%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : COM244_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 : n014.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 08:10:43 AM UTC 2026 % Result : Theorem 0.37s 0.68s % Output : Proof 0.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : COM244_1 : TPTP v9.3.0. Released v9.3.0. % 0.00/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n014.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 20:32:28 EDT 2026 % 0.17/0.34 % CPUTime : % 0.31/0.52 %----Proving TF0_NAR, FOF, or CNF % 0.37/0.68 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.37/0.68 % SZS status Theorem % 0.37/0.68 % SZS output start Proof % 0.37/0.68 ( % 0.37/0.68 (declare-sort tptp.vTy 0) % 0.37/0.68 (declare-sort tptp.vOptTerm 0) % 0.37/0.68 (declare-sort tptp.vTerm 0) % 0.37/0.68 (declare-const tptp.vptchecksimple (-> tptp.vTerm tptp.vTy Bool)) % 0.37/0.68 (declare-const tptp.vreduce (-> tptp.vTerm tptp.vOptTerm)) % 0.37/0.68 (declare-const tptp.vplusop (-> tptp.vTerm tptp.vTerm tptp.vTerm)) % 0.37/0.68 (declare-const tptp.visSomeTerm (-> tptp.vOptTerm Bool)) % 0.37/0.68 (declare-const tptp.visValue (-> tptp.vTerm Bool)) % 0.37/0.68 (declare-const tptp.visNV (-> tptp.vTerm Bool)) % 0.37/0.68 (declare-const tptp.vPlus (-> tptp.vTerm tptp.vTerm tptp.vTerm)) % 0.37/0.68 (declare-const tptp.vIszero (-> tptp.vTerm tptp.vTerm)) % 0.37/0.68 (declare-const tptp.vPred (-> tptp.vTerm tptp.vTerm)) % 0.37/0.68 (declare-const tptp.vSucc (-> tptp.vTerm tptp.vTerm)) % 0.37/0.68 (declare-const tptp.vIfelse (-> tptp.vTerm tptp.vTerm tptp.vTerm tptp.vTerm)) % 0.37/0.68 (declare-const tptp.vZero tptp.vTerm) % 0.37/0.68 (declare-const tptp.vFalse tptp.vTerm) % 0.37/0.68 (declare-const tptp.vTrue tptp.vTerm) % 0.37/0.68 (declare-const tptp.vsomeTerm (-> tptp.vTerm tptp.vOptTerm)) % 0.37/0.68 (declare-const tptp.vnoTerm tptp.vOptTerm) % 0.37/0.68 (declare-const tptp.vNat tptp.vTy) % 0.37/0.68 (declare-const tptp.vB tptp.vTy) % 0.37/0.68 (declare-const tptp.vgetTerm (-> tptp.vOptTerm tptp.vTerm)) % 0.37/0.68 (define @t1 () (@var "VTerm1" tptp.vTerm)) % 0.37/0.68 (define @t2 () (@var "VTerm0" tptp.vTerm)) % 0.37/0.68 (define @t3 () (tptp.vPlus @t2 @t1)) % 0.37/0.68 (define @t4 () (@var "VX" tptp.vTerm)) % 0.37/0.68 (define @t5 () (@list @t2 @t1)) % 0.37/0.68 (define @t6 () (tptp.vIszero @t2)) % 0.37/0.68 (define @t7 () (@list @t2)) % 0.37/0.68 (define @t8 () (tptp.vPred @t2)) % 0.37/0.68 (define @t9 () (tptp.vSucc @t2)) % 0.37/0.68 (define @t10 () (@var "VTerm2" tptp.vTerm)) % 0.37/0.68 (define @t11 () (tptp.vIfelse @t2 @t1 @t10)) % 0.37/0.68 (define @t12 () (@list @t2 @t1 @t10)) % 0.37/0.68 (define @t13 () (@var "VTerm5" tptp.vTerm)) % 0.37/0.68 (define @t14 () (@var "VTerm4" tptp.vTerm)) % 0.37/0.68 (define @t15 () (@var "VTerm3" tptp.vTerm)) % 0.37/0.68 (define @t16 () (= @t2 @t1)) % 0.37/0.68 (define @t17 () (tptp.vPred @t1)) % 0.37/0.68 (define @t18 () (tptp.vIszero @t1)) % 0.37/0.68 (define @t19 () (@list @t2 @t1 @t10 @t15)) % 0.37/0.68 (define @t20 () (tptp.vPlus @t1 @t10)) % 0.37/0.68 (define @t21 () (tptp.vsomeTerm @t2)) % 0.37/0.68 (define @t22 () (@var "VX" tptp.vOptTerm)) % 0.37/0.68 (define @t23 () (@var "VX" tptp.vTy)) % 0.37/0.68 (define @t24 () (@var "Vt" tptp.vTerm)) % 0.37/0.68 (define @t25 () (tptp.visNV tptp.vZero)) % 0.37/0.68 (define @t26 () (@var "Vnv" tptp.vTerm)) % 0.37/0.68 (define @t27 () (tptp.visNV @t26)) % 0.37/0.68 (define @t28 () (tptp.vSucc @t26)) % 0.37/0.68 (define @t29 () (@list @t26)) % 0.37/0.68 (define @t30 () (@var "VwildcardName0" tptp.vTerm)) % 0.37/0.68 (define @t31 () (@var "Vnv0" tptp.vTerm)) % 0.37/0.68 (define @t32 () (tptp.vSucc @t31)) % 0.37/0.68 (define @t33 () (@list @t31)) % 0.37/0.68 (define @t34 () (forall @t33 (not (= @t30 @t32)))) % 0.37/0.68 (define @t35 () (not (= @t30 tptp.vZero))) % 0.37/0.68 (define @t36 () (@list @t30)) % 0.37/0.68 (define @t37 () (= @t2 @t28)) % 0.37/0.68 (define @t38 () (tptp.visNV @t2)) % 0.37/0.68 (define @t39 () (not @t27)) % 0.37/0.68 (define @t40 () (not @t38)) % 0.37/0.68 (define @t41 () (tptp.visValue tptp.vTrue)) % 0.37/0.68 (define @t42 () (tptp.visValue tptp.vFalse)) % 0.37/0.68 (define @t43 () (@var "Vt1" tptp.vTerm)) % 0.37/0.68 (define @t44 () (tptp.visNV @t43)) % 0.37/0.68 (define @t45 () (not (= @t43 tptp.vFalse))) % 0.37/0.68 (define @t46 () (not (= @t43 tptp.vTrue))) % 0.37/0.68 (define @t47 () (@list @t43)) % 0.37/0.68 (define @t48 () (= @t2 @t43)) % 0.37/0.68 (define @t49 () (tptp.visValue @t2)) % 0.37/0.68 (define @t50 () (not @t44)) % 0.37/0.68 (define @t51 () (and @t46 @t45 @t48 @t50)) % 0.37/0.68 (define @t52 () (exists @t47 @t51)) % 0.37/0.68 (define @t53 () (not @t49)) % 0.37/0.68 (define @t54 () (=> @t53 @t52)) % 0.37/0.68 (define @t55 () (forall @t7 @t54)) % 0.37/0.68 (define @t56 () (tptp.vsomeTerm @t30)) % 0.37/0.68 (define @t57 () (@var "VOptTerm0" tptp.vOptTerm)) % 0.37/0.68 (define @t58 () (tptp.visSomeTerm @t57)) % 0.37/0.68 (define @t59 () (@list @t57)) % 0.37/0.68 (define @t60 () (@var "Vt2" tptp.vTerm)) % 0.37/0.68 (define @t61 () (@var "Vt3" tptp.vTerm)) % 0.37/0.68 (define @t62 () (tptp.vplusop @t60 @t61)) % 0.37/0.68 (define @t63 () (@list @t60 @t61)) % 0.37/0.68 (define @t64 () (@var "Vt30" tptp.vTerm)) % 0.37/0.68 (define @t65 () (tptp.vSucc @t64)) % 0.37/0.68 (define @t66 () (@var "Vt31" tptp.vTerm)) % 0.37/0.68 (define @t67 () (tptp.vplusop @t2 @t1)) % 0.37/0.68 (define @t68 () (@var "Vt22" tptp.vTerm)) % 0.37/0.68 (define @t69 () (@var "Vt3000" tptp.vTerm)) % 0.37/0.68 (define @t70 () (@var "Vt21" tptp.vTerm)) % 0.37/0.68 (define @t71 () (@var "Vt20" tptp.vTerm)) % 0.37/0.68 (define @t72 () (tptp.vreduce @t43)) % 0.37/0.68 (define @t73 () (tptp.vgetTerm @t72)) % 0.37/0.68 (define @t74 () (tptp.vIfelse @t43 @t60 @t61)) % 0.37/0.68 (define @t75 () (tptp.vreduce @t74)) % 0.37/0.68 (define @t76 () (tptp.visSomeTerm @t72)) % 0.37/0.68 (define @t77 () (@var "Vt301" tptp.vTerm)) % 0.37/0.68 (define @t78 () (@var "Vt201" tptp.vTerm)) % 0.37/0.68 (define @t79 () (forall (@list @t78 @t77) (or @t45 (not (= @t60 @t78)) (not (= @t61 @t77))))) % 0.37/0.68 (define @t80 () (@var "Vt300" tptp.vTerm)) % 0.37/0.68 (define @t81 () (@var "Vt200" tptp.vTerm)) % 0.37/0.68 (define @t82 () (forall (@list @t81 @t80) (or @t46 (not (= @t60 @t81)) (not (= @t61 @t80))))) % 0.37/0.68 (define @t83 () (@list @t43 @t60 @t61)) % 0.37/0.68 (define @t84 () (not @t76)) % 0.37/0.68 (define @t85 () (tptp.vSucc @t43)) % 0.37/0.68 (define @t86 () (tptp.vreduce @t85)) % 0.37/0.68 (define @t87 () (tptp.vsomeTerm tptp.vZero)) % 0.37/0.68 (define @t88 () (tptp.vPred tptp.vZero)) % 0.37/0.68 (define @t89 () (tptp.vreduce (tptp.vPred @t28))) % 0.37/0.68 (define @t90 () (tptp.vreduce @t28)) % 0.37/0.68 (define @t91 () (tptp.vgetTerm @t90)) % 0.37/0.68 (define @t92 () (tptp.visSomeTerm @t90)) % 0.37/0.68 (define @t93 () (and @t39 @t92)) % 0.37/0.68 (define @t94 () (and @t39 (not @t92))) % 0.37/0.68 (define @t95 () (tptp.vPred @t43)) % 0.37/0.68 (define @t96 () (tptp.vreduce @t95)) % 0.37/0.68 (define @t97 () (@var "Vnv00" tptp.vTerm)) % 0.37/0.68 (define @t98 () (forall (@list @t97) (not (= @t43 (tptp.vSucc @t97))))) % 0.37/0.68 (define @t99 () (not (= @t43 tptp.vZero))) % 0.37/0.68 (define @t100 () (and @t99 @t98 @t76)) % 0.37/0.68 (define @t101 () (and @t99 @t98 @t84)) % 0.37/0.68 (define @t102 () (tptp.vsomeTerm tptp.vTrue)) % 0.37/0.68 (define @t103 () (tptp.vIszero tptp.vZero)) % 0.37/0.68 (define @t104 () (tptp.vsomeTerm tptp.vFalse)) % 0.37/0.68 (define @t105 () (tptp.vreduce (tptp.vIszero @t28))) % 0.37/0.68 (define @t106 () (tptp.vIszero @t43)) % 0.37/0.68 (define @t107 () (tptp.vreduce @t106)) % 0.37/0.68 (define @t108 () (tptp.vPlus @t43 @t60)) % 0.37/0.68 (define @t109 () (tptp.vreduce @t108)) % 0.37/0.68 (define @t110 () (tptp.visNV @t60)) % 0.37/0.68 (define @t111 () (@list @t43 @t60)) % 0.37/0.68 (define @t112 () (tptp.vreduce @t60)) % 0.37/0.68 (define @t113 () (tptp.visSomeTerm @t112)) % 0.37/0.68 (define @t114 () (not @t110)) % 0.37/0.68 (define @t115 () (= @t109 tptp.vnoTerm)) % 0.37/0.68 (define @t116 () (@var "Vt10" tptp.vTerm)) % 0.37/0.68 (define @t117 () (@list @t116)) % 0.37/0.68 (define @t118 () (tptp.vPred @t32)) % 0.37/0.68 (define @t119 () (@list @t71 @t64)) % 0.37/0.68 (define @t120 () (tptp.vIfelse tptp.vTrue @t71 @t64)) % 0.37/0.68 (define @t121 () (tptp.vreduce @t2)) % 0.37/0.68 (define @t122 () (= @t121 tptp.vnoTerm)) % 0.37/0.68 (define @t123 () (@var "VwildcardName00" tptp.vTerm)) % 0.37/0.68 (define @t124 () (@var "Vt2080" tptp.vTerm)) % 0.37/0.68 (define @t125 () (@var "Vt1040" tptp.vTerm)) % 0.37/0.68 (define @t126 () (@var "Vt1030" tptp.vTerm)) % 0.37/0.68 (define @t127 () (@var "Vnv050" tptp.vTerm)) % 0.37/0.68 (define @t128 () (@var "Vt1020" tptp.vTerm)) % 0.37/0.68 (define @t129 () (@var "Vnv040" tptp.vTerm)) % 0.37/0.68 (define @t130 () (@var "Vt1010" tptp.vTerm)) % 0.37/0.68 (define @t131 () (@var "Vt3070" tptp.vTerm)) % 0.37/0.68 (define @t132 () (@var "Vt2070" tptp.vTerm)) % 0.37/0.68 (define @t133 () (@var "Vt1000" tptp.vTerm)) % 0.37/0.68 (define @t134 () (@var "Vt3060" tptp.vTerm)) % 0.37/0.68 (define @t135 () (@var "Vt2060" tptp.vTerm)) % 0.37/0.68 (define @t136 () (@var "Vt3050" tptp.vTerm)) % 0.37/0.68 (define @t137 () (@var "Vt2050" tptp.vTerm)) % 0.37/0.68 (define @t138 () (@var "Vt28" tptp.vTerm)) % 0.37/0.68 (define @t139 () (@var "Vt112" tptp.vTerm)) % 0.37/0.68 (define @t140 () (@var "Vot13" tptp.vOptTerm)) % 0.37/0.68 (define @t141 () (@var "Vt27" tptp.vTerm)) % 0.37/0.68 (define @t142 () (@var "Vot12" tptp.vOptTerm)) % 0.37/0.68 (define @t143 () (@var "Vt111" tptp.vTerm)) % 0.37/0.68 (define @t144 () (@var "Vt26" tptp.vTerm)) % 0.37/0.68 (define @t145 () (@var "Vt110" tptp.vTerm)) % 0.37/0.68 (define @t146 () (@var "Vot211" tptp.vOptTerm)) % 0.37/0.68 (define @t147 () (@var "Vot210" tptp.vOptTerm)) % 0.37/0.68 (define @t148 () (@var "Vt19" tptp.vTerm)) % 0.37/0.68 (define @t149 () (@var "Vt25" tptp.vTerm)) % 0.37/0.68 (define @t150 () (@var "Vt24" tptp.vTerm)) % 0.37/0.68 (define @t151 () (@var "Vt18" tptp.vTerm)) % 0.37/0.68 (define @t152 () (@var "Vt17" tptp.vTerm)) % 0.37/0.68 (define @t153 () (@var "Vot29" tptp.vOptTerm)) % 0.37/0.68 (define @t154 () (@var "Vnv030" tptp.vTerm)) % 0.37/0.68 (define @t155 () (@var "Vot28" tptp.vOptTerm)) % 0.37/0.68 (define @t156 () (@var "Vt16" tptp.vTerm)) % 0.37/0.68 (define @t157 () (@var "Vnv020" tptp.vTerm)) % 0.37/0.68 (define @t158 () (@var "Vnv5" tptp.vTerm)) % 0.37/0.68 (define @t159 () (tptp.vSucc @t158)) % 0.37/0.68 (define @t160 () (@var "Vot27" tptp.vOptTerm)) % 0.37/0.68 (define @t161 () (@var "Vot26" tptp.vOptTerm)) % 0.37/0.68 (define @t162 () (@var "Vnv4" tptp.vTerm)) % 0.37/0.68 (define @t163 () (tptp.vSucc @t162)) % 0.37/0.68 (define @t164 () (@var "Vnv3" tptp.vTerm)) % 0.37/0.68 (define @t165 () (@var "Vt15" tptp.vTerm)) % 0.37/0.68 (define @t166 () (@var "Vot25" tptp.vOptTerm)) % 0.37/0.68 (define @t167 () (@var "Vnv010" tptp.vTerm)) % 0.37/0.68 (define @t168 () (@var "Vot24" tptp.vOptTerm)) % 0.37/0.68 (define @t169 () (@var "Vt14" tptp.vTerm)) % 0.37/0.68 (define @t170 () (@var "Vnv000" tptp.vTerm)) % 0.37/0.68 (define @t171 () (@var "Vnv2" tptp.vTerm)) % 0.37/0.68 (define @t172 () (tptp.vSucc @t171)) % 0.37/0.68 (define @t173 () (@var "Vot23" tptp.vOptTerm)) % 0.37/0.68 (define @t174 () (@var "Vot22" tptp.vOptTerm)) % 0.37/0.68 (define @t175 () (@var "Vnv1" tptp.vTerm)) % 0.37/0.68 (define @t176 () (tptp.vSucc @t175)) % 0.37/0.68 (define @t177 () (@var "Vt13" tptp.vTerm)) % 0.37/0.68 (define @t178 () (@var "Vot21" tptp.vOptTerm)) % 0.37/0.68 (define @t179 () (@var "Vot20" tptp.vOptTerm)) % 0.37/0.68 (define @t180 () (@var "Vt12" tptp.vTerm)) % 0.37/0.68 (define @t181 () (@var "Vt33" tptp.vTerm)) % 0.37/0.68 (define @t182 () (@var "Vt23" tptp.vTerm)) % 0.37/0.68 (define @t183 () (@var "Vt11" tptp.vTerm)) % 0.37/0.68 (define @t184 () (@var "Vot11" tptp.vOptTerm)) % 0.37/0.68 (define @t185 () (@var "Vt3040" tptp.vTerm)) % 0.37/0.68 (define @t186 () (@var "Vt2040" tptp.vTerm)) % 0.37/0.68 (define @t187 () (@var "Vt3030" tptp.vTerm)) % 0.37/0.68 (define @t188 () (@var "Vt2030" tptp.vTerm)) % 0.37/0.68 (define @t189 () (@var "Vt32" tptp.vTerm)) % 0.37/0.68 (define @t190 () (@var "Vot10" tptp.vOptTerm)) % 0.37/0.68 (define @t191 () (@var "Vt3020" tptp.vTerm)) % 0.37/0.68 (define @t192 () (@var "Vt2020" tptp.vTerm)) % 0.37/0.68 (define @t193 () (@var "Vt3010" tptp.vTerm)) % 0.37/0.68 (define @t194 () (@var "Vt2010" tptp.vTerm)) % 0.37/0.68 (define @t195 () (@var "VT" tptp.vTy)) % 0.37/0.68 (define @t196 () (tptp.vptchecksimple @t74 @t195)) % 0.37/0.68 (define @t197 () (tptp.vptchecksimple @t61 @t195)) % 0.37/0.68 (define @t198 () (tptp.vptchecksimple @t60 @t195)) % 0.37/0.68 (define @t199 () (tptp.vptchecksimple @t43 tptp.vB)) % 0.37/0.68 (define @t200 () (@list @t43 @t60 @t61 @t195)) % 0.37/0.68 (define @t201 () (= @t195 tptp.vNat)) % 0.37/0.68 (define @t202 () (tptp.vptchecksimple tptp.vZero @t195)) % 0.37/0.68 (define @t203 () (@list @t195)) % 0.37/0.68 (define @t204 () (tptp.vptchecksimple @t85 tptp.vNat)) % 0.37/0.68 (define @t205 () (tptp.vptchecksimple @t43 tptp.vNat)) % 0.37/0.68 (define @t206 () (@list @t43 @t195)) % 0.37/0.68 (define @t207 () (tptp.vptchecksimple @t95 tptp.vNat)) % 0.37/0.68 (define @t208 () (tptp.vptchecksimple @t106 tptp.vB)) % 0.37/0.68 (define @t209 () (tptp.vptchecksimple @t108 tptp.vNat)) % 0.37/0.68 (define @t210 () (tptp.vptchecksimple @t60 tptp.vNat)) % 0.37/0.68 (define @t211 () (tptp.vreduce tptp.vZero)) % 0.37/0.68 (define @t212 () (not (= @t211 tptp.vnoTerm))) % 0.37/0.68 (define @t213 () (tptp.visValue tptp.vZero)) % 0.37/0.68 (define @t214 () (not @t213)) % 0.37/0.68 (define @t215 () (and @t202 @t214)) % 0.37/0.68 (define @t216 () (=> @t215 @t212)) % 0.37/0.68 (define @t217 () (forall @t203 @t216)) % 0.37/0.68 (define @t218 () (not @t217)) % 0.37/0.68 (define @t219 () (@var "BOUND_VARIABLE_8683" tptp.vTerm)) % 0.37/0.68 (define @t220 () (forall (@list @t219) (or (not (tptp.visNV @t219)) (tptp.visValue @t219)))) % 0.37/0.68 (define @t221 () (not (= tptp.vFalse tptp.vFalse))) % 0.37/0.68 (define @t222 () (or @t221 @t42)) % 0.37/0.68 (define @t223 () (@var "BOUND_VARIABLE_8675" tptp.vTerm)) % 0.37/0.68 (define @t224 () (tptp.visValue @t223)) % 0.37/0.68 (define @t225 () (not (= tptp.vFalse @t223))) % 0.37/0.68 (define @t226 () (@list @t223)) % 0.37/0.68 (define @t227 () (or @t225 @t225 @t224)) % 0.37/0.68 (define @t228 () (or @t225 @t224)) % 0.37/0.68 (define @t229 () (forall @t226 @t228)) % 0.37/0.68 (define @t230 () (not (= tptp.vTrue tptp.vTrue))) % 0.37/0.68 (define @t231 () (or @t230 @t41)) % 0.37/0.68 (define @t232 () (@var "BOUND_VARIABLE_8667" tptp.vTerm)) % 0.37/0.68 (define @t233 () (tptp.visValue @t232)) % 0.37/0.68 (define @t234 () (not (= tptp.vTrue @t232))) % 0.37/0.68 (define @t235 () (@list @t232)) % 0.37/0.68 (define @t236 () (or @t234 @t234 @t233)) % 0.37/0.68 (define @t237 () (or @t234 @t233)) % 0.37/0.68 (define @t238 () (forall @t235 @t237)) % 0.37/0.68 (define @t239 () (or @t40 @t49)) % 0.37/0.68 (define @t240 () (forall @t7 @t239)) % 0.37/0.68 (define @t241 () (@list @t2)) % 0.37/0.68 (define @t242 () (= tptp.vFalse @t2)) % 0.37/0.68 (define @t243 () (not @t242)) % 0.37/0.68 (define @t244 () (or @t243 @t49)) % 0.37/0.68 (define @t245 () (forall @t7 @t244)) % 0.37/0.68 (define @t246 () (= tptp.vTrue @t2)) % 0.37/0.68 (define @t247 () (not @t246)) % 0.37/0.68 (define @t248 () (or @t247 @t49)) % 0.37/0.68 (define @t249 () (forall @t7 @t248)) % 0.37/0.68 (define @t250 () (and @t249 @t245 @t240)) % 0.37/0.68 (define @t251 () (and @t248 @t244 @t239)) % 0.37/0.68 (define @t252 () (and @t243 @t40)) % 0.37/0.68 (define @t253 () (and @t247 @t243 @t40)) % 0.37/0.68 (define @t254 () (or @t253 @t49)) % 0.37/0.68 (define @t255 () (or @t49 @t253)) % 0.37/0.68 (define @t256 () (or @t246 @t242 @t38)) % 0.37/0.68 (define @t257 () (not @t256)) % 0.37/0.68 (define @t258 () (not (= @t2 @t2))) % 0.37/0.68 (define @t259 () (or @t246 @t242 @t258 @t38)) % 0.37/0.68 (define @t260 () (not @t48)) % 0.37/0.68 (define @t261 () (= tptp.vFalse @t43)) % 0.37/0.68 (define @t262 () (= tptp.vTrue @t43)) % 0.37/0.68 (define @t263 () (or @t260 @t262 @t261 @t260 @t44)) % 0.37/0.68 (define @t264 () (or @t262 @t261 @t260 @t44)) % 0.37/0.68 (define @t265 () (not @t50)) % 0.37/0.68 (define @t266 () (not @t261)) % 0.37/0.68 (define @t267 () (not @t266)) % 0.37/0.68 (define @t268 () (not @t262)) % 0.37/0.68 (define @t269 () (not @t268)) % 0.37/0.68 (define @t270 () (or @t269 @t267 @t260 @t265)) % 0.37/0.68 (define @t271 () (and @t268 @t266 @t48 @t50)) % 0.37/0.68 (define @t272 () (forall @t47 (not @t271))) % 0.37/0.68 (define @t273 () (not @t272)) % 0.37/0.68 (define @t274 () (not @t202)) % 0.37/0.68 (define @t275 () (not (= tptp.vnoTerm @t211))) % 0.37/0.68 (define @t276 () (or @t213 @t275 @t274)) % 0.37/0.68 (define @t277 () (or @t274 @t213 @t275)) % 0.37/0.68 (define @t278 () (not @t25)) % 0.37/0.68 (define @t279 () (or @t278 @t213)) % 0.37/0.68 (define @t280 () (not @t279)) % 0.37/0.68 (define @t281 () (@list true false)) % 0.37/0.68 (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))))) % 0.37/0.68 (assume @p2 (forall (@list @t15 @t10 @t1 @t14 @t2 @t13) (=> (= @t11 (tptp.vIfelse @t15 @t14 @t13)) (and (= @t2 @t15) (= @t1 @t14) (= @t10 @t13))))) % 0.37/0.68 (assume @p3 (forall @t5 (=> (= @t9 (tptp.vSucc @t1)) @t16))) % 0.37/0.68 (assume @p4 (forall @t5 (=> (= @t8 @t17) @t16))) % 0.37/0.68 (assume @p5 (forall @t5 (=> (= @t6 @t18) @t16))) % 0.37/0.68 (assume @p6 (forall @t19 (=> (= @t3 (tptp.vPlus @t10 @t15)) (and (= @t2 @t10) (= @t1 @t15))))) % 0.37/0.68 (assume @p7 (not (= tptp.vTrue tptp.vFalse))) % 0.37/0.68 (assume @p8 (forall @t12 (not (= tptp.vTrue @t11)))) % 0.37/0.68 (assume @p9 (not (= tptp.vTrue tptp.vZero))) % 0.37/0.68 (assume @p10 (forall @t7 (not (= tptp.vTrue @t9)))) % 0.37/0.68 (assume @p11 (forall @t7 (not (= tptp.vTrue @t8)))) % 0.37/0.68 (assume @p12 (forall @t7 (not (= tptp.vTrue @t6)))) % 0.37/0.68 (assume @p13 (forall @t5 (not (= tptp.vTrue @t3)))) % 0.37/0.68 (assume @p14 (forall @t12 (not (= tptp.vFalse @t11)))) % 0.37/0.68 (assume @p15 (not (= tptp.vFalse tptp.vZero))) % 0.37/0.68 (assume @p16 (forall @t7 (not (= tptp.vFalse @t9)))) % 0.37/0.68 (assume @p17 (forall @t7 (not (= tptp.vFalse @t8)))) % 0.37/0.68 (assume @p18 (forall @t7 (not (= tptp.vFalse @t6)))) % 0.37/0.68 (assume @p19 (forall @t5 (not (= tptp.vFalse @t3)))) % 0.37/0.68 (assume @p20 (forall @t12 (not (= @t11 tptp.vZero)))) % 0.37/0.68 (assume @p21 (forall @t19 (not (= @t11 (tptp.vSucc @t15))))) % 0.37/0.68 (assume @p22 (forall @t19 (not (= @t11 (tptp.vPred @t15))))) % 0.37/0.68 (assume @p23 (forall @t19 (not (= @t11 (tptp.vIszero @t15))))) % 0.37/0.68 (assume @p24 (forall (@list @t15 @t10 @t1 @t14 @t2) (not (= @t11 (tptp.vPlus @t15 @t14))))) % 0.37/0.68 (assume @p25 (forall @t7 (not (= tptp.vZero @t9)))) % 0.37/0.68 (assume @p26 (forall @t7 (not (= tptp.vZero @t8)))) % 0.37/0.68 (assume @p27 (forall @t7 (not (= tptp.vZero @t6)))) % 0.37/0.68 (assume @p28 (forall @t5 (not (= tptp.vZero @t3)))) % 0.37/0.68 (assume @p29 (forall @t5 (not (= @t9 @t17)))) % 0.37/0.68 (assume @p30 (forall @t5 (not (= @t9 @t18)))) % 0.37/0.68 (assume @p31 (forall @t12 (not (= @t9 @t20)))) % 0.37/0.68 (assume @p32 (forall @t5 (not (= @t8 @t18)))) % 0.37/0.68 (assume @p33 (forall @t12 (not (= @t8 @t20)))) % 0.37/0.68 (assume @p34 (forall @t12 (not (= @t6 @t20)))) % 0.37/0.68 (assume @p35 (forall (@list @t22) (or (= @t22 tptp.vnoTerm) (exists @t7 (= @t22 @t21))))) % 0.37/0.68 (assume @p36 (forall @t5 (=> (= @t21 (tptp.vsomeTerm @t1)) @t16))) % 0.37/0.68 (assume @p37 (forall @t7 (not (= tptp.vnoTerm @t21)))) % 0.37/0.68 (assume @p38 (forall (@list @t23) (or (= @t23 tptp.vB) (= @t23 tptp.vNat)))) % 0.37/0.68 (assume @p39 (not (= tptp.vB tptp.vNat))) % 0.37/0.68 (assume @p40 (forall (@list @t24) (= (tptp.vgetTerm (tptp.vsomeTerm @t24)) @t24))) % 0.37/0.68 (assume @p41 @t25) % 0.37/0.68 (assume @p42 (forall @t29 (= (tptp.visNV @t28) @t27))) % 0.37/0.68 (assume @p43 (forall @t36 (=> (and @t35 @t34) (not (tptp.visNV @t30))))) % 0.37/0.68 (assume @p44 (forall @t7 (=> @t38 (or (= @t2 tptp.vZero) (exists @t29 (and @t37 @t27)))))) % 0.37/0.68 (assume @p45 (forall @t7 (=> @t40 (or (exists @t29 (and @t37 @t39)) (exists @t36 (and @t35 @t34 (= @t2 @t30))))))) % 0.37/0.68 (assume @p46 @t41) % 0.37/0.68 (assume @p47 @t42) % 0.37/0.68 (assume @p48 (forall @t47 (=> (and @t46 @t45) (= (tptp.visValue @t43) @t44)))) % 0.37/0.68 (assume @p49 (forall @t7 (=> @t49 (or (= @t2 tptp.vTrue) (= @t2 tptp.vFalse) (exists @t47 (and @t46 @t45 @t48 @t44)))))) % 0.37/0.68 (assume @p50 @t55) % 0.37/0.68 (assume @p51 (not (tptp.visSomeTerm tptp.vnoTerm))) % 0.37/0.68 (assume @p52 (forall @t36 (tptp.visSomeTerm @t56))) % 0.37/0.68 (assume @p53 (forall @t59 (=> @t58 (exists @t36 (= @t57 @t56))))) % 0.37/0.68 (assume @p54 (forall @t59 (=> (not @t58) (= @t57 tptp.vnoTerm)))) % 0.37/0.68 (assume @p55 (forall (@list @t60) (= (tptp.vplusop @t60 tptp.vZero) @t60))) % 0.37/0.68 (assume @p56 (forall @t63 (= (tptp.vplusop @t60 (tptp.vSucc @t61)) (tptp.vSucc @t62)))) % 0.37/0.68 (assume @p57 (forall (@list @t61 @t60) (=> (and (not (= @t61 tptp.vZero)) (forall (@list @t64) (not (= @t61 @t65)))) (= @t62 @t61)))) % 0.37/0.68 (assume @p58 (forall @t5 (or (exists (@list @t71) (and (= @t2 @t71) (= @t1 tptp.vZero) (= @t67 @t71))) (exists (@list @t64 @t70) (and (= @t2 @t70) (= @t1 @t65) (= @t67 (tptp.vSucc (tptp.vplusop @t70 @t64))))) (exists (@list @t66 @t68) (and (not (= @t66 tptp.vZero)) (forall (@list @t69) (not (= @t66 (tptp.vSucc @t69)))) (= @t2 @t68) (= @t1 @t66) (= @t67 @t66)))))) % 0.37/0.68 (assume @p59 (forall @t63 (= (tptp.vreduce (tptp.vIfelse tptp.vTrue @t60 @t61)) (tptp.vsomeTerm @t60)))) % 0.37/0.68 (assume @p60 (forall @t63 (= (tptp.vreduce (tptp.vIfelse tptp.vFalse @t60 @t61)) (tptp.vsomeTerm @t61)))) % 0.37/0.68 (assume @p61 (forall @t83 (=> (and @t82 @t79 @t76) (= @t75 (tptp.vsomeTerm (tptp.vIfelse @t73 @t60 @t61)))))) % 0.37/0.68 (assume @p62 (forall @t83 (=> (and @t82 @t79 @t84) (= @t75 tptp.vnoTerm)))) % 0.37/0.68 (assume @p63 (forall @t47 (=> @t76 (= @t86 (tptp.vsomeTerm (tptp.vSucc @t73)))))) % 0.37/0.68 (assume @p64 (forall @t47 (=> @t84 (= @t86 tptp.vnoTerm)))) % 0.37/0.68 (assume @p65 (= (tptp.vreduce @t88) @t87)) % 0.37/0.68 (assume @p66 (forall @t29 (=> @t27 (= @t89 (tptp.vsomeTerm @t26))))) % 0.37/0.68 (assume @p67 (forall @t29 (=> @t93 (= @t89 (tptp.vsomeTerm (tptp.vPred @t91)))))) % 0.37/0.68 (assume @p68 (forall @t29 (=> @t94 (= @t89 tptp.vnoTerm)))) % 0.37/0.68 (assume @p69 (forall @t47 (=> @t100 (= @t96 (tptp.vsomeTerm (tptp.vPred @t73)))))) % 0.37/0.68 (assume @p70 (forall @t47 (=> @t101 (= @t96 tptp.vnoTerm)))) % 0.37/0.68 (assume @p71 (= (tptp.vreduce @t103) @t102)) % 0.37/0.68 (assume @p72 (forall @t29 (=> @t27 (= @t105 @t104)))) % 0.37/0.68 (assume @p73 (forall @t29 (=> @t93 (= @t105 (tptp.vsomeTerm (tptp.vIszero @t91)))))) % 0.37/0.68 (assume @p74 (forall @t29 (=> @t94 (= @t105 tptp.vnoTerm)))) % 0.37/0.68 (assume @p75 (forall @t47 (=> @t100 (= @t107 (tptp.vsomeTerm (tptp.vIszero @t73)))))) % 0.37/0.68 (assume @p76 (forall @t47 (=> @t101 (= @t107 tptp.vnoTerm)))) % 0.37/0.68 (assume @p77 (forall @t111 (=> (and @t44 @t110) (= @t109 (tptp.vsomeTerm (tptp.vplusop @t43 @t60)))))) % 0.37/0.68 (assume @p78 (forall @t111 (=> (and @t44 @t114 @t113) (= @t109 (tptp.vsomeTerm (tptp.vPlus @t43 (tptp.vgetTerm @t112))))))) % 0.37/0.68 (assume @p79 (forall @t111 (=> (and @t44 @t114 (not @t113)) @t115))) % 0.37/0.68 (assume @p80 (forall @t111 (=> (and @t50 @t76) (= @t109 (tptp.vsomeTerm (tptp.vPlus @t73 @t60)))))) % 0.37/0.68 (assume @p81 (forall @t111 (=> (and @t50 @t84) @t115))) % 0.37/0.68 (assume @p82 (forall @t36 (=> (and (forall @t119 (not (= @t30 @t120))) (forall @t119 (not (= @t30 (tptp.vIfelse tptp.vFalse @t71 @t64)))) (forall (@list @t116 @t71 @t64) (not (= @t30 (tptp.vIfelse @t116 @t71 @t64)))) (forall @t117 (not (= @t30 (tptp.vSucc @t116)))) (not (= @t30 @t88)) (forall @t33 (not (= @t30 @t118))) (forall @t117 (not (= @t30 (tptp.vPred @t116)))) (not (= @t30 @t103)) (forall @t33 (not (= @t30 (tptp.vIszero @t32)))) (forall @t117 (not (= @t30 (tptp.vIszero @t116)))) (forall (@list @t116 @t71) (not (= @t30 (tptp.vPlus @t116 @t71))))) (= (tptp.vreduce @t30) tptp.vnoTerm)))) % 0.37/0.68 (assume @p83 (forall @t7 (or (exists @t119 (and (= @t2 @t120) (= @t121 (tptp.vsomeTerm @t71)))) (exists (@list @t70 @t66) (and (= @t2 (tptp.vIfelse tptp.vFalse @t70 @t66)) (= @t121 (tptp.vsomeTerm @t66)))) (exists (@list @t116 @t68 @t189 @t190) (and (forall (@list @t194 @t193) (or (not (= @t116 tptp.vTrue)) (not (= @t68 @t194)) (not (= @t189 @t193)))) (forall (@list @t192 @t191) (or (not (= @t116 tptp.vFalse)) (not (= @t68 @t192)) (not (= @t189 @t191)))) (= @t190 (tptp.vreduce @t116)) (tptp.visSomeTerm @t190) (= @t2 (tptp.vIfelse @t116 @t68 @t189)) (= @t121 (tptp.vsomeTerm (tptp.vIfelse (tptp.vgetTerm @t190) @t68 @t189))))) (exists (@list @t183 @t182 @t181 @t184) (and (forall (@list @t188 @t187) (or (not (= @t183 tptp.vTrue)) (not (= @t182 @t188)) (not (= @t181 @t187)))) (forall (@list @t186 @t185) (or (not (= @t183 tptp.vFalse)) (not (= @t182 @t186)) (not (= @t181 @t185)))) (= @t184 (tptp.vreduce @t183)) (not (tptp.visSomeTerm @t184)) (= @t2 (tptp.vIfelse @t183 @t182 @t181)) @t122)) (exists (@list @t180 @t179) (and (= @t179 (tptp.vreduce @t180)) (tptp.visSomeTerm @t179) (= @t2 (tptp.vSucc @t180)) (= @t121 (tptp.vsomeTerm (tptp.vSucc (tptp.vgetTerm @t179)))))) (exists (@list @t177 @t178) (and (= @t178 (tptp.vreduce @t177)) (not (tptp.visSomeTerm @t178)) (= @t2 (tptp.vSucc @t177)) @t122)) (and (= @t2 @t88) (= @t121 @t87)) (exists @t33 (and (tptp.visNV @t31) (= @t2 @t118) (= @t121 (tptp.vsomeTerm @t31)))) (exists (@list @t175 @t174) (and (not (tptp.visNV @t175)) (= @t174 (tptp.vreduce @t176)) (tptp.visSomeTerm @t174) (= @t2 (tptp.vPred @t176)) (= @t121 (tptp.vsomeTerm (tptp.vPred (tptp.vgetTerm @t174)))))) (exists (@list @t171 @t173) (and (not (tptp.visNV @t171)) (= @t173 (tptp.vreduce @t172)) (not (tptp.visSomeTerm @t173)) (= @t2 (tptp.vPred @t172)) @t122)) (exists (@list @t169 @t168) (and (not (= @t169 tptp.vZero)) (forall (@list @t170) (not (= @t169 (tptp.vSucc @t170)))) (= @t168 (tptp.vreduce @t169)) (tptp.visSomeTerm @t168) (= @t2 (tptp.vPred @t169)) (= @t121 (tptp.vsomeTerm (tptp.vPred (tptp.vgetTerm @t168)))))) (exists (@list @t165 @t166) (and (not (= @t165 tptp.vZero)) (forall (@list @t167) (not (= @t165 (tptp.vSucc @t167)))) (= @t166 (tptp.vreduce @t165)) (not (tptp.visSomeTerm @t166)) (= @t2 (tptp.vPred @t165)) @t122)) (and (= @t2 @t103) (= @t121 @t102)) (exists (@list @t164) (and (tptp.visNV @t164) (= @t2 (tptp.vIszero (tptp.vSucc @t164))) (= @t121 @t104))) (exists (@list @t162 @t161) (and (not (tptp.visNV @t162)) (= @t161 (tptp.vreduce @t163)) (tptp.visSomeTerm @t161) (= @t2 (tptp.vIszero @t163)) (= @t121 (tptp.vsomeTerm (tptp.vIszero (tptp.vgetTerm @t161)))))) (exists (@list @t158 @t160) (and (not (tptp.visNV @t158)) (= @t160 (tptp.vreduce @t159)) (not (tptp.visSomeTerm @t160)) (= @t2 (tptp.vIszero @t159)) @t122)) (exists (@list @t156 @t155) (and (not (= @t156 tptp.vZero)) (forall (@list @t157) (not (= @t156 (tptp.vSucc @t157)))) (= @t155 (tptp.vreduce @t156)) (tptp.visSomeTerm @t155) (= @t2 (tptp.vIszero @t156)) (= @t121 (tptp.vsomeTerm (tptp.vIszero (tptp.vgetTerm @t155)))))) (exists (@list @t152 @t153) (and (not (= @t152 tptp.vZero)) (forall (@list @t154) (not (= @t152 (tptp.vSucc @t154)))) (= @t153 (tptp.vreduce @t152)) (not (tptp.visSomeTerm @t153)) (= @t2 (tptp.vIszero @t152)) @t122)) (exists (@list @t151 @t150) (and (tptp.visNV @t151) (tptp.visNV @t150) (= @t2 (tptp.vPlus @t151 @t150)) (= @t121 (tptp.vsomeTerm (tptp.vplusop @t151 @t150))))) (exists (@list @t148 @t149 @t147) (and (tptp.visNV @t148) (not (tptp.visNV @t149)) (= @t147 (tptp.vreduce @t149)) (tptp.visSomeTerm @t147) (= @t2 (tptp.vPlus @t148 @t149)) (= @t121 (tptp.vsomeTerm (tptp.vPlus @t148 (tptp.vgetTerm @t147)))))) (exists (@list @t145 @t144 @t146) (and (tptp.visNV @t145) (not (tptp.visNV @t144)) (= @t146 (tptp.vreduce @t144)) (not (tptp.visSomeTerm @t146)) (= @t2 (tptp.vPlus @t145 @t144)) @t122)) (exists (@list @t143 @t141 @t142) (and (not (tptp.visNV @t143)) (= @t142 (tptp.vreduce @t143)) (tptp.visSomeTerm @t142) (= @t2 (tptp.vPlus @t143 @t141)) (= @t121 (tptp.vsomeTerm (tptp.vPlus (tptp.vgetTerm @t142) @t141))))) (exists (@list @t139 @t138 @t140) (and (not (tptp.visNV @t139)) (= @t140 (tptp.vreduce @t139)) (not (tptp.visSomeTerm @t140)) (= @t2 (tptp.vPlus @t139 @t138)) @t122)) (exists (@list @t123) (and (forall (@list @t137 @t136) (not (= @t123 (tptp.vIfelse tptp.vTrue @t137 @t136)))) (forall (@list @t135 @t134) (not (= @t123 (tptp.vIfelse tptp.vFalse @t135 @t134)))) (forall (@list @t133 @t132 @t131) (not (= @t123 (tptp.vIfelse @t133 @t132 @t131)))) (forall (@list @t130) (not (= @t123 (tptp.vSucc @t130)))) (not (= @t123 @t88)) (forall (@list @t129) (not (= @t123 (tptp.vPred (tptp.vSucc @t129))))) (forall (@list @t128) (not (= @t123 (tptp.vPred @t128)))) (not (= @t123 @t103)) (forall (@list @t127) (not (= @t123 (tptp.vIszero (tptp.vSucc @t127))))) (forall (@list @t126) (not (= @t123 (tptp.vIszero @t126)))) (forall (@list @t125 @t124) (not (= @t123 (tptp.vPlus @t125 @t124)))) (= @t2 @t123) @t122))))) % 0.37/0.68 (assume @p84 (tptp.vptchecksimple tptp.vTrue tptp.vB)) % 0.37/0.68 (assume @p85 (tptp.vptchecksimple tptp.vFalse tptp.vB)) % 0.37/0.68 (assume @p86 (forall (@list @t43 @t60 @t195 @t61) (=> (and @t199 @t198 @t197) @t196))) % 0.37/0.68 (assume @p87 (forall @t200 (=> @t196 @t199))) % 0.37/0.68 (assume @p88 (forall @t200 (=> @t196 @t198))) % 0.37/0.68 (assume @p89 (forall @t200 (=> @t196 @t197))) % 0.37/0.68 (assume @p90 (tptp.vptchecksimple tptp.vZero tptp.vNat)) % 0.37/0.68 (assume @p91 (forall @t203 (=> @t202 @t201))) % 0.37/0.68 (assume @p92 (forall @t47 (=> @t205 @t204))) % 0.37/0.68 (assume @p93 (forall @t206 (=> (tptp.vptchecksimple @t85 @t195) @t201))) % 0.37/0.68 (assume @p94 (forall @t47 (=> @t204 @t205))) % 0.37/0.68 (assume @p95 (forall @t47 (=> @t205 @t207))) % 0.37/0.68 (assume @p96 (forall @t47 (=> @t207 @t205))) % 0.37/0.68 (assume @p97 (forall @t206 (=> (tptp.vptchecksimple @t95 @t195) @t201))) % 0.37/0.68 (assume @p98 (forall @t47 (=> @t205 @t208))) % 0.37/0.68 (assume @p99 (forall @t47 (=> @t208 @t205))) % 0.37/0.68 (assume @p100 (forall @t206 (=> (tptp.vptchecksimple @t106 @t195) (= @t195 tptp.vB)))) % 0.37/0.68 (assume @p101 (forall @t111 (=> (and @t205 @t210) @t209))) % 0.37/0.68 (assume @p102 (forall (@list @t43 @t60 @t195) (=> (tptp.vptchecksimple @t108 @t195) @t201))) % 0.37/0.68 (assume @p103 (forall @t111 (=> @t209 @t205))) % 0.37/0.68 (assume @p104 (forall @t111 (=> @t209 @t210))) % 0.37/0.68 (assume @p105 @t218) % 0.37/0.68 (assume @p106 true) % 0.37/0.68 (step @p107 :rule refl :args (@t220)) % 0.37/0.68 (step @p108 :rule aci_norm :args ((= (or false @t42) @t42))) % 0.37/0.68 (step @p109 :rule refl :args (@t42)) % 0.37/0.68 (step @p110 :rule evaluate :args ((not true))) % 0.37/0.68 (step @p111 :rule eq-refl :args (tptp.vFalse)) % 0.37/0.68 (step @p112 :rule cong :premises (@p111) :args (@t221)) % 0.37/0.68 (step @p113 :rule trans :premises (@p112 @p110)) % 0.37/0.68 (step @p114 :rule nary_cong :premises (@p113 @p109) :args (@t222)) % 0.37/0.68 (step @p115 :rule trans :premises (@p114 @p108)) % 0.37/0.68 (step @p116 :rule quant-var-elim-eq :args ((= (forall @t226 (or (not (= @t223 tptp.vFalse)) @t225 @t224)) @t222))) % 0.37/0.68 (step @p117 :rule refl :args (@t224)) % 0.37/0.68 (step @p118 :rule refl :args (@t225)) % 0.37/0.68 (step @p119 :rule eq-symm :args (tptp.vFalse @t223)) % 0.37/0.68 (step @p120 :rule cong :premises (@p119) :args (@t225)) % 0.37/0.68 (step @p121 :rule nary_cong :premises (@p120 @p118 @p117) :args (@t227)) % 0.37/0.68 (step @p122 :rule aci_norm :args ((= @t228 @t227))) % 0.37/0.68 (step @p123 :rule trans :premises (@p122 @p121)) % 0.37/0.68 (step @p124 :rule cong :premises (@p123) :args (@t229)) % 0.37/0.68 (step @p125 :rule trans :premises (@p124 @p116)) % 0.37/0.68 (step @p126 :rule trans :premises (@p125 @p115)) % 0.37/0.68 (step @p127 :rule aci_norm :args ((= (or false @t41) @t41))) % 0.37/0.68 (step @p128 :rule refl :args (@t41)) % 0.37/0.68 (step @p129 :rule eq-refl :args (tptp.vTrue)) % 0.37/0.68 (step @p130 :rule cong :premises (@p129) :args (@t230)) % 0.37/0.68 (step @p131 :rule trans :premises (@p130 @p110)) % 0.37/0.68 (step @p132 :rule nary_cong :premises (@p131 @p128) :args (@t231)) % 0.37/0.68 (step @p133 :rule trans :premises (@p132 @p127)) % 0.37/0.68 (step @p134 :rule quant-var-elim-eq :args ((= (forall @t235 (or (not (= @t232 tptp.vTrue)) @t234 @t233)) @t231))) % 0.37/0.68 (step @p135 :rule refl :args (@t233)) % 0.37/0.68 (step @p136 :rule refl :args (@t234)) % 0.37/0.68 (step @p137 :rule eq-symm :args (tptp.vTrue @t232)) % 0.37/0.68 (step @p138 :rule cong :premises (@p137) :args (@t234)) % 0.37/0.68 (step @p139 :rule nary_cong :premises (@p138 @p136 @p135) :args (@t236)) % 0.37/0.68 (step @p140 :rule aci_norm :args ((= @t237 @t236))) % 0.37/0.68 (step @p141 :rule trans :premises (@p140 @p139)) % 0.37/0.68 (step @p142 :rule cong :premises (@p141) :args (@t238)) % 0.37/0.68 (step @p143 :rule trans :premises (@p142 @p134)) % 0.37/0.68 (step @p144 :rule trans :premises (@p143 @p133)) % 0.37/0.68 (step @p145 :rule nary_cong :premises (@p144 @p126 @p107) :args ((and @t238 @t229 @t220))) % 0.37/0.68 (step @p146 :rule alpha_equiv :args (@t240 @t241 (@list @t219))) % 0.37/0.68 (step @p147 :rule alpha_equiv :args (@t245 @t241 (@list @t223))) % 0.37/0.68 (step @p148 :rule alpha_equiv :args (@t249 @t241 (@list @t232))) % 0.37/0.68 (step @p149 :rule nary_cong :premises (@p148 @p147 @p146) :args (@t250)) % 0.37/0.68 (step @p150 :rule quant-miniscope-and :args ((= (forall @t7 @t251) @t250))) % 0.37/0.68 (step @p151 :rule trans :premises (@p150 @p149)) % 0.37/0.68 (step @p152 :rule trans :premises (@p151 @p145)) % 0.37/0.68 (step @p153 :rule aci_norm :args ((= (and @t248 (and @t244 @t239)) @t251))) % 0.37/0.68 (step @p154 :rule bool-or-and-distrib :args (@t243 @t40 true @t49 false)) % 0.37/0.68 (step @p155 :rule refl :args (@t248)) % 0.37/0.68 (step @p156 :rule nary_cong :premises (@p155 @p154) :args ((and @t248 (or @t252 @t49)))) % 0.37/0.68 (step @p157 :rule bool-or-and-distrib :args (@t247 @t243 (and @t40) @t49 false)) % 0.37/0.68 (step @p158 :rule trans :premises (@p157 @p156)) % 0.37/0.68 (step @p159 :rule trans :premises (@p158 @p153)) % 0.37/0.68 (step @p160 :rule cong :premises (@p159) :args ((forall @t7 @t254))) % 0.37/0.68 (step @p161 :rule trans :premises (@p160 @p152)) % 0.37/0.68 (step @p162 :rule aci_norm :args ((= @t255 @t254))) % 0.37/0.68 (step @p163 :rule cong :premises (@p162) :args ((forall @t7 @t255))) % 0.37/0.68 (step @p164 :rule trans :premises (@p163 @p161)) % 0.37/0.68 (step @p165 :rule aci_norm :args ((= (and @t247 @t252) @t253))) % 0.37/0.68 (step @p166 :rule bool-or-de-morgan :args (@t242 @t38 false)) % 0.37/0.68 (step @p167 :rule refl :args (@t247)) % 0.37/0.68 (step @p168 :rule nary_cong :premises (@p167 @p166) :args ((and @t247 (not (or @t242 @t38))))) % 0.37/0.68 (step @p169 :rule bool-or-de-morgan :args (@t246 @t242 (or @t38))) % 0.37/0.68 (step @p170 :rule trans :premises (@p169 @p168)) % 0.37/0.68 (step @p171 :rule trans :premises (@p170 @p165)) % 0.37/0.68 (step @p172 :rule refl :args (@t49)) % 0.37/0.68 (step @p173 :rule nary_cong :premises (@p172 @p171) :args ((or @t49 @t257))) % 0.37/0.68 (step @p174 :rule refl :args (@t257)) % 0.37/0.68 (step @p175 :rule bool-double-not-elim :args (@t49)) % 0.37/0.68 (step @p176 :rule nary_cong :premises (@p175 @p174) :args ((or (not @t53) @t257))) % 0.37/0.68 (step @p177 :rule bool-impl-elim :args (@t53 @t257)) % 0.37/0.68 (step @p178 :rule trans :premises (@p177 @p176)) % 0.37/0.68 (step @p179 :rule trans :premises (@p178 @p173)) % 0.37/0.68 (step @p180 :rule cong :premises (@p179) :args ((forall @t7 (=> @t53 @t257)))) % 0.37/0.68 (step @p181 :rule trans :premises (@p180 @p164)) % 0.37/0.68 (step @p182 :rule aci_norm :args ((= (or @t246 @t242 false @t38) @t256))) % 0.37/0.68 (step @p183 :rule refl :args (@t38)) % 0.37/0.68 (step @p184 :rule eq-refl :args (@t2)) % 0.37/0.68 (step @p185 :rule cong :premises (@p184) :args (@t258)) % 0.37/0.68 (step @p186 :rule trans :premises (@p185 @p110)) % 0.37/0.68 (step @p187 :rule refl :args (@t242)) % 0.37/0.68 (step @p188 :rule refl :args (@t246)) % 0.37/0.68 (step @p189 :rule nary_cong :premises (@p188 @p187 @p186 @p183) :args (@t259)) % 0.37/0.68 (step @p190 :rule trans :premises (@p189 @p182)) % 0.37/0.68 (step @p191 :rule quant-var-elim-eq :args ((= (forall @t47 (or (not (= @t43 @t2)) @t262 @t261 @t260 @t44)) @t259))) % 0.37/0.68 (step @p192 :rule refl :args (@t44)) % 0.37/0.68 (step @p193 :rule refl :args (@t260)) % 0.37/0.68 (step @p194 :rule refl :args (@t261)) % 0.37/0.68 (step @p195 :rule refl :args (@t262)) % 0.37/0.68 (step @p196 :rule eq-symm :args (@t2 @t43)) % 0.37/0.68 (step @p197 :rule cong :premises (@p196) :args (@t260)) % 0.37/0.68 (step @p198 :rule nary_cong :premises (@p197 @p195 @p194 @p193 @p192) :args (@t263)) % 0.37/0.68 (step @p199 :rule aci_norm :args ((= @t264 @t263))) % 0.37/0.68 (step @p200 :rule trans :premises (@p199 @p198)) % 0.37/0.68 (step @p201 :rule cong :premises (@p200) :args ((forall @t47 @t264))) % 0.37/0.68 (step @p202 :rule trans :premises (@p201 @p191)) % 0.37/0.68 (step @p203 :rule trans :premises (@p202 @p190)) % 0.37/0.68 (step @p204 :rule bool-double-not-elim :args (@t44)) % 0.37/0.68 (step @p205 :rule bool-double-not-elim :args (@t261)) % 0.37/0.68 (step @p206 :rule bool-double-not-elim :args (@t262)) % 0.37/0.68 (step @p207 :rule nary_cong :premises (@p206 @p205 @p193 @p204) :args (@t270)) % 0.37/0.68 (step @p208 :rule aci_norm :args ((= (or @t269 (or @t267 (or @t260 @t265))) @t270))) % 0.37/0.68 (step @p209 :rule trans :premises (@p208 @p207)) % 0.37/0.68 (step @p210 :rule bool-and-de-morgan :args (@t48 @t50 true)) % 0.37/0.68 (step @p211 :rule refl :args (@t267)) % 0.37/0.68 (step @p212 :rule nary_cong :premises (@p211 @p210) :args ((or @t267 (not (and @t48 @t50))))) % 0.37/0.68 (step @p213 :rule bool-and-de-morgan :args (@t266 @t48 (and @t50))) % 0.37/0.68 (step @p214 :rule trans :premises (@p213 @p212)) % 0.37/0.68 (step @p215 :rule refl :args (@t269)) % 0.37/0.68 (step @p216 :rule nary_cong :premises (@p215 @p214) :args ((or @t269 (not (and @t266 @t48 @t50))))) % 0.37/0.68 (step @p217 :rule bool-and-de-morgan :args (@t268 @t266 (and @t48 @t50))) % 0.37/0.68 (step @p218 :rule trans :premises (@p217 @p216)) % 0.37/0.68 (step @p219 :rule trans :premises (@p218 @p209)) % 0.37/0.68 (step @p220 :rule cong :premises (@p219) :args (@t272)) % 0.37/0.68 (step @p221 :rule trans :premises (@p220 @p203)) % 0.37/0.68 (step @p222 :rule cong :premises (@p221) :args (@t273)) % 0.37/0.68 (step @p223 :rule exists-elim :args ((= (exists @t47 @t271) @t273))) % 0.37/0.68 (step @p224 :rule trans :premises (@p223 @p222)) % 0.37/0.68 (step @p225 :rule refl :args (@t50)) % 0.37/0.68 (step @p226 :rule refl :args (@t48)) % 0.37/0.68 (step @p227 :rule eq-symm :args (@t43 tptp.vFalse)) % 0.37/0.68 (step @p228 :rule cong :premises (@p227) :args (@t45)) % 0.37/0.68 (step @p229 :rule eq-symm :args (@t43 tptp.vTrue)) % 0.37/0.68 (step @p230 :rule cong :premises (@p229) :args (@t46)) % 0.37/0.68 (step @p231 :rule nary_cong :premises (@p230 @p228 @p226 @p225) :args (@t51)) % 0.37/0.68 (step @p232 :rule cong :premises (@p231) :args (@t52)) % 0.37/0.68 (step @p233 :rule trans :premises (@p232 @p224)) % 0.37/0.68 (step @p234 :rule refl :args (@t53)) % 0.37/0.68 (step @p235 :rule cong :premises (@p234 @p233) :args (@t54)) % 0.37/0.68 (step @p236 :rule cong :premises (@p235) :args (@t55)) % 0.37/0.68 (step @p237 :rule trans :premises (@p236 @p181)) % 0.37/0.68 (step @p238 :rule eq_resolve :premises (@p50 @p237)) % 0.37/0.68 (step @p239 :rule and_elim :premises (@p238) :args (2)) % 0.37/0.68 (step @p240 :rule quant-miniscope-or :args ((= (forall @t203 @t276) (or @t213 @t275 (forall @t203 @t274))))) % 0.37/0.68 (step @p241 :rule aci_norm :args ((= @t277 @t276))) % 0.37/0.68 (step @p242 :rule cong :premises (@p241) :args ((forall @t203 @t277))) % 0.37/0.68 (step @p243 :rule trans :premises (@p242 @p240)) % 0.37/0.68 (step @p244 :rule aci_norm :args ((= (or (or @t274 @t213) @t275) @t277))) % 0.37/0.68 (step @p245 :rule refl :args (@t275)) % 0.37/0.68 (step @p246 :rule bool-double-not-elim :args (@t213)) % 0.37/0.68 (step @p247 :rule refl :args (@t274)) % 0.37/0.68 (step @p248 :rule nary_cong :premises (@p247 @p246) :args ((or @t274 (not @t214)))) % 0.37/0.68 (step @p249 :rule bool-and-de-morgan :args (@t202 @t214 true)) % 0.37/0.68 (step @p250 :rule trans :premises (@p249 @p248)) % 0.37/0.68 (step @p251 :rule nary_cong :premises (@p250 @p245) :args ((or (not @t215) @t275))) % 0.37/0.68 (step @p252 :rule trans :premises (@p251 @p244)) % 0.37/0.68 (step @p253 :rule bool-impl-elim :args (@t215 @t275)) % 0.37/0.68 (step @p254 :rule trans :premises (@p253 @p252)) % 0.37/0.68 (step @p255 :rule cong :premises (@p254) :args ((forall @t203 (=> @t215 @t275)))) % 0.37/0.68 (step @p256 :rule trans :premises (@p255 @p243)) % 0.37/0.68 (step @p257 :rule eq-symm :args (@t211 tptp.vnoTerm)) % 0.37/0.68 (step @p258 :rule cong :premises (@p257) :args (@t212)) % 0.37/0.68 (step @p259 :rule refl :args (@t215)) % 0.37/0.68 (step @p260 :rule cong :premises (@p259 @p258) :args (@t216)) % 0.37/0.68 (step @p261 :rule cong :premises (@p260) :args (@t217)) % 0.37/0.68 (step @p262 :rule trans :premises (@p261 @p256)) % 0.37/0.68 (step @p263 :rule cong :premises (@p262) :args (@t218)) % 0.37/0.68 (step @p264 :rule eq_resolve :premises (@p105 @p263)) % 0.37/0.68 (step @p265 :rule not_or_elim :premises (@p264) :args (0)) % 0.37/0.68 (step @p266 :rule cnf_or_pos :args (@t279)) % 0.37/0.68 (step @p267 :rule reordering :premises (@p266) :args ((or @t213 @t278 @t280))) % 0.37/0.68 (step @p268 :rule chain_m_resolution :premises (@p267 @p265 @p41) :args (@t280 @t281 (@list @t213 @t25))) % 0.37/0.68 (assume-push @p275 @t220) % 0.37/0.68 (step @p270 :rule instantiate :premises (@p239) :args ((@list tptp.vZero))) % 0.37/0.68 (step-pop @p276 :rule scope :premises (@p270)) % 0.37/0.68 (step @p271 :rule process_scope :premises (@p276) :args (@t279)) % 0.37/0.68 (step @p273 :rule implies_elim :premises (@p271)) % 0.37/0.68 (step @p274 false :rule chain_m_resolution :premises (@p273 @p268 @p239) :args (false @t281 (@list @t279 @t220))) % 0.37/0.68 ) % 0.37/0.68 % SZS output end Proof % 0.37/0.68 % cvc5 exiting %------------------------------------------------------------------------------