%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : RNG103+2 : 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 08:45:41 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 : RNG103+2 : 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 14:07:23 EDT 2026 % 0.16/0.35 % CPUTime : % 0.32/0.51 %----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 $$unsorted 0) % 0.39/0.62 (declare-const tptp.xv $$unsorted) % 0.39/0.62 (declare-const tptp.xu $$unsorted) % 0.39/0.62 (declare-const tptp.xx $$unsorted) % 0.39/0.62 (declare-const tptp.xy $$unsorted) % 0.39/0.62 (declare-const tptp.slsdtgt0 (-> $$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 $$unsorted)) % 0.39/0.62 (declare-const tptp.xc $$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.xz $$unsorted) % 0.39/0.62 (declare-const tptp.sdtpldt1 (-> $$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 () (and (= (tptp.sdtasdt0 @t1 @t12) (tptp.sdtpldt0 @t10 @t17)) (= (tptp.sdtasdt0 @t12 @t1) (tptp.sdtpldt0 @t16 (tptp.sdtasdt0 @t11 @t1))))) % 0.39/0.62 (define @t19 () (forall @t15 (=> @t14 @t18))) % 0.39/0.62 (define @t20 () (tptp.smndt0 tptp.sz10)) % 0.39/0.62 (define @t21 () (= @t5 tptp.sz00)) % 0.39/0.62 (define @t22 () (= @t1 tptp.sz00)) % 0.39/0.62 (define @t23 () (tptp.aSet0 @t1)) % 0.39/0.62 (define @t24 () (tptp.aElementOf0 @t5 @t1)) % 0.39/0.62 (define @t25 () (@list @t5)) % 0.39/0.62 (define @t26 () (tptp.aElementOf0 @t11 @t1)) % 0.39/0.62 (define @t27 () (tptp.aElementOf0 @t11 @t5)) % 0.39/0.62 (define @t28 () (@list @t11)) % 0.39/0.62 (define @t29 () (tptp.aSet0 @t5)) % 0.39/0.62 (define @t30 () (and @t23 @t29)) % 0.39/0.62 (define @t31 () (@var "W3" $$unsorted)) % 0.39/0.62 (define @t32 () (@var "W5" $$unsorted)) % 0.39/0.62 (define @t33 () (@var "W4" $$unsorted)) % 0.39/0.62 (define @t34 () (tptp.aElementOf0 @t31 @t11)) % 0.39/0.62 (define @t35 () (@list @t31)) % 0.39/0.62 (define @t36 () (tptp.aSet0 @t11)) % 0.39/0.62 (define @t37 () (tptp.sdtpldt1 @t1 @t5)) % 0.39/0.62 (define @t38 () (tptp.sdtasasdt0 @t1 @t5)) % 0.39/0.62 (define @t39 () (tptp.sdtasdt0 @t11 @t5)) % 0.39/0.62 (define @t40 () (tptp.aIdeal0 @t1)) % 0.39/0.62 (define @t41 () (and @t40 (tptp.aIdeal0 @t5))) % 0.39/0.62 (define @t42 () (tptp.aElement0 @t31)) % 0.39/0.62 (define @t43 () (@list @t11 @t31)) % 0.39/0.62 (define @t44 () (tptp.aNaturalNumber0 @t1)) % 0.39/0.62 (define @t45 () (tptp.aElement0 tptp.xc)) % 0.39/0.62 (define @t46 () (tptp.slsdtgt0 tptp.xc)) % 0.39/0.62 (define @t47 () (tptp.sdtasdt0 tptp.xc @t1)) % 0.39/0.62 (define @t48 () (tptp.sdtasdt0 tptp.xc tptp.xu)) % 0.39/0.62 (define @t49 () (tptp.aElement0 tptp.xu)) % 0.39/0.62 (define @t50 () (tptp.sdtasdt0 tptp.xc tptp.xv)) % 0.39/0.62 (define @t51 () (tptp.aElement0 tptp.xv)) % 0.39/0.62 (define @t52 () (tptp.sdtpldt0 tptp.xu tptp.xv)) % 0.39/0.62 (define @t53 () (tptp.sdtasdt0 tptp.xc @t52)) % 0.39/0.62 (define @t54 () (tptp.sdtpldt0 @t48 @t50)) % 0.39/0.62 (define @t55 () (= @t53 @t54)) % 0.39/0.62 (define @t56 () (= @t54 @t53)) % 0.39/0.62 (define @t57 () (and @t55 (= (tptp.sdtasdt0 @t52 tptp.xc) (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xu tptp.xc) (tptp.sdtasdt0 tptp.xv tptp.xc))))) % 0.39/0.62 (define @t58 () (not @t57)) % 0.39/0.62 (define @t59 () (not @t13)) % 0.39/0.62 (define @t60 () (not @t7)) % 0.39/0.62 (define @t61 () (not @t2)) % 0.39/0.62 (define @t62 () (or @t61 @t60 @t59)) % 0.39/0.62 (define @t63 () (not @t51)) % 0.39/0.62 (define @t64 () (not @t49)) % 0.39/0.62 (define @t65 () (not @t45)) % 0.39/0.62 (define @t66 () (or @t65 @t64 @t63 @t57)) % 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 @t19) % 0.39/0.62 (assume @p15 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t20 @t1) @t4) (= @t4 (tptp.sdtasdt0 @t1 @t20)))))) % 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 @t22 @t21))))) % 0.39/0.62 (assume @p18 (not (= tptp.sz10 tptp.sz00))) % 0.39/0.62 (assume @p19 (forall @t3 (=> @t23 true))) % 0.39/0.62 (assume @p20 (forall @t3 (=> @t23 (forall @t25 (=> @t24 @t7))))) % 0.39/0.62 (assume @p21 (forall @t9 (=> @t30 (=> (and (forall @t28 (=> @t26 @t27)) (forall @t28 (=> @t27 @t26))) (= @t1 @t5))))) % 0.39/0.62 (assume @p22 (forall @t9 (=> @t30 (forall @t28 (= (= @t11 @t37) (and @t36 (forall @t35 (= @t34 (exists (@list @t33 @t32) (and (tptp.aElementOf0 @t33 @t1) (tptp.aElementOf0 @t32 @t5) (= (tptp.sdtpldt0 @t33 @t32) @t31))))))))))) % 0.39/0.62 (assume @p23 (forall @t9 (=> @t30 (forall @t28 (= (= @t11 @t38) (and @t36 (forall @t35 (= @t34 (and (tptp.aElementOf0 @t31 @t1) (tptp.aElementOf0 @t31 @t5)))))))))) % 0.39/0.62 (assume @p24 (forall @t3 (= @t40 (and @t23 (forall @t25 (=> @t24 (and (forall @t28 (=> @t26 (tptp.aElementOf0 @t12 @t1))) (forall @t28 (=> @t13 (tptp.aElementOf0 @t39 @t1)))))))))) % 0.39/0.62 (assume @p25 (forall @t9 (=> @t41 (tptp.aIdeal0 @t37)))) % 0.39/0.62 (assume @p26 (forall @t9 (=> @t41 (tptp.aIdeal0 @t38)))) % 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 (=> @t41 (=> (forall @t28 (=> @t13 (tptp.aElementOf0 @t11 @t37))) (forall @t43 (=> (and @t13 @t42) (exists (@list @t33) (and (tptp.aElement0 @t33) (tptp.sdteqdtlpzmzozddtrp0 @t33 @t11 @t1) (tptp.sdteqdtlpzmzozddtrp0 @t33 @t31 @t5))))))))) % 0.39/0.62 (assume @p29 (forall @t3 (=> @t44 true))) % 0.39/0.62 (assume @p30 (forall @t3 (=> (and @t2 (not @t22)) (tptp.aNaturalNumber0 (tptp.sbrdtbr0 @t1))))) % 0.39/0.62 (assume @p31 (forall @t9 (=> (and @t44 (tptp.aNaturalNumber0 @t5)) (=> (tptp.iLess0 @t1 @t5) true)))) % 0.39/0.62 (assume @p32 (forall @t9 (=> (and @t2 @t7 (not @t21)) (exists @t43 (and @t13 @t42 (= @t1 (tptp.sdtpldt0 @t39 @t31)) (=> (not (= @t31 tptp.sz00)) (tptp.iLess0 (tptp.sbrdtbr0 @t31) (tptp.sbrdtbr0 @t5)))))))) % 0.39/0.62 (assume @p33 (forall @t9 (=> @t8 (= (tptp.doDivides0 @t1 @t5) (exists @t28 (and @t13 (= @t17 @t5))))))) % 0.39/0.62 (assume @p34 (forall @t3 (=> @t2 (forall @t25 (= (tptp.aDivisorOf0 @t5 @t1) (and @t7 (tptp.doDivides0 @t5 @t1))))))) % 0.39/0.62 (assume @p35 (forall @t9 (=> @t8 (forall @t28 (= (tptp.aGcdOfAnd0 @t11 @t1 @t5) (and (tptp.aDivisorOf0 @t11 @t1) (tptp.aDivisorOf0 @t11 @t5) (forall @t35 (=> (and (tptp.aDivisorOf0 @t31 @t1) (tptp.aDivisorOf0 @t31 @t5)) (tptp.doDivides0 @t31 @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 @t25 (= (= @t5 (tptp.slsdtgt0 @t1)) (and @t29 (forall @t28 (= @t27 (exists @t35 (and @t42 (= (tptp.sdtasdt0 @t1 @t31) @t11))))))))))) % 0.39/0.62 (assume @p38 @t45) % 0.39/0.62 (assume @p39 (and (exists @t3 (and @t2 (= @t47 tptp.xx))) (tptp.aElementOf0 tptp.xx @t46) (exists @t3 (and @t2 (= @t47 tptp.xy))) (tptp.aElementOf0 tptp.xy @t46) (tptp.aElement0 tptp.xz))) % 0.39/0.62 (assume @p40 (and @t49 (= @t48 tptp.xx))) % 0.39/0.62 (assume @p41 (and @t51 (= @t50 tptp.xy))) % 0.39/0.62 (assume @p42 (not (= (tptp.sdtpldt0 tptp.xx tptp.xy) @t53))) % 0.39/0.62 (assume @p43 true) % 0.39/0.62 (step @p44 :rule and_elim :premises (@p40) :args (0)) % 0.39/0.62 (step @p45 :rule and_elim :premises (@p41) :args (0)) % 0.39/0.62 (step @p46 :rule bool-eq-false :args (@t55)) % 0.39/0.62 (step @p47 :rule symm :premises (@p46)) % 0.39/0.62 (step @p48 :rule eq-symm :args (@t54 @t53)) % 0.39/0.62 (step @p49 :rule cong :premises (@p48) :args ((not @t56))) % 0.39/0.62 (step @p50 :rule bool-eq-false :args (@t56)) % 0.39/0.62 (step @p51 :rule trans :premises (@p50 @p49)) % 0.39/0.62 (step @p52 :rule trans :premises (@p51 @p47)) % 0.39/0.62 (step @p53 :rule false_intro :premises (@p42)) % 0.39/0.62 (step @p54 :rule refl :args (@t53)) % 0.39/0.62 (step @p55 :rule and_elim :premises (@p41) :args (1)) % 0.39/0.62 (step @p56 :rule and_elim :premises (@p40) :args (1)) % 0.39/0.62 (step @p57 :rule cong :premises (@p56 @p55) :args (@t54)) % 0.39/0.62 (step @p58 :rule cong :premises (@p57 @p54) :args (@t56)) % 0.39/0.62 (step @p59 :rule trans :premises (@p58 @p53)) % 0.39/0.62 (step @p60 :rule eq_resolve :premises (@p59 @p52)) % 0.39/0.62 (step @p61 :rule false_elim :premises (@p60)) % 0.39/0.62 (step @p62 :rule cnf_and_pos :args (@t57 0)) % 0.39/0.62 (step @p63 :rule reordering :premises (@p62) :args ((or @t55 @t58))) % 0.39/0.62 (step @p64 :rule chain_m_resolution :premises (@p63 @p61) :args (@t58 (@list true) (@list @t55))) % 0.39/0.62 (step @p65 :rule aci_norm :args ((= (or @t62 @t18) (or @t61 @t60 @t59 @t18)))) % 0.39/0.62 (step @p66 :rule refl :args (@t18)) % 0.39/0.62 (step @p67 :rule aci_norm :args ((= (or @t61 (or @t60 @t59)) @t62))) % 0.39/0.62 (step @p68 :rule bool-and-de-morgan :args (@t7 @t13 true)) % 0.39/0.62 (step @p69 :rule refl :args (@t61)) % 0.39/0.62 (step @p70 :rule nary_cong :premises (@p69 @p68) :args ((or @t61 (not (and @t7 @t13))))) % 0.39/0.62 (step @p71 :rule bool-and-de-morgan :args (@t2 @t7 (and @t13))) % 0.39/0.62 (step @p72 :rule trans :premises (@p71 @p70)) % 0.39/0.62 (step @p73 :rule trans :premises (@p72 @p67)) % 0.39/0.62 (step @p74 :rule nary_cong :premises (@p73 @p66) :args ((or (not @t14) @t18))) % 0.39/0.62 (step @p75 :rule trans :premises (@p74 @p65)) % 0.39/0.62 (step @p76 :rule bool-impl-elim :args (@t14 @t18)) % 0.39/0.62 (step @p77 :rule trans :premises (@p76 @p75)) % 0.39/0.62 (step @p78 :rule cong :premises (@p77) :args (@t19)) % 0.39/0.62 (step @p79 :rule eq_resolve :premises (@p14 @p78)) % 0.39/0.62 (step @p80 :rule instantiate :premises (@p79) :args ((@list tptp.xc tptp.xu tptp.xv))) % 0.39/0.62 (step @p81 :rule cnf_or_pos :args (@t66)) % 0.39/0.62 (step @p82 :rule reordering :premises (@p81) :args ((or @t65 @t64 @t63 @t57 (not @t66)))) % 0.39/0.62 (step @p83 false :rule chain_m_resolution :premises (@p82 @p80 @p64 @p45 @p44 @p38) :args (false (@list false true false false false) (@list @t66 @t57 @t51 @t49 @t45))) % 0.39/0.62 ) % 0.39/0.62 % SZS output end Proof % 0.39/0.62 % cvc5 exiting %------------------------------------------------------------------------------