%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : RNG116+4 : 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 : n018.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 0.46s 0.65s % Output : Proof 0.46s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : RNG116+4 : 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 : n018.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 14:08:20 EDT 2026 % 0.16/0.34 % CPUTime : % 0.29/0.50 %----Proving TF0_NAR, FOF, or CNF % 0.46/0.65 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.46/0.65 % SZS status Theorem % 0.46/0.65 % SZS output start Proof % 0.46/0.65 ( % 0.46/0.65 (declare-sort $$unsorted 0) % 0.46/0.65 (declare-const tptp.xu $$unsorted) % 0.46/0.65 (declare-const tptp.xI $$unsorted) % 0.46/0.65 (declare-const tptp.xc $$unsorted) % 0.46/0.65 (declare-const tptp.xa $$unsorted) % 0.46/0.65 (declare-const tptp.slsdtgt0 (-> $$unsorted $$unsorted)) % 0.46/0.65 (declare-const tptp.aDivisorOf0 (-> $$unsorted $$unsorted Bool)) % 0.46/0.65 (declare-const tptp.iLess0 (-> $$unsorted $$unsorted Bool)) % 0.46/0.65 (declare-const tptp.sbrdtbr0 (-> $$unsorted $$unsorted)) % 0.46/0.65 (declare-const tptp.aElement0 (-> $$unsorted Bool)) % 0.46/0.65 (declare-const tptp.sz00 $$unsorted) % 0.46/0.65 (declare-const tptp.sz10 $$unsorted) % 0.46/0.65 (declare-const tptp.aGcdOfAnd0 (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.46/0.65 (declare-const tptp.smndt0 (-> $$unsorted $$unsorted)) % 0.46/0.65 (declare-const tptp.sdtpldt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.46/0.65 (declare-const tptp.sdtasasdt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.46/0.65 (declare-const tptp.xk $$unsorted) % 0.46/0.65 (declare-const tptp.aIdeal0 (-> $$unsorted Bool)) % 0.46/0.65 (declare-const tptp.misRelativelyPrime0 (-> $$unsorted $$unsorted Bool)) % 0.46/0.65 (declare-const tptp.sdtasdt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.46/0.65 (declare-const tptp.doDivides0 (-> $$unsorted $$unsorted Bool)) % 0.46/0.65 (declare-const tptp.aSet0 (-> $$unsorted Bool)) % 0.46/0.65 (declare-const tptp.xl $$unsorted) % 0.46/0.65 (declare-const tptp.aElementOf0 (-> $$unsorted $$unsorted Bool)) % 0.46/0.65 (declare-const tptp.sdteqdtlpzmzozddtrp0 (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.46/0.65 (declare-const tptp.xb $$unsorted) % 0.46/0.65 (declare-const tptp.sdtpldt1 (-> $$unsorted $$unsorted $$unsorted)) % 0.46/0.65 (declare-const tptp.aNaturalNumber0 (-> $$unsorted Bool)) % 0.46/0.65 (define @t1 () (@var "W0" $$unsorted)) % 0.46/0.65 (define @t2 () (tptp.aElement0 @t1)) % 0.46/0.65 (define @t3 () (@list @t1)) % 0.46/0.65 (define @t4 () (tptp.smndt0 @t1)) % 0.46/0.65 (define @t5 () (@var "W1" $$unsorted)) % 0.46/0.65 (define @t6 () (tptp.sdtpldt0 @t1 @t5)) % 0.46/0.65 (define @t7 () (tptp.aElement0 @t5)) % 0.46/0.65 (define @t8 () (and @t2 @t7)) % 0.46/0.65 (define @t9 () (@list @t1 @t5)) % 0.46/0.65 (define @t10 () (tptp.sdtasdt0 @t1 @t5)) % 0.46/0.65 (define @t11 () (@var "W2" $$unsorted)) % 0.46/0.65 (define @t12 () (tptp.sdtpldt0 @t5 @t11)) % 0.46/0.65 (define @t13 () (tptp.aElement0 @t11)) % 0.46/0.65 (define @t14 () (and @t2 @t7 @t13)) % 0.46/0.65 (define @t15 () (@list @t1 @t5 @t11)) % 0.46/0.65 (define @t16 () (tptp.sdtasdt0 @t5 @t1)) % 0.46/0.65 (define @t17 () (tptp.sdtasdt0 @t1 @t11)) % 0.46/0.65 (define @t18 () (tptp.smndt0 tptp.sz10)) % 0.46/0.65 (define @t19 () (= @t5 tptp.sz00)) % 0.46/0.65 (define @t20 () (= @t1 tptp.sz00)) % 0.46/0.65 (define @t21 () (tptp.aSet0 @t1)) % 0.46/0.65 (define @t22 () (tptp.aElementOf0 @t5 @t1)) % 0.46/0.65 (define @t23 () (@list @t5)) % 0.46/0.65 (define @t24 () (tptp.aElementOf0 @t11 @t1)) % 0.46/0.65 (define @t25 () (tptp.aElementOf0 @t11 @t5)) % 0.46/0.65 (define @t26 () (@list @t11)) % 0.46/0.65 (define @t27 () (tptp.aSet0 @t5)) % 0.46/0.65 (define @t28 () (and @t21 @t27)) % 0.46/0.65 (define @t29 () (@var "W3" $$unsorted)) % 0.46/0.65 (define @t30 () (@var "W5" $$unsorted)) % 0.46/0.65 (define @t31 () (@var "W4" $$unsorted)) % 0.46/0.65 (define @t32 () (tptp.aElementOf0 @t29 @t11)) % 0.46/0.65 (define @t33 () (@list @t29)) % 0.46/0.65 (define @t34 () (tptp.aSet0 @t11)) % 0.46/0.65 (define @t35 () (tptp.sdtpldt1 @t1 @t5)) % 0.46/0.65 (define @t36 () (tptp.sdtasasdt0 @t1 @t5)) % 0.46/0.65 (define @t37 () (tptp.sdtasdt0 @t11 @t5)) % 0.46/0.65 (define @t38 () (tptp.aIdeal0 @t1)) % 0.46/0.65 (define @t39 () (and @t38 (tptp.aIdeal0 @t5))) % 0.46/0.65 (define @t40 () (tptp.aElement0 @t29)) % 0.46/0.65 (define @t41 () (@list @t11 @t29)) % 0.46/0.65 (define @t42 () (tptp.aNaturalNumber0 @t1)) % 0.46/0.65 (define @t43 () (tptp.sbrdtbr0 @t1)) % 0.46/0.65 (define @t44 () (not @t20)) % 0.46/0.65 (define @t45 () (tptp.slsdtgt0 @t1)) % 0.46/0.65 (define @t46 () (tptp.sdtasdt0 tptp.xc @t1)) % 0.46/0.65 (define @t47 () (tptp.aElement0 tptp.xc)) % 0.46/0.65 (define @t48 () (tptp.slsdtgt0 tptp.xb)) % 0.46/0.65 (define @t49 () (tptp.slsdtgt0 tptp.xa)) % 0.46/0.65 (define @t50 () (tptp.sdtpldt1 @t49 @t48)) % 0.46/0.65 (define @t51 () (tptp.aElementOf0 @t5 @t49)) % 0.46/0.65 (define @t52 () (exists (@list @t5 @t11) (and @t51 (tptp.aElementOf0 @t11 @t48) (= @t12 @t1)))) % 0.46/0.65 (define @t53 () (tptp.aElementOf0 @t1 tptp.xI)) % 0.46/0.65 (define @t54 () (tptp.sdtasdt0 tptp.xb @t5)) % 0.46/0.65 (define @t55 () (tptp.aElementOf0 @t1 @t49)) % 0.46/0.65 (define @t56 () (tptp.sdtasdt0 tptp.xb @t1)) % 0.46/0.65 (define @t57 () (tptp.sdtasdt0 tptp.xa @t1)) % 0.46/0.65 (define @t58 () (tptp.aElementOf0 @t5 @t48)) % 0.46/0.65 (define @t59 () (tptp.sdtasdt0 tptp.xu @t1)) % 0.46/0.65 (define @t60 () (tptp.sdtpldt0 tptp.xk tptp.xl)) % 0.46/0.65 (define @t61 () (= tptp.xu @t60)) % 0.46/0.65 (define @t62 () (= @t56 tptp.xl)) % 0.46/0.65 (define @t63 () (and @t2 @t62)) % 0.46/0.65 (define @t64 () (exists @t3 @t63)) % 0.46/0.65 (define @t65 () (= @t57 tptp.xk)) % 0.46/0.65 (define @t66 () (and @t2 @t65)) % 0.46/0.65 (define @t67 () (exists @t3 @t66)) % 0.46/0.65 (define @t68 () (= tptp.xu (tptp.sdtpldt0 @t57 @t54))) % 0.46/0.65 (define @t69 () (and @t2 @t7 @t68)) % 0.46/0.65 (define @t70 () (exists @t9 @t69)) % 0.46/0.65 (define @t71 () (not @t70)) % 0.46/0.65 (define @t72 () (forall @t3 (not @t66))) % 0.46/0.65 (define @t73 () (not @t72)) % 0.46/0.65 (define @t74 () (not @t2)) % 0.46/0.65 (define @t75 () (forall @t3 (or @t74 (not @t65)))) % 0.46/0.65 (define @t76 () (@quantifiers_skolemize @t75 0)) % 0.46/0.65 (define @t77 () (tptp.sdtasdt0 tptp.xa @t76)) % 0.46/0.65 (define @t78 () (= tptp.xk @t77)) % 0.46/0.65 (define @t79 () (not @t78)) % 0.46/0.65 (define @t80 () (tptp.aElement0 @t76)) % 0.46/0.65 (define @t81 () (not @t80)) % 0.46/0.65 (define @t82 () (or @t81 @t79)) % 0.46/0.65 (define @t83 () (not @t82)) % 0.46/0.65 (define @t84 () (not @t75)) % 0.46/0.65 (define @t85 () (not (= @t77 tptp.xk))) % 0.46/0.65 (define @t86 () (or @t81 @t85)) % 0.46/0.65 (define @t87 () (not @t86)) % 0.46/0.65 (define @t88 () (@list true)) % 0.46/0.65 (define @t89 () (@list @t82)) % 0.46/0.65 (define @t90 () (forall @t3 (not @t63))) % 0.46/0.65 (define @t91 () (not @t90)) % 0.46/0.65 (define @t92 () (forall @t3 (or @t74 (not @t62)))) % 0.46/0.65 (define @t93 () (@quantifiers_skolemize @t92 0)) % 0.46/0.65 (define @t94 () (tptp.sdtasdt0 tptp.xb @t93)) % 0.46/0.65 (define @t95 () (= tptp.xl @t94)) % 0.46/0.65 (define @t96 () (not @t95)) % 0.46/0.65 (define @t97 () (tptp.aElement0 @t93)) % 0.46/0.65 (define @t98 () (not @t97)) % 0.46/0.65 (define @t99 () (or @t98 @t96)) % 0.46/0.65 (define @t100 () (not @t99)) % 0.46/0.65 (define @t101 () (not @t92)) % 0.46/0.65 (define @t102 () (not (= @t94 tptp.xl))) % 0.46/0.65 (define @t103 () (or @t98 @t102)) % 0.46/0.65 (define @t104 () (not @t103)) % 0.46/0.65 (define @t105 () (@list @t99)) % 0.46/0.65 (define @t106 () (not @t68)) % 0.46/0.65 (define @t107 () (not @t7)) % 0.46/0.65 (define @t108 () (or @t74 @t107 @t106)) % 0.46/0.65 (define @t109 () (forall @t9 (not @t69))) % 0.46/0.65 (define @t110 () (not @t109)) % 0.46/0.65 (define @t111 () (= tptp.xu (tptp.sdtpldt0 @t77 @t94))) % 0.46/0.65 (define @t112 () (not @t111)) % 0.46/0.65 (define @t113 () (or @t81 @t98 @t112)) % 0.46/0.65 (define @t114 () (not @t61)) % 0.46/0.65 (define @t115 () (and @t111 @t112)) % 0.46/0.65 (assume @p1 (forall @t3 (=> @t2 true))) % 0.46/0.65 (assume @p2 (tptp.aElement0 tptp.sz00)) % 0.46/0.65 (assume @p3 (tptp.aElement0 tptp.sz10)) % 0.46/0.65 (assume @p4 (forall @t3 (=> @t2 (tptp.aElement0 @t4)))) % 0.46/0.65 (assume @p5 (forall @t9 (=> @t8 (tptp.aElement0 @t6)))) % 0.46/0.65 (assume @p6 (forall @t9 (=> @t8 (tptp.aElement0 @t10)))) % 0.46/0.65 (assume @p7 (forall @t9 (=> @t8 (= @t6 (tptp.sdtpldt0 @t5 @t1))))) % 0.46/0.65 (assume @p8 (forall @t15 (=> @t14 (= (tptp.sdtpldt0 @t6 @t11) (tptp.sdtpldt0 @t1 @t12))))) % 0.46/0.65 (assume @p9 (forall @t3 (=> @t2 (and (= (tptp.sdtpldt0 @t1 tptp.sz00) @t1) (= @t1 (tptp.sdtpldt0 tptp.sz00 @t1)))))) % 0.46/0.65 (assume @p10 (forall @t3 (=> @t2 (and (= (tptp.sdtpldt0 @t1 @t4) tptp.sz00) (= tptp.sz00 (tptp.sdtpldt0 @t4 @t1)))))) % 0.46/0.65 (assume @p11 (forall @t9 (=> @t8 (= @t10 @t16)))) % 0.46/0.65 (assume @p12 (forall @t15 (=> @t14 (= (tptp.sdtasdt0 @t10 @t11) (tptp.sdtasdt0 @t1 (tptp.sdtasdt0 @t5 @t11)))))) % 0.46/0.65 (assume @p13 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz10) @t1) (= @t1 (tptp.sdtasdt0 tptp.sz10 @t1)))))) % 0.46/0.65 (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))))))) % 0.46/0.65 (assume @p15 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t18 @t1) @t4) (= @t4 (tptp.sdtasdt0 @t1 @t18)))))) % 0.46/0.65 (assume @p16 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz00) tptp.sz00) (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 @t1)))))) % 0.46/0.65 (assume @p17 (forall @t9 (=> @t8 (=> (= @t10 tptp.sz00) (or @t20 @t19))))) % 0.46/0.65 (assume @p18 (not (= tptp.sz10 tptp.sz00))) % 0.46/0.65 (assume @p19 (forall @t3 (=> @t21 true))) % 0.46/0.65 (assume @p20 (forall @t3 (=> @t21 (forall @t23 (=> @t22 @t7))))) % 0.46/0.65 (assume @p21 (forall @t9 (=> @t28 (=> (and (forall @t26 (=> @t24 @t25)) (forall @t26 (=> @t25 @t24))) (= @t1 @t5))))) % 0.46/0.65 (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))))))))))) % 0.46/0.65 (assume @p23 (forall @t9 (=> @t28 (forall @t26 (= (= @t11 @t36) (and @t34 (forall @t33 (= @t32 (and (tptp.aElementOf0 @t29 @t1) (tptp.aElementOf0 @t29 @t5)))))))))) % 0.46/0.65 (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)))))))))) % 0.46/0.65 (assume @p25 (forall @t9 (=> @t39 (tptp.aIdeal0 @t35)))) % 0.46/0.65 (assume @p26 (forall @t9 (=> @t39 (tptp.aIdeal0 @t36)))) % 0.46/0.65 (assume @p27 (forall @t15 (=> (and @t2 @t7 (tptp.aIdeal0 @t11)) (= (tptp.sdteqdtlpzmzozddtrp0 @t1 @t5 @t11) (tptp.aElementOf0 (tptp.sdtpldt0 @t1 (tptp.smndt0 @t5)) @t11))))) % 0.46/0.65 (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))))))))) % 0.46/0.65 (assume @p29 (forall @t3 (=> @t42 true))) % 0.46/0.65 (assume @p30 (forall @t3 (=> (and @t2 @t44) (tptp.aNaturalNumber0 @t43)))) % 0.46/0.65 (assume @p31 (forall @t9 (=> (and @t42 (tptp.aNaturalNumber0 @t5)) (=> (tptp.iLess0 @t1 @t5) true)))) % 0.46/0.65 (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)))))))) % 0.46/0.65 (assume @p33 (forall @t9 (=> @t8 (= (tptp.doDivides0 @t1 @t5) (exists @t26 (and @t13 (= @t17 @t5))))))) % 0.46/0.65 (assume @p34 (forall @t3 (=> @t2 (forall @t23 (= (tptp.aDivisorOf0 @t5 @t1) (and @t7 (tptp.doDivides0 @t5 @t1))))))) % 0.46/0.65 (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))))))))) % 0.46/0.65 (assume @p36 (forall @t9 (=> @t8 (= (tptp.misRelativelyPrime0 @t1 @t5) (tptp.aGcdOfAnd0 tptp.sz10 @t1 @t5))))) % 0.46/0.65 (assume @p37 (forall @t3 (=> @t2 (forall @t23 (= (= @t5 @t45) (and @t27 (forall @t26 (= @t25 (exists @t33 (and @t40 (= (tptp.sdtasdt0 @t1 @t29) @t11))))))))))) % 0.46/0.65 (assume @p38 (forall @t3 (=> @t2 (tptp.aIdeal0 @t45)))) % 0.46/0.65 (assume @p39 (and (tptp.aElement0 tptp.xa) (tptp.aElement0 tptp.xb))) % 0.46/0.65 (assume @p40 (or (not (= tptp.xa tptp.sz00)) (not (= tptp.xb tptp.sz00)))) % 0.46/0.65 (assume @p41 (and @t47 (exists @t3 (and @t2 (= @t46 tptp.xa))) (tptp.doDivides0 tptp.xc tptp.xa) (tptp.aDivisorOf0 tptp.xc tptp.xa) @t47 (exists @t3 (and @t2 (= @t46 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))) % 0.46/0.65 (assume @p42 (and (tptp.aSet0 tptp.xI) (forall @t3 (=> @t53 (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 @t48) (exists @t23 (and @t7 (= @t54 @t1))))) (forall @t3 (= @t53 @t52)) (= tptp.xI @t50))) % 0.46/0.65 (assume @p43 (and (exists @t3 (and @t2 (= @t57 tptp.sz00))) (tptp.aElementOf0 tptp.sz00 @t49) (exists @t3 (and @t2 (= @t57 tptp.xa))) (tptp.aElementOf0 tptp.xa @t49) (exists @t3 (and @t2 (= @t56 tptp.sz00))) (tptp.aElementOf0 tptp.sz00 @t48) (exists @t3 (and @t2 (= @t56 tptp.xb))) (tptp.aElementOf0 tptp.xb @t48))) % 0.46/0.65 (assume @p44 (exists @t3 (and (forall @t23 (= @t51 (exists @t26 (and @t13 (= (tptp.sdtasdt0 tptp.xa @t11) @t5))))) (forall @t23 (= @t58 (exists @t26 (and @t13 (= (tptp.sdtasdt0 tptp.xb @t11) @t5))))) @t52 (tptp.aElementOf0 @t1 @t50) @t44))) % 0.46/0.65 (assume @p45 (and (exists @t9 (and @t55 @t58 (= @t6 tptp.xu))) (tptp.aElementOf0 tptp.xu tptp.xI) (not (= tptp.xu tptp.sz00)) (forall @t3 (=> (and (or @t52 @t53) @t44) (not (tptp.iLess0 @t43 (tptp.sbrdtbr0 tptp.xu))))))) % 0.46/0.65 (assume @p46 (not (and (or (exists @t3 (and @t2 (= @t59 tptp.xa))) (tptp.doDivides0 tptp.xu tptp.xa) (tptp.aDivisorOf0 tptp.xu tptp.xa)) (or (exists @t3 (and @t2 (= @t59 tptp.xb))) (tptp.doDivides0 tptp.xu tptp.xb) (tptp.aDivisorOf0 tptp.xu tptp.xb))))) % 0.46/0.65 (assume @p47 (and @t67 (tptp.aElementOf0 tptp.xk @t49) @t64 (tptp.aElementOf0 tptp.xl @t48) @t61)) % 0.46/0.65 (assume @p48 @t71) % 0.46/0.65 (assume @p49 true) % 0.46/0.65 (step @p50 :rule and_elim :premises (@p47) :args (4)) % 0.46/0.65 (step @p51 :rule bool-and-de-morgan :args (@t2 @t65 true)) % 0.46/0.65 (step @p52 :rule cong :premises (@p51) :args (@t72)) % 0.46/0.65 (step @p53 :rule cong :premises (@p52) :args (@t73)) % 0.46/0.65 (step @p54 :rule exists-elim :args ((= @t67 @t73))) % 0.46/0.65 (step @p55 :rule trans :premises (@p54 @p53)) % 0.46/0.65 (step @p56 :rule and_elim :premises (@p47) :args (0)) % 0.46/0.65 (step @p57 :rule eq_resolve :premises (@p56 @p55)) % 0.46/0.65 (step @p58 :rule refl :args (@t83)) % 0.46/0.65 (step @p59 :rule bool-double-not-elim :args (@t75)) % 0.46/0.65 (step @p60 :rule nary_cong :premises (@p59 @p58) :args ((or (not @t84) @t83))) % 0.46/0.65 (step @p61 :rule eq-symm :args (@t77 tptp.xk)) % 0.46/0.65 (step @p62 :rule cong :premises (@p61) :args (@t85)) % 0.46/0.65 (step @p63 :rule refl :args (@t81)) % 0.46/0.65 (step @p64 :rule nary_cong :premises (@p63 @p62) :args (@t86)) % 0.46/0.65 (step @p65 :rule cong :premises (@p64) :args (@t87)) % 0.46/0.65 (step @p66 :rule refl :args (@t84)) % 0.46/0.65 (step @p67 :rule cong :premises (@p66 @p65) :args ((=> @t84 @t87))) % 0.46/0.65 (assume-push @p181 @t84) % 0.46/0.65 (step @p69 :rule skolemize :premises (@p57)) % 0.46/0.65 (step-pop @p182 :rule scope :premises (@p69)) % 0.46/0.65 (step @p70 :rule process_scope :premises (@p182) :args (@t87)) % 0.46/0.65 (step @p72 :rule eq_resolve :premises (@p70 @p67)) % 0.46/0.65 (step @p73 :rule implies_elim :premises (@p72)) % 0.46/0.65 (step @p74 :rule eq_resolve :premises (@p73 @p60)) % 0.46/0.65 (step @p75 :rule chain_m_resolution :premises (@p74 @p57) :args (@t83 @t88 (@list @t75))) % 0.46/0.65 (step @p76 :rule bool-double-not-elim :args (@t78)) % 0.46/0.65 (step @p77 :rule refl :args (@t82)) % 0.46/0.65 (step @p78 :rule nary_cong :premises (@p77 @p76) :args ((or @t82 (not @t79)))) % 0.46/0.65 (step @p79 :rule cnf_or_neg :args (@t82 1)) % 0.46/0.65 (step @p80 :rule eq_resolve :premises (@p79 @p78)) % 0.46/0.65 (step @p81 :rule reordering :premises (@p80) :args ((or @t78 @t82))) % 0.46/0.65 (step @p82 :rule chain_m_resolution :premises (@p81 @p75) :args (@t78 @t88 @t89)) % 0.46/0.65 (step @p83 :rule bool-and-de-morgan :args (@t2 @t62 true)) % 0.46/0.65 (step @p84 :rule cong :premises (@p83) :args (@t90)) % 0.46/0.65 (step @p85 :rule cong :premises (@p84) :args (@t91)) % 0.46/0.65 (step @p86 :rule exists-elim :args ((= @t64 @t91))) % 0.46/0.65 (step @p87 :rule trans :premises (@p86 @p85)) % 0.46/0.65 (step @p88 :rule and_elim :premises (@p47) :args (2)) % 0.46/0.65 (step @p89 :rule eq_resolve :premises (@p88 @p87)) % 0.46/0.65 (step @p90 :rule refl :args (@t100)) % 0.46/0.65 (step @p91 :rule bool-double-not-elim :args (@t92)) % 0.46/0.65 (step @p92 :rule nary_cong :premises (@p91 @p90) :args ((or (not @t101) @t100))) % 0.46/0.65 (step @p93 :rule eq-symm :args (@t94 tptp.xl)) % 0.46/0.65 (step @p94 :rule cong :premises (@p93) :args (@t102)) % 0.46/0.65 (step @p95 :rule refl :args (@t98)) % 0.46/0.65 (step @p96 :rule nary_cong :premises (@p95 @p94) :args (@t103)) % 0.46/0.65 (step @p97 :rule cong :premises (@p96) :args (@t104)) % 0.46/0.65 (step @p98 :rule refl :args (@t101)) % 0.46/0.65 (step @p99 :rule cong :premises (@p98 @p97) :args ((=> @t101 @t104))) % 0.46/0.65 (assume-push @p183 @t101) % 0.46/0.65 (step @p101 :rule skolemize :premises (@p89)) % 0.46/0.65 (step-pop @p184 :rule scope :premises (@p101)) % 0.46/0.65 (step @p102 :rule process_scope :premises (@p184) :args (@t104)) % 0.46/0.65 (step @p104 :rule eq_resolve :premises (@p102 @p99)) % 0.46/0.65 (step @p105 :rule implies_elim :premises (@p104)) % 0.46/0.65 (step @p106 :rule eq_resolve :premises (@p105 @p92)) % 0.46/0.65 (step @p107 :rule chain_m_resolution :premises (@p106 @p89) :args (@t100 @t88 (@list @t92))) % 0.46/0.65 (step @p108 :rule bool-double-not-elim :args (@t95)) % 0.46/0.65 (step @p109 :rule refl :args (@t99)) % 0.46/0.65 (step @p110 :rule nary_cong :premises (@p109 @p108) :args ((or @t99 (not @t96)))) % 0.46/0.65 (step @p111 :rule cnf_or_neg :args (@t99 1)) % 0.46/0.65 (step @p112 :rule eq_resolve :premises (@p111 @p110)) % 0.46/0.65 (step @p113 :rule reordering :premises (@p112) :args ((or @t95 @t99))) % 0.46/0.65 (step @p114 :rule chain_m_resolution :premises (@p113 @p107) :args (@t95 @t88 @t105)) % 0.46/0.65 (step @p115 :rule bool-double-not-elim :args ((forall @t9 @t108))) % 0.46/0.65 (step @p116 :rule aci_norm :args ((= (or @t74 (or @t107 @t106)) @t108))) % 0.46/0.65 (step @p117 :rule bool-and-de-morgan :args (@t7 @t68 true)) % 0.46/0.65 (step @p118 :rule refl :args (@t74)) % 0.46/0.65 (step @p119 :rule nary_cong :premises (@p118 @p117) :args ((or @t74 (not (and @t7 @t68))))) % 0.46/0.65 (step @p120 :rule bool-and-de-morgan :args (@t2 @t7 (and @t68))) % 0.46/0.65 (step @p121 :rule trans :premises (@p120 @p119)) % 0.46/0.65 (step @p122 :rule trans :premises (@p121 @p116)) % 0.46/0.65 (step @p123 :rule cong :premises (@p122) :args (@t109)) % 0.46/0.65 (step @p124 :rule cong :premises (@p123) :args (@t110)) % 0.46/0.65 (step @p125 :rule exists-elim :args ((= @t70 @t110))) % 0.46/0.65 (step @p126 :rule trans :premises (@p125 @p124)) % 0.46/0.65 (step @p127 :rule cong :premises (@p126) :args (@t71)) % 0.46/0.65 (step @p128 :rule trans :premises (@p127 @p115)) % 0.46/0.65 (step @p129 :rule eq_resolve :premises (@p48 @p128)) % 0.46/0.65 (step @p130 :rule instantiate :premises (@p129) :args ((@list @t76 @t93))) % 0.46/0.65 (step @p131 :rule bool-double-not-elim :args (@t97)) % 0.46/0.65 (step @p132 :rule nary_cong :premises (@p109 @p131) :args ((or @t99 (not @t98)))) % 0.46/0.65 (step @p133 :rule cnf_or_neg :args (@t99 0)) % 0.46/0.65 (step @p134 :rule eq_resolve :premises (@p133 @p132)) % 0.46/0.65 (step @p135 :rule reordering :premises (@p134) :args ((or @t97 @t99))) % 0.46/0.65 (step @p136 :rule chain_m_resolution :premises (@p135 @p107) :args (@t97 @t88 @t105)) % 0.46/0.65 (step @p137 :rule bool-double-not-elim :args (@t80)) % 0.46/0.65 (step @p138 :rule nary_cong :premises (@p77 @p137) :args ((or @t82 (not @t81)))) % 0.46/0.65 (step @p139 :rule cnf_or_neg :args (@t82 0)) % 0.46/0.65 (step @p140 :rule eq_resolve :premises (@p139 @p138)) % 0.46/0.65 (step @p141 :rule reordering :premises (@p140) :args ((or @t80 @t82))) % 0.46/0.65 (step @p142 :rule chain_m_resolution :premises (@p141 @p75) :args (@t80 @t88 @t89)) % 0.46/0.65 (step @p143 :rule cnf_or_pos :args (@t113)) % 0.46/0.65 (step @p144 :rule reordering :premises (@p143) :args ((or @t81 @t98 @t112 (not @t113)))) % 0.46/0.65 (step @p145 :rule chain_m_resolution :premises (@p144 @p142 @p136 @p130) :args (@t112 (@list false false false) (@list @t80 @t97 @t113))) % 0.46/0.65 (step @p146 :rule bool-double-not-elim :args (@t111)) % 0.46/0.65 (step @p147 :rule refl :args (@t96)) % 0.46/0.65 (step @p148 :rule refl :args (@t79)) % 0.46/0.65 (step @p149 :rule refl :args (@t114)) % 0.46/0.65 (step @p150 :rule nary_cong :premises (@p149 @p148 @p147 @p146) :args ((or @t114 @t79 @t96 (not @t112)))) % 0.46/0.65 (assume-push @p185 @t111) % 0.46/0.65 (assume-push @p186 @t112) % 0.46/0.65 (step @p153 :rule evaluate :args ((= true false))) % 0.46/0.65 (step @p154 :rule false_intro :premises (@p145)) % 0.46/0.65 (step @p155 :rule cong :premises (@p82 @p114) :args (@t60)) % 0.46/0.65 (step @p156 :rule and_elim :premises (@p47) :args (4)) % 0.46/0.65 (step @p157 :rule trans :premises (@p156 @p155)) % 0.46/0.65 (step @p158 :rule true_intro :premises (@p157)) % 0.46/0.65 (step @p159 :rule symm :premises (@p158)) % 0.46/0.65 (step @p160 :rule trans :premises (@p159 @p154)) % 0.46/0.65 (step @p161 false :rule eq_resolve :premises (@p160 @p153)) % 0.46/0.65 (step-pop @p187 :rule scope :premises (@p161)) % 0.46/0.65 (step-pop @p188 :rule scope :premises (@p187)) % 0.46/0.65 (step @p162 :rule process_scope :premises (@p188) :args (false)) % 0.46/0.65 (assume-push @p189 @t61) % 0.46/0.65 (assume-push @p190 @t78) % 0.46/0.65 (assume-push @p191 @t95) % 0.46/0.65 (assume-push @p192 @t112) % 0.46/0.65 (step @p155 :rule cong :premises (@p82 @p114) :args (@t60)) % 0.46/0.65 (step @p169 :rule trans :premises (@p50 @p155)) % 0.46/0.65 (step @p170 :rule and_intro :premises (@p169 @p145)) % 0.46/0.65 (step-pop @p193 :rule scope :premises (@p170)) % 0.46/0.65 (step-pop @p194 :rule scope :premises (@p193)) % 0.46/0.65 (step-pop @p195 :rule scope :premises (@p194)) % 0.46/0.65 (step-pop @p196 :rule scope :premises (@p195)) % 0.46/0.65 (step @p171 :rule process_scope :premises (@p196) :args (@t115)) % 0.46/0.65 (step @p176 :rule implies_elim :premises (@p171)) % 0.46/0.65 (step @p177 :rule resolution :premises (@p176 @p162) :args (true @t115)) % 0.46/0.65 (step @p178 :rule not_and :premises (@p177)) % 0.46/0.65 (step @p179 :rule eq_resolve :premises (@p178 @p150)) % 0.46/0.65 (step @p180 false :rule chain_m_resolution :premises (@p179 @p145 @p114 @p82 @p50) :args (false (@list true false false false) (@list @t111 @t95 @t78 @t61))) % 0.46/0.65 ) % 0.46/0.65 % SZS output end Proof % 0.46/0.65 % cvc5 exiting %------------------------------------------------------------------------------