%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM667^1 : TPTP v9.2.1. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n019.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 08:40:18 AM UTC 2026 % Result : Theorem 0.28s 0.55s % Output : Proof 0.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM667^1 : TPTP v9.2.1. Released v3.7.0. % 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 : n019.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 11:48:34 EDT 2026 % 0.16/0.34 % CPUTime : % 0.28/0.49 %----Proving TH0 % 0.28/0.55 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.28/0.55 % SZS status Theorem % 0.28/0.55 % SZS output start Proof % 0.28/0.55 ( % 0.28/0.55 (declare-sort tptp.nat 0) % 0.28/0.55 (declare-const tptp.z tptp.nat) % 0.28/0.55 (declare-const tptp.less (-> tptp.nat tptp.nat Bool)) % 0.28/0.55 (declare-const tptp.x tptp.nat) % 0.28/0.55 (declare-const tptp.y tptp.nat) % 0.28/0.55 (define @t1 () (= tptp.x tptp.y)) % 0.28/0.55 (define @t2 () (_ tptp.less tptp.x)) % 0.28/0.55 (define @t3 () (_ @t2 tptp.y)) % 0.28/0.55 (define @t4 () (not @t3)) % 0.28/0.55 (define @t5 () (=> @t4 @t1)) % 0.28/0.55 (define @t6 () (= tptp.y tptp.z)) % 0.28/0.55 (define @t7 () (_ (_ tptp.less tptp.y) tptp.z)) % 0.28/0.55 (define @t8 () (not @t7)) % 0.28/0.55 (define @t9 () (=> @t8 @t6)) % 0.28/0.55 (define @t10 () (@var "Xa" Bool)) % 0.28/0.55 (define @t11 () (@var "Xz" tptp.nat)) % 0.28/0.55 (define @t12 () (@var "Xx" tptp.nat)) % 0.28/0.55 (define @t13 () (_ tptp.less @t12)) % 0.28/0.55 (define @t14 () (_ @t13 @t11)) % 0.28/0.55 (define @t15 () (@var "Xy" tptp.nat)) % 0.28/0.55 (define @t16 () (_ (_ tptp.less @t15) @t11)) % 0.28/0.55 (define @t17 () (=> @t16 @t14)) % 0.28/0.55 (define @t18 () (= @t12 @t15)) % 0.28/0.55 (define @t19 () (_ @t13 @t15)) % 0.28/0.55 (define @t20 () (not @t19)) % 0.28/0.55 (define @t21 () (=> @t20 @t18)) % 0.28/0.55 (define @t22 () (@list @t12 @t15 @t11)) % 0.28/0.55 (define @t23 () (forall @t22 (=> @t21 @t17))) % 0.28/0.55 (define @t24 () (not @t16)) % 0.28/0.55 (define @t25 () (= tptp.x tptp.z)) % 0.28/0.55 (define @t26 () (_ @t2 tptp.z)) % 0.28/0.55 (define @t27 () (not @t26)) % 0.28/0.55 (define @t28 () (=> @t27 @t25)) % 0.28/0.55 (define @t29 () (not @t28)) % 0.28/0.55 (define @t30 () (tptp.less tptp.x tptp.z)) % 0.28/0.55 (define @t31 () (not @t1)) % 0.28/0.55 (define @t32 () (tptp.less tptp.x tptp.y)) % 0.28/0.55 (define @t33 () (not @t32)) % 0.28/0.55 (define @t34 () (and @t33 @t31)) % 0.28/0.55 (define @t35 () (not @t34)) % 0.28/0.55 (define @t36 () (tptp.less @t12 @t11)) % 0.28/0.55 (define @t37 () (tptp.less @t15 @t11)) % 0.28/0.55 (define @t38 () (not @t18)) % 0.28/0.55 (define @t39 () (tptp.less @t12 @t15)) % 0.28/0.55 (define @t40 () (and @t20 @t38)) % 0.28/0.55 (define @t41 () (or @t40 @t24 @t14)) % 0.28/0.55 (define @t42 () (tptp.less tptp.y tptp.z)) % 0.28/0.55 (define @t43 () (not @t42)) % 0.28/0.55 (define @t44 () (or @t34 @t43 @t30)) % 0.28/0.55 (define @t45 () (not @t6)) % 0.28/0.55 (define @t46 () (not @t30)) % 0.28/0.55 (define @t47 () (and @t32 @t6 @t46)) % 0.28/0.55 (define @t48 () (@list true)) % 0.28/0.55 (define @t49 () (not @t25)) % 0.28/0.55 (define @t50 () (and @t1 @t49)) % 0.28/0.55 (assume @p1 @t5) % 0.28/0.55 (assume @p2 @t9) % 0.28/0.55 (assume @p3 (forall (@list @t10) (=> (not (not @t10)) @t10))) % 0.28/0.55 (assume @p4 @t23) % 0.28/0.55 (assume @p5 (forall @t22 (=> @t19 (=> (=> @t24 (= @t15 @t11)) @t14)))) % 0.28/0.55 (assume @p6 @t29) % 0.28/0.55 (assume @p7 true) % 0.28/0.55 (step @p8 :rule refl :args (@t25)) % 0.28/0.55 (step @p9 :rule refl :args (@t30)) % 0.28/0.55 (step @p10 :rule refl :args (@t26)) % 0.28/0.55 (step @p11 :rule cong :premises (@p10 @p9) :args ((= @t26 @t30))) % 0.28/0.55 (step @p12 :rule symm :premises (@p11)) % 0.28/0.55 (step @p13 :rule eq_resolve :premises (@p10 @p12)) % 0.28/0.55 (step @p14 :rule cong :premises (@p13) :args (@t27)) % 0.28/0.55 (step @p15 :rule cong :premises (@p14 @p8) :args (@t28)) % 0.28/0.55 (step @p16 :rule cong :premises (@p15) :args (@t29)) % 0.28/0.55 (step @p17 :rule eq_resolve :premises (@p6 @p16)) % 0.28/0.55 (step @p18 :rule not_implies_elim2 :premises (@p17)) % 0.28/0.55 (step @p19 :rule cnf_and_pos :args (@t34 0)) % 0.28/0.55 (step @p20 :rule reordering :premises (@p19) :args ((or @t33 @t35))) % 0.28/0.55 (step @p21 :rule not_implies_elim1 :premises (@p17)) % 0.28/0.55 (step @p22 :rule refl :args (@t36)) % 0.28/0.55 (step @p23 :rule refl :args (@t14)) % 0.28/0.55 (step @p24 :rule cong :premises (@p23 @p22) :args ((= @t14 @t36))) % 0.28/0.55 (step @p25 :rule symm :premises (@p24)) % 0.28/0.55 (step @p26 :rule eq_resolve :premises (@p23 @p25)) % 0.28/0.55 (step @p27 :rule refl :args (@t37)) % 0.28/0.55 (step @p28 :rule refl :args (@t16)) % 0.28/0.55 (step @p29 :rule cong :premises (@p28 @p27) :args ((= @t16 @t37))) % 0.28/0.55 (step @p30 :rule symm :premises (@p29)) % 0.28/0.55 (step @p31 :rule eq_resolve :premises (@p28 @p30)) % 0.28/0.55 (step @p32 :rule cong :premises (@p31) :args (@t24)) % 0.28/0.55 (step @p33 :rule refl :args (@t38)) % 0.28/0.55 (step @p34 :rule refl :args (@t39)) % 0.28/0.55 (step @p35 :rule refl :args (@t19)) % 0.28/0.55 (step @p36 :rule cong :premises (@p35 @p34) :args ((= @t19 @t39))) % 0.28/0.55 (step @p37 :rule symm :premises (@p36)) % 0.28/0.55 (step @p38 :rule eq_resolve :premises (@p35 @p37)) % 0.28/0.55 (step @p39 :rule cong :premises (@p38) :args (@t20)) % 0.28/0.55 (step @p40 :rule nary_cong :premises (@p39 @p33) :args (@t40)) % 0.28/0.55 (step @p41 :rule nary_cong :premises (@p40 @p32 @p26) :args (@t41)) % 0.28/0.55 (step @p42 :rule cong :premises (@p41) :args ((forall @t22 @t41))) % 0.28/0.55 (step @p43 :rule aci_norm :args ((= (or @t40 (or @t24 @t14)) @t41))) % 0.28/0.55 (step @p44 :rule bool-impl-elim :args (@t16 @t14)) % 0.28/0.55 (step @p45 :rule bool-implies-de-morgan :args (@t20 @t18)) % 0.28/0.55 (step @p46 :rule nary_cong :premises (@p45 @p44) :args ((or (not @t21) @t17))) % 0.28/0.55 (step @p47 :rule trans :premises (@p46 @p43)) % 0.28/0.55 (step @p48 :rule bool-impl-elim :args (@t21 @t17)) % 0.28/0.55 (step @p49 :rule trans :premises (@p48 @p47)) % 0.28/0.55 (step @p50 :rule cong :premises (@p49) :args (@t23)) % 0.28/0.55 (step @p51 :rule trans :premises (@p50 @p42)) % 0.28/0.55 (step @p52 :rule eq_resolve :premises (@p4 @p51)) % 0.28/0.55 (step @p53 :rule instantiate :premises (@p52) :args ((@list tptp.x tptp.y tptp.z))) % 0.28/0.55 (step @p54 :rule cnf_or_pos :args (@t44)) % 0.28/0.55 (step @p55 :rule reordering :premises (@p54) :args ((or @t43 @t30 @t34 (not @t44)))) % 0.28/0.55 (step @p56 :rule refl :args (@t6)) % 0.28/0.55 (step @p57 :rule bool-double-not-elim :args (@t42)) % 0.28/0.55 (step @p58 :rule nary_cong :premises (@p57 @p56) :args ((or (not @t43) @t6))) % 0.28/0.55 (step @p59 :rule refl :args (@t42)) % 0.28/0.55 (step @p60 :rule refl :args (@t7)) % 0.28/0.55 (step @p61 :rule cong :premises (@p60 @p59) :args ((= @t7 @t42))) % 0.28/0.55 (step @p62 :rule symm :premises (@p61)) % 0.28/0.55 (step @p63 :rule eq_resolve :premises (@p60 @p62)) % 0.28/0.55 (step @p64 :rule cong :premises (@p63) :args (@t8)) % 0.28/0.55 (step @p65 :rule cong :premises (@p64 @p56) :args (@t9)) % 0.28/0.55 (step @p66 :rule eq_resolve :premises (@p2 @p65)) % 0.28/0.55 (step @p67 :rule implies_elim :premises (@p66)) % 0.28/0.55 (step @p68 :rule eq_resolve :premises (@p67 @p58)) % 0.28/0.55 (step @p69 :rule reordering :premises (@p68) :args ((or @t6 @t42))) % 0.28/0.55 (step @p70 :rule bool-double-not-elim :args (@t30)) % 0.28/0.55 (step @p71 :rule refl :args (@t33)) % 0.28/0.55 (step @p72 :rule refl :args (@t45)) % 0.28/0.55 (step @p73 :rule nary_cong :premises (@p72 @p71 @p70) :args ((or @t45 @t33 (not @t46)))) % 0.28/0.55 (assume-push @p151 @t32) % 0.28/0.55 (assume-push @p152 @t6) % 0.28/0.55 (assume-push @p153 @t46) % 0.28/0.55 (step @p77 :rule evaluate :args ((= false true))) % 0.28/0.55 (step @p78 :rule true_intro :premises (@p151)) % 0.28/0.55 (step @p79 :rule symm :premises (@p152)) % 0.28/0.55 (step @p80 :rule refl :args (tptp.x)) % 0.28/0.55 (step @p81 :rule cong :premises (@p80 @p79) :args (@t30)) % 0.28/0.55 (step @p82 :rule false_intro :premises (@p21)) % 0.28/0.55 (step @p83 :rule symm :premises (@p82)) % 0.28/0.55 (step @p84 :rule trans :premises (@p83 @p81 @p78)) % 0.28/0.55 (step @p85 false :rule eq_resolve :premises (@p84 @p77)) % 0.28/0.55 (step-pop @p154 :rule scope :premises (@p85)) % 0.28/0.55 (step-pop @p155 :rule scope :premises (@p154)) % 0.28/0.55 (step-pop @p156 :rule scope :premises (@p155)) % 0.28/0.55 (step @p86 :rule process_scope :premises (@p156) :args (false)) % 0.28/0.55 (assume-push @p157 @t6) % 0.28/0.55 (assume-push @p158 @t32) % 0.28/0.55 (assume-push @p159 @t46) % 0.28/0.55 (step @p93 :rule and_intro :premises (@p158 @p157 @p21)) % 0.28/0.55 (step-pop @p160 :rule scope :premises (@p93)) % 0.28/0.55 (step-pop @p161 :rule scope :premises (@p160)) % 0.28/0.55 (step-pop @p162 :rule scope :premises (@p161)) % 0.28/0.55 (step @p94 :rule process_scope :premises (@p162) :args (@t47)) % 0.28/0.55 (step @p98 :rule implies_elim :premises (@p94)) % 0.28/0.55 (step @p99 :rule resolution :premises (@p98 @p86) :args (true @t47)) % 0.28/0.55 (step @p100 :rule not_and :premises (@p99)) % 0.28/0.55 (step @p101 :rule eq_resolve :premises (@p100 @p73)) % 0.28/0.55 (step @p102 :rule reordering :premises (@p101) :args ((or @t33 @t30 @t45))) % 0.28/0.55 (step @p103 :rule chain_m_resolution :premises (@p102 @p21 @p69 @p55 @p53 @p21 @p20) :args (@t33 (@list true false true false true true) (@list @t30 @t6 @t42 @t44 @t30 @t34))) % 0.28/0.55 (step @p104 :rule refl :args (@t1)) % 0.28/0.55 (step @p105 :rule bool-double-not-elim :args (@t32)) % 0.28/0.55 (step @p106 :rule nary_cong :premises (@p105 @p104) :args ((or (not @t33) @t1))) % 0.28/0.55 (step @p107 :rule refl :args (@t32)) % 0.28/0.55 (step @p108 :rule refl :args (@t3)) % 0.28/0.55 (step @p109 :rule cong :premises (@p108 @p107) :args ((= @t3 @t32))) % 0.28/0.55 (step @p110 :rule symm :premises (@p109)) % 0.28/0.55 (step @p111 :rule eq_resolve :premises (@p108 @p110)) % 0.28/0.55 (step @p112 :rule cong :premises (@p111) :args (@t4)) % 0.28/0.55 (step @p113 :rule cong :premises (@p112 @p104) :args (@t5)) % 0.28/0.55 (step @p114 :rule eq_resolve :premises (@p1 @p113)) % 0.28/0.55 (step @p115 :rule implies_elim :premises (@p114)) % 0.28/0.55 (step @p116 :rule eq_resolve :premises (@p115 @p106)) % 0.28/0.55 (step @p117 :rule reordering :premises (@p116) :args ((or @t1 @t32))) % 0.28/0.55 (step @p118 :rule chain_m_resolution :premises (@p117 @p103) :args (@t1 @t48 (@list @t32))) % 0.28/0.55 (step @p119 :rule cnf_and_pos :args (@t34 1)) % 0.28/0.55 (step @p120 :rule reordering :premises (@p119) :args ((or @t31 @t35))) % 0.28/0.55 (step @p121 :rule chain_m_resolution :premises (@p120 @p118) :args (@t35 (@list false) (@list @t1))) % 0.38/0.55 (step @p122 :rule chain_m_resolution :premises (@p55 @p21 @p121 @p53) :args (@t43 (@list true true false) (@list @t30 @t34 @t44))) % 0.38/0.55 (step @p123 :rule chain_m_resolution :premises (@p69 @p122) :args (@t6 @t48 (@list @t42))) % 0.38/0.55 (step @p124 :rule bool-double-not-elim :args (@t25)) % 0.38/0.55 (step @p125 :rule refl :args (@t31)) % 0.38/0.55 (step @p126 :rule nary_cong :premises (@p125 @p124 @p72) :args ((or @t31 (not @t49) @t45))) % 0.38/0.55 (assume-push @p163 @t1) % 0.38/0.55 (assume-push @p164 @t49) % 0.38/0.55 (assume-push @p165 @t49) % 0.38/0.55 (assume-push @p166 @t1) % 0.38/0.55 (step @p131 :rule false_intro :premises (@p18)) % 0.38/0.55 (step @p132 :rule refl :args (tptp.z)) % 0.38/0.55 (step @p133 :rule symm :premises (@p163)) % 0.38/0.55 (step @p134 :rule cong :premises (@p133 @p132) :args (@t6)) % 0.38/0.55 (step @p135 :rule trans :premises (@p134 @p131)) % 0.38/0.55 (step @p136 :rule false_elim :premises (@p135)) % 0.38/0.55 (step-pop @p167 :rule scope :premises (@p136)) % 0.38/0.55 (step-pop @p168 :rule scope :premises (@p167)) % 0.38/0.55 (step @p137 :rule process_scope :premises (@p168) :args (@t45)) % 0.38/0.55 (step @p140 :rule and_intro :premises (@p18 @p163)) % 0.38/0.55 (step @p141 :rule modus_ponens :premises (@p140 @p137)) % 0.38/0.55 (step-pop @p169 :rule scope :premises (@p141)) % 0.38/0.55 (step-pop @p170 :rule scope :premises (@p169)) % 0.38/0.55 (step @p142 :rule process_scope :premises (@p170) :args (@t45)) % 0.38/0.55 (step @p145 :rule implies_elim :premises (@p142)) % 0.38/0.55 (step @p146 :rule cnf_and_neg :args (@t50)) % 0.38/0.55 (step @p147 :rule resolution :premises (@p146 @p145) :args (true @t50)) % 0.38/0.55 (step @p148 :rule eq_resolve :premises (@p147 @p126)) % 0.38/0.55 (step @p149 :rule reordering :premises (@p148) :args ((or @t25 @t31 @t45))) % 0.38/0.55 (step @p150 false :rule chain_m_resolution :premises (@p149 @p123 @p118 @p18) :args (false (@list false false true) (@list @t6 @t1 @t25))) % 0.38/0.55 ) % 0.38/0.55 % SZS output end Proof % 0.38/0.55 % cvc5 exiting %------------------------------------------------------------------------------