%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM464+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 08:39:30 AM UTC 2026 % Result : Theorem 0.40s 0.58s % Output : Proof 0.40s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM464+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 % 0.17/0.34 % Computer : n025.cluster.edu % 0.17/0.34 % Model : x86_64 x86_64 % 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.34 % Memory : 8042.1875MB % 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.34 % CPULimit : 300 % 0.17/0.34 % WCLimit : 300 % 0.17/0.34 % DateTime : Tue Jun 2 11:22:01 EDT 2026 % 0.17/0.34 % CPUTime : % 0.29/0.49 %----Proving TF0_NAR, FOF, or CNF % 0.40/0.58 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.40/0.58 % SZS status Theorem % 0.40/0.58 % SZS output start Proof % 0.40/0.58 ( % 0.40/0.58 (declare-sort $$unsorted 0) % 0.40/0.58 (declare-const tptp.xm $$unsorted) % 0.40/0.58 (declare-const tptp.sdtmndt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.40/0.58 (declare-const tptp.sdtasdt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.40/0.58 (declare-const tptp.sdtlseqdt0 (-> $$unsorted $$unsorted Bool)) % 0.40/0.58 (declare-const tptp.sdtpldt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.40/0.58 (declare-const tptp.xn $$unsorted) % 0.40/0.58 (declare-const tptp.sz10 $$unsorted) % 0.40/0.58 (declare-const tptp.sz00 $$unsorted) % 0.40/0.58 (declare-const tptp.aNaturalNumber0 (-> $$unsorted Bool)) % 0.40/0.58 (define @t1 () (@var "W0" $$unsorted)) % 0.40/0.58 (define @t2 () (tptp.aNaturalNumber0 @t1)) % 0.40/0.58 (define @t3 () (@list @t1)) % 0.40/0.58 (define @t4 () (tptp.aNaturalNumber0 tptp.sz10)) % 0.40/0.58 (define @t5 () (@var "W1" $$unsorted)) % 0.40/0.58 (define @t6 () (tptp.sdtpldt0 @t1 @t5)) % 0.40/0.58 (define @t7 () (tptp.aNaturalNumber0 @t5)) % 0.40/0.58 (define @t8 () (and @t2 @t7)) % 0.40/0.58 (define @t9 () (@list @t1 @t5)) % 0.40/0.58 (define @t10 () (tptp.sdtasdt0 @t1 @t5)) % 0.40/0.58 (define @t11 () (tptp.sdtpldt0 @t5 @t1)) % 0.40/0.58 (define @t12 () (@var "W2" $$unsorted)) % 0.40/0.58 (define @t13 () (tptp.sdtpldt0 @t5 @t12)) % 0.40/0.58 (define @t14 () (tptp.aNaturalNumber0 @t12)) % 0.40/0.58 (define @t15 () (and @t2 @t7 @t14)) % 0.40/0.58 (define @t16 () (@list @t1 @t5 @t12)) % 0.40/0.58 (define @t17 () (tptp.sdtasdt0 @t5 @t1)) % 0.40/0.58 (define @t18 () (tptp.sdtasdt0 @t12 @t1)) % 0.40/0.58 (define @t19 () (tptp.sdtasdt0 @t1 @t12)) % 0.40/0.58 (define @t20 () (= @t5 @t12)) % 0.40/0.58 (define @t21 () (tptp.sdtpldt0 @t12 @t1)) % 0.40/0.58 (define @t22 () (tptp.sdtpldt0 @t1 @t12)) % 0.40/0.58 (define @t23 () (= @t17 @t18)) % 0.40/0.58 (define @t24 () (= @t10 @t19)) % 0.40/0.58 (define @t25 () (= @t1 tptp.sz00)) % 0.40/0.58 (define @t26 () (not @t25)) % 0.40/0.58 (define @t27 () (= @t5 tptp.sz00)) % 0.40/0.58 (define @t28 () (and @t14 (= @t22 @t5))) % 0.40/0.58 (define @t29 () (@list @t12)) % 0.40/0.58 (define @t30 () (tptp.sdtlseqdt0 @t1 @t5)) % 0.40/0.58 (define @t31 () (= @t1 @t5)) % 0.40/0.58 (define @t32 () (tptp.sdtlseqdt0 @t5 @t1)) % 0.40/0.58 (define @t33 () (tptp.sdtlseqdt0 @t5 @t12)) % 0.40/0.58 (define @t34 () (not (= @t5 @t1))) % 0.40/0.58 (define @t35 () (and @t34 @t32)) % 0.40/0.58 (define @t36 () (or @t30 @t35)) % 0.40/0.58 (define @t37 () (=> @t8 @t36)) % 0.40/0.58 (define @t38 () (forall @t9 @t37)) % 0.40/0.58 (define @t39 () (tptp.sdtpldt0 @t12 @t5)) % 0.40/0.58 (define @t40 () (not @t31)) % 0.40/0.58 (define @t41 () (tptp.sdtlseqdt0 tptp.sz10 @t1)) % 0.40/0.58 (define @t42 () (not (= tptp.sz10 @t1))) % 0.40/0.58 (define @t43 () (and @t42 @t41)) % 0.40/0.58 (define @t44 () (= @t1 tptp.sz10)) % 0.40/0.58 (define @t45 () (or @t25 @t44 @t43)) % 0.40/0.58 (define @t46 () (=> @t2 @t45)) % 0.40/0.58 (define @t47 () (forall @t3 @t46)) % 0.40/0.58 (define @t48 () (tptp.aNaturalNumber0 tptp.xm)) % 0.40/0.58 (define @t49 () (tptp.sdtlseqdt0 tptp.sz10 tptp.xm)) % 0.40/0.58 (define @t50 () (tptp.sdtpldt0 tptp.sz10 @t1)) % 0.40/0.58 (define @t51 () (and @t2 (= @t50 tptp.xm))) % 0.40/0.58 (define @t52 () (exists @t3 @t51)) % 0.40/0.58 (define @t53 () (or @t52 @t49)) % 0.40/0.58 (define @t54 () (= tptp.xm tptp.sz00)) % 0.40/0.58 (define @t55 () (not @t54)) % 0.40/0.58 (define @t56 () (=> @t55 @t53)) % 0.40/0.58 (define @t57 () (not @t56)) % 0.40/0.58 (define @t58 () (and @t40 @t32)) % 0.40/0.58 (define @t59 () (not @t7)) % 0.40/0.58 (define @t60 () (not @t2)) % 0.40/0.58 (define @t61 () (or @t30 @t58)) % 0.40/0.58 (define @t62 () (= tptp.xm @t50)) % 0.40/0.58 (define @t63 () (and @t2 @t62)) % 0.40/0.58 (define @t64 () (forall @t3 (not @t63))) % 0.40/0.58 (define @t65 () (not @t64)) % 0.40/0.58 (define @t66 () (= tptp.sz10 tptp.xm)) % 0.40/0.58 (define @t67 () (not @t66)) % 0.40/0.58 (define @t68 () (and @t67 (tptp.sdtlseqdt0 tptp.xm tptp.sz10))) % 0.40/0.58 (define @t69 () (not @t48)) % 0.40/0.58 (define @t70 () (not @t4)) % 0.40/0.58 (define @t71 () (or @t70 @t69 @t49 @t68)) % 0.40/0.58 (define @t72 () (and (not @t44) @t41)) % 0.40/0.58 (define @t73 () (or @t60 @t25 @t44 @t72)) % 0.40/0.58 (define @t74 () (or @t25 @t44 @t72)) % 0.40/0.58 (define @t75 () (= tptp.xm tptp.sz10)) % 0.40/0.58 (define @t76 () (not @t75)) % 0.40/0.58 (define @t77 () (and @t76 @t49)) % 0.40/0.58 (define @t78 () (or @t69 @t54 @t75 @t77)) % 0.40/0.58 (define @t79 () (forall @t3 @t73)) % 0.40/0.58 (define @t80 () (and @t67 @t49)) % 0.40/0.58 (define @t81 () (= tptp.sz00 tptp.xm)) % 0.40/0.58 (define @t82 () (or @t69 @t81 @t66 @t80)) % 0.40/0.58 (define @t83 () (not @t80)) % 0.40/0.58 (assume @p1 (forall @t3 (=> @t2 true))) % 0.40/0.58 (assume @p2 (tptp.aNaturalNumber0 tptp.sz00)) % 0.40/0.58 (assume @p3 (and @t4 (not (= tptp.sz10 tptp.sz00)))) % 0.40/0.58 (assume @p4 (forall @t9 (=> @t8 (tptp.aNaturalNumber0 @t6)))) % 0.40/0.58 (assume @p5 (forall @t9 (=> @t8 (tptp.aNaturalNumber0 @t10)))) % 0.40/0.58 (assume @p6 (forall @t9 (=> @t8 (= @t6 @t11)))) % 0.40/0.58 (assume @p7 (forall @t16 (=> @t15 (= (tptp.sdtpldt0 @t6 @t12) (tptp.sdtpldt0 @t1 @t13))))) % 0.40/0.58 (assume @p8 (forall @t3 (=> @t2 (and (= (tptp.sdtpldt0 @t1 tptp.sz00) @t1) (= @t1 (tptp.sdtpldt0 tptp.sz00 @t1)))))) % 0.40/0.58 (assume @p9 (forall @t9 (=> @t8 (= @t10 @t17)))) % 0.40/0.58 (assume @p10 (forall @t16 (=> @t15 (= (tptp.sdtasdt0 @t10 @t12) (tptp.sdtasdt0 @t1 (tptp.sdtasdt0 @t5 @t12)))))) % 0.40/0.58 (assume @p11 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz10) @t1) (= @t1 (tptp.sdtasdt0 tptp.sz10 @t1)))))) % 0.40/0.58 (assume @p12 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz00) tptp.sz00) (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 @t1)))))) % 0.40/0.58 (assume @p13 (forall @t16 (=> @t15 (and (= (tptp.sdtasdt0 @t1 @t13) (tptp.sdtpldt0 @t10 @t19)) (= (tptp.sdtasdt0 @t13 @t1) (tptp.sdtpldt0 @t17 @t18)))))) % 0.40/0.58 (assume @p14 (forall @t16 (=> @t15 (=> (or (= @t6 @t22) (= @t11 @t21)) @t20)))) % 0.40/0.58 (assume @p15 (forall @t3 (=> @t2 (=> @t26 (forall (@list @t5 @t12) (=> (and @t7 @t14) (=> (or @t24 @t23) @t20))))))) % 0.40/0.58 (assume @p16 (forall @t9 (=> @t8 (=> (= @t6 tptp.sz00) (and @t25 @t27))))) % 0.40/0.58 (assume @p17 (forall @t9 (=> @t8 (=> (= @t10 tptp.sz00) (or @t25 @t27))))) % 0.40/0.58 (assume @p18 (forall @t9 (=> @t8 (= @t30 (exists @t29 @t28))))) % 0.40/0.58 (assume @p19 (forall @t9 (=> @t8 (=> @t30 (forall @t29 (= (= @t12 (tptp.sdtmndt0 @t5 @t1)) @t28)))))) % 0.40/0.58 (assume @p20 (forall @t3 (=> @t2 (tptp.sdtlseqdt0 @t1 @t1)))) % 0.40/0.58 (assume @p21 (forall @t9 (=> @t8 (=> (and @t30 @t32) @t31)))) % 0.40/0.58 (assume @p22 (forall @t16 (=> @t15 (=> (and @t30 @t33) (tptp.sdtlseqdt0 @t1 @t12))))) % 0.40/0.58 (assume @p23 @t38) % 0.40/0.58 (assume @p24 (forall @t9 (=> @t8 (=> (and @t40 @t30) (forall @t29 (=> @t14 (and (not (= @t21 @t39)) (tptp.sdtlseqdt0 @t21 @t39) (not (= @t22 @t13)) (tptp.sdtlseqdt0 @t22 @t13)))))))) % 0.40/0.58 (assume @p25 (forall @t16 (=> @t15 (=> (and @t26 (not @t20) @t33) (and (not @t24) (tptp.sdtlseqdt0 @t10 @t19) (not @t23) (tptp.sdtlseqdt0 @t17 @t18)))))) % 0.40/0.58 (assume @p26 @t47) % 0.40/0.58 (assume @p27 (and @t48 (tptp.aNaturalNumber0 tptp.xn))) % 0.40/0.58 (assume @p28 @t57) % 0.40/0.58 (assume @p29 true) % 0.40/0.58 (step @p30 :rule aci_norm :args ((= (or (or @t60 @t59) @t61) (or @t60 @t59 @t30 @t58)))) % 0.40/0.58 (step @p31 :rule refl :args (@t61)) % 0.40/0.58 (step @p32 :rule bool-and-de-morgan :args (@t2 @t7 true)) % 0.40/0.58 (step @p33 :rule nary_cong :premises (@p32 @p31) :args ((or (not @t8) @t61))) % 0.40/0.58 (step @p34 :rule trans :premises (@p33 @p30)) % 0.40/0.58 (step @p35 :rule bool-impl-elim :args (@t8 @t61)) % 0.40/0.58 (step @p36 :rule trans :premises (@p35 @p34)) % 0.40/0.58 (step @p37 :rule cong :premises (@p36) :args ((forall @t9 (=> @t8 @t61)))) % 0.40/0.58 (step @p38 :rule refl :args (@t32)) % 0.40/0.58 (step @p39 :rule eq-symm :args (@t5 @t1)) % 0.40/0.58 (step @p40 :rule cong :premises (@p39) :args (@t34)) % 0.40/0.58 (step @p41 :rule nary_cong :premises (@p40 @p38) :args (@t35)) % 0.40/0.58 (step @p42 :rule refl :args (@t30)) % 0.40/0.58 (step @p43 :rule nary_cong :premises (@p42 @p41) :args (@t36)) % 0.40/0.58 (step @p44 :rule refl :args (@t8)) % 0.40/0.58 (step @p45 :rule cong :premises (@p44 @p43) :args (@t37)) % 0.40/0.58 (step @p46 :rule cong :premises (@p45) :args (@t38)) % 0.40/0.58 (step @p47 :rule trans :premises (@p46 @p37)) % 0.40/0.58 (step @p48 :rule eq_resolve :premises (@p23 @p47)) % 0.40/0.58 (step @p49 :rule instantiate :premises (@p48) :args ((@list tptp.sz10 tptp.xm))) % 0.40/0.58 (step @p50 :rule and_elim :premises (@p27) :args (0)) % 0.40/0.58 (step @p51 :rule and_elim :premises (@p3) :args (0)) % 0.40/0.58 (step @p52 :rule refl :args (@t49)) % 0.40/0.58 (step @p53 :rule bool-and-de-morgan :args (@t2 @t62 true)) % 0.40/0.58 (step @p54 :rule cong :premises (@p53) :args (@t64)) % 0.40/0.58 (step @p55 :rule cong :premises (@p54) :args (@t65)) % 0.40/0.58 (step @p56 :rule exists-elim :args ((= (exists @t3 @t63) @t65))) % 0.40/0.58 (step @p57 :rule trans :premises (@p56 @p55)) % 0.40/0.58 (step @p58 :rule eq-symm :args (@t50 tptp.xm)) % 0.40/0.58 (step @p59 :rule refl :args (@t2)) % 0.40/0.58 (step @p60 :rule nary_cong :premises (@p59 @p58) :args (@t51)) % 0.40/0.58 (step @p61 :rule cong :premises (@p60) :args (@t52)) % 0.40/0.58 (step @p62 :rule trans :premises (@p61 @p57)) % 0.40/0.58 (step @p63 :rule nary_cong :premises (@p62 @p52) :args (@t53)) % 0.40/0.58 (step @p64 :rule eq-symm :args (tptp.xm tptp.sz00)) % 0.40/0.58 (step @p65 :rule cong :premises (@p64) :args (@t55)) % 0.40/0.58 (step @p66 :rule cong :premises (@p65 @p63) :args (@t56)) % 0.40/0.58 (step @p67 :rule cong :premises (@p66) :args (@t57)) % 0.40/0.58 (step @p68 :rule eq_resolve :premises (@p28 @p67)) % 0.40/0.58 (step @p69 :rule not_implies_elim2 :premises (@p68)) % 0.40/0.58 (step @p70 :rule not_or_elim :premises (@p69) :args (1)) % 0.40/0.58 (step @p71 :rule cnf_or_pos :args (@t71)) % 0.40/0.58 (step @p72 :rule reordering :premises (@p71) :args ((or @t49 @t70 @t69 @t68 (not @t71)))) % 0.40/0.58 (step @p73 :rule chain_m_resolution :premises (@p72 @p70 @p51 @p50 @p49) :args (@t68 (@list true false false false) (@list @t49 @t4 @t48 @t71))) % 0.40/0.58 (step @p74 :rule aci_norm :args ((= (or @t60 @t74) @t73))) % 0.40/0.58 (step @p75 :rule bool-impl-elim :args (@t2 @t74)) % 0.40/0.58 (step @p76 :rule trans :premises (@p75 @p74)) % 0.40/0.58 (step @p77 :rule cong :premises (@p76) :args ((forall @t3 (=> @t2 @t74)))) % 0.40/0.58 (step @p78 :rule refl :args (@t41)) % 0.40/0.58 (step @p79 :rule eq-symm :args (tptp.sz10 @t1)) % 0.40/0.58 (step @p80 :rule cong :premises (@p79) :args (@t42)) % 0.40/0.58 (step @p81 :rule nary_cong :premises (@p80 @p78) :args (@t43)) % 0.40/0.58 (step @p82 :rule refl :args (@t44)) % 0.40/0.58 (step @p83 :rule refl :args (@t25)) % 0.40/0.58 (step @p84 :rule nary_cong :premises (@p83 @p82 @p81) :args (@t45)) % 0.40/0.58 (step @p85 :rule cong :premises (@p59 @p84) :args (@t46)) % 0.40/0.58 (step @p86 :rule cong :premises (@p85) :args (@t47)) % 0.40/0.58 (step @p87 :rule trans :premises (@p86 @p77)) % 0.40/0.58 (step @p88 :rule eq_resolve :premises (@p26 @p87)) % 0.40/0.58 (step @p89 :rule eq-symm :args (tptp.xm tptp.sz10)) % 0.40/0.58 (step @p90 :rule cong :premises (@p89) :args (@t76)) % 0.40/0.58 (step @p91 :rule nary_cong :premises (@p90 @p52) :args (@t77)) % 0.40/0.58 (step @p92 :rule refl :args (@t69)) % 0.40/0.58 (step @p93 :rule nary_cong :premises (@p92 @p64 @p89 @p91) :args (@t78)) % 0.40/0.58 (step @p94 :rule refl :args (@t79)) % 0.40/0.58 (step @p95 :rule cong :premises (@p94 @p93) :args ((=> @t79 @t78))) % 0.40/0.58 (assume-push @p113 @t79) % 0.40/0.58 (step @p97 :rule instantiate :premises (@p88) :args ((@list tptp.xm))) % 0.40/0.58 (step-pop @p114 :rule scope :premises (@p97)) % 0.40/0.58 (step @p98 :rule process_scope :premises (@p114) :args (@t78)) % 0.40/0.58 (step @p100 :rule eq_resolve :premises (@p98 @p95)) % 0.40/0.58 (step @p101 :rule implies_elim :premises (@p100)) % 0.40/0.58 (step @p102 :rule chain_m_resolution :premises (@p101 @p88) :args (@t82 (@list false) (@list @t79))) % 0.40/0.58 (step @p103 :rule cnf_and_pos :args (@t80 1)) % 0.40/0.58 (step @p104 :rule reordering :premises (@p103) :args ((or @t49 @t83))) % 0.40/0.58 (step @p105 :rule chain_m_resolution :premises (@p104 @p70) :args (@t83 (@list true) (@list @t49))) % 0.40/0.58 (step @p106 :rule not_implies_elim1 :premises (@p68)) % 0.40/0.58 (step @p107 :rule cnf_or_pos :args (@t82)) % 0.40/0.58 (step @p108 :rule reordering :premises (@p107) :args ((or @t81 @t69 @t66 @t80 (not @t82)))) % 0.40/0.58 (step @p109 :rule chain_m_resolution :premises (@p108 @p106 @p50 @p105 @p102) :args (@t66 (@list true false true false) (@list @t81 @t48 @t80 @t82))) % 0.40/0.58 (step @p110 :rule cnf_and_pos :args (@t68 0)) % 0.40/0.58 (step @p111 :rule reordering :premises (@p110) :args ((or @t67 (not @t68)))) % 0.40/0.58 (step @p112 false :rule chain_m_resolution :premises (@p111 @p109 @p73) :args (false (@list false false) (@list @t66 @t68))) % 0.40/0.58 ) % 0.40/0.58 % SZS output end Proof % 0.40/0.58 % cvc5 exiting %------------------------------------------------------------------------------