%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYO208^5 : 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 : n001.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 09:12:14 AM UTC 2026 % Result : Theorem 1.33s 1.54s % Output : Proof 1.33s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.13/0.13 % Problem : SYO208^5 : TPTP v9.2.1. Released v4.0.0. % 0.13/0.14 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.19/0.36 % Computer : n001.cluster.edu % 0.19/0.36 % Model : x86_64 x86_64 % 0.19/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.19/0.36 % Memory : 8042.1875MB % 0.19/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.19/0.36 % CPULimit : 300 % 0.19/0.36 % WCLimit : 300 % 0.19/0.36 % DateTime : Wed Jun 3 00:01:20 EDT 2026 % 0.19/0.36 % CPUTime : % 0.32/0.51 %----Proving TH0 % 1.33/1.54 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 1.33/1.54 % SZS status Theorem % 1.33/1.54 % SZS output start Proof % 1.33/1.54 ( % 1.33/1.54 (declare-sort tptp.a 0) % 1.33/1.54 (define @t1 () (@var "Xf" (-> tptp.a Bool))) % 1.33/1.54 (define @t2 () (@var "Xj" tptp.a)) % 1.33/1.54 (define @t3 () (@var "Xg" (-> tptp.a tptp.a Bool))) % 1.33/1.54 (define @t4 () (_ @t3 @t2)) % 1.33/1.54 (define @t5 () (= (= @t4 @t1) (= @t1 @t1))) % 1.33/1.54 (define @t6 () (@list @t2)) % 1.33/1.54 (define @t7 () (exists @t6 @t5)) % 1.33/1.54 (define @t8 () (@list @t1)) % 1.33/1.54 (define @t9 () (forall @t8 @t7)) % 1.33/1.54 (define @t10 () (@list @t3)) % 1.33/1.54 (define @t11 () (exists @t10 @t9)) % 1.33/1.54 (define @t12 () (= @t1 @t4)) % 1.33/1.54 (define @t13 () (not (forall @t6 (not @t12)))) % 1.33/1.54 (define @t14 () (forall @t8 @t13)) % 1.33/1.54 (define @t15 () (forall @t10 (not @t14))) % 1.33/1.54 (define @t16 () (not @t15)) % 1.33/1.54 (define @t17 () (@quantifiers_skolemize @t15 0)) % 1.33/1.54 (define @t18 () (_ @t17 @t2)) % 1.33/1.54 (define @t19 () (forall @t8 (not (forall @t6 (not (= @t1 @t18)))))) % 1.33/1.54 (define @t20 () (not (not @t19))) % 1.33/1.54 (define @t21 () (@list true)) % 1.33/1.54 (define @t22 () (@var "BOUND_VARIABLE_14546" tptp.a)) % 1.33/1.54 (define @t23 () (not (_ @t17 @t22 @t22))) % 1.33/1.54 (define @t24 () (@list @t22)) % 1.33/1.54 (define @t25 () (lambda @t24 @t23)) % 1.33/1.54 (define @t26 () (not (= @t25 @t18))) % 1.33/1.54 (define @t27 () (forall @t6 @t26)) % 1.33/1.54 (define @t28 () (not @t27)) % 1.33/1.54 (define @t29 () (forall @t6 (not (= @t18 @t25)))) % 1.33/1.54 (define @t30 () (not @t29)) % 1.33/1.54 (define @t31 () (@purify @t25)) % 1.33/1.54 (define @t32 () (@quantifiers_skolemize @t29 0)) % 1.33/1.54 (define @t33 () (_ @t17 @t32)) % 1.33/1.54 (define @t34 () (= @t33 @t31)) % 1.33/1.54 (define @t35 () (= @t25 @t33)) % 1.33/1.54 (define @t36 () (= @t33 @t25)) % 1.33/1.54 (define @t37 () (not (not @t36))) % 1.33/1.54 (define @t38 () (_ @t31 @t22)) % 1.33/1.54 (define @t39 () (_ @t25 @t22)) % 1.33/1.54 (define @t40 () (= @t38 @t39)) % 1.33/1.54 (define @t41 () (forall @t24 @t40)) % 1.33/1.54 (define @t42 () (_ @t31 @t32)) % 1.33/1.54 (define @t43 () (_ @t17 @t32 @t32)) % 1.33/1.54 (define @t44 () (not @t43)) % 1.33/1.54 (define @t45 () (= @t44 @t42)) % 1.33/1.54 (define @t46 () (not @t45)) % 1.33/1.54 (define @t47 () (not @t44)) % 1.33/1.54 (define @t48 () (not @t42)) % 1.33/1.54 (define @t49 () (not @t34)) % 1.33/1.54 (define @t50 () (and @t42 @t44 @t34)) % 1.33/1.54 (define @t51 () (and @t48 @t43 @t34)) % 1.33/1.54 (assume @p1 (not (not @t11))) % 1.33/1.54 (assume @p2 true) % 1.33/1.54 (step @p3 :rule exists-elim :args ((= (exists @t10 @t14) @t16))) % 1.33/1.54 (step @p4 :rule exists-elim :args ((= (exists @t6 @t12) @t13))) % 1.33/1.54 (step @p5 :rule bool-eq-true :args (@t12)) % 1.33/1.54 (step @p6 :rule eq-refl :args (@t1)) % 1.33/1.54 (step @p7 :rule eq-symm :args (@t4 @t1)) % 1.33/1.54 (step @p8 :rule cong :premises (@p7 @p6) :args (@t5)) % 1.33/1.54 (step @p9 :rule trans :premises (@p8 @p5)) % 1.33/1.54 (step @p10 :rule cong :premises (@p9) :args (@t7)) % 1.33/1.54 (step @p11 :rule trans :premises (@p10 @p4)) % 1.33/1.54 (step @p12 :rule cong :premises (@p11) :args (@t9)) % 1.33/1.54 (step @p13 :rule cong :premises (@p12) :args (@t11)) % 1.33/1.54 (step @p14 :rule trans :premises (@p13 @p3)) % 1.33/1.54 (step @p15 :rule bool-double-not-elim :args (@t11)) % 1.33/1.54 (step @p16 :rule trans :premises (@p15 @p14)) % 1.33/1.54 (step @p17 :rule eq_resolve :premises (@p1 @p16)) % 1.33/1.54 (step @p18 :rule refl :args (@t19)) % 1.33/1.54 (step @p19 :rule bool-double-not-elim :args (@t15)) % 1.33/1.54 (step @p20 :rule nary_cong :premises (@p19 @p18) :args ((or (not @t16) @t19))) % 1.33/1.54 (step @p21 :rule bool-double-not-elim :args (@t19)) % 1.33/1.54 (step @p22 :rule refl :args (@t16)) % 1.33/1.54 (step @p23 :rule cong :premises (@p22 @p21) :args ((=> @t16 @t20))) % 1.33/1.54 (assume-push @p165 @t16) % 1.33/1.54 (step @p25 :rule skolemize :premises (@p17)) % 1.33/1.54 (step-pop @p166 :rule scope :premises (@p25)) % 1.33/1.54 (step @p26 :rule process_scope :premises (@p166) :args (@t20)) % 1.33/1.54 (step @p28 :rule eq_resolve :premises (@p26 @p23)) % 1.33/1.54 (step @p29 :rule implies_elim :premises (@p28)) % 1.33/1.54 (step @p30 :rule eq_resolve :premises (@p29 @p20)) % 1.33/1.54 (step @p31 :rule chain_m_resolution :premises (@p30 @p17) :args (@t19 @t21 (@list @t15))) % 1.33/1.54 (step @p32 :rule eq-symm :args (@t25 @t18)) % 1.33/1.54 (step @p33 :rule cong :premises (@p32) :args (@t26)) % 1.33/1.54 (step @p34 :rule cong :premises (@p33) :args (@t27)) % 1.33/1.54 (step @p35 :rule cong :premises (@p34) :args (@t28)) % 1.33/1.54 (step @p36 :rule cong :premises (@p18 @p35) :args ((=> @t19 @t28))) % 1.33/1.54 (assume-push @p167 @t19) % 1.33/1.54 (step @p38 :rule instantiate :premises (@p31) :args ((@list @t25))) % 1.33/1.54 (step-pop @p168 :rule scope :premises (@p38)) % 1.33/1.54 (step @p39 :rule process_scope :premises (@p168) :args (@t28)) % 1.33/1.54 (step @p41 :rule eq_resolve :premises (@p39 @p36)) % 1.33/1.54 (step @p42 :rule implies_elim :premises (@p41)) % 1.33/1.54 (step @p43 :rule chain_m_resolution :premises (@p42 @p31) :args (@t30 (@list false) (@list @t19))) % 1.33/1.54 (step @p44 :rule refl :args (@t34)) % 1.33/1.54 (step @p45 :rule bool-double-not-elim :args (@t29)) % 1.33/1.54 (step @p46 :rule nary_cong :premises (@p45 @p44) :args ((or (not @t30) @t34))) % 1.33/1.54 (step @p47 :rule eq-symm :args (@t31 @t33)) % 1.33/1.54 (step @p48 :rule refl :args (@t33)) % 1.33/1.54 (step @p49 :rule eq-refl :args (@t25)) % 1.33/1.54 (step @p50 :rule skolem_intro :args (@t31)) % 1.33/1.54 (step @p51 :rule refl :args (@t25)) % 1.33/1.54 (step @p52 :rule cong :premises (@p51 @p50) :args ((= @t25 @t31))) % 1.33/1.54 (step @p53 :rule trans :premises (@p52 @p49)) % 1.33/1.54 (step @p54 :rule true_elim :premises (@p53)) % 1.33/1.54 (step @p55 :rule cong :premises (@p54 @p48) :args (@t35)) % 1.33/1.54 (step @p56 :rule trans :premises (@p55 @p47)) % 1.33/1.54 (step @p57 :rule refl :args (@t30)) % 1.33/1.54 (step @p58 :rule cong :premises (@p57 @p56) :args ((=> @t30 @t35))) % 1.33/1.54 (step @p59 :rule eq-symm :args (@t33 @t25)) % 1.33/1.54 (step @p60 :rule bool-double-not-elim :args (@t36)) % 1.33/1.54 (step @p61 :rule trans :premises (@p60 @p59)) % 1.33/1.54 (step @p62 :rule cong :premises (@p57 @p61) :args ((=> @t30 @t37))) % 1.33/1.54 (step @p63 :rule trans :premises (@p62 @p58)) % 1.33/1.54 (assume-push @p169 @t30) % 1.33/1.54 (step @p65 :rule skolemize :premises (@p43)) % 1.33/1.54 (step-pop @p170 :rule scope :premises (@p65)) % 1.33/1.54 (step @p66 :rule process_scope :premises (@p170) :args (@t37)) % 1.33/1.54 (step @p68 :rule eq_resolve :premises (@p66 @p63)) % 1.33/1.54 (step @p69 :rule implies_elim :premises (@p68)) % 1.33/1.54 (step @p70 :rule eq_resolve :premises (@p69 @p46)) % 1.33/1.54 (step @p71 :rule chain_m_resolution :premises (@p70 @p43) :args (@t34 @t21 (@list @t29))) % 1.33/1.54 (step @p72 :rule eq-symm :args (@t38 @t23)) % 1.33/1.54 (step @p73 :rule beta-reduce :args ((= @t39 @t23))) % 1.33/1.54 (step @p74 :rule refl :args (@t38)) % 1.33/1.54 (step @p75 :rule cong :premises (@p74 @p73) :args (@t40)) % 1.33/1.54 (step @p76 :rule trans :premises (@p75 @p72)) % 1.33/1.54 (step @p77 :rule cong :premises (@p76) :args (@t41)) % 1.33/1.54 (step @p78 :rule quant-unused-vars :args ((= (forall @t24 true) true))) % 1.33/1.54 (step @p79 :rule eq-refl :args (@t39)) % 1.33/1.54 (step @p80 :rule cong :premises (@p79) :args ((forall @t24 (= @t39 @t39)))) % 1.33/1.54 (step @p81 :rule trans :premises (@p80 @p78)) % 1.33/1.54 (step @p82 :rule refl :args (@t39)) % 1.33/1.54 (step @p83 :rule refl :args (@t22)) % 1.33/1.54 (step @p84 :rule ho_cong :premises (@p50 @p83)) % 1.33/1.54 (step @p85 :rule cong :premises (@p84 @p82) :args (@t40)) % 1.33/1.54 (step @p86 :rule cong :premises (@p85) :args (@t41)) % 1.33/1.54 (step @p87 :rule trans :premises (@p86 @p81)) % 1.33/1.54 (step @p88 :rule true_elim :premises (@p87)) % 1.33/1.54 (step @p89 :rule eq_resolve :premises (@p88 @p77)) % 1.33/1.54 (step @p90 :rule instantiate :premises (@p89) :args ((@list @t32))) % 1.33/1.54 (step @p91 :rule refl :args (@t42)) % 1.33/1.54 (step @p92 :rule bool-double-not-elim :args (@t43)) % 1.33/1.54 (step @p93 :rule refl :args (@t46)) % 1.33/1.54 (step @p94 :rule nary_cong :premises (@p93 @p92 @p91) :args ((or @t46 @t47 @t42))) % 1.33/1.54 (step @p95 :rule cnf_equiv_pos1 :args (@t45)) % 1.33/1.54 (step @p96 :rule eq_resolve :premises (@p95 @p94)) % 1.33/1.54 (step @p97 :rule reordering :premises (@p96) :args ((or @t43 @t42 @t46))) % 1.33/1.54 (step @p98 :rule refl :args (@t48)) % 1.33/1.54 (step @p99 :rule refl :args (@t49)) % 1.33/1.54 (step @p100 :rule nary_cong :premises (@p99 @p92 @p98) :args ((or @t49 @t47 @t48))) % 1.33/1.54 (assume-push @p171 @t42) % 1.33/1.54 (assume-push @p172 @t44) % 1.33/1.54 (assume-push @p173 @t34) % 1.33/1.54 (step @p104 :rule evaluate :args ((= true false))) % 1.33/1.54 (step @p105 :rule false_intro :premises (@p172)) % 1.33/1.54 (step @p106 :rule refl :args (@t43)) % 1.33/1.54 (step @p107 :rule symm :premises (@p106)) % 1.33/1.54 (step @p108 :rule refl :args (@t32)) % 1.33/1.54 (step @p109 :rule symm :premises (@p71)) % 1.33/1.54 (step @p110 :rule ho_cong :premises (@p109 @p108)) % 1.33/1.54 (step @p111 :rule refl :args (@t42)) % 1.33/1.54 (step @p112 :rule true_intro :premises (@p171)) % 1.33/1.54 (step @p113 :rule symm :premises (@p112)) % 1.33/1.54 (step @p114 :rule trans :premises (@p113 @p111 @p110 @p107 @p105)) % 1.33/1.54 (step @p115 false :rule eq_resolve :premises (@p114 @p104)) % 1.33/1.54 (step-pop @p174 :rule scope :premises (@p115)) % 1.33/1.54 (step-pop @p175 :rule scope :premises (@p174)) % 1.33/1.54 (step-pop @p176 :rule scope :premises (@p175)) % 1.33/1.54 (step @p116 :rule process_scope :premises (@p176) :args (false)) % 1.33/1.54 (assume-push @p177 @t34) % 1.33/1.54 (assume-push @p178 @t44) % 1.33/1.54 (assume-push @p179 @t42) % 1.33/1.54 (step @p123 :rule and_intro :premises (@p179 @p178 @p71)) % 1.33/1.54 (step-pop @p180 :rule scope :premises (@p123)) % 1.33/1.54 (step-pop @p181 :rule scope :premises (@p180)) % 1.33/1.54 (step-pop @p182 :rule scope :premises (@p181)) % 1.33/1.54 (step @p124 :rule process_scope :premises (@p182) :args (@t50)) % 1.33/1.54 (step @p128 :rule implies_elim :premises (@p124)) % 1.33/1.54 (step @p129 :rule resolution :premises (@p128 @p116) :args (true @t50)) % 1.33/1.54 (step @p130 :rule not_and :premises (@p129)) % 1.33/1.54 (step @p131 :rule eq_resolve :premises (@p130 @p100)) % 1.33/1.54 (step @p132 :rule chain_m_resolution :premises (@p131 @p71 @p97 @p90) :args (@t43 (@list false false false) (@list @t34 @t42 @t45))) % 1.33/1.54 (step @p133 :rule cnf_equiv_pos2 :args (@t45)) % 1.33/1.54 (step @p134 :rule reordering :premises (@p133) :args ((or @t44 @t48 @t46))) % 1.33/1.54 (step @p135 :rule chain_m_resolution :premises (@p134 @p132 @p90) :args (@t48 (@list false false) (@list @t43 @t45))) % 1.33/1.54 (step @p136 :rule bool-double-not-elim :args (@t42)) % 1.33/1.54 (step @p137 :rule refl :args (@t44)) % 1.33/1.54 (step @p138 :rule nary_cong :premises (@p99 @p137 @p136) :args ((or @t49 @t44 (not @t48)))) % 1.33/1.54 (assume-push @p183 @t48) % 1.33/1.54 (assume-push @p184 @t43) % 1.33/1.54 (assume-push @p185 @t34) % 1.33/1.54 (step @p142 :rule evaluate :args ((= false true))) % 1.33/1.54 (step @p143 :rule true_intro :premises (@p184)) % 1.33/1.54 (step @p106 :rule refl :args (@t43)) % 1.33/1.54 (step @p107 :rule symm :premises (@p106)) % 1.33/1.54 (step @p108 :rule refl :args (@t32)) % 1.33/1.54 (step @p109 :rule symm :premises (@p71)) % 1.33/1.54 (step @p110 :rule ho_cong :premises (@p109 @p108)) % 1.33/1.54 (step @p111 :rule refl :args (@t42)) % 1.33/1.54 (step @p144 :rule false_intro :premises (@p183)) % 1.33/1.54 (step @p145 :rule symm :premises (@p144)) % 1.33/1.54 (step @p146 :rule trans :premises (@p145 @p111 @p110 @p107 @p143)) % 1.33/1.54 (step @p147 false :rule eq_resolve :premises (@p146 @p142)) % 1.33/1.54 (step-pop @p186 :rule scope :premises (@p147)) % 1.33/1.54 (step-pop @p187 :rule scope :premises (@p186)) % 1.33/1.54 (step-pop @p188 :rule scope :premises (@p187)) % 1.33/1.54 (step @p148 :rule process_scope :premises (@p188) :args (false)) % 1.33/1.54 (assume-push @p189 @t34) % 1.33/1.54 (assume-push @p190 @t43) % 1.33/1.54 (assume-push @p191 @t48) % 1.33/1.54 (step @p155 :rule and_intro :premises (@p191 @p190 @p71)) % 1.33/1.54 (step-pop @p192 :rule scope :premises (@p155)) % 1.33/1.54 (step-pop @p193 :rule scope :premises (@p192)) % 1.33/1.54 (step-pop @p194 :rule scope :premises (@p193)) % 1.33/1.54 (step @p156 :rule process_scope :premises (@p194) :args (@t51)) % 1.33/1.54 (step @p160 :rule implies_elim :premises (@p156)) % 1.33/1.54 (step @p161 :rule resolution :premises (@p160 @p148) :args (true @t51)) % 1.33/1.54 (step @p162 :rule not_and :premises (@p161)) % 1.33/1.54 (step @p163 :rule eq_resolve :premises (@p162 @p138)) % 1.33/1.54 (step @p164 false :rule chain_m_resolution :premises (@p163 @p135 @p132 @p71) :args (false (@list true false false) (@list @t42 @t43 @t34))) % 1.33/1.54 ) % 1.33/1.54 % SZS output end Proof % 1.33/1.54 % cvc5 exiting %------------------------------------------------------------------------------