%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : RNG115+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 : n020.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 0.45s 0.65s % Output : Proof 0.45s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : RNG115+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 : n020.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 14:08:25 EDT 2026 % 0.17/0.34 % CPUTime : % 0.28/0.50 %----Proving TF0_NAR, FOF, or CNF % 0.45/0.65 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.45/0.65 % SZS status Theorem % 0.45/0.65 % SZS output start Proof % 0.45/0.65 ( % 0.45/0.65 (declare-sort $$unsorted 0) % 0.45/0.65 (declare-const tptp.xu $$unsorted) % 0.45/0.65 (declare-const tptp.xI $$unsorted) % 0.45/0.65 (declare-const tptp.xc $$unsorted) % 0.45/0.65 (declare-const tptp.xa $$unsorted) % 0.45/0.65 (declare-const tptp.slsdtgt0 (-> $$unsorted $$unsorted)) % 0.45/0.65 (declare-const tptp.aDivisorOf0 (-> $$unsorted $$unsorted Bool)) % 0.45/0.65 (declare-const tptp.iLess0 (-> $$unsorted $$unsorted Bool)) % 0.45/0.65 (declare-const tptp.sbrdtbr0 (-> $$unsorted $$unsorted)) % 0.45/0.65 (declare-const tptp.aElement0 (-> $$unsorted Bool)) % 0.45/0.65 (declare-const tptp.sz00 $$unsorted) % 0.45/0.65 (declare-const tptp.sz10 $$unsorted) % 0.45/0.65 (declare-const tptp.aGcdOfAnd0 (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.45/0.65 (declare-const tptp.smndt0 (-> $$unsorted $$unsorted)) % 0.45/0.65 (declare-const tptp.sdtpldt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.45/0.65 (declare-const tptp.sdtasasdt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.45/0.65 (declare-const tptp.aIdeal0 (-> $$unsorted Bool)) % 0.45/0.65 (declare-const tptp.misRelativelyPrime0 (-> $$unsorted $$unsorted Bool)) % 0.45/0.65 (declare-const tptp.sdtasdt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.45/0.65 (declare-const tptp.doDivides0 (-> $$unsorted $$unsorted Bool)) % 0.45/0.65 (declare-const tptp.aSet0 (-> $$unsorted Bool)) % 0.45/0.65 (declare-const tptp.aElementOf0 (-> $$unsorted $$unsorted Bool)) % 0.45/0.65 (declare-const tptp.sdteqdtlpzmzozddtrp0 (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.45/0.65 (declare-const tptp.xb $$unsorted) % 0.45/0.65 (declare-const tptp.sdtpldt1 (-> $$unsorted $$unsorted $$unsorted)) % 0.45/0.65 (declare-const tptp.aNaturalNumber0 (-> $$unsorted Bool)) % 0.45/0.65 (define @t1 () (@var "W0" $$unsorted)) % 0.45/0.65 (define @t2 () (tptp.aElement0 @t1)) % 0.45/0.65 (define @t3 () (@list @t1)) % 0.45/0.65 (define @t4 () (tptp.smndt0 @t1)) % 0.45/0.65 (define @t5 () (@var "W1" $$unsorted)) % 0.45/0.65 (define @t6 () (tptp.sdtpldt0 @t1 @t5)) % 0.45/0.65 (define @t7 () (tptp.aElement0 @t5)) % 0.45/0.65 (define @t8 () (and @t2 @t7)) % 0.45/0.65 (define @t9 () (@list @t1 @t5)) % 0.45/0.65 (define @t10 () (tptp.sdtasdt0 @t1 @t5)) % 0.45/0.65 (define @t11 () (@var "W2" $$unsorted)) % 0.45/0.65 (define @t12 () (tptp.sdtpldt0 @t5 @t11)) % 0.45/0.65 (define @t13 () (tptp.aElement0 @t11)) % 0.45/0.65 (define @t14 () (and @t2 @t7 @t13)) % 0.45/0.65 (define @t15 () (@list @t1 @t5 @t11)) % 0.45/0.65 (define @t16 () (tptp.sdtasdt0 @t5 @t1)) % 0.45/0.65 (define @t17 () (tptp.sdtasdt0 @t1 @t11)) % 0.45/0.65 (define @t18 () (tptp.smndt0 tptp.sz10)) % 0.45/0.65 (define @t19 () (= @t5 tptp.sz00)) % 0.45/0.65 (define @t20 () (= @t1 tptp.sz00)) % 0.45/0.65 (define @t21 () (tptp.aSet0 @t1)) % 0.45/0.65 (define @t22 () (tptp.aElementOf0 @t5 @t1)) % 0.45/0.65 (define @t23 () (@list @t5)) % 0.45/0.65 (define @t24 () (tptp.aElementOf0 @t11 @t1)) % 0.45/0.65 (define @t25 () (tptp.aElementOf0 @t11 @t5)) % 0.45/0.65 (define @t26 () (@list @t11)) % 0.45/0.65 (define @t27 () (tptp.aSet0 @t5)) % 0.45/0.65 (define @t28 () (and @t21 @t27)) % 0.45/0.65 (define @t29 () (@var "W3" $$unsorted)) % 0.45/0.65 (define @t30 () (@var "W5" $$unsorted)) % 0.45/0.65 (define @t31 () (@var "W4" $$unsorted)) % 0.45/0.65 (define @t32 () (tptp.aElementOf0 @t29 @t11)) % 0.45/0.65 (define @t33 () (@list @t29)) % 0.45/0.65 (define @t34 () (tptp.aSet0 @t11)) % 0.45/0.65 (define @t35 () (tptp.sdtpldt1 @t1 @t5)) % 0.45/0.65 (define @t36 () (tptp.sdtasasdt0 @t1 @t5)) % 0.45/0.65 (define @t37 () (tptp.sdtasdt0 @t11 @t5)) % 0.45/0.65 (define @t38 () (tptp.aIdeal0 @t1)) % 0.45/0.65 (define @t39 () (and @t38 (tptp.aIdeal0 @t5))) % 0.45/0.65 (define @t40 () (tptp.aElement0 @t29)) % 0.45/0.65 (define @t41 () (@list @t11 @t29)) % 0.45/0.65 (define @t42 () (tptp.aNaturalNumber0 @t1)) % 0.45/0.65 (define @t43 () (tptp.sbrdtbr0 @t1)) % 0.45/0.65 (define @t44 () (not @t20)) % 0.45/0.65 (define @t45 () (tptp.slsdtgt0 @t1)) % 0.45/0.65 (define @t46 () (tptp.aElement0 tptp.xb)) % 0.45/0.65 (define @t47 () (tptp.sdtasdt0 tptp.xc @t1)) % 0.45/0.65 (define @t48 () (tptp.aElement0 tptp.xc)) % 0.45/0.65 (define @t49 () (tptp.slsdtgt0 tptp.xb)) % 0.45/0.65 (define @t50 () (tptp.slsdtgt0 tptp.xa)) % 0.45/0.65 (define @t51 () (tptp.sdtpldt1 @t50 @t49)) % 0.45/0.65 (define @t52 () (tptp.aElementOf0 @t5 @t50)) % 0.45/0.65 (define @t53 () (exists (@list @t5 @t11) (and @t52 (tptp.aElementOf0 @t11 @t49) (= @t12 @t1)))) % 0.45/0.65 (define @t54 () (tptp.aElementOf0 @t1 tptp.xI)) % 0.45/0.65 (define @t55 () (tptp.aElementOf0 @t1 @t50)) % 0.45/0.65 (define @t56 () (tptp.sdtasdt0 tptp.xb @t1)) % 0.45/0.65 (define @t57 () (tptp.sdtasdt0 tptp.xa @t1)) % 0.45/0.65 (define @t58 () (tptp.sdtasdt0 tptp.xb @t11)) % 0.45/0.65 (define @t59 () (and @t13 (= @t58 @t5))) % 0.45/0.65 (define @t60 () (exists @t26 @t59)) % 0.45/0.65 (define @t61 () (tptp.aElementOf0 @t5 @t49)) % 0.45/0.65 (define @t62 () (tptp.sdtasdt0 tptp.xa @t11)) % 0.45/0.65 (define @t63 () (= @t6 tptp.xu)) % 0.45/0.65 (define @t64 () (and @t55 @t61 @t63)) % 0.45/0.65 (define @t65 () (exists @t9 @t64)) % 0.45/0.65 (define @t66 () (tptp.sdtasdt0 tptp.xu @t1)) % 0.45/0.65 (define @t67 () (or @t60 @t61)) % 0.45/0.65 (define @t68 () (and @t13 (= @t62 @t1))) % 0.45/0.65 (define @t69 () (exists @t26 @t68)) % 0.45/0.65 (define @t70 () (or @t69 @t55)) % 0.45/0.65 (define @t71 () (and @t70 @t67 (= tptp.xu @t6))) % 0.45/0.65 (define @t72 () (exists @t9 @t71)) % 0.45/0.65 (define @t73 () (not @t72)) % 0.45/0.65 (define @t74 () (not @t63)) % 0.45/0.65 (define @t75 () (not @t61)) % 0.45/0.65 (define @t76 () (not @t55)) % 0.45/0.65 (define @t77 () (or @t76 @t75 @t74)) % 0.45/0.65 (define @t78 () (forall @t9 (not @t64))) % 0.45/0.65 (define @t79 () (not @t78)) % 0.45/0.65 (define @t80 () (forall @t9 @t77)) % 0.45/0.65 (define @t81 () (@quantifiers_skolemize @t80 1)) % 0.45/0.65 (define @t82 () (@quantifiers_skolemize @t80 0)) % 0.45/0.65 (define @t83 () (tptp.sdtpldt0 @t82 @t81)) % 0.45/0.65 (define @t84 () (= tptp.xu @t83)) % 0.45/0.65 (define @t85 () (not @t84)) % 0.45/0.65 (define @t86 () (tptp.aElementOf0 @t81 @t49)) % 0.45/0.65 (define @t87 () (not @t86)) % 0.45/0.65 (define @t88 () (tptp.aElementOf0 @t82 @t50)) % 0.45/0.65 (define @t89 () (not @t88)) % 0.45/0.65 (define @t90 () (or @t89 @t87 @t85)) % 0.45/0.65 (define @t91 () (not @t90)) % 0.45/0.65 (define @t92 () (not @t80)) % 0.45/0.65 (define @t93 () (not (= @t83 tptp.xu))) % 0.45/0.65 (define @t94 () (or @t89 @t87 @t93)) % 0.45/0.65 (define @t95 () (not @t94)) % 0.45/0.65 (define @t96 () (@list true)) % 0.45/0.65 (define @t97 () (@list @t90)) % 0.45/0.65 (define @t98 () (@var "BOUND_VARIABLE_8691" $$unsorted)) % 0.45/0.65 (define @t99 () (or (not (tptp.aElement0 @t98)) (not (= @t5 (tptp.sdtasdt0 tptp.xb @t98))))) % 0.45/0.65 (define @t100 () (and @t99 @t75)) % 0.45/0.65 (define @t101 () (@var "BOUND_VARIABLE_8682" $$unsorted)) % 0.45/0.65 (define @t102 () (or (not (tptp.aElement0 @t101)) (not (= @t1 (tptp.sdtasdt0 tptp.xa @t101))))) % 0.45/0.65 (define @t103 () (and @t102 @t76)) % 0.45/0.65 (define @t104 () (or @t103 @t100 @t74)) % 0.45/0.65 (define @t105 () (forall (@list @t1 @t5 @t101 @t98) @t104)) % 0.45/0.65 (define @t106 () (forall (@list @t101 @t98) @t104)) % 0.45/0.65 (define @t107 () (@list @t98)) % 0.45/0.65 (define @t108 () (forall @t107 @t75)) % 0.45/0.65 (define @t109 () (forall @t107 @t99)) % 0.45/0.65 (define @t110 () (@list @t11)) % 0.45/0.65 (define @t111 () (and @t109 @t108)) % 0.45/0.65 (define @t112 () (forall @t107 @t100)) % 0.45/0.65 (define @t113 () (@list @t101)) % 0.45/0.65 (define @t114 () (forall @t113 @t76)) % 0.45/0.65 (define @t115 () (forall @t113 @t102)) % 0.45/0.65 (define @t116 () (and @t115 @t114)) % 0.45/0.65 (define @t117 () (forall @t113 @t103)) % 0.45/0.65 (define @t118 () (or @t117 @t112 @t74)) % 0.45/0.65 (define @t119 () (= @t5 @t58)) % 0.45/0.65 (define @t120 () (not @t13)) % 0.45/0.65 (define @t121 () (forall @t26 (or @t120 (not @t119)))) % 0.45/0.65 (define @t122 () (= @t1 @t62)) % 0.45/0.65 (define @t123 () (forall @t26 (or @t120 (not @t122)))) % 0.45/0.65 (define @t124 () (not @t121)) % 0.45/0.65 (define @t125 () (not @t123)) % 0.45/0.65 (define @t126 () (or @t124 @t61)) % 0.45/0.65 (define @t127 () (not @t126)) % 0.45/0.65 (define @t128 () (or @t125 @t55)) % 0.45/0.65 (define @t129 () (not @t128)) % 0.45/0.65 (define @t130 () (or @t129 @t127 @t74)) % 0.45/0.65 (define @t131 () (and @t128 @t126 @t63)) % 0.45/0.65 (define @t132 () (forall @t9 (not @t131))) % 0.45/0.65 (define @t133 () (not @t132)) % 0.45/0.65 (define @t134 () (and @t13 @t119)) % 0.45/0.65 (define @t135 () (forall @t26 (not @t134))) % 0.45/0.65 (define @t136 () (not @t135)) % 0.45/0.65 (define @t137 () (and @t13 @t122)) % 0.45/0.65 (define @t138 () (forall @t26 (not @t137))) % 0.45/0.65 (define @t139 () (not @t138)) % 0.45/0.65 (define @t140 () (not @t46)) % 0.45/0.65 (define @t141 () (and (or @t140 (not (= @t81 (tptp.sdtasdt0 tptp.xb tptp.xb)))) @t87)) % 0.45/0.65 (define @t142 () (and (or @t140 (not (= @t82 (tptp.sdtasdt0 tptp.xa tptp.xb)))) @t89)) % 0.45/0.65 (define @t143 () (or @t142 @t141 @t93)) % 0.45/0.65 (define @t144 () (or @t142 @t141 @t85)) % 0.45/0.65 (define @t145 () (@list false)) % 0.45/0.65 (define @t146 () (not @t142)) % 0.45/0.65 (define @t147 () (not @t141)) % 0.45/0.65 (assume @p1 (forall @t3 (=> @t2 true))) % 0.45/0.65 (assume @p2 (tptp.aElement0 tptp.sz00)) % 0.45/0.65 (assume @p3 (tptp.aElement0 tptp.sz10)) % 0.45/0.65 (assume @p4 (forall @t3 (=> @t2 (tptp.aElement0 @t4)))) % 0.45/0.65 (assume @p5 (forall @t9 (=> @t8 (tptp.aElement0 @t6)))) % 0.45/0.65 (assume @p6 (forall @t9 (=> @t8 (tptp.aElement0 @t10)))) % 0.45/0.65 (assume @p7 (forall @t9 (=> @t8 (= @t6 (tptp.sdtpldt0 @t5 @t1))))) % 0.45/0.65 (assume @p8 (forall @t15 (=> @t14 (= (tptp.sdtpldt0 @t6 @t11) (tptp.sdtpldt0 @t1 @t12))))) % 0.45/0.65 (assume @p9 (forall @t3 (=> @t2 (and (= (tptp.sdtpldt0 @t1 tptp.sz00) @t1) (= @t1 (tptp.sdtpldt0 tptp.sz00 @t1)))))) % 0.45/0.65 (assume @p10 (forall @t3 (=> @t2 (and (= (tptp.sdtpldt0 @t1 @t4) tptp.sz00) (= tptp.sz00 (tptp.sdtpldt0 @t4 @t1)))))) % 0.45/0.65 (assume @p11 (forall @t9 (=> @t8 (= @t10 @t16)))) % 0.45/0.65 (assume @p12 (forall @t15 (=> @t14 (= (tptp.sdtasdt0 @t10 @t11) (tptp.sdtasdt0 @t1 (tptp.sdtasdt0 @t5 @t11)))))) % 0.45/0.65 (assume @p13 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz10) @t1) (= @t1 (tptp.sdtasdt0 tptp.sz10 @t1)))))) % 0.45/0.65 (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))))))) % 0.45/0.65 (assume @p15 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t18 @t1) @t4) (= @t4 (tptp.sdtasdt0 @t1 @t18)))))) % 0.45/0.65 (assume @p16 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz00) tptp.sz00) (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 @t1)))))) % 0.45/0.65 (assume @p17 (forall @t9 (=> @t8 (=> (= @t10 tptp.sz00) (or @t20 @t19))))) % 0.45/0.65 (assume @p18 (not (= tptp.sz10 tptp.sz00))) % 0.45/0.65 (assume @p19 (forall @t3 (=> @t21 true))) % 0.45/0.65 (assume @p20 (forall @t3 (=> @t21 (forall @t23 (=> @t22 @t7))))) % 0.45/0.65 (assume @p21 (forall @t9 (=> @t28 (=> (and (forall @t26 (=> @t24 @t25)) (forall @t26 (=> @t25 @t24))) (= @t1 @t5))))) % 0.45/0.65 (assume @p22 (forall @t9 (=> @t28 (forall @t26 (= (= @t11 @t35) (and @t34 (forall @t33 (= @t32 (exists (@list @t31 @t30) (and (tptp.aElementOf0 @t31 @t1) (tptp.aElementOf0 @t30 @t5) (= (tptp.sdtpldt0 @t31 @t30) @t29))))))))))) % 0.45/0.65 (assume @p23 (forall @t9 (=> @t28 (forall @t26 (= (= @t11 @t36) (and @t34 (forall @t33 (= @t32 (and (tptp.aElementOf0 @t29 @t1) (tptp.aElementOf0 @t29 @t5)))))))))) % 0.45/0.65 (assume @p24 (forall @t3 (= @t38 (and @t21 (forall @t23 (=> @t22 (and (forall @t26 (=> @t24 (tptp.aElementOf0 @t12 @t1))) (forall @t26 (=> @t13 (tptp.aElementOf0 @t37 @t1)))))))))) % 0.45/0.65 (assume @p25 (forall @t9 (=> @t39 (tptp.aIdeal0 @t35)))) % 0.45/0.65 (assume @p26 (forall @t9 (=> @t39 (tptp.aIdeal0 @t36)))) % 0.45/0.65 (assume @p27 (forall @t15 (=> (and @t2 @t7 (tptp.aIdeal0 @t11)) (= (tptp.sdteqdtlpzmzozddtrp0 @t1 @t5 @t11) (tptp.aElementOf0 (tptp.sdtpldt0 @t1 (tptp.smndt0 @t5)) @t11))))) % 0.45/0.65 (assume @p28 (forall @t9 (=> @t39 (=> (forall @t26 (=> @t13 (tptp.aElementOf0 @t11 @t35))) (forall @t41 (=> (and @t13 @t40) (exists (@list @t31) (and (tptp.aElement0 @t31) (tptp.sdteqdtlpzmzozddtrp0 @t31 @t11 @t1) (tptp.sdteqdtlpzmzozddtrp0 @t31 @t29 @t5))))))))) % 0.45/0.65 (assume @p29 (forall @t3 (=> @t42 true))) % 0.45/0.65 (assume @p30 (forall @t3 (=> (and @t2 @t44) (tptp.aNaturalNumber0 @t43)))) % 0.45/0.65 (assume @p31 (forall @t9 (=> (and @t42 (tptp.aNaturalNumber0 @t5)) (=> (tptp.iLess0 @t1 @t5) true)))) % 0.45/0.65 (assume @p32 (forall @t9 (=> (and @t2 @t7 (not @t19)) (exists @t41 (and @t13 @t40 (= @t1 (tptp.sdtpldt0 @t37 @t29)) (=> (not (= @t29 tptp.sz00)) (tptp.iLess0 (tptp.sbrdtbr0 @t29) (tptp.sbrdtbr0 @t5)))))))) % 0.45/0.65 (assume @p33 (forall @t9 (=> @t8 (= (tptp.doDivides0 @t1 @t5) (exists @t26 (and @t13 (= @t17 @t5))))))) % 0.45/0.65 (assume @p34 (forall @t3 (=> @t2 (forall @t23 (= (tptp.aDivisorOf0 @t5 @t1) (and @t7 (tptp.doDivides0 @t5 @t1))))))) % 0.45/0.65 (assume @p35 (forall @t9 (=> @t8 (forall @t26 (= (tptp.aGcdOfAnd0 @t11 @t1 @t5) (and (tptp.aDivisorOf0 @t11 @t1) (tptp.aDivisorOf0 @t11 @t5) (forall @t33 (=> (and (tptp.aDivisorOf0 @t29 @t1) (tptp.aDivisorOf0 @t29 @t5)) (tptp.doDivides0 @t29 @t11))))))))) % 0.45/0.65 (assume @p36 (forall @t9 (=> @t8 (= (tptp.misRelativelyPrime0 @t1 @t5) (tptp.aGcdOfAnd0 tptp.sz10 @t1 @t5))))) % 0.45/0.65 (assume @p37 (forall @t3 (=> @t2 (forall @t23 (= (= @t5 @t45) (and @t27 (forall @t26 (= @t25 (exists @t33 (and @t40 (= (tptp.sdtasdt0 @t1 @t29) @t11))))))))))) % 0.45/0.65 (assume @p38 (forall @t3 (=> @t2 (tptp.aIdeal0 @t45)))) % 0.45/0.65 (assume @p39 (and (tptp.aElement0 tptp.xa) @t46)) % 0.45/0.65 (assume @p40 (or (not (= tptp.xa tptp.sz00)) (not (= tptp.xb tptp.sz00)))) % 0.45/0.65 (assume @p41 (and @t48 (exists @t3 (and @t2 (= @t47 tptp.xa))) (tptp.doDivides0 tptp.xc tptp.xa) (tptp.aDivisorOf0 tptp.xc tptp.xa) @t48 (exists @t3 (and @t2 (= @t47 tptp.xb))) (tptp.doDivides0 tptp.xc tptp.xb) (tptp.aDivisorOf0 tptp.xc tptp.xb) (forall @t3 (=> (and (or (and @t2 (or (exists @t23 (and @t7 (= @t10 tptp.xa))) (tptp.doDivides0 @t1 tptp.xa))) (tptp.aDivisorOf0 @t1 tptp.xa)) (or (exists @t23 (and @t7 (= @t10 tptp.xb))) (tptp.doDivides0 @t1 tptp.xb) (tptp.aDivisorOf0 @t1 tptp.xb))) (and (exists @t23 (and @t7 (= @t10 tptp.xc))) (tptp.doDivides0 @t1 tptp.xc)))) (tptp.aGcdOfAnd0 tptp.xc tptp.xa tptp.xb))) % 0.45/0.65 (assume @p42 (and (tptp.aSet0 tptp.xI) (forall @t3 (=> @t54 (and (forall @t23 (=> (tptp.aElementOf0 @t5 tptp.xI) (tptp.aElementOf0 @t6 tptp.xI))) (forall @t23 (=> @t7 (tptp.aElementOf0 @t16 tptp.xI)))))) (tptp.aIdeal0 tptp.xI) (forall @t3 (= @t55 (exists @t23 (and @t7 (= (tptp.sdtasdt0 tptp.xa @t5) @t1))))) (forall @t3 (= (tptp.aElementOf0 @t1 @t49) (exists @t23 (and @t7 (= (tptp.sdtasdt0 tptp.xb @t5) @t1))))) (forall @t3 (= @t54 @t53)) (= tptp.xI @t51))) % 0.45/0.65 (assume @p43 (and (exists @t3 (and @t2 (= @t57 tptp.sz00))) (tptp.aElementOf0 tptp.sz00 @t50) (exists @t3 (and @t2 (= @t57 tptp.xa))) (tptp.aElementOf0 tptp.xa @t50) (exists @t3 (and @t2 (= @t56 tptp.sz00))) (tptp.aElementOf0 tptp.sz00 @t49) (exists @t3 (and @t2 (= @t56 tptp.xb))) (tptp.aElementOf0 tptp.xb @t49))) % 0.45/0.65 (assume @p44 (exists @t3 (and (forall @t23 (= @t52 (exists @t26 (and @t13 (= @t62 @t5))))) (forall @t23 (= @t61 @t60)) @t53 (tptp.aElementOf0 @t1 @t51) @t44))) % 0.45/0.65 (assume @p45 (and @t65 (tptp.aElementOf0 tptp.xu tptp.xI) (not (= tptp.xu tptp.sz00)) (forall @t3 (=> (and (or @t53 @t54) @t44) (not (tptp.iLess0 @t43 (tptp.sbrdtbr0 tptp.xu))))))) % 0.45/0.65 (assume @p46 (not (and (or (exists @t3 (and @t2 (= @t66 tptp.xa))) (tptp.doDivides0 tptp.xu tptp.xa) (tptp.aDivisorOf0 tptp.xu tptp.xa)) (or (exists @t3 (and @t2 (= @t66 tptp.xb))) (tptp.doDivides0 tptp.xu tptp.xb) (tptp.aDivisorOf0 tptp.xu tptp.xb))))) % 0.45/0.65 (assume @p47 @t73) % 0.45/0.65 (assume @p48 true) % 0.45/0.65 (step @p49 :rule aci_norm :args ((= (or @t76 (or @t75 @t74)) @t77))) % 0.45/0.65 (step @p50 :rule bool-and-de-morgan :args (@t61 @t63 true)) % 0.45/0.65 (step @p51 :rule refl :args (@t76)) % 0.45/0.65 (step @p52 :rule nary_cong :premises (@p51 @p50) :args ((or @t76 (not (and @t61 @t63))))) % 0.45/0.65 (step @p53 :rule bool-and-de-morgan :args (@t55 @t61 (and @t63))) % 0.45/0.65 (step @p54 :rule trans :premises (@p53 @p52)) % 0.45/0.65 (step @p55 :rule trans :premises (@p54 @p49)) % 0.45/0.65 (step @p56 :rule cong :premises (@p55) :args (@t78)) % 0.45/0.65 (step @p57 :rule cong :premises (@p56) :args (@t79)) % 0.45/0.65 (step @p58 :rule exists-elim :args ((= @t65 @t79))) % 0.45/0.65 (step @p59 :rule trans :premises (@p58 @p57)) % 0.45/0.65 (step @p60 :rule and_elim :premises (@p45) :args (0)) % 0.45/0.65 (step @p61 :rule eq_resolve :premises (@p60 @p59)) % 0.45/0.65 (step @p62 :rule refl :args (@t91)) % 0.45/0.65 (step @p63 :rule bool-double-not-elim :args (@t80)) % 0.45/0.65 (step @p64 :rule nary_cong :premises (@p63 @p62) :args ((or (not @t92) @t91))) % 0.45/0.65 (step @p65 :rule eq-symm :args (@t83 tptp.xu)) % 0.45/0.65 (step @p66 :rule cong :premises (@p65) :args (@t93)) % 0.45/0.65 (step @p67 :rule refl :args (@t87)) % 0.45/0.65 (step @p68 :rule refl :args (@t89)) % 0.45/0.65 (step @p69 :rule nary_cong :premises (@p68 @p67 @p66) :args (@t94)) % 0.45/0.65 (step @p70 :rule cong :premises (@p69) :args (@t95)) % 0.45/0.65 (step @p71 :rule refl :args (@t92)) % 0.45/0.65 (step @p72 :rule cong :premises (@p71 @p70) :args ((=> @t92 @t95))) % 0.45/0.65 (assume-push @p193 @t92) % 0.45/0.65 (step @p74 :rule skolemize :premises (@p61)) % 0.45/0.65 (step-pop @p194 :rule scope :premises (@p74)) % 0.45/0.65 (step @p75 :rule process_scope :premises (@p194) :args (@t95)) % 0.45/0.65 (step @p77 :rule eq_resolve :premises (@p75 @p72)) % 0.45/0.65 (step @p78 :rule implies_elim :premises (@p77)) % 0.45/0.65 (step @p79 :rule eq_resolve :premises (@p78 @p64)) % 0.45/0.65 (step @p80 :rule chain_m_resolution :premises (@p79 @p61) :args (@t91 @t96 (@list @t80))) % 0.45/0.65 (step @p81 :rule bool-double-not-elim :args (@t84)) % 0.45/0.65 (step @p82 :rule refl :args (@t90)) % 0.45/0.65 (step @p83 :rule nary_cong :premises (@p82 @p81) :args ((or @t90 (not @t85)))) % 0.45/0.65 (step @p84 :rule cnf_or_neg :args (@t90 2)) % 0.45/0.65 (step @p85 :rule eq_resolve :premises (@p84 @p83)) % 0.45/0.65 (step @p86 :rule reordering :premises (@p85) :args ((or @t84 @t90))) % 0.45/0.65 (step @p87 :rule chain_m_resolution :premises (@p86 @p80) :args (@t84 @t96 @t97)) % 0.45/0.65 (step @p88 :rule bool-double-not-elim :args (@t105)) % 0.45/0.65 (step @p89 :rule quant-merge-prenex :args ((= (forall @t9 @t106) @t105))) % 0.45/0.65 (step @p90 :rule refl :args (@t74)) % 0.45/0.65 (step @p91 :rule quant-unused-vars :args ((= @t108 @t75))) % 0.45/0.65 (step @p92 :rule alpha_equiv :args (@t109 (@list @t98) @t110)) % 0.45/0.65 (step @p93 :rule nary_cong :premises (@p92 @p91) :args (@t111)) % 0.45/0.65 (step @p94 :rule quant-miniscope-and :args ((= @t112 @t111))) % 0.45/0.65 (step @p95 :rule trans :premises (@p94 @p93)) % 0.45/0.65 (step @p96 :rule quant-unused-vars :args ((= @t114 @t76))) % 0.45/0.65 (step @p97 :rule alpha_equiv :args (@t115 (@list @t101) @t110)) % 0.45/0.65 (step @p98 :rule nary_cong :premises (@p97 @p96) :args (@t116)) % 0.45/0.65 (step @p99 :rule quant-miniscope-and :args ((= @t117 @t116))) % 0.45/0.65 (step @p100 :rule trans :premises (@p99 @p98)) % 0.45/0.65 (step @p101 :rule nary_cong :premises (@p100 @p95 @p90) :args (@t118)) % 0.45/0.65 (step @p102 :rule quant-miniscope-or :args ((= @t106 @t118))) % 0.45/0.65 (step @p103 :rule trans :premises (@p102 @p101)) % 0.45/0.65 (step @p104 :rule symm :premises (@p103)) % 0.45/0.65 (step @p105 :rule cong :premises (@p104) :args ((forall @t9 (or (and @t123 @t76) (and @t121 @t75) @t74)))) % 0.45/0.65 (step @p106 :rule trans :premises (@p105 @p89)) % 0.45/0.65 (step @p107 :rule refl :args (@t75)) % 0.45/0.65 (step @p108 :rule bool-double-not-elim :args (@t121)) % 0.45/0.65 (step @p109 :rule nary_cong :premises (@p108 @p107) :args ((and (not @t124) @t75))) % 0.45/0.65 (step @p110 :rule bool-or-de-morgan :args (@t124 @t61 false)) % 0.45/0.65 (step @p111 :rule trans :premises (@p110 @p109)) % 0.45/0.65 (step @p112 :rule bool-double-not-elim :args (@t123)) % 0.45/0.65 (step @p113 :rule nary_cong :premises (@p112 @p51) :args ((and (not @t125) @t76))) % 0.45/0.65 (step @p114 :rule bool-or-de-morgan :args (@t125 @t55 false)) % 0.45/0.65 (step @p115 :rule trans :premises (@p114 @p113)) % 0.45/0.65 (step @p116 :rule nary_cong :premises (@p115 @p111 @p90) :args (@t130)) % 0.45/0.65 (step @p117 :rule aci_norm :args ((= (or @t129 (or @t127 @t74)) @t130))) % 0.45/0.65 (step @p118 :rule bool-and-de-morgan :args (@t126 @t63 true)) % 0.45/0.65 (step @p119 :rule refl :args (@t129)) % 0.45/0.65 (step @p120 :rule nary_cong :premises (@p119 @p118) :args ((or @t129 (not (and @t126 @t63))))) % 0.45/0.65 (step @p121 :rule bool-and-de-morgan :args (@t128 @t126 (and @t63))) % 0.45/0.65 (step @p122 :rule trans :premises (@p121 @p120)) % 0.45/0.65 (step @p123 :rule trans :premises (@p122 @p117)) % 0.45/0.65 (step @p124 :rule trans :premises (@p123 @p116)) % 0.45/0.65 (step @p125 :rule cong :premises (@p124) :args (@t132)) % 0.45/0.65 (step @p126 :rule trans :premises (@p125 @p106)) % 0.45/0.65 (step @p127 :rule cong :premises (@p126) :args (@t133)) % 0.45/0.65 (step @p128 :rule exists-elim :args ((= (exists @t9 @t131) @t133))) % 0.45/0.65 (step @p129 :rule trans :premises (@p128 @p127)) % 0.45/0.65 (step @p130 :rule eq-symm :args (tptp.xu @t6)) % 0.45/0.65 (step @p131 :rule refl :args (@t61)) % 0.45/0.65 (step @p132 :rule bool-and-de-morgan :args (@t13 @t119 true)) % 0.45/0.65 (step @p133 :rule cong :premises (@p132) :args (@t135)) % 0.45/0.65 (step @p134 :rule cong :premises (@p133) :args (@t136)) % 0.45/0.65 (step @p135 :rule exists-elim :args ((= (exists @t26 @t134) @t136))) % 0.45/0.65 (step @p136 :rule trans :premises (@p135 @p134)) % 0.45/0.65 (step @p137 :rule eq-symm :args (@t58 @t5)) % 0.45/0.65 (step @p138 :rule refl :args (@t13)) % 0.45/0.65 (step @p139 :rule nary_cong :premises (@p138 @p137) :args (@t59)) % 0.45/0.65 (step @p140 :rule cong :premises (@p139) :args (@t60)) % 0.45/0.65 (step @p141 :rule trans :premises (@p140 @p136)) % 0.45/0.65 (step @p142 :rule nary_cong :premises (@p141 @p131) :args (@t67)) % 0.45/0.65 (step @p143 :rule refl :args (@t55)) % 0.45/0.65 (step @p144 :rule bool-and-de-morgan :args (@t13 @t122 true)) % 0.45/0.65 (step @p145 :rule cong :premises (@p144) :args (@t138)) % 0.45/0.65 (step @p146 :rule cong :premises (@p145) :args (@t139)) % 0.45/0.65 (step @p147 :rule exists-elim :args ((= (exists @t26 @t137) @t139))) % 0.45/0.65 (step @p148 :rule trans :premises (@p147 @p146)) % 0.45/0.65 (step @p149 :rule eq-symm :args (@t62 @t1)) % 0.45/0.65 (step @p150 :rule nary_cong :premises (@p138 @p149) :args (@t68)) % 0.45/0.65 (step @p151 :rule cong :premises (@p150) :args (@t69)) % 0.45/0.65 (step @p152 :rule trans :premises (@p151 @p148)) % 0.45/0.65 (step @p153 :rule nary_cong :premises (@p152 @p143) :args (@t70)) % 0.45/0.65 (step @p154 :rule nary_cong :premises (@p153 @p142 @p130) :args (@t71)) % 0.45/0.65 (step @p155 :rule cong :premises (@p154) :args (@t72)) % 0.45/0.65 (step @p156 :rule trans :premises (@p155 @p129)) % 0.45/0.65 (step @p157 :rule cong :premises (@p156) :args (@t73)) % 0.45/0.65 (step @p158 :rule trans :premises (@p157 @p88)) % 0.45/0.65 (step @p159 :rule eq_resolve :premises (@p47 @p158)) % 0.45/0.65 (step @p160 :rule refl :args (@t141)) % 0.45/0.65 (step @p161 :rule refl :args (@t142)) % 0.45/0.65 (step @p162 :rule nary_cong :premises (@p161 @p160 @p66) :args (@t143)) % 0.45/0.65 (step @p163 :rule refl :args (@t105)) % 0.45/0.65 (step @p164 :rule cong :premises (@p163 @p162) :args ((=> @t105 @t143))) % 0.45/0.65 (assume-push @p195 @t105) % 0.45/0.65 (step @p166 :rule instantiate :premises (@p159) :args ((@list @t82 @t81 tptp.xb tptp.xb))) % 0.45/0.65 (step-pop @p196 :rule scope :premises (@p166)) % 0.45/0.65 (step @p167 :rule process_scope :premises (@p196) :args (@t143)) % 0.45/0.65 (step @p169 :rule eq_resolve :premises (@p167 @p164)) % 0.45/0.65 (step @p170 :rule implies_elim :premises (@p169)) % 0.45/0.65 (step @p171 :rule chain_m_resolution :premises (@p170 @p159) :args (@t144 @t145 (@list @t105))) % 0.45/0.66 (step @p172 :rule bool-double-not-elim :args (@t88)) % 0.45/0.66 (step @p173 :rule nary_cong :premises (@p82 @p172) :args ((or @t90 (not @t89)))) % 0.45/0.66 (step @p174 :rule cnf_or_neg :args (@t90 0)) % 0.45/0.66 (step @p175 :rule eq_resolve :premises (@p174 @p173)) % 0.45/0.66 (step @p176 :rule reordering :premises (@p175) :args ((or @t88 @t90))) % 0.45/0.66 (step @p177 :rule chain_m_resolution :premises (@p176 @p80) :args (@t88 @t96 @t97)) % 0.45/0.66 (step @p178 :rule cnf_and_pos :args (@t142 1)) % 0.45/0.66 (step @p179 :rule reordering :premises (@p178) :args ((or @t89 @t146))) % 0.45/0.66 (step @p180 :rule chain_m_resolution :premises (@p179 @p177) :args (@t146 @t145 (@list @t88))) % 0.45/0.66 (step @p181 :rule bool-double-not-elim :args (@t86)) % 0.45/0.66 (step @p182 :rule nary_cong :premises (@p82 @p181) :args ((or @t90 (not @t87)))) % 0.45/0.66 (step @p183 :rule cnf_or_neg :args (@t90 1)) % 0.45/0.66 (step @p184 :rule eq_resolve :premises (@p183 @p182)) % 0.45/0.66 (step @p185 :rule reordering :premises (@p184) :args ((or @t86 @t90))) % 0.45/0.66 (step @p186 :rule chain_m_resolution :premises (@p185 @p80) :args (@t86 @t96 @t97)) % 0.45/0.66 (step @p187 :rule cnf_and_pos :args (@t141 1)) % 0.45/0.66 (step @p188 :rule reordering :premises (@p187) :args ((or @t87 @t147))) % 0.45/0.66 (step @p189 :rule chain_m_resolution :premises (@p188 @p186) :args (@t147 @t145 (@list @t86))) % 0.45/0.66 (step @p190 :rule cnf_or_pos :args (@t144)) % 0.45/0.66 (step @p191 :rule reordering :premises (@p190) :args ((or @t85 @t142 @t141 (not @t144)))) % 0.45/0.66 (step @p192 false :rule chain_m_resolution :premises (@p191 @p189 @p180 @p171 @p87) :args (false (@list true true false false) (@list @t141 @t142 @t144 @t84))) % 0.45/0.66 ) % 0.45/0.66 % SZS output end Proof % 0.45/0.66 % cvc5 exiting %------------------------------------------------------------------------------