%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : RNG112+4 : TPTP v9.2.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n004.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 08:45:43 AM UTC 2026 % Result : Theorem 4.32s 4.55s % Output : Proof 4.32s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : RNG112+4 : TPTP v9.2.1. Released v4.0.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.15/0.34 % Computer : n004.cluster.edu % 0.15/0.34 % Model : x86_64 x86_64 % 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.34 % Memory : 8042.1875MB % 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.34 % CPULimit : 300 % 0.15/0.34 % WCLimit : 300 % 0.15/0.34 % DateTime : Tue Jun 2 14:08:07 EDT 2026 % 0.15/0.34 % CPUTime : % 0.30/0.50 %----Proving TF0_NAR, FOF, or CNF % 4.32/4.55 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 4.32/4.55 % SZS status Theorem % 4.32/4.55 % SZS output start Proof % 4.32/4.55 ( % 4.32/4.55 (declare-sort $$unsorted 0) % 4.32/4.55 (declare-const tptp.xI $$unsorted) % 4.32/4.55 (declare-const tptp.xc $$unsorted) % 4.32/4.55 (declare-const tptp.xa $$unsorted) % 4.32/4.55 (declare-const tptp.slsdtgt0 (-> $$unsorted $$unsorted)) % 4.32/4.55 (declare-const tptp.aDivisorOf0 (-> $$unsorted $$unsorted Bool)) % 4.32/4.55 (declare-const tptp.iLess0 (-> $$unsorted $$unsorted Bool)) % 4.32/4.55 (declare-const tptp.sbrdtbr0 (-> $$unsorted $$unsorted)) % 4.32/4.55 (declare-const tptp.aElement0 (-> $$unsorted Bool)) % 4.32/4.55 (declare-const tptp.sz00 $$unsorted) % 4.32/4.55 (declare-const tptp.sz10 $$unsorted) % 4.32/4.55 (declare-const tptp.aGcdOfAnd0 (-> $$unsorted $$unsorted $$unsorted Bool)) % 4.32/4.55 (declare-const tptp.smndt0 (-> $$unsorted $$unsorted)) % 4.32/4.55 (declare-const tptp.sdtpldt0 (-> $$unsorted $$unsorted $$unsorted)) % 4.32/4.55 (declare-const tptp.sdtasasdt0 (-> $$unsorted $$unsorted $$unsorted)) % 4.32/4.55 (declare-const tptp.aIdeal0 (-> $$unsorted Bool)) % 4.32/4.55 (declare-const tptp.misRelativelyPrime0 (-> $$unsorted $$unsorted Bool)) % 4.32/4.55 (declare-const tptp.sdtasdt0 (-> $$unsorted $$unsorted $$unsorted)) % 4.32/4.55 (declare-const tptp.doDivides0 (-> $$unsorted $$unsorted Bool)) % 4.32/4.55 (declare-const tptp.aSet0 (-> $$unsorted Bool)) % 4.32/4.55 (declare-const tptp.aElementOf0 (-> $$unsorted $$unsorted Bool)) % 4.32/4.55 (declare-const tptp.sdteqdtlpzmzozddtrp0 (-> $$unsorted $$unsorted $$unsorted Bool)) % 4.32/4.55 (declare-const tptp.xb $$unsorted) % 4.32/4.55 (declare-const tptp.sdtpldt1 (-> $$unsorted $$unsorted $$unsorted)) % 4.32/4.55 (declare-const tptp.aNaturalNumber0 (-> $$unsorted Bool)) % 4.32/4.55 (define @t1 () (@var "W0" $$unsorted)) % 4.32/4.55 (define @t2 () (tptp.aElement0 @t1)) % 4.32/4.55 (define @t3 () (@list @t1)) % 4.32/4.55 (define @t4 () (tptp.smndt0 @t1)) % 4.32/4.55 (define @t5 () (@var "W1" $$unsorted)) % 4.32/4.55 (define @t6 () (tptp.sdtpldt0 @t1 @t5)) % 4.32/4.55 (define @t7 () (tptp.aElement0 @t5)) % 4.32/4.55 (define @t8 () (and @t2 @t7)) % 4.32/4.55 (define @t9 () (@list @t1 @t5)) % 4.32/4.55 (define @t10 () (tptp.sdtasdt0 @t1 @t5)) % 4.32/4.55 (define @t11 () (@var "W2" $$unsorted)) % 4.32/4.55 (define @t12 () (tptp.sdtpldt0 @t5 @t11)) % 4.32/4.55 (define @t13 () (tptp.aElement0 @t11)) % 4.32/4.55 (define @t14 () (and @t2 @t7 @t13)) % 4.32/4.55 (define @t15 () (@list @t1 @t5 @t11)) % 4.32/4.55 (define @t16 () (tptp.sdtasdt0 @t5 @t1)) % 4.32/4.55 (define @t17 () (tptp.sdtasdt0 @t1 @t11)) % 4.32/4.55 (define @t18 () (tptp.smndt0 tptp.sz10)) % 4.32/4.55 (define @t19 () (= @t5 tptp.sz00)) % 4.32/4.55 (define @t20 () (= @t1 tptp.sz00)) % 4.32/4.55 (define @t21 () (tptp.aSet0 @t1)) % 4.32/4.55 (define @t22 () (tptp.aElementOf0 @t5 @t1)) % 4.32/4.55 (define @t23 () (@list @t5)) % 4.32/4.55 (define @t24 () (tptp.aElementOf0 @t11 @t1)) % 4.32/4.55 (define @t25 () (tptp.aElementOf0 @t11 @t5)) % 4.32/4.55 (define @t26 () (@list @t11)) % 4.32/4.55 (define @t27 () (tptp.aSet0 @t5)) % 4.32/4.55 (define @t28 () (and @t21 @t27)) % 4.32/4.55 (define @t29 () (@var "W3" $$unsorted)) % 4.32/4.55 (define @t30 () (@var "W5" $$unsorted)) % 4.32/4.55 (define @t31 () (@var "W4" $$unsorted)) % 4.32/4.55 (define @t32 () (tptp.aElementOf0 @t29 @t11)) % 4.32/4.55 (define @t33 () (@list @t29)) % 4.32/4.55 (define @t34 () (tptp.aSet0 @t11)) % 4.32/4.55 (define @t35 () (tptp.sdtpldt1 @t1 @t5)) % 4.32/4.55 (define @t36 () (tptp.sdtasasdt0 @t1 @t5)) % 4.32/4.55 (define @t37 () (tptp.sdtasdt0 @t11 @t5)) % 4.32/4.55 (define @t38 () (tptp.aIdeal0 @t1)) % 4.32/4.55 (define @t39 () (and @t38 (tptp.aIdeal0 @t5))) % 4.32/4.55 (define @t40 () (tptp.aElement0 @t29)) % 4.32/4.55 (define @t41 () (@list @t11 @t29)) % 4.32/4.55 (define @t42 () (tptp.aNaturalNumber0 @t1)) % 4.32/4.55 (define @t43 () (tptp.sbrdtbr0 @t1)) % 4.32/4.55 (define @t44 () (not @t20)) % 4.32/4.55 (define @t45 () (tptp.sbrdtbr0 @t5)) % 4.32/4.55 (define @t46 () (not @t19)) % 4.32/4.55 (define @t47 () (tptp.slsdtgt0 @t1)) % 4.32/4.55 (define @t48 () (tptp.sdtasdt0 tptp.xc @t1)) % 4.32/4.55 (define @t49 () (tptp.aElement0 tptp.xc)) % 4.32/4.55 (define @t50 () (tptp.slsdtgt0 tptp.xb)) % 4.32/4.55 (define @t51 () (tptp.slsdtgt0 tptp.xa)) % 4.32/4.55 (define @t52 () (tptp.sdtpldt1 @t51 @t50)) % 4.32/4.55 (define @t53 () (tptp.aElementOf0 @t11 @t50)) % 4.32/4.55 (define @t54 () (tptp.aElementOf0 @t5 @t51)) % 4.32/4.55 (define @t55 () (and @t54 @t53 (= @t12 @t1))) % 4.32/4.55 (define @t56 () (@list @t5 @t11)) % 4.32/4.55 (define @t57 () (exists @t56 @t55)) % 4.32/4.55 (define @t58 () (tptp.aElementOf0 @t1 tptp.xI)) % 4.32/4.55 (define @t59 () (tptp.aElementOf0 @t5 tptp.xI)) % 4.32/4.55 (define @t60 () (tptp.sdtasdt0 tptp.xb @t1)) % 4.32/4.55 (define @t61 () (tptp.aElementOf0 tptp.sz00 @t50)) % 4.32/4.55 (define @t62 () (tptp.sdtasdt0 tptp.xa @t1)) % 4.32/4.55 (define @t63 () (tptp.aElementOf0 tptp.sz00 @t51)) % 4.32/4.55 (define @t64 () (tptp.aElementOf0 @t1 @t52)) % 4.32/4.55 (define @t65 () (tptp.sdtasdt0 tptp.xb @t11)) % 4.32/4.55 (define @t66 () (and @t13 (= @t65 @t5))) % 4.32/4.55 (define @t67 () (exists @t26 @t66)) % 4.32/4.55 (define @t68 () (tptp.aElementOf0 @t5 @t50)) % 4.32/4.55 (define @t69 () (= @t68 @t67)) % 4.32/4.55 (define @t70 () (forall @t23 @t69)) % 4.32/4.55 (define @t71 () (tptp.sdtasdt0 tptp.xa @t11)) % 4.32/4.55 (define @t72 () (and @t13 (= @t71 @t5))) % 4.32/4.55 (define @t73 () (exists @t26 @t72)) % 4.32/4.55 (define @t74 () (= @t54 @t73)) % 4.32/4.55 (define @t75 () (forall @t23 @t74)) % 4.32/4.55 (define @t76 () (and @t75 @t70 @t57 @t64 @t44)) % 4.32/4.55 (define @t77 () (exists @t3 @t76)) % 4.32/4.55 (define @t78 () (tptp.sbrdtbr0 @t11)) % 4.32/4.55 (define @t79 () (not (tptp.iLess0 @t78 @t45))) % 4.32/4.55 (define @t80 () (not (= @t11 tptp.sz00))) % 4.32/4.55 (define @t81 () (tptp.aElementOf0 @t11 tptp.xI)) % 4.32/4.55 (define @t82 () (tptp.sdtpldt0 @t29 @t31)) % 4.32/4.55 (define @t83 () (tptp.aElementOf0 @t31 @t50)) % 4.32/4.55 (define @t84 () (tptp.aElementOf0 @t29 @t51)) % 4.32/4.55 (define @t85 () (and @t84 @t83 (= @t82 @t11))) % 4.32/4.55 (define @t86 () (@list @t29 @t31)) % 4.32/4.55 (define @t87 () (exists @t86 @t85)) % 4.32/4.55 (define @t88 () (or @t87 @t81)) % 4.32/4.55 (define @t89 () (and @t88 @t80)) % 4.32/4.55 (define @t90 () (=> @t89 @t79)) % 4.32/4.55 (define @t91 () (forall @t26 @t90)) % 4.32/4.55 (define @t92 () (tptp.sdtpldt0 @t11 @t29)) % 4.32/4.55 (define @t93 () (tptp.aElementOf0 @t29 @t50)) % 4.32/4.55 (define @t94 () (tptp.aElementOf0 @t11 @t51)) % 4.32/4.55 (define @t95 () (and @t94 @t93 (= @t92 @t5))) % 4.32/4.55 (define @t96 () (exists @t41 @t95)) % 4.32/4.55 (define @t97 () (and @t96 @t59 @t46 @t91)) % 4.32/4.55 (define @t98 () (exists @t23 @t97)) % 4.32/4.55 (define @t99 () (or @t57 @t58)) % 4.32/4.55 (define @t100 () (and @t99 @t44)) % 4.32/4.55 (define @t101 () (=> @t100 @t98)) % 4.32/4.55 (define @t102 () (forall @t3 @t101)) % 4.32/4.55 (define @t103 () (not (tptp.iLess0 @t45 @t43))) % 4.32/4.55 (define @t104 () (and @t96 @t59 @t46)) % 4.32/4.55 (define @t105 () (=> @t104 @t103)) % 4.32/4.55 (define @t106 () (forall @t23 @t105)) % 4.32/4.55 (define @t107 () (and @t99 @t44 @t106)) % 4.32/4.55 (define @t108 () (exists @t3 @t107)) % 4.32/4.55 (define @t109 () (not @t108)) % 4.32/4.55 (define @t110 () (@var "BOUND_VARIABLE_8727" $$unsorted)) % 4.32/4.55 (define @t111 () (not (tptp.aElementOf0 @t110 @t50))) % 4.32/4.55 (define @t112 () (@var "BOUND_VARIABLE_8725" $$unsorted)) % 4.32/4.55 (define @t113 () (not (tptp.aElementOf0 @t112 @t51))) % 4.32/4.55 (define @t114 () (tptp.sdtpldt0 @t112 @t110)) % 4.32/4.55 (define @t115 () (tptp.sbrdtbr0 @t114)) % 4.32/4.55 (define @t116 () (not (tptp.iLess0 @t115 @t43))) % 4.32/4.55 (define @t117 () (= tptp.sz00 @t114)) % 4.32/4.55 (define @t118 () (not (tptp.aElementOf0 @t114 tptp.xI))) % 4.32/4.55 (define @t119 () (or @t118 @t117 @t116 @t113 @t111)) % 4.32/4.55 (define @t120 () (@list @t112 @t110)) % 4.32/4.55 (define @t121 () (forall @t120 @t119)) % 4.32/4.55 (define @t122 () (not @t121)) % 4.32/4.55 (define @t123 () (not @t58)) % 4.32/4.55 (define @t124 () (@var "BOUND_VARIABLE_8766" $$unsorted)) % 4.32/4.55 (define @t125 () (@var "BOUND_VARIABLE_8764" $$unsorted)) % 4.32/4.55 (define @t126 () (or (not (tptp.aElementOf0 @t125 @t51)) (not (tptp.aElementOf0 @t124 @t50)) (not (= @t1 (tptp.sdtpldt0 @t125 @t124))))) % 4.32/4.55 (define @t127 () (and @t126 @t123)) % 4.32/4.55 (define @t128 () (or @t127 @t20 @t122)) % 4.32/4.55 (define @t129 () (forall (@list @t1 @t125 @t124) @t128)) % 4.32/4.55 (define @t130 () (@list @t125 @t124)) % 4.32/4.55 (define @t131 () (forall @t130 @t128)) % 4.32/4.55 (define @t132 () (forall @t130 @t123)) % 4.32/4.55 (define @t133 () (forall @t130 @t126)) % 4.32/4.55 (define @t134 () (@list @t5 @t11)) % 4.32/4.55 (define @t135 () (and @t133 @t132)) % 4.32/4.55 (define @t136 () (forall @t130 @t127)) % 4.32/4.55 (define @t137 () (or @t136 @t20 @t122)) % 4.32/4.55 (define @t138 () (= @t1 @t12)) % 4.32/4.55 (define @t139 () (not @t138)) % 4.32/4.55 (define @t140 () (not @t53)) % 4.32/4.55 (define @t141 () (not @t54)) % 4.32/4.55 (define @t142 () (or @t141 @t140 @t139)) % 4.32/4.55 (define @t143 () (forall @t56 @t142)) % 4.32/4.55 (define @t144 () (and @t143 @t123)) % 4.32/4.55 (define @t145 () (not @t143)) % 4.32/4.55 (define @t146 () (not @t145)) % 4.32/4.55 (define @t147 () (or @t145 @t58)) % 4.32/4.55 (define @t148 () (not @t147)) % 4.32/4.55 (define @t149 () (not @t44)) % 4.32/4.55 (define @t150 () (or @t148 @t149 @t122)) % 4.32/4.55 (define @t151 () (and @t147 @t44 @t121)) % 4.32/4.55 (define @t152 () (forall @t3 (not @t151))) % 4.32/4.55 (define @t153 () (not @t152)) % 4.32/4.55 (define @t154 () (not (= @t114 @t114))) % 4.32/4.55 (define @t155 () (or @t118 @t117 @t116 @t113 @t111 @t154)) % 4.32/4.55 (define @t156 () (not (= @t5 @t114))) % 4.32/4.55 (define @t157 () (= tptp.sz00 @t5)) % 4.32/4.55 (define @t158 () (not @t59)) % 4.32/4.55 (define @t159 () (or @t156 @t158 @t157 @t103 @t113 @t111 @t156)) % 4.32/4.55 (define @t160 () (or @t158 @t157 @t103 @t113 @t111 @t156)) % 4.32/4.55 (define @t161 () (forall @t23 @t160)) % 4.32/4.55 (define @t162 () (forall @t120 @t161)) % 4.32/4.55 (define @t163 () (forall (@list @t112 @t110 @t5) @t160)) % 4.32/4.55 (define @t164 () (@list @t5 @t112 @t110)) % 4.32/4.55 (define @t165 () (or @t113 @t111 @t156)) % 4.32/4.55 (define @t166 () (or @t165 @t158 @t157 @t103)) % 4.32/4.55 (define @t167 () (forall @t164 @t166)) % 4.32/4.55 (define @t168 () (forall @t120 @t166)) % 4.32/4.55 (define @t169 () (forall @t120 @t165)) % 4.32/4.55 (define @t170 () (@list @t11 @t29)) % 4.32/4.55 (define @t171 () (or @t169 @t158 @t157 @t103)) % 4.32/4.55 (define @t172 () (= @t5 @t92)) % 4.32/4.55 (define @t173 () (not @t172)) % 4.32/4.55 (define @t174 () (not @t93)) % 4.32/4.55 (define @t175 () (not @t94)) % 4.32/4.55 (define @t176 () (or @t175 @t174 @t173)) % 4.32/4.55 (define @t177 () (forall @t41 @t176)) % 4.32/4.55 (define @t178 () (or @t177 @t158 @t157 @t103)) % 4.32/4.55 (define @t179 () (not @t157)) % 4.32/4.55 (define @t180 () (not @t179)) % 4.32/4.55 (define @t181 () (not @t177)) % 4.32/4.55 (define @t182 () (not @t181)) % 4.32/4.55 (define @t183 () (or @t182 @t158 @t180)) % 4.32/4.55 (define @t184 () (and @t181 @t59 @t179)) % 4.32/4.55 (define @t185 () (and @t94 @t93 @t172)) % 4.32/4.55 (define @t186 () (forall @t41 (not @t185))) % 4.32/4.55 (define @t187 () (not @t186)) % 4.32/4.55 (define @t188 () (and @t54 @t53 @t138)) % 4.32/4.55 (define @t189 () (forall @t56 (not @t188))) % 4.32/4.55 (define @t190 () (not @t189)) % 4.32/4.55 (define @t191 () (@var "BOUND_VARIABLE_8657" $$unsorted)) % 4.32/4.55 (define @t192 () (not (tptp.aElementOf0 @t191 @t50))) % 4.32/4.55 (define @t193 () (@var "BOUND_VARIABLE_8655" $$unsorted)) % 4.32/4.55 (define @t194 () (not (tptp.aElementOf0 @t193 @t51))) % 4.32/4.55 (define @t195 () (tptp.sdtpldt0 @t193 @t191)) % 4.32/4.55 (define @t196 () (= tptp.sz00 @t11)) % 4.32/4.55 (define @t197 () (not @t81)) % 4.32/4.55 (define @t198 () (@var "BOUND_VARIABLE_8633" $$unsorted)) % 4.32/4.55 (define @t199 () (@var "BOUND_VARIABLE_8631" $$unsorted)) % 4.32/4.55 (define @t200 () (or (not (tptp.aElementOf0 @t199 @t51)) (not (tptp.aElementOf0 @t198 @t50)) (not (= @t11 (tptp.sdtpldt0 @t199 @t198))))) % 4.32/4.55 (define @t201 () (and @t200 @t197)) % 4.32/4.55 (define @t202 () (@list @t11 @t199 @t198)) % 4.32/4.55 (define @t203 () (not (forall @t202 (or @t201 @t196 (not (tptp.iLess0 @t78 (tptp.sbrdtbr0 @t195))))))) % 4.32/4.55 (define @t204 () (= tptp.sz00 @t195)) % 4.32/4.55 (define @t205 () (not (tptp.aElementOf0 @t195 tptp.xI))) % 4.32/4.55 (define @t206 () (or @t205 @t204 @t203 @t194 @t192)) % 4.32/4.55 (define @t207 () (@list @t193 @t191)) % 4.32/4.55 (define @t208 () (forall @t207 @t206)) % 4.32/4.55 (define @t209 () (@quantifiers_skolemize @t208 1)) % 4.32/4.55 (define @t210 () (@quantifiers_skolemize @t208 0)) % 4.32/4.55 (define @t211 () (tptp.sdtpldt0 @t210 @t209)) % 4.32/4.55 (define @t212 () (tptp.sbrdtbr0 @t211)) % 4.32/4.55 (define @t213 () (forall @t120 (or @t118 @t117 (not (tptp.iLess0 @t115 @t212)) @t113 @t111))) % 4.32/4.55 (define @t214 () (not @t213)) % 4.32/4.55 (define @t215 () (tptp.aElementOf0 @t211 tptp.xI)) % 4.32/4.55 (define @t216 () (not @t215)) % 4.32/4.55 (define @t217 () (@var "BOUND_VARIABLE_8562" $$unsorted)) % 4.32/4.55 (define @t218 () (not (tptp.aElementOf0 @t217 @t50))) % 4.32/4.55 (define @t219 () (@var "BOUND_VARIABLE_8560" $$unsorted)) % 4.32/4.55 (define @t220 () (not (tptp.aElementOf0 @t219 @t51))) % 4.32/4.55 (define @t221 () (tptp.sdtpldt0 @t219 @t217)) % 4.32/4.55 (define @t222 () (= tptp.sz00 @t221)) % 4.32/4.55 (define @t223 () (not (tptp.aElementOf0 @t221 @t52))) % 4.32/4.55 (define @t224 () (or @t223 @t222 @t220 @t218)) % 4.32/4.55 (define @t225 () (@list @t219 @t217)) % 4.32/4.55 (define @t226 () (forall @t225 @t224)) % 4.32/4.55 (define @t227 () (@quantifiers_skolemize @t226 1)) % 4.32/4.55 (define @t228 () (@quantifiers_skolemize @t226 0)) % 4.32/4.55 (define @t229 () (tptp.sdtpldt0 @t228 @t227)) % 4.32/4.55 (define @t230 () (not (= @t211 @t229))) % 4.32/4.55 (define @t231 () (not (tptp.aElementOf0 @t227 @t50))) % 4.32/4.55 (define @t232 () (not (tptp.aElementOf0 @t228 @t51))) % 4.32/4.55 (define @t233 () (or @t232 @t231 @t230)) % 4.32/4.55 (define @t234 () (and @t233 @t216)) % 4.32/4.55 (define @t235 () (or @t234 (= @t211 tptp.sz00) @t214)) % 4.32/4.55 (define @t236 () (= tptp.sz00 @t211)) % 4.32/4.55 (define @t237 () (and (or @t232 @t231 (not (= @t229 @t211))) @t216)) % 4.32/4.55 (define @t238 () (or @t237 @t236 @t214)) % 4.32/4.55 (define @t239 () (@list false)) % 4.32/4.55 (define @t240 () (not (= @t221 @t221))) % 4.32/4.55 (define @t241 () (or @t223 (= @t221 tptp.sz00) @t220 @t218 @t240)) % 4.32/4.55 (define @t242 () (not (= @t1 @t221))) % 4.32/4.55 (define @t243 () (not @t64)) % 4.32/4.55 (define @t244 () (or @t242 @t243 @t20 @t220 @t218 @t242)) % 4.32/4.55 (define @t245 () (or @t243 @t20 @t220 @t218 @t242)) % 4.32/4.55 (define @t246 () (forall @t3 @t245)) % 4.32/4.55 (define @t247 () (forall @t225 @t246)) % 4.32/4.55 (define @t248 () (forall (@list @t219 @t217 @t1) @t245)) % 4.32/4.55 (define @t249 () (@list @t1 @t219 @t217)) % 4.32/4.55 (define @t250 () (or @t220 @t218 @t242)) % 4.32/4.55 (define @t251 () (or @t250 @t243 @t20)) % 4.32/4.55 (define @t252 () (forall @t249 @t251)) % 4.32/4.55 (define @t253 () (forall @t225 @t251)) % 4.32/4.55 (define @t254 () (forall @t225 @t250)) % 4.32/4.55 (define @t255 () (or @t254 @t243 @t20)) % 4.32/4.55 (define @t256 () (or @t143 @t243 @t20)) % 4.32/4.55 (define @t257 () (forall @t3 @t256)) % 4.32/4.55 (define @t258 () (= @t5 @t65)) % 4.32/4.55 (define @t259 () (not @t13)) % 4.32/4.55 (define @t260 () (forall @t23 (= @t68 (not (forall @t26 (or @t259 (not @t258))))))) % 4.32/4.55 (define @t261 () (not @t260)) % 4.32/4.55 (define @t262 () (= @t5 @t71)) % 4.32/4.55 (define @t263 () (forall @t23 (= @t54 (not (forall @t26 (or @t259 (not @t262))))))) % 4.32/4.55 (define @t264 () (not @t263)) % 4.32/4.55 (define @t265 () (or @t264 @t261 @t257)) % 4.32/4.55 (define @t266 () (or @t264 @t261 @t256)) % 4.32/4.55 (define @t267 () (or @t264 @t261 @t143 @t243 @t20)) % 4.32/4.55 (define @t268 () (or @t264 @t261 @t146 @t243 @t149)) % 4.32/4.55 (define @t269 () (and @t263 @t260 @t145 @t64 @t44)) % 4.32/4.55 (define @t270 () (forall @t3 (not @t269))) % 4.32/4.55 (define @t271 () (not @t270)) % 4.32/4.55 (define @t272 () (and @t13 @t258)) % 4.32/4.55 (define @t273 () (forall @t26 (not @t272))) % 4.32/4.55 (define @t274 () (not @t273)) % 4.32/4.55 (define @t275 () (and @t13 @t262)) % 4.32/4.55 (define @t276 () (forall @t26 (not @t275))) % 4.32/4.55 (define @t277 () (not @t276)) % 4.32/4.55 (define @t278 () (tptp.aElementOf0 @t229 @t52)) % 4.32/4.55 (define @t279 () (= tptp.sz00 @t229)) % 4.32/4.55 (define @t280 () (not @t278)) % 4.32/4.55 (define @t281 () (or @t280 @t279 @t232 @t231)) % 4.32/4.55 (define @t282 () (@list true)) % 4.32/4.55 (define @t283 () (@list @t281)) % 4.32/4.55 (define @t284 () (tptp.aElementOf0 @t229 tptp.xI)) % 4.32/4.55 (define @t285 () (not @t284)) % 4.32/4.55 (define @t286 () (and (or (not @t63) (not @t61) (not (= @t229 (tptp.sdtpldt0 tptp.sz00 tptp.sz00)))) @t285)) % 4.32/4.55 (define @t287 () (not @t286)) % 4.32/4.55 (define @t288 () (or @t286 @t279)) % 4.32/4.55 (define @t289 () (not @t288)) % 4.32/4.55 (define @t290 () (or @t286 (= @t229 tptp.sz00))) % 4.32/4.55 (define @t291 () (@var "BOUND_VARIABLE_8702" $$unsorted)) % 4.32/4.55 (define @t292 () (@var "BOUND_VARIABLE_8700" $$unsorted)) % 4.32/4.55 (define @t293 () (or (not (tptp.aElementOf0 @t292 @t51)) (not (tptp.aElementOf0 @t291 @t50)) (not (= @t1 (tptp.sdtpldt0 @t292 @t291))))) % 4.32/4.55 (define @t294 () (and @t293 @t123)) % 4.32/4.55 (define @t295 () (or @t294 @t20)) % 4.32/4.55 (define @t296 () (forall (@list @t1 @t292 @t291) @t295)) % 4.32/4.55 (define @t297 () (@list @t292 @t291)) % 4.32/4.55 (define @t298 () (forall @t297 @t295)) % 4.32/4.55 (define @t299 () (forall @t297 @t123)) % 4.32/4.55 (define @t300 () (forall @t297 @t293)) % 4.32/4.55 (define @t301 () (and @t300 @t299)) % 4.32/4.55 (define @t302 () (forall @t297 @t294)) % 4.32/4.55 (define @t303 () (or @t302 @t20)) % 4.32/4.55 (define @t304 () (or @t144 @t20)) % 4.32/4.55 (define @t305 () (forall @t3 @t304)) % 4.32/4.55 (define @t306 () (not @t208)) % 4.32/4.55 (define @t307 () (or @t306 @t305)) % 4.32/4.55 (define @t308 () (or @t306 @t304)) % 4.32/4.55 (define @t309 () (or @t144 @t20 @t306)) % 4.32/4.55 (define @t310 () (and @t147 @t44)) % 4.32/4.55 (define @t311 () (not (= @t195 @t195))) % 4.32/4.55 (define @t312 () (or @t205 @t204 @t203 @t194 @t192 @t311)) % 4.32/4.55 (define @t313 () (not (= @t5 @t195))) % 4.32/4.55 (define @t314 () (or @t201 @t196 @t79)) % 4.32/4.55 (define @t315 () (forall @t202 @t314)) % 4.32/4.55 (define @t316 () (not @t315)) % 4.32/4.55 (define @t317 () (or @t313 @t158 @t157 @t316 @t194 @t192 @t313)) % 4.32/4.55 (define @t318 () (or @t158 @t157 @t316 @t194 @t192 @t313)) % 4.32/4.55 (define @t319 () (forall @t23 @t318)) % 4.32/4.55 (define @t320 () (forall @t207 @t319)) % 4.32/4.55 (define @t321 () (forall (@list @t193 @t191 @t5) @t318)) % 4.32/4.55 (define @t322 () (@list @t5 @t193 @t191)) % 4.32/4.55 (define @t323 () (or @t194 @t192 @t313)) % 4.32/4.55 (define @t324 () (or @t323 @t158 @t157 @t316)) % 4.32/4.55 (define @t325 () (forall @t322 @t324)) % 4.32/4.55 (define @t326 () (forall @t207 @t324)) % 4.32/4.55 (define @t327 () (forall @t207 @t323)) % 4.32/4.55 (define @t328 () (or @t327 @t158 @t157 @t316)) % 4.32/4.55 (define @t329 () (or @t182 @t158 @t180 @t316)) % 4.32/4.55 (define @t330 () (and @t181 @t59 @t179 @t315)) % 4.32/4.55 (define @t331 () (forall @t23 (not @t330))) % 4.32/4.55 (define @t332 () (not @t331)) % 4.32/4.55 (define @t333 () (@list @t199 @t198)) % 4.32/4.55 (define @t334 () (forall @t333 @t314)) % 4.32/4.55 (define @t335 () (forall @t333 @t197)) % 4.32/4.55 (define @t336 () (forall @t333 @t200)) % 4.32/4.55 (define @t337 () (and @t336 @t335)) % 4.32/4.55 (define @t338 () (forall @t333 @t201)) % 4.32/4.55 (define @t339 () (or @t338 @t196 @t79)) % 4.32/4.55 (define @t340 () (= @t11 @t82)) % 4.32/4.55 (define @t341 () (not @t340)) % 4.32/4.55 (define @t342 () (not @t83)) % 4.32/4.55 (define @t343 () (not @t84)) % 4.32/4.55 (define @t344 () (or @t343 @t342 @t341)) % 4.32/4.55 (define @t345 () (forall @t86 @t344)) % 4.32/4.55 (define @t346 () (and @t345 @t197)) % 4.32/4.55 (define @t347 () (or @t346 @t196 @t79)) % 4.32/4.55 (define @t348 () (not @t345)) % 4.32/4.55 (define @t349 () (or @t348 @t81)) % 4.32/4.55 (define @t350 () (not @t349)) % 4.32/4.55 (define @t351 () (not @t196)) % 4.32/4.55 (define @t352 () (and @t349 @t351)) % 4.32/4.55 (define @t353 () (and @t84 @t83 @t340)) % 4.32/4.55 (define @t354 () (forall @t86 (not @t353))) % 4.32/4.55 (define @t355 () (not @t354)) % 4.32/4.55 (define @t356 () (forall @t202 (or @t201 @t196 (not (tptp.iLess0 @t78 @t212))))) % 4.32/4.55 (define @t357 () (not @t356)) % 4.32/4.55 (define @t358 () (or @t216 @t236 @t357 (not (tptp.aElementOf0 @t210 @t51)) (not (tptp.aElementOf0 @t209 @t50)))) % 4.32/4.55 (define @t359 () (not @t358)) % 4.32/4.55 (define @t360 () (@list @t358)) % 4.32/4.55 (define @t361 () (not @t237)) % 4.32/4.55 (define @t362 () (@quantifiers_skolemize @t213 1)) % 4.32/4.55 (define @t363 () (@quantifiers_skolemize @t213 0)) % 4.32/4.55 (define @t364 () (tptp.sdtpldt0 @t363 @t362)) % 4.32/4.55 (define @t365 () (tptp.iLess0 (tptp.sbrdtbr0 @t364) @t212)) % 4.32/4.55 (define @t366 () (not @t365)) % 4.32/4.55 (define @t367 () (= tptp.sz00 @t364)) % 4.32/4.55 (define @t368 () (tptp.aElementOf0 @t364 tptp.xI)) % 4.32/4.55 (define @t369 () (not @t368)) % 4.32/4.55 (define @t370 () (or @t369 @t367 @t366 (not (tptp.aElementOf0 @t363 @t51)) (not (tptp.aElementOf0 @t362 @t50)))) % 4.32/4.55 (define @t371 () (not @t370)) % 4.32/4.55 (define @t372 () (@list @t370)) % 4.32/4.55 (define @t373 () (@quantifiers_skolemize @t356 2)) % 4.32/4.55 (define @t374 () (@quantifiers_skolemize (forall @t56 (or @t141 @t140 (not (= @t12 @t211)))) 0)) % 4.32/4.55 (define @t375 () (and (or (not (tptp.aElementOf0 @t374 @t51)) (not (tptp.aElementOf0 @t373 @t50)) (not (= @t364 (tptp.sdtpldt0 @t374 @t373)))) @t369)) % 4.32/4.55 (define @t376 () (not @t375)) % 4.32/4.55 (define @t377 () (or @t375 @t367 @t366)) % 4.32/4.55 (assume @p1 (forall @t3 (=> @t2 true))) % 4.32/4.55 (assume @p2 (tptp.aElement0 tptp.sz00)) % 4.32/4.55 (assume @p3 (tptp.aElement0 tptp.sz10)) % 4.32/4.55 (assume @p4 (forall @t3 (=> @t2 (tptp.aElement0 @t4)))) % 4.32/4.55 (assume @p5 (forall @t9 (=> @t8 (tptp.aElement0 @t6)))) % 4.32/4.55 (assume @p6 (forall @t9 (=> @t8 (tptp.aElement0 @t10)))) % 4.32/4.55 (assume @p7 (forall @t9 (=> @t8 (= @t6 (tptp.sdtpldt0 @t5 @t1))))) % 4.32/4.55 (assume @p8 (forall @t15 (=> @t14 (= (tptp.sdtpldt0 @t6 @t11) (tptp.sdtpldt0 @t1 @t12))))) % 4.32/4.55 (assume @p9 (forall @t3 (=> @t2 (and (= (tptp.sdtpldt0 @t1 tptp.sz00) @t1) (= @t1 (tptp.sdtpldt0 tptp.sz00 @t1)))))) % 4.32/4.55 (assume @p10 (forall @t3 (=> @t2 (and (= (tptp.sdtpldt0 @t1 @t4) tptp.sz00) (= tptp.sz00 (tptp.sdtpldt0 @t4 @t1)))))) % 4.32/4.55 (assume @p11 (forall @t9 (=> @t8 (= @t10 @t16)))) % 4.32/4.55 (assume @p12 (forall @t15 (=> @t14 (= (tptp.sdtasdt0 @t10 @t11) (tptp.sdtasdt0 @t1 (tptp.sdtasdt0 @t5 @t11)))))) % 4.32/4.55 (assume @p13 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz10) @t1) (= @t1 (tptp.sdtasdt0 tptp.sz10 @t1)))))) % 4.32/4.55 (assume @p14 (forall @t15 (=> @t14 (and (= (tptp.sdtasdt0 @t1 @t12) (tptp.sdtpldt0 @t10 @t17)) (= (tptp.sdtasdt0 @t12 @t1) (tptp.sdtpldt0 @t16 (tptp.sdtasdt0 @t11 @t1))))))) % 4.32/4.55 (assume @p15 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t18 @t1) @t4) (= @t4 (tptp.sdtasdt0 @t1 @t18)))))) % 4.32/4.55 (assume @p16 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz00) tptp.sz00) (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 @t1)))))) % 4.32/4.55 (assume @p17 (forall @t9 (=> @t8 (=> (= @t10 tptp.sz00) (or @t20 @t19))))) % 4.32/4.55 (assume @p18 (not (= tptp.sz10 tptp.sz00))) % 4.32/4.55 (assume @p19 (forall @t3 (=> @t21 true))) % 4.32/4.55 (assume @p20 (forall @t3 (=> @t21 (forall @t23 (=> @t22 @t7))))) % 4.32/4.55 (assume @p21 (forall @t9 (=> @t28 (=> (and (forall @t26 (=> @t24 @t25)) (forall @t26 (=> @t25 @t24))) (= @t1 @t5))))) % 4.32/4.55 (assume @p22 (forall @t9 (=> @t28 (forall @t26 (= (= @t11 @t35) (and @t34 (forall @t33 (= @t32 (exists (@list @t31 @t30) (and (tptp.aElementOf0 @t31 @t1) (tptp.aElementOf0 @t30 @t5) (= (tptp.sdtpldt0 @t31 @t30) @t29))))))))))) % 4.32/4.55 (assume @p23 (forall @t9 (=> @t28 (forall @t26 (= (= @t11 @t36) (and @t34 (forall @t33 (= @t32 (and (tptp.aElementOf0 @t29 @t1) (tptp.aElementOf0 @t29 @t5)))))))))) % 4.32/4.55 (assume @p24 (forall @t3 (= @t38 (and @t21 (forall @t23 (=> @t22 (and (forall @t26 (=> @t24 (tptp.aElementOf0 @t12 @t1))) (forall @t26 (=> @t13 (tptp.aElementOf0 @t37 @t1)))))))))) % 4.32/4.55 (assume @p25 (forall @t9 (=> @t39 (tptp.aIdeal0 @t35)))) % 4.32/4.55 (assume @p26 (forall @t9 (=> @t39 (tptp.aIdeal0 @t36)))) % 4.32/4.55 (assume @p27 (forall @t15 (=> (and @t2 @t7 (tptp.aIdeal0 @t11)) (= (tptp.sdteqdtlpzmzozddtrp0 @t1 @t5 @t11) (tptp.aElementOf0 (tptp.sdtpldt0 @t1 (tptp.smndt0 @t5)) @t11))))) % 4.32/4.55 (assume @p28 (forall @t9 (=> @t39 (=> (forall @t26 (=> @t13 (tptp.aElementOf0 @t11 @t35))) (forall @t41 (=> (and @t13 @t40) (exists (@list @t31) (and (tptp.aElement0 @t31) (tptp.sdteqdtlpzmzozddtrp0 @t31 @t11 @t1) (tptp.sdteqdtlpzmzozddtrp0 @t31 @t29 @t5))))))))) % 4.32/4.55 (assume @p29 (forall @t3 (=> @t42 true))) % 4.32/4.55 (assume @p30 (forall @t3 (=> (and @t2 @t44) (tptp.aNaturalNumber0 @t43)))) % 4.32/4.55 (assume @p31 (forall @t9 (=> (and @t42 (tptp.aNaturalNumber0 @t5)) (=> (tptp.iLess0 @t1 @t5) true)))) % 4.32/4.55 (assume @p32 (forall @t9 (=> (and @t2 @t7 @t46) (exists @t41 (and @t13 @t40 (= @t1 (tptp.sdtpldt0 @t37 @t29)) (=> (not (= @t29 tptp.sz00)) (tptp.iLess0 (tptp.sbrdtbr0 @t29) @t45))))))) % 4.32/4.55 (assume @p33 (forall @t9 (=> @t8 (= (tptp.doDivides0 @t1 @t5) (exists @t26 (and @t13 (= @t17 @t5))))))) % 4.32/4.55 (assume @p34 (forall @t3 (=> @t2 (forall @t23 (= (tptp.aDivisorOf0 @t5 @t1) (and @t7 (tptp.doDivides0 @t5 @t1))))))) % 4.32/4.55 (assume @p35 (forall @t9 (=> @t8 (forall @t26 (= (tptp.aGcdOfAnd0 @t11 @t1 @t5) (and (tptp.aDivisorOf0 @t11 @t1) (tptp.aDivisorOf0 @t11 @t5) (forall @t33 (=> (and (tptp.aDivisorOf0 @t29 @t1) (tptp.aDivisorOf0 @t29 @t5)) (tptp.doDivides0 @t29 @t11))))))))) % 4.32/4.55 (assume @p36 (forall @t9 (=> @t8 (= (tptp.misRelativelyPrime0 @t1 @t5) (tptp.aGcdOfAnd0 tptp.sz10 @t1 @t5))))) % 4.32/4.55 (assume @p37 (forall @t3 (=> @t2 (forall @t23 (= (= @t5 @t47) (and @t27 (forall @t26 (= @t25 (exists @t33 (and @t40 (= (tptp.sdtasdt0 @t1 @t29) @t11))))))))))) % 4.32/4.55 (assume @p38 (forall @t3 (=> @t2 (tptp.aIdeal0 @t47)))) % 4.32/4.55 (assume @p39 (and (tptp.aElement0 tptp.xa) (tptp.aElement0 tptp.xb))) % 4.32/4.55 (assume @p40 (or (not (= tptp.xa tptp.sz00)) (not (= tptp.xb tptp.sz00)))) % 4.32/4.55 (assume @p41 (and @t49 (exists @t3 (and @t2 (= @t48 tptp.xa))) (tptp.doDivides0 tptp.xc tptp.xa) (tptp.aDivisorOf0 tptp.xc tptp.xa) @t49 (exists @t3 (and @t2 (= @t48 tptp.xb))) (tptp.doDivides0 tptp.xc tptp.xb) (tptp.aDivisorOf0 tptp.xc tptp.xb) (forall @t3 (=> (and (or (and @t2 (or (exists @t23 (and @t7 (= @t10 tptp.xa))) (tptp.doDivides0 @t1 tptp.xa))) (tptp.aDivisorOf0 @t1 tptp.xa)) (or (exists @t23 (and @t7 (= @t10 tptp.xb))) (tptp.doDivides0 @t1 tptp.xb) (tptp.aDivisorOf0 @t1 tptp.xb))) (and (exists @t23 (and @t7 (= @t10 tptp.xc))) (tptp.doDivides0 @t1 tptp.xc)))) (tptp.aGcdOfAnd0 tptp.xc tptp.xa tptp.xb))) % 4.32/4.55 (assume @p42 (and (tptp.aSet0 tptp.xI) (forall @t3 (=> @t58 (and (forall @t23 (=> @t59 (tptp.aElementOf0 @t6 tptp.xI))) (forall @t23 (=> @t7 (tptp.aElementOf0 @t16 tptp.xI)))))) (tptp.aIdeal0 tptp.xI) (forall @t3 (= (tptp.aElementOf0 @t1 @t51) (exists @t23 (and @t7 (= (tptp.sdtasdt0 tptp.xa @t5) @t1))))) (forall @t3 (= (tptp.aElementOf0 @t1 @t50) (exists @t23 (and @t7 (= (tptp.sdtasdt0 tptp.xb @t5) @t1))))) (forall @t3 (= @t58 @t57)) (= tptp.xI @t52))) % 4.32/4.55 (assume @p43 (and (exists @t3 (and @t2 (= @t62 tptp.sz00))) @t63 (exists @t3 (and @t2 (= @t62 tptp.xa))) (tptp.aElementOf0 tptp.xa @t51) (exists @t3 (and @t2 (= @t60 tptp.sz00))) @t61 (exists @t3 (and @t2 (= @t60 tptp.xb))) (tptp.aElementOf0 tptp.xb @t50))) % 4.32/4.55 (assume @p44 @t77) % 4.32/4.55 (assume @p45 @t102) % 4.32/4.55 (assume @p46 @t109) % 4.32/4.55 (assume @p47 true) % 4.32/4.55 (step @p48 :rule bool-double-not-elim :args (@t129)) % 4.32/4.55 (step @p49 :rule quant-merge-prenex :args ((= (forall @t3 @t131) @t129))) % 4.32/4.55 (step @p50 :rule refl :args (@t122)) % 4.32/4.55 (step @p51 :rule refl :args (@t20)) % 4.32/4.55 (step @p52 :rule quant-unused-vars :args ((= @t132 @t123))) % 4.32/4.55 (step @p53 :rule alpha_equiv :args (@t133 (@list @t125 @t124) @t134)) % 4.32/4.55 (step @p54 :rule nary_cong :premises (@p53 @p52) :args (@t135)) % 4.32/4.55 (step @p55 :rule quant-miniscope-and :args ((= @t136 @t135))) % 4.32/4.55 (step @p56 :rule trans :premises (@p55 @p54)) % 4.32/4.55 (step @p57 :rule nary_cong :premises (@p56 @p51 @p50) :args (@t137)) % 4.32/4.55 (step @p58 :rule quant-miniscope-or :args ((= @t131 @t137))) % 4.32/4.55 (step @p59 :rule trans :premises (@p58 @p57)) % 4.32/4.55 (step @p60 :rule symm :premises (@p59)) % 4.32/4.55 (step @p61 :rule cong :premises (@p60) :args ((forall @t3 (or @t144 @t20 @t122)))) % 4.32/4.55 (step @p62 :rule trans :premises (@p61 @p49)) % 4.32/4.55 (step @p63 :rule refl :args (@t123)) % 4.32/4.55 (step @p64 :rule bool-double-not-elim :args (@t143)) % 4.32/4.55 (step @p65 :rule nary_cong :premises (@p64 @p63) :args ((and @t146 @t123))) % 4.32/4.55 (step @p66 :rule bool-or-de-morgan :args (@t145 @t58 false)) % 4.32/4.55 (step @p67 :rule trans :premises (@p66 @p65)) % 4.32/4.55 (step @p68 :rule nary_cong :premises (@p67 @p51 @p50) :args ((or @t148 @t20 @t122))) % 4.32/4.55 (step @p69 :rule bool-double-not-elim :args (@t20)) % 4.32/4.55 (step @p70 :rule refl :args (@t148)) % 4.32/4.55 (step @p71 :rule nary_cong :premises (@p70 @p69 @p50) :args (@t150)) % 4.32/4.55 (step @p72 :rule aci_norm :args ((= (or @t148 (or @t149 @t122)) @t150))) % 4.32/4.55 (step @p73 :rule trans :premises (@p72 @p71)) % 4.32/4.55 (step @p74 :rule bool-and-de-morgan :args (@t44 @t121 true)) % 4.32/4.55 (step @p75 :rule nary_cong :premises (@p70 @p74) :args ((or @t148 (not (and @t44 @t121))))) % 4.32/4.55 (step @p76 :rule bool-and-de-morgan :args (@t147 @t44 (and @t121))) % 4.32/4.55 (step @p77 :rule trans :premises (@p76 @p75)) % 4.32/4.55 (step @p78 :rule trans :premises (@p77 @p73)) % 4.32/4.55 (step @p79 :rule trans :premises (@p78 @p68)) % 4.32/4.55 (step @p80 :rule cong :premises (@p79) :args (@t152)) % 4.32/4.55 (step @p81 :rule trans :premises (@p80 @p62)) % 4.32/4.55 (step @p82 :rule cong :premises (@p81) :args (@t153)) % 4.32/4.55 (step @p83 :rule exists-elim :args ((= (exists @t3 @t151) @t153))) % 4.32/4.55 (step @p84 :rule trans :premises (@p83 @p82)) % 4.32/4.55 (step @p85 :rule aci_norm :args ((= (or @t118 @t117 @t116 @t113 @t111 false) @t119))) % 4.32/4.55 (step @p86 :rule evaluate :args ((not true))) % 4.32/4.55 (step @p87 :rule eq-refl :args (@t114)) % 4.32/4.55 (step @p88 :rule cong :premises (@p87) :args (@t154)) % 4.32/4.55 (step @p89 :rule trans :premises (@p88 @p86)) % 4.32/4.55 (step @p90 :rule refl :args (@t111)) % 4.32/4.55 (step @p91 :rule refl :args (@t113)) % 4.32/4.55 (step @p92 :rule refl :args (@t116)) % 4.32/4.55 (step @p93 :rule refl :args (@t117)) % 4.32/4.55 (step @p94 :rule refl :args (@t118)) % 4.32/4.55 (step @p95 :rule nary_cong :premises (@p94 @p93 @p92 @p91 @p90 @p89) :args (@t155)) % 4.32/4.55 (step @p96 :rule trans :premises (@p95 @p85)) % 4.32/4.55 (step @p97 :rule cong :premises (@p96) :args ((forall @t120 @t155))) % 4.32/4.55 (step @p98 :rule quant-var-elim-eq :args ((= (forall @t23 @t159) @t155))) % 4.32/4.55 (step @p99 :rule aci_norm :args ((= @t160 @t159))) % 4.32/4.55 (step @p100 :rule cong :premises (@p99) :args (@t161)) % 4.32/4.55 (step @p101 :rule trans :premises (@p100 @p98)) % 4.32/4.55 (step @p102 :rule cong :premises (@p101) :args (@t162)) % 4.32/4.55 (step @p103 :rule quant-merge-prenex :args ((= @t162 @t163))) % 4.32/4.55 (step @p104 :rule symm :premises (@p103)) % 4.32/4.55 (step @p105 :rule quant_var_reordering :args ((= (forall @t164 @t160) @t163))) % 4.32/4.55 (step @p106 :rule trans :premises (@p105 @p104 @p102)) % 4.32/4.55 (step @p107 :rule trans :premises (@p106 @p97)) % 4.32/4.55 (step @p108 :rule aci_norm :args ((= @t166 @t160))) % 4.32/4.55 (step @p109 :rule cong :premises (@p108) :args (@t167)) % 4.32/4.55 (step @p110 :rule trans :premises (@p109 @p107)) % 4.32/4.55 (step @p111 :rule quant-merge-prenex :args ((= (forall @t23 @t168) @t167))) % 4.32/4.55 (step @p112 :rule refl :args (@t103)) % 4.32/4.55 (step @p113 :rule refl :args (@t157)) % 4.32/4.55 (step @p114 :rule refl :args (@t158)) % 4.32/4.55 (step @p115 :rule alpha_equiv :args (@t169 (@list @t112 @t110) @t170)) % 4.32/4.55 (step @p116 :rule nary_cong :premises (@p115 @p114 @p113 @p112) :args (@t171)) % 4.32/4.55 (step @p117 :rule quant-miniscope-or :args ((= @t168 @t171))) % 4.32/4.55 (step @p118 :rule trans :premises (@p117 @p116)) % 4.32/4.55 (step @p119 :rule symm :premises (@p118)) % 4.32/4.55 (step @p120 :rule cong :premises (@p119) :args ((forall @t23 @t178))) % 4.32/4.55 (step @p121 :rule trans :premises (@p120 @p111)) % 4.32/4.55 (step @p122 :rule trans :premises (@p121 @p110)) % 4.32/4.55 (step @p123 :rule aci_norm :args ((= (or (or @t177 @t158 @t157) @t103) @t178))) % 4.32/4.55 (step @p124 :rule bool-double-not-elim :args (@t157)) % 4.32/4.55 (step @p125 :rule bool-double-not-elim :args (@t177)) % 4.32/4.55 (step @p126 :rule nary_cong :premises (@p125 @p114 @p124) :args (@t183)) % 4.32/4.55 (step @p127 :rule aci_norm :args ((= (or @t182 (or @t158 @t180)) @t183))) % 4.32/4.55 (step @p128 :rule trans :premises (@p127 @p126)) % 4.32/4.55 (step @p129 :rule bool-and-de-morgan :args (@t59 @t179 true)) % 4.32/4.55 (step @p130 :rule refl :args (@t182)) % 4.32/4.55 (step @p131 :rule nary_cong :premises (@p130 @p129) :args ((or @t182 (not (and @t59 @t179))))) % 4.32/4.55 (step @p132 :rule bool-and-de-morgan :args (@t181 @t59 (and @t179))) % 4.32/4.55 (step @p133 :rule trans :premises (@p132 @p131)) % 4.32/4.55 (step @p134 :rule trans :premises (@p133 @p128)) % 4.32/4.55 (step @p135 :rule nary_cong :premises (@p134 @p112) :args ((or (not @t184) @t103))) % 4.32/4.55 (step @p136 :rule trans :premises (@p135 @p123)) % 4.32/4.55 (step @p137 :rule bool-impl-elim :args (@t184 @t103)) % 4.32/4.55 (step @p138 :rule trans :premises (@p137 @p136)) % 4.32/4.55 (step @p139 :rule cong :premises (@p138) :args ((forall @t23 (=> @t184 @t103)))) % 4.32/4.55 (step @p140 :rule trans :premises (@p139 @p122)) % 4.32/4.55 (step @p141 :rule refl :args (@t103)) % 4.32/4.55 (step @p142 :rule eq-symm :args (@t5 tptp.sz00)) % 4.32/4.55 (step @p143 :rule cong :premises (@p142) :args (@t46)) % 4.32/4.55 (step @p144 :rule refl :args (@t59)) % 4.32/4.55 (step @p145 :rule aci_norm :args ((= (or @t175 (or @t174 @t173)) @t176))) % 4.32/4.55 (step @p146 :rule bool-and-de-morgan :args (@t93 @t172 true)) % 4.32/4.55 (step @p147 :rule refl :args (@t175)) % 4.32/4.55 (step @p148 :rule nary_cong :premises (@p147 @p146) :args ((or @t175 (not (and @t93 @t172))))) % 4.32/4.55 (step @p149 :rule bool-and-de-morgan :args (@t94 @t93 (and @t172))) % 4.32/4.55 (step @p150 :rule trans :premises (@p149 @p148)) % 4.32/4.55 (step @p151 :rule trans :premises (@p150 @p145)) % 4.32/4.55 (step @p152 :rule cong :premises (@p151) :args (@t186)) % 4.32/4.55 (step @p153 :rule cong :premises (@p152) :args (@t187)) % 4.32/4.55 (step @p154 :rule exists-elim :args ((= (exists @t41 @t185) @t187))) % 4.32/4.55 (step @p155 :rule trans :premises (@p154 @p153)) % 4.32/4.55 (step @p156 :rule eq-symm :args (@t92 @t5)) % 4.32/4.55 (step @p157 :rule refl :args (@t93)) % 4.32/4.55 (step @p158 :rule refl :args (@t94)) % 4.32/4.55 (step @p159 :rule nary_cong :premises (@p158 @p157 @p156) :args (@t95)) % 4.32/4.55 (step @p160 :rule cong :premises (@p159) :args (@t96)) % 4.32/4.55 (step @p161 :rule trans :premises (@p160 @p155)) % 4.32/4.55 (step @p162 :rule nary_cong :premises (@p161 @p144 @p143) :args (@t104)) % 4.32/4.55 (step @p163 :rule cong :premises (@p162 @p141) :args (@t105)) % 4.32/4.55 (step @p164 :rule cong :premises (@p163) :args (@t106)) % 4.32/4.55 (step @p165 :rule trans :premises (@p164 @p140)) % 4.32/4.55 (step @p166 :rule refl :args (@t44)) % 4.32/4.55 (step @p167 :rule refl :args (@t58)) % 4.32/4.55 (step @p168 :rule aci_norm :args ((= (or @t141 (or @t140 @t139)) @t142))) % 4.32/4.55 (step @p169 :rule bool-and-de-morgan :args (@t53 @t138 true)) % 4.32/4.55 (step @p170 :rule refl :args (@t141)) % 4.32/4.55 (step @p171 :rule nary_cong :premises (@p170 @p169) :args ((or @t141 (not (and @t53 @t138))))) % 4.32/4.55 (step @p172 :rule bool-and-de-morgan :args (@t54 @t53 (and @t138))) % 4.32/4.55 (step @p173 :rule trans :premises (@p172 @p171)) % 4.32/4.55 (step @p174 :rule trans :premises (@p173 @p168)) % 4.32/4.55 (step @p175 :rule cong :premises (@p174) :args (@t189)) % 4.32/4.55 (step @p176 :rule cong :premises (@p175) :args (@t190)) % 4.32/4.55 (step @p177 :rule exists-elim :args ((= (exists @t56 @t188) @t190))) % 4.32/4.55 (step @p178 :rule trans :premises (@p177 @p176)) % 4.32/4.55 (step @p179 :rule eq-symm :args (@t12 @t1)) % 4.32/4.55 (step @p180 :rule refl :args (@t53)) % 4.32/4.55 (step @p181 :rule refl :args (@t54)) % 4.32/4.55 (step @p182 :rule nary_cong :premises (@p181 @p180 @p179) :args (@t55)) % 4.32/4.55 (step @p183 :rule cong :premises (@p182) :args (@t57)) % 4.32/4.55 (step @p184 :rule trans :premises (@p183 @p178)) % 4.32/4.55 (step @p185 :rule nary_cong :premises (@p184 @p167) :args (@t99)) % 4.32/4.55 (step @p186 :rule nary_cong :premises (@p185 @p166 @p165) :args (@t107)) % 4.32/4.55 (step @p187 :rule cong :premises (@p186) :args (@t108)) % 4.32/4.55 (step @p188 :rule trans :premises (@p187 @p84)) % 4.32/4.55 (step @p189 :rule cong :premises (@p188) :args (@t109)) % 4.32/4.55 (step @p190 :rule trans :premises (@p189 @p48)) % 4.32/4.55 (step @p191 :rule eq_resolve :premises (@p46 @p190)) % 4.32/4.55 (step @p192 :rule refl :args (@t214)) % 4.32/4.55 (step @p193 :rule eq-symm :args (@t211 tptp.sz00)) % 4.32/4.55 (step @p194 :rule refl :args (@t216)) % 4.32/4.55 (step @p195 :rule eq-symm :args (@t211 @t229)) % 4.32/4.55 (step @p196 :rule cong :premises (@p195) :args (@t230)) % 4.32/4.55 (step @p197 :rule refl :args (@t231)) % 4.32/4.55 (step @p198 :rule refl :args (@t232)) % 4.32/4.55 (step @p199 :rule nary_cong :premises (@p198 @p197 @p196) :args (@t233)) % 4.32/4.55 (step @p200 :rule nary_cong :premises (@p199 @p194) :args (@t234)) % 4.32/4.55 (step @p201 :rule nary_cong :premises (@p200 @p193 @p192) :args (@t235)) % 4.32/4.55 (step @p202 :rule refl :args (@t129)) % 4.32/4.55 (step @p203 :rule cong :premises (@p202 @p201) :args ((=> @t129 @t235))) % 4.32/4.55 (assume-push @p558 @t129) % 4.32/4.55 (step @p205 :rule instantiate :premises (@p191) :args ((@list @t211 @t228 @t227))) % 4.32/4.55 (step-pop @p559 :rule scope :premises (@p205)) % 4.32/4.55 (step @p206 :rule process_scope :premises (@p559) :args (@t235)) % 4.32/4.55 (step @p208 :rule eq_resolve :premises (@p206 @p203)) % 4.32/4.55 (step @p209 :rule implies_elim :premises (@p208)) % 4.32/4.55 (step @p210 :rule chain_m_resolution :premises (@p209 @p191) :args (@t238 @t239 (@list @t129))) % 4.32/4.55 (step @p211 :rule aci_norm :args ((= (or @t223 @t222 @t220 @t218 false) @t224))) % 4.32/4.55 (step @p212 :rule eq-refl :args (@t221)) % 4.32/4.55 (step @p213 :rule cong :premises (@p212) :args (@t240)) % 4.32/4.55 (step @p214 :rule trans :premises (@p213 @p86)) % 4.32/4.55 (step @p215 :rule refl :args (@t218)) % 4.32/4.55 (step @p216 :rule refl :args (@t220)) % 4.32/4.55 (step @p217 :rule eq-symm :args (@t221 tptp.sz00)) % 4.32/4.55 (step @p218 :rule refl :args (@t223)) % 4.32/4.55 (step @p219 :rule nary_cong :premises (@p218 @p217 @p216 @p215 @p214) :args (@t241)) % 4.32/4.55 (step @p220 :rule trans :premises (@p219 @p211)) % 4.32/4.55 (step @p221 :rule cong :premises (@p220) :args ((forall @t225 @t241))) % 4.32/4.55 (step @p222 :rule quant-var-elim-eq :args ((= (forall @t3 @t244) @t241))) % 4.32/4.55 (step @p223 :rule aci_norm :args ((= @t245 @t244))) % 4.32/4.55 (step @p224 :rule cong :premises (@p223) :args (@t246)) % 4.32/4.55 (step @p225 :rule trans :premises (@p224 @p222)) % 4.32/4.55 (step @p226 :rule cong :premises (@p225) :args (@t247)) % 4.32/4.55 (step @p227 :rule quant-merge-prenex :args ((= @t247 @t248))) % 4.32/4.55 (step @p228 :rule symm :premises (@p227)) % 4.32/4.55 (step @p229 :rule quant_var_reordering :args ((= (forall @t249 @t245) @t248))) % 4.32/4.55 (step @p230 :rule trans :premises (@p229 @p228 @p226)) % 4.32/4.55 (step @p231 :rule trans :premises (@p230 @p221)) % 4.32/4.55 (step @p232 :rule aci_norm :args ((= @t251 @t245))) % 4.32/4.55 (step @p233 :rule cong :premises (@p232) :args (@t252)) % 4.32/4.55 (step @p234 :rule trans :premises (@p233 @p231)) % 4.32/4.55 (step @p235 :rule quant-merge-prenex :args ((= (forall @t3 @t253) @t252))) % 4.32/4.55 (step @p236 :rule refl :args (@t243)) % 4.32/4.55 (step @p237 :rule alpha_equiv :args (@t254 (@list @t219 @t217) @t134)) % 4.32/4.55 (step @p238 :rule nary_cong :premises (@p237 @p236 @p51) :args (@t255)) % 4.32/4.55 (step @p239 :rule quant-miniscope-or :args ((= @t253 @t255))) % 4.32/4.55 (step @p240 :rule trans :premises (@p239 @p238)) % 4.32/4.55 (step @p241 :rule symm :premises (@p240)) % 4.32/4.55 (step @p242 :rule cong :premises (@p241) :args (@t257)) % 4.32/4.55 (step @p243 :rule trans :premises (@p242 @p235)) % 4.32/4.55 (step @p244 :rule trans :premises (@p243 @p234)) % 4.32/4.55 (step @p245 :rule refl :args (@t261)) % 4.32/4.55 (step @p246 :rule refl :args (@t264)) % 4.32/4.55 (step @p247 :rule nary_cong :premises (@p246 @p245 @p244) :args (@t265)) % 4.32/4.55 (step @p248 :rule quant-miniscope-or :args ((= (forall @t3 @t266) @t265))) % 4.32/4.55 (step @p249 :rule aci_norm :args ((= @t267 @t266))) % 4.32/4.55 (step @p250 :rule cong :premises (@p249) :args ((forall @t3 @t267))) % 4.32/4.55 (step @p251 :rule trans :premises (@p250 @p248)) % 4.32/4.55 (step @p252 :rule trans :premises (@p251 @p247)) % 4.32/4.55 (step @p253 :rule refl :args (@t261)) % 4.32/4.55 (step @p254 :rule refl :args (@t264)) % 4.32/4.55 (step @p255 :rule nary_cong :premises (@p254 @p253 @p64 @p236 @p69) :args (@t268)) % 4.32/4.55 (step @p256 :rule aci_norm :args ((= (or @t264 (or @t261 (or @t146 (or @t243 @t149)))) @t268))) % 4.32/4.55 (step @p257 :rule trans :premises (@p256 @p255)) % 4.32/4.55 (step @p258 :rule bool-and-de-morgan :args (@t64 @t44 true)) % 4.32/4.55 (step @p259 :rule refl :args (@t146)) % 4.32/4.55 (step @p260 :rule nary_cong :premises (@p259 @p258) :args ((or @t146 (not (and @t64 @t44))))) % 4.32/4.55 (step @p261 :rule bool-and-de-morgan :args 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4.32/4.57 (step @p501 :rule refl :args (@t358)) % 4.32/4.57 (step @p502 :rule nary_cong :premises (@p501 @p500) :args ((or @t358 (not @t216)))) % 4.32/4.57 (step @p503 :rule cnf_or_neg :args (@t358 0)) % 4.32/4.57 (step @p504 :rule eq_resolve :premises (@p503 @p502)) % 4.32/4.57 (step @p505 :rule reordering :premises (@p504) :args ((or @t215 @t358))) % 4.32/4.57 (step @p506 :rule chain_m_resolution :premises (@p505 @p499) :args (@t215 @t282 @t360)) % 4.32/4.57 (step @p507 :rule cnf_and_pos :args (@t237 1)) % 4.32/4.57 (step @p508 :rule reordering :premises (@p507) :args ((or @t216 @t361))) % 4.32/4.57 (step @p509 :rule chain_m_resolution :premises (@p508 @p506) :args (@t361 @t239 (@list @t215))) % 4.32/4.57 (step @p510 :rule cnf_or_neg :args (@t358 1)) % 4.32/4.57 (step @p511 :rule chain_m_resolution :premises (@p510 @p499) :args ((not @t236) @t282 @t360)) % 4.32/4.57 (step @p512 :rule cnf_or_pos :args (@t238)) % 4.32/4.57 (step @p513 :rule reordering :premises (@p512) :args ((or @t236 @t214 @t237 (not @t238)))) % 4.32/4.57 (step @p514 :rule chain_m_resolution :premises (@p513 @p511 @p509 @p210) :args (@t214 (@list true true false) (@list @t236 @t237 @t238))) % 4.32/4.57 (step @p515 :rule refl :args (@t371)) % 4.32/4.57 (step @p516 :rule bool-double-not-elim :args (@t213)) % 4.32/4.57 (step @p517 :rule nary_cong :premises (@p516 @p515) :args ((or (not @t214) @t371))) % 4.32/4.57 (assume-push @p564 @t214) % 4.32/4.57 (step @p519 :rule skolemize :premises (@p564)) % 4.32/4.57 (step-pop @p565 :rule scope :premises (@p519)) % 4.32/4.57 (step @p520 :rule process_scope :premises (@p565) :args (@t371)) % 4.32/4.57 (step @p522 :rule implies_elim :premises (@p520)) % 4.32/4.57 (step @p523 :rule eq_resolve :premises (@p522 @p517)) % 4.32/4.57 (step @p524 :rule chain_m_resolution :premises (@p523 @p514) :args (@t371 @t282 (@list @t213))) % 4.32/4.57 (step @p525 :rule cnf_or_neg :args (@t370 1)) % 4.32/4.57 (step @p526 :rule chain_m_resolution :premises (@p525 @p524) :args ((not @t367) @t282 @t372)) % 4.32/4.57 (step @p527 :rule bool-double-not-elim :args (@t365)) % 4.32/4.57 (step @p528 :rule refl :args (@t370)) % 4.32/4.57 (step @p529 :rule nary_cong :premises (@p528 @p527) :args ((or @t370 (not @t366)))) % 4.32/4.57 (step @p530 :rule cnf_or_neg :args (@t370 2)) % 4.32/4.57 (step @p531 :rule eq_resolve :premises (@p530 @p529)) % 4.32/4.57 (step @p532 :rule reordering :premises (@p531) :args ((or @t365 @t370))) % 4.32/4.57 (step @p533 :rule chain_m_resolution :premises (@p532 @p524) :args (@t365 @t282 @t372)) % 4.32/4.57 (step @p534 :rule bool-double-not-elim :args (@t368)) % 4.32/4.57 (step @p535 :rule nary_cong :premises (@p528 @p534) :args ((or @t370 (not @t369)))) % 4.32/4.57 (step @p536 :rule cnf_or_neg :args (@t370 0)) % 4.32/4.57 (step @p537 :rule eq_resolve :premises (@p536 @p535)) % 4.32/4.57 (step @p538 :rule reordering :premises (@p537) :args ((or @t368 @t370))) % 4.32/4.57 (step @p539 :rule chain_m_resolution :premises (@p538 @p524) :args (@t368 @t282 @t372)) % 4.32/4.57 (step @p540 :rule cnf_and_pos :args (@t375 1)) % 4.32/4.57 (step @p541 :rule reordering :premises (@p540) :args ((or @t369 @t376))) % 4.32/4.57 (step @p542 :rule chain_m_resolution :premises (@p541 @p539) :args (@t376 @t239 (@list @t368))) % 4.32/4.57 (step @p543 :rule bool-double-not-elim :args (@t356)) % 4.32/4.57 (step @p544 :rule nary_cong :premises (@p501 @p543) :args ((or @t358 (not @t357)))) % 4.32/4.57 (step @p545 :rule cnf_or_neg :args (@t358 2)) % 4.32/4.57 (step @p546 :rule eq_resolve :premises (@p545 @p544)) % 4.32/4.57 (step @p547 :rule reordering :premises (@p546) :args ((or @t356 @t358))) % 4.32/4.57 (step @p548 :rule chain_m_resolution :premises (@p547 @p499) :args (@t356 @t282 @t360)) % 4.32/4.57 (assume-push @p566 @t356) % 4.32/4.57 (step @p550 :rule instantiate :premises (@p566) :args ((@list @t364 @t374 @t373))) % 4.32/4.57 (step-pop @p567 :rule scope :premises (@p550)) % 4.32/4.57 (step @p551 :rule process_scope :premises (@p567) :args (@t377)) % 4.32/4.57 (step @p553 :rule implies_elim :premises (@p551)) % 4.32/4.57 (step @p554 :rule chain_m_resolution :premises (@p553 @p548) :args (@t377 @t239 (@list @t356))) % 4.32/4.57 (step @p555 :rule cnf_or_pos :args (@t377)) % 4.32/4.57 (step @p556 :rule reordering :premises (@p555) :args ((or @t367 @t366 @t375 (not @t377)))) % 4.32/4.57 (step @p557 false :rule chain_m_resolution :premises (@p556 @p554 @p542 @p533 @p526) :args (false (@list false true false true) (@list @t377 @t375 @t365 @t367))) % 4.32/4.57 ) % 4.32/4.57 % SZS output end Proof % 4.32/4.57 % cvc5 exiting %------------------------------------------------------------------------------