%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : PRO029^16 : TPTP v9.2.1. Released v8.1.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n002.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Jun 3 08:43:48 AM UTC 2026 % Result : Theorem 0.37s 0.64s % Output : Proof 0.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : PRO029^16 : TPTP v9.2.1. Released v8.1.0. % 0.12/0.14 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.35 % Computer : n002.cluster.edu % 0.17/0.35 % Model : x86_64 x86_64 % 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.35 % Memory : 8042.1875MB % 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.35 % CPULimit : 300 % 0.17/0.35 % WCLimit : 300 % 0.17/0.35 % DateTime : Tue Jun 2 13:11:33 EDT 2026 % 0.17/0.35 % CPUTime : % 0.28/0.51 %----Proving TH0 % 0.37/0.64 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.37/0.64 % SZS status Theorem % 0.37/0.64 % SZS output start Proof % 0.37/0.64 ( % 0.37/0.64 (declare-sort tptp.mindex 0) % 0.37/0.64 (declare-sort tptp.mworld 0) % 0.37/0.64 (declare-const tptp.mactual tptp.mworld) % 0.37/0.64 (declare-const tptp.mrel (-> tptp.mindex tptp.mworld tptp.mworld Bool)) % 0.37/0.64 (declare-const tptp.charge (-> tptp.mworld Bool)) % 0.37/0.64 (declare-const tptp.paid (-> tptp.mworld Bool)) % 0.37/0.64 (declare-const tptp.called (-> tptp.mworld Bool)) % 0.37/0.64 (declare-const |tptp.'#u'| tptp.mindex) % 0.37/0.64 (declare-const |tptp.'#c'| tptp.mindex) % 0.37/0.64 (define tptp.mlocal () (let ((_let_1 (@var "Phi" (-> tptp.mworld Bool)))) (lambda (@list _let_1) (_ _let_1 tptp.mactual)))) % 0.37/0.64 (define tptp.mnot () (let ((_let_1 (@var "W" tptp.mworld))) (let ((_let_2 (@var "A" (-> tptp.mworld Bool)))) (lambda (@list _let_2 _let_1) (not (_ _let_2 _let_1)))))) % 0.37/0.64 (define tptp.mand () (let ((_let_1 (@var "W" tptp.mworld))) (let ((_let_2 (@var "B" (-> tptp.mworld Bool)))) (let ((_let_3 (@var "A" (-> tptp.mworld Bool)))) (lambda (@list _let_3 _let_2 _let_1) (and (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.37/0.64 (define tptp.mor () (let ((_let_1 (@var "W" tptp.mworld))) (let ((_let_2 (@var "B" (-> tptp.mworld Bool)))) (let ((_let_3 (@var "A" (-> tptp.mworld Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.37/0.64 (define tptp.mimplies () (let ((_let_1 (@var "W" tptp.mworld))) (let ((_let_2 (@var "B" (-> tptp.mworld Bool)))) (let ((_let_3 (@var "A" (-> tptp.mworld Bool)))) (lambda (@list _let_3 _let_2 _let_1) (=> (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.37/0.64 (define tptp.mequiv () (let ((_let_1 (@var "W" tptp.mworld))) (let ((_let_2 (@var "B" (-> tptp.mworld Bool)))) (let ((_let_3 (@var "A" (-> tptp.mworld Bool)))) (lambda (@list _let_3 _let_2 _let_1) (= (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.37/0.64 (define tptp.mbox () (let ((_let_1 (@var "V" tptp.mworld))) (let ((_let_2 (@var "Phi" (-> tptp.mworld Bool)))) (let ((_let_3 (@var "W" tptp.mworld))) (let ((_let_4 (@var "R" tptp.mindex))) (lambda (@list _let_4 _let_2 _let_3) (forall (@list _let_1) (=> (_ (_ (_ tptp.mrel _let_4) _let_3) _let_1) (_ _let_2 _let_1))))))))) % 0.37/0.64 (define tptp.mdia () (let ((_let_1 (@var "V" tptp.mworld))) (let ((_let_2 (@var "Phi" (-> tptp.mworld Bool)))) (let ((_let_3 (@var "W" tptp.mworld))) (let ((_let_4 (@var "R" tptp.mindex))) (lambda (@list _let_4 _let_2 _let_3) (exists (@list _let_1) (and (_ (_ (_ tptp.mrel _let_4) _let_3) _let_1) (_ _let_2 _let_1))))))))) % 0.37/0.64 (define @t1 () (@var "W" tptp.mworld)) % 0.37/0.64 (define @t2 () (_ tptp.mrel |tptp.'#c'|)) % 0.37/0.64 (define @t3 () (_ @t2 @t1)) % 0.37/0.64 (define @t4 () (_ @t3 @t1)) % 0.37/0.64 (define @t5 () (@list @t1)) % 0.37/0.64 (define @t6 () (forall @t5 @t4)) % 0.37/0.64 (define @t7 () (@var "U" tptp.mworld)) % 0.37/0.64 (define @t8 () (@var "V" tptp.mworld)) % 0.37/0.64 (define @t9 () (@list @t1 @t8 @t7)) % 0.37/0.64 (define @t10 () (_ tptp.mrel |tptp.'#u'|)) % 0.37/0.64 (define @t11 () (_ @t10 @t1)) % 0.37/0.64 (define @t12 () (_ tptp.mimplies tptp.paid)) % 0.37/0.64 (define @t13 () (_ tptp.mbox |tptp.'#c'|)) % 0.37/0.64 (define @t14 () (_ tptp.mbox |tptp.'#u'|)) % 0.37/0.64 (define @t15 () (_ tptp.mimplies tptp.charge)) % 0.37/0.64 (define @t16 () (_ @t13 tptp.called)) % 0.37/0.64 (define @t17 () (_ @t14 tptp.paid)) % 0.37/0.64 (define @t18 () (_ tptp.mnot @t16)) % 0.37/0.64 (define @t19 () (_ tptp.mnot @t17)) % 0.37/0.64 (define @t20 () (_ tptp.mnot (_ @t15 (_ (_ tptp.mand tptp.called) (_ tptp.mnot tptp.paid))))) % 0.37/0.64 (define @t21 () (not (_ tptp.mlocal (_ (_ tptp.mimplies @t20) (_ @t14 @t20))))) % 0.37/0.64 (define @t22 () (@var "Phi" (-> tptp.mworld Bool))) % 0.37/0.64 (define @t23 () (lambda (@list @t22) (_ @t22 tptp.mactual))) % 0.37/0.64 (define @t24 () (@var "A" (-> tptp.mworld Bool))) % 0.37/0.64 (define @t25 () (_ @t24 @t1)) % 0.37/0.64 (define @t26 () (lambda (@list @t24 @t1) (not @t25))) % 0.37/0.64 (define @t27 () (@var "B" (-> tptp.mworld Bool))) % 0.37/0.64 (define @t28 () (_ @t27 @t1)) % 0.37/0.64 (define @t29 () (@list @t24 @t27 @t1)) % 0.37/0.64 (define @t30 () (lambda @t29 (and @t25 @t28))) % 0.37/0.64 (define @t31 () (lambda @t29 (or @t25 @t28))) % 0.37/0.64 (define @t32 () (lambda @t29 (=> @t25 @t28))) % 0.37/0.64 (define @t33 () (lambda @t29 (= @t25 @t28))) % 0.37/0.64 (define @t34 () (_ @t22 @t8)) % 0.37/0.64 (define @t35 () (@var "R" tptp.mindex)) % 0.37/0.64 (define @t36 () (_ (_ (_ tptp.mrel @t35) @t1) @t8)) % 0.37/0.64 (define @t37 () (@list @t8)) % 0.37/0.64 (define @t38 () (forall @t37 (=> @t36 @t34))) % 0.37/0.64 (define @t39 () (@list @t35 @t22 @t1)) % 0.37/0.64 (define @t40 () (lambda @t39 @t38)) % 0.37/0.64 (define @t41 () (lambda @t39 (exists @t37 (and @t36 @t34)))) % 0.37/0.64 (define @t42 () (@var "BOUND_VARIABLE_7829" tptp.mworld)) % 0.37/0.64 (define @t43 () (tptp.paid @t42)) % 0.37/0.64 (define @t44 () (not (tptp.mrel |tptp.'#u'| @t8 @t42))) % 0.37/0.64 (define @t45 () (tptp.paid @t8)) % 0.37/0.64 (define @t46 () (not @t45)) % 0.37/0.64 (define @t47 () (not (tptp.mrel |tptp.'#c'| tptp.mactual @t8))) % 0.37/0.64 (define @t48 () (@list @t8 @t42)) % 0.37/0.64 (define @t49 () (forall @t48 (or @t47 @t46 @t44 @t43))) % 0.37/0.64 (define @t50 () (not (tptp.mrel |tptp.'#c'| @t1 @t8))) % 0.37/0.64 (define @t51 () (or @t50 @t46 @t44 @t43)) % 0.37/0.64 (define @t52 () (lambda @t5 (forall @t48 @t51))) % 0.37/0.64 (define @t53 () (_ @t52 tptp.mactual)) % 0.37/0.64 (define @t54 () (or @t44 @t43)) % 0.37/0.64 (define @t55 () (or @t50 @t46 @t54)) % 0.37/0.64 (define @t56 () (forall @t48 @t55)) % 0.37/0.64 (define @t57 () (@list @t42)) % 0.37/0.64 (define @t58 () (forall @t57 @t55)) % 0.37/0.64 (define @t59 () (forall @t57 @t54)) % 0.37/0.64 (define @t60 () (@var "BOUND_VARIABLE_7803" tptp.mworld)) % 0.37/0.64 (define @t61 () (@list @t60)) % 0.37/0.64 (define @t62 () (or @t50 @t46 @t59)) % 0.37/0.64 (define @t63 () (tptp.paid @t60)) % 0.37/0.64 (define @t64 () (@list @t60)) % 0.37/0.64 (define @t65 () (forall @t64 (or (not (tptp.mrel |tptp.'#u'| @t8 @t60)) @t63))) % 0.37/0.64 (define @t66 () (_ tptp.paid @t8)) % 0.37/0.64 (define @t67 () (not @t66)) % 0.37/0.64 (define @t68 () (or @t50 @t67 @t65)) % 0.37/0.64 (define @t69 () (=> @t66 @t65)) % 0.37/0.64 (define @t70 () (or @t50 @t69)) % 0.37/0.64 (define @t71 () (_ tptp.paid @t1)) % 0.37/0.64 (define @t72 () (not (tptp.mrel |tptp.'#u'| @t1 @t8))) % 0.37/0.64 (define @t73 () (forall @t37 (or @t72 @t45))) % 0.37/0.64 (define @t74 () (@list @t8)) % 0.37/0.64 (define @t75 () (=> @t71 @t73)) % 0.37/0.64 (define @t76 () (lambda @t5 @t75)) % 0.37/0.64 (define @t77 () (or @t50 (_ @t76 @t8))) % 0.37/0.64 (define @t78 () (forall @t37 @t77)) % 0.37/0.64 (define @t79 () (lambda @t5 @t78)) % 0.37/0.64 (define @t80 () (_ @t22 @t8)) % 0.37/0.64 (define @t81 () (@list @t22 @t1)) % 0.37/0.64 (define @t82 () (lambda @t81 (forall @t37 (or @t50 @t80)))) % 0.37/0.64 (define @t83 () (lambda @t5 @t73)) % 0.37/0.64 (define @t84 () (_ @t83 @t1)) % 0.37/0.64 (define @t85 () (=> @t71 @t84)) % 0.37/0.64 (define @t86 () (lambda @t5 @t85)) % 0.37/0.64 (define @t87 () (@list @t27 @t1)) % 0.37/0.64 (define @t88 () (lambda @t87 (=> @t71 @t28))) % 0.37/0.64 (define @t89 () (lambda @t81 (forall @t37 (or @t72 @t80)))) % 0.37/0.64 (define @t90 () (tptp.mrel @t35 @t1 @t8)) % 0.37/0.64 (define @t91 () (lambda @t39 (forall @t37 (or (not @t90) @t80)))) % 0.37/0.64 (define @t92 () (_ @t91 |tptp.'#u'|)) % 0.37/0.64 (define @t93 () (not @t36)) % 0.37/0.64 (define @t94 () (or @t93 @t34)) % 0.37/0.64 (define @t95 () (tptp.mrel |tptp.'#c'| @t1 @t1)) % 0.37/0.64 (define @t96 () (@list tptp.mactual)) % 0.37/0.64 (define @t97 () (tptp.called @t8)) % 0.37/0.64 (define @t98 () (not @t97)) % 0.37/0.64 (define @t99 () (tptp.charge @t8)) % 0.37/0.64 (define @t100 () (and @t99 (or @t98 @t45))) % 0.37/0.64 (define @t101 () (not (tptp.mrel |tptp.'#u'| tptp.mactual @t8))) % 0.37/0.64 (define @t102 () (forall @t37 (or @t101 @t100))) % 0.37/0.64 (define @t103 () (tptp.paid tptp.mactual)) % 0.37/0.64 (define @t104 () (_ tptp.paid tptp.mactual)) % 0.37/0.64 (define @t105 () (not @t104)) % 0.37/0.64 (define @t106 () (tptp.called tptp.mactual)) % 0.37/0.64 (define @t107 () (_ tptp.called tptp.mactual)) % 0.37/0.64 (define @t108 () (and @t107 @t105)) % 0.37/0.64 (define @t109 () (tptp.charge tptp.mactual)) % 0.37/0.64 (define @t110 () (_ tptp.charge tptp.mactual)) % 0.37/0.64 (define @t111 () (=> @t110 @t108)) % 0.37/0.64 (define @t112 () (not @t111)) % 0.37/0.64 (define @t113 () (=> @t112 @t102)) % 0.37/0.64 (define @t114 () (forall @t37 (or @t72 @t100))) % 0.37/0.64 (define @t115 () (not @t71)) % 0.37/0.64 (define @t116 () (_ tptp.called @t1)) % 0.37/0.64 (define @t117 () (and @t116 @t115)) % 0.37/0.64 (define @t118 () (_ tptp.charge @t1)) % 0.37/0.64 (define @t119 () (=> @t118 @t117)) % 0.37/0.64 (define @t120 () (not @t119)) % 0.37/0.64 (define @t121 () (lambda @t5 (=> @t120 @t114))) % 0.37/0.64 (define @t122 () (_ @t121 tptp.mactual)) % 0.37/0.64 (define @t123 () (lambda @t5 @t114)) % 0.37/0.64 (define @t124 () (_ @t123 @t1)) % 0.37/0.64 (define @t125 () (=> @t120 @t124)) % 0.37/0.64 (define @t126 () (lambda @t5 @t125)) % 0.37/0.64 (define @t127 () (_ tptp.called @t8)) % 0.37/0.64 (define @t128 () (not @t127)) % 0.37/0.64 (define @t129 () (or @t128 @t66)) % 0.37/0.64 (define @t130 () (_ tptp.charge @t8)) % 0.37/0.64 (define @t131 () (and @t130 @t129)) % 0.37/0.64 (define @t132 () (or @t72 @t131)) % 0.37/0.64 (define @t133 () (and @t127 @t67)) % 0.37/0.64 (define @t134 () (not (=> @t130 @t133))) % 0.37/0.64 (define @t135 () (or @t72 @t134)) % 0.37/0.64 (define @t136 () (lambda @t5 @t120)) % 0.37/0.64 (define @t137 () (_ @t136 @t8)) % 0.37/0.64 (define @t138 () (or @t72 @t137)) % 0.37/0.64 (define @t139 () (forall @t37 @t138)) % 0.37/0.64 (define @t140 () (lambda @t5 @t139)) % 0.37/0.64 (define @t141 () (lambda @t5 @t119)) % 0.37/0.64 (define @t142 () (_ @t141 @t1)) % 0.37/0.64 (define @t143 () (not @t142)) % 0.37/0.64 (define @t144 () (lambda @t5 @t143)) % 0.37/0.64 (define @t145 () (lambda @t5 @t117)) % 0.37/0.64 (define @t146 () (_ @t145 @t1)) % 0.37/0.64 (define @t147 () (=> @t118 @t146)) % 0.37/0.64 (define @t148 () (lambda @t5 @t147)) % 0.37/0.64 (define @t149 () (lambda @t87 (=> @t118 @t28))) % 0.37/0.64 (define @t150 () (lambda @t5 @t115)) % 0.37/0.64 (define @t151 () (_ @t150 @t1)) % 0.37/0.64 (define @t152 () (and @t116 @t151)) % 0.37/0.64 (define @t153 () (lambda @t5 @t152)) % 0.37/0.64 (define @t154 () (lambda @t87 (and @t116 @t28))) % 0.37/0.64 (define @t155 () (_ @t26 tptp.paid)) % 0.37/0.64 (define @t156 () (_ @t30 tptp.called)) % 0.37/0.64 (define @t157 () (_ @t32 tptp.charge)) % 0.37/0.64 (define @t158 () (_ @t136 @t1)) % 0.37/0.64 (define @t159 () (=> @t158 @t28)) % 0.37/0.64 (define @t160 () (lambda @t87 @t159)) % 0.37/0.64 (define @t161 () (_ @t26 (_ @t157 (_ @t156 @t155)))) % 0.37/0.64 (define @t162 () (forall @t37 (or @t101 @t99))) % 0.37/0.64 (define @t163 () (and @t162 (forall @t37 (or @t47 @t99)))) % 0.37/0.64 (define @t164 () (=> @t110 @t163)) % 0.37/0.64 (define @t165 () (forall @t37 (or @t50 @t99))) % 0.37/0.64 (define @t166 () (forall @t37 (or @t72 @t99))) % 0.37/0.64 (define @t167 () (and @t166 @t165)) % 0.37/0.64 (define @t168 () (lambda @t5 (=> @t118 @t167))) % 0.37/0.64 (define @t169 () (_ @t168 tptp.mactual)) % 0.37/0.64 (define @t170 () (lambda @t5 @t167)) % 0.37/0.64 (define @t171 () (_ @t170 @t1)) % 0.37/0.64 (define @t172 () (=> @t118 @t171)) % 0.37/0.64 (define @t173 () (lambda @t5 @t172)) % 0.37/0.64 (define @t174 () (lambda @t5 @t165)) % 0.37/0.64 (define @t175 () (_ @t174 @t1)) % 0.37/0.64 (define @t176 () (and @t166 @t175)) % 0.37/0.64 (define @t177 () (lambda @t5 @t176)) % 0.37/0.64 (define @t178 () (lambda @t5 @t166)) % 0.37/0.64 (define @t179 () (_ @t178 @t1)) % 0.37/0.64 (define @t180 () (and @t179 @t28)) % 0.37/0.64 (define @t181 () (lambda @t87 @t180)) % 0.37/0.64 (define @t182 () (@list false)) % 0.37/0.64 (define @t183 () (@quantifiers_skolemize @t102 0)) % 0.37/0.64 (define @t184 () (@list @t183)) % 0.37/0.64 (define @t185 () (tptp.mrel |tptp.'#u'| tptp.mactual @t183)) % 0.37/0.64 (define @t186 () (tptp.paid @t183)) % 0.37/0.64 (define @t187 () (tptp.called @t183)) % 0.37/0.64 (define @t188 () (not @t187)) % 0.37/0.64 (define @t189 () (or @t188 @t186)) % 0.37/0.64 (define @t190 () (tptp.charge @t183)) % 0.37/0.64 (define @t191 () (and @t190 @t189)) % 0.37/0.64 (define @t192 () (not @t185)) % 0.37/0.64 (define @t193 () (or @t192 @t191)) % 0.37/0.64 (define @t194 () (@list true)) % 0.37/0.64 (define @t195 () (@list @t193)) % 0.37/0.64 (define @t196 () (or @t192 @t190)) % 0.37/0.64 (define @t197 () (@list false false)) % 0.37/0.64 (define @t198 () (@list true false)) % 0.37/0.64 (define @t199 () (@list @t189)) % 0.37/0.64 (define @t200 () (or @t192 @t186)) % 0.37/0.64 (define @t201 () (not @t200)) % 0.37/0.64 (define @t202 () (forall @t37 (or @t101 @t45))) % 0.37/0.64 (define @t203 () (not @t202)) % 0.37/0.64 (define @t204 () (@quantifiers_skolemize @t202 0)) % 0.37/0.64 (define @t205 () (tptp.paid @t204)) % 0.37/0.64 (define @t206 () (tptp.mrel |tptp.'#u'| tptp.mactual @t204)) % 0.37/0.64 (define @t207 () (not @t206)) % 0.37/0.64 (define @t208 () (or @t207 @t205)) % 0.37/0.64 (define @t209 () (not @t208)) % 0.37/0.64 (define @t210 () (@list @t208)) % 0.37/0.64 (define @t211 () (@var "BOUND_VARIABLE_7869" tptp.mworld)) % 0.37/0.64 (define @t212 () (tptp.called @t211)) % 0.37/0.64 (define @t213 () (@list @t211)) % 0.37/0.64 (define @t214 () (forall @t213 (or (not (tptp.mrel |tptp.'#c'| @t183 @t211)) @t212))) % 0.37/0.64 (define @t215 () (@quantifiers_skolemize @t214 0)) % 0.37/0.64 (define @t216 () (tptp.mrel |tptp.'#c'| @t183 @t215)) % 0.37/0.64 (define @t217 () (tptp.called @t215)) % 0.37/0.64 (define @t218 () (not @t216)) % 0.37/0.64 (define @t219 () (or @t218 @t217)) % 0.37/0.64 (define @t220 () (@var "BOUND_VARIABLE_7766" tptp.mworld)) % 0.37/0.64 (define @t221 () (tptp.called @t220)) % 0.37/0.64 (define @t222 () (not (tptp.mrel |tptp.'#c'| @t8 @t220))) % 0.37/0.64 (define @t223 () (@list @t8 @t220)) % 0.37/0.64 (define @t224 () (or @t72 @t98 @t222 @t221)) % 0.37/0.64 (define @t225 () (lambda @t5 (forall @t223 @t224))) % 0.37/0.64 (define @t226 () (_ @t225 tptp.mactual)) % 0.37/0.64 (define @t227 () (or @t222 @t221)) % 0.37/0.64 (define @t228 () (or @t72 @t98 @t227)) % 0.37/0.64 (define @t229 () (forall @t223 @t228)) % 0.37/0.64 (define @t230 () (@list @t220)) % 0.37/0.64 (define @t231 () (forall @t230 @t228)) % 0.37/0.64 (define @t232 () (forall @t230 @t227)) % 0.37/0.64 (define @t233 () (@var "BOUND_VARIABLE_7740" tptp.mworld)) % 0.37/0.64 (define @t234 () (@list @t233)) % 0.37/0.64 (define @t235 () (or @t72 @t98 @t232)) % 0.37/0.64 (define @t236 () (tptp.called @t233)) % 0.37/0.64 (define @t237 () (@list @t233)) % 0.37/0.64 (define @t238 () (forall @t237 (or (not (tptp.mrel |tptp.'#c'| @t8 @t233)) @t236))) % 0.37/0.64 (define @t239 () (or @t72 @t128 @t238)) % 0.37/0.64 (define @t240 () (=> @t127 @t238)) % 0.37/0.64 (define @t241 () (or @t72 @t240)) % 0.37/0.64 (define @t242 () (forall @t37 (or @t50 @t97))) % 0.37/0.64 (define @t243 () (=> @t116 @t242)) % 0.37/0.64 (define @t244 () (lambda @t5 @t243)) % 0.37/0.64 (define @t245 () (or @t72 (_ @t244 @t8))) % 0.37/0.64 (define @t246 () (forall @t37 @t245)) % 0.37/0.64 (define @t247 () (lambda @t5 @t246)) % 0.37/0.64 (define @t248 () (lambda @t5 @t242)) % 0.37/0.64 (define @t249 () (_ @t248 @t1)) % 0.37/0.64 (define @t250 () (=> @t116 @t249)) % 0.37/0.64 (define @t251 () (lambda @t5 @t250)) % 0.37/0.64 (define @t252 () (lambda @t87 (=> @t116 @t28))) % 0.37/0.64 (define @t253 () (or @t192 @t188 @t218 @t217)) % 0.37/0.64 (define @t254 () (not @t219)) % 0.37/0.64 (define @t255 () (not @t214)) % 0.37/0.64 (define @t256 () (or @t192 @t255)) % 0.37/0.64 (define @t257 () (not @t256)) % 0.37/0.64 (define @t258 () (not (forall @t213 (or (not (tptp.mrel |tptp.'#c'| @t8 @t211)) @t212)))) % 0.37/0.64 (define @t259 () (forall @t37 (or @t101 @t258))) % 0.37/0.64 (define @t260 () (forall @t37 (or @t47 @t97))) % 0.37/0.64 (define @t261 () (not @t260)) % 0.37/0.64 (define @t262 () (forall @t37 (or @t72 @t258))) % 0.37/0.64 (define @t263 () (not @t242)) % 0.37/0.64 (define @t264 () (lambda @t5 (=> @t263 @t262))) % 0.37/0.64 (define @t265 () (_ @t264 tptp.mactual)) % 0.37/0.64 (define @t266 () (lambda @t5 @t262)) % 0.37/0.64 (define @t267 () (_ @t266 @t1)) % 0.37/0.64 (define @t268 () (=> @t263 @t267)) % 0.37/0.64 (define @t269 () (lambda @t5 @t268)) % 0.37/0.64 (define @t270 () (lambda @t5 @t263)) % 0.37/0.64 (define @t271 () (or @t72 (_ @t270 @t8))) % 0.37/0.64 (define @t272 () (forall @t37 @t271)) % 0.37/0.64 (define @t273 () (lambda @t5 @t272)) % 0.37/0.64 (define @t274 () (not @t249)) % 0.37/0.64 (define @t275 () (lambda @t5 @t274)) % 0.37/0.64 (define @t276 () (_ @t270 @t1)) % 0.37/0.64 (define @t277 () (=> @t276 @t28)) % 0.37/0.64 (define @t278 () (lambda @t87 @t277)) % 0.37/0.64 (define @t279 () (tptp.mrel |tptp.'#c'| tptp.mactual tptp.mactual)) % 0.37/0.64 (define @t280 () (not @t279)) % 0.37/0.64 (define @t281 () (or @t280 @t106)) % 0.37/0.64 (define @t282 () (not @t106)) % 0.37/0.64 (define @t283 () (not @t103)) % 0.37/0.64 (define @t284 () (or @t280 @t283 @t207 @t205)) % 0.37/0.64 (define @t285 () (not @t284)) % 0.37/0.64 (assume @p1 @t6) % 0.37/0.64 (assume @p2 (forall @t9 (=> (and (_ @t3 @t8) (_ (_ @t2 @t8) @t7)) (_ @t3 @t7)))) % 0.37/0.64 (assume @p3 (forall @t5 (_ @t11 @t1))) % 0.37/0.64 (assume @p4 (forall @t9 (=> (and (_ @t11 @t8) (_ (_ @t10 @t8) @t7)) (_ @t11 @t7)))) % 0.37/0.64 (assume @p5 (_ tptp.mlocal (_ @t12 tptp.called))) % 0.37/0.64 (assume @p6 (_ tptp.mlocal (_ @t15 (_ (_ tptp.mand (_ @t14 tptp.charge)) (_ @t13 tptp.charge))))) % 0.37/0.64 (assume @p7 (_ tptp.mlocal (_ @t14 (_ (_ tptp.mimplies tptp.called) @t16)))) % 0.37/0.64 (assume @p8 (_ tptp.mlocal (_ @t13 (_ @t12 @t17)))) % 0.37/0.64 (assume @p9 (_ tptp.mlocal (_ (_ tptp.mimplies @t18) (_ @t14 @t18)))) % 0.37/0.64 (assume @p10 (_ tptp.mlocal (_ (_ tptp.mimplies @t19) (_ @t13 @t19)))) % 0.37/0.64 (assume @p11 @t21) % 0.37/0.64 (assume @p12 true) % 0.37/0.64 (step @p13 (= 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0.37/0.64 (step @p28 :rule refl :args (@t46)) % 0.37/0.64 (step @p29 :rule refl :args (@t50)) % 0.37/0.64 (step @p30 :rule nary_cong :premises (@p29 @p28 @p27) :args (@t62)) % 0.37/0.64 (step @p31 :rule quant-miniscope-or :args ((= @t58 @t62))) % 0.37/0.64 (step @p32 :rule trans :premises (@p31 @p30)) % 0.37/0.64 (step @p33 :rule symm :premises (@p32)) % 0.37/0.64 (step @p34 :rule cong :premises (@p33) :args ((forall @t37 (or @t50 @t46 @t65)))) % 0.37/0.64 (step @p35 :rule trans :premises (@p34 @p26)) % 0.37/0.64 (step @p36 :rule trans :premises (@p35 @p25)) % 0.37/0.64 (step @p37 :rule refl :args (@t65)) % 0.37/0.64 (step @p38 :rule refl :args (@t45)) % 0.37/0.64 (step @p39 :rule refl :args (@t66)) % 0.37/0.64 (step @p40 :rule cong :premises (@p39 @p38) :args ((= @t66 @t45))) % 0.37/0.64 (step @p41 :rule symm :premises (@p40)) % 0.37/0.64 (step @p42 :rule eq_resolve :premises (@p39 @p41)) % 0.37/0.64 (step @p43 :rule cong :premises (@p42) :args (@t67)) % 0.37/0.64 (step @p44 :rule 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(step @p58 :rule cong :premises (@p57) :args (@t76)) % 0.37/0.64 (step @p59 :rule ho_cong :premises (@p58 @p54)) % 0.37/0.64 (step @p60 :rule trans :premises (@p59 @p53)) % 0.37/0.64 (step @p61 :rule refl :args (@t50)) % 0.37/0.64 (step @p62 :rule nary_cong :premises (@p61 @p60) :args (@t77)) % 0.37/0.64 (step @p63 :rule cong :premises (@p62) :args (@t78)) % 0.37/0.64 (step @p64 :rule trans :premises (@p63 @p52)) % 0.37/0.64 (step @p65 :rule cong :premises (@p64) :args (@t79)) % 0.37/0.64 (step @p66 :rule beta-reduce :args ((= (_ @t82 @t76) @t79))) % 0.37/0.64 (step @p67 :rule trans :premises (@p66 @p65)) % 0.37/0.64 (step @p68 :rule beta-reduce :args ((= @t84 @t73))) % 0.37/0.64 (step @p69 :rule refl :args (@t71)) % 0.37/0.64 (step @p70 :rule cong :premises (@p69 @p68) :args (@t85)) % 0.37/0.64 (step @p71 :rule cong :premises (@p70) :args (@t86)) % 0.37/0.64 (step @p72 :rule beta-reduce :args ((= (_ @t88 @t83) @t86))) % 0.37/0.64 (step @p73 :rule trans :premises (@p72 @p71)) % 0.37/0.64 (step @p74 :rule beta-reduce :args ((= (_ @t89 tptp.paid) @t83))) % 0.37/0.64 (step @p75 :rule refl :args (tptp.paid)) % 0.37/0.64 (step @p76 :rule beta-reduce :args ((= @t92 @t89))) % 0.37/0.64 (step @p77 :rule ho_cong :premises (@p76 @p75)) % 0.37/0.64 (step @p78 :rule trans :premises (@p77 @p74)) % 0.37/0.64 (step @p79 :rule beta-reduce :args ((= (_ @t32 tptp.paid) @t88))) % 0.37/0.64 (step @p80 :rule ho_cong :premises (@p79 @p78)) % 0.37/0.64 (step @p81 :rule trans :premises (@p80 @p73)) % 0.37/0.64 (step @p82 :rule beta-reduce :args ((= (_ @t91 |tptp.'#c'|) @t82))) % 0.37/0.64 (step @p83 :rule ho_cong :premises (@p82 @p81)) % 0.37/0.64 (step @p84 :rule trans :premises (@p83 @p67)) % 0.37/0.64 (step @p85 :rule refl :args (@t23)) % 0.37/0.64 (step @p86 :rule ho_cong :premises (@p85 @p84)) % 0.37/0.64 (step @p87 :rule trans :premises (@p86 @p23)) % 0.37/0.64 (step @p88 :rule refl :args (|tptp.'#u'|)) % 0.37/0.64 (step @p89 :rule refl :args (@t80)) % 0.37/0.64 (step @p90 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0.37/0.64 (step @p106 :rule trans :premises (@p19 @p105)) % 0.37/0.64 (step @p107 :rule ho_cong :premises (@p106 @p88)) % 0.37/0.64 (step @p108 :rule ho_cong :premises (@p107 @p75)) % 0.37/0.64 (step @p109 :rule ho_cong :premises (@p17 @p75)) % 0.37/0.64 (step @p110 :rule ho_cong :premises (@p109 @p108)) % 0.37/0.64 (step @p111 :rule refl :args (|tptp.'#c'|)) % 0.37/0.64 (step @p112 :rule ho_cong :premises (@p106 @p111)) % 0.37/0.64 (step @p113 :rule ho_cong :premises (@p112 @p110)) % 0.37/0.64 (step @p114 :rule ho_cong :premises (@p13 @p113)) % 0.37/0.64 (step @p115 :rule trans :premises (@p114 @p87)) % 0.37/0.64 (step @p116 :rule eq_resolve :premises (@p8 @p115)) % 0.37/0.64 (step @p117 :rule refl :args (@t95)) % 0.37/0.64 (step @p118 :rule refl :args (@t4)) % 0.37/0.64 (step @p119 :rule cong :premises (@p118 @p117) :args ((= @t4 @t95))) % 0.37/0.64 (step @p120 :rule symm :premises (@p119)) % 0.37/0.64 (step @p121 :rule eq_resolve :premises (@p118 @p120)) % 0.37/0.64 (step @p122 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((or @t192 @t188 @t218 @t217 (not @t253)))) % 0.37/0.64 (step @p427 :rule chain_m_resolution :premises (@p426 @p424 @p363 @p312 @p356 @p355) :args (@t219 (@list false false false true false) (@list @t253 @t187 @t185 @t217 @t216))) % 0.37/0.64 (step @p428 :rule refl :args (@t254)) % 0.37/0.64 (step @p429 :rule bool-double-not-elim :args (@t214)) % 0.37/0.64 (step @p430 :rule nary_cong :premises (@p429 @p428) :args ((or (not @t255) @t254))) % 0.37/0.64 (assume-push @p529 @t255) % 0.37/0.64 (step @p432 :rule skolemize :premises (@p529)) % 0.37/0.64 (step-pop @p530 :rule scope :premises (@p432)) % 0.37/0.64 (step @p433 :rule process_scope :premises (@p530) :args (@t254)) % 0.37/0.64 (step @p435 :rule implies_elim :premises (@p433)) % 0.37/0.64 (step @p436 :rule eq_resolve :premises (@p435 @p430)) % 0.37/0.64 (step @p437 :rule chain_m_resolution :premises (@p436 @p427) :args (@t214 @t182 (@list @t219))) % 0.37/0.64 (step @p438 :rule cnf_or_pos :args (@t256)) % 0.37/0.64 (step @p439 :rule reordering :premises (@p438) :args ((or @t192 @t255 @t257))) % 0.37/0.64 (step @p440 :rule chain_m_resolution :premises (@p439 @p312 @p437) :args (@t257 @t197 (@list @t185 @t214))) % 0.37/0.64 (assume-push @p531 @t259) % 0.37/0.64 (step @p442 :rule instantiate :premises (@p531) :args (@t184)) % 0.37/0.64 (step-pop @p532 :rule scope :premises (@p442)) % 0.37/0.64 (step @p443 :rule process_scope :premises (@p532) :args (@t256)) % 0.37/0.64 (step @p445 :rule implies_elim :premises (@p443)) % 0.37/0.64 (step @p446 :rule chain_m_resolution :premises (@p445 @p440) :args ((not @t259) @t194 (@list @t256))) % 0.37/0.64 (step @p447 :rule refl :args (@t259)) % 0.37/0.64 (step @p448 :rule bool-double-not-elim :args (@t260)) % 0.37/0.64 (step @p449 :rule nary_cong :premises (@p448 @p447) :args ((or (not @t261) @t259))) % 0.37/0.64 (step @p450 :rule beta-reduce :args ((= @t265 (=> @t261 @t259)))) % 0.37/0.64 (step @p451 :rule beta-reduce :args ((= (_ @t23 @t264) @t265))) % 0.37/0.64 (step @p452 :rule trans :premises (@p451 @p450)) % 0.37/0.64 (step @p453 :rule beta-reduce :args ((= @t267 @t262))) % 0.37/0.64 (step @p454 :rule refl :args (@t263)) % 0.37/0.64 (step @p455 :rule cong :premises (@p454 @p453) :args (@t268)) % 0.37/0.64 (step @p456 :rule cong :premises (@p455) :args (@t269)) % 0.37/0.64 (step @p457 :rule beta-reduce :args ((= (_ (lambda @t87 (=> @t263 @t28)) @t266) @t269))) % 0.37/0.64 (step @p458 :rule trans :premises (@p457 @p456)) % 0.37/0.64 (step @p459 :rule beta-reduce :args ((= (_ (lambda @t5 (not (forall @t213 (or (not (tptp.mrel |tptp.'#c'| @t1 @t211)) @t212)))) @t8) @t258))) % 0.37/0.64 (step @p460 :rule alpha_equiv :args (@t242 @t74 (@list @t211))) % 0.37/0.64 (step @p461 :rule cong :premises (@p460) :args (@t263)) % 0.37/0.64 (step @p462 :rule cong :premises (@p461) :args (@t270)) % 0.37/0.64 (step @p463 :rule ho_cong :premises (@p462 @p54)) % 0.37/0.64 (step @p464 :rule trans :premises (@p463 @p459)) % 0.37/0.64 (step @p465 :rule nary_cong :premises (@p184 @p464) :args (@t271)) % 0.37/0.64 (step @p466 :rule cong :premises (@p465) :args (@t272)) % 0.37/0.64 (step @p467 :rule cong :premises (@p466) :args (@t273)) % 0.37/0.64 (step @p468 :rule beta-reduce :args ((= (_ @t89 @t270) @t273))) % 0.37/0.64 (step @p469 :rule trans :premises (@p468 @p467)) % 0.37/0.64 (step @p470 :rule cong :premises (@p402) :args (@t274)) % 0.37/0.64 (step @p471 :rule cong :premises (@p470) :args (@t275)) % 0.37/0.64 (step @p472 :rule beta-reduce :args ((= (_ @t26 @t248) @t275))) % 0.37/0.64 (step @p473 :rule trans :premises (@p472 @p471)) % 0.37/0.64 (step @p474 :rule ho_cong :premises (@p215 @p409)) % 0.37/0.64 (step @p475 :rule trans :premises (@p474 @p473)) % 0.37/0.64 (step @p476 :rule ho_cong :premises (@p76 @p475)) % 0.37/0.64 (step @p477 :rule trans :premises (@p476 @p469)) % 0.37/0.64 (step @p478 :rule beta-reduce :args ((= @t276 @t263))) % 0.37/0.64 (step @p479 :rule cong :premises (@p478 @p220) :args (@t277)) % 0.37/0.64 (step @p480 :rule cong :premises (@p479) :args (@t278)) % 0.37/0.64 (step @p481 :rule beta-reduce :args ((= (_ @t32 @t270) @t278))) % 0.37/0.64 (step @p482 :rule trans :premises (@p481 @p480)) % 0.37/0.64 (step @p483 :rule ho_cong :premises (@p226 @p475)) % 0.37/0.64 (step @p484 :rule trans :premises (@p483 @p482)) % 0.37/0.64 (step @p485 :rule ho_cong :premises (@p484 @p477)) % 0.37/0.64 (step @p486 :rule trans :premises (@p485 @p458)) % 0.37/0.64 (step @p487 :rule ho_cong :premises (@p85 @p486)) % 0.37/0.64 (step @p488 :rule trans :premises (@p487 @p452)) % 0.37/0.64 (step @p489 :rule ho_cong :premises (@p14 @p417)) % 0.37/0.64 (step @p490 :rule ho_cong :premises (@p107 @p489)) % 0.37/0.64 (step @p491 :rule ho_cong :premises (@p17 @p489)) % 0.37/0.64 (step @p492 :rule ho_cong :premises (@p491 @p490)) % 0.37/0.64 (step @p493 :rule ho_cong :premises (@p13 @p492)) % 0.37/0.64 (step @p494 :rule trans :premises (@p493 @p488)) % 0.37/0.64 (step @p495 :rule eq_resolve :premises (@p9 @p494)) % 0.37/0.64 (step @p496 :rule implies_elim :premises (@p495)) % 0.37/0.64 (step @p497 :rule eq_resolve :premises (@p496 @p449)) % 0.37/0.64 (step @p498 :rule chain_m_resolution :premises (@p497 @p446) :args (@t260 @t194 (@list @t259))) % 0.37/0.64 (assume-push @p533 @t260) % 0.37/0.64 (step @p500 :rule instantiate :premises (@p533) :args (@t96)) % 0.37/0.64 (step-pop @p534 :rule scope :premises (@p500)) % 0.37/0.64 (step @p501 :rule process_scope :premises (@p534) :args (@t281)) % 0.37/0.64 (step @p503 :rule implies_elim :premises (@p501)) % 0.37/0.64 (step @p504 :rule chain_m_resolution :premises (@p503 @p498) :args (@t281 @t182 (@list @t260))) % 0.37/0.64 (step @p505 :rule cnf_or_pos :args (@t281)) % 0.37/0.64 (step @p506 :rule reordering :premises (@p505) :args ((or @t106 @t280 (not @t281)))) % 0.37/0.64 (step @p507 :rule chain_m_resolution :premises (@p506 @p124 @p504) :args (@t106 @t197 (@list @t279 @t281))) % 0.37/0.64 (step @p508 :rule bool-double-not-elim :args (@t103)) % 0.37/0.64 (step @p509 :rule refl :args (@t282)) % 0.37/0.64 (step @p510 :rule nary_cong :premises (@p509 @p508) :args ((or @t282 (not @t283)))) % 0.37/0.64 (step @p511 :rule not_implies_elim2 :premises (@p250)) % 0.37/0.64 (step @p512 :rule not_and :premises (@p511)) % 0.37/0.64 (step @p513 :rule eq_resolve :premises (@p512 @p510)) % 0.37/0.64 (step @p514 :rule reordering :premises (@p513) :args ((or @t103 @t282))) % 0.37/0.64 (step @p515 :rule chain_m_resolution :premises (@p514 @p507) :args (@t103 @t182 (@list @t106))) % 0.37/0.64 (step @p516 :rule cnf_or_pos :args (@t284)) % 0.37/0.64 (step @p517 :rule reordering :premises (@p516) :args ((or @t283 @t207 @t205 @t280 @t285))) % 0.37/0.64 (step @p518 :rule chain_m_resolution :premises (@p517 @p515 @p349 @p342 @p124) :args (@t285 (@list false false true false) (@list @t103 @t206 @t205 @t279))) % 0.37/0.64 (assume-push @p535 @t49) % 0.37/0.64 (step @p520 :rule instantiate :premises (@p116) :args ((@list tptp.mactual @t204))) % 0.37/0.64 (step-pop @p536 :rule scope :premises (@p520)) % 0.37/0.64 (step @p521 :rule process_scope :premises (@p536) :args (@t284)) % 0.37/0.64 (step @p523 :rule implies_elim :premises (@p521)) % 0.37/0.64 (step @p524 false :rule chain_m_resolution :premises (@p523 @p518 @p116) :args (false @t198 (@list @t284 @t49))) % 0.37/0.64 ) % 0.37/0.64 % SZS output end Proof % 0.37/0.64 % cvc5 exiting %------------------------------------------------------------------------------