%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM448+5 : TPTP v9.2.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n011.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 08:39:26 AM UTC 2026 % Result : Theorem 15.44s 15.92s % Output : Proof 15.44s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM448+5 : TPTP v9.2.1. Released v4.0.0. % 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 : n011.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 : Tue Jun 2 11:20:19 EDT 2026 % 0.17/0.35 % CPUTime : % 0.31/0.50 %----Proving TF0_NAR, FOF, or CNF % 15.44/15.92 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 15.44/15.92 --- Run --no-e-matching --full-saturate-quant at 6... % 15.44/15.92 % SZS status Theorem % 15.44/15.92 % SZS output start Proof % 15.44/15.92 ( % 15.44/15.92 (declare-sort $$unsorted 0) % 15.44/15.92 (declare-const tptp.cS2076 $$unsorted) % 15.44/15.92 (declare-const tptp.isClosed0 (-> $$unsorted Bool)) % 15.44/15.92 (declare-const tptp.isOpen0 (-> $$unsorted Bool)) % 15.44/15.92 (declare-const tptp.stldt0 (-> $$unsorted $$unsorted)) % 15.44/15.92 (declare-const tptp.sdtslmnbsdt0 (-> $$unsorted $$unsorted $$unsorted)) % 15.44/15.92 (declare-const tptp.cS1395 $$unsorted) % 15.44/15.92 (declare-const tptp.sdtbsmnsldt0 (-> $$unsorted $$unsorted $$unsorted)) % 15.44/15.92 (declare-const tptp.aDivisorOf0 (-> $$unsorted $$unsorted Bool)) % 15.44/15.92 (declare-const tptp.xS $$unsorted) % 15.44/15.92 (declare-const tptp.szAzrzSzezqlpdtcmdtrp0 (-> $$unsorted $$unsorted $$unsorted)) % 15.44/15.92 (declare-const tptp.sbsmnsldt0 (-> $$unsorted $$unsorted)) % 15.44/15.92 (declare-const tptp.sdteqdtlpzmzozddtrp0 (-> $$unsorted $$unsorted $$unsorted Bool)) % 15.44/15.92 (declare-const tptp.cS2043 $$unsorted) % 15.44/15.92 (declare-const tptp.sz10 $$unsorted) % 15.44/15.92 (declare-const tptp.aSubsetOf0 (-> $$unsorted $$unsorted Bool)) % 15.44/15.92 (declare-const tptp.smndt0 (-> $$unsorted $$unsorted)) % 15.44/15.92 (declare-const tptp.aInteger0 (-> $$unsorted Bool)) % 15.44/15.92 (declare-const tptp.sz00 $$unsorted) % 15.44/15.92 (declare-const tptp.aSet0 (-> $$unsorted Bool)) % 15.44/15.92 (declare-const tptp.isPrime0 (-> $$unsorted Bool)) % 15.44/15.92 (declare-const tptp.sdtpldt0 (-> $$unsorted $$unsorted $$unsorted)) % 15.44/15.92 (declare-const tptp.sdtasdt0 (-> $$unsorted $$unsorted $$unsorted)) % 15.44/15.92 (declare-const tptp.aElementOf0 (-> $$unsorted $$unsorted Bool)) % 15.44/15.92 (declare-const tptp.isFinite0 (-> $$unsorted Bool)) % 15.44/15.92 (define @t1 () (@var "W0" $$unsorted)) % 15.44/15.92 (define @t2 () (tptp.aInteger0 @t1)) % 15.44/15.92 (define @t3 () (@list @t1)) % 15.44/15.92 (define @t4 () (tptp.aInteger0 tptp.sz10)) % 15.44/15.92 (define @t5 () (tptp.smndt0 @t1)) % 15.44/15.92 (define @t6 () (tptp.aInteger0 @t5)) % 15.44/15.92 (define @t7 () (forall @t3 (=> @t2 @t6))) % 15.44/15.92 (define @t8 () (@var "W1" $$unsorted)) % 15.44/15.92 (define @t9 () (tptp.sdtpldt0 @t1 @t8)) % 15.44/15.92 (define @t10 () (tptp.aInteger0 @t8)) % 15.44/15.92 (define @t11 () (and @t2 @t10)) % 15.44/15.92 (define @t12 () (@list @t1 @t8)) % 15.44/15.92 (define @t13 () (tptp.sdtasdt0 @t1 @t8)) % 15.44/15.92 (define @t14 () (tptp.aInteger0 @t13)) % 15.44/15.92 (define @t15 () (forall @t12 (=> @t11 @t14))) % 15.44/15.92 (define @t16 () (@var "W2" $$unsorted)) % 15.44/15.92 (define @t17 () (tptp.sdtpldt0 @t8 @t16)) % 15.44/15.92 (define @t18 () (tptp.aInteger0 @t16)) % 15.44/15.92 (define @t19 () (and @t2 @t10 @t18)) % 15.44/15.92 (define @t20 () (@list @t1 @t8 @t16)) % 15.44/15.92 (define @t21 () (tptp.sdtasdt0 @t8 @t16)) % 15.44/15.92 (define @t22 () (= (tptp.sdtasdt0 @t1 @t21) (tptp.sdtasdt0 @t13 @t16))) % 15.44/15.92 (define @t23 () (forall @t20 (=> @t19 @t22))) % 15.44/15.92 (define @t24 () (= @t13 (tptp.sdtasdt0 @t8 @t1))) % 15.44/15.92 (define @t25 () (forall @t12 (=> @t11 @t24))) % 15.44/15.92 (define @t26 () (= @t1 (tptp.sdtasdt0 tptp.sz10 @t1))) % 15.44/15.92 (define @t27 () (tptp.sdtasdt0 @t1 tptp.sz10)) % 15.44/15.92 (define @t28 () (and (= @t27 @t1) @t26)) % 15.44/15.92 (define @t29 () (=> @t2 @t28)) % 15.44/15.92 (define @t30 () (forall @t3 @t29)) % 15.44/15.92 (define @t31 () (tptp.sdtasdt0 @t1 @t16)) % 15.44/15.92 (define @t32 () (tptp.smndt0 tptp.sz10)) % 15.44/15.92 (define @t33 () (= @t5 (tptp.sdtasdt0 @t1 @t32))) % 15.44/15.92 (define @t34 () (tptp.sdtasdt0 @t32 @t1)) % 15.44/15.92 (define @t35 () (and (= @t34 @t5) @t33)) % 15.44/15.92 (define @t36 () (=> @t2 @t35)) % 15.44/15.92 (define @t37 () (forall @t3 @t36)) % 15.44/15.92 (define @t38 () (= @t8 tptp.sz00)) % 15.44/15.92 (define @t39 () (= @t1 tptp.sz00)) % 15.44/15.92 (define @t40 () (and @t18 (= @t21 @t1))) % 15.44/15.92 (define @t41 () (@list @t16)) % 15.44/15.92 (define @t42 () (exists @t41 @t40)) % 15.44/15.92 (define @t43 () (not @t38)) % 15.44/15.92 (define @t44 () (and @t10 @t43 @t42)) % 15.44/15.92 (define @t45 () (tptp.aDivisorOf0 @t8 @t1)) % 15.44/15.92 (define @t46 () (@list @t8)) % 15.44/15.92 (define @t47 () (tptp.sdteqdtlpzmzozddtrp0 @t1 @t8 @t16)) % 15.44/15.92 (define @t48 () (not (= @t16 tptp.sz00))) % 15.44/15.92 (define @t49 () (and @t2 @t10 @t18 @t48)) % 15.44/15.92 (define @t50 () (and @t2 @t10 @t43)) % 15.44/15.92 (define @t51 () (@var "W3" $$unsorted)) % 15.44/15.92 (define @t52 () (tptp.aInteger0 @t51)) % 15.44/15.92 (define @t53 () (@list @t1 @t8 @t16 @t51)) % 15.44/15.92 (define @t54 () (= @t1 @t32)) % 15.44/15.92 (define @t55 () (= @t1 tptp.sz10)) % 15.44/15.92 (define @t56 () (and (not @t55) (not @t54))) % 15.44/15.92 (define @t57 () (tptp.isPrime0 @t8)) % 15.44/15.92 (define @t58 () (and @t45 @t57)) % 15.44/15.92 (define @t59 () (exists @t46 @t58)) % 15.44/15.92 (define @t60 () (= @t59 @t56)) % 15.44/15.92 (define @t61 () (=> @t2 @t60)) % 15.44/15.92 (define @t62 () (forall @t3 @t61)) % 15.44/15.92 (define @t63 () (tptp.aSet0 @t1)) % 15.44/15.92 (define @t64 () (tptp.aElementOf0 @t8 @t1)) % 15.44/15.92 (define @t65 () (tptp.aElementOf0 @t16 @t1)) % 15.44/15.92 (define @t66 () (tptp.aElementOf0 @t16 @t8)) % 15.44/15.92 (define @t67 () (tptp.aSet0 @t8)) % 15.44/15.92 (define @t68 () (tptp.isFinite0 @t1)) % 15.44/15.92 (define @t69 () (tptp.aElementOf0 @t51 @t8)) % 15.44/15.92 (define @t70 () (tptp.aElementOf0 @t51 @t1)) % 15.44/15.92 (define @t71 () (tptp.aElementOf0 @t51 @t16)) % 15.44/15.92 (define @t72 () (@list @t51)) % 15.44/15.92 (define @t73 () (tptp.aSet0 @t16)) % 15.44/15.92 (define @t74 () (tptp.sdtbsmnsldt0 @t1 @t8)) % 15.44/15.92 (define @t75 () (tptp.aSubsetOf0 @t8 tptp.cS1395)) % 15.44/15.92 (define @t76 () (tptp.aSubsetOf0 @t1 tptp.cS1395)) % 15.44/15.92 (define @t77 () (and @t76 @t75)) % 15.44/15.92 (define @t78 () (tptp.sdtslmnbsdt0 @t1 @t8)) % 15.44/15.92 (define @t79 () (tptp.sbsmnsldt0 @t1)) % 15.44/15.92 (define @t80 () (tptp.stldt0 @t1)) % 15.44/15.92 (define @t81 () (tptp.szAzrzSzezqlpdtcmdtrp0 @t1 @t8)) % 15.44/15.92 (define @t82 () (tptp.isOpen0 @t1)) % 15.44/15.92 (define @t83 () (tptp.isClosed0 @t1)) % 15.44/15.92 (define @t84 () (tptp.isOpen0 @t8)) % 15.44/15.92 (define @t85 () (tptp.isClosed0 @t8)) % 15.44/15.92 (define @t86 () (tptp.aElementOf0 @t1 tptp.xS)) % 15.44/15.92 (define @t87 () (tptp.szAzrzSzezqlpdtcmdtrp0 tptp.sz00 @t8)) % 15.44/15.92 (define @t88 () (= @t87 @t1)) % 15.44/15.92 (define @t89 () (tptp.aElementOf0 @t16 @t87)) % 15.44/15.92 (define @t90 () (tptp.sdteqdtlpzmzozddtrp0 @t16 tptp.sz00 @t8)) % 15.44/15.92 (define @t91 () (tptp.sdtpldt0 @t16 (tptp.smndt0 tptp.sz00))) % 15.44/15.92 (define @t92 () (tptp.aDivisorOf0 @t8 @t91)) % 15.44/15.92 (define @t93 () (exists @t72 (and @t52 (= (tptp.sdtasdt0 @t8 @t51) @t91)))) % 15.44/15.92 (define @t94 () (forall @t41 (and (=> @t89 (and @t18 @t93 @t92 @t90)) (=> (and @t18 (or @t93 @t92 @t90)) @t89)))) % 15.44/15.92 (define @t95 () (tptp.aSet0 @t87)) % 15.44/15.92 (define @t96 () (tptp.sbsmnsldt0 tptp.xS)) % 15.44/15.92 (define @t97 () (tptp.stldt0 @t96)) % 15.44/15.92 (define @t98 () (or @t55 @t54)) % 15.44/15.92 (define @t99 () (tptp.aElementOf0 @t1 @t97)) % 15.44/15.92 (define @t100 () (= @t99 @t98)) % 15.44/15.92 (define @t101 () (forall @t3 @t100)) % 15.44/15.92 (define @t102 () (or @t101 (= @t97 tptp.cS2076))) % 15.44/15.92 (define @t103 () (tptp.aElementOf0 @t1 @t96)) % 15.44/15.92 (define @t104 () (not @t103)) % 15.44/15.92 (define @t105 () (and @t2 @t104)) % 15.44/15.92 (define @t106 () (= @t99 @t105)) % 15.44/15.92 (define @t107 () (forall @t3 @t106)) % 15.44/15.92 (define @t108 () (tptp.aSet0 @t97)) % 15.44/15.92 (define @t109 () (and @t108 @t107)) % 15.44/15.92 (define @t110 () (=> @t109 @t102)) % 15.44/15.92 (define @t111 () (tptp.aElementOf0 @t1 @t8)) % 15.44/15.92 (define @t112 () (tptp.aElementOf0 @t8 tptp.xS)) % 15.44/15.92 (define @t113 () (and @t112 @t111)) % 15.44/15.92 (define @t114 () (exists @t46 @t113)) % 15.44/15.92 (define @t115 () (and @t2 @t114)) % 15.44/15.92 (define @t116 () (= @t103 @t115)) % 15.44/15.92 (define @t117 () (forall @t3 @t116)) % 15.44/15.92 (define @t118 () (tptp.aSet0 @t96)) % 15.44/15.92 (define @t119 () (and @t118 @t117)) % 15.44/15.92 (define @t120 () (=> @t119 @t110)) % 15.44/15.92 (define @t121 () (and @t114 @t103)) % 15.44/15.92 (define @t122 () (or @t44 @t45)) % 15.44/15.92 (define @t123 () (and @t122 @t57)) % 15.44/15.92 (define @t124 () (exists @t46 @t123)) % 15.44/15.92 (define @t125 () (=> @t124 @t121)) % 15.44/15.92 (define @t126 () (and @t10 @t43 @t42 @t45 @t57)) % 15.44/15.92 (define @t127 () (exists @t46 @t126)) % 15.44/15.92 (define @t128 () (or @t114 @t103)) % 15.44/15.92 (define @t129 () (=> @t128 @t127)) % 15.44/15.92 (define @t130 () (and @t129 @t125)) % 15.44/15.92 (define @t131 () (=> @t2 @t130)) % 15.44/15.92 (define @t132 () (forall @t3 @t131)) % 15.44/15.92 (define @t133 () (=> @t132 @t120)) % 15.44/15.92 (define @t134 () (not @t133)) % 15.44/15.92 (define @t135 () (and (= @t1 @t27) @t26)) % 15.44/15.92 (define @t136 () (tptp.sdtasdt0 tptp.sz10 tptp.sz10)) % 15.44/15.92 (define @t137 () (= tptp.sz10 @t136)) % 15.44/15.92 (define @t138 () (and @t137 @t137)) % 15.44/15.92 (define @t139 () (not @t4)) % 15.44/15.92 (define @t140 () (or @t139 @t138)) % 15.44/15.92 (define @t141 () (not @t2)) % 15.44/15.92 (define @t142 () (forall @t3 (or @t141 @t135))) % 15.44/15.92 (define @t143 () (@list tptp.sz10)) % 15.44/15.92 (define @t144 () (or @t139 @t137)) % 15.44/15.92 (define @t145 () (@list false)) % 15.44/15.92 (define @t146 () (@list false false)) % 15.44/15.92 (define @t147 () (not @t18)) % 15.44/15.92 (define @t148 () (not @t10)) % 15.44/15.92 (define @t149 () (or @t141 @t148 @t147)) % 15.44/15.92 (define @t150 () (tptp.aInteger0 @t32)) % 15.44/15.92 (define @t151 () (or @t139 @t150)) % 15.44/15.92 (define @t152 () (tptp.sdtasdt0 @t136 @t32)) % 15.44/15.92 (define @t153 () (tptp.sdtasdt0 tptp.sz10 @t32)) % 15.44/15.92 (define @t154 () (= (tptp.sdtasdt0 tptp.sz10 @t153) @t152)) % 15.44/15.92 (define @t155 () (not @t150)) % 15.44/15.92 (define @t156 () (or @t139 @t139 @t155 @t154)) % 15.44/15.92 (define @t157 () (@list false false false)) % 15.44/15.92 (define @t158 () (or @t141 @t148)) % 15.44/15.92 (define @t159 () (not @t11)) % 15.44/15.92 (define @t160 () (@list tptp.sz10 @t32)) % 15.44/15.92 (define @t161 () (tptp.sdtasdt0 @t32 tptp.sz10)) % 15.44/15.92 (define @t162 () (= @t153 @t161)) % 15.44/15.92 (define @t163 () (or @t139 @t155 @t162)) % 15.44/15.92 (define @t164 () (and (= @t5 @t34) @t33)) % 15.44/15.92 (define @t165 () (= @t32 @t161)) % 15.44/15.92 (define @t166 () (and @t165 (= @t32 @t153))) % 15.44/15.92 (define @t167 () (or @t139 @t166)) % 15.44/15.92 (define @t168 () (tptp.sbsmnsldt0 tptp.cS2043)) % 15.44/15.92 (define @t169 () (tptp.stldt0 @t168)) % 15.44/15.92 (define @t170 () (= tptp.cS2076 @t169)) % 15.44/15.92 (define @t171 () (tptp.aElementOf0 @t1 @t169)) % 15.44/15.92 (define @t172 () (forall @t3 (= @t171 @t98))) % 15.44/15.92 (define @t173 () (or @t172 @t170)) % 15.44/15.92 (define @t174 () (tptp.aElementOf0 @t1 @t168)) % 15.44/15.92 (define @t175 () (not @t174)) % 15.44/15.92 (define @t176 () (and @t2 @t175)) % 15.44/15.92 (define @t177 () (forall @t3 (= @t171 @t176))) % 15.44/15.92 (define @t178 () (tptp.aSet0 @t169)) % 15.44/15.92 (define @t179 () (and @t178 @t177)) % 15.44/15.92 (define @t180 () (=> @t179 @t173)) % 15.44/15.92 (define @t181 () (not @t111)) % 15.44/15.92 (define @t182 () (not (tptp.aElementOf0 @t8 tptp.cS2043))) % 15.44/15.92 (define @t183 () (not (forall @t46 (or @t182 @t181)))) % 15.44/15.92 (define @t184 () (and (tptp.aSet0 @t168) (forall @t3 (= @t174 (and @t2 @t183))))) % 15.44/15.92 (define @t185 () (=> @t184 @t180)) % 15.44/15.92 (define @t186 () (@var "BOUND_VARIABLE_8578" $$unsorted)) % 15.44/15.92 (define @t187 () (not (tptp.isPrime0 @t186))) % 15.44/15.92 (define @t188 () (@var "BOUND_VARIABLE_8580" $$unsorted)) % 15.44/15.92 (define @t189 () (and (or (not (tptp.aInteger0 @t186)) (= tptp.sz00 @t186) (not (tptp.aInteger0 @t188)) (not (= @t1 (tptp.sdtasdt0 @t186 @t188)))) (not (tptp.aDivisorOf0 @t186 @t1)))) % 15.44/15.92 (define @t190 () (@var "BOUND_VARIABLE_8512" $$unsorted)) % 15.44/15.92 (define @t191 () (tptp.sdtasdt0 @t8 @t190)) % 15.44/15.92 (define @t192 () (not (= @t1 @t191))) % 15.44/15.92 (define @t193 () (not (tptp.aInteger0 @t190))) % 15.44/15.92 (define @t194 () (not @t57)) % 15.44/15.92 (define @t195 () (not @t45)) % 15.44/15.92 (define @t196 () (= tptp.sz00 @t8)) % 15.44/15.92 (define @t197 () (or @t148 @t196 @t195 @t194 @t193 @t192)) % 15.44/15.92 (define @t198 () (@list @t8 @t190)) % 15.44/15.92 (define @t199 () (not (forall @t198 @t197))) % 15.44/15.92 (define @t200 () (@var "BOUND_VARIABLE_8569" $$unsorted)) % 15.44/15.92 (define @t201 () (not (tptp.aElementOf0 @t1 @t200))) % 15.44/15.92 (define @t202 () (@list @t1 @t200 @t186 @t188)) % 15.44/15.92 (define @t203 () (forall @t202 (or @t141 (and (or (and (or (not (tptp.aElementOf0 @t200 tptp.cS2043)) @t201) @t175) @t199) (or (and @t183 @t174) @t189 @t187))))) % 15.44/15.92 (define @t204 () (=> @t203 @t185)) % 15.44/15.92 (define @t205 () (= tptp.cS2076 @t97)) % 15.44/15.92 (define @t206 () (or @t101 @t205)) % 15.44/15.92 (define @t207 () (=> @t109 @t206)) % 15.44/15.92 (define @t208 () (not @t112)) % 15.44/15.92 (define @t209 () (or @t208 @t181)) % 15.44/15.92 (define @t210 () (forall @t46 @t209)) % 15.44/15.92 (define @t211 () (not @t210)) % 15.44/15.92 (define @t212 () (and @t2 @t211)) % 15.44/15.92 (define @t213 () (= @t103 @t212)) % 15.44/15.92 (define @t214 () (forall @t3 @t213)) % 15.44/15.92 (define @t215 () (and @t118 @t214)) % 15.44/15.92 (define @t216 () (=> @t215 @t207)) % 15.44/15.92 (define @t217 () (and @t211 @t103)) % 15.44/15.92 (define @t218 () (or @t217 @t189 @t187)) % 15.44/15.92 (define @t219 () (tptp.aElementOf0 @t200 tptp.xS)) % 15.44/15.92 (define @t220 () (not @t219)) % 15.44/15.92 (define @t221 () (or @t220 @t201)) % 15.44/15.92 (define @t222 () (and @t221 @t104)) % 15.44/15.92 (define @t223 () (or @t222 @t199)) % 15.44/15.92 (define @t224 () (and @t223 @t218)) % 15.44/15.92 (define @t225 () (or @t141 @t224)) % 15.44/15.92 (define @t226 () (forall @t202 @t225)) % 15.44/15.92 (define @t227 () (=> @t226 @t216)) % 15.44/15.92 (define @t228 () (forall @t46 (not @t113))) % 15.44/15.92 (define @t229 () (not @t228)) % 15.44/15.92 (define @t230 () (or @t189 @t187)) % 15.44/15.92 (define @t231 () (or @t230 @t217)) % 15.44/15.92 (define @t232 () (and @t223 @t231)) % 15.44/15.92 (define @t233 () (or @t141 @t232)) % 15.44/15.92 (define @t234 () (forall @t202 @t233)) % 15.44/15.92 (define @t235 () (@list @t200 @t186 @t188)) % 15.44/15.92 (define @t236 () (forall @t235 @t233)) % 15.44/15.92 (define @t237 () (@list @t186 @t188)) % 15.44/15.92 (define @t238 () (forall @t237 @t230)) % 15.44/15.92 (define @t239 () (@var "BOUND_VARIABLE_8539" $$unsorted)) % 15.44/15.92 (define @t240 () (or @t238 @t217)) % 15.44/15.92 (define @t241 () (forall @t237 @t231)) % 15.44/15.92 (define @t242 () (forall @t235 @t231)) % 15.44/15.92 (define @t243 () (@list @t200)) % 15.44/15.92 (define @t244 () (forall @t243 @t104)) % 15.44/15.92 (define @t245 () (forall @t243 @t221)) % 15.44/15.92 (define @t246 () (and @t245 @t244)) % 15.44/15.92 (define @t247 () (forall @t243 @t222)) % 15.44/15.92 (define @t248 () (or @t247 @t199)) % 15.44/15.92 (define @t249 () (forall @t243 @t223)) % 15.44/15.92 (define @t250 () (forall @t235 @t223)) % 15.44/15.92 (define @t251 () (and @t250 @t242)) % 15.44/15.92 (define @t252 () (forall @t235 @t232)) % 15.44/15.92 (define @t253 () (or @t141 @t252)) % 15.44/15.92 (define @t254 () (not (= @t1 (tptp.sdtasdt0 @t8 @t239)))) % 15.44/15.92 (define @t255 () (not (tptp.aInteger0 @t239))) % 15.44/15.92 (define @t256 () (or @t148 @t196 @t255 @t254)) % 15.44/15.92 (define @t257 () (@list @t8 @t239)) % 15.44/15.92 (define @t258 () (forall @t257 (or (and @t256 @t195) @t194))) % 15.44/15.92 (define @t259 () (not @t258)) % 15.44/15.92 (define @t260 () (or @t211 @t103)) % 15.44/15.92 (define @t261 () (and (=> @t260 @t199) (=> @t259 @t217))) % 15.44/15.92 (define @t262 () (or @t255 @t254)) % 15.44/15.92 (define @t263 () (or @t148 @t196 @t262)) % 15.44/15.92 (define @t264 () (and @t263 @t195)) % 15.44/15.92 (define @t265 () (or @t264 @t194)) % 15.44/15.92 (define @t266 () (forall @t257 @t265)) % 15.44/15.92 (define @t267 () (@list @t239)) % 15.44/15.92 (define @t268 () (forall @t267 @t265)) % 15.44/15.92 (define @t269 () (forall @t267 @t195)) % 15.44/15.92 (define @t270 () (forall @t267 @t262)) % 15.44/15.92 (define @t271 () (@list @t16)) % 15.44/15.92 (define @t272 () (or @t148 @t196 @t270)) % 15.44/15.92 (define @t273 () (forall @t267 @t263)) % 15.44/15.92 (define @t274 () (and @t273 @t269)) % 15.44/15.92 (define @t275 () (forall @t267 @t264)) % 15.44/15.92 (define @t276 () (or @t275 @t194)) % 15.44/15.92 (define @t277 () (= @t1 @t21)) % 15.44/15.92 (define @t278 () (forall @t41 (or @t147 (not @t277)))) % 15.44/15.92 (define @t279 () (not @t278)) % 15.44/15.92 (define @t280 () (not @t279)) % 15.44/15.92 (define @t281 () (not @t196)) % 15.44/15.92 (define @t282 () (not @t281)) % 15.44/15.92 (define @t283 () (or @t148 @t282 @t280)) % 15.44/15.92 (define @t284 () (and @t10 @t281 @t279)) % 15.44/15.92 (define @t285 () (or @t284 @t45)) % 15.44/15.92 (define @t286 () (and @t285 @t57)) % 15.44/15.92 (define @t287 () (forall @t46 (not @t286))) % 15.44/15.92 (define @t288 () (not @t287)) % 15.44/15.92 (define @t289 () (and @t18 @t277)) % 15.44/15.92 (define @t290 () (forall @t41 (not @t289))) % 15.44/15.92 (define @t291 () (not @t290)) % 15.44/15.92 (define @t292 () (or @t193 @t192)) % 15.44/15.92 (define @t293 () (or @t148 @t196 @t292 @t195 @t194)) % 15.44/15.92 (define @t294 () (forall @t198 @t293)) % 15.44/15.92 (define @t295 () (@list @t190)) % 15.44/15.92 (define @t296 () (forall @t295 @t293)) % 15.44/15.92 (define @t297 () (forall @t295 @t292)) % 15.44/15.92 (define @t298 () (or @t148 @t196 @t297 @t195 @t194)) % 15.44/15.92 (define @t299 () (or @t148 @t282 @t280 @t195 @t194)) % 15.44/15.92 (define @t300 () (or @t195 @t194)) % 15.44/15.92 (define @t301 () (not @t58)) % 15.44/15.92 (define @t302 () (and @t10 @t281 @t279 @t45 @t57)) % 15.44/15.92 (define @t303 () (forall @t46 (not @t302))) % 15.44/15.92 (define @t304 () (not @t303)) % 15.44/15.92 (define @t305 () (forall @t3 (= @t98 @t171))) % 15.44/15.92 (define @t306 () (@quantifiers_skolemize @t305 0)) % 15.44/15.92 (define @t307 () (= @t32 @t306)) % 15.44/15.92 (define @t308 () (= tptp.sz10 @t306)) % 15.44/15.92 (define @t309 () (or @t308 @t307)) % 15.44/15.92 (define @t310 () (tptp.aElementOf0 @t306 @t169)) % 15.44/15.92 (define @t311 () (= @t310 @t309)) % 15.44/15.92 (define @t312 () (not @t311)) % 15.44/15.92 (define @t313 () (not @t305)) % 15.44/15.92 (define @t314 () (= @t306 @t32)) % 15.44/15.92 (define @t315 () (= @t306 tptp.sz10)) % 15.44/15.92 (define @t316 () (or @t315 @t314)) % 15.44/15.92 (define @t317 () (= @t316 @t310)) % 15.44/15.92 (define @t318 () (not @t317)) % 15.44/15.92 (define @t319 () (@list true)) % 15.44/15.92 (define @t320 () (tptp.aElementOf0 @t306 @t168)) % 15.44/15.92 (define @t321 () (not @t320)) % 15.44/15.92 (define @t322 () (tptp.aInteger0 @t306)) % 15.44/15.92 (define @t323 () (and @t322 @t321)) % 15.44/15.92 (define @t324 () (forall @t3 (= @t176 @t171))) % 15.44/15.92 (define @t325 () (= @t323 @t310)) % 15.44/15.92 (define @t326 () (@list @t306)) % 15.44/15.92 (define @t327 () (= @t310 @t323)) % 15.44/15.92 (define @t328 () (not @t327)) % 15.44/15.92 (define @t329 () (not @t310)) % 15.44/15.92 (define @t330 () (not @t323)) % 15.44/15.92 (define @t331 () (not @t307)) % 15.44/15.92 (define @t332 () (not @t308)) % 15.44/15.92 (define @t333 () (and @t332 @t331)) % 15.44/15.92 (define @t334 () (tptp.sdtasdt0 tptp.sz10 @t306)) % 15.44/15.92 (define @t335 () (tptp.sdtasdt0 @t306 tptp.sz10)) % 15.44/15.92 (define @t336 () (= @t306 @t335)) % 15.44/15.92 (define @t337 () (and @t336 (= @t306 @t334))) % 15.44/15.92 (define @t338 () (not @t322)) % 15.44/15.92 (define @t339 () (or @t338 @t337)) % 15.44/15.92 (define @t340 () (@list tptp.sz10 @t306)) % 15.44/15.92 (define @t341 () (tptp.aInteger0 @t334)) % 15.44/15.92 (define @t342 () (or @t139 @t338 @t341)) % 15.44/15.92 (define @t343 () (= @t334 @t335)) % 15.44/15.92 (define @t344 () (or @t139 @t338 @t343)) % 15.44/15.92 (define @t345 () (not (forall @t46 @t300))) % 15.44/15.92 (define @t346 () (= @t56 @t345)) % 15.44/15.92 (define @t347 () (forall @t46 @t301)) % 15.44/15.92 (define @t348 () (not @t347)) % 15.44/15.92 (define @t349 () (forall @t46 (or (not (tptp.aDivisorOf0 @t8 @t306)) @t194))) % 15.44/15.92 (define @t350 () (not @t349)) % 15.44/15.92 (define @t351 () (not @t314)) % 15.44/15.92 (define @t352 () (not @t315)) % 15.44/15.92 (define @t353 () (and @t352 @t351)) % 15.44/15.92 (define @t354 () (= @t353 @t350)) % 15.44/15.92 (define @t355 () (or @t338 @t354)) % 15.44/15.92 (define @t356 () (forall @t3 (or @t141 @t346))) % 15.44/15.92 (define @t357 () (= @t350 @t333)) % 15.44/15.92 (define @t358 () (or @t338 @t357)) % 15.44/15.92 (define @t359 () (@list @t356)) % 15.44/15.92 (define @t360 () (@quantifiers_skolemize @t349 0)) % 15.44/15.92 (define @t361 () (tptp.isPrime0 @t360)) % 15.44/15.92 (define @t362 () (not @t361)) % 15.44/15.92 (define @t363 () (tptp.aDivisorOf0 @t360 @t334)) % 15.44/15.92 (define @t364 () (not @t363)) % 15.44/15.92 (define @t365 () (and (or (not (tptp.aInteger0 @t360)) (= tptp.sz00 @t360) @t139 (not (= @t334 (tptp.sdtasdt0 @t360 tptp.sz10)))) @t364)) % 15.44/15.92 (define @t366 () (tptp.aElementOf0 @t334 @t168)) % 15.44/15.92 (define @t367 () (and (not (forall @t46 (or @t182 (not (tptp.aElementOf0 @t334 @t8))))) @t366)) % 15.44/15.92 (define @t368 () (or @t367 @t365 @t362)) % 15.44/15.92 (define @t369 () (not (= @t334 @t191))) % 15.44/15.92 (define @t370 () (not (tptp.aDivisorOf0 @t8 @t334))) % 15.44/15.92 (define @t371 () (or @t148 @t196 @t370 @t194 @t193 @t369)) % 15.44/15.92 (define @t372 () (forall @t198 @t371)) % 15.44/15.92 (define @t373 () (not @t372)) % 15.44/15.92 (define @t374 () (not @t366)) % 15.44/15.92 (define @t375 () (not (tptp.aElementOf0 tptp.sz10 tptp.cS2043))) % 15.44/15.92 (define @t376 () (and (or @t375 (not (tptp.aElementOf0 @t334 tptp.sz10))) @t374)) % 15.44/15.92 (define @t377 () (or @t376 @t373)) % 15.44/15.92 (define @t378 () (and @t377 @t368)) % 15.44/15.92 (define @t379 () (not @t341)) % 15.44/15.92 (define @t380 () (or @t379 @t378)) % 15.44/15.92 (define @t381 () (forall @t198 (or @t148 @t196 @t370 @t194 @t193 (not (= @t191 @t334))))) % 15.44/15.92 (define @t382 () (not @t381)) % 15.44/15.92 (define @t383 () (or @t376 @t382)) % 15.44/15.92 (define @t384 () (and @t383 @t368)) % 15.44/15.92 (define @t385 () (or @t379 @t384)) % 15.44/15.92 (define @t386 () (not @t357)) % 15.44/15.92 (define @t387 () (not @t333)) % 15.44/15.92 (define @t388 () (not @t384)) % 15.44/15.92 (define @t389 () (tptp.aDivisorOf0 @t360 @t306)) % 15.44/15.92 (define @t390 () (not @t389)) % 15.44/15.92 (define @t391 () (or @t390 @t362)) % 15.44/15.92 (define @t392 () (not @t391)) % 15.44/15.92 (define @t393 () (not @t350)) % 15.44/15.92 (define @t394 () (not @t343)) % 15.44/15.92 (define @t395 () (not @t336)) % 15.44/15.92 (define @t396 () (not @t321)) % 15.44/15.92 (define @t397 () (and @t336 @t343 @t321)) % 15.44/15.92 (define @t398 () (and @t336 @t343 @t389)) % 15.44/15.92 (define @t399 () (not @t137)) % 15.44/15.92 (define @t400 () (tptp.aElementOf0 tptp.sz10 @t168)) % 15.44/15.92 (define @t401 () (not (tptp.aDivisorOf0 @t8 tptp.sz10))) % 15.44/15.92 (define @t402 () (forall @t198 (or @t148 @t196 @t401 @t194 @t193 (not (= tptp.sz10 @t191))))) % 15.44/15.92 (define @t403 () (not @t402)) % 15.44/15.92 (define @t404 () (not @t400)) % 15.44/15.92 (define @t405 () (and (or @t375 (not (tptp.aElementOf0 tptp.sz10 tptp.sz10))) @t404)) % 15.44/15.92 (define @t406 () (or @t405 @t403)) % 15.44/15.92 (define @t407 () (and @t406 (or (and (not (forall @t46 (or @t182 (not (tptp.aElementOf0 tptp.sz10 @t8))))) @t400) (and (or @t139 (= tptp.sz00 tptp.sz10) @t139 @t399) (not (tptp.aDivisorOf0 tptp.sz10 tptp.sz10))) (not (tptp.isPrime0 tptp.sz10))))) % 15.44/15.92 (define @t408 () (or @t139 @t407)) % 15.44/15.92 (define @t409 () (@quantifiers_skolemize @t402 0)) % 15.44/15.92 (define @t410 () (tptp.aDivisorOf0 @t409 tptp.sz10)) % 15.44/15.92 (define @t411 () (@quantifiers_skolemize @t402 1)) % 15.44/15.92 (define @t412 () (tptp.isPrime0 @t409)) % 15.44/15.92 (define @t413 () (not @t412)) % 15.44/15.92 (define @t414 () (not @t410)) % 15.44/15.92 (define @t415 () (or (not (tptp.aInteger0 @t409)) (= tptp.sz00 @t409) @t414 @t413 (not (tptp.aInteger0 @t411)) (not (= tptp.sz10 (tptp.sdtasdt0 @t409 @t411))))) % 15.44/15.92 (define @t416 () (forall @t46 (or @t401 @t194))) % 15.44/15.92 (define @t417 () (not @t416)) % 15.44/15.92 (define @t418 () (not (= tptp.sz10 @t32))) % 15.44/15.92 (define @t419 () (not (= tptp.sz10 tptp.sz10))) % 15.44/15.92 (define @t420 () (and @t419 @t418)) % 15.44/15.92 (define @t421 () (= @t420 @t417)) % 15.44/15.92 (define @t422 () (or @t139 @t421)) % 15.44/15.92 (define @t423 () (or @t139 @t416)) % 15.44/15.92 (define @t424 () (or @t414 @t413)) % 15.44/15.92 (define @t425 () (not @t415)) % 15.44/15.92 (define @t426 () (and @t4 @t404)) % 15.44/15.92 (define @t427 () (@list false true)) % 15.44/15.92 (define @t428 () (tptp.aElementOf0 tptp.sz10 @t169)) % 15.44/15.92 (define @t429 () (= @t426 @t428)) % 15.44/15.92 (define @t430 () (not @t428)) % 15.44/15.92 (define @t431 () (and @t428 @t308 @t329)) % 15.44/15.92 (define @t432 () (@list true false)) % 15.44/15.92 (define @t433 () (tptp.aInteger0 @t153)) % 15.44/15.92 (define @t434 () (or @t139 @t155 @t433)) % 15.44/15.92 (define @t435 () (tptp.sdtasdt0 @t136 @t306)) % 15.44/15.92 (define @t436 () (and @t307 @t137 @t165 @t433 @t154 @t162)) % 15.44/15.92 (define @t437 () (@list false false false false false false)) % 15.44/15.92 (define @t438 () (and @t307 @t165 @t433 @t162)) % 15.44/15.92 (define @t439 () (and @t307 @t137 @t165 @t154 @t162 @t320)) % 15.44/15.92 (define @t440 () (not @t376)) % 15.44/15.92 (define @t441 () (@quantifiers_skolemize @t381 1)) % 15.44/15.92 (define @t442 () (@quantifiers_skolemize @t381 0)) % 15.44/15.92 (define @t443 () (tptp.sdtasdt0 @t442 @t441)) % 15.44/15.92 (define @t444 () (not (tptp.aInteger0 @t441))) % 15.44/15.92 (define @t445 () (tptp.isPrime0 @t442)) % 15.44/15.92 (define @t446 () (not @t445)) % 15.44/15.92 (define @t447 () (tptp.aDivisorOf0 @t442 @t334)) % 15.44/15.92 (define @t448 () (not @t447)) % 15.44/15.92 (define @t449 () (= tptp.sz00 @t442)) % 15.44/15.92 (define @t450 () (not (tptp.aInteger0 @t442))) % 15.44/15.92 (define @t451 () (or @t450 @t449 @t448 @t446 @t444 (not (= @t334 @t443)))) % 15.44/15.92 (define @t452 () (not @t451)) % 15.44/15.92 (define @t453 () (not (= @t443 @t334))) % 15.44/15.92 (define @t454 () (or @t450 @t449 @t448 @t446 @t444 @t453)) % 15.44/15.92 (define @t455 () (not @t454)) % 15.44/15.92 (define @t456 () (@list @t451)) % 15.44/15.92 (define @t457 () (tptp.aDivisorOf0 @t442 @t306)) % 15.44/15.92 (define @t458 () (not @t457)) % 15.44/15.92 (define @t459 () (or @t458 @t446)) % 15.44/15.92 (define @t460 () (not @t162)) % 15.44/15.92 (define @t461 () (not @t154)) % 15.44/15.92 (define @t462 () (not @t165)) % 15.44/15.92 (define @t463 () (and @t458 @t307 @t165 @t162 @t137 @t154 @t447)) % 15.44/15.92 (assume @p1 (forall @t3 (=> @t2 true))) % 15.44/15.92 (assume @p2 (tptp.aInteger0 tptp.sz00)) % 15.44/15.92 (assume @p3 @t4) % 15.44/15.92 (assume @p4 @t7) % 15.44/15.92 (assume @p5 (forall @t12 (=> @t11 (tptp.aInteger0 @t9)))) % 15.44/15.92 (assume @p6 @t15) % 15.44/15.92 (assume @p7 (forall @t20 (=> @t19 (= (tptp.sdtpldt0 @t1 @t17) (tptp.sdtpldt0 @t9 @t16))))) % 15.44/15.92 (assume @p8 (forall @t12 (=> @t11 (= @t9 (tptp.sdtpldt0 @t8 @t1))))) % 15.44/15.92 (assume @p9 (forall @t3 (=> @t2 (and (= (tptp.sdtpldt0 @t1 tptp.sz00) @t1) (= @t1 (tptp.sdtpldt0 tptp.sz00 @t1)))))) % 15.44/15.92 (assume @p10 (forall @t3 (=> @t2 (and (= (tptp.sdtpldt0 @t1 @t5) tptp.sz00) (= tptp.sz00 (tptp.sdtpldt0 @t5 @t1)))))) % 15.44/15.92 (assume @p11 @t23) % 15.44/15.92 (assume @p12 @t25) % 15.44/15.92 (assume @p13 @t30) % 15.44/15.92 (assume @p14 (forall @t20 (=> @t19 (and (= (tptp.sdtasdt0 @t1 @t17) (tptp.sdtpldt0 @t13 @t31)) (= (tptp.sdtasdt0 @t9 @t16) (tptp.sdtpldt0 @t31 @t21)))))) % 15.44/15.92 (assume @p15 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz00) tptp.sz00) (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 @t1)))))) % 15.44/15.92 (assume @p16 @t37) % 15.44/15.92 (assume @p17 (forall @t12 (=> @t11 (=> (= @t13 tptp.sz00) (or @t39 @t38))))) % 15.44/15.92 (assume @p18 (forall @t3 (=> @t2 (forall @t46 (= @t45 @t44))))) % 15.44/15.92 (assume @p19 (forall @t20 (=> @t49 (= @t47 (tptp.aDivisorOf0 @t16 (tptp.sdtpldt0 @t1 (tptp.smndt0 @t8))))))) % 15.44/15.92 (assume @p20 (forall @t12 (=> @t50 (tptp.sdteqdtlpzmzozddtrp0 @t1 @t1 @t8)))) % 15.44/15.92 (assume @p21 (forall @t20 (=> @t49 (=> @t47 (tptp.sdteqdtlpzmzozddtrp0 @t8 @t1 @t16))))) % 15.44/15.92 (assume @p22 (forall @t53 (=> (and @t2 @t10 @t18 @t48 @t52) (=> (and @t47 (tptp.sdteqdtlpzmzozddtrp0 @t8 @t51 @t16)) (tptp.sdteqdtlpzmzozddtrp0 @t1 @t51 @t16))))) % 15.44/15.92 (assume @p23 (forall @t53 (=> (and @t2 @t10 @t18 @t48 @t52 (not (= @t51 tptp.sz00))) (=> (tptp.sdteqdtlpzmzozddtrp0 @t1 @t8 (tptp.sdtasdt0 @t16 @t51)) (and @t47 (tptp.sdteqdtlpzmzozddtrp0 @t1 @t8 @t51)))))) % 15.44/15.92 (assume @p24 (forall @t3 (=> (and @t2 (not @t39)) (=> (tptp.isPrime0 @t1) true)))) % 15.44/15.92 (assume @p25 @t62) % 15.44/15.92 (assume @p26 (forall @t3 (=> @t63 true))) % 15.44/15.92 (assume @p27 (forall @t3 (=> @t63 (forall @t46 (=> @t64 true))))) % 15.44/15.92 (assume @p28 (forall @t3 (=> @t63 (forall @t46 (= (tptp.aSubsetOf0 @t8 @t1) (and @t67 (forall @t41 (=> @t66 @t65)))))))) % 15.44/15.92 (assume @p29 (forall @t3 (=> @t63 (=> @t68 true)))) % 15.44/15.92 (assume @p30 (forall @t12 (=> @t77 (forall @t41 (= (= @t16 @t74) (and @t73 (forall @t72 (= @t71 (and @t52 (or @t70 @t69)))))))))) % 15.44/15.92 (assume @p31 (forall @t12 (=> @t77 (forall @t41 (= (= @t16 @t78) (and @t73 (forall @t72 (= @t71 (and @t52 @t70 @t69))))))))) % 15.44/15.92 (assume @p32 (forall @t3 (=> (and @t63 (forall @t46 (=> @t64 @t75))) (forall @t46 (= (= @t8 @t79) (and @t67 (forall @t41 (= @t66 (and @t18 (exists @t72 (and @t70 (tptp.aElementOf0 @t16 @t51)))))))))))) % 15.44/15.92 (assume @p33 (forall @t3 (=> @t76 (forall @t46 (= (= @t8 @t80) (and @t67 (forall @t41 (= @t66 (and @t18 (not @t65)))))))))) % 15.44/15.92 (assume @p34 (forall @t12 (=> @t50 (forall @t41 (= (= @t16 @t81) (and @t73 (forall @t72 (= @t71 (and @t52 (tptp.sdteqdtlpzmzozddtrp0 @t51 @t1 @t8)))))))))) % 15.44/15.92 (assume @p35 (forall @t3 (=> @t76 (= @t82 (forall @t46 (=> @t64 (exists @t41 (and @t18 @t48 (tptp.aSubsetOf0 (tptp.szAzrzSzezqlpdtcmdtrp0 @t8 @t16) @t1))))))))) % 15.44/15.92 (assume @p36 (forall @t3 (=> @t76 (= @t83 (tptp.isOpen0 @t80))))) % 15.44/15.92 (assume @p37 (forall @t3 (=> (and @t63 (forall @t46 (=> @t64 (and @t75 @t84)))) (tptp.isOpen0 @t79)))) % 15.44/15.92 (assume @p38 (forall @t12 (=> (and @t76 @t75 @t82 @t84) (tptp.isOpen0 @t78)))) % 15.44/15.92 (assume @p39 (forall @t12 (=> (and @t76 @t75 @t83 @t85) (tptp.isClosed0 @t74)))) % 15.44/15.92 (assume @p40 (forall @t3 (=> (and @t63 @t68 (forall @t46 (=> @t64 (and @t75 @t85)))) (tptp.isClosed0 @t79)))) % 15.44/15.92 (assume @p41 (forall @t12 (=> @t50 (and (tptp.aSubsetOf0 @t81 tptp.cS1395) (tptp.isClosed0 @t81))))) % 15.44/15.92 (assume @p42 (and (tptp.aSet0 tptp.xS) (forall @t3 (and (=> @t86 (exists @t46 (and @t10 @t43 @t57 @t95 @t94 @t88))) (=> (exists @t46 (and @t10 @t43 @t57 (=> (and @t95 @t94) @t88))) @t86))) (= tptp.xS tptp.cS2043))) % 15.44/15.92 (assume @p43 @t134) % 15.44/15.92 (assume @p44 true) % 15.44/15.92 (step @p45 :rule bool-impl-elim :args (@t2 @t135)) % 15.44/15.92 (step @p46 :rule cong :premises (@p45) :args ((forall @t3 (=> @t2 @t135)))) % 15.44/15.92 (step @p47 :rule refl :args (@t26)) % 15.44/15.92 (step @p48 :rule eq-symm :args (@t27 @t1)) % 15.44/15.92 (step @p49 :rule nary_cong :premises (@p48 @p47) :args (@t28)) % 15.44/15.92 (step @p50 :rule refl :args (@t2)) % 15.44/15.92 (step @p51 :rule cong :premises (@p50 @p49) :args (@t29)) % 15.44/15.92 (step @p52 :rule cong :premises (@p51) :args (@t30)) % 15.44/15.92 (step @p53 :rule trans :premises (@p52 @p46)) % 15.44/15.92 (step @p54 :rule eq_resolve :premises (@p13 @p53)) % 15.44/15.92 (step @p55 :rule aci_norm :args ((= @t138 @t137))) % 15.44/15.92 (step @p56 :rule refl :args (@t139)) % 15.44/15.92 (step @p57 :rule nary_cong :premises (@p56 @p55) :args (@t140)) % 15.44/15.92 (step @p58 :rule refl :args (@t142)) % 15.44/15.92 (step @p59 :rule cong :premises (@p58 @p57) :args ((=> @t142 @t140))) % 15.44/15.92 (assume-push @p960 @t142) % 15.44/15.92 (step @p61 :rule instantiate :premises (@p54) :args (@t143)) % 15.44/15.92 (step-pop @p961 :rule scope :premises (@p61)) % 15.44/15.92 (step @p62 :rule process_scope :premises (@p961) :args (@t140)) % 15.44/15.92 (step @p64 :rule eq_resolve :premises (@p62 @p59)) % 15.44/15.92 (step @p65 :rule implies_elim :premises (@p64)) % 15.44/15.92 (step @p66 :rule chain_m_resolution :premises (@p65 @p54) :args (@t144 @t145 (@list @t142))) % 15.44/15.92 (step @p67 :rule cnf_or_pos :args (@t144)) % 15.44/15.92 (step @p68 :rule reordering :premises (@p67) :args ((or @t139 @t137 (not @t144)))) % 15.44/15.92 (step @p69 :rule chain_m_resolution :premises (@p68 @p3 @p66) :args (@t137 @t146 (@list @t4 @t144))) % 15.44/15.92 (step @p70 :rule aci_norm :args ((= (or @t149 @t22) (or @t141 @t148 @t147 @t22)))) % 15.44/15.92 (step @p71 :rule refl :args (@t22)) % 15.44/15.92 (step @p72 :rule aci_norm :args ((= (or @t141 (or @t148 @t147)) @t149))) % 15.44/15.92 (step @p73 :rule bool-and-de-morgan :args (@t10 @t18 true)) % 15.44/15.92 (step @p74 :rule refl :args (@t141)) % 15.44/15.92 (step @p75 :rule nary_cong :premises (@p74 @p73) :args ((or @t141 (not (and @t10 @t18))))) % 15.44/15.92 (step @p76 :rule bool-and-de-morgan :args (@t2 @t10 (and @t18))) % 15.44/15.92 (step @p77 :rule trans :premises (@p76 @p75)) % 15.44/15.92 (step @p78 :rule trans :premises (@p77 @p72)) % 15.44/15.92 (step @p79 :rule nary_cong :premises (@p78 @p71) :args ((or (not @t19) @t22))) % 15.44/15.92 (step @p80 :rule trans :premises (@p79 @p70)) % 15.44/15.92 (step @p81 :rule bool-impl-elim :args (@t19 @t22)) % 15.44/15.92 (step @p82 :rule trans :premises (@p81 @p80)) % 15.44/15.92 (step @p83 :rule cong :premises (@p82) :args (@t23)) % 15.44/15.92 (step @p84 :rule eq_resolve :premises (@p11 @p83)) % 15.44/15.92 (step @p85 :rule instantiate :premises (@p84) :args ((@list tptp.sz10 tptp.sz10 @t32))) % 15.44/15.92 (step @p86 :rule bool-impl-elim :args (@t2 @t6)) % 15.44/15.92 (step @p87 :rule cong :premises (@p86) :args (@t7)) % 15.44/15.92 (step @p88 :rule eq_resolve :premises (@p4 @p87)) % 15.44/15.92 (step @p89 :rule instantiate :premises (@p88) :args (@t143)) % 15.44/15.92 (step @p90 :rule cnf_or_pos :args (@t151)) % 15.44/15.92 (step @p91 :rule reordering :premises (@p90) :args ((or @t139 @t150 (not @t151)))) % 15.44/15.92 (step @p92 :rule chain_m_resolution :premises (@p91 @p3 @p89) :args (@t150 @t146 (@list @t4 @t151))) % 15.44/15.92 (step @p93 :rule cnf_or_pos :args (@t156)) % 15.44/15.92 (step @p94 :rule factoring :premises (@p93)) % 15.44/15.92 (step @p95 :rule reordering :premises (@p94) :args ((or @t139 @t155 @t154 (not @t156)))) % 15.44/15.92 (step @p96 :rule chain_m_resolution :premises (@p95 @p3 @p92 @p85) :args (@t154 @t157 (@list @t4 @t150 @t156))) % 15.44/15.92 (step @p97 :rule aci_norm :args ((= (or @t158 @t24) (or @t141 @t148 @t24)))) % 15.44/15.92 (step @p98 :rule refl :args (@t24)) % 15.44/15.92 (step @p99 :rule bool-and-de-morgan :args (@t2 @t10 true)) % 15.44/15.92 (step @p100 :rule nary_cong :premises (@p99 @p98) :args ((or @t159 @t24))) % 15.44/15.92 (step @p101 :rule trans :premises (@p100 @p97)) % 15.44/15.92 (step @p102 :rule bool-impl-elim :args (@t11 @t24)) % 15.44/15.92 (step @p103 :rule trans :premises (@p102 @p101)) % 15.44/15.92 (step @p104 :rule cong :premises (@p103) :args (@t25)) % 15.44/15.92 (step @p105 :rule eq_resolve :premises (@p12 @p104)) % 15.44/15.92 (step @p106 :rule instantiate :premises (@p105) :args (@t160)) % 15.44/15.92 (step @p107 :rule cnf_or_pos :args (@t163)) % 15.44/15.92 (step @p108 :rule reordering :premises (@p107) :args ((or @t139 @t155 @t162 (not @t163)))) % 15.44/15.92 (step @p109 :rule chain_m_resolution :premises (@p108 @p3 @p92 @p106) :args (@t162 @t157 (@list @t4 @t150 @t163))) % 15.44/15.92 (step @p110 :rule bool-impl-elim :args (@t2 @t164)) % 15.44/15.92 (step @p111 :rule cong :premises (@p110) :args ((forall @t3 (=> @t2 @t164)))) % 15.44/15.92 (step @p112 :rule refl :args (@t33)) % 15.44/15.92 (step @p113 :rule eq-symm :args (@t34 @t5)) % 15.44/15.92 (step @p114 :rule nary_cong :premises (@p113 @p112) :args (@t35)) % 15.44/15.92 (step @p115 :rule cong :premises (@p50 @p114) :args (@t36)) % 15.44/15.92 (step @p116 :rule cong :premises (@p115) :args (@t37)) % 15.44/15.92 (step @p117 :rule trans :premises (@p116 @p111)) % 15.44/15.92 (step @p118 :rule eq_resolve :premises (@p16 @p117)) % 15.44/15.92 (step @p119 :rule instantiate :premises (@p118) :args (@t143)) % 15.44/15.92 (step @p120 :rule cnf_or_pos :args (@t167)) % 15.44/15.92 (step @p121 :rule reordering :premises (@p120) :args ((or @t139 @t166 (not @t167)))) % 15.44/15.92 (step @p122 :rule chain_m_resolution :premises (@p121 @p3 @p119) :args (@t166 @t146 (@list @t4 @t167))) % 15.44/15.92 (step @p123 :rule cnf_and_pos :args (@t166 0)) % 15.44/15.92 (step @p124 :rule reordering :premises (@p123) :args ((or @t165 (not @t166)))) % 15.44/15.92 (step @p125 :rule chain_m_resolution :premises (@p124 @p122) :args (@t165 @t145 (@list @t166))) % 15.44/15.92 (step @p126 :rule refl :args (@t170)) % 15.44/15.92 (step @p127 :rule eq-symm :args (@t171 @t98)) % 15.44/15.92 (step @p128 :rule cong :premises (@p127) :args (@t172)) % 15.44/15.92 (step @p129 :rule nary_cong :premises (@p128 @p126) :args (@t173)) % 15.44/15.92 (step @p130 :rule eq-symm :args (@t171 @t176)) % 15.44/15.92 (step @p131 :rule cong :premises (@p130) :args (@t177)) % 15.44/15.92 (step @p132 :rule refl :args (@t178)) % 15.44/15.92 (step @p133 :rule nary_cong :premises (@p132 @p131) :args (@t179)) % 15.44/15.92 (step @p134 :rule cong :premises (@p133 @p129) :args (@t180)) % 15.44/15.92 (step @p135 :rule refl :args (@t184)) % 15.44/15.92 (step @p136 :rule cong :premises (@p135 @p134) :args (@t185)) % 15.44/15.92 (step @p137 :rule refl :args (@t203)) % 15.44/15.92 (step @p138 :rule cong :premises (@p137 @p136) :args (@t204)) % 15.44/15.92 (step @p139 :rule cong :premises (@p138) :args ((not @t204))) % 15.44/15.92 (step @p140 :rule and_elim :premises (@p42) :args (2)) % 15.44/15.92 (step @p141 :rule cong :premises (@p140) :args (@t96)) % 15.44/15.92 (step @p142 :rule cong :premises (@p141) :args (@t97)) % 15.44/15.92 (step @p143 :rule refl :args (tptp.cS2076)) % 15.44/15.92 (step @p144 :rule cong :premises (@p143 @p142) :args (@t205)) % 15.44/15.92 (step @p145 :rule refl :args (@t98)) % 15.44/15.92 (step @p146 :rule refl :args (@t1)) % 15.44/15.92 (step @p147 :rule cong :premises (@p146 @p142) :args (@t99)) % 15.44/15.92 (step @p148 :rule cong :premises (@p147 @p145) :args (@t100)) % 15.44/15.92 (step @p149 :rule cong :premises (@p148) :args (@t101)) % 15.44/15.92 (step @p150 :rule nary_cong :premises (@p149 @p144) :args (@t206)) % 15.44/15.92 (step @p151 :rule cong :premises (@p146 @p141) :args (@t103)) % 15.44/15.92 (step @p152 :rule cong :premises (@p151) :args (@t104)) % 15.44/15.92 (step @p153 :rule nary_cong :premises (@p50 @p152) :args (@t105)) % 15.44/15.92 (step @p154 :rule cong :premises (@p147 @p153) :args (@t106)) % 15.44/15.92 (step @p155 :rule cong :premises (@p154) :args (@t107)) % 15.44/15.92 (step @p156 :rule cong :premises (@p142) :args (@t108)) % 15.44/15.92 (step @p157 :rule nary_cong :premises (@p156 @p155) :args (@t109)) % 15.44/15.92 (step @p158 :rule cong :premises (@p157 @p150) :args (@t207)) % 15.44/15.92 (step @p159 :rule refl :args (@t181)) % 15.44/15.92 (step @p160 :rule refl :args (@t8)) % 15.44/15.92 (step @p161 :rule cong :premises (@p160 @p140) :args (@t112)) % 15.44/15.92 (step @p162 :rule cong :premises (@p161) :args (@t208)) % 15.44/15.92 (step @p163 :rule nary_cong :premises (@p162 @p159) :args (@t209)) % 15.44/15.92 (step @p164 :rule cong :premises (@p163) :args (@t210)) % 15.44/15.92 (step @p165 :rule cong :premises (@p164) :args (@t211)) % 15.44/15.92 (step @p166 :rule nary_cong :premises (@p50 @p165) :args (@t212)) % 15.44/15.92 (step @p167 :rule cong :premises (@p151 @p166) :args (@t213)) % 15.44/15.92 (step @p168 :rule cong :premises (@p167) :args (@t214)) % 15.44/15.92 (step @p169 :rule cong :premises (@p141) :args (@t118)) % 15.44/15.92 (step @p170 :rule nary_cong :premises (@p169 @p168) :args (@t215)) % 15.44/15.92 (step @p171 :rule cong :premises (@p170 @p158) :args (@t216)) % 15.44/15.92 (step @p172 :rule refl :args (@t187)) % 15.44/15.92 (step @p173 :rule refl :args (@t189)) % 15.44/15.92 (step @p174 :rule nary_cong :premises (@p165 @p151) :args (@t217)) % 15.44/15.92 (step @p175 :rule nary_cong :premises (@p174 @p173 @p172) :args (@t218)) % 15.44/15.92 (step @p176 :rule refl :args (@t199)) % 15.44/15.92 (step @p177 :rule refl :args (@t201)) % 15.44/15.92 (step @p178 :rule refl :args (@t200)) % 15.44/15.92 (step @p179 :rule cong :premises (@p178 @p140) :args (@t219)) % 15.44/15.92 (step @p180 :rule cong :premises (@p179) :args (@t220)) % 15.44/15.92 (step @p181 :rule nary_cong :premises (@p180 @p177) :args (@t221)) % 15.44/15.92 (step @p182 :rule nary_cong :premises (@p181 @p152) :args (@t222)) % 15.44/15.92 (step @p183 :rule nary_cong :premises (@p182 @p176) :args (@t223)) % 15.44/15.92 (step @p184 :rule nary_cong :premises (@p183 @p175) :args (@t224)) % 15.44/15.92 (step @p185 :rule refl :args (@t141)) % 15.44/15.92 (step @p186 :rule nary_cong :premises (@p185 @p184) :args (@t225)) % 15.44/15.92 (step @p187 :rule cong :premises (@p186) :args (@t226)) % 15.44/15.92 (step @p188 :rule cong :premises (@p187 @p171) :args (@t227)) % 15.44/15.92 (step @p189 :rule cong :premises (@p188) :args ((not @t227))) % 15.44/15.92 (step @p190 :rule trans :premises (@p189 @p139)) % 15.44/15.92 (step @p191 :rule eq-symm :args (@t97 tptp.cS2076)) % 15.44/15.92 (step @p192 :rule refl :args (@t101)) % 15.44/15.92 (step @p193 :rule nary_cong :premises (@p192 @p191) :args (@t102)) % 15.44/15.92 (step @p194 :rule refl :args (@t109)) % 15.44/15.92 (step @p195 :rule cong :premises (@p194 @p193) :args (@t110)) % 15.44/15.92 (step @p196 :rule bool-and-de-morgan :args (@t112 @t111 true)) % 15.44/15.92 (step @p197 :rule cong :premises (@p196) :args (@t228)) % 15.44/15.92 (step @p198 :rule cong :premises (@p197) :args (@t229)) % 15.44/15.92 (step @p199 :rule exists-elim :args ((= @t114 @t229))) % 15.44/15.92 (step @p200 :rule trans :premises (@p199 @p198)) % 15.44/15.92 (step @p201 :rule nary_cong :premises (@p50 @p200) :args (@t115)) % 15.44/15.92 (step @p202 :rule refl :args (@t103)) % 15.44/15.92 (step @p203 :rule cong :premises (@p202 @p201) :args (@t116)) % 15.44/15.92 (step @p204 :rule cong :premises (@p203) :args (@t117)) % 15.44/15.92 (step @p205 :rule refl :args (@t118)) % 15.44/15.92 (step @p206 :rule nary_cong :premises (@p205 @p204) :args (@t119)) % 15.44/15.92 (step @p207 :rule cong :premises (@p206 @p195) :args (@t120)) % 15.44/15.92 (step @p208 :rule aci_norm :args ((= @t231 @t218))) % 15.44/15.92 (step @p209 :rule refl :args (@t223)) % 15.44/15.92 (step @p210 :rule nary_cong :premises (@p209 @p208) :args (@t232)) % 15.44/15.92 (step @p211 :rule nary_cong :premises (@p185 @p210) :args (@t233)) % 15.44/15.92 (step @p212 :rule cong :premises (@p211) :args (@t234)) % 15.44/15.92 (step @p213 :rule quant-merge-prenex :args ((= (forall @t3 @t236) @t234))) % 15.44/15.92 (step @p214 :rule refl :args (@t217)) % 15.44/15.92 (step @p215 :rule alpha_equiv :args (@t238 (@list @t186 @t188) (@list @t8 @t239))) % 15.44/15.92 (step @p216 :rule nary_cong :premises (@p215 @p214) :args (@t240)) % 15.44/15.92 (step @p217 :rule quant-miniscope-or :args ((= @t241 @t240))) % 15.44/15.92 (step @p218 :rule quant-unused-vars :args ((= @t242 @t241))) % 15.44/15.92 (step @p219 :rule trans :premises (@p218 @p217)) % 15.44/15.92 (step @p220 :rule trans :premises (@p219 @p216)) % 15.44/15.92 (step @p221 :rule refl :args (@t199)) % 15.44/15.92 (step @p222 :rule quant-unused-vars :args ((= @t244 @t104))) % 15.44/15.92 (step @p223 :rule alpha_equiv :args (@t245 (@list @t200) (@list @t8))) % 15.44/15.92 (step @p224 :rule nary_cong :premises (@p223 @p222) :args (@t246)) % 15.44/15.92 (step @p225 :rule quant-miniscope-and :args ((= @t247 @t246))) % 15.44/15.92 (step @p226 :rule trans :premises (@p225 @p224)) % 15.44/15.92 (step @p227 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:args (@t459)) % 15.44/15.92 (step @p903 :rule reordering :premises (@p902) :args ((or @t446 @t458 (not @t459)))) % 15.44/15.92 (step @p904 :rule chain_m_resolution :premises (@p903 @p901 @p895) :args (@t458 @t146 (@list @t445 @t459))) % 15.44/15.92 (step @p905 :rule bool-double-not-elim :args (@t457)) % 15.44/15.92 (step @p906 :rule refl :args (@t460)) % 15.44/15.92 (step @p907 :rule refl :args (@t461)) % 15.44/15.92 (step @p908 :rule refl :args (@t462)) % 15.44/15.92 (step @p909 :rule refl :args (@t399)) % 15.44/15.92 (step @p910 :rule refl :args (@t331)) % 15.44/15.92 (step @p911 :rule nary_cong :premises (@p910 @p909 @p908 @p907 @p906 @p858 @p905) :args ((or @t331 @t399 @t462 @t461 @t460 @t448 (not @t458)))) % 15.44/15.92 (assume-push @p1080 @t458) % 15.44/15.92 (assume-push @p1081 @t307) % 15.44/15.92 (assume-push @p1082 @t165) % 15.44/15.92 (assume-push @p1083 @t162) % 15.44/15.92 (assume-push @p1084 @t137) % 15.44/15.92 (assume-push @p1085 @t154) % 15.44/15.92 (assume-push @p1086 @t447) % 15.44/15.92 (step @p919 :rule evaluate :args ((= true false))) % 15.44/15.92 (step @p920 :rule false_intro :premises (@p1080)) % 15.44/15.92 (step @p817 :rule symm :premises (@p125)) % 15.44/15.92 (step @p729 :rule refl :args (@t32)) % 15.44/15.92 (step @p730 :rule symm :premises (@p69)) % 15.44/15.92 (step @p731 :rule cong :premises (@p730 @p729) :args (@t152)) % 15.44/15.92 (step @p732 :rule symm :premises (@p109)) % 15.44/15.92 (step @p921 :rule symm :premises (@p1081)) % 15.44/15.92 (step @p922 :rule trans :premises (@p921 @p125 @p732)) % 15.44/15.92 (step @p923 :rule cong :premises (@p730 @p922) :args (@t435)) % 15.44/15.92 (step @p736 :rule refl :args (@t306)) % 15.44/15.92 (step @p737 :rule cong :premises (@p69 @p736) :args (@t334)) % 15.44/15.92 (step @p924 :rule trans :premises (@p737 @p923 @p96 @p731 @p109 @p817 @p1081)) % 15.44/15.92 (step @p925 :rule refl :args (@t442)) % 15.44/15.92 (step @p926 :rule cong :premises (@p925 @p924) :args (@t447)) % 15.44/15.92 (step @p927 :rule true_intro :premises (@p1086)) % 15.44/15.92 (step @p928 :rule symm :premises (@p927)) % 15.44/15.92 (step @p929 :rule trans :premises (@p928 @p926 @p920)) % 15.44/15.92 (step @p930 false :rule eq_resolve :premises (@p929 @p919)) % 15.44/15.92 (step-pop @p1087 :rule scope :premises (@p930)) % 15.44/15.92 (step-pop @p1088 :rule scope :premises (@p1087)) % 15.44/15.92 (step-pop @p1089 :rule scope :premises (@p1088)) % 15.44/15.92 (step-pop @p1090 :rule scope :premises (@p1089)) % 15.44/15.92 (step-pop @p1091 :rule scope :premises (@p1090)) % 15.44/15.92 (step-pop @p1092 :rule scope :premises (@p1091)) % 15.44/15.92 (step-pop @p1093 :rule scope :premises (@p1092)) % 15.44/15.92 (step @p931 :rule process_scope :premises (@p1093) :args (false)) % 15.44/15.92 (assume-push @p1094 @t307) % 15.44/15.92 (assume-push @p1095 @t137) % 15.44/15.92 (assume-push @p1096 @t165) % 15.44/15.92 (assume-push @p1097 @t154) % 15.44/15.92 (assume-push @p1098 @t162) % 15.44/15.92 (assume-push @p1099 @t447) % 15.44/15.92 (assume-push @p1100 @t458) % 15.44/15.92 (step @p946 :rule and_intro :premises (@p1100 @p1094 @p125 @p109 @p69 @p96 @p1099)) % 15.44/15.92 (step-pop @p1101 :rule scope :premises (@p946)) % 15.44/15.92 (step-pop @p1102 :rule scope :premises (@p1101)) % 15.44/15.92 (step-pop @p1103 :rule scope :premises (@p1102)) % 15.44/15.92 (step-pop @p1104 :rule scope :premises (@p1103)) % 15.44/15.92 (step-pop @p1105 :rule scope :premises (@p1104)) % 15.44/15.92 (step-pop @p1106 :rule scope :premises (@p1105)) % 15.44/15.92 (step-pop @p1107 :rule scope :premises (@p1106)) % 15.44/15.92 (step @p947 :rule process_scope :premises (@p1107) :args (@t463)) % 15.44/15.92 (step @p955 :rule implies_elim :premises (@p947)) % 15.44/15.92 (step @p956 :rule resolution :premises (@p955 @p931) :args (true @t463)) % 15.44/15.92 (step @p957 :rule not_and :premises (@p956)) % 15.44/15.92 (step @p958 :rule eq_resolve :premises (@p957 @p911)) % 15.44/15.92 (step @p959 false :rule chain_m_resolution :premises (@p958 @p904 @p879 @p711 @p125 @p109 @p96 @p69) :args (false (@list true false false false false false false) (@list @t457 @t447 @t307 @t165 @t162 @t154 @t137))) % 15.44/15.92 ) % 15.44/15.92 % SZS output end Proof % 15.44/15.92 % cvc5 exiting %------------------------------------------------------------------------------