%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : COM216_1 : TPTP v9.3.0. Released v9.3.0. % 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 08:10:40 AM UTC 2026 % Result : Theorem 0.38s 0.69s % Output : Proof 0.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : COM216_1 : TPTP v9.3.0. Released v9.3.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n017.cluster.edu % 0.17/0.34 % Model : x86_64 x86_64 % 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.34 % Memory : 8042.1875MB % 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.34 % CPULimit : 300 % 0.17/0.34 % WCLimit : 300 % 0.17/0.34 % DateTime : Mon Jun 1 20:31:16 EDT 2026 % 0.17/0.34 % CPUTime : % 0.33/0.52 %----Proving TF0_NAR, FOF, or CNF % 0.38/0.69 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.38/0.69 % SZS status Theorem % 0.38/0.69 % SZS output start Proof % 0.38/0.69 ( % 0.38/0.69 (declare-sort tptp.vTy 0) % 0.38/0.69 (declare-sort tptp.vOptTerm 0) % 0.38/0.69 (declare-sort tptp.vTerm 0) % 0.38/0.69 (declare-const tptp.vptchecksimple (-> tptp.vTerm tptp.vTy Bool)) % 0.38/0.69 (declare-const tptp.vreduce (-> tptp.vTerm tptp.vOptTerm)) % 0.38/0.69 (declare-const tptp.vplusop (-> tptp.vTerm tptp.vTerm tptp.vTerm)) % 0.38/0.69 (declare-const tptp.visSomeTerm (-> tptp.vOptTerm Bool)) % 0.38/0.69 (declare-const tptp.visValue (-> tptp.vTerm Bool)) % 0.38/0.69 (declare-const tptp.visNV (-> tptp.vTerm Bool)) % 0.38/0.69 (declare-const tptp.vPlus (-> tptp.vTerm tptp.vTerm tptp.vTerm)) % 0.38/0.69 (declare-const tptp.vIszero (-> tptp.vTerm tptp.vTerm)) % 0.38/0.69 (declare-const tptp.vPred (-> tptp.vTerm tptp.vTerm)) % 0.38/0.69 (declare-const tptp.vSucc (-> tptp.vTerm tptp.vTerm)) % 0.38/0.69 (declare-const tptp.vIfelse (-> tptp.vTerm tptp.vTerm tptp.vTerm tptp.vTerm)) % 0.38/0.69 (declare-const tptp.vZero tptp.vTerm) % 0.38/0.69 (declare-const tptp.vFalse tptp.vTerm) % 0.38/0.69 (declare-const tptp.vTrue tptp.vTerm) % 0.38/0.69 (declare-const tptp.vsomeTerm (-> tptp.vTerm tptp.vOptTerm)) % 0.38/0.69 (declare-const tptp.vnoTerm tptp.vOptTerm) % 0.38/0.69 (declare-const tptp.vNat tptp.vTy) % 0.38/0.69 (declare-const tptp.vB tptp.vTy) % 0.38/0.69 (declare-const tptp.vgetTerm (-> tptp.vOptTerm tptp.vTerm)) % 0.38/0.69 (define @t1 () (@var "VTerm1" tptp.vTerm)) % 0.38/0.69 (define @t2 () (@var "VTerm0" tptp.vTerm)) % 0.38/0.69 (define @t3 () (tptp.vPlus @t2 @t1)) % 0.38/0.69 (define @t4 () (@var "VX" tptp.vTerm)) % 0.38/0.69 (define @t5 () (@list @t2 @t1)) % 0.38/0.69 (define @t6 () (tptp.vIszero @t2)) % 0.38/0.69 (define @t7 () (@list @t2)) % 0.38/0.69 (define @t8 () (tptp.vPred @t2)) % 0.38/0.69 (define @t9 () (tptp.vSucc @t2)) % 0.38/0.69 (define @t10 () (@var "VTerm2" tptp.vTerm)) % 0.38/0.69 (define @t11 () (tptp.vIfelse @t2 @t1 @t10)) % 0.38/0.69 (define @t12 () (@list @t2 @t1 @t10)) % 0.38/0.69 (define @t13 () (@var "VTerm5" tptp.vTerm)) % 0.38/0.69 (define @t14 () (@var "VTerm4" tptp.vTerm)) % 0.38/0.69 (define @t15 () (@var "VTerm3" tptp.vTerm)) % 0.38/0.69 (define @t16 () (= @t2 @t1)) % 0.38/0.69 (define @t17 () (tptp.vPred @t1)) % 0.38/0.69 (define @t18 () (tptp.vIszero @t1)) % 0.38/0.69 (define @t19 () (@list @t2 @t1 @t10 @t15)) % 0.38/0.69 (define @t20 () (forall @t12 (not (= tptp.vFalse @t11)))) % 0.38/0.69 (define @t21 () (forall @t7 (not (= tptp.vFalse @t9)))) % 0.38/0.69 (define @t22 () (forall @t7 (not (= tptp.vFalse @t8)))) % 0.38/0.69 (define @t23 () (forall @t7 (not (= tptp.vFalse @t6)))) % 0.38/0.69 (define @t24 () (forall @t5 (not (= tptp.vFalse @t3)))) % 0.38/0.69 (define @t25 () (tptp.vPlus @t1 @t10)) % 0.38/0.69 (define @t26 () (tptp.vsomeTerm @t2)) % 0.38/0.69 (define @t27 () (@var "VX" tptp.vOptTerm)) % 0.38/0.69 (define @t28 () (@var "VX" tptp.vTy)) % 0.38/0.69 (define @t29 () (@var "Vt" tptp.vTerm)) % 0.38/0.69 (define @t30 () (@var "Vnv" tptp.vTerm)) % 0.38/0.69 (define @t31 () (tptp.visNV @t30)) % 0.38/0.69 (define @t32 () (tptp.vSucc @t30)) % 0.38/0.69 (define @t33 () (@list @t30)) % 0.38/0.69 (define @t34 () (@var "VwildcardName0" tptp.vTerm)) % 0.38/0.69 (define @t35 () (@var "Vnv0" tptp.vTerm)) % 0.38/0.69 (define @t36 () (tptp.vSucc @t35)) % 0.38/0.69 (define @t37 () (@list @t35)) % 0.38/0.69 (define @t38 () (forall @t37 (not (= @t34 @t36)))) % 0.38/0.69 (define @t39 () (not (= @t34 tptp.vZero))) % 0.38/0.69 (define @t40 () (@list @t34)) % 0.38/0.69 (define @t41 () (= @t2 @t32)) % 0.38/0.69 (define @t42 () (tptp.visNV @t2)) % 0.38/0.69 (define @t43 () (not @t31)) % 0.38/0.69 (define @t44 () (@var "Vt1" tptp.vTerm)) % 0.38/0.69 (define @t45 () (tptp.visNV @t44)) % 0.38/0.69 (define @t46 () (not (= @t44 tptp.vFalse))) % 0.38/0.69 (define @t47 () (not (= @t44 tptp.vTrue))) % 0.38/0.69 (define @t48 () (@list @t44)) % 0.38/0.69 (define @t49 () (= @t2 @t44)) % 0.38/0.69 (define @t50 () (tptp.visValue @t2)) % 0.38/0.69 (define @t51 () (not @t45)) % 0.38/0.69 (define @t52 () (tptp.vsomeTerm @t34)) % 0.38/0.69 (define @t53 () (@var "VOptTerm0" tptp.vOptTerm)) % 0.38/0.69 (define @t54 () (tptp.visSomeTerm @t53)) % 0.38/0.69 (define @t55 () (@list @t53)) % 0.38/0.69 (define @t56 () (@var "Vt2" tptp.vTerm)) % 0.38/0.69 (define @t57 () (@var "Vt3" tptp.vTerm)) % 0.38/0.69 (define @t58 () (tptp.vplusop @t56 @t57)) % 0.38/0.69 (define @t59 () (@list @t56 @t57)) % 0.38/0.69 (define @t60 () (@var "Vt30" tptp.vTerm)) % 0.38/0.69 (define @t61 () (tptp.vSucc @t60)) % 0.38/0.69 (define @t62 () (@var "Vt31" tptp.vTerm)) % 0.38/0.69 (define @t63 () (tptp.vplusop @t2 @t1)) % 0.38/0.69 (define @t64 () (@var "Vt22" tptp.vTerm)) % 0.38/0.69 (define @t65 () (@var "Vt3000" tptp.vTerm)) % 0.38/0.69 (define @t66 () (@var "Vt21" tptp.vTerm)) % 0.38/0.69 (define @t67 () (@var "Vt20" tptp.vTerm)) % 0.38/0.69 (define @t68 () (tptp.vreduce @t44)) % 0.38/0.69 (define @t69 () (tptp.vgetTerm @t68)) % 0.38/0.69 (define @t70 () (tptp.vIfelse @t44 @t56 @t57)) % 0.38/0.69 (define @t71 () (tptp.vreduce @t70)) % 0.38/0.69 (define @t72 () (tptp.visSomeTerm @t68)) % 0.38/0.69 (define @t73 () (@var "Vt301" tptp.vTerm)) % 0.38/0.69 (define @t74 () (@var "Vt201" tptp.vTerm)) % 0.38/0.69 (define @t75 () (forall (@list @t74 @t73) (or @t46 (not (= @t56 @t74)) (not (= @t57 @t73))))) % 0.38/0.69 (define @t76 () (@var "Vt300" tptp.vTerm)) % 0.38/0.69 (define @t77 () (@var "Vt200" tptp.vTerm)) % 0.38/0.69 (define @t78 () (forall (@list @t77 @t76) (or @t47 (not (= @t56 @t77)) (not (= @t57 @t76))))) % 0.38/0.69 (define @t79 () (@list @t44 @t56 @t57)) % 0.38/0.69 (define @t80 () (not @t72)) % 0.38/0.69 (define @t81 () (tptp.vSucc @t44)) % 0.38/0.69 (define @t82 () (tptp.vreduce @t81)) % 0.38/0.69 (define @t83 () (tptp.vsomeTerm tptp.vZero)) % 0.38/0.69 (define @t84 () (tptp.vPred tptp.vZero)) % 0.38/0.69 (define @t85 () (tptp.vreduce (tptp.vPred @t32))) % 0.38/0.69 (define @t86 () (tptp.vreduce @t32)) % 0.38/0.69 (define @t87 () (tptp.vgetTerm @t86)) % 0.38/0.69 (define @t88 () (tptp.visSomeTerm @t86)) % 0.38/0.69 (define @t89 () (and @t43 @t88)) % 0.38/0.69 (define @t90 () (and @t43 (not @t88))) % 0.38/0.69 (define @t91 () (tptp.vPred @t44)) % 0.38/0.69 (define @t92 () (tptp.vreduce @t91)) % 0.38/0.69 (define @t93 () (@var "Vnv00" tptp.vTerm)) % 0.38/0.69 (define @t94 () (forall (@list @t93) (not (= @t44 (tptp.vSucc @t93))))) % 0.38/0.69 (define @t95 () (not (= @t44 tptp.vZero))) % 0.38/0.69 (define @t96 () (and @t95 @t94 @t72)) % 0.38/0.69 (define @t97 () (and @t95 @t94 @t80)) % 0.38/0.69 (define @t98 () (tptp.vsomeTerm tptp.vTrue)) % 0.38/0.69 (define @t99 () (tptp.vIszero tptp.vZero)) % 0.38/0.69 (define @t100 () (tptp.vsomeTerm tptp.vFalse)) % 0.38/0.69 (define @t101 () (tptp.vreduce (tptp.vIszero @t32))) % 0.38/0.69 (define @t102 () (tptp.vIszero @t44)) % 0.38/0.69 (define @t103 () (tptp.vreduce @t102)) % 0.38/0.69 (define @t104 () (tptp.vPlus @t44 @t56)) % 0.38/0.69 (define @t105 () (tptp.vreduce @t104)) % 0.38/0.69 (define @t106 () (tptp.visNV @t56)) % 0.38/0.69 (define @t107 () (@list @t44 @t56)) % 0.38/0.69 (define @t108 () (tptp.vreduce @t56)) % 0.38/0.69 (define @t109 () (tptp.visSomeTerm @t108)) % 0.38/0.69 (define @t110 () (not @t106)) % 0.38/0.69 (define @t111 () (= @t105 tptp.vnoTerm)) % 0.38/0.69 (define @t112 () (tptp.vreduce @t34)) % 0.38/0.69 (define @t113 () (@var "Vt10" tptp.vTerm)) % 0.38/0.69 (define @t114 () (tptp.vPlus @t113 @t67)) % 0.38/0.69 (define @t115 () (@list @t113 @t67)) % 0.38/0.69 (define @t116 () (forall @t115 (not (= @t34 @t114)))) % 0.38/0.69 (define @t117 () (tptp.vIszero @t113)) % 0.38/0.69 (define @t118 () (@list @t113)) % 0.38/0.69 (define @t119 () (forall @t118 (not (= @t34 @t117)))) % 0.38/0.69 (define @t120 () (tptp.vIszero @t36)) % 0.38/0.69 (define @t121 () (forall @t37 (not (= @t34 @t120)))) % 0.38/0.69 (define @t122 () (= @t34 @t99)) % 0.38/0.69 (define @t123 () (not @t122)) % 0.38/0.69 (define @t124 () (tptp.vPred @t113)) % 0.38/0.69 (define @t125 () (forall @t118 (not (= @t34 @t124)))) % 0.38/0.69 (define @t126 () (tptp.vPred @t36)) % 0.38/0.69 (define @t127 () (forall @t37 (not (= @t34 @t126)))) % 0.38/0.69 (define @t128 () (= @t34 @t84)) % 0.38/0.69 (define @t129 () (not @t128)) % 0.38/0.69 (define @t130 () (tptp.vSucc @t113)) % 0.38/0.69 (define @t131 () (forall @t118 (not (= @t34 @t130)))) % 0.38/0.69 (define @t132 () (tptp.vIfelse @t113 @t67 @t60)) % 0.38/0.69 (define @t133 () (@list @t113 @t67 @t60)) % 0.38/0.69 (define @t134 () (forall @t133 (not (= @t34 @t132)))) % 0.38/0.69 (define @t135 () (tptp.vIfelse tptp.vFalse @t67 @t60)) % 0.38/0.69 (define @t136 () (@list @t67 @t60)) % 0.38/0.69 (define @t137 () (forall @t136 (not (= @t34 @t135)))) % 0.38/0.69 (define @t138 () (tptp.vIfelse tptp.vTrue @t67 @t60)) % 0.38/0.69 (define @t139 () (forall @t136 (not (= @t34 @t138)))) % 0.38/0.69 (define @t140 () (and @t139 @t137 @t134 @t131 @t129 @t127 @t125 @t123 @t121 @t119 @t116)) % 0.38/0.69 (define @t141 () (=> @t140 (= @t112 tptp.vnoTerm))) % 0.38/0.69 (define @t142 () (forall @t40 @t141)) % 0.38/0.69 (define @t143 () (tptp.vreduce @t2)) % 0.38/0.69 (define @t144 () (= @t143 tptp.vnoTerm)) % 0.38/0.69 (define @t145 () (@var "VwildcardName00" tptp.vTerm)) % 0.38/0.69 (define @t146 () (@var "Vt2080" tptp.vTerm)) % 0.38/0.69 (define @t147 () (@var "Vt1040" tptp.vTerm)) % 0.38/0.69 (define @t148 () (@var "Vt1030" tptp.vTerm)) % 0.38/0.69 (define @t149 () (@var "Vnv050" tptp.vTerm)) % 0.38/0.69 (define @t150 () (@var "Vt1020" tptp.vTerm)) % 0.38/0.69 (define @t151 () (@var "Vnv040" tptp.vTerm)) % 0.38/0.69 (define @t152 () (@var "Vt1010" tptp.vTerm)) % 0.38/0.69 (define @t153 () (@var "Vt3070" tptp.vTerm)) % 0.38/0.69 (define @t154 () (@var "Vt2070" tptp.vTerm)) % 0.38/0.69 (define @t155 () (@var "Vt1000" tptp.vTerm)) % 0.38/0.69 (define @t156 () (@var "Vt3060" tptp.vTerm)) % 0.38/0.69 (define @t157 () (@var "Vt2060" tptp.vTerm)) % 0.38/0.69 (define @t158 () (@var "Vt3050" tptp.vTerm)) % 0.38/0.69 (define @t159 () (@var "Vt2050" tptp.vTerm)) % 0.38/0.69 (define @t160 () (@var "Vt28" tptp.vTerm)) % 0.38/0.69 (define @t161 () (@var "Vt112" tptp.vTerm)) % 0.38/0.69 (define @t162 () (@var "Vot13" tptp.vOptTerm)) % 0.38/0.69 (define @t163 () (@var "Vt27" tptp.vTerm)) % 0.38/0.69 (define @t164 () (@var "Vot12" tptp.vOptTerm)) % 0.38/0.69 (define @t165 () (@var "Vt111" tptp.vTerm)) % 0.38/0.69 (define @t166 () (@var "Vt26" tptp.vTerm)) % 0.38/0.69 (define @t167 () (@var "Vt110" tptp.vTerm)) % 0.38/0.69 (define @t168 () (@var "Vot211" tptp.vOptTerm)) % 0.38/0.69 (define @t169 () (@var "Vot210" tptp.vOptTerm)) % 0.38/0.69 (define @t170 () (@var "Vt19" tptp.vTerm)) % 0.38/0.69 (define @t171 () (@var "Vt25" tptp.vTerm)) % 0.38/0.69 (define @t172 () (@var "Vt24" tptp.vTerm)) % 0.38/0.69 (define @t173 () (@var "Vt18" tptp.vTerm)) % 0.38/0.69 (define @t174 () (@var "Vt17" tptp.vTerm)) % 0.38/0.69 (define @t175 () (@var "Vot29" tptp.vOptTerm)) % 0.38/0.69 (define @t176 () (@var "Vnv030" tptp.vTerm)) % 0.38/0.69 (define @t177 () (@var "Vot28" tptp.vOptTerm)) % 0.38/0.69 (define @t178 () (@var "Vt16" tptp.vTerm)) % 0.38/0.69 (define @t179 () (@var "Vnv020" tptp.vTerm)) % 0.38/0.69 (define @t180 () (@var "Vnv5" tptp.vTerm)) % 0.38/0.69 (define @t181 () (tptp.vSucc @t180)) % 0.38/0.69 (define @t182 () (@var "Vot27" tptp.vOptTerm)) % 0.38/0.69 (define @t183 () (@var "Vot26" tptp.vOptTerm)) % 0.38/0.69 (define @t184 () (@var "Vnv4" tptp.vTerm)) % 0.38/0.69 (define @t185 () (tptp.vSucc @t184)) % 0.38/0.69 (define @t186 () (@var "Vnv3" tptp.vTerm)) % 0.38/0.69 (define @t187 () (@var "Vt15" tptp.vTerm)) % 0.38/0.69 (define @t188 () (@var "Vot25" tptp.vOptTerm)) % 0.38/0.69 (define @t189 () (@var "Vnv010" tptp.vTerm)) % 0.38/0.69 (define @t190 () (@var "Vot24" tptp.vOptTerm)) % 0.38/0.69 (define @t191 () (@var "Vt14" tptp.vTerm)) % 0.38/0.69 (define @t192 () (@var "Vnv000" tptp.vTerm)) % 0.38/0.69 (define @t193 () (@var "Vnv2" tptp.vTerm)) % 0.38/0.69 (define @t194 () (tptp.vSucc @t193)) % 0.38/0.69 (define @t195 () (@var "Vot23" tptp.vOptTerm)) % 0.38/0.69 (define @t196 () (@var "Vot22" tptp.vOptTerm)) % 0.38/0.69 (define @t197 () (@var "Vnv1" tptp.vTerm)) % 0.38/0.69 (define @t198 () (tptp.vSucc @t197)) % 0.38/0.69 (define @t199 () (@var "Vt13" tptp.vTerm)) % 0.38/0.69 (define @t200 () (@var "Vot21" tptp.vOptTerm)) % 0.38/0.69 (define @t201 () (@var "Vot20" tptp.vOptTerm)) % 0.38/0.69 (define @t202 () (@var "Vt12" tptp.vTerm)) % 0.38/0.69 (define @t203 () (@var "Vt33" tptp.vTerm)) % 0.38/0.69 (define @t204 () (@var "Vt23" tptp.vTerm)) % 0.38/0.69 (define @t205 () (@var "Vt11" tptp.vTerm)) % 0.38/0.69 (define @t206 () (@var "Vot11" tptp.vOptTerm)) % 0.38/0.69 (define @t207 () (@var "Vt3040" tptp.vTerm)) % 0.38/0.69 (define @t208 () (@var "Vt2040" tptp.vTerm)) % 0.38/0.69 (define @t209 () (@var "Vt3030" tptp.vTerm)) % 0.38/0.69 (define @t210 () (@var "Vt2030" tptp.vTerm)) % 0.38/0.69 (define @t211 () (@var "Vt32" tptp.vTerm)) % 0.38/0.69 (define @t212 () (@var "Vot10" tptp.vOptTerm)) % 0.38/0.69 (define @t213 () (@var "Vt3020" tptp.vTerm)) % 0.38/0.69 (define @t214 () (@var "Vt2020" tptp.vTerm)) % 0.38/0.69 (define @t215 () (@var "Vt3010" tptp.vTerm)) % 0.38/0.69 (define @t216 () (@var "Vt2010" tptp.vTerm)) % 0.38/0.69 (define @t217 () (@var "VT" tptp.vTy)) % 0.38/0.69 (define @t218 () (tptp.vptchecksimple @t70 @t217)) % 0.38/0.69 (define @t219 () (tptp.vptchecksimple @t57 @t217)) % 0.38/0.69 (define @t220 () (tptp.vptchecksimple @t56 @t217)) % 0.38/0.69 (define @t221 () (tptp.vptchecksimple @t44 tptp.vB)) % 0.38/0.69 (define @t222 () (@list @t44 @t56 @t57 @t217)) % 0.38/0.69 (define @t223 () (= @t217 tptp.vNat)) % 0.38/0.69 (define @t224 () (tptp.vptchecksimple @t81 tptp.vNat)) % 0.38/0.69 (define @t225 () (tptp.vptchecksimple @t44 tptp.vNat)) % 0.38/0.69 (define @t226 () (@list @t44 @t217)) % 0.38/0.69 (define @t227 () (tptp.vptchecksimple @t91 tptp.vNat)) % 0.38/0.69 (define @t228 () (tptp.vptchecksimple @t102 tptp.vB)) % 0.38/0.69 (define @t229 () (tptp.vptchecksimple @t104 tptp.vNat)) % 0.38/0.69 (define @t230 () (tptp.vptchecksimple @t56 tptp.vNat)) % 0.38/0.69 (define @t231 () (@var "Vtres" tptp.vTerm)) % 0.38/0.69 (define @t232 () (tptp.vptchecksimple @t231 @t217)) % 0.38/0.69 (define @t233 () (tptp.vreduce tptp.vFalse)) % 0.38/0.69 (define @t234 () (= @t233 (tptp.vsomeTerm @t231))) % 0.38/0.69 (define @t235 () (tptp.vptchecksimple tptp.vFalse @t217)) % 0.38/0.69 (define @t236 () (and @t235 @t234)) % 0.38/0.69 (define @t237 () (@list @t217 @t231)) % 0.38/0.69 (define @t238 () (forall @t237 (=> @t236 @t232))) % 0.38/0.69 (define @t239 () (not @t238)) % 0.38/0.69 (define @t240 () (= tptp.vnoTerm @t112)) % 0.38/0.69 (define @t241 () (not @t116)) % 0.38/0.69 (define @t242 () (not @t119)) % 0.38/0.69 (define @t243 () (not @t121)) % 0.38/0.69 (define @t244 () (not @t125)) % 0.38/0.69 (define @t245 () (not @t127)) % 0.38/0.69 (define @t246 () (not @t131)) % 0.38/0.69 (define @t247 () (not @t134)) % 0.38/0.69 (define @t248 () (not @t137)) % 0.38/0.69 (define @t249 () (not @t139)) % 0.38/0.69 (define @t250 () (not @t123)) % 0.38/0.69 (define @t251 () (not @t129)) % 0.38/0.69 (define @t252 () (or @t249 @t248 @t247 @t246 @t251 @t245 @t244 @t250 @t243 @t242 @t241)) % 0.38/0.69 (define @t253 () (not @t234)) % 0.38/0.69 (define @t254 () (not @t235)) % 0.38/0.69 (define @t255 () (or @t254 @t253 @t232)) % 0.38/0.69 (define @t256 () (forall @t237 @t255)) % 0.38/0.69 (define @t257 () (@quantifiers_skolemize @t256 1)) % 0.38/0.69 (define @t258 () (= @t233 (tptp.vsomeTerm @t257))) % 0.38/0.69 (define @t259 () (@quantifiers_skolemize @t256 0)) % 0.38/0.69 (define @t260 () (not @t258)) % 0.38/0.69 (define @t261 () (or (not (tptp.vptchecksimple tptp.vFalse @t259)) @t260 (tptp.vptchecksimple @t257 @t259))) % 0.38/0.69 (define @t262 () (@list true)) % 0.38/0.69 (define @t263 () (= tptp.vnoTerm @t233)) % 0.38/0.69 (define @t264 () (forall @t115 (not (= tptp.vFalse @t114)))) % 0.38/0.69 (define @t265 () (@list false)) % 0.38/0.69 (define @t266 () (@list @t2)) % 0.38/0.69 (define @t267 () (@list @t113)) % 0.38/0.69 (define @t268 () (forall @t118 (not (= tptp.vFalse @t117)))) % 0.38/0.69 (define @t269 () (forall @t37 (not (= tptp.vFalse @t120)))) % 0.38/0.69 (define @t270 () (tptp.vSucc (@quantifiers_skolemize @t269 0))) % 0.38/0.69 (define @t271 () (= tptp.vFalse (tptp.vIszero @t270))) % 0.38/0.69 (define @t272 () (not @t269)) % 0.38/0.69 (define @t273 () (not (not @t271))) % 0.38/0.69 (define @t274 () (forall @t118 (not (= tptp.vFalse @t124)))) % 0.38/0.69 (define @t275 () (forall @t37 (not (= tptp.vFalse @t126)))) % 0.38/0.69 (define @t276 () (tptp.vSucc (@quantifiers_skolemize @t275 0))) % 0.38/0.69 (define @t277 () (= tptp.vFalse (tptp.vPred @t276))) % 0.38/0.69 (define @t278 () (not @t275)) % 0.38/0.69 (define @t279 () (not (not @t277))) % 0.38/0.69 (define @t280 () (forall @t118 (not (= tptp.vFalse @t130)))) % 0.38/0.69 (define @t281 () (forall @t133 (not (= tptp.vFalse @t132)))) % 0.38/0.69 (define @t282 () (@list tptp.vZero)) % 0.38/0.69 (define @t283 () (forall @t136 (not (= tptp.vFalse @t138)))) % 0.38/0.69 (define @t284 () (@quantifiers_skolemize @t283 1)) % 0.38/0.69 (define @t285 () (@quantifiers_skolemize @t283 0)) % 0.38/0.69 (define @t286 () (= tptp.vFalse (tptp.vIfelse tptp.vTrue @t285 @t284))) % 0.38/0.69 (define @t287 () (not @t283)) % 0.38/0.69 (define @t288 () (not (not @t286))) % 0.38/0.69 (define @t289 () (forall @t136 (not (= tptp.vFalse @t135)))) % 0.38/0.69 (define @t290 () (@quantifiers_skolemize @t289 1)) % 0.38/0.69 (define @t291 () (@quantifiers_skolemize @t289 0)) % 0.38/0.69 (define @t292 () (= tptp.vFalse (tptp.vIfelse tptp.vFalse @t291 @t290))) % 0.38/0.69 (define @t293 () (not @t289)) % 0.38/0.69 (define @t294 () (not (not @t292))) % 0.38/0.69 (define @t295 () (not @t264)) % 0.38/0.69 (define @t296 () (not @t268)) % 0.38/0.69 (define @t297 () (= tptp.vFalse @t99)) % 0.38/0.69 (define @t298 () (not @t274)) % 0.38/0.69 (define @t299 () (= tptp.vFalse @t84)) % 0.38/0.69 (define @t300 () (not @t280)) % 0.38/0.69 (define @t301 () (not @t281)) % 0.38/0.69 (define @t302 () (or @t287 @t293 @t301 @t300 @t299 @t278 @t298 @t297 @t272 @t296 @t295 @t263)) % 0.38/0.69 (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))))) % 0.38/0.69 (assume @p2 (forall (@list @t15 @t10 @t1 @t14 @t2 @t13) (=> (= @t11 (tptp.vIfelse @t15 @t14 @t13)) (and (= @t2 @t15) (= @t1 @t14) (= @t10 @t13))))) % 0.38/0.69 (assume @p3 (forall @t5 (=> (= @t9 (tptp.vSucc @t1)) @t16))) % 0.38/0.69 (assume @p4 (forall @t5 (=> (= @t8 @t17) @t16))) % 0.38/0.69 (assume @p5 (forall @t5 (=> (= @t6 @t18) @t16))) % 0.38/0.69 (assume @p6 (forall @t19 (=> (= @t3 (tptp.vPlus @t10 @t15)) (and (= @t2 @t10) (= @t1 @t15))))) % 0.38/0.69 (assume @p7 (not (= tptp.vTrue tptp.vFalse))) % 0.38/0.69 (assume @p8 (forall @t12 (not (= tptp.vTrue @t11)))) % 0.38/0.69 (assume @p9 (not (= tptp.vTrue tptp.vZero))) % 0.38/0.69 (assume @p10 (forall @t7 (not (= tptp.vTrue @t9)))) % 0.38/0.69 (assume @p11 (forall @t7 (not (= tptp.vTrue @t8)))) % 0.38/0.69 (assume @p12 (forall @t7 (not (= tptp.vTrue @t6)))) % 0.38/0.69 (assume @p13 (forall @t5 (not (= tptp.vTrue @t3)))) % 0.38/0.69 (assume @p14 @t20) % 0.38/0.69 (assume @p15 (not (= tptp.vFalse tptp.vZero))) % 0.38/0.69 (assume @p16 @t21) % 0.38/0.69 (assume @p17 @t22) % 0.38/0.69 (assume @p18 @t23) % 0.38/0.69 (assume @p19 @t24) % 0.38/0.69 (assume @p20 (forall @t12 (not (= @t11 tptp.vZero)))) % 0.38/0.69 (assume @p21 (forall @t19 (not (= @t11 (tptp.vSucc @t15))))) % 0.38/0.69 (assume @p22 (forall @t19 (not (= @t11 (tptp.vPred @t15))))) % 0.38/0.69 (assume @p23 (forall @t19 (not (= @t11 (tptp.vIszero @t15))))) % 0.38/0.69 (assume @p24 (forall (@list @t15 @t10 @t1 @t14 @t2) (not (= @t11 (tptp.vPlus @t15 @t14))))) % 0.38/0.69 (assume @p25 (forall @t7 (not (= tptp.vZero @t9)))) % 0.38/0.69 (assume @p26 (forall @t7 (not (= tptp.vZero @t8)))) % 0.38/0.69 (assume @p27 (forall @t7 (not (= tptp.vZero @t6)))) % 0.38/0.69 (assume @p28 (forall @t5 (not (= tptp.vZero @t3)))) % 0.38/0.69 (assume @p29 (forall @t5 (not (= @t9 @t17)))) % 0.38/0.69 (assume @p30 (forall @t5 (not (= @t9 @t18)))) % 0.38/0.69 (assume @p31 (forall @t12 (not (= @t9 @t25)))) % 0.38/0.69 (assume @p32 (forall @t5 (not (= @t8 @t18)))) % 0.38/0.69 (assume @p33 (forall @t12 (not (= @t8 @t25)))) % 0.38/0.69 (assume @p34 (forall @t12 (not (= @t6 @t25)))) % 0.38/0.69 (assume @p35 (forall (@list @t27) (or (= @t27 tptp.vnoTerm) (exists @t7 (= @t27 @t26))))) % 0.38/0.69 (assume @p36 (forall @t5 (=> (= @t26 (tptp.vsomeTerm @t1)) @t16))) % 0.38/0.69 (assume @p37 (forall @t7 (not (= tptp.vnoTerm @t26)))) % 0.38/0.69 (assume @p38 (forall (@list @t28) (or (= @t28 tptp.vB) (= @t28 tptp.vNat)))) % 0.38/0.69 (assume @p39 (not (= tptp.vB tptp.vNat))) % 0.38/0.69 (assume @p40 (forall (@list @t29) (= (tptp.vgetTerm (tptp.vsomeTerm @t29)) @t29))) % 0.38/0.69 (assume @p41 (tptp.visNV tptp.vZero)) % 0.38/0.69 (assume @p42 (forall @t33 (= (tptp.visNV @t32) @t31))) % 0.38/0.69 (assume @p43 (forall @t40 (=> (and @t39 @t38) (not (tptp.visNV @t34))))) % 0.38/0.69 (assume @p44 (forall @t7 (=> @t42 (or (= @t2 tptp.vZero) (exists @t33 (and @t41 @t31)))))) % 0.38/0.69 (assume @p45 (forall @t7 (=> (not @t42) (or (exists @t33 (and @t41 @t43)) (exists @t40 (and @t39 @t38 (= @t2 @t34))))))) % 0.38/0.69 (assume @p46 (tptp.visValue tptp.vTrue)) % 0.38/0.69 (assume @p47 (tptp.visValue tptp.vFalse)) % 0.38/0.69 (assume @p48 (forall @t48 (=> (and @t47 @t46) (= (tptp.visValue @t44) @t45)))) % 0.38/0.69 (assume @p49 (forall @t7 (=> @t50 (or (= @t2 tptp.vTrue) (= @t2 tptp.vFalse) (exists @t48 (and @t47 @t46 @t49 @t45)))))) % 0.38/0.69 (assume @p50 (forall @t7 (=> (not @t50) (exists @t48 (and @t47 @t46 @t49 @t51))))) % 0.38/0.69 (assume @p51 (not (tptp.visSomeTerm tptp.vnoTerm))) % 0.38/0.69 (assume @p52 (forall @t40 (tptp.visSomeTerm @t52))) % 0.38/0.69 (assume @p53 (forall @t55 (=> @t54 (exists @t40 (= @t53 @t52))))) % 0.38/0.69 (assume @p54 (forall @t55 (=> (not @t54) (= @t53 tptp.vnoTerm)))) % 0.38/0.69 (assume @p55 (forall (@list @t56) (= (tptp.vplusop @t56 tptp.vZero) @t56))) % 0.38/0.69 (assume @p56 (forall @t59 (= (tptp.vplusop @t56 (tptp.vSucc @t57)) (tptp.vSucc @t58)))) % 0.38/0.69 (assume @p57 (forall (@list @t57 @t56) (=> (and (not (= @t57 tptp.vZero)) (forall (@list @t60) (not (= @t57 @t61)))) (= @t58 @t57)))) % 0.38/0.69 (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)))))) % 0.38/0.69 (assume @p59 (forall @t59 (= (tptp.vreduce (tptp.vIfelse tptp.vTrue @t56 @t57)) (tptp.vsomeTerm @t56)))) % 0.38/0.69 (assume @p60 (forall @t59 (= (tptp.vreduce (tptp.vIfelse tptp.vFalse @t56 @t57)) (tptp.vsomeTerm @t57)))) % 0.38/0.69 (assume @p61 (forall @t79 (=> (and @t78 @t75 @t72) (= @t71 (tptp.vsomeTerm (tptp.vIfelse @t69 @t56 @t57)))))) % 0.38/0.69 (assume @p62 (forall @t79 (=> (and @t78 @t75 @t80) (= @t71 tptp.vnoTerm)))) % 0.38/0.69 (assume @p63 (forall @t48 (=> @t72 (= @t82 (tptp.vsomeTerm (tptp.vSucc @t69)))))) % 0.38/0.69 (assume @p64 (forall @t48 (=> @t80 (= @t82 tptp.vnoTerm)))) % 0.38/0.69 (assume @p65 (= (tptp.vreduce @t84) @t83)) % 0.38/0.69 (assume @p66 (forall @t33 (=> @t31 (= @t85 (tptp.vsomeTerm @t30))))) % 0.38/0.69 (assume @p67 (forall @t33 (=> @t89 (= @t85 (tptp.vsomeTerm (tptp.vPred @t87)))))) % 0.38/0.69 (assume @p68 (forall @t33 (=> @t90 (= @t85 tptp.vnoTerm)))) % 0.38/0.69 (assume @p69 (forall @t48 (=> @t96 (= @t92 (tptp.vsomeTerm (tptp.vPred @t69)))))) % 0.38/0.69 (assume @p70 (forall @t48 (=> @t97 (= @t92 tptp.vnoTerm)))) % 0.38/0.69 (assume @p71 (= (tptp.vreduce @t99) @t98)) % 0.38/0.69 (assume @p72 (forall @t33 (=> @t31 (= @t101 @t100)))) % 0.38/0.69 (assume @p73 (forall @t33 (=> @t89 (= @t101 (tptp.vsomeTerm (tptp.vIszero @t87)))))) % 0.38/0.69 (assume @p74 (forall @t33 (=> @t90 (= @t101 tptp.vnoTerm)))) % 0.38/0.69 (assume @p75 (forall @t48 (=> @t96 (= @t103 (tptp.vsomeTerm (tptp.vIszero @t69)))))) % 0.38/0.69 (assume @p76 (forall @t48 (=> @t97 (= @t103 tptp.vnoTerm)))) % 0.38/0.69 (assume @p77 (forall @t107 (=> (and @t45 @t106) (= @t105 (tptp.vsomeTerm (tptp.vplusop @t44 @t56)))))) % 0.38/0.69 (assume @p78 (forall @t107 (=> (and @t45 @t110 @t109) (= @t105 (tptp.vsomeTerm (tptp.vPlus @t44 (tptp.vgetTerm @t108))))))) % 0.38/0.69 (assume @p79 (forall @t107 (=> (and @t45 @t110 (not @t109)) @t111))) % 0.38/0.69 (assume @p80 (forall @t107 (=> (and @t51 @t72) (= @t105 (tptp.vsomeTerm (tptp.vPlus @t69 @t56)))))) % 0.38/0.69 (assume @p81 (forall @t107 (=> (and @t51 @t80) @t111))) % 0.38/0.69 (assume @p82 @t142) % 0.38/0.69 (assume @p83 (forall @t7 (or (exists @t136 (and (= @t2 @t138) (= @t143 (tptp.vsomeTerm @t67)))) (exists (@list @t66 @t62) (and (= @t2 (tptp.vIfelse tptp.vFalse @t66 @t62)) (= @t143 (tptp.vsomeTerm @t62)))) (exists (@list @t113 @t64 @t211 @t212) (and (forall (@list @t216 @t215) (or (not (= @t113 tptp.vTrue)) (not (= @t64 @t216)) (not (= @t211 @t215)))) (forall (@list @t214 @t213) (or (not (= @t113 tptp.vFalse)) (not (= @t64 @t214)) (not (= @t211 @t213)))) (= @t212 (tptp.vreduce @t113)) (tptp.visSomeTerm @t212) (= @t2 (tptp.vIfelse @t113 @t64 @t211)) (= @t143 (tptp.vsomeTerm (tptp.vIfelse (tptp.vgetTerm @t212) @t64 @t211))))) (exists (@list @t205 @t204 @t203 @t206) (and (forall (@list @t210 @t209) (or (not (= @t205 tptp.vTrue)) (not (= @t204 @t210)) (not (= @t203 @t209)))) (forall (@list @t208 @t207) (or (not (= @t205 tptp.vFalse)) (not (= @t204 @t208)) (not (= @t203 @t207)))) (= @t206 (tptp.vreduce @t205)) (not (tptp.visSomeTerm @t206)) (= @t2 (tptp.vIfelse @t205 @t204 @t203)) @t144)) (exists (@list @t202 @t201) (and (= @t201 (tptp.vreduce @t202)) (tptp.visSomeTerm @t201) (= @t2 (tptp.vSucc @t202)) (= @t143 (tptp.vsomeTerm (tptp.vSucc (tptp.vgetTerm @t201)))))) (exists (@list @t199 @t200) (and (= @t200 (tptp.vreduce @t199)) (not (tptp.visSomeTerm @t200)) (= @t2 (tptp.vSucc @t199)) @t144)) (and (= @t2 @t84) (= @t143 @t83)) (exists @t37 (and (tptp.visNV @t35) (= @t2 @t126) (= @t143 (tptp.vsomeTerm @t35)))) (exists (@list @t197 @t196) (and (not (tptp.visNV @t197)) (= @t196 (tptp.vreduce @t198)) (tptp.visSomeTerm @t196) (= @t2 (tptp.vPred @t198)) (= @t143 (tptp.vsomeTerm (tptp.vPred (tptp.vgetTerm @t196)))))) (exists (@list @t193 @t195) (and (not (tptp.visNV @t193)) (= @t195 (tptp.vreduce @t194)) (not (tptp.visSomeTerm @t195)) (= @t2 (tptp.vPred @t194)) @t144)) (exists (@list @t191 @t190) (and (not (= @t191 tptp.vZero)) (forall (@list @t192) (not (= @t191 (tptp.vSucc @t192)))) (= @t190 (tptp.vreduce @t191)) (tptp.visSomeTerm @t190) (= @t2 (tptp.vPred @t191)) (= @t143 (tptp.vsomeTerm (tptp.vPred (tptp.vgetTerm @t190)))))) (exists (@list @t187 @t188) (and (not (= @t187 tptp.vZero)) (forall (@list @t189) (not (= @t187 (tptp.vSucc @t189)))) (= @t188 (tptp.vreduce @t187)) (not (tptp.visSomeTerm @t188)) (= @t2 (tptp.vPred @t187)) @t144)) (and (= @t2 @t99) (= @t143 @t98)) (exists (@list @t186) (and (tptp.visNV @t186) (= @t2 (tptp.vIszero (tptp.vSucc @t186))) (= @t143 @t100))) (exists (@list @t184 @t183) (and (not (tptp.visNV @t184)) (= @t183 (tptp.vreduce @t185)) (tptp.visSomeTerm @t183) (= @t2 (tptp.vIszero @t185)) (= @t143 (tptp.vsomeTerm (tptp.vIszero (tptp.vgetTerm @t183)))))) (exists (@list @t180 @t182) (and (not (tptp.visNV @t180)) (= @t182 (tptp.vreduce @t181)) (not (tptp.visSomeTerm @t182)) (= @t2 (tptp.vIszero @t181)) @t144)) (exists (@list @t178 @t177) (and (not (= @t178 tptp.vZero)) (forall (@list @t179) (not (= @t178 (tptp.vSucc @t179)))) (= @t177 (tptp.vreduce @t178)) (tptp.visSomeTerm @t177) (= @t2 (tptp.vIszero @t178)) (= @t143 (tptp.vsomeTerm (tptp.vIszero (tptp.vgetTerm @t177)))))) (exists (@list @t174 @t175) (and (not (= @t174 tptp.vZero)) (forall (@list @t176) (not (= @t174 (tptp.vSucc @t176)))) (= @t175 (tptp.vreduce @t174)) (not 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@t287) % 0.38/0.69 (step @p245 :rule skolemize :premises (@p274)) % 0.38/0.69 (step-pop @p275 :rule scope :premises (@p245)) % 0.38/0.69 (step @p246 :rule process_scope :premises (@p275) :args (@t288)) % 0.38/0.69 (step @p248 :rule eq_resolve :premises (@p246 @p243)) % 0.38/0.69 (step @p249 :rule implies_elim :premises (@p248)) % 0.38/0.69 (step @p250 :rule eq_resolve :premises (@p249 @p240)) % 0.38/0.69 (step @p251 :rule chain_m_resolution :premises (@p250 @p237) :args (@t283 @t262 (@list @t286))) % 0.38/0.69 (step @p252 :rule instantiate :premises (@p14) :args ((@list tptp.vFalse @t291 @t290))) % 0.38/0.69 (step @p253 :rule refl :args (@t292)) % 0.38/0.69 (step @p254 :rule bool-double-not-elim :args (@t289)) % 0.38/0.69 (step @p255 :rule nary_cong :premises (@p254 @p253) :args ((or (not @t293) @t292))) % 0.38/0.69 (step @p256 :rule bool-double-not-elim :args (@t292)) % 0.38/0.69 (step @p257 :rule refl :args (@t293)) % 0.38/0.69 (step @p258 :rule cong :premises (@p257 @p256) :args ((=> @t293 @t294))) % 0.38/0.69 (assume-push @p276 @t293) % 0.38/0.69 (step @p260 :rule skolemize :premises (@p276)) % 0.38/0.69 (step-pop @p277 :rule scope :premises (@p260)) % 0.38/0.69 (step @p261 :rule process_scope :premises (@p277) :args (@t294)) % 0.38/0.69 (step @p263 :rule eq_resolve :premises (@p261 @p258)) % 0.38/0.69 (step @p264 :rule implies_elim :premises (@p263)) % 0.38/0.69 (step @p265 :rule eq_resolve :premises (@p264 @p255)) % 0.38/0.69 (step @p266 :rule chain_m_resolution :premises (@p265 @p252) :args (@t289 @t262 (@list @t292))) % 0.38/0.69 (step @p267 :rule cnf_or_pos :args (@t302)) % 0.38/0.69 (step @p268 :rule reordering :premises (@p267) :args ((or @t299 @t297 @t287 @t293 @t301 @t300 @t278 @t298 @t272 @t296 @t295 @t263 (not @t302)))) % 0.38/0.69 (step @p269 false :rule chain_m_resolution :premises (@p268 @p266 @p251 @p236 @p235 @p234 @p231 @p228 @p213 @p210 @p195 @p192 @p189 @p165) :args (false (@list false false true true false false false false false false false true false) (@list @t289 @t283 @t299 @t297 @t281 @t280 @t275 @t274 @t269 @t268 @t264 @t263 @t302))) % 0.38/0.69 ) % 0.38/0.69 % SZS output end Proof % 0.38/0.69 % cvc5 exiting %------------------------------------------------------------------------------