%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET587^5 : 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 : n008.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 08:48:07 AM UTC 2026 % Result : Theorem 0.29s 0.55s % Output : Proof 0.29s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET587^5 : 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 % 0.16/0.34 % Computer : n008.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 16:03:48 EDT 2026 % 0.16/0.34 % CPUTime : % 0.29/0.48 %----Proving TH0 % 0.29/0.55 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.29/0.55 % SZS status Theorem % 0.29/0.55 % SZS output start Proof % 0.29/0.55 ( % 0.29/0.55 (declare-sort tptp.a 0) % 0.29/0.55 (define @t1 () (@var "Xx" tptp.a)) % 0.29/0.55 (define @t2 () (@var "Y" (-> tptp.a Bool))) % 0.29/0.55 (define @t3 () (_ @t2 @t1)) % 0.29/0.55 (define @t4 () (@var "X" (-> tptp.a Bool))) % 0.29/0.55 (define @t5 () (_ @t4 @t1)) % 0.29/0.55 (define @t6 () (@list @t1)) % 0.29/0.55 (define @t7 () (forall @t6 (=> @t5 @t3))) % 0.29/0.55 (define @t8 () (lambda @t6 false)) % 0.29/0.55 (define @t9 () (not @t3)) % 0.29/0.55 (define @t10 () (and @t5 @t9)) % 0.29/0.55 (define @t11 () (lambda @t6 @t10)) % 0.29/0.55 (define @t12 () (= @t11 @t8)) % 0.29/0.55 (define @t13 () (= @t12 @t7)) % 0.29/0.55 (define @t14 () (@list @t4 @t2)) % 0.29/0.55 (define @t15 () (forall @t14 @t13)) % 0.29/0.55 (define @t16 () (not @t15)) % 0.29/0.55 (define @t17 () (_ @t2 @t1)) % 0.29/0.55 (define @t18 () (_ @t4 @t1)) % 0.29/0.55 (define @t19 () (lambda @t6 (and @t18 (not @t17)))) % 0.29/0.55 (define @t20 () (@var "BOUND_VARIABLE_7491" tptp.a)) % 0.29/0.55 (define @t21 () (lambda (@list @t20) false)) % 0.29/0.55 (define @t22 () (forall @t6 (or (not @t18) @t17))) % 0.29/0.55 (define @t23 () (= @t19 @t21)) % 0.29/0.55 (define @t24 () (= @t11 @t21)) % 0.29/0.55 (define @t25 () (= @t24 @t22)) % 0.29/0.55 (define @t26 () (not @t5)) % 0.29/0.55 (define @t27 () (or @t26 @t3)) % 0.29/0.55 (define @t28 () (@purify @t21)) % 0.29/0.55 (define @t29 () (forall @t14 (= @t22 (= @t21 @t19)))) % 0.29/0.55 (define @t30 () (@quantifiers_skolemize @t29 1)) % 0.29/0.55 (define @t31 () (_ @t30 @t1)) % 0.29/0.55 (define @t32 () (not @t31)) % 0.29/0.55 (define @t33 () (@quantifiers_skolemize @t29 0)) % 0.29/0.55 (define @t34 () (_ @t33 @t1)) % 0.29/0.55 (define @t35 () (and @t34 @t32)) % 0.29/0.55 (define @t36 () (lambda @t6 @t35)) % 0.29/0.55 (define @t37 () (@purify @t36)) % 0.29/0.55 (define @t38 () (= @t37 @t28)) % 0.29/0.55 (define @t39 () (not @t34)) % 0.29/0.55 (define @t40 () (forall @t6 (or @t39 @t31))) % 0.29/0.55 (define @t41 () (= @t40 @t38)) % 0.29/0.55 (define @t42 () (not @t41)) % 0.29/0.55 (define @t43 () (not @t29)) % 0.29/0.55 (define @t44 () (= @t21 @t36)) % 0.29/0.55 (define @t45 () (= @t40 @t44)) % 0.29/0.55 (define @t46 () (not @t45)) % 0.29/0.55 (define @t47 () (@const 0 tptp.a)) % 0.29/0.55 (define @t48 () (_ @t30 @t47)) % 0.29/0.55 (define @t49 () (not @t48)) % 0.29/0.55 (define @t50 () (_ @t33 @t47)) % 0.29/0.55 (define @t51 () (and @t50 @t49)) % 0.29/0.55 (define @t52 () (_ @t21 @t47)) % 0.29/0.55 (define @t53 () (_ @t28 @t47)) % 0.29/0.55 (define @t54 () (= (_ @t36 @t47) @t51)) % 0.29/0.55 (define @t55 () (_ @t37 @t47)) % 0.29/0.55 (define @t56 () (= @t55 @t53)) % 0.29/0.55 (define @t57 () (not @t56)) % 0.29/0.55 (define @t58 () (or @t38 @t57)) % 0.29/0.55 (define @t59 () (not @t51)) % 0.29/0.55 (define @t60 () (not @t50)) % 0.29/0.55 (define @t61 () (or @t60 @t48)) % 0.29/0.55 (define @t62 () (forall @t6 (= @t35 false))) % 0.29/0.55 (define @t63 () (=> @t38 @t62)) % 0.29/0.55 (assume @p1 @t16) % 0.29/0.55 (assume @p2 true) % 0.29/0.55 (step @p3 :rule eq-symm :args (@t19 @t21)) % 0.29/0.55 (step @p4 :rule refl :args (@t22)) % 0.29/0.55 (step @p5 :rule cong :premises (@p4 @p3) :args ((= @t22 @t23))) % 0.29/0.55 (step @p6 :rule eq-symm :args (@t23 @t22)) % 0.29/0.55 (step @p7 :rule trans :premises (@p6 @p5)) % 0.29/0.55 (step @p8 :rule cong :premises (@p7) :args ((forall @t14 (= @t23 @t22)))) % 0.29/0.55 (step @p9 :rule refl :args (@t22)) % 0.29/0.55 (step @p10 :rule refl :args (@t21)) % 0.29/0.55 (step @p11 :rule refl :args (@t17)) % 0.29/0.55 (step @p12 :rule refl :args (@t3)) % 0.29/0.55 (step @p13 :rule cong :premises (@p12 @p11) :args ((= @t3 @t17))) % 0.29/0.55 (step @p14 :rule symm :premises (@p13)) % 0.29/0.55 (step @p15 :rule eq_resolve :premises (@p12 @p14)) % 0.29/0.55 (step @p16 :rule cong :premises (@p15) :args (@t9)) % 0.29/0.55 (step @p17 :rule refl :args (@t18)) % 0.29/0.55 (step @p18 :rule refl :args (@t5)) % 0.29/0.55 (step @p19 :rule cong :premises (@p18 @p17) :args ((= @t5 @t18))) % 0.29/0.55 (step @p20 :rule symm :premises (@p19)) % 0.29/0.55 (step @p21 :rule eq_resolve :premises (@p18 @p20)) % 0.29/0.55 (step @p22 :rule nary_cong :premises (@p21 @p16) :args (@t10)) % 0.29/0.55 (step @p23 :rule cong :premises (@p22) :args (@t11)) % 0.29/0.55 (step @p24 :rule cong :premises (@p23 @p10) :args (@t24)) % 0.29/0.55 (step @p25 :rule cong :premises (@p24 @p9) :args (@t25)) % 0.29/0.55 (step @p26 :rule cong :premises (@p25) :args ((forall @t14 @t25))) % 0.29/0.55 (step @p27 :rule trans :premises (@p26 @p8)) % 0.29/0.55 (step @p28 :rule cong :premises (@p21) :args (@t26)) % 0.29/0.55 (step @p29 :rule nary_cong :premises (@p28 @p15) :args (@t27)) % 0.29/0.55 (step @p30 :rule cong :premises (@p29) :args ((forall @t6 @t27))) % 0.29/0.55 (step @p31 :rule bool-impl-elim :args (@t5 @t3)) % 0.29/0.55 (step @p32 :rule cong :premises (@p31) :args (@t7)) % 0.29/0.55 (step @p33 :rule trans :premises (@p32 @p30)) % 0.29/0.55 (step @p34 :rule refl :args (@t21)) % 0.29/0.55 (step @p35 :rule symm :premises (@p34)) % 0.29/0.55 (step @p36 :rule alpha_equiv :args (@t8 (@list @t1) (@list @t20))) % 0.29/0.55 (step @p37 :rule trans :premises (@p36 @p35)) % 0.29/0.55 (step @p38 :rule refl :args (@t11)) % 0.29/0.55 (step @p39 :rule cong :premises (@p38 @p37) :args (@t12)) % 0.29/0.55 (step @p40 :rule cong :premises (@p39 @p33) :args (@t13)) % 0.29/0.55 (step @p41 :rule cong :premises (@p40) :args (@t15)) % 0.29/0.55 (step @p42 :rule trans :premises (@p41 @p27)) % 0.29/0.55 (step @p43 :rule cong :premises (@p42) :args (@t16)) % 0.29/0.55 (step @p44 :rule eq_resolve :premises (@p1 @p43)) % 0.29/0.55 (step @p45 :rule refl :args (@t42)) % 0.29/0.55 (step @p46 :rule bool-double-not-elim :args (@t29)) % 0.29/0.55 (step @p47 :rule nary_cong :premises (@p46 @p45) :args ((or (not @t43) @t42))) % 0.29/0.55 (step @p48 :rule eq-symm :args (@t28 @t37)) % 0.29/0.55 (step @p49 :rule eq-refl :args (@t36)) % 0.29/0.55 (step @p50 :rule skolem_intro :args (@t37)) % 0.29/0.55 (step @p51 :rule refl :args (@t36)) % 0.29/0.55 (step @p52 :rule cong :premises (@p51 @p50) :args ((= @t36 @t37))) % 0.29/0.55 (step @p53 :rule trans :premises (@p52 @p49)) % 0.29/0.55 (step @p54 :rule true_elim :premises (@p53)) % 0.29/0.55 (step @p55 :rule eq-refl :args (@t21)) % 0.29/0.55 (step @p56 :rule refl :args (@t21)) % 0.29/0.55 (step @p57 :rule cong :premises (@p56 @p35) :args ((= @t21 @t21))) % 0.29/0.55 (step @p58 :rule trans :premises (@p57 @p55)) % 0.29/0.55 (step @p59 :rule skolem_intro :args (@t28)) % 0.29/0.55 (step @p60 :rule cong :premises (@p56 @p59) :args ((= @t21 @t28))) % 0.29/0.55 (step @p61 :rule trans :premises (@p60 @p58)) % 0.29/0.55 (step @p62 :rule true_elim :premises (@p61)) % 0.29/0.55 (step @p63 :rule cong :premises (@p62 @p54) :args (@t44)) % 0.29/0.55 (step @p64 :rule trans :premises (@p63 @p48)) % 0.29/0.55 (step @p65 :rule refl :args (@t40)) % 0.29/0.55 (step @p66 :rule cong :premises (@p65 @p64) :args (@t45)) % 0.29/0.55 (step @p67 :rule cong :premises (@p66) :args (@t46)) % 0.29/0.55 (step @p68 :rule refl :args (@t43)) % 0.29/0.55 (step @p69 :rule cong :premises (@p68 @p67) :args ((=> @t43 @t46))) % 0.29/0.55 (assume-push @p138 @t43) % 0.29/0.55 (step @p71 :rule skolemize :premises (@p44)) % 0.29/0.55 (step-pop @p139 :rule scope :premises (@p71)) % 0.29/0.55 (step @p72 :rule process_scope :premises (@p139) :args (@t46)) % 0.29/0.55 (step @p74 :rule eq_resolve :premises (@p72 @p69)) % 0.29/0.55 (step @p75 :rule implies_elim :premises (@p74)) % 0.29/0.55 (step @p76 :rule eq_resolve :premises (@p75 @p47)) % 0.29/0.55 (step @p77 :rule chain_m_resolution :premises (@p76 @p44) :args (@t42 (@list true) (@list @t29))) % 0.29/0.55 (step @p78 :rule cnf_equiv_neg2 :args (@t41)) % 0.29/0.55 (step @p79 :rule bool-double-not-elim :args (@t51)) % 0.29/0.55 (step @p80 :rule bool-eq-false :args (@t51)) % 0.29/0.55 (step @p81 :rule evaluate :args ((not false))) % 0.29/0.55 (step @p82 :rule beta-reduce :args ((= @t52 false))) % 0.29/0.55 (step @p83 :rule cong :premises (@p82) :args ((not @t52))) % 0.29/0.55 (step @p84 :rule trans :premises (@p83 @p81)) % 0.29/0.55 (step @p85 :rule refl :args (@t47)) % 0.29/0.55 (step @p86 :rule ho_cong :premises (@p59 @p85)) % 0.29/0.55 (step @p87 :rule cong :premises (@p86) :args ((not @t53))) % 0.29/0.55 (step @p88 :rule bool-eq-false :args (@t53)) % 0.29/0.55 (step @p89 :rule trans :premises (@p88 @p87 @p84)) % 0.29/0.55 (step @p90 :rule true_elim :premises (@p89)) % 0.29/0.55 (step @p91 :rule eq-refl :args (@t51)) % 0.29/0.55 (step @p92 :rule refl :args (@t51)) % 0.29/0.55 (step @p93 :rule beta-reduce :args (@t54)) % 0.29/0.55 (step @p94 :rule cong :premises (@p93 @p92) :args (@t54)) % 0.29/0.55 (step @p95 :rule trans :premises (@p94 @p91)) % 0.29/0.55 (step @p96 :rule ho_cong :premises (@p50 @p85)) % 0.29/0.55 (step @p97 :rule cong :premises (@p96 @p92) :args ((= @t55 @t51))) % 0.29/0.55 (step @p98 :rule trans :premises (@p97 @p95)) % 0.29/0.55 (step @p99 :rule true_elim :premises (@p98)) % 0.29/0.55 (step @p100 :rule cong :premises (@p99 @p90) :args (@t56)) % 0.29/0.55 (step @p101 :rule trans :premises (@p100 @p80)) % 0.29/0.55 (step @p102 :rule cong :premises (@p101) :args (@t57)) % 0.29/0.55 (step @p103 :rule trans :premises (@p102 @p79)) % 0.29/0.55 (step @p104 :rule refl :args (@t38)) % 0.29/0.55 (step @p105 :rule nary_cong :premises (@p104 @p103) :args (@t58)) % 0.29/0.55 ; WARNING: add trust step for TRUST % 0.29/0.55 ; trust TRUST THEORY_LEMMA % 0.29/0.55 (step @p106 :rule trust :premises () :args (@t58)) % 0.29/0.55 (step @p107 :rule eq_resolve :premises (@p106 @p105)) % 0.29/0.55 (step @p108 :rule cnf_and_pos :args (@t51 0)) % 0.29/0.55 (step @p109 :rule reordering :premises (@p108) :args ((or @t50 @t59))) % 0.29/0.55 (step @p110 :rule cnf_and_pos :args (@t51 1)) % 0.29/0.55 (step @p111 :rule reordering :premises (@p110) :args ((or @t49 @t59))) % 0.29/0.55 (step @p112 :rule cnf_or_pos :args (@t61)) % 0.29/0.55 (step @p113 :rule reordering :premises (@p112) :args ((or @t48 @t60 (not @t61)))) % 0.29/0.55 (assume-push @p140 @t40) % 0.29/0.55 (step @p115 :rule instantiate :premises (@p140) :args ((@list @t47))) % 0.29/0.55 (step-pop @p141 :rule scope :premises (@p115)) % 0.29/0.55 (step @p116 :rule process_scope :premises (@p141) :args (@t61)) % 0.29/0.55 (step @p118 :rule implies_elim :premises (@p116)) % 0.29/0.55 (step @p119 :rule chain_m_resolution :premises (@p118 @p113 @p111 @p109 @p107 @p78 @p77) :args ((not @t40) (@list true true false false true true) (@list @t61 @t48 @t50 @t51 @t38 @t41))) % 0.29/0.55 (step @p120 :rule cnf_equiv_neg1 :args (@t41)) % 0.29/0.55 (step @p121 :rule reordering :premises (@p120) :args ((or @t40 @t38 @t41))) % 0.29/0.55 (step @p122 :rule chain_m_resolution :premises (@p121 @p119 @p77) :args (@t38 (@list true true) (@list @t40 @t41))) % 0.29/0.55 (step @p123 :rule bool-double-not-elim :args (@t31)) % 0.29/0.55 (step @p124 :rule refl :args (@t39)) % 0.29/0.55 (step @p125 :rule nary_cong :premises (@p124 @p123) :args ((or @t39 (not @t32)))) % 0.29/0.55 (step @p126 :rule bool-and-de-morgan :args (@t34 @t32 true)) % 0.29/0.55 (step @p127 :rule trans :premises (@p126 @p125)) % 0.29/0.55 (step @p128 :rule cong :premises (@p127) :args ((forall @t6 (not @t35)))) % 0.29/0.55 (step @p129 :rule bool-eq-false :args (@t35)) % 0.29/0.55 (step @p130 :rule cong :premises (@p129) :args (@t62)) % 0.29/0.55 (step @p131 :rule trans :premises (@p130 @p128)) % 0.29/0.55 (step @p132 :rule cong :premises (@p104 @p131) :args (@t63)) % 0.29/0.55 ; trust TRUST THEORY_LEMMA % 0.29/0.55 (step @p133 :rule trust :premises () :args (@t63)) % 0.29/0.55 (step @p134 :rule eq_resolve :premises (@p133 @p132)) % 0.29/0.55 (step @p135 :rule implies_elim :premises (@p134)) % 0.29/0.55 (step @p136 :rule reordering :premises (@p135) :args ((or @t40 (not @t38)))) % 0.29/0.55 (step @p137 false :rule chain_m_resolution :premises (@p136 @p122 @p119) :args (false (@list false true) (@list @t38 @t40))) % 0.29/0.55 ) % 0.29/0.55 % SZS output end Proof % 0.29/0.55 % cvc5 exiting %------------------------------------------------------------------------------