src/HOL/SMT_Examples/Boogie_Dijkstra.certs2

--- a/src/HOL/SMT_Examples/Boogie_Dijkstra.certs2	Tue Jun 03 16:02:42 2014 +0200
+++ b/src/HOL/SMT_Examples/Boogie_Dijkstra.certs2	Tue Jun 03 16:22:59 2014 +0200
@@ -1,3139 +1,3045 @@
-4130cc2c7db4aedd246ade86526a1512dc2d3ec1 3138 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 ((?x2200 (* (- 1) (v_b_SP_G_2$ ?v0!19))))
-(let ((?x2198 (v_b_SP_G_2$ ?v1!18)))
-(let ((?x2191 (b_G$ (pair$ ?v1!18 ?v0!19))))
-(let (($x2202 (>= (+ ?x2191 ?x2198 ?x2200) 0)))
-(let (($x2194 (<= (+ b_Infinity$ (* (- 1) ?x2191)) 0)))
-(let (($x2189 (fun_app$ v_b_Visited_G_2$ ?v1!18)))
-(let (($x3065 (not $x2189)))
-(let (($x3080 (or $x3065 $x2194 $x2202)))
-(let (($x3085 (not $x3080)))
-(let (($x3977 (forall ((?v1 B_Vertex$) )(!(let ((?x2217 (v_b_SP_G_2$ ?v0!20)))
-(let ((?x2218 (* (- 1) ?x2217)))
-(let ((?x220 (v_b_SP_G_2$ ?v1)))
-(let (($x2528 (= (+ ?x220 ?x2218 (b_G$ (pair$ ?v1 ?v0!20))) 0)))
-(let (($x238 (fun_app$ v_b_Visited_G_2$ ?v1)))
-(let (($x247 (not $x238)))
-(or (>= (+ ?x220 ?x2218) 0) $x247 (not $x2528)))))))) :pattern ( (v_b_SP_G_2$ ?v1) ) :pattern ( (fun_app$ v_b_Visited_G_2$ ?v1) ) :pattern ( (pair$ ?v1 ?v0!20) )))
-))
-(let (($x3982 (not $x3977)))
-(let (($x2220 (<= (+ b_Infinity$ (* (- 1) (v_b_SP_G_2$ ?v0!20))) 0)))
-(let (($x2215 (= ?v0!20 b_Source$)))
-(let (($x3968 (forall ((?v0 B_Vertex$) (?v1 B_Vertex$) )(!(let ((?x220 (v_b_SP_G_2$ ?v1)))
-(let ((?x102 (b_G$ (pair$ ?v1 ?v0))))
-(let (($x1621 (>= (+ ?x102 ?x220 (* (- 1) (v_b_SP_G_2$ ?v0))) 0)))
-(let (($x1303 (<= (+ b_Infinity$ (* (- 1) ?x102)) 0)))
-(let (($x238 (fun_app$ v_b_Visited_G_2$ ?v1)))
-(let (($x247 (not $x238)))
-(or $x247 $x1303 $x1621))))))) :pattern ( (pair$ ?v1 ?v0) )))
-))
-(let (($x3973 (not $x3968)))
-(let (($x3985 (or $x3973 $x2215 $x2220 $x3982)))
-(let (($x3988 (not $x3985)))
-(let (($x3991 (or $x3085 $x3988)))
-(let (($x3994 (not $x3991)))
-(let (($x3960 (forall ((?v0 B_Vertex$) (?v1 B_Vertex$) )(!(let (($x1601 (>= (+ (v_b_SP_G_2$ ?v1) (* (- 1) (v_b_SP_G_2$ ?v0))) 0)))
-(let (($x238 (fun_app$ v_b_Visited_G_2$ ?v1)))
-(or $x238 (not (fun_app$ v_b_Visited_G_2$ ?v0)) $x1601))) :pattern ( (v_b_SP_G_2$ ?v1) (v_b_SP_G_2$ ?v0) )))
-))
-(let (($x3997 (or (not $x3960) $x3994)))
-(let (($x4000 (not $x3997)))
-(let (($x2175 (>= (+ (v_b_SP_G_2$ ?v1!16) (* (- 1) (v_b_SP_G_2$ ?v0!17))) 0)))
-(let (($x2168 (fun_app$ v_b_Visited_G_2$ ?v0!17)))
-(let (($x3019 (not $x2168)))
-(let (($x2166 (fun_app$ v_b_Visited_G_2$ ?v1!16)))
-(let (($x3034 (or $x2166 $x3019 $x2175)))
-(let (($x3943 (forall ((?v0 B_Vertex$) )(!(let ((?x121 (fun_app$c v_b_SP_G_1$ ?v0)))
-(let ((?x220 (v_b_SP_G_2$ ?v0)))
-(let (($x225 (= ?x220 ?x121)))
-(let (($x238 (fun_app$ v_b_Visited_G_2$ ?v0)))
-(let (($x247 (not $x238)))
-(or $x247 $x225)))))) :pattern ( (fun_app$ v_b_Visited_G_2$ ?v0) ) :pattern ( (v_b_SP_G_2$ ?v0) ) :pattern ( (fun_app$c v_b_SP_G_1$ ?v0) )))
-))
-(let (($x3039 (not $x3034)))
-(let (($x4003 (or $x3039 $x4000)))
-(let (($x4006 (not $x4003)))
-(let (($x3951 (forall ((?v0 B_Vertex$) )(!(let ((?x220 (v_b_SP_G_2$ ?v0)))
-(>= ?x220 0)) :pattern ( (v_b_SP_G_2$ ?v0) )))
-))
-(let (($x4009 (or (not $x3951) $x4006)))
-(let (($x4012 (not $x4009)))
-(let ((?x2152 (v_b_SP_G_2$ ?v0!15)))
-(let (($x2153 (>= ?x2152 0)))
-(let (($x2154 (not $x2153)))
-(let ((?x243 (v_b_SP_G_2$ b_Source$)))
-(let (($x244 (= ?x243 0)))
-(let (($x913 (not $x244)))
-(let (($x4015 (or $x913 $x2154 $x4012)))
-(let (($x4018 (not $x4015)))
-(let (($x3948 (not $x3943)))
-(let (($x4021 (or $x3948 $x4018)))
-(let (($x4024 (not $x4021)))
-(let ((?x2136 (fun_app$c v_b_SP_G_1$ ?v0!14)))
-(let ((?x2135 (v_b_SP_G_2$ ?v0!14)))
-(let (($x2137 (= ?x2135 ?x2136)))
-(let (($x2133 (fun_app$ v_b_Visited_G_2$ ?v0!14)))
-(let (($x2134 (not $x2133)))
-(let (($x2138 (or $x2134 $x2137)))
-(let ((@x8891 (unit-resolution (def-axiom (or $x2138 $x2133)) (hypothesis (not $x2138)) $x2133)))
-(let (($x3646 (not $x2137)))
-(let ((@x8820 (unit-resolution (def-axiom (or $x2138 $x3646)) (hypothesis (not $x2138)) $x3646)))
-(let ((?x212 (fun_app$a (fun_app$b (fun_upd$ v_b_Visited_G_1$) v_b_v_G_1$) true)))
-(let (($x213 (= v_b_Visited_G_2$ ?x212)))
-(let (($x2139 (not $x2138)))
-(let (($x4027 (or $x2139 $x4024)))
-(let (($x4030 (not $x4027)))
-(let (($x3934 (forall ((?v0 B_Vertex$) )(!(>= (+ (fun_app$c v_b_SP_G_1$ ?v0) (* (- 1) (v_b_SP_G_2$ ?v0))) 0) :pattern ( (fun_app$c v_b_SP_G_1$ ?v0) ) :pattern ( (v_b_SP_G_2$ ?v0) )))
-))
-(let (($x3939 (not $x3934)))
-(let (($x4033 (or $x3939 $x4030)))
-(let (($x4036 (not $x4033)))
-(let (($x2121 (>= (+ (fun_app$c v_b_SP_G_1$ ?v0!13) (* (- 1) (v_b_SP_G_2$ ?v0!13))) 0)))
-(let (($x2122 (not $x2121)))
-(let (($x4039 (or $x2122 $x4036)))
-(let (($x4042 (not $x4039)))
-(let (($x3926 (forall ((?v0 B_Vertex$) )(!(let ((?x121 (fun_app$c v_b_SP_G_1$ ?v0)))
-(let ((?x220 (v_b_SP_G_2$ ?v0)))
-(let (($x225 (= ?x220 ?x121)))
-(let ((?x204 (fun_app$c v_b_SP_G_1$ v_b_v_G_1$)))
-(let ((?x1520 (* (- 1) ?x204)))
-(let (($x1547 (<= (+ ?x121 ?x1520 (* (- 1) (b_G$ (pair$ v_b_v_G_1$ ?v0)))) 0)))
-(let (($x1540 (<= (+ b_Infinity$ (* (- 1) (b_G$ (pair$ v_b_v_G_1$ ?v0)))) 0)))
-(let (($x2991 (or $x1540 $x1547)))
-(let (($x2992 (not $x2991)))
-(or $x2992 $x225)))))))))) :pattern ( (pair$ v_b_v_G_1$ ?v0) ) :pattern ( (fun_app$c v_b_SP_G_1$ ?v0) ) :pattern ( (v_b_SP_G_2$ ?v0) )))
-))
-(let (($x3931 (not $x3926)))
-(let (($x3918 (forall ((?v0 B_Vertex$) )(!(let ((?x220 (v_b_SP_G_2$ ?v0)))
-(let ((?x1560 (* (- 1) ?x220)))
-(let ((?x215 (b_G$ (pair$ v_b_v_G_1$ ?v0))))
-(let ((?x204 (fun_app$c v_b_SP_G_1$ v_b_v_G_1$)))
-(let (($x1559 (= (+ ?x204 ?x215 ?x1560) 0)))
-(let (($x1547 (<= (+ (fun_app$c v_b_SP_G_1$ ?v0) (* (- 1) ?x204) (* (- 1) ?x215)) 0)))
-(let (($x1540 (<= (+ b_Infinity$ (* (- 1) ?x215)) 0)))
-(or $x1540 $x1547 $x1559)))))))) :pattern ( (pair$ v_b_v_G_1$ ?v0) ) :pattern ( (fun_app$c v_b_SP_G_1$ ?v0) ) :pattern ( (v_b_SP_G_2$ ?v0) )))
-))
-(let (($x3923 (not $x3918)))
-(let (($x3196 (not $x213)))
-(let (($x3908 (forall ((?v0 B_Vertex$) )(!(let ((?x204 (fun_app$c v_b_SP_G_1$ v_b_v_G_1$)))
-(let ((?x1520 (* (- 1) ?x204)))
-(let ((?x121 (fun_app$c v_b_SP_G_1$ ?v0)))
-(let (($x125 (fun_app$ v_b_Visited_G_1$ ?v0)))
-(or $x125 (>= (+ ?x121 ?x1520) 0)))))) :pattern ( (fun_app$ v_b_Visited_G_1$ ?v0) ) :pattern ( (fun_app$c v_b_SP_G_1$ ?v0) )))
-))
-(let (($x3913 (not $x3908)))
-(let (($x1522 (<= (+ b_Infinity$ (* (- 1) (fun_app$c v_b_SP_G_1$ v_b_v_G_1$))) 0)))
-(let (($x202 (fun_app$ v_b_Visited_G_1$ v_b_v_G_1$)))
-(let (($x2087 (<= (+ b_Infinity$ (* (- 1) (fun_app$c v_b_SP_G_1$ ?v0!12))) 0)))
-(let (($x2082 (fun_app$ v_b_Visited_G_1$ ?v0!12)))
-(let (($x4045 (or $x2082 $x2087 $x202 $x1522 $x3913 $x3196 $x3923 $x3931 $x4042)))
-(let (($x4048 (not $x4045)))
-(let (($x193 (= (fun_app$c v_b_SP_G_3$ b_Source$) 0)))
-(let (($x3870 (forall ((?v0 B_Vertex$) (?v1 B_Vertex$) )(!(let ((?x177 (fun_app$c v_b_SP_G_3$ ?v1)))
-(let ((?x102 (b_G$ (pair$ ?v1 ?v0))))
-(let (($x1493 (>= (+ ?x102 ?x177 (* (- 1) (fun_app$c v_b_SP_G_3$ ?v0))) 0)))
-(let (($x1303 (<= (+ b_Infinity$ (* (- 1) ?x102)) 0)))
-(let (($x1448 (<= (+ b_Infinity$ (* (- 1) ?x177)) 0)))
-(or $x1448 $x1303 $x1493)))))) :pattern ( (pair$ ?v1 ?v0) )))
-))
-(let (($x3878 (or (not $x3870) $x193)))
-(let (($x3881 (not $x3878)))
-(let ((?x2036 (b_G$ (pair$ ?v1!10 ?v0!11))))
-(let ((?x2030 (fun_app$c v_b_SP_G_3$ ?v1!10)))
-(let (($x2497 (>= (+ ?x2030 ?x2036 (* (- 1) (fun_app$c v_b_SP_G_3$ ?v0!11))) 0)))
-(let (($x2039 (<= (+ b_Infinity$ (* (- 1) ?x2036)) 0)))
-(let (($x2033 (<= (+ b_Infinity$ (* (- 1) ?x2030)) 0)))
-(let (($x2919 (or $x2033 $x2039 $x2497)))
-(let (($x2924 (not $x2919)))
-(let (($x3884 (or $x2924 $x3881)))
-(let (($x3887 (not $x3884)))
-(let (($x3862 (forall ((?v0 B_Vertex$) )(!(let ((?x177 (fun_app$c v_b_SP_G_3$ ?v0)))
-(let ((?x2479 (+ ?x177 (* (- 1) (fun_app$c v_b_SP_G_3$ (?v1!9 ?v0))) (* (- 1) (b_G$ (pair$ (?v1!9 ?v0) ?v0))))))
-(let (($x2480 (= ?x2479 0)))
-(let (($x2464 (<= (+ ?x177 (* (- 1) (fun_app$c v_b_SP_G_3$ (?v1!9 ?v0)))) 0)))
-(let (($x2891 (not (or $x2464 (not $x2480)))))
-(let (($x1448 (<= (+ b_Infinity$ (* (- 1) ?x177)) 0)))
-(let (($x74 (= ?v0 b_Source$)))
-(or $x74 $x1448 $x2891)))))))) :pattern ( (fun_app$c v_b_SP_G_3$ ?v0) )))
-))
-(let (($x3890 (or (not $x3862) $x3887)))
-(let (($x3893 (not $x3890)))
-(let (($x3848 (forall ((?v1 B_Vertex$) )(!(let ((?x1970 (fun_app$c v_b_SP_G_3$ ?v0!8)))
-(let ((?x1971 (* (- 1) ?x1970)))
-(let ((?x177 (fun_app$c v_b_SP_G_3$ ?v1)))
-(let (($x2436 (= (+ ?x177 ?x1971 (b_G$ (pair$ ?v1 ?v0!8))) 0)))
-(or (>= (+ ?x177 ?x1971) 0) (not $x2436)))))) :pattern ( (fun_app$c v_b_SP_G_3$ ?v1) ) :pattern ( (pair$ ?v1 ?v0!8) )))
-))
-(let (($x3853 (not $x3848)))
-(let (($x1973 (<= (+ b_Infinity$ (* (- 1) (fun_app$c v_b_SP_G_3$ ?v0!8))) 0)))
-(let (($x1968 (= ?v0!8 b_Source$)))
-(let (($x3856 (or $x1968 $x1973 $x3853)))
-(let (($x3859 (not $x3856)))
-(let (($x3896 (or $x3859 $x3893)))
-(let (($x3899 (not $x3896)))
-(let (($x164 (= v_b_SP_G_3$ v_b_SP_G_1$)))
-(let (($x2982 (not $x164)))
-(let (($x3838 (forall ((?v0 B_Vertex$) )(!(let (($x1395 (<= (+ b_Infinity$ (* (- 1) (fun_app$c v_b_SP_G_1$ ?v0))) 0)))
-(let (($x125 (fun_app$ v_b_Visited_G_1$ ?v0)))
-(or $x125 $x1395))) :pattern ( (fun_app$ v_b_Visited_G_1$ ?v0) ) :pattern ( (fun_app$c v_b_SP_G_1$ ?v0) )))
-))
-(let (($x3843 (not $x3838)))
-(let (($x3902 (or $x3843 (not (= v_b_Visited_G_3$ v_b_Visited_G_1$)) (not (= v_b_v_G_2$ v_b_v_G_0$)) $x2982 (not (= v_b_oldSP_G_1$ v_b_oldSP_G_0$)) $x3899)))
-(let (($x5759 (>= (+ ?x2030 (* (- 1) (fun_app$c v_b_SP_G_1$ ?v1!10))) 0)))
-(let ((?x4698 (fun_app$c v_b_SP_G_1$ ?v1!10)))
-(let (($x6220 (= ?x2030 ?x4698)))
-(let (($x3905 (not $x3902)))
-(let ((@x5698 (hypothesis $x3905)))
-(let ((@x5699 (unit-resolution (def-axiom (or $x3902 $x164)) @x5698 $x164)))
-(let ((@x7384 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x6220) $x5759)) (monotonicity @x5699 $x6220) $x5759)))
-(let (($x3668 (not $x2497)))
-(let (($x4677 (>= (+ ?x2036 (* (- 1) (fun_app$c v_b_SP_G_1$ ?v0!11)) ?x4698) 0)))
-(let (($x4697 (fun_app$ v_b_Visited_G_1$ ?v1!10)))
-(let (($x4492 (<= (+ b_Infinity$ (* (- 1) ?x4698)) 0)))
-(let (($x5659 (not $x4492)))
-(let (($x2034 (not $x2033)))
-(let ((?x119 (fun_app$c v_b_SP_G_1$ b_Source$)))
-(let (($x120 (= ?x119 0)))
-(let (($x4051 (or $x3905 $x4048)))
-(let (($x4054 (not $x4051)))
-(let (($x3829 (forall ((?v0 B_Vertex$) )(!(let ((?x121 (fun_app$c v_b_SP_G_1$ ?v0)))
-(let ((?x2416 (+ ?x121 (* (- 1) (fun_app$c v_b_SP_G_1$ (?v1!7 ?v0))) (* (- 1) (b_G$ (pair$ (?v1!7 ?v0) ?v0))))))
-(let (($x2417 (= ?x2416 0)))
-(let (($x2401 (<= (+ ?x121 (* (- 1) (fun_app$c v_b_SP_G_1$ (?v1!7 ?v0)))) 0)))
-(let (($x2825 (not (or $x2401 (not (fun_app$ v_b_Visited_G_1$ (?v1!7 ?v0))) (not $x2417)))))
-(let (($x1395 (<= (+ b_Infinity$ (* (- 1) ?x121)) 0)))
-(let (($x74 (= ?v0 b_Source$)))
-(or $x74 $x1395 $x2825)))))))) :pattern ( (fun_app$c v_b_SP_G_1$ ?v0) )))
-))
-(let (($x3834 (not $x3829)))
-(let (($x3821 (forall ((?v0 B_Vertex$) (?v1 B_Vertex$) )(!(let ((?x121 (fun_app$c v_b_SP_G_1$ ?v1)))
-(let ((?x102 (b_G$ (pair$ ?v1 ?v0))))
-(let (($x1384 (>= (+ ?x102 ?x121 (* (- 1) (fun_app$c v_b_SP_G_1$ ?v0))) 0)))
-(let (($x1303 (<= (+ b_Infinity$ (* (- 1) ?x102)) 0)))
-(let (($x125 (fun_app$ v_b_Visited_G_1$ ?v1)))
-(let (($x126 (not $x125)))
-(or $x126 $x1303 $x1384))))))) :pattern ( (pair$ ?v1 ?v0) )))
-))
-(let (($x3826 (not $x3821)))
-(let (($x3813 (forall ((?v0 B_Vertex$) (?v1 B_Vertex$) )(!(let ((?x121 (fun_app$c v_b_SP_G_1$ ?v1)))
-(let (($x1367 (>= (+ ?x121 (* (- 1) (fun_app$c v_b_SP_G_1$ ?v0))) 0)))
-(let (($x125 (fun_app$ v_b_Visited_G_1$ ?v1)))
-(or $x125 (not (fun_app$ v_b_Visited_G_1$ ?v0)) $x1367)))) :pattern ( (fun_app$ v_b_Visited_G_1$ ?v1) (fun_app$ v_b_Visited_G_1$ ?v0) )))
-))
-(let (($x3818 (not $x3813)))
-(let (($x3804 (forall ((?v0 B_Vertex$) )(!(let ((?x121 (fun_app$c v_b_SP_G_1$ ?v0)))
-(>= ?x121 0)) :pattern ( (fun_app$c v_b_SP_G_1$ ?v0) )))
-))
-(let (($x3809 (not $x3804)))
-(let (($x3213 (not $x120)))
-(let (($x3795 (forall ((?v0 B_Vertex$) )(!(let ((?x75 (v_b_SP_G_0$ ?v0)))
-(let ((?x2378 (+ ?x75 (* (- 1) (v_b_SP_G_0$ (?v1!6 ?v0))) (* (- 1) (b_G$ (pair$ (?v1!6 ?v0) ?v0))))))
-(let (($x2379 (= ?x2378 0)))
-(let (($x2363 (<= (+ ?x75 (* (- 1) (v_b_SP_G_0$ (?v1!6 ?v0)))) 0)))
-(let (($x2752 (not (or $x2363 (not (v_b_Visited_G_0$ (?v1!6 ?v0))) (not $x2379)))))
-(let (($x1330 (<= (+ b_Infinity$ (* (- 1) ?x75)) 0)))
-(let (($x74 (= ?v0 b_Source$)))
-(or $x74 $x1330 $x2752)))))))) :pattern ( (v_b_SP_G_0$ ?v0) )))
-))
-(let (($x4057 (or (not $x3795) $x3213 $x3809 $x3818 $x3826 $x3834 $x4054)))
-(let (($x4060 (not $x4057)))
-(let (($x3781 (forall ((?v1 B_Vertex$) )(!(let ((?x1849 (v_b_SP_G_0$ ?v0!5)))
-(let ((?x1850 (* (- 1) ?x1849)))
-(let ((?x75 (v_b_SP_G_0$ ?v1)))
-(let (($x83 (v_b_Visited_G_0$ ?v1)))
-(let (($x84 (not $x83)))
-(or (>= (+ ?x75 ?x1850) 0) $x84 (not (= (+ ?x75 ?x1850 (b_G$ (pair$ ?v1 ?v0!5))) 0)))))))) :pattern ( (v_b_SP_G_0$ ?v1) ) :pattern ( (v_b_Visited_G_0$ ?v1) ) :pattern ( (pair$ ?v1 ?v0!5) )))
-))
-(let (($x1852 (<= (+ b_Infinity$ (* (- 1) (v_b_SP_G_0$ ?v0!5))) 0)))
-(let (($x1847 (= ?v0!5 b_Source$)))
-(let (($x3789 (or $x1847 $x1852 (not $x3781))))
-(let (($x3792 (not $x3789)))
-(let (($x4063 (or $x3792 $x4060)))
-(let (($x4066 (not $x4063)))
-(let (($x3772 (forall ((?v0 B_Vertex$) (?v1 B_Vertex$) )(!(let ((?x102 (b_G$ (pair$ ?v1 ?v0))))
-(let ((?x75 (v_b_SP_G_0$ ?v1)))
-(let (($x1316 (>= (+ ?x75 (* (- 1) (v_b_SP_G_0$ ?v0)) ?x102) 0)))
-(let (($x1303 (<= (+ b_Infinity$ (* (- 1) ?x102)) 0)))
-(let (($x83 (v_b_Visited_G_0$ ?v1)))
-(let (($x84 (not $x83)))
-(or $x84 $x1303 $x1316))))))) :pattern ( (pair$ ?v1 ?v0) )))
-))
-(let (($x4069 (or (not $x3772) $x4066)))
-(let (($x4072 (not $x4069)))
-(let ((?x1823 (b_G$ (pair$ ?v1!3 ?v0!4))))
-(let (($x2336 (>= (+ ?x1823 (v_b_SP_G_0$ ?v1!3) (* (- 1) (v_b_SP_G_0$ ?v0!4))) 0)))
-(let (($x1826 (<= (+ b_Infinity$ (* (- 1) ?x1823)) 0)))
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-(let ((@x496 (monotonicity (quant-intro (rewrite (= (=> $x128 $x130) $x430)) (= $x132 $x433)) (monotonicity @x450 @x490 (= (and $x137 $x147) (and $x448 $x481))) (= $x149 (and $x433 (and $x448 $x481))))))
-(let ((@x501 (trans @x496 (rewrite (= (and $x433 (and $x448 $x481)) (and $x433 $x448 $x481))) (= $x149 (and $x433 $x448 $x481)))))
-(let ((@x509 (trans (monotonicity @x501 (= $x150 (and $x123 (and $x433 $x448 $x481)))) @x507 (= $x150 (and $x123 $x433 $x448 $x481)))))
-(let ((@x517 (trans (monotonicity @x509 (= $x151 (and $x120 (and $x123 $x433 $x448 $x481)))) (rewrite (= (and $x120 (and $x123 $x433 $x448 $x481)) $x513)) (= $x151 $x513))))
-(let ((@x524 (trans (monotonicity @x517 (= $x152 $x518)) (rewrite (= $x518 $x513)) (= $x152 $x513))))
-(let ((@x528 (trans (monotonicity @x524 (= $x153 $x518)) (rewrite (= $x518 $x513)) (= $x153 $x513))))
-(let (($x414 (exists ((?v1 B_Vertex$) )(let ((?x97 (v_b_SP_G_0$ ?0)))
-(let (($x112 (= ?x97 (+ (v_b_SP_G_0$ ?v1) (b_G$ (pair$ ?v1 ?0))))))
-(let (($x83 (v_b_Visited_G_0$ ?v1)))
-(let ((?x75 (v_b_SP_G_0$ ?v1)))
-(let (($x98 (<= ?x97 ?x75)))
-(let (($x403 (not $x98)))
-(and $x403 $x83 $x112))))))))
-))
-(let (($x421 (or (not (and $x79 (not (<= b_Infinity$ (v_b_SP_G_0$ ?0))))) $x414)))
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-(let (($x83 (v_b_Visited_G_0$ ?v1)))
-(and (< (v_b_SP_G_0$ ?v1) ?x97) (and $x83 $x112))))))
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-(let (($x116 (=> (and $x79 (< (v_b_SP_G_0$ ?0) b_Infinity$)) $x115)))
-(let (($x422 (= (=> (and $x79 (not (<= b_Infinity$ (v_b_SP_G_0$ ?0)))) $x414) $x421)))
-(let (($x418 (= $x116 (=> (and $x79 (not (<= b_Infinity$ (v_b_SP_G_0$ ?0)))) $x414))))
-(let ((?x97 (v_b_SP_G_0$ ?1)))
-(let (($x112 (= ?x97 (+ (v_b_SP_G_0$ ?0) ?x102))))
-(let (($x83 (v_b_Visited_G_0$ ?0)))
-(let ((?x75 (v_b_SP_G_0$ ?0)))
-(let (($x98 (<= ?x97 ?x75)))
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-(let (($x114 (and (< ?x75 ?x97) (and $x83 $x112))))
-(let ((@x408 (monotonicity (rewrite (= (< ?x75 ?x97) $x403)) (= $x114 (and $x403 (and $x83 $x112))))))
-(let ((@x413 (trans @x408 (rewrite (= (and $x403 (and $x83 $x112)) $x409)) (= $x114 $x409))))
-(let (($x397 (not (<= b_Infinity$ ?x75))))
-(let (($x400 (and $x79 $x397)))
-(let ((@x402 (monotonicity (rewrite (= (< ?x75 b_Infinity$) $x397)) (= (and $x79 (< ?x75 b_Infinity$)) $x400))))
-(let ((@x425 (trans (monotonicity @x402 (quant-intro @x413 (= $x115 $x414)) $x418) (rewrite $x422) (= $x116 $x421))))
-(let ((@x531 (monotonicity (quant-intro @x425 (= $x117 $x426)) @x528 (= $x154 (and $x426 $x513)))))
-(let ((@x960 (monotonicity (trans @x531 (rewrite (= (and $x426 $x513) $x532)) (= $x154 $x532)) @x957 (= $x285 (=> $x532 $x955)))))
-(let ((@x969 (monotonicity (quant-intro @x425 (= $x117 $x426)) (trans @x960 (rewrite (= (=> $x532 $x955) $x962)) (= $x285 $x962)) (= (and $x117 $x285) $x967))))
-(let (($x106 (<= ?x97 (+ ?x75 ?x102))))
-(let (($x388 (or (not (and $x83 $x378)) $x106)))
-(let (($x107 (=> (and $x83 (< ?x102 b_Infinity$)) $x106)))
-(let ((@x383 (monotonicity @x380 (= (and $x83 (< ?x102 b_Infinity$)) (and $x83 $x378)))))
-(let ((@x392 (trans (monotonicity @x383 (= $x107 (=> (and $x83 $x378) $x106))) (rewrite (= (=> (and $x83 $x378) $x106) $x388)) (= $x107 $x388))))
-(let ((@x972 (monotonicity (quant-intro @x392 (= $x108 $x393)) @x969 (= $x287 (=> $x393 $x967)))))
-(let ((@x981 (monotonicity (quant-intro @x392 (= $x108 $x393)) (trans @x972 (rewrite (= (=> $x393 $x967) $x974)) (= $x287 $x974)) (= (and $x108 $x287) $x979))))
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-(let (($x96 (and $x84 $x95)))
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-(let (($x371 (or $x370 $x98)))
-(let ((@x984 (monotonicity (quant-intro (rewrite (= (=> $x96 $x98) $x371)) (= $x100 $x374)) @x981 (= $x289 (=> $x374 $x979)))))
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-(let ((@x1002 (trans (monotonicity @x993 (= $x291 (=> $x94 $x991))) (rewrite (= (=> $x94 $x991) $x998)) (= $x291 $x998))))
-(let ((@x1008 (monotonicity (monotonicity @x1002 (= (and $x94 $x291) $x1003)) (= $x293 (=> $x92 $x1003)))))
-(let ((@x1017 (monotonicity (trans @x1008 (rewrite (= (=> $x92 $x1003) $x1010)) (= $x293 $x1010)) (= (and $x92 $x293) $x1015))))
-(let (($x340 (or $x74 (= ?x75 b_Infinity$))))
-(let ((@x345 (quant-intro (rewrite (= (=> $x79 (= ?x75 b_Infinity$)) $x340)) (= $x82 $x343))))
-(let ((@x350 (monotonicity @x345 (rewrite (= (and $x85 true) $x85)) (= (and $x82 (and $x85 true)) (and $x343 $x85)))))
-(let ((@x339 (quant-intro (rewrite (= (=> $x74 (= ?x75 0)) (or $x79 (= ?x75 0)))) (= $x78 $x337))))
-(let ((@x358 (trans (monotonicity @x339 @x350 (= $x88 (and $x337 (and $x343 $x85)))) (rewrite (= (and $x337 (and $x343 $x85)) $x354)) (= $x88 $x354))))
-(let ((@x365 (trans (monotonicity @x358 (= $x89 (and true $x354))) (rewrite (= (and true $x354) $x354)) (= $x89 $x354))))
-(let ((@x369 (trans (monotonicity @x365 (= $x90 (and true $x354))) (rewrite (= (and true $x354) $x354)) (= $x90 $x354))))
-(let ((@x1026 (trans (monotonicity @x369 @x1017 (= $x295 (=> $x354 $x1015))) (rewrite (= (=> $x354 $x1015) $x1022)) (= $x295 $x1022))))
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-(let ((@x1031 (not-or-elim @x1030 $x354)))
-(let ((@x1780 (mp~ (mp (and-elim @x1031 $x85) (rewrite* (= $x85 $x85)) $x85) @x1779 $x85)))
-(let ((@x4210 (unit-resolution ((_ quant-inst ?v1!3) (or (not $x3748) $x2668)) (mp @x1780 @x3752 $x3748) (hypothesis $x1821) false)))
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-(let (($x1798 (v_b_Visited_G_0$ ?v1!1)))
-(let (($x2637 (or $x1798 $x2622 $x1807)))
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-(let ((?x1784 (v_b_SP_G_0$ ?v0!0)))
-(let (($x1785 (>= ?x1784 0)))
-(let (($x307 (not (<= b_Infinity$ 0))))
-(let ((@x310 (mp (asserted (< 0 b_Infinity$)) (rewrite (= (< 0 b_Infinity$) $x307)) $x307)))
-(let (($x3424 (= b_Infinity$ ?x1784)))
-(let ((@x3416 (symm (commutativity (= $x3424 (= ?x1784 b_Infinity$))) (= (= ?x1784 b_Infinity$) $x3424))))
-(let (($x3481 (= ?x1784 b_Infinity$)))
-(let (($x5544 (= ?v0!0 b_Source$)))
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-(let ((@x3411 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not (= ?x1784 0)) $x1785)) (hypothesis (not $x1785)) (not (= ?x1784 0)))))
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-(or $x79 (= (v_b_SP_G_0$ ?v0) 0)))) :pattern ( (v_b_SP_G_0$ ?v0) )))
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-(let ((@x3739 (quant-intro (refl (= (or $x79 (= ?x75 0)) (or $x79 (= ?x75 0)))) (= $x337 $x3735))))
-(let ((@x1769 (nnf-pos (refl (~ (or $x79 (= ?x75 0)) (or $x79 (= ?x75 0)))) (~ $x337 $x337))))
-(let ((@x1770 (mp~ (mp (and-elim @x1031 $x337) (rewrite* (= $x337 $x337)) $x337) @x1769 $x337)))
-(let (($x3446 (= (or (not $x3735) (or $x5542 (= ?x1784 0))) (or (not $x3735) $x5542 (= ?x1784 0)))))
-(let ((@x3448 (mp ((_ quant-inst ?v0!0) (or (not $x3735) (or $x5542 (= ?x1784 0)))) (rewrite $x3446) (or (not $x3735) $x5542 (= ?x1784 0)))))
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-(or $x74 (= (v_b_SP_G_0$ ?v0) b_Infinity$))) :pattern ( (v_b_SP_G_0$ ?v0) )))
-))
-(let ((@x1775 (mp~ (mp (and-elim @x1031 $x343) (rewrite* (= $x343 $x343)) $x343) (nnf-pos (refl (~ $x340 $x340)) (~ $x343 $x343)) $x343)))
-(let ((@x3440 (rewrite (= (or (not $x3741) (or $x5544 $x3481)) (or (not $x3741) $x5544 $x3481)))))
-(let ((@x3430 (mp ((_ quant-inst ?v0!0) (or (not $x3741) (or $x5544 $x3481))) @x3440 (or (not $x3741) $x5544 $x3481))))
-(let ((@x3417 (unit-resolution @x3430 (mp @x1775 (quant-intro (refl (= $x340 $x340)) (= $x343 $x3741)) $x3741) (unit-resolution @x3448 (mp @x1770 @x3739 $x3735) @x3411 $x5542) $x3481)))
-(let ((@x3399 ((_ th-lemma arith triangle-eq) (or (not $x3424) (<= (+ b_Infinity$ (* (- 1) ?x1784)) 0)))))
-(let ((@x3400 (unit-resolution @x3399 (mp @x3417 @x3416 $x3424) (<= (+ b_Infinity$ (* (- 1) ?x1784)) 0))))
-(let ((@x3331 (unit-resolution ((_ th-lemma arith farkas 1 1) (or (<= ?x1784 0) $x1785)) (hypothesis (not $x1785)) (<= ?x1784 0))))
-(let ((@x3301 ((_ th-lemma arith farkas 1 -1 1) @x3331 @x3400 (mp @x310 (rewrite* (= $x307 $x307)) $x307) false)))
-(let (($x3437 (not $x3735)))
-(let (($x3312 (or $x3437 $x92)))
-(let ((@x3294 (monotonicity (rewrite (= (= b_Source$ b_Source$) true)) (= (not (= b_Source$ b_Source$)) (not true)))))
-(let ((@x3309 (trans @x3294 (rewrite (= (not true) false)) (= (not (= b_Source$ b_Source$)) false))))
-(let ((@x3315 (monotonicity @x3309 (= (or (not (= b_Source$ b_Source$)) $x92) (or false $x92)))))
-(let ((@x3319 (trans @x3315 (rewrite (= (or false $x92) $x92)) (= (or (not (= b_Source$ b_Source$)) $x92) $x92))))
-(let ((@x3291 (monotonicity @x3319 (= (or $x3437 (or (not (= b_Source$ b_Source$)) $x92)) $x3312))))
-(let ((@x3299 (trans @x3291 (rewrite (= $x3312 $x3312)) (= (or $x3437 (or (not (= b_Source$ b_Source$)) $x92)) $x3312))))
-(let ((@x3300 (mp ((_ quant-inst b_Source$) (or $x3437 (or (not (= b_Source$ b_Source$)) $x92))) @x3299 $x3312)))
-(let ((@x4116 (lemma (unit-resolution @x3300 (mp @x1770 @x3739 $x3735) (hypothesis $x1009) false) $x92)))
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-(let ((?x220 (v_b_SP_G_2$ ?v1)))
-(let (($x2528 (= (+ ?x220 ?x2218 (b_G$ (pair$ ?v1 ?v0!20))) 0)))
-(let (($x238 (fun_app$ v_b_Visited_G_2$ ?v1)))
-(let (($x247 (not $x238)))
-(or (>= (+ ?x220 ?x2218) 0) $x247 (not $x2528)))))))))
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-(or $x247 $x1303 $x1621))))))))
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-(or $x238 (not (fun_app$ v_b_Visited_G_2$ ?v0)) $x1601))))
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-(let (($x1595 (forall ((?v0 B_Vertex$) )(let ((?x220 (v_b_SP_G_2$ ?v0)))
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-(let (($x3163 (or $x913 $x2154 $x3158)))
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-(let ((?x204 (fun_app$c v_b_SP_G_1$ v_b_v_G_1$)))
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-(let (($x1547 (<= (+ ?x121 ?x1520 (* (- 1) (b_G$ (pair$ v_b_v_G_1$ ?v0)))) 0)))
-(let (($x1540 (<= (+ b_Infinity$ (* (- 1) (b_G$ (pair$ v_b_v_G_1$ ?v0)))) 0)))
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-(let (($x1540 (<= (+ b_Infinity$ (* (- 1) ?x215)) 0)))
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-(let (($x125 (fun_app$ v_b_Visited_G_1$ ?v0)))
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-(let (($x74 (= ?v0 b_Source$)))
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-(let ((@x3915 (monotonicity (quant-intro (refl (= $x1532 $x1532)) (= $x1535 $x3908)) (= (not $x1535) $x3913))))
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-(let ((@x3845 (monotonicity (quant-intro (refl (= $x2839 $x2839)) (= $x2850 $x3838)) (= (not $x2850) $x3843))))
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-(let ((@x3836 (monotonicity (quant-intro (refl (= $x2831 $x2831)) (= $x2836 $x3829)) (= (not $x2836) $x3834))))
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-(let ((@x3802 (monotonicity (quant-intro (refl (= $x2758 $x2758)) (= $x2763 $x3795)) (= (not $x2763) (not $x3795)))))
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-(let ((@x3788 (monotonicity (quant-intro (refl (= $x2714 $x2714)) (= $x2725 $x3781)) (= (not $x2725) (not $x3781)))))
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-(let ((@x3779 (monotonicity (quant-intro (refl (= $x2705 $x2705)) (= $x2710 $x3772)) (= (not $x2710) (not $x3772)))))
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-(let ((@x3770 (monotonicity (quant-intro (refl (= $x2660 $x2660)) (= $x2665 $x3763)) (= (not $x2665) (not $x3763)))))
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-(let ((@x3758 (quant-intro (refl (= (>= ?x75 0) (>= ?x75 0))) (= $x1280 $x3754))))
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-(let ((@x4101 (monotonicity (monotonicity @x4095 (= $x3261 $x4096)) (= $x3266 (or $x1009 $x1786 $x4096)))))
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-(let (($x2436 (= (+ ?x177 ?x1971 (b_G$ (pair$ ?v1 ?v0!8))) 0)))
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-(let (($x1974 (not $x1973)))
-(let (($x1969 (not $x1968)))
-(let (($x2451 (and $x1969 $x1974 $x2445)))
-(let (($x2512 (or $x2451 $x2509)))
-(let (($x1950 (forall ((?v0 B_Vertex$) )(let (($x1395 (<= (+ b_Infinity$ (* (- 1) (fun_app$c v_b_SP_G_1$ ?v0))) 0)))
-(let (($x1398 (not $x1395)))
-(let (($x125 (fun_app$ v_b_Visited_G_1$ ?v0)))
-(let (($x126 (not $x125)))
-(let (($x1431 (and $x126 $x1398)))
-(not $x1431)))))))
-))
-(let (($x2518 (and $x1950 $x159 $x162 $x164 $x167 $x2512)))
-(let (($x2586 (or $x2518 $x2581)))
-(let (($x2428 (forall ((?v0 B_Vertex$) )(let ((?x121 (fun_app$c v_b_SP_G_1$ ?v0)))
-(let ((?x2416 (+ ?x121 (* (- 1) (fun_app$c v_b_SP_G_1$ (?v1!7 ?v0))) (* (- 1) (b_G$ (pair$ (?v1!7 ?v0) ?v0))))))
-(let (($x2417 (= ?x2416 0)))
-(let ((?x1922 (?v1!7 ?v0)))
-(let (($x1927 (fun_app$ v_b_Visited_G_1$ ?x1922)))
-(let (($x2422 (and (not (<= (+ ?x121 (* (- 1) (fun_app$c v_b_SP_G_1$ ?x1922))) 0)) $x1927 $x2417)))
-(let (($x1395 (<= (+ b_Infinity$ (* (- 1) ?x121)) 0)))
-(let (($x1398 (not $x1395)))
-(let (($x74 (= ?v0 b_Source$)))
-(let (($x79 (not $x74)))
-(let (($x1401 (and $x79 $x1398)))
-(let (($x1404 (not $x1401)))
-(or $x1404 $x2422))))))))))))))
-))
-(let (($x1390 (forall ((?v0 B_Vertex$) (?v1 B_Vertex$) )(let ((?x121 (fun_app$c v_b_SP_G_1$ ?v1)))
-(let ((?x102 (b_G$ (pair$ ?v1 ?v0))))
-(let (($x1384 (>= (+ ?x102 ?x121 (* (- 1) (fun_app$c v_b_SP_G_1$ ?v0))) 0)))
-(let (($x1303 (<= (+ b_Infinity$ (* (- 1) ?x102)) 0)))
-(let (($x1306 (not $x1303)))
-(let (($x125 (fun_app$ v_b_Visited_G_1$ ?v1)))
-(let (($x1377 (and $x125 $x1306)))
-(let (($x1380 (not $x1377)))
-(or $x1380 $x1384))))))))))
-))
-(let (($x1374 (forall ((?v0 B_Vertex$) (?v1 B_Vertex$) )(let ((?x121 (fun_app$c v_b_SP_G_1$ ?v1)))
-(let (($x1367 (>= (+ ?x121 (* (- 1) (fun_app$c v_b_SP_G_1$ ?v0))) 0)))
-(let (($x127 (fun_app$ v_b_Visited_G_1$ ?v0)))
-(let (($x125 (fun_app$ v_b_Visited_G_1$ ?v1)))
-(let (($x126 (not $x125)))
-(let (($x128 (and $x126 $x127)))
-(let (($x429 (not $x128)))
-(or $x429 $x1367)))))))))
-))
-(let (($x2390 (forall ((?v0 B_Vertex$) )(let ((?x75 (v_b_SP_G_0$ ?v0)))
-(let ((?x2378 (+ ?x75 (* (- 1) (v_b_SP_G_0$ (?v1!6 ?v0))) (* (- 1) (b_G$ (pair$ (?v1!6 ?v0) ?v0))))))
-(let (($x2379 (= ?x2378 0)))
-(let ((?x1887 (?v1!6 ?v0)))
-(let (($x1892 (v_b_Visited_G_0$ ?x1887)))
-(let (($x2384 (and (not (<= (+ ?x75 (* (- 1) (v_b_SP_G_0$ ?x1887))) 0)) $x1892 $x2379)))
-(let (($x74 (= ?v0 b_Source$)))
-(let (($x79 (not $x74)))
-(let (($x1336 (and $x79 (not (<= (+ b_Infinity$ (* (- 1) ?x75)) 0)))))
-(let (($x1339 (not $x1336)))
-(or $x1339 $x2384))))))))))))
-))
-(let (($x2595 (and $x2390 $x120 $x1363 $x1374 $x1390 $x2428 $x2586)))
-(let (($x1876 (forall ((?v1 B_Vertex$) )(let ((?x1849 (v_b_SP_G_0$ ?v0!5)))
-(let ((?x1850 (* (- 1) ?x1849)))
-(let ((?x75 (v_b_SP_G_0$ ?v1)))
-(let (($x83 (v_b_Visited_G_0$ ?v1)))
-(let (($x1863 (and (not (>= (+ ?x75 ?x1850) 0)) $x83 (= (+ ?x75 ?x1850 (b_G$ (pair$ ?v1 ?v0!5))) 0))))
-(not $x1863)))))))
-))
-(let (($x1853 (not $x1852)))
-(let (($x1848 (not $x1847)))
-(let (($x2350 (and $x1848 $x1853 $x1876)))
-(let (($x2600 (or $x2350 $x2595)))
-(let (($x1322 (forall ((?v0 B_Vertex$) (?v1 B_Vertex$) )(let ((?x102 (b_G$ (pair$ ?v1 ?v0))))
-(let ((?x75 (v_b_SP_G_0$ ?v1)))
-(let (($x1316 (>= (+ ?x75 (* (- 1) (v_b_SP_G_0$ ?v0)) ?x102) 0)))
-(let (($x1303 (<= (+ b_Infinity$ (* (- 1) ?x102)) 0)))
-(let (($x1306 (not $x1303)))
-(let (($x83 (v_b_Visited_G_0$ ?v1)))
-(let (($x1309 (and $x83 $x1306)))
-(let (($x1312 (not $x1309)))
-(or $x1312 $x1316))))))))))
-))
-(let (($x2603 (and $x1322 $x2600)))
-(let (($x1829 (not (and $x1821 (not $x1826)))))
-(let (($x2339 (or $x1829 $x2336)))
-(let (($x2342 (not $x2339)))
-(let (($x2606 (or $x2342 $x2603)))
-(let (($x1295 (forall ((?v0 B_Vertex$) (?v1 B_Vertex$) )(let (($x1288 (>= (+ (v_b_SP_G_0$ ?v1) (* (- 1) (v_b_SP_G_0$ ?v0))) 0)))
-(let (($x95 (v_b_Visited_G_0$ ?v0)))
-(let (($x83 (v_b_Visited_G_0$ ?v1)))
-(let (($x84 (not $x83)))
-(let (($x96 (and $x84 $x95)))
-(let (($x370 (not $x96)))
-(or $x370 $x1288))))))))
-))
-(let (($x2609 (and $x1295 $x2606)))
-(let (($x1802 (not (and (not $x1798) $x1800))))
-(let (($x1808 (or $x1802 $x1807)))
-(let (($x1809 (not $x1808)))
-(let (($x2612 (or $x1809 $x2609)))
-(let (($x2615 (and $x1280 $x2612)))
-(let (($x2618 (or $x1009 $x1786 $x2615)))
-(let ((@x3203 (rewrite (= (and $x2083 $x2088 $x203 $x1525 $x1535 $x213 $x3010 $x3016 $x3189) $x3201))))
-(let (($x2531 (and (not (>= (+ ?x220 (* (- 1) (v_b_SP_G_2$ ?v0!20))) 0)) $x238 $x2528)))
-(let (($x2534 (not $x2531)))
-(let ((@x3117 (monotonicity (rewrite (= $x2531 (not $x3111))) (= $x2534 (not (not $x3111))))))
-(let ((@x3124 (quant-intro (trans @x3117 (rewrite (= (not (not $x3111)) $x3111)) (= $x2534 $x3111)) (= $x2537 $x3122))))
-(let (($x1306 (not $x1303)))
-(let (($x1615 (and $x238 $x1306)))
-(let (($x1618 (not $x1615)))
-(let (($x1625 (or $x1618 $x1621)))
-(let ((@x3094 (monotonicity (rewrite (= $x1615 (not (or $x247 $x1303)))) (= $x1618 (not (not (or $x247 $x1303)))))))
-(let ((@x3098 (trans @x3094 (rewrite (= (not (not (or $x247 $x1303))) (or $x247 $x1303))) (= $x1618 (or $x247 $x1303)))))
-(let ((@x3106 (trans (monotonicity @x3098 (= $x1625 (or (or $x247 $x1303) $x1621))) (rewrite (= (or (or $x247 $x1303) $x1621) $x3102)) (= $x1625 $x3102))))
-(let ((@x3127 (monotonicity (quant-intro @x3106 (= $x1628 $x3107)) @x3124 (= $x2546 (and $x3107 $x2216 $x2221 $x3122)))))
-(let ((@x3135 (trans @x3127 (rewrite (= (and $x3107 $x2216 $x2221 $x3122) $x3131)) (= $x2546 $x3131))))
-(let ((@x3072 (monotonicity (rewrite (= (and $x2189 (not $x2194)) (not (or $x3065 $x2194)))) (= $x2197 (not (not (or $x3065 $x2194)))))))
-(let ((@x3076 (trans @x3072 (rewrite (= (not (not (or $x3065 $x2194))) (or $x3065 $x2194))) (= $x2197 (or $x3065 $x2194)))))
-(let ((@x3084 (trans (monotonicity @x3076 (= $x2203 (or (or $x3065 $x2194) $x2202))) (rewrite (= (or (or $x3065 $x2194) $x2202) $x3080)) (= $x2203 $x3080))))
-(let ((@x3138 (monotonicity (monotonicity @x3084 (= $x2204 $x3085)) @x3135 (= $x2551 $x3136))))
-(let (($x3058 (= (or (or $x238 (not (fun_app$ v_b_Visited_G_2$ ?1))) $x1601) $x3057)))
-(let (($x1606 (or $x798 $x1601)))
-(let (($x3055 (= $x1606 (or (or $x238 (not (fun_app$ v_b_Visited_G_2$ ?1))) $x1601))))
-(let (($x3043 (or $x238 (not (fun_app$ v_b_Visited_G_2$ ?1)))))
-(let ((@x3049 (monotonicity (rewrite (= $x249 (not $x3043))) (= $x798 (not (not $x3043))))))
-(let ((@x3056 (monotonicity (trans @x3049 (rewrite (= (not (not $x3043)) $x3043)) (= $x798 $x3043)) $x3055)))
-(let ((@x3064 (quant-intro (trans @x3056 (rewrite $x3058) (= $x1606 $x3057)) (= $x1609 $x3062))))
-(let ((@x3149 (trans (monotonicity @x3064 @x3138 (= $x2554 (and $x3062 $x3136))) (rewrite (= (and $x3062 $x3136) $x3145)) (= $x2554 $x3145))))
-(let ((@x3026 (monotonicity (rewrite (= (and (not $x2166) $x2168) (not (or $x2166 $x3019)))) (= $x2170 (not (not (or $x2166 $x3019)))))))
-(let ((@x3030 (trans @x3026 (rewrite (= (not (not (or $x2166 $x3019))) (or $x2166 $x3019))) (= $x2170 (or $x2166 $x3019)))))
-(let ((@x3038 (trans (monotonicity @x3030 (= $x2176 (or (or $x2166 $x3019) $x2175))) (rewrite (= (or (or $x2166 $x3019) $x2175) $x3034)) (= $x2176 $x3034))))
-(let ((@x3152 (monotonicity (monotonicity @x3038 (= $x2177 $x3039)) @x3149 (= $x2557 $x3150))))
-(let ((@x3162 (trans (monotonicity @x3152 (= $x2560 (and $x1595 $x3150))) (rewrite (= (and $x1595 $x3150) $x3158)) (= $x2560 $x3158))))
-(let ((@x3168 (monotonicity (monotonicity @x3162 (= $x2563 $x3163)) (= $x2566 (and $x786 $x3163)))))
-(let ((@x3178 (monotonicity (trans @x3168 (rewrite (= (and $x786 $x3163) $x3171)) (= $x2566 $x3171)) (= $x2569 $x3176))))
-(let ((@x3188 (trans (monotonicity @x3178 (= $x2572 (and $x1586 $x3176))) (rewrite (= (and $x1586 $x3176) $x3184)) (= $x2572 $x3184))))
-(let ((@x3015 (monotonicity (rewrite (= (and (not $x1540) (not $x1547)) $x2992)) (= (or (and (not $x1540) (not $x1547)) $x225) $x3013))))
-(let ((@x2997 (monotonicity (rewrite (= (and (not $x1540) (not $x1547)) $x2992)) (= (not (and (not $x1540) (not $x1547))) (not $x2992)))))
-(let ((@x3001 (trans @x2997 (rewrite (= (not $x2992) $x2991)) (= (not (and (not $x1540) (not $x1547))) $x2991))))
-(let ((@x3004 (monotonicity @x3001 (= (or (not (and (not $x1540) (not $x1547))) $x1559) (or $x2991 $x1559)))))
-(let ((@x3009 (trans @x3004 (rewrite (= (or $x2991 $x1559) $x3005)) (= (or (not (and (not $x1540) (not $x1547))) $x1559) $x3005))))
-(let ((@x3194 (monotonicity (quant-intro @x3009 (= $x1567 $x3010)) (quant-intro @x3015 (= $x1573 $x3016)) (monotonicity @x3188 (= $x2575 $x3189)) (= $x2581 (and $x2083 $x2088 $x203 $x1525 $x1535 $x213 $x3010 $x3016 $x3189)))))
-(let (($x1451 (not $x1448)))
-(let (($x1487 (and $x1451 $x1306)))
-(let (($x1490 (not $x1487)))
-(let (($x1496 (or $x1490 $x1493)))
-(let ((@x2933 (monotonicity (rewrite (= $x1487 (not (or $x1448 $x1303)))) (= $x1490 (not (not (or $x1448 $x1303)))))))
-(let ((@x2937 (trans @x2933 (rewrite (= (not (not (or $x1448 $x1303))) (or $x1448 $x1303))) (= $x1490 (or $x1448 $x1303)))))
-(let ((@x2945 (trans (monotonicity @x2937 (= $x1496 (or (or $x1448 $x1303) $x1493))) (rewrite (= (or (or $x1448 $x1303) $x1493) $x2941)) (= $x1496 $x2941))))
-(let ((@x2951 (monotonicity (quant-intro @x2945 (= $x1499 $x2946)) (= $x2061 (and $x2946 $x2058)))))
-(let ((@x2911 (monotonicity (rewrite (= (and $x2034 (not $x2039)) (not (or $x2033 $x2039)))) (= $x2042 (not (not (or $x2033 $x2039)))))))
-(let ((@x2915 (trans @x2911 (rewrite (= (not (not (or $x2033 $x2039))) (or $x2033 $x2039))) (= $x2042 (or $x2033 $x2039)))))
-(let ((@x2923 (trans (monotonicity @x2915 (= $x2500 (or (or $x2033 $x2039) $x2497))) (rewrite (= (or (or $x2033 $x2039) $x2497) $x2919)) (= $x2500 $x2919))))
-(let ((@x2961 (monotonicity (monotonicity @x2923 (= $x2503 $x2924)) (trans @x2951 (rewrite (= (and $x2946 $x2058) $x2954)) (= $x2061 $x2954)) (= $x2506 $x2959))))
-(let (($x2485 (and (not $x2464) $x2480)))
-(let (($x1454 (and $x79 $x1451)))
-(let (($x1457 (not $x1454)))
-(let (($x2488 (or $x1457 $x2485)))
-(let ((@x2884 (monotonicity (rewrite (= $x1454 (not (or $x74 $x1448)))) (= $x1457 (not (not (or $x74 $x1448)))))))
-(let ((@x2888 (trans @x2884 (rewrite (= (not (not (or $x74 $x1448))) (or $x74 $x1448))) (= $x1457 (or $x74 $x1448)))))
-(let ((@x2896 (monotonicity @x2888 (rewrite (= $x2485 $x2891)) (= $x2488 (or (or $x74 $x1448) $x2891)))))
-(let ((@x2901 (trans @x2896 (rewrite (= (or (or $x74 $x1448) $x2891) $x2897)) (= $x2488 $x2897))))
-(let ((@x2964 (monotonicity (quant-intro @x2901 (= $x2491 $x2902)) @x2961 (= $x2509 (and $x2902 $x2959)))))
-(let (($x2439 (and (not (>= (+ ?x177 ?x1971) 0)) $x2436)))
-(let (($x2442 (not $x2439)))
-(let ((@x2860 (monotonicity (rewrite (= $x2439 (not $x2854))) (= $x2442 (not (not $x2854))))))
-(let ((@x2867 (quant-intro (trans @x2860 (rewrite (= (not (not $x2854)) $x2854)) (= $x2442 $x2854)) (= $x2445 $x2865))))
-(let ((@x2877 (trans (monotonicity @x2867 (= $x2451 (and $x1969 $x1974 $x2865))) (rewrite (= (and $x1969 $x1974 $x2865) $x2873)) (= $x2451 $x2873))))
-(let ((@x2975 (monotonicity @x2877 (trans @x2964 (rewrite (= (and $x2902 $x2959) $x2968)) (= $x2509 $x2968)) (= $x2512 $x2973))))
-(let ((@x2845 (monotonicity (rewrite (= (and $x126 (not $x1395)) (not $x2839))) (= (not (and $x126 (not $x1395))) (not (not $x2839))))))
-(let ((@x2849 (trans @x2845 (rewrite (= (not (not $x2839)) $x2839)) (= (not (and $x126 (not $x1395))) $x2839))))
-(let ((@x2978 (monotonicity (quant-intro @x2849 (= $x1950 $x2850)) @x2975 (= $x2518 (and $x2850 $x159 $x162 $x164 $x167 $x2973)))))
-(let ((@x2990 (trans @x2978 (rewrite (= (and $x2850 $x159 $x162 $x164 $x167 $x2973) $x2986)) (= $x2518 $x2986))))
-(let ((?x1922 (?v1!7 ?0)))
-(let (($x1927 (fun_app$ v_b_Visited_G_1$ ?x1922)))
-(let (($x2422 (and (not $x2401) $x1927 $x2417)))
-(let (($x1398 (not $x1395)))
-(let (($x1401 (and $x79 $x1398)))
-(let (($x1404 (not $x1401)))
-(let (($x2425 (or $x1404 $x2422)))
-(let ((@x2817 (monotonicity (rewrite (= $x1401 (not (or $x74 $x1395)))) (= $x1404 (not (not (or $x74 $x1395)))))))
-(let ((@x2821 (trans @x2817 (rewrite (= (not (not (or $x74 $x1395))) (or $x74 $x1395))) (= $x1404 (or $x74 $x1395)))))
-(let ((@x2830 (monotonicity @x2821 (rewrite (= $x2422 $x2825)) (= $x2425 (or (or $x74 $x1395) $x2825)))))
-(let ((@x2835 (trans @x2830 (rewrite (= (or (or $x74 $x1395) $x2825) $x2831)) (= $x2425 $x2831))))
-(let ((@x2795 (monotonicity (rewrite (= (and $x125 $x1306) (not (or $x126 $x1303)))) (= (not (and $x125 $x1306)) (not (not (or $x126 $x1303)))))))
-(let ((@x2799 (trans @x2795 (rewrite (= (not (not (or $x126 $x1303))) (or $x126 $x1303))) (= (not (and $x125 $x1306)) (or $x126 $x1303)))))
-(let ((@x2802 (monotonicity @x2799 (= (or (not (and $x125 $x1306)) $x1384) (or (or $x126 $x1303) $x1384)))))
-(let ((@x2807 (trans @x2802 (rewrite (= (or (or $x126 $x1303) $x1384) $x2803)) (= (or (not (and $x125 $x1306)) $x1384) $x2803))))
-(let ((@x2775 (rewrite (= (not (not (or $x125 (not $x127)))) (or $x125 (not $x127))))))
-(let ((@x2773 (monotonicity (rewrite (= $x128 (not (or $x125 (not $x127))))) (= $x429 (not (not (or $x125 (not $x127))))))))
-(let ((@x2780 (monotonicity (trans @x2773 @x2775 (= $x429 (or $x125 (not $x127)))) (= (or $x429 $x1367) (or (or $x125 (not $x127)) $x1367)))))
-(let ((@x2785 (trans @x2780 (rewrite (= (or (or $x125 (not $x127)) $x1367) $x2781)) (= (or $x429 $x1367) $x2781))))
-(let ((?x1887 (?v1!6 ?0)))
-(let (($x1892 (v_b_Visited_G_0$ ?x1887)))
-(let (($x2384 (and (not $x2363) $x1892 $x2379)))
-(let (($x1336 (and $x79 (not $x1330))))
-(let (($x1339 (not $x1336)))
-(let (($x2387 (or $x1339 $x2384)))
-(let ((@x2744 (monotonicity (rewrite (= $x1336 (not (or $x74 $x1330)))) (= $x1339 (not (not (or $x74 $x1330)))))))
-(let ((@x2748 (trans @x2744 (rewrite (= (not (not (or $x74 $x1330))) (or $x74 $x1330))) (= $x1339 (or $x74 $x1330)))))
-(let ((@x2757 (monotonicity @x2748 (rewrite (= $x2384 $x2752)) (= $x2387 (or (or $x74 $x1330) $x2752)))))
-(let ((@x2762 (trans @x2757 (rewrite (= (or (or $x74 $x1330) $x2752) $x2758)) (= $x2387 $x2758))))
-(let ((@x3211 (monotonicity (quant-intro @x2762 (= $x2390 $x2763)) (quant-intro @x2785 (= $x1374 $x2786)) (quant-intro @x2807 (= $x1390 $x2808)) (quant-intro @x2835 (= $x2428 $x2836)) (monotonicity @x2990 (trans @x3194 @x3203 (= $x2581 $x3201)) (= $x2586 $x3206)) (= $x2595 (and $x2763 $x120 $x1363 $x2786 $x2808 $x2836 $x3206)))))
-(let ((@x3224 (trans @x3211 (rewrite (= (and $x2763 $x120 $x1363 $x2786 $x2808 $x2836 $x3206) $x3220)) (= $x2595 $x3220))))
-(let (($x1863 (and (not (>= (+ ?x75 (* (- 1) (v_b_SP_G_0$ ?v0!5))) 0)) $x83 $x1862)))
-(let (($x1873 (not $x1863)))
-(let ((@x2720 (monotonicity (rewrite (= $x1863 (not $x2714))) (= $x1873 (not (not $x2714))))))
-(let ((@x2727 (quant-intro (trans @x2720 (rewrite (= (not (not $x2714)) $x2714)) (= $x1873 $x2714)) (= $x1876 $x2725))))
-(let ((@x2737 (trans (monotonicity @x2727 (= $x2350 (and $x1848 $x1853 $x2725))) (rewrite (= (and $x1848 $x1853 $x2725) $x2733)) (= $x2350 $x2733))))
-(let ((@x2697 (monotonicity (rewrite (= (and $x83 $x1306) (not (or $x84 $x1303)))) (= (not (and $x83 $x1306)) (not (not (or $x84 $x1303)))))))
-(let ((@x2701 (trans @x2697 (rewrite (= (not (not (or $x84 $x1303))) (or $x84 $x1303))) (= (not (and $x83 $x1306)) (or $x84 $x1303)))))
-(let ((@x2704 (monotonicity @x2701 (= (or (not (and $x83 $x1306)) $x1316) (or (or $x84 $x1303) $x1316)))))
-(let ((@x2709 (trans @x2704 (rewrite (= (or (or $x84 $x1303) $x1316) $x2705)) (= (or (not (and $x83 $x1306)) $x1316) $x2705))))
-(let ((@x3230 (monotonicity (quant-intro @x2709 (= $x1322 $x2710)) (monotonicity @x2737 @x3224 (= $x2600 $x3225)) (= $x2603 (and $x2710 $x3225)))))
-(let ((@x2675 (monotonicity (rewrite (= (and $x1821 (not $x1826)) (not (or $x2668 $x1826)))) (= $x1829 (not (not (or $x2668 $x1826)))))))
-(let ((@x2679 (trans @x2675 (rewrite (= (not (not (or $x2668 $x1826))) (or $x2668 $x1826))) (= $x1829 (or $x2668 $x1826)))))
-(let ((@x2687 (trans (monotonicity @x2679 (= $x2339 (or (or $x2668 $x1826) $x2336))) (rewrite (= (or (or $x2668 $x1826) $x2336) $x2683)) (= $x2339 $x2683))))
-(let ((@x3241 (monotonicity (monotonicity @x2687 (= $x2342 $x2688)) (trans @x3230 (rewrite (= (and $x2710 $x3225) $x3234)) (= $x2603 $x3234)) (= $x2606 $x3239))))
-(let ((@x2654 (rewrite (= (not (not (or $x83 (not $x95)))) (or $x83 (not $x95))))))
-(let ((@x2652 (monotonicity (rewrite (= $x96 (not (or $x83 (not $x95))))) (= $x370 (not (not (or $x83 (not $x95))))))))
-(let ((@x2659 (monotonicity (trans @x2652 @x2654 (= $x370 (or $x83 (not $x95)))) (= (or $x370 $x1288) (or (or $x83 (not $x95)) $x1288)))))
-(let ((@x2664 (trans @x2659 (rewrite (= (or (or $x83 (not $x95)) $x1288) $x2660)) (= (or $x370 $x1288) $x2660))))
-(let ((@x3244 (monotonicity (quant-intro @x2664 (= $x1295 $x2665)) @x3241 (= $x2609 (and $x2665 $x3239)))))
-(let ((@x2629 (monotonicity (rewrite (= (and (not $x1798) $x1800) (not (or $x1798 $x2622)))) (= $x1802 (not (not (or $x1798 $x2622)))))))
-(let ((@x2633 (trans @x2629 (rewrite (= (not (not (or $x1798 $x2622))) (or $x1798 $x2622))) (= $x1802 (or $x1798 $x2622)))))
-(let ((@x2641 (trans (monotonicity @x2633 (= $x1808 (or (or $x1798 $x2622) $x1807))) (rewrite (= (or (or $x1798 $x2622) $x1807) $x2637)) (= $x1808 $x2637))))
-(let ((@x3255 (monotonicity (monotonicity @x2641 (= $x1809 $x2642)) (trans @x3244 (rewrite (= (and $x2665 $x3239) $x3248)) (= $x2609 $x3248)) (= $x2612 $x3253))))
-(let ((@x3265 (trans (monotonicity @x3255 (= $x2615 (and $x1280 $x3253))) (rewrite (= (and $x1280 $x3253) $x3261)) (= $x2615 $x3261))))
-(let (($x2244 (forall ((?v1 B_Vertex$) )(let ((?x2217 (v_b_SP_G_2$ ?v0!20)))
-(let ((?x2218 (* (- 1) ?x2217)))
-(let ((?x220 (v_b_SP_G_2$ ?v1)))
-(let (($x238 (fun_app$ v_b_Visited_G_2$ ?v1)))
-(let (($x2231 (and (not (>= (+ ?x220 ?x2218) 0)) $x238 (= (+ (b_G$ (pair$ ?v1 ?v0!20)) ?x220 ?x2218) 0))))
-(not $x2231)))))))
-))
-(let (($x2238 (not (not (and $x2216 $x2221)))))
-(let (($x2248 (and $x2238 $x2244)))
-(let (($x2253 (and $x1628 $x2248)))
-(let (($x2257 (or $x2204 $x2253)))
-(let (($x2261 (and $x1609 $x2257)))
-(let (($x2265 (or $x2177 $x2261)))
-(let (($x2269 (and $x1595 $x2265)))
-(let (($x2273 (or $x913 $x2154 $x2269)))
-(let (($x2277 (and $x786 $x2273)))
-(let (($x2281 (or $x2139 $x2277)))
-(let (($x2285 (and $x1586 $x2281)))
-(let (($x2289 (or $x2122 $x2285)))
-(let (($x2110 (and (and $x2083 $x2088) $x203 $x1525 $x1535 $x213 $x1567 $x1573)))
-(let (($x2293 (and $x2110 $x2289)))
-(let (($x2047 (or $x2042 (>= (+ ?x2036 ?x2030 (* (- 1) (fun_app$c v_b_SP_G_3$ ?v0!11))) 0))))
-(let (($x2048 (not $x2047)))
-(let (($x2065 (or $x2048 $x2061)))
-(let (($x2022 (forall ((?v0 B_Vertex$) )(let ((?x177 (fun_app$c v_b_SP_G_3$ ?v0)))
-(let ((?x1446 (* (- 1) ?x177)))
-(let ((?x2008 (fun_app$c v_b_SP_G_3$ (?v1!9 ?v0))))
-(let ((?x2013 (b_G$ (pair$ (?v1!9 ?v0) ?v0))))
-(let (($x2015 (= (+ ?x2013 ?x2008 ?x1446) 0)))
-(let (($x2016 (and (not (>= (+ ?x2008 ?x1446) 0)) $x2015)))
-(let (($x1448 (<= (+ b_Infinity$ ?x1446) 0)))
-(let (($x1451 (not $x1448)))
-(let (($x74 (= ?v0 b_Source$)))
-(let (($x79 (not $x74)))
-(let (($x1454 (and $x79 $x1451)))
-(let (($x1457 (not $x1454)))
-(or $x1457 $x2016))))))))))))))
-))
-(let (($x2069 (and $x2022 $x2065)))
-(let (($x1996 (forall ((?v1 B_Vertex$) )(let ((?x1970 (fun_app$c v_b_SP_G_3$ ?v0!8)))
-(let ((?x1971 (* (- 1) ?x1970)))
-(let ((?x177 (fun_app$c v_b_SP_G_3$ ?v1)))
-(let (($x1984 (and (not (>= (+ ?x177 ?x1971) 0)) (= (+ (b_G$ (pair$ ?v1 ?v0!8)) ?x177 ?x1971) 0))))
-(not $x1984))))))
-))
-(let (($x1990 (not (not (and $x1969 $x1974)))))
-(let (($x2000 (and $x1990 $x1996)))
-(let (($x2073 (or $x2000 $x2069)))
-(let (($x1961 (and $x1950 $x159 $x162 $x164 $x167)))
-(let (($x2077 (and $x1961 $x2073)))
-(let (($x2297 (or $x2077 $x2293)))
-(let (($x1938 (forall ((?v0 B_Vertex$) )(let ((?x121 (fun_app$c v_b_SP_G_1$ ?v0)))
-(let ((?x1393 (* (- 1) ?x121)))
-(let ((?x1922 (?v1!7 ?v0)))
-(let ((?x1923 (fun_app$c v_b_SP_G_1$ ?x1922)))
-(let ((?x1929 (b_G$ (pair$ ?x1922 ?v0))))
-(let (($x1931 (= (+ ?x1929 ?x1923 ?x1393) 0)))
-(let (($x1927 (fun_app$ v_b_Visited_G_1$ ?x1922)))
-(let (($x1932 (and (not (>= (+ ?x1923 ?x1393) 0)) $x1927 $x1931)))
-(let (($x1395 (<= (+ b_Infinity$ ?x1393) 0)))
-(let (($x1398 (not $x1395)))
-(let (($x74 (= ?v0 b_Source$)))
-(let (($x79 (not $x74)))
-(let (($x1401 (and $x79 $x1398)))
-(let (($x1404 (not $x1401)))
-(or $x1404 $x1932))))))))))))))))
-))
-(let (($x1903 (forall ((?v0 B_Vertex$) )(let ((?x1894 (b_G$ (pair$ (?v1!6 ?v0) ?v0))))
-(let ((?x75 (v_b_SP_G_0$ ?v0)))
-(let ((?x1328 (* (- 1) ?x75)))
-(let ((?x1887 (?v1!6 ?v0)))
-(let ((?x1888 (v_b_SP_G_0$ ?x1887)))
-(let (($x1896 (= (+ ?x1888 ?x1328 ?x1894) 0)))
-(let (($x1892 (v_b_Visited_G_0$ ?x1887)))
-(let (($x1897 (and (not (>= (+ ?x1888 ?x1328) 0)) $x1892 $x1896)))
-(let (($x74 (= ?v0 b_Source$)))
-(let (($x79 (not $x74)))
-(let (($x1336 (and $x79 (not (<= (+ b_Infinity$ ?x1328) 0)))))
-(let (($x1339 (not $x1336)))
-(or $x1339 $x1897))))))))))))))
-))
-(let (($x1941 (and $x1903 $x120 $x1363 $x1374 $x1390 $x1938)))
-(let (($x2301 (and $x1941 $x2297)))
-(let (($x1870 (not (not (and $x1848 $x1853)))))
-(let (($x1880 (and $x1870 $x1876)))
-(let (($x2305 (or $x1880 $x2301)))
-(let (($x2309 (and $x1322 $x2305)))
-(let (($x1834 (>= (+ (v_b_SP_G_0$ ?v1!3) (* (- 1) (v_b_SP_G_0$ ?v0!4)) ?x1823) 0)))
-(let (($x1836 (not (or $x1829 $x1834))))
-(let (($x2313 (or $x1836 $x2309)))
-(let (($x2317 (and $x1295 $x2313)))
-(let (($x2321 (or $x1809 $x2317)))
-(let (($x2325 (and $x1280 $x2321)))
-(let (($x2329 (or $x1009 $x1786 $x2325)))
-(let (($x2230 (= (+ (b_G$ (pair$ ?0 ?v0!20)) ?x220 (* (- 1) (v_b_SP_G_2$ ?v0!20))) 0)))
-(let (($x2231 (and (not (>= (+ ?x220 (* (- 1) (v_b_SP_G_2$ ?v0!20))) 0)) $x238 $x2230)))
-(let (($x2241 (not $x2231)))
-(let (($x2526 (= (+ (b_G$ (pair$ ?0 ?v0!20)) ?x220 (* (- 1) (v_b_SP_G_2$ ?v0!20))) (+ ?x220 (* (- 1) (v_b_SP_G_2$ ?v0!20)) (b_G$ (pair$ ?0 ?v0!20))))))
-(let ((@x2533 (monotonicity (monotonicity (rewrite $x2526) (= $x2230 $x2528)) (= $x2231 $x2531))))
-(let ((@x2542 (monotonicity (rewrite (= $x2238 (and $x2216 $x2221))) (quant-intro (monotonicity @x2533 (= $x2241 $x2534)) (= $x2244 $x2537)) (= $x2248 (and (and $x2216 $x2221) $x2537)))))
-(let ((@x2550 (trans (monotonicity @x2542 (= $x2253 (and $x1628 (and (and $x2216 $x2221) $x2537)))) (rewrite (= (and $x1628 (and (and $x2216 $x2221) $x2537)) $x2546)) (= $x2253 $x2546))))
-(let ((@x2559 (monotonicity (monotonicity (monotonicity @x2550 (= $x2257 $x2551)) (= $x2261 $x2554)) (= $x2265 $x2557))))
-(let ((@x2568 (monotonicity (monotonicity (monotonicity @x2559 (= $x2269 $x2560)) (= $x2273 $x2563)) (= $x2277 $x2566))))
-(let ((@x2577 (monotonicity (monotonicity (monotonicity @x2568 (= $x2281 $x2569)) (= $x2285 $x2572)) (= $x2289 $x2575))))
-(let ((@x2585 (trans (monotonicity @x2577 (= $x2293 (and $x2110 $x2575))) (rewrite (= (and $x2110 $x2575) $x2581)) (= $x2293 $x2581))))
-(let (($x2498 (= (>= (+ ?x2036 ?x2030 (* (- 1) (fun_app$c v_b_SP_G_3$ ?v0!11))) 0) $x2497)))
-(let (($x2495 (= (+ ?x2036 ?x2030 (* (- 1) (fun_app$c v_b_SP_G_3$ ?v0!11))) (+ ?x2030 ?x2036 (* (- 1) (fun_app$c v_b_SP_G_3$ ?v0!11))))))
-(let ((@x2505 (monotonicity (monotonicity (monotonicity (rewrite $x2495) $x2498) (= $x2047 $x2500)) (= $x2048 $x2503))))
-(let ((?x1446 (* (- 1) ?x177)))
-(let ((?x2008 (fun_app$c v_b_SP_G_3$ (?v1!9 ?0))))
-(let ((?x2013 (b_G$ (pair$ (?v1!9 ?0) ?0))))
-(let (($x2015 (= (+ ?x2013 ?x2008 ?x1446) 0)))
-(let (($x2016 (and (not (>= (+ ?x2008 ?x1446) 0)) $x2015)))
-(let (($x2019 (or $x1457 $x2016)))
-(let ((@x2477 (monotonicity (rewrite (= (+ ?x2013 ?x2008 ?x1446) (+ ?x1446 ?x2008 ?x2013))) (= $x2015 (= (+ ?x1446 ?x2008 ?x2013) 0)))))
-(let ((@x2484 (trans @x2477 (rewrite (= (= (+ ?x1446 ?x2008 ?x2013) 0) $x2480)) (= $x2015 $x2480))))
-(let ((@x2461 (monotonicity (rewrite (= (+ ?x2008 ?x1446) (+ ?x1446 ?x2008))) (= (>= (+ ?x2008 ?x1446) 0) (>= (+ ?x1446 ?x2008) 0)))))
-(let ((@x2468 (trans @x2461 (rewrite (= (>= (+ ?x1446 ?x2008) 0) $x2464)) (= (>= (+ ?x2008 ?x1446) 0) $x2464))))
-(let ((@x2487 (monotonicity (monotonicity @x2468 (= (not (>= (+ ?x2008 ?x1446) 0)) (not $x2464))) @x2484 (= $x2016 $x2485))))
-(let ((@x2511 (monotonicity (quant-intro (monotonicity @x2487 (= $x2019 $x2488)) (= $x2022 $x2491)) (monotonicity @x2505 (= $x2065 $x2506)) (= $x2069 $x2509))))
-(let (($x1984 (and (not (>= (+ ?x177 ?x1971) 0)) (= (+ (b_G$ (pair$ ?0 ?v0!8)) ?x177 ?x1971) 0))))
-(let (($x1993 (not $x1984)))
-(let (($x2434 (= (+ (b_G$ (pair$ ?0 ?v0!8)) ?x177 ?x1971) (+ ?x177 ?x1971 (b_G$ (pair$ ?0 ?v0!8))))))
-(let ((@x2438 (monotonicity (rewrite $x2434) (= (= (+ (b_G$ (pair$ ?0 ?v0!8)) ?x177 ?x1971) 0) $x2436))))
-(let ((@x2447 (quant-intro (monotonicity (monotonicity @x2438 (= $x1984 $x2439)) (= $x1993 $x2442)) (= $x1996 $x2445))))
-(let ((@x2450 (monotonicity (rewrite (= $x1990 (and $x1969 $x1974))) @x2447 (= $x2000 (and (and $x1969 $x1974) $x2445)))))
-(let ((@x2455 (trans @x2450 (rewrite (= (and (and $x1969 $x1974) $x2445) $x2451)) (= $x2000 $x2451))))
-(let ((@x2517 (monotonicity (monotonicity @x2455 @x2511 (= $x2073 $x2512)) (= $x2077 (and $x1961 $x2512)))))
-(let ((@x2588 (monotonicity (trans @x2517 (rewrite (= (and $x1961 $x2512) $x2518)) (= $x2077 $x2518)) @x2585 (= $x2297 $x2586))))
-(let ((?x1393 (* (- 1) ?x121)))
-(let ((?x1923 (fun_app$c v_b_SP_G_1$ ?x1922)))
-(let ((?x1929 (b_G$ (pair$ ?x1922 ?0))))
-(let (($x1931 (= (+ ?x1929 ?x1923 ?x1393) 0)))
-(let (($x1932 (and (not (>= (+ ?x1923 ?x1393) 0)) $x1927 $x1931)))
-(let (($x1935 (or $x1404 $x1932)))
-(let ((@x2414 (monotonicity (rewrite (= (+ ?x1929 ?x1923 ?x1393) (+ ?x1393 ?x1923 ?x1929))) (= $x1931 (= (+ ?x1393 ?x1923 ?x1929) 0)))))
-(let ((@x2421 (trans @x2414 (rewrite (= (= (+ ?x1393 ?x1923 ?x1929) 0) $x2417)) (= $x1931 $x2417))))
-(let ((@x2398 (monotonicity (rewrite (= (+ ?x1923 ?x1393) (+ ?x1393 ?x1923))) (= (>= (+ ?x1923 ?x1393) 0) (>= (+ ?x1393 ?x1923) 0)))))
-(let ((@x2405 (trans @x2398 (rewrite (= (>= (+ ?x1393 ?x1923) 0) $x2401)) (= (>= (+ ?x1923 ?x1393) 0) $x2401))))
-(let ((@x2424 (monotonicity (monotonicity @x2405 (= (not (>= (+ ?x1923 ?x1393) 0)) (not $x2401))) @x2421 (= $x1932 $x2422))))
-(let (($x1896 (= (+ (v_b_SP_G_0$ ?x1887) (* (- 1) ?x75) (b_G$ (pair$ ?x1887 ?0))) 0)))
-(let (($x1897 (and (not (>= (+ (v_b_SP_G_0$ ?x1887) (* (- 1) ?x75)) 0)) $x1892 $x1896)))
-(let (($x1900 (or $x1339 $x1897)))
-(let (($x2374 (= (+ (* (- 1) ?x75) (v_b_SP_G_0$ ?x1887) (b_G$ (pair$ ?x1887 ?0))) 0)))
-(let (($x2372 (= (+ (v_b_SP_G_0$ ?x1887) (* (- 1) ?x75) (b_G$ (pair$ ?x1887 ?0))) (+ (* (- 1) ?x75) (v_b_SP_G_0$ ?x1887) (b_G$ (pair$ ?x1887 ?0))))))
-(let ((@x2383 (trans (monotonicity (rewrite $x2372) (= $x1896 $x2374)) (rewrite (= $x2374 $x2379)) (= $x1896 $x2379))))
-(let (($x2369 (= (not (>= (+ (v_b_SP_G_0$ ?x1887) (* (- 1) ?x75)) 0)) (not $x2363))))
-(let (($x1890 (>= (+ (v_b_SP_G_0$ ?x1887) (* (- 1) ?x75)) 0)))
-(let (($x2356 (= (+ (v_b_SP_G_0$ ?x1887) (* (- 1) ?x75)) (+ (* (- 1) ?x75) (v_b_SP_G_0$ ?x1887)))))
-(let ((@x2360 (monotonicity (rewrite $x2356) (= $x1890 (>= (+ (* (- 1) ?x75) (v_b_SP_G_0$ ?x1887)) 0)))))
-(let ((@x2367 (trans @x2360 (rewrite (= (>= (+ (* (- 1) ?x75) (v_b_SP_G_0$ ?x1887)) 0) $x2363)) (= $x1890 $x2363))))
-(let ((@x2389 (monotonicity (monotonicity (monotonicity @x2367 $x2369) @x2383 (= $x1897 $x2384)) (= $x1900 $x2387))))
-(let ((@x2591 (monotonicity (quant-intro @x2389 (= $x1903 $x2390)) (quant-intro (monotonicity @x2424 (= $x1935 $x2425)) (= $x1938 $x2428)) (= $x1941 (and $x2390 $x120 $x1363 $x1374 $x1390 $x2428)))))
-(let ((@x2594 (monotonicity @x2591 @x2588 (= $x2301 (and (and $x2390 $x120 $x1363 $x1374 $x1390 $x2428) $x2586)))))
-(let ((@x2599 (trans @x2594 (rewrite (= (and (and $x2390 $x120 $x1363 $x1374 $x1390 $x2428) $x2586) $x2595)) (= $x2301 $x2595))))
-(let ((@x2349 (monotonicity (rewrite (= $x1870 (and $x1848 $x1853))) (= $x1880 (and (and $x1848 $x1853) $x1876)))))
-(let ((@x2354 (trans @x2349 (rewrite (= (and (and $x1848 $x1853) $x1876) $x2350)) (= $x1880 $x2350))))
-(let ((@x2605 (monotonicity (monotonicity @x2354 @x2599 (= $x2305 $x2600)) (= $x2309 $x2603))))
-(let (($x2334 (= (+ (v_b_SP_G_0$ ?v1!3) (* (- 1) (v_b_SP_G_0$ ?v0!4)) ?x1823) (+ ?x1823 (v_b_SP_G_0$ ?v1!3) (* (- 1) (v_b_SP_G_0$ ?v0!4))))))
-(let ((@x2341 (monotonicity (monotonicity (rewrite $x2334) (= $x1834 $x2336)) (= (or $x1829 $x1834) $x2339))))
-(let ((@x2608 (monotonicity (monotonicity @x2341 (= $x1836 $x2342)) @x2605 (= $x2313 $x2606))))
-(let ((@x2617 (monotonicity (monotonicity (monotonicity @x2608 (= $x2317 $x2609)) (= $x2321 $x2612)) (= $x2325 $x2615))))
-(let (($x1662 (forall ((?v0 B_Vertex$) )(let (($x1656 (exists ((?v1 B_Vertex$) )(let ((?x220 (v_b_SP_G_2$ ?v1)))
-(let ((?x102 (b_G$ (pair$ ?v1 ?v0))))
-(let (($x238 (fun_app$ v_b_Visited_G_2$ ?v1)))
-(and (not (>= (+ ?x220 (* (- 1) (v_b_SP_G_2$ ?v0))) 0)) $x238 (= (+ ?x102 ?x220 (* (- 1) (v_b_SP_G_2$ ?v0))) 0))))))
-))
-(let (($x74 (= ?v0 b_Source$)))
-(let (($x79 (not $x74)))
-(let (($x1641 (and $x79 (not (<= (+ b_Infinity$ (* (- 1) (v_b_SP_G_2$ ?v0))) 0)))))
-(or (not $x1641) $x1656))))))
-))
-(let (($x1631 (not $x1628)))
-(let (($x1665 (or $x1631 $x1662)))
-(let (($x1668 (and $x1628 $x1665)))
-(let (($x1612 (not $x1609)))
-(let (($x1671 (or $x1612 $x1668)))
-(let (($x1674 (and $x1609 $x1671)))
-(let (($x1677 (or $x1598 $x1674)))
-(let (($x1680 (and $x244 $x1595 $x1677)))
-(let (($x1683 (or $x925 $x1680)))
-(let (($x1686 (and $x786 $x1683)))
-(let (($x1689 (or $x1589 $x1686)))
-(let (($x1692 (and $x1586 $x1689)))
-(let (($x1434 (exists ((?v0 B_Vertex$) )(let (($x1395 (<= (+ b_Infinity$ (* (- 1) (fun_app$c v_b_SP_G_1$ ?v0))) 0)))
-(let (($x1398 (not $x1395)))
-(let (($x125 (fun_app$ v_b_Visited_G_1$ ?v0)))
-(let (($x126 (not $x125)))
-(and $x126 $x1398))))))
-))
-(let (($x1576 (and $x1434 $x203 $x1525 $x1535 $x213 $x1567 $x1573)))
-(let (($x1579 (not $x1576)))
-(let (($x1695 (or $x1579 $x1692)))
-(let (($x1502 (not $x1499)))
-(let (($x1505 (or $x1502 $x193)))
-(let (($x1508 (and $x1499 $x1505)))
-(let (($x1481 (forall ((?v0 B_Vertex$) )(let (($x1475 (exists ((?v1 B_Vertex$) )(let ((?x177 (fun_app$c v_b_SP_G_3$ ?v1)))
-(let ((?x102 (b_G$ (pair$ ?v1 ?v0))))
-(and (not (>= (+ ?x177 (* (- 1) (fun_app$c v_b_SP_G_3$ ?v0))) 0)) (= (+ ?x102 ?x177 (* (- 1) (fun_app$c v_b_SP_G_3$ ?v0))) 0)))))
-))
-(let (($x1448 (<= (+ b_Infinity$ (* (- 1) (fun_app$c v_b_SP_G_3$ ?v0))) 0)))
-(let (($x1451 (not $x1448)))
-(let (($x74 (= ?v0 b_Source$)))
-(let (($x79 (not $x74)))
-(let (($x1454 (and $x79 $x1451)))
-(let (($x1457 (not $x1454)))
-(or $x1457 $x1475)))))))))
-))
-(let (($x1484 (not $x1481)))
-(let (($x1511 (or $x1484 $x1508)))
-(let (($x1514 (and $x1481 $x1511)))
-(let (($x1437 (not $x1434)))
-(let (($x1440 (and $x1437 $x159 $x162 $x164 $x167)))
-(let (($x1443 (not $x1440)))
-(let (($x1517 (or $x1443 $x1514)))
-(let (($x1698 (and $x1517 $x1695)))
-(let (($x1422 (forall ((?v0 B_Vertex$) )(let (($x1416 (exists ((?v1 B_Vertex$) )(let ((?x121 (fun_app$c v_b_SP_G_1$ ?v1)))
-(let ((?x102 (b_G$ (pair$ ?v1 ?v0))))
-(let (($x125 (fun_app$ v_b_Visited_G_1$ ?v1)))
-(and (not (>= (+ ?x121 (* (- 1) (fun_app$c v_b_SP_G_1$ ?v0))) 0)) $x125 (= (+ ?x102 ?x121 (* (- 1) (fun_app$c v_b_SP_G_1$ ?v0))) 0))))))
-))
-(let (($x1395 (<= (+ b_Infinity$ (* (- 1) (fun_app$c v_b_SP_G_1$ ?v0))) 0)))
-(let (($x1398 (not $x1395)))
-(let (($x74 (= ?v0 b_Source$)))
-(let (($x79 (not $x74)))
-(let (($x1401 (and $x79 $x1398)))
-(let (($x1404 (not $x1401)))
-(or $x1404 $x1416)))))))))
-))
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-(let (($x1336 (and $x79 (not (<= (+ b_Infinity$ (* (- 1) (v_b_SP_G_0$ ?v0))) 0)))))
-(let (($x1339 (not $x1336)))
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-))
-(let (($x1425 (and $x1357 $x120 $x1363 $x1374 $x1390 $x1422)))
-(let (($x1428 (not $x1425)))
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-(let (($x1710 (and $x1322 $x1707)))
-(let (($x1298 (not $x1295)))
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-(let (($x1716 (and $x1295 $x1713)))
-(let (($x1719 (or $x1283 $x1716)))
-(let (($x1725 (not (and $x92 $x1280 $x1719))))
-(let (($x2232 (exists ((?v1 B_Vertex$) )(let ((?x2217 (v_b_SP_G_2$ ?v0!20)))
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-(let ((?x220 (v_b_SP_G_2$ ?v1)))
-(let (($x238 (fun_app$ v_b_Visited_G_2$ ?v1)))
-(and (not (>= (+ ?x220 ?x2218) 0)) $x238 (= (+ (b_G$ (pair$ ?v1 ?v0!20)) ?x220 ?x2218) 0)))))))
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-(let ((@x2250 (nnf-neg (refl (~ $x2238 $x2238)) (nnf-neg (refl (~ $x2241 $x2241)) (~ (not $x2232) $x2244)) (~ (not (or (not (and $x2216 $x2221)) $x2232)) $x2248))))
-(let ((@x2252 (trans (sk (~ (not $x1662) (not (or (not (and $x2216 $x2221)) $x2232)))) @x2250 (~ (not $x1662) $x2248))))
-(let ((@x2213 (nnf-neg (nnf-pos (refl (~ $x1625 $x1625)) (~ $x1628 $x1628)) (~ (not $x1631) $x1628))))
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-(let ((@x2186 (nnf-neg (nnf-pos (refl (~ $x1606 $x1606)) (~ $x1609 $x1609)) (~ (not $x1612) $x1609))))
-(let ((@x2268 (nnf-neg (sk (~ $x1612 $x2177)) (nnf-neg @x2186 @x2260 (~ (not $x1671) $x2261)) (~ (not $x1674) $x2265))))
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-(let ((@x2276 (nnf-neg (refl (~ $x913 $x913)) (sk (~ $x1598 $x2154)) (nnf-neg @x2163 @x2268 (~ (not $x1677) $x2269)) (~ (not $x1680) $x2273))))
-(let ((@x2148 (nnf-neg (nnf-pos (refl (~ $x783 $x783)) (~ $x786 $x786)) (~ (not $x925) $x786))))
-(let ((@x2284 (nnf-neg (sk (~ $x925 $x2139)) (nnf-neg @x2148 @x2276 (~ (not $x1683) $x2277)) (~ (not $x1686) $x2281))))
-(let ((@x2131 (nnf-neg (nnf-pos (refl (~ $x1582 $x1582)) (~ $x1586 $x1586)) (~ (not $x1589) $x1586))))
-(let ((@x2292 (nnf-neg (sk (~ $x1589 $x2122)) (nnf-neg @x2131 @x2284 (~ (not $x1689) $x2285)) (~ (not $x1692) $x2289))))
-(let (($x1553 (and (not $x1540) (not $x1547))))
-(let (($x1570 (or $x1553 $x225)))
-(let ((@x2105 (nnf-pos (refl (~ (or (not $x1553) $x1559) (or (not $x1553) $x1559))) (~ $x1567 $x1567))))
-(let ((@x2112 (monotonicity (sk (~ $x1434 (and $x2083 $x2088))) (refl (~ $x203 $x203)) (refl (~ $x1525 $x1525)) (nnf-pos (refl (~ $x1532 $x1532)) (~ $x1535 $x1535)) (refl (~ $x213 $x213)) @x2105 (nnf-pos (refl (~ $x1570 $x1570)) (~ $x1573 $x1573)) (~ $x1576 $x2110))))
-(let ((@x2296 (nnf-neg (nnf-neg @x2112 (~ (not $x1579) $x2110)) @x2292 (~ (not $x1695) $x2293))))
-(let ((@x2057 (nnf-neg (nnf-pos (refl (~ $x1496 $x1496)) (~ $x1499 $x1499)) (~ (not $x1502) $x1499))))
-(let ((@x2068 (nnf-neg (sk (~ $x1502 $x2048)) (nnf-neg @x2057 (refl (~ $x2058 $x2058)) (~ (not $x1505) $x2061)) (~ (not $x1508) $x2065))))
-(let (($x1475 (exists ((?v1 B_Vertex$) )(let ((?x177 (fun_app$c v_b_SP_G_3$ ?v1)))
-(let ((?x102 (b_G$ (pair$ ?v1 ?0))))
-(and (not (>= (+ ?x177 (* (- 1) (fun_app$c v_b_SP_G_3$ ?0))) 0)) (= (+ ?x102 ?x177 (* (- 1) (fun_app$c v_b_SP_G_3$ ?0))) 0)))))
-))
-(let (($x1478 (or $x1457 $x1475)))
-(let ((@x2024 (nnf-pos (monotonicity (refl (~ $x1457 $x1457)) (sk (~ $x1475 $x2016)) (~ $x1478 $x2019)) (~ $x1481 $x2022))))
-(let ((@x2072 (nnf-neg (nnf-neg @x2024 (~ (not $x1484) $x2022)) @x2068 (~ (not $x1511) $x2069))))
-(let (($x1985 (exists ((?v1 B_Vertex$) )(let ((?x1970 (fun_app$c v_b_SP_G_3$ ?v0!8)))
-(let ((?x1971 (* (- 1) ?x1970)))
-(let ((?x177 (fun_app$c v_b_SP_G_3$ ?v1)))
-(and (not (>= (+ ?x177 ?x1971) 0)) (= (+ (b_G$ (pair$ ?v1 ?v0!8)) ?x177 ?x1971) 0))))))
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-(let ((@x2002 (nnf-neg (refl (~ $x1990 $x1990)) (nnf-neg (refl (~ $x1993 $x1993)) (~ (not $x1985) $x1996)) (~ (not (or (not (and $x1969 $x1974)) $x1985)) $x2000))))
-(let ((@x2004 (trans (sk (~ $x1484 (not (or (not (and $x1969 $x1974)) $x1985)))) @x2002 (~ $x1484 $x2000))))
-(let ((@x1952 (nnf-neg (refl (~ (not (and $x126 $x1398)) (not (and $x126 $x1398)))) (~ $x1437 $x1950))))
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-(let ((@x2080 (nnf-neg (nnf-neg @x1963 (~ (not $x1443) $x1961)) (nnf-neg @x2004 @x2072 (~ (not $x1514) $x2073)) (~ (not $x1517) $x2077))))
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-(let ((?x102 (b_G$ (pair$ ?v1 ?0))))
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-(and (not (>= (+ ?x121 (* (- 1) (fun_app$c v_b_SP_G_1$ ?0))) 0)) $x125 (= (+ ?x102 ?x121 (* (- 1) (fun_app$c v_b_SP_G_1$ ?0))) 0))))))
-))
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-(let ((@x1940 (nnf-pos (monotonicity (refl (~ $x1404 $x1404)) (sk (~ $x1416 $x1932)) (~ $x1419 $x1935)) (~ $x1422 $x1938))))
-(let ((@x1917 (refl (~ (or (not (and $x125 $x1306)) $x1384) (or (not (and $x125 $x1306)) $x1384)))))
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-(and (not (>= (+ ?x75 (* (- 1) (v_b_SP_G_0$ ?0))) 0)) $x83 (= (+ ?x75 (* (- 1) (v_b_SP_G_0$ ?0)) ?x102) 0))))))
-))
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-(let ((?x75 (v_b_SP_G_0$ ?v1)))
-(let (($x83 (v_b_Visited_G_0$ ?v1)))
-(and (not (>= (+ ?x75 ?x1850) 0)) $x83 (= (+ ?x75 ?x1850 (b_G$ (pair$ ?v1 ?v0!5))) 0)))))))
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-(let (($x1075 (or $x949 (and $x237 (or $x937 (and $x786 (or $x925 (and $x244 $x246 $x902))))))))
-(let (($x1082 (and $x374 (or $x985 (and $x393 (or $x973 (and $x426 (or $x961 (and $x678 $x1075)))))))))
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-(let (($x238 (fun_app$ v_b_Visited_G_2$ ?v1)))
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-(let (($x74 (= ?v0 b_Source$)))
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-(let ((?x180 (fun_app$c v_b_SP_G_3$ ?v0)))
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-(let ((?x180 (fun_app$c v_b_SP_G_3$ ?v0)))
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-(let (($x125 (fun_app$ v_b_Visited_G_1$ ?v1)))
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-(let ((?x1184 (+ ?x102 ?x220)))
-(let (($x1199 (= ?x250 ?x1184)))
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-(let ((@x1640 (monotonicity (rewrite $x1636) (= $x821 (not (<= (+ b_Infinity$ (* (- 1) ?x220)) 0))))))
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-(let ((@x1308 (monotonicity (rewrite (= (<= b_Infinity$ ?x102) $x1303)) (= $x378 $x1306))))
-(let ((@x1627 (monotonicity (monotonicity (monotonicity @x1308 (= $x805 $x1615)) (= $x811 $x1618)) (rewrite (= (<= ?x250 ?x1184) $x1621)) (= (or $x811 (<= ?x250 ?x1184)) $x1625))))
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-(let ((@x1611 (quant-intro (monotonicity (rewrite (= $x251 $x1601)) (= $x799 $x1606)) (= $x802 $x1609))))
-(let ((@x1673 (monotonicity (monotonicity @x1611 (= $x889 $x1612)) (monotonicity (quant-intro @x1627 (= $x1193 $x1628)) @x1667 (= $x1217 $x1668)) (= $x1220 $x1671))))
-(let ((@x1597 (quant-intro (rewrite (= (<= 0 ?x220) (>= ?x220 0))) (= $x246 $x1595))))
-(let ((@x1679 (monotonicity (monotonicity @x1597 (= $x901 $x1598)) (monotonicity @x1611 @x1673 (= $x1223 $x1674)) (= $x1226 $x1677))))
-(let ((@x1685 (monotonicity (monotonicity @x1597 @x1679 (= $x1229 $x1680)) (= $x1232 $x1683))))
-(let ((@x1591 (monotonicity (quant-intro (rewrite (= (<= ?x220 ?x121) $x1582)) (= $x237 $x1586)) (= $x937 $x1589))))
-(let ((@x1691 (monotonicity @x1591 (monotonicity @x1685 (= $x1235 $x1686)) (= $x1238 $x1689))))
-(let ((@x1694 (monotonicity (quant-intro (rewrite (= (<= ?x220 ?x121) $x1582)) (= $x237 $x1586)) @x1691 (= $x1241 $x1692))))
-(let ((@x1552 (monotonicity (rewrite (= (<= ?x121 ?x217) $x1547)) (= $x698 (not $x1547)))))
-(let ((@x1545 (monotonicity (rewrite (= (<= b_Infinity$ ?x215) $x1540)) (= $x694 (not $x1540)))))
-(let ((@x1572 (monotonicity (monotonicity @x1545 @x1552 (= $x701 $x1553)) (= $x721 $x1570))))
-(let ((@x1558 (monotonicity (monotonicity @x1545 @x1552 (= $x701 $x1553)) (= $x707 (not $x1553)))))
-(let ((@x1566 (monotonicity @x1558 (rewrite (= $x221 $x1559)) (= $x708 (or (not $x1553) $x1559)))))
-(let ((@x1534 (monotonicity (rewrite (= $x206 (>= (+ ?x121 (* (- 1) ?x204)) 0))) (= $x687 $x1532))))
-(let ((@x1527 (monotonicity (rewrite (= (<= b_Infinity$ ?x204) $x1522)) (= $x684 $x1525))))
-(let ((@x1400 (monotonicity (rewrite (= (<= b_Infinity$ ?x121) $x1395)) (= $x452 $x1398))))
-(let ((@x1436 (quant-intro (monotonicity @x1400 (= $x537 (and $x126 $x1398))) (= $x540 $x1434))))
-(let ((@x1578 (monotonicity @x1436 @x1527 (quant-intro @x1534 (= $x690 $x1535)) (quant-intro @x1566 (= $x713 $x1567)) (quant-intro @x1572 (= $x726 $x1573)) (= $x767 $x1576))))
-(let ((@x1697 (monotonicity (monotonicity @x1578 (= $x949 $x1579)) @x1694 (= $x1244 $x1695))))
-(let ((@x1453 (monotonicity (rewrite (= (<= b_Infinity$ ?x177) $x1448)) (= $x598 $x1451))))
-(let ((@x1492 (monotonicity (monotonicity @x1453 @x1308 (= $x626 $x1487)) (= $x632 $x1490))))
-(let ((@x1498 (monotonicity @x1492 (rewrite (= (<= ?x180 (+ ?x102 ?x177)) $x1493)) (= (or $x632 (<= ?x180 (+ ?x102 ?x177))) $x1496))))
-(let ((@x1507 (monotonicity (monotonicity (quant-intro @x1498 (= $x1163 $x1499)) (= $x1166 $x1502)) (= $x1169 $x1505))))
-(let (($x1145 (exists ((?v1 B_Vertex$) )(let ((?x177 (fun_app$c v_b_SP_G_3$ ?v1)))
-(let ((?x102 (b_G$ (pair$ ?v1 ?0))))
-(let ((?x1136 (+ ?x102 ?x177)))
-(let ((?x180 (fun_app$c v_b_SP_G_3$ ?0)))
-(let (($x1139 (= ?x180 ?x1136)))
-(let (($x605 (not (<= ?x180 ?x177))))
-(and $x605 $x1139))))))))
-))
-(let (($x1148 (or $x617 $x1145)))
-(let (($x1472 (and (not (>= (+ ?x177 (* (- 1) ?x180)) 0)) (= (+ ?x102 ?x177 (* (- 1) ?x180)) 0))))
-(let ((?x1136 (+ ?x102 ?x177)))
-(let (($x1139 (= ?x180 ?x1136)))
-(let (($x1142 (and $x605 $x1139)))
-(let ((@x1467 (monotonicity (rewrite (= (<= ?x180 ?x177) (>= (+ ?x177 (* (- 1) ?x180)) 0))) (= $x605 (not (>= (+ ?x177 (* (- 1) ?x180)) 0))))))
-(let ((@x1474 (monotonicity @x1467 (rewrite (= $x1139 (= (+ ?x102 ?x177 (* (- 1) ?x180)) 0))) (= $x1142 $x1472))))
-(let ((@x1480 (monotonicity (monotonicity (monotonicity @x1453 (= $x601 $x1454)) (= $x617 $x1457)) (quant-intro @x1474 (= $x1145 $x1475)) (= $x1148 $x1478))))
-(let ((@x1513 (monotonicity (monotonicity (quant-intro @x1480 (= $x1151 $x1481)) (= $x1154 $x1484)) (monotonicity (quant-intro @x1498 (= $x1163 $x1499)) @x1507 (= $x1172 $x1508)) (= $x1175 $x1511))))
-(let ((@x1445 (monotonicity (monotonicity (monotonicity @x1436 (= $x543 $x1437)) (= $x581 $x1440)) (= $x677 $x1443))))
-(let ((@x1519 (monotonicity @x1445 (monotonicity (quant-intro @x1480 (= $x1151 $x1481)) @x1513 (= $x1178 $x1514)) (= $x1181 $x1517))))
-(let (($x1121 (exists ((?v1 B_Vertex$) )(let ((?x121 (fun_app$c v_b_SP_G_1$ ?v1)))
-(let ((?x102 (b_G$ (pair$ ?v1 ?0))))
-(let ((?x1102 (+ ?x102 ?x121)))
-(let ((?x129 (fun_app$c v_b_SP_G_1$ ?0)))
-(let (($x1115 (= ?x129 ?x1102)))
-(let (($x125 (fun_app$ v_b_Visited_G_1$ ?v1)))
-(let (($x130 (<= ?x129 ?x121)))
-(let (($x458 (not $x130)))
-(and $x458 $x125 $x1115))))))))))
-))
-(let (($x1124 (or $x475 $x1121)))
-(let ((?x1102 (+ ?x102 ?x121)))
-(let (($x1115 (= ?x129 ?x1102)))
-(let (($x1118 (and $x458 $x125 $x1115)))
-(let (($x1414 (= $x1118 (and (not $x1367) $x125 (= (+ ?x102 ?x121 (* (- 1) ?x129)) 0)))))
-(let ((@x1415 (monotonicity (monotonicity (rewrite (= $x130 $x1367)) (= $x458 (not $x1367))) (rewrite (= $x1115 (= (+ ?x102 ?x121 (* (- 1) ?x129)) 0))) $x1414)))
-(let ((@x1421 (monotonicity (monotonicity (monotonicity @x1400 (= $x455 $x1401)) (= $x475 $x1404)) (quant-intro @x1415 (= $x1121 $x1416)) (= $x1124 $x1419))))
-(let ((@x1382 (monotonicity (monotonicity @x1308 (= $x436 (and $x125 $x1306))) (= $x442 (not (and $x125 $x1306))))))
-(let ((@x1389 (monotonicity @x1382 (rewrite (= (<= ?x129 ?x1102) $x1384)) (= (or $x442 (<= ?x129 ?x1102)) (or (not (and $x125 $x1306)) $x1384)))))
-(let ((@x1376 (quant-intro (monotonicity (rewrite (= $x130 $x1367)) (= $x430 (or $x429 $x1367))) (= $x433 $x1374))))
-(let ((@x1365 (quant-intro (rewrite (= (<= 0 ?x121) (>= ?x121 0))) (= $x123 $x1363))))
-(let (($x1349 (= $x409 (and (not $x1288) $x83 (= (+ ?x75 (* (- 1) ?x97) ?x102) 0)))))
-(let ((@x1350 (monotonicity (monotonicity (rewrite (= $x98 $x1288)) (= $x403 (not $x1288))) (rewrite (= $x112 (= (+ ?x75 (* (- 1) ?x97) ?x102) 0))) $x1349)))
-(let ((@x1335 (monotonicity (rewrite (= (<= b_Infinity$ ?x75) $x1330)) (= $x397 (not $x1330)))))
-(let ((@x1341 (monotonicity (monotonicity @x1335 (= $x400 $x1336)) (= (not $x400) $x1339))))
-(let ((@x1359 (quant-intro (monotonicity @x1341 (quant-intro @x1350 (= $x414 $x1351)) (= $x421 $x1354)) (= $x426 $x1357))))
-(let ((@x1427 (monotonicity @x1359 @x1365 @x1376 (quant-intro @x1389 (= $x1112 $x1390)) (quant-intro @x1421 (= $x1127 $x1422)) (= $x1130 $x1425))))
-(let ((@x1703 (monotonicity (monotonicity @x1427 (= $x1133 $x1428)) (monotonicity @x1519 @x1697 (= $x1247 $x1698)) (= $x1250 $x1701))))
-(let ((@x1314 (monotonicity (monotonicity @x1308 (= (and $x83 $x378) (and $x83 $x1306))) (= (not (and $x83 $x378)) (not (and $x83 $x1306))))))
-(let ((@x1321 (monotonicity @x1314 (rewrite (= $x106 $x1316)) (= $x388 (or (not (and $x83 $x1306)) $x1316)))))
-(let ((@x1709 (monotonicity (monotonicity (quant-intro @x1321 (= $x393 $x1322)) (= $x973 $x1325)) (monotonicity @x1359 @x1703 (= $x1253 $x1704)) (= $x1256 $x1707))))
-(let ((@x1297 (quant-intro (monotonicity (rewrite (= $x98 $x1288)) (= $x371 (or $x370 $x1288))) (= $x374 $x1295))))
-(let ((@x1715 (monotonicity (monotonicity @x1297 (= $x985 $x1298)) (monotonicity (quant-intro @x1321 (= $x393 $x1322)) @x1709 (= $x1259 $x1710)) (= $x1262 $x1713))))
-(let ((@x1282 (quant-intro (rewrite (= (<= 0 ?x75) (>= ?x75 0))) (= $x94 $x1280))))
-(let ((@x1721 (monotonicity (monotonicity @x1282 (= $x997 $x1283)) (monotonicity @x1297 @x1715 (= $x1265 $x1716)) (= $x1268 $x1719))))
-(let ((@x1727 (monotonicity (monotonicity @x1282 @x1721 (= $x1271 (and $x92 $x1280 $x1719))) (= (not $x1271) $x1725))))
-(let (($x1263 (= (or $x985 (and $x393 (or $x973 (and $x426 (or $x961 (and $x678 $x1075)))))) $x1262)))
-(let (($x1260 (= (and $x393 (or $x973 (and $x426 (or $x961 (and $x678 $x1075))))) $x1259)))
-(let (($x1242 (= (and $x237 (or $x937 (and $x786 (or $x925 (and $x244 $x246 $x902))))) $x1241)))
-(let ((@x1204 (monotonicity (monotonicity (rewrite (= ?x255 ?x1184)) (= $x262 $x1199)) (= $x833 $x1202))))
-(let ((@x1213 (quant-intro (monotonicity (quant-intro @x1204 (= $x838 $x1205)) (= $x845 $x1208)) (= $x850 $x1211))))
-(let ((@x1192 (monotonicity (monotonicity (rewrite (= ?x255 ?x1184)) (= $x256 (<= ?x250 ?x1184))) (= $x812 (or $x811 (<= ?x250 ?x1184))))))
-(let ((@x1198 (monotonicity (quant-intro @x1192 (= $x817 $x1193)) (= (not $x817) $x1196))))
-(let ((@x1219 (monotonicity (quant-intro @x1192 (= $x817 $x1193)) (monotonicity @x1198 @x1213 (= $x878 $x1214)) (= $x883 $x1217))))
-(let ((@x1228 (monotonicity (monotonicity (monotonicity @x1219 (= $x890 $x1220)) (= $x895 $x1223)) (= $x902 $x1226))))
-(let ((@x1234 (monotonicity (monotonicity @x1228 (= (and $x244 $x246 $x902) $x1229)) (= (or $x925 (and $x244 $x246 $x902)) $x1232))))
-(let ((@x1237 (monotonicity @x1234 (= (and $x786 (or $x925 (and $x244 $x246 $x902))) $x1235))))
-(let ((@x1240 (monotonicity @x1237 (= (or $x937 (and $x786 (or $x925 (and $x244 $x246 $x902)))) $x1238))))
-(let ((@x1162 (monotonicity (monotonicity (rewrite (= ?x182 ?x1136)) (= $x189 (<= ?x180 ?x1136))) (= $x633 (or $x632 (<= ?x180 ?x1136))))))
-(let ((@x1168 (monotonicity (quant-intro @x1162 (= $x638 $x1163)) (= (not $x638) $x1166))))
-(let ((@x1174 (monotonicity (quant-intro @x1162 (= $x638 $x1163)) (monotonicity @x1168 (= $x654 $x1169)) (= $x659 $x1172))))
-(let ((@x1144 (monotonicity (monotonicity (rewrite (= ?x182 ?x1136)) (= $x183 $x1139)) (= $x608 $x1142))))
-(let ((@x1153 (quant-intro (monotonicity (quant-intro @x1144 (= $x611 $x1145)) (= $x618 $x1148)) (= $x623 $x1151))))
-(let ((@x1177 (monotonicity (monotonicity @x1153 (= (not $x623) $x1154)) @x1174 (= $x666 $x1175))))
-(let ((@x1183 (monotonicity (monotonicity @x1153 @x1177 (= $x671 $x1178)) (= $x678 $x1181))))
-(let ((@x1249 (monotonicity @x1183 (monotonicity (monotonicity @x1240 $x1242) (= $x1075 $x1244)) (= (and $x678 $x1075) $x1247))))
-(let ((@x1120 (monotonicity (monotonicity (rewrite (= ?x134 ?x1102)) (= $x141 $x1115)) (= $x464 $x1118))))
-(let ((@x1129 (quant-intro (monotonicity (quant-intro @x1120 (= $x469 $x1121)) (= $x476 $x1124)) (= $x481 $x1127))))
-(let ((@x1111 (monotonicity (monotonicity (rewrite (= ?x134 ?x1102)) (= $x135 (<= ?x129 ?x1102))) (= $x443 (or $x442 (<= ?x129 ?x1102))))))
-(let ((@x1135 (monotonicity (monotonicity (quant-intro @x1111 (= $x448 $x1112)) @x1129 (= $x532 $x1130)) (= $x961 $x1133))))
-(let ((@x1255 (monotonicity (monotonicity @x1135 @x1249 (= (or $x961 (and $x678 $x1075)) $x1250)) (= (and $x426 (or $x961 (and $x678 $x1075))) $x1253))))
-(let ((@x1258 (monotonicity @x1255 (= (or $x973 (and $x426 (or $x961 (and $x678 $x1075)))) $x1256))))
-(let ((@x1267 (monotonicity (monotonicity (monotonicity @x1258 $x1260) $x1263) (= $x1082 $x1265))))
-(let ((@x1273 (monotonicity (monotonicity @x1267 (= (or $x997 $x1082) $x1268)) (= (and $x92 $x94 (or $x997 $x1082)) $x1271))))
-(let ((@x1729 (trans (monotonicity @x1273 (= $x1084 (not $x1271))) @x1727 (= $x1084 $x1725))))
-(let ((@x1088 (mp (not-or-elim @x1030 (not $x1015)) (rewrite* (= (not $x1015) $x1084)) $x1084)))
-(let ((@x2621 (mp (mp~ (mp @x1088 @x1729 $x1725) @x2331 $x2329) (monotonicity @x2617 (= $x2329 $x2618)) $x2618)))
-(let ((@x4102 (mp (mp @x2621 (monotonicity @x3265 (= $x2618 $x3266)) $x3266) @x4101 (or $x1009 $x1786 $x4096))))
-(let ((@x5459 (unit-resolution (def-axiom (or $x4093 $x4087)) (unit-resolution @x4102 @x4116 (lemma @x3301 $x1785) $x4096) $x4087)))
-(let ((@x4213 (unit-resolution ((_ quant-inst ?v0!2) (or (not $x3748) $x2622)) (mp @x1780 @x3752 $x3748) (hypothesis $x1800) false)))
-(let ((@x5512 (unit-resolution (def-axiom (or $x4090 $x2642 $x4084)) (unit-resolution (def-axiom (or $x2637 $x1800)) (lemma @x4213 $x2622) $x2637) @x5459 $x4084)))
-(let ((@x5451 (unit-resolution (def-axiom (or $x4078 $x2688 $x4072)) (unit-resolution (def-axiom (or $x4081 $x4075)) @x5512 $x4075) (unit-resolution (def-axiom (or $x2683 $x1821)) (lemma @x4210 $x2668) $x2683) $x4072)))
-(let ((?x1849 (v_b_SP_G_0$ ?v0!5)))
-(let (($x4261 (= b_Infinity$ ?x1849)))
-(let ((@x4269 (symm (commutativity (= $x4261 (= ?x1849 b_Infinity$))) (= (= ?x1849 b_Infinity$) $x4261))))
-(let (($x4170 (= ?x1849 b_Infinity$)))
-(let ((@x4259 (rewrite (= (or (not $x3741) (or $x1847 $x4170)) (or (not $x3741) $x1847 $x4170)))))
-(let ((@x4260 (mp ((_ quant-inst ?v0!5) (or (not $x3741) (or $x1847 $x4170))) @x4259 (or (not $x3741) $x1847 $x4170))))
-(let ((@x4263 (unit-resolution @x4260 (mp @x1775 (quant-intro (refl (= $x340 $x340)) (= $x343 $x3741)) $x3741) (unit-resolution (def-axiom (or $x3789 $x1848)) (hypothesis $x3792) $x1848) $x4170)))
-(let ((@x4249 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x4261) $x1852)) (unit-resolution (def-axiom (or $x3789 $x1853)) (hypothesis $x3792) $x1853) (not $x4261))))
-(let ((@x5453 (unit-resolution (def-axiom (or $x4066 $x3792 $x4060)) (lemma (unit-resolution @x4249 (mp @x4263 @x4269 $x4261) false) $x3789) (unit-resolution (def-axiom (or $x4069 $x4063)) @x5451 $x4063) $x4060)))
-(let ((@x5456 (unit-resolution (def-axiom (or $x4057 $x120)) @x5453 $x120)))
-(let ((@x5702 (trans (monotonicity @x5699 (= (fun_app$c v_b_SP_G_3$ b_Source$) ?x119)) @x5456 $x193)))
-(let (($x4338 (<= (+ b_Infinity$ (* (- 1) (fun_app$c v_b_SP_G_1$ ?v0!8))) 0)))
-(let (($x4960 (not $x4338)))
-(let (($x4484 (>= (+ ?x1970 (* (- 1) (fun_app$c v_b_SP_G_1$ ?v0!8))) 0)))
-(let ((@x6411 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not (= ?x1970 (fun_app$c v_b_SP_G_1$ ?v0!8))) $x4484)) (monotonicity @x5699 (= ?x1970 (fun_app$c v_b_SP_G_1$ ?v0!8))) $x4484)))
-(let ((@x4754 (lemma ((_ th-lemma arith farkas 1 -1 1) (hypothesis $x4484) (hypothesis $x4338) (hypothesis $x1974) false) (or $x4960 (not $x4484) $x1973))))
-(let (($x5013 (<= (+ ?x1970 (* (- 1) (fun_app$c v_b_SP_G_3$ (?v1!7 ?v0!8)))) 0)))
-(let ((?x4355 (* (- 1) (fun_app$c v_b_SP_G_1$ (?v1!7 ?v0!8)))))
-(let ((?x4335 (fun_app$c v_b_SP_G_1$ ?v0!8)))
-(let (($x4361 (<= (+ ?x4335 ?x4355) 0)))
-(let (($x4332 (not $x4361)))
-(let ((?x4366 (+ ?x4335 ?x4355 (* (- 1) (b_G$ (pair$ (?v1!7 ?v0!8) ?v0!8))))))
-(let (($x4371 (= ?x4366 0)))
-(let (($x4372 (not $x4371)))
-(let (($x4370 (or $x4361 (not (fun_app$ v_b_Visited_G_1$ (?v1!7 ?v0!8))) $x4372)))
-(let (($x4373 (not $x4370)))
-(let ((@x4406 (unit-resolution (def-axiom (or $x4057 $x3829)) @x5453 $x3829)))
-(let ((@x4343 (rewrite (= (or $x3834 (or $x1968 $x4338 $x4373)) (or $x3834 $x1968 $x4338 $x4373)))))
-(let ((@x4329 (mp ((_ quant-inst ?v0!8) (or $x3834 (or $x1968 $x4338 $x4373))) @x4343 (or $x3834 $x1968 $x4338 $x4373))))
-(let ((@x4408 (unit-resolution @x4329 @x4406 (unit-resolution (def-axiom (or $x3856 $x1969)) (hypothesis $x3859) $x1969) (hypothesis $x4960) $x4373)))
-(let ((@x4463 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not (= ?x1970 ?x4335)) $x4484)) (monotonicity (hypothesis $x164) (= ?x1970 ?x4335)) $x4484)))
-(let (($x4500 (<= (+ (fun_app$c v_b_SP_G_3$ (?v1!7 ?v0!8)) ?x4355) 0)))
-(let ((?x4341 (?v1!7 ?v0!8)))
-(let ((?x4288 (fun_app$c v_b_SP_G_3$ ?x4341)))
-(let ((@x5080 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not (= ?x4288 (fun_app$c v_b_SP_G_1$ ?x4341))) $x4500)) (monotonicity (hypothesis $x164) (= ?x4288 (fun_app$c v_b_SP_G_1$ ?x4341))) $x4500)))
-(let ((@x5445 ((_ th-lemma arith farkas 1 -1 -1 1) (hypothesis $x4484) (hypothesis $x5013) (hypothesis $x4500) (hypothesis $x4332) false)))
-(let ((@x4647 (unit-resolution (lemma @x5445 (or (not $x5013) (not $x4484) (not $x4500) $x4361)) @x5080 @x4463 (unit-resolution (def-axiom (or $x4370 $x4332)) @x4408 $x4332) (not $x5013))))
-(let ((?x4700 (+ ?x1970 (* (- 1) ?x4288) (* (- 1) (b_G$ (pair$ ?x4341 ?v0!8))))))
-(let (($x4722 (= ?x4700 0)))
-(let (($x4489 (>= ?x4700 0)))
-(let (($x4331 (>= ?x4366 0)))
-(let ((@x4769 (unit-resolution ((_ th-lemma arith triangle-eq) (or $x4372 $x4331)) (unit-resolution (def-axiom (or $x4370 $x4371)) @x4408 $x4371) $x4331)))
-(let ((@x5050 (unit-resolution ((_ th-lemma arith assign-bounds -1 -1 1) (or $x4489 (not $x4331) (not $x4484) (not $x4500))) @x4769 @x4463 @x5080 $x4489)))
-(let (($x5088 (<= ?x4700 0)))
-(let (($x4912 (>= (+ ?x4288 ?x4355) 0)))
-(let ((@x6226 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not (= ?x4288 (fun_app$c v_b_SP_G_1$ ?x4341))) $x4912)) (monotonicity (hypothesis $x164) (= ?x4288 (fun_app$c v_b_SP_G_1$ ?x4341))) $x4912)))
-(let (($x4483 (<= (+ ?x1970 (* (- 1) ?x4335)) 0)))
-(let ((@x4788 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not (= ?x1970 ?x4335)) $x4483)) (monotonicity (hypothesis $x164) (= ?x1970 ?x4335)) $x4483)))
-(let (($x4330 (<= ?x4366 0)))
-(let ((@x4407 (unit-resolution ((_ th-lemma arith triangle-eq) (or $x4372 $x4330)) (unit-resolution (def-axiom (or $x4370 $x4371)) @x4408 $x4371) $x4330)))
-(let ((@x5001 (unit-resolution ((_ th-lemma arith assign-bounds -1 -1 1) (or $x5088 (not $x4330) (not $x4483) (not $x4912))) @x4407 @x4788 @x6226 $x5088)))
-(let ((@x4974 (unit-resolution ((_ th-lemma arith triangle-eq) (or $x4722 (not $x5088) (not $x4489))) @x5001 @x5050 $x4722)))
-(let (($x5094 (not $x4722)))
-(let (($x4624 (or $x5013 $x5094)))
-(let (($x4764 (or $x3853 $x5013 $x5094)))
-(let (($x4299 (>= (+ ?x4288 ?x1971) 0)))
-(let (($x4989 (or $x3853 (or $x4299 (not (= (+ ?x4288 ?x1971 (b_G$ (pair$ ?x4341 ?v0!8))) 0))))))
-(let (($x4626 (= (or $x4299 (not (= (+ ?x4288 ?x1971 (b_G$ (pair$ ?x4341 ?v0!8))) 0))) $x4624)))
-(let ((@x4723 (rewrite (= (= (+ ?x1971 ?x4288 (b_G$ (pair$ ?x4341 ?v0!8))) 0) $x4722))))
-(let (($x4286 (= (+ ?x4288 ?x1971 (b_G$ (pair$ ?x4341 ?v0!8))) 0)))
-(let (($x4839 (= (+ ?x4288 ?x1971 (b_G$ (pair$ ?x4341 ?v0!8))) (+ ?x1971 ?x4288 (b_G$ (pair$ ?x4341 ?v0!8))))))
-(let ((@x4695 (monotonicity (rewrite $x4839) (= $x4286 (= (+ ?x1971 ?x4288 (b_G$ (pair$ ?x4341 ?v0!8))) 0)))))
-(let ((@x4401 (monotonicity (trans @x4695 @x4723 (= $x4286 $x4722)) (= (not $x4286) $x5094))))
-(let ((@x5263 (monotonicity (rewrite (= (+ ?x4288 ?x1971) (+ ?x1971 ?x4288))) (= $x4299 (>= (+ ?x1971 ?x4288) 0)))))
-(let ((@x4841 (trans @x5263 (rewrite (= (>= (+ ?x1971 ?x4288) 0) $x5013)) (= $x4299 $x5013))))
-(let ((@x5186 (trans (monotonicity (monotonicity @x4841 @x4401 $x4626) (= $x4989 (or $x3853 $x4624))) (rewrite (= (or $x3853 $x4624) $x4764)) (= $x4989 $x4764))))
-(let ((@x5499 (unit-resolution (mp ((_ quant-inst (?v1!7 ?v0!8)) $x4989) @x5186 $x4764) (unit-resolution (def-axiom (or $x3856 $x3848)) (hypothesis $x3859) $x3848) $x4624)))
-(let ((@x5708 (unit-resolution (lemma (unit-resolution @x5499 @x4974 @x4647 false) (or $x3856 $x2982 $x4338)) @x5699 (unit-resolution @x4754 @x6411 (hypothesis $x1974) $x4960) $x3856)))
-(let ((@x5837 (unit-resolution (def-axiom (or $x3899 $x3859 $x3893)) @x5708 (unit-resolution (def-axiom (or $x3902 $x3896)) @x5698 $x3896) $x3893)))
-(let ((@x5839 (unit-resolution (def-axiom (or $x3887 $x2924 $x3881)) (unit-resolution (def-axiom (or $x3890 $x3884)) @x5837 $x3884) (unit-resolution (def-axiom (or $x3878 $x2058)) @x5702 $x3878) $x2924)))
-(let ((@x5847 (monotonicity (symm @x5699 (= v_b_SP_G_1$ v_b_SP_G_3$)) (= ?x4698 ?x2030))))
-(let ((@x6414 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x6220) $x5759)) (symm @x5847 $x6220) $x5759)))
-(let ((@x6168 (lemma ((_ th-lemma arith farkas 1 -1 1) (hypothesis $x5759) (hypothesis $x4492) (hypothesis $x2034) false) (or $x5659 (not $x5759) $x2033))))
-(let ((@x5991 (unit-resolution @x6168 @x6414 (unit-resolution (def-axiom (or $x2919 $x2034)) @x5839 $x2034) $x5659)))
-(let ((@x4386 (mp ((_ quant-inst ?v1!10) (or $x3843 (or $x4697 $x4492))) (rewrite (= (or $x3843 (or $x4697 $x4492)) (or $x3843 $x4697 $x4492))) (or $x3843 $x4697 $x4492))))
-(let ((@x5999 (unit-resolution @x4386 (unit-resolution (def-axiom (or $x3902 $x3838)) @x5698 $x3838) (or $x4697 $x4492))))
-(let ((@x6172 (unit-resolution (def-axiom (or $x4057 $x3821)) @x5453 $x3821)))
-(let (($x4384 (not $x4697)))
-(let (($x5846 (or $x3826 $x4384 $x2039 $x4677)))
-(let (($x4673 (or $x4384 $x2039 (>= (+ ?x2036 ?x4698 (* (- 1) (fun_app$c v_b_SP_G_1$ ?v0!11))) 0))))
-(let (($x5849 (or $x3826 $x4673)))
-(let (($x4614 (= (>= (+ ?x2036 ?x4698 (* (- 1) (fun_app$c v_b_SP_G_1$ ?v0!11))) 0) $x4677)))
-(let (($x4674 (= (+ ?x2036 ?x4698 (* (- 1) (fun_app$c v_b_SP_G_1$ ?v0!11))) (+ ?x2036 (* (- 1) (fun_app$c v_b_SP_G_1$ ?v0!11)) ?x4698))))
-(let ((@x5516 (monotonicity (monotonicity (rewrite $x4674) $x4614) (= $x4673 (or $x4384 $x2039 $x4677)))))
-(let ((@x5314 (trans (monotonicity @x5516 (= $x5849 (or $x3826 (or $x4384 $x2039 $x4677)))) (rewrite (= (or $x3826 (or $x4384 $x2039 $x4677)) $x5846)) (= $x5849 $x5846))))
-(let ((@x6307 (unit-resolution (mp ((_ quant-inst ?v0!11 ?v1!10) $x5849) @x5314 $x5846) @x6172 (unit-resolution (def-axiom (or $x2919 (not $x2039))) @x5839 (not $x2039)) (or $x4384 $x4677))))
-(let ((?x4518 (fun_app$c v_b_SP_G_1$ ?v0!11)))
-(let ((?x4546 (* (- 1) ?x4518)))
-(let ((?x2043 (fun_app$c v_b_SP_G_3$ ?v0!11)))
-(let ((@x6142 (monotonicity (symm @x5699 (= v_b_SP_G_1$ v_b_SP_G_3$)) (= ?x4518 ?x2043))))
-(let ((@x5800 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not (= ?x2043 ?x4518)) (<= (+ ?x2043 ?x4546) 0))) (symm @x6142 (= ?x2043 ?x4518)) (<= (+ ?x2043 ?x4546) 0))))
-(let ((@x5815 ((_ th-lemma arith farkas -1 -1 1 1) @x5800 (unit-resolution (def-axiom (or $x2919 $x3668)) @x5839 $x3668) @x6414 (unit-resolution @x6307 (unit-resolution @x5999 @x5991 $x4697) $x4677) false)))
-(let ((@x7385 (unit-resolution (def-axiom (or $x3856 $x1974)) (unit-resolution (lemma @x5815 (or $x3902 $x1973)) @x5698 $x1973) $x3856)))
-(let ((@x7411 (unit-resolution (def-axiom (or $x3899 $x3859 $x3893)) @x7385 (unit-resolution (def-axiom (or $x3902 $x3896)) @x5698 $x3896) $x3893)))
-(let ((@x7356 (unit-resolution (def-axiom (or $x3887 $x2924 $x3881)) (unit-resolution (def-axiom (or $x3878 $x2058)) @x5702 $x3878) (unit-resolution (def-axiom (or $x3890 $x3884)) @x7411 $x3884) $x2924)))
-(let ((@x7398 (unit-resolution @x6168 (unit-resolution (def-axiom (or $x2919 $x2034)) @x7356 $x2034) @x7384 $x5659)))
-(let ((@x7318 (unit-resolution @x4386 (unit-resolution (def-axiom (or $x3902 $x3838)) @x5698 $x3838) @x7398 $x4697)))
-(let ((@x5937 (unit-resolution (mp ((_ quant-inst ?v0!11 ?v1!10) $x5849) @x5314 $x5846) @x6172 (unit-resolution (def-axiom (or $x2919 (not $x2039))) @x7356 (not $x2039)) @x7318 $x4677)))
-(let ((@x6020 ((_ th-lemma arith farkas 1 -1 -1 1) @x5937 @x5800 (unit-resolution (def-axiom (or $x2919 $x3668)) @x7356 $x3668) @x7384 false)))
-(let ((@x8163 (unit-resolution (def-axiom (or $x4054 $x3905 $x4048)) (unit-resolution (def-axiom (or $x4057 $x4051)) @x5453 $x4051) $x4051)))
-(let ((@x8164 (unit-resolution @x8163 (lemma @x6020 $x3902) $x4048)))
-(let ((@x8214 (unit-resolution (def-axiom (or $x4045 $x213)) @x8164 $x213)))
-(let ((@x8302 (unit-resolution (def-axiom (or $x4045 $x3926)) @x8164 $x3926)))
-(let (($x5115 (fun_app$ ?x212 ?v0!14)))
-(let ((@x7409 (monotonicity (symm (hypothesis $x213) (= ?x212 v_b_Visited_G_2$)) (= $x5115 $x2133))))
-(let (($x6262 (fun_app$ v_b_Visited_G_1$ ?v0!14)))
-(let (($x5230 (= ?v0!14 v_b_v_G_1$)))
-(let (($x7438 (or $x5230 $x6262)))
-(let (($x7443 (= $x5115 $x7438)))
-(let (($x3716 (forall ((?v0 B_Vertex_bool_fun$) (?v1 B_Vertex$) (?v2 Bool) (?v3 B_Vertex$) )(!(let (($x56 (fun_app$ (fun_app$a (fun_app$b (fun_upd$ ?v0) ?v1) ?v2) ?v3)))
-(= $x56 (ite (= ?v3 ?v1) ?v2 (fun_app$ ?v0 ?v3)))) :pattern ( (fun_app$ (fun_app$a (fun_app$b (fun_upd$ ?v0) ?v1) ?v2) ?v3) )))
-))
-(let (($x1099 (forall ((?v0 B_Vertex_bool_fun$) (?v1 B_Vertex$) (?v2 Bool) (?v3 B_Vertex$) )(let (($x56 (fun_app$ (fun_app$a (fun_app$b (fun_upd$ ?v0) ?v1) ?v2) ?v3)))
-(= $x56 (ite (= ?v3 ?v1) ?v2 (fun_app$ ?v0 ?v3)))))
-))
-(let (($x56 (fun_app$ (fun_app$a (fun_app$b (fun_upd$ ?3) ?2) ?1) ?0)))
-(let (($x1095 (= $x56 (ite (= ?0 ?2) ?1 (fun_app$ ?3 ?0)))))
-(let (($x61 (forall ((?v0 B_Vertex_bool_fun$) (?v1 B_Vertex$) (?v2 Bool) (?v3 B_Vertex$) )(let (($x56 (fun_app$ (fun_app$a (fun_app$b (fun_upd$ ?v0) ?v1) ?v2) ?v3)))
-(= $x56 (ite (= ?v3 ?v1) ?v2 (fun_app$ ?v0 ?v3)))))
-))
-(let ((@x1098 (rewrite (= (= $x56 (ite (= ?0 ?2) ?1 (fun_app$ ?3 ?0))) $x1095))))
-(let ((@x1104 (mp (mp (asserted $x61) (rewrite* (= $x61 $x61)) $x61) (quant-intro @x1098 (= $x61 $x1099)) $x1099)))
-(let ((@x3721 (mp (mp~ @x1104 (nnf-pos (refl (~ $x1095 $x1095)) (~ $x1099 $x1099)) $x1099) (quant-intro (refl (= $x1095 $x1095)) (= $x1099 $x3716)) $x3716)))
-(let (($x5105 (not $x3716)))
-(let (($x7445 (or $x5105 $x7443)))
-(let ((@x7444 (monotonicity (rewrite (= (ite $x5230 true $x6262) $x7438)) (= (= $x5115 (ite $x5230 true $x6262)) $x7443))))
-(let ((@x7449 (monotonicity @x7444 (= (or $x5105 (= $x5115 (ite $x5230 true $x6262))) $x7445))))
-(let ((@x7452 (trans @x7449 (rewrite (= $x7445 $x7445)) (= (or $x5105 (= $x5115 (ite $x5230 true $x6262))) $x7445))))
-(let ((@x7453 (mp ((_ quant-inst v_b_Visited_G_1$ v_b_v_G_1$ true ?v0!14) (or $x5105 (= $x5115 (ite $x5230 true $x6262)))) @x7452 $x7445)))
-(let (($x7425 (not $x7438)))
-(let (($x6006 (not $x6262)))
-(let (($x7455 (>= (+ ?x204 (* (- 1) ?x2136)) 0)))
-(let (($x7487 (not $x7455)))
-(let (($x5623 (>= (+ ?x204 (* (- 1) ?x2136) (b_G$ (pair$ v_b_v_G_1$ ?v0!14))) 0)))
-(let (($x5890 (not $x5623)))
-(let (($x6101 (<= (+ b_Infinity$ (* (- 1) (b_G$ (pair$ v_b_v_G_1$ ?v0!14)))) 0)))
-(let (($x5590 (or $x6101 $x5623)))
-(let (($x5624 (not $x5590)))
-(let ((@x5806 (hypothesis $x3646)))
-(let ((@x6086 (hypothesis $x3926)))
-(let (($x5930 (or $x3931 $x5624 $x2137)))
-(let ((?x6353 (b_G$ (pair$ v_b_v_G_1$ ?v0!14))))
-(let ((?x6397 (* (- 1) ?x6353)))
-(let ((?x1520 (* (- 1) ?x204)))
-(let (($x6154 (<= (+ ?x2136 ?x1520 ?x6397) 0)))
-(let (($x5925 (or $x3931 (or (not (or $x6101 $x6154)) $x2137))))
-(let ((@x5231 (monotonicity (rewrite (= (+ ?x2136 ?x1520 ?x6397) (+ ?x1520 ?x2136 ?x6397))) (= $x6154 (<= (+ ?x1520 ?x2136 ?x6397) 0)))))
-(let ((@x5207 (trans @x5231 (rewrite (= (<= (+ ?x1520 ?x2136 ?x6397) 0) $x5623)) (= $x6154 $x5623))))
-(let ((@x5636 (monotonicity (monotonicity @x5207 (= (or $x6101 $x6154) $x5590)) (= (not (or $x6101 $x6154)) $x5624))))
-(let ((@x5641 (monotonicity @x5636 (= (or (not (or $x6101 $x6154)) $x2137) (or $x5624 $x2137)))))
-(let ((@x5869 (trans (monotonicity @x5641 (= $x5925 (or $x3931 (or $x5624 $x2137)))) (rewrite (= (or $x3931 (or $x5624 $x2137)) $x5930)) (= $x5925 $x5930))))
-(let ((@x6877 (unit-resolution (def-axiom (or $x5590 $x5890)) (unit-resolution (mp ((_ quant-inst ?v0!14) $x5925) @x5869 $x5930) @x6086 @x5806 $x5624) $x5890)))
-(let (($x5403 (= v_b_v_G_1$ ?v0!14)))
-(let (($x5399 (<= ?x6353 0)))
-(let ((@x6842 (hypothesis $x5890)))
-(let ((@x7496 (unit-resolution ((_ th-lemma arith assign-bounds 1 1) (or $x5399 $x5623 $x7487)) (hypothesis $x7455) @x6842 $x5399)))
-(let (($x3728 (forall ((?v0 B_Vertex$) (?v1 B_Vertex$) )(!(let (($x319 (not (<= (b_G$ (pair$ ?v0 ?v1)) 0))))
-(let (($x64 (= ?v0 ?v1)))
-(or $x64 $x319))) :pattern ( (pair$ ?v0 ?v1) )))
-))
-(let (($x330 (forall ((?v0 B_Vertex$) (?v1 B_Vertex$) )(let (($x319 (not (<= (b_G$ (pair$ ?v0 ?v1)) 0))))
-(let (($x64 (= ?v0 ?v1)))
-(or $x64 $x319))))
-))
-(let (($x319 (not (<= (b_G$ (pair$ ?1 ?0)) 0))))
-(let (($x64 (= ?1 ?0)))
-(let (($x325 (or $x64 $x319)))
-(let (($x72 (forall ((?v0 B_Vertex$) (?v1 B_Vertex$) )(let (($x64 (= ?v0 ?v1)))
-(let (($x69 (not $x64)))
-(=> $x69 (< 0 (b_G$ (pair$ ?v0 ?v1)))))))
-))
-(let (($x69 (not $x64)))
-(let (($x71 (=> $x69 (< 0 (b_G$ (pair$ ?1 ?0))))))
-(let ((@x324 (monotonicity (rewrite (= (< 0 (b_G$ (pair$ ?1 ?0))) $x319)) (= $x71 (=> $x69 $x319)))))
-(let ((@x332 (quant-intro (trans @x324 (rewrite (= (=> $x69 $x319) $x325)) (= $x71 $x325)) (= $x72 $x330))))
-(let ((@x1765 (mp~ (mp (mp (asserted $x72) @x332 $x330) (rewrite* (= $x330 $x330)) $x330) (nnf-pos (refl (~ $x325 $x325)) (~ $x330 $x330)) $x330)))
-(let ((@x3733 (mp @x1765 (quant-intro (refl (= $x325 $x325)) (= $x330 $x3728)) $x3728)))
-(let (($x7466 (= (or (not $x3728) (or $x5403 (not $x5399))) (or (not $x3728) $x5403 (not $x5399)))))
-(let ((@x7468 (mp ((_ quant-inst v_b_v_G_1$ ?v0!14) (or (not $x3728) (or $x5403 (not $x5399)))) (rewrite $x7466) (or (not $x3728) $x5403 (not $x5399)))))
-(let ((@x7498 (unit-resolution (unit-resolution @x7468 @x3733 (or $x5403 (not $x5399))) @x7496 $x5403)))
-(let ((@x7502 (unit-resolution ((_ th-lemma arith assign-bounds -1 1) (or (not (>= ?x6353 0)) $x5623 $x7487)) (hypothesis $x7455) @x6842 (not (>= ?x6353 0)))))
-(let ((@x7506 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not (= ?x6353 0)) (>= ?x6353 0))) @x7502 (not (= ?x6353 0)))))
-(let (($x3722 (forall ((?v0 B_Vertex$) (?v1 B_Vertex$) )(!(let (($x64 (= ?v0 ?v1)))
-(let (($x69 (not $x64)))
-(or $x69 (= (b_G$ (pair$ ?v0 ?v1)) 0)))) :pattern ( (pair$ ?v0 ?v1) )))
-))
-(let (($x314 (forall ((?v0 B_Vertex$) (?v1 B_Vertex$) )(let (($x64 (= ?v0 ?v1)))
-(let (($x69 (not $x64)))
-(or $x69 (= (b_G$ (pair$ ?v0 ?v1)) 0)))))
-))
-(let (($x311 (or $x69 (= (b_G$ (pair$ ?1 ?0)) 0))))
-(let (($x68 (forall ((?v0 B_Vertex$) (?v1 B_Vertex$) )(let (($x64 (= ?v0 ?v1)))
-(=> $x64 (= (b_G$ (pair$ ?v0 ?v1)) 0))))
-))
-(let ((@x316 (quant-intro (rewrite (= (=> $x64 (= (b_G$ (pair$ ?1 ?0)) 0)) $x311)) (= $x68 $x314))))
-(let ((@x1760 (mp~ (mp (mp (asserted $x68) @x316 $x314) (rewrite* (= $x314 $x314)) $x314) (nnf-pos (refl (~ $x311 $x311)) (~ $x314 $x314)) $x314)))
-(let ((@x3727 (mp @x1760 (quant-intro (refl (= $x311 $x311)) (= $x314 $x3722)) $x3722)))
-(let (($x7472 (= (or (not $x3722) (or (not $x5403) (= ?x6353 0))) (or (not $x3722) (not $x5403) (= ?x6353 0)))))
-(let ((@x7474 (mp ((_ quant-inst v_b_v_G_1$ ?v0!14) (or (not $x3722) (or (not $x5403) (= ?x6353 0)))) (rewrite $x7472) (or (not $x3722) (not $x5403) (= ?x6353 0)))))
-(let ((@x7508 (unit-resolution (unit-resolution @x7474 @x3727 (or (not $x5403) (= ?x6353 0))) @x7506 @x7498 false)))
-(let ((@x6970 (unit-resolution (def-axiom (or $x4057 $x3813)) @x5453 $x3813)))
-(let ((@x7100 (rewrite (= (or $x3818 (or $x202 $x6006 $x7455)) (or $x3818 $x202 $x6006 $x7455)))))
-(let ((@x7101 (mp ((_ quant-inst ?v0!14 v_b_v_G_1$) (or $x3818 (or $x202 $x6006 $x7455))) @x7100 (or $x3818 $x202 $x6006 $x7455))))
-(let ((@x5643 (unit-resolution @x7101 @x6970 (hypothesis $x203) (hypothesis $x6262) (hypothesis $x7487) false)))
-(let ((@x7476 (unit-resolution (lemma @x5643 (or $x6006 $x202 $x7455)) (unit-resolution (lemma @x7508 (or $x7487 $x5623)) @x6877 $x7487) (hypothesis $x203) $x6006)))
-(let ((?x3394 (v_b_SP_G_2$ v_b_v_G_1$)))
-(let (($x3329 (= ?x3394 ?x204)))
-(let ((?x3404 (b_G$ (pair$ v_b_v_G_1$ v_b_v_G_1$))))
-(let (($x3390 (>= ?x3404 0)))
-(let (($x4586 (or (<= (+ b_Infinity$ (* (- 1) ?x3404)) 0) $x3390)))
-(let (($x4394 (= ?x3404 0)))
-(let (($x4439 (not $x3722)))
-(let (($x4440 (or $x4439 $x4394)))
-(let ((@x4427 (monotonicity (rewrite (= (= v_b_v_G_1$ v_b_v_G_1$) true)) (= (not (= v_b_v_G_1$ v_b_v_G_1$)) (not true)))))
-(let ((@x4447 (trans @x4427 (rewrite (= (not true) false)) (= (not (= v_b_v_G_1$ v_b_v_G_1$)) false))))
-(let ((@x4434 (monotonicity @x4447 (= (or (not (= v_b_v_G_1$ v_b_v_G_1$)) $x4394) (or false $x4394)))))
-(let ((@x4438 (trans @x4434 (rewrite (= (or false $x4394) $x4394)) (= (or (not (= v_b_v_G_1$ v_b_v_G_1$)) $x4394) $x4394))))
-(let ((@x4450 (monotonicity @x4438 (= (or $x4439 (or (not (= v_b_v_G_1$ v_b_v_G_1$)) $x4394)) $x4440))))
-(let ((@x4451 (trans @x4450 (rewrite (= $x4440 $x4440)) (= (or $x4439 (or (not (= v_b_v_G_1$ v_b_v_G_1$)) $x4394)) $x4440))))
-(let ((@x4452 (mp ((_ quant-inst v_b_v_G_1$ v_b_v_G_1$) (or $x4439 (or (not (= v_b_v_G_1$ v_b_v_G_1$)) $x4394))) @x4451 $x4440)))
-(let ((@x4473 (lemma (unit-resolution @x4452 @x3727 (hypothesis (not $x4394)) false) $x4394)))
-(let ((@x6229 (unit-resolution (def-axiom (or $x4586 (not $x3390))) (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x4394) $x3390)) @x4473 $x3390) $x4586)))
-(let (($x4589 (not $x4586)))
-(let (($x5387 (or $x3931 $x4589 $x3329)))
-(let (($x3393 (<= (+ ?x204 ?x1520 (* (- 1) ?x3404)) 0)))
-(let (($x3330 (or (not (or (<= (+ b_Infinity$ (* (- 1) ?x3404)) 0) $x3393)) $x3329)))
-(let (($x4517 (or $x3931 $x3330)))
-(let (($x4592 (= (not (or (<= (+ b_Infinity$ (* (- 1) ?x3404)) 0) $x3393)) $x4589)))
-(let ((@x3389 (monotonicity (rewrite (= (+ ?x204 ?x1520 (* (- 1) ?x3404)) (* (- 1) ?x3404))) (= $x3393 (<= (* (- 1) ?x3404) 0)))))
-(let ((@x3371 (trans @x3389 (rewrite (= (<= (* (- 1) ?x3404) 0) $x3390)) (= $x3393 $x3390))))
-(let ((@x5175 (monotonicity @x3371 (= (or (<= (+ b_Infinity$ (* (- 1) ?x3404)) 0) $x3393) $x4586))))
-(let ((@x4575 (monotonicity (monotonicity (monotonicity @x5175 $x4592) (= $x3330 (or $x4589 $x3329))) (= $x4517 (or $x3931 (or $x4589 $x3329))))))
-(let ((@x5481 (trans @x4575 (rewrite (= (or $x3931 (or $x4589 $x3329)) $x5387)) (= $x4517 $x5387))))
-(let ((@x6230 (unit-resolution (mp ((_ quant-inst v_b_v_G_1$) $x4517) @x5481 $x5387) @x6086 @x6229 $x3329)))
-(let ((@x7480 (trans (monotonicity (hypothesis $x5230) (= ?x2135 ?x3394)) (hypothesis $x3329) (= ?x2135 ?x204))))
-(let ((@x7483 (trans @x7480 (symm (monotonicity (hypothesis $x5230) (= ?x2136 ?x204)) (= ?x204 ?x2136)) $x2137)))
-(let ((@x7489 (lemma (unit-resolution @x5806 @x7483 false) (or (not $x5230) $x2137 (not $x3329)))))
-(let ((@x7479 (unit-resolution (def-axiom (or $x7425 $x5230 $x6262)) (unit-resolution @x7489 @x5806 @x6230 (not $x5230)) (or $x7425 $x6262))))
-(let ((@x7373 (unit-resolution (def-axiom (or (not $x7443) (not $x5115) $x7438)) (unit-resolution @x7479 @x7476 $x7425) (unit-resolution @x7453 @x3721 $x7443) (not $x5115))))
-(let ((@x7491 (unit-resolution @x7373 (mp (hypothesis $x2133) (symm @x7409 (= $x2133 $x5115)) $x5115) false)))
-(let ((@x5912 (unit-resolution (lemma @x7491 (or $x2134 $x3196 $x202 $x3931 $x2137)) (unit-resolution (def-axiom (or $x4045 $x203)) @x8164 $x203) @x8302 @x8214 $x2138)))
-(let ((@x8165 (unit-resolution (def-axiom (or $x4045 $x3918)) @x8164 $x3918)))
-(let ((?x6546 (b_G$ (pair$ v_b_v_G_1$ ?v0!13))))
-(let ((?x2118 (v_b_SP_G_2$ ?v0!13)))
-(let ((?x2119 (* (- 1) ?x2118)))
-(let ((?x6581 (+ ?x204 ?x2119 ?x6546)))
-(let (($x6584 (= ?x6581 0)))
-(let (($x6576 (>= (+ ?x204 (* (- 1) (fun_app$c v_b_SP_G_1$ ?v0!13)) ?x6546) 0)))
-(let (($x6555 (<= (+ b_Infinity$ (* (- 1) ?x6546)) 0)))
-(let (($x6633 (or $x6555 $x6576)))
-(let (($x6635 (not $x6633)))
-(let (($x6716 (not (= (fun_app$c v_b_SP_G_1$ ?v0!13) ?x2118))))
-(let ((?x2117 (fun_app$c v_b_SP_G_1$ ?v0!13)))
-(let (($x6631 (= ?x2118 ?x2117)))
-(let ((@x6726 (monotonicity (commutativity (= (= ?x2117 ?x2118) $x6631)) (= $x6716 (not $x6631)))))
-(let ((@x6727 (mp (unit-resolution ((_ th-lemma arith triangle-eq) (or $x6716 $x2121)) (hypothesis $x2122) $x6716) @x6726 (not $x6631))))
-(let (($x6620 (or $x6635 $x6631)))
-(let (($x6613 (or $x3931 $x6635 $x6631)))
-(let (($x6614 (or $x3931 (or (not (or $x6555 (<= (+ ?x2117 ?x1520 (* (- 1) ?x6546)) 0))) $x6631))))
-(let (($x6610 (= (or (not (or $x6555 (<= (+ ?x2117 ?x1520 (* (- 1) ?x6546)) 0))) $x6631) $x6620)))
-(let (($x6556 (<= (+ ?x2117 ?x1520 (* (- 1) ?x6546)) 0)))
-(let ((@x6595 (rewrite (= (+ ?x2117 ?x1520 (* (- 1) ?x6546)) (+ ?x1520 ?x2117 (* (- 1) ?x6546))))))
-(let ((@x6574 (monotonicity @x6595 (= $x6556 (<= (+ ?x1520 ?x2117 (* (- 1) ?x6546)) 0)))))
-(let ((@x6580 (trans @x6574 (rewrite (= (<= (+ ?x1520 ?x2117 (* (- 1) ?x6546)) 0) $x6576)) (= $x6556 $x6576))))
-(let ((@x6619 (monotonicity (monotonicity @x6580 (= (or $x6555 $x6556) $x6633)) (= (not (or $x6555 $x6556)) $x6635))))
-(let ((@x6624 (trans (monotonicity (monotonicity @x6619 $x6610) (= $x6614 (or $x3931 $x6620))) (rewrite (= (or $x3931 $x6620) $x6613)) (= $x6614 $x6613))))
-(let ((@x6732 (unit-resolution (unit-resolution (mp ((_ quant-inst ?v0!13) $x6614) @x6624 $x6613) @x6086 $x6620) @x6727 $x6635)))
-(let (($x6587 (or $x6555 $x6576 $x6584)))
-(let ((@x4512 (hypothesis $x3918)))
-(let (($x6590 (or $x3923 $x6555 $x6576 $x6584)))
-(let (($x6591 (or $x3923 (or $x6555 $x6556 (= (+ ?x204 ?x6546 ?x2119) 0)))))
-(let ((@x6586 (monotonicity (rewrite (= (+ ?x204 ?x6546 ?x2119) ?x6581)) (= (= (+ ?x204 ?x6546 ?x2119) 0) $x6584))))
-(let ((@x6589 (monotonicity @x6580 @x6586 (= (or $x6555 $x6556 (= (+ ?x204 ?x6546 ?x2119) 0)) $x6587))))
-(let ((@x6601 (trans (monotonicity @x6589 (= $x6591 (or $x3923 $x6587))) (rewrite (= (or $x3923 $x6587) $x6590)) (= $x6591 $x6590))))
-(let ((@x6735 (unit-resolution (unit-resolution (mp ((_ quant-inst ?v0!13) $x6591) @x6601 $x6590) @x4512 $x6587) (unit-resolution (def-axiom (or $x6633 (not $x6576))) @x6732 (not $x6576)) (unit-resolution (def-axiom (or $x6633 (not $x6555))) @x6732 (not $x6555)) $x6584)))
-(let ((@x6746 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x6584) (>= ?x6581 0))) @x6735 (>= ?x6581 0))))
-(let ((@x6748 (unit-resolution ((_ th-lemma arith farkas 1 1) (or (<= (+ ?x2117 ?x2119) 0) $x2121)) (hypothesis $x2122) (<= (+ ?x2117 ?x2119) 0))))
-(let ((@x6749 ((_ th-lemma arith farkas 1 -1 1) @x6748 (unit-resolution (def-axiom (or $x6633 (not $x6576))) @x6732 (not $x6576)) @x6746 false)))
-(let ((@x8304 (unit-resolution (def-axiom (or $x4042 $x2122 $x4036)) (unit-resolution (lemma @x6749 (or $x2121 $x3923 $x3931)) @x8165 @x8302 $x2121) (unit-resolution (def-axiom (or $x4045 $x4039)) @x8164 $x4039) $x4036)))
-(let ((@x8619 (unit-resolution (def-axiom (or $x4030 $x2139 $x4024)) (unit-resolution (def-axiom (or $x4033 $x4027)) @x8304 $x4027) $x4027)))
-(let ((@x10488 (unit-resolution @x8619 (lemma (unit-resolution @x5912 @x8820 @x8891 false) $x2138) $x4024)))
-(let ((@x10489 (unit-resolution (def-axiom (or $x4021 $x3943)) @x10488 $x3943)))
-(let (($x4687 (= ?v0!17 v_b_v_G_1$)))
-(let (($x4718 (fun_app$ v_b_Visited_G_1$ ?v0!17)))
-(let (($x7386 (or $x4687 $x4718)))
-(let (($x4686 (fun_app$ ?x212 ?v0!17)))
-(let (($x7429 (= $x4686 $x7386)))
-(let (($x7431 (or $x5105 $x7429)))
-(let ((@x7423 (monotonicity (rewrite (= (ite $x4687 true $x4718) $x7386)) (= (= $x4686 (ite $x4687 true $x4718)) $x7429))))
-(let ((@x7457 (monotonicity @x7423 (= (or $x5105 (= $x4686 (ite $x4687 true $x4718))) $x7431))))
-(let ((@x7375 (trans @x7457 (rewrite (= $x7431 $x7431)) (= (or $x5105 (= $x4686 (ite $x4687 true $x4718))) $x7431))))
-(let ((@x7402 (mp ((_ quant-inst v_b_Visited_G_1$ v_b_v_G_1$ true ?v0!17) (or $x5105 (= $x4686 (ite $x4687 true $x4718)))) @x7375 $x7431)))
-(let ((@x8181 (symm (monotonicity (symm @x8214 (= ?x212 v_b_Visited_G_2$)) (= $x4686 $x2168)) (= $x2168 $x4686))))
-(let ((@x8115 (mp (unit-resolution (def-axiom (or $x3034 $x2168)) (hypothesis $x3039) $x2168) @x8181 $x4686)))
-(let ((@x8116 (unit-resolution (def-axiom (or (not $x7429) (not $x4686) $x7386)) @x8115 (unit-resolution @x7402 @x3721 $x7429) $x7386)))
-(let (($x7513 (not $x4718)))
-(let (($x8244 (>= (+ ?x204 (* (- 1) (fun_app$c v_b_SP_G_1$ ?v0!17))) 0)))
-(let (($x8196 (not $x8244)))
-(let (($x7753 (<= (+ ?x204 (* (- 1) (fun_app$c v_b_SP_G_1$ ?v1!16))) 0)))
-(let (($x4600 (fun_app$ v_b_Visited_G_1$ ?v1!16)))
-(let (($x4599 (= ?v1!16 v_b_v_G_1$)))
-(let (($x7324 (or $x4599 $x4600)))
-(let (($x4598 (fun_app$ ?x212 ?v1!16)))
-(let (($x7351 (= $x4598 $x7324)))
-(let (($x5310 (or $x5105 $x7351)))
-(let ((@x4543 (monotonicity (rewrite (= (ite $x4599 true $x4600) $x7324)) (= (= $x4598 (ite $x4599 true $x4600)) $x7351))))
-(let ((@x7173 (monotonicity @x4543 (= (or $x5105 (= $x4598 (ite $x4599 true $x4600))) $x5310))))
-(let ((@x7233 (trans @x7173 (rewrite (= $x5310 $x5310)) (= (or $x5105 (= $x4598 (ite $x4599 true $x4600))) $x5310))))
-(let ((@x7234 (mp ((_ quant-inst v_b_Visited_G_1$ v_b_v_G_1$ true ?v1!16) (or $x5105 (= $x4598 (ite $x4599 true $x4600)))) @x7233 $x5310)))
-(let ((@x8188 (symm (monotonicity (symm @x8214 (= ?x212 v_b_Visited_G_2$)) (= $x4598 $x2166)) (= $x2166 $x4598))))
-(let (($x2167 (not $x2166)))
-(let ((@x8189 (hypothesis $x3039)))
-(let ((@x7882 (mp (unit-resolution (def-axiom (or $x3034 $x2167)) @x8189 $x2167) (monotonicity @x8188 (= $x2167 (not $x4598))) (not $x4598))))
-(let ((@x7883 (unit-resolution (def-axiom (or (not $x7351) $x4598 (not $x7324))) @x7882 (unit-resolution @x7234 @x3721 $x7351) (not $x7324))))
-(let (($x7758 (or $x4600 $x7753)))
-(let (($x7761 (or $x3913 $x4600 $x7753)))
-(let (($x7762 (or $x3913 (or $x4600 (>= (+ (fun_app$c v_b_SP_G_1$ ?v1!16) ?x1520) 0)))))
-(let (($x7759 (= (or $x4600 (>= (+ (fun_app$c v_b_SP_G_1$ ?v1!16) ?x1520) 0)) $x7758)))
-(let ((@x7755 (rewrite (= (>= (+ ?x1520 (fun_app$c v_b_SP_G_1$ ?v1!16)) 0) $x7753))))
-(let (($x5376 (>= (+ (fun_app$c v_b_SP_G_1$ ?v1!16) ?x1520) 0)))
-(let (($x7728 (= (+ (fun_app$c v_b_SP_G_1$ ?v1!16) ?x1520) (+ ?x1520 (fun_app$c v_b_SP_G_1$ ?v1!16)))))
-(let ((@x7751 (monotonicity (rewrite $x7728) (= $x5376 (>= (+ ?x1520 (fun_app$c v_b_SP_G_1$ ?v1!16)) 0)))))
-(let ((@x7766 (monotonicity (monotonicity (trans @x7751 @x7755 (= $x5376 $x7753)) $x7759) (= $x7762 (or $x3913 $x7758)))))
-(let ((@x7771 (mp ((_ quant-inst ?v1!16) $x7762) (trans @x7766 (rewrite (= (or $x3913 $x7758) $x7761)) (= $x7762 $x7761)) $x7761)))
-(let ((@x7873 (unit-resolution @x7771 (unit-resolution (def-axiom (or $x4045 $x3908)) @x8164 $x3908) $x7758)))
-(let ((@x7874 (unit-resolution @x7873 (unit-resolution (def-axiom (or $x7324 (not $x4600))) @x7883 (not $x4600)) $x7753)))
-(let ((?x4523 (b_G$ (pair$ v_b_v_G_1$ ?v1!16))))
-(let (($x8224 (<= ?x4523 0)))
-(let (($x8225 (not $x8224)))
-(let (($x8223 (= v_b_v_G_1$ ?v1!16)))
-(let (($x8293 (not $x8223)))
-(let ((@x8351 (unit-resolution (hypothesis (not $x4599)) (symm (hypothesis $x8223) $x4599) false)))
-(let ((@x7877 (unit-resolution (lemma @x8351 (or $x8293 $x4599)) (unit-resolution (def-axiom (or $x7324 (not $x4599))) @x7883 (not $x4599)) $x8293)))
-(let ((@x8233 (rewrite (= (or (not $x3728) (or $x8223 $x8225)) (or (not $x3728) $x8223 $x8225)))))
-(let ((@x8234 (mp ((_ quant-inst v_b_v_G_1$ ?v1!16) (or (not $x3728) (or $x8223 $x8225))) @x8233 (or (not $x3728) $x8223 $x8225))))
-(let ((@x6202 (lemma (unit-resolution @x8234 @x3733 (hypothesis $x8224) (hypothesis $x8293) false) (or $x8225 $x8223))))
-(let (($x3634 (not $x2175)))
-(let ((@x8299 (hypothesis $x3634)))
-(let (($x7624 (<= (+ (v_b_SP_G_2$ ?v0!17) (* (- 1) (fun_app$c v_b_SP_G_1$ ?v0!17))) 0)))
-(let ((@x8305 (unit-resolution (def-axiom (or $x4033 $x3934)) @x8304 $x3934)))
-(let (($x7629 (or $x3939 $x7624)))
-(let (($x5070 (>= (+ (fun_app$c v_b_SP_G_1$ ?v0!17) (* (- 1) (v_b_SP_G_2$ ?v0!17))) 0)))
-(let (($x7620 (>= (+ (* (- 1) (v_b_SP_G_2$ ?v0!17)) (fun_app$c v_b_SP_G_1$ ?v0!17)) 0)))
-(let (($x7616 (= (+ (fun_app$c v_b_SP_G_1$ ?v0!17) (* (- 1) (v_b_SP_G_2$ ?v0!17))) (+ (* (- 1) (v_b_SP_G_2$ ?v0!17)) (fun_app$c v_b_SP_G_1$ ?v0!17)))))
-(let ((@x7628 (trans (monotonicity (rewrite $x7616) (= $x5070 $x7620)) (rewrite (= $x7620 $x7624)) (= $x5070 $x7624))))
-(let ((@x7636 (trans (monotonicity @x7628 (= (or $x3939 $x5070) $x7629)) (rewrite (= $x7629 $x7629)) (= (or $x3939 $x5070) $x7629))))
-(let ((@x8222 (hypothesis $x8244)))
-(let (($x7884 (or $x8196 $x2175 (not (<= (+ ?x204 (* (- 1) (v_b_SP_G_2$ ?v1!16)) ?x4523) 0)) $x8224 (not $x7624))))
-(let ((@x8211 (unit-resolution ((_ th-lemma arith assign-bounds 1 1 1 1) $x7884) @x8222 (unit-resolution (mp ((_ quant-inst ?v0!17) (or $x3939 $x5070)) @x7636 $x7629) @x8305 $x7624) (hypothesis $x8225) @x8299 (not (<= (+ ?x204 (* (- 1) (v_b_SP_G_2$ ?v1!16)) ?x4523) 0)))))
-(let (($x8251 (or (not (= (+ ?x204 (* (- 1) (v_b_SP_G_2$ ?v1!16)) ?x4523) 0)) (<= (+ ?x204 (* (- 1) (v_b_SP_G_2$ ?v1!16)) ?x4523) 0))))
-(let ((@x8191 (unit-resolution ((_ th-lemma arith triangle-eq) $x8251) @x8211 (not (= (+ ?x204 (* (- 1) (v_b_SP_G_2$ ?v1!16)) ?x4523) 0)))))
-(let (($x7559 (>= (+ ?x204 ?x4523 (* (- 1) (fun_app$c v_b_SP_G_1$ ?v1!16))) 0)))
-(let (($x4525 (<= (+ b_Infinity$ (* (- 1) ?x4523)) 0)))
-(let (($x7564 (or $x4525 $x7559)))
-(let (($x7567 (not $x7564)))
-(let (($x7592 (>= (+ (v_b_SP_G_2$ ?v1!16) (* (- 1) (fun_app$c v_b_SP_G_1$ ?v1!16))) 0)))
-(let ((@x8198 ((_ th-lemma arith farkas -1 -1 1 1 1) (hypothesis $x7592) @x8222 (unit-resolution (mp ((_ quant-inst ?v0!17) (or $x3939 $x5070)) @x7636 $x7629) @x8305 $x7624) @x8299 (hypothesis $x7753) false)))
-(let ((@x8177 (unit-resolution (lemma @x8198 (or $x8196 (not $x7592) $x2175 (not $x7753))) @x8222 @x8299 (hypothesis $x7753) (not $x7592))))
-(let (($x8284 (or (not (= (v_b_SP_G_2$ ?v1!16) (fun_app$c v_b_SP_G_1$ ?v1!16))) $x7592)))
-(let ((@x8185 (unit-resolution ((_ th-lemma arith triangle-eq) $x8284) @x8177 (not (= (v_b_SP_G_2$ ?v1!16) (fun_app$c v_b_SP_G_1$ ?v1!16))))))
-(let ((?x4855 (fun_app$c v_b_SP_G_1$ ?v1!16)))
-(let ((?x2171 (v_b_SP_G_2$ ?v1!16)))
-(let (($x4497 (= ?x2171 ?x4855)))
-(let (($x7570 (or $x7567 $x4497)))
-(let (($x7573 (or $x3931 $x7567 $x4497)))
-(let (($x7574 (or $x3931 (or (not (or $x4525 (<= (+ ?x4855 ?x1520 (* (- 1) ?x4523)) 0))) $x4497))))
-(let (($x7571 (= (or (not (or $x4525 (<= (+ ?x4855 ?x1520 (* (- 1) ?x4523)) 0))) $x4497) $x7570)))
-(let (($x4527 (<= (+ ?x4855 ?x1520 (* (- 1) ?x4523)) 0)))
-(let ((@x7554 (rewrite (= (+ ?x4855 ?x1520 (* (- 1) ?x4523)) (+ ?x1520 (* (- 1) ?x4523) ?x4855)))))
-(let ((@x7557 (monotonicity @x7554 (= $x4527 (<= (+ ?x1520 (* (- 1) ?x4523) ?x4855) 0)))))
-(let ((@x7563 (trans @x7557 (rewrite (= (<= (+ ?x1520 (* (- 1) ?x4523) ?x4855) 0) $x7559)) (= $x4527 $x7559))))
-(let ((@x7569 (monotonicity (monotonicity @x7563 (= (or $x4525 $x4527) $x7564)) (= (not (or $x4525 $x4527)) $x7567))))
-(let ((@x7582 (trans (monotonicity (monotonicity @x7569 $x7571) (= $x7574 (or $x3931 $x7570))) (rewrite (= (or $x3931 $x7570) $x7573)) (= $x7574 $x7573))))
-(let ((@x7879 (unit-resolution (unit-resolution (mp ((_ quant-inst ?v1!16) $x7574) @x7582 $x7573) @x8302 $x7570) @x8185 $x7567)))
-(let ((?x7593 (+ ?x204 (* (- 1) ?x2171) ?x4523)))
-(let (($x7596 (= ?x7593 0)))
-(let (($x7599 (or $x4525 $x7559 $x7596)))
-(let (($x7602 (or $x3923 $x4525 $x7559 $x7596)))
-(let (($x7603 (or $x3923 (or $x4525 $x4527 (= (+ ?x204 ?x4523 (* (- 1) ?x2171)) 0)))))
-(let ((@x7598 (monotonicity (rewrite (= (+ ?x204 ?x4523 (* (- 1) ?x2171)) ?x7593)) (= (= (+ ?x204 ?x4523 (* (- 1) ?x2171)) 0) $x7596))))
-(let ((@x7601 (monotonicity @x7563 @x7598 (= (or $x4525 $x4527 (= (+ ?x204 ?x4523 (* (- 1) ?x2171)) 0)) $x7599))))
-(let ((@x7611 (trans (monotonicity @x7601 (= $x7603 (or $x3923 $x7599))) (rewrite (= (or $x3923 $x7599) $x7602)) (= $x7603 $x7602))))
-(let ((@x7886 (unit-resolution (unit-resolution (mp ((_ quant-inst ?v1!16) $x7603) @x7611 $x7602) @x8165 $x7599) (unit-resolution (def-axiom (or $x7564 (not $x7559))) @x7879 (not $x7559)) (unit-resolution (def-axiom (or $x7564 (not $x4525))) @x7879 (not $x4525)) @x8191 false)))
-(let ((@x7891 (unit-resolution (lemma @x7886 (or $x8196 $x8224 $x2175 (not $x7753))) (unit-resolution @x6202 @x7877 $x8225) (unit-resolution (def-axiom (or $x3034 $x3634)) @x8189 $x3634) @x7874 $x8196)))
-(let ((@x8258 (rewrite (= (or $x3818 (or $x202 $x7513 $x8244)) (or $x3818 $x202 $x7513 $x8244)))))
-(let ((@x8259 (mp ((_ quant-inst ?v0!17 v_b_v_G_1$) (or $x3818 (or $x202 $x7513 $x8244))) @x8258 (or $x3818 $x202 $x7513 $x8244))))
-(let ((@x8237 (unit-resolution @x8259 @x6970 (unit-resolution (def-axiom (or $x4045 $x203)) @x8164 $x203) (hypothesis $x4718) (hypothesis $x8196) false)))
-(let ((@x7896 (unit-resolution (def-axiom (or (not $x7386) $x4687 $x4718)) (unit-resolution (lemma @x8237 (or $x7513 $x8244)) @x7891 $x7513) @x8116 $x4687)))
-(let ((?x2172 (v_b_SP_G_2$ ?v0!17)))
-(let (($x8143 (= ?x2172 ?x3394)))
-(let (($x8113 (not $x8143)))
-(let (($x3298 (>= (+ ?x204 (* (- 1) ?x3394)) 0)))
-(let ((@x8142 (unit-resolution ((_ quant-inst v_b_v_G_1$) (or $x3939 $x3298)) @x8305 $x3298)))
-(let (($x7700 (>= (+ ?x2172 (* (- 1) (fun_app$c v_b_SP_G_1$ ?v0!17))) 0)))
-(let ((?x4678 (fun_app$c v_b_SP_G_1$ ?v0!17)))
-(let (($x4679 (= ?x2172 ?x4678)))
-(let ((@x7441 (mp ((_ quant-inst ?v0!17) (or $x3948 (or $x3019 $x4679))) (rewrite (= (or $x3948 (or $x3019 $x4679)) (or $x3948 $x3019 $x4679))) (or $x3948 $x3019 $x4679))))
-(let ((@x7894 (unit-resolution @x7441 (hypothesis $x3943) (unit-resolution (def-axiom (or $x3034 $x2168)) @x8189 $x2168) $x4679)))
-(let (($x7901 (or $x8244 (not (<= (+ ?x2172 (* (- 1) ?x3394)) 0)) (not $x7700) (not $x3298))))
-(let ((@x5877 (unit-resolution ((_ th-lemma arith assign-bounds 1 -1 -1) $x7901) @x7891 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x4679) $x7700)) @x7894 $x7700) @x8142 (not (<= (+ ?x2172 (* (- 1) ?x3394)) 0)))))
-(let ((@x5587 (unit-resolution ((_ th-lemma arith triangle-eq) (or $x8113 (<= (+ ?x2172 (* (- 1) ?x3394)) 0))) @x5877 $x8113)))
-(let ((@x8137 (unit-resolution (hypothesis $x8113) (monotonicity (hypothesis $x4687) $x8143) false)))
-(let ((@x5143 (lemma (unit-resolution (lemma @x8137 (or (not $x4687) $x8143)) @x5587 @x7896 false) (or $x3034 $x3948))))
-(let ((@x7027 (hypothesis $x2154)))
-(let ((@x5873 (hypothesis $x4048)))
-(let ((@x5974 (unit-resolution (def-axiom (or $x4045 $x3926)) @x5873 $x3926)))
-(let ((@x5247 (unit-resolution (def-axiom (or $x4045 $x3918)) @x5873 $x3918)))
-(let ((?x6040 (b_G$ (pair$ v_b_v_G_1$ ?v0!15))))
-(let ((?x6162 (+ ?x204 (* (- 1) ?x2152) ?x6040)))
-(let (($x5552 (= ?x6162 0)))
-(let (($x7159 (not $x5552)))
-(let (($x6237 (<= ?x6162 0)))
-(let (($x7034 (not $x6237)))
-(let ((?x3280 (?v1!7 v_b_v_G_1$)))
-(let ((?x3281 (fun_app$c v_b_SP_G_1$ ?x3280)))
-(let ((?x3282 (* (- 1) ?x3281)))
-(let (($x4633 (<= (+ b_Infinity$ ?x3282) 0)))
-(let (($x6507 (not $x4633)))
-(let (($x4951 (>= (+ ?x204 ?x3282) 0)))
-(let (($x3284 (<= (+ ?x204 ?x3282) 0)))
-(let (($x4138 (not $x3284)))
-(let (($x4244 (fun_app$ v_b_Visited_G_1$ b_Source$)))
-(let (($x5095 (not $x4244)))
-(let (($x3279 (= v_b_v_G_1$ b_Source$)))
-(let (($x6104 (not (= (+ ?x204 (* (- 1) (b_G$ (pair$ ?x3280 v_b_v_G_1$))) ?x3282) 0))))
-(let (($x5949 (or $x3284 (not (fun_app$ v_b_Visited_G_1$ ?x3280)) $x6104)))
-(let (($x4583 (not $x5949)))
-(let (($x4896 (or $x3834 $x3279 $x1522 $x4583)))
-(let (($x4103 (not (= (+ ?x204 ?x3282 (* (- 1) (b_G$ (pair$ ?x3280 v_b_v_G_1$)))) 0))))
-(let (($x4106 (or $x3279 $x1522 (not (or $x3284 (not (fun_app$ v_b_Visited_G_1$ ?x3280)) $x4103)))))
-(let (($x4926 (or $x3834 $x4106)))
-(let (($x4565 (= (not (or $x3284 (not (fun_app$ v_b_Visited_G_1$ ?x3280)) $x4103)) $x4583)))
-(let (($x5863 (= (= (+ ?x204 ?x3282 (* (- 1) (b_G$ (pair$ ?x3280 v_b_v_G_1$)))) 0) (= (+ ?x204 (* (- 1) (b_G$ (pair$ ?x3280 v_b_v_G_1$))) ?x3282) 0))))
-(let (($x5947 (= (+ ?x204 ?x3282 (* (- 1) (b_G$ (pair$ ?x3280 v_b_v_G_1$)))) (+ ?x204 (* (- 1) (b_G$ (pair$ ?x3280 v_b_v_G_1$))) ?x3282))))
-(let ((@x5489 (monotonicity (monotonicity (monotonicity (rewrite $x5947) $x5863) (= $x4103 $x6104)) (= (or $x3284 (not (fun_app$ v_b_Visited_G_1$ ?x3280)) $x4103) $x5949))))
-(let ((@x4548 (monotonicity (monotonicity (monotonicity @x5489 $x4565) (= $x4106 (or $x3279 $x1522 $x4583))) (= $x4926 (or $x3834 (or $x3279 $x1522 $x4583))))))
-(let ((@x4802 (trans @x4548 (rewrite (= (or $x3834 (or $x3279 $x1522 $x4583)) $x4896)) (= $x4926 $x4896))))
-(let ((@x6065 (unit-resolution (mp ((_ quant-inst v_b_v_G_1$) $x4926) @x4802 $x4896) @x4406 (unit-resolution (def-axiom (or $x4045 $x1525)) @x5873 $x1525) (unit-resolution (def-axiom (or $x5949 $x4138)) (hypothesis $x3284) $x5949) $x3279)))
-(let ((@x5493 (mp (unit-resolution (def-axiom (or $x4045 $x203)) @x5873 $x203) (monotonicity (monotonicity @x6065 (= $x202 $x4244)) (= $x203 $x5095)) $x5095)))
-(let ((@x5435 (unit-resolution (def-axiom (or $x4042 $x2122 $x4036)) (unit-resolution (lemma @x6749 (or $x2121 $x3923 $x3931)) @x5247 @x5974 $x2121) (unit-resolution (def-axiom (or $x4045 $x4039)) @x5873 $x4039) $x4036)))
-(let ((@x7140 (symm (commutativity (= (= b_Source$ ?v0!15) (= ?v0!15 b_Source$))) (= (= ?v0!15 b_Source$) (= b_Source$ ?v0!15)))))
-(let ((@x7142 (monotonicity @x7140 (= (not (= ?v0!15 b_Source$)) (not (= b_Source$ ?v0!15))))))
-(let (($x6380 (= ?v0!15 b_Source$)))
-(let (($x6990 (not $x6380)))
-(let (($x6954 (or $x6380 (fun_app$ v_b_Visited_G_1$ ?v0!15))))
-(let ((?x6005 (fun_app$a (fun_app$b (fun_upd$ v_b_Visited_G_1$) b_Source$) true)))
-(let (($x6887 (fun_app$ ?x6005 ?v0!15)))
-(let (($x6951 (= $x6887 $x6954)))
-(let (($x6959 (or $x5105 $x6951)))
-(let (($x6960 (or $x5105 (= $x6887 (ite $x6380 true (fun_app$ v_b_Visited_G_1$ ?v0!15))))))
-(let (($x6957 (= (= $x6887 (ite $x6380 true (fun_app$ v_b_Visited_G_1$ ?v0!15))) $x6951)))
-(let ((@x6956 (rewrite (= (ite $x6380 true (fun_app$ v_b_Visited_G_1$ ?v0!15)) $x6954))))
-(let ((@x6989 (trans (monotonicity (monotonicity @x6956 $x6957) (= $x6960 $x6959)) (rewrite (= $x6959 $x6959)) (= $x6960 $x6959))))
-(let (($x6793 (= (fun_app$b (fun_upd$ v_b_Visited_G_1$) b_Source$) (fun_app$b (fun_upd$ v_b_Visited_G_1$) v_b_v_G_1$))))
-(let ((@x5780 (hypothesis $x3279)))
-(let ((@x5781 (symm @x5780 (= b_Source$ v_b_v_G_1$))))
-(let ((@x6803 (trans (monotonicity (monotonicity @x5781 $x6793) (= ?x6005 ?x212)) (symm (hypothesis $x213) (= ?x212 v_b_Visited_G_2$)) (= ?x6005 v_b_Visited_G_2$))))
-(let ((@x7131 (symm (monotonicity @x6803 (= $x6887 (fun_app$ v_b_Visited_G_2$ ?v0!15))) (= (fun_app$ v_b_Visited_G_2$ ?v0!15) $x6887))))
-(let ((@x7133 (monotonicity @x7131 (= (not (fun_app$ v_b_Visited_G_2$ ?v0!15)) (not $x6887)))))
-(let (($x5938 (fun_app$ v_b_Visited_G_2$ ?v0!15)))
-(let (($x5943 (not $x5938)))
-(let ((?x5971 (fun_app$c v_b_SP_G_1$ ?v0!15)))
-(let (($x6392 (>= ?x5971 0)))
-(let ((@x5502 (unit-resolution (def-axiom (or $x4057 $x3804)) @x5453 $x3804)))
-(let ((@x7119 ((_ th-lemma arith assign-bounds -1 1) (or (not (>= (+ ?x2152 (* (- 1) ?x5971)) 0)) $x2153 (not $x6392)))))
-(let ((@x7120 (unit-resolution @x7119 (unit-resolution ((_ quant-inst ?v0!15) (or $x3809 $x6392)) @x5502 $x6392) @x7027 (not (>= (+ ?x2152 (* (- 1) ?x5971)) 0)))))
-(let ((@x7123 ((_ th-lemma arith triangle-eq) (or (not (= ?x2152 ?x5971)) (>= (+ ?x2152 (* (- 1) ?x5971)) 0)))))
-(let (($x5994 (= (or $x3948 (or $x5943 (= ?x2152 ?x5971))) (or $x3948 $x5943 (= ?x2152 ?x5971)))))
-(let ((@x6100 (mp ((_ quant-inst ?v0!15) (or $x3948 (or $x5943 (= ?x2152 ?x5971)))) (rewrite $x5994) (or $x3948 $x5943 (= ?x2152 ?x5971)))))
-(let ((@x7127 (unit-resolution (unit-resolution @x6100 (hypothesis $x3943) (or $x5943 (= ?x2152 ?x5971))) (unit-resolution @x7123 @x7120 (not (= ?x2152 ?x5971))) $x5943)))
-(let ((@x7135 (unit-resolution (def-axiom (or (not $x6951) $x6887 (not $x6954))) (mp @x7127 @x7133 (not $x6887)) (unit-resolution (mp ((_ quant-inst v_b_Visited_G_1$ b_Source$ true ?v0!15) $x6960) @x6989 $x6959) @x3721 $x6951) (not $x6954))))
-(let ((@x7143 (mp (unit-resolution (def-axiom (or $x6954 $x6990)) @x7135 $x6990) @x7142 (not (= b_Source$ ?v0!15)))))
-(let ((?x7024 (b_G$ (pair$ b_Source$ ?v0!15))))
-(let (($x7048 (<= ?x7024 0)))
-(let (($x7084 (>= (+ ?x6040 (* (- 1) ?x7024)) 0)))
-(let ((@x7145 (monotonicity @x5781 (= (pair$ b_Source$ ?v0!15) (pair$ v_b_v_G_1$ ?v0!15)))))
-(let ((@x7152 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not (= ?x6040 ?x7024)) $x7084)) (symm (monotonicity @x7145 (= ?x7024 ?x6040)) (= ?x6040 ?x7024)) $x7084)))
-(let (($x6014 (<= (+ ?x119 ?x1520) 0)))
-(let ((@x5742 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not (= ?x119 ?x204)) $x6014)) (symm (monotonicity @x5780 (= ?x204 ?x119)) (= ?x119 ?x204)) $x6014)))
-(let (($x3478 (>= ?x119 0)))
-(let ((@x6523 (unit-resolution ((_ th-lemma arith triangle-eq) (or $x3213 $x3478)) @x5456 $x3478)))
-(let (($x5984 (>= (+ ?x204 (* (- 1) ?x5971) ?x6040) 0)))
-(let (($x6042 (<= (+ b_Infinity$ (* (- 1) ?x6040)) 0)))
-(let (($x5545 (or $x6042 $x5984)))
-(let (($x5577 (not $x5545)))
-(let (($x5972 (= ?x2152 ?x5971)))
-(let (($x6132 (or $x5577 $x5972)))
-(let (($x6394 (or $x3931 $x5577 $x5972)))
-(let (($x6213 (or $x3931 (or (not (or $x6042 (<= (+ ?x5971 ?x1520 (* (- 1) ?x6040)) 0))) $x5972))))
-(let (($x6240 (= (or (not (or $x6042 (<= (+ ?x5971 ?x1520 (* (- 1) ?x6040)) 0))) $x5972) $x6132)))
-(let (($x6044 (<= (+ ?x5971 ?x1520 (* (- 1) ?x6040)) 0)))
-(let ((@x6156 (rewrite (= (+ ?x5971 ?x1520 (* (- 1) ?x6040)) (+ ?x1520 ?x5971 (* (- 1) ?x6040))))))
-(let ((@x5992 (monotonicity @x6156 (= $x6044 (<= (+ ?x1520 ?x5971 (* (- 1) ?x6040)) 0)))))
-(let ((@x5651 (trans @x5992 (rewrite (= (<= (+ ?x1520 ?x5971 (* (- 1) ?x6040)) 0) $x5984)) (= $x6044 $x5984))))
-(let ((@x5893 (monotonicity (monotonicity @x5651 (= (or $x6042 $x6044) $x5545)) (= (not (or $x6042 $x6044)) $x5577))))
-(let ((@x5887 (trans (monotonicity (monotonicity @x5893 $x6240) (= $x6213 (or $x3931 $x6132))) (rewrite (= (or $x3931 $x6132) $x6394)) (= $x6213 $x6394))))
-(let ((@x7154 (unit-resolution (unit-resolution (mp ((_ quant-inst ?v0!15) $x6213) @x5887 $x6394) @x6086 $x6132) (unit-resolution @x7123 @x7120 (not $x5972)) $x5577)))
-(let (($x5495 (or $x6042 $x5984 $x5552)))
-(let (($x5652 (or $x3923 $x6042 $x5984 $x5552)))
-(let (($x5496 (or $x3923 (or $x6042 $x6044 (= (+ ?x204 ?x6040 (* (- 1) ?x2152)) 0)))))
-(let ((@x5529 (monotonicity (rewrite (= (+ ?x204 ?x6040 (* (- 1) ?x2152)) ?x6162)) (= (= (+ ?x204 ?x6040 (* (- 1) ?x2152)) 0) $x5552))))
-(let ((@x5649 (monotonicity @x5651 @x5529 (= (or $x6042 $x6044 (= (+ ?x204 ?x6040 (* (- 1) ?x2152)) 0)) $x5495))))
-(let ((@x5906 (trans (monotonicity @x5649 (= $x5496 (or $x3923 $x5495))) (rewrite (= (or $x3923 $x5495) $x5652)) (= $x5496 $x5652))))
-(let ((@x7158 (unit-resolution (unit-resolution (mp ((_ quant-inst ?v0!15) $x5496) @x5906 $x5652) @x4512 $x5495) (unit-resolution (def-axiom (or $x5545 (not $x5984))) @x7154 (not $x5984)) (unit-resolution (def-axiom (or $x5545 (not $x6042))) @x7154 (not $x6042)) $x5552)))
-(let ((@x7166 (unit-resolution ((_ th-lemma arith assign-bounds 1 1 1 1 1) (or $x7048 (not $x7084) $x2153 $x7034 (not $x6014) (not $x3478))) (unit-resolution ((_ th-lemma arith triangle-eq) (or $x7159 $x6237)) @x7158 $x6237) @x6523 @x5742 @x7027 @x7152 $x7048)))
-(let (($x7062 (= (or (not $x3728) (or (= b_Source$ ?v0!15) (not $x7048))) (or (not $x3728) (= b_Source$ ?v0!15) (not $x7048)))))
-(let ((@x7064 (mp ((_ quant-inst b_Source$ ?v0!15) (or (not $x3728) (or (= b_Source$ ?v0!15) (not $x7048)))) (rewrite $x7062) (or (not $x3728) (= b_Source$ ?v0!15) (not $x7048)))))
-(let ((@x7168 (unit-resolution (unit-resolution @x7064 @x3733 (or (= b_Source$ ?v0!15) (not $x7048))) @x7166 @x7143 false)))
-(let ((@x6972 (unit-resolution (lemma @x7168 (or $x3948 $x2153 (not $x3279) $x3196 $x3923 $x3931)) @x6065 @x7027 (unit-resolution (def-axiom (or $x4045 $x213)) @x5873 $x213) @x5247 @x5974 $x3948)))
-(let ((@x6196 (unit-resolution (def-axiom (or $x4030 $x2139 $x4024)) (unit-resolution (def-axiom (or $x4021 $x3943)) @x6972 $x4021) (unit-resolution (def-axiom (or $x4033 $x4027)) @x5435 $x4027) $x2139)))
-(let (($x6189 (>= (+ ?x6353 (* (- 1) (b_G$ (pair$ b_Source$ ?v0!14)))) 0)))
-(let ((@x5870 (monotonicity @x5780 (= (pair$ v_b_v_G_1$ ?v0!14) (pair$ b_Source$ ?v0!14)))))
-(let ((@x6892 ((_ th-lemma arith triangle-eq) (or (not (= ?x6353 (b_G$ (pair$ b_Source$ ?v0!14)))) $x6189))))
-(let ((@x6893 (unit-resolution @x6892 (monotonicity @x5870 (= ?x6353 (b_G$ (pair$ b_Source$ ?v0!14)))) $x6189)))
-(let ((?x6449 (b_G$ (pair$ b_Source$ ?v0!14))))
-(let (($x6497 (<= ?x6449 0)))
-(let (($x6702 (not $x6497)))
-(let (($x6238 (= b_Source$ ?v0!14)))
-(let (($x6704 (not $x6238)))
-(let ((@x5923 (monotonicity (symm (hypothesis $x6238) (= ?v0!14 b_Source$)) (= ?x2136 ?x119))))
-(let ((@x5826 (monotonicity (symm (hypothesis $x6238) (= ?v0!14 b_Source$)) (= ?x2135 ?x243))))
-(let ((@x5929 (trans (trans @x5826 (monotonicity @x5781 (= ?x243 ?x3394)) (= ?x2135 ?x3394)) (hypothesis $x3329) (= ?x2135 ?x204))))
-(let ((@x6701 (trans (trans @x5929 (monotonicity @x5780 (= ?x204 ?x119)) (= ?x2135 ?x119)) (symm @x5923 (= ?x119 ?x2136)) $x2137)))
-(let ((@x6754 (lemma (unit-resolution @x5806 @x6701 false) (or $x6704 $x2137 (not $x3329) (not $x3279)))))
-(let ((@x6858 (rewrite (= (or (not $x3728) (or $x6238 $x6702)) (or (not $x3728) $x6238 $x6702)))))
-(let ((@x6859 (mp ((_ quant-inst b_Source$ ?v0!14) (or (not $x3728) (or $x6238 $x6702))) @x6858 (or (not $x3728) $x6238 $x6702))))
-(let ((@x6879 (unit-resolution @x6859 @x3733 (unit-resolution @x6754 @x5806 @x6230 @x5780 $x6704) $x6702)))
-(let (($x5364 (= ?v0!14 b_Source$)))
-(let (($x6300 (or $x5364 $x6262)))
-(let (($x6211 (fun_app$ ?x6005 ?v0!14)))
-(let (($x6870 (= $x6211 $x6300)))
-(let (($x6873 (or $x5105 $x6870)))
-(let ((@x6868 (monotonicity (rewrite (= (ite $x5364 true $x6262) $x6300)) (= (= $x6211 (ite $x5364 true $x6262)) $x6870))))
-(let ((@x6944 (monotonicity @x6868 (= (or $x5105 (= $x6211 (ite $x5364 true $x6262))) $x6873))))
-(let ((@x6946 (trans @x6944 (rewrite (= $x6873 $x6873)) (= (or $x5105 (= $x6211 (ite $x5364 true $x6262))) $x6873))))
-(let ((@x6947 (mp ((_ quant-inst v_b_Visited_G_1$ b_Source$ true ?v0!14) (or $x5105 (= $x6211 (ite $x5364 true $x6262)))) @x6946 $x6873)))
-(let ((@x6885 (mp (hypothesis $x2133) (symm (monotonicity @x6803 (= $x6211 $x2133)) (= $x2133 $x6211)) $x6211)))
-(let ((@x6923 (unit-resolution (def-axiom (or (not $x6870) (not $x6211) $x6300)) @x6885 (unit-resolution @x6947 @x3721 $x6870) $x6300)))
-(let (($x6603 (>= (+ ?x119 (* (- 1) ?x2136)) 0)))
-(let ((@x6948 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not (= ?x6449 0)) $x6497)) (hypothesis $x6702) (not (= ?x6449 0)))))
-(let (($x6718 (= (or $x4439 (or $x6704 (= ?x6449 0))) (or $x4439 $x6704 (= ?x6449 0)))))
-(let ((@x5740 (mp ((_ quant-inst b_Source$ ?v0!14) (or $x4439 (or $x6704 (= ?x6449 0)))) (rewrite $x6718) (or $x4439 $x6704 (= ?x6449 0)))))
-(let ((@x6975 (unit-resolution (unit-resolution @x5740 @x3727 (or $x6704 (= ?x6449 0))) @x6948 $x6704)))
-(let ((@x6981 (mp @x6975 (monotonicity (commutativity (= $x6238 $x5364)) (= $x6704 (not $x5364))) (not $x5364))))
-(let ((@x6938 (unit-resolution (def-axiom (or (not $x6300) $x5364 $x6262)) @x6981 (hypothesis $x6300) $x6262)))
-(let ((@x6605 (rewrite (= (or $x3818 (or $x4244 $x6006 $x6603)) (or $x3818 $x4244 $x6006 $x6603)))))
-(let ((@x6664 (mp ((_ quant-inst ?v0!14 b_Source$) (or $x3818 (or $x4244 $x6006 $x6603))) @x6605 (or $x3818 $x4244 $x6006 $x6603))))
-(let ((@x6832 (unit-resolution ((_ th-lemma arith farkas 1 1) (or (>= ?x6449 0) $x6497)) (hypothesis $x6702) (>= ?x6449 0))))
-(let ((@x6833 ((_ th-lemma arith farkas 1 1 -1 -1 1) @x6832 (hypothesis $x6189) @x6842 (hypothesis $x6014) (unit-resolution @x6664 @x6970 (hypothesis $x5095) @x6938 $x6603) false)))
-(let ((@x6924 (unit-resolution (lemma @x6833 (or $x6497 (not $x6189) $x5623 (not $x6014) $x4244 (not $x6300))) @x6923 @x6879 @x6877 @x5742 (hypothesis $x5095) @x6893 false)))
-(let ((@x6199 (unit-resolution (lemma @x6924 (or $x2134 $x4244 $x3196 (not $x3279) $x3931 $x2137)) (unit-resolution (def-axiom (or $x2138 $x3646)) @x6196 $x3646) (unit-resolution (def-axiom (or $x2138 $x2133)) @x6196 $x2133) (unit-resolution (def-axiom (or $x4045 $x213)) @x5873 $x213) @x6065 @x5974 @x5493 false)))
-(let ((@x7353 (unit-resolution ((_ th-lemma arith farkas 1 1) (or $x3284 $x4951)) (unit-resolution (lemma @x6199 (or $x4045 $x2153 $x4138)) @x5873 @x7027 $x4138) $x4951)))
-(let ((@x7331 (unit-resolution ((_ th-lemma arith assign-bounds 1 1) (or $x6507 $x1522 (not $x4951))) @x7353 (unit-resolution (def-axiom (or $x4045 $x1525)) @x5873 $x1525) $x6507)))
-(let (($x6440 (= v_b_v_G_1$ ?v0!15)))
-(let (($x6441 (<= ?x6040 0)))
-(let (($x6477 (<= (+ ?x119 ?x3282) 0)))
-(let (($x4627 (= ?x3280 b_Source$)))
-(let ((?x5260 (+ ?x3281 (* (- 1) (fun_app$c v_b_SP_G_1$ (?v1!7 ?x3280))) (* (- 1) (b_G$ (pair$ (?v1!7 ?x3280) ?x3280))))))
-(let (($x5252 (<= (+ ?x3281 (* (- 1) (fun_app$c v_b_SP_G_1$ (?v1!7 ?x3280)))) 0)))
-(let (($x4638 (or $x5252 (not (fun_app$ v_b_Visited_G_1$ (?v1!7 ?x3280))) (not (= ?x5260 0)))))
-(let ((@x7029 (hypothesis $x4951)))
-(let ((@x7028 (hypothesis $x6237)))
-(let ((@x7030 (hypothesis (not $x5252))))
-(let (($x6656 (>= (fun_app$c v_b_SP_G_1$ (?v1!7 ?x3280)) 0)))
-(let ((@x6836 (unit-resolution ((_ th-lemma arith assign-bounds 1 1 1 1 1) (or $x6441 (not $x4951) (not $x6656) $x5252 $x2153 $x7034)) @x7030 @x7029 @x7028 @x7027 (unit-resolution ((_ quant-inst (?v1!7 ?x3280)) (or $x3809 $x6656)) @x5502 $x6656) $x6441)))
-(let (($x6469 (= (or (not $x3728) (or $x6440 (not $x6441))) (or (not $x3728) $x6440 (not $x6441)))))
-(let ((@x6472 (mp ((_ quant-inst v_b_v_G_1$ ?v0!15) (or (not $x3728) (or $x6440 (not $x6441)))) (rewrite $x6469) (or (not $x3728) $x6440 (not $x6441)))))
-(let ((@x7025 (unit-resolution (unit-resolution @x6472 @x3733 (or $x6440 (not $x6441))) (hypothesis $x6441) $x6440)))
-(let (($x6466 (= ?x6040 0)))
-(let (($x7038 (not $x6466)))
-(let (($x7031 (not (>= ?x6040 0))))
-(let ((@x7037 (unit-resolution ((_ th-lemma arith assign-bounds 1 1 1 1 1) (or $x7031 (not $x4951) (not $x6656) $x5252 $x2153 $x7034)) @x7030 @x7029 @x7028 @x7027 (unit-resolution ((_ quant-inst (?v1!7 ?x3280)) (or $x3809 $x6656)) @x5502 $x6656) $x7031)))
-(let ((@x6480 (rewrite (= (or $x4439 (or (not $x6440) $x6466)) (or $x4439 (not $x6440) $x6466)))))
-(let ((@x6481 (mp ((_ quant-inst v_b_v_G_1$ ?v0!15) (or $x4439 (or (not $x6440) $x6466))) @x6480 (or $x4439 (not $x6440) $x6466))))
-(let ((@x7043 (unit-resolution (unit-resolution @x6481 @x3727 (or (not $x6440) $x6466)) (unit-resolution ((_ th-lemma arith triangle-eq) (or $x7038 (>= ?x6040 0))) @x7037 $x7038) @x7025 false)))
-(let ((@x6866 (unit-resolution (lemma @x7043 (or (not $x6441) $x5252 (not $x4951) $x7034 $x2153)) @x6836 @x7030 @x7029 @x7028 @x7027 false)))
-(let ((@x6500 (unit-resolution (lemma @x6866 (or $x5252 (not $x4951) $x7034 $x2153)) @x7028 @x7029 @x7027 $x5252)))
-(let (($x5562 (= (or $x3834 (or $x4627 $x4633 (not $x4638))) (or $x3834 $x4627 $x4633 (not $x4638)))))
-(let ((@x5564 (mp ((_ quant-inst (?v1!7 v_b_v_G_1$)) (or $x3834 (or $x4627 $x4633 (not $x4638)))) (rewrite $x5562) (or $x3834 $x4627 $x4633 (not $x4638)))))
-(let ((@x6514 (unit-resolution (unit-resolution @x5564 @x4406 (hypothesis $x6507) (or $x4627 (not $x4638))) (unit-resolution (def-axiom (or $x4638 (not $x5252))) @x6500 $x4638) $x4627)))
-(let ((@x6521 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not (= ?x119 ?x3281)) $x6477)) (symm (monotonicity @x6514 (= ?x3281 ?x119)) (= ?x119 ?x3281)) $x6477)))
-(let ((@x6529 (unit-resolution ((_ th-lemma arith assign-bounds 1 1 1 1 1) (or $x6441 (not $x4951) $x2153 $x7034 (not $x3478) (not $x6477))) @x7028 @x6523 @x7029 @x7027 @x6521 $x6441)))
-(let ((@x6534 (unit-resolution (unit-resolution @x6472 @x3733 (or $x6440 (not $x6441))) @x6529 $x6440)))
-(let ((@x6536 (unit-resolution ((_ th-lemma arith assign-bounds 1 -1 -1 1 -1) (or $x7031 (not $x4951) $x2153 $x7034 (not $x3478) (not $x6477))) @x7028 @x6523 @x7029 @x7027 @x6521 $x7031)))
-(let ((@x6538 (unit-resolution (unit-resolution @x6481 @x3727 (or (not $x6440) $x6466)) (unit-resolution ((_ th-lemma arith triangle-eq) (or $x7038 (>= ?x6040 0))) @x6536 $x7038) @x6534 false)))
-(let ((@x7332 (unit-resolution (lemma @x6538 (or $x7034 (not $x4951) $x2153 $x4633)) @x7353 @x7027 @x7331 $x7034)))
-(let ((@x7339 (unit-resolution (mp ((_ quant-inst ?v0!15) $x5496) @x5906 $x5652) @x4512 (hypothesis $x7159) $x5545)))
-(let ((@x7377 (unit-resolution @x7339 (unit-resolution (def-axiom (or $x5545 (not $x5984))) @x7154 (not $x5984)) (unit-resolution (def-axiom (or $x5545 (not $x6042))) @x7154 (not $x6042)) false)))
-(let ((@x7334 (unit-resolution (lemma @x7377 (or $x5552 $x3923 $x3931 $x2153)) (unit-resolution ((_ th-lemma arith triangle-eq) (or $x7159 $x6237)) @x7332 $x7159) @x5247 @x5974 @x7027 false)))
-(let (($x4282 (= ?x243 ?x119)))
-(let (($x4455 (<= (b_G$ (pair$ v_b_v_G_1$ b_Source$)) 0)))
-(let (($x4147 (>= ?x204 0)))
-(let (($x3479 (<= ?x119 0)))
-(let (($x4279 (<= (+ ?x119 ?x1520 (* (- 1) (b_G$ (pair$ v_b_v_G_1$ b_Source$)))) 0)))
-(let (($x4277 (<= (+ b_Infinity$ (* (- 1) (b_G$ (pair$ v_b_v_G_1$ b_Source$)))) 0)))
-(let (($x4281 (not (or $x4277 $x4279))))
-(let (($x4909 (not $x4282)))
-(let ((@x4883 (hypothesis $x913)))
-(let ((@x4907 (mp (hypothesis $x4282) (monotonicity (hypothesis $x120) (= $x4282 $x244)) $x244)))
-(let ((@x6051 (unit-resolution (lemma (unit-resolution @x4883 @x4907 false) (or $x4909 $x244 $x3213)) @x5456 (or $x4909 $x244))))
-(let ((@x5597 (mp ((_ quant-inst b_Source$) (or $x3931 (or $x4281 $x4282))) (rewrite (= (or $x3931 (or $x4281 $x4282)) (or $x3931 $x4281 $x4282))) (or $x3931 $x4281 $x4282))))
-(let ((@x5875 (unit-resolution (unit-resolution @x5597 @x6086 (or $x4281 $x4282)) (unit-resolution @x6051 @x4883 $x4909) $x4281)))
-(let ((@x5520 (unit-resolution (def-axiom (or (or $x4277 $x4279) (not $x4279))) @x5875 (not $x4279))))
-(let ((@x6090 (unit-resolution ((_ th-lemma arith assign-bounds 1 1 1) (or $x4455 (not $x3479) (not $x4147) $x4279)) @x5520 (unit-resolution ((_ th-lemma arith triangle-eq) (or $x3213 $x3479)) @x5456 $x3479) (unit-resolution ((_ quant-inst v_b_v_G_1$) (or $x3809 $x4147)) @x5502 $x4147) $x4455)))
-(let (($x5519 (= (or (not $x3728) (or $x3279 (not $x4455))) (or (not $x3728) $x3279 (not $x4455)))))
-(let ((@x6055 (mp ((_ quant-inst v_b_v_G_1$ b_Source$) (or (not $x3728) (or $x3279 (not $x4455)))) (rewrite $x5519) (or (not $x3728) $x3279 (not $x4455)))))
-(let ((@x6223 (symm (unit-resolution @x6055 @x3733 @x6090 $x3279) (= b_Source$ v_b_v_G_1$))))
-(let ((@x5727 (trans (trans (monotonicity @x6223 (= ?x243 ?x3394)) @x6230 (= ?x243 ?x204)) (monotonicity (unit-resolution @x6055 @x3733 @x6090 $x3279) (= ?x204 ?x119)) $x4282)))
-(let ((@x5312 (lemma (unit-resolution @x4883 (trans @x5727 @x5456 $x244) false) (or $x244 $x3931))))
-(let ((@x8382 (unit-resolution (def-axiom (or $x4018 $x913 $x2154 $x4012)) (unit-resolution @x5312 @x8302 $x244) (unit-resolution (lemma @x7334 (or $x4045 $x2153)) @x8164 $x2153) (or $x4018 $x4012))))
-(let ((@x9064 (unit-resolution @x8382 (unit-resolution (def-axiom (or $x4021 $x4015)) @x10488 $x4015) $x4012)))
-(let ((@x10157 (unit-resolution (def-axiom (or $x4006 $x3039 $x4000)) (unit-resolution (def-axiom (or $x4009 $x4003)) @x9064 $x4003) (unit-resolution @x5143 @x10489 $x3034) $x4000)))
-(let ((@x8593 (hypothesis $x3988)))
-(let ((?x4618 (fun_app$c v_b_SP_G_1$ ?v0!20)))
-(let (($x4870 (<= (+ ?x4618 (* (- 1) (fun_app$c v_b_SP_G_1$ (?v1!7 ?v0!20)))) 0)))
-(let ((@x5730 (hypothesis $x2221)))
-(let (($x8567 (>= (+ (v_b_SP_G_2$ ?v0!20) (* (- 1) ?x4618)) 0)))
-(let ((?x2217 (v_b_SP_G_2$ ?v0!20)))
-(let (($x4625 (= ?x2217 ?x4618)))
-(let ((?x4660 (b_G$ (pair$ v_b_v_G_1$ ?v0!20))))
-(let ((?x4661 (* (- 1) ?x4660)))
-(let ((?x3395 (* (- 1) ?x3394)))
-(let ((?x8452 (+ ?x2217 ?x3395 ?x4661)))
-(let (($x8388 (<= ?x8452 0)))
-(let (($x8780 (>= ?x8452 0)))
-(let ((@x6097 (unit-resolution ((_ th-lemma arith farkas 1 1) (or $x8780 $x8388)) (hypothesis (not $x8388)) $x8780)))
-(let (($x4663 (<= (+ b_Infinity$ ?x4661) 0)))
-(let (($x4368 (fun_app$ v_b_Visited_G_2$ v_b_v_G_1$)))
-(let ((@x8557 (symm (monotonicity @x8214 (= $x4368 (fun_app$ ?x212 v_b_v_G_1$))) (= (fun_app$ ?x212 v_b_v_G_1$) $x4368))))
-(let (($x3413 (fun_app$ ?x212 v_b_v_G_1$)))
-(let (($x3709 (forall ((?v0 B_Vertex_bool_fun$) (?v1 B_Vertex$) (?v2 Bool) )(!(= (fun_app$ (fun_app$a (fun_app$b (fun_upd$ ?v0) ?v1) ?v2) ?v1) ?v2) :pattern ( (fun_app$a (fun_app$b (fun_upd$ ?v0) ?v1) ?v2) )))
-))
-(let (($x1092 (forall ((?v0 B_Vertex_bool_fun$) (?v1 B_Vertex$) (?v2 Bool) )(= (fun_app$ (fun_app$a (fun_app$b (fun_upd$ ?v0) ?v1) ?v2) ?v1) ?v2))
-))
-(let (($x1089 (= (fun_app$ (fun_app$a (fun_app$b (fun_upd$ ?2) ?1) ?0) ?1) ?0)))
-(let (($x49 (forall ((?v0 B_Vertex_bool_fun$) (?v1 B_Vertex$) (?v2 Bool) )(= (fun_app$ (fun_app$a (fun_app$b (fun_upd$ ?v0) ?v1) ?v2) ?v1) ?v2))
-))
-(let (($x48 (= (fun_app$ (fun_app$a (fun_app$b (fun_upd$ ?2) ?1) ?0) ?1) ?0)))
-(let ((@x1097 (mp (mp (asserted $x49) (rewrite* (= $x49 $x49)) $x49) (quant-intro (rewrite (= $x48 $x1089)) (= $x49 $x1092)) $x1092)))
-(let ((@x3714 (mp (mp~ @x1097 (nnf-pos (refl (~ $x1089 $x1089)) (~ $x1092 $x1092)) $x1092) (quant-intro (refl (= $x1089 $x1089)) (= $x1092 $x3709)) $x3709)))
-(let (($x4545 (or (not $x3709) $x3413)))
-(let ((@x6188 (monotonicity (rewrite (= (= $x3413 true) $x3413)) (= (or (not $x3709) (= $x3413 true)) $x4545))))
-(let ((@x5812 (trans @x6188 (rewrite (= $x4545 $x4545)) (= (or (not $x3709) (= $x3413 true)) $x4545))))
-(let ((@x8745 (unit-resolution (mp ((_ quant-inst v_b_Visited_G_1$ v_b_v_G_1$ true) (or (not $x3709) (= $x3413 true))) @x5812 $x4545) @x3714 $x3413)))
-(let ((@x6205 (hypothesis $x3968)))
-(let (($x4369 (not $x4368)))
-(let (($x9030 (or $x3973 $x4369 $x4663 $x8388)))
-(let (($x9031 (or $x3973 (or $x4369 $x4663 (>= (+ ?x4660 ?x3394 (* (- 1) ?x2217)) 0)))))
-(let (($x8458 (= (or $x4369 $x4663 (>= (+ ?x4660 ?x3394 (* (- 1) ?x2217)) 0)) (or $x4369 $x4663 $x8388))))
-(let (($x8517 (>= (+ ?x4660 ?x3394 (* (- 1) ?x2217)) 0)))
-(let ((@x8896 (rewrite (= (+ ?x4660 ?x3394 (* (- 1) ?x2217)) (+ (* (- 1) ?x2217) ?x3394 ?x4660)))))
-(let ((@x8448 (monotonicity @x8896 (= $x8517 (>= (+ (* (- 1) ?x2217) ?x3394 ?x4660) 0)))))
-(let ((@x8455 (trans @x8448 (rewrite (= (>= (+ (* (- 1) ?x2217) ?x3394 ?x4660) 0) $x8388)) (= $x8517 $x8388))))
-(let ((@x9127 (monotonicity (monotonicity @x8455 $x8458) (= $x9031 (or $x3973 (or $x4369 $x4663 $x8388))))))
-(let ((@x8184 (trans @x9127 (rewrite (= (or $x3973 (or $x4369 $x4663 $x8388)) $x9030)) (= $x9031 $x9030))))
-(let ((@x6333 (unit-resolution (mp ((_ quant-inst ?v0!20 v_b_v_G_1$) $x9031) @x8184 $x9030) @x6205 (mp @x8745 @x8557 $x4368) (hypothesis (not $x8388)) $x4663)))
-(let ((@x5997 (unit-resolution ((_ th-lemma arith assign-bounds 1 -1) (or $x6014 (not $x4147) (not $x3479))) (unit-resolution ((_ quant-inst v_b_v_G_1$) (or $x3809 $x4147)) @x5502 $x4147) (unit-resolution ((_ th-lemma arith triangle-eq) (or $x3213 $x3479)) @x5456 $x3479) $x6014)))
-(let (($x6242 (= ?x204 ?x3394)))
-(let ((@x9345 (mp (unit-resolution (mp ((_ quant-inst v_b_v_G_1$) $x4517) @x5481 $x5387) @x8302 @x6229 $x3329) (symm (commutativity (= $x6242 $x3329)) (= $x3329 $x6242)) $x6242)))
-(let ((@x8936 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x6242) (<= (+ ?x204 ?x3395) 0))) @x9345 (<= (+ ?x204 ?x3395) 0))))
-(let ((@x5629 (lemma ((_ th-lemma arith farkas 1 1 1 1 1 1) @x8936 @x5997 @x6523 @x6333 @x6097 @x5730 false) (or $x8388 $x2220 $x3973))))
-(let ((@x10145 (unit-resolution @x5629 (unit-resolution (def-axiom (or $x3985 $x3968)) @x8593 $x3968) @x5730 $x8388)))
-(let (($x8926 (<= (+ ?x2217 ?x3395) 0)))
-(let (($x8453 (= ?x8452 0)))
-(let ((?x2218 (* (- 1) ?x2217)))
-(let ((?x8793 (+ ?x204 ?x2218 ?x4660)))
-(let (($x8622 (<= ?x8793 0)))
-(let (($x8798 (= ?x8793 0)))
-(let (($x8551 (>= (+ ?x204 (* (- 1) ?x4618) ?x4660) 0)))
-(let (($x8822 (or $x4663 $x8551)))
-(let (($x8685 (not $x8822)))
-(let (($x8574 (or $x8685 $x4625)))
-(let (($x8550 (or $x3931 $x8685 $x4625)))
-(let (($x8571 (or $x3931 (or (not (or $x4663 (<= (+ ?x4618 ?x1520 ?x4661) 0))) $x4625))))
-(let ((@x9375 (monotonicity (rewrite (= (+ ?x4618 ?x1520 ?x4661) (+ ?x1520 ?x4618 ?x4661))) (= (<= (+ ?x4618 ?x1520 ?x4661) 0) (<= (+ ?x1520 ?x4618 ?x4661) 0)))))
-(let ((@x8823 (trans @x9375 (rewrite (= (<= (+ ?x1520 ?x4618 ?x4661) 0) $x8551)) (= (<= (+ ?x4618 ?x1520 ?x4661) 0) $x8551))))
-(let ((@x8684 (monotonicity @x8823 (= (or $x4663 (<= (+ ?x4618 ?x1520 ?x4661) 0)) $x8822))))
-(let ((@x8549 (monotonicity @x8684 (= (not (or $x4663 (<= (+ ?x4618 ?x1520 ?x4661) 0))) $x8685))))
-(let ((@x8576 (monotonicity @x8549 (= (or (not (or $x4663 (<= (+ ?x4618 ?x1520 ?x4661) 0))) $x4625) $x8574))))
-(let ((@x8764 (trans (monotonicity @x8576 (= $x8571 (or $x3931 $x8574))) (rewrite (= (or $x3931 $x8574) $x8550)) (= $x8571 $x8550))))
-(let ((@x10339 (unit-resolution (unit-resolution (mp ((_ quant-inst ?v0!20) $x8571) @x8764 $x8550) @x8302 $x8574) (hypothesis (not $x4625)) $x8685)))
-(let ((@x10165 (unit-resolution (def-axiom (or $x8822 (not $x4663))) (hypothesis $x8685) (not $x4663))))
-(let ((@x10166 (unit-resolution (def-axiom (or $x8822 (not $x8551))) (hypothesis $x8685) (not $x8551))))
-(let (($x8800 (or $x4663 $x8551 $x8798)))
-(let (($x8659 (or $x3923 $x4663 $x8551 $x8798)))
-(let (($x4665 (<= (+ ?x4618 ?x1520 ?x4661) 0)))
-(let (($x9296 (or $x3923 (or $x4663 $x4665 (= (+ ?x204 ?x4660 ?x2218) 0)))))
-(let ((@x8797 (monotonicity (rewrite (= (+ ?x204 ?x4660 ?x2218) ?x8793)) (= (= (+ ?x204 ?x4660 ?x2218) 0) $x8798))))
-(let ((@x8638 (monotonicity @x8823 @x8797 (= (or $x4663 $x4665 (= (+ ?x204 ?x4660 ?x2218) 0)) $x8800))))
-(let ((@x9312 (trans (monotonicity @x8638 (= $x9296 (or $x3923 $x8800))) (rewrite (= (or $x3923 $x8800) $x8659)) (= $x9296 $x8659))))
-(let ((@x10167 (unit-resolution (unit-resolution (mp ((_ quant-inst ?v0!20) $x9296) @x9312 $x8659) @x8165 $x8800) @x10166 @x10165 (hypothesis (not $x8798)) false)))
-(let ((@x10348 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x8798) $x8622)) (unit-resolution (lemma @x10167 (or $x8822 $x8798)) @x10339 $x8798) $x8622)))
-(let ((@x10388 (unit-resolution ((_ th-lemma arith assign-bounds 1 -1) (or (not $x8622) $x8780 (not $x3298))) @x8142 (or (not $x8622) $x8780))))
-(let ((@x10484 (unit-resolution ((_ th-lemma arith triangle-eq) (or $x8453 (not $x8388) (not $x8780))) (hypothesis $x8388) (or $x8453 (not $x8780)))))
-(let ((@x11844 (hypothesis $x3977)))
-(let (($x8695 (not $x8453)))
-(let (($x8690 (or $x3982 $x8926 $x4369 $x8695)))
-(let (($x4741 (>= (+ ?x3394 ?x2218) 0)))
-(let (($x8692 (or $x3982 (or $x4741 $x4369 (not (= (+ ?x3394 ?x2218 ?x4660) 0))))))
-(let (($x9019 (= (or $x4741 $x4369 (not (= (+ ?x3394 ?x2218 ?x4660) 0))) (or $x8926 $x4369 $x8695))))
-(let ((@x8997 (monotonicity (rewrite (= (+ ?x3394 ?x2218 ?x4660) (+ ?x2218 ?x3394 ?x4660))) (= (= (+ ?x3394 ?x2218 ?x4660) 0) (= (+ ?x2218 ?x3394 ?x4660) 0)))))
-(let ((@x9034 (trans @x8997 (rewrite (= (= (+ ?x2218 ?x3394 ?x4660) 0) $x8453)) (= (= (+ ?x3394 ?x2218 ?x4660) 0) $x8453))))
-(let ((@x8397 (monotonicity (rewrite (= (+ ?x3394 ?x2218) (+ ?x2218 ?x3394))) (= $x4741 (>= (+ ?x2218 ?x3394) 0)))))
-(let ((@x9139 (trans @x8397 (rewrite (= (>= (+ ?x2218 ?x3394) 0) $x8926)) (= $x4741 $x8926))))
-(let ((@x9020 (monotonicity @x9139 (monotonicity @x9034 (= (not (= (+ ?x3394 ?x2218 ?x4660) 0)) $x8695)) $x9019)))
-(let ((@x8404 (trans (monotonicity @x9020 (= $x8692 (or $x3982 (or $x8926 $x4369 $x8695)))) (rewrite (= (or $x3982 (or $x8926 $x4369 $x8695)) $x8690)) (= $x8692 $x8690))))
-(let ((@x10486 (unit-resolution (mp ((_ quant-inst v_b_v_G_1$) $x8692) @x8404 $x8690) @x11844 (mp @x8745 @x8557 $x4368) (or $x8926 $x8695))))
-(let ((@x10481 (unit-resolution @x10486 (unit-resolution @x10484 (unit-resolution @x10388 @x10348 $x8780) $x8453) $x8926)))
-(let (($x6460 (not (<= ?x4660 0))))
-(let ((@x10539 (commutativity (= (= v_b_v_G_1$ ?v0!20) (= ?v0!20 v_b_v_G_1$)))))
-(let ((@x10627 (monotonicity (symm @x10539 (= (= ?v0!20 v_b_v_G_1$) (= v_b_v_G_1$ ?v0!20))) (= (not (= ?v0!20 v_b_v_G_1$)) (not (= v_b_v_G_1$ ?v0!20))))))
-(let (($x7719 (= ?v0!20 v_b_v_G_1$)))
-(let (($x10690 (not $x7719)))
-(let (($x10582 (or $x7719 (fun_app$ v_b_Visited_G_1$ ?v0!20))))
-(let (($x7724 (fun_app$ ?x212 ?v0!20)))
-(let (($x10917 (= $x7724 $x10582)))
-(let (($x10865 (or $x5105 $x10917)))
-(let (($x10888 (or $x5105 (= $x7724 (ite $x7719 true (fun_app$ v_b_Visited_G_1$ ?v0!20))))))
-(let (($x10747 (= (= $x7724 (ite $x7719 true (fun_app$ v_b_Visited_G_1$ ?v0!20))) $x10917)))
-(let ((@x9484 (rewrite (= (ite $x7719 true (fun_app$ v_b_Visited_G_1$ ?v0!20)) $x10582))))
-(let ((@x10687 (trans (monotonicity (monotonicity @x9484 $x10747) (= $x10888 $x10865)) (rewrite (= $x10865 $x10865)) (= $x10888 $x10865))))
-(let ((@x8210 (symm @x8214 (= ?x212 v_b_Visited_G_2$))))
-(let ((@x10510 (symm (monotonicity @x8210 (= $x7724 (fun_app$ v_b_Visited_G_2$ ?v0!20))) (= (fun_app$ v_b_Visited_G_2$ ?v0!20) $x7724))))
-(let ((@x10542 (monotonicity @x10510 (= (not (fun_app$ v_b_Visited_G_2$ ?v0!20)) (not $x7724)))))
-(let (($x4503 (fun_app$ v_b_Visited_G_2$ ?v0!20)))
-(let (($x4504 (not $x4503)))
-(let ((@x10611 (mp ((_ quant-inst ?v0!20) (or $x3948 (or $x4504 $x4625))) (rewrite (= (or $x3948 (or $x4504 $x4625)) (or $x3948 $x4504 $x4625))) (or $x3948 $x4504 $x4625))))
-(let ((@x10491 (unit-resolution (unit-resolution @x10611 @x10489 (or $x4504 $x4625)) (hypothesis (not $x4625)) $x4504)))
-(let ((@x10518 (unit-resolution (def-axiom (or (not $x10917) $x7724 (not $x10582))) (mp @x10491 @x10542 (not $x7724)) (unit-resolution (mp ((_ quant-inst v_b_Visited_G_1$ v_b_v_G_1$ true ?v0!20) $x10888) @x10687 $x10865) @x3721 $x10917) (not $x10582))))
-(let ((@x10563 (mp (unit-resolution (def-axiom (or $x10582 $x10690)) @x10518 $x10690) @x10627 (not (= v_b_v_G_1$ ?v0!20)))))
-(let (($x9114 (= (or (not $x3728) (or (= v_b_v_G_1$ ?v0!20) $x6460)) (or (not $x3728) (= v_b_v_G_1$ ?v0!20) $x6460))))
-(let ((@x9115 (mp ((_ quant-inst v_b_v_G_1$ ?v0!20) (or (not $x3728) (or (= v_b_v_G_1$ ?v0!20) $x6460))) (rewrite $x9114) (or (not $x3728) (= v_b_v_G_1$ ?v0!20) $x6460))))
-(let ((@x10566 (unit-resolution (unit-resolution @x9115 @x3733 (or (= v_b_v_G_1$ ?v0!20) $x6460)) @x10563 $x6460)))
-(let ((@x10568 (lemma ((_ th-lemma arith farkas -1 -1 1 1) @x8142 @x10566 @x10348 @x10481 false) (or $x4625 $x3982 (not $x8388)))))
-(let ((@x10170 (unit-resolution @x10568 (unit-resolution (def-axiom (or $x3985 $x3977)) @x8593 $x3977) @x10145 $x4625)))
-(let ((?x4866 (?v1!7 ?v0!20)))
-(let (($x8671 (fun_app$ v_b_Visited_G_2$ ?x4866)))
-(let (($x8672 (not $x8671)))
-(let ((@x11435 (symm (monotonicity @x8210 (= (fun_app$ ?x212 ?x4866) $x8671)) (= $x8671 (fun_app$ ?x212 ?x4866)))))
-(let (($x6693 (<= (+ b_Infinity$ (* (- 1) (b_G$ (pair$ ?x4866 ?v0!20)))) 0)))
-(let (($x11835 (not $x6693)))
-(let ((?x4874 (b_G$ (pair$ ?x4866 ?v0!20))))
-(let ((?x4875 (* (- 1) ?x4874)))
-(let ((?x4876 (+ ?x4618 (* (- 1) (fun_app$c v_b_SP_G_1$ ?x4866)) ?x4875)))
-(let (($x8645 (>= ?x4876 0)))
-(let (($x4877 (= ?x4876 0)))
-(let (($x4878 (not $x4877)))
-(let (($x4879 (or $x4870 (not (fun_app$ v_b_Visited_G_1$ ?x4866)) $x4878)))
-(let (($x4880 (not $x4879)))
-(let (($x4865 (<= (+ b_Infinity$ (* (- 1) ?x4618)) 0)))
-(let (($x8667 (not $x4865)))
-(let ((@x8893 (hypothesis $x8567)))
-(let ((@x8402 (lemma ((_ th-lemma arith farkas 1 -1 1) @x8893 (hypothesis $x4865) @x5730 false) (or $x8667 (not $x8567) $x2220))))
-(let ((@x9038 (rewrite (= (or $x3834 (or $x2215 $x4865 $x4880)) (or $x3834 $x2215 $x4865 $x4880)))))
-(let ((@x9039 (mp ((_ quant-inst ?v0!20) (or $x3834 (or $x2215 $x4865 $x4880))) @x9038 (or $x3834 $x2215 $x4865 $x4880))))
-(let ((@x9273 (unit-resolution (unit-resolution @x9039 @x4406 (hypothesis $x2216) (or $x4865 $x4880)) (unit-resolution @x8402 @x8893 @x5730 $x8667) $x4880)))
-(let ((@x11282 (unit-resolution ((_ th-lemma arith triangle-eq) (or $x4878 $x8645)) (unit-resolution (def-axiom (or $x4879 $x4877)) @x9273 $x4877) $x8645)))
-(let ((?x4867 (fun_app$c v_b_SP_G_1$ ?x4866)))
-(let (($x5337 (>= ?x4867 0)))
-(let ((@x11717 (unit-resolution ((_ th-lemma arith assign-bounds -1 -1 -1 -1) (or $x11835 (not $x8645) $x2220 (not $x8567) (not $x5337))) (unit-resolution ((_ quant-inst (?v1!7 ?v0!20)) (or $x3809 $x5337)) @x5502 $x5337) @x5730 @x8893 @x11282 $x11835)))
-(let (($x9233 (<= ?x4876 0)))
-(let ((@x11182 (unit-resolution ((_ th-lemma arith triangle-eq) (or $x4878 $x9233)) (unit-resolution (def-axiom (or $x4879 $x4877)) @x9273 $x4877) $x9233)))
-(let ((?x8643 (v_b_SP_G_2$ ?x4866)))
-(let ((?x9203 (* (- 1) ?x8643)))
-(let ((?x9103 (+ ?x2217 ?x4875 ?x9203)))
-(let (($x10503 (>= ?x9103 0)))
-(let (($x6233 (>= (+ ?x4867 ?x9203) 0)))
-(let ((@x11833 (unit-resolution ((_ th-lemma arith assign-bounds 1 1 1) (or $x10503 (not $x6233) (not $x8645) (not $x8567))) (hypothesis $x8645) @x8893 (unit-resolution ((_ quant-inst (?v1!7 ?v0!20)) (or $x3939 $x6233)) @x8305 $x6233) $x10503)))
-(let (($x10448 (<= (+ ?x2217 ?x9203) 0)))
-(let (($x11011 (= ?x9103 0)))
-(let (($x10912 (<= ?x9103 0)))
-(let (($x10744 (or $x8672 $x6693 $x10912)))
-(let (($x10746 (or $x3973 $x8672 $x6693 $x10912)))
-(let (($x10750 (or $x3973 (or $x8672 $x6693 (>= (+ ?x4874 ?x8643 ?x2218) 0)))))
-(let ((@x9876 (monotonicity (rewrite (= (+ ?x4874 ?x8643 ?x2218) (+ ?x2218 ?x4874 ?x8643))) (= (>= (+ ?x4874 ?x8643 ?x2218) 0) (>= (+ ?x2218 ?x4874 ?x8643) 0)))))
-(let ((@x10867 (trans @x9876 (rewrite (= (>= (+ ?x2218 ?x4874 ?x8643) 0) $x10912)) (= (>= (+ ?x4874 ?x8643 ?x2218) 0) $x10912))))
-(let ((@x10745 (monotonicity @x10867 (= (or $x8672 $x6693 (>= (+ ?x4874 ?x8643 ?x2218) 0)) $x10744))))
-(let ((@x10734 (trans (monotonicity @x10745 (= $x10750 (or $x3973 $x10744))) (rewrite (= (or $x3973 $x10744) $x10746)) (= $x10750 $x10746))))
-(let ((@x11838 (unit-resolution (unit-resolution (mp ((_ quant-inst ?v0!20 (?v1!7 ?v0!20)) $x10750) @x10734 $x10746) @x6205 $x10744) (hypothesis $x8671) (hypothesis $x11835) $x10912)))
-(let ((@x11843 (unit-resolution ((_ th-lemma arith triangle-eq) (or $x11011 (not $x10912) (not $x10503))) @x11833 @x11838 $x11011)))
-(let (($x10804 (not $x11011)))
-(let (($x11040 (or $x10448 $x8672 $x10804)))
-(let (($x10301 (or $x3982 $x10448 $x8672 $x10804)))
-(let (($x6994 (>= (+ ?x8643 ?x2218) 0)))
-(let (($x10896 (or $x3982 (or $x6994 $x8672 (not (= (+ ?x8643 ?x2218 ?x4874) 0))))))
-(let ((@x11010 (monotonicity (rewrite (= (+ ?x8643 ?x2218 ?x4874) (+ ?x2218 ?x4874 ?x8643))) (= (= (+ ?x8643 ?x2218 ?x4874) 0) (= (+ ?x2218 ?x4874 ?x8643) 0)))))
-(let ((@x10803 (trans @x11010 (rewrite (= (= (+ ?x2218 ?x4874 ?x8643) 0) $x11011)) (= (= (+ ?x8643 ?x2218 ?x4874) 0) $x11011))))
-(let ((@x10440 (monotonicity (rewrite (= (+ ?x8643 ?x2218) (+ ?x2218 ?x8643))) (= $x6994 (>= (+ ?x2218 ?x8643) 0)))))
-(let ((@x10354 (trans @x10440 (rewrite (= (>= (+ ?x2218 ?x8643) 0) $x10448)) (= $x6994 $x10448))))
-(let ((@x10595 (monotonicity @x10354 (monotonicity @x10803 (= (not (= (+ ?x8643 ?x2218 ?x4874) 0)) $x10804)) (= (or $x6994 $x8672 (not (= (+ ?x8643 ?x2218 ?x4874) 0))) $x11040))))
-(let ((@x10685 (trans (monotonicity @x10595 (= $x10896 (or $x3982 $x11040))) (rewrite (= (or $x3982 $x11040) $x10301)) (= $x10896 $x10301))))
-(let ((@x11846 (unit-resolution (unit-resolution (mp ((_ quant-inst (?v1!7 ?v0!20)) $x10896) @x10685 $x10301) @x11844 $x11040) @x11843 (hypothesis $x8671) $x10448)))
-(let ((@x11850 (lemma ((_ th-lemma arith farkas -1 1 -1 1) @x11846 @x11833 (hypothesis $x9233) (hypothesis (not $x4870)) false) (or $x8672 (not $x9233) $x4870 $x3982 (not $x8645) (not $x8567) $x6693 $x3973))))
-(let ((@x11185 (unit-resolution @x11850 @x11182 (hypothesis (not $x4870)) @x11844 @x11282 @x8893 @x11717 @x6205 $x8672)))
-(let ((@x11550 (mp @x11185 (monotonicity @x11435 (= $x8672 (not (fun_app$ ?x212 ?x4866)))) (not (fun_app$ ?x212 ?x4866)))))
-(let (($x11789 (fun_app$ ?x212 ?x4866)))
-(let (($x4871 (fun_app$ v_b_Visited_G_1$ ?x4866)))
-(let (($x11792 (or (= ?x4866 v_b_v_G_1$) $x4871)))
-(let (($x11795 (= $x11789 $x11792)))
-(let (($x11638 (or $x5105 $x11795)))
-(let (($x11557 (= (or $x5105 (= $x11789 (ite (= ?x4866 v_b_v_G_1$) true $x4871))) $x11638)))
-(let ((@x11797 (monotonicity (rewrite (= (ite (= ?x4866 v_b_v_G_1$) true $x4871) $x11792)) (= (= $x11789 (ite (= ?x4866 v_b_v_G_1$) true $x4871)) $x11795))))
-(let ((@x11556 ((_ quant-inst v_b_Visited_G_1$ v_b_v_G_1$ true (?v1!7 ?v0!20)) (or $x5105 (= $x11789 (ite (= ?x4866 v_b_v_G_1$) true $x4871))))))
-(let ((@x11621 (mp @x11556 (trans (monotonicity @x11797 $x11557) (rewrite (= $x11638 $x11638)) $x11557) $x11638)))
-(let ((@x11379 (unit-resolution (def-axiom (or $x11792 (not $x4871))) (unit-resolution (def-axiom (or $x4879 $x4871)) @x9273 $x4871) $x11792)))
-(let ((@x11588 (unit-resolution (def-axiom (or (not $x11795) $x11789 (not $x11792))) @x11379 (or (not $x11795) $x11789))))
-(let ((@x11409 (unit-resolution (unit-resolution @x11588 (unit-resolution @x11621 @x3721 $x11795) $x11789) @x11550 false)))
-(let ((@x9681 (unit-resolution (lemma @x11409 (or (not $x8567) $x4870 $x3982 $x3973 $x2220 $x2215)) (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x4625) $x8567)) @x10170 $x8567) (unit-resolution (def-axiom (or $x3985 $x3977)) @x8593 $x3977) (unit-resolution (def-axiom (or $x3985 $x3968)) @x8593 $x3968) @x5730 (unit-resolution (def-axiom (or $x3985 $x2216)) @x8593 $x2216) $x4870)))
-(let ((@x9302 (unit-resolution @x8402 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x4625) $x8567)) @x10170 $x8567) @x5730 $x8667)))
-(let ((@x10155 (unit-resolution @x9039 @x4406 (unit-resolution (def-axiom (or $x3985 $x2216)) @x8593 $x2216) (or $x4865 $x4880))))
-(let ((@x10236 (unit-resolution (def-axiom (or $x4879 (not $x4870))) (unit-resolution @x10155 @x9302 $x4880) @x9681 false)))
-(let ((@x10357 (unit-resolution (lemma @x10236 (or $x3985 $x2220)) (unit-resolution (def-axiom (or $x3985 $x2221)) @x8593 $x2221) @x8593 false)))
-(let ((@x8697 (unit-resolution (def-axiom (or $x3994 $x3085 $x3988)) (lemma @x10357 $x3985) (unit-resolution (def-axiom (or $x3997 $x3991)) @x10157 $x3991) $x3085)))
-(let (($x2195 (not $x2194)))
-(let (($x4939 (<= (+ b_Infinity$ (* (- 1) (b_G$ (pair$ v_b_v_G_1$ ?v0!19)))) 0)))
-(let ((?x4936 (b_G$ (pair$ v_b_v_G_1$ ?v0!19))))
-(let ((?x4520 (fun_app$c v_b_SP_G_1$ ?v0!19)))
-(let ((?x4919 (* (- 1) ?x4520)))
-(let (($x7104 (>= (+ ?x204 ?x4919 ?x4936) 0)))
-(let (($x8037 (>= (+ ?x2191 (* (- 1) ?x4936)) 0)))
-(let (($x4552 (= ?v1!18 v_b_v_G_1$)))
-(let (($x4560 (fun_app$ v_b_Visited_G_1$ ?v1!18)))
-(let (($x4584 (not $x4560)))
-(let (($x3626 (not $x2202)))
-(let ((@x9184 (hypothesis $x3626)))
-(let (($x8491 (>= (+ ?x2198 (* (- 1) (fun_app$c v_b_SP_G_1$ ?v1!18))) 0)))
-(let ((?x4539 (fun_app$c v_b_SP_G_1$ ?v1!18)))
-(let (($x4537 (= ?x2198 ?x4539)))
-(let ((@x8063 (mp ((_ quant-inst ?v1!18) (or $x3948 (or $x3065 $x4537))) (rewrite (= (or $x3948 (or $x3065 $x4537)) (or $x3948 $x3065 $x4537))) (or $x3948 $x3065 $x4537))))
-(let ((@x10071 (unit-resolution @x8063 @x10489 (unit-resolution (def-axiom (or $x3080 $x2189)) (hypothesis $x3085) $x2189) $x4537)))
-(let (($x9200 (<= (+ (v_b_SP_G_2$ ?v0!19) ?x4919) 0)))
-(let (($x9219 (or $x3939 $x9200)))
-(let ((@x6015 (monotonicity (rewrite (= (+ ?x4520 ?x2200) (+ ?x2200 ?x4520))) (= (>= (+ ?x4520 ?x2200) 0) (>= (+ ?x2200 ?x4520) 0)))))
-(let ((@x9261 (trans @x6015 (rewrite (= (>= (+ ?x2200 ?x4520) 0) $x9200)) (= (>= (+ ?x4520 ?x2200) 0) $x9200))))
-(let ((@x8768 (trans (monotonicity @x9261 (= (or $x3939 (>= (+ ?x4520 ?x2200) 0)) $x9219)) (rewrite (= $x9219 $x9219)) (= (or $x3939 (>= (+ ?x4520 ?x2200) 0)) $x9219))))
-(let ((@x9207 (unit-resolution (mp ((_ quant-inst ?v0!19) (or $x3939 (>= (+ ?x4520 ?x2200) 0))) @x8768 $x9219) @x8305 $x9200)))
-(let ((@x9209 ((_ th-lemma arith farkas 1 -1 -1 1) (hypothesis (>= (+ ?x2191 ?x4919 ?x4539) 0)) @x9207 @x9184 (hypothesis $x8491) false)))
-(let ((@x9157 (lemma @x9209 (or (not (>= (+ ?x2191 ?x4919 ?x4539) 0)) $x2202 (not $x8491)))))
-(let ((@x10062 (unit-resolution @x9157 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x4537) $x8491)) @x10071 $x8491) @x9184 (not (>= (+ ?x2191 ?x4919 ?x4539) 0)))))
-(let (($x8396 (>= (+ ?x2191 ?x4919 ?x4539) 0)))
-(let (($x7250 (or $x3826 $x4584 $x2194 $x8396)))
-(let (($x7254 (or $x3826 (or $x4584 $x2194 (>= (+ ?x2191 ?x4539 ?x4919) 0)))))
-(let (($x7281 (= (or $x4584 $x2194 (>= (+ ?x2191 ?x4539 ?x4919) 0)) (or $x4584 $x2194 $x8396))))
-(let ((@x7279 (monotonicity (rewrite (= (+ ?x2191 ?x4539 ?x4919) (+ ?x2191 ?x4919 ?x4539))) (= (>= (+ ?x2191 ?x4539 ?x4919) 0) $x8396))))
-(let ((@x7262 (monotonicity (monotonicity @x7279 $x7281) (= $x7254 (or $x3826 (or $x4584 $x2194 $x8396))))))
-(let ((@x7275 (trans @x7262 (rewrite (= (or $x3826 (or $x4584 $x2194 $x8396)) $x7250)) (= $x7254 $x7250))))
-(let ((@x10063 (unit-resolution (mp ((_ quant-inst ?v0!19 ?v1!18) $x7254) @x7275 $x7250) @x6172 (unit-resolution (def-axiom (or $x3080 $x2195)) (hypothesis $x3085) $x2195) (or $x4584 $x8396))))
-(let (($x8064 (or $x4552 $x4560)))
-(let (($x4569 (fun_app$ ?x212 ?v1!18)))
-(let (($x7915 (= $x4569 $x8064)))
-(let (($x5802 (or $x5105 $x7915)))
-(let ((@x7808 (monotonicity (rewrite (= (ite $x4552 true $x4560) $x8064)) (= (= $x4569 (ite $x4552 true $x4560)) $x7915))))
-(let ((@x8409 (monotonicity @x7808 (= (or $x5105 (= $x4569 (ite $x4552 true $x4560))) $x5802))))
-(let ((@x8439 (trans @x8409 (rewrite (= $x5802 $x5802)) (= (or $x5105 (= $x4569 (ite $x4552 true $x4560))) $x5802))))
-(let ((@x9247 (mp ((_ quant-inst v_b_Visited_G_1$ v_b_v_G_1$ true ?v1!18) (or $x5105 (= $x4569 (ite $x4552 true $x4560)))) @x8439 $x5802)))
-(let ((@x10467 (mp (unit-resolution (def-axiom (or $x3080 $x2189)) (hypothesis $x3085) $x2189) (symm (monotonicity @x8210 (= $x4569 $x2189)) (= $x2189 $x4569)) $x4569)))
-(let ((@x10247 (unit-resolution (def-axiom (or (not $x7915) (not $x4569) $x8064)) @x10467 (unit-resolution @x9247 @x3721 $x7915) $x8064)))
-(let ((@x10216 (unit-resolution (def-axiom (or (not $x8064) $x4552 $x4560)) @x10247 (unit-resolution @x10063 @x10062 $x4584) $x4552)))
-(let ((@x10847 (monotonicity @x10216 (= (pair$ ?v1!18 ?v0!19) (pair$ v_b_v_G_1$ ?v0!19)))))
-(let ((@x10848 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not (= ?x2191 ?x4936)) $x8037)) (monotonicity @x10847 (= ?x2191 ?x4936)) $x8037)))
-(let (($x8038 (>= (+ ?x2198 ?x3395) 0)))
-(let ((@x10005 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not (= ?x2198 ?x3394)) $x8038)) (monotonicity @x10216 (= ?x2198 ?x3394)) $x8038)))
-(let ((@x8468 ((_ th-lemma arith farkas -1 1 -1 -1 1 1) (hypothesis $x8038) @x8936 (hypothesis $x8037) (hypothesis $x7104) @x9207 @x9184 false)))
-(let ((@x9577 (unit-resolution (lemma @x8468 (or (not $x7104) (not $x8038) (not $x8037) $x2202)) @x10005 @x9184 @x10848 (not $x7104))))
-(let ((@x8883 ((_ th-lemma arith farkas -1 1 -1 -1 1) (hypothesis $x8038) @x8936 (hypothesis $x8037) (hypothesis (>= (+ ?x204 ?x2200 ?x4936) 0)) @x9184 false)))
-(let ((@x9326 (lemma @x8883 (or (not (>= (+ ?x204 ?x2200 ?x4936) 0)) (not $x8038) (not $x8037) $x2202))))
-(let ((@x9398 (unit-resolution @x9326 @x10848 @x9184 @x10005 (not (>= (+ ?x204 ?x2200 ?x4936) 0)))))
-(let ((?x7186 (+ ?x204 ?x2200 ?x4936)))
-(let (($x7258 (>= ?x7186 0)))
-(let ((@x8781 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not (= ?x7186 0)) $x7258)) @x9398 (not (= ?x7186 0)))))
-(let (($x7111 (= ?x7186 0)))
-(let (($x7222 (or $x4939 $x7104 $x7111)))
-(let (($x7201 (or $x3923 $x4939 $x7104 $x7111)))
-(let (($x4941 (<= (+ ?x4520 ?x1520 (* (- 1) ?x4936)) 0)))
-(let (($x7208 (or $x3923 (or $x4939 $x4941 (= (+ ?x204 ?x4936 ?x2200) 0)))))
-(let ((@x7190 (monotonicity (rewrite (= (+ ?x204 ?x4936 ?x2200) ?x7186)) (= (= (+ ?x204 ?x4936 ?x2200) 0) $x7111))))
-(let ((@x7077 (rewrite (= (+ ?x4520 ?x1520 (* (- 1) ?x4936)) (+ ?x1520 ?x4520 (* (- 1) ?x4936))))))
-(let ((@x7001 (monotonicity @x7077 (= $x4941 (<= (+ ?x1520 ?x4520 (* (- 1) ?x4936)) 0)))))
-(let ((@x7110 (trans @x7001 (rewrite (= (<= (+ ?x1520 ?x4520 (* (- 1) ?x4936)) 0) $x7104)) (= $x4941 $x7104))))
-(let ((@x7200 (monotonicity @x7110 @x7190 (= (or $x4939 $x4941 (= (+ ?x204 ?x4936 ?x2200) 0)) $x7222))))
-(let ((@x7230 (trans (monotonicity @x7200 (= $x7208 (or $x3923 $x7222))) (rewrite (= (or $x3923 $x7222) $x7201)) (= $x7208 $x7201))))
-(let ((@x8782 (unit-resolution (unit-resolution (mp ((_ quant-inst ?v0!19) $x7208) @x7230 $x7201) @x8165 $x7222) @x8781 @x9577 $x4939)))
-(let ((@x7246 ((_ th-lemma arith farkas 1 -1 1) @x10848 @x8782 (unit-resolution (def-axiom (or $x3080 $x2195)) (hypothesis $x3085) $x2195) false)))
-(unit-resolution (lemma @x7246 (or $x3080 $x2202)) (unit-resolution (def-axiom (or $x3080 $x3626)) @x8697 $x3626) @x8697 false)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
-
+e3d9ca1db0784558fae8ee48f75145c34159be22 3044 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) )))
+))
+(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$) )(!(let ((?x303 (v_b_SP_G_2$ ?v0)))
+(let ((?x1263 (* (- 1) ?x303)))
+(let ((?x273 (v_b_SP_G_2$ ?v1)))
+(let ((?x155 (b_G$ (pair$ ?v1 ?v0))))
+(let (($x1282 (>= (+ ?x155 ?x273 ?x1263) 0)))
+(let (($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) )))
+))
+(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 ((@x8092 (hypothesis $x3740)))
+(let ((@x3222 (def-axiom (or $x3737 $x3720))))
+(let (($x4161 (>= ?x3104 0)))
+(let (($x3703 (forall ((?v0 B_Vertex$) )(!(let ((?x273 (v_b_SP_G_2$ ?v0)))
+(>= ?x273 0)) :pattern ( (v_b_SP_G_2$ ?v0) )))
+))
+(let (($x3743 (or $x2811 $x3740)))
+(let (($x3746 (not $x3743)))
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+(let (($x301 (fun_app$ v_b_Visited_G_2$ ?v0)))
+(let (($x2768 (not $x301)))
+(let (($x291 (fun_app$ v_b_Visited_G_2$ ?v1)))
+(or $x291 $x2768 $x1262))))) :pattern ( (v_b_SP_G_2$ ?v1) (v_b_SP_G_2$ ?v0) )))
+))
+(let (($x3717 (not $x3712)))
+(let (($x3749 (or $x3717 $x3746)))
+(let (($x3752 (not $x3749)))
+(let (($x1869 (>= (+ (v_b_SP_G_2$ ?v1!16) (* (- 1) (v_b_SP_G_2$ ?v0!17))) 0)))
+(let (($x1862 (fun_app$ v_b_Visited_G_2$ ?v0!17)))
+(let (($x2745 (not $x1862)))
+(let (($x1860 (fun_app$ v_b_Visited_G_2$ ?v1!16)))
+(let (($x2760 (or $x1860 $x2745 $x1869)))
+(let (($x2765 (not $x2760)))
+(let (($x3755 (or $x2765 $x3752)))
+(let (($x3758 (not $x3755)))
+(let (($x3708 (not $x3703)))
+(let (($x3761 (or $x3708 $x3758)))
+(let (($x3764 (not $x3761)))
+(let ((?x1846 (v_b_SP_G_2$ ?v0!15)))
+(let (($x1847 (>= ?x1846 0)))
+(let ((?x257 (fun_app$c v_b_SP_G_1$ v_b_v_G_1$)))
+(let (($x3904 (>= ?x257 0)))
+(let (($x3556 (forall ((?v0 B_Vertex$) )(!(let ((?x174 (fun_app$c v_b_SP_G_1$ ?v0)))
+(>= ?x174 0)) :pattern ( (fun_app$c v_b_SP_G_1$ ?v0) )))
+))
+(let (($x1848 (not $x1847)))
+(let (($x3767 (or $x1848 $x3764)))
+(let (($x3770 (not $x3767)))
+(let ((?x296 (v_b_SP_G_2$ b_Source$)))
+(let (($x297 (= ?x296 0)))
+(let (($x773 (not $x297)))
+(let (($x3773 (or $x773 $x3770)))
+(let (($x3776 (not $x3773)))
+(let (($x3779 (or $x773 $x3776)))
+(let (($x3782 (not $x3779)))
+(let (($x3695 (forall ((?v0 B_Vertex$) )(!(let ((?x174 (fun_app$c v_b_SP_G_1$ ?v0)))
+(let ((?x273 (v_b_SP_G_2$ ?v0)))
+(let (($x278 (= ?x273 ?x174)))
+(let (($x291 (fun_app$ v_b_Visited_G_2$ ?v0)))
+(let (($x300 (not $x291)))
+(or $x300 $x278)))))) :pattern ( (fun_app$ v_b_Visited_G_2$ ?v0) ) :pattern ( (v_b_SP_G_2$ ?v0) ) :pattern ( (fun_app$c v_b_SP_G_1$ ?v0) )))
+))
+(let (($x3700 (not $x3695)))
+(let (($x3785 (or $x3700 $x3782)))
+(let (($x3788 (not $x3785)))
+(let ((?x1827 (fun_app$c v_b_SP_G_1$ ?v0!14)))
+(let ((?x1826 (v_b_SP_G_2$ ?v0!14)))
+(let (($x1828 (= ?x1826 ?x1827)))
+(let (($x1829 (or (not (fun_app$ v_b_Visited_G_2$ ?v0!14)) $x1828)))
+(let (($x1830 (not $x1829)))
+(let (($x3791 (or $x1830 $x3788)))
+(let (($x3794 (not $x3791)))
+(let (($x3686 (forall ((?v0 B_Vertex$) )(!(>= (+ (fun_app$c v_b_SP_G_1$ ?v0) (* (- 1) (v_b_SP_G_2$ ?v0))) 0) :pattern ( (fun_app$c v_b_SP_G_1$ ?v0) ) :pattern ( (v_b_SP_G_2$ ?v0) )))
+))
+(let (($x3691 (not $x3686)))
+(let (($x3797 (or $x3691 $x3794)))
+(let (($x3800 (not $x3797)))
+(let ((?x1809 (v_b_SP_G_2$ ?v0!13)))
+(let ((?x1810 (* (- 1) ?x1809)))
+(let ((?x1808 (fun_app$c v_b_SP_G_1$ ?v0!13)))
+(let ((?x1811 (+ ?x1808 ?x1810)))
+(let (($x1812 (>= ?x1811 0)))
+(let (($x1813 (not $x1812)))
+(let (($x3803 (or $x1813 $x3800)))
+(let (($x3806 (not $x3803)))
+(let (($x3678 (forall ((?v0 B_Vertex$) )(!(let ((?x174 (fun_app$c v_b_SP_G_1$ ?v0)))
+(let ((?x273 (v_b_SP_G_2$ ?v0)))
+(let (($x278 (= ?x273 ?x174)))
+(let ((?x257 (fun_app$c v_b_SP_G_1$ v_b_v_G_1$)))
+(let ((?x1173 (* (- 1) ?x257)))
+(let (($x1175 (<= (+ ?x174 ?x1173 (* (- 1) (b_G$ (pair$ v_b_v_G_1$ ?v0)))) 0)))
+(let (($x1169 (<= (+ b_Infinity$ (* (- 1) (b_G$ (pair$ v_b_v_G_1$ ?v0)))) 0)))
+(let (($x2717 (or $x1169 $x1175)))
+(let (($x2718 (not $x2717)))
+(or $x2718 $x278)))))))))) :pattern ( (pair$ v_b_v_G_1$ ?v0) ) :pattern ( (fun_app$c v_b_SP_G_1$ ?v0) ) :pattern ( (v_b_SP_G_2$ ?v0) )))
+))
+(let (($x3683 (not $x3678)))
+(let (($x3670 (forall ((?v0 B_Vertex$) )(!(let ((?x273 (v_b_SP_G_2$ ?v0)))
+(let ((?x1186 (* (- 1) ?x273)))
+(let ((?x268 (b_G$ (pair$ v_b_v_G_1$ ?v0))))
+(let ((?x257 (fun_app$c v_b_SP_G_1$ v_b_v_G_1$)))
+(let (($x1185 (= (+ ?x257 ?x268 ?x1186) 0)))
+(let (($x1175 (<= (+ (fun_app$c v_b_SP_G_1$ ?v0) (* (- 1) ?x257) (* (- 1) ?x268)) 0)))
+(let (($x1169 (<= (+ b_Infinity$ (* (- 1) ?x268)) 0)))
+(or $x1169 $x1175 $x1185)))))))) :pattern ( (pair$ v_b_v_G_1$ ?v0) ) :pattern ( (fun_app$c v_b_SP_G_1$ ?v0) ) :pattern ( (v_b_SP_G_2$ ?v0) )))
+))
+(let (($x3675 (not $x3670)))
+(let ((?x263 (fun_upd$ v_b_Visited_G_1$)))
+(let ((?x264 (fun_app$b ?x263 v_b_v_G_1$)))
+(let ((?x265 (fun_app$a ?x264 true)))
+(let (($x266 (= v_b_Visited_G_2$ ?x265)))
+(let (($x2935 (not $x266)))
+(let (($x3660 (forall ((?v0 B_Vertex$) )(!(let ((?x257 (fun_app$c v_b_SP_G_1$ v_b_v_G_1$)))
+(let ((?x1173 (* (- 1) ?x257)))
+(let ((?x174 (fun_app$c v_b_SP_G_1$ ?v0)))
+(let (($x178 (fun_app$ v_b_Visited_G_1$ ?v0)))
+(or $x178 (>= (+ ?x174 ?x1173) 0)))))) :pattern ( (fun_app$ v_b_Visited_G_1$ ?v0) ) :pattern ( (fun_app$c v_b_SP_G_1$ ?v0) )))
+))
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+(let ((?x1173 (* (- 1) ?x257)))
+(let ((?x1212 (+ b_Infinity$ ?x1173)))
+(let (($x1213 (<= ?x1212 0)))
+(let (($x255 (fun_app$ v_b_Visited_G_1$ v_b_v_G_1$)))
+(let ((?x1775 (fun_app$c v_b_SP_G_1$ ?v0!12)))
+(let ((?x1776 (* (- 1) ?x1775)))
+(let ((?x1777 (+ b_Infinity$ ?x1776)))
+(let (($x1778 (<= ?x1777 0)))
+(let (($x1773 (fun_app$ v_b_Visited_G_1$ ?v0!12)))
+(let (($x3809 (or $x1773 $x1778 $x255 $x1213 $x3665 $x2935 $x3675 $x3683 $x3806)))
+(let (($x3812 (not $x3809)))
+(let ((?x245 (fun_app$c v_b_SP_G_3$ b_Source$)))
+(let (($x246 (= ?x245 0)))
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+(let ((?x155 (b_G$ (pair$ ?v1 ?v0))))
+(let (($x1140 (>= (+ ?x155 ?x230 (* (- 1) (fun_app$c v_b_SP_G_3$ ?v0))) 0)))
+(let (($x922 (<= (+ b_Infinity$ (* (- 1) ?x155)) 0)))
+(let (($x1099 (<= (+ b_Infinity$ (* (- 1) ?x230)) 0)))
+(or $x1099 $x922 $x1140)))))) :pattern ( (pair$ ?v1 ?v0) )))
+))
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+(let ((?x1734 (fun_app$c v_b_SP_G_3$ ?v0!11)))
+(let ((?x1735 (* (- 1) ?x1734)))
+(let ((?x1726 (pair$ ?v1!10 ?v0!11)))
+(let ((?x1727 (b_G$ ?x1726)))
+(let ((?x1721 (fun_app$c v_b_SP_G_3$ ?v1!10)))
+(let ((?x2206 (+ ?x1721 ?x1727 ?x1735)))
+(let (($x2209 (>= ?x2206 0)))
+(let (($x1730 (<= (+ b_Infinity$ (* (- 1) ?x1727)) 0)))
+(let (($x1724 (<= (+ b_Infinity$ (* (- 1) ?x1721)) 0)))
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+(let (($x3636 (or $x2650 $x3633)))
+(let (($x3639 (not $x3636)))
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+(let ((?x2191 (+ ?x230 (* (- 1) (fun_app$c v_b_SP_G_3$ (?v1!9 ?v0))) (* (- 1) (b_G$ (pair$ (?v1!9 ?v0) ?v0))))))
+(let (($x2192 (= ?x2191 0)))
+(let (($x2176 (<= (+ ?x230 (* (- 1) (fun_app$c v_b_SP_G_3$ (?v1!9 ?v0)))) 0)))
+(let (($x2617 (not (or $x2176 (not $x2192)))))
+(let (($x1099 (<= (+ b_Infinity$ (* (- 1) ?x230)) 0)))
+(let (($x127 (= ?v0 b_Source$)))
+(or $x127 $x1099 $x2617)))))))) :pattern ( (fun_app$c v_b_SP_G_3$ ?v0) )))
+))
+(let (($x3619 (not $x3614)))
+(let (($x3642 (or $x3619 $x3639)))
+(let (($x3645 (not $x3642)))
+(let (($x3600 (forall ((?v1 B_Vertex$) )(!(let ((?x1661 (fun_app$c v_b_SP_G_3$ ?v0!8)))
+(let ((?x1662 (* (- 1) ?x1661)))
+(let ((?x230 (fun_app$c v_b_SP_G_3$ ?v1)))
+(let (($x2148 (= (+ ?x230 ?x1662 (b_G$ (pair$ ?v1 ?v0!8))) 0)))
+(or (>= (+ ?x230 ?x1662) 0) (not $x2148)))))) :pattern ( (fun_app$c v_b_SP_G_3$ ?v1) ) :pattern ( (pair$ ?v1 ?v0!8) )))
+))
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+(let (($x1664 (<= (+ b_Infinity$ (* (- 1) (fun_app$c v_b_SP_G_3$ ?v0!8))) 0)))
+(let (($x1659 (= ?v0!8 b_Source$)))
+(let (($x3608 (or $x1659 $x1664 $x3605)))
+(let (($x3611 (not $x3608)))
+(let (($x3648 (or $x3611 $x3645)))
+(let (($x3651 (not $x3648)))
+(let (($x220 (= v_b_oldSP_G_1$ v_b_oldSP_G_0$)))
+(let (($x2709 (not $x220)))
+(let (($x217 (= v_b_SP_G_3$ v_b_SP_G_1$)))
+(let (($x2708 (not $x217)))
+(let (($x215 (= v_b_v_G_2$ v_b_v_G_0$)))
+(let (($x2707 (not $x215)))
+(let (($x212 (= v_b_Visited_G_3$ v_b_Visited_G_1$)))
+(let (($x2706 (not $x212)))
+(let (($x3590 (forall ((?v0 B_Vertex$) )(!(let (($x1002 (<= (+ b_Infinity$ (* (- 1) (fun_app$c v_b_SP_G_1$ ?v0))) 0)))
+(let (($x178 (fun_app$ v_b_Visited_G_1$ ?v0)))
+(or $x178 $x1002))) :pattern ( (fun_app$ v_b_Visited_G_1$ ?v0) ) :pattern ( (fun_app$c v_b_SP_G_1$ ?v0) )))
+))
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+(let (($x3654 (or $x3595 $x2706 $x2707 $x2708 $x2709 $x3651)))
+(let (($x3657 (not $x3654)))
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+(let (($x3581 (forall ((?v0 B_Vertex$) )(!(let ((?x174 (fun_app$c v_b_SP_G_1$ ?v0)))
+(let ((?x2128 (+ ?x174 (* (- 1) (fun_app$c v_b_SP_G_1$ (?v1!7 ?v0))) (* (- 1) (b_G$ (pair$ (?v1!7 ?v0) ?v0))))))
+(let (($x2129 (= ?x2128 0)))
+(let (($x2113 (<= (+ ?x174 (* (- 1) (fun_app$c v_b_SP_G_1$ (?v1!7 ?v0)))) 0)))
+(let (($x2551 (not (or $x2113 (not (fun_app$ v_b_Visited_G_1$ (?v1!7 ?v0))) (not $x2129)))))
+(let (($x1002 (<= (+ b_Infinity$ (* (- 1) ?x174)) 0)))
+(let (($x127 (= ?v0 b_Source$)))
+(or $x127 $x1002 $x2551)))))))) :pattern ( (fun_app$c v_b_SP_G_1$ ?v0) )))
+))
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+(let ((?x155 (b_G$ (pair$ ?v1 ?v0))))
+(let (($x990 (>= (+ ?x155 ?x174 (* (- 1) (fun_app$c v_b_SP_G_1$ ?v0))) 0)))
+(let (($x922 (<= (+ b_Infinity$ (* (- 1) ?x155)) 0)))
+(let (($x178 (fun_app$ v_b_Visited_G_1$ ?v1)))
+(let (($x179 (not $x178)))
+(or $x179 $x922 $x990))))))) :pattern ( (pair$ ?v1 ?v0) )))
+))
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+(let (($x1015 (>= (+ ?x174 (* (- 1) (fun_app$c v_b_SP_G_1$ ?v0))) 0)))
+(let (($x178 (fun_app$ v_b_Visited_G_1$ ?v1)))
+(or $x178 (not (fun_app$ v_b_Visited_G_1$ ?v0)) $x1015)))) :pattern ( (fun_app$ v_b_Visited_G_1$ ?v1) (fun_app$ v_b_Visited_G_1$ ?v0) )))
+))
+(let (($x3570 (not $x3565)))
+(let (($x3561 (not $x3556)))
+(let ((?x172 (fun_app$c v_b_SP_G_1$ b_Source$)))
+(let (($x173 (= ?x172 0)))
+(let (($x2952 (not $x173)))
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+(let ((?x2090 (+ ?x128 (* (- 1) (v_b_SP_G_0$ (?v1!6 ?v0))) (* (- 1) (b_G$ (pair$ (?v1!6 ?v0) ?v0))))))
+(let (($x2091 (= ?x2090 0)))
+(let (($x2075 (<= (+ ?x128 (* (- 1) (v_b_SP_G_0$ (?v1!6 ?v0)))) 0)))
+(let (($x2478 (not (or $x2075 (not (v_b_Visited_G_0$ (?v1!6 ?v0))) (not $x2091)))))
+(let (($x947 (<= (+ b_Infinity$ (* (- 1) ?x128)) 0)))
+(let (($x127 (= ?v0 b_Source$)))
+(or $x127 $x947 $x2478)))))))) :pattern ( (v_b_SP_G_0$ ?v0) )))
+))
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+(let ((?x1541 (* (- 1) ?x1540)))
+(let ((?x128 (v_b_SP_G_0$ ?v1)))
+(let (($x136 (v_b_Visited_G_0$ ?v1)))
+(let (($x137 (not $x136)))
+(or (>= (+ ?x128 ?x1541) 0) $x137 (not (= (+ ?x128 ?x1541 (b_G$ (pair$ ?v1 ?v0!5))) 0)))))))) :pattern ( (v_b_SP_G_0$ ?v1) ) :pattern ( (v_b_Visited_G_0$ ?v1) ) :pattern ( (pair$ ?v1 ?v0!5) )))
+))
+(let (($x3538 (not $x3533)))
+(let ((?x1540 (v_b_SP_G_0$ ?v0!5)))
+(let ((?x1541 (* (- 1) ?x1540)))
+(let ((?x1542 (+ b_Infinity$ ?x1541)))
+(let (($x1543 (<= ?x1542 0)))
+(let (($x1538 (= ?v0!5 b_Source$)))
+(let (($x3541 (or $x1538 $x1543 $x3538)))
+(let (($x1539 (not $x1538)))
+(let ((@x6246 (unit-resolution (def-axiom (or $x3541 $x1539)) (hypothesis (not $x3541)) $x1539)))
+(let (($x5625 (= b_Infinity$ ?x1540)))
+(let (($x6457 (not $x5625)))
+(let (($x1544 (not $x1543)))
+(let ((@x6514 (unit-resolution (def-axiom (or $x3541 $x1544)) (hypothesis (not $x3541)) $x1544)))
+(let ((@x5778 (symm (commutativity (= $x5625 (= ?x1540 b_Infinity$))) (= (= ?x1540 b_Infinity$) $x5625))))
+(let (($x5616 (= ?x1540 b_Infinity$)))
+(let (($x3493 (forall ((?v0 B_Vertex$) )(!(let (($x127 (= ?v0 b_Source$)))
+(or $x127 (= (v_b_SP_G_0$ ?v0) b_Infinity$))) :pattern ( (v_b_SP_G_0$ ?v0) )))
+))
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+(or $x127 (= (v_b_SP_G_0$ ?v0) b_Infinity$))))
+))
+(let (($x127 (= ?0 b_Source$)))
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+(let (($x138 (forall ((?v0 B_Vertex$) )(let (($x136 (v_b_Visited_G_0$ ?v0)))
+(not $x136)))
+))
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+(let (($x132 (not $x127)))
+(or $x132 (= (v_b_SP_G_0$ ?v0) 0)))))
+))
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+(let (($x1329 (forall ((?v0 B_Vertex$) )(let (($x1323 (exists ((?v1 B_Vertex$) )(let ((?x303 (v_b_SP_G_2$ ?v0)))
+(let ((?x1263 (* (- 1) ?x303)))
+(let ((?x273 (v_b_SP_G_2$ ?v1)))
+(let ((?x155 (b_G$ (pair$ ?v1 ?v0))))
+(let (($x1306 (= (+ ?x155 ?x273 ?x1263) 0)))
+(let (($x291 (fun_app$ v_b_Visited_G_2$ ?v1)))
+(let (($x1262 (>= (+ ?x273 ?x1263) 0)))
+(let (($x1309 (not $x1262)))
+(and $x1309 $x291 $x1306))))))))))
+))
+(let (($x127 (= ?v0 b_Source$)))
+(let (($x132 (not $x127)))
+(let (($x1300 (and $x132 (not (<= (+ b_Infinity$ (* (- 1) (v_b_SP_G_2$ ?v0))) 0)))))
+(or (not $x1300) $x1323))))))
+))
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+(let ((?x1263 (* (- 1) ?x303)))
+(let ((?x273 (v_b_SP_G_2$ ?v1)))
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+(let (($x1232 (and $x1080 (and $x256 (and $x1214 (and $x1209 (and $x266 (and $x1193 $x1199))))))))
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+(let ((?x270 (+ ?x257 ?x268)))
+(let (($x274 (= ?x273 ?x270)))
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+(let (($x608 (or $x277 $x274)))
+(let ((@x1184 (monotonicity (monotonicity @x1172 @x1178 (= $x272 $x1179)) (= $x277 $x1182))))
+(let ((@x1195 (quant-intro (monotonicity @x1184 (rewrite (= $x274 $x1185)) (= $x608 $x1190)) (= $x611 $x1193))))
+(let ((@x1219 (monotonicity @x1195 (quant-intro @x1198 (= $x617 $x1199)) (= $x620 (and $x1193 $x1199)))))
+(let (($x178 (fun_app$ v_b_Visited_G_1$ ?0)))
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+(let (($x602 (or $x178 $x259)))
+(let ((@x1208 (monotonicity (rewrite (= $x259 (>= (+ ?x174 ?x1173) 0))) (= $x602 $x1206))))
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+(let (($x1002 (<= (+ b_Infinity$ (* (- 1) ?x174)) 0)))
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+(let (($x179 (not $x178)))
+(let (($x1077 (and $x179 $x1003)))
+(let ((@x1079 (monotonicity (rewrite (= (< ?x174 b_Infinity$) $x1003)) (= (and $x179 (< ?x174 b_Infinity$)) $x1077))))
+(let ((@x1234 (monotonicity (quant-intro @x1079 (= $x209 $x1080)) (monotonicity @x1228 $x1230) (= $x635 $x1232))))
+(let ((@x1242 (monotonicity (trans @x1234 (rewrite (= $x1232 $x1235)) (= $x635 $x1235)) (= (not $x635) $x1240))))
+(let ((@x1370 (monotonicity @x1242 (monotonicity @x1249 @x1364 (= $x803 $x1365)) (= $x810 $x1368))))
+(let ((?x230 (fun_app$c v_b_SP_G_3$ ?0)))
+(let (($x1140 (>= (+ ?x155 ?x230 (* (- 1) (fun_app$c v_b_SP_G_3$ ?1))) 0)))
+(let (($x1099 (<= (+ b_Infinity$ (* (- 1) ?x230)) 0)))
+(let (($x1100 (not $x1099)))
+(let (($x1134 (and $x1100 $x923)))
+(let (($x1137 (not $x1134)))
+(let (($x1143 (or $x1137 $x1140)))
+(let ((?x521 (+ ?x155 ?x230)))
+(let ((?x233 (fun_app$c v_b_SP_G_3$ ?1)))
+(let (($x545 (<= ?x233 ?x521)))
+(let (($x552 (or (not (and (< ?x230 b_Infinity$) (< ?x155 b_Infinity$))) $x545)))
+(let ((@x1136 (monotonicity (rewrite (= (< ?x230 b_Infinity$) $x1100)) @x925 (= (and (< ?x230 b_Infinity$) (< ?x155 b_Infinity$)) $x1134))))
+(let ((@x1139 (monotonicity @x1136 (= (not (and (< ?x230 b_Infinity$) (< ?x155 b_Infinity$))) $x1137))))
+(let ((@x1148 (quant-intro (monotonicity @x1139 (rewrite (= $x545 $x1140)) (= $x552 $x1143)) (= $x557 $x1146))))
+(let ((@x1154 (monotonicity (monotonicity @x1148 (= (not $x557) $x1149)) (= $x573 $x1152))))
+(let (($x1122 (exists ((?v1 B_Vertex$) )(let ((?x230 (fun_app$c v_b_SP_G_3$ ?v1)))
+(let ((?x155 (b_G$ (pair$ ?v1 ?0))))
+(and (not (>= (+ ?x230 (* (- 1) (fun_app$c v_b_SP_G_3$ ?0))) 0)) (= (+ ?x155 ?x230 (* (- 1) (fun_app$c v_b_SP_G_3$ ?0))) 0)))))
+))
+(let (($x1103 (and $x132 $x1100)))
+(let (($x1106 (not $x1103)))
+(let (($x1125 (or $x1106 $x1122)))
+(let (($x530 (exists ((?v1 B_Vertex$) )(let ((?x230 (fun_app$c v_b_SP_G_3$ ?v1)))
+(let ((?x155 (b_G$ (pair$ ?v1 ?0))))
+(let ((?x521 (+ ?x155 ?x230)))
+(let ((?x233 (fun_app$c v_b_SP_G_3$ ?0)))
+(let (($x524 (= ?x233 ?x521)))
+(let (($x234 (< ?x230 ?x233)))
+(and $x234 $x524))))))))
+))
+(let (($x537 (or (not (and $x132 (< ?x230 b_Infinity$))) $x530)))
+(let (($x1119 (and (not (>= (+ ?x230 (* (- 1) ?x233)) 0)) (= (+ ?x155 ?x230 (* (- 1) ?x233)) 0))))
+(let (($x524 (= ?x233 ?x521)))
+(let (($x234 (< ?x230 ?x233)))
+(let (($x527 (and $x234 $x524)))
+(let ((@x1121 (monotonicity (rewrite (= $x234 (not (>= (+ ?x230 (* (- 1) ?x233)) 0)))) (rewrite (= $x524 (= (+ ?x155 ?x230 (* (- 1) ?x233)) 0))) (= $x527 $x1119))))
+(let ((@x1105 (monotonicity (rewrite (= (< ?x230 b_Infinity$) $x1100)) (= (and $x132 (< ?x230 b_Infinity$)) $x1103))))
+(let ((@x1127 (monotonicity (monotonicity @x1105 (= (not (and $x132 (< ?x230 b_Infinity$))) $x1106)) (quant-intro @x1121 (= $x530 $x1122)) (= $x537 $x1125))))
+(let ((@x1133 (monotonicity (quant-intro @x1127 (= $x542 $x1128)) (= (not $x542) $x1131))))
+(let ((@x1160 (monotonicity @x1133 (monotonicity @x1148 @x1154 (= $x578 $x1155)) (= $x585 $x1158))))
+(let ((@x1091 (rewrite (= (and $x1083 (and $x212 (and $x215 (and $x217 $x220)))) $x1089))))
+(let (($x493 (and $x212 (and $x215 (and $x217 $x220)))))
+(let (($x507 (and $x210 $x493)))
+(let ((@x1088 (monotonicity (monotonicity (quant-intro @x1079 (= $x209 $x1080)) (= $x210 $x1083)) (= $x507 (and $x1083 $x493)))))
+(let ((@x1096 (monotonicity (trans @x1088 @x1091 (= $x507 $x1089)) (= (not $x507) $x1094))))
+(let ((@x1166 (monotonicity @x1096 (monotonicity (quant-intro @x1127 (= $x542 $x1128)) @x1160 (= $x590 $x1161)) (= $x597 $x1164))))
+(let (($x1070 (= (and $x980 (and $x173 (and $x1051 (and $x1045 (and $x997 $x1037))))) $x1069)))
+(let (($x1067 (= $x482 (and $x980 (and $x173 (and $x1051 (and $x1045 (and $x997 $x1037))))))))
+(let (($x1031 (exists ((?v1 B_Vertex$) )(let ((?x174 (fun_app$c v_b_SP_G_1$ ?v1)))
+(let ((?x155 (b_G$ (pair$ ?v1 ?0))))
+(let (($x1012 (= (+ ?x155 ?x174 (* (- 1) (fun_app$c v_b_SP_G_1$ ?0))) 0)))
+(let (($x178 (fun_app$ v_b_Visited_G_1$ ?v1)))
+(let (($x1015 (>= (+ ?x174 (* (- 1) (fun_app$c v_b_SP_G_1$ ?0))) 0)))
+(let (($x1017 (not $x1015)))
+(and $x1017 $x178 $x1012))))))))
+))
+(let (($x1006 (and $x132 $x1003)))
+(let (($x1009 (not $x1006)))
+(let (($x1034 (or $x1009 $x1031)))
+(let (($x437 (exists ((?v1 B_Vertex$) )(let ((?x174 (fun_app$c v_b_SP_G_1$ ?v1)))
+(let ((?x155 (b_G$ (pair$ ?v1 ?0))))
+(let ((?x410 (+ ?x155 ?x174)))
+(let ((?x182 (fun_app$c v_b_SP_G_1$ ?0)))
+(let (($x428 (= ?x182 ?x410)))
+(let (($x178 (fun_app$ v_b_Visited_G_1$ ?v1)))
+(let (($x431 (and $x178 $x428)))
+(let (($x193 (< ?x174 ?x182)))
+(and $x193 $x431))))))))))
+))
+(let (($x444 (or (not (and $x132 (< ?x174 b_Infinity$))) $x437)))
+(let (($x1012 (= (+ ?x155 ?x174 (* (- 1) (fun_app$c v_b_SP_G_1$ ?1))) 0)))
+(let (($x1015 (>= (+ ?x174 (* (- 1) (fun_app$c v_b_SP_G_1$ ?1))) 0)))
+(let (($x1017 (not $x1015)))
+(let (($x1026 (and $x1017 $x178 $x1012)))
+(let ((?x410 (+ ?x155 ?x174)))
+(let ((?x182 (fun_app$c v_b_SP_G_1$ ?1)))
+(let (($x428 (= ?x182 ?x410)))
+(let (($x431 (and $x178 $x428)))
+(let (($x193 (< ?x174 ?x182)))
+(let (($x434 (and $x193 $x431)))
+(let ((@x1025 (monotonicity (rewrite (= $x193 $x1017)) (monotonicity (rewrite (= $x428 $x1012)) (= $x431 (and $x178 $x1012))) (= $x434 (and $x1017 (and $x178 $x1012))))))
+(let ((@x1030 (trans @x1025 (rewrite (= (and $x1017 (and $x178 $x1012)) $x1026)) (= $x434 $x1026))))
+(let ((@x1008 (monotonicity (rewrite (= (< ?x174 b_Infinity$) $x1003)) (= (and $x132 (< ?x174 b_Infinity$)) $x1006))))
+(let ((@x1036 (monotonicity (monotonicity @x1008 (= (not (and $x132 (< ?x174 b_Infinity$))) $x1009)) (quant-intro @x1030 (= $x437 $x1031)) (= $x444 $x1034))))
+(let (($x990 (>= (+ ?x155 ?x174 (* (- 1) ?x182)) 0)))
+(let (($x983 (and $x178 $x923)))
+(let (($x986 (not $x983)))
+(let (($x994 (or $x986 $x990)))
+(let (($x413 (<= ?x182 ?x410)))
+(let (($x420 (or (not (and $x178 (< ?x155 b_Infinity$))) $x413)))
+(let ((@x988 (monotonicity (monotonicity @x925 (= (and $x178 (< ?x155 b_Infinity$)) $x983)) (= (not (and $x178 (< ?x155 b_Infinity$))) $x986))))
+(let ((@x999 (quant-intro (monotonicity @x988 (rewrite (= $x413 $x990)) (= $x420 $x994)) (= $x425 $x997))))
+(let ((@x1056 (monotonicity @x999 (quant-intro @x1036 (= $x449 $x1037)) (= $x459 (and $x997 $x1037)))))
+(let (($x180 (fun_app$ v_b_Visited_G_1$ ?1)))
+(let (($x181 (and $x179 $x180)))
+(let (($x403 (not $x181)))
+(let (($x1042 (or $x403 $x1015)))
+(let (($x183 (<= ?x182 ?x174)))
+(let (($x404 (or $x403 $x183)))
+(let ((@x1047 (quant-intro (monotonicity (rewrite (= $x183 $x1015)) (= $x404 $x1042)) (= $x407 $x1045))))
+(let ((@x1053 (quant-intro (rewrite (= (<= 0 ?x174) (>= ?x174 0))) (= $x176 $x1051))))
+(let ((@x1062 (monotonicity @x1053 (monotonicity @x1047 @x1056 (= $x462 (and $x1045 (and $x997 $x1037)))) (= $x465 (and $x1051 (and $x1045 (and $x997 $x1037)))))))
+(let ((@x1065 (monotonicity @x1062 (= $x468 (and $x173 (and $x1051 (and $x1045 (and $x997 $x1037))))))))
+(let (($x974 (exists ((?v1 B_Vertex$) )(let ((?x155 (b_G$ (pair$ ?v1 ?0))))
+(let ((?x128 (v_b_SP_G_0$ ?v1)))
+(let (($x957 (= (+ ?x128 (* (- 1) (v_b_SP_G_0$ ?0)) ?x155) 0)))
+(let (($x136 (v_b_Visited_G_0$ ?v1)))
+(let (($x907 (>= (+ ?x128 (* (- 1) (v_b_SP_G_0$ ?0))) 0)))
+(let (($x960 (not $x907)))
+(and $x960 $x136 $x957))))))))
+))
+(let (($x951 (and $x132 (not (<= (+ b_Infinity$ (* (- 1) (v_b_SP_G_0$ ?0))) 0)))))
+(let (($x954 (not $x951)))
+(let (($x977 (or $x954 $x974)))
+(let (($x168 (exists ((?v1 B_Vertex$) )(let (($x136 (v_b_Visited_G_0$ ?v1)))
+(let (($x166 (and $x136 (= (v_b_SP_G_0$ ?0) (+ (v_b_SP_G_0$ ?v1) (b_G$ (pair$ ?v1 ?0)))))))
+(and (< (v_b_SP_G_0$ ?v1) (v_b_SP_G_0$ ?0)) $x166))))
+))
+(let (($x397 (or (not (and $x132 (< (v_b_SP_G_0$ ?0) b_Infinity$))) $x168)))
+(let (($x957 (= (+ (v_b_SP_G_0$ ?0) (* (- 1) (v_b_SP_G_0$ ?1)) ?x155) 0)))
+(let (($x136 (v_b_Visited_G_0$ ?0)))
+(let (($x907 (>= (+ (v_b_SP_G_0$ ?0) (* (- 1) (v_b_SP_G_0$ ?1))) 0)))
+(let (($x960 (not $x907)))
+(let (($x969 (and $x960 $x136 $x957)))
+(let (($x167 (and (< (v_b_SP_G_0$ ?0) (v_b_SP_G_0$ ?1)) (and $x136 (= (v_b_SP_G_0$ ?1) (+ (v_b_SP_G_0$ ?0) ?x155))))))
+(let (($x964 (= (and $x136 (= (v_b_SP_G_0$ ?1) (+ (v_b_SP_G_0$ ?0) ?x155))) (and $x136 $x957))))
+(let ((@x959 (rewrite (= (= (v_b_SP_G_0$ ?1) (+ (v_b_SP_G_0$ ?0) ?x155)) $x957))))
+(let ((@x968 (monotonicity (rewrite (= (< (v_b_SP_G_0$ ?0) (v_b_SP_G_0$ ?1)) $x960)) (monotonicity @x959 $x964) (= $x167 (and $x960 (and $x136 $x957))))))
+(let ((@x973 (trans @x968 (rewrite (= (and $x960 (and $x136 $x957)) $x969)) (= $x167 $x969))))
+(let (($x949 (= (< (v_b_SP_G_0$ ?0) b_Infinity$) (not (<= (+ b_Infinity$ (* (- 1) (v_b_SP_G_0$ ?0))) 0)))))
+(let ((@x953 (monotonicity (rewrite $x949) (= (and $x132 (< (v_b_SP_G_0$ ?0) b_Infinity$)) $x951))))
+(let ((@x956 (monotonicity @x953 (= (not (and $x132 (< (v_b_SP_G_0$ ?0) b_Infinity$))) $x954))))
+(let ((@x982 (quant-intro (monotonicity @x956 (quant-intro @x973 (= $x168 $x974)) (= $x397 $x977)) (= $x400 $x980))))
+(let ((@x1076 (monotonicity (trans (monotonicity @x982 @x1065 $x1067) (rewrite $x1070) (= $x482 $x1069)) (= (not $x482) $x1074))))
+(let ((@x1376 (monotonicity @x1076 (monotonicity @x1166 @x1370 (= $x815 $x1371)) (= $x822 $x1374))))
+(let (($x933 (>= (+ (v_b_SP_G_0$ ?0) (* (- 1) (v_b_SP_G_0$ ?1)) ?x155) 0)))
+(let (($x926 (and $x136 $x923)))
+(let (($x929 (not $x926)))
+(let (($x936 (or $x929 $x933)))
+(let ((?x150 (v_b_SP_G_0$ ?1)))
+(let (($x159 (<= ?x150 (+ (v_b_SP_G_0$ ?0) ?x155))))
+(let (($x390 (or (not (and $x136 (< ?x155 b_Infinity$))) $x159)))
+(let ((@x931 (monotonicity (monotonicity @x925 (= (and $x136 (< ?x155 b_Infinity$)) $x926)) (= (not (and $x136 (< ?x155 b_Infinity$))) $x929))))
+(let ((@x941 (quant-intro (monotonicity @x931 (rewrite (= $x159 $x933)) (= $x390 $x936)) (= $x393 $x939))))
+(let ((@x1382 (monotonicity (monotonicity @x941 (= (not $x393) $x942)) (monotonicity @x982 @x1376 (= $x827 $x1377)) (= $x834 $x1380))))
+(let (($x148 (v_b_Visited_G_0$ ?1)))
+(let (($x137 (not $x136)))
+(let (($x149 (and $x137 $x148)))
+(let (($x382 (not $x149)))
+(let (($x911 (or $x382 $x907)))
+(let ((?x128 (v_b_SP_G_0$ ?0)))
+(let (($x151 (<= ?x150 ?x128)))
+(let (($x383 (or $x382 $x151)))
+(let ((@x916 (quant-intro (monotonicity (rewrite (= $x151 $x907)) (= $x383 $x911)) (= $x386 $x914))))
+(let ((@x1388 (monotonicity (monotonicity @x916 (= (not $x386) $x917)) (monotonicity @x941 @x1382 (= $x839 $x1383)) (= $x846 $x1386))))
+(let ((@x901 (quant-intro (rewrite (= (<= 0 ?x128) (>= ?x128 0))) (= $x147 $x899))))
+(let ((@x1394 (monotonicity (monotonicity @x901 (= (not $x147) $x902)) (monotonicity @x916 @x1388 (= $x851 $x1389)) (= $x858 $x1392))))
+(let ((@x1400 (monotonicity (monotonicity @x901 @x1394 (= $x863 $x1395)) (= $x870 $x1398))))
+(let ((@x895 (monotonicity (rewrite (= (and $x354 (and $x360 $x138)) $x890)) (= (not (and $x354 (and $x360 $x138))) (not $x890)))))
+(let ((@x1406 (monotonicity @x895 (monotonicity @x1400 (= $x875 $x1401)) (= $x882 (or (not $x890) $x1401)))))
+(let (($x318 (exists ((?v1 B_Vertex$) )(let (($x291 (fun_app$ v_b_Visited_G_2$ ?v1)))
+(let (($x316 (and $x291 (= (v_b_SP_G_2$ ?0) (+ (v_b_SP_G_2$ ?v1) (b_G$ (pair$ ?v1 ?0)))))))
+(let ((?x303 (v_b_SP_G_2$ ?0)))
+(let ((?x273 (v_b_SP_G_2$ ?v1)))
+(let (($x314 (< ?x273 ?x303)))
+(and $x314 $x316)))))))
+))
+(let (($x313 (and $x132 (< ?x273 b_Infinity$))))
+(let (($x319 (=> $x313 $x318)))
+(let ((@x691 (monotonicity (rewrite (= (+ ?x273 ?x155) ?x671)) (= (= ?x303 (+ ?x273 ?x155)) $x689))))
+(let ((@x697 (monotonicity (monotonicity @x691 (= (and $x291 (= ?x303 (+ ?x273 ?x155))) $x692)) (= (and $x314 (and $x291 (= ?x303 (+ ?x273 ?x155)))) $x695))))
+(let ((@x703 (monotonicity (quant-intro @x697 (= $x318 $x698)) (= $x319 (=> $x313 $x698)))))
+(let ((@x712 (quant-intro (trans @x703 (rewrite (= (=> $x313 $x698) $x705)) (= $x319 $x705)) (= $x320 $x710))))
+(let ((@x719 (trans (monotonicity @x712 (= $x321 (and $x710 false))) (rewrite (= (and $x710 false) false)) (= $x321 false))))
+(let ((@x726 (trans (monotonicity @x719 (= $x322 (=> false true))) (rewrite (= (=> false true) true)) (= $x322 true))))
+(let ((@x733 (trans (monotonicity @x712 @x726 (= $x323 (and $x710 true))) (rewrite (= (and $x710 true) $x710)) (= $x323 $x710))))
+(let (($x156 (< ?x155 b_Infinity$)))
+(let (($x307 (and $x291 $x156)))
+(let (($x310 (=> $x307 (<= ?x303 (+ ?x273 ?x155)))))
+(let ((@x676 (monotonicity (rewrite (= (+ ?x273 ?x155) ?x671)) (= (<= ?x303 (+ ?x273 ?x155)) $x674))))
+(let ((@x685 (trans (monotonicity @x676 (= $x310 (=> $x307 $x674))) (rewrite (= (=> $x307 $x674) $x681)) (= $x310 $x681))))
+(let ((@x736 (monotonicity (quant-intro @x685 (= $x311 $x686)) @x733 (= $x324 (=> $x686 $x710)))))
+(let ((@x745 (monotonicity (quant-intro @x685 (= $x311 $x686)) (trans @x736 (rewrite (= (=> $x686 $x710) $x738)) (= $x324 $x738)) (= (and $x311 $x324) $x743))))
+(let ((@x748 (monotonicity (quant-intro (rewrite (= (=> $x302 $x304) $x665)) (= $x306 $x668)) @x745 (= $x326 (=> $x668 $x743)))))
+(let ((@x757 (monotonicity (quant-intro (rewrite (= (=> $x302 $x304) $x665)) (= $x306 $x668)) (trans @x748 (rewrite (= (=> $x668 $x743) $x750)) (= $x326 $x750)) (= (and $x306 $x326) $x755))))
+(let ((@x766 (trans (monotonicity @x757 (= $x328 (=> $x299 $x755))) (rewrite (= (=> $x299 $x755) $x762)) (= $x328 $x762))))
+(let ((@x772 (monotonicity (monotonicity @x766 (= (and $x299 $x328) $x767)) (= $x330 (=> $x297 $x767)))))
+(let ((@x781 (monotonicity (trans @x772 (rewrite (= (=> $x297 $x767) $x774)) (= $x330 $x774)) (= (and $x297 $x330) $x779))))
+(let ((@x654 (quant-intro (rewrite (= (=> $x291 $x278) (or $x300 $x278))) (= $x293 $x652))))
+(let ((@x659 (monotonicity @x654 (rewrite (= (and true true) true)) (= $x295 (and $x652 true)))))
+(let ((@x784 (monotonicity (trans @x659 (rewrite (= (and $x652 true) $x652)) (= $x295 $x652)) @x781 (= $x332 (=> $x652 $x779)))))
+(let ((@x793 (monotonicity @x654 (trans @x784 (rewrite (= (=> $x652 $x779) $x786)) (= $x332 $x786)) (= (and $x293 $x332) $x791))))
+(let ((@x802 (trans (monotonicity @x793 (= $x334 (=> $x290 $x791))) (rewrite (= (=> $x290 $x791) $x798)) (= $x334 $x798))))
+(let (($x633 (= (and $x256 (and $x258 (and $x261 (and $x266 (and $x276 $x280))))) $x632)))
+(let ((@x622 (monotonicity (quant-intro (rewrite (= (=> $x272 $x274) $x608)) (= $x276 $x611)) (quant-intro (rewrite (= (=> $x277 $x278) $x614)) (= $x280 $x617)) (= (and $x276 $x280) $x620))))
+(let ((@x628 (monotonicity (quant-intro (rewrite (= (=> $x179 $x259) $x602)) (= $x261 $x605)) (monotonicity @x622 (= (and $x266 (and $x276 $x280)) $x623)) (= (and $x261 (and $x266 (and $x276 $x280))) $x626))))
+(let ((@x631 (monotonicity @x628 (= (and $x258 (and $x261 (and $x266 (and $x276 $x280)))) $x629))))
+(let ((@x640 (monotonicity (monotonicity (monotonicity @x631 $x633) (= $x286 $x635)) (= $x287 (and true $x635)))))
+(let ((@x646 (monotonicity (trans @x640 (rewrite (= (and true $x635) $x635)) (= $x287 $x635)) (= $x288 (and true $x635)))))
+(let ((@x808 (monotonicity (trans @x646 (rewrite (= (and true $x635) $x635)) (= $x288 $x635)) (monotonicity @x802 (= (and $x290 $x334) $x803)) (= $x336 (=> $x635 $x803)))))
+(let ((@x564 (monotonicity (rewrite (= (=> $x246 true) true)) (= $x248 (and $x246 true)))))
+(let (($x231 (< ?x230 b_Infinity$)))
+(let (($x241 (and $x231 $x156)))
+(let (($x243 (=> $x241 (<= ?x233 (+ ?x230 ?x155)))))
+(let ((@x547 (monotonicity (rewrite (= (+ ?x230 ?x155) ?x521)) (= (<= ?x233 (+ ?x230 ?x155)) $x545))))
+(let ((@x556 (trans (monotonicity @x547 (= $x243 (=> $x241 $x545))) (rewrite (= (=> $x241 $x545) $x552)) (= $x243 $x552))))
+(let ((@x571 (monotonicity (quant-intro @x556 (= $x244 $x557)) (trans @x564 (rewrite (= (and $x246 true) $x246)) (= $x248 $x246)) (= $x249 (=> $x557 $x246)))))
+(let ((@x580 (monotonicity (quant-intro @x556 (= $x244 $x557)) (trans @x571 (rewrite (= (=> $x557 $x246) $x573)) (= $x249 $x573)) (= (and $x244 $x249) $x578))))
+(let (($x238 (exists ((?v1 B_Vertex$) )(let ((?x155 (b_G$ (pair$ ?v1 ?0))))
+(let ((?x230 (fun_app$c v_b_SP_G_3$ ?v1)))
+(let ((?x235 (+ ?x230 ?x155)))
+(let ((?x233 (fun_app$c v_b_SP_G_3$ ?0)))
+(let (($x234 (< ?x230 ?x233)))
+(and $x234 (= ?x233 ?x235))))))))
+))
+(let (($x232 (and $x132 $x231)))
+(let (($x239 (=> $x232 $x238)))
+(let ((@x526 (monotonicity (rewrite (= (+ ?x230 ?x155) ?x521)) (= (= ?x233 (+ ?x230 ?x155)) $x524))))
+(let ((@x532 (quant-intro (monotonicity @x526 (= (and $x234 (= ?x233 (+ ?x230 ?x155))) $x527)) (= $x238 $x530))))
+(let ((@x541 (trans (monotonicity @x532 (= $x239 (=> $x232 $x530))) (rewrite (= (=> $x232 $x530) $x537)) (= $x239 $x537))))
+(let ((@x583 (monotonicity (quant-intro @x541 (= $x240 $x542)) @x580 (= $x251 (=> $x542 $x578)))))
+(let ((@x592 (monotonicity (quant-intro @x541 (= $x240 $x542)) (trans @x583 (rewrite (= (=> $x542 $x578) $x585)) (= $x251 $x585)) (= (and $x240 $x251) $x590))))
+(let (($x491 (= (and $x215 (and $x217 (and $x220 true))) (and $x215 (and $x217 $x220)))))
+(let ((@x489 (monotonicity (rewrite (= (and $x220 true) $x220)) (= (and $x217 (and $x220 true)) (and $x217 $x220)))))
+(let ((@x495 (monotonicity (monotonicity @x489 $x491) (= (and $x212 (and $x215 (and $x217 (and $x220 true)))) $x493))))
+(let ((@x502 (trans (monotonicity @x495 (= $x225 (and true $x493))) (rewrite (= (and true $x493) $x493)) (= $x225 $x493))))
+(let ((@x506 (trans (monotonicity @x502 (= $x226 (and true $x493))) (rewrite (= (and true $x493) $x493)) (= $x226 $x493))))
+(let ((@x512 (monotonicity (monotonicity @x506 (= (and $x210 $x226) $x507)) (= $x228 (and true $x507)))))
+(let ((@x518 (monotonicity (trans @x512 (rewrite (= (and true $x507) $x507)) (= $x228 $x507)) (= $x229 (and true $x507)))))
+(let ((@x595 (monotonicity (trans @x518 (rewrite (= (and true $x507) $x507)) (= $x229 $x507)) @x592 (= $x253 (=> $x507 $x590)))))
+(let ((@x817 (monotonicity (trans @x595 (rewrite (= (=> $x507 $x590) $x597)) (= $x253 $x597)) (trans @x808 (rewrite (= (=> $x635 $x803) $x810)) (= $x336 $x810)) (= (and $x253 $x336) $x815))))
+(let (($x197 (exists ((?v1 B_Vertex$) )(let ((?x155 (b_G$ (pair$ ?v1 ?0))))
+(let ((?x174 (fun_app$c v_b_SP_G_1$ ?v1)))
+(let ((?x187 (+ ?x174 ?x155)))
+(let ((?x182 (fun_app$c v_b_SP_G_1$ ?0)))
+(let (($x178 (fun_app$ v_b_Visited_G_1$ ?v1)))
+(let (($x193 (< ?x174 ?x182)))
+(and $x193 (and $x178 (= ?x182 ?x187))))))))))
+))
+(let (($x191 (< ?x174 b_Infinity$)))
+(let (($x192 (and $x132 $x191)))
+(let (($x198 (=> $x192 $x197)))
+(let ((@x430 (monotonicity (rewrite (= (+ ?x174 ?x155) ?x410)) (= (= ?x182 (+ ?x174 ?x155)) $x428))))
+(let ((@x436 (monotonicity (monotonicity @x430 (= (and $x178 (= ?x182 (+ ?x174 ?x155))) $x431)) (= (and $x193 (and $x178 (= ?x182 (+ ?x174 ?x155)))) $x434))))
+(let ((@x442 (monotonicity (quant-intro @x436 (= $x197 $x437)) (= $x198 (=> $x192 $x437)))))
+(let ((@x451 (quant-intro (trans @x442 (rewrite (= (=> $x192 $x437) $x444)) (= $x198 $x444)) (= $x199 $x449))))
+(let ((@x458 (trans (monotonicity @x451 (= $x200 (and $x449 true))) (rewrite (= (and $x449 true) $x449)) (= $x200 $x449))))
+(let (($x186 (and $x178 $x156)))
+(let (($x189 (=> $x186 (<= ?x182 (+ ?x174 ?x155)))))
+(let ((@x415 (monotonicity (rewrite (= (+ ?x174 ?x155) ?x410)) (= (<= ?x182 (+ ?x174 ?x155)) $x413))))
+(let ((@x424 (trans (monotonicity @x415 (= $x189 (=> $x186 $x413))) (rewrite (= (=> $x186 $x413) $x420)) (= $x189 $x420))))
+(let ((@x461 (monotonicity (quant-intro @x424 (= $x190 $x425)) @x458 (= (and $x190 $x200) $x459))))
+(let ((@x464 (monotonicity (quant-intro (rewrite (= (=> $x181 $x183) $x404)) (= $x185 $x407)) @x461 (= (and $x185 (and $x190 $x200)) $x462))))
+(let ((@x470 (monotonicity (monotonicity @x464 (= (and $x176 (and $x185 (and $x190 $x200))) $x465)) (= (and $x173 (and $x176 (and $x185 (and $x190 $x200)))) $x468))))
+(let ((@x477 (trans (monotonicity @x470 (= $x205 (and true $x468))) (rewrite (= (and true $x468) $x468)) (= $x205 $x468))))
+(let ((@x481 (trans (monotonicity @x477 (= $x206 (and true $x468))) (rewrite (= (and true $x468) $x468)) (= $x206 $x468))))
+(let ((@x402 (quant-intro (rewrite (= (=> (and $x132 (< ?x128 b_Infinity$)) $x168) $x397)) (= $x170 $x400))))
+(let ((@x820 (monotonicity (monotonicity @x402 @x481 (= (and $x170 $x206) $x482)) @x817 (= $x338 (=> $x482 $x815)))))
+(let ((@x829 (monotonicity @x402 (trans @x820 (rewrite (= (=> $x482 $x815) $x822)) (= $x338 $x822)) (= (and $x170 $x338) $x827))))
+(let ((@x395 (quant-intro (rewrite (= (=> (and $x136 $x156) $x159) $x390)) (= $x161 $x393))))
+(let ((@x838 (trans (monotonicity @x395 @x829 (= $x340 (=> $x393 $x827))) (rewrite (= (=> $x393 $x827) $x834)) (= $x340 $x834))))
+(let ((@x844 (monotonicity (quant-intro (rewrite (= (=> $x149 $x151) $x383)) (= $x153 $x386)) (monotonicity @x395 @x838 (= (and $x161 $x340) $x839)) (= $x342 (=> $x386 $x839)))))
+(let ((@x853 (monotonicity (quant-intro (rewrite (= (=> $x149 $x151) $x383)) (= $x153 $x386)) (trans @x844 (rewrite (= (=> $x386 $x839) $x846)) (= $x342 $x846)) (= (and $x153 $x342) $x851))))
+(let ((@x862 (trans (monotonicity @x853 (= $x344 (=> $x147 $x851))) (rewrite (= (=> $x147 $x851) $x858)) (= $x344 $x858))))
+(let ((@x868 (monotonicity (monotonicity @x862 (= (and $x147 $x344) $x863)) (= $x346 (=> $x145 $x863)))))
+(let ((@x877 (monotonicity (trans @x868 (rewrite (= (=> $x145 $x863) $x870)) (= $x346 $x870)) (= (and $x145 $x346) $x875))))
+(let (($x368 (and $x354 (and $x360 $x138))))
+(let (($x371 (and true $x368)))
+(let ((@x362 (quant-intro (rewrite (= (=> $x132 (= ?x128 b_Infinity$)) $x357)) (= $x135 $x360))))
+(let ((@x367 (monotonicity @x362 (rewrite (= (and $x138 true) $x138)) (= (and $x135 (and $x138 true)) (and $x360 $x138)))))
+(let ((@x356 (quant-intro (rewrite (= (=> $x127 (= ?x128 0)) (or $x132 (= ?x128 0)))) (= $x131 $x354))))
+(let ((@x370 (monotonicity @x356 @x367 (= (and $x131 (and $x135 (and $x138 true))) $x368))))
+(let ((@x377 (trans (monotonicity @x370 (= $x142 $x371)) (rewrite (= $x371 $x368)) (= $x142 $x368))))
+(let ((@x381 (trans (monotonicity @x377 (= $x143 $x371)) (rewrite (= $x371 $x368)) (= $x143 $x368))))
+(let ((@x886 (trans (monotonicity @x381 @x877 (= $x348 (=> $x368 $x875))) (rewrite (= (=> $x368 $x875) $x882)) (= $x348 $x882))))
+(let ((@x1411 (trans (monotonicity @x886 (= $x349 (not $x882))) (monotonicity @x1406 (= (not $x882) $x1407)) (= $x349 $x1407))))
+(let ((@x1413 (not-or-elim (mp (asserted $x349) @x1411 $x1407) $x890)))
+(let ((@x1463 (mp~ (and-elim @x1413 $x360) (nnf-pos (refl (~ $x357 $x357)) (~ $x360 $x360)) $x360)))
+(let ((@x3498 (mp @x1463 (quant-intro (refl (= $x357 $x357)) (= $x360 $x3493)) $x3493)))
+(let ((@x6489 (rewrite (= (or (not $x3493) (or $x1538 $x5616)) (or (not $x3493) $x1538 $x5616)))))
+(let ((@x5602 (mp ((_ quant-inst ?v0!5) (or (not $x3493) (or $x1538 $x5616))) @x6489 (or (not $x3493) $x1538 $x5616))))
+(let ((@x5777 (unit-resolution (hypothesis $x6457) (mp (unit-resolution @x5602 @x3498 (hypothesis $x1539) $x5616) @x5778 $x5625) false)))
+(let ((@x5735 (unit-resolution (lemma @x5777 (or $x5625 $x1538)) (unit-resolution ((_ th-lemma arith triangle-eq) (or $x6457 $x1543)) @x6514 $x6457) @x6246 false)))
+(let (($x3544 (not $x3541)))
+(let (($x3827 (or $x3544 $x3824)))
+(let (($x3830 (not $x3827)))
+(let (($x3524 (forall ((?v0 B_Vertex$) (?v1 B_Vertex$) )(!(let ((?x155 (b_G$ (pair$ ?v1 ?v0))))
+(let ((?x128 (v_b_SP_G_0$ ?v1)))
+(let (($x933 (>= (+ ?x128 (* (- 1) (v_b_SP_G_0$ ?v0)) ?x155) 0)))
+(let (($x922 (<= (+ b_Infinity$ (* (- 1) ?x155)) 0)))
+(let (($x136 (v_b_Visited_G_0$ ?v1)))
+(let (($x137 (not $x136)))
+(or $x137 $x922 $x933))))))) :pattern ( (pair$ ?v1 ?v0) )))
+))
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+(let (($x3833 (or $x3529 $x3830)))
+(let (($x3836 (not $x3833)))
+(let ((?x1522 (v_b_SP_G_0$ ?v0!4)))
+(let ((?x1523 (* (- 1) ?x1522)))
+(let ((?x1521 (v_b_SP_G_0$ ?v1!3)))
+(let ((?x1513 (pair$ ?v1!3 ?v0!4)))
+(let ((?x1514 (b_G$ ?x1513)))
+(let ((?x2045 (+ ?x1514 ?x1521 ?x1523)))
+(let (($x2048 (>= ?x2045 0)))
+(let (($x1517 (<= (+ b_Infinity$ (* (- 1) ?x1514)) 0)))
+(let (($x1512 (v_b_Visited_G_0$ ?v1!3)))
+(let (($x2394 (not $x1512)))
+(let (($x2409 (or $x2394 $x1517 $x2048)))
+(let (($x3500 (forall ((?v0 B_Vertex$) )(!(let (($x136 (v_b_Visited_G_0$ ?v0)))
+(not $x136)) :pattern ( (v_b_Visited_G_0$ ?v0) )))
+))
+(let ((@x1468 (mp~ (and-elim @x1413 $x138) (nnf-pos (refl (~ $x137 $x137)) (~ $x138 $x138)) $x138)))
+(let ((@x3505 (mp @x1468 (quant-intro (refl (= $x137 $x137)) (= $x138 $x3500)) $x3500)))
+(let ((@x3073 (unit-resolution ((_ quant-inst ?v1!3) (or (not $x3500) $x2394)) @x3505 (hypothesis $x1512) false)))
+(let (($x2414 (not $x2409)))
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+(or $x136 (not (v_b_Visited_G_0$ ?v0)) $x907))) :pattern ( (v_b_Visited_G_0$ ?v1) (v_b_Visited_G_0$ ?v0) )))
+))
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+(let (($x3845 (or $x3520 $x3842)))
+(let (($x3848 (not $x3845)))
+(let (($x1498 (>= (+ (v_b_SP_G_0$ ?v1!1) (* (- 1) (v_b_SP_G_0$ ?v0!2))) 0)))
+(let (($x1491 (v_b_Visited_G_0$ ?v0!2)))
+(let (($x2348 (not $x1491)))
+(let (($x1489 (v_b_Visited_G_0$ ?v1!1)))
+(let (($x2363 (or $x1489 $x2348 $x1498)))
+(let (($x2368 (not $x2363)))
+(let (($x3851 (or $x2368 $x3848)))
+(let (($x3854 (not $x3851)))
+(let (($x3506 (forall ((?v0 B_Vertex$) )(!(let ((?x128 (v_b_SP_G_0$ ?v0)))
+(>= ?x128 0)) :pattern ( (v_b_SP_G_0$ ?v0) )))
+))
+(let (($x3511 (not $x3506)))
+(let (($x3857 (or $x3511 $x3854)))
+(let (($x3860 (not $x3857)))
+(let ((?x1475 (v_b_SP_G_0$ ?v0!0)))
+(let (($x1476 (>= ?x1475 0)))
+(let (($x1477 (not $x1476)))
+(let ((@x5848 (hypothesis $x1477)))
+(let (($x5440 (<= ?x1475 0)))
+(let (($x86 (<= b_Infinity$ 0)))
+(let (($x87 (not $x86)))
+(let ((@x90 (mp (asserted (< 0 b_Infinity$)) (rewrite (= (< 0 b_Infinity$) $x87)) $x87)))
+(let (($x5734 (= b_Infinity$ ?x1475)))
+(let ((@x4994 (symm (commutativity (= $x5734 (= ?x1475 b_Infinity$))) (= (= ?x1475 b_Infinity$) $x5734))))
+(let (($x5461 (= ?x1475 b_Infinity$)))
+(let (($x5589 (= ?v0!0 b_Source$)))
+(let (($x4695 (not $x5589)))
+(let ((@x5096 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not (= ?x1475 0)) $x1476)) @x5848 (not (= ?x1475 0)))))
+(let (($x3487 (forall ((?v0 B_Vertex$) )(!(let (($x127 (= ?v0 b_Source$)))
+(let (($x132 (not $x127)))
+(or $x132 (= (v_b_SP_G_0$ ?v0) 0)))) :pattern ( (v_b_SP_G_0$ ?v0) )))
+))
+(let ((@x3491 (quant-intro (refl (= (or $x132 (= ?x128 0)) (or $x132 (= ?x128 0)))) (= $x354 $x3487))))
+(let ((@x1457 (nnf-pos (refl (~ (or $x132 (= ?x128 0)) (or $x132 (= ?x128 0)))) (~ $x354 $x354))))
+(let ((@x3492 (mp (mp~ (and-elim @x1413 $x354) @x1457 $x354) @x3491 $x3487)))
+(let (($x5571 (= (or (not $x3487) (or $x4695 (= ?x1475 0))) (or (not $x3487) $x4695 (= ?x1475 0)))))
+(let ((@x5058 (mp ((_ quant-inst ?v0!0) (or (not $x3487) (or $x4695 (= ?x1475 0)))) (rewrite $x5571) (or (not $x3487) $x4695 (= ?x1475 0)))))
+(let ((@x5156 (rewrite (= (or (not $x3493) (or $x5589 $x5461)) (or (not $x3493) $x5589 $x5461)))))
+(let ((@x5542 (mp ((_ quant-inst ?v0!0) (or (not $x3493) (or $x5589 $x5461))) @x5156 (or (not $x3493) $x5589 $x5461))))
+(let ((@x5003 (mp (unit-resolution @x5542 @x3498 (unit-resolution @x5058 @x3492 @x5096 $x4695) $x5461) @x4994 $x5734)))
+(let ((@x5457 ((_ th-lemma arith triangle-eq) (or (not $x5734) (<= (+ b_Infinity$ (* (- 1) ?x1475)) 0)))))
+(let ((@x5462 (unit-resolution @x5457 @x5003 (<= (+ b_Infinity$ (* (- 1) ?x1475)) 0))))
+(let ((@x5446 (lemma ((_ th-lemma arith farkas 1 -1 1) (hypothesis $x5440) @x5462 @x90 false) (or (not $x5440) $x1476))))
+(let ((@x6353 (unit-resolution @x5446 (unit-resolution ((_ th-lemma arith farkas 1 1) (or $x5440 $x1476)) @x5848 $x5440) @x5848 false)))
+(let (($x3863 (or $x1477 $x3860)))
+(let (($x3866 (not $x3863)))
+(let (($x3869 (or $x869 $x3866)))
+(let (($x3872 (not $x3869)))
+(let (($x5983 (not $x3487)))
+(let (($x3194 (or $x5983 $x145)))
+(let ((@x5448 (monotonicity (rewrite (= (= b_Source$ b_Source$) true)) (= (not (= b_Source$ b_Source$)) (not true)))))
+(let ((@x5820 (trans @x5448 (rewrite (= (not true) false)) (= (not (= b_Source$ b_Source$)) false))))
+(let ((@x5657 (monotonicity @x5820 (= (or (not (= b_Source$ b_Source$)) $x145) (or false $x145)))))
+(let ((@x5707 (trans @x5657 (rewrite (= (or false $x145) $x145)) (= (or (not (= b_Source$ b_Source$)) $x145) $x145))))
+(let ((@x5373 (monotonicity @x5707 (= (or $x5983 (or (not (= b_Source$ b_Source$)) $x145)) $x3194))))
+(let ((@x5431 (trans @x5373 (rewrite (= $x3194 $x3194)) (= (or $x5983 (or (not (= b_Source$ b_Source$)) $x145)) $x3194))))
+(let ((@x5763 (mp ((_ quant-inst b_Source$) (or $x5983 (or (not (= b_Source$ b_Source$)) $x145))) @x5431 $x3194)))
+(let (($x3875 (or $x869 $x3872)))
+(let (($x2848 (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 $x2242)))))))))
+))
+(let (($x2833 (forall ((?v0 B_Vertex$) (?v1 B_Vertex$) )(let ((?x303 (v_b_SP_G_2$ ?v0)))
+(let ((?x1263 (* (- 1) ?x303)))
+(let ((?x273 (v_b_SP_G_2$ ?v1)))
+(let ((?x155 (b_G$ (pair$ ?v1 ?v0))))
+(let (($x1282 (>= (+ ?x155 ?x273 ?x1263) 0)))
+(let (($x922 (<= (+ b_Infinity$ (* (- 1) ?x155)) 0)))
+(let (($x291 (fun_app$ v_b_Visited_G_2$ ?v1)))
+(let (($x300 (not $x291)))
+(or $x300 $x922 $x1282))))))))))
+))
+(let (($x2857 (not (or (not $x2833) $x1909 $x1914 (not $x2848)))))
+(let (($x2862 (or $x2811 $x2857)))
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+(or $x291 $x2768 $x1262))))))
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+(let ((?x273 (v_b_SP_G_2$ ?v0)))
+(let (($x278 (= ?x273 ?x174)))
+(let ((?x257 (fun_app$c v_b_SP_G_1$ v_b_v_G_1$)))
+(let ((?x1173 (* (- 1) ?x257)))
+(let (($x1175 (<= (+ ?x174 ?x1173 (* (- 1) (b_G$ (pair$ v_b_v_G_1$ ?v0)))) 0)))
+(let (($x1169 (<= (+ b_Infinity$ (* (- 1) (b_G$ (pair$ v_b_v_G_1$ ?v0)))) 0)))
+(let (($x2717 (or $x1169 $x1175)))
+(let (($x2718 (not $x2717)))
+(or $x2718 $x278)))))))))))
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+(let ((?x1186 (* (- 1) ?x273)))
+(let ((?x268 (b_G$ (pair$ v_b_v_G_1$ ?v0))))
+(let ((?x257 (fun_app$c v_b_SP_G_1$ v_b_v_G_1$)))
+(let (($x1185 (= (+ ?x257 ?x268 ?x1186) 0)))
+(let (($x1175 (<= (+ (fun_app$c v_b_SP_G_1$ ?v0) (* (- 1) ?x257) (* (- 1) ?x268)) 0)))
+(let (($x1169 (<= (+ b_Infinity$ (* (- 1) ?x268)) 0)))
+(or $x1169 $x1175 $x1185)))))))))
+))
+(let (($x2939 (or $x1773 $x1778 $x255 $x1213 (not $x1209) $x2935 (not $x2736) (not $x2742) (not $x2928))))
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+(let ((?x155 (b_G$ (pair$ ?v1 ?v0))))
+(let (($x1140 (>= (+ ?x155 ?x230 (* (- 1) (fun_app$c v_b_SP_G_3$ ?v0))) 0)))
+(let (($x922 (<= (+ b_Infinity$ (* (- 1) ?x155)) 0)))
+(let (($x1099 (<= (+ b_Infinity$ (* (- 1) ?x230)) 0)))
+(or $x1099 $x922 $x1140)))))))
+))
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+(let (($x2685 (or $x2650 $x2680)))
+(let (($x2628 (forall ((?v0 B_Vertex$) )(let ((?x230 (fun_app$c v_b_SP_G_3$ ?v0)))
+(let ((?x2191 (+ ?x230 (* (- 1) (fun_app$c v_b_SP_G_3$ (?v1!9 ?v0))) (* (- 1) (b_G$ (pair$ (?v1!9 ?v0) ?v0))))))
+(let (($x2192 (= ?x2191 0)))
+(let (($x2176 (<= (+ ?x230 (* (- 1) (fun_app$c v_b_SP_G_3$ (?v1!9 ?v0)))) 0)))
+(let (($x2617 (not (or $x2176 (not $x2192)))))
+(let (($x1099 (<= (+ b_Infinity$ (* (- 1) ?x230)) 0)))
+(let (($x127 (= ?v0 b_Source$)))
+(or $x127 $x1099 $x2617)))))))))
+))
+(let (($x2694 (not (or (not $x2628) (not $x2685)))))
+(let (($x2591 (forall ((?v1 B_Vertex$) )(let ((?x1661 (fun_app$c v_b_SP_G_3$ ?v0!8)))
+(let ((?x1662 (* (- 1) ?x1661)))
+(let ((?x230 (fun_app$c v_b_SP_G_3$ ?v1)))
+(let (($x2148 (= (+ ?x230 ?x1662 (b_G$ (pair$ ?v1 ?v0!8))) 0)))
+(or (>= (+ ?x230 ?x1662) 0) (not $x2148)))))))
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+(let (($x2599 (not (or $x1659 $x1664 (not $x2591)))))
+(let (($x2699 (or $x2599 $x2694)))
+(let (($x2576 (forall ((?v0 B_Vertex$) )(let (($x1002 (<= (+ b_Infinity$ (* (- 1) (fun_app$c v_b_SP_G_1$ ?v0))) 0)))
+(let (($x178 (fun_app$ v_b_Visited_G_1$ ?v0)))
+(or $x178 $x1002))))
+))
+(let (($x2712 (not (or (not $x2576) $x2706 $x2707 $x2708 $x2709 (not $x2699)))))
+(let (($x2945 (or $x2712 $x2940)))
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+(let ((?x2128 (+ ?x174 (* (- 1) (fun_app$c v_b_SP_G_1$ (?v1!7 ?v0))) (* (- 1) (b_G$ (pair$ (?v1!7 ?v0) ?v0))))))
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+(let (($x2113 (<= (+ ?x174 (* (- 1) (fun_app$c v_b_SP_G_1$ (?v1!7 ?v0)))) 0)))
+(let (($x2551 (not (or $x2113 (not (fun_app$ v_b_Visited_G_1$ (?v1!7 ?v0))) (not $x2129)))))
+(let (($x1002 (<= (+ b_Infinity$ (* (- 1) ?x174)) 0)))
+(let (($x127 (= ?v0 b_Source$)))
+(or $x127 $x1002 $x2551)))))))))
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+(let (($x990 (>= (+ ?x155 ?x174 (* (- 1) (fun_app$c v_b_SP_G_1$ ?v0))) 0)))
+(let (($x922 (<= (+ b_Infinity$ (* (- 1) ?x155)) 0)))
+(let (($x178 (fun_app$ v_b_Visited_G_1$ ?v1)))
+(let (($x179 (not $x178)))
+(or $x179 $x922 $x990))))))))
+))
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+(let (($x178 (fun_app$ v_b_Visited_G_1$ ?v1)))
+(or $x178 (not (fun_app$ v_b_Visited_G_1$ ?v0)) $x1015)))))
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+(let ((?x2090 (+ ?x128 (* (- 1) (v_b_SP_G_0$ (?v1!6 ?v0))) (* (- 1) (b_G$ (pair$ (?v1!6 ?v0) ?v0))))))
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+(let (($x2075 (<= (+ ?x128 (* (- 1) (v_b_SP_G_0$ (?v1!6 ?v0)))) 0)))
+(let (($x2478 (not (or $x2075 (not (v_b_Visited_G_0$ (?v1!6 ?v0))) (not $x2091)))))
+(let (($x947 (<= (+ b_Infinity$ (* (- 1) ?x128)) 0)))
+(let (($x127 (= ?v0 b_Source$)))
+(or $x127 $x947 $x2478)))))))))
+))
+(let (($x2958 (or (not $x2489) $x2952 (not $x1051) (not $x2512) (not $x2534) (not $x2562) (not $x2945))))
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+(let ((?x1541 (* (- 1) ?x1540)))
+(let ((?x128 (v_b_SP_G_0$ ?v1)))
+(let (($x136 (v_b_Visited_G_0$ ?v1)))
+(let (($x137 (not $x136)))
+(or (>= (+ ?x128 ?x1541) 0) $x137 (not (= (+ ?x128 ?x1541 (b_G$ (pair$ ?v1 ?v0!5))) 0)))))))))
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+(let (($x2964 (or $x2459 $x2959)))
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+(let (($x933 (>= (+ ?x128 (* (- 1) (v_b_SP_G_0$ ?v0)) ?x155) 0)))
+(let (($x922 (<= (+ b_Infinity$ (* (- 1) ?x155)) 0)))
+(let (($x136 (v_b_Visited_G_0$ ?v1)))
+(let (($x137 (not $x136)))
+(or $x137 $x922 $x933))))))))
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+(let (($x2973 (not (or (not $x2436) (not $x2964)))))
+(let (($x2978 (or $x2414 $x2973)))
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+(let (($x136 (v_b_Visited_G_0$ ?v1)))
+(or $x136 (not (v_b_Visited_G_0$ ?v0)) $x907))))
+))
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+(let (($x2992 (or $x2368 $x2987)))
+(let (($x3000 (not (or $x902 (not $x2992)))))
+(let (($x3005 (or $x1477 $x3000)))
+(let (($x3013 (not (or $x869 (not $x3005)))))
+(let (($x3018 (or $x869 $x3013)))
+(let (($x2837 (or (>= (+ ?x273 (* (- 1) ?x1911)) 0) $x300 (not (= (+ ?x273 (* (- 1) ?x1911) (b_G$ (pair$ ?0 ?v0!20))) 0)))))
+(let ((@x3736 (monotonicity (quant-intro (refl (= $x2837 $x2837)) (= $x2848 $x3729)) (= (not $x2848) $x3734))))
+(let ((@x3724 (quant-intro (refl (= (or $x300 $x922 $x1282) (or $x300 $x922 $x1282))) (= $x2833 $x3720))))
+(let ((@x3739 (monotonicity (monotonicity @x3724 (= (not $x2833) $x3725)) @x3736 (= (or (not $x2833) $x1909 $x1914 (not $x2848)) $x3737))))
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+(let ((@x3716 (quant-intro (refl (= (or $x291 (not $x301) $x1262) (or $x291 (not $x301) $x1262))) (= $x2788 $x3712))))
+(let ((@x3751 (monotonicity (monotonicity @x3716 (= (not $x2788) $x3717)) @x3748 (= (or (not $x2788) (not $x2862)) $x3749))))
+(let ((@x3760 (monotonicity (monotonicity (monotonicity @x3751 (= $x2871 $x3752)) (= $x2876 $x3755)) (= (not $x2876) $x3758))))
+(let ((@x3707 (quant-intro (refl (= (>= ?x273 0) (>= ?x273 0))) (= $x1256 $x3703))))
+(let ((@x3763 (monotonicity (monotonicity @x3707 (= $x1259 $x3708)) @x3760 (= (or $x1259 (not $x2876)) $x3761))))
+(let ((@x3772 (monotonicity (monotonicity (monotonicity @x3763 (= $x2884 $x3764)) (= $x2889 $x3767)) (= (not $x2889) $x3770))))
+(let ((@x3778 (monotonicity (monotonicity @x3772 (= (or $x773 (not $x2889)) $x3773)) (= $x2897 $x3776))))
+(let ((@x3784 (monotonicity (monotonicity @x3778 (= $x2902 $x3779)) (= (not $x2902) $x3782))))
+(let ((@x3699 (quant-intro (refl (= (or $x300 $x278) (or $x300 $x278))) (= $x652 $x3695))))
+(let ((@x3787 (monotonicity (monotonicity @x3699 (= $x785 $x3700)) @x3784 (= (or $x785 (not $x2902)) $x3785))))
+(let ((@x3796 (monotonicity (monotonicity (monotonicity @x3787 (= $x2910 $x3788)) (= $x2915 $x3791)) (= (not $x2915) $x3794))))
+(let ((@x3693 (monotonicity (quant-intro (refl (= $x1243 $x1243)) (= $x1247 $x3686)) (= $x1250 $x3691))))
+(let ((@x3802 (monotonicity (monotonicity @x3693 @x3796 (= (or $x1250 (not $x2915)) $x3797)) (= $x2923 $x3800))))
+(let ((@x3808 (monotonicity (monotonicity @x3802 (= $x2928 $x3803)) (= (not $x2928) $x3806))))
+(let ((@x3680 (refl (= (or (not (or $x1169 $x1175)) $x278) (or (not (or $x1169 $x1175)) $x278)))))
+(let ((@x3685 (monotonicity (quant-intro @x3680 (= $x2742 $x3678)) (= (not $x2742) $x3683))))
+(let ((@x3674 (quant-intro (refl (= (or $x1169 $x1175 $x1185) (or $x1169 $x1175 $x1185))) (= $x2736 $x3670))))
+(let ((@x3667 (monotonicity (quant-intro (refl (= $x1206 $x1206)) (= $x1209 $x3660)) (= (not $x1209) $x3665))))
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+(let ((@x3626 (quant-intro (refl (= (or $x1099 $x922 $x1140) (or $x1099 $x922 $x1140))) (= $x2672 $x3622))))
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+(let ((@x3641 (monotonicity (monotonicity (monotonicity @x3632 (= $x2680 $x3633)) (= $x2685 $x3636)) (= (not $x2685) $x3639))))
+(let ((?x2191 (+ ?x230 (* (- 1) (fun_app$c v_b_SP_G_3$ (?v1!9 ?0))) (* (- 1) (b_G$ (pair$ (?v1!9 ?0) ?0))))))
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+(let (($x2176 (<= (+ ?x230 (* (- 1) (fun_app$c v_b_SP_G_3$ (?v1!9 ?0)))) 0)))
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+(let (($x2623 (or $x127 $x1099 $x2617)))
+(let ((@x3621 (monotonicity (quant-intro (refl (= $x2623 $x2623)) (= $x2628 $x3614)) (= (not $x2628) $x3619))))
+(let ((@x3647 (monotonicity (monotonicity @x3621 @x3641 (= (or (not $x2628) (not $x2685)) $x3642)) (= $x2694 $x3645))))
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+(let (($x2580 (or (>= (+ ?x230 ?x1662) 0) (not $x2148))))
+(let ((@x3607 (monotonicity (quant-intro (refl (= $x2580 $x2580)) (= $x2591 $x3600)) (= (not $x2591) $x3605))))
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+(let ((@x3653 (monotonicity (monotonicity @x3613 @x3647 (= $x2699 $x3648)) (= (not $x2699) $x3651))))
+(let ((@x3594 (quant-intro (refl (= (or $x178 $x1002) (or $x178 $x1002))) (= $x2576 $x3590))))
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+(let ((@x3817 (monotonicity (monotonicity @x3656 (= $x2712 $x3657)) (monotonicity @x3811 (= $x2940 $x3812)) (= $x2945 $x3815))))
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+(let (($x2557 (or $x127 $x1002 $x2551)))
+(let ((@x3588 (monotonicity (quant-intro (refl (= $x2557 $x2557)) (= $x2562 $x3581)) (= (not $x2562) $x3586))))
+(let ((@x3577 (quant-intro (refl (= (or $x179 $x922 $x990) (or $x179 $x922 $x990))) (= $x2534 $x3573))))
+(let ((@x3569 (quant-intro (refl (= (or $x178 (not $x180) $x1015) (or $x178 (not $x180) $x1015))) (= $x2512 $x3565))))
+(let ((@x3560 (quant-intro (refl (= (>= ?x174 0) (>= ?x174 0))) (= $x1051 $x3556))))
+(let ((?x2090 (+ ?x128 (* (- 1) (v_b_SP_G_0$ (?v1!6 ?0))) (* (- 1) (b_G$ (pair$ (?v1!6 ?0) ?0))))))
+(let (($x2091 (= ?x2090 0)))
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+(let ((@x3554 (monotonicity (quant-intro (refl (= $x2484 $x2484)) (= $x2489 $x3547)) (= (not $x2489) $x3552))))
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+(let ((@x3540 (monotonicity (quant-intro (refl (= $x2440 $x2440)) (= $x2451 $x3533)) (= (not $x2451) $x3538))))
+(let ((@x3546 (monotonicity (monotonicity @x3540 (= (or $x1538 $x1543 (not $x2451)) $x3541)) (= $x2459 $x3544))))
+(let ((@x3829 (monotonicity @x3546 (monotonicity @x3823 (= $x2959 $x3824)) (= $x2964 $x3827))))
+(let ((@x3528 (quant-intro (refl (= (or $x137 $x922 $x933) (or $x137 $x922 $x933))) (= $x2436 $x3524))))
+(let ((@x3835 (monotonicity (monotonicity @x3528 (= (not $x2436) $x3529)) (monotonicity @x3829 (= (not $x2964) $x3830)) (= (or (not $x2436) (not $x2964)) $x3833))))
+(let ((@x3844 (monotonicity (monotonicity (monotonicity @x3835 (= $x2973 $x3836)) (= $x2978 $x3839)) (= (not $x2978) $x3842))))
+(let ((@x3519 (quant-intro (refl (= (or $x136 (not $x148) $x907) (or $x136 (not $x148) $x907))) (= $x2391 $x3515))))
+(let ((@x3847 (monotonicity (monotonicity @x3519 (= (not $x2391) $x3520)) @x3844 (= (or (not $x2391) (not $x2978)) $x3845))))
+(let ((@x3856 (monotonicity (monotonicity (monotonicity @x3847 (= $x2987 $x3848)) (= $x2992 $x3851)) (= (not $x2992) $x3854))))
+(let ((@x3510 (quant-intro (refl (= (>= ?x128 0) (>= ?x128 0))) (= $x899 $x3506))))
+(let ((@x3859 (monotonicity (monotonicity @x3510 (= $x902 $x3511)) @x3856 (= (or $x902 (not $x2992)) $x3857))))
+(let ((@x3868 (monotonicity (monotonicity (monotonicity @x3859 (= $x3000 $x3860)) (= $x3005 $x3863)) (= (not $x3005) $x3866))))
+(let ((@x3874 (monotonicity (monotonicity @x3868 (= (or $x869 (not $x3005)) $x3869)) (= $x3013 $x3872))))
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+(let ((?x1912 (* (- 1) ?x1911)))
+(let ((?x273 (v_b_SP_G_2$ ?v1)))
+(let (($x2242 (= (+ ?x273 ?x1912 (b_G$ (pair$ ?v1 ?v0!20))) 0)))
+(let (($x291 (fun_app$ v_b_Visited_G_2$ ?v1)))
+(let (($x2245 (and (not (>= (+ ?x273 ?x1912) 0)) $x291 $x2242)))
+(not $x2245))))))))
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+(let (($x2283 (or $x773 $x2280)))
+(let (($x2286 (and $x652 $x2283)))
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+(let (($x2215 (not $x2212)))
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+(let ((?x2191 (+ ?x230 (* (- 1) (fun_app$c v_b_SP_G_3$ (?v1!9 ?v0))) (* (- 1) (b_G$ (pair$ (?v1!9 ?v0) ?v0))))))
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+(let (($x2176 (<= (+ ?x230 (* (- 1) (fun_app$c v_b_SP_G_3$ (?v1!9 ?v0)))) 0)))
+(let (($x2197 (and (not $x2176) $x2192)))
+(let (($x1099 (<= (+ b_Infinity$ (* (- 1) ?x230)) 0)))
+(let (($x1100 (not $x1099)))
+(let (($x127 (= ?v0 b_Source$)))
+(let (($x132 (not $x127)))
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+(let ((?x1662 (* (- 1) ?x1661)))
+(let ((?x230 (fun_app$c v_b_SP_G_3$ ?v1)))
+(let (($x2148 (= (+ ?x230 ?x1662 (b_G$ (pair$ ?v1 ?v0!8))) 0)))
+(let (($x2151 (and (not (>= (+ ?x230 ?x1662) 0)) $x2148)))
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+(let (($x179 (not $x178)))
+(let (($x1077 (and $x179 $x1003)))
+(not $x1077)))))))
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+(let (($x2306 (or $x2230 $x2301)))
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+(let ((?x2128 (+ ?x174 (* (- 1) (fun_app$c v_b_SP_G_1$ (?v1!7 ?v0))) (* (- 1) (b_G$ (pair$ (?v1!7 ?v0) ?v0))))))
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+(let ((?x1613 (?v1!7 ?v0)))
+(let (($x1618 (fun_app$ v_b_Visited_G_1$ ?x1613)))
+(let (($x2134 (and (not (<= (+ ?x174 (* (- 1) (fun_app$c v_b_SP_G_1$ ?x1613))) 0)) $x1618 $x2129)))
+(let (($x1002 (<= (+ b_Infinity$ (* (- 1) ?x174)) 0)))
+(let (($x1003 (not $x1002)))
+(let (($x127 (= ?v0 b_Source$)))
+(let (($x132 (not $x127)))
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+(let (($x1009 (not $x1006)))
+(or $x1009 $x2134))))))))))))))
+))
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+(let ((?x2090 (+ ?x128 (* (- 1) (v_b_SP_G_0$ (?v1!6 ?v0))) (* (- 1) (b_G$ (pair$ (?v1!6 ?v0) ?v0))))))
+(let (($x2091 (= ?x2090 0)))
+(let ((?x1578 (?v1!6 ?v0)))
+(let (($x1583 (v_b_Visited_G_0$ ?x1578)))
+(let (($x2096 (and (not (<= (+ ?x128 (* (- 1) (v_b_SP_G_0$ ?x1578))) 0)) $x1583 $x2091)))
+(let (($x127 (= ?v0 b_Source$)))
+(let (($x132 (not $x127)))
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+(let (($x954 (not $x951)))
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+))
+(let (($x2315 (and $x2102 $x173 $x1051 $x1045 $x997 $x2140 $x2306)))
+(let (($x1567 (forall ((?v1 B_Vertex$) )(let ((?x1540 (v_b_SP_G_0$ ?v0!5)))
+(let ((?x1541 (* (- 1) ?x1540)))
+(let ((?x128 (v_b_SP_G_0$ ?v1)))
+(let (($x136 (v_b_Visited_G_0$ ?v1)))
+(let (($x1554 (and (not (>= (+ ?x128 ?x1541) 0)) $x136 (= (+ ?x128 ?x1541 (b_G$ (pair$ ?v1 ?v0!5))) 0))))
+(not $x1554)))))))
+))
+(let (($x2062 (and $x1539 $x1544 $x1567)))
+(let (($x2320 (or $x2062 $x2315)))
+(let (($x2323 (and $x939 $x2320)))
+(let (($x1520 (not (and $x1512 (not $x1517)))))
+(let (($x2051 (or $x1520 $x2048)))
+(let (($x2054 (not $x2051)))
+(let (($x2326 (or $x2054 $x2323)))
+(let (($x2329 (and $x914 $x2326)))
+(let (($x1493 (not (and (not $x1489) $x1491))))
+(let (($x1499 (or $x1493 $x1498)))
+(let (($x1500 (not $x1499)))
+(let (($x2332 (or $x1500 $x2329)))
+(let (($x2335 (and $x899 $x2332)))
+(let (($x2338 (or $x1477 $x2335)))
+(let (($x2341 (and $x145 $x2338)))
+(let (($x2344 (or $x869 $x2341)))
+(let ((@x2942 (rewrite (= (and $x1774 $x1779 $x256 $x1214 $x1209 $x266 $x2736 $x2742 $x2928) $x2940))))
+(let (($x2242 (= (+ ?x273 (* (- 1) ?x1911) (b_G$ (pair$ ?0 ?v0!20))) 0)))
+(let (($x2245 (and (not (>= (+ ?x273 (* (- 1) ?x1911)) 0)) $x291 $x2242)))
+(let (($x2248 (not $x2245)))
+(let ((@x2843 (monotonicity (rewrite (= $x2245 (not $x2837))) (= $x2248 (not (not $x2837))))))
+(let ((@x2850 (quant-intro (trans @x2843 (rewrite (= (not (not $x2837)) $x2837)) (= $x2248 $x2837)) (= $x2251 $x2848))))
+(let ((@x2820 (monotonicity (rewrite (= $x1276 (not (or $x300 $x922)))) (= $x1279 (not (not (or $x300 $x922)))))))
+(let ((@x2824 (trans @x2820 (rewrite (= (not (not (or $x300 $x922))) (or $x300 $x922))) (= $x1279 (or $x300 $x922)))))
+(let ((@x2832 (trans (monotonicity @x2824 (= $x1286 (or (or $x300 $x922) $x1282))) (rewrite (= (or (or $x300 $x922) $x1282) (or $x300 $x922 $x1282))) (= $x1286 (or $x300 $x922 $x1282)))))
+(let ((@x2853 (monotonicity (quant-intro @x2832 (= $x1289 $x2833)) @x2850 (= $x2260 (and $x2833 $x1910 $x1915 $x2848)))))
+(let ((@x2861 (trans @x2853 (rewrite (= (and $x2833 $x1910 $x1915 $x2848) $x2857)) (= $x2260 $x2857))))
+(let ((@x2798 (monotonicity (rewrite (= (and $x1883 (not $x1888)) (not (or $x2791 $x1888)))) (= $x1891 (not (not (or $x2791 $x1888)))))))
+(let ((@x2802 (trans @x2798 (rewrite (= (not (not (or $x2791 $x1888))) (or $x2791 $x1888))) (= $x1891 (or $x2791 $x1888)))))
+(let ((@x2810 (trans (monotonicity @x2802 (= $x1897 (or (or $x2791 $x1888) $x1896))) (rewrite (= (or (or $x2791 $x1888) $x1896) $x2806)) (= $x1897 $x2806))))
+(let ((@x2864 (monotonicity (monotonicity @x2810 (= $x1898 $x2811)) @x2861 (= $x2265 $x2862))))
+(let ((@x2785 (rewrite (= (or (or $x291 (not $x301)) $x1262) (or $x291 (not $x301) $x1262)))))
+(let ((@x2777 (rewrite (= (not (not (or $x291 (not $x301)))) (or $x291 (not $x301))))))
+(let ((@x2775 (monotonicity (rewrite (= $x302 (not (or $x291 (not $x301))))) (= $x664 (not (not (or $x291 (not $x301))))))))
+(let ((@x2782 (monotonicity (trans @x2775 @x2777 (= $x664 (or $x291 (not $x301)))) (= $x1267 (or (or $x291 (not $x301)) $x1262)))))
+(let ((@x2790 (quant-intro (trans @x2782 @x2785 (= $x1267 (or $x291 (not $x301) $x1262))) (= $x1270 $x2788))))
+(let ((@x2875 (trans (monotonicity @x2790 @x2864 (= $x2268 (and $x2788 $x2862))) (rewrite (= (and $x2788 $x2862) $x2871)) (= $x2268 $x2871))))
+(let ((@x2752 (monotonicity (rewrite (= (and (not $x1860) $x1862) (not (or $x1860 $x2745)))) (= $x1864 (not (not (or $x1860 $x2745)))))))
+(let ((@x2756 (trans @x2752 (rewrite (= (not (not (or $x1860 $x2745))) (or $x1860 $x2745))) (= $x1864 (or $x1860 $x2745)))))
+(let ((@x2764 (trans (monotonicity @x2756 (= $x1870 (or (or $x1860 $x2745) $x1869))) (rewrite (= (or (or $x1860 $x2745) $x1869) $x2760)) (= $x1870 $x2760))))
+(let ((@x2878 (monotonicity (monotonicity @x2764 (= $x1871 $x2765)) @x2875 (= $x2271 $x2876))))
+(let ((@x2888 (trans (monotonicity @x2878 (= $x2274 (and $x1256 $x2876))) (rewrite (= (and $x1256 $x2876) $x2884)) (= $x2274 $x2884))))
+(let ((@x2894 (monotonicity (monotonicity @x2888 (= $x2277 $x2889)) (= $x2280 (and $x297 $x2889)))))
+(let ((@x2904 (monotonicity (trans @x2894 (rewrite (= (and $x297 $x2889) $x2897)) (= $x2280 $x2897)) (= $x2283 $x2902))))
+(let ((@x2914 (trans (monotonicity @x2904 (= $x2286 (and $x652 $x2902))) (rewrite (= (and $x652 $x2902) $x2910)) (= $x2286 $x2910))))
+(let ((@x2920 (monotonicity (monotonicity @x2914 (= $x2289 $x2915)) (= $x2292 (and $x1247 $x2915)))))
+(let ((@x2930 (monotonicity (trans @x2920 (rewrite (= (and $x1247 $x2915) $x2923)) (= $x2292 $x2923)) (= $x2295 $x2928))))
+(let ((@x2741 (monotonicity (rewrite (= $x1179 (not (or $x1169 $x1175)))) (= $x1196 (or (not (or $x1169 $x1175)) $x278)))))
+(let ((@x2723 (monotonicity (rewrite (= $x1179 (not (or $x1169 $x1175)))) (= $x1182 (not (not (or $x1169 $x1175)))))))
+(let ((@x2727 (trans @x2723 (rewrite (= (not (not (or $x1169 $x1175))) (or $x1169 $x1175))) (= $x1182 (or $x1169 $x1175)))))
+(let ((@x2735 (trans (monotonicity @x2727 (= $x1190 (or (or $x1169 $x1175) $x1185))) (rewrite (= (or (or $x1169 $x1175) $x1185) (or $x1169 $x1175 $x1185))) (= $x1190 (or $x1169 $x1175 $x1185)))))
+(let ((@x2933 (monotonicity (quant-intro @x2735 (= $x1193 $x2736)) (quant-intro @x2741 (= $x1199 $x2742)) @x2930 (= $x2301 (and $x1774 $x1779 $x256 $x1214 $x1209 $x266 $x2736 $x2742 $x2928)))))
+(let ((@x2659 (monotonicity (rewrite (= $x1134 (not (or $x1099 $x922)))) (= $x1137 (not (not (or $x1099 $x922)))))))
+(let ((@x2663 (trans @x2659 (rewrite (= (not (not (or $x1099 $x922))) (or $x1099 $x922))) (= $x1137 (or $x1099 $x922)))))
+(let ((@x2671 (trans (monotonicity @x2663 (= $x1143 (or (or $x1099 $x922) $x1140))) (rewrite (= (or (or $x1099 $x922) $x1140) (or $x1099 $x922 $x1140))) (= $x1143 (or $x1099 $x922 $x1140)))))
+(let ((@x2677 (monotonicity (quant-intro @x2671 (= $x1146 $x2672)) (= $x1752 (and $x2672 $x1749)))))
+(let ((@x2637 (monotonicity (rewrite (= (and (not $x1724) (not $x1730)) (not (or $x1724 $x1730)))) (= $x1733 (not (not (or $x1724 $x1730)))))))
+(let ((@x2641 (trans @x2637 (rewrite (= (not (not (or $x1724 $x1730))) (or $x1724 $x1730))) (= $x1733 (or $x1724 $x1730)))))
+(let ((@x2649 (trans (monotonicity @x2641 (= $x2212 (or (or $x1724 $x1730) $x2209))) (rewrite (= (or (or $x1724 $x1730) $x2209) $x2645)) (= $x2212 $x2645))))
+(let ((@x2687 (monotonicity (monotonicity @x2649 (= $x2215 $x2650)) (trans @x2677 (rewrite (= (and $x2672 $x1749) $x2680)) (= $x1752 $x2680)) (= $x2218 $x2685))))
+(let ((@x2610 (monotonicity (rewrite (= $x1103 (not (or $x127 $x1099)))) (= $x1106 (not (not (or $x127 $x1099)))))))
+(let ((@x2614 (trans @x2610 (rewrite (= (not (not (or $x127 $x1099))) (or $x127 $x1099))) (= $x1106 (or $x127 $x1099)))))
+(let ((@x2622 (monotonicity @x2614 (rewrite (= (and (not $x2176) $x2192) $x2617)) (= (or $x1106 (and (not $x2176) $x2192)) (or (or $x127 $x1099) $x2617)))))
+(let ((@x2627 (trans @x2622 (rewrite (= (or (or $x127 $x1099) $x2617) $x2623)) (= (or $x1106 (and (not $x2176) $x2192)) $x2623))))
+(let ((@x2690 (monotonicity (quant-intro @x2627 (= $x2203 $x2628)) @x2687 (= $x2221 (and $x2628 $x2685)))))
+(let (($x2151 (and (not (>= (+ ?x230 ?x1662) 0)) $x2148)))
+(let (($x2154 (not $x2151)))
+(let ((@x2586 (monotonicity (rewrite (= $x2151 (not $x2580))) (= $x2154 (not (not $x2580))))))
+(let ((@x2593 (quant-intro (trans @x2586 (rewrite (= (not (not $x2580)) $x2580)) (= $x2154 $x2580)) (= $x2157 $x2591))))
+(let ((@x2603 (trans (monotonicity @x2593 (= $x2163 (and $x1660 $x1665 $x2591))) (rewrite (= (and $x1660 $x1665 $x2591) $x2599)) (= $x2163 $x2599))))
+(let ((@x2701 (monotonicity @x2603 (trans @x2690 (rewrite (= (and $x2628 $x2685) $x2694)) (= $x2221 $x2694)) (= $x2224 $x2699))))
+(let ((@x2571 (monotonicity (rewrite (= $x1077 (not (or $x178 $x1002)))) (= (not $x1077) (not (not (or $x178 $x1002)))))))
+(let ((@x2575 (trans @x2571 (rewrite (= (not (not (or $x178 $x1002))) (or $x178 $x1002))) (= (not $x1077) (or $x178 $x1002)))))
+(let ((@x2704 (monotonicity (quant-intro @x2575 (= $x1641 $x2576)) @x2701 (= $x2230 (and $x2576 $x212 $x215 $x217 $x220 $x2699)))))
+(let ((@x2716 (trans @x2704 (rewrite (= (and $x2576 $x212 $x215 $x217 $x220 $x2699) $x2712)) (= $x2230 $x2712))))
+(let ((?x1613 (?v1!7 ?0)))
+(let (($x1618 (fun_app$ v_b_Visited_G_1$ ?x1613)))
+(let (($x2134 (and (not $x2113) $x1618 $x2129)))
+(let (($x2137 (or $x1009 $x2134)))
+(let ((@x2543 (monotonicity (rewrite (= $x1006 (not (or $x127 $x1002)))) (= $x1009 (not (not (or $x127 $x1002)))))))
+(let ((@x2547 (trans @x2543 (rewrite (= (not (not (or $x127 $x1002))) (or $x127 $x1002))) (= $x1009 (or $x127 $x1002)))))
+(let ((@x2556 (monotonicity @x2547 (rewrite (= $x2134 $x2551)) (= $x2137 (or (or $x127 $x1002) $x2551)))))
+(let ((@x2561 (trans @x2556 (rewrite (= (or (or $x127 $x1002) $x2551) $x2557)) (= $x2137 $x2557))))
+(let ((@x2521 (monotonicity (rewrite (= $x983 (not (or $x179 $x922)))) (= $x986 (not (not (or $x179 $x922)))))))
+(let ((@x2525 (trans @x2521 (rewrite (= (not (not (or $x179 $x922))) (or $x179 $x922))) (= $x986 (or $x179 $x922)))))
+(let ((@x2533 (trans (monotonicity @x2525 (= $x994 (or (or $x179 $x922) $x990))) (rewrite (= (or (or $x179 $x922) $x990) (or $x179 $x922 $x990))) (= $x994 (or $x179 $x922 $x990)))))
+(let ((@x2509 (rewrite (= (or (or $x178 (not $x180)) $x1015) (or $x178 (not $x180) $x1015)))))
+(let ((@x2501 (rewrite (= (not (not (or $x178 (not $x180)))) (or $x178 (not $x180))))))
+(let ((@x2499 (monotonicity (rewrite (= $x181 (not (or $x178 (not $x180))))) (= $x403 (not (not (or $x178 (not $x180))))))))
+(let ((@x2506 (monotonicity (trans @x2499 @x2501 (= $x403 (or $x178 (not $x180)))) (= $x1042 (or (or $x178 (not $x180)) $x1015)))))
+(let ((@x2514 (quant-intro (trans @x2506 @x2509 (= $x1042 (or $x178 (not $x180) $x1015))) (= $x1045 $x2512))))
+(let ((?x1578 (?v1!6 ?0)))
+(let (($x1583 (v_b_Visited_G_0$ ?x1578)))
+(let (($x2096 (and (not $x2075) $x1583 $x2091)))
+(let (($x2099 (or $x954 $x2096)))
+(let ((@x2470 (monotonicity (rewrite (= $x951 (not (or $x127 $x947)))) (= $x954 (not (not (or $x127 $x947)))))))
+(let ((@x2474 (trans @x2470 (rewrite (= (not (not (or $x127 $x947))) (or $x127 $x947))) (= $x954 (or $x127 $x947)))))
+(let ((@x2483 (monotonicity @x2474 (rewrite (= $x2096 $x2478)) (= $x2099 (or (or $x127 $x947) $x2478)))))
+(let ((@x2488 (trans @x2483 (rewrite (= (or (or $x127 $x947) $x2478) $x2484)) (= $x2099 $x2484))))
+(let ((@x2950 (monotonicity (quant-intro @x2488 (= $x2102 $x2489)) @x2514 (quant-intro @x2533 (= $x997 $x2534)) (quant-intro @x2561 (= $x2140 $x2562)) (monotonicity @x2716 (trans @x2933 @x2942 (= $x2301 $x2940)) (= $x2306 $x2945)) (= $x2315 (and $x2489 $x173 $x1051 $x2512 $x2534 $x2562 $x2945)))))
+(let ((@x2963 (trans @x2950 (rewrite (= (and $x2489 $x173 $x1051 $x2512 $x2534 $x2562 $x2945) $x2959)) (= $x2315 $x2959))))
+(let (($x1554 (and (not (>= (+ ?x128 ?x1541) 0)) $x136 (= (+ ?x128 ?x1541 (b_G$ (pair$ ?0 ?v0!5))) 0))))
+(let (($x1564 (not $x1554)))
+(let ((@x2446 (monotonicity (rewrite (= $x1554 (not $x2440))) (= $x1564 (not (not $x2440))))))
+(let ((@x2453 (quant-intro (trans @x2446 (rewrite (= (not (not $x2440)) $x2440)) (= $x1564 $x2440)) (= $x1567 $x2451))))
+(let ((@x2463 (trans (monotonicity @x2453 (= $x2062 (and $x1539 $x1544 $x2451))) (rewrite (= (and $x1539 $x1544 $x2451) $x2459)) (= $x2062 $x2459))))
+(let ((@x2423 (monotonicity (rewrite (= $x926 (not (or $x137 $x922)))) (= $x929 (not (not (or $x137 $x922)))))))
+(let ((@x2427 (trans @x2423 (rewrite (= (not (not (or $x137 $x922))) (or $x137 $x922))) (= $x929 (or $x137 $x922)))))
+(let ((@x2435 (trans (monotonicity @x2427 (= $x936 (or (or $x137 $x922) $x933))) (rewrite (= (or (or $x137 $x922) $x933) (or $x137 $x922 $x933))) (= $x936 (or $x137 $x922 $x933)))))
+(let ((@x2969 (monotonicity (quant-intro @x2435 (= $x939 $x2436)) (monotonicity @x2463 @x2963 (= $x2320 $x2964)) (= $x2323 (and $x2436 $x2964)))))
+(let ((@x2401 (monotonicity (rewrite (= (and $x1512 (not $x1517)) (not (or $x2394 $x1517)))) (= $x1520 (not (not (or $x2394 $x1517)))))))
+(let ((@x2405 (trans @x2401 (rewrite (= (not (not (or $x2394 $x1517))) (or $x2394 $x1517))) (= $x1520 (or $x2394 $x1517)))))
+(let ((@x2413 (trans (monotonicity @x2405 (= $x2051 (or (or $x2394 $x1517) $x2048))) (rewrite (= (or (or $x2394 $x1517) $x2048) $x2409)) (= $x2051 $x2409))))
+(let ((@x2980 (monotonicity (monotonicity @x2413 (= $x2054 $x2414)) (trans @x2969 (rewrite (= (and $x2436 $x2964) $x2973)) (= $x2323 $x2973)) (= $x2326 $x2978))))
+(let ((@x2388 (rewrite (= (or (or $x136 (not $x148)) $x907) (or $x136 (not $x148) $x907)))))
+(let ((@x2380 (rewrite (= (not (not (or $x136 (not $x148)))) (or $x136 (not $x148))))))
+(let ((@x2378 (monotonicity (rewrite (= $x149 (not (or $x136 (not $x148))))) (= $x382 (not (not (or $x136 (not $x148))))))))
+(let ((@x2385 (monotonicity (trans @x2378 @x2380 (= $x382 (or $x136 (not $x148)))) (= $x911 (or (or $x136 (not $x148)) $x907)))))
+(let ((@x2393 (quant-intro (trans @x2385 @x2388 (= $x911 (or $x136 (not $x148) $x907))) (= $x914 $x2391))))
+(let ((@x2991 (trans (monotonicity @x2393 @x2980 (= $x2329 (and $x2391 $x2978))) (rewrite (= (and $x2391 $x2978) $x2987)) (= $x2329 $x2987))))
+(let ((@x2355 (monotonicity (rewrite (= (and (not $x1489) $x1491) (not (or $x1489 $x2348)))) (= $x1493 (not (not (or $x1489 $x2348)))))))
+(let ((@x2359 (trans @x2355 (rewrite (= (not (not (or $x1489 $x2348))) (or $x1489 $x2348))) (= $x1493 (or $x1489 $x2348)))))
+(let ((@x2367 (trans (monotonicity @x2359 (= $x1499 (or (or $x1489 $x2348) $x1498))) (rewrite (= (or (or $x1489 $x2348) $x1498) $x2363)) (= $x1499 $x2363))))
+(let ((@x2994 (monotonicity (monotonicity @x2367 (= $x1500 $x2368)) @x2991 (= $x2332 $x2992))))
+(let ((@x3004 (trans (monotonicity @x2994 (= $x2335 (and $x899 $x2992))) (rewrite (= (and $x899 $x2992) $x3000)) (= $x2335 $x3000))))
+(let ((@x3010 (monotonicity (monotonicity @x3004 (= $x2338 $x3005)) (= $x2341 (and $x145 $x3005)))))
+(let ((@x3020 (monotonicity (trans @x3010 (rewrite (= (and $x145 $x3005) $x3013)) (= $x2341 $x3013)) (= $x2344 $x3018))))
+(let (($x1938 (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 (($x291 (fun_app$ v_b_Visited_G_2$ ?v1)))
+(let (($x1925 (and (not (>= (+ ?x273 ?x1912) 0)) $x291 (= (+ (b_G$ (pair$ ?v1 ?v0!20)) ?x273 ?x1912) 0))))
+(not $x1925)))))))
+))
+(let (($x1932 (not (not (and $x1910 $x1915)))))
+(let (($x1942 (and $x1932 $x1938)))
+(let (($x1947 (and $x1289 $x1942)))
+(let (($x1951 (or $x1898 $x1947)))
+(let (($x1955 (and $x1270 $x1951)))
+(let (($x1959 (or $x1871 $x1955)))
+(let (($x1963 (and $x1256 $x1959)))
+(let (($x1967 (or $x1848 $x1963)))
+(let (($x1842 (not $x773)))
+(let (($x1971 (and $x1842 $x1967)))
+(let (($x1975 (or $x773 $x1971)))
+(let (($x1979 (and $x652 $x1975)))
+(let (($x1983 (or $x1830 $x1979)))
+(let (($x1987 (and $x1247 $x1983)))
+(let (($x1991 (or $x1813 $x1987)))
+(let (($x1801 (and (and $x1774 $x1779) $x256 $x1214 $x1209 $x266 $x1193 $x1199)))
+(let (($x1995 (and $x1801 $x1991)))
+(let (($x1739 (not (or $x1733 (>= (+ ?x1727 ?x1721 ?x1735) 0)))))
+(let (($x1756 (or $x1739 $x1752)))
+(let (($x1713 (forall ((?v0 B_Vertex$) )(let ((?x230 (fun_app$c v_b_SP_G_3$ ?v0)))
+(let ((?x1097 (* (- 1) ?x230)))
+(let ((?x1699 (fun_app$c v_b_SP_G_3$ (?v1!9 ?v0))))
+(let ((?x1704 (b_G$ (pair$ (?v1!9 ?v0) ?v0))))
+(let (($x1706 (= (+ ?x1704 ?x1699 ?x1097) 0)))
+(let (($x1707 (and (not (>= (+ ?x1699 ?x1097) 0)) $x1706)))
+(let (($x1099 (<= (+ b_Infinity$ ?x1097) 0)))
+(let (($x1100 (not $x1099)))
+(let (($x127 (= ?v0 b_Source$)))
+(let (($x132 (not $x127)))
+(let (($x1103 (and $x132 $x1100)))
+(let (($x1106 (not $x1103)))
+(or $x1106 $x1707))))))))))))))
+))
+(let (($x1760 (and $x1713 $x1756)))
+(let (($x1687 (forall ((?v1 B_Vertex$) )(let ((?x1661 (fun_app$c v_b_SP_G_3$ ?v0!8)))
+(let ((?x1662 (* (- 1) ?x1661)))
+(let ((?x230 (fun_app$c v_b_SP_G_3$ ?v1)))
+(let (($x1675 (and (not (>= (+ ?x230 ?x1662) 0)) (= (+ (b_G$ (pair$ ?v1 ?v0!8)) ?x230 ?x1662) 0))))
+(not $x1675))))))
+))
+(let (($x1681 (not (not (and $x1660 $x1665)))))
+(let (($x1691 (and $x1681 $x1687)))
+(let (($x1764 (or $x1691 $x1760)))
+(let (($x1652 (and $x1641 $x212 $x215 $x217 $x220)))
+(let (($x1768 (and $x1652 $x1764)))
+(let (($x1999 (or $x1768 $x1995)))
+(let (($x1629 (forall ((?v0 B_Vertex$) )(let ((?x174 (fun_app$c v_b_SP_G_1$ ?v0)))
+(let ((?x1000 (* (- 1) ?x174)))
+(let ((?x1613 (?v1!7 ?v0)))
+(let ((?x1614 (fun_app$c v_b_SP_G_1$ ?x1613)))
+(let ((?x1620 (b_G$ (pair$ ?x1613 ?v0))))
+(let (($x1622 (= (+ ?x1620 ?x1614 ?x1000) 0)))
+(let (($x1618 (fun_app$ v_b_Visited_G_1$ ?x1613)))
+(let (($x1623 (and (not (>= (+ ?x1614 ?x1000) 0)) $x1618 $x1622)))
+(let (($x1002 (<= (+ b_Infinity$ ?x1000) 0)))
+(let (($x1003 (not $x1002)))
+(let (($x127 (= ?v0 b_Source$)))
+(let (($x132 (not $x127)))
+(let (($x1006 (and $x132 $x1003)))
+(let (($x1009 (not $x1006)))
+(or $x1009 $x1623))))))))))))))))
+))
+(let (($x1594 (forall ((?v0 B_Vertex$) )(let ((?x1585 (b_G$ (pair$ (?v1!6 ?v0) ?v0))))
+(let ((?x128 (v_b_SP_G_0$ ?v0)))
+(let ((?x945 (* (- 1) ?x128)))
+(let ((?x1578 (?v1!6 ?v0)))
+(let ((?x1579 (v_b_SP_G_0$ ?x1578)))
+(let (($x1587 (= (+ ?x1579 ?x945 ?x1585) 0)))
+(let (($x1583 (v_b_Visited_G_0$ ?x1578)))
+(let (($x1588 (and (not (>= (+ ?x1579 ?x945) 0)) $x1583 $x1587)))
+(let (($x127 (= ?v0 b_Source$)))
+(let (($x132 (not $x127)))
+(let (($x951 (and $x132 (not (<= (+ b_Infinity$ ?x945) 0)))))
+(let (($x954 (not $x951)))
+(or $x954 $x1588))))))))))))))
+))
+(let (($x1632 (and $x1594 $x173 $x1051 $x1045 $x997 $x1629)))
+(let (($x2003 (and $x1632 $x1999)))
+(let (($x1561 (not (not (and $x1539 $x1544)))))
+(let (($x1571 (and $x1561 $x1567)))
+(let (($x2007 (or $x1571 $x2003)))
+(let (($x2011 (and $x939 $x2007)))
+(let (($x1527 (not (or $x1520 (>= (+ ?x1521 ?x1523 ?x1514) 0)))))
+(let (($x2015 (or $x1527 $x2011)))
+(let (($x2019 (and $x914 $x2015)))
+(let (($x2023 (or $x1500 $x2019)))
+(let (($x2027 (and $x899 $x2023)))
+(let (($x2031 (or $x1477 $x2027)))
+(let (($x1471 (not $x869)))
+(let (($x2035 (and $x1471 $x2031)))
+(let (($x2039 (or $x869 $x2035)))
+(let (($x1925 (and (not (>= (+ ?x273 (* (- 1) ?x1911)) 0)) $x291 (= (+ (b_G$ (pair$ ?0 ?v0!20)) ?x273 (* (- 1) ?x1911)) 0))))
+(let (($x1935 (not $x1925)))
+(let (($x2243 (= (= (+ (b_G$ (pair$ ?0 ?v0!20)) ?x273 (* (- 1) ?x1911)) 0) $x2242)))
+(let (($x2240 (= (+ (b_G$ (pair$ ?0 ?v0!20)) ?x273 (* (- 1) ?x1911)) (+ ?x273 (* (- 1) ?x1911) (b_G$ (pair$ ?0 ?v0!20))))))
+(let ((@x2250 (monotonicity (monotonicity (monotonicity (rewrite $x2240) $x2243) (= $x1925 $x2245)) (= $x1935 $x2248))))
+(let ((@x2256 (monotonicity (rewrite (= $x1932 (and $x1910 $x1915))) (quant-intro @x2250 (= $x1938 $x2251)) (= $x1942 (and (and $x1910 $x1915) $x2251)))))
+(let ((@x2264 (trans (monotonicity @x2256 (= $x1947 (and $x1289 (and (and $x1910 $x1915) $x2251)))) (rewrite (= (and $x1289 (and (and $x1910 $x1915) $x2251)) $x2260)) (= $x1947 $x2260))))
+(let ((@x2273 (monotonicity (monotonicity (monotonicity @x2264 (= $x1951 $x2265)) (= $x1955 $x2268)) (= $x1959 $x2271))))
+(let ((@x2282 (monotonicity (rewrite (= $x1842 $x297)) (monotonicity (monotonicity @x2273 (= $x1963 $x2274)) (= $x1967 $x2277)) (= $x1971 $x2280))))
+(let ((@x2291 (monotonicity (monotonicity (monotonicity @x2282 (= $x1975 $x2283)) (= $x1979 $x2286)) (= $x1983 $x2289))))
+(let ((@x2300 (monotonicity (monotonicity (monotonicity @x2291 (= $x1987 $x2292)) (= $x1991 $x2295)) (= $x1995 (and $x1801 $x2295)))))
+(let ((@x2211 (monotonicity (rewrite (= (+ ?x1727 ?x1721 ?x1735) ?x2206)) (= (>= (+ ?x1727 ?x1721 ?x1735) 0) $x2209))))
+(let ((@x2214 (monotonicity @x2211 (= (or $x1733 (>= (+ ?x1727 ?x1721 ?x1735) 0)) $x2212))))
+(let (($x2197 (and (not $x2176) $x2192)))
+(let (($x2200 (or $x1106 $x2197)))
+(let ((?x1097 (* (- 1) ?x230)))
+(let ((?x1699 (fun_app$c v_b_SP_G_3$ (?v1!9 ?0))))
+(let ((?x1704 (b_G$ (pair$ (?v1!9 ?0) ?0))))
+(let (($x1706 (= (+ ?x1704 ?x1699 ?x1097) 0)))
+(let (($x1707 (and (not (>= (+ ?x1699 ?x1097) 0)) $x1706)))
+(let (($x1710 (or $x1106 $x1707)))
+(let ((@x2189 (monotonicity (rewrite (= (+ ?x1704 ?x1699 ?x1097) (+ ?x1097 ?x1699 ?x1704))) (= $x1706 (= (+ ?x1097 ?x1699 ?x1704) 0)))))
+(let ((@x2196 (trans @x2189 (rewrite (= (= (+ ?x1097 ?x1699 ?x1704) 0) $x2192)) (= $x1706 $x2192))))
+(let ((@x2173 (monotonicity (rewrite (= (+ ?x1699 ?x1097) (+ ?x1097 ?x1699))) (= (>= (+ ?x1699 ?x1097) 0) (>= (+ ?x1097 ?x1699) 0)))))
+(let ((@x2180 (trans @x2173 (rewrite (= (>= (+ ?x1097 ?x1699) 0) $x2176)) (= (>= (+ ?x1699 ?x1097) 0) $x2176))))
+(let ((@x2199 (monotonicity (monotonicity @x2180 (= (not (>= (+ ?x1699 ?x1097) 0)) (not $x2176))) @x2196 (= $x1707 $x2197))))
+(let ((@x2223 (monotonicity (quant-intro (monotonicity @x2199 (= $x1710 $x2200)) (= $x1713 $x2203)) (monotonicity (monotonicity @x2214 (= $x1739 $x2215)) (= $x1756 $x2218)) (= $x1760 $x2221))))
+(let (($x1675 (and (not (>= (+ ?x230 ?x1662) 0)) (= (+ (b_G$ (pair$ ?0 ?v0!8)) ?x230 ?x1662) 0))))
+(let (($x1684 (not $x1675)))
+(let (($x2146 (= (+ (b_G$ (pair$ ?0 ?v0!8)) ?x230 ?x1662) (+ ?x230 ?x1662 (b_G$ (pair$ ?0 ?v0!8))))))
+(let ((@x2150 (monotonicity (rewrite $x2146) (= (= (+ (b_G$ (pair$ ?0 ?v0!8)) ?x230 ?x1662) 0) $x2148))))
+(let ((@x2159 (quant-intro (monotonicity (monotonicity @x2150 (= $x1675 $x2151)) (= $x1684 $x2154)) (= $x1687 $x2157))))
+(let ((@x2162 (monotonicity (rewrite (= $x1681 (and $x1660 $x1665))) @x2159 (= $x1691 (and (and $x1660 $x1665) $x2157)))))
+(let ((@x2167 (trans @x2162 (rewrite (= (and (and $x1660 $x1665) $x2157) $x2163)) (= $x1691 $x2163))))
+(let ((@x2229 (monotonicity (monotonicity @x2167 @x2223 (= $x1764 $x2224)) (= $x1768 (and $x1652 $x2224)))))
+(let ((@x2308 (monotonicity (trans @x2229 (rewrite (= (and $x1652 $x2224) $x2230)) (= $x1768 $x2230)) (trans @x2300 (rewrite (= (and $x1801 $x2295) $x2301)) (= $x1995 $x2301)) (= $x1999 $x2306))))
+(let ((?x1000 (* (- 1) ?x174)))
+(let ((?x1614 (fun_app$c v_b_SP_G_1$ ?x1613)))
+(let ((?x1620 (b_G$ (pair$ ?x1613 ?0))))
+(let (($x1622 (= (+ ?x1620 ?x1614 ?x1000) 0)))
+(let (($x1623 (and (not (>= (+ ?x1614 ?x1000) 0)) $x1618 $x1622)))
+(let (($x1626 (or $x1009 $x1623)))
+(let ((@x2126 (monotonicity (rewrite (= (+ ?x1620 ?x1614 ?x1000) (+ ?x1000 ?x1614 ?x1620))) (= $x1622 (= (+ ?x1000 ?x1614 ?x1620) 0)))))
+(let ((@x2133 (trans @x2126 (rewrite (= (= (+ ?x1000 ?x1614 ?x1620) 0) $x2129)) (= $x1622 $x2129))))
+(let ((@x2110 (monotonicity (rewrite (= (+ ?x1614 ?x1000) (+ ?x1000 ?x1614))) (= (>= (+ ?x1614 ?x1000) 0) (>= (+ ?x1000 ?x1614) 0)))))
+(let ((@x2117 (trans @x2110 (rewrite (= (>= (+ ?x1000 ?x1614) 0) $x2113)) (= (>= (+ ?x1614 ?x1000) 0) $x2113))))
+(let ((@x2136 (monotonicity (monotonicity @x2117 (= (not (>= (+ ?x1614 ?x1000) 0)) (not $x2113))) @x2133 (= $x1623 $x2134))))
+(let (($x1587 (= (+ (v_b_SP_G_0$ ?x1578) (* (- 1) ?x128) (b_G$ (pair$ ?x1578 ?0))) 0)))
+(let (($x1588 (and (not (>= (+ (v_b_SP_G_0$ ?x1578) (* (- 1) ?x128)) 0)) $x1583 $x1587)))
+(let (($x1591 (or $x954 $x1588)))
+(let (($x2086 (= (+ (* (- 1) ?x128) (v_b_SP_G_0$ ?x1578) (b_G$ (pair$ ?x1578 ?0))) 0)))
+(let (($x2084 (= (+ (v_b_SP_G_0$ ?x1578) (* (- 1) ?x128) (b_G$ (pair$ ?x1578 ?0))) (+ (* (- 1) ?x128) (v_b_SP_G_0$ ?x1578) (b_G$ (pair$ ?x1578 ?0))))))
+(let ((@x2095 (trans (monotonicity (rewrite $x2084) (= $x1587 $x2086)) (rewrite (= $x2086 $x2091)) (= $x1587 $x2091))))
+(let (($x2081 (= (not (>= (+ (v_b_SP_G_0$ ?x1578) (* (- 1) ?x128)) 0)) (not $x2075))))
+(let (($x1581 (>= (+ (v_b_SP_G_0$ ?x1578) (* (- 1) ?x128)) 0)))
+(let (($x2068 (= (+ (v_b_SP_G_0$ ?x1578) (* (- 1) ?x128)) (+ (* (- 1) ?x128) (v_b_SP_G_0$ ?x1578)))))
+(let ((@x2072 (monotonicity (rewrite $x2068) (= $x1581 (>= (+ (* (- 1) ?x128) (v_b_SP_G_0$ ?x1578)) 0)))))
+(let ((@x2079 (trans @x2072 (rewrite (= (>= (+ (* (- 1) ?x128) (v_b_SP_G_0$ ?x1578)) 0) $x2075)) (= $x1581 $x2075))))
+(let ((@x2101 (monotonicity (monotonicity (monotonicity @x2079 $x2081) @x2095 (= $x1588 $x2096)) (= $x1591 $x2099))))
+(let ((@x2311 (monotonicity (quant-intro @x2101 (= $x1594 $x2102)) (quant-intro (monotonicity @x2136 (= $x1626 $x2137)) (= $x1629 $x2140)) (= $x1632 (and $x2102 $x173 $x1051 $x1045 $x997 $x2140)))))
+(let ((@x2314 (monotonicity @x2311 @x2308 (= $x2003 (and (and $x2102 $x173 $x1051 $x1045 $x997 $x2140) $x2306)))))
+(let ((@x2319 (trans @x2314 (rewrite (= (and (and $x2102 $x173 $x1051 $x1045 $x997 $x2140) $x2306) $x2315)) (= $x2003 $x2315))))
+(let ((@x2061 (monotonicity (rewrite (= $x1561 (and $x1539 $x1544))) (= $x1571 (and (and $x1539 $x1544) $x1567)))))
+(let ((@x2066 (trans @x2061 (rewrite (= (and (and $x1539 $x1544) $x1567) $x2062)) (= $x1571 $x2062))))
+(let ((@x2325 (monotonicity (monotonicity @x2066 @x2319 (= $x2007 $x2320)) (= $x2011 $x2323))))
+(let ((@x2050 (monotonicity (rewrite (= (+ ?x1521 ?x1523 ?x1514) ?x2045)) (= (>= (+ ?x1521 ?x1523 ?x1514) 0) $x2048))))
+(let ((@x2053 (monotonicity @x2050 (= (or $x1520 (>= (+ ?x1521 ?x1523 ?x1514) 0)) $x2051))))
+(let ((@x2328 (monotonicity (monotonicity @x2053 (= $x1527 $x2054)) @x2325 (= $x2015 $x2326))))
+(let ((@x2337 (monotonicity (monotonicity (monotonicity @x2328 (= $x2019 $x2329)) (= $x2023 $x2332)) (= $x2027 $x2335))))
+(let ((@x2343 (monotonicity (rewrite (= $x1471 $x145)) (monotonicity @x2337 (= $x2031 $x2338)) (= $x2035 $x2341))))
+(let (($x1926 (exists ((?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 (($x291 (fun_app$ v_b_Visited_G_2$ ?v1)))
+(and (not (>= (+ ?x273 ?x1912) 0)) $x291 (= (+ (b_G$ (pair$ ?v1 ?v0!20)) ?x273 ?x1912) 0)))))))
+))
+(let ((@x1944 (nnf-neg (refl (~ $x1932 $x1932)) (nnf-neg (refl (~ $x1935 $x1935)) (~ (not $x1926) $x1938)) (~ (not (or (not (and $x1910 $x1915)) $x1926)) $x1942))))
+(let ((@x1946 (trans (sk (~ (not $x1329) (not (or (not (and $x1910 $x1915)) $x1926)))) @x1944 (~ (not $x1329) $x1942))))
+(let ((@x1907 (nnf-neg (nnf-pos (refl (~ $x1286 $x1286)) (~ $x1289 $x1289)) (~ (not $x1292) $x1289))))
+(let ((@x1954 (nnf-neg (sk (~ $x1292 $x1898)) (nnf-neg @x1907 @x1946 (~ (not $x1332) $x1947)) (~ (not $x1335) $x1951))))
+(let ((@x1880 (nnf-neg (nnf-pos (refl (~ $x1267 $x1267)) (~ $x1270 $x1270)) (~ (not $x1273) $x1270))))
+(let ((@x1962 (nnf-neg (sk (~ $x1273 $x1871)) (nnf-neg @x1880 @x1954 (~ (not $x1338) $x1955)) (~ (not $x1341) $x1959))))
+(let ((@x1857 (nnf-neg (nnf-pos (refl (~ (>= ?x273 0) (>= ?x273 0))) (~ $x1256 $x1256)) (~ (not $x1259) $x1256))))
+(let ((@x1970 (nnf-neg (sk (~ $x1259 $x1848)) (nnf-neg @x1857 @x1962 (~ (not $x1344) $x1963)) (~ (not $x1347) $x1967))))
+(let ((@x1978 (nnf-neg (refl (~ $x773 $x773)) (nnf-neg (refl (~ $x1842 $x1842)) @x1970 (~ (not $x1350) $x1971)) (~ (not $x1353) $x1975))))
+(let ((@x1839 (nnf-neg (nnf-pos (refl (~ (or $x300 $x278) (or $x300 $x278))) (~ $x652 $x652)) (~ (not $x785) $x652))))
+(let ((@x1986 (nnf-neg (sk (~ $x785 $x1830)) (nnf-neg @x1839 @x1978 (~ (not $x1356) $x1979)) (~ (not $x1359) $x1983))))
+(let ((@x1822 (nnf-neg (nnf-pos (refl (~ $x1243 $x1243)) (~ $x1247 $x1247)) (~ (not $x1250) $x1247))))
+(let ((@x1994 (nnf-neg (sk (~ $x1250 $x1813)) (nnf-neg @x1822 @x1986 (~ (not $x1362) $x1987)) (~ (not $x1365) $x1991))))
+(let ((@x1803 (monotonicity (sk (~ $x1080 (and $x1774 $x1779))) (refl (~ $x256 $x256)) (refl (~ $x1214 $x1214)) (nnf-pos (refl (~ $x1206 $x1206)) (~ $x1209 $x1209)) (refl (~ $x266 $x266)) (nnf-pos (refl (~ $x1190 $x1190)) (~ $x1193 $x1193)) (nnf-pos (refl (~ $x1196 $x1196)) (~ $x1199 $x1199)) (~ $x1235 $x1801))))
+(let ((@x1998 (nnf-neg (nnf-neg @x1803 (~ (not $x1240) $x1801)) @x1994 (~ (not $x1368) $x1995))))
+(let ((@x1748 (nnf-neg (nnf-pos (refl (~ $x1143 $x1143)) (~ $x1146 $x1146)) (~ (not $x1149) $x1146))))
+(let ((@x1759 (nnf-neg (sk (~ $x1149 $x1739)) (nnf-neg @x1748 (refl (~ $x1749 $x1749)) (~ (not $x1152) $x1752)) (~ (not $x1155) $x1756))))
+(let ((@x1715 (nnf-pos (monotonicity (refl (~ $x1106 $x1106)) (sk (~ $x1122 $x1707)) (~ $x1125 $x1710)) (~ $x1128 $x1713))))
+(let ((@x1763 (nnf-neg (nnf-neg @x1715 (~ (not $x1131) $x1713)) @x1759 (~ (not $x1158) $x1760))))
+(let (($x1676 (exists ((?v1 B_Vertex$) )(let ((?x1661 (fun_app$c v_b_SP_G_3$ ?v0!8)))
+(let ((?x1662 (* (- 1) ?x1661)))
+(let ((?x230 (fun_app$c v_b_SP_G_3$ ?v1)))
+(and (not (>= (+ ?x230 ?x1662) 0)) (= (+ (b_G$ (pair$ ?v1 ?v0!8)) ?x230 ?x1662) 0))))))
+))
+(let ((@x1693 (nnf-neg (refl (~ $x1681 $x1681)) (nnf-neg (refl (~ $x1684 $x1684)) (~ (not $x1676) $x1687)) (~ (not (or (not (and $x1660 $x1665)) $x1676)) $x1691))))
+(let ((@x1695 (trans (sk (~ $x1131 (not (or (not (and $x1660 $x1665)) $x1676)))) @x1693 (~ $x1131 $x1691))))
+(let ((@x1654 (monotonicity (nnf-neg (refl (~ (not $x1077) (not $x1077))) (~ $x1083 $x1641)) (refl (~ $x212 $x212)) (refl (~ $x215 $x215)) (refl (~ $x217 $x217)) (refl (~ $x220 $x220)) (~ $x1089 $x1652))))
+(let ((@x1771 (nnf-neg (nnf-neg @x1654 (~ (not $x1094) $x1652)) (nnf-neg @x1695 @x1763 (~ (not $x1161) $x1764)) (~ (not $x1164) $x1768))))
+(let ((@x1631 (nnf-pos (monotonicity (refl (~ $x1009 $x1009)) (sk (~ $x1031 $x1623)) (~ $x1034 $x1626)) (~ $x1037 $x1629))))
+(let ((@x1596 (nnf-pos (monotonicity (refl (~ $x954 $x954)) (sk (~ $x974 $x1588)) (~ $x977 $x1591)) (~ $x980 $x1594))))
+(let ((@x1634 (monotonicity @x1596 (refl (~ $x173 $x173)) (nnf-pos (refl (~ (>= ?x174 0) (>= ?x174 0))) (~ $x1051 $x1051)) (nnf-pos (refl (~ $x1042 $x1042)) (~ $x1045 $x1045)) (nnf-pos (refl (~ $x994 $x994)) (~ $x997 $x997)) @x1631 (~ $x1069 $x1632))))
+(let ((@x2006 (nnf-neg (nnf-neg @x1634 (~ (not $x1074) $x1632)) (nnf-neg @x1771 @x1998 (~ (not $x1371) $x1999)) (~ (not $x1374) $x2003))))
+(let (($x1555 (exists ((?v1 B_Vertex$) )(let ((?x1540 (v_b_SP_G_0$ ?v0!5)))
+(let ((?x1541 (* (- 1) ?x1540)))
+(let ((?x128 (v_b_SP_G_0$ ?v1)))
+(let (($x136 (v_b_Visited_G_0$ ?v1)))
+(and (not (>= (+ ?x128 ?x1541) 0)) $x136 (= (+ ?x128 ?x1541 (b_G$ (pair$ ?v1 ?v0!5))) 0)))))))
+))
+(let ((@x1573 (nnf-neg (refl (~ $x1561 $x1561)) (nnf-neg (refl (~ $x1564 $x1564)) (~ (not $x1555) $x1567)) (~ (not (or (not (and $x1539 $x1544)) $x1555)) $x1571))))
+(let ((@x1575 (trans (sk (~ (not $x980) (not (or (not (and $x1539 $x1544)) $x1555)))) @x1573 (~ (not $x980) $x1571))))
+(let ((@x1536 (nnf-neg (nnf-pos (refl (~ $x936 $x936)) (~ $x939 $x939)) (~ (not $x942) $x939))))
+(let ((@x2014 (nnf-neg @x1536 (nnf-neg @x1575 @x2006 (~ (not $x1377) $x2007)) (~ (not $x1380) $x2011))))
+(let ((@x1509 (nnf-neg (nnf-pos (refl (~ $x911 $x911)) (~ $x914 $x914)) (~ (not $x917) $x914))))
+(let ((@x2022 (nnf-neg @x1509 (nnf-neg (sk (~ $x942 $x1527)) @x2014 (~ (not $x1383) $x2015)) (~ (not $x1386) $x2019))))
+(let ((@x1486 (nnf-neg (nnf-pos (refl (~ (>= ?x128 0) (>= ?x128 0))) (~ $x899 $x899)) (~ (not $x902) $x899))))
+(let ((@x2030 (nnf-neg @x1486 (nnf-neg (sk (~ $x917 $x1500)) @x2022 (~ (not $x1389) $x2023)) (~ (not $x1392) $x2027))))
+(let ((@x2038 (nnf-neg (refl (~ $x1471 $x1471)) (nnf-neg (sk (~ $x902 $x1477)) @x2030 (~ (not $x1395) $x2031)) (~ (not $x1398) $x2035))))
+(let ((@x2042 (mp~ (not-or-elim (mp (asserted $x349) @x1411 $x1407) (not $x1401)) (nnf-neg (refl (~ $x869 $x869)) @x2038 (~ (not $x1401) $x2039)) $x2039)))
+(let ((@x3878 (mp (mp (mp @x2042 (monotonicity @x2343 (= $x2039 $x2344)) $x2344) @x3020 $x3018) (monotonicity @x3874 (= $x3018 $x3875)) $x3875)))
+(let ((@x4209 (unit-resolution @x3878 (lemma (unit-resolution @x5763 @x3492 (hypothesis $x869) false) $x145) $x3872)))
+(let ((@x4211 (unit-resolution (def-axiom (or $x3866 $x1477 $x3860)) (unit-resolution (def-axiom (or $x3869 $x3863)) @x4209 $x3863) (lemma @x6353 $x1476) $x3860)))
+(let ((@x6165 (unit-resolution ((_ quant-inst ?v0!2) (or (not $x3500) $x2348)) @x3505 (hypothesis $x1491) false)))
+(let ((@x4215 (unit-resolution (def-axiom (or $x3854 $x2368 $x3848)) (unit-resolution (def-axiom (or $x2363 $x1491)) (lemma @x6165 $x2348) $x2363) (unit-resolution (def-axiom (or $x3857 $x3851)) @x4211 $x3851) $x3848)))
+(let ((@x4217 (unit-resolution (def-axiom (or $x3842 $x2414 $x3836)) (unit-resolution (def-axiom (or $x3845 $x3839)) @x4215 $x3839) (unit-resolution (def-axiom (or $x2409 $x1512)) (lemma @x3073 $x2394) $x2409) $x3836)))
+(let ((@x4219 (unit-resolution (def-axiom (or $x3830 $x3544 $x3824)) (unit-resolution (def-axiom (or $x3833 $x3827)) @x4217 $x3827) (lemma @x5735 $x3541) $x3824)))
+(let ((@x5955 (unit-resolution (def-axiom (or $x3821 $x3556)) @x4219 $x3556)))
+(let (($x4373 (or $x3561 $x3904)))
+(let ((@x4363 ((_ quant-inst v_b_v_G_1$) $x4373)))
+(let ((@x5049 (unit-resolution @x4363 @x5955 $x3904)))
+(let ((?x5210 (pair$ v_b_v_G_1$ ?v0!15)))
+(let ((?x5018 (b_G$ ?x5210)))
+(let ((?x4456 (* (- 1) ?x1846)))
+(let ((?x6267 (+ ?x257 ?x4456 ?x5018)))
+(let (($x5853 (<= ?x6267 0)))
+(let (($x6128 (= ?x6267 0)))
+(let (($x6822 (>= (+ ?x257 (* (- 1) (fun_app$c v_b_SP_G_1$ ?v0!15)) ?x5018) 0)))
+(let (($x4911 (<= (+ b_Infinity$ (* (- 1) ?x5018)) 0)))
+(let (($x6706 (or $x4911 $x6822)))
+(let (($x6711 (not $x6706)))
+(let ((@x5703 (hypothesis $x1848)))
+(let (($x5745 (or (not (>= (+ ?x1846 (* (- 1) (fun_app$c v_b_SP_G_1$ ?v0!15))) 0)) $x1847)))
+(let ((?x4480 (fun_app$c v_b_SP_G_1$ ?v0!15)))
+(let (($x5850 (>= ?x4480 0)))
+(let ((@x5698 ((_ th-lemma arith farkas -1 1 1) @x5703 (hypothesis (>= (+ ?x1846 (* (- 1) ?x4480)) 0)) (unit-resolution ((_ quant-inst ?v0!15) (or $x3561 $x5850)) @x5955 $x5850) false)))
+(let ((@x6183 (unit-resolution (lemma @x5698 $x5745) @x5703 (not (>= (+ ?x1846 (* (- 1) ?x4480)) 0)))))
+(let ((@x6242 ((_ th-lemma arith triangle-eq) (or (not (= ?x1846 ?x4480)) (>= (+ ?x1846 (* (- 1) ?x4480)) 0)))))
+(let ((@x4529 (unit-resolution (def-axiom (or $x3821 $x173)) @x4219 $x173)))
+(let ((@x5142 (hypothesis $x3657)))
+(let ((@x4265 (unit-resolution (def-axiom (or $x3654 $x217)) @x5142 $x217)))
+(let ((?x5667 (fun_app$c v_b_SP_G_1$ ?v1!10)))
+(let ((?x5152 (fun_app$c v_b_SP_G_1$ ?v0!11)))
+(let ((?x5630 (* (- 1) ?x5152)))
+(let (($x4072 (>= (+ ?x1727 ?x5630 ?x5667) 0)))
+(let (($x5699 (fun_app$ v_b_Visited_G_1$ ?v1!10)))
+(let (($x1725 (not $x1724)))
+(let ((@x4170 (hypothesis $x2650)))
+(let (($x4150 (>= (+ ?x1721 (* (- 1) ?x5667)) 0)))
+(let ((@x4195 (monotonicity (symm (hypothesis $x217) (= v_b_SP_G_1$ v_b_SP_G_3$)) (= ?x5667 ?x1721))))
+(let ((@x4203 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not (= ?x1721 ?x5667)) $x4150)) (symm @x4195 (= ?x1721 ?x5667)) $x4150)))
+(let (($x4167 (or (not (<= (+ b_Infinity$ (* (- 1) ?x5667)) 0)) (not $x4150) $x1724)))
+(let ((@x4163 ((_ th-lemma arith farkas 1 -1 1) (hypothesis $x4150) (hypothesis (<= (+ b_Infinity$ (* (- 1) ?x5667)) 0)) (hypothesis $x1725) false)))
+(let ((@x4204 (unit-resolution (lemma @x4163 $x4167) @x4203 (unit-resolution (def-axiom (or $x2645 $x1725)) @x4170 $x1725) (not (<= (+ b_Infinity$ (* (- 1) ?x5667)) 0)))))
+(let (($x6045 (<= (+ b_Infinity$ (* (- 1) ?x5667)) 0)))
+(let (($x5247 (or $x5699 $x6045)))
+(let ((@x3048 (mp ((_ quant-inst ?v1!10) (or $x3595 $x5247)) (rewrite (= (or $x3595 $x5247) (or $x3595 $x5699 $x6045))) (or $x3595 $x5699 $x6045))))
+(let ((@x4206 (unit-resolution (unit-resolution @x3048 (hypothesis $x3590) $x5247) @x4204 $x5699)))
+(let ((@x4223 (unit-resolution (def-axiom (or $x3821 $x3573)) @x4219 $x3573)))
+(let (($x5758 (not $x5699)))
+(let (($x4064 (or $x3578 $x5758 $x1730 $x4072)))
+(let (($x5845 (or $x5758 $x1730 (>= (+ ?x1727 ?x5667 ?x5630) 0))))
+(let (($x4065 (or $x3578 $x5845)))
+(let ((@x4061 (monotonicity (rewrite (= (+ ?x1727 ?x5667 ?x5630) (+ ?x1727 ?x5630 ?x5667))) (= (>= (+ ?x1727 ?x5667 ?x5630) 0) $x4072))))
+(let ((@x4102 (monotonicity (monotonicity @x4061 (= $x5845 (or $x5758 $x1730 $x4072))) (= $x4065 (or $x3578 (or $x5758 $x1730 $x4072))))))
+(let ((@x4106 (trans @x4102 (rewrite (= (or $x3578 (or $x5758 $x1730 $x4072)) $x4064)) (= $x4065 $x4064))))
+(let ((@x4225 (unit-resolution (mp ((_ quant-inst ?v0!11 ?v1!10) $x4065) @x4106 $x4064) @x4223 (unit-resolution (def-axiom (or $x2645 (not $x1730))) @x4170 (not $x1730)) (or $x5758 $x4072))))
+(let ((@x4228 (monotonicity (symm (hypothesis $x217) (= v_b_SP_G_1$ v_b_SP_G_3$)) (= ?x5152 ?x1734))))
+(let ((@x4234 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not (= ?x1734 ?x5152)) (<= (+ ?x1734 ?x5630) 0))) (symm @x4228 (= ?x1734 ?x5152)) (<= (+ ?x1734 ?x5630) 0))))
+(let ((@x4235 ((_ th-lemma arith farkas -1 -1 1 1) @x4234 (unit-resolution (def-axiom (or $x2645 (not $x2209))) @x4170 (not $x2209)) @x4203 (unit-resolution @x4225 @x4206 $x4072) false)))
+(let ((@x4885 (unit-resolution (lemma @x4235 (or $x2645 $x3595 $x2708)) @x4265 (unit-resolution (def-axiom (or $x3654 $x3590)) @x5142 $x3590) $x2645)))
+(let (($x4595 (<= (+ ?x1661 (* (- 1) (fun_app$c v_b_SP_G_3$ (?v1!7 ?v0!8)))) 0)))
+(let ((?x3922 (?v1!7 ?v0!8)))
+(let ((?x3910 (fun_app$c v_b_SP_G_1$ ?x3922)))
+(let ((?x3989 (* (- 1) ?x3910)))
+(let ((?x3142 (fun_app$c v_b_SP_G_1$ ?v0!8)))
+(let (($x3936 (<= (+ ?x3142 ?x3989) 0)))
+(let (($x4266 (not $x3936)))
+(let ((?x3945 (pair$ ?x3922 ?v0!8)))
+(let ((?x3946 (b_G$ ?x3945)))
+(let ((?x3031 (* (- 1) ?x3946)))
+(let ((?x3056 (+ ?x3142 ?x3989 ?x3031)))
+(let (($x3032 (= ?x3056 0)))
+(let (($x3033 (not $x3032)))
+(let (($x3034 (or $x3936 (not (fun_app$ v_b_Visited_G_1$ ?x3922)) $x3033)))
+(let (($x3049 (not $x3034)))
+(let ((@x3978 (hypothesis $x1665)))
+(let ((?x3144 (* (- 1) ?x3142)))
+(let ((?x3984 (+ ?x1661 ?x3144)))
+(let (($x3969 (>= ?x3984 0)))
+(let ((@x4544 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not (= ?x1661 ?x3142)) $x3969)) (monotonicity @x4265 (= ?x1661 ?x3142)) $x3969)))
+(let ((@x3973 ((_ th-lemma arith farkas 1 -1 1) (hypothesis $x3969) (hypothesis (<= (+ b_Infinity$ ?x3144) 0)) @x3978 false)))
+(let ((@x4027 (lemma @x3973 (or (not (<= (+ b_Infinity$ ?x3144) 0)) (not $x3969) $x1664))))
+(let ((@x4552 (unit-resolution @x4027 @x4544 @x3978 (not (<= (+ b_Infinity$ ?x3144) 0)))))
+(let ((@x3425 (def-axiom (or $x3630 $x1749))))
+(let ((@x4543 (unit-resolution @x3425 (trans (monotonicity @x4265 (= ?x245 ?x172)) @x4529 $x246) $x3630)))
+(let ((@x3134 (def-axiom (or $x3639 $x2650 $x3633))))
+(let ((@x3138 (def-axiom (or $x3642 $x3636))))
+(let ((@x3120 (def-axiom (or $x3651 $x3611 $x3645))))
+(let ((@x4905 (unit-resolution @x3120 (unit-resolution @x3138 (unit-resolution @x3134 @x4543 @x4885 $x3639) $x3642) (unit-resolution (def-axiom (or $x3654 $x3648)) @x5142 $x3648) $x3611)))
+(let ((@x4545 (unit-resolution (def-axiom (or $x3821 $x3581)) @x4219 $x3581)))
+(let (($x4738 (= (or $x3586 (or $x1659 (<= (+ b_Infinity$ ?x3144) 0) $x3049)) (or $x3586 $x1659 (<= (+ b_Infinity$ ?x3144) 0) $x3049))))
+(let ((@x4737 ((_ quant-inst ?v0!8) (or $x3586 (or $x1659 (<= (+ b_Infinity$ ?x3144) 0) $x3049)))))
+(let ((@x5209 (mp @x4737 (rewrite $x4738) (or $x3586 $x1659 (<= (+ b_Infinity$ ?x3144) 0) $x3049))))
+(let ((@x4406 (unit-resolution @x5209 @x4545 (unit-resolution (def-axiom (or $x3608 $x1660)) @x4905 $x1660) @x4552 $x3049)))
+(let ((?x3126 (fun_app$c v_b_SP_G_3$ ?x3922)))
+(let ((?x4327 (+ ?x3126 ?x3989)))
+(let (($x4402 (<= ?x4327 0)))
+(let ((@x4541 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not (= ?x3126 ?x3910)) $x4402)) (monotonicity @x4265 (= ?x3126 ?x3910)) $x4402)))
+(let ((@x4852 ((_ th-lemma arith farkas 1 -1 -1 1) (hypothesis $x3969) (hypothesis $x4595) (hypothesis $x4402) (hypothesis $x4266) false)))
+(let ((@x4542 (unit-resolution (lemma @x4852 (or (not $x4595) (not $x3969) (not $x4402) $x3936)) @x4544 @x4541 (unit-resolution (def-axiom (or $x3034 $x4266)) @x4406 $x4266) (not $x4595))))
+(let ((?x5182 (* (- 1) ?x3126)))
+(let ((?x4179 (+ ?x1661 ?x5182 ?x3031)))
+(let (($x5089 (= ?x4179 0)))
+(let (($x3918 (>= ?x4179 0)))
+(let (($x5284 (>= ?x3056 0)))
+(let ((@x4264 (unit-resolution ((_ th-lemma arith triangle-eq) (or $x3033 $x5284)) (unit-resolution (def-axiom (or $x3034 $x3032)) @x4406 $x3032) $x5284)))
+(let ((@x5267 (unit-resolution ((_ th-lemma arith assign-bounds -1 -1 1) (or $x3918 (not $x5284) (not $x3969) (not $x4402))) @x4264 @x4544 @x4541 $x3918)))
+(let (($x3917 (<= ?x4179 0)))
+(let (($x4407 (>= ?x4327 0)))
+(let ((@x4549 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not (= ?x3126 ?x3910)) $x4407)) (monotonicity @x4265 (= ?x3126 ?x3910)) $x4407)))
+(let (($x3979 (<= ?x3984 0)))
+(let ((@x6239 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not (= ?x1661 ?x3142)) $x3979)) (monotonicity @x4265 (= ?x1661 ?x3142)) $x3979)))
+(let (($x5179 (<= ?x3056 0)))
+(let ((@x3960 (unit-resolution ((_ th-lemma arith triangle-eq) (or $x3033 $x5179)) (unit-resolution (def-axiom (or $x3034 $x3032)) @x4406 $x3032) $x5179)))
+(let ((@x4631 (unit-resolution ((_ th-lemma arith assign-bounds -1 -1 1) (or $x3917 (not $x5179) (not $x3979) (not $x4407))) @x3960 @x6239 @x4549 $x3917)))
+(let ((@x4760 (unit-resolution ((_ th-lemma arith triangle-eq) (or $x5089 (not $x3917) (not $x3918))) @x4631 @x5267 $x5089)))
+(let (($x4746 (not $x5089)))
+(let (($x4181 (or $x4595 $x4746)))
+(let (($x3184 (or $x3605 $x4595 $x4746)))
+(let (($x5980 (>= (+ ?x3126 ?x1662) 0)))
+(let (($x5913 (or $x5980 (not (= (+ ?x3126 ?x1662 ?x3946) 0)))))
+(let (($x3976 (or $x3605 $x5913)))
+(let ((@x4178 (monotonicity (rewrite (= (+ ?x3126 ?x1662 ?x3946) (+ ?x1662 ?x3126 ?x3946))) (= (= (+ ?x3126 ?x1662 ?x3946) 0) (= (+ ?x1662 ?x3126 ?x3946) 0)))))
+(let ((@x4745 (trans @x4178 (rewrite (= (= (+ ?x1662 ?x3126 ?x3946) 0) $x5089)) (= (= (+ ?x3126 ?x1662 ?x3946) 0) $x5089))))
+(let ((@x5181 (monotonicity (rewrite (= (+ ?x3126 ?x1662) (+ ?x1662 ?x3126))) (= $x5980 (>= (+ ?x1662 ?x3126) 0)))))
+(let ((@x4634 (trans @x5181 (rewrite (= (>= (+ ?x1662 ?x3126) 0) $x4595)) (= $x5980 $x4595))))
+(let ((@x4184 (monotonicity @x4634 (monotonicity @x4745 (= (not (= (+ ?x3126 ?x1662 ?x3946) 0)) $x4746)) (= $x5913 $x4181))))
+(let ((@x3916 (trans (monotonicity @x4184 (= $x3976 (or $x3605 $x4181))) (rewrite (= (or $x3605 $x4181) $x3184)) (= $x3976 $x3184))))
+(let ((@x5060 (unit-resolution (mp ((_ quant-inst (?v1!7 ?v0!8)) $x3976) @x3916 $x3184) (unit-resolution (def-axiom (or $x3608 $x3600)) @x4905 $x3600) $x4181)))
+(let ((@x6153 (unit-resolution (lemma (unit-resolution @x5060 @x4760 @x4542 false) (or $x3654 $x1664)) @x5142 $x1664)))
+(let ((@x6273 (unit-resolution @x3120 (unit-resolution (def-axiom (or $x3608 $x1665)) @x6153 $x3608) (unit-resolution (def-axiom (or $x3654 $x3648)) @x5142 $x3648) $x3645)))
+(let ((@x5939 (unit-resolution @x3425 (unit-resolution @x3134 (unit-resolution @x3138 @x6273 $x3636) @x4885 $x3633) $x1749)))
+(let ((@x5914 (unit-resolution @x5939 (trans (monotonicity @x4265 (= ?x245 ?x172)) @x4529 $x246) false)))
+(let ((@x6386 (unit-resolution (def-axiom (or $x3818 $x3657 $x3812)) (unit-resolution (def-axiom (or $x3821 $x3815)) @x4219 $x3815) $x3815)))
+(let ((@x6181 (unit-resolution @x6386 (lemma @x5914 $x3654) $x3812)))
+(let ((@x5944 (unit-resolution (def-axiom (or $x3809 $x3678)) @x6181 $x3678)))
+(let (($x4481 (= ?x1846 ?x4480)))
+(let (($x3188 (or $x3683 $x6711 $x4481)))
+(let (($x5285 (or (not (or $x4911 (<= (+ ?x4480 ?x1173 (* (- 1) ?x5018)) 0))) $x4481)))
+(let (($x6363 (or $x3683 $x5285)))
+(let (($x5370 (<= (+ ?x4480 ?x1173 (* (- 1) ?x5018)) 0)))
+(let ((@x4465 (rewrite (= (+ ?x4480 ?x1173 (* (- 1) ?x5018)) (+ ?x1173 ?x4480 (* (- 1) ?x5018))))))
+(let ((@x6818 (monotonicity @x4465 (= $x5370 (<= (+ ?x1173 ?x4480 (* (- 1) ?x5018)) 0)))))
+(let ((@x6705 (trans @x6818 (rewrite (= (<= (+ ?x1173 ?x4480 (* (- 1) ?x5018)) 0) $x6822)) (= $x5370 $x6822))))
+(let ((@x5840 (monotonicity (monotonicity @x6705 (= (or $x4911 $x5370) $x6706)) (= (not (or $x4911 $x5370)) $x6711))))
+(let ((@x6545 (monotonicity (monotonicity @x5840 (= $x5285 (or $x6711 $x4481))) (= $x6363 (or $x3683 (or $x6711 $x4481))))))
+(let ((@x4811 (trans @x6545 (rewrite (= (or $x3683 (or $x6711 $x4481)) $x3188)) (= $x6363 $x3188))))
+(let ((@x6726 (unit-resolution (mp ((_ quant-inst ?v0!15) $x6363) @x4811 $x3188) @x5944 (unit-resolution @x6242 @x6183 (not $x4481)) $x6711)))
+(let ((@x6470 (unit-resolution (def-axiom (or $x6706 (not $x4911))) (hypothesis $x6711) (not $x4911))))
+(let ((@x6494 (unit-resolution (def-axiom (or $x6706 (not $x6822))) (hypothesis $x6711) (not $x6822))))
+(let (($x6511 (or $x4911 $x6822 $x6128)))
+(let ((@x6588 (unit-resolution (def-axiom (or $x3809 $x3670)) @x6181 $x3670)))
+(let (($x6235 (or $x3675 $x4911 $x6822 $x6128)))
+(let (($x6510 (or $x4911 $x5370 (= (+ ?x257 ?x5018 ?x4456) 0))))
+(let (($x6263 (or $x3675 $x6510)))
+(let ((@x6480 (monotonicity (rewrite (= (+ ?x257 ?x5018 ?x4456) ?x6267)) (= (= (+ ?x257 ?x5018 ?x4456) 0) $x6128))))
+(let ((@x4472 (monotonicity (monotonicity @x6705 @x6480 (= $x6510 $x6511)) (= $x6263 (or $x3675 $x6511)))))
+(let ((@x5852 (mp ((_ quant-inst ?v0!15) $x6263) (trans @x4472 (rewrite (= (or $x3675 $x6511) $x6235)) (= $x6263 $x6235)) $x6235)))
+(let ((@x6501 (unit-resolution (unit-resolution @x5852 @x6588 $x6511) @x6494 @x6470 (hypothesis (not $x6128)) false)))
+(let ((@x4608 (lemma @x6501 (or $x6706 $x6128))))
+(let ((@x6959 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x6128) $x5853)) (unit-resolution @x4608 @x6726 $x6128) $x5853)))
+(let (($x6603 (>= ?x5018 0)))
+(let (($x6582 (<= ?x5018 0)))
+(let (($x6583 (not $x6582)))
+(let (($x6156 (= v_b_v_G_1$ ?v0!15)))
+(let (($x5538 (not $x6156)))
+(let ((@x7337 (symm (commutativity (= $x6156 (= ?v0!15 v_b_v_G_1$))) (= (= ?v0!15 v_b_v_G_1$) $x6156))))
+(let (($x6631 (= ?v0!15 v_b_v_G_1$)))
+(let (($x7483 (not $x6631)))
+(let (($x6269 (fun_app$ v_b_Visited_G_1$ ?v0!15)))
+(let (($x7698 (or $x6631 $x6269)))
+(let (($x6630 (fun_app$ ?x265 ?v0!15)))
+(let (($x7702 (= $x6630 $x7698)))
+(let (($x3468 (forall ((?v0 B_Vertex_bool_fun$) (?v1 B_Vertex$) (?v2 Bool) (?v3 B_Vertex$) )(!(let (($x67 (fun_app$ (fun_app$a (fun_app$b (fun_upd$ ?v0) ?v1) ?v2) ?v3)))
+(= $x67 (ite (= ?v3 ?v1) ?v2 (fun_app$ ?v0 ?v3)))) :pattern ( (fun_app$ (fun_app$a (fun_app$b (fun_upd$ ?v0) ?v1) ?v2) ?v3) )))
+))
+(let (($x77 (forall ((?v0 B_Vertex_bool_fun$) (?v1 B_Vertex$) (?v2 Bool) (?v3 B_Vertex$) )(let (($x67 (fun_app$ (fun_app$a (fun_app$b (fun_upd$ ?v0) ?v1) ?v2) ?v3)))
+(= $x67 (ite (= ?v3 ?v1) ?v2 (fun_app$ ?v0 ?v3)))))
+))
+(let (($x67 (fun_app$ (fun_app$a (fun_app$b (fun_upd$ ?3) ?2) ?1) ?0)))
+(let (($x74 (= $x67 (ite (= ?0 ?2) ?1 (fun_app$ ?3 ?0)))))
+(let (($x72 (forall ((?v0 B_Vertex_bool_fun$) (?v1 B_Vertex$) (?v2 Bool) (?v3 B_Vertex$) )(let (($x67 (fun_app$ (fun_app$a (fun_app$b (fun_upd$ ?v0) ?v1) ?v2) ?v3)))
+(= $x67 (ite (= ?v3 ?v1) ?v2 (fun_app$ ?v0 ?v3)))))
+))
+(let ((@x76 (rewrite (= (= $x67 (ite (= ?0 ?2) ?1 (fun_app$ ?3 ?0))) $x74))))
+(let ((@x1443 (mp~ (mp (asserted $x72) (quant-intro @x76 (= $x72 $x77)) $x77) (nnf-pos (refl (~ $x74 $x74)) (~ $x77 $x77)) $x77)))
+(let ((@x3473 (mp @x1443 (quant-intro (refl (= $x74 $x74)) (= $x77 $x3468)) $x3468)))
+(let (($x4114 (not $x3468)))
+(let (($x6435 (or $x4114 $x7702)))
+(let ((@x5925 (monotonicity (rewrite (= (ite $x6631 true $x6269) $x7698)) (= (= $x6630 (ite $x6631 true $x6269)) $x7702))))
+(let ((@x6213 (monotonicity @x5925 (= (or $x4114 (= $x6630 (ite $x6631 true $x6269))) $x6435))))
+(let ((@x7487 (trans @x6213 (rewrite (= $x6435 $x6435)) (= (or $x4114 (= $x6630 (ite $x6631 true $x6269))) $x6435))))
+(let ((@x7488 (mp ((_ quant-inst v_b_Visited_G_1$ v_b_v_G_1$ true ?v0!15) (or $x4114 (= $x6630 (ite $x6631 true $x6269)))) @x7487 $x6435)))
+(let ((@x5875 (symm (unit-resolution (def-axiom (or $x3809 $x266)) @x6181 $x266) (= ?x265 v_b_Visited_G_2$))))
+(let ((@x7321 (symm (monotonicity @x5875 (= $x6630 (fun_app$ v_b_Visited_G_2$ ?v0!15))) (= (fun_app$ v_b_Visited_G_2$ ?v0!15) $x6630))))
+(let ((@x7322 (monotonicity @x7321 (= (not (fun_app$ v_b_Visited_G_2$ ?v0!15)) (not $x6630)))))
+(let (($x4415 (fun_app$ v_b_Visited_G_2$ ?v0!15)))
+(let (($x4479 (not $x4415)))
+(let ((?x5054 (b_G$ (pair$ v_b_v_G_1$ ?v0!13))))
+(let ((?x4706 (+ ?x257 ?x1810 ?x5054)))
+(let (($x4687 (= ?x4706 0)))
+(let (($x5187 (>= (+ ?x257 (* (- 1) ?x1808) ?x5054) 0)))
+(let (($x5051 (<= (+ b_Infinity$ (* (- 1) ?x5054)) 0)))
+(let (($x5186 (or $x5051 $x5187)))
+(let (($x5221 (not $x5186)))
+(let ((@x5744 (monotonicity (commutativity (= (= ?x1808 ?x1809) (= ?x1809 ?x1808))) (= (not (= ?x1808 ?x1809)) (not (= ?x1809 ?x1808))))))
+(let (($x5690 (not (= ?x1808 ?x1809))))
+(let ((@x5726 (mp (unit-resolution ((_ th-lemma arith triangle-eq) (or $x5690 $x1812)) (hypothesis $x1813) $x5690) @x5744 (not (= ?x1809 ?x1808)))))
+(let (($x5270 (= ?x1809 ?x1808)))
+(let (($x5230 (or $x5221 $x5270)))
+(let ((@x4739 (hypothesis $x3678)))
+(let (($x5327 (or $x3683 $x5221 $x5270)))
+(let (($x5333 (or (not (or $x5051 (<= (+ ?x1808 ?x1173 (* (- 1) ?x5054)) 0))) $x5270)))
+(let (($x5268 (or $x3683 $x5333)))
+(let (($x5095 (<= (+ ?x1808 ?x1173 (* (- 1) ?x5054)) 0)))
+(let ((@x5120 (rewrite (= (+ ?x1808 ?x1173 (* (- 1) ?x5054)) (+ ?x1173 ?x1808 (* (- 1) ?x5054))))))
+(let ((@x5127 (monotonicity @x5120 (= $x5095 (<= (+ ?x1173 ?x1808 (* (- 1) ?x5054)) 0)))))
+(let ((@x4705 (trans @x5127 (rewrite (= (<= (+ ?x1173 ?x1808 (* (- 1) ?x5054)) 0) $x5187)) (= $x5095 $x5187))))
+(let ((@x5229 (monotonicity (monotonicity @x4705 (= (or $x5051 $x5095) $x5186)) (= (not (or $x5051 $x5095)) $x5221))))
+(let ((@x5269 (monotonicity (monotonicity @x5229 (= $x5333 $x5230)) (= $x5268 (or $x3683 $x5230)))))
+(let ((@x5432 (mp ((_ quant-inst ?v0!13) $x5268) (trans @x5269 (rewrite (= (or $x3683 $x5230) $x5327)) (= $x5268 $x5327)) $x5327)))
+(let ((@x5729 (unit-resolution (def-axiom (or $x5186 (not $x5051))) (unit-resolution (unit-resolution @x5432 @x4739 $x5230) @x5726 $x5221) (not $x5051))))
+(let ((@x5749 (unit-resolution (def-axiom (or $x5186 (not $x5187))) (unit-resolution (unit-resolution @x5432 @x4739 $x5230) @x5726 $x5221) (not $x5187))))
+(let (($x5211 (or $x5051 $x5187 $x4687)))
+(let ((@x5807 (hypothesis $x3670)))
+(let (($x5189 (or $x3675 $x5051 $x5187 $x4687)))
+(let (($x5102 (or $x5051 $x5095 (= (+ ?x257 ?x5054 ?x1810) 0))))
+(let (($x5163 (or $x3675 $x5102)))
+(let ((@x5164 (monotonicity (rewrite (= (+ ?x257 ?x5054 ?x1810) ?x4706)) (= (= (+ ?x257 ?x5054 ?x1810) 0) $x4687))))
+(let ((@x5215 (monotonicity (monotonicity @x4705 @x5164 (= $x5102 $x5211)) (= $x5163 (or $x3675 $x5211)))))
+(let ((@x5376 (mp ((_ quant-inst ?v0!13) $x5163) (trans @x5215 (rewrite (= (or $x3675 $x5211) $x5189)) (= $x5163 $x5189)) $x5189)))
+(let ((@x5714 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x4687) (>= ?x4706 0))) (unit-resolution (unit-resolution @x5376 @x5807 $x5211) @x5749 @x5729 $x4687) (>= ?x4706 0))))
+(let ((@x5723 (unit-resolution ((_ th-lemma arith farkas 1 1) (or (<= ?x1811 0) $x1812)) (hypothesis $x1813) (<= ?x1811 0))))
+(let ((@x6888 (unit-resolution (lemma ((_ th-lemma arith farkas 1 -1 1) @x5723 @x5749 @x5714 false) (or $x1812 $x3675 $x3683)) @x6588 @x5944 $x1812)))
+(let ((@x6891 (unit-resolution (def-axiom (or $x3806 $x1813 $x3800)) @x6888 (unit-resolution (def-axiom (or $x3809 $x3803)) @x6181 $x3803) $x3800)))
+(let (($x6050 (= ?v0!14 v_b_v_G_1$)))
+(let (($x5678 (fun_app$ v_b_Visited_G_1$ ?v0!14)))
+(let (($x4963 (or $x6050 $x5678)))
+(let (($x6049 (fun_app$ ?x265 ?v0!14)))
+(let (($x6452 (= $x6049 $x4963)))
+(let (($x5869 (or $x4114 $x6452)))
+(let ((@x6355 (monotonicity (rewrite (= (ite $x6050 true $x5678) $x4963)) (= (= $x6049 (ite $x6050 true $x5678)) $x6452))))
+(let ((@x5854 (monotonicity @x6355 (= (or $x4114 (= $x6049 (ite $x6050 true $x5678))) $x5869))))
+(let ((@x6366 (trans @x5854 (rewrite (= $x5869 $x5869)) (= (or $x4114 (= $x6049 (ite $x6050 true $x5678))) $x5869))))
+(let ((@x6233 (mp ((_ quant-inst v_b_Visited_G_1$ v_b_v_G_1$ true ?v0!14) (or $x4114 (= $x6049 (ite $x6050 true $x5678)))) @x6366 $x5869)))
+(let ((@x6372 (symm (monotonicity @x5875 (= $x6049 (fun_app$ v_b_Visited_G_2$ ?v0!14))) (= (fun_app$ v_b_Visited_G_2$ ?v0!14) $x6049))))
+(let (($x1824 (fun_app$ v_b_Visited_G_2$ ?v0!14)))
+(let ((@x4837 (mp (unit-resolution (def-axiom (or $x1829 $x1824)) (hypothesis $x1830) $x1824) @x6372 $x6049)))
+(let ((@x5037 (unit-resolution (def-axiom (or (not $x6452) (not $x6049) $x4963)) @x4837 (unit-resolution @x6233 @x3473 $x6452) $x4963)))
+(let (($x4290 (not $x5678)))
+(let ((?x5658 (* (- 1) ?x1827)))
+(let ((?x4907 (+ ?x257 ?x5658)))
+(let (($x6523 (>= ?x4907 0)))
+(let (($x6556 (not $x6523)))
+(let (($x4887 (>= (+ ?x257 ?x5658 (b_G$ (pair$ v_b_v_G_1$ ?v0!14))) 0)))
+(let (($x4812 (not $x4887)))
+(let (($x4783 (<= (+ b_Infinity$ (* (- 1) (b_G$ (pair$ v_b_v_G_1$ ?v0!14)))) 0)))
+(let (($x5110 (or $x4783 $x4887)))
+(let (($x5079 (not $x5110)))
+(let ((@x5065 (unit-resolution (def-axiom (or $x1829 (not $x1828))) (hypothesis $x1830) (not $x1828))))
+(let (($x4844 (or $x3683 $x5079 $x1828)))
+(let (($x4891 (<= (+ ?x1827 ?x1173 (* (- 1) (b_G$ (pair$ v_b_v_G_1$ ?v0!14)))) 0)))
+(let (($x5552 (or (not (or $x4783 $x4891)) $x1828)))
+(let (($x4766 (or $x3683 $x5552)))
+(let (($x4493 (<= (+ ?x1173 ?x1827 (* (- 1) (b_G$ (pair$ v_b_v_G_1$ ?v0!14)))) 0)))
+(let (($x5019 (= (+ ?x1827 ?x1173 (* (- 1) (b_G$ (pair$ v_b_v_G_1$ ?v0!14)))) (+ ?x1173 ?x1827 (* (- 1) (b_G$ (pair$ v_b_v_G_1$ ?v0!14)))))))
+(let ((@x5288 (trans (monotonicity (rewrite $x5019) (= $x4891 $x4493)) (rewrite (= $x4493 $x4887)) (= $x4891 $x4887))))
+(let ((@x5082 (monotonicity (monotonicity @x5288 (= (or $x4783 $x4891) $x5110)) (= (not (or $x4783 $x4891)) $x5079))))
+(let ((@x5868 (monotonicity (monotonicity @x5082 (= $x5552 (or $x5079 $x1828))) (= $x4766 (or $x3683 (or $x5079 $x1828))))))
+(let ((@x5811 (trans @x5868 (rewrite (= (or $x3683 (or $x5079 $x1828)) $x4844)) (= $x4766 $x4844))))
+(let ((@x6433 (unit-resolution (def-axiom (or $x5110 $x4812)) (unit-resolution (mp ((_ quant-inst ?v0!14) $x4766) @x5811 $x4844) @x5944 @x5065 $x5079) $x4812)))
+(let ((?x6047 (pair$ v_b_v_G_1$ ?v0!14)))
+(let ((?x6491 (b_G$ ?x6047)))
+(let (($x5826 (>= ?x6491 0)))
+(let ((@x6283 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not (= ?x6491 0)) $x5826)) (hypothesis (not $x5826)) (not (= ?x6491 0)))))
+(let (($x5742 (= v_b_v_G_1$ ?v0!14)))
+(let (($x5751 (<= ?x6491 0)))
+(let ((@x6302 (unit-resolution ((_ th-lemma arith farkas 1 1) (or $x5826 $x5751)) (hypothesis (not $x5826)) $x5751)))
+(let (($x5738 (or $x5742 (not $x5751))))
+(let (($x3480 (forall ((?v0 B_Vertex$) (?v1 B_Vertex$) )(!(let (($x84 (= ?v0 ?v1)))
+(or $x84 (not (<= (b_G$ (pair$ ?v0 ?v1)) 0)))) :pattern ( (pair$ ?v0 ?v1) )))
+))
+(let (($x120 (forall ((?v0 B_Vertex$) (?v1 B_Vertex$) )(let (($x84 (= ?v0 ?v1)))
+(or $x84 (not (<= (b_G$ (pair$ ?v0 ?v1)) 0)))))
+))
+(let (($x84 (= ?1 ?0)))
+(let (($x117 (or $x84 (not (<= (b_G$ (pair$ ?1 ?0)) 0)))))
+(let (($x105 (forall ((?v0 B_Vertex$) (?v1 B_Vertex$) )(let ((?x29 (pair$ ?v0 ?v1)))
+(let ((?x85 (b_G$ ?x29)))
+(let (($x102 (< 0 ?x85)))
+(=> (not (= ?v0 ?v1)) $x102)))))
+))
+(let (($x110 (forall ((?v0 B_Vertex$) (?v1 B_Vertex$) )(let ((?x29 (pair$ ?v0 ?v1)))
+(let ((?x85 (b_G$ ?x29)))
+(let (($x102 (< 0 ?x85)))
+(let (($x84 (= ?v0 ?v1)))
+(or $x84 $x102))))))
+))
+(let ((?x29 (pair$ ?1 ?0)))
+(let ((?x85 (b_G$ ?x29)))
+(let (($x102 (< 0 ?x85)))
+(let ((@x119 (monotonicity (rewrite (= $x102 (not (<= ?x85 0)))) (= (or $x84 $x102) $x117))))
+(let ((@x112 (quant-intro (rewrite (= (=> (not $x84) $x102) (or $x84 $x102))) (= $x105 $x110))))
+(let ((@x125 (mp (asserted $x105) (trans @x112 (quant-intro @x119 (= $x110 $x120)) (= $x105 $x120)) $x120)))
+(let ((@x3485 (mp (mp~ @x125 (nnf-pos (refl (~ $x117 $x117)) (~ $x120 $x120)) $x120) (quant-intro (refl (= $x117 $x117)) (= $x120 $x3480)) $x3480)))
+(let ((@x5780 (mp ((_ quant-inst v_b_v_G_1$ ?v0!14) (or (not $x3480) $x5738)) (rewrite (= (or (not $x3480) $x5738) (or (not $x3480) $x5742 (not $x5751)))) (or (not $x3480) $x5742 (not $x5751)))))
+(let (($x5739 (= ?x6491 0)))
+(let (($x5781 (or (not $x5742) $x5739)))
+(let (($x3474 (forall ((?v0 B_Vertex$) (?v1 B_Vertex$) )(!(or (not (= ?v0 ?v1)) (= (b_G$ (pair$ ?v0 ?v1)) 0)) :pattern ( (pair$ ?v0 ?v1) )))
+))
+(let (($x99 (forall ((?v0 B_Vertex$) (?v1 B_Vertex$) )(or (not (= ?v0 ?v1)) (= (b_G$ (pair$ ?v0 ?v1)) 0)))
+))
+(let ((@x3476 (refl (= (or (not $x84) (= ?x85 0)) (or (not $x84) (= ?x85 0))))))
+(let ((@x1447 (refl (~ (or (not $x84) (= ?x85 0)) (or (not $x84) (= ?x85 0))))))
+(let (($x93 (forall ((?v0 B_Vertex$) (?v1 B_Vertex$) )(let (($x84 (= ?v0 ?v1)))
+(=> $x84 (= (b_G$ (pair$ ?v0 ?v1)) 0))))
+))
+(let ((@x98 (rewrite (= (=> $x84 (= ?x85 0)) (or (not $x84) (= ?x85 0))))))
+(let ((@x1448 (mp~ (mp (asserted $x93) (quant-intro @x98 (= $x93 $x99)) $x99) (nnf-pos @x1447 (~ $x99 $x99)) $x99)))
+(let ((@x3479 (mp @x1448 (quant-intro @x3476 (= $x99 $x3474)) $x3474)))
+(let ((@x5817 (mp ((_ quant-inst v_b_v_G_1$ ?v0!14) (or (not $x3474) $x5781)) (rewrite (= (or (not $x3474) $x5781) (or (not $x3474) (not $x5742) $x5739))) (or (not $x3474) (not $x5742) $x5739))))
+(let ((@x6306 (unit-resolution (unit-resolution @x5817 @x3479 $x5781) (unit-resolution (unit-resolution @x5780 @x3485 $x5738) @x6302 $x5742) @x6283 false)))
+(let ((@x6555 ((_ th-lemma arith farkas 1 -1 1) (lemma @x6306 $x5826) (hypothesis $x4812) (hypothesis $x6523) false)))
+(let ((@x6225 (unit-resolution (def-axiom (or $x3809 $x256)) @x6181 $x256)))
+(let ((@x5748 (unit-resolution (def-axiom (or $x3821 $x3565)) @x4219 $x3565)))
+(let ((@x6018 (rewrite (= (or $x3570 (or $x255 $x4290 $x6523)) (or $x3570 $x255 $x4290 $x6523)))))
+(let ((@x6055 (mp ((_ quant-inst ?v0!14 v_b_v_G_1$) (or $x3570 (or $x255 $x4290 $x6523))) @x6018 (or $x3570 $x255 $x4290 $x6523))))
+(let ((@x6222 (unit-resolution @x6055 @x5748 @x6225 (hypothesis $x5678) (hypothesis $x6556) false)))
+(let ((@x5057 (unit-resolution (lemma @x6222 (or $x4290 $x6523)) (unit-resolution (lemma @x6555 (or $x6556 $x4887)) @x6433 $x6556) $x4290)))
+(let ((@x6293 (monotonicity (unit-resolution (def-axiom (or (not $x4963) $x6050 $x5678)) @x5057 @x5037 $x6050) (= ?x1827 ?x257))))
+(let (($x3052 (= ?x3104 ?x257)))
+(let ((?x3130 (pair$ v_b_v_G_1$ v_b_v_G_1$)))
+(let ((?x3096 (b_G$ ?x3130)))
+(let (($x3079 (>= ?x3096 0)))
+(let (($x3088 (<= (+ b_Infinity$ (* (- 1) ?x3096)) 0)))
+(let (($x4242 (or $x3088 $x3079)))
+(let (($x4785 (= ?x3096 0)))
+(let (($x3151 (not $x3474)))
+(let (($x4816 (or $x3151 $x4785)))
+(let ((@x4770 (monotonicity (rewrite (= (= v_b_v_G_1$ v_b_v_G_1$) true)) (= (not (= v_b_v_G_1$ v_b_v_G_1$)) (not true)))))
+(let ((@x4775 (trans @x4770 (rewrite (= (not true) false)) (= (not (= v_b_v_G_1$ v_b_v_G_1$)) false))))
+(let ((@x4767 (monotonicity @x4775 (= (or (not (= v_b_v_G_1$ v_b_v_G_1$)) $x4785) (or false $x4785)))))
+(let ((@x4773 (trans @x4767 (rewrite (= (or false $x4785) $x4785)) (= (or (not (= v_b_v_G_1$ v_b_v_G_1$)) $x4785) $x4785))))
+(let ((@x4820 (monotonicity @x4773 (= (or $x3151 (or (not (= v_b_v_G_1$ v_b_v_G_1$)) $x4785)) $x4816))))
+(let ((@x4821 (trans @x4820 (rewrite (= $x4816 $x4816)) (= (or $x3151 (or (not (= v_b_v_G_1$ v_b_v_G_1$)) $x4785)) $x4816))))
+(let ((@x4822 (mp ((_ quant-inst v_b_v_G_1$ v_b_v_G_1$) (or $x3151 (or (not (= v_b_v_G_1$ v_b_v_G_1$)) $x4785))) @x4821 $x4816)))
+(let ((@x4849 (lemma (unit-resolution @x4822 @x3479 (hypothesis (not $x4785)) false) $x4785)))
+(let ((@x6019 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x4785) $x3079)) @x4849 $x3079)))
+(let ((@x4316 (def-axiom (or $x4242 (not $x3079)))))
+(let (($x4245 (not $x4242)))
+(let (($x3975 (or $x3683 $x4245 $x3052)))
+(let (($x3053 (or (not (or $x3088 (<= (+ ?x257 ?x1173 (* (- 1) ?x3096)) 0))) $x3052)))
+(let (($x3958 (or $x3683 $x3053)))
+(let (($x3103 (<= (+ ?x257 ?x1173 (* (- 1) ?x3096)) 0)))
+(let ((@x4023 (monotonicity (rewrite (= (+ ?x257 ?x1173 (* (- 1) ?x3096)) (* (- 1) ?x3096))) (= $x3103 (<= (* (- 1) ?x3096) 0)))))
+(let ((@x4044 (trans @x4023 (rewrite (= (<= (* (- 1) ?x3096) 0) $x3079)) (= $x3103 $x3079))))
+(let ((@x4247 (monotonicity (monotonicity @x4044 (= (or $x3088 $x3103) $x4242)) (= (not (or $x3088 $x3103)) $x4245))))
+(let ((@x4254 (monotonicity (monotonicity @x4247 (= $x3053 (or $x4245 $x3052))) (= $x3958 (or $x3683 (or $x4245 $x3052))))))
+(let ((@x4258 (trans @x4254 (rewrite (= (or $x3683 (or $x4245 $x3052)) $x3975)) (= $x3958 $x3975))))
+(let ((@x4259 (mp ((_ quant-inst v_b_v_G_1$) $x3958) @x4258 $x3975)))
+(let ((@x6268 (monotonicity (unit-resolution (def-axiom (or (not $x4963) $x6050 $x5678)) @x5057 @x5037 $x6050) (= ?x1826 ?x3104))))
+(let ((@x6107 (trans @x6268 (unit-resolution @x4259 @x5944 (unit-resolution @x4316 @x6019 $x4242) $x3052) (= ?x1826 ?x257))))
+(let ((@x6162 (unit-resolution @x5065 (trans @x6107 (symm @x6293 (= ?x257 ?x1827)) $x1828) false)))
+(let ((@x7615 (unit-resolution (def-axiom (or $x3794 $x1830 $x3788)) (lemma @x6162 $x1829) (unit-resolution (def-axiom (or $x3797 $x3791)) @x6891 $x3791) $x3788)))
+(let ((@x7616 (unit-resolution (def-axiom (or $x3785 $x3695)) @x7615 $x3695)))
+(let ((@x7443 (mp ((_ quant-inst ?v0!15) (or $x3700 (or $x4479 $x4481))) (rewrite (= (or $x3700 (or $x4479 $x4481)) (or $x3700 $x4479 $x4481))) (or $x3700 $x4479 $x4481))))
+(let ((@x7323 (mp (unit-resolution @x7443 @x7616 (unit-resolution @x6242 @x6183 (not $x4481)) $x4479) @x7322 (not $x6630))))
+(let ((@x7334 (unit-resolution (def-axiom (or (not $x7702) $x6630 (not $x7698))) @x7323 (unit-resolution @x7488 @x3473 $x7702) (not $x7698))))
+(let ((@x7344 (mp (unit-resolution (def-axiom (or $x7698 $x7483)) @x7334 $x7483) (monotonicity @x7337 (= $x7483 $x5538)) $x5538)))
+(let (($x5470 (or $x6156 $x6583)))
+(let ((@x6577 (mp ((_ quant-inst v_b_v_G_1$ ?v0!15) (or (not $x3480) $x5470)) (rewrite (= (or (not $x3480) $x5470) (or (not $x3480) $x6156 $x6583))) (or (not $x3480) $x6156 $x6583))))
+(let ((@x7345 (unit-resolution ((_ th-lemma arith farkas 1 1) (or $x6603 $x6582)) (unit-resolution (unit-resolution @x6577 @x3485 $x5470) @x7344 $x6583) $x6603)))
+(let (($x4153 (<= ?x296 0)))
+(let ((?x4058 (* (- 1) ?x296)))
+(let ((?x4124 (+ ?x172 ?x4058)))
+(let (($x4125 (>= ?x4124 0)))
+(let ((@x6892 (unit-resolution (def-axiom (or $x3797 $x3686)) @x6891 $x3686)))
+(let (($x4878 (or $x3691 $x4125)))
+(let ((@x4880 ((_ quant-inst b_Source$) $x4878)))
+(let (($x3198 (<= ?x172 0)))
+(let ((@x4532 (unit-resolution ((_ th-lemma arith triangle-eq) (or $x2952 $x3198)) @x4529 $x3198)))
+(let ((@x6899 (unit-resolution ((_ th-lemma arith assign-bounds -1 1) (or $x4153 (not $x3198) (not $x4125))) @x4532 (or $x4153 (not $x4125)))))
+(let ((@x6900 (unit-resolution @x6899 (unit-resolution @x4880 @x6892 $x4125) $x4153)))
+(let (($x3887 (= v_b_v_G_1$ b_Source$)))
+(let (($x5313 (not $x3887)))
+(let ((@x5202 (hypothesis $x773)))
+(let ((?x4565 (pair$ b_Source$ b_Source$)))
+(let ((?x4566 (b_G$ ?x4565)))
+(let ((?x4567 (* (- 1) ?x4566)))
+(let ((?x4041 (pair$ v_b_v_G_1$ b_Source$)))
+(let ((?x4042 (b_G$ ?x4041)))
+(let ((@x4671 (monotonicity (symm (hypothesis $x3887) (= b_Source$ v_b_v_G_1$)) (= ?x4565 ?x4041))))
+(let ((@x4659 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not (= ?x4042 ?x4566)) (>= (+ ?x4042 ?x4567) 0))) (monotonicity (symm @x4671 (= ?x4041 ?x4565)) (= ?x4042 ?x4566)) (>= (+ ?x4042 ?x4567) 0))))
+(let ((?x4049 (* (- 1) ?x4042)))
+(let ((?x5672 (+ ?x3096 ?x4049)))
+(let (($x5674 (>= ?x5672 0)))
+(let ((@x4664 (monotonicity (monotonicity (hypothesis $x3887) (= ?x3130 ?x4041)) (= ?x3096 ?x4042))))
+(let (($x4315 (not $x3079)))
+(let ((@x4728 (trans (monotonicity (hypothesis $x3887) (= ?x257 ?x172)) @x4529 (= ?x257 0))))
+(let ((@x4830 (monotonicity (monotonicity (hypothesis $x3887) (= ?x3104 ?x296)) @x4728 (= $x3052 $x297))))
+(let ((@x4736 (mp @x5202 (monotonicity (symm @x4830 (= $x297 $x3052)) (= $x773 (not $x3052))) (not $x3052))))
+(let ((@x5369 (unit-resolution @x4316 (unit-resolution (unit-resolution @x4259 @x4739 (or $x4245 $x3052)) @x4736 $x4245) $x4315)))
+(let (($x4601 (= ?x4566 0)))
+(let (($x4613 (or $x3151 $x4601)))
+(let ((@x4604 (monotonicity @x5820 (= (or (not (= b_Source$ b_Source$)) $x4601) (or false $x4601)))))
+(let ((@x4630 (trans @x4604 (rewrite (= (or false $x4601) $x4601)) (= (or (not (= b_Source$ b_Source$)) $x4601) $x4601))))
+(let ((@x4617 (monotonicity @x4630 (= (or $x3151 (or (not (= b_Source$ b_Source$)) $x4601)) $x4613))))
+(let ((@x4620 (trans @x4617 (rewrite (= $x4613 $x4613)) (= (or $x3151 (or (not (= b_Source$ b_Source$)) $x4601)) $x4613))))
+(let ((@x4621 (mp ((_ quant-inst b_Source$ b_Source$) (or $x3151 (or (not (= b_Source$ b_Source$)) $x4601))) @x4620 $x4613)))
+(let ((@x5180 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x4601) (>= ?x4566 0))) (unit-resolution @x4621 @x3479 $x4601) (>= ?x4566 0))))
+(let ((@x5283 ((_ th-lemma arith farkas 1 -1 1 1) @x5180 @x5369 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not (= ?x3096 ?x4042)) $x5674)) @x4664 $x5674) @x4659 false)))
+(let (($x5310 (<= ?x4042 0)))
+(let ((?x4076 (+ ?x257 ?x4058 ?x4042)))
+(let (($x4096 (<= ?x4076 0)))
+(let (($x4079 (= ?x4076 0)))
+(let (($x4053 (<= (+ ?x172 ?x1173 ?x4049) 0)))
+(let (($x4051 (<= (+ b_Infinity$ ?x4049) 0)))
+(let (($x4054 (or $x4051 $x4053)))
+(let (($x4055 (not $x4054)))
+(let ((@x5609 (symm (monotonicity @x4529 (= (= ?x296 ?x172) $x297)) (= $x297 (= ?x296 ?x172)))))
+(let ((@x5618 (mp @x5202 (monotonicity @x5609 (= $x773 (not (= ?x296 ?x172)))) (not (= ?x296 ?x172)))))
+(let (($x4056 (= ?x296 ?x172)))
+(let (($x4057 (or $x4055 $x4056)))
+(let (($x4295 (or $x3683 $x4055 $x4056)))
+(let ((@x4884 (mp ((_ quant-inst b_Source$) (or $x3683 $x4057)) (rewrite (= (or $x3683 $x4057) $x4295)) $x4295)))
+(let ((@x5791 (unit-resolution (def-axiom (or $x4054 (not $x4051))) (hypothesis $x4055) (not $x4051))))
+(let ((@x5806 (unit-resolution (def-axiom (or $x4054 (not $x4053))) (hypothesis $x4055) (not $x4053))))
+(let (($x4082 (or $x4051 $x4053 $x4079)))
+(let (($x4085 (or $x3675 $x4051 $x4053 $x4079)))
+(let (($x4075 (or $x4051 $x4053 (= (+ ?x257 ?x4042 ?x4058) 0))))
+(let (($x4086 (or $x3675 $x4075)))
+(let ((@x4081 (monotonicity (rewrite (= (+ ?x257 ?x4042 ?x4058) ?x4076)) (= (= (+ ?x257 ?x4042 ?x4058) 0) $x4079))))
+(let ((@x4090 (monotonicity (monotonicity @x4081 (= $x4075 $x4082)) (= $x4086 (or $x3675 $x4082)))))
+(let ((@x4095 (mp ((_ quant-inst b_Source$) $x4086) (trans @x4090 (rewrite (= (or $x3675 $x4082) $x4085)) (= $x4086 $x4085)) $x4085)))
+(let ((@x5789 (unit-resolution (unit-resolution @x4095 @x5807 $x4082) @x5806 @x5791 (hypothesis (not $x4079)) false)))
+(let ((@x5623 (unit-resolution (lemma @x5789 (or $x4054 $x4079 $x3675)) (unit-resolution (unit-resolution @x4884 @x4739 $x4057) @x5618 $x4055) @x5807 $x4079)))
+(let ((@x5923 (hypothesis $x4096)))
+(let ((@x5933 ((_ th-lemma arith farkas -1 1 -1 1) (hypothesis $x3904) (hypothesis $x4153) (hypothesis (not $x5310)) @x5923 false)))
+(let ((@x5938 (lemma @x5933 (or $x5310 (not $x3904) (not $x4153) (not $x4096)))))
+(let ((@x5596 (unit-resolution @x5938 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x4079) $x4096)) @x5623 $x4096) (hypothesis $x4153) @x5049 $x5310)))
+(let (($x5886 (= (or (not $x3480) (or $x3887 (not $x5310))) (or (not $x3480) $x3887 (not $x5310)))))
+(let ((@x5952 (mp ((_ quant-inst v_b_v_G_1$ b_Source$) (or (not $x3480) (or $x3887 (not $x5310)))) (rewrite $x5886) (or (not $x3480) $x3887 (not $x5310)))))
+(let ((@x5597 (unit-resolution @x5952 @x3485 @x5596 (unit-resolution (lemma @x5283 (or $x5313 $x3683 $x297)) @x5202 @x4739 $x5313) false)))
+(let ((@x6788 (unit-resolution (lemma @x5597 (or $x297 (not $x4153) $x3675 $x3683)) @x6900 @x6588 @x5944 $x297)))
+(let ((@x7810 (unit-resolution (def-axiom (or $x3782 $x773 $x3776)) (unit-resolution (def-axiom (or $x3785 $x3779)) @x7615 $x3779) @x6788 $x3776)))
+(let ((@x3347 (def-axiom (or $x3770 $x1848 $x3764))))
+(let ((@x9293 (unit-resolution @x3347 (unit-resolution (def-axiom (or $x3773 $x3767)) @x7810 $x3767) $x3767)))
+(let ((@x9294 (unit-resolution @x9293 (lemma ((_ th-lemma arith farkas 1 1 -1 1) @x5703 @x7345 @x6959 @x5049 false) $x1847) $x3764)))
+(let ((@x3367 (def-axiom (or $x3761 $x3703))))
+(let (($x4335 (or $x3708 $x4161)))
+(let ((@x4337 ((_ quant-inst v_b_v_G_1$) $x4335)))
+(let (($x4126 (fun_app$ v_b_Visited_G_2$ v_b_v_G_1$)))
+(let (($x3136 (fun_app$ ?x265 v_b_v_G_1$)))
+(let (($x3461 (forall ((?v0 B_Vertex_bool_fun$) (?v1 B_Vertex$) (?v2 Bool) )(!(= (fun_app$ (fun_app$a (fun_app$b (fun_upd$ ?v0) ?v1) ?v2) ?v1) ?v2) :pattern ( (fun_app$a (fun_app$b (fun_upd$ ?v0) ?v1) ?v2) )))
+))
+(let (($x57 (forall ((?v0 B_Vertex_bool_fun$) (?v1 B_Vertex$) (?v2 Bool) )(= (fun_app$ (fun_app$a (fun_app$b (fun_upd$ ?v0) ?v1) ?v2) ?v1) ?v2))
+))
+(let (($x54 (= (fun_app$ (fun_app$a (fun_app$b (fun_upd$ ?2) ?1) ?0) ?1) ?0)))
+(let (($x52 (forall ((?v0 B_Vertex_bool_fun$) (?v1 B_Vertex$) (?v2 Bool) )(= (fun_app$ (fun_app$a (fun_app$b (fun_upd$ ?v0) ?v1) ?v2) ?v1) ?v2))
+))
+(let (($x51 (= (fun_app$ (fun_app$a (fun_app$b (fun_upd$ ?2) ?1) ?0) ?1) ?0)))
+(let ((@x62 (mp (asserted $x52) (quant-intro (rewrite (= $x51 $x54)) (= $x52 $x57)) $x57)))
+(let ((@x3466 (mp (mp~ @x62 (nnf-pos (refl (~ $x54 $x54)) (~ $x57 $x57)) $x57) (quant-intro (refl (= $x54 $x54)) (= $x57 $x3461)) $x3461)))
+(let (($x6140 (or (not $x3461) $x3136)))
+(let ((@x6106 (monotonicity (rewrite (= (= $x3136 true) $x3136)) (= (or (not $x3461) (= $x3136 true)) $x6140))))
+(let ((@x5837 (trans @x6106 (rewrite (= $x6140 $x6140)) (= (or (not $x3461) (= $x3136 true)) $x6140))))
+(let ((@x5928 (mp ((_ quant-inst v_b_Visited_G_1$ v_b_v_G_1$ true) (or (not $x3461) (= $x3136 true))) @x5837 $x6140)))
+(let ((@x7482 (mp (unit-resolution @x5928 @x3466 $x3136) (monotonicity @x5875 (= $x3136 $x4126)) $x4126)))
+(let (($x4570 (>= ?x4546 0)))
+(let ((@x5420 (unit-resolution ((_ th-lemma arith farkas 1 1) (or $x4570 $x4569)) (hypothesis (not $x4569)) $x4570)))
+(let (($x4438 (<= (+ b_Infinity$ ?x4436) 0)))
+(let (($x4127 (not $x4126)))
+(let (($x5352 (or $x3725 $x4127 $x4438 $x4569)))
+(let (($x5336 (>= (+ ?x4435 ?x3104 (* (- 1) ?x1911)) 0)))
+(let (($x5339 (or $x4127 $x4438 $x5336)))
+(let (($x5353 (or $x3725 $x5339)))
+(let ((@x5341 (rewrite (= (+ ?x4435 ?x3104 (* (- 1) ?x1911)) (+ (* (- 1) ?x1911) ?x3104 ?x4435)))))
+(let ((@x5344 (monotonicity @x5341 (= $x5336 (>= (+ (* (- 1) ?x1911) ?x3104 ?x4435) 0)))))
+(let ((@x5348 (trans @x5344 (rewrite (= (>= (+ (* (- 1) ?x1911) ?x3104 ?x4435) 0) $x4569)) (= $x5336 $x4569))))
+(let ((@x5357 (monotonicity (monotonicity @x5348 (= $x5339 (or $x4127 $x4438 $x4569))) (= $x5353 (or $x3725 (or $x4127 $x4438 $x4569))))))
+(let ((@x5361 (trans @x5357 (rewrite (= (or $x3725 (or $x4127 $x4438 $x4569)) $x5352)) (= $x5353 $x5352))))
+(let ((@x5424 (unit-resolution (mp ((_ quant-inst ?v0!20 v_b_v_G_1$) $x5353) @x5361 $x5352) (hypothesis $x3720) (hypothesis $x4126) (hypothesis (not $x4569)) $x4438)))
+(let ((@x5428 (lemma ((_ th-lemma arith farkas 1 1 1 1) @x5424 (hypothesis $x4161) @x5420 (hypothesis $x1915) false) (or $x4569 (not $x4161) $x1914 $x3725 $x4127))))
+(let ((@x7692 (unit-resolution (unit-resolution @x5428 @x7482 (or $x4569 (not $x4161) $x1914 $x3725)) (unit-resolution @x4337 (unit-resolution @x3367 @x9294 $x3703) $x4161) (or $x4569 $x1914 $x3725))))
+(let ((@x7751 (unit-resolution @x7692 (unit-resolution (def-axiom (or $x3737 $x1915)) @x8092 $x1915) (unit-resolution @x3222 @x8092 $x3720) $x4569)))
+(let (($x5386 (= v_b_v_G_1$ ?v0!20)))
+(let (($x5390 (not $x5386)))
+(let ((@x9325 (symm (commutativity (= $x5386 (= ?v0!20 v_b_v_G_1$))) (= (= ?v0!20 v_b_v_G_1$) $x5386))))
+(let (($x5240 (= ?v0!20 v_b_v_G_1$)))
+(let (($x9145 (not $x5240)))
+(let (($x4609 (fun_app$ v_b_Visited_G_1$ ?v0!20)))
+(let (($x9130 (or $x5240 $x4609)))
+(let (($x5237 (fun_app$ ?x265 ?v0!20)))
+(let (($x9133 (= $x5237 $x9130)))
+(let (($x9136 (or $x4114 $x9133)))
+(let ((@x9135 (monotonicity (rewrite (= (ite $x5240 true $x4609) $x9130)) (= (= $x5237 (ite $x5240 true $x4609)) $x9133))))
+(let ((@x9140 (monotonicity @x9135 (= (or $x4114 (= $x5237 (ite $x5240 true $x4609))) $x9136))))
+(let ((@x9143 (trans @x9140 (rewrite (= $x9136 $x9136)) (= (or $x4114 (= $x5237 (ite $x5240 true $x4609))) $x9136))))
+(let ((@x9144 (mp ((_ quant-inst v_b_Visited_G_1$ v_b_v_G_1$ true ?v0!20) (or $x4114 (= $x5237 (ite $x5240 true $x4609)))) @x9143 $x9136)))
+(let ((@x9316 (symm (monotonicity @x5875 (= $x5237 (fun_app$ v_b_Visited_G_2$ ?v0!20))) (= (fun_app$ v_b_Visited_G_2$ ?v0!20) $x5237))))
+(let ((@x9318 (monotonicity @x9316 (= (not (fun_app$ v_b_Visited_G_2$ ?v0!20)) (not $x5237)))))
+(let (($x4278 (fun_app$ v_b_Visited_G_2$ ?v0!20)))
+(let (($x4279 (not $x4278)))
+(let (($x4403 (or $x4279 $x4400)))
+(let ((@x8012 (mp ((_ quant-inst ?v0!20) (or $x3700 $x4403)) (rewrite (= (or $x3700 $x4403) (or $x3700 $x4279 $x4400))) (or $x3700 $x4279 $x4400))))
+(let ((@x9292 (unit-resolution (unit-resolution @x8012 @x7616 $x4403) (hypothesis (not $x4400)) $x4279)))
+(let ((@x9320 (unit-resolution (def-axiom (or (not $x9133) $x5237 (not $x9130))) (mp @x9292 @x9318 (not $x5237)) (unit-resolution @x9144 @x3473 $x9133) (not $x9130))))
+(let ((@x9328 (mp (unit-resolution (def-axiom (or $x9130 $x9145)) @x9320 $x9145) (monotonicity @x9325 (= $x9145 $x5390)) $x5390)))
+(let (($x5387 (<= ?x4435 0)))
+(let (($x5391 (= ?x4435 0)))
+(let ((?x3106 (+ ?x257 ?x3096 ?x3105)))
+(let (($x4239 (<= ?x3106 0)))
+(let ((?x3884 (+ ?x257 ?x3105)))
+(let (($x3885 (<= ?x3884 0)))
+(let (($x6004 (= ?x257 ?x3104)))
+(let ((@x7828 (mp (unit-resolution @x4259 @x5944 (unit-resolution @x4316 @x6019 $x4242) $x3052) (symm (commutativity (= $x6004 $x3052)) (= $x3052 $x6004)) $x6004)))
+(let (($x4177 (<= ?x3096 0)))
+(let ((@x6933 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x4785) $x4177)) @x4849 $x4177)))
+(let ((@x7838 (unit-resolution ((_ th-lemma arith assign-bounds 1 1) (or $x4239 (not $x3885) (not $x4177))) @x6933 (or $x4239 (not $x3885)))))
+(let ((@x7839 (unit-resolution @x7838 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x6004) $x3885)) @x7828 $x3885) $x4239)))
+(let (($x3044 (>= ?x3106 0)))
+(let (($x3886 (>= ?x3884 0)))
+(let (($x5927 (or $x3691 $x3886)))
+(let ((@x5941 ((_ quant-inst v_b_v_G_1$) $x5927)))
+(let ((@x6925 (unit-resolution @x5941 @x6892 $x3886)))
+(let ((@x6929 (unit-resolution ((_ th-lemma arith assign-bounds -1 -1) (or $x3044 $x4315 (not $x3886))) @x6019 (or $x3044 (not $x3886)))))
+(let ((@x6930 (unit-resolution @x6929 @x6925 $x3044)))
+(let ((?x4381 (+ ?x1911 ?x3105)))
+(let (($x7049 (<= ?x4381 0)))
+(let (($x7135 (= ?x4546 0)))
+(let ((?x1912 (* (- 1) ?x1911)))
+(let ((?x4487 (+ ?x257 ?x1912 ?x4435)))
+(let (($x4507 (<= ?x4487 0)))
+(let (($x5673 (= ?x4487 0)))
+(let (($x6827 (>= (+ ?x257 ?x4418 ?x4435) 0)))
+(let (($x6723 (or $x4438 $x6827)))
+(let (($x6684 (not $x6723)))
+(let (($x6831 (or $x6684 $x4400)))
+(let (($x6789 (or $x3683 $x6684 $x4400)))
+(let (($x4443 (or (not (or $x4438 (<= (+ ?x4393 ?x1173 ?x4436) 0))) $x4400)))
+(let (($x6790 (or $x3683 $x4443)))
+(let ((@x6945 (monotonicity (rewrite (= (+ ?x4393 ?x1173 ?x4436) (+ ?x1173 ?x4393 ?x4436))) (= (<= (+ ?x4393 ?x1173 ?x4436) 0) (<= (+ ?x1173 ?x4393 ?x4436) 0)))))
+(let ((@x6725 (trans @x6945 (rewrite (= (<= (+ ?x1173 ?x4393 ?x4436) 0) $x6827)) (= (<= (+ ?x4393 ?x1173 ?x4436) 0) $x6827))))
+(let ((@x6730 (monotonicity @x6725 (= (or $x4438 (<= (+ ?x4393 ?x1173 ?x4436) 0)) $x6723))))
+(let ((@x6830 (monotonicity @x6730 (= (not (or $x4438 (<= (+ ?x4393 ?x1173 ?x4436) 0))) $x6684))))
+(let ((@x6829 (monotonicity (monotonicity @x6830 (= $x4443 $x6831)) (= $x6790 (or $x3683 $x6831)))))
+(let ((@x6824 (mp ((_ quant-inst ?v0!20) $x6790) (trans @x6829 (rewrite (= (or $x3683 $x6831) $x6789)) (= $x6790 $x6789)) $x6789)))
+(let ((@x9281 (unit-resolution (unit-resolution @x6824 @x5944 $x6831) (hypothesis (not $x4400)) $x6684)))
+(let ((@x7436 (unit-resolution (def-axiom (or $x6723 (not $x4438))) (hypothesis $x6684) (not $x4438))))
+(let ((@x7494 (unit-resolution (def-axiom (or $x6723 (not $x6827))) (hypothesis $x6684) (not $x6827))))
+(let (($x6621 (or $x4438 $x6827 $x5673)))
+(let (($x6987 (or $x3675 $x4438 $x6827 $x5673)))
+(let (($x4440 (<= (+ ?x4393 ?x1173 ?x4436) 0)))
+(let (($x4486 (or $x4438 $x4440 (= (+ ?x257 ?x4435 ?x1912) 0))))
+(let (($x6624 (or $x3675 $x4486)))
+(let ((@x5324 (monotonicity (rewrite (= (+ ?x257 ?x4435 ?x1912) ?x4487)) (= (= (+ ?x257 ?x4435 ?x1912) 0) $x5673))))
+(let ((@x6996 (monotonicity (monotonicity @x6725 @x5324 (= $x4486 $x6621)) (= $x6624 (or $x3675 $x6621)))))
+(let ((@x7057 (mp ((_ quant-inst ?v0!20) $x6624) (trans @x6996 (rewrite (= (or $x3675 $x6621) $x6987)) (= $x6624 $x6987)) $x6987)))
+(let ((@x7649 (unit-resolution (unit-resolution @x7057 @x6588 $x6621) @x7494 @x7436 (hypothesis (not $x5673)) false)))
+(let ((@x7699 (lemma @x7649 (or $x6723 $x5673))))
+(let ((@x9285 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x5673) $x4507)) (unit-resolution @x7699 @x9281 $x5673) $x4507)))
+(let ((@x9287 (unit-resolution ((_ th-lemma arith assign-bounds 1 -1) (or (not $x4507) $x4570 (not $x3886))) @x6925 (or (not $x4507) $x4570))))
+(let ((@x7251 (unit-resolution ((_ th-lemma arith triangle-eq) (or $x7135 (not $x4569) (not $x4570))) (hypothesis $x4569) (or $x7135 (not $x4570)))))
+(let (($x7151 (not $x7135)))
+(let (($x7157 (or $x3734 $x7049 $x4127 $x7151)))
+(let (($x4516 (>= (+ ?x3104 ?x1912) 0)))
+(let (($x4528 (or $x4516 $x4127 (not (= (+ ?x3104 ?x1912 ?x4435) 0)))))
+(let (($x7317 (or $x3734 $x4528)))
+(let ((@x7137 (monotonicity (rewrite (= (+ ?x3104 ?x1912 ?x4435) (+ ?x1912 ?x3104 ?x4435))) (= (= (+ ?x3104 ?x1912 ?x4435) 0) (= (+ ?x1912 ?x3104 ?x4435) 0)))))
+(let ((@x7149 (trans @x7137 (rewrite (= (= (+ ?x1912 ?x3104 ?x4435) 0) $x7135)) (= (= (+ ?x3104 ?x1912 ?x4435) 0) $x7135))))
+(let ((@x7063 (monotonicity (rewrite (= (+ ?x3104 ?x1912) (+ ?x1912 ?x3104))) (= $x4516 (>= (+ ?x1912 ?x3104) 0)))))
+(let ((@x7144 (trans @x7063 (rewrite (= (>= (+ ?x1912 ?x3104) 0) $x7049)) (= $x4516 $x7049))))
+(let ((@x7156 (monotonicity @x7144 (monotonicity @x7149 (= (not (= (+ ?x3104 ?x1912 ?x4435) 0)) $x7151)) (= $x4528 (or $x7049 $x4127 $x7151)))))
+(let ((@x7313 (trans (monotonicity @x7156 (= $x7317 (or $x3734 (or $x7049 $x4127 $x7151)))) (rewrite (= (or $x3734 (or $x7049 $x4127 $x7151)) $x7157)) (= $x7317 $x7157))))
+(let ((@x7502 (unit-resolution (mp ((_ quant-inst v_b_v_G_1$) $x7317) @x7313 $x7157) (hypothesis $x3729) @x7482 (or $x7049 $x7151))))
+(let ((@x9290 (unit-resolution @x7502 (unit-resolution @x7251 (unit-resolution @x9287 @x9285 $x4570) $x7135) $x7049)))
+(let (($x4382 (>= ?x4381 0)))
+(let (($x6813 (= ?v1!16 v_b_v_G_1$)))
+(let (($x7202 (= v_b_v_G_1$ ?v1!16)))
+(let ((?x6481 (pair$ v_b_v_G_1$ ?v1!16)))
+(let ((?x6374 (b_G$ ?x6481)))
+(let (($x7203 (<= ?x6374 0)))
+(let ((?x1866 (v_b_SP_G_2$ ?v0!17)))
+(let ((?x6890 (+ ?x1866 ?x3105)))
+(let (($x6886 (<= ?x6890 0)))
+(let ((?x4496 (fun_app$c v_b_SP_G_1$ ?v0!17)))
+(let ((?x6307 (* (- 1) ?x4496)))
+(let ((?x5972 (+ ?x257 ?x6307)))
+(let (($x7220 (>= ?x5972 0)))
+(let (($x3187 (fun_app$ v_b_Visited_G_1$ ?v0!17)))
+(let (($x4478 (= ?v0!17 v_b_v_G_1$)))
+(let (($x4499 (or $x4478 $x3187)))
+(let (($x4471 (fun_app$ ?x265 ?v0!17)))
+(let (($x4593 (= $x4471 $x4499)))
+(let (($x4712 (or $x4114 $x4593)))
+(let ((@x4495 (monotonicity (rewrite (= (ite $x4478 true $x3187) $x4499)) (= (= $x4471 (ite $x4478 true $x3187)) $x4593))))
+(let ((@x5371 (monotonicity @x4495 (= (or $x4114 (= $x4471 (ite $x4478 true $x3187))) $x4712))))
+(let ((@x5958 (trans @x5371 (rewrite (= $x4712 $x4712)) (= (or $x4114 (= $x4471 (ite $x4478 true $x3187))) $x4712))))
+(let ((@x6125 (mp ((_ quant-inst v_b_Visited_G_1$ v_b_v_G_1$ true ?v0!17) (or $x4114 (= $x4471 (ite $x4478 true $x3187)))) @x5958 $x4712)))
+(let ((@x8166 (mp (unit-resolution (def-axiom (or $x2760 $x1862)) (hypothesis $x2765) $x1862) (symm (monotonicity @x5875 (= $x4471 $x1862)) (= $x1862 $x4471)) $x4471)))
+(let ((@x8237 (unit-resolution (def-axiom (or (not $x4593) (not $x4471) $x4499)) @x8166 (unit-resolution @x6125 @x3473 $x4593) $x4499)))
+(let (($x6485 (not $x4478)))
+(let (($x8046 (<= (+ ?x257 (* (- 1) (fun_app$c v_b_SP_G_1$ ?v1!16))) 0)))
+(let (($x6814 (fun_app$ v_b_Visited_G_1$ ?v1!16)))
+(let (($x8334 (or $x6813 $x6814)))
+(let (($x6812 (fun_app$ ?x265 ?v1!16)))
+(let (($x7683 (= $x6812 $x8334)))
+(let (($x6622 (or $x4114 $x7683)))
+(let ((@x6719 (monotonicity (rewrite (= (ite $x6813 true $x6814) $x8334)) (= (= $x6812 (ite $x6813 true $x6814)) $x7683))))
+(let ((@x8777 (monotonicity @x6719 (= (or $x4114 (= $x6812 (ite $x6813 true $x6814))) $x6622))))
+(let ((@x8650 (trans @x8777 (rewrite (= $x6622 $x6622)) (= (or $x4114 (= $x6812 (ite $x6813 true $x6814))) $x6622))))
+(let ((@x8651 (mp ((_ quant-inst v_b_Visited_G_1$ v_b_v_G_1$ true ?v1!16) (or $x4114 (= $x6812 (ite $x6813 true $x6814)))) @x8650 $x6622)))
+(let ((@x8121 (monotonicity (symm (monotonicity @x5875 (= $x6812 $x1860)) (= $x1860 $x6812)) (= (not $x1860) (not $x6812)))))
+(let (($x1861 (not $x1860)))
+(let ((@x7803 (hypothesis $x2765)))
+(let ((@x8141 (mp (unit-resolution (def-axiom (or $x2760 $x1861)) @x7803 $x1861) @x8121 (not $x6812))))
+(let ((@x8147 (unit-resolution (def-axiom (or (not $x7683) $x6812 (not $x8334))) @x8141 (unit-resolution @x8651 @x3473 $x7683) (not $x8334))))
+(let (($x8156 (or $x6814 $x8046)))
+(let (($x8160 (or $x3665 $x6814 $x8046)))
+(let (($x6666 (>= (+ (fun_app$c v_b_SP_G_1$ ?v1!16) ?x1173) 0)))
+(let (($x6673 (or $x6814 $x6666)))
+(let (($x8163 (or $x3665 $x6673)))
+(let ((@x7990 (rewrite (= (>= (+ ?x1173 (fun_app$c v_b_SP_G_1$ ?v1!16)) 0) $x8046))))
+(let (($x8213 (= (+ (fun_app$c v_b_SP_G_1$ ?v1!16) ?x1173) (+ ?x1173 (fun_app$c v_b_SP_G_1$ ?v1!16)))))
+(let ((@x8047 (monotonicity (rewrite $x8213) (= $x6666 (>= (+ ?x1173 (fun_app$c v_b_SP_G_1$ ?v1!16)) 0)))))
+(let ((@x8089 (monotonicity (monotonicity (trans @x8047 @x7990 (= $x6666 $x8046)) (= $x6673 $x8156)) (= $x8163 (or $x3665 $x8156)))))
+(let ((@x8093 (mp ((_ quant-inst ?v1!16) $x8163) (trans @x8089 (rewrite (= (or $x3665 $x8156) $x8160)) (= $x8163 $x8160)) $x8160)))
+(let ((@x8217 (unit-resolution @x8093 (unit-resolution (def-axiom (or $x3809 $x3660)) @x6181 $x3660) $x8156)))
+(let ((@x8239 (unit-resolution @x8217 (unit-resolution (def-axiom (or $x8334 (not $x6814))) @x8147 (not $x6814)) $x8046)))
+(let (($x3386 (not $x1869)))
+(let ((@x3390 (def-axiom (or $x2760 $x3386))))
+(let ((@x8240 (unit-resolution @x3390 @x7803 $x3386)))
+(let ((?x6009 (pair$ v_b_v_G_1$ ?v0!17)))
+(let ((?x6010 (b_G$ ?x6009)))
+(let ((?x1867 (* (- 1) ?x1866)))
+(let ((?x6187 (+ ?x257 ?x1867 ?x6010)))
+(let ((@x8743 (monotonicity (monotonicity (hypothesis $x4478) (= ?x6009 ?x3130)) (= ?x6010 ?x3096))))
+(let (($x6889 (= ?x1866 ?x3104)))
+(let ((@x6922 (hypothesis $x4478)))
+(let ((@x6921 (unit-resolution (hypothesis (not $x6889)) (monotonicity @x6922 $x6889) false)))
+(let ((@x6939 (lemma @x6921 (or $x6485 $x6889))))
+(let ((@x6214 ((_ th-lemma arith triangle-eq) (or (not $x6889) $x6886))))
+(let (($x7675 (>= ?x6890 0)))
+(let ((@x8362 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x6889) $x7675)) (unit-resolution @x6939 @x6922 $x6889) $x7675)))
+(let ((@x7970 ((_ th-lemma arith eq-propagate 1 1 1 1 -1 -1) @x8362 (unit-resolution @x6214 (unit-resolution @x6939 @x6922 $x6889) $x6886) @x6019 @x6933 @x6930 @x7839 (= ?x6010 ?x6187))))
+(let ((@x8765 (trans (trans (symm @x7970 (= ?x6187 ?x6010)) @x8743 (= ?x6187 ?x3096)) @x4849 (= ?x6187 0))))
+(let (($x6564 (>= ?x6187 0)))
+(let (($x7274 (not $x6564)))
+(let ((@x7271 (hypothesis $x3386)))
+(let ((?x1865 (v_b_SP_G_2$ ?v1!16)))
+(let ((?x6126 (* (- 1) ?x1865)))
+(let ((?x6400 (+ ?x257 ?x6126 ?x6374)))
+(let (($x6319 (<= ?x6400 0)))
+(let (($x8008 (= ?x6400 0)))
+(let (($x6238 (<= (+ b_Infinity$ (* (- 1) ?x6374)) 0)))
+(let (($x8646 (not $x6238)))
+(let (($x7241 (>= (+ ?x257 (* (- 1) (fun_app$c v_b_SP_G_1$ ?v1!16)) ?x6374) 0)))
+(let (($x7239 (or $x6238 $x7241)))
+(let (($x4416 (not $x7239)))
+(let ((?x6234 (fun_app$c v_b_SP_G_1$ ?v1!16)))
+(let (($x6378 (= ?x1865 ?x6234)))
+(let (($x8565 (not $x6378)))
+(let (($x8664 (>= (+ ?x1865 (* (- 1) ?x6234)) 0)))
+(let (($x8549 (not $x8664)))
+(let ((@x8517 ((_ th-lemma arith assign-bounds -1 -1 -1 -1 1) (or $x8549 (not $x8046) $x1869 (not $x6886) (not $x4177) (not $x3044)))))
+(let ((@x8321 (unit-resolution @x8517 (unit-resolution @x6214 (unit-resolution @x6939 @x6922 $x6889) $x6886) @x6933 @x6930 @x7271 (hypothesis $x8046) $x8549)))
+(let (($x8358 (or $x4416 $x6378)))
+(let (($x8640 (or $x3683 $x4416 $x6378)))
+(let (($x6219 (or (not (or $x6238 (<= (+ ?x6234 ?x1173 (* (- 1) ?x6374)) 0))) $x6378)))
+(let (($x8252 (or $x3683 $x6219)))
+(let (($x6539 (<= (+ ?x6234 ?x1173 (* (- 1) ?x6374)) 0)))
+(let ((@x7664 (rewrite (= (+ ?x6234 ?x1173 (* (- 1) ?x6374)) (+ ?x1173 ?x6234 (* (- 1) ?x6374))))))
+(let ((@x7697 (monotonicity @x7664 (= $x6539 (<= (+ ?x1173 ?x6234 (* (- 1) ?x6374)) 0)))))
+(let ((@x4371 (trans @x7697 (rewrite (= (<= (+ ?x1173 ?x6234 (* (- 1) ?x6374)) 0) $x7241)) (= $x6539 $x7241))))
+(let ((@x8352 (monotonicity (monotonicity @x4371 (= (or $x6238 $x6539) $x7239)) (= (not (or $x6238 $x6539)) $x4416))))
+(let ((@x8173 (monotonicity (monotonicity @x8352 (= $x6219 $x8358)) (= $x8252 (or $x3683 $x8358)))))
+(let ((@x8649 (mp ((_ quant-inst ?v1!16) $x8252) (trans @x8173 (rewrite (= (or $x3683 $x8358) $x8640)) (= $x8252 $x8640)) $x8640)))
+(let ((@x8632 (unit-resolution (unit-resolution @x8649 @x5944 $x8358) (unit-resolution ((_ th-lemma arith triangle-eq) (or $x8565 $x8664)) @x8321 $x8565) $x4416)))
+(let (($x8029 (or $x6238 $x7241 $x8008)))
+(let (($x8118 (or $x3675 $x6238 $x7241 $x8008)))
+(let (($x6399 (or $x6238 $x6539 (= (+ ?x257 ?x6374 ?x6126) 0))))
+(let (($x8113 (or $x3675 $x6399)))
+(let ((@x8010 (monotonicity (rewrite (= (+ ?x257 ?x6374 ?x6126) ?x6400)) (= (= (+ ?x257 ?x6374 ?x6126) 0) $x8008))))
+(let ((@x5909 (monotonicity (monotonicity @x4371 @x8010 (= $x6399 $x8029)) (= $x8113 (or $x3675 $x8029)))))
+(let ((@x7712 (mp ((_ quant-inst ?v1!16) $x8113) (trans @x5909 (rewrite (= (or $x3675 $x8029) $x8118)) (= $x8113 $x8118)) $x8118)))
+(let ((@x8635 (unit-resolution (unit-resolution @x7712 @x6588 $x8029) (unit-resolution (def-axiom (or $x7239 (not $x7241))) @x8632 (not $x7241)) (unit-resolution (def-axiom (or $x7239 $x8646)) @x8632 $x8646) $x8008)))
+(let ((@x7288 (monotonicity (commutativity (= (= v_b_v_G_1$ ?v0!17) $x4478)) (= (not (= v_b_v_G_1$ ?v0!17)) $x6485))))
+(let (($x7176 (= v_b_v_G_1$ ?v0!17)))
+(let (($x7180 (not $x7176)))
+(let (($x7177 (<= ?x6010 0)))
+(let (($x7178 (not $x7177)))
+(let (($x7206 (not $x7203)))
+(let ((@x7267 (monotonicity (symm (commutativity (= $x7202 $x6813)) (= $x6813 $x7202)) (= (not $x6813) (not $x7202)))))
+(let (($x7207 (or $x7202 $x7206)))
+(let ((@x7215 (mp ((_ quant-inst v_b_v_G_1$ ?v1!16) (or (not $x3480) $x7207)) (rewrite (= (or (not $x3480) $x7207) (or (not $x3480) $x7202 $x7206))) (or (not $x3480) $x7202 $x7206))))
+(let ((@x7270 (unit-resolution (unit-resolution @x7215 @x3485 $x7207) (mp (hypothesis (not $x6813)) @x7267 (not $x7202)) $x7206)))
+(let ((@x7278 (unit-resolution ((_ th-lemma arith assign-bounds 1 1 1 1) (or $x7178 $x7274 $x1869 $x7203 (not $x6319))) (hypothesis $x6319) (hypothesis $x6564) @x7271 @x7270 $x7178)))
+(let ((@x7282 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not (= ?x6010 0)) $x7177)) @x7278 (not (= ?x6010 0)))))
+(let (($x7181 (= ?x6010 0)))
+(let (($x7188 (or $x7180 $x7181)))
+(let ((@x7196 (mp ((_ quant-inst v_b_v_G_1$ ?v0!17) (or $x3151 $x7188)) (rewrite (= (or $x3151 $x7188) (or $x3151 $x7180 $x7181))) (or $x3151 $x7180 $x7181))))
+(let ((@x7289 (mp (unit-resolution (unit-resolution @x7196 @x3479 $x7188) @x7282 $x7180) @x7288 $x6485)))
+(let ((@x5812 (def-axiom (or (not $x4499) $x4478 $x3187))))
+(let (($x7229 (= (or $x3570 (or $x255 (not $x3187) $x7220)) (or $x3570 $x255 (not $x3187) $x7220))))
+(let ((@x7231 (mp ((_ quant-inst ?v0!17 v_b_v_G_1$) (or $x3570 (or $x255 (not $x3187) $x7220))) (rewrite $x7229) (or $x3570 $x255 (not $x3187) $x7220))))
+(let ((@x7291 (unit-resolution @x7231 @x5748 @x6225 (unit-resolution @x5812 @x7289 (hypothesis $x4499) $x3187) $x7220)))
+(let (($x6327 (<= (+ ?x1866 ?x6307) 0)))
+(let (($x6088 (or $x3691 $x6327)))
+(let ((@x6464 (monotonicity (rewrite (= (+ ?x4496 ?x1867) (+ ?x1867 ?x4496))) (= (>= (+ ?x4496 ?x1867) 0) (>= (+ ?x1867 ?x4496) 0)))))
+(let ((@x5905 (trans @x6464 (rewrite (= (>= (+ ?x1867 ?x4496) 0) $x6327)) (= (>= (+ ?x4496 ?x1867) 0) $x6327))))
+(let ((@x5843 (trans (monotonicity @x5905 (= (or $x3691 (>= (+ ?x4496 ?x1867) 0)) $x6088)) (rewrite (= $x6088 $x6088)) (= (or $x3691 (>= (+ ?x4496 ?x1867) 0)) $x6088))))
+(let ((@x7292 (unit-resolution (mp ((_ quant-inst ?v0!17) (or $x3691 (>= (+ ?x4496 ?x1867) 0))) @x5843 $x6088) @x6892 $x6327)))
+(let ((@x7295 (lemma ((_ th-lemma arith farkas 1 1 1 1 1) @x7292 @x7271 @x7270 (hypothesis $x6319) @x7291 false) (or (not $x6319) $x1869 (not $x4499) $x7274 $x6813))))
+(let ((@x8734 (unit-resolution @x7295 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x8008) $x6319)) @x8635 $x6319) (hypothesis $x4499) (hypothesis (not $x6813)) @x7271 $x7274)))
+(let ((@x8324 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not (= ?x6187 0)) $x6564)) @x8734 (not (= ?x6187 0)))))
+(let ((@x8494 (lemma (unit-resolution @x8324 @x8765 false) (or $x6485 (not $x4499) $x6813 $x1869 (not $x8046)))))
+(let ((@x8211 (unit-resolution @x8494 @x8237 (unit-resolution (def-axiom (or $x8334 (not $x6813))) @x8147 (not $x6813)) @x8240 @x8239 $x6485)))
+(let ((@x8909 (unit-resolution @x7231 @x5748 @x6225 (hypothesis $x3187) (hypothesis (not $x7220)) false)))
+(let ((@x8256 (unit-resolution (lemma @x8909 (or (not $x3187) $x7220)) (unit-resolution @x5812 @x8211 @x8237 $x3187) $x7220)))
+(let ((@x8314 (unit-resolution ((_ th-lemma arith assign-bounds 1 -1 1 -1) (or $x6886 (not $x7220) (not $x6327) $x4315 (not $x4239))) @x7292 @x7839 @x8256 @x6019 $x6886)))
+(let ((@x8385 (unit-resolution ((_ th-lemma arith triangle-eq) (or $x8565 $x8664)) (unit-resolution @x8517 @x8314 @x6933 @x6930 @x8240 @x8239 $x8549) $x8565)))
+(let ((@x8386 (unit-resolution (def-axiom (or $x7239 $x8646)) (unit-resolution (unit-resolution @x8649 @x5944 $x8358) @x8385 $x4416) $x8646)))
+(let (($x8654 (not $x7241)))
+(let ((@x8390 (unit-resolution (def-axiom (or $x7239 $x8654)) (unit-resolution (unit-resolution @x8649 @x5944 $x8358) @x8385 $x4416) $x8654)))
+(let ((@x8410 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x8008) $x6319)) (unit-resolution (unit-resolution @x7712 @x6588 $x8029) @x8390 @x8386 $x8008) $x6319)))
+(let ((@x8411 ((_ th-lemma arith assign-bounds 1 1 1 1 1) (or $x7203 (not $x6319) $x1869 (not $x6886) (not $x4177) (not $x3044)))))
+(let ((@x8413 (unit-resolution @x7215 @x3485 (unit-resolution @x8411 @x8410 @x6933 @x6930 @x8240 @x8314 $x7203) $x7202)))
+(let ((@x8417 (unit-resolution (unit-resolution (def-axiom (or $x8334 (not $x6813))) @x8147 (not $x6813)) (symm @x8413 $x6813) false)))
+(let ((@x3365 (def-axiom (or $x3758 $x2765 $x3752))))
+(let ((@x9296 (unit-resolution @x3365 (lemma @x8417 $x2760) (unit-resolution (def-axiom (or $x3761 $x3755)) @x9294 $x3755) $x3752)))
+(let ((@x8225 (rewrite (= (or $x3717 (or $x4278 $x4127 $x4382)) (or $x3717 $x4278 $x4127 $x4382)))))
+(let ((@x8229 (mp ((_ quant-inst v_b_v_G_1$ ?v0!20) (or $x3717 (or $x4278 $x4127 $x4382))) @x8225 (or $x3717 $x4278 $x4127 $x4382))))
+(let ((@x9299 (unit-resolution @x8229 (unit-resolution (def-axiom (or $x3749 $x3712)) @x9296 $x3712) @x7482 (or $x4278 $x4382))))
+(let (($x4508 (>= ?x4487 0)))
+(let ((@x9304 (unit-resolution ((_ th-lemma arith assign-bounds 1 -1) (or $x4508 (not $x4569) (not $x3886))) @x6925 (or $x4508 (not $x4569)))))
+(let ((@x9306 ((_ th-lemma arith eq-propagate -1 -1 -1 -1 -1 -1 1 1) (unit-resolution @x9304 (hypothesis $x4569) $x4508) @x9285 (unit-resolution @x9299 @x9292 $x4382) @x9290 @x6019 @x6933 @x6930 @x7839 $x5391)))
+(let (($x5388 (not $x5387)))
+(let (($x5389 (or $x5386 $x5388)))
+(let ((@x7598 (mp ((_ quant-inst v_b_v_G_1$ ?v0!20) (or (not $x3480) $x5389)) (rewrite (= (or (not $x3480) $x5389) (or (not $x3480) $x5386 $x5388))) (or (not $x3480) $x5386 $x5388))))
+(let ((@x9311 (unit-resolution (unit-resolution @x7598 @x3485 $x5389) (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x5391) $x5387)) @x9306 $x5387) $x5386)))
+(let ((@x8045 (unit-resolution (lemma (unit-resolution @x9311 @x9328 false) (or $x4400 $x3734 (not $x4569))) (unit-resolution (def-axiom (or $x3737 $x3729)) @x8092 $x3729) @x7751 $x4400)))
+(let ((@x8812 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x4400) $x5977)) @x8045 $x5977)))
+(let ((?x4641 (?v1!7 ?v0!20)))
+(let ((?x4648 (pair$ ?x4641 ?v0!20)))
+(let ((?x4649 (b_G$ ?x4648)))
+(let ((?x4650 (* (- 1) ?x4649)))
+(let ((?x4642 (fun_app$c v_b_SP_G_1$ ?x4641)))
+(let ((?x4643 (* (- 1) ?x4642)))
+(let ((?x4651 (+ ?x4393 ?x4643 ?x4650)))
+(let (($x4391 (>= ?x4651 0)))
+(let (($x4652 (= ?x4651 0)))
+(let (($x4653 (not $x4652)))
+(let (($x4646 (fun_app$ v_b_Visited_G_1$ ?x4641)))
+(let (($x4647 (not $x4646)))
+(let ((?x4644 (+ ?x4393 ?x4643)))
+(let (($x4645 (<= ?x4644 0)))
+(let (($x4654 (or $x4645 $x4647 $x4653)))
+(let (($x4655 (not $x4654)))
+(let (($x4640 (<= (+ b_Infinity$ ?x4418) 0)))
+(let (($x7886 (not $x4640)))
+(let ((@x8816 (unit-resolution ((_ th-lemma arith assign-bounds 1 -1) (or (not $x5977) $x1914 $x7886)) @x8812 (unit-resolution (def-axiom (or $x3737 $x1915)) @x8092 $x1915) $x7886)))
+(let ((@x7414 (rewrite (= (or $x3586 (or $x1909 $x4640 $x4655)) (or $x3586 $x1909 $x4640 $x4655)))))
+(let ((@x7415 (mp ((_ quant-inst ?v0!20) (or $x3586 (or $x1909 $x4640 $x4655))) @x7414 (or $x3586 $x1909 $x4640 $x4655))))
+(let ((@x8817 (unit-resolution @x7415 @x4545 (unit-resolution (def-axiom (or $x3737 $x1910)) @x8092 $x1910) (or $x4640 $x4655))))
+(let ((@x8826 (unit-resolution @x8817 @x8816 $x4655)))
+(let ((@x6085 (unit-resolution ((_ th-lemma arith triangle-eq) (or $x4653 $x4391)) (unit-resolution (def-axiom (or $x4654 $x4652)) @x8826 $x4652) $x4391)))
+(let (($x7707 (<= ?x4651 0)))
+(let ((@x8177 (unit-resolution ((_ th-lemma arith triangle-eq) (or $x4653 $x7707)) (unit-resolution (def-axiom (or $x4654 $x4652)) @x8826 $x4652) $x7707)))
+(let (($x4689 (fun_app$ v_b_Visited_G_2$ ?x4641)))
+(let ((@x6032 (monotonicity (symm (hypothesis $x266) (= ?x265 v_b_Visited_G_2$)) (= (fun_app$ ?x265 ?x4641) $x4689))))
+(let ((@x6036 (monotonicity (symm @x6032 (= $x4689 (fun_app$ ?x265 ?x4641))) (= (not $x4689) (not (fun_app$ ?x265 ?x4641))))))
+(let (($x5978 (fun_app$ ?x265 ?x4641)))
+(let (($x5985 (= ?x4641 v_b_v_G_1$)))
+(let (($x5988 (or $x5985 $x4646)))
+(let (($x5991 (= $x5978 $x5988)))
+(let (($x5994 (or $x4114 $x5991)))
+(let ((@x5993 (monotonicity (rewrite (= (ite $x5985 true $x4646) $x5988)) (= (= $x5978 (ite $x5985 true $x4646)) $x5991))))
+(let ((@x5998 (monotonicity @x5993 (= (or $x4114 (= $x5978 (ite $x5985 true $x4646))) $x5994))))
+(let ((@x6001 (trans @x5998 (rewrite (= $x5994 $x5994)) (= (or $x4114 (= $x5978 (ite $x5985 true $x4646))) $x5994))))
+(let ((@x6002 (mp ((_ quant-inst v_b_Visited_G_1$ v_b_v_G_1$ true (?v1!7 ?v0!20)) (or $x4114 (= $x5978 (ite $x5985 true $x4646)))) @x6001 $x5994)))
+(let ((@x6025 (unit-resolution (def-axiom (or (not $x5991) $x5978 (not $x5988))) (unit-resolution (def-axiom (or $x5988 $x4647)) (hypothesis $x4646) $x5988) (or (not $x5991) $x5978))))
+(let ((@x6038 (unit-resolution (unit-resolution @x6025 (unit-resolution @x6002 @x3473 $x5991) $x5978) (mp (hypothesis (not $x4689)) @x6036 (not $x5978)) false)))
+(let ((@x8986 (unit-resolution (lemma @x6038 (or $x4689 $x2935 $x4647)) (unit-resolution (def-axiom (or $x3809 $x266)) @x6181 $x266) (or $x4689 $x4647))))
+(let ((@x8987 (unit-resolution @x8986 (unit-resolution (def-axiom (or $x4654 $x4646)) @x8826 $x4646) $x4689)))
+(let ((?x4697 (v_b_SP_G_2$ ?x4641)))
+(let ((?x4700 (* (- 1) ?x4697)))
+(let ((?x4868 (+ ?x1911 ?x4700)))
+(let (($x9248 (<= ?x4868 0)))
+(let (($x8507 (not $x9248)))
+(let ((?x4701 (+ ?x4642 ?x4700)))
+(let (($x4708 (>= ?x4701 0)))
+(let ((@x8348 (unit-resolution ((_ th-lemma arith assign-bounds -1 -1 -1) (or $x8507 (not $x4708) $x4645 (not $x5977))) @x8812 (unit-resolution ((_ quant-inst (?v1!7 ?v0!20)) (or $x3691 $x4708)) @x6892 $x4708) (unit-resolution (def-axiom (or $x4654 (not $x4645))) @x8826 (not $x4645)) $x8507)))
+(let ((?x8311 (+ ?x1911 ?x4650 ?x4700)))
+(let (($x8266 (>= ?x8311 0)))
+(let ((@x10143 (unit-resolution ((_ th-lemma arith assign-bounds -1 -1 -1) (or $x8266 (not $x4391) (not $x4708) (not $x5977))) (unit-resolution ((_ quant-inst (?v1!7 ?v0!20)) (or $x3691 $x4708)) @x6892 $x4708) (hypothesis $x4391) (hypothesis $x5977) $x8266)))
+(let (($x8534 (<= ?x8311 0)))
+(let (($x5038 (<= ?x4701 0)))
+(let (($x5863 (= ?x4642 ?x4697)))
+(let ((@x10149 (symm (commutativity (= $x5863 (= ?x4697 ?x4642))) (= (= ?x4697 ?x4642) $x5863))))
+(let (($x4698 (= ?x4697 ?x4642)))
+(let ((@x7939 (rewrite (= (or $x3700 (or (not $x4689) $x4698)) (or $x3700 (not $x4689) $x4698)))))
+(let ((@x7943 (mp ((_ quant-inst (?v1!7 ?v0!20)) (or $x3700 (or (not $x4689) $x4698))) @x7939 (or $x3700 (not $x4689) $x4698))))
+(let ((@x7980 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x5863) $x5038)) (mp (unit-resolution @x7943 @x7616 (hypothesis $x4689) $x4698) @x10149 $x5863) $x5038)))
+(let (($x8014 (<= ?x4419 0)))
+(let (($x8221 (or $x3691 $x8014)))
+(let ((@x8001 (monotonicity (rewrite (= (+ ?x4393 ?x1912) (+ ?x1912 ?x4393))) (= (>= (+ ?x4393 ?x1912) 0) (>= (+ ?x1912 ?x4393) 0)))))
+(let ((@x8035 (trans @x8001 (rewrite (= (>= (+ ?x1912 ?x4393) 0) $x8014)) (= (>= (+ ?x4393 ?x1912) 0) $x8014))))
+(let ((@x8178 (trans (monotonicity @x8035 (= (or $x3691 (>= (+ ?x4393 ?x1912) 0)) $x8221)) (rewrite (= $x8221 $x8221)) (= (or $x3691 (>= (+ ?x4393 ?x1912) 0)) $x8221))))
+(let ((@x8659 (unit-resolution (mp ((_ quant-inst ?v0!20) (or $x3691 (>= (+ ?x4393 ?x1912) 0))) @x8178 $x8221) @x6892 $x8014)))
+(let ((@x8083 (unit-resolution ((_ th-lemma arith assign-bounds -1 -1 -1) (or $x8534 (not $x7707) (not $x5038) (not $x8014))) @x8659 (hypothesis $x7707) @x7980 $x8534)))
+(let (($x9251 (= ?x8311 0)))
+(let (($x8749 (not $x9251)))
+(let (($x4690 (not $x4689)))
+(let (($x8567 (or $x3734 $x9248 $x4690 $x8749)))
+(let (($x4857 (>= (+ ?x4697 ?x1912) 0)))
+(let (($x4861 (or $x4857 $x4690 (not (= (+ ?x4697 ?x1912 ?x4649) 0)))))
+(let (($x8927 (or $x3734 $x4861)))
+(let ((@x8955 (monotonicity (rewrite (= (+ ?x4697 ?x1912 ?x4649) (+ ?x1912 ?x4649 ?x4697))) (= (= (+ ?x4697 ?x1912 ?x4649) 0) (= (+ ?x1912 ?x4649 ?x4697) 0)))))
+(let ((@x8627 (trans @x8955 (rewrite (= (= (+ ?x1912 ?x4649 ?x4697) 0) $x9251)) (= (= (+ ?x4697 ?x1912 ?x4649) 0) $x9251))))
+(let ((@x8965 (monotonicity (rewrite (= (+ ?x4697 ?x1912) (+ ?x1912 ?x4697))) (= $x4857 (>= (+ ?x1912 ?x4697) 0)))))
+(let ((@x8985 (trans @x8965 (rewrite (= (>= (+ ?x1912 ?x4697) 0) $x9248)) (= $x4857 $x9248))))
+(let ((@x9087 (monotonicity @x8985 (monotonicity @x8627 (= (not (= (+ ?x4697 ?x1912 ?x4649) 0)) $x8749)) (= $x4861 (or $x9248 $x4690 $x8749)))))
+(let ((@x8874 (trans (monotonicity @x9087 (= $x8927 (or $x3734 (or $x9248 $x4690 $x8749)))) (rewrite (= (or $x3734 (or $x9248 $x4690 $x8749)) $x8567)) (= $x8927 $x8567))))
+(let ((@x8397 (unit-resolution (mp ((_ quant-inst (?v1!7 ?v0!20)) $x8927) @x8874 $x8567) (hypothesis $x3729) (hypothesis $x4689) (or $x9248 $x8749))))
+(let ((@x5592 (unit-resolution ((_ th-lemma arith triangle-eq) (or $x9251 (not $x8534) (not $x8266))) (unit-resolution @x8397 (hypothesis $x8507) $x8749) @x8083 @x10143 false)))
+(let ((@x8013 (unit-resolution (lemma @x5592 (or $x9248 $x3734 $x4690 (not $x7707) (not $x4391) (not $x5977))) @x8348 (unit-resolution (def-axiom (or $x3737 $x3729)) @x8092 $x3729) @x8987 @x8177 @x6085 @x8812 false)))
+(let ((@x3278 (def-axiom (or $x3746 $x2811 $x3740))))
+(let ((@x8433 (unit-resolution @x3278 (unit-resolution (def-axiom (or $x3749 $x3743)) @x9296 $x3743) $x3743)))
+(let (($x3378 (not $x1896)))
+(let ((@x3380 (def-axiom (or $x2806 $x3378))))
+(let ((@x8434 (unit-resolution @x3380 (unit-resolution @x8433 (lemma @x8013 $x3737) $x2811) $x3378)))
+(let ((?x6619 (fun_app$c v_b_SP_G_1$ ?v1!18)))
+(let (($x6615 (= ?x1892 ?x6619)))
+(let (($x7618 (not $x6615)))
+(let ((@x7591 (hypothesis $x2811)))
+(let ((@x7607 (unit-resolution (def-axiom (or $x2806 $x1883)) @x7591 $x1883)))
+(let ((@x7571 (hypothesis $x3378)))
+(let (($x1889 (not $x1888)))
+(let ((@x7592 (unit-resolution (def-axiom (or $x2806 $x1889)) @x7591 $x1889)))
+(let ((?x7110 (pair$ v_b_v_G_1$ ?v0!19)))
+(let ((?x7111 (b_G$ ?x7110)))
+(let ((?x7100 (* (- 1) ?x7111)))
+(let ((?x7554 (+ ?x1885 ?x7100)))
+(let (($x7556 (>= ?x7554 0)))
+(let (($x7003 (= ?x1885 ?x7111)))
+(let (($x7243 (= ?v1!18 v_b_v_G_1$)))
+(let (($x7246 (fun_app$ v_b_Visited_G_1$ ?v1!18)))
+(let (($x6211 (not $x7246)))
+(let (($x7248 (>= (+ ?x1885 ?x6619 (* (- 1) (fun_app$c v_b_SP_G_1$ ?v0!19))) 0)))
+(let (($x7499 (not $x7248)))
+(let ((?x6721 (* (- 1) ?x6619)))
+(let ((?x5600 (+ ?x1892 ?x6721)))
+(let (($x7353 (>= ?x5600 0)))
+(let ((@x8658 (unit-resolution ((_ th-lemma arith triangle-eq) (or $x7618 $x7353)) (hypothesis $x6615) $x7353)))
+(let (($x7076 (<= (+ ?x1893 (* (- 1) (fun_app$c v_b_SP_G_1$ ?v0!19))) 0)))
+(let (($x7084 (or $x3691 $x7076)))
+(let (($x7081 (= (or $x3691 (>= (+ (fun_app$c v_b_SP_G_1$ ?v0!19) ?x1894) 0)) $x7084)))
+(let ((@x7078 (rewrite (= (>= (+ ?x1894 (fun_app$c v_b_SP_G_1$ ?v0!19)) 0) $x7076))))
+(let (($x7048 (>= (+ (fun_app$c v_b_SP_G_1$ ?v0!19) ?x1894) 0)))
+(let (($x7069 (= (+ (fun_app$c v_b_SP_G_1$ ?v0!19) ?x1894) (+ ?x1894 (fun_app$c v_b_SP_G_1$ ?v0!19)))))
+(let ((@x7073 (monotonicity (rewrite $x7069) (= $x7048 (>= (+ ?x1894 (fun_app$c v_b_SP_G_1$ ?v0!19)) 0)))))
+(let ((@x7090 (trans (monotonicity (trans @x7073 @x7078 (= $x7048 $x7076)) $x7081) (rewrite (= $x7084 $x7084)) $x7081)))
+(let ((@x7496 (unit-resolution (mp ((_ quant-inst ?v0!19) (or $x3691 $x7048)) @x7090 $x7084) @x6892 $x7076)))
+(let ((@x7501 (lemma ((_ th-lemma arith farkas 1 -1 -1 1) (hypothesis $x7248) @x7571 @x7496 (hypothesis $x7353) false) (or $x7499 $x1896 (not $x7353)))))
+(let ((@x6992 (rewrite (= (or $x3578 (or $x6211 $x1888 $x7248)) (or $x3578 $x6211 $x1888 $x7248)))))
+(let ((@x7051 (mp ((_ quant-inst ?v0!19 ?v1!18) (or $x3578 (or $x6211 $x1888 $x7248))) @x6992 (or $x3578 $x6211 $x1888 $x7248))))
+(let ((@x8673 (unit-resolution (unit-resolution @x7051 @x4223 (hypothesis $x1889) (or $x6211 $x7248)) (unit-resolution @x7501 @x8658 @x7571 $x7499) $x6211)))
+(let (($x7222 (or $x7243 $x7246)))
+(let (($x6667 (fun_app$ ?x265 ?v1!18)))
+(let (($x6740 (= $x6667 $x7222)))
+(let (($x6746 (or $x4114 $x6740)))
+(let ((@x6743 (monotonicity (rewrite (= (ite $x7243 true $x7246) $x7222)) (= (= $x6667 (ite $x7243 true $x7246)) $x6740))))
+(let ((@x6845 (monotonicity @x6743 (= (or $x4114 (= $x6667 (ite $x7243 true $x7246))) $x6746))))
+(let ((@x4954 (trans @x6845 (rewrite (= $x6746 $x6746)) (= (or $x4114 (= $x6667 (ite $x7243 true $x7246))) $x6746))))
+(let ((@x6537 (mp ((_ quant-inst v_b_Visited_G_1$ v_b_v_G_1$ true ?v1!18) (or $x4114 (= $x6667 (ite $x7243 true $x7246)))) @x4954 $x6746)))
+(let ((@x8675 (mp (hypothesis $x1883) (symm (monotonicity @x5875 (= $x6667 $x1883)) (= $x1883 $x6667)) $x6667)))
+(let ((@x8676 (unit-resolution (def-axiom (or (not $x6740) (not $x6667) $x7222)) @x8675 (unit-resolution @x6537 @x3473 $x6740) $x7222)))
+(let ((@x4955 (def-axiom (or (not $x7222) $x7243 $x7246))))
+(let ((@x7000 (unit-resolution (hypothesis (not $x7003)) (monotonicity (monotonicity (hypothesis $x7243) (= ?x1884 ?x7110)) $x7003) false)))
+(let ((@x7002 (lemma @x7000 (or (not $x7243) $x7003))))
+(let ((@x7011 ((_ th-lemma arith triangle-eq) (or (not $x7003) $x7556))))
+(let ((@x8679 (unit-resolution @x7011 (unit-resolution @x7002 (unit-resolution @x4955 @x8676 @x8673 $x7243) $x7003) $x7556)))
+(let (($x7102 (<= (+ b_Infinity$ ?x7100) 0)))
+(let ((?x7171 (+ ?x257 ?x1894 ?x7111)))
+(let (($x7252 (>= ?x7171 0)))
+(let (($x7576 (not $x7252)))
+(let (($x7366 (<= (+ ?x257 ?x6721) 0)))
+(let (($x8449 (or $x3665 $x7246 $x7366)))
+(let (($x7357 (>= (+ ?x6619 ?x1173) 0)))
+(let (($x7358 (or $x7246 $x7357)))
+(let (($x8450 (or $x3665 $x7358)))
+(let ((@x8441 (monotonicity (rewrite (= (+ ?x6619 ?x1173) (+ ?x1173 ?x6619))) (= $x7357 (>= (+ ?x1173 ?x6619) 0)))))
+(let ((@x8445 (trans @x8441 (rewrite (= (>= (+ ?x1173 ?x6619) 0) $x7366)) (= $x7357 $x7366))))
+(let ((@x8454 (monotonicity (monotonicity @x8445 (= $x7358 (or $x7246 $x7366))) (= $x8450 (or $x3665 (or $x7246 $x7366))))))
+(let ((@x8458 (trans @x8454 (rewrite (= (or $x3665 (or $x7246 $x7366)) $x8449)) (= $x8450 $x8449))))
+(let ((@x8681 (unit-resolution (mp ((_ quant-inst ?v1!18) $x8450) @x8458 $x8449) (unit-resolution (def-axiom (or $x3809 $x3660)) @x6181 $x3660) @x8673 $x7366)))
+(let ((@x8685 (unit-resolution ((_ th-lemma arith assign-bounds -1 1 -1 1) (or $x7576 $x1896 (not $x7353) (not $x7366) (not $x7556))) @x8681 @x8679 @x7571 @x8658 $x7576)))
+(let ((@x8686 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not (= ?x7171 0)) $x7252)) @x8685 (not (= ?x7171 0)))))
+(let (($x7117 (>= (+ ?x257 (* (- 1) (fun_app$c v_b_SP_G_1$ ?v0!19)) ?x7111) 0)))
+(let (($x7161 (not $x7117)))
+(let ((@x8688 ((_ th-lemma arith assign-bounds -1 -1 1 -1 1) (or $x7161 (not $x7076) $x1896 (not $x7353) (not $x7366) (not $x7556)))))
+(let (($x7174 (= ?x7171 0)))
+(let (($x7184 (or $x7102 $x7117 $x7174)))
+(let (($x7186 (or $x3675 $x7102 $x7117 $x7174)))
+(let (($x7104 (<= (+ (fun_app$c v_b_SP_G_1$ ?v0!19) ?x1173 ?x7100) 0)))
+(let (($x7165 (or $x7102 $x7104 (= (+ ?x257 ?x7111 ?x1894) 0))))
+(let (($x7187 (or $x3675 $x7165)))
+(let ((@x7183 (monotonicity (rewrite (= (+ ?x257 ?x7111 ?x1894) ?x7171)) (= (= (+ ?x257 ?x7111 ?x1894) 0) $x7174))))
+(let ((@x7119 (rewrite (= (<= (+ ?x1173 (fun_app$c v_b_SP_G_1$ ?v0!19) ?x7100) 0) $x7117))))
+(let (($x7112 (= (+ (fun_app$c v_b_SP_G_1$ ?v0!19) ?x1173 ?x7100) (+ ?x1173 (fun_app$c v_b_SP_G_1$ ?v0!19) ?x7100))))
+(let ((@x7115 (monotonicity (rewrite $x7112) (= $x7104 (<= (+ ?x1173 (fun_app$c v_b_SP_G_1$ ?v0!19) ?x7100) 0)))))
+(let ((@x7205 (monotonicity (monotonicity (trans @x7115 @x7119 (= $x7104 $x7117)) @x7183 (= $x7165 $x7184)) (= $x7187 (or $x3675 $x7184)))))
+(let ((@x7250 (mp ((_ quant-inst ?v0!19) $x7187) (trans @x7205 (rewrite (= (or $x3675 $x7184) $x7186)) (= $x7187 $x7186)) $x7186)))
+(let ((@x8690 (unit-resolution (unit-resolution @x7250 @x6588 $x7184) (unit-resolution @x8688 @x8681 @x8679 @x7571 @x8658 @x7496 $x7161) @x8686 $x7102)))
+(let ((@x8693 (lemma ((_ th-lemma arith farkas -1 1 1) @x8690 @x8679 (hypothesis $x1889) false) (or $x7618 $x1888 $x1896 $x2791))))
+(let ((@x7245 (mp ((_ quant-inst ?v1!18) (or $x3700 (or $x2791 $x6615))) (rewrite (= (or $x3700 (or $x2791 $x6615)) (or $x3700 $x2791 $x6615))) (or $x3700 $x2791 $x6615))))
+(let ((@x8285 (unit-resolution @x7245 @x7616 @x7607 (unit-resolution @x8693 @x7592 @x7571 @x7607 $x7618) false)))
+(unit-resolution (lemma @x8285 (or $x2806 $x1896)) @x8434 (unit-resolution @x8433 (lemma @x8013 $x3737) $x2811) false))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
+