%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM468+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 : n011.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 08:39:31 AM UTC 2026 % Result : Theorem 0.39s 0.62s % Output : Proof 0.36s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.13/0.12 % Problem : NUM468+2 : TPTP v9.2.1. Released v4.0.0. % 0.13/0.14 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.18/0.35 % Computer : n011.cluster.edu % 0.18/0.35 % Model : x86_64 x86_64 % 0.18/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.18/0.35 % Memory : 8042.1875MB % 0.18/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.18/0.35 % CPULimit : 300 % 0.18/0.35 % WCLimit : 300 % 0.18/0.35 % DateTime : Tue Jun 2 11:21:50 EDT 2026 % 0.18/0.35 % 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 $$unsorted 0) % 0.39/0.62 (declare-const tptp.xl $$unsorted) % 0.39/0.62 (declare-const tptp.xm $$unsorted) % 0.39/0.62 (declare-const tptp.iLess0 (-> $$unsorted $$unsorted Bool)) % 0.39/0.62 (declare-const tptp.sdtmndt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.39/0.62 (declare-const tptp.sdtasdt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.39/0.62 (declare-const tptp.sdtsldt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.39/0.62 (declare-const tptp.sdtlseqdt0 (-> $$unsorted $$unsorted Bool)) % 0.39/0.62 (declare-const tptp.sdtpldt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.39/0.62 (declare-const tptp.sz10 $$unsorted) % 0.39/0.62 (declare-const tptp.doDivides0 (-> $$unsorted $$unsorted Bool)) % 0.39/0.62 (declare-const tptp.sz00 $$unsorted) % 0.39/0.62 (declare-const tptp.xn $$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.aNaturalNumber0 @t1)) % 0.39/0.62 (define @t3 () (@list @t1)) % 0.39/0.62 (define @t4 () (@var "W1" $$unsorted)) % 0.39/0.62 (define @t5 () (tptp.sdtpldt0 @t1 @t4)) % 0.39/0.62 (define @t6 () (tptp.aNaturalNumber0 @t4)) % 0.39/0.62 (define @t7 () (and @t2 @t6)) % 0.39/0.62 (define @t8 () (@list @t1 @t4)) % 0.39/0.62 (define @t9 () (tptp.sdtasdt0 @t1 @t4)) % 0.39/0.62 (define @t10 () (tptp.sdtpldt0 @t4 @t1)) % 0.39/0.62 (define @t11 () (@var "W2" $$unsorted)) % 0.39/0.62 (define @t12 () (tptp.sdtpldt0 @t4 @t11)) % 0.39/0.62 (define @t13 () (tptp.aNaturalNumber0 @t11)) % 0.39/0.62 (define @t14 () (and @t2 @t6 @t13)) % 0.39/0.62 (define @t15 () (@list @t1 @t4 @t11)) % 0.39/0.62 (define @t16 () (tptp.sdtasdt0 @t4 @t1)) % 0.39/0.62 (define @t17 () (tptp.sdtasdt0 @t11 @t1)) % 0.39/0.62 (define @t18 () (tptp.sdtasdt0 @t1 @t11)) % 0.39/0.62 (define @t19 () (and (= (tptp.sdtasdt0 @t1 @t12) (tptp.sdtpldt0 @t9 @t18)) (= (tptp.sdtasdt0 @t12 @t1) (tptp.sdtpldt0 @t16 @t17)))) % 0.39/0.62 (define @t20 () (forall @t15 (=> @t14 @t19))) % 0.39/0.62 (define @t21 () (= @t4 @t11)) % 0.39/0.62 (define @t22 () (tptp.sdtpldt0 @t11 @t1)) % 0.39/0.62 (define @t23 () (tptp.sdtpldt0 @t1 @t11)) % 0.39/0.62 (define @t24 () (= @t16 @t17)) % 0.39/0.62 (define @t25 () (= @t9 @t18)) % 0.39/0.62 (define @t26 () (and @t6 @t13)) % 0.39/0.62 (define @t27 () (= @t1 tptp.sz00)) % 0.39/0.62 (define @t28 () (not @t27)) % 0.39/0.62 (define @t29 () (= @t4 tptp.sz00)) % 0.39/0.62 (define @t30 () (and @t13 (= @t23 @t4))) % 0.39/0.62 (define @t31 () (@list @t11)) % 0.39/0.62 (define @t32 () (tptp.sdtlseqdt0 @t1 @t4)) % 0.39/0.62 (define @t33 () (= @t1 @t4)) % 0.39/0.62 (define @t34 () (tptp.sdtlseqdt0 @t4 @t1)) % 0.39/0.62 (define @t35 () (tptp.sdtlseqdt0 @t4 @t11)) % 0.39/0.62 (define @t36 () (tptp.sdtpldt0 @t11 @t4)) % 0.39/0.62 (define @t37 () (and (not @t33) @t32)) % 0.39/0.62 (define @t38 () (tptp.iLess0 @t1 @t4)) % 0.39/0.62 (define @t39 () (and @t13 (= @t4 @t18))) % 0.39/0.62 (define @t40 () (tptp.doDivides0 @t1 @t4)) % 0.39/0.62 (define @t41 () (tptp.aNaturalNumber0 tptp.xl)) % 0.39/0.62 (define @t42 () (tptp.sdtasdt0 tptp.xl @t1)) % 0.39/0.62 (define @t43 () (tptp.sdtsldt0 tptp.xn tptp.xl)) % 0.39/0.62 (define @t44 () (tptp.sdtsldt0 tptp.xm tptp.xl)) % 0.39/0.62 (define @t45 () (tptp.sdtpldt0 @t44 @t43)) % 0.39/0.62 (define @t46 () (tptp.sdtasdt0 tptp.xl @t45)) % 0.39/0.62 (define @t47 () (tptp.sdtasdt0 tptp.xl @t43)) % 0.39/0.62 (define @t48 () (tptp.aNaturalNumber0 @t43)) % 0.39/0.62 (define @t49 () (tptp.sdtasdt0 tptp.xl @t44)) % 0.39/0.62 (define @t50 () (tptp.aNaturalNumber0 @t44)) % 0.39/0.62 (define @t51 () (=> (and @t50 (= tptp.xm @t49)) (=> (and @t48 (= tptp.xn @t47)) (= (tptp.sdtpldt0 tptp.xm tptp.xn) @t46)))) % 0.39/0.62 (define @t52 () (not (= tptp.xl tptp.sz00))) % 0.39/0.62 (define @t53 () (=> @t52 @t51)) % 0.39/0.62 (define @t54 () (not @t53)) % 0.39/0.62 (define @t55 () (tptp.sdtpldt0 @t49 @t47)) % 0.39/0.62 (define @t56 () (= @t46 @t55)) % 0.39/0.62 (define @t57 () (= @t55 @t46)) % 0.39/0.62 (define @t58 () (and @t56 (= (tptp.sdtasdt0 @t45 tptp.xl) (tptp.sdtpldt0 (tptp.sdtasdt0 @t44 tptp.xl) (tptp.sdtasdt0 @t43 tptp.xl))))) % 0.39/0.62 (define @t59 () (not @t58)) % 0.39/0.62 (define @t60 () (not @t13)) % 0.39/0.62 (define @t61 () (not @t6)) % 0.39/0.62 (define @t62 () (not @t2)) % 0.39/0.62 (define @t63 () (or @t62 @t61 @t60)) % 0.39/0.62 (define @t64 () (not @t48)) % 0.39/0.62 (define @t65 () (not @t50)) % 0.39/0.62 (define @t66 () (not @t41)) % 0.39/0.62 (define @t67 () (or @t66 @t65 @t64 @t58)) % 0.39/0.62 (assume @p1 (forall @t3 (=> @t2 true))) % 0.39/0.62 (assume @p2 (tptp.aNaturalNumber0 tptp.sz00)) % 0.39/0.62 (assume @p3 (and (tptp.aNaturalNumber0 tptp.sz10) (not (= tptp.sz10 tptp.sz00)))) % 0.39/0.62 (assume @p4 (forall @t8 (=> @t7 (tptp.aNaturalNumber0 @t5)))) % 0.39/0.62 (assume @p5 (forall @t8 (=> @t7 (tptp.aNaturalNumber0 @t9)))) % 0.39/0.62 (assume @p6 (forall @t8 (=> @t7 (= @t5 @t10)))) % 0.39/0.62 (assume @p7 (forall @t15 (=> @t14 (= (tptp.sdtpldt0 @t5 @t11) (tptp.sdtpldt0 @t1 @t12))))) % 0.39/0.62 (assume @p8 (forall @t3 (=> @t2 (and (= (tptp.sdtpldt0 @t1 tptp.sz00) @t1) (= @t1 (tptp.sdtpldt0 tptp.sz00 @t1)))))) % 0.39/0.62 (assume @p9 (forall @t8 (=> @t7 (= @t9 @t16)))) % 0.39/0.62 (assume @p10 (forall @t15 (=> @t14 (= (tptp.sdtasdt0 @t9 @t11) (tptp.sdtasdt0 @t1 (tptp.sdtasdt0 @t4 @t11)))))) % 0.39/0.62 (assume @p11 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz10) @t1) (= @t1 (tptp.sdtasdt0 tptp.sz10 @t1)))))) % 0.39/0.62 (assume @p12 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz00) tptp.sz00) (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 @t1)))))) % 0.39/0.62 (assume @p13 @t20) % 0.39/0.62 (assume @p14 (forall @t15 (=> @t14 (=> (or (= @t5 @t23) (= @t10 @t22)) @t21)))) % 0.39/0.62 (assume @p15 (forall @t3 (=> @t2 (=> @t28 (forall (@list @t4 @t11) (=> @t26 (=> (or @t25 @t24) @t21))))))) % 0.39/0.62 (assume @p16 (forall @t8 (=> @t7 (=> (= @t5 tptp.sz00) (and @t27 @t29))))) % 0.39/0.62 (assume @p17 (forall @t8 (=> @t7 (=> (= @t9 tptp.sz00) (or @t27 @t29))))) % 0.39/0.62 (assume @p18 (forall @t8 (=> @t7 (= @t32 (exists @t31 @t30))))) % 0.39/0.62 (assume @p19 (forall @t8 (=> @t7 (=> @t32 (forall @t31 (= (= @t11 (tptp.sdtmndt0 @t4 @t1)) @t30)))))) % 0.39/0.62 (assume @p20 (forall @t3 (=> @t2 (tptp.sdtlseqdt0 @t1 @t1)))) % 0.39/0.62 (assume @p21 (forall @t8 (=> @t7 (=> (and @t32 @t34) @t33)))) % 0.39/0.62 (assume @p22 (forall @t15 (=> @t14 (=> (and @t32 @t35) (tptp.sdtlseqdt0 @t1 @t11))))) % 0.39/0.62 (assume @p23 (forall @t8 (=> @t7 (or @t32 (and (not (= @t4 @t1)) @t34))))) % 0.39/0.62 (assume @p24 (forall @t8 (=> @t7 (=> @t37 (forall @t31 (=> @t13 (and (not (= @t22 @t36)) (tptp.sdtlseqdt0 @t22 @t36) (not (= @t23 @t12)) (tptp.sdtlseqdt0 @t23 @t12)))))))) % 0.39/0.62 (assume @p25 (forall @t15 (=> @t14 (=> (and @t28 (not @t21) @t35) (and (not @t25) (tptp.sdtlseqdt0 @t9 @t18) (not @t24) (tptp.sdtlseqdt0 @t16 @t17)))))) % 0.39/0.62 (assume @p26 (forall @t3 (=> @t2 (or @t27 (= @t1 tptp.sz10) (and (not (= tptp.sz10 @t1)) (tptp.sdtlseqdt0 tptp.sz10 @t1)))))) % 0.39/0.62 (assume @p27 (forall @t8 (=> @t7 (=> @t28 (tptp.sdtlseqdt0 @t4 @t16))))) % 0.39/0.62 (assume @p28 (forall @t8 (=> @t7 (=> @t38 true)))) % 0.39/0.62 (assume @p29 (forall @t8 (=> @t7 (=> @t37 @t38)))) % 0.39/0.62 (assume @p30 (forall @t8 (=> @t7 (= @t40 (exists @t31 @t39))))) % 0.39/0.62 (assume @p31 (forall @t8 (=> @t7 (=> (and @t28 @t40) (forall @t31 (= (= @t11 (tptp.sdtsldt0 @t4 @t1)) @t39)))))) % 0.39/0.62 (assume @p32 (forall @t15 (=> @t14 (=> (and @t40 (tptp.doDivides0 @t4 @t11)) (tptp.doDivides0 @t1 @t11))))) % 0.39/0.62 (assume @p33 (and @t41 (tptp.aNaturalNumber0 tptp.xm) (tptp.aNaturalNumber0 tptp.xn))) % 0.39/0.62 (assume @p34 (and (exists @t3 (and @t2 (= tptp.xm @t42))) (tptp.doDivides0 tptp.xl tptp.xm) (exists @t3 (and @t2 (= tptp.xn @t42))) (tptp.doDivides0 tptp.xl tptp.xn))) % 0.39/0.62 (assume @p35 @t54) % 0.39/0.62 (assume @p36 true) % 0.39/0.62 (step @p37 :rule and_elim :premises (@p33) :args (0)) % 0.39/0.62 (step @p38 :rule refl :args (@t51)) % 0.39/0.62 (step @p39 :rule eq-symm :args (tptp.xl tptp.sz00)) % 0.39/0.62 (step @p40 :rule cong :premises (@p39) :args (@t52)) % 0.39/0.62 (step @p41 :rule cong :premises (@p40 @p38) :args (@t53)) % 0.39/0.62 (step @p42 :rule cong :premises (@p41) :args (@t54)) % 0.39/0.62 (step @p43 :rule eq_resolve :premises (@p35 @p42)) % 0.39/0.62 (step @p44 :rule not_implies_elim2 :premises (@p43)) % 0.39/0.62 (step @p45 :rule not_implies_elim1 :premises (@p44)) % 0.39/0.62 (step @p46 :rule and_elim :premises (@p45) :args (0)) % 0.39/0.62 (step @p47 :rule not_implies_elim2 :premises (@p44)) % 0.39/0.62 (step @p48 :rule not_implies_elim1 :premises (@p47)) % 0.39/0.62 (step @p49 :rule and_elim :premises (@p48) :args (0)) % 0.39/0.62 (step @p50 :rule bool-eq-false :args (@t56)) % 0.39/0.62 (step @p51 :rule symm :premises (@p50)) % 0.39/0.62 (step @p52 :rule eq-symm :args (@t55 @t46)) % 0.39/0.62 (step @p53 :rule cong :premises (@p52) :args ((not @t57))) % 0.39/0.62 (step @p54 :rule bool-eq-false :args (@t57)) % 0.39/0.62 (step @p55 :rule trans :premises (@p54 @p53)) % 0.39/0.62 (step @p56 :rule trans :premises (@p55 @p51)) % 0.39/0.62 (step @p57 :rule not_implies_elim2 :premises (@p47)) % 0.39/0.62 (step @p58 :rule false_intro :premises (@p57)) % 0.39/0.62 (step @p59 :rule refl :args (@t46)) % 0.39/0.62 (step @p60 :rule and_elim :premises (@p48) :args (1)) % 0.39/0.62 (step @p61 :rule symm :premises (@p60)) % 0.39/0.62 (step @p62 :rule and_elim :premises (@p45) :args (1)) % 0.39/0.62 (step @p63 :rule symm :premises (@p62)) % 0.39/0.62 (step @p64 :rule cong :premises (@p63 @p61) :args (@t55)) % 0.39/0.62 (step @p65 :rule cong :premises (@p64 @p59) :args (@t57)) % 0.39/0.62 (step @p66 :rule trans :premises (@p65 @p58)) % 0.39/0.62 (step @p67 :rule eq_resolve :premises (@p66 @p56)) % 0.36/0.63 (step @p68 :rule false_elim :premises (@p67)) % 0.36/0.63 (step @p69 :rule cnf_and_pos :args (@t58 0)) % 0.36/0.63 (step @p70 :rule reordering :premises (@p69) :args ((or @t56 @t59))) % 0.36/0.63 (step @p71 :rule chain_m_resolution :premises (@p70 @p68) :args (@t59 (@list true) (@list @t56))) % 0.36/0.63 (step @p72 :rule aci_norm :args ((= (or @t63 @t19) (or @t62 @t61 @t60 @t19)))) % 0.36/0.63 (step @p73 :rule refl :args (@t19)) % 0.36/0.63 (step @p74 :rule aci_norm :args ((= (or @t62 (or @t61 @t60)) @t63))) % 0.36/0.63 (step @p75 :rule bool-and-de-morgan :args (@t6 @t13 true)) % 0.36/0.63 (step @p76 :rule refl :args (@t62)) % 0.36/0.63 (step @p77 :rule nary_cong :premises (@p76 @p75) :args ((or @t62 (not @t26)))) % 0.36/0.63 (step @p78 :rule bool-and-de-morgan :args (@t2 @t6 (and @t13))) % 0.36/0.63 (step @p79 :rule trans :premises (@p78 @p77)) % 0.36/0.63 (step @p80 :rule trans :premises (@p79 @p74)) % 0.36/0.63 (step @p81 :rule nary_cong :premises (@p80 @p73) :args ((or (not @t14) @t19))) % 0.36/0.63 (step @p82 :rule trans :premises (@p81 @p72)) % 0.36/0.63 (step @p83 :rule bool-impl-elim :args (@t14 @t19)) % 0.36/0.63 (step @p84 :rule trans :premises (@p83 @p82)) % 0.36/0.63 (step @p85 :rule cong :premises (@p84) :args (@t20)) % 0.36/0.63 (step @p86 :rule eq_resolve :premises (@p13 @p85)) % 0.36/0.63 (step @p87 :rule instantiate :premises (@p86) :args ((@list tptp.xl @t44 @t43))) % 0.36/0.63 (step @p88 :rule cnf_or_pos :args (@t67)) % 0.36/0.63 (step @p89 :rule reordering :premises (@p88) :args ((or @t66 @t65 @t64 @t58 (not @t67)))) % 0.36/0.63 (step @p90 false :rule chain_m_resolution :premises (@p89 @p87 @p71 @p49 @p46 @p37) :args (false (@list false true false false false) (@list @t67 @t58 @t48 @t50 @t41))) % 0.36/0.63 ) % 0.36/0.63 % SZS output end Proof % 0.36/0.63 % cvc5 exiting %------------------------------------------------------------------------------