%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET594^5 : 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 : 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 08:48:08 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 % 0.12/0.12 % Problem : SET594^5 : TPTP v9.2.1. Released v4.0.0. % 0.12/0.14 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.35 % Computer : n003.cluster.edu % 0.17/0.35 % Model : x86_64 x86_64 % 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.35 % Memory : 8042.1875MB % 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.35 % CPULimit : 300 % 0.17/0.35 % WCLimit : 300 % 0.17/0.35 % DateTime : Tue Jun 2 16:03:44 EDT 2026 % 0.17/0.35 % CPUTime : % 0.32/0.50 %----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 "Xx" 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 "Y" (-> tptp.a Bool))) % 0.39/0.56 (define @t5 () (_ @t4 @t1)) % 0.39/0.56 (define @t6 () (or @t5 @t3)) % 0.39/0.56 (define @t7 () (@var "X" (-> tptp.a Bool))) % 0.39/0.56 (define @t8 () (_ @t7 @t1)) % 0.39/0.56 (define @t9 () (@list @t1)) % 0.39/0.56 (define @t10 () (forall @t9 (=> @t8 @t6))) % 0.39/0.56 (define @t11 () (@var "Xz" tptp.a)) % 0.39/0.56 (define @t12 () (_ @t2 @t11)) % 0.39/0.56 (define @t13 () (_ @t7 @t11)) % 0.39/0.56 (define @t14 () (and @t13 @t12)) % 0.39/0.56 (define @t15 () (_ @t4 @t11)) % 0.39/0.56 (define @t16 () (and @t13 @t15)) % 0.39/0.56 (define @t17 () (or @t16 @t14)) % 0.39/0.56 (define @t18 () (@list @t11)) % 0.39/0.56 (define @t19 () (lambda @t18 @t17)) % 0.39/0.56 (define @t20 () (=> (= @t19 @t7) @t10)) % 0.39/0.56 (define @t21 () (@list @t7 @t4 @t2)) % 0.39/0.56 (define @t22 () (forall @t21 @t20)) % 0.39/0.56 (define @t23 () (not @t22)) % 0.39/0.56 (define @t24 () (@var "BOUND_VARIABLE_7459" tptp.a)) % 0.39/0.56 (define @t25 () (_ @t2 @t24)) % 0.39/0.56 (define @t26 () (_ @t4 @t24)) % 0.39/0.56 (define @t27 () (not (_ @t7 @t24))) % 0.39/0.56 (define @t28 () (_ @t2 @t11)) % 0.39/0.56 (define @t29 () (_ @t7 @t11)) % 0.39/0.56 (define @t30 () (_ @t4 @t11)) % 0.39/0.56 (define @t31 () (not (= @t7 (lambda @t18 (or (and @t29 @t30) (and @t29 @t28)))))) % 0.39/0.56 (define @t32 () (or @t31 @t27 @t26 @t25)) % 0.39/0.56 (define @t33 () (or @t27 @t26 @t25)) % 0.39/0.56 (define @t34 () (or @t31 @t33)) % 0.39/0.56 (define @t35 () (@list @t7 @t4 @t2 @t24)) % 0.39/0.56 (define @t36 () (forall @t35 @t34)) % 0.39/0.56 (define @t37 () (@list @t24)) % 0.39/0.56 (define @t38 () (forall @t37 @t34)) % 0.39/0.56 (define @t39 () (forall @t37 @t33)) % 0.39/0.56 (define @t40 () (or @t31 @t39)) % 0.39/0.56 (define @t41 () (_ @t2 @t1)) % 0.39/0.56 (define @t42 () (_ @t4 @t1)) % 0.39/0.56 (define @t43 () (_ @t7 @t1)) % 0.39/0.56 (define @t44 () (forall @t9 (or (not @t43) @t42 @t41))) % 0.39/0.56 (define @t45 () (= @t7 @t19)) % 0.39/0.56 (define @t46 () (not @t45)) % 0.39/0.56 (define @t47 () (or @t46 @t44)) % 0.39/0.56 (define @t48 () (not @t8)) % 0.39/0.56 (define @t49 () (or @t48 @t5 @t3)) % 0.39/0.56 (define @t50 () (forall @t35 @t32)) % 0.39/0.56 (define @t51 () (@quantifiers_skolemize @t50 3)) % 0.39/0.56 (define @t52 () (@quantifiers_skolemize @t50 2)) % 0.39/0.56 (define @t53 () (_ @t52 @t51)) % 0.39/0.56 (define @t54 () (@quantifiers_skolemize @t50 1)) % 0.39/0.56 (define @t55 () (_ @t54 @t51)) % 0.39/0.56 (define @t56 () (@quantifiers_skolemize @t50 0)) % 0.39/0.56 (define @t57 () (_ @t56 @t51)) % 0.39/0.56 (define @t58 () (not @t57)) % 0.39/0.56 (define @t59 () (_ @t56 @t11)) % 0.39/0.56 (define @t60 () (lambda @t18 (or (and @t59 (_ @t54 @t11)) (and @t59 (_ @t52 @t11))))) % 0.39/0.56 (define @t61 () (@purify @t60)) % 0.39/0.56 (define @t62 () (= @t56 @t61)) % 0.39/0.56 (define @t63 () (not @t62)) % 0.39/0.56 (define @t64 () (or @t63 @t58 @t55 @t53)) % 0.39/0.56 (define @t65 () (not @t64)) % 0.39/0.56 (define @t66 () (not @t50)) % 0.39/0.56 (define @t67 () (= @t56 @t60)) % 0.39/0.56 (define @t68 () (not @t67)) % 0.39/0.56 (define @t69 () (or @t68 @t58 @t55 @t53)) % 0.39/0.56 (define @t70 () (not @t69)) % 0.39/0.56 (define @t71 () (@list true)) % 0.39/0.56 (define @t72 () (@list @t64)) % 0.39/0.56 (define @t73 () (and @t57 @t53)) % 0.39/0.56 (define @t74 () (and @t57 @t55)) % 0.39/0.56 (define @t75 () (or @t74 @t73)) % 0.39/0.56 (define @t76 () (= @t57 @t75)) % 0.39/0.56 (define @t77 () (not @t73)) % 0.39/0.56 (define @t78 () (not @t74)) % 0.39/0.56 (define @t79 () (not @t75)) % 0.39/0.56 (assume @p1 @t23) % 0.39/0.56 (assume @p2 true) % 0.39/0.56 (step @p3 :rule aci_norm :args ((= @t34 @t32))) % 0.39/0.56 (step @p4 :rule cong :premises (@p3) :args (@t36)) % 0.39/0.56 (step @p5 :rule quant-merge-prenex :args ((= (forall @t21 @t38) @t36))) % 0.39/0.56 (step @p6 :rule alpha_equiv :args (@t39 (@list @t24) (@list @t1))) % 0.39/0.56 (step @p7 :rule refl :args (@t31)) % 0.39/0.56 (step @p8 :rule nary_cong :premises (@p7 @p6) :args (@t40)) % 0.39/0.56 (step @p9 :rule quant-miniscope-or :args ((= @t38 @t40))) % 0.39/0.56 (step @p10 :rule trans :premises (@p9 @p8)) % 0.39/0.56 (step @p11 :rule symm :premises (@p10)) % 0.39/0.56 (step @p12 :rule cong :premises (@p11) :args ((forall @t21 (or @t31 @t44)))) % 0.39/0.56 (step @p13 :rule trans :premises (@p12 @p5)) % 0.39/0.56 (step @p14 :rule trans :premises (@p13 @p4)) % 0.39/0.56 (step @p15 :rule refl :args (@t44)) % 0.39/0.56 (step @p16 :rule refl :args (@t28)) % 0.39/0.56 (step @p17 :rule refl :args (@t12)) % 0.39/0.56 (step @p18 :rule cong :premises (@p17 @p16) :args ((= @t12 @t28))) % 0.39/0.56 (step @p19 :rule symm :premises (@p18)) % 0.39/0.56 (step @p20 :rule eq_resolve :premises (@p17 @p19)) % 0.39/0.56 (step @p21 :rule refl :args (@t29)) % 0.39/0.56 (step @p22 :rule refl :args (@t13)) % 0.39/0.56 (step @p23 :rule cong :premises (@p22 @p21) :args ((= @t13 @t29))) % 0.39/0.56 (step @p24 :rule symm :premises (@p23)) % 0.39/0.56 (step @p25 :rule eq_resolve :premises (@p22 @p24)) % 0.39/0.56 (step @p26 :rule nary_cong :premises (@p25 @p20) :args (@t14)) % 0.39/0.56 (step @p27 :rule refl :args (@t30)) % 0.39/0.56 (step @p28 :rule refl :args (@t15)) % 0.39/0.56 (step @p29 :rule cong :premises (@p28 @p27) :args ((= @t15 @t30))) % 0.39/0.56 (step @p30 :rule symm :premises (@p29)) % 0.39/0.56 (step @p31 :rule eq_resolve :premises (@p28 @p30)) % 0.39/0.56 (step @p32 :rule nary_cong :premises (@p25 @p31) :args (@t16)) % 0.39/0.56 (step @p33 :rule nary_cong :premises (@p32 @p26) :args (@t17)) % 0.39/0.56 (step @p34 :rule cong :premises (@p33) :args (@t19)) % 0.39/0.56 (step @p35 :rule refl :args (@t7)) % 0.39/0.56 (step @p36 :rule cong :premises (@p35 @p34) :args (@t45)) % 0.39/0.56 (step @p37 :rule cong :premises (@p36) :args (@t46)) % 0.39/0.56 (step @p38 :rule nary_cong :premises (@p37 @p15) :args (@t47)) % 0.39/0.56 (step @p39 :rule cong :premises (@p38) :args ((forall @t21 @t47))) % 0.39/0.56 (step @p40 :rule trans :premises (@p39 @p14)) % 0.39/0.56 (step @p41 :rule bool-impl-elim :args (@t45 @t44)) % 0.39/0.56 (step @p42 :rule cong :premises (@p41) :args ((forall @t21 (=> @t45 @t44)))) % 0.39/0.56 (step @p43 :rule trans :premises (@p42 @p40)) % 0.39/0.56 (step @p44 :rule refl :args (@t41)) % 0.39/0.56 (step @p45 :rule refl :args (@t3)) % 0.39/0.56 (step @p46 :rule cong :premises (@p45 @p44) :args ((= @t3 @t41))) % 0.39/0.56 (step @p47 :rule symm :premises (@p46)) % 0.39/0.56 (step @p48 :rule eq_resolve :premises (@p45 @p47)) % 0.39/0.56 (step @p49 :rule refl :args (@t42)) % 0.39/0.56 (step @p50 :rule refl :args (@t5)) % 0.39/0.56 (step @p51 :rule cong :premises (@p50 @p49) :args ((= @t5 @t42))) % 0.39/0.56 (step @p52 :rule symm :premises (@p51)) % 0.39/0.56 (step @p53 :rule eq_resolve :premises (@p50 @p52)) % 0.39/0.56 (step @p54 :rule refl :args (@t43)) % 0.39/0.56 (step @p55 :rule refl :args (@t8)) % 0.39/0.56 (step @p56 :rule cong :premises (@p55 @p54) :args ((= @t8 @t43))) % 0.39/0.56 (step @p57 :rule symm :premises (@p56)) % 0.39/0.56 (step @p58 :rule eq_resolve :premises (@p55 @p57)) % 0.39/0.56 (step @p59 :rule cong :premises (@p58) :args (@t48)) % 0.39/0.56 (step @p60 :rule nary_cong :premises (@p59 @p53 @p48) :args (@t49)) % 0.39/0.56 (step @p61 :rule cong :premises (@p60) :args ((forall @t9 @t49))) % 0.39/0.56 (step @p62 :rule aci_norm :args ((= (or @t48 @t6) @t49))) % 0.39/0.56 (step @p63 :rule bool-impl-elim :args (@t8 @t6)) % 0.39/0.56 (step @p64 :rule trans :premises (@p63 @p62)) % 0.39/0.56 (step @p65 :rule cong :premises (@p64) :args (@t10)) % 0.39/0.56 (step @p66 :rule trans :premises (@p65 @p61)) % 0.39/0.56 (step @p67 :rule eq-symm :args (@t19 @t7)) % 0.39/0.56 (step @p68 :rule cong :premises (@p67 @p66) :args (@t20)) % 0.39/0.56 (step @p69 :rule cong :premises (@p68) :args (@t22)) % 0.39/0.56 (step @p70 :rule trans :premises (@p69 @p43)) % 0.39/0.56 (step @p71 :rule cong :premises (@p70) :args (@t23)) % 0.39/0.56 (step @p72 :rule eq_resolve :premises (@p1 @p71)) % 0.39/0.56 (step @p73 :rule refl :args (@t65)) % 0.39/0.56 (step @p74 :rule bool-double-not-elim :args (@t50)) % 0.39/0.56 (step @p75 :rule nary_cong :premises (@p74 @p73) :args ((or (not @t66) @t65))) % 0.39/0.56 (step @p76 :rule refl :args (@t53)) % 0.39/0.56 (step @p77 :rule refl :args (@t55)) % 0.39/0.56 (step @p78 :rule refl :args (@t58)) % 0.39/0.56 (step @p79 :rule eq-refl :args (@t60)) % 0.39/0.56 (step @p80 :rule skolem_intro :args (@t61)) % 0.39/0.56 (step @p81 :rule refl :args (@t60)) % 0.39/0.56 (step @p82 :rule cong :premises (@p81 @p80) :args ((= @t60 @t61))) % 0.39/0.56 (step @p83 :rule trans :premises (@p82 @p79)) % 0.39/0.56 (step @p84 :rule true_elim :premises (@p83)) % 0.39/0.56 (step @p85 :rule refl :args (@t56)) % 0.39/0.56 (step @p86 :rule cong :premises (@p85 @p84) :args (@t67)) % 0.39/0.56 (step @p87 :rule cong :premises (@p86) :args (@t68)) % 0.39/0.56 (step @p88 :rule nary_cong :premises (@p87 @p78 @p77 @p76) :args (@t69)) % 0.39/0.56 (step @p89 :rule cong :premises (@p88) :args (@t70)) % 0.39/0.56 (step @p90 :rule refl :args (@t66)) % 0.39/0.56 (step @p91 :rule cong :premises (@p90 @p89) :args ((=> @t66 @t70))) % 0.39/0.56 (assume-push @p132 @t66) % 0.39/0.56 (step @p93 :rule skolemize :premises (@p72)) % 0.39/0.56 (step-pop @p133 :rule scope :premises (@p93)) % 0.39/0.56 (step @p94 :rule process_scope :premises (@p133) :args (@t70)) % 0.39/0.56 (step @p96 :rule eq_resolve :premises (@p94 @p91)) % 0.39/0.56 (step @p97 :rule implies_elim :premises (@p96)) % 0.39/0.56 (step @p98 :rule eq_resolve :premises (@p97 @p75)) % 0.39/0.56 (step @p99 :rule chain_m_resolution :premises (@p98 @p72) :args (@t65 @t71 (@list @t50))) % 0.39/0.56 (step @p100 :rule bool-double-not-elim :args (@t57)) % 0.39/0.56 (step @p101 :rule refl :args (@t64)) % 0.39/0.56 (step @p102 :rule nary_cong :premises (@p101 @p100) :args ((or @t64 (not @t58)))) % 0.39/0.56 (step @p103 :rule cnf_or_neg :args (@t64 1)) % 0.39/0.56 (step @p104 :rule eq_resolve :premises (@p103 @p102)) % 0.39/0.56 (step @p105 :rule reordering :premises (@p104) :args ((or @t57 @t64))) % 0.39/0.57 (step @p106 :rule chain_m_resolution :premises (@p105 @p99) :args (@t57 @t71 @t72)) % 0.39/0.57 (step @p107 :rule bool-double-not-elim :args (@t62)) % 0.39/0.57 (step @p108 :rule nary_cong :premises (@p101 @p107) :args ((or @t64 (not @t63)))) % 0.39/0.57 (step @p109 :rule cnf_or_neg :args (@t64 0)) % 0.39/0.57 (step @p110 :rule eq_resolve :premises (@p109 @p108)) % 0.39/0.57 (step @p111 :rule reordering :premises (@p110) :args ((or @t62 @t64))) % 0.39/0.57 (step @p112 :rule chain_m_resolution :premises (@p111 @p99) :args (@t62 @t71 @t72)) % 0.39/0.57 ; WARNING: add trust step for TRUST % 0.39/0.57 ; trust TRUST THEORY_LEMMA % 0.39/0.57 (step @p113 :rule trust :premises () :args ((=> @t62 @t76))) % 0.39/0.57 (step @p114 :rule implies_elim :premises (@p113)) % 0.39/0.57 (step @p115 :rule chain_m_resolution :premises (@p114 @p112) :args (@t76 (@list false) (@list @t62))) % 0.39/0.57 (step @p116 :rule cnf_or_neg :args (@t64 3)) % 0.39/0.57 (step @p117 :rule chain_m_resolution :premises (@p116 @p99) :args ((not @t53) @t71 @t72)) % 0.39/0.57 (step @p118 :rule cnf_and_pos :args (@t73 1)) % 0.39/0.57 (step @p119 :rule reordering :premises (@p118) :args ((or @t53 @t77))) % 0.39/0.57 (step @p120 :rule chain_m_resolution :premises (@p119 @p117) :args (@t77 @t71 (@list @t53))) % 0.39/0.57 (step @p121 :rule cnf_or_neg :args (@t64 2)) % 0.39/0.57 (step @p122 :rule chain_m_resolution :premises (@p121 @p99) :args ((not @t55) @t71 @t72)) % 0.39/0.57 (step @p123 :rule cnf_and_pos :args (@t74 1)) % 0.39/0.57 (step @p124 :rule reordering :premises (@p123) :args ((or @t55 @t78))) % 0.39/0.57 (step @p125 :rule chain_m_resolution :premises (@p124 @p122) :args (@t78 @t71 (@list @t55))) % 0.39/0.57 (step @p126 :rule cnf_or_pos :args (@t75)) % 0.39/0.57 (step @p127 :rule reordering :premises (@p126) :args ((or @t74 @t73 @t79))) % 0.39/0.57 (step @p128 :rule chain_m_resolution :premises (@p127 @p125 @p120) :args (@t79 (@list true true) (@list @t74 @t73))) % 0.39/0.57 (step @p129 :rule cnf_equiv_pos1 :args (@t76)) % 0.39/0.57 (step @p130 :rule reordering :premises (@p129) :args ((or @t58 @t75 (not @t76)))) % 0.39/0.57 (step @p131 false :rule chain_m_resolution :premises (@p130 @p128 @p115 @p106) :args (false (@list true false false) (@list @t75 @t76 @t57))) % 0.39/0.57 ) % 0.39/0.57 % SZS output end Proof % 0.39/0.57 % cvc5 exiting %------------------------------------------------------------------------------