%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM670^1 : TPTP v9.2.1. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n003.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 08:40:19 AM UTC 2026 % Result : Theorem 0.53s 0.71s % Output : Proof 0.53s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM670^1 : TPTP v9.2.1. Released v3.7.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n003.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 11:48:44 EDT 2026 % 0.16/0.34 % CPUTime : % 0.31/0.48 %----Proving TH0 % 0.53/0.71 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.53/0.71 % SZS status Theorem % 0.53/0.71 % SZS output start Proof % 0.53/0.71 ( % 0.53/0.71 (declare-sort tptp.nat 0) % 0.53/0.71 (declare-const tptp.z tptp.nat) % 0.53/0.71 (declare-const tptp.x tptp.nat) % 0.53/0.71 (declare-const tptp.pl (-> tptp.nat tptp.nat tptp.nat)) % 0.53/0.71 (declare-const tptp.y tptp.nat) % 0.53/0.71 (define @t1 () (@var "Xx_0" tptp.nat)) % 0.53/0.71 (define @t2 () (_ tptp.pl tptp.y)) % 0.53/0.71 (define @t3 () (_ @t2 @t1)) % 0.53/0.71 (define @t4 () (= tptp.x @t3)) % 0.53/0.71 (define @t5 () (not @t4)) % 0.53/0.71 (define @t6 () (@list @t1)) % 0.53/0.71 (define @t7 () (forall @t6 @t5)) % 0.53/0.71 (define @t8 () (not @t7)) % 0.53/0.71 (define @t9 () (@var "Xa" Bool)) % 0.53/0.71 (define @t10 () (@var "Xx" tptp.nat)) % 0.53/0.71 (define @t11 () (@var "Xy" tptp.nat)) % 0.53/0.71 (define @t12 () (_ tptp.pl @t11)) % 0.53/0.71 (define @t13 () (_ @t12 @t10)) % 0.53/0.71 (define @t14 () (_ tptp.pl @t10)) % 0.53/0.71 (define @t15 () (_ @t14 @t11)) % 0.53/0.71 (define @t16 () (= @t15 @t13)) % 0.53/0.71 (define @t17 () (forall (@list @t10 @t11) @t16)) % 0.53/0.71 (define @t18 () (@var "Xz" tptp.nat)) % 0.53/0.71 (define @t19 () (_ @t12 @t18)) % 0.53/0.71 (define @t20 () (_ @t14 @t19)) % 0.53/0.71 (define @t21 () (_ (_ tptp.pl @t15) @t18)) % 0.53/0.71 (define @t22 () (= @t21 @t20)) % 0.53/0.71 (define @t23 () (forall (@list @t10 @t11 @t18) @t22)) % 0.53/0.71 (define @t24 () (_ @t2 tptp.z)) % 0.53/0.71 (define @t25 () (_ (_ tptp.pl @t24) @t1)) % 0.53/0.71 (define @t26 () (_ (_ tptp.pl tptp.x) tptp.z)) % 0.53/0.71 (define @t27 () (= @t26 @t25)) % 0.53/0.71 (define @t28 () (not @t27)) % 0.53/0.71 (define @t29 () (forall @t6 @t28)) % 0.53/0.71 (define @t30 () (tptp.pl tptp.y tptp.z)) % 0.53/0.71 (define @t31 () (tptp.pl @t30 @t1)) % 0.53/0.71 (define @t32 () (tptp.pl tptp.x tptp.z)) % 0.53/0.71 (define @t33 () (tptp.pl @t11 @t10)) % 0.53/0.71 (define @t34 () (tptp.pl @t10 @t11)) % 0.53/0.71 (define @t35 () (tptp.pl tptp.y @t1)) % 0.53/0.71 (define @t36 () (forall @t6 (not (= tptp.x @t35)))) % 0.53/0.71 (define @t37 () (@quantifiers_skolemize @t36 0)) % 0.53/0.71 (define @t38 () (tptp.pl @t11 @t18)) % 0.53/0.71 (define @t39 () (tptp.pl @t10 @t38)) % 0.53/0.71 (define @t40 () (tptp.pl @t34 @t18)) % 0.53/0.71 (define @t41 () (= tptp.x (tptp.pl tptp.y @t37))) % 0.53/0.71 (define @t42 () (not @t36)) % 0.53/0.71 (define @t43 () (not (not @t41))) % 0.53/0.71 (define @t44 () (forall @t6 (not (= @t32 @t31)))) % 0.53/0.71 (define @t45 () (= @t32 (tptp.pl @t30 @t37))) % 0.53/0.71 (assume @p1 @t8) % 0.53/0.71 (assume @p2 (forall (@list @t9) (=> (not (not @t9)) @t9))) % 0.53/0.71 (assume @p3 @t17) % 0.53/0.71 (assume @p4 @t23) % 0.53/0.71 (assume @p5 (not (not @t29))) % 0.53/0.71 (assume @p6 true) % 0.53/0.71 (step @p7 :rule refl :args ((tptp.pl @t24 @t1))) % 0.53/0.71 (step @p8 :rule refl :args (@t1)) % 0.53/0.71 (step @p9 :rule refl :args (@t30)) % 0.53/0.71 (step @p10 :rule cong :premises (@p9 @p8) :args (@t31)) % 0.53/0.71 (step @p11 :rule trans :premises (@p10 @p7)) % 0.53/0.71 (step @p12 :rule refl :args (tptp.pl)) % 0.53/0.71 (step @p13 :rule ho_cong :premises (@p12 @p9)) % 0.53/0.71 (step @p14 :rule ho_cong :premises (@p13 @p8)) % 0.53/0.71 (step @p15 :rule cong :premises (@p14 @p11) :args ((= (_ (_ tptp.pl @t30) @t1) @t31))) % 0.53/0.71 (step @p16 :rule symm :premises (@p15)) % 0.53/0.71 (step @p17 :rule refl :args (@t25)) % 0.53/0.71 (step @p18 :rule eq_resolve :premises (@p17 @p16)) % 0.53/0.71 (step @p19 :rule refl :args (@t24)) % 0.53/0.71 (step @p20 :rule cong :premises (@p19 @p9) :args ((= @t24 @t30))) % 0.53/0.71 (step @p21 :rule symm :premises (@p20)) % 0.53/0.71 (step @p22 :rule eq_resolve :premises (@p19 @p21)) % 0.53/0.71 (step @p23 :rule ho_cong :premises (@p12 @p22)) % 0.53/0.71 (step @p24 :rule ho_cong :premises (@p23 @p8)) % 0.53/0.71 (step @p25 :rule trans :premises (@p24 @p18)) % 0.53/0.71 (step @p26 :rule refl :args (@t32)) % 0.53/0.71 (step @p27 :rule refl :args (@t26)) % 0.53/0.71 (step @p28 :rule cong :premises (@p27 @p26) :args ((= @t26 @t32))) % 0.53/0.71 (step @p29 :rule symm :premises (@p28)) % 0.53/0.71 (step @p30 :rule eq_resolve :premises (@p27 @p29)) % 0.53/0.71 (step @p31 :rule cong :premises (@p30 @p25) :args (@t27)) % 0.53/0.71 (step @p32 :rule cong :premises (@p31) :args (@t28)) % 0.53/0.71 (step @p33 :rule cong :premises (@p32) :args (@t29)) % 0.53/0.71 (step @p34 :rule bool-double-not-elim :args (@t29)) % 0.53/0.71 (step @p35 :rule trans :premises (@p34 @p33)) % 0.53/0.71 (step @p36 :rule eq_resolve :premises (@p5 @p35)) % 0.53/0.71 (step @p37 :rule refl :args (@t33)) % 0.53/0.71 (step @p38 :rule refl :args (@t13)) % 0.53/0.71 (step @p39 :rule cong :premises (@p38 @p37) :args ((= @t13 @t33))) % 0.53/0.71 (step @p40 :rule symm :premises (@p39)) % 0.53/0.71 (step @p41 :rule eq_resolve :premises (@p38 @p40)) % 0.53/0.71 (step @p42 :rule refl :args (@t34)) % 0.53/0.71 (step @p43 :rule refl :args (@t15)) % 0.53/0.71 (step @p44 :rule cong :premises (@p43 @p42) :args ((= @t15 @t34))) % 0.53/0.71 (step @p45 :rule symm :premises (@p44)) % 0.53/0.71 (step @p46 :rule eq_resolve :premises (@p43 @p45)) % 0.53/0.71 (step @p47 :rule cong :premises (@p46 @p41) :args (@t16)) % 0.53/0.71 (step @p48 :rule cong :premises (@p47) :args (@t17)) % 0.53/0.71 (step @p49 :rule eq_resolve :premises (@p3 @p48)) % 0.53/0.71 (step @p50 :rule instantiate :premises (@p49) :args ((@list @t37 @t30))) % 0.53/0.71 (step @p51 :rule refl :args ((tptp.pl @t10 @t19))) % 0.53/0.71 (step @p52 :rule refl :args (@t38)) % 0.53/0.71 (step @p53 :rule refl :args (@t10)) % 0.53/0.71 (step @p54 :rule cong :premises (@p53 @p52) :args (@t39)) % 0.53/0.71 (step @p55 :rule trans :premises (@p54 @p51)) % 0.53/0.71 (step @p56 :rule refl :args (@t14)) % 0.53/0.71 (step @p57 :rule ho_cong :premises (@p56 @p52)) % 0.53/0.71 (step @p58 :rule cong :premises (@p57 @p55) :args ((= (_ @t14 @t38) @t39))) % 0.53/0.71 (step @p59 :rule symm :premises (@p58)) % 0.53/0.71 (step @p60 :rule refl :args (@t20)) % 0.53/0.71 (step @p61 :rule eq_resolve :premises (@p60 @p59)) % 0.53/0.71 (step @p62 :rule refl :args (@t19)) % 0.53/0.71 (step @p63 :rule cong :premises (@p62 @p52) :args ((= @t19 @t38))) % 0.53/0.71 (step @p64 :rule symm :premises (@p63)) % 0.53/0.71 (step @p65 :rule eq_resolve :premises (@p62 @p64)) % 0.53/0.71 (step @p66 :rule ho_cong :premises (@p56 @p65)) % 0.53/0.71 (step @p67 :rule trans :premises (@p66 @p61)) % 0.53/0.71 (step @p68 :rule refl :args ((tptp.pl @t15 @t18))) % 0.53/0.71 (step @p69 :rule refl :args (@t18)) % 0.53/0.71 (step @p70 :rule cong :premises (@p42 @p69) :args (@t40)) % 0.53/0.71 (step @p71 :rule trans :premises (@p70 @p68)) % 0.53/0.71 (step @p72 :rule ho_cong :premises (@p12 @p42)) % 0.53/0.71 (step @p73 :rule ho_cong :premises (@p72 @p69)) % 0.53/0.71 (step @p74 :rule cong :premises (@p73 @p71) :args ((= (_ (_ tptp.pl @t34) @t18) @t40))) % 0.53/0.71 (step @p75 :rule symm :premises (@p74)) % 0.53/0.71 (step @p76 :rule refl :args (@t21)) % 0.53/0.71 (step @p77 :rule eq_resolve :premises (@p76 @p75)) % 0.53/0.71 (step @p78 :rule ho_cong :premises (@p12 @p46)) % 0.53/0.71 (step @p79 :rule ho_cong :premises (@p78 @p69)) % 0.53/0.71 (step @p80 :rule trans :premises (@p79 @p77)) % 0.53/0.71 (step @p81 :rule cong :premises (@p80 @p67) :args (@t22)) % 0.53/0.71 (step @p82 :rule cong :premises (@p81) :args (@t23)) % 0.53/0.71 (step @p83 :rule eq_resolve :premises (@p4 @p82)) % 0.53/0.71 (step @p84 :rule instantiate :premises (@p83) :args ((@list @t37 tptp.y tptp.z))) % 0.53/0.71 (step @p85 :rule refl :args (tptp.z)) % 0.53/0.71 (step @p86 :rule instantiate :premises (@p49) :args ((@list tptp.y @t37))) % 0.53/0.71 (step @p87 :rule refl :args (@t35)) % 0.53/0.71 (step @p88 :rule refl :args (@t3)) % 0.53/0.71 (step @p89 :rule cong :premises (@p88 @p87) :args ((= @t3 @t35))) % 0.53/0.71 (step @p90 :rule symm :premises (@p89)) % 0.53/0.71 (step @p91 :rule eq_resolve :premises (@p88 @p90)) % 0.53/0.71 (step @p92 :rule refl :args (tptp.x)) % 0.53/0.71 (step @p93 :rule cong :premises (@p92 @p91) :args (@t4)) % 0.53/0.71 (step @p94 :rule cong :premises (@p93) :args (@t5)) % 0.53/0.71 (step @p95 :rule cong :premises (@p94) :args (@t7)) % 0.53/0.71 (step @p96 :rule cong :premises (@p95) :args (@t8)) % 0.53/0.71 (step @p97 :rule eq_resolve :premises (@p1 @p96)) % 0.53/0.71 (step @p98 :rule refl :args (@t41)) % 0.53/0.71 (step @p99 :rule bool-double-not-elim :args (@t36)) % 0.53/0.71 (step @p100 :rule nary_cong :premises (@p99 @p98) :args ((or (not @t42) @t41))) % 0.53/0.71 (step @p101 :rule bool-double-not-elim :args (@t41)) % 0.53/0.71 (step @p102 :rule refl :args (@t42)) % 0.53/0.71 (step @p103 :rule cong :premises (@p102 @p101) :args ((=> @t42 @t43))) % 0.53/0.71 (assume-push @p121 @t42) % 0.53/0.71 (step @p105 :rule skolemize :premises (@p97)) % 0.53/0.71 (step-pop @p122 :rule scope :premises (@p105)) % 0.53/0.71 (step @p106 :rule process_scope :premises (@p122) :args (@t43)) % 0.53/0.71 (step @p108 :rule eq_resolve :premises (@p106 @p103)) % 0.53/0.71 (step @p109 :rule implies_elim :premises (@p108)) % 0.53/0.71 (step @p110 :rule eq_resolve :premises (@p109 @p100)) % 0.53/0.71 (step @p111 :rule chain_m_resolution :premises (@p110 @p97) :args (@t41 (@list true) (@list @t36))) % 0.53/0.71 (step @p112 :rule trans :premises (@p111 @p86)) % 0.53/0.71 (step @p113 :rule cong :premises (@p112 @p85) :args (@t32)) % 0.53/0.71 (step @p114 :rule trans :premises (@p113 @p84 @p50)) % 0.53/0.71 (assume-push @p123 @t44) % 0.53/0.71 (step @p116 :rule instantiate :premises (@p36) :args ((@list @t37))) % 0.53/0.71 (step-pop @p124 :rule scope :premises (@p116)) % 0.53/0.71 (step @p117 :rule process_scope :premises (@p124) :args ((not @t45))) % 0.53/0.71 (step @p119 :rule implies_elim :premises (@p117)) % 0.53/0.71 (step @p120 false :rule chain_m_resolution :premises (@p119 @p114 @p36) :args (false (@list false false) (@list @t45 @t44))) % 0.53/0.71 ) % 0.53/0.71 % SZS output end Proof % 0.53/0.71 % cvc5 exiting %------------------------------------------------------------------------------