# HG changeset patch # User wenzelm # Date 1614975998 -3600 # Node ID 3c5a7746ffa4b22590b1cd221c55c77e6f1ef6d2 # Parent 3fdb94d87e0e819044e99b5b49e8ac10fcac555b# Parent f3378101f555d44005cbf49ef6534cc3d1c7928d merged diff -r 3fdb94d87e0e -r 3c5a7746ffa4 NEWS --- a/NEWS Fri Mar 05 15:01:59 2021 +0100 +++ b/NEWS Fri Mar 05 21:26:38 2021 +0100 @@ -7,6 +7,16 @@ New in this Isabelle version ---------------------------- +*** General *** + +* Timeouts for Isabelle/ML tools are subject to system option +"timeout_scale" --- this already used for the overall session build +process before, and allows to adapt to slow machines. The underlying +Timeout.apply in Isabelle/ML treats an original timeout specification 0 +as no timeout; before it meant immediate timeout. Rare INCOMPATIBILITY +in boundary cases. + + *** HOL *** * Theory Multiset: dedicated predicate "multiset" is gone, use diff -r 3fdb94d87e0e -r 3c5a7746ffa4 etc/options --- a/etc/options Fri Mar 05 15:01:59 2021 +0100 +++ b/etc/options Fri Mar 05 21:26:38 2021 +0100 @@ -66,7 +66,7 @@ -- "additional print modes for prover output (separated by commas)" -section "Parallel Processing" +section "Parallel Processing and Timing" public option threads : int = 0 -- "maximum number of worker threads for prover process (0 = hardware max.)" @@ -87,6 +87,9 @@ option command_timing_threshold : real = 0.1 -- "default threshold for persistent command timing (seconds)" +public option timeout_scale : real = 1.0 + -- "scale factor for timeout in Isabelle/ML and session build" + section "Detail of Proof Checking" @@ -108,9 +111,6 @@ option timeout : real = 0 -- "timeout for session build job (seconds > 0)" -option timeout_scale : real = 1.0 - -- "scale factor for session timeout" - option process_output_limit : int = 100 -- "build process output limit (in million characters, 0 = unlimited)" diff -r 3fdb94d87e0e -r 3c5a7746ffa4 src/HOL/Library/refute.ML --- a/src/HOL/Library/refute.ML Fri Mar 05 15:01:59 2021 +0100 +++ b/src/HOL/Library/refute.ML Fri Mar 05 21:26:38 2021 +0100 @@ -993,7 +993,7 @@ else error ("Unexpected outcome: " ^ quote outcome_code ^ ".") fun wrapper () = let - val timer = Timer.startRealTimer () + val time_start = Time.now () val t = if no_assms then t else if negate then Logic.list_implies (assm_ts, t) @@ -1029,9 +1029,9 @@ else () fun find_model_loop universe = let - val msecs_spent = Time.toMilliseconds (Timer.checkRealTimer timer) - val _ = maxtime = 0 orelse msecs_spent < 1000 * maxtime - orelse raise Timeout.TIMEOUT (Time.fromMilliseconds msecs_spent) + val time_spent = Time.now () - time_start + val _ = maxtime = 0 orelse time_spent < Timeout.scale_time (Time.fromSeconds maxtime) + orelse raise Timeout.TIMEOUT time_spent val init_model = (universe, []) val init_args = {maxvars = maxvars, def_eq = false, next_idx = 1, bounds = [], wellformed = True} @@ -1114,15 +1114,13 @@ writeln ("Trying to find a model that " ^ (if negate then "refutes" else "satisfies") ^ ": " ^ Syntax.string_of_term ctxt t); - if maxtime > 0 then ( - Timeout.apply (Time.fromSeconds maxtime) - wrapper () - handle Timeout.TIMEOUT _ => - (writeln ("Search terminated, time limit (" ^ - string_of_int maxtime - ^ (if maxtime=1 then " second" else " seconds") ^ ") exceeded."); - check_expect "unknown") - ) else wrapper () + Timeout.apply (Time.fromSeconds maxtime) + wrapper () + handle Timeout.TIMEOUT _ => + (writeln ("Search terminated, time limit (" ^ + string_of_int maxtime + ^ (if maxtime=1 then " second" else " seconds") ^ ") exceeded."); + check_expect "unknown") end; diff -r 3fdb94d87e0e -r 3c5a7746ffa4 src/HOL/Nitpick_Examples/minipick.ML --- a/src/HOL/Nitpick_Examples/minipick.ML Fri Mar 05 15:01:59 2021 +0100 +++ b/src/HOL/Nitpick_Examples/minipick.ML Fri Mar 05 21:26:38 2021 +0100 @@ -430,7 +430,7 @@ fun solve_any_kodkod_problem thy problems = let val {debug, overlord, timeout, ...} = Nitpick_Commands.default_params thy [] - val deadline = Time.now () + timeout + val deadline = Timeout.end_time timeout val max_threads = 1 val max_solutions = 1 in diff -r 3fdb94d87e0e -r 3c5a7746ffa4 src/HOL/SMT.thy --- a/src/HOL/SMT.thy Fri Mar 05 15:01:59 2021 +0100 +++ b/src/HOL/SMT.thy Fri Mar 05 21:26:38 2021 +0100 @@ -663,7 +663,7 @@ (given in seconds) to restrict their runtime. \ -declare [[smt_timeout = 1000000]] +declare [[smt_timeout = 0]] text \ SMT solvers apply randomized heuristics. In case a problem is not diff -r 3fdb94d87e0e -r 3c5a7746ffa4 src/HOL/SMT_Examples/Boogie_Dijkstra.certs --- a/src/HOL/SMT_Examples/Boogie_Dijkstra.certs Fri Mar 05 15:01:59 2021 +0100 +++ b/src/HOL/SMT_Examples/Boogie_Dijkstra.certs Fri Mar 05 21:26:38 2021 +0100 @@ -1,3020 +1,4 @@ -9d6b81d96fb21c8c08e3f1fd649ce37bdafb5f92 3015 0 -unsat -((set-logic AUFLIA) -(declare-fun ?v0!19 () B_Vertex$) -(declare-fun ?v1!18 () B_Vertex$) -(declare-fun ?v0!20 () B_Vertex$) -(declare-fun ?v0!17 () B_Vertex$) -(declare-fun ?v1!16 () B_Vertex$) -(declare-fun ?v0!15 () B_Vertex$) -(declare-fun ?v0!14 () B_Vertex$) -(declare-fun ?v0!13 () B_Vertex$) -(declare-fun ?v0!12 () B_Vertex$) -(declare-fun ?v0!11 () B_Vertex$) -(declare-fun ?v1!10 () B_Vertex$) -(declare-fun ?v1!9 (B_Vertex$) B_Vertex$) -(declare-fun ?v0!8 () B_Vertex$) -(declare-fun ?v1!7 (B_Vertex$) B_Vertex$) -(declare-fun ?v1!6 (B_Vertex$) B_Vertex$) -(declare-fun ?v0!5 () B_Vertex$) -(declare-fun ?v0!4 () B_Vertex$) -(declare-fun ?v1!3 () B_Vertex$) -(declare-fun ?v0!2 () B_Vertex$) -(declare-fun ?v1!1 () B_Vertex$) -(declare-fun ?v0!0 () B_Vertex$) -(proof -(let ((?x1893 (v_b_SP_G_2$ ?v0!19))) -(let ((?x1894 (* (- 1) ?x1893))) -(let ((?x1892 (v_b_SP_G_2$ ?v1!18))) -(let ((?x1884 (pair$ ?v1!18 ?v0!19))) -(let ((?x1885 (b_G$ ?x1884))) -(let (($x1896 (>= (+ ?x1885 ?x1892 ?x1894) 0))) -(let (($x1888 (<= (+ b_Infinity$ (* (- 1) ?x1885)) 0))) -(let (($x1883 (fun_app$ v_b_Visited_G_2$ ?v1!18))) -(let (($x2791 (not $x1883))) -(let (($x2806 (or $x2791 $x1888 $x1896))) -(let (($x2811 (not $x2806))) -(let (($x3729 (forall ((?v1 B_Vertex$) )(! (let ((?x1911 (v_b_SP_G_2$ ?v0!20))) -(let ((?x1912 (* (- 1) ?x1911))) -(let ((?x273 (v_b_SP_G_2$ ?v1))) -(let (($x2242 (= (+ ?x273 ?x1912 (b_G$ (pair$ ?v1 ?v0!20))) 0))) -(let (($x291 (fun_app$ v_b_Visited_G_2$ ?v1))) -(let (($x300 (not $x291))) -(or (>= (+ ?x273 ?x1912) 0) $x300 (not $x2242)))))))) :pattern ( (v_b_SP_G_2$ ?v1) ) :pattern ( (fun_app$ v_b_Visited_G_2$ ?v1) ) :pattern ( (pair$ ?v1 ?v0!20) ) :qid k!42)) -)) -(let (($x3734 (not $x3729))) -(let (($x1914 (<= (+ b_Infinity$ (* (- 1) (v_b_SP_G_2$ ?v0!20))) 0))) -(let (($x1909 (= ?v0!20 b_Source$))) -(let (($x3720 (forall ((?v0 B_Vertex$) (?v1 B_Vertex$) )(! (let ((?x273 (v_b_SP_G_2$ ?v1))) -(let ((?x155 (b_G$ (pair$ ?v1 ?v0)))) -(let (($x1282 (>= (+ ?x155 ?x273 (* (- 1) (v_b_SP_G_2$ ?v0))) 0))) -(let (($x922 (<= (+ b_Infinity$ (* (- 1) ?x155)) 0))) -(let (($x291 (fun_app$ v_b_Visited_G_2$ ?v1))) -(let (($x300 (not $x291))) -(or $x300 $x922 $x1282))))))) :pattern ( (pair$ ?v1 ?v0) ) :qid k!42)) -)) -(let (($x3725 (not $x3720))) -(let (($x3737 (or $x3725 $x1909 $x1914 $x3734))) -(let ((?x4393 (fun_app$c v_b_SP_G_1$ ?v0!20))) -(let ((?x4418 (* (- 1) ?x4393))) -(let ((?x1911 (v_b_SP_G_2$ ?v0!20))) -(let ((?x4419 (+ ?x1911 ?x4418))) -(let (($x5977 (>= ?x4419 0))) -(let (($x4400 (= ?x1911 ?x4393))) -(let ((?x4434 (pair$ v_b_v_G_1$ ?v0!20))) -(let ((?x4435 (b_G$ ?x4434))) -(let ((?x4436 (* (- 1) ?x4435))) -(let ((?x3104 (v_b_SP_G_2$ v_b_v_G_1$))) -(let ((?x3105 (* (- 1) ?x3104))) -(let ((?x4546 (+ ?x1911 ?x3105 ?x4436))) -(let (($x4569 (<= ?x4546 0))) -(let (($x3740 (not $x3737))) -(let ((@x4391 (hypothesis $x3740))) -(let ((@x3222 (def-axiom (or $x3737 $x3720)))) -(let (($x4161 (>= ?x3104 0))) -(let (($x3703 (forall ((?v0 B_Vertex$) )(! 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(let ((?x10078 (b_S_ptr$ b_T_T_u1$ v_b_P_H_arr$))) -(let ((?x10079 (b_S_ref$ ?x10078))) -(let ((?x10076 (b_S_array$ b_T_T_u1$ v_b_P_H_len$))) -(let ((?x10080 (b_S_ptr$ ?x10076 ?x10079))) -(let ((?x21014 (b_S_ref$ ?x10080))) -(let ((?x21983 (b_S_ptr$ ?x10076 ?x21014))) -(let ((?x22357 (b_S_read_n_version$ v_b_S_s$ ?x21983))) -(let ((?x22358 (b_S_ver_n_domain$ ?x22357))) -(let ((?x22234 (b_S_typ$ ?x21983))) -(let (($x22353 (b_S_has_n_volatile_n_owns_n_set$ ?x22234))) -(or $x22353 (not (b_S_set_n_in$ ?v3 (b_S_owns$ v_b_S_s$ ?x21983))) (b_S_set_n_in2$ ?v3 ?x22358)))))))))))) :pattern ( (b_S_set_n_in$ ?v3 (b_S_owns$ v_b_S_s$ (b_S_ptr$ (b_S_array$ b_T_T_u1$ v_b_P_H_len$) (b_S_ref$ (b_S_ptr$ (b_S_array$ b_T_T_u1$ v_b_P_H_len$) (b_S_ref$ (b_S_ptr$ b_T_T_u1$ v_b_P_H_arr$))))))) ) :qid k!564)) -)) -(let (($x22363 (not $x22362))) -(let (($x22248 (b_S_closed$ v_b_S_s$ ?x21983))) -(let (($x22272 (not $x22248))) -(let (($x22352 (not $x22344))) -(let (($x22364 (or $x22352 $x22272 $x22363))) -(let (($x22365 (not $x22364))) -(let (($x22318 (b_S_in_n_domain$ v_b_S_s$ ?x21983 ?x21983))) -(let (($x22317 (b_S_in_n_domain_n_lab$ v_b_S_s$ ?x21983 ?x21983 b_l_H_public$))) -(let (($x22326 (= $x22317 $x22318))) -(let (($x8728 (forall ((?v0 B_S_state$) (?v1 B_S_ptr$) (?v2 B_S_ptr$) (?v3 B_S_label$) )(! 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$x15636 (<= (+ (* (- 1) v_b_L_H_max_G_3$) ?x15634) 0))))) -(let ((@x15897 (trans @x15890 (rewrite (= (<= (+ (* (- 1) v_b_L_H_max_G_3$) ?x15634) 0) $x15893)) (= $x15636 $x15893)))) -(let ((@x15868 (monotonicity (rewrite (= (+ ?v0!14 ?x11581) (+ ?x11581 ?v0!14))) (= (>= (+ ?v0!14 ?x11581) 0) (>= (+ ?x11581 ?v0!14) 0))))) -(let ((@x15875 (trans @x15868 (rewrite (= (>= (+ ?x11581 ?v0!14) 0) $x15871)) (= (>= (+ ?v0!14 ?x11581) 0) $x15871)))) -(let ((@x15881 (monotonicity (monotonicity @x15875 (= (not (>= (+ ?v0!14 ?x11581) 0)) $x15876)) (= (and $x15626 $x15627 (not (>= (+ ?v0!14 ?x11581) 0))) $x15879)))) -(let ((@x15884 (monotonicity @x15881 (= (not (and $x15626 $x15627 (not (>= (+ ?v0!14 ?x11581) 0)))) $x15882)))) -(let ((@x15906 (monotonicity (monotonicity (monotonicity @x15884 @x15897 $x15899) (= $x15638 $x15901)) (= $x15655 $x15904)))) -(let ((@x15912 (monotonicity (monotonicity (rewrite (= $x15622 $x11608)) @x15906 (= $x15659 $x15907)) (= $x15663 $x15910)))) -(let ((@x15915 (monotonicity (rewrite (= $x15617 $x13358)) @x15912 (= $x15667 (and $x13358 $x15910))))) -(let ((@x15923 (monotonicity (trans @x15915 (rewrite (= (and $x13358 $x15910) $x15916)) (= $x15667 $x15916)) (= $x15671 $x15921)))) -(let ((@x15958 (monotonicity (rewrite (= $x15695 $x11725)) @x15923 (= $x15698 (and $x11725 $x15921))))) -(let ((@x15926 (monotonicity (rewrite (= $x15608 $x11562)) @x15923 (= $x15675 (and $x11562 $x15921))))) -(let ((@x15934 (monotonicity (trans @x15926 (rewrite (= (and $x11562 $x15921) $x15927)) (= $x15675 $x15927)) (= $x15679 $x15932)))) -(let ((@x15937 (monotonicity (rewrite (= $x15596 $x10323)) @x15934 (= $x15683 (and $x10323 $x15932))))) -(let ((@x15945 (monotonicity (trans @x15937 (rewrite (= (and $x10323 $x15932) $x15938)) (= $x15683 $x15938)) (= $x15687 $x15943)))) -(let ((@x15948 (monotonicity (rewrite (= $x15605 $x11527)) @x15945 (= $x15691 (and $x11527 $x15943))))) -(let ((@x15966 (monotonicity (trans @x15948 (rewrite (= (and $x11527 $x15943) $x15949)) (= 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(= $x15833 $x16115)))) -(let (($x13451 (exists ((?v0 Int) )(! (let ((?x10163 (b_S_read_n_u1$ v_b_S_s$ (b_S_idx$ (b_S_ptr$ b_T_T_u1$ v_b_P_H_arr$) ?v0 b_T_T_u1$)))) -(let (($x10238 (= ?x10163 v_b_S_result_G_0$))) -(let (($x11800 (>= (+ ?v0 (* (- 1) v_b_P_H_len$)) 0))) -(let (($x11802 (not $x11800))) -(let (($x12168 (<= ?v0 4294967295))) -(let (($x2815 (>= ?v0 0))) -(and $x2815 $x12168 $x11802 $x10238))))))) :qid k!704)) -)) -(let (($x13445 (not $x13442))) -(let (($x13454 (or $x13445 $x13451))) -(let (($x13457 (and $x13442 $x13454))) -(let (($x13460 (or $x11797 $x13457))) -(let (($x13463 (and b_S_position_n_marker$ $x13460))) -(let (($x13466 (or $x11777 $x13463))) -(let (($x13376 (not $x13373))) -(let (($x13379 (or $x13376 $x11651))) -(let (($x13382 (and $x13373 $x13379))) -(let (($x13385 (or $x11612 $x13382))) -(let (($x13388 (and $x11608 $x13385))) -(let (($x13391 (or $x13361 $x13388))) -(let (($x13394 (and $x11570 $x13353 $x13391))) -(let (($x13412 (or $x11730 $x13394))) -(let (($x13397 (or $x11567 $x13394))) -(let (($x13400 (and $x10321 $x10324 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(refl (~ $x15593 $x15593)) (nnf-neg (refl (~ $x15596 $x15596)) @x15713 (~ (not $x13424) $x15714)) (~ (not $x13427) $x15718)))) -(let ((@x15788 (nnf-neg (nnf-neg (refl (~ $x15587 $x15587)) @x15721 (~ (not $x13430) $x15722)) @x15784 (~ (not $x13469) $x15785)))) -(let ((@x15580 (monotonicity (refl (~ $x11260 $x11260)) (refl (~ $x10167 $x10167)) (refl (~ $x11911 $x11911)) (refl (~ $x13304 $x13304)) (refl (~ $x13315 $x13315)) (refl (~ $x11901 $x11901)) (refl (~ $x13326 $x13326)) (refl (~ $x11898 $x11898)) (nnf-pos (refl (~ $x13337 $x13337)) (~ $x13340 $x13340)) (refl (~ $x11868 $x11868)) (refl (~ $x10192 $x10192)) (refl (~ $x11429 $x11429)) (refl (~ $x11432 $x11432)) (~ $x13343 $x13343)))) -(let ((@x15792 (nnf-neg (nnf-neg @x15580 (~ (not $x13346) $x13343)) (refl (~ $x15584 $x15584)) @x15788 (~ (not $x13472) $x15789)))) -(let ((@x15796 (nnf-neg (refl (~ $x15545 $x15545)) (refl (~ $x15548 $x15548)) @x15792 (~ (not $x13475) $x15793)))) -(let ((@x15544 (nnf-neg (nnf-pos (refl (~ $x13289 $x13289)) (~ $x13292 $x13292)) (~ (not $x13295) $x13292)))) -(let ((@x15804 (nnf-neg (sk (~ $x13295 $x15535)) (nnf-neg @x15544 @x15796 (~ (not $x13478) $x15797)) (~ (not $x13481) $x15801)))) -(let ((@x15812 (nnf-neg (refl (~ $x11385 $x11385)) (nnf-neg (refl (~ $x15519 $x15519)) @x15804 (~ (not $x13484) $x15805)) (~ (not $x13487) $x15809)))) -(let ((@x15820 (nnf-neg (refl (~ $x15502 $x15502)) (refl (~ $x15511 $x15511)) (nnf-neg (refl (~ $x15514 $x15514)) @x15812 (~ (not $x13490) $x15813)) (~ (not $x13493) $x15817)))) -(let ((@x15828 (nnf-neg (refl (~ $x15502 $x15502)) (refl (~ $x15505 $x15505)) (nnf-neg (refl (~ $x15508 $x15508)) @x15820 (~ (not $x13496) $x15821)) (~ (not $x13499) $x15825)))) -(let ((@x15835 (nnf-neg (refl (~ $x11221 $x11221)) (nnf-neg (refl (~ $x15499 $x15499)) @x15828 (~ (not $x13502) $x15829)) (~ $x13508 $x15833)))) -(let (($x6441 (= b_S_max_o_u4$ 4294967295))) -(let ((@x6435 (monotonicity (rewrite (= (* 65536 65536) 4294967296)) (= (- (* 65536 65536) 1) (- 4294967296 1))))) -(let ((@x6440 (trans @x6435 (rewrite (= (- 4294967296 1) 4294967295)) (= (- (* 65536 65536) 1) 4294967295)))) -(let ((@x6443 (monotonicity @x6440 (= (= b_S_max_o_u4$ (- (* 65536 65536) 1)) $x6441)))) -(let ((@x6446 (mp (asserted (= b_S_max_o_u4$ (- (* 65536 65536) 1))) @x6443 $x6441))) -(let ((@x12140 (trans (monotonicity @x6446 (= ?x3113 (* (- 1) 4294967295))) (rewrite (= (* (- 1) 4294967295) (- 4294967295))) (= ?x3113 (- 4294967295))))) -(let ((@x12164 (trans (monotonicity @x12140 (= ?x3114 (+ ?0 (- 4294967295)))) (rewrite (= (+ ?0 (- 4294967295)) (+ (- 4294967295) ?0))) (= ?x3114 (+ (- 4294967295) ?0))))) -(let ((@x12172 (trans (monotonicity @x12164 (= $x3115 (<= (+ (- 4294967295) ?0) 0))) (rewrite (= (<= (+ (- 4294967295) ?0) 0) $x12168)) (= $x3115 $x12168)))) -(let ((@x13453 (quant-intro (monotonicity @x12172 (= $x11839 (and $x2815 $x12168 $x11802 $x10238))) (= $x11844 $x13451)))) -(let ((@x13441 (monotonicity (monotonicity (monotonicity @x12172 (= $x11808 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(monotonicity (monotonicity @x13357 (= $x11600 $x13358)) (= $x11605 $x13361)) (monotonicity @x13387 (= $x11663 $x13388)) (= $x11666 $x13391)))) -(let ((@x13414 (monotonicity (monotonicity @x13357 @x13393 (= $x11672 $x13394)) (= $x11733 $x13412)))) -(let ((@x13399 (monotonicity (monotonicity @x13357 @x13393 (= $x11672 $x13394)) (= $x11677 $x13397)))) -(let ((@x13408 (monotonicity (monotonicity (monotonicity @x13399 (= $x11683 $x13400)) (= $x11688 $x13403)) (= $x11694 $x13406)))) -(let ((@x13417 (monotonicity (monotonicity @x13408 (= $x11699 $x13409)) @x13414 (= $x11736 $x13415)))) -(let ((@x13426 (monotonicity (monotonicity (monotonicity @x13417 (= $x11739 $x13418)) (= $x11745 $x13421)) (= $x11750 $x13424)))) -(let ((@x13471 (monotonicity (monotonicity (monotonicity @x13426 (= $x11756 $x13427)) (= $x11761 $x13430)) (monotonicity (monotonicity @x13462 (= $x11856 $x13463)) (= $x11859 $x13466)) (= $x11862 $x13469)))) -(let ((@x13339 (monotonicity (monotonicity (monotonicity @x12172 (= 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(let (($x6905 (b_S_typed$ ?v0 (b_S_idx$ (b_S_ptr$ (b_S_array$ ?v2 ?v3) ?v1) ?v4 ?v2)))) -(let ((?x6897 (b_S_typemap$ ?v0))) -(let ((?x6899 (b_S_select_o_tm$ ?x6897 (b_S_idx$ (b_S_ptr$ (b_S_array$ ?v2 ?v3) ?v1) ?v4 ?v2)))) -(let (($x6904 (b_S_ts_n_is_n_array_n_elt$ ?x6899))) -(let (($x17952 (or (not (= (b_S_ts_n_emb$ ?x6899) (b_S_ptr$ (b_S_array$ ?v2 ?v3) ?v1))) (b_S_ts_n_is_n_volatile$ ?x6899) (not $x6904) (not $x6905)))) -(let (($x17953 (not $x17952))) -(let (($x4862 (>= (+ ?v4 (* (- 1) ?v3)) 0))) -(let (($x2815 (>= ?v4 0))) -(let (($x3763 (not $x2815))) -(or (not (b_S_typed$ ?v0 (b_S_ptr$ (b_S_array$ ?v2 ?v3) ?v1))) $x3763 $x4862 $x17953)))))))))) :pattern ( (b_S_select_o_sm$ (b_S_statusmap$ ?v0) (b_S_idx$ (b_S_ptr$ ?v2 ?v1) ?v4 ?v2)) (b_S_ptr$ (b_S_array$ ?v2 ?v3) ?v1) ) :pattern ( (b_S_select_o_tm$ (b_S_typemap$ ?v0) (b_S_idx$ (b_S_ptr$ ?v2 ?v1) ?v4 ?v2)) (b_S_ptr$ (b_S_array$ ?v2 ?v3) ?v1) ) :qid k!493)) -)) -(let (($x6943 (forall ((?v0 B_S_state$) (?v1 Int) (?v2 B_S_ctype$) (?v3 Int) (?v4 Int) )(! (let (($x6905 (b_S_typed$ ?v0 (b_S_idx$ (b_S_ptr$ (b_S_array$ ?v2 ?v3) ?v1) ?v4 ?v2)))) -(let ((?x6897 (b_S_typemap$ ?v0))) -(let ((?x6899 (b_S_select_o_tm$ ?x6897 (b_S_idx$ (b_S_ptr$ (b_S_array$ ?v2 ?v3) ?v1) ?v4 ?v2)))) -(let (($x6904 (b_S_ts_n_is_n_array_n_elt$ ?x6899))) -(let ((?x6894 (b_S_ptr$ (b_S_array$ ?v2 ?v3) ?v1))) -(let (($x6901 (= (b_S_ts_n_emb$ ?x6899) ?x6894))) -(let (($x6937 (and $x6901 (not (b_S_ts_n_is_n_volatile$ ?x6899)) $x6904 $x6905))) -(let (($x4862 (>= (+ ?v4 (* (- 1) ?v3)) 0))) -(let (($x6603 (not $x4862))) -(let (($x2815 (>= ?v4 0))) -(let (($x6895 (b_S_typed$ ?v0 ?x6894))) -(let (($x6929 (and $x6895 $x2815 $x6603))) -(let (($x6934 (not $x6929))) -(or $x6934 $x6937)))))))))))))) :pattern ( (b_S_select_o_sm$ (b_S_statusmap$ ?v0) (b_S_idx$ (b_S_ptr$ ?v2 ?v1) ?v4 ?v2)) (b_S_ptr$ (b_S_array$ ?v2 ?v3) ?v1) ) :pattern ( (b_S_select_o_tm$ (b_S_typemap$ ?v0) (b_S_idx$ (b_S_ptr$ ?v2 ?v1) ?v4 ?v2)) (b_S_ptr$ (b_S_array$ ?v2 ?v3) ?v1) ) :qid k!493)) -)) -(let (($x6905 (b_S_typed$ ?4 (b_S_idx$ (b_S_ptr$ (b_S_array$ ?2 ?1) ?3) ?0 ?2)))) -(let ((?x6897 (b_S_typemap$ ?4))) -(let ((?x6899 (b_S_select_o_tm$ ?x6897 (b_S_idx$ (b_S_ptr$ (b_S_array$ ?2 ?1) ?3) ?0 ?2)))) -(let (($x6904 (b_S_ts_n_is_n_array_n_elt$ ?x6899))) -(let (($x17952 (or (not (= (b_S_ts_n_emb$ ?x6899) (b_S_ptr$ (b_S_array$ ?2 ?1) ?3))) (b_S_ts_n_is_n_volatile$ ?x6899) (not $x6904) (not $x6905)))) -(let (($x17953 (not $x17952))) -(let (($x4862 (>= (+ ?0 (* (- 1) ?1)) 0))) -(let (($x17959 (or (not (b_S_typed$ ?4 (b_S_ptr$ (b_S_array$ ?2 ?1) ?3))) $x3763 $x4862 $x17953))) -(let ((?x6894 (b_S_ptr$ (b_S_array$ ?2 ?1) ?3))) -(let (($x6901 (= (b_S_ts_n_emb$ ?x6899) ?x6894))) -(let (($x6937 (and $x6901 (not (b_S_ts_n_is_n_volatile$ ?x6899)) $x6904 $x6905))) -(let (($x6603 (not $x4862))) -(let (($x6895 (b_S_typed$ ?4 ?x6894))) -(let (($x6929 (and $x6895 $x2815 $x6603))) -(let (($x6934 (not $x6929))) -(let (($x6940 (or $x6934 $x6937))) -(let (($x17938 (or (not $x6895) $x3763 $x4862))) -(let ((@x17944 (monotonicity (rewrite (= $x6929 (not $x17938))) (= $x6934 (not (not $x17938)))))) -(let ((@x17958 (monotonicity (trans @x17944 (rewrite (= (not (not $x17938)) $x17938)) (= $x6934 $x17938)) (rewrite (= $x6937 $x17953)) (= $x6940 (or $x17938 $x17953))))) -(let ((@x17966 (quant-intro (trans @x17958 (rewrite (= (or $x17938 $x17953) $x17959)) (= $x6940 $x17959)) (= $x6943 $x17964)))) -(let (($x6917 (forall ((?v0 B_S_state$) (?v1 Int) (?v2 B_S_ctype$) (?v3 Int) (?v4 Int) )(! (let (($x6905 (b_S_typed$ ?v0 (b_S_idx$ (b_S_ptr$ (b_S_array$ ?v2 ?v3) ?v1) ?v4 ?v2)))) -(let ((?x6897 (b_S_typemap$ ?v0))) -(let ((?x6899 (b_S_select_o_tm$ ?x6897 (b_S_idx$ (b_S_ptr$ (b_S_array$ ?v2 ?v3) ?v1) ?v4 ?v2)))) -(let (($x6904 (b_S_ts_n_is_n_array_n_elt$ ?x6899))) -(let ((?x6894 (b_S_ptr$ (b_S_array$ ?v2 ?v3) ?v1))) -(let (($x6901 (= (b_S_ts_n_emb$ ?x6899) ?x6894))) -(let (($x6908 (and $x6901 (and (not (b_S_ts_n_is_n_volatile$ ?x6899)) (and $x6904 $x6905))))) -(let (($x2766 (<= 0 ?v4))) -(let (($x6566 (and $x2766 (< ?v4 ?v3)))) -(let (($x6895 (b_S_typed$ ?v0 ?x6894))) -(let (($x6896 (and $x6895 $x6566))) -(=> $x6896 $x6908)))))))))))) :pattern ( (b_S_select_o_sm$ (b_S_statusmap$ ?v0) (b_S_idx$ (b_S_ptr$ ?v2 ?v1) ?v4 ?v2)) (b_S_ptr$ (b_S_array$ ?v2 ?v3) ?v1) ) :pattern ( (b_S_select_o_tm$ (b_S_typemap$ ?v0) (b_S_idx$ (b_S_ptr$ ?v2 ?v1) ?v4 ?v2)) (b_S_ptr$ (b_S_array$ ?v2 ?v3) ?v1) ) :qid k!493)) -)) -(let (($x6923 (forall ((?v0 B_S_state$) (?v1 Int) (?v2 B_S_ctype$) (?v3 Int) (?v4 Int) )(! 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(and $x6904 $x6905))))) -(let (($x6920 (or (not (and $x6895 (and $x2766 (< ?0 ?1)))) $x6908))) -(let (($x6566 (and $x2766 (< ?0 ?1)))) -(let (($x6896 (and $x6895 $x6566))) -(let ((@x6608 (monotonicity @x2814 (rewrite (= (< ?0 ?1) $x6603)) (= $x6566 (and $x2815 $x6603))))) -(let ((@x6933 (trans (monotonicity @x6608 (= $x6896 (and $x6895 (and $x2815 $x6603)))) (rewrite (= (and $x6895 (and $x2815 $x6603)) $x6929)) (= $x6896 $x6929)))) -(let ((@x6942 (monotonicity (monotonicity @x6933 (= (not $x6896) $x6934)) (rewrite (= $x6908 $x6937)) (= $x6920 $x6940)))) -(let ((@x6947 (trans (quant-intro (rewrite (= (=> $x6896 $x6908) $x6920)) (= $x6917 $x6923)) (quant-intro @x6942 (= $x6923 $x6943)) (= $x6917 $x6943)))) -(let ((@x14355 (mp~ (mp (asserted $x6917) @x6947 $x6943) (nnf-pos (refl (~ $x6940 $x6940)) (~ $x6943 $x6943)) $x6943))) -(let ((@x17967 (mp @x14355 @x17966 $x17964))) -(let (($x23539 (not $x23538))) -(let (($x23587 (not $x17964))) -(let (($x23588 (or $x23587 $x23539 $x11259 $x23557))) 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((@x22763 (monotonicity (monotonicity (symm @x23704 (= ?x22658 ?x22805)) (= ?x22663 ?x22806)) (= ?x22664 ?x22809)))) -(let (($x22767 (not (or $x22665 (not (b_S_is_n_non_n_primitive$ ?x22663)))))) -(let (($x19234 (forall ((?v0 B_S_type_n_state$) )(! 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(let (($x9543 (= (b_S_kind_n_of$ (b_S_typ$ (b_S_ts_n_emb$ ?v0))) b_S_kind_n_primitive$))) -(and (not $x9543) (b_S_is_n_non_n_primitive$ (b_S_typ$ (b_S_ts_n_emb$ ?v0))))) :pattern ( (b_S_ts_n_emb$ ?v0) ) :qid k!618)) -)) -(let (($x9543 (= (b_S_kind_n_of$ (b_S_typ$ (b_S_ts_n_emb$ ?0))) b_S_kind_n_primitive$))) -(let (($x19230 (or $x9543 (not (b_S_is_n_non_n_primitive$ (b_S_typ$ (b_S_ts_n_emb$ ?0))))))) -(let (($x9546 (and (not $x9543) (b_S_is_n_non_n_primitive$ (b_S_typ$ (b_S_ts_n_emb$ ?0)))))) -(let ((@x15316 (mp~ (asserted $x9548) (nnf-pos (refl (~ $x9546 $x9546)) (~ $x9548 $x9548)) $x9548))) -(let ((@x19237 (mp @x15316 (quant-intro (rewrite (= $x9546 (not $x19230))) (= $x9548 $x19234)) $x19234))) -(let ((@x23507 (def-axiom (or (or $x22665 (not (b_S_is_n_non_n_primitive$ ?x22663))) (not $x22665))))) -(let ((@x23501 (unit-resolution @x23507 (unit-resolution ((_ quant-inst (b_S_select_o_tm$ ?x10272 ?x22505)) (or (not $x19234) $x22767)) @x19237 $x22767) (not $x22665)))) -(let ((@x23573 (lemma (unit-resolution @x23501 (trans @x22763 (hypothesis $x22810) $x22665) false) (or $x22807 (not $x22506))))) -(let (($x22432 (not (or (not $x22602) (not (b_S_closed$ v_b_S_s$ ?x22805)))))) -(let (($x22436 (= (b_S_kind_n_of$ ?x22514) b_S_kind_n_primitive$))) -(let (($x22427 (not $x22436))) -(let (($x22455 (or $x22427 $x22432 $x22810 (not (or $x22451 (b_S_in_n_wrapped_n_domain$ v_b_S_s$ ?x22805)))))) -(let (($x22447 (or (= (b_S_owner$ v_b_S_s$ ?x10137) b_S_me$) (b_S_in_n_wrapped_n_domain$ v_b_S_s$ ?x10137)))) -(let (($x22456 (not $x22455))) -(let (($x22463 (not (or $x22456 (not (or $x22436 (not $x22447))))))) -(let (($x22464 (or $x15505 $x22463))) -(let (($x22465 (not $x22464))) -(let (($x22466 (= $x10141 $x22465))) -(let (($x19072 (forall ((?v0 B_S_state$) (?v1 B_S_ptr$) )(! 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false)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) - -06100f97c3a244ddafdb8cd3437991e2729cce2c 3051 0 -unsat -((set-logic AUFLIA) -(declare-fun ?v0!14 () Int) -(declare-fun ?v0!15 () Int) -(declare-fun ?v0!13 () Int) -(proof -(let ((?x11604 (* (- 1) v_b_SL_H_witness_G_1$))) -(let ((?x20744 (+ v_b_SL_H_witness_G_0$ ?x11604))) -(let (($x20746 (>= ?x20744 0))) -(let (($x20743 (= v_b_SL_H_witness_G_0$ v_b_SL_H_witness_G_1$))) -(let ((@x25111 (commutativity (= $x20743 (= v_b_SL_H_witness_G_1$ v_b_SL_H_witness_G_0$))))) -(let ((@x25113 (symm @x25111 (= (= v_b_SL_H_witness_G_1$ v_b_SL_H_witness_G_0$) $x20743)))) -(let (($x10351 (= v_b_SL_H_witness_G_1$ v_b_SL_H_witness_G_0$))) -(let ((?x10037 (b_S_ptr$ b_T_T_u1$ v_b_P_H_arr$))) -(let ((?x10331 (b_S_idx$ ?x10037 v_b_SL_H_witness_G_1$ b_T_T_u1$))) -(let ((?x10332 (b_S_read_n_u1$ v_b_S_s$ ?x10331))) -(let (($x10333 (= ?x10332 v_b_L_H_max_G_3$))) -(let (($x11606 (<= (+ v_b_P_H_len$ ?x11604) 0))) -(let (($x19430 (or $x11606 (not $x10333)))) -(let (($x19431 (not $x19430))) -(let (($x20349 (forall ((?v0 Int) )(! (let ((?x11590 (* (- 1) v_b_L_H_max_G_3$))) -(let ((?x10037 (b_S_ptr$ b_T_T_u1$ v_b_P_H_arr$))) -(let ((?x10121 (b_S_idx$ ?x10037 ?v0 b_T_T_u1$))) -(let ((?x10122 (b_S_read_n_u1$ v_b_S_s$ ?x10121))) -(let (($x11592 (<= (+ ?x10122 ?x11590) 0))) -(let (($x11574 (>= (+ ?v0 (* (- 1) v_b_L_H_p_G_1$)) 0))) -(let (($x12489 (<= ?v0 4294967295))) -(let (($x16571 (not $x12489))) -(let (($x2815 (>= ?v0 0))) -(let (($x3743 (not $x2815))) -(or $x3743 $x16571 $x11574 $x11592))))))))))) :pattern ( (b_S_idx$ (b_S_ptr$ b_T_T_u1$ v_b_P_H_arr$) ?v0 b_T_T_u1$) ) :qid k!705)) -)) -(let (($x20354 (not $x20349))) -(let (($x20357 (or $x20354 $x19431))) -(let (($x20360 (not $x20357))) -(let ((?x15673 (b_S_idx$ ?x10037 ?v0!14 b_T_T_u1$))) -(let ((?x15674 (b_S_read_n_u1$ v_b_S_s$ ?x15673))) -(let ((?x15920 (* (- 1) ?x15674))) -(let (($x15922 (>= (+ v_b_L_H_max_G_3$ ?x15920) 0))) -(let (($x15900 (<= (+ v_b_L_H_p_G_1$ (* (- 1) ?v0!14)) 0))) -(let (($x15667 (<= ?v0!14 4294967295))) -(let (($x19384 (not $x15667))) -(let (($x15666 (>= ?v0!14 0))) -(let (($x19383 (not $x15666))) -(let (($x19399 (or $x19383 $x19384 $x15900 $x15922))) -(let (($x19404 (not $x19399))) -(let (($x20363 (or $x19404 $x20360))) -(let (($x20366 (not $x20363))) -(let ((?x11540 (* (- 1) v_b_L_H_p_G_1$))) -(let ((?x11568 (+ v_b_P_H_len$ ?x11540))) -(let (($x11567 (>= ?x11568 0))) -(let (($x11571 (not $x11567))) -(let (($x20369 (or $x11571 $x20366))) -(let (($x20372 (not $x20369))) -(let (($x20375 (or $x11571 $x20372))) -(let (($x20378 (not $x20375))) -(let (($x11495 (>= v_b_SL_H_witness_G_1$ 0))) -(let (($x19473 (not $x11495))) -(let (($x11537 (>= v_b_L_H_p_G_1$ 2))) -(let (($x19472 (not $x11537))) -(let (($x10317 (b_S_local_n_value_n_is$ v_b_S_s$ b_H_tok_S_1_T_16_o_24$ b_H_loc_o_p$ v_b_L_H_p_G_1$ b_T_T_u4$))) -(let (($x19471 (not $x10317))) -(let ((?x11541 (+ v_b_L_H_p_G_0$ ?x11540))) -(let (($x11539 (= ?x11541 (- 1)))) -(let (($x19470 (not $x11539))) -(let (($x12582 (<= v_b_L_H_p_G_0$ 4294967294))) -(let (($x15654 (not 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(($x20408 (not $x20405))) -(let (($x20411 (or $x15630 $x15633 $x20408))) -(let (($x20414 (not $x20411))) -(let (($x20417 (or $x11475 $x19492 $x19519 $x20414))) -(let (($x24901 (= v_b_L_H_p_G_0$ v_b_SL_H_witness_G_1$))) -(let ((@x24227 (hypothesis $x20396))) -(let ((@x24923 (unit-resolution (def-axiom (or $x20393 $x10299)) @x24227 $x10299))) -(let (($x24944 (not $x24901))) -(let ((@x25016 (unit-resolution (def-axiom (or $x20393 $x10292)) @x24227 $x10292))) -(let ((@x24980 (unit-resolution (def-axiom (or $x20393 $x10297)) @x24227 $x10297))) -(let ((?x24895 (+ v_b_L_H_p_G_0$ ?x11604))) -(let (($x24790 (>= ?x24895 0))) -(let ((@x24834 ((_ th-lemma arith triangle-eq) (or $x24944 $x24790)))) -(let ((@x25134 (monotonicity (monotonicity (hypothesis $x10299) (= ?x10331 ?x10279)) (= ?x10332 ?x10286)))) -(let ((@x25137 (trans @x25134 (symm (hypothesis $x10292) (= ?x10286 v_b_L_H_max_G_2$)) (= ?x10332 v_b_L_H_max_G_2$)))) -(let ((@x25138 (trans @x25137 (symm (hypothesis $x10297) (= 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(let ((?x9808 (b_S_kind_n_of$ ?v0))) -(let (($x9842 (= ?x9808 b_S_kind_n_primitive$))) -(let (($x2704 (b_S_is_n_primitive$ ?v0))) -(= $x2704 $x9842)))) :pattern ( (b_S_is_n_primitive$ ?v0) ) :qid k!665)) -)) -(let ((?x9808 (b_S_kind_n_of$ ?0))) -(let (($x9842 (= ?x9808 b_S_kind_n_primitive$))) -(let (($x2704 (b_S_is_n_primitive$ ?0))) -(let (($x9847 (= $x2704 $x9842))) -(let (($x9845 (forall ((?v0 B_S_ctype$) )(! (let ((?x9808 (b_S_kind_n_of$ ?v0))) -(let (($x9842 (= ?x9808 b_S_kind_n_primitive$))) -(let (($x2704 (b_S_is_n_primitive$ ?v0))) -(= $x2704 $x9842)))) :pattern ( (b_S_is_n_primitive$ ?v0) ) :qid k!665)) -)) -(let ((@x9855 (mp (asserted $x9845) (quant-intro (rewrite (= (= $x2704 $x9842) $x9847)) (= $x9845 $x9850)) $x9850))) -(let ((@x15496 (mp~ @x9855 (nnf-pos (refl (~ $x9847 $x9847)) (~ $x9850 $x9850)) $x9850))) -(let (($x21227 (not $x9850))) -(let (($x21486 (or $x21227 $x21483))) -(let ((@x21487 ((_ quant-inst b_T_T_u1$) $x21486))) -(let ((@x9728 (asserted $x9727))) -(let ((@x23038 (unit-resolution (def-axiom (or (not $x21483) (not $x9727) $x21476)) @x9728 (or (not $x21483) $x21476)))) -(let ((?x23196 (b_S_typ$ ?x10279))) -(let (($x23197 (= ?x23196 b_T_T_u1$))) -(let (($x23206 (= $x10280 $x23197))) -(let (($x20261 (forall ((?v0 B_S_ptr$) (?v1 B_S_ctype$) )(! (let ((?x6595 (b_S_typ$ ?v0))) -(let (($x7824 (= ?x6595 ?v1))) -(let (($x9555 (b_S_is$ ?v0 ?v1))) -(= $x9555 $x7824)))) :pattern ( (b_S_is$ ?v0 ?v1) ) :qid k!624)) -)) -(let (($x9576 (forall ((?v0 B_S_ptr$) (?v1 B_S_ctype$) )(! (let ((?x6595 (b_S_typ$ ?v0))) -(let (($x7824 (= ?x6595 ?v1))) -(let (($x9555 (b_S_is$ ?v0 ?v1))) -(= $x9555 $x7824)))) :qid k!624)) -)) -(let ((?x6595 (b_S_typ$ ?1))) -(let (($x7824 (= ?x6595 ?0))) -(let (($x9555 (b_S_is$ ?1 ?0))) -(let (($x9573 (= $x9555 $x7824))) -(let (($x9570 (forall ((?v0 B_S_ptr$) (?v1 B_S_ctype$) )(! 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(let (($x6864 (b_S_typed$ ?v0 (b_S_idx$ (b_S_ptr$ (b_S_array$ ?v2 ?v3) ?v1) ?v4 ?v2)))) -(let ((?x6856 (b_S_typemap$ ?v0))) -(let ((?x6858 (b_S_select_o_tm$ ?x6856 (b_S_idx$ (b_S_ptr$ (b_S_array$ ?v2 ?v3) ?v1) ?v4 ?v2)))) -(let (($x6863 (b_S_ts_n_is_n_array_n_elt$ ?x6858))) -(let (($x17970 (or (not (= (b_S_ts_n_emb$ ?x6858) (b_S_ptr$ (b_S_array$ ?v2 ?v3) ?v1))) (b_S_ts_n_is_n_volatile$ ?x6858) (not $x6863) (not $x6864)))) -(let (($x17971 (not $x17970))) -(let (($x4831 (>= (+ ?v4 (* (- 1) ?v3)) 0))) -(let (($x2815 (>= ?v4 0))) -(let (($x3743 (not $x2815))) -(or (not (b_S_typed$ ?v0 (b_S_ptr$ (b_S_array$ ?v2 ?v3) ?v1))) $x3743 $x4831 $x17971)))))))))) :pattern ( (b_S_select_o_sm$ (b_S_statusmap$ ?v0) (b_S_idx$ (b_S_ptr$ ?v2 ?v1) ?v4 ?v2)) (b_S_ptr$ (b_S_array$ ?v2 ?v3) ?v1) ) :pattern ( (b_S_select_o_tm$ (b_S_typemap$ ?v0) (b_S_idx$ (b_S_ptr$ ?v2 ?v1) ?v4 ?v2)) (b_S_ptr$ (b_S_array$ ?v2 ?v3) ?v1) ) :qid k!494)) -)) -(let (($x6902 (forall ((?v0 B_S_state$) (?v1 Int) (?v2 B_S_ctype$) (?v3 Int) (?v4 Int) )(! (let (($x6864 (b_S_typed$ ?v0 (b_S_idx$ (b_S_ptr$ (b_S_array$ ?v2 ?v3) ?v1) ?v4 ?v2)))) -(let ((?x6856 (b_S_typemap$ ?v0))) -(let ((?x6858 (b_S_select_o_tm$ ?x6856 (b_S_idx$ (b_S_ptr$ (b_S_array$ ?v2 ?v3) ?v1) ?v4 ?v2)))) -(let (($x6863 (b_S_ts_n_is_n_array_n_elt$ ?x6858))) -(let ((?x6853 (b_S_ptr$ (b_S_array$ ?v2 ?v3) ?v1))) -(let (($x6860 (= (b_S_ts_n_emb$ ?x6858) ?x6853))) -(let (($x6896 (and $x6860 (not (b_S_ts_n_is_n_volatile$ ?x6858)) $x6863 $x6864))) -(let (($x4831 (>= (+ ?v4 (* (- 1) ?v3)) 0))) -(let (($x6562 (not $x4831))) -(let (($x2815 (>= ?v4 0))) -(let (($x6854 (b_S_typed$ ?v0 ?x6853))) -(let (($x6888 (and $x6854 $x2815 $x6562))) -(let (($x6893 (not $x6888))) -(or $x6893 $x6896)))))))))))))) :pattern ( (b_S_select_o_sm$ (b_S_statusmap$ ?v0) (b_S_idx$ (b_S_ptr$ ?v2 ?v1) ?v4 ?v2)) (b_S_ptr$ (b_S_array$ ?v2 ?v3) ?v1) ) :pattern ( (b_S_select_o_tm$ (b_S_typemap$ ?v0) (b_S_idx$ (b_S_ptr$ ?v2 ?v1) ?v4 ?v2)) (b_S_ptr$ (b_S_array$ ?v2 ?v3) ?v1) ) :qid k!494)) -)) -(let (($x6864 (b_S_typed$ ?4 (b_S_idx$ (b_S_ptr$ (b_S_array$ ?2 ?1) ?3) ?0 ?2)))) -(let ((?x6856 (b_S_typemap$ ?4))) -(let ((?x6858 (b_S_select_o_tm$ ?x6856 (b_S_idx$ (b_S_ptr$ (b_S_array$ ?2 ?1) ?3) ?0 ?2)))) -(let (($x6863 (b_S_ts_n_is_n_array_n_elt$ ?x6858))) -(let (($x17970 (or (not (= (b_S_ts_n_emb$ ?x6858) (b_S_ptr$ (b_S_array$ ?2 ?1) ?3))) (b_S_ts_n_is_n_volatile$ ?x6858) (not $x6863) (not $x6864)))) -(let (($x17971 (not $x17970))) -(let (($x4831 (>= (+ ?0 (* (- 1) ?1)) 0))) -(let (($x17977 (or (not (b_S_typed$ ?4 (b_S_ptr$ (b_S_array$ ?2 ?1) ?3))) $x3743 $x4831 $x17971))) -(let ((?x6853 (b_S_ptr$ (b_S_array$ ?2 ?1) ?3))) -(let (($x6860 (= (b_S_ts_n_emb$ ?x6858) ?x6853))) -(let (($x6896 (and $x6860 (not (b_S_ts_n_is_n_volatile$ ?x6858)) $x6863 $x6864))) -(let (($x6562 (not $x4831))) -(let (($x6854 (b_S_typed$ ?4 ?x6853))) -(let (($x6888 (and $x6854 $x2815 $x6562))) -(let (($x6893 (not $x6888))) -(let (($x6899 (or $x6893 $x6896))) -(let (($x17956 (or (not $x6854) $x3743 $x4831))) -(let ((@x17962 (monotonicity (rewrite (= $x6888 (not $x17956))) (= $x6893 (not (not $x17956)))))) -(let ((@x17976 (monotonicity (trans @x17962 (rewrite (= (not (not $x17956)) $x17956)) (= $x6893 $x17956)) (rewrite (= $x6896 $x17971)) (= $x6899 (or $x17956 $x17971))))) -(let ((@x17984 (quant-intro (trans @x17976 (rewrite (= (or $x17956 $x17971) $x17977)) (= $x6899 $x17977)) (= $x6902 $x17982)))) -(let (($x6876 (forall ((?v0 B_S_state$) (?v1 Int) (?v2 B_S_ctype$) (?v3 Int) (?v4 Int) )(! (let (($x6864 (b_S_typed$ ?v0 (b_S_idx$ (b_S_ptr$ (b_S_array$ ?v2 ?v3) ?v1) ?v4 ?v2)))) -(let ((?x6856 (b_S_typemap$ ?v0))) -(let ((?x6858 (b_S_select_o_tm$ ?x6856 (b_S_idx$ (b_S_ptr$ (b_S_array$ ?v2 ?v3) ?v1) ?v4 ?v2)))) -(let (($x6863 (b_S_ts_n_is_n_array_n_elt$ ?x6858))) -(let ((?x6853 (b_S_ptr$ (b_S_array$ ?v2 ?v3) ?v1))) -(let (($x6860 (= (b_S_ts_n_emb$ ?x6858) ?x6853))) -(let (($x6867 (and $x6860 (and (not (b_S_ts_n_is_n_volatile$ ?x6858)) (and $x6863 $x6864))))) -(let (($x2766 (<= 0 ?v4))) -(let (($x6525 (and $x2766 (< ?v4 ?v3)))) -(let (($x6854 (b_S_typed$ ?v0 ?x6853))) -(let (($x6855 (and $x6854 $x6525))) -(=> $x6855 $x6867)))))))))))) :pattern ( (b_S_select_o_sm$ (b_S_statusmap$ ?v0) (b_S_idx$ (b_S_ptr$ ?v2 ?v1) ?v4 ?v2)) (b_S_ptr$ (b_S_array$ ?v2 ?v3) ?v1) ) :pattern ( (b_S_select_o_tm$ (b_S_typemap$ ?v0) (b_S_idx$ (b_S_ptr$ ?v2 ?v1) ?v4 ?v2)) (b_S_ptr$ (b_S_array$ ?v2 ?v3) ?v1) ) :qid k!494)) -)) -(let (($x6882 (forall ((?v0 B_S_state$) (?v1 Int) (?v2 B_S_ctype$) (?v3 Int) (?v4 Int) )(! (let (($x6864 (b_S_typed$ ?v0 (b_S_idx$ (b_S_ptr$ (b_S_array$ ?v2 ?v3) ?v1) ?v4 ?v2)))) -(let ((?x6856 (b_S_typemap$ ?v0))) -(let ((?x6858 (b_S_select_o_tm$ ?x6856 (b_S_idx$ (b_S_ptr$ (b_S_array$ ?v2 ?v3) ?v1) ?v4 ?v2)))) -(let (($x6863 (b_S_ts_n_is_n_array_n_elt$ ?x6858))) -(let ((?x6853 (b_S_ptr$ (b_S_array$ ?v2 ?v3) ?v1))) -(let (($x6860 (= (b_S_ts_n_emb$ ?x6858) ?x6853))) -(let (($x6867 (and $x6860 (and (not (b_S_ts_n_is_n_volatile$ ?x6858)) (and $x6863 $x6864))))) -(let (($x2766 (<= 0 ?v4))) -(let (($x6525 (and $x2766 (< ?v4 ?v3)))) -(let (($x6854 (b_S_typed$ ?v0 ?x6853))) -(let (($x6855 (and $x6854 $x6525))) -(or (not $x6855) $x6867)))))))))))) :pattern ( (b_S_select_o_sm$ (b_S_statusmap$ ?v0) (b_S_idx$ (b_S_ptr$ ?v2 ?v1) ?v4 ?v2)) (b_S_ptr$ (b_S_array$ ?v2 ?v3) ?v1) ) :pattern ( (b_S_select_o_tm$ (b_S_typemap$ ?v0) (b_S_idx$ (b_S_ptr$ ?v2 ?v1) ?v4 ?v2)) (b_S_ptr$ (b_S_array$ ?v2 ?v3) ?v1) ) :qid k!494)) -)) -(let (($x6867 (and $x6860 (and (not (b_S_ts_n_is_n_volatile$ ?x6858)) (and $x6863 $x6864))))) -(let (($x6879 (or (not (and $x6854 (and $x2766 (< ?0 ?1)))) $x6867))) -(let (($x6525 (and $x2766 (< ?0 ?1)))) -(let (($x6855 (and $x6854 $x6525))) -(let ((@x6567 (monotonicity @x2814 (rewrite (= (< ?0 ?1) $x6562)) (= $x6525 (and $x2815 $x6562))))) -(let ((@x6892 (trans (monotonicity @x6567 (= $x6855 (and $x6854 (and $x2815 $x6562)))) (rewrite (= (and $x6854 (and $x2815 $x6562)) $x6888)) (= $x6855 $x6888)))) -(let ((@x6901 (monotonicity (monotonicity @x6892 (= (not $x6855) $x6893)) (rewrite (= $x6867 $x6896)) (= $x6879 $x6899)))) -(let ((@x6906 (trans (quant-intro (rewrite (= (=> $x6855 $x6867) $x6879)) (= $x6876 $x6882)) (quant-intro @x6901 (= $x6882 $x6902)) (= $x6876 $x6902)))) -(let ((@x14395 (mp~ (mp (asserted $x6876) @x6906 $x6902) (nnf-pos (refl (~ $x6899 $x6899)) (~ $x6902 $x6902)) $x6902))) -(let ((@x17985 (mp @x14395 @x17984 $x17982))) -(let (($x23544 (not $x23015))) -(let (($x23814 (not $x17982))) -(let (($x23815 (or $x23814 $x23544 $x11218 $x23302))) -(let (($x23303 (or $x23544 $x22571 $x22573 $x23302))) -(let (($x23827 (or $x23814 $x23303))) -(let ((@x23821 (trans (monotonicity @x22612 @x22606 (= $x23303 (or $x23544 false $x11218 $x23302))) (rewrite (= (or $x23544 false $x11218 $x23302) (or $x23544 $x11218 $x23302))) (= $x23303 (or $x23544 $x11218 $x23302))))) -(let ((@x23844 (trans (monotonicity @x23821 (= $x23827 (or $x23814 (or $x23544 $x11218 $x23302)))) (rewrite (= (or $x23814 (or $x23544 $x11218 $x23302)) $x23815)) (= $x23827 $x23815)))) -(let ((@x23877 (unit-resolution (mp ((_ quant-inst v_b_S_s$ v_b_P_H_arr$ b_T_T_u1$ v_b_P_H_len$ 0) $x23827) @x23844 $x23815) @x17985 @x12000 @x23423 (hypothesis $x23309) false))) -(let ((@x23450 (monotonicity (symm (hypothesis $x22509) (= ?x22508 ?x10096)) (= (b_S_ref$ ?x22508) ?x22488)))) -(let ((?x23516 (* (- 1) ?x23421))) -(let ((?x23517 (+ ?x21017 ?x23516))) -(let (($x23500 (<= ?x23517 0))) -(let ((@x23651 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not (= ?x21017 ?x23421)) 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(unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x22694) $x22698)) (symm (monotonicity (symm @x23661 (= ?x22542 ?x10096)) (= ?x22620 ?x22488)) $x22694) $x22698))) -(let (($x22699 (>= ?x22695 0))) -(let ((@x23712 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x22694) $x22699)) (symm (monotonicity (symm @x23661 (= ?x22542 ?x10096)) (= ?x22620 ?x22488)) $x22694) $x22699))) -(let ((?x23417 (* (- 1) ?x21017))) -(let ((?x22615 (+ ?x10038 ?x23417))) -(let (($x22616 (<= ?x22615 0))) -(let (($x23418 (= ?x10038 ?x21017))) -(let (($x21189 (= ?x21017 ?x10038))) -(let (($x21194 (or $x21155 $x21189))) -(let ((@x21195 ((_ quant-inst (b_S_array$ b_T_T_u1$ v_b_P_H_len$) (b_S_ref$ ?x10037)) $x21194))) -(let ((@x23725 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x23418) $x22616)) (symm (unit-resolution @x21195 @x20273 $x21189) $x23418) $x22616))) -(let (($x22617 (>= ?x22615 0))) -(let ((@x23656 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x23418) 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@x23725 @x23712 @x23695 @x23938 @x23935 @x23654 @x23651 (= ?x22742 ?x23437)))) -(let ((@x23945 (monotonicity (trans (symm @x23940 (= ?x23437 ?x22742)) @x23450 (= ?x23437 ?x22488)) (= ?x23445 ?x22508)))) -(let ((@x23946 (trans (monotonicity @x23790 (= ?x23234 ?x23405)) (hypothesis $x23447) (= ?x23234 ?x23445)))) -(let ((@x23949 (symm (monotonicity (trans @x23946 @x23945 (= ?x23234 ?x22508)) (= ?x23235 ?x22652)) (= ?x22652 ?x23235)))) -(let ((@x23951 (trans (monotonicity @x23949 (= ?x22655 ?x23228)) (unit-resolution (def-axiom (or $x23309 $x23052)) (lemma @x23877 $x23302) $x23052) (= ?x22655 ?x22567)))) -(let ((@x23955 (trans (monotonicity (trans @x23951 @x23788 (= ?x22655 ?x10039)) (= ?x22663 ?x10041)) @x12002 $x22664))) -(let ((@x23959 (lemma (unit-resolution (hypothesis (not $x22664)) @x23955 false) (or $x23475 $x22664 (not $x22509))))) -(let ((@x23694 (unit-resolution (def-axiom (or $x22666 (not $x22664))) (unit-resolution @x23959 @x22967 @x23560 $x22664) $x22666))) -(let (($x23385 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(unit-resolution (def-axiom (or $x20505 $x20341)) @x24355 $x20341))) -(let (($x23047 (= v_b_L_H_max_G_1$ v_b_S_result_G_0$))) -(let ((@x23243 (symm (unit-resolution (def-axiom (or $x20493 $x10181)) (hypothesis $x20496) $x10181) $x23047))) -(let (($x23245 (or (not $x23047) (<= (+ v_b_L_H_max_G_1$ (* (- 1) v_b_S_result_G_0$)) 0)))) -(let ((@x23247 (unit-resolution ((_ th-lemma arith triangle-eq) $x23245) @x23243 (<= (+ v_b_L_H_max_G_1$ (* (- 1) v_b_S_result_G_0$)) 0)))) -(let ((@x23136 (trans (hypothesis $x10151) (symm (hypothesis $x10181) $x23047) (= ?x10150 v_b_S_result_G_0$)))) -(let (($x23099 (not (= ?x10150 v_b_S_result_G_0$)))) -(let (($x23104 (or $x20478 $x19519 $x19674 $x11826 $x23099))) -(let (($x22996 (>= (+ v_b_SL_H_witness_G_0$ (* (- 1) v_b_P_H_len$)) 0))) -(let (($x23100 (or $x19519 $x19674 $x22996 $x23099))) -(let (($x23105 (or $x20478 $x23100))) -(let (($x23006 (= (>= (+ (* (- 1) v_b_P_H_len$) v_b_SL_H_witness_G_0$) 0) $x11826))) -(let (($x23004 (= $x22996 (>= (+ (* (- 1) 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$x10151) (hypothesis $x12382) $x20478))) -(let ((@x23251 (unit-resolution (def-axiom (or $x20490 $x19598 $x20484)) (unit-resolution (def-axiom (or $x20481 $x20473)) @x23249 $x20481) (unit-resolution (def-axiom (or $x20493 $x20487)) (hypothesis $x20496) $x20487) $x19598))) -(let (($x23147 (>= (+ v_b_L_H_max_G_1$ ?x16058) 0))) -(let (($x23239 (or (not (<= (+ v_b_L_H_p_G_0$ (* (- 1) ?v0!15)) 0)) $x16038 $x11446))) -(let ((@x23237 ((_ th-lemma arith farkas -1 1 1) (hypothesis $x16043) (hypothesis (<= (+ v_b_L_H_p_G_0$ (* (- 1) ?v0!15)) 0)) (hypothesis $x11445) false))) -(let ((@x23255 (unit-resolution (lemma @x23237 $x23239) (unit-resolution (def-axiom (or $x19593 $x16043)) @x23251 $x16043) (unit-resolution (def-axiom (or $x20493 $x11445)) (hypothesis $x20496) $x11445) (not (<= (+ v_b_L_H_p_G_0$ (* (- 1) ?v0!15)) 0))))) -(let (($x23127 (<= (+ v_b_L_H_p_G_0$ (* (- 1) ?v0!15)) 0))) -(let (($x23155 (or $x20346 $x19577 $x19578 $x23127 $x23147))) -(let (($x23093 (<= (+ ?x15781 (* (- 1) 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$x23156 $x23155)))) -(let ((@x23260 (unit-resolution (mp ((_ quant-inst ?v0!15) $x23156) @x23164 $x23155) (hypothesis $x20341) (unit-resolution (def-axiom (or $x19593 $x15773)) @x23251 $x15773) (unit-resolution (def-axiom (or $x19593 $x15774)) @x23251 $x15774) (or $x23127 $x23147)))) -(let ((@x23262 ((_ th-lemma arith farkas -1 1 1) (unit-resolution @x23260 @x23255 $x23147) (unit-resolution (def-axiom (or $x19593 (not $x16060))) @x23251 (not $x16060)) @x23247 false))) -(let ((@x24798 (unit-resolution (lemma @x23262 (or $x20493 $x20346 $x11826 $x19519 $x19679 $x19674)) @x24540 (unit-resolution (def-axiom (or $x20505 $x11827)) @x24355 $x11827) (unit-resolution (def-axiom (or $x20505 $x11391)) @x24355 $x11391) @x24795 (unit-resolution (def-axiom (or $x20505 $x12382)) @x24355 $x12382) $x20493))) -(let ((@x24803 (unit-resolution (def-axiom (or $x20502 $x20462 $x20496)) @x24798 (unit-resolution (def-axiom (or $x20505 $x20499)) @x24355 $x20499) $x20462))) -(let ((@x24804 (unit-resolution (def-axiom (or $x20459 $x11446)) @x24803 $x11446))) -(let ((@x24203 (unit-resolution (def-axiom (or $x20505 $x11860)) @x24355 $x11860))) -(let (($x24182 (or $x22580 $x20989 $x21492 $x22569 $x19675 $x11445 $x23433))) -(let (($x23429 (>= (+ v_b_L_H_p_G_0$ (* (- 1) v_b_P_H_len$)) 0))) -(let (($x23434 (or $x20989 $x21492 $x22569 $x19675 $x23429 $x23433))) -(let (($x24183 (or $x22580 $x23434))) -(let ((@x24147 (rewrite (= (>= (+ (* (- 1) v_b_P_H_len$) v_b_L_H_p_G_0$) 0) $x11445)))) -(let (($x24139 (= (+ v_b_L_H_p_G_0$ (* (- 1) v_b_P_H_len$)) (+ (* (- 1) v_b_P_H_len$) v_b_L_H_p_G_0$)))) -(let ((@x24148 (monotonicity (rewrite $x24139) (= $x23429 (>= (+ (* (- 1) v_b_P_H_len$) v_b_L_H_p_G_0$) 0))))) -(let ((@x24179 (monotonicity (trans @x24148 @x24147 (= $x23429 $x11445)) (= $x23434 (or $x20989 $x21492 $x22569 $x19675 $x11445 $x23433))))) -(let ((@x24189 (monotonicity @x24179 (= $x24183 (or $x22580 (or $x20989 $x21492 $x22569 $x19675 $x11445 $x23433)))))) -(let ((@x24193 (trans @x24189 (rewrite (= (or $x22580 (or $x20989 $x21492 $x22569 $x19675 $x11445 $x23433)) $x24182)) (= $x24183 $x24182)))) -(let ((@x24194 (mp ((_ quant-inst v_b_S_s$ v_b_P_H_arr$ (b_S_ptr$ ?x10035 ?x21017) v_b_P_H_len$ v_b_L_H_p_G_0$ b_T_T_u1$) $x24183) @x24193 $x24182))) -(let ((@x24207 (unit-resolution @x24194 @x18688 @x9728 @x12009 @x24203 @x24804 @x22724 (hypothesis $x23432) false))) -(let ((@x24208 (lemma @x24207 $x23433))) -(let ((@x24497 (unit-resolution (def-axiom (or $x24247 $x24257)) (mp (unit-resolution (def-axiom (or $x23432 $x23317)) @x24208 $x23317) @x24487 $x24258) $x24247))) -(let (($x24284 (b_S_in_n_wrapped_n_domain$ v_b_S_s$ ?x24595))) -(let ((?x24260 (b_S_owner$ v_b_S_s$ ?x24595))) -(let (($x24283 (= ?x24260 b_S_me$))) -(let (($x24285 (or $x24283 $x24284))) -(let (($x24286 (not $x24285))) -(let ((?x24251 (b_S_typ$ ?x24595))) -(let ((?x24252 (b_S_kind_n_of$ ?x24251))) -(let (($x24259 (= ?x24252 b_S_kind_n_primitive$))) -(let (($x24250 (not $x24247))) -(let (($x24256 (not $x24255))) -(let 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false)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) - diff -r 3fdb94d87e0e -r 3c5a7746ffa4 src/HOL/SMT_Examples/Boogie_Max.certs --- a/src/HOL/SMT_Examples/Boogie_Max.certs Fri Mar 05 15:01:59 2021 +0100 +++ b/src/HOL/SMT_Examples/Boogie_Max.certs Fri Mar 05 21:26:38 2021 +0100 @@ -1,4 +1,4 @@ -9c420ec314a920506e90cf4b4e40b4ee3ab35dec 778 0 +ae712ba60be9be1bab4bc3570ac5c4aec9bad512 778 0 unsat ((set-logic AUFLIA) (declare-fun ?v0!3 () Int) @@ -777,782 +777,3 @@ (let ((@x2111 (unit-resolution (lemma @x1971 (or $x951 (not $x1522) $x1858 $x689 $x1895 $x1359 $x1361)) @x2102 (or $x951 (not $x1522) $x689 $x1895 $x1359 $x1361)))) (unit-resolution @x2111 @x2109 @x2121 (unit-resolution (def-axiom (or $x1898 $x692)) @x2025 $x692) (unit-resolution (def-axiom (or $x1898 $x1892)) @x2025 $x1892) (unit-resolution (def-axiom (or $x1898 $x104)) @x2025 $x104) (unit-resolution (def-axiom (or $x1898 $x109)) @x2025 $x109) 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(def-axiom (or $x1274 (not $x1011))) @x2096 (not $x1011)) @x2084 false))) -(let ((@x2114 (unit-resolution (def-axiom (or $x1925 $x1875 $x1919)) (lemma @x2106 $x1872) (unit-resolution (def-axiom (or $x1928 $x1922)) @x2094 $x1922) $x1919))) -(let ((@x2001 (unit-resolution (def-axiom (or $x1913 $x1901 $x1907)) (unit-resolution (def-axiom (or $x1916 $x1910)) @x2114 $x1910) $x1910))) -(let ((@x2025 (unit-resolution @x2001 @x2179 $x1901))) -(let ((@x1557 (trans (monotonicity (hypothesis $x107) (= ?x135 ?x101)) (symm (hypothesis $x104) (= ?x101 v_b_max_G_2$)) (= ?x135 v_b_max_G_2$)))) -(let ((@x1975 (trans @x1557 (symm (hypothesis $x109) (= v_b_max_G_2$ v_b_max_G_3$)) $x136))) -(let ((@x1978 (lemma (unit-resolution (hypothesis $x951) @x1975 false) (or $x136 $x1361 $x1359 $x1360)))) -(let ((@x2121 (unit-resolution @x1978 (unit-resolution (def-axiom (or $x1898 $x109)) @x2025 $x109) (unit-resolution (def-axiom (or $x1898 $x104)) @x2025 $x104) (unit-resolution (def-axiom (or $x1898 $x107)) @x2025 $x107) $x136))) -(let ((@x2109 (unit-resolution ((_ th-lemma arith triangle-eq) (or $x1362 $x1522)) (unit-resolution (def-axiom (or $x1898 $x684)) @x2025 $x684) $x1522))) -(let ((@x1460 (unit-resolution @x1808 (unit-resolution @x1523 (hypothesis $x136) $x1886) (hypothesis $x1892) $x1318))) -(let ((@x1539 (def-axiom (or $x1313 $x1053)))) -(let (($x1965 (not $x1560))) -(let (($x1597 (<= (+ ?x101 ?x744) 0))) -(let ((@x1431 (trans (symm (hypothesis $x104) (= ?x101 v_b_max_G_2$)) (symm (hypothesis $x109) (= v_b_max_G_2$ v_b_max_G_3$)) (= ?x101 v_b_max_G_3$)))) -(let ((@x1435 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not (= ?x101 v_b_max_G_3$)) $x1597)) @x1431 $x1597))) -(let ((@x1437 (lemma ((_ th-lemma arith farkas -1 -1 1) (hypothesis $x1436) (hypothesis $x1597) (hypothesis $x1445) false) (or $x1453 $x1070 (not $x1597))))) -(let ((@x1952 (unit-resolution @x1565 (unit-resolution @x1437 (unit-resolution @x1812 @x1460 $x1436) @x1435 $x1453) $x1563))) -(let ((@x1958 (unit-resolution ((_ th-lemma arith assign-bounds 1 1 1) (or $x1955 $x1070 (not $x1597) $x689)) (unit-resolution @x1812 @x1460 $x1436) @x1435 (hypothesis $x692) $x1955))) -(let ((@x1962 (unit-resolution (mp ((_ quant-inst ?v0!3) $x1464) @x1450 $x1476) (hypothesis $x1853) (unit-resolution (def-axiom (or $x1313 $x931)) @x1460 $x931) (or $x1511 $x1488)))) -(let ((@x1969 (unit-resolution ((_ th-lemma arith triangle-eq) (or $x1558 (not $x1511) $x1965)) (unit-resolution @x1962 @x1958 $x1511) (or $x1558 $x1965)))) -(let ((@x1971 ((_ th-lemma arith farkas -1 1 1) (unit-resolution @x1969 (unit-resolution @x1540 @x1952 (not $x1558)) $x1965) (hypothesis $x1522) (unit-resolution @x1539 @x1460 $x1053) false))) -(let ((@x2111 (unit-resolution (lemma @x1971 (or $x951 (not $x1522) $x1858 $x689 $x1895 $x1359 $x1361)) @x2102 (or $x951 (not $x1522) $x689 $x1895 $x1359 $x1361)))) -(unit-resolution @x2111 @x2109 @x2121 (unit-resolution (def-axiom (or $x1898 $x692)) @x2025 $x692) (unit-resolution (def-axiom (or $x1898 $x1892)) @x2025 $x1892) (unit-resolution (def-axiom (or $x1898 $x104)) @x2025 $x104) (unit-resolution (def-axiom (or $x1898 $x109)) @x2025 $x109) false)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) - diff -r 3fdb94d87e0e -r 3c5a7746ffa4 src/HOL/SMT_Examples/SMT_Examples.certs --- a/src/HOL/SMT_Examples/SMT_Examples.certs Fri Mar 05 15:01:59 2021 +0100 +++ b/src/HOL/SMT_Examples/SMT_Examples.certs Fri Mar 05 21:26:38 2021 +0100 @@ -1,920 +1,11 @@ -c6761b6a026c6bf2d28c35e9faf633fc441c84c5 45 0 -unsat -((set-logic AUFLIA) -(proof -(let ((?x44 (id$ x$))) -(let (($x46 (= ?x44 x$))) -(let (($x73 (not $x46))) -(let (($x47 (id$a true))) -(let (($x510 (forall ((?v0 Bool) )(! (let (($x33 (id$a ?v0))) -(= $x33 ?v0)) :pattern ( (id$a ?v0) ) :qid k!9)) -)) -(let (($x40 (forall ((?v0 Bool) )(! (let (($x33 (id$a ?v0))) -(= $x33 ?v0)) :qid k!9)) -)) -(let ((@x514 (quant-intro (refl (= (= (id$a ?0) ?0) (= (id$a ?0) ?0))) (= $x40 $x510)))) -(let ((@x69 (nnf-pos (refl (~ (= (id$a ?0) ?0) (= (id$a ?0) ?0))) (~ $x40 $x40)))) -(let (($x35 (forall ((?v0 Bool) )(! (let (($x33 (id$a ?v0))) -(= $x33 ?v0)) :qid k!9)) -)) -(let ((@x42 (quant-intro (rewrite (= (= (id$a ?0) ?0) (= (id$a ?0) ?0))) (= $x35 $x40)))) -(let ((@x515 (mp (mp~ (mp (asserted $x35) @x42 $x40) @x69 $x40) @x514 $x510))) -(let (($x87 (or (not $x510) $x47))) -(let ((@x176 (monotonicity (rewrite (= (= $x47 true) $x47)) (= (or (not $x510) (= $x47 true)) $x87)))) -(let ((@x179 (trans @x176 (rewrite (= $x87 $x87)) (= (or (not $x510) (= $x47 true)) $x87)))) -(let ((@x495 (unit-resolution (mp ((_ quant-inst true) (or (not $x510) (= $x47 true))) @x179 $x87) @x515 (hypothesis (not $x47)) false))) -(let (($x71 (or $x73 (not $x47)))) -(let ((@x79 (monotonicity (rewrite (= (and $x46 $x47) (not $x71))) (= (not (and $x46 $x47)) (not (not $x71)))))) -(let ((@x83 (trans @x79 (rewrite (= (not (not $x71)) $x71)) (= (not (and $x46 $x47)) $x71)))) -(let (($x54 (and $x46 $x47))) -(let (($x57 (not $x54))) -(let ((@x56 (monotonicity (rewrite (= (= $x47 true) $x47)) (= (and $x46 (= $x47 true)) $x54)))) -(let ((@x62 (mp (asserted (not (and $x46 (= $x47 true)))) (monotonicity @x56 (= (not (and $x46 (= $x47 true))) $x57)) $x57))) -(let ((@x84 (mp @x62 @x83 $x71))) -(let (($x503 (forall ((?v0 A$) )(! (let ((?x28 (id$ ?v0))) -(= ?x28 ?v0)) :pattern ( (id$ ?v0) ) :qid k!8)) -)) -(let (($x30 (forall ((?v0 A$) )(! (let ((?x28 (id$ ?v0))) -(= ?x28 ?v0)) :qid k!8)) -)) -(let ((@x507 (quant-intro (refl (= (= (id$ ?0) ?0) (= (id$ ?0) ?0))) (= $x30 $x503)))) -(let ((@x64 (nnf-pos (refl (~ (= (id$ ?0) ?0) (= (id$ ?0) ?0))) (~ $x30 $x30)))) -(let ((@x508 (mp (mp~ (asserted $x30) @x64 $x30) @x507 $x503))) -(let (($x163 (or (not $x503) $x46))) -(let ((@x496 ((_ quant-inst x$) $x163))) -(unit-resolution @x496 @x508 (unit-resolution @x84 (lemma @x495 $x47) $x73) false))))))))))))))))))))))))))))))))) - -23f5eb3b530a4577da2f8947333286ff70ed557f 11 0 -unsat -((set-logic AUFLIA) -(proof -(let (($x29 (exists ((?v0 A$) )(! (g$ ?v0) :qid k!7)) -)) -(let (($x30 (f$ $x29))) -(let (($x31 (=> $x30 true))) -(let (($x32 (not $x31))) -(let ((@x42 (trans (monotonicity (rewrite (= $x31 true)) (= $x32 (not true))) (rewrite (= (not true) false)) (= $x32 false)))) -(mp (asserted $x32) @x42 false)))))))) - -174a4beaccbbd473470bdf78d1dd5655decaaf38 51 0 -unsat -((set-logic AUFLIA) -(proof -(let ((?x61 (fun_app$ f$ i$))) -(let ((?x57 (fun_upd$ f$ i1$ v1$))) -(let ((?x59 (fun_upd$ ?x57 i2$ v2$))) -(let ((?x60 (fun_app$ ?x59 i$))) -(let (($x62 (= ?x60 ?x61))) -(let ((?x189 (fun_app$ ?x57 i$))) -(let (($x197 (= ?x189 ?x61))) -(let (($x196 (= ?x189 v1$))) -(let (($x49 (= i$ i1$))) -(let (($x476 (ite $x49 $x196 $x197))) -(let (($x524 (forall ((?v0 A_b_fun$) (?v1 A$) (?v2 B$) (?v3 A$) )(! (let (($x41 (= ?v3 ?v1))) -(ite $x41 (= (fun_app$ (fun_upd$ ?v0 ?v1 ?v2) ?v3) ?v2) (= (fun_app$ (fun_upd$ ?v0 ?v1 ?v2) ?v3) (fun_app$ ?v0 ?v3)))) :pattern ( (fun_app$ (fun_upd$ ?v0 ?v1 ?v2) ?v3) ) :qid k!16)) -)) -(let (($x94 (forall ((?v0 A_b_fun$) (?v1 A$) (?v2 B$) (?v3 A$) )(! (let (($x41 (= ?v3 ?v1))) -(ite $x41 (= (fun_app$ (fun_upd$ ?v0 ?v1 ?v2) ?v3) ?v2) (= (fun_app$ (fun_upd$ ?v0 ?v1 ?v2) ?v3) (fun_app$ ?v0 ?v3)))) :qid k!16)) -)) -(let (($x41 (= ?0 ?2))) -(let (($x89 (ite $x41 (= (fun_app$ (fun_upd$ ?3 ?2 ?1) ?0) ?1) (= (fun_app$ (fun_upd$ ?3 ?2 ?1) ?0) (fun_app$ ?3 ?0))))) -(let (($x45 (forall ((?v0 A_b_fun$) (?v1 A$) (?v2 B$) (?v3 A$) )(! (let ((?x40 (fun_app$ (fun_upd$ ?v0 ?v1 ?v2) ?v3))) -(= ?x40 (ite (= ?v3 ?v1) ?v2 (fun_app$ ?v0 ?v3)))) :qid k!16)) -)) -(let ((?x40 (fun_app$ (fun_upd$ ?3 ?2 ?1) ?0))) -(let (($x44 (= ?x40 (ite $x41 ?1 (fun_app$ ?3 ?0))))) -(let ((@x82 (mp~ (asserted $x45) (nnf-pos (refl (~ $x44 $x44)) (~ $x45 $x45)) $x45))) -(let ((@x97 (mp @x82 (quant-intro (rewrite (= $x44 $x89)) (= $x45 $x94)) $x94))) -(let ((@x529 (mp @x97 (quant-intro (refl (= $x89 $x89)) (= $x94 $x524)) $x524))) -(let (($x163 (not $x524))) -(let (($x478 (or $x163 $x476))) -(let ((@x479 ((_ quant-inst f$ i1$ v1$ i$) $x478))) -(let (($x50 (not $x49))) -(let (($x52 (= i$ i2$))) -(let (($x53 (not $x52))) -(let (($x54 (and $x50 $x53))) -(let ((@x72 (monotonicity (rewrite (= (=> $x54 $x62) (or (not $x54) $x62))) (= (not (=> $x54 $x62)) (not (or (not $x54) $x62)))))) -(let ((@x73 (not-or-elim (mp (asserted (not (=> $x54 $x62))) @x72 (not (or (not $x54) $x62))) $x54))) -(let ((@x74 (and-elim @x73 $x50))) -(let ((@x313 (unit-resolution (def-axiom (or (not $x476) $x49 $x197)) @x74 (or (not $x476) $x197)))) -(let (($x192 (= ?x60 ?x189))) -(let (($x188 (= ?x60 v2$))) -(let (($x171 (ite $x52 $x188 $x192))) -(let (($x293 (or $x163 $x171))) -(let ((@x503 ((_ quant-inst (fun_upd$ f$ i1$ v1$) i2$ v2$ i$) $x293))) -(let ((@x76 (and-elim @x73 $x53))) -(let ((@x458 (unit-resolution (def-axiom (or (not $x171) $x52 $x192)) @x76 (or (not $x171) $x192)))) -(let ((@x462 (trans (unit-resolution @x458 (unit-resolution @x503 @x529 $x171) $x192) (unit-resolution @x313 (unit-resolution @x479 @x529 $x476) $x197) $x62))) -(let ((@x78 (not-or-elim (mp (asserted (not (=> $x54 $x62))) @x72 (not (or (not $x54) $x62))) (not $x62)))) -(unit-resolution @x78 @x462 false))))))))))))))))))))))))))))))))))))))))))) - -3aa17d1c77bc1a92bca05df291d11d81c645a931 6 0 +f4ff5c44833ca360a0e6110670545870e993732e 6 0 unsat ((set-logic AUFLIA) (proof (let ((@x30 (rewrite (= (not true) false)))) (mp (asserted (not true)) @x30 false)))) -feaa6ef662dd489cf55f86209489c2992ff08d28 46 0 -unsat -((set-logic AUFLIA) -(proof -(let ((?x61 (fun_app$a le$ 3))) -(let (($x63 (fun_app$ ?x61 42))) -(let (($x75 (not $x63))) -(let (($x59 (= le$ uu$))) -(let ((@x73 (monotonicity (rewrite (= (=> $x59 $x63) (or (not $x59) $x63))) (= (not (=> $x59 $x63)) (not (or (not $x59) $x63)))))) -(let ((@x74 (not-or-elim (mp (asserted (not (=> $x59 $x63))) @x73 (not (or (not $x59) $x63))) $x59))) -(let ((@x482 (monotonicity (symm @x74 (= uu$ le$)) (= (fun_app$a uu$ 3) ?x61)))) -(let ((@x484 (symm (monotonicity @x482 (= (fun_app$ (fun_app$a uu$ 3) 42) $x63)) (= $x63 (fun_app$ (fun_app$a uu$ 3) 42))))) -(let ((@x472 (monotonicity @x484 (= $x75 (not (fun_app$ (fun_app$a uu$ 3) 42)))))) -(let ((@x77 (not-or-elim (mp (asserted (not (=> $x59 $x63))) @x73 (not (or (not $x59) $x63))) $x75))) -(let ((?x79 (fun_app$a uu$ 3))) -(let (($x168 (fun_app$ ?x79 42))) -(let (($x52 (forall ((?v0 Int) (?v1 Int) )(! (let (($x46 (<= (+ ?v0 (* (- 1) ?v1)) 0))) -(let (($x31 (fun_app$ (fun_app$a uu$ ?v0) ?v1))) -(= $x31 $x46))) :pattern ( (fun_app$ (fun_app$a uu$ ?v0) ?v1) ) :qid k!10)) -)) -(let (($x46 (<= (+ ?1 (* (- 1) ?0)) 0))) -(let (($x31 (fun_app$ (fun_app$a uu$ ?1) ?0))) -(let (($x49 (= $x31 $x46))) -(let (($x35 (forall ((?v0 Int) (?v1 Int) )(! (let (($x32 (<= ?v0 ?v1))) -(let (($x31 (fun_app$ (fun_app$a uu$ ?v0) ?v1))) -(= $x31 $x32))) :pattern ( (fun_app$ (fun_app$a uu$ ?v0) ?v1) ) :qid k!10)) -)) -(let (($x40 (forall ((?v0 Int) (?v1 Int) )(! (let (($x32 (<= ?v0 ?v1))) -(let (($x31 (fun_app$ (fun_app$a uu$ ?v0) ?v1))) -(= $x31 $x32))) :pattern ( (fun_app$ (fun_app$a uu$ ?v0) ?v1) ) :qid k!10)) -)) -(let ((@x51 (monotonicity (rewrite (= (<= ?1 ?0) $x46)) (= (= $x31 (<= ?1 ?0)) $x49)))) -(let ((@x42 (quant-intro (rewrite (= (= $x31 (<= ?1 ?0)) (= $x31 (<= ?1 ?0)))) (= $x35 $x40)))) -(let ((@x57 (mp (asserted $x35) (trans @x42 (quant-intro @x51 (= $x40 $x52)) (= $x35 $x52)) $x52))) -(let ((@x78 (mp~ @x57 (nnf-pos (refl (~ $x49 $x49)) (~ $x52 $x52)) $x52))) -(let (($x134 (or (not $x52) $x168))) -(let (($x137 (= (or (not $x52) (= $x168 (<= (+ 3 (* (- 1) 42)) 0))) $x134))) -(let ((?x169 (* (- 1) 42))) -(let ((?x170 (+ 3 ?x169))) -(let (($x160 (<= ?x170 0))) -(let (($x171 (= $x168 $x160))) -(let ((@x158 (trans (monotonicity (rewrite (= ?x169 (- 42))) (= ?x170 (+ 3 (- 42)))) (rewrite (= (+ 3 (- 42)) (- 39))) (= ?x170 (- 39))))) -(let ((@x497 (trans (monotonicity @x158 (= $x160 (<= (- 39) 0))) (rewrite (= (<= (- 39) 0) true)) (= $x160 true)))) -(let ((@x131 (trans (monotonicity @x497 (= $x171 (= $x168 true))) (rewrite (= (= $x168 true) $x168)) (= $x171 $x168)))) -(let ((@x478 (mp ((_ quant-inst 3 42) (or (not $x52) $x171)) (trans (monotonicity @x131 $x137) (rewrite (= $x134 $x134)) $x137) $x134))) -(unit-resolution (unit-resolution @x478 @x78 $x168) (mp @x77 @x472 (not $x168)) false))))))))))))))))))))))))))))))))))) - -60f1b32e9c6a2229b64c85dcfb0bde9c2bd5433a 11 0 -unsat -((set-logic AUFLIA) -(proof -(let (($x29 (forall ((?v0 A$) )(! (g$ ?v0) :qid k!7)) -)) -(let (($x30 (f$ $x29))) -(let (($x31 (=> $x30 true))) -(let (($x32 (not $x31))) -(let ((@x42 (trans (monotonicity (rewrite (= $x31 true)) (= $x32 (not true))) (rewrite (= (not true) false)) (= $x32 false)))) -(mp (asserted $x32) @x42 false)))))))) - -9cdd1051dbf4e0648f71536fbc74bbab8e0e744e 75 0 -unsat -((set-logic AUFLIA) -(proof -(let ((?x78 (cons$ 2 nil$))) -(let ((?x79 (cons$ 1 ?x78))) -(let ((?x74 (cons$ 1 nil$))) -(let ((?x75 (cons$ 0 ?x74))) -(let ((?x76 (map$ uu$ ?x75))) -(let (($x80 (= ?x76 ?x79))) -(let ((?x185 (map$ uu$ ?x74))) -(let ((?x189 (map$ uu$ nil$))) -(let ((?x188 (fun_app$ uu$ 1))) -(let ((?x160 (cons$ ?x188 ?x189))) -(let (($x290 (= ?x185 ?x160))) -(let (($x521 (forall ((?v0 Int_int_fun$) (?v1 Int) (?v2 Int_list$) )(! (= (map$ ?v0 (cons$ ?v1 ?v2)) (cons$ (fun_app$ ?v0 ?v1) (map$ ?v0 ?v2))) :pattern ( (map$ ?v0 (cons$ ?v1 ?v2)) ) :pattern ( (cons$ (fun_app$ ?v0 ?v1) (map$ ?v0 ?v2)) ) :qid k!13)) -)) -(let (($x72 (forall ((?v0 Int_int_fun$) (?v1 Int) (?v2 Int_list$) )(! (= (map$ ?v0 (cons$ ?v1 ?v2)) (cons$ (fun_app$ ?v0 ?v1) (map$ ?v0 ?v2))) :qid k!13)) -)) -(let (($x71 (= (map$ ?2 (cons$ ?1 ?0)) (cons$ (fun_app$ ?2 ?1) (map$ ?2 ?0))))) -(let ((@x97 (mp~ (asserted $x72) (nnf-pos (refl (~ $x71 $x71)) (~ $x72 $x72)) $x72))) -(let ((@x526 (mp @x97 (quant-intro (refl (= $x71 $x71)) (= $x72 $x521)) $x521))) -(let (($x173 (or (not $x521) $x290))) -(let ((@x506 ((_ quant-inst uu$ 1 nil$) $x173))) -(let (($x492 (= ?x189 nil$))) -(let (($x513 (forall ((?v0 Int_int_fun$) )(! (= (map$ ?v0 nil$) nil$) :pattern ( (map$ ?v0 nil$) ) :qid k!12)) -)) -(let (($x61 (forall ((?v0 Int_int_fun$) )(! (= (map$ ?v0 nil$) nil$) :qid k!12)) -)) -(let ((@x515 (refl (= (= (map$ ?0 nil$) nil$) (= (map$ ?0 nil$) nil$))))) -(let ((@x83 (refl (~ (= (map$ ?0 nil$) nil$) (= (map$ ?0 nil$) nil$))))) -(let ((@x518 (mp (mp~ (asserted $x61) (nnf-pos @x83 (~ $x61 $x61)) $x61) (quant-intro @x515 (= $x61 $x513)) $x513))) -(let (($x495 (or (not $x513) $x492))) -(let ((@x496 ((_ quant-inst uu$) $x495))) -(let (($x136 (= ?x188 2))) -(let (($x51 (forall ((?v0 Int) )(! (= (+ ?v0 (* (- 1) (fun_app$ uu$ ?v0))) (- 1)) :pattern ( (fun_app$ uu$ ?v0) ) :qid k!11)) -)) -(let (($x47 (= (+ ?0 (* (- 1) (fun_app$ uu$ ?0))) (- 1)))) -(let (($x34 (forall ((?v0 Int) )(! (let ((?x29 (fun_app$ uu$ ?v0))) -(= ?x29 (+ ?v0 1))) :pattern ( (fun_app$ uu$ ?v0) ) :qid k!11)) -)) -(let (($x42 (forall ((?v0 Int) )(! (let ((?x29 (fun_app$ uu$ ?v0))) -(= ?x29 (+ 1 ?v0))) :pattern ( (fun_app$ uu$ ?v0) ) :qid k!11)) -)) -(let ((@x53 (quant-intro (rewrite (= (= (fun_app$ uu$ ?0) (+ 1 ?0)) $x47)) (= $x42 $x51)))) -(let ((?x29 (fun_app$ uu$ ?0))) -(let (($x39 (= ?x29 (+ 1 ?0)))) -(let ((@x41 (monotonicity (rewrite (= (+ ?0 1) (+ 1 ?0))) (= (= ?x29 (+ ?0 1)) $x39)))) -(let ((@x56 (mp (asserted $x34) (trans (quant-intro @x41 (= $x34 $x42)) @x53 (= $x34 $x51)) $x51))) -(let ((@x85 (mp~ @x56 (nnf-pos (refl (~ $x47 $x47)) (~ $x51 $x51)) $x51))) -(let (($x145 (not $x51))) -(let (($x499 (or $x145 $x136))) -(let ((@x498 (rewrite (= (= (+ 1 (* (- 1) ?x188)) (- 1)) $x136)))) -(let ((@x204 (monotonicity @x498 (= (or $x145 (= (+ 1 (* (- 1) ?x188)) (- 1))) $x499)))) -(let ((@x207 (trans @x204 (rewrite (= $x499 $x499)) (= (or $x145 (= (+ 1 (* (- 1) ?x188)) (- 1))) $x499)))) -(let ((@x104 (mp ((_ quant-inst 1) (or $x145 (= (+ 1 (* (- 1) ?x188)) (- 1)))) @x207 $x499))) -(let ((@x191 (monotonicity (symm (unit-resolution @x104 @x85 $x136) (= 2 ?x188)) (symm (unit-resolution @x496 @x518 $x492) (= nil$ ?x189)) (= ?x78 ?x160)))) -(let ((@x473 (trans @x191 (symm (unit-resolution @x506 @x526 $x290) (= ?x160 ?x185)) (= ?x78 ?x185)))) -(let ((?x182 (fun_app$ uu$ 0))) -(let (($x163 (= ?x182 1))) -(let (($x487 (or $x145 $x163))) -(let ((@x501 (monotonicity (rewrite (= (+ 0 (* (- 1) ?x182)) (* (- 1) ?x182))) (= (= (+ 0 (* (- 1) ?x182)) (- 1)) (= (* (- 1) ?x182) (- 1)))))) -(let ((@x503 (trans @x501 (rewrite (= (= (* (- 1) ?x182) (- 1)) $x163)) (= (= (+ 0 (* (- 1) ?x182)) (- 1)) $x163)))) -(let ((@x151 (monotonicity @x503 (= (or $x145 (= (+ 0 (* (- 1) ?x182)) (- 1))) $x487)))) -(let ((@x490 (trans @x151 (rewrite (= $x487 $x487)) (= (or $x145 (= (+ 0 (* (- 1) ?x182)) (- 1))) $x487)))) -(let ((@x491 (mp ((_ quant-inst 0) (or $x145 (= (+ 0 (* (- 1) ?x182)) (- 1)))) @x490 $x487))) -(let ((@x478 (monotonicity (symm (unit-resolution @x491 @x85 $x163) (= 1 ?x182)) @x473 (= ?x79 (cons$ ?x182 ?x185))))) -(let ((?x186 (cons$ ?x182 ?x185))) -(let (($x187 (= ?x76 ?x186))) -(let (($x504 (or (not $x521) $x187))) -(let ((@x505 ((_ quant-inst uu$ 0 (cons$ 1 nil$)) $x504))) -(let ((@x466 (trans (unit-resolution @x505 @x526 $x187) (symm @x478 (= ?x186 ?x79)) $x80))) -(let (($x81 (not $x80))) -(let ((@x82 (asserted $x81))) -(unit-resolution @x82 @x466 false)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) - -40c61a0200976d6203302a7343af5b7ad1e6ce36 11 0 -unsat -((set-logic AUFLIA) -(proof -(let (($x29 (forall ((?v0 A$) )(! 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(let (($x55 (>= ?v0 10))) -(ite $x55 (= (dec_10$ ?v0) (dec_10$ (+ (- 10) ?v0))) (= (dec_10$ ?v0) ?v0))) :qid k!5)) -)) -(let (($x55 (>= ?0 10))) -(let (($x87 (ite $x55 (= (dec_10$ ?0) (dec_10$ (+ (- 10) ?0))) (= (dec_10$ ?0) ?0)))) -(let (($x68 (forall ((?v0 Int) )(! (let ((?x38 (+ (- 10) ?v0))) -(let ((?x41 (dec_10$ ?x38))) -(let (($x55 (>= ?v0 10))) -(let ((?x60 (ite $x55 ?x41 ?v0))) -(let ((?x28 (dec_10$ ?v0))) -(= ?x28 ?x60)))))) :qid k!5)) -)) -(let ((?x38 (+ (- 10) ?0))) -(let ((?x41 (dec_10$ ?x38))) -(let ((?x60 (ite $x55 ?x41 ?0))) -(let ((?x28 (dec_10$ ?0))) -(let (($x65 (= ?x28 ?x60))) -(let (($x35 (forall ((?v0 Int) )(! (let ((?x28 (dec_10$ ?v0))) -(= ?x28 (ite (< ?v0 10) ?v0 (dec_10$ (- ?v0 10))))) :qid k!5)) -)) -(let (($x50 (forall ((?v0 Int) )(! 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(let (($x97 (less_eq$ ?v0 ?v2))) -(let (($x95 (less_eq$ ?v1 ?v2))) -(let (($x93 (less_eq$ ?v0 ?v1))) -(let (($x96 (and $x93 $x95))) -(=> $x96 $x97))))) :qid k!17)) -)) -(let ((@x110 (mp (asserted $x99) (quant-intro (rewrite (= (=> $x96 $x97) $x102)) (= $x99 $x105)) $x105))) -(let ((@x159 (mp (mp~ @x110 (nnf-pos (refl (~ $x102 $x102)) (~ $x105 $x105)) $x105) (quant-intro @x155 (= $x105 $x156)) $x156))) -(let ((@x584 (mp @x159 @x583 $x578))) -(let (($x247 (not $x115))) -(let (($x160 (not $x113))) -(let (($x251 (not $x578))) -(let (($x252 (or $x251 $x160 $x247 $x117))) -(let ((@x570 (mp ((_ quant-inst (sup$ ?x108) (sup$ ?x111) (sup$ ?x108)) (or $x251 (or $x160 $x247 $x117))) (rewrite (= (or $x251 (or $x160 $x247 $x117)) $x252)) $x252))) -(unit-resolution @x570 @x584 @x114 @x116 @x119 false))))))))))))))))))))))))))))))))))))))) - -4e8ab14f236ad601aa67494ca8ea18b2ba6a1a79 25 0 -unsat -((set-logic AUFLIA) -(proof -(let (($x142 (pred$e 1))) -(let (($x144 (not $x142))) -(let ((@x145 (asserted $x144))) -(let (($x615 (forall ((?v0 Int) )(! (pred$e ?v0) :pattern ( (pred$e ?v0) ) :qid k!29)) -)) -(let (($x138 (forall ((?v0 Int) )(! (pred$e ?v0) :qid k!29)) -)) -(let (($x127 (forall ((?v0 Int) )(! (let (($x125 (or (pred$d (cons$d ?v0 nil$d)) (not (pred$d (cons$d ?v0 nil$d)))))) -(let (($x119 (pred$e ?v0))) -(and $x119 $x125))) :qid k!29)) -)) -(let (($x119 (pred$e ?0))) -(let (($x125 (or (pred$d (cons$d ?0 nil$d)) (not (pred$d (cons$d ?0 nil$d)))))) -(let (($x126 (and $x119 $x125))) -(let ((@x133 (monotonicity (rewrite (= $x125 true)) (= $x126 (and $x119 true))))) -(let ((@x140 (quant-intro (trans @x133 (rewrite (= (and $x119 true) $x119)) (= $x126 $x119)) (= $x127 $x138)))) -(let ((@x170 (mp~ (mp (asserted $x127) @x140 $x138) (nnf-pos (refl (~ $x119 $x119)) (~ $x138 $x138)) $x138))) -(let ((@x620 (mp @x170 (quant-intro (refl (= $x119 $x119)) (= $x138 $x615)) $x615))) -(let (($x257 (or (not $x615) $x142))) -(let ((@x258 ((_ quant-inst 1) $x257))) -(unit-resolution @x258 @x620 @x145 false)))))))))))))))))) - -b4b100f728c8f0d6f96483e4de44e248cc4be1aa 101 0 -unsat -((set-logic AUFLIA) -(proof -(let ((?x124 (some$a true))) -(let ((?x125 (g$b ?x124))) -(let ((?x122 (some$ 3))) -(let ((?x123 (g$ ?x122))) -(let (($x126 (= ?x123 ?x125))) -(let ((?x269 (cons$a true nil$a))) -(let ((?x270 (g$c ?x269))) -(let (($x587 (= ?x125 ?x270))) -(let (($x604 (forall ((?v0 Bool) )(! (= (g$b (some$a ?v0)) (g$c (cons$a ?v0 nil$a))) :pattern ( (some$a ?v0) ) :pattern ( (cons$a ?v0 nil$a) ) :qid k!33)) -)) -(let (($x43 (forall ((?v0 Bool) )(! (= (g$b (some$a ?v0)) (g$c (cons$a ?v0 nil$a))) :qid k!33)) -)) -(let (($x42 (= (g$b (some$a ?0)) (g$c (cons$a ?0 nil$a))))) -(let ((@x160 (mp~ (asserted $x43) (nnf-pos (refl (~ $x42 $x42)) (~ $x43 $x43)) $x43))) -(let ((@x609 (mp @x160 (quant-intro (refl (= $x42 $x42)) (= $x43 $x604)) $x604))) -(let (($x254 (or (not $x604) $x587))) -(let ((@x255 ((_ quant-inst true) $x254))) -(let ((?x227 (size$ ?x269))) -(let (($x569 (= ?x270 ?x227))) -(let (($x612 (forall ((?v0 Bool_list$) )(! (let ((?x61 (size$ ?v0))) -(let ((?x60 (g$c ?v0))) -(= ?x60 ?x61))) :pattern ( (g$c ?v0) ) :pattern ( (size$ ?v0) ) :qid k!38)) -)) -(let (($x63 (forall ((?v0 Bool_list$) )(! (let ((?x61 (size$ ?v0))) -(let ((?x60 (g$c ?v0))) -(= ?x60 ?x61))) :qid k!38)) -)) -(let ((@x616 (quant-intro (refl (= (= (g$c ?0) (size$ ?0)) (= (g$c ?0) (size$ ?0)))) (= $x63 $x612)))) -(let ((@x142 (nnf-pos (refl (~ (= (g$c ?0) (size$ ?0)) (= (g$c ?0) (size$ ?0)))) (~ $x63 $x63)))) -(let ((@x617 (mp (mp~ (asserted $x63) @x142 $x63) @x616 $x612))) -(let (($x571 (or (not $x612) $x569))) -(let ((@x572 ((_ quant-inst (cons$a true nil$a)) $x571))) -(let ((?x89 (suc$ zero$))) -(let ((?x105 (size$ nil$a))) -(let ((?x233 (plus$ ?x105 ?x89))) -(let (($x570 (= ?x227 ?x233))) -(let (($x657 (forall ((?v0 Bool) (?v1 Bool_list$) )(! (= (size$ (cons$a ?v0 ?v1)) (plus$ (size$ ?v1) (suc$ zero$))) :pattern ( (cons$a ?v0 ?v1) ) :qid k!46)) -)) -(let (($x114 (forall ((?v0 Bool) (?v1 Bool_list$) )(! (= (size$ (cons$a ?v0 ?v1)) (plus$ (size$ ?v1) (suc$ zero$))) :qid k!46)) -)) -(let (($x113 (= (size$ (cons$a ?1 ?0)) (plus$ (size$ ?0) ?x89)))) -(let ((@x173 (mp~ (asserted $x114) (nnf-pos (refl (~ $x113 $x113)) (~ $x114 $x114)) $x114))) -(let ((@x662 (mp @x173 (quant-intro (refl (= $x113 $x113)) (= $x114 $x657)) $x657))) -(let (($x576 (or (not $x657) $x570))) -(let ((@x213 ((_ quant-inst true nil$a) $x576))) -(let ((?x108 (size$a nil$))) -(let (($x109 (= ?x108 zero$))) -(let ((@x110 (asserted $x109))) -(let (($x106 (= ?x105 zero$))) -(let ((@x107 (asserted $x106))) -(let ((@x287 (monotonicity (trans @x107 (symm @x110 (= zero$ ?x108)) (= ?x105 ?x108)) (= ?x233 (plus$ ?x108 ?x89))))) -(let ((?x246 (plus$ ?x108 ?x89))) -(let ((?x256 (cons$ 3 nil$))) -(let ((?x588 (size$a ?x256))) -(let (($x584 (= ?x588 ?x246))) -(let (($x664 (forall ((?v0 Int) (?v1 Int_list$) )(! (= (size$a (cons$ ?v0 ?v1)) (plus$ (size$a ?v1) (suc$ zero$))) :pattern ( (cons$ ?v0 ?v1) ) :qid k!47)) -)) -(let (($x119 (forall ((?v0 Int) (?v1 Int_list$) )(! (= (size$a (cons$ ?v0 ?v1)) (plus$ (size$a ?v1) (suc$ zero$))) :qid k!47)) -)) -(let (($x118 (= (size$a (cons$ ?1 ?0)) (plus$ (size$a ?0) ?x89)))) -(let ((@x178 (mp~ (asserted $x119) (nnf-pos (refl (~ $x118 $x118)) (~ $x119 $x119)) $x119))) -(let ((@x669 (mp @x178 (quant-intro (refl (= $x118 $x118)) (= $x119 $x664)) $x664))) -(let (($x231 (or (not $x664) $x584))) -(let ((@x232 ((_ quant-inst 3 nil$) $x231))) -(let ((?x267 (g$a ?x256))) -(let (($x592 (= ?x267 ?x588))) -(let (($x620 (forall ((?v0 Int_list$) )(! (let ((?x67 (size$a ?v0))) -(let ((?x66 (g$a ?v0))) -(= ?x66 ?x67))) :pattern ( (g$a ?v0) ) :pattern ( (size$a ?v0) ) :qid k!39)) -)) -(let (($x69 (forall ((?v0 Int_list$) )(! (let ((?x67 (size$a ?v0))) -(let ((?x66 (g$a ?v0))) -(= ?x66 ?x67))) :qid k!39)) -)) -(let ((@x622 (refl (= (= (g$a ?0) (size$a ?0)) (= (g$a ?0) (size$a ?0)))))) -(let ((@x129 (nnf-pos (refl (~ (= (g$a ?0) (size$a ?0)) (= (g$a ?0) (size$a ?0)))) (~ $x69 $x69)))) -(let ((@x625 (mp (mp~ (asserted $x69) @x129 $x69) (quant-intro @x622 (= $x69 $x620)) $x620))) -(let (($x248 (or (not $x620) $x592))) -(let ((@x585 ((_ quant-inst (cons$ 3 nil$)) $x248))) -(let (($x268 (= ?x123 ?x267))) -(let (($x596 (forall ((?v0 Int) )(! (= (g$ (some$ ?v0)) (g$a (cons$ ?v0 nil$))) :pattern ( (some$ ?v0) ) :pattern ( (cons$ ?v0 nil$) ) :qid k!32)) -)) -(let (($x34 (forall ((?v0 Int) )(! (= (g$ (some$ ?v0)) (g$a (cons$ ?v0 nil$))) :qid k!32)) -)) -(let (($x33 (= (g$ (some$ ?0)) (g$a (cons$ ?0 nil$))))) -(let ((@x157 (mp~ (asserted $x34) (nnf-pos (refl (~ $x33 $x33)) (~ $x34 $x34)) $x34))) -(let ((@x601 (mp @x157 (quant-intro (refl (= $x33 $x33)) (= $x34 $x596)) $x596))) -(let (($x250 (or (not $x596) $x268))) -(let ((@x586 ((_ quant-inst 3) $x250))) -(let ((@x275 (trans (unit-resolution @x586 @x601 $x268) (unit-resolution @x585 @x625 $x592) (= ?x123 ?x588)))) -(let ((@x280 (trans (trans @x275 (unit-resolution @x232 @x669 $x584) (= ?x123 ?x246)) (symm @x287 (= ?x246 ?x233)) (= ?x123 ?x233)))) -(let ((@x558 (trans @x280 (symm (unit-resolution @x213 @x662 $x570) (= ?x233 ?x227)) (= ?x123 ?x227)))) -(let ((@x560 (trans @x558 (symm (unit-resolution @x572 @x617 $x569) (= ?x227 ?x270)) (= ?x123 ?x270)))) -(let ((@x546 (trans @x560 (symm (unit-resolution @x255 @x609 $x587) (= ?x270 ?x125)) $x126))) -(let (($x127 (not $x126))) -(let ((@x128 (asserted $x127))) -(unit-resolution @x128 @x546 false))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) - -572677daa32981bf8212986300f1362edf42a0c1 7 0 +44c9e70361e406cdaa5515db0484a14de1f3823e 7 0 unsat ((set-logic AUFLIA) (proof @@ -922,7 +13,7 @@ (let ((@x40 (trans @x36 (rewrite (= (not true) false)) (= (not (or p$ (not p$))) false)))) (mp (asserted (not (or p$ (not p$)))) @x40 false))))) -dfd95b23f80baacb2acdc442487bd8121f072035 9 0 +642064746d4dfc4babb357dafe234a81ef017f2c 9 0 unsat ((set-logic AUFLIA) (proof @@ -932,7 +23,7 @@ (let ((@x47 (trans @x43 (rewrite (= (not true) false)) (= (not (= (and p$ true) p$)) false)))) (mp (asserted (not (= (and p$ true) p$))) @x47 false))))))) -8d6b87f1242925c8eefb2ec3e8ab8eefcd64e572 13 0 +0a1454d805d51972201b1f0614ae4d2b1ee0c238 13 0 unsat ((set-logic AUFLIA) (proof @@ -946,7 +37,19 @@ (let (($x29 (or p$ q$))) (mp (and-elim (not-or-elim @x44 (and $x29 (not p$))) $x29) @x58 false))))))))))) -dfb7aeab4f33cdf91b335d72ad619dbd0d65fb62 23 0 +34112335b57502835b641cecdefffafb46f85d80 11 0 +unsat +((set-logic AUFLIA) +(proof +(let (($x32 (and c$ d$))) +(let (($x29 (and a$ b$))) +(let (($x33 (or $x29 $x32))) +(let (($x34 (=> $x33 $x33))) +(let (($x35 (not $x34))) +(let ((@x45 (trans (monotonicity (rewrite (= $x34 true)) (= $x35 (not true))) (rewrite (= (not true) false)) (= $x35 false)))) +(mp (asserted $x35) @x45 false))))))))) + +20bc477eba70622207284dac695d9d5d493c254c 23 0 unsat ((set-logic AUFLIA) (proof @@ -970,19 +73,7 @@ (let ((@x58 (monotonicity (trans @x49 (rewrite (= (=> $x31 $x44) $x51)) (= $x37 $x51)) (= $x38 $x56)))) (mp (asserted $x38) (trans @x58 @x67 (= $x38 false)) false))))))))))))))))))))) -a021a5fec5486f23204e54770f9c04c64baf7e25 11 0 -unsat -((set-logic AUFLIA) -(proof -(let (($x32 (and c$ d$))) -(let (($x29 (and a$ b$))) -(let (($x33 (or $x29 $x32))) -(let (($x34 (=> $x33 $x33))) -(let (($x35 (not $x34))) -(let ((@x45 (trans (monotonicity (rewrite (= $x34 true)) (= $x35 (not true))) (rewrite (= (not true) false)) (= $x35 false)))) -(mp (asserted $x35) @x45 false))))))))) - -3efca8956be216e9acda1b32436ba8f01358d35e 24 0 +31d9c9d3ff37ebd83ab46c7b87647ef17b2c57d5 24 0 unsat ((set-logic AUFLIA) (proof @@ -1007,35 +98,7 @@ (let ((@x82 (trans (monotonicity @x75 (= $x37 (not true))) (rewrite (= (not true) false)) (= $x37 false)))) (mp (asserted $x37) @x82 false)))))))))))))))))))))) -143f46ba7acb4b0a8f67b0de474b0a249f30985b 27 0 -unsat -((set-logic AUFLIA) -(proof -(let ((?x38 (symm_f$ b$ a$))) -(let ((?x37 (symm_f$ a$ b$))) -(let (($x39 (= ?x37 ?x38))) -(let (($x52 (not $x39))) -(let ((@x47 (monotonicity (rewrite (= (= a$ a$) true)) (= (and (= a$ a$) $x39) (and true $x39))))) -(let ((@x51 (trans @x47 (rewrite (= (and true $x39) $x39)) (= (and (= a$ a$) $x39) $x39)))) -(let ((@x57 (mp (asserted (not (and (= a$ a$) $x39))) (monotonicity @x51 (= (not (and (= a$ a$) $x39)) $x52)) $x52))) -(let (($x480 (forall ((?v0 A$) (?v1 A$) )(! (let ((?x30 (symm_f$ ?v1 ?v0))) -(let ((?x29 (symm_f$ ?v0 ?v1))) -(= ?x29 ?x30))) :pattern ( (symm_f$ ?v0 ?v1) ) :pattern ( (symm_f$ ?v1 ?v0) ) :qid k!8)) -)) -(let (($x32 (forall ((?v0 A$) (?v1 A$) )(! (let ((?x30 (symm_f$ ?v1 ?v0))) -(let ((?x29 (symm_f$ ?v0 ?v1))) -(= ?x29 ?x30))) :qid k!8)) -)) -(let ((?x30 (symm_f$ ?0 ?1))) -(let ((?x29 (symm_f$ ?1 ?0))) -(let (($x31 (= ?x29 ?x30))) -(let ((@x60 (mp~ (asserted $x32) (nnf-pos (refl (~ $x31 $x31)) (~ $x32 $x32)) $x32))) -(let ((@x485 (mp @x60 (quant-intro (refl (= $x31 $x31)) (= $x32 $x480)) $x480))) -(let (($x149 (or (not $x480) $x39))) -(let ((@x61 ((_ quant-inst a$ b$) $x149))) -(unit-resolution @x61 @x485 @x57 false))))))))))))))))))) - -d600888ef4325a32ff87997035fed7a7c01e4767 39 0 +330b2c9cc52cf5f35a134a2209b0d4127652f7c0 39 0 unsat ((set-logic AUFLIA) (proof @@ -1075,7 +138,35 @@ (let ((@x40 (mp (asserted (or a$ (or b$ (or c$ d$)))) (rewrite (= (or a$ (or b$ (or c$ d$))) $x37)) $x37))) (mp @x40 @x202 false))))))))))))))))))))))))))))))))))))) -a6dd135a0c109f49b36d7266dc7a6becc640e496 637 0 +ad87d7e797bdb9354f6592e3ce911c29af823c87 27 0 +unsat +((set-logic AUFLIA) +(proof +(let ((?x38 (symm_f$ b$ a$))) +(let ((?x37 (symm_f$ a$ b$))) +(let (($x39 (= ?x37 ?x38))) +(let (($x52 (not $x39))) +(let ((@x47 (monotonicity (rewrite (= (= a$ a$) true)) (= (and (= a$ a$) $x39) (and true $x39))))) +(let ((@x51 (trans @x47 (rewrite (= (and true $x39) $x39)) (= (and (= a$ a$) $x39) $x39)))) +(let ((@x57 (mp (asserted (not (and (= a$ a$) $x39))) (monotonicity @x51 (= (not (and (= a$ a$) $x39)) $x52)) $x52))) +(let (($x480 (forall ((?v0 A$) (?v1 A$) )(! (let ((?x30 (symm_f$ ?v1 ?v0))) +(let ((?x29 (symm_f$ ?v0 ?v1))) +(= ?x29 ?x30))) :pattern ( (symm_f$ ?v0 ?v1) ) :pattern ( (symm_f$ ?v1 ?v0) ) :qid k!8)) +)) +(let (($x32 (forall ((?v0 A$) (?v1 A$) )(! (let ((?x30 (symm_f$ ?v1 ?v0))) +(let ((?x29 (symm_f$ ?v0 ?v1))) +(= ?x29 ?x30))) :qid k!8)) +)) +(let ((?x30 (symm_f$ ?0 ?1))) +(let ((?x29 (symm_f$ ?1 ?0))) +(let (($x31 (= ?x29 ?x30))) +(let ((@x60 (mp~ (asserted $x32) (nnf-pos (refl (~ $x31 $x31)) (~ $x32 $x32)) $x32))) +(let ((@x485 (mp @x60 (quant-intro (refl (= $x31 $x31)) (= $x32 $x480)) $x480))) +(let (($x149 (or (not $x480) $x39))) +(let ((@x61 ((_ quant-inst a$ b$) $x149))) +(unit-resolution @x61 @x485 @x57 false))))))))))))))))))) + +475916706487c818c9d90b517b53e98cbd0b98a4 637 0 unsat ((set-logic AUFLIA) (proof @@ -1713,7 +804,7 @@ (let ((@x1722 (unit-resolution @x1662 (unit-resolution @x472 @x1718 $x467) (unit-resolution @x565 @x1715 $x482) $x355))) (unit-resolution @x1647 @x1722 (unit-resolution @x472 @x1718 $x467) (unit-resolution @x565 @x1715 $x482) (unit-resolution @x480 @x1718 $x397) false))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -cc18a32517b61d11530e29950c780e58afa4da51 38 0 +53d98ae38981e94d40d6d86fc0074ee3a2e0fb7e 38 0 unsat ((set-logic AUFLIA) (declare-fun ?v0!0 () Int) @@ -1752,7 +843,7 @@ (let ((@x79 (and-elim (mp @x72 @x77 (and $x48 $x63)) $x48))) (unit-resolution @x79 @x81 false)))))))))))))))))))) -f69da5e318af2ccb1aaa30033e9780c0075e7706 53 0 +e22c0f9d8d283fe65facdddeef75c43b520c8702 53 0 unsat ((set-logic AUFLIA) (declare-fun ?v0!0 () A$) @@ -1806,7 +897,7 @@ (let ((@x161 ((_ quant-inst c$) $x160))) (unit-resolution @x161 @x485 (unit-resolution @x525 @x485 $x517) false))))))))))))))))))))))))))))))))))))))) -853b35db7beb7a5b039f102f0403b2d296edcda0 53 0 +3b83f9f26b0c0bdbb99d25d8249a78edb7dbd8f3 53 0 unsat ((set-logic AUFLIA) (declare-fun ?v0!3 () A$) @@ -1860,7 +951,7 @@ (let ((@x211 ((_ quant-inst c$) $x549))) (unit-resolution @x211 @x199 (unit-resolution @x592 @x199 $x584) false))))))))))))))))))))))))))))))))))))))) -ee1b9a27124d1797593a214fc9b1585b73aca864 26 0 +c5dafcf16dd97b4d38e39a04bbc990e4ad5fdbd3 26 0 unsat ((set-logic AUFLIA) (proof @@ -1887,7 +978,7 @@ (let ((@x70 ((_ quant-inst x$) $x156))) (unit-resolution @x70 @x491 @x49 false))))))))))))))))))) -1b3bdde0d609ebf7ad7472d1510134c9c367d283 7 0 +c810fdd7e33dce88857a4a5d351d4d48aeec706d 7 0 unsat ((set-logic AUFLIA) (proof @@ -1895,7 +986,7 @@ (let ((@x39 (trans @x35 (rewrite (= (not true) false)) (= (not (= 3 3)) false)))) (mp (asserted (not (= 3 3))) @x39 false))))) -a90c5a0ce94c691b0e4756f87e5d5fdbfd876893 7 0 +4405deb1e8af2d0b383b4c76fef214640ee54b60 7 0 unsat ((set-logic AUFLIRA) (proof @@ -1903,7 +994,7 @@ (let ((@x39 (trans @x35 (rewrite (= (not true) false)) (= (not (= 3.0 3.0)) false)))) (mp (asserted (not (= 3.0 3.0))) @x39 false))))) -16d237209133b15bdc9c24699c793f8bdc748cd0 9 0 +9db6968bb918051eba4a8f252eb4d7b31abc0008 9 0 unsat ((set-logic AUFLIA) (proof @@ -1913,7 +1004,7 @@ (let ((@x48 (trans @x44 (rewrite (= (not true) false)) (= (not (= (+ 3 1) 4)) false)))) (mp (asserted (not (= (+ 3 1) 4))) @x48 false))))))) -bc021898e31cb7c6419a072d70191b97605bee76 16 0 +4236229b55c8c35ee3fdabff17499992a72bc2e9 16 0 unsat ((set-logic AUFLIA) (proof @@ -1930,7 +1021,7 @@ (let ((@x63 (trans (monotonicity @x56 (= $x35 (not true))) (rewrite (= (not true) false)) (= $x35 false)))) (mp (asserted $x35) @x63 false)))))))))))))) -31045f736583ed0b58ba51e123c31f8bb6c0267d 11 0 +edfffa3c123ab0c63cd525084a50aa3c5ed5a484 11 0 unsat ((set-logic AUFLIA) (proof @@ -1942,20 +1033,7 @@ (let ((@x59 (trans @x55 (rewrite (= (not true) false)) (= (not (< 5 (ite (<= 3 8) 8 3))) false)))) (mp (asserted (not (< 5 (ite (<= 3 8) 8 3)))) @x59 false))))))))) -c4e20de399740e8f0c9a87abad030298d74bc47b 12 0 -unsat -((set-logic AUFLIA) -(proof -(let ((?x31 (p$ true))) -(let (($x29 (< 2 3))) -(let ((?x30 (p$ $x29))) -(let (($x32 (= ?x30 ?x31))) -(let ((@x42 (monotonicity (monotonicity (rewrite (= $x29 true)) $x32) (= $x32 (= ?x31 ?x31))))) -(let ((@x49 (monotonicity (trans @x42 (rewrite (= (= ?x31 ?x31) true)) (= $x32 true)) (= (not $x32) (not true))))) -(let ((@x53 (trans @x49 (rewrite (= (not true) false)) (= (not $x32) false)))) -(mp (asserted (not $x32)) @x53 false)))))))))) - -6b0b089fbe179e8a27509c818f9a5e6847ac6bf2 88 0 +f9514ad0d68d1d07ca6390dfeefcb474eb113622 88 0 unsat ((set-logic AUFLIRA) (proof @@ -2044,7 +1122,20 @@ (let ((@x234 (unit-resolution @x136 (unit-resolution @x138 (lemma @x231 (not $x134)) $x83) $x133))) ((_ th-lemma arith farkas -2 1 -1 -1 1) (unit-resolution @x138 (lemma @x231 (not $x134)) $x83) @x221 @x126 @x226 (unit-resolution @x159 @x234 $x149) false)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -d63ee5062f9a1d0a0bd17f51adaa0ac5e8f9ec16 16 0 +dfe0238fb899e04c38457f444509fee29d6fc513 12 0 +unsat +((set-logic AUFLIA) +(proof +(let ((?x31 (p$ true))) +(let (($x29 (< 2 3))) +(let ((?x30 (p$ $x29))) +(let (($x32 (= ?x30 ?x31))) +(let ((@x42 (monotonicity (monotonicity (rewrite (= $x29 true)) $x32) (= $x32 (= ?x31 ?x31))))) +(let ((@x49 (monotonicity (trans @x42 (rewrite (= (= ?x31 ?x31) true)) (= $x32 true)) (= (not $x32) (not true))))) +(let ((@x53 (trans @x49 (rewrite (= (not true) false)) (= (not $x32) false)))) +(mp (asserted (not $x32)) @x53 false)))))))))) + +46bed4652ccbc7e1a58c0efb03590e49ee15643a 16 0 unsat ((set-logic AUFLIA) (proof @@ -2061,7 +1152,7 @@ (let ((@x70 (trans @x48 @x68 (= (not (or (<= 4 (+ x$ 3)) $x33)) false)))) (mp (asserted (not (or (<= 4 (+ x$ 3)) $x33))) @x70 false)))))))))))))) -ea0e16fa50db2870878476eccdef4f64568acd55 18 0 +ef89c4f1b53c97f5cf2e25105c9bb8f92779adb7 18 0 unsat ((set-logic AUFLIA) (proof @@ -2080,7 +1171,7 @@ (let ((@x83 (mp (asserted $x58) (trans (monotonicity @x66 (= $x58 $x67)) @x80 (= $x58 $x70)) $x70))) (mp @x83 @x90 false)))))))))))))))) -2389277f3547499e520f2b3ac28991b30ac7c1a8 11 0 +77b18cda19c5fffd05747f5d9240aebf138e344d 11 0 unsat ((set-logic AUFLIA) (proof @@ -2092,7 +1183,27 @@ (let ((@x57 (trans @x53 (rewrite (= (not true) false)) (= (not (not (= (+ 2 2) 5))) false)))) (mp (asserted (not (not (= (+ 2 2) 5)))) @x57 false))))))))) -3a6df2b095b936aac9a1d533e306f2d31b4fb44e 22 0 +42e94ca5e1eca47637b565820dbeb8f0c3f0cfbe 19 0 +unsat +((set-logic AUFLIRA) +(proof +(let ((?x32 (* 7.0 a$))) +(let ((?x29 (* 3.0 x$))) +(let ((?x33 (+ ?x29 ?x32))) +(let (($x43 (>= ?x33 4.0))) +(let (($x41 (not $x43))) +(let ((@x40 (mp (asserted (< ?x33 4.0)) (rewrite (= (< ?x33 4.0) $x41)) $x41))) +(let ((?x38 (* 2.0 x$))) +(let (($x48 (<= ?x38 3.0))) +(let (($x49 (not $x48))) +(let ((@x52 (mp (asserted (< 3.0 ?x38)) (rewrite (= (< 3.0 ?x38) $x49)) $x49))) +(let (($x58 (>= a$ 0.0))) +(let ((@x62 (monotonicity (rewrite (= (< a$ 0.0) (not $x58))) (= (not (< a$ 0.0)) (not (not $x58)))))) +(let ((@x66 (trans @x62 (rewrite (= (not (not $x58)) $x58)) (= (not (< a$ 0.0)) $x58)))) +(let ((@x67 (mp (asserted (not (< a$ 0.0))) @x66 $x58))) +((_ th-lemma arith farkas 7 3/2 1) @x67 @x52 @x40 false))))))))))))))))) + +0be06fbd57421bc1e05bb76b65b7d775f798777d 22 0 unsat ((set-logic AUFLIA) (proof @@ -2115,27 +1226,167 @@ (let ((@x78 (trans (monotonicity @x71 (= $x40 (not true))) (rewrite (= (not true) false)) (= $x40 false)))) (mp (asserted $x40) @x78 false)))))))))))))))))))) -dfbbe6f3879b3c49e6d5f7ecff4f8f81ed746bd4 19 0 +d419775b36e6eb4a3ae9788e677f2c6bd6596508 159 0 unsat -((set-logic AUFLIRA) +((set-logic AUFLIA) (proof -(let ((?x32 (* 7.0 a$))) -(let ((?x29 (* 3.0 x$))) -(let ((?x33 (+ ?x29 ?x32))) -(let (($x43 (>= ?x33 4.0))) -(let (($x41 (not $x43))) -(let ((@x40 (mp (asserted (< ?x33 4.0)) (rewrite (= (< ?x33 4.0) $x41)) $x41))) -(let ((?x38 (* 2.0 x$))) -(let (($x48 (<= ?x38 3.0))) -(let (($x49 (not $x48))) -(let ((@x52 (mp (asserted (< 3.0 ?x38)) (rewrite (= (< 3.0 ?x38) $x49)) $x49))) -(let (($x58 (>= a$ 0.0))) -(let ((@x62 (monotonicity (rewrite (= (< a$ 0.0) (not $x58))) (= (not (< a$ 0.0)) (not (not $x58)))))) -(let ((@x66 (trans @x62 (rewrite (= (not (not $x58)) $x58)) (= (not (< a$ 0.0)) $x58)))) -(let ((@x67 (mp (asserted (not (< a$ 0.0))) @x66 $x58))) -((_ th-lemma arith farkas 7 3/2 1) @x67 @x52 @x40 false))))))))))))))))) +(let (($x44 (= m$ n$))) +(let ((@x480 (symm (commutativity (= $x44 (= n$ m$))) (= (= n$ m$) $x44)))) +(let (($x40 (= n$ m$))) +(let ((?x102 (* (- 1) m$))) +(let ((?x103 (+ n$ ?x102))) +(let (($x118 (>= ?x103 0))) +(let ((?x78 (* (- 1) n$a))) +(let ((?x96 (+ m$ ?x78))) +(let (($x127 (<= ?x96 0))) +(let ((?x79 (+ n$ ?x78))) +(let (($x88 (>= ?x79 0))) +(let (($x239 (or $x88 $x127))) +(let ((@x251 (monotonicity (rewrite (= (and (not $x88) (not $x127)) (not $x239))) (= (not (and (not $x88) (not $x127))) (not (not $x239)))))) +(let ((@x271 (trans @x251 (rewrite (= (not (not $x239)) $x239)) (= (not (and (not $x88) (not $x127))) $x239)))) +(let (($x128 (not $x127))) +(let (($x87 (not $x88))) +(let (($x143 (and $x87 $x128))) +(let (($x210 (not $x143))) +(let (($x50 (= n$a m$))) +(let (($x57 (and $x50 $x44))) +(let (($x80 (<= ?x79 0))) +(let (($x81 (not $x80))) +(let (($x33 (= m$ n$a))) +(let (($x84 (and $x33 $x81))) +(let (($x91 (and $x44 $x87))) +(let (($x95 (>= ?x96 0))) +(let (($x94 (not $x95))) +(let (($x99 (and $x94 $x81))) +(let (($x48 (= n$a n$))) +(let (($x104 (<= ?x103 0))) +(let (($x105 (not $x104))) +(let (($x108 (and $x105 $x48))) +(let (($x111 (and $x105 $x87))) +(let (($x114 (and $x50 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(($x73 (not $x72))) +(let (($x170 (or $x121 (or $x114 (or $x111 (or $x108 (or $x99 (or $x91 (or $x84 $x57))))))))) +(let (($x191 (or $x146 (or $x143 (or $x140 (or $x137 (or $x134 (or $x131 (or $x124 $x170))))))))) +(let (($x189 (= $x70 (or $x143 (or $x140 (or $x137 (or $x134 (or $x131 (or $x124 $x170))))))))) +(let (($x186 (= (or (and $x38 (< n$a m$)) (or (and $x40 (< m$ n$a)) $x67)) (or $x140 (or $x137 (or $x134 (or $x131 (or $x124 $x170)))))))) +(let (($x183 (= (or (and $x40 (< m$ n$a)) $x67) (or $x137 (or $x134 (or $x131 (or $x124 $x170))))))) +(let (($x171 (= (or (and $x48 (< n$ m$)) (or (and $x50 (< m$ n$)) $x62)) $x170))) +(let (($x168 (= (or (and $x50 (< m$ n$)) $x62) (or $x114 (or $x111 (or $x108 (or $x99 (or $x91 (or $x84 $x57))))))))) +(let (($x162 (= (or (and (< m$ n$) $x48) $x60) (or $x108 (or $x99 (or $x91 (or $x84 $x57))))))) +(let (($x156 (= (or (and $x44 (< n$ n$a)) (or (and $x33 (< n$a n$)) $x57)) (or $x91 (or $x84 $x57))))) +(let ((@x83 (rewrite (= (< n$a n$) $x81)))) +(let ((@x154 (monotonicity (monotonicity @x83 (= (and $x33 (< n$a n$)) $x84)) (= (or (and $x33 (< n$a n$)) $x57) (or $x84 $x57))))) +(let ((@x90 (rewrite (= (< n$ n$a) $x87)))) +(let ((@x157 (monotonicity (monotonicity @x90 (= (and $x44 (< n$ n$a)) $x91)) @x154 $x156))) +(let ((@x98 (rewrite (= (< m$ n$a) $x94)))) +(let ((@x101 (monotonicity @x98 @x83 (= (and (< m$ n$a) (< n$a n$)) $x99)))) +(let ((@x160 (monotonicity @x101 @x157 (= $x60 (or $x99 (or $x91 (or $x84 $x57))))))) +(let ((@x107 (rewrite (= (< m$ n$) $x105)))) +(let ((@x163 (monotonicity (monotonicity @x107 (= (and (< m$ n$) $x48) $x108)) @x160 $x162))) +(let ((@x113 (monotonicity @x107 @x90 (= (and (< m$ n$) (< n$ n$a)) $x111)))) +(let ((@x166 (monotonicity @x113 @x163 (= $x62 (or $x111 (or $x108 (or $x99 (or $x91 (or $x84 $x57))))))))) +(let ((@x169 (monotonicity (monotonicity @x107 (= (and $x50 (< m$ n$)) $x114)) @x166 $x168))) +(let ((@x120 (rewrite (= (< n$ m$) $x117)))) +(let ((@x172 (monotonicity (monotonicity @x120 (= (and $x48 (< n$ m$)) $x121)) @x169 $x171))) +(let ((@x126 (monotonicity @x83 @x120 (= (and (< n$a n$) (< n$ m$)) $x124)))) +(let ((@x130 (rewrite (= (< n$a m$) $x128)))) +(let ((@x178 (monotonicity (monotonicity @x130 (= (and (< n$a m$) $x44) $x131)) (monotonicity @x126 @x172 (= $x65 (or $x124 $x170))) (= (or (and (< n$a m$) $x44) $x65) (or $x131 (or $x124 $x170)))))) +(let ((@x136 (monotonicity @x130 @x107 (= (and (< n$a m$) (< m$ n$)) $x134)))) +(let ((@x181 (monotonicity @x136 @x178 (= $x67 (or $x134 (or $x131 (or $x124 $x170))))))) +(let ((@x184 (monotonicity (monotonicity @x98 (= (and $x40 (< m$ n$a)) $x137)) @x181 $x183))) +(let ((@x187 (monotonicity (monotonicity @x130 (= (and $x38 (< n$a m$)) $x140)) @x184 $x186))) +(let ((@x145 (monotonicity @x90 @x130 (= (and (< n$ n$a) (< n$a m$)) $x143)))) +(let ((@x193 (monotonicity (monotonicity @x120 (= (and (< n$ m$) $x33) $x146)) (monotonicity @x145 @x187 $x189) (= (or (and (< n$ m$) $x33) $x70) $x191)))) +(let ((@x151 (monotonicity @x120 @x98 (= (and (< n$ m$) (< m$ n$a)) $x149)))) +(let ((@x201 (trans (monotonicity @x151 @x193 (= $x72 (or $x149 $x191))) (rewrite (= (or $x149 $x191) $x197)) (= $x72 $x197)))) +(let ((@x205 (mp (asserted $x73) (monotonicity @x201 (= $x73 (not $x197))) (not $x197)))) +(let ((@x272 (mp (not-or-elim @x205 $x210) @x271 $x239))) +(let (($x273 (not $x38))) +(let (($x274 (or $x273 $x127))) +(let ((@x280 (monotonicity (rewrite (= $x140 (not $x274))) (= (not $x140) (not (not $x274)))))) +(let ((@x284 (trans @x280 (rewrite (= (not (not $x274)) $x274)) (= (not $x140) $x274)))) +(let ((@x285 (mp (not-or-elim @x205 (not $x140)) @x284 $x274))) +(let (($x286 (not $x40))) +(let (($x311 (not $x44))) +(let ((@x434 (hypothesis $x81))) +(let (($x386 (or $x95 $x80))) +(let ((@x392 (monotonicity (rewrite (= $x99 (not $x386))) (= (not $x99) (not (not $x386)))))) +(let ((@x396 (trans @x392 (rewrite (= (not (not $x386)) $x386)) (= (not $x99) $x386)))) +(let ((@x397 (mp (not-or-elim @x205 (not $x99)) @x396 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$x324))) (= (not $x124) (not (not $x324)))))) +(let ((@x334 (trans @x330 (rewrite (= (not (not $x324)) $x324)) (= (not $x124) $x324)))) +(let ((@x335 (mp (not-or-elim @x205 (not $x124)) @x334 $x324))) +(let (($x299 (or $x127 $x104))) +(let ((@x305 (monotonicity (rewrite (= $x134 (not $x299))) (= (not $x134) (not (not $x299)))))) +(let ((@x309 (trans @x305 (rewrite (= (not (not $x299)) $x299)) (= (not $x134) $x299)))) +(let ((@x310 (mp (not-or-elim @x205 (not $x134)) @x309 $x299))) +(let ((@x444 (unit-resolution ((_ th-lemma arith triangle-eq) (or $x40 $x105 $x117)) (unit-resolution @x310 @x440 $x104) (unit-resolution @x335 @x434 $x118) $x40))) +(let ((@x459 (unit-resolution ((_ th-lemma arith triangle-eq) (or $x38 $x81 $x87)) (lemma (unit-resolution @x444 @x450 false) $x80) (or $x38 $x87)))) +(let ((@x460 (unit-resolution @x459 (unit-resolution @x285 (hypothesis $x128) $x273) (unit-resolution @x272 (hypothesis $x128) $x88) false))) +(let ((@x461 (lemma @x460 $x127))) +(let (($x254 (or $x118 $x95))) +(let ((@x262 (monotonicity (rewrite (= $x149 (not $x254))) (= (not $x149) (not (not $x254)))))) +(let ((@x256 (trans @x262 (rewrite (= (not (not $x254)) $x254)) (= (not $x149) $x254)))) +(let ((@x257 (mp (not-or-elim @x205 (not $x149)) @x256 $x254))) +(let (($x247 (or $x118 $x246))) +(let ((@x259 (monotonicity (rewrite (= $x146 (not $x247))) (= (not $x146) (not (not $x247)))))) +(let ((@x245 (trans @x259 (rewrite (= (not (not $x247)) $x247)) (= (not $x146) $x247)))) +(let ((@x238 (mp (not-or-elim @x205 (not $x146)) @x245 $x247))) +(let ((@x465 (unit-resolution @x439 (unit-resolution @x238 (hypothesis $x117) $x246) (unit-resolution @x257 (hypothesis $x117) $x95) @x461 false))) +(let (($x336 (not $x48))) +(let (($x374 (or $x104 $x336))) +(let ((@x380 (monotonicity (rewrite (= $x108 (not $x374))) (= (not $x108) (not (not $x374)))))) +(let ((@x384 (trans @x380 (rewrite (= (not (not $x374)) $x374)) (= (not $x108) $x374)))) +(let ((@x385 (mp (not-or-elim @x205 (not $x108)) @x384 $x374))) +(let ((@x475 (mp (unit-resolution @x385 (hypothesis $x105) $x336) (monotonicity (commutativity (= $x48 $x38)) (= $x336 $x273)) $x273))) +(let (($x362 (or $x104 $x88))) +(let ((@x368 (monotonicity (rewrite (= $x111 (not $x362))) (= (not $x111) (not (not $x362)))))) +(let ((@x372 (trans @x368 (rewrite (= (not (not $x362)) $x362)) (= (not $x111) $x362)))) +(let ((@x373 (mp (not-or-elim @x205 (not $x111)) @x372 $x362))) +(let ((@x469 (unit-resolution @x459 (unit-resolution @x373 (hypothesis $x105) $x88) $x38))) +(let ((@x478 (unit-resolution ((_ th-lemma arith triangle-eq) (or $x40 $x105 $x117)) (lemma (unit-resolution @x469 @x475 false) $x104) (lemma @x465 $x118) $x40))) +(let (($x287 (or $x286 $x95))) +(let ((@x293 (monotonicity (rewrite (= $x137 (not $x287))) (= (not $x137) (not (not $x287)))))) +(let ((@x297 (trans @x293 (rewrite (= (not (not $x287)) $x287)) (= (not $x137) $x287)))) +(let ((@x298 (mp (not-or-elim @x205 (not $x137)) @x297 $x287))) +(let ((@x488 (mp (unit-resolution @x439 (unit-resolution @x298 @x478 $x95) @x461 $x33) (symm (commutativity (= $x50 $x33)) (= $x33 $x50)) $x50))) +(let (($x422 (or (not $x50) $x311))) +(let ((@x428 (monotonicity (rewrite (= $x57 (not $x422))) (= (not $x57) (not (not $x422)))))) +(let ((@x432 (trans @x428 (rewrite (= (not (not $x422)) $x422)) (= (not $x57) $x422)))) +(let ((@x433 (mp (not-or-elim @x205 (not $x57)) @x432 $x422))) +(unit-resolution @x433 @x488 (mp @x478 @x480 $x44) false))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -32286f9c5e71eb2b15c18f86f04c80931e2e307b 878 0 +8eb414a6a3d3ad6d5e5412da8fced2ed014e80e6 878 0 unsat ((set-logic AUFLIA) (proof @@ -3014,7 +2265,7 @@ (let ((@x1972 (unit-resolution @x623 (unit-resolution @x625 (unit-resolution @x1804 @x1969 $x823) $x363) $x620))) (unit-resolution @x926 @x1972 @x1966 false)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -5c29815a1036cbd6b831d4adbe102069cf0d830f 20 0 +acc0a8679fada55f807fa45c47b89f2dc4f0cc19 20 0 unsat ((set-logic AUFLIRA) (proof @@ -3035,167 +2286,7 @@ (let ((@x62 (monotonicity @x59 (= $x36 (not $x43))))) (mp (asserted $x36) (trans @x62 @x71 (= $x36 false)) false)))))))))))))))))) -7d3773a9d63ce2ada82ac001b84291cdc85d7ab8 159 0 -unsat -((set-logic AUFLIA) -(proof -(let (($x44 (= m$ n$))) -(let ((@x480 (symm (commutativity (= $x44 (= n$ m$))) (= (= n$ m$) $x44)))) -(let (($x40 (= n$ m$))) -(let ((?x102 (* (- 1) m$))) -(let ((?x103 (+ n$ ?x102))) -(let (($x118 (>= ?x103 0))) -(let ((?x78 (* (- 1) n$a))) -(let ((?x96 (+ m$ ?x78))) -(let (($x127 (<= ?x96 0))) -(let ((?x79 (+ n$ ?x78))) -(let (($x88 (>= ?x79 0))) -(let (($x239 (or $x88 $x127))) -(let ((@x251 (monotonicity (rewrite (= (and (not $x88) (not $x127)) (not $x239))) (= (not (and (not $x88) (not $x127))) (not (not $x239)))))) -(let ((@x271 (trans @x251 (rewrite (= (not (not $x239)) $x239)) (= (not (and (not $x88) (not $x127))) $x239)))) -(let (($x128 (not $x127))) -(let (($x87 (not $x88))) -(let (($x143 (and $x87 $x128))) -(let (($x210 (not 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$x57))))) -(let (($x62 (or (and (< m$ n$) (< n$ n$a)) (or (and (< m$ n$) $x48) $x60)))) -(let (($x65 (or (and (< n$a n$) (< n$ m$)) (or (and $x48 (< n$ m$)) (or (and $x50 (< m$ n$)) $x62))))) -(let (($x67 (or (and (< n$a m$) (< m$ n$)) (or (and (< n$a m$) $x44) $x65)))) -(let (($x70 (or (and (< n$ n$a) (< n$a m$)) (or (and $x38 (< n$a m$)) (or (and $x40 (< m$ n$a)) $x67))))) -(let (($x72 (or (and (< n$ m$) (< m$ n$a)) (or (and (< n$ m$) $x33) $x70)))) -(let (($x73 (not $x72))) -(let (($x170 (or $x121 (or $x114 (or $x111 (or $x108 (or $x99 (or $x91 (or $x84 $x57))))))))) -(let (($x191 (or $x146 (or $x143 (or $x140 (or $x137 (or $x134 (or $x131 (or $x124 $x170))))))))) -(let (($x189 (= $x70 (or $x143 (or $x140 (or $x137 (or $x134 (or $x131 (or $x124 $x170))))))))) -(let (($x186 (= (or (and $x38 (< n$a m$)) (or (and $x40 (< m$ n$a)) $x67)) (or $x140 (or $x137 (or $x134 (or $x131 (or $x124 $x170)))))))) -(let (($x183 (= (or (and $x40 (< m$ n$a)) $x67) (or $x137 (or $x134 (or $x131 (or 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((@x163 (monotonicity (monotonicity @x107 (= (and (< m$ n$) $x48) $x108)) @x160 $x162))) -(let ((@x113 (monotonicity @x107 @x90 (= (and (< m$ n$) (< n$ n$a)) $x111)))) -(let ((@x166 (monotonicity @x113 @x163 (= $x62 (or $x111 (or $x108 (or $x99 (or $x91 (or $x84 $x57))))))))) -(let ((@x169 (monotonicity (monotonicity @x107 (= (and $x50 (< m$ n$)) $x114)) @x166 $x168))) -(let ((@x120 (rewrite (= (< n$ m$) $x117)))) -(let ((@x172 (monotonicity (monotonicity @x120 (= (and $x48 (< n$ m$)) $x121)) @x169 $x171))) -(let ((@x126 (monotonicity @x83 @x120 (= (and (< n$a n$) (< n$ m$)) $x124)))) -(let ((@x130 (rewrite (= (< n$a m$) $x128)))) -(let ((@x178 (monotonicity (monotonicity @x130 (= (and (< n$a m$) $x44) $x131)) (monotonicity @x126 @x172 (= $x65 (or $x124 $x170))) (= (or (and (< n$a m$) $x44) $x65) (or $x131 (or $x124 $x170)))))) -(let ((@x136 (monotonicity @x130 @x107 (= (and (< n$a m$) (< m$ n$)) $x134)))) -(let ((@x181 (monotonicity @x136 @x178 (= $x67 (or $x134 (or $x131 (or $x124 $x170))))))) -(let ((@x184 (monotonicity (monotonicity @x98 (= (and $x40 (< m$ n$a)) $x137)) @x181 $x183))) -(let ((@x187 (monotonicity (monotonicity @x130 (= (and $x38 (< n$a m$)) $x140)) @x184 $x186))) -(let ((@x145 (monotonicity @x90 @x130 (= (and (< n$ n$a) (< n$a m$)) $x143)))) -(let ((@x193 (monotonicity (monotonicity @x120 (= (and (< n$ m$) $x33) $x146)) (monotonicity @x145 @x187 $x189) (= (or (and (< n$ m$) $x33) $x70) $x191)))) -(let ((@x151 (monotonicity @x120 @x98 (= (and (< n$ m$) (< m$ n$a)) $x149)))) -(let ((@x201 (trans (monotonicity @x151 @x193 (= $x72 (or $x149 $x191))) (rewrite (= (or $x149 $x191) $x197)) (= $x72 $x197)))) -(let ((@x205 (mp (asserted $x73) (monotonicity @x201 (= $x73 (not $x197))) (not $x197)))) -(let ((@x272 (mp (not-or-elim @x205 $x210) @x271 $x239))) -(let (($x273 (not $x38))) -(let (($x274 (or $x273 $x127))) -(let ((@x280 (monotonicity (rewrite (= $x140 (not $x274))) (= (not $x140) (not (not $x274)))))) -(let ((@x284 (trans @x280 (rewrite (= (not (not $x274)) $x274)) (= (not $x140) $x274)))) -(let ((@x285 (mp (not-or-elim @x205 (not $x140)) @x284 $x274))) -(let (($x286 (not $x40))) -(let (($x311 (not $x44))) -(let ((@x434 (hypothesis $x81))) -(let (($x386 (or $x95 $x80))) -(let ((@x392 (monotonicity (rewrite (= $x99 (not $x386))) (= (not $x99) (not (not $x386)))))) -(let ((@x396 (trans @x392 (rewrite (= (not (not $x386)) $x386)) (= (not $x99) $x386)))) -(let ((@x397 (mp (not-or-elim @x205 (not $x99)) @x396 $x386))) -(let (($x246 (not $x33))) -(let (($x410 (or $x246 $x80))) -(let ((@x416 (monotonicity (rewrite (= $x84 (not $x410))) (= (not $x84) (not (not $x410)))))) -(let ((@x420 (trans @x416 (rewrite (= (not (not $x410)) $x410)) (= (not $x84) $x410)))) -(let ((@x421 (mp (not-or-elim @x205 (not $x84)) @x420 $x410))) -(let ((@x439 ((_ th-lemma arith triangle-eq) (or $x33 $x128 $x94)))) -(let ((@x440 (unit-resolution @x439 (unit-resolution @x421 @x434 $x246) (unit-resolution @x397 @x434 $x95) $x128))) -(let (($x312 (or $x127 $x311))) -(let ((@x318 (monotonicity (rewrite (= $x131 (not $x312))) (= (not $x131) (not (not $x312)))))) -(let ((@x322 (trans @x318 (rewrite (= (not (not $x312)) $x312)) (= (not $x131) $x312)))) -(let ((@x323 (mp (not-or-elim @x205 (not $x131)) @x322 $x312))) -(let ((@x450 (mp (unit-resolution @x323 @x440 $x311) (monotonicity (commutativity (= $x44 $x40)) (= $x311 $x286)) $x286))) -(let (($x324 (or $x80 $x118))) -(let ((@x330 (monotonicity (rewrite (= $x124 (not $x324))) (= (not $x124) (not (not $x324)))))) -(let ((@x334 (trans @x330 (rewrite (= (not (not $x324)) $x324)) (= (not $x124) $x324)))) -(let ((@x335 (mp (not-or-elim @x205 (not $x124)) @x334 $x324))) -(let (($x299 (or $x127 $x104))) -(let ((@x305 (monotonicity (rewrite (= $x134 (not $x299))) (= (not $x134) (not (not $x299)))))) -(let ((@x309 (trans @x305 (rewrite (= (not (not $x299)) $x299)) (= (not $x134) $x299)))) -(let ((@x310 (mp (not-or-elim @x205 (not $x134)) @x309 $x299))) -(let ((@x444 (unit-resolution ((_ th-lemma arith triangle-eq) (or $x40 $x105 $x117)) (unit-resolution @x310 @x440 $x104) (unit-resolution @x335 @x434 $x118) $x40))) -(let ((@x459 (unit-resolution ((_ th-lemma arith triangle-eq) (or $x38 $x81 $x87)) (lemma (unit-resolution @x444 @x450 false) $x80) (or $x38 $x87)))) -(let ((@x460 (unit-resolution @x459 (unit-resolution @x285 (hypothesis $x128) $x273) (unit-resolution @x272 (hypothesis $x128) $x88) false))) -(let ((@x461 (lemma @x460 $x127))) -(let (($x254 (or $x118 $x95))) -(let ((@x262 (monotonicity (rewrite (= $x149 (not $x254))) (= (not $x149) (not (not $x254)))))) -(let ((@x256 (trans @x262 (rewrite (= (not (not $x254)) $x254)) (= (not $x149) $x254)))) -(let ((@x257 (mp (not-or-elim @x205 (not $x149)) @x256 $x254))) -(let (($x247 (or $x118 $x246))) -(let ((@x259 (monotonicity (rewrite (= $x146 (not $x247))) (= (not $x146) (not (not $x247)))))) -(let ((@x245 (trans @x259 (rewrite (= (not (not $x247)) $x247)) (= (not $x146) $x247)))) -(let ((@x238 (mp (not-or-elim @x205 (not $x146)) @x245 $x247))) -(let ((@x465 (unit-resolution @x439 (unit-resolution @x238 (hypothesis $x117) $x246) (unit-resolution @x257 (hypothesis $x117) $x95) @x461 false))) -(let (($x336 (not $x48))) -(let (($x374 (or $x104 $x336))) -(let ((@x380 (monotonicity (rewrite (= $x108 (not $x374))) (= (not $x108) (not (not $x374)))))) -(let ((@x384 (trans @x380 (rewrite (= (not (not $x374)) $x374)) (= (not $x108) $x374)))) -(let ((@x385 (mp (not-or-elim @x205 (not $x108)) @x384 $x374))) -(let ((@x475 (mp (unit-resolution @x385 (hypothesis $x105) $x336) (monotonicity (commutativity (= $x48 $x38)) (= $x336 $x273)) $x273))) -(let (($x362 (or $x104 $x88))) -(let ((@x368 (monotonicity (rewrite (= $x111 (not $x362))) (= (not $x111) (not (not $x362)))))) -(let ((@x372 (trans @x368 (rewrite (= (not (not $x362)) $x362)) (= (not $x111) $x362)))) -(let ((@x373 (mp (not-or-elim @x205 (not $x111)) @x372 $x362))) -(let ((@x469 (unit-resolution @x459 (unit-resolution @x373 (hypothesis $x105) $x88) $x38))) -(let ((@x478 (unit-resolution ((_ th-lemma arith triangle-eq) (or $x40 $x105 $x117)) (lemma (unit-resolution @x469 @x475 false) $x104) (lemma @x465 $x118) $x40))) -(let (($x287 (or $x286 $x95))) -(let ((@x293 (monotonicity (rewrite (= $x137 (not $x287))) (= (not $x137) (not (not $x287)))))) -(let ((@x297 (trans @x293 (rewrite (= (not (not $x287)) $x287)) (= (not $x137) $x287)))) -(let ((@x298 (mp (not-or-elim @x205 (not $x137)) @x297 $x287))) -(let ((@x488 (mp (unit-resolution @x439 (unit-resolution @x298 @x478 $x95) @x461 $x33) (symm (commutativity (= $x50 $x33)) (= $x33 $x50)) $x50))) -(let (($x422 (or (not $x50) $x311))) -(let ((@x428 (monotonicity (rewrite (= $x57 (not $x422))) (= (not $x57) (not (not $x422)))))) -(let ((@x432 (trans @x428 (rewrite (= (not (not $x422)) $x422)) (= (not $x57) $x422)))) -(let ((@x433 (mp (not-or-elim @x205 (not $x57)) @x432 $x422))) -(unit-resolution @x433 @x488 (mp @x478 @x480 $x44) false))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) - -0b997744cf42fde45b98a34c933b0698332e657f 113 0 +f2ecc8d02c730cd119d0a8be84bc5bf03ed0f98b 113 0 unsat ((set-logic ) (proof @@ -3309,7 +2400,7 @@ (let ((@x74 (mp (asserted $x36) @x73 $x67))) ((_ th-lemma arith farkas -1 1 1) @x74 (unit-resolution ((_ th-lemma arith) (or false $x305)) (true-axiom true) $x305) @x332 false)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -2e67f9e254b2a35a9d35027c6e63de01bc5086bd 112 0 +2b90909cb79318775a857f179e3de90ebc09360b 112 0 unsat ((set-logic ) (proof @@ -3422,7 +2513,7 @@ (let ((@x70 (mp (asserted (not (< (+ x$ (+ ?x29 ?x29)) (+ x$ 3)))) @x69 $x63))) ((_ th-lemma arith farkas -1 1 1) @x70 @x331 (unit-resolution ((_ th-lemma arith) (or false $x319)) (true-axiom true) $x319) false))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -3938db798ebafb55191dcdaf83a8615d1d59c0c3 32 0 +9e8bd1ccee1598c51f1f67ef729241282bee8975 32 0 unsat ((set-logic ) (proof @@ -3455,7 +2546,7 @@ (let ((@x117 (unit-resolution ((_ th-lemma arith assign-bounds 1) (or $x102 (not $x100))) (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x95) $x100)) @x98 $x100) $x102))) (unit-resolution ((_ th-lemma arith triangle-eq) (or $x28 (not $x101) (not $x102))) @x117 @x110 @x30 false)))))))))))))))))))))))))))))) -dcc9b986d57d4904aeadc1233210450bb15df4d3 12 0 +e975f8a0748f1ab04103c4bce1c336d67c9ddc7f 12 0 unsat ((set-logic AUFLIA) (proof @@ -3468,7 +2559,7 @@ (let ((@x46 (trans @x42 (rewrite (= (not true) false)) (= $x29 false)))) (mp (asserted $x29) @x46 false))))))))) -e33f4ac0207897c2b7abfeafedc87232f999a6d5 12 0 +693a453fa295b294a12bfe4fc2548b88f93af81d 12 0 unsat ((set-logic AUFLIRA) (proof @@ -3481,7 +2572,7 @@ (let ((@x46 (trans @x42 (rewrite (= (not true) false)) (= $x29 false)))) (mp (asserted $x29) @x46 false))))))))) -ef29919c373b650f8005a5573289548ab716b089 22 0 +da9745bea43c7d7581f4f1a982ea54a4f665c150 22 0 unsat ((set-logic AUFLIA) (proof @@ -3504,7 +2595,7 @@ (let ((@x49 (mp~ (mp (asserted $x30) (monotonicity @x40 (= $x30 $x41)) $x41) @x48 $x46))) (mp (mp @x49 @x54 $x52) (rewrite (= $x52 false)) false))))))))))))) -4d3a976164de7ccb5d4650a113f067b8a1c55b22 22 0 +d1b4498be99afb5671326f37a46458328653a778 22 0 unsat ((set-logic AUFLIRA) (proof @@ -3527,7 +2618,7 @@ (let ((@x48 (mp~ (mp (asserted $x29) (monotonicity @x39 (= $x29 $x40)) $x40) @x47 $x45))) (mp (mp @x48 @x53 $x51) (rewrite (= $x51 false)) false))))))))))))) -f28123a872d014e01ec45f8bb7163bb037909301 31 0 +47b866c871f79f79347596e68e9f0a6717e9f9ae 31 0 unsat ((set-logic AUFLIA) (declare-fun ?v0!0 () Int) @@ -3559,7 +2650,7 @@ (let ((@x74 (mp (mp~ (mp (asserted $x32) @x51 $x49) @x67 $x63) (quant-intro (rewrite (= $x60 $x54)) (= $x63 $x71)) $x71))) (mp @x74 (rewrite (= $x71 false)) false)))))))))))))))))) -574f579e644304e47945be9d8bd47347079730d4 22 0 +f8895baf351fb020e98a9589d9032cb37daead5c 22 0 unsat ((set-logic AUFLIA) (declare-fun ?v1!0 () Int) @@ -3582,7 +2673,7 @@ (let ((@x70 (trans (symm (and-elim @x65 (= ?v0!1 0)) (= 0 ?v0!1)) @x68 (= 0 ?v1!0)))) (mp (trans @x70 @x67 (= 0 1)) (rewrite (= (= 0 1) false)) false)))))))))))))))) -a24ff2e4a93d06b88e1d7717852cb82258ed11ed 55 0 +c6ae686b0a4faf5664648d4de310ae4c5a1de7ec 55 0 unsat ((set-logic AUFLIA) (proof @@ -3638,7 +2729,7 @@ (let ((@x50 (monotonicity @x47 (= $x36 $x48)))) (mp (asserted $x36) (trans @x50 @x101 (= $x36 false)) false))))))))))))))))))))))))))) -c446c8659459cda8dda1ecfd9aba54ce2a50f002 42 0 +326e4de3d7358a1ce81c3b38c63746b57dca63fa 42 0 unsat ((set-logic AUFLIA) (proof @@ -3681,7 +2772,7 @@ (let ((@x60 (monotonicity (quant-intro @x54 (= $x37 $x55)) (= $x38 $x58)))) (mp (asserted $x38) (trans @x60 @x97 (= $x38 false)) false)))))))))))))))))))))))))) -a6ee8724a53192e0bb5b41bbeed60d66d29cdc32 32 0 +8948c34be010e83eefa29947fdeb482617c77a6d 32 0 unsat ((set-logic AUFLIA) (proof @@ -3714,7 +2805,7 @@ (let ((@x53 (monotonicity @x50 (= $x37 $x51)))) (mp (asserted $x37) (trans @x53 @x76 (= $x37 false)) false))))))))))))))))))) -07f4cd3fa64b76806d385c4af8945a76e01f07d9 43 0 +933b139b2a650c91137f9f7c9b004c8f0d9521d1 43 0 unsat ((set-logic AUFLIA) (declare-fun ?v0!1 () Int) @@ -3758,7 +2849,7 @@ (let ((@x103 (not-or-elim @x102 $x81))) (unit-resolution (unit-resolution ((_ th-lemma arith triangle-eq) (or $x87 $x84 $x93)) @x103 (or $x87 $x93)) @x106 @x105 false))))))))))))))))))))))))))))))))) -7f22e563ec1d8ce90ee01f0d4b366d5b595fcdef 46 0 +b488c2ec223d613631144f2dcdf7e5867fbbb258 46 0 unsat ((set-logic AUFLIA) (declare-fun ?v0!0 () Int) @@ -3805,7 +2896,7 @@ (let ((@x109 (lemma @x108 $x84))) (unit-resolution (unit-resolution (def-axiom (or $x88 $x83 $x86)) @x92 (or $x83 $x86)) (unit-resolution ((_ th-lemma arith farkas 1 1) (or $x93 $x85)) @x109 $x93) (unit-resolution ((_ th-lemma arith farkas 1 1) (or $x87 $x85)) @x109 $x87) false))))))))))))))))))))))))))))))))) -e566ad249d308c74a627c15c9f02c271a6843a42 31 0 +da417520952f17eeef46bee85072a2ecad83fc46 31 0 unsat ((set-logic AUFLIA) (proof @@ -3837,7 +2928,7 @@ (let ((@x66 (mp~ (mp (asserted $x33) @x60 $x56) (nnf-pos (refl (~ $x53 $x53)) (~ $x56 $x56)) $x56))) (unit-resolution @x66 @x464 false))))))))))))))))))))))))) -a02ae6c9688537bbe4c3be0d3dcebbc703417864 62 0 +623edcfe9613936b08dbdc0269a0746af35c83aa 62 0 unsat ((set-logic AUFLIA) (declare-fun ?v0!1 () Int) @@ -3900,7 +2991,7 @@ (let ((@x515 (unit-resolution (def-axiom (or z3name!0 $x220)) (unit-resolution @x131 @x238 $x88) $x220))) (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x220) (>= ?x96 3))) @x515 @x245 false)))))))))))))))))))))))))))))))))))))))))))))))))))))) -9853592ad3514c1450e40271884a9f21f57ff85b 39 0 +42b10c0c66daf8181b08c93c22f4ecaa3220e964 39 0 unsat ((set-logic AUFLIA) (proof @@ -3940,7 +3031,7 @@ (let ((@x75 (trans @x71 (rewrite (= (not (not $x61)) $x61)) (= $x39 $x61)))) (mp (asserted $x39) (trans @x75 @x85 (= $x39 false)) false))))))))))))))))))))))) -7f619f54c20728881b08a920d22e08bbe3d76a4d 52 0 +a32c06c0a3798bb49bc988f268a9de26ca0e273b 52 0 unsat ((set-logic AUFLIA) (declare-fun ?v1!1 () Int) @@ -3993,7 +3084,7 @@ (let ((@x117 (and-elim (not-or-elim @x112 (and $x100 $x102)) $x102))) ((_ th-lemma arith farkas 1 1 1) @x117 @x116 @x118 false))))))))))))))))))))))))))))))))))) -9201a8009730b821ad6a3a2b64598e50ab5748ca 45 0 +dd6dcae1cf0d709ea38f21e7928a94234cce9953 45 0 unsat ((set-logic AUFLIRA) (declare-fun ?v1!1 () Int) @@ -4039,7 +3130,7 @@ (let ((@x115 (and-elim (not-or-elim @x111 (and $x100 (not (<= ?v2!0 0.0)))) $x100))) (unit-resolution ((_ th-lemma arith farkas 1 1) (or (not $x105) $x99)) @x115 @x117 false)))))))))))))))))))))))))))))) -d9fbfe5a894f4a224aaf7d1fa1f67325ad2e1497 110 0 +3eba422177cb1a37290b37910c836f326aae81a7 110 0 unsat ((set-logic AUFLIA) (proof @@ -4150,7 +3241,7 @@ (let ((@x125 (mp (mp @x110 (quant-intro @x115 (= $x107 $x116)) $x116) (quant-intro (rewrite (= $x113 $x104)) (= $x116 $x122)) $x122))) (mp (mp @x125 @x156 $x152) @x180 false)))))))))))))))))))))))))))))))))))))))))))))) -ae4f4fb9c10608b8e3b893cc6c99e3ec5d13a86c 23 0 +cf55ed5d5e3fbc48182cb17ef320bda064703b0c 23 0 unsat ((set-logic AUFLIA) (declare-fun ?v1!0 () Int) @@ -4174,7 +3265,7 @@ (let ((@x73 (not-or-elim @x70 $x62))) (unit-resolution ((_ th-lemma arith farkas 1 1) (or (not $x62) (not $x64))) @x73 @x74 false))))))))))))))))) -d98ad8f668dead6f610669a52351ea0176a811b0 26 0 +47c99edbec21b5ca2d3944c6aeff150e7def6e0b 26 0 unsat ((set-logic ) (proof @@ -4201,7 +3292,7 @@ (let ((@x73 (and-elim (not-or-elim (mp (asserted $x35) @x69 $x65) $x52) $x49))) ((_ th-lemma arith farkas 1 1 1) @x73 @x72 @x74 false)))))))))))))))))))))))) -271390ea915947de195c2202e30f90bb84689d60 26 0 +d19214170f32152ce058c34f982fe481da9e80ff 26 0 unsat ((set-logic ) (proof @@ -4228,7 +3319,7 @@ (let ((@x92 (trans @x88 (rewrite (= (not true) false)) (= $x39 false)))) (mp (asserted $x39) @x92 false)))))))))))))))))))))))) -b216c79478e44396acca3654b76845499fc18a04 23 0 +6338e51142f708a9900dc576fef69c89a46c7f58 23 0 unsat ((set-logic ) (proof @@ -4252,7 +3343,7 @@ (let ((@x82 (trans (monotonicity @x75 (= $x39 (not true))) (rewrite (= (not true) false)) (= $x39 false)))) (mp (asserted $x39) @x82 false))))))))))))))))))))) -9df6daf3cc37f0807bf370ee01536b85d300ecce 51 0 +760eefae5bab2da16eec8daa0cc978ac4329de62 51 0 unsat ((set-logic ) (proof @@ -4304,134 +3395,20 @@ (let ((@x152 (trans (monotonicity @x145 (= $x52 (not true))) (rewrite (= (not true) false)) (= $x52 false)))) (mp (asserted $x52) @x152 false))))))))))))))))))))))))))))))))))))))))))))))))) -49c385b161a0c500f84c45f85272a8ec9574fef4 126 0 +12dc1d685081b4234b95f046bcf34da3681d7c1e 12 0 unsat ((set-logic AUFLIA) (proof +(let ((@x39 (rewrite (= (= (* 2 (of_nat$ x$)) 1) false)))) (let ((?x29 (of_nat$ x$))) (let ((?x30 (* 2 ?x29))) -(let ((?x31 (nat$ ?x30))) -(let ((?x212 (of_nat$ ?x31))) -(let ((?x532 (* (- 1) ?x212))) -(let ((?x533 (+ ?x30 ?x532))) -(let (($x513 (<= ?x533 0))) -(let (($x531 (= ?x533 0))) -(let (($x193 (>= ?x29 0))) -(let (($x487 (>= ?x212 1))) -(let (($x485 (= ?x212 1))) -(let ((?x33 (nat$ 1))) -(let ((?x504 (of_nat$ ?x33))) -(let (($x505 (= ?x504 1))) -(let (($x546 (forall ((?v0 Int) )(! (let ((?x49 (nat$ ?v0))) -(let ((?x50 (of_nat$ ?x49))) -(let (($x51 (= ?x50 ?v0))) -(let (($x64 (>= ?v0 0))) -(let (($x65 (not $x64))) -(or $x65 $x51)))))) :pattern ( (nat$ ?v0) ) :qid k!10)) -)) -(let (($x71 (forall ((?v0 Int) )(! (let ((?x49 (nat$ ?v0))) -(let ((?x50 (of_nat$ ?x49))) -(let (($x51 (= ?x50 ?v0))) -(let (($x64 (>= ?v0 0))) -(let (($x65 (not $x64))) -(or $x65 $x51)))))) :qid k!10)) -)) -(let ((?x49 (nat$ ?0))) -(let ((?x50 (of_nat$ ?x49))) -(let (($x51 (= ?x50 ?0))) -(let (($x64 (>= ?0 0))) -(let (($x65 (not $x64))) -(let (($x68 (or $x65 $x51))) -(let (($x53 (forall ((?v0 Int) )(! (let ((?x49 (nat$ ?v0))) -(let ((?x50 (of_nat$ ?x49))) -(let (($x51 (= ?x50 ?v0))) -(let (($x48 (<= 0 ?v0))) -(=> $x48 $x51))))) :qid k!10)) -)) -(let (($x59 (forall ((?v0 Int) )(! (let ((?x49 (nat$ ?v0))) -(let ((?x50 (of_nat$ ?x49))) -(let (($x51 (= ?x50 ?v0))) -(or (not (<= 0 ?v0)) $x51)))) :qid k!10)) -)) -(let ((@x67 (monotonicity (rewrite (= (<= 0 ?0) $x64)) (= (not (<= 0 ?0)) $x65)))) -(let ((@x73 (quant-intro (monotonicity @x67 (= (or (not (<= 0 ?0)) $x51) $x68)) (= $x59 $x71)))) -(let ((@x58 (rewrite (= (=> (<= 0 ?0) $x51) (or (not (<= 0 ?0)) $x51))))) -(let ((@x76 (mp (asserted $x53) (trans (quant-intro @x58 (= $x53 $x59)) @x73 (= $x53 $x71)) $x71))) -(let ((@x551 (mp (mp~ @x76 (nnf-pos (refl (~ $x68 $x68)) (~ $x71 $x71)) $x71) (quant-intro (refl (= $x68 $x68)) (= $x71 $x546)) $x546))) -(let (($x526 (not $x546))) -(let (($x489 (or $x526 $x505))) -(let ((@x506 (rewrite (= (>= 1 0) true)))) -(let ((@x219 (trans (monotonicity @x506 (= (not (>= 1 0)) (not true))) (rewrite (= (not true) false)) (= (not (>= 1 0)) false)))) -(let ((@x223 (monotonicity @x219 (= (or (not (>= 1 0)) $x505) (or false $x505))))) -(let ((@x503 (trans @x223 (rewrite (= (or false $x505) $x505)) (= (or (not (>= 1 0)) $x505) $x505)))) -(let ((@x493 (monotonicity @x503 (= (or $x526 (or (not (>= 1 0)) $x505)) $x489)))) -(let ((@x496 (trans @x493 (rewrite (= $x489 $x489)) (= (or $x526 (or (not (>= 1 0)) $x505)) $x489)))) -(let ((@x497 (mp ((_ quant-inst 1) (or $x526 (or (not (>= 1 0)) $x505))) @x496 $x489))) -(let (($x34 (= ?x31 ?x33))) -(let ((@x42 (mp (asserted (not (not $x34))) (rewrite (= (not (not $x34)) $x34)) $x34))) -(let ((@x356 (trans (monotonicity @x42 (= ?x212 ?x504)) (unit-resolution @x497 @x551 $x505) $x485))) -(let ((@x371 (unit-resolution ((_ th-lemma arith farkas 1 1) (or (not $x487) (not (<= ?x212 0)))) (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x485) $x487)) @x356 $x487) (not (<= ?x212 0))))) -(let ((@x374 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not (= ?x212 0)) (<= ?x212 0))) @x371 (not (= ?x212 0))))) -(let (($x515 (= ?x212 0))) -(let (($x517 (or $x193 $x515))) -(let (($x552 (forall ((?v0 Int) )(! (let ((?x49 (nat$ ?v0))) -(let ((?x50 (of_nat$ ?x49))) -(let (($x78 (= ?x50 0))) -(let (($x64 (>= ?v0 0))) -(or $x64 $x78))))) :pattern ( (nat$ ?v0) ) :qid k!11)) -)) -(let (($x101 (forall ((?v0 Int) )(! (let ((?x49 (nat$ ?v0))) -(let ((?x50 (of_nat$ ?x49))) -(let (($x78 (= ?x50 0))) -(let (($x64 (>= ?v0 0))) -(or $x64 $x78))))) :qid k!11)) -)) -(let ((@x556 (quant-intro (refl (= (or $x64 (= ?x50 0)) (or $x64 (= ?x50 0)))) (= $x101 $x552)))) -(let ((@x120 (nnf-pos (refl (~ (or $x64 (= ?x50 0)) (or $x64 (= ?x50 0)))) (~ $x101 $x101)))) -(let (($x80 (forall ((?v0 Int) )(! (let ((?x49 (nat$ ?v0))) -(let ((?x50 (of_nat$ ?x49))) -(let (($x78 (= ?x50 0))) -(let (($x77 (< ?v0 0))) -(=> $x77 $x78))))) :qid k!11)) -)) -(let (($x86 (forall ((?v0 Int) )(! (let ((?x49 (nat$ ?v0))) -(let ((?x50 (of_nat$ ?x49))) -(let (($x78 (= ?x50 0))) -(let (($x77 (< ?v0 0))) -(let (($x82 (not $x77))) -(or $x82 $x78)))))) :qid k!11)) -)) -(let (($x78 (= ?x50 0))) -(let (($x98 (or $x64 $x78))) -(let (($x77 (< ?0 0))) -(let (($x82 (not $x77))) -(let (($x83 (or $x82 $x78))) -(let ((@x97 (trans (monotonicity (rewrite (= $x77 $x65)) (= $x82 (not $x65))) (rewrite (= (not $x65) $x64)) (= $x82 $x64)))) -(let ((@x105 (trans (quant-intro (rewrite (= (=> $x77 $x78) $x83)) (= $x80 $x86)) (quant-intro (monotonicity @x97 (= $x83 $x98)) (= $x86 $x101)) (= $x80 $x101)))) -(let ((@x557 (mp (mp~ (mp (asserted $x80) @x105 $x101) @x120 $x101) @x556 $x552))) -(let (($x156 (not $x552))) -(let (($x520 (or $x156 $x193 $x515))) -(let ((@x530 (rewrite (= (>= ?x30 0) $x193)))) -(let ((@x523 (monotonicity (monotonicity @x530 (= (or (>= ?x30 0) $x515) $x517)) (= (or $x156 (or (>= ?x30 0) $x515)) (or $x156 $x517))))) -(let ((@x215 (trans @x523 (rewrite (= (or $x156 $x517) $x520)) (= (or $x156 (or (>= ?x30 0) $x515)) $x520)))) -(let ((@x229 (mp ((_ quant-inst (* 2 ?x29)) (or $x156 (or (>= ?x30 0) $x515))) @x215 $x520))) -(let (($x185 (not $x193))) -(let (($x534 (or $x185 $x531))) -(let (($x188 (or $x526 $x185 $x531))) -(let (($x213 (= ?x212 ?x30))) -(let (($x208 (>= ?x30 0))) -(let (($x209 (not $x208))) -(let (($x214 (or $x209 $x213))) -(let (($x189 (or $x526 $x214))) -(let ((@x536 (monotonicity (monotonicity @x530 (= $x209 $x185)) (rewrite (= $x213 $x531)) (= $x214 $x534)))) -(let ((@x175 (trans (monotonicity @x536 (= $x189 (or $x526 $x534))) (rewrite (= (or $x526 $x534) $x188)) (= $x189 $x188)))) -(let ((@x176 (mp ((_ quant-inst (* 2 ?x29)) $x189) @x175 $x188))) -(let ((@x470 (unit-resolution (unit-resolution @x176 @x551 $x534) (unit-resolution (unit-resolution @x229 @x557 $x517) @x374 $x193) $x531))) -(let (($x514 (>= ?x533 0))) -(let (($x486 (<= ?x212 1))) -((_ th-lemma arith gcd-test -1/2 -1/2 -1/2 -1/2) (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x485) $x487)) @x356 $x487) (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x485) $x486)) @x356 $x486) (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x531) $x514)) @x470 $x514) (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x531) $x513)) @x470 $x513) false)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) +(let (($x32 (= ?x30 1))) +(let (($x33 (not $x32))) +(let (($x34 (not $x33))) +(let ((@x37 (rewrite (= $x34 $x32)))) +(mp (asserted $x34) (trans @x37 @x39 (= $x34 false)) false)))))))))) -1c2b6530334930f2f4f6e0d6b73f1d249b6c5fd8 23 0 +f2f21091bf9deb3a38832129de5449a872415f16 23 0 unsat ((set-logic AUFLIA) (proof @@ -4455,5072 +3432,7 @@ (let ((@x70 (not-or-elim (mp (asserted $x36) (trans @x44 @x66 (= $x36 $x64)) $x64) $x45))) (unit-resolution ((_ th-lemma arith farkas 1 1) $x61) @x70 @x71 false))))))))))))))))))))) -995f80f06d5874ea2208846fb3b3217c3a3b9bfd 147 0 -unsat -((set-logic AUFLIA) -(proof -(let ((?x29 (of_nat$ y$))) -(let ((?x30 (+ 1 ?x29))) -(let ((?x31 (nat$ ?x30))) -(let ((?x32 (of_nat$ ?x31))) -(let ((?x43 (* (- 1) ?x29))) -(let ((?x44 (+ ?x43 ?x32))) -(let ((?x47 (nat$ ?x44))) -(let ((?x50 (of_nat$ ?x47))) -(let ((?x567 (* (- 1) ?x32))) -(let ((?x255 (+ ?x29 ?x567 ?x50))) -(let (($x513 (>= ?x255 0))) -(let (($x532 (= ?x255 0))) -(let ((?x568 (+ ?x29 ?x567))) -(let (($x248 (<= ?x568 0))) -(let (($x551 (<= ?x568 (- 1)))) -(let (($x558 (= ?x568 (- 1)))) -(let (($x229 (>= ?x29 (- 1)))) -(let (($x387 (>= ?x29 0))) -(let ((?x154 (nat$ ?x29))) -(let ((?x388 (of_nat$ ?x154))) -(let (($x352 (= ?x388 0))) -(let (($x498 (or $x387 $x352))) -(let (($x584 (forall ((?v0 Int) )(! (let ((?x81 (nat$ ?v0))) -(let ((?x82 (of_nat$ ?x81))) -(let (($x110 (= ?x82 0))) -(let (($x95 (>= ?v0 0))) -(or $x95 $x110))))) :pattern ( (nat$ ?v0) ) :qid k!11)) -)) -(let (($x133 (forall ((?v0 Int) )(! (let ((?x81 (nat$ ?v0))) -(let ((?x82 (of_nat$ ?x81))) -(let (($x110 (= ?x82 0))) -(let (($x95 (>= ?v0 0))) -(or $x95 $x110))))) :qid k!11)) -)) -(let ((?x81 (nat$ ?0))) -(let ((?x82 (of_nat$ ?x81))) -(let (($x110 (= ?x82 0))) -(let (($x95 (>= ?0 0))) -(let (($x130 (or $x95 $x110))) -(let (($x112 (forall ((?v0 Int) )(! (let ((?x81 (nat$ ?v0))) -(let ((?x82 (of_nat$ ?x81))) -(let (($x110 (= ?x82 0))) -(let (($x109 (< ?v0 0))) -(=> $x109 $x110))))) :qid k!11)) -)) -(let (($x118 (forall ((?v0 Int) )(! (let ((?x81 (nat$ ?v0))) -(let ((?x82 (of_nat$ ?x81))) -(let (($x110 (= ?x82 0))) -(let (($x109 (< ?v0 0))) -(let (($x114 (not $x109))) -(or $x114 $x110)))))) :qid k!11)) -)) -(let ((@x125 (monotonicity (rewrite (= (< ?0 0) (not $x95))) (= (not (< ?0 0)) (not (not $x95)))))) -(let ((@x129 (trans @x125 (rewrite (= (not (not $x95)) $x95)) (= (not (< ?0 0)) $x95)))) -(let ((@x135 (quant-intro (monotonicity @x129 (= (or (not (< ?0 0)) $x110) $x130)) (= $x118 $x133)))) -(let ((@x117 (rewrite (= (=> (< ?0 0) $x110) (or (not (< ?0 0)) $x110))))) -(let ((@x138 (mp (asserted $x112) (trans (quant-intro @x117 (= $x112 $x118)) @x135 (= $x112 $x133)) $x133))) -(let ((@x589 (mp (mp~ @x138 (nnf-pos (refl (~ $x130 $x130)) (~ $x133 $x133)) $x133) (quant-intro (refl (= $x130 $x130)) (= $x133 $x584)) $x584))) -(let (($x555 (not $x584))) -(let (($x500 (or $x555 $x387 $x352))) -(let ((@x404 (mp ((_ quant-inst (of_nat$ y$)) (or $x555 $x498)) (rewrite (= (or $x555 $x498) $x500)) $x500))) -(let ((@x487 (unit-resolution (unit-resolution @x404 @x589 $x498) (hypothesis (not $x387)) $x352))) -(let (($x239 (= ?x154 y$))) -(let (($x570 (forall ((?v0 Nat$) )(! 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(let ((?x115 (nat$ ?v0))) -(let ((?x116 (of_nat$ ?x115))) -(let (($x117 (= ?x116 ?v0))) -(or (not (<= 0 ?v0)) $x117)))) :qid k!10)) -)) -(let (($x117 (= ?x116 ?0))) -(let (($x131 (not $x129))) -(let (($x134 (or $x131 $x117))) -(let (($x122 (or (not (<= 0 ?0)) $x117))) -(let ((@x133 (monotonicity (rewrite (= (<= 0 ?0) $x129)) (= (not (<= 0 ?0)) $x131)))) -(let ((@x127 (quant-intro (rewrite (= (=> (<= 0 ?0) $x117) $x122)) (= $x119 $x125)))) -(let ((@x141 (trans @x127 (quant-intro (monotonicity @x133 (= $x122 $x134)) (= $x125 $x137)) (= $x119 $x137)))) -(let ((@x196 (mp~ (mp (asserted $x119) @x141 $x137) (nnf-pos @x185 (~ $x137 $x137)) $x137))) -(let ((@x631 (mp @x196 (quant-intro @x628 (= $x137 $x626)) $x626))) -(let (($x269 (not $x626))) -(let (($x607 (or $x269 $x605 $x612))) -(let (($x273 (= ?x32 ?x30))) -(let (($x291 (>= ?x30 0))) -(let (($x292 (not $x291))) -(let (($x609 (or $x292 $x273))) -(let (($x271 (or $x269 $x609))) -(let ((@x268 (monotonicity (monotonicity (rewrite (= $x291 $x610)) (= $x292 $x605)) (rewrite (= $x273 $x612)) (= $x609 $x616)))) -(let ((@x593 (trans (monotonicity @x268 (= $x271 (or $x269 $x616))) (rewrite (= (or $x269 $x616) $x607)) (= $x271 $x607)))) -(let ((@x594 (mp ((_ quant-inst (+ 1 ?x29)) $x271) @x593 $x607))) -(let ((@x538 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x612) $x595)) (unit-resolution (unit-resolution @x594 @x631 $x616) @x545 $x612) $x595))) -((_ th-lemma arith farkas 1 -1 -1 1) (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x559) $x557)) @x539 $x557) @x106 @x538 @x457 false))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) - -7d4feac3284b531c122b21d3a2a25c87f1e3b93b 78 0 -unsat -((set-logic AUFLIA) -(proof -(let ((?x37 (* (- 1) x$))) -(let (($x55 (>= x$ 0))) -(let ((?x62 (ite $x55 x$ ?x37))) -(let ((?x554 (* (- 1) ?x62))) -(let ((?x217 (+ ?x37 ?x554))) -(let (($x562 (<= ?x217 0))) -(let (($x249 (= ?x37 ?x62))) -(let (($x56 (not $x55))) -(let (($x163 (= x$ ?x62))) -(let ((@x559 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x163) (<= (+ x$ ?x554) 0))) (unit-resolution (def-axiom (or $x56 $x163)) (hypothesis $x55) $x163) (<= (+ x$ ?x554) 0)))) -(let (($x254 (>= ?x62 0))) -(let (($x255 (not $x254))) -(let (($x588 (forall ((?v0 Int) )(! 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(let ((?x90 (nat$ ?v0))) -(let ((?x91 (of_nat$ ?x90))) -(let (($x92 (= ?x91 ?v0))) -(or (not (<= 0 ?v0)) $x92)))) :qid k!10)) -)) -(let ((@x108 (monotonicity (rewrite (= (<= 0 ?0) $x104)) (= (not (<= 0 ?0)) $x106)))) -(let ((@x114 (quant-intro (monotonicity @x108 (= (or (not (<= 0 ?0)) $x92) $x109)) (= $x100 $x112)))) -(let ((@x99 (rewrite (= (=> (<= 0 ?0) $x92) (or (not (<= 0 ?0)) $x92))))) -(let ((@x117 (mp (asserted $x94) (trans (quant-intro @x99 (= $x94 $x100)) @x114 (= $x94 $x112)) $x112))) -(let ((@x593 (mp (mp~ @x117 (nnf-pos (refl (~ $x109 $x109)) (~ $x112 $x112)) $x112) (quant-intro (refl (= $x109 $x109)) (= $x112 $x588)) $x588))) -(let ((?x67 (nat$ ?x62))) -(let ((?x70 (of_nat$ ?x67))) -(let (($x73 (= ?x70 ?x62))) -(let (($x76 (not $x73))) -(let (($x28 (< x$ 0))) -(let ((?x30 (ite $x28 (- x$) x$))) -(let (($x34 (not (= (of_nat$ (nat$ ?x30)) ?x30)))) -(let (($x77 (= (not (= (of_nat$ (nat$ (ite $x28 ?x37 x$))) (ite $x28 ?x37 x$))) $x76))) -(let ((?x40 (ite $x28 ?x37 x$))) -(let ((?x43 (nat$ ?x40))) -(let ((?x46 (of_nat$ ?x43))) -(let (($x49 (= ?x46 ?x40))) -(let ((@x66 (trans (monotonicity (rewrite (= $x28 $x56)) (= ?x40 (ite $x56 ?x37 x$))) (rewrite (= (ite $x56 ?x37 x$) ?x62)) (= ?x40 ?x62)))) -(let ((@x75 (monotonicity (monotonicity (monotonicity @x66 (= ?x43 ?x67)) (= ?x46 ?x70)) @x66 (= $x49 $x73)))) -(let ((@x45 (monotonicity (monotonicity (rewrite (= (- x$) ?x37)) (= ?x30 ?x40)) (= (nat$ ?x30) ?x43)))) -(let ((@x51 (monotonicity (monotonicity @x45 (= (of_nat$ (nat$ ?x30)) ?x46)) (monotonicity (rewrite (= (- x$) ?x37)) (= ?x30 ?x40)) (= (= (of_nat$ (nat$ ?x30)) ?x30) $x49)))) -(let ((@x80 (trans (monotonicity @x51 (= $x34 (not $x49))) (monotonicity @x75 $x77) (= $x34 $x76)))) -(let ((@x81 (mp (asserted $x34) @x80 $x76))) -(let (($x239 (or (not $x588) $x255 $x73))) -(let ((@x576 (mp ((_ quant-inst (ite $x55 x$ ?x37)) (or (not $x588) (or $x255 $x73))) (rewrite (= (or (not $x588) (or $x255 $x73)) $x239)) $x239))) -(let ((@x561 ((_ th-lemma arith farkas -1 1 1) (hypothesis $x55) (unit-resolution @x576 @x81 @x593 $x255) @x559 false))) -(let ((@x198 (lemma @x561 $x56))) -(let ((@x566 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x249) $x562)) (unit-resolution (def-axiom (or $x55 $x249)) @x198 $x249) $x562))) -(let (($x578 (<= ?x62 0))) -(let ((@x257 (unit-resolution ((_ th-lemma arith farkas 1 1) (or $x578 $x254)) (unit-resolution @x576 @x81 @x593 $x255) $x578))) -((_ th-lemma arith farkas 1 1 1) @x257 @x198 @x566 false))))))))))))))))))))))))))))))))))))))))))))))))))))))) - -ce85402875b83dc2f06a381810d29a2061933b9f 312 0 -unsat -((set-logic AUFLIA) -(declare-fun ?v1!0 (Nat$) Nat$) -(proof -(let ((?x89 (of_nat$ m$))) -(let ((?x90 (* 4 ?x89))) -(let ((?x98 (+ 1 ?x90))) -(let ((?x101 (nat$ ?x98))) -(let ((?x295 (of_nat$ ?x101))) -(let ((?x598 (* (- 1) ?x295))) -(let ((?x599 (+ ?x90 ?x598))) -(let (($x574 (>= ?x599 (- 1)))) -(let (($x597 (= ?x599 (- 1)))) -(let (($x610 (>= ?x89 0))) -(let (($x380 (<= ?x295 1))) -(let (($x687 (not $x380))) -(let (($x701 (forall ((?v1 Nat$) )(! (let ((?x89 (of_nat$ m$))) -(let ((?x90 (* 4 ?x89))) -(let ((?x98 (+ 1 ?x90))) -(let ((?x101 (nat$ ?x98))) -(let (($x382 (= ?v1 ?x101))) -(let ((?x34 (nat$ 1))) -(let (($x35 (= ?v1 ?x34))) -(let (($x381 (dvd$ ?v1 ?x101))) -(let (($x371 (not $x381))) -(or $x371 $x35 $x382)))))))))) :pattern ( (dvd$ ?v1 (nat$ (+ 1 (* 4 (of_nat$ m$))))) ) :qid k!10)) -)) -(let (($x702 (not $x701))) -(let (($x357 (or $x380 $x702))) -(let (($x487 (not $x357))) -(let (($x104 (prime_nat$ ?x101))) -(let (($x110 (not $x104))) -(let (($x697 (or $x110 $x487))) -(let ((?x703 (?v1!0 ?x101))) -(let (($x707 (= ?x703 ?x101))) -(let ((?x34 (nat$ 1))) -(let (($x706 (= ?x703 ?x34))) -(let (($x704 (dvd$ ?x703 ?x101))) -(let (($x705 (not $x704))) -(let (($x708 (or $x705 $x706 $x707))) -(let (($x698 (not $x708))) -(let (($x360 (or $x104 $x380 $x698))) -(let (($x700 (not $x360))) -(let (($x369 (not $x697))) -(let (($x342 (or $x369 $x700))) -(let (($x684 (not $x342))) -(let (($x738 (forall ((?v0 Nat$) )(! (let (($x219 (or (not (dvd$ (?v1!0 ?v0) ?v0)) (= (?v1!0 ?v0) (nat$ 1)) (= (?v1!0 ?v0) ?v0)))) -(let (($x220 (not $x219))) -(let ((?x30 (of_nat$ ?v0))) -(let (($x65 (<= ?x30 1))) -(let (($x28 (prime_nat$ ?v0))) -(let (($x245 (or $x28 $x65 $x220))) -(let (($x710 (forall ((?v1 Nat$) )(! (let ((?x34 (nat$ 1))) -(let (($x35 (= ?v1 ?x34))) -(or (not (dvd$ ?v1 ?v0)) $x35 (= ?v1 ?v0)))) :pattern ( (dvd$ ?v1 ?v0) ) :qid k!10)) -)) -(let (($x200 (not $x28))) -(not (or (not (or $x200 (not (or $x65 (not $x710))))) (not $x245))))))))))) :pattern ( (prime_nat$ ?v0) ) :pattern ( (of_nat$ ?v0) ) :qid k!10)) -)) -(let (($x290 (forall ((?v0 Nat$) )(! (let (($x219 (or (not (dvd$ (?v1!0 ?v0) ?v0)) (= (?v1!0 ?v0) (nat$ 1)) (= (?v1!0 ?v0) ?v0)))) -(let (($x220 (not $x219))) -(let ((?x30 (of_nat$ ?v0))) -(let (($x65 (<= ?x30 1))) -(let (($x28 (prime_nat$ ?v0))) -(let (($x245 (or $x28 $x65 $x220))) -(let (($x72 (forall ((?v1 Nat$) )(! (let ((?x34 (nat$ 1))) -(let (($x35 (= ?v1 ?x34))) -(or (not (dvd$ ?v1 ?v0)) $x35 (= ?v1 ?v0)))) :qid k!10)) -)) -(let (($x221 (not $x72))) -(let (($x273 (not (or $x65 $x221)))) -(let (($x200 (not $x28))) -(let (($x276 (or $x200 $x273))) -(not (or (not $x276) (not $x245)))))))))))))) :qid k!10)) -)) -(let (($x219 (or (not (dvd$ (?v1!0 ?0) ?0)) (= (?v1!0 ?0) ?x34) (= (?v1!0 ?0) ?0)))) -(let (($x220 (not $x219))) -(let ((?x30 (of_nat$ ?0))) -(let (($x65 (<= ?x30 1))) -(let (($x28 (prime_nat$ ?0))) -(let (($x245 (or $x28 $x65 $x220))) -(let (($x710 (forall ((?v1 Nat$) )(! (let ((?x34 (nat$ 1))) -(let (($x35 (= ?v1 ?x34))) -(or (not (dvd$ ?v1 ?0)) $x35 (= ?v1 ?0)))) :pattern ( (dvd$ ?v1 ?0) ) :qid k!10)) -)) -(let (($x200 (not $x28))) -(let (($x72 (forall ((?v1 Nat$) )(! (let ((?x34 (nat$ 1))) -(let (($x35 (= ?v1 ?x34))) -(or (not (dvd$ ?v1 ?0)) $x35 (= ?v1 ?0)))) :qid k!10)) -)) -(let (($x221 (not $x72))) -(let (($x273 (not (or $x65 $x221)))) -(let (($x276 (or $x200 $x273))) -(let (($x285 (not (or (not $x276) (not $x245))))) -(let (($x734 (= $x285 (not (or (not (or $x200 (not (or $x65 (not $x710))))) (not $x245)))))) -(let (($x731 (= (or (not $x276) (not $x245)) (or (not (or $x200 (not (or $x65 (not $x710))))) (not $x245))))) -(let (($x35 (= ?0 ?x34))) -(let (($x69 (or (not (dvd$ ?0 ?1)) $x35 (= ?0 ?1)))) -(let ((@x717 (monotonicity (quant-intro (refl (= $x69 $x69)) (= $x72 $x710)) (= $x221 (not $x710))))) -(let ((@x723 (monotonicity (monotonicity @x717 (= (or $x65 $x221) (or $x65 (not $x710)))) (= $x273 (not (or $x65 (not $x710))))))) -(let ((@x729 (monotonicity (monotonicity @x723 (= $x276 (or $x200 (not (or $x65 (not $x710)))))) (= (not $x276) (not (or $x200 (not (or $x65 (not $x710))))))))) -(let ((@x740 (quant-intro (monotonicity (monotonicity @x729 $x731) $x734) (= $x290 $x738)))) -(let (($x253 (forall ((?v0 Nat$) )(! (let (($x219 (or (not (dvd$ (?v1!0 ?v0) ?v0)) (= (?v1!0 ?v0) (nat$ 1)) (= (?v1!0 ?v0) ?v0)))) -(let (($x220 (not $x219))) -(let ((?x30 (of_nat$ ?v0))) -(let (($x65 (<= ?x30 1))) -(let (($x28 (prime_nat$ ?v0))) -(let (($x245 (or $x28 $x65 $x220))) -(let (($x72 (forall ((?v1 Nat$) )(! (let ((?x34 (nat$ 1))) -(let (($x35 (= ?v1 ?x34))) -(or (not (dvd$ ?v1 ?v0)) $x35 (= ?v1 ?v0)))) :qid k!10)) -)) -(let (($x66 (not $x65))) -(let (($x75 (and $x66 $x72))) -(let (($x200 (not $x28))) -(let (($x229 (or $x200 $x75))) -(and $x229 $x245)))))))))))) :qid k!10)) -)) -(let ((@x278 (monotonicity (rewrite (= (and (not $x65) $x72) $x273)) (= (or $x200 (and (not $x65) $x72)) $x276)))) -(let ((@x281 (monotonicity @x278 (= (and (or $x200 (and (not $x65) $x72)) $x245) (and $x276 $x245))))) -(let ((@x289 (trans @x281 (rewrite (= (and $x276 $x245) $x285)) (= (and (or $x200 (and (not $x65) $x72)) $x245) $x285)))) -(let (($x233 (forall ((?v0 Nat$) )(! (let (($x219 (or (not (dvd$ (?v1!0 ?v0) ?v0)) (= (?v1!0 ?v0) (nat$ 1)) (= (?v1!0 ?v0) ?v0)))) -(let (($x220 (not $x219))) -(let ((?x30 (of_nat$ ?v0))) -(let (($x65 (<= ?x30 1))) -(let (($x66 (not $x65))) -(let (($x211 (not $x66))) -(let (($x224 (or $x211 $x220))) -(let (($x28 (prime_nat$ ?v0))) -(let (($x228 (or $x28 $x224))) -(let (($x72 (forall ((?v1 Nat$) )(! (let ((?x34 (nat$ 1))) -(let (($x35 (= ?v1 ?x34))) -(or (not (dvd$ ?v1 ?v0)) $x35 (= ?v1 ?v0)))) :qid k!10)) -)) -(let (($x75 (and $x66 $x72))) -(let (($x200 (not $x28))) -(let (($x229 (or $x200 $x75))) -(and $x229 $x228)))))))))))))) :qid k!10)) -)) -(let (($x66 (not $x65))) -(let (($x75 (and $x66 $x72))) -(let (($x229 (or $x200 $x75))) -(let (($x250 (and $x229 $x245))) -(let (($x211 (not $x66))) -(let (($x224 (or $x211 $x220))) -(let (($x228 (or $x28 $x224))) -(let (($x230 (and $x229 $x228))) -(let ((@x244 (monotonicity (monotonicity (rewrite (= $x211 $x65)) (= $x224 (or $x65 $x220))) (= $x228 (or $x28 (or $x65 $x220)))))) -(let ((@x249 (trans @x244 (rewrite (= (or $x28 (or $x65 $x220)) $x245)) (= $x228 $x245)))) -(let (($x81 (forall ((?v0 Nat$) )(! (let (($x72 (forall ((?v1 Nat$) )(! (let ((?x34 (nat$ 1))) -(let (($x35 (= ?v1 ?x34))) -(or (not (dvd$ ?v1 ?v0)) $x35 (= ?v1 ?v0)))) :qid k!10)) -)) -(let ((?x30 (of_nat$ ?v0))) -(let (($x65 (<= ?x30 1))) -(let (($x66 (not $x65))) -(let (($x75 (and $x66 $x72))) -(let (($x28 (prime_nat$ ?v0))) -(= $x28 $x75))))))) :qid k!10)) -)) -(let ((@x227 (nnf-neg (refl (~ $x211 $x211)) (sk (~ $x221 $x220)) (~ (not $x75) $x224)))) -(let ((@x210 (monotonicity (refl (~ $x66 $x66)) (nnf-pos (refl (~ $x69 $x69)) (~ $x72 $x72)) (~ $x75 $x75)))) -(let ((@x232 (nnf-pos (refl (~ $x28 $x28)) (refl (~ $x200 $x200)) @x210 @x227 (~ (= $x28 $x75) $x230)))) -(let (($x42 (forall ((?v0 Nat$) )(! (let (($x39 (forall ((?v1 Nat$) )(! (let (($x33 (dvd$ ?v1 ?v0))) -(=> $x33 (or (= ?v1 (nat$ 1)) (= ?v1 ?v0)))) :qid k!10)) -)) -(let ((?x30 (of_nat$ ?v0))) -(let (($x31 (< 1 ?x30))) -(let (($x28 (prime_nat$ ?v0))) -(= $x28 (and $x31 $x39)))))) :qid k!10)) -)) -(let (($x62 (forall ((?v0 Nat$) )(! (let (($x48 (forall ((?v1 Nat$) )(! (or (not (dvd$ ?v1 ?v0)) (or (= ?v1 (nat$ 1)) (= ?v1 ?v0))) :qid k!10)) -)) -(let ((?x30 (of_nat$ ?v0))) -(let (($x31 (< 1 ?x30))) -(let (($x51 (and $x31 $x48))) -(let (($x28 (prime_nat$ ?v0))) -(= $x28 $x51)))))) :qid k!10)) -)) -(let (($x78 (= $x28 $x75))) -(let (($x48 (forall ((?v1 Nat$) )(! (or (not (dvd$ ?v1 ?0)) (or (= ?v1 (nat$ 1)) (= ?v1 ?0))) :qid k!10)) -)) -(let (($x31 (< 1 ?x30))) -(let (($x51 (and $x31 $x48))) -(let (($x57 (= $x28 $x51))) -(let ((@x71 (rewrite (= (or (not (dvd$ ?0 ?1)) (or $x35 (= ?0 ?1))) $x69)))) -(let ((@x77 (monotonicity (rewrite (= $x31 $x66)) (quant-intro @x71 (= $x48 $x72)) (= $x51 $x75)))) -(let (($x39 (forall ((?v1 Nat$) )(! (let (($x33 (dvd$ ?v1 ?0))) -(=> $x33 (or (= ?v1 (nat$ 1)) (= ?v1 ?0)))) :qid k!10)) -)) -(let (($x41 (= $x28 (and $x31 $x39)))) -(let (($x45 (or (not (dvd$ ?0 ?1)) (or $x35 (= ?0 ?1))))) -(let ((@x50 (quant-intro (rewrite (= (=> (dvd$ ?0 ?1) (or $x35 (= ?0 ?1))) $x45)) (= $x39 $x48)))) -(let ((@x56 (monotonicity (monotonicity @x50 (= (and $x31 $x39) $x51)) (= $x41 (= $x28 $x51))))) -(let ((@x64 (quant-intro (trans @x56 (rewrite (= (= $x28 $x51) $x57)) (= $x41 $x57)) (= $x42 $x62)))) -(let ((@x85 (trans @x64 (quant-intro (monotonicity @x77 (= $x57 $x78)) (= $x62 $x81)) (= $x42 $x81)))) -(let ((@x236 (mp~ (mp (asserted $x42) @x85 $x81) (nnf-pos @x232 (~ $x81 $x233)) $x233))) -(let ((@x256 (mp @x236 (quant-intro (monotonicity @x249 (= $x230 $x250)) (= $x233 $x253)) $x253))) -(let ((@x741 (mp (mp @x256 (quant-intro @x289 (= $x253 $x290)) $x290) @x740 $x738))) -(let (($x348 (or (not $x738) $x684))) -(let ((@x685 ((_ quant-inst (nat$ ?x98)) $x348))) -(let ((@x569 (unit-resolution (def-axiom (or $x342 $x697)) (unit-resolution @x685 @x741 $x684) $x697))) -(let (($x125 (not (or $x110 (>= ?x89 1))))) -(let (($x94 (<= 1 ?x89))) -(let (($x95 (=> (prime_nat$ (nat$ (+ ?x90 1))) $x94))) -(let (($x96 (not $x95))) -(let ((@x124 (monotonicity (rewrite (= $x94 (>= ?x89 1))) (= (or $x110 $x94) (or $x110 (>= ?x89 1)))))) -(let ((@x103 (monotonicity (rewrite (= (+ ?x90 1) ?x98)) (= (nat$ (+ ?x90 1)) ?x101)))) -(let ((@x109 (monotonicity (monotonicity @x103 (= (prime_nat$ (nat$ (+ ?x90 1))) $x104)) (= $x95 (=> $x104 $x94))))) -(let ((@x115 (trans @x109 (rewrite (= (=> $x104 $x94) (or $x110 $x94))) (= $x95 (or $x110 $x94))))) -(let ((@x129 (trans (monotonicity @x115 (= $x96 (not (or $x110 $x94)))) (monotonicity @x124 (= (not (or $x110 $x94)) $x125)) (= $x96 $x125)))) -(let ((@x131 (not-or-elim (mp (asserted $x96) @x129 $x125) $x104))) -(let ((@x572 (unit-resolution (unit-resolution (def-axiom (or $x369 $x110 $x487)) @x131 (or $x369 $x487)) @x569 $x487))) -(let ((@x530 (unit-resolution ((_ th-lemma arith farkas 1 1) (or (not (<= ?x295 0)) $x380)) (unit-resolution (def-axiom (or $x357 $x687)) @x572 $x687) (not (<= ?x295 0))))) -(let ((@x561 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not (= ?x295 0)) (<= ?x295 0))) @x530 (not (= ?x295 0))))) -(let (($x575 (= ?x295 0))) -(let (($x577 (or $x610 $x575))) -(let (($x756 (forall ((?v0 Int) )(! (let ((?x140 (nat$ ?v0))) -(let ((?x141 (of_nat$ ?x140))) -(let (($x169 (= ?x141 0))) -(let (($x155 (>= ?v0 0))) -(or $x155 $x169))))) :pattern ( (nat$ ?v0) ) :qid k!14)) -)) -(let (($x192 (forall ((?v0 Int) )(! (let ((?x140 (nat$ ?v0))) -(let ((?x141 (of_nat$ ?x140))) -(let (($x169 (= ?x141 0))) -(let (($x155 (>= ?v0 0))) -(or $x155 $x169))))) :qid k!14)) -)) -(let ((?x140 (nat$ ?0))) -(let ((?x141 (of_nat$ ?x140))) -(let (($x169 (= ?x141 0))) -(let (($x155 (>= ?0 0))) -(let (($x189 (or $x155 $x169))) -(let (($x171 (forall ((?v0 Int) )(! (let ((?x140 (nat$ ?v0))) -(let ((?x141 (of_nat$ ?x140))) -(let (($x169 (= ?x141 0))) -(let (($x168 (< ?v0 0))) -(=> $x168 $x169))))) :qid k!14)) -)) -(let (($x177 (forall ((?v0 Int) )(! (let ((?x140 (nat$ ?v0))) -(let ((?x141 (of_nat$ ?x140))) -(let (($x169 (= ?x141 0))) -(let (($x168 (< ?v0 0))) -(let (($x173 (not $x168))) -(or $x173 $x169)))))) :qid k!14)) -)) -(let ((@x184 (monotonicity (rewrite (= (< ?0 0) (not $x155))) (= (not (< ?0 0)) (not (not $x155)))))) -(let ((@x188 (trans @x184 (rewrite (= (not (not $x155)) $x155)) (= (not (< ?0 0)) $x155)))) -(let ((@x194 (quant-intro (monotonicity @x188 (= (or (not (< ?0 0)) $x169) $x189)) (= $x177 $x192)))) -(let ((@x176 (rewrite (= (=> (< ?0 0) $x169) (or (not (< ?0 0)) $x169))))) -(let ((@x197 (mp (asserted $x171) (trans (quant-intro @x176 (= $x171 $x177)) @x194 (= $x171 $x192)) $x192))) -(let ((@x761 (mp (mp~ @x197 (nnf-pos (refl (~ $x189 $x189)) (~ $x192 $x192)) $x192) (quant-intro (refl (= $x189 $x189)) (= $x192 $x756)) $x756))) -(let (($x580 (not $x756))) -(let (($x581 (or $x580 $x610 $x575))) -(let ((@x612 (rewrite (= (>= ?x98 0) $x610)))) -(let ((@x579 (monotonicity @x612 (= (or (>= ?x98 0) $x575) $x577)))) -(let ((@x555 (monotonicity @x579 (= (or $x580 (or (>= ?x98 0) $x575)) (or $x580 $x577))))) -(let ((@x564 (trans @x555 (rewrite (= (or $x580 $x577) $x581)) (= (or $x580 (or (>= ?x98 0) $x575)) $x581)))) -(let ((@x565 (mp ((_ quant-inst (+ 1 ?x90)) (or $x580 (or (>= ?x98 0) $x575))) @x564 $x581))) -(let (($x613 (not $x610))) -(let (($x600 (or $x613 $x597))) -(let (($x750 (forall ((?v0 Int) )(! (let ((?x140 (nat$ ?v0))) -(let ((?x141 (of_nat$ ?x140))) -(let (($x142 (= ?x141 ?v0))) -(let (($x155 (>= ?v0 0))) -(let (($x156 (not $x155))) -(or $x156 $x142)))))) :pattern ( (nat$ ?v0) ) :qid k!13)) -)) -(let (($x162 (forall ((?v0 Int) )(! (let ((?x140 (nat$ ?v0))) -(let ((?x141 (of_nat$ ?x140))) -(let (($x142 (= ?x141 ?v0))) -(let (($x155 (>= ?v0 0))) -(let (($x156 (not $x155))) -(or $x156 $x142)))))) :qid k!13)) -)) -(let ((@x752 (refl (= (or (not $x155) (= ?x141 ?0)) (or (not $x155) (= ?x141 ?0)))))) -(let ((@x263 (refl (~ (or (not $x155) (= ?x141 ?0)) (or (not $x155) (= ?x141 ?0)))))) -(let (($x144 (forall ((?v0 Int) )(! (let ((?x140 (nat$ ?v0))) -(let ((?x141 (of_nat$ ?x140))) -(let (($x142 (= ?x141 ?v0))) -(let (($x139 (<= 0 ?v0))) -(=> $x139 $x142))))) :qid k!13)) -)) -(let (($x150 (forall ((?v0 Int) )(! (let ((?x140 (nat$ ?v0))) -(let ((?x141 (of_nat$ ?x140))) -(let (($x142 (= ?x141 ?v0))) -(or (not (<= 0 ?v0)) $x142)))) :qid k!13)) -)) -(let (($x142 (= ?x141 ?0))) -(let (($x156 (not $x155))) -(let (($x159 (or $x156 $x142))) -(let (($x147 (or (not (<= 0 ?0)) $x142))) -(let ((@x158 (monotonicity (rewrite (= (<= 0 ?0) $x155)) (= (not (<= 0 ?0)) $x156)))) -(let ((@x152 (quant-intro (rewrite (= (=> (<= 0 ?0) $x142) $x147)) (= $x144 $x150)))) -(let ((@x166 (trans @x152 (quant-intro (monotonicity @x158 (= $x147 $x159)) (= $x150 $x162)) (= $x144 $x162)))) -(let ((@x266 (mp~ (mp (asserted $x144) @x166 $x162) (nnf-pos @x263 (~ $x162 $x162)) $x162))) -(let ((@x755 (mp @x266 (quant-intro @x752 (= $x162 $x750)) $x750))) -(let (($x603 (not $x750))) -(let (($x604 (or $x603 $x613 $x597))) -(let (($x608 (= ?x295 ?x98))) -(let (($x618 (>= ?x98 0))) -(let (($x619 (not $x618))) -(let (($x609 (or $x619 $x608))) -(let (($x605 (or $x603 $x609))) -(let ((@x602 (monotonicity (monotonicity @x612 (= $x619 $x613)) (rewrite (= $x608 $x597)) (= $x609 $x600)))) -(let ((@x590 (trans (monotonicity @x602 (= $x605 (or $x603 $x600))) (rewrite (= (or $x603 $x600) $x604)) (= $x605 $x604)))) -(let ((@x591 (mp ((_ quant-inst (+ 1 ?x90)) $x605) @x590 $x604))) -(let ((@x532 (unit-resolution (unit-resolution @x591 @x755 $x600) (unit-resolution (unit-resolution @x565 @x761 $x577) @x561 $x610) $x597))) -(let ((@x133 (not-or-elim (mp (asserted $x96) @x129 $x125) (not (>= ?x89 1))))) -((_ th-lemma arith farkas -4 1 1) @x133 (unit-resolution (def-axiom (or $x357 $x687)) @x572 $x687) (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x597) $x574)) @x532 $x574) false))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) - -5e90e9139eb4e9a7c2678bca8dda6cda05861f4c 23 0 -unsat -((set-logic AUFLIA) -(proof -(let (($x40 (= x$ a$))) -(let ((?x36 (pair$ x$ y$))) -(let ((?x37 (fst$ ?x36))) -(let (($x39 (= ?x37 a$))) -(let ((@x50 (monotonicity (rewrite (= (=> $x39 $x40) (or (not $x39) $x40))) (= (not (=> $x39 $x40)) (not (or (not $x39) $x40)))))) -(let ((@x51 (not-or-elim (mp (asserted (not (=> $x39 $x40))) @x50 (not (or (not $x39) $x40))) $x39))) -(let (($x56 (= ?x37 x$))) -(let (($x478 (forall ((?v0 A$) (?v1 B$) )(! (= (fst$ (pair$ ?v0 ?v1)) ?v0) :pattern ( (pair$ ?v0 ?v1) ) :qid k!12)) -)) -(let (($x32 (forall ((?v0 A$) (?v1 B$) )(! (= (fst$ (pair$ ?v0 ?v1)) ?v0) :qid k!12)) -)) -(let (($x31 (= (fst$ (pair$ ?1 ?0)) ?1))) -(let ((@x55 (mp~ (asserted $x32) (nnf-pos (refl (~ $x31 $x31)) (~ $x32 $x32)) $x32))) -(let ((@x483 (mp @x55 (quant-intro (refl (= $x31 $x31)) (= $x32 $x478)) $x478))) -(let (($x62 (or (not $x478) $x56))) -(let ((@x149 ((_ quant-inst x$ y$) $x62))) -(let ((@x150 (trans (symm (unit-resolution @x149 @x483 $x56) (= x$ ?x37)) @x51 $x40))) -(let ((@x54 (not-or-elim (mp (asserted (not (=> $x39 $x40))) @x50 (not (or (not $x39) $x40))) (not $x40)))) -(unit-resolution @x54 @x150 false))))))))))))))))))) - -53d3d89ffb6e574b15fcea58a111b4eecba9beb5 42 0 -unsat -((set-logic AUFLIA) -(proof -(let ((?x59 (snd$a p2$))) -(let ((?x58 (fst$a p1$))) -(let (($x60 (= ?x58 ?x59))) -(let ((?x55 (pair$ y$ x$))) -(let (($x56 (= p2$ ?x55))) -(let ((?x52 (pair$a x$ y$))) -(let (($x53 (= p1$ ?x52))) -(let (($x57 (and $x53 $x56))) -(let ((@x70 (monotonicity (rewrite (= (=> $x57 $x60) (or (not $x57) $x60))) (= (not (=> $x57 $x60)) (not (or (not $x57) $x60)))))) -(let ((@x71 (not-or-elim (mp (asserted (not (=> $x57 $x60))) @x70 (not (or (not $x57) $x60))) $x57))) -(let ((@x74 (and-elim @x71 $x56))) -(let ((@x504 (symm (monotonicity @x74 (= ?x59 (snd$a ?x55))) (= (snd$a ?x55) ?x59)))) -(let ((?x100 (snd$a ?x55))) -(let (($x185 (= ?x100 x$))) -(let (($x534 (forall ((?v0 B$) (?v1 A$) )(! (= (snd$a (pair$ ?v0 ?v1)) ?v1) :pattern ( (pair$ ?v0 ?v1) ) :qid k!21)) -)) -(let (($x47 (forall ((?v0 B$) (?v1 A$) )(! (= (snd$a (pair$ ?v0 ?v1)) ?v1) :qid k!21)) -)) -(let (($x46 (= (snd$a (pair$ ?1 ?0)) ?0))) -(let ((@x96 (mp~ (asserted $x47) (nnf-pos (refl (~ $x46 $x46)) (~ $x47 $x47)) $x47))) -(let ((@x539 (mp @x96 (quant-intro (refl (= $x46 $x46)) (= $x47 $x534)) $x534))) -(let (($x190 (or (not $x534) $x185))) -(let ((@x191 ((_ quant-inst y$ x$) $x190))) -(let ((?x187 (fst$a ?x52))) -(let (($x188 (= ?x187 x$))) -(let (($x522 (forall ((?v0 A$) (?v1 B$) )(! (= (fst$a (pair$a ?v0 ?v1)) ?v0) :pattern ( (pair$a ?v0 ?v1) ) :qid k!19)) -)) -(let (($x39 (forall ((?v0 A$) (?v1 B$) )(! (= (fst$a (pair$a ?v0 ?v1)) ?v0) :qid k!19)) -)) -(let (($x38 (= (fst$a (pair$a ?1 ?0)) ?1))) -(let ((@x90 (mp~ (asserted $x39) (nnf-pos (refl (~ $x38 $x38)) (~ $x39 $x39)) $x39))) -(let ((@x527 (mp @x90 (quant-intro (refl (= $x38 $x38)) (= $x39 $x522)) $x522))) -(let (($x162 (or (not $x522) $x188))) -(let ((@x292 ((_ quant-inst x$ y$) $x162))) -(let ((@x505 (trans (monotonicity (and-elim @x71 $x53) (= ?x58 ?x187)) (unit-resolution @x292 @x527 $x188) (= ?x58 x$)))) -(let ((@x489 (trans @x505 (symm (unit-resolution @x191 @x539 $x185) (= x$ ?x100)) (= ?x58 ?x100)))) -(let ((@x76 (not-or-elim (mp (asserted (not (=> $x57 $x60))) @x70 (not (or (not $x57) $x60))) (not $x60)))) -(unit-resolution @x76 (trans @x489 @x504 $x60) false)))))))))))))))))))))))))))))))))))) - -541ab286f481dab3994e7cef5aa3ab01f0d6487a 24 0 -unsat -((set-logic AUFLIA) -(proof -(let (($x29 (f$ g$ x$))) -(let (($x73 (not $x29))) -(let (($x65 (not (or (= $x29 (fun_app$ g$ x$)) $x29 (fun_app$ g$ x$))))) -(let (($x32 (= $x29 (and (fun_app$ g$ x$) true)))) -(let (($x37 (not (or $x32 (or (= $x29 true) (= (fun_app$ g$ x$) true)))))) -(let (($x30 (fun_app$ g$ x$))) -(let (($x44 (= $x29 $x30))) -(let (($x56 (or $x44 (or $x29 $x30)))) -(let ((@x67 (monotonicity (rewrite (= $x56 (or $x44 $x29 $x30))) (= (not $x56) $x65)))) -(let ((@x55 (monotonicity (rewrite (= (= $x29 true) $x29)) (rewrite (= (= $x30 true) $x30)) (= (or (= $x29 true) (= $x30 true)) (or $x29 $x30))))) -(let ((@x43 (monotonicity (rewrite (= (and $x30 true) $x30)) (= $x32 (= $x29 $x30))))) -(let ((@x58 (monotonicity (trans @x43 (rewrite (= (= $x29 $x30) $x44)) (= $x32 $x44)) @x55 (= (or $x32 (or (= $x29 true) (= $x30 true))) $x56)))) -(let ((@x69 (trans (monotonicity @x58 (= $x37 (not $x56))) @x67 (= $x37 $x65)))) -(let ((@x70 (mp (asserted $x37) @x69 $x65))) -(let ((@x87 (monotonicity (iff-false (not-or-elim @x70 (not $x30)) (= $x30 false)) (= (= $x73 $x30) (= $x73 false))))) -(let ((@x91 (trans @x87 (rewrite (= (= $x73 false) $x29)) (= (= $x73 $x30) $x29)))) -(let ((@x93 (trans @x91 (iff-false (not-or-elim @x70 $x73) (= $x29 false)) (= (= $x73 $x30) false)))) -(let (($x77 (= $x73 $x30))) -(let ((@x80 (mp (not-or-elim @x70 (not $x44)) (rewrite (= (not $x44) $x77)) $x77))) -(mp @x80 @x93 false)))))))))))))))))))))) - -303e836701682600d31f180dbf7164cb66aa7e90 5 0 -unsat -( -a0 -a1 -) -b1682b5d9334f1f753211625091194aee8feeee0 5 0 -unsat -( -a3 -a2 -) -e480713ec1d59b302d3665ef6cf6d4bde9acf881 5 0 -unsat -( -a0 -a1 -) -32a8fd63d6c57c114d55e5b029c6c7c0a22bfc9e 5 0 -unsat -( -a1 -a0 -) -8e5b0b49054ab51d88db63de1bbe5f826bed3499 2 0 -sat -(error "Cannot get an unsat core unless immediately preceded by UNSAT/VALID response.") -0ca8132e17307584a7bf84322b4f8062f2f2c658 2 0 -sat -(error "Cannot get an unsat core unless immediately preceded by UNSAT/VALID response.") -256aa6c949586ab7b008ef9578a05ed9d8811969 7 0 -unsat -( -a73 -a77 -a97 -a98 -) -6b21e8fbdb4a81ae46f60a001dcc2f2cfa2bb055 5 0 -unsat -( -a0 -a1 -) -9aca5c922a21ee8af6f8c447405fbb253f6c0e3d 2 0 -sat -(error "Cannot get an unsat core unless immediately preceded by UNSAT/VALID response.") -bbd5549a4514d443e2da4c190a400b7bb7fad211 8 0 -unsat -( -a2 -a1 -a6 -a5 -a4 -) -5d3180378cd70f7c6a038fcc3edc01a1f8acce33 8 0 -unsat -( -a2 -a1 -a5 -a4 -a3 -) -b697e9e1f1623fa76652384cbd62f909744566cf 2 0 -sat -(error "Cannot get an unsat core unless immediately preceded by UNSAT/VALID response.") -93d4ee1f0414a974916a0daf16114650cca034a6 2 0 -sat -(error "Cannot get an unsat core unless immediately preceded by UNSAT/VALID response.") -3e0697d22f6063be90ed182054dfac4e59e65728 2 0 -sat -(error "Cannot get an unsat core unless immediately preceded by UNSAT/VALID response.") -132bc98466cbf8cf9a94f930b1fd690c493fcf96 100 0 -unsat -( -a93 -a40 -a42 -a79 -a45 -a69 -a154 -a76 -a32 -a62 -a15 -a17 -a39 -a41 -a16 -a50 -a23 -a140 -a31 -a29 -a139 -a70 -a128 -a143 -a7 -a30 -a38 -a27 -a35 -a135 -a129 -a151 -a148 -a36 -a25 -a33 -a182 -a144 -a138 -a159 -a113 -a75 -a117 -a133 -a158 -a137 -a37 -a147 -a155 -a46 -a61 -a13 -a48 -a124 -a18 -a43 -a44 -a14 -a47 -a26 -a34 -a116 -a149 -a120 -a73 -a130 -a156 -a142 -a118 -a127 -a150 -a96 -a152 -a121 -a160 -a49 -a24 -a8 -a136 -a28 -a114 -a72 -a141 -a162 -a122 -a145 -a146 -a74 -a184 -a153 -a169 -a119 -a183 -a157 -a161 -a115 -a71 -) -c3d7cbf937c8a42adee3dea055fc94c0d5fa9f09 2 0 -sat -(error "Cannot get an unsat core unless immediately preceded by UNSAT/VALID response.") -bdab860f909efa4b33522c132777f2e16f390f0d 97 0 -unsat -( -a22 -a15 -a45 -a16 -a24 -a46 -a26 -a65 -a18 -a62 -a71 -a5 -a25 -a27 -a68 -a83 -a51 -a87 -a14 -a2 -a13 -a66 -a21 -a64 -a63 -a31 -a32 -a79 -a78 -a73 -a30 -a81 -a92 -a41 -a52 -a42 -a93 -a90 -a39 -a80 -a69 -a19 -a3 -a29 -a4 -a70 -a20 -a72 -a1 -a23 -a11 -a60 -a74 -a10 -a59 -a76 -a77 -a28 -a89 -a38 -a55 -a6 -a43 -a94 -a37 -a88 -a17 -a86 -a35 -a36 -a58 -a9 -a50 -a67 -a7 -a56 -a84 -a85 -a34 -a57 -a8 -a33 -a61 -a12 -a53 -a91 -a40 -a54 -a82 -a96 -a44 -a95 -a97 -a75 -) -7b0531750ec3111a052894242409998ff73f0d8e 2 0 -sat -(error "Cannot get an unsat core unless immediately preceded by UNSAT/VALID response.") -0c77f4fcdf3c7cc2416cd1c79a1e4ffa770ccdd9 2 0 -sat -(error "Cannot get an unsat core unless immediately preceded by UNSAT/VALID response.") -b5cac27259e12d93b0f91244374657bda3651301 2 0 -sat -(error "Cannot get an unsat core unless immediately preceded by UNSAT/VALID response.") -8f371242ee130c5b7f7049f82612acd4b70ba898 2 0 -sat -(error "Cannot get an unsat core unless immediately preceded by UNSAT/VALID response.") -947377c6f6ef2e11f5ddd7a677e90d51d4d4ca09 2 0 -sat -(error "Cannot get an unsat core unless immediately preceded by UNSAT/VALID response.") -445ee9b6220decad197f092fe7e63a050fceb831 2 0 -sat -(error "Cannot get an unsat core unless immediately preceded by UNSAT/VALID response.") -51d11b605d2a9a01009f9f814fb688a96656112f 2 0 -sat -(error "Cannot get an unsat core unless immediately preceded by UNSAT/VALID response.") -425ffc08f16b7f80d0cbe2998f660aa2f786acbf 2 0 -sat -(error "Cannot get an unsat core unless immediately preceded by UNSAT/VALID response.") -1db6aab13ff3e14aca462e31d60bcc91d1d91ba4 2 0 -sat -(error "Cannot get an unsat core unless immediately preceded by UNSAT/VALID response.") -a67d9819b8a80d46a99da882dbc773b1daa04f46 2 0 -sat -(error "Cannot get an unsat core unless immediately preceded by UNSAT/VALID response.") -57ced68ab36f2fcdb9d24788830e8652a2d56817 2 0 -sat -(error "Cannot get an unsat core unless immediately preceded by UNSAT/VALID response.") -f6c7d41773bef5bed37f5e86a6fa287578c04f2d 90 0 -unsat -( -a15 -a39 -a13 -a32 -a66 -a89 -a54 -a18 -a41 -a65 -a75 -a48 -a23 -a20 -a42 -a63 -a55 -a11 -a24 -a88 -a51 -a12 -a31 -a25 -a64 -a76 -a5 -a93 -a83 -a72 -a22 -a43 -a26 -a28 -a44 -a1 -a36 -a38 -a50 -a49 -a62 -a87 -a70 -a77 -a34 -a84 -a60 -a40 -a3 -a52 -a85 -a35 -a37 -a46 -a45 -a47 -a33 -a27 -a29 -a86 -a56 -a10 -a61 -a91 -a9 -a80 -a90 -a58 -a8 -a79 -a92 -a59 -a78 -a2 -a67 -a53 -a4 -a69 -a21 -a71 -a68 -a17 -a6 -a14 -a57 -a7 -a30 -) -ac0ffc3882f6c09968ced3592e058a6fb86a87c7 2 0 -sat -(error "Cannot get an unsat core unless immediately preceded by UNSAT/VALID response.") -85bbaf5a5aa1611b4cf32fa801006fbfc15c02d7 5 0 -unsat -( -a0 -a1 -) -926b60197ebba006da54aed0737eebccf8577396 5 0 -unsat -( -a1 -a0 -) -700af424f8dda45d1d02de88a120ee19f4cfb835 4 0 -unsat -( -a0 -) -5c1e9490994c9407572cee32f5d1f714ddc35898 4 0 -unsat -( -a0 -) -60f0eb26fb928f5be2217521c55fd281c68657ab 12 0 -unsat -((set-logic AUFLIA) -(proof -(let ((@x39 (rewrite (= (= (* 2 (of_nat$ x$)) 1) false)))) -(let ((?x29 (of_nat$ x$))) -(let ((?x30 (* 2 ?x29))) -(let (($x32 (= ?x30 1))) -(let (($x33 (not $x32))) -(let (($x34 (not $x33))) -(let ((@x37 (rewrite (= $x34 $x32)))) -(mp (asserted $x34) (trans @x37 @x39 (= $x34 false)) false)))))))))) - -8add3cdd73f5b10c545c377441668f38198ca42e 23 0 -unsat -((set-logic AUFLIA) -(proof -(let ((?x28 (of_nat$ a$))) -(let (($x57 (>= ?x28 4))) -(let (($x47 (>= ?x28 3))) -(let (($x61 (or $x47 (not $x57)))) -(let (($x64 (not $x61))) -(let ((@x51 (monotonicity (rewrite (= (< ?x28 3) (not $x47))) (= (not (< ?x28 3)) (not (not $x47)))))) -(let ((@x55 (trans @x51 (rewrite (= (not (not $x47)) $x47)) (= (not (< ?x28 3)) $x47)))) -(let ((@x63 (monotonicity @x55 (rewrite (= (< (* 2 ?x28) 7) (not $x57))) (= (or (not (< ?x28 3)) (< (* 2 ?x28) 7)) $x61)))) -(let ((@x66 (monotonicity @x63 (= (not (or (not (< ?x28 3)) (< (* 2 ?x28) 7))) $x64)))) -(let (($x36 (not (=> (< ?x28 3) (< (* 2 ?x28) 7))))) -(let (($x34 (< (* 2 ?x28) 7))) -(let (($x30 (< ?x28 3))) -(let (($x38 (not $x30))) -(let (($x39 (or $x38 $x34))) -(let ((@x44 (monotonicity (rewrite (= (=> $x30 $x34) $x39)) (= $x36 (not $x39))))) -(let ((@x71 (not-or-elim (mp (asserted $x36) (trans @x44 @x66 (= $x36 $x64)) $x64) $x57))) -(let (($x45 (not $x47))) -(let ((@x70 (not-or-elim (mp (asserted $x36) (trans @x44 @x66 (= $x36 $x64)) $x64) $x45))) -(unit-resolution ((_ th-lemma arith farkas 1 1) $x61) @x70 @x71 false))))))))))))))))))))) - -4c6f37a2909344bd2a4d64422c28ae3c0bb6baa4 22 0 -unsat -((set-logic AUFLIA) -(proof -(let ((?x29 (of_nat$ y$))) -(let ((?x30 (+ 1 ?x29))) -(let ((?x33 (- ?x30 ?x29))) -(let (($x32 (< ?x30 ?x29))) -(let ((?x34 (ite $x32 0 ?x33))) -(let ((?x31 (* 0 ?x30))) -(let (($x35 (< ?x31 ?x34))) -(let (($x36 (not $x35))) -(let ((@x55 (monotonicity (rewrite (= $x32 false)) (= (ite $x32 0 1) (ite false 0 1))))) -(let ((@x59 (trans @x55 (rewrite (= (ite false 0 1) 1)) (= (ite $x32 0 1) 1)))) -(let ((@x62 (monotonicity @x59 (= (< 0 (ite $x32 0 1)) (< 0 1))))) -(let ((@x66 (trans @x62 (rewrite (= (< 0 1) true)) (= (< 0 (ite $x32 0 1)) true)))) -(let ((@x69 (monotonicity @x66 (= (not (< 0 (ite $x32 0 1))) (not true))))) -(let ((@x73 (trans @x69 (rewrite (= (not true) false)) (= (not (< 0 (ite $x32 0 1))) false)))) -(let ((@x44 (monotonicity (rewrite (= ?x33 1)) (= ?x34 (ite $x32 0 1))))) -(let ((@x47 (monotonicity (rewrite (= ?x31 0)) @x44 (= $x35 (< 0 (ite $x32 0 1)))))) -(let ((@x50 (monotonicity @x47 (= $x36 (not (< 0 (ite $x32 0 1))))))) -(mp (asserted $x36) (trans @x50 @x73 (= $x36 false)) false)))))))))))))))))))) - -b714679c599d34ff47961092cf8a68a58c263339 37 0 -unsat -((set-logic AUFLIA) -(proof -(let ((?x29 (of_nat$ y$))) -(let (($x91 (>= ?x29 0))) -(let ((@x126 (mp (asserted (<= 0 ?x29)) (rewrite (= (<= 0 ?x29) $x91)) $x91))) -(let (($x86 (<= ?x29 (- 1)))) -(let (($x111 (not (or (= (not $x86) (= (ite $x91 ?x29 0) ?x29)) (not $x86))))) -(let (($x39 (=> (not (ite (< 0 (+ 1 ?x29)) true false)) false))) -(let (($x36 (= (ite (< (+ 1 ?x29) 1) 0 (- (+ 1 ?x29) 1)) ?x29))) -(let ((?x30 (+ 1 ?x29))) -(let (($x31 (< 0 ?x30))) -(let (($x32 (ite $x31 true false))) -(let (($x37 (= $x32 $x36))) -(let (($x41 (or false (or $x37 $x39)))) -(let (($x42 (not $x41))) -(let (($x112 (= (not (or (= $x31 (= (ite (< ?x30 1) 0 ?x29) ?x29)) $x31)) $x111))) -(let (($x33 (< ?x30 1))) -(let ((?x48 (ite $x33 0 ?x29))) -(let (($x51 (= ?x48 ?x29))) -(let (($x57 (= $x31 $x51))) -(let (($x72 (or $x57 $x31))) -(let (($x109 (= $x72 (or (= (not $x86) (= (ite $x91 ?x29 0) ?x29)) (not $x86))))) -(let ((@x96 (monotonicity (rewrite (= $x33 (not $x91))) (= ?x48 (ite (not $x91) 0 ?x29))))) -(let ((@x101 (trans @x96 (rewrite (= (ite (not $x91) 0 ?x29) (ite $x91 ?x29 0))) (= ?x48 (ite $x91 ?x29 0))))) -(let ((@x107 (monotonicity (rewrite (= $x31 (not $x86))) (monotonicity @x101 (= $x51 (= (ite $x91 ?x29 0) ?x29))) (= $x57 (= (not $x86) (= (ite $x91 ?x29 0) ?x29)))))) -(let ((@x113 (monotonicity (monotonicity @x107 (rewrite (= $x31 (not $x86))) $x109) $x112))) -(let ((@x67 (monotonicity (monotonicity (rewrite (= $x32 $x31)) (= (not $x32) (not $x31))) (= $x39 (=> (not $x31) false))))) -(let ((@x71 (trans @x67 (rewrite (= (=> (not $x31) false) $x31)) (= $x39 $x31)))) -(let ((@x50 (monotonicity (rewrite (= (- ?x30 1) ?x29)) (= (ite $x33 0 (- ?x30 1)) ?x48)))) -(let ((@x56 (monotonicity (rewrite (= $x32 $x31)) (monotonicity @x50 (= $x36 $x51)) (= $x37 (= $x31 $x51))))) -(let ((@x74 (monotonicity (trans @x56 (rewrite (= (= $x31 $x51) $x57)) (= $x37 $x57)) @x71 (= (or $x37 $x39) $x72)))) -(let ((@x81 (trans (monotonicity @x74 (= $x41 (or false $x72))) (rewrite (= (or false $x72) $x72)) (= $x41 $x72)))) -(let ((@x115 (trans (monotonicity @x81 (= $x42 (not $x72))) @x113 (= $x42 $x111)))) -(let ((@x119 (not-or-elim (mp (asserted $x42) @x115 $x111) $x86))) -(unit-resolution ((_ th-lemma arith farkas 1 1) (or (not $x86) (not $x91))) @x119 @x126 false))))))))))))))))))))))))))))))))))) - -37308e9e03de5831baac25fd010c0af7fb3ac06c 64 0 -unsat -((set-logic AUFLIA) -(proof -(let ((?x58 (* (- 1) x$))) -(let (($x76 (>= x$ 0))) -(let ((?x83 (ite $x76 x$ ?x58))) -(let ((?x536 (* (- 1) ?x83))) -(let ((?x539 (+ ?x58 ?x536))) -(let (($x237 (<= ?x539 0))) -(let (($x229 (= ?x58 ?x83))) -(let (($x77 (not $x76))) -(let (($x143 (= x$ ?x83))) -(let ((@x182 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x143) (<= (+ x$ ?x536) 0))) (unit-resolution (def-axiom (or $x77 $x143)) (hypothesis $x76) $x143) (<= (+ x$ ?x536) 0)))) -(let (($x232 (>= ?x83 0))) -(let (($x337 (not $x232))) -(let ((?x88 (nat$ ?x83))) -(let ((?x91 (of_nat$ ?x88))) -(let (($x233 (= ?x91 0))) -(let (($x94 (= ?x91 ?x83))) -(let (($x234 (ite $x232 $x94 $x233))) -(let (($x560 (forall ((?v0 Int) )(! (let (($x39 (>= ?v0 0))) -(ite $x39 (= (of_nat$ (nat$ ?v0)) ?v0) (= (of_nat$ (nat$ ?v0)) 0))) :pattern ( (nat$ ?v0) ) :qid k!8)) -)) -(let (($x139 (forall ((?v0 Int) )(! (let (($x39 (>= ?v0 0))) -(ite $x39 (= (of_nat$ (nat$ ?v0)) ?v0) (= (of_nat$ (nat$ ?v0)) 0))) :qid k!8)) -)) -(let (($x39 (>= ?0 0))) -(let (($x136 (ite $x39 (= (of_nat$ (nat$ ?0)) ?0) (= (of_nat$ (nat$ ?0)) 0)))) -(let (($x46 (forall ((?v0 Int) )(! (let ((?x29 (of_nat$ (nat$ ?v0)))) -(= ?x29 (ite (>= ?v0 0) ?v0 0))) :qid k!8)) -)) -(let ((@x141 (quant-intro (rewrite (= (= (of_nat$ (nat$ ?0)) (ite $x39 ?0 0)) $x136)) (= $x46 $x139)))) -(let ((?x29 (of_nat$ (nat$ ?0)))) -(let (($x43 (= ?x29 (ite $x39 ?0 0)))) -(let (($x33 (forall ((?v0 Int) )(! (let ((?x29 (of_nat$ (nat$ ?v0)))) -(= ?x29 (ite (<= 0 ?v0) ?v0 0))) :qid k!8)) -)) -(let ((@x42 (monotonicity (rewrite (= (<= 0 ?0) $x39)) (= (ite (<= 0 ?0) ?0 0) (ite $x39 ?0 0))))) -(let ((@x45 (monotonicity @x42 (= (= ?x29 (ite (<= 0 ?0) ?0 0)) $x43)))) -(let ((@x122 (mp~ (mp (asserted $x33) (quant-intro @x45 (= $x33 $x46)) $x46) (nnf-pos (refl (~ $x43 $x43)) (~ $x46 $x46)) $x46))) -(let ((@x565 (mp (mp @x122 @x141 $x139) (quant-intro (refl (= $x136 $x136)) (= $x139 $x560)) $x560))) -(let (($x551 (or (not $x560) $x234))) -(let ((@x552 ((_ quant-inst (ite $x76 x$ ?x58)) $x551))) -(let (($x97 (not $x94))) -(let (($x36 (< x$ 0))) -(let ((?x51 (ite $x36 (- x$) x$))) -(let (($x55 (not (= (of_nat$ (nat$ ?x51)) ?x51)))) -(let (($x98 (= (not (= (of_nat$ (nat$ (ite $x36 ?x58 x$))) (ite $x36 ?x58 x$))) $x97))) -(let ((?x61 (ite $x36 ?x58 x$))) -(let ((?x64 (nat$ ?x61))) -(let ((?x67 (of_nat$ ?x64))) -(let (($x70 (= ?x67 ?x61))) -(let ((@x87 (trans (monotonicity (rewrite (= $x36 $x77)) (= ?x61 (ite $x77 ?x58 x$))) (rewrite (= (ite $x77 ?x58 x$) ?x83)) (= ?x61 ?x83)))) -(let ((@x96 (monotonicity (monotonicity (monotonicity @x87 (= ?x64 ?x88)) (= ?x67 ?x91)) @x87 (= $x70 $x94)))) -(let ((@x66 (monotonicity (monotonicity (rewrite (= (- x$) ?x58)) (= ?x51 ?x61)) (= (nat$ ?x51) ?x64)))) -(let ((@x72 (monotonicity (monotonicity @x66 (= (of_nat$ (nat$ ?x51)) ?x67)) (monotonicity (rewrite (= (- x$) ?x58)) (= ?x51 ?x61)) (= (= (of_nat$ (nat$ ?x51)) ?x51) $x70)))) -(let ((@x101 (trans (monotonicity @x72 (= $x55 (not $x70))) (monotonicity @x96 $x98) (= $x55 $x97)))) -(let ((@x102 (mp (asserted $x55) @x101 $x97))) -(let ((@x545 (unit-resolution (def-axiom (or (not $x234) $x337 $x94)) @x102 (or (not $x234) $x337)))) -(let ((@x532 ((_ th-lemma arith farkas -1 1 1) (hypothesis $x76) (unit-resolution @x545 (unit-resolution @x552 @x565 $x234) $x337) @x182 false))) -(let ((@x533 (lemma @x532 $x77))) -(let ((@x526 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x229) $x237)) (unit-resolution (def-axiom (or $x76 $x229)) @x533 $x229) $x237))) -((_ th-lemma arith farkas 1 1 1) (unit-resolution @x545 (unit-resolution @x552 @x565 $x234) $x337) @x533 @x526 false)))))))))))))))))))))))))))))))))))))))))))))))))))))) - -ed82050c49ac6c4c1fb3e26f7f8f9a2dd0dd0173 264 0 -unsat -((set-logic AUFLIA) -(declare-fun ?v1!0 (Nat$) Nat$) -(proof -(let ((?x89 (of_nat$ m$))) -(let ((?x90 (* 4 ?x89))) -(let ((?x98 (+ 1 ?x90))) -(let ((?x101 (nat$ ?x98))) -(let ((?x276 (of_nat$ ?x101))) -(let ((?x581 (* (- 1) ?x276))) -(let ((?x582 (+ ?x90 ?x581))) -(let (($x555 (>= ?x582 (- 1)))) -(let (($x580 (= ?x582 (- 1)))) -(let (($x574 (= ?x276 0))) -(let (($x622 (>= ?x89 0))) -(let (($x583 (ite $x622 $x580 $x574))) -(let (($x737 (forall ((?v0 Int) )(! (let (($x160 (>= ?v0 0))) -(ite $x160 (= (of_nat$ (nat$ ?v0)) ?v0) (= (of_nat$ (nat$ ?v0)) 0))) :pattern ( (nat$ ?v0) ) :qid k!14)) -)) -(let (($x271 (forall ((?v0 Int) )(! (let (($x160 (>= ?v0 0))) -(ite $x160 (= (of_nat$ (nat$ ?v0)) ?v0) (= (of_nat$ (nat$ ?v0)) 0))) :qid k!14)) -)) -(let (($x160 (>= ?0 0))) -(let (($x268 (ite $x160 (= (of_nat$ (nat$ ?0)) ?0) (= (of_nat$ (nat$ ?0)) 0)))) -(let (($x167 (forall ((?v0 Int) )(! (let ((?x149 (nat$ ?v0))) -(let ((?x150 (of_nat$ ?x149))) -(= ?x150 (ite (>= ?v0 0) ?v0 0)))) :qid k!14)) -)) -(let ((@x273 (quant-intro (rewrite (= (= (of_nat$ (nat$ ?0)) (ite $x160 ?0 0)) $x268)) (= $x167 $x271)))) -(let ((?x149 (nat$ ?0))) -(let ((?x150 (of_nat$ ?x149))) -(let (($x164 (= ?x150 (ite $x160 ?0 0)))) -(let (($x154 (forall ((?v0 Int) )(! (let ((?x149 (nat$ ?v0))) -(let ((?x150 (of_nat$ ?x149))) -(= ?x150 (ite (<= 0 ?v0) ?v0 0)))) :qid k!14)) -)) -(let ((@x163 (monotonicity (rewrite (= (<= 0 ?0) $x160)) (= (ite (<= 0 ?0) ?0 0) (ite $x160 ?0 0))))) -(let ((@x166 (monotonicity @x163 (= (= ?x150 (ite (<= 0 ?0) ?0 0)) $x164)))) -(let ((@x243 (mp~ (mp (asserted $x154) (quant-intro @x166 (= $x154 $x167)) $x167) (nnf-pos (refl (~ $x164 $x164)) (~ $x167 $x167)) $x167))) -(let ((@x742 (mp (mp @x243 @x273 $x271) (quant-intro (refl (= $x268 $x268)) (= $x271 $x737)) $x737))) -(let (($x587 (or (not $x737) $x583))) -(let ((@x585 (monotonicity (rewrite (= (>= ?x98 0) $x622)) (rewrite (= (= ?x276 ?x98) $x580)) (= (ite (>= ?x98 0) (= ?x276 ?x98) $x574) $x583)))) -(let ((@x568 (monotonicity @x585 (= (or (not $x737) (ite (>= ?x98 0) (= ?x276 ?x98) $x574)) $x587)))) -(let ((@x571 (trans @x568 (rewrite (= $x587 $x587)) (= (or (not $x737) (ite (>= ?x98 0) (= ?x276 ?x98) $x574)) $x587)))) -(let ((@x572 (mp ((_ quant-inst (+ 1 ?x90)) (or (not $x737) (ite (>= ?x98 0) (= ?x276 ?x98) $x574))) @x571 $x587))) -(let (($x723 (forall ((?v0 Nat$) )(! (let ((?x30 (of_nat$ ?v0))) -(>= ?x30 0)) :pattern ( (of_nat$ ?v0) ) :qid k!12)) -)) -(let (($x142 (forall ((?v0 Nat$) )(! (let ((?x30 (of_nat$ ?v0))) -(>= ?x30 0)) :qid k!12)) -)) -(let ((@x727 (quant-intro (refl (= (>= (of_nat$ ?0) 0) (>= (of_nat$ ?0) 0))) (= $x142 $x723)))) -(let ((@x232 (nnf-pos (refl (~ (>= (of_nat$ ?0) 0) (>= (of_nat$ ?0) 0))) (~ $x142 $x142)))) -(let (($x135 (forall ((?v0 Nat$) )(! (let ((?x30 (of_nat$ ?v0))) -(<= 0 ?x30)) :qid k!12)) -)) -(let ((@x144 (quant-intro (rewrite (= (<= 0 (of_nat$ ?0)) (>= (of_nat$ ?0) 0))) (= $x135 $x142)))) -(let ((@x728 (mp (mp~ (mp (asserted $x135) @x144 $x142) @x232 $x142) @x727 $x723))) -(let (($x593 (or (not $x723) $x622))) -(let ((@x594 ((_ quant-inst m$) $x593))) -(let ((@x547 (unit-resolution (def-axiom (or (not $x583) (not $x622) $x580)) (unit-resolution @x594 @x728 $x622) (or (not $x583) $x580)))) -(let ((@x551 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x580) $x555)) (unit-resolution @x547 (unit-resolution @x572 @x742 $x583) $x580) $x555))) -(let (($x361 (<= ?x276 1))) -(let (($x668 (not $x361))) -(let (($x346 (forall ((?v1 Nat$) )(! (let ((?x89 (of_nat$ m$))) -(let ((?x90 (* 4 ?x89))) -(let ((?x98 (+ 1 ?x90))) -(let ((?x101 (nat$ ?x98))) -(let ((?x276 (of_nat$ ?x101))) -(let ((?x30 (of_nat$ ?v1))) -(let (($x363 (= ?x30 ?x276))) -(let (($x34 (= ?x30 1))) -(let (($x362 (dvd$ ?v1 ?x101))) -(let (($x352 (not $x362))) -(or $x352 $x34 $x363))))))))))) :pattern ( (dvd$ ?v1 (nat$ (+ 1 (* 4 (of_nat$ m$))))) ) :pattern ( (of_nat$ ?v1) ) :qid k!10)) -)) -(let (($x682 (not $x346))) -(let (($x683 (or $x361 $x682))) -(let (($x338 (not $x683))) -(let (($x104 (prime_nat$ ?x101))) -(let (($x110 (not $x104))) -(let (($x468 (or $x110 $x338))) -(let ((?x351 (?v1!0 ?x101))) -(let ((?x686 (of_nat$ ?x351))) -(let (($x688 (= ?x686 ?x276))) -(let (($x687 (= ?x686 1))) -(let (($x684 (dvd$ ?x351 ?x101))) -(let (($x685 (not $x684))) -(let (($x689 (or $x685 $x687 $x688))) -(let (($x679 (not $x689))) -(let (($x344 (or $x104 $x361 $x679))) -(let (($x681 (not $x344))) -(let (($x678 (not $x468))) -(let (($x323 (or $x678 $x681))) -(let (($x665 (not $x323))) -(let (($x719 (forall ((?v0 Nat$) )(! (let (($x191 (or (not (dvd$ (?v1!0 ?v0) ?v0)) (= (of_nat$ (?v1!0 ?v0)) 1) (= (of_nat$ (?v1!0 ?v0)) (of_nat$ ?v0))))) -(let (($x192 (not $x191))) -(let ((?x30 (of_nat$ ?v0))) -(let (($x65 (<= ?x30 1))) -(let (($x28 (prime_nat$ ?v0))) -(let (($x217 (or $x28 $x65 $x192))) -(let (($x692 (forall ((?v1 Nat$) )(! (let ((?x30 (of_nat$ ?v1))) -(let (($x34 (= ?x30 1))) -(or (not (dvd$ ?v1 ?v0)) $x34 (= ?x30 (of_nat$ ?v0))))) :pattern ( (dvd$ ?v1 ?v0) ) :pattern ( (of_nat$ ?v1) ) :qid k!10)) -)) -(let (($x177 (not $x28))) -(not (or (not (or $x177 (not (or $x65 (not $x692))))) (not $x217))))))))))) :pattern ( (prime_nat$ ?v0) ) :pattern ( (of_nat$ ?v0) ) :qid k!10)) -)) -(let (($x262 (forall ((?v0 Nat$) )(! (let (($x191 (or (not (dvd$ (?v1!0 ?v0) ?v0)) (= (of_nat$ (?v1!0 ?v0)) 1) (= (of_nat$ (?v1!0 ?v0)) (of_nat$ ?v0))))) -(let (($x192 (not $x191))) -(let ((?x30 (of_nat$ ?v0))) -(let (($x65 (<= ?x30 1))) -(let (($x28 (prime_nat$ ?v0))) -(let (($x217 (or $x28 $x65 $x192))) -(let (($x72 (forall ((?v1 Nat$) )(! (let ((?x30 (of_nat$ ?v1))) -(let (($x34 (= ?x30 1))) -(or (not (dvd$ ?v1 ?v0)) $x34 (= ?x30 (of_nat$ ?v0))))) :qid k!10)) -)) -(let (($x193 (not $x72))) -(let (($x245 (not (or $x65 $x193)))) -(let (($x177 (not $x28))) -(let (($x248 (or $x177 $x245))) -(not (or (not $x248) (not $x217)))))))))))))) :qid k!10)) -)) -(let (($x191 (or (not (dvd$ (?v1!0 ?0) ?0)) (= (of_nat$ (?v1!0 ?0)) 1) (= (of_nat$ (?v1!0 ?0)) (of_nat$ ?0))))) -(let (($x192 (not $x191))) -(let ((?x30 (of_nat$ ?0))) -(let (($x65 (<= ?x30 1))) -(let (($x28 (prime_nat$ ?0))) -(let (($x217 (or $x28 $x65 $x192))) -(let (($x692 (forall ((?v1 Nat$) )(! (let ((?x30 (of_nat$ ?v1))) -(let (($x34 (= ?x30 1))) -(or (not (dvd$ ?v1 ?0)) $x34 (= ?x30 (of_nat$ ?0))))) :pattern ( (dvd$ ?v1 ?0) ) :pattern ( (of_nat$ ?v1) ) :qid k!10)) -)) -(let (($x177 (not $x28))) -(let (($x72 (forall ((?v1 Nat$) )(! (let ((?x30 (of_nat$ ?v1))) -(let (($x34 (= ?x30 1))) -(or (not (dvd$ ?v1 ?0)) $x34 (= ?x30 (of_nat$ ?0))))) :qid k!10)) -)) -(let (($x193 (not $x72))) -(let (($x245 (not (or $x65 $x193)))) -(let (($x248 (or $x177 $x245))) -(let (($x257 (not (or (not $x248) (not $x217))))) -(let (($x716 (= $x257 (not (or (not (or $x177 (not (or $x65 (not $x692))))) (not $x217)))))) -(let (($x713 (= (or (not $x248) (not $x217)) (or (not (or $x177 (not (or $x65 (not $x692))))) (not $x217))))) -(let (($x34 (= ?x30 1))) -(let (($x69 (or (not (dvd$ ?0 ?1)) $x34 (= ?x30 (of_nat$ ?1))))) -(let ((@x699 (monotonicity (quant-intro (refl (= $x69 $x69)) (= $x72 $x692)) (= $x193 (not $x692))))) -(let ((@x705 (monotonicity (monotonicity @x699 (= (or $x65 $x193) (or $x65 (not $x692)))) (= $x245 (not (or $x65 (not $x692))))))) -(let ((@x711 (monotonicity (monotonicity @x705 (= $x248 (or $x177 (not (or $x65 (not $x692)))))) (= (not $x248) (not (or $x177 (not (or $x65 (not $x692))))))))) -(let ((@x721 (quant-intro (monotonicity (monotonicity @x711 $x713) $x716) (= $x262 $x719)))) -(let (($x225 (forall ((?v0 Nat$) )(! (let (($x191 (or (not (dvd$ (?v1!0 ?v0) ?v0)) (= (of_nat$ (?v1!0 ?v0)) 1) (= (of_nat$ (?v1!0 ?v0)) (of_nat$ ?v0))))) -(let (($x192 (not $x191))) -(let ((?x30 (of_nat$ ?v0))) -(let (($x65 (<= ?x30 1))) -(let (($x28 (prime_nat$ ?v0))) -(let (($x217 (or $x28 $x65 $x192))) -(let (($x72 (forall ((?v1 Nat$) )(! (let ((?x30 (of_nat$ ?v1))) -(let (($x34 (= ?x30 1))) -(or (not (dvd$ ?v1 ?v0)) $x34 (= ?x30 (of_nat$ ?v0))))) :qid k!10)) -)) -(let (($x66 (not $x65))) -(let (($x75 (and $x66 $x72))) -(let (($x177 (not $x28))) -(let (($x201 (or $x177 $x75))) -(and $x201 $x217)))))))))))) :qid k!10)) -)) -(let ((@x250 (monotonicity (rewrite (= (and (not $x65) $x72) $x245)) (= (or $x177 (and (not $x65) $x72)) $x248)))) -(let ((@x253 (monotonicity @x250 (= (and (or $x177 (and (not $x65) $x72)) $x217) (and $x248 $x217))))) -(let ((@x261 (trans @x253 (rewrite (= (and $x248 $x217) $x257)) (= (and (or $x177 (and (not $x65) $x72)) $x217) $x257)))) -(let (($x205 (forall ((?v0 Nat$) )(! (let (($x191 (or (not (dvd$ (?v1!0 ?v0) ?v0)) (= (of_nat$ (?v1!0 ?v0)) 1) (= (of_nat$ (?v1!0 ?v0)) (of_nat$ ?v0))))) -(let (($x192 (not $x191))) -(let ((?x30 (of_nat$ ?v0))) -(let (($x65 (<= ?x30 1))) -(let (($x66 (not $x65))) -(let (($x182 (not $x66))) -(let (($x196 (or $x182 $x192))) -(let (($x28 (prime_nat$ ?v0))) -(let (($x200 (or $x28 $x196))) -(let (($x72 (forall ((?v1 Nat$) )(! (let ((?x30 (of_nat$ ?v1))) -(let (($x34 (= ?x30 1))) -(or (not (dvd$ ?v1 ?v0)) $x34 (= ?x30 (of_nat$ ?v0))))) :qid k!10)) -)) -(let (($x75 (and $x66 $x72))) -(let (($x177 (not $x28))) -(let (($x201 (or $x177 $x75))) -(and $x201 $x200)))))))))))))) :qid k!10)) -)) -(let (($x66 (not $x65))) -(let (($x75 (and $x66 $x72))) -(let (($x201 (or $x177 $x75))) -(let (($x222 (and $x201 $x217))) -(let (($x182 (not $x66))) -(let (($x196 (or $x182 $x192))) -(let (($x200 (or $x28 $x196))) -(let (($x202 (and $x201 $x200))) -(let ((@x216 (monotonicity (monotonicity (rewrite (= $x182 $x65)) (= $x196 (or $x65 $x192))) (= $x200 (or $x28 (or $x65 $x192)))))) -(let ((@x221 (trans @x216 (rewrite (= (or $x28 (or $x65 $x192)) $x217)) (= $x200 $x217)))) -(let (($x81 (forall ((?v0 Nat$) )(! (let (($x72 (forall ((?v1 Nat$) )(! (let ((?x30 (of_nat$ ?v1))) -(let (($x34 (= ?x30 1))) -(or (not (dvd$ ?v1 ?v0)) $x34 (= ?x30 (of_nat$ ?v0))))) :qid k!10)) -)) -(let ((?x30 (of_nat$ ?v0))) -(let (($x65 (<= ?x30 1))) -(let (($x66 (not $x65))) -(let (($x75 (and $x66 $x72))) -(let (($x28 (prime_nat$ ?v0))) -(= $x28 $x75))))))) :qid k!10)) -)) -(let ((@x199 (nnf-neg (refl (~ $x182 $x182)) (sk (~ $x193 $x192)) (~ (not $x75) $x196)))) -(let ((@x181 (monotonicity (refl (~ $x66 $x66)) (nnf-pos (refl (~ $x69 $x69)) (~ $x72 $x72)) (~ $x75 $x75)))) -(let ((@x204 (nnf-pos (refl (~ $x28 $x28)) (refl (~ $x177 $x177)) @x181 @x199 (~ (= $x28 $x75) $x202)))) -(let (($x42 (forall ((?v0 Nat$) )(! (let (($x39 (forall ((?v1 Nat$) )(! (let (($x33 (dvd$ ?v1 ?v0))) -(=> $x33 (or (= (of_nat$ ?v1) 1) (= (of_nat$ ?v1) (of_nat$ ?v0))))) :qid k!10)) -)) -(let ((?x30 (of_nat$ ?v0))) -(let (($x31 (< 1 ?x30))) -(let (($x28 (prime_nat$ ?v0))) -(= $x28 (and $x31 $x39)))))) :qid k!10)) -)) -(let (($x62 (forall ((?v0 Nat$) )(! (let (($x48 (forall ((?v1 Nat$) )(! (or (not (dvd$ ?v1 ?v0)) (or (= (of_nat$ ?v1) 1) (= (of_nat$ ?v1) (of_nat$ ?v0)))) :qid k!10)) -)) -(let ((?x30 (of_nat$ ?v0))) -(let (($x31 (< 1 ?x30))) -(let (($x51 (and $x31 $x48))) -(let (($x28 (prime_nat$ ?v0))) -(= $x28 $x51)))))) :qid k!10)) -)) -(let (($x78 (= $x28 $x75))) -(let (($x48 (forall ((?v1 Nat$) )(! (or (not (dvd$ ?v1 ?0)) (or (= (of_nat$ ?v1) 1) (= (of_nat$ ?v1) (of_nat$ ?0)))) :qid k!10)) -)) -(let (($x31 (< 1 ?x30))) -(let (($x51 (and $x31 $x48))) -(let (($x57 (= $x28 $x51))) -(let (($x45 (or (not (dvd$ ?0 ?1)) (or $x34 (= ?x30 (of_nat$ ?1)))))) -(let ((@x77 (monotonicity (rewrite (= $x31 $x66)) (quant-intro (rewrite (= $x45 $x69)) (= $x48 $x72)) (= $x51 $x75)))) -(let (($x39 (forall ((?v1 Nat$) )(! (let (($x33 (dvd$ ?v1 ?0))) -(=> $x33 (or (= (of_nat$ ?v1) 1) (= (of_nat$ ?v1) (of_nat$ ?0))))) :qid k!10)) -)) -(let (($x41 (= $x28 (and $x31 $x39)))) -(let ((@x47 (rewrite (= (=> (dvd$ ?0 ?1) (or $x34 (= ?x30 (of_nat$ ?1)))) $x45)))) -(let ((@x53 (monotonicity (quant-intro @x47 (= $x39 $x48)) (= (and $x31 $x39) $x51)))) -(let ((@x61 (trans (monotonicity @x53 (= $x41 (= $x28 $x51))) (rewrite (= (= $x28 $x51) $x57)) (= $x41 $x57)))) -(let ((@x85 (trans (quant-intro @x61 (= $x42 $x62)) (quant-intro (monotonicity @x77 (= $x57 $x78)) (= $x62 $x81)) (= $x42 $x81)))) -(let ((@x208 (mp~ (mp (asserted $x42) @x85 $x81) (nnf-pos @x204 (~ $x81 $x205)) $x205))) -(let ((@x228 (mp @x208 (quant-intro (monotonicity @x221 (= $x202 $x222)) (= $x205 $x225)) $x225))) -(let ((@x722 (mp (mp @x228 (quant-intro @x261 (= $x225 $x262)) $x262) @x721 $x719))) -(let (($x329 (or (not $x719) $x665))) -(let ((@x667 ((_ quant-inst (nat$ ?x98)) $x329))) -(let ((@x553 (unit-resolution (def-axiom (or $x323 $x468)) (unit-resolution @x667 @x722 $x665) $x468))) -(let (($x125 (not (or $x110 (>= ?x89 1))))) -(let (($x94 (<= 1 ?x89))) -(let (($x95 (=> (prime_nat$ (nat$ (+ ?x90 1))) $x94))) -(let (($x96 (not $x95))) -(let ((@x124 (monotonicity (rewrite (= $x94 (>= ?x89 1))) (= (or $x110 $x94) (or $x110 (>= ?x89 1)))))) -(let ((@x103 (monotonicity (rewrite (= (+ ?x90 1) ?x98)) (= (nat$ (+ ?x90 1)) ?x101)))) -(let ((@x109 (monotonicity (monotonicity @x103 (= (prime_nat$ (nat$ (+ ?x90 1))) $x104)) (= $x95 (=> $x104 $x94))))) -(let ((@x115 (trans @x109 (rewrite (= (=> $x104 $x94) (or $x110 $x94))) (= $x95 (or $x110 $x94))))) -(let ((@x129 (trans (monotonicity @x115 (= $x96 (not (or $x110 $x94)))) (monotonicity @x124 (= (not (or $x110 $x94)) $x125)) (= $x96 $x125)))) -(let ((@x131 (not-or-elim (mp (asserted $x96) @x129 $x125) $x104))) -(let ((@x479 (unit-resolution (unit-resolution (def-axiom (or $x678 $x110 $x338)) @x131 (or $x678 $x338)) @x553 $x338))) -(let ((@x133 (not-or-elim (mp (asserted $x96) @x129 $x125) (not (>= ?x89 1))))) -((_ th-lemma arith farkas -4 1 1) @x133 (unit-resolution (def-axiom (or $x683 $x668)) @x479 $x668) @x551 false)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) - -032a981d2d971a3ae58910db408d3838b7de586f 7 0 -unsat -((set-logic AUFLIA) -(proof -(let ((@x36 (monotonicity (rewrite (= (or p$ (not p$)) true)) (= (not (or p$ (not p$))) (not true))))) -(let ((@x40 (trans @x36 (rewrite (= (not true) false)) (= (not (or p$ (not p$))) false)))) -(mp (asserted (not (or p$ (not p$)))) @x40 false))))) - -d251ca4335382db5b789cf4827abd98b9e46f2bf 9 0 -unsat -((set-logic AUFLIA) -(proof -(let ((@x36 (monotonicity (rewrite (= (and p$ true) p$)) (= (= (and p$ true) p$) (= p$ p$))))) -(let ((@x40 (trans @x36 (rewrite (= (= p$ p$) true)) (= (= (and p$ true) p$) true)))) -(let ((@x43 (monotonicity @x40 (= (not (= (and p$ true) p$)) (not true))))) -(let ((@x47 (trans @x43 (rewrite (= (not true) false)) (= (not (= (and p$ true) p$)) false)))) -(mp (asserted (not (= (and p$ true) p$))) @x47 false))))))) - -98b44ed25900b5731029a0f9910e7ccad7cfa5cf 13 0 -unsat -((set-logic AUFLIA) -(proof -(let (($x33 (not (=> (and (or p$ q$) (not p$)) q$)))) -(let (($x37 (= (=> (and (or p$ q$) (not p$)) q$) (or (not (and (or p$ q$) (not p$))) q$)))) -(let ((@x41 (monotonicity (rewrite $x37) (= $x33 (not (or (not (and (or p$ q$) (not p$))) q$)))))) -(let ((@x44 (mp (asserted $x33) @x41 (not (or (not (and (or p$ q$) (not p$))) q$))))) -(let ((@x45 (and-elim (not-or-elim @x44 (and (or p$ q$) (not p$))) (not p$)))) -(let ((@x54 (monotonicity (iff-false @x45 (= p$ false)) (iff-false (not-or-elim @x44 (not q$)) (= q$ false)) (= (or p$ q$) (or false false))))) -(let ((@x58 (trans @x54 (rewrite (= (or false false) false)) (= (or p$ q$) false)))) -(let (($x29 (or p$ q$))) -(mp (and-elim (not-or-elim @x44 (and $x29 (not p$))) $x29) @x58 false))))))))))) - -c4510ae6be30b994919ed3a724999fe0329aac46 6 0 -unsat -((set-logic AUFLIA) -(proof -(let ((@x30 (rewrite (= (not true) false)))) -(mp (asserted (not true)) @x30 false)))) - -d79b20c3fa2c3156619ed0d2d824ef5eb5776ea3 11 0 -unsat -((set-logic AUFLIA) -(proof -(let (($x32 (and c$ d$))) -(let (($x29 (and a$ b$))) -(let (($x33 (or $x29 $x32))) -(let (($x34 (=> $x33 $x33))) -(let (($x35 (not $x34))) -(let ((@x45 (trans (monotonicity (rewrite (= $x34 true)) (= $x35 (not true))) (rewrite (= (not true) false)) (= $x35 false)))) -(mp (asserted $x35) @x45 false))))))))) - -2b81235bea88ad32b47b62d270d5f8604cdbea46 24 0 -unsat -((set-logic AUFLIA) -(proof -(let (($x28 (= p$ p$))) -(let (($x29 (= $x28 p$))) -(let (($x30 (= $x29 p$))) -(let (($x31 (= $x30 p$))) -(let (($x32 (= $x31 p$))) -(let (($x33 (= $x32 p$))) -(let (($x34 (= $x33 p$))) -(let (($x35 (= $x34 p$))) -(let (($x36 (= $x35 p$))) -(let (($x37 (not $x36))) -(let ((@x40 (rewrite (= $x28 true)))) -(let ((@x45 (rewrite (= (= true p$) p$)))) -(let ((@x47 (trans (monotonicity @x40 (= $x29 (= true p$))) @x45 (= $x29 p$)))) -(let ((@x53 (monotonicity (trans (monotonicity @x47 (= $x30 $x28)) @x40 (= $x30 true)) (= $x31 (= true p$))))) -(let ((@x59 (trans (monotonicity (trans @x53 @x45 (= $x31 p$)) (= $x32 $x28)) @x40 (= $x32 true)))) -(let ((@x63 (trans (monotonicity @x59 (= $x33 (= true p$))) @x45 (= $x33 p$)))) -(let ((@x69 (monotonicity (trans (monotonicity @x63 (= $x34 $x28)) @x40 (= $x34 true)) (= $x35 (= true p$))))) -(let ((@x75 (trans (monotonicity (trans @x69 @x45 (= $x35 p$)) (= $x36 $x28)) @x40 (= $x36 true)))) -(let ((@x82 (trans (monotonicity @x75 (= $x37 (not true))) (rewrite (= (not true) false)) (= $x37 false)))) -(mp (asserted $x37) @x82 false)))))))))))))))))))))) - -bd97c872cfd055e1504521fb8cd9167911452904 23 0 -unsat -((set-logic AUFLIA) -(proof -(let (($x33 (and p1$ p3$))) -(let (($x32 (and p3$ p2$))) -(let (($x34 (or $x32 $x33))) -(let (($x35 (=> p1$ $x34))) -(let (($x36 (or $x35 p1$))) -(let (($x29 (and p1$ p2$))) -(let (($x31 (or $x29 p3$))) -(let (($x37 (=> $x31 $x36))) -(let (($x38 (not $x37))) -(let (($x40 (not p1$))) -(let (($x41 (or $x40 $x34))) -(let (($x44 (or $x41 p1$))) -(let (($x50 (not $x31))) -(let (($x51 (or $x50 $x44))) -(let (($x56 (not $x51))) -(let ((@x67 (trans (monotonicity (rewrite (= $x51 true)) (= $x56 (not true))) (rewrite (= (not true) false)) (= $x56 false)))) -(let ((@x49 (monotonicity (monotonicity (rewrite (= $x35 $x41)) (= $x36 $x44)) (= $x37 (=> $x31 $x44))))) -(let ((@x58 (monotonicity (trans @x49 (rewrite (= (=> $x31 $x44) $x51)) (= $x37 $x51)) (= $x38 $x56)))) -(mp (asserted $x38) (trans @x58 @x67 (= $x38 false)) false))))))))))))))))))))) - -a4102e588c1974e32fabf0cded52102a5448e5f2 39 0 -unsat -((set-logic AUFLIA) -(proof -(let (($x100 (not d$))) -(let (($x45 (not c$))) -(let (($x112 (or p$ (and q$ (not q$))))) -(let (($x113 (and (not p$) $x112))) -(let (($x114 (or c$ $x113))) -(let (($x115 (not $x114))) -(let ((@x121 (monotonicity (rewrite (= (and q$ (not q$)) false)) (= $x112 (or p$ false))))) -(let ((@x128 (monotonicity (trans @x121 (rewrite (= (or p$ false) p$)) (= $x112 p$)) (= $x113 (and (not p$) p$))))) -(let ((@x132 (trans @x128 (rewrite (= (and (not p$) p$) false)) (= $x113 false)))) -(let ((@x139 (trans (monotonicity @x132 (= $x114 (or c$ false))) (rewrite (= (or c$ false) c$)) (= $x114 c$)))) -(let ((@x153 (iff-false (mp (asserted $x115) (monotonicity @x139 (= $x115 $x45)) $x45) (= c$ false)))) -(let ((@x147 (trans (monotonicity @x153 (= (or $x100 c$) (or $x100 false))) (rewrite (= (or $x100 false) $x100)) (= (or $x100 c$) $x100)))) -(let (($x103 (or $x100 c$))) -(let ((@x102 (monotonicity (rewrite (= (or d$ false) d$)) (= (not (or d$ false)) $x100)))) -(let ((@x108 (mp (asserted (or (not (or d$ false)) c$)) (monotonicity @x102 (= (or (not (or d$ false)) c$) $x103)) $x103))) -(let (($x87 (not b$))) -(let ((@x164 (trans (monotonicity @x153 (= (or $x87 c$) (or $x87 false))) (rewrite (= (or $x87 false) $x87)) (= (or $x87 c$) $x87)))) -(let (($x90 (or $x87 c$))) -(let ((@x82 (monotonicity (rewrite (= (or x$ (not x$)) true)) (= (and b$ (or x$ (not x$))) (and b$ true))))) -(let ((@x86 (trans @x82 (rewrite (= (and b$ true) b$)) (= (and b$ (or x$ (not x$))) b$)))) -(let ((@x92 (monotonicity (monotonicity @x86 (= (not (and b$ (or x$ (not x$)))) $x87)) (= (or (not (and b$ (or x$ (not x$)))) c$) $x90)))) -(let ((@x95 (mp (asserted (or (not (and b$ (or x$ (not x$)))) c$)) @x92 $x90))) -(let (($x64 (not a$))) -(let ((@x170 (monotonicity (iff-false (mp @x95 @x164 $x87) (= b$ false)) (= (or $x64 b$) (or $x64 false))))) -(let ((@x174 (trans @x170 (rewrite (= (or $x64 false) $x64)) (= (or $x64 b$) $x64)))) -(let (($x67 (or $x64 b$))) -(let ((@x59 (monotonicity (rewrite (= (and c$ $x45) false)) (= (or a$ (and c$ $x45)) (or a$ false))))) -(let ((@x63 (trans @x59 (rewrite (= (or a$ false) a$)) (= (or a$ (and c$ $x45)) a$)))) -(let ((@x69 (monotonicity (monotonicity @x63 (= (not (or a$ (and c$ $x45))) $x64)) (= (or (not (or a$ (and c$ $x45))) b$) $x67)))) -(let ((@x175 (mp (mp (asserted (or (not (or a$ (and c$ $x45))) b$)) @x69 $x67) @x174 $x64))) -(let ((@x198 (monotonicity (iff-false @x175 (= a$ false)) (iff-false (mp @x95 @x164 $x87) (= b$ false)) @x153 (iff-false (mp @x108 @x147 $x100) (= d$ false)) (= (or a$ b$ c$ d$) (or false false false false))))) -(let ((@x202 (trans @x198 (rewrite (= (or false false false false) false)) (= (or a$ b$ c$ d$) false)))) -(let (($x37 (or a$ b$ c$ d$))) -(let ((@x40 (mp (asserted (or a$ (or b$ (or c$ d$)))) (rewrite (= (or a$ (or b$ (or c$ d$))) $x37)) $x37))) -(mp @x40 @x202 false))))))))))))))))))))))))))))))))))))) - -2281aab3f66d02faebd1a91e2e39f2078773cec5 27 0 -unsat -((set-logic AUFLIA) -(proof -(let ((?x38 (symm_f$ b$ a$))) -(let ((?x37 (symm_f$ a$ b$))) -(let (($x39 (= ?x37 ?x38))) -(let (($x52 (not $x39))) -(let ((@x47 (monotonicity (rewrite (= (= a$ a$) true)) (= (and (= a$ a$) $x39) (and true $x39))))) -(let ((@x51 (trans @x47 (rewrite (= (and true $x39) $x39)) (= (and (= a$ a$) $x39) $x39)))) -(let ((@x57 (mp (asserted (not (and (= a$ a$) $x39))) (monotonicity @x51 (= (not (and (= a$ a$) $x39)) $x52)) $x52))) -(let (($x480 (forall ((?v0 A$) (?v1 A$) )(! 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x22$))) -(let ((@x1705 (unit-resolution (unit-resolution @x325 @x1665 (or x26$ x56$)) (unit-resolution @x612 @x1702 $x610) x26$))) -(let ((@x1709 (unit-resolution @x222 (unit-resolution @x616 @x1702 $x539) @x897 @x1692 x16$))) -(let ((@x1713 (unit-resolution @x269 (unit-resolution @x664 @x1705 $x596) (unit-resolution (asserted (or $x609 $x595)) @x1702 $x595) (unit-resolution @x527 @x1709 $x525) x20$))) -(let ((@x1714 (unit-resolution @x590 @x1713 (unit-resolution @x307 (unit-resolution @x662 @x1705 $x657) x54$) false))) -(let ((@x1715 (lemma @x1714 x17$))) -(let ((@x1718 (unit-resolution (unit-resolution @x1569 @x1665 (or $x609 x11$)) (unit-resolution @x1671 (unit-resolution @x561 @x1715 $x553) x22$) x11$))) -(let ((@x1722 (unit-resolution @x1662 (unit-resolution @x472 @x1718 $x467) (unit-resolution @x565 @x1715 $x482) $x355))) -(unit-resolution @x1647 @x1722 (unit-resolution @x472 @x1718 $x467) (unit-resolution @x565 @x1715 $x482) (unit-resolution @x480 @x1718 $x397) false))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) - -5b5847cff590025b823cc0b87a8a109505cf26d0 38 0 -unsat -((set-logic AUFLIA) -(declare-fun ?v0!0 () Int) -(declare-fun ?v1!1 () Int) -(proof -(let (($x48 (p$ ?v0!0))) -(let (($x50 (not $x48))) -(let (($x63 (not (or $x48 (p$ ?v1!1))))) -(let ((@x77 (monotonicity (rewrite (= (not $x50) $x48)) (= (and (not $x50) $x63) (and $x48 $x63))))) -(let (($x57 (not $x50))) -(let (($x67 (and $x57 $x63))) -(let (($x41 (forall ((?v0 Int) )(! (let (($x32 (forall ((?v1 Int) )(! (let (($x28 (p$ ?v1))) -(or (p$ ?v0) $x28)) :qid k!5)) -)) -(or (not (p$ ?v0)) $x32)) :qid k!5)) -)) -(let (($x44 (not $x41))) -(let (($x52 (forall ((?v1 Int) )(! (let (($x28 (p$ ?v1))) -(let (($x48 (p$ ?v0!0))) -(or $x48 $x28))) :qid k!5)) -)) -(let ((@x69 (nnf-neg (refl (~ $x57 $x57)) (sk (~ (not $x52) $x63)) (~ (not (or $x50 $x52)) $x67)))) -(let (($x34 (forall ((?v0 Int) )(! (let (($x32 (forall ((?v1 Int) )(! (let (($x28 (p$ ?v1))) -(or (p$ ?v0) $x28)) :qid k!5)) -)) -(let (($x28 (p$ ?v0))) -(=> $x28 $x32))) :qid k!5)) -)) -(let (($x35 (not $x34))) -(let (($x32 (forall ((?v1 Int) )(! (let (($x28 (p$ ?v1))) -(or (p$ ?0) $x28)) :qid k!5)) -)) -(let ((@x43 (quant-intro (rewrite (= (=> (p$ ?0) $x32) (or (not (p$ ?0)) $x32))) (= $x34 $x41)))) -(let ((@x72 (mp~ (mp (asserted $x35) (monotonicity @x43 (= $x35 $x44)) $x44) (trans (sk (~ $x44 (not (or $x50 $x52)))) @x69 (~ $x44 $x67)) $x67))) -(let ((@x81 (not-or-elim (and-elim (mp @x72 @x77 (and $x48 $x63)) $x63) $x50))) -(let ((@x79 (and-elim (mp @x72 @x77 (and $x48 $x63)) $x48))) -(unit-resolution @x79 @x81 false)))))))))))))))))))) - -373c19e76251b161134a463d5e2a74af5c6b8f8c 53 0 -unsat -((set-logic AUFLIA) -(declare-fun ?v0!0 () A$) -(proof -(let (($x517 (forall ((?v0 A$) )(! (let (($x40 (p$ x$ ?v0))) -(not $x40)) :pattern ( (p$ x$ ?v0) ) :qid k!9)) -)) -(let (($x44 (p$ x$ c$))) -(let (($x91 (= $x44 x$))) -(let (($x510 (forall ((?v0 Bool) (?v1 A$) )(! (let (($x29 (p$ ?v0 ?v1))) -(= $x29 ?v0)) :pattern ( (p$ ?v0 ?v1) ) :qid k!8)) -)) -(let (($x36 (forall ((?v0 Bool) (?v1 A$) )(! (let (($x29 (p$ ?v0 ?v1))) -(= $x29 ?v0)) :qid k!8)) -)) -(let ((@x514 (quant-intro (refl (= (= (p$ ?1 ?0) ?1) (= (p$ ?1 ?0) ?1))) (= $x36 $x510)))) -(let ((@x64 (nnf-pos (refl (~ (= (p$ ?1 ?0) ?1) (= (p$ ?1 ?0) ?1))) (~ $x36 $x36)))) -(let (($x31 (forall ((?v0 Bool) (?v1 A$) )(! (let (($x29 (p$ ?v0 ?v1))) -(= $x29 ?v0)) :qid k!8)) -)) -(let ((@x38 (quant-intro (rewrite (= (= (p$ ?1 ?0) ?1) (= (p$ ?1 ?0) ?1))) (= $x31 $x36)))) -(let ((@x515 (mp (mp~ (mp (asserted $x31) @x38 $x36) @x64 $x36) @x514 $x510))) -(let (($x170 (or (not $x510) $x91))) -(let ((@x503 ((_ quant-inst x$ c$) $x170))) -(let (($x73 (p$ x$ ?v0!0))) -(let (($x179 (= $x73 x$))) -(let (($x85 (or $x73 $x44))) -(let (($x81 (not $x44))) -(let (($x69 (forall ((?v0 A$) )(! (let (($x40 (p$ x$ ?v0))) -(not $x40)) :qid k!9)) -)) -(let (($x84 (or $x69 $x81))) -(let (($x42 (exists ((?v0 A$) )(! (p$ x$ ?v0) :qid k!9)) -)) -(let (($x54 (not $x42))) -(let (($x55 (= $x54 $x44))) -(let ((@x71 (nnf-neg (refl (~ (not (p$ x$ ?0)) (not (p$ x$ ?0)))) (~ $x54 $x69)))) -(let ((@x88 (nnf-pos @x71 (nnf-neg (sk (~ $x42 $x73)) (~ (not $x54) $x73)) (refl (~ $x44 $x44)) (refl (~ $x81 $x81)) (~ $x55 (and $x85 $x84))))) -(let ((@x53 (monotonicity (rewrite (= (= $x42 $x44) (= $x42 $x44))) (= (not (= $x42 $x44)) (not (= $x42 $x44)))))) -(let ((@x59 (trans @x53 (rewrite (= (not (= $x42 $x44)) $x55)) (= (not (= $x42 $x44)) $x55)))) -(let ((@x89 (mp~ (mp (asserted (not (= $x42 $x44))) @x59 $x55) @x88 (and $x85 $x84)))) -(let ((@x92 (and-elim @x89 $x85))) -(let ((@x484 (unit-resolution (def-axiom (or (not $x179) (not $x73) x$)) (unit-resolution @x92 (hypothesis $x81) $x73) (or (not $x179) x$)))) -(let ((@x145 (unit-resolution @x484 (unit-resolution ((_ quant-inst x$ ?v0!0) (or (not $x510) $x179)) @x515 $x179) x$))) -(let ((@x147 (unit-resolution (def-axiom (or (not $x91) $x44 (not x$))) (hypothesis $x81) (or (not $x91) (not x$))))) -(let ((@x485 (lemma (unit-resolution @x147 @x145 (unit-resolution @x503 @x515 $x91) false) $x44))) -(let (($x522 (or $x517 $x81))) -(let ((@x521 (quant-intro (refl (= (not (p$ x$ ?0)) (not (p$ x$ ?0)))) (= $x69 $x517)))) -(let ((@x525 (mp (and-elim @x89 $x84) (monotonicity @x521 (= $x84 $x522)) $x522))) -(let (($x160 (or (not $x517) $x81))) -(let ((@x161 ((_ quant-inst c$) $x160))) -(unit-resolution @x161 @x485 (unit-resolution @x525 @x485 $x517) false))))))))))))))))))))))))))))))))))))))) - -73d33aacc4f76cc1b4edd5b56d4a9b1cb27da391 53 0 -unsat -((set-logic AUFLIA) -(declare-fun ?v0!3 () A$) -(proof -(let (($x584 (forall ((?v0 A$) )(! (let (($x52 (p$ x$ ?v0))) -(not $x52)) :pattern ( (p$ x$ ?v0) ) :qid k!10)) -)) -(let (($x55 (p$ x$ c$))) -(let (($x230 (= $x55 x$))) -(let (($x561 (forall ((?v0 Bool) (?v1 A$) )(! (let (($x29 (p$ ?v0 ?v1))) -(= $x29 ?v0)) :pattern ( (p$ ?v0 ?v1) ) :qid k!8)) -)) -(let (($x36 (forall ((?v0 Bool) (?v1 A$) )(! (let (($x29 (p$ ?v0 ?v1))) -(= $x29 ?v0)) :qid k!8)) -)) -(let ((@x565 (quant-intro (refl (= (= (p$ ?1 ?0) ?1) (= (p$ ?1 ?0) ?1))) (= $x36 $x561)))) -(let ((@x75 (nnf-pos (refl (~ (= (p$ ?1 ?0) ?1) (= (p$ ?1 ?0) ?1))) (~ $x36 $x36)))) -(let (($x31 (forall ((?v0 Bool) (?v1 A$) )(! (let (($x29 (p$ ?v0 ?v1))) -(= $x29 ?v0)) :qid k!8)) -)) -(let ((@x38 (quant-intro (rewrite (= (= (p$ ?1 ?0) ?1) (= (p$ ?1 ?0) ?1))) (= $x31 $x36)))) -(let ((@x566 (mp (mp~ (mp (asserted $x31) @x38 $x36) @x75 $x36) @x565 $x561))) -(let (($x220 (or (not $x561) $x230))) -(let ((@x221 ((_ quant-inst x$ c$) $x220))) -(let (($x124 (p$ x$ ?v0!3))) -(let (($x141 (= $x124 x$))) -(let (($x136 (or $x124 $x55))) -(let (($x132 (not $x55))) -(let (($x120 (forall ((?v0 A$) )(! (let (($x52 (p$ x$ ?v0))) -(not $x52)) :qid k!10)) -)) -(let (($x135 (or $x120 $x132))) -(let (($x54 (exists ((?v0 A$) )(! (p$ x$ ?v0) :qid k!10)) -)) -(let (($x65 (not $x54))) -(let (($x66 (= $x65 $x55))) -(let ((@x122 (nnf-neg (refl (~ (not (p$ x$ ?0)) (not (p$ x$ ?0)))) (~ $x65 $x120)))) -(let ((@x139 (nnf-pos @x122 (nnf-neg (sk (~ $x54 $x124)) (~ (not $x65) $x124)) (refl (~ $x55 $x55)) (refl (~ $x132 $x132)) (~ $x66 (and $x136 $x135))))) -(let ((@x64 (monotonicity (rewrite (= (= $x54 $x55) (= $x54 $x55))) (= (not (= $x54 $x55)) (not (= $x54 $x55)))))) -(let ((@x70 (trans @x64 (rewrite (= (not (= $x54 $x55)) $x66)) (= (not (= $x54 $x55)) $x66)))) -(let ((@x140 (mp~ (mp (asserted (not (= $x54 $x55))) @x70 $x66) @x139 (and $x136 $x135)))) -(let ((@x143 (and-elim @x140 $x136))) -(let ((@x193 (unit-resolution (def-axiom (or (not $x141) (not $x124) x$)) (unit-resolution @x143 (hypothesis $x132) $x124) (or (not $x141) x$)))) -(let ((@x535 (unit-resolution @x193 (unit-resolution ((_ quant-inst x$ ?v0!3) (or (not $x561) $x141)) @x566 $x141) x$))) -(let ((@x197 (unit-resolution (def-axiom (or (not $x230) $x55 (not x$))) (hypothesis $x132) (or (not $x230) (not x$))))) -(let ((@x199 (lemma (unit-resolution @x197 @x535 (unit-resolution @x221 @x566 $x230) false) $x55))) -(let (($x589 (or $x584 $x132))) -(let ((@x588 (quant-intro (refl (= (not (p$ x$ ?0)) (not (p$ x$ ?0)))) (= $x120 $x584)))) -(let ((@x592 (mp (and-elim @x140 $x135) (monotonicity @x588 (= $x135 $x589)) $x589))) -(let (($x549 (or (not $x584) $x132))) -(let ((@x211 ((_ quant-inst c$) $x549))) -(unit-resolution @x211 @x199 (unit-resolution @x592 @x199 $x584) false))))))))))))))))))))))))))))))))))))))) - -5865554a06d92ae737f15d4517f201cb6a56c4e7 26 0 -unsat -((set-logic AUFLIA) -(proof -(let (($x28 (p$ x$))) -(let ((@x48 (monotonicity (rewrite (= (=> $x28 (p$ y$)) (or (not $x28) (p$ y$)))) (= (not (=> $x28 (p$ y$))) (not (or (not $x28) (p$ y$))))))) -(let ((@x51 (mp (asserted (not (=> $x28 (p$ y$)))) @x48 (not (or (not $x28) (p$ y$)))))) -(let ((@x49 (not-or-elim @x51 $x28))) -(let (($x486 (forall ((?v0 A$) )(! (let (($x30 (p$ ?v0))) -(not $x30)) :pattern ( (p$ ?v0) ) :qid k!8)) -)) -(let (($x34 (forall ((?v0 A$) )(! (let (($x30 (p$ ?v0))) -(not $x30)) :qid k!8)) -)) -(let ((@x490 (quant-intro (refl (= (not (p$ ?0)) (not (p$ ?0)))) (= $x34 $x486)))) -(let (($x31 (exists ((?v0 A$) )(! (p$ ?v0) :qid k!8)) -)) -(let (($x32 (not $x31))) -(let ((@x59 (monotonicity (iff-true @x49 (= $x28 true)) (= (ite $x28 $x32 $x34) (ite true $x32 $x34))))) -(let ((@x63 (trans @x59 (rewrite (= (ite true $x32 $x34) $x32)) (= (ite $x28 $x32 $x34) $x32)))) -(let ((@x67 (mp~ (mp (asserted (ite $x28 $x32 $x34)) @x63 $x32) (nnf-neg (refl (~ (not (p$ ?0)) (not (p$ ?0)))) (~ $x32 $x34)) $x34))) -(let ((@x491 (mp @x67 @x490 $x486))) -(let (($x42 (not $x28))) -(let (($x156 (or (not $x486) $x42))) -(let ((@x70 ((_ quant-inst x$) $x156))) -(unit-resolution @x70 @x491 @x49 false))))))))))))))))))) - -2e7aa15df0632240a3bbe8b448df847c6a5afa7c 7 0 -unsat -((set-logic AUFLIA) -(proof -(let ((@x35 (monotonicity (rewrite (= (= 3 3) true)) (= (not (= 3 3)) (not true))))) -(let ((@x39 (trans @x35 (rewrite (= (not true) false)) (= (not (= 3 3)) false)))) -(mp (asserted (not (= 3 3))) @x39 false))))) - -b2313f7d5e8f2049d0fc86a5290b5b01c50a1956 7 0 -unsat -((set-logic AUFLIRA) -(proof -(let ((@x35 (monotonicity (rewrite (= (= 3.0 3.0) true)) (= (not (= 3.0 3.0)) (not true))))) -(let ((@x39 (trans @x35 (rewrite (= (not true) false)) (= (not (= 3.0 3.0)) false)))) -(mp (asserted (not (= 3.0 3.0))) @x39 false))))) - -6114093ed426a317c79d6cee4b92be3fd329859f 9 0 -unsat -((set-logic AUFLIA) -(proof -(let ((@x37 (monotonicity (rewrite (= (+ 3 1) 4)) (= (= (+ 3 1) 4) (= 4 4))))) -(let ((@x41 (trans @x37 (rewrite (= (= 4 4) true)) (= (= (+ 3 1) 4) true)))) -(let ((@x44 (monotonicity @x41 (= (not (= (+ 3 1) 4)) (not true))))) -(let ((@x48 (trans @x44 (rewrite (= (not true) false)) (= (not (= (+ 3 1) 4)) false)))) -(mp (asserted (not (= (+ 3 1) 4))) @x48 false))))))) - -a203b3db2a53411ee3d79b9aeda0b90634f85bed 16 0 -unsat -((set-logic AUFLIA) -(proof -(let ((?x32 (+ z$ x$))) -(let ((?x33 (+ y$ ?x32))) -(let ((?x30 (+ y$ z$))) -(let ((?x31 (+ x$ ?x30))) -(let (($x34 (= ?x31 ?x33))) -(let (($x35 (not $x34))) -(let ((@x45 (monotonicity (rewrite (= ?x32 (+ x$ z$))) (= ?x33 (+ y$ (+ x$ z$)))))) -(let ((@x49 (trans @x45 (rewrite (= (+ y$ (+ x$ z$)) (+ x$ y$ z$))) (= ?x33 (+ x$ y$ z$))))) -(let ((@x52 (monotonicity (rewrite (= ?x31 (+ x$ y$ z$))) @x49 (= $x34 (= (+ x$ y$ z$) (+ x$ y$ z$)))))) -(let ((@x56 (trans @x52 (rewrite (= (= (+ x$ y$ z$) (+ x$ y$ z$)) true)) (= $x34 true)))) -(let ((@x63 (trans (monotonicity @x56 (= $x35 (not true))) (rewrite (= (not true) false)) (= $x35 false)))) -(mp (asserted $x35) @x63 false)))))))))))))) - -2a15e56e254da2b0d703c710a918cea09184c4fd 11 0 -unsat -((set-logic AUFLIA) -(proof -(let ((@x41 (monotonicity (rewrite (= (<= 3 8) true)) (= (ite (<= 3 8) 8 3) (ite true 8 3))))) -(let ((@x45 (trans @x41 (rewrite (= (ite true 8 3) 8)) (= (ite (<= 3 8) 8 3) 8)))) -(let ((@x48 (monotonicity @x45 (= (< 5 (ite (<= 3 8) 8 3)) (< 5 8))))) -(let ((@x52 (trans @x48 (rewrite (= (< 5 8) true)) (= (< 5 (ite (<= 3 8) 8 3)) true)))) -(let ((@x55 (monotonicity @x52 (= (not (< 5 (ite (<= 3 8) 8 3))) (not true))))) -(let ((@x59 (trans @x55 (rewrite (= (not true) false)) (= (not (< 5 (ite (<= 3 8) 8 3))) false)))) -(mp (asserted (not (< 5 (ite (<= 3 8) 8 3)))) @x59 false))))))))) - -e5c3e298abc0852046f636c11356417cc1ca2609 88 0 -unsat -((set-logic AUFLIRA) -(proof -(let ((?x44 (* (- 1.0) x$))) -(let (($x83 (>= x$ 0.0))) -(let ((?x90 (ite $x83 x$ ?x44))) -(let ((?x113 (* (- 1.0) ?x90))) -(let ((?x148 (+ x$ ?x113))) -(let (($x149 (<= ?x148 0.0))) -(let (($x133 (= x$ ?x90))) -(let ((?x45 (* (- 1.0) y$))) -(let ((?x46 (+ ?x44 ?x45))) -(let ((?x29 (+ x$ y$))) -(let (($x71 (>= ?x29 0.0))) -(let ((?x78 (ite $x71 ?x29 ?x46))) -(let ((?x151 (* (- 1.0) ?x78))) -(let ((?x179 (+ ?x46 ?x151))) -(let (($x181 (>= ?x179 0.0))) -(let (($x130 (= ?x46 ?x78))) -(let (($x72 (not $x71))) -(let (($x95 (>= y$ 0.0))) -(let (($x96 (not $x95))) -(let (($x154 (>= (+ ?x29 ?x151) 0.0))) -(let (($x129 (= ?x29 ?x78))) -(let (($x190 (not $x181))) -(let ((@x161 (hypothesis $x95))) -(let ((?x102 (ite $x95 y$ ?x45))) -(let ((?x114 (* (- 1.0) ?x102))) -(let ((?x115 (+ 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-(let ((@x221 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x140) $x178)) (unit-resolution (def-axiom (or $x95 $x140)) @x206 $x140) $x178))) -(let ((@x222 ((_ th-lemma arith farkas 2 1 1 1 1) @x206 @x221 @x126 @x216 (unit-resolution @x159 (unit-resolution @x136 @x212 $x133) $x149) false))) -(let ((@x226 (unit-resolution @x199 (unit-resolution @x132 (lemma @x222 $x72) $x130) $x181))) -(let ((@x231 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x134) $x153)) (hypothesis $x134) (lemma ((_ th-lemma arith farkas 1 -1 -1 1) @x221 @x126 @x226 (hypothesis $x153) false) (not $x153)) false))) -(let ((@x234 (unit-resolution @x136 (unit-resolution @x138 (lemma @x231 (not $x134)) $x83) $x133))) -((_ th-lemma arith farkas -2 1 -1 -1 1) (unit-resolution @x138 (lemma @x231 (not $x134)) $x83) @x221 @x126 @x226 (unit-resolution @x159 @x234 $x149) false)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) - 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(* (- 1) y$)) 0))) -(let ((@x76 (monotonicity (rewrite (= (< 0 (+ (* (- 1) x$) y$)) (not $x70))) (= (not (< 0 (+ (* (- 1) x$) y$))) (not (not $x70)))))) -(let ((@x80 (trans @x76 (rewrite (= (not (not $x70)) $x70)) (= (not (< 0 (+ (* (- 1) x$) y$))) $x70)))) -(let (($x64 (< 0 (+ (* (- 1) x$) y$)))) -(let (($x67 (not $x64))) -(let (($x58 (not (< 0 (- y$ x$))))) -(let ((@x66 (monotonicity (rewrite (= (- y$ x$) (+ (* (- 1) x$) y$))) (= (< 0 (- y$ x$)) $x64)))) -(let ((@x83 (mp (asserted $x58) (trans (monotonicity @x66 (= $x58 $x67)) @x80 (= $x58 $x70)) $x70))) -(mp @x83 @x90 false)))))))))))))))) - -895fc717670fb918a1eb39f2d045d84196651462 11 0 -unsat -((set-logic AUFLIA) -(proof -(let ((@x39 (monotonicity (rewrite (= (+ 2 2) 4)) (= (= (+ 2 2) 5) (= 4 5))))) -(let ((@x43 (trans @x39 (rewrite (= (= 4 5) false)) (= (= (+ 2 2) 5) false)))) -(let ((@x46 (monotonicity @x43 (= (not (= (+ 2 2) 5)) (not false))))) -(let ((@x50 (trans @x46 (rewrite (= (not false) true)) (= (not (= (+ 2 2) 5)) 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@x1767 @x1762 (unit-resolution @x569 (unit-resolution @x1279 @x1754 @x1698 $x92) $x582) false))) -(let ((@x1770 (lemma @x1768 (or $x288 $x438)))) -(let ((@x891 (unit-resolution @x1770 @x1370 $x438))) -(let ((@x783 (unit-resolution ((_ th-lemma arith assign-bounds -2 2 -2 -2 2 -1) (or $x932 $x817 $x818 $x706 $x364 $x743 $x903)) @x698 @x812 (or $x932 $x817 $x706 $x364 $x903)))) -(let ((@x795 (unit-resolution (unit-resolution @x783 @x1538 @x1617 (or $x932 $x364 $x903)) (unit-resolution @x828 (unit-resolution @x599 @x891 $x596) $x669) (unit-resolution @x1645 @x1370 $x363) $x932))) -(let ((@x809 (unit-resolution (unit-resolution @x709 @x1617 (or $x463 $x339 $x439 $x707)) @x889 @x688 @x891 $x339))) -(let ((@x821 (unit-resolution ((_ th-lemma arith assign-bounds 2 -1) (or $x675 $x439 $x784)) (unit-resolution @x693 (unit-resolution @x599 @x891 $x596) $x678) @x891 $x675))) -(let ((@x836 (lemma (unit-resolution @x1734 @x821 @x809 @x1370 @x795 @x890 @x889 false) (or $x288 $x463)))) -(let ((@x918 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(< ?0 ?v1) :qid k!4)) -)) -(let ((@x42 (rewrite (= (< ?1 ?0) (not (<= (+ ?0 (* (- 1) ?1)) 0)))))) -(let ((@x51 (monotonicity (quant-intro (quant-intro @x42 (= $x30 $x43)) (= $x31 $x46)) (= $x32 $x49)))) -(let ((@x74 (mp (mp~ (mp (asserted $x32) @x51 $x49) @x67 $x63) (quant-intro (rewrite (= $x60 $x54)) (= $x63 $x71)) $x71))) -(mp @x74 (rewrite (= $x71 false)) false)))))))))))))))))) - -3c28d4739f1b1a92e69b6d9cc30eb0a41a881398 22 0 -unsat -((set-logic AUFLIA) -(declare-fun ?v1!0 () Int) -(declare-fun ?v0!1 () Int) -(proof -(let (($x53 (= ?v1!0 1))) -(let (($x59 (not (or (not (and (= ?v0!1 0) $x53)) (not (= ?v0!1 ?v1!0)))))) -(let (($x43 (forall ((?v0 Int) (?v1 Int) )(! (or (not (and (= ?v0 0) (= ?v1 1))) (not (= ?v0 ?v1))) :qid k!4)) -)) -(let (($x46 (not $x43))) -(let (($x36 (forall ((?v0 Int) (?v1 Int) )(! (=> (and (= ?v0 0) (= ?v1 1)) (not (= ?v0 ?v1))) :qid k!4)) -)) -(let (($x37 (not $x36))) -(let (($x41 (= (=> (and (= ?1 0) (= ?0 1)) (not (= ?1 ?0))) (or (not (and (= ?1 0) (= ?0 1))) (not (= ?1 ?0)))))) -(let ((@x48 (monotonicity (quant-intro (rewrite $x41) (= $x36 $x43)) (= $x37 $x46)))) -(let ((@x65 (not-or-elim (mp~ (mp (asserted $x37) @x48 $x46) (sk (~ $x46 $x59)) $x59) (and (= ?v0!1 0) $x53)))) -(let ((@x67 (and-elim @x65 $x53))) -(let (($x56 (= ?v0!1 ?v1!0))) -(let ((@x68 (not-or-elim (mp~ (mp (asserted $x37) @x48 $x46) (sk (~ $x46 $x59)) $x59) $x56))) -(let ((@x70 (trans (symm (and-elim @x65 (= ?v0!1 0)) (= 0 ?v0!1)) @x68 (= 0 ?v1!0)))) -(mp (trans @x70 @x67 (= 0 1)) (rewrite (= (= 0 1) false)) false)))))))))))))))) - -67d24fd230a14f7ae0f516e21c1c266eaa6a1dee 55 0 -unsat -((set-logic AUFLIA) -(proof -(let (($x35 (exists ((?v0 Int) )(! (forall ((?v1 Int) )(! (let (($x31 (<= 0 ?v1))) -(let (($x30 (< ?v1 0))) -(let (($x32 (or $x30 $x31))) -(let (($x29 (< ?v0 ?v1))) -(=> $x29 $x32))))) :qid k!4)) - :qid k!4)) -)) -(let (($x36 (not $x35))) -(let (($x45 (exists ((?v0 Int) )(! (forall ((?v1 Int) )(! (let (($x31 (<= 0 ?v1))) -(let (($x30 (< ?v1 0))) -(let (($x32 (or $x30 $x31))) -(let (($x29 (< ?v0 ?v1))) -(let (($x38 (not $x29))) -(or $x38 $x32)))))) :qid k!4)) - :qid k!4)) -)) -(let (($x48 (not $x45))) -(let (($x88 (exists ((?v0 Int) )(! true :qid k!4)) -)) -(let (($x42 (forall ((?v1 Int) )(! (let (($x31 (<= 0 ?v1))) -(let (($x30 (< ?v1 0))) -(let (($x32 (or $x30 $x31))) -(let (($x29 (< ?0 ?v1))) -(let (($x38 (not $x29))) -(or $x38 $x32)))))) :qid k!4)) -)) -(let (($x81 (forall ((?v1 Int) )(! true :qid k!4)) -)) -(let (($x31 (<= 0 ?0))) -(let (($x30 (< ?0 0))) -(let (($x32 (or $x30 $x31))) -(let (($x29 (< ?1 ?0))) -(let (($x38 (not $x29))) -(let (($x39 (or $x38 $x32))) -(let (($x60 (<= (+ ?0 (* (- 1) ?1)) 0))) -(let ((@x78 (rewrite (= (or $x60 (or (not (>= ?0 0)) (>= ?0 0))) true)))) -(let ((@x73 (monotonicity (rewrite (= $x30 (not (>= ?0 0)))) (rewrite (= $x31 (>= ?0 0))) (= $x32 (or (not (>= ?0 0)) (>= ?0 0)))))) -(let ((@x66 (monotonicity (rewrite (= $x29 (not $x60))) (= $x38 (not (not $x60)))))) -(let ((@x76 (monotonicity (trans @x66 (rewrite (= (not (not $x60)) $x60)) (= $x38 $x60)) @x73 (= $x39 (or $x60 (or (not (>= ?0 0)) (>= ?0 0))))))) -(let ((@x87 (trans (quant-intro (trans @x76 @x78 (= $x39 true)) (= $x42 $x81)) (elim-unused (= $x81 true)) (= $x42 true)))) -(let ((@x94 (trans (quant-intro @x87 (= $x45 $x88)) (elim-unused (= $x88 true)) (= $x45 true)))) -(let ((@x101 (trans (monotonicity @x94 (= $x48 (not true))) (rewrite (= (not true) false)) (= $x48 false)))) -(let (($x34 (forall ((?v1 Int) )(! (let (($x31 (<= 0 ?v1))) -(let (($x30 (< ?v1 0))) -(let (($x32 (or $x30 $x31))) -(let (($x29 (< ?0 ?v1))) -(=> $x29 $x32))))) :qid k!4)) -)) -(let ((@x47 (quant-intro (quant-intro (rewrite (= (=> $x29 $x32) $x39)) (= $x34 $x42)) (= $x35 $x45)))) -(let ((@x50 (monotonicity @x47 (= $x36 $x48)))) -(mp (asserted $x36) (trans @x50 @x101 (= $x36 false)) false))))))))))))))))))))))))))) - -9b33558f7e3d33274980f3cf1408c789ce3fe411 42 0 -unsat -((set-logic AUFLIA) -(proof -(let (($x37 (forall ((?v0 Int) (?v1 Int) )(! (let ((?x34 (* 2 ?v1))) -(let ((?x31 (* 2 ?v0))) -(let ((?x33 (+ ?x31 1))) -(let (($x35 (< ?x33 ?x34))) -(let (($x29 (< ?v0 ?v1))) -(=> $x29 $x35)))))) :qid k!4)) -)) -(let (($x38 (not $x37))) -(let (($x55 (forall ((?v0 Int) (?v1 Int) )(! (let ((?x34 (* 2 ?v1))) -(let ((?x31 (* 2 ?v0))) -(let ((?x40 (+ 1 ?x31))) -(let (($x43 (< ?x40 ?x34))) -(let (($x29 (< ?v0 ?v1))) -(let (($x49 (not $x29))) -(or $x49 $x43))))))) :qid k!4)) -)) -(let (($x58 (not $x55))) -(let (($x84 (forall ((?v0 Int) (?v1 Int) )(! true :qid k!4)) -)) -(let ((?x34 (* 2 ?0))) -(let ((?x31 (* 2 ?1))) -(let ((?x40 (+ 1 ?x31))) -(let (($x43 (< ?x40 ?x34))) -(let (($x29 (< ?1 ?0))) -(let (($x49 (not $x29))) -(let (($x50 (or $x49 $x43))) -(let (($x63 (>= (+ ?1 (* (- 1) ?0)) 0))) -(let (($x62 (not $x63))) -(let ((@x74 (trans (monotonicity (rewrite (= $x29 $x62)) (= $x49 (not $x62))) (rewrite (= (not $x62) $x63)) (= $x49 $x63)))) -(let ((@x79 (monotonicity @x74 (rewrite (= $x43 $x62)) (= $x50 (or $x63 $x62))))) -(let ((@x86 (quant-intro (trans @x79 (rewrite (= (or $x63 $x62) true)) (= $x50 true)) (= $x55 $x84)))) -(let ((@x93 (monotonicity (trans @x86 (elim-unused (= $x84 true)) (= $x55 true)) (= $x58 (not true))))) -(let ((@x97 (trans @x93 (rewrite (= (not true) false)) (= $x58 false)))) -(let ((@x45 (monotonicity (rewrite (= (+ ?x31 1) ?x40)) (= (< (+ ?x31 1) ?x34) $x43)))) -(let ((@x48 (monotonicity @x45 (= (=> $x29 (< (+ ?x31 1) ?x34)) (=> $x29 $x43))))) -(let ((@x54 (trans @x48 (rewrite (= (=> $x29 $x43) $x50)) (= (=> $x29 (< (+ ?x31 1) ?x34)) $x50)))) -(let ((@x60 (monotonicity (quant-intro @x54 (= $x37 $x55)) (= $x38 $x58)))) -(mp (asserted $x38) (trans @x60 @x97 (= $x38 false)) false)))))))))))))))))))))))))) - -c91b2faa74b6f14adc03f118d0ebf326186d3e82 32 0 -unsat -((set-logic AUFLIA) -(proof -(let (($x36 (forall ((?v0 Int) (?v1 Int) )(! (let ((?x33 (* 2 ?v1))) -(let ((?x30 (* 2 ?v0))) -(let ((?x32 (+ ?x30 1))) -(let (($x34 (= ?x32 ?x33))) -(not $x34))))) :qid k!4)) -)) -(let (($x37 (not $x36))) -(let (($x48 (forall ((?v0 Int) (?v1 Int) )(! (let ((?x33 (* 2 ?v1))) -(let ((?x30 (* 2 ?v0))) -(let ((?x39 (+ 1 ?x30))) -(let (($x42 (= ?x39 ?x33))) -(not $x42))))) :qid k!4)) -)) -(let (($x51 (not $x48))) -(let (($x63 (forall ((?v0 Int) (?v1 Int) )(! true :qid k!4)) -)) -(let ((?x33 (* 2 ?0))) -(let ((?x30 (* 2 ?1))) -(let ((?x39 (+ 1 ?x30))) -(let (($x42 (= ?x39 ?x33))) -(let (($x45 (not $x42))) -(let ((@x62 (trans (monotonicity (rewrite (= $x42 false)) (= $x45 (not false))) (rewrite (= (not false) true)) (= $x45 true)))) -(let ((@x69 (trans (quant-intro @x62 (= $x48 $x63)) (elim-unused (= $x63 true)) (= $x48 true)))) -(let ((@x76 (trans (monotonicity @x69 (= $x51 (not true))) (rewrite (= (not true) false)) (= $x51 false)))) -(let ((@x44 (monotonicity (rewrite (= (+ ?x30 1) ?x39)) (= (= (+ ?x30 1) ?x33) $x42)))) -(let ((@x50 (quant-intro (monotonicity @x44 (= (not (= (+ ?x30 1) ?x33)) $x45)) (= $x36 $x48)))) -(let ((@x53 (monotonicity @x50 (= $x37 $x51)))) -(mp (asserted $x37) (trans @x53 @x76 (= $x37 false)) false))))))))))))))))))) - -5e6af334bdbf0a7d43561ad8b7c602bb6c3adb5b 43 0 -unsat -((set-logic AUFLIA) -(declare-fun ?v0!1 () Int) -(declare-fun ?v1!0 () Int) -(proof -(let ((?x78 (+ ?v1!0 ?v0!1))) -(let (($x90 (>= ?x78 2))) -(let (($x93 (not $x90))) -(let (($x87 (= ?x78 2))) -(let (($x81 (<= ?x78 2))) -(let (($x84 (not $x81))) -(let (($x73 (or (not (<= (+ ?v0!1 ?v1!0) 2)) (= (+ ?v0!1 ?v1!0) 2) (not (>= (+ ?v0!1 ?v1!0) 2))))) -(let (($x74 (not $x73))) -(let ((@x80 (rewrite (= (+ ?v0!1 ?v1!0) ?x78)))) -(let ((@x95 (monotonicity (monotonicity @x80 (= (>= (+ ?v0!1 ?v1!0) 2) $x90)) (= (not (>= (+ ?v0!1 ?v1!0) 2)) $x93)))) -(let ((@x86 (monotonicity (monotonicity @x80 (= (<= (+ ?v0!1 ?v1!0) 2) $x81)) (= (not (<= (+ ?v0!1 ?v1!0) 2)) $x84)))) -(let ((@x98 (monotonicity @x86 (monotonicity @x80 (= (= (+ ?v0!1 ?v1!0) 2) $x87)) @x95 (= $x73 (or $x84 $x87 $x93))))) -(let (($x60 (forall ((?v0 Int) (?v1 Int) )(! (let (($x41 (not (>= (+ ?v0 ?v1) 2)))) -(let ((?x30 (+ ?v0 ?v1))) -(let (($x32 (= ?x30 2))) -(let (($x46 (not (<= ?x30 2)))) -(or $x46 $x32 $x41))))) :qid k!4)) -)) -(let (($x63 (not $x60))) -(let (($x36 (forall ((?v0 Int) (?v1 Int) )(! (or (< 2 (+ ?v0 ?v1)) (or (= (+ ?v0 ?v1) 2) (< (+ ?v0 ?v1) 2))) :qid k!4)) -)) -(let (($x37 (not $x36))) -(let (($x41 (not (>= (+ ?1 ?0) 2)))) -(let ((?x30 (+ ?1 ?0))) -(let (($x32 (= ?x30 2))) -(let (($x46 (not (<= ?x30 2)))) -(let (($x55 (or $x46 $x32 $x41))) -(let (($x35 (or (< 2 ?x30) (or $x32 (< ?x30 2))))) -(let ((@x51 (monotonicity (rewrite (= (< ?x30 2) $x41)) (= (or $x32 (< ?x30 2)) (or $x32 $x41))))) -(let ((@x54 (monotonicity (rewrite (= (< 2 ?x30) $x46)) @x51 (= $x35 (or $x46 (or $x32 $x41)))))) -(let ((@x59 (trans @x54 (rewrite (= (or $x46 (or $x32 $x41)) $x55)) (= $x35 $x55)))) -(let ((@x66 (mp (asserted $x37) (monotonicity (quant-intro @x59 (= $x36 $x60)) (= $x37 $x63)) $x63))) -(let ((@x102 (mp (mp~ @x66 (sk (~ $x63 $x74)) $x74) (monotonicity @x98 (= $x74 (not (or $x84 $x87 $x93)))) (not (or $x84 $x87 $x93))))) -(let ((@x105 (not-or-elim @x102 (not $x87)))) -(let ((@x106 (not-or-elim @x102 $x90))) -(let ((@x103 (not-or-elim @x102 $x81))) -(unit-resolution (unit-resolution ((_ th-lemma arith triangle-eq) (or $x87 $x84 $x93)) @x103 (or $x87 $x93)) @x106 @x105 false))))))))))))))))))))))))))))))))) - -225395f9fe2308e0df959c87e4b0367c509ed3da 46 0 -unsat -((set-logic AUFLIA) -(declare-fun ?v0!0 () Int) -(proof -(let (($x86 (<= ?v0!0 (- 1)))) -(let (($x87 (not $x86))) -(let (($x84 (>= ?v0!0 1))) -(let (($x83 (<= ?v0!0 0))) -(let (($x93 (not $x83))) -(let (($x85 (not $x84))) -(let (($x88 (ite $x83 $x85 $x87))) -(let (($x89 (not $x88))) -(let (($x73 (forall ((?v0 Int) )(! (let (($x58 (not (<= ?v0 (- 1))))) -(let (($x61 (not (>= ?v0 1)))) -(ite (<= ?v0 0) $x61 $x58))) :qid k!4)) -)) -(let (($x76 (not $x73))) -(let (($x34 (forall ((?v0 Int) )(! (let (($x32 (< ?v0 1))) -(let (($x28 (< 0 ?v0))) -(ite $x28 (< 0 (+ ?v0 1)) $x32))) :qid k!4)) -)) -(let (($x35 (not $x34))) -(let (($x46 (forall ((?v0 Int) )(! (let (($x32 (< ?v0 1))) -(let (($x40 (< 0 (+ 1 ?v0)))) -(let (($x28 (< 0 ?v0))) -(ite $x28 $x40 $x32)))) :qid k!4)) -)) -(let (($x58 (not (<= ?0 (- 1))))) -(let (($x61 (not (>= ?0 1)))) -(let (($x68 (ite (<= ?0 0) $x61 $x58))) -(let (($x32 (< ?0 1))) -(let (($x40 (< 0 (+ 1 ?0)))) -(let (($x28 (< 0 ?0))) -(let (($x43 (ite $x28 $x40 $x32))) -(let ((@x67 (monotonicity (rewrite (= $x28 (not (<= ?0 0)))) (rewrite (= $x40 $x58)) (rewrite (= $x32 $x61)) (= $x43 (ite (not (<= ?0 0)) $x58 $x61))))) -(let ((@x72 (trans @x67 (rewrite (= (ite (not (<= ?0 0)) $x58 $x61) $x68)) (= $x43 $x68)))) -(let ((@x78 (monotonicity (quant-intro @x72 (= $x46 $x73)) (= (not $x46) $x76)))) -(let ((@x42 (monotonicity (rewrite (= (+ ?0 1) (+ 1 ?0))) (= (< 0 (+ ?0 1)) $x40)))) -(let ((@x45 (monotonicity @x42 (= (ite $x28 (< 0 (+ ?0 1)) $x32) $x43)))) -(let ((@x51 (monotonicity (quant-intro @x45 (= $x34 $x46)) (= $x35 (not $x46))))) -(let ((@x92 (mp~ (mp (asserted $x35) (trans @x51 @x78 (= $x35 $x76)) $x76) (sk (~ $x76 $x89)) $x89))) -(let ((@x105 (unit-resolution (unit-resolution (def-axiom (or $x88 $x93 $x84)) @x92 (or $x93 $x84)) (hypothesis $x85) $x93))) -(let ((@x108 (unit-resolution ((_ th-lemma arith farkas 1 1) (or $x83 $x84)) @x105 (hypothesis $x85) false))) -(let ((@x109 (lemma @x108 $x84))) -(unit-resolution (unit-resolution (def-axiom (or $x88 $x83 $x86)) @x92 (or $x83 $x86)) (unit-resolution ((_ th-lemma arith farkas 1 1) (or $x93 $x85)) @x109 $x93) (unit-resolution ((_ th-lemma arith farkas 1 1) (or $x87 $x85)) @x109 $x87) false))))))))))))))))))))))))))))))))) - -588d2c3e5f2a3b0948546d186f05535d11e37c8d 31 0 -unsat -((set-logic AUFLIA) -(proof -(let (($x56 (forall ((?v0 Int) )(! (let (($x50 (not (<= ?v0 0)))) -(let (($x45 (not (>= ?v0 0)))) -(or $x45 $x50))) :qid k!4)) -)) -(let (($x458 (not $x56))) -(let (($x153 (<= 0 0))) -(let (($x68 (not $x153))) -(let (($x158 (>= 0 0))) -(let (($x143 (not $x158))) -(let (($x154 (or $x143 $x68))) -(let (($x119 (or $x458 $x154))) -(let ((@x137 (trans (monotonicity (rewrite (= $x153 true)) (= $x68 (not true))) (rewrite (= (not true) false)) (= $x68 false)))) -(let ((@x261 (trans (monotonicity (rewrite (= $x158 true)) (= $x143 (not true))) (rewrite (= (not true) false)) (= $x143 false)))) -(let ((@x116 (trans (monotonicity @x261 @x137 (= $x154 (or false false))) (rewrite (= (or false false) false)) (= $x154 false)))) -(let ((@x463 (trans (monotonicity @x116 (= $x119 (or $x458 false))) (rewrite (= (or $x458 false) $x458)) (= $x119 $x458)))) -(let ((@x464 (mp ((_ quant-inst 0) $x119) @x463 $x458))) -(let (($x50 (not (<= ?0 0)))) -(let (($x45 (not (>= ?0 0)))) -(let (($x53 (or $x45 $x50))) -(let (($x31 (forall ((?v0 Int) )(! (or (< ?v0 0) (< 0 ?v0)) :qid k!4)) -)) -(let (($x33 (not (ite $x31 false true)))) -(let ((@x55 (monotonicity (rewrite (= (< ?0 0) $x45)) (rewrite (= (< 0 ?0) $x50)) (= (or (< ?0 0) (< 0 ?0)) $x53)))) -(let ((@x40 (monotonicity (rewrite (= (ite $x31 false true) (not $x31))) (= $x33 (not (not $x31)))))) -(let ((@x60 (trans (trans @x40 (rewrite (= (not (not $x31)) $x31)) (= $x33 $x31)) (quant-intro @x55 (= $x31 $x56)) (= $x33 $x56)))) -(let ((@x66 (mp~ (mp (asserted $x33) @x60 $x56) (nnf-pos (refl (~ $x53 $x53)) (~ $x56 $x56)) $x56))) -(unit-resolution @x66 @x464 false))))))))))))))))))))))))) - -c3173310bcd1c740d9eae3d871d668c6d70c7e74 62 0 -unsat -((set-logic AUFLIA) -(declare-fun ?v0!1 () Int) -(declare-fun z3name!0 () Bool) -(proof -(let ((?x96 (ite z3name!0 (- 1) 3))) -(let (($x99 (<= ?x96 0))) -(let (($x62 (forall ((?v0 Int) )(! (let (($x56 (not (<= ?v0 0)))) -(let (($x51 (not (>= ?v0 0)))) -(or $x51 $x56))) :qid k!4)) -)) -(let ((?x65 (ite $x62 (- 1) 3))) -(let (($x71 (<= ?x65 0))) -(let ((@x93 (intro-def (and (or (not z3name!0) $x62) (or z3name!0 (not $x62)))))) -(let ((@x101 (monotonicity (monotonicity (apply-def @x93 (~ $x62 z3name!0)) (= ?x65 ?x96)) (= $x71 $x99)))) -(let (($x31 (forall ((?v0 Int) )(! (or (< ?v0 0) (< 0 ?v0)) :qid k!4)) -)) -(let (($x37 (not (< 0 (ite $x31 (- 1) 3))))) -(let (($x56 (not (<= ?0 0)))) -(let (($x51 (not (>= ?0 0)))) -(let (($x59 (or $x51 $x56))) -(let ((@x61 (monotonicity (rewrite (= (< ?0 0) $x51)) (rewrite (= (< 0 ?0) $x56)) (= (or (< ?0 0) (< 0 ?0)) $x59)))) -(let ((@x67 (monotonicity (quant-intro @x61 (= $x31 $x62)) (= (ite $x31 (- 1) 3) ?x65)))) -(let ((@x70 (monotonicity @x67 (= (< 0 (ite $x31 (- 1) 3)) (< 0 ?x65))))) -(let ((@x76 (trans @x70 (rewrite (= (< 0 ?x65) (not $x71))) (= (< 0 (ite $x31 (- 1) 3)) (not $x71))))) -(let ((@x79 (monotonicity @x76 (= (not (< 0 (ite $x31 (- 1) 3))) (not (not $x71)))))) -(let ((@x83 (trans @x79 (rewrite (= (not (not $x71)) $x71)) (= (not (< 0 (ite $x31 (- 1) 3))) $x71)))) -(let ((?x42 (ite $x31 (- 1) 3))) -(let (($x45 (< 0 ?x42))) -(let ((@x44 (monotonicity (rewrite (= (- 1) (- 1))) (= (ite $x31 (- 1) 3) ?x42)))) -(let ((@x50 (monotonicity (monotonicity @x44 (= (< 0 (ite $x31 (- 1) 3)) $x45)) (= $x37 (not $x45))))) -(let ((@x128 (mp (mp (asserted $x37) (trans @x50 @x83 (= $x37 $x71)) $x71) @x101 $x99))) -(let ((@x245 (unit-resolution ((_ th-lemma arith farkas 1 1) (or (not (>= ?x96 3)) (not $x99))) @x128 (not (>= ?x96 3))))) -(let (($x220 (= ?x96 3))) -(let (($x88 (not z3name!0))) -(let (($x90 (not $x62))) -(let (($x323 (<= 0 0))) -(let (($x533 (not $x323))) -(let (($x542 (>= 0 0))) -(let (($x179 (not $x542))) -(let (($x206 (or $x179 $x533))) -(let (($x529 (or $x90 $x206))) -(let ((@x527 (trans (monotonicity (rewrite (= $x323 true)) (= $x533 (not true))) (rewrite (= (not true) false)) (= $x533 false)))) -(let ((@x200 (trans (monotonicity (rewrite (= $x542 true)) (= $x179 (not true))) (rewrite (= (not true) false)) (= $x179 false)))) -(let ((@x528 (trans (monotonicity @x200 @x527 (= $x206 (or false false))) (rewrite (= (or false false) false)) (= $x206 false)))) -(let ((@x237 (trans (monotonicity @x528 (= $x529 (or $x90 false))) (rewrite (= (or $x90 false) $x90)) (= $x529 $x90)))) -(let ((@x238 (mp ((_ quant-inst 0) $x529) @x237 $x90))) -(let (($x89 (or $x88 $x62))) -(let (($x115 (<= ?v0!1 0))) -(let (($x116 (not $x115))) -(let (($x113 (>= ?v0!1 0))) -(let (($x114 (not $x113))) -(let (($x117 (or $x114 $x116))) -(let (($x118 (not $x117))) -(let (($x121 (or z3name!0 $x118))) -(let ((@x123 (monotonicity (refl (~ z3name!0 z3name!0)) (sk (~ $x90 $x118)) (~ (or z3name!0 $x90) $x121)))) -(let ((@x109 (monotonicity (refl (~ $x88 $x88)) (nnf-pos (refl (~ $x59 $x59)) (~ $x62 $x62)) (~ $x89 $x89)))) -(let ((@x126 (monotonicity @x109 @x123 (~ (and $x89 (or z3name!0 $x90)) (and $x89 $x121))))) -(let ((@x131 (and-elim (mp~ @x93 @x126 (and $x89 $x121)) $x89))) -(let ((@x515 (unit-resolution (def-axiom (or z3name!0 $x220)) (unit-resolution @x131 @x238 $x88) $x220))) -(unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x220) (>= ?x96 3))) @x515 @x245 false)))))))))))))))))))))))))))))))))))))))))))))))))))))) - -774e453e6283d3bbc1a31f77b233e45c4351f009 39 0 -unsat -((set-logic AUFLIA) -(proof -(let (($x38 (exists ((?v0 Int) (?v1 Int) (?v2 Int) )(! (let ((?x33 (- 6))) -(let ((?x34 (* ?x33 ?v1))) -(let ((?x31 (* 4 ?v0))) -(let ((?x35 (+ ?x31 ?x34))) -(= ?x35 1))))) :qid k!4)) -)) -(let (($x29 (not $x38))) -(let (($x39 (not $x29))) -(let (($x61 (exists ((?v0 Int) (?v1 Int) )(! (let ((?x58 (* (- 6) ?v1))) -(let ((?x57 (* 4 ?v0))) -(let ((?x59 (+ ?x57 ?x58))) -(= ?x59 1)))) :qid k!4)) -)) -(let (($x77 (exists ((?v0 Int) (?v1 Int) )(! false :qid k!4)) -)) -(let ((@x81 (quant-intro (rewrite (= (= (+ (* 4 ?1) (* (- 6) ?0)) 1) false)) (= $x61 $x77)))) -(let ((@x85 (trans @x81 (elim-unused (= $x77 false)) (= $x61 false)))) -(let (($x53 (exists ((?v0 Int) (?v1 Int) (?v2 Int) )(! 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(or (< 0 ?v1) (< ?v1 1)) :qid k!4)) -)) -(let (($x32 (or (< 0 ?0) (< ?0 1)))) -(let ((@x51 (monotonicity (rewrite (= (< 0 ?0) (not (<= ?0 0)))) (rewrite (= (< ?0 1) (not (>= ?0 1)))) (= $x32 (or (not (<= ?0 0)) (not (>= ?0 1))))))) -(let ((@x57 (monotonicity (quant-intro @x51 (= $x35 $x52)) (= (not $x35) $x55)))) -(let ((@x59 (trans (monotonicity (elim-unused (= $x33 $x35)) (= $x27 (not $x35))) @x57 (= $x27 $x55)))) -(let ((@x70 (mp~ (mp (asserted $x27) @x59 $x55) (sk (~ $x55 (not (or (not (<= ?v1!0 0)) (not $x64))))) (not (or (not (<= ?v1!0 0)) (not $x64)))))) -(let ((@x74 (not-or-elim @x70 $x64))) -(let (($x62 (<= ?v1!0 0))) -(let ((@x73 (not-or-elim @x70 $x62))) -(unit-resolution ((_ th-lemma arith farkas 1 1) (or (not $x62) (not $x64))) @x73 @x74 false))))))))))))))))) - -1ce41c6c9b94498d7f0910606954c5a3eb9e79cc 26 0 -unsat -((set-logic ) -(proof -(let (($x58 (<= b$ 0))) -(let (($x62 (or (not (and (not (<= a$ 0)) (not (<= (* a$ b$) 0)))) (not $x58)))) -(let (($x65 (not $x62))) -(let (($x35 (not (=> (and (< 0 a$) (< 0 (* a$ b$))) (< 0 b$))))) -(let (($x33 (< 0 b$))) -(let (($x38 (or (not (and (< 0 a$) (< 0 (* a$ b$)))) $x33))) -(let (($x56 (= (not (and (< 0 a$) (< 0 (* a$ b$)))) (not (and (not (<= a$ 0)) (not (<= (* a$ b$) 0))))))) -(let ((?x30 (* a$ b$))) -(let (($x48 (<= ?x30 0))) -(let (($x49 (not $x48))) -(let (($x44 (<= a$ 0))) -(let (($x45 (not $x44))) -(let (($x52 (and $x45 $x49))) -(let (($x32 (and (< 0 a$) (< 0 ?x30)))) -(let ((@x54 (monotonicity (rewrite (= (< 0 a$) $x45)) (rewrite (= (< 0 ?x30) $x49)) (= $x32 $x52)))) -(let ((@x64 (monotonicity (monotonicity @x54 $x56) (rewrite (= $x33 (not $x58))) (= $x38 $x62)))) -(let ((@x43 (monotonicity (rewrite (= (=> $x32 $x33) $x38)) (= $x35 (not $x38))))) -(let ((@x69 (trans @x43 (monotonicity @x64 (= (not $x38) $x65)) (= $x35 $x65)))) -(let ((@x74 (not-or-elim (mp (asserted $x35) @x69 $x65) $x58))) -(let ((@x72 (and-elim (not-or-elim (mp (asserted $x35) @x69 $x65) $x52) $x45))) -(let ((@x73 (and-elim (not-or-elim (mp (asserted $x35) @x69 $x65) $x52) $x49))) -((_ th-lemma arith farkas 1 1 1) @x73 @x72 @x74 false)))))))))))))))))))))))) - -120e7571f7a3d5bdf7efb7d07b2863a6d193cfc4 26 0 -unsat -((set-logic ) -(proof -(let ((?x35 (+ y$ 1))) -(let ((?x36 (* a$ ?x35))) -(let ((?x34 (* a$ x$))) -(let ((?x37 (+ ?x34 ?x36))) -(let ((?x30 (+ x$ 1))) -(let ((?x32 (+ ?x30 y$))) -(let ((?x33 (* a$ ?x32))) -(let (($x38 (= ?x33 ?x37))) -(let (($x39 (not $x38))) -(let (($x82 (= (= (+ a$ ?x34 (* a$ y$)) (+ a$ ?x34 (* a$ y$))) true))) -(let (($x80 (= $x38 (= (+ a$ ?x34 (* a$ y$)) (+ a$ ?x34 (* a$ y$)))))) -(let ((@x76 (rewrite (= (+ ?x34 (+ a$ (* a$ y$))) (+ a$ ?x34 (* a$ y$)))))) -(let ((@x66 (monotonicity (rewrite (= ?x35 (+ 1 y$))) (= ?x36 (* a$ (+ 1 y$)))))) -(let ((@x71 (trans @x66 (rewrite (= (* a$ (+ 1 y$)) (+ a$ (* a$ y$)))) (= ?x36 (+ a$ (* a$ y$)))))) -(let ((@x78 (trans (monotonicity @x71 (= ?x37 (+ ?x34 (+ a$ (* a$ y$))))) @x76 (= ?x37 (+ a$ ?x34 (* a$ y$)))))) -(let ((@x58 (rewrite (= (* a$ (+ 1 x$ y$)) (+ a$ ?x34 (* a$ y$)))))) -(let ((@x46 (monotonicity (rewrite (= ?x30 (+ 1 x$))) (= ?x32 (+ (+ 1 x$) y$))))) -(let ((@x51 (trans @x46 (rewrite (= (+ (+ 1 x$) y$) (+ 1 x$ y$))) (= ?x32 (+ 1 x$ y$))))) -(let ((@x60 (trans (monotonicity @x51 (= ?x33 (* a$ (+ 1 x$ y$)))) @x58 (= ?x33 (+ a$ ?x34 (* a$ y$)))))) -(let ((@x88 (monotonicity (trans (monotonicity @x60 @x78 $x80) (rewrite $x82) (= $x38 true)) (= $x39 (not true))))) -(let ((@x92 (trans @x88 (rewrite (= (not true) false)) (= $x39 false)))) -(mp (asserted $x39) @x92 false)))))))))))))))))))))))) - -9643a0be0523c30ccea2649b7d41baba98b9e1c7 23 0 -unsat -((set-logic ) -(proof -(let ((?x36 (* 2.0 x$))) -(let ((?x37 (* ?x36 y$))) -(let ((?x32 (- 1.0 y$))) -(let ((?x33 (* x$ ?x32))) -(let ((?x30 (+ 1.0 y$))) -(let ((?x31 (* x$ ?x30))) -(let ((?x34 (- ?x31 ?x33))) -(let (($x38 (= ?x34 ?x37))) -(let (($x39 (not $x38))) -(let ((@x73 (rewrite (= (= (* 2.0 (* x$ y$)) (* 2.0 (* x$ y$))) true)))) -(let ((?x41 (* x$ y$))) -(let ((?x63 (* 2.0 ?x41))) -(let ((@x56 (rewrite (= (* x$ (+ 1.0 (* (- 1.0) y$))) (+ x$ (* (- 1.0) ?x41)))))) -(let ((@x52 (monotonicity (rewrite (= ?x32 (+ 1.0 (* (- 1.0) y$)))) (= ?x33 (* x$ (+ 1.0 (* (- 1.0) y$))))))) -(let ((@x61 (monotonicity (rewrite (= ?x31 (+ x$ ?x41))) (trans @x52 @x56 (= ?x33 (+ x$ (* (- 1.0) ?x41)))) (= ?x34 (- (+ x$ ?x41) (+ x$ (* (- 1.0) ?x41))))))) -(let ((@x66 (trans @x61 (rewrite (= (- (+ x$ ?x41) (+ x$ (* (- 1.0) ?x41))) ?x63)) (= ?x34 ?x63)))) -(let ((@x75 (trans (monotonicity @x66 (rewrite (= ?x37 ?x63)) (= $x38 (= ?x63 ?x63))) @x73 (= $x38 true)))) -(let ((@x82 (trans (monotonicity @x75 (= $x39 (not true))) (rewrite (= (not true) false)) (= $x39 false)))) -(mp (asserted $x39) @x82 false))))))))))))))))))))) - -cf35af4ec81d7dbaa379643034cb419106fa4ff8 51 0 -unsat -((set-logic ) -(proof -(let ((?x47 (+ b$ d$))) -(let ((?x48 (+ ?x47 e$))) -(let ((?x30 (+ 1 p$))) -(let ((?x49 (* ?x30 ?x48))) -(let ((?x44 (* d$ p$))) -(let ((?x42 (* ?x30 d$))) -(let ((?x33 (+ b$ e$))) -(let ((?x40 (* 2 ?x30))) -(let ((?x41 (* ?x40 ?x33))) -(let ((?x43 (+ ?x41 ?x42))) -(let ((?x45 (+ ?x43 ?x44))) -(let ((?x46 (+ u$ ?x45))) -(let ((?x50 (- ?x46 ?x49))) -(let ((?x37 (* p$ d$))) -(let ((?x34 (* ?x30 ?x33))) -(let ((?x35 (+ u$ ?x34))) -(let ((?x38 (+ ?x35 ?x37))) -(let (($x51 (= ?x38 ?x50))) -(let (($x52 (not $x51))) -(let ((?x55 (* p$ e$))) -(let ((?x54 (* p$ b$))) -(let ((?x70 (+ u$ b$ e$ ?x37 ?x54 ?x55))) -(let ((?x127 (+ b$ e$ d$ ?x37 ?x54 ?x55))) -(let ((?x85 (* 2 ?x55))) -(let ((?x83 (* 2 ?x54))) -(let ((?x84 (* 2 e$))) -(let ((?x82 (* 2 b$))) -(let ((?x116 (+ u$ ?x82 ?x84 d$ (* 2 ?x37) ?x83 ?x85))) -(let ((@x126 (monotonicity (rewrite (= ?x48 (+ b$ e$ d$))) (= ?x49 (* ?x30 (+ b$ e$ d$)))))) -(let ((@x131 (trans @x126 (rewrite (= (* ?x30 (+ b$ e$ d$)) ?x127)) (= ?x49 ?x127)))) -(let ((@x118 (rewrite (= (+ u$ (+ ?x82 ?x84 d$ (* 2 ?x37) ?x83 ?x85)) ?x116)))) -(let ((?x108 (+ ?x82 ?x84 d$ (* 2 ?x37) ?x83 ?x85))) -(let ((?x97 (+ ?x82 ?x84 d$ ?x37 ?x83 ?x85))) -(let ((@x88 (rewrite (= (* (+ 2 (* 2 p$)) ?x33) (+ ?x82 ?x84 ?x83 ?x85))))) -(let ((@x81 (monotonicity (rewrite (= ?x40 (+ 2 (* 2 p$)))) (= ?x41 (* (+ 2 (* 2 p$)) ?x33))))) -(let ((@x96 (monotonicity (trans @x81 @x88 (= ?x41 (+ ?x82 ?x84 ?x83 ?x85))) (rewrite (= ?x42 (+ d$ ?x37))) (= ?x43 (+ (+ ?x82 ?x84 ?x83 ?x85) (+ d$ ?x37)))))) -(let ((@x101 (trans @x96 (rewrite (= (+ (+ ?x82 ?x84 ?x83 ?x85) (+ d$ ?x37)) ?x97)) (= ?x43 ?x97)))) -(let ((@x112 (trans (monotonicity @x101 (rewrite (= ?x44 ?x37)) (= ?x45 (+ ?x97 ?x37))) (rewrite (= (+ ?x97 ?x37) ?x108)) (= ?x45 ?x108)))) -(let ((@x120 (trans (monotonicity @x112 (= ?x46 (+ u$ ?x108))) @x118 (= ?x46 ?x116)))) -(let ((@x139 (trans (monotonicity @x120 @x131 (= ?x50 (- ?x116 ?x127))) (rewrite (= (- ?x116 ?x127) ?x70)) (= ?x50 ?x70)))) -(let ((@x64 (rewrite (= (+ u$ (+ b$ e$ ?x54 ?x55)) (+ u$ b$ e$ ?x54 ?x55))))) -(let ((@x61 (monotonicity (rewrite (= ?x34 (+ b$ e$ ?x54 ?x55))) (= ?x35 (+ u$ (+ b$ e$ ?x54 ?x55)))))) -(let ((@x69 (monotonicity (trans @x61 @x64 (= ?x35 (+ u$ b$ e$ ?x54 ?x55))) (= ?x38 (+ (+ u$ b$ e$ ?x54 ?x55) ?x37))))) -(let ((@x74 (trans @x69 (rewrite (= (+ (+ u$ b$ e$ ?x54 ?x55) ?x37) ?x70)) (= ?x38 ?x70)))) -(let ((@x145 (trans (monotonicity @x74 @x139 (= $x51 (= ?x70 ?x70))) (rewrite (= (= ?x70 ?x70) true)) (= $x51 true)))) -(let ((@x152 (trans (monotonicity @x145 (= $x52 (not true))) (rewrite (= (not true) false)) (= $x52 false)))) -(mp (asserted $x52) @x152 false))))))))))))))))))))))))))))))))))))))))))))))))) - -1d394bb8e58206d50a13d379fbea25a1cbf1305d 12 0 -unsat -((set-logic AUFLIA) -(proof -(let ((@x39 (rewrite (= (= (* 2 (of_nat$ x$)) 1) false)))) -(let ((?x29 (of_nat$ x$))) -(let ((?x30 (* 2 ?x29))) -(let (($x32 (= ?x30 1))) -(let (($x33 (not $x32))) -(let (($x34 (not $x33))) -(let ((@x37 (rewrite (= $x34 $x32)))) -(mp (asserted $x34) (trans @x37 @x39 (= $x34 false)) false)))))))))) - -7e42c634f1307c931bb3205b7d29a61bf5cbb1dd 23 0 -unsat -((set-logic AUFLIA) -(proof -(let ((?x28 (of_nat$ a$))) -(let (($x57 (>= ?x28 4))) -(let (($x47 (>= ?x28 3))) -(let (($x61 (or $x47 (not $x57)))) -(let (($x64 (not $x61))) -(let ((@x51 (monotonicity (rewrite (= (< ?x28 3) (not $x47))) (= (not (< ?x28 3)) (not (not $x47)))))) -(let ((@x55 (trans @x51 (rewrite (= (not (not $x47)) $x47)) (= (not (< ?x28 3)) $x47)))) -(let ((@x63 (monotonicity @x55 (rewrite (= (< (* 2 ?x28) 7) (not $x57))) (= (or (not (< ?x28 3)) (< (* 2 ?x28) 7)) $x61)))) -(let ((@x66 (monotonicity @x63 (= (not (or (not (< ?x28 3)) (< (* 2 ?x28) 7))) $x64)))) -(let (($x36 (not (=> (< ?x28 3) (< (* 2 ?x28) 7))))) -(let (($x34 (< (* 2 ?x28) 7))) -(let (($x30 (< ?x28 3))) -(let (($x38 (not $x30))) -(let (($x39 (or $x38 $x34))) -(let ((@x44 (monotonicity (rewrite (= (=> $x30 $x34) $x39)) (= $x36 (not $x39))))) -(let ((@x71 (not-or-elim (mp (asserted $x36) (trans @x44 @x66 (= $x36 $x64)) $x64) $x57))) -(let (($x45 (not $x47))) -(let ((@x70 (not-or-elim (mp (asserted $x36) (trans @x44 @x66 (= $x36 $x64)) $x64) $x45))) -(unit-resolution ((_ th-lemma arith farkas 1 1) $x61) @x70 @x71 false))))))))))))))))))))) - -c9b8971d778e9001682f5b3a4e16c461840b29c5 22 0 +dbe03d888710bfc170c0322723b6fe3d138c2de7 22 0 unsat ((set-logic AUFLIA) (proof @@ -9543,7 +3455,7 @@ (let ((@x50 (monotonicity @x47 (= $x36 (not (< 0 (ite $x32 0 1))))))) (mp (asserted $x36) (trans @x50 @x73 (= $x36 false)) false)))))))))))))))))))) -cbf2808ec09a5b4982758153f97196673f93edba 37 0 +30cc2762602a7a30eb3ec186f081112e21381d17 37 0 unsat ((set-logic AUFLIA) (proof @@ -9581,7 +3493,7 @@ (let ((@x119 (not-or-elim (mp (asserted $x42) @x115 $x111) $x86))) (unit-resolution ((_ th-lemma arith farkas 1 1) (or (not $x86) (not $x91))) @x119 @x126 false))))))))))))))))))))))))))))))))))) -b06d43652b73c2768eef10e5038b2c417733fa71 64 0 +093b4bdc35e8040f16c5dca022c87a6f58a6b797 64 0 unsat ((set-logic AUFLIA) (proof @@ -9646,7 +3558,7 @@ (let ((@x526 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x229) $x237)) (unit-resolution (def-axiom (or $x76 $x229)) @x533 $x229) $x237))) ((_ th-lemma arith farkas 1 1 1) (unit-resolution @x545 (unit-resolution @x552 @x565 $x234) $x337) @x533 @x526 false)))))))))))))))))))))))))))))))))))))))))))))))))))))) -678cc460f8a4ff76257174915fd3463bc39fc2f5 264 0 +c03c5a5464afed237861dfdc891e37969d566ebb 264 0 unsat ((set-logic AUFLIA) (declare-fun ?v1!0 (Nat$) Nat$) @@ -9911,7 +3823,7 @@ (let ((@x133 (not-or-elim (mp (asserted $x96) @x129 $x125) (not (>= ?x89 1))))) ((_ th-lemma arith farkas -4 1 1) @x133 (unit-resolution (def-axiom (or $x683 $x668)) @x479 $x668) @x551 false)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -f6c311f26c2b2fcfdbba6a5ea33668ca436fbf9f 23 0 +60d94e0cd230c2f830228f101b7544d16a19dfd6 23 0 unsat ((set-logic AUFLIA) (proof @@ -9935,7 +3847,7 @@ (let ((@x54 (not-or-elim (mp (asserted (not (=> $x39 $x40))) @x50 (not (or (not $x39) $x40))) (not $x40)))) (unit-resolution @x54 @x150 false))))))))))))))))))) -197edb4480e92508ed0f53a2d22e3b77c6f0c371 42 0 +abc6aef55894d3d204d52d3df341120d4c77014e 42 0 unsat ((set-logic AUFLIA) (proof @@ -9978,7 +3890,7 @@ (let ((@x76 (not-or-elim (mp (asserted (not (=> $x57 $x60))) @x70 (not (or (not $x57) $x60))) (not $x60)))) (unit-resolution @x76 (trans @x489 @x504 $x60) false)))))))))))))))))))))))))))))))))))) -cc9c148ca28c075f5144e44f79eebd527c2d0a6e 51 0 +d251f21fb3589ab6ed61bce83e553bbcd5ee429c 51 0 unsat ((set-logic AUFLIA) (proof @@ -10030,7 +3942,7 @@ (let ((@x78 (not-or-elim (mp (asserted (not (=> $x54 $x62))) @x72 (not (or (not $x54) $x62))) (not $x62)))) (unit-resolution @x78 @x462 false))))))))))))))))))))))))))))))))))))))))))) -94f8dc0b729718a91a4b2c16a293ab5ccce66764 24 0 +481375169802669da2461e9c7ce3d0e407b7bc16 24 0 unsat ((set-logic AUFLIA) (proof @@ -10055,7 +3967,7 @@ (let ((@x80 (mp (not-or-elim @x70 (not $x44)) (rewrite (= (not $x44) $x77)) $x77))) (mp @x80 @x93 false)))))))))))))))))))))) -08613a28dc6a32b8391e714c444a61d28a9dfe5b 45 0 +847a42093e0c7ebac5b356b94c79945004bf96e9 45 0 unsat ((set-logic AUFLIA) (proof @@ -10101,7 +4013,7 @@ (let ((@x496 ((_ quant-inst x$) $x163))) (unit-resolution @x496 @x508 (unit-resolution @x84 (lemma @x495 $x47) $x73) false))))))))))))))))))))))))))))))))) -4f66483c86f0c5a32686585d9e938dbb7086da72 11 0 +7db89748bff125dc0b538776ae3b570548832266 11 0 unsat ((set-logic AUFLIA) (proof @@ -10113,7 +4025,7 @@ (let ((@x42 (trans (monotonicity (rewrite (= $x31 true)) (= $x32 (not true))) (rewrite (= (not true) false)) (= $x32 false)))) (mp (asserted $x32) @x42 false)))))))) -756c9cf46ff832b47dec2dc62b830e47ac31bac1 11 0 +f60c850fda8f88ddfddcac265e198fed2855c01b 11 0 unsat ((set-logic AUFLIA) (proof @@ -10125,7 +4037,7 @@ (let ((@x42 (trans (monotonicity (rewrite (= $x31 true)) (= $x32 (not true))) (rewrite (= (not true) false)) (= $x32 false)))) (mp (asserted $x32) @x42 false)))))))) -8ddba6affa2abbe3cf3994f41ccb915988ccdafd 46 0 +f9e10e513fd0588f5d6c281610f4889bb0668a34 46 0 unsat ((set-logic AUFLIA) (proof @@ -10172,7 +4084,7 @@ (let ((@x478 (mp ((_ quant-inst 3 42) (or (not $x52) $x171)) (trans (monotonicity @x131 $x137) (rewrite (= $x134 $x134)) $x137) $x134))) (unit-resolution (unit-resolution @x478 @x78 $x168) (mp @x77 @x472 (not $x168)) false))))))))))))))))))))))))))))))))))) -1a5b849ab8104f63cc08e8abf718c3988390afde 75 0 +88fa92ffd8ea964848bdbb197defe1efa7fdd2e7 75 0 unsat ((set-logic AUFLIA) (proof @@ -10248,7 +4160,7 @@ (let ((@x82 (asserted $x81))) (unit-resolution @x82 @x466 false)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -b4e508855de4e3fc04daa5e54a806efd9a7631e0 11 0 +f06072929c8d142e53379b87462f703ce8c8fca8 11 0 unsat ((set-logic AUFLIA) (proof @@ -10260,7 +4172,7 @@ (let ((@x42 (trans (monotonicity (rewrite (= $x31 true)) (= $x32 (not true))) (rewrite (= (not true) false)) (= $x32 false)))) (mp (asserted $x32) @x42 false)))))))) -4fd0a6f6e50e6e78d532ce03c828f7347a53b208 109 0 +c36d2d391586c8a6d1e6b8e7a73bd245b4c2def7 109 0 unsat ((set-logic AUFLIA) (proof @@ -10370,7 +4282,7 @@ (let ((@x81 (asserted $x80))) (unit-resolution @x81 (trans @x397 ((_ th-lemma arith eq-propagate 1 1 -4 -4) @x410 @x422 @x428 @x438 (= ?x490 6)) $x79) false))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -a09daf2232b40165a00a066ec5933156007bdafb 348 0 +703387d92be4ef7e4f1bc652b2328a3b33f53830 348 0 unsat ((set-logic ) (proof @@ -10719,7 +4631,7 @@ (let ((@x895 (unit-resolution ((_ th-lemma arith triangle-eq) (or $x117 $x807 (not $x673))) @x891 (or $x807 (not $x673))))) ((_ th-lemma arith farkas -2 -2 1 -1 1 1) (unit-resolution @x895 @x889 $x807) @x485 @x745 @x488 (unit-resolution ((_ th-lemma arith triangle-eq) (or $x134 $x679)) @x584 $x679) (unit-resolution ((_ th-lemma arith) (or false $x564)) @x26 $x564) false))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -d8a2ea999dd5c80012745e4f4f27b069ecc2aed2 64 0 +9c0ac00b9444829edc9751ffc537b6a41af5144b 64 0 unsat ((set-logic AUFLIA) (proof @@ -10784,7 +4696,7 @@ (let ((@x570 (mp ((_ quant-inst (sup$ ?x108) (sup$ ?x111) (sup$ ?x108)) (or $x251 (or $x160 $x247 $x117))) (rewrite (= (or $x251 (or $x160 $x247 $x117)) $x252)) $x252))) (unit-resolution @x570 @x584 @x114 @x116 @x119 false))))))))))))))))))))))))))))))))))))))) -6e9f5761c7179fbcc82d651f00cba7c8afa1e7bd 25 0 +3d46cc152552934c74a9b7e72f528acd2da80760 25 0 unsat ((set-logic AUFLIA) (proof @@ -10810,7 +4722,7 @@ (let ((@x258 ((_ quant-inst 1) $x257))) (unit-resolution @x258 @x620 @x145 false)))))))))))))))))) -8cb478278000a15878db9a263de25709c0d86abf 101 0 +83f2e868ac360af426c9844684088eb79f31b9ad 101 0 unsat ((set-logic AUFLIA) (proof diff -r 3fdb94d87e0e -r 3c5a7746ffa4 src/HOL/SMT_Examples/SMT_Examples_Verit.certs --- a/src/HOL/SMT_Examples/SMT_Examples_Verit.certs Fri Mar 05 15:01:59 2021 +0100 +++ b/src/HOL/SMT_Examples/SMT_Examples_Verit.certs Fri Mar 05 21:26:38 2021 +0100 @@ -1,21 +1,3 @@ -d4888d8ad473d347e6ab6d509244a7583a7babd4 17 0 -unsat -(assume a0 (! (not (! (= (! (and p$ true) :named @p_1) p$) :named @p_3)) :named @p_5)) -(step t2 (cl (= @p_1 (! (and p$) :named @p_2))) :rule and_simplify) -(step t3 (cl (= @p_2 p$)) :rule and_simplify) -(step t4 (cl @p_3) :rule trans :premises (t2 t3)) -(step t5 (cl (= @p_3 (! (= p$ p$) :named @p_4))) :rule cong :premises (t4)) -(step t6 (cl (= @p_4 true)) :rule equiv_simplify) -(step t7 (cl (= @p_3 true)) :rule trans :premises (t5 t6)) -(step t8 (cl (= @p_5 (! (not true) :named @p_6))) :rule cong :premises (t7)) -(step t9 (cl (= @p_6 false)) :rule not_simplify) -(step t10 (cl (! (= @p_5 false) :named @p_7)) :rule trans :premises (t8 t9)) -(step t11 (cl (! (not @p_7) :named @p_9) (! (not @p_5) :named @p_8) false) :rule equiv_pos2) -(step t12 (cl (not @p_8) @p_3) :rule not_not) -(step t13 (cl @p_9 @p_3 false) :rule th_resolution :premises (t12 t11)) -(step t14 (cl false) :rule th_resolution :premises (a0 t10 t13)) -(step t15 (cl (not false)) :rule false) -(step t16 (cl) :rule resolution :premises (t14 t15)) 95a654bfff554e647800fe77ff2ba30347402e24 9 0 unsat (assume a0 (! (not true) :named @p_1)) @@ -39,6 +21,40 @@ (step t9 (cl false) :rule th_resolution :premises (a0 t5 t8)) (step t10 (cl (not false)) :rule false) (step t11 (cl) :rule resolution :premises (t9 t10)) +d4888d8ad473d347e6ab6d509244a7583a7babd4 17 0 +unsat +(assume a0 (! (not (! (= (! (and p$ true) :named @p_1) p$) :named @p_3)) :named @p_5)) +(step t2 (cl (= @p_1 (! (and p$) :named @p_2))) :rule and_simplify) +(step t3 (cl (= @p_2 p$)) :rule and_simplify) +(step t4 (cl @p_3) :rule trans :premises (t2 t3)) +(step t5 (cl (= @p_3 (! (= p$ p$) :named @p_4))) :rule cong :premises (t4)) +(step t6 (cl (= @p_4 true)) :rule equiv_simplify) +(step t7 (cl (= @p_3 true)) :rule trans :premises (t5 t6)) +(step t8 (cl (= @p_5 (! (not true) :named @p_6))) :rule cong :premises (t7)) +(step t9 (cl (= @p_6 false)) :rule not_simplify) +(step t10 (cl (! (= @p_5 false) :named @p_7)) :rule trans :premises (t8 t9)) +(step t11 (cl (! (not @p_7) :named @p_9) (! (not @p_5) :named @p_8) false) :rule equiv_pos2) +(step t12 (cl (not @p_8) @p_3) :rule not_not) +(step t13 (cl @p_9 @p_3 false) :rule th_resolution :premises (t12 t11)) +(step t14 (cl false) :rule th_resolution :premises (a0 t10 t13)) +(step t15 (cl (not false)) :rule false) +(step t16 (cl) :rule resolution :premises (t14 t15)) +337e2bffaa7ce02e1ab772f593ffdbb243d5e449 15 0 +unsat +(assume a0 (! (not (! (=> (! (and (! (or p$ q$) :named @p_8) (! (not p$) :named @p_9)) :named @p_2) q$) :named @p_6)) :named @p_1)) +(step t2 (cl (! (= @p_1 (! (and @p_2 (! (not q$) :named @p_10)) :named @p_4)) :named @p_3)) :rule bool_simplify) +(step t3 (cl (! (not @p_3) :named @p_7) (! (not @p_1) :named @p_5) @p_4) :rule equiv_pos2) +(step t4 (cl (not @p_5) @p_6) :rule not_not) +(step t5 (cl @p_7 @p_6 @p_4) :rule th_resolution :premises (t4 t3)) +(step t6 (cl @p_4) :rule th_resolution :premises (a0 t2 t5)) +(step t7 (cl (! (= @p_4 (! (and @p_8 @p_9 @p_10) :named @p_12)) :named @p_11)) :rule ac_simp) +(step t8 (cl (not @p_11) (not @p_4) @p_12) :rule equiv_pos2) +(step t9 (cl @p_12) :rule th_resolution :premises (t6 t7 t8)) +(step t10 (cl @p_8) :rule and :premises (t9)) +(step t11 (cl p$ q$) :rule or :premises (t10)) +(step t12 (cl @p_9) :rule and :premises (t9)) +(step t13 (cl @p_10) :rule and :premises (t9)) +(step t14 (cl) :rule resolution :premises (t11 t12 t13)) 10d84ea161ad298d0be18624997ac708a1f26ba1 12 0 unsat (assume a0 (! (not (! (=> (! (or (and a$ b$) (and c$ d$)) :named @p_1) @p_1) :named @p_6)) :named @p_2)) @@ -65,22 +81,36 @@ (step t9 (cl p1$) :rule not_implies1 :premises (t8)) (step t10 (cl (not p1$)) :rule not_or :premises (t7)) (step t11 (cl) :rule resolution :premises (t10 t9)) -337e2bffaa7ce02e1ab772f593ffdbb243d5e449 15 0 +f8dcc171fd9ab79494da2e1c5e4771e075fd9d51 29 0 unsat -(assume a0 (! (not (! (=> (! (and (! (or p$ q$) :named @p_8) (! (not p$) :named @p_9)) :named @p_2) q$) :named @p_6)) :named @p_1)) -(step t2 (cl (! (= @p_1 (! (and @p_2 (! (not q$) :named @p_10)) :named @p_4)) :named @p_3)) :rule bool_simplify) -(step t3 (cl (! (not @p_3) :named @p_7) (! (not @p_1) :named @p_5) @p_4) :rule equiv_pos2) -(step t4 (cl (not @p_5) @p_6) :rule not_not) -(step t5 (cl @p_7 @p_6 @p_4) :rule th_resolution :premises (t4 t3)) -(step t6 (cl @p_4) :rule th_resolution :premises (a0 t2 t5)) -(step t7 (cl (! (= @p_4 (! (and @p_8 @p_9 @p_10) :named @p_12)) :named @p_11)) :rule ac_simp) -(step t8 (cl (not @p_11) (not @p_4) @p_12) :rule equiv_pos2) -(step t9 (cl @p_12) :rule th_resolution :premises (t6 t7 t8)) -(step t10 (cl @p_8) :rule and :premises (t9)) -(step t11 (cl p$ q$) :rule or :premises (t10)) -(step t12 (cl @p_9) :rule and :premises (t9)) -(step t13 (cl @p_10) :rule and :premises (t9)) -(step t14 (cl) :rule resolution :premises (t11 t12 t13)) +(assume a0 (! (not (! (= (! (= (! (= (! (= (! (= (! (= (! (= (! (= (! (= p$ p$) :named @p_1) p$) :named @p_2) p$) :named @p_4) p$) :named @p_5) p$) :named @p_6) p$) :named @p_7) p$) :named @p_8) p$) :named @p_9) p$) :named @p_10)) :named @p_11)) +(step t2 (cl (= @p_1 true)) :rule equiv_simplify) +(step t3 (cl (= @p_2 (! (= true p$) :named @p_3))) :rule cong :premises (t2)) +(step t4 (cl (= @p_3 p$)) :rule equiv_simplify) +(step t5 (cl @p_4) :rule trans :premises (t3 t4)) +(step t6 (cl (= @p_4 @p_1)) :rule cong :premises (t5)) +(step t7 (cl (= @p_4 true)) :rule trans :premises (t6 t2)) +(step t8 (cl (= @p_5 @p_3)) :rule cong :premises (t7)) +(step t9 (cl @p_6) :rule trans :premises (t8 t4)) +(step t10 (cl (= @p_6 @p_1)) :rule cong :premises (t9)) +(step t11 (cl (= @p_6 true)) :rule trans :premises (t10 t2)) +(step t12 (cl (= @p_7 @p_3)) :rule cong :premises (t11)) +(step t13 (cl @p_8) :rule trans :premises (t12 t4)) +(step t14 (cl (= @p_8 @p_1)) :rule cong :premises (t13)) +(step t15 (cl (= @p_8 true)) :rule trans :premises (t14 t2)) +(step t16 (cl (= @p_9 @p_3)) :rule cong :premises (t15)) +(step t17 (cl @p_10) :rule trans :premises (t16 t4)) +(step t18 (cl (= @p_10 @p_1)) :rule cong :premises (t17)) +(step t19 (cl (= @p_10 true)) :rule trans :premises (t18 t2)) +(step t20 (cl (= @p_11 (! (not true) :named @p_12))) :rule cong :premises (t19)) +(step t21 (cl (= @p_12 false)) :rule not_simplify) +(step t22 (cl (! (= @p_11 false) :named @p_13)) :rule trans :premises (t20 t21)) +(step t23 (cl (! (not @p_13) :named @p_15) (! (not @p_11) :named @p_14) false) :rule equiv_pos2) +(step t24 (cl (not @p_14) @p_10) :rule not_not) +(step t25 (cl @p_15 @p_10 false) :rule th_resolution :premises (t24 t23)) +(step t26 (cl false) :rule th_resolution :premises (a0 t22 t25)) +(step t27 (cl (not false)) :rule false) +(step t28 (cl) :rule resolution :premises (t26 t27)) ef250e7a4e9499952e8416cff69ed029a37c7aa3 59 0 unsat (assume a0 (! (or a$ (or b$ (or c$ d$))) :named @p_1)) @@ -141,36 +171,6 @@ (step t56 (cl @p_26) :rule resolution :premises (t54 t50)) (step t57 (cl a$) :rule resolution :premises (t51 t55 t50 t56)) (step t58 (cl) :rule resolution :premises (t52 t55 t57)) -f8dcc171fd9ab79494da2e1c5e4771e075fd9d51 29 0 -unsat -(assume a0 (! (not (! (= (! (= (! (= (! (= (! (= (! (= (! (= (! (= (! (= p$ p$) :named @p_1) p$) :named @p_2) p$) :named @p_4) p$) :named @p_5) p$) :named @p_6) p$) :named @p_7) p$) :named @p_8) p$) :named @p_9) p$) :named @p_10)) :named @p_11)) -(step t2 (cl (= @p_1 true)) :rule equiv_simplify) -(step t3 (cl (= @p_2 (! (= true p$) :named @p_3))) :rule cong :premises (t2)) -(step t4 (cl (= @p_3 p$)) :rule equiv_simplify) -(step t5 (cl @p_4) :rule trans :premises (t3 t4)) -(step t6 (cl (= @p_4 @p_1)) :rule cong :premises (t5)) -(step t7 (cl (= @p_4 true)) :rule trans :premises (t6 t2)) -(step t8 (cl (= @p_5 @p_3)) :rule cong :premises (t7)) -(step t9 (cl @p_6) :rule trans :premises (t8 t4)) -(step t10 (cl (= @p_6 @p_1)) :rule cong :premises (t9)) -(step t11 (cl (= @p_6 true)) :rule trans :premises (t10 t2)) -(step t12 (cl (= @p_7 @p_3)) :rule cong :premises (t11)) -(step t13 (cl @p_8) :rule trans :premises (t12 t4)) -(step t14 (cl (= @p_8 @p_1)) :rule cong :premises (t13)) -(step t15 (cl (= @p_8 true)) :rule trans :premises (t14 t2)) -(step t16 (cl (= @p_9 @p_3)) :rule cong :premises (t15)) -(step t17 (cl @p_10) :rule trans :premises (t16 t4)) -(step t18 (cl (= @p_10 @p_1)) :rule cong :premises (t17)) -(step t19 (cl (= @p_10 true)) :rule trans :premises (t18 t2)) -(step t20 (cl (= @p_11 (! (not true) :named @p_12))) :rule cong :premises (t19)) -(step t21 (cl (= @p_12 false)) :rule not_simplify) -(step t22 (cl (! (= @p_11 false) :named @p_13)) :rule trans :premises (t20 t21)) -(step t23 (cl (! (not @p_13) :named @p_15) (! (not @p_11) :named @p_14) false) :rule equiv_pos2) -(step t24 (cl (not @p_14) @p_10) :rule not_not) -(step t25 (cl @p_15 @p_10 false) :rule th_resolution :premises (t24 t23)) -(step t26 (cl false) :rule th_resolution :premises (a0 t22 t25)) -(step t27 (cl (not false)) :rule false) -(step t28 (cl) :rule resolution :premises (t26 t27)) a331481eed4f18a666baadda4e1010ca7a295ccf 38 0 unsat (assume a0 (! (forall ((?v0 A$) (?v1 A$)) (! (= (! (symm_f$ ?v0 ?v1) :named @p_2) (! (symm_f$ ?v1 ?v0) :named @p_6)) :named @p_8)) :named @p_1)) @@ -210,661 +210,6 @@ (step t19 (cl (or (! (not @p_18) :named @p_29) @p_21)) :rule forall_inst :args ((:= veriT_vr2 a$) (:= veriT_vr3 b$))) (step t20 (cl @p_29 @p_21) :rule or :premises (t19)) (step t21 (cl) :rule resolution :premises (t20 t8 t18)) -8616c6debd3ebae49adf8409b8c1ecb6665bc881 654 0 -unsat -(assume a0 (! (forall ((?v0 Int)) (! (= (! (fun_app$ uua$ ?v0) :named @p_13) (! (line_integral_exists$ f$ (! (insert$ j$ bot$) :named @p_7)) :named @p_12)) :named @p_15)) :named @p_11)) -(assume a1 (! (forall ((?v0 Int)) (! (= (! (fun_app$ uu$ ?v0) :named @p_25) (! (line_integral_exists$ f$ (! (insert$ i$ bot$) :named @p_5)) :named @p_24)) :named @p_27)) :named @p_23)) -(assume a2 (! (forall ((?v0 Int_real_real_real_prod_fun_bool_fun_fun$) (?v1 Int_real_real_real_prod_fun_prod$)) (! (= (! (case_prod$ ?v0 ?v1) :named @p_36) (! (fun_app$a (! (fun_app$ ?v0 (! (fst$ ?v1) :named @p_40)) :named @p_42) (! (snd$ ?v1) :named @p_44)) :named @p_46)) :named @p_48)) :named @p_35)) -(assume a3 (! (forall ((?v0 Real_real_prod$) (?v1 Real_real_prod$)) (! (=> (! (= (! (insert$ ?v0 bot$) :named @p_3) (! (insert$ ?v1 bot$) :named @p_64)) :named @p_66) (! (= ?v0 ?v1) :named @p_70)) :named @p_72)) :named @p_62)) -(assume a4 (! (forall ((?v0 Int) (?v1 Real_real_real_prod_fun$)) (! (= ?v1 (! (snd$ (! (pair$ ?v0 ?v1) :named @p_87)) :named @p_89)) :named @p_91)) :named @p_85)) -(assume a5 (! (forall ((?v0 Real) (?v1 Real)) (! (= ?v1 (! (snd$a (! (fun_app$b (! (pair$a ?v0) :named @p_102) ?v1) :named @p_105)) :named @p_107)) :named @p_109)) :named @p_101)) -(assume a6 (! (member$ (! (pair$ k$ g$) :named @p_403) one_chain_typeI$) :named @p_402)) -(assume a7 (! (forall ((?v0 Real_real_prod_set$) (?v1 Real_real_prod$) (?v2 Real_real_prod_set$)) (! (= (! (= bot$ (! (inf$ ?v0 (! (insert$ ?v1 ?v2) :named @p_1)) :named @p_122)) :named @p_124) (! (and (! (not (! (member$a ?v1 ?v0) :named @p_128)) :named @p_130) (! (= bot$ (! (inf$ ?v0 ?v2) :named @p_133)) :named @p_135)) :named @p_137)) :named @p_139)) :named @p_120)) -(assume a8 (! (finite$ bot$) :named @p_414)) -(assume a9 (! (forall ((?v0 Real_real_prod_set$) (?v1 Real_real_prod$)) (! (=> (! (finite$ ?v0) :named @p_4) (! (finite$ (! (insert$ ?v1 ?v0) :named @p_160)) :named @p_162)) :named @p_164)) :named @p_157)) -(assume a10 (! (= i$ (! (fun_app$b (pair$a 1.0) 0.0) :named @p_417)) :named @p_499)) -(assume a11 (! (forall ((?v0 Real_real_prod$) (?v1 Real_real_prod_set$)) (! (=> (! (member$a ?v0 ?v1) :named @p_176) (! (= ?v1 (! (insert$ ?v0 ?v1) :named @p_2)) :named @p_181)) :named @p_183)) :named @p_175)) -(assume a12 (! (= j$ (! (fun_app$b (pair$a 0.0) 1.0) :named @p_419)) :named @p_500)) -(assume a13 (! (forall ((?v0 Real_real_prod_set$)) (! (= bot$ (! (inf$ ?v0 bot$) :named @p_196)) :named @p_198)) :named @p_195)) -(assume a14 (! (forall ((?v0 Real_real_prod$) (?v1 Real_real_prod$) (?v2 Real_real_prod_set$)) (! (= (! (insert$ ?v0 @p_1) :named @p_208) (! (insert$ ?v1 (! (insert$ ?v0 ?v2) :named @p_213)) :named @p_215)) :named @p_217)) :named @p_206)) -(assume a15 (! (forall ((?v0 Real_real_prod$) (?v1 Real_real_prod_set$)) (! (= @p_2 (! (sup$ @p_3 ?v1) :named @p_236)) :named @p_238)) :named @p_231)) -(assume a16 (! (forall ((?v0 Real_real_prod_set$) (?v1 Real_real_prod_real_real_prod_fun$) (?v2 Real_real_prod_set$) (?v3 Real_real_real_prod_fun$) (?v4 Real_real_prod_set$)) (! (=> (! (and @p_4 (! (and (! (fun_app$a (! (line_integral_exists$ ?v1 ?v2) :named @p_252) ?v3) :named @p_254) (! (and (! (fun_app$a (! (line_integral_exists$ ?v1 ?v4) :named @p_257) ?v3) :named @p_260) (! (and (! (= ?v0 (! (sup$ ?v2 ?v4) :named @p_265)) :named @p_267) (! (= bot$ (! (inf$ ?v2 ?v4) :named @p_269)) :named @p_271)) :named @p_273)) :named @p_275)) :named @p_277)) :named @p_279) (! (= (! (line_integral$ ?v1 ?v0 ?v3) :named @p_281) (! (+ (! (line_integral$ ?v1 ?v2 ?v3) :named @p_283) (! (line_integral$ ?v1 ?v4 ?v3) :named @p_285)) :named @p_287)) :named @p_289)) :named @p_291)) :named @p_250)) -(assume a17 (! (and (! (= (one_chain_line_integral$ f$ @p_5 one_chain_typeI$) (one_chain_line_integral$ f$ @p_5 one_chain_typeII$)) :named @p_337) (! (and (! (forall ((?v0 Int_real_real_real_prod_fun_prod$)) (! (=> (! (member$ ?v0 one_chain_typeI$) :named @p_9) (! (case_prod$ uu$ ?v0) :named @p_6)) :named @p_326)) :named @p_322) (! (forall ((?v0 Int_real_real_real_prod_fun_prod$)) (! (=> (! (member$ ?v0 one_chain_typeII$) :named @p_8) @p_6) :named @p_331)) :named @p_328)) :named @p_333)) :named @p_336)) -(assume a18 (! (and (! (= (one_chain_line_integral$ f$ @p_7 one_chain_typeII$) (one_chain_line_integral$ f$ @p_7 one_chain_typeI$)) :named @p_377) (! (and (! (forall ((?v0 Int_real_real_real_prod_fun_prod$)) (! (=> @p_8 (! (case_prod$ uua$ ?v0) :named @p_10)) :named @p_366)) :named @p_362) (! (forall ((?v0 Int_real_real_real_prod_fun_prod$)) (! (=> @p_9 @p_10) :named @p_371)) :named @p_368)) :named @p_373)) :named @p_376)) -(assume a19 (not (! (= (! (line_integral$ f$ (! (insert$ i$ @p_7) :named @p_407) g$) :named @p_462) (! (+ (! (line_integral$ f$ @p_5 g$) :named @p_404) (! (line_integral$ f$ @p_7 g$) :named @p_405)) :named @p_463)) :named @p_410))) -(anchor :step t21 :args ((:= ?v0 veriT_vr0))) -(step t21.t1 (cl (= ?v0 veriT_vr0)) :rule refl) -(step t21.t2 (cl (= @p_13 (! (fun_app$ uua$ veriT_vr0) :named @p_14))) :rule cong :premises (t21.t1)) -(step t21.t3 (cl (= @p_15 (! (= @p_12 @p_14) :named @p_16))) :rule cong :premises (t21.t2)) -(step t21 (cl (! (= @p_11 (! (forall ((veriT_vr0 Int)) @p_16) :named @p_18)) :named @p_17)) :rule bind) -(step t22 (cl (not @p_17) (not @p_11) @p_18) :rule equiv_pos2) -(step t23 (cl @p_18) :rule th_resolution :premises (a0 t21 t22)) -(anchor :step t24 :args ((:= veriT_vr0 veriT_vr1))) -(step t24.t1 (cl (= veriT_vr0 veriT_vr1)) :rule refl) -(step t24.t2 (cl (= @p_14 (! (fun_app$ uua$ veriT_vr1) :named @p_19))) :rule cong :premises (t24.t1)) -(step t24.t3 (cl (= @p_16 (! (= @p_12 @p_19) :named @p_20))) :rule cong :premises (t24.t2)) -(step t24 (cl (! (= @p_18 (! (forall ((veriT_vr1 Int)) @p_20) :named @p_22)) :named @p_21)) :rule bind) -(step t25 (cl (not @p_21) (not @p_18) @p_22) :rule equiv_pos2) -(step t26 (cl @p_22) :rule th_resolution :premises (t23 t24 t25)) -(anchor :step t27 :args ((:= ?v0 veriT_vr2))) -(step t27.t1 (cl (= ?v0 veriT_vr2)) :rule refl) -(step t27.t2 (cl (= @p_25 (! (fun_app$ uu$ veriT_vr2) :named @p_26))) :rule cong :premises (t27.t1)) -(step t27.t3 (cl (= @p_27 (! (= @p_24 @p_26) :named @p_28))) :rule cong :premises (t27.t2)) -(step t27 (cl (! (= @p_23 (! (forall ((veriT_vr2 Int)) @p_28) :named @p_30)) :named @p_29)) :rule bind) -(step t28 (cl (not @p_29) (not @p_23) @p_30) :rule equiv_pos2) -(step t29 (cl @p_30) :rule th_resolution :premises (a1 t27 t28)) -(anchor :step t30 :args ((:= veriT_vr2 veriT_vr3))) -(step t30.t1 (cl (= veriT_vr2 veriT_vr3)) :rule refl) -(step t30.t2 (cl (= @p_26 (! (fun_app$ uu$ veriT_vr3) :named @p_31))) :rule cong :premises (t30.t1)) -(step t30.t3 (cl (= @p_28 (! (= @p_24 @p_31) :named @p_32))) :rule cong :premises (t30.t2)) -(step t30 (cl (! (= @p_30 (! (forall ((veriT_vr3 Int)) @p_32) :named @p_34)) :named @p_33)) :rule bind) -(step t31 (cl (not @p_33) (not @p_30) @p_34) :rule equiv_pos2) -(step t32 (cl @p_34) :rule th_resolution :premises (t29 t30 t31)) -(anchor :step t33 :args ((:= ?v0 veriT_vr4) (:= ?v1 veriT_vr5))) -(step t33.t1 (cl (! (= ?v0 veriT_vr4) :named @p_38)) :rule refl) -(step t33.t2 (cl (! (= ?v1 veriT_vr5) :named @p_39)) :rule refl) -(step t33.t3 (cl (= @p_36 (! (case_prod$ veriT_vr4 veriT_vr5) :named @p_37))) :rule cong :premises (t33.t1 t33.t2)) -(step t33.t4 (cl @p_38) :rule refl) -(step t33.t5 (cl @p_39) :rule refl) -(step t33.t6 (cl (= @p_40 (! (fst$ veriT_vr5) :named @p_41))) :rule cong :premises (t33.t5)) -(step t33.t7 (cl (= @p_42 (! (fun_app$ veriT_vr4 @p_41) :named @p_43))) :rule cong :premises (t33.t4 t33.t6)) -(step t33.t8 (cl @p_39) :rule refl) -(step t33.t9 (cl (= @p_44 (! (snd$ veriT_vr5) :named @p_45))) :rule cong :premises (t33.t8)) -(step t33.t10 (cl (= @p_46 (! (fun_app$a @p_43 @p_45) :named @p_47))) :rule cong :premises (t33.t7 t33.t9)) -(step t33.t11 (cl (= @p_48 (! (= @p_37 @p_47) :named @p_49))) :rule cong :premises (t33.t3 t33.t10)) -(step t33 (cl (! (= @p_35 (! (forall ((veriT_vr4 Int_real_real_real_prod_fun_bool_fun_fun$) (veriT_vr5 Int_real_real_real_prod_fun_prod$)) @p_49) :named @p_51)) :named @p_50)) :rule bind) -(step t34 (cl (not @p_50) (not @p_35) @p_51) :rule equiv_pos2) -(step t35 (cl @p_51) :rule th_resolution :premises (a2 t33 t34)) -(anchor :step t36 :args ((:= veriT_vr4 veriT_vr6) (:= veriT_vr5 veriT_vr7))) -(step t36.t1 (cl (! (= veriT_vr4 veriT_vr6) :named @p_53)) :rule refl) -(step t36.t2 (cl (! (= veriT_vr5 veriT_vr7) :named @p_54)) :rule refl) -(step t36.t3 (cl (= @p_37 (! (case_prod$ veriT_vr6 veriT_vr7) :named @p_52))) :rule cong :premises (t36.t1 t36.t2)) -(step t36.t4 (cl @p_53) :rule refl) -(step t36.t5 (cl @p_54) :rule refl) -(step t36.t6 (cl (= @p_41 (! (fst$ veriT_vr7) :named @p_55))) :rule cong :premises (t36.t5)) -(step t36.t7 (cl (= @p_43 (! (fun_app$ veriT_vr6 @p_55) :named @p_56))) :rule cong :premises (t36.t4 t36.t6)) -(step t36.t8 (cl @p_54) :rule refl) -(step t36.t9 (cl (= @p_45 (! (snd$ veriT_vr7) :named @p_57))) :rule cong :premises (t36.t8)) -(step t36.t10 (cl (= @p_47 (! (fun_app$a @p_56 @p_57) :named @p_58))) :rule cong :premises (t36.t7 t36.t9)) -(step t36.t11 (cl (= @p_49 (! (= @p_52 @p_58) :named @p_59))) :rule cong :premises (t36.t3 t36.t10)) -(step t36 (cl (! (= @p_51 (! (forall ((veriT_vr6 Int_real_real_real_prod_fun_bool_fun_fun$) (veriT_vr7 Int_real_real_real_prod_fun_prod$)) @p_59) :named @p_61)) :named @p_60)) :rule bind) -(step t37 (cl (not @p_60) (not @p_51) @p_61) :rule equiv_pos2) -(step t38 (cl @p_61) :rule th_resolution :premises (t35 t36 t37)) -(anchor :step t39 :args ((:= ?v0 veriT_vr8) (:= ?v1 veriT_vr9))) -(step t39.t1 (cl (! (= ?v0 veriT_vr8) :named @p_68)) :rule refl) -(step t39.t2 (cl (= @p_3 (! (insert$ veriT_vr8 bot$) :named @p_63))) :rule cong :premises (t39.t1)) -(step t39.t3 (cl (! (= ?v1 veriT_vr9) :named @p_69)) :rule refl) -(step t39.t4 (cl (= @p_64 (! (insert$ veriT_vr9 bot$) :named @p_65))) :rule cong :premises (t39.t3)) -(step t39.t5 (cl (= @p_66 (! (= @p_63 @p_65) :named @p_67))) :rule cong :premises (t39.t2 t39.t4)) -(step t39.t6 (cl @p_68) :rule refl) -(step t39.t7 (cl @p_69) :rule refl) -(step t39.t8 (cl (= @p_70 (! (= veriT_vr8 veriT_vr9) :named @p_71))) :rule cong :premises (t39.t6 t39.t7)) -(step t39.t9 (cl (= @p_72 (! (=> @p_67 @p_71) :named @p_73))) :rule cong :premises (t39.t5 t39.t8)) -(step t39 (cl (! (= @p_62 (! (forall ((veriT_vr8 Real_real_prod$) (veriT_vr9 Real_real_prod$)) @p_73) :named @p_75)) :named @p_74)) :rule bind) -(step t40 (cl (not @p_74) (not @p_62) @p_75) :rule equiv_pos2) -(step t41 (cl @p_75) :rule th_resolution :premises (a3 t39 t40)) -(anchor :step t42 :args ((:= veriT_vr8 veriT_vr10) (:= veriT_vr9 veriT_vr11))) -(step t42.t1 (cl (! (= veriT_vr8 veriT_vr10) :named @p_79)) :rule refl) -(step t42.t2 (cl (= @p_63 (! (insert$ veriT_vr10 bot$) :named @p_76))) :rule cong :premises (t42.t1)) -(step t42.t3 (cl (! (= veriT_vr9 veriT_vr11) :named @p_80)) :rule refl) -(step t42.t4 (cl (= @p_65 (! (insert$ veriT_vr11 bot$) :named @p_77))) :rule cong :premises (t42.t3)) -(step t42.t5 (cl (= @p_67 (! (= @p_76 @p_77) :named @p_78))) :rule cong :premises (t42.t2 t42.t4)) -(step t42.t6 (cl @p_79) :rule refl) -(step t42.t7 (cl @p_80) :rule refl) -(step t42.t8 (cl (= @p_71 (! (= veriT_vr10 veriT_vr11) :named @p_81))) :rule cong :premises (t42.t6 t42.t7)) -(step t42.t9 (cl (= @p_73 (! (=> @p_78 @p_81) :named @p_82))) :rule cong :premises (t42.t5 t42.t8)) -(step t42 (cl (! (= @p_75 (! (forall ((veriT_vr10 Real_real_prod$) (veriT_vr11 Real_real_prod$)) @p_82) :named @p_84)) :named @p_83)) :rule bind) -(step t43 (cl (not @p_83) (not @p_75) @p_84) :rule equiv_pos2) -(step t44 (cl @p_84) :rule th_resolution :premises (t41 t42 t43)) -(anchor :step t45 :args ((:= ?v0 veriT_vr12) (:= ?v1 veriT_vr13))) -(step t45.t1 (cl (! (= ?v1 veriT_vr13) :named @p_86)) :rule refl) -(step t45.t2 (cl (= ?v0 veriT_vr12)) :rule refl) -(step t45.t3 (cl @p_86) :rule refl) -(step t45.t4 (cl (= @p_87 (! (pair$ veriT_vr12 veriT_vr13) :named @p_88))) :rule cong :premises (t45.t2 t45.t3)) -(step t45.t5 (cl (= @p_89 (! (snd$ @p_88) :named @p_90))) :rule cong :premises (t45.t4)) -(step t45.t6 (cl (= @p_91 (! (= veriT_vr13 @p_90) :named @p_92))) :rule cong :premises (t45.t1 t45.t5)) -(step t45 (cl (! (= @p_85 (! (forall ((veriT_vr12 Int) (veriT_vr13 Real_real_real_prod_fun$)) @p_92) :named @p_94)) :named @p_93)) :rule bind) -(step t46 (cl (not @p_93) (not @p_85) @p_94) :rule equiv_pos2) -(step t47 (cl @p_94) :rule th_resolution :premises (a4 t45 t46)) -(anchor :step t48 :args ((:= veriT_vr12 veriT_vr14) (:= veriT_vr13 veriT_vr15))) -(step t48.t1 (cl (! (= veriT_vr13 veriT_vr15) :named @p_95)) :rule refl) -(step t48.t2 (cl (= veriT_vr12 veriT_vr14)) :rule refl) -(step t48.t3 (cl @p_95) :rule refl) -(step t48.t4 (cl (= @p_88 (! (pair$ veriT_vr14 veriT_vr15) :named @p_96))) :rule cong :premises (t48.t2 t48.t3)) -(step t48.t5 (cl (= @p_90 (! (snd$ @p_96) :named @p_97))) :rule cong :premises (t48.t4)) -(step t48.t6 (cl (= @p_92 (! (= veriT_vr15 @p_97) :named @p_98))) :rule cong :premises (t48.t1 t48.t5)) -(step t48 (cl (! (= @p_94 (! (forall ((veriT_vr14 Int) (veriT_vr15 Real_real_real_prod_fun$)) @p_98) :named @p_100)) :named @p_99)) :rule bind) -(step t49 (cl (not @p_99) (not @p_94) @p_100) :rule equiv_pos2) -(step t50 (cl @p_100) :rule th_resolution :premises (t47 t48 t49)) -(anchor :step t51 :args ((:= ?v0 veriT_vr16) (:= ?v1 veriT_vr17))) -(step t51.t1 (cl (! (= ?v1 veriT_vr17) :named @p_104)) :rule refl) -(step t51.t2 (cl (= ?v0 veriT_vr16)) :rule refl) -(step t51.t3 (cl (= @p_102 (! (pair$a veriT_vr16) :named @p_103))) :rule cong :premises (t51.t2)) -(step t51.t4 (cl @p_104) :rule refl) -(step t51.t5 (cl (= @p_105 (! (fun_app$b @p_103 veriT_vr17) :named @p_106))) :rule cong :premises (t51.t3 t51.t4)) -(step t51.t6 (cl (= @p_107 (! (snd$a @p_106) :named @p_108))) :rule cong :premises (t51.t5)) -(step t51.t7 (cl (= @p_109 (! (= veriT_vr17 @p_108) :named @p_110))) :rule cong :premises (t51.t1 t51.t6)) -(step t51 (cl (! (= @p_101 (! (forall ((veriT_vr16 Real) (veriT_vr17 Real)) @p_110) :named @p_112)) :named @p_111)) :rule bind) -(step t52 (cl (not @p_111) (not @p_101) @p_112) :rule equiv_pos2) -(step t53 (cl @p_112) :rule th_resolution :premises (a5 t51 t52)) -(anchor :step t54 :args ((:= veriT_vr16 veriT_vr18) (:= veriT_vr17 veriT_vr19))) -(step t54.t1 (cl (! (= veriT_vr17 veriT_vr19) :named @p_114)) :rule refl) -(step t54.t2 (cl (= veriT_vr16 veriT_vr18)) :rule refl) -(step t54.t3 (cl (= @p_103 (! (pair$a veriT_vr18) :named @p_113))) :rule cong :premises (t54.t2)) -(step t54.t4 (cl @p_114) :rule refl) -(step t54.t5 (cl (= @p_106 (! (fun_app$b @p_113 veriT_vr19) :named @p_115))) :rule cong :premises (t54.t3 t54.t4)) -(step t54.t6 (cl (= @p_108 (! (snd$a @p_115) :named @p_116))) :rule cong :premises (t54.t5)) -(step t54.t7 (cl (= @p_110 (! (= veriT_vr19 @p_116) :named @p_117))) :rule cong :premises (t54.t1 t54.t6)) -(step t54 (cl (! (= @p_112 (! (forall ((veriT_vr18 Real) (veriT_vr19 Real)) @p_117) :named @p_119)) :named @p_118)) :rule bind) -(step t55 (cl (not @p_118) (not @p_112) @p_119) :rule equiv_pos2) -(step t56 (cl @p_119) :rule th_resolution :premises (t53 t54 t55)) -(anchor :step t57 :args ((:= ?v0 veriT_vr20) (:= ?v1 veriT_vr21) (:= ?v2 veriT_vr22))) -(step t57.t1 (cl (! (= ?v0 veriT_vr20) :named @p_127)) :rule refl) -(step t57.t2 (cl (! (= ?v1 veriT_vr21) :named @p_126)) :rule refl) -(step t57.t3 (cl (! (= ?v2 veriT_vr22) :named @p_132)) :rule refl) -(step t57.t4 (cl (= @p_1 (! (insert$ veriT_vr21 veriT_vr22) :named @p_121))) :rule cong :premises (t57.t2 t57.t3)) -(step t57.t5 (cl (= @p_122 (! (inf$ veriT_vr20 @p_121) :named @p_123))) :rule cong :premises (t57.t1 t57.t4)) -(step t57.t6 (cl (= @p_124 (! (= bot$ @p_123) :named @p_125))) :rule cong :premises (t57.t5)) -(step t57.t7 (cl @p_126) :rule refl) -(step t57.t8 (cl @p_127) :rule refl) -(step t57.t9 (cl (= @p_128 (! (member$a veriT_vr21 veriT_vr20) :named @p_129))) :rule cong :premises (t57.t7 t57.t8)) -(step t57.t10 (cl (= @p_130 (! (not @p_129) :named @p_131))) :rule cong :premises (t57.t9)) -(step t57.t11 (cl @p_127) :rule refl) -(step t57.t12 (cl @p_132) :rule refl) -(step t57.t13 (cl (= @p_133 (! (inf$ veriT_vr20 veriT_vr22) :named @p_134))) :rule cong :premises (t57.t11 t57.t12)) -(step t57.t14 (cl (= @p_135 (! (= bot$ @p_134) :named @p_136))) :rule cong :premises (t57.t13)) -(step t57.t15 (cl (= @p_137 (! (and @p_131 @p_136) :named @p_138))) :rule cong :premises (t57.t10 t57.t14)) -(step t57.t16 (cl (= @p_139 (! (= @p_125 @p_138) :named @p_140))) :rule cong :premises (t57.t6 t57.t15)) -(step t57 (cl (! (= @p_120 (! (forall ((veriT_vr20 Real_real_prod_set$) (veriT_vr21 Real_real_prod$) (veriT_vr22 Real_real_prod_set$)) @p_140) :named @p_142)) :named @p_141)) :rule bind) -(step t58 (cl (not @p_141) (not @p_120) @p_142) :rule equiv_pos2) -(step t59 (cl @p_142) :rule th_resolution :premises (a7 t57 t58)) -(anchor :step t60 :args ((:= veriT_vr20 veriT_vr23) (:= veriT_vr21 veriT_vr24) (:= veriT_vr22 veriT_vr25))) -(step t60.t1 (cl (! (= veriT_vr20 veriT_vr23) :named @p_147)) :rule refl) -(step t60.t2 (cl (! (= veriT_vr21 veriT_vr24) :named @p_146)) :rule refl) -(step t60.t3 (cl (! (= veriT_vr22 veriT_vr25) :named @p_150)) :rule refl) -(step t60.t4 (cl (= @p_121 (! (insert$ veriT_vr24 veriT_vr25) :named @p_143))) :rule cong :premises (t60.t2 t60.t3)) -(step t60.t5 (cl (= @p_123 (! (inf$ veriT_vr23 @p_143) :named @p_144))) :rule cong :premises (t60.t1 t60.t4)) -(step t60.t6 (cl (= @p_125 (! (= bot$ @p_144) :named @p_145))) :rule cong :premises (t60.t5)) -(step t60.t7 (cl @p_146) :rule refl) -(step t60.t8 (cl @p_147) :rule refl) -(step t60.t9 (cl (= @p_129 (! (member$a veriT_vr24 veriT_vr23) :named @p_148))) :rule cong :premises (t60.t7 t60.t8)) -(step t60.t10 (cl (= @p_131 (! (not @p_148) :named @p_149))) :rule cong :premises (t60.t9)) -(step t60.t11 (cl @p_147) :rule refl) -(step t60.t12 (cl @p_150) :rule refl) -(step t60.t13 (cl (= @p_134 (! (inf$ veriT_vr23 veriT_vr25) :named @p_151))) :rule cong :premises (t60.t11 t60.t12)) -(step t60.t14 (cl (= @p_136 (! (= bot$ @p_151) :named @p_152))) :rule cong :premises (t60.t13)) -(step t60.t15 (cl (= @p_138 (! (and @p_149 @p_152) :named @p_153))) :rule cong :premises (t60.t10 t60.t14)) -(step t60.t16 (cl (= @p_140 (! (= @p_145 @p_153) :named @p_154))) :rule cong :premises (t60.t6 t60.t15)) -(step t60 (cl (! (= @p_142 (! (forall ((veriT_vr23 Real_real_prod_set$) (veriT_vr24 Real_real_prod$) (veriT_vr25 Real_real_prod_set$)) @p_154) :named @p_156)) :named @p_155)) :rule bind) -(step t61 (cl (not @p_155) (not @p_142) @p_156) :rule equiv_pos2) -(step t62 (cl @p_156) :rule th_resolution :premises (t59 t60 t61)) -(anchor :step t63 :args ((:= ?v0 veriT_vr26) (:= ?v1 veriT_vr27))) -(step t63.t1 (cl (! (= ?v0 veriT_vr26) :named @p_159)) :rule refl) -(step t63.t2 (cl (= @p_4 (! (finite$ veriT_vr26) :named @p_158))) :rule cong :premises (t63.t1)) -(step t63.t3 (cl (= ?v1 veriT_vr27)) :rule refl) -(step t63.t4 (cl @p_159) :rule refl) -(step t63.t5 (cl (= @p_160 (! (insert$ veriT_vr27 veriT_vr26) :named @p_161))) :rule cong :premises (t63.t3 t63.t4)) -(step t63.t6 (cl (= @p_162 (! (finite$ @p_161) :named @p_163))) :rule cong :premises (t63.t5)) -(step t63.t7 (cl (= @p_164 (! (=> @p_158 @p_163) :named @p_165))) :rule cong :premises (t63.t2 t63.t6)) -(step t63 (cl (! (= @p_157 (! (forall ((veriT_vr26 Real_real_prod_set$) (veriT_vr27 Real_real_prod$)) @p_165) :named @p_167)) :named @p_166)) :rule bind) -(step t64 (cl (not @p_166) (not @p_157) @p_167) :rule equiv_pos2) -(step t65 (cl @p_167) :rule th_resolution :premises (a9 t63 t64)) -(anchor :step t66 :args ((:= veriT_vr26 veriT_vr28) (:= veriT_vr27 veriT_vr29))) -(step t66.t1 (cl (! (= veriT_vr26 veriT_vr28) :named @p_169)) :rule refl) -(step t66.t2 (cl (= @p_158 (! (finite$ veriT_vr28) :named @p_168))) :rule cong :premises (t66.t1)) -(step t66.t3 (cl (= veriT_vr27 veriT_vr29)) :rule refl) -(step t66.t4 (cl @p_169) :rule refl) -(step t66.t5 (cl (= @p_161 (! (insert$ veriT_vr29 veriT_vr28) :named @p_170))) :rule cong :premises (t66.t3 t66.t4)) -(step t66.t6 (cl (= @p_163 (! (finite$ @p_170) :named @p_171))) :rule cong :premises (t66.t5)) -(step t66.t7 (cl (= @p_165 (! (=> @p_168 @p_171) :named @p_172))) :rule cong :premises (t66.t2 t66.t6)) -(step t66 (cl (! (= @p_167 (! (forall ((veriT_vr28 Real_real_prod_set$) (veriT_vr29 Real_real_prod$)) @p_172) :named @p_174)) :named @p_173)) :rule bind) -(step t67 (cl (not @p_173) (not @p_167) @p_174) :rule equiv_pos2) -(step t68 (cl @p_174) :rule th_resolution :premises (t65 t66 t67)) -(anchor :step t69 :args ((:= ?v0 veriT_vr30) (:= ?v1 veriT_vr31))) -(step t69.t1 (cl (! (= ?v0 veriT_vr30) :named @p_179)) :rule refl) -(step t69.t2 (cl (! (= ?v1 veriT_vr31) :named @p_178)) :rule refl) -(step t69.t3 (cl (= @p_176 (! (member$a veriT_vr30 veriT_vr31) :named @p_177))) :rule cong :premises (t69.t1 t69.t2)) -(step t69.t4 (cl @p_178) :rule refl) -(step t69.t5 (cl @p_179) :rule refl) -(step t69.t6 (cl @p_178) :rule refl) -(step t69.t7 (cl (= @p_2 (! (insert$ veriT_vr30 veriT_vr31) :named @p_180))) :rule cong :premises (t69.t5 t69.t6)) -(step t69.t8 (cl (= @p_181 (! (= veriT_vr31 @p_180) :named @p_182))) :rule cong :premises (t69.t4 t69.t7)) -(step t69.t9 (cl (= @p_183 (! (=> @p_177 @p_182) :named @p_184))) :rule cong :premises (t69.t3 t69.t8)) -(step t69 (cl (! (= @p_175 (! (forall ((veriT_vr30 Real_real_prod$) (veriT_vr31 Real_real_prod_set$)) @p_184) :named @p_186)) :named @p_185)) :rule bind) -(step t70 (cl (not @p_185) (not @p_175) @p_186) :rule equiv_pos2) -(step t71 (cl @p_186) :rule th_resolution :premises (a11 t69 t70)) -(anchor :step t72 :args ((:= veriT_vr30 veriT_vr32) (:= veriT_vr31 veriT_vr33))) -(step t72.t1 (cl (! (= veriT_vr30 veriT_vr32) :named @p_189)) :rule refl) -(step t72.t2 (cl (! (= veriT_vr31 veriT_vr33) :named @p_188)) :rule refl) -(step t72.t3 (cl (= @p_177 (! (member$a veriT_vr32 veriT_vr33) :named @p_187))) :rule cong :premises (t72.t1 t72.t2)) -(step t72.t4 (cl @p_188) :rule refl) -(step t72.t5 (cl @p_189) :rule refl) -(step t72.t6 (cl @p_188) :rule refl) -(step t72.t7 (cl (= @p_180 (! (insert$ veriT_vr32 veriT_vr33) :named @p_190))) :rule cong :premises (t72.t5 t72.t6)) -(step t72.t8 (cl (= @p_182 (! (= veriT_vr33 @p_190) :named @p_191))) :rule cong :premises (t72.t4 t72.t7)) -(step t72.t9 (cl (= @p_184 (! (=> @p_187 @p_191) :named @p_192))) :rule cong :premises (t72.t3 t72.t8)) -(step t72 (cl (! (= @p_186 (! (forall ((veriT_vr32 Real_real_prod$) (veriT_vr33 Real_real_prod_set$)) @p_192) :named @p_194)) :named @p_193)) :rule bind) -(step t73 (cl (not @p_193) (not @p_186) @p_194) :rule equiv_pos2) -(step t74 (cl @p_194) :rule th_resolution :premises (t71 t72 t73)) -(anchor :step t75 :args ((:= ?v0 veriT_vr34))) -(step t75.t1 (cl (= ?v0 veriT_vr34)) :rule refl) -(step t75.t2 (cl (= @p_196 (! (inf$ veriT_vr34 bot$) :named @p_197))) :rule cong :premises (t75.t1)) -(step t75.t3 (cl (= @p_198 (! (= bot$ @p_197) :named @p_199))) :rule cong :premises (t75.t2)) -(step t75 (cl (! (= @p_195 (! (forall ((veriT_vr34 Real_real_prod_set$)) @p_199) :named @p_201)) :named @p_200)) :rule bind) -(step t76 (cl (not @p_200) (not @p_195) @p_201) :rule equiv_pos2) -(step t77 (cl @p_201) :rule th_resolution :premises (a13 t75 t76)) -(anchor :step t78 :args ((:= veriT_vr34 veriT_vr35))) -(step t78.t1 (cl (= veriT_vr34 veriT_vr35)) :rule refl) -(step t78.t2 (cl (= @p_197 (! (inf$ veriT_vr35 bot$) :named @p_202))) :rule cong :premises (t78.t1)) -(step t78.t3 (cl (= @p_199 (! (= bot$ @p_202) :named @p_203))) :rule cong :premises (t78.t2)) -(step t78 (cl (! (= @p_201 (! (forall ((veriT_vr35 Real_real_prod_set$)) @p_203) :named @p_205)) :named @p_204)) :rule bind) -(step t79 (cl (not @p_204) (not @p_201) @p_205) :rule equiv_pos2) -(step t80 (cl @p_205) :rule th_resolution :premises (t77 t78 t79)) -(anchor :step t81 :args ((:= ?v0 veriT_vr36) (:= ?v1 veriT_vr37) (:= ?v2 veriT_vr38))) -(step t81.t1 (cl (! (= ?v0 veriT_vr36) :named @p_211)) :rule refl) -(step t81.t2 (cl (! (= ?v1 veriT_vr37) :named @p_210)) :rule refl) -(step t81.t3 (cl (! (= ?v2 veriT_vr38) :named @p_212)) :rule refl) -(step t81.t4 (cl (= @p_1 (! (insert$ veriT_vr37 veriT_vr38) :named @p_207))) :rule cong :premises (t81.t2 t81.t3)) -(step t81.t5 (cl (= @p_208 (! (insert$ veriT_vr36 @p_207) :named @p_209))) :rule cong :premises (t81.t1 t81.t4)) -(step t81.t6 (cl @p_210) :rule refl) -(step t81.t7 (cl @p_211) :rule refl) -(step t81.t8 (cl @p_212) :rule refl) -(step t81.t9 (cl (= @p_213 (! (insert$ veriT_vr36 veriT_vr38) :named @p_214))) :rule cong :premises (t81.t7 t81.t8)) -(step t81.t10 (cl (= @p_215 (! (insert$ veriT_vr37 @p_214) :named @p_216))) :rule cong :premises (t81.t6 t81.t9)) -(step t81.t11 (cl (= @p_217 (! (= @p_209 @p_216) :named @p_218))) :rule cong :premises (t81.t5 t81.t10)) -(step t81 (cl (! (= @p_206 (! (forall ((veriT_vr36 Real_real_prod$) (veriT_vr37 Real_real_prod$) (veriT_vr38 Real_real_prod_set$)) @p_218) :named @p_220)) :named @p_219)) :rule bind) -(step t82 (cl (not @p_219) (not @p_206) @p_220) :rule equiv_pos2) -(step t83 (cl @p_220) :rule th_resolution :premises (a14 t81 t82)) -(anchor :step t84 :args ((:= veriT_vr36 veriT_vr39) (:= veriT_vr37 veriT_vr40) (:= veriT_vr38 veriT_vr41))) -(step t84.t1 (cl (! (= veriT_vr36 veriT_vr39) :named @p_224)) :rule refl) -(step t84.t2 (cl (! (= veriT_vr37 veriT_vr40) :named @p_223)) :rule refl) -(step t84.t3 (cl (! (= veriT_vr38 veriT_vr41) :named @p_225)) :rule refl) -(step t84.t4 (cl (= @p_207 (! (insert$ veriT_vr40 veriT_vr41) :named @p_221))) :rule cong :premises (t84.t2 t84.t3)) -(step t84.t5 (cl (= @p_209 (! (insert$ veriT_vr39 @p_221) :named @p_222))) :rule cong :premises (t84.t1 t84.t4)) -(step t84.t6 (cl @p_223) :rule refl) -(step t84.t7 (cl @p_224) :rule refl) -(step t84.t8 (cl @p_225) :rule refl) -(step t84.t9 (cl (= @p_214 (! 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(= veriT_vr43 veriT_vr45) :named @p_245)) :rule refl) -(step t90.t3 (cl (= @p_232 (! (insert$ veriT_vr44 veriT_vr45) :named @p_242))) :rule cong :premises (t90.t1 t90.t2)) -(step t90.t4 (cl @p_243) :rule refl) -(step t90.t5 (cl (= @p_234 (! (insert$ veriT_vr44 bot$) :named @p_244))) :rule cong :premises (t90.t4)) -(step t90.t6 (cl @p_245) :rule refl) -(step t90.t7 (cl (= @p_237 (! (sup$ @p_244 veriT_vr45) :named @p_246))) :rule cong :premises (t90.t5 t90.t6)) -(step t90.t8 (cl (= @p_239 (! (= @p_242 @p_246) :named @p_247))) :rule cong :premises (t90.t3 t90.t7)) -(step t90 (cl (! (= @p_241 (! (forall ((veriT_vr44 Real_real_prod$) (veriT_vr45 Real_real_prod_set$)) @p_247) :named @p_249)) :named @p_248)) :rule bind) -(step t91 (cl (not @p_248) (not @p_241) @p_249) :rule equiv_pos2) -(step t92 (cl @p_249) :rule th_resolution :premises (t89 t90 t91)) -(anchor :step t93 :args ((:= ?v0 veriT_vr46) (:= ?v1 veriT_vr47) (:= ?v2 veriT_vr48) (:= ?v3 veriT_vr49) (:= ?v4 veriT_vr50))) -(step t93.t1 (cl (! (= ?v0 veriT_vr46) :named @p_262)) :rule refl) -(step t93.t2 (cl (= @p_4 (! (finite$ veriT_vr46) :named @p_251))) :rule cong :premises (t93.t1)) -(step t93.t3 (cl (! (= ?v1 veriT_vr47) :named @p_256)) :rule refl) -(step t93.t4 (cl (! (= ?v2 veriT_vr48) :named @p_263)) :rule refl) -(step t93.t5 (cl (= @p_252 (! (line_integral_exists$ veriT_vr47 veriT_vr48) :named @p_253))) :rule cong :premises (t93.t3 t93.t4)) -(step t93.t6 (cl (! (= ?v3 veriT_vr49) :named @p_259)) :rule refl) -(step t93.t7 (cl (= @p_254 (! (fun_app$a @p_253 veriT_vr49) :named @p_255))) :rule cong :premises (t93.t5 t93.t6)) -(step t93.t8 (cl @p_256) :rule refl) -(step t93.t9 (cl (! (= ?v4 veriT_vr50) :named @p_264)) :rule refl) -(step t93.t10 (cl (= @p_257 (! (line_integral_exists$ veriT_vr47 veriT_vr50) :named @p_258))) :rule cong :premises (t93.t8 t93.t9)) -(step t93.t11 (cl @p_259) :rule refl) -(step t93.t12 (cl (= @p_260 (! (fun_app$a @p_258 veriT_vr49) :named @p_261))) :rule cong :premises (t93.t10 t93.t11)) -(step t93.t13 (cl @p_262) :rule refl) -(step t93.t14 (cl @p_263) :rule refl) -(step t93.t15 (cl @p_264) :rule refl) -(step t93.t16 (cl (= @p_265 (! (sup$ veriT_vr48 veriT_vr50) :named @p_266))) :rule cong :premises (t93.t14 t93.t15)) -(step t93.t17 (cl (= @p_267 (! (= veriT_vr46 @p_266) :named @p_268))) :rule cong :premises (t93.t13 t93.t16)) -(step t93.t18 (cl @p_263) :rule refl) -(step t93.t19 (cl @p_264) :rule refl) -(step t93.t20 (cl (= @p_269 (! 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(forall ((veriT_vr46 Real_real_prod_set$) (veriT_vr47 Real_real_prod_real_real_prod_fun$) (veriT_vr48 Real_real_prod_set$) (veriT_vr49 Real_real_real_prod_fun$) (veriT_vr50 Real_real_prod_set$)) @p_292) :named @p_294)) :named @p_293)) :rule bind) -(step t94 (cl (not @p_293) (not @p_250) @p_294) :rule equiv_pos2) -(step t95 (cl @p_294) :rule th_resolution :premises (a16 t93 t94)) -(anchor :step t96 :args (veriT_vr46 veriT_vr47 veriT_vr48 veriT_vr49 veriT_vr50)) -(step t96.t1 (cl (= @p_280 (! (and @p_251 @p_255 @p_261 @p_268 @p_272) :named @p_295))) :rule ac_simp) -(step t96.t2 (cl (= @p_292 (! (=> @p_295 @p_290) :named @p_296))) :rule cong :premises (t96.t1)) -(step t96 (cl (! (= @p_294 (! (forall ((veriT_vr46 Real_real_prod_set$) (veriT_vr47 Real_real_prod_real_real_prod_fun$) (veriT_vr48 Real_real_prod_set$) (veriT_vr49 Real_real_real_prod_fun$) (veriT_vr50 Real_real_prod_set$)) @p_296) :named @p_298)) :named @p_297)) :rule bind) -(step t97 (cl (not @p_297) (not @p_294) @p_298) :rule equiv_pos2) -(step t98 (cl @p_298) :rule th_resolution :premises (t95 t96 t97)) -(anchor :step t99 :args ((:= veriT_vr46 veriT_vr51) (:= veriT_vr47 veriT_vr52) (:= veriT_vr48 veriT_vr53) (:= veriT_vr49 veriT_vr54) (:= veriT_vr50 veriT_vr55))) -(step t99.t1 (cl (! (= veriT_vr46 veriT_vr51) :named @p_306)) :rule refl) -(step t99.t2 (cl (= @p_251 (! (finite$ veriT_vr51) :named @p_299))) :rule cong :premises (t99.t1)) -(step t99.t3 (cl (! (= veriT_vr47 veriT_vr52) :named @p_302)) :rule refl) -(step t99.t4 (cl (! (= veriT_vr48 veriT_vr53) :named @p_307)) :rule refl) -(step t99.t5 (cl (= @p_253 (! 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(forall ((veriT_vr51 Real_real_prod_set$) (veriT_vr52 Real_real_prod_real_real_prod_fun$) (veriT_vr53 Real_real_prod_set$) (veriT_vr54 Real_real_real_prod_fun$) (veriT_vr55 Real_real_prod_set$)) @p_319) :named @p_321)) :named @p_320)) :rule bind) -(step t100 (cl (not @p_320) (not @p_298) @p_321) :rule equiv_pos2) -(step t101 (cl @p_321) :rule th_resolution :premises (t98 t99 t100)) -(anchor :step t102 :args ((:= ?v0 veriT_vr56))) -(step t102.t1 (cl (! (= ?v0 veriT_vr56) :named @p_324)) :rule refl) -(step t102.t2 (cl (= @p_9 (! (member$ veriT_vr56 one_chain_typeI$) :named @p_323))) :rule cong :premises (t102.t1)) -(step t102.t3 (cl @p_324) :rule refl) -(step t102.t4 (cl (! (= @p_6 (! (case_prod$ uu$ veriT_vr56) :named @p_325)) :named @p_330)) :rule cong :premises (t102.t3)) -(step t102.t5 (cl (= @p_326 (! (=> @p_323 @p_325) :named @p_327))) :rule cong :premises (t102.t2 t102.t4)) -(step t102 (cl (= @p_322 (! (forall ((veriT_vr56 Int_real_real_real_prod_fun_prod$)) @p_327) :named @p_334))) :rule bind) -(anchor :step t103 :args ((:= ?v0 veriT_vr56))) -(step t103.t1 (cl @p_324) :rule refl) -(step t103.t2 (cl (= @p_8 (! (member$ veriT_vr56 one_chain_typeII$) :named @p_329))) :rule cong :premises (t103.t1)) -(step t103.t3 (cl @p_324) :rule refl) -(step t103.t4 (cl @p_330) :rule cong :premises (t103.t3)) -(step t103.t5 (cl (= @p_331 (! (=> @p_329 @p_325) :named @p_332))) :rule cong :premises (t103.t2 t103.t4)) -(step t103 (cl (= @p_328 (! (forall ((veriT_vr56 Int_real_real_real_prod_fun_prod$)) @p_332) :named @p_335))) :rule bind) -(step t104 (cl (= @p_333 (! (and @p_334 @p_335) :named @p_338))) :rule cong :premises (t102 t103)) -(step t105 (cl (! (= @p_336 (! (and @p_337 @p_338) :named @p_340)) :named @p_339)) :rule cong :premises (t104)) -(step t106 (cl (not @p_339) (not @p_336) @p_340) :rule equiv_pos2) -(step t107 (cl @p_340) :rule th_resolution :premises (a17 t105 t106)) -(step t108 (cl (! (= @p_340 (! (and @p_337 @p_334 @p_335) :named @p_342)) :named @p_341)) :rule ac_simp) -(step t109 (cl (not @p_341) (not @p_340) @p_342) :rule equiv_pos2) -(step t110 (cl @p_342) :rule th_resolution :premises (t107 t108 t109)) -(anchor :step t111 :args ((:= veriT_vr56 veriT_vr57))) -(step t111.t1 (cl (! (= veriT_vr56 veriT_vr57) :named @p_344)) :rule refl) -(step t111.t2 (cl (= @p_329 (! (member$ veriT_vr57 one_chain_typeII$) :named @p_343))) :rule cong :premises (t111.t1)) -(step t111.t3 (cl @p_344) :rule refl) -(step t111.t4 (cl (= @p_325 (! (case_prod$ uu$ veriT_vr57) :named @p_345))) :rule cong :premises (t111.t3)) -(step t111.t5 (cl (= @p_332 (! (=> @p_343 @p_345) :named @p_346))) :rule cong :premises (t111.t2 t111.t4)) -(step t111 (cl (= @p_335 (! (forall ((veriT_vr57 Int_real_real_real_prod_fun_prod$)) @p_346) :named @p_347))) :rule bind) -(step t112 (cl (! (= @p_342 (! (and @p_337 @p_334 @p_347) :named @p_349)) :named @p_348)) :rule cong :premises (t111)) -(step t113 (cl (not @p_348) (not @p_342) @p_349) :rule equiv_pos2) -(step t114 (cl @p_349) :rule th_resolution :premises (t110 t112 t113)) -(anchor :step t115 :args ((:= veriT_vr56 veriT_vr58))) -(step t115.t1 (cl (! (= veriT_vr56 veriT_vr58) :named @p_351)) :rule refl) -(step t115.t2 (cl (= @p_323 (! (member$ veriT_vr58 one_chain_typeI$) :named @p_350))) :rule cong :premises (t115.t1)) -(step t115.t3 (cl @p_351) :rule refl) -(step t115.t4 (cl (= @p_325 (! (case_prod$ uu$ veriT_vr58) :named @p_352))) :rule cong :premises (t115.t3)) -(step t115.t5 (cl (= @p_327 (! (=> @p_350 @p_352) :named @p_353))) :rule cong :premises (t115.t2 t115.t4)) -(step t115 (cl (= @p_334 (! (forall ((veriT_vr58 Int_real_real_real_prod_fun_prod$)) @p_353) :named @p_358))) :rule bind) -(anchor :step t116 :args ((:= veriT_vr57 veriT_vr59))) -(step t116.t1 (cl (! (= veriT_vr57 veriT_vr59) :named @p_355)) :rule refl) -(step t116.t2 (cl (= @p_343 (! (member$ veriT_vr59 one_chain_typeII$) :named @p_354))) :rule cong :premises (t116.t1)) -(step t116.t3 (cl @p_355) :rule refl) -(step t116.t4 (cl (= @p_345 (! (case_prod$ uu$ veriT_vr59) :named @p_356))) :rule cong :premises (t116.t3)) -(step t116.t5 (cl (= @p_346 (! (=> @p_354 @p_356) :named @p_357))) :rule cong :premises (t116.t2 t116.t4)) -(step t116 (cl (= @p_347 (! (forall ((veriT_vr59 Int_real_real_real_prod_fun_prod$)) @p_357) :named @p_359))) :rule bind) -(step t117 (cl (! (= @p_349 (! (and @p_337 @p_358 @p_359) :named @p_361)) :named @p_360)) :rule cong :premises (t115 t116)) -(step t118 (cl (not @p_360) (not @p_349) @p_361) :rule equiv_pos2) -(step t119 (cl @p_361) :rule th_resolution :premises (t114 t117 t118)) -(anchor :step t120 :args ((:= ?v0 veriT_vr60))) -(step t120.t1 (cl (! (= ?v0 veriT_vr60) :named @p_364)) :rule refl) -(step t120.t2 (cl (= @p_8 (! (member$ veriT_vr60 one_chain_typeII$) :named @p_363))) :rule cong :premises (t120.t1)) -(step t120.t3 (cl @p_364) :rule refl) -(step t120.t4 (cl (! (= @p_10 (! (case_prod$ uua$ veriT_vr60) :named @p_365)) :named @p_370)) :rule cong :premises (t120.t3)) -(step t120.t5 (cl (= @p_366 (! (=> @p_363 @p_365) :named @p_367))) :rule cong :premises (t120.t2 t120.t4)) -(step t120 (cl (= @p_362 (! (forall ((veriT_vr60 Int_real_real_real_prod_fun_prod$)) @p_367) :named @p_374))) :rule bind) -(anchor :step t121 :args ((:= ?v0 veriT_vr60))) -(step t121.t1 (cl @p_364) :rule refl) -(step t121.t2 (cl (= @p_9 (! (member$ veriT_vr60 one_chain_typeI$) :named @p_369))) :rule cong :premises (t121.t1)) -(step t121.t3 (cl @p_364) :rule refl) -(step t121.t4 (cl @p_370) :rule cong :premises (t121.t3)) -(step t121.t5 (cl (= @p_371 (! (=> @p_369 @p_365) :named @p_372))) :rule cong :premises (t121.t2 t121.t4)) -(step t121 (cl (= @p_368 (! (forall ((veriT_vr60 Int_real_real_real_prod_fun_prod$)) @p_372) :named @p_375))) :rule bind) -(step t122 (cl (= @p_373 (! (and @p_374 @p_375) :named @p_378))) :rule cong :premises (t120 t121)) -(step t123 (cl (! (= @p_376 (! (and @p_377 @p_378) :named @p_380)) :named @p_379)) :rule cong :premises (t122)) -(step t124 (cl (not @p_379) (not @p_376) @p_380) :rule equiv_pos2) -(step t125 (cl @p_380) :rule th_resolution :premises (a18 t123 t124)) -(step t126 (cl (! (= @p_380 (! (and @p_377 @p_374 @p_375) :named @p_382)) :named @p_381)) :rule ac_simp) -(step t127 (cl (not @p_381) (not @p_380) @p_382) :rule equiv_pos2) -(step t128 (cl @p_382) :rule th_resolution :premises (t125 t126 t127)) -(anchor :step t129 :args ((:= veriT_vr60 veriT_vr61))) -(step t129.t1 (cl (! (= veriT_vr60 veriT_vr61) :named @p_384)) :rule refl) -(step t129.t2 (cl (= @p_369 (! (member$ veriT_vr61 one_chain_typeI$) :named @p_383))) :rule cong :premises (t129.t1)) -(step t129.t3 (cl @p_384) :rule refl) -(step t129.t4 (cl (= @p_365 (! (case_prod$ uua$ veriT_vr61) :named @p_385))) :rule cong :premises (t129.t3)) -(step t129.t5 (cl (= @p_372 (! (=> @p_383 @p_385) :named @p_386))) :rule cong :premises (t129.t2 t129.t4)) -(step t129 (cl (= @p_375 (! (forall ((veriT_vr61 Int_real_real_real_prod_fun_prod$)) @p_386) :named @p_387))) :rule bind) -(step t130 (cl (! (= @p_382 (! (and @p_377 @p_374 @p_387) :named @p_389)) :named @p_388)) :rule cong :premises (t129)) -(step t131 (cl (not @p_388) (not @p_382) @p_389) :rule equiv_pos2) -(step t132 (cl @p_389) :rule th_resolution :premises (t128 t130 t131)) -(anchor :step t133 :args ((:= veriT_vr60 veriT_vr62))) -(step t133.t1 (cl (! (= veriT_vr60 veriT_vr62) :named @p_391)) :rule refl) -(step t133.t2 (cl (= @p_363 (! (member$ veriT_vr62 one_chain_typeII$) :named @p_390))) :rule cong :premises (t133.t1)) -(step t133.t3 (cl @p_391) :rule refl) -(step t133.t4 (cl (= @p_365 (! (case_prod$ uua$ veriT_vr62) :named @p_392))) :rule cong :premises (t133.t3)) -(step t133.t5 (cl (= @p_367 (! (=> @p_390 @p_392) :named @p_393))) :rule cong :premises (t133.t2 t133.t4)) -(step t133 (cl (= @p_374 (! (forall ((veriT_vr62 Int_real_real_real_prod_fun_prod$)) @p_393) :named @p_398))) :rule bind) -(anchor :step t134 :args ((:= veriT_vr61 veriT_vr63))) -(step t134.t1 (cl (! (= veriT_vr61 veriT_vr63) :named @p_395)) :rule refl) -(step t134.t2 (cl (= @p_383 (! (member$ veriT_vr63 one_chain_typeI$) :named @p_394))) :rule cong :premises (t134.t1)) -(step t134.t3 (cl @p_395) :rule refl) -(step t134.t4 (cl (= @p_385 (! (case_prod$ uua$ veriT_vr63) :named @p_396))) :rule cong :premises (t134.t3)) -(step t134.t5 (cl (= @p_386 (! (=> @p_394 @p_396) :named @p_397))) :rule cong :premises (t134.t2 t134.t4)) -(step t134 (cl (= @p_387 (! (forall ((veriT_vr63 Int_real_real_real_prod_fun_prod$)) @p_397) :named @p_399))) :rule bind) -(step t135 (cl (! (= @p_389 (! (and @p_377 @p_398 @p_399) :named @p_401)) :named @p_400)) :rule cong :premises (t133 t134)) -(step t136 (cl (not @p_400) (not @p_389) @p_401) :rule equiv_pos2) -(step t137 (cl @p_401) :rule th_resolution :premises (t132 t135 t136)) -(step t138 (cl @p_358) :rule and :premises (t119)) -(step t139 (cl @p_399) :rule and :premises (t137)) -(step t140 (cl (or (! (not @p_399) :named @p_422) (! (=> @p_402 (! (case_prod$ uua$ @p_403) :named @p_421)) :named @p_420))) :rule forall_inst :args ((:= veriT_vr63 @p_403))) -(step t141 (cl (or (! (not @p_358) :named @p_427) (! (=> @p_402 (! (case_prod$ uu$ @p_403) :named @p_426)) :named @p_424))) :rule forall_inst :args ((:= veriT_vr58 @p_403))) -(step t142 (cl (or (! (not @p_321) :named @p_406) (! (=> (! (and (! (finite$ @p_5) :named @p_415) (! (fun_app$a @p_12 g$) :named @p_409) (! (fun_app$a @p_24 g$) :named @p_408) (! (= @p_5 (! (sup$ @p_7 @p_5) :named @p_466)) :named @p_430) (! (= bot$ (inf$ @p_7 @p_5)) :named @p_431)) :named @p_429) (! (= @p_404 (! (+ @p_405 @p_404) :named @p_528)) :named @p_433)) :named @p_432))) :rule forall_inst :args ((:= veriT_vr51 @p_5) (:= veriT_vr52 f$) (:= veriT_vr53 @p_7) (:= veriT_vr54 g$) (:= veriT_vr55 @p_5))) -(step t143 (cl (or @p_406 (! (=> (! (and (! (finite$ @p_407) :named @p_412) @p_408 @p_409 (! (= @p_407 (sup$ @p_5 @p_7)) :named @p_411) (! (= bot$ (inf$ @p_5 @p_7)) :named @p_437)) :named @p_434) @p_410) :named @p_438))) :rule forall_inst :args ((:= veriT_vr51 @p_407) (:= veriT_vr52 f$) (:= veriT_vr53 @p_5) (:= veriT_vr54 g$) (:= veriT_vr55 @p_7))) -(step t144 (cl (or (! (not @p_249) :named @p_441) @p_411)) :rule forall_inst :args ((:= veriT_vr44 i$) (:= veriT_vr45 @p_7))) -(step t145 (cl (or (! (not @p_230) :named @p_442) (! (= @p_407 (! (insert$ j$ @p_5) :named @p_467)) :named @p_443))) :rule forall_inst :args ((:= veriT_vr39 j$) (:= veriT_vr40 i$) (:= veriT_vr41 bot$))) -(step t146 (cl (or (! (not @p_194) :named @p_447) (! (=> (! (member$a i$ @p_7) :named @p_445) (! (= @p_7 @p_407) :named @p_446)) :named @p_444))) :rule forall_inst :args ((:= veriT_vr32 i$) (:= veriT_vr33 @p_7))) -(step t147 (cl (or (! (not @p_174) :named @p_413) (! (=> (! (finite$ @p_7) :named @p_416) @p_412) :named @p_448))) :rule forall_inst :args ((:= veriT_vr28 @p_7) (:= veriT_vr29 i$))) -(step t148 (cl (or @p_413 (! (=> @p_414 @p_415) :named @p_449))) :rule forall_inst :args ((:= veriT_vr28 bot$) (:= veriT_vr29 i$))) -(step t149 (cl (or @p_413 (! (=> @p_414 @p_416) :named @p_451))) :rule forall_inst :args ((:= veriT_vr28 bot$) (:= veriT_vr29 j$))) -(step t150 (cl (or (! (not @p_119) :named @p_418) (! (= 0.0 (! (snd$a @p_417) :named @p_495)) :named @p_454))) :rule forall_inst :args ((:= veriT_vr18 1.0) (:= veriT_vr19 0.0))) -(step t151 (cl (or @p_418 (! (= 1.0 (! (snd$a @p_419) :named @p_496)) :named @p_455))) :rule forall_inst :args ((:= veriT_vr18 0.0) (:= veriT_vr19 1.0))) -(step t152 (cl (or (! (not @p_100) :named @p_456) (! (= g$ (! (snd$ @p_403) :named @p_471)) :named @p_457))) :rule forall_inst :args ((:= veriT_vr14 k$) (:= veriT_vr15 g$))) -(step t153 (cl (or (! (not @p_84) :named @p_461) (! (=> (! (= @p_7 @p_5) :named @p_459) (! (= j$ i$) :named @p_460)) :named @p_458))) :rule forall_inst :args ((:= veriT_vr10 i$) (:= veriT_vr11 j$))) -(step t154 (cl (! (not @p_420) :named @p_423) (! (not @p_402) :named @p_425) @p_421) :rule implies_pos) -(step t155 (cl @p_422 @p_420) :rule or :premises (t140)) -(step t156 (cl @p_423 @p_421) :rule resolution :premises (t154 a6)) -(step t157 (cl @p_420) :rule resolution :premises (t155 t139)) -(step t158 (cl @p_421) :rule resolution :premises (t156 t157)) -(step t159 (cl (! (not @p_424) :named @p_428) @p_425 @p_426) :rule implies_pos) -(step t160 (cl @p_427 @p_424) :rule or :premises (t141)) -(step t161 (cl @p_428 @p_426) :rule resolution :premises (t159 a6)) -(step t162 (cl @p_424) :rule resolution :premises (t160 t138)) -(step t163 (cl @p_426) :rule resolution :premises (t161 t162)) -(step t164 (cl @p_429 (not @p_415) (! (not @p_409) :named @p_436) (! (not @p_408) :named @p_435) (not @p_430) (not @p_431)) :rule and_neg) -(step t165 (cl (not @p_432) (not @p_429) @p_433) :rule implies_pos) -(step t166 (cl @p_406 @p_432) :rule or :premises (t142)) -(step t167 (cl @p_432) :rule resolution :premises (t166 t101)) -(step t168 (cl @p_434 (not @p_412) @p_435 @p_436 (not @p_411) (! (not @p_437) :named @p_515)) :rule and_neg) -(step t169 (cl (! (not @p_438) :named @p_439) (! (not @p_434) :named @p_440) @p_410) :rule implies_pos) -(step t170 (cl @p_406 @p_438) :rule or :premises (t143)) -(step t171 (cl @p_439 @p_440) :rule resolution :premises (t169 a19)) -(step t172 (cl @p_438) :rule resolution :premises (t170 t101)) -(step t173 (cl @p_440) :rule resolution :premises (t171 t172)) -(step t174 (cl @p_441 @p_411) :rule or :premises (t144)) -(step t175 (cl @p_411) :rule resolution :premises (t174 t92)) -(step t176 (cl @p_442 @p_443) :rule or :premises (t145)) -(step t177 (cl @p_443) :rule resolution :premises (t176 t86)) -(step t178 (cl (not @p_444) (! (not @p_445) :named @p_470) @p_446) :rule implies_pos) -(step t179 (cl @p_447 @p_444) :rule or :premises (t146)) -(step t180 (cl @p_444) :rule resolution :premises (t179 t74)) -(step t181 (cl (not @p_448) (not @p_416) @p_412) :rule implies_pos) -(step t182 (cl @p_413 @p_448) :rule or :premises (t147)) -(step t183 (cl @p_448) :rule resolution :premises (t182 t68)) -(step t184 (cl (! (not @p_449) :named @p_450) (! (not @p_414) :named @p_452) @p_415) :rule implies_pos) -(step t185 (cl @p_413 @p_449) :rule or :premises (t148)) -(step t186 (cl @p_450 @p_415) :rule resolution :premises (t184 a8)) -(step t187 (cl @p_449) :rule resolution :premises (t185 t68)) -(step t188 (cl @p_415) :rule resolution :premises (t186 t187)) -(step t189 (cl (! (not @p_451) :named @p_453) @p_452 @p_416) :rule implies_pos) -(step t190 (cl @p_413 @p_451) :rule or :premises (t149)) -(step t191 (cl @p_453 @p_416) :rule resolution :premises (t189 a8)) -(step t192 (cl @p_451) :rule resolution :premises (t190 t68)) -(step t193 (cl @p_416) :rule resolution :premises (t191 t192)) -(step t194 (cl @p_412) :rule resolution :premises (t181 t193 t183)) -(step t195 (cl @p_418 @p_454) :rule or :premises (t150)) -(step t196 (cl @p_454) :rule resolution :premises (t195 t56)) -(step t197 (cl @p_418 @p_455) :rule or :premises (t151)) -(step t198 (cl @p_455) :rule resolution :premises (t197 t56)) -(step t199 (cl @p_456 @p_457) :rule or :premises (t152)) -(step t200 (cl @p_457) :rule resolution :premises (t199 t50)) -(step t201 (cl (not @p_458) (! (not @p_459) :named @p_507) @p_460) :rule implies_pos) -(step t202 (cl @p_461 @p_458) :rule or :premises (t153)) -(step t203 (cl @p_458) :rule resolution :premises (t202 t44)) -(step t204 (cl (or @p_410 (! (not (! (<= @p_462 @p_463) :named @p_534)) :named @p_464) (! (not (! (<= @p_463 @p_462) :named @p_535)) :named @p_465))) :rule la_disequality) -(step t205 (cl @p_410 @p_464 @p_465) :rule or :premises (t204)) -(step t206 (cl @p_464 @p_465) :rule resolution :premises (t205 a19)) -(step t207 (cl (or @p_441 (! (= @p_466 @p_467) :named @p_474))) :rule forall_inst :args ((:= veriT_vr44 j$) (:= veriT_vr45 @p_5))) -(step t208 (cl (or @p_447 (! (=> (! (member$a j$ @p_5) :named @p_468) (! (= @p_5 @p_467) :named @p_477)) :named @p_475))) :rule forall_inst :args ((:= veriT_vr32 j$) (:= veriT_vr33 @p_5))) -(step t209 (cl (or (! (not @p_156) :named @p_469) (! (= @p_437 (! (and (! (not @p_468) :named @p_476) (! (= bot$ (inf$ @p_5 bot$)) :named @p_479)) :named @p_478)) :named @p_482))) :rule forall_inst :args ((:= veriT_vr23 @p_5) (:= veriT_vr24 j$) (:= veriT_vr25 bot$))) -(step t210 (cl (or @p_469 (! (= @p_431 (! (and @p_470 (! (= bot$ (inf$ @p_7 bot$)) :named @p_485)) :named @p_483)) :named @p_487))) :rule forall_inst :args ((:= veriT_vr23 @p_7) (:= veriT_vr24 i$) (:= veriT_vr25 bot$))) -(step t211 (cl (or (! (not @p_61) :named @p_472) (! (= @p_426 (! (fun_app$a (! (fun_app$ uu$ (! (fst$ @p_403) :named @p_473)) :named @p_508) @p_471) :named @p_489)) :named @p_488))) :rule forall_inst :args ((:= veriT_vr6 uu$) (:= veriT_vr7 @p_403))) -(step t212 (cl (or @p_472 (! (= @p_421 (! (fun_app$a (! (fun_app$ uua$ @p_473) :named @p_509) @p_471) :named @p_492)) :named @p_491))) :rule forall_inst :args ((:= veriT_vr6 uua$) (:= veriT_vr7 @p_403))) -(step t213 (cl @p_441 @p_474) :rule or :premises (t207)) -(step t214 (cl @p_474) :rule resolution :premises (t213 t92)) -(step t215 (cl (not @p_475) @p_476 @p_477) :rule implies_pos) -(step t216 (cl @p_447 @p_475) :rule or :premises (t208)) -(step t217 (cl @p_475) :rule resolution :premises (t216 t74)) -(step t218 (cl (not (! (not @p_470) :named @p_484)) @p_445) :rule not_not) -(step t219 (cl @p_478 (! (not @p_476) :named @p_480) (! (not @p_479) :named @p_481)) :rule and_neg) -(step t220 (cl (not @p_480) @p_468) :rule not_not) -(step t221 (cl @p_478 @p_468 @p_481) :rule th_resolution :premises (t220 t219)) -(step t222 (cl (not @p_482) @p_437 (! (not @p_478) :named @p_516)) :rule equiv_pos1) -(step t223 (cl @p_469 @p_482) :rule or :premises (t209)) -(step t224 (cl @p_482) :rule resolution :premises (t223 t62)) -(step t225 (cl @p_483 @p_484 (! (not @p_485) :named @p_486)) :rule and_neg) -(step t226 (cl @p_483 @p_445 @p_486) :rule th_resolution :premises (t218 t225)) -(step t227 (cl (not @p_487) @p_431 (not @p_483)) :rule equiv_pos1) -(step t228 (cl @p_469 @p_487) :rule or :premises (t210)) -(step t229 (cl @p_487) :rule resolution :premises (t228 t62)) -(step t230 (cl (! (not @p_488) :named @p_490) (not @p_426) @p_489) :rule equiv_pos2) -(step t231 (cl @p_472 @p_488) :rule or :premises (t211)) -(step t232 (cl @p_490 @p_489) :rule resolution :premises (t230 t163)) -(step t233 (cl @p_488) :rule resolution :premises (t231 t38)) -(step t234 (cl @p_489) :rule resolution :premises (t232 t233)) -(step t235 (cl (! (not @p_491) :named @p_493) (not @p_421) @p_492) :rule equiv_pos2) -(step t236 (cl @p_472 @p_491) :rule or :premises (t212)) -(step t237 (cl @p_493 @p_492) :rule resolution :premises (t235 t158)) -(step t238 (cl @p_491) :rule resolution :premises (t236 t38)) -(step t239 (cl @p_492) :rule resolution :premises (t237 t238)) -(step t240 (cl (or (! (not @p_205) :named @p_494) @p_479)) :rule forall_inst :args ((:= veriT_vr35 @p_5))) -(step t241 (cl (or @p_494 @p_485)) :rule forall_inst :args ((:= veriT_vr35 @p_7))) -(step t242 (cl @p_494 @p_479) :rule or :premises (t240)) -(step t243 (cl @p_479) :rule resolution :premises (t242 t80)) -(step t244 (cl @p_494 @p_485) :rule or :premises (t241)) -(step t245 (cl @p_485) :rule resolution :premises (t244 t80)) -(step t246 (cl (! (= @p_7 @p_7) :named @p_520)) :rule eq_reflexive) -(step t247 (cl (not (! (= 1.0 0.0) :named @p_497))) :rule la_generic :args ((- 1))) -(step t248 (cl (! (not @p_455) :named @p_505) (not (! (= @p_495 @p_496) :named @p_498)) (! (not @p_454) :named @p_506) @p_497) :rule eq_transitive) -(step t249 (cl (not (! (= @p_417 @p_419) :named @p_501)) @p_498) :rule eq_congruent) -(step t250 (cl (! (not @p_499) :named @p_502) (! (not @p_460) :named @p_503) (! (not @p_500) :named @p_504) @p_501) :rule eq_transitive) -(step t251 (cl @p_498 @p_502 @p_503 @p_504) :rule th_resolution :premises (t249 t250)) -(step t252 (cl @p_505 @p_506 @p_497 @p_502 @p_503 @p_504) :rule th_resolution :premises (t248 t251)) -(step t253 (cl @p_505 @p_506 @p_502 @p_503 @p_504) :rule th_resolution :premises (t247 t252)) -(step t254 (cl @p_503) :rule resolution :premises (t253 a10 a12 t196 t198)) -(step t255 (cl @p_507) :rule resolution :premises (t201 t254 t203)) -(step t256 (cl (! (= f$ f$) :named @p_523)) :rule eq_reflexive) -(step t257 (cl (! (= g$ g$) :named @p_524)) :rule eq_reflexive) -(step t258 (cl (! (= @p_405 @p_405) :named @p_527)) :rule eq_reflexive) -(step t259 (cl (or (! (not @p_34) :named @p_510) (! (= @p_24 @p_508) :named @p_511))) :rule forall_inst :args ((:= veriT_vr3 @p_473))) -(step t260 (cl (or (! (not @p_22) :named @p_512) (! (= @p_12 @p_509) :named @p_513))) :rule forall_inst :args ((:= veriT_vr1 @p_473))) -(step t261 (cl @p_510 @p_511) :rule or :premises (t259)) -(step t262 (cl @p_511) :rule resolution :premises (t261 t32)) -(step t263 (cl @p_512 @p_513) :rule or :premises (t260)) -(step t264 (cl @p_513) :rule resolution :premises (t263 t26)) -(step t265 (cl (not @p_511) (! (not @p_457) :named @p_514) @p_408 (not @p_489)) :rule eq_congruent_pred) -(step t266 (cl @p_408) :rule resolution :premises (t265 t200 t234 t262)) -(step t267 (cl (not @p_513) @p_514 @p_409 (not @p_492)) :rule eq_congruent_pred) -(step t268 (cl @p_409) :rule resolution :premises (t267 t200 t239 t264)) -(step t269 (cl @p_515) :rule resolution :premises (t168 t268 t194 t173 t175 t266)) -(step t270 (cl @p_516) :rule resolution :premises (t222 t269 t224)) -(step t271 (cl @p_468) :rule resolution :premises (t221 t270 t243)) -(step t272 (cl @p_477) :rule resolution :premises (t215 t271 t217)) -(step t273 (cl (! (not @p_477) :named @p_517) (not @p_474) @p_430) :rule eq_transitive) -(step t274 (cl @p_430) :rule resolution :premises (t273 t214 t272)) -(step t275 (cl @p_517 (! (not @p_443) :named @p_518) (! (= @p_5 @p_407) :named @p_519)) :rule eq_transitive) -(step t276 (cl @p_518 @p_517 @p_519) :rule eq_transitive) -(step t277 (cl (not @p_520) (! (not @p_446) :named @p_521) (! (not @p_519) :named @p_522) @p_459) :rule eq_transitive) -(step t278 (cl @p_521 @p_522 @p_459) :rule th_resolution :premises (t277 t246)) -(step t279 (cl @p_521 @p_459 @p_518 @p_517) :rule th_resolution :premises (t278 t276)) -(step t280 (cl @p_521) :rule resolution :premises (t279 t177 t255 t272)) -(step t281 (cl (not @p_523) @p_522 (! (not @p_524) :named @p_525) (! (= @p_462 @p_404) :named @p_526)) :rule eq_congruent) -(step t282 (cl @p_522 @p_525 @p_526) :rule th_resolution :premises (t281 t256)) -(step t283 (cl @p_522 @p_526) :rule th_resolution :premises (t282 t257)) -(step t284 (cl @p_526 @p_517 @p_518) :rule th_resolution :premises (t283 t275)) -(step t285 (cl @p_470) :rule resolution :premises (t178 t280 t180)) -(step t286 (cl @p_483) :rule resolution :premises (t226 t285 t245)) -(step t287 (cl @p_431) :rule resolution :premises (t227 t286 t229)) -(step t288 (cl @p_429) :rule resolution :premises (t164 t287 t188 t266 t268 t274)) -(step t289 (cl @p_433) :rule resolution :premises (t165 t288 t167)) -(step t290 (cl (not @p_527) (! (not @p_526) :named @p_529) (! (= (! (+ @p_405 @p_462) :named @p_531) @p_528) :named @p_530)) :rule eq_congruent) -(step t291 (cl @p_529 @p_530) :rule th_resolution :premises (t290 t258)) -(step t292 (cl @p_530 @p_517 @p_518) :rule th_resolution :premises (t291 t284)) -(step t293 (cl (! (not @p_433) :named @p_532) (not @p_530) (! (= @p_404 @p_531) :named @p_533)) :rule eq_transitive) -(step t294 (cl @p_532 @p_533 @p_517 @p_518) :rule th_resolution :premises (t293 t292)) -(step t295 (cl @p_534 @p_529 (! (not @p_533) :named @p_536)) :rule la_generic :args (1.0 (- 2) (- 1))) -(step t296 (cl @p_534 @p_517 @p_518 @p_532) :rule th_resolution :premises (t295 t284 t294)) -(step t297 (cl @p_534) :rule resolution :premises (t296 t289 t177 t272)) -(step t298 (cl @p_465) :rule resolution :premises (t206 t297)) -(step t299 (cl @p_535 @p_529 @p_536) :rule la_generic :args (1.0 2 1)) -(step t300 (cl @p_535 @p_517 @p_518 @p_532) :rule th_resolution :premises (t299 t284 t294)) -(step t301 (cl) :rule resolution :premises (t300 t289 t177 t298 t272)) a5b152c08be1e0a4da353f094af8f11f36a16f52 333 0 unsat (assume a0 (not x0$)) @@ -1622,9 +967,9 @@ (step t36 (cl (or @p_30 @p_44)) :rule forall_inst :args ((:= veriT_vr2 x$))) (step t37 (cl @p_30 @p_44) :rule or :premises (t36)) (step t38 (cl) :rule resolution :premises (t37 t34 t35)) -fa126f313953bee2fb2b0380ecf176cbb28700f5 12 0 +ccb9d5509f5273cf85143c83133df9d0fe59cf61 12 0 unsat -(assume a0 (! (not (! (= 3.0 3.0) :named @p_1)) :named @p_2)) +(assume a0 (! (not (! (= 3 3) :named @p_1)) :named @p_2)) (step t2 (cl (= @p_1 true)) :rule eq_simplify) (step t3 (cl (= @p_2 (! (not true) :named @p_3))) :rule cong :premises (t2)) (step t4 (cl (= @p_3 false)) :rule not_simplify) @@ -1635,9 +980,9 @@ (step t9 (cl false) :rule th_resolution :premises (a0 t5 t8)) (step t10 (cl (not false)) :rule false) (step t11 (cl) :rule resolution :premises (t9 t10)) -ccb9d5509f5273cf85143c83133df9d0fe59cf61 12 0 +fa126f313953bee2fb2b0380ecf176cbb28700f5 12 0 unsat -(assume a0 (! (not (! (= 3 3) :named @p_1)) :named @p_2)) +(assume a0 (! (not (! (= 3.0 3.0) :named @p_1)) :named @p_2)) (step t2 (cl (= @p_1 true)) :rule eq_simplify) (step t3 (cl (= @p_2 (! (not true) :named @p_3))) :rule cong :premises (t2)) (step t4 (cl (= @p_3 false)) :rule not_simplify) @@ -5549,6 +4894,661 @@ (step t591 (cl @p_1136) :rule eq_reflexive) (step t592 (cl @p_1135 @p_790 @p_1092) :rule th_resolution :premises (t590 t591)) (step t593 (cl) :rule resolution :premises (t592 a24 t588 t586)) +8616c6debd3ebae49adf8409b8c1ecb6665bc881 654 0 +unsat +(assume a0 (! (forall ((?v0 Int)) (! (= (! (fun_app$ uua$ ?v0) :named @p_13) (! (line_integral_exists$ f$ (! (insert$ j$ bot$) :named @p_7)) :named @p_12)) :named @p_15)) :named @p_11)) +(assume a1 (! (forall ((?v0 Int)) (! (= (! (fun_app$ uu$ ?v0) :named @p_25) (! (line_integral_exists$ f$ (! (insert$ i$ bot$) :named @p_5)) :named @p_24)) :named @p_27)) :named @p_23)) +(assume a2 (! (forall ((?v0 Int_real_real_real_prod_fun_bool_fun_fun$) (?v1 Int_real_real_real_prod_fun_prod$)) (! (= (! (case_prod$ ?v0 ?v1) :named @p_36) (! (fun_app$a (! (fun_app$ ?v0 (! (fst$ ?v1) :named @p_40)) :named @p_42) (! (snd$ ?v1) :named @p_44)) :named @p_46)) :named @p_48)) :named @p_35)) +(assume a3 (! (forall ((?v0 Real_real_prod$) (?v1 Real_real_prod$)) (! (=> (! (= (! (insert$ ?v0 bot$) :named @p_3) (! (insert$ ?v1 bot$) :named @p_64)) :named @p_66) (! (= ?v0 ?v1) :named @p_70)) :named @p_72)) :named @p_62)) +(assume a4 (! (forall ((?v0 Int) (?v1 Real_real_real_prod_fun$)) (! (= ?v1 (! (snd$ (! (pair$ ?v0 ?v1) :named @p_87)) :named @p_89)) :named @p_91)) :named @p_85)) +(assume a5 (! (forall ((?v0 Real) (?v1 Real)) (! (= ?v1 (! (snd$a (! (fun_app$b (! (pair$a ?v0) :named @p_102) ?v1) :named @p_105)) :named @p_107)) :named @p_109)) :named @p_101)) +(assume a6 (! (member$ (! (pair$ k$ g$) :named @p_403) one_chain_typeI$) :named @p_402)) +(assume a7 (! (forall ((?v0 Real_real_prod_set$) (?v1 Real_real_prod$) (?v2 Real_real_prod_set$)) (! (= (! (= bot$ (! (inf$ ?v0 (! (insert$ ?v1 ?v2) :named @p_1)) :named @p_122)) :named @p_124) (! (and (! (not (! (member$a ?v1 ?v0) :named @p_128)) :named @p_130) (! (= bot$ (! (inf$ ?v0 ?v2) :named @p_133)) :named @p_135)) :named @p_137)) :named @p_139)) :named @p_120)) +(assume a8 (! (finite$ bot$) :named @p_414)) +(assume a9 (! (forall ((?v0 Real_real_prod_set$) (?v1 Real_real_prod$)) (! (=> (! (finite$ ?v0) :named @p_4) (! (finite$ (! (insert$ ?v1 ?v0) :named @p_160)) :named @p_162)) :named @p_164)) :named @p_157)) +(assume a10 (! (= i$ (! (fun_app$b (pair$a 1.0) 0.0) :named @p_417)) :named @p_499)) +(assume a11 (! (forall ((?v0 Real_real_prod$) (?v1 Real_real_prod_set$)) (! (=> (! (member$a ?v0 ?v1) :named @p_176) (! (= ?v1 (! (insert$ ?v0 ?v1) :named @p_2)) :named @p_181)) :named @p_183)) :named @p_175)) +(assume a12 (! (= j$ (! (fun_app$b (pair$a 0.0) 1.0) :named @p_419)) :named @p_500)) +(assume a13 (! (forall ((?v0 Real_real_prod_set$)) (! (= bot$ (! (inf$ ?v0 bot$) :named @p_196)) :named @p_198)) :named @p_195)) +(assume a14 (! (forall ((?v0 Real_real_prod$) (?v1 Real_real_prod$) (?v2 Real_real_prod_set$)) (! (= (! (insert$ ?v0 @p_1) :named @p_208) (! (insert$ ?v1 (! (insert$ ?v0 ?v2) :named @p_213)) :named @p_215)) :named @p_217)) :named @p_206)) +(assume a15 (! (forall ((?v0 Real_real_prod$) (?v1 Real_real_prod_set$)) (! (= @p_2 (! (sup$ @p_3 ?v1) :named @p_236)) :named @p_238)) :named @p_231)) +(assume a16 (! (forall ((?v0 Real_real_prod_set$) (?v1 Real_real_prod_real_real_prod_fun$) (?v2 Real_real_prod_set$) (?v3 Real_real_real_prod_fun$) (?v4 Real_real_prod_set$)) (! (=> (! (and @p_4 (! (and (! (fun_app$a (! (line_integral_exists$ ?v1 ?v2) :named @p_252) ?v3) :named @p_254) (! (and (! (fun_app$a (! (line_integral_exists$ ?v1 ?v4) :named @p_257) ?v3) :named @p_260) (! (and (! (= ?v0 (! (sup$ ?v2 ?v4) :named @p_265)) :named @p_267) (! (= bot$ (! (inf$ ?v2 ?v4) :named @p_269)) :named @p_271)) :named @p_273)) :named @p_275)) :named @p_277)) :named @p_279) (! (= (! (line_integral$ ?v1 ?v0 ?v3) :named @p_281) (! (+ (! (line_integral$ ?v1 ?v2 ?v3) :named @p_283) (! (line_integral$ ?v1 ?v4 ?v3) :named @p_285)) :named @p_287)) :named @p_289)) :named @p_291)) :named @p_250)) +(assume a17 (! (and (! (= (one_chain_line_integral$ f$ @p_5 one_chain_typeI$) (one_chain_line_integral$ f$ @p_5 one_chain_typeII$)) :named @p_337) (! (and (! (forall ((?v0 Int_real_real_real_prod_fun_prod$)) (! (=> (! (member$ ?v0 one_chain_typeI$) :named @p_9) (! (case_prod$ uu$ ?v0) :named @p_6)) :named @p_326)) :named @p_322) (! (forall ((?v0 Int_real_real_real_prod_fun_prod$)) (! (=> (! (member$ ?v0 one_chain_typeII$) :named @p_8) @p_6) :named @p_331)) :named @p_328)) :named @p_333)) :named @p_336)) +(assume a18 (! (and (! (= (one_chain_line_integral$ f$ @p_7 one_chain_typeII$) (one_chain_line_integral$ f$ @p_7 one_chain_typeI$)) :named @p_377) (! (and (! (forall ((?v0 Int_real_real_real_prod_fun_prod$)) (! (=> @p_8 (! (case_prod$ uua$ ?v0) :named @p_10)) :named @p_366)) :named @p_362) (! (forall ((?v0 Int_real_real_real_prod_fun_prod$)) (! (=> @p_9 @p_10) :named @p_371)) :named @p_368)) :named @p_373)) :named @p_376)) +(assume a19 (not (! (= (! (line_integral$ f$ (! (insert$ i$ @p_7) :named @p_407) g$) :named @p_462) (! (+ (! (line_integral$ f$ @p_5 g$) :named @p_404) (! (line_integral$ f$ @p_7 g$) :named @p_405)) :named @p_463)) :named @p_410))) +(anchor :step t21 :args ((:= ?v0 veriT_vr0))) +(step t21.t1 (cl (= ?v0 veriT_vr0)) :rule refl) +(step t21.t2 (cl (= @p_13 (! (fun_app$ uua$ veriT_vr0) :named @p_14))) :rule cong :premises (t21.t1)) +(step t21.t3 (cl (= @p_15 (! (= @p_12 @p_14) :named @p_16))) :rule cong :premises (t21.t2)) +(step t21 (cl (! (= @p_11 (! (forall ((veriT_vr0 Int)) @p_16) :named @p_18)) :named @p_17)) :rule bind) +(step t22 (cl (not @p_17) (not @p_11) @p_18) :rule equiv_pos2) +(step t23 (cl @p_18) :rule th_resolution :premises (a0 t21 t22)) +(anchor :step t24 :args ((:= veriT_vr0 veriT_vr1))) +(step t24.t1 (cl (= veriT_vr0 veriT_vr1)) :rule refl) +(step t24.t2 (cl (= @p_14 (! (fun_app$ uua$ veriT_vr1) :named @p_19))) :rule cong :premises (t24.t1)) +(step t24.t3 (cl (= @p_16 (! (= @p_12 @p_19) :named @p_20))) :rule cong :premises (t24.t2)) +(step t24 (cl (! (= @p_18 (! (forall ((veriT_vr1 Int)) @p_20) :named @p_22)) :named @p_21)) :rule bind) +(step t25 (cl (not @p_21) (not @p_18) @p_22) :rule equiv_pos2) +(step t26 (cl @p_22) :rule th_resolution :premises (t23 t24 t25)) +(anchor :step t27 :args ((:= ?v0 veriT_vr2))) +(step t27.t1 (cl (= ?v0 veriT_vr2)) :rule refl) +(step t27.t2 (cl (= @p_25 (! (fun_app$ uu$ veriT_vr2) :named @p_26))) :rule cong :premises (t27.t1)) +(step t27.t3 (cl (= @p_27 (! (= @p_24 @p_26) :named @p_28))) :rule cong :premises (t27.t2)) +(step t27 (cl (! (= @p_23 (! (forall ((veriT_vr2 Int)) @p_28) :named @p_30)) :named @p_29)) :rule bind) +(step t28 (cl (not @p_29) (not @p_23) @p_30) :rule equiv_pos2) +(step t29 (cl @p_30) :rule th_resolution :premises (a1 t27 t28)) +(anchor :step t30 :args ((:= veriT_vr2 veriT_vr3))) +(step t30.t1 (cl (= veriT_vr2 veriT_vr3)) :rule refl) +(step t30.t2 (cl (= @p_26 (! (fun_app$ uu$ veriT_vr3) :named @p_31))) :rule cong :premises (t30.t1)) +(step t30.t3 (cl (= @p_28 (! (= @p_24 @p_31) :named @p_32))) :rule cong :premises (t30.t2)) +(step t30 (cl (! (= @p_30 (! (forall ((veriT_vr3 Int)) @p_32) :named @p_34)) :named @p_33)) :rule bind) +(step t31 (cl (not @p_33) (not @p_30) @p_34) :rule equiv_pos2) +(step t32 (cl @p_34) :rule th_resolution :premises (t29 t30 t31)) +(anchor :step t33 :args ((:= ?v0 veriT_vr4) (:= ?v1 veriT_vr5))) +(step t33.t1 (cl (! (= ?v0 veriT_vr4) :named @p_38)) :rule refl) +(step t33.t2 (cl (! (= ?v1 veriT_vr5) :named @p_39)) :rule refl) +(step t33.t3 (cl (= @p_36 (! (case_prod$ veriT_vr4 veriT_vr5) :named @p_37))) :rule cong :premises (t33.t1 t33.t2)) +(step t33.t4 (cl @p_38) :rule refl) +(step t33.t5 (cl @p_39) :rule refl) +(step t33.t6 (cl (= @p_40 (! (fst$ veriT_vr5) :named @p_41))) :rule cong :premises (t33.t5)) +(step t33.t7 (cl (= @p_42 (! (fun_app$ veriT_vr4 @p_41) :named @p_43))) :rule cong :premises (t33.t4 t33.t6)) +(step t33.t8 (cl @p_39) :rule refl) +(step t33.t9 (cl (= @p_44 (! (snd$ veriT_vr5) :named @p_45))) :rule cong :premises (t33.t8)) +(step t33.t10 (cl (= @p_46 (! (fun_app$a @p_43 @p_45) :named @p_47))) :rule cong :premises (t33.t7 t33.t9)) +(step t33.t11 (cl (= @p_48 (! (= @p_37 @p_47) :named @p_49))) :rule cong :premises (t33.t3 t33.t10)) +(step t33 (cl (! (= @p_35 (! 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(forall ((veriT_vr56 Int_real_real_real_prod_fun_prod$)) @p_327) :named @p_334))) :rule bind) +(anchor :step t103 :args ((:= ?v0 veriT_vr56))) +(step t103.t1 (cl @p_324) :rule refl) +(step t103.t2 (cl (= @p_8 (! (member$ veriT_vr56 one_chain_typeII$) :named @p_329))) :rule cong :premises (t103.t1)) +(step t103.t3 (cl @p_324) :rule refl) +(step t103.t4 (cl @p_330) :rule cong :premises (t103.t3)) +(step t103.t5 (cl (= @p_331 (! (=> @p_329 @p_325) :named @p_332))) :rule cong :premises (t103.t2 t103.t4)) +(step t103 (cl (= @p_328 (! (forall ((veriT_vr56 Int_real_real_real_prod_fun_prod$)) @p_332) :named @p_335))) :rule bind) +(step t104 (cl (= @p_333 (! (and @p_334 @p_335) :named @p_338))) :rule cong :premises (t102 t103)) +(step t105 (cl (! (= @p_336 (! (and @p_337 @p_338) :named @p_340)) :named @p_339)) :rule cong :premises (t104)) +(step t106 (cl (not @p_339) (not @p_336) @p_340) :rule equiv_pos2) +(step t107 (cl @p_340) :rule th_resolution :premises (a17 t105 t106)) +(step t108 (cl (! (= @p_340 (! (and @p_337 @p_334 @p_335) :named @p_342)) :named @p_341)) :rule ac_simp) +(step t109 (cl (not @p_341) (not @p_340) @p_342) :rule equiv_pos2) +(step t110 (cl @p_342) :rule th_resolution :premises (t107 t108 t109)) +(anchor :step t111 :args ((:= veriT_vr56 veriT_vr57))) +(step t111.t1 (cl (! (= veriT_vr56 veriT_vr57) :named @p_344)) :rule refl) +(step t111.t2 (cl (= @p_329 (! (member$ veriT_vr57 one_chain_typeII$) :named @p_343))) :rule cong :premises (t111.t1)) +(step t111.t3 (cl @p_344) :rule refl) +(step t111.t4 (cl (= @p_325 (! (case_prod$ uu$ veriT_vr57) :named @p_345))) :rule cong :premises (t111.t3)) +(step t111.t5 (cl (= @p_332 (! (=> @p_343 @p_345) :named @p_346))) :rule cong :premises (t111.t2 t111.t4)) +(step t111 (cl (= @p_335 (! (forall ((veriT_vr57 Int_real_real_real_prod_fun_prod$)) @p_346) :named @p_347))) :rule bind) +(step t112 (cl (! (= @p_342 (! (and @p_337 @p_334 @p_347) :named @p_349)) :named @p_348)) :rule cong :premises (t111)) +(step t113 (cl (not @p_348) (not @p_342) @p_349) :rule equiv_pos2) +(step t114 (cl @p_349) :rule th_resolution :premises (t110 t112 t113)) +(anchor :step t115 :args ((:= veriT_vr56 veriT_vr58))) +(step t115.t1 (cl (! (= veriT_vr56 veriT_vr58) :named @p_351)) :rule refl) +(step t115.t2 (cl (= @p_323 (! (member$ veriT_vr58 one_chain_typeI$) :named @p_350))) :rule cong :premises (t115.t1)) +(step t115.t3 (cl @p_351) :rule refl) +(step t115.t4 (cl (= @p_325 (! (case_prod$ uu$ veriT_vr58) :named @p_352))) :rule cong :premises (t115.t3)) +(step t115.t5 (cl (= @p_327 (! (=> @p_350 @p_352) :named @p_353))) :rule cong :premises (t115.t2 t115.t4)) +(step t115 (cl (= @p_334 (! (forall ((veriT_vr58 Int_real_real_real_prod_fun_prod$)) @p_353) :named @p_358))) :rule bind) +(anchor :step t116 :args ((:= veriT_vr57 veriT_vr59))) +(step t116.t1 (cl (! (= veriT_vr57 veriT_vr59) :named @p_355)) :rule refl) +(step t116.t2 (cl (= @p_343 (! (member$ veriT_vr59 one_chain_typeII$) :named @p_354))) :rule cong :premises (t116.t1)) +(step t116.t3 (cl @p_355) :rule refl) +(step t116.t4 (cl (= @p_345 (! (case_prod$ uu$ veriT_vr59) :named @p_356))) :rule cong :premises (t116.t3)) +(step t116.t5 (cl (= @p_346 (! (=> @p_354 @p_356) :named @p_357))) :rule cong :premises (t116.t2 t116.t4)) +(step t116 (cl (= @p_347 (! (forall ((veriT_vr59 Int_real_real_real_prod_fun_prod$)) @p_357) :named @p_359))) :rule bind) +(step t117 (cl (! (= @p_349 (! (and @p_337 @p_358 @p_359) :named @p_361)) :named @p_360)) :rule cong :premises (t115 t116)) +(step t118 (cl (not @p_360) (not @p_349) @p_361) :rule equiv_pos2) +(step t119 (cl @p_361) :rule th_resolution :premises (t114 t117 t118)) +(anchor :step t120 :args ((:= ?v0 veriT_vr60))) +(step t120.t1 (cl (! (= ?v0 veriT_vr60) :named @p_364)) :rule refl) +(step t120.t2 (cl (= @p_8 (! (member$ veriT_vr60 one_chain_typeII$) :named @p_363))) :rule cong :premises (t120.t1)) +(step t120.t3 (cl @p_364) :rule refl) +(step t120.t4 (cl (! (= @p_10 (! (case_prod$ uua$ veriT_vr60) :named @p_365)) :named @p_370)) :rule cong :premises (t120.t3)) +(step t120.t5 (cl (= @p_366 (! (=> @p_363 @p_365) :named @p_367))) :rule cong :premises (t120.t2 t120.t4)) +(step t120 (cl (= @p_362 (! (forall ((veriT_vr60 Int_real_real_real_prod_fun_prod$)) @p_367) :named @p_374))) :rule bind) +(anchor :step t121 :args ((:= ?v0 veriT_vr60))) +(step t121.t1 (cl @p_364) :rule refl) +(step t121.t2 (cl (= @p_9 (! (member$ veriT_vr60 one_chain_typeI$) :named @p_369))) :rule cong :premises (t121.t1)) +(step t121.t3 (cl @p_364) :rule refl) +(step t121.t4 (cl @p_370) :rule cong :premises (t121.t3)) +(step t121.t5 (cl (= @p_371 (! (=> @p_369 @p_365) :named @p_372))) :rule cong :premises (t121.t2 t121.t4)) +(step t121 (cl (= @p_368 (! (forall ((veriT_vr60 Int_real_real_real_prod_fun_prod$)) @p_372) :named @p_375))) :rule bind) +(step t122 (cl (= @p_373 (! (and @p_374 @p_375) :named @p_378))) :rule cong :premises (t120 t121)) +(step t123 (cl (! (= @p_376 (! (and @p_377 @p_378) :named @p_380)) :named @p_379)) :rule cong :premises (t122)) +(step t124 (cl (not @p_379) (not @p_376) @p_380) :rule equiv_pos2) +(step t125 (cl @p_380) :rule th_resolution :premises (a18 t123 t124)) +(step t126 (cl (! (= @p_380 (! (and @p_377 @p_374 @p_375) :named @p_382)) :named @p_381)) :rule ac_simp) +(step t127 (cl (not @p_381) (not @p_380) @p_382) :rule equiv_pos2) +(step t128 (cl @p_382) :rule th_resolution :premises (t125 t126 t127)) +(anchor :step t129 :args ((:= veriT_vr60 veriT_vr61))) +(step t129.t1 (cl (! (= veriT_vr60 veriT_vr61) :named @p_384)) :rule refl) +(step t129.t2 (cl (= @p_369 (! (member$ veriT_vr61 one_chain_typeI$) :named @p_383))) :rule cong :premises (t129.t1)) +(step t129.t3 (cl @p_384) :rule refl) +(step t129.t4 (cl (= @p_365 (! (case_prod$ uua$ veriT_vr61) :named @p_385))) :rule cong :premises (t129.t3)) +(step t129.t5 (cl (= @p_372 (! (=> @p_383 @p_385) :named @p_386))) :rule cong :premises (t129.t2 t129.t4)) +(step t129 (cl (= @p_375 (! (forall ((veriT_vr61 Int_real_real_real_prod_fun_prod$)) @p_386) :named @p_387))) :rule bind) +(step t130 (cl (! (= @p_382 (! (and @p_377 @p_374 @p_387) :named @p_389)) :named @p_388)) :rule cong :premises (t129)) +(step t131 (cl (not @p_388) (not @p_382) @p_389) :rule equiv_pos2) +(step t132 (cl @p_389) :rule th_resolution :premises (t128 t130 t131)) +(anchor :step t133 :args ((:= veriT_vr60 veriT_vr62))) +(step t133.t1 (cl (! (= veriT_vr60 veriT_vr62) :named @p_391)) :rule refl) +(step t133.t2 (cl (= @p_363 (! (member$ veriT_vr62 one_chain_typeII$) :named @p_390))) :rule cong :premises (t133.t1)) +(step t133.t3 (cl @p_391) :rule refl) +(step t133.t4 (cl (= @p_365 (! (case_prod$ uua$ veriT_vr62) :named @p_392))) :rule cong :premises (t133.t3)) +(step t133.t5 (cl (= @p_367 (! (=> @p_390 @p_392) :named @p_393))) :rule cong :premises (t133.t2 t133.t4)) +(step t133 (cl (= @p_374 (! (forall ((veriT_vr62 Int_real_real_real_prod_fun_prod$)) @p_393) :named @p_398))) :rule bind) +(anchor :step t134 :args ((:= veriT_vr61 veriT_vr63))) +(step t134.t1 (cl (! (= veriT_vr61 veriT_vr63) :named @p_395)) :rule refl) +(step t134.t2 (cl (= @p_383 (! (member$ veriT_vr63 one_chain_typeI$) :named @p_394))) :rule cong :premises (t134.t1)) +(step t134.t3 (cl @p_395) :rule refl) +(step t134.t4 (cl (= @p_385 (! (case_prod$ uua$ veriT_vr63) :named @p_396))) :rule cong :premises (t134.t3)) +(step t134.t5 (cl (= @p_386 (! (=> @p_394 @p_396) :named @p_397))) :rule cong :premises (t134.t2 t134.t4)) +(step t134 (cl (= @p_387 (! (forall ((veriT_vr63 Int_real_real_real_prod_fun_prod$)) @p_397) :named @p_399))) :rule bind) +(step t135 (cl (! (= @p_389 (! (and @p_377 @p_398 @p_399) :named @p_401)) :named @p_400)) :rule cong :premises (t133 t134)) +(step t136 (cl (not @p_400) (not @p_389) @p_401) :rule equiv_pos2) +(step t137 (cl @p_401) :rule th_resolution :premises (t132 t135 t136)) +(step t138 (cl @p_358) :rule and :premises (t119)) +(step t139 (cl @p_399) :rule and :premises (t137)) +(step t140 (cl (or (! (not @p_399) :named @p_422) (! (=> @p_402 (! (case_prod$ uua$ @p_403) :named @p_421)) :named @p_420))) :rule forall_inst :args ((:= veriT_vr63 @p_403))) +(step t141 (cl (or (! (not @p_358) :named @p_427) (! (=> @p_402 (! (case_prod$ uu$ @p_403) :named @p_426)) :named @p_424))) :rule forall_inst :args ((:= veriT_vr58 @p_403))) +(step t142 (cl (or (! (not @p_321) :named @p_406) (! (=> (! (and (! (finite$ @p_5) :named @p_415) (! (fun_app$a @p_12 g$) :named @p_409) (! (fun_app$a @p_24 g$) :named @p_408) (! (= @p_5 (! (sup$ @p_7 @p_5) :named @p_466)) :named @p_430) (! (= bot$ (inf$ @p_7 @p_5)) :named @p_431)) :named @p_429) (! (= @p_404 (! (+ @p_405 @p_404) :named @p_528)) :named @p_433)) :named @p_432))) :rule forall_inst :args ((:= veriT_vr51 @p_5) (:= veriT_vr52 f$) (:= veriT_vr53 @p_7) (:= veriT_vr54 g$) (:= veriT_vr55 @p_5))) +(step t143 (cl (or @p_406 (! (=> (! (and (! (finite$ @p_407) :named @p_412) @p_408 @p_409 (! (= @p_407 (sup$ @p_5 @p_7)) :named @p_411) (! (= bot$ (inf$ @p_5 @p_7)) :named @p_437)) :named @p_434) @p_410) :named @p_438))) :rule forall_inst :args ((:= veriT_vr51 @p_407) (:= veriT_vr52 f$) (:= veriT_vr53 @p_5) (:= veriT_vr54 g$) (:= veriT_vr55 @p_7))) +(step t144 (cl (or (! (not @p_249) :named @p_441) @p_411)) :rule forall_inst :args ((:= veriT_vr44 i$) (:= veriT_vr45 @p_7))) +(step t145 (cl (or (! (not @p_230) :named @p_442) (! (= @p_407 (! (insert$ j$ @p_5) :named @p_467)) :named @p_443))) :rule forall_inst :args ((:= veriT_vr39 j$) (:= veriT_vr40 i$) (:= veriT_vr41 bot$))) +(step t146 (cl (or (! (not @p_194) :named @p_447) (! (=> (! (member$a i$ @p_7) :named @p_445) (! (= @p_7 @p_407) :named @p_446)) :named @p_444))) :rule forall_inst :args ((:= veriT_vr32 i$) (:= veriT_vr33 @p_7))) +(step t147 (cl (or (! (not @p_174) :named @p_413) (! (=> (! (finite$ @p_7) :named @p_416) @p_412) :named @p_448))) :rule forall_inst :args ((:= veriT_vr28 @p_7) (:= veriT_vr29 i$))) +(step t148 (cl (or @p_413 (! (=> @p_414 @p_415) :named @p_449))) :rule forall_inst :args ((:= veriT_vr28 bot$) (:= veriT_vr29 i$))) +(step t149 (cl (or @p_413 (! (=> @p_414 @p_416) :named @p_451))) :rule forall_inst :args ((:= veriT_vr28 bot$) (:= veriT_vr29 j$))) +(step t150 (cl (or (! (not @p_119) :named @p_418) (! (= 0.0 (! (snd$a @p_417) :named @p_495)) :named @p_454))) :rule forall_inst :args ((:= veriT_vr18 1.0) (:= veriT_vr19 0.0))) +(step t151 (cl (or @p_418 (! (= 1.0 (! (snd$a @p_419) :named @p_496)) :named @p_455))) :rule forall_inst :args ((:= veriT_vr18 0.0) (:= veriT_vr19 1.0))) +(step t152 (cl (or (! (not @p_100) :named @p_456) (! (= g$ (! (snd$ @p_403) :named @p_471)) :named @p_457))) :rule forall_inst :args ((:= veriT_vr14 k$) (:= veriT_vr15 g$))) +(step t153 (cl (or (! (not @p_84) :named @p_461) (! (=> (! (= @p_7 @p_5) :named @p_459) (! (= j$ i$) :named @p_460)) :named @p_458))) :rule forall_inst :args ((:= veriT_vr10 i$) (:= veriT_vr11 j$))) +(step t154 (cl (! (not @p_420) :named @p_423) (! (not @p_402) :named @p_425) @p_421) :rule implies_pos) +(step t155 (cl @p_422 @p_420) :rule or :premises (t140)) +(step t156 (cl @p_423 @p_421) :rule resolution :premises (t154 a6)) +(step t157 (cl @p_420) :rule resolution :premises (t155 t139)) +(step t158 (cl @p_421) :rule resolution :premises (t156 t157)) +(step t159 (cl (! (not @p_424) :named @p_428) @p_425 @p_426) :rule implies_pos) +(step t160 (cl @p_427 @p_424) :rule or :premises (t141)) +(step t161 (cl @p_428 @p_426) :rule resolution :premises (t159 a6)) +(step t162 (cl @p_424) :rule resolution :premises (t160 t138)) +(step t163 (cl @p_426) :rule resolution :premises (t161 t162)) +(step t164 (cl @p_429 (not @p_415) (! (not @p_409) :named @p_436) (! (not @p_408) :named @p_435) (not @p_430) (not @p_431)) :rule and_neg) +(step t165 (cl (not @p_432) (not @p_429) @p_433) :rule implies_pos) +(step t166 (cl @p_406 @p_432) :rule or :premises (t142)) +(step t167 (cl @p_432) :rule resolution :premises (t166 t101)) +(step t168 (cl @p_434 (not @p_412) @p_435 @p_436 (not @p_411) (! (not @p_437) :named @p_515)) :rule and_neg) +(step t169 (cl (! (not @p_438) :named @p_439) (! (not @p_434) :named @p_440) @p_410) :rule implies_pos) +(step t170 (cl @p_406 @p_438) :rule or :premises (t143)) +(step t171 (cl @p_439 @p_440) :rule resolution :premises (t169 a19)) +(step t172 (cl @p_438) :rule resolution :premises (t170 t101)) +(step t173 (cl @p_440) :rule resolution :premises (t171 t172)) +(step t174 (cl @p_441 @p_411) :rule or :premises (t144)) +(step t175 (cl @p_411) :rule resolution :premises (t174 t92)) +(step t176 (cl @p_442 @p_443) :rule or :premises (t145)) +(step t177 (cl @p_443) :rule resolution :premises (t176 t86)) +(step t178 (cl (not @p_444) (! (not @p_445) :named @p_470) @p_446) :rule implies_pos) +(step t179 (cl @p_447 @p_444) :rule or :premises (t146)) +(step t180 (cl @p_444) :rule resolution :premises (t179 t74)) +(step t181 (cl (not @p_448) (not @p_416) @p_412) :rule implies_pos) +(step t182 (cl @p_413 @p_448) :rule or :premises (t147)) +(step t183 (cl @p_448) :rule resolution :premises (t182 t68)) +(step t184 (cl (! (not @p_449) :named @p_450) (! (not @p_414) :named @p_452) @p_415) :rule implies_pos) +(step t185 (cl @p_413 @p_449) :rule or :premises (t148)) +(step t186 (cl @p_450 @p_415) :rule resolution :premises (t184 a8)) +(step t187 (cl @p_449) :rule resolution :premises (t185 t68)) +(step t188 (cl @p_415) :rule resolution :premises (t186 t187)) +(step t189 (cl (! (not @p_451) :named @p_453) @p_452 @p_416) :rule implies_pos) +(step t190 (cl @p_413 @p_451) :rule or :premises (t149)) +(step t191 (cl @p_453 @p_416) :rule resolution :premises (t189 a8)) +(step t192 (cl @p_451) :rule resolution :premises (t190 t68)) +(step t193 (cl @p_416) :rule resolution :premises (t191 t192)) +(step t194 (cl @p_412) :rule resolution :premises (t181 t193 t183)) +(step t195 (cl @p_418 @p_454) :rule or :premises (t150)) +(step t196 (cl @p_454) :rule resolution :premises (t195 t56)) +(step t197 (cl @p_418 @p_455) :rule or :premises (t151)) +(step t198 (cl @p_455) :rule resolution :premises (t197 t56)) +(step t199 (cl @p_456 @p_457) :rule or :premises (t152)) +(step t200 (cl @p_457) :rule resolution :premises (t199 t50)) +(step t201 (cl (not @p_458) (! (not @p_459) :named @p_507) @p_460) :rule implies_pos) +(step t202 (cl @p_461 @p_458) :rule or :premises (t153)) +(step t203 (cl @p_458) :rule resolution :premises (t202 t44)) +(step t204 (cl (or @p_410 (! (not (! (<= @p_462 @p_463) :named @p_534)) :named @p_464) (! (not (! (<= @p_463 @p_462) :named @p_535)) :named @p_465))) :rule la_disequality) +(step t205 (cl @p_410 @p_464 @p_465) :rule or :premises (t204)) +(step t206 (cl @p_464 @p_465) :rule resolution :premises (t205 a19)) +(step t207 (cl (or @p_441 (! (= @p_466 @p_467) :named @p_474))) :rule forall_inst :args ((:= veriT_vr44 j$) (:= veriT_vr45 @p_5))) +(step t208 (cl (or @p_447 (! (=> (! (member$a j$ @p_5) :named @p_468) (! (= @p_5 @p_467) :named @p_477)) :named @p_475))) :rule forall_inst :args ((:= veriT_vr32 j$) (:= veriT_vr33 @p_5))) +(step t209 (cl (or (! (not @p_156) :named @p_469) (! (= @p_437 (! (and (! (not @p_468) :named @p_476) (! (= bot$ (inf$ @p_5 bot$)) :named @p_479)) :named @p_478)) :named @p_482))) :rule forall_inst :args ((:= veriT_vr23 @p_5) (:= veriT_vr24 j$) (:= veriT_vr25 bot$))) +(step t210 (cl (or @p_469 (! (= @p_431 (! (and @p_470 (! (= bot$ (inf$ @p_7 bot$)) :named @p_485)) :named @p_483)) :named @p_487))) :rule forall_inst :args ((:= veriT_vr23 @p_7) (:= veriT_vr24 i$) (:= veriT_vr25 bot$))) +(step t211 (cl (or (! (not @p_61) :named @p_472) (! (= @p_426 (! (fun_app$a (! (fun_app$ uu$ (! (fst$ @p_403) :named @p_473)) :named @p_508) @p_471) :named @p_489)) :named @p_488))) :rule forall_inst :args ((:= veriT_vr6 uu$) (:= veriT_vr7 @p_403))) +(step t212 (cl (or @p_472 (! (= @p_421 (! (fun_app$a (! (fun_app$ uua$ @p_473) :named @p_509) @p_471) :named @p_492)) :named @p_491))) :rule forall_inst :args ((:= veriT_vr6 uua$) (:= veriT_vr7 @p_403))) +(step t213 (cl @p_441 @p_474) :rule or :premises (t207)) +(step t214 (cl @p_474) :rule resolution :premises (t213 t92)) +(step t215 (cl (not @p_475) @p_476 @p_477) :rule implies_pos) +(step t216 (cl @p_447 @p_475) :rule or :premises (t208)) +(step t217 (cl @p_475) :rule resolution :premises (t216 t74)) +(step t218 (cl (not (! (not @p_470) :named @p_484)) @p_445) :rule not_not) +(step t219 (cl @p_478 (! (not @p_476) :named @p_480) (! (not @p_479) :named @p_481)) :rule and_neg) +(step t220 (cl (not @p_480) @p_468) :rule not_not) +(step t221 (cl @p_478 @p_468 @p_481) :rule th_resolution :premises (t220 t219)) +(step t222 (cl (not @p_482) @p_437 (! (not @p_478) :named @p_516)) :rule equiv_pos1) +(step t223 (cl @p_469 @p_482) :rule or :premises (t209)) +(step t224 (cl @p_482) :rule resolution :premises (t223 t62)) +(step t225 (cl @p_483 @p_484 (! (not @p_485) :named @p_486)) :rule and_neg) +(step t226 (cl @p_483 @p_445 @p_486) :rule th_resolution :premises (t218 t225)) +(step t227 (cl (not @p_487) @p_431 (not @p_483)) :rule equiv_pos1) +(step t228 (cl @p_469 @p_487) :rule or :premises (t210)) +(step t229 (cl @p_487) :rule resolution :premises (t228 t62)) +(step t230 (cl (! (not @p_488) :named @p_490) (not @p_426) @p_489) :rule equiv_pos2) +(step t231 (cl @p_472 @p_488) :rule or :premises (t211)) +(step t232 (cl @p_490 @p_489) :rule resolution :premises (t230 t163)) +(step t233 (cl @p_488) :rule resolution :premises (t231 t38)) +(step t234 (cl @p_489) :rule resolution :premises (t232 t233)) +(step t235 (cl (! (not @p_491) :named @p_493) (not @p_421) @p_492) :rule equiv_pos2) +(step t236 (cl @p_472 @p_491) :rule or :premises (t212)) +(step t237 (cl @p_493 @p_492) :rule resolution :premises (t235 t158)) +(step t238 (cl @p_491) :rule resolution :premises (t236 t38)) +(step t239 (cl @p_492) :rule resolution :premises (t237 t238)) +(step t240 (cl (or (! 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(not @p_500) :named @p_504) @p_501) :rule eq_transitive) +(step t251 (cl @p_498 @p_502 @p_503 @p_504) :rule th_resolution :premises (t249 t250)) +(step t252 (cl @p_505 @p_506 @p_497 @p_502 @p_503 @p_504) :rule th_resolution :premises (t248 t251)) +(step t253 (cl @p_505 @p_506 @p_502 @p_503 @p_504) :rule th_resolution :premises (t247 t252)) +(step t254 (cl @p_503) :rule resolution :premises (t253 a10 a12 t196 t198)) +(step t255 (cl @p_507) :rule resolution :premises (t201 t254 t203)) +(step t256 (cl (! (= f$ f$) :named @p_523)) :rule eq_reflexive) +(step t257 (cl (! (= g$ g$) :named @p_524)) :rule eq_reflexive) +(step t258 (cl (! (= @p_405 @p_405) :named @p_527)) :rule eq_reflexive) +(step t259 (cl (or (! (not @p_34) :named @p_510) (! (= @p_24 @p_508) :named @p_511))) :rule forall_inst :args ((:= veriT_vr3 @p_473))) +(step t260 (cl (or (! (not @p_22) :named @p_512) (! (= @p_12 @p_509) :named @p_513))) :rule forall_inst :args ((:= veriT_vr1 @p_473))) +(step t261 (cl @p_510 @p_511) :rule or :premises (t259)) +(step t262 (cl @p_511) :rule resolution :premises (t261 t32)) +(step t263 (cl @p_512 @p_513) :rule or :premises (t260)) +(step t264 (cl @p_513) :rule resolution :premises (t263 t26)) +(step t265 (cl (not @p_511) (! (not @p_457) :named @p_514) @p_408 (not @p_489)) :rule eq_congruent_pred) +(step t266 (cl @p_408) :rule resolution :premises (t265 t200 t234 t262)) +(step t267 (cl (not @p_513) @p_514 @p_409 (not @p_492)) :rule eq_congruent_pred) +(step t268 (cl @p_409) :rule resolution :premises (t267 t200 t239 t264)) +(step t269 (cl @p_515) :rule resolution :premises (t168 t268 t194 t173 t175 t266)) +(step t270 (cl @p_516) :rule resolution :premises (t222 t269 t224)) +(step t271 (cl @p_468) :rule resolution :premises (t221 t270 t243)) +(step t272 (cl @p_477) :rule resolution :premises (t215 t271 t217)) +(step t273 (cl (! (not @p_477) :named @p_517) (not @p_474) @p_430) :rule eq_transitive) +(step t274 (cl @p_430) :rule resolution :premises (t273 t214 t272)) +(step t275 (cl @p_517 (! (not @p_443) :named @p_518) (! (= @p_5 @p_407) :named @p_519)) :rule eq_transitive) +(step t276 (cl @p_518 @p_517 @p_519) :rule eq_transitive) +(step t277 (cl (not @p_520) (! (not @p_446) :named @p_521) (! (not @p_519) :named @p_522) @p_459) :rule eq_transitive) +(step t278 (cl @p_521 @p_522 @p_459) :rule th_resolution :premises (t277 t246)) +(step t279 (cl @p_521 @p_459 @p_518 @p_517) :rule th_resolution :premises (t278 t276)) +(step t280 (cl @p_521) :rule resolution :premises (t279 t177 t255 t272)) +(step t281 (cl (not @p_523) @p_522 (! (not @p_524) :named @p_525) (! (= @p_462 @p_404) :named @p_526)) :rule eq_congruent) +(step t282 (cl @p_522 @p_525 @p_526) :rule th_resolution :premises (t281 t256)) +(step t283 (cl @p_522 @p_526) :rule th_resolution :premises (t282 t257)) +(step t284 (cl @p_526 @p_517 @p_518) :rule th_resolution :premises (t283 t275)) +(step t285 (cl @p_470) :rule resolution :premises (t178 t280 t180)) +(step t286 (cl @p_483) :rule resolution :premises (t226 t285 t245)) +(step t287 (cl @p_431) :rule resolution :premises (t227 t286 t229)) +(step t288 (cl @p_429) :rule resolution :premises (t164 t287 t188 t266 t268 t274)) +(step t289 (cl @p_433) :rule resolution :premises (t165 t288 t167)) +(step t290 (cl (not @p_527) (! (not @p_526) :named @p_529) (! (= (! (+ @p_405 @p_462) :named @p_531) @p_528) :named @p_530)) :rule eq_congruent) +(step t291 (cl @p_529 @p_530) :rule th_resolution :premises (t290 t258)) +(step t292 (cl @p_530 @p_517 @p_518) :rule th_resolution :premises (t291 t284)) +(step t293 (cl (! (not @p_433) :named @p_532) (not @p_530) (! (= @p_404 @p_531) :named @p_533)) :rule eq_transitive) +(step t294 (cl @p_532 @p_533 @p_517 @p_518) :rule th_resolution :premises (t293 t292)) +(step t295 (cl @p_534 @p_529 (! (not @p_533) :named @p_536)) :rule la_generic :args (1.0 (- 2) (- 1))) +(step t296 (cl @p_534 @p_517 @p_518 @p_532) :rule th_resolution :premises (t295 t284 t294)) +(step t297 (cl @p_534) :rule resolution :premises (t296 t289 t177 t272)) +(step t298 (cl @p_465) :rule resolution :premises (t206 t297)) +(step t299 (cl @p_535 @p_529 @p_536) :rule la_generic :args (1.0 2 1)) +(step t300 (cl @p_535 @p_517 @p_518 @p_532) :rule th_resolution :premises (t299 t284 t294)) +(step t301 (cl) :rule resolution :premises (t300 t289 t177 t298 t272)) 7d1d28af77b48e47cf45f7abbbccb64bffffc3f9 6 0 unsat (assume a0 (! (< 0.0 (+ x$ (! (* 2.0 y$) :named @p_1))) :named @p_2)) @@ -7396,526 +7396,6 @@ (step t210 (cl @p_456 @p_452 @p_455) :rule th_resolution :premises (t206 t209)) (step t211 (cl @p_457 @p_458 @p_440 @p_456 @p_455) :rule th_resolution :premises (t205 t210)) (step t212 (cl) :rule resolution :premises (t211 t116 t156 t193 t202 t204)) -ba9da4ba7350e0a8fc453119da89963e8ee28018 323 0 -unsat -(assume a1 (! (not (! (=> (! (forall ((?v0 Real_a_fun$) (?v1 B_list$)) (! (= (! (=> (! (and (! (= (! (rec_join$ ?v1) :named @p_3) ?v0) :named @p_68) (! (and (! (=> (! (and (! (= ?v1 nil$) :named @p_4) (! (= uu$ ?v0) :named @p_72)) :named @p_74) false) :named @p_76) (! (and (! (forall ((?v2 B$)) (! (=> (! (and (! (= ?v1 (! (cons$ ?v2 nil$) :named @p_8)) :named @p_5) (! (= ?v0 (! (coeff_cube_to_path$ ?v2) :named @p_1)) :named @p_82)) :named @p_84) false) :named @p_86)) :named @p_78) (! (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (! (=> (! (and (! (= ?v1 (! (cons$ ?v2 (! 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(not @p_85) :named @p_211))) :rule implies_simplify) -(step t32.t2 (cl (= @p_79 (! (forall ((veriT_vr4 B$)) @p_211) :named @p_210))) :rule bind) -(anchor :step t32.t3 :args (veriT_vr4 veriT_vr5 veriT_vr6)) -(step t32.t3.t1 (cl (= @p_102 (! (not @p_100) :named @p_213))) :rule implies_simplify) -(step t32.t3 (cl (= @p_89 (! (forall ((veriT_vr4 B$) (veriT_vr5 B$) (veriT_vr6 B_list$)) @p_213) :named @p_212))) :rule bind) -(step t32.t4 (cl (= @p_195 (! (and @p_69 @p_209 @p_210 @p_212) :named @p_214))) :rule cong :premises (t32.t1 t32.t2 t32.t3)) -(step t32.t5 (cl (= @p_196 (! (=> @p_214 false) :named @p_215))) :rule cong :premises (t32.t4)) -(step t32.t6 (cl (= @p_215 (! (not @p_214) :named @p_216))) :rule implies_simplify) -(step t32.t7 (cl (= @p_196 @p_216)) :rule trans :premises (t32.t5 t32.t6)) -(step t32.t8 (cl (! (= @p_113 true) :named @p_228)) :rule eq_simplify) -(step t32.t9 (cl (! (= @p_120 (! (not @p_118) :named @p_217)) :named @p_229)) :rule implies_simplify) -(anchor :step t32.t10 :args (veriT_vr4)) -(step t32.t10.t1 (cl (! (= @p_130 (! (not @p_128) :named @p_219)) :named @p_231)) :rule implies_simplify) -(step t32.t10 (cl (! (= @p_122 (! (forall ((veriT_vr4 B$)) @p_219) :named @p_218)) :named @p_230)) :rule bind) -(anchor :step t32.t11 :args (veriT_vr4 veriT_vr5 veriT_vr6)) -(step t32.t11.t1 (cl (! (= @p_142 (! (not @p_140) :named @p_221)) :named @p_233)) :rule implies_simplify) -(step t32.t11 (cl (! (= @p_132 (! (forall ((veriT_vr4 B$) (veriT_vr5 B$) (veriT_vr6 B_list$)) @p_221) :named @p_220)) :named @p_232)) :rule bind) -(step t32.t12 (cl (! (= @p_197 (! (and true @p_217 @p_218 @p_220) :named @p_222)) :named @p_234)) :rule cong :premises (t32.t8 t32.t9 t32.t10 t32.t11)) -(step t32.t13 (cl (! (= @p_222 (! (and @p_217 @p_218 @p_220) :named @p_223)) :named @p_235)) :rule and_simplify) -(step t32.t14 (cl (! (= @p_197 @p_223) :named @p_236)) :rule trans :premises (t32.t12 t32.t13)) -(step t32.t15 (cl (! (= @p_198 (! (=> @p_223 false) :named @p_224)) :named @p_237)) :rule cong :premises (t32.t14)) -(step t32.t16 (cl (! (= @p_224 (! (not @p_223) :named @p_225)) :named @p_238)) :rule implies_simplify) -(step t32.t17 (cl (! (= @p_198 @p_225) :named @p_239)) :rule trans :premises (t32.t15 t32.t16)) -(step t32.t18 (cl (= @p_199 (! (= @p_216 @p_225) :named @p_226))) :rule cong :premises (t32.t7 t32.t17)) -(step t32.t19 (cl (= @p_226 (! (= @p_214 @p_223) :named @p_227))) :rule equiv_simplify) -(step t32.t20 (cl (= @p_199 @p_227)) :rule trans :premises (t32.t18 t32.t19)) -(step t32 (cl (= @p_205 (! (forall ((veriT_vr2 Real_a_fun$) (veriT_vr3 B_list$)) @p_227) :named @p_243))) :rule bind) -(anchor :step t33 :args (veriT_vr3)) -(step t33.t1 (cl @p_228) :rule eq_simplify) -(step t33.t2 (cl @p_229) :rule implies_simplify) -(anchor :step t33.t3 :args (veriT_vr4)) -(step t33.t3.t1 (cl @p_231) :rule implies_simplify) -(step t33.t3 (cl @p_230) :rule bind) -(anchor :step t33.t4 :args (veriT_vr4 veriT_vr5 veriT_vr6)) -(step t33.t4.t1 (cl @p_233) :rule implies_simplify) -(step t33.t4 (cl @p_232) :rule bind) -(step t33.t5 (cl @p_234) :rule cong :premises (t33.t1 t33.t2 t33.t3 t33.t4)) -(step t33.t6 (cl @p_235) :rule and_simplify) -(step t33.t7 (cl @p_236) :rule trans :premises (t33.t5 t33.t6)) -(step t33.t8 (cl @p_237) :rule cong :premises (t33.t7)) -(step t33.t9 (cl @p_238) :rule implies_simplify) -(step t33.t10 (cl @p_239) :rule trans :premises (t33.t8 t33.t9)) -(step t33 (cl (= @p_202 (! (forall ((veriT_vr3 B_list$)) @p_225) :named @p_240))) :rule bind) -(step t34 (cl (= @p_204 (! (= @p_240 @p_240) :named @p_241))) :rule cong :premises (t33 t33)) -(step t35 (cl (= @p_241 true)) :rule equiv_simplify) -(step t36 (cl (= @p_204 true)) :rule trans :premises (t34 t35)) -(step t37 (cl (= @p_206 (! (not true) :named @p_242))) :rule cong :premises (t36)) -(step t38 (cl (= @p_242 false)) :rule not_simplify) -(step t39 (cl (= @p_206 false)) :rule trans :premises (t37 t38)) -(step t40 (cl (= @p_208 (! (and @p_243 false) :named @p_244))) :rule cong :premises (t32 t39)) -(step t41 (cl (= @p_244 false)) :rule and_simplify) -(step t42 (cl (! (= @p_208 false) :named @p_245)) :rule trans :premises (t40 t41)) -(step t43 (cl (not @p_245) (not @p_208) false) :rule equiv_pos2) -(step t44 (cl false) :rule th_resolution :premises (t31 t42 t43)) -(step t45 (cl (not false)) :rule false) -(step t46 (cl) :rule resolution :premises (t44 t45)) -2da165964e2359aec5a20e66969cc8494006e9ba 36 0 -unsat -(assume a4 (! (forall ((?v0 Int)) (! (and (! (pred$e ?v0) :named @p_4) (! (or (! (pred$d (! (cons$d ?v0 nil$d) :named @p_7)) :named @p_1) (! (not @p_1) :named @p_11)) :named @p_13)) :named @p_15)) :named @p_2)) -(assume a5 (not (! (pred$e 1) :named @p_26))) -(anchor :step t3 :args ((:= ?v0 veriT_vr8))) -(step t3.t1 (cl (! (= ?v0 veriT_vr8) :named @p_6)) :rule refl) -(step t3.t2 (cl (= @p_4 (! (pred$e veriT_vr8) :named @p_5))) :rule cong :premises (t3.t1)) -(step t3.t3 (cl @p_6) :rule refl) -(step t3.t4 (cl (! (= @p_7 (! (cons$d veriT_vr8 nil$d) :named @p_8)) :named @p_9)) :rule cong :premises (t3.t3)) -(step t3.t5 (cl (! (= @p_1 (! (pred$d @p_8) :named @p_3)) :named @p_10)) :rule cong :premises (t3.t4)) -(step t3.t6 (cl @p_6) :rule refl) -(step t3.t7 (cl @p_9) :rule cong :premises (t3.t6)) -(step t3.t8 (cl @p_10) :rule cong :premises (t3.t7)) -(step t3.t9 (cl (= @p_11 (! (not @p_3) :named @p_12))) :rule cong :premises (t3.t8)) -(step t3.t10 (cl (= @p_13 (! (or @p_3 @p_12) :named @p_14))) :rule cong :premises (t3.t5 t3.t9)) -(step t3.t11 (cl (= @p_15 (! (and @p_5 @p_14) :named @p_16))) :rule cong :premises (t3.t2 t3.t10)) -(step t3 (cl (! (= @p_2 (! (forall ((veriT_vr8 Int)) @p_16) :named @p_18)) :named @p_17)) :rule bind) -(step t4 (cl (not @p_17) (not @p_2) @p_18) :rule equiv_pos2) -(step t5 (cl @p_18) :rule th_resolution :premises (a4 t3 t4)) -(anchor :step t6 :args (veriT_vr8)) -(step t6.t1 (cl (= @p_14 true)) :rule or_simplify) -(step t6.t2 (cl (= @p_16 (! (and @p_5 true) :named @p_19))) :rule cong :premises (t6.t1)) -(step t6.t3 (cl (= @p_19 (! (and @p_5) :named @p_20))) :rule and_simplify) -(step t6.t4 (cl (= @p_20 @p_5)) :rule and_simplify) -(step t6.t5 (cl (= @p_16 @p_5)) :rule trans :premises (t6.t2 t6.t3 t6.t4)) -(step t6 (cl (! (= @p_18 (! (forall ((veriT_vr8 Int)) @p_5) :named @p_22)) :named @p_21)) :rule bind) -(step t7 (cl (not @p_21) (not @p_18) @p_22) :rule equiv_pos2) -(step t8 (cl @p_22) :rule th_resolution :premises (t5 t6 t7)) -(anchor :step t9 :args ((:= veriT_vr8 veriT_vr9))) -(step t9.t1 (cl (= veriT_vr8 veriT_vr9)) :rule refl) -(step t9.t2 (cl (= @p_5 (! (pred$e veriT_vr9) :named @p_23))) :rule cong :premises (t9.t1)) -(step t9 (cl (! (= @p_22 (! (forall ((veriT_vr9 Int)) @p_23) :named @p_25)) :named @p_24)) :rule bind) -(step t10 (cl (not @p_24) (not @p_22) @p_25) :rule equiv_pos2) -(step t11 (cl @p_25) :rule th_resolution :premises (t8 t9 t10)) -(step t12 (cl (or (! (not @p_25) :named @p_27) @p_26)) :rule forall_inst :args ((:= veriT_vr9 1))) -(step t13 (cl @p_27 @p_26) :rule or :premises (t12)) -(step t14 (cl) :rule resolution :premises (t13 t11 a5)) -f9bb7f97f8819ceceaefe0cdf934d0eda3431a5b 158 0 -unsat -(assume a0 (! (forall ((?v0 Int)) (! (= (! (g$ (! (some$ ?v0) :named @p_5)) :named @p_7) (! (g$a (! (cons$ ?v0 nil$) :named @p_10)) :named @p_12)) :named @p_14)) :named @p_4)) -(assume a1 (forall ((?v0 Bool)) (= (g$b (some$a ?v0)) (g$c (cons$a ?v0 nil$a))))) -(assume a6 (! (forall ((?v0 Bool_list$)) (! (= (! (g$c ?v0) :named @p_27) (! (size$ ?v0) :named @p_30)) :named @p_32)) :named @p_26)) -(assume a7 (! (forall ((?v0 Int_list$)) (! (= (! (g$a ?v0) :named @p_43) (! (size$a ?v0) :named @p_46)) :named @p_48)) :named @p_42)) -(assume a12 (! (= zero$ (! (size$ nil$a) :named @p_118)) :named @p_143)) -(assume a13 (! (= zero$ (! (size$a nil$) :named @p_133)) :named @p_144)) -(assume a14 (forall ((?v0 Bool) (?v1 Bool_list$)) (= (size$ (cons$a ?v0 ?v1)) (! (plus$ (! (size$ ?v1) :named @p_60) (! (suc$ zero$) :named @p_1)) :named @p_3)))) -(assume a15 (! (forall ((?v0 Int) (?v1 Int_list$)) (! (= (! (size$a (! (cons$ ?v0 ?v1) :named @p_96)) :named @p_98) (! (plus$ (! (size$a ?v1) :named @p_101) @p_1) :named @p_103)) :named @p_105)) :named @p_95)) -(assume a16 (not (! (= (! (g$ (some$ 3)) :named @p_124) (! (g$b (some$a true)) :named @p_2)) :named @p_141))) -(step t10 (cl (and (= (g$b (some$a false)) (g$c (! (cons$a false nil$a) :named @p_119))) (! (= @p_2 (! (g$c (! (cons$a true nil$a) :named @p_121)) :named @p_122)) :named @p_117))) :rule bfun_elim :premises (a1)) -(step t11 (cl (! (forall ((?v1 Bool_list$)) (! (and (! (= @p_3 (! (size$ (! (cons$a false ?v1) :named @p_63)) :named @p_65)) :named @p_67) (! (= @p_3 (! (size$ (! (cons$a true ?v1) :named @p_71)) :named @p_73)) :named @p_75)) :named @p_77)) :named @p_58)) :rule bfun_elim :premises (a14)) -(anchor :step t12 :args ((:= ?v0 veriT_vr0))) -(step t12.t1 (cl (! (= ?v0 veriT_vr0) :named @p_9)) :rule refl) -(step t12.t2 (cl (= @p_5 (! (some$ veriT_vr0) :named @p_6))) :rule cong :premises (t12.t1)) -(step t12.t3 (cl (= @p_7 (! (g$ @p_6) :named @p_8))) :rule cong :premises (t12.t2)) -(step t12.t4 (cl @p_9) :rule refl) -(step t12.t5 (cl (= @p_10 (! 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(forall ((veriT_vr2 Bool_list$)) @p_33) :named @p_35)) :named @p_34)) :rule bind) -(step t19 (cl (not @p_34) (not @p_26) @p_35) :rule equiv_pos2) -(step t20 (cl @p_35) :rule th_resolution :premises (a6 t18 t19)) -(anchor :step t21 :args ((:= veriT_vr2 veriT_vr3))) -(step t21.t1 (cl (! (= veriT_vr2 veriT_vr3) :named @p_37)) :rule refl) -(step t21.t2 (cl (= @p_28 (! (g$c veriT_vr3) :named @p_36))) :rule cong :premises (t21.t1)) -(step t21.t3 (cl @p_37) :rule refl) -(step t21.t4 (cl (= @p_31 (! (size$ veriT_vr3) :named @p_38))) :rule cong :premises (t21.t3)) -(step t21.t5 (cl (= @p_33 (! (= @p_36 @p_38) :named @p_39))) :rule cong :premises (t21.t2 t21.t4)) -(step t21 (cl (! (= @p_35 (! (forall ((veriT_vr3 Bool_list$)) @p_39) :named @p_41)) :named @p_40)) :rule bind) -(step t22 (cl (not @p_40) (not @p_35) @p_41) :rule equiv_pos2) -(step t23 (cl @p_41) :rule th_resolution :premises (t20 t21 t22)) -(anchor :step t24 :args ((:= ?v0 veriT_vr4))) -(step t24.t1 (cl (! (= ?v0 veriT_vr4) :named @p_45)) :rule refl) -(step t24.t2 (cl (= @p_43 (! (g$a veriT_vr4) :named @p_44))) :rule cong :premises (t24.t1)) -(step t24.t3 (cl @p_45) :rule refl) -(step t24.t4 (cl (= @p_46 (! (size$a veriT_vr4) :named @p_47))) :rule cong :premises (t24.t3)) -(step t24.t5 (cl (= @p_48 (! (= @p_44 @p_47) :named @p_49))) :rule cong :premises (t24.t2 t24.t4)) -(step t24 (cl (! (= @p_42 (! (forall ((veriT_vr4 Int_list$)) @p_49) :named @p_51)) :named @p_50)) :rule bind) -(step t25 (cl (not @p_50) (not @p_42) @p_51) :rule equiv_pos2) -(step t26 (cl @p_51) :rule th_resolution :premises (a7 t24 t25)) -(anchor :step t27 :args ((:= veriT_vr4 veriT_vr5))) -(step t27.t1 (cl (! (= veriT_vr4 veriT_vr5) :named @p_53)) :rule refl) -(step t27.t2 (cl (= @p_44 (! (g$a veriT_vr5) :named @p_52))) :rule cong :premises (t27.t1)) -(step t27.t3 (cl @p_53) :rule refl) -(step t27.t4 (cl (= @p_47 (! (size$a veriT_vr5) :named @p_54))) :rule cong :premises (t27.t3)) -(step t27.t5 (cl (= @p_49 (! (= @p_52 @p_54) :named @p_55))) :rule cong :premises (t27.t2 t27.t4)) -(step t27 (cl (! (= @p_51 (! (forall ((veriT_vr5 Int_list$)) @p_55) :named @p_57)) :named @p_56)) :rule bind) -(step t28 (cl (not @p_56) (not @p_51) @p_57) :rule equiv_pos2) -(step t29 (cl @p_57) :rule th_resolution :premises (t26 t27 t28)) -(anchor :step t30 :args ((:= ?v1 veriT_vr20))) -(step t30.t1 (cl (! (= ?v1 veriT_vr20) :named @p_62)) :rule refl) -(step t30.t2 (cl (! (= @p_60 (! (size$ veriT_vr20) :named @p_61)) :named @p_69)) :rule cong :premises (t30.t1)) -(step t30.t3 (cl (! (= @p_3 (! (plus$ @p_61 @p_1) :named @p_59)) :named @p_70)) :rule cong :premises (t30.t2)) -(step t30.t4 (cl @p_62) :rule refl) -(step t30.t5 (cl (= @p_63 (! (cons$a false veriT_vr20) :named @p_64))) :rule cong :premises (t30.t4)) -(step t30.t6 (cl (= @p_65 (! (size$ @p_64) :named @p_66))) :rule cong :premises (t30.t5)) -(step t30.t7 (cl (= @p_67 (! 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(= veriT_vr20 veriT_vr21) :named @p_83)) :rule refl) -(step t33.t2 (cl (! (= @p_61 (! (size$ veriT_vr21) :named @p_82)) :named @p_87)) :rule cong :premises (t33.t1)) -(step t33.t3 (cl (! (= @p_59 (! (plus$ @p_82 @p_1) :named @p_81)) :named @p_88)) :rule cong :premises (t33.t2)) -(step t33.t4 (cl @p_83) :rule refl) -(step t33.t5 (cl (= @p_64 (! (cons$a false veriT_vr21) :named @p_84))) :rule cong :premises (t33.t4)) -(step t33.t6 (cl (= @p_66 (! (size$ @p_84) :named @p_85))) :rule cong :premises (t33.t5)) -(step t33.t7 (cl (= @p_68 (! (= @p_81 @p_85) :named @p_86))) :rule cong :premises (t33.t3 t33.t6)) -(step t33.t8 (cl @p_83) :rule refl) -(step t33.t9 (cl @p_87) :rule cong :premises (t33.t8)) -(step t33.t10 (cl @p_88) :rule cong :premises (t33.t9)) -(step t33.t11 (cl @p_83) :rule refl) -(step t33.t12 (cl (= @p_72 (! (cons$a true veriT_vr21) :named @p_89))) :rule cong :premises (t33.t11)) -(step t33.t13 (cl (= @p_74 (! (size$ @p_89) :named @p_90))) :rule cong :premises (t33.t12)) -(step t33.t14 (cl (= @p_76 (! (= @p_81 @p_90) :named @p_91))) :rule cong :premises (t33.t10 t33.t13)) -(step t33.t15 (cl (= @p_78 (! (and @p_86 @p_91) :named @p_92))) :rule cong :premises (t33.t7 t33.t14)) -(step t33 (cl (! (= @p_80 (! (forall ((veriT_vr21 Bool_list$)) @p_92) :named @p_94)) :named @p_93)) :rule bind) -(step t34 (cl (not @p_93) (not @p_80) @p_94) :rule equiv_pos2) -(step t35 (cl @p_94) :rule th_resolution :premises (t32 t33 t34)) -(anchor :step t36 :args ((:= ?v0 veriT_vr22) (:= ?v1 veriT_vr23))) -(step t36.t1 (cl (= ?v0 veriT_vr22)) :rule refl) -(step t36.t2 (cl (! (= ?v1 veriT_vr23) :named @p_100)) :rule refl) -(step t36.t3 (cl (= @p_96 (! (cons$ veriT_vr22 veriT_vr23) :named @p_97))) :rule cong :premises (t36.t1 t36.t2)) -(step t36.t4 (cl (= @p_98 (! (size$a @p_97) :named @p_99))) :rule cong :premises (t36.t3)) -(step t36.t5 (cl @p_100) :rule refl) -(step t36.t6 (cl (= @p_101 (! (size$a veriT_vr23) :named @p_102))) :rule cong :premises (t36.t5)) -(step t36.t7 (cl (= @p_103 (! (plus$ @p_102 @p_1) :named @p_104))) :rule cong :premises (t36.t6)) -(step t36.t8 (cl (= @p_105 (! (= @p_99 @p_104) :named @p_106))) :rule cong :premises (t36.t4 t36.t7)) -(step t36 (cl (! (= @p_95 (! (forall ((veriT_vr22 Int) (veriT_vr23 Int_list$)) @p_106) :named @p_108)) :named @p_107)) :rule bind) -(step t37 (cl (not @p_107) (not @p_95) @p_108) :rule equiv_pos2) -(step t38 (cl @p_108) :rule th_resolution :premises (a15 t36 t37)) -(anchor :step t39 :args ((:= veriT_vr22 veriT_vr24) (:= veriT_vr23 veriT_vr25))) -(step t39.t1 (cl (= veriT_vr22 veriT_vr24)) :rule refl) -(step t39.t2 (cl (! (= veriT_vr23 veriT_vr25) :named @p_111)) :rule refl) -(step t39.t3 (cl (= @p_97 (! (cons$ veriT_vr24 veriT_vr25) :named @p_109))) :rule cong :premises (t39.t1 t39.t2)) -(step t39.t4 (cl (= @p_99 (! (size$a @p_109) :named @p_110))) :rule cong :premises (t39.t3)) -(step t39.t5 (cl @p_111) :rule refl) -(step t39.t6 (cl (= @p_102 (! (size$a veriT_vr25) :named @p_112))) :rule cong :premises (t39.t5)) -(step t39.t7 (cl (= @p_104 (! (plus$ @p_112 @p_1) :named @p_113))) :rule cong :premises (t39.t6)) -(step t39.t8 (cl (= @p_106 (! (= @p_110 @p_113) :named @p_114))) :rule cong :premises (t39.t4 t39.t7)) -(step t39 (cl (! (= @p_108 (! (forall ((veriT_vr24 Int) (veriT_vr25 Int_list$)) @p_114) :named @p_116)) :named @p_115)) :rule bind) -(step t40 (cl (not @p_115) (not @p_108) @p_116) :rule equiv_pos2) -(step t41 (cl @p_116) :rule th_resolution :premises (t38 t39 t40)) -(step t42 (cl @p_117) :rule and :premises (t10)) -(step t43 (cl (or (! (not @p_94) :named @p_127) (! (and (= (! (plus$ @p_118 @p_1) :named @p_120) (size$ @p_119)) (! (= @p_120 (! (size$ @p_121) :named @p_123)) :named @p_126)) :named @p_125))) :rule forall_inst :args ((:= veriT_vr21 nil$a))) -(step t44 (cl (or (! (not @p_41) :named @p_128) (! (= @p_122 @p_123) :named @p_129))) :rule forall_inst :args ((:= veriT_vr3 @p_121))) -(step t45 (cl (or (! (not @p_25) :named @p_130) (! (= @p_124 (! (g$a (! (cons$ 3 nil$) :named @p_132)) :named @p_134)) :named @p_131))) :rule forall_inst :args ((:= veriT_vr1 3))) -(step t46 (cl (not @p_125) @p_126) :rule and_pos) -(step t47 (cl @p_127 @p_125) :rule or :premises (t43)) -(step t48 (cl @p_125) :rule resolution :premises (t47 t35)) -(step t49 (cl @p_126) :rule resolution :premises (t46 t48)) -(step t50 (cl @p_128 @p_129) :rule or :premises (t44)) -(step t51 (cl @p_129) :rule resolution :premises (t50 t23)) -(step t52 (cl @p_130 @p_131) :rule or :premises (t45)) -(step t53 (cl @p_131) :rule resolution :premises (t52 t17)) -(step t54 (cl (or (! (not @p_116) :named @p_136) (! (= (! (size$a @p_132) :named @p_135) (! (plus$ @p_133 @p_1) :named @p_140)) :named @p_137))) :rule forall_inst :args ((:= veriT_vr24 3) (:= veriT_vr25 nil$))) -(step t55 (cl (or (! (not @p_57) :named @p_138) (! (= @p_134 @p_135) :named @p_139))) :rule forall_inst :args ((:= veriT_vr5 @p_132))) -(step t56 (cl @p_136 @p_137) :rule or :premises (t54)) -(step t57 (cl @p_137) :rule resolution :premises (t56 t41)) -(step t58 (cl @p_138 @p_139) :rule or :premises (t55)) -(step t59 (cl @p_139) :rule resolution :premises (t58 t29)) -(step t60 (cl (! (not @p_131) :named @p_150) (! (not @p_139) :named @p_151) (! (not @p_137) :named @p_152) (not (! (= @p_120 @p_140) :named @p_142)) (! (not @p_126) :named @p_153) (! (not @p_129) :named @p_154) (! (not @p_117) :named @p_155) @p_141) :rule eq_transitive) -(step t61 (cl (not (! (= @p_118 @p_133) :named @p_145)) (! (not (! (= @p_1 @p_1) :named @p_149)) :named @p_146) @p_142) :rule eq_congruent) -(step t62 (cl (! (not @p_143) :named @p_147) (! (not @p_144) :named @p_148) @p_145) :rule eq_transitive) -(step t63 (cl @p_146 @p_142 @p_147 @p_148) :rule th_resolution :premises (t61 t62)) -(step t64 (cl @p_149) :rule eq_reflexive) -(step t65 (cl @p_142 @p_147 @p_148) :rule th_resolution :premises (t63 t64)) -(step t66 (cl @p_150 @p_151 @p_152 @p_153 @p_154 @p_155 @p_141 @p_147 @p_148) :rule th_resolution :premises (t60 t65)) -(step t67 (cl) :rule resolution :premises (t66 t42 a12 a13 a16 t49 t51 t53 t57 t59)) 672f5a048dc0215d5adebfbf2f0a3a36f69e286e 873 0 unsat (define-fun veriT_sk0 () V$ (! (choice ((veriT_vr65 V$)) (not (! (not (! (= x2$ (! (rraise$ veriT_vr65) :named @p_369)) :named @p_370)) :named @p_368))) :named @p_382)) @@ -8790,3 +8270,523 @@ (step t303 (cl @p_681 @p_682 @p_531 @p_573 @p_574 @p_381) :rule th_resolution :premises (t302 t230)) (step t304 (cl @p_682 @p_531 @p_573 @p_574 @p_381 @p_678 @p_677 @p_666 @p_538) :rule th_resolution :premises (t303 t297)) (step t305 (cl) :rule resolution :premises (t304 t299 t146 t235 t301 t164 t171 t196 t198 t282)) +ba9da4ba7350e0a8fc453119da89963e8ee28018 323 0 +unsat +(assume a1 (! (not (! (=> (! (forall ((?v0 Real_a_fun$) (?v1 B_list$)) (! (= (! (=> (! (and (! (= (! (rec_join$ ?v1) :named @p_3) ?v0) :named @p_68) (! (and (! (=> (! (and (! (= ?v1 nil$) :named @p_4) (! (= uu$ ?v0) :named @p_72)) :named @p_74) false) :named @p_76) (! (and (! (forall ((?v2 B$)) (! (=> (! (and (! (= ?v1 (! (cons$ ?v2 nil$) :named @p_8)) :named @p_5) (! (= ?v0 (! (coeff_cube_to_path$ ?v2) :named @p_1)) :named @p_82)) :named @p_84) false) :named @p_86)) :named @p_78) (! (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (! (=> (! (and (! (= ?v1 (! (cons$ ?v2 (! (cons$ ?v3 ?v4) :named @p_2)) :named @p_9)) :named @p_6) (! (= ?v0 (! (joinpaths$ @p_1 (! (rec_join$ @p_2) :named @p_95)) :named @p_7)) :named @p_97)) :named @p_99) false) :named @p_101)) :named @p_88)) :named @p_103)) :named @p_105)) :named @p_107) false) :named @p_109) (! (=> (! (and (! (= @p_3 @p_3) :named @p_112) (! (and (! (=> (! (and @p_4 (! (= uu$ @p_3) :named @p_115)) :named @p_117) false) :named @p_119) (! (and (! (forall ((?v2 B$)) (! (=> (! (and @p_5 (! (= @p_3 @p_1) :named @p_125)) :named @p_127) false) :named @p_129)) :named @p_121) (! (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (! (=> (! (and @p_6 (! (= @p_3 @p_7) :named @p_137)) :named @p_139) false) :named @p_141)) :named @p_131)) :named @p_143)) :named @p_145)) :named @p_147) false) :named @p_149)) :named @p_151)) :named @p_53) (! (= (! (forall ((?v0 B_list$) (?v1 Real_a_fun$)) (! (=> (! (and (! (= (! 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(forall ((?v1 B$) (?v2 B$) (?v3 B_list$)) (! (=> (! (and (! (= ?v0 (! (cons$ ?v1 (! (cons$ ?v2 ?v3) :named @p_13)) :named @p_169)) :named @p_170) (! (= @p_10 (! (joinpaths$ @p_12 (! (rec_join$ @p_13) :named @p_175)) :named @p_176)) :named @p_177)) :named @p_178) false) :named @p_179)) :named @p_168)) :named @p_180)) :named @p_181)) :named @p_182) false) :named @p_183)) :named @p_51)) :named @p_49)) :named @p_52)) :named @p_55)) +(anchor :step t2 :args (?v0 (:= ?v1 @p_10))) +(step t2.t1 (cl @p_19) :rule refl) +(step t2.t2 (cl (= @p_19 @p_15)) :rule cong :premises (t2.t1)) +(step t2.t3 (cl @p_19) :rule refl) +(step t2.t4 (cl (= @p_20 @p_21)) :rule cong :premises (t2.t3)) +(step t2.t5 (cl (= @p_22 @p_23)) :rule cong :premises (t2.t4)) +(step t2.t6 (cl (= @p_24 @p_16)) :rule cong :premises (t2.t5)) +(anchor :step t2.t7 :args (?v2)) +(step t2.t7.t1 (cl @p_19) :rule refl) +(step t2.t7.t2 (cl (= @p_27 (! 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(= ?v1 veriT_vr3) :named @p_70)) :rule refl) +(step t10.t2 (cl (! (= @p_3 (! (rec_join$ veriT_vr3) :named @p_63)) :named @p_111)) :rule cong :premises (t10.t1)) +(step t10.t3 (cl (! (= ?v0 veriT_vr2) :named @p_71)) :rule refl) +(step t10.t4 (cl (= @p_68 (! (= veriT_vr2 @p_63) :named @p_69))) :rule cong :premises (t10.t2 t10.t3)) +(step t10.t5 (cl @p_70) :rule refl) +(step t10.t6 (cl (! (= @p_4 (! (= nil$ veriT_vr3) :named @p_64)) :named @p_114)) :rule cong :premises (t10.t5)) +(step t10.t7 (cl @p_71) :rule refl) +(step t10.t8 (cl (= @p_72 (! (= uu$ veriT_vr2) :named @p_73))) :rule cong :premises (t10.t7)) +(step t10.t9 (cl (= @p_74 (! (and @p_64 @p_73) :named @p_75))) :rule cong :premises (t10.t6 t10.t8)) +(step t10.t10 (cl (= @p_76 (! (=> @p_75 false) :named @p_77))) :rule cong :premises (t10.t9)) +(anchor :step t10.t11 :args ((:= ?v2 veriT_vr4))) +(step t10.t11.t1 (cl @p_70) :rule refl) +(step t10.t11.t2 (cl (! (= ?v2 veriT_vr4) :named @p_81)) :rule refl) +(step t10.t11.t3 (cl (! 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(= ?v0 veriT_vr4) :named @p_45)) :rule refl) +(step t24.t2 (cl (= @p_43 (! (g$a veriT_vr4) :named @p_44))) :rule cong :premises (t24.t1)) +(step t24.t3 (cl @p_45) :rule refl) +(step t24.t4 (cl (= @p_46 (! (size$a veriT_vr4) :named @p_47))) :rule cong :premises (t24.t3)) +(step t24.t5 (cl (= @p_48 (! (= @p_44 @p_47) :named @p_49))) :rule cong :premises (t24.t2 t24.t4)) +(step t24 (cl (! (= @p_42 (! (forall ((veriT_vr4 Int_list$)) @p_49) :named @p_51)) :named @p_50)) :rule bind) +(step t25 (cl (not @p_50) (not @p_42) @p_51) :rule equiv_pos2) +(step t26 (cl @p_51) :rule th_resolution :premises (a7 t24 t25)) +(anchor :step t27 :args ((:= veriT_vr4 veriT_vr5))) +(step t27.t1 (cl (! (= veriT_vr4 veriT_vr5) :named @p_53)) :rule refl) +(step t27.t2 (cl (= @p_44 (! (g$a veriT_vr5) :named @p_52))) :rule cong :premises (t27.t1)) +(step t27.t3 (cl @p_53) :rule refl) +(step t27.t4 (cl (= @p_47 (! (size$a veriT_vr5) :named @p_54))) :rule cong :premises (t27.t3)) +(step t27.t5 (cl (= @p_49 (! (= @p_52 @p_54) :named @p_55))) :rule cong :premises (t27.t2 t27.t4)) +(step t27 (cl (! (= @p_51 (! (forall ((veriT_vr5 Int_list$)) @p_55) :named @p_57)) :named @p_56)) :rule bind) +(step t28 (cl (not @p_56) (not @p_51) @p_57) :rule equiv_pos2) +(step t29 (cl @p_57) :rule th_resolution :premises (t26 t27 t28)) +(anchor :step t30 :args ((:= ?v1 veriT_vr20))) +(step t30.t1 (cl (! (= ?v1 veriT_vr20) :named @p_62)) :rule refl) +(step t30.t2 (cl (! (= @p_60 (! (size$ veriT_vr20) :named @p_61)) :named @p_69)) :rule cong :premises (t30.t1)) +(step t30.t3 (cl (! (= @p_3 (! (plus$ @p_61 @p_1) :named @p_59)) :named @p_70)) :rule cong :premises (t30.t2)) +(step t30.t4 (cl @p_62) :rule refl) +(step t30.t5 (cl (= @p_63 (! (cons$a false veriT_vr20) :named @p_64))) :rule cong :premises (t30.t4)) +(step t30.t6 (cl (= @p_65 (! (size$ @p_64) :named @p_66))) :rule cong :premises (t30.t5)) +(step t30.t7 (cl (= @p_67 (! (= @p_59 @p_66) :named @p_68))) :rule cong :premises (t30.t3 t30.t6)) +(step t30.t8 (cl @p_62) :rule refl) +(step t30.t9 (cl @p_69) :rule cong :premises (t30.t8)) +(step t30.t10 (cl @p_70) :rule cong :premises (t30.t9)) +(step t30.t11 (cl @p_62) :rule refl) +(step t30.t12 (cl (= @p_71 (! (cons$a true veriT_vr20) :named @p_72))) :rule cong :premises (t30.t11)) +(step t30.t13 (cl (= @p_73 (! (size$ @p_72) :named @p_74))) :rule cong :premises (t30.t12)) +(step t30.t14 (cl (= @p_75 (! (= @p_59 @p_74) :named @p_76))) :rule cong :premises (t30.t10 t30.t13)) +(step t30.t15 (cl (= @p_77 (! (and @p_68 @p_76) :named @p_78))) :rule cong :premises (t30.t7 t30.t14)) +(step t30 (cl (! (= @p_58 (! (forall ((veriT_vr20 Bool_list$)) @p_78) :named @p_80)) :named @p_79)) :rule bind) +(step t31 (cl (not @p_79) (not @p_58) @p_80) :rule equiv_pos2) +(step t32 (cl @p_80) :rule th_resolution :premises (t11 t30 t31)) +(anchor :step t33 :args ((:= veriT_vr20 veriT_vr21))) +(step t33.t1 (cl (! (= veriT_vr20 veriT_vr21) :named @p_83)) :rule refl) +(step t33.t2 (cl (! (= @p_61 (! (size$ veriT_vr21) :named @p_82)) :named @p_87)) :rule cong :premises (t33.t1)) +(step t33.t3 (cl (! (= @p_59 (! (plus$ @p_82 @p_1) :named @p_81)) :named @p_88)) :rule cong :premises (t33.t2)) +(step t33.t4 (cl @p_83) :rule refl) +(step t33.t5 (cl (= @p_64 (! (cons$a false veriT_vr21) :named @p_84))) :rule cong :premises (t33.t4)) +(step t33.t6 (cl (= @p_66 (! (size$ @p_84) :named @p_85))) :rule cong :premises (t33.t5)) +(step t33.t7 (cl (= @p_68 (! (= @p_81 @p_85) :named @p_86))) :rule cong :premises (t33.t3 t33.t6)) +(step t33.t8 (cl @p_83) :rule refl) +(step t33.t9 (cl @p_87) :rule cong :premises (t33.t8)) +(step t33.t10 (cl @p_88) :rule cong :premises (t33.t9)) +(step t33.t11 (cl @p_83) :rule refl) +(step t33.t12 (cl (= @p_72 (! (cons$a true veriT_vr21) :named @p_89))) :rule cong :premises (t33.t11)) +(step t33.t13 (cl (= @p_74 (! (size$ @p_89) :named @p_90))) :rule cong :premises (t33.t12)) +(step t33.t14 (cl (= @p_76 (! (= @p_81 @p_90) :named @p_91))) :rule cong :premises (t33.t10 t33.t13)) +(step t33.t15 (cl (= @p_78 (! (and @p_86 @p_91) :named @p_92))) :rule cong :premises (t33.t7 t33.t14)) +(step t33 (cl (! (= @p_80 (! (forall ((veriT_vr21 Bool_list$)) @p_92) :named @p_94)) :named @p_93)) :rule bind) +(step t34 (cl (not @p_93) (not @p_80) @p_94) :rule equiv_pos2) +(step t35 (cl @p_94) :rule th_resolution :premises (t32 t33 t34)) +(anchor :step t36 :args ((:= ?v0 veriT_vr22) (:= ?v1 veriT_vr23))) +(step t36.t1 (cl (= ?v0 veriT_vr22)) :rule refl) +(step t36.t2 (cl (! (= ?v1 veriT_vr23) :named @p_100)) :rule refl) +(step t36.t3 (cl (= @p_96 (! (cons$ veriT_vr22 veriT_vr23) :named @p_97))) :rule cong :premises (t36.t1 t36.t2)) +(step t36.t4 (cl (= @p_98 (! (size$a @p_97) :named @p_99))) :rule cong :premises (t36.t3)) +(step t36.t5 (cl @p_100) :rule refl) +(step t36.t6 (cl (= @p_101 (! (size$a veriT_vr23) :named @p_102))) :rule cong :premises (t36.t5)) +(step t36.t7 (cl (= @p_103 (! (plus$ @p_102 @p_1) :named @p_104))) :rule cong :premises (t36.t6)) +(step t36.t8 (cl (= @p_105 (! (= @p_99 @p_104) :named @p_106))) :rule cong :premises (t36.t4 t36.t7)) +(step t36 (cl (! (= @p_95 (! (forall ((veriT_vr22 Int) (veriT_vr23 Int_list$)) @p_106) :named @p_108)) :named @p_107)) :rule bind) +(step t37 (cl (not @p_107) (not @p_95) @p_108) :rule equiv_pos2) +(step t38 (cl @p_108) :rule th_resolution :premises (a15 t36 t37)) +(anchor :step t39 :args ((:= veriT_vr22 veriT_vr24) (:= veriT_vr23 veriT_vr25))) +(step t39.t1 (cl (= veriT_vr22 veriT_vr24)) :rule refl) +(step t39.t2 (cl (! (= veriT_vr23 veriT_vr25) :named @p_111)) :rule refl) +(step t39.t3 (cl (= @p_97 (! (cons$ veriT_vr24 veriT_vr25) :named @p_109))) :rule cong :premises (t39.t1 t39.t2)) +(step t39.t4 (cl (= @p_99 (! (size$a @p_109) :named @p_110))) :rule cong :premises (t39.t3)) +(step t39.t5 (cl @p_111) :rule refl) +(step t39.t6 (cl (= @p_102 (! (size$a veriT_vr25) :named @p_112))) :rule cong :premises (t39.t5)) +(step t39.t7 (cl (= @p_104 (! (plus$ @p_112 @p_1) :named @p_113))) :rule cong :premises (t39.t6)) +(step t39.t8 (cl (= @p_106 (! (= @p_110 @p_113) :named @p_114))) :rule cong :premises (t39.t4 t39.t7)) +(step t39 (cl (! (= @p_108 (! (forall ((veriT_vr24 Int) (veriT_vr25 Int_list$)) @p_114) :named @p_116)) :named @p_115)) :rule bind) +(step t40 (cl (not @p_115) (not @p_108) @p_116) :rule equiv_pos2) +(step t41 (cl @p_116) :rule th_resolution :premises (t38 t39 t40)) +(step t42 (cl @p_117) :rule and :premises (t10)) +(step t43 (cl (or (! (not @p_94) :named @p_127) (! (and (= (! (plus$ @p_118 @p_1) :named @p_120) (size$ @p_119)) (! (= @p_120 (! (size$ @p_121) :named @p_123)) :named @p_126)) :named @p_125))) :rule forall_inst :args ((:= veriT_vr21 nil$a))) +(step t44 (cl (or (! (not @p_41) :named @p_128) (! (= @p_122 @p_123) :named @p_129))) :rule forall_inst :args ((:= veriT_vr3 @p_121))) +(step t45 (cl (or (! (not @p_25) :named @p_130) (! (= @p_124 (! (g$a (! (cons$ 3 nil$) :named @p_132)) :named @p_134)) :named @p_131))) :rule forall_inst :args ((:= veriT_vr1 3))) +(step t46 (cl (not @p_125) @p_126) :rule and_pos) +(step t47 (cl @p_127 @p_125) :rule or :premises (t43)) +(step t48 (cl @p_125) :rule resolution :premises (t47 t35)) +(step t49 (cl @p_126) :rule resolution :premises (t46 t48)) +(step t50 (cl @p_128 @p_129) :rule or :premises (t44)) +(step t51 (cl @p_129) :rule resolution :premises (t50 t23)) +(step t52 (cl @p_130 @p_131) :rule or :premises (t45)) +(step t53 (cl @p_131) :rule resolution :premises (t52 t17)) +(step t54 (cl (or (! (not @p_116) :named @p_136) (! (= (! (size$a @p_132) :named @p_135) (! (plus$ @p_133 @p_1) :named @p_140)) :named @p_137))) :rule forall_inst :args ((:= veriT_vr24 3) (:= veriT_vr25 nil$))) +(step t55 (cl (or (! (not @p_57) :named @p_138) (! (= @p_134 @p_135) :named @p_139))) :rule forall_inst :args ((:= veriT_vr5 @p_132))) +(step t56 (cl @p_136 @p_137) :rule or :premises (t54)) +(step t57 (cl @p_137) :rule resolution :premises (t56 t41)) +(step t58 (cl @p_138 @p_139) :rule or :premises (t55)) +(step t59 (cl @p_139) :rule resolution :premises (t58 t29)) +(step t60 (cl (! (not @p_131) :named @p_150) (! (not @p_139) :named @p_151) (! (not @p_137) :named @p_152) (not (! (= @p_120 @p_140) :named @p_142)) (! (not @p_126) :named @p_153) (! (not @p_129) :named @p_154) (! (not @p_117) :named @p_155) @p_141) :rule eq_transitive) +(step t61 (cl (not (! (= @p_118 @p_133) :named @p_145)) (! (not (! (= @p_1 @p_1) :named @p_149)) :named @p_146) @p_142) :rule eq_congruent) +(step t62 (cl (! (not @p_143) :named @p_147) (! (not @p_144) :named @p_148) @p_145) :rule eq_transitive) +(step t63 (cl @p_146 @p_142 @p_147 @p_148) :rule th_resolution :premises (t61 t62)) +(step t64 (cl @p_149) :rule eq_reflexive) +(step t65 (cl @p_142 @p_147 @p_148) :rule th_resolution :premises (t63 t64)) +(step t66 (cl @p_150 @p_151 @p_152 @p_153 @p_154 @p_155 @p_141 @p_147 @p_148) :rule th_resolution :premises (t60 t65)) +(step t67 (cl) :rule resolution :premises (t66 t42 a12 a13 a16 t49 t51 t53 t57 t59)) diff -r 3fdb94d87e0e -r 3c5a7746ffa4 src/HOL/SMT_Examples/SMT_Word_Examples.certs --- a/src/HOL/SMT_Examples/SMT_Word_Examples.certs Fri Mar 05 15:01:59 2021 +0100 +++ b/src/HOL/SMT_Examples/SMT_Word_Examples.certs Fri Mar 05 21:26:38 2021 +0100 @@ -1,12 +1,4 @@ -152f808e76881b6ae41a49c63654f988bc675b52 7 0 -unsat -((set-logic ) -(proof -(let ((@x35 (monotonicity (rewrite (= (= (_ bv11 4) (_ bv11 4)) true)) (= (not (= (_ bv11 4) (_ bv11 4))) (not true))))) -(let ((@x39 (trans @x35 (rewrite (= (not true) false)) (= (not (= (_ bv11 4) (_ bv11 4))) false)))) -(mp (asserted (not (= (_ bv11 4) (_ bv11 4)))) @x39 false))))) - -9fbec967ab26119b905e134e9f6da22a94ff68aa 8 0 +a5d69231f52771aee13986f9557d0f15deceb578 8 0 unsat ((set-logic ) (proof @@ -15,7 +7,15 @@ (let ((@x49 (trans (monotonicity @x42 (= (not (= (_ bv11 4) (bvneg (_ bv5 4)))) (not true))) (rewrite (= (not true) false)) (= (not (= (_ bv11 4) (bvneg (_ bv5 4)))) false)))) (mp (asserted (not (= (_ bv11 4) (bvneg (_ bv5 4))))) @x49 false)))))) -55b7bec34258b475381a754439390616488c924c 7 0 +ce29313a11444a23d27ac32aa304904b58c5ef48 7 0 +unsat +((set-logic ) +(proof +(let ((@x35 (monotonicity (rewrite (= (= (_ bv11 4) (_ bv11 4)) true)) (= (not (= (_ bv11 4) (_ bv11 4))) (not true))))) +(let ((@x39 (trans @x35 (rewrite (= (not true) false)) (= (not (= (_ bv11 4) (_ bv11 4))) false)))) +(mp (asserted (not (= (_ bv11 4) (_ bv11 4)))) @x39 false))))) + +bb95b2d5c073512432c61cceeaca86ea168b5973 7 0 unsat ((set-logic ) (proof @@ -23,7 +23,7 @@ (let ((@x42 (trans @x38 (rewrite (= (not true) false)) (= (not (bvult (_ bv23 8) (_ bv27 8))) false)))) (mp (asserted (not (bvult (_ bv23 8) (_ bv27 8)))) @x42 false))))) -fa462c1327b4231dc12d6f379b9bb280ea17bfd3 9 0 +26bb2ac93ef8c385bfbf217919bbafac305e5636 9 0 unsat ((set-logic ) (proof @@ -33,7 +33,7 @@ (let ((@x49 (trans @x45 (rewrite (= (not true) false)) (= (not (= (bvadd (_ bv27 5) (_ bv11 5)) (_ bv6 5))) false)))) (mp (asserted (not (= (bvadd (_ bv27 5) (_ bv11 5)) (_ bv6 5)))) @x49 false))))))) -bf6c2eb2daf9373dd063355969e25afc57fc44fe 9 0 +0e3ec4ac7c67aebfff2a5df85b922b50d3602563 9 0 unsat ((set-logic ) (proof @@ -43,7 +43,7 @@ (let ((@x49 (trans @x45 (rewrite (= (not true) false)) (= (not (= (bvmul (_ bv7 8) (_ bv3 8)) (_ bv21 8))) false)))) (mp (asserted (not (= (bvmul (_ bv7 8) (_ bv3 8)) (_ bv21 8)))) @x49 false))))))) -21dcbc62e4a0d275653bc7c57a948d4bf6975168 9 0 +9cf93e929e27dc04c30894bd14ced90c3cc565db 9 0 unsat ((set-logic ) (proof @@ -53,7 +53,7 @@ (let ((@x54 (trans @x50 (rewrite (= (not true) false)) (= (not (= (bvsub (_ bv11 8) (_ bv27 8)) (bvneg (_ bv16 8)))) false)))) (mp (asserted (not (= (bvsub (_ bv11 8) (_ bv27 8)) (bvneg (_ bv16 8))))) @x54 false))))))) -6dd961e81bf75734a230f5a110b28edf98e90aaf 7 0 +4bf6f825855790123eb3af10c0a8ece72a2696c0 7 0 unsat ((set-logic ) (proof @@ -61,7 +61,7 @@ (let ((@x39 (trans @x35 (rewrite (= (not true) false)) (= (not (= (_ bv11 5) (_ bv11 5))) false)))) (mp (asserted (not (= (_ bv11 5) (_ bv11 5)))) @x39 false))))) -10d0fe43a5dca47373c59ffadf5d4a9049a8df88 11 0 +faad761e2741d8b647fa62db13d8b0e649fb03d0 11 0 unsat ((set-logic ) (proof @@ -73,7 +73,7 @@ (let ((@x63 (trans @x59 (rewrite (= (not true) false)) (= (not (= (bvadd (bvneg (_ bv40 7)) (_ bv1 7)) (bvneg (_ bv39 7)))) false)))) (mp (asserted (not (= (bvadd (bvneg (_ bv40 7)) (_ bv1 7)) (bvneg (_ bv39 7))))) @x63 false))))))))) -de1bc26329091943d56ccf83cf9662c0b2001c97 19 0 +e913ddebe8fd3723faed676f00550d0f85717e48 19 0 unsat ((set-logic ) (proof @@ -93,7 +93,7 @@ (let ((@x67 (trans @x63 (rewrite (= (not true) false)) (= $x38 false)))) (mp (asserted $x38) @x67 false))))))))))))))))) -821acdf5acf235899fac29bcb5ad69c40cffe88f 18 0 +a481dcd4c078eb4bbc4578997c1becc3d0588892 18 0 unsat ((set-logic ) (proof @@ -112,7 +112,7 @@ (let ((@x84 (trans (monotonicity @x77 (= (not (= (_ bv4 4) ?x31)) (not true))) (rewrite (= (not true) false)) (= (not (= (_ bv4 4) ?x31)) false)))) (mp (not-or-elim (mp (asserted $x34) @x60 $x56) (not (= (_ bv4 4) ?x31))) @x84 false)))))))))))))))) -fb4d74278af64850ed8084451a8ff7a7075dbdfe 9 0 +1cd4bc28651d39e32aab684ecfdd3be7c1dd0a2c 9 0 unsat ((set-logic ) (proof @@ -122,7 +122,7 @@ (let ((@x48 (trans @x44 (rewrite (= (not true) false)) (= (not (= (bvand (_ bv6 32) (_ bv5 32)) (_ bv4 32))) false)))) (mp (asserted (not (= (bvand (_ bv6 32) (_ bv5 32)) (_ bv4 32)))) @x48 false))))))) -5a9d6d65605763b3b0286a0d4717a93a4da85a34 9 0 +178251ca0606b596bae71a7cf9b656088f51af57 9 0 unsat ((set-logic ) (proof @@ -132,7 +132,7 @@ (let ((@x48 (trans @x44 (rewrite (= (not true) false)) (= (not (= (bvor (_ bv6 8) (_ bv3 8)) (_ bv7 8))) false)))) (mp (asserted (not (= (bvor (_ bv6 8) (_ bv3 8)) (_ bv7 8)))) @x48 false))))))) -71f993d99975ef37af8d8478a6f1c26548b6f4a7 9 0 +769bdf70860c69df30d176b7eb677294e426fc4b 9 0 unsat ((set-logic ) (proof @@ -142,7 +142,7 @@ (let ((@x48 (trans @x44 (rewrite (= (not true) false)) (= (not (= (bvxor (_ bv240 8) (_ bv255 8)) (_ bv15 8))) false)))) (mp (asserted (not (= (bvxor (_ bv240 8) (_ bv255 8)) (_ bv15 8)))) @x48 false))))))) -353b2591bd8c22d0df29b19faf56739aac7b9b6d 8 0 +c2fb3d6f1f3f3e6dd3836f7f610e92c43dd7dfff 8 0 unsat ((set-logic ) (proof @@ -151,7 +151,7 @@ (let ((@x47 (trans (monotonicity @x40 (= (not (= (bvnot (_ bv240 16)) (_ bv65295 16))) (not true))) (rewrite (= (not true) false)) (= (not (= (bvnot (_ bv240 16)) (_ bv65295 16))) false)))) (mp (asserted (not (= (bvnot (_ bv240 16)) (_ bv65295 16)))) @x47 false)))))) -88af7aeb0e9a24cb60cf70ebed32fe4a6b94a809 9 0 +62fc6678382dfb5f2112f46aac810939a87814fd 9 0 unsat ((set-logic ) (proof @@ -161,7 +161,7 @@ (let ((@x48 (trans @x44 (rewrite (= (not true) false)) (= (not (= (concat (_ bv11 4) (_ bv27 8)) (_ bv2843 12))) false)))) (mp (asserted (not (= (concat (_ bv11 4) (_ bv27 8)) (_ bv2843 12)))) @x48 false))))))) -98fd1bf6fea1dce9107b6a84cfa810d8ae0827ad 9 0 +584cf4e60989598a0043c67a2cbfb9786830972b 9 0 unsat ((set-logic ) (proof @@ -171,7 +171,16 @@ (let ((@x48 (trans @x44 (rewrite (= (not true) false)) (= (not (= (concat (_ bv3 4) (_ bv15 6)) (_ bv207 10))) false)))) (mp (asserted (not (= (concat (_ bv3 4) (_ bv15 6)) (_ bv207 10)))) @x48 false))))))) -44630a6139544aa8cc936f2dcdd464d5967b2876 9 0 +c4ba99a31bff950f61b48e2df91d0092a4605b5b 8 0 +unsat +((set-logic ) +(proof +(let ((@x36 (monotonicity (rewrite (= ((_ extract 2 1) (_ bv6 4)) (_ bv3 2))) (= (= ((_ extract 2 1) (_ bv6 4)) (_ bv3 2)) (= (_ bv3 2) (_ bv3 2)))))) +(let ((@x40 (trans @x36 (rewrite (= (= (_ bv3 2) (_ bv3 2)) true)) (= (= ((_ extract 2 1) (_ bv6 4)) (_ bv3 2)) true)))) +(let ((@x47 (trans (monotonicity @x40 (= (not (= ((_ extract 2 1) (_ bv6 4)) (_ bv3 2))) (not true))) (rewrite (= (not true) false)) (= (not (= ((_ extract 2 1) (_ bv6 4)) (_ bv3 2))) false)))) +(mp (asserted (not (= ((_ extract 2 1) (_ bv6 4)) (_ bv3 2)))) @x47 false)))))) + +597573e2f4fd839e604ae52ba364ae11700dace1 9 0 unsat ((set-logic ) (proof @@ -181,16 +190,7 @@ (let ((@x47 (trans @x43 (rewrite (= (not true) false)) (= (not (= ((_ zero_extend 6) (_ bv10 4)) (_ bv10 10))) false)))) (mp (asserted (not (= ((_ zero_extend 6) (_ bv10 4)) (_ bv10 10)))) @x47 false))))))) -36033c98ec9d88c28e82a4d5b423281f56a42859 8 0 -unsat -((set-logic ) -(proof -(let ((@x36 (monotonicity (rewrite (= ((_ extract 2 1) (_ bv6 4)) (_ bv3 2))) (= (= ((_ extract 2 1) (_ bv6 4)) (_ bv3 2)) (= (_ bv3 2) (_ bv3 2)))))) -(let ((@x40 (trans @x36 (rewrite (= (= (_ bv3 2) (_ bv3 2)) true)) (= (= ((_ extract 2 1) (_ bv6 4)) (_ bv3 2)) true)))) -(let ((@x47 (trans (monotonicity @x40 (= (not (= ((_ extract 2 1) (_ bv6 4)) (_ bv3 2))) (not true))) (rewrite (= (not true) false)) (= (not (= ((_ extract 2 1) (_ bv6 4)) (_ bv3 2))) false)))) -(mp (asserted (not (= ((_ extract 2 1) (_ bv6 4)) (_ bv3 2)))) @x47 false)))))) - -2b91c33c03a89b80ac6fb984f384bd9814c2b51d 9 0 +10141671f4de43526d88d4ecd79c12df4bdb4825 9 0 unsat ((set-logic ) (proof @@ -200,7 +200,7 @@ (let ((@x47 (trans @x43 (rewrite (= (not true) false)) (= (not (= ((_ sign_extend 2) (_ bv10 4)) (_ bv58 6))) false)))) (mp (asserted (not (= ((_ sign_extend 2) (_ bv10 4)) (_ bv58 6)))) @x47 false))))))) -80e93d77c56b62b509cae750a834ba3c2a6545e3 9 0 +9db301365e8ecb55d7eee63724f390087c022cac 9 0 unsat ((set-logic ) (proof @@ -210,7 +210,7 @@ (let ((@x48 (trans @x44 (rewrite (= (not true) false)) (= (not (= (bvshl (_ bv19 8) (_ bv2 8)) (_ bv76 8))) false)))) (mp (asserted (not (= (bvshl (_ bv19 8) (_ bv2 8)) (_ bv76 8)))) @x48 false))))))) -08e3a62c0a330f1ab742b05e694f723668925d10 9 0 +a14cf81020b4c017a44794d9f507892fc994a0aa 9 0 unsat ((set-logic ) (proof @@ -220,7 +220,7 @@ (let ((@x48 (trans @x44 (rewrite (= (not true) false)) (= (not (= (bvlshr (_ bv25 8) (_ bv2 8)) (_ bv6 8))) false)))) (mp (asserted (not (= (bvlshr (_ bv25 8) (_ bv2 8)) (_ bv6 8)))) @x48 false))))))) -d1e9761fb935892f82a21268d39aac76f75ee282 9 0 +f043e921c4475109c2fdff12856bf28a46f470e8 9 0 unsat ((set-logic ) (proof @@ -230,7 +230,7 @@ (let ((@x48 (trans @x44 (rewrite (= (not true) false)) (= (not (= (bvashr (_ bv19 8) (_ bv2 8)) (_ bv4 8))) false)))) (mp (asserted (not (= (bvashr (_ bv19 8) (_ bv2 8)) (_ bv4 8)))) @x48 false))))))) -1b01af1c33961b4a329d46a526471313f71130ca 9 0 +1737667dcdf52add3cf7ec23188f82da46dd2b0a 9 0 unsat ((set-logic ) (proof @@ -240,7 +240,7 @@ (let ((@x47 (trans @x43 (rewrite (= (not true) false)) (= (not (= ((_ rotate_right 2) (_ bv6 4)) (_ bv9 4))) false)))) (mp (asserted (not (= ((_ rotate_right 2) (_ bv6 4)) (_ bv9 4)))) @x47 false))))))) -a14e30a88e731b5e605d4726dbb1f583497ab894 9 0 +4c62aea85c861b1e65021c56cee22174328eedc0 9 0 unsat ((set-logic ) (proof @@ -250,7 +250,7 @@ (let ((@x47 (trans @x43 (rewrite (= (not true) false)) (= (not (= ((_ rotate_left 1) (_ bv14 4)) (_ bv13 4))) false)))) (mp (asserted (not (= ((_ rotate_left 1) (_ bv14 4)) (_ bv13 4)))) @x47 false))))))) -08dd0af4f9cea470363f78957650260a900928c8 17 0 +dfec96be9ace458cbe9ee12898f33db7192c335c 17 0 unsat ((set-logic ) (proof @@ -268,7 +268,7 @@ (let ((@x55 (unit-resolution ((_ th-lemma bv) $x53) @x26 @x26 @x26 @x26 @x26 @x26 @x26 @x26 @x26 @x26 @x26 @x26 @x26 @x26 @x26 @x26 $x52))) (unit-resolution @x55 @x63 false))))))))))))))) -cffe711faa89f3f62e8e8e58173aaeb3cedc5d63 51 0 +73db5e04efabac69390d8eaa510230b30d68aff6 51 0 unsat ((set-logic ) (proof @@ -320,7 +320,7 @@ (let ((@x314 (unit-resolution ((_ th-lemma bv) $x312) @x26 @x26 @x26 @x26 @x26 @x26 @x26 @x26 (unit-resolution (def-axiom (or $x95 (not $x74))) @x303 (not $x74)) (unit-resolution (def-axiom (or $x95 (not $x75))) @x303 (not $x75)) (unit-resolution (def-axiom (or $x95 (not $x76))) @x303 (not $x76)) (unit-resolution (def-axiom (or $x95 (not $x77))) @x303 (not $x77)) (unit-resolution (def-axiom (or $x95 (not $x78))) @x303 (not $x78)) (unit-resolution (def-axiom (or $x95 (not $x79))) @x303 (not $x79)) (unit-resolution (def-axiom (or $x95 (not $x80))) @x303 (not $x80)) (unit-resolution (def-axiom (or $x95 $x264)) @x303 $x264) $x300))) (unit-resolution @x314 @x322 false))))))))))))))))))))))))))))))))))))))))))))))))) -024e51ae2c856c79195e59dfbc39c68dcf8ab939 29 0 +7378269c0bf8c864db559557bebcaf1734a4d5b0 29 0 unsat ((set-logic ) (proof @@ -350,7 +350,7 @@ (let ((@x30 (asserted $x29))) (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x29) $x183)) @x30 (unit-resolution @x189 @x180 $x184) false))))))))))))))))))) -20245d49b4c03da63c3124c5910beafc837f359a 12 0 +ed93cefa9922cae76b281457731fa49405ea5f1e 12 0 unsat ((set-logic ) (proof diff -r 3fdb94d87e0e -r 3c5a7746ffa4 src/HOL/SMT_Examples/VCC_Max.certs --- a/src/HOL/SMT_Examples/VCC_Max.certs Fri Mar 05 15:01:59 2021 +0100 +++ b/src/HOL/SMT_Examples/VCC_Max.certs Fri Mar 05 21:26:38 2021 +0100 @@ -1,4 +1,4 @@ -8ec9d30fc9fdbc0ea292e0fdf148a6230c16dbca 2924 0 +bb3039fa3c51c2ff1e3d9c4077fcbaf0fc7ae1b5 2924 0 unsat ((set-logic ) (declare-fun ?v0!15 () Int) @@ -2923,2928 +2923,3 @@ (let ((@x24927 (lemma (unit-resolution (hypothesis $x24385) @x24924 false) (or $x24726 $x24332 $x24607)))) (unit-resolution (unit-resolution @x24927 @x23880 (or $x24332 $x24607)) @x24156 @x24149 false)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -b45f2460a495d881fc6020fbfa5928aede1a58f0 2924 0 -unsat -((set-logic ) -(declare-fun ?v0!15 () Int) -(declare-fun ?v0!14 () Int) -(declare-fun ?v0!13 () Int) -(proof -(let ((?x10076 (b_S_array$ b_T_T_u1$ v_b_P_H_len$))) -(let ((?x22595 (b_S_ptr$ ?x10076 v_b_P_H_arr$))) -(let ((?x24598 (b_S_idx$ ?x22595 v_b_L_H_p_G_0$ b_T_T_u1$))) -(let ((?x10272 (b_S_typemap$ v_b_S_s$))) -(let ((?x24302 (b_S_select_o_tm$ ?x10272 ?x24598))) -(let ((?x24605 (b_S_ts_n_emb$ ?x24302))) -(let (($x24606 (= ?x24605 ?x22595))) -(let (($x24611 (b_S_typed$ v_b_S_s$ ?x24598))) -(let (($x24614 (not $x24611))) -(let (($x24608 (b_S_ts_n_is_n_volatile$ ?x24302))) -(let (($x24607 (not $x24606))) -(let (($x24615 (or $x24607 $x24608 (not (b_S_ts_n_is_n_array_n_elt$ ?x24302)) $x24614))) -(let (($x24616 (not $x24615))) -(let (($x11901 (>= v_b_L_H_p_G_0$ 0))) -(let (($x20030 (forall ((?v0 Int) )(! (let ((?x10163 (b_S_read_n_u1$ v_b_S_s$ (b_S_idx$ (b_S_ptr$ b_T_T_u1$ v_b_P_H_arr$) ?v0 b_T_T_u1$)))) -(let (($x10238 (= ?x10163 v_b_S_result_G_0$))) -(let (($x11800 (>= (+ ?v0 (* (- 1) v_b_P_H_len$)) 0))) -(let (($x12168 (<= ?v0 4294967295))) -(let (($x16553 (not $x12168))) -(let (($x2815 (>= ?v0 0))) -(let (($x3763 (not $x2815))) -(or $x3763 $x16553 $x11800 (not $x10238))))))))) :pattern ( (b_S_idx$ (b_S_ptr$ b_T_T_u1$ v_b_P_H_arr$) ?v0 b_T_T_u1$) ) :qid k!704)) -)) -(let (($x20035 (not $x20030))) -(let (($x20022 (forall ((?v0 Int) )(! (let ((?x11816 (* (- 1) v_b_S_result_G_0$))) -(let ((?x10163 (b_S_read_n_u1$ v_b_S_s$ (b_S_idx$ (b_S_ptr$ b_T_T_u1$ v_b_P_H_arr$) ?v0 b_T_T_u1$)))) -(let (($x11818 (<= (+ ?x10163 ?x11816) 0))) -(let (($x11800 (>= (+ ?v0 (* (- 1) v_b_P_H_len$)) 0))) -(let (($x12168 (<= ?v0 4294967295))) -(let (($x16553 (not $x12168))) -(let (($x2815 (>= ?v0 0))) -(let (($x3763 (not $x2815))) -(or $x3763 $x16553 $x11800 $x11818))))))))) :pattern ( (b_S_idx$ (b_S_ptr$ b_T_T_u1$ v_b_P_H_arr$) ?v0 b_T_T_u1$) ) :qid k!704)) -)) -(let (($x20027 (not $x20022))) -(let (($x20038 (or $x20027 $x20035))) -(let (($x20041 (not $x20038))) -(let ((?x10078 (b_S_ptr$ b_T_T_u1$ v_b_P_H_arr$))) -(let ((?x15743 (b_S_idx$ ?x10078 ?v0!15 b_T_T_u1$))) -(let ((?x15744 (b_S_read_n_u1$ v_b_S_s$ ?x15743))) -(let ((?x16029 (* (- 1) ?x15744))) -(let (($x16031 (>= (+ v_b_S_result_G_0$ ?x16029) 0))) -(let (($x16009 (<= (+ v_b_P_H_len$ (* (- 1) ?v0!15)) 0))) -(let (($x15737 (<= ?v0!15 4294967295))) -(let (($x19560 (not $x15737))) -(let (($x15736 (>= ?v0!15 0))) -(let (($x19559 (not $x15736))) -(let (($x19575 (or $x19559 $x19560 $x16009 $x16031))) -(let (($x19580 (not $x19575))) -(let (($x20044 (or $x19580 $x20041))) -(let (($x20047 (not $x20044))) -(let (($x10222 (= v_b_S_result_G_0$ v_b_L_H_max_G_1$))) -(let (($x19640 (not $x10222))) -(let (($x10220 (= v_b_SL_H_witness_G_2$ v_b_SL_H_witness_G_0$))) -(let (($x19639 (not $x10220))) -(let (($x10218 (= v_b_L_H_p_G_2$ v_b_L_H_p_G_0$))) -(let (($x19638 (not $x10218))) -(let (($x10216 (= v_b_L_H_max_G_4$ v_b_L_H_max_G_1$))) -(let (($x19637 (not $x10216))) -(let (($x11432 (>= v_b_SL_H_witness_G_0$ 0))) -(let (($x19501 (not $x11432))) -(let (($x11429 (>= v_b_L_H_p_G_0$ 1))) -(let (($x19474 (not $x11429))) -(let (($x15729 (not b_S_position_n_marker$))) -(let (($x20050 (or $x15729 $x19474 $x19501 $x19637 $x19638 $x19639 $x19640 $x20047))) -(let (($x20053 (not $x20050))) -(let (($x20056 (or $x15729 $x20053))) -(let (($x20059 (not $x20056))) -(let ((?x11484 (* (- 1) v_b_L_H_p_G_0$))) -(let ((?x11485 (+ v_b_P_H_len$ ?x11484))) -(let (($x11486 (<= ?x11485 0))) -(let (($x11487 (not $x11486))) -(let (($x20062 (or $x11487 $x19474 $x19501 $x20059))) -(let (($x20065 (not $x20062))) -(let ((?x10372 (b_S_idx$ ?x10078 v_b_SL_H_witness_G_1$ b_T_T_u1$))) -(let ((?x10373 (b_S_read_n_u1$ v_b_S_s$ ?x10372))) -(let (($x10374 (= ?x10373 v_b_L_H_max_G_3$))) -(let (($x19411 (not $x10374))) -(let (($x11647 (<= (+ v_b_P_H_len$ (* (- 1) v_b_SL_H_witness_G_1$)) 0))) -(let (($x19412 (or $x11647 $x19411))) -(let (($x19413 (not $x19412))) -(let (($x19906 (forall ((?v0 Int) )(! (let ((?x11631 (* (- 1) v_b_L_H_max_G_3$))) -(let ((?x10163 (b_S_read_n_u1$ v_b_S_s$ (b_S_idx$ (b_S_ptr$ b_T_T_u1$ v_b_P_H_arr$) ?v0 b_T_T_u1$)))) -(let (($x11633 (<= (+ ?x10163 ?x11631) 0))) -(let (($x11615 (>= (+ ?v0 (* (- 1) v_b_L_H_p_G_1$)) 0))) -(let (($x12168 (<= ?v0 4294967295))) -(let (($x16553 (not $x12168))) -(let (($x2815 (>= ?v0 0))) -(let (($x3763 (not $x2815))) -(or $x3763 $x16553 $x11615 $x11633))))))))) :pattern ( (b_S_idx$ (b_S_ptr$ b_T_T_u1$ v_b_P_H_arr$) ?v0 b_T_T_u1$) ) :qid k!704)) -)) -(let (($x19911 (not $x19906))) -(let (($x19914 (or $x19911 $x19413))) -(let (($x19917 (not $x19914))) -(let ((?x15633 (b_S_idx$ ?x10078 ?v0!14 b_T_T_u1$))) -(let ((?x15634 (b_S_read_n_u1$ v_b_S_s$ ?x15633))) -(let ((?x15891 (* (- 1) ?x15634))) -(let (($x15893 (>= (+ v_b_L_H_max_G_3$ ?x15891) 0))) -(let (($x15871 (<= (+ v_b_L_H_p_G_1$ (* (- 1) ?v0!14)) 0))) -(let (($x15627 (<= ?v0!14 4294967295))) -(let (($x19366 (not $x15627))) -(let (($x15626 (>= ?v0!14 0))) -(let (($x19365 (not $x15626))) -(let (($x19381 (or $x19365 $x19366 $x15871 $x15893))) -(let (($x19386 (not $x19381))) -(let (($x19920 (or $x19386 $x19917))) -(let (($x19923 (not $x19920))) -(let (($x11608 (>= (+ v_b_P_H_len$ (* (- 1) v_b_L_H_p_G_1$)) 0))) -(let (($x11612 (not $x11608))) -(let (($x19926 (or $x11612 $x19923))) -(let (($x19929 (not $x19926))) -(let (($x19932 (or $x11612 $x19929))) -(let (($x19935 (not $x19932))) -(let (($x11536 (>= v_b_SL_H_witness_G_1$ 0))) -(let (($x19455 (not $x11536))) -(let (($x11578 (>= v_b_L_H_p_G_1$ 2))) -(let (($x19454 (not $x11578))) -(let (($x10358 (b_S_local_n_value_n_is$ v_b_S_s$ b_H_tok_S_1_T_16_o_24$ b_H_loc_o_p$ v_b_L_H_p_G_1$ b_T_T_u4$))) -(let (($x19453 (not $x10358))) -(let ((?x11581 (* (- 1) v_b_L_H_p_G_1$))) -(let ((?x11582 (+ v_b_L_H_p_G_0$ ?x11581))) -(let (($x11580 (= ?x11582 (- 1)))) -(let (($x19452 (not $x11580))) -(let (($x13353 (<= v_b_L_H_p_G_0$ 4294967294))) -(let (($x15614 (not $x13353))) -(let (($x11570 (>= v_b_L_H_p_G_0$ (- 1)))) -(let (($x15611 (not $x11570))) -(let (($x19938 (or $x15611 $x15614 $x19452 $x19453 $x19454 $x19455 $x19935))) -(let (($x19941 (not $x19938))) -(let (($x19944 (or $x15611 $x15614 $x19941))) -(let (($x19947 (not $x19944))) -(let (($x10392 (= v_b_SL_H_witness_G_1$ v_b_SL_H_witness_G_0$))) -(let (($x19513 (not $x10392))) -(let (($x10391 (= v_b_L_H_max_G_3$ v_b_L_H_max_G_1$))) -(let (($x19512 (not $x10391))) -(let ((?x10320 (b_S_idx$ ?x10078 v_b_L_H_p_G_0$ b_T_T_u1$))) -(let ((?x10327 (b_S_read_n_u1$ v_b_S_s$ ?x10320))) -(let ((?x11517 (* (- 1) ?x10327))) -(let (($x11516 (>= (+ v_b_L_H_max_G_1$ ?x11517) 0))) -(let (($x11515 (not $x11516))) -(let (($x19980 (or $x11515 $x19501 $x19512 $x19513 $x19474 $x19455 $x19947))) -(let (($x19983 (not $x19980))) -(let (($x10340 (= v_b_SL_H_witness_G_1$ v_b_L_H_p_G_0$))) -(let (($x19473 (not $x10340))) -(let (($x10338 (= v_b_L_H_max_G_3$ v_b_L_H_max_G_2$))) -(let (($x19472 (not $x10338))) -(let (($x10335 (b_S_local_n_value_n_is$ v_b_S_s$ b_H_tok_S_1_T_24_o_47$ b_H_loc_o_witness$ v_b_L_H_p_G_0$ b_T_T_u4$))) -(let (($x19471 (not $x10335))) -(let (($x10334 (b_S_local_n_value_n_is$ v_b_S_s$ b_H_tok_S_1_T_23_o_7$ b_H_loc_o_max$ v_b_L_H_max_G_2$ b_T_T_u1$))) -(let (($x19470 (not $x10334))) -(let (($x10333 (= v_b_L_H_max_G_2$ ?x10327))) -(let (($x19469 (not $x10333))) -(let (($x10324 (b_S_thread_n_local$ v_b_S_s$ ?x10320))) -(let (($x15599 (not $x10324))) -(let (($x10321 (b_S_is$ ?x10320 b_T_T_u1$))) -(let (($x15590 (not $x10321))) -(let (($x19950 (or $x15590 $x15599 $x19469 $x19470 $x19471 $x19472 $x19473 $x19474 $x19455 $x19947))) -(let (($x19953 (not $x19950))) -(let (($x19956 (or $x15590 $x15599 $x19953))) -(let (($x19959 (not $x19956))) -(let (($x10322 (b_S_typed$ v_b_S_s$ ?x10320))) -(let (($x15593 (not $x10322))) -(let (($x19962 (or $x15590 $x15593 $x19959))) -(let (($x19965 (not $x19962))) -(let (($x19968 (or $x15590 $x15593 $x19965))) -(let (($x19971 (not $x19968))) -(let (($x19974 (or $x11516 $x19474 $x19501 $x19971))) -(let (($x19977 (not $x19974))) -(let (($x19986 (or $x19977 $x19983))) -(let (($x19989 (not $x19986))) -(let (($x19992 (or $x15590 $x15599 $x19474 $x19501 $x19989))) -(let (($x19995 (not $x19992))) -(let (($x19998 (or $x15590 $x15599 $x19995))) -(let (($x20001 (not $x19998))) -(let (($x20004 (or $x15590 $x15593 $x20001))) -(let (($x20007 (not $x20004))) -(let (($x20010 (or $x15590 $x15593 $x20007))) -(let (($x20013 (not $x20010))) -(let (($x20016 (or $x11486 $x19474 $x19501 $x20013))) -(let (($x20019 (not $x20016))) -(let (($x20068 (or $x20019 $x20065))) -(let (($x20071 (not $x20068))) -(let ((?x2238 (b_S_ptr_n_to$ b_T_T_u1$))) -(let (($x10296 (b_S_local_n_value_n_is_n_ptr$ v_b_S_s$ b_H_tok_S_1_T_16_o_3$ b_H_loc_o_arr$ ?x10078 ?x2238))) -(let (($x19683 (not $x10296))) -(let ((?x10105 (b_S_ptr_n_to_n_int$ ?x10078))) -(let (($x10295 (b_S_local_n_value_n_is$ v_b_S_s$ b_H_tok_S_1_T_16_o_3$ b_H_loc_o_arr$ ?x10105 ?x2238))) -(let (($x19682 (not $x10295))) -(let (($x10294 (b_S_local_n_value_n_is$ v_b_S_s$ 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(monotonicity (monotonicity @x19894 (= (not $x19340) $x19895)) @x20085 (= (or (not $x19340) (not $x19691)) $x20086)))) -(let ((@x20097 (monotonicity (monotonicity (monotonicity @x20088 (= $x19700 $x20089)) (= $x19705 $x20092)) (= (not $x19705) $x20095)))) -(let ((@x20103 (monotonicity (monotonicity @x20097 (= (or $x11385 (not $x19705)) $x20098)) (= $x19713 $x20101)))) -(let ((@x20109 (monotonicity (monotonicity @x20103 (= $x19718 $x20104)) (= (not $x19718) $x20107)))) -(let ((@x20112 (monotonicity @x20109 (= (or $x15502 $x15511 $x19724 $x19725 $x19726 $x19727 (not $x19718)) $x20110)))) -(let ((@x20121 (monotonicity (monotonicity (monotonicity @x20112 (= $x19730 $x20113)) (= $x19735 $x20116)) (= (not $x19735) $x20119)))) -(let ((@x20127 (monotonicity (monotonicity @x20121 (= (or $x15502 $x15505 (not $x19735)) $x20122)) (= $x19743 $x20125)))) -(let ((@x20133 (monotonicity (monotonicity @x20127 (= $x19748 $x20128)) (= (not $x19748) $x20131)))) -(let ((@x20139 (monotonicity (monotonicity @x20133 (= (or $x11221 (not $x19748)) $x20134)) (= $x19756 $x20137)))) -(let (($x15761 (forall ((?v0 Int) )(! (let ((?x10163 (b_S_read_n_u1$ v_b_S_s$ (b_S_idx$ (b_S_ptr$ b_T_T_u1$ v_b_P_H_arr$) ?v0 b_T_T_u1$)))) -(let (($x10238 (= ?x10163 v_b_S_result_G_0$))) -(let (($x11800 (>= (+ ?v0 (* (- 1) v_b_P_H_len$)) 0))) -(let (($x11802 (not $x11800))) -(let (($x12168 (<= ?v0 4294967295))) -(let (($x2815 (>= ?v0 0))) -(let (($x13448 (and $x2815 $x12168 $x11802 $x10238))) -(not $x13448)))))))) :qid k!704)) -)) -(let (($x13442 (forall ((?v0 Int) )(! 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(let ((?x11887 (* (- 1) v_b_L_H_max_G_1$))) -(let ((?x10163 (b_S_read_n_u1$ v_b_S_s$ (b_S_idx$ (b_S_ptr$ b_T_T_u1$ v_b_P_H_arr$) ?v0 b_T_T_u1$)))) -(let (($x11889 (<= (+ ?x10163 ?x11887) 0))) -(let (($x11871 (>= (+ ?v0 (* (- 1) v_b_L_H_p_G_0$)) 0))) -(let (($x11873 (not $x11871))) -(let (($x12168 (<= ?v0 4294967295))) -(let (($x2815 (>= ?v0 0))) -(let (($x13331 (and $x2815 $x12168 $x11873))) -(let (($x13334 (not $x13331))) -(or $x13334 $x11889)))))))))) :qid k!704)) -)) -(let (($x16070 (and $x11260 $x10167 $x11911 $x13304 $x13315 $x11901 $x13326 $x11898 $x13340 $x11868 $x10192 $x10284 $x10204 $x10097 $x10291 $x10292 $x10293 $x10294 $x10295 $x10296 $x11429 $x11432 $x16064))) -(let (($x16075 (or $x11259 $x15548 $x16070))) -(let (($x13292 (forall ((?v0 Int) )(! (let ((?x10163 (b_S_read_n_u1$ v_b_S_s$ (b_S_idx$ (b_S_ptr$ b_T_T_u1$ v_b_P_H_arr$) ?v0 b_T_T_u1$)))) -(let (($x11404 (>= (+ v_b_L_H_max_G_0$ (* (- 1) ?x10163)) 0))) -(let (($x11388 (>= ?v0 1))) -(let (($x11389 (not $x11388))) -(let (($x12168 (<= ?v0 4294967295))) -(let (($x2815 (>= ?v0 0))) -(let (($x13283 (and $x2815 $x12168 $x11389))) -(let (($x13286 (not $x13283))) -(or $x13286 $x11404))))))))) :qid k!704)) -)) -(let (($x16078 (and $x13292 $x16075))) -(let (($x15528 (not (and $x15523 $x15524 (not $x15525))))) -(let (($x15534 (or $x15528 $x15533))) -(let (($x15535 (not $x15534))) -(let (($x16081 (or $x15535 $x16078))) -(let (($x16084 (and $x11382 $x16081))) -(let (($x16087 (or $x11385 $x16084))) -(let (($x16093 (and $x10138 $x10141 $x10145 $x10146 $x10147 $x10148 $x16087))) -(let (($x16098 (or $x15502 $x15511 $x16093))) -(let (($x16104 (and $x10138 $x10139 $x16098))) -(let (($x16109 (or $x15502 $x15505 $x16104))) -(let (($x16112 (and $x10136 $x16109))) -(let (($x16115 (or $x11221 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$x19381)))) -(let ((@x19435 (monotonicity (monotonicity @x19385 (= $x15901 $x19386)) (trans @x19425 (rewrite (= (and $x19408 $x19412) $x19428)) (= $x15651 $x19428)) (= $x15904 $x19433)))) -(let ((@x19445 (trans (monotonicity @x19435 (= $x15907 (and $x11608 $x19433))) (rewrite (= (and $x11608 $x19433) $x19441)) (= $x15907 $x19441)))) -(let ((@x19451 (monotonicity (monotonicity @x19445 (= $x15910 $x19446)) (= $x15916 (and $x11570 $x13353 $x11580 $x10358 $x11578 $x11536 $x19446))))) -(let ((@x19462 (trans @x19451 (rewrite (= (and $x11570 $x13353 $x11580 $x10358 $x11578 $x11536 $x19446) $x19458)) (= $x15916 $x19458)))) -(let ((@x19511 (monotonicity (monotonicity @x19462 (= $x15921 $x19463)) (= $x15959 (and $x11516 $x11432 $x10391 $x10392 $x11429 $x11536 $x19463))))) -(let ((@x19519 (trans @x19511 (rewrite (= (and $x11516 $x11432 $x10391 $x10392 $x11429 $x11536 $x19463) $x19515)) (= $x15959 $x19515)))) -(let ((@x19479 (rewrite (= (and $x10321 $x10324 $x10333 $x10334 $x10335 $x10338 $x10340 $x11429 $x11536 $x19463) $x19477)))) -(let ((@x19468 (monotonicity (monotonicity @x19462 (= $x15921 $x19463)) (= $x15927 (and $x10321 $x10324 $x10333 $x10334 $x10335 $x10338 $x10340 $x11429 $x11536 $x19463))))) -(let ((@x19487 (monotonicity (monotonicity (trans @x19468 @x19479 (= $x15927 $x19477)) (= $x15932 $x19482)) (= $x15938 (and $x10321 $x10322 $x19482))))) -(let ((@x19494 (trans @x19487 (rewrite (= (and $x10321 $x10322 $x19482) $x19490)) (= $x15938 $x19490)))) -(let ((@x19500 (monotonicity (monotonicity @x19494 (= $x15943 $x19495)) (= $x15949 (and $x11515 $x11429 $x11432 $x19495))))) -(let ((@x19508 (trans @x19500 (rewrite (= (and $x11515 $x11429 $x11432 $x19495) $x19504)) (= $x15949 $x19504)))) -(let ((@x19525 (monotonicity (monotonicity @x19508 @x19519 (= $x15964 $x19520)) (= $x15970 (and $x10321 $x10324 $x11429 $x11432 $x19520))))) -(let ((@x19532 (trans @x19525 (rewrite (= (and $x10321 $x10324 $x11429 $x11432 $x19520) $x19528)) (= $x15970 $x19528)))) -(let ((@x19538 (monotonicity (monotonicity @x19532 (= $x15975 $x19533)) (= $x15981 (and $x10321 $x10322 $x19533))))) -(let ((@x19545 (trans @x19538 (rewrite (= (and $x10321 $x10322 $x19533) $x19541)) (= $x15981 $x19541)))) -(let ((@x19551 (monotonicity (monotonicity @x19545 (= $x15986 $x19546)) (= $x15992 (and $x11487 $x11429 $x11432 $x19546))))) -(let ((@x19558 (trans @x19551 (rewrite (= (and $x11487 $x11429 $x11432 $x19546) $x19554)) (= $x15992 $x19554)))) -(let ((@x19359 (rewrite (= (or (or $x3763 $x16553 $x11871) $x11889) (or $x3763 $x16553 $x11871 $x11889))))) -(let (($x13331 (and $x2815 $x12168 $x11873))) -(let (($x13334 (not $x13331))) -(let (($x13337 (or $x13334 $x11889))) -(let ((@x19349 (monotonicity (rewrite (= $x13331 (not (or $x3763 $x16553 $x11871)))) (= $x13334 (not (not (or $x3763 $x16553 $x11871))))))) -(let ((@x19353 (trans @x19349 (rewrite (= (not (not (or $x3763 $x16553 $x11871))) (or $x3763 $x16553 $x11871))) (= $x13334 (or $x3763 $x16553 $x11871))))) -(let ((@x19361 (trans (monotonicity @x19353 (= $x13337 (or (or $x3763 $x16553 $x11871) $x11889))) @x19359 (= $x13337 (or $x3763 $x16553 $x11871 $x11889))))) -(let ((@x19666 (monotonicity (quant-intro @x19361 (= $x13340 $x19362)) (monotonicity @x19558 @x19660 (= $x16064 $x19661)) (= $x16070 $x19664)))) -(let ((@x19693 (monotonicity (trans @x19666 (rewrite (= $x19664 $x19686)) (= $x16070 $x19686)) (= $x16075 $x19691)))) -(let ((@x19337 (rewrite (= (or (or $x3763 $x16553 $x11388) $x11404) (or $x3763 $x16553 $x11388 $x11404))))) -(let (($x13283 (and $x2815 $x12168 $x11389))) -(let (($x13286 (not $x13283))) -(let (($x13289 (or $x13286 $x11404))) -(let ((@x19327 (monotonicity (rewrite (= $x13283 (not (or $x3763 $x16553 $x11388)))) (= $x13286 (not (not (or $x3763 $x16553 $x11388))))))) -(let ((@x19331 (trans @x19327 (rewrite (= (not (not (or $x3763 $x16553 $x11388))) (or $x3763 $x16553 $x11388))) (= $x13286 (or $x3763 $x16553 $x11388))))) -(let ((@x19339 (trans (monotonicity @x19331 (= $x13289 (or (or $x3763 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(= $x15833 $x16115)))) -(let (($x13451 (exists ((?v0 Int) )(! (let ((?x10163 (b_S_read_n_u1$ v_b_S_s$ (b_S_idx$ (b_S_ptr$ b_T_T_u1$ v_b_P_H_arr$) ?v0 b_T_T_u1$)))) -(let (($x10238 (= ?x10163 v_b_S_result_G_0$))) -(let (($x11800 (>= (+ ?v0 (* (- 1) v_b_P_H_len$)) 0))) -(let (($x11802 (not $x11800))) -(let (($x12168 (<= ?v0 4294967295))) -(let (($x2815 (>= ?v0 0))) -(and $x2815 $x12168 $x11802 $x10238))))))) :qid k!704)) -)) -(let (($x13445 (not $x13442))) -(let (($x13454 (or $x13445 $x13451))) -(let (($x13457 (and $x13442 $x13454))) -(let (($x13460 (or $x11797 $x13457))) -(let (($x13463 (and b_S_position_n_marker$ $x13460))) -(let (($x13466 (or $x11777 $x13463))) -(let (($x13376 (not $x13373))) -(let (($x13379 (or $x13376 $x11651))) -(let (($x13382 (and $x13373 $x13379))) -(let (($x13385 (or $x11612 $x13382))) -(let (($x13388 (and $x11608 $x13385))) -(let (($x13391 (or $x13361 $x13388))) -(let (($x13394 (and $x11570 $x13353 $x13391))) -(let (($x13412 (or $x11730 $x13394))) -(let (($x13397 (or $x11567 $x13394))) -(let (($x13400 (and $x10321 $x10324 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(let (($x6905 (b_S_typed$ ?v0 (b_S_idx$ (b_S_ptr$ (b_S_array$ ?v2 ?v3) ?v1) ?v4 ?v2)))) -(let ((?x6897 (b_S_typemap$ ?v0))) -(let ((?x6899 (b_S_select_o_tm$ ?x6897 (b_S_idx$ (b_S_ptr$ (b_S_array$ ?v2 ?v3) ?v1) ?v4 ?v2)))) -(let (($x6904 (b_S_ts_n_is_n_array_n_elt$ ?x6899))) -(let (($x17952 (or (not (= (b_S_ts_n_emb$ ?x6899) (b_S_ptr$ (b_S_array$ ?v2 ?v3) ?v1))) (b_S_ts_n_is_n_volatile$ ?x6899) (not $x6904) (not $x6905)))) -(let (($x17953 (not $x17952))) -(let (($x4862 (>= (+ ?v4 (* (- 1) ?v3)) 0))) -(let (($x2815 (>= ?v4 0))) -(let (($x3763 (not $x2815))) -(or (not (b_S_typed$ ?v0 (b_S_ptr$ (b_S_array$ ?v2 ?v3) ?v1))) $x3763 $x4862 $x17953)))))))))) :pattern ( (b_S_select_o_sm$ (b_S_statusmap$ ?v0) (b_S_idx$ (b_S_ptr$ ?v2 ?v1) ?v4 ?v2)) (b_S_ptr$ (b_S_array$ ?v2 ?v3) ?v1) ) :pattern ( (b_S_select_o_tm$ (b_S_typemap$ ?v0) (b_S_idx$ (b_S_ptr$ ?v2 ?v1) ?v4 ?v2)) (b_S_ptr$ (b_S_array$ ?v2 ?v3) ?v1) ) :qid k!493)) -)) -(let (($x6943 (forall ((?v0 B_S_state$) (?v1 Int) (?v2 B_S_ctype$) (?v3 Int) (?v4 Int) )(! (let (($x6905 (b_S_typed$ ?v0 (b_S_idx$ (b_S_ptr$ (b_S_array$ ?v2 ?v3) ?v1) ?v4 ?v2)))) -(let ((?x6897 (b_S_typemap$ ?v0))) -(let ((?x6899 (b_S_select_o_tm$ ?x6897 (b_S_idx$ (b_S_ptr$ (b_S_array$ ?v2 ?v3) ?v1) ?v4 ?v2)))) -(let (($x6904 (b_S_ts_n_is_n_array_n_elt$ ?x6899))) -(let ((?x6894 (b_S_ptr$ (b_S_array$ ?v2 ?v3) ?v1))) -(let (($x6901 (= (b_S_ts_n_emb$ ?x6899) ?x6894))) -(let (($x6937 (and $x6901 (not (b_S_ts_n_is_n_volatile$ ?x6899)) $x6904 $x6905))) -(let (($x4862 (>= (+ ?v4 (* (- 1) ?v3)) 0))) -(let (($x6603 (not $x4862))) -(let (($x2815 (>= ?v4 0))) -(let (($x6895 (b_S_typed$ ?v0 ?x6894))) -(let (($x6929 (and $x6895 $x2815 $x6603))) -(let (($x6934 (not $x6929))) -(or $x6934 $x6937)))))))))))))) :pattern ( (b_S_select_o_sm$ (b_S_statusmap$ ?v0) (b_S_idx$ (b_S_ptr$ ?v2 ?v1) ?v4 ?v2)) (b_S_ptr$ (b_S_array$ ?v2 ?v3) ?v1) ) :pattern ( (b_S_select_o_tm$ (b_S_typemap$ ?v0) (b_S_idx$ (b_S_ptr$ ?v2 ?v1) ?v4 ?v2)) (b_S_ptr$ (b_S_array$ ?v2 ?v3) ?v1) ) :qid k!493)) -)) -(let (($x6905 (b_S_typed$ ?4 (b_S_idx$ (b_S_ptr$ (b_S_array$ ?2 ?1) ?3) ?0 ?2)))) -(let ((?x6897 (b_S_typemap$ ?4))) -(let ((?x6899 (b_S_select_o_tm$ ?x6897 (b_S_idx$ (b_S_ptr$ (b_S_array$ ?2 ?1) ?3) ?0 ?2)))) -(let (($x6904 (b_S_ts_n_is_n_array_n_elt$ ?x6899))) -(let (($x17952 (or (not (= (b_S_ts_n_emb$ ?x6899) (b_S_ptr$ (b_S_array$ ?2 ?1) ?3))) (b_S_ts_n_is_n_volatile$ ?x6899) (not $x6904) (not $x6905)))) -(let (($x17953 (not $x17952))) -(let (($x4862 (>= (+ ?0 (* (- 1) ?1)) 0))) -(let (($x17959 (or (not (b_S_typed$ ?4 (b_S_ptr$ (b_S_array$ ?2 ?1) ?3))) $x3763 $x4862 $x17953))) -(let ((?x6894 (b_S_ptr$ (b_S_array$ ?2 ?1) ?3))) -(let (($x6901 (= (b_S_ts_n_emb$ ?x6899) ?x6894))) -(let (($x6937 (and $x6901 (not (b_S_ts_n_is_n_volatile$ ?x6899)) $x6904 $x6905))) -(let (($x6603 (not $x4862))) -(let (($x6895 (b_S_typed$ ?4 ?x6894))) -(let (($x6929 (and $x6895 $x2815 $x6603))) -(let (($x6934 (not $x6929))) -(let (($x6940 (or $x6934 $x6937))) -(let (($x17938 (or (not $x6895) $x3763 $x4862))) -(let ((@x17944 (monotonicity (rewrite (= $x6929 (not $x17938))) (= $x6934 (not (not $x17938)))))) -(let ((@x17958 (monotonicity (trans @x17944 (rewrite (= (not (not $x17938)) $x17938)) (= $x6934 $x17938)) (rewrite (= $x6937 $x17953)) (= $x6940 (or $x17938 $x17953))))) -(let ((@x17966 (quant-intro (trans @x17958 (rewrite (= (or $x17938 $x17953) $x17959)) (= $x6940 $x17959)) (= $x6943 $x17964)))) -(let (($x6917 (forall ((?v0 B_S_state$) (?v1 Int) (?v2 B_S_ctype$) (?v3 Int) (?v4 Int) )(! (let (($x6905 (b_S_typed$ ?v0 (b_S_idx$ (b_S_ptr$ (b_S_array$ ?v2 ?v3) ?v1) ?v4 ?v2)))) -(let ((?x6897 (b_S_typemap$ ?v0))) -(let ((?x6899 (b_S_select_o_tm$ ?x6897 (b_S_idx$ (b_S_ptr$ (b_S_array$ ?v2 ?v3) ?v1) ?v4 ?v2)))) -(let (($x6904 (b_S_ts_n_is_n_array_n_elt$ ?x6899))) -(let ((?x6894 (b_S_ptr$ (b_S_array$ ?v2 ?v3) ?v1))) -(let (($x6901 (= (b_S_ts_n_emb$ ?x6899) ?x6894))) -(let (($x6908 (and $x6901 (and (not (b_S_ts_n_is_n_volatile$ ?x6899)) (and $x6904 $x6905))))) -(let (($x2766 (<= 0 ?v4))) -(let (($x6566 (and $x2766 (< ?v4 ?v3)))) -(let (($x6895 (b_S_typed$ ?v0 ?x6894))) -(let (($x6896 (and $x6895 $x6566))) -(=> $x6896 $x6908)))))))))))) :pattern ( (b_S_select_o_sm$ (b_S_statusmap$ ?v0) (b_S_idx$ (b_S_ptr$ ?v2 ?v1) ?v4 ?v2)) (b_S_ptr$ (b_S_array$ ?v2 ?v3) ?v1) ) :pattern ( (b_S_select_o_tm$ (b_S_typemap$ ?v0) (b_S_idx$ (b_S_ptr$ ?v2 ?v1) ?v4 ?v2)) (b_S_ptr$ (b_S_array$ ?v2 ?v3) ?v1) ) :qid k!493)) -)) -(let (($x6923 (forall ((?v0 B_S_state$) (?v1 Int) (?v2 B_S_ctype$) (?v3 Int) (?v4 Int) )(! (let (($x6905 (b_S_typed$ ?v0 (b_S_idx$ (b_S_ptr$ (b_S_array$ ?v2 ?v3) ?v1) ?v4 ?v2)))) -(let ((?x6897 (b_S_typemap$ ?v0))) -(let ((?x6899 (b_S_select_o_tm$ ?x6897 (b_S_idx$ (b_S_ptr$ (b_S_array$ ?v2 ?v3) ?v1) ?v4 ?v2)))) -(let (($x6904 (b_S_ts_n_is_n_array_n_elt$ ?x6899))) -(let ((?x6894 (b_S_ptr$ (b_S_array$ ?v2 ?v3) ?v1))) -(let (($x6901 (= (b_S_ts_n_emb$ ?x6899) ?x6894))) -(let (($x6908 (and $x6901 (and (not (b_S_ts_n_is_n_volatile$ ?x6899)) (and $x6904 $x6905))))) -(let (($x2766 (<= 0 ?v4))) -(let (($x6566 (and $x2766 (< ?v4 ?v3)))) -(let (($x6895 (b_S_typed$ ?v0 ?x6894))) -(let (($x6896 (and $x6895 $x6566))) -(or (not $x6896) $x6908)))))))))))) :pattern ( (b_S_select_o_sm$ (b_S_statusmap$ ?v0) (b_S_idx$ (b_S_ptr$ ?v2 ?v1) ?v4 ?v2)) (b_S_ptr$ (b_S_array$ ?v2 ?v3) ?v1) ) :pattern ( (b_S_select_o_tm$ (b_S_typemap$ ?v0) (b_S_idx$ (b_S_ptr$ ?v2 ?v1) ?v4 ?v2)) (b_S_ptr$ (b_S_array$ ?v2 ?v3) ?v1) ) :qid k!493)) -)) -(let (($x6908 (and $x6901 (and (not (b_S_ts_n_is_n_volatile$ ?x6899)) (and $x6904 $x6905))))) -(let (($x6920 (or (not (and $x6895 (and $x2766 (< ?0 ?1)))) $x6908))) -(let (($x6566 (and $x2766 (< ?0 ?1)))) -(let (($x6896 (and $x6895 $x6566))) -(let ((@x6608 (monotonicity @x2814 (rewrite (= (< ?0 ?1) $x6603)) (= $x6566 (and $x2815 $x6603))))) -(let ((@x6933 (trans (monotonicity @x6608 (= $x6896 (and $x6895 (and $x2815 $x6603)))) (rewrite (= (and $x6895 (and $x2815 $x6603)) $x6929)) (= $x6896 $x6929)))) -(let ((@x6942 (monotonicity (monotonicity @x6933 (= (not $x6896) $x6934)) (rewrite (= $x6908 $x6937)) (= $x6920 $x6940)))) -(let ((@x6947 (trans (quant-intro (rewrite (= (=> $x6896 $x6908) $x6920)) (= $x6917 $x6923)) (quant-intro @x6942 (= $x6923 $x6943)) (= $x6917 $x6943)))) -(let ((@x14355 (mp~ (mp (asserted $x6917) @x6947 $x6943) (nnf-pos (refl (~ $x6940 $x6940)) (~ $x6943 $x6943)) $x6943))) -(let ((@x17967 (mp @x14355 @x17966 $x17964))) -(let (($x23539 (not $x23538))) -(let (($x23587 (not $x17964))) -(let (($x23588 (or $x23587 $x23539 $x11259 $x23557))) -(let (($x23558 (or $x23539 $x22599 $x22601 $x23557))) -(let (($x23589 (or $x23587 $x23558))) -(let ((@x23586 (trans (monotonicity @x22711 @x22706 (= $x23558 (or $x23539 false $x11259 $x23557))) (rewrite (= (or $x23539 false $x11259 $x23557) (or $x23539 $x11259 $x23557))) (= $x23558 (or $x23539 $x11259 $x23557))))) -(let ((@x23610 (trans (monotonicity @x23586 (= $x23589 (or $x23587 (or $x23539 $x11259 $x23557)))) (rewrite (= (or $x23587 (or $x23539 $x11259 $x23557)) $x23588)) (= $x23589 $x23588)))) -(let ((@x23661 (unit-resolution (mp ((_ quant-inst v_b_S_s$ v_b_P_H_arr$ b_T_T_u1$ v_b_P_H_len$ 0) $x23589) @x23610 $x23588) @x17967 @x12041 @x23608 (hypothesis $x23556) false))) -(let ((@x23442 (hypothesis $x22506))) -(let ((@x23451 (symm @x23444 (= ?x22553 ?x10137)))) -(let ((@x23449 (monotonicity (symm @x23445 (= v_b_P_H_arr$ ?x10079)) (= ?x10078 ?x22553)))) -(let (($x21186 (= ?x21014 ?x10079))) -(let (($x21191 (or $x21152 $x21186))) -(let ((@x21192 ((_ quant-inst (b_S_array$ b_T_T_u1$ v_b_P_H_len$) (b_S_ref$ ?x10078)) $x21191))) -(let ((@x23674 (trans (monotonicity @x23670 (= ?x23622 ?x21014)) (unit-resolution @x21192 @x19840 $x21186) (= ?x23622 ?x10079)))) -(let ((@x23682 (trans @x23680 (unit-resolution @x22000 @x15336 @x12044 $x21990) (= ?x22595 ?x21983)))) -(let ((@x23781 (trans (monotonicity @x23682 (= ?x23546 ?x23613)) (hypothesis $x23639) (= ?x23546 ?x23636)))) -(let ((@x23782 (trans @x23781 (monotonicity (trans @x23674 @x23445 (= ?x23622 v_b_P_H_arr$)) (= ?x23636 ?x10078)) (= ?x23546 ?x10078)))) -(let ((@x23785 (trans (trans (trans @x23782 @x23449 (= ?x23546 ?x22553)) @x23451 (= ?x23546 ?x10137)) @x23442 (= ?x23546 ?x22505)))) -(let ((@x23787 (symm (monotonicity @x23785 (= ?x23547 (b_S_select_o_tm$ ?x10272 ?x22505))) (= (b_S_select_o_tm$ ?x10272 ?x22505) ?x23547)))) -(let ((@x23788 (monotonicity @x23787 (= (b_S_ts_n_emb$ (b_S_select_o_tm$ ?x10272 ?x22505)) ?x23548)))) -(let ((@x23704 (monotonicity (monotonicity @x23442 (= ?x22478 (b_S_select_o_tm$ ?x10272 ?x22505))) (= ?x22805 (b_S_ts_n_emb$ (b_S_select_o_tm$ ?x10272 ?x22505)))))) -(let ((@x23790 (trans (trans @x23704 @x23788 (= ?x22805 ?x23548)) (unit-resolution (def-axiom (or $x23556 $x23549)) (lemma @x23661 $x23557) $x23549) (= ?x22805 ?x22595)))) -(let ((@x23794 (trans (monotonicity (trans @x23790 @x23680 (= ?x22805 ?x10080)) (= ?x22433 ?x10082)) @x12043 $x22451))) -(let ((@x23797 (lemma (unit-resolution (hypothesis (not $x22451)) @x23794 false) (or $x23642 $x22451 (not $x22506))))) -(let ((@x24045 (unit-resolution (unit-resolution @x23797 @x24001 (or $x22451 (not $x22506))) @x23969 $x22451))) -(let ((?x22806 (b_S_typ$ ?x22805))) -(let ((?x22809 (b_S_kind_n_of$ ?x22806))) -(let (($x22810 (= ?x22809 b_S_kind_n_primitive$))) -(let (($x22807 (not $x22810))) -(let ((?x22655 (b_S_select_o_tm$ ?x10272 ?x22505))) -(let ((?x22658 (b_S_ts_n_emb$ ?x22655))) -(let ((?x22663 (b_S_typ$ ?x22658))) -(let ((?x22664 (b_S_kind_n_of$ ?x22663))) -(let (($x22665 (= ?x22664 b_S_kind_n_primitive$))) -(let ((@x22763 (monotonicity (monotonicity (symm @x23704 (= ?x22658 ?x22805)) (= ?x22663 ?x22806)) (= ?x22664 ?x22809)))) -(let (($x22767 (not (or $x22665 (not (b_S_is_n_non_n_primitive$ ?x22663)))))) -(let (($x19234 (forall ((?v0 B_S_type_n_state$) )(! 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$x22568 $x24110) $x23999)))) -(let ((@x23967 (mp ((_ quant-inst (b_S_ptr$ b_T_T_u1$ v_b_P_H_arr$) v_b_L_H_p_G_0$ b_T_T_u1$) (or $x22568 $x24110)) (trans @x23964 (rewrite (= $x23999 $x23999)) (= (or $x22568 $x24110) $x23999)) $x23999))) -(let ((@x24824 (unit-resolution (def-axiom (or $x23973 $x23925)) (unit-resolution @x23967 @x18183 $x23975) $x23925))) -(let ((?x24252 (+ ?x10079 ?x23287 (* (- 1) (b_S_ref$ ?x24114))))) -(let (($x24242 (= ?x24252 0))) -(let (($x24247 (or $x21152 $x24242))) -(let ((@x24254 (monotonicity (rewrite (= (= (b_S_ref$ ?x24114) ?x24111) $x24242)) (= (or $x21152 (= (b_S_ref$ ?x24114) ?x24111)) $x24247)))) -(let ((@x24256 (trans @x24254 (rewrite (= $x24247 $x24247)) (= (or $x21152 (= (b_S_ref$ ?x24114) ?x24111)) $x24247)))) -(let ((@x24827 (unit-resolution (mp ((_ quant-inst b_T_T_u1$ (+ ?x10079 ?x23287)) (or $x21152 (= (b_S_ref$ ?x24114) ?x24111))) @x24256 $x24247) @x19840 $x24242))) -(let ((@x24831 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x24242) (<= ?x24252 0))) @x24827 (<= ?x24252 0)))) -(let ((@x24834 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x24242) (>= ?x24252 0))) @x24827 (>= ?x24252 0)))) -(let (($x24814 (= ?x24111 ?x24715))) -(let ((?x24815 (* (- 1) ?x24715))) -(let ((?x24818 (+ ?x24111 ?x24815))) -(let (($x24819 (<= ?x24818 0))) -(let ((?x24234 (* (- 1) ?x21014))) -(let ((?x24214 (+ ?x10079 ?x24234))) -(let (($x24215 (<= ?x24214 0))) -(let ((@x24854 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not (= ?x10079 ?x21014)) $x24215)) (symm (unit-resolution @x21192 @x19840 $x21186) (= ?x10079 ?x21014)) $x24215))) -(let ((?x24751 (* (- 1) ?x23622))) -(let ((?x24752 (+ ?x21014 ?x24751))) -(let (($x24753 (<= ?x24752 0))) -(let ((@x24857 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not (= ?x21014 ?x23622)) $x24753)) (symm (monotonicity @x23670 (= ?x23622 ?x21014)) (= ?x21014 ?x23622)) $x24753))) -(let ((@x24862 (unit-resolution ((_ th-lemma arith assign-bounds -1 -1) (or $x24819 (not $x24753) (not $x24215))) @x24857 @x24854 $x24819))) -(let (($x24820 (>= ?x24818 0))) -(let (($x24216 (>= ?x24214 0))) -(let ((@x24841 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not (= ?x10079 ?x21014)) $x24216)) (symm (unit-resolution @x21192 @x19840 $x21186) (= ?x10079 ?x21014)) $x24216))) -(let (($x24754 (>= ?x24752 0))) -(let ((@x24846 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not (= ?x21014 ?x23622)) $x24754)) (symm (monotonicity @x23670 (= ?x23622 ?x21014)) (= ?x21014 ?x23622)) $x24754))) -(let ((@x24851 (unit-resolution ((_ th-lemma arith assign-bounds -1 -1) (or $x24820 (not $x24754) (not $x24216))) @x24846 @x24841 $x24820))) -(let ((@x24907 (unit-resolution ((_ th-lemma arith triangle-eq) (or $x24814 (not $x24819) (not $x24820))) @x24851 @x24862 $x24814))) -(let ((@x24911 (trans (symm @x24907 (= ?x24715 ?x24111)) ((_ th-lemma arith eq-propagate -1 -1) @x24834 @x24831 (= ?x24111 (b_S_ref$ ?x24114))) (= ?x24715 (b_S_ref$ ?x24114))))) -(let ((@x24912 (trans @x24911 (monotonicity (symm @x24824 (= ?x24114 ?x10320)) (= (b_S_ref$ ?x24114) ?x24147)) (= ?x24715 ?x24147)))) -(let ((@x24915 (trans (monotonicity @x23682 (= ?x24598 ?x24697)) (hypothesis $x24723) (= ?x24598 ?x24720)))) -(let ((@x24917 (monotonicity (trans @x24915 (monotonicity @x24912 (= ?x24720 ?x24169)) (= ?x24598 ?x24169)) (= ?x24302 ?x24320)))) -(let ((@x24920 (trans (monotonicity (symm @x24917 (= ?x24320 ?x24302)) (= ?x24323 ?x24605)) (hypothesis $x24606) (= ?x24323 ?x22595)))) -(let ((@x24924 (trans (monotonicity (trans @x24920 @x23680 (= ?x24323 ?x10080)) (= ?x24331 ?x10082)) @x12043 $x24332))) -(let ((@x24927 (lemma (unit-resolution (hypothesis $x24385) @x24924 false) (or $x24726 $x24332 $x24607)))) -(unit-resolution (unit-resolution @x24927 @x23880 (or $x24332 $x24607)) @x24156 @x24149 false)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) - diff -r 3fdb94d87e0e -r 3c5a7746ffa4 src/HOL/Tools/Nitpick/nitpick.ML --- a/src/HOL/Tools/Nitpick/nitpick.ML Fri Mar 05 15:01:59 2021 +0100 +++ b/src/HOL/Tools/Nitpick/nitpick.ML Fri Mar 05 21:26:38 2021 +0100 @@ -201,7 +201,6 @@ subst def_assm_ts nondef_assm_ts orig_t = let val time_start = Time.now () - val timer = Timer.startRealTimer () val thy = Proof.theory_of state val ctxt = Proof.context_of state val keywords = Thy_Header.get_keywords thy @@ -933,8 +932,7 @@ handle Timeout.TIMEOUT _ => (print_nt (fn () => excipit "ran out of time after checking"); if !met_potential > 0 then potentialN else unknownN) - val _ = print_v (fn () => - "Total time: " ^ string_of_time (Timer.checkRealTimer timer)) + val _ = print_v (fn () => "Total time: " ^ string_of_time (Time.now () - time_start)) val _ = spying spy (fn () => (state, i, "outcome: " ^ outcome_code)) in (outcome_code, Queue.content (Synchronized.value outcome)) end @@ -949,7 +947,7 @@ in let val unknown_outcome = (unknownN, []) - val deadline = Time.now () + timeout + val deadline = Timeout.end_time timeout val outcome as (outcome_code, _) = Timeout.apply (timeout + timeout_bonus) (pick_them_nits_in_term deadline state params mode i n step subst diff -r 3fdb94d87e0e -r 3c5a7746ffa4 src/HOL/Tools/Nitpick/nitpick_tests.ML --- a/src/HOL/Tools/Nitpick/nitpick_tests.ML Fri Mar 05 15:01:59 2021 +0100 +++ b/src/HOL/Tools/Nitpick/nitpick_tests.ML Fri Mar 05 21:26:38 2021 +0100 @@ -211,7 +211,7 @@ fun run_all_tests () = let val {debug, overlord, timeout, ...} = Nitpick_Commands.default_params \<^theory> [] - val deadline = Time.now () + timeout + val deadline = Timeout.end_time timeout val max_threads = 1 val max_solutions = 1 in diff -r 3fdb94d87e0e -r 3c5a7746ffa4 src/HOL/Tools/Nunchaku/nunchaku.ML --- a/src/HOL/Tools/Nunchaku/nunchaku.ML Fri Mar 05 15:01:59 2021 +0100 +++ b/src/HOL/Tools/Nunchaku/nunchaku.ML Fri Mar 05 21:26:38 2021 +0100 @@ -159,7 +159,7 @@ let val ctxt = Proof.context_of state; - val timer = Timer.startRealTimer () + val time_start = Time.now () val print = writeln; val print_n = if mode = Normal then writeln else K (); @@ -310,10 +310,10 @@ val _ = spying spy (fn () => (state, i, "starting " ^ str_of_mode mode ^ " mode")); val outcome as (outcome_code, _) = - Timeout.apply (Time.+ (timeout, timeout_slack)) run () + Timeout.apply (timeout + timeout_slack) run () handle Timeout.TIMEOUT _ => (print_n "Time out"; (unknownN, NONE)); - val _ = print_v (fn () => "Total time: " ^ string_of_time (Timer.checkRealTimer timer)); + val _ = print_v (fn () => "Total time: " ^ string_of_time (Time.now () - time_start)); val _ = spying spy (fn () => (state, i, "outcome: " ^ outcome_code)); in diff -r 3fdb94d87e0e -r 3c5a7746ffa4 src/HOL/Tools/SMT/smt_config.ML --- a/src/HOL/Tools/SMT/smt_config.ML Fri Mar 05 15:01:59 2021 +0100 +++ b/src/HOL/Tools/SMT/smt_config.ML Fri Mar 05 21:26:38 2021 +0100 @@ -41,6 +41,7 @@ val compress_verit_proofs: Proof.context -> bool (*tools*) + val get_timeout: Proof.context -> Time.time option val with_time_limit: Proof.context -> real Config.T -> ('a -> 'b) -> 'a -> 'b val with_timeout: Proof.context -> ('a -> 'b) -> 'a -> 'b @@ -178,7 +179,7 @@ (* options *) val oracle = Attrib.setup_config_bool \<^binding>\smt_oracle\ (K true) -val timeout = Attrib.setup_config_real \<^binding>\smt_timeout\ (K 1000000.0) +val timeout = Attrib.setup_config_real \<^binding>\smt_timeout\ (K 0.0) val reconstruction_step_timeout = Attrib.setup_config_real \<^binding>\smt_reconstruction_step_timeout\ (K 10.0) val random_seed = Attrib.setup_config_int \<^binding>\smt_random_seed\ (K 1) val read_only_certificates = Attrib.setup_config_bool \<^binding>\smt_read_only_certificates\ (K false) @@ -218,6 +219,10 @@ (* tools *) +fun get_timeout ctxt = + let val t = seconds (Config.get ctxt timeout); + in if Timeout.ignored t then NONE else SOME (Timeout.scale_time t) end; + fun with_time_limit ctxt timeout_config f x = Timeout.apply (seconds (Config.get ctxt timeout_config)) f x handle Timeout.TIMEOUT _ => raise SMT_Failure.SMT SMT_Failure.Time_Out diff -r 3fdb94d87e0e -r 3c5a7746ffa4 src/HOL/Tools/SMT/smt_systems.ML --- a/src/HOL/Tools/SMT/smt_systems.ML Fri Mar 05 15:01:59 2021 +0100 +++ b/src/HOL/Tools/SMT/smt_systems.ML Fri Mar 05 21:26:38 2021 +0100 @@ -57,10 +57,12 @@ (* CVC3 *) local - fun cvc3_options ctxt = [ - "-seed", string_of_int (Config.get ctxt SMT_Config.random_seed), - "-lang", "smt2", - "-timeout", string_of_int (Real.ceil (Config.get ctxt SMT_Config.timeout))] + fun cvc3_options ctxt = + ["-seed", string_of_int (Config.get ctxt SMT_Config.random_seed), + "-lang", "smt2"] @ + (case SMT_Config.get_timeout ctxt of + NONE => [] + | SOME t => ["-timeout", string_of_int (Real.ceil (Time.toReal t))]) in val cvc3: SMT_Solver.solver_config = { @@ -83,11 +85,13 @@ val cvc4_extensions = Attrib.setup_config_bool \<^binding>\cvc4_extensions\ (K false) local - fun cvc4_options ctxt = [ - "--no-stats", - "--random-seed=" ^ string_of_int (Config.get ctxt SMT_Config.random_seed), - "--lang=smt2", - "--tlimit", string_of_int (Real.ceil (1000.0 * Config.get ctxt SMT_Config.timeout))] + fun cvc4_options ctxt = + ["--no-stats", + "--random-seed=" ^ string_of_int (Config.get ctxt SMT_Config.random_seed), + "--lang=smt2"] @ + (case SMT_Config.get_timeout ctxt of + NONE => [] + | SOME t => ["--tlimit", string_of_int (Time.toMilliseconds t)]) fun select_class ctxt = if Config.get ctxt cvc4_extensions then @@ -125,6 +129,15 @@ SMTLIB_Interface.hosmtlibC else SMTLIB_Interface.smtlibC + + fun veriT_options ctxt = + ["--proof-with-sharing", + "--proof-define-skolems", + "--proof-prune", + "--proof-merge", + "--disable-print-success", + "--disable-banner"] @ + Verit_Proof.veriT_current_strategy (Context.Proof ctxt) in val veriT: SMT_Solver.solver_config = { @@ -132,14 +145,7 @@ class = select_class, avail = is_some o check_tool "ISABELLE_VERIT", command = the o check_tool "ISABELLE_VERIT", - options = (fn ctxt => [ - "--proof-with-sharing", - "--proof-define-skolems", - "--proof-prune", - "--proof-merge", - "--disable-print-success", - "--disable-banner"] @ - Verit_Proof.veriT_current_strategy (Context.Proof ctxt)), + options = veriT_options, smt_options = [(":produce-proofs", "true")], default_max_relevant = 200 (* FUDGE *), outcome = on_first_non_unsupported_line (outcome_of "unsat" "sat" "unknown" "timeout"), @@ -156,9 +162,11 @@ local fun z3_options ctxt = ["smt.random_seed=" ^ string_of_int (Config.get ctxt SMT_Config.random_seed), - "smt.refine_inj_axioms=false", - "-T:" ^ string_of_int (Real.ceil (Config.get ctxt SMT_Config.timeout)), - "-smt2"] + "smt.refine_inj_axioms=false"] @ + (case SMT_Config.get_timeout ctxt of + NONE => [] + | SOME t => ["-T:" ^ string_of_int (Real.ceil (Time.toReal t))]) @ + ["-smt2"] fun select_class ctxt = if Config.get ctxt z3_extensions then Z3_Interface.smtlib_z3C else SMTLIB_Interface.smtlibC diff -r 3fdb94d87e0e -r 3c5a7746ffa4 src/HOL/Tools/Sledgehammer/sledgehammer.ML --- a/src/HOL/Tools/Sledgehammer/sledgehammer.ML Fri Mar 05 15:01:59 2021 +0100 +++ b/src/HOL/Tools/Sledgehammer/sledgehammer.ML Fri Mar 05 21:26:38 2021 +0100 @@ -123,7 +123,7 @@ let val ctxt = Proof.context_of state - val hard_timeout = time_mult 5.0 timeout + val hard_timeout = Time.scale 5.0 timeout val _ = spying spy (fn () => (state, subgoal, name, "Launched")); val max_facts = max_facts |> the_default (default_max_facts_of_prover ctxt name) val num_facts = length facts |> not only ? Integer.min max_facts diff -r 3fdb94d87e0e -r 3c5a7746ffa4 src/HOL/Tools/Sledgehammer/sledgehammer_isar_compress.ML --- a/src/HOL/Tools/Sledgehammer/sledgehammer_isar_compress.ML Fri Mar 05 15:01:59 2021 +0100 +++ b/src/HOL/Tools/Sledgehammer/sledgehammer_isar_compress.ML Fri Mar 05 21:26:38 2021 +0100 @@ -129,7 +129,7 @@ val merge_slack_factor = 1.5 fun adjust_merge_timeout max time = - let val timeout = time_mult merge_slack_factor (merge_slack_time + time) in + let val timeout = Time.scale merge_slack_factor (merge_slack_time + time) in if max < timeout then max else timeout end diff -r 3fdb94d87e0e -r 3c5a7746ffa4 src/HOL/Tools/Sledgehammer/sledgehammer_isar_preplay.ML --- a/src/HOL/Tools/Sledgehammer/sledgehammer_isar_preplay.ML Fri Mar 05 15:01:59 2021 +0100 +++ b/src/HOL/Tools/Sledgehammer/sledgehammer_isar_preplay.ML Fri Mar 05 21:26:38 2021 +0100 @@ -57,7 +57,7 @@ else let val y = f timeout x in (case get_time y of - SOME time => next_timeout := time_min (time, !next_timeout) + SOME time => next_timeout := Time.min (time, !next_timeout) | _ => ()); SOME y end diff -r 3fdb94d87e0e -r 3c5a7746ffa4 src/HOL/Tools/Sledgehammer/sledgehammer_mash.ML --- a/src/HOL/Tools/Sledgehammer/sledgehammer_mash.ML Fri Mar 05 15:01:59 2021 +0100 +++ b/src/HOL/Tools/Sledgehammer/sledgehammer_mash.ML Fri Mar 05 21:26:38 2021 +0100 @@ -1264,9 +1264,9 @@ fun launch_thread timeout task = let - val hard_timeout = time_mult learn_timeout_slack timeout + val hard_timeout = Time.scale learn_timeout_slack timeout val birth_time = Time.now () - val death_time = birth_time + hard_timeout + val death_time = birth_time + Timeout.scale_time hard_timeout val desc = ("Machine learner for Sledgehammer", "") in Async_Manager_Legacy.thread MaShN birth_time death_time desc task @@ -1546,7 +1546,7 @@ fun maybe_launch_thread exact min_num_facts_to_learn = if not (Async_Manager_Legacy.has_running_threads MaShN) andalso Time.toSeconds timeout >= min_secs_for_learning then - let val timeout = time_mult learn_timeout_slack timeout in + let val timeout = Time.scale learn_timeout_slack timeout in (if verbose then writeln ("Started MaShing through " ^ (if exact then "" else "up to ") ^ string_of_int min_num_facts_to_learn ^ diff -r 3fdb94d87e0e -r 3c5a7746ffa4 src/HOL/Tools/Sledgehammer/sledgehammer_util.ML --- a/src/HOL/Tools/Sledgehammer/sledgehammer_util.ML Fri Mar 05 15:01:59 2021 +0100 +++ b/src/HOL/Tools/Sledgehammer/sledgehammer_util.ML Fri Mar 05 21:26:38 2021 +0100 @@ -13,8 +13,6 @@ val serial_commas : string -> string list -> string list val simplify_spaces : string -> string val with_cleanup : ('a -> unit) -> ('a -> 'b) -> 'a -> 'b - val time_mult : real -> Time.time -> Time.time - val time_min : Time.time * Time.time -> Time.time val parse_bool_option : bool -> string -> string -> bool option val parse_time : string -> string -> Time.time val subgoal_count : Proof.state -> int @@ -49,9 +47,6 @@ |> tap (fn _ => clean_up x) |> Exn.release -fun time_mult k t = Time.fromMilliseconds (Real.ceil (k * Real.fromInt (Time.toMilliseconds t))) -fun time_min (x, y) = if x < y then x else y - fun parse_bool_option option name s = (case s of "smart" => if option then NONE else raise Option.Option diff -r 3fdb94d87e0e -r 3c5a7746ffa4 src/HOL/Tools/try0.ML --- a/src/HOL/Tools/try0.ML Fri Mar 05 15:01:59 2021 +0100 +++ b/src/HOL/Tools/try0.ML Fri Mar 05 21:26:38 2021 +0100 @@ -34,9 +34,9 @@ end; fun apply_generic timeout_opt name command pre post apply st = - let val timer = Timer.startRealTimer () in + let val time_start = Time.now () in if try (can_apply timeout_opt pre post apply) st = SOME true then - SOME (name, command, Time.toMilliseconds (Timer.checkRealTimer timer)) + SOME (name, command, Time.toMilliseconds (Time.now () - time_start)) else NONE end; diff -r 3fdb94d87e0e -r 3c5a7746ffa4 src/Pure/Concurrent/timeout.ML --- a/src/Pure/Concurrent/timeout.ML Fri Mar 05 15:01:59 2021 +0100 +++ b/src/Pure/Concurrent/timeout.ML Fri Mar 05 21:26:38 2021 +0100 @@ -1,12 +1,18 @@ (* Title: Pure/Concurrent/timeout.ML Author: Makarius -Execution with (relative) timeout. +Execution with relative timeout: + - timeout specification < 1ms means no timeout + - actual timeout is subject to system option "timeout_scale" *) signature TIMEOUT = sig exception TIMEOUT of Time.time + val ignored: Time.time -> bool + val scale: unit -> real + val scale_time: Time.time -> Time.time + val end_time: Time.time -> Time.time val apply: Time.time -> ('a -> 'b) -> 'a -> 'b val print: Time.time -> string end; @@ -16,26 +22,35 @@ exception TIMEOUT of Time.time; +fun ignored timeout = timeout < Time.fromMilliseconds 1; + +fun scale () = Options.default_real "timeout_scale"; +fun scale_time t = Time.scale (scale ()) t; + +fun end_time timeout = Time.now () + scale_time timeout; + fun apply timeout f x = - Thread_Attributes.with_attributes Thread_Attributes.no_interrupts (fn orig_atts => - let - val self = Thread.self (); - val start = Time.now (); + if ignored timeout then f x + else + Thread_Attributes.with_attributes Thread_Attributes.no_interrupts (fn orig_atts => + let + val self = Thread.self (); + val start = Time.now (); - val request = - Event_Timer.request {physical = false} (start + timeout) - (fn () => Isabelle_Thread.interrupt_unsynchronized self); - val result = - Exn.capture (fn () => Thread_Attributes.with_attributes orig_atts (fn _ => f x)) (); + val request = + Event_Timer.request {physical = false} (start + scale_time timeout) + (fn () => Isabelle_Thread.interrupt_unsynchronized self); + val result = + Exn.capture (fn () => Thread_Attributes.with_attributes orig_atts (fn _ => f x)) (); - val stop = Time.now (); - val was_timeout = not (Event_Timer.cancel request); - val test = Exn.capture Thread_Attributes.expose_interrupt (); - in - if was_timeout andalso (Exn.is_interrupt_exn result orelse Exn.is_interrupt_exn test) - then raise TIMEOUT (stop - start) - else (Exn.release test; Exn.release result) - end); + val stop = Time.now (); + val was_timeout = not (Event_Timer.cancel request); + val test = Exn.capture Thread_Attributes.expose_interrupt (); + in + if was_timeout andalso (Exn.is_interrupt_exn result orelse Exn.is_interrupt_exn test) + then raise TIMEOUT (stop - start) + else (Exn.release test; Exn.release result) + end); fun print t = "Timeout after " ^ Value.print_time t ^ "s"; diff -r 3fdb94d87e0e -r 3c5a7746ffa4 src/Pure/General/time.ML --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/src/Pure/General/time.ML Fri Mar 05 21:26:38 2021 +0100 @@ -0,0 +1,25 @@ +(* Title: Pure/General/time.scala + Author: Makarius + +Time based on nanoseconds (idealized). +*) + +signature TIME = +sig + include TIME + val min: time * time -> time + val max: time * time -> time + val scale: real -> time -> time +end; + +structure Time: TIME = +struct + +open Time; + +fun min (t1, t2) = if t1 < t2 then t1 else t2; +fun max (t1, t2) = if t1 > t2 then t1 else t2; + +fun scale s t = Time.fromNanoseconds (Real.ceil (s * Real.fromInt (Time.toNanoseconds t))); + +end; diff -r 3fdb94d87e0e -r 3c5a7746ffa4 src/Pure/General/time.scala --- a/src/Pure/General/time.scala Fri Mar 05 15:01:59 2021 +0100 +++ b/src/Pure/General/time.scala Fri Mar 05 21:26:38 2021 +0100 @@ -21,7 +21,6 @@ def now(): Time = ms(System.currentTimeMillis()) val zero: Time = ms(0) - val start: Time = now() def print_seconds(s: Double): String = String.format(Locale.ROOT, "%.3f", s.asInstanceOf[AnyRef]) diff -r 3fdb94d87e0e -r 3c5a7746ffa4 src/Pure/ML/ml_init.ML --- a/src/Pure/ML/ml_init.ML Fri Mar 05 15:01:59 2021 +0100 +++ b/src/Pure/ML/ml_init.ML Fri Mar 05 21:26:38 2021 +0100 @@ -33,19 +33,3 @@ if n = 1 then String.str (String.sub (s, i)) else String.substring (s, i, n); end; - -(* FIXME workaround for 100% CPU usage in OS.Process.sleep *) -structure OS = -struct - open OS; - structure Process = - struct - open Process; - fun sleep t = - let - open Thread; - val lock = Mutex.mutex (); - val cond = ConditionVar.conditionVar (); - in ConditionVar.waitUntil (cond, lock, Time.now () + t) end; - end; -end; diff -r 3fdb94d87e0e -r 3c5a7746ffa4 src/Pure/ML/ml_statistics.ML --- a/src/Pure/ML/ml_statistics.ML Fri Mar 05 15:01:59 2021 +0100 +++ b/src/Pure/ML/ml_statistics.ML Fri Mar 05 21:26:38 2021 +0100 @@ -141,22 +141,6 @@ (* monitor process *) -(* FIXME workaround for 100% CPU usage in OS.Process.sleep *) -structure OS = -struct - open OS; - structure Process = - struct - open Process; - fun sleep t = - let - open Thread; - val lock = Mutex.mutex (); - val cond = ConditionVar.conditionVar (); - in ConditionVar.waitUntil (cond, lock, Time.now () + t) end; - end; -end; - fun monitor pid delay = let fun loop () = diff -r 3fdb94d87e0e -r 3c5a7746ffa4 src/Pure/ROOT.ML --- a/src/Pure/ROOT.ML Fri Mar 05 15:01:59 2021 +0100 +++ b/src/Pure/ROOT.ML Fri Mar 05 21:26:38 2021 +0100 @@ -85,6 +85,7 @@ ML_file "General/binding.ML"; ML_file "General/socket_io.ML"; ML_file "General/seq.ML"; +ML_file "General/time.ML"; ML_file "General/timing.ML"; ML_file "General/sha1.ML";