%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : RNG123+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 : 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 08:45:45 AM UTC 2026 % Result : Theorem 0.43s 0.68s % Output : Proof 0.43s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : RNG123+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 : n020.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 14:08:55 EDT 2026 % 0.16/0.34 % CPUTime : % 0.27/0.51 %----Proving TF0_NAR, FOF, or CNF % 0.43/0.68 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.43/0.68 % SZS status Theorem % 0.43/0.68 % SZS output start Proof % 0.43/0.68 ( % 0.43/0.68 (declare-sort $$unsorted 0) % 0.43/0.68 (declare-const tptp.xu $$unsorted) % 0.43/0.68 (declare-const tptp.xr $$unsorted) % 0.43/0.68 (declare-const tptp.xI $$unsorted) % 0.43/0.68 (declare-const tptp.xc $$unsorted) % 0.43/0.68 (declare-const tptp.xa $$unsorted) % 0.43/0.68 (declare-const tptp.slsdtgt0 (-> $$unsorted $$unsorted)) % 0.43/0.68 (declare-const tptp.aDivisorOf0 (-> $$unsorted $$unsorted Bool)) % 0.43/0.68 (declare-const tptp.iLess0 (-> $$unsorted $$unsorted Bool)) % 0.43/0.68 (declare-const tptp.sbrdtbr0 (-> $$unsorted $$unsorted)) % 0.43/0.68 (declare-const tptp.aElement0 (-> $$unsorted Bool)) % 0.43/0.68 (declare-const tptp.sz00 $$unsorted) % 0.43/0.68 (declare-const tptp.xq $$unsorted) % 0.43/0.68 (declare-const tptp.sz10 $$unsorted) % 0.43/0.68 (declare-const tptp.aGcdOfAnd0 (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.43/0.68 (declare-const tptp.smndt0 (-> $$unsorted $$unsorted)) % 0.43/0.68 (declare-const tptp.sdtpldt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.43/0.68 (declare-const tptp.sdtasasdt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.43/0.68 (declare-const tptp.aIdeal0 (-> $$unsorted Bool)) % 0.43/0.68 (declare-const tptp.misRelativelyPrime0 (-> $$unsorted $$unsorted Bool)) % 0.43/0.68 (declare-const tptp.sdtasdt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.43/0.68 (declare-const tptp.doDivides0 (-> $$unsorted $$unsorted Bool)) % 0.43/0.68 (declare-const tptp.aSet0 (-> $$unsorted Bool)) % 0.43/0.68 (declare-const tptp.aElementOf0 (-> $$unsorted $$unsorted Bool)) % 0.43/0.68 (declare-const tptp.sdteqdtlpzmzozddtrp0 (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.43/0.68 (declare-const tptp.xb $$unsorted) % 0.43/0.68 (declare-const tptp.sdtpldt1 (-> $$unsorted $$unsorted $$unsorted)) % 0.43/0.68 (declare-const tptp.aNaturalNumber0 (-> $$unsorted Bool)) % 0.43/0.68 (define @t1 () (@var "W0" $$unsorted)) % 0.43/0.68 (define @t2 () (tptp.aElement0 @t1)) % 0.43/0.68 (define @t3 () (@list @t1)) % 0.43/0.68 (define @t4 () (tptp.aElement0 tptp.sz10)) % 0.43/0.68 (define @t5 () (tptp.smndt0 @t1)) % 0.43/0.68 (define @t6 () (@var "W1" $$unsorted)) % 0.43/0.68 (define @t7 () (tptp.sdtpldt0 @t1 @t6)) % 0.43/0.68 (define @t8 () (tptp.aElement0 @t6)) % 0.43/0.68 (define @t9 () (and @t2 @t8)) % 0.43/0.68 (define @t10 () (@list @t1 @t6)) % 0.43/0.68 (define @t11 () (tptp.sdtasdt0 @t1 @t6)) % 0.43/0.68 (define @t12 () (@var "W2" $$unsorted)) % 0.43/0.68 (define @t13 () (tptp.sdtpldt0 @t6 @t12)) % 0.43/0.68 (define @t14 () (tptp.aElement0 @t12)) % 0.43/0.68 (define @t15 () (and @t2 @t8 @t14)) % 0.43/0.68 (define @t16 () (@list @t1 @t6 @t12)) % 0.43/0.68 (define @t17 () (tptp.sdtasdt0 @t6 @t1)) % 0.43/0.68 (define @t18 () (tptp.sdtasdt0 @t1 @t12)) % 0.43/0.68 (define @t19 () (tptp.smndt0 tptp.sz10)) % 0.43/0.68 (define @t20 () (= @t6 tptp.sz00)) % 0.43/0.68 (define @t21 () (= @t1 tptp.sz00)) % 0.43/0.68 (define @t22 () (tptp.aSet0 @t1)) % 0.43/0.68 (define @t23 () (tptp.aElementOf0 @t6 @t1)) % 0.43/0.68 (define @t24 () (@list @t6)) % 0.43/0.68 (define @t25 () (tptp.aElementOf0 @t12 @t1)) % 0.43/0.68 (define @t26 () (tptp.aElementOf0 @t12 @t6)) % 0.43/0.68 (define @t27 () (@list @t12)) % 0.43/0.68 (define @t28 () (tptp.aSet0 @t6)) % 0.43/0.68 (define @t29 () (and @t22 @t28)) % 0.43/0.68 (define @t30 () (@var "W3" $$unsorted)) % 0.43/0.68 (define @t31 () (@var "W5" $$unsorted)) % 0.43/0.68 (define @t32 () (@var "W4" $$unsorted)) % 0.43/0.68 (define @t33 () (tptp.aElementOf0 @t30 @t12)) % 0.43/0.68 (define @t34 () (@list @t30)) % 0.43/0.68 (define @t35 () (tptp.aSet0 @t12)) % 0.43/0.68 (define @t36 () (tptp.sdtpldt1 @t1 @t6)) % 0.43/0.68 (define @t37 () (tptp.sdtasasdt0 @t1 @t6)) % 0.43/0.68 (define @t38 () (tptp.sdtasdt0 @t12 @t6)) % 0.43/0.68 (define @t39 () (tptp.aIdeal0 @t1)) % 0.43/0.68 (define @t40 () (and @t39 (tptp.aIdeal0 @t6))) % 0.43/0.68 (define @t41 () (tptp.aElement0 @t30)) % 0.43/0.68 (define @t42 () (@list @t12 @t30)) % 0.43/0.68 (define @t43 () (tptp.aNaturalNumber0 @t1)) % 0.43/0.68 (define @t44 () (tptp.sbrdtbr0 @t1)) % 0.43/0.68 (define @t45 () (not @t21)) % 0.43/0.68 (define @t46 () (tptp.slsdtgt0 @t1)) % 0.43/0.68 (define @t47 () (tptp.sdtasdt0 tptp.xc @t1)) % 0.43/0.68 (define @t48 () (tptp.aElement0 tptp.xc)) % 0.43/0.68 (define @t49 () (tptp.slsdtgt0 tptp.xb)) % 0.43/0.68 (define @t50 () (tptp.slsdtgt0 tptp.xa)) % 0.43/0.68 (define @t51 () (tptp.sdtpldt1 @t50 @t49)) % 0.43/0.68 (define @t52 () (tptp.aElementOf0 @t6 @t50)) % 0.43/0.68 (define @t53 () (exists (@list @t6 @t12) (and @t52 (tptp.aElementOf0 @t12 @t49) (= @t13 @t1)))) % 0.43/0.68 (define @t54 () (tptp.aElementOf0 @t1 tptp.xI)) % 0.43/0.68 (define @t55 () (tptp.sdtasdt0 tptp.xb @t6)) % 0.43/0.68 (define @t56 () (tptp.aElementOf0 @t1 @t50)) % 0.43/0.68 (define @t57 () (tptp.aElementOf0 @t17 tptp.xI)) % 0.43/0.68 (define @t58 () (forall @t24 (=> @t8 @t57))) % 0.43/0.68 (define @t59 () (tptp.aElementOf0 @t7 tptp.xI)) % 0.43/0.68 (define @t60 () (tptp.aElementOf0 @t6 tptp.xI)) % 0.43/0.68 (define @t61 () (forall @t24 (=> @t60 @t59))) % 0.43/0.68 (define @t62 () (and @t61 @t58)) % 0.43/0.68 (define @t63 () (=> @t54 @t62)) % 0.43/0.68 (define @t64 () (forall @t3 @t63)) % 0.43/0.68 (define @t65 () (tptp.sdtasdt0 tptp.xb @t1)) % 0.43/0.68 (define @t66 () (tptp.sdtasdt0 tptp.xa @t1)) % 0.43/0.68 (define @t67 () (tptp.aElementOf0 @t6 @t49)) % 0.43/0.68 (define @t68 () (tptp.sbrdtbr0 tptp.xu)) % 0.43/0.68 (define @t69 () (tptp.doDivides0 tptp.xu tptp.xb)) % 0.43/0.68 (define @t70 () (tptp.sdtasdt0 tptp.xu @t1)) % 0.43/0.68 (define @t71 () (exists @t3 (and @t2 (= @t70 tptp.xb)))) % 0.43/0.68 (define @t72 () (tptp.doDivides0 tptp.xu tptp.xa)) % 0.43/0.68 (define @t73 () (exists @t3 (and @t2 (= @t70 tptp.xa)))) % 0.43/0.68 (define @t74 () (= tptp.xr tptp.sz00)) % 0.43/0.68 (define @t75 () (tptp.sdtasdt0 tptp.xq tptp.xu)) % 0.43/0.68 (define @t76 () (tptp.smndt0 @t75)) % 0.43/0.68 (define @t77 () (tptp.aElementOf0 @t76 tptp.xI)) % 0.43/0.68 (define @t78 () (tptp.aElementOf0 tptp.xb tptp.xI)) % 0.43/0.68 (define @t79 () (exists @t10 (and @t56 @t67 (= @t7 tptp.xb)))) % 0.43/0.68 (define @t80 () (tptp.sdtpldt0 @t76 tptp.xb)) % 0.43/0.68 (define @t81 () (tptp.aElementOf0 tptp.xr tptp.xI)) % 0.43/0.68 (define @t82 () (= @t7 tptp.xr)) % 0.43/0.68 (define @t83 () (and @t56 @t67 @t82)) % 0.43/0.68 (define @t84 () (exists @t10 @t83)) % 0.43/0.68 (define @t85 () (or @t84 @t81)) % 0.43/0.68 (define @t86 () (not @t85)) % 0.43/0.68 (define @t87 () (@var "BOUND_VARIABLE_8463" $$unsorted)) % 0.43/0.68 (define @t88 () (or (not (tptp.aElement0 @t87)) (tptp.aElementOf0 (tptp.sdtasdt0 @t87 @t1) tptp.xI))) % 0.43/0.68 (define @t89 () (@var "BOUND_VARIABLE_8456" $$unsorted)) % 0.43/0.68 (define @t90 () (or (not (tptp.aElementOf0 @t89 tptp.xI)) (tptp.aElementOf0 (tptp.sdtpldt0 @t1 @t89) tptp.xI))) % 0.43/0.68 (define @t91 () (and @t90 @t88)) % 0.43/0.68 (define @t92 () (not @t54)) % 0.43/0.68 (define @t93 () (or @t92 @t91)) % 0.43/0.68 (define @t94 () (@list @t89 @t87)) % 0.43/0.68 (define @t95 () (forall @t94 @t93)) % 0.43/0.68 (define @t96 () (forall (@list @t87) @t88)) % 0.43/0.68 (define @t97 () (@list @t6)) % 0.43/0.68 (define @t98 () (forall @t94 @t88)) % 0.43/0.68 (define @t99 () (forall (@list @t89) @t90)) % 0.43/0.68 (define @t100 () (forall @t94 @t90)) % 0.43/0.68 (define @t101 () (and @t100 @t98)) % 0.43/0.68 (define @t102 () (forall @t94 @t91)) % 0.43/0.68 (define @t103 () (or @t92 @t102)) % 0.43/0.68 (define @t104 () (and (forall @t24 (or (not @t60) @t59)) (forall @t24 (or (not @t8) @t57)))) % 0.43/0.68 (define @t105 () (tptp.aElementOf0 @t80 tptp.xI)) % 0.43/0.68 (define @t106 () (not @t78)) % 0.43/0.68 (define @t107 () (or @t106 @t105)) % 0.43/0.68 (define @t108 () (and @t107 (or (not @t4) (tptp.aElementOf0 (tptp.sdtasdt0 tptp.sz10 @t76) tptp.xI)))) % 0.43/0.68 (define @t109 () (not @t77)) % 0.43/0.68 (define @t110 () (or @t109 @t108)) % 0.43/0.68 (define @t111 () (@list false false)) % 0.43/0.68 (define @t112 () (not @t82)) % 0.43/0.68 (define @t113 () (not @t67)) % 0.43/0.68 (define @t114 () (not @t56)) % 0.43/0.68 (define @t115 () (forall @t10 (not @t83))) % 0.43/0.68 (define @t116 () (not @t115)) % 0.43/0.68 (assume @p1 (forall @t3 (=> @t2 true))) % 0.43/0.68 (assume @p2 (tptp.aElement0 tptp.sz00)) % 0.43/0.68 (assume @p3 @t4) % 0.43/0.68 (assume @p4 (forall @t3 (=> @t2 (tptp.aElement0 @t5)))) % 0.43/0.68 (assume @p5 (forall @t10 (=> @t9 (tptp.aElement0 @t7)))) % 0.43/0.68 (assume @p6 (forall @t10 (=> @t9 (tptp.aElement0 @t11)))) % 0.43/0.68 (assume @p7 (forall @t10 (=> @t9 (= @t7 (tptp.sdtpldt0 @t6 @t1))))) % 0.43/0.68 (assume @p8 (forall @t16 (=> @t15 (= (tptp.sdtpldt0 @t7 @t12) (tptp.sdtpldt0 @t1 @t13))))) % 0.43/0.68 (assume @p9 (forall @t3 (=> @t2 (and (= (tptp.sdtpldt0 @t1 tptp.sz00) @t1) (= @t1 (tptp.sdtpldt0 tptp.sz00 @t1)))))) % 0.43/0.68 (assume @p10 (forall @t3 (=> @t2 (and (= (tptp.sdtpldt0 @t1 @t5) tptp.sz00) (= tptp.sz00 (tptp.sdtpldt0 @t5 @t1)))))) % 0.43/0.68 (assume @p11 (forall @t10 (=> @t9 (= @t11 @t17)))) % 0.43/0.68 (assume @p12 (forall @t16 (=> @t15 (= (tptp.sdtasdt0 @t11 @t12) (tptp.sdtasdt0 @t1 (tptp.sdtasdt0 @t6 @t12)))))) % 0.43/0.68 (assume @p13 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz10) @t1) (= @t1 (tptp.sdtasdt0 tptp.sz10 @t1)))))) % 0.43/0.68 (assume @p14 (forall @t16 (=> @t15 (and (= (tptp.sdtasdt0 @t1 @t13) (tptp.sdtpldt0 @t11 @t18)) (= (tptp.sdtasdt0 @t13 @t1) (tptp.sdtpldt0 @t17 (tptp.sdtasdt0 @t12 @t1))))))) % 0.43/0.68 (assume @p15 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t19 @t1) @t5) (= @t5 (tptp.sdtasdt0 @t1 @t19)))))) % 0.43/0.68 (assume @p16 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz00) tptp.sz00) (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 @t1)))))) % 0.43/0.68 (assume @p17 (forall @t10 (=> @t9 (=> (= @t11 tptp.sz00) (or @t21 @t20))))) % 0.43/0.68 (assume @p18 (not (= tptp.sz10 tptp.sz00))) % 0.43/0.68 (assume @p19 (forall @t3 (=> @t22 true))) % 0.43/0.68 (assume @p20 (forall @t3 (=> @t22 (forall @t24 (=> @t23 @t8))))) % 0.43/0.68 (assume @p21 (forall @t10 (=> @t29 (=> (and (forall @t27 (=> @t25 @t26)) (forall @t27 (=> @t26 @t25))) (= @t1 @t6))))) % 0.43/0.68 (assume @p22 (forall @t10 (=> @t29 (forall @t27 (= (= @t12 @t36) (and @t35 (forall @t34 (= @t33 (exists (@list @t32 @t31) (and (tptp.aElementOf0 @t32 @t1) (tptp.aElementOf0 @t31 @t6) (= (tptp.sdtpldt0 @t32 @t31) @t30))))))))))) % 0.43/0.68 (assume @p23 (forall @t10 (=> @t29 (forall @t27 (= (= @t12 @t37) (and @t35 (forall @t34 (= @t33 (and (tptp.aElementOf0 @t30 @t1) (tptp.aElementOf0 @t30 @t6)))))))))) % 0.43/0.68 (assume @p24 (forall @t3 (= @t39 (and @t22 (forall @t24 (=> @t23 (and (forall @t27 (=> @t25 (tptp.aElementOf0 @t13 @t1))) (forall @t27 (=> @t14 (tptp.aElementOf0 @t38 @t1)))))))))) % 0.43/0.68 (assume @p25 (forall @t10 (=> @t40 (tptp.aIdeal0 @t36)))) % 0.43/0.68 (assume @p26 (forall @t10 (=> @t40 (tptp.aIdeal0 @t37)))) % 0.43/0.68 (assume @p27 (forall @t16 (=> (and @t2 @t8 (tptp.aIdeal0 @t12)) (= (tptp.sdteqdtlpzmzozddtrp0 @t1 @t6 @t12) (tptp.aElementOf0 (tptp.sdtpldt0 @t1 (tptp.smndt0 @t6)) @t12))))) % 0.43/0.68 (assume @p28 (forall @t10 (=> @t40 (=> (forall @t27 (=> @t14 (tptp.aElementOf0 @t12 @t36))) (forall @t42 (=> (and @t14 @t41) (exists (@list @t32) (and (tptp.aElement0 @t32) (tptp.sdteqdtlpzmzozddtrp0 @t32 @t12 @t1) (tptp.sdteqdtlpzmzozddtrp0 @t32 @t30 @t6))))))))) % 0.43/0.68 (assume @p29 (forall @t3 (=> @t43 true))) % 0.43/0.68 (assume @p30 (forall @t3 (=> (and @t2 @t45) (tptp.aNaturalNumber0 @t44)))) % 0.43/0.68 (assume @p31 (forall @t10 (=> (and @t43 (tptp.aNaturalNumber0 @t6)) (=> (tptp.iLess0 @t1 @t6) true)))) % 0.43/0.68 (assume @p32 (forall @t10 (=> (and @t2 @t8 (not @t20)) (exists @t42 (and @t14 @t41 (= @t1 (tptp.sdtpldt0 @t38 @t30)) (=> (not (= @t30 tptp.sz00)) (tptp.iLess0 (tptp.sbrdtbr0 @t30) (tptp.sbrdtbr0 @t6)))))))) % 0.43/0.68 (assume @p33 (forall @t10 (=> @t9 (= (tptp.doDivides0 @t1 @t6) (exists @t27 (and @t14 (= @t18 @t6))))))) % 0.43/0.68 (assume @p34 (forall @t3 (=> @t2 (forall @t24 (= (tptp.aDivisorOf0 @t6 @t1) (and @t8 (tptp.doDivides0 @t6 @t1))))))) % 0.43/0.68 (assume @p35 (forall @t10 (=> @t9 (forall @t27 (= (tptp.aGcdOfAnd0 @t12 @t1 @t6) (and (tptp.aDivisorOf0 @t12 @t1) (tptp.aDivisorOf0 @t12 @t6) (forall @t34 (=> (and (tptp.aDivisorOf0 @t30 @t1) (tptp.aDivisorOf0 @t30 @t6)) (tptp.doDivides0 @t30 @t12))))))))) % 0.43/0.68 (assume @p36 (forall @t10 (=> @t9 (= (tptp.misRelativelyPrime0 @t1 @t6) (tptp.aGcdOfAnd0 tptp.sz10 @t1 @t6))))) % 0.43/0.68 (assume @p37 (forall @t3 (=> @t2 (forall @t24 (= (= @t6 @t46) (and @t28 (forall @t27 (= @t26 (exists @t34 (and @t41 (= (tptp.sdtasdt0 @t1 @t30) @t12))))))))))) % 0.43/0.68 (assume @p38 (forall @t3 (=> @t2 (tptp.aIdeal0 @t46)))) % 0.43/0.68 (assume @p39 (and (tptp.aElement0 tptp.xa) (tptp.aElement0 tptp.xb))) % 0.43/0.68 (assume @p40 (or (not (= tptp.xa tptp.sz00)) (not (= tptp.xb tptp.sz00)))) % 0.43/0.68 (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 @t24 (and @t8 (= @t11 tptp.xa))) (tptp.doDivides0 @t1 tptp.xa))) (tptp.aDivisorOf0 @t1 tptp.xa)) (or (exists @t24 (and @t8 (= @t11 tptp.xb))) (tptp.doDivides0 @t1 tptp.xb) (tptp.aDivisorOf0 @t1 tptp.xb))) (and (exists @t24 (and @t8 (= @t11 tptp.xc))) (tptp.doDivides0 @t1 tptp.xc)))) (tptp.aGcdOfAnd0 tptp.xc tptp.xa tptp.xb))) % 0.43/0.68 (assume @p42 (and (tptp.aSet0 tptp.xI) @t64 (tptp.aIdeal0 tptp.xI) (forall @t3 (= @t56 (exists @t24 (and @t8 (= (tptp.sdtasdt0 tptp.xa @t6) @t1))))) (forall @t3 (= (tptp.aElementOf0 @t1 @t49) (exists @t24 (and @t8 (= @t55 @t1))))) (forall @t3 (= @t54 @t53)) (= tptp.xI @t51))) % 0.43/0.68 (assume @p43 (and (exists @t3 (and @t2 (= @t66 tptp.sz00))) (tptp.aElementOf0 tptp.sz00 @t50) (exists @t3 (and @t2 (= @t66 tptp.xa))) (tptp.aElementOf0 tptp.xa @t50) (exists @t3 (and @t2 (= @t65 tptp.sz00))) (tptp.aElementOf0 tptp.sz00 @t49) (exists @t3 (and @t2 (= @t65 tptp.xb))) (tptp.aElementOf0 tptp.xb @t49))) % 0.43/0.68 (assume @p44 (exists @t3 (and (forall @t24 (= @t52 (exists @t27 (and @t14 (= (tptp.sdtasdt0 tptp.xa @t12) @t6))))) (forall @t24 (= @t67 (exists @t27 (and @t14 (= (tptp.sdtasdt0 tptp.xb @t12) @t6))))) @t53 (tptp.aElementOf0 @t1 @t51) @t45))) % 0.43/0.68 (assume @p45 (and (exists @t10 (and @t56 @t67 (= @t7 tptp.xu))) (tptp.aElementOf0 tptp.xu tptp.xI) (not (= tptp.xu tptp.sz00)) (forall @t3 (=> (and (or @t53 @t54) @t45) (not (tptp.iLess0 @t44 @t68)))))) % 0.43/0.68 (assume @p46 (not (and (or @t73 @t72 (tptp.aDivisorOf0 tptp.xu tptp.xa)) (or @t71 @t69 (tptp.aDivisorOf0 tptp.xu tptp.xb))))) % 0.43/0.68 (assume @p47 (exists @t10 (and @t2 @t8 (= tptp.xu (tptp.sdtpldt0 @t66 @t55))))) % 0.43/0.68 (assume @p48 (not (not (and @t73 @t72)))) % 0.43/0.68 (assume @p49 (not (or @t71 @t69))) % 0.43/0.68 (assume @p50 (and (tptp.aElement0 tptp.xq) (tptp.aElement0 tptp.xr) (= tptp.xb (tptp.sdtpldt0 @t75 tptp.xr)) (or @t74 (tptp.iLess0 (tptp.sbrdtbr0 tptp.xr) @t68)))) % 0.43/0.68 (assume @p51 (not @t74)) % 0.43/0.68 (assume @p52 (and (exists @t10 (and @t56 @t67 (= @t7 @t76))) @t77)) % 0.43/0.68 (assume @p53 (and @t79 @t79 @t78)) % 0.43/0.68 (assume @p54 (= tptp.xr @t80)) % 0.43/0.68 (assume @p55 @t86) % 0.43/0.68 (assume @p56 true) % 0.43/0.68 (step @p57 :rule evaluate :args ((= false true))) % 0.43/0.68 (step @p58 :rule quant-merge-prenex :args ((= (forall @t3 @t95) (forall (@list @t1 @t89 @t87) @t93)))) % 0.43/0.68 (step @p59 :rule alpha_equiv :args (@t96 (@list @t87) @t97)) % 0.43/0.68 (step @p60 :rule quant-unused-vars :args ((= @t98 @t96))) % 0.43/0.68 (step @p61 :rule trans :premises (@p60 @p59)) % 0.43/0.68 (step @p62 :rule alpha_equiv :args (@t99 (@list @t89) @t97)) % 0.43/0.68 (step @p63 :rule quant-unused-vars :args ((= @t100 @t99))) % 0.43/0.68 (step @p64 :rule trans :premises (@p63 @p62)) % 0.43/0.68 (step @p65 :rule nary_cong :premises (@p64 @p61) :args (@t101)) % 0.43/0.68 (step @p66 :rule quant-miniscope-and :args ((= @t102 @t101))) % 0.43/0.68 (step @p67 :rule trans :premises (@p66 @p65)) % 0.43/0.68 (step @p68 :rule refl :args (@t92)) % 0.43/0.68 (step @p69 :rule nary_cong :premises (@p68 @p67) :args (@t103)) % 0.43/0.68 (step @p70 :rule quant-miniscope-or :args ((= @t95 @t103))) % 0.43/0.68 (step @p71 :rule trans :premises (@p70 @p69)) % 0.43/0.68 (step @p72 :rule symm :premises (@p71)) % 0.43/0.68 (step @p73 :rule cong :premises (@p72) :args ((forall @t3 (or @t92 @t104)))) % 0.43/0.68 (step @p74 :rule trans :premises (@p73 @p58)) % 0.43/0.68 (step @p75 :rule bool-impl-elim :args (@t54 @t104)) % 0.43/0.68 (step @p76 :rule cong :premises (@p75) :args ((forall @t3 (=> @t54 @t104)))) % 0.43/0.68 (step @p77 :rule trans :premises (@p76 @p74)) % 0.43/0.68 (step @p78 :rule bool-impl-elim :args (@t8 @t57)) % 0.43/0.68 (step @p79 :rule cong :premises (@p78) :args (@t58)) % 0.43/0.68 (step @p80 :rule bool-impl-elim :args (@t60 @t59)) % 0.43/0.68 (step @p81 :rule cong :premises (@p80) :args (@t61)) % 0.43/0.68 (step @p82 :rule nary_cong :premises (@p81 @p79) :args (@t62)) % 0.43/0.68 (step @p83 :rule refl :args (@t54)) % 0.43/0.68 (step @p84 :rule cong :premises (@p83 @p82) :args (@t63)) % 0.43/0.68 (step @p85 :rule cong :premises (@p84) :args (@t64)) % 0.43/0.68 (step @p86 :rule trans :premises (@p85 @p77)) % 0.43/0.68 (step @p87 :rule and_elim :premises (@p42) :args (1)) % 0.43/0.68 (step @p88 :rule eq_resolve :premises (@p87 @p86)) % 0.43/0.68 (step @p89 :rule instantiate :premises (@p88) :args ((@list @t76 tptp.xb tptp.sz10))) % 0.43/0.68 (step @p90 :rule and_elim :premises (@p52) :args (1)) % 0.43/0.68 (step @p91 :rule cnf_or_pos :args (@t110)) % 0.43/0.68 (step @p92 :rule reordering :premises (@p91) :args ((or @t109 @t108 (not @t110)))) % 0.43/0.68 (step @p93 :rule chain_m_resolution :premises (@p92 @p90 @p89) :args (@t108 @t111 (@list @t77 @t110))) % 0.43/0.68 (step @p94 :rule cnf_and_pos :args (@t108 0)) % 0.43/0.68 (step @p95 :rule reordering :premises (@p94) :args ((or @t107 (not @t108)))) % 0.43/0.68 (step @p96 :rule chain_m_resolution :premises (@p95 @p93) :args (@t107 (@list false) (@list @t108))) % 0.43/0.68 (step @p97 :rule and_elim :premises (@p53) :args (2)) % 0.43/0.68 (step @p98 :rule cnf_or_pos :args (@t107)) % 0.43/0.68 (step @p99 :rule reordering :premises (@p98) :args ((or @t106 @t105 (not @t107)))) % 0.43/0.68 (step @p100 :rule chain_m_resolution :premises (@p99 @p97 @p96) :args (@t105 @t111 (@list @t78 @t107))) % 0.43/0.68 (step @p101 :rule true_intro :premises (@p100)) % 0.43/0.68 (step @p102 :rule refl :args (tptp.xI)) % 0.43/0.68 (step @p103 :rule cong :premises (@p54 @p102) :args (@t81)) % 0.43/0.68 (step @p104 :rule refl :args (@t81)) % 0.43/0.68 (step @p105 :rule aci_norm :args ((= (or @t114 (or @t113 @t112)) (or @t114 @t113 @t112)))) % 0.43/0.68 (step @p106 :rule bool-and-de-morgan :args (@t67 @t82 true)) % 0.43/0.68 (step @p107 :rule refl :args (@t114)) % 0.43/0.68 (step @p108 :rule nary_cong :premises (@p107 @p106) :args ((or @t114 (not (and @t67 @t82))))) % 0.43/0.68 (step @p109 :rule bool-and-de-morgan :args (@t56 @t67 (and @t82))) % 0.43/0.68 (step @p110 :rule trans :premises (@p109 @p108)) % 0.43/0.68 (step @p111 :rule trans :premises (@p110 @p105)) % 0.43/0.68 (step @p112 :rule cong :premises (@p111) :args (@t115)) % 0.43/0.68 (step @p113 :rule cong :premises (@p112) :args (@t116)) % 0.43/0.68 (step @p114 :rule exists-elim :args ((= @t84 @t116))) % 0.43/0.68 (step @p115 :rule trans :premises (@p114 @p113)) % 0.43/0.68 (step @p116 :rule nary_cong :premises (@p115 @p104) :args (@t85)) % 0.43/0.68 (step @p117 :rule cong :premises (@p116) :args (@t86)) % 0.43/0.68 (step @p118 :rule eq_resolve :premises (@p55 @p117)) % 0.43/0.68 (step @p119 :rule not_or_elim :premises (@p118) :args (1)) % 0.43/0.68 (step @p120 :rule false_intro :premises (@p119)) % 0.43/0.68 (step @p121 :rule symm :premises (@p120)) % 0.43/0.68 (step @p122 :rule trans :premises (@p121 @p103 @p101)) % 0.43/0.68 (step @p123 false :rule eq_resolve :premises (@p122 @p57)) % 0.43/0.68 ) % 0.43/0.68 % SZS output end Proof % 0.43/0.68 % cvc5 exiting %------------------------------------------------------------------------------