%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : RNG126+4 : 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 : n006.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 08:45:46 AM UTC 2026 % Result : Theorem 27.87s 28.09s % Output : Proof 27.87s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : RNG126+4 : 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 : n006.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 14:09:04 EDT 2026 % 0.17/0.34 % CPUTime : % 0.31/0.50 %----Proving TF0_NAR, FOF, or CNF % 27.87/28.09 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 27.87/28.09 --- Run --no-e-matching --full-saturate-quant at 6... % 27.87/28.09 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 6... % 27.87/28.09 --- Run --finite-model-find --uf-ss=no-minimal at 6... % 27.87/28.09 % SZS status Theorem % 27.87/28.09 % SZS output start Proof % 27.87/28.09 ( % 27.87/28.09 (declare-sort $$unsorted 0) % 27.87/28.09 (declare-const tptp.xu $$unsorted) % 27.87/28.09 (declare-const tptp.xI $$unsorted) % 27.87/28.09 (declare-const tptp.xc $$unsorted) % 27.87/28.09 (declare-const tptp.xa $$unsorted) % 27.87/28.09 (declare-const tptp.slsdtgt0 (-> $$unsorted $$unsorted)) % 27.87/28.09 (declare-const tptp.aDivisorOf0 (-> $$unsorted $$unsorted Bool)) % 27.87/28.09 (declare-const tptp.iLess0 (-> $$unsorted $$unsorted Bool)) % 27.87/28.09 (declare-const tptp.sbrdtbr0 (-> $$unsorted $$unsorted)) % 27.87/28.09 (declare-const tptp.aElement0 (-> $$unsorted Bool)) % 27.87/28.09 (declare-const tptp.sz00 $$unsorted) % 27.87/28.09 (declare-const tptp.sz10 $$unsorted) % 27.87/28.09 (declare-const tptp.aGcdOfAnd0 (-> $$unsorted $$unsorted $$unsorted Bool)) % 27.87/28.09 (declare-const tptp.smndt0 (-> $$unsorted $$unsorted)) % 27.87/28.09 (declare-const tptp.sdtpldt0 (-> $$unsorted $$unsorted $$unsorted)) % 27.87/28.09 (declare-const tptp.sdtasasdt0 (-> $$unsorted $$unsorted $$unsorted)) % 27.87/28.09 (declare-const tptp.aIdeal0 (-> $$unsorted Bool)) % 27.87/28.09 (declare-const tptp.misRelativelyPrime0 (-> $$unsorted $$unsorted Bool)) % 27.87/28.09 (declare-const tptp.sdtasdt0 (-> $$unsorted $$unsorted $$unsorted)) % 27.87/28.09 (declare-const tptp.doDivides0 (-> $$unsorted $$unsorted Bool)) % 27.87/28.09 (declare-const tptp.aSet0 (-> $$unsorted Bool)) % 27.87/28.09 (declare-const tptp.aElementOf0 (-> $$unsorted $$unsorted Bool)) % 27.87/28.09 (declare-const tptp.sdteqdtlpzmzozddtrp0 (-> $$unsorted $$unsorted $$unsorted Bool)) % 27.87/28.09 (declare-const tptp.xb $$unsorted) % 27.87/28.09 (declare-const tptp.sdtpldt1 (-> $$unsorted $$unsorted $$unsorted)) % 27.87/28.09 (declare-const tptp.aNaturalNumber0 (-> $$unsorted Bool)) % 27.87/28.09 (define @t1 () (@var "W0" $$unsorted)) % 27.87/28.09 (define @t2 () (tptp.aElement0 @t1)) % 27.87/28.09 (define @t3 () (@list @t1)) % 27.87/28.09 (define @t4 () (tptp.smndt0 @t1)) % 27.87/28.09 (define @t5 () (@var "W1" $$unsorted)) % 27.87/28.09 (define @t6 () (tptp.sdtpldt0 @t1 @t5)) % 27.87/28.09 (define @t7 () (tptp.aElement0 @t5)) % 27.87/28.09 (define @t8 () (and @t2 @t7)) % 27.87/28.09 (define @t9 () (@list @t1 @t5)) % 27.87/28.09 (define @t10 () (tptp.sdtasdt0 @t1 @t5)) % 27.87/28.09 (define @t11 () (@var "W2" $$unsorted)) % 27.87/28.09 (define @t12 () (tptp.sdtpldt0 @t5 @t11)) % 27.87/28.09 (define @t13 () (tptp.aElement0 @t11)) % 27.87/28.09 (define @t14 () (and @t2 @t7 @t13)) % 27.87/28.09 (define @t15 () (@list @t1 @t5 @t11)) % 27.87/28.09 (define @t16 () (tptp.sdtasdt0 @t5 @t1)) % 27.87/28.09 (define @t17 () (= @t10 @t16)) % 27.87/28.09 (define @t18 () (forall @t9 (=> @t8 @t17))) % 27.87/28.09 (define @t19 () (tptp.sdtasdt0 @t1 @t11)) % 27.87/28.09 (define @t20 () (tptp.smndt0 tptp.sz10)) % 27.87/28.09 (define @t21 () (= @t5 tptp.sz00)) % 27.87/28.09 (define @t22 () (= @t1 tptp.sz00)) % 27.87/28.09 (define @t23 () (tptp.aSet0 @t1)) % 27.87/28.09 (define @t24 () (tptp.aElementOf0 @t5 @t1)) % 27.87/28.09 (define @t25 () (@list @t5)) % 27.87/28.09 (define @t26 () (forall @t25 (=> @t24 @t7))) % 27.87/28.09 (define @t27 () (=> @t23 @t26)) % 27.87/28.09 (define @t28 () (forall @t3 @t27)) % 27.87/28.09 (define @t29 () (tptp.aElementOf0 @t11 @t1)) % 27.87/28.09 (define @t30 () (tptp.aElementOf0 @t11 @t5)) % 27.87/28.09 (define @t31 () (@list @t11)) % 27.87/28.09 (define @t32 () (tptp.aSet0 @t5)) % 27.87/28.09 (define @t33 () (and @t23 @t32)) % 27.87/28.09 (define @t34 () (@var "W3" $$unsorted)) % 27.87/28.09 (define @t35 () (@var "W5" $$unsorted)) % 27.87/28.09 (define @t36 () (@var "W4" $$unsorted)) % 27.87/28.09 (define @t37 () (tptp.aElementOf0 @t34 @t11)) % 27.87/28.09 (define @t38 () (@list @t34)) % 27.87/28.09 (define @t39 () (tptp.aSet0 @t11)) % 27.87/28.09 (define @t40 () (tptp.sdtpldt1 @t1 @t5)) % 27.87/28.09 (define @t41 () (tptp.sdtasasdt0 @t1 @t5)) % 27.87/28.09 (define @t42 () (tptp.sdtasdt0 @t11 @t5)) % 27.87/28.09 (define @t43 () (tptp.aIdeal0 @t1)) % 27.87/28.09 (define @t44 () (and @t43 (tptp.aIdeal0 @t5))) % 27.87/28.09 (define @t45 () (tptp.aElement0 @t34)) % 27.87/28.09 (define @t46 () (@list @t11 @t34)) % 27.87/28.09 (define @t47 () (tptp.aNaturalNumber0 @t1)) % 27.87/28.09 (define @t48 () (tptp.sbrdtbr0 @t1)) % 27.87/28.09 (define @t49 () (not @t22)) % 27.87/28.09 (define @t50 () (tptp.slsdtgt0 @t1)) % 27.87/28.09 (define @t51 () (tptp.sdtasdt0 tptp.xc @t1)) % 27.87/28.09 (define @t52 () (tptp.aElement0 tptp.xc)) % 27.87/28.09 (define @t53 () (tptp.slsdtgt0 tptp.xb)) % 27.87/28.09 (define @t54 () (tptp.slsdtgt0 tptp.xa)) % 27.87/28.09 (define @t55 () (tptp.sdtpldt1 @t54 @t53)) % 27.87/28.09 (define @t56 () (tptp.aElementOf0 @t5 @t54)) % 27.87/28.09 (define @t57 () (exists (@list @t5 @t11) (and @t56 (tptp.aElementOf0 @t11 @t53) (= @t12 @t1)))) % 27.87/28.09 (define @t58 () (tptp.aElementOf0 @t1 tptp.xI)) % 27.87/28.09 (define @t59 () (tptp.sdtasdt0 tptp.xb @t5)) % 27.87/28.09 (define @t60 () (and @t7 (= @t59 @t1))) % 27.87/28.09 (define @t61 () (exists @t25 @t60)) % 27.87/28.09 (define @t62 () (tptp.aElementOf0 @t1 @t53)) % 27.87/28.09 (define @t63 () (= @t62 @t61)) % 27.87/28.09 (define @t64 () (forall @t3 @t63)) % 27.87/28.09 (define @t65 () (tptp.sdtasdt0 tptp.xa @t5)) % 27.87/28.09 (define @t66 () (and @t7 (= @t65 @t1))) % 27.87/28.09 (define @t67 () (exists @t25 @t66)) % 27.87/28.09 (define @t68 () (tptp.aElementOf0 @t1 @t54)) % 27.87/28.09 (define @t69 () (= @t68 @t67)) % 27.87/28.09 (define @t70 () (forall @t3 @t69)) % 27.87/28.09 (define @t71 () (tptp.aElementOf0 @t16 tptp.xI)) % 27.87/28.09 (define @t72 () (forall @t25 (=> @t7 @t71))) % 27.87/28.09 (define @t73 () (tptp.aElementOf0 @t6 tptp.xI)) % 27.87/28.09 (define @t74 () (tptp.aElementOf0 @t5 tptp.xI)) % 27.87/28.09 (define @t75 () (forall @t25 (=> @t74 @t73))) % 27.87/28.09 (define @t76 () (and @t75 @t72)) % 27.87/28.09 (define @t77 () (=> @t58 @t76)) % 27.87/28.09 (define @t78 () (forall @t3 @t77)) % 27.87/28.09 (define @t79 () (tptp.aSet0 tptp.xI)) % 27.87/28.09 (define @t80 () (tptp.sdtasdt0 tptp.xb @t1)) % 27.87/28.09 (define @t81 () (tptp.sdtasdt0 tptp.xa @t1)) % 27.87/28.09 (define @t82 () (tptp.aElementOf0 @t5 @t53)) % 27.87/28.09 (define @t83 () (tptp.aElementOf0 tptp.xu tptp.xI)) % 27.87/28.09 (define @t84 () (tptp.sdtasdt0 tptp.xu @t1)) % 27.87/28.09 (define @t85 () (and @t2 (= @t84 tptp.xc))) % 27.87/28.09 (define @t86 () (exists @t3 @t85)) % 27.87/28.09 (define @t87 () (tptp.aElementOf0 tptp.xc @t55)) % 27.87/28.09 (define @t88 () (= @t6 tptp.xc)) % 27.87/28.09 (define @t89 () (and @t68 @t82 @t88)) % 27.87/28.09 (define @t90 () (exists @t9 @t89)) % 27.87/28.09 (define @t91 () (or @t90 @t87)) % 27.87/28.09 (define @t92 () (=> @t64 @t91)) % 27.87/28.09 (define @t93 () (=> @t70 @t92)) % 27.87/28.09 (define @t94 () (not @t93)) % 27.87/28.09 (define @t95 () (not @t88)) % 27.87/28.09 (define @t96 () (not @t82)) % 27.87/28.09 (define @t97 () (not @t68)) % 27.87/28.09 (define @t98 () (forall @t9 (not @t89))) % 27.87/28.09 (define @t99 () (not @t98)) % 27.87/28.09 (define @t100 () (= @t1 @t59)) % 27.87/28.09 (define @t101 () (and @t7 @t100)) % 27.87/28.09 (define @t102 () (forall @t25 (not @t101))) % 27.87/28.09 (define @t103 () (not @t102)) % 27.87/28.09 (define @t104 () (= @t1 @t65)) % 27.87/28.09 (define @t105 () (and @t7 @t104)) % 27.87/28.09 (define @t106 () (forall @t25 (not @t105))) % 27.87/28.09 (define @t107 () (not @t106)) % 27.87/28.09 (define @t108 () (= tptp.xc @t84)) % 27.87/28.09 (define @t109 () (and @t2 @t108)) % 27.87/28.09 (define @t110 () (forall @t3 (not @t109))) % 27.87/28.09 (define @t111 () (not @t110)) % 27.87/28.09 (define @t112 () (not @t2)) % 27.87/28.09 (define @t113 () (@quantifiers_skolemize (forall @t3 (or @t112 (not @t108))) 0)) % 27.87/28.09 (define @t114 () (tptp.sdtasdt0 tptp.xu @t113)) % 27.87/28.09 (define @t115 () (= tptp.xc @t114)) % 27.87/28.09 (define @t116 () (not @t115)) % 27.87/28.09 (define @t117 () (tptp.aElement0 @t113)) % 27.87/28.09 (define @t118 () (not @t117)) % 27.87/28.09 (define @t119 () (or @t118 @t116)) % 27.87/28.09 (define @t120 () (@list true)) % 27.87/28.09 (define @t121 () (@list @t119)) % 27.87/28.09 (define @t122 () (not @t7)) % 27.87/28.09 (define @t123 () (@var "BOUND_VARIABLE_7978" $$unsorted)) % 27.87/28.09 (define @t124 () (tptp.aElement0 @t123)) % 27.87/28.09 (define @t125 () (not (tptp.aElementOf0 @t123 @t1))) % 27.87/28.09 (define @t126 () (not @t23)) % 27.87/28.09 (define @t127 () (or @t125 @t124)) % 27.87/28.09 (define @t128 () (or @t126 @t127)) % 27.87/28.09 (define @t129 () (forall (@list @t1 @t123) @t128)) % 27.87/28.09 (define @t130 () (@list @t123)) % 27.87/28.09 (define @t131 () (forall @t130 @t128)) % 27.87/28.09 (define @t132 () (forall @t130 @t127)) % 27.87/28.09 (define @t133 () (@list @t5)) % 27.87/28.09 (define @t134 () (or @t126 @t132)) % 27.87/28.09 (define @t135 () (forall @t25 (or (not @t24) @t7))) % 27.87/28.09 (define @t136 () (tptp.aElement0 tptp.xu)) % 27.87/28.09 (define @t137 () (tptp.aElementOf0 tptp.xu @t55)) % 27.87/28.09 (define @t138 () (not @t137)) % 27.87/28.09 (define @t139 () (tptp.aSet0 @t55)) % 27.87/28.09 (define @t140 () (not @t139)) % 27.87/28.09 (define @t141 () (or @t140 @t138 @t136)) % 27.87/28.09 (define @t142 () (@list false false false)) % 27.87/28.09 (define @t143 () (tptp.sdtasdt0 @t113 tptp.xu)) % 27.87/28.09 (define @t144 () (= @t114 @t143)) % 27.87/28.09 (define @t145 () (not @t136)) % 27.87/28.09 (define @t146 () (or @t145 @t118 @t144)) % 27.87/28.09 (define @t147 () (tptp.aElementOf0 @t143 @t55)) % 27.87/28.09 (define @t148 () (@var "BOUND_VARIABLE_8429" $$unsorted)) % 27.87/28.09 (define @t149 () (tptp.sdtasdt0 @t148 @t1)) % 27.87/28.09 (define @t150 () (tptp.aElementOf0 @t149 tptp.xI)) % 27.87/28.09 (define @t151 () (not (tptp.aElement0 @t148))) % 27.87/28.09 (define @t152 () (or @t151 @t150)) % 27.87/28.09 (define @t153 () (@var "BOUND_VARIABLE_8422" $$unsorted)) % 27.87/28.09 (define @t154 () (tptp.sdtpldt0 @t1 @t153)) % 27.87/28.09 (define @t155 () (tptp.aElementOf0 @t154 tptp.xI)) % 27.87/28.09 (define @t156 () (tptp.aElementOf0 @t153 tptp.xI)) % 27.87/28.09 (define @t157 () (not @t156)) % 27.87/28.09 (define @t158 () (or @t157 @t155)) % 27.87/28.09 (define @t159 () (and @t158 @t152)) % 27.87/28.09 (define @t160 () (not @t58)) % 27.87/28.09 (define @t161 () (or @t160 @t159)) % 27.87/28.09 (define @t162 () (forall (@list @t1 @t153 @t148) @t161)) % 27.87/28.09 (define @t163 () (@list @t153 @t148)) % 27.87/28.09 (define @t164 () (forall @t163 @t161)) % 27.87/28.09 (define @t165 () (forall (@list @t148) @t152)) % 27.87/28.09 (define @t166 () (forall @t163 @t152)) % 27.87/28.09 (define @t167 () (forall (@list @t153) @t158)) % 27.87/28.09 (define @t168 () (forall @t163 @t158)) % 27.87/28.09 (define @t169 () (and @t168 @t166)) % 27.87/28.09 (define @t170 () (forall @t163 @t159)) % 27.87/28.09 (define @t171 () (or @t160 @t170)) % 27.87/28.09 (define @t172 () (and (forall @t25 (or (not @t74) @t73)) (forall @t25 (or @t122 @t71)))) % 27.87/28.09 (define @t173 () (or @t118 @t147)) % 27.87/28.09 (define @t174 () (and (or (not (tptp.aElementOf0 tptp.sz00 @t55)) (tptp.aElementOf0 (tptp.sdtpldt0 tptp.xu tptp.sz00) @t55)) @t173)) % 27.87/28.09 (define @t175 () (or @t138 @t174)) % 27.87/28.09 (define @t176 () (@list false false)) % 27.87/28.09 (assume @p1 (forall @t3 (=> @t2 true))) % 27.87/28.09 (assume @p2 (tptp.aElement0 tptp.sz00)) % 27.87/28.09 (assume @p3 (tptp.aElement0 tptp.sz10)) % 27.87/28.09 (assume @p4 (forall @t3 (=> @t2 (tptp.aElement0 @t4)))) % 27.87/28.09 (assume @p5 (forall @t9 (=> @t8 (tptp.aElement0 @t6)))) % 27.87/28.09 (assume @p6 (forall @t9 (=> @t8 (tptp.aElement0 @t10)))) % 27.87/28.09 (assume @p7 (forall @t9 (=> @t8 (= @t6 (tptp.sdtpldt0 @t5 @t1))))) % 27.87/28.09 (assume @p8 (forall @t15 (=> @t14 (= (tptp.sdtpldt0 @t6 @t11) (tptp.sdtpldt0 @t1 @t12))))) % 27.87/28.09 (assume @p9 (forall @t3 (=> @t2 (and (= (tptp.sdtpldt0 @t1 tptp.sz00) @t1) (= @t1 (tptp.sdtpldt0 tptp.sz00 @t1)))))) % 27.87/28.09 (assume @p10 (forall @t3 (=> @t2 (and (= (tptp.sdtpldt0 @t1 @t4) tptp.sz00) (= tptp.sz00 (tptp.sdtpldt0 @t4 @t1)))))) % 27.87/28.09 (assume @p11 @t18) % 27.87/28.09 (assume @p12 (forall @t15 (=> @t14 (= (tptp.sdtasdt0 @t10 @t11) (tptp.sdtasdt0 @t1 (tptp.sdtasdt0 @t5 @t11)))))) % 27.87/28.09 (assume @p13 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz10) @t1) (= @t1 (tptp.sdtasdt0 tptp.sz10 @t1)))))) % 27.87/28.09 (assume @p14 (forall @t15 (=> @t14 (and (= (tptp.sdtasdt0 @t1 @t12) (tptp.sdtpldt0 @t10 @t19)) (= (tptp.sdtasdt0 @t12 @t1) (tptp.sdtpldt0 @t16 (tptp.sdtasdt0 @t11 @t1))))))) % 27.87/28.09 (assume @p15 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t20 @t1) @t4) (= @t4 (tptp.sdtasdt0 @t1 @t20)))))) % 27.87/28.09 (assume @p16 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz00) tptp.sz00) (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 @t1)))))) % 27.87/28.09 (assume @p17 (forall @t9 (=> @t8 (=> (= @t10 tptp.sz00) (or @t22 @t21))))) % 27.87/28.09 (assume @p18 (not (= tptp.sz10 tptp.sz00))) % 27.87/28.09 (assume @p19 (forall @t3 (=> @t23 true))) % 27.87/28.09 (assume @p20 @t28) % 27.87/28.09 (assume @p21 (forall @t9 (=> @t33 (=> (and (forall @t31 (=> @t29 @t30)) (forall @t31 (=> @t30 @t29))) (= @t1 @t5))))) % 27.87/28.09 (assume @p22 (forall @t9 (=> @t33 (forall @t31 (= (= @t11 @t40) (and @t39 (forall @t38 (= @t37 (exists (@list @t36 @t35) (and (tptp.aElementOf0 @t36 @t1) (tptp.aElementOf0 @t35 @t5) (= (tptp.sdtpldt0 @t36 @t35) @t34))))))))))) % 27.87/28.09 (assume @p23 (forall @t9 (=> @t33 (forall @t31 (= (= @t11 @t41) (and @t39 (forall @t38 (= @t37 (and (tptp.aElementOf0 @t34 @t1) (tptp.aElementOf0 @t34 @t5)))))))))) % 27.87/28.09 (assume @p24 (forall @t3 (= @t43 (and @t23 (forall @t25 (=> @t24 (and (forall @t31 (=> @t29 (tptp.aElementOf0 @t12 @t1))) (forall @t31 (=> @t13 (tptp.aElementOf0 @t42 @t1)))))))))) % 27.87/28.09 (assume @p25 (forall @t9 (=> @t44 (tptp.aIdeal0 @t40)))) % 27.87/28.09 (assume @p26 (forall @t9 (=> @t44 (tptp.aIdeal0 @t41)))) % 27.87/28.09 (assume @p27 (forall @t15 (=> (and @t2 @t7 (tptp.aIdeal0 @t11)) (= (tptp.sdteqdtlpzmzozddtrp0 @t1 @t5 @t11) (tptp.aElementOf0 (tptp.sdtpldt0 @t1 (tptp.smndt0 @t5)) @t11))))) % 27.87/28.09 (assume @p28 (forall @t9 (=> @t44 (=> (forall @t31 (=> @t13 (tptp.aElementOf0 @t11 @t40))) (forall @t46 (=> (and @t13 @t45) (exists (@list @t36) (and (tptp.aElement0 @t36) (tptp.sdteqdtlpzmzozddtrp0 @t36 @t11 @t1) (tptp.sdteqdtlpzmzozddtrp0 @t36 @t34 @t5))))))))) % 27.87/28.09 (assume @p29 (forall @t3 (=> @t47 true))) % 27.87/28.09 (assume @p30 (forall @t3 (=> (and @t2 @t49) (tptp.aNaturalNumber0 @t48)))) % 27.87/28.09 (assume @p31 (forall @t9 (=> (and @t47 (tptp.aNaturalNumber0 @t5)) (=> (tptp.iLess0 @t1 @t5) true)))) % 27.87/28.09 (assume @p32 (forall @t9 (=> (and @t2 @t7 (not @t21)) (exists @t46 (and @t13 @t45 (= @t1 (tptp.sdtpldt0 @t42 @t34)) (=> (not (= @t34 tptp.sz00)) (tptp.iLess0 (tptp.sbrdtbr0 @t34) (tptp.sbrdtbr0 @t5)))))))) % 27.87/28.09 (assume @p33 (forall @t9 (=> @t8 (= (tptp.doDivides0 @t1 @t5) (exists @t31 (and @t13 (= @t19 @t5))))))) % 27.87/28.09 (assume @p34 (forall @t3 (=> @t2 (forall @t25 (= (tptp.aDivisorOf0 @t5 @t1) (and @t7 (tptp.doDivides0 @t5 @t1))))))) % 27.87/28.09 (assume @p35 (forall @t9 (=> @t8 (forall @t31 (= (tptp.aGcdOfAnd0 @t11 @t1 @t5) (and (tptp.aDivisorOf0 @t11 @t1) (tptp.aDivisorOf0 @t11 @t5) (forall @t38 (=> (and (tptp.aDivisorOf0 @t34 @t1) (tptp.aDivisorOf0 @t34 @t5)) (tptp.doDivides0 @t34 @t11))))))))) % 27.87/28.09 (assume @p36 (forall @t9 (=> @t8 (= (tptp.misRelativelyPrime0 @t1 @t5) (tptp.aGcdOfAnd0 tptp.sz10 @t1 @t5))))) % 27.87/28.09 (assume @p37 (forall @t3 (=> @t2 (forall @t25 (= (= @t5 @t50) (and @t32 (forall @t31 (= @t30 (exists @t38 (and @t45 (= (tptp.sdtasdt0 @t1 @t34) @t11))))))))))) % 27.87/28.09 (assume @p38 (forall @t3 (=> @t2 (tptp.aIdeal0 @t50)))) % 27.87/28.09 (assume @p39 (and (tptp.aElement0 tptp.xa) (tptp.aElement0 tptp.xb))) % 27.87/28.09 (assume @p40 (or (not (= tptp.xa tptp.sz00)) (not (= tptp.xb tptp.sz00)))) % 27.87/28.09 (assume @p41 (and @t52 (exists @t3 (and @t2 (= @t51 tptp.xa))) (tptp.doDivides0 tptp.xc tptp.xa) (tptp.aDivisorOf0 tptp.xc tptp.xa) @t52 (exists @t3 (and @t2 (= @t51 tptp.xb))) (tptp.doDivides0 tptp.xc tptp.xb) (tptp.aDivisorOf0 tptp.xc tptp.xb) (forall @t3 (=> (and (or (and @t2 (or (exists @t25 (and @t7 (= @t10 tptp.xa))) (tptp.doDivides0 @t1 tptp.xa))) (tptp.aDivisorOf0 @t1 tptp.xa)) (or (exists @t25 (and @t7 (= @t10 tptp.xb))) (tptp.doDivides0 @t1 tptp.xb) (tptp.aDivisorOf0 @t1 tptp.xb))) (and (exists @t25 (and @t7 (= @t10 tptp.xc))) (tptp.doDivides0 @t1 tptp.xc)))) (tptp.aGcdOfAnd0 tptp.xc tptp.xa tptp.xb))) % 27.87/28.09 (assume @p42 (and @t79 @t78 (tptp.aIdeal0 tptp.xI) @t70 @t64 (forall @t3 (= @t58 @t57)) (= tptp.xI @t55))) % 27.87/28.09 (assume @p43 (and (exists @t3 (and @t2 (= @t81 tptp.sz00))) (tptp.aElementOf0 tptp.sz00 @t54) (exists @t3 (and @t2 (= @t81 tptp.xa))) (tptp.aElementOf0 tptp.xa @t54) (exists @t3 (and @t2 (= @t80 tptp.sz00))) (tptp.aElementOf0 tptp.sz00 @t53) (exists @t3 (and @t2 (= @t80 tptp.xb))) (tptp.aElementOf0 tptp.xb @t53))) % 27.87/28.09 (assume @p44 (exists @t3 (and (forall @t25 (= @t56 (exists @t31 (and @t13 (= (tptp.sdtasdt0 tptp.xa @t11) @t5))))) (forall @t25 (= @t82 (exists @t31 (and @t13 (= (tptp.sdtasdt0 tptp.xb @t11) @t5))))) @t57 (tptp.aElementOf0 @t1 @t55) @t49))) % 27.87/28.09 (assume @p45 (and (exists @t9 (and @t68 @t82 (= @t6 tptp.xu))) @t83 (not (= tptp.xu tptp.sz00)) (forall @t3 (=> (and (or @t57 @t58) @t49) (not (tptp.iLess0 @t48 (tptp.sbrdtbr0 tptp.xu))))))) % 27.87/28.09 (assume @p46 (and (exists @t3 (and @t2 (= @t84 tptp.xa))) (tptp.doDivides0 tptp.xu tptp.xa) (tptp.aDivisorOf0 tptp.xu tptp.xa) (exists @t3 (and @t2 (= @t84 tptp.xb))) (tptp.doDivides0 tptp.xu tptp.xb) (tptp.aDivisorOf0 tptp.xu tptp.xb))) % 27.87/28.09 (assume @p47 @t86) % 27.87/28.09 (assume @p48 @t94) % 27.87/28.09 (assume @p49 true) % 27.87/28.09 (step @p50 :rule evaluate :args ((= true false))) % 27.87/28.09 (step @p51 :rule refl :args (@t87)) % 27.87/28.09 (step @p52 :rule aci_norm :args ((= (or @t97 (or @t96 @t95)) (or @t97 @t96 @t95)))) % 27.87/28.09 (step @p53 :rule bool-and-de-morgan :args (@t82 @t88 true)) % 27.87/28.09 (step @p54 :rule refl :args (@t97)) % 27.87/28.09 (step @p55 :rule nary_cong :premises (@p54 @p53) :args ((or @t97 (not (and @t82 @t88))))) % 27.87/28.09 (step @p56 :rule bool-and-de-morgan :args (@t68 @t82 (and @t88))) % 27.87/28.09 (step @p57 :rule trans :premises (@p56 @p55)) % 27.87/28.09 (step @p58 :rule trans :premises (@p57 @p52)) % 27.87/28.09 (step @p59 :rule cong :premises (@p58) :args (@t98)) % 27.87/28.09 (step @p60 :rule cong :premises (@p59) :args (@t99)) % 27.87/28.09 (step @p61 :rule exists-elim :args ((= @t90 @t99))) % 27.87/28.09 (step @p62 :rule trans :premises (@p61 @p60)) % 27.87/28.09 (step @p63 :rule nary_cong :premises (@p62 @p51) :args (@t91)) % 27.87/28.09 (step @p64 :rule bool-and-de-morgan :args (@t7 @t100 true)) % 27.87/28.09 (step @p65 :rule cong :premises (@p64) :args (@t102)) % 27.87/28.09 (step @p66 :rule cong :premises (@p65) :args (@t103)) % 27.87/28.09 (step @p67 :rule exists-elim :args ((= (exists @t25 @t101) @t103))) % 27.87/28.09 (step @p68 :rule trans :premises (@p67 @p66)) % 27.87/28.09 (step @p69 :rule eq-symm :args (@t59 @t1)) % 27.87/28.09 (step @p70 :rule refl :args (@t7)) % 27.87/28.09 (step @p71 :rule nary_cong :premises (@p70 @p69) :args (@t60)) % 27.87/28.09 (step @p72 :rule cong :premises (@p71) :args (@t61)) % 27.87/28.09 (step @p73 :rule trans :premises (@p72 @p68)) % 27.87/28.09 (step @p74 :rule refl :args (@t62)) % 27.87/28.09 (step @p75 :rule cong :premises (@p74 @p73) :args (@t63)) % 27.87/28.09 (step @p76 :rule cong :premises (@p75) :args (@t64)) % 27.87/28.09 (step @p77 :rule cong :premises (@p76 @p63) :args (@t92)) % 27.87/28.09 (step @p78 :rule bool-and-de-morgan :args (@t7 @t104 true)) % 27.87/28.09 (step @p79 :rule cong :premises (@p78) :args (@t106)) % 27.87/28.09 (step @p80 :rule cong :premises (@p79) :args (@t107)) % 27.87/28.09 (step @p81 :rule exists-elim :args ((= (exists @t25 @t105) @t107))) % 27.87/28.09 (step @p82 :rule trans :premises (@p81 @p80)) % 27.87/28.09 (step @p83 :rule eq-symm :args (@t65 @t1)) % 27.87/28.09 (step @p84 :rule nary_cong :premises (@p70 @p83) :args (@t66)) % 27.87/28.09 (step @p85 :rule cong :premises (@p84) :args (@t67)) % 27.87/28.09 (step @p86 :rule trans :premises (@p85 @p82)) % 27.87/28.09 (step @p87 :rule refl :args (@t68)) % 27.87/28.09 (step @p88 :rule cong :premises (@p87 @p86) :args (@t69)) % 27.87/28.09 (step @p89 :rule cong :premises (@p88) :args (@t70)) % 27.87/28.09 (step @p90 :rule cong :premises (@p89 @p77) :args (@t93)) % 27.87/28.09 (step @p91 :rule cong :premises (@p90) :args (@t94)) % 27.87/28.09 (step @p92 :rule eq_resolve :premises (@p48 @p91)) % 27.87/28.09 (step @p93 :rule not_implies_elim2 :premises (@p92)) % 27.87/28.09 (step @p94 :rule not_implies_elim2 :premises (@p93)) % 27.87/28.09 (step @p95 :rule not_or_elim :premises (@p94) :args (1)) % 27.87/28.09 (step @p96 :rule false_intro :premises (@p95)) % 27.87/28.09 (step @p97 :rule refl :args (@t55)) % 27.87/28.09 (step @p98 :rule bool-and-de-morgan :args (@t2 @t108 true)) % 27.87/28.09 (step @p99 :rule cong :premises (@p98) :args (@t110)) % 27.87/28.09 (step @p100 :rule cong :premises (@p99) :args (@t111)) % 27.87/28.09 (step @p101 :rule exists-elim :args ((= (exists @t3 @t109) @t111))) % 27.87/28.09 (step @p102 :rule trans :premises (@p101 @p100)) % 27.87/28.09 (step @p103 :rule eq-symm :args (@t84 tptp.xc)) % 27.87/28.09 (step @p104 :rule refl :args (@t2)) % 27.87/28.09 (step @p105 :rule nary_cong :premises (@p104 @p103) :args (@t85)) % 27.87/28.09 (step @p106 :rule cong :premises (@p105) :args (@t86)) % 27.87/28.09 (step @p107 :rule trans :premises (@p106 @p102)) % 27.87/28.09 (step @p108 :rule eq_resolve :premises (@p47 @p107)) % 27.87/28.09 (step @p109 :rule skolemize :premises (@p108)) % 27.87/28.09 (step @p110 :rule bool-double-not-elim :args (@t115)) % 27.87/28.09 (step @p111 :rule refl :args (@t119)) % 27.87/28.09 (step @p112 :rule nary_cong :premises (@p111 @p110) :args ((or @t119 (not @t116)))) % 27.87/28.09 (step @p113 :rule cnf_or_neg :args (@t119 1)) % 27.87/28.09 (step @p114 :rule eq_resolve :premises (@p113 @p112)) % 27.87/28.09 (step @p115 :rule reordering :premises (@p114) :args ((or @t115 @t119))) % 27.87/28.09 (step @p116 :rule chain_m_resolution :premises (@p115 @p109) :args (@t115 @t120 @t121)) % 27.87/28.09 (step @p117 :rule symm :premises (@p116)) % 27.87/28.09 (step @p118 :rule aci_norm :args ((= (or (or @t112 @t122) @t17) (or @t112 @t122 @t17)))) % 27.87/28.09 (step @p119 :rule refl :args (@t17)) % 27.87/28.09 (step @p120 :rule bool-and-de-morgan :args (@t2 @t7 true)) % 27.87/28.09 (step @p121 :rule nary_cong :premises (@p120 @p119) :args ((or (not @t8) @t17))) % 27.87/28.09 (step @p122 :rule trans :premises (@p121 @p118)) % 27.87/28.09 (step @p123 :rule bool-impl-elim :args (@t8 @t17)) % 27.87/28.09 (step @p124 :rule trans :premises (@p123 @p122)) % 27.87/28.09 (step @p125 :rule cong :premises (@p124) :args (@t18)) % 27.87/28.09 (step @p126 :rule eq_resolve :premises (@p11 @p125)) % 27.87/28.09 (step @p127 :rule instantiate :premises (@p126) :args ((@list tptp.xu @t113))) % 27.87/28.09 (step @p128 :rule aci_norm :args ((= @t128 (or @t126 @t125 @t124)))) % 27.87/28.09 (step @p129 :rule cong :premises (@p128) :args (@t129)) % 27.87/28.09 (step @p130 :rule quant-merge-prenex :args ((= (forall @t3 @t131) @t129))) % 27.87/28.09 (step @p131 :rule alpha_equiv :args (@t132 (@list @t123) @t133)) % 27.87/28.09 (step @p132 :rule refl :args (@t126)) % 27.87/28.09 (step @p133 :rule nary_cong :premises (@p132 @p131) :args (@t134)) % 27.87/28.09 (step @p134 :rule quant-miniscope-or :args ((= @t131 @t134))) % 27.87/28.09 (step @p135 :rule trans :premises (@p134 @p133)) % 27.87/28.09 (step @p136 :rule symm :premises (@p135)) % 27.87/28.09 (step @p137 :rule cong :premises (@p136) :args ((forall @t3 (or @t126 @t135)))) % 27.87/28.09 (step @p138 :rule trans :premises (@p137 @p130)) % 27.87/28.09 (step @p139 :rule trans :premises (@p138 @p129)) % 27.87/28.09 (step @p140 :rule bool-impl-elim :args (@t23 @t135)) % 27.87/28.09 (step @p141 :rule cong :premises (@p140) :args ((forall @t3 (=> @t23 @t135)))) % 27.87/28.09 (step @p142 :rule trans :premises (@p141 @p139)) % 27.87/28.09 (step @p143 :rule bool-impl-elim :args (@t24 @t7)) % 27.87/28.09 (step @p144 :rule cong :premises (@p143) :args (@t26)) % 27.87/28.09 (step @p145 :rule refl :args (@t23)) % 27.87/28.09 (step @p146 :rule cong :premises (@p145 @p144) :args (@t27)) % 27.87/28.09 (step @p147 :rule cong :premises (@p146) :args (@t28)) % 27.87/28.09 (step @p148 :rule trans :premises (@p147 @p142)) % 27.87/28.09 (step @p149 :rule eq_resolve :premises (@p20 @p148)) % 27.87/28.09 (step @p150 :rule instantiate :premises (@p149) :args ((@list @t55 tptp.xu))) % 27.87/28.09 (step @p151 :rule and_elim :premises (@p42) :args (6)) % 27.87/28.09 (step @p152 :rule refl :args (tptp.xu)) % 27.87/28.09 (step @p153 :rule cong :premises (@p152 @p151) :args (@t83)) % 27.87/28.09 (step @p154 :rule and_elim :premises (@p45) :args (1)) % 27.87/28.09 (step @p155 :rule eq_resolve :premises (@p154 @p153)) % 27.87/28.09 (step @p156 :rule cong :premises (@p151) :args (@t79)) % 27.87/28.09 (step @p157 :rule and_elim :premises (@p42) :args (0)) % 27.87/28.09 (step @p158 :rule eq_resolve :premises (@p157 @p156)) % 27.87/28.09 (step @p159 :rule cnf_or_pos :args (@t141)) % 27.87/28.09 (step @p160 :rule reordering :premises (@p159) :args ((or @t140 @t138 @t136 (not @t141)))) % 27.87/28.09 (step @p161 :rule chain_m_resolution :premises (@p160 @p158 @p155 @p150) :args (@t136 @t142 (@list @t139 @t137 @t141))) % 27.87/28.09 (step @p162 :rule bool-double-not-elim :args (@t117)) % 27.87/28.09 (step @p163 :rule nary_cong :premises (@p111 @p162) :args ((or @t119 (not @t118)))) % 27.87/28.09 (step @p164 :rule cnf_or_neg :args (@t119 0)) % 27.87/28.09 (step @p165 :rule eq_resolve :premises (@p164 @p163)) % 27.87/28.09 (step @p166 :rule reordering :premises (@p165) :args ((or @t117 @t119))) % 27.87/28.09 (step @p167 :rule chain_m_resolution :premises (@p166 @p109) :args (@t117 @t120 @t121)) % 27.87/28.09 (step @p168 :rule cnf_or_pos :args (@t146)) % 27.87/28.09 (step @p169 :rule reordering :premises (@p168) :args ((or @t118 @t145 @t144 (not @t146)))) % 27.87/28.09 (step @p170 :rule chain_m_resolution :premises (@p169 @p167 @p161 @p127) :args (@t144 @t142 (@list @t117 @t136 @t146))) % 27.87/28.09 (step @p171 :rule symm :premises (@p170)) % 27.87/28.09 (step @p172 :rule trans :premises (@p171 @p117)) % 27.87/28.09 (step @p173 :rule cong :premises (@p172 @p97) :args (@t147)) % 27.87/28.09 (step @p174 :rule refl :args (@t149)) % 27.87/28.09 (step @p175 :rule cong :premises (@p174 @p151) :args (@t150)) % 27.87/28.09 (step @p176 :rule refl :args (@t151)) % 27.87/28.09 (step @p177 :rule nary_cong :premises (@p176 @p175) :args (@t152)) % 27.87/28.09 (step @p178 :rule refl :args (@t154)) % 27.87/28.09 (step @p179 :rule cong :premises (@p178 @p151) :args (@t155)) % 27.87/28.09 (step @p180 :rule refl :args (@t153)) % 27.87/28.09 (step @p181 :rule cong :premises (@p180 @p151) :args (@t156)) % 27.87/28.09 (step @p182 :rule cong :premises (@p181) :args (@t157)) % 27.87/28.09 (step @p183 :rule nary_cong :premises (@p182 @p179) :args (@t158)) % 27.87/28.09 (step @p184 :rule nary_cong :premises (@p183 @p177) :args (@t159)) % 27.87/28.09 (step @p185 :rule refl :args (@t1)) % 27.87/28.09 (step @p186 :rule cong :premises (@p185 @p151) :args (@t58)) % 27.87/28.09 (step @p187 :rule cong :premises (@p186) :args (@t160)) % 27.87/28.09 (step @p188 :rule nary_cong :premises (@p187 @p184) :args (@t161)) % 27.87/28.09 (step @p189 :rule cong :premises (@p188) :args (@t162)) % 27.87/28.09 (step @p190 :rule quant-merge-prenex :args ((= (forall @t3 @t164) @t162))) % 27.87/28.09 (step @p191 :rule alpha_equiv :args (@t165 (@list @t148) @t133)) % 27.87/28.09 (step @p192 :rule quant-unused-vars :args ((= @t166 @t165))) % 27.87/28.09 (step @p193 :rule trans :premises (@p192 @p191)) % 27.87/28.09 (step @p194 :rule alpha_equiv :args (@t167 (@list @t153) @t133)) % 27.87/28.09 (step @p195 :rule quant-unused-vars :args ((= @t168 @t167))) % 27.87/28.09 (step @p196 :rule trans :premises (@p195 @p194)) % 27.87/28.09 (step @p197 :rule nary_cong :premises (@p196 @p193) :args (@t169)) % 27.87/28.09 (step @p198 :rule quant-miniscope-and :args ((= @t170 @t169))) % 27.87/28.09 (step @p199 :rule trans :premises (@p198 @p197)) % 27.87/28.09 (step @p200 :rule refl :args (@t160)) % 27.87/28.09 (step @p201 :rule nary_cong :premises (@p200 @p199) :args (@t171)) % 27.87/28.09 (step @p202 :rule quant-miniscope-or :args ((= @t164 @t171))) % 27.87/28.09 (step @p203 :rule trans :premises (@p202 @p201)) % 27.87/28.09 (step @p204 :rule symm :premises (@p203)) % 27.87/28.09 (step @p205 :rule cong :premises (@p204) :args ((forall @t3 (or @t160 @t172)))) % 27.87/28.09 (step @p206 :rule trans :premises (@p205 @p190)) % 27.87/28.09 (step @p207 :rule bool-impl-elim :args (@t58 @t172)) % 27.87/28.09 (step @p208 :rule cong :premises (@p207) :args ((forall @t3 (=> @t58 @t172)))) % 27.87/28.09 (step @p209 :rule trans :premises (@p208 @p206)) % 27.87/28.09 (step @p210 :rule bool-impl-elim :args (@t7 @t71)) % 27.87/28.09 (step @p211 :rule cong :premises (@p210) :args (@t72)) % 27.87/28.09 (step @p212 :rule bool-impl-elim :args (@t74 @t73)) % 27.87/28.09 (step @p213 :rule cong :premises (@p212) :args (@t75)) % 27.87/28.09 (step @p214 :rule nary_cong :premises (@p213 @p211) :args (@t76)) % 27.87/28.09 (step @p215 :rule refl :args (@t58)) % 27.87/28.09 (step @p216 :rule cong :premises (@p215 @p214) :args (@t77)) % 27.87/28.09 (step @p217 :rule cong :premises (@p216) :args (@t78)) % 27.87/28.09 (step @p218 :rule trans :premises (@p217 @p209)) % 27.87/28.09 (step @p219 :rule trans :premises (@p218 @p189)) % 27.87/28.09 (step @p220 :rule and_elim :premises (@p42) :args (1)) % 27.87/28.09 (step @p221 :rule eq_resolve :premises (@p220 @p219)) % 27.87/28.09 (step @p222 :rule instantiate :premises (@p221) :args ((@list tptp.xu tptp.sz00 @t113))) % 27.87/28.09 (step @p223 :rule cnf_or_pos :args (@t175)) % 27.87/28.09 (step @p224 :rule reordering :premises (@p223) :args ((or @t138 @t174 (not @t175)))) % 27.87/28.09 (step @p225 :rule chain_m_resolution :premises (@p224 @p155 @p222) :args (@t174 @t176 (@list @t137 @t175))) % 27.87/28.09 (step @p226 :rule cnf_and_pos :args (@t174 1)) % 27.87/28.09 (step @p227 :rule reordering :premises (@p226) :args ((or @t173 (not @t174)))) % 27.87/28.09 (step @p228 :rule chain_m_resolution :premises (@p227 @p225) :args (@t173 (@list false) (@list @t174))) % 27.87/28.09 (step @p229 :rule cnf_or_pos :args (@t173)) % 27.87/28.09 (step @p230 :rule reordering :premises (@p229) :args ((or @t118 @t147 (not @t173)))) % 27.87/28.09 (step @p231 :rule chain_m_resolution :premises (@p230 @p167 @p228) :args (@t147 @t176 (@list @t117 @t173))) % 27.87/28.09 (step @p232 :rule true_intro :premises (@p231)) % 27.87/28.09 (step @p233 :rule symm :premises (@p232)) % 27.87/28.09 (step @p234 :rule trans :premises (@p233 @p173 @p96)) % 27.87/28.09 (step @p235 false :rule eq_resolve :premises (@p234 @p50)) % 27.87/28.09 ) % 27.87/28.09 % SZS output end Proof % 27.87/28.09 % cvc5 exiting %------------------------------------------------------------------------------