%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : RNG116+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 : n004.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Jun 3 08:45:44 AM UTC 2026 % Result : Theorem 17.72s 18.00s % Output : Proof 17.72s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : RNG116+1 : TPTP v9.2.1. Released v4.0.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n004.cluster.edu % 0.16/0.34 % Model : x86_64 x86_64 % 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.34 % Memory : 8042.1875MB % 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.34 % CPULimit : 300 % 0.16/0.34 % WCLimit : 300 % 0.16/0.34 % DateTime : Tue Jun 2 14:08:22 EDT 2026 % 0.16/0.34 % CPUTime : % 0.30/0.50 %----Proving TF0_NAR, FOF, or CNF % 17.72/18.00 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 17.72/18.00 --- Run --no-e-matching --full-saturate-quant at 6... % 17.72/18.00 % SZS status Theorem % 17.72/18.00 % SZS output start Proof % 17.72/18.00 ( % 17.72/18.00 (declare-sort $$unsorted 0) % 17.72/18.00 (declare-const tptp.xk $$unsorted) % 17.72/18.00 (declare-const tptp.xu $$unsorted) % 17.72/18.00 (declare-const tptp.xc $$unsorted) % 17.72/18.00 (declare-const tptp.xa $$unsorted) % 17.72/18.00 (declare-const tptp.xI $$unsorted) % 17.72/18.00 (declare-const tptp.slsdtgt0 (-> $$unsorted $$unsorted)) % 17.72/18.00 (declare-const tptp.aDivisorOf0 (-> $$unsorted $$unsorted Bool)) % 17.72/18.00 (declare-const tptp.iLess0 (-> $$unsorted $$unsorted Bool)) % 17.72/18.00 (declare-const tptp.sbrdtbr0 (-> $$unsorted $$unsorted)) % 17.72/18.00 (declare-const tptp.xl $$unsorted) % 17.72/18.00 (declare-const tptp.aElement0 (-> $$unsorted Bool)) % 17.72/18.00 (declare-const tptp.sz00 $$unsorted) % 17.72/18.00 (declare-const tptp.sz10 $$unsorted) % 17.72/18.00 (declare-const tptp.aGcdOfAnd0 (-> $$unsorted $$unsorted $$unsorted Bool)) % 17.72/18.00 (declare-const tptp.smndt0 (-> $$unsorted $$unsorted)) % 17.72/18.00 (declare-const tptp.sdtpldt0 (-> $$unsorted $$unsorted $$unsorted)) % 17.72/18.00 (declare-const tptp.sdtasasdt0 (-> $$unsorted $$unsorted $$unsorted)) % 17.72/18.00 (declare-const tptp.aIdeal0 (-> $$unsorted Bool)) % 17.72/18.00 (declare-const tptp.misRelativelyPrime0 (-> $$unsorted $$unsorted Bool)) % 17.72/18.00 (declare-const tptp.sdtasdt0 (-> $$unsorted $$unsorted $$unsorted)) % 17.72/18.00 (declare-const tptp.doDivides0 (-> $$unsorted $$unsorted Bool)) % 17.72/18.00 (declare-const tptp.aSet0 (-> $$unsorted Bool)) % 17.72/18.00 (declare-const tptp.aElementOf0 (-> $$unsorted $$unsorted Bool)) % 17.72/18.00 (declare-const tptp.sdteqdtlpzmzozddtrp0 (-> $$unsorted $$unsorted $$unsorted Bool)) % 17.72/18.00 (declare-const tptp.xb $$unsorted) % 17.72/18.00 (declare-const tptp.sdtpldt1 (-> $$unsorted $$unsorted $$unsorted)) % 17.72/18.00 (declare-const tptp.aNaturalNumber0 (-> $$unsorted Bool)) % 17.72/18.00 (define @t1 () (@var "W0" $$unsorted)) % 17.72/18.00 (define @t2 () (tptp.aElement0 @t1)) % 17.72/18.00 (define @t3 () (@list @t1)) % 17.72/18.00 (define @t4 () (tptp.smndt0 @t1)) % 17.72/18.00 (define @t5 () (@var "W1" $$unsorted)) % 17.72/18.00 (define @t6 () (tptp.sdtpldt0 @t1 @t5)) % 17.72/18.00 (define @t7 () (tptp.aElement0 @t5)) % 17.72/18.00 (define @t8 () (and @t2 @t7)) % 17.72/18.00 (define @t9 () (@list @t1 @t5)) % 17.72/18.00 (define @t10 () (tptp.sdtasdt0 @t1 @t5)) % 17.72/18.00 (define @t11 () (@var "W2" $$unsorted)) % 17.72/18.00 (define @t12 () (tptp.sdtpldt0 @t5 @t11)) % 17.72/18.00 (define @t13 () (tptp.aElement0 @t11)) % 17.72/18.00 (define @t14 () (and @t2 @t7 @t13)) % 17.72/18.00 (define @t15 () (@list @t1 @t5 @t11)) % 17.72/18.00 (define @t16 () (tptp.sdtasdt0 @t5 @t1)) % 17.72/18.00 (define @t17 () (tptp.sdtasdt0 @t1 @t11)) % 17.72/18.00 (define @t18 () (tptp.smndt0 tptp.sz10)) % 17.72/18.00 (define @t19 () (= @t5 tptp.sz00)) % 17.72/18.00 (define @t20 () (= @t1 tptp.sz00)) % 17.72/18.00 (define @t21 () (tptp.aSet0 @t1)) % 17.72/18.00 (define @t22 () (tptp.aElementOf0 @t5 @t1)) % 17.72/18.00 (define @t23 () (@list @t5)) % 17.72/18.00 (define @t24 () (tptp.aElementOf0 @t11 @t1)) % 17.72/18.00 (define @t25 () (tptp.aElementOf0 @t11 @t5)) % 17.72/18.00 (define @t26 () (@list @t11)) % 17.72/18.00 (define @t27 () (tptp.aSet0 @t5)) % 17.72/18.00 (define @t28 () (and @t21 @t27)) % 17.72/18.00 (define @t29 () (@var "W3" $$unsorted)) % 17.72/18.00 (define @t30 () (@var "W5" $$unsorted)) % 17.72/18.00 (define @t31 () (@var "W4" $$unsorted)) % 17.72/18.00 (define @t32 () (tptp.aElementOf0 @t29 @t11)) % 17.72/18.00 (define @t33 () (@list @t29)) % 17.72/18.00 (define @t34 () (tptp.aSet0 @t11)) % 17.72/18.00 (define @t35 () (tptp.sdtpldt1 @t1 @t5)) % 17.72/18.00 (define @t36 () (tptp.sdtasasdt0 @t1 @t5)) % 17.72/18.00 (define @t37 () (tptp.sdtasdt0 @t11 @t5)) % 17.72/18.00 (define @t38 () (tptp.aIdeal0 @t1)) % 17.72/18.00 (define @t39 () (and @t38 (tptp.aIdeal0 @t5))) % 17.72/18.00 (define @t40 () (tptp.aElement0 @t29)) % 17.72/18.00 (define @t41 () (@list @t11 @t29)) % 17.72/18.00 (define @t42 () (tptp.aNaturalNumber0 @t1)) % 17.72/18.00 (define @t43 () (tptp.sbrdtbr0 @t1)) % 17.72/18.00 (define @t44 () (not @t20)) % 17.72/18.00 (define @t45 () (tptp.sdtasdt0 @t1 @t29)) % 17.72/18.00 (define @t46 () (and @t40 (= @t45 @t11))) % 17.72/18.00 (define @t47 () (exists @t33 @t46)) % 17.72/18.00 (define @t48 () (= @t25 @t47)) % 17.72/18.00 (define @t49 () (forall @t26 @t48)) % 17.72/18.00 (define @t50 () (and @t27 @t49)) % 17.72/18.00 (define @t51 () (tptp.slsdtgt0 @t1)) % 17.72/18.00 (define @t52 () (= @t5 @t51)) % 17.72/18.00 (define @t53 () (= @t52 @t50)) % 17.72/18.00 (define @t54 () (forall @t23 @t53)) % 17.72/18.00 (define @t55 () (=> @t2 @t54)) % 17.72/18.00 (define @t56 () (forall @t3 @t55)) % 17.72/18.00 (define @t57 () (tptp.aElement0 tptp.xb)) % 17.72/18.00 (define @t58 () (tptp.aElement0 tptp.xa)) % 17.72/18.00 (define @t59 () (tptp.slsdtgt0 tptp.xb)) % 17.72/18.00 (define @t60 () (tptp.slsdtgt0 tptp.xa)) % 17.72/18.00 (define @t61 () (tptp.sdtpldt1 @t60 @t59)) % 17.72/18.00 (define @t62 () (tptp.sdtpldt0 tptp.xk tptp.xl)) % 17.72/18.00 (define @t63 () (tptp.aElementOf0 tptp.xl @t59)) % 17.72/18.00 (define @t64 () (tptp.aElementOf0 tptp.xk @t60)) % 17.72/18.00 (define @t65 () (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xa @t1) (tptp.sdtasdt0 tptp.xb @t5))) % 17.72/18.00 (define @t66 () (= tptp.xu @t65)) % 17.72/18.00 (define @t67 () (and @t2 @t7 @t66)) % 17.72/18.00 (define @t68 () (exists @t9 @t67)) % 17.72/18.00 (define @t69 () (not @t68)) % 17.72/18.00 (define @t70 () (@var "BOUND_VARIABLE_8172" $$unsorted)) % 17.72/18.00 (define @t71 () (tptp.aElementOf0 @t11 @t70)) % 17.72/18.00 (define @t72 () (= @t11 @t45)) % 17.72/18.00 (define @t73 () (not @t40)) % 17.72/18.00 (define @t74 () (not (forall @t33 (or @t73 (not @t72))))) % 17.72/18.00 (define @t75 () (forall @t26 (= @t71 @t74))) % 17.72/18.00 (define @t76 () (tptp.aSet0 @t70)) % 17.72/18.00 (define @t77 () (and @t76 @t75)) % 17.72/18.00 (define @t78 () (= (= @t70 @t51) @t77)) % 17.72/18.00 (define @t79 () (not @t2)) % 17.72/18.00 (define @t80 () (or @t79 @t78)) % 17.72/18.00 (define @t81 () (@list @t1 @t70)) % 17.72/18.00 (define @t82 () (forall @t81 @t80)) % 17.72/18.00 (define @t83 () (@list @t70)) % 17.72/18.00 (define @t84 () (forall @t83 @t80)) % 17.72/18.00 (define @t85 () (forall @t83 @t78)) % 17.72/18.00 (define @t86 () (or @t79 @t85)) % 17.72/18.00 (define @t87 () (forall @t23 (= @t52 (and @t27 (forall @t26 (= @t25 @t74)))))) % 17.72/18.00 (define @t88 () (and @t40 @t72)) % 17.72/18.00 (define @t89 () (forall @t33 (not @t88))) % 17.72/18.00 (define @t90 () (not @t89)) % 17.72/18.00 (define @t91 () (tptp.sdtasdt0 tptp.xa @t29)) % 17.72/18.00 (define @t92 () (not (forall @t33 (or @t73 (not (= @t11 @t91)))))) % 17.72/18.00 (define @t93 () (tptp.aElementOf0 @t11 @t60)) % 17.72/18.00 (define @t94 () (forall @t26 (= @t93 @t92))) % 17.72/18.00 (define @t95 () (tptp.aSet0 @t60)) % 17.72/18.00 (define @t96 () (and @t95 @t94)) % 17.72/18.00 (define @t97 () (forall @t26 (= @t92 @t93))) % 17.72/18.00 (define @t98 () (and @t95 @t97)) % 17.72/18.00 (define @t99 () (= (= @t60 @t60) @t98)) % 17.72/18.00 (define @t100 () (not @t58)) % 17.72/18.00 (define @t101 () (or @t100 @t99)) % 17.72/18.00 (define @t102 () (forall @t81 (or @t79 (= (= @t51 @t70) (and @t76 (forall @t26 (= @t74 @t71))))))) % 17.72/18.00 (define @t103 () (or @t100 @t96)) % 17.72/18.00 (define @t104 () (@list false)) % 17.72/18.00 (define @t105 () (@list @t102)) % 17.72/18.00 (define @t106 () (@list false false)) % 17.72/18.00 (define @t107 () (forall @t33 (or @t73 (not (= tptp.xk @t91))))) % 17.72/18.00 (define @t108 () (not @t107)) % 17.72/18.00 (define @t109 () (= @t64 @t108)) % 17.72/18.00 (define @t110 () (@quantifiers_skolemize @t107 0)) % 17.72/18.00 (define @t111 () (tptp.sdtasdt0 tptp.xa @t110)) % 17.72/18.00 (define @t112 () (= tptp.xk @t111)) % 17.72/18.00 (define @t113 () (not @t112)) % 17.72/18.00 (define @t114 () (tptp.aElement0 @t110)) % 17.72/18.00 (define @t115 () (not @t114)) % 17.72/18.00 (define @t116 () (or @t115 @t113)) % 17.72/18.00 (define @t117 () (@list true)) % 17.72/18.00 (define @t118 () (@list @t116)) % 17.72/18.00 (define @t119 () (tptp.sdtasdt0 tptp.xb @t29)) % 17.72/18.00 (define @t120 () (not (forall @t33 (or @t73 (not (= @t11 @t119)))))) % 17.72/18.00 (define @t121 () (tptp.aElementOf0 @t11 @t59)) % 17.72/18.00 (define @t122 () (forall @t26 (= @t121 @t120))) % 17.72/18.00 (define @t123 () (tptp.aSet0 @t59)) % 17.72/18.00 (define @t124 () (and @t123 @t122)) % 17.72/18.00 (define @t125 () (forall @t26 (= @t120 @t121))) % 17.72/18.00 (define @t126 () (and @t123 @t125)) % 17.72/18.00 (define @t127 () (= (= @t59 @t59) @t126)) % 17.72/18.00 (define @t128 () (not @t57)) % 17.72/18.00 (define @t129 () (or @t128 @t127)) % 17.72/18.00 (define @t130 () (or @t128 @t124)) % 17.72/18.00 (define @t131 () (forall @t33 (or @t73 (not (= tptp.xl @t119))))) % 17.72/18.00 (define @t132 () (not @t131)) % 17.72/18.00 (define @t133 () (= @t63 @t132)) % 17.72/18.00 (define @t134 () (@quantifiers_skolemize @t131 0)) % 17.72/18.00 (define @t135 () (tptp.sdtasdt0 tptp.xb @t134)) % 17.72/18.00 (define @t136 () (= tptp.xl @t135)) % 17.72/18.00 (define @t137 () (not @t136)) % 17.72/18.00 (define @t138 () (tptp.aElement0 @t134)) % 17.72/18.00 (define @t139 () (not @t138)) % 17.72/18.00 (define @t140 () (or @t139 @t137)) % 17.72/18.00 (define @t141 () (@list @t140)) % 17.72/18.00 (define @t142 () (not @t66)) % 17.72/18.00 (define @t143 () (not @t7)) % 17.72/18.00 (define @t144 () (or @t79 @t143 @t142)) % 17.72/18.00 (define @t145 () (forall @t9 @t144)) % 17.72/18.00 (define @t146 () (forall @t9 (not @t67))) % 17.72/18.00 (define @t147 () (not @t146)) % 17.72/18.00 (define @t148 () (= @t62 (tptp.sdtpldt0 @t111 @t135))) % 17.72/18.00 (define @t149 () (not @t148)) % 17.72/18.00 (define @t150 () (or @t115 @t139 @t149)) % 17.72/18.00 (define @t151 () (and @t149 @t148)) % 17.72/18.00 (assume @p1 (forall @t3 (=> @t2 true))) % 17.72/18.00 (assume @p2 (tptp.aElement0 tptp.sz00)) % 17.72/18.00 (assume @p3 (tptp.aElement0 tptp.sz10)) % 17.72/18.00 (assume @p4 (forall @t3 (=> @t2 (tptp.aElement0 @t4)))) % 17.72/18.00 (assume @p5 (forall @t9 (=> @t8 (tptp.aElement0 @t6)))) % 17.72/18.00 (assume @p6 (forall @t9 (=> @t8 (tptp.aElement0 @t10)))) % 17.72/18.00 (assume @p7 (forall @t9 (=> @t8 (= @t6 (tptp.sdtpldt0 @t5 @t1))))) % 17.72/18.00 (assume @p8 (forall @t15 (=> @t14 (= (tptp.sdtpldt0 @t6 @t11) (tptp.sdtpldt0 @t1 @t12))))) % 17.72/18.00 (assume @p9 (forall @t3 (=> @t2 (and (= (tptp.sdtpldt0 @t1 tptp.sz00) @t1) (= @t1 (tptp.sdtpldt0 tptp.sz00 @t1)))))) % 17.72/18.00 (assume @p10 (forall @t3 (=> @t2 (and (= (tptp.sdtpldt0 @t1 @t4) tptp.sz00) (= tptp.sz00 (tptp.sdtpldt0 @t4 @t1)))))) % 17.72/18.00 (assume @p11 (forall @t9 (=> @t8 (= @t10 @t16)))) % 17.72/18.00 (assume @p12 (forall @t15 (=> @t14 (= (tptp.sdtasdt0 @t10 @t11) (tptp.sdtasdt0 @t1 (tptp.sdtasdt0 @t5 @t11)))))) % 17.72/18.00 (assume @p13 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz10) @t1) (= @t1 (tptp.sdtasdt0 tptp.sz10 @t1)))))) % 17.72/18.00 (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))))))) % 17.72/18.00 (assume @p15 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t18 @t1) @t4) (= @t4 (tptp.sdtasdt0 @t1 @t18)))))) % 17.72/18.00 (assume @p16 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz00) tptp.sz00) (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 @t1)))))) % 17.72/18.00 (assume @p17 (forall @t9 (=> @t8 (=> (= @t10 tptp.sz00) (or @t20 @t19))))) % 17.72/18.00 (assume @p18 (not (= tptp.sz10 tptp.sz00))) % 17.72/18.00 (assume @p19 (forall @t3 (=> @t21 true))) % 17.72/18.00 (assume @p20 (forall @t3 (=> @t21 (forall @t23 (=> @t22 @t7))))) % 17.72/18.00 (assume @p21 (forall @t9 (=> @t28 (=> (and (forall @t26 (=> @t24 @t25)) (forall @t26 (=> @t25 @t24))) (= @t1 @t5))))) % 17.72/18.00 (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))))))))))) % 17.72/18.00 (assume @p23 (forall @t9 (=> @t28 (forall @t26 (= (= @t11 @t36) (and @t34 (forall @t33 (= @t32 (and (tptp.aElementOf0 @t29 @t1) (tptp.aElementOf0 @t29 @t5)))))))))) % 17.72/18.00 (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)))))))))) % 17.72/18.00 (assume @p25 (forall @t9 (=> @t39 (tptp.aIdeal0 @t35)))) % 17.72/18.00 (assume @p26 (forall @t9 (=> @t39 (tptp.aIdeal0 @t36)))) % 17.72/18.00 (assume @p27 (forall @t15 (=> (and @t2 @t7 (tptp.aIdeal0 @t11)) (= (tptp.sdteqdtlpzmzozddtrp0 @t1 @t5 @t11) (tptp.aElementOf0 (tptp.sdtpldt0 @t1 (tptp.smndt0 @t5)) @t11))))) % 17.72/18.00 (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))))))))) % 17.72/18.00 (assume @p29 (forall @t3 (=> @t42 true))) % 17.72/18.00 (assume @p30 (forall @t3 (=> (and @t2 @t44) (tptp.aNaturalNumber0 @t43)))) % 17.72/18.00 (assume @p31 (forall @t9 (=> (and @t42 (tptp.aNaturalNumber0 @t5)) (=> (tptp.iLess0 @t1 @t5) true)))) % 17.72/18.00 (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)))))))) % 17.72/18.00 (assume @p33 (forall @t9 (=> @t8 (= (tptp.doDivides0 @t1 @t5) (exists @t26 (and @t13 (= @t17 @t5))))))) % 17.72/18.00 (assume @p34 (forall @t3 (=> @t2 (forall @t23 (= (tptp.aDivisorOf0 @t5 @t1) (and @t7 (tptp.doDivides0 @t5 @t1))))))) % 17.72/18.00 (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))))))))) % 17.72/18.00 (assume @p36 (forall @t9 (=> @t8 (= (tptp.misRelativelyPrime0 @t1 @t5) (tptp.aGcdOfAnd0 tptp.sz10 @t1 @t5))))) % 17.72/18.00 (assume @p37 @t56) % 17.72/18.00 (assume @p38 (forall @t3 (=> @t2 (tptp.aIdeal0 @t51)))) % 17.72/18.00 (assume @p39 (and @t58 @t57)) % 17.72/18.00 (assume @p40 (or (not (= tptp.xa tptp.sz00)) (not (= tptp.xb tptp.sz00)))) % 17.72/18.00 (assume @p41 (tptp.aGcdOfAnd0 tptp.xc tptp.xa tptp.xb)) % 17.72/18.00 (assume @p42 (and (tptp.aIdeal0 tptp.xI) (= tptp.xI @t61))) % 17.72/18.00 (assume @p43 (and (tptp.aElementOf0 tptp.sz00 @t60) (tptp.aElementOf0 tptp.xa @t60) (tptp.aElementOf0 tptp.sz00 @t59) (tptp.aElementOf0 tptp.xb @t59))) % 17.72/18.00 (assume @p44 (exists @t3 (and (tptp.aElementOf0 @t1 @t61) @t44))) % 17.72/18.00 (assume @p45 (and (tptp.aElementOf0 tptp.xu tptp.xI) (not (= tptp.xu tptp.sz00)) (forall @t3 (=> (and (tptp.aElementOf0 @t1 tptp.xI) @t44) (not (tptp.iLess0 @t43 (tptp.sbrdtbr0 tptp.xu))))))) % 17.72/18.00 (assume @p46 (not (and (tptp.aDivisorOf0 tptp.xu tptp.xa) (tptp.aDivisorOf0 tptp.xu tptp.xb)))) % 17.72/18.00 (assume @p47 (and @t64 @t63 (= tptp.xu @t62))) % 17.72/18.00 (assume @p48 @t69) % 17.72/18.00 (assume @p49 true) % 17.72/18.00 (step @p50 :rule eq-symm :args (@t71 @t74)) % 17.72/18.00 (step @p51 :rule cong :premises (@p50) :args (@t75)) % 17.72/18.00 (step @p52 :rule refl :args (@t76)) % 17.72/18.00 (step @p53 :rule nary_cong :premises (@p52 @p51) :args (@t77)) % 17.72/18.00 (step @p54 :rule eq-symm :args (@t70 @t51)) % 17.72/18.00 (step @p55 :rule cong :premises (@p54 @p53) :args (@t78)) % 17.72/18.00 (step @p56 :rule refl :args (@t79)) % 17.72/18.00 (step @p57 :rule nary_cong :premises (@p56 @p55) :args (@t80)) % 17.72/18.00 (step @p58 :rule cong :premises (@p57) :args (@t82)) % 17.72/18.00 (step @p59 :rule quant-merge-prenex :args ((= (forall @t3 @t84) @t82))) % 17.72/18.00 (step @p60 :rule alpha_equiv :args (@t85 (@list @t70) (@list @t5))) % 17.72/18.00 (step @p61 :rule refl :args (@t79)) % 17.72/18.00 (step @p62 :rule nary_cong :premises (@p61 @p60) :args (@t86)) % 17.72/18.00 (step @p63 :rule quant-miniscope-or :args ((= @t84 @t86))) % 17.72/18.00 (step @p64 :rule trans :premises (@p63 @p62)) % 17.72/18.00 (step @p65 :rule symm :premises (@p64)) % 17.72/18.00 (step @p66 :rule cong :premises (@p65) :args ((forall @t3 (or @t79 @t87)))) % 17.72/18.00 (step @p67 :rule trans :premises (@p66 @p59)) % 17.72/18.00 (step @p68 :rule trans :premises (@p67 @p58)) % 17.72/18.00 (step @p69 :rule bool-impl-elim :args (@t2 @t87)) % 17.72/18.00 (step @p70 :rule cong :premises (@p69) :args ((forall @t3 (=> @t2 @t87)))) % 17.72/18.00 (step @p71 :rule trans :premises (@p70 @p68)) % 17.72/18.00 (step @p72 :rule bool-and-de-morgan :args (@t40 @t72 true)) % 17.72/18.00 (step @p73 :rule cong :premises (@p72) :args (@t89)) % 17.72/18.00 (step @p74 :rule cong :premises (@p73) :args (@t90)) % 17.72/18.00 (step @p75 :rule exists-elim :args ((= (exists @t33 @t88) @t90))) % 17.72/18.00 (step @p76 :rule trans :premises (@p75 @p74)) % 17.72/18.00 (step @p77 :rule eq-symm :args (@t45 @t11)) % 17.72/18.00 (step @p78 :rule refl :args (@t40)) % 17.72/18.00 (step @p79 :rule nary_cong :premises (@p78 @p77) :args (@t46)) % 17.72/18.00 (step @p80 :rule cong :premises (@p79) :args (@t47)) % 17.72/18.00 (step @p81 :rule trans :premises (@p80 @p76)) % 17.72/18.00 (step @p82 :rule refl :args (@t25)) % 17.72/18.00 (step @p83 :rule cong :premises (@p82 @p81) :args (@t48)) % 17.72/18.00 (step @p84 :rule cong :premises (@p83) :args (@t49)) % 17.72/18.00 (step @p85 :rule refl :args (@t27)) % 17.72/18.00 (step @p86 :rule nary_cong :premises (@p85 @p84) :args (@t50)) % 17.72/18.00 (step @p87 :rule refl :args (@t52)) % 17.72/18.00 (step @p88 :rule cong :premises (@p87 @p86) :args (@t53)) % 17.72/18.00 (step @p89 :rule cong :premises (@p88) :args (@t54)) % 17.72/18.00 (step @p90 :rule refl :args (@t2)) % 17.72/18.00 (step @p91 :rule cong :premises (@p90 @p89) :args (@t55)) % 17.72/18.00 (step @p92 :rule cong :premises (@p91) :args (@t56)) % 17.72/18.00 (step @p93 :rule trans :premises (@p92 @p71)) % 17.72/18.00 (step @p94 :rule eq_resolve :premises (@p37 @p93)) % 17.72/18.00 (step @p95 :rule bool-eq-true :args (@t96)) % 17.72/18.00 (step @p96 :rule eq-symm :args (true @t96)) % 17.72/18.00 (step @p97 :rule trans :premises (@p96 @p95)) % 17.72/18.00 (step @p98 :rule eq-symm :args (@t92 @t93)) % 17.72/18.00 (step @p99 :rule cong :premises (@p98) :args (@t97)) % 17.72/18.00 (step @p100 :rule refl :args (@t95)) % 17.72/18.00 (step @p101 :rule nary_cong :premises (@p100 @p99) :args (@t98)) % 17.72/18.00 (step @p102 :rule eq-refl :args (@t60)) % 17.72/18.00 (step @p103 :rule cong :premises (@p102 @p101) :args (@t99)) % 17.72/18.00 (step @p104 :rule trans :premises (@p103 @p97)) % 17.72/18.00 (step @p105 :rule refl :args (@t100)) % 17.72/18.00 (step @p106 :rule nary_cong :premises (@p105 @p104) :args (@t101)) % 17.72/18.00 (step @p107 :rule refl :args (@t102)) % 17.72/18.00 (step @p108 :rule cong :premises (@p107 @p106) :args ((=> @t102 @t101))) % 17.72/18.00 (assume-push @p246 @t102) % 17.72/18.00 (step @p110 :rule instantiate :premises (@p94) :args ((@list tptp.xa @t60))) % 17.72/18.00 (step-pop @p247 :rule scope :premises (@p110)) % 17.72/18.00 (step @p111 :rule process_scope :premises (@p247) :args (@t101)) % 17.72/18.00 (step @p113 :rule eq_resolve :premises (@p111 @p108)) % 17.72/18.00 (step @p114 :rule implies_elim :premises (@p113)) % 17.72/18.00 (step @p115 :rule chain_m_resolution :premises (@p114 @p94) :args (@t103 @t104 @t105)) % 17.72/18.00 (step @p116 :rule and_elim :premises (@p39) :args (0)) % 17.72/18.00 (step @p117 :rule cnf_or_pos :args (@t103)) % 17.72/18.00 (step @p118 :rule reordering :premises (@p117) :args ((or @t100 @t96 (not @t103)))) % 17.72/18.00 (step @p119 :rule chain_m_resolution :premises (@p118 @p116 @p115) :args (@t96 @t106 (@list @t58 @t103))) % 17.72/18.00 (step @p120 :rule cnf_and_pos :args (@t96 1)) % 17.72/18.00 (step @p121 :rule reordering :premises (@p120) :args ((or @t94 (not @t96)))) % 17.72/18.00 (step @p122 :rule chain_m_resolution :premises (@p121 @p119) :args (@t94 @t104 (@list @t96))) % 17.72/18.00 (step @p123 :rule instantiate :premises (@p122) :args ((@list tptp.xk))) % 17.72/18.00 (step @p124 :rule and_elim :premises (@p47) :args (0)) % 17.72/18.00 (step @p125 :rule cnf_equiv_pos1 :args (@t109)) % 17.72/18.00 (step @p126 :rule reordering :premises (@p125) :args ((or (not @t64) @t108 (not @t109)))) % 17.72/18.00 (step @p127 :rule chain_m_resolution :premises (@p126 @p124 @p123) :args (@t108 @t106 (@list @t64 @t109))) % 17.72/18.00 (step @p128 :rule skolemize :premises (@p127)) % 17.72/18.00 (step @p129 :rule bool-double-not-elim :args (@t112)) % 17.72/18.00 (step @p130 :rule refl :args (@t116)) % 17.72/18.00 (step @p131 :rule nary_cong :premises (@p130 @p129) :args ((or @t116 (not @t113)))) % 17.72/18.00 (step @p132 :rule cnf_or_neg :args (@t116 1)) % 17.72/18.00 (step @p133 :rule eq_resolve :premises (@p132 @p131)) % 17.72/18.00 (step @p134 :rule reordering :premises (@p133) :args ((or @t112 @t116))) % 17.72/18.00 (step @p135 :rule chain_m_resolution :premises (@p134 @p128) :args (@t112 @t117 @t118)) % 17.72/18.00 (step @p136 :rule bool-eq-true :args (@t124)) % 17.72/18.00 (step @p137 :rule eq-symm :args (true @t124)) % 17.72/18.00 (step @p138 :rule trans :premises (@p137 @p136)) % 17.72/18.00 (step @p139 :rule eq-symm :args (@t120 @t121)) % 17.72/18.00 (step @p140 :rule cong :premises (@p139) :args (@t125)) % 17.72/18.00 (step @p141 :rule refl :args (@t123)) % 17.72/18.00 (step @p142 :rule nary_cong :premises (@p141 @p140) :args (@t126)) % 17.72/18.00 (step @p143 :rule eq-refl :args (@t59)) % 17.72/18.00 (step @p144 :rule cong :premises (@p143 @p142) :args (@t127)) % 17.72/18.00 (step @p145 :rule trans :premises (@p144 @p138)) % 17.72/18.00 (step @p146 :rule refl :args (@t128)) % 17.72/18.00 (step @p147 :rule nary_cong :premises (@p146 @p145) :args (@t129)) % 17.72/18.00 (step @p148 :rule cong :premises (@p107 @p147) :args ((=> @t102 @t129))) % 17.72/18.00 (assume-push @p248 @t102) % 17.72/18.00 (step @p150 :rule instantiate :premises (@p94) :args ((@list tptp.xb @t59))) % 17.72/18.00 (step-pop @p249 :rule scope :premises (@p150)) % 17.72/18.00 (step @p151 :rule process_scope :premises (@p249) :args (@t129)) % 17.72/18.00 (step @p153 :rule eq_resolve :premises (@p151 @p148)) % 17.72/18.00 (step @p154 :rule implies_elim :premises (@p153)) % 17.72/18.00 (step @p155 :rule chain_m_resolution :premises (@p154 @p94) :args (@t130 @t104 @t105)) % 17.72/18.00 (step @p156 :rule and_elim :premises (@p39) :args (1)) % 17.72/18.00 (step @p157 :rule cnf_or_pos :args (@t130)) % 17.72/18.00 (step @p158 :rule reordering :premises (@p157) :args ((or @t128 @t124 (not @t130)))) % 17.72/18.00 (step @p159 :rule chain_m_resolution :premises (@p158 @p156 @p155) :args (@t124 @t106 (@list @t57 @t130))) % 17.72/18.00 (step @p160 :rule cnf_and_pos :args (@t124 1)) % 17.72/18.00 (step @p161 :rule reordering :premises (@p160) :args ((or @t122 (not @t124)))) % 17.72/18.00 (step @p162 :rule chain_m_resolution :premises (@p161 @p159) :args (@t122 @t104 (@list @t124))) % 17.72/18.00 (step @p163 :rule instantiate :premises (@p162) :args ((@list tptp.xl))) % 17.72/18.00 (step @p164 :rule and_elim :premises (@p47) :args (1)) % 17.72/18.00 (step @p165 :rule cnf_equiv_pos1 :args (@t133)) % 17.72/18.00 (step @p166 :rule reordering :premises (@p165) :args ((or (not @t63) @t132 (not @t133)))) % 17.72/18.00 (step @p167 :rule chain_m_resolution :premises (@p166 @p164 @p163) :args (@t132 @t106 (@list @t63 @t133))) % 17.72/18.00 (step @p168 :rule skolemize :premises (@p167)) % 17.72/18.00 (step @p169 :rule bool-double-not-elim :args (@t136)) % 17.72/18.00 (step @p170 :rule refl :args (@t140)) % 17.72/18.00 (step @p171 :rule nary_cong :premises (@p170 @p169) :args ((or @t140 (not @t137)))) % 17.72/18.00 (step @p172 :rule cnf_or_neg :args (@t140 1)) % 17.72/18.00 (step @p173 :rule eq_resolve :premises (@p172 @p171)) % 17.72/18.00 (step @p174 :rule reordering :premises (@p173) :args ((or @t136 @t140))) % 17.72/18.00 (step @p175 :rule chain_m_resolution :premises (@p174 @p168) :args (@t136 @t117 @t141)) % 17.72/18.00 (step @p176 :rule refl :args (@t65)) % 17.72/18.00 (step @p177 :rule and_elim :premises (@p47) :args (2)) % 17.72/18.00 (step @p178 :rule cong :premises (@p177 @p176) :args (@t66)) % 17.72/18.00 (step @p179 :rule cong :premises (@p178) :args (@t142)) % 17.72/18.00 (step @p180 :rule refl :args (@t143)) % 17.72/18.00 (step @p181 :rule nary_cong :premises (@p56 @p180 @p179) :args (@t144)) % 17.72/18.00 (step @p182 :rule cong :premises (@p181) :args (@t145)) % 17.72/18.00 (step @p183 :rule bool-double-not-elim :args (@t145)) % 17.72/18.00 (step @p184 :rule aci_norm :args ((= (or @t79 (or @t143 @t142)) @t144))) % 17.72/18.00 (step @p185 :rule bool-and-de-morgan :args (@t7 @t66 true)) % 17.72/18.00 (step @p186 :rule nary_cong :premises (@p61 @p185) :args ((or @t79 (not (and @t7 @t66))))) % 17.72/18.00 (step @p187 :rule bool-and-de-morgan :args (@t2 @t7 (and @t66))) % 17.72/18.00 (step @p188 :rule trans :premises (@p187 @p186)) % 17.72/18.00 (step @p189 :rule trans :premises (@p188 @p184)) % 17.72/18.00 (step @p190 :rule cong :premises (@p189) :args (@t146)) % 17.72/18.00 (step @p191 :rule cong :premises (@p190) :args (@t147)) % 17.72/18.00 (step @p192 :rule exists-elim :args ((= @t68 @t147))) % 17.72/18.00 (step @p193 :rule trans :premises (@p192 @p191)) % 17.72/18.00 (step @p194 :rule cong :premises (@p193) :args (@t69)) % 17.72/18.00 (step @p195 :rule trans :premises (@p194 @p183)) % 17.72/18.00 (step @p196 :rule trans :premises (@p195 @p182)) % 17.72/18.00 (step @p197 :rule eq_resolve :premises (@p48 @p196)) % 17.72/18.00 (step @p198 :rule instantiate :premises (@p197) :args ((@list @t110 @t134))) % 17.72/18.00 (step @p199 :rule bool-double-not-elim :args (@t138)) % 17.72/18.00 (step @p200 :rule nary_cong :premises (@p170 @p199) :args ((or @t140 (not @t139)))) % 17.72/18.00 (step @p201 :rule cnf_or_neg :args (@t140 0)) % 17.72/18.00 (step @p202 :rule eq_resolve :premises (@p201 @p200)) % 17.72/18.00 (step @p203 :rule reordering :premises (@p202) :args ((or @t138 @t140))) % 17.72/18.00 (step @p204 :rule chain_m_resolution :premises (@p203 @p168) :args (@t138 @t117 @t141)) % 17.72/18.00 (step @p205 :rule bool-double-not-elim :args (@t114)) % 17.72/18.00 (step @p206 :rule nary_cong :premises (@p130 @p205) :args ((or @t116 (not @t115)))) % 17.72/18.00 (step @p207 :rule cnf_or_neg :args (@t116 0)) % 17.72/18.00 (step @p208 :rule eq_resolve :premises (@p207 @p206)) % 17.72/18.00 (step @p209 :rule reordering :premises (@p208) :args ((or @t114 @t116))) % 17.72/18.00 (step @p210 :rule chain_m_resolution :premises (@p209 @p128) :args (@t114 @t117 @t118)) % 17.72/18.00 (step @p211 :rule cnf_or_pos :args (@t150)) % 17.72/18.00 (step @p212 :rule reordering :premises (@p211) :args ((or @t115 @t139 @t149 (not @t150)))) % 17.72/18.00 (step @p213 :rule chain_m_resolution :premises (@p212 @p210 @p204 @p198) :args (@t149 (@list false false false) (@list @t114 @t138 @t150))) % 17.72/18.00 (step @p214 :rule bool-double-not-elim :args (@t148)) % 17.72/18.00 (step @p215 :rule refl :args (@t137)) % 17.72/18.00 (step @p216 :rule refl :args (@t113)) % 17.72/18.00 (step @p217 :rule nary_cong :premises (@p216 @p215 @p214) :args ((or @t113 @t137 (not @t149)))) % 17.72/18.00 (assume-push @p250 @t149) % 17.72/18.00 (assume-push @p251 @t148) % 17.72/18.00 (step @p220 :rule evaluate :args ((= true false))) % 17.72/18.00 (step @p221 :rule false_intro :premises (@p213)) % 17.72/18.00 (step @p222 :rule chain_m_resolution :premises (@p174 @p168) :args (@t136 @t117 @t141)) % 17.72/18.00 (step @p223 :rule chain_m_resolution :premises (@p134 @p128) :args (@t112 @t117 @t118)) % 17.72/18.00 (step @p224 :rule cong :premises (@p223 @p222) :args (@t62)) % 17.72/18.00 (step @p225 :rule true_intro :premises (@p224)) % 17.72/18.00 (step @p226 :rule symm :premises (@p225)) % 17.72/18.00 (step @p227 :rule trans :premises (@p226 @p221)) % 17.72/18.00 (step @p228 false :rule eq_resolve :premises (@p227 @p220)) % 17.72/18.00 (step-pop @p252 :rule scope :premises (@p228)) % 17.72/18.00 (step-pop @p253 :rule scope :premises (@p252)) % 17.72/18.00 (step @p229 :rule process_scope :premises (@p253) :args (false)) % 17.72/18.00 (assume-push @p254 @t112) % 17.72/18.00 (assume-push @p255 @t136) % 17.72/18.00 (assume-push @p256 @t149) % 17.72/18.00 (step @p235 :rule cong :premises (@p135 @p175) :args (@t62)) % 17.72/18.00 (step @p236 :rule and_intro :premises (@p213 @p235)) % 17.72/18.00 (step-pop @p257 :rule scope :premises (@p236)) % 17.72/18.00 (step-pop @p258 :rule scope :premises (@p257)) % 17.72/18.00 (step-pop @p259 :rule scope :premises (@p258)) % 17.72/18.00 (step @p237 :rule process_scope :premises (@p259) :args (@t151)) % 17.72/18.00 (step @p241 :rule implies_elim :premises (@p237)) % 17.72/18.00 (step @p242 :rule resolution :premises (@p241 @p229) :args (true @t151)) % 17.72/18.00 (step @p243 :rule not_and :premises (@p242)) % 17.72/18.00 (step @p244 :rule eq_resolve :premises (@p243 @p217)) % 17.72/18.00 (step @p245 false :rule chain_m_resolution :premises (@p244 @p213 @p175 @p135) :args (false (@list true false false) (@list @t148 @t136 @t112))) % 17.72/18.00 ) % 17.72/18.00 % SZS output end Proof % 17.72/18.00 % cvc5 exiting %------------------------------------------------------------------------------