%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET557^1 : TPTP v9.2.1. Released v3.6.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n021.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 08:48:03 AM UTC 2026 % Result : Theorem 1.41s 1.60s % Output : Proof 1.41s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.11 % Problem : SET557^1 : TPTP v9.2.1. Released v3.6.0. % 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.15/0.33 % Computer : n021.cluster.edu % 0.15/0.33 % Model : x86_64 x86_64 % 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.33 % Memory : 8042.1875MB % 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.33 % CPULimit : 300 % 0.15/0.33 % WCLimit : 300 % 0.15/0.33 % DateTime : Tue Jun 2 16:02:05 EDT 2026 % 0.15/0.33 % CPUTime : % 0.30/0.47 %----Proving TH0 % 1.41/1.60 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 1.41/1.60 % SZS status Theorem % 1.41/1.60 % SZS output start Proof % 1.41/1.60 ( % 1.41/1.60 (declare-sort $$unsorted 0) % 1.41/1.60 (define @t1 () (@var "F" (-> $$unsorted Bool))) % 1.41/1.60 (define @t2 () (@var "X" $$unsorted)) % 1.41/1.60 (define @t3 () (@var "G" (-> $$unsorted $$unsorted Bool))) % 1.41/1.60 (define @t4 () (_ @t3 @t2)) % 1.41/1.60 (define @t5 () (@list @t2)) % 1.41/1.60 (define @t6 () (exists @t5 (= @t4 @t1))) % 1.41/1.60 (define @t7 () (@list @t1)) % 1.41/1.60 (define @t8 () (forall @t7 @t6)) % 1.41/1.60 (define @t9 () (@list @t3)) % 1.41/1.60 (define @t10 () (exists @t9 @t8)) % 1.41/1.60 (define @t11 () (= @t1 @t4)) % 1.41/1.60 (define @t12 () (not (forall @t5 (not @t11)))) % 1.41/1.60 (define @t13 () (forall @t7 @t12)) % 1.41/1.60 (define @t14 () (forall @t9 (not @t13))) % 1.41/1.60 (define @t15 () (not @t14)) % 1.41/1.60 (define @t16 () (@quantifiers_skolemize @t14 0)) % 1.41/1.60 (define @t17 () (_ @t16 @t2)) % 1.41/1.60 (define @t18 () (forall @t7 (not (forall @t5 (not (= @t1 @t17)))))) % 1.41/1.60 (define @t19 () (not (not @t18))) % 1.41/1.60 (define @t20 () (@list true)) % 1.41/1.60 (define @t21 () (@var "BOUND_VARIABLE_14542" $$unsorted)) % 1.41/1.60 (define @t22 () (not (_ @t16 @t21 @t21))) % 1.41/1.60 (define @t23 () (@list @t21)) % 1.41/1.60 (define @t24 () (lambda @t23 @t22)) % 1.41/1.60 (define @t25 () (not (= @t24 @t17))) % 1.41/1.60 (define @t26 () (forall @t5 @t25)) % 1.41/1.60 (define @t27 () (not @t26)) % 1.41/1.60 (define @t28 () (forall @t5 (not (= @t17 @t24)))) % 1.41/1.60 (define @t29 () (not @t28)) % 1.41/1.60 (define @t30 () (@purify @t24)) % 1.41/1.60 (define @t31 () (@quantifiers_skolemize @t28 0)) % 1.41/1.60 (define @t32 () (_ @t16 @t31)) % 1.41/1.60 (define @t33 () (= @t32 @t30)) % 1.41/1.60 (define @t34 () (= @t24 @t32)) % 1.41/1.60 (define @t35 () (= @t32 @t24)) % 1.41/1.60 (define @t36 () (not (not @t35))) % 1.41/1.60 (define @t37 () (_ @t30 @t21)) % 1.41/1.60 (define @t38 () (_ @t24 @t21)) % 1.41/1.60 (define @t39 () (= @t37 @t38)) % 1.41/1.60 (define @t40 () (forall @t23 @t39)) % 1.41/1.60 (define @t41 () (_ @t30 @t31)) % 1.41/1.60 (define @t42 () (_ @t16 @t31 @t31)) % 1.41/1.60 (define @t43 () (not @t42)) % 1.41/1.60 (define @t44 () (= @t43 @t41)) % 1.41/1.60 (define @t45 () (not @t44)) % 1.41/1.60 (define @t46 () (not @t43)) % 1.41/1.60 (define @t47 () (not @t41)) % 1.41/1.60 (define @t48 () (not @t33)) % 1.41/1.60 (define @t49 () (and @t41 @t43 @t33)) % 1.41/1.60 (define @t50 () (and @t47 @t42 @t33)) % 1.41/1.60 (assume @p1 (not (not @t10))) % 1.41/1.60 (assume @p2 true) % 1.41/1.60 (step @p3 :rule exists-elim :args ((= (exists @t9 @t13) @t15))) % 1.41/1.60 (step @p4 :rule exists-elim :args ((= (exists @t5 @t11) @t12))) % 1.41/1.60 (step @p5 :rule eq-symm :args (@t4 @t1)) % 1.41/1.60 (step @p6 :rule cong :premises (@p5) :args (@t6)) % 1.41/1.60 (step @p7 :rule trans :premises (@p6 @p4)) % 1.41/1.60 (step @p8 :rule cong :premises (@p7) :args (@t8)) % 1.41/1.60 (step @p9 :rule cong :premises (@p8) :args (@t10)) % 1.41/1.60 (step @p10 :rule trans :premises (@p9 @p3)) % 1.41/1.60 (step @p11 :rule bool-double-not-elim :args (@t10)) % 1.41/1.60 (step @p12 :rule trans :premises (@p11 @p10)) % 1.41/1.60 (step @p13 :rule eq_resolve :premises (@p1 @p12)) % 1.41/1.60 (step @p14 :rule refl :args (@t18)) % 1.41/1.60 (step @p15 :rule bool-double-not-elim :args (@t14)) % 1.41/1.60 (step @p16 :rule nary_cong :premises (@p15 @p14) :args ((or (not @t15) @t18))) % 1.41/1.60 (step @p17 :rule bool-double-not-elim :args (@t18)) % 1.41/1.60 (step @p18 :rule refl :args (@t15)) % 1.41/1.60 (step @p19 :rule cong :premises (@p18 @p17) :args ((=> @t15 @t19))) % 1.41/1.60 (assume-push @p161 @t15) % 1.41/1.60 (step @p21 :rule skolemize :premises (@p13)) % 1.41/1.60 (step-pop @p162 :rule scope :premises (@p21)) % 1.41/1.60 (step @p22 :rule process_scope :premises (@p162) :args (@t19)) % 1.41/1.60 (step @p24 :rule eq_resolve :premises (@p22 @p19)) % 1.41/1.60 (step @p25 :rule implies_elim :premises (@p24)) % 1.41/1.60 (step @p26 :rule eq_resolve :premises (@p25 @p16)) % 1.41/1.60 (step @p27 :rule chain_m_resolution :premises (@p26 @p13) :args (@t18 @t20 (@list @t14))) % 1.41/1.60 (step @p28 :rule eq-symm :args (@t24 @t17)) % 1.41/1.60 (step @p29 :rule cong :premises (@p28) :args (@t25)) % 1.41/1.60 (step @p30 :rule cong :premises (@p29) :args (@t26)) % 1.41/1.60 (step @p31 :rule cong :premises (@p30) :args (@t27)) % 1.41/1.60 (step @p32 :rule cong :premises (@p14 @p31) :args ((=> @t18 @t27))) % 1.41/1.60 (assume-push @p163 @t18) % 1.41/1.60 (step @p34 :rule instantiate :premises (@p27) :args ((@list @t24))) % 1.41/1.60 (step-pop @p164 :rule scope :premises (@p34)) % 1.41/1.60 (step @p35 :rule process_scope :premises (@p164) :args (@t27)) % 1.41/1.60 (step @p37 :rule eq_resolve :premises (@p35 @p32)) % 1.41/1.60 (step @p38 :rule implies_elim :premises (@p37)) % 1.41/1.60 (step @p39 :rule chain_m_resolution :premises (@p38 @p27) :args (@t29 (@list false) (@list @t18))) % 1.41/1.60 (step @p40 :rule refl :args (@t33)) % 1.41/1.60 (step @p41 :rule bool-double-not-elim :args (@t28)) % 1.41/1.60 (step @p42 :rule nary_cong :premises (@p41 @p40) :args ((or (not @t29) @t33))) % 1.41/1.60 (step @p43 :rule eq-symm :args (@t30 @t32)) % 1.41/1.60 (step @p44 :rule refl :args (@t32)) % 1.41/1.60 (step @p45 :rule eq-refl :args (@t24)) % 1.41/1.60 (step @p46 :rule skolem_intro :args (@t30)) % 1.41/1.60 (step @p47 :rule refl :args (@t24)) % 1.41/1.60 (step @p48 :rule cong :premises (@p47 @p46) :args ((= @t24 @t30))) % 1.41/1.60 (step @p49 :rule trans :premises (@p48 @p45)) % 1.41/1.60 (step @p50 :rule true_elim :premises (@p49)) % 1.41/1.60 (step @p51 :rule cong :premises (@p50 @p44) :args (@t34)) % 1.41/1.60 (step @p52 :rule trans :premises (@p51 @p43)) % 1.41/1.60 (step @p53 :rule refl :args (@t29)) % 1.41/1.60 (step @p54 :rule cong :premises (@p53 @p52) :args ((=> @t29 @t34))) % 1.41/1.60 (step @p55 :rule eq-symm :args (@t32 @t24)) % 1.41/1.60 (step @p56 :rule bool-double-not-elim :args (@t35)) % 1.41/1.60 (step @p57 :rule trans :premises (@p56 @p55)) % 1.41/1.60 (step @p58 :rule cong :premises (@p53 @p57) :args ((=> @t29 @t36))) % 1.41/1.60 (step @p59 :rule trans :premises (@p58 @p54)) % 1.41/1.60 (assume-push @p165 @t29) % 1.41/1.60 (step @p61 :rule skolemize :premises (@p39)) % 1.41/1.60 (step-pop @p166 :rule scope :premises (@p61)) % 1.41/1.60 (step @p62 :rule process_scope :premises (@p166) :args (@t36)) % 1.41/1.60 (step @p64 :rule eq_resolve :premises (@p62 @p59)) % 1.41/1.60 (step @p65 :rule implies_elim :premises (@p64)) % 1.41/1.60 (step @p66 :rule eq_resolve :premises (@p65 @p42)) % 1.41/1.60 (step @p67 :rule chain_m_resolution :premises (@p66 @p39) :args (@t33 @t20 (@list @t28))) % 1.41/1.60 (step @p68 :rule eq-symm :args (@t37 @t22)) % 1.41/1.60 (step @p69 :rule beta-reduce :args ((= @t38 @t22))) % 1.41/1.60 (step @p70 :rule refl :args (@t37)) % 1.41/1.60 (step @p71 :rule cong :premises (@p70 @p69) :args (@t39)) % 1.41/1.60 (step @p72 :rule trans :premises (@p71 @p68)) % 1.41/1.60 (step @p73 :rule cong :premises (@p72) :args (@t40)) % 1.41/1.60 (step @p74 :rule quant-unused-vars :args ((= (forall @t23 true) true))) % 1.41/1.60 (step @p75 :rule eq-refl :args (@t38)) % 1.41/1.60 (step @p76 :rule cong :premises (@p75) :args ((forall @t23 (= @t38 @t38)))) % 1.41/1.60 (step @p77 :rule trans :premises (@p76 @p74)) % 1.41/1.60 (step @p78 :rule refl :args (@t38)) % 1.41/1.60 (step @p79 :rule refl :args (@t21)) % 1.41/1.60 (step @p80 :rule ho_cong :premises (@p46 @p79)) % 1.41/1.60 (step @p81 :rule cong :premises (@p80 @p78) :args (@t39)) % 1.41/1.60 (step @p82 :rule cong :premises (@p81) :args (@t40)) % 1.41/1.60 (step @p83 :rule trans :premises (@p82 @p77)) % 1.41/1.60 (step @p84 :rule true_elim :premises (@p83)) % 1.41/1.60 (step @p85 :rule eq_resolve :premises (@p84 @p73)) % 1.41/1.60 (step @p86 :rule instantiate :premises (@p85) :args ((@list @t31))) % 1.41/1.60 (step @p87 :rule refl :args (@t41)) % 1.41/1.60 (step @p88 :rule bool-double-not-elim :args (@t42)) % 1.41/1.60 (step @p89 :rule refl :args (@t45)) % 1.41/1.60 (step @p90 :rule nary_cong :premises (@p89 @p88 @p87) :args ((or @t45 @t46 @t41))) % 1.41/1.60 (step @p91 :rule cnf_equiv_pos1 :args (@t44)) % 1.41/1.60 (step @p92 :rule eq_resolve :premises (@p91 @p90)) % 1.41/1.60 (step @p93 :rule reordering :premises (@p92) :args ((or @t42 @t41 @t45))) % 1.41/1.60 (step @p94 :rule refl :args (@t47)) % 1.41/1.60 (step @p95 :rule refl :args (@t48)) % 1.41/1.60 (step @p96 :rule nary_cong :premises (@p95 @p88 @p94) :args ((or @t48 @t46 @t47))) % 1.41/1.60 (assume-push @p167 @t41) % 1.41/1.60 (assume-push @p168 @t43) % 1.41/1.60 (assume-push @p169 @t33) % 1.41/1.60 (step @p100 :rule evaluate :args ((= true false))) % 1.41/1.60 (step @p101 :rule false_intro :premises (@p168)) % 1.41/1.60 (step @p102 :rule refl :args (@t42)) % 1.41/1.60 (step @p103 :rule symm :premises (@p102)) % 1.41/1.60 (step @p104 :rule refl :args (@t31)) % 1.41/1.60 (step @p105 :rule symm :premises (@p67)) % 1.41/1.60 (step @p106 :rule ho_cong :premises (@p105 @p104)) % 1.41/1.60 (step @p107 :rule refl :args (@t41)) % 1.41/1.60 (step @p108 :rule true_intro :premises (@p167)) % 1.41/1.60 (step @p109 :rule symm :premises (@p108)) % 1.41/1.60 (step @p110 :rule trans :premises (@p109 @p107 @p106 @p103 @p101)) % 1.41/1.60 (step @p111 false :rule eq_resolve :premises (@p110 @p100)) % 1.41/1.60 (step-pop @p170 :rule scope :premises (@p111)) % 1.41/1.60 (step-pop @p171 :rule scope :premises (@p170)) % 1.41/1.60 (step-pop @p172 :rule scope :premises (@p171)) % 1.41/1.60 (step @p112 :rule process_scope :premises (@p172) :args (false)) % 1.41/1.60 (assume-push @p173 @t33) % 1.41/1.60 (assume-push @p174 @t43) % 1.41/1.60 (assume-push @p175 @t41) % 1.41/1.60 (step @p119 :rule and_intro :premises (@p175 @p174 @p67)) % 1.41/1.60 (step-pop @p176 :rule scope :premises (@p119)) % 1.41/1.60 (step-pop @p177 :rule scope :premises (@p176)) % 1.41/1.60 (step-pop @p178 :rule scope :premises (@p177)) % 1.41/1.60 (step @p120 :rule process_scope :premises (@p178) :args (@t49)) % 1.41/1.60 (step @p124 :rule implies_elim :premises (@p120)) % 1.41/1.60 (step @p125 :rule resolution :premises (@p124 @p112) :args (true @t49)) % 1.41/1.60 (step @p126 :rule not_and :premises (@p125)) % 1.41/1.60 (step @p127 :rule eq_resolve :premises (@p126 @p96)) % 1.41/1.60 (step @p128 :rule chain_m_resolution :premises (@p127 @p67 @p93 @p86) :args (@t42 (@list false false false) (@list @t33 @t41 @t44))) % 1.41/1.60 (step @p129 :rule cnf_equiv_pos2 :args (@t44)) % 1.41/1.60 (step @p130 :rule reordering :premises (@p129) :args ((or @t43 @t47 @t45))) % 1.41/1.60 (step @p131 :rule chain_m_resolution :premises (@p130 @p128 @p86) :args (@t47 (@list false false) (@list @t42 @t44))) % 1.41/1.60 (step @p132 :rule bool-double-not-elim :args (@t41)) % 1.41/1.60 (step @p133 :rule refl :args (@t43)) % 1.41/1.60 (step @p134 :rule nary_cong :premises (@p95 @p133 @p132) :args ((or @t48 @t43 (not @t47)))) % 1.41/1.60 (assume-push @p179 @t47) % 1.41/1.60 (assume-push @p180 @t42) % 1.41/1.60 (assume-push @p181 @t33) % 1.41/1.60 (step @p138 :rule evaluate :args ((= false true))) % 1.41/1.60 (step @p139 :rule true_intro :premises (@p180)) % 1.41/1.60 (step @p102 :rule refl :args (@t42)) % 1.41/1.60 (step @p103 :rule symm :premises (@p102)) % 1.41/1.60 (step @p104 :rule refl :args (@t31)) % 1.41/1.60 (step @p105 :rule symm :premises (@p67)) % 1.41/1.60 (step @p106 :rule ho_cong :premises (@p105 @p104)) % 1.41/1.60 (step @p107 :rule refl :args (@t41)) % 1.41/1.60 (step @p140 :rule false_intro :premises (@p179)) % 1.41/1.60 (step @p141 :rule symm :premises (@p140)) % 1.41/1.60 (step @p142 :rule trans :premises (@p141 @p107 @p106 @p103 @p139)) % 1.41/1.60 (step @p143 false :rule eq_resolve :premises (@p142 @p138)) % 1.41/1.60 (step-pop @p182 :rule scope :premises (@p143)) % 1.41/1.60 (step-pop @p183 :rule scope :premises (@p182)) % 1.41/1.60 (step-pop @p184 :rule scope :premises (@p183)) % 1.41/1.60 (step @p144 :rule process_scope :premises (@p184) :args (false)) % 1.41/1.60 (assume-push @p185 @t33) % 1.41/1.60 (assume-push @p186 @t42) % 1.41/1.60 (assume-push @p187 @t47) % 1.41/1.60 (step @p151 :rule and_intro :premises (@p187 @p186 @p67)) % 1.41/1.60 (step-pop @p188 :rule scope :premises (@p151)) % 1.41/1.60 (step-pop @p189 :rule scope :premises (@p188)) % 1.41/1.60 (step-pop @p190 :rule scope :premises (@p189)) % 1.41/1.60 (step @p152 :rule process_scope :premises (@p190) :args (@t50)) % 1.41/1.60 (step @p156 :rule implies_elim :premises (@p152)) % 1.41/1.60 (step @p157 :rule resolution :premises (@p156 @p144) :args (true @t50)) % 1.41/1.60 (step @p158 :rule not_and :premises (@p157)) % 1.41/1.60 (step @p159 :rule eq_resolve :premises (@p158 @p134)) % 1.41/1.60 (step @p160 false :rule chain_m_resolution :premises (@p159 @p131 @p128 @p67) :args (false (@list true false false) (@list @t41 @t42 @t33))) % 1.41/1.60 ) % 1.41/1.60 % SZS output end Proof % 1.41/1.60 % cvc5 exiting %------------------------------------------------------------------------------