%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET636^5 : 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 : n011.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 08:48:20 AM UTC 2026 % Result : Theorem 0.33s 0.56s % Output : Proof 0.33s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SET636^5 : TPTP v9.2.1. Released v4.0.0. % 0.11/0.14 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.18/0.35 % Computer : n011.cluster.edu % 0.18/0.35 % Model : x86_64 x86_64 % 0.18/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.18/0.35 % Memory : 8042.1875MB % 0.18/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.18/0.35 % CPULimit : 300 % 0.18/0.35 % WCLimit : 300 % 0.18/0.35 % DateTime : Tue Jun 2 16:05:20 EDT 2026 % 0.18/0.35 % CPUTime : % 0.33/0.50 %----Proving TH0 % 0.33/0.56 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.33/0.56 % SZS status Theorem % 0.33/0.56 % SZS output start Proof % 0.33/0.56 ( % 0.33/0.56 (declare-sort tptp.a 0) % 0.33/0.56 (define @t1 () (@var "Xx" tptp.a)) % 0.33/0.56 (define @t2 () (@list @t1)) % 0.33/0.56 (define @t3 () (lambda @t2 false)) % 0.33/0.56 (define @t4 () (@var "Y" (-> tptp.a Bool))) % 0.33/0.56 (define @t5 () (_ @t4 @t1)) % 0.33/0.56 (define @t6 () (@var "X" (-> tptp.a Bool))) % 0.33/0.56 (define @t7 () (_ @t6 @t1)) % 0.33/0.56 (define @t8 () (and @t7 @t5)) % 0.33/0.56 (define @t9 () (lambda @t2 @t8)) % 0.33/0.56 (define @t10 () (= @t9 @t3)) % 0.33/0.56 (define @t11 () (exists @t2 @t8)) % 0.33/0.56 (define @t12 () (not @t11)) % 0.33/0.56 (define @t13 () (= @t12 @t10)) % 0.33/0.56 (define @t14 () (@list @t6 @t4)) % 0.33/0.56 (define @t15 () (forall @t14 @t13)) % 0.33/0.56 (define @t16 () (not @t15)) % 0.33/0.56 (define @t17 () (_ @t4 @t1)) % 0.33/0.56 (define @t18 () (_ @t6 @t1)) % 0.33/0.56 (define @t19 () (lambda @t2 (and @t18 @t17))) % 0.33/0.56 (define @t20 () (@var "BOUND_VARIABLE_7495" tptp.a)) % 0.33/0.56 (define @t21 () (lambda (@list @t20) false)) % 0.33/0.56 (define @t22 () (forall @t2 (or (not @t18) (not @t17)))) % 0.33/0.56 (define @t23 () (= @t22 (= @t19 @t21))) % 0.33/0.56 (define @t24 () (= @t9 @t21)) % 0.33/0.56 (define @t25 () (= @t22 @t24)) % 0.33/0.56 (define @t26 () (not @t5)) % 0.33/0.56 (define @t27 () (not @t7)) % 0.33/0.56 (define @t28 () (or @t27 @t26)) % 0.33/0.56 (define @t29 () (forall @t2 (not @t8))) % 0.33/0.56 (define @t30 () (not @t29)) % 0.33/0.56 (define @t31 () (@purify @t21)) % 0.33/0.56 (define @t32 () (forall @t14 (= @t22 (= @t21 @t19)))) % 0.33/0.56 (define @t33 () (@quantifiers_skolemize @t32 1)) % 0.33/0.56 (define @t34 () (_ @t33 @t1)) % 0.33/0.56 (define @t35 () (@quantifiers_skolemize @t32 0)) % 0.33/0.56 (define @t36 () (_ @t35 @t1)) % 0.33/0.56 (define @t37 () (and @t36 @t34)) % 0.33/0.56 (define @t38 () (lambda @t2 @t37)) % 0.33/0.56 (define @t39 () (@purify @t38)) % 0.33/0.56 (define @t40 () (= @t39 @t31)) % 0.33/0.56 (define @t41 () (forall @t2 (or (not @t36) (not @t34)))) % 0.33/0.56 (define @t42 () (= @t41 @t40)) % 0.33/0.56 (define @t43 () (not @t42)) % 0.33/0.56 (define @t44 () (not @t32)) % 0.33/0.56 (define @t45 () (= @t21 @t38)) % 0.33/0.56 (define @t46 () (= @t41 @t45)) % 0.33/0.56 (define @t47 () (not @t46)) % 0.33/0.56 (define @t48 () (@const 0 tptp.a)) % 0.33/0.56 (define @t49 () (_ @t33 @t48)) % 0.33/0.56 (define @t50 () (_ @t35 @t48)) % 0.33/0.56 (define @t51 () (and @t50 @t49)) % 0.33/0.56 (define @t52 () (_ @t21 @t48)) % 0.33/0.56 (define @t53 () (_ @t31 @t48)) % 0.33/0.56 (define @t54 () (= (_ @t38 @t48) @t51)) % 0.33/0.56 (define @t55 () (_ @t39 @t48)) % 0.33/0.56 (define @t56 () (= @t55 @t53)) % 0.33/0.56 (define @t57 () (not @t56)) % 0.33/0.56 (define @t58 () (or @t40 @t57)) % 0.33/0.56 (define @t59 () (not @t51)) % 0.33/0.56 (define @t60 () (not @t49)) % 0.33/0.56 (define @t61 () (not @t50)) % 0.33/0.56 (define @t62 () (or @t61 @t60)) % 0.33/0.56 (define @t63 () (forall @t2 (= @t37 false))) % 0.33/0.56 (define @t64 () (=> @t40 @t63)) % 0.33/0.56 (assume @p1 @t16) % 0.33/0.56 (assume @p2 true) % 0.33/0.56 (step @p3 :rule eq-symm :args (@t19 @t21)) % 0.33/0.56 (step @p4 :rule refl :args (@t22)) % 0.33/0.56 (step @p5 :rule cong :premises (@p4 @p3) :args (@t23)) % 0.33/0.56 (step @p6 :rule cong :premises (@p5) :args ((forall @t14 @t23))) % 0.33/0.56 (step @p7 :rule refl :args (@t21)) % 0.33/0.56 (step @p8 :rule refl :args (@t17)) % 0.33/0.56 (step @p9 :rule refl :args (@t5)) % 0.33/0.56 (step @p10 :rule cong :premises (@p9 @p8) :args ((= @t5 @t17))) % 0.33/0.56 (step @p11 :rule symm :premises (@p10)) % 0.33/0.56 (step @p12 :rule eq_resolve :premises (@p9 @p11)) % 0.33/0.56 (step @p13 :rule refl :args (@t18)) % 0.33/0.56 (step @p14 :rule refl :args (@t7)) % 0.33/0.56 (step @p15 :rule cong :premises (@p14 @p13) :args ((= @t7 @t18))) % 0.33/0.56 (step @p16 :rule symm :premises (@p15)) % 0.33/0.56 (step @p17 :rule eq_resolve :premises (@p14 @p16)) % 0.33/0.56 (step @p18 :rule nary_cong :premises (@p17 @p12) :args (@t8)) % 0.33/0.56 (step @p19 :rule cong :premises (@p18) :args (@t9)) % 0.33/0.56 (step @p20 :rule cong :premises (@p19 @p7) :args (@t24)) % 0.33/0.56 (step @p21 :rule refl :args (@t22)) % 0.33/0.56 (step @p22 :rule cong :premises (@p21 @p20) :args (@t25)) % 0.33/0.56 (step @p23 :rule cong :premises (@p22) :args ((forall @t14 @t25))) % 0.33/0.56 (step @p24 :rule trans :premises (@p23 @p6)) % 0.33/0.56 (step @p25 :rule refl :args (@t21)) % 0.33/0.56 (step @p26 :rule symm :premises (@p25)) % 0.33/0.56 (step @p27 :rule alpha_equiv :args (@t3 (@list @t1) (@list @t20))) % 0.33/0.56 (step @p28 :rule trans :premises (@p27 @p26)) % 0.33/0.56 (step @p29 :rule refl :args (@t9)) % 0.33/0.56 (step @p30 :rule cong :premises (@p29 @p28) :args (@t10)) % 0.33/0.56 (step @p31 :rule bool-double-not-elim :args (@t22)) % 0.33/0.56 (step @p32 :rule cong :premises (@p12) :args (@t26)) % 0.33/0.56 (step @p33 :rule cong :premises (@p17) :args (@t27)) % 0.33/0.56 (step @p34 :rule nary_cong :premises (@p33 @p32) :args (@t28)) % 0.33/0.56 (step @p35 :rule cong :premises (@p34) :args ((forall @t2 @t28))) % 0.33/0.56 (step @p36 :rule bool-and-de-morgan :args (@t7 @t5 true)) % 0.33/0.56 (step @p37 :rule cong :premises (@p36) :args (@t29)) % 0.33/0.56 (step @p38 :rule trans :premises (@p37 @p35)) % 0.33/0.56 (step @p39 :rule cong :premises (@p38) :args (@t30)) % 0.33/0.56 (step @p40 :rule exists-elim :args ((= @t11 @t30))) % 0.33/0.56 (step @p41 :rule trans :premises (@p40 @p39)) % 0.33/0.56 (step @p42 :rule cong :premises (@p41) :args (@t12)) % 0.33/0.56 (step @p43 :rule trans :premises (@p42 @p31)) % 0.33/0.56 (step @p44 :rule cong :premises (@p43 @p30) :args (@t13)) % 0.33/0.56 (step @p45 :rule cong :premises (@p44) :args (@t15)) % 0.33/0.56 (step @p46 :rule trans :premises (@p45 @p24)) % 0.33/0.56 (step @p47 :rule cong :premises (@p46) :args (@t16)) % 0.33/0.56 (step @p48 :rule eq_resolve :premises (@p1 @p47)) % 0.33/0.56 (step @p49 :rule refl :args (@t43)) % 0.33/0.56 (step @p50 :rule bool-double-not-elim :args (@t32)) % 0.33/0.56 (step @p51 :rule nary_cong :premises (@p50 @p49) :args ((or (not @t44) @t43))) % 0.33/0.56 (step @p52 :rule eq-symm :args (@t31 @t39)) % 0.33/0.56 (step @p53 :rule eq-refl :args (@t38)) % 0.33/0.56 (step @p54 :rule skolem_intro :args (@t39)) % 0.33/0.56 (step @p55 :rule refl :args (@t38)) % 0.33/0.56 (step @p56 :rule cong :premises (@p55 @p54) :args ((= @t38 @t39))) % 0.33/0.56 (step @p57 :rule trans :premises (@p56 @p53)) % 0.33/0.56 (step @p58 :rule true_elim :premises (@p57)) % 0.33/0.56 (step @p59 :rule eq-refl :args (@t21)) % 0.33/0.56 (step @p60 :rule refl :args (@t21)) % 0.33/0.56 (step @p61 :rule cong :premises (@p60 @p26) :args ((= @t21 @t21))) % 0.33/0.56 (step @p62 :rule trans :premises (@p61 @p59)) % 0.33/0.56 (step @p63 :rule skolem_intro :args (@t31)) % 0.33/0.56 (step @p64 :rule cong :premises (@p60 @p63) :args ((= @t21 @t31))) % 0.33/0.56 (step @p65 :rule trans :premises (@p64 @p62)) % 0.33/0.56 (step @p66 :rule true_elim :premises (@p65)) % 0.33/0.56 (step @p67 :rule cong :premises (@p66 @p58) :args (@t45)) % 0.33/0.56 (step @p68 :rule trans :premises (@p67 @p52)) % 0.33/0.56 (step @p69 :rule refl :args (@t41)) % 0.33/0.56 (step @p70 :rule cong :premises (@p69 @p68) :args (@t46)) % 0.33/0.56 (step @p71 :rule cong :premises (@p70) :args (@t47)) % 0.33/0.56 (step @p72 :rule refl :args (@t44)) % 0.33/0.56 (step @p73 :rule cong :premises (@p72 @p71) :args ((=> @t44 @t47))) % 0.33/0.56 (assume-push @p138 @t44) % 0.33/0.56 (step @p75 :rule skolemize :premises (@p48)) % 0.33/0.56 (step-pop @p139 :rule scope :premises (@p75)) % 0.33/0.56 (step @p76 :rule process_scope :premises (@p139) :args (@t47)) % 0.33/0.56 (step @p78 :rule eq_resolve :premises (@p76 @p73)) % 0.33/0.56 (step @p79 :rule implies_elim :premises (@p78)) % 0.33/0.56 (step @p80 :rule eq_resolve :premises (@p79 @p51)) % 0.33/0.56 (step @p81 :rule chain_m_resolution :premises (@p80 @p48) :args (@t43 (@list true) (@list @t32))) % 0.33/0.56 (step @p82 :rule cnf_equiv_neg2 :args (@t42)) % 0.33/0.56 (step @p83 :rule bool-double-not-elim :args (@t51)) % 0.33/0.56 (step @p84 :rule bool-eq-false :args (@t51)) % 0.33/0.56 (step @p85 :rule evaluate :args ((not false))) % 0.33/0.56 (step @p86 :rule beta-reduce :args ((= @t52 false))) % 0.33/0.56 (step @p87 :rule cong :premises (@p86) :args ((not @t52))) % 0.33/0.56 (step @p88 :rule trans :premises (@p87 @p85)) % 0.33/0.56 (step @p89 :rule refl :args (@t48)) % 0.33/0.56 (step @p90 :rule ho_cong :premises (@p63 @p89)) % 0.33/0.56 (step @p91 :rule cong :premises (@p90) :args ((not @t53))) % 0.33/0.56 (step @p92 :rule bool-eq-false :args (@t53)) % 0.33/0.56 (step @p93 :rule trans :premises (@p92 @p91 @p88)) % 0.33/0.56 (step @p94 :rule true_elim :premises (@p93)) % 0.33/0.56 (step @p95 :rule eq-refl :args (@t51)) % 0.33/0.56 (step @p96 :rule refl :args (@t51)) % 0.33/0.56 (step @p97 :rule beta-reduce :args (@t54)) % 0.33/0.56 (step @p98 :rule cong :premises (@p97 @p96) :args (@t54)) % 0.33/0.56 (step @p99 :rule trans :premises (@p98 @p95)) % 0.33/0.56 (step @p100 :rule ho_cong :premises (@p54 @p89)) % 0.33/0.56 (step @p101 :rule cong :premises (@p100 @p96) :args ((= @t55 @t51))) % 0.33/0.56 (step @p102 :rule trans :premises (@p101 @p99)) % 0.33/0.56 (step @p103 :rule true_elim :premises (@p102)) % 0.33/0.56 (step @p104 :rule cong :premises (@p103 @p94) :args (@t56)) % 0.33/0.56 (step @p105 :rule trans :premises (@p104 @p84)) % 0.33/0.56 (step @p106 :rule cong :premises (@p105) :args (@t57)) % 0.33/0.56 (step @p107 :rule trans :premises (@p106 @p83)) % 0.33/0.56 (step @p108 :rule refl :args (@t40)) % 0.33/0.56 (step @p109 :rule nary_cong :premises (@p108 @p107) :args (@t58)) % 0.33/0.56 ; WARNING: add trust step for TRUST % 0.33/0.56 ; trust TRUST THEORY_LEMMA % 0.33/0.56 (step @p110 :rule trust :premises () :args (@t58)) % 0.33/0.56 (step @p111 :rule eq_resolve :premises (@p110 @p109)) % 0.33/0.56 (step @p112 :rule cnf_and_pos :args (@t51 0)) % 0.33/0.56 (step @p113 :rule reordering :premises (@p112) :args ((or @t50 @t59))) % 0.33/0.56 (step @p114 :rule cnf_and_pos :args (@t51 1)) % 0.33/0.56 (step @p115 :rule reordering :premises (@p114) :args ((or @t49 @t59))) % 0.33/0.57 (step @p116 :rule cnf_or_pos :args (@t62)) % 0.33/0.57 (step @p117 :rule reordering :premises (@p116) :args ((or @t61 @t60 (not @t62)))) % 0.33/0.57 (assume-push @p140 @t41) % 0.33/0.57 (step @p119 :rule instantiate :premises (@p140) :args ((@list @t48))) % 0.33/0.57 (step-pop @p141 :rule scope :premises (@p119)) % 0.33/0.57 (step @p120 :rule process_scope :premises (@p141) :args (@t62)) % 0.33/0.57 (step @p122 :rule implies_elim :premises (@p120)) % 0.33/0.57 (step @p123 :rule chain_m_resolution :premises (@p122 @p117 @p115 @p113 @p111 @p82 @p81) :args ((not @t41) (@list true false false false true true) (@list @t62 @t49 @t50 @t51 @t40 @t42))) % 0.33/0.57 (step @p124 :rule cnf_equiv_neg1 :args (@t42)) % 0.33/0.57 (step @p125 :rule reordering :premises (@p124) :args ((or @t41 @t40 @t42))) % 0.33/0.57 (step @p126 :rule chain_m_resolution :premises (@p125 @p123 @p81) :args (@t40 (@list true true) (@list @t41 @t42))) % 0.33/0.57 (step @p127 :rule bool-and-de-morgan :args (@t36 @t34 true)) % 0.33/0.57 (step @p128 :rule cong :premises (@p127) :args ((forall @t2 (not @t37)))) % 0.33/0.57 (step @p129 :rule bool-eq-false :args (@t37)) % 0.33/0.57 (step @p130 :rule cong :premises (@p129) :args (@t63)) % 0.33/0.57 (step @p131 :rule trans :premises (@p130 @p128)) % 0.33/0.57 (step @p132 :rule cong :premises (@p108 @p131) :args (@t64)) % 0.33/0.57 ; trust TRUST THEORY_LEMMA % 0.33/0.57 (step @p133 :rule trust :premises () :args (@t64)) % 0.33/0.57 (step @p134 :rule eq_resolve :premises (@p133 @p132)) % 0.33/0.57 (step @p135 :rule implies_elim :premises (@p134)) % 0.33/0.57 (step @p136 :rule reordering :premises (@p135) :args ((or @t41 (not @t40)))) % 0.33/0.57 (step @p137 false :rule chain_m_resolution :premises (@p136 @p126 @p123) :args (false (@list false true) (@list @t40 @t41))) % 0.33/0.57 ) % 0.33/0.57 % SZS output end Proof % 0.33/0.57 % cvc5 exiting %------------------------------------------------------------------------------