%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM457+1 : 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 : n001.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 08:39:28 AM UTC 2026 % Result : Theorem 0.36s 0.60s % Output : Proof 0.36s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM457+1 : 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 : n001.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 11:22:05 EDT 2026 % 0.16/0.35 % CPUTime : % 0.31/0.50 %----Proving TF0_NAR, FOF, or CNF % 0.36/0.60 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.36/0.60 % SZS status Theorem % 0.36/0.60 % SZS output start Proof % 0.36/0.60 ( % 0.36/0.60 (declare-sort $$unsorted 0) % 0.36/0.60 (declare-const tptp.xn $$unsorted) % 0.36/0.60 (declare-const tptp.sdtasdt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.60 (declare-const tptp.sdtpldt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.60 (declare-const tptp.xm $$unsorted) % 0.36/0.60 (declare-const tptp.sz10 $$unsorted) % 0.36/0.60 (declare-const tptp.sz00 $$unsorted) % 0.36/0.60 (declare-const tptp.aNaturalNumber0 (-> $$unsorted Bool)) % 0.36/0.60 (define @t1 () (@var "W0" $$unsorted)) % 0.36/0.60 (define @t2 () (tptp.aNaturalNumber0 @t1)) % 0.36/0.60 (define @t3 () (@list @t1)) % 0.36/0.60 (define @t4 () (tptp.aNaturalNumber0 tptp.sz00)) % 0.36/0.60 (define @t5 () (@var "W1" $$unsorted)) % 0.36/0.60 (define @t6 () (tptp.sdtpldt0 @t1 @t5)) % 0.36/0.60 (define @t7 () (tptp.aNaturalNumber0 @t5)) % 0.36/0.60 (define @t8 () (and @t2 @t7)) % 0.36/0.60 (define @t9 () (@list @t1 @t5)) % 0.36/0.60 (define @t10 () (tptp.sdtasdt0 @t1 @t5)) % 0.36/0.60 (define @t11 () (tptp.sdtpldt0 @t5 @t1)) % 0.36/0.60 (define @t12 () (@var "W2" $$unsorted)) % 0.36/0.60 (define @t13 () (tptp.sdtpldt0 @t5 @t12)) % 0.36/0.60 (define @t14 () (tptp.aNaturalNumber0 @t12)) % 0.36/0.60 (define @t15 () (and @t2 @t7 @t14)) % 0.36/0.60 (define @t16 () (@list @t1 @t5 @t12)) % 0.36/0.60 (define @t17 () (tptp.sdtasdt0 @t5 @t1)) % 0.36/0.60 (define @t18 () (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 @t1))) % 0.36/0.60 (define @t19 () (tptp.sdtasdt0 @t1 tptp.sz00)) % 0.36/0.60 (define @t20 () (and (= @t19 tptp.sz00) @t18)) % 0.36/0.60 (define @t21 () (=> @t2 @t20)) % 0.36/0.60 (define @t22 () (forall @t3 @t21)) % 0.36/0.60 (define @t23 () (tptp.sdtasdt0 @t12 @t1)) % 0.36/0.60 (define @t24 () (tptp.sdtasdt0 @t1 @t12)) % 0.36/0.60 (define @t25 () (= @t5 @t12)) % 0.36/0.60 (define @t26 () (= @t17 @t23)) % 0.36/0.60 (define @t27 () (= @t10 @t24)) % 0.36/0.60 (define @t28 () (or @t27 @t26)) % 0.36/0.60 (define @t29 () (=> @t28 @t25)) % 0.36/0.60 (define @t30 () (and @t7 @t14)) % 0.36/0.60 (define @t31 () (@list @t5 @t12)) % 0.36/0.60 (define @t32 () (forall @t31 (=> @t30 @t29))) % 0.36/0.60 (define @t33 () (= @t1 tptp.sz00)) % 0.36/0.60 (define @t34 () (not @t33)) % 0.36/0.60 (define @t35 () (=> @t34 @t32)) % 0.36/0.60 (define @t36 () (=> @t2 @t35)) % 0.36/0.60 (define @t37 () (forall @t3 @t36)) % 0.36/0.60 (define @t38 () (tptp.aNaturalNumber0 tptp.xn)) % 0.36/0.60 (define @t39 () (tptp.aNaturalNumber0 tptp.xm)) % 0.36/0.60 (define @t40 () (= tptp.xm tptp.sz00)) % 0.36/0.60 (define @t41 () (or @t40 (= tptp.xn tptp.sz00))) % 0.36/0.60 (define @t42 () (tptp.sdtasdt0 tptp.xm tptp.xn)) % 0.36/0.60 (define @t43 () (=> (= @t42 tptp.sz00) @t41)) % 0.36/0.60 (define @t44 () (not @t43)) % 0.36/0.60 (define @t45 () (@var "BOUND_VARIABLE_7611" $$unsorted)) % 0.36/0.60 (define @t46 () (@var "BOUND_VARIABLE_7609" $$unsorted)) % 0.36/0.60 (define @t47 () (= @t46 @t45)) % 0.36/0.60 (define @t48 () (and (not (= (tptp.sdtasdt0 @t1 @t46) (tptp.sdtasdt0 @t1 @t45))) (not (= (tptp.sdtasdt0 @t46 @t1) (tptp.sdtasdt0 @t45 @t1))))) % 0.36/0.60 (define @t49 () (not (tptp.aNaturalNumber0 @t45))) % 0.36/0.60 (define @t50 () (not (tptp.aNaturalNumber0 @t46))) % 0.36/0.60 (define @t51 () (not @t2)) % 0.36/0.60 (define @t52 () (or @t51 @t33 @t50 @t49 @t48 @t47)) % 0.36/0.60 (define @t53 () (or @t50 @t49 @t48 @t47)) % 0.36/0.60 (define @t54 () (or @t51 @t33 @t53)) % 0.36/0.60 (define @t55 () (@list @t1 @t46 @t45)) % 0.36/0.60 (define @t56 () (forall @t55 @t54)) % 0.36/0.60 (define @t57 () (@list @t46 @t45)) % 0.36/0.60 (define @t58 () (forall @t57 @t54)) % 0.36/0.60 (define @t59 () (forall @t57 @t53)) % 0.36/0.60 (define @t60 () (or @t51 @t33 @t59)) % 0.36/0.60 (define @t61 () (and (not @t27) (not @t26))) % 0.36/0.60 (define @t62 () (not @t14)) % 0.36/0.60 (define @t63 () (not @t7)) % 0.36/0.60 (define @t64 () (or @t63 @t62 @t61 @t25)) % 0.36/0.60 (define @t65 () (forall @t31 @t64)) % 0.36/0.60 (define @t66 () (or @t51 @t33 @t65)) % 0.36/0.60 (define @t67 () (=> @t34 @t65)) % 0.36/0.60 (define @t68 () (= tptp.sz00 tptp.xn)) % 0.36/0.60 (define @t69 () (tptp.sdtasdt0 tptp.sz00 tptp.xm)) % 0.36/0.60 (define @t70 () (tptp.sdtasdt0 tptp.xn tptp.xm)) % 0.36/0.60 (define @t71 () (not (= @t69 @t70))) % 0.36/0.60 (define @t72 () (tptp.sdtasdt0 tptp.xm tptp.sz00)) % 0.36/0.60 (define @t73 () (not (= @t72 @t42))) % 0.36/0.60 (define @t74 () (and @t73 @t71)) % 0.36/0.60 (define @t75 () (not @t38)) % 0.36/0.60 (define @t76 () (not @t4)) % 0.36/0.60 (define @t77 () (not @t39)) % 0.36/0.60 (define @t78 () (or @t77 @t40 @t76 @t75 @t74 @t68)) % 0.36/0.60 (define @t79 () (forall @t55 @t52)) % 0.36/0.60 (define @t80 () (not (= @t42 @t72))) % 0.36/0.60 (define @t81 () (and @t80 (not (= @t70 @t69)))) % 0.36/0.60 (define @t82 () (= tptp.sz00 tptp.xm)) % 0.36/0.60 (define @t83 () (or @t77 @t82 @t76 @t75 @t81 @t68)) % 0.36/0.60 (define @t84 () (@list false)) % 0.36/0.60 (define @t85 () (and (= tptp.sz00 @t19) @t18)) % 0.36/0.60 (define @t86 () (= tptp.sz00 @t72)) % 0.36/0.60 (define @t87 () (and @t86 (= tptp.sz00 @t69))) % 0.36/0.60 (define @t88 () (or @t77 @t87)) % 0.36/0.60 (assume @p1 (forall @t3 (=> @t2 true))) % 0.36/0.60 (assume @p2 @t4) % 0.36/0.60 (assume @p3 (and (tptp.aNaturalNumber0 tptp.sz10) (not (= tptp.sz10 tptp.sz00)))) % 0.36/0.60 (assume @p4 (forall @t9 (=> @t8 (tptp.aNaturalNumber0 @t6)))) % 0.36/0.60 (assume @p5 (forall @t9 (=> @t8 (tptp.aNaturalNumber0 @t10)))) % 0.36/0.60 (assume @p6 (forall @t9 (=> @t8 (= @t6 @t11)))) % 0.36/0.60 (assume @p7 (forall @t16 (=> @t15 (= (tptp.sdtpldt0 @t6 @t12) (tptp.sdtpldt0 @t1 @t13))))) % 0.36/0.60 (assume @p8 (forall @t3 (=> @t2 (and (= (tptp.sdtpldt0 @t1 tptp.sz00) @t1) (= @t1 (tptp.sdtpldt0 tptp.sz00 @t1)))))) % 0.36/0.60 (assume @p9 (forall @t9 (=> @t8 (= @t10 @t17)))) % 0.36/0.60 (assume @p10 (forall @t16 (=> @t15 (= (tptp.sdtasdt0 @t10 @t12) (tptp.sdtasdt0 @t1 (tptp.sdtasdt0 @t5 @t12)))))) % 0.36/0.60 (assume @p11 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz10) @t1) (= @t1 (tptp.sdtasdt0 tptp.sz10 @t1)))))) % 0.36/0.60 (assume @p12 @t22) % 0.36/0.60 (assume @p13 (forall @t16 (=> @t15 (and (= (tptp.sdtasdt0 @t1 @t13) (tptp.sdtpldt0 @t10 @t24)) (= (tptp.sdtasdt0 @t13 @t1) (tptp.sdtpldt0 @t17 @t23)))))) % 0.36/0.60 (assume @p14 (forall @t16 (=> @t15 (=> (or (= @t6 (tptp.sdtpldt0 @t1 @t12)) (= @t11 (tptp.sdtpldt0 @t12 @t1))) @t25)))) % 0.36/0.60 (assume @p15 @t37) % 0.36/0.60 (assume @p16 (forall @t9 (=> @t8 (=> (= @t6 tptp.sz00) (and @t33 (= @t5 tptp.sz00)))))) % 0.36/0.60 (assume @p17 (and @t39 @t38)) % 0.36/0.60 (assume @p18 @t44) % 0.36/0.60 (assume @p19 true) % 0.36/0.60 (step @p20 :rule evaluate :args ((= true false))) % 0.36/0.60 (step @p21 :rule aci_norm :args ((= @t54 @t52))) % 0.36/0.60 (step @p22 :rule cong :premises (@p21) :args (@t56)) % 0.36/0.60 (step @p23 :rule quant-merge-prenex :args ((= (forall @t3 @t58) @t56))) % 0.36/0.60 (step @p24 :rule alpha_equiv :args (@t59 (@list @t46 @t45) (@list @t5 @t12))) % 0.36/0.60 (step @p25 :rule refl :args (@t33)) % 0.36/0.60 (step @p26 :rule refl :args (@t51)) % 0.36/0.60 (step @p27 :rule nary_cong :premises (@p26 @p25 @p24) :args (@t60)) % 0.36/0.60 (step @p28 :rule quant-miniscope-or :args ((= @t58 @t60))) % 0.36/0.60 (step @p29 :rule trans :premises (@p28 @p27)) % 0.36/0.60 (step @p30 :rule symm :premises (@p29)) % 0.36/0.60 (step @p31 :rule cong :premises (@p30) :args ((forall @t3 @t66))) % 0.36/0.60 (step @p32 :rule trans :premises (@p31 @p23)) % 0.36/0.60 (step @p33 :rule trans :premises (@p32 @p22)) % 0.36/0.60 (step @p34 :rule aci_norm :args ((= (or @t51 (or @t33 @t65)) @t66))) % 0.36/0.60 (step @p35 :rule refl :args (@t65)) % 0.36/0.60 (step @p36 :rule bool-double-not-elim :args (@t33)) % 0.36/0.60 (step @p37 :rule nary_cong :premises (@p36 @p35) :args ((or (not @t34) @t65))) % 0.36/0.60 (step @p38 :rule bool-impl-elim :args (@t34 @t65)) % 0.36/0.60 (step @p39 :rule trans :premises (@p38 @p37)) % 0.36/0.60 (step @p40 :rule nary_cong :premises (@p26 @p39) :args ((or @t51 @t67))) % 0.36/0.60 (step @p41 :rule trans :premises (@p40 @p34)) % 0.36/0.60 (step @p42 :rule bool-impl-elim :args (@t2 @t67)) % 0.36/0.60 (step @p43 :rule trans :premises (@p42 @p41)) % 0.36/0.60 (step @p44 :rule cong :premises (@p43) :args ((forall @t3 (=> @t2 @t67)))) % 0.36/0.60 (step @p45 :rule trans :premises (@p44 @p33)) % 0.36/0.60 (step @p46 :rule aci_norm :args ((= (or (or @t63 @t62) (or @t61 @t25)) @t64))) % 0.36/0.60 (step @p47 :rule refl :args (@t25)) % 0.36/0.60 (step @p48 :rule bool-or-de-morgan :args (@t27 @t26 false)) % 0.36/0.60 (step @p49 :rule nary_cong :premises (@p48 @p47) :args ((or (not @t28) @t25))) % 0.36/0.60 (step @p50 :rule bool-impl-elim :args (@t28 @t25)) % 0.36/0.60 (step @p51 :rule trans :premises (@p50 @p49)) % 0.36/0.60 (step @p52 :rule bool-and-de-morgan :args (@t7 @t14 true)) % 0.36/0.60 (step @p53 :rule nary_cong :premises (@p52 @p51) :args ((or (not @t30) @t29))) % 0.36/0.60 (step @p54 :rule trans :premises (@p53 @p46)) % 0.36/0.60 (step @p55 :rule bool-impl-elim :args (@t30 @t29)) % 0.36/0.60 (step @p56 :rule trans :premises (@p55 @p54)) % 0.36/0.60 (step @p57 :rule cong :premises (@p56) :args (@t32)) % 0.36/0.60 (step @p58 :rule refl :args (@t34)) % 0.36/0.60 (step @p59 :rule cong :premises (@p58 @p57) :args (@t35)) % 0.36/0.60 (step @p60 :rule refl :args (@t2)) % 0.36/0.60 (step @p61 :rule cong :premises (@p60 @p59) :args (@t36)) % 0.36/0.60 (step @p62 :rule cong :premises (@p61) :args (@t37)) % 0.36/0.60 (step @p63 :rule trans :premises (@p62 @p45)) % 0.36/0.60 (step @p64 :rule eq_resolve :premises (@p15 @p63)) % 0.36/0.60 (step @p65 :rule refl :args (@t68)) % 0.36/0.60 (step @p66 :rule eq-symm :args (@t69 @t70)) % 0.36/0.60 (step @p67 :rule cong :premises (@p66) :args (@t71)) % 0.36/0.60 (step @p68 :rule eq-symm :args (@t72 @t42)) % 0.36/0.60 (step @p69 :rule cong :premises (@p68) :args (@t73)) % 0.36/0.60 (step @p70 :rule nary_cong :premises (@p69 @p67) :args (@t74)) % 0.36/0.60 (step @p71 :rule refl :args (@t75)) % 0.36/0.60 (step @p72 :rule refl :args (@t76)) % 0.36/0.60 (step @p73 :rule eq-symm :args (tptp.xm tptp.sz00)) % 0.36/0.60 (step @p74 :rule refl :args (@t77)) % 0.36/0.60 (step @p75 :rule nary_cong :premises (@p74 @p73 @p72 @p71 @p70 @p65) :args (@t78)) % 0.36/0.60 (step @p76 :rule refl :args (@t79)) % 0.36/0.60 (step @p77 :rule cong :premises (@p76 @p75) :args ((=> @t79 @t78))) % 0.36/0.60 (assume-push @p126 @t79) % 0.36/0.60 (step @p79 :rule instantiate :premises (@p64) :args ((@list tptp.xm tptp.sz00 tptp.xn))) % 0.36/0.60 (step-pop @p127 :rule scope :premises (@p79)) % 0.36/0.60 (step @p80 :rule process_scope :premises (@p127) :args (@t78)) % 0.36/0.60 (step @p82 :rule eq_resolve :premises (@p80 @p77)) % 0.36/0.60 (step @p83 :rule implies_elim :premises (@p82)) % 0.36/0.60 (step @p84 :rule chain_m_resolution :premises (@p83 @p64) :args (@t83 @t84 (@list @t79))) % 0.36/0.60 (step @p85 :rule and_elim :premises (@p17) :args (1)) % 0.36/0.60 (step @p86 :rule and_elim :premises (@p17) :args (0)) % 0.36/0.60 (step @p87 :rule eq-symm :args (tptp.xn tptp.sz00)) % 0.36/0.60 (step @p88 :rule nary_cong :premises (@p73 @p87) :args (@t41)) % 0.36/0.60 (step @p89 :rule eq-symm :args (@t42 tptp.sz00)) % 0.36/0.60 (step @p90 :rule cong :premises (@p89 @p88) :args (@t43)) % 0.36/0.60 (step @p91 :rule cong :premises (@p90) :args (@t44)) % 0.36/0.60 (step @p92 :rule eq_resolve :premises (@p18 @p91)) % 0.36/0.60 (step @p93 :rule not_implies_elim2 :premises (@p92)) % 0.36/0.60 (step @p94 :rule not_or_elim :premises (@p93) :args (1)) % 0.36/0.60 (step @p95 :rule not_or_elim :premises (@p93) :args (0)) % 0.36/0.60 (step @p96 :rule cnf_or_pos :args (@t83)) % 0.36/0.60 (step @p97 :rule reordering :premises (@p96) :args ((or @t82 @t68 @t76 @t77 @t75 @t81 (not @t83)))) % 0.36/0.60 (step @p98 :rule chain_m_resolution :premises (@p97 @p95 @p94 @p2 @p86 @p85 @p84) :args (@t81 (@list true true false false false false) (@list @t82 @t68 @t4 @t39 @t38 @t83))) % 0.36/0.60 (step @p99 :rule cnf_and_pos :args (@t81 0)) % 0.36/0.60 (step @p100 :rule reordering :premises (@p99) :args ((or @t80 (not @t81)))) % 0.36/0.60 (step @p101 :rule chain_m_resolution :premises (@p100 @p98) :args (@t80 @t84 (@list @t81))) % 0.36/0.60 (step @p102 :rule false_intro :premises (@p101)) % 0.36/0.60 (step @p103 :rule bool-impl-elim :args (@t2 @t85)) % 0.36/0.60 (step @p104 :rule cong :premises (@p103) :args ((forall @t3 (=> @t2 @t85)))) % 0.36/0.60 (step @p105 :rule refl :args (@t18)) % 0.36/0.60 (step @p106 :rule eq-symm :args (@t19 tptp.sz00)) % 0.36/0.60 (step @p107 :rule nary_cong :premises (@p106 @p105) :args (@t20)) % 0.36/0.60 (step @p108 :rule cong :premises (@p60 @p107) :args (@t21)) % 0.36/0.60 (step @p109 :rule cong :premises (@p108) :args (@t22)) % 0.36/0.60 (step @p110 :rule trans :premises (@p109 @p104)) % 0.36/0.60 (step @p111 :rule eq_resolve :premises (@p12 @p110)) % 0.36/0.60 (step @p112 :rule instantiate :premises (@p111) :args ((@list tptp.xm))) % 0.36/0.60 (step @p113 :rule cnf_or_pos :args (@t88)) % 0.36/0.60 (step @p114 :rule reordering :premises (@p113) :args ((or @t77 @t87 (not @t88)))) % 0.36/0.60 (step @p115 :rule chain_m_resolution :premises (@p114 @p86 @p112) :args (@t87 (@list false false) (@list @t39 @t88))) % 0.36/0.60 (step @p116 :rule cnf_and_pos :args (@t87 0)) % 0.36/0.60 (step @p117 :rule reordering :premises (@p116) :args ((or @t86 (not @t87)))) % 0.36/0.60 (step @p118 :rule chain_m_resolution :premises (@p117 @p115) :args (@t86 @t84 (@list @t87))) % 0.36/0.60 (step @p119 :rule not_implies_elim1 :premises (@p92)) % 0.36/0.60 (step @p120 :rule symm :premises (@p119)) % 0.36/0.60 (step @p121 :rule trans :premises (@p120 @p118)) % 0.36/0.60 (step @p122 :rule true_intro :premises (@p121)) % 0.36/0.60 (step @p123 :rule symm :premises (@p122)) % 0.36/0.60 (step @p124 :rule trans :premises (@p123 @p102)) % 0.36/0.60 (step @p125 false :rule eq_resolve :premises (@p124 @p20)) % 0.36/0.60 ) % 0.36/0.60 % SZS output end Proof % 0.36/0.60 % cvc5 exiting %------------------------------------------------------------------------------