%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : RNG115+1 : 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 : n029.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 38.12s 38.37s % Output : Proof 38.12s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : RNG115+1 : 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 % 0.16/0.34 % Computer : n029.cluster.edu % 0.16/0.34 % Model : x86_64 x86_64 % 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.34 % Memory : 8042.1875MB % 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.35 % CPULimit : 300 % 0.16/0.35 % WCLimit : 300 % 0.16/0.35 % DateTime : Tue Jun 2 14:07:47 EDT 2026 % 0.16/0.35 % CPUTime : % 0.30/0.51 %----Proving TF0_NAR, FOF, or CNF % 38.12/38.37 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 38.12/38.37 --- Run --no-e-matching --full-saturate-quant at 6... % 38.12/38.37 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 6... % 38.12/38.37 --- Run --finite-model-find --uf-ss=no-minimal at 6... % 38.12/38.37 --- Run --multi-trigger-when-single --full-saturate-quant at 30... % 38.12/38.37 % SZS status Theorem % 38.12/38.37 % SZS output start Proof % 38.12/38.37 ( % 38.12/38.37 (declare-sort $$unsorted 0) % 38.12/38.37 (declare-const tptp.xu $$unsorted) % 38.12/38.37 (declare-const tptp.xc $$unsorted) % 38.12/38.37 (declare-const tptp.xa $$unsorted) % 38.12/38.37 (declare-const tptp.xI $$unsorted) % 38.12/38.37 (declare-const tptp.slsdtgt0 (-> $$unsorted $$unsorted)) % 38.12/38.37 (declare-const tptp.aDivisorOf0 (-> $$unsorted $$unsorted Bool)) % 38.12/38.37 (declare-const tptp.iLess0 (-> $$unsorted $$unsorted Bool)) % 38.12/38.37 (declare-const tptp.sbrdtbr0 (-> $$unsorted $$unsorted)) % 38.12/38.37 (declare-const tptp.aElement0 (-> $$unsorted Bool)) % 38.12/38.37 (declare-const tptp.sz00 $$unsorted) % 38.12/38.37 (declare-const tptp.sz10 $$unsorted) % 38.12/38.37 (declare-const tptp.aGcdOfAnd0 (-> $$unsorted $$unsorted $$unsorted Bool)) % 38.12/38.37 (declare-const tptp.smndt0 (-> $$unsorted $$unsorted)) % 38.12/38.37 (declare-const tptp.sdtpldt0 (-> $$unsorted $$unsorted $$unsorted)) % 38.12/38.37 (declare-const tptp.sdtasasdt0 (-> $$unsorted $$unsorted $$unsorted)) % 38.12/38.37 (declare-const tptp.aIdeal0 (-> $$unsorted Bool)) % 38.12/38.37 (declare-const tptp.misRelativelyPrime0 (-> $$unsorted $$unsorted Bool)) % 38.12/38.37 (declare-const tptp.sdtasdt0 (-> $$unsorted $$unsorted $$unsorted)) % 38.12/38.37 (declare-const tptp.doDivides0 (-> $$unsorted $$unsorted Bool)) % 38.12/38.37 (declare-const tptp.aSet0 (-> $$unsorted Bool)) % 38.12/38.37 (declare-const tptp.aElementOf0 (-> $$unsorted $$unsorted Bool)) % 38.12/38.37 (declare-const tptp.sdteqdtlpzmzozddtrp0 (-> $$unsorted $$unsorted $$unsorted Bool)) % 38.12/38.37 (declare-const tptp.xb $$unsorted) % 38.12/38.37 (declare-const tptp.sdtpldt1 (-> $$unsorted $$unsorted $$unsorted)) % 38.12/38.37 (declare-const tptp.aNaturalNumber0 (-> $$unsorted Bool)) % 38.12/38.37 (define @t1 () (@var "W0" $$unsorted)) % 38.12/38.37 (define @t2 () (tptp.aElement0 @t1)) % 38.12/38.37 (define @t3 () (@list @t1)) % 38.12/38.37 (define @t4 () (tptp.smndt0 @t1)) % 38.12/38.37 (define @t5 () (@var "W1" $$unsorted)) % 38.12/38.37 (define @t6 () (tptp.sdtpldt0 @t1 @t5)) % 38.12/38.37 (define @t7 () (tptp.aElement0 @t5)) % 38.12/38.37 (define @t8 () (and @t2 @t7)) % 38.12/38.37 (define @t9 () (@list @t1 @t5)) % 38.12/38.37 (define @t10 () (tptp.sdtasdt0 @t1 @t5)) % 38.12/38.37 (define @t11 () (@var "W2" $$unsorted)) % 38.12/38.37 (define @t12 () (tptp.sdtpldt0 @t5 @t11)) % 38.12/38.37 (define @t13 () (tptp.aElement0 @t11)) % 38.12/38.37 (define @t14 () (and @t2 @t7 @t13)) % 38.12/38.37 (define @t15 () (@list @t1 @t5 @t11)) % 38.12/38.37 (define @t16 () (tptp.sdtasdt0 @t5 @t1)) % 38.12/38.37 (define @t17 () (tptp.sdtasdt0 @t1 @t11)) % 38.12/38.37 (define @t18 () (tptp.smndt0 tptp.sz10)) % 38.12/38.37 (define @t19 () (= @t5 tptp.sz00)) % 38.12/38.37 (define @t20 () (= @t1 tptp.sz00)) % 38.12/38.37 (define @t21 () (tptp.aSet0 @t1)) % 38.12/38.37 (define @t22 () (tptp.aElementOf0 @t5 @t1)) % 38.12/38.37 (define @t23 () (@list @t5)) % 38.12/38.37 (define @t24 () (tptp.aElementOf0 @t11 @t1)) % 38.12/38.37 (define @t25 () (tptp.aElementOf0 @t11 @t5)) % 38.12/38.37 (define @t26 () (@list @t11)) % 38.12/38.37 (define @t27 () (tptp.aSet0 @t5)) % 38.12/38.37 (define @t28 () (and @t21 @t27)) % 38.12/38.37 (define @t29 () (@var "W3" $$unsorted)) % 38.12/38.37 (define @t30 () (@var "W5" $$unsorted)) % 38.12/38.37 (define @t31 () (@var "W4" $$unsorted)) % 38.12/38.37 (define @t32 () (tptp.sdtpldt0 @t31 @t30)) % 38.12/38.37 (define @t33 () (tptp.aElementOf0 @t30 @t5)) % 38.12/38.37 (define @t34 () (tptp.aElementOf0 @t31 @t1)) % 38.12/38.37 (define @t35 () (and @t34 @t33 (= @t32 @t29))) % 38.12/38.37 (define @t36 () (@list @t31 @t30)) % 38.12/38.37 (define @t37 () (exists @t36 @t35)) % 38.12/38.37 (define @t38 () (tptp.aElementOf0 @t29 @t11)) % 38.12/38.37 (define @t39 () (= @t38 @t37)) % 38.12/38.37 (define @t40 () (@list @t29)) % 38.12/38.37 (define @t41 () (forall @t40 @t39)) % 38.12/38.37 (define @t42 () (tptp.aSet0 @t11)) % 38.12/38.37 (define @t43 () (and @t42 @t41)) % 38.12/38.37 (define @t44 () (tptp.sdtpldt1 @t1 @t5)) % 38.12/38.37 (define @t45 () (= @t11 @t44)) % 38.12/38.37 (define @t46 () (= @t45 @t43)) % 38.12/38.37 (define @t47 () (forall @t26 @t46)) % 38.12/38.37 (define @t48 () (=> @t28 @t47)) % 38.12/38.37 (define @t49 () (forall @t9 @t48)) % 38.12/38.37 (define @t50 () (tptp.sdtasasdt0 @t1 @t5)) % 38.12/38.37 (define @t51 () (tptp.sdtasdt0 @t11 @t5)) % 38.12/38.37 (define @t52 () (tptp.aElementOf0 @t51 @t1)) % 38.12/38.37 (define @t53 () (forall @t26 (=> @t13 @t52))) % 38.12/38.37 (define @t54 () (tptp.aElementOf0 @t12 @t1)) % 38.12/38.37 (define @t55 () (forall @t26 (=> @t24 @t54))) % 38.12/38.37 (define @t56 () (and @t55 @t53)) % 38.12/38.37 (define @t57 () (=> @t22 @t56)) % 38.12/38.37 (define @t58 () (forall @t23 @t57)) % 38.12/38.37 (define @t59 () (and @t21 @t58)) % 38.12/38.37 (define @t60 () (tptp.aIdeal0 @t1)) % 38.12/38.37 (define @t61 () (= @t60 @t59)) % 38.12/38.37 (define @t62 () (forall @t3 @t61)) % 38.12/38.37 (define @t63 () (and @t60 (tptp.aIdeal0 @t5))) % 38.12/38.37 (define @t64 () (tptp.aElement0 @t29)) % 38.12/38.37 (define @t65 () (@list @t11 @t29)) % 38.12/38.37 (define @t66 () (tptp.aNaturalNumber0 @t1)) % 38.12/38.37 (define @t67 () (tptp.sbrdtbr0 @t1)) % 38.12/38.37 (define @t68 () (not @t20)) % 38.12/38.37 (define @t69 () (tptp.slsdtgt0 @t1)) % 38.12/38.37 (define @t70 () (tptp.aIdeal0 @t69)) % 38.12/38.37 (define @t71 () (forall @t3 (=> @t2 @t70))) % 38.12/38.37 (define @t72 () (tptp.aElement0 tptp.xb)) % 38.12/38.37 (define @t73 () (tptp.aElement0 tptp.xa)) % 38.12/38.37 (define @t74 () (tptp.slsdtgt0 tptp.xb)) % 38.12/38.37 (define @t75 () (tptp.slsdtgt0 tptp.xa)) % 38.12/38.37 (define @t76 () (tptp.sdtpldt1 @t75 @t74)) % 38.12/38.37 (define @t77 () (tptp.aElementOf0 tptp.xu tptp.xI)) % 38.12/38.37 (define @t78 () (tptp.aElementOf0 @t5 @t74)) % 38.12/38.37 (define @t79 () (tptp.aElementOf0 @t1 @t75)) % 38.12/38.37 (define @t80 () (and @t79 @t78 (= tptp.xu @t6))) % 38.12/38.37 (define @t81 () (exists @t9 @t80)) % 38.12/38.37 (define @t82 () (not @t81)) % 38.12/38.37 (define @t83 () (= @t6 tptp.xu)) % 38.12/38.37 (define @t84 () (not @t83)) % 38.12/38.37 (define @t85 () (not @t78)) % 38.12/38.37 (define @t86 () (not @t79)) % 38.12/38.37 (define @t87 () (or @t86 @t85 @t84)) % 38.12/38.37 (define @t88 () (forall @t9 @t87)) % 38.12/38.37 (define @t89 () (and @t79 @t78 @t83)) % 38.12/38.37 (define @t90 () (forall @t9 (not @t89))) % 38.12/38.37 (define @t91 () (not @t90)) % 38.12/38.37 (define @t92 () (not (tptp.aElementOf0 @t30 @t74))) % 38.12/38.37 (define @t93 () (not (tptp.aElementOf0 @t31 @t75))) % 38.12/38.37 (define @t94 () (forall @t36 (or @t93 @t92 (not (= @t32 tptp.xu))))) % 38.12/38.37 (define @t95 () (@list false)) % 38.12/38.37 (define @t96 () (@var "BOUND_VARIABLE_7916" $$unsorted)) % 38.12/38.37 (define @t97 () (tptp.aElementOf0 @t29 @t96)) % 38.12/38.37 (define @t98 () (= @t29 @t32)) % 38.12/38.37 (define @t99 () (not @t98)) % 38.12/38.37 (define @t100 () (not @t33)) % 38.12/38.37 (define @t101 () (not @t34)) % 38.12/38.37 (define @t102 () (or @t101 @t100 @t99)) % 38.12/38.37 (define @t103 () (not (forall @t36 @t102))) % 38.12/38.37 (define @t104 () (forall @t40 (= @t97 @t103))) % 38.12/38.37 (define @t105 () (tptp.aSet0 @t96)) % 38.12/38.37 (define @t106 () (and @t105 @t104)) % 38.12/38.37 (define @t107 () (= (= @t96 @t44) @t106)) % 38.12/38.37 (define @t108 () (not @t27)) % 38.12/38.37 (define @t109 () (not @t21)) % 38.12/38.37 (define @t110 () (or @t109 @t108 @t107)) % 38.12/38.37 (define @t111 () (@list @t1 @t5 @t96)) % 38.12/38.37 (define @t112 () (forall @t111 @t110)) % 38.12/38.37 (define @t113 () (@list @t96)) % 38.12/38.37 (define @t114 () (forall @t113 @t110)) % 38.12/38.37 (define @t115 () (forall @t113 @t107)) % 38.12/38.37 (define @t116 () (@list @t11)) % 38.12/38.37 (define @t117 () (or @t109 @t108 @t115)) % 38.12/38.37 (define @t118 () (forall @t26 (= @t45 (and @t42 (forall @t40 (= @t38 @t103)))))) % 38.12/38.37 (define @t119 () (or @t109 @t108 @t118)) % 38.12/38.37 (define @t120 () (and @t34 @t33 @t98)) % 38.12/38.37 (define @t121 () (forall @t36 (not @t120))) % 38.12/38.37 (define @t122 () (not @t121)) % 38.12/38.37 (define @t123 () (not (forall @t36 (or @t93 @t92 @t99)))) % 38.12/38.37 (define @t124 () (tptp.aElementOf0 @t29 @t76)) % 38.12/38.37 (define @t125 () (forall @t40 (= @t124 @t123))) % 38.12/38.37 (define @t126 () (tptp.aSet0 @t76)) % 38.12/38.37 (define @t127 () (and @t126 @t125)) % 38.12/38.37 (define @t128 () (forall @t40 (= @t123 @t124))) % 38.12/38.37 (define @t129 () (and @t126 @t128)) % 38.12/38.37 (define @t130 () (= (= @t76 @t76) @t129)) % 38.12/38.37 (define @t131 () (tptp.aSet0 @t74)) % 38.12/38.37 (define @t132 () (not @t131)) % 38.12/38.37 (define @t133 () (tptp.aSet0 @t75)) % 38.12/38.37 (define @t134 () (not @t133)) % 38.12/38.37 (define @t135 () (or @t134 @t132 @t130)) % 38.12/38.37 (define @t136 () (forall @t111 (or @t109 @t108 (= (= @t44 @t96) (and @t105 (forall @t40 (= @t103 @t97))))))) % 38.12/38.37 (define @t137 () (or @t134 @t132 @t127)) % 38.12/38.37 (define @t138 () (@var "BOUND_VARIABLE_7974" $$unsorted)) % 38.12/38.37 (define @t139 () (tptp.sdtasdt0 @t138 @t5)) % 38.12/38.37 (define @t140 () (not (tptp.aElement0 @t138))) % 38.12/38.37 (define @t141 () (or @t140 (tptp.aElementOf0 @t139 @t1))) % 38.12/38.37 (define @t142 () (@var "BOUND_VARIABLE_7967" $$unsorted)) % 38.12/38.37 (define @t143 () (tptp.sdtpldt0 @t5 @t142)) % 38.12/38.37 (define @t144 () (or (not (tptp.aElementOf0 @t142 @t1)) (tptp.aElementOf0 @t143 @t1))) % 38.12/38.37 (define @t145 () (and @t144 @t141)) % 38.12/38.37 (define @t146 () (not @t22)) % 38.12/38.37 (define @t147 () (or @t146 @t145)) % 38.12/38.37 (define @t148 () (@list @t5 @t142 @t138)) % 38.12/38.37 (define @t149 () (@list @t142 @t138)) % 38.12/38.37 (define @t150 () (forall @t149 @t147)) % 38.12/38.37 (define @t151 () (forall (@list @t138) @t141)) % 38.12/38.37 (define @t152 () (forall @t149 @t141)) % 38.12/38.37 (define @t153 () (forall (@list @t142) @t144)) % 38.12/38.37 (define @t154 () (forall @t149 @t144)) % 38.12/38.37 (define @t155 () (and @t154 @t152)) % 38.12/38.37 (define @t156 () (forall @t149 @t145)) % 38.12/38.37 (define @t157 () (or @t146 @t156)) % 38.12/38.37 (define @t158 () (and (forall @t26 (or (not @t24) @t54)) (forall @t26 (or (not @t13) @t52)))) % 38.12/38.37 (define @t159 () (tptp.aIdeal0 @t74)) % 38.12/38.37 (define @t160 () (not @t72)) % 38.12/38.37 (define @t161 () (or @t160 @t159)) % 38.12/38.37 (define @t162 () (@list false false)) % 38.12/38.37 (define @t163 () (and @t131 (forall @t148 (or @t85 (and (or (not (tptp.aElementOf0 @t142 @t74)) (tptp.aElementOf0 @t143 @t74)) (or @t140 (tptp.aElementOf0 @t139 @t74))))))) % 38.12/38.37 (define @t164 () (= @t159 @t163)) % 38.12/38.37 (define @t165 () (tptp.aIdeal0 @t75)) % 38.12/38.37 (define @t166 () (not @t73)) % 38.12/38.37 (define @t167 () (or @t166 @t165)) % 38.12/38.37 (define @t168 () (and @t133 (forall @t148 (or (not (tptp.aElementOf0 @t5 @t75)) (and (or (not (tptp.aElementOf0 @t142 @t75)) (tptp.aElementOf0 @t143 @t75)) (or @t140 (tptp.aElementOf0 @t139 @t75))))))) % 38.12/38.37 (define @t169 () (= @t165 @t168)) % 38.12/38.37 (define @t170 () (@list false false false)) % 38.12/38.37 (define @t171 () (not (= tptp.xu @t32))) % 38.12/38.37 (define @t172 () (or @t93 @t92 @t171)) % 38.12/38.37 (define @t173 () (forall @t36 @t172)) % 38.12/38.37 (define @t174 () (not @t173)) % 38.12/38.37 (define @t175 () (tptp.aElementOf0 tptp.xu @t76)) % 38.12/38.37 (define @t176 () (= @t175 @t174)) % 38.12/38.37 (define @t177 () (not @t94)) % 38.12/38.37 (define @t178 () (= @t175 @t177)) % 38.12/38.37 (assume @p1 (forall @t3 (=> @t2 true))) % 38.12/38.37 (assume @p2 (tptp.aElement0 tptp.sz00)) % 38.12/38.37 (assume @p3 (tptp.aElement0 tptp.sz10)) % 38.12/38.37 (assume @p4 (forall @t3 (=> @t2 (tptp.aElement0 @t4)))) % 38.12/38.37 (assume @p5 (forall @t9 (=> @t8 (tptp.aElement0 @t6)))) % 38.12/38.37 (assume @p6 (forall @t9 (=> @t8 (tptp.aElement0 @t10)))) % 38.12/38.37 (assume @p7 (forall @t9 (=> @t8 (= @t6 (tptp.sdtpldt0 @t5 @t1))))) % 38.12/38.37 (assume @p8 (forall @t15 (=> @t14 (= (tptp.sdtpldt0 @t6 @t11) (tptp.sdtpldt0 @t1 @t12))))) % 38.12/38.37 (assume @p9 (forall @t3 (=> @t2 (and (= (tptp.sdtpldt0 @t1 tptp.sz00) @t1) (= @t1 (tptp.sdtpldt0 tptp.sz00 @t1)))))) % 38.12/38.37 (assume @p10 (forall @t3 (=> @t2 (and (= (tptp.sdtpldt0 @t1 @t4) tptp.sz00) (= tptp.sz00 (tptp.sdtpldt0 @t4 @t1)))))) % 38.12/38.37 (assume @p11 (forall @t9 (=> @t8 (= @t10 @t16)))) % 38.12/38.37 (assume @p12 (forall @t15 (=> @t14 (= (tptp.sdtasdt0 @t10 @t11) (tptp.sdtasdt0 @t1 (tptp.sdtasdt0 @t5 @t11)))))) % 38.12/38.37 (assume @p13 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz10) @t1) (= @t1 (tptp.sdtasdt0 tptp.sz10 @t1)))))) % 38.12/38.37 (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))))))) % 38.12/38.37 (assume @p15 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t18 @t1) @t4) (= @t4 (tptp.sdtasdt0 @t1 @t18)))))) % 38.12/38.37 (assume @p16 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz00) tptp.sz00) (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 @t1)))))) % 38.12/38.37 (assume @p17 (forall @t9 (=> @t8 (=> (= @t10 tptp.sz00) (or @t20 @t19))))) % 38.12/38.37 (assume @p18 (not (= tptp.sz10 tptp.sz00))) % 38.12/38.37 (assume @p19 (forall @t3 (=> @t21 true))) % 38.12/38.37 (assume @p20 (forall @t3 (=> @t21 (forall @t23 (=> @t22 @t7))))) % 38.12/38.37 (assume @p21 (forall @t9 (=> @t28 (=> (and (forall @t26 (=> @t24 @t25)) (forall @t26 (=> @t25 @t24))) (= @t1 @t5))))) % 38.12/38.37 (assume @p22 @t49) % 38.12/38.37 (assume @p23 (forall @t9 (=> @t28 (forall @t26 (= (= @t11 @t50) (and @t42 (forall @t40 (= @t38 (and (tptp.aElementOf0 @t29 @t1) (tptp.aElementOf0 @t29 @t5)))))))))) % 38.12/38.37 (assume @p24 @t62) % 38.12/38.37 (assume @p25 (forall @t9 (=> @t63 (tptp.aIdeal0 @t44)))) % 38.12/38.37 (assume @p26 (forall @t9 (=> @t63 (tptp.aIdeal0 @t50)))) % 38.12/38.37 (assume @p27 (forall @t15 (=> (and @t2 @t7 (tptp.aIdeal0 @t11)) (= (tptp.sdteqdtlpzmzozddtrp0 @t1 @t5 @t11) (tptp.aElementOf0 (tptp.sdtpldt0 @t1 (tptp.smndt0 @t5)) @t11))))) % 38.12/38.37 (assume @p28 (forall @t9 (=> @t63 (=> (forall @t26 (=> @t13 (tptp.aElementOf0 @t11 @t44))) (forall @t65 (=> (and @t13 @t64) (exists (@list @t31) (and (tptp.aElement0 @t31) (tptp.sdteqdtlpzmzozddtrp0 @t31 @t11 @t1) (tptp.sdteqdtlpzmzozddtrp0 @t31 @t29 @t5))))))))) % 38.12/38.37 (assume @p29 (forall @t3 (=> @t66 true))) % 38.12/38.37 (assume @p30 (forall @t3 (=> (and @t2 @t68) (tptp.aNaturalNumber0 @t67)))) % 38.12/38.37 (assume @p31 (forall @t9 (=> (and @t66 (tptp.aNaturalNumber0 @t5)) (=> (tptp.iLess0 @t1 @t5) true)))) % 38.12/38.37 (assume @p32 (forall @t9 (=> (and @t2 @t7 (not @t19)) (exists @t65 (and @t13 @t64 (= @t1 (tptp.sdtpldt0 @t51 @t29)) (=> (not (= @t29 tptp.sz00)) (tptp.iLess0 (tptp.sbrdtbr0 @t29) (tptp.sbrdtbr0 @t5)))))))) % 38.12/38.37 (assume @p33 (forall @t9 (=> @t8 (= (tptp.doDivides0 @t1 @t5) (exists @t26 (and @t13 (= @t17 @t5))))))) % 38.12/38.37 (assume @p34 (forall @t3 (=> @t2 (forall @t23 (= (tptp.aDivisorOf0 @t5 @t1) (and @t7 (tptp.doDivides0 @t5 @t1))))))) % 38.12/38.37 (assume @p35 (forall @t9 (=> @t8 (forall @t26 (= (tptp.aGcdOfAnd0 @t11 @t1 @t5) (and (tptp.aDivisorOf0 @t11 @t1) (tptp.aDivisorOf0 @t11 @t5) (forall @t40 (=> (and (tptp.aDivisorOf0 @t29 @t1) (tptp.aDivisorOf0 @t29 @t5)) (tptp.doDivides0 @t29 @t11))))))))) % 38.12/38.37 (assume @p36 (forall @t9 (=> @t8 (= (tptp.misRelativelyPrime0 @t1 @t5) (tptp.aGcdOfAnd0 tptp.sz10 @t1 @t5))))) % 38.12/38.37 (assume @p37 (forall @t3 (=> @t2 (forall @t23 (= (= @t5 @t69) (and @t27 (forall @t26 (= @t25 (exists @t40 (and @t64 (= (tptp.sdtasdt0 @t1 @t29) @t11))))))))))) % 38.12/38.37 (assume @p38 @t71) % 38.12/38.37 (assume @p39 (and @t73 @t72)) % 38.12/38.37 (assume @p40 (or (not (= tptp.xa tptp.sz00)) (not (= tptp.xb tptp.sz00)))) % 38.12/38.37 (assume @p41 (tptp.aGcdOfAnd0 tptp.xc tptp.xa tptp.xb)) % 38.12/38.37 (assume @p42 (and (tptp.aIdeal0 tptp.xI) (= tptp.xI @t76))) % 38.12/38.37 (assume @p43 (and (tptp.aElementOf0 tptp.sz00 @t75) (tptp.aElementOf0 tptp.xa @t75) (tptp.aElementOf0 tptp.sz00 @t74) (tptp.aElementOf0 tptp.xb @t74))) % 38.12/38.37 (assume @p44 (exists @t3 (and (tptp.aElementOf0 @t1 @t76) @t68))) % 38.12/38.37 (assume @p45 (and @t77 (not (= tptp.xu tptp.sz00)) (forall @t3 (=> (and (tptp.aElementOf0 @t1 tptp.xI) @t68) (not (tptp.iLess0 @t67 (tptp.sbrdtbr0 tptp.xu))))))) % 38.12/38.37 (assume @p46 (not (and (tptp.aDivisorOf0 tptp.xu tptp.xa) (tptp.aDivisorOf0 tptp.xu tptp.xb)))) % 38.12/38.37 (assume @p47 @t82) % 38.12/38.37 (assume @p48 true) % 38.12/38.37 (step @p49 :rule and_elim :premises (@p42) :args (1)) % 38.12/38.37 (step @p50 :rule refl :args (tptp.xu)) % 38.12/38.37 (step @p51 :rule cong :premises (@p50 @p49) :args (@t77)) % 38.12/38.37 (step @p52 :rule and_elim :premises (@p45) :args (0)) % 38.12/38.37 (step @p53 :rule eq_resolve :premises (@p52 @p51)) % 38.12/38.37 (step @p54 :rule bool-double-not-elim :args (@t88)) % 38.12/38.37 (step @p55 :rule aci_norm :args ((= (or @t86 (or @t85 @t84)) @t87))) % 38.12/38.37 (step @p56 :rule bool-and-de-morgan :args (@t78 @t83 true)) % 38.12/38.37 (step @p57 :rule refl :args (@t86)) % 38.12/38.37 (step @p58 :rule nary_cong :premises (@p57 @p56) :args ((or @t86 (not (and @t78 @t83))))) % 38.12/38.37 (step @p59 :rule bool-and-de-morgan :args (@t79 @t78 (and @t83))) % 38.12/38.37 (step @p60 :rule trans :premises (@p59 @p58)) % 38.12/38.37 (step @p61 :rule trans :premises (@p60 @p55)) % 38.12/38.37 (step @p62 :rule cong :premises (@p61) :args (@t90)) % 38.12/38.37 (step @p63 :rule cong :premises (@p62) :args (@t91)) % 38.12/38.37 (step @p64 :rule exists-elim :args ((= (exists @t9 @t89) @t91))) % 38.12/38.37 (step @p65 :rule trans :premises (@p64 @p63)) % 38.12/38.37 (step @p66 :rule eq-symm :args (tptp.xu @t6)) % 38.12/38.37 (step @p67 :rule refl :args (@t78)) % 38.12/38.37 (step @p68 :rule refl :args (@t79)) % 38.12/38.37 (step @p69 :rule nary_cong :premises (@p68 @p67 @p66) :args (@t80)) % 38.12/38.37 (step @p70 :rule cong :premises (@p69) :args (@t81)) % 38.12/38.37 (step @p71 :rule trans :premises (@p70 @p65)) % 38.12/38.37 (step @p72 :rule cong :premises (@p71) :args (@t82)) % 38.12/38.37 (step @p73 :rule trans :premises (@p72 @p54)) % 38.12/38.37 (step @p74 :rule eq_resolve :premises (@p47 @p73)) % 38.12/38.37 (step @p75 :rule alpha_equiv :args (@t88 (@list @t1 @t5) (@list @t31 @t30))) % 38.12/38.37 (step @p76 :rule equiv_elim1 :premises (@p75)) % 38.12/38.37 (step @p77 :rule chain_m_resolution :premises (@p76 @p74) :args (@t94 @t95 (@list @t88))) % 38.12/38.37 (step @p78 :rule eq-symm :args (@t97 @t103)) % 38.12/38.37 (step @p79 :rule cong :premises (@p78) :args (@t104)) % 38.12/38.37 (step @p80 :rule refl :args (@t105)) % 38.12/38.37 (step @p81 :rule nary_cong :premises (@p80 @p79) :args (@t106)) % 38.12/38.37 (step @p82 :rule eq-symm :args (@t96 @t44)) % 38.12/38.37 (step @p83 :rule cong :premises (@p82 @p81) :args (@t107)) % 38.12/38.37 (step @p84 :rule refl :args (@t108)) % 38.12/38.37 (step @p85 :rule refl :args (@t109)) % 38.12/38.37 (step @p86 :rule nary_cong :premises (@p85 @p84 @p83) :args (@t110)) % 38.12/38.37 (step @p87 :rule cong :premises (@p86) :args (@t112)) % 38.12/38.37 (step @p88 :rule quant-merge-prenex :args ((= (forall @t9 @t114) @t112))) % 38.12/38.37 (step @p89 :rule alpha_equiv :args (@t115 (@list @t96) @t116)) % 38.12/38.37 (step @p90 :rule refl :args (@t108)) % 38.12/38.37 (step @p91 :rule refl :args (@t109)) % 38.12/38.37 (step @p92 :rule nary_cong :premises (@p91 @p90 @p89) :args (@t117)) % 38.12/38.37 (step @p93 :rule quant-miniscope-or :args ((= @t114 @t117))) % 38.12/38.37 (step @p94 :rule trans :premises (@p93 @p92)) % 38.12/38.37 (step @p95 :rule symm :premises (@p94)) % 38.12/38.37 (step @p96 :rule cong :premises (@p95) :args ((forall @t9 @t119))) % 38.12/38.37 (step @p97 :rule trans :premises (@p96 @p88)) % 38.12/38.37 (step @p98 :rule trans :premises (@p97 @p87)) % 38.12/38.37 (step @p99 :rule aci_norm :args ((= (or (or @t109 @t108) @t118) @t119))) % 38.12/38.37 (step @p100 :rule refl :args (@t118)) % 38.12/38.37 (step @p101 :rule bool-and-de-morgan :args (@t21 @t27 true)) % 38.12/38.37 (step @p102 :rule nary_cong :premises (@p101 @p100) :args ((or (not @t28) @t118))) % 38.12/38.37 (step @p103 :rule trans :premises (@p102 @p99)) % 38.12/38.37 (step @p104 :rule bool-impl-elim :args (@t28 @t118)) % 38.12/38.37 (step @p105 :rule trans :premises (@p104 @p103)) % 38.12/38.37 (step @p106 :rule cong :premises (@p105) :args ((forall @t9 (=> @t28 @t118)))) % 38.12/38.37 (step @p107 :rule trans :premises (@p106 @p98)) % 38.12/38.37 (step @p108 :rule aci_norm :args ((= (or @t101 (or @t100 @t99)) @t102))) % 38.12/38.37 (step @p109 :rule bool-and-de-morgan :args (@t33 @t98 true)) % 38.12/38.37 (step @p110 :rule refl :args (@t101)) % 38.12/38.37 (step @p111 :rule nary_cong :premises (@p110 @p109) :args ((or @t101 (not (and @t33 @t98))))) % 38.12/38.37 (step @p112 :rule bool-and-de-morgan :args (@t34 @t33 (and @t98))) % 38.12/38.37 (step @p113 :rule trans :premises (@p112 @p111)) % 38.12/38.37 (step @p114 :rule trans :premises (@p113 @p108)) % 38.12/38.37 (step @p115 :rule cong :premises (@p114) :args (@t121)) % 38.12/38.37 (step @p116 :rule cong :premises (@p115) :args (@t122)) % 38.12/38.37 (step @p117 :rule exists-elim :args ((= (exists @t36 @t120) @t122))) % 38.12/38.37 (step @p118 :rule trans :premises (@p117 @p116)) % 38.12/38.37 (step @p119 :rule eq-symm :args (@t32 @t29)) % 38.12/38.37 (step @p120 :rule refl :args (@t33)) % 38.12/38.37 (step @p121 :rule refl :args (@t34)) % 38.12/38.37 (step @p122 :rule nary_cong :premises (@p121 @p120 @p119) :args (@t35)) % 38.12/38.37 (step @p123 :rule cong :premises (@p122) :args (@t37)) % 38.12/38.37 (step @p124 :rule trans :premises (@p123 @p118)) % 38.12/38.37 (step @p125 :rule refl :args (@t38)) % 38.12/38.37 (step @p126 :rule cong :premises (@p125 @p124) :args (@t39)) % 38.12/38.37 (step @p127 :rule cong :premises (@p126) :args (@t41)) % 38.12/38.37 (step @p128 :rule refl :args (@t42)) % 38.12/38.37 (step @p129 :rule nary_cong :premises (@p128 @p127) :args (@t43)) % 38.12/38.37 (step @p130 :rule refl :args (@t45)) % 38.12/38.37 (step @p131 :rule cong :premises (@p130 @p129) :args (@t46)) % 38.12/38.37 (step @p132 :rule cong :premises (@p131) :args (@t47)) % 38.12/38.37 (step @p133 :rule refl :args (@t28)) % 38.12/38.37 (step @p134 :rule cong :premises (@p133 @p132) :args (@t48)) % 38.12/38.37 (step @p135 :rule cong :premises (@p134) :args (@t49)) % 38.12/38.37 (step @p136 :rule trans :premises (@p135 @p107)) % 38.12/38.37 (step @p137 :rule eq_resolve :premises (@p22 @p136)) % 38.12/38.37 (step @p138 :rule bool-eq-true :args (@t127)) % 38.12/38.37 (step @p139 :rule eq-symm :args (true @t127)) % 38.12/38.37 (step @p140 :rule trans :premises (@p139 @p138)) % 38.12/38.37 (step @p141 :rule eq-symm :args (@t123 @t124)) % 38.12/38.37 (step @p142 :rule cong :premises (@p141) :args (@t128)) % 38.12/38.37 (step @p143 :rule refl :args (@t126)) % 38.12/38.37 (step @p144 :rule nary_cong :premises (@p143 @p142) :args (@t129)) % 38.12/38.37 (step @p145 :rule eq-refl :args (@t76)) % 38.12/38.37 (step @p146 :rule cong :premises (@p145 @p144) :args (@t130)) % 38.12/38.37 (step @p147 :rule trans :premises (@p146 @p140)) % 38.12/38.37 (step @p148 :rule refl :args (@t132)) % 38.12/38.37 (step @p149 :rule refl :args (@t134)) % 38.12/38.37 (step @p150 :rule nary_cong :premises (@p149 @p148 @p147) :args (@t135)) % 38.12/38.37 (step @p151 :rule refl :args (@t136)) % 38.12/38.37 (step @p152 :rule cong :premises (@p151 @p150) :args ((=> @t136 @t135))) % 38.12/38.37 (assume-push @p249 @t136) % 38.12/38.37 (step @p154 :rule instantiate :premises (@p137) :args ((@list @t75 @t74 @t76))) % 38.12/38.37 (step-pop @p250 :rule scope :premises (@p154)) % 38.12/38.37 (step @p155 :rule process_scope :premises (@p250) :args (@t135)) % 38.12/38.37 (step @p157 :rule eq_resolve :premises (@p155 @p152)) % 38.12/38.37 (step @p158 :rule implies_elim :premises (@p157)) % 38.12/38.37 (step @p159 :rule chain_m_resolution :premises (@p158 @p137) :args (@t137 @t95 (@list @t136))) % 38.12/38.37 (step @p160 :rule quant-merge-prenex :args ((= (forall @t23 @t150) (forall @t148 @t147)))) % 38.12/38.37 (step @p161 :rule alpha_equiv :args (@t151 (@list @t138) @t116)) % 38.12/38.37 (step @p162 :rule quant-unused-vars :args ((= @t152 @t151))) % 38.12/38.37 (step @p163 :rule trans :premises (@p162 @p161)) % 38.12/38.37 (step @p164 :rule alpha_equiv :args (@t153 (@list @t142) @t116)) % 38.12/38.37 (step @p165 :rule quant-unused-vars :args ((= @t154 @t153))) % 38.12/38.37 (step @p166 :rule trans :premises (@p165 @p164)) % 38.12/38.37 (step @p167 :rule nary_cong :premises (@p166 @p163) :args (@t155)) % 38.12/38.37 (step @p168 :rule quant-miniscope-and :args ((= @t156 @t155))) % 38.12/38.37 (step @p169 :rule trans :premises (@p168 @p167)) % 38.12/38.37 (step @p170 :rule refl :args (@t146)) % 38.12/38.37 (step @p171 :rule nary_cong :premises (@p170 @p169) :args (@t157)) % 38.12/38.37 (step @p172 :rule quant-miniscope-or :args ((= @t150 @t157))) % 38.12/38.37 (step @p173 :rule trans :premises (@p172 @p171)) % 38.12/38.37 (step @p174 :rule symm :premises (@p173)) % 38.12/38.37 (step @p175 :rule cong :premises (@p174) :args ((forall @t23 (or @t146 @t158)))) % 38.12/38.37 (step @p176 :rule trans :premises (@p175 @p160)) % 38.12/38.37 (step @p177 :rule bool-impl-elim :args (@t22 @t158)) % 38.12/38.37 (step @p178 :rule cong :premises (@p177) :args ((forall @t23 (=> @t22 @t158)))) % 38.12/38.37 (step @p179 :rule trans :premises (@p178 @p176)) % 38.12/38.37 (step @p180 :rule bool-impl-elim :args (@t13 @t52)) % 38.12/38.37 (step @p181 :rule cong :premises (@p180) :args (@t53)) % 38.12/38.37 (step @p182 :rule bool-impl-elim :args (@t24 @t54)) % 38.12/38.37 (step @p183 :rule cong :premises (@p182) :args (@t55)) % 38.12/38.37 (step @p184 :rule nary_cong :premises (@p183 @p181) :args (@t56)) % 38.12/38.37 (step @p185 :rule refl :args (@t22)) % 38.12/38.37 (step @p186 :rule cong :premises (@p185 @p184) :args (@t57)) % 38.12/38.37 (step @p187 :rule cong :premises (@p186) :args (@t58)) % 38.12/38.37 (step @p188 :rule trans :premises (@p187 @p179)) % 38.12/38.37 (step @p189 :rule refl :args (@t21)) % 38.12/38.37 (step @p190 :rule nary_cong :premises (@p189 @p188) :args (@t59)) % 38.12/38.37 (step @p191 :rule refl :args (@t60)) % 38.12/38.37 (step @p192 :rule cong :premises (@p191 @p190) :args (@t61)) % 38.12/38.37 (step @p193 :rule cong :premises (@p192) :args (@t62)) % 38.12/38.37 (step @p194 :rule eq_resolve :premises (@p24 @p193)) % 38.12/38.37 (step @p195 :rule instantiate :premises (@p194) :args ((@list @t74))) % 38.12/38.37 (step @p196 :rule bool-impl-elim :args (@t2 @t70)) % 38.12/38.37 (step @p197 :rule cong :premises (@p196) :args (@t71)) % 38.12/38.37 (step @p198 :rule eq_resolve :premises (@p38 @p197)) % 38.12/38.37 (step @p199 :rule instantiate :premises (@p198) :args ((@list tptp.xb))) % 38.12/38.37 (step @p200 :rule and_elim :premises (@p39) :args (1)) % 38.12/38.37 (step @p201 :rule cnf_or_pos :args (@t161)) % 38.12/38.37 (step @p202 :rule reordering :premises (@p201) :args ((or @t160 @t159 (not @t161)))) % 38.12/38.37 (step @p203 :rule chain_m_resolution :premises (@p202 @p200 @p199) :args (@t159 @t162 (@list @t72 @t161))) % 38.12/38.37 (step @p204 :rule cnf_equiv_pos1 :args (@t164)) % 38.12/38.37 (step @p205 :rule reordering :premises (@p204) :args ((or (not @t159) @t163 (not @t164)))) % 38.12/38.37 (step @p206 :rule chain_m_resolution :premises (@p205 @p203 @p195) :args (@t163 @t162 (@list @t159 @t164))) % 38.12/38.37 (step @p207 :rule cnf_and_pos :args (@t163 0)) % 38.12/38.37 (step @p208 :rule reordering :premises (@p207) :args ((or @t131 (not @t163)))) % 38.12/38.37 (step @p209 :rule chain_m_resolution :premises (@p208 @p206) :args (@t131 @t95 (@list @t163))) % 38.12/38.37 (step @p210 :rule instantiate :premises (@p194) :args ((@list @t75))) % 38.12/38.37 (step @p211 :rule instantiate :premises (@p198) :args ((@list tptp.xa))) % 38.12/38.37 (step @p212 :rule and_elim :premises (@p39) :args (0)) % 38.12/38.37 (step @p213 :rule cnf_or_pos :args (@t167)) % 38.12/38.37 (step @p214 :rule reordering :premises (@p213) :args ((or @t166 @t165 (not @t167)))) % 38.12/38.37 (step @p215 :rule chain_m_resolution :premises (@p214 @p212 @p211) :args (@t165 @t162 (@list @t73 @t167))) % 38.12/38.37 (step @p216 :rule cnf_equiv_pos1 :args (@t169)) % 38.12/38.37 (step @p217 :rule reordering :premises (@p216) :args ((or (not @t165) @t168 (not @t169)))) % 38.12/38.37 (step @p218 :rule chain_m_resolution :premises (@p217 @p215 @p210) :args (@t168 @t162 (@list @t165 @t169))) % 38.12/38.37 (step @p219 :rule cnf_and_pos :args (@t168 0)) % 38.12/38.37 (step @p220 :rule reordering :premises (@p219) :args ((or @t133 (not @t168)))) % 38.12/38.37 (step @p221 :rule chain_m_resolution :premises (@p220 @p218) :args (@t133 @t95 (@list @t168))) % 38.12/38.37 (step @p222 :rule cnf_or_pos :args (@t137)) % 38.12/38.37 (step @p223 :rule reordering :premises (@p222) :args ((or @t134 @t132 @t127 (not @t137)))) % 38.12/38.37 (step @p224 :rule chain_m_resolution :premises (@p223 @p221 @p209 @p159) :args (@t127 @t170 (@list @t133 @t131 @t137))) % 38.12/38.37 (step @p225 :rule cnf_and_pos :args (@t127 1)) % 38.12/38.37 (step @p226 :rule reordering :premises (@p225) :args ((or @t125 (not @t127)))) % 38.12/38.37 (step @p227 :rule chain_m_resolution :premises (@p226 @p224) :args (@t125 @t95 (@list @t127))) % 38.12/38.37 (step @p228 :rule eq-symm :args (tptp.xu @t32)) % 38.12/38.37 (step @p229 :rule cong :premises (@p228) :args (@t171)) % 38.12/38.37 (step @p230 :rule refl :args (@t92)) % 38.12/38.37 (step @p231 :rule refl :args (@t93)) % 38.12/38.37 (step @p232 :rule nary_cong :premises (@p231 @p230 @p229) :args (@t172)) % 38.12/38.37 (step @p233 :rule cong :premises (@p232) :args (@t173)) % 38.12/38.37 (step @p234 :rule cong :premises (@p233) :args (@t174)) % 38.12/38.37 (step @p235 :rule refl :args (@t175)) % 38.12/38.37 (step @p236 :rule cong :premises (@p235 @p234) :args (@t176)) % 38.12/38.37 (step @p237 :rule refl :args (@t125)) % 38.12/38.37 (step @p238 :rule cong :premises (@p237 @p236) :args ((=> @t125 @t176))) % 38.12/38.38 (assume-push @p251 @t125) % 38.12/38.38 (step @p240 :rule instantiate :premises (@p227) :args ((@list tptp.xu))) % 38.12/38.38 (step-pop @p252 :rule scope :premises (@p240)) % 38.12/38.38 (step @p241 :rule process_scope :premises (@p252) :args (@t176)) % 38.12/38.38 (step @p243 :rule eq_resolve :premises (@p241 @p238)) % 38.12/38.38 (step @p244 :rule implies_elim :premises (@p243)) % 38.12/38.38 (step @p245 :rule chain_m_resolution :premises (@p244 @p227) :args (@t178 @t95 (@list @t125))) % 38.12/38.38 (step @p246 :rule cnf_equiv_pos1 :args (@t178)) % 38.12/38.38 (step @p247 :rule reordering :premises (@p246) :args ((or (not @t175) @t177 (not @t178)))) % 38.12/38.38 (step @p248 false :rule chain_m_resolution :premises (@p247 @p245 @p77 @p53) :args (false @t170 (@list @t178 @t94 @t175))) % 38.12/38.38 ) % 38.12/38.38 % SZS output end Proof % 38.12/38.38 % cvc5 exiting %------------------------------------------------------------------------------