%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM472+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 08:39:31 AM UTC 2026 % Result : Theorem 0.45s 0.65s % Output : Proof 0.45s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : NUM472+1 : TPTP v9.2.1. Released v4.0.0. % 0.12/0.14 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.16/0.35 % Computer : n006.cluster.edu % 0.16/0.35 % Model : x86_64 x86_64 % 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.35 % Memory : 8042.1875MB % 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.35 % CPULimit : 300 % 0.16/0.35 % WCLimit : 300 % 0.16/0.35 % DateTime : Tue Jun 2 11:22:19 EDT 2026 % 0.16/0.35 % CPUTime : % 0.33/0.51 %----Proving TF0_NAR, FOF, or CNF % 0.45/0.65 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.45/0.65 % SZS status Theorem % 0.45/0.65 % SZS output start Proof % 0.45/0.65 ( % 0.45/0.65 (declare-sort $$unsorted 0) % 0.45/0.65 (declare-const tptp.xq $$unsorted) % 0.45/0.65 (declare-const tptp.xp $$unsorted) % 0.45/0.65 (declare-const tptp.sz10 $$unsorted) % 0.45/0.65 (declare-const tptp.xl $$unsorted) % 0.45/0.65 (declare-const tptp.sdtpldt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.45/0.65 (declare-const tptp.sdtlseqdt0 (-> $$unsorted $$unsorted Bool)) % 0.45/0.65 (declare-const tptp.aNaturalNumber0 (-> $$unsorted Bool)) % 0.45/0.65 (declare-const tptp.sz00 $$unsorted) % 0.45/0.65 (declare-const tptp.sdtsldt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.45/0.65 (declare-const tptp.sdtasdt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.45/0.65 (declare-const tptp.sdtmndt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.45/0.65 (declare-const tptp.xn $$unsorted) % 0.45/0.65 (declare-const tptp.iLess0 (-> $$unsorted $$unsorted Bool)) % 0.45/0.65 (declare-const tptp.doDivides0 (-> $$unsorted $$unsorted Bool)) % 0.45/0.65 (declare-const tptp.xm $$unsorted) % 0.45/0.65 (define @t1 () (@var "W0" $$unsorted)) % 0.45/0.65 (define @t2 () (tptp.aNaturalNumber0 @t1)) % 0.45/0.65 (define @t3 () (@list @t1)) % 0.45/0.65 (define @t4 () (@var "W1" $$unsorted)) % 0.45/0.65 (define @t5 () (tptp.sdtpldt0 @t1 @t4)) % 0.45/0.65 (define @t6 () (tptp.aNaturalNumber0 @t5)) % 0.45/0.65 (define @t7 () (tptp.aNaturalNumber0 @t4)) % 0.45/0.65 (define @t8 () (and @t2 @t7)) % 0.45/0.65 (define @t9 () (@list @t1 @t4)) % 0.45/0.65 (define @t10 () (forall @t9 (=> @t8 @t6))) % 0.45/0.65 (define @t11 () (tptp.sdtasdt0 @t1 @t4)) % 0.45/0.65 (define @t12 () (tptp.sdtpldt0 @t4 @t1)) % 0.45/0.65 (define @t13 () (@var "W2" $$unsorted)) % 0.45/0.65 (define @t14 () (tptp.sdtpldt0 @t4 @t13)) % 0.45/0.65 (define @t15 () (tptp.aNaturalNumber0 @t13)) % 0.45/0.65 (define @t16 () (and @t2 @t7 @t15)) % 0.45/0.65 (define @t17 () (@list @t1 @t4 @t13)) % 0.45/0.65 (define @t18 () (tptp.sdtasdt0 @t4 @t1)) % 0.45/0.65 (define @t19 () (tptp.sdtasdt0 @t13 @t1)) % 0.45/0.65 (define @t20 () (tptp.sdtasdt0 @t1 @t13)) % 0.45/0.65 (define @t21 () (= @t4 @t13)) % 0.45/0.65 (define @t22 () (tptp.sdtpldt0 @t13 @t1)) % 0.45/0.65 (define @t23 () (tptp.sdtpldt0 @t1 @t13)) % 0.45/0.65 (define @t24 () (= @t18 @t19)) % 0.45/0.65 (define @t25 () (= @t11 @t20)) % 0.45/0.65 (define @t26 () (= @t1 tptp.sz00)) % 0.45/0.65 (define @t27 () (not @t26)) % 0.45/0.65 (define @t28 () (= @t4 tptp.sz00)) % 0.45/0.65 (define @t29 () (and @t15 (= @t23 @t4))) % 0.45/0.65 (define @t30 () (@list @t13)) % 0.45/0.65 (define @t31 () (exists @t30 @t29)) % 0.45/0.65 (define @t32 () (tptp.sdtlseqdt0 @t1 @t4)) % 0.45/0.65 (define @t33 () (= @t32 @t31)) % 0.45/0.65 (define @t34 () (=> @t8 @t33)) % 0.45/0.65 (define @t35 () (forall @t9 @t34)) % 0.45/0.65 (define @t36 () (= @t1 @t4)) % 0.45/0.65 (define @t37 () (tptp.sdtlseqdt0 @t4 @t1)) % 0.45/0.65 (define @t38 () (tptp.sdtlseqdt0 @t4 @t13)) % 0.45/0.65 (define @t39 () (tptp.sdtpldt0 @t13 @t4)) % 0.45/0.65 (define @t40 () (and (not @t36) @t32)) % 0.45/0.65 (define @t41 () (tptp.iLess0 @t1 @t4)) % 0.45/0.65 (define @t42 () (and @t15 (= @t4 @t20))) % 0.45/0.65 (define @t43 () (tptp.doDivides0 @t1 @t4)) % 0.45/0.65 (define @t44 () (tptp.doDivides0 @t1 @t13)) % 0.45/0.65 (define @t45 () (tptp.aNaturalNumber0 tptp.xn)) % 0.45/0.65 (define @t46 () (tptp.aNaturalNumber0 tptp.xm)) % 0.45/0.65 (define @t47 () (tptp.sdtpldt0 tptp.xm tptp.xn)) % 0.45/0.65 (define @t48 () (tptp.sdtlseqdt0 tptp.xm @t47)) % 0.45/0.65 (define @t49 () (= @t4 @t23)) % 0.45/0.65 (define @t50 () (not @t15)) % 0.45/0.65 (define @t51 () (= @t32 (not (forall @t30 (or @t50 (not @t49)))))) % 0.45/0.65 (define @t52 () (not @t7)) % 0.45/0.65 (define @t53 () (not @t2)) % 0.45/0.65 (define @t54 () (or @t53 @t52)) % 0.45/0.65 (define @t55 () (not @t8)) % 0.45/0.65 (define @t56 () (and @t15 @t49)) % 0.45/0.65 (define @t57 () (forall @t30 (not @t56))) % 0.45/0.65 (define @t58 () (not @t57)) % 0.45/0.65 (define @t59 () (tptp.aNaturalNumber0 @t47)) % 0.45/0.65 (define @t60 () (not @t45)) % 0.45/0.65 (define @t61 () (not @t46)) % 0.45/0.65 (define @t62 () (or @t61 @t60 @t59)) % 0.45/0.65 (define @t63 () (@list false false false)) % 0.45/0.65 (define @t64 () (forall @t30 (or @t50 (not (= @t47 (tptp.sdtpldt0 tptp.xm @t13)))))) % 0.45/0.65 (define @t65 () (not @t64)) % 0.45/0.65 (define @t66 () (= @t48 @t65)) % 0.45/0.65 (define @t67 () (not @t59)) % 0.45/0.65 (define @t68 () (or @t61 @t67 @t66)) % 0.45/0.65 (define @t69 () (not @t66)) % 0.45/0.65 (define @t70 () (not (= @t47 @t47))) % 0.45/0.65 (define @t71 () (or @t60 @t70)) % 0.45/0.65 (assume @p1 (forall @t3 (=> @t2 true))) % 0.45/0.65 (assume @p2 (tptp.aNaturalNumber0 tptp.sz00)) % 0.45/0.65 (assume @p3 (and (tptp.aNaturalNumber0 tptp.sz10) (not (= tptp.sz10 tptp.sz00)))) % 0.45/0.65 (assume @p4 @t10) % 0.45/0.65 (assume @p5 (forall @t9 (=> @t8 (tptp.aNaturalNumber0 @t11)))) % 0.45/0.65 (assume @p6 (forall @t9 (=> @t8 (= @t5 @t12)))) % 0.45/0.65 (assume @p7 (forall @t17 (=> @t16 (= (tptp.sdtpldt0 @t5 @t13) (tptp.sdtpldt0 @t1 @t14))))) % 0.45/0.65 (assume @p8 (forall @t3 (=> @t2 (and (= (tptp.sdtpldt0 @t1 tptp.sz00) @t1) (= @t1 (tptp.sdtpldt0 tptp.sz00 @t1)))))) % 0.45/0.65 (assume @p9 (forall @t9 (=> @t8 (= @t11 @t18)))) % 0.45/0.65 (assume @p10 (forall @t17 (=> @t16 (= (tptp.sdtasdt0 @t11 @t13) (tptp.sdtasdt0 @t1 (tptp.sdtasdt0 @t4 @t13)))))) % 0.45/0.65 (assume @p11 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz10) @t1) (= @t1 (tptp.sdtasdt0 tptp.sz10 @t1)))))) % 0.45/0.65 (assume @p12 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz00) tptp.sz00) (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 @t1)))))) % 0.45/0.65 (assume @p13 (forall @t17 (=> @t16 (and (= (tptp.sdtasdt0 @t1 @t14) (tptp.sdtpldt0 @t11 @t20)) (= (tptp.sdtasdt0 @t14 @t1) (tptp.sdtpldt0 @t18 @t19)))))) % 0.45/0.65 (assume @p14 (forall @t17 (=> @t16 (=> (or (= @t5 @t23) (= @t12 @t22)) @t21)))) % 0.45/0.65 (assume @p15 (forall @t3 (=> @t2 (=> @t27 (forall (@list @t4 @t13) (=> (and @t7 @t15) (=> (or @t25 @t24) @t21))))))) % 0.45/0.65 (assume @p16 (forall @t9 (=> @t8 (=> (= @t5 tptp.sz00) (and @t26 @t28))))) % 0.45/0.65 (assume @p17 (forall @t9 (=> @t8 (=> (= @t11 tptp.sz00) (or @t26 @t28))))) % 0.45/0.65 (assume @p18 @t35) % 0.45/0.65 (assume @p19 (forall @t9 (=> @t8 (=> @t32 (forall @t30 (= (= @t13 (tptp.sdtmndt0 @t4 @t1)) @t29)))))) % 0.45/0.65 (assume @p20 (forall @t3 (=> @t2 (tptp.sdtlseqdt0 @t1 @t1)))) % 0.45/0.65 (assume @p21 (forall @t9 (=> @t8 (=> (and @t32 @t37) @t36)))) % 0.45/0.65 (assume @p22 (forall @t17 (=> @t16 (=> (and @t32 @t38) (tptp.sdtlseqdt0 @t1 @t13))))) % 0.45/0.65 (assume @p23 (forall @t9 (=> @t8 (or @t32 (and (not (= @t4 @t1)) @t37))))) % 0.45/0.65 (assume @p24 (forall @t9 (=> @t8 (=> @t40 (forall @t30 (=> @t15 (and (not (= @t22 @t39)) (tptp.sdtlseqdt0 @t22 @t39) (not (= @t23 @t14)) (tptp.sdtlseqdt0 @t23 @t14)))))))) % 0.45/0.65 (assume @p25 (forall @t17 (=> @t16 (=> (and @t27 (not @t21) @t38) (and (not @t25) (tptp.sdtlseqdt0 @t11 @t20) (not @t24) (tptp.sdtlseqdt0 @t18 @t19)))))) % 0.45/0.65 (assume @p26 (forall @t3 (=> @t2 (or @t26 (= @t1 tptp.sz10) (and (not (= tptp.sz10 @t1)) (tptp.sdtlseqdt0 tptp.sz10 @t1)))))) % 0.45/0.65 (assume @p27 (forall @t9 (=> @t8 (=> @t27 (tptp.sdtlseqdt0 @t4 @t18))))) % 0.45/0.65 (assume @p28 (forall @t9 (=> @t8 (=> @t41 true)))) % 0.45/0.65 (assume @p29 (forall @t9 (=> @t8 (=> @t40 @t41)))) % 0.45/0.65 (assume @p30 (forall @t9 (=> @t8 (= @t43 (exists @t30 @t42))))) % 0.45/0.65 (assume @p31 (forall @t9 (=> @t8 (=> (and @t27 @t43) (forall @t30 (= (= @t13 (tptp.sdtsldt0 @t4 @t1)) @t42)))))) % 0.45/0.65 (assume @p32 (forall @t17 (=> @t16 (=> (and @t43 (tptp.doDivides0 @t4 @t13)) @t44)))) % 0.45/0.65 (assume @p33 (forall @t17 (=> @t16 (=> (and @t43 @t44) (tptp.doDivides0 @t1 @t14))))) % 0.45/0.65 (assume @p34 (and (tptp.aNaturalNumber0 tptp.xl) @t46 @t45)) % 0.45/0.65 (assume @p35 (and (tptp.doDivides0 tptp.xl tptp.xm) (tptp.doDivides0 tptp.xl @t47))) % 0.45/0.65 (assume @p36 (not (= tptp.xl tptp.sz00))) % 0.45/0.65 (assume @p37 (= tptp.xp (tptp.sdtsldt0 tptp.xm tptp.xl))) % 0.45/0.65 (assume @p38 (= tptp.xq (tptp.sdtsldt0 @t47 tptp.xl))) % 0.45/0.65 (assume @p39 (not @t48)) % 0.45/0.65 (assume @p40 true) % 0.45/0.65 (step @p41 :rule and_elim :premises (@p34) :args (2)) % 0.45/0.65 (step @p42 :rule aci_norm :args ((= (or @t54 @t51) (or @t53 @t52 @t51)))) % 0.45/0.65 (step @p43 :rule refl :args (@t51)) % 0.45/0.65 (step @p44 :rule bool-and-de-morgan :args (@t2 @t7 true)) % 0.45/0.65 (step @p45 :rule nary_cong :premises (@p44 @p43) :args ((or @t55 @t51))) % 0.45/0.65 (step @p46 :rule trans :premises (@p45 @p42)) % 0.45/0.65 (step @p47 :rule bool-impl-elim :args (@t8 @t51)) % 0.45/0.65 (step @p48 :rule trans :premises (@p47 @p46)) % 0.45/0.65 (step @p49 :rule cong :premises (@p48) :args ((forall @t9 (=> @t8 @t51)))) % 0.45/0.65 (step @p50 :rule bool-and-de-morgan :args (@t15 @t49 true)) % 0.45/0.65 (step @p51 :rule cong :premises (@p50) :args (@t57)) % 0.45/0.65 (step @p52 :rule cong :premises (@p51) :args (@t58)) % 0.45/0.65 (step @p53 :rule exists-elim :args ((= (exists @t30 @t56) @t58))) % 0.45/0.65 (step @p54 :rule trans :premises (@p53 @p52)) % 0.45/0.65 (step @p55 :rule eq-symm :args (@t23 @t4)) % 0.45/0.65 (step @p56 :rule refl :args (@t15)) % 0.45/0.65 (step @p57 :rule nary_cong :premises (@p56 @p55) :args (@t29)) % 0.45/0.65 (step @p58 :rule cong :premises (@p57) :args (@t31)) % 0.45/0.65 (step @p59 :rule trans :premises (@p58 @p54)) % 0.45/0.65 (step @p60 :rule refl :args (@t32)) % 0.45/0.65 (step @p61 :rule cong :premises (@p60 @p59) :args (@t33)) % 0.45/0.65 (step @p62 :rule refl :args (@t8)) % 0.45/0.65 (step @p63 :rule cong :premises (@p62 @p61) :args (@t34)) % 0.45/0.65 (step @p64 :rule cong :premises (@p63) :args (@t35)) % 0.45/0.65 (step @p65 :rule trans :premises (@p64 @p49)) % 0.45/0.65 (step @p66 :rule eq_resolve :premises (@p18 @p65)) % 0.45/0.65 (step @p67 :rule instantiate :premises (@p66) :args ((@list tptp.xm @t47))) % 0.45/0.65 (step @p68 :rule aci_norm :args ((= (or @t54 @t6) (or @t53 @t52 @t6)))) % 0.45/0.65 (step @p69 :rule refl :args (@t6)) % 0.45/0.65 (step @p70 :rule nary_cong :premises (@p44 @p69) :args ((or @t55 @t6))) % 0.45/0.65 (step @p71 :rule trans :premises (@p70 @p68)) % 0.45/0.65 (step @p72 :rule bool-impl-elim :args (@t8 @t6)) % 0.45/0.65 (step @p73 :rule trans :premises (@p72 @p71)) % 0.45/0.65 (step @p74 :rule cong :premises (@p73) :args (@t10)) % 0.45/0.65 (step @p75 :rule eq_resolve :premises (@p4 @p74)) % 0.45/0.65 (step @p76 :rule instantiate :premises (@p75) :args ((@list tptp.xm tptp.xn))) % 0.45/0.65 (step @p77 :rule and_elim :premises (@p34) :args (1)) % 0.45/0.65 (step @p78 :rule cnf_or_pos :args (@t62)) % 0.45/0.65 (step @p79 :rule reordering :premises (@p78) :args ((or @t61 @t60 @t59 (not @t62)))) % 0.45/0.65 (step @p80 :rule chain_m_resolution :premises (@p79 @p77 @p41 @p76) :args (@t59 @t63 (@list @t46 @t45 @t62))) % 0.45/0.65 (step @p81 :rule cnf_or_pos :args (@t68)) % 0.45/0.65 (step @p82 :rule reordering :premises (@p81) :args ((or @t61 @t67 @t66 (not @t68)))) % 0.45/0.65 (step @p83 :rule chain_m_resolution :premises (@p82 @p77 @p80 @p67) :args (@t66 @t63 (@list @t46 @t59 @t68))) % 0.45/0.65 (step @p84 :rule bool-double-not-elim :args (@t64)) % 0.45/0.65 (step @p85 :rule refl :args (@t48)) % 0.45/0.65 (step @p86 :rule refl :args (@t69)) % 0.45/0.65 (step @p87 :rule nary_cong :premises (@p86 @p85 @p84) :args ((or @t69 @t48 (not @t65)))) % 0.45/0.65 (step @p88 :rule cnf_equiv_pos2 :args (@t66)) % 0.45/0.65 (step @p89 :rule eq_resolve :premises (@p88 @p87)) % 0.45/0.65 (step @p90 :rule reordering :premises (@p89) :args ((or @t48 @t64 @t69))) % 0.45/0.65 (step @p91 :rule chain_m_resolution :premises (@p90 @p39 @p83) :args (@t64 (@list true false) (@list @t48 @t66))) % 0.45/0.65 (step @p92 :rule aci_norm :args ((= (or @t60 false) @t60))) % 0.45/0.65 (step @p93 :rule evaluate :args ((not true))) % 0.45/0.65 (step @p94 :rule eq-refl :args (@t47)) % 0.45/0.65 (step @p95 :rule cong :premises (@p94) :args (@t70)) % 0.45/0.65 (step @p96 :rule trans :premises (@p95 @p93)) % 0.45/0.65 (step @p97 :rule refl :args (@t60)) % 0.45/0.65 (step @p98 :rule nary_cong :premises (@p97 @p96) :args (@t71)) % 0.45/0.65 (step @p99 :rule trans :premises (@p98 @p92)) % 0.45/0.65 (step @p100 :rule refl :args (@t64)) % 0.45/0.65 (step @p101 :rule cong :premises (@p100 @p99) :args ((=> @t64 @t71))) % 0.45/0.65 (assume-push @p110 @t64) % 0.45/0.65 (step @p103 :rule instantiate :premises (@p91) :args ((@list tptp.xn))) % 0.45/0.65 (step-pop @p111 :rule scope :premises (@p103)) % 0.45/0.65 (step @p104 :rule process_scope :premises (@p111) :args (@t71)) % 0.45/0.65 (step @p106 :rule eq_resolve :premises (@p104 @p101)) % 0.45/0.65 (step @p107 :rule implies_elim :premises (@p106)) % 0.45/0.65 (step @p108 :rule reordering :premises (@p107) :args ((or @t60 @t65))) % 0.45/0.65 (step @p109 false :rule chain_m_resolution :premises (@p108 @p91 @p41) :args (false (@list false false) (@list @t64 @t45))) % 0.45/0.65 ) % 0.45/0.65 % SZS output end Proof % 0.45/0.65 % cvc5 exiting %------------------------------------------------------------------------------