%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET169^5 : 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 : 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 08:47:33 AM UTC 2026 % Result : Theorem 0.39s 0.56s % Output : Proof 0.39s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET169^5 : 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 % 0.18/0.34 % Computer : n021.cluster.edu % 0.18/0.34 % Model : x86_64 x86_64 % 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.18/0.34 % Memory : 8042.1875MB % 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.18/0.34 % CPULimit : 300 % 0.18/0.34 % WCLimit : 300 % 0.18/0.34 % DateTime : Tue Jun 2 15:07:05 EDT 2026 % 0.18/0.35 % CPUTime : % 0.31/0.49 %----Proving TH0 % 0.39/0.56 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.39/0.56 % SZS status Theorem % 0.39/0.56 % SZS output start Proof % 0.39/0.56 ( % 0.39/0.56 (declare-sort tptp.a 0) % 0.39/0.56 (define @t1 () (@var "Xz" tptp.a)) % 0.39/0.56 (define @t2 () (@var "Z" (-> tptp.a Bool))) % 0.39/0.56 (define @t3 () (_ @t2 @t1)) % 0.39/0.56 (define @t4 () (@var "X" (-> tptp.a Bool))) % 0.39/0.56 (define @t5 () (_ @t4 @t1)) % 0.39/0.56 (define @t6 () (and @t5 @t3)) % 0.39/0.56 (define @t7 () (@var "Y" (-> tptp.a Bool))) % 0.39/0.56 (define @t8 () (_ @t7 @t1)) % 0.39/0.56 (define @t9 () (and @t5 @t8)) % 0.39/0.56 (define @t10 () (or @t9 @t6)) % 0.39/0.56 (define @t11 () (@list @t1)) % 0.39/0.56 (define @t12 () (lambda @t11 @t10)) % 0.39/0.56 (define @t13 () (@var "Xx" tptp.a)) % 0.39/0.56 (define @t14 () (_ @t2 @t13)) % 0.39/0.56 (define @t15 () (_ @t7 @t13)) % 0.39/0.56 (define @t16 () (or @t15 @t14)) % 0.39/0.56 (define @t17 () (_ @t4 @t13)) % 0.39/0.56 (define @t18 () (and @t17 @t16)) % 0.39/0.56 (define @t19 () (@list @t13)) % 0.39/0.56 (define @t20 () (lambda @t19 @t18)) % 0.39/0.56 (define @t21 () (= @t20 @t12)) % 0.39/0.56 (define @t22 () (@list @t4 @t7 @t2)) % 0.39/0.56 (define @t23 () (forall @t22 @t21)) % 0.39/0.56 (define @t24 () (not @t23)) % 0.39/0.56 (define @t25 () (@const 0 tptp.a)) % 0.39/0.56 (define @t26 () (_ @t2 @t1)) % 0.39/0.56 (define @t27 () (_ @t4 @t1)) % 0.39/0.56 (define @t28 () (_ @t7 @t1)) % 0.39/0.56 (define @t29 () (_ @t2 @t13)) % 0.39/0.56 (define @t30 () (_ @t7 @t13)) % 0.39/0.56 (define @t31 () (_ @t4 @t13)) % 0.39/0.56 (define @t32 () (forall @t22 (= (lambda @t19 (and @t31 (or @t30 @t29))) (lambda @t11 (or (and @t27 @t28) (and @t27 @t26)))))) % 0.39/0.56 (define @t33 () (@quantifiers_skolemize @t32 2)) % 0.39/0.56 (define @t34 () (_ @t33 @t25)) % 0.39/0.56 (define @t35 () (@quantifiers_skolemize @t32 1)) % 0.39/0.56 (define @t36 () (_ @t35 @t25)) % 0.39/0.56 (define @t37 () (or @t36 @t34)) % 0.39/0.56 (define @t38 () (@quantifiers_skolemize @t32 0)) % 0.39/0.56 (define @t39 () (_ @t38 @t25)) % 0.39/0.56 (define @t40 () (and @t39 @t36)) % 0.39/0.56 (define @t41 () (and @t39 @t37)) % 0.39/0.56 (define @t42 () (and @t39 @t34)) % 0.39/0.56 (define @t43 () (or @t40 @t42)) % 0.39/0.56 (define @t44 () (lambda @t19 (and (_ @t38 @t13) (or (_ @t35 @t13) (_ @t33 @t13))))) % 0.39/0.56 (define @t45 () (@purify @t44)) % 0.39/0.56 (define @t46 () (_ @t38 @t1)) % 0.39/0.56 (define @t47 () (lambda @t11 (or (and @t46 (_ @t35 @t1)) (and @t46 (_ @t33 @t1))))) % 0.39/0.56 (define @t48 () (@purify @t47)) % 0.39/0.56 (define @t49 () (= @t48 @t45)) % 0.39/0.56 (define @t50 () (not @t49)) % 0.39/0.56 (define @t51 () (not @t32)) % 0.39/0.56 (define @t52 () (= @t44 @t47)) % 0.39/0.56 (define @t53 () (not @t52)) % 0.39/0.56 (define @t54 () (@list true)) % 0.39/0.56 (define @t55 () (= (_ @t44 @t25) @t41)) % 0.39/0.56 (define @t56 () (_ @t45 @t25)) % 0.39/0.56 (define @t57 () (= (_ @t47 @t25) @t43)) % 0.39/0.56 (define @t58 () (_ @t48 @t25)) % 0.39/0.56 (define @t59 () (= @t58 @t56)) % 0.39/0.56 (define @t60 () (not @t59)) % 0.39/0.56 (define @t61 () (or @t49 @t60)) % 0.39/0.56 (define @t62 () (= @t41 @t43)) % 0.39/0.56 (define @t63 () (not @t39)) % 0.39/0.56 (define @t64 () (@list true false false false false)) % 0.39/0.56 (define @t65 () (not @t40)) % 0.39/0.56 (define @t66 () (not @t42)) % 0.39/0.56 (define @t67 () (not @t41)) % 0.39/0.56 (define @t68 () (@list @t39)) % 0.39/0.56 (assume @p1 @t24) % 0.39/0.56 (assume @p2 true) % 0.39/0.56 (step @p3 :rule cnf_or_neg :args (@t37 0)) % 0.39/0.56 (step @p4 :rule cnf_and_neg :args (@t40)) % 0.39/0.56 (step @p5 :rule cnf_and_neg :args (@t41)) % 0.39/0.56 (step @p6 :rule cnf_or_neg :args (@t43 0)) % 0.39/0.56 (step @p7 :rule refl :args (@t26)) % 0.39/0.56 (step @p8 :rule refl :args (@t3)) % 0.39/0.56 (step @p9 :rule cong :premises (@p8 @p7) :args ((= @t3 @t26))) % 0.39/0.56 (step @p10 :rule symm :premises (@p9)) % 0.39/0.56 (step @p11 :rule eq_resolve :premises (@p8 @p10)) % 0.39/0.56 (step @p12 :rule refl :args (@t27)) % 0.39/0.56 (step @p13 :rule refl :args (@t5)) % 0.39/0.56 (step @p14 :rule cong :premises (@p13 @p12) :args ((= @t5 @t27))) % 0.39/0.56 (step @p15 :rule symm :premises (@p14)) % 0.39/0.56 (step @p16 :rule eq_resolve :premises (@p13 @p15)) % 0.39/0.56 (step @p17 :rule nary_cong :premises (@p16 @p11) :args (@t6)) % 0.39/0.56 (step @p18 :rule refl :args (@t28)) % 0.39/0.56 (step @p19 :rule refl :args (@t8)) % 0.39/0.56 (step @p20 :rule cong :premises (@p19 @p18) :args ((= @t8 @t28))) % 0.39/0.56 (step @p21 :rule symm :premises (@p20)) % 0.39/0.56 (step @p22 :rule eq_resolve :premises (@p19 @p21)) % 0.39/0.56 (step @p23 :rule nary_cong :premises (@p16 @p22) :args (@t9)) % 0.39/0.56 (step @p24 :rule nary_cong :premises (@p23 @p17) :args (@t10)) % 0.39/0.56 (step @p25 :rule cong :premises (@p24) :args (@t12)) % 0.39/0.56 (step @p26 :rule refl :args (@t29)) % 0.39/0.56 (step @p27 :rule refl :args (@t14)) % 0.39/0.56 (step @p28 :rule cong :premises (@p27 @p26) :args ((= @t14 @t29))) % 0.39/0.56 (step @p29 :rule symm :premises (@p28)) % 0.39/0.56 (step @p30 :rule eq_resolve :premises (@p27 @p29)) % 0.39/0.56 (step @p31 :rule refl :args (@t30)) % 0.39/0.56 (step @p32 :rule refl :args (@t15)) % 0.39/0.56 (step @p33 :rule cong :premises (@p32 @p31) :args ((= @t15 @t30))) % 0.39/0.56 (step @p34 :rule symm :premises (@p33)) % 0.39/0.56 (step @p35 :rule eq_resolve :premises (@p32 @p34)) % 0.39/0.56 (step @p36 :rule nary_cong :premises (@p35 @p30) :args (@t16)) % 0.39/0.56 (step @p37 :rule refl :args (@t31)) % 0.39/0.56 (step @p38 :rule refl :args (@t17)) % 0.39/0.56 (step @p39 :rule cong :premises (@p38 @p37) :args ((= @t17 @t31))) % 0.39/0.56 (step @p40 :rule symm :premises (@p39)) % 0.39/0.56 (step @p41 :rule eq_resolve :premises (@p38 @p40)) % 0.39/0.56 (step @p42 :rule nary_cong :premises (@p41 @p36) :args (@t18)) % 0.39/0.56 (step @p43 :rule cong :premises (@p42) :args (@t20)) % 0.39/0.56 (step @p44 :rule cong :premises (@p43 @p25) :args (@t21)) % 0.39/0.56 (step @p45 :rule cong :premises (@p44) :args (@t23)) % 0.39/0.56 (step @p46 :rule cong :premises (@p45) :args (@t24)) % 0.39/0.56 (step @p47 :rule eq_resolve :premises (@p1 @p46)) % 0.39/0.56 (step @p48 :rule refl :args (@t50)) % 0.39/0.56 (step @p49 :rule bool-double-not-elim :args (@t32)) % 0.39/0.56 (step @p50 :rule nary_cong :premises (@p49 @p48) :args ((or (not @t51) @t50))) % 0.39/0.56 (step @p51 :rule eq-symm :args (@t45 @t48)) % 0.39/0.56 (step @p52 :rule eq-refl :args (@t47)) % 0.39/0.56 (step @p53 :rule skolem_intro :args (@t48)) % 0.39/0.56 (step @p54 :rule refl :args (@t47)) % 0.39/0.56 (step @p55 :rule cong :premises (@p54 @p53) :args ((= @t47 @t48))) % 0.39/0.56 (step @p56 :rule trans :premises (@p55 @p52)) % 0.39/0.56 (step @p57 :rule true_elim :premises (@p56)) % 0.39/0.56 (step @p58 :rule eq-refl :args (@t44)) % 0.39/0.56 (step @p59 :rule skolem_intro :args (@t45)) % 0.39/0.56 (step @p60 :rule refl :args (@t44)) % 0.39/0.56 (step @p61 :rule cong :premises (@p60 @p59) :args ((= @t44 @t45))) % 0.39/0.56 (step @p62 :rule trans :premises (@p61 @p58)) % 0.39/0.56 (step @p63 :rule true_elim :premises (@p62)) % 0.39/0.56 (step @p64 :rule cong :premises (@p63 @p57) :args (@t52)) % 0.39/0.56 (step @p65 :rule trans :premises (@p64 @p51)) % 0.39/0.56 (step @p66 :rule cong :premises (@p65) :args (@t53)) % 0.39/0.56 (step @p67 :rule refl :args (@t51)) % 0.39/0.56 (step @p68 :rule cong :premises (@p67 @p66) :args ((=> @t51 @t53))) % 0.39/0.56 (assume-push @p135 @t51) % 0.39/0.56 (step @p70 :rule skolemize :premises (@p47)) % 0.39/0.56 (step-pop @p136 :rule scope :premises (@p70)) % 0.39/0.56 (step @p71 :rule process_scope :premises (@p136) :args (@t53)) % 0.39/0.56 (step @p73 :rule eq_resolve :premises (@p71 @p68)) % 0.39/0.56 (step @p74 :rule implies_elim :premises (@p73)) % 0.39/0.56 (step @p75 :rule eq_resolve :premises (@p74 @p50)) % 0.39/0.56 (step @p76 :rule chain_m_resolution :premises (@p75 @p47) :args (@t50 @t54 (@list @t32))) % 0.39/0.56 (step @p77 :rule eq-symm :args (@t43 @t41)) % 0.39/0.56 (step @p78 :rule eq-refl :args (@t41)) % 0.39/0.56 (step @p79 :rule refl :args (@t41)) % 0.39/0.56 (step @p80 :rule beta-reduce :args (@t55)) % 0.39/0.56 (step @p81 :rule cong :premises (@p80 @p79) :args (@t55)) % 0.39/0.56 (step @p82 :rule trans :premises (@p81 @p78)) % 0.39/0.56 (step @p83 :rule refl :args (@t25)) % 0.39/0.56 (step @p84 :rule ho_cong :premises (@p59 @p83)) % 0.39/0.56 (step @p85 :rule cong :premises (@p84 @p79) :args ((= @t56 @t41))) % 0.39/0.56 (step @p86 :rule trans :premises (@p85 @p82)) % 0.39/0.56 (step @p87 :rule true_elim :premises (@p86)) % 0.39/0.56 (step @p88 :rule eq-refl :args (@t43)) % 0.39/0.56 (step @p89 :rule refl :args (@t43)) % 0.39/0.56 (step @p90 :rule beta-reduce :args (@t57)) % 0.39/0.56 (step @p91 :rule cong :premises (@p90 @p89) :args (@t57)) % 0.39/0.56 (step @p92 :rule trans :premises (@p91 @p88)) % 0.39/0.56 (step @p93 :rule ho_cong :premises (@p53 @p83)) % 0.39/0.56 (step @p94 :rule cong :premises (@p93 @p89) :args ((= @t58 @t43))) % 0.39/0.56 (step @p95 :rule trans :premises (@p94 @p92)) % 0.39/0.56 (step @p96 :rule true_elim :premises (@p95)) % 0.39/0.56 (step @p97 :rule cong :premises (@p96 @p87) :args (@t59)) % 0.39/0.56 (step @p98 :rule trans :premises (@p97 @p77)) % 0.39/0.56 (step @p99 :rule cong :premises (@p98) :args (@t60)) % 0.39/0.56 (step @p100 :rule refl :args (@t49)) % 0.39/0.56 (step @p101 :rule nary_cong :premises (@p100 @p99) :args (@t61)) % 0.39/0.56 ; WARNING: add trust step for TRUST % 0.39/0.56 ; trust TRUST THEORY_LEMMA % 0.39/0.56 (step @p102 :rule trust :premises () :args (@t61)) % 0.39/0.56 (step @p103 :rule eq_resolve :premises (@p102 @p101)) % 0.39/0.56 (step @p104 :rule chain_m_resolution :premises (@p103 @p76) :args ((not @t62) @t54 (@list @t49))) % 0.39/0.56 (step @p105 :rule cnf_equiv_neg2 :args (@t62)) % 0.39/0.56 (step @p106 :rule chain_m_resolution :premises (@p105 @p104 @p6 @p5 @p4 @p3) :args ((or @t63 (not @t36)) @t64 (@list @t62 @t43 @t41 @t40 @t37))) % 0.39/0.56 (step @p107 :rule cnf_and_pos :args (@t40 1)) % 0.39/0.56 (step @p108 :rule reordering :premises (@p107) :args ((or @t36 @t65))) % 0.39/0.56 (step @p109 :rule cnf_or_neg :args (@t37 1)) % 0.39/0.56 (step @p110 :rule cnf_and_neg :args (@t42)) % 0.39/0.56 (step @p111 :rule cnf_or_neg :args (@t43 1)) % 0.39/0.56 (step @p112 :rule chain_m_resolution :premises (@p105 @p104 @p111 @p5 @p110 @p109) :args ((or @t63 (not @t34)) @t64 (@list @t62 @t43 @t41 @t42 @t37))) % 0.39/0.56 (step @p113 :rule cnf_or_pos :args (@t37)) % 0.39/0.56 (step @p114 :rule reordering :premises (@p113) :args ((or @t36 @t34 (not @t37)))) % 0.39/0.56 (step @p115 :rule cnf_and_pos :args (@t42 1)) % 0.39/0.56 (step @p116 :rule reordering :premises (@p115) :args ((or @t34 @t66))) % 0.39/0.56 (step @p117 :rule cnf_and_pos :args (@t41 1)) % 0.39/0.56 (step @p118 :rule reordering :premises (@p117) :args ((or @t37 @t67))) % 0.39/0.56 (step @p119 :rule cnf_or_pos :args (@t43)) % 0.39/0.56 (step @p120 :rule reordering :premises (@p119) :args ((or @t40 @t42 (not @t43)))) % 0.39/0.56 (step @p121 :rule cnf_equiv_neg1 :args (@t62)) % 0.39/0.56 (step @p122 :rule reordering :premises (@p121) :args ((or @t41 @t43 @t62))) % 0.39/0.56 (step @p123 :rule chain_m_resolution :premises (@p122 @p104 @p120 @p118 @p116 @p114 @p112 @p108 @p106) :args (@t63 (@list true true true true true true true true) (@list @t62 @t43 @t41 @t42 @t37 @t34 @t40 @t36))) % 0.39/0.56 (step @p124 :rule cnf_and_pos :args (@t40 0)) % 0.39/0.56 (step @p125 :rule reordering :premises (@p124) :args ((or @t39 @t65))) % 0.39/0.56 (step @p126 :rule chain_m_resolution :premises (@p125 @p123) :args (@t65 @t54 @t68)) % 0.39/0.56 (step @p127 :rule cnf_and_pos :args (@t42 0)) % 0.39/0.56 (step @p128 :rule reordering :premises (@p127) :args ((or @t39 @t66))) % 0.39/0.56 (step @p129 :rule chain_m_resolution :premises (@p128 @p123) :args (@t66 @t54 @t68)) % 0.39/0.56 (step @p130 :rule cnf_and_pos :args (@t41 0)) % 0.39/0.56 (step @p131 :rule reordering :premises (@p130) :args ((or @t39 @t67))) % 0.39/0.56 (step @p132 :rule chain_m_resolution :premises (@p131 @p123) :args (@t67 @t54 @t68)) % 0.39/0.56 (step @p133 :rule chain_m_resolution :premises (@p122 @p132 @p104) :args (@t43 (@list true true) (@list @t41 @t62))) % 0.39/0.56 (step @p134 false :rule chain_m_resolution :premises (@p120 @p133 @p129 @p126) :args (false (@list false true true) (@list @t43 @t42 @t40))) % 0.39/0.56 ) % 0.39/0.56 % SZS output end Proof % 0.39/0.56 % cvc5 exiting %------------------------------------------------------------------------------