%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : RNG124+1 : TPTP v9.2.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n006.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 0.39s 0.62s % Output : Proof 0.39s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : RNG124+1 : TPTP v9.2.1. Released v4.0.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n006.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 14:08:49 EDT 2026 % 0.16/0.34 % CPUTime : % 0.30/0.50 %----Proving TF0_NAR, FOF, or CNF % 0.39/0.62 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.39/0.62 % SZS status Theorem % 0.39/0.62 % SZS output start Proof % 0.39/0.62 ( % 0.39/0.62 (declare-sort $$unsorted 0) % 0.39/0.62 (declare-const tptp.xq $$unsorted) % 0.39/0.62 (declare-const tptp.xu $$unsorted) % 0.39/0.62 (declare-const tptp.xc $$unsorted) % 0.39/0.62 (declare-const tptp.xa $$unsorted) % 0.39/0.62 (declare-const tptp.xI $$unsorted) % 0.39/0.62 (declare-const tptp.slsdtgt0 (-> $$unsorted $$unsorted)) % 0.39/0.62 (declare-const tptp.aDivisorOf0 (-> $$unsorted $$unsorted Bool)) % 0.39/0.62 (declare-const tptp.iLess0 (-> $$unsorted $$unsorted Bool)) % 0.39/0.62 (declare-const tptp.sbrdtbr0 (-> $$unsorted $$unsorted)) % 0.39/0.62 (declare-const tptp.aElement0 (-> $$unsorted Bool)) % 0.39/0.62 (declare-const tptp.sz00 $$unsorted) % 0.39/0.62 (declare-const tptp.sz10 $$unsorted) % 0.39/0.62 (declare-const tptp.aGcdOfAnd0 (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.39/0.62 (declare-const tptp.smndt0 (-> $$unsorted $$unsorted)) % 0.39/0.62 (declare-const tptp.xr $$unsorted) % 0.39/0.62 (declare-const tptp.sdtpldt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.39/0.62 (declare-const tptp.sdtasasdt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.39/0.62 (declare-const tptp.aIdeal0 (-> $$unsorted Bool)) % 0.39/0.62 (declare-const tptp.misRelativelyPrime0 (-> $$unsorted $$unsorted Bool)) % 0.39/0.62 (declare-const tptp.sdtasdt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.39/0.62 (declare-const tptp.doDivides0 (-> $$unsorted $$unsorted Bool)) % 0.39/0.62 (declare-const tptp.aSet0 (-> $$unsorted Bool)) % 0.39/0.62 (declare-const tptp.aElementOf0 (-> $$unsorted $$unsorted Bool)) % 0.39/0.62 (declare-const tptp.sdteqdtlpzmzozddtrp0 (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.39/0.62 (declare-const tptp.xb $$unsorted) % 0.39/0.62 (declare-const tptp.sdtpldt1 (-> $$unsorted $$unsorted $$unsorted)) % 0.39/0.62 (declare-const tptp.aNaturalNumber0 (-> $$unsorted Bool)) % 0.39/0.62 (define @t1 () (@var "W0" $$unsorted)) % 0.39/0.62 (define @t2 () (tptp.aElement0 @t1)) % 0.39/0.62 (define @t3 () (@list @t1)) % 0.39/0.62 (define @t4 () (tptp.smndt0 @t1)) % 0.39/0.62 (define @t5 () (@var "W1" $$unsorted)) % 0.39/0.62 (define @t6 () (tptp.sdtpldt0 @t1 @t5)) % 0.39/0.62 (define @t7 () (tptp.aElement0 @t5)) % 0.39/0.62 (define @t8 () (and @t2 @t7)) % 0.39/0.62 (define @t9 () (@list @t1 @t5)) % 0.39/0.62 (define @t10 () (tptp.sdtasdt0 @t1 @t5)) % 0.39/0.62 (define @t11 () (@var "W2" $$unsorted)) % 0.39/0.62 (define @t12 () (tptp.sdtpldt0 @t5 @t11)) % 0.39/0.62 (define @t13 () (tptp.aElement0 @t11)) % 0.39/0.62 (define @t14 () (and @t2 @t7 @t13)) % 0.39/0.62 (define @t15 () (@list @t1 @t5 @t11)) % 0.39/0.62 (define @t16 () (tptp.sdtasdt0 @t5 @t1)) % 0.39/0.62 (define @t17 () (tptp.sdtasdt0 @t1 @t11)) % 0.39/0.62 (define @t18 () (tptp.smndt0 tptp.sz10)) % 0.39/0.62 (define @t19 () (= @t5 tptp.sz00)) % 0.39/0.62 (define @t20 () (= @t1 tptp.sz00)) % 0.39/0.62 (define @t21 () (tptp.aSet0 @t1)) % 0.39/0.62 (define @t22 () (tptp.aElementOf0 @t5 @t1)) % 0.39/0.62 (define @t23 () (@list @t5)) % 0.39/0.62 (define @t24 () (tptp.aElementOf0 @t11 @t1)) % 0.39/0.62 (define @t25 () (tptp.aElementOf0 @t11 @t5)) % 0.39/0.62 (define @t26 () (@list @t11)) % 0.39/0.62 (define @t27 () (tptp.aSet0 @t5)) % 0.39/0.62 (define @t28 () (and @t21 @t27)) % 0.39/0.62 (define @t29 () (@var "W3" $$unsorted)) % 0.39/0.62 (define @t30 () (@var "W5" $$unsorted)) % 0.39/0.62 (define @t31 () (@var "W4" $$unsorted)) % 0.39/0.62 (define @t32 () (tptp.aElementOf0 @t29 @t11)) % 0.39/0.62 (define @t33 () (@list @t29)) % 0.39/0.62 (define @t34 () (tptp.aSet0 @t11)) % 0.39/0.62 (define @t35 () (tptp.sdtpldt1 @t1 @t5)) % 0.39/0.62 (define @t36 () (tptp.sdtasasdt0 @t1 @t5)) % 0.39/0.62 (define @t37 () (tptp.sdtasdt0 @t11 @t5)) % 0.39/0.62 (define @t38 () (tptp.aIdeal0 @t1)) % 0.39/0.62 (define @t39 () (and @t38 (tptp.aIdeal0 @t5))) % 0.39/0.62 (define @t40 () (tptp.aElement0 @t29)) % 0.39/0.62 (define @t41 () (@list @t11 @t29)) % 0.39/0.62 (define @t42 () (tptp.aNaturalNumber0 @t1)) % 0.39/0.62 (define @t43 () (tptp.sbrdtbr0 @t1)) % 0.39/0.62 (define @t44 () (not @t20)) % 0.39/0.62 (define @t45 () (tptp.slsdtgt0 @t1)) % 0.39/0.62 (define @t46 () (tptp.slsdtgt0 tptp.xb)) % 0.39/0.62 (define @t47 () (tptp.slsdtgt0 tptp.xa)) % 0.39/0.62 (define @t48 () (tptp.sdtpldt1 @t47 @t46)) % 0.39/0.62 (define @t49 () (tptp.sbrdtbr0 tptp.xu)) % 0.39/0.62 (define @t50 () (not (tptp.iLess0 @t43 @t49))) % 0.39/0.62 (define @t51 () (tptp.aElementOf0 @t1 tptp.xI)) % 0.39/0.62 (define @t52 () (and @t51 @t44)) % 0.39/0.62 (define @t53 () (forall @t3 (=> @t52 @t50))) % 0.39/0.62 (define @t54 () (tptp.iLess0 (tptp.sbrdtbr0 tptp.xr) @t49)) % 0.39/0.62 (define @t55 () (= tptp.xr tptp.sz00)) % 0.39/0.62 (define @t56 () (or @t55 @t54)) % 0.39/0.62 (define @t57 () (tptp.sdtasdt0 tptp.xq tptp.xu)) % 0.39/0.62 (define @t58 () (tptp.smndt0 @t57)) % 0.39/0.62 (define @t59 () (tptp.aElementOf0 tptp.xr tptp.xI)) % 0.39/0.62 (define @t60 () (not @t51)) % 0.39/0.62 (define @t61 () (or @t60 @t20 @t50)) % 0.39/0.62 (define @t62 () (= tptp.sz00 tptp.xr)) % 0.39/0.62 (define @t63 () (not @t54)) % 0.39/0.62 (define @t64 () (not @t59)) % 0.39/0.62 (define @t65 () (or @t64 @t62 @t63)) % 0.39/0.62 (define @t66 () (not @t65)) % 0.39/0.62 (define @t67 () (or @t64 @t55 @t63)) % 0.39/0.62 (define @t68 () (forall @t3 @t61)) % 0.39/0.62 (assume @p1 (forall @t3 (=> @t2 true))) % 0.39/0.62 (assume @p2 (tptp.aElement0 tptp.sz00)) % 0.39/0.62 (assume @p3 (tptp.aElement0 tptp.sz10)) % 0.39/0.62 (assume @p4 (forall @t3 (=> @t2 (tptp.aElement0 @t4)))) % 0.39/0.62 (assume @p5 (forall @t9 (=> @t8 (tptp.aElement0 @t6)))) % 0.39/0.62 (assume @p6 (forall @t9 (=> @t8 (tptp.aElement0 @t10)))) % 0.39/0.62 (assume @p7 (forall @t9 (=> @t8 (= @t6 (tptp.sdtpldt0 @t5 @t1))))) % 0.39/0.62 (assume @p8 (forall @t15 (=> @t14 (= (tptp.sdtpldt0 @t6 @t11) (tptp.sdtpldt0 @t1 @t12))))) % 0.39/0.62 (assume @p9 (forall @t3 (=> @t2 (and (= (tptp.sdtpldt0 @t1 tptp.sz00) @t1) (= @t1 (tptp.sdtpldt0 tptp.sz00 @t1)))))) % 0.39/0.62 (assume @p10 (forall @t3 (=> @t2 (and (= (tptp.sdtpldt0 @t1 @t4) tptp.sz00) (= tptp.sz00 (tptp.sdtpldt0 @t4 @t1)))))) % 0.39/0.62 (assume @p11 (forall @t9 (=> @t8 (= @t10 @t16)))) % 0.39/0.62 (assume @p12 (forall @t15 (=> @t14 (= (tptp.sdtasdt0 @t10 @t11) (tptp.sdtasdt0 @t1 (tptp.sdtasdt0 @t5 @t11)))))) % 0.39/0.62 (assume @p13 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz10) @t1) (= @t1 (tptp.sdtasdt0 tptp.sz10 @t1)))))) % 0.39/0.62 (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))))))) % 0.39/0.62 (assume @p15 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t18 @t1) @t4) (= @t4 (tptp.sdtasdt0 @t1 @t18)))))) % 0.39/0.62 (assume @p16 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz00) tptp.sz00) (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 @t1)))))) % 0.39/0.62 (assume @p17 (forall @t9 (=> @t8 (=> (= @t10 tptp.sz00) (or @t20 @t19))))) % 0.39/0.62 (assume @p18 (not (= tptp.sz10 tptp.sz00))) % 0.39/0.62 (assume @p19 (forall @t3 (=> @t21 true))) % 0.39/0.62 (assume @p20 (forall @t3 (=> @t21 (forall @t23 (=> @t22 @t7))))) % 0.39/0.62 (assume @p21 (forall @t9 (=> @t28 (=> (and (forall @t26 (=> @t24 @t25)) (forall @t26 (=> @t25 @t24))) (= @t1 @t5))))) % 0.39/0.62 (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))))))))))) % 0.39/0.62 (assume @p23 (forall @t9 (=> @t28 (forall @t26 (= (= @t11 @t36) (and @t34 (forall @t33 (= @t32 (and (tptp.aElementOf0 @t29 @t1) (tptp.aElementOf0 @t29 @t5)))))))))) % 0.39/0.62 (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)))))))))) % 0.39/0.62 (assume @p25 (forall @t9 (=> @t39 (tptp.aIdeal0 @t35)))) % 0.39/0.62 (assume @p26 (forall @t9 (=> @t39 (tptp.aIdeal0 @t36)))) % 0.39/0.62 (assume @p27 (forall @t15 (=> (and @t2 @t7 (tptp.aIdeal0 @t11)) (= (tptp.sdteqdtlpzmzozddtrp0 @t1 @t5 @t11) (tptp.aElementOf0 (tptp.sdtpldt0 @t1 (tptp.smndt0 @t5)) @t11))))) % 0.39/0.62 (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))))))))) % 0.39/0.62 (assume @p29 (forall @t3 (=> @t42 true))) % 0.39/0.62 (assume @p30 (forall @t3 (=> (and @t2 @t44) (tptp.aNaturalNumber0 @t43)))) % 0.39/0.62 (assume @p31 (forall @t9 (=> (and @t42 (tptp.aNaturalNumber0 @t5)) (=> (tptp.iLess0 @t1 @t5) true)))) % 0.39/0.62 (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)))))))) % 0.39/0.62 (assume @p33 (forall @t9 (=> @t8 (= (tptp.doDivides0 @t1 @t5) (exists @t26 (and @t13 (= @t17 @t5))))))) % 0.39/0.62 (assume @p34 (forall @t3 (=> @t2 (forall @t23 (= (tptp.aDivisorOf0 @t5 @t1) (and @t7 (tptp.doDivides0 @t5 @t1))))))) % 0.39/0.62 (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))))))))) % 0.39/0.62 (assume @p36 (forall @t9 (=> @t8 (= (tptp.misRelativelyPrime0 @t1 @t5) (tptp.aGcdOfAnd0 tptp.sz10 @t1 @t5))))) % 0.39/0.62 (assume @p37 (forall @t3 (=> @t2 (forall @t23 (= (= @t5 @t45) (and @t27 (forall @t26 (= @t25 (exists @t33 (and @t40 (= (tptp.sdtasdt0 @t1 @t29) @t11))))))))))) % 0.39/0.62 (assume @p38 (forall @t3 (=> @t2 (tptp.aIdeal0 @t45)))) % 0.39/0.62 (assume @p39 (and (tptp.aElement0 tptp.xa) (tptp.aElement0 tptp.xb))) % 0.39/0.62 (assume @p40 (or (not (= tptp.xa tptp.sz00)) (not (= tptp.xb tptp.sz00)))) % 0.39/0.62 (assume @p41 (tptp.aGcdOfAnd0 tptp.xc tptp.xa tptp.xb)) % 0.39/0.62 (assume @p42 (and (tptp.aIdeal0 tptp.xI) (= tptp.xI @t48))) % 0.39/0.62 (assume @p43 (and (tptp.aElementOf0 tptp.sz00 @t47) (tptp.aElementOf0 tptp.xa @t47) (tptp.aElementOf0 tptp.sz00 @t46) (tptp.aElementOf0 tptp.xb @t46))) % 0.39/0.62 (assume @p44 (exists @t3 (and (tptp.aElementOf0 @t1 @t48) @t44))) % 0.39/0.62 (assume @p45 (and (tptp.aElementOf0 tptp.xu tptp.xI) (not (= tptp.xu tptp.sz00)) @t53)) % 0.39/0.62 (assume @p46 (not (and (tptp.aDivisorOf0 tptp.xu tptp.xa) (tptp.aDivisorOf0 tptp.xu tptp.xb)))) % 0.39/0.62 (assume @p47 (exists @t9 (and @t2 @t7 (= tptp.xu (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xa @t1) (tptp.sdtasdt0 tptp.xb @t5)))))) % 0.39/0.62 (assume @p48 (not (not (tptp.doDivides0 tptp.xu tptp.xa)))) % 0.39/0.62 (assume @p49 (not (tptp.doDivides0 tptp.xu tptp.xb))) % 0.39/0.62 (assume @p50 (and (tptp.aElement0 tptp.xq) (tptp.aElement0 tptp.xr) (= tptp.xb (tptp.sdtpldt0 @t57 tptp.xr)) @t56)) % 0.39/0.62 (assume @p51 (not @t55)) % 0.39/0.62 (assume @p52 (tptp.aElementOf0 @t58 tptp.xI)) % 0.39/0.62 (assume @p53 (tptp.aElementOf0 tptp.xb tptp.xI)) % 0.39/0.62 (assume @p54 (= tptp.xr (tptp.sdtpldt0 @t58 tptp.xb))) % 0.39/0.62 (assume @p55 @t59) % 0.39/0.62 (assume @p56 (not false)) % 0.39/0.62 (assume @p57 true) % 0.39/0.62 (step @p58 :rule aci_norm :args ((= (or (or @t60 @t20) @t50) @t61))) % 0.39/0.62 (step @p59 :rule refl :args (@t50)) % 0.39/0.62 (step @p60 :rule bool-double-not-elim :args (@t20)) % 0.39/0.62 (step @p61 :rule refl :args (@t60)) % 0.39/0.62 (step @p62 :rule nary_cong :premises (@p61 @p60) :args ((or @t60 (not @t44)))) % 0.39/0.62 (step @p63 :rule bool-and-de-morgan :args (@t51 @t44 true)) % 0.39/0.62 (step @p64 :rule trans :premises (@p63 @p62)) % 0.39/0.62 (step @p65 :rule nary_cong :premises (@p64 @p59) :args ((or (not @t52) @t50))) % 0.39/0.62 (step @p66 :rule trans :premises (@p65 @p58)) % 0.39/0.62 (step @p67 :rule bool-impl-elim :args (@t52 @t50)) % 0.39/0.62 (step @p68 :rule trans :premises (@p67 @p66)) % 0.39/0.62 (step @p69 :rule cong :premises (@p68) :args (@t53)) % 0.39/0.62 (step @p70 :rule and_elim :premises (@p45) :args (2)) % 0.39/0.62 (step @p71 :rule eq_resolve :premises (@p70 @p69)) % 0.39/0.62 (step @p72 :rule symm :premises (@p51)) % 0.39/0.62 (step @p73 :rule refl :args (@t54)) % 0.39/0.62 (step @p74 :rule eq-symm :args (tptp.xr tptp.sz00)) % 0.39/0.62 (step @p75 :rule nary_cong :premises (@p74 @p73) :args (@t56)) % 0.39/0.62 (step @p76 :rule and_elim :premises (@p50) :args (3)) % 0.39/0.62 (step @p77 :rule eq_resolve :premises (@p76 @p75)) % 0.39/0.62 (step @p78 :rule reordering :premises (@p77) :args ((or @t54 @t62))) % 0.39/0.62 (step @p79 :rule chain_m_resolution :premises (@p78 @p72) :args (@t54 (@list true) (@list @t62))) % 0.39/0.62 (step @p80 :rule cnf_or_pos :args (@t65)) % 0.39/0.62 (step @p81 :rule reordering :premises (@p80) :args ((or @t62 @t63 @t64 @t66))) % 0.39/0.62 (step @p82 :rule chain_m_resolution :premises (@p81 @p72 @p79 @p55) :args (@t66 (@list true false false) (@list @t62 @t54 @t59))) % 0.39/0.62 (step @p83 :rule refl :args (@t63)) % 0.39/0.62 (step @p84 :rule refl :args (@t64)) % 0.39/0.62 (step @p85 :rule nary_cong :premises (@p84 @p74 @p83) :args (@t67)) % 0.39/0.62 (step @p86 :rule refl :args (@t68)) % 0.39/0.62 (step @p87 :rule cong :premises (@p86 @p85) :args ((=> @t68 @t67))) % 0.39/0.62 (assume-push @p95 @t68) % 0.39/0.62 (step @p89 :rule instantiate :premises (@p71) :args ((@list tptp.xr))) % 0.39/0.62 (step-pop @p96 :rule scope :premises (@p89)) % 0.39/0.62 (step @p90 :rule process_scope :premises (@p96) :args (@t67)) % 0.39/0.62 (step @p92 :rule eq_resolve :premises (@p90 @p87)) % 0.39/0.62 (step @p93 :rule implies_elim :premises (@p92)) % 0.39/0.62 (step @p94 false :rule chain_m_resolution :premises (@p93 @p82 @p71) :args (false (@list true false) (@list @t65 @t68))) % 0.39/0.62 ) % 0.39/0.62 % SZS output end Proof % 0.39/0.62 % cvc5 exiting %------------------------------------------------------------------------------