%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : ITP004_2 : TPTP v9.2.1. Bugfixed v7.5.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n013.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 08:24:23 AM UTC 2026 % Result : Theorem 3.57s 3.89s % Output : Proof 0.33s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : ITP004_2 : TPTP v9.2.1. Bugfixed v7.5.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.14/0.33 % Computer : n013.cluster.edu % 0.14/0.33 % Model : x86_64 x86_64 % 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.33 % Memory : 8042.1875MB % 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.33 % CPULimit : 300 % 0.14/0.33 % WCLimit : 300 % 0.14/0.33 % DateTime : Tue Jun 2 03:37:00 EDT 2026 % 0.14/0.34 % CPUTime : % 0.27/0.50 %----Proving TF0_NAR, FOF, or CNF % 3.57/3.89 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 3.57/3.89 % SZS status Theorem % 3.57/3.89 % SZS output start Proof % 3.57/3.89 ( % 3.57/3.89 (declare-sort tptp.tp__o 0) % 3.57/3.89 (declare-sort tptp.del 0) % 3.57/3.89 (declare-sort $$unsorted 0) % 3.57/3.89 (declare-const tptp.c_2Ebool_2E_21 (-> tptp.del $$unsorted)) % 3.57/3.89 (declare-const tptp.c_2Emin_2E_3D (-> tptp.del $$unsorted)) % 3.57/3.89 (declare-const tptp.c_2Epred__set_2EREST (-> tptp.del $$unsorted)) % 3.57/3.89 (declare-const tptp.c_2Epred__set_2EDELETE (-> tptp.del $$unsorted)) % 3.57/3.89 (declare-const tptp.c_2Epred__set_2ECHOICE (-> tptp.del $$unsorted)) % 3.57/3.89 (declare-const tptp.fo__c_2Ebool_2E_2F_5C (-> tptp.tp__o tptp.tp__o tptp.tp__o)) % 3.57/3.89 (declare-const tptp.c_2Ebool_2E_2F_5C $$unsorted) % 3.57/3.89 (declare-const tptp.c_2Ebool_2EIN (-> tptp.del $$unsorted)) % 3.57/3.89 (declare-const tptp.ap (-> $$unsorted $$unsorted $$unsorted)) % 3.57/3.89 (declare-const tptp.fo__c_2Ebool_2E_7E (-> tptp.tp__o tptp.tp__o)) % 3.57/3.89 (declare-const tptp.mem (-> $$unsorted tptp.del Bool)) % 3.57/3.89 (declare-const tptp.arr (-> tptp.del tptp.del tptp.del)) % 3.57/3.89 (declare-const tptp.p (-> $$unsorted Bool)) % 3.57/3.89 (declare-const tptp.bool tptp.del) % 3.57/3.89 (declare-const tptp.k (-> tptp.del $$unsorted $$unsorted)) % 3.57/3.89 (declare-const tptp.i (-> tptp.del $$unsorted)) % 3.57/3.89 (declare-const tptp.fo__c_2Emin_2E_3D_3D_3E (-> tptp.tp__o tptp.tp__o tptp.tp__o)) % 3.57/3.89 (declare-const tptp.inj__o (-> tptp.tp__o $$unsorted)) % 3.57/3.89 (declare-const tptp.c_2Ebool_2E_7E $$unsorted) % 3.57/3.89 (declare-const tptp.surj__o (-> $$unsorted tptp.tp__o)) % 3.57/3.89 (declare-const tptp.c_2Emin_2E_3D_3D_3E $$unsorted) % 3.57/3.89 (declare-const tptp.c_2Epred__set_2ESUBSET (-> tptp.del $$unsorted)) % 3.57/3.89 (define @t1 () (@var "B" tptp.del)) % 3.57/3.89 (define @t2 () (@var "X" $$unsorted)) % 3.57/3.89 (define @t3 () (@var "F" $$unsorted)) % 3.57/3.89 (define @t4 () (tptp.ap @t3 @t2)) % 3.57/3.89 (define @t5 () (tptp.mem @t4 @t1)) % 3.57/3.89 (define @t6 () (@var "A" tptp.del)) % 3.57/3.89 (define @t7 () (tptp.mem @t2 @t6)) % 3.57/3.89 (define @t8 () (@list @t2)) % 3.57/3.89 (define @t9 () (forall @t8 (=> @t7 @t5))) % 3.57/3.89 (define @t10 () (tptp.arr @t6 @t1)) % 3.57/3.89 (define @t11 () (tptp.mem @t3 @t10)) % 3.57/3.89 (define @t12 () (=> @t11 @t9)) % 3.57/3.89 (define @t13 () (@list @t6 @t1 @t3)) % 3.57/3.89 (define @t14 () (forall @t13 @t12)) % 3.57/3.89 (define @t15 () (@var "R" $$unsorted)) % 3.57/3.89 (define @t16 () (@var "Q" $$unsorted)) % 3.57/3.89 (define @t17 () (tptp.p @t15)) % 3.57/3.89 (define @t18 () (tptp.p @t16)) % 3.57/3.89 (define @t19 () (tptp.mem @t15 tptp.bool)) % 3.57/3.89 (define @t20 () (@list @t15)) % 3.57/3.89 (define @t21 () (tptp.mem @t16 tptp.bool)) % 3.57/3.89 (define @t22 () (@list @t16)) % 3.57/3.89 (define @t23 () (@var "G" $$unsorted)) % 3.57/3.89 (define @t24 () (@var "Y" $$unsorted)) % 3.57/3.89 (define @t25 () (@list @t6 @t2)) % 3.57/3.89 (define @t26 () (@var "X" tptp.tp__o)) % 3.57/3.89 (define @t27 () (tptp.inj__o @t26)) % 3.57/3.89 (define @t28 () (@list @t26)) % 3.57/3.89 (define @t29 () (tptp.arr tptp.bool tptp.bool)) % 3.57/3.89 (define @t30 () (tptp.arr tptp.bool @t29)) % 3.57/3.89 (define @t31 () (@var "X1" tptp.tp__o)) % 3.57/3.89 (define @t32 () (tptp.inj__o @t31)) % 3.57/3.89 (define @t33 () (@var "X0" tptp.tp__o)) % 3.57/3.89 (define @t34 () (tptp.inj__o @t33)) % 3.57/3.89 (define @t35 () (@list @t33 @t31)) % 3.57/3.89 (define @t36 () (@var "A_27a" tptp.del)) % 3.57/3.89 (define @t37 () (tptp.arr @t36 tptp.bool)) % 3.57/3.89 (define @t38 () (tptp.arr @t37 tptp.bool)) % 3.57/3.89 (define @t39 () (tptp.c_2Epred__set_2ESUBSET @t36)) % 3.57/3.89 (define @t40 () (@list @t36)) % 3.57/3.89 (define @t41 () (tptp.c_2Ebool_2EIN @t36)) % 3.57/3.89 (define @t42 () (tptp.c_2Epred__set_2ECHOICE @t36)) % 3.57/3.89 (define @t43 () (tptp.arr @t36 @t37)) % 3.57/3.89 (define @t44 () (tptp.c_2Epred__set_2EDELETE @t36)) % 3.57/3.89 (define @t45 () (tptp.c_2Epred__set_2EREST @t36)) % 3.57/3.89 (define @t46 () (@var "V1t" $$unsorted)) % 3.57/3.89 (define @t47 () (@var "V2x" $$unsorted)) % 3.57/3.89 (define @t48 () (tptp.ap @t41 @t47)) % 3.57/3.89 (define @t49 () (tptp.p (tptp.ap @t48 @t46))) % 3.57/3.89 (define @t50 () (@var "V0s" $$unsorted)) % 3.57/3.89 (define @t51 () (tptp.p (tptp.ap @t48 @t50))) % 3.57/3.89 (define @t52 () (=> @t51 @t49)) % 3.57/3.89 (define @t53 () (tptp.mem @t47 @t36)) % 3.57/3.89 (define @t54 () (@list @t47)) % 3.57/3.89 (define @t55 () (forall @t54 (=> @t53 @t52))) % 3.57/3.89 (define @t56 () (tptp.ap @t39 @t50)) % 3.57/3.89 (define @t57 () (tptp.p (tptp.ap @t56 @t46))) % 3.57/3.89 (define @t58 () (= @t57 @t55)) % 3.57/3.89 (define @t59 () (tptp.mem @t46 @t37)) % 3.57/3.89 (define @t60 () (=> @t59 @t58)) % 3.57/3.89 (define @t61 () (@list @t46)) % 3.57/3.89 (define @t62 () (forall @t61 @t60)) % 3.57/3.89 (define @t63 () (tptp.mem @t50 @t37)) % 3.57/3.89 (define @t64 () (=> @t63 @t62)) % 3.57/3.89 (define @t65 () (@list @t36 @t50)) % 3.57/3.89 (define @t66 () (forall @t65 @t64)) % 3.57/3.89 (define @t67 () (@var "V2y" $$unsorted)) % 3.57/3.89 (define @t68 () (@var "V1x" $$unsorted)) % 3.57/3.89 (define @t69 () (tptp.ap @t41 @t68)) % 3.57/3.89 (define @t70 () (tptp.p (tptp.ap @t69 @t50))) % 3.57/3.89 (define @t71 () (tptp.ap @t44 @t50)) % 3.57/3.89 (define @t72 () (= (tptp.p (tptp.ap @t69 (tptp.ap @t71 @t67))) (and @t70 (not (= @t68 @t67))))) % 3.57/3.89 (define @t73 () (tptp.mem @t67 @t36)) % 3.57/3.89 (define @t74 () (@list @t67)) % 3.57/3.89 (define @t75 () (forall @t74 (=> @t73 @t72))) % 3.57/3.89 (define @t76 () (tptp.mem @t68 @t36)) % 3.57/3.89 (define @t77 () (=> @t76 @t75)) % 3.57/3.89 (define @t78 () (@list @t68)) % 3.57/3.89 (define @t79 () (forall @t78 @t77)) % 3.57/3.89 (define @t80 () (=> @t63 @t79)) % 3.57/3.89 (define @t81 () (forall @t65 @t80)) % 3.57/3.89 (define @t82 () (tptp.ap @t45 @t50)) % 3.57/3.89 (define @t83 () (= @t82 (tptp.ap @t71 (tptp.ap @t42 @t50)))) % 3.57/3.89 (define @t84 () (forall @t65 (=> @t63 @t83))) % 3.57/3.89 (define @t85 () (tptp.p (tptp.ap (tptp.ap @t39 @t82) @t50))) % 3.57/3.89 (define @t86 () (forall @t65 (=> @t63 @t85))) % 3.57/3.89 (define @t87 () (not @t86)) % 3.57/3.89 (define @t88 () (not @t63)) % 3.57/3.89 (define @t89 () (forall @t65 (or @t88 @t85))) % 3.57/3.89 (define @t90 () (@quantifiers_skolemize @t89 1)) % 3.57/3.89 (define @t91 () (@quantifiers_skolemize @t89 0)) % 3.57/3.89 (define @t92 () (tptp.arr @t91 tptp.bool)) % 3.57/3.89 (define @t93 () (tptp.mem @t90 @t92)) % 3.57/3.89 (define @t94 () (tptp.c_2Epred__set_2EREST @t91)) % 3.57/3.89 (define @t95 () (tptp.ap @t94 @t90)) % 3.57/3.89 (define @t96 () (tptp.p (tptp.ap (tptp.ap (tptp.c_2Epred__set_2ESUBSET @t91) @t95) @t90))) % 3.57/3.89 (define @t97 () (not @t93)) % 3.57/3.89 (define @t98 () (or @t97 @t96)) % 3.57/3.89 (define @t99 () (@list true)) % 3.57/3.89 (define @t100 () (@list @t98)) % 3.57/3.89 (define @t101 () (tptp.c_2Epred__set_2ECHOICE @t91)) % 3.57/3.89 (define @t102 () (tptp.ap @t101 @t90)) % 3.57/3.89 (define @t103 () (tptp.ap (tptp.ap (tptp.c_2Epred__set_2EDELETE @t91) @t90) @t102)) % 3.57/3.89 (define @t104 () (= @t95 @t103)) % 3.57/3.89 (define @t105 () (or @t97 @t104)) % 3.57/3.89 (define @t106 () (@var "BOUND_VARIABLE_7877" $$unsorted)) % 3.57/3.89 (define @t107 () (not @t51)) % 3.57/3.89 (define @t108 () (not @t53)) % 3.57/3.89 (define @t109 () (= (tptp.p (tptp.ap @t56 @t106)) (forall @t54 (or @t108 @t107 (tptp.p (tptp.ap @t48 @t106)))))) % 3.57/3.89 (define @t110 () (not (tptp.mem @t106 @t37))) % 3.57/3.89 (define @t111 () (or @t110 @t109)) % 3.57/3.89 (define @t112 () (or @t88 @t111)) % 3.57/3.89 (define @t113 () (forall (@list @t36 @t50 @t106) @t112)) % 3.57/3.89 (define @t114 () (@list @t106)) % 3.57/3.89 (define @t115 () (forall @t114 @t112)) % 3.57/3.89 (define @t116 () (forall @t114 @t111)) % 3.57/3.89 (define @t117 () (or @t88 @t116)) % 3.57/3.89 (define @t118 () (or @t108 @t107 @t49)) % 3.57/3.89 (define @t119 () (= @t57 (forall @t54 @t118))) % 3.57/3.89 (define @t120 () (forall @t61 (or (not @t59) @t119))) % 3.57/3.89 (define @t121 () (@var "BOUND_VARIABLE_7688" $$unsorted)) % 3.57/3.89 (define @t122 () (tptp.mem (tptp.ap @t3 @t121) @t1)) % 3.57/3.89 (define @t123 () (not (tptp.mem @t121 @t6))) % 3.57/3.89 (define @t124 () (not @t11)) % 3.57/3.89 (define @t125 () (or @t123 @t122)) % 3.57/3.89 (define @t126 () (or @t124 @t125)) % 3.57/3.89 (define @t127 () (forall (@list @t6 @t1 @t3 @t121) @t126)) % 3.57/3.89 (define @t128 () (@list @t121)) % 3.57/3.89 (define @t129 () (forall @t128 @t126)) % 3.57/3.89 (define @t130 () (forall @t128 @t125)) % 3.57/3.89 (define @t131 () (or @t124 @t130)) % 3.57/3.89 (define @t132 () (forall @t8 (or (not @t7) @t5))) % 3.57/3.89 (define @t133 () (@list @t91)) % 3.57/3.89 (define @t134 () (tptp.mem @t95 @t92)) % 3.57/3.89 (define @t135 () (tptp.mem @t94 (tptp.arr @t92 @t92))) % 3.57/3.89 (define @t136 () (not @t135)) % 3.57/3.89 (define @t137 () (or @t136 @t97 @t134)) % 3.57/3.89 (define @t138 () (@list false false false)) % 3.57/3.89 (define @t139 () (tptp.c_2Ebool_2EIN @t91)) % 3.57/3.89 (define @t140 () (tptp.ap @t139 @t47)) % 3.57/3.89 (define @t141 () (forall @t54 (or (not (tptp.mem @t47 @t91)) (not (tptp.p (tptp.ap @t140 @t95))) (tptp.p (tptp.ap @t140 @t90))))) % 3.57/3.89 (define @t142 () (= @t96 @t141)) % 3.57/3.89 (define @t143 () (not @t134)) % 3.57/3.89 (define @t144 () (or @t143 @t97 @t142)) % 3.57/3.89 (define @t145 () (not @t141)) % 3.57/3.89 (define @t146 () (@list true false)) % 3.57/3.89 (define @t147 () (@quantifiers_skolemize @t141 0)) % 3.57/3.89 (define @t148 () (tptp.ap @t139 @t147)) % 3.57/3.89 (define @t149 () (tptp.p (tptp.ap @t148 @t95))) % 3.57/3.89 (define @t150 () (tptp.p (tptp.ap @t148 @t90))) % 3.57/3.89 (define @t151 () (not @t149)) % 3.57/3.89 (define @t152 () (tptp.mem @t147 @t91)) % 3.57/3.89 (define @t153 () (not @t152)) % 3.57/3.89 (define @t154 () (or @t153 @t151 @t150)) % 3.57/3.89 (define @t155 () (@list @t154)) % 3.57/3.89 (define @t156 () (@var "BOUND_VARIABLE_7926" $$unsorted)) % 3.57/3.89 (define @t157 () (@var "BOUND_VARIABLE_7924" $$unsorted)) % 3.57/3.89 (define @t158 () (tptp.ap @t41 @t157)) % 3.57/3.89 (define @t159 () (= (tptp.p (tptp.ap @t158 (tptp.ap @t71 @t156))) (and (tptp.p (tptp.ap @t158 @t50)) (not (= @t157 @t156))))) % 3.57/3.89 (define @t160 () (not (tptp.mem @t156 @t36))) % 3.57/3.89 (define @t161 () (not (tptp.mem @t157 @t36))) % 3.57/3.89 (define @t162 () (or @t88 @t161 @t160 @t159)) % 3.57/3.89 (define @t163 () (or @t161 @t160 @t159)) % 3.57/3.89 (define @t164 () (or @t88 @t163)) % 3.57/3.89 (define @t165 () (@list @t36 @t50 @t157 @t156)) % 3.57/3.89 (define @t166 () (forall @t165 @t164)) % 3.57/3.89 (define @t167 () (@list @t157 @t156)) % 3.57/3.89 (define @t168 () (forall @t167 @t164)) % 3.57/3.89 (define @t169 () (forall @t167 @t163)) % 3.57/3.89 (define @t170 () (@var "BOUND_VARIABLE_7903" $$unsorted)) % 3.57/3.89 (define @t171 () (or @t88 @t169)) % 3.57/3.89 (define @t172 () (= (tptp.p (tptp.ap @t69 (tptp.ap @t71 @t170))) (and @t70 (not (= @t68 @t170))))) % 3.57/3.89 (define @t173 () (not (tptp.mem @t170 @t36))) % 3.57/3.89 (define @t174 () (not @t76)) % 3.57/3.89 (define @t175 () (or @t174 @t173 @t172)) % 3.57/3.89 (define @t176 () (@list @t68 @t170)) % 3.57/3.89 (define @t177 () (forall @t176 @t175)) % 3.57/3.89 (define @t178 () (or @t173 @t172)) % 3.57/3.89 (define @t179 () (or @t174 @t178)) % 3.57/3.89 (define @t180 () (forall @t176 @t179)) % 3.57/3.89 (define @t181 () (@list @t170)) % 3.57/3.89 (define @t182 () (forall @t181 @t179)) % 3.57/3.89 (define @t183 () (forall @t181 @t178)) % 3.57/3.89 (define @t184 () (or @t174 @t183)) % 3.57/3.89 (define @t185 () (forall @t74 (or (not @t73) @t72))) % 3.57/3.89 (define @t186 () (not (= @t147 @t102))) % 3.57/3.89 (define @t187 () (and @t150 @t186)) % 3.57/3.89 (define @t188 () (tptp.ap @t148 @t103)) % 3.57/3.89 (define @t189 () (tptp.p @t188)) % 3.57/3.89 (define @t190 () (= @t189 @t187)) % 3.57/3.89 (define @t191 () (tptp.mem @t102 @t91)) % 3.57/3.89 (define @t192 () (not @t191)) % 3.57/3.89 (define @t193 () (or @t97 @t153 @t192 @t190)) % 3.57/3.89 (define @t194 () (forall @t165 @t162)) % 3.57/3.89 (define @t195 () (and @t150 (not (= @t102 @t147)))) % 3.57/3.89 (define @t196 () (= @t189 @t195)) % 3.57/3.89 (define @t197 () (or @t97 @t153 @t192 @t196)) % 3.57/3.89 (define @t198 () (tptp.mem @t101 (tptp.arr @t92 @t91))) % 3.57/3.89 (define @t199 () (not @t198)) % 3.57/3.89 (define @t200 () (or @t199 @t97 @t191)) % 3.57/3.89 (define @t201 () (not @t195)) % 3.57/3.89 (define @t202 () (not @t189)) % 3.57/3.89 (define @t203 () (and @t104 @t149)) % 3.57/3.89 (assume @p1 @t14) % 3.57/3.89 (assume @p2 (forall @t22 (=> @t21 (forall @t20 (=> @t19 (=> (= @t18 @t17) (= @t16 @t15))))))) % 3.57/3.89 (assume @p3 (forall @t13 (=> @t11 (forall (@list @t23) (=> (tptp.mem @t23 @t10) (=> (forall @t8 (=> @t7 (= @t4 (tptp.ap @t23 @t2)))) (= @t3 @t23))))))) % 3.57/3.89 (assume @p4 (forall (@list @t6 @t24 @t2) (=> @t7 (= (tptp.ap (tptp.k @t6 @t24) @t2) @t24)))) % 3.57/3.89 (assume @p5 (forall @t25 (=> @t7 (= (tptp.ap (tptp.i @t6) @t2) @t2)))) % 3.57/3.89 (assume @p6 (forall @t28 (= (tptp.surj__o @t27) @t26))) % 3.57/3.89 (assume @p7 (forall @t28 (tptp.mem @t27 tptp.bool))) % 3.57/3.89 (assume @p8 (forall @t8 (=> (tptp.mem @t2 tptp.bool) (= @t2 (tptp.inj__o (tptp.surj__o @t2)))))) % 3.57/3.89 (assume @p9 (tptp.mem tptp.c_2Emin_2E_3D_3D_3E @t30)) % 3.57/3.89 (assume @p10 (forall @t35 (= (tptp.inj__o (tptp.fo__c_2Emin_2E_3D_3D_3E @t33 @t31)) (tptp.ap (tptp.ap tptp.c_2Emin_2E_3D_3D_3E @t34) @t32)))) % 3.57/3.89 (assume @p11 (forall @t22 (=> @t21 (forall @t20 (=> @t19 (= (tptp.p (tptp.ap (tptp.ap tptp.c_2Emin_2E_3D_3D_3E @t16) @t15)) (=> @t18 @t17))))))) % 3.57/3.89 (assume @p12 (forall @t40 (tptp.mem @t39 (tptp.arr @t37 @t38)))) % 3.57/3.89 (assume @p13 (tptp.mem tptp.c_2Ebool_2E_7E @t29)) % 3.57/3.89 (assume @p14 (forall (@list @t33) (= (tptp.inj__o (tptp.fo__c_2Ebool_2E_7E @t33)) (tptp.ap tptp.c_2Ebool_2E_7E @t34)))) % 3.57/3.89 (assume @p15 (forall @t22 (=> @t21 (= (tptp.p (tptp.ap tptp.c_2Ebool_2E_7E @t16)) (not @t18))))) % 3.57/3.89 (assume @p16 (tptp.mem tptp.c_2Ebool_2E_2F_5C @t30)) % 3.57/3.89 (assume @p17 (forall @t35 (= (tptp.inj__o (tptp.fo__c_2Ebool_2E_2F_5C @t33 @t31)) (tptp.ap (tptp.ap tptp.c_2Ebool_2E_2F_5C @t34) @t32)))) % 3.57/3.89 (assume @p18 (forall @t22 (=> @t21 (forall @t20 (=> @t19 (= (tptp.p (tptp.ap (tptp.ap tptp.c_2Ebool_2E_2F_5C @t16) @t15)) (and @t18 @t17))))))) % 3.57/3.89 (assume @p19 (forall @t40 (tptp.mem @t41 (tptp.arr @t36 @t38)))) % 3.57/3.89 (assume @p20 (forall @t40 (tptp.mem @t42 (tptp.arr @t37 @t36)))) % 3.57/3.89 (assume @p21 (forall @t40 (tptp.mem @t44 (tptp.arr @t37 @t43)))) % 3.57/3.89 (assume @p22 (forall @t40 (tptp.mem @t45 (tptp.arr @t37 @t37)))) % 3.57/3.89 (assume @p23 (forall @t40 (tptp.mem (tptp.c_2Emin_2E_3D @t36) @t43))) % 3.57/3.89 (assume @p24 (forall @t25 (=> @t7 (forall (@list @t24) (=> (tptp.mem @t24 @t6) (= (tptp.p (tptp.ap (tptp.ap (tptp.c_2Emin_2E_3D @t6) @t2) @t24)) (= @t2 @t24))))))) % 3.57/3.89 (assume @p25 (forall @t40 (tptp.mem (tptp.c_2Ebool_2E_21 @t36) @t38))) % 3.57/3.89 (assume @p26 (forall (@list @t6 @t16) (=> (tptp.mem @t16 (tptp.arr @t6 tptp.bool)) (= (tptp.p (tptp.ap (tptp.c_2Ebool_2E_21 @t6) @t16)) (forall @t8 (=> @t7 (tptp.p (tptp.ap @t16 @t2)))))))) % 3.57/3.89 (assume @p27 @t66) % 3.57/3.89 (assume @p28 @t81) % 3.57/3.89 (assume @p29 @t84) % 3.57/3.89 (assume @p30 @t87) % 3.57/3.89 (assume @p31 true) % 3.57/3.89 (step @p32 :rule bool-impl-elim :args (@t63 @t83)) % 3.57/3.89 (step @p33 :rule cong :premises (@p32) :args (@t84)) % 3.57/3.89 (step @p34 :rule eq_resolve :premises (@p29 @p33)) % 3.57/3.89 (step @p35 :rule instantiate :premises (@p34) :args ((@list @t91 @t90))) % 3.57/3.89 (step @p36 :rule bool-impl-elim :args (@t63 @t85)) % 3.57/3.89 (step @p37 :rule cong :premises (@p36) :args (@t86)) % 3.57/3.89 (step @p38 :rule cong :premises (@p37) :args (@t87)) % 3.57/3.89 (step @p39 :rule eq_resolve :premises (@p30 @p38)) % 3.57/3.89 (step @p40 :rule skolemize :premises (@p39)) % 3.57/3.89 (step @p41 :rule bool-double-not-elim :args (@t93)) % 3.57/3.89 (step @p42 :rule refl :args (@t98)) % 3.57/3.89 (step @p43 :rule nary_cong :premises (@p42 @p41) :args ((or @t98 (not @t97)))) % 3.57/3.89 (step @p44 :rule cnf_or_neg :args (@t98 0)) % 3.57/3.89 (step @p45 :rule eq_resolve :premises (@p44 @p43)) % 3.57/3.89 (step @p46 :rule reordering :premises (@p45) :args ((or @t93 @t98))) % 3.57/3.89 (step @p47 :rule chain_m_resolution :premises (@p46 @p40) :args (@t93 @t99 @t100)) % 3.57/3.89 (step @p48 :rule cnf_or_pos :args (@t105)) % 3.57/3.89 (step @p49 :rule reordering :premises (@p48) :args ((or @t97 @t104 (not @t105)))) % 3.57/3.89 (step @p50 :rule chain_m_resolution :premises (@p49 @p47 @p35) :args (@t104 (@list false false) (@list @t93 @t105))) % 3.57/3.89 (step @p51 :rule aci_norm :args ((= @t112 (or @t88 @t110 @t109)))) % 3.57/3.89 (step @p52 :rule cong :premises (@p51) :args (@t113)) % 3.57/3.89 (step @p53 :rule quant-merge-prenex :args ((= (forall @t65 @t115) @t113))) % 3.57/3.89 (step @p54 :rule alpha_equiv :args (@t116 (@list @t106) (@list @t46))) % 3.57/3.89 (step @p55 :rule refl :args (@t88)) % 3.57/3.89 (step @p56 :rule nary_cong :premises (@p55 @p54) :args (@t117)) % 3.57/3.89 (step @p57 :rule quant-miniscope-or :args ((= @t115 @t117))) % 3.57/3.89 (step @p58 :rule trans :premises (@p57 @p56)) % 3.57/3.89 (step @p59 :rule symm :premises (@p58)) % 3.57/3.89 (step @p60 :rule cong :premises (@p59) :args ((forall @t65 (or @t88 @t120)))) % 3.57/3.89 (step @p61 :rule trans :premises (@p60 @p53)) % 3.57/3.89 (step @p62 :rule trans :premises (@p61 @p52)) % 3.57/3.89 (step @p63 :rule bool-impl-elim :args (@t63 @t120)) % 3.57/3.89 (step @p64 :rule cong :premises (@p63) :args ((forall @t65 (=> @t63 @t120)))) % 3.57/3.89 (step @p65 :rule trans :premises (@p64 @p62)) % 3.57/3.89 (step @p66 :rule bool-impl-elim :args (@t59 @t119)) % 3.57/3.89 (step @p67 :rule cong :premises (@p66) :args ((forall @t61 (=> @t59 @t119)))) % 3.57/3.89 (step @p68 :rule aci_norm :args ((= (or @t108 (or @t107 @t49)) @t118))) % 3.57/3.89 (step @p69 :rule bool-impl-elim :args (@t51 @t49)) % 3.57/3.89 (step @p70 :rule refl :args (@t108)) % 3.57/3.89 (step @p71 :rule nary_cong :premises (@p70 @p69) :args ((or @t108 @t52))) % 3.57/3.89 (step @p72 :rule trans :premises (@p71 @p68)) % 3.57/3.89 (step @p73 :rule bool-impl-elim :args (@t53 @t52)) % 3.57/3.89 (step @p74 :rule trans :premises (@p73 @p72)) % 3.57/3.89 (step @p75 :rule cong :premises (@p74) :args (@t55)) % 3.57/3.89 (step @p76 :rule refl :args (@t57)) % 3.57/3.89 (step @p77 :rule cong :premises (@p76 @p75) :args (@t58)) % 3.57/3.89 (step @p78 :rule refl :args (@t59)) % 3.57/3.89 (step @p79 :rule cong :premises (@p78 @p77) :args (@t60)) % 3.57/3.89 (step @p80 :rule cong :premises (@p79) :args (@t62)) % 3.57/3.89 (step @p81 :rule trans :premises (@p80 @p67)) % 3.57/3.89 (step @p82 :rule refl :args (@t63)) % 3.57/3.89 (step @p83 :rule cong :premises (@p82 @p81) :args (@t64)) % 3.57/3.89 (step @p84 :rule cong :premises (@p83) :args (@t66)) % 3.57/3.89 (step @p85 :rule trans :premises (@p84 @p65)) % 3.57/3.89 (step @p86 :rule eq_resolve :premises (@p27 @p85)) % 3.57/3.89 (step @p87 :rule instantiate :premises (@p86) :args ((@list @t91 @t95 @t90))) % 3.57/3.89 (step @p88 :rule aci_norm :args ((= @t126 (or @t124 @t123 @t122)))) % 3.57/3.89 (step @p89 :rule cong :premises (@p88) :args (@t127)) % 3.57/3.89 (step @p90 :rule quant-merge-prenex :args ((= (forall @t13 @t129) @t127))) % 3.57/3.89 (step @p91 :rule alpha_equiv :args (@t130 (@list @t121) (@list @t2))) % 3.57/3.89 (step @p92 :rule refl :args (@t124)) % 3.57/3.89 (step @p93 :rule nary_cong :premises (@p92 @p91) :args (@t131)) % 3.57/3.89 (step @p94 :rule quant-miniscope-or :args ((= @t129 @t131))) % 3.57/3.89 (step @p95 :rule trans :premises (@p94 @p93)) % 3.57/3.89 (step @p96 :rule symm :premises (@p95)) % 3.57/3.89 (step @p97 :rule cong :premises (@p96) :args ((forall @t13 (or @t124 @t132)))) % 3.57/3.89 (step @p98 :rule trans :premises (@p97 @p90)) % 3.57/3.89 (step @p99 :rule trans :premises (@p98 @p89)) % 3.57/3.89 (step @p100 :rule bool-impl-elim :args (@t11 @t132)) % 3.57/3.89 (step @p101 :rule cong :premises (@p100) :args ((forall @t13 (=> @t11 @t132)))) % 3.57/3.89 (step @p102 :rule trans :premises (@p101 @p99)) % 3.57/3.89 (step @p103 :rule bool-impl-elim :args (@t7 @t5)) % 3.57/3.89 (step @p104 :rule cong :premises (@p103) :args (@t9)) % 3.57/3.89 (step @p105 :rule refl :args (@t11)) % 3.57/3.89 (step @p106 :rule cong :premises (@p105 @p104) :args (@t12)) % 3.57/3.89 (step @p107 :rule cong :premises (@p106) :args (@t14)) % 3.57/3.89 (step @p108 :rule trans :premises (@p107 @p102)) % 3.57/3.89 (step @p109 :rule eq_resolve :premises (@p1 @p108)) % 3.57/3.89 (step @p110 :rule instantiate :premises (@p109) :args ((@list @t92 @t92 @t94 @t90))) % 3.57/3.89 (step @p111 :rule instantiate :premises (@p22) :args (@t133)) % 3.57/3.89 (step @p112 :rule cnf_or_pos :args (@t137)) % 3.57/3.89 (step @p113 :rule reordering :premises (@p112) :args ((or @t97 @t134 @t136 (not @t137)))) % 3.57/3.89 (step @p114 :rule chain_m_resolution :premises (@p113 @p47 @p111 @p110) :args (@t134 @t138 (@list @t93 @t135 @t137))) % 3.57/3.89 (step @p115 :rule cnf_or_pos :args (@t144)) % 3.57/3.89 (step @p116 :rule reordering :premises (@p115) :args ((or @t97 @t143 @t142 (not @t144)))) % 3.57/3.89 (step @p117 :rule chain_m_resolution :premises (@p116 @p47 @p114 @p87) :args (@t142 @t138 (@list @t93 @t134 @t144))) % 3.57/3.89 (step @p118 :rule cnf_or_neg :args (@t98 1)) % 3.57/3.89 (step @p119 :rule chain_m_resolution :premises (@p118 @p40) :args ((not @t96) @t99 @t100)) % 3.57/3.89 (step @p120 :rule cnf_equiv_pos2 :args (@t142)) % 3.57/3.89 (step @p121 :rule reordering :premises (@p120) :args ((or @t96 @t145 (not @t142)))) % 3.57/3.89 (step @p122 :rule chain_m_resolution :premises (@p121 @p119 @p117) :args (@t145 @t146 (@list @t96 @t142))) % 3.57/3.89 (step @p123 :rule skolemize :premises (@p122)) % 3.57/3.89 (step @p124 :rule bool-double-not-elim :args (@t149)) % 3.57/3.89 (step @p125 :rule refl :args (@t154)) % 3.57/3.89 (step @p126 :rule nary_cong :premises (@p125 @p124) :args ((or @t154 (not @t151)))) % 3.57/3.89 (step @p127 :rule cnf_or_neg :args (@t154 1)) % 3.57/3.89 (step @p128 :rule eq_resolve :premises (@p127 @p126)) % 3.57/3.89 (step @p129 :rule reordering :premises (@p128) :args ((or @t149 @t154))) % 3.57/3.89 (step @p130 :rule chain_m_resolution :premises (@p129 @p123) :args (@t149 @t99 @t155)) % 3.57/3.89 (step @p131 :rule aci_norm :args ((= @t164 @t162))) % 3.57/3.89 (step @p132 :rule cong :premises (@p131) :args (@t166)) % 3.57/3.89 (step @p133 :rule quant-merge-prenex :args ((= (forall @t65 @t168) @t166))) % 3.57/3.89 (step @p134 :rule alpha_equiv :args (@t169 (@list @t157 @t156) (@list @t68 @t170))) % 3.57/3.89 (step @p135 :rule nary_cong :premises (@p55 @p134) :args (@t171)) % 3.57/3.89 (step @p136 :rule quant-miniscope-or :args ((= @t168 @t171))) % 3.57/3.89 (step @p137 :rule trans :premises (@p136 @p135)) % 3.57/3.89 (step @p138 :rule symm :premises (@p137)) % 3.57/3.89 (step @p139 :rule cong :premises (@p138) :args ((forall @t65 (or @t88 @t177)))) % 3.57/3.89 (step @p140 :rule trans :premises (@p139 @p133)) % 3.57/3.89 (step @p141 :rule trans :premises (@p140 @p132)) % 3.57/3.89 (step @p142 :rule bool-impl-elim :args (@t63 @t177)) % 3.57/3.89 (step @p143 :rule cong :premises (@p142) :args ((forall @t65 (=> @t63 @t177)))) % 3.57/3.89 (step @p144 :rule trans :premises (@p143 @p141)) % 3.57/3.89 (step @p145 :rule aci_norm :args ((= @t179 @t175))) % 3.57/3.89 (step @p146 :rule cong :premises (@p145) :args (@t180)) % 3.57/3.89 (step @p147 :rule quant-merge-prenex :args ((= (forall @t78 @t182) @t180))) % 3.57/3.89 (step @p148 :rule alpha_equiv :args (@t183 (@list @t170) (@list @t67))) % 3.57/3.89 (step @p149 :rule refl :args (@t174)) % 3.57/3.89 (step @p150 :rule nary_cong :premises (@p149 @p148) :args (@t184)) % 3.57/3.89 (step @p151 :rule quant-miniscope-or :args ((= @t182 @t184))) % 3.57/3.89 (step @p152 :rule trans :premises (@p151 @p150)) % 3.57/3.89 (step @p153 :rule symm :premises (@p152)) % 3.57/3.89 (step @p154 :rule cong :premises (@p153) :args ((forall @t78 (or @t174 @t185)))) % 3.57/3.89 (step @p155 :rule trans :premises (@p154 @p147)) % 3.57/3.89 (step @p156 :rule trans :premises (@p155 @p146)) % 3.57/3.89 (step @p157 :rule bool-impl-elim :args (@t76 @t185)) % 3.57/3.89 (step @p158 :rule cong :premises (@p157) :args ((forall @t78 (=> @t76 @t185)))) % 3.57/3.89 (step @p159 :rule trans :premises (@p158 @p156)) % 3.57/3.89 (step @p160 :rule bool-impl-elim :args (@t73 @t72)) % 3.57/3.89 (step @p161 :rule cong :premises (@p160) :args (@t75)) % 3.57/3.89 (step @p162 :rule refl :args (@t76)) % 3.57/3.89 (step @p163 :rule cong :premises (@p162 @p161) :args (@t77)) % 3.57/3.89 (step @p164 :rule cong :premises (@p163) :args (@t79)) % 3.57/3.89 (step @p165 :rule trans :premises (@p164 @p159)) % 3.57/3.89 (step @p166 :rule cong :premises (@p82 @p165) :args (@t80)) % 0.33/3.90 (step @p167 :rule cong :premises (@p166) :args (@t81)) % 0.33/3.90 (step @p168 :rule trans :premises (@p167 @p144)) % 0.33/3.90 (step @p169 :rule eq_resolve :premises (@p28 @p168)) % 0.33/3.90 (step @p170 :rule eq-symm :args (@t147 @t102)) % 0.33/3.90 (step @p171 :rule cong :premises (@p170) :args (@t186)) % 0.33/3.90 (step @p172 :rule refl :args (@t150)) % 0.33/3.90 (step @p173 :rule nary_cong :premises (@p172 @p171) :args (@t187)) % 0.33/3.90 (step @p174 :rule refl :args (@t189)) % 0.33/3.90 (step @p175 :rule cong :premises (@p174 @p173) :args (@t190)) % 0.33/3.90 (step @p176 :rule refl :args (@t192)) % 0.33/3.90 (step @p177 :rule refl :args (@t153)) % 0.33/3.90 (step @p178 :rule refl :args (@t97)) % 0.33/3.90 (step @p179 :rule nary_cong :premises (@p178 @p177 @p176 @p175) :args (@t193)) % 0.33/3.90 (step @p180 :rule refl :args (@t194)) % 0.33/3.90 (step @p181 :rule cong :premises (@p180 @p179) :args ((=> @t194 @t193))) % 0.33/3.90 (assume-push @p227 @t194) % 0.33/3.90 (step @p183 :rule instantiate :premises (@p169) :args ((@list @t91 @t90 @t147 @t102))) % 0.33/3.90 (step-pop @p228 :rule scope :premises (@p183)) % 0.33/3.90 (step @p184 :rule process_scope :premises (@p228) :args (@t193)) % 0.33/3.90 (step @p186 :rule eq_resolve :premises (@p184 @p181)) % 0.33/3.90 (step @p187 :rule implies_elim :premises (@p186)) % 0.33/3.90 (step @p188 :rule chain_m_resolution :premises (@p187 @p169) :args (@t197 (@list false) (@list @t194))) % 0.33/3.90 (step @p189 :rule bool-double-not-elim :args (@t152)) % 0.33/3.90 (step @p190 :rule nary_cong :premises (@p125 @p189) :args ((or @t154 (not @t153)))) % 0.33/3.90 (step @p191 :rule cnf_or_neg :args (@t154 0)) % 0.33/3.90 (step @p192 :rule eq_resolve :premises (@p191 @p190)) % 0.33/3.90 (step @p193 :rule reordering :premises (@p192) :args ((or @t152 @t154))) % 0.33/3.90 (step @p194 :rule chain_m_resolution :premises (@p193 @p123) :args (@t152 @t99 @t155)) % 0.33/3.90 (step @p195 :rule instantiate :premises (@p109) :args ((@list @t92 @t91 @t101 @t90))) % 0.33/3.90 (step @p196 :rule instantiate :premises (@p20) :args (@t133)) % 0.33/3.90 (step @p197 :rule cnf_or_pos :args (@t200)) % 0.33/3.90 (step @p198 :rule reordering :premises (@p197) :args ((or @t97 @t199 @t191 (not @t200)))) % 0.33/3.90 (step @p199 :rule chain_m_resolution :premises (@p198 @p47 @p196 @p195) :args (@t191 @t138 (@list @t93 @t198 @t200))) % 0.33/3.90 (step @p200 :rule cnf_or_pos :args (@t197)) % 0.33/3.90 (step @p201 :rule reordering :premises (@p200) :args ((or @t97 @t192 @t153 @t196 (not @t197)))) % 0.33/3.90 (step @p202 :rule chain_m_resolution :premises (@p201 @p47 @p199 @p194 @p188) :args (@t196 (@list false false false false) (@list @t93 @t191 @t152 @t197))) % 0.33/3.90 (step @p203 :rule cnf_or_neg :args (@t154 2)) % 0.33/3.90 (step @p204 :rule chain_m_resolution :premises (@p203 @p123) :args ((not @t150) @t99 @t155)) % 0.33/3.90 (step @p205 :rule cnf_and_pos :args (@t195 0)) % 0.33/3.90 (step @p206 :rule reordering :premises (@p205) :args ((or @t150 @t201))) % 0.33/3.90 (step @p207 :rule chain_m_resolution :premises (@p206 @p204) :args (@t201 @t99 (@list @t150))) % 0.33/3.90 (step @p208 :rule cnf_equiv_pos1 :args (@t196)) % 0.33/3.90 (step @p209 :rule reordering :premises (@p208) :args ((or @t195 @t202 (not @t196)))) % 0.33/3.90 (step @p210 :rule chain_m_resolution :premises (@p209 @p207 @p202) :args (@t202 @t146 (@list @t195 @t196))) % 0.33/3.90 (assume-push @p229 @t104) % 0.33/3.90 (assume-push @p230 @t149) % 0.33/3.90 (step @p213 :rule true_intro :premises (@p130)) % 0.33/3.90 (step @p214 :rule symm :premises (@p50)) % 0.33/3.90 (step @p215 :rule refl :args (@t148)) % 0.33/3.90 (step @p216 :rule cong :premises (@p215 @p214) :args (@t188)) % 0.33/3.90 (step @p217 :rule cong :premises (@p216) :args (@t189)) % 0.33/3.90 (step @p218 :rule trans :premises (@p217 @p213)) % 0.33/3.90 (step @p219 :rule true_elim :premises (@p218)) % 0.33/3.90 (step-pop @p231 :rule scope :premises (@p219)) % 0.33/3.90 (step-pop @p232 :rule scope :premises (@p231)) % 0.33/3.90 (step @p220 :rule process_scope :premises (@p232) :args (@t189)) % 0.33/3.90 (step @p223 :rule implies_elim :premises (@p220)) % 0.33/3.90 (step @p224 :rule cnf_and_neg :args (@t203)) % 0.33/3.90 (step @p225 :rule resolution :premises (@p224 @p223) :args (true @t203)) % 0.33/3.90 (step @p226 false :rule chain_m_resolution :premises (@p225 @p210 @p130 @p50) :args (false (@list true false false) (@list @t189 @t149 @t104))) % 0.33/3.90 ) % 0.33/3.90 % SZS output end Proof % 0.33/3.90 % cvc5 exiting %------------------------------------------------------------------------------