%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : ITP023_2 : TPTP v9.2.1. Bugfixed v7.5.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n001.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 08:24:47 AM UTC 2026 % Result : Theorem 36.11s 36.37s % Output : Proof 36.11s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : ITP023_2 : TPTP v9.2.1. Bugfixed v7.5.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n001.cluster.edu % 0.16/0.34 % Model : x86_64 x86_64 % 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.34 % Memory : 8042.1875MB % 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.34 % CPULimit : 300 % 0.16/0.34 % WCLimit : 300 % 0.16/0.34 % DateTime : Tue Jun 2 04:05:50 EDT 2026 % 0.16/0.34 % CPUTime : % 0.31/0.51 %----Proving TF0_NAR, FOF, or CNF % 36.11/36.37 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 36.11/36.37 --- Run --no-e-matching --full-saturate-quant at 6... % 36.11/36.37 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 6... % 36.11/36.37 --- Run --finite-model-find --uf-ss=no-minimal at 6... % 36.11/36.37 --- Run --multi-trigger-when-single --full-saturate-quant at 30... % 36.11/36.37 % SZS status Theorem % 36.11/36.37 % SZS output start Proof % 36.11/36.37 ( % 36.11/36.37 (declare-sort tptp.tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal 0) % 36.11/36.37 (declare-sort tptp.tp__ty_2Erealax_2Ereal 0) % 36.11/36.37 (declare-sort tptp.tp__o 0) % 36.11/36.37 (declare-sort tptp.del 0) % 36.11/36.37 (declare-sort $$unsorted 0) % 36.11/36.37 (declare-const tptp.c_2Ebool_2E_21 (-> tptp.del $$unsorted)) % 36.11/36.37 (declare-const tptp.fo__c_2Ebool_2E_7E (-> tptp.tp__o tptp.tp__o)) % 36.11/36.37 (declare-const tptp.c_2Ebool_2E_7E $$unsorted) % 36.11/36.37 (declare-const tptp.c_2Ebool_2E_2F_5C $$unsorted) % 36.11/36.37 (declare-const tptp.fo__c_2Ebool_2E_5C_2F (-> tptp.tp__o tptp.tp__o tptp.tp__o)) % 36.11/36.37 (declare-const tptp.inj__ty_2Erealax_2Ereal (-> tptp.tp__ty_2Erealax_2Ereal $$unsorted)) % 36.11/36.37 (declare-const tptp.fo__c_2Ebool_2ET tptp.tp__o) % 36.11/36.37 (declare-const tptp.c_2Ebool_2ET $$unsorted) % 36.11/36.37 (declare-const tptp.surj__o (-> $$unsorted tptp.tp__o)) % 36.11/36.37 (declare-const tptp.inj__o (-> tptp.tp__o $$unsorted)) % 36.11/36.37 (declare-const tptp.c_2Emin_2E_3D (-> tptp.del $$unsorted)) % 36.11/36.37 (declare-const tptp.i (-> tptp.del $$unsorted)) % 36.11/36.37 (declare-const tptp.fo__c_2Ereal__topology_2Ecball (-> tptp.tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal tptp.tp__ty_2Erealax_2Ereal tptp.tp__o)) % 36.11/36.37 (declare-const tptp.k (-> tptp.del $$unsorted $$unsorted)) % 36.11/36.37 (declare-const tptp.c_2Ereal__topology_2Ecball $$unsorted) % 36.11/36.37 (declare-const tptp.p (-> $$unsorted Bool)) % 36.11/36.37 (declare-const tptp.arr (-> tptp.del tptp.del tptp.del)) % 36.11/36.37 (declare-const tptp.fo__c_2Ereal__topology_2Eball (-> tptp.tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal tptp.tp__ty_2Erealax_2Ereal tptp.tp__o)) % 36.11/36.37 (declare-const tptp.mem (-> $$unsorted tptp.del Bool)) % 36.11/36.37 (declare-const tptp.ap (-> $$unsorted $$unsorted $$unsorted)) % 36.11/36.37 (declare-const tptp.c_2Epair_2E_2C (-> tptp.del tptp.del $$unsorted)) % 36.11/36.37 (declare-const tptp.surj__ty_2Erealax_2Ereal (-> $$unsorted tptp.tp__ty_2Erealax_2Ereal)) % 36.11/36.37 (declare-const tptp.c_2Emin_2E_3D_3D_3E $$unsorted) % 36.11/36.37 (declare-const tptp.c_2Ebool_2E_5C_2F $$unsorted) % 36.11/36.37 (declare-const tptp.ty_2Erealax_2Ereal tptp.del) % 36.11/36.37 (declare-const tptp.c_2Epred__set_2ESUBSET (-> tptp.del $$unsorted)) % 36.11/36.37 (declare-const tptp.fo__c_2Ebool_2EF tptp.tp__o) % 36.11/36.37 (declare-const tptp.surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (-> $$unsorted tptp.tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal)) % 36.11/36.37 (declare-const tptp.fo__c_2Ebool_2E_2F_5C (-> tptp.tp__o tptp.tp__o tptp.tp__o)) % 36.11/36.37 (declare-const tptp.ty_2Epair_2Eprod (-> tptp.del tptp.del tptp.del)) % 36.11/36.37 (declare-const tptp.bool tptp.del) % 36.11/36.37 (declare-const tptp.c_2Ereal__topology_2Eball $$unsorted) % 36.11/36.37 (declare-const tptp.inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (-> tptp.tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal $$unsorted)) % 36.11/36.37 (declare-const tptp.c_2Ereal__topology_2Ebounded__def $$unsorted) % 36.11/36.37 (declare-const tptp.c_2Ebool_2EF $$unsorted) % 36.11/36.37 (declare-const tptp.c_2Ebool_2E_3F (-> tptp.del $$unsorted)) % 36.11/36.37 (declare-const tptp.fo__c_2Emin_2E_3D_3D_3E (-> tptp.tp__o tptp.tp__o tptp.tp__o)) % 36.11/36.37 (define @t1 () (@var "B" tptp.del)) % 36.11/36.37 (define @t2 () (@var "X" $$unsorted)) % 36.11/36.37 (define @t3 () (@var "F" $$unsorted)) % 36.11/36.37 (define @t4 () (tptp.ap @t3 @t2)) % 36.11/36.37 (define @t5 () (tptp.mem @t4 @t1)) % 36.11/36.37 (define @t6 () (@var "A" tptp.del)) % 36.11/36.37 (define @t7 () (tptp.mem @t2 @t6)) % 36.11/36.37 (define @t8 () (@list @t2)) % 36.11/36.37 (define @t9 () (forall @t8 (=> @t7 @t5))) % 36.11/36.37 (define @t10 () (tptp.arr @t6 @t1)) % 36.11/36.37 (define @t11 () (tptp.mem @t3 @t10)) % 36.11/36.37 (define @t12 () (=> @t11 @t9)) % 36.11/36.37 (define @t13 () (@list @t6 @t1 @t3)) % 36.11/36.37 (define @t14 () (forall @t13 @t12)) % 36.11/36.37 (define @t15 () (@var "R" $$unsorted)) % 36.11/36.37 (define @t16 () (@var "Q" $$unsorted)) % 36.11/36.37 (define @t17 () (tptp.p @t15)) % 36.11/36.37 (define @t18 () (tptp.p @t16)) % 36.11/36.37 (define @t19 () (tptp.mem @t15 tptp.bool)) % 36.11/36.37 (define @t20 () (@list @t15)) % 36.11/36.37 (define @t21 () (tptp.mem @t16 tptp.bool)) % 36.11/36.37 (define @t22 () (@list @t16)) % 36.11/36.37 (define @t23 () (@var "G" $$unsorted)) % 36.11/36.37 (define @t24 () (@var "Y" $$unsorted)) % 36.11/36.37 (define @t25 () (@list @t6 @t2)) % 36.11/36.37 (define @t26 () (@var "X" tptp.tp__o)) % 36.11/36.37 (define @t27 () (tptp.inj__o @t26)) % 36.11/36.37 (define @t28 () (@list @t26)) % 36.11/36.37 (define @t29 () (@var "A_27a" tptp.del)) % 36.11/36.37 (define @t30 () (tptp.arr @t29 tptp.bool)) % 36.11/36.37 (define @t31 () (tptp.arr @t30 tptp.bool)) % 36.11/36.37 (define @t32 () (@list @t29)) % 36.11/36.37 (define @t33 () (tptp.p (tptp.ap @t16 @t2))) % 36.11/36.37 (define @t34 () (tptp.mem @t16 (tptp.arr @t6 tptp.bool))) % 36.11/36.37 (define @t35 () (@list @t6 @t16)) % 36.11/36.37 (define @t36 () (@var "X" tptp.tp__ty_2Erealax_2Ereal)) % 36.11/36.37 (define @t37 () (tptp.inj__ty_2Erealax_2Ereal @t36)) % 36.11/36.37 (define @t38 () (@list @t36)) % 36.11/36.37 (define @t39 () (@var "X" tptp.tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal)) % 36.11/36.37 (define @t40 () (tptp.inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @t39)) % 36.11/36.37 (define @t41 () (@list @t39)) % 36.11/36.37 (define @t42 () (tptp.ty_2Epair_2Eprod tptp.ty_2Erealax_2Ereal tptp.ty_2Erealax_2Ereal)) % 36.11/36.37 (define @t43 () (tptp.arr tptp.ty_2Erealax_2Ereal tptp.bool)) % 36.11/36.37 (define @t44 () (tptp.arr @t42 @t43)) % 36.11/36.37 (define @t45 () (tptp.mem tptp.c_2Ereal__topology_2Eball @t44)) % 36.11/36.37 (define @t46 () (@var "X1" tptp.tp__ty_2Erealax_2Ereal)) % 36.11/36.37 (define @t47 () (tptp.inj__ty_2Erealax_2Ereal @t46)) % 36.11/36.37 (define @t48 () (@var "X0" tptp.tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal)) % 36.11/36.37 (define @t49 () (tptp.inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @t48)) % 36.11/36.37 (define @t50 () (@list @t48 @t46)) % 36.11/36.37 (define @t51 () (@var "A_27b" tptp.del)) % 36.11/36.37 (define @t52 () (tptp.mem tptp.c_2Ereal__topology_2Ecball @t44)) % 36.11/36.37 (define @t53 () (tptp.arr tptp.bool tptp.bool)) % 36.11/36.37 (define @t54 () (tptp.arr tptp.bool @t53)) % 36.11/36.37 (define @t55 () (@var "X1" tptp.tp__o)) % 36.11/36.37 (define @t56 () (tptp.inj__o @t55)) % 36.11/36.37 (define @t57 () (@var "X0" tptp.tp__o)) % 36.11/36.37 (define @t58 () (tptp.inj__o @t57)) % 36.11/36.37 (define @t59 () (@list @t57 @t55)) % 36.11/36.37 (define @t60 () (@var "V1t2" tptp.tp__o)) % 36.11/36.37 (define @t61 () (tptp.p (tptp.inj__o @t60))) % 36.11/36.37 (define @t62 () (@var "V0t1" tptp.tp__o)) % 36.11/36.37 (define @t63 () (tptp.p (tptp.inj__o @t62))) % 36.11/36.37 (define @t64 () (@var "V0t" tptp.tp__o)) % 36.11/36.37 (define @t65 () (tptp.p (tptp.inj__o @t64))) % 36.11/36.37 (define @t66 () (not @t65)) % 36.11/36.37 (define @t67 () (=> @t65 false)) % 36.11/36.37 (define @t68 () (@list @t64)) % 36.11/36.37 (define @t69 () (forall @t68 (= (not @t66) @t65))) % 36.11/36.37 (define @t70 () (@var "V0x" $$unsorted)) % 36.11/36.37 (define @t71 () (@var "V1y" $$unsorted)) % 36.11/36.37 (define @t72 () (@var "V2x" $$unsorted)) % 36.11/36.37 (define @t73 () (@var "V0P" $$unsorted)) % 36.11/36.37 (define @t74 () (@var "V1x" $$unsorted)) % 36.11/36.37 (define @t75 () (@var "V2C" tptp.tp__o)) % 36.11/36.37 (define @t76 () (@var "V1B" tptp.tp__o)) % 36.11/36.37 (define @t77 () (tptp.p (tptp.inj__o @t76))) % 36.11/36.37 (define @t78 () (@var "V0A" tptp.tp__o)) % 36.11/36.37 (define @t79 () (tptp.p (tptp.inj__o @t78))) % 36.11/36.37 (define @t80 () (or @t79 @t77 (tptp.p (tptp.inj__o @t75)))) % 36.11/36.37 (define @t81 () (or @t79 @t77)) % 36.11/36.37 (define @t82 () (@list @t78 @t76)) % 36.11/36.37 (define @t83 () (not @t77)) % 36.11/36.37 (define @t84 () (not @t79)) % 36.11/36.37 (define @t85 () (not @t81)) % 36.11/36.37 (define @t86 () (@var "V1e" tptp.tp__ty_2Erealax_2Ereal)) % 36.11/36.37 (define @t87 () (@var "V0x" tptp.tp__ty_2Erealax_2Ereal)) % 36.11/36.37 (define @t88 () (tptp.c_2Epair_2E_2C tptp.ty_2Erealax_2Ereal tptp.ty_2Erealax_2Ereal)) % 36.11/36.37 (define @t89 () (tptp.ap (tptp.ap @t88 (tptp.inj__ty_2Erealax_2Ereal @t87)) (tptp.inj__ty_2Erealax_2Ereal @t86))) % 36.11/36.37 (define @t90 () (tptp.ap tptp.c_2Ereal__topology_2Ecball @t89)) % 36.11/36.37 (define @t91 () (tptp.ap tptp.c_2Ereal__topology_2Eball @t89)) % 36.11/36.37 (define @t92 () (tptp.c_2Epred__set_2ESUBSET tptp.ty_2Erealax_2Ereal)) % 36.11/36.37 (define @t93 () (@list @t87 @t86)) % 36.11/36.37 (define @t94 () (@var "V0s" $$unsorted)) % 36.11/36.37 (define @t95 () (tptp.p (tptp.ap tptp.c_2Ereal__topology_2Ebounded__def @t94))) % 36.11/36.37 (define @t96 () (@var "V1t" $$unsorted)) % 36.11/36.37 (define @t97 () (tptp.ap @t92 @t94)) % 36.11/36.37 (define @t98 () (tptp.p (tptp.ap @t97 @t96))) % 36.11/36.37 (define @t99 () (tptp.p (tptp.ap tptp.c_2Ereal__topology_2Ebounded__def @t96))) % 36.11/36.37 (define @t100 () (and @t99 @t98)) % 36.11/36.37 (define @t101 () (=> @t100 @t95)) % 36.11/36.37 (define @t102 () (tptp.mem @t96 @t43)) % 36.11/36.37 (define @t103 () (@list @t96)) % 36.11/36.37 (define @t104 () (forall @t103 (=> @t102 @t101))) % 36.11/36.37 (define @t105 () (tptp.mem @t94 @t43)) % 36.11/36.37 (define @t106 () (=> @t105 @t104)) % 36.11/36.37 (define @t107 () (@list @t94)) % 36.11/36.37 (define @t108 () (forall @t107 @t106)) % 36.11/36.37 (define @t109 () (=> @t84 false)) % 36.11/36.37 (define @t110 () (@list @t78)) % 36.11/36.37 (define @t111 () (=> @t83 false)) % 36.11/36.37 (define @t112 () (=> @t79 false)) % 36.11/36.37 (define @t113 () (@var "V0p" tptp.tp__o)) % 36.11/36.37 (define @t114 () (tptp.p (tptp.inj__o @t113))) % 36.11/36.37 (define @t115 () (not @t114)) % 36.11/36.37 (define @t116 () (@var "V1q" tptp.tp__o)) % 36.11/36.37 (define @t117 () (tptp.p (tptp.inj__o @t116))) % 36.11/36.37 (define @t118 () (not @t117)) % 36.11/36.37 (define @t119 () (@var "V2r" tptp.tp__o)) % 36.11/36.37 (define @t120 () (tptp.p (tptp.inj__o @t119))) % 36.11/36.37 (define @t121 () (not @t120)) % 36.11/36.37 (define @t122 () (@list @t113 @t116 @t119)) % 36.11/36.37 (define @t123 () (or @t114 @t121)) % 36.11/36.37 (define @t124 () (or @t114 @t117)) % 36.11/36.37 (define @t125 () (forall @t93 (tptp.p (tptp.ap tptp.c_2Ereal__topology_2Ebounded__def @t91)))) % 36.11/36.37 (define @t126 () (@quantifiers_skolemize @t125 1)) % 36.11/36.37 (define @t127 () (@quantifiers_skolemize @t125 0)) % 36.11/36.37 (define @t128 () (@list @t127 @t126)) % 36.11/36.37 (define @t129 () (@var "BOUND_VARIABLE_8268" $$unsorted)) % 36.11/36.37 (define @t130 () (not (tptp.p (tptp.ap @t97 @t129)))) % 36.11/36.37 (define @t131 () (not (tptp.p (tptp.ap tptp.c_2Ereal__topology_2Ebounded__def @t129)))) % 36.11/36.37 (define @t132 () (not (tptp.mem @t129 @t43))) % 36.11/36.37 (define @t133 () (not @t105)) % 36.11/36.37 (define @t134 () (or @t132 @t131 @t130)) % 36.11/36.37 (define @t135 () (or @t133 @t95 @t134)) % 36.11/36.37 (define @t136 () (forall (@list @t94 @t129) @t135)) % 36.11/36.37 (define @t137 () (@list @t129)) % 36.11/36.37 (define @t138 () (forall @t137 @t135)) % 36.11/36.37 (define @t139 () (forall @t137 @t134)) % 36.11/36.37 (define @t140 () (or @t133 @t95 @t139)) % 36.11/36.37 (define @t141 () (not @t98)) % 36.11/36.37 (define @t142 () (not @t99)) % 36.11/36.37 (define @t143 () (not @t102)) % 36.11/36.37 (define @t144 () (or @t143 @t142 @t141)) % 36.11/36.37 (define @t145 () (forall @t103 @t144)) % 36.11/36.37 (define @t146 () (or @t133 @t95 @t145)) % 36.11/36.37 (define @t147 () (or @t95 @t145)) % 36.11/36.37 (define @t148 () (or @t95 @t144)) % 36.11/36.37 (define @t149 () (or @t143 @t142 @t141 @t95)) % 36.11/36.37 (define @t150 () (or @t142 @t141 @t95)) % 36.11/36.37 (define @t151 () (tptp.inj__ty_2Erealax_2Ereal @t126)) % 36.11/36.37 (define @t152 () (tptp.inj__ty_2Erealax_2Ereal @t127)) % 36.11/36.37 (define @t153 () (tptp.ap @t88 @t152)) % 36.11/36.37 (define @t154 () (tptp.ap @t153 @t151)) % 36.11/36.37 (define @t155 () (tptp.ap tptp.c_2Ereal__topology_2Ecball @t154)) % 36.11/36.37 (define @t156 () (tptp.ap tptp.c_2Ereal__topology_2Eball @t154)) % 36.11/36.37 (define @t157 () (@var "BOUND_VARIABLE_7958" $$unsorted)) % 36.11/36.37 (define @t158 () (tptp.mem (tptp.ap @t3 @t157) @t1)) % 36.11/36.37 (define @t159 () (not (tptp.mem @t157 @t6))) % 36.11/36.37 (define @t160 () (not @t11)) % 36.11/36.37 (define @t161 () (or @t159 @t158)) % 36.11/36.37 (define @t162 () (or @t160 @t161)) % 36.11/36.37 (define @t163 () (forall (@list @t6 @t1 @t3 @t157) @t162)) % 36.11/36.37 (define @t164 () (@list @t157)) % 36.11/36.37 (define @t165 () (forall @t164 @t162)) % 36.11/36.37 (define @t166 () (forall @t164 @t161)) % 36.11/36.37 (define @t167 () (or @t160 @t166)) % 36.11/36.37 (define @t168 () (forall @t8 (or (not @t7) @t5))) % 36.11/36.37 (define @t169 () (tptp.arr tptp.ty_2Erealax_2Ereal @t42)) % 36.11/36.37 (define @t170 () (tptp.mem @t153 @t169)) % 36.11/36.37 (define @t171 () (tptp.mem @t152 tptp.ty_2Erealax_2Ereal)) % 36.11/36.37 (define @t172 () (not @t171)) % 36.11/36.37 (define @t173 () (tptp.mem @t88 (tptp.arr tptp.ty_2Erealax_2Ereal @t169))) % 36.11/36.37 (define @t174 () (not @t173)) % 36.11/36.37 (define @t175 () (or @t174 @t172 @t170)) % 36.11/36.37 (define @t176 () (@list false false false)) % 36.11/36.37 (define @t177 () (tptp.mem @t154 @t42)) % 36.11/36.37 (define @t178 () (tptp.mem @t151 tptp.ty_2Erealax_2Ereal)) % 36.11/36.37 (define @t179 () (not @t178)) % 36.11/36.37 (define @t180 () (not @t170)) % 36.11/36.37 (define @t181 () (or @t180 @t179 @t177)) % 36.11/36.37 (define @t182 () (tptp.mem @t155 @t43)) % 36.11/36.37 (define @t183 () (not @t177)) % 36.11/36.37 (define @t184 () (not @t52)) % 36.11/36.37 (define @t185 () (or @t184 @t183 @t182)) % 36.11/36.37 (define @t186 () (tptp.mem @t156 @t43)) % 36.11/36.37 (define @t187 () (not @t45)) % 36.11/36.37 (define @t188 () (or @t187 @t183 @t186)) % 36.11/36.37 (define @t189 () (tptp.p (tptp.ap (tptp.ap @t92 @t156) @t155))) % 36.11/36.37 (define @t190 () (not @t189)) % 36.11/36.37 (define @t191 () (tptp.p (tptp.ap tptp.c_2Ereal__topology_2Ebounded__def @t155))) % 36.11/36.37 (define @t192 () (not @t191)) % 36.11/36.37 (define @t193 () (not @t182)) % 36.11/36.37 (define @t194 () (tptp.p (tptp.ap tptp.c_2Ereal__topology_2Ebounded__def @t156))) % 36.11/36.37 (define @t195 () (not @t186)) % 36.11/36.37 (define @t196 () (or @t195 @t194 @t193 @t192 @t190)) % 36.11/36.37 (assume @p1 @t14) % 36.11/36.37 (assume @p2 (forall @t22 (=> @t21 (forall @t20 (=> @t19 (=> (= @t18 @t17) (= @t16 @t15))))))) % 36.11/36.37 (assume @p3 (forall @t13 (=> @t11 (forall (@list @t23) (=> (tptp.mem @t23 @t10) (=> (forall @t8 (=> @t7 (= @t4 (tptp.ap @t23 @t2)))) (= @t3 @t23))))))) % 36.11/36.37 (assume @p4 (forall (@list @t6 @t24 @t2) (=> @t7 (= (tptp.ap (tptp.k @t6 @t24) @t2) @t24)))) % 36.11/36.37 (assume @p5 (forall @t25 (=> @t7 (= (tptp.ap (tptp.i @t6) @t2) @t2)))) % 36.11/36.38 (assume @p6 (forall @t28 (= (tptp.surj__o @t27) @t26))) % 36.11/36.38 (assume @p7 (forall @t28 (tptp.mem @t27 tptp.bool))) % 36.11/36.38 (assume @p8 (forall @t8 (=> (tptp.mem @t2 tptp.bool) (= @t2 (tptp.inj__o (tptp.surj__o @t2)))))) % 36.11/36.38 (assume @p9 (tptp.mem tptp.c_2Ebool_2ET tptp.bool)) % 36.11/36.38 (assume @p10 (= (tptp.inj__o tptp.fo__c_2Ebool_2ET) tptp.c_2Ebool_2ET)) % 36.11/36.38 (assume @p11 (tptp.p tptp.c_2Ebool_2ET)) % 36.11/36.38 (assume @p12 (forall @t32 (tptp.mem (tptp.c_2Ebool_2E_3F @t29) @t31))) % 36.11/36.38 (assume @p13 (forall @t35 (=> @t34 (= (tptp.p (tptp.ap (tptp.c_2Ebool_2E_3F @t6) @t16)) (exists @t8 (and @t7 @t33)))))) % 36.11/36.38 (assume @p14 (forall @t38 (= (tptp.surj__ty_2Erealax_2Ereal @t37) @t36))) % 36.11/36.38 (assume @p15 (forall @t38 (tptp.mem @t37 tptp.ty_2Erealax_2Ereal))) % 36.11/36.38 (assume @p16 (forall @t8 (=> (tptp.mem @t2 tptp.ty_2Erealax_2Ereal) (= @t2 (tptp.inj__ty_2Erealax_2Ereal (tptp.surj__ty_2Erealax_2Ereal @t2)))))) % 36.11/36.38 (assume @p17 (forall @t41 (= (tptp.surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @t40) @t39))) % 36.11/36.38 (assume @p18 (forall @t41 (tptp.mem @t40 @t42))) % 36.11/36.38 (assume @p19 (forall @t8 (=> (tptp.mem @t2 @t42) (= @t2 (tptp.inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (tptp.surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @t2)))))) % 36.11/36.38 (assume @p20 @t45) % 36.11/36.38 (assume @p21 (forall @t50 (= (tptp.inj__o (tptp.fo__c_2Ereal__topology_2Eball @t48 @t46)) (tptp.ap (tptp.ap tptp.c_2Ereal__topology_2Eball @t49) @t47)))) % 36.11/36.38 (assume @p22 (forall @t32 (tptp.mem (tptp.c_2Epred__set_2ESUBSET @t29) (tptp.arr @t30 @t31)))) % 36.11/36.38 (assume @p23 (forall (@list @t29 @t51) (tptp.mem (tptp.c_2Epair_2E_2C @t29 @t51) (tptp.arr @t29 (tptp.arr @t51 (tptp.ty_2Epair_2Eprod @t29 @t51)))))) % 36.11/36.38 (assume @p24 @t52) % 36.11/36.38 (assume @p25 (forall @t50 (= (tptp.inj__o (tptp.fo__c_2Ereal__topology_2Ecball @t48 @t46)) (tptp.ap (tptp.ap tptp.c_2Ereal__topology_2Ecball @t49) @t47)))) % 36.11/36.38 (assume @p26 (tptp.mem tptp.c_2Ereal__topology_2Ebounded__def (tptp.arr @t43 tptp.bool))) % 36.11/36.38 (assume @p27 (tptp.mem tptp.c_2Ebool_2EF tptp.bool)) % 36.11/36.38 (assume @p28 (= (tptp.inj__o tptp.fo__c_2Ebool_2EF) tptp.c_2Ebool_2EF)) % 36.11/36.38 (assume @p29 (not (tptp.p tptp.c_2Ebool_2EF))) % 36.11/36.38 (assume @p30 (tptp.mem tptp.c_2Emin_2E_3D_3D_3E @t54)) % 36.11/36.38 (assume @p31 (forall @t59 (= (tptp.inj__o (tptp.fo__c_2Emin_2E_3D_3D_3E @t57 @t55)) (tptp.ap (tptp.ap tptp.c_2Emin_2E_3D_3D_3E @t58) @t56)))) % 36.11/36.38 (assume @p32 (forall @t22 (=> @t21 (forall @t20 (=> @t19 (= (tptp.p (tptp.ap (tptp.ap tptp.c_2Emin_2E_3D_3D_3E @t16) @t15)) (=> @t18 @t17))))))) % 36.11/36.38 (assume @p33 (tptp.mem tptp.c_2Ebool_2E_5C_2F @t54)) % 36.11/36.38 (assume @p34 (forall @t59 (= (tptp.inj__o (tptp.fo__c_2Ebool_2E_5C_2F @t57 @t55)) (tptp.ap (tptp.ap tptp.c_2Ebool_2E_5C_2F @t58) @t56)))) % 36.11/36.38 (assume @p35 (forall @t22 (=> @t21 (forall @t20 (=> @t19 (= (tptp.p (tptp.ap (tptp.ap tptp.c_2Ebool_2E_5C_2F @t16) @t15)) (or @t18 @t17))))))) % 36.11/36.38 (assume @p36 (tptp.mem tptp.c_2Ebool_2E_2F_5C @t54)) % 36.11/36.38 (assume @p37 (forall @t59 (= (tptp.inj__o (tptp.fo__c_2Ebool_2E_2F_5C @t57 @t55)) (tptp.ap (tptp.ap tptp.c_2Ebool_2E_2F_5C @t58) @t56)))) % 36.11/36.38 (assume @p38 (forall @t22 (=> @t21 (forall @t20 (=> @t19 (= (tptp.p (tptp.ap (tptp.ap tptp.c_2Ebool_2E_2F_5C @t16) @t15)) (and @t18 @t17))))))) % 36.11/36.38 (assume @p39 (tptp.mem tptp.c_2Ebool_2E_7E @t53)) % 36.11/36.38 (assume @p40 (forall (@list @t57) (= (tptp.inj__o (tptp.fo__c_2Ebool_2E_7E @t57)) (tptp.ap tptp.c_2Ebool_2E_7E @t58)))) % 36.11/36.38 (assume @p41 (forall @t22 (=> @t21 (= (tptp.p (tptp.ap tptp.c_2Ebool_2E_7E @t16)) (not @t18))))) % 36.11/36.38 (assume @p42 (forall @t32 (tptp.mem (tptp.c_2Emin_2E_3D @t29) (tptp.arr @t29 @t30)))) % 36.11/36.38 (assume @p43 (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))))))) % 36.11/36.38 (assume @p44 (forall @t32 (tptp.mem (tptp.c_2Ebool_2E_21 @t29) @t31))) % 36.11/36.38 (assume @p45 (forall @t35 (=> @t34 (= (tptp.p (tptp.ap (tptp.c_2Ebool_2E_21 @t6) @t16)) (forall @t8 (=> @t7 @t33)))))) % 36.11/36.38 (assume @p46 true) % 36.11/36.38 (assume @p47 (forall (@list @t62 @t60) (=> (=> @t63 @t61) (=> (=> @t61 @t63) (= @t63 @t61))))) % 36.11/36.38 (assume @p48 (forall @t68 (=> @t67 @t66))) % 36.11/36.38 (assume @p49 (forall @t68 (=> @t66 @t67))) % 36.11/36.38 (assume @p50 (forall @t68 (and (= (=> true @t65) @t65) (= (=> @t65 true) true) (= (=> false @t65) true) (= (=> @t65 @t65) true) (= @t67 @t66)))) % 36.11/36.38 (assume @p51 (and @t69 (= (not true) false) (= (not false) true))) % 36.11/36.38 (assume @p52 (forall (@list @t29 @t70) (=> (tptp.mem @t70 @t29) (forall (@list @t71) (=> (tptp.mem @t71 @t29) (= (= @t70 @t71) (= @t71 @t70))))))) % 36.11/36.38 (assume @p53 (forall @t68 (and (= (= true @t65) @t65) (= (= @t65 true) @t65) (= (= false @t65) @t66) (= (= @t65 false) @t66)))) % 36.11/36.38 (assume @p54 (forall (@list @t29 @t73) (=> (tptp.mem @t73 @t30) (= (not (forall (@list @t74) (=> (tptp.mem @t74 @t29) (tptp.p (tptp.ap @t73 @t74))))) (exists (@list @t72) (and (tptp.mem @t72 @t29) (not (tptp.p (tptp.ap @t73 @t72))))))))) % 36.11/36.38 (assume @p55 (forall (@list @t78 @t76 @t75) (= @t80 @t80))) % 36.11/36.38 (assume @p56 (forall @t82 (= @t81 (or @t77 @t79)))) % 36.11/36.38 (assume @p57 (forall @t82 (and (= (not (and @t79 @t77)) (or @t84 @t83)) (= @t85 (and @t84 @t83))))) % 36.11/36.38 (assume @p58 (forall @t93 (tptp.p (tptp.ap (tptp.ap @t92 @t91) @t90)))) % 36.11/36.38 (assume @p59 @t108) % 36.11/36.38 (assume @p60 (forall @t93 (tptp.p (tptp.ap tptp.c_2Ereal__topology_2Ebounded__def @t90)))) % 36.11/36.38 (assume @p61 @t69) % 36.11/36.38 (assume @p62 (forall @t110 (=> @t79 @t109))) % 36.11/36.38 (assume @p63 (forall @t82 (= (=> @t85 false) (=> @t112 @t111)))) % 36.11/36.38 (assume @p64 (forall @t82 (= (=> (not (or @t84 @t77)) false) (=> @t79 @t111)))) % 36.11/36.38 (assume @p65 (forall @t110 (=> @t109 (=> @t112 false)))) % 36.11/36.38 (assume @p66 (forall @t122 (= (= @t114 (= @t117 @t120)) (and (or @t114 @t117 @t120) (or @t114 @t121 @t118) (or @t117 @t121 @t115) (or @t120 @t118 @t115))))) % 36.11/36.38 (assume @p67 (forall @t122 (= (= @t114 (and @t117 @t120)) (and (or @t114 @t118 @t121) (or @t117 @t115) (or @t120 @t115))))) % 36.11/36.38 (assume @p68 (forall @t122 (= (= @t114 (or @t117 @t120)) (and (or @t114 @t118) @t123 (or @t117 @t120 @t115))))) % 36.11/36.38 (assume @p69 (forall @t122 (= (= @t114 (=> @t117 @t120)) (and @t124 @t123 (or @t118 @t120 @t115))))) % 36.11/36.38 (assume @p70 (forall (@list @t113 @t116) (= (= @t114 @t118) (and @t124 (or @t118 @t115))))) % 36.11/36.38 (assume @p71 (not @t125)) % 36.11/36.38 (step @p72 :rule skolemize :premises (@p71)) % 36.11/36.38 (step @p73 :rule instantiate :premises (@p58) :args (@t128)) % 36.11/36.38 (step @p74 :rule instantiate :premises (@p60) :args (@t128)) % 36.11/36.38 (step @p75 :rule aci_norm :args ((= @t135 (or @t133 @t95 @t132 @t131 @t130)))) % 36.11/36.38 (step @p76 :rule cong :premises (@p75) :args (@t136)) % 36.11/36.38 (step @p77 :rule quant-merge-prenex :args ((= (forall @t107 @t138) @t136))) % 36.11/36.38 (step @p78 :rule alpha_equiv :args (@t139 (@list @t129) (@list @t96))) % 36.11/36.38 (step @p79 :rule refl :args (@t95)) % 36.11/36.38 (step @p80 :rule refl :args (@t133)) % 36.11/36.38 (step @p81 :rule nary_cong :premises (@p80 @p79 @p78) :args (@t140)) % 36.11/36.38 (step @p82 :rule quant-miniscope-or :args ((= @t138 @t140))) % 36.11/36.38 (step @p83 :rule trans :premises (@p82 @p81)) % 36.11/36.38 (step @p84 :rule symm :premises (@p83)) % 36.11/36.38 (step @p85 :rule cong :premises (@p84) :args ((forall @t107 @t146))) % 36.11/36.38 (step @p86 :rule trans :premises (@p85 @p77)) % 36.11/36.38 (step @p87 :rule trans :premises (@p86 @p76)) % 36.11/36.38 (step @p88 :rule aci_norm :args ((= (or @t133 @t147) @t146))) % 36.11/36.38 (step @p89 :rule bool-impl-elim :args (@t105 @t147)) % 36.11/36.38 (step @p90 :rule trans :premises (@p89 @p88)) % 36.11/36.38 (step @p91 :rule cong :premises (@p90) :args ((forall @t107 (=> @t105 @t147)))) % 36.11/36.38 (step @p92 :rule trans :premises (@p91 @p87)) % 36.11/36.38 (step @p93 :rule quant-miniscope-or :args ((= (forall @t103 @t148) @t147))) % 36.11/36.38 (step @p94 :rule aci_norm :args ((= @t149 @t148))) % 36.11/36.38 (step @p95 :rule cong :premises (@p94) :args ((forall @t103 @t149))) % 36.11/36.38 (step @p96 :rule trans :premises (@p95 @p93)) % 36.11/36.38 (step @p97 :rule aci_norm :args ((= (or @t143 @t150) @t149))) % 36.11/36.38 (step @p98 :rule aci_norm :args ((= (or (or @t142 @t141) @t95) @t150))) % 36.11/36.38 (step @p99 :rule bool-and-de-morgan :args (@t99 @t98 true)) % 36.11/36.38 (step @p100 :rule nary_cong :premises (@p99 @p79) :args ((or (not @t100) @t95))) % 36.11/36.38 (step @p101 :rule trans :premises (@p100 @p98)) % 36.11/36.38 (step @p102 :rule bool-impl-elim :args (@t100 @t95)) % 36.11/36.38 (step @p103 :rule trans :premises (@p102 @p101)) % 36.11/36.38 (step @p104 :rule refl :args (@t143)) % 36.11/36.38 (step @p105 :rule nary_cong :premises (@p104 @p103) :args ((or @t143 @t101))) % 36.11/36.38 (step @p106 :rule trans :premises (@p105 @p97)) % 36.11/36.38 (step @p107 :rule bool-impl-elim :args (@t102 @t101)) % 36.11/36.38 (step @p108 :rule trans :premises (@p107 @p106)) % 36.11/36.38 (step @p109 :rule cong :premises (@p108) :args (@t104)) % 36.11/36.38 (step @p110 :rule trans :premises (@p109 @p96)) % 36.11/36.38 (step @p111 :rule refl :args (@t105)) % 36.11/36.38 (step @p112 :rule cong :premises (@p111 @p110) :args (@t106)) % 36.11/36.38 (step @p113 :rule cong :premises (@p112) :args (@t108)) % 36.11/36.38 (step @p114 :rule trans :premises (@p113 @p92)) % 36.11/36.38 (step @p115 :rule eq_resolve :premises (@p59 @p114)) % 36.11/36.38 (step @p116 :rule instantiate :premises (@p115) :args ((@list @t156 @t155))) % 36.11/36.38 (step @p117 :rule aci_norm :args ((= @t162 (or @t160 @t159 @t158)))) % 36.11/36.38 (step @p118 :rule cong :premises (@p117) :args (@t163)) % 36.11/36.38 (step @p119 :rule quant-merge-prenex :args ((= (forall @t13 @t165) @t163))) % 36.11/36.38 (step @p120 :rule alpha_equiv :args (@t166 (@list @t157) (@list @t2))) % 36.11/36.38 (step @p121 :rule refl :args (@t160)) % 36.11/36.38 (step @p122 :rule nary_cong :premises (@p121 @p120) :args (@t167)) % 36.11/36.38 (step @p123 :rule quant-miniscope-or :args ((= @t165 @t167))) % 36.11/36.38 (step @p124 :rule trans :premises (@p123 @p122)) % 36.11/36.38 (step @p125 :rule symm :premises (@p124)) % 36.11/36.38 (step @p126 :rule cong :premises (@p125) :args ((forall @t13 (or @t160 @t168)))) % 36.11/36.38 (step @p127 :rule trans :premises (@p126 @p119)) % 36.11/36.38 (step @p128 :rule trans :premises (@p127 @p118)) % 36.11/36.38 (step @p129 :rule bool-impl-elim :args (@t11 @t168)) % 36.11/36.38 (step @p130 :rule cong :premises (@p129) :args ((forall @t13 (=> @t11 @t168)))) % 36.11/36.38 (step @p131 :rule trans :premises (@p130 @p128)) % 36.11/36.38 (step @p132 :rule bool-impl-elim :args (@t7 @t5)) % 36.11/36.38 (step @p133 :rule cong :premises (@p132) :args (@t9)) % 36.11/36.38 (step @p134 :rule refl :args (@t11)) % 36.11/36.38 (step @p135 :rule cong :premises (@p134 @p133) :args (@t12)) % 36.11/36.38 (step @p136 :rule cong :premises (@p135) :args (@t14)) % 36.11/36.38 (step @p137 :rule trans :premises (@p136 @p131)) % 36.11/36.38 (step @p138 :rule eq_resolve :premises (@p1 @p137)) % 36.11/36.38 (step @p139 :rule instantiate :premises (@p138) :args ((@list @t42 @t43 tptp.c_2Ereal__topology_2Ecball @t154))) % 36.11/36.38 (step @p140 :rule instantiate :premises (@p138) :args ((@list tptp.ty_2Erealax_2Ereal @t42 @t153 @t151))) % 36.11/36.38 (step @p141 :rule instantiate :premises (@p138) :args ((@list tptp.ty_2Erealax_2Ereal @t169 @t88 @t152))) % 36.11/36.38 (step @p142 :rule instantiate :premises (@p23) :args ((@list tptp.ty_2Erealax_2Ereal tptp.ty_2Erealax_2Ereal))) % 36.11/36.38 (step @p143 :rule instantiate :premises (@p15) :args ((@list @t127))) % 36.11/36.38 (step @p144 :rule cnf_or_pos :args (@t175)) % 36.11/36.38 (step @p145 :rule reordering :premises (@p144) :args ((or @t172 @t174 @t170 (not @t175)))) % 36.11/36.38 (step @p146 :rule chain_m_resolution :premises (@p145 @p143 @p142 @p141) :args (@t170 @t176 (@list @t171 @t173 @t175))) % 36.11/36.38 (step @p147 :rule instantiate :premises (@p15) :args ((@list @t126))) % 36.11/36.38 (step @p148 :rule cnf_or_pos :args (@t181)) % 36.11/36.38 (step @p149 :rule reordering :premises (@p148) :args ((or @t179 @t180 @t177 (not @t181)))) % 36.11/36.38 (step @p150 :rule chain_m_resolution :premises (@p149 @p147 @p146 @p140) :args (@t177 @t176 (@list @t178 @t170 @t181))) % 36.11/36.38 (step @p151 :rule cnf_or_pos :args (@t185)) % 36.11/36.38 (step @p152 :rule reordering :premises (@p151) :args ((or @t184 @t182 @t183 (not @t185)))) % 36.11/36.38 (step @p153 :rule chain_m_resolution :premises (@p152 @p24 @p150 @p139) :args (@t182 @t176 (@list @t52 @t177 @t185))) % 36.11/36.38 (step @p154 :rule instantiate :premises (@p138) :args ((@list @t42 @t43 tptp.c_2Ereal__topology_2Eball @t154))) % 36.11/36.38 (step @p155 :rule cnf_or_pos :args (@t188)) % 36.11/36.38 (step @p156 :rule reordering :premises (@p155) :args ((or @t187 @t186 @t183 (not @t188)))) % 36.11/36.38 (step @p157 :rule chain_m_resolution :premises (@p156 @p20 @p150 @p154) :args (@t186 @t176 (@list @t45 @t177 @t188))) % 36.11/36.38 (step @p158 :rule cnf_or_pos :args (@t196)) % 36.11/36.38 (step @p159 :rule reordering :premises (@p158) :args ((or @t194 @t190 @t192 @t195 @t193 (not @t196)))) % 36.11/36.38 (step @p160 false :rule chain_m_resolution :premises (@p159 @p157 @p153 @p116 @p74 @p73 @p72) :args (false (@list false false false false false true) (@list @t186 @t182 @t196 @t191 @t189 @t194))) % 36.11/36.38 ) % 36.11/36.38 % SZS output end Proof % 36.11/36.38 % cvc5 exiting %------------------------------------------------------------------------------