%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : RNG124+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 : n013.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 08:45:45 AM UTC 2026 % Result : Theorem 0.36s 0.70s % Output : Proof 0.36s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : RNG124+4 : TPTP v9.2.1. Released v4.0.0. % 0.12/0.14 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.35 % Computer : n013.cluster.edu % 0.17/0.35 % Model : x86_64 x86_64 % 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.35 % Memory : 8042.1875MB % 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.35 % CPULimit : 300 % 0.17/0.35 % WCLimit : 300 % 0.17/0.35 % DateTime : Tue Jun 2 14:08:45 EDT 2026 % 0.17/0.35 % CPUTime : % 0.28/0.52 %----Proving TF0_NAR, FOF, or CNF % 0.36/0.70 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.36/0.70 % SZS status Theorem % 0.36/0.70 % SZS output start Proof % 0.36/0.70 ( % 0.36/0.70 (declare-sort $$unsorted 0) % 0.36/0.70 (declare-const tptp.xu $$unsorted) % 0.36/0.70 (declare-const tptp.xr $$unsorted) % 0.36/0.70 (declare-const tptp.xI $$unsorted) % 0.36/0.70 (declare-const tptp.xc $$unsorted) % 0.36/0.70 (declare-const tptp.xa $$unsorted) % 0.36/0.70 (declare-const tptp.slsdtgt0 (-> $$unsorted $$unsorted)) % 0.36/0.70 (declare-const tptp.aDivisorOf0 (-> $$unsorted $$unsorted Bool)) % 0.36/0.70 (declare-const tptp.iLess0 (-> $$unsorted $$unsorted Bool)) % 0.36/0.70 (declare-const tptp.sbrdtbr0 (-> $$unsorted $$unsorted)) % 0.36/0.70 (declare-const tptp.aElement0 (-> $$unsorted Bool)) % 0.36/0.70 (declare-const tptp.sz00 $$unsorted) % 0.36/0.70 (declare-const tptp.xq $$unsorted) % 0.36/0.70 (declare-const tptp.sz10 $$unsorted) % 0.36/0.70 (declare-const tptp.aGcdOfAnd0 (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.36/0.70 (declare-const tptp.smndt0 (-> $$unsorted $$unsorted)) % 0.36/0.70 (declare-const tptp.sdtpldt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.70 (declare-const tptp.sdtasasdt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.70 (declare-const tptp.aIdeal0 (-> $$unsorted Bool)) % 0.36/0.70 (declare-const tptp.misRelativelyPrime0 (-> $$unsorted $$unsorted Bool)) % 0.36/0.70 (declare-const tptp.sdtasdt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.70 (declare-const tptp.doDivides0 (-> $$unsorted $$unsorted Bool)) % 0.36/0.70 (declare-const tptp.aSet0 (-> $$unsorted Bool)) % 0.36/0.70 (declare-const tptp.aElementOf0 (-> $$unsorted $$unsorted Bool)) % 0.36/0.70 (declare-const tptp.sdteqdtlpzmzozddtrp0 (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.36/0.70 (declare-const tptp.xb $$unsorted) % 0.36/0.70 (declare-const tptp.sdtpldt1 (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.70 (declare-const tptp.aNaturalNumber0 (-> $$unsorted Bool)) % 0.36/0.70 (define @t1 () (@var "W0" $$unsorted)) % 0.36/0.70 (define @t2 () (tptp.aElement0 @t1)) % 0.36/0.70 (define @t3 () (@list @t1)) % 0.36/0.70 (define @t4 () (tptp.smndt0 @t1)) % 0.36/0.70 (define @t5 () (@var "W1" $$unsorted)) % 0.36/0.70 (define @t6 () (tptp.sdtpldt0 @t1 @t5)) % 0.36/0.70 (define @t7 () (tptp.aElement0 @t5)) % 0.36/0.70 (define @t8 () (and @t2 @t7)) % 0.36/0.70 (define @t9 () (@list @t1 @t5)) % 0.36/0.70 (define @t10 () (tptp.sdtasdt0 @t1 @t5)) % 0.36/0.70 (define @t11 () (@var "W2" $$unsorted)) % 0.36/0.70 (define @t12 () (tptp.sdtpldt0 @t5 @t11)) % 0.36/0.70 (define @t13 () (tptp.aElement0 @t11)) % 0.36/0.70 (define @t14 () (and @t2 @t7 @t13)) % 0.36/0.70 (define @t15 () (@list @t1 @t5 @t11)) % 0.36/0.70 (define @t16 () (tptp.sdtasdt0 @t5 @t1)) % 0.36/0.70 (define @t17 () (tptp.sdtasdt0 @t1 @t11)) % 0.36/0.70 (define @t18 () (tptp.smndt0 tptp.sz10)) % 0.36/0.70 (define @t19 () (= @t5 tptp.sz00)) % 0.36/0.70 (define @t20 () (= @t1 tptp.sz00)) % 0.36/0.70 (define @t21 () (tptp.aSet0 @t1)) % 0.36/0.70 (define @t22 () (tptp.aElementOf0 @t5 @t1)) % 0.36/0.70 (define @t23 () (@list @t5)) % 0.36/0.70 (define @t24 () (tptp.aElementOf0 @t11 @t1)) % 0.36/0.70 (define @t25 () (tptp.aElementOf0 @t11 @t5)) % 0.36/0.70 (define @t26 () (@list @t11)) % 0.36/0.70 (define @t27 () (tptp.aSet0 @t5)) % 0.36/0.70 (define @t28 () (and @t21 @t27)) % 0.36/0.70 (define @t29 () (@var "W3" $$unsorted)) % 0.36/0.70 (define @t30 () (@var "W5" $$unsorted)) % 0.36/0.70 (define @t31 () (@var "W4" $$unsorted)) % 0.36/0.70 (define @t32 () (tptp.aElementOf0 @t29 @t11)) % 0.36/0.70 (define @t33 () (@list @t29)) % 0.36/0.70 (define @t34 () (tptp.aSet0 @t11)) % 0.36/0.70 (define @t35 () (tptp.sdtpldt1 @t1 @t5)) % 0.36/0.70 (define @t36 () (tptp.sdtasasdt0 @t1 @t5)) % 0.36/0.70 (define @t37 () (tptp.sdtasdt0 @t11 @t5)) % 0.36/0.70 (define @t38 () (tptp.aIdeal0 @t1)) % 0.36/0.70 (define @t39 () (and @t38 (tptp.aIdeal0 @t5))) % 0.36/0.70 (define @t40 () (tptp.aElement0 @t29)) % 0.36/0.70 (define @t41 () (@list @t11 @t29)) % 0.36/0.70 (define @t42 () (tptp.aNaturalNumber0 @t1)) % 0.36/0.70 (define @t43 () (tptp.sbrdtbr0 @t1)) % 0.36/0.70 (define @t44 () (not @t20)) % 0.36/0.70 (define @t45 () (tptp.slsdtgt0 @t1)) % 0.36/0.70 (define @t46 () (tptp.sdtasdt0 tptp.xc @t1)) % 0.36/0.70 (define @t47 () (tptp.aElement0 tptp.xc)) % 0.36/0.70 (define @t48 () (tptp.slsdtgt0 tptp.xb)) % 0.36/0.70 (define @t49 () (tptp.slsdtgt0 tptp.xa)) % 0.36/0.70 (define @t50 () (tptp.sdtpldt1 @t49 @t48)) % 0.36/0.70 (define @t51 () (tptp.aElementOf0 @t11 @t48)) % 0.36/0.70 (define @t52 () (tptp.aElementOf0 @t5 @t49)) % 0.36/0.70 (define @t53 () (and @t52 @t51 (= @t12 @t1))) % 0.36/0.70 (define @t54 () (@list @t5 @t11)) % 0.36/0.70 (define @t55 () (exists @t54 @t53)) % 0.36/0.70 (define @t56 () (tptp.aElementOf0 @t1 tptp.xI)) % 0.36/0.70 (define @t57 () (tptp.sdtasdt0 tptp.xb @t5)) % 0.36/0.70 (define @t58 () (tptp.aElementOf0 @t1 @t49)) % 0.36/0.70 (define @t59 () (tptp.sdtasdt0 tptp.xb @t1)) % 0.36/0.70 (define @t60 () (tptp.sdtasdt0 tptp.xa @t1)) % 0.36/0.70 (define @t61 () (tptp.aElementOf0 @t5 @t48)) % 0.36/0.70 (define @t62 () (tptp.sbrdtbr0 tptp.xu)) % 0.36/0.70 (define @t63 () (not (tptp.iLess0 @t43 @t62))) % 0.36/0.70 (define @t64 () (or @t55 @t56)) % 0.36/0.70 (define @t65 () (and @t64 @t44)) % 0.36/0.70 (define @t66 () (=> @t65 @t63)) % 0.36/0.70 (define @t67 () (forall @t3 @t66)) % 0.36/0.70 (define @t68 () (= @t6 tptp.xu)) % 0.36/0.70 (define @t69 () (tptp.doDivides0 tptp.xu tptp.xb)) % 0.36/0.70 (define @t70 () (tptp.sdtasdt0 tptp.xu @t1)) % 0.36/0.70 (define @t71 () (exists @t3 (and @t2 (= @t70 tptp.xb)))) % 0.36/0.70 (define @t72 () (tptp.doDivides0 tptp.xu tptp.xa)) % 0.36/0.70 (define @t73 () (exists @t3 (and @t2 (= @t70 tptp.xa)))) % 0.36/0.70 (define @t74 () (tptp.iLess0 (tptp.sbrdtbr0 tptp.xr) @t62)) % 0.36/0.70 (define @t75 () (= tptp.xr tptp.sz00)) % 0.36/0.70 (define @t76 () (or @t75 @t74)) % 0.36/0.70 (define @t77 () (tptp.sdtasdt0 tptp.xq tptp.xu)) % 0.36/0.70 (define @t78 () (tptp.smndt0 @t77)) % 0.36/0.70 (define @t79 () (exists @t9 (and @t58 @t61 (= @t6 tptp.xb)))) % 0.36/0.70 (define @t80 () (tptp.aElementOf0 tptp.xr tptp.xI)) % 0.36/0.70 (define @t81 () (= tptp.sz00 tptp.xr)) % 0.36/0.70 (define @t82 () (not @t80)) % 0.36/0.70 (define @t83 () (forall @t9 (or (not @t58) (not @t61) (not @t68)))) % 0.36/0.70 (define @t84 () (@quantifiers_skolemize @t83 1)) % 0.36/0.70 (define @t85 () (@quantifiers_skolemize @t83 0)) % 0.36/0.70 (define @t86 () (and (or (not (tptp.aElementOf0 @t85 @t49)) (not (tptp.aElementOf0 @t84 @t48)) (not (= tptp.xr (tptp.sdtpldt0 @t85 @t84)))) @t82)) % 0.36/0.70 (define @t87 () (not @t86)) % 0.36/0.70 (define @t88 () (@list false)) % 0.36/0.70 (define @t89 () (not @t56)) % 0.36/0.70 (define @t90 () (@var "BOUND_VARIABLE_8651" $$unsorted)) % 0.36/0.70 (define @t91 () (@var "BOUND_VARIABLE_8649" $$unsorted)) % 0.36/0.70 (define @t92 () (or (not (tptp.aElementOf0 @t91 @t49)) (not (tptp.aElementOf0 @t90 @t48)) (not (= @t1 (tptp.sdtpldt0 @t91 @t90))))) % 0.36/0.70 (define @t93 () (and @t92 @t89)) % 0.36/0.70 (define @t94 () (or @t93 @t20 @t63)) % 0.36/0.70 (define @t95 () (forall (@list @t1 @t91 @t90) @t94)) % 0.36/0.70 (define @t96 () (@list @t91 @t90)) % 0.36/0.70 (define @t97 () (forall @t96 @t94)) % 0.36/0.70 (define @t98 () (forall @t96 @t89)) % 0.36/0.70 (define @t99 () (forall @t96 @t92)) % 0.36/0.70 (define @t100 () (and @t99 @t98)) % 0.36/0.70 (define @t101 () (forall @t96 @t93)) % 0.36/0.70 (define @t102 () (or @t101 @t20 @t63)) % 0.36/0.70 (define @t103 () (= @t1 @t12)) % 0.36/0.70 (define @t104 () (not @t103)) % 0.36/0.70 (define @t105 () (not @t51)) % 0.36/0.70 (define @t106 () (not @t52)) % 0.36/0.70 (define @t107 () (or @t106 @t105 @t104)) % 0.36/0.70 (define @t108 () (forall @t54 @t107)) % 0.36/0.70 (define @t109 () (and @t108 @t89)) % 0.36/0.70 (define @t110 () (or @t109 @t20 @t63)) % 0.36/0.70 (define @t111 () (not @t108)) % 0.36/0.70 (define @t112 () (or @t111 @t56)) % 0.36/0.70 (define @t113 () (not @t112)) % 0.36/0.70 (define @t114 () (and @t112 @t44)) % 0.36/0.70 (define @t115 () (and @t52 @t51 @t103)) % 0.36/0.70 (define @t116 () (forall @t54 (not @t115))) % 0.36/0.70 (define @t117 () (not @t116)) % 0.36/0.70 (define @t118 () (not @t74)) % 0.36/0.70 (define @t119 () (or @t86 @t75 @t118)) % 0.36/0.70 (define @t120 () (or @t86 @t81 @t118)) % 0.36/0.70 (assume @p1 (forall @t3 (=> @t2 true))) % 0.36/0.70 (assume @p2 (tptp.aElement0 tptp.sz00)) % 0.36/0.70 (assume @p3 (tptp.aElement0 tptp.sz10)) % 0.36/0.70 (assume @p4 (forall @t3 (=> @t2 (tptp.aElement0 @t4)))) % 0.36/0.70 (assume @p5 (forall @t9 (=> @t8 (tptp.aElement0 @t6)))) % 0.36/0.70 (assume @p6 (forall @t9 (=> @t8 (tptp.aElement0 @t10)))) % 0.36/0.70 (assume @p7 (forall @t9 (=> @t8 (= @t6 (tptp.sdtpldt0 @t5 @t1))))) % 0.36/0.70 (assume @p8 (forall @t15 (=> @t14 (= (tptp.sdtpldt0 @t6 @t11) (tptp.sdtpldt0 @t1 @t12))))) % 0.36/0.70 (assume @p9 (forall @t3 (=> @t2 (and (= (tptp.sdtpldt0 @t1 tptp.sz00) @t1) (= @t1 (tptp.sdtpldt0 tptp.sz00 @t1)))))) % 0.36/0.70 (assume @p10 (forall @t3 (=> @t2 (and (= (tptp.sdtpldt0 @t1 @t4) tptp.sz00) (= tptp.sz00 (tptp.sdtpldt0 @t4 @t1)))))) % 0.36/0.70 (assume @p11 (forall @t9 (=> @t8 (= @t10 @t16)))) % 0.36/0.70 (assume @p12 (forall @t15 (=> @t14 (= (tptp.sdtasdt0 @t10 @t11) (tptp.sdtasdt0 @t1 (tptp.sdtasdt0 @t5 @t11)))))) % 0.36/0.70 (assume @p13 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz10) @t1) (= @t1 (tptp.sdtasdt0 tptp.sz10 @t1)))))) % 0.36/0.70 (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))))))) % 0.36/0.70 (assume @p15 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t18 @t1) @t4) (= @t4 (tptp.sdtasdt0 @t1 @t18)))))) % 0.36/0.70 (assume @p16 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz00) tptp.sz00) (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 @t1)))))) % 0.36/0.70 (assume @p17 (forall @t9 (=> @t8 (=> (= @t10 tptp.sz00) (or @t20 @t19))))) % 0.36/0.70 (assume @p18 (not (= tptp.sz10 tptp.sz00))) % 0.36/0.70 (assume @p19 (forall @t3 (=> @t21 true))) % 0.36/0.70 (assume @p20 (forall @t3 (=> @t21 (forall @t23 (=> @t22 @t7))))) % 0.36/0.70 (assume @p21 (forall @t9 (=> @t28 (=> (and (forall @t26 (=> @t24 @t25)) (forall @t26 (=> @t25 @t24))) (= @t1 @t5))))) % 0.36/0.70 (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))))))))))) % 0.36/0.70 (assume @p23 (forall @t9 (=> @t28 (forall @t26 (= (= @t11 @t36) (and @t34 (forall @t33 (= @t32 (and (tptp.aElementOf0 @t29 @t1) (tptp.aElementOf0 @t29 @t5)))))))))) % 0.36/0.70 (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)))))))))) % 0.36/0.70 (assume @p25 (forall @t9 (=> @t39 (tptp.aIdeal0 @t35)))) % 0.36/0.70 (assume @p26 (forall @t9 (=> @t39 (tptp.aIdeal0 @t36)))) % 0.36/0.70 (assume @p27 (forall @t15 (=> (and @t2 @t7 (tptp.aIdeal0 @t11)) (= (tptp.sdteqdtlpzmzozddtrp0 @t1 @t5 @t11) (tptp.aElementOf0 (tptp.sdtpldt0 @t1 (tptp.smndt0 @t5)) @t11))))) % 0.36/0.70 (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))))))))) % 0.36/0.70 (assume @p29 (forall @t3 (=> @t42 true))) % 0.36/0.70 (assume @p30 (forall @t3 (=> (and @t2 @t44) (tptp.aNaturalNumber0 @t43)))) % 0.36/0.70 (assume @p31 (forall @t9 (=> (and @t42 (tptp.aNaturalNumber0 @t5)) (=> (tptp.iLess0 @t1 @t5) true)))) % 0.36/0.70 (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)))))))) % 0.36/0.70 (assume @p33 (forall @t9 (=> @t8 (= (tptp.doDivides0 @t1 @t5) (exists @t26 (and @t13 (= @t17 @t5))))))) % 0.36/0.70 (assume @p34 (forall @t3 (=> @t2 (forall @t23 (= (tptp.aDivisorOf0 @t5 @t1) (and @t7 (tptp.doDivides0 @t5 @t1))))))) % 0.36/0.70 (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))))))))) % 0.36/0.70 (assume @p36 (forall @t9 (=> @t8 (= (tptp.misRelativelyPrime0 @t1 @t5) (tptp.aGcdOfAnd0 tptp.sz10 @t1 @t5))))) % 0.36/0.70 (assume @p37 (forall @t3 (=> @t2 (forall @t23 (= (= @t5 @t45) (and @t27 (forall @t26 (= @t25 (exists @t33 (and @t40 (= (tptp.sdtasdt0 @t1 @t29) @t11))))))))))) % 0.36/0.70 (assume @p38 (forall @t3 (=> @t2 (tptp.aIdeal0 @t45)))) % 0.36/0.70 (assume @p39 (and (tptp.aElement0 tptp.xa) (tptp.aElement0 tptp.xb))) % 0.36/0.70 (assume @p40 (or (not (= tptp.xa tptp.sz00)) (not (= tptp.xb tptp.sz00)))) % 0.36/0.70 (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))) % 0.36/0.70 (assume @p42 (and (tptp.aSet0 tptp.xI) (forall @t3 (=> @t56 (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 (= @t58 (exists @t23 (and @t7 (= (tptp.sdtasdt0 tptp.xa @t5) @t1))))) (forall @t3 (= (tptp.aElementOf0 @t1 @t48) (exists @t23 (and @t7 (= @t57 @t1))))) (forall @t3 (= @t56 @t55)) (= tptp.xI @t50))) % 0.36/0.70 (assume @p43 (and (exists @t3 (and @t2 (= @t60 tptp.sz00))) (tptp.aElementOf0 tptp.sz00 @t49) (exists @t3 (and @t2 (= @t60 tptp.xa))) (tptp.aElementOf0 tptp.xa @t49) (exists @t3 (and @t2 (= @t59 tptp.sz00))) (tptp.aElementOf0 tptp.sz00 @t48) (exists @t3 (and @t2 (= @t59 tptp.xb))) (tptp.aElementOf0 tptp.xb @t48))) % 0.36/0.70 (assume @p44 (exists @t3 (and (forall @t23 (= @t52 (exists @t26 (and @t13 (= (tptp.sdtasdt0 tptp.xa @t11) @t5))))) (forall @t23 (= @t61 (exists @t26 (and @t13 (= (tptp.sdtasdt0 tptp.xb @t11) @t5))))) @t55 (tptp.aElementOf0 @t1 @t50) @t44))) % 0.36/0.70 (assume @p45 (and (exists @t9 (and @t58 @t61 @t68)) (tptp.aElementOf0 tptp.xu tptp.xI) (not (= tptp.xu tptp.sz00)) @t67)) % 0.36/0.70 (assume @p46 (not (and (or @t73 @t72 (tptp.aDivisorOf0 tptp.xu tptp.xa)) (or @t71 @t69 (tptp.aDivisorOf0 tptp.xu tptp.xb))))) % 0.36/0.70 (assume @p47 (exists @t9 (and @t2 @t7 (= tptp.xu (tptp.sdtpldt0 @t60 @t57))))) % 0.36/0.70 (assume @p48 (not (not (and @t73 @t72)))) % 0.36/0.70 (assume @p49 (not (or @t71 @t69))) % 0.36/0.70 (assume @p50 (and (tptp.aElement0 tptp.xq) (tptp.aElement0 tptp.xr) (= tptp.xb (tptp.sdtpldt0 @t77 tptp.xr)) @t76)) % 0.36/0.70 (assume @p51 (not @t75)) % 0.36/0.70 (assume @p52 (and (exists @t9 (and @t58 @t61 (= @t6 @t78))) (tptp.aElementOf0 @t78 tptp.xI))) % 0.36/0.70 (assume @p53 (and @t79 @t79 (tptp.aElementOf0 tptp.xb tptp.xI))) % 0.36/0.70 (assume @p54 (= tptp.xr (tptp.sdtpldt0 @t78 tptp.xb))) % 0.36/0.70 (assume @p55 (and (exists @t9 (and @t58 @t61 (= @t6 tptp.xr))) @t80)) % 0.36/0.70 (assume @p56 (not false)) % 0.36/0.70 (assume @p57 true) % 0.36/0.70 (step @p58 :rule symm :premises (@p51)) % 0.36/0.70 (step @p59 :rule refl :args (@t74)) % 0.36/0.70 (step @p60 :rule eq-symm :args (tptp.xr tptp.sz00)) % 0.36/0.70 (step @p61 :rule nary_cong :premises (@p60 @p59) :args (@t76)) % 0.36/0.70 (step @p62 :rule and_elim :premises (@p50) :args (3)) % 0.36/0.70 (step @p63 :rule eq_resolve :premises (@p62 @p61)) % 0.36/0.70 (step @p64 :rule reordering :premises (@p63) :args ((or @t74 @t81))) % 0.36/0.70 (step @p65 :rule chain_m_resolution :premises (@p64 @p58) :args (@t74 (@list true) (@list @t81))) % 0.36/0.70 (step @p66 :rule and_elim :premises (@p55) :args (1)) % 0.36/0.70 (step @p67 :rule cnf_and_pos :args (@t86 1)) % 0.36/0.70 (step @p68 :rule reordering :premises (@p67) :args ((or @t82 @t87))) % 0.36/0.70 (step @p69 :rule chain_m_resolution :premises (@p68 @p66) :args (@t87 @t88 (@list @t80))) % 0.36/0.70 (step @p70 :rule quant-merge-prenex :args ((= (forall @t3 @t97) @t95))) % 0.36/0.70 (step @p71 :rule refl :args (@t63)) % 0.36/0.70 (step @p72 :rule refl :args (@t20)) % 0.36/0.70 (step @p73 :rule quant-unused-vars :args ((= @t98 @t89))) % 0.36/0.70 (step @p74 :rule alpha_equiv :args (@t99 (@list @t91 @t90) (@list @t5 @t11))) % 0.36/0.70 (step @p75 :rule nary_cong :premises (@p74 @p73) :args (@t100)) % 0.36/0.70 (step @p76 :rule quant-miniscope-and :args ((= @t101 @t100))) % 0.36/0.70 (step @p77 :rule trans :premises (@p76 @p75)) % 0.36/0.70 (step @p78 :rule nary_cong :premises (@p77 @p72 @p71) :args (@t102)) % 0.36/0.70 (step @p79 :rule quant-miniscope-or :args ((= @t97 @t102))) % 0.36/0.70 (step @p80 :rule trans :premises (@p79 @p78)) % 0.36/0.70 (step @p81 :rule symm :premises (@p80)) % 0.36/0.70 (step @p82 :rule cong :premises (@p81) :args ((forall @t3 @t110))) % 0.36/0.70 (step @p83 :rule trans :premises (@p82 @p70)) % 0.36/0.70 (step @p84 :rule aci_norm :args ((= (or (or @t109 @t20) @t63) @t110))) % 0.36/0.70 (step @p85 :rule refl :args (@t89)) % 0.36/0.70 (step @p86 :rule bool-double-not-elim :args (@t108)) % 0.36/0.70 (step @p87 :rule nary_cong :premises (@p86 @p85) :args ((and (not @t111) @t89))) % 0.36/0.70 (step @p88 :rule bool-or-de-morgan :args (@t111 @t56 false)) % 0.36/0.70 (step @p89 :rule trans :premises (@p88 @p87)) % 0.36/0.70 (step @p90 :rule nary_cong :premises (@p89 @p72) :args ((or @t113 @t20))) % 0.36/0.70 (step @p91 :rule bool-double-not-elim :args (@t20)) % 0.36/0.70 (step @p92 :rule refl :args (@t113)) % 0.36/0.70 (step @p93 :rule nary_cong :premises (@p92 @p91) :args ((or @t113 (not @t44)))) % 0.36/0.70 (step @p94 :rule bool-and-de-morgan :args (@t112 @t44 true)) % 0.36/0.70 (step @p95 :rule trans :premises (@p94 @p93)) % 0.36/0.70 (step @p96 :rule trans :premises (@p95 @p90)) % 0.36/0.70 (step @p97 :rule nary_cong :premises (@p96 @p71) :args ((or (not @t114) @t63))) % 0.36/0.70 (step @p98 :rule trans :premises (@p97 @p84)) % 0.36/0.70 (step @p99 :rule bool-impl-elim :args (@t114 @t63)) % 0.36/0.70 (step @p100 :rule trans :premises (@p99 @p98)) % 0.36/0.70 (step @p101 :rule cong :premises (@p100) :args ((forall @t3 (=> @t114 @t63)))) % 0.36/0.70 (step @p102 :rule trans :premises (@p101 @p83)) % 0.36/0.70 (step @p103 :rule refl :args (@t63)) % 0.36/0.70 (step @p104 :rule refl :args (@t44)) % 0.36/0.70 (step @p105 :rule refl :args (@t56)) % 0.36/0.70 (step @p106 :rule aci_norm :args ((= (or @t106 (or @t105 @t104)) @t107))) % 0.36/0.70 (step @p107 :rule bool-and-de-morgan :args (@t51 @t103 true)) % 0.36/0.70 (step @p108 :rule refl :args (@t106)) % 0.36/0.70 (step @p109 :rule nary_cong :premises (@p108 @p107) :args ((or @t106 (not (and @t51 @t103))))) % 0.36/0.70 (step @p110 :rule bool-and-de-morgan :args (@t52 @t51 (and @t103))) % 0.36/0.70 (step @p111 :rule trans :premises (@p110 @p109)) % 0.36/0.71 (step @p112 :rule trans :premises (@p111 @p106)) % 0.36/0.71 (step @p113 :rule cong :premises (@p112) :args (@t116)) % 0.36/0.71 (step @p114 :rule cong :premises (@p113) :args (@t117)) % 0.36/0.71 (step @p115 :rule exists-elim :args ((= (exists @t54 @t115) @t117))) % 0.36/0.71 (step @p116 :rule trans :premises (@p115 @p114)) % 0.36/0.71 (step @p117 :rule eq-symm :args (@t12 @t1)) % 0.36/0.71 (step @p118 :rule refl :args (@t51)) % 0.36/0.71 (step @p119 :rule refl :args (@t52)) % 0.36/0.71 (step @p120 :rule nary_cong :premises (@p119 @p118 @p117) :args (@t53)) % 0.36/0.71 (step @p121 :rule cong :premises (@p120) :args (@t55)) % 0.36/0.71 (step @p122 :rule trans :premises (@p121 @p116)) % 0.36/0.71 (step @p123 :rule nary_cong :premises (@p122 @p105) :args (@t64)) % 0.36/0.71 (step @p124 :rule nary_cong :premises (@p123 @p104) :args (@t65)) % 0.36/0.71 (step @p125 :rule cong :premises (@p124 @p103) :args (@t66)) % 0.36/0.71 (step @p126 :rule cong :premises (@p125) :args (@t67)) % 0.36/0.71 (step @p127 :rule trans :premises (@p126 @p102)) % 0.36/0.71 (step @p128 :rule and_elim :premises (@p45) :args (3)) % 0.36/0.71 (step @p129 :rule eq_resolve :premises (@p128 @p127)) % 0.36/0.71 (step @p130 :rule refl :args (@t118)) % 0.36/0.71 (step @p131 :rule refl :args (@t86)) % 0.36/0.71 (step @p132 :rule nary_cong :premises (@p131 @p60 @p130) :args (@t119)) % 0.36/0.71 (step @p133 :rule refl :args (@t95)) % 0.36/0.71 (step @p134 :rule cong :premises (@p133 @p132) :args ((=> @t95 @t119))) % 0.36/0.71 (assume-push @p145 @t95) % 0.36/0.71 (step @p136 :rule instantiate :premises (@p129) :args ((@list tptp.xr @t85 @t84))) % 0.36/0.71 (step-pop @p146 :rule scope :premises (@p136)) % 0.36/0.71 (step @p137 :rule process_scope :premises (@p146) :args (@t119)) % 0.36/0.71 (step @p139 :rule eq_resolve :premises (@p137 @p134)) % 0.36/0.71 (step @p140 :rule implies_elim :premises (@p139)) % 0.36/0.71 (step @p141 :rule chain_m_resolution :premises (@p140 @p129) :args (@t120 @t88 (@list @t95))) % 0.36/0.71 (step @p142 :rule cnf_or_pos :args (@t120)) % 0.36/0.71 (step @p143 :rule reordering :premises (@p142) :args ((or @t81 @t118 @t86 (not @t120)))) % 0.36/0.71 (step @p144 false :rule chain_m_resolution :premises (@p143 @p141 @p69 @p65 @p58) :args (false (@list false true false true) (@list @t120 @t86 @t74 @t81))) % 0.36/0.71 ) % 0.36/0.71 % SZS output end Proof % 0.36/0.71 % cvc5 exiting %------------------------------------------------------------------------------