%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM475+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 : n025.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 08:39:32 AM UTC 2026 % Result : Theorem 2.53s 2.75s % Output : Proof 2.53s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM475+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 % 0.19/0.35 % Computer : n025.cluster.edu % 0.19/0.35 % Model : x86_64 x86_64 % 0.19/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.19/0.35 % Memory : 8042.1875MB % 0.19/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.19/0.35 % CPULimit : 300 % 0.19/0.35 % WCLimit : 300 % 0.19/0.35 % DateTime : Tue Jun 2 11:22:46 EDT 2026 % 0.19/0.35 % CPUTime : % 0.31/0.51 %----Proving TF0_NAR, FOF, or CNF % 2.53/2.75 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 2.53/2.75 % SZS status Theorem % 2.53/2.75 % SZS output start Proof % 2.53/2.75 ( % 2.53/2.75 (declare-sort $$unsorted 0) % 2.53/2.75 (declare-const tptp.xq $$unsorted) % 2.53/2.75 (declare-const tptp.xp $$unsorted) % 2.53/2.75 (declare-const tptp.xr $$unsorted) % 2.53/2.75 (declare-const tptp.sz10 $$unsorted) % 2.53/2.75 (declare-const tptp.xl $$unsorted) % 2.53/2.75 (declare-const tptp.sdtpldt0 (-> $$unsorted $$unsorted $$unsorted)) % 2.53/2.75 (declare-const tptp.sdtlseqdt0 (-> $$unsorted $$unsorted Bool)) % 2.53/2.75 (declare-const tptp.aNaturalNumber0 (-> $$unsorted Bool)) % 2.53/2.75 (declare-const tptp.sz00 $$unsorted) % 2.53/2.75 (declare-const tptp.sdtsldt0 (-> $$unsorted $$unsorted $$unsorted)) % 2.53/2.75 (declare-const tptp.sdtasdt0 (-> $$unsorted $$unsorted $$unsorted)) % 2.53/2.75 (declare-const tptp.sdtmndt0 (-> $$unsorted $$unsorted $$unsorted)) % 2.53/2.75 (declare-const tptp.xn $$unsorted) % 2.53/2.75 (declare-const tptp.iLess0 (-> $$unsorted $$unsorted Bool)) % 2.53/2.75 (declare-const tptp.doDivides0 (-> $$unsorted $$unsorted Bool)) % 2.53/2.75 (declare-const tptp.xm $$unsorted) % 2.53/2.75 (define @t1 () (@var "W0" $$unsorted)) % 2.53/2.75 (define @t2 () (tptp.aNaturalNumber0 @t1)) % 2.53/2.75 (define @t3 () (@list @t1)) % 2.53/2.75 (define @t4 () (@var "W1" $$unsorted)) % 2.53/2.75 (define @t5 () (tptp.sdtpldt0 @t1 @t4)) % 2.53/2.75 (define @t6 () (tptp.aNaturalNumber0 @t4)) % 2.53/2.75 (define @t7 () (and @t2 @t6)) % 2.53/2.75 (define @t8 () (@list @t1 @t4)) % 2.53/2.75 (define @t9 () (tptp.sdtasdt0 @t1 @t4)) % 2.53/2.75 (define @t10 () (tptp.aNaturalNumber0 @t9)) % 2.53/2.75 (define @t11 () (forall @t8 (=> @t7 @t10))) % 2.53/2.75 (define @t12 () (tptp.sdtpldt0 @t4 @t1)) % 2.53/2.75 (define @t13 () (@var "W2" $$unsorted)) % 2.53/2.75 (define @t14 () (tptp.sdtpldt0 @t4 @t13)) % 2.53/2.75 (define @t15 () (tptp.aNaturalNumber0 @t13)) % 2.53/2.75 (define @t16 () (and @t2 @t6 @t15)) % 2.53/2.75 (define @t17 () (@list @t1 @t4 @t13)) % 2.53/2.75 (define @t18 () (tptp.sdtasdt0 @t4 @t1)) % 2.53/2.75 (define @t19 () (tptp.sdtasdt0 @t13 @t1)) % 2.53/2.75 (define @t20 () (tptp.sdtasdt0 @t1 @t13)) % 2.53/2.75 (define @t21 () (= @t4 @t13)) % 2.53/2.75 (define @t22 () (tptp.sdtpldt0 @t13 @t1)) % 2.53/2.75 (define @t23 () (= @t12 @t22)) % 2.53/2.75 (define @t24 () (tptp.sdtpldt0 @t1 @t13)) % 2.53/2.75 (define @t25 () (= @t5 @t24)) % 2.53/2.75 (define @t26 () (or @t25 @t23)) % 2.53/2.75 (define @t27 () (=> @t26 @t21)) % 2.53/2.75 (define @t28 () (forall @t17 (=> @t16 @t27))) % 2.53/2.75 (define @t29 () (= @t18 @t19)) % 2.53/2.75 (define @t30 () (= @t9 @t20)) % 2.53/2.75 (define @t31 () (and @t6 @t15)) % 2.53/2.75 (define @t32 () (= @t1 tptp.sz00)) % 2.53/2.75 (define @t33 () (not @t32)) % 2.53/2.75 (define @t34 () (= @t4 tptp.sz00)) % 2.53/2.75 (define @t35 () (and @t15 (= @t24 @t4))) % 2.53/2.75 (define @t36 () (@list @t13)) % 2.53/2.75 (define @t37 () (tptp.sdtlseqdt0 @t1 @t4)) % 2.53/2.75 (define @t38 () (= @t1 @t4)) % 2.53/2.75 (define @t39 () (tptp.sdtlseqdt0 @t4 @t1)) % 2.53/2.75 (define @t40 () (tptp.sdtlseqdt0 @t4 @t13)) % 2.53/2.75 (define @t41 () (tptp.sdtpldt0 @t13 @t4)) % 2.53/2.75 (define @t42 () (and (not @t38) @t37)) % 2.53/2.75 (define @t43 () (tptp.iLess0 @t1 @t4)) % 2.53/2.75 (define @t44 () (and @t15 (= @t4 @t20))) % 2.53/2.75 (define @t45 () (tptp.doDivides0 @t1 @t4)) % 2.53/2.75 (define @t46 () (tptp.doDivides0 @t1 @t13)) % 2.53/2.75 (define @t47 () (tptp.aNaturalNumber0 tptp.xn)) % 2.53/2.75 (define @t48 () (tptp.aNaturalNumber0 tptp.xl)) % 2.53/2.75 (define @t49 () (tptp.sdtpldt0 tptp.xm tptp.xn)) % 2.53/2.75 (define @t50 () (tptp.sdtasdt0 tptp.xl @t1)) % 2.53/2.75 (define @t51 () (tptp.sdtasdt0 tptp.xl tptp.xp)) % 2.53/2.75 (define @t52 () (tptp.aNaturalNumber0 tptp.xr)) % 2.53/2.75 (define @t53 () (tptp.sdtpldt0 @t51 tptp.xn)) % 2.53/2.75 (define @t54 () (tptp.sdtasdt0 tptp.xl tptp.xr)) % 2.53/2.75 (define @t55 () (tptp.sdtpldt0 @t51 @t54)) % 2.53/2.75 (define @t56 () (= @t55 @t53)) % 2.53/2.75 (define @t57 () (= tptp.xn @t54)) % 2.53/2.75 (define @t58 () (tptp.aNaturalNumber0 @t51)) % 2.53/2.75 (define @t59 () (not @t6)) % 2.53/2.75 (define @t60 () (not @t2)) % 2.53/2.75 (define @t61 () (tptp.aNaturalNumber0 @t54)) % 2.53/2.75 (define @t62 () (not @t52)) % 2.53/2.75 (define @t63 () (not @t48)) % 2.53/2.75 (define @t64 () (or @t63 @t62 @t61)) % 2.53/2.75 (define @t65 () (tptp.sdtpldt0 tptp.xn @t51)) % 2.53/2.75 (define @t66 () (tptp.sdtpldt0 @t54 @t51)) % 2.53/2.75 (define @t67 () (not @t56)) % 2.53/2.75 (define @t68 () (and @t67 (not (= @t66 @t65)))) % 2.53/2.75 (define @t69 () (not @t68)) % 2.53/2.75 (define @t70 () (@list false)) % 2.53/2.75 (define @t71 () (and (not @t25) (not @t23))) % 2.53/2.75 (define @t72 () (not @t15)) % 2.53/2.75 (define @t73 () (or @t60 @t59 @t72 @t71 @t21)) % 2.53/2.75 (define @t74 () (or @t60 @t59 @t72)) % 2.53/2.75 (define @t75 () (not (= @t65 @t66))) % 2.53/2.75 (define @t76 () (not (= @t53 @t55))) % 2.53/2.75 (define @t77 () (and @t76 @t75)) % 2.53/2.75 (define @t78 () (not @t61)) % 2.53/2.75 (define @t79 () (not @t47)) % 2.53/2.75 (define @t80 () (not @t58)) % 2.53/2.75 (define @t81 () (or @t80 @t79 @t78 @t77 @t57)) % 2.53/2.75 (define @t82 () (forall @t17 @t73)) % 2.53/2.75 (define @t83 () (or @t80 @t79 @t78 @t68 @t57)) % 2.53/2.75 (assume @p1 (forall @t3 (=> @t2 true))) % 2.53/2.75 (assume @p2 (tptp.aNaturalNumber0 tptp.sz00)) % 2.53/2.75 (assume @p3 (and (tptp.aNaturalNumber0 tptp.sz10) (not (= tptp.sz10 tptp.sz00)))) % 2.53/2.75 (assume @p4 (forall @t8 (=> @t7 (tptp.aNaturalNumber0 @t5)))) % 2.53/2.75 (assume @p5 @t11) % 2.53/2.75 (assume @p6 (forall @t8 (=> @t7 (= @t5 @t12)))) % 2.53/2.75 (assume @p7 (forall @t17 (=> @t16 (= (tptp.sdtpldt0 @t5 @t13) (tptp.sdtpldt0 @t1 @t14))))) % 2.53/2.75 (assume @p8 (forall @t3 (=> @t2 (and (= (tptp.sdtpldt0 @t1 tptp.sz00) @t1) (= @t1 (tptp.sdtpldt0 tptp.sz00 @t1)))))) % 2.53/2.75 (assume @p9 (forall @t8 (=> @t7 (= @t9 @t18)))) % 2.53/2.75 (assume @p10 (forall @t17 (=> @t16 (= (tptp.sdtasdt0 @t9 @t13) (tptp.sdtasdt0 @t1 (tptp.sdtasdt0 @t4 @t13)))))) % 2.53/2.75 (assume @p11 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz10) @t1) (= @t1 (tptp.sdtasdt0 tptp.sz10 @t1)))))) % 2.53/2.75 (assume @p12 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz00) tptp.sz00) (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 @t1)))))) % 2.53/2.75 (assume @p13 (forall @t17 (=> @t16 (and (= (tptp.sdtasdt0 @t1 @t14) (tptp.sdtpldt0 @t9 @t20)) (= (tptp.sdtasdt0 @t14 @t1) (tptp.sdtpldt0 @t18 @t19)))))) % 2.53/2.75 (assume @p14 @t28) % 2.53/2.75 (assume @p15 (forall @t3 (=> @t2 (=> @t33 (forall (@list @t4 @t13) (=> @t31 (=> (or @t30 @t29) @t21))))))) % 2.53/2.75 (assume @p16 (forall @t8 (=> @t7 (=> (= @t5 tptp.sz00) (and @t32 @t34))))) % 2.53/2.75 (assume @p17 (forall @t8 (=> @t7 (=> (= @t9 tptp.sz00) (or @t32 @t34))))) % 2.53/2.75 (assume @p18 (forall @t8 (=> @t7 (= @t37 (exists @t36 @t35))))) % 2.53/2.75 (assume @p19 (forall @t8 (=> @t7 (=> @t37 (forall @t36 (= (= @t13 (tptp.sdtmndt0 @t4 @t1)) @t35)))))) % 2.53/2.75 (assume @p20 (forall @t3 (=> @t2 (tptp.sdtlseqdt0 @t1 @t1)))) % 2.53/2.75 (assume @p21 (forall @t8 (=> @t7 (=> (and @t37 @t39) @t38)))) % 2.53/2.75 (assume @p22 (forall @t17 (=> @t16 (=> (and @t37 @t40) (tptp.sdtlseqdt0 @t1 @t13))))) % 2.53/2.75 (assume @p23 (forall @t8 (=> @t7 (or @t37 (and (not (= @t4 @t1)) @t39))))) % 2.53/2.75 (assume @p24 (forall @t8 (=> @t7 (=> @t42 (forall @t36 (=> @t15 (and (not (= @t22 @t41)) (tptp.sdtlseqdt0 @t22 @t41) (not (= @t24 @t14)) (tptp.sdtlseqdt0 @t24 @t14)))))))) % 2.53/2.75 (assume @p25 (forall @t17 (=> @t16 (=> (and @t33 (not @t21) @t40) (and (not @t30) (tptp.sdtlseqdt0 @t9 @t20) (not @t29) (tptp.sdtlseqdt0 @t18 @t19)))))) % 2.53/2.75 (assume @p26 (forall @t3 (=> @t2 (or @t32 (= @t1 tptp.sz10) (and (not (= tptp.sz10 @t1)) (tptp.sdtlseqdt0 tptp.sz10 @t1)))))) % 2.53/2.75 (assume @p27 (forall @t8 (=> @t7 (=> @t33 (tptp.sdtlseqdt0 @t4 @t18))))) % 2.53/2.75 (assume @p28 (forall @t8 (=> @t7 (=> @t43 true)))) % 2.53/2.75 (assume @p29 (forall @t8 (=> @t7 (=> @t42 @t43)))) % 2.53/2.75 (assume @p30 (forall @t8 (=> @t7 (= @t45 (exists @t36 @t44))))) % 2.53/2.75 (assume @p31 (forall @t8 (=> @t7 (=> (and @t33 @t45) (forall @t36 (= (= @t13 (tptp.sdtsldt0 @t4 @t1)) @t44)))))) % 2.53/2.75 (assume @p32 (forall @t17 (=> @t16 (=> (and @t45 (tptp.doDivides0 @t4 @t13)) @t46)))) % 2.53/2.75 (assume @p33 (forall @t17 (=> @t16 (=> (and @t45 @t46) (tptp.doDivides0 @t1 @t14))))) % 2.53/2.75 (assume @p34 (and @t48 (tptp.aNaturalNumber0 tptp.xm) @t47)) % 2.53/2.75 (assume @p35 (and (exists @t3 (and @t2 (= tptp.xm @t50))) (tptp.doDivides0 tptp.xl tptp.xm) (exists @t3 (and @t2 (= @t49 @t50))) (tptp.doDivides0 tptp.xl @t49))) % 2.53/2.75 (assume @p36 (not (= tptp.xl tptp.sz00))) % 2.53/2.75 (assume @p37 (and (tptp.aNaturalNumber0 tptp.xp) (= tptp.xm @t51) (= tptp.xp (tptp.sdtsldt0 tptp.xm tptp.xl)))) % 2.53/2.75 (assume @p38 (and (tptp.aNaturalNumber0 tptp.xq) (= @t49 (tptp.sdtasdt0 tptp.xl tptp.xq)) (= tptp.xq (tptp.sdtsldt0 @t49 tptp.xl)))) % 2.53/2.75 (assume @p39 (and (exists @t3 (and @t2 (= (tptp.sdtpldt0 tptp.xp @t1) tptp.xq))) (tptp.sdtlseqdt0 tptp.xp tptp.xq))) % 2.53/2.75 (assume @p40 (and @t52 (= (tptp.sdtpldt0 tptp.xp tptp.xr) tptp.xq) (= tptp.xr (tptp.sdtmndt0 tptp.xq tptp.xp)))) % 2.53/2.75 (assume @p41 @t56) % 2.53/2.75 (assume @p42 (not @t57)) % 2.53/2.75 (assume @p43 true) % 2.53/2.75 (step @p44 :rule and_elim :premises (@p34) :args (2)) % 2.53/2.75 (step @p45 :rule and_elim :premises (@p34) :args (1)) % 2.53/2.75 (step @p46 :rule true_intro :premises (@p45)) % 2.53/2.75 (step @p47 :rule and_elim :premises (@p37) :args (1)) % 2.53/2.75 (step @p48 :rule symm :premises (@p47)) % 2.53/2.75 (step @p49 :rule cong :premises (@p48) :args (@t58)) % 2.53/2.75 (step @p50 :rule trans :premises (@p49 @p46)) % 2.53/2.75 (step @p51 :rule true_elim :premises (@p50)) % 2.53/2.75 (step @p52 :rule aci_norm :args ((= (or (or @t60 @t59) @t10) (or @t60 @t59 @t10)))) % 2.53/2.76 (step @p53 :rule refl :args (@t10)) % 2.53/2.76 (step @p54 :rule bool-and-de-morgan :args (@t2 @t6 true)) % 2.53/2.76 (step @p55 :rule nary_cong :premises (@p54 @p53) :args ((or (not @t7) @t10))) % 2.53/2.76 (step @p56 :rule trans :premises (@p55 @p52)) % 2.53/2.76 (step @p57 :rule bool-impl-elim :args (@t7 @t10)) % 2.53/2.76 (step @p58 :rule trans :premises (@p57 @p56)) % 2.53/2.76 (step @p59 :rule cong :premises (@p58) :args (@t11)) % 2.53/2.76 (step @p60 :rule eq_resolve :premises (@p5 @p59)) % 2.53/2.76 (step @p61 :rule instantiate :premises (@p60) :args ((@list tptp.xl tptp.xr))) % 2.53/2.76 (step @p62 :rule and_elim :premises (@p40) :args (0)) % 2.53/2.76 (step @p63 :rule and_elim :premises (@p34) :args (0)) % 2.53/2.76 (step @p64 :rule cnf_or_pos :args (@t64)) % 2.53/2.76 (step @p65 :rule reordering :premises (@p64) :args ((or @t63 @t62 @t61 (not @t64)))) % 2.53/2.76 (step @p66 :rule chain_m_resolution :premises (@p65 @p63 @p62 @p61) :args (@t61 (@list false false false) (@list @t48 @t52 @t64))) % 2.53/2.76 (step @p67 :rule cnf_and_pos :args (@t68 0)) % 2.53/2.76 (step @p68 :rule reordering :premises (@p67) :args ((or @t67 @t69))) % 2.53/2.76 (step @p69 :rule chain_m_resolution :premises (@p68 @p41) :args (@t69 @t70 (@list @t56))) % 2.53/2.76 (step @p70 :rule aci_norm :args ((= (or @t74 (or @t71 @t21)) @t73))) % 2.53/2.76 (step @p71 :rule refl :args (@t21)) % 2.53/2.76 (step @p72 :rule bool-or-de-morgan :args (@t25 @t23 false)) % 2.53/2.76 (step @p73 :rule nary_cong :premises (@p72 @p71) :args ((or (not @t26) @t21))) % 2.53/2.76 (step @p74 :rule bool-impl-elim :args (@t26 @t21)) % 2.53/2.76 (step @p75 :rule trans :premises (@p74 @p73)) % 2.53/2.76 (step @p76 :rule aci_norm :args ((= (or @t60 (or @t59 @t72)) @t74))) % 2.53/2.76 (step @p77 :rule bool-and-de-morgan :args (@t6 @t15 true)) % 2.53/2.76 (step @p78 :rule refl :args (@t60)) % 2.53/2.76 (step @p79 :rule nary_cong :premises (@p78 @p77) :args ((or @t60 (not @t31)))) % 2.53/2.76 (step @p80 :rule bool-and-de-morgan :args (@t2 @t6 (and @t15))) % 2.53/2.76 (step @p81 :rule trans :premises (@p80 @p79)) % 2.53/2.76 (step @p82 :rule trans :premises (@p81 @p76)) % 2.53/2.76 (step @p83 :rule nary_cong :premises (@p82 @p75) :args ((or (not @t16) @t27))) % 2.53/2.76 (step @p84 :rule trans :premises (@p83 @p70)) % 2.53/2.76 (step @p85 :rule bool-impl-elim :args (@t16 @t27)) % 2.53/2.76 (step @p86 :rule trans :premises (@p85 @p84)) % 2.53/2.76 (step @p87 :rule cong :premises (@p86) :args (@t28)) % 2.53/2.76 (step @p88 :rule eq_resolve :premises (@p14 @p87)) % 2.53/2.76 (step @p89 :rule refl :args (@t57)) % 2.53/2.76 (step @p90 :rule eq-symm :args (@t65 @t66)) % 2.53/2.76 (step @p91 :rule cong :premises (@p90) :args (@t75)) % 2.53/2.76 (step @p92 :rule eq-symm :args (@t53 @t55)) % 2.53/2.76 (step @p93 :rule cong :premises (@p92) :args (@t76)) % 2.53/2.76 (step @p94 :rule nary_cong :premises (@p93 @p91) :args (@t77)) % 2.53/2.76 (step @p95 :rule refl :args (@t78)) % 2.53/2.76 (step @p96 :rule refl :args (@t79)) % 2.53/2.76 (step @p97 :rule refl :args (@t80)) % 2.53/2.76 (step @p98 :rule nary_cong :premises (@p97 @p96 @p95 @p94 @p89) :args (@t81)) % 2.53/2.76 (step @p99 :rule refl :args (@t82)) % 2.53/2.76 (step @p100 :rule cong :premises (@p99 @p98) :args ((=> @t82 @t81))) % 2.53/2.76 (assume-push @p111 @t82) % 2.53/2.76 (step @p102 :rule instantiate :premises (@p88) :args ((@list @t51 tptp.xn @t54))) % 2.53/2.76 (step-pop @p112 :rule scope :premises (@p102)) % 2.53/2.76 (step @p103 :rule process_scope :premises (@p112) :args (@t81)) % 2.53/2.76 (step @p105 :rule eq_resolve :premises (@p103 @p100)) % 2.53/2.76 (step @p106 :rule implies_elim :premises (@p105)) % 2.53/2.76 (step @p107 :rule chain_m_resolution :premises (@p106 @p88) :args (@t83 @t70 (@list @t82))) % 2.53/2.76 (step @p108 :rule cnf_or_pos :args (@t83)) % 2.53/2.76 (step @p109 :rule reordering :premises (@p108) :args ((or @t57 @t79 @t80 @t78 @t68 (not @t83)))) % 2.53/2.76 (step @p110 false :rule chain_m_resolution :premises (@p109 @p107 @p69 @p66 @p51 @p42 @p44) :args (false (@list false true false false true false) (@list @t83 @t68 @t61 @t58 @t57 @t47))) % 2.53/2.76 ) % 2.53/2.76 % SZS output end Proof % 2.53/2.76 % cvc5 exiting %------------------------------------------------------------------------------