%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : COM144+1 : TPTP v9.2.1. Released v6.4.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n017.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 08:10:35 AM UTC 2026 % Result : Theorem 0.43s 0.64s % Output : Proof 0.43s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : COM144+1 : TPTP v9.2.1. Released v6.4.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.15/0.34 % Computer : n017.cluster.edu % 0.15/0.34 % Model : x86_64 x86_64 % 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.34 % Memory : 8042.1875MB % 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.34 % CPULimit : 300 % 0.15/0.34 % WCLimit : 300 % 0.15/0.34 % DateTime : Mon Jun 1 20:29:31 EDT 2026 % 0.15/0.34 % CPUTime : % 0.30/0.51 %----Proving TF0_NAR, FOF, or CNF % 0.43/0.64 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.43/0.64 % SZS status Theorem % 0.43/0.64 % SZS output start Proof % 0.43/0.64 ( % 0.43/0.64 (declare-sort $$unsorted 0) % 0.43/0.64 (declare-const tptp.ve1 $$unsorted) % 0.43/0.64 (declare-const tptp.varrow (-> $$unsorted $$unsorted $$unsorted)) % 0.43/0.64 (declare-const tptp.vgetSomeExp (-> $$unsorted $$unsorted)) % 0.43/0.64 (declare-const tptp.vsomeExp (-> $$unsorted $$unsorted)) % 0.43/0.64 (declare-const tptp.vnoExp $$unsorted) % 0.43/0.64 (declare-const tptp.vsubst (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.43/0.64 (declare-const tptp.vgensym (-> $$unsorted $$unsorted)) % 0.43/0.64 (declare-const tptp.vapp (-> $$unsorted $$unsorted $$unsorted)) % 0.43/0.64 (declare-const tptp.visValue (-> $$unsorted Bool)) % 0.43/0.64 (declare-const tptp.vempty $$unsorted) % 0.43/0.64 (declare-const tptp.vbind (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.43/0.64 (declare-const tptp.vnoType $$unsorted) % 0.43/0.64 (declare-const tptp.visFreeVar (-> $$unsorted $$unsorted Bool)) % 0.43/0.64 (declare-const tptp.vtcheck (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.43/0.64 (declare-const tptp.vsomeType (-> $$unsorted $$unsorted)) % 0.43/0.64 (declare-const tptp.visSomeExp (-> $$unsorted Bool)) % 0.43/0.64 (declare-const tptp.vvar (-> $$unsorted $$unsorted)) % 0.43/0.64 (declare-const tptp.vlookup (-> $$unsorted $$unsorted $$unsorted)) % 0.43/0.64 (declare-const tptp.vabs (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.43/0.64 (declare-const tptp.visSomeType (-> $$unsorted Bool)) % 0.43/0.64 (declare-const tptp.vreduce (-> $$unsorted $$unsorted)) % 0.43/0.64 (declare-const tptp.vgetSomeType (-> $$unsorted $$unsorted)) % 0.43/0.64 (define @t1 () (@var "VVar1" $$unsorted)) % 0.43/0.64 (define @t2 () (@var "VVar0" $$unsorted)) % 0.43/0.64 (define @t3 () (tptp.vvar @t2)) % 0.43/0.64 (define @t4 () (= @t3 (tptp.vvar @t1))) % 0.43/0.64 (define @t5 () (= @t2 @t1)) % 0.43/0.64 (define @t6 () (@var "VExp1" $$unsorted)) % 0.43/0.64 (define @t7 () (@var "VTyp1" $$unsorted)) % 0.43/0.64 (define @t8 () (@var "VExp0" $$unsorted)) % 0.43/0.64 (define @t9 () (@var "VTyp0" $$unsorted)) % 0.43/0.64 (define @t10 () (tptp.vabs @t2 @t9 @t8)) % 0.43/0.64 (define @t11 () (= @t10 (tptp.vabs @t1 @t7 @t6))) % 0.43/0.64 (define @t12 () (= @t8 @t6)) % 0.43/0.64 (define @t13 () (= @t9 @t7)) % 0.43/0.64 (define @t14 () (and @t5 @t13 @t12)) % 0.43/0.64 (define @t15 () (@var "VExp3" $$unsorted)) % 0.43/0.64 (define @t16 () (@var "VExp2" $$unsorted)) % 0.43/0.64 (define @t17 () (tptp.vapp @t8 @t6)) % 0.43/0.64 (define @t18 () (= @t17 (tptp.vapp @t16 @t15))) % 0.43/0.64 (define @t19 () (and (= @t8 @t16) (= @t6 @t15))) % 0.43/0.64 (define @t20 () (tptp.visValue @t8)) % 0.43/0.64 (define @t21 () (@var "Ve" $$unsorted)) % 0.43/0.64 (define @t22 () (@var "VS" $$unsorted)) % 0.43/0.64 (define @t23 () (@var "Vx" $$unsorted)) % 0.43/0.64 (define @t24 () (tptp.vabs @t23 @t22 @t21)) % 0.43/0.64 (define @t25 () (= @t8 @t24)) % 0.43/0.64 (define @t26 () (not @t20)) % 0.43/0.64 (define @t27 () (tptp.vvar @t23)) % 0.43/0.64 (define @t28 () (= @t8 @t27)) % 0.43/0.64 (define @t29 () (@var "Ve2" $$unsorted)) % 0.43/0.64 (define @t30 () (@var "Ve1" $$unsorted)) % 0.43/0.64 (define @t31 () (tptp.vapp @t30 @t29)) % 0.43/0.64 (define @t32 () (= @t8 @t31)) % 0.43/0.64 (define @t33 () (@var "Vv" $$unsorted)) % 0.43/0.64 (define @t34 () (= @t23 @t33)) % 0.43/0.64 (define @t35 () (tptp.visFreeVar @t2 @t8)) % 0.43/0.64 (define @t36 () (= @t2 @t33)) % 0.43/0.64 (define @t37 () (tptp.visFreeVar @t33 @t21)) % 0.43/0.64 (define @t38 () (and (not @t34) @t37)) % 0.43/0.64 (define @t39 () (@var "VT" $$unsorted)) % 0.43/0.64 (define @t40 () (or (tptp.visFreeVar @t33 @t30) (tptp.visFreeVar @t33 @t29))) % 0.43/0.64 (define @t41 () (= tptp.vempty tptp.vempty)) % 0.43/0.64 (define @t42 () (@var "VCtx1" $$unsorted)) % 0.43/0.64 (define @t43 () (@var "VCtx0" $$unsorted)) % 0.43/0.64 (define @t44 () (tptp.vbind @t2 @t9 @t43)) % 0.43/0.64 (define @t45 () (= @t44 (tptp.vbind @t1 @t7 @t42))) % 0.43/0.64 (define @t46 () (and @t5 @t13 (= @t43 @t42))) % 0.43/0.64 (define @t47 () (= tptp.vnoType tptp.vnoType)) % 0.43/0.64 (define @t48 () (tptp.vsomeType @t9)) % 0.43/0.64 (define @t49 () (= @t48 (tptp.vsomeType @t7))) % 0.43/0.64 (define @t50 () (@var "VOptTyp0" $$unsorted)) % 0.43/0.64 (define @t51 () (tptp.visSomeType @t50)) % 0.43/0.64 (define @t52 () (= @t50 (tptp.vsomeType @t21))) % 0.43/0.64 (define @t53 () (@var "RESULT" $$unsorted)) % 0.43/0.64 (define @t54 () (= @t53 @t21)) % 0.43/0.64 (define @t55 () (= @t53 tptp.vnoType)) % 0.43/0.64 (define @t56 () (tptp.vlookup @t2 @t43)) % 0.43/0.64 (define @t57 () (= @t53 @t56)) % 0.43/0.64 (define @t58 () (= @t43 tptp.vempty)) % 0.43/0.64 (define @t59 () (= @t2 @t23)) % 0.43/0.64 (define @t60 () (@var "VTy" $$unsorted)) % 0.43/0.64 (define @t61 () (= @t53 (tptp.vsomeType @t60))) % 0.43/0.64 (define @t62 () (@var "Vy" $$unsorted)) % 0.43/0.64 (define @t63 () (= @t23 @t62)) % 0.43/0.64 (define @t64 () (@var "VC" $$unsorted)) % 0.43/0.64 (define @t65 () (tptp.vbind @t62 @t60 @t64)) % 0.43/0.64 (define @t66 () (= @t43 @t65)) % 0.43/0.64 (define @t67 () (and @t59 @t66)) % 0.43/0.64 (define @t68 () (tptp.vlookup @t23 @t64)) % 0.43/0.64 (define @t69 () (= @t53 @t68)) % 0.43/0.64 (define @t70 () (not @t63)) % 0.43/0.64 (define @t71 () (@list @t23)) % 0.43/0.64 (define @t72 () (@var "VTx" $$unsorted)) % 0.43/0.64 (define @t73 () (tptp.vbind @t23 @t72 @t64)) % 0.43/0.64 (define @t74 () (tptp.vtcheck (tptp.vbind @t23 @t72 @t65) @t21 @t39)) % 0.43/0.64 (define @t75 () (@list @t62 @t60 @t23 @t72 @t64 @t21 @t39)) % 0.43/0.64 (define @t76 () (tptp.vsubst @t2 @t8 @t6)) % 0.43/0.64 (define @t77 () (= @t53 @t76)) % 0.43/0.64 (define @t78 () (tptp.vvar @t62)) % 0.43/0.64 (define @t79 () (= @t6 @t78)) % 0.43/0.64 (define @t80 () (= @t8 @t21)) % 0.43/0.64 (define @t81 () (and @t59 @t80 @t79)) % 0.43/0.64 (define @t82 () (= @t53 @t78)) % 0.43/0.64 (define @t83 () (tptp.vsubst @t23 @t21 @t29)) % 0.43/0.64 (define @t84 () (tptp.vsubst @t23 @t21 @t30)) % 0.43/0.64 (define @t85 () (= @t53 (tptp.vapp @t84 @t83))) % 0.43/0.64 (define @t86 () (= @t6 @t31)) % 0.43/0.64 (define @t87 () (tptp.vabs @t62 @t39 @t30)) % 0.43/0.64 (define @t88 () (= @t53 @t87)) % 0.43/0.64 (define @t89 () (= @t6 @t87)) % 0.43/0.64 (define @t90 () (and @t59 @t80 @t89)) % 0.43/0.64 (define @t91 () (@var "Vfresh" $$unsorted)) % 0.43/0.64 (define @t92 () (= @t53 (tptp.vsubst @t23 @t21 (tptp.vabs @t91 @t39 (tptp.vsubst @t62 (tptp.vvar @t91) @t30))))) % 0.43/0.64 (define @t93 () (= @t91 (tptp.vgensym (tptp.vapp (tptp.vapp @t21 @t30) @t27)))) % 0.43/0.64 (define @t94 () (tptp.visFreeVar @t62 @t21)) % 0.43/0.64 (define @t95 () (= @t53 (tptp.vabs @t62 @t39 @t84))) % 0.43/0.64 (define @t96 () (not @t94)) % 0.43/0.64 (define @t97 () (= tptp.vnoExp tptp.vnoExp)) % 0.43/0.64 (define @t98 () (tptp.vsomeExp @t8)) % 0.43/0.64 (define @t99 () (= @t98 (tptp.vsomeExp @t6))) % 0.43/0.64 (define @t100 () (@list @t8)) % 0.43/0.64 (define @t101 () (@var "VOptExp0" $$unsorted)) % 0.43/0.64 (define @t102 () (tptp.visSomeExp @t101)) % 0.43/0.64 (define @t103 () (= @t101 (tptp.vsomeExp @t21))) % 0.43/0.64 (define @t104 () (= @t53 tptp.vnoExp)) % 0.43/0.64 (define @t105 () (tptp.vreduce @t8)) % 0.43/0.64 (define @t106 () (= @t53 @t105)) % 0.43/0.64 (define @t107 () (=> @t106 @t104)) % 0.43/0.64 (define @t108 () (@list @t23 @t22 @t21 @t8 @t53)) % 0.43/0.64 (define @t109 () (forall @t108 (=> @t25 @t107))) % 0.43/0.64 (define @t110 () (@var "Ve2red" $$unsorted)) % 0.43/0.64 (define @t111 () (tptp.vabs @t23 @t22 @t30)) % 0.43/0.64 (define @t112 () (= @t53 (tptp.vsomeExp (tptp.vapp @t111 (tptp.vgetSomeExp @t110))))) % 0.43/0.64 (define @t113 () (tptp.visSomeExp @t110)) % 0.43/0.64 (define @t114 () (= @t110 (tptp.vreduce @t29))) % 0.43/0.64 (define @t115 () (= @t8 (tptp.vapp @t111 @t29))) % 0.43/0.64 (define @t116 () (= @t53 (tptp.vsomeExp (tptp.vsubst @t23 @t29 @t30)))) % 0.43/0.64 (define @t117 () (tptp.visValue @t29)) % 0.43/0.64 (define @t118 () (not @t113)) % 0.43/0.64 (define @t119 () (not @t117)) % 0.43/0.64 (define @t120 () (@var "Ve1red" $$unsorted)) % 0.43/0.64 (define @t121 () (= @t53 (tptp.vsomeExp (tptp.vapp (tptp.vgetSomeExp @t120) @t29)))) % 0.43/0.64 (define @t122 () (tptp.visSomeExp @t120)) % 0.43/0.64 (define @t123 () (= @t120 (tptp.vreduce @t30))) % 0.43/0.64 (define @t124 () (@var "VVe10" $$unsorted)) % 0.43/0.64 (define @t125 () (@var "VVS0" $$unsorted)) % 0.43/0.64 (define @t126 () (@var "VVx0" $$unsorted)) % 0.43/0.64 (define @t127 () (forall (@list @t126 @t125 @t124) (not (= @t30 (tptp.vabs @t126 @t125 @t124))))) % 0.43/0.64 (define @t128 () (and @t32 @t127)) % 0.43/0.64 (define @t129 () (not @t122)) % 0.43/0.64 (define @t130 () (@list @t23 @t22 @t21)) % 0.43/0.64 (define @t131 () (@var "VTyp3" $$unsorted)) % 0.43/0.64 (define @t132 () (@var "VTyp2" $$unsorted)) % 0.43/0.64 (define @t133 () (= (tptp.varrow @t9 @t7) (tptp.varrow @t132 @t131))) % 0.43/0.64 (define @t134 () (and (= @t9 @t132) (= @t7 @t131))) % 0.43/0.64 (define @t135 () (= @t68 (tptp.vsomeType @t39))) % 0.43/0.64 (define @t136 () (tptp.varrow @t22 @t39)) % 0.43/0.64 (define @t137 () (tptp.vtcheck (tptp.vbind @t23 @t22 @t64) @t21 @t39)) % 0.43/0.64 (define @t138 () (tptp.vtcheck @t64 @t29 @t22)) % 0.43/0.64 (define @t139 () (tptp.vtcheck @t64 @t30 @t136)) % 0.43/0.64 (define @t140 () (@var "VT2" $$unsorted)) % 0.43/0.64 (define @t141 () (@var "VT1" $$unsorted)) % 0.43/0.64 (define @t142 () (tptp.vtcheck @t64 @t21 @t39)) % 0.43/0.64 (define @t143 () (not (tptp.visFreeVar @t23 @t21))) % 0.43/0.64 (define @t144 () (@list @t23 @t22 @t64 @t21 @t39)) % 0.43/0.64 (define @t145 () (@var "Veout" $$unsorted)) % 0.43/0.64 (define @t146 () (tptp.vtcheck @t64 @t145 @t39)) % 0.43/0.64 (define @t147 () (tptp.vsomeExp @t145)) % 0.43/0.64 (define @t148 () (tptp.vabs @t23 @t22 tptp.ve1)) % 0.43/0.64 (define @t149 () (tptp.vtcheck @t64 @t148 @t39)) % 0.43/0.64 (define @t150 () (tptp.vreduce @t148)) % 0.43/0.64 (define @t151 () (and (= @t150 @t147) @t149)) % 0.43/0.64 (define @t152 () (=> @t151 @t146)) % 0.43/0.64 (define @t153 () (@list @t23 @t22 @t64 @t145 @t39)) % 0.43/0.64 (define @t154 () (forall @t153 @t152)) % 0.43/0.64 (define @t155 () (not @t154)) % 0.43/0.64 (define @t156 () (not @t149)) % 0.43/0.64 (define @t157 () (= @t147 @t150)) % 0.43/0.64 (define @t158 () (not @t157)) % 0.43/0.64 (define @t159 () (or @t158 @t156 @t146)) % 0.43/0.64 (define @t160 () (and @t157 @t149)) % 0.43/0.64 (define @t161 () (forall @t153 @t159)) % 0.43/0.64 (define @t162 () (@quantifiers_skolemize @t161 1)) % 0.43/0.64 (define @t163 () (@quantifiers_skolemize @t161 0)) % 0.43/0.64 (define @t164 () (tptp.vabs @t163 @t162 tptp.ve1)) % 0.43/0.64 (define @t165 () (tptp.vreduce @t164)) % 0.43/0.64 (define @t166 () (@quantifiers_skolemize @t161 3)) % 0.43/0.64 (define @t167 () (tptp.vsomeExp @t166)) % 0.43/0.64 (define @t168 () (= @t167 @t165)) % 0.43/0.64 (define @t169 () (@quantifiers_skolemize @t161 4)) % 0.43/0.64 (define @t170 () (@quantifiers_skolemize @t161 2)) % 0.43/0.64 (define @t171 () (not @t168)) % 0.43/0.64 (define @t172 () (or @t171 (not (tptp.vtcheck @t170 @t164 @t169)) (tptp.vtcheck @t170 @t166 @t169))) % 0.43/0.64 (define @t173 () (tptp.vreduce @t24)) % 0.43/0.64 (define @t174 () (= tptp.vnoExp @t173)) % 0.43/0.64 (define @t175 () (not (= @t173 @t173))) % 0.43/0.64 (define @t176 () (or @t175 (= @t173 tptp.vnoExp))) % 0.43/0.64 (define @t177 () (not (= @t53 @t173))) % 0.43/0.64 (define @t178 () (or @t177 @t177 @t104)) % 0.43/0.64 (define @t179 () (@list @t53)) % 0.43/0.64 (define @t180 () (or @t177 @t104)) % 0.43/0.64 (define @t181 () (forall @t179 @t180)) % 0.43/0.64 (define @t182 () (forall @t130 @t181)) % 0.43/0.64 (define @t183 () (@list @t23 @t22 @t21 @t53)) % 0.43/0.64 (define @t184 () (not (= @t24 @t24))) % 0.43/0.64 (define @t185 () (or @t184 @t177 @t104)) % 0.43/0.64 (define @t186 () (not @t106)) % 0.43/0.64 (define @t187 () (not @t25)) % 0.43/0.64 (define @t188 () (or @t187 @t187 @t186 @t104)) % 0.43/0.64 (define @t189 () (or @t187 @t186 @t104)) % 0.43/0.64 (define @t190 () (forall @t100 @t189)) % 0.43/0.64 (define @t191 () (forall @t183 @t190)) % 0.43/0.64 (define @t192 () (forall (@list @t23 @t22 @t21 @t53 @t8) @t189)) % 0.43/0.64 (define @t193 () (= tptp.vnoExp @t165)) % 0.43/0.64 (define @t194 () (not @t193)) % 0.43/0.64 (define @t195 () (= tptp.vnoExp @t167)) % 0.43/0.64 (define @t196 () (not @t195)) % 0.43/0.64 (define @t197 () (and @t168 @t196)) % 0.43/0.64 (assume @p1 (forall (@list @t2 @t1) (and (=> @t4 @t5) (=> @t5 @t4)))) % 0.43/0.64 (assume @p2 (forall (@list @t2 @t9 @t8 @t1 @t7 @t6) (and (=> @t11 @t14) (=> @t14 @t11)))) % 0.43/0.64 (assume @p3 (forall (@list @t8 @t6 @t16 @t15) (and (=> @t18 @t19) (=> @t19 @t18)))) % 0.43/0.64 (assume @p4 (forall (@list @t2 @t1 @t9 @t8) (not (= @t3 (tptp.vabs @t1 @t9 @t8))))) % 0.43/0.64 (assume @p5 (forall (@list @t2 @t8 @t6) (not (= @t3 @t17)))) % 0.43/0.64 (assume @p6 (forall (@list @t2 @t9 @t8 @t6 @t16) (not (= @t10 (tptp.vapp @t6 @t16))))) % 0.43/0.64 (assume @p7 (forall (@list @t23 @t22 @t21 @t8) (=> @t25 @t20))) % 0.43/0.64 (assume @p8 (forall (@list @t23 @t8) (=> @t28 @t26))) % 0.43/0.64 (assume @p9 (forall (@list @t30 @t29 @t8) (=> @t32 @t26))) % 0.43/0.64 (assume @p10 (forall (@list @t2 @t8 @t23 @t33) (=> (and @t36 @t28) (and (=> @t34 @t35) (=> @t35 @t34))))) % 0.43/0.64 (assume @p11 (forall (@list @t39 @t2 @t8 @t23 @t33 @t21) (=> (and @t36 (= @t8 (tptp.vabs @t23 @t39 @t21))) (and (=> @t38 @t35) (=> @t35 @t38))))) % 0.43/0.64 (assume @p12 (forall (@list @t2 @t8 @t30 @t33 @t29) (=> (and @t36 @t32) (and (=> @t40 @t35) (=> @t35 @t40))))) % 0.43/0.64 (assume @p13 (and (=> @t41 true) (=> true @t41))) % 0.43/0.64 (assume @p14 (forall (@list @t2 @t9 @t43 @t1 @t7 @t42) (and (=> @t45 @t46) (=> @t46 @t45)))) % 0.43/0.64 (assume @p15 (and (=> @t47 true) (=> true @t47))) % 0.43/0.64 (assume @p16 (forall (@list @t9 @t7) (and (=> @t49 @t13) (=> @t13 @t49)))) % 0.43/0.64 (assume @p17 (forall (@list @t2 @t9 @t43) (not (= tptp.vempty @t44)))) % 0.43/0.64 (assume @p18 (forall (@list @t9) (not (= tptp.vnoType @t48)))) % 0.43/0.64 (assume @p19 (forall (@list @t50) (=> (= @t50 tptp.vnoType) (not @t51)))) % 0.43/0.64 (assume @p20 (forall (@list @t21 @t50) (=> @t52 @t51))) % 0.43/0.64 (assume @p21 (forall (@list @t50 @t53 @t21) (=> @t52 (=> (= @t53 (tptp.vgetSomeType @t50)) @t54)))) % 0.43/0.64 (assume @p22 (forall (@list @t23 @t2 @t43 @t53) (=> (and @t59 @t58) (=> @t57 @t55)))) % 0.43/0.64 (assume @p23 (forall (@list @t64 @t23 @t62 @t2 @t43 @t53 @t60) (=> @t67 (=> @t63 (=> @t57 @t61))))) % 0.43/0.64 (assume @p24 (forall (@list @t60 @t62 @t2 @t43 @t53 @t23 @t64) (=> @t67 (=> @t70 (=> @t57 @t69))))) % 0.43/0.64 (assume @p25 (forall (@list @t2 @t43 @t53) (=> (= @t56 @t53) (or (exists @t71 (and @t59 @t58 @t55)) (exists (@list @t64 @t23 @t62 @t60) (and @t59 @t66 @t63 @t61)) (exists (@list @t60 @t62 @t23 @t64) (and @t59 @t66 @t70 @t69)))))) % 0.43/0.64 (assume @p26 (forall @t75 (=> (and @t63 @t74) (tptp.vtcheck @t73 @t21 @t39)))) % 0.43/0.64 (assume @p27 (forall @t75 (=> (and @t70 @t74) (tptp.vtcheck (tptp.vbind @t62 @t60 @t73) @t21 @t39)))) % 0.43/0.64 (assume @p28 (forall (@list @t33 @t21) (=> (= (tptp.vgensym @t21) @t33) (not @t37)))) % 0.43/0.64 (assume @p29 (forall (@list @t23 @t62 @t2 @t8 @t6 @t53 @t21) (=> @t81 (=> @t63 (=> @t77 @t54))))) % 0.43/0.64 (assume @p30 (forall (@list @t21 @t23 @t2 @t8 @t6 @t53 @t62) (=> @t81 (=> @t70 (=> @t77 @t82))))) % 0.43/0.64 (assume @p31 (forall (@list @t2 @t8 @t6 @t53 @t30 @t23 @t21 @t29) (=> (and @t59 @t80 @t86) (=> @t77 @t85)))) % 0.43/0.64 (assume @p32 (forall (@list @t21 @t23 @t2 @t8 @t6 @t53 @t62 @t39 @t30) (=> @t90 (=> @t63 (=> @t77 @t88))))) % 0.43/0.64 (assume @p33 (forall (@list @t2 @t8 @t6 @t53 @t23 @t21 @t39 @t62 @t91 @t30) (=> @t90 (=> (and @t70 @t94 @t93) (=> @t77 @t92))))) % 0.43/0.64 (assume @p34 (forall (@list @t2 @t8 @t6 @t53 @t62 @t39 @t23 @t21 @t30) (=> @t90 (=> (and @t70 @t96) (=> @t77 @t95))))) % 0.43/0.64 (assume @p35 (forall (@list @t2 @t8 @t6 @t53) (=> (= @t76 @t53) (or (exists (@list @t23 @t62 @t21) (and @t59 @t80 @t79 @t63 @t54)) (exists (@list @t21 @t23 @t62) (and @t59 @t80 @t79 @t70 @t82)) (exists (@list @t30 @t23 @t21 @t29) (and @t59 @t80 @t86 @t85)) (exists (@list @t21 @t23 @t62 @t39 @t30) (and @t59 @t80 @t89 @t63 @t88)) (exists (@list @t23 @t21 @t39 @t62 @t91 @t30) (and @t59 @t80 @t89 @t70 @t94 @t93 @t92)) (exists (@list @t62 @t39 @t23 @t21 @t30) (and @t59 @t80 @t89 @t70 @t96 @t95)))))) % 0.43/0.64 (assume @p36 (and (=> @t97 true) (=> true @t97))) % 0.43/0.64 (assume @p37 (forall (@list @t8 @t6) (and (=> @t99 @t12) (=> @t12 @t99)))) % 0.43/0.64 (assume @p38 (forall @t100 (not (= tptp.vnoExp @t98)))) % 0.43/0.64 (assume @p39 (forall (@list @t101) (=> (= @t101 tptp.vnoExp) (not @t102)))) % 0.43/0.64 (assume @p40 (forall (@list @t21 @t101) (=> @t103 @t102))) % 0.43/0.64 (assume @p41 (forall (@list @t101 @t53 @t21) (=> @t103 (=> (= @t53 (tptp.vgetSomeExp @t101)) @t54)))) % 0.43/0.64 (assume @p42 (forall (@list @t23 @t8 @t53) (=> @t28 @t107))) % 0.43/0.64 (assume @p43 @t109) % 0.43/0.64 (assume @p44 (forall (@list @t29 @t8 @t53 @t23 @t22 @t30 @t110) (=> @t115 (=> (and @t114 @t113) (=> @t106 @t112))))) % 0.43/0.64 (assume @p45 (forall (@list @t22 @t110 @t8 @t53 @t23 @t29 @t30) (=> @t115 (=> (and @t114 @t118 @t117) (=> @t106 @t116))))) % 0.43/0.64 (assume @p46 (forall (@list @t23 @t22 @t30 @t110 @t29 @t8 @t53) (=> @t115 (=> (and @t114 @t118 @t119) @t107)))) % 0.43/0.64 (assume @p47 (forall (@list @t30 @t8 @t53 @t120 @t29) (=> @t128 (=> (and @t123 @t122) (=> @t106 @t121))))) % 0.43/0.64 (assume @p48 (forall (@list @t29 @t30 @t120 @t8 @t53) (=> @t128 (=> (and @t123 @t129) @t107)))) % 0.43/0.64 (assume @p49 (forall (@list @t8 @t53) (=> (= @t105 @t53) (or (exists @t71 (and @t28 @t104)) (exists @t130 (and @t25 @t104)) (exists (@list @t29 @t23 @t22 @t30 @t110) (and @t115 @t114 @t113 @t112)) (exists (@list @t22 @t110 @t23 @t29 @t30) (and @t115 @t114 @t118 @t117 @t116)) (exists (@list @t23 @t22 @t30 @t110 @t29) (and @t115 @t114 @t118 @t119 @t104)) (exists (@list @t30 @t120 @t29) (and @t32 @t127 @t123 @t122 @t121)) (exists (@list @t29 @t30 @t120) (and @t32 @t127 @t123 @t129 @t104)))))) % 0.43/0.64 (assume @p50 (forall (@list @t9 @t7 @t132 @t131) (and (=> @t133 @t134) (=> @t134 @t133)))) % 0.43/0.64 (assume @p51 (forall (@list @t64 @t23 @t39) (=> @t135 (tptp.vtcheck @t64 @t27 @t39)))) % 0.43/0.64 (assume @p52 (forall (@list @t64 @t23 @t21 @t22 @t39) (=> @t137 (tptp.vtcheck @t64 @t24 @t136)))) % 0.43/0.64 (assume @p53 (forall (@list @t22 @t64 @t30 @t29 @t39) (=> (and @t139 @t138) (tptp.vtcheck @t64 @t31 @t39)))) % 0.43/0.64 (assume @p54 (forall (@list @t21 @t39 @t64) (=> @t142 (or (exists @t71 (and (= @t21 @t27) @t135)) (exists (@list @t23 @t29 @t141 @t140) (and (= @t21 (tptp.vabs @t23 @t141 @t29)) (= @t39 (tptp.varrow @t141 @t140)) (tptp.vtcheck (tptp.vbind @t23 @t141 @t64) @t29 @t140))) (exists (@list @t30 @t29 @t22) (and (= @t21 @t31) @t139 @t138)))))) % 0.43/0.64 (assume @p55 (forall @t144 (=> (and @t143 @t142) @t137))) % 0.43/0.64 (assume @p56 (forall (@list @t39 @t64 @t23 @t21 @t29 @t140) (=> (and @t142 (tptp.vtcheck (tptp.vbind @t23 @t39 @t64) @t29 @t140)) (tptp.vtcheck @t64 @t83 @t140)))) % 0.43/0.64 (assume @p57 (forall @t144 (=> (and (= @t68 tptp.vnoType) @t142) @t137))) % 0.43/0.64 (assume @p58 (forall @t144 (=> (and @t143 @t137) @t142))) % 0.43/0.64 (assume @p59 (forall (@list @t64 @t145 @t39) (=> (and (= (tptp.vreduce tptp.ve1) @t147) (tptp.vtcheck @t64 tptp.ve1 @t39)) @t146))) % 0.43/0.64 (assume @p60 @t155) % 0.43/0.64 (assume @p61 true) % 0.43/0.64 (step @p62 :rule aci_norm :args ((= (or (or @t158 @t156) @t146) @t159))) % 0.43/0.64 (step @p63 :rule refl :args (@t146)) % 0.43/0.64 (step @p64 :rule bool-and-de-morgan :args (@t157 @t149 true)) % 0.43/0.64 (step @p65 :rule nary_cong :premises (@p64 @p63) :args ((or (not @t160) @t146))) % 0.43/0.64 (step @p66 :rule trans :premises (@p65 @p62)) % 0.43/0.64 (step @p67 :rule bool-impl-elim :args (@t160 @t146)) % 0.43/0.64 (step @p68 :rule trans :premises (@p67 @p66)) % 0.43/0.64 (step @p69 :rule cong :premises (@p68) :args ((forall @t153 (=> @t160 @t146)))) % 0.43/0.64 (step @p70 :rule refl :args (@t146)) % 0.43/0.64 (step @p71 :rule refl :args (@t149)) % 0.43/0.64 (step @p72 :rule eq-symm :args (@t150 @t147)) % 0.43/0.64 (step @p73 :rule nary_cong :premises (@p72 @p71) :args (@t151)) % 0.43/0.64 (step @p74 :rule cong :premises (@p73 @p70) :args (@t152)) % 0.43/0.64 (step @p75 :rule cong :premises (@p74) :args (@t154)) % 0.43/0.64 (step @p76 :rule trans :premises (@p75 @p69)) % 0.43/0.64 (step @p77 :rule cong :premises (@p76) :args (@t155)) % 0.43/0.64 (step @p78 :rule eq_resolve :premises (@p60 @p77)) % 0.43/0.64 (step @p79 :rule skolemize :premises (@p78)) % 0.43/0.64 (step @p80 :rule bool-double-not-elim :args (@t168)) % 0.43/0.64 (step @p81 :rule refl :args (@t172)) % 0.43/0.64 (step @p82 :rule nary_cong :premises (@p81 @p80) :args ((or @t172 (not @t171)))) % 0.43/0.65 (step @p83 :rule cnf_or_neg :args (@t172 0)) % 0.43/0.65 (step @p84 :rule eq_resolve :premises (@p83 @p82)) % 0.43/0.65 (step @p85 :rule reordering :premises (@p84) :args ((or @t168 @t172))) % 0.43/0.65 (step @p86 :rule chain_m_resolution :premises (@p85 @p79) :args (@t168 (@list true) (@list @t172))) % 0.43/0.65 (step @p87 :rule instantiate :premises (@p38) :args ((@list @t166))) % 0.43/0.65 (step @p88 :rule aci_norm :args ((= (or false @t174) @t174))) % 0.43/0.65 (step @p89 :rule eq-symm :args (@t173 tptp.vnoExp)) % 0.43/0.65 (step @p90 :rule evaluate :args ((not true))) % 0.43/0.65 (step @p91 :rule eq-refl :args (@t173)) % 0.43/0.65 (step @p92 :rule cong :premises (@p91) :args (@t175)) % 0.43/0.65 (step @p93 :rule trans :premises (@p92 @p90)) % 0.43/0.65 (step @p94 :rule nary_cong :premises (@p93 @p89) :args (@t176)) % 0.43/0.65 (step @p95 :rule trans :premises (@p94 @p88)) % 0.43/0.65 (step @p96 :rule cong :premises (@p95) :args ((forall @t130 @t176))) % 0.43/0.65 (step @p97 :rule quant-var-elim-eq :args ((= (forall @t179 @t178) @t176))) % 0.43/0.65 (step @p98 :rule aci_norm :args ((= @t180 @t178))) % 0.43/0.65 (step @p99 :rule cong :premises (@p98) :args (@t181)) % 0.43/0.65 (step @p100 :rule trans :premises (@p99 @p97)) % 0.43/0.65 (step @p101 :rule cong :premises (@p100) :args (@t182)) % 0.43/0.65 (step @p102 :rule quant-merge-prenex :args ((= @t182 (forall @t183 @t180)))) % 0.43/0.65 (step @p103 :rule symm :premises (@p102)) % 0.43/0.65 (step @p104 :rule trans :premises (@p103 @p101)) % 0.43/0.65 (step @p105 :rule trans :premises (@p104 @p96)) % 0.43/0.65 (step @p106 :rule aci_norm :args ((= (or false @t177 @t104) @t180))) % 0.43/0.65 (step @p107 :rule refl :args (@t104)) % 0.43/0.65 (step @p108 :rule refl :args (@t177)) % 0.43/0.65 (step @p109 :rule eq-refl :args (@t24)) % 0.43/0.65 (step @p110 :rule cong :premises (@p109) :args (@t184)) % 0.43/0.65 (step @p111 :rule trans :premises (@p110 @p90)) % 0.43/0.65 (step @p112 :rule nary_cong :premises (@p111 @p108 @p107) :args (@t185)) % 0.43/0.65 (step @p113 :rule trans :premises (@p112 @p106)) % 0.43/0.65 (step @p114 :rule cong :premises (@p113) :args ((forall @t183 @t185))) % 0.43/0.65 (step @p115 :rule trans :premises (@p114 @p105)) % 0.43/0.65 (step @p116 :rule quant-var-elim-eq :args ((= (forall @t100 @t188) @t185))) % 0.43/0.65 (step @p117 :rule aci_norm :args ((= @t189 @t188))) % 0.43/0.65 (step @p118 :rule cong :premises (@p117) :args (@t190)) % 0.43/0.65 (step @p119 :rule trans :premises (@p118 @p116)) % 0.43/0.65 (step @p120 :rule cong :premises (@p119) :args (@t191)) % 0.43/0.65 (step @p121 :rule quant-merge-prenex :args ((= @t191 @t192))) % 0.43/0.65 (step @p122 :rule symm :premises (@p121)) % 0.43/0.65 (step @p123 :rule quant_var_reordering :args ((= (forall @t108 @t189) @t192))) % 0.43/0.65 (step @p124 :rule trans :premises (@p123 @p122 @p120)) % 0.43/0.65 (step @p125 :rule trans :premises (@p124 @p115)) % 0.43/0.65 (step @p126 :rule aci_norm :args ((= (or @t187 (or @t186 @t104)) @t189))) % 0.43/0.65 (step @p127 :rule bool-impl-elim :args (@t106 @t104)) % 0.43/0.65 (step @p128 :rule refl :args (@t187)) % 0.43/0.65 (step @p129 :rule nary_cong :premises (@p128 @p127) :args ((or @t187 @t107))) % 0.43/0.65 (step @p130 :rule trans :premises (@p129 @p126)) % 0.43/0.65 (step @p131 :rule bool-impl-elim :args (@t25 @t107)) % 0.43/0.65 (step @p132 :rule trans :premises (@p131 @p130)) % 0.43/0.65 (step @p133 :rule cong :premises (@p132) :args (@t109)) % 0.43/0.65 (step @p134 :rule trans :premises (@p133 @p125)) % 0.43/0.65 (step @p135 :rule eq_resolve :premises (@p43 @p134)) % 0.43/0.65 (step @p136 :rule instantiate :premises (@p135) :args ((@list @t163 @t162 tptp.ve1))) % 0.43/0.65 (step @p137 :rule refl :args (@t194)) % 0.43/0.65 (step @p138 :rule bool-double-not-elim :args (@t195)) % 0.43/0.65 (step @p139 :rule refl :args (@t171)) % 0.43/0.65 (step @p140 :rule nary_cong :premises (@p139 @p138 @p137) :args ((or @t171 (not @t196) @t194))) % 0.43/0.65 (assume-push @p157 @t168) % 0.43/0.65 (assume-push @p158 @t196) % 0.43/0.65 (step @p143 :rule false_intro :premises (@p87)) % 0.43/0.65 (step @p144 :rule symm :premises (@p86)) % 0.43/0.65 (step @p145 :rule refl :args (tptp.vnoExp)) % 0.43/0.65 (step @p146 :rule cong :premises (@p145 @p144) :args (@t193)) % 0.43/0.65 (step @p147 :rule trans :premises (@p146 @p143)) % 0.43/0.65 (step @p148 :rule false_elim :premises (@p147)) % 0.43/0.65 (step-pop @p159 :rule scope :premises (@p148)) % 0.43/0.65 (step-pop @p160 :rule scope :premises (@p159)) % 0.43/0.65 (step @p149 :rule process_scope :premises (@p160) :args (@t194)) % 0.43/0.65 (step @p152 :rule implies_elim :premises (@p149)) % 0.43/0.65 (step @p153 :rule cnf_and_neg :args (@t197)) % 0.43/0.65 (step @p154 :rule resolution :premises (@p153 @p152) :args (true @t197)) % 0.43/0.65 (step @p155 :rule eq_resolve :premises (@p154 @p140)) % 0.43/0.65 (step @p156 false :rule chain_m_resolution :premises (@p155 @p136 @p87 @p86) :args (false (@list false true false) (@list @t193 @t195 @t168))) % 0.43/0.65 ) % 0.43/0.65 % SZS output end Proof % 0.43/0.65 % cvc5 exiting %------------------------------------------------------------------------------