%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : RNG118+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 08:45:44 AM UTC 2026 % Result : Theorem 204.38s 204.65s % Output : Proof 204.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : RNG118+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 % 0.15/0.34 % Computer : n029.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 14:08:47 EDT 2026 % 0.15/0.34 % CPUTime : % 0.30/0.49 %----Proving TF0_NAR, FOF, or CNF % 204.38/204.65 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 204.38/204.65 --- Run --no-e-matching --full-saturate-quant at 6... % 204.38/204.65 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 6... % 204.38/204.65 --- Run --finite-model-find --uf-ss=no-minimal at 6... % 204.38/204.65 --- Run --multi-trigger-when-single --full-saturate-quant at 30... % 204.38/204.65 --- Run --trigger-sel=max --full-saturate-quant at 15... % 204.38/204.65 --- Run --multi-trigger-when-single --multi-trigger-priority --full-saturate-quant at 33... % 204.38/204.65 --- Run --multi-trigger-cache --full-saturate-quant at 15... % 204.38/204.65 --- Run --prenex-quant=none --full-saturate-quant at 30... % 204.38/204.65 --- Run --enum-inst-interleave --decision=internal --full-saturate-quant at 15... % 204.38/204.65 --- Run --relevant-triggers --full-saturate-quant at 30... % 204.38/204.65 --- Run --finite-model-find --e-matching --sort-inference --uf-ss-fair at 15... % 204.38/204.65 % SZS status Theorem % 204.38/204.65 % SZS output start Proof % 204.38/204.65 ( % 204.38/204.65 (declare-sort $$unsorted 0) % 204.38/204.65 (declare-const tptp.xu $$unsorted) % 204.38/204.65 (declare-const tptp.xc $$unsorted) % 204.38/204.65 (declare-const tptp.xa $$unsorted) % 204.38/204.65 (declare-const tptp.xI $$unsorted) % 204.38/204.65 (declare-const tptp.slsdtgt0 (-> $$unsorted $$unsorted)) % 204.38/204.65 (declare-const tptp.aDivisorOf0 (-> $$unsorted $$unsorted Bool)) % 204.38/204.65 (declare-const tptp.iLess0 (-> $$unsorted $$unsorted Bool)) % 204.38/204.65 (declare-const tptp.sbrdtbr0 (-> $$unsorted $$unsorted)) % 204.38/204.65 (declare-const tptp.aElement0 (-> $$unsorted Bool)) % 204.38/204.65 (declare-const tptp.sz00 $$unsorted) % 204.38/204.65 (declare-const tptp.sz10 $$unsorted) % 204.38/204.65 (declare-const tptp.aGcdOfAnd0 (-> $$unsorted $$unsorted $$unsorted Bool)) % 204.38/204.65 (declare-const tptp.smndt0 (-> $$unsorted $$unsorted)) % 204.38/204.65 (declare-const tptp.sdtpldt0 (-> $$unsorted $$unsorted $$unsorted)) % 204.38/204.65 (declare-const tptp.sdtasasdt0 (-> $$unsorted $$unsorted $$unsorted)) % 204.38/204.65 (declare-const tptp.aIdeal0 (-> $$unsorted Bool)) % 204.38/204.65 (declare-const tptp.misRelativelyPrime0 (-> $$unsorted $$unsorted Bool)) % 204.38/204.65 (declare-const tptp.sdtasdt0 (-> $$unsorted $$unsorted $$unsorted)) % 204.38/204.65 (declare-const tptp.doDivides0 (-> $$unsorted $$unsorted Bool)) % 204.38/204.65 (declare-const tptp.aSet0 (-> $$unsorted Bool)) % 204.38/204.65 (declare-const tptp.aElementOf0 (-> $$unsorted $$unsorted Bool)) % 204.38/204.65 (declare-const tptp.sdteqdtlpzmzozddtrp0 (-> $$unsorted $$unsorted $$unsorted Bool)) % 204.38/204.65 (declare-const tptp.xb $$unsorted) % 204.38/204.65 (declare-const tptp.sdtpldt1 (-> $$unsorted $$unsorted $$unsorted)) % 204.38/204.65 (declare-const tptp.aNaturalNumber0 (-> $$unsorted Bool)) % 204.38/204.65 (define @t1 () (@var "W0" $$unsorted)) % 204.38/204.65 (define @t2 () (tptp.aElement0 @t1)) % 204.38/204.65 (define @t3 () (@list @t1)) % 204.38/204.65 (define @t4 () (tptp.smndt0 @t1)) % 204.38/204.65 (define @t5 () (@var "W1" $$unsorted)) % 204.38/204.65 (define @t6 () (tptp.sdtpldt0 @t1 @t5)) % 204.38/204.65 (define @t7 () (tptp.aElement0 @t6)) % 204.38/204.65 (define @t8 () (tptp.aElement0 @t5)) % 204.38/204.65 (define @t9 () (and @t2 @t8)) % 204.38/204.65 (define @t10 () (@list @t1 @t5)) % 204.38/204.65 (define @t11 () (forall @t10 (=> @t9 @t7))) % 204.38/204.65 (define @t12 () (tptp.sdtasdt0 @t1 @t5)) % 204.38/204.65 (define @t13 () (tptp.aElement0 @t12)) % 204.38/204.65 (define @t14 () (forall @t10 (=> @t9 @t13))) % 204.38/204.65 (define @t15 () (= @t6 (tptp.sdtpldt0 @t5 @t1))) % 204.38/204.65 (define @t16 () (forall @t10 (=> @t9 @t15))) % 204.38/204.65 (define @t17 () (@var "W2" $$unsorted)) % 204.38/204.65 (define @t18 () (tptp.sdtpldt0 @t5 @t17)) % 204.38/204.65 (define @t19 () (tptp.aElement0 @t17)) % 204.38/204.65 (define @t20 () (and @t2 @t8 @t19)) % 204.38/204.65 (define @t21 () (@list @t1 @t5 @t17)) % 204.38/204.65 (define @t22 () (tptp.sdtasdt0 @t5 @t1)) % 204.38/204.65 (define @t23 () (tptp.sdtasdt0 @t1 @t17)) % 204.38/204.65 (define @t24 () (tptp.smndt0 tptp.sz10)) % 204.38/204.65 (define @t25 () (= @t5 tptp.sz00)) % 204.38/204.65 (define @t26 () (= @t1 tptp.sz00)) % 204.38/204.65 (define @t27 () (tptp.aSet0 @t1)) % 204.38/204.65 (define @t28 () (tptp.aElementOf0 @t5 @t1)) % 204.38/204.65 (define @t29 () (@list @t5)) % 204.38/204.65 (define @t30 () (tptp.aElementOf0 @t17 @t1)) % 204.38/204.65 (define @t31 () (tptp.aElementOf0 @t17 @t5)) % 204.38/204.65 (define @t32 () (@list @t17)) % 204.38/204.65 (define @t33 () (tptp.aSet0 @t5)) % 204.38/204.65 (define @t34 () (and @t27 @t33)) % 204.38/204.65 (define @t35 () (@var "W3" $$unsorted)) % 204.38/204.65 (define @t36 () (@var "W5" $$unsorted)) % 204.38/204.65 (define @t37 () (@var "W4" $$unsorted)) % 204.38/204.65 (define @t38 () (tptp.aElementOf0 @t35 @t17)) % 204.38/204.65 (define @t39 () (@list @t35)) % 204.38/204.65 (define @t40 () (tptp.aSet0 @t17)) % 204.38/204.65 (define @t41 () (tptp.sdtpldt1 @t1 @t5)) % 204.38/204.65 (define @t42 () (tptp.sdtasasdt0 @t1 @t5)) % 204.38/204.65 (define @t43 () (tptp.sdtasdt0 @t17 @t5)) % 204.38/204.65 (define @t44 () (tptp.aIdeal0 @t1)) % 204.38/204.65 (define @t45 () (and @t44 (tptp.aIdeal0 @t5))) % 204.38/204.65 (define @t46 () (tptp.aElement0 @t35)) % 204.38/204.65 (define @t47 () (@list @t17 @t35)) % 204.38/204.65 (define @t48 () (tptp.aNaturalNumber0 @t1)) % 204.38/204.65 (define @t49 () (tptp.sbrdtbr0 @t1)) % 204.38/204.65 (define @t50 () (not @t26)) % 204.38/204.65 (define @t51 () (tptp.sbrdtbr0 @t5)) % 204.38/204.65 (define @t52 () (tptp.iLess0 (tptp.sbrdtbr0 @t35) @t51)) % 204.38/204.65 (define @t53 () (not (= @t35 tptp.sz00))) % 204.38/204.65 (define @t54 () (=> @t53 @t52)) % 204.38/204.65 (define @t55 () (= @t1 (tptp.sdtpldt0 @t43 @t35))) % 204.38/204.65 (define @t56 () (and @t19 @t46 @t55 @t54)) % 204.38/204.65 (define @t57 () (exists @t47 @t56)) % 204.38/204.65 (define @t58 () (not @t25)) % 204.38/204.65 (define @t59 () (and @t2 @t8 @t58)) % 204.38/204.65 (define @t60 () (=> @t59 @t57)) % 204.38/204.65 (define @t61 () (forall @t10 @t60)) % 204.38/204.65 (define @t62 () (tptp.slsdtgt0 @t1)) % 204.38/204.65 (define @t63 () (tptp.aElement0 tptp.xb)) % 204.38/204.65 (define @t64 () (tptp.aElement0 tptp.xa)) % 204.38/204.65 (define @t65 () (tptp.slsdtgt0 tptp.xb)) % 204.38/204.65 (define @t66 () (tptp.slsdtgt0 tptp.xa)) % 204.38/204.65 (define @t67 () (tptp.sdtpldt1 @t66 @t65)) % 204.38/204.65 (define @t68 () (tptp.sbrdtbr0 tptp.xu)) % 204.38/204.65 (define @t69 () (= tptp.xu (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xa @t1) (tptp.sdtasdt0 tptp.xb @t5)))) % 204.38/204.65 (define @t70 () (and @t2 @t8 @t69)) % 204.38/204.65 (define @t71 () (exists @t10 @t70)) % 204.38/204.65 (define @t72 () (tptp.iLess0 @t51 @t68)) % 204.38/204.65 (define @t73 () (or @t25 @t72)) % 204.38/204.65 (define @t74 () (= tptp.xb (tptp.sdtpldt0 (tptp.sdtasdt0 @t1 tptp.xu) @t5))) % 204.38/204.65 (define @t75 () (and @t2 @t8 @t74 @t73)) % 204.38/204.65 (define @t76 () (exists @t10 @t75)) % 204.38/204.65 (define @t77 () (not @t76)) % 204.38/204.65 (define @t78 () (not @t8)) % 204.38/204.65 (define @t79 () (not @t2)) % 204.38/204.65 (define @t80 () (or @t79 @t78)) % 204.38/204.65 (define @t81 () (not @t9)) % 204.38/204.65 (define @t82 () (not @t69)) % 204.38/204.65 (define @t83 () (or @t79 @t78 @t82)) % 204.38/204.65 (define @t84 () (forall @t10 @t83)) % 204.38/204.65 (define @t85 () (@quantifiers_skolemize @t84 0)) % 204.38/204.65 (define @t86 () (tptp.sdtasdt0 tptp.xa @t85)) % 204.38/204.65 (define @t87 () (@quantifiers_skolemize @t84 1)) % 204.38/204.65 (define @t88 () (tptp.sdtasdt0 tptp.xb @t87)) % 204.38/204.65 (define @t89 () (forall @t10 (not @t70))) % 204.38/204.65 (define @t90 () (not @t89)) % 204.38/204.65 (define @t91 () (tptp.aElement0 @t87)) % 204.38/204.65 (define @t92 () (tptp.sdtpldt0 @t86 @t88)) % 204.38/204.65 (define @t93 () (= tptp.xu @t92)) % 204.38/204.65 (define @t94 () (not @t93)) % 204.38/204.65 (define @t95 () (not @t91)) % 204.38/204.65 (define @t96 () (tptp.aElement0 @t85)) % 204.38/204.65 (define @t97 () (not @t96)) % 204.38/204.65 (define @t98 () (or @t97 @t95 @t94)) % 204.38/204.65 (define @t99 () (@list true)) % 204.38/204.65 (define @t100 () (@list @t98)) % 204.38/204.65 (define @t101 () (tptp.aElement0 @t88)) % 204.38/204.65 (define @t102 () (not @t63)) % 204.38/204.65 (define @t103 () (or @t102 @t95 @t101)) % 204.38/204.65 (define @t104 () (@list false false false)) % 204.38/204.65 (define @t105 () (tptp.aElement0 @t86)) % 204.38/204.65 (define @t106 () (not @t64)) % 204.38/204.65 (define @t107 () (or @t106 @t97 @t105)) % 204.38/204.65 (define @t108 () (tptp.sdtpldt0 @t88 @t86)) % 204.38/204.65 (define @t109 () (tptp.aElement0 @t108)) % 204.38/204.65 (define @t110 () (not @t105)) % 204.38/204.65 (define @t111 () (not @t101)) % 204.38/204.65 (define @t112 () (or @t111 @t110 @t109)) % 204.38/204.65 (define @t113 () (= @t92 @t108)) % 204.38/204.65 (define @t114 () (or @t110 @t111 @t113)) % 204.38/204.65 (define @t115 () (tptp.aElement0 tptp.xu)) % 204.38/204.65 (define @t116 () (@const 0 (-> $$unsorted it_88_$$unsorted))) % 204.38/204.65 (define @t117 () (_ @t116 @t5)) % 204.38/204.65 (define @t118 () (_ @t116 @t35)) % 204.38/204.65 (define @t119 () (@const 1 (-> it_88_$$unsorted it_88_$$unsorted Bool))) % 204.38/204.65 (define @t120 () (not (= tptp.sz00 @t35))) % 204.38/204.65 (define @t121 () (not @t55)) % 204.38/204.65 (define @t122 () (not @t46)) % 204.38/204.65 (define @t123 () (not @t19)) % 204.38/204.65 (define @t124 () (= tptp.sz00 @t5)) % 204.38/204.65 (define @t125 () (not (forall @t47 (or @t123 @t122 @t121 (and @t120 (not @t52)))))) % 204.38/204.65 (define @t126 () (or @t79 @t78 @t124 @t125)) % 204.38/204.65 (define @t127 () (not @t124)) % 204.38/204.65 (define @t128 () (not @t127)) % 204.38/204.65 (define @t129 () (or @t79 @t78 @t128)) % 204.38/204.65 (define @t130 () (and @t2 @t8 @t127)) % 204.38/204.65 (define @t131 () (=> @t120 @t52)) % 204.38/204.65 (define @t132 () (not @t131)) % 204.38/204.65 (define @t133 () (or @t123 @t122 @t121 @t132)) % 204.38/204.65 (define @t134 () (and @t19 @t46 @t55 @t131)) % 204.38/204.65 (define @t135 () (forall @t47 (not @t134))) % 204.38/204.65 (define @t136 () (not @t135)) % 204.38/204.65 (define @t137 () (_ @t116 tptp.xu)) % 204.38/204.65 (define @t138 () (not @t74)) % 204.38/204.65 (define @t139 () (forall @t10 (or @t79 @t78 @t138 (and @t127 (not (_ @t119 @t117 @t137)))))) % 204.38/204.65 (define @t140 () (forall @t10 (or @t79 @t78 @t138 (and @t127 (not @t72))))) % 204.38/204.65 (define @t141 () (or @t124 @t72)) % 204.38/204.65 (define @t142 () (not @t141)) % 204.38/204.65 (define @t143 () (or @t79 @t78 @t138 @t142)) % 204.38/204.65 (define @t144 () (and @t2 @t8 @t74 @t141)) % 204.38/204.65 (define @t145 () (forall @t10 (not @t144))) % 204.38/204.65 (define @t146 () (not @t145)) % 204.38/204.65 (define @t147 () (forall @t47 (or @t123 @t122 (not (= tptp.xb (tptp.sdtpldt0 (tptp.sdtasdt0 @t17 tptp.xu) @t35))) (and @t120 (not (_ @t119 @t118 @t137)))))) % 204.38/204.65 (define @t148 () (not @t147)) % 204.38/204.65 (define @t149 () (= tptp.sz00 tptp.xu)) % 204.38/204.65 (define @t150 () (not @t115)) % 204.38/204.65 (define @t151 () (or @t102 @t150 @t149 @t148)) % 204.38/204.65 (assume @p1 (forall @t3 (=> @t2 true))) % 204.38/204.65 (assume @p2 (tptp.aElement0 tptp.sz00)) % 204.38/204.65 (assume @p3 (tptp.aElement0 tptp.sz10)) % 204.38/204.65 (assume @p4 (forall @t3 (=> @t2 (tptp.aElement0 @t4)))) % 204.38/204.65 (assume @p5 @t11) % 204.38/204.65 (assume @p6 @t14) % 204.38/204.65 (assume @p7 @t16) % 204.38/204.65 (assume @p8 (forall @t21 (=> @t20 (= (tptp.sdtpldt0 @t6 @t17) (tptp.sdtpldt0 @t1 @t18))))) % 204.38/204.65 (assume @p9 (forall @t3 (=> @t2 (and (= (tptp.sdtpldt0 @t1 tptp.sz00) @t1) (= @t1 (tptp.sdtpldt0 tptp.sz00 @t1)))))) % 204.38/204.65 (assume @p10 (forall @t3 (=> @t2 (and (= (tptp.sdtpldt0 @t1 @t4) tptp.sz00) (= tptp.sz00 (tptp.sdtpldt0 @t4 @t1)))))) % 204.38/204.65 (assume @p11 (forall @t10 (=> @t9 (= @t12 @t22)))) % 204.38/204.65 (assume @p12 (forall @t21 (=> @t20 (= (tptp.sdtasdt0 @t12 @t17) (tptp.sdtasdt0 @t1 (tptp.sdtasdt0 @t5 @t17)))))) % 204.38/204.65 (assume @p13 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz10) @t1) (= @t1 (tptp.sdtasdt0 tptp.sz10 @t1)))))) % 204.38/204.65 (assume @p14 (forall @t21 (=> @t20 (and (= (tptp.sdtasdt0 @t1 @t18) (tptp.sdtpldt0 @t12 @t23)) (= (tptp.sdtasdt0 @t18 @t1) (tptp.sdtpldt0 @t22 (tptp.sdtasdt0 @t17 @t1))))))) % 204.38/204.65 (assume @p15 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t24 @t1) @t4) (= @t4 (tptp.sdtasdt0 @t1 @t24)))))) % 204.38/204.65 (assume @p16 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz00) tptp.sz00) (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 @t1)))))) % 204.38/204.65 (assume @p17 (forall @t10 (=> @t9 (=> (= @t12 tptp.sz00) (or @t26 @t25))))) % 204.38/204.65 (assume @p18 (not (= tptp.sz10 tptp.sz00))) % 204.38/204.65 (assume @p19 (forall @t3 (=> @t27 true))) % 204.38/204.65 (assume @p20 (forall @t3 (=> @t27 (forall @t29 (=> @t28 @t8))))) % 204.38/204.65 (assume @p21 (forall @t10 (=> @t34 (=> (and (forall @t32 (=> @t30 @t31)) (forall @t32 (=> @t31 @t30))) (= @t1 @t5))))) % 204.38/204.65 (assume @p22 (forall @t10 (=> @t34 (forall @t32 (= (= @t17 @t41) (and @t40 (forall @t39 (= @t38 (exists (@list @t37 @t36) (and (tptp.aElementOf0 @t37 @t1) (tptp.aElementOf0 @t36 @t5) (= (tptp.sdtpldt0 @t37 @t36) @t35))))))))))) % 204.38/204.65 (assume @p23 (forall @t10 (=> @t34 (forall @t32 (= (= @t17 @t42) (and @t40 (forall @t39 (= @t38 (and (tptp.aElementOf0 @t35 @t1) (tptp.aElementOf0 @t35 @t5)))))))))) % 204.38/204.65 (assume @p24 (forall @t3 (= @t44 (and @t27 (forall @t29 (=> @t28 (and (forall @t32 (=> @t30 (tptp.aElementOf0 @t18 @t1))) (forall @t32 (=> @t19 (tptp.aElementOf0 @t43 @t1)))))))))) % 204.38/204.65 (assume @p25 (forall @t10 (=> @t45 (tptp.aIdeal0 @t41)))) % 204.38/204.65 (assume @p26 (forall @t10 (=> @t45 (tptp.aIdeal0 @t42)))) % 204.38/204.65 (assume @p27 (forall @t21 (=> (and @t2 @t8 (tptp.aIdeal0 @t17)) (= (tptp.sdteqdtlpzmzozddtrp0 @t1 @t5 @t17) (tptp.aElementOf0 (tptp.sdtpldt0 @t1 (tptp.smndt0 @t5)) @t17))))) % 204.38/204.65 (assume @p28 (forall @t10 (=> @t45 (=> (forall @t32 (=> @t19 (tptp.aElementOf0 @t17 @t41))) (forall @t47 (=> (and @t19 @t46) (exists (@list @t37) (and (tptp.aElement0 @t37) (tptp.sdteqdtlpzmzozddtrp0 @t37 @t17 @t1) (tptp.sdteqdtlpzmzozddtrp0 @t37 @t35 @t5))))))))) % 204.38/204.65 (assume @p29 (forall @t3 (=> @t48 true))) % 204.38/204.65 (assume @p30 (forall @t3 (=> (and @t2 @t50) (tptp.aNaturalNumber0 @t49)))) % 204.38/204.65 (assume @p31 (forall @t10 (=> (and @t48 (tptp.aNaturalNumber0 @t5)) (=> (tptp.iLess0 @t1 @t5) true)))) % 204.38/204.65 (assume @p32 @t61) % 204.38/204.65 (assume @p33 (forall @t10 (=> @t9 (= (tptp.doDivides0 @t1 @t5) (exists @t32 (and @t19 (= @t23 @t5))))))) % 204.38/204.65 (assume @p34 (forall @t3 (=> @t2 (forall @t29 (= (tptp.aDivisorOf0 @t5 @t1) (and @t8 (tptp.doDivides0 @t5 @t1))))))) % 204.38/204.65 (assume @p35 (forall @t10 (=> @t9 (forall @t32 (= (tptp.aGcdOfAnd0 @t17 @t1 @t5) (and (tptp.aDivisorOf0 @t17 @t1) (tptp.aDivisorOf0 @t17 @t5) (forall @t39 (=> (and (tptp.aDivisorOf0 @t35 @t1) (tptp.aDivisorOf0 @t35 @t5)) (tptp.doDivides0 @t35 @t17))))))))) % 204.38/204.65 (assume @p36 (forall @t10 (=> @t9 (= (tptp.misRelativelyPrime0 @t1 @t5) (tptp.aGcdOfAnd0 tptp.sz10 @t1 @t5))))) % 204.38/204.65 (assume @p37 (forall @t3 (=> @t2 (forall @t29 (= (= @t5 @t62) (and @t33 (forall @t32 (= @t31 (exists @t39 (and @t46 (= (tptp.sdtasdt0 @t1 @t35) @t17))))))))))) % 204.38/204.65 (assume @p38 (forall @t3 (=> @t2 (tptp.aIdeal0 @t62)))) % 204.38/204.65 (assume @p39 (and @t64 @t63)) % 204.38/204.65 (assume @p40 (or (not (= tptp.xa tptp.sz00)) (not (= tptp.xb tptp.sz00)))) % 204.38/204.65 (assume @p41 (tptp.aGcdOfAnd0 tptp.xc tptp.xa tptp.xb)) % 204.38/204.65 (assume @p42 (and (tptp.aIdeal0 tptp.xI) (= tptp.xI @t67))) % 204.38/204.65 (assume @p43 (and (tptp.aElementOf0 tptp.sz00 @t66) (tptp.aElementOf0 tptp.xa @t66) (tptp.aElementOf0 tptp.sz00 @t65) (tptp.aElementOf0 tptp.xb @t65))) % 204.38/204.65 (assume @p44 (exists @t3 (and (tptp.aElementOf0 @t1 @t67) @t50))) % 204.38/204.65 (assume @p45 (and (tptp.aElementOf0 tptp.xu tptp.xI) (not (= tptp.xu tptp.sz00)) (forall @t3 (=> (and (tptp.aElementOf0 @t1 tptp.xI) @t50) (not (tptp.iLess0 @t49 @t68)))))) % 204.38/204.65 (assume @p46 (not (and (tptp.aDivisorOf0 tptp.xu tptp.xa) (tptp.aDivisorOf0 tptp.xu tptp.xb)))) % 204.38/204.65 (assume @p47 @t71) % 204.38/204.65 (assume @p48 (not (not (tptp.doDivides0 tptp.xu tptp.xa)))) % 204.38/204.65 (assume @p49 (not (tptp.doDivides0 tptp.xu tptp.xb))) % 204.38/204.65 (assume @p50 @t77) % 204.38/204.65 (assume @p51 true) % 204.38/204.65 (step @p52 :rule evaluate :args ((= false true))) % 204.38/204.65 (step @p53 :rule aci_norm :args ((= (or @t80 @t7) (or @t79 @t78 @t7)))) % 204.38/204.65 (step @p54 :rule refl :args (@t7)) % 204.38/204.65 (step @p55 :rule bool-and-de-morgan :args (@t2 @t8 true)) % 204.38/204.65 (step @p56 :rule nary_cong :premises (@p55 @p54) :args ((or @t81 @t7))) % 204.38/204.65 (step @p57 :rule trans :premises (@p56 @p53)) % 204.38/204.65 (step @p58 :rule bool-impl-elim :args (@t9 @t7)) % 204.38/204.65 (step @p59 :rule trans :premises (@p58 @p57)) % 204.38/204.65 (step @p60 :rule cong :premises (@p59) :args (@t11)) % 204.38/204.65 (step @p61 :rule eq_resolve :premises (@p5 @p60)) % 204.38/204.65 (step @p62 :rule instantiate :premises (@p61) :args ((@list @t88 @t86))) % 204.38/204.65 (step @p63 :rule aci_norm :args ((= (or @t80 @t13) (or @t79 @t78 @t13)))) % 204.38/204.65 (step @p64 :rule refl :args (@t13)) % 204.38/204.65 (step @p65 :rule nary_cong :premises (@p55 @p64) :args ((or @t81 @t13))) % 204.38/204.65 (step @p66 :rule trans :premises (@p65 @p63)) % 204.38/204.65 (step @p67 :rule bool-impl-elim :args (@t9 @t13)) % 204.38/204.65 (step @p68 :rule trans :premises (@p67 @p66)) % 204.38/204.65 (step @p69 :rule cong :premises (@p68) :args (@t14)) % 204.38/204.65 (step @p70 :rule eq_resolve :premises (@p6 @p69)) % 204.38/204.65 (step @p71 :rule instantiate :premises (@p70) :args ((@list tptp.xb @t87))) % 204.38/204.65 (step @p72 :rule aci_norm :args ((= (or @t79 (or @t78 @t82)) @t83))) % 204.38/204.65 (step @p73 :rule bool-and-de-morgan :args (@t8 @t69 true)) % 204.38/204.65 (step @p74 :rule refl :args (@t79)) % 204.38/204.65 (step @p75 :rule nary_cong :premises (@p74 @p73) :args ((or @t79 (not (and @t8 @t69))))) % 204.38/204.65 (step @p76 :rule bool-and-de-morgan :args (@t2 @t8 (and @t69))) % 204.38/204.65 (step @p77 :rule trans :premises (@p76 @p75)) % 204.38/204.65 (step @p78 :rule trans :premises (@p77 @p72)) % 204.38/204.65 (step @p79 :rule cong :premises (@p78) :args (@t89)) % 204.38/204.65 (step @p80 :rule cong :premises (@p79) :args (@t90)) % 204.38/204.65 (step @p81 :rule exists-elim :args ((= @t71 @t90))) % 204.38/204.65 (step @p82 :rule trans :premises (@p81 @p80)) % 204.38/204.65 (step @p83 :rule eq_resolve :premises (@p47 @p82)) % 204.38/204.65 (step @p84 :rule skolemize :premises (@p83)) % 204.38/204.65 (step @p85 :rule bool-double-not-elim :args (@t91)) % 204.38/204.65 (step @p86 :rule refl :args (@t98)) % 204.38/204.65 (step @p87 :rule nary_cong :premises (@p86 @p85) :args ((or @t98 (not @t95)))) % 204.38/204.65 (step @p88 :rule cnf_or_neg :args (@t98 1)) % 204.38/204.65 (step @p89 :rule eq_resolve :premises (@p88 @p87)) % 204.38/204.65 (step @p90 :rule reordering :premises (@p89) :args ((or @t91 @t98))) % 204.38/204.65 (step @p91 :rule chain_m_resolution :premises (@p90 @p84) :args (@t91 @t99 @t100)) % 204.38/204.65 (step @p92 :rule and_elim :premises (@p39) :args (1)) % 204.38/204.65 (step @p93 :rule cnf_or_pos :args (@t103)) % 204.38/204.65 (step @p94 :rule reordering :premises (@p93) :args ((or @t102 @t95 @t101 (not @t103)))) % 204.38/204.65 (step @p95 :rule chain_m_resolution :premises (@p94 @p92 @p91 @p71) :args (@t101 @t104 (@list @t63 @t91 @t103))) % 204.38/204.65 (step @p96 :rule instantiate :premises (@p70) :args ((@list tptp.xa @t85))) % 204.38/204.65 (step @p97 :rule bool-double-not-elim :args (@t96)) % 204.38/204.65 (step @p98 :rule nary_cong :premises (@p86 @p97) :args ((or @t98 (not @t97)))) % 204.38/204.65 (step @p99 :rule cnf_or_neg :args (@t98 0)) % 204.38/204.65 (step @p100 :rule eq_resolve :premises (@p99 @p98)) % 204.38/204.65 (step @p101 :rule reordering :premises (@p100) :args ((or @t96 @t98))) % 204.38/204.65 (step @p102 :rule chain_m_resolution :premises (@p101 @p84) :args (@t96 @t99 @t100)) % 204.38/204.65 (step @p103 :rule and_elim :premises (@p39) :args (0)) % 204.38/204.65 (step @p104 :rule cnf_or_pos :args (@t107)) % 204.38/204.65 (step @p105 :rule reordering :premises (@p104) :args ((or @t106 @t97 @t105 (not @t107)))) % 204.38/204.65 (step @p106 :rule chain_m_resolution :premises (@p105 @p103 @p102 @p96) :args (@t105 @t104 (@list @t64 @t96 @t107))) % 204.38/204.65 (step @p107 :rule cnf_or_pos :args (@t112)) % 204.38/204.65 (step @p108 :rule reordering :premises (@p107) :args ((or @t110 @t111 @t109 (not @t112)))) % 204.38/204.65 (step @p109 :rule chain_m_resolution :premises (@p108 @p106 @p95 @p62) :args (@t109 @t104 (@list @t105 @t101 @t112))) % 204.38/204.65 (step @p110 :rule true_intro :premises (@p109)) % 204.38/204.65 (step @p111 :rule aci_norm :args ((= (or @t80 @t15) (or @t79 @t78 @t15)))) % 204.38/204.65 (step @p112 :rule refl :args (@t15)) % 204.38/204.65 (step @p113 :rule nary_cong :premises (@p55 @p112) :args ((or @t81 @t15))) % 204.38/204.65 (step @p114 :rule trans :premises (@p113 @p111)) % 204.38/204.65 (step @p115 :rule bool-impl-elim :args (@t9 @t15)) % 204.38/204.65 (step @p116 :rule trans :premises (@p115 @p114)) % 204.38/204.65 (step @p117 :rule cong :premises (@p116) :args (@t16)) % 204.38/204.65 (step @p118 :rule eq_resolve :premises (@p7 @p117)) % 204.38/204.65 (step @p119 :rule instantiate :premises (@p118) :args ((@list @t86 @t88))) % 204.38/204.65 (step @p120 :rule cnf_or_pos :args (@t114)) % 204.38/204.65 (step @p121 :rule reordering :premises (@p120) :args ((or @t110 @t111 @t113 (not @t114)))) % 204.38/204.65 (step @p122 :rule chain_m_resolution :premises (@p121 @p106 @p95 @p119) :args (@t113 @t104 (@list @t105 @t101 @t114))) % 204.38/204.65 (step @p123 :rule bool-double-not-elim :args (@t93)) % 204.38/204.65 (step @p124 :rule nary_cong :premises (@p86 @p123) :args ((or @t98 (not @t94)))) % 204.38/204.65 (step @p125 :rule cnf_or_neg :args (@t98 2)) % 204.38/204.65 (step @p126 :rule eq_resolve :premises (@p125 @p124)) % 204.38/204.65 (step @p127 :rule reordering :premises (@p126) :args ((or @t93 @t98))) % 204.38/204.65 (step @p128 :rule chain_m_resolution :premises (@p127 @p84) :args (@t93 @t99 @t100)) % 204.38/204.65 (step @p129 :rule trans :premises (@p128 @p122)) % 204.38/204.65 (step @p130 :rule cong :premises (@p129) :args (@t115)) % 204.38/204.65 ; WARNING: add trust step for TRUST % 204.38/204.65 ; trust TRUST PREPROCESS_SORT_INFER % 204.38/204.65 (step @p131 :rule trust :premises () :args ((= (forall @t10 @t126) (forall @t10 (or @t79 @t78 @t124 (not (forall @t47 (or @t123 @t122 @t121 (and @t120 (not (_ @t119 @t118 @t117))))))))))) % 204.38/204.65 (step @p132 :rule aci_norm :args ((= (or (or @t79 @t78 @t124) @t125) @t126))) % 204.38/204.65 (step @p133 :rule refl :args (@t125)) % 204.38/204.65 (step @p134 :rule bool-double-not-elim :args (@t124)) % 204.38/204.65 (step @p135 :rule refl :args (@t78)) % 204.38/204.65 (step @p136 :rule nary_cong :premises (@p74 @p135 @p134) :args (@t129)) % 204.38/204.65 (step @p137 :rule aci_norm :args ((= (or @t79 (or @t78 @t128)) @t129))) % 204.38/204.65 (step @p138 :rule trans :premises (@p137 @p136)) % 204.38/204.65 (step @p139 :rule bool-and-de-morgan :args (@t8 @t127 true)) % 204.38/204.65 (step @p140 :rule nary_cong :premises (@p74 @p139) :args ((or @t79 (not (and @t8 @t127))))) % 204.38/204.65 (step @p141 :rule bool-and-de-morgan :args (@t2 @t8 (and @t127))) % 204.38/204.65 (step @p142 :rule trans :premises (@p141 @p140)) % 204.38/204.65 (step @p143 :rule trans :premises (@p142 @p138)) % 204.38/204.65 (step @p144 :rule nary_cong :premises (@p143 @p133) :args ((or (not @t130) @t125))) % 204.38/204.65 (step @p145 :rule trans :premises (@p144 @p132)) % 204.38/204.65 (step @p146 :rule bool-impl-elim :args (@t130 @t125)) % 204.38/204.65 (step @p147 :rule trans :premises (@p146 @p145)) % 204.38/204.65 (step @p148 :rule cong :premises (@p147) :args ((forall @t10 (=> @t130 @t125)))) % 204.38/204.65 (step @p149 :rule bool-implies-de-morgan :args (@t120 @t52)) % 204.38/204.65 (step @p150 :rule refl :args (@t121)) % 204.38/204.65 (step @p151 :rule refl :args (@t122)) % 204.38/204.65 (step @p152 :rule refl :args (@t123)) % 204.38/204.65 (step @p153 :rule nary_cong :premises (@p152 @p151 @p150 @p149) :args (@t133)) % 204.38/204.65 (step @p154 :rule aci_norm :args ((= (or @t123 (or @t122 (or @t121 @t132))) @t133))) % 204.38/204.65 (step @p155 :rule bool-and-de-morgan :args (@t55 @t131 true)) % 204.38/204.65 (step @p156 :rule nary_cong :premises (@p151 @p155) :args ((or @t122 (not (and @t55 @t131))))) % 204.38/204.65 (step @p157 :rule bool-and-de-morgan :args (@t46 @t55 (and @t131))) % 204.38/204.65 (step @p158 :rule trans :premises (@p157 @p156)) % 204.38/204.65 (step @p159 :rule nary_cong :premises (@p152 @p158) :args ((or @t123 (not (and @t46 @t55 @t131))))) % 204.38/204.65 (step @p160 :rule bool-and-de-morgan :args (@t19 @t46 (and @t55 @t131))) % 204.38/204.65 (step @p161 :rule trans :premises (@p160 @p159)) % 204.38/204.65 (step @p162 :rule trans :premises (@p161 @p154)) % 204.38/204.65 (step @p163 :rule trans :premises (@p162 @p153)) % 204.38/204.65 (step @p164 :rule cong :premises (@p163) :args (@t135)) % 204.38/204.65 (step @p165 :rule cong :premises (@p164) :args (@t136)) % 204.38/204.65 (step @p166 :rule exists-elim :args ((= (exists @t47 @t134) @t136))) % 204.38/204.65 (step @p167 :rule trans :premises (@p166 @p165)) % 204.38/204.65 (step @p168 :rule refl :args (@t52)) % 204.38/204.65 (step @p169 :rule eq-symm :args (@t35 tptp.sz00)) % 204.38/204.65 (step @p170 :rule cong :premises (@p169) :args (@t53)) % 204.38/204.65 (step @p171 :rule cong :premises (@p170 @p168) :args (@t54)) % 204.38/204.65 (step @p172 :rule refl :args (@t55)) % 204.38/204.65 (step @p173 :rule refl :args (@t46)) % 204.38/204.65 (step @p174 :rule refl :args (@t19)) % 204.38/204.65 (step @p175 :rule nary_cong :premises (@p174 @p173 @p172 @p171) :args (@t56)) % 204.38/204.65 (step @p176 :rule cong :premises (@p175) :args (@t57)) % 204.38/204.65 (step @p177 :rule trans :premises (@p176 @p167)) % 204.38/204.65 (step @p178 :rule eq-symm :args (@t5 tptp.sz00)) % 204.38/204.65 (step @p179 :rule cong :premises (@p178) :args (@t58)) % 204.38/204.65 (step @p180 :rule refl :args (@t8)) % 204.38/204.65 (step @p181 :rule refl :args (@t2)) % 204.38/204.65 (step @p182 :rule nary_cong :premises (@p181 @p180 @p179) :args (@t59)) % 204.38/204.65 (step @p183 :rule cong :premises (@p182 @p177) :args (@t60)) % 204.38/204.65 (step @p184 :rule cong :premises (@p183) :args (@t61)) % 204.38/204.65 (step @p185 :rule trans :premises (@p184 @p148)) % 204.38/204.65 (step @p186 :rule trans :premises (@p185 @p131)) % 204.38/204.65 (step @p187 :rule eq_resolve :premises (@p32 @p186)) % 204.38/204.65 (step @p188 :rule instantiate :premises (@p187) :args ((@list tptp.xb tptp.xu))) % 204.38/204.65 ; trust TRUST PREPROCESS_SORT_INFER % 204.38/204.65 (step @p189 :rule trust :premises () :args ((= @t140 @t139))) % 204.38/204.65 (step @p190 :rule bool-double-not-elim :args (@t140)) % 204.38/204.65 (step @p191 :rule bool-or-de-morgan :args (@t124 @t72 false)) % 204.38/204.65 (step @p192 :rule refl :args (@t138)) % 204.38/204.65 (step @p193 :rule nary_cong :premises (@p74 @p135 @p192 @p191) :args (@t143)) % 204.38/204.65 (step @p194 :rule aci_norm :args ((= (or @t79 (or @t78 (or @t138 @t142))) @t143))) % 204.38/204.65 (step @p195 :rule bool-and-de-morgan :args (@t74 @t141 true)) % 204.38/204.65 (step @p196 :rule nary_cong :premises (@p135 @p195) :args ((or @t78 (not (and @t74 @t141))))) % 204.38/204.65 (step @p197 :rule bool-and-de-morgan :args (@t8 @t74 (and @t141))) % 204.38/204.65 (step @p198 :rule trans :premises (@p197 @p196)) % 204.38/204.65 (step @p199 :rule nary_cong :premises (@p74 @p198) :args ((or @t79 (not (and @t8 @t74 @t141))))) % 204.38/204.65 (step @p200 :rule bool-and-de-morgan :args (@t2 @t8 (and @t74 @t141))) % 204.38/204.65 (step @p201 :rule trans :premises (@p200 @p199)) % 204.38/204.65 (step @p202 :rule trans :premises (@p201 @p194)) % 204.38/204.65 (step @p203 :rule trans :premises (@p202 @p193)) % 204.38/204.65 (step @p204 :rule cong :premises (@p203) :args (@t145)) % 204.38/204.65 (step @p205 :rule cong :premises (@p204) :args (@t146)) % 204.38/204.65 (step @p206 :rule exists-elim :args ((= (exists @t10 @t144) @t146))) % 204.38/204.65 (step @p207 :rule trans :premises (@p206 @p205)) % 204.38/204.65 (step @p208 :rule refl :args (@t72)) % 204.38/204.65 (step @p209 :rule nary_cong :premises (@p178 @p208) :args (@t73)) % 204.38/204.65 (step @p210 :rule refl :args (@t74)) % 204.38/204.65 (step @p211 :rule nary_cong :premises (@p181 @p180 @p210 @p209) :args (@t75)) % 204.38/204.65 (step @p212 :rule cong :premises (@p211) :args (@t76)) % 204.38/204.65 (step @p213 :rule trans :premises (@p212 @p207)) % 204.38/204.65 (step @p214 :rule cong :premises (@p213) :args (@t77)) % 204.38/204.65 (step @p215 :rule trans :premises (@p214 @p190)) % 204.38/204.65 (step @p216 :rule trans :premises (@p215 @p189)) % 204.38/204.65 (step @p217 :rule eq_resolve :premises (@p50 @p216)) % 204.38/204.65 (step @p218 :rule alpha_equiv :args (@t139 (@list @t1 @t5) (@list @t17 @t35))) % 204.38/204.65 (step @p219 :rule equiv_elim1 :premises (@p218)) % 204.38/204.65 (step @p220 :rule chain_m_resolution :premises (@p219 @p217) :args (@t147 (@list false) (@list @t139))) % 204.38/204.65 (step @p221 :rule and_elim :premises (@p45) :args (1)) % 204.38/204.65 (step @p222 :rule symm :premises (@p221)) % 204.38/204.65 (step @p223 :rule cnf_or_pos :args (@t151)) % 204.38/204.65 (step @p224 :rule reordering :premises (@p223) :args ((or @t149 @t102 @t150 @t148 (not @t151)))) % 204.38/204.65 (step @p225 :rule chain_m_resolution :premises (@p224 @p222 @p92 @p220 @p188) :args (@t150 (@list true false false false) (@list @t149 @t63 @t147 @t151))) % 204.38/204.65 (step @p226 :rule false_intro :premises (@p225)) % 204.38/204.65 (step @p227 :rule symm :premises (@p226)) % 204.38/204.65 (step @p228 :rule trans :premises (@p227 @p130 @p110)) % 204.38/204.65 (step @p229 false :rule eq_resolve :premises (@p228 @p52)) % 204.38/204.65 ) % 204.38/204.65 % SZS output end Proof % 204.38/204.65 % cvc5 exiting %------------------------------------------------------------------------------