src/HOL/SMT_Examples/SMT_Examples.certs
changeset 66740 ece9435ca78e
parent 66298 5ff9fe3fee66
child 67972 959b0aed2ce5
     1.1 --- a/src/HOL/SMT_Examples/SMT_Examples.certs	Sun Oct 01 15:17:31 2017 +0200
     1.2 +++ b/src/HOL/SMT_Examples/SMT_Examples.certs	Sun Oct 01 15:17:43 2017 +0200
     1.3 @@ -1,3 +1,113 @@
     1.4 +c6761b6a026c6bf2d28c35e9faf633fc441c84c5 45 0
     1.5 +unsat
     1.6 +((set-logic AUFLIA)
     1.7 +(proof
     1.8 +(let ((?x44 (id$ x$)))
     1.9 +(let (($x46 (= ?x44 x$)))
    1.10 +(let (($x73 (not $x46)))
    1.11 +(let (($x47 (id$a true)))
    1.12 +(let (($x510 (forall ((?v0 Bool) )(! (let (($x33 (id$a ?v0)))
    1.13 +(= $x33 ?v0)) :pattern ( (id$a ?v0) ) :qid k!9))
    1.14 +))
    1.15 +(let (($x40 (forall ((?v0 Bool) )(! (let (($x33 (id$a ?v0)))
    1.16 +(= $x33 ?v0)) :qid k!9))
    1.17 +))
    1.18 +(let ((@x514 (quant-intro (refl (= (= (id$a ?0) ?0) (= (id$a ?0) ?0))) (= $x40 $x510))))
    1.19 +(let ((@x69 (nnf-pos (refl (~ (= (id$a ?0) ?0) (= (id$a ?0) ?0))) (~ $x40 $x40))))
    1.20 +(let (($x35 (forall ((?v0 Bool) )(! (let (($x33 (id$a ?v0)))
    1.21 +(= $x33 ?v0)) :qid k!9))
    1.22 +))
    1.23 +(let ((@x42 (quant-intro (rewrite (= (= (id$a ?0) ?0) (= (id$a ?0) ?0))) (= $x35 $x40))))
    1.24 +(let ((@x515 (mp (mp~ (mp (asserted $x35) @x42 $x40) @x69 $x40) @x514 $x510)))
    1.25 +(let (($x87 (or (not $x510) $x47)))
    1.26 +(let ((@x176 (monotonicity (rewrite (= (= $x47 true) $x47)) (= (or (not $x510) (= $x47 true)) $x87))))
    1.27 +(let ((@x179 (trans @x176 (rewrite (= $x87 $x87)) (= (or (not $x510) (= $x47 true)) $x87))))
    1.28 +(let ((@x495 (unit-resolution (mp ((_ quant-inst true) (or (not $x510) (= $x47 true))) @x179 $x87) @x515 (hypothesis (not $x47)) false)))
    1.29 +(let (($x71 (or $x73 (not $x47))))
    1.30 +(let ((@x79 (monotonicity (rewrite (= (and $x46 $x47) (not $x71))) (= (not (and $x46 $x47)) (not (not $x71))))))
    1.31 +(let ((@x83 (trans @x79 (rewrite (= (not (not $x71)) $x71)) (= (not (and $x46 $x47)) $x71))))
    1.32 +(let (($x54 (and $x46 $x47)))
    1.33 +(let (($x57 (not $x54)))
    1.34 +(let ((@x56 (monotonicity (rewrite (= (= $x47 true) $x47)) (= (and $x46 (= $x47 true)) $x54))))
    1.35 +(let ((@x62 (mp (asserted (not (and $x46 (= $x47 true)))) (monotonicity @x56 (= (not (and $x46 (= $x47 true))) $x57)) $x57)))
    1.36 +(let ((@x84 (mp @x62 @x83 $x71)))
    1.37 +(let (($x503 (forall ((?v0 A$) )(! (let ((?x28 (id$ ?v0)))
    1.38 +(= ?x28 ?v0)) :pattern ( (id$ ?v0) ) :qid k!8))
    1.39 +))
    1.40 +(let (($x30 (forall ((?v0 A$) )(! (let ((?x28 (id$ ?v0)))
    1.41 +(= ?x28 ?v0)) :qid k!8))
    1.42 +))
    1.43 +(let ((@x507 (quant-intro (refl (= (= (id$ ?0) ?0) (= (id$ ?0) ?0))) (= $x30 $x503))))
    1.44 +(let ((@x64 (nnf-pos (refl (~ (= (id$ ?0) ?0) (= (id$ ?0) ?0))) (~ $x30 $x30))))
    1.45 +(let ((@x508 (mp (mp~ (asserted $x30) @x64 $x30) @x507 $x503)))
    1.46 +(let (($x163 (or (not $x503) $x46)))
    1.47 +(let ((@x496 ((_ quant-inst x$) $x163)))
    1.48 +(unit-resolution @x496 @x508 (unit-resolution @x84 (lemma @x495 $x47) $x73) false)))))))))))))))))))))))))))))))))
    1.49 +
    1.50 +23f5eb3b530a4577da2f8947333286ff70ed557f 11 0
    1.51 +unsat
    1.52 +((set-logic AUFLIA)
    1.53 +(proof
    1.54 +(let (($x29 (exists ((?v0 A$) )(! (g$ ?v0) :qid k!7))
    1.55 +))
    1.56 +(let (($x30 (f$ $x29)))
    1.57 +(let (($x31 (=> $x30 true)))
    1.58 +(let (($x32 (not $x31)))
    1.59 +(let ((@x42 (trans (monotonicity (rewrite (= $x31 true)) (= $x32 (not true))) (rewrite (= (not true) false)) (= $x32 false))))
    1.60 +(mp (asserted $x32) @x42 false))))))))
    1.61 +
    1.62 +174a4beaccbbd473470bdf78d1dd5655decaaf38 51 0
    1.63 +unsat
    1.64 +((set-logic AUFLIA)
    1.65 +(proof
    1.66 +(let ((?x61 (fun_app$ f$ i$)))
    1.67 +(let ((?x57 (fun_upd$ f$ i1$ v1$)))
    1.68 +(let ((?x59 (fun_upd$ ?x57 i2$ v2$)))
    1.69 +(let ((?x60 (fun_app$ ?x59 i$)))
    1.70 +(let (($x62 (= ?x60 ?x61)))
    1.71 +(let ((?x189 (fun_app$ ?x57 i$)))
    1.72 +(let (($x197 (= ?x189 ?x61)))
    1.73 +(let (($x196 (= ?x189 v1$)))
    1.74 +(let (($x49 (= i$ i1$)))
    1.75 +(let (($x476 (ite $x49 $x196 $x197)))
    1.76 +(let (($x524 (forall ((?v0 A_b_fun$) (?v1 A$) (?v2 B$) (?v3 A$) )(! (let (($x41 (= ?v3 ?v1)))
    1.77 +(ite $x41 (= (fun_app$ (fun_upd$ ?v0 ?v1 ?v2) ?v3) ?v2) (= (fun_app$ (fun_upd$ ?v0 ?v1 ?v2) ?v3) (fun_app$ ?v0 ?v3)))) :pattern ( (fun_app$ (fun_upd$ ?v0 ?v1 ?v2) ?v3) ) :qid k!16))
    1.78 +))
    1.79 +(let (($x94 (forall ((?v0 A_b_fun$) (?v1 A$) (?v2 B$) (?v3 A$) )(! (let (($x41 (= ?v3 ?v1)))
    1.80 +(ite $x41 (= (fun_app$ (fun_upd$ ?v0 ?v1 ?v2) ?v3) ?v2) (= (fun_app$ (fun_upd$ ?v0 ?v1 ?v2) ?v3) (fun_app$ ?v0 ?v3)))) :qid k!16))
    1.81 +))
    1.82 +(let (($x41 (= ?0 ?2)))
    1.83 +(let (($x89 (ite $x41 (= (fun_app$ (fun_upd$ ?3 ?2 ?1) ?0) ?1) (= (fun_app$ (fun_upd$ ?3 ?2 ?1) ?0) (fun_app$ ?3 ?0)))))
    1.84 +(let (($x45 (forall ((?v0 A_b_fun$) (?v1 A$) (?v2 B$) (?v3 A$) )(! (let ((?x40 (fun_app$ (fun_upd$ ?v0 ?v1 ?v2) ?v3)))
    1.85 +(= ?x40 (ite (= ?v3 ?v1) ?v2 (fun_app$ ?v0 ?v3)))) :qid k!16))
    1.86 +))
    1.87 +(let ((?x40 (fun_app$ (fun_upd$ ?3 ?2 ?1) ?0)))
    1.88 +(let (($x44 (= ?x40 (ite $x41 ?1 (fun_app$ ?3 ?0)))))
    1.89 +(let ((@x82 (mp~ (asserted $x45) (nnf-pos (refl (~ $x44 $x44)) (~ $x45 $x45)) $x45)))
    1.90 +(let ((@x97 (mp @x82 (quant-intro (rewrite (= $x44 $x89)) (= $x45 $x94)) $x94)))
    1.91 +(let ((@x529 (mp @x97 (quant-intro (refl (= $x89 $x89)) (= $x94 $x524)) $x524)))
    1.92 +(let (($x163 (not $x524)))
    1.93 +(let (($x478 (or $x163 $x476)))
    1.94 +(let ((@x479 ((_ quant-inst f$ i1$ v1$ i$) $x478)))
    1.95 +(let (($x50 (not $x49)))
    1.96 +(let (($x52 (= i$ i2$)))
    1.97 +(let (($x53 (not $x52)))
    1.98 +(let (($x54 (and $x50 $x53)))
    1.99 +(let ((@x72 (monotonicity (rewrite (= (=> $x54 $x62) (or (not $x54) $x62))) (= (not (=> $x54 $x62)) (not (or (not $x54) $x62))))))
   1.100 +(let ((@x73 (not-or-elim (mp (asserted (not (=> $x54 $x62))) @x72 (not (or (not $x54) $x62))) $x54)))
   1.101 +(let ((@x74 (and-elim @x73 $x50)))
   1.102 +(let ((@x313 (unit-resolution (def-axiom (or (not $x476) $x49 $x197)) @x74 (or (not $x476) $x197))))
   1.103 +(let (($x192 (= ?x60 ?x189)))
   1.104 +(let (($x188 (= ?x60 v2$)))
   1.105 +(let (($x171 (ite $x52 $x188 $x192)))
   1.106 +(let (($x293 (or $x163 $x171)))
   1.107 +(let ((@x503 ((_ quant-inst (fun_upd$ f$ i1$ v1$) i2$ v2$ i$) $x293)))
   1.108 +(let ((@x76 (and-elim @x73 $x53)))
   1.109 +(let ((@x458 (unit-resolution (def-axiom (or (not $x171) $x52 $x192)) @x76 (or (not $x171) $x192))))
   1.110 +(let ((@x462 (trans (unit-resolution @x458 (unit-resolution @x503 @x529 $x171) $x192) (unit-resolution @x313 (unit-resolution @x479 @x529 $x476) $x197) $x62)))
   1.111 +(let ((@x78 (not-or-elim (mp (asserted (not (=> $x54 $x62))) @x72 (not (or (not $x54) $x62))) (not $x62))))
   1.112 +(unit-resolution @x78 @x462 false)))))))))))))))))))))))))))))))))))))))))))
   1.113 +
   1.114  3aa17d1c77bc1a92bca05df291d11d81c645a931 6 0
   1.115  unsat
   1.116  ((set-logic AUFLIA)
   1.117 @@ -5,6 +115,805 @@
   1.118  (let ((@x30 (rewrite (= (not true) false))))
   1.119  (mp (asserted (not true)) @x30 false))))
   1.120  
   1.121 +feaa6ef662dd489cf55f86209489c2992ff08d28 46 0
   1.122 +unsat
   1.123 +((set-logic AUFLIA)
   1.124 +(proof
   1.125 +(let ((?x61 (fun_app$a le$ 3)))
   1.126 +(let (($x63 (fun_app$ ?x61 42)))
   1.127 +(let (($x75 (not $x63)))
   1.128 +(let (($x59 (= le$ uu$)))
   1.129 +(let ((@x73 (monotonicity (rewrite (= (=> $x59 $x63) (or (not $x59) $x63))) (= (not (=> $x59 $x63)) (not (or (not $x59) $x63))))))
   1.130 +(let ((@x74 (not-or-elim (mp (asserted (not (=> $x59 $x63))) @x73 (not (or (not $x59) $x63))) $x59)))
   1.131 +(let ((@x482 (monotonicity (symm @x74 (= uu$ le$)) (= (fun_app$a uu$ 3) ?x61))))
   1.132 +(let ((@x484 (symm (monotonicity @x482 (= (fun_app$ (fun_app$a uu$ 3) 42) $x63)) (= $x63 (fun_app$ (fun_app$a uu$ 3) 42)))))
   1.133 +(let ((@x472 (monotonicity @x484 (= $x75 (not (fun_app$ (fun_app$a uu$ 3) 42))))))
   1.134 +(let ((@x77 (not-or-elim (mp (asserted (not (=> $x59 $x63))) @x73 (not (or (not $x59) $x63))) $x75)))
   1.135 +(let ((?x79 (fun_app$a uu$ 3)))
   1.136 +(let (($x168 (fun_app$ ?x79 42)))
   1.137 +(let (($x52 (forall ((?v0 Int) (?v1 Int) )(! (let (($x46 (<= (+ ?v0 (* (- 1) ?v1)) 0)))
   1.138 +(let (($x31 (fun_app$ (fun_app$a uu$ ?v0) ?v1)))
   1.139 +(= $x31 $x46))) :pattern ( (fun_app$ (fun_app$a uu$ ?v0) ?v1) ) :qid k!10))
   1.140 +))
   1.141 +(let (($x46 (<= (+ ?1 (* (- 1) ?0)) 0)))
   1.142 +(let (($x31 (fun_app$ (fun_app$a uu$ ?1) ?0)))
   1.143 +(let (($x49 (= $x31 $x46)))
   1.144 +(let (($x35 (forall ((?v0 Int) (?v1 Int) )(! (let (($x32 (<= ?v0 ?v1)))
   1.145 +(let (($x31 (fun_app$ (fun_app$a uu$ ?v0) ?v1)))
   1.146 +(= $x31 $x32))) :pattern ( (fun_app$ (fun_app$a uu$ ?v0) ?v1) ) :qid k!10))
   1.147 +))
   1.148 +(let (($x40 (forall ((?v0 Int) (?v1 Int) )(! (let (($x32 (<= ?v0 ?v1)))
   1.149 +(let (($x31 (fun_app$ (fun_app$a uu$ ?v0) ?v1)))
   1.150 +(= $x31 $x32))) :pattern ( (fun_app$ (fun_app$a uu$ ?v0) ?v1) ) :qid k!10))
   1.151 +))
   1.152 +(let ((@x51 (monotonicity (rewrite (= (<= ?1 ?0) $x46)) (= (= $x31 (<= ?1 ?0)) $x49))))
   1.153 +(let ((@x42 (quant-intro (rewrite (= (= $x31 (<= ?1 ?0)) (= $x31 (<= ?1 ?0)))) (= $x35 $x40))))
   1.154 +(let ((@x57 (mp (asserted $x35) (trans @x42 (quant-intro @x51 (= $x40 $x52)) (= $x35 $x52)) $x52)))
   1.155 +(let ((@x78 (mp~ @x57 (nnf-pos (refl (~ $x49 $x49)) (~ $x52 $x52)) $x52)))
   1.156 +(let (($x134 (or (not $x52) $x168)))
   1.157 +(let (($x137 (= (or (not $x52) (= $x168 (<= (+ 3 (* (- 1) 42)) 0))) $x134)))
   1.158 +(let ((?x169 (* (- 1) 42)))
   1.159 +(let ((?x170 (+ 3 ?x169)))
   1.160 +(let (($x160 (<= ?x170 0)))
   1.161 +(let (($x171 (= $x168 $x160)))
   1.162 +(let ((@x158 (trans (monotonicity (rewrite (= ?x169 (- 42))) (= ?x170 (+ 3 (- 42)))) (rewrite (= (+ 3 (- 42)) (- 39))) (= ?x170 (- 39)))))
   1.163 +(let ((@x497 (trans (monotonicity @x158 (= $x160 (<= (- 39) 0))) (rewrite (= (<= (- 39) 0) true)) (= $x160 true))))
   1.164 +(let ((@x131 (trans (monotonicity @x497 (= $x171 (= $x168 true))) (rewrite (= (= $x168 true) $x168)) (= $x171 $x168))))
   1.165 +(let ((@x478 (mp ((_ quant-inst 3 42) (or (not $x52) $x171)) (trans (monotonicity @x131 $x137) (rewrite (= $x134 $x134)) $x137) $x134)))
   1.166 +(unit-resolution (unit-resolution @x478 @x78 $x168) (mp @x77 @x472 (not $x168)) false)))))))))))))))))))))))))))))))))))
   1.167 +
   1.168 +60f1b32e9c6a2229b64c85dcfb0bde9c2bd5433a 11 0
   1.169 +unsat
   1.170 +((set-logic AUFLIA)
   1.171 +(proof
   1.172 +(let (($x29 (forall ((?v0 A$) )(! (g$ ?v0) :qid k!7))
   1.173 +))
   1.174 +(let (($x30 (f$ $x29)))
   1.175 +(let (($x31 (=> $x30 true)))
   1.176 +(let (($x32 (not $x31)))
   1.177 +(let ((@x42 (trans (monotonicity (rewrite (= $x31 true)) (= $x32 (not true))) (rewrite (= (not true) false)) (= $x32 false))))
   1.178 +(mp (asserted $x32) @x42 false))))))))
   1.179 +
   1.180 +9cdd1051dbf4e0648f71536fbc74bbab8e0e744e 75 0
   1.181 +unsat
   1.182 +((set-logic AUFLIA)
   1.183 +(proof
   1.184 +(let ((?x78 (cons$ 2 nil$)))
   1.185 +(let ((?x79 (cons$ 1 ?x78)))
   1.186 +(let ((?x74 (cons$ 1 nil$)))
   1.187 +(let ((?x75 (cons$ 0 ?x74)))
   1.188 +(let ((?x76 (map$ uu$ ?x75)))
   1.189 +(let (($x80 (= ?x76 ?x79)))
   1.190 +(let ((?x185 (map$ uu$ ?x74)))
   1.191 +(let ((?x189 (map$ uu$ nil$)))
   1.192 +(let ((?x188 (fun_app$ uu$ 1)))
   1.193 +(let ((?x160 (cons$ ?x188 ?x189)))
   1.194 +(let (($x290 (= ?x185 ?x160)))
   1.195 +(let (($x521 (forall ((?v0 Int_int_fun$) (?v1 Int) (?v2 Int_list$) )(! (= (map$ ?v0 (cons$ ?v1 ?v2)) (cons$ (fun_app$ ?v0 ?v1) (map$ ?v0 ?v2))) :pattern ( (map$ ?v0 (cons$ ?v1 ?v2)) ) :pattern ( (cons$ (fun_app$ ?v0 ?v1) (map$ ?v0 ?v2)) ) :qid k!13))
   1.196 +))
   1.197 +(let (($x72 (forall ((?v0 Int_int_fun$) (?v1 Int) (?v2 Int_list$) )(! (= (map$ ?v0 (cons$ ?v1 ?v2)) (cons$ (fun_app$ ?v0 ?v1) (map$ ?v0 ?v2))) :qid k!13))
   1.198 +))
   1.199 +(let (($x71 (= (map$ ?2 (cons$ ?1 ?0)) (cons$ (fun_app$ ?2 ?1) (map$ ?2 ?0)))))
   1.200 +(let ((@x97 (mp~ (asserted $x72) (nnf-pos (refl (~ $x71 $x71)) (~ $x72 $x72)) $x72)))
   1.201 +(let ((@x526 (mp @x97 (quant-intro (refl (= $x71 $x71)) (= $x72 $x521)) $x521)))
   1.202 +(let (($x173 (or (not $x521) $x290)))
   1.203 +(let ((@x506 ((_ quant-inst uu$ 1 nil$) $x173)))
   1.204 +(let (($x492 (= ?x189 nil$)))
   1.205 +(let (($x513 (forall ((?v0 Int_int_fun$) )(! (= (map$ ?v0 nil$) nil$) :pattern ( (map$ ?v0 nil$) ) :qid k!12))
   1.206 +))
   1.207 +(let (($x61 (forall ((?v0 Int_int_fun$) )(! (= (map$ ?v0 nil$) nil$) :qid k!12))
   1.208 +))
   1.209 +(let ((@x515 (refl (= (= (map$ ?0 nil$) nil$) (= (map$ ?0 nil$) nil$)))))
   1.210 +(let ((@x83 (refl (~ (= (map$ ?0 nil$) nil$) (= (map$ ?0 nil$) nil$)))))
   1.211 +(let ((@x518 (mp (mp~ (asserted $x61) (nnf-pos @x83 (~ $x61 $x61)) $x61) (quant-intro @x515 (= $x61 $x513)) $x513)))
   1.212 +(let (($x495 (or (not $x513) $x492)))
   1.213 +(let ((@x496 ((_ quant-inst uu$) $x495)))
   1.214 +(let (($x136 (= ?x188 2)))
   1.215 +(let (($x51 (forall ((?v0 Int) )(! (= (+ ?v0 (* (- 1) (fun_app$ uu$ ?v0))) (- 1)) :pattern ( (fun_app$ uu$ ?v0) ) :qid k!11))
   1.216 +))
   1.217 +(let (($x47 (= (+ ?0 (* (- 1) (fun_app$ uu$ ?0))) (- 1))))
   1.218 +(let (($x34 (forall ((?v0 Int) )(! (let ((?x29 (fun_app$ uu$ ?v0)))
   1.219 +(= ?x29 (+ ?v0 1))) :pattern ( (fun_app$ uu$ ?v0) ) :qid k!11))
   1.220 +))
   1.221 +(let (($x42 (forall ((?v0 Int) )(! (let ((?x29 (fun_app$ uu$ ?v0)))
   1.222 +(= ?x29 (+ 1 ?v0))) :pattern ( (fun_app$ uu$ ?v0) ) :qid k!11))
   1.223 +))
   1.224 +(let ((@x53 (quant-intro (rewrite (= (= (fun_app$ uu$ ?0) (+ 1 ?0)) $x47)) (= $x42 $x51))))
   1.225 +(let ((?x29 (fun_app$ uu$ ?0)))
   1.226 +(let (($x39 (= ?x29 (+ 1 ?0))))
   1.227 +(let ((@x41 (monotonicity (rewrite (= (+ ?0 1) (+ 1 ?0))) (= (= ?x29 (+ ?0 1)) $x39))))
   1.228 +(let ((@x56 (mp (asserted $x34) (trans (quant-intro @x41 (= $x34 $x42)) @x53 (= $x34 $x51)) $x51)))
   1.229 +(let ((@x85 (mp~ @x56 (nnf-pos (refl (~ $x47 $x47)) (~ $x51 $x51)) $x51)))
   1.230 +(let (($x145 (not $x51)))
   1.231 +(let (($x499 (or $x145 $x136)))
   1.232 +(let ((@x498 (rewrite (= (= (+ 1 (* (- 1) ?x188)) (- 1)) $x136))))
   1.233 +(let ((@x204 (monotonicity @x498 (= (or $x145 (= (+ 1 (* (- 1) ?x188)) (- 1))) $x499))))
   1.234 +(let ((@x207 (trans @x204 (rewrite (= $x499 $x499)) (= (or $x145 (= (+ 1 (* (- 1) ?x188)) (- 1))) $x499))))
   1.235 +(let ((@x104 (mp ((_ quant-inst 1) (or $x145 (= (+ 1 (* (- 1) ?x188)) (- 1)))) @x207 $x499)))
   1.236 +(let ((@x191 (monotonicity (symm (unit-resolution @x104 @x85 $x136) (= 2 ?x188)) (symm (unit-resolution @x496 @x518 $x492) (= nil$ ?x189)) (= ?x78 ?x160))))
   1.237 +(let ((@x473 (trans @x191 (symm (unit-resolution @x506 @x526 $x290) (= ?x160 ?x185)) (= ?x78 ?x185))))
   1.238 +(let ((?x182 (fun_app$ uu$ 0)))
   1.239 +(let (($x163 (= ?x182 1)))
   1.240 +(let (($x487 (or $x145 $x163)))
   1.241 +(let ((@x501 (monotonicity (rewrite (= (+ 0 (* (- 1) ?x182)) (* (- 1) ?x182))) (= (= (+ 0 (* (- 1) ?x182)) (- 1)) (= (* (- 1) ?x182) (- 1))))))
   1.242 +(let ((@x503 (trans @x501 (rewrite (= (= (* (- 1) ?x182) (- 1)) $x163)) (= (= (+ 0 (* (- 1) ?x182)) (- 1)) $x163))))
   1.243 +(let ((@x151 (monotonicity @x503 (= (or $x145 (= (+ 0 (* (- 1) ?x182)) (- 1))) $x487))))
   1.244 +(let ((@x490 (trans @x151 (rewrite (= $x487 $x487)) (= (or $x145 (= (+ 0 (* (- 1) ?x182)) (- 1))) $x487))))
   1.245 +(let ((@x491 (mp ((_ quant-inst 0) (or $x145 (= (+ 0 (* (- 1) ?x182)) (- 1)))) @x490 $x487)))
   1.246 +(let ((@x478 (monotonicity (symm (unit-resolution @x491 @x85 $x163) (= 1 ?x182)) @x473 (= ?x79 (cons$ ?x182 ?x185)))))
   1.247 +(let ((?x186 (cons$ ?x182 ?x185)))
   1.248 +(let (($x187 (= ?x76 ?x186)))
   1.249 +(let (($x504 (or (not $x521) $x187)))
   1.250 +(let ((@x505 ((_ quant-inst uu$ 0 (cons$ 1 nil$)) $x504)))
   1.251 +(let ((@x466 (trans (unit-resolution @x505 @x526 $x187) (symm @x478 (= ?x186 ?x79)) $x80)))
   1.252 +(let (($x81 (not $x80)))
   1.253 +(let ((@x82 (asserted $x81)))
   1.254 +(unit-resolution @x82 @x466 false))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
   1.255 +
   1.256 +40c61a0200976d6203302a7343af5b7ad1e6ce36 11 0
   1.257 +unsat
   1.258 +((set-logic AUFLIA)
   1.259 +(proof
   1.260 +(let (($x29 (forall ((?v0 A$) )(! (p$ ?v0) :qid k!6))
   1.261 +))
   1.262 +(let (($x30 (not $x29)))
   1.263 +(let (($x31 (or $x29 $x30)))
   1.264 +(let (($x32 (not $x31)))
   1.265 +(let ((@x42 (trans (monotonicity (rewrite (= $x31 true)) (= $x32 (not true))) (rewrite (= (not true) false)) (= $x32 false))))
   1.266 +(mp (asserted $x32) @x42 false))))))))
   1.267 +
   1.268 +f17a5e4d5f1a5a93fbc847f858c7c845c29d8349 109 0
   1.269 +unsat
   1.270 +((set-logic AUFLIA)
   1.271 +(proof
   1.272 +(let ((?x75 (dec_10$ 4)))
   1.273 +(let ((?x76 (* 4 ?x75)))
   1.274 +(let ((?x77 (dec_10$ ?x76)))
   1.275 +(let (($x79 (= ?x77 6)))
   1.276 +(let (($x150 (<= ?x75 4)))
   1.277 +(let (($x174 (= ?x75 4)))
   1.278 +(let (($x513 (forall ((?v0 Int) )(! (let (($x55 (>= ?v0 10)))
   1.279 +(ite $x55 (= (dec_10$ ?v0) (dec_10$ (+ (- 10) ?v0))) (= (dec_10$ ?v0) ?v0))) :pattern ( (dec_10$ ?v0) ) :qid k!5))
   1.280 +))
   1.281 +(let (($x92 (forall ((?v0 Int) )(! (let (($x55 (>= ?v0 10)))
   1.282 +(ite $x55 (= (dec_10$ ?v0) (dec_10$ (+ (- 10) ?v0))) (= (dec_10$ ?v0) ?v0))) :qid k!5))
   1.283 +))
   1.284 +(let (($x55 (>= ?0 10)))
   1.285 +(let (($x87 (ite $x55 (= (dec_10$ ?0) (dec_10$ (+ (- 10) ?0))) (= (dec_10$ ?0) ?0))))
   1.286 +(let (($x68 (forall ((?v0 Int) )(! (let ((?x38 (+ (- 10) ?v0)))
   1.287 +(let ((?x41 (dec_10$ ?x38)))
   1.288 +(let (($x55 (>= ?v0 10)))
   1.289 +(let ((?x60 (ite $x55 ?x41 ?v0)))
   1.290 +(let ((?x28 (dec_10$ ?v0)))
   1.291 +(= ?x28 ?x60)))))) :qid k!5))
   1.292 +))
   1.293 +(let ((?x38 (+ (- 10) ?0)))
   1.294 +(let ((?x41 (dec_10$ ?x38)))
   1.295 +(let ((?x60 (ite $x55 ?x41 ?0)))
   1.296 +(let ((?x28 (dec_10$ ?0)))
   1.297 +(let (($x65 (= ?x28 ?x60)))
   1.298 +(let (($x35 (forall ((?v0 Int) )(! (let ((?x28 (dec_10$ ?v0)))
   1.299 +(= ?x28 (ite (< ?v0 10) ?v0 (dec_10$ (- ?v0 10))))) :qid k!5))
   1.300 +))
   1.301 +(let (($x50 (forall ((?v0 Int) )(! (let ((?x38 (+ (- 10) ?v0)))
   1.302 +(let ((?x41 (dec_10$ ?x38)))
   1.303 +(let (($x30 (< ?v0 10)))
   1.304 +(let ((?x44 (ite $x30 ?v0 ?x41)))
   1.305 +(let ((?x28 (dec_10$ ?v0)))
   1.306 +(= ?x28 ?x44)))))) :qid k!5))
   1.307 +))
   1.308 +(let ((@x59 (monotonicity (rewrite (= (< ?0 10) (not $x55))) (= (ite (< ?0 10) ?0 ?x41) (ite (not $x55) ?0 ?x41)))))
   1.309 +(let ((@x64 (trans @x59 (rewrite (= (ite (not $x55) ?0 ?x41) ?x60)) (= (ite (< ?0 10) ?0 ?x41) ?x60))))
   1.310 +(let ((@x67 (monotonicity @x64 (= (= ?x28 (ite (< ?0 10) ?0 ?x41)) $x65))))
   1.311 +(let (($x30 (< ?0 10)))
   1.312 +(let ((?x44 (ite $x30 ?0 ?x41)))
   1.313 +(let (($x47 (= ?x28 ?x44)))
   1.314 +(let ((@x43 (monotonicity (rewrite (= (- ?0 10) ?x38)) (= (dec_10$ (- ?0 10)) ?x41))))
   1.315 +(let ((@x49 (monotonicity (monotonicity @x43 (= (ite $x30 ?0 (dec_10$ (- ?0 10))) ?x44)) (= (= ?x28 (ite $x30 ?0 (dec_10$ (- ?0 10)))) $x47))))
   1.316 +(let ((@x72 (trans (quant-intro @x49 (= $x35 $x50)) (quant-intro @x67 (= $x50 $x68)) (= $x35 $x68))))
   1.317 +(let ((@x86 (mp~ (mp (asserted $x35) @x72 $x68) (nnf-pos (refl (~ $x65 $x65)) (~ $x68 $x68)) $x68)))
   1.318 +(let ((@x95 (mp @x86 (quant-intro (rewrite (= $x65 $x87)) (= $x68 $x92)) $x92)))
   1.319 +(let ((@x518 (mp @x95 (quant-intro (refl (= $x87 $x87)) (= $x92 $x513)) $x513)))
   1.320 +(let (($x501 (not $x513)))
   1.321 +(let (($x163 (or $x501 $x174)))
   1.322 +(let ((?x97 (+ (- 10) 4)))
   1.323 +(let ((?x183 (dec_10$ ?x97)))
   1.324 +(let (($x184 (= ?x75 ?x183)))
   1.325 +(let (($x96 (>= 4 10)))
   1.326 +(let (($x185 (ite $x96 $x184 $x174)))
   1.327 +(let ((@x172 (monotonicity (monotonicity (rewrite (= ?x97 (- 6))) (= ?x183 (dec_10$ (- 6)))) (= $x184 (= ?x75 (dec_10$ (- 6)))))))
   1.328 +(let ((@x507 (monotonicity (rewrite (= $x96 false)) @x172 (= $x185 (ite false (= ?x75 (dec_10$ (- 6))) $x174)))))
   1.329 +(let ((@x511 (trans @x507 (rewrite (= (ite false (= ?x75 (dec_10$ (- 6))) $x174) $x174)) (= $x185 $x174))))
   1.330 +(let ((@x148 (trans (monotonicity @x511 (= (or $x501 $x185) $x163)) (rewrite (= $x163 $x163)) (= (or $x501 $x185) $x163))))
   1.331 +(let ((@x149 (mp ((_ quant-inst 4) (or $x501 $x185)) @x148 $x163)))
   1.332 +(let ((@x438 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x174) $x150)) (unit-resolution @x149 @x518 $x174) $x150)))
   1.333 +(let (($x151 (>= ?x75 4)))
   1.334 +(let ((@x428 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x174) $x151)) (unit-resolution @x149 @x518 $x174) $x151)))
   1.335 +(let ((?x489 (+ (- 10) ?x76)))
   1.336 +(let ((?x490 (dec_10$ ?x489)))
   1.337 +(let ((?x448 (* (- 1) ?x490)))
   1.338 +(let ((?x449 (+ ?x76 ?x448)))
   1.339 +(let (($x444 (<= ?x449 10)))
   1.340 +(let (($x292 (= ?x449 10)))
   1.341 +(let ((?x455 (+ (- 20) ?x76)))
   1.342 +(let ((?x458 (dec_10$ ?x455)))
   1.343 +(let (($x461 (= ?x490 ?x458)))
   1.344 +(let (($x310 (>= ?x75 5)))
   1.345 +(let (($x450 (ite $x310 $x461 $x292)))
   1.346 +(let (($x453 (or $x501 $x450)))
   1.347 +(let (($x470 (= ?x490 ?x489)))
   1.348 +(let ((?x467 (+ (- 10) ?x489)))
   1.349 +(let ((?x468 (dec_10$ ?x467)))
   1.350 +(let (($x469 (= ?x490 ?x468)))
   1.351 +(let (($x466 (>= ?x489 10)))
   1.352 +(let (($x471 (ite $x466 $x469 $x470)))
   1.353 +(let ((@x463 (monotonicity (monotonicity (rewrite (= ?x467 ?x455)) (= ?x468 ?x458)) (= $x469 $x461))))
   1.354 +(let ((@x452 (monotonicity (rewrite (= $x466 $x310)) @x463 (rewrite (= $x470 $x292)) (= $x471 $x450))))
   1.355 +(let ((@x442 (trans (monotonicity @x452 (= (or $x501 $x471) $x453)) (rewrite (= $x453 $x453)) (= (or $x501 $x471) $x453))))
   1.356 +(let ((@x443 (mp ((_ quant-inst (+ (- 10) ?x76)) (or $x501 $x471)) @x442 $x453)))
   1.357 +(let (($x346 (not $x310)))
   1.358 +(let ((@x418 (unit-resolution (def-axiom (or (not $x450) $x310 $x292)) (unit-resolution ((_ th-lemma arith farkas 1 1) (or $x346 (not $x150))) @x438 $x346) (or (not $x450) $x292))))
   1.359 +(let ((@x422 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x292) $x444)) (unit-resolution @x418 (unit-resolution @x443 @x518 $x450) $x292) $x444)))
   1.360 +(let (($x336 (>= ?x449 10)))
   1.361 +(let ((@x410 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x292) $x336)) (unit-resolution @x418 (unit-resolution @x443 @x518 $x450) $x292) $x336)))
   1.362 +(let (($x491 (= ?x77 ?x490)))
   1.363 +(let ((?x499 (* (- 1) ?x77)))
   1.364 +(let ((?x485 (+ ?x76 ?x499)))
   1.365 +(let (($x497 (= ?x485 0)))
   1.366 +(let (($x131 (>= ?x75 3)))
   1.367 +(let (($x486 (ite $x131 $x491 $x497)))
   1.368 +(let (($x205 (or $x501 $x486)))
   1.369 +(let ((@x204 (monotonicity (rewrite (= (>= ?x76 10) $x131)) (rewrite (= (= ?x77 ?x76) $x497)) (= (ite (>= ?x76 10) $x491 (= ?x77 ?x76)) $x486))))
   1.370 +(let ((@x479 (monotonicity @x204 (= (or $x501 (ite (>= ?x76 10) $x491 (= ?x77 ?x76))) $x205))))
   1.371 +(let ((@x212 (trans @x479 (rewrite (= $x205 $x205)) (= (or $x501 (ite (>= ?x76 10) $x491 (= ?x77 ?x76))) $x205))))
   1.372 +(let ((@x481 (mp ((_ quant-inst (* 4 ?x75)) (or $x501 (ite (>= ?x76 10) $x491 (= ?x77 ?x76)))) @x212 $x205)))
   1.373 +(let ((@x397 (unit-resolution (def-axiom (or (not $x486) (not $x131) $x491)) (unit-resolution ((_ th-lemma arith farkas 1 1) (or $x131 (not $x151))) @x428 $x131) (unit-resolution @x481 @x518 $x486) $x491)))
   1.374 +(let (($x80 (not $x79)))
   1.375 +(let ((@x81 (asserted $x80)))
   1.376 +(unit-resolution @x81 (trans @x397 ((_ th-lemma arith eq-propagate 1 1 -4 -4) @x410 @x422 @x428 @x438 (= ?x490 6)) $x79) false)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
   1.377 +
   1.378 +b6d44e20599d4862894eecfa4c98fcb043a6336d 348 0
   1.379 +unsat
   1.380 +((set-logic <null>)
   1.381 +(proof
   1.382 +(let ((?x96 (map$ uu$ xs$)))
   1.383 +(let ((?x97 (eval_dioph$ ks$ ?x96)))
   1.384 +(let ((?x424 (+ l$ ?x97)))
   1.385 +(let ((?x425 (mod ?x424 2)))
   1.386 +(let (($x482 (>= ?x425 2)))
   1.387 +(let (($x564 (not $x482)))
   1.388 +(let ((@x26 (true-axiom true)))
   1.389 +(let ((?x369 (* (- 1) l$)))
   1.390 +(let ((?x93 (eval_dioph$ ks$ xs$)))
   1.391 +(let ((?x678 (+ ?x93 ?x369)))
   1.392 +(let (($x679 (<= ?x678 0)))
   1.393 +(let (($x95 (= ?x93 l$)))
   1.394 +(let ((?x110 (* (- 1) ?x97)))
   1.395 +(let ((?x111 (+ l$ ?x110)))
   1.396 +(let ((?x114 (divide$ ?x111 2)))
   1.397 +(let ((?x101 (map$ uua$ xs$)))
   1.398 +(let ((?x102 (eval_dioph$ ks$ ?x101)))
   1.399 +(let (($x117 (= ?x102 ?x114)))
   1.400 +(let (($x282 (not $x117)))
   1.401 +(let ((?x99 (modulo$ l$ 2)))
   1.402 +(let ((?x98 (modulo$ ?x97 2)))
   1.403 +(let (($x100 (= ?x98 ?x99)))
   1.404 +(let (($x281 (not $x100)))
   1.405 +(let (($x283 (or $x281 $x282)))
   1.406 +(let (($x465 (>= ?x425 0)))
   1.407 +(let ((?x496 (* (- 2) ?x102)))
   1.408 +(let ((?x497 (+ ?x93 ?x110 ?x496)))
   1.409 +(let (($x504 (<= ?x497 0)))
   1.410 +(let (($x498 (= ?x497 0)))
   1.411 +(let (($x304 (forall ((?v0 Int_list$) (?v1 Int_list$) )(! (let ((?x45 (eval_dioph$ ?v0 ?v1)))
   1.412 +(let ((?x83 (+ ?x45 (* (- 1) (eval_dioph$ ?v0 (map$ uu$ ?v1))) (* (- 2) (eval_dioph$ ?v0 (map$ uua$ ?v1))))))
   1.413 +(= ?x83 0))) :pattern ( (eval_dioph$ ?v0 (map$ uu$ ?v1)) ) :pattern ( (eval_dioph$ ?v0 (map$ uua$ ?v1)) ) :qid k!19))
   1.414 +))
   1.415 +(let (($x85 (forall ((?v0 Int_list$) (?v1 Int_list$) )(! (let ((?x45 (eval_dioph$ ?v0 ?v1)))
   1.416 +(let ((?x83 (+ ?x45 (* (- 1) (eval_dioph$ ?v0 (map$ uu$ ?v1))) (* (- 2) (eval_dioph$ ?v0 (map$ uua$ ?v1))))))
   1.417 +(= ?x83 0))) :qid k!19))
   1.418 +))
   1.419 +(let ((?x45 (eval_dioph$ ?1 ?0)))
   1.420 +(let ((?x83 (+ ?x45 (* (- 1) (eval_dioph$ ?1 (map$ uu$ ?0))) (* (- 2) (eval_dioph$ ?1 (map$ uua$ ?0))))))
   1.421 +(let (($x79 (= ?x83 0)))
   1.422 +(let (($x58 (forall ((?v0 Int_list$) (?v1 Int_list$) )(! (let ((?x45 (eval_dioph$ ?v0 ?v1)))
   1.423 +(let ((?x48 (eval_dioph$ ?v0 (map$ uu$ ?v1))))
   1.424 +(let ((?x56 (+ (* (eval_dioph$ ?v0 (map$ uua$ ?v1)) 2) ?x48)))
   1.425 +(= ?x56 ?x45)))) :qid k!19))
   1.426 +))
   1.427 +(let (($x74 (forall ((?v0 Int_list$) (?v1 Int_list$) )(! (let ((?x45 (eval_dioph$ ?v0 ?v1)))
   1.428 +(let ((?x54 (eval_dioph$ ?v0 (map$ uua$ ?v1))))
   1.429 +(let ((?x60 (* 2 ?x54)))
   1.430 +(let ((?x48 (eval_dioph$ ?v0 (map$ uu$ ?v1))))
   1.431 +(let ((?x66 (+ ?x48 ?x60)))
   1.432 +(= ?x66 ?x45)))))) :qid k!19))
   1.433 +))
   1.434 +(let ((?x54 (eval_dioph$ ?1 (map$ uua$ ?0))))
   1.435 +(let ((?x60 (* 2 ?x54)))
   1.436 +(let ((?x48 (eval_dioph$ ?1 (map$ uu$ ?0))))
   1.437 +(let ((?x66 (+ ?x48 ?x60)))
   1.438 +(let (($x71 (= ?x66 ?x45)))
   1.439 +(let ((@x65 (monotonicity (rewrite (= (* ?x54 2) ?x60)) (= (+ (* ?x54 2) ?x48) (+ ?x60 ?x48)))))
   1.440 +(let ((@x70 (trans @x65 (rewrite (= (+ ?x60 ?x48) ?x66)) (= (+ (* ?x54 2) ?x48) ?x66))))
   1.441 +(let ((@x76 (quant-intro (monotonicity @x70 (= (= (+ (* ?x54 2) ?x48) ?x45) $x71)) (= $x58 $x74))))
   1.442 +(let ((@x89 (trans @x76 (quant-intro (rewrite (= $x71 $x79)) (= $x74 $x85)) (= $x58 $x85))))
   1.443 +(let ((@x270 (mp~ (mp (asserted $x58) @x89 $x85) (nnf-pos (refl (~ $x79 $x79)) (~ $x85 $x85)) $x85)))
   1.444 +(let ((@x309 (mp @x270 (quant-intro (refl (= $x79 $x79)) (= $x85 $x304)) $x304)))
   1.445 +(let (($x502 (or (not $x304) $x498)))
   1.446 +(let ((@x503 ((_ quant-inst ks$ xs$) $x502)))
   1.447 +(let ((@x795 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x498) $x504)) (unit-resolution @x503 @x309 $x498) $x504)))
   1.448 +(let (($x815 (not $x679)))
   1.449 +(let (($x680 (>= ?x678 0)))
   1.450 +(let ((?x592 (mod ?x97 2)))
   1.451 +(let ((?x619 (* (- 1) ?x592)))
   1.452 +(let ((?x511 (mod l$ 2)))
   1.453 +(let ((?x538 (* (- 1) ?x511)))
   1.454 +(let ((?x776 (* (- 1) ?x102)))
   1.455 +(let ((?x759 (+ l$ ?x98 ?x776 ?x538 (* (- 1) (div l$ 2)) ?x619 (* (- 1) (div ?x97 2)))))
   1.456 +(let (($x760 (>= ?x759 1)))
   1.457 +(let (($x747 (not $x760)))
   1.458 +(let ((?x674 (* (- 1) ?x99)))
   1.459 +(let ((?x675 (+ ?x98 ?x674)))
   1.460 +(let (($x676 (<= ?x675 0)))
   1.461 +(let (($x284 (not $x283)))
   1.462 +(let ((@x493 (hypothesis $x284)))
   1.463 +(let ((@x781 (unit-resolution ((_ th-lemma arith triangle-eq) (or $x281 $x676)) (unit-resolution (def-axiom (or $x283 $x100)) @x493 $x100) $x676)))
   1.464 +(let ((?x670 (* (- 1) ?x114)))
   1.465 +(let ((?x671 (+ ?x102 ?x670)))
   1.466 +(let (($x673 (>= ?x671 0)))
   1.467 +(let ((@x787 (unit-resolution ((_ th-lemma arith triangle-eq) (or $x282 $x673)) (unit-resolution (def-axiom (or $x283 $x117)) @x493 $x117) $x673)))
   1.468 +(let ((?x557 (div l$ 2)))
   1.469 +(let ((?x570 (* (- 2) ?x557)))
   1.470 +(let ((?x571 (+ l$ ?x538 ?x570)))
   1.471 +(let (($x576 (<= ?x571 0)))
   1.472 +(let (($x569 (= ?x571 0)))
   1.473 +(let ((@x568 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x569) $x576)) (unit-resolution ((_ th-lemma arith) (or false $x569)) @x26 $x569) $x576)))
   1.474 +(let ((?x620 (+ ?x98 ?x619)))
   1.475 +(let (($x635 (<= ?x620 0)))
   1.476 +(let (($x621 (= ?x620 0)))
   1.477 +(let (($x318 (forall ((?v0 Int) (?v1 Int) )(! (let ((?x200 (mod ?v0 ?v1)))
   1.478 +(let ((?x157 (* (- 1) ?v1)))
   1.479 +(let ((?x154 (* (- 1) ?v0)))
   1.480 +(let ((?x208 (mod ?x154 ?x157)))
   1.481 +(let ((?x214 (* (- 1) ?x208)))
   1.482 +(let (($x175 (<= ?v1 0)))
   1.483 +(let ((?x234 (ite $x175 ?x214 ?x200)))
   1.484 +(let (($x143 (= ?v1 0)))
   1.485 +(let ((?x239 (ite $x143 ?v0 ?x234)))
   1.486 +(let ((?x199 (modulo$ ?v0 ?v1)))
   1.487 +(= ?x199 ?x239))))))))))) :pattern ( (modulo$ ?v0 ?v1) ) :qid k!22))
   1.488 +))
   1.489 +(let (($x245 (forall ((?v0 Int) (?v1 Int) )(! (let ((?x200 (mod ?v0 ?v1)))
   1.490 +(let ((?x157 (* (- 1) ?v1)))
   1.491 +(let ((?x154 (* (- 1) ?v0)))
   1.492 +(let ((?x208 (mod ?x154 ?x157)))
   1.493 +(let ((?x214 (* (- 1) ?x208)))
   1.494 +(let (($x175 (<= ?v1 0)))
   1.495 +(let ((?x234 (ite $x175 ?x214 ?x200)))
   1.496 +(let (($x143 (= ?v1 0)))
   1.497 +(let ((?x239 (ite $x143 ?v0 ?x234)))
   1.498 +(let ((?x199 (modulo$ ?v0 ?v1)))
   1.499 +(= ?x199 ?x239))))))))))) :qid k!22))
   1.500 +))
   1.501 +(let ((?x200 (mod ?1 ?0)))
   1.502 +(let ((?x157 (* (- 1) ?0)))
   1.503 +(let ((?x154 (* (- 1) ?1)))
   1.504 +(let ((?x208 (mod ?x154 ?x157)))
   1.505 +(let ((?x214 (* (- 1) ?x208)))
   1.506 +(let (($x175 (<= ?0 0)))
   1.507 +(let ((?x234 (ite $x175 ?x214 ?x200)))
   1.508 +(let (($x143 (= ?0 0)))
   1.509 +(let ((?x239 (ite $x143 ?1 ?x234)))
   1.510 +(let ((?x199 (modulo$ ?1 ?0)))
   1.511 +(let (($x242 (= ?x199 ?x239)))
   1.512 +(let (($x206 (forall ((?v0 Int) (?v1 Int) )(! (let (($x143 (= ?v1 0)))
   1.513 +(let ((?x204 (ite $x143 ?v0 (ite (< 0 ?v1) (mod ?v0 ?v1) (- (mod (- ?v0) (- ?v1)))))))
   1.514 +(let ((?x199 (modulo$ ?v0 ?v1)))
   1.515 +(= ?x199 ?x204)))) :qid k!22))
   1.516 +))
   1.517 +(let (($x228 (forall ((?v0 Int) (?v1 Int) )(! (let ((?x157 (* (- 1) ?v1)))
   1.518 +(let ((?x154 (* (- 1) ?v0)))
   1.519 +(let ((?x208 (mod ?x154 ?x157)))
   1.520 +(let ((?x214 (* (- 1) ?x208)))
   1.521 +(let ((?x200 (mod ?v0 ?v1)))
   1.522 +(let (($x144 (< 0 ?v1)))
   1.523 +(let ((?x219 (ite $x144 ?x200 ?x214)))
   1.524 +(let (($x143 (= ?v1 0)))
   1.525 +(let ((?x222 (ite $x143 ?v0 ?x219)))
   1.526 +(let ((?x199 (modulo$ ?v0 ?v1)))
   1.527 +(= ?x199 ?x222))))))))))) :qid k!22))
   1.528 +))
   1.529 +(let ((@x233 (monotonicity (rewrite (= (< 0 ?0) (not $x175))) (= (ite (< 0 ?0) ?x200 ?x214) (ite (not $x175) ?x200 ?x214)))))
   1.530 +(let ((@x238 (trans @x233 (rewrite (= (ite (not $x175) ?x200 ?x214) ?x234)) (= (ite (< 0 ?0) ?x200 ?x214) ?x234))))
   1.531 +(let ((@x241 (monotonicity @x238 (= (ite $x143 ?1 (ite (< 0 ?0) ?x200 ?x214)) ?x239))))
   1.532 +(let ((@x244 (monotonicity @x241 (= (= ?x199 (ite $x143 ?1 (ite (< 0 ?0) ?x200 ?x214))) $x242))))
   1.533 +(let (($x144 (< 0 ?0)))
   1.534 +(let ((?x219 (ite $x144 ?x200 ?x214)))
   1.535 +(let ((?x222 (ite $x143 ?1 ?x219)))
   1.536 +(let (($x225 (= ?x199 ?x222)))
   1.537 +(let (($x226 (= (= ?x199 (ite $x143 ?1 (ite $x144 ?x200 (- (mod (- ?1) (- ?0)))))) $x225)))
   1.538 +(let ((@x210 (monotonicity (rewrite (= (- ?1) ?x154)) (rewrite (= (- ?0) ?x157)) (= (mod (- ?1) (- ?0)) ?x208))))
   1.539 +(let ((@x218 (trans (monotonicity @x210 (= (- (mod (- ?1) (- ?0))) (- ?x208))) (rewrite (= (- ?x208) ?x214)) (= (- (mod (- ?1) (- ?0))) ?x214))))
   1.540 +(let ((@x221 (monotonicity @x218 (= (ite $x144 ?x200 (- (mod (- ?1) (- ?0)))) ?x219))))
   1.541 +(let ((@x224 (monotonicity @x221 (= (ite $x143 ?1 (ite $x144 ?x200 (- (mod (- ?1) (- ?0))))) ?x222))))
   1.542 +(let ((@x249 (trans (quant-intro (monotonicity @x224 $x226) (= $x206 $x228)) (quant-intro @x244 (= $x228 $x245)) (= $x206 $x245))))
   1.543 +(let ((@x280 (mp~ (mp (asserted $x206) @x249 $x245) (nnf-pos (refl (~ $x242 $x242)) (~ $x245 $x245)) $x245)))
   1.544 +(let ((@x323 (mp @x280 (quant-intro (refl (= $x242 $x242)) (= $x245 $x318)) $x318)))
   1.545 +(let (($x545 (not $x318)))
   1.546 +(let (($x626 (or $x545 $x621)))
   1.547 +(let ((?x359 (* (- 1) 2)))
   1.548 +(let ((?x590 (mod ?x110 ?x359)))
   1.549 +(let ((?x591 (* (- 1) ?x590)))
   1.550 +(let (($x357 (<= 2 0)))
   1.551 +(let ((?x593 (ite $x357 ?x591 ?x592)))
   1.552 +(let (($x356 (= 2 0)))
   1.553 +(let ((?x594 (ite $x356 ?x97 ?x593)))
   1.554 +(let (($x595 (= ?x98 ?x594)))
   1.555 +(let ((@x601 (monotonicity (monotonicity (rewrite (= ?x359 (- 2))) (= ?x590 (mod ?x110 (- 2)))) (= ?x591 (* (- 1) (mod ?x110 (- 2)))))))
   1.556 +(let ((@x368 (rewrite (= $x357 false))))
   1.557 +(let ((@x604 (monotonicity @x368 @x601 (= ?x593 (ite false (* (- 1) (mod ?x110 (- 2))) ?x592)))))
   1.558 +(let ((@x608 (trans @x604 (rewrite (= (ite false (* (- 1) (mod ?x110 (- 2))) ?x592) ?x592)) (= ?x593 ?x592))))
   1.559 +(let ((@x366 (rewrite (= $x356 false))))
   1.560 +(let ((@x615 (trans (monotonicity @x366 @x608 (= ?x594 (ite false ?x97 ?x592))) (rewrite (= (ite false ?x97 ?x592) ?x592)) (= ?x594 ?x592))))
   1.561 +(let ((@x625 (trans (monotonicity @x615 (= $x595 (= ?x98 ?x592))) (rewrite (= (= ?x98 ?x592) $x621)) (= $x595 $x621))))
   1.562 +(let ((@x633 (trans (monotonicity @x625 (= (or $x545 $x595) $x626)) (rewrite (= $x626 $x626)) (= (or $x545 $x595) $x626))))
   1.563 +(let ((@x634 (mp ((_ quant-inst (eval_dioph$ ks$ ?x96) 2) (or $x545 $x595)) @x633 $x626)))
   1.564 +(let ((@x431 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x621) $x635)) (unit-resolution @x634 @x323 $x621) $x635)))
   1.565 +(let ((?x637 (div ?x97 2)))
   1.566 +(let ((?x650 (* (- 2) ?x637)))
   1.567 +(let ((?x651 (+ ?x97 ?x619 ?x650)))
   1.568 +(let (($x656 (<= ?x651 0)))
   1.569 +(let (($x649 (= ?x651 0)))
   1.570 +(let ((@x661 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x649) $x656)) (unit-resolution ((_ th-lemma arith) (or false $x649)) @x26 $x649) $x656)))
   1.571 +(let ((?x539 (+ ?x99 ?x538)))
   1.572 +(let (($x555 (<= ?x539 0)))
   1.573 +(let (($x540 (= ?x539 0)))
   1.574 +(let (($x546 (or $x545 $x540)))
   1.575 +(let ((?x506 (mod ?x369 ?x359)))
   1.576 +(let ((?x507 (* (- 1) ?x506)))
   1.577 +(let ((?x512 (ite $x357 ?x507 ?x511)))
   1.578 +(let ((?x513 (ite $x356 l$ ?x512)))
   1.579 +(let (($x514 (= ?x99 ?x513)))
   1.580 +(let ((@x520 (monotonicity (monotonicity (rewrite (= ?x359 (- 2))) (= ?x506 (mod ?x369 (- 2)))) (= ?x507 (* (- 1) (mod ?x369 (- 2)))))))
   1.581 +(let ((@x523 (monotonicity @x368 @x520 (= ?x512 (ite false (* (- 1) (mod ?x369 (- 2))) ?x511)))))
   1.582 +(let ((@x527 (trans @x523 (rewrite (= (ite false (* (- 1) (mod ?x369 (- 2))) ?x511) ?x511)) (= ?x512 ?x511))))
   1.583 +(let ((@x534 (trans (monotonicity @x366 @x527 (= ?x513 (ite false l$ ?x511))) (rewrite (= (ite false l$ ?x511) ?x511)) (= ?x513 ?x511))))
   1.584 +(let ((@x544 (trans (monotonicity @x534 (= $x514 (= ?x99 ?x511))) (rewrite (= (= ?x99 ?x511) $x540)) (= $x514 $x540))))
   1.585 +(let ((@x553 (trans (monotonicity @x544 (= (or $x545 $x514) $x546)) (rewrite (= $x546 $x546)) (= (or $x545 $x514) $x546))))
   1.586 +(let ((@x554 (mp ((_ quant-inst l$ 2) (or $x545 $x514)) @x553 $x546)))
   1.587 +(let ((@x668 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x540) $x555)) (unit-resolution @x554 @x323 $x540) $x555)))
   1.588 +(let ((?x361 (div ?x111 2)))
   1.589 +(let ((?x395 (* (- 1) ?x361)))
   1.590 +(let ((?x396 (+ ?x114 ?x395)))
   1.591 +(let (($x414 (>= ?x396 0)))
   1.592 +(let (($x397 (= ?x396 0)))
   1.593 +(let (($x311 (forall ((?v0 Int) (?v1 Int) )(! (let ((?x145 (div ?v0 ?v1)))
   1.594 +(let ((?x157 (* (- 1) ?v1)))
   1.595 +(let ((?x154 (* (- 1) ?v0)))
   1.596 +(let ((?x160 (div ?x154 ?x157)))
   1.597 +(let (($x175 (<= ?v1 0)))
   1.598 +(let ((?x182 (ite $x175 ?x160 ?x145)))
   1.599 +(let (($x143 (= ?v1 0)))
   1.600 +(let ((?x141 (divide$ ?v0 ?v1)))
   1.601 +(= ?x141 (ite $x143 0 ?x182)))))))))) :pattern ( (divide$ ?v0 ?v1) ) :qid k!21))
   1.602 +))
   1.603 +(let (($x193 (forall ((?v0 Int) (?v1 Int) )(! (let ((?x145 (div ?v0 ?v1)))
   1.604 +(let ((?x157 (* (- 1) ?v1)))
   1.605 +(let ((?x154 (* (- 1) ?v0)))
   1.606 +(let ((?x160 (div ?x154 ?x157)))
   1.607 +(let (($x175 (<= ?v1 0)))
   1.608 +(let ((?x182 (ite $x175 ?x160 ?x145)))
   1.609 +(let (($x143 (= ?v1 0)))
   1.610 +(let ((?x141 (divide$ ?v0 ?v1)))
   1.611 +(= ?x141 (ite $x143 0 ?x182)))))))))) :qid k!21))
   1.612 +))
   1.613 +(let ((?x141 (divide$ ?1 ?0)))
   1.614 +(let (($x190 (= ?x141 (ite $x143 0 (ite $x175 (div ?x154 ?x157) (div ?1 ?0))))))
   1.615 +(let (($x152 (forall ((?v0 Int) (?v1 Int) )(! (let (($x143 (= ?v1 0)))
   1.616 +(let ((?x150 (ite $x143 0 (ite (< 0 ?v1) (div ?v0 ?v1) (div (- ?v0) (- ?v1))))))
   1.617 +(let ((?x141 (divide$ ?v0 ?v1)))
   1.618 +(= ?x141 ?x150)))) :qid k!21))
   1.619 +))
   1.620 +(let (($x172 (forall ((?v0 Int) (?v1 Int) )(! (let ((?x157 (* (- 1) ?v1)))
   1.621 +(let ((?x154 (* (- 1) ?v0)))
   1.622 +(let ((?x160 (div ?x154 ?x157)))
   1.623 +(let ((?x145 (div ?v0 ?v1)))
   1.624 +(let (($x144 (< 0 ?v1)))
   1.625 +(let ((?x163 (ite $x144 ?x145 ?x160)))
   1.626 +(let (($x143 (= ?v1 0)))
   1.627 +(let ((?x166 (ite $x143 0 ?x163)))
   1.628 +(let ((?x141 (divide$ ?v0 ?v1)))
   1.629 +(= ?x141 ?x166)))))))))) :qid k!21))
   1.630 +))
   1.631 +(let ((?x160 (div ?x154 ?x157)))
   1.632 +(let ((?x145 (div ?1 ?0)))
   1.633 +(let ((?x163 (ite $x144 ?x145 ?x160)))
   1.634 +(let ((?x166 (ite $x143 0 ?x163)))
   1.635 +(let (($x169 (= ?x141 ?x166)))
   1.636 +(let ((@x181 (monotonicity (rewrite (= $x144 (not $x175))) (= ?x163 (ite (not $x175) ?x145 ?x160)))))
   1.637 +(let ((@x186 (trans @x181 (rewrite (= (ite (not $x175) ?x145 ?x160) (ite $x175 ?x160 ?x145))) (= ?x163 (ite $x175 ?x160 ?x145)))))
   1.638 +(let ((@x192 (monotonicity (monotonicity @x186 (= ?x166 (ite $x143 0 (ite $x175 ?x160 ?x145)))) (= $x169 $x190))))
   1.639 +(let (($x170 (= (= ?x141 (ite $x143 0 (ite $x144 ?x145 (div (- ?1) (- ?0))))) $x169)))
   1.640 +(let ((@x162 (monotonicity (rewrite (= (- ?1) ?x154)) (rewrite (= (- ?0) ?x157)) (= (div (- ?1) (- ?0)) ?x160))))
   1.641 +(let ((@x168 (monotonicity (monotonicity @x162 (= (ite $x144 ?x145 (div (- ?1) (- ?0))) ?x163)) (= (ite $x143 0 (ite $x144 ?x145 (div (- ?1) (- ?0)))) ?x166))))
   1.642 +(let ((@x197 (trans (quant-intro (monotonicity @x168 $x170) (= $x152 $x172)) (quant-intro @x192 (= $x172 $x193)) (= $x152 $x193))))
   1.643 +(let ((@x275 (mp~ (mp (asserted $x152) @x197 $x193) (nnf-pos (refl (~ $x190 $x190)) (~ $x193 $x193)) $x193)))
   1.644 +(let ((@x316 (mp @x275 (quant-intro (refl (= $x190 $x190)) (= $x193 $x311)) $x311)))
   1.645 +(let (($x403 (or (not $x311) $x397)))
   1.646 +(let ((?x358 (* (- 1) ?x111)))
   1.647 +(let ((?x360 (div ?x358 ?x359)))
   1.648 +(let ((?x362 (ite $x357 ?x360 ?x361)))
   1.649 +(let ((?x363 (ite $x356 0 ?x362)))
   1.650 +(let (($x364 (= ?x114 ?x363)))
   1.651 +(let ((@x374 (rewrite (= ?x359 (- 2)))))
   1.652 +(let ((@x377 (monotonicity (rewrite (= ?x358 (+ ?x369 ?x97))) @x374 (= ?x360 (div (+ ?x369 ?x97) (- 2))))))
   1.653 +(let ((@x380 (monotonicity @x368 @x377 (= ?x362 (ite false (div (+ ?x369 ?x97) (- 2)) ?x361)))))
   1.654 +(let ((@x384 (trans @x380 (rewrite (= (ite false (div (+ ?x369 ?x97) (- 2)) ?x361) ?x361)) (= ?x362 ?x361))))
   1.655 +(let ((@x391 (trans (monotonicity @x366 @x384 (= ?x363 (ite false 0 ?x361))) (rewrite (= (ite false 0 ?x361) ?x361)) (= ?x363 ?x361))))
   1.656 +(let ((@x401 (trans (monotonicity @x391 (= $x364 (= ?x114 ?x361))) (rewrite (= (= ?x114 ?x361) $x397)) (= $x364 $x397))))
   1.657 +(let ((@x410 (trans (monotonicity @x401 (= (or (not $x311) $x364) $x403)) (rewrite (= $x403 $x403)) (= (or (not $x311) $x364) $x403))))
   1.658 +(let ((@x411 (mp ((_ quant-inst (+ l$ ?x110) 2) (or (not $x311) $x364)) @x410 $x403)))
   1.659 +(let ((@x485 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x397) $x414)) (unit-resolution @x411 @x316 $x397) $x414)))
   1.660 +(let ((?x436 (* (- 1) ?x425)))
   1.661 +(let ((?x435 (* (- 2) ?x361)))
   1.662 +(let ((?x437 (+ l$ ?x110 ?x435 ?x436)))
   1.663 +(let (($x442 (<= ?x437 0)))
   1.664 +(let (($x434 (= ?x437 0)))
   1.665 +(let ((@x745 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x434) $x442)) (unit-resolution ((_ th-lemma arith) (or false $x434)) @x26 $x434) $x442)))
   1.666 +(let ((@x746 ((_ th-lemma arith farkas 1 -2 -2 -2 1 1 1 1 1 1) @x745 @x485 (hypothesis $x673) (hypothesis $x760) (hypothesis $x676) @x668 @x661 @x431 @x568 (unit-resolution ((_ th-lemma arith) (or false $x564)) @x26 $x564) false)))
   1.667 +(let ((@x788 (unit-resolution (lemma @x746 (or $x747 (not $x673) (not $x676))) @x787 @x781 $x747)))
   1.668 +(let (($x677 (>= ?x675 0)))
   1.669 +(let ((@x812 (unit-resolution ((_ th-lemma arith triangle-eq) (or $x281 $x677)) (unit-resolution (def-axiom (or $x283 $x100)) @x493 $x100) $x677)))
   1.670 +(let (($x577 (>= ?x571 0)))
   1.671 +(let ((@x778 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x569) $x577)) (unit-resolution ((_ th-lemma arith) (or false $x569)) @x26 $x569) $x577)))
   1.672 +(let (($x556 (>= ?x539 0)))
   1.673 +(let ((@x645 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x540) $x556)) (unit-resolution @x554 @x323 $x540) $x556)))
   1.674 +(let (($x636 (>= ?x620 0)))
   1.675 +(let ((@x652 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x621) $x636)) (unit-resolution @x634 @x323 $x621) $x636)))
   1.676 +(let (($x505 (>= ?x497 0)))
   1.677 +(let ((@x488 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x498) $x505)) (unit-resolution @x503 @x309 $x498) $x505)))
   1.678 +(let (($x657 (>= ?x651 0)))
   1.679 +(let ((@x581 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x649) $x657)) (unit-resolution ((_ th-lemma arith) (or false $x649)) @x26 $x649) $x657)))
   1.680 +(let ((@x582 ((_ th-lemma arith farkas -1/2 -1/2 -1/2 1/2 -1/2 -1/2 -1/2 1) @x581 (hypothesis $x677) @x488 (hypothesis (not $x680)) @x652 @x645 @x778 (hypothesis $x747) false)))
   1.681 +(let ((@x813 (unit-resolution (lemma @x582 (or $x680 (not $x677) $x760)) @x812 @x788 $x680)))
   1.682 +(let (($x134 (not $x95)))
   1.683 +(let (($x290 (= $x95 $x283)))
   1.684 +(let ((@x289 (monotonicity (rewrite (= (and $x100 $x117) $x284)) (= (= $x134 (and $x100 $x117)) (= $x134 $x284)))))
   1.685 +(let ((@x294 (trans @x289 (rewrite (= (= $x134 $x284) $x290)) (= (= $x134 (and $x100 $x117)) $x290))))
   1.686 +(let (($x120 (and $x100 $x117)))
   1.687 +(let (($x135 (= $x134 $x120)))
   1.688 +(let (($x107 (= $x95 (and $x100 (= ?x102 (divide$ (- l$ ?x97) 2))))))
   1.689 +(let (($x108 (not $x107)))
   1.690 +(let ((@x116 (monotonicity (rewrite (= (- l$ ?x97) ?x111)) (= (divide$ (- l$ ?x97) 2) ?x114))))
   1.691 +(let ((@x122 (monotonicity (monotonicity @x116 (= (= ?x102 (divide$ (- l$ ?x97) 2)) $x117)) (= (and $x100 (= ?x102 (divide$ (- l$ ?x97) 2))) $x120))))
   1.692 +(let ((@x130 (trans (monotonicity @x122 (= $x107 (= $x95 $x120))) (rewrite (= (= $x95 $x120) (= $x95 $x120))) (= $x107 (= $x95 $x120)))))
   1.693 +(let ((@x139 (trans (monotonicity @x130 (= $x108 (not (= $x95 $x120)))) (rewrite (= (not (= $x95 $x120)) $x135)) (= $x108 $x135))))
   1.694 +(let ((@x295 (mp (mp (asserted $x108) @x139 $x135) @x294 $x290)))
   1.695 +(let ((@x344 (unit-resolution (def-axiom (or $x134 $x283 (not $x290))) @x295 (or $x134 $x283))))
   1.696 +(let ((@x819 (unit-resolution ((_ th-lemma arith triangle-eq) (or $x95 $x815 (not $x680))) (unit-resolution @x344 @x493 $x134) (or $x815 (not $x680)))))
   1.697 +(let (($x672 (<= ?x671 0)))
   1.698 +(let ((@x823 (unit-resolution ((_ th-lemma arith triangle-eq) (or $x282 $x672)) (unit-resolution (def-axiom (or $x283 $x117)) @x493 $x117) $x672)))
   1.699 +(let (($x413 (<= ?x396 0)))
   1.700 +(let ((@x802 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x397) $x413)) (unit-resolution @x411 @x316 $x397) $x413)))
   1.701 +(let (($x443 (>= ?x437 0)))
   1.702 +(let ((@x826 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x434) $x443)) (unit-resolution ((_ th-lemma arith) (or false $x434)) @x26 $x434) $x443)))
   1.703 +(let ((@x827 ((_ th-lemma arith farkas 1 -2 -2 1 -1 1) @x826 @x802 @x823 (unit-resolution @x819 @x813 $x815) @x795 (unit-resolution ((_ th-lemma arith) (or false $x465)) @x26 $x465) false)))
   1.704 +(let ((@x828 (lemma @x827 $x283)))
   1.705 +(let ((@x340 (unit-resolution (def-axiom (or $x95 $x284 (not $x290))) @x295 (or $x95 $x284))))
   1.706 +(let ((@x584 (unit-resolution @x340 @x828 $x95)))
   1.707 +(let (($x807 (not $x672)))
   1.708 +(let ((@x888 ((_ th-lemma arith assign-bounds 1 -1/2 -1/2 1/2 -1/2) (or $x673 (not $x413) (not $x465) (not $x443) (not $x504) (not $x680)))))
   1.709 +(let ((@x889 (unit-resolution @x888 (unit-resolution ((_ th-lemma arith triangle-eq) (or $x134 $x680)) @x584 $x680) @x802 @x826 (unit-resolution ((_ th-lemma arith) (or false $x465)) @x26 $x465) @x795 $x673)))
   1.710 +(let ((@x728 (monotonicity (symm @x584 (= l$ ?x93)) (= ?x99 (modulo$ ?x93 2)))))
   1.711 +(let ((?x499 (modulo$ ?x93 2)))
   1.712 +(let (($x500 (= ?x499 ?x98)))
   1.713 +(let (($x297 (forall ((?v0 Int_list$) (?v1 Int_list$) )(! (= (modulo$ (eval_dioph$ ?v0 ?v1) 2) (modulo$ (eval_dioph$ ?v0 (map$ uu$ ?v1)) 2)) :pattern ( (eval_dioph$ ?v0 (map$ uu$ ?v1)) ) :qid k!18))
   1.714 +))
   1.715 +(let (($x51 (forall ((?v0 Int_list$) (?v1 Int_list$) )(! (= (modulo$ (eval_dioph$ ?v0 ?v1) 2) (modulo$ (eval_dioph$ ?v0 (map$ uu$ ?v1)) 2)) :qid k!18))
   1.716 +))
   1.717 +(let (($x50 (= (modulo$ ?x45 2) (modulo$ ?x48 2))))
   1.718 +(let ((@x265 (mp~ (asserted $x51) (nnf-pos (refl (~ $x50 $x50)) (~ $x51 $x51)) $x51)))
   1.719 +(let ((@x302 (mp @x265 (quant-intro (refl (= $x50 $x50)) (= $x51 $x297)) $x297)))
   1.720 +(let (($x464 (or (not $x297) $x500)))
   1.721 +(let ((@x578 ((_ quant-inst ks$ xs$) $x464)))
   1.722 +(let ((@x748 (trans (symm (unit-resolution @x578 @x302 $x500) (= ?x98 ?x499)) (symm @x728 (= ?x499 ?x99)) $x100)))
   1.723 +(let ((@x891 (unit-resolution (unit-resolution (def-axiom (or $x284 $x281 $x282)) @x828 $x283) (lemma (unit-resolution (hypothesis $x281) @x748 false) $x100) $x282)))
   1.724 +(let ((@x895 (unit-resolution ((_ th-lemma arith triangle-eq) (or $x117 $x807 (not $x673))) @x891 (or $x807 (not $x673)))))
   1.725 +((_ th-lemma arith farkas -2 -2 1 -1 1 1) (unit-resolution @x895 @x889 $x807) @x485 @x745 @x488 (unit-resolution ((_ th-lemma arith triangle-eq) (or $x134 $x679)) @x584 $x679) (unit-resolution ((_ th-lemma arith) (or false $x564)) @x26 $x564) false)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
   1.726 +
   1.727 +db184ed715734759b60f9bdc99290a92283563f5 64 0
   1.728 +unsat
   1.729 +((set-logic AUFLIA)
   1.730 +(proof
   1.731 +(let ((?x108 (collect$ uu$)))
   1.732 +(let ((?x109 (sup$ ?x108)))
   1.733 +(let (($x117 (less_eq$ ?x109 ?x109)))
   1.734 +(let (($x118 (not $x117)))
   1.735 +(let ((@x119 (asserted $x118)))
   1.736 +(let ((?x111 (collect$ uua$)))
   1.737 +(let ((?x112 (sup$ ?x111)))
   1.738 +(let (($x115 (less_eq$ ?x112 ?x109)))
   1.739 +(let ((@x116 (asserted $x115)))
   1.740 +(let (($x113 (less_eq$ ?x109 ?x112)))
   1.741 +(let ((@x114 (asserted $x113)))
   1.742 +(let (($x578 (forall ((?v0 A$) (?v1 A$) (?v2 A$) )(! (let (($x97 (less_eq$ ?v0 ?v2)))
   1.743 +(let (($x95 (less_eq$ ?v1 ?v2)))
   1.744 +(let (($x138 (not $x95)))
   1.745 +(let (($x93 (less_eq$ ?v0 ?v1)))
   1.746 +(let (($x137 (not $x93)))
   1.747 +(or $x137 $x138 $x97)))))) :pattern ( (less_eq$ ?v0 ?v1) (less_eq$ ?v1 ?v2) ) :qid k!17))
   1.748 +))
   1.749 +(let (($x156 (forall ((?v0 A$) (?v1 A$) (?v2 A$) )(! (let (($x97 (less_eq$ ?v0 ?v2)))
   1.750 +(let (($x95 (less_eq$ ?v1 ?v2)))
   1.751 +(let (($x138 (not $x95)))
   1.752 +(let (($x93 (less_eq$ ?v0 ?v1)))
   1.753 +(let (($x137 (not $x93)))
   1.754 +(or $x137 $x138 $x97)))))) :qid k!17))
   1.755 +))
   1.756 +(let ((@x583 (trans (rewrite (= $x156 $x578)) (rewrite (= $x578 $x578)) (= $x156 $x578))))
   1.757 +(let (($x105 (forall ((?v0 A$) (?v1 A$) (?v2 A$) )(! (let (($x97 (less_eq$ ?v0 ?v2)))
   1.758 +(let (($x95 (less_eq$ ?v1 ?v2)))
   1.759 +(let (($x93 (less_eq$ ?v0 ?v1)))
   1.760 +(let (($x96 (and $x93 $x95)))
   1.761 +(let (($x101 (not $x96)))
   1.762 +(or $x101 $x97)))))) :qid k!17))
   1.763 +))
   1.764 +(let (($x97 (less_eq$ ?2 ?0)))
   1.765 +(let (($x95 (less_eq$ ?1 ?0)))
   1.766 +(let (($x138 (not $x95)))
   1.767 +(let (($x93 (less_eq$ ?2 ?1)))
   1.768 +(let (($x137 (not $x93)))
   1.769 +(let (($x151 (or $x137 $x138 $x97)))
   1.770 +(let (($x96 (and $x93 $x95)))
   1.771 +(let (($x101 (not $x96)))
   1.772 +(let (($x102 (or $x101 $x97)))
   1.773 +(let ((@x143 (monotonicity (rewrite (= $x96 (not (or $x137 $x138)))) (= $x101 (not (not (or $x137 $x138)))))))
   1.774 +(let ((@x147 (trans @x143 (rewrite (= (not (not (or $x137 $x138))) (or $x137 $x138))) (= $x101 (or $x137 $x138)))))
   1.775 +(let ((@x155 (trans (monotonicity @x147 (= $x102 (or (or $x137 $x138) $x97))) (rewrite (= (or (or $x137 $x138) $x97) $x151)) (= $x102 $x151))))
   1.776 +(let (($x99 (forall ((?v0 A$) (?v1 A$) (?v2 A$) )(! (let (($x97 (less_eq$ ?v0 ?v2)))
   1.777 +(let (($x95 (less_eq$ ?v1 ?v2)))
   1.778 +(let (($x93 (less_eq$ ?v0 ?v1)))
   1.779 +(let (($x96 (and $x93 $x95)))
   1.780 +(=> $x96 $x97))))) :qid k!17))
   1.781 +))
   1.782 +(let ((@x110 (mp (asserted $x99) (quant-intro (rewrite (= (=> $x96 $x97) $x102)) (= $x99 $x105)) $x105)))
   1.783 +(let ((@x159 (mp (mp~ @x110 (nnf-pos (refl (~ $x102 $x102)) (~ $x105 $x105)) $x105) (quant-intro @x155 (= $x105 $x156)) $x156)))
   1.784 +(let ((@x584 (mp @x159 @x583 $x578)))
   1.785 +(let (($x247 (not $x115)))
   1.786 +(let (($x160 (not $x113)))
   1.787 +(let (($x251 (not $x578)))
   1.788 +(let (($x252 (or $x251 $x160 $x247 $x117)))
   1.789 +(let ((@x570 (mp ((_ quant-inst (sup$ ?x108) (sup$ ?x111) (sup$ ?x108)) (or $x251 (or $x160 $x247 $x117))) (rewrite (= (or $x251 (or $x160 $x247 $x117)) $x252)) $x252)))
   1.790 +(unit-resolution @x570 @x584 @x114 @x116 @x119 false)))))))))))))))))))))))))))))))))))))))
   1.791 +
   1.792 +4e8ab14f236ad601aa67494ca8ea18b2ba6a1a79 25 0
   1.793 +unsat
   1.794 +((set-logic AUFLIA)
   1.795 +(proof
   1.796 +(let (($x142 (pred$e 1)))
   1.797 +(let (($x144 (not $x142)))
   1.798 +(let ((@x145 (asserted $x144)))
   1.799 +(let (($x615 (forall ((?v0 Int) )(! (pred$e ?v0) :pattern ( (pred$e ?v0) ) :qid k!29))
   1.800 +))
   1.801 +(let (($x138 (forall ((?v0 Int) )(! (pred$e ?v0) :qid k!29))
   1.802 +))
   1.803 +(let (($x127 (forall ((?v0 Int) )(! (let (($x125 (or (pred$d (cons$d ?v0 nil$d)) (not (pred$d (cons$d ?v0 nil$d))))))
   1.804 +(let (($x119 (pred$e ?v0)))
   1.805 +(and $x119 $x125))) :qid k!29))
   1.806 +))
   1.807 +(let (($x119 (pred$e ?0)))
   1.808 +(let (($x125 (or (pred$d (cons$d ?0 nil$d)) (not (pred$d (cons$d ?0 nil$d))))))
   1.809 +(let (($x126 (and $x119 $x125)))
   1.810 +(let ((@x133 (monotonicity (rewrite (= $x125 true)) (= $x126 (and $x119 true)))))
   1.811 +(let ((@x140 (quant-intro (trans @x133 (rewrite (= (and $x119 true) $x119)) (= $x126 $x119)) (= $x127 $x138))))
   1.812 +(let ((@x170 (mp~ (mp (asserted $x127) @x140 $x138) (nnf-pos (refl (~ $x119 $x119)) (~ $x138 $x138)) $x138)))
   1.813 +(let ((@x620 (mp @x170 (quant-intro (refl (= $x119 $x119)) (= $x138 $x615)) $x615)))
   1.814 +(let (($x257 (or (not $x615) $x142)))
   1.815 +(let ((@x258 ((_ quant-inst 1) $x257)))
   1.816 +(unit-resolution @x258 @x620 @x145 false))))))))))))))))))
   1.817 +
   1.818 +b4b100f728c8f0d6f96483e4de44e248cc4be1aa 101 0
   1.819 +unsat
   1.820 +((set-logic AUFLIA)
   1.821 +(proof
   1.822 +(let ((?x124 (some$a true)))
   1.823 +(let ((?x125 (g$b ?x124)))
   1.824 +(let ((?x122 (some$ 3)))
   1.825 +(let ((?x123 (g$ ?x122)))
   1.826 +(let (($x126 (= ?x123 ?x125)))
   1.827 +(let ((?x269 (cons$a true nil$a)))
   1.828 +(let ((?x270 (g$c ?x269)))
   1.829 +(let (($x587 (= ?x125 ?x270)))
   1.830 +(let (($x604 (forall ((?v0 Bool) )(! (= (g$b (some$a ?v0)) (g$c (cons$a ?v0 nil$a))) :pattern ( (some$a ?v0) ) :pattern ( (cons$a ?v0 nil$a) ) :qid k!33))
   1.831 +))
   1.832 +(let (($x43 (forall ((?v0 Bool) )(! (= (g$b (some$a ?v0)) (g$c (cons$a ?v0 nil$a))) :qid k!33))
   1.833 +))
   1.834 +(let (($x42 (= (g$b (some$a ?0)) (g$c (cons$a ?0 nil$a)))))
   1.835 +(let ((@x160 (mp~ (asserted $x43) (nnf-pos (refl (~ $x42 $x42)) (~ $x43 $x43)) $x43)))
   1.836 +(let ((@x609 (mp @x160 (quant-intro (refl (= $x42 $x42)) (= $x43 $x604)) $x604)))
   1.837 +(let (($x254 (or (not $x604) $x587)))
   1.838 +(let ((@x255 ((_ quant-inst true) $x254)))
   1.839 +(let ((?x227 (size$ ?x269)))
   1.840 +(let (($x569 (= ?x270 ?x227)))
   1.841 +(let (($x612 (forall ((?v0 Bool_list$) )(! (let ((?x61 (size$ ?v0)))
   1.842 +(let ((?x60 (g$c ?v0)))
   1.843 +(= ?x60 ?x61))) :pattern ( (g$c ?v0) ) :pattern ( (size$ ?v0) ) :qid k!38))
   1.844 +))
   1.845 +(let (($x63 (forall ((?v0 Bool_list$) )(! (let ((?x61 (size$ ?v0)))
   1.846 +(let ((?x60 (g$c ?v0)))
   1.847 +(= ?x60 ?x61))) :qid k!38))
   1.848 +))
   1.849 +(let ((@x616 (quant-intro (refl (= (= (g$c ?0) (size$ ?0)) (= (g$c ?0) (size$ ?0)))) (= $x63 $x612))))
   1.850 +(let ((@x142 (nnf-pos (refl (~ (= (g$c ?0) (size$ ?0)) (= (g$c ?0) (size$ ?0)))) (~ $x63 $x63))))
   1.851 +(let ((@x617 (mp (mp~ (asserted $x63) @x142 $x63) @x616 $x612)))
   1.852 +(let (($x571 (or (not $x612) $x569)))
   1.853 +(let ((@x572 ((_ quant-inst (cons$a true nil$a)) $x571)))
   1.854 +(let ((?x89 (suc$ zero$)))
   1.855 +(let ((?x105 (size$ nil$a)))
   1.856 +(let ((?x233 (plus$ ?x105 ?x89)))
   1.857 +(let (($x570 (= ?x227 ?x233)))
   1.858 +(let (($x657 (forall ((?v0 Bool) (?v1 Bool_list$) )(! (= (size$ (cons$a ?v0 ?v1)) (plus$ (size$ ?v1) (suc$ zero$))) :pattern ( (cons$a ?v0 ?v1) ) :qid k!46))
   1.859 +))
   1.860 +(let (($x114 (forall ((?v0 Bool) (?v1 Bool_list$) )(! (= (size$ (cons$a ?v0 ?v1)) (plus$ (size$ ?v1) (suc$ zero$))) :qid k!46))
   1.861 +))
   1.862 +(let (($x113 (= (size$ (cons$a ?1 ?0)) (plus$ (size$ ?0) ?x89))))
   1.863 +(let ((@x173 (mp~ (asserted $x114) (nnf-pos (refl (~ $x113 $x113)) (~ $x114 $x114)) $x114)))
   1.864 +(let ((@x662 (mp @x173 (quant-intro (refl (= $x113 $x113)) (= $x114 $x657)) $x657)))
   1.865 +(let (($x576 (or (not $x657) $x570)))
   1.866 +(let ((@x213 ((_ quant-inst true nil$a) $x576)))
   1.867 +(let ((?x108 (size$a nil$)))
   1.868 +(let (($x109 (= ?x108 zero$)))
   1.869 +(let ((@x110 (asserted $x109)))
   1.870 +(let (($x106 (= ?x105 zero$)))
   1.871 +(let ((@x107 (asserted $x106)))
   1.872 +(let ((@x287 (monotonicity (trans @x107 (symm @x110 (= zero$ ?x108)) (= ?x105 ?x108)) (= ?x233 (plus$ ?x108 ?x89)))))
   1.873 +(let ((?x246 (plus$ ?x108 ?x89)))
   1.874 +(let ((?x256 (cons$ 3 nil$)))
   1.875 +(let ((?x588 (size$a ?x256)))
   1.876 +(let (($x584 (= ?x588 ?x246)))
   1.877 +(let (($x664 (forall ((?v0 Int) (?v1 Int_list$) )(! (= (size$a (cons$ ?v0 ?v1)) (plus$ (size$a ?v1) (suc$ zero$))) :pattern ( (cons$ ?v0 ?v1) ) :qid k!47))
   1.878 +))
   1.879 +(let (($x119 (forall ((?v0 Int) (?v1 Int_list$) )(! (= (size$a (cons$ ?v0 ?v1)) (plus$ (size$a ?v1) (suc$ zero$))) :qid k!47))
   1.880 +))
   1.881 +(let (($x118 (= (size$a (cons$ ?1 ?0)) (plus$ (size$a ?0) ?x89))))
   1.882 +(let ((@x178 (mp~ (asserted $x119) (nnf-pos (refl (~ $x118 $x118)) (~ $x119 $x119)) $x119)))
   1.883 +(let ((@x669 (mp @x178 (quant-intro (refl (= $x118 $x118)) (= $x119 $x664)) $x664)))
   1.884 +(let (($x231 (or (not $x664) $x584)))
   1.885 +(let ((@x232 ((_ quant-inst 3 nil$) $x231)))
   1.886 +(let ((?x267 (g$a ?x256)))
   1.887 +(let (($x592 (= ?x267 ?x588)))
   1.888 +(let (($x620 (forall ((?v0 Int_list$) )(! (let ((?x67 (size$a ?v0)))
   1.889 +(let ((?x66 (g$a ?v0)))
   1.890 +(= ?x66 ?x67))) :pattern ( (g$a ?v0) ) :pattern ( (size$a ?v0) ) :qid k!39))
   1.891 +))
   1.892 +(let (($x69 (forall ((?v0 Int_list$) )(! (let ((?x67 (size$a ?v0)))
   1.893 +(let ((?x66 (g$a ?v0)))
   1.894 +(= ?x66 ?x67))) :qid k!39))
   1.895 +))
   1.896 +(let ((@x622 (refl (= (= (g$a ?0) (size$a ?0)) (= (g$a ?0) (size$a ?0))))))
   1.897 +(let ((@x129 (nnf-pos (refl (~ (= (g$a ?0) (size$a ?0)) (= (g$a ?0) (size$a ?0)))) (~ $x69 $x69))))
   1.898 +(let ((@x625 (mp (mp~ (asserted $x69) @x129 $x69) (quant-intro @x622 (= $x69 $x620)) $x620)))
   1.899 +(let (($x248 (or (not $x620) $x592)))
   1.900 +(let ((@x585 ((_ quant-inst (cons$ 3 nil$)) $x248)))
   1.901 +(let (($x268 (= ?x123 ?x267)))
   1.902 +(let (($x596 (forall ((?v0 Int) )(! (= (g$ (some$ ?v0)) (g$a (cons$ ?v0 nil$))) :pattern ( (some$ ?v0) ) :pattern ( (cons$ ?v0 nil$) ) :qid k!32))
   1.903 +))
   1.904 +(let (($x34 (forall ((?v0 Int) )(! (= (g$ (some$ ?v0)) (g$a (cons$ ?v0 nil$))) :qid k!32))
   1.905 +))
   1.906 +(let (($x33 (= (g$ (some$ ?0)) (g$a (cons$ ?0 nil$)))))
   1.907 +(let ((@x157 (mp~ (asserted $x34) (nnf-pos (refl (~ $x33 $x33)) (~ $x34 $x34)) $x34)))
   1.908 +(let ((@x601 (mp @x157 (quant-intro (refl (= $x33 $x33)) (= $x34 $x596)) $x596)))
   1.909 +(let (($x250 (or (not $x596) $x268)))
   1.910 +(let ((@x586 ((_ quant-inst 3) $x250)))
   1.911 +(let ((@x275 (trans (unit-resolution @x586 @x601 $x268) (unit-resolution @x585 @x625 $x592) (= ?x123 ?x588))))
   1.912 +(let ((@x280 (trans (trans @x275 (unit-resolution @x232 @x669 $x584) (= ?x123 ?x246)) (symm @x287 (= ?x246 ?x233)) (= ?x123 ?x233))))
   1.913 +(let ((@x558 (trans @x280 (symm (unit-resolution @x213 @x662 $x570) (= ?x233 ?x227)) (= ?x123 ?x227))))
   1.914 +(let ((@x560 (trans @x558 (symm (unit-resolution @x572 @x617 $x569) (= ?x227 ?x270)) (= ?x123 ?x270))))
   1.915 +(let ((@x546 (trans @x560 (symm (unit-resolution @x255 @x609 $x587) (= ?x270 ?x125)) $x126)))
   1.916 +(let (($x127 (not $x126)))
   1.917 +(let ((@x128 (asserted $x127)))
   1.918 +(unit-resolution @x128 @x546 false)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
   1.919 +
   1.920  572677daa32981bf8212986300f1362edf42a0c1 7 0
   1.921  unsat
   1.922  ((set-logic AUFLIA)
   1.923 @@ -37,18 +946,6 @@
   1.924  (let (($x29 (or p$ q$)))
   1.925  (mp (and-elim (not-or-elim @x44 (and $x29 (not p$))) $x29) @x58 false)))))))))))
   1.926  
   1.927 -a021a5fec5486f23204e54770f9c04c64baf7e25 11 0
   1.928 -unsat
   1.929 -((set-logic AUFLIA)
   1.930 -(proof
   1.931 -(let (($x32 (and c$ d$)))
   1.932 -(let (($x29 (and a$ b$)))
   1.933 -(let (($x33 (or $x29 $x32)))
   1.934 -(let (($x34 (=> $x33 $x33)))
   1.935 -(let (($x35 (not $x34)))
   1.936 -(let ((@x45 (trans (monotonicity (rewrite (= $x34 true)) (= $x35 (not true))) (rewrite (= (not true) false)) (= $x35 false))))
   1.937 -(mp (asserted $x35) @x45 false)))))))))
   1.938 -
   1.939  dfb7aeab4f33cdf91b335d72ad619dbd0d65fb62 23 0
   1.940  unsat
   1.941  ((set-logic AUFLIA)
   1.942 @@ -73,6 +970,18 @@
   1.943  (let ((@x58 (monotonicity (trans @x49 (rewrite (= (=> $x31 $x44) $x51)) (= $x37 $x51)) (= $x38 $x56))))
   1.944  (mp (asserted $x38) (trans @x58 @x67 (= $x38 false)) false)))))))))))))))))))))
   1.945  
   1.946 +a021a5fec5486f23204e54770f9c04c64baf7e25 11 0
   1.947 +unsat
   1.948 +((set-logic AUFLIA)
   1.949 +(proof
   1.950 +(let (($x32 (and c$ d$)))
   1.951 +(let (($x29 (and a$ b$)))
   1.952 +(let (($x33 (or $x29 $x32)))
   1.953 +(let (($x34 (=> $x33 $x33)))
   1.954 +(let (($x35 (not $x34)))
   1.955 +(let ((@x45 (trans (monotonicity (rewrite (= $x34 true)) (= $x35 (not true))) (rewrite (= (not true) false)) (= $x35 false))))
   1.956 +(mp (asserted $x35) @x45 false)))))))))
   1.957 +
   1.958  3efca8956be216e9acda1b32436ba8f01358d35e 24 0
   1.959  unsat
   1.960  ((set-logic AUFLIA)
   1.961 @@ -98,6 +1007,34 @@
   1.962  (let ((@x82 (trans (monotonicity @x75 (= $x37 (not true))) (rewrite (= (not true) false)) (= $x37 false))))
   1.963  (mp (asserted $x37) @x82 false))))))))))))))))))))))
   1.964  
   1.965 +143f46ba7acb4b0a8f67b0de474b0a249f30985b 27 0
   1.966 +unsat
   1.967 +((set-logic AUFLIA)
   1.968 +(proof
   1.969 +(let ((?x38 (symm_f$ b$ a$)))
   1.970 +(let ((?x37 (symm_f$ a$ b$)))
   1.971 +(let (($x39 (= ?x37 ?x38)))
   1.972 +(let (($x52 (not $x39)))
   1.973 +(let ((@x47 (monotonicity (rewrite (= (= a$ a$) true)) (= (and (= a$ a$) $x39) (and true $x39)))))
   1.974 +(let ((@x51 (trans @x47 (rewrite (= (and true $x39) $x39)) (= (and (= a$ a$) $x39) $x39))))
   1.975 +(let ((@x57 (mp (asserted (not (and (= a$ a$) $x39))) (monotonicity @x51 (= (not (and (= a$ a$) $x39)) $x52)) $x52)))
   1.976 +(let (($x480 (forall ((?v0 A$) (?v1 A$) )(! (let ((?x30 (symm_f$ ?v1 ?v0)))
   1.977 +(let ((?x29 (symm_f$ ?v0 ?v1)))
   1.978 +(= ?x29 ?x30))) :pattern ( (symm_f$ ?v0 ?v1) ) :pattern ( (symm_f$ ?v1 ?v0) ) :qid k!8))
   1.979 +))
   1.980 +(let (($x32 (forall ((?v0 A$) (?v1 A$) )(! (let ((?x30 (symm_f$ ?v1 ?v0)))
   1.981 +(let ((?x29 (symm_f$ ?v0 ?v1)))
   1.982 +(= ?x29 ?x30))) :qid k!8))
   1.983 +))
   1.984 +(let ((?x30 (symm_f$ ?0 ?1)))
   1.985 +(let ((?x29 (symm_f$ ?1 ?0)))
   1.986 +(let (($x31 (= ?x29 ?x30)))
   1.987 +(let ((@x60 (mp~ (asserted $x32) (nnf-pos (refl (~ $x31 $x31)) (~ $x32 $x32)) $x32)))
   1.988 +(let ((@x485 (mp @x60 (quant-intro (refl (= $x31 $x31)) (= $x32 $x480)) $x480)))
   1.989 +(let (($x149 (or (not $x480) $x39)))
   1.990 +(let ((@x61 ((_ quant-inst a$ b$) $x149)))
   1.991 +(unit-resolution @x61 @x485 @x57 false)))))))))))))))))))
   1.992 +
   1.993  d600888ef4325a32ff87997035fed7a7c01e4767 39 0
   1.994  unsat
   1.995  ((set-logic AUFLIA)
   1.996 @@ -138,34 +1075,6 @@
   1.997  (let ((@x40 (mp (asserted (or a$ (or b$ (or c$ d$)))) (rewrite (= (or a$ (or b$ (or c$ d$))) $x37)) $x37)))
   1.998  (mp @x40 @x202 false)))))))))))))))))))))))))))))))))))))
   1.999  
  1.1000 -143f46ba7acb4b0a8f67b0de474b0a249f30985b 27 0
  1.1001 -unsat
  1.1002 -((set-logic AUFLIA)
  1.1003 -(proof
  1.1004 -(let ((?x38 (symm_f$ b$ a$)))
  1.1005 -(let ((?x37 (symm_f$ a$ b$)))
  1.1006 -(let (($x39 (= ?x37 ?x38)))
  1.1007 -(let (($x52 (not $x39)))
  1.1008 -(let ((@x47 (monotonicity (rewrite (= (= a$ a$) true)) (= (and (= a$ a$) $x39) (and true $x39)))))
  1.1009 -(let ((@x51 (trans @x47 (rewrite (= (and true $x39) $x39)) (= (and (= a$ a$) $x39) $x39))))
  1.1010 -(let ((@x57 (mp (asserted (not (and (= a$ a$) $x39))) (monotonicity @x51 (= (not (and (= a$ a$) $x39)) $x52)) $x52)))
  1.1011 -(let (($x480 (forall ((?v0 A$) (?v1 A$) )(! (let ((?x30 (symm_f$ ?v1 ?v0)))
  1.1012 -(let ((?x29 (symm_f$ ?v0 ?v1)))
  1.1013 -(= ?x29 ?x30))) :pattern ( (symm_f$ ?v0 ?v1) ) :pattern ( (symm_f$ ?v1 ?v0) ) :qid k!8))
  1.1014 -))
  1.1015 -(let (($x32 (forall ((?v0 A$) (?v1 A$) )(! (let ((?x30 (symm_f$ ?v1 ?v0)))
  1.1016 -(let ((?x29 (symm_f$ ?v0 ?v1)))
  1.1017 -(= ?x29 ?x30))) :qid k!8))
  1.1018 -))
  1.1019 -(let ((?x30 (symm_f$ ?0 ?1)))
  1.1020 -(let ((?x29 (symm_f$ ?1 ?0)))
  1.1021 -(let (($x31 (= ?x29 ?x30)))
  1.1022 -(let ((@x60 (mp~ (asserted $x32) (nnf-pos (refl (~ $x31 $x31)) (~ $x32 $x32)) $x32)))
  1.1023 -(let ((@x485 (mp @x60 (quant-intro (refl (= $x31 $x31)) (= $x32 $x480)) $x480)))
  1.1024 -(let (($x149 (or (not $x480) $x39)))
  1.1025 -(let ((@x61 ((_ quant-inst a$ b$) $x149)))
  1.1026 -(unit-resolution @x61 @x485 @x57 false)))))))))))))))))))
  1.1027 -
  1.1028  a6dd135a0c109f49b36d7266dc7a6becc640e496 637 0
  1.1029  unsat
  1.1030  ((set-logic AUFLIA)
  1.1031 @@ -1033,6 +1942,19 @@
  1.1032  (let ((@x59 (trans @x55 (rewrite (= (not true) false)) (= (not (< 5 (ite (<= 3 8) 8 3))) false))))
  1.1033  (mp (asserted (not (< 5 (ite (<= 3 8) 8 3)))) @x59 false)))))))))
  1.1034  
  1.1035 +c4e20de399740e8f0c9a87abad030298d74bc47b 12 0
  1.1036 +unsat
  1.1037 +((set-logic AUFLIA)
  1.1038 +(proof
  1.1039 +(let ((?x31 (p$ true)))
  1.1040 +(let (($x29 (< 2 3)))
  1.1041 +(let ((?x30 (p$ $x29)))
  1.1042 +(let (($x32 (= ?x30 ?x31)))
  1.1043 +(let ((@x42 (monotonicity (monotonicity (rewrite (= $x29 true)) $x32) (= $x32 (= ?x31 ?x31)))))
  1.1044 +(let ((@x49 (monotonicity (trans @x42 (rewrite (= (= ?x31 ?x31) true)) (= $x32 true)) (= (not $x32) (not true)))))
  1.1045 +(let ((@x53 (trans @x49 (rewrite (= (not true) false)) (= (not $x32) false))))
  1.1046 +(mp (asserted (not $x32)) @x53 false))))))))))
  1.1047 +
  1.1048  6b0b089fbe179e8a27509c818f9a5e6847ac6bf2 88 0
  1.1049  unsat
  1.1050  ((set-logic AUFLIRA)
  1.1051 @@ -1122,23 +2044,6 @@
  1.1052  (let ((@x234 (unit-resolution @x136 (unit-resolution @x138 (lemma @x231 (not $x134)) $x83) $x133)))
  1.1053  ((_ th-lemma arith farkas -2 1 -1 -1 1) (unit-resolution @x138 (lemma @x231 (not $x134)) $x83) @x221 @x126 @x226 (unit-resolution @x159 @x234 $x149) false))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
  1.1054  
  1.1055 -bc11d479eb44aa63c2efc812af856ec331477415 16 0
  1.1056 -unsat
  1.1057 -((set-logic AUFLIA)
  1.1058 -(proof
  1.1059 -(let ((?x32 (p$ true)))
  1.1060 -(let (($x29 (< 2 3)))
  1.1061 -(let (($x30 (ite $x29 true false)))
  1.1062 -(let ((?x31 (p$ $x30)))
  1.1063 -(let (($x33 (= ?x31 ?x32)))
  1.1064 -(let (($x34 (not $x33)))
  1.1065 -(let ((@x52 (monotonicity (monotonicity (rewrite (= $x29 true)) (= (p$ $x29) ?x32)) (= (= (p$ $x29) ?x32) (= ?x32 ?x32)))))
  1.1066 -(let ((@x56 (trans @x52 (rewrite (= (= ?x32 ?x32) true)) (= (= (p$ $x29) ?x32) true))))
  1.1067 -(let ((@x63 (trans (monotonicity @x56 (= (not (= (p$ $x29) ?x32)) (not true))) (rewrite (= (not true) false)) (= (not (= (p$ $x29) ?x32)) false))))
  1.1068 -(let ((@x43 (monotonicity (monotonicity (rewrite (= $x30 $x29)) (= ?x31 (p$ $x29))) (= $x33 (= (p$ $x29) ?x32)))))
  1.1069 -(let ((@x46 (monotonicity @x43 (= $x34 (not (= (p$ $x29) ?x32))))))
  1.1070 -(mp (asserted $x34) (trans @x46 @x63 (= $x34 false)) false))))))))))))))
  1.1071 -
  1.1072  d63ee5062f9a1d0a0bd17f51adaa0ac5e8f9ec16 16 0
  1.1073  unsat
  1.1074  ((set-logic AUFLIA)
  1.1075 @@ -1230,166 +2135,6 @@
  1.1076  (let ((@x67 (mp (asserted (not (< a$ 0.0))) @x66 $x58)))
  1.1077  ((_ th-lemma arith farkas 7 3/2 1) @x67 @x52 @x40 false)))))))))))))))))
  1.1078  
  1.1079 -7d3773a9d63ce2ada82ac001b84291cdc85d7ab8 159 0
  1.1080 -unsat
  1.1081 -((set-logic AUFLIA)
  1.1082 -(proof
  1.1083 -(let (($x44 (= m$ n$)))
  1.1084 -(let ((@x480 (symm (commutativity (= $x44 (= n$ m$))) (= (= n$ m$) $x44))))
  1.1085 -(let (($x40 (= n$ m$)))
  1.1086 -(let ((?x102 (* (- 1) m$)))
  1.1087 -(let ((?x103 (+ n$ ?x102)))
  1.1088 -(let (($x118 (>= ?x103 0)))
  1.1089 -(let ((?x78 (* (- 1) n$a)))
  1.1090 -(let ((?x96 (+ m$ ?x78)))
  1.1091 -(let (($x127 (<= ?x96 0)))
  1.1092 -(let ((?x79 (+ n$ ?x78)))
  1.1093 -(let (($x88 (>= ?x79 0)))
  1.1094 -(let (($x239 (or $x88 $x127)))
  1.1095 -(let ((@x251 (monotonicity (rewrite (= (and (not $x88) (not $x127)) (not $x239))) (= (not (and (not $x88) (not $x127))) (not (not $x239))))))
  1.1096 -(let ((@x271 (trans @x251 (rewrite (= (not (not $x239)) $x239)) (= (not (and (not $x88) (not $x127))) $x239))))
  1.1097 -(let (($x128 (not $x127)))
  1.1098 -(let (($x87 (not $x88)))
  1.1099 -(let (($x143 (and $x87 $x128)))
  1.1100 -(let (($x210 (not $x143)))
  1.1101 -(let (($x50 (= n$a m$)))
  1.1102 -(let (($x57 (and $x50 $x44)))
  1.1103 -(let (($x80 (<= ?x79 0)))
  1.1104 -(let (($x81 (not $x80)))
  1.1105 -(let (($x33 (= m$ n$a)))
  1.1106 -(let (($x84 (and $x33 $x81)))
  1.1107 -(let (($x91 (and $x44 $x87)))
  1.1108 -(let (($x95 (>= ?x96 0)))
  1.1109 -(let (($x94 (not $x95)))
  1.1110 -(let (($x99 (and $x94 $x81)))
  1.1111 -(let (($x48 (= n$a n$)))
  1.1112 -(let (($x104 (<= ?x103 0)))
  1.1113 -(let (($x105 (not $x104)))
  1.1114 -(let (($x108 (and $x105 $x48)))
  1.1115 -(let (($x111 (and $x105 $x87)))
  1.1116 -(let (($x114 (and $x50 $x105)))
  1.1117 -(let (($x117 (not $x118)))
  1.1118 -(let (($x121 (and $x48 $x117)))
  1.1119 -(let (($x124 (and $x81 $x117)))
  1.1120 -(let (($x131 (and $x128 $x44)))
  1.1121 -(let (($x134 (and $x128 $x105)))
  1.1122 -(let (($x137 (and $x40 $x94)))
  1.1123 -(let (($x38 (= n$ n$a)))
  1.1124 -(let (($x140 (and $x38 $x128)))
  1.1125 -(let (($x146 (and $x117 $x33)))
  1.1126 -(let (($x149 (and $x117 $x94)))
  1.1127 -(let (($x197 (or $x149 $x146 $x143 $x140 $x137 $x134 $x131 $x124 $x121 $x114 $x111 $x108 $x99 $x91 $x84 $x57)))
  1.1128 -(let (($x60 (or (and (< m$ n$a) (< n$a n$)) (or (and $x44 (< n$ n$a)) (or (and $x33 (< n$a n$)) $x57)))))
  1.1129 -(let (($x62 (or (and (< m$ n$) (< n$ n$a)) (or (and (< m$ n$) $x48) $x60))))
  1.1130 -(let (($x65 (or (and (< n$a n$) (< n$ m$)) (or (and $x48 (< n$ m$)) (or (and $x50 (< m$ n$)) $x62)))))
  1.1131 -(let (($x67 (or (and (< n$a m$) (< m$ n$)) (or (and (< n$a m$) $x44) $x65))))
  1.1132 -(let (($x70 (or (and (< n$ n$a) (< n$a m$)) (or (and $x38 (< n$a m$)) (or (and $x40 (< m$ n$a)) $x67)))))
  1.1133 -(let (($x72 (or (and (< n$ m$) (< m$ n$a)) (or (and (< n$ m$) $x33) $x70))))
  1.1134 -(let (($x73 (not $x72)))
  1.1135 -(let (($x170 (or $x121 (or $x114 (or $x111 (or $x108 (or $x99 (or $x91 (or $x84 $x57)))))))))
  1.1136 -(let (($x191 (or $x146 (or $x143 (or $x140 (or $x137 (or $x134 (or $x131 (or $x124 $x170)))))))))
  1.1137 -(let (($x189 (= $x70 (or $x143 (or $x140 (or $x137 (or $x134 (or $x131 (or $x124 $x170)))))))))
  1.1138 -(let (($x186 (= (or (and $x38 (< n$a m$)) (or (and $x40 (< m$ n$a)) $x67)) (or $x140 (or $x137 (or $x134 (or $x131 (or $x124 $x170))))))))
  1.1139 -(let (($x183 (= (or (and $x40 (< m$ n$a)) $x67) (or $x137 (or $x134 (or $x131 (or $x124 $x170)))))))
  1.1140 -(let (($x171 (= (or (and $x48 (< n$ m$)) (or (and $x50 (< m$ n$)) $x62)) $x170)))
  1.1141 -(let (($x168 (= (or (and $x50 (< m$ n$)) $x62) (or $x114 (or $x111 (or $x108 (or $x99 (or $x91 (or $x84 $x57)))))))))
  1.1142 -(let (($x162 (= (or (and (< m$ n$) $x48) $x60) (or $x108 (or $x99 (or $x91 (or $x84 $x57)))))))
  1.1143 -(let (($x156 (= (or (and $x44 (< n$ n$a)) (or (and $x33 (< n$a n$)) $x57)) (or $x91 (or $x84 $x57)))))
  1.1144 -(let ((@x83 (rewrite (= (< n$a n$) $x81))))
  1.1145 -(let ((@x154 (monotonicity (monotonicity @x83 (= (and $x33 (< n$a n$)) $x84)) (= (or (and $x33 (< n$a n$)) $x57) (or $x84 $x57)))))
  1.1146 -(let ((@x90 (rewrite (= (< n$ n$a) $x87))))
  1.1147 -(let ((@x157 (monotonicity (monotonicity @x90 (= (and $x44 (< n$ n$a)) $x91)) @x154 $x156)))
  1.1148 -(let ((@x98 (rewrite (= (< m$ n$a) $x94))))
  1.1149 -(let ((@x101 (monotonicity @x98 @x83 (= (and (< m$ n$a) (< n$a n$)) $x99))))
  1.1150 -(let ((@x160 (monotonicity @x101 @x157 (= $x60 (or $x99 (or $x91 (or $x84 $x57)))))))
  1.1151 -(let ((@x107 (rewrite (= (< m$ n$) $x105))))
  1.1152 -(let ((@x163 (monotonicity (monotonicity @x107 (= (and (< m$ n$) $x48) $x108)) @x160 $x162)))
  1.1153 -(let ((@x113 (monotonicity @x107 @x90 (= (and (< m$ n$) (< n$ n$a)) $x111))))
  1.1154 -(let ((@x166 (monotonicity @x113 @x163 (= $x62 (or $x111 (or $x108 (or $x99 (or $x91 (or $x84 $x57)))))))))
  1.1155 -(let ((@x169 (monotonicity (monotonicity @x107 (= (and $x50 (< m$ n$)) $x114)) @x166 $x168)))
  1.1156 -(let ((@x120 (rewrite (= (< n$ m$) $x117))))
  1.1157 -(let ((@x172 (monotonicity (monotonicity @x120 (= (and $x48 (< n$ m$)) $x121)) @x169 $x171)))
  1.1158 -(let ((@x126 (monotonicity @x83 @x120 (= (and (< n$a n$) (< n$ m$)) $x124))))
  1.1159 -(let ((@x130 (rewrite (= (< n$a m$) $x128))))
  1.1160 -(let ((@x178 (monotonicity (monotonicity @x130 (= (and (< n$a m$) $x44) $x131)) (monotonicity @x126 @x172 (= $x65 (or $x124 $x170))) (= (or (and (< n$a m$) $x44) $x65) (or $x131 (or $x124 $x170))))))
  1.1161 -(let ((@x136 (monotonicity @x130 @x107 (= (and (< n$a m$) (< m$ n$)) $x134))))
  1.1162 -(let ((@x181 (monotonicity @x136 @x178 (= $x67 (or $x134 (or $x131 (or $x124 $x170)))))))
  1.1163 -(let ((@x184 (monotonicity (monotonicity @x98 (= (and $x40 (< m$ n$a)) $x137)) @x181 $x183)))
  1.1164 -(let ((@x187 (monotonicity (monotonicity @x130 (= (and $x38 (< n$a m$)) $x140)) @x184 $x186)))
  1.1165 -(let ((@x145 (monotonicity @x90 @x130 (= (and (< n$ n$a) (< n$a m$)) $x143))))
  1.1166 -(let ((@x193 (monotonicity (monotonicity @x120 (= (and (< n$ m$) $x33) $x146)) (monotonicity @x145 @x187 $x189) (= (or (and (< n$ m$) $x33) $x70) $x191))))
  1.1167 -(let ((@x151 (monotonicity @x120 @x98 (= (and (< n$ m$) (< m$ n$a)) $x149))))
  1.1168 -(let ((@x201 (trans (monotonicity @x151 @x193 (= $x72 (or $x149 $x191))) (rewrite (= (or $x149 $x191) $x197)) (= $x72 $x197))))
  1.1169 -(let ((@x205 (mp (asserted $x73) (monotonicity @x201 (= $x73 (not $x197))) (not $x197))))
  1.1170 -(let ((@x272 (mp (not-or-elim @x205 $x210) @x271 $x239)))
  1.1171 -(let (($x273 (not $x38)))
  1.1172 -(let (($x274 (or $x273 $x127)))
  1.1173 -(let ((@x280 (monotonicity (rewrite (= $x140 (not $x274))) (= (not $x140) (not (not $x274))))))
  1.1174 -(let ((@x284 (trans @x280 (rewrite (= (not (not $x274)) $x274)) (= (not $x140) $x274))))
  1.1175 -(let ((@x285 (mp (not-or-elim @x205 (not $x140)) @x284 $x274)))
  1.1176 -(let (($x286 (not $x40)))
  1.1177 -(let (($x311 (not $x44)))
  1.1178 -(let ((@x434 (hypothesis $x81)))
  1.1179 -(let (($x386 (or $x95 $x80)))
  1.1180 -(let ((@x392 (monotonicity (rewrite (= $x99 (not $x386))) (= (not $x99) (not (not $x386))))))
  1.1181 -(let ((@x396 (trans @x392 (rewrite (= (not (not $x386)) $x386)) (= (not $x99) $x386))))
  1.1182 -(let ((@x397 (mp (not-or-elim @x205 (not $x99)) @x396 $x386)))
  1.1183 -(let (($x246 (not $x33)))
  1.1184 -(let (($x410 (or $x246 $x80)))
  1.1185 -(let ((@x416 (monotonicity (rewrite (= $x84 (not $x410))) (= (not $x84) (not (not $x410))))))
  1.1186 -(let ((@x420 (trans @x416 (rewrite (= (not (not $x410)) $x410)) (= (not $x84) $x410))))
  1.1187 -(let ((@x421 (mp (not-or-elim @x205 (not $x84)) @x420 $x410)))
  1.1188 -(let ((@x439 ((_ th-lemma arith triangle-eq) (or $x33 $x128 $x94))))
  1.1189 -(let ((@x440 (unit-resolution @x439 (unit-resolution @x421 @x434 $x246) (unit-resolution @x397 @x434 $x95) $x128)))
  1.1190 -(let (($x312 (or $x127 $x311)))
  1.1191 -(let ((@x318 (monotonicity (rewrite (= $x131 (not $x312))) (= (not $x131) (not (not $x312))))))
  1.1192 -(let ((@x322 (trans @x318 (rewrite (= (not (not $x312)) $x312)) (= (not $x131) $x312))))
  1.1193 -(let ((@x323 (mp (not-or-elim @x205 (not $x131)) @x322 $x312)))
  1.1194 -(let ((@x450 (mp (unit-resolution @x323 @x440 $x311) (monotonicity (commutativity (= $x44 $x40)) (= $x311 $x286)) $x286)))
  1.1195 -(let (($x324 (or $x80 $x118)))
  1.1196 -(let ((@x330 (monotonicity (rewrite (= $x124 (not $x324))) (= (not $x124) (not (not $x324))))))
  1.1197 -(let ((@x334 (trans @x330 (rewrite (= (not (not $x324)) $x324)) (= (not $x124) $x324))))
  1.1198 -(let ((@x335 (mp (not-or-elim @x205 (not $x124)) @x334 $x324)))
  1.1199 -(let (($x299 (or $x127 $x104)))
  1.1200 -(let ((@x305 (monotonicity (rewrite (= $x134 (not $x299))) (= (not $x134) (not (not $x299))))))
  1.1201 -(let ((@x309 (trans @x305 (rewrite (= (not (not $x299)) $x299)) (= (not $x134) $x299))))
  1.1202 -(let ((@x310 (mp (not-or-elim @x205 (not $x134)) @x309 $x299)))
  1.1203 -(let ((@x444 (unit-resolution ((_ th-lemma arith triangle-eq) (or $x40 $x105 $x117)) (unit-resolution @x310 @x440 $x104) (unit-resolution @x335 @x434 $x118) $x40)))
  1.1204 -(let ((@x459 (unit-resolution ((_ th-lemma arith triangle-eq) (or $x38 $x81 $x87)) (lemma (unit-resolution @x444 @x450 false) $x80) (or $x38 $x87))))
  1.1205 -(let ((@x460 (unit-resolution @x459 (unit-resolution @x285 (hypothesis $x128) $x273) (unit-resolution @x272 (hypothesis $x128) $x88) false)))
  1.1206 -(let ((@x461 (lemma @x460 $x127)))
  1.1207 -(let (($x254 (or $x118 $x95)))
  1.1208 -(let ((@x262 (monotonicity (rewrite (= $x149 (not $x254))) (= (not $x149) (not (not $x254))))))
  1.1209 -(let ((@x256 (trans @x262 (rewrite (= (not (not $x254)) $x254)) (= (not $x149) $x254))))
  1.1210 -(let ((@x257 (mp (not-or-elim @x205 (not $x149)) @x256 $x254)))
  1.1211 -(let (($x247 (or $x118 $x246)))
  1.1212 -(let ((@x259 (monotonicity (rewrite (= $x146 (not $x247))) (= (not $x146) (not (not $x247))))))
  1.1213 -(let ((@x245 (trans @x259 (rewrite (= (not (not $x247)) $x247)) (= (not $x146) $x247))))
  1.1214 -(let ((@x238 (mp (not-or-elim @x205 (not $x146)) @x245 $x247)))
  1.1215 -(let ((@x465 (unit-resolution @x439 (unit-resolution @x238 (hypothesis $x117) $x246) (unit-resolution @x257 (hypothesis $x117) $x95) @x461 false)))
  1.1216 -(let (($x336 (not $x48)))
  1.1217 -(let (($x374 (or $x104 $x336)))
  1.1218 -(let ((@x380 (monotonicity (rewrite (= $x108 (not $x374))) (= (not $x108) (not (not $x374))))))
  1.1219 -(let ((@x384 (trans @x380 (rewrite (= (not (not $x374)) $x374)) (= (not $x108) $x374))))
  1.1220 -(let ((@x385 (mp (not-or-elim @x205 (not $x108)) @x384 $x374)))
  1.1221 -(let ((@x475 (mp (unit-resolution @x385 (hypothesis $x105) $x336) (monotonicity (commutativity (= $x48 $x38)) (= $x336 $x273)) $x273)))
  1.1222 -(let (($x362 (or $x104 $x88)))
  1.1223 -(let ((@x368 (monotonicity (rewrite (= $x111 (not $x362))) (= (not $x111) (not (not $x362))))))
  1.1224 -(let ((@x372 (trans @x368 (rewrite (= (not (not $x362)) $x362)) (= (not $x111) $x362))))
  1.1225 -(let ((@x373 (mp (not-or-elim @x205 (not $x111)) @x372 $x362)))
  1.1226 -(let ((@x469 (unit-resolution @x459 (unit-resolution @x373 (hypothesis $x105) $x88) $x38)))
  1.1227 -(let ((@x478 (unit-resolution ((_ th-lemma arith triangle-eq) (or $x40 $x105 $x117)) (lemma (unit-resolution @x469 @x475 false) $x104) (lemma @x465 $x118) $x40)))
  1.1228 -(let (($x287 (or $x286 $x95)))
  1.1229 -(let ((@x293 (monotonicity (rewrite (= $x137 (not $x287))) (= (not $x137) (not (not $x287))))))
  1.1230 -(let ((@x297 (trans @x293 (rewrite (= (not (not $x287)) $x287)) (= (not $x137) $x287))))
  1.1231 -(let ((@x298 (mp (not-or-elim @x205 (not $x137)) @x297 $x287)))
  1.1232 -(let ((@x488 (mp (unit-resolution @x439 (unit-resolution @x298 @x478 $x95) @x461 $x33) (symm (commutativity (= $x50 $x33)) (= $x33 $x50)) $x50)))
  1.1233 -(let (($x422 (or (not $x50) $x311)))
  1.1234 -(let ((@x428 (monotonicity (rewrite (= $x57 (not $x422))) (= (not $x57) (not (not $x422))))))
  1.1235 -(let ((@x432 (trans @x428 (rewrite (= (not (not $x422)) $x422)) (= (not $x57) $x422))))
  1.1236 -(let ((@x433 (mp (not-or-elim @x205 (not $x57)) @x432 $x422)))
  1.1237 -(unit-resolution @x433 @x488 (mp @x478 @x480 $x44) false)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
  1.1238 -
  1.1239  32286f9c5e71eb2b15c18f86f04c80931e2e307b 878 0
  1.1240  unsat
  1.1241  ((set-logic AUFLIA)
  1.1242 @@ -2290,13 +3035,173 @@
  1.1243  (let ((@x62 (monotonicity @x59 (= $x36 (not $x43)))))
  1.1244  (mp (asserted $x36) (trans @x62 @x71 (= $x36 false)) false))))))))))))))))))
  1.1245  
  1.1246 -faae12ee7efe4347f92e42776a0e0e57a624319c 113 0
  1.1247 +7d3773a9d63ce2ada82ac001b84291cdc85d7ab8 159 0
  1.1248 +unsat
  1.1249 +((set-logic AUFLIA)
  1.1250 +(proof
  1.1251 +(let (($x44 (= m$ n$)))
  1.1252 +(let ((@x480 (symm (commutativity (= $x44 (= n$ m$))) (= (= n$ m$) $x44))))
  1.1253 +(let (($x40 (= n$ m$)))
  1.1254 +(let ((?x102 (* (- 1) m$)))
  1.1255 +(let ((?x103 (+ n$ ?x102)))
  1.1256 +(let (($x118 (>= ?x103 0)))
  1.1257 +(let ((?x78 (* (- 1) n$a)))
  1.1258 +(let ((?x96 (+ m$ ?x78)))
  1.1259 +(let (($x127 (<= ?x96 0)))
  1.1260 +(let ((?x79 (+ n$ ?x78)))
  1.1261 +(let (($x88 (>= ?x79 0)))
  1.1262 +(let (($x239 (or $x88 $x127)))
  1.1263 +(let ((@x251 (monotonicity (rewrite (= (and (not $x88) (not $x127)) (not $x239))) (= (not (and (not $x88) (not $x127))) (not (not $x239))))))
  1.1264 +(let ((@x271 (trans @x251 (rewrite (= (not (not $x239)) $x239)) (= (not (and (not $x88) (not $x127))) $x239))))
  1.1265 +(let (($x128 (not $x127)))
  1.1266 +(let (($x87 (not $x88)))
  1.1267 +(let (($x143 (and $x87 $x128)))
  1.1268 +(let (($x210 (not $x143)))
  1.1269 +(let (($x50 (= n$a m$)))
  1.1270 +(let (($x57 (and $x50 $x44)))
  1.1271 +(let (($x80 (<= ?x79 0)))
  1.1272 +(let (($x81 (not $x80)))
  1.1273 +(let (($x33 (= m$ n$a)))
  1.1274 +(let (($x84 (and $x33 $x81)))
  1.1275 +(let (($x91 (and $x44 $x87)))
  1.1276 +(let (($x95 (>= ?x96 0)))
  1.1277 +(let (($x94 (not $x95)))
  1.1278 +(let (($x99 (and $x94 $x81)))
  1.1279 +(let (($x48 (= n$a n$)))
  1.1280 +(let (($x104 (<= ?x103 0)))
  1.1281 +(let (($x105 (not $x104)))
  1.1282 +(let (($x108 (and $x105 $x48)))
  1.1283 +(let (($x111 (and $x105 $x87)))
  1.1284 +(let (($x114 (and $x50 $x105)))
  1.1285 +(let (($x117 (not $x118)))
  1.1286 +(let (($x121 (and $x48 $x117)))
  1.1287 +(let (($x124 (and $x81 $x117)))
  1.1288 +(let (($x131 (and $x128 $x44)))
  1.1289 +(let (($x134 (and $x128 $x105)))
  1.1290 +(let (($x137 (and $x40 $x94)))
  1.1291 +(let (($x38 (= n$ n$a)))
  1.1292 +(let (($x140 (and $x38 $x128)))
  1.1293 +(let (($x146 (and $x117 $x33)))
  1.1294 +(let (($x149 (and $x117 $x94)))
  1.1295 +(let (($x197 (or $x149 $x146 $x143 $x140 $x137 $x134 $x131 $x124 $x121 $x114 $x111 $x108 $x99 $x91 $x84 $x57)))
  1.1296 +(let (($x60 (or (and (< m$ n$a) (< n$a n$)) (or (and $x44 (< n$ n$a)) (or (and $x33 (< n$a n$)) $x57)))))
  1.1297 +(let (($x62 (or (and (< m$ n$) (< n$ n$a)) (or (and (< m$ n$) $x48) $x60))))
  1.1298 +(let (($x65 (or (and (< n$a n$) (< n$ m$)) (or (and $x48 (< n$ m$)) (or (and $x50 (< m$ n$)) $x62)))))
  1.1299 +(let (($x67 (or (and (< n$a m$) (< m$ n$)) (or (and (< n$a m$) $x44) $x65))))
  1.1300 +(let (($x70 (or (and (< n$ n$a) (< n$a m$)) (or (and $x38 (< n$a m$)) (or (and $x40 (< m$ n$a)) $x67)))))
  1.1301 +(let (($x72 (or (and (< n$ m$) (< m$ n$a)) (or (and (< n$ m$) $x33) $x70))))
  1.1302 +(let (($x73 (not $x72)))
  1.1303 +(let (($x170 (or $x121 (or $x114 (or $x111 (or $x108 (or $x99 (or $x91 (or $x84 $x57)))))))))
  1.1304 +(let (($x191 (or $x146 (or $x143 (or $x140 (or $x137 (or $x134 (or $x131 (or $x124 $x170)))))))))
  1.1305 +(let (($x189 (= $x70 (or $x143 (or $x140 (or $x137 (or $x134 (or $x131 (or $x124 $x170)))))))))
  1.1306 +(let (($x186 (= (or (and $x38 (< n$a m$)) (or (and $x40 (< m$ n$a)) $x67)) (or $x140 (or $x137 (or $x134 (or $x131 (or $x124 $x170))))))))
  1.1307 +(let (($x183 (= (or (and $x40 (< m$ n$a)) $x67) (or $x137 (or $x134 (or $x131 (or $x124 $x170)))))))
  1.1308 +(let (($x171 (= (or (and $x48 (< n$ m$)) (or (and $x50 (< m$ n$)) $x62)) $x170)))
  1.1309 +(let (($x168 (= (or (and $x50 (< m$ n$)) $x62) (or $x114 (or $x111 (or $x108 (or $x99 (or $x91 (or $x84 $x57)))))))))
  1.1310 +(let (($x162 (= (or (and (< m$ n$) $x48) $x60) (or $x108 (or $x99 (or $x91 (or $x84 $x57)))))))
  1.1311 +(let (($x156 (= (or (and $x44 (< n$ n$a)) (or (and $x33 (< n$a n$)) $x57)) (or $x91 (or $x84 $x57)))))
  1.1312 +(let ((@x83 (rewrite (= (< n$a n$) $x81))))
  1.1313 +(let ((@x154 (monotonicity (monotonicity @x83 (= (and $x33 (< n$a n$)) $x84)) (= (or (and $x33 (< n$a n$)) $x57) (or $x84 $x57)))))
  1.1314 +(let ((@x90 (rewrite (= (< n$ n$a) $x87))))
  1.1315 +(let ((@x157 (monotonicity (monotonicity @x90 (= (and $x44 (< n$ n$a)) $x91)) @x154 $x156)))
  1.1316 +(let ((@x98 (rewrite (= (< m$ n$a) $x94))))
  1.1317 +(let ((@x101 (monotonicity @x98 @x83 (= (and (< m$ n$a) (< n$a n$)) $x99))))
  1.1318 +(let ((@x160 (monotonicity @x101 @x157 (= $x60 (or $x99 (or $x91 (or $x84 $x57)))))))
  1.1319 +(let ((@x107 (rewrite (= (< m$ n$) $x105))))
  1.1320 +(let ((@x163 (monotonicity (monotonicity @x107 (= (and (< m$ n$) $x48) $x108)) @x160 $x162)))
  1.1321 +(let ((@x113 (monotonicity @x107 @x90 (= (and (< m$ n$) (< n$ n$a)) $x111))))
  1.1322 +(let ((@x166 (monotonicity @x113 @x163 (= $x62 (or $x111 (or $x108 (or $x99 (or $x91 (or $x84 $x57)))))))))
  1.1323 +(let ((@x169 (monotonicity (monotonicity @x107 (= (and $x50 (< m$ n$)) $x114)) @x166 $x168)))
  1.1324 +(let ((@x120 (rewrite (= (< n$ m$) $x117))))
  1.1325 +(let ((@x172 (monotonicity (monotonicity @x120 (= (and $x48 (< n$ m$)) $x121)) @x169 $x171)))
  1.1326 +(let ((@x126 (monotonicity @x83 @x120 (= (and (< n$a n$) (< n$ m$)) $x124))))
  1.1327 +(let ((@x130 (rewrite (= (< n$a m$) $x128))))
  1.1328 +(let ((@x178 (monotonicity (monotonicity @x130 (= (and (< n$a m$) $x44) $x131)) (monotonicity @x126 @x172 (= $x65 (or $x124 $x170))) (= (or (and (< n$a m$) $x44) $x65) (or $x131 (or $x124 $x170))))))
  1.1329 +(let ((@x136 (monotonicity @x130 @x107 (= (and (< n$a m$) (< m$ n$)) $x134))))
  1.1330 +(let ((@x181 (monotonicity @x136 @x178 (= $x67 (or $x134 (or $x131 (or $x124 $x170)))))))
  1.1331 +(let ((@x184 (monotonicity (monotonicity @x98 (= (and $x40 (< m$ n$a)) $x137)) @x181 $x183)))
  1.1332 +(let ((@x187 (monotonicity (monotonicity @x130 (= (and $x38 (< n$a m$)) $x140)) @x184 $x186)))
  1.1333 +(let ((@x145 (monotonicity @x90 @x130 (= (and (< n$ n$a) (< n$a m$)) $x143))))
  1.1334 +(let ((@x193 (monotonicity (monotonicity @x120 (= (and (< n$ m$) $x33) $x146)) (monotonicity @x145 @x187 $x189) (= (or (and (< n$ m$) $x33) $x70) $x191))))
  1.1335 +(let ((@x151 (monotonicity @x120 @x98 (= (and (< n$ m$) (< m$ n$a)) $x149))))
  1.1336 +(let ((@x201 (trans (monotonicity @x151 @x193 (= $x72 (or $x149 $x191))) (rewrite (= (or $x149 $x191) $x197)) (= $x72 $x197))))
  1.1337 +(let ((@x205 (mp (asserted $x73) (monotonicity @x201 (= $x73 (not $x197))) (not $x197))))
  1.1338 +(let ((@x272 (mp (not-or-elim @x205 $x210) @x271 $x239)))
  1.1339 +(let (($x273 (not $x38)))
  1.1340 +(let (($x274 (or $x273 $x127)))
  1.1341 +(let ((@x280 (monotonicity (rewrite (= $x140 (not $x274))) (= (not $x140) (not (not $x274))))))
  1.1342 +(let ((@x284 (trans @x280 (rewrite (= (not (not $x274)) $x274)) (= (not $x140) $x274))))
  1.1343 +(let ((@x285 (mp (not-or-elim @x205 (not $x140)) @x284 $x274)))
  1.1344 +(let (($x286 (not $x40)))
  1.1345 +(let (($x311 (not $x44)))
  1.1346 +(let ((@x434 (hypothesis $x81)))
  1.1347 +(let (($x386 (or $x95 $x80)))
  1.1348 +(let ((@x392 (monotonicity (rewrite (= $x99 (not $x386))) (= (not $x99) (not (not $x386))))))
  1.1349 +(let ((@x396 (trans @x392 (rewrite (= (not (not $x386)) $x386)) (= (not $x99) $x386))))
  1.1350 +(let ((@x397 (mp (not-or-elim @x205 (not $x99)) @x396 $x386)))
  1.1351 +(let (($x246 (not $x33)))
  1.1352 +(let (($x410 (or $x246 $x80)))
  1.1353 +(let ((@x416 (monotonicity (rewrite (= $x84 (not $x410))) (= (not $x84) (not (not $x410))))))
  1.1354 +(let ((@x420 (trans @x416 (rewrite (= (not (not $x410)) $x410)) (= (not $x84) $x410))))
  1.1355 +(let ((@x421 (mp (not-or-elim @x205 (not $x84)) @x420 $x410)))
  1.1356 +(let ((@x439 ((_ th-lemma arith triangle-eq) (or $x33 $x128 $x94))))
  1.1357 +(let ((@x440 (unit-resolution @x439 (unit-resolution @x421 @x434 $x246) (unit-resolution @x397 @x434 $x95) $x128)))
  1.1358 +(let (($x312 (or $x127 $x311)))
  1.1359 +(let ((@x318 (monotonicity (rewrite (= $x131 (not $x312))) (= (not $x131) (not (not $x312))))))
  1.1360 +(let ((@x322 (trans @x318 (rewrite (= (not (not $x312)) $x312)) (= (not $x131) $x312))))
  1.1361 +(let ((@x323 (mp (not-or-elim @x205 (not $x131)) @x322 $x312)))
  1.1362 +(let ((@x450 (mp (unit-resolution @x323 @x440 $x311) (monotonicity (commutativity (= $x44 $x40)) (= $x311 $x286)) $x286)))
  1.1363 +(let (($x324 (or $x80 $x118)))
  1.1364 +(let ((@x330 (monotonicity (rewrite (= $x124 (not $x324))) (= (not $x124) (not (not $x324))))))
  1.1365 +(let ((@x334 (trans @x330 (rewrite (= (not (not $x324)) $x324)) (= (not $x124) $x324))))
  1.1366 +(let ((@x335 (mp (not-or-elim @x205 (not $x124)) @x334 $x324)))
  1.1367 +(let (($x299 (or $x127 $x104)))
  1.1368 +(let ((@x305 (monotonicity (rewrite (= $x134 (not $x299))) (= (not $x134) (not (not $x299))))))
  1.1369 +(let ((@x309 (trans @x305 (rewrite (= (not (not $x299)) $x299)) (= (not $x134) $x299))))
  1.1370 +(let ((@x310 (mp (not-or-elim @x205 (not $x134)) @x309 $x299)))
  1.1371 +(let ((@x444 (unit-resolution ((_ th-lemma arith triangle-eq) (or $x40 $x105 $x117)) (unit-resolution @x310 @x440 $x104) (unit-resolution @x335 @x434 $x118) $x40)))
  1.1372 +(let ((@x459 (unit-resolution ((_ th-lemma arith triangle-eq) (or $x38 $x81 $x87)) (lemma (unit-resolution @x444 @x450 false) $x80) (or $x38 $x87))))
  1.1373 +(let ((@x460 (unit-resolution @x459 (unit-resolution @x285 (hypothesis $x128) $x273) (unit-resolution @x272 (hypothesis $x128) $x88) false)))
  1.1374 +(let ((@x461 (lemma @x460 $x127)))
  1.1375 +(let (($x254 (or $x118 $x95)))
  1.1376 +(let ((@x262 (monotonicity (rewrite (= $x149 (not $x254))) (= (not $x149) (not (not $x254))))))
  1.1377 +(let ((@x256 (trans @x262 (rewrite (= (not (not $x254)) $x254)) (= (not $x149) $x254))))
  1.1378 +(let ((@x257 (mp (not-or-elim @x205 (not $x149)) @x256 $x254)))
  1.1379 +(let (($x247 (or $x118 $x246)))
  1.1380 +(let ((@x259 (monotonicity (rewrite (= $x146 (not $x247))) (= (not $x146) (not (not $x247))))))
  1.1381 +(let ((@x245 (trans @x259 (rewrite (= (not (not $x247)) $x247)) (= (not $x146) $x247))))
  1.1382 +(let ((@x238 (mp (not-or-elim @x205 (not $x146)) @x245 $x247)))
  1.1383 +(let ((@x465 (unit-resolution @x439 (unit-resolution @x238 (hypothesis $x117) $x246) (unit-resolution @x257 (hypothesis $x117) $x95) @x461 false)))
  1.1384 +(let (($x336 (not $x48)))
  1.1385 +(let (($x374 (or $x104 $x336)))
  1.1386 +(let ((@x380 (monotonicity (rewrite (= $x108 (not $x374))) (= (not $x108) (not (not $x374))))))
  1.1387 +(let ((@x384 (trans @x380 (rewrite (= (not (not $x374)) $x374)) (= (not $x108) $x374))))
  1.1388 +(let ((@x385 (mp (not-or-elim @x205 (not $x108)) @x384 $x374)))
  1.1389 +(let ((@x475 (mp (unit-resolution @x385 (hypothesis $x105) $x336) (monotonicity (commutativity (= $x48 $x38)) (= $x336 $x273)) $x273)))
  1.1390 +(let (($x362 (or $x104 $x88)))
  1.1391 +(let ((@x368 (monotonicity (rewrite (= $x111 (not $x362))) (= (not $x111) (not (not $x362))))))
  1.1392 +(let ((@x372 (trans @x368 (rewrite (= (not (not $x362)) $x362)) (= (not $x111) $x362))))
  1.1393 +(let ((@x373 (mp (not-or-elim @x205 (not $x111)) @x372 $x362)))
  1.1394 +(let ((@x469 (unit-resolution @x459 (unit-resolution @x373 (hypothesis $x105) $x88) $x38)))
  1.1395 +(let ((@x478 (unit-resolution ((_ th-lemma arith triangle-eq) (or $x40 $x105 $x117)) (lemma (unit-resolution @x469 @x475 false) $x104) (lemma @x465 $x118) $x40)))
  1.1396 +(let (($x287 (or $x286 $x95)))
  1.1397 +(let ((@x293 (monotonicity (rewrite (= $x137 (not $x287))) (= (not $x137) (not (not $x287))))))
  1.1398 +(let ((@x297 (trans @x293 (rewrite (= (not (not $x287)) $x287)) (= (not $x137) $x287))))
  1.1399 +(let ((@x298 (mp (not-or-elim @x205 (not $x137)) @x297 $x287)))
  1.1400 +(let ((@x488 (mp (unit-resolution @x439 (unit-resolution @x298 @x478 $x95) @x461 $x33) (symm (commutativity (= $x50 $x33)) (= $x33 $x50)) $x50)))
  1.1401 +(let (($x422 (or (not $x50) $x311)))
  1.1402 +(let ((@x428 (monotonicity (rewrite (= $x57 (not $x422))) (= (not $x57) (not (not $x422))))))
  1.1403 +(let ((@x432 (trans @x428 (rewrite (= (not (not $x422)) $x422)) (= (not $x57) $x422))))
  1.1404 +(let ((@x433 (mp (not-or-elim @x205 (not $x57)) @x432 $x422)))
  1.1405 +(unit-resolution @x433 @x488 (mp @x478 @x480 $x44) false)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
  1.1406 +
  1.1407 +0b997744cf42fde45b98a34c933b0698332e657f 113 0
  1.1408  unsat
  1.1409  ((set-logic <null>)
  1.1410  (proof
  1.1411  (let ((?x228 (mod x$ 2)))
  1.1412  (let ((?x262 (* (- 1) ?x228)))
  1.1413 -(let ((?x31 (mod$ x$ 2)))
  1.1414 +(let ((?x31 (modulo$ x$ 2)))
  1.1415  (let ((?x263 (+ ?x31 ?x262)))
  1.1416  (let (($x280 (>= ?x263 0)))
  1.1417  (let (($x264 (= ?x263 0)))
  1.1418 @@ -2309,8 +3214,8 @@
  1.1419  (let ((?x170 (ite $x111 ?x150 ?x136)))
  1.1420  (let (($x78 (= ?v1 0)))
  1.1421  (let ((?x175 (ite $x78 ?v0 ?x170)))
  1.1422 -(let ((?x135 (mod$ ?v0 ?v1)))
  1.1423 -(= ?x135 ?x175))))))))))) :pattern ( (mod$ ?v0 ?v1) ) :qid k!9))
  1.1424 +(let ((?x135 (modulo$ ?v0 ?v1)))
  1.1425 +(= ?x135 ?x175))))))))))) :pattern ( (modulo$ ?v0 ?v1) ) :qid k!9))
  1.1426  ))
  1.1427  (let (($x181 (forall ((?v0 Int) (?v1 Int) )(! (let ((?x136 (mod ?v0 ?v1)))
  1.1428  (let ((?x93 (* (- 1) ?v1)))
  1.1429 @@ -2321,7 +3226,7 @@
  1.1430  (let ((?x170 (ite $x111 ?x150 ?x136)))
  1.1431  (let (($x78 (= ?v1 0)))
  1.1432  (let ((?x175 (ite $x78 ?v0 ?x170)))
  1.1433 -(let ((?x135 (mod$ ?v0 ?v1)))
  1.1434 +(let ((?x135 (modulo$ ?v0 ?v1)))
  1.1435  (= ?x135 ?x175))))))))))) :qid k!9))
  1.1436  ))
  1.1437  (let ((?x136 (mod ?1 ?0)))
  1.1438 @@ -2333,11 +3238,11 @@
  1.1439  (let ((?x170 (ite $x111 ?x150 ?x136)))
  1.1440  (let (($x78 (= ?0 0)))
  1.1441  (let ((?x175 (ite $x78 ?1 ?x170)))
  1.1442 -(let ((?x135 (mod$ ?1 ?0)))
  1.1443 +(let ((?x135 (modulo$ ?1 ?0)))
  1.1444  (let (($x178 (= ?x135 ?x175)))
  1.1445  (let (($x142 (forall ((?v0 Int) (?v1 Int) )(! (let (($x78 (= ?v1 0)))
  1.1446  (let ((?x140 (ite $x78 ?v0 (ite (< 0 ?v1) (mod ?v0 ?v1) (- (mod (- ?v0) (- ?v1)))))))
  1.1447 -(let ((?x135 (mod$ ?v0 ?v1)))
  1.1448 +(let ((?x135 (modulo$ ?v0 ?v1)))
  1.1449  (= ?x135 ?x140)))) :qid k!9))
  1.1450  ))
  1.1451  (let (($x164 (forall ((?v0 Int) (?v1 Int) )(! (let ((?x93 (* (- 1) ?v1)))
  1.1452 @@ -2349,7 +3254,7 @@
  1.1453  (let ((?x155 (ite $x79 ?x136 ?x150)))
  1.1454  (let (($x78 (= ?v1 0)))
  1.1455  (let ((?x158 (ite $x78 ?v0 ?x155)))
  1.1456 -(let ((?x135 (mod$ ?v0 ?v1)))
  1.1457 +(let ((?x135 (modulo$ ?v0 ?v1)))
  1.1458  (= ?x135 ?x158))))))))))) :qid k!9))
  1.1459  ))
  1.1460  (let ((@x169 (monotonicity (rewrite (= (< 0 ?0) (not $x111))) (= (ite (< 0 ?0) ?x136 ?x150) (ite (not $x111) ?x136 ?x150)))))
  1.1461 @@ -2404,7 +3309,7 @@
  1.1462  (let ((@x74 (mp (asserted $x36) @x73 $x67)))
  1.1463  ((_ th-lemma arith farkas -1 1 1) @x74 (unit-resolution ((_ th-lemma arith) (or false $x305)) (true-axiom true) $x305) @x332 false))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
  1.1464  
  1.1465 -57f344c9e787868c98d1e622f158c445c1899c96 112 0
  1.1466 +2e67f9e254b2a35a9d35027c6e63de01bc5086bd 112 0
  1.1467  unsat
  1.1468  ((set-logic <null>)
  1.1469  (proof
  1.1470 @@ -2412,7 +3317,7 @@
  1.1471  (let (($x318 (>= ?x224 2)))
  1.1472  (let (($x319 (not $x318)))
  1.1473  (let ((?x258 (* (- 1) ?x224)))
  1.1474 -(let ((?x29 (mod$ x$ 2)))
  1.1475 +(let ((?x29 (modulo$ x$ 2)))
  1.1476  (let ((?x259 (+ ?x29 ?x258)))
  1.1477  (let (($x275 (<= ?x259 0)))
  1.1478  (let (($x260 (= ?x259 0)))
  1.1479 @@ -2425,8 +3330,8 @@
  1.1480  (let ((?x166 (ite $x107 ?x146 ?x132)))
  1.1481  (let (($x74 (= ?v1 0)))
  1.1482  (let ((?x171 (ite $x74 ?v0 ?x166)))
  1.1483 -(let ((?x131 (mod$ ?v0 ?v1)))
  1.1484 -(= ?x131 ?x171))))))))))) :pattern ( (mod$ ?v0 ?v1) ) :qid k!9))
  1.1485 +(let ((?x131 (modulo$ ?v0 ?v1)))
  1.1486 +(= ?x131 ?x171))))))))))) :pattern ( (modulo$ ?v0 ?v1) ) :qid k!9))
  1.1487  ))
  1.1488  (let (($x177 (forall ((?v0 Int) (?v1 Int) )(! (let ((?x132 (mod ?v0 ?v1)))
  1.1489  (let ((?x89 (* (- 1) ?v1)))
  1.1490 @@ -2437,7 +3342,7 @@
  1.1491  (let ((?x166 (ite $x107 ?x146 ?x132)))
  1.1492  (let (($x74 (= ?v1 0)))
  1.1493  (let ((?x171 (ite $x74 ?v0 ?x166)))
  1.1494 -(let ((?x131 (mod$ ?v0 ?v1)))
  1.1495 +(let ((?x131 (modulo$ ?v0 ?v1)))
  1.1496  (= ?x131 ?x171))))))))))) :qid k!9))
  1.1497  ))
  1.1498  (let ((?x132 (mod ?1 ?0)))
  1.1499 @@ -2449,11 +3354,11 @@
  1.1500  (let ((?x166 (ite $x107 ?x146 ?x132)))
  1.1501  (let (($x74 (= ?0 0)))
  1.1502  (let ((?x171 (ite $x74 ?1 ?x166)))
  1.1503 -(let ((?x131 (mod$ ?1 ?0)))
  1.1504 +(let ((?x131 (modulo$ ?1 ?0)))
  1.1505  (let (($x174 (= ?x131 ?x171)))
  1.1506  (let (($x138 (forall ((?v0 Int) (?v1 Int) )(! (let (($x74 (= ?v1 0)))
  1.1507  (let ((?x136 (ite $x74 ?v0 (ite (< 0 ?v1) (mod ?v0 ?v1) (- (mod (- ?v0) (- ?v1)))))))
  1.1508 -(let ((?x131 (mod$ ?v0 ?v1)))
  1.1509 +(let ((?x131 (modulo$ ?v0 ?v1)))
  1.1510  (= ?x131 ?x136)))) :qid k!9))
  1.1511  ))
  1.1512  (let (($x160 (forall ((?v0 Int) (?v1 Int) )(! (let ((?x89 (* (- 1) ?v1)))
  1.1513 @@ -2465,7 +3370,7 @@
  1.1514  (let ((?x151 (ite $x75 ?x132 ?x146)))
  1.1515  (let (($x74 (= ?v1 0)))
  1.1516  (let ((?x154 (ite $x74 ?v0 ?x151)))
  1.1517 -(let ((?x131 (mod$ ?v0 ?v1)))
  1.1518 +(let ((?x131 (modulo$ ?v0 ?v1)))
  1.1519  (= ?x131 ?x154))))))))))) :qid k!9))
  1.1520  ))
  1.1521  (let ((@x165 (monotonicity (rewrite (= (< 0 ?0) (not $x107))) (= (ite (< 0 ?0) ?x132 ?x146) (ite (not $x107) ?x132 ?x146)))))
  1.1522 @@ -3399,3733 +4304,133 @@
  1.1523  (let ((@x152 (trans (monotonicity @x145 (= $x52 (not true))) (rewrite (= (not true) false)) (= $x52 false))))
  1.1524  (mp (asserted $x52) @x152 false)))))))))))))))))))))))))))))))))))))))))))))))))
  1.1525  
  1.1526 -5e90e9139eb4e9a7c2678bca8dda6cda05861f4c 23 0
  1.1527 -unsat
  1.1528 -((set-logic AUFLIA)
  1.1529 -(proof
  1.1530 -(let (($x40 (= x$ a$)))
  1.1531 -(let ((?x36 (pair$ x$ y$)))
  1.1532 -(let ((?x37 (fst$ ?x36)))
  1.1533 -(let (($x39 (= ?x37 a$)))
  1.1534 -(let ((@x50 (monotonicity (rewrite (= (=> $x39 $x40) (or (not $x39) $x40))) (= (not (=> $x39 $x40)) (not (or (not $x39) $x40))))))
  1.1535 -(let ((@x51 (not-or-elim (mp (asserted (not (=> $x39 $x40))) @x50 (not (or (not $x39) $x40))) $x39)))
  1.1536 -(let (($x56 (= ?x37 x$)))
  1.1537 -(let (($x478 (forall ((?v0 A$) (?v1 B$) )(! (= (fst$ (pair$ ?v0 ?v1)) ?v0) :pattern ( (pair$ ?v0 ?v1) ) :qid k!12))
  1.1538 -))
  1.1539 -(let (($x32 (forall ((?v0 A$) (?v1 B$) )(! (= (fst$ (pair$ ?v0 ?v1)) ?v0) :qid k!12))
  1.1540 -))
  1.1541 -(let (($x31 (= (fst$ (pair$ ?1 ?0)) ?1)))
  1.1542 -(let ((@x55 (mp~ (asserted $x32) (nnf-pos (refl (~ $x31 $x31)) (~ $x32 $x32)) $x32)))
  1.1543 -(let ((@x483 (mp @x55 (quant-intro (refl (= $x31 $x31)) (= $x32 $x478)) $x478)))
  1.1544 -(let (($x62 (or (not $x478) $x56)))
  1.1545 -(let ((@x149 ((_ quant-inst x$ y$) $x62)))
  1.1546 -(let ((@x150 (trans (symm (unit-resolution @x149 @x483 $x56) (= x$ ?x37)) @x51 $x40)))
  1.1547 -(let ((@x54 (not-or-elim (mp (asserted (not (=> $x39 $x40))) @x50 (not (or (not $x39) $x40))) (not $x40))))
  1.1548 -(unit-resolution @x54 @x150 false)))))))))))))))))))
  1.1549 -
  1.1550 -53d3d89ffb6e574b15fcea58a111b4eecba9beb5 42 0
  1.1551 -unsat
  1.1552 -((set-logic AUFLIA)
  1.1553 -(proof
  1.1554 -(let ((?x59 (snd$a p2$)))
  1.1555 -(let ((?x58 (fst$a p1$)))
  1.1556 -(let (($x60 (= ?x58 ?x59)))
  1.1557 -(let ((?x55 (pair$ y$ x$)))
  1.1558 -(let (($x56 (= p2$ ?x55)))
  1.1559 -(let ((?x52 (pair$a x$ y$)))
  1.1560 -(let (($x53 (= p1$ ?x52)))
  1.1561 -(let (($x57 (and $x53 $x56)))
  1.1562 -(let ((@x70 (monotonicity (rewrite (= (=> $x57 $x60) (or (not $x57) $x60))) (= (not (=> $x57 $x60)) (not (or (not $x57) $x60))))))
  1.1563 -(let ((@x71 (not-or-elim (mp (asserted (not (=> $x57 $x60))) @x70 (not (or (not $x57) $x60))) $x57)))
  1.1564 -(let ((@x74 (and-elim @x71 $x56)))
  1.1565 -(let ((@x504 (symm (monotonicity @x74 (= ?x59 (snd$a ?x55))) (= (snd$a ?x55) ?x59))))
  1.1566 -(let ((?x100 (snd$a ?x55)))
  1.1567 -(let (($x185 (= ?x100 x$)))
  1.1568 -(let (($x534 (forall ((?v0 B$) (?v1 A$) )(! (= (snd$a (pair$ ?v0 ?v1)) ?v1) :pattern ( (pair$ ?v0 ?v1) ) :qid k!21))
  1.1569 -))
  1.1570 -(let (($x47 (forall ((?v0 B$) (?v1 A$) )(! (= (snd$a (pair$ ?v0 ?v1)) ?v1) :qid k!21))
  1.1571 -))
  1.1572 -(let (($x46 (= (snd$a (pair$ ?1 ?0)) ?0)))
  1.1573 -(let ((@x96 (mp~ (asserted $x47) (nnf-pos (refl (~ $x46 $x46)) (~ $x47 $x47)) $x47)))
  1.1574 -(let ((@x539 (mp @x96 (quant-intro (refl (= $x46 $x46)) (= $x47 $x534)) $x534)))
  1.1575 -(let (($x190 (or (not $x534) $x185)))
  1.1576 -(let ((@x191 ((_ quant-inst y$ x$) $x190)))
  1.1577 -(let ((?x187 (fst$a ?x52)))
  1.1578 -(let (($x188 (= ?x187 x$)))
  1.1579 -(let (($x522 (forall ((?v0 A$) (?v1 B$) )(! (= (fst$a (pair$a ?v0 ?v1)) ?v0) :pattern ( (pair$a ?v0 ?v1) ) :qid k!19))
  1.1580 -))
  1.1581 -(let (($x39 (forall ((?v0 A$) (?v1 B$) )(! (= (fst$a (pair$a ?v0 ?v1)) ?v0) :qid k!19))
  1.1582 -))
  1.1583 -(let (($x38 (= (fst$a (pair$a ?1 ?0)) ?1)))
  1.1584 -(let ((@x90 (mp~ (asserted $x39) (nnf-pos (refl (~ $x38 $x38)) (~ $x39 $x39)) $x39)))
  1.1585 -(let ((@x527 (mp @x90 (quant-intro (refl (= $x38 $x38)) (= $x39 $x522)) $x522)))
  1.1586 -(let (($x162 (or (not $x522) $x188)))
  1.1587 -(let ((@x292 ((_ quant-inst x$ y$) $x162)))
  1.1588 -(let ((@x505 (trans (monotonicity (and-elim @x71 $x53) (= ?x58 ?x187)) (unit-resolution @x292 @x527 $x188) (= ?x58 x$))))
  1.1589 -(let ((@x489 (trans @x505 (symm (unit-resolution @x191 @x539 $x185) (= x$ ?x100)) (= ?x58 ?x100))))
  1.1590 -(let ((@x76 (not-or-elim (mp (asserted (not (=> $x57 $x60))) @x70 (not (or (not $x57) $x60))) (not $x60))))
  1.1591 -(unit-resolution @x76 (trans @x489 @x504 $x60) false))))))))))))))))))))))))))))))))))))
  1.1592 -
  1.1593 -f501ac3814a9ff559897f8057e18657ad1030d2a 60 0
  1.1594 -unsat
  1.1595 -((set-logic AUFLIA)
  1.1596 -(proof
  1.1597 -(let ((?x69 (fun_app$ f$ i$)))
  1.1598 -(let ((?x60 (fun_upd$ f$)))
  1.1599 -(let ((?x61 (fun_app$b ?x60 i1$)))
  1.1600 -(let ((?x63 (fun_app$a ?x61 v1$)))
  1.1601 -(let ((?x64 (fun_upd$ ?x63)))
  1.1602 -(let ((?x65 (fun_app$b ?x64 i2$)))
  1.1603 -(let ((?x67 (fun_app$a ?x65 v2$)))
  1.1604 -(let ((?x68 (fun_app$ ?x67 i$)))
  1.1605 -(let (($x70 (= ?x68 ?x69)))
  1.1606 -(let ((?x197 (fun_app$ ?x63 i$)))
  1.1607 -(let (($x205 (= ?x197 ?x69)))
  1.1608 -(let (($x204 (= ?x197 v1$)))
  1.1609 -(let (($x53 (= i$ i1$)))
  1.1610 -(let (($x484 (ite $x53 $x204 $x205)))
  1.1611 -(let (($x531 (forall ((?v0 A_b_fun$) (?v1 A$) (?v2 B$) (?v3 A$) )(! (let ((?x46 (fun_app$ ?v0 ?v3)))
  1.1612 -(let ((?x44 (fun_app$ (fun_app$a (fun_app$b (fun_upd$ ?v0) ?v1) ?v2) ?v3)))
  1.1613 -(let (($x45 (= ?v3 ?v1)))
  1.1614 -(ite $x45 (= ?x44 ?v2) (= ?x44 ?x46))))) :pattern ( (fun_app$ (fun_app$a (fun_app$b (fun_upd$ ?v0) ?v1) ?v2) ?v3) ) :qid k!20))
  1.1615 -))
  1.1616 -(let (($x102 (forall ((?v0 A_b_fun$) (?v1 A$) (?v2 B$) (?v3 A$) )(! (let ((?x46 (fun_app$ ?v0 ?v3)))
  1.1617 -(let ((?x44 (fun_app$ (fun_app$a (fun_app$b (fun_upd$ ?v0) ?v1) ?v2) ?v3)))
  1.1618 -(let (($x45 (= ?v3 ?v1)))
  1.1619 -(ite $x45 (= ?x44 ?v2) (= ?x44 ?x46))))) :qid k!20))
  1.1620 -))
  1.1621 -(let ((?x46 (fun_app$ ?3 ?0)))
  1.1622 -(let ((?x44 (fun_app$ (fun_app$a (fun_app$b (fun_upd$ ?3) ?2) ?1) ?0)))
  1.1623 -(let (($x45 (= ?0 ?2)))
  1.1624 -(let (($x97 (ite $x45 (= ?x44 ?1) (= ?x44 ?x46))))
  1.1625 -(let (($x49 (forall ((?v0 A_b_fun$) (?v1 A$) (?v2 B$) (?v3 A$) )(! (let ((?x44 (fun_app$ (fun_app$a (fun_app$b (fun_upd$ ?v0) ?v1) ?v2) ?v3)))
  1.1626 -(= ?x44 (ite (= ?v3 ?v1) ?v2 (fun_app$ ?v0 ?v3)))) :qid k!20))
  1.1627 -))
  1.1628 -(let ((@x104 (quant-intro (rewrite (= (= ?x44 (ite $x45 ?1 ?x46)) $x97)) (= $x49 $x102))))
  1.1629 -(let ((@x91 (refl (~ (= ?x44 (ite $x45 ?1 ?x46)) (= ?x44 (ite $x45 ?1 ?x46))))))
  1.1630 -(let ((@x105 (mp (mp~ (asserted $x49) (nnf-pos @x91 (~ $x49 $x49)) $x49) @x104 $x102)))
  1.1631 -(let ((@x536 (mp @x105 (quant-intro (refl (= $x97 $x97)) (= $x102 $x531)) $x531)))
  1.1632 -(let (($x171 (not $x531)))
  1.1633 -(let (($x486 (or $x171 $x484)))
  1.1634 -(let ((@x487 ((_ quant-inst f$ i1$ v1$ i$) $x486)))
  1.1635 -(let (($x54 (not $x53)))
  1.1636 -(let (($x56 (= i$ i2$)))
  1.1637 -(let (($x57 (not $x56)))
  1.1638 -(let (($x58 (and $x54 $x57)))
  1.1639 -(let ((@x80 (monotonicity (rewrite (= (=> $x58 $x70) (or (not $x58) $x70))) (= (not (=> $x58 $x70)) (not (or (not $x58) $x70))))))
  1.1640 -(let ((@x81 (not-or-elim (mp (asserted (not (=> $x58 $x70))) @x80 (not (or (not $x58) $x70))) $x58)))
  1.1641 -(let ((@x82 (and-elim @x81 $x54)))
  1.1642 -(let ((@x321 (unit-resolution (def-axiom (or (not $x484) $x53 $x205)) @x82 (or (not $x484) $x205))))
  1.1643 -(let (($x200 (= ?x68 ?x197)))
  1.1644 -(let (($x196 (= ?x68 v2$)))
  1.1645 -(let (($x179 (ite $x56 $x196 $x200)))
  1.1646 -(let (($x301 (or $x171 $x179)))
  1.1647 -(let ((@x511 ((_ quant-inst (fun_app$a ?x61 v1$) i2$ v2$ i$) $x301)))
  1.1648 -(let ((@x84 (and-elim @x81 $x57)))
  1.1649 -(let ((@x466 (unit-resolution (def-axiom (or (not $x179) $x56 $x200)) @x84 (or (not $x179) $x200))))
  1.1650 -(let ((@x470 (trans (unit-resolution @x466 (unit-resolution @x511 @x536 $x179) $x200) (unit-resolution @x321 (unit-resolution @x487 @x536 $x484) $x205) $x70)))
  1.1651 -(let ((@x86 (not-or-elim (mp (asserted (not (=> $x58 $x70))) @x80 (not (or (not $x58) $x70))) (not $x70))))
  1.1652 -(unit-resolution @x86 @x470 false))))))))))))))))))))))))))))))))))))))))))))))))
  1.1653 -
  1.1654 -541ab286f481dab3994e7cef5aa3ab01f0d6487a 24 0
  1.1655 -unsat
  1.1656 -((set-logic AUFLIA)
  1.1657 -(proof
  1.1658 -(let (($x29 (f$ g$ x$)))
  1.1659 -(let (($x73 (not $x29)))
  1.1660 -(let (($x65 (not (or (= $x29 (fun_app$ g$ x$)) $x29 (fun_app$ g$ x$)))))
  1.1661 -(let (($x32 (= $x29 (and (fun_app$ g$ x$) true))))
  1.1662 -(let (($x37 (not (or $x32 (or (= $x29 true) (= (fun_app$ g$ x$) true))))))
  1.1663 -(let (($x30 (fun_app$ g$ x$)))
  1.1664 -(let (($x44 (= $x29 $x30)))
  1.1665 -(let (($x56 (or $x44 (or $x29 $x30))))
  1.1666 -(let ((@x67 (monotonicity (rewrite (= $x56 (or $x44 $x29 $x30))) (= (not $x56) $x65))))
  1.1667 -(let ((@x55 (monotonicity (rewrite (= (= $x29 true) $x29)) (rewrite (= (= $x30 true) $x30)) (= (or (= $x29 true) (= $x30 true)) (or $x29 $x30)))))
  1.1668 -(let ((@x43 (monotonicity (rewrite (= (and $x30 true) $x30)) (= $x32 (= $x29 $x30)))))
  1.1669 -(let ((@x58 (monotonicity (trans @x43 (rewrite (= (= $x29 $x30) $x44)) (= $x32 $x44)) @x55 (= (or $x32 (or (= $x29 true) (= $x30 true))) $x56))))
  1.1670 -(let ((@x69 (trans (monotonicity @x58 (= $x37 (not $x56))) @x67 (= $x37 $x65))))
  1.1671 -(let ((@x70 (mp (asserted $x37) @x69 $x65)))
  1.1672 -(let ((@x87 (monotonicity (iff-false (not-or-elim @x70 (not $x30)) (= $x30 false)) (= (= $x73 $x30) (= $x73 false)))))
  1.1673 -(let ((@x91 (trans @x87 (rewrite (= (= $x73 false) $x29)) (= (= $x73 $x30) $x29))))
  1.1674 -(let ((@x93 (trans @x91 (iff-false (not-or-elim @x70 $x73) (= $x29 false)) (= (= $x73 $x30) false))))
  1.1675 -(let (($x77 (= $x73 $x30)))
  1.1676 -(let ((@x80 (mp (not-or-elim @x70 (not $x44)) (rewrite (= (not $x44) $x77)) $x77)))
  1.1677 -(mp @x80 @x93 false))))))))))))))))))))))
  1.1678 -
  1.1679 -c6761b6a026c6bf2d28c35e9faf633fc441c84c5 45 0
  1.1680 -unsat
  1.1681 -((set-logic AUFLIA)
  1.1682 -(proof
  1.1683 -(let ((?x44 (id$ x$)))
  1.1684 -(let (($x46 (= ?x44 x$)))
  1.1685 -(let (($x73 (not $x46)))
  1.1686 -(let (($x47 (id$a true)))
  1.1687 -(let (($x510 (forall ((?v0 Bool) )(! (let (($x33 (id$a ?v0)))
  1.1688 -(= $x33 ?v0)) :pattern ( (id$a ?v0) ) :qid k!9))
  1.1689 -))
  1.1690 -(let (($x40 (forall ((?v0 Bool) )(! (let (($x33 (id$a ?v0)))
  1.1691 -(= $x33 ?v0)) :qid k!9))
  1.1692 -))
  1.1693 -(let ((@x514 (quant-intro (refl (= (= (id$a ?0) ?0) (= (id$a ?0) ?0))) (= $x40 $x510))))
  1.1694 -(let ((@x69 (nnf-pos (refl (~ (= (id$a ?0) ?0) (= (id$a ?0) ?0))) (~ $x40 $x40))))
  1.1695 -(let (($x35 (forall ((?v0 Bool) )(! (let (($x33 (id$a ?v0)))
  1.1696 -(= $x33 ?v0)) :qid k!9))
  1.1697 -))
  1.1698 -(let ((@x42 (quant-intro (rewrite (= (= (id$a ?0) ?0) (= (id$a ?0) ?0))) (= $x35 $x40))))
  1.1699 -(let ((@x515 (mp (mp~ (mp (asserted $x35) @x42 $x40) @x69 $x40) @x514 $x510)))
  1.1700 -(let (($x87 (or (not $x510) $x47)))
  1.1701 -(let ((@x176 (monotonicity (rewrite (= (= $x47 true) $x47)) (= (or (not $x510) (= $x47 true)) $x87))))
  1.1702 -(let ((@x179 (trans @x176 (rewrite (= $x87 $x87)) (= (or (not $x510) (= $x47 true)) $x87))))
  1.1703 -(let ((@x495 (unit-resolution (mp ((_ quant-inst true) (or (not $x510) (= $x47 true))) @x179 $x87) @x515 (hypothesis (not $x47)) false)))
  1.1704 -(let (($x71 (or $x73 (not $x47))))
  1.1705 -(let ((@x79 (monotonicity (rewrite (= (and $x46 $x47) (not $x71))) (= (not (and $x46 $x47)) (not (not $x71))))))
  1.1706 -(let ((@x83 (trans @x79 (rewrite (= (not (not $x71)) $x71)) (= (not (and $x46 $x47)) $x71))))
  1.1707 -(let (($x54 (and $x46 $x47)))
  1.1708 -(let (($x57 (not $x54)))
  1.1709 -(let ((@x56 (monotonicity (rewrite (= (= $x47 true) $x47)) (= (and $x46 (= $x47 true)) $x54))))
  1.1710 -(let ((@x62 (mp (asserted (not (and $x46 (= $x47 true)))) (monotonicity @x56 (= (not (and $x46 (= $x47 true))) $x57)) $x57)))
  1.1711 -(let ((@x84 (mp @x62 @x83 $x71)))
  1.1712 -(let (($x503 (forall ((?v0 A$) )(! (let ((?x28 (id$ ?v0)))
  1.1713 -(= ?x28 ?v0)) :pattern ( (id$ ?v0) ) :qid k!8))
  1.1714 -))
  1.1715 -(let (($x30 (forall ((?v0 A$) )(! (let ((?x28 (id$ ?v0)))
  1.1716 -(= ?x28 ?v0)) :qid k!8))
  1.1717 -))
  1.1718 -(let ((@x507 (quant-intro (refl (= (= (id$ ?0) ?0) (= (id$ ?0) ?0))) (= $x30 $x503))))
  1.1719 -(let ((@x64 (nnf-pos (refl (~ (= (id$ ?0) ?0) (= (id$ ?0) ?0))) (~ $x30 $x30))))
  1.1720 -(let ((@x508 (mp (mp~ (asserted $x30) @x64 $x30) @x507 $x503)))
  1.1721 -(let (($x163 (or (not $x503) $x46)))
  1.1722 -(let ((@x496 ((_ quant-inst x$) $x163)))
  1.1723 -(unit-resolution @x496 @x508 (unit-resolution @x84 (lemma @x495 $x47) $x73) false)))))))))))))))))))))))))))))))))
  1.1724 -
  1.1725 -50e0d27d5994794dc9d5826e8afa4b3217acf731 14 0
  1.1726 -unsat
  1.1727 -((set-logic AUFLIA)
  1.1728 -(proof
  1.1729 -(let (($x29 (exists ((?v0 A$) )(! (g$ ?v0) :qid k!7))
  1.1730 -))
  1.1731 -(let (($x30 (ite $x29 true false)))
  1.1732 -(let (($x31 (f$ $x30)))
  1.1733 -(let (($x32 (=> $x31 true)))
  1.1734 -(let (($x33 (not $x32)))
  1.1735 -(let ((@x42 (monotonicity (monotonicity (rewrite (= $x30 $x29)) (= $x31 (f$ $x29))) (= $x32 (=> (f$ $x29) true)))))
  1.1736 -(let ((@x46 (trans @x42 (rewrite (= (=> (f$ $x29) true) true)) (= $x32 true))))
  1.1737 -(let ((@x53 (trans (monotonicity @x46 (= $x33 (not true))) (rewrite (= (not true) false)) (= $x33 false))))
  1.1738 -(mp (asserted $x33) @x53 false)))))))))))
  1.1739 -
  1.1740 -8b09776b03122aeacc9dd9526e1f0e5d41a07f14 14 0
  1.1741 -unsat
  1.1742 -((set-logic AUFLIA)
  1.1743 -(proof
  1.1744 -(let (($x29 (forall ((?v0 A$) )(! (g$ ?v0) :qid k!7))
  1.1745 -))
  1.1746 -(let (($x30 (ite $x29 true false)))
  1.1747 -(let (($x31 (f$ $x30)))
  1.1748 -(let (($x32 (=> $x31 true)))
  1.1749 -(let (($x33 (not $x32)))
  1.1750 -(let ((@x42 (monotonicity (monotonicity (rewrite (= $x30 $x29)) (= $x31 (f$ $x29))) (= $x32 (=> (f$ $x29) true)))))
  1.1751 -(let ((@x46 (trans @x42 (rewrite (= (=> (f$ $x29) true) true)) (= $x32 true))))
  1.1752 -(let ((@x53 (trans (monotonicity @x46 (= $x33 (not true))) (rewrite (= (not true) false)) (= $x33 false))))
  1.1753 -(mp (asserted $x33) @x53 false)))))))))))
  1.1754 -
  1.1755 -feaa6ef662dd489cf55f86209489c2992ff08d28 46 0
  1.1756 -unsat
  1.1757 -((set-logic AUFLIA)
  1.1758 -(proof
  1.1759 -(let ((?x61 (fun_app$a le$ 3)))
  1.1760 -(let (($x63 (fun_app$ ?x61 42)))
  1.1761 -(let (($x75 (not $x63)))
  1.1762 -(let (($x59 (= le$ uu$)))
  1.1763 -(let ((@x73 (monotonicity (rewrite (= (=> $x59 $x63) (or (not $x59) $x63))) (= (not (=> $x59 $x63)) (not (or (not $x59) $x63))))))
  1.1764 -(let ((@x74 (not-or-elim (mp (asserted (not (=> $x59 $x63))) @x73 (not (or (not $x59) $x63))) $x59)))
  1.1765 -(let ((@x482 (monotonicity (symm @x74 (= uu$ le$)) (= (fun_app$a uu$ 3) ?x61))))
  1.1766 -(let ((@x484 (symm (monotonicity @x482 (= (fun_app$ (fun_app$a uu$ 3) 42) $x63)) (= $x63 (fun_app$ (fun_app$a uu$ 3) 42)))))
  1.1767 -(let ((@x472 (monotonicity @x484 (= $x75 (not (fun_app$ (fun_app$a uu$ 3) 42))))))
  1.1768 -(let ((@x77 (not-or-elim (mp (asserted (not (=> $x59 $x63))) @x73 (not (or (not $x59) $x63))) $x75)))
  1.1769 -(let ((?x79 (fun_app$a uu$ 3)))
  1.1770 -(let (($x168 (fun_app$ ?x79 42)))
  1.1771 -(let (($x52 (forall ((?v0 Int) (?v1 Int) )(! (let (($x46 (<= (+ ?v0 (* (- 1) ?v1)) 0)))
  1.1772 -(let (($x31 (fun_app$ (fun_app$a uu$ ?v0) ?v1)))
  1.1773 -(= $x31 $x46))) :pattern ( (fun_app$ (fun_app$a uu$ ?v0) ?v1) ) :qid k!10))
  1.1774 -))
  1.1775 -(let (($x46 (<= (+ ?1 (* (- 1) ?0)) 0)))
  1.1776 -(let (($x31 (fun_app$ (fun_app$a uu$ ?1) ?0)))
  1.1777 -(let (($x49 (= $x31 $x46)))
  1.1778 -(let (($x35 (forall ((?v0 Int) (?v1 Int) )(! (let (($x32 (<= ?v0 ?v1)))
  1.1779 -(let (($x31 (fun_app$ (fun_app$a uu$ ?v0) ?v1)))
  1.1780 -(= $x31 $x32))) :pattern ( (fun_app$ (fun_app$a uu$ ?v0) ?v1) ) :qid k!10))
  1.1781 -))
  1.1782 -(let (($x40 (forall ((?v0 Int) (?v1 Int) )(! (let (($x32 (<= ?v0 ?v1)))
  1.1783 -(let (($x31 (fun_app$ (fun_app$a uu$ ?v0) ?v1)))
  1.1784 -(= $x31 $x32))) :pattern ( (fun_app$ (fun_app$a uu$ ?v0) ?v1) ) :qid k!10))
  1.1785 -))
  1.1786 -(let ((@x51 (monotonicity (rewrite (= (<= ?1 ?0) $x46)) (= (= $x31 (<= ?1 ?0)) $x49))))
  1.1787 -(let ((@x42 (quant-intro (rewrite (= (= $x31 (<= ?1 ?0)) (= $x31 (<= ?1 ?0)))) (= $x35 $x40))))
  1.1788 -(let ((@x57 (mp (asserted $x35) (trans @x42 (quant-intro @x51 (= $x40 $x52)) (= $x35 $x52)) $x52)))
  1.1789 -(let ((@x78 (mp~ @x57 (nnf-pos (refl (~ $x49 $x49)) (~ $x52 $x52)) $x52)))
  1.1790 -(let (($x134 (or (not $x52) $x168)))
  1.1791 -(let (($x137 (= (or (not $x52) (= $x168 (<= (+ 3 (* (- 1) 42)) 0))) $x134)))
  1.1792 -(let ((?x169 (* (- 1) 42)))
  1.1793 -(let ((?x170 (+ 3 ?x169)))
  1.1794 -(let (($x160 (<= ?x170 0)))
  1.1795 -(let (($x171 (= $x168 $x160)))
  1.1796 -(let ((@x158 (trans (monotonicity (rewrite (= ?x169 (- 42))) (= ?x170 (+ 3 (- 42)))) (rewrite (= (+ 3 (- 42)) (- 39))) (= ?x170 (- 39)))))
  1.1797 -(let ((@x497 (trans (monotonicity @x158 (= $x160 (<= (- 39) 0))) (rewrite (= (<= (- 39) 0) true)) (= $x160 true))))
  1.1798 -(let ((@x131 (trans (monotonicity @x497 (= $x171 (= $x168 true))) (rewrite (= (= $x168 true) $x168)) (= $x171 $x168))))
  1.1799 -(let ((@x478 (mp ((_ quant-inst 3 42) (or (not $x52) $x171)) (trans (monotonicity @x131 $x137) (rewrite (= $x134 $x134)) $x137) $x134)))
  1.1800 -(unit-resolution (unit-resolution @x478 @x78 $x168) (mp @x77 @x472 (not $x168)) false)))))))))))))))))))))))))))))))))))
  1.1801 -
  1.1802 -9cdd1051dbf4e0648f71536fbc74bbab8e0e744e 75 0
  1.1803 -unsat
  1.1804 -((set-logic AUFLIA)
  1.1805 -(proof
  1.1806 -(let ((?x78 (cons$ 2 nil$)))
  1.1807 -(let ((?x79 (cons$ 1 ?x78)))
  1.1808 -(let ((?x74 (cons$ 1 nil$)))
  1.1809 -(let ((?x75 (cons$ 0 ?x74)))
  1.1810 -(let ((?x76 (map$ uu$ ?x75)))
  1.1811 -(let (($x80 (= ?x76 ?x79)))
  1.1812 -(let ((?x185 (map$ uu$ ?x74)))
  1.1813 -(let ((?x189 (map$ uu$ nil$)))
  1.1814 -(let ((?x188 (fun_app$ uu$ 1)))
  1.1815 -(let ((?x160 (cons$ ?x188 ?x189)))
  1.1816 -(let (($x290 (= ?x185 ?x160)))
  1.1817 -(let (($x521 (forall ((?v0 Int_int_fun$) (?v1 Int) (?v2 Int_list$) )(! (= (map$ ?v0 (cons$ ?v1 ?v2)) (cons$ (fun_app$ ?v0 ?v1) (map$ ?v0 ?v2))) :pattern ( (map$ ?v0 (cons$ ?v1 ?v2)) ) :pattern ( (cons$ (fun_app$ ?v0 ?v1) (map$ ?v0 ?v2)) ) :qid k!13))
  1.1818 -))
  1.1819 -(let (($x72 (forall ((?v0 Int_int_fun$) (?v1 Int) (?v2 Int_list$) )(! (= (map$ ?v0 (cons$ ?v1 ?v2)) (cons$ (fun_app$ ?v0 ?v1) (map$ ?v0 ?v2))) :qid k!13))
  1.1820 -))
  1.1821 -(let (($x71 (= (map$ ?2 (cons$ ?1 ?0)) (cons$ (fun_app$ ?2 ?1) (map$ ?2 ?0)))))
  1.1822 -(let ((@x97 (mp~ (asserted $x72) (nnf-pos (refl (~ $x71 $x71)) (~ $x72 $x72)) $x72)))
  1.1823 -(let ((@x526 (mp @x97 (quant-intro (refl (= $x71 $x71)) (= $x72 $x521)) $x521)))
  1.1824 -(let (($x173 (or (not $x521) $x290)))
  1.1825 -(let ((@x506 ((_ quant-inst uu$ 1 nil$) $x173)))
  1.1826 -(let (($x492 (= ?x189 nil$)))
  1.1827 -(let (($x513 (forall ((?v0 Int_int_fun$) )(! (= (map$ ?v0 nil$) nil$) :pattern ( (map$ ?v0 nil$) ) :qid k!12))
  1.1828 -))
  1.1829 -(let (($x61 (forall ((?v0 Int_int_fun$) )(! (= (map$ ?v0 nil$) nil$) :qid k!12))
  1.1830 -))
  1.1831 -(let ((@x515 (refl (= (= (map$ ?0 nil$) nil$) (= (map$ ?0 nil$) nil$)))))
  1.1832 -(let ((@x83 (refl (~ (= (map$ ?0 nil$) nil$) (= (map$ ?0 nil$) nil$)))))
  1.1833 -(let ((@x518 (mp (mp~ (asserted $x61) (nnf-pos @x83 (~ $x61 $x61)) $x61) (quant-intro @x515 (= $x61 $x513)) $x513)))
  1.1834 -(let (($x495 (or (not $x513) $x492)))
  1.1835 -(let ((@x496 ((_ quant-inst uu$) $x495)))
  1.1836 -(let (($x136 (= ?x188 2)))
  1.1837 -(let (($x51 (forall ((?v0 Int) )(! (= (+ ?v0 (* (- 1) (fun_app$ uu$ ?v0))) (- 1)) :pattern ( (fun_app$ uu$ ?v0) ) :qid k!11))
  1.1838 -))
  1.1839 -(let (($x47 (= (+ ?0 (* (- 1) (fun_app$ uu$ ?0))) (- 1))))
  1.1840 -(let (($x34 (forall ((?v0 Int) )(! (let ((?x29 (fun_app$ uu$ ?v0)))
  1.1841 -(= ?x29 (+ ?v0 1))) :pattern ( (fun_app$ uu$ ?v0) ) :qid k!11))
  1.1842 -))
  1.1843 -(let (($x42 (forall ((?v0 Int) )(! (let ((?x29 (fun_app$ uu$ ?v0)))
  1.1844 -(= ?x29 (+ 1 ?v0))) :pattern ( (fun_app$ uu$ ?v0) ) :qid k!11))
  1.1845 -))
  1.1846 -(let ((@x53 (quant-intro (rewrite (= (= (fun_app$ uu$ ?0) (+ 1 ?0)) $x47)) (= $x42 $x51))))
  1.1847 -(let ((?x29 (fun_app$ uu$ ?0)))
  1.1848 -(let (($x39 (= ?x29 (+ 1 ?0))))
  1.1849 -(let ((@x41 (monotonicity (rewrite (= (+ ?0 1) (+ 1 ?0))) (= (= ?x29 (+ ?0 1)) $x39))))
  1.1850 -(let ((@x56 (mp (asserted $x34) (trans (quant-intro @x41 (= $x34 $x42)) @x53 (= $x34 $x51)) $x51)))
  1.1851 -(let ((@x85 (mp~ @x56 (nnf-pos (refl (~ $x47 $x47)) (~ $x51 $x51)) $x51)))
  1.1852 -(let (($x145 (not $x51)))
  1.1853 -(let (($x499 (or $x145 $x136)))
  1.1854 -(let ((@x498 (rewrite (= (= (+ 1 (* (- 1) ?x188)) (- 1)) $x136))))
  1.1855 -(let ((@x204 (monotonicity @x498 (= (or $x145 (= (+ 1 (* (- 1) ?x188)) (- 1))) $x499))))
  1.1856 -(let ((@x207 (trans @x204 (rewrite (= $x499 $x499)) (= (or $x145 (= (+ 1 (* (- 1) ?x188)) (- 1))) $x499))))
  1.1857 -(let ((@x104 (mp ((_ quant-inst 1) (or $x145 (= (+ 1 (* (- 1) ?x188)) (- 1)))) @x207 $x499)))
  1.1858 -(let ((@x191 (monotonicity (symm (unit-resolution @x104 @x85 $x136) (= 2 ?x188)) (symm (unit-resolution @x496 @x518 $x492) (= nil$ ?x189)) (= ?x78 ?x160))))
  1.1859 -(let ((@x473 (trans @x191 (symm (unit-resolution @x506 @x526 $x290) (= ?x160 ?x185)) (= ?x78 ?x185))))
  1.1860 -(let ((?x182 (fun_app$ uu$ 0)))
  1.1861 -(let (($x163 (= ?x182 1)))
  1.1862 -(let (($x487 (or $x145 $x163)))
  1.1863 -(let ((@x501 (monotonicity (rewrite (= (+ 0 (* (- 1) ?x182)) (* (- 1) ?x182))) (= (= (+ 0 (* (- 1) ?x182)) (- 1)) (= (* (- 1) ?x182) (- 1))))))
  1.1864 -(let ((@x503 (trans @x501 (rewrite (= (= (* (- 1) ?x182) (- 1)) $x163)) (= (= (+ 0 (* (- 1) ?x182)) (- 1)) $x163))))
  1.1865 -(let ((@x151 (monotonicity @x503 (= (or $x145 (= (+ 0 (* (- 1) ?x182)) (- 1))) $x487))))
  1.1866 -(let ((@x490 (trans @x151 (rewrite (= $x487 $x487)) (= (or $x145 (= (+ 0 (* (- 1) ?x182)) (- 1))) $x487))))
  1.1867 -(let ((@x491 (mp ((_ quant-inst 0) (or $x145 (= (+ 0 (* (- 1) ?x182)) (- 1)))) @x490 $x487)))
  1.1868 -(let ((@x478 (monotonicity (symm (unit-resolution @x491 @x85 $x163) (= 1 ?x182)) @x473 (= ?x79 (cons$ ?x182 ?x185)))))
  1.1869 -(let ((?x186 (cons$ ?x182 ?x185)))
  1.1870 -(let (($x187 (= ?x76 ?x186)))
  1.1871 -(let (($x504 (or (not $x521) $x187)))
  1.1872 -(let ((@x505 ((_ quant-inst uu$ 0 (cons$ 1 nil$)) $x504)))
  1.1873 -(let ((@x466 (trans (unit-resolution @x505 @x526 $x187) (symm @x478 (= ?x186 ?x79)) $x80)))
  1.1874 -(let (($x81 (not $x80)))
  1.1875 -(let ((@x82 (asserted $x81)))
  1.1876 -(unit-resolution @x82 @x466 false))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
  1.1877 -
  1.1878 -40c61a0200976d6203302a7343af5b7ad1e6ce36 11 0
  1.1879 -unsat
  1.1880 -((set-logic AUFLIA)
  1.1881 -(proof
  1.1882 -(let (($x29 (forall ((?v0 A$) )(! (p$ ?v0) :qid k!6))
  1.1883 -))
  1.1884 -(let (($x30 (not $x29)))
  1.1885 -(let (($x31 (or $x29 $x30)))
  1.1886 -(let (($x32 (not $x31)))
  1.1887 -(let ((@x42 (trans (monotonicity (rewrite (= $x31 true)) (= $x32 (not true))) (rewrite (= (not true) false)) (= $x32 false))))
  1.1888 -(mp (asserted $x32) @x42 false))))))))
  1.1889 -
  1.1890 -f17a5e4d5f1a5a93fbc847f858c7c845c29d8349 109 0
  1.1891 -unsat
  1.1892 -((set-logic AUFLIA)
  1.1893 -(proof
  1.1894 -(let ((?x75 (dec_10$ 4)))
  1.1895 -(let ((?x76 (* 4 ?x75)))
  1.1896 -(let ((?x77 (dec_10$ ?x76)))
  1.1897 -(let (($x79 (= ?x77 6)))
  1.1898 -(let (($x150 (<= ?x75 4)))
  1.1899 -(let (($x174 (= ?x75 4)))
  1.1900 -(let (($x513 (forall ((?v0 Int) )(! (let (($x55 (>= ?v0 10)))
  1.1901 -(ite $x55 (= (dec_10$ ?v0) (dec_10$ (+ (- 10) ?v0))) (= (dec_10$ ?v0) ?v0))) :pattern ( (dec_10$ ?v0) ) :qid k!5))
  1.1902 -))
  1.1903 -(let (($x92 (forall ((?v0 Int) )(! (let (($x55 (>= ?v0 10)))
  1.1904 -(ite $x55 (= (dec_10$ ?v0) (dec_10$ (+ (- 10) ?v0))) (= (dec_10$ ?v0) ?v0))) :qid k!5))
  1.1905 -))
  1.1906 -(let (($x55 (>= ?0 10)))
  1.1907 -(let (($x87 (ite $x55 (= (dec_10$ ?0) (dec_10$ (+ (- 10) ?0))) (= (dec_10$ ?0) ?0))))
  1.1908 -(let (($x68 (forall ((?v0 Int) )(! (let ((?x38 (+ (- 10) ?v0)))
  1.1909 -(let ((?x41 (dec_10$ ?x38)))
  1.1910 -(let (($x55 (>= ?v0 10)))
  1.1911 -(let ((?x60 (ite $x55 ?x41 ?v0)))
  1.1912 -(let ((?x28 (dec_10$ ?v0)))
  1.1913 -(= ?x28 ?x60)))))) :qid k!5))
  1.1914 -))
  1.1915 -(let ((?x38 (+ (- 10) ?0)))
  1.1916 -(let ((?x41 (dec_10$ ?x38)))
  1.1917 -(let ((?x60 (ite $x55 ?x41 ?0)))
  1.1918 -(let ((?x28 (dec_10$ ?0)))
  1.1919 -(let (($x65 (= ?x28 ?x60)))
  1.1920 -(let (($x35 (forall ((?v0 Int) )(! (let ((?x28 (dec_10$ ?v0)))
  1.1921 -(= ?x28 (ite (< ?v0 10) ?v0 (dec_10$ (- ?v0 10))))) :qid k!5))
  1.1922 -))
  1.1923 -(let (($x50 (forall ((?v0 Int) )(! (let ((?x38 (+ (- 10) ?v0)))
  1.1924 -(let ((?x41 (dec_10$ ?x38)))
  1.1925 -(let (($x30 (< ?v0 10)))
  1.1926 -(let ((?x44 (ite $x30 ?v0 ?x41)))
  1.1927 -(let ((?x28 (dec_10$ ?v0)))
  1.1928 -(= ?x28 ?x44)))))) :qid k!5))
  1.1929 -))
  1.1930 -(let ((@x59 (monotonicity (rewrite (= (< ?0 10) (not $x55))) (= (ite (< ?0 10) ?0 ?x41) (ite (not $x55) ?0 ?x41)))))
  1.1931 -(let ((@x64 (trans @x59 (rewrite (= (ite (not $x55) ?0 ?x41) ?x60)) (= (ite (< ?0 10) ?0 ?x41) ?x60))))
  1.1932 -(let ((@x67 (monotonicity @x64 (= (= ?x28 (ite (< ?0 10) ?0 ?x41)) $x65))))
  1.1933 -(let (($x30 (< ?0 10)))
  1.1934 -(let ((?x44 (ite $x30 ?0 ?x41)))
  1.1935 -(let (($x47 (= ?x28 ?x44)))
  1.1936 -(let ((@x43 (monotonicity (rewrite (= (- ?0 10) ?x38)) (= (dec_10$ (- ?0 10)) ?x41))))
  1.1937 -(let ((@x49 (monotonicity (monotonicity @x43 (= (ite $x30 ?0 (dec_10$ (- ?0 10))) ?x44)) (= (= ?x28 (ite $x30 ?0 (dec_10$ (- ?0 10)))) $x47))))
  1.1938 -(let ((@x72 (trans (quant-intro @x49 (= $x35 $x50)) (quant-intro @x67 (= $x50 $x68)) (= $x35 $x68))))
  1.1939 -(let ((@x86 (mp~ (mp (asserted $x35) @x72 $x68) (nnf-pos (refl (~ $x65 $x65)) (~ $x68 $x68)) $x68)))
  1.1940 -(let ((@x95 (mp @x86 (quant-intro (rewrite (= $x65 $x87)) (= $x68 $x92)) $x92)))
  1.1941 -(let ((@x518 (mp @x95 (quant-intro (refl (= $x87 $x87)) (= $x92 $x513)) $x513)))
  1.1942 -(let (($x501 (not $x513)))
  1.1943 -(let (($x163 (or $x501 $x174)))
  1.1944 -(let ((?x97 (+ (- 10) 4)))
  1.1945 -(let ((?x183 (dec_10$ ?x97)))
  1.1946 -(let (($x184 (= ?x75 ?x183)))
  1.1947 -(let (($x96 (>= 4 10)))
  1.1948 -(let (($x185 (ite $x96 $x184 $x174)))
  1.1949 -(let ((@x172 (monotonicity (monotonicity (rewrite (= ?x97 (- 6))) (= ?x183 (dec_10$ (- 6)))) (= $x184 (= ?x75 (dec_10$ (- 6)))))))
  1.1950 -(let ((@x507 (monotonicity (rewrite (= $x96 false)) @x172 (= $x185 (ite false (= ?x75 (dec_10$ (- 6))) $x174)))))
  1.1951 -(let ((@x511 (trans @x507 (rewrite (= (ite false (= ?x75 (dec_10$ (- 6))) $x174) $x174)) (= $x185 $x174))))
  1.1952 -(let ((@x148 (trans (monotonicity @x511 (= (or $x501 $x185) $x163)) (rewrite (= $x163 $x163)) (= (or $x501 $x185) $x163))))
  1.1953 -(let ((@x149 (mp ((_ quant-inst 4) (or $x501 $x185)) @x148 $x163)))
  1.1954 -(let ((@x438 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x174) $x150)) (unit-resolution @x149 @x518 $x174) $x150)))
  1.1955 -(let (($x151 (>= ?x75 4)))
  1.1956 -(let ((@x428 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x174) $x151)) (unit-resolution @x149 @x518 $x174) $x151)))
  1.1957 -(let ((?x489 (+ (- 10) ?x76)))
  1.1958 -(let ((?x490 (dec_10$ ?x489)))
  1.1959 -(let ((?x448 (* (- 1) ?x490)))
  1.1960 -(let ((?x449 (+ ?x76 ?x448)))
  1.1961 -(let (($x444 (<= ?x449 10)))
  1.1962 -(let (($x292 (= ?x449 10)))
  1.1963 -(let ((?x455 (+ (- 20) ?x76)))
  1.1964 -(let ((?x458 (dec_10$ ?x455)))
  1.1965 -(let (($x461 (= ?x490 ?x458)))
  1.1966 -(let (($x310 (>= ?x75 5)))
  1.1967 -(let (($x450 (ite $x310 $x461 $x292)))
  1.1968 -(let (($x453 (or $x501 $x450)))
  1.1969 -(let (($x470 (= ?x490 ?x489)))
  1.1970 -(let ((?x467 (+ (- 10) ?x489)))
  1.1971 -(let ((?x468 (dec_10$ ?x467)))
  1.1972 -(let (($x469 (= ?x490 ?x468)))
  1.1973 -(let (($x466 (>= ?x489 10)))
  1.1974 -(let (($x471 (ite $x466 $x469 $x470)))
  1.1975 -(let ((@x463 (monotonicity (monotonicity (rewrite (= ?x467 ?x455)) (= ?x468 ?x458)) (= $x469 $x461))))
  1.1976 -(let ((@x452 (monotonicity (rewrite (= $x466 $x310)) @x463 (rewrite (= $x470 $x292)) (= $x471 $x450))))
  1.1977 -(let ((@x442 (trans (monotonicity @x452 (= (or $x501 $x471) $x453)) (rewrite (= $x453 $x453)) (= (or $x501 $x471) $x453))))
  1.1978 -(let ((@x443 (mp ((_ quant-inst (+ (- 10) ?x76)) (or $x501 $x471)) @x442 $x453)))
  1.1979 -(let (($x346 (not $x310)))
  1.1980 -(let ((@x418 (unit-resolution (def-axiom (or (not $x450) $x310 $x292)) (unit-resolution ((_ th-lemma arith farkas 1 1) (or $x346 (not $x150))) @x438 $x346) (or (not $x450) $x292))))
  1.1981 -(let ((@x422 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x292) $x444)) (unit-resolution @x418 (unit-resolution @x443 @x518 $x450) $x292) $x444)))
  1.1982 -(let (($x336 (>= ?x449 10)))
  1.1983 -(let ((@x410 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x292) $x336)) (unit-resolution @x418 (unit-resolution @x443 @x518 $x450) $x292) $x336)))
  1.1984 -(let (($x491 (= ?x77 ?x490)))
  1.1985 -(let ((?x499 (* (- 1) ?x77)))
  1.1986 -(let ((?x485 (+ ?x76 ?x499)))
  1.1987 -(let (($x497 (= ?x485 0)))
  1.1988 -(let (($x131 (>= ?x75 3)))
  1.1989 -(let (($x486 (ite $x131 $x491 $x497)))
  1.1990 -(let (($x205 (or $x501 $x486)))
  1.1991 -(let ((@x204 (monotonicity (rewrite (= (>= ?x76 10) $x131)) (rewrite (= (= ?x77 ?x76) $x497)) (= (ite (>= ?x76 10) $x491 (= ?x77 ?x76)) $x486))))
  1.1992 -(let ((@x479 (monotonicity @x204 (= (or $x501 (ite (>= ?x76 10) $x491 (= ?x77 ?x76))) $x205))))
  1.1993 -(let ((@x212 (trans @x479 (rewrite (= $x205 $x205)) (= (or $x501 (ite (>= ?x76 10) $x491 (= ?x77 ?x76))) $x205))))
  1.1994 -(let ((@x481 (mp ((_ quant-inst (* 4 ?x75)) (or $x501 (ite (>= ?x76 10) $x491 (= ?x77 ?x76)))) @x212 $x205)))
  1.1995 -(let ((@x397 (unit-resolution (def-axiom (or (not $x486) (not $x131) $x491)) (unit-resolution ((_ th-lemma arith farkas 1 1) (or $x131 (not $x151))) @x428 $x131) (unit-resolution @x481 @x518 $x486) $x491)))
  1.1996 -(let (($x80 (not $x79)))
  1.1997 -(let ((@x81 (asserted $x80)))
  1.1998 -(unit-resolution @x81 (trans @x397 ((_ th-lemma arith eq-propagate 1 1 -4 -4) @x410 @x422 @x428 @x438 (= ?x490 6)) $x79) false)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
  1.1999 -
  1.2000 -8c0c900f4d4a92edc7d6113704948dc9280df015 348 0
  1.2001 -unsat
  1.2002 -((set-logic <null>)
  1.2003 -(proof
  1.2004 -(let ((?x96 (map$ uu$ xs$)))
  1.2005 -(let ((?x97 (eval_dioph$ ks$ ?x96)))
  1.2006 -(let ((?x424 (+ l$ ?x97)))
  1.2007 -(let ((?x425 (mod ?x424 2)))
  1.2008 -(let (($x482 (>= ?x425 2)))
  1.2009 -(let (($x564 (not $x482)))
  1.2010 -(let ((@x26 (true-axiom true)))
  1.2011 -(let ((?x369 (* (- 1) l$)))
  1.2012 -(let ((?x93 (eval_dioph$ ks$ xs$)))
  1.2013 -(let ((?x678 (+ ?x93 ?x369)))
  1.2014 -(let (($x679 (<= ?x678 0)))
  1.2015 -(let (($x95 (= ?x93 l$)))
  1.2016 -(let ((?x110 (* (- 1) ?x97)))
  1.2017 -(let ((?x111 (+ l$ ?x110)))
  1.2018 -(let ((?x114 (div$ ?x111 2)))
  1.2019 -(let ((?x101 (map$ uua$ xs$)))
  1.2020 -(let ((?x102 (eval_dioph$ ks$ ?x101)))
  1.2021 -(let (($x117 (= ?x102 ?x114)))
  1.2022 -(let (($x282 (not $x117)))
  1.2023 -(let ((?x99 (mod$ l$ 2)))
  1.2024 -(let ((?x98 (mod$ ?x97 2)))
  1.2025 -(let (($x100 (= ?x98 ?x99)))
  1.2026 -(let (($x281 (not $x100)))
  1.2027 -(let (($x283 (or $x281 $x282)))
  1.2028 -(let (($x465 (>= ?x425 0)))
  1.2029 -(let ((?x496 (* (- 2) ?x102)))
  1.2030 -(let ((?x497 (+ ?x93 ?x110 ?x496)))
  1.2031 -(let (($x504 (<= ?x497 0)))
  1.2032 -(let (($x498 (= ?x497 0)))
  1.2033 -(let (($x304 (forall ((?v0 Int_list$) (?v1 Int_list$) )(! (let ((?x45 (eval_dioph$ ?v0 ?v1)))
  1.2034 -(let ((?x83 (+ ?x45 (* (- 1) (eval_dioph$ ?v0 (map$ uu$ ?v1))) (* (- 2) (eval_dioph$ ?v0 (map$ uua$ ?v1))))))
  1.2035 -(= ?x83 0))) :pattern ( (eval_dioph$ ?v0 (map$ uu$ ?v1)) ) :pattern ( (eval_dioph$ ?v0 (map$ uua$ ?v1)) ) :qid k!19))
  1.2036 -))
  1.2037 -(let (($x85 (forall ((?v0 Int_list$) (?v1 Int_list$) )(! (let ((?x45 (eval_dioph$ ?v0 ?v1)))
  1.2038 -(let ((?x83 (+ ?x45 (* (- 1) (eval_dioph$ ?v0 (map$ uu$ ?v1))) (* (- 2) (eval_dioph$ ?v0 (map$ uua$ ?v1))))))
  1.2039 -(= ?x83 0))) :qid k!19))
  1.2040 -))
  1.2041 -(let ((?x45 (eval_dioph$ ?1 ?0)))
  1.2042 -(let ((?x83 (+ ?x45 (* (- 1) (eval_dioph$ ?1 (map$ uu$ ?0))) (* (- 2) (eval_dioph$ ?1 (map$ uua$ ?0))))))
  1.2043 -(let (($x79 (= ?x83 0)))
  1.2044 -(let (($x58 (forall ((?v0 Int_list$) (?v1 Int_list$) )(! (let ((?x45 (eval_dioph$ ?v0 ?v1)))
  1.2045 -(let ((?x48 (eval_dioph$ ?v0 (map$ uu$ ?v1))))
  1.2046 -(let ((?x56 (+ (* (eval_dioph$ ?v0 (map$ uua$ ?v1)) 2) ?x48)))
  1.2047 -(= ?x56 ?x45)))) :qid k!19))
  1.2048 -))
  1.2049 -(let (($x74 (forall ((?v0 Int_list$) (?v1 Int_list$) )(! (let ((?x45 (eval_dioph$ ?v0 ?v1)))
  1.2050 -(let ((?x54 (eval_dioph$ ?v0 (map$ uua$ ?v1))))
  1.2051 -(let ((?x60 (* 2 ?x54)))
  1.2052 -(let ((?x48 (eval_dioph$ ?v0 (map$ uu$ ?v1))))
  1.2053 -(let ((?x66 (+ ?x48 ?x60)))
  1.2054 -(= ?x66 ?x45)))))) :qid k!19))
  1.2055 -))
  1.2056 -(let ((?x54 (eval_dioph$ ?1 (map$ uua$ ?0))))
  1.2057 -(let ((?x60 (* 2 ?x54)))
  1.2058 -(let ((?x48 (eval_dioph$ ?1 (map$ uu$ ?0))))
  1.2059 -(let ((?x66 (+ ?x48 ?x60)))
  1.2060 -(let (($x71 (= ?x66 ?x45)))
  1.2061 -(let ((@x65 (monotonicity (rewrite (= (* ?x54 2) ?x60)) (= (+ (* ?x54 2) ?x48) (+ ?x60 ?x48)))))
  1.2062 -(let ((@x70 (trans @x65 (rewrite (= (+ ?x60 ?x48) ?x66)) (= (+ (* ?x54 2) ?x48) ?x66))))
  1.2063 -(let ((@x76 (quant-intro (monotonicity @x70 (= (= (+ (* ?x54 2) ?x48) ?x45) $x71)) (= $x58 $x74))))
  1.2064 -(let ((@x89 (trans @x76 (quant-intro (rewrite (= $x71 $x79)) (= $x74 $x85)) (= $x58 $x85))))
  1.2065 -(let ((@x270 (mp~ (mp (asserted $x58) @x89 $x85) (nnf-pos (refl (~ $x79 $x79)) (~ $x85 $x85)) $x85)))
  1.2066 -(let ((@x309 (mp @x270 (quant-intro (refl (= $x79 $x79)) (= $x85 $x304)) $x304)))
  1.2067 -(let (($x502 (or (not $x304) $x498)))
  1.2068 -(let ((@x503 ((_ quant-inst ks$ xs$) $x502)))
  1.2069 -(let ((@x795 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x498) $x504)) (unit-resolution @x503 @x309 $x498) $x504)))
  1.2070 -(let (($x815 (not $x679)))
  1.2071 -(let (($x680 (>= ?x678 0)))
  1.2072 -(let ((?x592 (mod ?x97 2)))
  1.2073 -(let ((?x619 (* (- 1) ?x592)))
  1.2074 -(let ((?x511 (mod l$ 2)))
  1.2075 -(let ((?x538 (* (- 1) ?x511)))
  1.2076 -(let ((?x776 (* (- 1) ?x102)))
  1.2077 -(let ((?x759 (+ l$ ?x98 ?x776 ?x538 (* (- 1) (div l$ 2)) ?x619 (* (- 1) (div ?x97 2)))))
  1.2078 -(let (($x760 (>= ?x759 1)))
  1.2079 -(let (($x747 (not $x760)))
  1.2080 -(let ((?x674 (* (- 1) ?x99)))
  1.2081 -(let ((?x675 (+ ?x98 ?x674)))
  1.2082 -(let (($x676 (<= ?x675 0)))
  1.2083 -(let (($x284 (not $x283)))
  1.2084 -(let ((@x493 (hypothesis $x284)))
  1.2085 -(let ((@x781 (unit-resolution ((_ th-lemma arith triangle-eq) (or $x281 $x676)) (unit-resolution (def-axiom (or $x283 $x100)) @x493 $x100) $x676)))
  1.2086 -(let ((?x670 (* (- 1) ?x114)))
  1.2087 -(let ((?x671 (+ ?x102 ?x670)))
  1.2088 -(let (($x673 (>= ?x671 0)))
  1.2089 -(let ((@x787 (unit-resolution ((_ th-lemma arith triangle-eq) (or $x282 $x673)) (unit-resolution (def-axiom (or $x283 $x117)) @x493 $x117) $x673)))
  1.2090 -(let ((?x557 (div l$ 2)))
  1.2091 -(let ((?x570 (* (- 2) ?x557)))
  1.2092 -(let ((?x571 (+ l$ ?x538 ?x570)))
  1.2093 -(let (($x576 (<= ?x571 0)))
  1.2094 -(let (($x569 (= ?x571 0)))
  1.2095 -(let ((@x568 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x569) $x576)) (unit-resolution ((_ th-lemma arith) (or false $x569)) @x26 $x569) $x576)))
  1.2096 -(let ((?x620 (+ ?x98 ?x619)))
  1.2097 -(let (($x635 (<= ?x620 0)))
  1.2098 -(let (($x621 (= ?x620 0)))
  1.2099 -(let (($x318 (forall ((?v0 Int) (?v1 Int) )(! (let ((?x200 (mod ?v0 ?v1)))
  1.2100 -(let ((?x157 (* (- 1) ?v1)))
  1.2101 -(let ((?x154 (* (- 1) ?v0)))
  1.2102 -(let ((?x208 (mod ?x154 ?x157)))
  1.2103 -(let ((?x214 (* (- 1) ?x208)))
  1.2104 -(let (($x175 (<= ?v1 0)))
  1.2105 -(let ((?x234 (ite $x175 ?x214 ?x200)))
  1.2106 -(let (($x143 (= ?v1 0)))
  1.2107 -(let ((?x239 (ite $x143 ?v0 ?x234)))
  1.2108 -(let ((?x199 (mod$ ?v0 ?v1)))
  1.2109 -(= ?x199 ?x239))))))))))) :pattern ( (mod$ ?v0 ?v1) ) :qid k!22))
  1.2110 -))
  1.2111 -(let (($x245 (forall ((?v0 Int) (?v1 Int) )(! (let ((?x200 (mod ?v0 ?v1)))
  1.2112 -(let ((?x157 (* (- 1) ?v1)))
  1.2113 -(let ((?x154 (* (- 1) ?v0)))
  1.2114 -(let ((?x208 (mod ?x154 ?x157)))
  1.2115 -(let ((?x214 (* (- 1) ?x208)))
  1.2116 -(let (($x175 (<= ?v1 0)))
  1.2117 -(let ((?x234 (ite $x175 ?x214 ?x200)))
  1.2118 -(let (($x143 (= ?v1 0)))
  1.2119 -(let ((?x239 (ite $x143 ?v0 ?x234)))
  1.2120 -(let ((?x199 (mod$ ?v0 ?v1)))
  1.2121 -(= ?x199 ?x239))))))))))) :qid k!22))
  1.2122 -))
  1.2123 -(let ((?x200 (mod ?1 ?0)))
  1.2124 -(let ((?x157 (* (- 1) ?0)))
  1.2125 -(let ((?x154 (* (- 1) ?1)))
  1.2126 -(let ((?x208 (mod ?x154 ?x157)))
  1.2127 -(let ((?x214 (* (- 1) ?x208)))
  1.2128 -(let (($x175 (<= ?0 0)))
  1.2129 -(let ((?x234 (ite $x175 ?x214 ?x200)))
  1.2130 -(let (($x143 (= ?0 0)))
  1.2131 -(let ((?x239 (ite $x143 ?1 ?x234)))
  1.2132 -(let ((?x199 (mod$ ?1 ?0)))
  1.2133 -(let (($x242 (= ?x199 ?x239)))
  1.2134 -(let (($x206 (forall ((?v0 Int) (?v1 Int) )(! (let (($x143 (= ?v1 0)))
  1.2135 -(let ((?x204 (ite $x143 ?v0 (ite (< 0 ?v1) (mod ?v0 ?v1) (- (mod (- ?v0) (- ?v1)))))))
  1.2136 -(let ((?x199 (mod$ ?v0 ?v1)))
  1.2137 -(= ?x199 ?x204)))) :qid k!22))
  1.2138 -))
  1.2139 -(let (($x228 (forall ((?v0 Int) (?v1 Int) )(! (let ((?x157 (* (- 1) ?v1)))
  1.2140 -(let ((?x154 (* (- 1) ?v0)))
  1.2141 -(let ((?x208 (mod ?x154 ?x157)))
  1.2142 -(let ((?x214 (* (- 1) ?x208)))
  1.2143 -(let ((?x200 (mod ?v0 ?v1)))
  1.2144 -(let (($x144 (< 0 ?v1)))
  1.2145 -(let ((?x219 (ite $x144 ?x200 ?x214)))
  1.2146 -(let (($x143 (= ?v1 0)))
  1.2147 -(let ((?x222 (ite $x143 ?v0 ?x219)))
  1.2148 -(let ((?x199 (mod$ ?v0 ?v1)))
  1.2149 -(= ?x199 ?x222))))))))))) :qid k!22))
  1.2150 -))
  1.2151 -(let ((@x233 (monotonicity (rewrite (= (< 0 ?0) (not $x175))) (= (ite (< 0 ?0) ?x200 ?x214) (ite (not $x175) ?x200 ?x214)))))
  1.2152 -(let ((@x238 (trans @x233 (rewrite (= (ite (not $x175) ?x200 ?x214) ?x234)) (= (ite (< 0 ?0) ?x200 ?x214) ?x234))))
  1.2153 -(let ((@x241 (monotonicity @x238 (= (ite $x143 ?1 (ite (< 0 ?0) ?x200 ?x214)) ?x239))))
  1.2154 -(let ((@x244 (monotonicity @x241 (= (= ?x199 (ite $x143 ?1 (ite (< 0 ?0) ?x200 ?x214))) $x242))))
  1.2155 -(let (($x144 (< 0 ?0)))
  1.2156 -(let ((?x219 (ite $x144 ?x200 ?x214)))
  1.2157 -(let ((?x222 (ite $x143 ?1 ?x219)))
  1.2158 -(let (($x225 (= ?x199 ?x222)))
  1.2159 -(let (($x226 (= (= ?x199 (ite $x143 ?1 (ite $x144 ?x200 (- (mod (- ?1) (- ?0)))))) $x225)))
  1.2160 -(let ((@x210 (monotonicity (rewrite (= (- ?1) ?x154)) (rewrite (= (- ?0) ?x157)) (= (mod (- ?1) (- ?0)) ?x208))))
  1.2161 -(let ((@x218 (trans (monotonicity @x210 (= (- (mod (- ?1) (- ?0))) (- ?x208))) (rewrite (= (- ?x208) ?x214)) (= (- (mod (- ?1) (- ?0))) ?x214))))
  1.2162 -(let ((@x221 (monotonicity @x218 (= (ite $x144 ?x200 (- (mod (- ?1) (- ?0)))) ?x219))))
  1.2163 -(let ((@x224 (monotonicity @x221 (= (ite $x143 ?1 (ite $x144 ?x200 (- (mod (- ?1) (- ?0))))) ?x222))))
  1.2164 -(let ((@x249 (trans (quant-intro (monotonicity @x224 $x226) (= $x206 $x228)) (quant-intro @x244 (= $x228 $x245)) (= $x206 $x245))))
  1.2165 -(let ((@x280 (mp~ (mp (asserted $x206) @x249 $x245) (nnf-pos (refl (~ $x242 $x242)) (~ $x245 $x245)) $x245)))
  1.2166 -(let ((@x323 (mp @x280 (quant-intro (refl (= $x242 $x242)) (= $x245 $x318)) $x318)))
  1.2167 -(let (($x545 (not $x318)))
  1.2168 -(let (($x626 (or $x545 $x621)))
  1.2169 -(let ((?x359 (* (- 1) 2)))
  1.2170 -(let ((?x590 (mod ?x110 ?x359)))
  1.2171 -(let ((?x591 (* (- 1) ?x590)))
  1.2172 -(let (($x357 (<= 2 0)))
  1.2173 -(let ((?x593 (ite $x357 ?x591 ?x592)))
  1.2174 -(let (($x356 (= 2 0)))
  1.2175 -(let ((?x594 (ite $x356 ?x97 ?x593)))
  1.2176 -(let (($x595 (= ?x98 ?x594)))
  1.2177 -(let ((@x601 (monotonicity (monotonicity (rewrite (= ?x359 (- 2))) (= ?x590 (mod ?x110 (- 2)))) (= ?x591 (* (- 1) (mod ?x110 (- 2)))))))
  1.2178 -(let ((@x368 (rewrite (= $x357 false))))
  1.2179 -(let ((@x604 (monotonicity @x368 @x601 (= ?x593 (ite false (* (- 1) (mod ?x110 (- 2))) ?x592)))))
  1.2180 -(let ((@x608 (trans @x604 (rewrite (= (ite false (* (- 1) (mod ?x110 (- 2))) ?x592) ?x592)) (= ?x593 ?x592))))
  1.2181 -(let ((@x366 (rewrite (= $x356 false))))
  1.2182 -(let ((@x615 (trans (monotonicity @x366 @x608 (= ?x594 (ite false ?x97 ?x592))) (rewrite (= (ite false ?x97 ?x592) ?x592)) (= ?x594 ?x592))))
  1.2183 -(let ((@x625 (trans (monotonicity @x615 (= $x595 (= ?x98 ?x592))) (rewrite (= (= ?x98 ?x592) $x621)) (= $x595 $x621))))
  1.2184 -(let ((@x633 (trans (monotonicity @x625 (= (or $x545 $x595) $x626)) (rewrite (= $x626 $x626)) (= (or $x545 $x595) $x626))))
  1.2185 -(let ((@x634 (mp ((_ quant-inst (eval_dioph$ ks$ ?x96) 2) (or $x545 $x595)) @x633 $x626)))
  1.2186 -(let ((@x431 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x621) $x635)) (unit-resolution @x634 @x323 $x621) $x635)))
  1.2187 -(let ((?x637 (div ?x97 2)))
  1.2188 -(let ((?x650 (* (- 2) ?x637)))
  1.2189 -(let ((?x651 (+ ?x97 ?x619 ?x650)))
  1.2190 -(let (($x656 (<= ?x651 0)))
  1.2191 -(let (($x649 (= ?x651 0)))
  1.2192 -(let ((@x661 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x649) $x656)) (unit-resolution ((_ th-lemma arith) (or false $x649)) @x26 $x649) $x656)))
  1.2193 -(let ((?x539 (+ ?x99 ?x538)))
  1.2194 -(let (($x555 (<= ?x539 0)))
  1.2195 -(let (($x540 (= ?x539 0)))
  1.2196 -(let (($x546 (or $x545 $x540)))
  1.2197 -(let ((?x506 (mod ?x369 ?x359)))
  1.2198 -(let ((?x507 (* (- 1) ?x506)))
  1.2199 -(let ((?x512 (ite $x357 ?x507 ?x511)))
  1.2200 -(let ((?x513 (ite $x356 l$ ?x512)))
  1.2201 -(let (($x514 (= ?x99 ?x513)))
  1.2202 -(let ((@x520 (monotonicity (monotonicity (rewrite (= ?x359 (- 2))) (= ?x506 (mod ?x369 (- 2)))) (= ?x507 (* (- 1) (mod ?x369 (- 2)))))))
  1.2203 -(let ((@x523 (monotonicity @x368 @x520 (= ?x512 (ite false (* (- 1) (mod ?x369 (- 2))) ?x511)))))
  1.2204 -(let ((@x527 (trans @x523 (rewrite (= (ite false (* (- 1) (mod ?x369 (- 2))) ?x511) ?x511)) (= ?x512 ?x511))))
  1.2205 -(let ((@x534 (trans (monotonicity @x366 @x527 (= ?x513 (ite false l$ ?x511))) (rewrite (= (ite false l$ ?x511) ?x511)) (= ?x513 ?x511))))
  1.2206 -(let ((@x544 (trans (monotonicity @x534 (= $x514 (= ?x99 ?x511))) (rewrite (= (= ?x99 ?x511) $x540)) (= $x514 $x540))))
  1.2207 -(let ((@x553 (trans (monotonicity @x544 (= (or $x545 $x514) $x546)) (rewrite (= $x546 $x546)) (= (or $x545 $x514) $x546))))
  1.2208 -(let ((@x554 (mp ((_ quant-inst l$ 2) (or $x545 $x514)) @x553 $x546)))
  1.2209 -(let ((@x668 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x540) $x555)) (unit-resolution @x554 @x323 $x540) $x555)))
  1.2210 -(let ((?x361 (div ?x111 2)))
  1.2211 -(let ((?x395 (* (- 1) ?x361)))
  1.2212 -(let ((?x396 (+ ?x114 ?x395)))
  1.2213 -(let (($x414 (>= ?x396 0)))
  1.2214 -(let (($x397 (= ?x396 0)))
  1.2215 -(let (($x311 (forall ((?v0 Int) (?v1 Int) )(! (let ((?x145 (div ?v0 ?v1)))
  1.2216 -(let ((?x157 (* (- 1) ?v1)))
  1.2217 -(let ((?x154 (* (- 1) ?v0)))
  1.2218 -(let ((?x160 (div ?x154 ?x157)))
  1.2219 -(let (($x175 (<= ?v1 0)))
  1.2220 -(let ((?x182 (ite $x175 ?x160 ?x145)))
  1.2221 -(let (($x143 (= ?v1 0)))
  1.2222 -(let ((?x141 (div$ ?v0 ?v1)))
  1.2223 -(= ?x141 (ite $x143 0 ?x182)))))))))) :pattern ( (div$ ?v0 ?v1) ) :qid k!21))
  1.2224 -))
  1.2225 -(let (($x193 (forall ((?v0 Int) (?v1 Int) )(! (let ((?x145 (div ?v0 ?v1)))
  1.2226 -(let ((?x157 (* (- 1) ?v1)))
  1.2227 -(let ((?x154 (* (- 1) ?v0)))
  1.2228 -(let ((?x160 (div ?x154 ?x157)))
  1.2229 -(let (($x175 (<= ?v1 0)))
  1.2230 -(let ((?x182 (ite $x175 ?x160 ?x145)))
  1.2231 -(let (($x143 (= ?v1 0)))
  1.2232 -(let ((?x141 (div$ ?v0 ?v1)))
  1.2233 -(= ?x141 (ite $x143 0 ?x182)))))))))) :qid k!21))
  1.2234 -))
  1.2235 -(let ((?x141 (div$ ?1 ?0)))
  1.2236 -(let (($x190 (= ?x141 (ite $x143 0 (ite $x175 (div ?x154 ?x157) (div ?1 ?0))))))
  1.2237 -(let (($x152 (forall ((?v0 Int) (?v1 Int) )(! (let (($x143 (= ?v1 0)))
  1.2238 -(let ((?x150 (ite $x143 0 (ite (< 0 ?v1) (div ?v0 ?v1) (div (- ?v0) (- ?v1))))))
  1.2239 -(let ((?x141 (div$ ?v0 ?v1)))
  1.2240 -(= ?x141 ?x150)))) :qid k!21))
  1.2241 -))
  1.2242 -(let (($x172 (forall ((?v0 Int) (?v1 Int) )(! (let ((?x157 (* (- 1) ?v1)))
  1.2243 -(let ((?x154 (* (- 1) ?v0)))
  1.2244 -(let ((?x160 (div ?x154 ?x157)))
  1.2245 -(let ((?x145 (div ?v0 ?v1)))
  1.2246 -(let (($x144 (< 0 ?v1)))
  1.2247 -(let ((?x163 (ite $x144 ?x145 ?x160)))
  1.2248 -(let (($x143 (= ?v1 0)))
  1.2249 -(let ((?x166 (ite $x143 0 ?x163)))
  1.2250 -(let ((?x141 (div$ ?v0 ?v1)))
  1.2251 -(= ?x141 ?x166)))))))))) :qid k!21))
  1.2252 -))
  1.2253 -(let ((?x160 (div ?x154 ?x157)))
  1.2254 -(let ((?x145 (div ?1 ?0)))
  1.2255 -(let ((?x163 (ite $x144 ?x145 ?x160)))
  1.2256 -(let ((?x166 (ite $x143 0 ?x163)))
  1.2257 -(let (($x169 (= ?x141 ?x166)))
  1.2258 -(let ((@x181 (monotonicity (rewrite (= $x144 (not $x175))) (= ?x163 (ite (not $x175) ?x145 ?x160)))))
  1.2259 -(let ((@x186 (trans @x181 (rewrite (= (ite (not $x175) ?x145 ?x160) (ite $x175 ?x160 ?x145))) (= ?x163 (ite $x175 ?x160 ?x145)))))
  1.2260 -(let ((@x192 (monotonicity (monotonicity @x186 (= ?x166 (ite $x143 0 (ite $x175 ?x160 ?x145)))) (= $x169 $x190))))
  1.2261 -(let (($x170 (= (= ?x141 (ite $x143 0 (ite $x144 ?x145 (div (- ?1) (- ?0))))) $x169)))
  1.2262 -(let ((@x162 (monotonicity (rewrite (= (- ?1) ?x154)) (rewrite (= (- ?0) ?x157)) (= (div (- ?1) (- ?0)) ?x160))))
  1.2263 -(let ((@x168 (monotonicity (monotonicity @x162 (= (ite $x144 ?x145 (div (- ?1) (- ?0))) ?x163)) (= (ite $x143 0 (ite $x144 ?x145 (div (- ?1) (- ?0)))) ?x166))))
  1.2264 -(let ((@x197 (trans (quant-intro (monotonicity @x168 $x170) (= $x152 $x172)) (quant-intro @x192 (= $x172 $x193)) (= $x152 $x193))))
  1.2265 -(let ((@x275 (mp~ (mp (asserted $x152) @x197 $x193) (nnf-pos (refl (~ $x190 $x190)) (~ $x193 $x193)) $x193)))
  1.2266 -(let ((@x316 (mp @x275 (quant-intro (refl (= $x190 $x190)) (= $x193 $x311)) $x311)))
  1.2267 -(let (($x403 (or (not $x311) $x397)))
  1.2268 -(let ((?x358 (* (- 1) ?x111)))
  1.2269 -(let ((?x360 (div ?x358 ?x359)))
  1.2270 -(let ((?x362 (ite $x357 ?x360 ?x361)))
  1.2271 -(let ((?x363 (ite $x356 0 ?x362)))
  1.2272 -(let (($x364 (= ?x114 ?x363)))
  1.2273 -(let ((@x374 (rewrite (= ?x359 (- 2)))))
  1.2274 -(let ((@x377 (monotonicity (rewrite (= ?x358 (+ ?x369 ?x97))) @x374 (= ?x360 (div (+ ?x369 ?x97) (- 2))))))
  1.2275 -(let ((@x380 (monotonicity @x368 @x377 (= ?x362 (ite false (div (+ ?x369 ?x97) (- 2)) ?x361)))))
  1.2276 -(let ((@x384 (trans @x380 (rewrite (= (ite false (div (+ ?x369 ?x97) (- 2)) ?x361) ?x361)) (= ?x362 ?x361))))
  1.2277 -(let ((@x391 (trans (monotonicity @x366 @x384 (= ?x363 (ite false 0 ?x361))) (rewrite (= (ite false 0 ?x361) ?x361)) (= ?x363 ?x361))))
  1.2278 -(let ((@x401 (trans (monotonicity @x391 (= $x364 (= ?x114 ?x361))) (rewrite (= (= ?x114 ?x361) $x397)) (= $x364 $x397))))
  1.2279 -(let ((@x410 (trans (monotonicity @x401 (= (or (not $x311) $x364) $x403)) (rewrite (= $x403 $x403)) (= (or (not $x311) $x364) $x403))))
  1.2280 -(let ((@x411 (mp ((_ quant-inst (+ l$ ?x110) 2) (or (not $x311) $x364)) @x410 $x403)))
  1.2281 -(let ((@x485 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x397) $x414)) (unit-resolution @x411 @x316 $x397) $x414)))
  1.2282 -(let ((?x436 (* (- 1) ?x425)))
  1.2283 -(let ((?x435 (* (- 2) ?x361)))
  1.2284 -(let ((?x437 (+ l$ ?x110 ?x435 ?x436)))
  1.2285 -(let (($x442 (<= ?x437 0)))
  1.2286 -(let (($x434 (= ?x437 0)))
  1.2287 -(let ((@x745 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x434) $x442)) (unit-resolution ((_ th-lemma arith) (or false $x434)) @x26 $x434) $x442)))
  1.2288 -(let ((@x746 ((_ th-lemma arith farkas 1 -2 -2 -2 1 1 1 1 1 1) @x745 @x485 (hypothesis $x673) (hypothesis $x760) (hypothesis $x676) @x668 @x661 @x431 @x568 (unit-resolution ((_ th-lemma arith) (or false $x564)) @x26 $x564) false)))
  1.2289 -(let ((@x788 (unit-resolution (lemma @x746 (or $x747 (not $x673) (not $x676))) @x787 @x781 $x747)))
  1.2290 -(let (($x677 (>= ?x675 0)))
  1.2291 -(let ((@x812 (unit-resolution ((_ th-lemma arith triangle-eq) (or $x281 $x677)) (unit-resolution (def-axiom (or $x283 $x100)) @x493 $x100) $x677)))
  1.2292 -(let (($x577 (>= ?x571 0)))
  1.2293 -(let ((@x778 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x569) $x577)) (unit-resolution ((_ th-lemma arith) (or false $x569)) @x26 $x569) $x577)))
  1.2294 -(let (($x556 (>= ?x539 0)))
  1.2295 -(let ((@x645 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x540) $x556)) (unit-resolution @x554 @x323 $x540) $x556)))
  1.2296 -(let (($x636 (>= ?x620 0)))
  1.2297 -(let ((@x652 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x621) $x636)) (unit-resolution @x634 @x323 $x621) $x636)))
  1.2298 -(let (($x505 (>= ?x497 0)))
  1.2299 -(let ((@x488 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x498) $x505)) (unit-resolution @x503 @x309 $x498) $x505)))
  1.2300 -(let (($x657 (>= ?x651 0)))
  1.2301 -(let ((@x581 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x649) $x657)) (unit-resolution ((_ th-lemma arith) (or false $x649)) @x26 $x649) $x657)))
  1.2302 -(let ((@x582 ((_ th-lemma arith farkas -1/2 -1/2 -1/2 1/2 -1/2 -1/2 -1/2 1) @x581 (hypothesis $x677) @x488 (hypothesis (not $x680)) @x652 @x645 @x778 (hypothesis $x747) false)))
  1.2303 -(let ((@x813 (unit-resolution (lemma @x582 (or $x680 (not $x677) $x760)) @x812 @x788 $x680)))
  1.2304 -(let (($x134 (not $x95)))
  1.2305 -(let (($x290 (= $x95 $x283)))
  1.2306 -(let ((@x289 (monotonicity (rewrite (= (and $x100 $x117) $x284)) (= (= $x134 (and $x100 $x117)) (= $x134 $x284)))))
  1.2307 -(let ((@x294 (trans @x289 (rewrite (= (= $x134 $x284) $x290)) (= (= $x134 (and $x100 $x117)) $x290))))
  1.2308 -(let (($x120 (and $x100 $x117)))
  1.2309 -(let (($x135 (= $x134 $x120)))
  1.2310 -(let (($x107 (= $x95 (and $x100 (= ?x102 (div$ (- l$ ?x97) 2))))))
  1.2311 -(let (($x108 (not $x107)))
  1.2312 -(let ((@x116 (monotonicity (rewrite (= (- l$ ?x97) ?x111)) (= (div$ (- l$ ?x97) 2) ?x114))))
  1.2313 -(let ((@x122 (monotonicity (monotonicity @x116 (= (= ?x102 (div$ (- l$ ?x97) 2)) $x117)) (= (and $x100 (= ?x102 (div$ (- l$ ?x97) 2))) $x120))))
  1.2314 -(let ((@x130 (trans (monotonicity @x122 (= $x107 (= $x95 $x120))) (rewrite (= (= $x95 $x120) (= $x95 $x120))) (= $x107 (= $x95 $x120)))))
  1.2315 -(let ((@x139 (trans (monotonicity @x130 (= $x108 (not (= $x95 $x120)))) (rewrite (= (not (= $x95 $x120)) $x135)) (= $x108 $x135))))
  1.2316 -(let ((@x295 (mp (mp (asserted $x108) @x139 $x135) @x294 $x290)))
  1.2317 -(let ((@x344 (unit-resolution (def-axiom (or $x134 $x283 (not $x290))) @x295 (or $x134 $x283))))
  1.2318 -(let ((@x819 (unit-resolution ((_ th-lemma arith triangle-eq) (or $x95 $x815 (not $x680))) (unit-resolution @x344 @x493 $x134) (or $x815 (not $x680)))))
  1.2319 -(let (($x672 (<= ?x671 0)))
  1.2320 -(let ((@x823 (unit-resolution ((_ th-lemma arith triangle-eq) (or $x282 $x672)) (unit-resolution (def-axiom (or $x283 $x117)) @x493 $x117) $x672)))
  1.2321 -(let (($x413 (<= ?x396 0)))
  1.2322 -(let ((@x802 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x397) $x413)) (unit-resolution @x411 @x316 $x397) $x413)))
  1.2323 -(let (($x443 (>= ?x437 0)))
  1.2324 -(let ((@x826 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x434) $x443)) (unit-resolution ((_ th-lemma arith) (or false $x434)) @x26 $x434) $x443)))
  1.2325 -(let ((@x827 ((_ th-lemma arith farkas 1 -2 -2 1 -1 1) @x826 @x802 @x823 (unit-resolution @x819 @x813 $x815) @x795 (unit-resolution ((_ th-lemma arith) (or false $x465)) @x26 $x465) false)))
  1.2326 -(let ((@x828 (lemma @x827 $x283)))
  1.2327 -(let ((@x340 (unit-resolution (def-axiom (or $x95 $x284 (not $x290))) @x295 (or $x95 $x284))))
  1.2328 -(let ((@x584 (unit-resolution @x340 @x828 $x95)))
  1.2329 -(let (($x807 (not $x672)))
  1.2330 -(let ((@x888 ((_ th-lemma arith assign-bounds 1 -1/2 -1/2 1/2 -1/2) (or $x673 (not $x413) (not $x465) (not $x443) (not $x504) (not $x680)))))
  1.2331 -(let ((@x889 (unit-resolution @x888 (unit-resolution ((_ th-lemma arith triangle-eq) (or $x134 $x680)) @x584 $x680) @x802 @x826 (unit-resolution ((_ th-lemma arith) (or false $x465)) @x26 $x465) @x795 $x673)))
  1.2332 -(let ((@x741 (symm (monotonicity (symm @x584 (= l$ ?x93)) (= ?x99 (mod$ ?x93 2))) (= (mod$ ?x93 2) ?x99))))
  1.2333 -(let ((?x499 (mod$ ?x93 2)))
  1.2334 -(let (($x500 (= ?x499 ?x98)))
  1.2335 -(let (($x297 (forall ((?v0 Int_list$) (?v1 Int_list$) )(! (= (mod$ (eval_dioph$ ?v0 ?v1) 2) (mod$ (eval_dioph$ ?v0 (map$ uu$ ?v1)) 2)) :pattern ( (eval_dioph$ ?v0 (map$ uu$ ?v1)) ) :qid k!18))
  1.2336 -))
  1.2337 -(let (($x51 (forall ((?v0 Int_list$) (?v1 Int_list$) )(! (= (mod$ (eval_dioph$ ?v0 ?v1) 2) (mod$ (eval_dioph$ ?v0 (map$ uu$ ?v1)) 2)) :qid k!18))
  1.2338 -))
  1.2339 -(let (($x50 (= (mod$ ?x45 2) (mod$ ?x48 2))))
  1.2340 -(let ((@x265 (mp~ (asserted $x51) (nnf-pos (refl (~ $x50 $x50)) (~ $x51 $x51)) $x51)))
  1.2341 -(let ((@x302 (mp @x265 (quant-intro (refl (= $x50 $x50)) (= $x51 $x297)) $x297)))
  1.2342 -(let (($x464 (or (not $x297) $x500)))
  1.2343 -(let ((@x578 ((_ quant-inst ks$ xs$) $x464)))
  1.2344 -(let ((@x748 (trans (symm (unit-resolution @x578 @x302 $x500) (= ?x98 ?x499)) @x741 $x100)))
  1.2345 -(let ((@x891 (unit-resolution (unit-resolution (def-axiom (or $x284 $x281 $x282)) @x828 $x283) (lemma (unit-resolution (hypothesis $x281) @x748 false) $x100) $x282)))
  1.2346 -(let ((@x895 (unit-resolution ((_ th-lemma arith triangle-eq) (or $x117 $x807 (not $x673))) @x891 (or $x807 (not $x673)))))
  1.2347 -((_ th-lemma arith farkas -2 -2 1 -1 1 1) (unit-resolution @x895 @x889 $x807) @x485 @x745 @x488 (unit-resolution ((_ th-lemma arith triangle-eq) (or $x134 $x679)) @x584 $x679) (unit-resolution ((_ th-lemma arith) (or false $x564)) @x26 $x564) false)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
  1.2348 -
  1.2349 -db184ed715734759b60f9bdc99290a92283563f5 64 0
  1.2350 -unsat
  1.2351 -((set-logic AUFLIA)
  1.2352 -(proof
  1.2353 -(let ((?x108 (collect$ uu$)))
  1.2354 -(let ((?x109 (sup$ ?x108)))
  1.2355 -(let (($x117 (less_eq$ ?x109 ?x109)))
  1.2356 -(let (($x118 (not $x117)))
  1.2357 -(let ((@x119 (asserted $x118)))
  1.2358 -(let ((?x111 (collect$ uua$)))
  1.2359 -(let ((?x112 (sup$ ?x111)))
  1.2360 -(let (($x115 (less_eq$ ?x112 ?x109)))
  1.2361 -(let ((@x116 (asserted $x115)))
  1.2362 -(let (($x113 (less_eq$ ?x109 ?x112)))
  1.2363 -(let ((@x114 (asserted $x113)))
  1.2364 -(let (($x578 (forall ((?v0 A$) (?v1 A$) (?v2 A$) )(! (let (($x97 (less_eq$ ?v0 ?v2)))
  1.2365 -(let (($x95 (less_eq$ ?v1 ?v2)))
  1.2366 -(let (($x138 (not $x95)))
  1.2367 -(let (($x93 (less_eq$ ?v0 ?v1)))
  1.2368 -(let (($x137 (not $x93)))
  1.2369 -(or $x137 $x138 $x97)))))) :pattern ( (less_eq$ ?v0 ?v1) (less_eq$ ?v1 ?v2) ) :qid k!17))
  1.2370 -))
  1.2371 -(let (($x156 (forall ((?v0 A$) (?v1 A$) (?v2 A$) )(! (let (($x97 (less_eq$ ?v0 ?v2)))
  1.2372 -(let (($x95 (less_eq$ ?v1 ?v2)))
  1.2373 -(let (($x138 (not $x95)))
  1.2374 -(let (($x93 (less_eq$ ?v0 ?v1)))
  1.2375 -(let (($x137 (not $x93)))
  1.2376 -(or $x137 $x138 $x97)))))) :qid k!17))
  1.2377 -))
  1.2378 -(let ((@x583 (trans (rewrite (= $x156 $x578)) (rewrite (= $x578 $x578)) (= $x156 $x578))))
  1.2379 -(let (($x105 (forall ((?v0 A$) (?v1 A$) (?v2 A$) )(! (let (($x97 (less_eq$ ?v0 ?v2)))
  1.2380 -(let (($x95 (less_eq$ ?v1 ?v2)))
  1.2381 -(let (($x93 (less_eq$ ?v0 ?v1)))
  1.2382 -(let (($x96 (and $x93 $x95)))
  1.2383 -(let (($x101 (not $x96)))
  1.2384 -(or $x101 $x97)))))) :qid k!17))
  1.2385 -))
  1.2386 -(let (($x97 (less_eq$ ?2 ?0)))
  1.2387 -(let (($x95 (less_eq$ ?1 ?0)))
  1.2388 -(let (($x138 (not $x95)))
  1.2389 -(let (($x93 (less_eq$ ?2 ?1)))
  1.2390 -(let (($x137 (not $x93)))
  1.2391 -(let (($x151 (or $x137 $x138 $x97)))
  1.2392 -(let (($x96 (and $x93 $x95)))
  1.2393 -(let (($x101 (not $x96)))
  1.2394 -(let (($x102 (or $x101 $x97)))
  1.2395 -(let ((@x143 (monotonicity (rewrite (= $x96 (not (or $x137 $x138)))) (= $x101 (not (not (or $x137 $x138)))))))
  1.2396 -(let ((@x147 (trans @x143 (rewrite (= (not (not (or $x137 $x138))) (or $x137 $x138))) (= $x101 (or $x137 $x138)))))
  1.2397 -(let ((@x155 (trans (monotonicity @x147 (= $x102 (or (or $x137 $x138) $x97))) (rewrite (= (or (or $x137 $x138) $x97) $x151)) (= $x102 $x151))))
  1.2398 -(let (($x99 (forall ((?v0 A$) (?v1 A$) (?v2 A$) )(! (let (($x97 (less_eq$ ?v0 ?v2)))
  1.2399 -(let (($x95 (less_eq$ ?v1 ?v2)))
  1.2400 -(let (($x93 (less_eq$ ?v0 ?v1)))
  1.2401 -(let (($x96 (and $x93 $x95)))
  1.2402 -(=> $x96 $x97))))) :qid k!17))
  1.2403 -))
  1.2404 -(let ((@x110 (mp (asserted $x99) (quant-intro (rewrite (= (=> $x96 $x97) $x102)) (= $x99 $x105)) $x105)))
  1.2405 -(let ((@x159 (mp (mp~ @x110 (nnf-pos (refl (~ $x102 $x102)) (~ $x105 $x105)) $x105) (quant-intro @x155 (= $x105 $x156)) $x156)))
  1.2406 -(let ((@x584 (mp @x159 @x583 $x578)))
  1.2407 -(let (($x247 (not $x115)))
  1.2408 -(let (($x160 (not $x113)))
  1.2409 -(let (($x251 (not $x578)))
  1.2410 -(let (($x252 (or $x251 $x160 $x247 $x117)))
  1.2411 -(let ((@x570 (mp ((_ quant-inst (sup$ ?x108) (sup$ ?x111) (sup$ ?x108)) (or $x251 (or $x160 $x247 $x117))) (rewrite (= (or $x251 (or $x160 $x247 $x117)) $x252)) $x252)))
  1.2412 -(unit-resolution @x570 @x584 @x114 @x116 @x119 false)))))))))))))))))))))))))))))))))))))))
  1.2413 -
  1.2414 -4e8ab14f236ad601aa67494ca8ea18b2ba6a1a79 25 0
  1.2415 -unsat
  1.2416 -((set-logic AUFLIA)
  1.2417 -(proof
  1.2418 -(let (($x142 (pred$e 1)))
  1.2419 -(let (($x144 (not $x142)))
  1.2420 -(let ((@x145 (asserted $x144)))
  1.2421 -(let (($x615 (forall ((?v0 Int) )(! (pred$e ?v0) :pattern ( (pred$e ?v0) ) :qid k!29))
  1.2422 -))
  1.2423 -(let (($x138 (forall ((?v0 Int) )(! (pred$e ?v0) :qid k!29))
  1.2424 -))
  1.2425 -(let (($x127 (forall ((?v0 Int) )(! (let (($x125 (or (pred$d (cons$d ?v0 nil$d)) (not (pred$d (cons$d ?v0 nil$d))))))
  1.2426 -(let (($x119 (pred$e ?v0)))
  1.2427 -(and $x119 $x125))) :qid k!29))
  1.2428 -))
  1.2429 -(let (($x119 (pred$e ?0)))
  1.2430 -(let (($x125 (or (pred$d (cons$d ?0 nil$d)) (not (pred$d (cons$d ?0 nil$d))))))
  1.2431 -(let (($x126 (and $x119 $x125)))
  1.2432 -(let ((@x133 (monotonicity (rewrite (= $x125 true)) (= $x126 (and $x119 true)))))
  1.2433 -(let ((@x140 (quant-intro (trans @x133 (rewrite (= (and $x119 true) $x119)) (= $x126 $x119)) (= $x127 $x138))))
  1.2434 -(let ((@x170 (mp~ (mp (asserted $x127) @x140 $x138) (nnf-pos (refl (~ $x119 $x119)) (~ $x138 $x138)) $x138)))
  1.2435 -(let ((@x620 (mp @x170 (quant-intro (refl (= $x119 $x119)) (= $x138 $x615)) $x615)))
  1.2436 -(let (($x257 (or (not $x615) $x142)))
  1.2437 -(let ((@x258 ((_ quant-inst 1) $x257)))
  1.2438 -(unit-resolution @x258 @x620 @x145 false))))))))))))))))))
  1.2439 -
  1.2440 -b4b100f728c8f0d6f96483e4de44e248cc4be1aa 101 0
  1.2441 +49c385b161a0c500f84c45f85272a8ec9574fef4 126 0
  1.2442  unsat
  1.2443  ((set-logic AUFLIA)
  1.2444  (proof
  1.2445 -(let ((?x124 (some$a true)))
  1.2446 -(let ((?x125 (g$b ?x124)))
  1.2447 -(let ((?x122 (some$ 3)))
  1.2448 -(let ((?x123 (g$ ?x122)))
  1.2449 -(let (($x126 (= ?x123 ?x125)))
  1.2450 -(let ((?x269 (cons$a true nil$a)))
  1.2451 -(let ((?x270 (g$c ?x269)))
  1.2452 -(let (($x587 (= ?x125 ?x270)))
  1.2453 -(let (($x604 (forall ((?v0 Bool) )(! (= (g$b (some$a ?v0)) (g$c (cons$a ?v0 nil$a))) :pattern ( (some$a ?v0) ) :pattern ( (cons$a ?v0 nil$a) ) :qid k!33))
  1.2454 -))
  1.2455 -(let (($x43 (forall ((?v0 Bool) )(! (= (g$b (some$a ?v0)) (g$c (cons$a ?v0 nil$a))) :qid k!33))
  1.2456 -))
  1.2457 -(let (($x42 (= (g$b (some$a ?0)) (g$c (cons$a ?0 nil$a)))))
  1.2458 -(let ((@x160 (mp~ (asserted $x43) (nnf-pos (refl (~ $x42 $x42)) (~ $x43 $x43)) $x43)))
  1.2459 -(let ((@x609 (mp @x160 (quant-intro (refl (= $x42 $x42)) (= $x43 $x604)) $x604)))
  1.2460 -(let (($x254 (or (not $x604) $x587)))
  1.2461 -(let ((@x255 ((_ quant-inst true) $x254)))
  1.2462 -(let ((?x227 (size$ ?x269)))
  1.2463 -(let (($x569 (= ?x270 ?x227)))
  1.2464 -(let (($x612 (forall ((?v0 Bool_list$) )(! (let ((?x61 (size$ ?v0)))
  1.2465 -(let ((?x60 (g$c ?v0)))
  1.2466 -(= ?x60 ?x61))) :pattern ( (g$c ?v0) ) :pattern ( (size$ ?v0) ) :qid k!38))
  1.2467 -))
  1.2468 -(let (($x63 (forall ((?v0 Bool_list$) )(! (let ((?x61 (size$ ?v0)))
  1.2469 -(let ((?x60 (g$c ?v0)))
  1.2470 -(= ?x60 ?x61))) :qid k!38))
  1.2471 -))
  1.2472 -(let ((@x616 (quant-intro (refl (= (= (g$c ?0) (size$ ?0)) (= (g$c ?0) (size$ ?0)))) (= $x63 $x612))))
  1.2473 -(let ((@x142 (nnf-pos (refl (~ (= (g$c ?0) (size$ ?0)) (= (g$c ?0) (size$ ?0)))) (~ $x63 $x63))))
  1.2474 -(let ((@x617 (mp (mp~ (asserted $x63) @x142 $x63) @x616 $x612)))
  1.2475 -(let (($x571 (or (not $x612) $x569)))
  1.2476 -(let ((@x572 ((_ quant-inst (cons$a true nil$a)) $x571)))
  1.2477 -(let ((?x89 (suc$ zero$)))
  1.2478 -(let ((?x105 (size$ nil$a)))
  1.2479 -(let ((?x233 (plus$ ?x105 ?x89)))
  1.2480 -(let (($x570 (= ?x227 ?x233)))
  1.2481 -(let (($x657 (forall ((?v0 Bool) (?v1 Bool_list$) )(! (= (size$ (cons$a ?v0 ?v1)) (plus$ (size$ ?v1) (suc$ zero$))) :pattern ( (cons$a ?v0 ?v1) ) :qid k!46))
  1.2482 -))
  1.2483 -(let (($x114 (forall ((?v0 Bool) (?v1 Bool_list$) )(! (= (size$ (cons$a ?v0 ?v1)) (plus$ (size$ ?v1) (suc$ zero$))) :qid k!46))
  1.2484 -))
  1.2485 -(let (($x113 (= (size$ (cons$a ?1 ?0)) (plus$ (size$ ?0) ?x89))))
  1.2486 -(let ((@x173 (mp~ (asserted $x114) (nnf-pos (refl (~ $x113 $x113)) (~ $x114 $x114)) $x114)))
  1.2487 -(let ((@x662 (mp @x173 (quant-intro (refl (= $x113 $x113)) (= $x114 $x657)) $x657)))
  1.2488 -(let (($x576 (or (not $x657) $x570)))
  1.2489 -(let ((@x213 ((_ quant-inst true nil$a) $x576)))
  1.2490 -(let ((?x108 (size$a nil$)))
  1.2491 -(let (($x109 (= ?x108 zero$)))
  1.2492 -(let ((@x110 (asserted $x109)))
  1.2493 -(let (($x106 (= ?x105 zero$)))
  1.2494 -(let ((@x107 (asserted $x106)))
  1.2495 -(let ((@x287 (monotonicity (trans @x107 (symm @x110 (= zero$ ?x108)) (= ?x105 ?x108)) (= ?x233 (plus$ ?x108 ?x89)))))
  1.2496 -(let ((?x246 (plus$ ?x108 ?x89)))
  1.2497 -(let ((?x256 (cons$ 3 nil$)))
  1.2498 -(let ((?x588 (size$a ?x256)))
  1.2499 -(let (($x584 (= ?x588 ?x246)))
  1.2500 -(let (($x664 (forall ((?v0 Int) (?v1 Int_list$) )(! (= (size$a (cons$ ?v0 ?v1)) (plus$ (size$a ?v1) (suc$ zero$))) :pattern ( (cons$ ?v0 ?v1) ) :qid k!47))
  1.2501 -))
  1.2502 -(let (($x119 (forall ((?v0 Int) (?v1 Int_list$) )(! (= (size$a (cons$ ?v0 ?v1)) (plus$ (size$a ?v1) (suc$ zero$))) :qid k!47))
  1.2503 -))
  1.2504 -(let (($x118 (= (size$a (cons$ ?1 ?0)) (plus$ (size$a ?0) ?x89))))
  1.2505 -(let ((@x178 (mp~ (asserted $x119) (nnf-pos (refl (~ $x118 $x118)) (~ $x119 $x119)) $x119)))
  1.2506 -(let ((@x669 (mp @x178 (quant-intro (refl (= $x118 $x118)) (= $x119 $x664)) $x664)))
  1.2507 -(let (($x231 (or (not $x664) $x584)))
  1.2508 -(let ((@x232 ((_ quant-inst 3 nil$) $x231)))
  1.2509 -(let ((?x267 (g$a ?x256)))
  1.2510 -(let (($x592 (= ?x267 ?x588)))
  1.2511 -(let (($x620 (forall ((?v0 Int_list$) )(! (let ((?x67 (size$a ?v0)))
  1.2512 -(let ((?x66 (g$a ?v0)))
  1.2513 -(= ?x66 ?x67))) :pattern ( (g$a ?v0) ) :pattern ( (size$a ?v0) ) :qid k!39))
  1.2514 -))
  1.2515 -(let (($x69 (forall ((?v0 Int_list$) )(! (let ((?x67 (size$a ?v0)))
  1.2516 -(let ((?x66 (g$a ?v0)))
  1.2517 -(= ?x66 ?x67))) :qid k!39))
  1.2518 -))
  1.2519 -(let ((@x622 (refl (= (= (g$a ?0) (size$a ?0)) (= (g$a ?0) (size$a ?0))))))
  1.2520 -(let ((@x129 (nnf-pos (refl (~ (= (g$a ?0) (size$a ?0)) (= (g$a ?0) (size$a ?0)))) (~ $x69 $x69))))
  1.2521 -(let ((@x625 (mp (mp~ (asserted $x69) @x129 $x69) (quant-intro @x622 (= $x69 $x620)) $x620)))
  1.2522 -(let (($x248 (or (not $x620) $x592)))
  1.2523 -(let ((@x585 ((_ quant-inst (cons$ 3 nil$)) $x248)))
  1.2524 -(let (($x268 (= ?x123 ?x267)))
  1.2525 -(let (($x596 (forall ((?v0 Int) )(! (= (g$ (some$ ?v0)) (g$a (cons$ ?v0 nil$))) :pattern ( (some$ ?v0) ) :pattern ( (cons$ ?v0 nil$) ) :qid k!32))
  1.2526 -))
  1.2527 -(let (($x34 (forall ((?v0 Int) )(! (= (g$ (some$ ?v0)) (g$a (cons$ ?v0 nil$))) :qid k!32))
  1.2528 -))
  1.2529 -(let (($x33 (= (g$ (some$ ?0)) (g$a (cons$ ?0 nil$)))))
  1.2530 -(let ((@x157 (mp~ (asserted $x34) (nnf-pos (refl (~ $x33 $x33)) (~ $x34 $x34)) $x34)))
  1.2531 -(let ((@x601 (mp @x157 (quant-intro (refl (= $x33 $x33)) (= $x34 $x596)) $x596)))
  1.2532 -(let (($x250 (or (not $x596) $x268)))
  1.2533 -(let ((@x586 ((_ quant-inst 3) $x250)))
  1.2534 -(let ((@x275 (trans (unit-resolution @x586 @x601 $x268) (unit-resolution @x585 @x625 $x592) (= ?x123 ?x588))))
  1.2535 -(let ((@x280 (trans (trans @x275 (unit-resolution @x232 @x669 $x584) (= ?x123 ?x246)) (symm @x287 (= ?x246 ?x233)) (= ?x123 ?x233))))
  1.2536 -(let ((@x558 (trans @x280 (symm (unit-resolution @x213 @x662 $x570) (= ?x233 ?x227)) (= ?x123 ?x227))))
  1.2537 -(let ((@x560 (trans @x558 (symm (unit-resolution @x572 @x617 $x569) (= ?x227 ?x270)) (= ?x123 ?x270))))
  1.2538 -(let ((@x546 (trans @x560 (symm (unit-resolution @x255 @x609 $x587) (= ?x270 ?x125)) $x126)))
  1.2539 -(let (($x127 (not $x126)))
  1.2540 -(let ((@x128 (asserted $x127)))
  1.2541 -(unit-resolution @x128 @x546 false)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
  1.2542 -
  1.2543 -0f7f4a10f8a84029fd3a6efddc4408fa429b0cda 113 0
  1.2544 -unsat
  1.2545 -((set-logic <null>)
  1.2546 -(proof
  1.2547 -(let ((?x228 (mod x$ 2)))
  1.2548 -(let ((?x262 (* (- 1) ?x228)))
  1.2549 -(let ((?x31 (mod$ x$ 2)))
  1.2550 -(let ((?x263 (+ ?x31 ?x262)))
  1.2551 -(let (($x280 (>= ?x263 0)))
  1.2552 -(let (($x264 (= ?x263 0)))
  1.2553 -(let (($x205 (forall ((?v0 Int) (?v1 Int) )(!(let ((?x136 (mod ?v0 ?v1)))
  1.2554 -(let ((?x93 (* (- 1) ?v1)))
  1.2555 -(let ((?x90 (* (- 1) ?v0)))
  1.2556 -(let ((?x144 (mod ?x90 ?x93)))
  1.2557 -(let ((?x150 (* (- 1) ?x144)))
  1.2558 -(let (($x111 (<= ?v1 0)))
  1.2559 -(let ((?x170 (ite $x111 ?x150 ?x136)))
  1.2560 -(let (($x78 (= ?v1 0)))
  1.2561 -(let ((?x175 (ite $x78 ?v0 ?x170)))
  1.2562 -(let ((?x135 (mod$ ?v0 ?v1)))
  1.2563 -(= ?x135 ?x175))))))))))) :pattern ( (mod$ ?v0 ?v1) )))
  1.2564 -))
  1.2565 -(let (($x181 (forall ((?v0 Int) (?v1 Int) )(let ((?x136 (mod ?v0 ?v1)))
  1.2566 -(let ((?x93 (* (- 1) ?v1)))
  1.2567 -(let ((?x90 (* (- 1) ?v0)))
  1.2568 -(let ((?x144 (mod ?x90 ?x93)))
  1.2569 -(let ((?x150 (* (- 1) ?x144)))
  1.2570 -(let (($x111 (<= ?v1 0)))
  1.2571 -(let ((?x170 (ite $x111 ?x150 ?x136)))
  1.2572 -(let (($x78 (= ?v1 0)))
  1.2573 -(let ((?x175 (ite $x78 ?v0 ?x170)))
  1.2574 -(let ((?x135 (mod$ ?v0 ?v1)))
  1.2575 -(= ?x135 ?x175))))))))))))
  1.2576 -))
  1.2577 -(let ((?x136 (mod ?1 ?0)))
  1.2578 -(let ((?x93 (* (- 1) ?0)))
  1.2579 -(let ((?x90 (* (- 1) ?1)))
  1.2580 -(let ((?x144 (mod ?x90 ?x93)))
  1.2581 -(let ((?x150 (* (- 1) ?x144)))
  1.2582 -(let (($x111 (<= ?0 0)))
  1.2583 -(let ((?x170 (ite $x111 ?x150 ?x136)))
  1.2584 -(let (($x78 (= ?0 0)))
  1.2585 -(let ((?x175 (ite $x78 ?1 ?x170)))
  1.2586 -(let ((?x135 (mod$ ?1 ?0)))
  1.2587 -(let (($x178 (= ?x135 ?x175)))
  1.2588 -(let (($x142 (forall ((?v0 Int) (?v1 Int) )(let (($x78 (= ?v1 0)))
  1.2589 -(let ((?x140 (ite $x78 ?v0 (ite (< 0 ?v1) (mod ?v0 ?v1) (- (mod (- ?v0) (- ?v1)))))))
  1.2590 -(let ((?x135 (mod$ ?v0 ?v1)))
  1.2591 -(= ?x135 ?x140)))))
  1.2592 -))
  1.2593 -(let (($x164 (forall ((?v0 Int) (?v1 Int) )(let ((?x93 (* (- 1) ?v1)))
  1.2594 -(let ((?x90 (* (- 1) ?v0)))
  1.2595 -(let ((?x144 (mod ?x90 ?x93)))
  1.2596 -(let ((?x150 (* (- 1) ?x144)))
  1.2597 -(let ((?x136 (mod ?v0 ?v1)))
  1.2598 -(let (($x79 (< 0 ?v1)))
  1.2599 -(let ((?x155 (ite $x79 ?x136 ?x150)))
  1.2600 -(let (($x78 (= ?v1 0)))
  1.2601 -(let ((?x158 (ite $x78 ?v0 ?x155)))
  1.2602 -(let ((?x135 (mod$ ?v0 ?v1)))
  1.2603 -(= ?x135 ?x158))))))))))))
  1.2604 -))
  1.2605 -(let ((@x169 (monotonicity (rewrite (= (< 0 ?0) (not $x111))) (= (ite (< 0 ?0) ?x136 ?x150) (ite (not $x111) ?x136 ?x150)))))
  1.2606 -(let ((@x174 (trans @x169 (rewrite (= (ite (not $x111) ?x136 ?x150) ?x170)) (= (ite (< 0 ?0) ?x136 ?x150) ?x170))))
  1.2607 -(let ((@x177 (monotonicity @x174 (= (ite $x78 ?1 (ite (< 0 ?0) ?x136 ?x150)) ?x175))))
  1.2608 -(let ((@x180 (monotonicity @x177 (= (= ?x135 (ite $x78 ?1 (ite (< 0 ?0) ?x136 ?x150))) $x178))))
  1.2609 -(let (($x79 (< 0 ?0)))
  1.2610 -(let ((?x155 (ite $x79 ?x136 ?x150)))
  1.2611 -(let ((?x158 (ite $x78 ?1 ?x155)))
  1.2612 -(let (($x161 (= ?x135 ?x158)))
  1.2613 -(let (($x162 (= (= ?x135 (ite $x78 ?1 (ite $x79 ?x136 (- (mod (- ?1) (- ?0)))))) $x161)))
  1.2614 -(let ((@x146 (monotonicity (rewrite (= (- ?1) ?x90)) (rewrite (= (- ?0) ?x93)) (= (mod (- ?1) (- ?0)) ?x144))))
  1.2615 -(let ((@x154 (trans (monotonicity @x146 (= (- (mod (- ?1) (- ?0))) (- ?x144))) (rewrite (= (- ?x144) ?x150)) (= (- (mod (- ?1) (- ?0))) ?x150))))
  1.2616 -(let ((@x157 (monotonicity @x154 (= (ite $x79 ?x136 (- (mod (- ?1) (- ?0)))) ?x155))))
  1.2617 -(let ((@x160 (monotonicity @x157 (= (ite $x78 ?1 (ite $x79 ?x136 (- (mod (- ?1) (- ?0))))) ?x158))))
  1.2618 -(let ((@x185 (trans (quant-intro (monotonicity @x160 $x162) (= $x142 $x164)) (quant-intro @x180 (= $x164 $x181)) (= $x142 $x181))))
  1.2619 -(let ((@x196 (mp~ (mp (asserted $x142) @x185 $x181) (nnf-pos (refl (~ $x178 $x178)) (~ $x181 $x181)) $x181)))
  1.2620 -(let ((@x210 (mp @x196 (quant-intro (refl (= $x178 $x178)) (= $x181 $x205)) $x205)))
  1.2621 -(let (($x270 (or (not $x205) $x264)))
  1.2622 -(let ((?x225 (* (- 1) 2)))
  1.2623 -(let ((?x224 (* (- 1) x$)))
  1.2624 -(let ((?x226 (mod ?x224 ?x225)))
  1.2625 -(let ((?x227 (* (- 1) ?x226)))
  1.2626 -(let (($x223 (<= 2 0)))
  1.2627 -(let ((?x229 (ite $x223 ?x227 ?x228)))
  1.2628 -(let (($x222 (= 2 0)))
  1.2629 -(let ((?x230 (ite $x222 x$ ?x229)))
  1.2630 -(let (($x231 (= ?x31 ?x230)))
  1.2631 -(let ((@x244 (monotonicity (monotonicity (rewrite (= ?x225 (- 2))) (= ?x226 (mod ?x224 (- 2)))) (= ?x227 (* (- 1) (mod ?x224 (- 2)))))))
  1.2632 -(let ((@x247 (monotonicity (rewrite (= $x223 false)) @x244 (= ?x229 (ite false (* (- 1) (mod ?x224 (- 2))) ?x228)))))
  1.2633 -(let ((@x251 (trans @x247 (rewrite (= (ite false (* (- 1) (mod ?x224 (- 2))) ?x228) ?x228)) (= ?x229 ?x228))))
  1.2634 -(let ((@x254 (monotonicity (rewrite (= $x222 false)) @x251 (= ?x230 (ite false x$ ?x228)))))
  1.2635 -(let ((@x261 (monotonicity (trans @x254 (rewrite (= (ite false x$ ?x228) ?x228)) (= ?x230 ?x228)) (= $x231 (= ?x31 ?x228)))))
  1.2636 -(let ((@x274 (monotonicity (trans @x261 (rewrite (= (= ?x31 ?x228) $x264)) (= $x231 $x264)) (= (or (not $x205) $x231) $x270))))
  1.2637 -(let ((@x277 (trans @x274 (rewrite (= $x270 $x270)) (= (or (not $x205) $x231) $x270))))
  1.2638 -(let ((@x278 (mp ((_ quant-inst x$ 2) (or (not $x205) $x231)) @x277 $x270)))
  1.2639 -(let ((@x337 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x264) $x280)) (unit-resolution @x278 @x210 $x264) $x280)))
  1.2640 -(let (($x305 (>= ?x228 0)))
  1.2641 -(let (($x64 (>= ?x31 0)))
  1.2642 -(let (($x67 (not $x64)))
  1.2643 -(let (($x36 (not (<= (+ x$ 1) (+ x$ (+ (* 2 ?x31) 1))))))
  1.2644 -(let ((@x69 (monotonicity (rewrite (= (>= (* 2 ?x31) 0) $x64)) (= (not (>= (* 2 ?x31) 0)) $x67))))
  1.2645 -(let ((?x32 (* 2 ?x31)))
  1.2646 -(let ((?x47 (+ 1 x$ ?x32)))
  1.2647 -(let (($x52 (<= (+ 1 x$) ?x47)))
  1.2648 -(let (($x55 (not $x52)))
  1.2649 -(let ((@x63 (monotonicity (rewrite (= $x52 (>= ?x32 0))) (= $x55 (not (>= ?x32 0))))))
  1.2650 -(let ((@x46 (monotonicity (rewrite (= (+ ?x32 1) (+ 1 ?x32))) (= (+ x$ (+ ?x32 1)) (+ x$ (+ 1 ?x32))))))
  1.2651 -(let ((@x51 (trans @x46 (rewrite (= (+ x$ (+ 1 ?x32)) ?x47)) (= (+ x$ (+ ?x32 1)) ?x47))))
  1.2652 -(let ((@x54 (monotonicity (rewrite (= (+ x$ 1) (+ 1 x$))) @x51 (= (<= (+ x$ 1) (+ x$ (+ ?x32 1))) $x52))))
  1.2653 -(let ((@x73 (trans (monotonicity @x54 (= $x36 $x55)) (trans @x63 @x69 (= $x55 $x67)) (= $x36 $x67))))
  1.2654 -(let ((@x74 (mp (asserted $x36) @x73 $x67)))
  1.2655 -((_ th-lemma arith farkas -1 1 1) @x74 (unit-resolution ((_ th-lemma arith) (or false $x305)) (true-axiom true) $x305) @x337 false))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
  1.2656 -
  1.2657 -fa5abc269019f00f5093218b287856c2a08c0adf 112 0
  1.2658 -unsat
  1.2659 -((set-logic <null>)
  1.2660 -(proof
  1.2661 -(let ((?x224 (mod x$ 2)))
  1.2662 -(let (($x318 (>= ?x224 2)))
  1.2663 -(let (($x319 (not $x318)))
  1.2664 -(let ((?x258 (* (- 1) ?x224)))
  1.2665 -(let ((?x29 (mod$ x$ 2)))
  1.2666 -(let ((?x259 (+ ?x29 ?x258)))
  1.2667 -(let (($x275 (<= ?x259 0)))
  1.2668 -(let (($x260 (= ?x259 0)))
  1.2669 -(let (($x201 (forall ((?v0 Int) (?v1 Int) )(!(let ((?x132 (mod ?v0 ?v1)))
  1.2670 -(let ((?x89 (* (- 1) ?v1)))
  1.2671 -(let ((?x86 (* (- 1) ?v0)))
  1.2672 -(let ((?x140 (mod ?x86 ?x89)))
  1.2673 -(let ((?x146 (* (- 1) ?x140)))
  1.2674 -(let (($x107 (<= ?v1 0)))
  1.2675 -(let ((?x166 (ite $x107 ?x146 ?x132)))
  1.2676 -(let (($x74 (= ?v1 0)))
  1.2677 -(let ((?x171 (ite $x74 ?v0 ?x166)))
  1.2678 -(let ((?x131 (mod$ ?v0 ?v1)))
  1.2679 -(= ?x131 ?x171))))))))))) :pattern ( (mod$ ?v0 ?v1) )))
  1.2680 -))
  1.2681 -(let (($x177 (forall ((?v0 Int) (?v1 Int) )(let ((?x132 (mod ?v0 ?v1)))
  1.2682 -(let ((?x89 (* (- 1) ?v1)))
  1.2683 -(let ((?x86 (* (- 1) ?v0)))
  1.2684 -(let ((?x140 (mod ?x86 ?x89)))
  1.2685 -(let ((?x146 (* (- 1) ?x140)))
  1.2686 -(let (($x107 (<= ?v1 0)))
  1.2687 -(let ((?x166 (ite $x107 ?x146 ?x132)))
  1.2688 -(let (($x74 (= ?v1 0)))
  1.2689 -(let ((?x171 (ite $x74 ?v0 ?x166)))
  1.2690 -(let ((?x131 (mod$ ?v0 ?v1)))
  1.2691 -(= ?x131 ?x171))))))))))))
  1.2692 -))
  1.2693 -(let ((?x132 (mod ?1 ?0)))
  1.2694 -(let ((?x89 (* (- 1) ?0)))
  1.2695 -(let ((?x86 (* (- 1) ?1)))
  1.2696 -(let ((?x140 (mod ?x86 ?x89)))
  1.2697 -(let ((?x146 (* (- 1) ?x140)))
  1.2698 -(let (($x107 (<= ?0 0)))
  1.2699 -(let ((?x166 (ite $x107 ?x146 ?x132)))
  1.2700 -(let (($x74 (= ?0 0)))
  1.2701 -(let ((?x171 (ite $x74 ?1 ?x166)))
  1.2702 -(let ((?x131 (mod$ ?1 ?0)))
  1.2703 -(let (($x174 (= ?x131 ?x171)))
  1.2704 -(let (($x138 (forall ((?v0 Int) (?v1 Int) )(let (($x74 (= ?v1 0)))
  1.2705 -(let ((?x136 (ite $x74 ?v0 (ite (< 0 ?v1) (mod ?v0 ?v1) (- (mod (- ?v0) (- ?v1)))))))
  1.2706 -(let ((?x131 (mod$ ?v0 ?v1)))
  1.2707 -(= ?x131 ?x136)))))
  1.2708 -))
  1.2709 -(let (($x160 (forall ((?v0 Int) (?v1 Int) )(let ((?x89 (* (- 1) ?v1)))
  1.2710 -(let ((?x86 (* (- 1) ?v0)))
  1.2711 -(let ((?x140 (mod ?x86 ?x89)))
  1.2712 -(let ((?x146 (* (- 1) ?x140)))
  1.2713 -(let ((?x132 (mod ?v0 ?v1)))
  1.2714 -(let (($x75 (< 0 ?v1)))
  1.2715 -(let ((?x151 (ite $x75 ?x132 ?x146)))
  1.2716 -(let (($x74 (= ?v1 0)))
  1.2717 -(let ((?x154 (ite $x74 ?v0 ?x151)))
  1.2718 -(let ((?x131 (mod$ ?v0 ?v1)))
  1.2719 -(= ?x131 ?x154))))))))))))
  1.2720 -))
  1.2721 -(let ((@x165 (monotonicity (rewrite (= (< 0 ?0) (not $x107))) (= (ite (< 0 ?0) ?x132 ?x146) (ite (not $x107) ?x132 ?x146)))))
  1.2722 -(let ((@x170 (trans @x165 (rewrite (= (ite (not $x107) ?x132 ?x146) ?x166)) (= (ite (< 0 ?0) ?x132 ?x146) ?x166))))
  1.2723 -(let ((@x173 (monotonicity @x170 (= (ite $x74 ?1 (ite (< 0 ?0) ?x132 ?x146)) ?x171))))
  1.2724 -(let ((@x176 (monotonicity @x173 (= (= ?x131 (ite $x74 ?1 (ite (< 0 ?0) ?x132 ?x146))) $x174))))
  1.2725 -(let (($x75 (< 0 ?0)))
  1.2726 -(let ((?x151 (ite $x75 ?x132 ?x146)))
  1.2727 -(let ((?x154 (ite $x74 ?1 ?x151)))
  1.2728 -(let (($x157 (= ?x131 ?x154)))
  1.2729 -(let (($x158 (= (= ?x131 (ite $x74 ?1 (ite $x75 ?x132 (- (mod (- ?1) (- ?0)))))) $x157)))
  1.2730 -(let ((@x142 (monotonicity (rewrite (= (- ?1) ?x86)) (rewrite (= (- ?0) ?x89)) (= (mod (- ?1) (- ?0)) ?x140))))
  1.2731 -(let ((@x150 (trans (monotonicity @x142 (= (- (mod (- ?1) (- ?0))) (- ?x140))) (rewrite (= (- ?x140) ?x146)) (= (- (mod (- ?1) (- ?0))) ?x146))))
  1.2732 -(let ((@x153 (monotonicity @x150 (= (ite $x75 ?x132 (- (mod (- ?1) (- ?0)))) ?x151))))
  1.2733 -(let ((@x156 (monotonicity @x153 (= (ite $x74 ?1 (ite $x75 ?x132 (- (mod (- ?1) (- ?0))))) ?x154))))
  1.2734 -(let ((@x181 (trans (quant-intro (monotonicity @x156 $x158) (= $x138 $x160)) (quant-intro @x176 (= $x160 $x177)) (= $x138 $x177))))
  1.2735 -(let ((@x192 (mp~ (mp (asserted $x138) @x181 $x177) (nnf-pos (refl (~ $x174 $x174)) (~ $x177 $x177)) $x177)))
  1.2736 -(let ((@x206 (mp @x192 (quant-intro (refl (= $x174 $x174)) (= $x177 $x201)) $x201)))
  1.2737 -(let (($x266 (or (not $x201) $x260)))
  1.2738 -(let ((?x221 (* (- 1) 2)))
  1.2739 -(let ((?x220 (* (- 1) x$)))
  1.2740 -(let ((?x222 (mod ?x220 ?x221)))
  1.2741 -(let ((?x223 (* (- 1) ?x222)))
  1.2742 -(let (($x219 (<= 2 0)))
  1.2743 -(let ((?x225 (ite $x219 ?x223 ?x224)))
  1.2744 -(let (($x218 (= 2 0)))
  1.2745 -(let ((?x226 (ite $x218 x$ ?x225)))
  1.2746 -(let (($x227 (= ?x29 ?x226)))
  1.2747 -(let ((@x240 (monotonicity (monotonicity (rewrite (= ?x221 (- 2))) (= ?x222 (mod ?x220 (- 2)))) (= ?x223 (* (- 1) (mod ?x220 (- 2)))))))
  1.2748 -(let ((@x243 (monotonicity (rewrite (= $x219 false)) @x240 (= ?x225 (ite false (* (- 1) (mod ?x220 (- 2))) ?x224)))))
  1.2749 -(let ((@x247 (trans @x243 (rewrite (= (ite false (* (- 1) (mod ?x220 (- 2))) ?x224) ?x224)) (= ?x225 ?x224))))
  1.2750 -(let ((@x250 (monotonicity (rewrite (= $x218 false)) @x247 (= ?x226 (ite false x$ ?x224)))))
  1.2751 -(let ((@x257 (monotonicity (trans @x250 (rewrite (= (ite false x$ ?x224) ?x224)) (= ?x226 ?x224)) (= $x227 (= ?x29 ?x224)))))
  1.2752 -(let ((@x270 (monotonicity (trans @x257 (rewrite (= (= ?x29 ?x224) $x260)) (= $x227 $x260)) (= (or (not $x201) $x227) $x266))))
  1.2753 -(let ((@x273 (trans @x270 (rewrite (= $x266 $x266)) (= (or (not $x201) $x227) $x266))))
  1.2754 -(let ((@x274 (mp ((_ quant-inst x$ 2) (or (not $x201) $x227)) @x273 $x266)))
  1.2755 -(let ((@x336 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x260) $x275)) (unit-resolution @x274 @x206 $x260) $x275)))
  1.2756 -(let (($x63 (>= ?x29 2)))
  1.2757 -(let ((?x37 (* 2 ?x29)))
  1.2758 -(let (($x56 (>= ?x37 3)))
  1.2759 -(let (($x46 (< (+ x$ ?x37) (+ 3 x$))))
  1.2760 -(let (($x49 (not $x46)))
  1.2761 -(let ((@x58 (monotonicity (rewrite (= $x46 (not $x56))) (= $x49 (not (not $x56))))))
  1.2762 -(let ((@x67 (trans (trans @x58 (rewrite (= (not (not $x56)) $x56)) (= $x49 $x56)) (rewrite (= $x56 $x63)) (= $x49 $x63))))
  1.2763 -(let ((@x42 (monotonicity (rewrite (= (+ ?x29 ?x29) ?x37)) (= (+ x$ (+ ?x29 ?x29)) (+ x$ ?x37)))))
  1.2764 -(let ((@x48 (monotonicity @x42 (rewrite (= (+ x$ 3) (+ 3 x$))) (= (< (+ x$ (+ ?x29 ?x29)) (+ x$ 3)) $x46))))
  1.2765 -(let ((@x51 (monotonicity @x48 (= (not (< (+ x$ (+ ?x29 ?x29)) (+ x$ 3))) $x49))))
  1.2766 -(let ((@x69 (trans @x51 @x67 (= (not (< (+ x$ (+ ?x29 ?x29)) (+ x$ 3))) $x63))))
  1.2767 -(let ((@x70 (mp (asserted (not (< (+ x$ (+ ?x29 ?x29)) (+ x$ 3)))) @x69 $x63)))
  1.2768 -((_ th-lemma arith farkas -1 1 1) @x70 @x336 (unit-resolution ((_ th-lemma arith) (or false $x319)) (true-axiom true) $x319) false)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
  1.2769 -
  1.2770 -1880f0ed1cb3d1cfa006dff17f1b5553ce3a5158 236 0
  1.2771 -unsat
  1.2772 -((set-logic <null>)
  1.2773 -(proof
  1.2774 -(let ((?x410 (div n$ 2)))
  1.2775 -(let ((?x704 (* (- 1) ?x410)))
  1.2776 -(let ((?x381 (div n$ 4)))
  1.2777 -(let ((?x601 (* (- 2) ?x381)))
  1.2778 -(let ((?x329 (mod n$ 4)))
  1.2779 -(let ((?x363 (* (- 1) ?x329)))
  1.2780 -(let ((?x35 (mod$ n$ 4)))
  1.2781 -(let ((?x705 (+ n$ ?x35 ?x363 ?x601 ?x704)))
  1.2782 -(let (($x706 (>= ?x705 2)))
  1.2783 -(let ((?x39 (mod$ n$ 2)))
  1.2784 -(let (($x515 (>= ?x39 1)))
  1.2785 -(let (($x725 (not $x515)))
  1.2786 -(let (($x514 (<= ?x39 1)))
  1.2787 -(let ((?x519 (mod n$ 2)))
  1.2788 -(let ((?x534 (* (- 1) ?x519)))
  1.2789 -(let ((?x535 (+ ?x39 ?x534)))
  1.2790 -(let (($x408 (<= ?x535 0)))
  1.2791 -(let (($x490 (= ?x535 0)))
  1.2792 -(let (($x191 (forall ((?v0 Int) (?v1 Int) )(!(let ((?x108 (mod ?v0 ?v1)))
  1.2793 -(let ((?x65 (* (- 1) ?v1)))
  1.2794 -(let ((?x62 (* (- 1) ?v0)))
  1.2795 -(let ((?x116 (mod ?x62 ?x65)))
  1.2796 -(let ((?x122 (* (- 1) ?x116)))
  1.2797 -(let (($x83 (<= ?v1 0)))
  1.2798 -(let ((?x142 (ite $x83 ?x122 ?x108)))
  1.2799 -(let (($x50 (= ?v1 0)))
  1.2800 -(let ((?x147 (ite $x50 ?v0 ?x142)))
  1.2801 -(let ((?x107 (mod$ ?v0 ?v1)))
  1.2802 -(= ?x107 ?x147))))))))))) :pattern ( (mod$ ?v0 ?v1) )))
  1.2803 -))
  1.2804 -(let (($x153 (forall ((?v0 Int) (?v1 Int) )(let ((?x108 (mod ?v0 ?v1)))
  1.2805 -(let ((?x65 (* (- 1) ?v1)))
  1.2806 -(let ((?x62 (* (- 1) ?v0)))
  1.2807 -(let ((?x116 (mod ?x62 ?x65)))
  1.2808 -(let ((?x122 (* (- 1) ?x116)))
  1.2809 -(let (($x83 (<= ?v1 0)))
  1.2810 -(let ((?x142 (ite $x83 ?x122 ?x108)))
  1.2811 -(let (($x50 (= ?v1 0)))
  1.2812 -(let ((?x147 (ite $x50 ?v0 ?x142)))
  1.2813 -(let ((?x107 (mod$ ?v0 ?v1)))
  1.2814 -(= ?x107 ?x147))))))))))))
  1.2815 -))
  1.2816 -(let ((?x108 (mod ?1 ?0)))
  1.2817 -(let ((?x65 (* (- 1) ?0)))
  1.2818 -(let ((?x62 (* (- 1) ?1)))
  1.2819 -(let ((?x116 (mod ?x62 ?x65)))
  1.2820 -(let ((?x122 (* (- 1) ?x116)))
  1.2821 -(let (($x83 (<= ?0 0)))
  1.2822 -(let ((?x142 (ite $x83 ?x122 ?x108)))
  1.2823 -(let (($x50 (= ?0 0)))
  1.2824 -(let ((?x147 (ite $x50 ?1 ?x142)))
  1.2825 -(let ((?x107 (mod$ ?1 ?0)))
  1.2826 -(let (($x150 (= ?x107 ?x147)))
  1.2827 -(let (($x114 (forall ((?v0 Int) (?v1 Int) )(let (($x50 (= ?v1 0)))
  1.2828 -(let ((?x112 (ite $x50 ?v0 (ite (< 0 ?v1) (mod ?v0 ?v1) (- (mod (- ?v0) (- ?v1)))))))
  1.2829 -(let ((?x107 (mod$ ?v0 ?v1)))
  1.2830 -(= ?x107 ?x112)))))
  1.2831 -))
  1.2832 -(let (($x136 (forall ((?v0 Int) (?v1 Int) )(let ((?x65 (* (- 1) ?v1)))
  1.2833 -(let ((?x62 (* (- 1) ?v0)))
  1.2834 -(let ((?x116 (mod ?x62 ?x65)))
  1.2835 -(let ((?x122 (* (- 1) ?x116)))
  1.2836 -(let ((?x108 (mod ?v0 ?v1)))
  1.2837 -(let (($x51 (< 0 ?v1)))
  1.2838 -(let ((?x127 (ite $x51 ?x108 ?x122)))
  1.2839 -(let (($x50 (= ?v1 0)))
  1.2840 -(let ((?x130 (ite $x50 ?v0 ?x127)))
  1.2841 -(let ((?x107 (mod$ ?v0 ?v1)))
  1.2842 -(= ?x107 ?x130))))))))))))
  1.2843 -))
  1.2844 -(let ((@x141 (monotonicity (rewrite (= (< 0 ?0) (not $x83))) (= (ite (< 0 ?0) ?x108 ?x122) (ite (not $x83) ?x108 ?x122)))))
  1.2845 -(let ((@x146 (trans @x141 (rewrite (= (ite (not $x83) ?x108 ?x122) ?x142)) (= (ite (< 0 ?0) ?x108 ?x122) ?x142))))
  1.2846 -(let ((@x149 (monotonicity @x146 (= (ite $x50 ?1 (ite (< 0 ?0) ?x108 ?x122)) ?x147))))
  1.2847 -(let ((@x152 (monotonicity @x149 (= (= ?x107 (ite $x50 ?1 (ite (< 0 ?0) ?x108 ?x122))) $x150))))
  1.2848 -(let (($x51 (< 0 ?0)))
  1.2849 -(let ((?x127 (ite $x51 ?x108 ?x122)))
  1.2850 -(let ((?x130 (ite $x50 ?1 ?x127)))
  1.2851 -(let (($x133 (= ?x107 ?x130)))
  1.2852 -(let (($x134 (= (= ?x107 (ite $x50 ?1 (ite $x51 ?x108 (- (mod (- ?1) (- ?0)))))) $x133)))
  1.2853 -(let ((@x118 (monotonicity (rewrite (= (- ?1) ?x62)) (rewrite (= (- ?0) ?x65)) (= (mod (- ?1) (- ?0)) ?x116))))
  1.2854 -(let ((@x126 (trans (monotonicity @x118 (= (- (mod (- ?1) (- ?0))) (- ?x116))) (rewrite (= (- ?x116) ?x122)) (= (- (mod (- ?1) (- ?0))) ?x122))))
  1.2855 -(let ((@x129 (monotonicity @x126 (= (ite $x51 ?x108 (- (mod (- ?1) (- ?0)))) ?x127))))
  1.2856 -(let ((@x132 (monotonicity @x129 (= (ite $x50 ?1 (ite $x51 ?x108 (- (mod (- ?1) (- ?0))))) ?x130))))
  1.2857 -(let ((@x157 (trans (quant-intro (monotonicity @x132 $x134) (= $x114 $x136)) (quant-intro @x152 (= $x136 $x153)) (= $x114 $x153))))
  1.2858 -(let ((@x168 (mp~ (mp (asserted $x114) @x157 $x153) (nnf-pos (refl (~ $x150 $x150)) (~ $x153 $x153)) $x153)))
  1.2859 -(let ((@x196 (mp @x168 (quant-intro (refl (= $x150 $x150)) (= $x153 $x191)) $x191)))
  1.2860 -(let (($x260 (not $x191)))
  1.2861 -(let (($x541 (or $x260 $x490)))
  1.2862 -(let ((?x211 (* (- 1) 2)))
  1.2863 -(let ((?x222 (* (- 1) n$)))
  1.2864 -(let ((?x517 (mod ?x222 ?x211)))
  1.2865 -(let ((?x518 (* (- 1) ?x517)))
  1.2866 -(let (($x209 (<= 2 0)))
  1.2867 -(let ((?x520 (ite $x209 ?x518 ?x519)))
  1.2868 -(let (($x208 (= 2 0)))
  1.2869 -(let ((?x521 (ite $x208 n$ ?x520)))
  1.2870 -(let (($x485 (= ?x39 ?x521)))
  1.2871 -(let ((@x593 (monotonicity (monotonicity (rewrite (= ?x211 (- 2))) (= ?x517 (mod ?x222 (- 2)))) (= ?x518 (* (- 1) (mod ?x222 (- 2)))))))
  1.2872 -(let ((@x221 (rewrite (= $x209 false))))
  1.2873 -(let ((@x596 (monotonicity @x221 @x593 (= ?x520 (ite false (* (- 1) (mod ?x222 (- 2))) ?x519)))))
  1.2874 -(let ((@x599 (trans @x596 (rewrite (= (ite false (* (- 1) (mod ?x222 (- 2))) ?x519) ?x519)) (= ?x520 ?x519))))
  1.2875 -(let ((@x219 (rewrite (= $x208 false))))
  1.2876 -(let ((@x487 (trans (monotonicity @x219 @x599 (= ?x521 (ite false n$ ?x519))) (rewrite (= (ite false n$ ?x519) ?x519)) (= ?x521 ?x519))))
  1.2877 -(let ((@x538 (trans (monotonicity @x487 (= $x485 (= ?x39 ?x519))) (rewrite (= (= ?x39 ?x519) $x490)) (= $x485 $x490))))
  1.2878 -(let ((@x406 (trans (monotonicity @x538 (= (or $x260 $x485) $x541)) (rewrite (= $x541 $x541)) (= (or $x260 $x485) $x541))))
  1.2879 -(let ((@x407 (mp ((_ quant-inst n$ 2) (or $x260 $x485)) @x406 $x541)))
  1.2880 -(let ((@x715 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x490) $x408)) (unit-resolution @x407 @x196 $x490) $x408)))
  1.2881 -(let (($x303 (>= ?x519 2)))
  1.2882 -(let (($x304 (not $x303)))
  1.2883 -(let ((@x26 (true-axiom true)))
  1.2884 -(let ((@x722 (unit-resolution ((_ th-lemma arith assign-bounds 1 1) (or $x514 $x303 (not $x408))) (unit-resolution ((_ th-lemma arith) (or false $x304)) @x26 $x304) @x715 $x514)))
  1.2885 -(let (($x41 (= ?x39 1)))
  1.2886 -(let (($x169 (not $x41)))
  1.2887 -(let ((?x42 (mod$ m$ 2)))
  1.2888 -(let (($x43 (= ?x42 1)))
  1.2889 -(let ((?x29 (+ n$ m$)))
  1.2890 -(let ((?x214 (mod ?x29 2)))
  1.2891 -(let ((?x253 (* (- 1) ?x214)))
  1.2892 -(let ((?x31 (mod$ ?x29 2)))
  1.2893 -(let ((?x603 (+ n$ m$ ?x31 ?x35 ?x253 (* (- 1) (div ?x29 2)) ?x363 ?x601 (* (- 1) (div m$ 2)))))
  1.2894 -(let (($x604 (>= ?x603 2)))
  1.2895 -(let (($x523 (>= ?x42 1)))
  1.2896 -(let (($x609 (not $x523)))
  1.2897 -(let (($x522 (<= ?x42 1)))
  1.2898 -(let ((?x439 (mod m$ 2)))
  1.2899 -(let ((?x466 (* (- 1) ?x439)))
  1.2900 -(let ((?x467 (+ ?x42 ?x466)))
  1.2901 -(let (($x482 (<= ?x467 0)))
  1.2902 -(let (($x468 (= ?x467 0)))
  1.2903 -(let (($x473 (or $x260 $x468)))
  1.2904 -(let ((?x440 (ite $x209 (* (- 1) (mod (* (- 1) m$) ?x211)) ?x439)))
  1.2905 -(let ((?x441 (ite $x208 m$ ?x440)))
  1.2906 -(let (($x442 (= ?x42 ?x441)))
  1.2907 -(let ((@x453 (rewrite (= (ite false (* (- 1) (mod (* (- 1) m$) (- 2))) ?x439) ?x439))))
  1.2908 -(let (($x447 (= (* (- 1) (mod (* (- 1) m$) ?x211)) (* (- 1) (mod (* (- 1) m$) (- 2))))))
  1.2909 -(let ((@x229 (rewrite (= ?x211 (- 2)))))
  1.2910 -(let ((@x445 (monotonicity @x229 (= (mod (* (- 1) m$) ?x211) (mod (* (- 1) m$) (- 2))))))
  1.2911 -(let ((@x451 (monotonicity @x221 (monotonicity @x445 $x447) (= ?x440 (ite false (* (- 1) (mod (* (- 1) m$) (- 2))) ?x439)))))
  1.2912 -(let ((@x458 (monotonicity @x219 (trans @x451 @x453 (= ?x440 ?x439)) (= ?x441 (ite false m$ ?x439)))))
  1.2913 -(let ((@x465 (monotonicity (trans @x458 (rewrite (= (ite false m$ ?x439) ?x439)) (= ?x441 ?x439)) (= $x442 (= ?x42 ?x439)))))
  1.2914 -(let ((@x477 (monotonicity (trans @x465 (rewrite (= (= ?x42 ?x439) $x468)) (= $x442 $x468)) (= (or $x260 $x442) $x473))))
  1.2915 -(let ((@x481 (mp ((_ quant-inst m$ 2) (or $x260 $x442)) (trans @x477 (rewrite (= $x473 $x473)) (= (or $x260 $x442) $x473)) $x473)))
  1.2916 -(let ((@x277 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x468) $x482)) (unit-resolution @x481 @x196 $x468) $x482)))
  1.2917 -(let ((@x386 (unit-resolution ((_ th-lemma arith) (or false (not (>= ?x439 2)))) @x26 (not (>= ?x439 2)))))
  1.2918 -(let ((@x384 (unit-resolution ((_ th-lemma arith assign-bounds 1 1) (or $x522 (>= ?x439 2) (not $x482))) @x386 @x277 $x522)))
  1.2919 -(let ((@x564 (unit-resolution ((_ th-lemma arith triangle-eq) (or $x43 (not $x522) $x609)) (hypothesis (not $x43)) (or (not $x522) $x609))))
  1.2920 -(let ((?x272 (div ?x29 2)))
  1.2921 -(let ((?x288 (* (- 2) ?x272)))
  1.2922 -(let ((?x289 (+ n$ m$ ?x253 ?x288)))
  1.2923 -(let (($x294 (<= ?x289 0)))
  1.2924 -(let (($x287 (= ?x289 0)))
  1.2925 -(let ((@x617 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x287) $x294)) (unit-resolution ((_ th-lemma arith) (or false $x287)) @x26 $x287) $x294)))
  1.2926 -(let (($x433 (<= ?x31 0)))
  1.2927 -(let (($x32 (= ?x31 0)))
  1.2928 -(let ((@x33 (asserted $x32)))
  1.2929 -(let ((?x254 (+ ?x31 ?x253)))
  1.2930 -(let (($x270 (<= ?x254 0)))
  1.2931 -(let (($x255 (= ?x254 0)))
  1.2932 -(let (($x261 (or $x260 $x255)))
  1.2933 -(let ((?x215 (ite $x209 (* (- 1) (mod (* (- 1) ?x29) ?x211)) ?x214)))
  1.2934 -(let ((?x216 (ite $x208 ?x29 ?x215)))
  1.2935 -(let (($x217 (= ?x31 ?x216)))
  1.2936 -(let (($x239 (= (ite false (* (- 1) (mod (+ ?x222 (* (- 1) m$)) (- 2))) ?x214) ?x214)))
  1.2937 -(let (($x237 (= ?x215 (ite false (* (- 1) (mod (+ ?x222 (* (- 1) m$)) (- 2))) ?x214))))
  1.2938 -(let (($x234 (= (* (- 1) (mod (* (- 1) ?x29) ?x211)) (* (- 1) (mod (+ ?x222 (* (- 1) m$)) (- 2))))))
  1.2939 -(let ((@x232 (monotonicity (rewrite (= (* (- 1) ?x29) (+ ?x222 (* (- 1) m$)))) @x229 (= (mod (* (- 1) ?x29) ?x211) (mod (+ ?x222 (* (- 1) m$)) (- 2))))))
  1.2940 -(let ((@x242 (trans (monotonicity @x221 (monotonicity @x232 $x234) $x237) (rewrite $x239) (= ?x215 ?x214))))
  1.2941 -(let ((@x249 (trans (monotonicity @x219 @x242 (= ?x216 (ite false ?x29 ?x214))) (rewrite (= (ite false ?x29 ?x214) ?x214)) (= ?x216 ?x214))))
  1.2942 -(let ((@x259 (trans (monotonicity @x249 (= $x217 (= ?x31 ?x214))) (rewrite (= (= ?x31 ?x214) $x255)) (= $x217 $x255))))
  1.2943 -(let ((@x268 (trans (monotonicity @x259 (= (or $x260 $x217) $x261)) (rewrite (= $x261 $x261)) (= (or $x260 $x217) $x261))))
  1.2944 -(let ((@x269 (mp ((_ quant-inst (+ n$ m$) 2) (or $x260 $x217)) @x268 $x261)))
  1.2945 -(let ((@x626 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x255) $x270)) (unit-resolution @x269 @x196 $x255) $x270)))
  1.2946 -(let ((?x498 (+ m$ ?x466 (* (- 2) (div m$ 2)))))
  1.2947 -(let (($x496 (= ?x498 0)))
  1.2948 -(let ((@x633 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x496) (<= ?x498 0))) (unit-resolution ((_ th-lemma arith) (or false $x496)) @x26 $x496) (<= ?x498 0))))
  1.2949 -(let ((?x397 (* (- 4) ?x381)))
  1.2950 -(let ((?x398 (+ n$ ?x363 ?x397)))
  1.2951 -(let (($x403 (<= ?x398 0)))
  1.2952 -(let (($x396 (= ?x398 0)))
  1.2953 -(let ((@x640 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x396) $x403)) (unit-resolution ((_ th-lemma arith) (or false $x396)) @x26 $x396) $x403)))
  1.2954 -(let ((?x364 (+ ?x35 ?x363)))
  1.2955 -(let (($x379 (<= ?x364 0)))
  1.2956 -(let (($x365 (= ?x364 0)))
  1.2957 -(let (($x370 (or $x260 $x365)))
  1.2958 -(let ((?x330 (ite (<= 4 0) (* (- 1) (mod ?x222 (* (- 1) 4))) ?x329)))
  1.2959 -(let ((?x331 (ite (= 4 0) n$ ?x330)))
  1.2960 -(let (($x332 (= ?x35 ?x331)))
  1.2961 -(let ((@x342 (monotonicity (rewrite (= (* (- 1) 4) (- 4))) (= (mod ?x222 (* (- 1) 4)) (mod ?x222 (- 4))))))
  1.2962 -(let ((@x345 (monotonicity @x342 (= (* (- 1) (mod ?x222 (* (- 1) 4))) (* (- 1) (mod ?x222 (- 4)))))))
  1.2963 -(let ((@x348 (monotonicity (rewrite (= (<= 4 0) false)) @x345 (= ?x330 (ite false (* (- 1) (mod ?x222 (- 4))) ?x329)))))
  1.2964 -(let ((@x352 (trans @x348 (rewrite (= (ite false (* (- 1) (mod ?x222 (- 4))) ?x329) ?x329)) (= ?x330 ?x329))))
  1.2965 -(let ((@x355 (monotonicity (rewrite (= (= 4 0) false)) @x352 (= ?x331 (ite false n$ ?x329)))))
  1.2966 -(let ((@x362 (monotonicity (trans @x355 (rewrite (= (ite false n$ ?x329) ?x329)) (= ?x331 ?x329)) (= $x332 (= ?x35 ?x329)))))
  1.2967 -(let ((@x374 (monotonicity (trans @x362 (rewrite (= (= ?x35 ?x329) $x365)) (= $x332 $x365)) (= (or $x260 $x332) $x370))))
  1.2968 -(let ((@x378 (mp ((_ quant-inst n$ 4) (or $x260 $x332)) (trans @x374 (rewrite (= $x370 $x370)) (= (or $x260 $x332) $x370)) $x370)))
  1.2969 -(let ((@x645 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x365) $x379)) (unit-resolution @x378 @x196 $x365) $x379)))
  1.2970 -(let (($x435 (<= ?x35 3)))
  1.2971 -(let (($x37 (= ?x35 3)))
  1.2972 -(let ((@x38 (asserted $x37)))
  1.2973 -(let ((@x655 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x468) (>= ?x467 0))) (unit-resolution @x481 @x196 $x468) (>= ?x467 0))))
  1.2974 -(let ((@x656 ((_ th-lemma arith farkas -1 1 -2 1 1 1 1 1 1 1) @x655 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x37) $x435)) @x38 $x435) (hypothesis $x604) @x645 @x640 @x633 @x626 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x32) $x433)) @x33 $x433) @x617 (hypothesis $x609) false)))
  1.2975 -(let ((@x565 (unit-resolution (lemma @x656 (or (not $x604) $x523)) (unit-resolution @x564 @x384 $x609) (not $x604))))
  1.2976 -(let (($x295 (>= ?x289 0)))
  1.2977 -(let ((@x566 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x287) $x295)) (unit-resolution ((_ th-lemma arith) (or false $x287)) @x26 $x287) $x295)))
  1.2978 -(let (($x434 (>= ?x31 0)))
  1.2979 -(let (($x271 (>= ?x254 0)))
  1.2980 -(let ((@x531 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x255) $x271)) (unit-resolution @x269 @x196 $x255) $x271)))
  1.2981 -(let ((@x537 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x496) (>= ?x498 0))) (unit-resolution ((_ th-lemma arith) (or false $x496)) @x26 $x496) (>= ?x498 0))))
  1.2982 -(let ((@x549 (unit-resolution ((_ th-lemma arith) (or false (>= ?x439 0))) @x26 (>= ?x439 0))))
  1.2983 -(let (($x404 (>= ?x398 0)))
  1.2984 -(let ((@x552 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x396) $x404)) (unit-resolution ((_ th-lemma arith) (or false $x396)) @x26 $x396) $x404)))
  1.2985 -(let (($x380 (>= ?x364 0)))
  1.2986 -(let ((@x273 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x365) $x380)) (unit-resolution @x378 @x196 $x365) $x380)))
  1.2987 -(let (($x436 (>= ?x35 3)))
  1.2988 -(let ((@x545 ((_ th-lemma arith farkas -1/2 -1/2 -1/2 -1/2 -1/2 -1/2 -1/2 -1/2 1) (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x37) $x436)) @x38 $x436) @x273 @x552 @x549 @x537 @x531 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x32) $x434)) @x33 $x434) @x566 @x565 false)))
  1.2989 -(let (($x171 (or $x169 (not $x43))))
  1.2990 -(let ((@x177 (monotonicity (rewrite (= (and $x41 $x43) (not $x171))) (= (not (and $x41 $x43)) (not (not $x171))))))
  1.2991 -(let ((@x181 (trans @x177 (rewrite (= (not (not $x171)) $x171)) (= (not (and $x41 $x43)) $x171))))
  1.2992 -(let ((@x182 (mp (asserted (not (and $x41 $x43))) @x181 $x171)))
  1.2993 -(let ((@x729 (unit-resolution ((_ th-lemma arith triangle-eq) (or $x41 (not $x514) $x725)) (unit-resolution @x182 (lemma @x545 $x43) $x169) (or (not $x514) $x725))))
  1.2994 -(let ((?x420 (* (- 2) ?x410)))
  1.2995 -(let ((?x421 (+ n$ ?x420 ?x534)))
  1.2996 -(let (($x426 (<= ?x421 0)))
  1.2997 -(let (($x419 (= ?x421 0)))
  1.2998 -(let ((@x737 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x419) $x426)) (unit-resolution ((_ th-lemma arith) (or false $x419)) @x26 $x419) $x426)))
  1.2999 -(let (($x409 (>= ?x535 0)))
  1.3000 -(let ((@x741 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x490) $x409)) (unit-resolution @x407 @x196 $x490) $x409)))
  1.3001 -(let ((@x742 ((_ th-lemma arith farkas -1 1 -2 1 1 1 1) @x741 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x37) $x435)) @x38 $x435) (hypothesis $x706) @x640 @x737 @x645 (unit-resolution @x729 @x722 $x725) false)))
  1.3002 -(let (($x427 (>= ?x421 0)))
  1.3003 -(let ((@x584 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x419) $x427)) (unit-resolution ((_ th-lemma arith) (or false $x419)) @x26 $x419) $x427)))
  1.3004 -(let (($x542 (>= ?x519 0)))
  1.3005 -((_ th-lemma arith farkas -1/2 -1/2 -1/2 -1/2 -1/2 1) (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x37) $x436)) @x38 $x436) @x552 (unit-resolution ((_ th-lemma arith) (or false $x542)) @x26 $x542) @x584 @x273 (lemma @x742 (not $x706)) false)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
  1.3006 -
  1.3007 -f6a4c40290fd6742c0b08a1fe90b3664e90c2143 336 0
  1.3008 -unsat
  1.3009 -((set-logic <null>)
  1.3010 -(proof
  1.3011 -(let ((?x99 (mod$ l$ 2)))
  1.3012 -(let ((?x96 (map$ uu$ xs$)))
  1.3013 -(let ((?x97 (eval_dioph$ ks$ ?x96)))
  1.3014 -(let ((?x98 (mod$ ?x97 2)))
  1.3015 -(let (($x100 (= ?x98 ?x99)))
  1.3016 -(let ((?x93 (eval_dioph$ ks$ xs$)))
  1.3017 -(let (($x95 (= ?x93 l$)))
  1.3018 -(let ((?x110 (* (- 1) ?x97)))
  1.3019 -(let ((?x111 (+ l$ ?x110)))
  1.3020 -(let ((?x114 (divide$ ?x111 2)))
  1.3021 -(let ((?x101 (map$ uua$ xs$)))
  1.3022 -(let ((?x102 (eval_dioph$ ks$ ?x101)))
  1.3023 -(let (($x117 (= ?x102 ?x114)))
  1.3024 -(let (($x282 (not $x117)))
  1.3025 -(let (($x281 (not $x100)))
  1.3026 -(let (($x283 (or $x281 $x282)))
  1.3027 -(let ((?x744 (div ?x93 2)))
  1.3028 -(let ((?x970 (* (- 1) ?x744)))
  1.3029 -(let ((?x699 (mod ?x93 2)))
  1.3030 -(let ((?x726 (* (- 1) ?x699)))
  1.3031 -(let ((?x516 (mod l$ 2)))
  1.3032 -(let ((?x543 (* (- 1) ?x516)))
  1.3033 -(let (($x972 (>= (+ l$ ?x99 ?x543 (* (- 1) (div l$ 2)) ?x726 ?x970) 1)))
  1.3034 -(let ((?x369 (* (- 1) l$)))
  1.3035 -(let ((?x693 (+ ?x93 ?x369)))
  1.3036 -(let (($x695 (>= ?x693 0)))
  1.3037 -(let (($x861 (not $x695)))
  1.3038 -(let (($x694 (<= ?x693 0)))
  1.3039 -(let ((?x686 (+ ?x102 (* (- 1) ?x114))))
  1.3040 -(let (($x687 (<= ?x686 0)))
  1.3041 -(let (($x284 (not $x283)))
  1.3042 -(let ((@x466 (hypothesis $x284)))
  1.3043 -(let ((@x856 (unit-resolution ((_ th-lemma arith triangle-eq) (or $x282 $x687)) (unit-resolution (def-axiom (or $x283 $x117)) @x466 $x117) $x687)))
  1.3044 -(let ((?x437 (+ l$ ?x110 (* (- 2) (div ?x111 2)) (* (- 1) (mod (+ l$ ?x97) 2)))))
  1.3045 -(let (($x443 (>= ?x437 0)))
  1.3046 -(let (($x434 (= ?x437 0)))
  1.3047 -(let ((@x26 (true-axiom true)))
  1.3048 -(let ((@x793 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x434) $x443)) (unit-resolution ((_ th-lemma arith) (or false $x434)) @x26 $x434) $x443)))
  1.3049 -(let ((?x501 (* (- 2) ?x102)))
  1.3050 -(let ((?x502 (+ ?x93 ?x110 ?x501)))
  1.3051 -(let (($x509 (<= ?x502 0)))
  1.3052 -(let (($x503 (= ?x502 0)))
  1.3053 -(let (($x304 (forall ((?v0 Int_list$) (?v1 Int_list$) )(!(let ((?x45 (eval_dioph$ ?v0 ?v1)))
  1.3054 -(let ((?x83 (+ ?x45 (* (- 1) (eval_dioph$ ?v0 (map$ uu$ ?v1))) (* (- 2) (eval_dioph$ ?v0 (map$ uua$ ?v1))))))
  1.3055 -(= ?x83 0))) :pattern ( (eval_dioph$ ?v0 (map$ uu$ ?v1)) ) :pattern ( (eval_dioph$ ?v0 (map$ uua$ ?v1)) )))
  1.3056 -))
  1.3057 -(let (($x85 (forall ((?v0 Int_list$) (?v1 Int_list$) )(let ((?x45 (eval_dioph$ ?v0 ?v1)))
  1.3058 -(let ((?x83 (+ ?x45 (* (- 1) (eval_dioph$ ?v0 (map$ uu$ ?v1))) (* (- 2) (eval_dioph$ ?v0 (map$ uua$ ?v1))))))
  1.3059 -(= ?x83 0))))
  1.3060 -))
  1.3061 -(let ((?x45 (eval_dioph$ ?1 ?0)))
  1.3062 -(let ((?x83 (+ ?x45 (* (- 1) (eval_dioph$ ?1 (map$ uu$ ?0))) (* (- 2) (eval_dioph$ ?1 (map$ uua$ ?0))))))
  1.3063 -(let (($x79 (= ?x83 0)))
  1.3064 -(let (($x58 (forall ((?v0 Int_list$) (?v1 Int_list$) )(let ((?x45 (eval_dioph$ ?v0 ?v1)))
  1.3065 -(let ((?x48 (eval_dioph$ ?v0 (map$ uu$ ?v1))))
  1.3066 -(let ((?x56 (+ (* (eval_dioph$ ?v0 (map$ uua$ ?v1)) 2) ?x48)))
  1.3067 -(= ?x56 ?x45)))))
  1.3068 -))
  1.3069 -(let (($x74 (forall ((?v0 Int_list$) (?v1 Int_list$) )(let ((?x45 (eval_dioph$ ?v0 ?v1)))
  1.3070 -(let ((?x54 (eval_dioph$ ?v0 (map$ uua$ ?v1))))
  1.3071 -(let ((?x60 (* 2 ?x54)))
  1.3072 -(let ((?x48 (eval_dioph$ ?v0 (map$ uu$ ?v1))))
  1.3073 -(let ((?x66 (+ ?x48 ?x60)))
  1.3074 -(= ?x66 ?x45)))))))
  1.3075 -))
  1.3076 -(let ((?x54 (eval_dioph$ ?1 (map$ uua$ ?0))))
  1.3077 -(let ((?x60 (* 2 ?x54)))
  1.3078 -(let ((?x48 (eval_dioph$ ?1 (map$ uu$ ?0))))
  1.3079 -(let ((?x66 (+ ?x48 ?x60)))
  1.3080 -(let (($x71 (= ?x66 ?x45)))
  1.3081 -(let ((@x65 (monotonicity (rewrite (= (* ?x54 2) ?x60)) (= (+ (* ?x54 2) ?x48) (+ ?x60 ?x48)))))
  1.3082 -(let ((@x70 (trans @x65 (rewrite (= (+ ?x60 ?x48) ?x66)) (= (+ (* ?x54 2) ?x48) ?x66))))
  1.3083 -(let ((@x76 (quant-intro (monotonicity @x70 (= (= (+ (* ?x54 2) ?x48) ?x45) $x71)) (= $x58 $x74))))
  1.3084 -(let ((@x89 (trans @x76 (quant-intro (rewrite (= $x71 $x79)) (= $x74 $x85)) (= $x58 $x85))))
  1.3085 -(let ((@x270 (mp~ (mp (asserted $x58) @x89 $x85) (nnf-pos (refl (~ $x79 $x79)) (~ $x85 $x85)) $x85)))
  1.3086 -(let ((@x309 (mp @x270 (quant-intro (refl (= $x79 $x79)) (= $x85 $x304)) $x304)))
  1.3087 -(let (($x507 (or (not $x304) $x503)))
  1.3088 -(let ((@x508 ((_ quant-inst ks$ xs$) $x507)))
  1.3089 -(let ((@x800 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x503) $x509)) (unit-resolution @x508 @x309 $x503) $x509)))
  1.3090 -(let ((?x396 (+ ?x114 (* (- 1) (div ?x111 2)))))
  1.3091 -(let (($x413 (<= ?x396 0)))
  1.3092 -(let (($x397 (= ?x396 0)))
  1.3093 -(let (($x311 (forall ((?v0 Int) (?v1 Int) )(!(let ((?x145 (div ?v0 ?v1)))
  1.3094 -(let ((?x157 (* (- 1) ?v1)))
  1.3095 -(let ((?x154 (* (- 1) ?v0)))
  1.3096 -(let ((?x160 (div ?x154 ?x157)))
  1.3097 -(let (($x175 (<= ?v1 0)))
  1.3098 -(let ((?x182 (ite $x175 ?x160 ?x145)))
  1.3099 -(let (($x143 (= ?v1 0)))
  1.3100 -(let ((?x141 (divide$ ?v0 ?v1)))
  1.3101 -(= ?x141 (ite $x143 0 ?x182)))))))))) :pattern ( (divide$ ?v0 ?v1) )))
  1.3102 -))
  1.3103 -(let (($x193 (forall ((?v0 Int) (?v1 Int) )(let ((?x145 (div ?v0 ?v1)))
  1.3104 -(let ((?x157 (* (- 1) ?v1)))
  1.3105 -(let ((?x154 (* (- 1) ?v0)))
  1.3106 -(let ((?x160 (div ?x154 ?x157)))
  1.3107 -(let (($x175 (<= ?v1 0)))
  1.3108 -(let ((?x182 (ite $x175 ?x160 ?x145)))
  1.3109 -(let (($x143 (= ?v1 0)))
  1.3110 -(let ((?x141 (divide$ ?v0 ?v1)))
  1.3111 -(= ?x141 (ite $x143 0 ?x182)))))))))))
  1.3112 -))
  1.3113 -(let ((?x145 (div ?1 ?0)))
  1.3114 -(let ((?x157 (* (- 1) ?0)))
  1.3115 -(let ((?x154 (* (- 1) ?1)))
  1.3116 -(let ((?x160 (div ?x154 ?x157)))
  1.3117 -(let (($x175 (<= ?0 0)))
  1.3118 -(let ((?x182 (ite $x175 ?x160 ?x145)))
  1.3119 -(let (($x143 (= ?0 0)))
  1.3120 -(let ((?x141 (divide$ ?1 ?0)))
  1.3121 -(let (($x190 (= ?x141 (ite $x143 0 ?x182))))
  1.3122 -(let (($x152 (forall ((?v0 Int) (?v1 Int) )(let (($x143 (= ?v1 0)))
  1.3123 -(let ((?x150 (ite $x143 0 (ite (< 0 ?v1) (div ?v0 ?v1) (div (- ?v0) (- ?v1))))))
  1.3124 -(let ((?x141 (divide$ ?v0 ?v1)))
  1.3125 -(= ?x141 ?x150)))))
  1.3126 -))
  1.3127 -(let (($x172 (forall ((?v0 Int) (?v1 Int) )(let ((?x157 (* (- 1) ?v1)))
  1.3128 -(let ((?x154 (* (- 1) ?v0)))
  1.3129 -(let ((?x160 (div ?x154 ?x157)))
  1.3130 -(let ((?x145 (div ?v0 ?v1)))
  1.3131 -(let (($x144 (< 0 ?v1)))
  1.3132 -(let ((?x163 (ite $x144 ?x145 ?x160)))
  1.3133 -(let (($x143 (= ?v1 0)))
  1.3134 -(let ((?x166 (ite $x143 0 ?x163)))
  1.3135 -(let ((?x141 (divide$ ?v0 ?v1)))
  1.3136 -(= ?x141 ?x166)))))))))))
  1.3137 -))
  1.3138 -(let (($x144 (< 0 ?0)))
  1.3139 -(let ((?x163 (ite $x144 ?x145 ?x160)))
  1.3140 -(let ((?x166 (ite $x143 0 ?x163)))
  1.3141 -(let ((@x181 (monotonicity (rewrite (= $x144 (not $x175))) (= ?x163 (ite (not $x175) ?x145 ?x160)))))
  1.3142 -(let ((@x186 (trans @x181 (rewrite (= (ite (not $x175) ?x145 ?x160) ?x182)) (= ?x163 ?x182))))
  1.3143 -(let ((@x192 (monotonicity (monotonicity @x186 (= ?x166 (ite $x143 0 ?x182))) (= (= ?x141 ?x166) $x190))))
  1.3144 -(let (($x169 (= ?x141 ?x166)))
  1.3145 -(let (($x170 (= (= ?x141 (ite $x143 0 (ite $x144 ?x145 (div (- ?1) (- ?0))))) $x169)))
  1.3146 -(let ((@x162 (monotonicity (rewrite (= (- ?1) ?x154)) (rewrite (= (- ?0) ?x157)) (= (div (- ?1) (- ?0)) ?x160))))
  1.3147 -(let ((@x168 (monotonicity (monotonicity @x162 (= (ite $x144 ?x145 (div (- ?1) (- ?0))) ?x163)) (= (ite $x143 0 (ite $x144 ?x145 (div (- ?1) (- ?0)))) ?x166))))
  1.3148 -(let ((@x197 (trans (quant-intro (monotonicity @x168 $x170) (= $x152 $x172)) (quant-intro @x192 (= $x172 $x193)) (= $x152 $x193))))
  1.3149 -(let ((@x275 (mp~ (mp (asserted $x152) @x197 $x193) (nnf-pos (refl (~ $x190 $x190)) (~ $x193 $x193)) $x193)))
  1.3150 -(let ((@x316 (mp @x275 (quant-intro (refl (= $x190 $x190)) (= $x193 $x311)) $x311)))
  1.3151 -(let (($x403 (or (not $x311) $x397)))
  1.3152 -(let ((?x361 (div ?x111 2)))
  1.3153 -(let (($x357 (<= 2 0)))
  1.3154 -(let ((?x362 (ite $x357 (div (* (- 1) ?x111) (* (- 1) 2)) ?x361)))
  1.3155 -(let (($x356 (= 2 0)))
  1.3156 -(let ((?x363 (ite $x356 0 ?x362)))
  1.3157 -(let (($x364 (= ?x114 ?x363)))
  1.3158 -(let ((@x374 (rewrite (= (* (- 1) 2) (- 2)))))
  1.3159 -(let ((@x377 (monotonicity (rewrite (= (* (- 1) ?x111) (+ ?x369 ?x97))) @x374 (= (div (* (- 1) ?x111) (* (- 1) 2)) (div (+ ?x369 ?x97) (- 2))))))
  1.3160 -(let ((@x368 (rewrite (= $x357 false))))
  1.3161 -(let ((@x380 (monotonicity @x368 @x377 (= ?x362 (ite false (div (+ ?x369 ?x97) (- 2)) ?x361)))))
  1.3162 -(let ((@x384 (trans @x380 (rewrite (= (ite false (div (+ ?x369 ?x97) (- 2)) ?x361) ?x361)) (= ?x362 ?x361))))
  1.3163 -(let ((@x366 (rewrite (= $x356 false))))
  1.3164 -(let ((@x391 (trans (monotonicity @x366 @x384 (= ?x363 (ite false 0 ?x361))) (rewrite (= (ite false 0 ?x361) ?x361)) (= ?x363 ?x361))))
  1.3165 -(let ((@x401 (trans (monotonicity @x391 (= $x364 (= ?x114 ?x361))) (rewrite (= (= ?x114 ?x361) $x397)) (= $x364 $x397))))
  1.3166 -(let ((@x410 (trans (monotonicity @x401 (= (or (not $x311) $x364) $x403)) (rewrite (= $x403 $x403)) (= (or (not $x311) $x364) $x403))))
  1.3167 -(let ((@x802 (unit-resolution (mp ((_ quant-inst (+ l$ ?x110) 2) (or (not $x311) $x364)) @x410 $x403) @x316 $x397)))
  1.3168 -(let ((?x425 (mod (+ l$ ?x97) 2)))
  1.3169 -(let (($x465 (>= ?x425 0)))
  1.3170 -(let ((@x810 ((_ th-lemma arith farkas 1 -2 -2 -1 1 1) (unit-resolution ((_ th-lemma arith) (or false $x465)) @x26 $x465) (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x397) $x413)) @x802 $x413) (hypothesis $x687) @x800 (hypothesis (not $x694)) @x793 false)))
  1.3171 -(let (($x134 (not $x95)))
  1.3172 -(let (($x290 (= $x95 $x283)))
  1.3173 -(let ((@x289 (monotonicity (rewrite (= (and $x100 $x117) $x284)) (= (= $x134 (and $x100 $x117)) (= $x134 $x284)))))
  1.3174 -(let ((@x294 (trans @x289 (rewrite (= (= $x134 $x284) $x290)) (= (= $x134 (and $x100 $x117)) $x290))))
  1.3175 -(let (($x120 (and $x100 $x117)))
  1.3176 -(let (($x135 (= $x134 $x120)))
  1.3177 -(let (($x107 (= $x95 (and $x100 (= ?x102 (divide$ (- l$ ?x97) 2))))))
  1.3178 -(let (($x108 (not $x107)))
  1.3179 -(let ((@x116 (monotonicity (rewrite (= (- l$ ?x97) ?x111)) (= (divide$ (- l$ ?x97) 2) ?x114))))
  1.3180 -(let ((@x122 (monotonicity (monotonicity @x116 (= (= ?x102 (divide$ (- l$ ?x97) 2)) $x117)) (= (and $x100 (= ?x102 (divide$ (- l$ ?x97) 2))) $x120))))
  1.3181 -(let ((@x130 (trans (monotonicity @x122 (= $x107 (= $x95 $x120))) (rewrite (= (= $x95 $x120) (= $x95 $x120))) (= $x107 (= $x95 $x120)))))
  1.3182 -(let ((@x139 (trans (monotonicity @x130 (= $x108 (not (= $x95 $x120)))) (rewrite (= (not (= $x95 $x120)) $x135)) (= $x108 $x135))))
  1.3183 -(let ((@x295 (mp (mp (asserted $x108) @x139 $x135) @x294 $x290)))
  1.3184 -(let ((@x344 (unit-resolution (def-axiom (or $x134 $x283 (not $x290))) @x295 (or $x134 $x283))))
  1.3185 -(let ((@x898 (unit-resolution ((_ th-lemma arith triangle-eq) (or $x95 (not $x694) $x861)) (unit-resolution @x344 @x466 $x134) (or (not $x694) $x861))))
  1.3186 -(let ((@x899 (unit-resolution @x898 (unit-resolution (lemma @x810 (or $x694 (not $x687))) @x856 $x694) $x861)))
  1.3187 -(let ((?x544 (+ ?x99 ?x543)))
  1.3188 -(let (($x561 (>= ?x544 0)))
  1.3189 -(let (($x545 (= ?x544 0)))
  1.3190 -(let (($x318 (forall ((?v0 Int) (?v1 Int) )(!(let ((?x200 (mod ?v0 ?v1)))
  1.3191 -(let ((?x157 (* (- 1) ?v1)))
  1.3192 -(let ((?x154 (* (- 1) ?v0)))
  1.3193 -(let ((?x208 (mod ?x154 ?x157)))
  1.3194 -(let ((?x214 (* (- 1) ?x208)))
  1.3195 -(let (($x175 (<= ?v1 0)))
  1.3196 -(let ((?x234 (ite $x175 ?x214 ?x200)))
  1.3197 -(let (($x143 (= ?v1 0)))
  1.3198 -(let ((?x239 (ite $x143 ?v0 ?x234)))
  1.3199 -(let ((?x199 (mod$ ?v0 ?v1)))
  1.3200 -(= ?x199 ?x239))))))))))) :pattern ( (mod$ ?v0 ?v1) )))
  1.3201 -))
  1.3202 -(let (($x245 (forall ((?v0 Int) (?v1 Int) )(let ((?x200 (mod ?v0 ?v1)))
  1.3203 -(let ((?x157 (* (- 1) ?v1)))
  1.3204 -(let ((?x154 (* (- 1) ?v0)))
  1.3205 -(let ((?x208 (mod ?x154 ?x157)))
  1.3206 -(let ((?x214 (* (- 1) ?x208)))
  1.3207 -(let (($x175 (<= ?v1 0)))
  1.3208 -(let ((?x234 (ite $x175 ?x214 ?x200)))
  1.3209 -(let (($x143 (= ?v1 0)))
  1.3210 -(let ((?x239 (ite $x143 ?v0 ?x234)))
  1.3211 -(let ((?x199 (mod$ ?v0 ?v1)))
  1.3212 -(= ?x199 ?x239))))))))))))
  1.3213 -))
  1.3214 -(let ((?x200 (mod ?1 ?0)))
  1.3215 -(let ((?x208 (mod ?x154 ?x157)))
  1.3216 -(let ((?x214 (* (- 1) ?x208)))
  1.3217 -(let ((?x234 (ite $x175 ?x214 ?x200)))
  1.3218 -(let ((?x239 (ite $x143 ?1 ?x234)))
  1.3219 -(let ((?x199 (mod$ ?1 ?0)))
  1.3220 -(let (($x242 (= ?x199 ?x239)))
  1.3221 -(let (($x206 (forall ((?v0 Int) (?v1 Int) )(let (($x143 (= ?v1 0)))
  1.3222 -(let ((?x204 (ite $x143 ?v0 (ite (< 0 ?v1) (mod ?v0 ?v1) (- (mod (- ?v0) (- ?v1)))))))
  1.3223 -(let ((?x199 (mod$ ?v0 ?v1)))
  1.3224 -(= ?x199 ?x204)))))
  1.3225 -))
  1.3226 -(let (($x228 (forall ((?v0 Int) (?v1 Int) )(let ((?x157 (* (- 1) ?v1)))
  1.3227 -(let ((?x154 (* (- 1) ?v0)))
  1.3228 -(let ((?x208 (mod ?x154 ?x157)))
  1.3229 -(let ((?x214 (* (- 1) ?x208)))
  1.3230 -(let ((?x200 (mod ?v0 ?v1)))
  1.3231 -(let (($x144 (< 0 ?v1)))
  1.3232 -(let ((?x219 (ite $x144 ?x200 ?x214)))
  1.3233 -(let (($x143 (= ?v1 0)))
  1.3234 -(let ((?x222 (ite $x143 ?v0 ?x219)))
  1.3235 -(let ((?x199 (mod$ ?v0 ?v1)))
  1.3236 -(= ?x199 ?x222))))))))))))
  1.3237 -))
  1.3238 -(let ((@x233 (monotonicity (rewrite (= $x144 (not $x175))) (= (ite $x144 ?x200 ?x214) (ite (not $x175) ?x200 ?x214)))))
  1.3239 -(let ((@x238 (trans @x233 (rewrite (= (ite (not $x175) ?x200 ?x214) ?x234)) (= (ite $x144 ?x200 ?x214) ?x234))))
  1.3240 -(let ((@x244 (monotonicity (monotonicity @x238 (= (ite $x143 ?1 (ite $x144 ?x200 ?x214)) ?x239)) (= (= ?x199 (ite $x143 ?1 (ite $x144 ?x200 ?x214))) $x242))))
  1.3241 -(let ((?x219 (ite $x144 ?x200 ?x214)))
  1.3242 -(let ((?x222 (ite $x143 ?1 ?x219)))
  1.3243 -(let (($x225 (= ?x199 ?x222)))
  1.3244 -(let (($x226 (= (= ?x199 (ite $x143 ?1 (ite $x144 ?x200 (- (mod (- ?1) (- ?0)))))) $x225)))
  1.3245 -(let ((@x210 (monotonicity (rewrite (= (- ?1) ?x154)) (rewrite (= (- ?0) ?x157)) (= (mod (- ?1) (- ?0)) ?x208))))
  1.3246 -(let ((@x218 (trans (monotonicity @x210 (= (- (mod (- ?1) (- ?0))) (- ?x208))) (rewrite (= (- ?x208) ?x214)) (= (- (mod (- ?1) (- ?0))) ?x214))))
  1.3247 -(let ((@x221 (monotonicity @x218 (= (ite $x144 ?x200 (- (mod (- ?1) (- ?0)))) ?x219))))
  1.3248 -(let ((@x224 (monotonicity @x221 (= (ite $x143 ?1 (ite $x144 ?x200 (- (mod (- ?1) (- ?0))))) ?x222))))
  1.3249 -(let ((@x249 (trans (quant-intro (monotonicity @x224 $x226) (= $x206 $x228)) (quant-intro @x244 (= $x228 $x245)) (= $x206 $x245))))
  1.3250 -(let ((@x280 (mp~ (mp (asserted $x206) @x249 $x245) (nnf-pos (refl (~ $x242 $x242)) (~ $x245 $x245)) $x245)))
  1.3251 -(let ((@x323 (mp @x280 (quant-intro (refl (= $x242 $x242)) (= $x245 $x318)) $x318)))
  1.3252 -(let (($x550 (not $x318)))
  1.3253 -(let (($x551 (or $x550 $x545)))
  1.3254 -(let ((?x359 (* (- 1) 2)))
  1.3255 -(let ((?x511 (mod ?x369 ?x359)))
  1.3256 -(let ((?x512 (* (- 1) ?x511)))
  1.3257 -(let ((?x517 (ite $x357 ?x512 ?x516)))
  1.3258 -(let ((?x518 (ite $x356 l$ ?x517)))
  1.3259 -(let (($x519 (= ?x99 ?x518)))
  1.3260 -(let ((@x525 (monotonicity (monotonicity @x374 (= ?x511 (mod ?x369 (- 2)))) (= ?x512 (* (- 1) (mod ?x369 (- 2)))))))
  1.3261 -(let ((@x528 (monotonicity @x368 @x525 (= ?x517 (ite false (* (- 1) (mod ?x369 (- 2))) ?x516)))))
  1.3262 -(let ((@x532 (trans @x528 (rewrite (= (ite false (* (- 1) (mod ?x369 (- 2))) ?x516) ?x516)) (= ?x517 ?x516))))
  1.3263 -(let ((@x539 (trans (monotonicity @x366 @x532 (= ?x518 (ite false l$ ?x516))) (rewrite (= (ite false l$ ?x516) ?x516)) (= ?x518 ?x516))))
  1.3264 -(let ((@x549 (trans (monotonicity @x539 (= $x519 (= ?x99 ?x516))) (rewrite (= (= ?x99 ?x516) $x545)) (= $x519 $x545))))
  1.3265 -(let ((@x558 (trans (monotonicity @x549 (= (or $x550 $x519) $x551)) (rewrite (= $x551 $x551)) (= (or $x550 $x519) $x551))))
  1.3266 -(let ((@x559 (mp ((_ quant-inst l$ 2) (or $x550 $x519)) @x558 $x551)))
  1.3267 -(let ((@x902 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x545) $x561)) (unit-resolution @x559 @x323 $x545) $x561)))
  1.3268 -(let ((?x757 (* (- 2) ?x744)))
  1.3269 -(let ((?x758 (+ ?x93 ?x726 ?x757)))
  1.3270 -(let (($x764 (>= ?x758 0)))
  1.3271 -(let (($x756 (= ?x758 0)))
  1.3272 -(let ((@x872 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x756) $x764)) (unit-resolution ((_ th-lemma arith) (or false $x756)) @x26 $x756) $x764)))
  1.3273 -(let ((?x562 (div l$ 2)))
  1.3274 -(let ((?x575 (* (- 2) ?x562)))
  1.3275 -(let ((?x576 (+ l$ ?x543 ?x575)))
  1.3276 -(let (($x582 (>= ?x576 0)))
  1.3277 -(let (($x574 (= ?x576 0)))
  1.3278 -(let ((@x880 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x574) $x582)) (unit-resolution ((_ th-lemma arith) (or false $x574)) @x26 $x574) $x582)))
  1.3279 -(let ((?x504 (mod$ ?x93 2)))
  1.3280 -(let ((?x727 (+ ?x504 ?x726)))
  1.3281 -(let (($x728 (= ?x727 0)))
  1.3282 -(let (($x733 (or $x550 $x728)))
  1.3283 -(let ((?x696 (* (- 1) ?x93)))
  1.3284 -(let ((?x697 (mod ?x696 ?x359)))
  1.3285 -(let ((?x698 (* (- 1) ?x697)))
  1.3286 -(let ((?x700 (ite $x357 ?x698 ?x699)))
  1.3287 -(let ((?x701 (ite $x356 ?x93 ?x700)))
  1.3288 -(let (($x702 (= ?x504 ?x701)))
  1.3289 -(let ((@x708 (monotonicity (monotonicity @x374 (= ?x697 (mod ?x696 (- 2)))) (= ?x698 (* (- 1) (mod ?x696 (- 2)))))))
  1.3290 -(let ((@x711 (monotonicity @x368 @x708 (= ?x700 (ite false (* (- 1) (mod ?x696 (- 2))) ?x699)))))
  1.3291 -(let ((@x715 (trans @x711 (rewrite (= (ite false (* (- 1) (mod ?x696 (- 2))) ?x699) ?x699)) (= ?x700 ?x699))))
  1.3292 -(let ((@x722 (trans (monotonicity @x366 @x715 (= ?x701 (ite false ?x93 ?x699))) (rewrite (= (ite false ?x93 ?x699) ?x699)) (= ?x701 ?x699))))
  1.3293 -(let ((@x732 (trans (monotonicity @x722 (= $x702 (= ?x504 ?x699))) (rewrite (= (= ?x504 ?x699) $x728)) (= $x702 $x728))))
  1.3294 -(let ((@x740 (trans (monotonicity @x732 (= (or $x550 $x702) $x733)) (rewrite (= $x733 $x733)) (= (or $x550 $x702) $x733))))
  1.3295 -(let ((@x427 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x728) (>= ?x727 0))) (unit-resolution (mp ((_ quant-inst (eval_dioph$ ks$ xs$) 2) (or $x550 $x702)) @x740 $x733) @x323 $x728) (>= ?x727 0))))
  1.3296 -(let ((?x783 (* (- 1) ?x504)))
  1.3297 -(let ((?x784 (+ ?x99 ?x783)))
  1.3298 -(let (($x786 (>= ?x784 0)))
  1.3299 -(let (($x782 (= ?x99 ?x504)))
  1.3300 -(let (($x821 (= ?x98 ?x504)))
  1.3301 -(let (($x505 (= ?x504 ?x98)))
  1.3302 -(let (($x297 (forall ((?v0 Int_list$) (?v1 Int_list$) )(!(= (mod$ (eval_dioph$ ?v0 ?v1) 2) (mod$ (eval_dioph$ ?v0 (map$ uu$ ?v1)) 2)) :pattern ( (eval_dioph$ ?v0 (map$ uu$ ?v1)) )))
  1.3303 -))
  1.3304 -(let (($x51 (forall ((?v0 Int_list$) (?v1 Int_list$) )(= (mod$ (eval_dioph$ ?v0 ?v1) 2) (mod$ (eval_dioph$ ?v0 (map$ uu$ ?v1)) 2)))
  1.3305 -))
  1.3306 -(let (($x50 (= (mod$ ?x45 2) (mod$ ?x48 2))))
  1.3307 -(let ((@x265 (mp~ (asserted $x51) (nnf-pos (refl (~ $x50 $x50)) (~ $x51 $x51)) $x51)))
  1.3308 -(let ((@x302 (mp @x265 (quant-intro (refl (= $x50 $x50)) (= $x51 $x297)) $x297)))
  1.3309 -(let (($x514 (or (not $x297) $x505)))
  1.3310 -(let ((@x515 ((_ quant-inst ks$ xs$) $x514)))
  1.3311 -(let ((@x824 (symm (unit-resolution (def-axiom (or $x283 $x100)) @x466 $x100) (= ?x99 ?x98))))
  1.3312 -(let ((@x939 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x782) $x786)) (trans @x824 (symm (unit-resolution @x515 @x302 $x505) $x821) $x782) $x786)))
  1.3313 -(let (($x785 (<= ?x784 0)))
  1.3314 -(let ((@x887 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x782) $x785)) (trans @x824 (symm (unit-resolution @x515 @x302 $x505) $x821) $x782) $x785)))
  1.3315 -(let (($x688 (>= ?x686 0)))
  1.3316 -(let ((@x855 (unit-resolution ((_ th-lemma arith triangle-eq) (or $x282 $x688)) (unit-resolution (def-axiom (or $x283 $x117)) @x466 $x117) $x688)))
  1.3317 -(let ((@x979 (unit-resolution ((_ th-lemma arith) (or false (not (>= ?x425 2)))) @x26 (not (>= ?x425 2)))))
  1.3318 -(let (($x560 (<= ?x544 0)))
  1.3319 -(let ((@x461 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x545) $x560)) (unit-resolution @x559 @x323 $x545) $x560)))
  1.3320 -(let (($x763 (<= ?x758 0)))
  1.3321 -(let ((@x658 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x756) $x763)) (unit-resolution ((_ th-lemma arith) (or false $x756)) @x26 $x756) $x763)))
  1.3322 -(let (($x581 (<= ?x576 0)))
  1.3323 -(let ((@x986 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x574) $x581)) (unit-resolution ((_ th-lemma arith) (or false $x574)) @x26 $x574) $x581)))
  1.3324 -(let ((@x989 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x728) (<= ?x727 0))) (unit-resolution (mp ((_ quant-inst (eval_dioph$ ks$ xs$) 2) (or $x550 $x702)) @x740 $x733) @x323 $x728) (<= ?x727 0))))
  1.3325 -(let (($x510 (>= ?x502 0)))
  1.3326 -(let ((@x994 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x503) $x510)) (unit-resolution @x508 @x309 $x503) $x510)))
  1.3327 -(let ((@x998 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x397) (>= ?x396 0))) @x802 (>= ?x396 0))))
  1.3328 -(let ((@x1001 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x434) (<= ?x437 0))) (unit-resolution ((_ th-lemma arith) (or false $x434)) @x26 $x434) (<= ?x437 0))))
  1.3329 -(let ((@x1002 ((_ th-lemma arith farkas 1 -2 -2 -1 -2 1 1 1 1 1 1) @x1001 @x998 (hypothesis $x688) @x994 (hypothesis $x972) (hypothesis $x785) @x989 @x986 @x658 @x461 @x979 false)))
  1.3330 -(let ((@x474 (unit-resolution (lemma @x1002 (or (not $x972) (not $x688) (not $x785))) @x855 @x887 (not $x972))))
  1.3331 -(let ((@x941 (unit-resolution @x474 ((_ th-lemma arith) @x939 @x427 @x880 @x872 @x902 @x899 $x972) false)))
  1.3332 -(let ((@x942 (lemma @x941 $x283)))
  1.3333 -(let ((@x340 (unit-resolution (def-axiom (or $x95 $x284 (not $x290))) @x295 (or $x95 $x284))))
  1.3334 -(let ((@x679 (unit-resolution @x340 @x942 $x95)))
  1.3335 -(let ((@x889 (trans (symm (unit-resolution @x515 @x302 $x505) $x821) (monotonicity @x679 (= ?x504 ?x99)) $x100)))
  1.3336 -(let (($x811 (not $x687)))
  1.3337 -(let ((@x845 ((_ th-lemma arith assign-bounds 1 -1/2 -1/2 1/2 -1/2) (or $x688 (not $x413) (not $x465) (not $x443) (not $x509) $x861))))
  1.3338 -(let ((@x892 (unit-resolution @x845 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x397) $x413)) @x802 $x413) (unit-resolution ((_ th-lemma arith triangle-eq) (or $x134 $x695)) @x679 $x695) @x793 (unit-resolution ((_ th-lemma arith) (or false $x465)) @x26 $x465) @x800 $x688)))
  1.3339 -(let ((@x935 (unit-resolution ((_ th-lemma arith triangle-eq) (or $x117 $x811 (not $x688))) (hypothesis $x282) (or $x811 (not $x688)))))
  1.3340 -(let ((@x955 ((_ th-lemma arith farkas -2 -2 1 -1 1 1) (unit-resolution @x935 @x892 $x811) @x998 @x1001 @x994 (unit-resolution ((_ th-lemma arith triangle-eq) (or $x134 $x694)) @x679 $x694) @x979 false)))
  1.3341 -(let ((@x472 (unit-resolution (unit-resolution (def-axiom (or $x284 $x281 $x282)) @x942 $x283) (lemma @x955 $x117) $x281)))
  1.3342 -(unit-resolution @x472 @x889 false)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
  1.3343 -
  1.3344 -0f7f4a10f8a84029fd3a6efddc4408fa429b0cda 113 0
  1.3345 -unsat
  1.3346 -((set-logic <null>)
  1.3347 -(proof
  1.3348 -(let ((?x228 (mod x$ 2)))
  1.3349 -(let ((?x262 (* (- 1) ?x228)))
  1.3350 -(let ((?x31 (mod$ x$ 2)))
  1.3351 -(let ((?x263 (+ ?x31 ?x262)))
  1.3352 -(let (($x280 (>= ?x263 0)))
  1.3353 -(let (($x264 (= ?x263 0)))
  1.3354 -(let (($x205 (forall ((?v0 Int) (?v1 Int) )(!(let ((?x136 (mod ?v0 ?v1)))
  1.3355 -(let ((?x93 (* (- 1) ?v1)))
  1.3356 -(let ((?x90 (* (- 1) ?v0)))
  1.3357 -(let ((?x144 (mod ?x90 ?x93)))
  1.3358 -(let ((?x150 (* (- 1) ?x144)))
  1.3359 -(let (($x111 (<= ?v1 0)))
  1.3360 -(let ((?x170 (ite $x111 ?x150 ?x136)))
  1.3361 -(let (($x78 (= ?v1 0)))
  1.3362 -(let ((?x175 (ite $x78 ?v0 ?x170)))
  1.3363 -(let ((?x135 (mod$ ?v0 ?v1)))
  1.3364 -(= ?x135 ?x175))))))))))) :pattern ( (mod$ ?v0 ?v1) )))
  1.3365 -))
  1.3366 -(let (($x181 (forall ((?v0 Int) (?v1 Int) )(let ((?x136 (mod ?v0 ?v1)))
  1.3367 -(let ((?x93 (* (- 1) ?v1)))
  1.3368 -(let ((?x90 (* (- 1) ?v0)))
  1.3369 -(let ((?x144 (mod ?x90 ?x93)))
  1.3370 -(let ((?x150 (* (- 1) ?x144)))
  1.3371 -(let (($x111 (<= ?v1 0)))
  1.3372 -(let ((?x170 (ite $x111 ?x150 ?x136)))
  1.3373 -(let (($x78 (= ?v1 0)))
  1.3374 -(let ((?x175 (ite $x78 ?v0 ?x170)))
  1.3375 -(let ((?x135 (mod$ ?v0 ?v1)))
  1.3376 -(= ?x135 ?x175))))))))))))
  1.3377 -))
  1.3378 -(let ((?x136 (mod ?1 ?0)))
  1.3379 -(let ((?x93 (* (- 1) ?0)))
  1.3380 -(let ((?x90 (* (- 1) ?1)))
  1.3381 -(let ((?x144 (mod ?x90 ?x93)))
  1.3382 -(let ((?x150 (* (- 1) ?x144)))
  1.3383 -(let (($x111 (<= ?0 0)))
  1.3384 -(let ((?x170 (ite $x111 ?x150 ?x136)))
  1.3385 -(let (($x78 (= ?0 0)))
  1.3386 -(let ((?x175 (ite $x78 ?1 ?x170)))
  1.3387 -(let ((?x135 (mod$ ?1 ?0)))
  1.3388 -(let (($x178 (= ?x135 ?x175)))
  1.3389 -(let (($x142 (forall ((?v0 Int) (?v1 Int) )(let (($x78 (= ?v1 0)))
  1.3390 -(let ((?x140 (ite $x78 ?v0 (ite (< 0 ?v1) (mod ?v0 ?v1) (- (mod (- ?v0) (- ?v1)))))))
  1.3391 -(let ((?x135 (mod$ ?v0 ?v1)))
  1.3392 -(= ?x135 ?x140)))))
  1.3393 -))
  1.3394 -(let (($x164 (forall ((?v0 Int) (?v1 Int) )(let ((?x93 (* (- 1) ?v1)))
  1.3395 -(let ((?x90 (* (- 1) ?v0)))
  1.3396 -(let ((?x144 (mod ?x90 ?x93)))
  1.3397 -(let ((?x150 (* (- 1) ?x144)))
  1.3398 -(let ((?x136 (mod ?v0 ?v1)))
  1.3399 -(let (($x79 (< 0 ?v1)))
  1.3400 -(let ((?x155 (ite $x79 ?x136 ?x150)))
  1.3401 -(let (($x78 (= ?v1 0)))
  1.3402 -(let ((?x158 (ite $x78 ?v0 ?x155)))
  1.3403 -(let ((?x135 (mod$ ?v0 ?v1)))
  1.3404 -(= ?x135 ?x158))))))))))))
  1.3405 -))
  1.3406 -(let ((@x169 (monotonicity (rewrite (= (< 0 ?0) (not $x111))) (= (ite (< 0 ?0) ?x136 ?x150) (ite (not $x111) ?x136 ?x150)))))
  1.3407 -(let ((@x174 (trans @x169 (rewrite (= (ite (not $x111) ?x136 ?x150) ?x170)) (= (ite (< 0 ?0) ?x136 ?x150) ?x170))))
  1.3408 -(let ((@x177 (monotonicity @x174 (= (ite $x78 ?1 (ite (< 0 ?0) ?x136 ?x150)) ?x175))))
  1.3409 -(let ((@x180 (monotonicity @x177 (= (= ?x135 (ite $x78 ?1 (ite (< 0 ?0) ?x136 ?x150))) $x178))))
  1.3410 -(let (($x79 (< 0 ?0)))
  1.3411 -(let ((?x155 (ite $x79 ?x136 ?x150)))
  1.3412 -(let ((?x158 (ite $x78 ?1 ?x155)))
  1.3413 -(let (($x161 (= ?x135 ?x158)))
  1.3414 -(let (($x162 (= (= ?x135 (ite $x78 ?1 (ite $x79 ?x136 (- (mod (- ?1) (- ?0)))))) $x161)))
  1.3415 -(let ((@x146 (monotonicity (rewrite (= (- ?1) ?x90)) (rewrite (= (- ?0) ?x93)) (= (mod (- ?1) (- ?0)) ?x144))))
  1.3416 -(let ((@x154 (trans (monotonicity @x146 (= (- (mod (- ?1) (- ?0))) (- ?x144))) (rewrite (= (- ?x144) ?x150)) (= (- (mod (- ?1) (- ?0))) ?x150))))
  1.3417 -(let ((@x157 (monotonicity @x154 (= (ite $x79 ?x136 (- (mod (- ?1) (- ?0)))) ?x155))))
  1.3418 -(let ((@x160 (monotonicity @x157 (= (ite $x78 ?1 (ite $x79 ?x136 (- (mod (- ?1) (- ?0))))) ?x158))))
  1.3419 -(let ((@x185 (trans (quant-intro (monotonicity @x160 $x162) (= $x142 $x164)) (quant-intro @x180 (= $x164 $x181)) (= $x142 $x181))))
  1.3420 -(let ((@x196 (mp~ (mp (asserted $x142) @x185 $x181) (nnf-pos (refl (~ $x178 $x178)) (~ $x181 $x181)) $x181)))
  1.3421 -(let ((@x210 (mp @x196 (quant-intro (refl (= $x178 $x178)) (= $x181 $x205)) $x205)))
  1.3422 -(let (($x270 (or (not $x205) $x264)))
  1.3423 -(let ((?x225 (* (- 1) 2)))
  1.3424 -(let ((?x224 (* (- 1) x$)))
  1.3425 -(let ((?x226 (mod ?x224 ?x225)))
  1.3426 -(let ((?x227 (* (- 1) ?x226)))
  1.3427 -(let (($x223 (<= 2 0)))
  1.3428 -(let ((?x229 (ite $x223 ?x227 ?x228)))
  1.3429 -(let (($x222 (= 2 0)))
  1.3430 -(let ((?x230 (ite $x222 x$ ?x229)))
  1.3431 -(let (($x231 (= ?x31 ?x230)))
  1.3432 -(let ((@x244 (monotonicity (monotonicity (rewrite (= ?x225 (- 2))) (= ?x226 (mod ?x224 (- 2)))) (= ?x227 (* (- 1) (mod ?x224 (- 2)))))))
  1.3433 -(let ((@x247 (monotonicity (rewrite (= $x223 false)) @x244 (= ?x229 (ite false (* (- 1) (mod ?x224 (- 2))) ?x228)))))
  1.3434 -(let ((@x251 (trans @x247 (rewrite (= (ite false (* (- 1) (mod ?x224 (- 2))) ?x228) ?x228)) (= ?x229 ?x228))))
  1.3435 -(let ((@x254 (monotonicity (rewrite (= $x222 false)) @x251 (= ?x230 (ite false x$ ?x228)))))
  1.3436 -(let ((@x261 (monotonicity (trans @x254 (rewrite (= (ite false x$ ?x228) ?x228)) (= ?x230 ?x228)) (= $x231 (= ?x31 ?x228)))))
  1.3437 -(let ((@x274 (monotonicity (trans @x261 (rewrite (= (= ?x31 ?x228) $x264)) (= $x231 $x264)) (= (or (not $x205) $x231) $x270))))
  1.3438 -(let ((@x277 (trans @x274 (rewrite (= $x270 $x270)) (= (or (not $x205) $x231) $x270))))
  1.3439 -(let ((@x278 (mp ((_ quant-inst x$ 2) (or (not $x205) $x231)) @x277 $x270)))
  1.3440 -(let ((@x337 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x264) $x280)) (unit-resolution @x278 @x210 $x264) $x280)))
  1.3441 -(let (($x305 (>= ?x228 0)))
  1.3442 -(let (($x64 (>= ?x31 0)))
  1.3443 -(let (($x67 (not $x64)))
  1.3444 -(let (($x36 (not (<= (+ x$ 1) (+ x$ (+ (* 2 ?x31) 1))))))
  1.3445 -(let ((@x69 (monotonicity (rewrite (= (>= (* 2 ?x31) 0) $x64)) (= (not (>= (* 2 ?x31) 0)) $x67))))
  1.3446 -(let ((?x32 (* 2 ?x31)))
  1.3447 -(let ((?x47 (+ 1 x$ ?x32)))
  1.3448 -(let (($x52 (<= (+ 1 x$) ?x47)))
  1.3449 -(let (($x55 (not $x52)))
  1.3450 -(let ((@x63 (monotonicity (rewrite (= $x52 (>= ?x32 0))) (= $x55 (not (>= ?x32 0))))))
  1.3451 -(let ((@x46 (monotonicity (rewrite (= (+ ?x32 1) (+ 1 ?x32))) (= (+ x$ (+ ?x32 1)) (+ x$ (+ 1 ?x32))))))
  1.3452 -(let ((@x51 (trans @x46 (rewrite (= (+ x$ (+ 1 ?x32)) ?x47)) (= (+ x$ (+ ?x32 1)) ?x47))))
  1.3453 -(let ((@x54 (monotonicity (rewrite (= (+ x$ 1) (+ 1 x$))) @x51 (= (<= (+ x$ 1) (+ x$ (+ ?x32 1))) $x52))))
  1.3454 -(let ((@x73 (trans (monotonicity @x54 (= $x36 $x55)) (trans @x63 @x69 (= $x55 $x67)) (= $x36 $x67))))
  1.3455 -(let ((@x74 (mp (asserted $x36) @x73 $x67)))
  1.3456 -((_ th-lemma arith farkas -1 1 1) @x74 (unit-resolution ((_ th-lemma arith) (or false $x305)) (true-axiom true) $x305) @x337 false))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
  1.3457 -
  1.3458 -fa5abc269019f00f5093218b287856c2a08c0adf 112 0
  1.3459 -unsat
  1.3460 -((set-logic <null>)
  1.3461 -(proof
  1.3462 -(let ((?x224 (mod x$ 2)))
  1.3463 -(let (($x318 (>= ?x224 2)))
  1.3464 -(let (($x319 (not $x318)))
  1.3465 -(let ((?x258 (* (- 1) ?x224)))
  1.3466 -(let ((?x29 (mod$ x$ 2)))
  1.3467 -(let ((?x259 (+ ?x29 ?x258)))
  1.3468 -(let (($x275 (<= ?x259 0)))
  1.3469 -(let (($x260 (= ?x259 0)))
  1.3470 -(let (($x201 (forall ((?v0 Int) (?v1 Int) )(!(let ((?x132 (mod ?v0 ?v1)))
  1.3471 -(let ((?x89 (* (- 1) ?v1)))
  1.3472 -(let ((?x86 (* (- 1) ?v0)))
  1.3473 -(let ((?x140 (mod ?x86 ?x89)))
  1.3474 -(let ((?x146 (* (- 1) ?x140)))
  1.3475 -(let (($x107 (<= ?v1 0)))
  1.3476 -(let ((?x166 (ite $x107 ?x146 ?x132)))
  1.3477 -(let (($x74 (= ?v1 0)))
  1.3478 -(let ((?x171 (ite $x74 ?v0 ?x166)))
  1.3479 -(let ((?x131 (mod$ ?v0 ?v1)))
  1.3480 -(= ?x131 ?x171))))))))))) :pattern ( (mod$ ?v0 ?v1) )))
  1.3481 -))
  1.3482 -(let (($x177 (forall ((?v0 Int) (?v1 Int) )(let ((?x132 (mod ?v0 ?v1)))
  1.3483 -(let ((?x89 (* (- 1) ?v1)))
  1.3484 -(let ((?x86 (* (- 1) ?v0)))
  1.3485 -(let ((?x140 (mod ?x86 ?x89)))
  1.3486 -(let ((?x146 (* (- 1) ?x140)))
  1.3487 -(let (($x107 (<= ?v1 0)))
  1.3488 -(let ((?x166 (ite $x107 ?x146 ?x132)))
  1.3489 -(let (($x74 (= ?v1 0)))
  1.3490 -(let ((?x171 (ite $x74 ?v0 ?x166)))
  1.3491 -(let ((?x131 (mod$ ?v0 ?v1)))
  1.3492 -(= ?x131 ?x171))))))))))))
  1.3493 -))
  1.3494 -(let ((?x132 (mod ?1 ?0)))
  1.3495 -(let ((?x89 (* (- 1) ?0)))
  1.3496 -(let ((?x86 (* (- 1) ?1)))
  1.3497 -(let ((?x140 (mod ?x86 ?x89)))
  1.3498 -(let ((?x146 (* (- 1) ?x140)))
  1.3499 -(let (($x107 (<= ?0 0)))
  1.3500 -(let ((?x166 (ite $x107 ?x146 ?x132)))
  1.3501 -(let (($x74 (= ?0 0)))
  1.3502 -(let ((?x171 (ite $x74 ?1 ?x166)))
  1.3503 -(let ((?x131 (mod$ ?1 ?0)))
  1.3504 -(let (($x174 (= ?x131 ?x171)))
  1.3505 -(let (($x138 (forall ((?v0 Int) (?v1 Int) )(let (($x74 (= ?v1 0)))
  1.3506 -(let ((?x136 (ite $x74 ?v0 (ite (< 0 ?v1) (mod ?v0 ?v1) (- (mod (- ?v0) (- ?v1)))))))
  1.3507 -(let ((?x131 (mod$ ?v0 ?v1)))
  1.3508 -(= ?x131 ?x136)))))
  1.3509 -))
  1.3510 -(let (($x160 (forall ((?v0 Int) (?v1 Int) )(let ((?x89 (* (- 1) ?v1)))
  1.3511 -(let ((?x86 (* (- 1) ?v0)))
  1.3512 -(let ((?x140 (mod ?x86 ?x89)))
  1.3513 -(let ((?x146 (* (- 1) ?x140)))
  1.3514 -(let ((?x132 (mod ?v0 ?v1)))
  1.3515 -(let (($x75 (< 0 ?v1)))
  1.3516 -(let ((?x151 (ite $x75 ?x132 ?x146)))
  1.3517 -(let (($x74 (= ?v1 0)))
  1.3518 -(let ((?x154 (ite $x74 ?v0 ?x151)))
  1.3519 -(let ((?x131 (mod$ ?v0 ?v1)))
  1.3520 -(= ?x131 ?x154))))))))))))
  1.3521 -))
  1.3522 -(let ((@x165 (monotonicity (rewrite (= (< 0 ?0) (not $x107))) (= (ite (< 0 ?0) ?x132 ?x146) (ite (not $x107) ?x132 ?x146)))))
  1.3523 -(let ((@x170 (trans @x165 (rewrite (= (ite (not $x107) ?x132 ?x146) ?x166)) (= (ite (< 0 ?0) ?x132 ?x146) ?x166))))
  1.3524 -(let ((@x173 (monotonicity @x170 (= (ite $x74 ?1 (ite (< 0 ?0) ?x132 ?x146)) ?x171))))
  1.3525 -(let ((@x176 (monotonicity @x173 (= (= ?x131 (ite $x74 ?1 (ite (< 0 ?0) ?x132 ?x146))) $x174))))
  1.3526 -(let (($x75 (< 0 ?0)))
  1.3527 -(let ((?x151 (ite $x75 ?x132 ?x146)))
  1.3528 -(let ((?x154 (ite $x74 ?1 ?x151)))
  1.3529 -(let (($x157 (= ?x131 ?x154)))
  1.3530 -(let (($x158 (= (= ?x131 (ite $x74 ?1 (ite $x75 ?x132 (- (mod (- ?1) (- ?0)))))) $x157)))
  1.3531 -(let ((@x142 (monotonicity (rewrite (= (- ?1) ?x86)) (rewrite (= (- ?0) ?x89)) (= (mod (- ?1) (- ?0)) ?x140))))
  1.3532 -(let ((@x150 (trans (monotonicity @x142 (= (- (mod (- ?1) (- ?0))) (- ?x140))) (rewrite (= (- ?x140) ?x146)) (= (- (mod (- ?1) (- ?0))) ?x146))))
  1.3533 -(let ((@x153 (monotonicity @x150 (= (ite $x75 ?x132 (- (mod (- ?1) (- ?0)))) ?x151))))
  1.3534 -(let ((@x156 (monotonicity @x153 (= (ite $x74 ?1 (ite $x75 ?x132 (- (mod (- ?1) (- ?0))))) ?x154))))
  1.3535 -(let ((@x181 (trans (quant-intro (monotonicity @x156 $x158) (= $x138 $x160)) (quant-intro @x176 (= $x160 $x177)) (= $x138 $x177))))
  1.3536 -(let ((@x192 (mp~ (mp (asserted $x138) @x181 $x177) (nnf-pos (refl (~ $x174 $x174)) (~ $x177 $x177)) $x177)))
  1.3537 -(let ((@x206 (mp @x192 (quant-intro (refl (= $x174 $x174)) (= $x177 $x201)) $x201)))
  1.3538 -(let (($x266 (or (not $x201) $x260)))
  1.3539 -(let ((?x221 (* (- 1) 2)))
  1.3540 -(let ((?x220 (* (- 1) x$)))
  1.3541 -(let ((?x222 (mod ?x220 ?x221)))
  1.3542 -(let ((?x223 (* (- 1) ?x222)))
  1.3543 -(let (($x219 (<= 2 0)))
  1.3544 -(let ((?x225 (ite $x219 ?x223 ?x224)))
  1.3545 -(let (($x218 (= 2 0)))
  1.3546 -(let ((?x226 (ite $x218 x$ ?x225)))
  1.3547 -(let (($x227 (= ?x29 ?x226)))
  1.3548 -(let ((@x240 (monotonicity (monotonicity (rewrite (= ?x221 (- 2))) (= ?x222 (mod ?x220 (- 2)))) (= ?x223 (* (- 1) (mod ?x220 (- 2)))))))
  1.3549 -(let ((@x243 (monotonicity (rewrite (= $x219 false)) @x240 (= ?x225 (ite false (* (- 1) (mod ?x220 (- 2))) ?x224)))))
  1.3550 -(let ((@x247 (trans @x243 (rewrite (= (ite false (* (- 1) (mod ?x220 (- 2))) ?x224) ?x224)) (= ?x225 ?x224))))
  1.3551 -(let ((@x250 (monotonicity (rewrite (= $x218 false)) @x247 (= ?x226 (ite false x$ ?x224)))))
  1.3552 -(let ((@x257 (monotonicity (trans @x250 (rewrite (= (ite false x$ ?x224) ?x224)) (= ?x226 ?x224)) (= $x227 (= ?x29 ?x224)))))
  1.3553 -(let ((@x270 (monotonicity (trans @x257 (rewrite (= (= ?x29 ?x224) $x260)) (= $x227 $x260)) (= (or (not $x201) $x227) $x266))))
  1.3554 -(let ((@x273 (trans @x270 (rewrite (= $x266 $x266)) (= (or (not $x201) $x227) $x266))))
  1.3555 -(let ((@x274 (mp ((_ quant-inst x$ 2) (or (not $x201) $x227)) @x273 $x266)))
  1.3556 -(let ((@x336 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x260) $x275)) (unit-resolution @x274 @x206 $x260) $x275)))
  1.3557 -(let (($x63 (>= ?x29 2)))
  1.3558 -(let ((?x37 (* 2 ?x29)))
  1.3559 -(let (($x56 (>= ?x37 3)))
  1.3560 -(let (($x46 (< (+ x$ ?x37) (+ 3 x$))))
  1.3561 -(let (($x49 (not $x46)))
  1.3562 -(let ((@x58 (monotonicity (rewrite (= $x46 (not $x56))) (= $x49 (not (not $x56))))))
  1.3563 -(let ((@x67 (trans (trans @x58 (rewrite (= (not (not $x56)) $x56)) (= $x49 $x56)) (rewrite (= $x56 $x63)) (= $x49 $x63))))
  1.3564 -(let ((@x42 (monotonicity (rewrite (= (+ ?x29 ?x29) ?x37)) (= (+ x$ (+ ?x29 ?x29)) (+ x$ ?x37)))))
  1.3565 -(let ((@x48 (monotonicity @x42 (rewrite (= (+ x$ 3) (+ 3 x$))) (= (< (+ x$ (+ ?x29 ?x29)) (+ x$ 3)) $x46))))
  1.3566 -(let ((@x51 (monotonicity @x48 (= (not (< (+ x$ (+ ?x29 ?x29)) (+ x$ 3))) $x49))))
  1.3567 -(let ((@x69 (trans @x51 @x67 (= (not (< (+ x$ (+ ?x29 ?x29)) (+ x$ 3))) $x63))))
  1.3568 -(let ((@x70 (mp (asserted (not (< (+ x$ (+ ?x29 ?x29)) (+ x$ 3)))) @x69 $x63)))
  1.3569 -((_ th-lemma arith farkas -1 1 1) @x70 @x336 (unit-resolution ((_ th-lemma arith) (or false $x319)) (true-axiom true) $x319) false)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
  1.3570 -
  1.3571 -1880f0ed1cb3d1cfa006dff17f1b5553ce3a5158 236 0
  1.3572 -unsat
  1.3573 -((set-logic <null>)
  1.3574 -(proof
  1.3575 -(let ((?x410 (div n$ 2)))
  1.3576 -(let ((?x704 (* (- 1) ?x410)))
  1.3577 -(let ((?x381 (div n$ 4)))
  1.3578 -(let ((?x601 (* (- 2) ?x381)))
  1.3579 -(let ((?x329 (mod n$ 4)))
  1.3580 -(let ((?x363 (* (- 1) ?x329)))
  1.3581 -(let ((?x35 (mod$ n$ 4)))
  1.3582 -(let ((?x705 (+ n$ ?x35 ?x363 ?x601 ?x704)))
  1.3583 -(let (($x706 (>= ?x705 2)))
  1.3584 -(let ((?x39 (mod$ n$ 2)))
  1.3585 -(let (($x515 (>= ?x39 1)))
  1.3586 -(let (($x725 (not $x515)))
  1.3587 -(let (($x514 (<= ?x39 1)))
  1.3588 -(let ((?x519 (mod n$ 2)))
  1.3589 -(let ((?x534 (* (- 1) ?x519)))
  1.3590 -(let ((?x535 (+ ?x39 ?x534)))
  1.3591 -(let (($x408 (<= ?x535 0)))
  1.3592 -(let (($x490 (= ?x535 0)))
  1.3593 -(let (($x191 (forall ((?v0 Int) (?v1 Int) )(!(let ((?x108 (mod ?v0 ?v1)))
  1.3594 -(let ((?x65 (* (- 1) ?v1)))
  1.3595 -(let ((?x62 (* (- 1) ?v0)))
  1.3596 -(let ((?x116 (mod ?x62 ?x65)))
  1.3597 -(let ((?x122 (* (- 1) ?x116)))
  1.3598 -(let (($x83 (<= ?v1 0)))
  1.3599 -(let ((?x142 (ite $x83 ?x122 ?x108)))
  1.3600 -(let (($x50 (= ?v1 0)))
  1.3601 -(let ((?x147 (ite $x50 ?v0 ?x142)))
  1.3602 -(let ((?x107 (mod$ ?v0 ?v1)))
  1.3603 -(= ?x107 ?x147))))))))))) :pattern ( (mod$ ?v0 ?v1) )))
  1.3604 -))
  1.3605 -(let (($x153 (forall ((?v0 Int) (?v1 Int) )(let ((?x108 (mod ?v0 ?v1)))
  1.3606 -(let ((?x65 (* (- 1) ?v1)))
  1.3607 -(let ((?x62 (* (- 1) ?v0)))
  1.3608 -(let ((?x116 (mod ?x62 ?x65)))
  1.3609 -(let ((?x122 (* (- 1) ?x116)))
  1.3610 -(let (($x83 (<= ?v1 0)))
  1.3611 -(let ((?x142 (ite $x83 ?x122 ?x108)))
  1.3612 -(let (($x50 (= ?v1 0)))
  1.3613 -(let ((?x147 (ite $x50 ?v0 ?x142)))
  1.3614 -(let ((?x107 (mod$ ?v0 ?v1)))
  1.3615 -(= ?x107 ?x147))))))))))))
  1.3616 -))
  1.3617 -(let ((?x108 (mod ?1 ?0)))
  1.3618 -(let ((?x65 (* (- 1) ?0)))
  1.3619 -(let ((?x62 (* (- 1) ?1)))
  1.3620 -(let ((?x116 (mod ?x62 ?x65)))
  1.3621 -(let ((?x122 (* (- 1) ?x116)))
  1.3622 -(let (($x83 (<= ?0 0)))
  1.3623 -(let ((?x142 (ite $x83 ?x122 ?x108)))
  1.3624 -(let (($x50 (= ?0 0)))
  1.3625 -(let ((?x147 (ite $x50 ?1 ?x142)))
  1.3626 -(let ((?x107 (mod$ ?1 ?0)))
  1.3627 -(let (($x150 (= ?x107 ?x147)))
  1.3628 -(let (($x114 (forall ((?v0 Int) (?v1 Int) )(let (($x50 (= ?v1 0)))
  1.3629 -(let ((?x112 (ite $x50 ?v0 (ite (< 0 ?v1) (mod ?v0 ?v1) (- (mod (- ?v0) (- ?v1)))))))
  1.3630 -(let ((?x107 (mod$ ?v0 ?v1)))
  1.3631 -(= ?x107 ?x112)))))
  1.3632 -))
  1.3633 -(let (($x136 (forall ((?v0 Int) (?v1 Int) )(let ((?x65 (* (- 1) ?v1)))
  1.3634 -(let ((?x62 (* (- 1) ?v0)))
  1.3635 -(let ((?x116 (mod ?x62 ?x65)))
  1.3636 -(let ((?x122 (* (- 1) ?x116)))
  1.3637 -(let ((?x108 (mod ?v0 ?v1)))
  1.3638 -(let (($x51 (< 0 ?v1)))
  1.3639 -(let ((?x127 (ite $x51 ?x108 ?x122)))
  1.3640 -(let (($x50 (= ?v1 0)))
  1.3641 -(let ((?x130 (ite $x50 ?v0 ?x127)))
  1.3642 -(let ((?x107 (mod$ ?v0 ?v1)))
  1.3643 -(= ?x107 ?x130))))))))))))
  1.3644 -))
  1.3645 -(let ((@x141 (monotonicity (rewrite (= (< 0 ?0) (not $x83))) (= (ite (< 0 ?0) ?x108 ?x122) (ite (not $x83) ?x108 ?x122)))))
  1.3646 -(let ((@x146 (trans @x141 (rewrite (= (ite (not $x83) ?x108 ?x122) ?x142)) (= (ite (< 0 ?0) ?x108 ?x122) ?x142))))
  1.3647 -(let ((@x149 (monotonicity @x146 (= (ite $x50 ?1 (ite (< 0 ?0) ?x108 ?x122)) ?x147))))
  1.3648 -(let ((@x152 (monotonicity @x149 (= (= ?x107 (ite $x50 ?1 (ite (< 0 ?0) ?x108 ?x122))) $x150))))
  1.3649 -(let (($x51 (< 0 ?0)))
  1.3650 -(let ((?x127 (ite $x51 ?x108 ?x122)))
  1.3651 -(let ((?x130 (ite $x50 ?1 ?x127)))
  1.3652 -(let (($x133 (= ?x107 ?x130)))
  1.3653 -(let (($x134 (= (= ?x107 (ite $x50 ?1 (ite $x51 ?x108 (- (mod (- ?1) (- ?0)))))) $x133)))
  1.3654 -(let ((@x118 (monotonicity (rewrite (= (- ?1) ?x62)) (rewrite (= (- ?0) ?x65)) (= (mod (- ?1) (- ?0)) ?x116))))
  1.3655 -(let ((@x126 (trans (monotonicity @x118 (= (- (mod (- ?1) (- ?0))) (- ?x116))) (rewrite (= (- ?x116) ?x122)) (= (- (mod (- ?1) (- ?0))) ?x122))))
  1.3656 -(let ((@x129 (monotonicity @x126 (= (ite $x51 ?x108 (- (mod (- ?1) (- ?0)))) ?x127))))
  1.3657 -(let ((@x132 (monotonicity @x129 (= (ite $x50 ?1 (ite $x51 ?x108 (- (mod (- ?1) (- ?0))))) ?x130))))
  1.3658 -(let ((@x157 (trans (quant-intro (monotonicity @x132 $x134) (= $x114 $x136)) (quant-intro @x152 (= $x136 $x153)) (= $x114 $x153))))
  1.3659 -(let ((@x168 (mp~ (mp (asserted $x114) @x157 $x153) (nnf-pos (refl (~ $x150 $x150)) (~ $x153 $x153)) $x153)))
  1.3660 -(let ((@x196 (mp @x168 (quant-intro (refl (= $x150 $x150)) (= $x153 $x191)) $x191)))
  1.3661 -(let (($x260 (not $x191)))
  1.3662 -(let (($x541 (or $x260 $x490)))
  1.3663 -(let ((?x211 (* (- 1) 2)))
  1.3664 -(let ((?x222 (* (- 1) n$)))
  1.3665 -(let ((?x517 (mod ?x222 ?x211)))
  1.3666 -(let ((?x518 (* (- 1) ?x517)))
  1.3667 -(let (($x209 (<= 2 0)))
  1.3668 -(let ((?x520 (ite $x209 ?x518 ?x519)))
  1.3669 -(let (($x208 (= 2 0)))
  1.3670 -(let ((?x521 (ite $x208 n$ ?x520)))
  1.3671 -(let (($x485 (= ?x39 ?x521)))
  1.3672 -(let ((@x593 (monotonicity (monotonicity (rewrite (= ?x211 (- 2))) (= ?x517 (mod ?x222 (- 2)))) (= ?x518 (* (- 1) (mod ?x222 (- 2)))))))
  1.3673 -(let ((@x221 (rewrite (= $x209 false))))
  1.3674 -(let ((@x596 (monotonicity @x221 @x593 (= ?x520 (ite false (* (- 1) (mod ?x222 (- 2))) ?x519)))))
  1.3675 -(let ((@x599 (trans @x596 (rewrite (= (ite false (* (- 1) (mod ?x222 (- 2))) ?x519) ?x519)) (= ?x520 ?x519))))
  1.3676 -(let ((@x219 (rewrite (= $x208 false))))
  1.3677 -(let ((@x487 (trans (monotonicity @x219 @x599 (= ?x521 (ite false n$ ?x519))) (rewrite (= (ite false n$ ?x519) ?x519)) (= ?x521 ?x519))))
  1.3678 -(let ((@x538 (trans (monotonicity @x487 (= $x485 (= ?x39 ?x519))) (rewrite (= (= ?x39 ?x519) $x490)) (= $x485 $x490))))
  1.3679 -(let ((@x406 (trans (monotonicity @x538 (= (or $x260 $x485) $x541)) (rewrite (= $x541 $x541)) (= (or $x260 $x485) $x541))))
  1.3680 -(let ((@x407 (mp ((_ quant-inst n$ 2) (or $x260 $x485)) @x406 $x541)))
  1.3681 -(let ((@x715 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x490) $x408)) (unit-resolution @x407 @x196 $x490) $x408)))
  1.3682 -(let (($x303 (>= ?x519 2)))
  1.3683 -(let (($x304 (not $x303)))
  1.3684 -(let ((@x26 (true-axiom true)))
  1.3685 -(let ((@x722 (unit-resolution ((_ th-lemma arith assign-bounds 1 1) (or $x514 $x303 (not $x408))) (unit-resolution ((_ th-lemma arith) (or false $x304)) @x26 $x304) @x715 $x514)))
  1.3686 -(let (($x41 (= ?x39 1)))
  1.3687 -(let (($x169 (not $x41)))
  1.3688 -(let ((?x42 (mod$ m$ 2)))
  1.3689 -(let (($x43 (= ?x42 1)))
  1.3690 -(let ((?x29 (+ n$ m$)))
  1.3691 -(let ((?x214 (mod ?x29 2)))
  1.3692 -(let ((?x253 (* (- 1) ?x214)))
  1.3693 -(let ((?x31 (mod$ ?x29 2)))
  1.3694 -(let ((?x603 (+ n$ m$ ?x31 ?x35 ?x253 (* (- 1) (div ?x29 2)) ?x363 ?x601 (* (- 1) (div m$ 2)))))
  1.3695 -(let (($x604 (>= ?x603 2)))
  1.3696 -(let (($x523 (>= ?x42 1)))
  1.3697 -(let (($x609 (not $x523)))
  1.3698 -(let (($x522 (<= ?x42 1)))
  1.3699 -(let ((?x439 (mod m$ 2)))
  1.3700 -(let ((?x466 (* (- 1) ?x439)))
  1.3701 -(let ((?x467 (+ ?x42 ?x466)))
  1.3702 -(let (($x482 (<= ?x467 0)))
  1.3703 -(let (($x468 (= ?x467 0)))
  1.3704 -(let (($x473 (or $x260 $x468)))
  1.3705 -(let ((?x440 (ite $x209 (* (- 1) (mod (* (- 1) m$) ?x211)) ?x439)))
  1.3706 -(let ((?x441 (ite $x208 m$ ?x440)))
  1.3707 -(let (($x442 (= ?x42 ?x441)))
  1.3708 -(let ((@x453 (rewrite (= (ite false (* (- 1) (mod (* (- 1) m$) (- 2))) ?x439) ?x439))))
  1.3709 -(let (($x447 (= (* (- 1) (mod (* (- 1) m$) ?x211)) (* (- 1) (mod (* (- 1) m$) (- 2))))))
  1.3710 -(let ((@x229 (rewrite (= ?x211 (- 2)))))
  1.3711 -(let ((@x445 (monotonicity @x229 (= (mod (* (- 1) m$) ?x211) (mod (* (- 1) m$) (- 2))))))
  1.3712 -(let ((@x451 (monotonicity @x221 (monotonicity @x445 $x447) (= ?x440 (ite false (* (- 1) (mod (* (- 1) m$) (- 2))) ?x439)))))
  1.3713 -(let ((@x458 (monotonicity @x219 (trans @x451 @x453 (= ?x440 ?x439)) (= ?x441 (ite false m$ ?x439)))))
  1.3714 -(let ((@x465 (monotonicity (trans @x458 (rewrite (= (ite false m$ ?x439) ?x439)) (= ?x441 ?x439)) (= $x442 (= ?x42 ?x439)))))
  1.3715 -(let ((@x477 (monotonicity (trans @x465 (rewrite (= (= ?x42 ?x439) $x468)) (= $x442 $x468)) (= (or $x260 $x442) $x473))))
  1.3716 -(let ((@x481 (mp ((_ quant-inst m$ 2) (or $x260 $x442)) (trans @x477 (rewrite (= $x473 $x473)) (= (or $x260 $x442) $x473)) $x473)))
  1.3717 -(let ((@x277 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x468) $x482)) (unit-resolution @x481 @x196 $x468) $x482)))
  1.3718 -(let ((@x386 (unit-resolution ((_ th-lemma arith) (or false (not (>= ?x439 2)))) @x26 (not (>= ?x439 2)))))
  1.3719 -(let ((@x384 (unit-resolution ((_ th-lemma arith assign-bounds 1 1) (or $x522 (>= ?x439 2) (not $x482))) @x386 @x277 $x522)))
  1.3720 -(let ((@x564 (unit-resolution ((_ th-lemma arith triangle-eq) (or $x43 (not $x522) $x609)) (hypothesis (not $x43)) (or (not $x522) $x609))))
  1.3721 -(let ((?x272 (div ?x29 2)))
  1.3722 -(let ((?x288 (* (- 2) ?x272)))
  1.3723 -(let ((?x289 (+ n$ m$ ?x253 ?x288)))
  1.3724 -(let (($x294 (<= ?x289 0)))
  1.3725 -(let (($x287 (= ?x289 0)))
  1.3726 -(let ((@x617 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x287) $x294)) (unit-resolution ((_ th-lemma arith) (or false $x287)) @x26 $x287) $x294)))
  1.3727 -(let (($x433 (<= ?x31 0)))
  1.3728 -(let (($x32 (= ?x31 0)))
  1.3729 -(let ((@x33 (asserted $x32)))
  1.3730 -(let ((?x254 (+ ?x31 ?x253)))
  1.3731 -(let (($x270 (<= ?x254 0)))
  1.3732 -(let (($x255 (= ?x254 0)))
  1.3733 -(let (($x261 (or $x260 $x255)))
  1.3734 -(let ((?x215 (ite $x209 (* (- 1) (mod (* (- 1) ?x29) ?x211)) ?x214)))
  1.3735 -(let ((?x216 (ite $x208 ?x29 ?x215)))
  1.3736 -(let (($x217 (= ?x31 ?x216)))
  1.3737 -(let (($x239 (= (ite false (* (- 1) (mod (+ ?x222 (* (- 1) m$)) (- 2))) ?x214) ?x214)))
  1.3738 -(let (($x237 (= ?x215 (ite false (* (- 1) (mod (+ ?x222 (* (- 1) m$)) (- 2))) ?x214))))
  1.3739 -(let (($x234 (= (* (- 1) (mod (* (- 1) ?x29) ?x211)) (* (- 1) (mod (+ ?x222 (* (- 1) m$)) (- 2))))))
  1.3740 -(let ((@x232 (monotonicity (rewrite (= (* (- 1) ?x29) (+ ?x222 (* (- 1) m$)))) @x229 (= (mod (* (- 1) ?x29) ?x211) (mod (+ ?x222 (* (- 1) m$)) (- 2))))))
  1.3741 -(let ((@x242 (trans (monotonicity @x221 (monotonicity @x232 $x234) $x237) (rewrite $x239) (= ?x215 ?x214))))
  1.3742 -(let ((@x249 (trans (monotonicity @x219 @x242 (= ?x216 (ite false ?x29 ?x214))) (rewrite (= (ite false ?x29 ?x214) ?x214)) (= ?x216 ?x214))))
  1.3743 -(let ((@x259 (trans (monotonicity @x249 (= $x217 (= ?x31 ?x214))) (rewrite (= (= ?x31 ?x214) $x255)) (= $x217 $x255))))
  1.3744 -(let ((@x268 (trans (monotonicity @x259 (= (or $x260 $x217) $x261)) (rewrite (= $x261 $x261)) (= (or $x260 $x217) $x261))))
  1.3745 -(let ((@x269 (mp ((_ quant-inst (+ n$ m$) 2) (or $x260 $x217)) @x268 $x261)))
  1.3746 -(let ((@x626 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x255) $x270)) (unit-resolution @x269 @x196 $x255) $x270)))
  1.3747 -(let ((?x498 (+ m$ ?x466 (* (- 2) (div m$ 2)))))
  1.3748 -(let (($x496 (= ?x498 0)))
  1.3749 -(let ((@x633 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x496) (<= ?x498 0))) (unit-resolution ((_ th-lemma arith) (or false $x496)) @x26 $x496) (<= ?x498 0))))
  1.3750 -(let ((?x397 (* (- 4) ?x381)))
  1.3751 -(let ((?x398 (+ n$ ?x363 ?x397)))
  1.3752 -(let (($x403 (<= ?x398 0)))
  1.3753 -(let (($x396 (= ?x398 0)))
  1.3754 -(let ((@x640 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x396) $x403)) (unit-resolution ((_ th-lemma arith) (or false $x396)) @x26 $x396) $x403)))
  1.3755 -(let ((?x364 (+ ?x35 ?x363)))
  1.3756 -(let (($x379 (<= ?x364 0)))
  1.3757 -(let (($x365 (= ?x364 0)))
  1.3758 -(let (($x370 (or $x260 $x365)))
  1.3759 -(let ((?x330 (ite (<= 4 0) (* (- 1) (mod ?x222 (* (- 1) 4))) ?x329)))
  1.3760 -(let ((?x331 (ite (= 4 0) n$ ?x330)))
  1.3761 -(let (($x332 (= ?x35 ?x331)))
  1.3762 -(let ((@x342 (monotonicity (rewrite (= (* (- 1) 4) (- 4))) (= (mod ?x222 (* (- 1) 4)) (mod ?x222 (- 4))))))
  1.3763 -(let ((@x345 (monotonicity @x342 (= (* (- 1) (mod ?x222 (* (- 1) 4))) (* (- 1) (mod ?x222 (- 4)))))))
  1.3764 -(let ((@x348 (monotonicity (rewrite (= (<= 4 0) false)) @x345 (= ?x330 (ite false (* (- 1) (mod ?x222 (- 4))) ?x329)))))
  1.3765 -(let ((@x352 (trans @x348 (rewrite (= (ite false (* (- 1) (mod ?x222 (- 4))) ?x329) ?x329)) (= ?x330 ?x329))))
  1.3766 -(let ((@x355 (monotonicity (rewrite (= (= 4 0) false)) @x352 (= ?x331 (ite false n$ ?x329)))))
  1.3767 -(let ((@x362 (monotonicity (trans @x355 (rewrite (= (ite false n$ ?x329) ?x329)) (= ?x331 ?x329)) (= $x332 (= ?x35 ?x329)))))
  1.3768 -(let ((@x374 (monotonicity (trans @x362 (rewrite (= (= ?x35 ?x329) $x365)) (= $x332 $x365)) (= (or $x260 $x332) $x370))))
  1.3769 -(let ((@x378 (mp ((_ quant-inst n$ 4) (or $x260 $x332)) (trans @x374 (rewrite (= $x370 $x370)) (= (or $x260 $x332) $x370)) $x370)))
  1.3770 -(let ((@x645 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x365) $x379)) (unit-resolution @x378 @x196 $x365) $x379)))
  1.3771 -(let (($x435 (<= ?x35 3)))
  1.3772 -(let (($x37 (= ?x35 3)))
  1.3773 -(let ((@x38 (asserted $x37)))
  1.3774 -(let ((@x655 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x468) (>= ?x467 0))) (unit-resolution @x481 @x196 $x468) (>= ?x467 0))))
  1.3775 -(let ((@x656 ((_ th-lemma arith farkas -1 1 -2 1 1 1 1 1 1 1) @x655 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x37) $x435)) @x38 $x435) (hypothesis $x604) @x645 @x640 @x633 @x626 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x32) $x433)) @x33 $x433) @x617 (hypothesis $x609) false)))
  1.3776 -(let ((@x565 (unit-resolution (lemma @x656 (or (not $x604) $x523)) (unit-resolution @x564 @x384 $x609) (not $x604))))
  1.3777 -(let (($x295 (>= ?x289 0)))
  1.3778 -(let ((@x566 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x287) $x295)) (unit-resolution ((_ th-lemma arith) (or false $x287)) @x26 $x287) $x295)))
  1.3779 -(let (($x434 (>= ?x31 0)))
  1.3780 -(let (($x271 (>= ?x254 0)))
  1.3781 -(let ((@x531 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x255) $x271)) (unit-resolution @x269 @x196 $x255) $x271)))
  1.3782 -(let ((@x537 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x496) (>= ?x498 0))) (unit-resolution ((_ th-lemma arith) (or false $x496)) @x26 $x496) (>= ?x498 0))))
  1.3783 -(let ((@x549 (unit-resolution ((_ th-lemma arith) (or false (>= ?x439 0))) @x26 (>= ?x439 0))))
  1.3784 -(let (($x404 (>= ?x398 0)))
  1.3785 -(let ((@x552 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x396) $x404)) (unit-resolution ((_ th-lemma arith) (or false $x396)) @x26 $x396) $x404)))
  1.3786 -(let (($x380 (>= ?x364 0)))
  1.3787 -(let ((@x273 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x365) $x380)) (unit-resolution @x378 @x196 $x365) $x380)))
  1.3788 -(let (($x436 (>= ?x35 3)))
  1.3789 -(let ((@x545 ((_ th-lemma arith farkas -1/2 -1/2 -1/2 -1/2 -1/2 -1/2 -1/2 -1/2 1) (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x37) $x436)) @x38 $x436) @x273 @x552 @x549 @x537 @x531 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x32) $x434)) @x33 $x434) @x566 @x565 false)))
  1.3790 -(let (($x171 (or $x169 (not $x43))))
  1.3791 -(let ((@x177 (monotonicity (rewrite (= (and $x41 $x43) (not $x171))) (= (not (and $x41 $x43)) (not (not $x171))))))
  1.3792 -(let ((@x181 (trans @x177 (rewrite (= (not (not $x171)) $x171)) (= (not (and $x41 $x43)) $x171))))
  1.3793 -(let ((@x182 (mp (asserted (not (and $x41 $x43))) @x181 $x171)))
  1.3794 -(let ((@x729 (unit-resolution ((_ th-lemma arith triangle-eq) (or $x41 (not $x514) $x725)) (unit-resolution @x182 (lemma @x545 $x43) $x169) (or (not $x514) $x725))))
  1.3795 -(let ((?x420 (* (- 2) ?x410)))
  1.3796 -(let ((?x421 (+ n$ ?x420 ?x534)))
  1.3797 -(let (($x426 (<= ?x421 0)))
  1.3798 -(let (($x419 (= ?x421 0)))
  1.3799 -(let ((@x737 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x419) $x426)) (unit-resolution ((_ th-lemma arith) (or false $x419)) @x26 $x419) $x426)))
  1.3800 -(let (($x409 (>= ?x535 0)))
  1.3801 -(let ((@x741 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x490) $x409)) (unit-resolution @x407 @x196 $x490) $x409)))
  1.3802 -(let ((@x742 ((_ th-lemma arith farkas -1 1 -2 1 1 1 1) @x741 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x37) $x435)) @x38 $x435) (hypothesis $x706) @x640 @x737 @x645 (unit-resolution @x729 @x722 $x725) false)))
  1.3803 -(let (($x427 (>= ?x421 0)))
  1.3804 -(let ((@x584 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x419) $x427)) (unit-resolution ((_ th-lemma arith) (or false $x419)) @x26 $x419) $x427)))
  1.3805 -(let (($x542 (>= ?x519 0)))
  1.3806 -((_ th-lemma arith farkas -1/2 -1/2 -1/2 -1/2 -1/2 1) (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x37) $x436)) @x38 $x436) @x552 (unit-resolution ((_ th-lemma arith) (or false $x542)) @x26 $x542) @x584 @x273 (lemma @x742 (not $x706)) false)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
  1.3807 +(let ((?x29 (of_nat$ x$)))
  1.3808 +(let ((?x30 (* 2 ?x29)))
  1.3809 +(let ((?x31 (nat$ ?x30)))
  1.3810 +(let ((?x212 (of_nat$ ?x31)))
  1.3811 +(let ((?x532 (* (- 1) ?x212)))
  1.3812 +(let ((?x533 (+ ?x30 ?x532)))
  1.3813 +(let (($x513 (<= ?x533 0)))
  1.3814 +(let (($x531 (= ?x533 0)))
  1.3815 +(let (($x193 (>= ?x29 0)))
  1.3816 +(let (($x487 (>= ?x212 1)))
  1.3817 +(let (($x485 (= ?x212 1)))
  1.3818 +(let ((?x33 (nat$ 1)))
  1.3819 +(let ((?x504 (of_nat$ ?x33)))
  1.3820 +(let (($x505 (= ?x504 1)))
  1.3821 +(let (($x546 (forall ((?v0 Int) )(! (let ((?x49 (nat$ ?v0)))
  1.3822 +(let ((?x50 (of_nat$ ?x49)))
  1.3823 +(let (($x51 (= ?x50 ?v0)))
  1.3824 +(let (($x64 (>= ?v0 0)))
  1.3825 +(let (($x65 (not $x64)))
  1.3826 +(or $x65 $x51)))))) :pattern ( (nat$ ?v0) ) :qid k!10))
  1.3827 +))
  1.3828 +(let (($x71 (forall ((?v0 Int) )(! (let ((?x49 (nat$ ?v0)))
  1.3829 +(let ((?x50 (of_nat$ ?x49)))
  1.3830 +(let (($x51 (= ?x50 ?v0)))
  1.3831 +(let (($x64 (>= ?v0 0)))
  1.3832 +(let (($x65 (not $x64)))
  1.3833 +(or $x65 $x51)))))) :qid k!10))
  1.3834 +))
  1.3835 +(let ((?x49 (nat$ ?0)))
  1.3836 +(let ((?x50 (of_nat$ ?x49)))
  1.3837 +(let (($x51 (= ?x50 ?0)))
  1.3838 +(let (($x64 (>= ?0 0)))
  1.3839 +(let (($x65 (not $x64)))
  1.3840 +(let (($x68 (or $x65 $x51)))
  1.3841 +(let (($x53 (forall ((?v0 Int) )(! (let ((?x49 (nat$ ?v0)))
  1.3842 +(let ((?x50 (of_nat$ ?x49)))
  1.3843 +(let (($x51 (= ?x50 ?v0)))
  1.3844 +(let (($x48 (<= 0 ?v0)))
  1.3845 +(=> $x48 $x51))))) :qid k!10))
  1.3846 +))
  1.3847 +(let (($x59 (forall ((?v0 Int) )(! (let ((?x49 (nat$ ?v0)))
  1.3848 +(let ((?x50 (of_nat$ ?x49)))
  1.3849 +(let (($x51 (= ?x50 ?v0)))
  1.3850 +(or (not (<= 0 ?v0)) $x51)))) :qid k!10))
  1.3851 +))
  1.3852 +(let ((@x67 (monotonicity (rewrite (= (<= 0 ?0) $x64)) (= (not (<= 0 ?0)) $x65))))
  1.3853 +(let ((@x73 (quant-intro (monotonicity @x67 (= (or (not (<= 0 ?0)) $x51) $x68)) (= $x59 $x71))))
  1.3854 +(let ((@x58 (rewrite (= (=> (<= 0 ?0) $x51) (or (not (<= 0 ?0)) $x51)))))
  1.3855 +(let ((@x76 (mp (asserted $x53) (trans (quant-intro @x58 (= $x53 $x59)) @x73 (= $x53 $x71)) $x71)))
  1.3856 +(let ((@x551 (mp (mp~ @x76 (nnf-pos (refl (~ $x68 $x68)) (~ $x71 $x71)) $x71) (quant-intro (refl (= $x68 $x68)) (= $x71 $x546)) $x546)))
  1.3857 +(let (($x526 (not $x546)))
  1.3858 +(let (($x489 (or $x526 $x505)))
  1.3859 +(let ((@x506 (rewrite (= (>= 1 0) true))))
  1.3860 +(let ((@x219 (trans (monotonicity @x506 (= (not (>= 1 0)) (not true))) (rewrite (= (not true) false)) (= (not (>= 1 0)) false))))
  1.3861 +(let ((@x223 (monotonicity @x219 (= (or (not (>= 1 0)) $x505) (or false $x505)))))
  1.3862 +(let ((@x503 (trans @x223 (rewrite (= (or false $x505) $x505)) (= (or (not (>= 1 0)) $x505) $x505))))
  1.3863 +(let ((@x493 (monotonicity @x503 (= (or $x526 (or (not (>= 1 0)) $x505)) $x489))))
  1.3864 +(let ((@x496 (trans @x493 (rewrite (= $x489 $x489)) (= (or $x526 (or (not (>= 1 0)) $x505)) $x489))))
  1.3865 +(let ((@x497 (mp ((_ quant-inst 1) (or $x526 (or (not (>= 1 0)) $x505))) @x496 $x489)))
  1.3866 +(let (($x34 (= ?x31 ?x33)))
  1.3867 +(let ((@x42 (mp (asserted (not (not $x34))) (rewrite (= (not (not $x34)) $x34)) $x34)))
  1.3868 +(let ((@x356 (trans (monotonicity @x42 (= ?x212 ?x504)) (unit-resolution @x497 @x551 $x505) $x485)))
  1.3869 +(let ((@x371 (unit-resolution ((_ th-lemma arith farkas 1 1) (or (not $x487) (not (<= ?x212 0)))) (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x485) $x487)) @x356 $x487) (not (<= ?x212 0)))))
  1.3870 +(let ((@x374 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not (= ?x212 0)) (<= ?x212 0))) @x371 (not (= ?x212 0)))))
  1.3871 +(let (($x515 (= ?x212 0)))
  1.3872 +(let (($x517 (or $x193 $x515)))
  1.3873 +(let (($x552 (forall ((?v0 Int) )(! (let ((?x49 (nat$ ?v0)))
  1.3874 +(let ((?x50 (of_nat$ ?x49)))
  1.3875 +(let (($x78 (= ?x50 0)))
  1.3876 +(let (($x64 (>= ?v0 0)))
  1.3877 +(or $x64 $x78))))) :pattern ( (nat$ ?v0) ) :qid k!11))
  1.3878 +))
  1.3879 +(let (($x101 (forall ((?v0 Int) )(! (let ((?x49 (nat$ ?v0)))
  1.3880 +(let ((?x50 (of_nat$ ?x49)))
  1.3881 +(let (($x78 (= ?x50 0)))
  1.3882 +(let (($x64 (>= ?v0 0)))
  1.3883 +(or $x64 $x78))))) :qid k!11))
  1.3884 +))
  1.3885 +(let ((@x556 (quant-intro (refl (= (or $x64 (= ?x50 0)) (or $x64 (= ?x50 0)))) (= $x101 $x552))))
  1.3886 +(let ((@x120 (nnf-pos (refl (~ (or $x64 (= ?x50 0)) (or $x64 (= ?x50 0)))) (~ $x101 $x101))))
  1.3887 +(let (($x80 (forall ((?v0 Int) )(! (let ((?x49 (nat$ ?v0)))
  1.3888 +(let ((?x50 (of_nat$ ?x49)))
  1.3889 +(let (($x78 (= ?x50 0)))
  1.3890 +(let (($x77 (< ?v0 0)))
  1.3891 +(=> $x77 $x78))))) :qid k!11))
  1.3892 +))
  1.3893 +(let (($x86 (forall ((?v0 Int) )(! (let ((?x49 (nat$ ?v0)))
  1.3894 +(let ((?x50 (of_nat$ ?x49)))
  1.3895 +(let (($x78 (= ?x50 0)))
  1.3896 +(let (($x77 (< ?v0 0)))
  1.3897 +(let (($x82 (not $x77)))
  1.3898 +(or $x82 $x78)))))) :qid k!11))
  1.3899 +))
  1.3900 +(let (($x78 (= ?x50 0)))
  1.3901 +(let (($x98 (or $x64 $x78)))
  1.3902 +(let (($x77 (< ?0 0)))
  1.3903 +(let (($x82 (not $x77)))
  1.3904 +(let (($x83 (or $x82 $x78)))
  1.3905 +(let ((@x97 (trans (monotonicity (rewrite (= $x77 $x65)) (= $x82 (not $x65))) (rewrite (= (not $x65) $x64)) (= $x82 $x64))))
  1.3906 +(let ((@x105 (trans (quant-intro (rewrite (= (=> $x77 $x78) $x83)) (= $x80 $x86)) (quant-intro (monotonicity @x97 (= $x83 $x98)) (= $x86 $x101)) (= $x80 $x101))))
  1.3907 +(let ((@x557 (mp (mp~ (mp (asserted $x80) @x105 $x101) @x120 $x101) @x556 $x552)))
  1.3908 +(let (($x156 (not $x552)))
  1.3909 +(let (($x520 (or $x156 $x193 $x515)))
  1.3910 +(let ((@x530 (rewrite (= (>= ?x30 0) $x193))))
  1.3911 +(let ((@x523 (monotonicity (monotonicity @x530 (= (or (>= ?x30 0) $x515) $x517)) (= (or $x156 (or (>= ?x30 0) $x515)) (or $x156 $x517)))))
  1.3912 +(let ((@x215 (trans @x523 (rewrite (= (or $x156 $x517) $x520)) (= (or $x156 (or (>= ?x30 0) $x515)) $x520))))
  1.3913 +(let ((@x229 (mp ((_ quant-inst (* 2 ?x29)) (or $x156 (or (>= ?x30 0) $x515))) @x215 $x520)))
  1.3914 +(let (($x185 (not $x193)))
  1.3915 +(let (($x534 (or $x185 $x531)))
  1.3916 +(let (($x188 (or $x526 $x185 $x531)))
  1.3917 +(let (($x213 (= ?x212 ?x30)))
  1.3918 +(let (($x208 (>= ?x30 0)))
  1.3919 +(let (($x209 (not $x208)))
  1.3920 +(let (($x214 (or $x209 $x213)))
  1.3921 +(let (($x189 (or $x526 $x214)))
  1.3922 +(let ((@x536 (monotonicity (monotonicity @x530 (= $x209 $x185)) (rewrite (= $x213 $x531)) (= $x214 $x534))))
  1.3923 +(let ((@x175 (trans (monotonicity @x536 (= $x189 (or $x526 $x534))) (rewrite (= (or $x526 $x534) $x188)) (= $x189 $x188))))
  1.3924 +(let ((@x176 (mp ((_ quant-inst (* 2 ?x29)) $x189) @x175 $x188)))
  1.3925 +(let ((@x470 (unit-resolution (unit-resolution @x176 @x551 $x534) (unit-resolution (unit-resolution @x229 @x557 $x517) @x374 $x193) $x531)))
  1.3926 +(let (($x514 (>= ?x533 0)))
  1.3927 +(let (($x486 (<= ?x212 1)))
  1.3928 +((_ th-lemma arith gcd-test -1/2 -1/2 -1/2 -1/2) (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x485) $x487)) @x356 $x487) (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x485) $x486)) @x356 $x486) (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x531) $x514)) @x470 $x514) (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x531) $x513)) @x470 $x513) false))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
  1.3929  
  1.3930 -f6a4c40290fd6742c0b08a1fe90b3664e90c2143 336 0
  1.3931 -unsat
  1.3932 -((set-logic <null>)
  1.3933 -(proof
  1.3934 -(let ((?x99 (mod$ l$ 2)))
  1.3935 -(let ((?x96 (map$ uu$ xs$)))
  1.3936 -(let ((?x97 (eval_dioph$ ks$ ?x96)))
  1.3937 -(let ((?x98 (mod$ ?x97 2)))
  1.3938 -(let (($x100 (= ?x98 ?x99)))
  1.3939 -(let ((?x93 (eval_dioph$ ks$ xs$)))
  1.3940 -(let (($x95 (= ?x93 l$)))
  1.3941 -(let ((?x110 (* (- 1) ?x97)))
  1.3942 -(let ((?x111 (+ l$ ?x110)))
  1.3943 -(let ((?x114 (divide$ ?x111 2)))
  1.3944 -(let ((?x101 (map$ uua$ xs$)))
  1.3945 -(let ((?x102 (eval_dioph$ ks$ ?x101)))
  1.3946 -(let (($x117 (= ?x102 ?x114)))
  1.3947 -(let (($x282 (not $x117)))
  1.3948 -(let (($x281 (not $x100)))
  1.3949 -(let (($x283 (or $x281 $x282)))
  1.3950 -(let ((?x744 (div ?x93 2)))
  1.3951 -(let ((?x970 (* (- 1) ?x744)))
  1.3952 -(let ((?x699 (mod ?x93 2)))
  1.3953 -(let ((?x726 (* (- 1) ?x699)))
  1.3954 -(let ((?x516 (mod l$ 2)))
  1.3955 -(let ((?x543 (* (- 1) ?x516)))
  1.3956 -(let (($x972 (>= (+ l$ ?x99 ?x543 (* (- 1) (div l$ 2)) ?x726 ?x970) 1)))
  1.3957 -(let ((?x369 (* (- 1) l$)))
  1.3958 -(let ((?x693 (+ ?x93 ?x369)))
  1.3959 -(let (($x695 (>= ?x693 0)))
  1.3960 -(let (($x861 (not $x695)))
  1.3961 -(let (($x694 (<= ?x693 0)))
  1.3962 -(let ((?x686 (+ ?x102 (* (- 1) ?x114))))
  1.3963 -(let (($x687 (<= ?x686 0)))
  1.3964 -(let (($x284 (not $x283)))
  1.3965 -(let ((@x466 (hypothesis $x284)))
  1.3966 -(let ((@x856 (unit-resolution ((_ th-lemma arith triangle-eq) (or $x282 $x687)) (unit-resolution (def-axiom (or $x283 $x117)) @x466 $x117) $x687)))
  1.3967 -(let ((?x437 (+ l$ ?x110 (* (- 2) (div ?x111 2)) (* (- 1) (mod (+ l$ ?x97) 2)))))
  1.3968 -(let (($x443 (>= ?x437 0)))
  1.3969 -(let (($x434 (= ?x437 0)))
  1.3970 -(let ((@x26 (true-axiom true)))
  1.3971 -(let ((@x793 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x434) $x443)) (unit-resolution ((_ th-lemma arith) (or false $x434)) @x26 $x434) $x443)))
  1.3972 -(let ((?x501 (* (- 2) ?x102)))
  1.3973 -(let ((?x502 (+ ?x93 ?x110 ?x501)))
  1.3974 -(let (($x509 (<= ?x502 0)))
  1.3975 -(let (($x503 (= ?x502 0)))
  1.3976 -(let (($x304 (forall ((?v0 Int_list$) (?v1 Int_list$) )(!(let ((?x45 (eval_dioph$ ?v0 ?v1)))
  1.3977 -(let ((?x83 (+ ?x45 (* (- 1) (eval_dioph$ ?v0 (map$ uu$ ?v1))) (* (- 2) (eval_dioph$ ?v0 (map$ uua$ ?v1))))))
  1.3978 -(= ?x83 0))) :pattern ( (eval_dioph$ ?v0 (map$ uu$ ?v1)) ) :pattern ( (eval_dioph$ ?v0 (map$ uua$ ?v1)) )))
  1.3979 -))
  1.3980 -(let (($x85 (forall ((?v0 Int_list$) (?v1 Int_list$) )(let ((?x45 (eval_dioph$ ?v0 ?v1)))
  1.3981 -(let ((?x83 (+ ?x45 (* (- 1) (eval_dioph$ ?v0 (map$ uu$ ?v1))) (* (- 2) (eval_dioph$ ?v0 (map$ uua$ ?v1))))))
  1.3982 -(= ?x83 0))))
  1.3983 -))
  1.3984 -(let ((?x45 (eval_dioph$ ?1 ?0)))
  1.3985 -(let ((?x83 (+ ?x45 (* (- 1) (eval_dioph$ ?1 (map$ uu$ ?0))) (* (- 2) (eval_dioph$ ?1 (map$ uua$ ?0))))))
  1.3986 -(let (($x79 (= ?x83 0)))
  1.3987 -(let (($x58 (forall ((?v0 Int_list$) (?v1 Int_list$) )(let ((?x45 (eval_dioph$ ?v0 ?v1)))
  1.3988 -(let ((?x48 (eval_dioph$ ?v0 (map$ uu$ ?v1))))
  1.3989 -(let ((?x56 (+ (* (eval_dioph$ ?v0 (map$ uua$ ?v1)) 2) ?x48)))
  1.3990 -(= ?x56 ?x45)))))
  1.3991 -))
  1.3992 -(let (($x74 (forall ((?v0 Int_list$) (?v1 Int_list$) )(let ((?x45 (eval_dioph$ ?v0 ?v1)))
  1.3993 -(let ((?x54 (eval_dioph$ ?v0 (map$ uua$ ?v1))))
  1.3994 -(let ((?x60 (* 2 ?x54)))
  1.3995 -(let ((?x48 (eval_dioph$ ?v0 (map$ uu$ ?v1))))
  1.3996 -(let ((?x66 (+ ?x48 ?x60)))
  1.3997 -(= ?x66 ?x45)))))))
  1.3998 -))
  1.3999 -(let ((?x54 (eval_dioph$ ?1 (map$ uua$ ?0))))
  1.4000 -(let ((?x60 (* 2 ?x54)))
  1.4001 -(let ((?x48 (eval_dioph$ ?1 (map$ uu$ ?0))))
  1.4002 -(let ((?x66 (+ ?x48 ?x60)))
  1.4003 -(let (($x71 (= ?x66 ?x45)))
  1.4004 -(let ((@x65 (monotonicity (rewrite (= (* ?x54 2) ?x60)) (= (+ (* ?x54 2) ?x48) (+ ?x60 ?x48)))))
  1.4005 -(let ((@x70 (trans @x65 (rewrite (= (+ ?x60 ?x48) ?x66)) (= (+ (* ?x54 2) ?x48) ?x66))))
  1.4006 -(let ((@x76 (quant-intro (monotonicity @x70 (= (= (+ (* ?x54 2) ?x48) ?x45) $x71)) (= $x58 $x74))))
  1.4007 -(let ((@x89 (trans @x76 (quant-intro (rewrite (= $x71 $x79)) (= $x74 $x85)) (= $x58 $x85))))
  1.4008 -(let ((@x270 (mp~ (mp (asserted $x58) @x89 $x85) (nnf-pos (refl (~ $x79 $x79)) (~ $x85 $x85)) $x85)))
  1.4009 -(let ((@x309 (mp @x270 (quant-intro (refl (= $x79 $x79)) (= $x85 $x304)) $x304)))
  1.4010 -(let (($x507 (or (not $x304) $x503)))
  1.4011 -(let ((@x508 ((_ quant-inst ks$ xs$) $x507)))
  1.4012 -(let ((@x800 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x503) $x509)) (unit-resolution @x508 @x309 $x503) $x509)))
  1.4013 -(let ((?x396 (+ ?x114 (* (- 1) (div ?x111 2)))))
  1.4014 -(let (($x413 (<= ?x396 0)))
  1.4015 -(let (($x397 (= ?x396 0)))
  1.4016 -(let (($x311 (forall ((?v0 Int) (?v1 Int) )(!(let ((?x145 (div ?v0 ?v1)))
  1.4017 -(let ((?x157 (* (- 1) ?v1)))
  1.4018 -(let ((?x154 (* (- 1) ?v0)))
  1.4019 -(let ((?x160 (div ?x154 ?x157)))
  1.4020 -(let (($x175 (<= ?v1 0)))
  1.4021 -(let ((?x182 (ite $x175 ?x160 ?x145)))
  1.4022 -(let (($x143 (= ?v1 0)))
  1.4023 -(let ((?x141 (divide$ ?v0 ?v1)))
  1.4024 -(= ?x141 (ite $x143 0 ?x182)))))))))) :pattern ( (divide$ ?v0 ?v1) )))
  1.4025 -))
  1.4026 -(let (($x193 (forall ((?v0 Int) (?v1 Int) )(let ((?x145 (div ?v0 ?v1)))
  1.4027 -(let ((?x157 (* (- 1) ?v1)))
  1.4028 -(let ((?x154 (* (- 1) ?v0)))
  1.4029 -(let ((?x160 (div ?x154 ?x157)))
  1.4030 -(let (($x175 (<= ?v1 0)))
  1.4031 -(let ((?x182 (ite $x175 ?x160 ?x145)))
  1.4032 -(let (($x143 (= ?v1 0)))
  1.4033 -(let ((?x141 (divide$ ?v0 ?v1)))
  1.4034 -(= ?x141 (ite $x143 0 ?x182)))))))))))
  1.4035 -))
  1.4036 -(let ((?x145 (div ?1 ?0)))
  1.4037 -(let ((?x157 (* (- 1) ?0)))
  1.4038 -(let ((?x154 (* (- 1) ?1)))
  1.4039 -(let ((?x160 (div ?x154 ?x157)))
  1.4040 -(let (($x175 (<= ?0 0)))
  1.4041 -(let ((?x182 (ite $x175 ?x160 ?x145)))
  1.4042 -(let (($x143 (= ?0 0)))
  1.4043 -(let ((?x141 (divide$ ?1 ?0)))
  1.4044 -(let (($x190 (= ?x141 (ite $x143 0 ?x182))))
  1.4045 -(let (($x152 (forall ((?v0 Int) (?v1 Int) )(let (($x143 (= ?v1 0)))
  1.4046 -(let ((?x150 (ite $x143 0 (ite (< 0 ?v1) (div ?v0 ?v1) (div (- ?v0) (- ?v1))))))
  1.4047 -(let ((?x141 (divide$ ?v0 ?v1)))
  1.4048 -(= ?x141 ?x150)))))
  1.4049 -))
  1.4050 -(let (($x172 (forall ((?v0 Int) (?v1 Int) )(let ((?x157 (* (- 1) ?v1)))
  1.4051 -(let ((?x154 (* (- 1) ?v0)))
  1.4052 -(let ((?x160 (div ?x154 ?x157)))
  1.4053 -(let ((?x145 (div ?v0 ?v1)))
  1.4054 -(let (($x144 (< 0 ?v1)))
  1.4055 -(let ((?x163 (ite $x144 ?x145 ?x160)))
  1.4056 -(let (($x143 (= ?v1 0)))
  1.4057 -(let ((?x166 (ite $x143 0 ?x163)))
  1.4058 -(let ((?x141 (divide$ ?v0 ?v1)))
  1.4059 -(= ?x141 ?x166)))))))))))
  1.4060 -))
  1.4061 -(let (($x144 (< 0 ?0)))
  1.4062 -(let ((?x163 (ite $x144 ?x145 ?x160)))
  1.4063 -(let ((?x166 (ite $x143 0 ?x163)))
  1.4064 -(let ((@x181 (monotonicity (rewrite (= $x144 (not $x175))) (= ?x163 (ite (not $x175) ?x145 ?x160)))))
  1.4065 -(let ((@x186 (trans @x181 (rewrite (= (ite (not $x175) ?x145 ?x160) ?x182)) (= ?x163 ?x182))))
  1.4066 -(let ((@x192 (monotonicity (monotonicity @x186 (= ?x166 (ite $x143 0 ?x182))) (= (= ?x141 ?x166) $x190))))
  1.4067 -(let (($x169 (= ?x141 ?x166)))
  1.4068 -(let (($x170 (= (= ?x141 (ite $x143 0 (ite $x144 ?x145 (div (- ?1) (- ?0))))) $x169)))
  1.4069 -(let ((@x162 (monotonicity (rewrite (= (- ?1) ?x154)) (rewrite (= (- ?0) ?x157)) (= (div (- ?1) (- ?0)) ?x160))))
  1.4070 -(let ((@x168 (monotonicity (monotonicity @x162 (= (ite $x144 ?x145 (div (- ?1) (- ?0))) ?x163)) (= (ite $x143 0 (ite $x144 ?x145 (div (- ?1) (- ?0)))) ?x166))))
  1.4071 -(let ((@x197 (trans (quant-intro (monotonicity @x168 $x170) (= $x152 $x172)) (quant-intro @x192 (= $x172 $x193)) (= $x152 $x193))))
  1.4072 -(let ((@x275 (mp~ (mp (asserted $x152) @x197 $x193) (nnf-pos (refl (~ $x190 $x190)) (~ $x193 $x193)) $x193)))
  1.4073 -(let ((@x316 (mp @x275 (quant-intro (refl (= $x190 $x190)) (= $x193 $x311)) $x311)))
  1.4074 -(let (($x403 (or (not $x311) $x397)))
  1.4075 -(let ((?x361 (div ?x111 2)))
  1.4076 -(let (($x357 (<= 2 0)))
  1.4077 -(let ((?x362 (ite $x357 (div (* (- 1) ?x111) (* (- 1) 2)) ?x361)))
  1.4078 -(let (($x356 (= 2 0)))
  1.4079 -(let ((?x363 (ite $x356 0 ?x362)))
  1.4080 -(let (($x364 (= ?x114 ?x363)))
  1.4081 -(let ((@x374 (rewrite (= (* (- 1) 2) (- 2)))))
  1.4082 -(let ((@x377 (monotonicity (rewrite (= (* (- 1) ?x111) (+ ?x369 ?x97))) @x374 (= (div (* (- 1) ?x111) (* (- 1) 2)) (div (+ ?x369 ?x97) (- 2))))))
  1.4083 -(let ((@x368 (rewrite (= $x357 false))))
  1.4084 -(let ((@x380 (monotonicity @x368 @x377 (= ?x362 (ite false (div (+ ?x369 ?x97) (- 2)) ?x361)))))
  1.4085 -(let ((@x384 (trans @x380 (rewrite (= (ite false (div (+ ?x369 ?x97) (- 2)) ?x361) ?x361)) (= ?x362 ?x361))))
  1.4086 -(let ((@x366 (rewrite (= $x356 false))))
  1.4087 -(let ((@x391 (trans (monotonicity @x366 @x384 (= ?x363 (ite false 0 ?x361))) (rewrite (= (ite false 0 ?x361) ?x361)) (= ?x363 ?x361))))
  1.4088 -(let ((@x401 (trans (monotonicity @x391 (= $x364 (= ?x114 ?x361))) (rewrite (= (= ?x114 ?x361) $x397)) (= $x364 $x397))))
  1.4089 -(let ((@x410 (trans (monotonicity @x401 (= (or (not $x311) $x364) $x403)) (rewrite (= $x403 $x403)) (= (or (not $x311) $x364) $x403))))
  1.4090 -(let ((@x802 (unit-resolution (mp ((_ quant-inst (+ l$ ?x110) 2) (or (not $x311) $x364)) @x410 $x403) @x316 $x397)))
  1.4091 -(let ((?x425 (mod (+ l$ ?x97) 2)))
  1.4092 -(let (($x465 (>= ?x425 0)))
  1.4093 -(let ((@x810 ((_ th-lemma arith farkas 1 -2 -2 -1 1 1) (unit-resolution ((_ th-lemma arith) (or false $x465)) @x26 $x465) (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x397) $x413)) @x802 $x413) (hypothesis $x687) @x800 (hypothesis (not $x694)) @x793 false)))
  1.4094 -(let (($x134 (not $x95)))
  1.4095 -(let (($x290 (= $x95 $x283)))
  1.4096 -(let ((@x289 (monotonicity (rewrite (= (and $x100 $x117) $x284)) (= (= $x134 (and $x100 $x117)) (= $x134 $x284)))))
  1.4097 -(let ((@x294 (trans @x289 (rewrite (= (= $x134 $x284) $x290)) (= (= $x134 (and $x100 $x117)) $x290))))
  1.4098 -(let (($x120 (and $x100 $x117)))
  1.4099 -(let (($x135 (= $x134 $x120)))
  1.4100 -(let (($x107 (= $x95 (and $x100 (= ?x102 (divide$ (- l$ ?x97) 2))))))
  1.4101 -(let (($x108 (not $x107)))
  1.4102 -(let ((@x116 (monotonicity (rewrite (= (- l$ ?x97) ?x111)) (= (divide$ (- l$ ?x97) 2) ?x114))))
  1.4103 -(let ((@x122 (monotonicity (monotonicity @x116 (= (= ?x102 (divide$ (- l$ ?x97) 2)) $x117)) (= (and $x100 (= ?x102 (divide$ (- l$ ?x97) 2))) $x120))))
  1.4104 -(let ((@x130 (trans (monotonicity @x122 (= $x107 (= $x95 $x120))) (rewrite (= (= $x95 $x120) (= $x95 $x120))) (= $x107 (= $x95 $x120)))))
  1.4105 -(let ((@x139 (trans (monotonicity @x130 (= $x108 (not (= $x95 $x120)))) (rewrite (= (not (= $x95 $x120)) $x135)) (= $x108 $x135))))
  1.4106 -(let ((@x295 (mp (mp (asserted $x108) @x139 $x135) @x294 $x290)))
  1.4107 -(let ((@x344 (unit-resolution (def-axiom (or $x134 $x283 (not $x290))) @x295 (or $x134 $x283))))
  1.4108 -(let ((@x898 (unit-resolution ((_ th-lemma arith triangle-eq) (or $x95 (not $x694) $x861)) (unit-resolution @x344 @x466 $x134) (or (not $x694) $x861))))
  1.4109 -(let ((@x899 (unit-resolution @x898 (unit-resolution (lemma @x810 (or $x694 (not $x687))) @x856 $x694) $x861)))
  1.4110 -(let ((?x544 (+ ?x99 ?x543)))
  1.4111 -(let (($x561 (>= ?x544 0)))
  1.4112 -(let (($x545 (= ?x544 0)))
  1.4113 -(let (($x318 (forall ((?v0 Int) (?v1 Int) )(!(let ((?x200 (mod ?v0 ?v1)))
  1.4114 -(let ((?x157 (* (- 1) ?v1)))
  1.4115 -(let ((?x154 (* (- 1) ?v0)))
  1.4116 -(let ((?x208 (mod ?x154 ?x157)))
  1.4117 -(let ((?x214 (* (- 1) ?x208)))
  1.4118 -(let (($x175 (<= ?v1 0)))
  1.4119 -(let ((?x234 (ite $x175 ?x214 ?x200)))
  1.4120 -(let (($x143 (= ?v1 0)))
  1.4121 -(let ((?x239 (ite $x143 ?v0 ?x234)))
  1.4122 -(let ((?x199 (mod$ ?v0 ?v1)))
  1.4123 -(= ?x199 ?x239))))))))))) :pattern ( (mod$ ?v0 ?v1) )))
  1.4124 -))
  1.4125 -(let (($x245 (forall ((?v0 Int) (?v1 Int) )(let ((?x200 (mod ?v0 ?v1)))
  1.4126 -(let ((?x157 (* (- 1) ?v1)))
  1.4127 -(let ((?x154 (* (- 1) ?v0)))
  1.4128 -(let ((?x208 (mod ?x154 ?x157)))
  1.4129 -(let ((?x214 (* (- 1) ?x208)))
  1.4130 -(let (($x175 (<= ?v1 0)))
  1.4131 -(let ((?x234 (ite $x175 ?x214 ?x200)))
  1.4132 -(let (($x143 (= ?v1 0)))
  1.4133 -(let ((?x239 (ite $x143 ?v0 ?x234)))
  1.4134 -(let ((?x199 (mod$ ?v0 ?v1)))
  1.4135 -(= ?x199 ?x239))))))))))))
  1.4136 -))
  1.4137 -(let ((?x200 (mod ?1 ?0)))
  1.4138 -(let ((?x208 (mod ?x154 ?x157)))
  1.4139 -(let ((?x214 (* (- 1) ?x208)))
  1.4140 -(let ((?x234 (ite $x175 ?x214 ?x200)))
  1.4141 -(let ((?x239 (ite $x143 ?1 ?x234)))
  1.4142 -(let ((?x199 (mod$ ?1 ?0)))
  1.4143 -(let (($x242 (= ?x199 ?x239)))
  1.4144 -(let (($x206 (forall ((?v0 Int) (?v1 Int) )(let (($x143 (= ?v1 0)))
  1.4145 -(let ((?x204 (ite $x143 ?v0 (ite (< 0 ?v1) (mod ?v0 ?v1) (- (mod (- ?v0) (- ?v1)))))))
  1.4146 -(let ((?x199 (mod$ ?v0 ?v1)))
  1.4147 -(= ?x199 ?x204)))))
  1.4148 -))
  1.4149 -(let (($x228 (forall ((?v0 Int) (?v1 Int) )(let ((?x157 (* (- 1) ?v1)))
  1.4150 -(let ((?x154 (* (- 1) ?v0)))
  1.4151 -(let ((?x208 (mod ?x154 ?x157)))
  1.4152 -(let ((?x214 (* (- 1) ?x208)))
  1.4153 -(let ((?x200 (mod ?v0 ?v1)))
  1.4154 -(let (($x144 (< 0 ?v1)))
  1.4155 -(let ((?x219 (ite $x144 ?x200 ?x214)))
  1.4156 -(let (($x143 (= ?v1 0)))
  1.4157 -(let ((?x222 (ite $x143 ?v0 ?x219)))
  1.4158 -(let ((?x199 (mod$ ?v0 ?v1)))
  1.4159 -(= ?x199 ?x222))))))))))))
  1.4160 -))
  1.4161 -(let ((@x233 (monotonicity (rewrite (= $x144 (not $x175))) (= (ite $x144 ?x200 ?x214) (ite (not $x175) ?x200 ?x214)))))
  1.4162 -(let ((@x238 (trans @x233 (rewrite (= (ite (not $x175) ?x200 ?x214) ?x234)) (= (ite $x144 ?x200 ?x214) ?x234))))
  1.4163 -(let ((@x244 (monotonicity (monotonicity @x238 (= (ite $x143 ?1 (ite $x144 ?x200 ?x214)) ?x239)) (= (= ?x199 (ite $x143 ?1 (ite $x144 ?x200 ?x214))) $x242))))
  1.4164 -(let ((?x219 (ite $x144 ?x200 ?x214)))
  1.4165 -(let ((?x222 (ite $x143 ?1 ?x219)))
  1.4166 -(let (($x225 (= ?x199 ?x222)))
  1.4167 -(let (($x226 (= (= ?x199 (ite $x143 ?1 (ite $x144 ?x200 (- (mod (- ?1) (- ?0)))))) $x225)))
  1.4168 -(let ((@x210 (monotonicity (rewrite (= (- ?1) ?x154)) (rewrite (= (- ?0) ?x157)) (= (mod (- ?1) (- ?0)) ?x208))))
  1.4169 -(let ((@x218 (trans (monotonicity @x210 (= (- (mod (- ?1) (- ?0))) (- ?x208))) (rewrite (= (- ?x208) ?x214)) (= (- (mod (- ?1) (- ?0))) ?x214))))
  1.4170 -(let ((@x221 (monotonicity @x218 (= (ite $x144 ?x200 (- (mod (- ?1) (- ?0)))) ?x219))))
  1.4171 -(let ((@x224 (monotonicity @x221 (= (ite $x143 ?1 (ite $x144 ?x200 (- (mod (- ?1) (- ?0))))) ?x222))))
  1.4172 -(let ((@x249 (trans (quant-intro (monotonicity @x224 $x226) (= $x206 $x228)) (quant-intro @x244 (= $x228 $x245)) (= $x206 $x245))))
  1.4173 -(let ((@x280 (mp~ (mp (asserted $x206) @x249 $x245) (nnf-pos (refl (~ $x242 $x242)) (~ $x245 $x245)) $x245)))
  1.4174 -(let ((@x323 (mp @x280 (quant-intro (refl (= $x242 $x242)) (= $x245 $x318)) $x318)))
  1.4175 -(let (($x550 (not $x318)))
  1.4176 -(let (($x551 (or $x550 $x545)))
  1.4177 -(let ((?x359 (* (- 1) 2)))
  1.4178 -(let ((?x511 (mod ?x369 ?x359)))
  1.4179 -(let ((?x512 (* (- 1) ?x511)))
  1.4180 -(let ((?x517 (ite $x357 ?x512 ?x516)))
  1.4181 -(let ((?x518 (ite $x356 l$ ?x517)))
  1.4182 -(let (($x519 (= ?x99 ?x518)))
  1.4183 -(let ((@x525 (monotonicity (monotonicity @x374 (= ?x511 (mod ?x369 (- 2)))) (= ?x512 (* (- 1) (mod ?x369 (- 2)))))))
  1.4184 -(let ((@x528 (monotonicity @x368 @x525 (= ?x517 (ite false (* (- 1) (mod ?x369 (- 2))) ?x516)))))
  1.4185 -(let ((@x532 (trans @x528 (rewrite (= (ite false (* (- 1) (mod ?x369 (- 2))) ?x516) ?x516)) (= ?x517 ?x516))))
  1.4186 -(let ((@x539 (trans (monotonicity @x366 @x532 (= ?x518 (ite false l$ ?x516))) (rewrite (= (ite false l$ ?x516) ?x516)) (= ?x518 ?x516))))
  1.4187 -(let ((@x549 (trans (monotonicity @x539 (= $x519 (= ?x99 ?x516))) (rewrite (= (= ?x99 ?x516) $x545)) (= $x519 $x545))))
  1.4188 -(let ((@x558 (trans (monotonicity @x549 (= (or $x550 $x519) $x551)) (rewrite (= $x551 $x551)) (= (or $x550 $x519) $x551))))
  1.4189 -(let ((@x559 (mp ((_ quant-inst l$ 2) (or $x550 $x519)) @x558 $x551)))
  1.4190 -(let ((@x902 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x545) $x561)) (unit-resolution @x559 @x323 $x545) $x561)))
  1.4191 -(let ((?x757 (* (- 2) ?x744)))
  1.4192 -(let ((?x758 (+ ?x93 ?x726 ?x757)))
  1.4193 -(let (($x764 (>= ?x758 0)))
  1.4194 -(let (($x756 (= ?x758 0)))
  1.4195 -(let ((@x872 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x756) $x764)) (unit-resolution ((_ th-lemma arith) (or false $x756)) @x26 $x756) $x764)))
  1.4196 -(let ((?x562 (div l$ 2)))
  1.4197 -(let ((?x575 (* (- 2) ?x562)))
  1.4198 -(let ((?x576 (+ l$ ?x543 ?x575)))
  1.4199 -(let (($x582 (>= ?x576 0)))
  1.4200 -(let (($x574 (= ?x576 0)))
  1.4201 -(let ((@x880 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x574) $x582)) (unit-resolution ((_ th-lemma arith) (or false $x574)) @x26 $x574) $x582)))
  1.4202 -(let ((?x504 (mod$ ?x93 2)))
  1.4203 -(let ((?x727 (+ ?x504 ?x726)))
  1.4204 -(let (($x728 (= ?x727 0)))
  1.4205 -(let (($x733 (or $x550 $x728)))
  1.4206 -(let ((?x696 (* (- 1) ?x93)))
  1.4207 -(let ((?x697 (mod ?x696 ?x359)))
  1.4208 -(let ((?x698 (* (- 1) ?x697)))
  1.4209 -(let ((?x700 (ite $x357 ?x698 ?x699)))
  1.4210 -(let ((?x701 (ite $x356 ?x93 ?x700)))
  1.4211 -(let (($x702 (= ?x504 ?x701)))
  1.4212 -(let ((@x708 (monotonicity (monotonicity @x374 (= ?x697 (mod ?x696 (- 2)))) (= ?x698 (* (- 1) (mod ?x696 (- 2)))))))
  1.4213 -(let ((@x711 (monotonicity @x368 @x708 (= ?x700 (ite false (* (- 1) (mod ?x696 (- 2))) ?x699)))))
  1.4214 -(let ((@x715 (trans @x711 (rewrite (= (ite false (* (- 1) (mod ?x696 (- 2))) ?x699) ?x699)) (= ?x700 ?x699))))
  1.4215 -(let ((@x722 (trans (monotonicity @x366 @x715 (= ?x701 (ite false ?x93 ?x699))) (rewrite (= (ite false ?x93 ?x699) ?x699)) (= ?x701 ?x699))))
  1.4216 -(let ((@x732 (trans (monotonicity @x722 (= $x702 (= ?x504 ?x699))) (rewrite (= (= ?x504 ?x699) $x728)) (= $x702 $x728))))
  1.4217 -(let ((@x740 (trans (monotonicity @x732 (= (or $x550 $x702) $x733)) (rewrite (= $x733 $x733)) (= (or $x550 $x702) $x733))))
  1.4218 -(let ((@x427 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x728) (>= ?x727 0))) (unit-resolution (mp ((_ quant-inst (eval_dioph$ ks$ xs$) 2) (or $x550 $x702)) @x740 $x733) @x323 $x728) (>= ?x727 0))))
  1.4219 -(let ((?x783 (* (- 1) ?x504)))
  1.4220 -(let ((?x784 (+ ?x99 ?x783)))
  1.4221 -(let (($x786 (>= ?x784 0)))
  1.4222 -(let (($x782 (= ?x99 ?x504)))
  1.4223 -(let (($x821 (= ?x98 ?x504)))
  1.4224 -(let (($x505 (= ?x504 ?x98)))
  1.4225 -(let (($x297 (forall ((?v0 Int_list$) (?v1 Int_list$) )(!(= (mod$ (eval_dioph$ ?v0 ?v1) 2) (mod$ (eval_dioph$ ?v0 (map$ uu$ ?v1)) 2)) :pattern ( (eval_dioph$ ?v0 (map$ uu$ ?v1)) )))
  1.4226 -))
  1.4227 -(let (($x51 (forall ((?v0 Int_list$) (?v1 Int_list$) )(= (mod$ (eval_dioph$ ?v0 ?v1) 2) (mod$ (eval_dioph$ ?v0 (map$ uu$ ?v1)) 2)))
  1.4228 -))
  1.4229 -(let (($x50 (= (mod$ ?x45 2) (mod$ ?x48 2))))
  1.4230 -(let ((@x265 (mp~ (asserted $x51) (nnf-pos (refl (~ $x50 $x50)) (~ $x51 $x51)) $x51)))
  1.4231 -(let ((@x302 (mp @x265 (quant-intro (refl (= $x50 $x50)) (= $x51 $x297)) $x297)))
  1.4232 -(let (($x514 (or (not $x297) $x505)))
  1.4233 -(let ((@x515 ((_ quant-inst ks$ xs$) $x514)))
  1.4234 -(let ((@x824 (symm (unit-resolution (def-axiom (or $x283 $x100)) @x466 $x100) (= ?x99 ?x98))))
  1.4235 -(let ((@x939 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x782) $x786)) (trans @x824 (symm (unit-resolution @x515 @x302 $x505) $x821) $x782) $x786)))
  1.4236 -(let (($x785 (<= ?x784 0)))
  1.4237 -(let ((@x887 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x782) $x785)) (trans @x824 (symm (unit-resolution @x515 @x302 $x505) $x821) $x782) $x785)))
  1.4238 -(let (($x688 (>= ?x686 0)))
  1.4239 -(let ((@x855 (unit-resolution ((_ th-lemma arith triangle-eq) (or $x282 $x688)) (unit-resolution (def-axiom (or $x283 $x117)) @x466 $x117) $x688)))
  1.4240 -(let ((@x979 (unit-resolution ((_ th-lemma arith) (or false (not (>= ?x425 2)))) @x26 (not (>= ?x425 2)))))
  1.4241 -(let (($x560 (<= ?x544 0)))
  1.4242 -(let ((@x461 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x545) $x560)) (unit-resolution @x559 @x323 $x545) $x560)))
  1.4243 -(let (($x763 (<= ?x758 0)))
  1.4244 -(let ((@x658 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x756) $x763)) (unit-resolution ((_ th-lemma arith) (or false $x756)) @x26 $x756) $x763)))
  1.4245 -(let (($x581 (<= ?x576 0)))
  1.4246 -(let ((@x986 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x574) $x581)) (unit-resolution ((_ th-lemma arith) (or false $x574)) @x26 $x574) $x581)))
  1.4247 -(let ((@x989 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x728) (<= ?x727 0))) (unit-resolution (mp ((_ quant-inst (eval_dioph$ ks$ xs$) 2) (or $x550 $x702)) @x740 $x733) @x323 $x728) (<= ?x727 0))))
  1.4248 -(let (($x510 (>= ?x502 0)))
  1.4249 -(let ((@x994 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x503) $x510)) (unit-resolution @x508 @x309 $x503) $x510)))
  1.4250 -(let ((@x998 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x397) (>= ?x396 0))) @x802 (>= ?x396 0))))
  1.4251 -(let ((@x1001 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x434) (<= ?x437 0))) (unit-resolution ((_ th-lemma arith) (or false $x434)) @x26 $x434) (<= ?x437 0))))
  1.4252 -(let ((@x1002 ((_ th-lemma arith farkas 1 -2 -2 -1 -2 1 1 1 1 1 1) @x1001 @x998 (hypothesis $x688) @x994 (hypothesis $x972) (hypothesis $x785) @x989 @x986 @x658 @x461 @x979 false)))
  1.4253 -(let ((@x474 (unit-resolution (lemma @x1002 (or (not $x972) (not $x688) (not $x785))) @x855 @x887 (not $x972))))
  1.4254 -(let ((@x941 (unit-resolution @x474 ((_ th-lemma arith) @x939 @x427 @x880 @x872 @x902 @x899 $x972) false)))
  1.4255 -(let ((@x942 (lemma @x941 $x283)))
  1.4256 -(let ((@x340 (unit-resolution (def-axiom (or $x95 $x284 (not $x290))) @x295 (or $x95 $x284))))
  1.4257 -(let ((@x679 (unit-resolution @x340 @x942 $x95)))
  1.4258 -(let ((@x889 (trans (symm (unit-resolution @x515 @x302 $x505) $x821) (monotonicity @x679 (= ?x504 ?x99)) $x100)))
  1.4259 -(let (($x811 (not $x687)))
  1.4260 -(let ((@x845 ((_ th-lemma arith assign-bounds 1 -1/2 -1/2 1/2 -1/2) (or $x688 (not $x413) (not $x465) (not $x443) (not $x509) $x861))))
  1.4261 -(let ((@x892 (unit-resolution @x845 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x397) $x413)) @x802 $x413) (unit-resolution ((_ th-lemma arith triangle-eq) (or $x134 $x695)) @x679 $x695) @x793 (unit-resolution ((_ th-lemma arith) (or false $x465)) @x26 $x465) @x800 $x688)))
  1.4262 -(let ((@x935 (unit-resolution ((_ th-lemma arith triangle-eq) (or $x117 $x811 (not $x688))) (hypothesis $x282) (or $x811 (not $x688)))))
  1.4263 -(let ((@x955 ((_ th-lemma arith farkas -2 -2 1 -1 1 1) (unit-resolution @x935 @x892 $x811) @x998 @x1001 @x994 (unit-resolution ((_ th-lemma arith triangle-eq) (or $x134 $x694)) @x679 $x694) @x979 false)))
  1.4264 -(let ((@x472 (unit-resolution (unit-resolution (def-axiom (or $x284 $x281 $x282)) @x942 $x283) (lemma @x955 $x117) $x281)))
  1.4265 -(unit-resolution @x472 @x889 false)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
  1.4266 -
  1.4267 -785615f585a02b3e6ed8608ecc9660ba5c4025e2 2 0
  1.4268 -sat
  1.4269 -(error "line 9 column 10: proof is not available")
  1.4270 -c4e20de399740e8f0c9a87abad030298d74bc47b 12 0
  1.4271 -unsat
  1.4272 -((set-logic AUFLIA)
  1.4273 -(proof
  1.4274 -(let ((?x31 (p$ true)))
  1.4275 -(let (($x29 (< 2 3)))
  1.4276 -(let ((?x30 (p$ $x29)))
  1.4277 -(let (($x32 (= ?x30 ?x31)))
  1.4278 -(let ((@x42 (monotonicity (monotonicity (rewrite (= $x29 true)) $x32) (= $x32 (= ?x31 ?x31)))))
  1.4279 -(let ((@x49 (monotonicity (trans @x42 (rewrite (= (= ?x31 ?x31) true)) (= $x32 true)) (= (not $x32) (not true)))))
  1.4280 -(let ((@x53 (trans @x49 (rewrite (= (not true) false)) (= (not $x32) false))))
  1.4281 -(mp (asserted (not $x32)) @x53 false))))))))))
  1.4282 -
  1.4283 -23f5eb3b530a4577da2f8947333286ff70ed557f 11 0
  1.4284 -unsat
  1.4285 -((set-logic AUFLIA)
  1.4286 -(proof
  1.4287 -(let (($x29 (exists ((?v0 A$) )(! (g$ ?v0) :qid k!7))
  1.4288 -))
  1.4289 -(let (($x30 (f$ $x29)))
  1.4290 -(let (($x31 (=> $x30 true)))
  1.4291 -(let (($x32 (not $x31)))
  1.4292 -(let ((@x42 (trans (monotonicity (rewrite (= $x31 true)) (= $x32 (not true))) (rewrite (= (not true) false)) (= $x32 false))))
  1.4293 -(mp (asserted $x32) @x42 false))))))))
  1.4294 -
  1.4295 -60f1b32e9c6a2229b64c85dcfb0bde9c2bd5433a 11 0
  1.4296 -unsat
  1.4297 -((set-logic AUFLIA)
  1.4298 -(proof
  1.4299 -(let (($x29 (forall ((?v0 A$) )(! (g$ ?v0) :qid k!7))
  1.4300 -))
  1.4301 -(let (($x30 (f$ $x29)))
  1.4302 -(let (($x31 (=> $x30 true)))
  1.4303 -(let (($x32 (not $x31)))
  1.4304 -(let ((@x42 (trans (monotonicity (rewrite (= $x31 true)) (= $x32 (not true))) (rewrite (= (not true) false)) (= $x32 false))))
  1.4305 -(mp (asserted $x32) @x42 false))))))))
  1.4306 -
  1.4307 -0b997744cf42fde45b98a34c933b0698332e657f 113 0
  1.4308 -unsat
  1.4309 -((set-logic <null>)
  1.4310 -(proof
  1.4311 -(let ((?x228 (mod x$ 2)))
  1.4312 -(let ((?x262 (* (- 1) ?x228)))
  1.4313 -(let ((?x31 (modulo$ x$ 2)))
  1.4314 -(let ((?x263 (+ ?x31 ?x262)))
  1.4315 -(let (($x280 (>= ?x263 0)))
  1.4316 -(let (($x264 (= ?x263 0)))
  1.4317 -(let (($x205 (forall ((?v0 Int) (?v1 Int) )(! (let ((?x136 (mod ?v0 ?v1)))
  1.4318 -(let ((?x93 (* (- 1) ?v1)))
  1.4319 -(let ((?x90 (* (- 1) ?v0)))
  1.4320 -(let ((?x144 (mod ?x90 ?x93)))
  1.4321 -(let ((?x150 (* (- 1) ?x144)))
  1.4322 -(let (($x111 (<= ?v1 0)))
  1.4323 -(let ((?x170 (ite $x111 ?x150 ?x136)))
  1.4324 -(let (($x78 (= ?v1 0)))
  1.4325 -(let ((?x175 (ite $x78 ?v0 ?x170)))
  1.4326 -(let ((?x135 (modulo$ ?v0 ?v1)))
  1.4327 -(= ?x135 ?x175))))))))))) :pattern ( (modulo$ ?v0 ?v1) ) :qid k!9))
  1.4328 -))
  1.4329 -(let (($x181 (forall ((?v0 Int) (?v1 Int) )(! (let ((?x136 (mod ?v0 ?v1)))
  1.4330 -(let ((?x93 (* (- 1) ?v1)))
  1.4331 -(let ((?x90 (* (- 1) ?v0)))
  1.4332 -(let ((?x144 (mod ?x90 ?x93)))
  1.4333 -(let ((?x150 (* (- 1) ?x144)))
  1.4334 -(let (($x111 (<= ?v1 0)))
  1.4335 -(let ((?x170 (ite $x111 ?x150 ?x136)))
  1.4336 -(let (($x78 (= ?v1 0)))
  1.4337 -(let ((?x175 (ite $x78 ?v0 ?x170)))
  1.4338 -(let ((?x135 (modulo$ ?v0 ?v1)))
  1.4339 -(= ?x135 ?x175))))))))))) :qid k!9))
  1.4340 -))
  1.4341 -(let ((?x136 (mod ?1 ?0)))
  1.4342 -(let ((?x93 (* (- 1) ?0)))
  1.4343 -(let ((?x90 (* (- 1) ?1)))
  1.4344 -(let ((?x144 (mod ?x90 ?x93)))
  1.4345 -(let ((?x150 (* (- 1) ?x144)))
  1.4346 -(let (($x111 (<= ?0 0)))
  1.4347 -(let ((?x170 (ite $x111 ?x150 ?x136)))
  1.4348 -(let (($x78 (= ?0 0)))
  1.4349 -(let ((?x175 (ite $x78 ?1 ?x170)))
  1.4350 -(let ((?x135 (modulo$ ?1 ?0)))
  1.4351 -(let (($x178 (= ?x135 ?x175)))
  1.4352 -(let (($x142 (forall ((?v0 Int) (?v1 Int) )(! (let (($x78 (= ?v1 0)))
  1.4353 -(let ((?x140 (ite $x78 ?v0 (ite (< 0 ?v1) (mod ?v0 ?v1) (- (mod (- ?v0) (- ?v1)))))))
  1.4354 -(let ((?x135 (modulo$ ?v0 ?v1)))
  1.4355 -(= ?x135 ?x140)))) :qid k!9))
  1.4356 -))
  1.4357 -(let (($x164 (forall ((?v0 Int) (?v1 Int) )(! (let ((?x93 (* (- 1) ?v1)))
  1.4358 -(let ((?x90 (* (- 1) ?v0)))
  1.4359 -(let ((?x144 (mod ?x90 ?x93)))
  1.4360 -(let ((?x150 (* (- 1) ?x144)))
  1.4361 -(let ((?x136 (mod ?v0 ?v1)))
  1.4362 -(let (($x79 (< 0 ?v1)))
  1.4363 -(let ((?x155 (ite $x79 ?x136 ?x150)))
  1.4364 -(let (($x78 (= ?v1 0)))
  1.4365 -(let ((?x158 (ite $x78 ?v0 ?x155)))
  1.4366 -(let ((?x135 (modulo$ ?v0 ?v1)))
  1.4367 -(= ?x135 ?x158))))))))))) :qid k!9))
  1.4368 -))
  1.4369 -(let ((@x169 (monotonicity (rewrite (= (< 0 ?0) (not $x111))) (= (ite (< 0 ?0) ?x136 ?x150) (ite (not $x111) ?x136 ?x150)))))
  1.4370 -(let ((@x174 (trans @x169 (rewrite (= (ite (not $x111) ?x136 ?x150) ?x170)) (= (ite (< 0 ?0) ?x136 ?x150) ?x170))))
  1.4371 -(let ((@x177 (monotonicity @x174 (= (ite $x78 ?1 (ite (< 0 ?0) ?x136 ?x150)) ?x175))))
  1.4372 -(let ((@x180 (monotonicity @x177 (= (= ?x135 (ite $x78 ?1 (ite (< 0 ?0) ?x136 ?x150))) $x178))))
  1.4373 -(let (($x79 (< 0 ?0)))
  1.4374 -(let ((?x155 (ite $x79 ?x136 ?x150)))
  1.4375 -(let ((?x158 (ite $x78 ?1 ?x155)))
  1.4376 -(let (($x161 (= ?x135 ?x158)))
  1.4377 -(let (($x162 (= (= ?x135 (ite $x78 ?1 (ite $x79 ?x136 (- (mod (- ?1) (- ?0)))))) $x161)))
  1.4378 -(let ((@x146 (monotonicity (rewrite (= (- ?1) ?x90)) (rewrite (= (- ?0) ?x93)) (= (mod (- ?1) (- ?0)) ?x144))))
  1.4379 -(let ((@x154 (trans (monotonicity @x146 (= (- (mod (- ?1) (- ?0))) (- ?x144))) (rewrite (= (- ?x144) ?x150)) (= (- (mod (- ?1) (- ?0))) ?x150))))
  1.4380 -(let ((@x157 (monotonicity @x154 (= (ite $x79 ?x136 (- (mod (- ?1) (- ?0)))) ?x155))))
  1.4381 -(let ((@x160 (monotonicity @x157 (= (ite $x78 ?1 (ite $x79 ?x136 (- (mod (- ?1) (- ?0))))) ?x158))))
  1.4382 -(let ((@x185 (trans (quant-intro (monotonicity @x160 $x162) (= $x142 $x164)) (quant-intro @x180 (= $x164 $x181)) (= $x142 $x181))))
  1.4383 -(let ((@x196 (mp~ (mp (asserted $x142) @x185 $x181) (nnf-pos (refl (~ $x178 $x178)) (~ $x181 $x181)) $x181)))
  1.4384 -(let ((@x210 (mp @x196 (quant-intro (refl (= $x178 $x178)) (= $x181 $x205)) $x205)))
  1.4385 -(let (($x270 (or (not $x205) $x264)))
  1.4386 -(let ((?x225 (* (- 1) 2)))
  1.4387 -(let ((?x224 (* (- 1) x$)))
  1.4388 -(let ((?x226 (mod ?x224 ?x225)))
  1.4389 -(let ((?x227 (* (- 1) ?x226)))
  1.4390 -(let (($x223 (<= 2 0)))
  1.4391 -(let ((?x229 (ite $x223 ?x227 ?x228)))
  1.4392 -(let (($x222 (= 2 0)))
  1.4393 -(let ((?x230 (ite $x222 x$ ?x229)))
  1.4394 -(let (($x231 (= ?x31 ?x230)))
  1.4395 -(let ((@x244 (monotonicity (monotonicity (rewrite (= ?x225 (- 2))) (= ?x226 (mod ?x224 (- 2)))) (= ?x227 (* (- 1) (mod ?x224 (- 2)))))))
  1.4396 -(let ((@x247 (monotonicity (rewrite (= $x223 false)) @x244 (= ?x229 (ite false (* (- 1) (mod ?x224 (- 2))) ?x228)))))
  1.4397 -(let ((@x251 (trans @x247 (rewrite (= (ite false (* (- 1) (mod ?x224 (- 2))) ?x228) ?x228)) (= ?x229 ?x228))))
  1.4398 -(let ((@x254 (monotonicity (rewrite (= $x222 false)) @x251 (= ?x230 (ite false x$ ?x228)))))
  1.4399 -(let ((@x261 (monotonicity (trans @x254 (rewrite (= (ite false x$ ?x228) ?x228)) (= ?x230 ?x228)) (= $x231 (= ?x31 ?x228)))))
  1.4400 -(let ((@x274 (monotonicity (trans @x261 (rewrite (= (= ?x31 ?x228) $x264)) (= $x231 $x264)) (= (or (not $x205) $x231) $x270))))
  1.4401 -(let ((@x277 (trans @x274 (rewrite (= $x270 $x270)) (= (or (not $x205) $x231) $x270))))
  1.4402 -(let ((@x278 (mp ((_ quant-inst x$ 2) (or (not $x205) $x231)) @x277 $x270)))
  1.4403 -(let ((@x332 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x264) $x280)) (unit-resolution @x278 @x210 $x264) $x280)))
  1.4404 -(let (($x305 (>= ?x228 0)))
  1.4405 -(let (($x64 (>= ?x31 0)))
  1.4406 -(let (($x67 (not $x64)))
  1.4407 -(let (($x36 (not (<= (+ x$ 1) (+ x$ (+ (* 2 ?x31) 1))))))
  1.4408 -(let ((@x69 (monotonicity (rewrite (= (>= (* 2 ?x31) 0) $x64)) (= (not (>= (* 2 ?x31) 0)) $x67))))
  1.4409 -(let ((?x32 (* 2 ?x31)))
  1.4410 -(let ((?x47 (+ 1 x$ ?x32)))
  1.4411 -(let (($x52 (<= (+ 1 x$) ?x47)))
  1.4412 -(let (($x55 (not $x52)))
  1.4413 -(let ((@x63 (monotonicity (rewrite (= $x52 (>= ?x32 0))) (= $x55 (not (>= ?x32 0))))))
  1.4414 -(let ((@x46 (monotonicity (rewrite (= (+ ?x32 1) (+ 1 ?x32))) (= (+ x$ (+ ?x32 1)) (+ x$ (+ 1 ?x32))))))
  1.4415 -(let ((@x51 (trans @x46 (rewrite (= (+ x$ (+ 1 ?x32)) ?x47)) (= (+ x$ (+ ?x32 1)) ?x47))))
  1.4416 -(let ((@x54 (monotonicity (rewrite (= (+ x$ 1) (+ 1 x$))) @x51 (= (<= (+ x$ 1) (+ x$ (+ ?x32 1))) $x52))))
  1.4417 -(let ((@x73 (trans (monotonicity @x54 (= $x36 $x55)) (trans @x63 @x69 (= $x55 $x67)) (= $x36 $x67))))
  1.4418 -(let ((@x74 (mp (asserted $x36) @x73 $x67)))
  1.4419 -((_ th-lemma arith farkas -1 1 1) @x74 (unit-resolution ((_ th-lemma arith) (or false $x305)) (true-axiom true) $x305) @x332 false))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
  1.4420 -
  1.4421 -2e67f9e254b2a35a9d35027c6e63de01bc5086bd 112 0
  1.4422 -unsat
  1.4423 -((set-logic <null>)
  1.4424 -(proof
  1.4425 -(let ((?x224 (mod x$ 2)))
  1.4426 -(let (($x318 (>= ?x224 2)))
  1.4427 -(let (($x319 (not $x318)))
  1.4428 -(let ((?x258 (* (- 1) ?x224)))
  1.4429 -(let ((?x29 (modulo$ x$ 2)))
  1.4430 -(let ((?x259 (+ ?x29 ?x258)))
  1.4431 -(let (($x275 (<= ?x259 0)))
  1.4432 -(let (($x260 (= ?x259 0)))
  1.4433 -(let (($x201 (forall ((?v0 Int) (?v1 Int) )(! (let ((?x132 (mod ?v0 ?v1)))
  1.4434 -(let ((?x89 (* (- 1) ?v1)))
  1.4435 -(let ((?x86 (* (- 1) ?v0)))
  1.4436 -(let ((?x140 (mod ?x86 ?x89)))
  1.4437 -(let ((?x146 (* (- 1) ?x140)))
  1.4438 -(let (($x107 (<= ?v1 0)))
  1.4439 -(let ((?x166 (ite $x107 ?x146 ?x132)))
  1.4440 -(let (($x74 (= ?v1 0)))
  1.4441 -(let ((?x171 (ite $x74 ?v0 ?x166)))
  1.4442 -(let ((?x131 (modulo$ ?v0 ?v1)))
  1.4443 -(= ?x131 ?x171))))))))))) :pattern ( (modulo$ ?v0 ?v1) ) :qid k!9))
  1.4444 -))
  1.4445 -(let (($x177 (forall ((?v0 Int) (?v1 Int) )(! (let ((?x132 (mod ?v0 ?v1)))
  1.4446 -(let ((?x89 (* (- 1) ?v1)))
  1.4447 -(let ((?x86 (* (- 1) ?v0)))
  1.4448 -(let ((?x140 (mod ?x86 ?x89)))
  1.4449 -(let ((?x146 (* (- 1) ?x140)))
  1.4450 -(let (($x107 (<= ?v1 0)))
  1.4451 -(let ((?x166 (ite $x107 ?x146 ?x132)))
  1.4452 -(let (($x74 (= ?v1 0)))
  1.4453 -(let ((?x171 (ite $x74 ?v0 ?x166)))
  1.4454 -(let ((?x131 (modulo$ ?v0 ?v1)))
  1.4455 -(= ?x131 ?x171))))))))))) :qid k!9))
  1.4456 -))
  1.4457 -(let ((?x132 (mod ?1 ?0)))
  1.4458 -(let ((?x89 (* (- 1) ?0)))
  1.4459 -(let ((?x86 (* (- 1) ?1)))
  1.4460 -(let ((?x140 (mod ?x86 ?x89)))
  1.4461 -(let ((?x146 (* (- 1) ?x140)))
  1.4462 -(let (($x107 (<= ?0 0)))
  1.4463 -(let ((?x166 (ite $x107 ?x146 ?x132)))
  1.4464 -(let (($x74 (= ?0 0)))
  1.4465 -(let ((?x171 (ite $x74 ?1 ?x166)))
  1.4466 -(let ((?x131 (modulo$ ?1 ?0)))
  1.4467 -(let (($x174 (= ?x131 ?x171)))
  1.4468 -(let (($x138 (forall ((?v0 Int) (?v1 Int) )(! (let (($x74 (= ?v1 0)))
  1.4469 -(let ((?x136 (ite $x74 ?v0 (ite (< 0 ?v1) (mod ?v0 ?v1) (- (mod (- ?v0) (- ?v1)))))))
  1.4470 -(let ((?x131 (modulo$ ?v0 ?v1)))
  1.4471 -(= ?x131 ?x136)))) :qid k!9))
  1.4472 -))
  1.4473 -(let (($x160 (forall ((?v0 Int) (?v1 Int) )(! (let ((?x89 (* (- 1) ?v1)))
  1.4474 -(let ((?x86 (* (- 1) ?v0)))
  1.4475 -(let ((?x140 (mod ?x86 ?x89)))
  1.4476 -(let ((?x146 (* (- 1) ?x140)))
  1.4477 -(let ((?x132 (mod ?v0 ?v1)))
  1.4478 -(let (($x75 (< 0 ?v1)))
  1.4479 -(let ((?x151 (ite $x75 ?x132 ?x146)))
  1.4480 -(let (($x74 (= ?v1 0)))
  1.4481 -(let ((?x154 (ite $x74 ?v0 ?x151)))
  1.4482 -(let ((?x131 (modulo$ ?v0 ?v1)))
  1.4483 -(= ?x131 ?x154))))))))))) :qid k!9))
  1.4484 -))
  1.4485 -(let ((@x165 (monotonicity (rewrite (= (< 0 ?0) (not $x107))) (= (ite (< 0 ?0) ?x132 ?x146) (ite (not $x107) ?x132 ?x146)))))
  1.4486 -(let ((@x170 (trans @x165 (rewrite (= (ite (not $x107) ?x132 ?x146) ?x166)) (= (ite (< 0 ?0) ?x132 ?x146) ?x166))))
  1.4487 -(let ((@x173 (monotonicity @x170 (= (ite $x74 ?1 (ite (< 0 ?0) ?x132 ?x146)) ?x171))))
  1.4488 -(let ((@x176 (monotonicity @x173 (= (= ?x131 (ite $x74 ?1 (ite (< 0 ?0) ?x132 ?x146))) $x174))))
  1.4489 -(let (($x75 (< 0 ?0)))
  1.4490 -(let ((?x151 (ite $x75 ?x132 ?x146)))
  1.4491 -(let ((?x154 (ite $x74 ?1 ?x151)))
  1.4492 -(let (($x157 (= ?x131 ?x154)))
  1.4493 -(let (($x158 (= (= ?x131 (ite $x74 ?1 (ite $x75 ?x132 (- (mod (- ?1) (- ?0)))))) $x157)))
  1.4494 -(let ((@x142 (monotonicity (rewrite (= (- ?1) ?x86)) (rewrite (= (- ?0) ?x89)) (= (mod (- ?1) (- ?0)) ?x140))))
  1.4495 -(let ((@x150 (trans (monotonicity @x142 (= (- (mod (- ?1) (- ?0))) (- ?x140))) (rewrite (= (- ?x140) ?x146)) (= (- (mod (- ?1) (- ?0))) ?x146))))
  1.4496 -(let ((@x153 (monotonicity @x150 (= (ite $x75 ?x132 (- (mod (- ?1) (- ?0)))) ?x151))))
  1.4497 -(let ((@x156 (monotonicity @x153 (= (ite $x74 ?1 (ite $x75 ?x132 (- (mod (- ?1) (- ?0))))) ?x154))))
  1.4498 -(let ((@x181 (trans (quant-intro (monotonicity @x156 $x158) (= $x138 $x160)) (quant-intro @x176 (= $x160 $x177)) (= $x138 $x177))))
  1.4499 -(let ((@x192 (mp~ (mp (asserted $x138) @x181 $x177) (nnf-pos (refl (~ $x174 $x174)) (~ $x177 $x177)) $x177)))
  1.4500 -(let ((@x206 (mp @x192 (quant-intro (refl (= $x174 $x174)) (= $x177 $x201)) $x201)))
  1.4501 -(let (($x266 (or (not $x201) $x260)))
  1.4502 -(let ((?x221 (* (- 1) 2)))
  1.4503 -(let ((?x220 (* (- 1) x$)))
  1.4504 -(let ((?x222 (mod ?x220 ?x221)))
  1.4505 -(let ((?x223 (* (- 1) ?x222)))
  1.4506 -(let (($x219 (<= 2 0)))
  1.4507 -(let ((?x225 (ite $x219 ?x223 ?x224)))
  1.4508 -(let (($x218 (= 2 0)))
  1.4509 -(let ((?x226 (ite $x218 x$ ?x225)))
  1.4510 -(let (($x227 (= ?x29 ?x226)))
  1.4511 -(let ((@x240 (monotonicity (monotonicity (rewrite (= ?x221 (- 2))) (= ?x222 (mod ?x220 (- 2)))) (= ?x223 (* (- 1) (mod ?x220 (- 2)))))))
  1.4512 -(let ((@x243 (monotonicity (rewrite (= $x219 false)) @x240 (= ?x225 (ite false (* (- 1) (mod ?x220 (- 2))) ?x224)))))
  1.4513 -(let ((@x247 (trans @x243 (rewrite (= (ite false (* (- 1) (mod ?x220 (- 2))) ?x224) ?x224)) (= ?x225 ?x224))))
  1.4514 -(let ((@x250 (monotonicity (rewrite (= $x218 false)) @x247 (= ?x226 (ite false x$ ?x224)))))
  1.4515 -(let ((@x257 (monotonicity (trans @x250 (rewrite (= (ite false x$ ?x224) ?x224)) (= ?x226 ?x224)) (= $x227 (= ?x29 ?x224)))))
  1.4516 -(let ((@x270 (monotonicity (trans @x257 (rewrite (= (= ?x29 ?x224) $x260)) (= $x227 $x260)) (= (or (not $x201) $x227) $x266))))
  1.4517 -(let ((@x273 (trans @x270 (rewrite (= $x266 $x266)) (= (or (not $x201) $x227) $x266))))
  1.4518 -(let ((@x274 (mp ((_ quant-inst x$ 2) (or (not $x201) $x227)) @x273 $x266)))
  1.4519 -(let ((@x331 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x260) $x275)) (unit-resolution @x274 @x206 $x260) $x275)))
  1.4520 -(let (($x63 (>= ?x29 2)))
  1.4521 -(let ((?x37 (* 2 ?x29)))
  1.4522 -(let (($x56 (>= ?x37 3)))
  1.4523 -(let (($x46 (< (+ x$ ?x37) (+ 3 x$))))
  1.4524 -(let (($x49 (not $x46)))
  1.4525 -(let ((@x58 (monotonicity (rewrite (= $x46 (not $x56))) (= $x49 (not (not $x56))))))
  1.4526 -(let ((@x67 (trans (trans @x58 (rewrite (= (not (not $x56)) $x56)) (= $x49 $x56)) (rewrite (= $x56 $x63)) (= $x49 $x63))))
  1.4527 -(let ((@x42 (monotonicity (rewrite (= (+ ?x29 ?x29) ?x37)) (= (+ x$ (+ ?x29 ?x29)) (+ x$ ?x37)))))
  1.4528 -(let ((@x48 (monotonicity @x42 (rewrite (= (+ x$ 3) (+ 3 x$))) (= (< (+ x$ (+ ?x29 ?x29)) (+ x$ 3)) $x46))))
  1.4529 -(let ((@x51 (monotonicity @x48 (= (not (< (+ x$ (+ ?x29 ?x29)) (+ x$ 3))) $x49))))
  1.4530 -(let ((@x69 (trans @x51 @x67 (= (not (< (+ x$ (+ ?x29 ?x29)) (+ x$ 3))) $x63))))
  1.4531 -(let ((@x70 (mp (asserted (not (< (+ x$ (+ ?x29 ?x29)) (+ x$ 3)))) @x69 $x63)))
  1.4532 -((_ th-lemma arith farkas -1 1 1) @x70 @x331 (unit-resolution ((_ th-lemma arith) (or false $x319)) (true-axiom true) $x319) false)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
  1.4533 -
  1.4534 -b6d44e20599d4862894eecfa4c98fcb043a6336d 348 0
  1.4535 -unsat
  1.4536 -((set-logic <null>)
  1.4537 -(proof
  1.4538 -(let ((?x96 (map$ uu$ xs$)))
  1.4539 -(let ((?x97 (eval_dioph$ ks$ ?x96)))
  1.4540 -(let ((?x424 (+ l$ ?x97)))
  1.4541 -(let ((?x425 (mod ?x424 2)))
  1.4542 -(let (($x482 (>= ?x425 2)))
  1.4543 -(let (($x564 (not $x482)))
  1.4544 -(let ((@x26 (true-axiom true)))
  1.4545 -(let ((?x369 (* (- 1) l$)))
  1.4546 -(let ((?x93 (eval_dioph$ ks$ xs$)))
  1.4547 -(let ((?x678 (+ ?x93 ?x369)))
  1.4548 -(let (($x679 (<= ?x678 0)))
  1.4549 -(let (($x95 (= ?x93 l$)))
  1.4550 -(let ((?x110 (* (- 1) ?x97)))
  1.4551 -(let ((?x111 (+ l$ ?x110)))
  1.4552 -(let ((?x114 (divide$ ?x111 2)))
  1.4553 -(let ((?x101 (map$ uua$ xs$)))
  1.4554 -(let ((?x102 (eval_dioph$ ks$ ?x101)))
  1.4555 -(let (($x117 (= ?x102 ?x114)))
  1.4556 -(let (($x282 (not $x117)))
  1.4557 -(let ((?x99 (modulo$ l$ 2)))
  1.4558 -(let ((?x98 (modulo$ ?x97 2)))
  1.4559 -(let (($x100 (= ?x98 ?x99)))
  1.4560 -(let (($x281 (not $x100)))
  1.4561 -(let (($x283 (or $x281 $x282)))
  1.4562 -(let (($x465 (>= ?x425 0)))
  1.4563 -(let ((?x496 (* (- 2) ?x102)))
  1.4564 -(let ((?x497 (+ ?x93 ?x110 ?x496)))
  1.4565 -(let (($x504 (<= ?x497 0)))
  1.4566 -(let (($x498 (= ?x497 0)))
  1.4567 -(let (($x304 (forall ((?v0 Int_list$) (?v1 Int_list$) )(! (let ((?x45 (eval_dioph$ ?v0 ?v1)))
  1.4568 -(let ((?x83 (+ ?x45 (* (- 1) (eval_dioph$ ?v0 (map$ uu$ ?v1))) (* (- 2) (eval_dioph$ ?v0 (map$ uua$ ?v1))))))
  1.4569 -(= ?x83 0))) :pattern ( (eval_dioph$ ?v0 (map$ uu$ ?v1)) ) :pattern ( (eval_dioph$ ?v0 (map$ uua$ ?v1)) ) :qid k!19))
  1.4570 -))
  1.4571 -(let (($x85 (forall ((?v0 Int_list$) (?v1 Int_list$) )(! (let ((?x45 (eval_dioph$ ?v0 ?v1)))
  1.4572 -(let ((?x83 (+ ?x45 (* (- 1) (eval_dioph$ ?v0 (map$ uu$ ?v1))) (* (- 2) (eval_dioph$ ?v0 (map$ uua$ ?v1))))))
  1.4573 -(= ?x83 0))) :qid k!19))
  1.4574 -))
  1.4575 -(let ((?x45 (eval_dioph$ ?1 ?0)))
  1.4576 -(let ((?x83 (+ ?x45 (* (- 1) (eval_dioph$ ?1 (map$ uu$ ?0))) (* (- 2) (eval_dioph$ ?1 (map$ uua$ ?0))))))
  1.4577 -(let (($x79 (= ?x83 0)))
  1.4578 -(let (($x58 (forall ((?v0 Int_list$) (?v1 Int_list$) )(! (let ((?x45 (eval_dioph$ ?v0 ?v1)))
  1.4579 -(let ((?x48 (eval_dioph$ ?v0 (map$ uu$ ?v1))))
  1.4580 -(let ((?x56 (+ (* (eval_dioph$ ?v0 (map$ uua$ ?v1)) 2) ?x48)))
  1.4581 -(= ?x56 ?x45)))) :qid k!19))
  1.4582 -))
  1.4583 -(let (($x74 (forall ((?v0 Int_list$) (?v1 Int_list$) )(! (let ((?x45 (eval_dioph$ ?v0 ?v1)))
  1.4584 -(let ((?x54 (eval_dioph$ ?v0 (map$ uua$ ?v1))))
  1.4585 -(let ((?x60 (* 2 ?x54)))
  1.4586 -(let ((?x48 (eval_dioph$ ?v0 (map$ uu$ ?v1))))
  1.4587 -(let ((?x66 (+ ?x48 ?x60)))
  1.4588 -(= ?x66 ?x45)))))) :qid k!19))
  1.4589 -))
  1.4590 -(let ((?x54 (eval_dioph$ ?1 (map$ uua$ ?0))))
  1.4591 -(let ((?x60 (* 2 ?x54)))
  1.4592 -(let ((?x48 (eval_dioph$ ?1 (map$ uu$ ?0))))
  1.4593 -(let ((?x66 (+ ?x48 ?x60)))
  1.4594 -(let (($x71 (= ?x66 ?x45)))
  1.4595 -(let ((@x65 (monotonicity (rewrite (= (* ?x54 2) ?x60)) (= (+ (* ?x54 2) ?x48) (+ ?x60 ?x48)))))
  1.4596 -(let ((@x70 (trans @x65 (rewrite (= (+ ?x60 ?x48) ?x66)) (= (+ (* ?x54 2) ?x48) ?x66))))
  1.4597 -(let ((@x76 (quant-intro (monotonicity @x70 (= (= (+ (* ?x54 2) ?x48) ?x45) $x71)) (= $x58 $x74))))
  1.4598 -(let ((@x89 (trans @x76 (quant-intro (rewrite (= $x71 $x79)) (= $x74 $x85)) (= $x58 $x85))))
  1.4599 -(let ((@x270 (mp~ (mp (asserted $x58) @x89 $x85) (nnf-pos (refl (~ $x79 $x79)) (~ $x85 $x85)) $x85)))
  1.4600 -(let ((@x309 (mp @x270 (quant-intro (refl (= $x79 $x79)) (= $x85 $x304)) $x304)))
  1.4601 -(let (($x502 (or (not $x304) $x498)))
  1.4602 -(let ((@x503 ((_ quant-inst ks$ xs$) $x502)))
  1.4603 -(let ((@x795 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x498) $x504)) (unit-resolution @x503 @x309 $x498) $x504)))
  1.4604 -(let (($x815 (not $x679)))
  1.4605 -(let (($x680 (>= ?x678 0)))
  1.4606 -(let ((?x592 (mod ?x97 2)))
  1.4607 -(let ((?x619 (* (- 1) ?x592)))
  1.4608 -(let ((?x511 (mod l$ 2)))
  1.4609 -(let ((?x538 (* (- 1) ?x511)))
  1.4610 -(let ((?x776 (* (- 1) ?x102)))
  1.4611 -(let ((?x759 (+ l$ ?x98 ?x776 ?x538 (* (- 1) (div l$ 2)) ?x619 (* (- 1) (div ?x97 2)))))
  1.4612 -(let (($x760 (>= ?x759 1)))
  1.4613 -(let (($x747 (not $x760)))
  1.4614 -(let ((?x674 (* (- 1) ?x99)))
  1.4615 -(let ((?x675 (+ ?x98 ?x674)))
  1.4616 -(let (($x676 (<= ?x675 0)))
  1.4617 -(let (($x284 (not $x283)))
  1.4618 -(let ((@x493 (hypothesis $x284)))
  1.4619 -(let ((@x781 (unit-resolution ((_ th-lemma arith triangle-eq) (or $x281 $x676)) (unit-resolution (def-axiom (or $x283 $x100)) @x493 $x100) $x676)))
  1.4620 -(let ((?x670 (* (- 1) ?x114)))
  1.4621 -(let ((?x671 (+ ?x102 ?x670)))
  1.4622 -(let (($x673 (>= ?x671 0)))
  1.4623 -(let ((@x787 (unit-resolution ((_ th-lemma arith triangle-eq) (or $x282 $x673)) (unit-resolution (def-axiom (or $x283 $x117)) @x493 $x117) $x673)))
  1.4624 -(let ((?x557 (div l$ 2)))
  1.4625 -(let ((?x570 (* (- 2) ?x557)))
  1.4626 -(let ((?x571 (+ l$ ?x538 ?x570)))
  1.4627 -(let (($x576 (<= ?x571 0)))
  1.4628 -(let (($x569 (= ?x571 0)))
  1.4629 -(let ((@x568 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x569) $x576)) (unit-resolution ((_ th-lemma arith) (or false $x569)) @x26 $x569) $x576)))
  1.4630 -(let ((?x620 (+ ?x98 ?x619)))
  1.4631 -(let (($x635 (<= ?x620 0)))
  1.4632 -(let (($x621 (= ?x620 0)))
  1.4633 -(let (($x318 (forall ((?v0 Int) (?v1 Int) )(! (let ((?x200 (mod ?v0 ?v1)))
  1.4634 -(let ((?x157 (* (- 1) ?v1)))
  1.4635 -(let ((?x154 (* (- 1) ?v0)))
  1.4636 -(let ((?x208 (mod ?x154 ?x157)))
  1.4637 -(let ((?x214 (* (- 1) ?x208)))
  1.4638 -(let (($x175 (<= ?v1 0)))
  1.4639 -(let ((?x234 (ite $x175 ?x214 ?x200)))
  1.4640 -(let (($x143 (= ?v1 0)))
  1.4641 -(let ((?x239 (ite $x143 ?v0 ?x234)))
  1.4642 -(let ((?x199 (modulo$ ?v0 ?v1)))
  1.4643 -(= ?x199 ?x239))))))))))) :pattern ( (modulo$ ?v0 ?v1) ) :qid k!22))
  1.4644 -))
  1.4645 -(let (($x245 (forall ((?v0 Int) (?v1 Int) )(! (let ((?x200 (mod ?v0 ?v1)))
  1.4646 -(let ((?x157 (* (- 1) ?v1)))
  1.4647 -(let ((?x154 (* (- 1) ?v0)))
  1.4648 -(let ((?x208 (mod ?x154 ?x157)))
  1.4649 -(let ((?x214 (* (- 1) ?x208)))
  1.4650 -(let (($x175 (<= ?v1 0)))
  1.4651 -(let ((?x234 (ite $x175 ?x214 ?x200)))
  1.4652 -(let (($x143 (= ?v1 0)))
  1.4653 -(let ((?x239 (ite $x143 ?v0 ?x234)))
  1.4654 -(let ((?x199 (modulo$ ?v0 ?v1)))
  1.4655 -(= ?x199 ?x239))))))))))) :qid k!22))
  1.4656 -))
  1.4657 -(let ((?x200 (mod ?1 ?0)))
  1.4658 -(let ((?x157 (* (- 1) ?0)))
  1.4659 -(let ((?x154 (* (- 1) ?1)))
  1.4660 -(let ((?x208 (mod ?x154 ?x157)))
  1.4661 -(let ((?x214 (* (- 1) ?x208)))
  1.4662 -(let (($x175 (<= ?0 0)))
  1.4663 -(let ((?x234 (ite $x175 ?x214 ?x200)))
  1.4664 -(let (($x143 (= ?0 0)))
  1.4665 -(let ((?x239 (ite $x143 ?1 ?x234)))
  1.4666 -(let ((?x199 (modulo$ ?1 ?0)))
  1.4667 -(let (($x242 (= ?x199 ?x239)))
  1.4668 -(let (($x206 (forall ((?v0 Int) (?v1 Int) )(! (let (($x143 (= ?v1 0)))
  1.4669 -(let ((?x204 (ite $x143 ?v0 (ite (< 0 ?v1) (mod ?v0 ?v1) (- (mod (- ?v0) (- ?v1)))))))
  1.4670 -(let ((?x199 (modulo$ ?v0 ?v1)))
  1.4671 -(= ?x199 ?x204)))) :qid k!22))
  1.4672 -))
  1.4673 -(let (($x228 (forall ((?v0 Int) (?v1 Int) )(! (let ((?x157 (* (- 1) ?v1)))
  1.4674 -(let ((?x154 (* (- 1) ?v0)))
  1.4675 -(let ((?x208 (mod ?x154 ?x157)))
  1.4676 -(let ((?x214 (* (- 1) ?x208)))
  1.4677 -(let ((?x200 (mod ?v0 ?v1)))
  1.4678 -(let (($x144 (< 0 ?v1)))
  1.4679 -(let ((?x219 (ite $x144 ?x200 ?x214)))
  1.4680 -(let (($x143 (= ?v1 0)))
  1.4681 -(let ((?x222 (ite $x143 ?v0 ?x219)))
  1.4682 -(let ((?x199 (modulo$ ?v0 ?v1)))
  1.4683 -(= ?x199 ?x222))))))))))) :qid k!22))
  1.4684 -))
  1.4685 -(let ((@x233 (monotonicity (rewrite (= (< 0 ?0) (not $x175))) (= (ite (< 0 ?0) ?x200 ?x214) (ite (not $x175) ?x200 ?x214)))))
  1.4686 -(let ((@x238 (trans @x233 (rewrite (= (ite (not $x175) ?x200 ?x214) ?x234)) (= (ite (< 0 ?0) ?x200 ?x214) ?x234))))
  1.4687 -(let ((@x241 (monotonicity @x238 (= (ite $x143 ?1 (ite (< 0 ?0) ?x200 ?x214)) ?x239))))
  1.4688 -(let ((@x244 (monotonicity @x241 (= (= ?x199 (ite $x143 ?1 (ite (< 0 ?0) ?x200 ?x214))) $x242))))
  1.4689 -(let (($x144 (< 0 ?0)))
  1.4690 -(let ((?x219 (ite $x144 ?x200 ?x214)))
  1.4691 -(let ((?x222 (ite $x143 ?1 ?x219)))
  1.4692 -(let (($x225 (= ?x199 ?x222)))
  1.4693 -(let (($x226 (= (= ?x199 (ite $x143 ?1 (ite $x144 ?x200 (- (mod (- ?1) (- ?0)))))) $x225)))
  1.4694 -(let ((@x210 (monotonicity (rewrite (= (- ?1) ?x154)) (rewrite (= (- ?0) ?x157)) (= (mod (- ?1) (- ?0)) ?x208))))
  1.4695 -(let ((@x218 (trans (monotonicity @x210 (= (- (mod (- ?1) (- ?0))) (- ?x208))) (rewrite (= (- ?x208) ?x214)) (= (- (mod (- ?1) (- ?0))) ?x214))))
  1.4696 -(let ((@x221 (monotonicity @x218 (= (ite $x144 ?x200 (- (mod (- ?1) (- ?0)))) ?x219))))
  1.4697 -(let ((@x224 (monotonicity @x221 (= (ite $x143 ?1 (ite $x144 ?x200 (- (mod (- ?1) (- ?0))))) ?x222))))
  1.4698 -(let ((@x249 (trans (quant-intro (monotonicity @x224 $x226) (= $x206 $x228)) (quant-intro @x244 (= $x228 $x245)) (= $x206 $x245))))
  1.4699 -(let ((@x280 (mp~ (mp (asserted $x206) @x249 $x245) (nnf-pos (refl (~ $x242 $x242)) (~ $x245 $x245)) $x245)))
  1.4700 -(let ((@x323 (mp @x280 (quant-intro (refl (= $x242 $x242)) (= $x245 $x318)) $x318)))
  1.4701 -(let (($x545 (not $x318)))
  1.4702 -(let (($x626 (or $x545 $x621)))
  1.4703 -(let ((?x359 (* (- 1) 2)))
  1.4704 -(let ((?x590 (mod ?x110 ?x359)))
  1.4705 -(let ((?x591 (* (- 1) ?x590)))
  1.4706 -(let (($x357 (<= 2 0)))
  1.4707 -(let ((?x593 (ite $x357 ?x591 ?x592)))
  1.4708 -(let (($x356 (= 2 0)))
  1.4709 -(let ((?x594 (ite $x356 ?x97 ?x593)))
  1.4710 -(let (($x595 (= ?x98 ?x594)))
  1.4711 -(let ((@x601 (monotonicity (monotonicity (rewrite (= ?x359 (- 2))) (= ?x590 (mod ?x110 (- 2)))) (= ?x591 (* (- 1) (mod ?x110 (- 2)))))))
  1.4712 -(let ((@x368 (rewrite (= $x357 false))))
  1.4713 -(let ((@x604 (monotonicity @x368 @x601 (= ?x593 (ite false (* (- 1) (mod ?x110 (- 2))) ?x592)))))
  1.4714 -(let ((@x608 (trans @x604 (rewrite (= (ite false (* (- 1) (mod ?x110 (- 2))) ?x592) ?x592)) (= ?x593 ?x592))))
  1.4715 -(let ((@x366 (rewrite (= $x356 false))))
  1.4716 -(let ((@x615 (trans (monotonicity @x366 @x608 (= ?x594 (ite false ?x97 ?x592))) (rewrite (= (ite false ?x97 ?x592) ?x592)) (= ?x594 ?x592))))
  1.4717 -(let ((@x625 (trans (monotonicity @x615 (= $x595 (= ?x98 ?x592))) (rewrite (= (= ?x98 ?x592) $x621)) (= $x595 $x621))))
  1.4718 -(let ((@x633 (trans (monotonicity @x625 (= (or $x545 $x595) $x626)) (rewrite (= $x626 $x626)) (= (or $x545 $x595) $x626))))
  1.4719 -(let ((@x634 (mp ((_ quant-inst (eval_dioph$ ks$ ?x96) 2) (or $x545 $x595)) @x633 $x626)))
  1.4720 -(let ((@x431 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x621) $x635)) (unit-resolution @x634 @x323 $x621) $x635)))
  1.4721 -(let ((?x637 (div ?x97 2)))
  1.4722 -(let ((?x650 (* (- 2) ?x637)))
  1.4723 -(let ((?x651 (+ ?x97 ?x619 ?x650)))
  1.4724 -(let (($x656 (<= ?x651 0)))
  1.4725 -(let (($x649 (= ?x651 0)))
  1.4726 -(let ((@x661 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x649) $x656)) (unit-resolution ((_ th-lemma arith) (or false $x649)) @x26 $x649) $x656)))
  1.4727 -(let ((?x539 (+ ?x99 ?x538)))
  1.4728 -(let (($x555 (<= ?x539 0)))
  1.4729 -(let (($x540 (= ?x539 0)))
  1.4730 -(let (($x546 (or $x545 $x540)))
  1.4731 -(let ((?x506 (mod ?x369 ?x359)))
  1.4732 -(let ((?x507 (* (- 1) ?x506)))
  1.4733 -(let ((?x512 (ite $x357 ?x507 ?x511)))
  1.4734 -(let ((?x513 (ite $x356 l$ ?x512)))
  1.4735 -(let (($x514 (= ?x99 ?x513)))
  1.4736 -(let ((@x520 (monotonicity (monotonicity (rewrite (= ?x359 (- 2))) (= ?x506 (mod ?x369 (- 2)))) (= ?x507 (* (- 1) (mod ?x369 (- 2)))))))
  1.4737 -(let ((@x523 (monotonicity @x368 @x520 (= ?x512 (ite false (* (- 1) (mod ?x369 (- 2))) ?x511)))))
  1.4738 -(let ((@x527 (trans @x523 (rewrite (= (ite false (* (- 1) (mod ?x369 (- 2))) ?x511) ?x511)) (= ?x512 ?x511))))
  1.4739 -(let ((@x534 (trans (monotonicity @x366 @x527 (= ?x513 (ite false l$ ?x511))) (rewrite (= (ite false l$ ?x511) ?x511)) (= ?x513 ?x511))))
  1.4740 -(let ((@x544 (trans (monotonicity @x534 (= $x514 (= ?x99 ?x511))) (rewrite (= (= ?x99 ?x511) $x540)) (= $x514 $x540))))
  1.4741 -(let ((@x553 (trans (monotonicity @x544 (= (or $x545 $x514) $x546)) (rewrite (= $x546 $x546)) (= (or $x545 $x514) $x546))))
  1.4742 -(let ((@x554 (mp ((_ quant-inst l$ 2) (or $x545 $x514)) @x553 $x546)))
  1.4743 -(let ((@x668 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x540) $x555)) (unit-resolution @x554 @x323 $x540) $x555)))
  1.4744 -(let ((?x361 (div ?x111 2)))
  1.4745 -(let ((?x395 (* (- 1) ?x361)))
  1.4746 -(let ((?x396 (+ ?x114 ?x395)))
  1.4747 -(let (($x414 (>= ?x396 0)))
  1.4748 -(let (($x397 (= ?x396 0)))
  1.4749 -(let (($x311 (forall ((?v0 Int) (?v1 Int) )(! (let ((?x145 (div ?v0 ?v1)))
  1.4750 -(let ((?x157 (* (- 1) ?v1)))
  1.4751 -(let ((?x154 (* (- 1) ?v0)))
  1.4752 -(let ((?x160 (div ?x154 ?x157)))
  1.4753 -(let (($x175 (<= ?v1 0)))
  1.4754 -(let ((?x182 (ite $x175 ?x160 ?x145)))
  1.4755 -(let (($x143 (= ?v1 0)))
  1.4756 -(let ((?x141 (divide$ ?v0 ?v1)))
  1.4757 -(= ?x141 (ite $x143 0 ?x182)))))))))) :pattern ( (divide$ ?v0 ?v1) ) :qid k!21))
  1.4758 -))
  1.4759 -(let (($x193 (forall ((?v0 Int) (?v1 Int) )(! (let ((?x145 (div ?v0 ?v1)))
  1.4760 -(let ((?x157 (* (- 1) ?v1)))
  1.4761 -(let ((?x154 (* (- 1) ?v0)))
  1.4762 -(let ((?x160 (div ?x154 ?x157)))
  1.4763 -(let (($x175 (<= ?v1 0)))
  1.4764 -(let ((?x182 (ite $x175 ?x160 ?x145)))
  1.4765 -(let (($x143 (= ?v1 0)))
  1.4766 -(let ((?x141 (divide$ ?v0 ?v1)))
  1.4767 -(= ?x141 (ite $x143 0 ?x182)))))))))) :qid k!21))
  1.4768 -))
  1.4769 -(let ((?x141 (divide$ ?1 ?0)))
  1.4770 -(let (($x190 (= ?x141 (ite $x143 0 (ite $x175 (div ?x154 ?x157) (div ?1 ?0))))))
  1.4771 -(let (($x152 (forall ((?v0 Int) (?v1 Int) )(! (let (($x143 (= ?v1 0)))
  1.4772 -(let ((?x150 (ite $x143 0 (ite (< 0 ?v1) (div ?v0 ?v1) (div (- ?v0) (- ?v1))))))
  1.4773 -(let ((?x141 (divide$ ?v0 ?v1)))
  1.4774 -(= ?x141 ?x150)))) :qid k!21))
  1.4775 -))
  1.4776 -(let (($x172 (forall ((?v0 Int) (?v1 Int) )(! (let ((?x157 (* (- 1) ?v1)))
  1.4777 -(let ((?x154 (* (- 1) ?v0)))
  1.4778 -(let ((?x160 (div ?x154 ?x157)))
  1.4779 -(let ((?x145 (div ?v0 ?v1)))
  1.4780 -(let (($x144 (< 0 ?v1)))
  1.4781 -(let ((?x163 (ite $x144 ?x145 ?x160)))
  1.4782 -(let (($x143 (= ?v1 0)))
  1.4783 -(let ((?x166 (ite $x143 0 ?x163)))
  1.4784 -(let ((?x141 (divide$ ?v0 ?v1)))
  1.4785 -(= ?x141 ?x166)))))))))) :qid k!21))
  1.4786 -))
  1.4787 -(let ((?x160 (div ?x154 ?x157)))
  1.4788 -(let ((?x145 (div ?1 ?0)))
  1.4789 -(let ((?x163 (ite $x144 ?x145 ?x160)))
  1.4790 -(let ((?x166 (ite $x143 0 ?x163)))
  1.4791 -(let (($x169 (= ?x141 ?x166)))
  1.4792 -(let ((@x181 (monotonicity (rewrite (= $x144 (not $x175))) (= ?x163 (ite (not $x175) ?x145 ?x160)))))
  1.4793 -(let ((@x186 (trans @x181 (rewrite (= (ite (not $x175) ?x145 ?x160) (ite $x175 ?x160 ?x145))) (= ?x163 (ite $x175 ?x160 ?x145)))))
  1.4794 -(let ((@x192 (monotonicity (monotonicity @x186 (= ?x166 (ite $x143 0 (ite $x175 ?x160 ?x145)))) (= $x169 $x190))))
  1.4795 -(let (($x170 (= (= ?x141 (ite $x143 0 (ite $x144 ?x145 (div (- ?1) (- ?0))))) $x169)))
  1.4796 -(let ((@x162 (monotonicity (rewrite (= (- ?1) ?x154)) (rewrite (= (- ?0) ?x157)) (= (div (- ?1) (- ?0)) ?x160))))
  1.4797 -(let ((@x168 (monotonicity (monotonicity @x162 (= (ite $x144 ?x145 (div (- ?1) (- ?0))) ?x163)) (= (ite $x143 0 (ite $x144 ?x145 (div (- ?1) (- ?0)))) ?x166))))
  1.4798 -(let ((@x197 (trans (quant-intro (monotonicity @x168 $x170) (= $x152 $x172)) (quant-intro @x192 (= $x172 $x193)) (= $x152 $x193))))
  1.4799 -(let ((@x275 (mp~ (mp (asserted $x152) @x197 $x193) (nnf-pos (refl (~ $x190 $x190)) (~ $x193 $x193)) $x193)))
  1.4800 -(let ((@x316 (mp @x275 (quant-intro (refl (= $x190 $x190)) (= $x193 $x311)) $x311)))
  1.4801 -(let (($x403 (or (not $x311) $x397)))
  1.4802 -(let ((?x358 (* (- 1) ?x111)))
  1.4803 -(let ((?x360 (div ?x358 ?x359)))
  1.4804 -(let ((?x362 (ite $x357 ?x360 ?x361)))
  1.4805 -(let ((?x363 (ite $x356 0 ?x362)))
  1.4806 -(let (($x364 (= ?x114 ?x363)))
  1.4807 -(let ((@x374 (rewrite (= ?x359 (- 2)))))
  1.4808 -(let ((@x377 (monotonicity (rewrite (= ?x358 (+ ?x369 ?x97))) @x374 (= ?x360 (div (+ ?x369 ?x97) (- 2))))))
  1.4809 -(let ((@x380 (monotonicity @x368 @x377 (= ?x362 (ite false (div (+ ?x369 ?x97) (- 2)) ?x361)))))
  1.4810 -(let ((@x384 (trans @x380 (rewrite (= (ite false (div (+ ?x369 ?x97) (- 2)) ?x361) ?x361)) (= ?x362 ?x361))))
  1.4811 -(let ((@x391 (trans (monotonicity @x366 @x384 (= ?x363 (ite false 0 ?x361))) (rewrite (= (ite false 0 ?x361) ?x361)) (= ?x363 ?x361))))
  1.4812 -(let ((@x401 (trans (monotonicity @x391 (= $x364 (= ?x114 ?x361))) (rewrite (= (= ?x114 ?x361) $x397)) (= $x364 $x397))))
  1.4813 -(let ((@x410 (trans (monotonicity @x401 (= (or (not $x311) $x364) $x403)) (rewrite (= $x403 $x403)) (= (or (not $x311) $x364) $x403))))
  1.4814 -(let ((@x411 (mp ((_ quant-inst (+ l$ ?x110) 2) (or (not $x311) $x364)) @x410 $x403)))
  1.4815 -(let ((@x485 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x397) $x414)) (unit-resolution @x411 @x316 $x397) $x414)))
  1.4816 -(let ((?x436 (* (- 1) ?x425)))
  1.4817 -(let ((?x435 (* (- 2) ?x361)))
  1.4818 -(let ((?x437 (+ l$ ?x110 ?x435 ?x436)))
  1.4819 -(let (($x442 (<= ?x437 0)))
  1.4820 -(let (($x434 (= ?x437 0)))
  1.4821 -(let ((@x745 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x434) $x442)) (unit-resolution ((_ th-lemma arith) (or false $x434)) @x26 $x434) $x442)))
  1.4822 -(let ((@x746 ((_ th-lemma arith farkas 1 -2 -2 -2 1 1 1 1 1 1) @x745 @x485 (hypothesis $x673) (hypothesis $x760) (hypothesis $x676) @x668 @x661 @x431 @x568 (unit-resolution ((_ th-lemma arith) (or false $x564)) @x26 $x564) false)))
  1.4823 -(let ((@x788 (unit-resolution (lemma @x746 (or $x747 (not $x673) (not $x676))) @x787 @x781 $x747)))
  1.4824 -(let (($x677 (>= ?x675 0)))
  1.4825 -(let ((@x812 (unit-resolution ((_ th-lemma arith triangle-eq) (or $x281 $x677)) (unit-resolution (def-axiom (or $x283 $x100)) @x493 $x100) $x677)))
  1.4826 -(let (($x577 (>= ?x571 0)))
  1.4827 -(let ((@x778 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x569) $x577)) (unit-resolution ((_ th-lemma arith) (or false $x569)) @x26 $x569) $x577)))
  1.4828 -(let (($x556 (>= ?x539 0)))
  1.4829 -(let ((@x645 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x540) $x556)) (unit-resolution @x554 @x323 $x540) $x556)))
  1.4830 -(let (($x636 (>= ?x620 0)))
  1.4831 -(let ((@x652 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x621) $x636)) (unit-resolution @x634 @x323 $x621) $x636)))
  1.4832 -(let (($x505 (>= ?x497 0)))
  1.4833 -(let ((@x488 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x498) $x505)) (unit-resolution @x503 @x309 $x498) $x505)))
  1.4834 -(let (($x657 (>= ?x651 0)))
  1.4835 -(let ((@x581 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x649) $x657)) (unit-resolution ((_ th-lemma arith) (or false $x649)) @x26 $x649) $x657)))
  1.4836 -(let ((@x582 ((_ th-lemma arith farkas -1/2 -1/2 -1/2 1/2 -1/2 -1/2 -1/2 1) @x581 (hypothesis $x677) @x488 (hypothesis (not $x680)) @x652 @x645 @x778 (hypothesis $x747) false)))
  1.4837 -(let ((@x813 (unit-resolution (lemma @x582 (or $x680 (not $x677) $x760)) @x812 @x788 $x680)))
  1.4838 -(let (($x134 (not $x95)))
  1.4839 -(let (($x290 (= $x95 $x283)))
  1.4840 -(let ((@x289 (monotonicity (rewrite (= (and $x100 $x117) $x284)) (= (= $x134 (and $x100 $x117)) (= $x134 $x284)))))
  1.4841 -(let ((@x294 (trans @x289 (rewrite (= (= $x134 $x284) $x290)) (= (= $x134 (and $x100 $x117)) $x290))))
  1.4842 -(let (($x120 (and $x100 $x117)))
  1.4843 -(let (($x135 (= $x134 $x120)))
  1.4844 -(let (($x107 (= $x95 (and $x100 (= ?x102 (divide$ (- l$ ?x97) 2))))))
  1.4845 -(let (($x108 (not $x107)))
  1.4846 -(let ((@x116 (monotonicity (rewrite (= (- l$ ?x97) ?x111)) (= (divide$ (- l$ ?x97) 2) ?x114))))
  1.4847 -(let ((@x122 (monotonicity (monotonicity @x116 (= (= ?x102 (divide$ (- l$ ?x97) 2)) $x117)) (= (and $x100 (= ?x102 (divide$ (- l$ ?x97) 2))) $x120))))
  1.4848 -(let ((@x130 (trans (monotonicity @x122 (= $x107 (= $x95 $x120))) (rewrite (= (= $x95 $x120) (= $x95 $x120))) (= $x107 (= $x95 $x120)))))
  1.4849 -(let ((@x139 (trans (monotonicity @x130 (= $x108 (not (= $x95 $x120)))) (rewrite (= (not (= $x95 $x120)) $x135)) (= $x108 $x135))))
  1.4850 -(let ((@x295 (mp (mp (asserted $x108) @x139 $x135) @x294 $x290)))
  1.4851 -(let ((@x344 (unit-resolution (def-axiom (or $x134 $x283 (not $x290))) @x295 (or $x134 $x283))))
  1.4852 -(let ((@x819 (unit-resolution ((_ th-lemma arith triangle-eq) (or $x95 $x815 (not $x680))) (unit-resolution @x344 @x493 $x134) (or $x815 (not $x680)))))
  1.4853 -(let (($x672 (<= ?x671 0)))
  1.4854 -(let ((@x823 (unit-resolution ((_ th-lemma arith triangle-eq) (or $x282 $x672)) (unit-resolution (def-axiom (or $x283 $x117)) @x493 $x117) $x672)))
  1.4855 -(let (($x413 (<= ?x396 0)))
  1.4856 -(let ((@x802 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x397) $x413)) (unit-resolution @x411 @x316 $x397) $x413)))
  1.4857 -(let (($x443 (>= ?x437 0)))
  1.4858 -(let ((@x826 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x434) $x443)) (unit-resolution ((_ th-lemma arith) (or false $x434)) @x26 $x434) $x443)))
  1.4859 -(let ((@x827 ((_ th-lemma arith farkas 1 -2 -2 1 -1 1) @x826 @x802 @x823 (unit-resolution @x819 @x813 $x815) @x795 (unit-resolution ((_ th-lemma arith) (or false $x465)) @x26 $x465) false)))
  1.4860 -(let ((@x828 (lemma @x827 $x283)))
  1.4861 -(let ((@x340 (unit-resolution (def-axiom (or $x95 $x284 (not $x290))) @x295 (or $x95 $x284))))
  1.4862 -(let ((@x584 (unit-resolution @x340 @x828 $x95)))
  1.4863 -(let (($x807 (not $x672)))
  1.4864 -(let ((@x888 ((_ th-lemma arith assign-bounds 1 -1/2 -1/2 1/2 -1/2) (or $x673 (not $x413) (not $x465) (not $x443) (not $x504) (not $x680)))))
  1.4865 -(let ((@x889 (unit-resolution @x888 (unit-resolution ((_ th-lemma arith triangle-eq) (or $x134 $x680)) @x584 $x680) @x802 @x826 (unit-resolution ((_ th-lemma arith) (or false $x465)) @x26 $x465) @x795 $x673)))
  1.4866 -(let ((@x728 (monotonicity (symm @x584 (= l$ ?x93)) (= ?x99 (modulo$ ?x93 2)))))
  1.4867 -(let ((?x499 (modulo$ ?x93 2)))
  1.4868 -(let (($x500 (= ?x499 ?x98)))
  1.4869 -(let (($x297 (forall ((?v0 Int_list$) (?v1 Int_list$) )(! (= (modulo$ (eval_dioph$ ?v0 ?v1) 2) (modulo$ (eval_dioph$ ?v0 (map$ uu$ ?v1)) 2)) :pattern ( (eval_dioph$ ?v0 (map$ uu$ ?v1)) ) :qid k!18))
  1.4870 -))
  1.4871 -(let (($x51 (forall ((?v0 Int_list$) (?v1 Int_list$) )(! (= (modulo$ (eval_dioph$ ?v0 ?v1) 2) (modulo$ (eval_dioph$ ?v0 (map$ uu$ ?v1)) 2)) :qid k!18))
  1.4872 -))
  1.4873 -(let (($x50 (= (modulo$ ?x45 2) (modulo$ ?x48 2))))
  1.4874 -(let ((@x265 (mp~ (asserted $x51) (nnf-pos (refl (~ $x50 $x50)) (~ $x51 $x51)) $x51)))
  1.4875 -(let ((@x302 (mp @x265 (quant-intro (refl (= $x50 $x50)) (= $x51 $x297)) $x297)))
  1.4876 -(let (($x464 (or (not $x297) $x500)))
  1.4877 -(let ((@x578 ((_ quant-inst ks$ xs$) $x464)))
  1.4878 -(let ((@x748 (trans (symm (unit-resolution @x578 @x302 $x500) (= ?x98 ?x499)) (symm @x728 (= ?x499 ?x99)) $x100)))
  1.4879 -(let ((@x891 (unit-resolution (unit-resolution (def-axiom (or $x284 $x281 $x282)) @x828 $x283) (lemma (unit-resolution (hypothesis $x281) @x748 false) $x100) $x282)))
  1.4880 -(let ((@x895 (unit-resolution ((_ th-lemma arith triangle-eq) (or $x117 $x807 (not $x673))) @x891 (or $x807 (not $x673)))))
  1.4881 -((_ th-lemma arith farkas -2 -2 1 -1 1 1) (unit-resolution @x895 @x889 $x807) @x485 @x745 @x488 (unit-resolution ((_ th-lemma arith triangle-eq) (or $x134 $x679)) @x584 $x679) (unit-resolution ((_ th-lemma arith) (or false $x564)) @x26 $x564) false)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
  1.4882 -
  1.4883 -d982bc989c38d6a72f2d807a1168e928070f463b 100 0
  1.4884 -unsat
  1.4885 -(
  1.4886 -a141
  1.4887 -a32
  1.4888 -a142
  1.4889 -a33
  1.4890 -a143
  1.4891 -a34
  1.4892 -a144
  1.4893 -a35
  1.4894 -a145
  1.4895 -a36
  1.4896 -a146
  1.4897 -a147
  1.4898 -a37
  1.4899 -a148
  1.4900 -a38
  1.4901 -a93
  1.4902 -a149
  1.4903 -a39
  1.4904 -a150
  1.4905 -a40
  1.4906 -a151
  1.4907 -a41
  1.4908 -a152
  1.4909 -a96
  1.4910 -a42
  1.4911 -a153
  1.4912 -a43
  1.4913 -a154
  1.4914 -a44
  1.4915 -a155
  1.4916 -a45
  1.4917 -a156
  1.4918 -a46
  1.4919 -a157
  1.4920 -a47
  1.4921 -a158
  1.4922 -a48
  1.4923 -a159
  1.4924 -a160
  1.4925 -a49
  1.4926 -a161
  1.4927 -a50
  1.4928 -a162
  1.4929 -a14
  1.4930 -a13
  1.4931 -a15
  1.4932 -a113
  1.4933 -a16
  1.4934 -a114
  1.4935 -a115
  1.4936 -a169
  1.4937 -a116
  1.4938 -a7
  1.4939 -a117
  1.4940 -a8
  1.4941 -a61
  1.4942 -a118
  1.4943 -a62
  1.4944 -a119
  1.4945 -a120
  1.4946 -a121
  1.4947 -a122
  1.4948 -a69
  1.4949 -a17
  1.4950 -a70
  1.4951 -a124
  1.4952 -a18
  1.4953 -a182
  1.4954 -a71
  1.4955 -a72
  1.4956 -a183
  1.4957 -a73
  1.4958 -a127
  1.4959 -a184
  1.4960 -a74
  1.4961 -a128
  1.4962 -a75
  1.4963 -a129
  1.4964 -a23
  1.4965 -a76
  1.4966 -a130
  1.4967 -a24
  1.4968 -a25
  1.4969 -a79
  1.4970 -a133
  1.4971 -a26
  1.4972 -a27
  1.4973 -a135
  1.4974 -a136
  1.4975 -a28
  1.4976 -a137
  1.4977 -a29
  1.4978 -a138
  1.4979 -a30
  1.4980 -a139
  1.4981 -a140
  1.4982 -a31
  1.4983 -)
  1.4984 -356e447dfc184b20563d0467365f8b5f8cef0ab1 97 0
  1.4985 -unsat
  1.4986 -(
  1.4987 -a29
  1.4988 -a80
  1.4989 -a81
  1.4990 -a30
  1.4991 -a31
  1.4992 -a82
  1.4993 -a32
  1.4994 -a83
  1.4995 -a33
  1.4996 -a84
  1.4997 -a85
  1.4998 -a34
  1.4999 -a86
  1.5000 -a35
  1.5001 -a87
  1.5002 -a36
  1.5003 -a88
  1.5004 -a37
  1.5005 -a89
  1.5006 -a38
  1.5007 -a90
  1.5008 -a39
  1.5009 -a91
  1.5010 -a40
  1.5011 -a92
  1.5012 -a41
  1.5013 -a93
  1.5014 -a42
  1.5015 -a94
  1.5016 -a43
  1.5017 -a95
  1.5018 -a44
  1.5019 -a45
  1.5020 -a96
  1.5021 -a46
  1.5022 -a97
  1.5023 -a50
  1.5024 -a51
  1.5025 -a1
  1.5026 -a52
  1.5027 -a2
  1.5028 -a53
  1.5029 -a3
  1.5030 -a4
  1.5031 -a54
  1.5032 -a5
  1.5033 -a55
  1.5034 -a6
  1.5035 -a56
  1.5036 -a7
  1.5037 -a57
  1.5038 -a8
  1.5039 -a58
  1.5040 -a9
  1.5041 -a59
  1.5042 -a10
  1.5043 -a60
  1.5044 -a11
  1.5045 -a61
  1.5046 -a12
  1.5047 -a62
  1.5048 -a13
  1.5049 -a63
  1.5050 -a14
  1.5051 -a64
  1.5052 -a15
  1.5053 -a65
  1.5054 -a16
  1.5055 -a66
  1.5056 -a17
  1.5057 -a67
  1.5058 -a18
  1.5059 -a68
  1.5060 -a69
  1.5061 -a19
  1.5062 -a70
  1.5063 -a20
  1.5064 -a71
  1.5065 -a21
  1.5066 -a72
  1.5067 -a22
  1.5068 -a73
  1.5069 -a23
  1.5070 -a74
  1.5071 -a24
  1.5072 -a75
  1.5073 -a25
  1.5074 -a76
  1.5075 -a26
  1.5076 -a77
  1.5077 -a27
  1.5078 -a78
  1.5079 -a28
  1.5080 -a79
  1.5081 -)
  1.5082 -52fd45adea6478e9d5ad83eff76800476c97a929 2 0
  1.5083 -sat
  1.5084 -(error "Cannot get an unsat core unless immediately preceded by UNSAT/VALID response.")
  1.5085 -986242bd9f42b2ccb6c2f7242f7302e1f4a543ef 2 0
  1.5086 -sat
  1.5087 -(error "Cannot get an unsat core unless immediately preceded by UNSAT/VALID response.")
  1.5088 -72ac661c77e89ad0f41fb5c62073e8267bf5a6c1 2 0
  1.5089 -sat
  1.5090 -(error "Cannot get an unsat core unless immediately preceded by UNSAT/VALID response.")
  1.5091 -707271ac37bbf9aba707687e1d6d62497810fc5d 2 0
  1.5092 -sat
  1.5093 -(error "Cannot get an unsat core unless immediately preceded by UNSAT/VALID response.")
  1.5094 -9882e692cde42bbd5ed7cdcd884340dfaa68b016 2 0
  1.5095 -sat
  1.5096 -(error "Cannot get an unsat core unless immediately preceded by UNSAT/VALID response.")
  1.5097 -763f8658cf70daf26cd303b055bde69d09e03192 2 0
  1.5098 -sat
  1.5099 -(error "Cannot get an unsat core unless immediately preceded by UNSAT/VALID response.")
  1.5100 -5ace894fbc0cab965d77619b71e294a7498ea670 2 0
  1.5101 -sat
  1.5102 -(error "Cannot get an unsat core unless immediately preceded by UNSAT/VALID response.")
  1.5103 -35953e5bdfb3c20982931376ab02561049c3d3ec 2 0
  1.5104 -sat
  1.5105 -(error "Cannot get an unsat core unless immediately preceded by UNSAT/VALID response.")
  1.5106 -834942f3e869aeabae6a62cc9136262f9e001d9b 2 0
  1.5107 -sat
  1.5108 -(error "Cannot get an unsat core unless immediately preceded by UNSAT/VALID response.")
  1.5109 -1915bb36fd704a827d0d979f7d3273ea47ac12ff 2 0
  1.5110 -sat
  1.5111 -(error "Cannot get an unsat core unless immediately preceded by UNSAT/VALID response.")
  1.5112 -112b71a74adbf7dc3d30f9548dd7e6e7e507b5cb 90 0
  1.5113 -unsat
  1.5114 -(
  1.5115 -a28
  1.5116 -a78
  1.5117 -a29
  1.5118 -a79
  1.5119 -a30
  1.5120 -a80
  1.5121 -a31
  1.5122 -a32
  1.5123 -a33
  1.5124 -a83
  1.5125 -a84
  1.5126 -a34
  1.5127 -a85
  1.5128 -a35
  1.5129 -a86
  1.5130 -a36
  1.5131 -a87
  1.5132 -a37
  1.5133 -a88
  1.5134 -a38
  1.5135 -a89
  1.5136 -a39
  1.5137 -a90
  1.5138 -a40
  1.5139 -a91
  1.5140 -a41
  1.5141 -a92
  1.5142 -a42
  1.5143 -a93
  1.5144 -a43
  1.5145 -a44
  1.5146 -a45
  1.5147 -a46
  1.5148 -a47
  1.5149 -a48
  1.5150 -a49
  1.5151 -a1
  1.5152 -a50
  1.5153 -a2
  1.5154 -a51
  1.5155 -a52
  1.5156 -a3
  1.5157 -a53
  1.5158 -a4
  1.5159 -a54
  1.5160 -a5
  1.5161 -a55
  1.5162 -a6
  1.5163 -a56
  1.5164 -a57
  1.5165 -a7
  1.5166 -a58
  1.5167 -a8
  1.5168 -a59
  1.5169 -a9
  1.5170 -a60
  1.5171 -a61
  1.5172 -a10
  1.5173 -a62
  1.5174 -a11
  1.5175 -a63
  1.5176 -a12
  1.5177 -a64
  1.5178 -a13
  1.5179 -a65
  1.5180 -a14
  1.5181 -a66
  1.5182 -a15
  1.5183 -a67
  1.5184 -a68
  1.5185 -a17
  1.5186 -a18
  1.5187 -a69
  1.5188 -a70
  1.5189 -a20
  1.5190 -a71
  1.5191 -a21
  1.5192 -a72
  1.5193 -a22
  1.5194 -a23
  1.5195 -a24
  1.5196 -a25
  1.5197 -a75
  1.5198 -a26
  1.5199 -a76
  1.5200 -a27
  1.5201 -a77
  1.5202 -)
  1.5203 -55c4468a22c3129940ee0f507180fb5cb8a244d5 2 0
  1.5204 -sat
  1.5205 -(error "Cannot get an unsat core unless immediately preceded by UNSAT/VALID response.")
  1.5206 -834270f8dd620f74a77f5565b14e1f3bada38fbc 13 0
  1.5207 -unsat
  1.5208 -(
  1.5209 -a0
  1.5210 -a1
  1.5211 -a2
  1.5212 -a3
  1.5213 -a4
  1.5214 -a5
  1.5215 -a6
  1.5216 -a7
  1.5217 -a8
  1.5218 -a9
  1.5219 -)
  1.5220 -f22198ac4ffd581fb59d39b6771250bce4f2b10c 13 0
  1.5221 -unsat
  1.5222 -(
  1.5223 -a0
  1.5224 -a1
  1.5225 -a2
  1.5226 -a3
  1.5227 -a4
  1.5228 -a5
  1.5229 -a6
  1.5230 -a7
  1.5231 -a8
  1.5232 -a9
  1.5233 -)
  1.5234 -c2cfe7fbd368fc0ecc0401a01b53f57caeef131a 4 0
  1.5235 -unsat
  1.5236 -(
  1.5237 -a0
  1.5238 -)
  1.5239 -1b75f6cb11115d60847d54399897af90dea90827 4 0
  1.5240 -unsat
  1.5241 -(
  1.5242 -a0
  1.5243 -)
  1.5244 -4998d5a79895ec5f3cef0120dc86abbbd8e29b48 4 0
  1.5245 -unsat
  1.5246 -(
  1.5247 -a2
  1.5248 -)
  1.5249 -1437414329c2da0f812cda22f62176795fe4b488 2 0
  1.5250 -sat
  1.5251 -(error "Cannot get an unsat core unless immediately preceded by UNSAT/VALID response.")
  1.5252 -6ca70dfdb60448a41d66f81903a82cf3bfc1d3c0 6 0
  1.5253 -unsat
  1.5254 -(
  1.5255 -a11
  1.5256 -a4
  1.5257 -a5
  1.5258 -)
  1.5259 -2998de44350b8173b123947e09d691282118e3a6 6 0
  1.5260 -unsat
  1.5261 -(
  1.5262 -a0
  1.5263 -a1
  1.5264 -a2
  1.5265 -)
  1.5266 -9e56e42500b1c152c4d6f34a9829575456349872 2 0
  1.5267 -sat
  1.5268 -(error "Cannot get an unsat core unless immediately preceded by UNSAT/VALID response.")
  1.5269 -20e7bc67dece8e9eee65bc5c217876381ad19805 7 0
  1.5270 -unsat
  1.5271 -(
  1.5272 -a44
  1.5273 -a5
  1.5274 -a6
  1.5275 -a40
  1.5276 -)
  1.5277 -47a88885e5196eac2e3922eb19ce30b6d748259f 7 0
  1.5278 -unsat
  1.5279 -(
  1.5280 -a0
  1.5281 -a1
  1.5282 -a3
  1.5283 -a5
  1.5284 -)
  1.5285 -e06991d1826b36a536b8ecef95433bd1f28774f6 2 0
  1.5286 -unknown
  1.5287 -(error "Cannot get an unsat core unless immediately preceded by UNSAT/VALID response.")
  1.5288 -5ecd136d06134f07af067717cf168158b90a4fe5 2 0
  1.5289 -unknown
  1.5290 -(error "Cannot get an unsat core unless immediately preceded by UNSAT/VALID response.")
  1.5291 -0b10533518bb68ba1619340435dfd68ab76ab077 6 0
  1.5292 -unsat
  1.5293 -(
  1.5294 -a0
  1.5295 -a3
  1.5296 -a104
  1.5297 -)
  1.5298 -2a33649206162ac011eff175206722d181426839 6 0
  1.5299 -unsat
  1.5300 -(
  1.5301 -a0
  1.5302 -a1
  1.5303 -a2
  1.5304 -)
  1.5305 -375c41e114323d3d731079fe1d402f74a9d2651f 2 0
  1.5306 -sat
  1.5307 -(error "Cannot get an unsat core unless immediately preceded by UNSAT/VALID response.")
  1.5308 -e666d5e185fdae30099fc5a288467b6b29dd2412 7 0
  1.5309 -unsat
  1.5310 -(
  1.5311 -a170
  1.5312 -a176
  1.5313 -a89
  1.5314 -a4
  1.5315 -)
  1.5316 -38448f458cf85259745f3f72f0ef85742b6132c3 7 0
  1.5317 -unsat
  1.5318 -(
  1.5319 -a0
  1.5320 -a1
  1.5321 -a2
  1.5322 -a3
  1.5323 -)
  1.5324 -3e59b0c055a1eaf3a70cee6780566e0c51865d4c 2 0
  1.5325 -sat
  1.5326 -(error "Cannot get an unsat core unless immediately preceded by UNSAT/VALID response.")
  1.5327 -40fc07c6890b8180980355c66bcf18270b94dbe2 5 0
  1.5328 -unsat
  1.5329 -(
  1.5330 -a0
  1.5331 -a2
  1.5332 -)
  1.5333 -a0984a525fc9fe1f8886060622bc7f06810aa427 2 0
  1.5334 -sat
  1.5335 -(error "Cannot get an unsat core unless immediately preceded by UNSAT/VALID response.")
  1.5336 -bdd84922010fb8a29483543e42719deb8169a21d 2 0
  1.5337 -sat
  1.5338 -(error "line 14 column 10: proof is not available")
  1.5339 -5229e4ae9267447d5281e256ba94b22471594333 2 0
  1.5340 -sat
  1.5341 -(error "line 15 column 10: proof is not available")
  1.5342 -9931ad6cacee040172b5200df33d2ff766d9ab3f 2 0
  1.5343 -sat
  1.5344 -(error "line 14 column 10: proof is not available")
  1.5345 -24fee7a6227ca691697261bdf9710f47f3306cf4 2 0
  1.5346 -sat
  1.5347 -(error "line 13 column 10: proof is not available")
  1.5348 -f5ea14decc68f09b91c21ca192729ed973297ac3 2 0
  1.5349 -sat
  1.5350 -(error "line 10 column 10: proof is not available")
  1.5351 -c2358f1bb12beb27e84bf6b9d4edbd4a7ce4c606 2 0
  1.5352 -sat
  1.5353 -(error "line 20 column 10: proof is not available")
  1.5354 -1e10ff820821c9cb846ff93eb2274f54845cd885 7 0
  1.5355 -unsat
  1.5356 -(
  1.5357 -a57
  1.5358 -a0
  1.5359 -a3
  1.5360 -a34
  1.5361 -)
  1.5362 -037b1f2d8c0f457a04260cddd88499544bfb551f 7 0
  1.5363 -unsat
  1.5364 -(
  1.5365 -a0
  1.5366 -a1
  1.5367 -a2
  1.5368 -a3
  1.5369 -)
  1.5370 -9f1937e419764d5c93a8821ef6d0e32a40427cf1 2 0
  1.5371 -unknown
  1.5372 -(error "Cannot get an unsat core unless immediately preceded by UNSAT/VALID response.")
  1.5373 -7eaf5e7924f7478914e32e3781267cee9333ddd4 2 0
  1.5374 -unknown
  1.5375 -(error "Cannot get an unsat core unless immediately preceded by UNSAT/VALID response.")
  1.5376  1c2b6530334930f2f4f6e0d6b73f1d249b6c5fd8 23 0
  1.5377  unsat
  1.5378  ((set-logic AUFLIA)
  1.5379 @@ -7298,147 +4603,6 @@
  1.5380  (let ((@x72 (mp (asserted $x38) (trans (monotonicity @x55 (= $x38 $x56)) @x69 (= $x38 $x59)) $x59)))
  1.5381  ((_ th-lemma arith farkas -1 -1 1) @x72 @x453 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x532) $x513)) @x459 $x513) false)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
  1.5382  
  1.5383 -49c385b161a0c500f84c45f85272a8ec9574fef4 126 0
  1.5384 -unsat
  1.5385 -((set-logic AUFLIA)
  1.5386 -(proof
  1.5387 -(let ((?x29 (of_nat$ x$)))
  1.5388 -(let ((?x30 (* 2 ?x29)))
  1.5389 -(let ((?x31 (nat$ ?x30)))
  1.5390 -(let ((?x212 (of_nat$ ?x31)))
  1.5391 -(let ((?x532 (* (- 1) ?x212)))
  1.5392 -(let ((?x533 (+ ?x30 ?x532)))
  1.5393 -(let (($x513 (<= ?x533 0)))
  1.5394 -(let (($x531 (= ?x533 0)))
  1.5395 -(let (($x193 (>= ?x29 0)))
  1.5396 -(let (($x487 (>= ?x212 1)))
  1.5397 -(let (($x485 (= ?x212 1)))
  1.5398 -(let ((?x33 (nat$ 1)))
  1.5399 -(let ((?x504 (of_nat$ ?x33)))
  1.5400 -(let (($x505 (= ?x504 1)))
  1.5401 -(let (($x546 (forall ((?v0 Int) )(! (let ((?x49 (nat$ ?v0)))
  1.5402 -(let ((?x50 (of_nat$ ?x49)))
  1.5403 -(let (($x51 (= ?x50 ?v0)))
  1.5404 -(let (($x64 (>= ?v0 0)))
  1.5405 -(let (($x65 (not $x64)))
  1.5406 -(or $x65 $x51)))))) :pattern ( (nat$ ?v0) ) :qid k!10))
  1.5407 -))
  1.5408 -(let (($x71 (forall ((?v0 Int) )(! (let ((?x49 (nat$ ?v0)))
  1.5409 -(let ((?x50 (of_nat$ ?x49)))
  1.5410 -(let (($x51 (= ?x50 ?v0)))
  1.5411 -(let (($x64 (>= ?v0 0)))
  1.5412 -(let (($x65 (not $x64)))
  1.5413 -(or $x65 $x51)))))) :qid k!10))
  1.5414 -))
  1.5415 -(let ((?x49 (nat$ ?0)))
  1.5416 -(let ((?x50 (of_nat$ ?x49)))
  1.5417 -(let (($x51 (= ?x50 ?0)))
  1.5418 -(let (($x64 (>= ?0 0)))
  1.5419 -(let (($x65 (not $x64)))
  1.5420 -(let (($x68 (or $x65 $x51)))
  1.5421 -(let (($x53 (forall ((?v0 Int) )(! (let ((?x49 (nat$ ?v0)))
  1.5422 -(let ((?x50 (of_nat$ ?x49)))
  1.5423 -(let (($x51 (= ?x50 ?v0)))
  1.5424 -(let (($x48 (<= 0 ?v0)))
  1.5425 -(=> $x48 $x51))))) :qid k!10))
  1.5426 -))
  1.5427 -(let (($x59 (forall ((?v0 Int) )(! (let ((?x49 (nat$ ?v0)))
  1.5428 -(let ((?x50 (of_nat$ ?x49)))
  1.5429 -(let (($x51 (= ?x50 ?v0)))
  1.5430 -(or (not (<= 0 ?v0)) $x51)))) :qid k!10))
  1.5431 -))
  1.5432 -(let ((@x67 (monotonicity (rewrite (= (<= 0 ?0) $x64)) (= (not (<= 0 ?0)) $x65))))
  1.5433 -(let ((@x73 (quant-intro (monotonicity @x67 (= (or (not (<= 0 ?0)) $x51) $x68)) (= $x59 $x71))))
  1.5434 -(let ((@x58 (rewrite (= (=> (<= 0 ?0) $x51) (or (not (<= 0 ?0)) $x51)))))
  1.5435 -(let ((@x76 (mp (asserted $x53) (trans (quant-intro @x58 (= $x53 $x59)) @x73 (= $x53 $x71)) $x71)))
  1.5436 -(let ((@x551 (mp (mp~ @x76 (nnf-pos (refl (~ $x68 $x68)) (~ $x71 $x71)) $x71) (quant-intro (refl (= $x68 $x68)) (= $x71 $x546)) $x546)))
  1.5437 -(let (($x526 (not $x546)))
  1.5438 -(let (($x489 (or $x526 $x505)))
  1.5439 -(let ((@x506 (rewrite (= (>= 1 0) true))))
  1.5440 -(let ((@x219 (trans (monotonicity @x506 (= (not (>= 1 0)) (not true))) (rewrite (= (not true) false)) (= (not (>= 1 0)) false))))
  1.5441 -(let ((@x223 (monotonicity @x219 (= (or (not (>= 1 0)) $x505) (or false $x505)))))
  1.5442 -(let ((@x503 (trans @x223 (rewrite (= (or false $x505) $x505)) (= (or (not (>= 1 0)) $x505) $x505))))
  1.5443 -(let ((@x493 (monotonicity @x503 (= (or $x526 (or (not (>= 1 0)) $x505)) $x489))))
  1.5444 -(let ((@x496 (trans @x493 (rewrite (= $x489 $x489)) (= (or $x526 (or (not (>= 1 0)) $x505)) $x489))))
  1.5445 -(let ((@x497 (mp ((_ quant-inst 1) (or $x526 (or (not (>= 1 0)) $x505))) @x496 $x489)))
  1.5446 -(let (($x34 (= ?x31 ?x33)))
  1.5447 -(let ((@x42 (mp (asserted (not (not $x34))) (rewrite (= (not (not $x34)) $x34)) $x34)))
  1.5448 -(let ((@x356 (trans (monotonicity @x42 (= ?x212 ?x504)) (unit-resolution @x497 @x551 $x505) $x485)))
  1.5449 -(let ((@x371 (unit-resolution ((_ th-lemma arith farkas 1 1) (or (not $x487) (not (<= ?x212 0)))) (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x485) $x487)) @x356 $x487) (not (<= ?x212 0)))))
  1.5450 -(let ((@x374 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not (= ?x212 0)) (<= ?x212 0))) @x371 (not (= ?x212 0)))))
  1.5451 -(let (($x515 (= ?x212 0)))
  1.5452 -(let (($x517 (or $x193 $x515)))
  1.5453 -(let (($x552 (forall ((?v0 Int) )(! (let ((?x49 (nat$ ?v0)))
  1.5454 -(let ((?x50 (of_nat$ ?x49)))
  1.5455 -(let (($x78 (= ?x50 0)))
  1.5456 -(let (($x64 (>= ?v0 0)))
  1.5457 -(or $x64 $x78))))) :pattern ( (nat$ ?v0) ) :qid k!11))
  1.5458 -))
  1.5459 -(let (($x101 (forall ((?v0 Int) )(! (let ((?x49 (nat$ ?v0)))
  1.5460 -(let ((?x50 (of_nat$ ?x49)))
  1.5461 -(let (($x78 (= ?x50 0)))
  1.5462 -(let (($x64 (>= ?v0 0)))
  1.5463 -(or $x64 $x78))))) :qid k!11))
  1.5464 -))
  1.5465 -(let ((@x556 (quant-intro (refl (= (or $x64 (= ?x50 0)) (or $x64 (= ?x50 0)))) (= $x101 $x552))))
  1.5466 -(let ((@x120 (nnf-pos (refl (~ (or $x64 (= ?x50 0)) (or $x64 (= ?x50 0)))) (~ $x101 $x101))))
  1.5467 -(let (($x80 (forall ((?v0 Int) )(! (let ((?x49 (nat$ ?v0)))
  1.5468 -(let ((?x50 (of_nat$ ?x49)))
  1.5469 -(let (($x78 (= ?x50 0)))
  1.5470 -(let (($x77 (< ?v0 0)))
  1.5471 -(=> $x77 $x78))))) :qid k!11))
  1.5472 -))
  1.5473 -(let (($x86 (forall ((?v0 Int) )(! (let ((?x49 (nat$ ?v0)))
  1.5474 -(let ((?x50 (of_nat$ ?x49)))
  1.5475 -(let (($x78 (= ?x50 0)))
  1.5476 -(let (($x77 (< ?v0 0)))
  1.5477 -(let (($x82 (not $x77)))
  1.5478 -(or $x82 $x78)))))) :qid k!11))
  1.5479 -))
  1.5480 -(let (($x78 (= ?x50 0)))
  1.5481 -(let (($x98 (or $x64 $x78)))
  1.5482 -(let (($x77 (< ?0 0)))
  1.5483 -(let (($x82 (not $x77)))
  1.5484 -(let (($x83 (or $x82 $x78)))
  1.5485 -(let ((@x97 (trans (monotonicity (rewrite (= $x77 $x65)) (= $x82 (not $x65))) (rewrite (= (not $x65) $x64)) (= $x82 $x64))))
  1.5486 -(let ((@x105 (trans (quant-intro (rewrite (= (=> $x77 $x78) $x83)) (= $x80 $x86)) (quant-intro (monotonicity @x97 (= $x83 $x98)) (= $x86 $x101)) (= $x80 $x101))))
  1.5487 -(let ((@x557 (mp (mp~ (mp (asserted $x80) @x105 $x101) @x120 $x101) @x556 $x552)))
  1.5488 -(let (($x156 (not $x552)))
  1.5489 -(let (($x520 (or $x156 $x193 $x515)))
  1.5490 -(let ((@x530 (rewrite (= (>= ?x30 0) $x193))))
  1.5491 -(let ((@x523 (monotonicity (monotonicity @x530 (= (or (>= ?x30 0) $x515) $x517)) (= (or $x156 (or (>= ?x30 0) $x515)) (or $x156 $x517)))))
  1.5492 -(let ((@x215 (trans @x523 (rewrite (= (or $x156 $x517) $x520)) (= (or $x156 (or (>= ?x30 0) $x515)) $x520))))
  1.5493 -(let ((@x229 (mp ((_ quant-inst (* 2 ?x29)) (or $x156 (or (>= ?x30 0) $x515))) @x215 $x520)))
  1.5494 -(let (($x185 (not $x193)))
  1.5495 -(let (($x534 (or $x185 $x531)))
  1.5496 -(let (($x188 (or $x526 $x185 $x531)))
  1.5497 -(let (($x213 (= ?x212 ?x30)))
  1.5498 -(let (($x208 (>= ?x30 0)))
  1.5499 -(let (($x209 (not $x208)))
  1.5500 -(let (($x214 (or $x209 $x213)))
  1.5501 -(let (($x189 (or $x526 $x214)))
  1.5502 -(let ((@x536 (monotonicity (monotonicity @x530 (= $x209 $x185)) (rewrite (= $x213 $x531)) (= $x214 $x534))))
  1.5503 -(let ((@x175 (trans (monotonicity @x536 (= $x189 (or $x526 $x534))) (rewrite (= (or $x526 $x534) $x188)) (= $x189 $x188))))
  1.5504 -(let ((@x176 (mp ((_ quant-inst (* 2 ?x29)) $x189) @x175 $x188)))
  1.5505 -(let ((@x470 (unit-resolution (unit-resolution @x176 @x551 $x534) (unit-resolution (unit-resolution @x229 @x557 $x517) @x374 $x193) $x531)))
  1.5506 -(let (($x514 (>= ?x533 0)))
  1.5507 -(let (($x486 (<= ?x212 1)))
  1.5508 -((_ th-lemma arith gcd-test -1/2 -1/2 -1/2 -1/2) (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x485) $x487)) @x356 $x487) (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x485) $x486)) @x356 $x486) (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x531) $x514)) @x470 $x514) (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x531) $x513)) @x470 $x513) false))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
  1.5509 -
  1.5510 -b2e870cca8f9ff26b649a7a2c6910fff2183e779 6 0
  1.5511 -unsat
  1.5512 -(
  1.5513 -a0
  1.5514 -a259
  1.5515 -a260
  1.5516 -)
  1.5517 -0df05630a046f3db612e71e7557cbf94daec55ea 6 0
  1.5518 -unsat
  1.5519 -(
  1.5520 -a0
  1.5521 -a2
  1.5522 -a3
  1.5523 -)
  1.5524  5d99a07ea08069a53b86d7f3330815887331e82a 145 0
  1.5525  unsat
  1.5526  ((set-logic AUFLIA)
  1.5527 @@ -7585,12 +4749,6 @@
  1.5528  (let ((@x538 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x612) $x595)) (unit-resolution (unit-resolution @x594 @x631 $x616) @x545 $x612) $x595)))
  1.5529  ((_ th-lemma arith farkas 1 -1 -1 1) (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x559) $x557)) @x539 $x557) @x106 @x538 @x457 false)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
  1.5530  
  1.5531 -09cc14017050c484625b3e0c3d671ae32b66851f 5 0
  1.5532 -unsat
  1.5533 -(
  1.5534 -a0
  1.5535 -a1
  1.5536 -)
  1.5537  7d4feac3284b531c122b21d3a2a25c87f1e3b93b 78 0
  1.5538  unsat
  1.5539  ((set-logic AUFLIA)
  1.5540 @@ -7670,35 +4828,6 @@
  1.5541  (let ((@x257 (unit-resolution ((_ th-lemma arith farkas 1 1) (or $x578 $x254)) (unit-resolution @x576 @x81 @x593 $x255) $x578)))
  1.5542  ((_ th-lemma arith farkas 1 1 1) @x257 @x198 @x566 false)))))))))))))))))))))))))))))))))))))))))))))))))))))))
  1.5543  
  1.5544 -74a1c0d44cbd0147017229e79a08e8dfcfe4eee2 7 0
  1.5545 -unsat
  1.5546 -(
  1.5547 -a2
  1.5548 -a189
  1.5549 -a138
  1.5550 -a7
  1.5551 -)
  1.5552 -1a98e6860e90be637d16c2d7127e7141065068af 5 0
  1.5553 -unsat
  1.5554 -(
  1.5555 -a0
  1.5556 -a1
  1.5557 -)
  1.5558 -14f8ad1280ad869e9c8ef4e6a613ceb808bfd5ab 7 0
  1.5559 -unsat
  1.5560 -(
  1.5561 -a0
  1.5562 -a1
  1.5563 -a2
  1.5564 -a4
  1.5565 -)
  1.5566 -15ec6864dfa5b932b5e4bed685e55140b1a81105 6 0
  1.5567 -unsat
  1.5568 -(
  1.5569 -a0
  1.5570 -a1
  1.5571 -a3
  1.5572 -)
  1.5573  ce85402875b83dc2f06a381810d29a2061933b9f 312 0
  1.5574  unsat
  1.5575  ((set-logic AUFLIA)
  1.5576 @@ -8012,95 +5141,520 @@
  1.5577  (let ((@x133 (not-or-elim (mp (asserted $x96) @x129 $x125) (not (>= ?x89 1)))))
  1.5578  ((_ th-lemma arith farkas -4 1 1) @x133 (unit-resolution (def-axiom (or $x357 $x687)) @x572 $x687) (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x597) $x574)) @x532 $x574) false)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
  1.5579  
  1.5580 -9e3a7cb6b1687db90ac27c1322f4180e0715e89a 7 0
  1.5581 +5e90e9139eb4e9a7c2678bca8dda6cda05861f4c 23 0
  1.5582 +unsat
  1.5583 +((set-logic AUFLIA)
  1.5584 +(proof
  1.5585 +(let (($x40 (= x$ a$)))
  1.5586 +(let ((?x36 (pair$ x$ y$)))
  1.5587 +(let ((?x37 (fst$ ?x36)))
  1.5588 +(let (($x39 (= ?x37 a$)))
  1.5589 +(let ((@x50 (monotonicity (rewrite (= (=> $x39 $x40) (or (not $x39) $x40))) (= (not (=> $x39 $x40)) (not (or (not $x39) $x40))))))
  1.5590 +(let ((@x51 (not-or-elim (mp (asserted (not (=> $x39 $x40))) @x50 (not (or (not $x39) $x40))) $x39)))
  1.5591 +(let (($x56 (= ?x37 x$)))
  1.5592 +(let (($x478 (forall ((?v0 A$) (?v1 B$) )(! (= (fst$ (pair$ ?v0 ?v1)) ?v0) :pattern ( (pair$ ?v0 ?v1) ) :qid k!12))
  1.5593 +))
  1.5594 +(let (($x32 (forall ((?v0 A$) (?v1 B$) )(! (= (fst$ (pair$ ?v0 ?v1)) ?v0) :qid k!12))
  1.5595 +))
  1.5596 +(let (($x31 (= (fst$ (pair$ ?1 ?0)) ?1)))
  1.5597 +(let ((@x55 (mp~ (asserted $x32) (nnf-pos (refl (~ $x31 $x31)) (~ $x32 $x32)) $x32)))
  1.5598 +(let ((@x483 (mp @x55 (quant-intro (refl (= $x31 $x31)) (= $x32 $x478)) $x478)))
  1.5599 +(let (($x62 (or (not $x478) $x56)))
  1.5600 +(let ((@x149 ((_ quant-inst x$ y$) $x62)))
  1.5601 +(let ((@x150 (trans (symm (unit-resolution @x149 @x483 $x56) (= x$ ?x37)) @x51 $x40)))
  1.5602 +(let ((@x54 (not-or-elim (mp (asserted (not (=> $x39 $x40))) @x50 (not (or (not $x39) $x40))) (not $x40))))
  1.5603 +(unit-resolution @x54 @x150 false)))))))))))))))))))
  1.5604 +
  1.5605 +53d3d89ffb6e574b15fcea58a111b4eecba9beb5 42 0
  1.5606  unsat
  1.5607 -(
  1.5608 -a1
  1.5609 -a169
  1.5610 -a170
  1.5611 -a94
  1.5612 -)
  1.5613 -0f29eff8af0baceae4a69ea0ceff00e3a8c44aaf 7 0
  1.5614 +((set-logic AUFLIA)
  1.5615 +(proof
  1.5616 +(let ((?x59 (snd$a p2$)))
  1.5617 +(let ((?x58 (fst$a p1$)))
  1.5618 +(let (($x60 (= ?x58 ?x59)))
  1.5619 +(let ((?x55 (pair$ y$ x$)))
  1.5620 +(let (($x56 (= p2$ ?x55)))
  1.5621 +(let ((?x52 (pair$a x$ y$)))
  1.5622 +(let (($x53 (= p1$ ?x52)))
  1.5623 +(let (($x57 (and $x53 $x56)))
  1.5624 +(let ((@x70 (monotonicity (rewrite (= (=> $x57 $x60) (or (not $x57) $x60))) (= (not (=> $x57 $x60)) (not (or (not $x57) $x60))))))
  1.5625 +(let ((@x71 (not-or-elim (mp (asserted (not (=> $x57 $x60))) @x70 (not (or (not $x57) $x60))) $x57)))
  1.5626 +(let ((@x74 (and-elim @x71 $x56)))
  1.5627 +(let ((@x504 (symm (monotonicity @x74 (= ?x59 (snd$a ?x55))) (= (snd$a ?x55) ?x59))))
  1.5628 +(let ((?x100 (snd$a ?x55)))
  1.5629 +(let (($x185 (= ?x100 x$)))
  1.5630 +(let (($x534 (forall ((?v0 B$) (?v1 A$) )(! (= (snd$a (pair$ ?v0 ?v1)) ?v1) :pattern ( (pair$ ?v0 ?v1) ) :qid k!21))
  1.5631 +))
  1.5632 +(let (($x47 (forall ((?v0 B$) (?v1 A$) )(! (= (snd$a (pair$ ?v0 ?v1)) ?v1) :qid k!21))
  1.5633 +))
  1.5634 +(let (($x46 (= (snd$a (pair$ ?1 ?0)) ?0)))
  1.5635 +(let ((@x96 (mp~ (asserted $x47) (nnf-pos (refl (~ $x46 $x46)) (~ $x47 $x47)) $x47)))
  1.5636 +(let ((@x539 (mp @x96 (quant-intro (refl (= $x46 $x46)) (= $x47 $x534)) $x534)))
  1.5637 +(let (($x190 (or (not $x534) $x185)))
  1.5638 +(let ((@x191 ((_ quant-inst y$ x$) $x190)))
  1.5639 +(let ((?x187 (fst$a ?x52)))
  1.5640 +(let (($x188 (= ?x187 x$)))
  1.5641 +(let (($x522 (forall ((?v0 A$) (?v1 B$) )(! (= (fst$a (pair$a ?v0 ?v1)) ?v0) :pattern ( (pair$a ?v0 ?v1) ) :qid k!19))
  1.5642 +))
  1.5643 +(let (($x39 (forall ((?v0 A$) (?v1 B$) )(! (= (fst$a (pair$a ?v0 ?v1)) ?v0) :qid k!19))
  1.5644 +))
  1.5645 +(let (($x38 (= (fst$a (pair$a ?1 ?0)) ?1)))
  1.5646 +(let ((@x90 (mp~ (asserted $x39) (nnf-pos (refl (~ $x38 $x38)) (~ $x39 $x39)) $x39)))
  1.5647 +(let ((@x527 (mp @x90 (quant-intro (refl (= $x38 $x38)) (= $x39 $x522)) $x522)))
  1.5648 +(let (($x162 (or (not $x522) $x188)))
  1.5649 +(let ((@x292 ((_ quant-inst x$ y$) $x162)))
  1.5650 +(let ((@x505 (trans (monotonicity (and-elim @x71 $x53) (= ?x58 ?x187)) (unit-resolution @x292 @x527 $x188) (= ?x58 x$))))
  1.5651 +(let ((@x489 (trans @x505 (symm (unit-resolution @x191 @x539 $x185) (= x$ ?x100)) (= ?x58 ?x100))))
  1.5652 +(let ((@x76 (not-or-elim (mp (asserted (not (=> $x57 $x60))) @x70 (not (or (not $x57) $x60))) (not $x60))))
  1.5653 +(unit-resolution @x76 (trans @x489 @x504 $x60) false))))))))))))))))))))))))))))))))))))
  1.5654 +
  1.5655 +541ab286f481dab3994e7cef5aa3ab01f0d6487a 24 0
  1.5656 +unsat
  1.5657 +((set-logic AUFLIA)
  1.5658 +(proof
  1.5659 +(let (($x29 (f$ g$ x$)))
  1.5660 +(let (($x73 (not $x29)))
  1.5661 +(let (($x65 (not (or (= $x29 (fun_app$ g$ x$)) $x29 (fun_app$ g$ x$)))))
  1.5662 +(let (($x32 (= $x29 (and (fun_app$ g$ x$) true))))
  1.5663 +(let (($x37 (not (or $x32 (or (= $x29 true) (= (fun_app$ g$ x$) true))))))
  1.5664 +(let (($x30 (fun_app$ g$ x$)))
  1.5665 +(let (($x44 (= $x29 $x30)))
  1.5666 +(let (($x56 (or $x44 (or $x29 $x30))))
  1.5667 +(let ((@x67 (monotonicity (rewrite (= $x56 (or $x44 $x29 $x30))) (= (not $x56) $x65))))
  1.5668 +(let ((@x55 (monotonicity (rewrite (= (= $x29 true) $x29)) (rewrite (= (= $x30 true) $x30)) (= (or (= $x29 true) (= $x30 true)) (or $x29 $x30)))))
  1.5669 +(let ((@x43 (monotonicity (rewrite (= (and $x30 true) $x30)) (= $x32 (= $x29 $x30)))))
  1.5670 +(let ((@x58 (monotonicity (trans @x43 (rewrite (= (= $x29 $x30) $x44)) (= $x32 $x44)) @x55 (= (or $x32 (or (= $x29 true) (= $x30 true))) $x56))))
  1.5671 +(let ((@x69 (trans (monotonicity @x58 (= $x37 (not $x56))) @x67 (= $x37 $x65))))
  1.5672 +(let ((@x70 (mp (asserted $x37) @x69 $x65)))
  1.5673 +(let ((@x87 (monotonicity (iff-false (not-or-elim @x70 (not $x30)) (= $x30 false)) (= (= $x73 $x30) (= $x73 false)))))
  1.5674 +(let ((@x91 (trans @x87 (rewrite (= (= $x73 false) $x29)) (= (= $x73 $x30) $x29))))
  1.5675 +(let ((@x93 (trans @x91 (iff-false (not-or-elim @x70 $x73) (= $x29 false)) (= (= $x73 $x30) false))))
  1.5676 +(let (($x77 (= $x73 $x30)))
  1.5677 +(let ((@x80 (mp (not-or-elim @x70 (not $x44)) (rewrite (= (not $x44) $x77)) $x77)))
  1.5678 +(mp @x80 @x93 false))))))))))))))))))))))
  1.5679 +
  1.5680 +303e836701682600d31f180dbf7164cb66aa7e90 5 0
  1.5681  unsat
  1.5682  (
  1.5683  a0
  1.5684  a1
  1.5685 -a3
  1.5686 -a4
  1.5687  )
  1.5688 -2f309a4750090c04f284fbecb4a976eedaa46ce9 7 0
  1.5689 +b1682b5d9334f1f753211625091194aee8feeee0 5 0
  1.5690  unsat
  1.5691  (
  1.5692 -a95
  1.5693 -a173
  1.5694 -a5
  1.5695 -a179
  1.5696 +a3
  1.5697 +a2
  1.5698  )
  1.5699 -e0764188710d396d7c3d8c7ed12e92df610f3d5d 6 0
  1.5700 -unsat
  1.5701 -(
  1.5702 -a0
  1.5703 -a2
  1.5704 -a3
  1.5705 -)
  1.5706 -ff18566d8fd433a50da07b998b8d9915d4e6d38c 7 0
  1.5707 +e480713ec1d59b302d3665ef6cf6d4bde9acf881 5 0
  1.5708  unsat
  1.5709  (
  1.5710  a0
  1.5711  a1
  1.5712 -a2
  1.5713 -a3
  1.5714  )
  1.5715 -85b5e78e459667d6880efd720fc8258c1f632634 5 0
  1.5716 +32a8fd63d6c57c114d55e5b029c6c7c0a22bfc9e 5 0
  1.5717  unsat
  1.5718  (
  1.5719 +a1
  1.5720  a0
  1.5721 -a2
  1.5722  )
  1.5723 -d9da06f46916827de91e55898f12e162fc4394a9 5 0
  1.5724 +8e5b0b49054ab51d88db63de1bbe5f826bed3499 2 0
  1.5725 +sat
  1.5726 +(error "Cannot get an unsat core unless immediately preceded by UNSAT/VALID response.")
  1.5727 +0ca8132e17307584a7bf84322b4f8062f2f2c658 2 0
  1.5728 +sat
  1.5729 +(error "Cannot get an unsat core unless immediately preceded by UNSAT/VALID response.")
  1.5730 +256aa6c949586ab7b008ef9578a05ed9d8811969 7 0
  1.5731  unsat
  1.5732  (
  1.5733 -a0
  1.5734 -a2
  1.5735 +a73
  1.5736 +a77
  1.5737 +a97
  1.5738 +a98
  1.5739  )
  1.5740 -0c5b279548a729dbbc42ad3281942c493cea61a9 2 0
  1.5741 -unknown
  1.5742 -(error "Cannot get an unsat core unless immediately preceded by UNSAT/VALID response.")
  1.5743 -f38355a9ae0344ba7fe2a48aa18389448f4b9cd2 2 0
  1.5744 -unknown
  1.5745 -(error "Cannot get an unsat core unless immediately preceded by UNSAT/VALID response.")
  1.5746 -bbdbbe6715d50b1bf20ff06d778334d19ea80167 5 0
  1.5747 +6b21e8fbdb4a81ae46f60a001dcc2f2cfa2bb055 5 0
  1.5748  unsat
  1.5749  (
  1.5750  a0
  1.5751  a1
  1.5752  )
  1.5753 -933c14ef800372ac93564be5a3ef60dc447e5229 5 0
  1.5754 +9aca5c922a21ee8af6f8c447405fbb253f6c0e3d 2 0
  1.5755 +sat
  1.5756 +(error "Cannot get an unsat core unless immediately preceded by UNSAT/VALID response.")
  1.5757 +bbd5549a4514d443e2da4c190a400b7bb7fad211 8 0
  1.5758 +unsat
  1.5759 +(
  1.5760 +a2
  1.5761 +a1
  1.5762 +a6
  1.5763 +a5
  1.5764 +a4
  1.5765 +)
  1.5766 +5d3180378cd70f7c6a038fcc3edc01a1f8acce33 8 0
  1.5767  unsat
  1.5768  (
  1.5769  a2
  1.5770 +a1
  1.5771 +a5
  1.5772 +a4
  1.5773  a3
  1.5774  )
  1.5775 -b2b6ec8367faf6099e2eb37a31144e974fe80a4d 5 0
  1.5776 +b697e9e1f1623fa76652384cbd62f909744566cf 2 0
  1.5777 +sat
  1.5778 +(error "Cannot get an unsat core unless immediately preceded by UNSAT/VALID response.")
  1.5779 +93d4ee1f0414a974916a0daf16114650cca034a6 2 0
  1.5780 +sat
  1.5781 +(error "Cannot get an unsat core unless immediately preceded by UNSAT/VALID response.")
  1.5782 +3e0697d22f6063be90ed182054dfac4e59e65728 2 0
  1.5783 +sat
  1.5784 +(error "Cannot get an unsat core unless immediately preceded by UNSAT/VALID response.")
  1.5785 +132bc98466cbf8cf9a94f930b1fd690c493fcf96 100 0
  1.5786 +unsat
  1.5787 +(
  1.5788 +a93
  1.5789 +a40
  1.5790 +a42
  1.5791 +a79
  1.5792 +a45
  1.5793 +a69
  1.5794 +a154
  1.5795 +a76
  1.5796 +a32
  1.5797 +a62
  1.5798 +a15
  1.5799 +a17
  1.5800 +a39
  1.5801 +a41
  1.5802 +a16
  1.5803 +a50
  1.5804 +a23
  1.5805 +a140
  1.5806 +a31
  1.5807 +a29
  1.5808 +a139
  1.5809 +a70
  1.5810 +a128
  1.5811 +a143
  1.5812 +a7
  1.5813 +a30
  1.5814 +a38
  1.5815 +a27
  1.5816 +a35
  1.5817 +a135
  1.5818 +a129
  1.5819 +a151
  1.5820 +a148
  1.5821 +a36
  1.5822 +a25
  1.5823 +a33
  1.5824 +a182
  1.5825 +a144
  1.5826 +a138
  1.5827 +a159
  1.5828 +a113
  1.5829 +a75
  1.5830 +a117
  1.5831 +a133
  1.5832 +a158
  1.5833 +a137
  1.5834 +a37
  1.5835 +a147
  1.5836 +a155
  1.5837 +a46
  1.5838 +a61
  1.5839 +a13
  1.5840 +a48
  1.5841 +a124
  1.5842 +a18
  1.5843 +a43
  1.5844 +a44
  1.5845 +a14
  1.5846 +a47
  1.5847 +a26
  1.5848 +a34
  1.5849 +a116
  1.5850 +a149
  1.5851 +a120
  1.5852 +a73
  1.5853 +a130
  1.5854 +a156
  1.5855 +a142
  1.5856 +a118
  1.5857 +a127
  1.5858 +a150
  1.5859 +a96
  1.5860 +a152
  1.5861 +a121
  1.5862 +a160
  1.5863 +a49
  1.5864 +a24
  1.5865 +a8
  1.5866 +a136
  1.5867 +a28
  1.5868 +a114
  1.5869 +a72
  1.5870 +a141
  1.5871 +a162
  1.5872 +a122
  1.5873 +a145
  1.5874 +a146
  1.5875 +a74
  1.5876 +a184
  1.5877 +a153
  1.5878 +a169
  1.5879 +a119
  1.5880 +a183
  1.5881 +a157
  1.5882 +a161
  1.5883 +a115
  1.5884 +a71
  1.5885 +)
  1.5886 +c3d7cbf937c8a42adee3dea055fc94c0d5fa9f09 2 0
  1.5887 +sat
  1.5888 +(error "Cannot get an unsat core unless immediately preceded by UNSAT/VALID response.")
  1.5889 +bdab860f909efa4b33522c132777f2e16f390f0d 97 0
  1.5890 +unsat
  1.5891 +(
  1.5892 +a22
  1.5893 +a15
  1.5894 +a45
  1.5895 +a16
  1.5896 +a24
  1.5897 +a46
  1.5898 +a26
  1.5899 +a65
  1.5900 +a18
  1.5901 +a62
  1.5902 +a71
  1.5903 +a5
  1.5904 +a25
  1.5905 +a27
  1.5906 +a68
  1.5907 +a83
  1.5908 +a51
  1.5909 +a87
  1.5910 +a14
  1.5911 +a2
  1.5912 +a13
  1.5913 +a66
  1.5914 +a21
  1.5915 +a64
  1.5916 +a63
  1.5917 +a31
  1.5918 +a32
  1.5919 +a79
  1.5920 +a78
  1.5921 +a73
  1.5922 +a30
  1.5923 +a81
  1.5924 +a92
  1.5925 +a41
  1.5926 +a52
  1.5927 +a42
  1.5928 +a93
  1.5929 +a90
  1.5930 +a39
  1.5931 +a80
  1.5932 +a69
  1.5933 +a19
  1.5934 +a3
  1.5935 +a29
  1.5936 +a4
  1.5937 +a70
  1.5938 +a20
  1.5939 +a72
  1.5940 +a1
  1.5941 +a23
  1.5942 +a11
  1.5943 +a60
  1.5944 +a74
  1.5945 +a10
  1.5946 +a59
  1.5947 +a76
  1.5948 +a77
  1.5949 +a28
  1.5950 +a89
  1.5951 +a38
  1.5952 +a55
  1.5953 +a6
  1.5954 +a43
  1.5955 +a94
  1.5956 +a37
  1.5957 +a88
  1.5958 +a17
  1.5959 +a86
  1.5960 +a35
  1.5961 +a36
  1.5962 +a58
  1.5963 +a9
  1.5964 +a50
  1.5965 +a67
  1.5966 +a7
  1.5967 +a56
  1.5968 +a84
  1.5969 +a85
  1.5970 +a34
  1.5971 +a57
  1.5972 +a8
  1.5973 +a33
  1.5974 +a61
  1.5975 +a12
  1.5976 +a53
  1.5977 +a91
  1.5978 +a40
  1.5979 +a54
  1.5980 +a82
  1.5981 +a96
  1.5982 +a44
  1.5983 +a95
  1.5984 +a97
  1.5985 +a75
  1.5986 +)
  1.5987 +7b0531750ec3111a052894242409998ff73f0d8e 2 0
  1.5988 +sat
  1.5989 +(error "Cannot get an unsat core unless immediately preceded by UNSAT/VALID response.")
  1.5990 +0c77f4fcdf3c7cc2416cd1c79a1e4ffa770ccdd9 2 0
  1.5991 +sat
  1.5992 +(error "Cannot get an unsat core unless immediately preceded by UNSAT/VALID response.")
  1.5993 +b5cac27259e12d93b0f91244374657bda3651301 2 0
  1.5994 +sat
  1.5995 +(error "Cannot get an unsat core unless immediately preceded by UNSAT/VALID response.")
  1.5996 +8f371242ee130c5b7f7049f82612acd4b70ba898 2 0
  1.5997 +sat
  1.5998 +(error "Cannot get an unsat core unless immediately preceded by UNSAT/VALID response.")
  1.5999 +947377c6f6ef2e11f5ddd7a677e90d51d4d4ca09 2 0
  1.6000 +sat
  1.6001 +(error "Cannot get an unsat core unless immediately preceded by UNSAT/VALID response.")
  1.6002 +445ee9b6220decad197f092fe7e63a050fceb831 2 0
  1.6003 +sat
  1.6004 +(error "Cannot get an unsat core unless immediately preceded by UNSAT/VALID response.")
  1.6005 +51d11b605d2a9a01009f9f814fb688a96656112f 2 0
  1.6006 +sat
  1.6007 +(error "Cannot get an unsat core unless immediately preceded by UNSAT/VALID response.")
  1.6008 +425ffc08f16b7f80d0cbe2998f660aa2f786acbf 2 0
  1.6009 +sat
  1.6010 +(error "Cannot get an unsat core unless immediately preceded by UNSAT/VALID response.")
  1.6011 +1db6aab13ff3e14aca462e31d60bcc91d1d91ba4 2 0
  1.6012 +sat
  1.6013 +(error "Cannot get an unsat core unless immediately preceded by UNSAT/VALID response.")
  1.6014 +a67d9819b8a80d46a99da882dbc773b1daa04f46 2 0
  1.6015 +sat
  1.6016 +(error "Cannot get an unsat core unless immediately preceded by UNSAT/VALID response.")
  1.6017 +57ced68ab36f2fcdb9d24788830e8652a2d56817 2 0
  1.6018 +sat
  1.6019 +(error "Cannot get an unsat core unless immediately preceded by UNSAT/VALID response.")
  1.6020 +f6c7d41773bef5bed37f5e86a6fa287578c04f2d 90 0
  1.6021 +unsat
  1.6022 +(
  1.6023 +a15
  1.6024 +a39
  1.6025 +a13
  1.6026 +a32
  1.6027 +a66
  1.6028 +a89
  1.6029 +a54
  1.6030 +a18
  1.6031 +a41
  1.6032 +a65
  1.6033 +a75
  1.6034 +a48
  1.6035 +a23
  1.6036 +a20
  1.6037 +a42
  1.6038 +a63
  1.6039 +a55
  1.6040 +a11
  1.6041 +a24
  1.6042 +a88
  1.6043 +a51
  1.6044 +a12
  1.6045 +a31
  1.6046 +a25
  1.6047 +a64
  1.6048 +a76
  1.6049 +a5
  1.6050 +a93
  1.6051 +a83
  1.6052 +a72
  1.6053 +a22
  1.6054 +a43
  1.6055 +a26
  1.6056 +a28
  1.6057 +a44
  1.6058 +a1
  1.6059 +a36
  1.6060 +a38
  1.6061 +a50
  1.6062 +a49
  1.6063 +a62
  1.6064 +a87
  1.6065 +a70
  1.6066 +a77
  1.6067 +a34
  1.6068 +a84
  1.6069 +a60
  1.6070 +a40
  1.6071 +a3
  1.6072 +a52
  1.6073 +a85
  1.6074 +a35
  1.6075 +a37
  1.6076 +a46
  1.6077 +a45
  1.6078 +a47
  1.6079 +a33
  1.6080 +a27
  1.6081 +a29
  1.6082 +a86
  1.6083 +a56
  1.6084 +a10
  1.6085 +a61
  1.6086 +a91
  1.6087 +a9
  1.6088 +a80
  1.6089 +a90
  1.6090 +a58
  1.6091 +a8
  1.6092 +a79
  1.6093 +a92
  1.6094 +a59
  1.6095 +a78
  1.6096 +a2
  1.6097 +a67
  1.6098 +a53
  1.6099 +a4
  1.6100 +a69
  1.6101 +a21
  1.6102 +a71
  1.6103 +a68
  1.6104 +a17
  1.6105 +a6
  1.6106 +a14
  1.6107 +a57
  1.6108 +a7
  1.6109 +a30
  1.6110 +)
  1.6111 +ac0ffc3882f6c09968ced3592e058a6fb86a87c7 2 0
  1.6112 +sat
  1.6113 +(error "Cannot get an unsat core unless immediately preceded by UNSAT/VALID response.")
  1.6114 +85bbaf5a5aa1611b4cf32fa801006fbfc15c02d7 5 0
  1.6115  unsat
  1.6116  (
  1.6117  a0
  1.6118  a1
  1.6119  )
  1.6120 -7d3ccc6fd748dc986de65f6b96355c1acc61633a 5 0
  1.6121 +926b60197ebba006da54aed0737eebccf8577396 5 0
  1.6122  unsat
  1.6123  (
  1.6124 +a1
  1.6125  a0
  1.6126 -a1
  1.6127  )
  1.6128 -502c6566fddc9f002ef331f2822f70acfc1eb0a6 2 0
  1.6129 -sat
  1.6130 -(error "Cannot get an unsat core unless immediately preceded by UNSAT/VALID response.")
  1.6131 -9a7dd691b0176ee4885324369fa4400bb78fa856 2 0
  1.6132 -sat
  1.6133 -(error "Cannot get an unsat core unless immediately preceded by UNSAT/VALID response.")
  1.6134 -5dee863399bac5f53042e3459e153dff890dd2a5 4 0
  1.6135 +700af424f8dda45d1d02de88a120ee19f4cfb835 4 0
  1.6136  unsat
  1.6137  (
  1.6138  a0
  1.6139  )
  1.6140 +5c1e9490994c9407572cee32f5d1f714ddc35898 4 0
  1.6141 +unsat
  1.6142 +(
  1.6143 +a0
  1.6144 +)