%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : COM212_1 : TPTP v9.3.0. Released v9.3.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n025.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 08:10:39 AM UTC 2026 % Result : Theorem 0.37s 0.67s % Output : Proof 0.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : COM212_1 : TPTP v9.3.0. Released v9.3.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n025.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 : Mon Jun 1 20:32:01 EDT 2026 % 0.16/0.35 % CPUTime : % 0.28/0.53 %----Proving TF0_NAR, FOF, or CNF % 0.37/0.67 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.37/0.67 % SZS status Theorem % 0.37/0.67 % SZS output start Proof % 0.37/0.67 ( % 0.37/0.67 (declare-sort tptp.vTy 0) % 0.37/0.67 (declare-sort tptp.vOptTerm 0) % 0.37/0.67 (declare-sort tptp.vTerm 0) % 0.37/0.67 (declare-const tptp.vptchecksimple (-> tptp.vTerm tptp.vTy Bool)) % 0.37/0.67 (declare-const tptp.vreduce (-> tptp.vTerm tptp.vOptTerm)) % 0.37/0.67 (declare-const tptp.vplusop (-> tptp.vTerm tptp.vTerm tptp.vTerm)) % 0.37/0.67 (declare-const tptp.visSomeTerm (-> tptp.vOptTerm Bool)) % 0.37/0.67 (declare-const tptp.visValue (-> tptp.vTerm Bool)) % 0.37/0.67 (declare-const tptp.visNV (-> tptp.vTerm Bool)) % 0.37/0.67 (declare-const tptp.vPlus (-> tptp.vTerm tptp.vTerm tptp.vTerm)) % 0.37/0.67 (declare-const tptp.vIszero (-> tptp.vTerm tptp.vTerm)) % 0.37/0.67 (declare-const tptp.vPred (-> tptp.vTerm tptp.vTerm)) % 0.37/0.67 (declare-const tptp.vSucc (-> tptp.vTerm tptp.vTerm)) % 0.37/0.67 (declare-const tptp.vIfelse (-> tptp.vTerm tptp.vTerm tptp.vTerm tptp.vTerm)) % 0.37/0.67 (declare-const tptp.vZero tptp.vTerm) % 0.37/0.67 (declare-const tptp.vFalse tptp.vTerm) % 0.37/0.67 (declare-const tptp.vTrue tptp.vTerm) % 0.37/0.67 (declare-const tptp.vsomeTerm (-> tptp.vTerm tptp.vOptTerm)) % 0.37/0.67 (declare-const tptp.vnoTerm tptp.vOptTerm) % 0.37/0.67 (declare-const tptp.vNat tptp.vTy) % 0.37/0.67 (declare-const tptp.vB tptp.vTy) % 0.37/0.67 (declare-const tptp.vgetTerm (-> tptp.vOptTerm tptp.vTerm)) % 0.37/0.67 (define @t1 () (@var "VTerm1" tptp.vTerm)) % 0.37/0.67 (define @t2 () (@var "VTerm0" tptp.vTerm)) % 0.37/0.67 (define @t3 () (tptp.vPlus @t2 @t1)) % 0.37/0.67 (define @t4 () (@var "VX" tptp.vTerm)) % 0.37/0.67 (define @t5 () (@list @t2 @t1)) % 0.37/0.67 (define @t6 () (tptp.vIszero @t2)) % 0.37/0.67 (define @t7 () (@list @t2)) % 0.37/0.67 (define @t8 () (tptp.vPred @t2)) % 0.37/0.67 (define @t9 () (tptp.vSucc @t2)) % 0.37/0.67 (define @t10 () (@var "VTerm2" tptp.vTerm)) % 0.37/0.67 (define @t11 () (tptp.vIfelse @t2 @t1 @t10)) % 0.37/0.67 (define @t12 () (@list @t2 @t1 @t10)) % 0.37/0.67 (define @t13 () (@var "VTerm5" tptp.vTerm)) % 0.37/0.67 (define @t14 () (@var "VTerm4" tptp.vTerm)) % 0.37/0.67 (define @t15 () (@var "VTerm3" tptp.vTerm)) % 0.37/0.67 (define @t16 () (= @t2 @t1)) % 0.37/0.67 (define @t17 () (tptp.vPred @t1)) % 0.37/0.67 (define @t18 () (tptp.vIszero @t1)) % 0.37/0.67 (define @t19 () (@list @t2 @t1 @t10 @t15)) % 0.37/0.67 (define @t20 () (forall @t7 (not (= tptp.vFalse @t9)))) % 0.37/0.67 (define @t21 () (tptp.vPlus @t1 @t10)) % 0.37/0.67 (define @t22 () (tptp.vsomeTerm @t2)) % 0.37/0.67 (define @t23 () (@var "VX" tptp.vOptTerm)) % 0.37/0.67 (define @t24 () (@var "VX" tptp.vTy)) % 0.37/0.67 (define @t25 () (@var "Vt" tptp.vTerm)) % 0.37/0.67 (define @t26 () (@var "Vnv" tptp.vTerm)) % 0.37/0.67 (define @t27 () (tptp.visNV @t26)) % 0.37/0.67 (define @t28 () (tptp.vSucc @t26)) % 0.37/0.67 (define @t29 () (@list @t26)) % 0.37/0.67 (define @t30 () (@var "VwildcardName0" tptp.vTerm)) % 0.37/0.67 (define @t31 () (not (tptp.visNV @t30))) % 0.37/0.67 (define @t32 () (@var "Vnv0" tptp.vTerm)) % 0.37/0.67 (define @t33 () (tptp.vSucc @t32)) % 0.37/0.67 (define @t34 () (@list @t32)) % 0.37/0.67 (define @t35 () (forall @t34 (not (= @t30 @t33)))) % 0.37/0.67 (define @t36 () (not (= @t30 tptp.vZero))) % 0.37/0.67 (define @t37 () (and @t36 @t35)) % 0.37/0.67 (define @t38 () (=> @t37 @t31)) % 0.37/0.67 (define @t39 () (@list @t30)) % 0.37/0.67 (define @t40 () (forall @t39 @t38)) % 0.37/0.67 (define @t41 () (= @t2 @t28)) % 0.37/0.67 (define @t42 () (tptp.visNV @t2)) % 0.37/0.67 (define @t43 () (not @t27)) % 0.37/0.67 (define @t44 () (@var "Vt1" tptp.vTerm)) % 0.37/0.67 (define @t45 () (tptp.visNV @t44)) % 0.37/0.67 (define @t46 () (not (= @t44 tptp.vFalse))) % 0.37/0.67 (define @t47 () (not (= @t44 tptp.vTrue))) % 0.37/0.67 (define @t48 () (@list @t44)) % 0.37/0.67 (define @t49 () (= @t2 @t44)) % 0.37/0.67 (define @t50 () (tptp.visValue @t2)) % 0.37/0.67 (define @t51 () (not @t45)) % 0.37/0.67 (define @t52 () (tptp.vsomeTerm @t30)) % 0.37/0.67 (define @t53 () (@var "VOptTerm0" tptp.vOptTerm)) % 0.37/0.67 (define @t54 () (tptp.visSomeTerm @t53)) % 0.37/0.67 (define @t55 () (@list @t53)) % 0.37/0.67 (define @t56 () (@var "Vt2" tptp.vTerm)) % 0.37/0.67 (define @t57 () (@var "Vt3" tptp.vTerm)) % 0.37/0.67 (define @t58 () (tptp.vplusop @t56 @t57)) % 0.37/0.67 (define @t59 () (@list @t56 @t57)) % 0.37/0.67 (define @t60 () (@var "Vt30" tptp.vTerm)) % 0.37/0.67 (define @t61 () (tptp.vSucc @t60)) % 0.37/0.67 (define @t62 () (@var "Vt31" tptp.vTerm)) % 0.37/0.67 (define @t63 () (tptp.vplusop @t2 @t1)) % 0.37/0.67 (define @t64 () (@var "Vt22" tptp.vTerm)) % 0.37/0.67 (define @t65 () (@var "Vt3000" tptp.vTerm)) % 0.37/0.67 (define @t66 () (@var "Vt21" tptp.vTerm)) % 0.37/0.67 (define @t67 () (@var "Vt20" tptp.vTerm)) % 0.37/0.67 (define @t68 () (tptp.vreduce @t44)) % 0.37/0.67 (define @t69 () (tptp.vgetTerm @t68)) % 0.37/0.67 (define @t70 () (tptp.vIfelse @t44 @t56 @t57)) % 0.37/0.67 (define @t71 () (tptp.vreduce @t70)) % 0.37/0.67 (define @t72 () (tptp.visSomeTerm @t68)) % 0.37/0.67 (define @t73 () (@var "Vt301" tptp.vTerm)) % 0.37/0.67 (define @t74 () (@var "Vt201" tptp.vTerm)) % 0.37/0.67 (define @t75 () (forall (@list @t74 @t73) (or @t46 (not (= @t56 @t74)) (not (= @t57 @t73))))) % 0.37/0.67 (define @t76 () (@var "Vt300" tptp.vTerm)) % 0.37/0.67 (define @t77 () (@var "Vt200" tptp.vTerm)) % 0.37/0.67 (define @t78 () (forall (@list @t77 @t76) (or @t47 (not (= @t56 @t77)) (not (= @t57 @t76))))) % 0.37/0.67 (define @t79 () (@list @t44 @t56 @t57)) % 0.37/0.67 (define @t80 () (not @t72)) % 0.37/0.67 (define @t81 () (tptp.vSucc @t44)) % 0.37/0.67 (define @t82 () (tptp.vreduce @t81)) % 0.37/0.67 (define @t83 () (tptp.vsomeTerm tptp.vZero)) % 0.37/0.67 (define @t84 () (tptp.vPred tptp.vZero)) % 0.37/0.67 (define @t85 () (tptp.vreduce (tptp.vPred @t28))) % 0.37/0.67 (define @t86 () (tptp.vreduce @t28)) % 0.37/0.67 (define @t87 () (tptp.vgetTerm @t86)) % 0.37/0.67 (define @t88 () (tptp.visSomeTerm @t86)) % 0.37/0.67 (define @t89 () (and @t43 @t88)) % 0.37/0.67 (define @t90 () (and @t43 (not @t88))) % 0.37/0.67 (define @t91 () (tptp.vPred @t44)) % 0.37/0.67 (define @t92 () (tptp.vreduce @t91)) % 0.37/0.67 (define @t93 () (@var "Vnv00" tptp.vTerm)) % 0.37/0.67 (define @t94 () (forall (@list @t93) (not (= @t44 (tptp.vSucc @t93))))) % 0.37/0.67 (define @t95 () (not (= @t44 tptp.vZero))) % 0.37/0.67 (define @t96 () (and @t95 @t94 @t72)) % 0.37/0.67 (define @t97 () (and @t95 @t94 @t80)) % 0.37/0.67 (define @t98 () (tptp.vsomeTerm tptp.vTrue)) % 0.37/0.67 (define @t99 () (tptp.vIszero tptp.vZero)) % 0.37/0.67 (define @t100 () (tptp.vsomeTerm tptp.vFalse)) % 0.37/0.67 (define @t101 () (tptp.vreduce (tptp.vIszero @t28))) % 0.37/0.67 (define @t102 () (tptp.vIszero @t44)) % 0.37/0.67 (define @t103 () (tptp.vreduce @t102)) % 0.37/0.67 (define @t104 () (tptp.vPlus @t44 @t56)) % 0.37/0.67 (define @t105 () (tptp.vreduce @t104)) % 0.37/0.67 (define @t106 () (tptp.visNV @t56)) % 0.37/0.67 (define @t107 () (@list @t44 @t56)) % 0.37/0.67 (define @t108 () (tptp.vreduce @t56)) % 0.37/0.67 (define @t109 () (tptp.visSomeTerm @t108)) % 0.37/0.67 (define @t110 () (not @t106)) % 0.37/0.67 (define @t111 () (= @t105 tptp.vnoTerm)) % 0.37/0.67 (define @t112 () (@var "Vt10" tptp.vTerm)) % 0.37/0.67 (define @t113 () (@list @t112)) % 0.37/0.67 (define @t114 () (tptp.vPred @t33)) % 0.37/0.67 (define @t115 () (@list @t67 @t60)) % 0.37/0.67 (define @t116 () (tptp.vIfelse tptp.vTrue @t67 @t60)) % 0.37/0.67 (define @t117 () (tptp.vreduce @t2)) % 0.37/0.67 (define @t118 () (= @t117 tptp.vnoTerm)) % 0.37/0.67 (define @t119 () (@var "VwildcardName00" tptp.vTerm)) % 0.37/0.67 (define @t120 () (@var "Vt2080" tptp.vTerm)) % 0.37/0.67 (define @t121 () (@var "Vt1040" tptp.vTerm)) % 0.37/0.67 (define @t122 () (@var "Vt1030" tptp.vTerm)) % 0.37/0.67 (define @t123 () (@var "Vnv050" tptp.vTerm)) % 0.37/0.67 (define @t124 () (@var "Vt1020" tptp.vTerm)) % 0.37/0.67 (define @t125 () (@var "Vnv040" tptp.vTerm)) % 0.37/0.67 (define @t126 () (@var "Vt1010" tptp.vTerm)) % 0.37/0.67 (define @t127 () (@var "Vt3070" tptp.vTerm)) % 0.37/0.67 (define @t128 () (@var "Vt2070" tptp.vTerm)) % 0.37/0.67 (define @t129 () (@var "Vt1000" tptp.vTerm)) % 0.37/0.67 (define @t130 () (@var "Vt3060" tptp.vTerm)) % 0.37/0.67 (define @t131 () (@var "Vt2060" tptp.vTerm)) % 0.37/0.67 (define @t132 () (@var "Vt3050" tptp.vTerm)) % 0.37/0.67 (define @t133 () (@var "Vt2050" tptp.vTerm)) % 0.37/0.67 (define @t134 () (@var "Vt28" tptp.vTerm)) % 0.37/0.67 (define @t135 () (@var "Vt112" tptp.vTerm)) % 0.37/0.67 (define @t136 () (@var "Vot13" tptp.vOptTerm)) % 0.37/0.67 (define @t137 () (@var "Vt27" tptp.vTerm)) % 0.37/0.67 (define @t138 () (@var "Vot12" tptp.vOptTerm)) % 0.37/0.67 (define @t139 () (@var "Vt111" tptp.vTerm)) % 0.37/0.67 (define @t140 () (@var "Vt26" tptp.vTerm)) % 0.37/0.67 (define @t141 () (@var "Vt110" tptp.vTerm)) % 0.37/0.67 (define @t142 () (@var "Vot211" tptp.vOptTerm)) % 0.37/0.67 (define @t143 () (@var "Vot210" tptp.vOptTerm)) % 0.37/0.67 (define @t144 () (@var "Vt19" tptp.vTerm)) % 0.37/0.67 (define @t145 () (@var "Vt25" tptp.vTerm)) % 0.37/0.67 (define @t146 () (@var "Vt24" tptp.vTerm)) % 0.37/0.67 (define @t147 () (@var "Vt18" tptp.vTerm)) % 0.37/0.67 (define @t148 () (@var "Vt17" tptp.vTerm)) % 0.37/0.67 (define @t149 () (@var "Vot29" tptp.vOptTerm)) % 0.37/0.67 (define @t150 () (@var "Vnv030" tptp.vTerm)) % 0.37/0.67 (define @t151 () (@var "Vot28" tptp.vOptTerm)) % 0.37/0.67 (define @t152 () (@var "Vt16" tptp.vTerm)) % 0.37/0.67 (define @t153 () (@var "Vnv020" tptp.vTerm)) % 0.37/0.67 (define @t154 () (@var "Vnv5" tptp.vTerm)) % 0.37/0.67 (define @t155 () (tptp.vSucc @t154)) % 0.37/0.67 (define @t156 () (@var "Vot27" tptp.vOptTerm)) % 0.37/0.67 (define @t157 () (@var "Vot26" tptp.vOptTerm)) % 0.37/0.67 (define @t158 () (@var "Vnv4" tptp.vTerm)) % 0.37/0.67 (define @t159 () (tptp.vSucc @t158)) % 0.37/0.67 (define @t160 () (@var "Vnv3" tptp.vTerm)) % 0.37/0.67 (define @t161 () (@var "Vt15" tptp.vTerm)) % 0.37/0.67 (define @t162 () (@var "Vot25" tptp.vOptTerm)) % 0.37/0.67 (define @t163 () (@var "Vnv010" tptp.vTerm)) % 0.37/0.67 (define @t164 () (@var "Vot24" tptp.vOptTerm)) % 0.37/0.67 (define @t165 () (@var "Vt14" tptp.vTerm)) % 0.37/0.67 (define @t166 () (@var "Vnv000" tptp.vTerm)) % 0.37/0.67 (define @t167 () (@var "Vnv2" tptp.vTerm)) % 0.37/0.67 (define @t168 () (tptp.vSucc @t167)) % 0.37/0.67 (define @t169 () (@var "Vot23" tptp.vOptTerm)) % 0.37/0.67 (define @t170 () (@var "Vot22" tptp.vOptTerm)) % 0.37/0.67 (define @t171 () (@var "Vnv1" tptp.vTerm)) % 0.37/0.67 (define @t172 () (tptp.vSucc @t171)) % 0.37/0.67 (define @t173 () (@var "Vt13" tptp.vTerm)) % 0.37/0.67 (define @t174 () (@var "Vot21" tptp.vOptTerm)) % 0.37/0.67 (define @t175 () (@var "Vot20" tptp.vOptTerm)) % 0.37/0.67 (define @t176 () (@var "Vt12" tptp.vTerm)) % 0.37/0.67 (define @t177 () (@var "Vt33" tptp.vTerm)) % 0.37/0.67 (define @t178 () (@var "Vt23" tptp.vTerm)) % 0.37/0.67 (define @t179 () (@var "Vt11" tptp.vTerm)) % 0.37/0.67 (define @t180 () (@var "Vot11" tptp.vOptTerm)) % 0.37/0.67 (define @t181 () (@var "Vt3040" tptp.vTerm)) % 0.37/0.67 (define @t182 () (@var "Vt2040" tptp.vTerm)) % 0.37/0.67 (define @t183 () (@var "Vt3030" tptp.vTerm)) % 0.37/0.67 (define @t184 () (@var "Vt2030" tptp.vTerm)) % 0.37/0.67 (define @t185 () (@var "Vt32" tptp.vTerm)) % 0.37/0.67 (define @t186 () (@var "Vot10" tptp.vOptTerm)) % 0.37/0.67 (define @t187 () (@var "Vt3020" tptp.vTerm)) % 0.37/0.67 (define @t188 () (@var "Vt2020" tptp.vTerm)) % 0.37/0.67 (define @t189 () (@var "Vt3010" tptp.vTerm)) % 0.37/0.67 (define @t190 () (@var "Vt2010" tptp.vTerm)) % 0.37/0.67 (define @t191 () (@var "VT" tptp.vTy)) % 0.37/0.67 (define @t192 () (tptp.vptchecksimple @t70 @t191)) % 0.37/0.67 (define @t193 () (tptp.vptchecksimple @t57 @t191)) % 0.37/0.67 (define @t194 () (tptp.vptchecksimple @t56 @t191)) % 0.37/0.67 (define @t195 () (tptp.vptchecksimple @t44 tptp.vB)) % 0.37/0.67 (define @t196 () (@list @t44 @t56 @t57 @t191)) % 0.37/0.67 (define @t197 () (= @t191 tptp.vNat)) % 0.37/0.67 (define @t198 () (tptp.vptchecksimple @t81 tptp.vNat)) % 0.37/0.67 (define @t199 () (tptp.vptchecksimple @t44 tptp.vNat)) % 0.37/0.67 (define @t200 () (@list @t44 @t191)) % 0.37/0.67 (define @t201 () (tptp.vptchecksimple @t91 tptp.vNat)) % 0.37/0.67 (define @t202 () (tptp.vptchecksimple @t102 tptp.vB)) % 0.37/0.67 (define @t203 () (tptp.vptchecksimple @t104 tptp.vNat)) % 0.37/0.67 (define @t204 () (tptp.vptchecksimple @t56 tptp.vNat)) % 0.37/0.67 (define @t205 () (tptp.visNV tptp.vFalse)) % 0.37/0.67 (define @t206 () (forall @t34 (not (= tptp.vFalse @t33)))) % 0.37/0.67 (define @t207 () (not @t35)) % 0.37/0.67 (define @t208 () (= tptp.vZero @t30)) % 0.37/0.67 (define @t209 () (not @t208)) % 0.37/0.67 (define @t210 () (and @t209 @t35)) % 0.37/0.67 (define @t211 () (not @t205)) % 0.37/0.67 (define @t212 () (not @t206)) % 0.37/0.67 (define @t213 () (= tptp.vZero tptp.vFalse)) % 0.37/0.67 (define @t214 () (or @t213 @t212 @t211)) % 0.37/0.67 (assume @p1 (forall (@list @t4) (or (= @t4 tptp.vTrue) (= @t4 tptp.vFalse) (exists @t12 (= @t4 @t11)) (= @t4 tptp.vZero) (exists @t7 (= @t4 @t9)) (exists @t7 (= @t4 @t8)) (exists @t7 (= @t4 @t6)) (exists @t5 (= @t4 @t3))))) % 0.37/0.67 (assume @p2 (forall (@list @t15 @t10 @t1 @t14 @t2 @t13) (=> (= @t11 (tptp.vIfelse @t15 @t14 @t13)) (and (= @t2 @t15) (= @t1 @t14) (= @t10 @t13))))) % 0.37/0.67 (assume @p3 (forall @t5 (=> (= @t9 (tptp.vSucc @t1)) @t16))) % 0.37/0.67 (assume @p4 (forall @t5 (=> (= @t8 @t17) @t16))) % 0.37/0.67 (assume @p5 (forall @t5 (=> (= @t6 @t18) @t16))) % 0.37/0.67 (assume @p6 (forall @t19 (=> (= @t3 (tptp.vPlus @t10 @t15)) (and (= @t2 @t10) (= @t1 @t15))))) % 0.37/0.67 (assume @p7 (not (= tptp.vTrue tptp.vFalse))) % 0.37/0.67 (assume @p8 (forall @t12 (not (= tptp.vTrue @t11)))) % 0.37/0.67 (assume @p9 (not (= tptp.vTrue tptp.vZero))) % 0.37/0.67 (assume @p10 (forall @t7 (not (= tptp.vTrue @t9)))) % 0.37/0.67 (assume @p11 (forall @t7 (not (= tptp.vTrue @t8)))) % 0.37/0.67 (assume @p12 (forall @t7 (not (= tptp.vTrue @t6)))) % 0.37/0.67 (assume @p13 (forall @t5 (not (= tptp.vTrue @t3)))) % 0.37/0.67 (assume @p14 (forall @t12 (not (= tptp.vFalse @t11)))) % 0.37/0.67 (assume @p15 (not (= tptp.vFalse tptp.vZero))) % 0.37/0.67 (assume @p16 @t20) % 0.37/0.67 (assume @p17 (forall @t7 (not (= tptp.vFalse @t8)))) % 0.37/0.67 (assume @p18 (forall @t7 (not (= tptp.vFalse @t6)))) % 0.37/0.67 (assume @p19 (forall @t5 (not (= tptp.vFalse @t3)))) % 0.37/0.67 (assume @p20 (forall @t12 (not (= @t11 tptp.vZero)))) % 0.37/0.67 (assume @p21 (forall @t19 (not (= @t11 (tptp.vSucc @t15))))) % 0.37/0.67 (assume @p22 (forall @t19 (not (= @t11 (tptp.vPred @t15))))) % 0.37/0.67 (assume @p23 (forall @t19 (not (= @t11 (tptp.vIszero @t15))))) % 0.37/0.67 (assume @p24 (forall (@list @t15 @t10 @t1 @t14 @t2) (not (= @t11 (tptp.vPlus @t15 @t14))))) % 0.37/0.67 (assume @p25 (forall @t7 (not (= tptp.vZero @t9)))) % 0.37/0.67 (assume @p26 (forall @t7 (not (= tptp.vZero @t8)))) % 0.37/0.67 (assume @p27 (forall @t7 (not (= tptp.vZero @t6)))) % 0.37/0.67 (assume @p28 (forall @t5 (not (= tptp.vZero @t3)))) % 0.37/0.67 (assume @p29 (forall @t5 (not (= @t9 @t17)))) % 0.37/0.67 (assume @p30 (forall @t5 (not (= @t9 @t18)))) % 0.37/0.67 (assume @p31 (forall @t12 (not (= @t9 @t21)))) % 0.37/0.67 (assume @p32 (forall @t5 (not (= @t8 @t18)))) % 0.37/0.67 (assume @p33 (forall @t12 (not (= @t8 @t21)))) % 0.37/0.67 (assume @p34 (forall @t12 (not (= @t6 @t21)))) % 0.37/0.67 (assume @p35 (forall (@list @t23) (or (= @t23 tptp.vnoTerm) (exists @t7 (= @t23 @t22))))) % 0.37/0.67 (assume @p36 (forall @t5 (=> (= @t22 (tptp.vsomeTerm @t1)) @t16))) % 0.37/0.67 (assume @p37 (forall @t7 (not (= tptp.vnoTerm @t22)))) % 0.37/0.67 (assume @p38 (forall (@list @t24) (or (= @t24 tptp.vB) (= @t24 tptp.vNat)))) % 0.37/0.67 (assume @p39 (not (= tptp.vB tptp.vNat))) % 0.37/0.67 (assume @p40 (forall (@list @t25) (= (tptp.vgetTerm (tptp.vsomeTerm @t25)) @t25))) % 0.37/0.67 (assume @p41 (tptp.visNV tptp.vZero)) % 0.37/0.67 (assume @p42 (forall @t29 (= (tptp.visNV @t28) @t27))) % 0.37/0.67 (assume @p43 @t40) % 0.37/0.67 (assume @p44 (forall @t7 (=> @t42 (or (= @t2 tptp.vZero) (exists @t29 (and @t41 @t27)))))) % 0.37/0.67 (assume @p45 (forall @t7 (=> (not @t42) (or (exists @t29 (and @t41 @t43)) (exists @t39 (and @t36 @t35 (= @t2 @t30))))))) % 0.37/0.67 (assume @p46 (tptp.visValue tptp.vTrue)) % 0.37/0.67 (assume @p47 (tptp.visValue tptp.vFalse)) % 0.37/0.67 (assume @p48 (forall @t48 (=> (and @t47 @t46) (= (tptp.visValue @t44) @t45)))) % 0.37/0.67 (assume @p49 (forall @t7 (=> @t50 (or (= @t2 tptp.vTrue) (= @t2 tptp.vFalse) (exists @t48 (and @t47 @t46 @t49 @t45)))))) % 0.37/0.67 (assume @p50 (forall @t7 (=> (not @t50) (exists @t48 (and @t47 @t46 @t49 @t51))))) % 0.37/0.67 (assume @p51 (not (tptp.visSomeTerm tptp.vnoTerm))) % 0.37/0.67 (assume @p52 (forall @t39 (tptp.visSomeTerm @t52))) % 0.37/0.67 (assume @p53 (forall @t55 (=> @t54 (exists @t39 (= @t53 @t52))))) % 0.37/0.67 (assume @p54 (forall @t55 (=> (not @t54) (= @t53 tptp.vnoTerm)))) % 0.37/0.67 (assume @p55 (forall (@list @t56) (= (tptp.vplusop @t56 tptp.vZero) @t56))) % 0.37/0.67 (assume @p56 (forall @t59 (= (tptp.vplusop @t56 (tptp.vSucc @t57)) (tptp.vSucc @t58)))) % 0.37/0.67 (assume @p57 (forall (@list @t57 @t56) (=> (and (not (= @t57 tptp.vZero)) (forall (@list @t60) (not (= @t57 @t61)))) (= @t58 @t57)))) % 0.37/0.67 (assume @p58 (forall @t5 (or (exists (@list @t67) (and (= @t2 @t67) (= @t1 tptp.vZero) (= @t63 @t67))) (exists (@list @t60 @t66) (and (= @t2 @t66) (= @t1 @t61) (= @t63 (tptp.vSucc (tptp.vplusop @t66 @t60))))) (exists (@list @t62 @t64) (and (not (= @t62 tptp.vZero)) (forall (@list @t65) (not (= @t62 (tptp.vSucc @t65)))) (= @t2 @t64) (= @t1 @t62) (= @t63 @t62)))))) % 0.37/0.67 (assume @p59 (forall @t59 (= (tptp.vreduce (tptp.vIfelse tptp.vTrue @t56 @t57)) (tptp.vsomeTerm @t56)))) % 0.37/0.67 (assume @p60 (forall @t59 (= (tptp.vreduce (tptp.vIfelse tptp.vFalse @t56 @t57)) (tptp.vsomeTerm @t57)))) % 0.37/0.67 (assume @p61 (forall @t79 (=> (and @t78 @t75 @t72) (= @t71 (tptp.vsomeTerm (tptp.vIfelse @t69 @t56 @t57)))))) % 0.37/0.67 (assume @p62 (forall @t79 (=> (and @t78 @t75 @t80) (= @t71 tptp.vnoTerm)))) % 0.37/0.67 (assume @p63 (forall @t48 (=> @t72 (= @t82 (tptp.vsomeTerm (tptp.vSucc @t69)))))) % 0.37/0.67 (assume @p64 (forall @t48 (=> @t80 (= @t82 tptp.vnoTerm)))) % 0.37/0.67 (assume @p65 (= (tptp.vreduce @t84) @t83)) % 0.37/0.67 (assume @p66 (forall @t29 (=> @t27 (= @t85 (tptp.vsomeTerm @t26))))) % 0.37/0.67 (assume @p67 (forall @t29 (=> @t89 (= @t85 (tptp.vsomeTerm (tptp.vPred @t87)))))) % 0.37/0.67 (assume @p68 (forall @t29 (=> @t90 (= @t85 tptp.vnoTerm)))) % 0.37/0.67 (assume @p69 (forall @t48 (=> @t96 (= @t92 (tptp.vsomeTerm (tptp.vPred @t69)))))) % 0.37/0.67 (assume @p70 (forall @t48 (=> @t97 (= @t92 tptp.vnoTerm)))) % 0.37/0.67 (assume @p71 (= (tptp.vreduce @t99) @t98)) % 0.37/0.67 (assume @p72 (forall @t29 (=> @t27 (= @t101 @t100)))) % 0.37/0.67 (assume @p73 (forall @t29 (=> @t89 (= @t101 (tptp.vsomeTerm (tptp.vIszero @t87)))))) % 0.37/0.67 (assume @p74 (forall @t29 (=> @t90 (= @t101 tptp.vnoTerm)))) % 0.37/0.67 (assume @p75 (forall @t48 (=> @t96 (= @t103 (tptp.vsomeTerm (tptp.vIszero @t69)))))) % 0.37/0.67 (assume @p76 (forall @t48 (=> @t97 (= @t103 tptp.vnoTerm)))) % 0.37/0.67 (assume @p77 (forall @t107 (=> (and @t45 @t106) (= @t105 (tptp.vsomeTerm (tptp.vplusop @t44 @t56)))))) % 0.37/0.67 (assume @p78 (forall @t107 (=> (and @t45 @t110 @t109) (= @t105 (tptp.vsomeTerm (tptp.vPlus @t44 (tptp.vgetTerm @t108))))))) % 0.37/0.67 (assume @p79 (forall @t107 (=> (and @t45 @t110 (not @t109)) @t111))) % 0.37/0.67 (assume @p80 (forall @t107 (=> (and @t51 @t72) (= @t105 (tptp.vsomeTerm (tptp.vPlus @t69 @t56)))))) % 0.37/0.67 (assume @p81 (forall @t107 (=> (and @t51 @t80) @t111))) % 0.37/0.67 (assume @p82 (forall @t39 (=> (and (forall @t115 (not (= @t30 @t116))) (forall @t115 (not (= @t30 (tptp.vIfelse tptp.vFalse @t67 @t60)))) (forall (@list @t112 @t67 @t60) (not (= @t30 (tptp.vIfelse @t112 @t67 @t60)))) (forall @t113 (not (= @t30 (tptp.vSucc @t112)))) (not (= @t30 @t84)) (forall @t34 (not (= @t30 @t114))) (forall @t113 (not (= @t30 (tptp.vPred @t112)))) (not (= @t30 @t99)) (forall @t34 (not (= @t30 (tptp.vIszero @t33)))) (forall @t113 (not (= @t30 (tptp.vIszero @t112)))) (forall (@list @t112 @t67) (not (= @t30 (tptp.vPlus @t112 @t67))))) (= (tptp.vreduce @t30) tptp.vnoTerm)))) % 0.37/0.67 (assume @p83 (forall @t7 (or (exists @t115 (and (= @t2 @t116) (= @t117 (tptp.vsomeTerm @t67)))) (exists (@list @t66 @t62) (and (= @t2 (tptp.vIfelse tptp.vFalse @t66 @t62)) (= @t117 (tptp.vsomeTerm @t62)))) (exists (@list @t112 @t64 @t185 @t186) (and (forall (@list @t190 @t189) (or (not (= @t112 tptp.vTrue)) (not (= @t64 @t190)) (not (= @t185 @t189)))) (forall (@list @t188 @t187) (or (not (= @t112 tptp.vFalse)) (not (= @t64 @t188)) (not (= @t185 @t187)))) (= @t186 (tptp.vreduce @t112)) (tptp.visSomeTerm @t186) (= @t2 (tptp.vIfelse @t112 @t64 @t185)) (= @t117 (tptp.vsomeTerm (tptp.vIfelse (tptp.vgetTerm @t186) @t64 @t185))))) (exists (@list @t179 @t178 @t177 @t180) (and (forall (@list @t184 @t183) (or (not (= @t179 tptp.vTrue)) (not (= @t178 @t184)) (not (= @t177 @t183)))) (forall (@list @t182 @t181) (or (not (= @t179 tptp.vFalse)) (not (= @t178 @t182)) (not (= @t177 @t181)))) (= @t180 (tptp.vreduce @t179)) (not (tptp.visSomeTerm @t180)) (= @t2 (tptp.vIfelse @t179 @t178 @t177)) @t118)) (exists (@list @t176 @t175) (and (= @t175 (tptp.vreduce @t176)) (tptp.visSomeTerm @t175) (= @t2 (tptp.vSucc @t176)) (= @t117 (tptp.vsomeTerm (tptp.vSucc (tptp.vgetTerm @t175)))))) (exists (@list @t173 @t174) (and (= @t174 (tptp.vreduce @t173)) (not (tptp.visSomeTerm @t174)) (= @t2 (tptp.vSucc @t173)) @t118)) (and (= @t2 @t84) (= @t117 @t83)) (exists @t34 (and (tptp.visNV @t32) (= @t2 @t114) (= @t117 (tptp.vsomeTerm @t32)))) (exists (@list @t171 @t170) (and (not (tptp.visNV @t171)) (= @t170 (tptp.vreduce @t172)) (tptp.visSomeTerm @t170) (= @t2 (tptp.vPred @t172)) (= @t117 (tptp.vsomeTerm (tptp.vPred (tptp.vgetTerm @t170)))))) (exists (@list @t167 @t169) (and (not (tptp.visNV @t167)) (= @t169 (tptp.vreduce @t168)) (not (tptp.visSomeTerm @t169)) (= @t2 (tptp.vPred @t168)) @t118)) (exists (@list @t165 @t164) (and (not (= @t165 tptp.vZero)) (forall (@list @t166) (not (= @t165 (tptp.vSucc @t166)))) (= @t164 (tptp.vreduce @t165)) (tptp.visSomeTerm @t164) (= @t2 (tptp.vPred @t165)) (= @t117 (tptp.vsomeTerm (tptp.vPred (tptp.vgetTerm @t164)))))) (exists (@list @t161 @t162) (and (not (= @t161 tptp.vZero)) (forall (@list @t163) (not (= @t161 (tptp.vSucc @t163)))) (= @t162 (tptp.vreduce @t161)) (not (tptp.visSomeTerm @t162)) (= @t2 (tptp.vPred @t161)) @t118)) (and (= @t2 @t99) (= @t117 @t98)) (exists (@list @t160) (and (tptp.visNV @t160) (= @t2 (tptp.vIszero (tptp.vSucc @t160))) (= @t117 @t100))) (exists (@list @t158 @t157) (and (not (tptp.visNV @t158)) (= @t157 (tptp.vreduce @t159)) (tptp.visSomeTerm @t157) (= @t2 (tptp.vIszero @t159)) (= @t117 (tptp.vsomeTerm (tptp.vIszero (tptp.vgetTerm @t157)))))) (exists (@list @t154 @t156) (and (not (tptp.visNV @t154)) (= @t156 (tptp.vreduce @t155)) (not (tptp.visSomeTerm @t156)) (= @t2 (tptp.vIszero @t155)) @t118)) (exists (@list @t152 @t151) (and (not (= @t152 tptp.vZero)) (forall (@list @t153) (not (= @t152 (tptp.vSucc @t153)))) (= @t151 (tptp.vreduce @t152)) (tptp.visSomeTerm @t151) (= @t2 (tptp.vIszero @t152)) (= @t117 (tptp.vsomeTerm (tptp.vIszero (tptp.vgetTerm @t151)))))) (exists (@list @t148 @t149) (and (not (= @t148 tptp.vZero)) (forall (@list @t150) (not (= @t148 (tptp.vSucc @t150)))) (= @t149 (tptp.vreduce @t148)) (not (tptp.visSomeTerm @t149)) (= @t2 (tptp.vIszero @t148)) @t118)) (exists (@list @t147 @t146) (and (tptp.visNV @t147) (tptp.visNV @t146) (= @t2 (tptp.vPlus @t147 @t146)) (= @t117 (tptp.vsomeTerm (tptp.vplusop @t147 @t146))))) (exists (@list @t144 @t145 @t143) (and (tptp.visNV @t144) (not (tptp.visNV @t145)) (= @t143 (tptp.vreduce @t145)) (tptp.visSomeTerm @t143) (= @t2 (tptp.vPlus @t144 @t145)) (= @t117 (tptp.vsomeTerm (tptp.vPlus @t144 (tptp.vgetTerm @t143)))))) (exists (@list @t141 @t140 @t142) (and (tptp.visNV @t141) (not (tptp.visNV @t140)) (= @t142 (tptp.vreduce @t140)) (not (tptp.visSomeTerm @t142)) (= @t2 (tptp.vPlus @t141 @t140)) @t118)) (exists (@list @t139 @t137 @t138) (and (not (tptp.visNV @t139)) (= @t138 (tptp.vreduce @t139)) (tptp.visSomeTerm @t138) (= @t2 (tptp.vPlus @t139 @t137)) (= @t117 (tptp.vsomeTerm (tptp.vPlus (tptp.vgetTerm @t138) @t137))))) (exists (@list @t135 @t134 @t136) (and (not (tptp.visNV @t135)) (= @t136 (tptp.vreduce @t135)) (not (tptp.visSomeTerm @t136)) (= @t2 (tptp.vPlus @t135 @t134)) @t118)) (exists (@list @t119) (and (forall (@list @t133 @t132) (not (= @t119 (tptp.vIfelse tptp.vTrue @t133 @t132)))) (forall (@list @t131 @t130) (not (= @t119 (tptp.vIfelse tptp.vFalse @t131 @t130)))) (forall (@list @t129 @t128 @t127) (not (= @t119 (tptp.vIfelse @t129 @t128 @t127)))) (forall (@list @t126) (not (= @t119 (tptp.vSucc @t126)))) (not (= @t119 @t84)) (forall (@list @t125) (not (= @t119 (tptp.vPred (tptp.vSucc @t125))))) (forall (@list @t124) (not (= @t119 (tptp.vPred @t124)))) (not (= @t119 @t99)) (forall (@list @t123) (not (= @t119 (tptp.vIszero (tptp.vSucc @t123))))) (forall (@list @t122) (not (= @t119 (tptp.vIszero @t122)))) (forall (@list @t121 @t120) (not (= @t119 (tptp.vPlus @t121 @t120)))) (= @t2 @t119) @t118))))) % 0.37/0.67 (assume @p84 (tptp.vptchecksimple tptp.vTrue tptp.vB)) % 0.37/0.67 (assume @p85 (tptp.vptchecksimple tptp.vFalse tptp.vB)) % 0.37/0.67 (assume @p86 (forall (@list @t44 @t56 @t191 @t57) (=> (and @t195 @t194 @t193) @t192))) % 0.37/0.67 (assume @p87 (forall @t196 (=> @t192 @t195))) % 0.37/0.67 (assume @p88 (forall @t196 (=> @t192 @t194))) % 0.37/0.67 (assume @p89 (forall @t196 (=> @t192 @t193))) % 0.37/0.67 (assume @p90 (tptp.vptchecksimple tptp.vZero tptp.vNat)) % 0.37/0.67 (assume @p91 (forall (@list @t191) (=> (tptp.vptchecksimple tptp.vZero @t191) @t197))) % 0.37/0.67 (assume @p92 (forall @t48 (=> @t199 @t198))) % 0.37/0.67 (assume @p93 (forall @t200 (=> (tptp.vptchecksimple @t81 @t191) @t197))) % 0.37/0.67 (assume @p94 (forall @t48 (=> @t198 @t199))) % 0.37/0.67 (assume @p95 (forall @t48 (=> @t199 @t201))) % 0.37/0.67 (assume @p96 (forall @t48 (=> @t201 @t199))) % 0.37/0.67 (assume @p97 (forall @t200 (=> (tptp.vptchecksimple @t91 @t191) @t197))) % 0.37/0.67 (assume @p98 (forall @t48 (=> @t199 @t202))) % 0.37/0.67 (assume @p99 (forall @t48 (=> @t202 @t199))) % 0.37/0.67 (assume @p100 (forall @t200 (=> (tptp.vptchecksimple @t102 @t191) (= @t191 tptp.vB)))) % 0.37/0.67 (assume @p101 (forall @t107 (=> (and @t199 @t204) @t203))) % 0.37/0.67 (assume @p102 (forall (@list @t44 @t56 @t191) (=> (tptp.vptchecksimple @t104 @t191) @t197))) % 0.37/0.67 (assume @p103 (forall @t107 (=> @t203 @t199))) % 0.37/0.67 (assume @p104 (forall @t107 (=> @t203 @t204))) % 0.37/0.67 (assume @p105 (not (=> @t205 (tptp.vptchecksimple tptp.vFalse tptp.vNat)))) % 0.37/0.67 (assume @p106 true) % 0.37/0.67 (step @p107 :rule symm :premises (@p15)) % 0.37/0.67 (step @p108 :rule not_implies_elim1 :premises (@p105)) % 0.37/0.67 (step @p109 :rule alpha_equiv :args (@t20 (@list @t2) (@list @t32))) % 0.37/0.67 (step @p110 :rule equiv_elim1 :premises (@p109)) % 0.37/0.67 (step @p111 :rule chain_m_resolution :premises (@p110 @p16) :args (@t206 (@list false) (@list @t20))) % 0.37/0.67 (step @p112 :rule aci_norm :args ((= (or (or @t208 @t207) @t31) (or @t208 @t207 @t31)))) % 0.37/0.67 (step @p113 :rule refl :args (@t31)) % 0.37/0.67 (step @p114 :rule refl :args (@t207)) % 0.37/0.67 (step @p115 :rule bool-double-not-elim :args (@t208)) % 0.37/0.67 (step @p116 :rule nary_cong :premises (@p115 @p114) :args ((or (not @t209) @t207))) % 0.37/0.67 (step @p117 :rule bool-and-de-morgan :args (@t209 @t35 true)) % 0.37/0.67 (step @p118 :rule trans :premises (@p117 @p116)) % 0.37/0.67 (step @p119 :rule nary_cong :premises (@p118 @p113) :args ((or (not @t210) @t31))) % 0.37/0.67 (step @p120 :rule trans :premises (@p119 @p112)) % 0.37/0.67 (step @p121 :rule bool-impl-elim :args (@t210 @t31)) % 0.37/0.67 (step @p122 :rule trans :premises (@p121 @p120)) % 0.37/0.67 (step @p123 :rule cong :premises (@p122) :args ((forall @t39 (=> @t210 @t31)))) % 0.37/0.67 (step @p124 :rule refl :args (@t31)) % 0.37/0.67 (step @p125 :rule refl :args (@t35)) % 0.37/0.67 (step @p126 :rule eq-symm :args (@t30 tptp.vZero)) % 0.37/0.67 (step @p127 :rule cong :premises (@p126) :args (@t36)) % 0.37/0.67 (step @p128 :rule nary_cong :premises (@p127 @p125) :args (@t37)) % 0.37/0.67 (step @p129 :rule cong :premises (@p128 @p124) :args (@t38)) % 0.37/0.67 (step @p130 :rule cong :premises (@p129) :args (@t40)) % 0.37/0.67 (step @p131 :rule trans :premises (@p130 @p123)) % 0.37/0.67 (step @p132 :rule eq_resolve :premises (@p43 @p131)) % 0.37/0.67 (step @p133 :rule instantiate :premises (@p132) :args ((@list tptp.vFalse))) % 0.37/0.67 (step @p134 :rule cnf_or_pos :args (@t214)) % 0.37/0.67 (step @p135 :rule reordering :premises (@p134) :args ((or @t213 @t211 @t212 (not @t214)))) % 0.37/0.67 (step @p136 false :rule chain_m_resolution :premises (@p135 @p133 @p111 @p108 @p107) :args (false (@list false false false true) (@list @t214 @t206 @t205 @t213))) % 0.37/0.67 ) % 0.37/0.67 % SZS output end Proof % 0.37/0.67 % cvc5 exiting %------------------------------------------------------------------------------