%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYN999^1 : TPTP v9.2.1. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n013.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 09:10:14 AM UTC 2026 % Result : Theorem 0.39s 0.63s % Output : Proof 0.39s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : SYN999^1 : TPTP v9.2.1. Released v3.7.0. % 0.12/0.14 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.16/0.35 % Computer : n013.cluster.edu % 0.16/0.35 % Model : x86_64 x86_64 % 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.35 % Memory : 8042.1875MB % 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.35 % CPULimit : 300 % 0.16/0.35 % WCLimit : 300 % 0.16/0.35 % DateTime : Tue Jun 2 23:51:15 EDT 2026 % 0.16/0.35 % CPUTime : % 0.31/0.50 %----Proving TH0 % 0.39/0.63 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.39/0.63 % SZS status Theorem % 0.39/0.63 % SZS output start Proof % 0.39/0.63 ( % 0.39/0.63 (declare-sort $$unsorted 0) % 0.39/0.63 (define tptp.leibeq () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" $$unsorted))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (=> (_ _let_2 _let_3) (_ _let_2 _let_1)))))))) % 0.39/0.63 (define @t1 () (@var "X" $$unsorted)) % 0.39/0.63 (define @t2 () (@var "Y" $$unsorted)) % 0.39/0.63 (define @t3 () (=> (_ (_ tptp.leibeq @t1) @t2) (_ (_ tptp.leibeq @t2) @t1))) % 0.39/0.63 (define @t4 () (@list @t1 @t2)) % 0.39/0.63 (define @t5 () (forall @t4 @t3)) % 0.39/0.63 (define @t6 () (not @t5)) % 0.39/0.63 (define @t7 () (@var "P" (-> $$unsorted Bool))) % 0.39/0.63 (define @t8 () (_ @t7 @t2)) % 0.39/0.63 (define @t9 () (_ @t7 @t1)) % 0.39/0.63 (define @t10 () (@list @t7)) % 0.39/0.63 (define @t11 () (forall @t10 (=> @t9 @t8))) % 0.39/0.63 (define @t12 () (lambda @t4 @t11)) % 0.39/0.63 (define @t13 () (@var "BOUND_VARIABLE_7477" (-> $$unsorted Bool))) % 0.39/0.63 (define @t14 () (_ @t13 @t1)) % 0.39/0.63 (define @t15 () (not (_ @t13 @t2))) % 0.39/0.63 (define @t16 () (_ @t7 @t2)) % 0.39/0.63 (define @t17 () (_ @t7 @t1)) % 0.39/0.63 (define @t18 () (not @t17)) % 0.39/0.63 (define @t19 () (forall @t10 (or @t18 @t16))) % 0.39/0.63 (define @t20 () (not @t19)) % 0.39/0.63 (define @t21 () (or @t20 @t15 @t14)) % 0.39/0.63 (define @t22 () (or @t15 @t14)) % 0.39/0.63 (define @t23 () (or @t20 @t22)) % 0.39/0.63 (define @t24 () (@list @t1 @t2 @t13)) % 0.39/0.63 (define @t25 () (forall @t24 @t23)) % 0.39/0.63 (define @t26 () (@list @t13)) % 0.39/0.63 (define @t27 () (forall @t26 @t23)) % 0.39/0.63 (define @t28 () (forall @t26 @t22)) % 0.39/0.63 (define @t29 () (or @t20 @t28)) % 0.39/0.63 (define @t30 () (not @t16)) % 0.39/0.63 (define @t31 () (forall @t10 (or @t30 @t17))) % 0.39/0.63 (define @t32 () (@var "BOUND_VARIABLE_7455" $$unsorted)) % 0.39/0.63 (define @t33 () (_ @t7 @t32)) % 0.39/0.63 (define @t34 () (lambda (@list @t32) (forall @t10 (or @t30 @t33)))) % 0.39/0.63 (define @t35 () (lambda @t4 @t19)) % 0.39/0.63 (define @t36 () (lambda (@list @t2) @t19)) % 0.39/0.63 (define @t37 () (_ @t35 @t1)) % 0.39/0.63 (define @t38 () (=> (_ @t37 @t2) (_ (_ @t35 @t2) @t1))) % 0.39/0.63 (define @t39 () (forall @t4 @t38)) % 0.39/0.63 (define @t40 () (not @t9)) % 0.39/0.63 (define @t41 () (or @t40 @t8)) % 0.39/0.63 (define @t42 () (forall @t24 @t21)) % 0.39/0.63 (define @t43 () (@quantifiers_skolemize @t42 0)) % 0.39/0.63 (define @t44 () (@quantifiers_skolemize @t42 2)) % 0.39/0.63 (define @t45 () (_ @t44 @t43)) % 0.39/0.63 (define @t46 () (@quantifiers_skolemize @t42 1)) % 0.39/0.63 (define @t47 () (_ @t44 @t46)) % 0.39/0.63 (define @t48 () (not @t47)) % 0.39/0.63 (define @t49 () (forall @t10 (or (not (_ @t7 @t43)) (_ @t7 @t46)))) % 0.39/0.63 (define @t50 () (not @t49)) % 0.39/0.63 (define @t51 () (or @t50 @t48 @t45)) % 0.39/0.63 (define @t52 () (@list true)) % 0.39/0.63 (define @t53 () (@list @t51)) % 0.39/0.63 (define @t54 () (= @t43 @t46)) % 0.39/0.63 (define @t55 () (@var "BOUND_VARIABLE_14634" $$unsorted)) % 0.39/0.63 (define @t56 () (lambda (@list @t55) (= @t55 @t43))) % 0.39/0.63 (define @t57 () (_ @t56 @t46)) % 0.39/0.63 (define @t58 () (_ @t56 @t43)) % 0.39/0.63 (define @t59 () (not @t58)) % 0.39/0.63 (define @t60 () (or @t59 @t57)) % 0.39/0.63 (assume @p1 @t6) % 0.39/0.63 (assume @p2 true) % 0.39/0.63 (step @p3 (= tptp.leibeq @t12) :rule refl :args (@t12)) % 0.39/0.63 (step @p4 :rule evaluate :args ((= true false))) % 0.39/0.63 (step @p5 :rule aci_norm :args ((= @t23 @t21))) % 0.39/0.63 (step @p6 :rule cong :premises (@p5) :args (@t25)) % 0.39/0.63 (step @p7 :rule quant-merge-prenex :args ((= (forall @t4 @t27) @t25))) % 0.39/0.63 (step @p8 :rule alpha_equiv :args (@t28 (@list @t13) (@list @t7))) % 0.39/0.63 (step @p9 :rule refl :args (@t20)) % 0.39/0.63 (step @p10 :rule nary_cong :premises (@p9 @p8) :args (@t29)) % 0.39/0.63 (step @p11 :rule quant-miniscope-or :args ((= @t27 @t29))) % 0.39/0.63 (step @p12 :rule trans :premises (@p11 @p10)) % 0.39/0.63 (step @p13 :rule symm :premises (@p12)) % 0.39/0.63 (step @p14 :rule cong :premises (@p13) :args ((forall @t4 (or @t20 @t31)))) % 0.39/0.63 (step @p15 :rule trans :premises (@p14 @p7)) % 0.39/0.63 (step @p16 :rule trans :premises (@p15 @p6)) % 0.39/0.63 (step @p17 :rule bool-impl-elim :args (@t19 @t31)) % 0.39/0.63 (step @p18 :rule cong :premises (@p17) :args ((forall @t4 (=> @t19 @t31)))) % 0.39/0.63 (step @p19 :rule trans :premises (@p18 @p16)) % 0.39/0.63 (step @p20 :rule beta-reduce :args ((= (_ @t34 @t1) @t31))) % 0.39/0.63 (step @p21 :rule refl :args (@t1)) % 0.39/0.63 (step @p22 :rule beta-reduce :args ((= (_ (lambda (@list @t1 @t32) (forall @t10 (or @t18 @t33))) @t2) @t34))) % 0.39/0.63 (step @p23 :rule refl :args (@t2)) % 0.39/0.63 (step @p24 :rule alpha_equiv :args (@t35 (@list @t2) (@list @t32))) % 0.39/0.63 (step @p25 :rule ho_cong :premises (@p24 @p23)) % 0.39/0.63 (step @p26 :rule trans :premises (@p25 @p22)) % 0.39/0.63 (step @p27 :rule ho_cong :premises (@p26 @p21)) % 0.39/0.63 (step @p28 :rule trans :premises (@p27 @p20)) % 0.39/0.63 (step @p29 :rule beta-reduce :args ((= (_ @t36 @t2) @t19))) % 0.39/0.63 (step @p30 :rule refl :args (@t2)) % 0.39/0.63 (step @p31 :rule beta-reduce :args ((= @t37 @t36))) % 0.39/0.63 (step @p32 :rule ho_cong :premises (@p31 @p30)) % 0.39/0.63 (step @p33 :rule trans :premises (@p32 @p29)) % 0.39/0.63 (step @p34 :rule cong :premises (@p33 @p28) :args (@t38)) % 0.39/0.63 (step @p35 :rule cong :premises (@p34) :args (@t39)) % 0.39/0.63 (step @p36 :rule trans :premises (@p35 @p19)) % 0.39/0.63 (step @p37 :rule cong :premises (@p36) :args ((not @t39))) % 0.39/0.63 (step @p38 :rule refl :args (@t16)) % 0.39/0.63 (step @p39 :rule refl :args (@t8)) % 0.39/0.63 (step @p40 :rule cong :premises (@p39 @p38) :args ((= @t8 @t16))) % 0.39/0.63 (step @p41 :rule symm :premises (@p40)) % 0.39/0.63 (step @p42 :rule eq_resolve :premises (@p39 @p41)) % 0.39/0.63 (step @p43 :rule refl :args (@t17)) % 0.39/0.63 (step @p44 :rule refl :args (@t9)) % 0.39/0.63 (step @p45 :rule cong :premises (@p44 @p43) :args ((= @t9 @t17))) % 0.39/0.63 (step @p46 :rule symm :premises (@p45)) % 0.39/0.63 (step @p47 :rule eq_resolve :premises (@p44 @p46)) % 0.39/0.63 (step @p48 :rule cong :premises (@p47) :args (@t40)) % 0.39/0.63 (step @p49 :rule nary_cong :premises (@p48 @p42) :args (@t41)) % 0.39/0.63 (step @p50 :rule cong :premises (@p49) :args ((forall @t10 @t41))) % 0.39/0.63 (step @p51 :rule bool-impl-elim :args (@t9 @t8)) % 0.39/0.63 (step @p52 :rule cong :premises (@p51) :args (@t11)) % 0.39/0.63 (step @p53 :rule trans :premises (@p52 @p50)) % 0.39/0.63 (step @p54 :rule cong :premises (@p53) :args (@t12)) % 0.39/0.63 (step @p55 :rule trans :premises (@p3 @p54)) % 0.39/0.63 (step @p56 :rule ho_cong :premises (@p55 @p30)) % 0.39/0.63 (step @p57 :rule ho_cong :premises (@p56 @p21)) % 0.39/0.63 (step @p58 :rule ho_cong :premises (@p55 @p21)) % 0.39/0.63 (step @p59 :rule ho_cong :premises (@p58 @p30)) % 0.39/0.63 (step @p60 :rule cong :premises (@p59 @p57) :args (@t3)) % 0.39/0.63 (step @p61 :rule cong :premises (@p60) :args (@t5)) % 0.39/0.63 (step @p62 :rule cong :premises (@p61) :args (@t6)) % 0.39/0.63 (step @p63 :rule trans :premises (@p62 @p37)) % 0.39/0.63 (step @p64 :rule eq_resolve :premises (@p1 @p63)) % 0.39/0.63 (step @p65 :rule skolemize :premises (@p64)) % 0.39/0.63 (step @p66 :rule cnf_or_neg :args (@t51 2)) % 0.39/0.63 (step @p67 :rule chain_m_resolution :premises (@p66 @p65) :args ((not @t45) @t52 @t53)) % 0.39/0.63 (step @p68 :rule false_intro :premises (@p67)) % 0.39/0.63 (step @p69 :rule refl :args (@t45)) % 0.39/0.63 (step @p70 :rule symm :premises (@p69)) % 0.39/0.63 (step @p71 :rule bool-double-not-elim :args (@t49)) % 0.39/0.63 (step @p72 :rule refl :args (@t51)) % 0.39/0.63 (step @p73 :rule nary_cong :premises (@p72 @p71) :args ((or @t51 (not @t50)))) % 0.39/0.63 (step @p74 :rule cnf_or_neg :args (@t51 0)) % 0.39/0.63 (step @p75 :rule eq_resolve :premises (@p74 @p73)) % 0.39/0.63 (step @p76 :rule reordering :premises (@p75) :args ((or @t49 @t51))) % 0.39/0.63 (step @p77 :rule chain_m_resolution :premises (@p76 @p65) :args (@t49 @t52 @t53)) % 0.39/0.63 (step @p78 :rule aci_norm :args ((= (or false @t54) @t54))) % 0.39/0.63 (step @p79 :rule eq-symm :args (@t46 @t43)) % 0.39/0.63 (step @p80 :rule beta-reduce :args ((= @t57 (= @t46 @t43)))) % 0.39/0.63 (step @p81 :rule trans :premises (@p80 @p79)) % 0.39/0.63 (step @p82 :rule evaluate :args ((not true))) % 0.39/0.63 (step @p83 :rule eq-refl :args (@t43)) % 0.39/0.63 (step @p84 :rule beta-reduce :args ((= @t58 (= @t43 @t43)))) % 0.39/0.63 (step @p85 :rule trans :premises (@p84 @p83)) % 0.39/0.63 (step @p86 :rule cong :premises (@p85) :args (@t59)) % 0.39/0.63 (step @p87 :rule trans :premises (@p86 @p82)) % 0.39/0.63 (step @p88 :rule nary_cong :premises (@p87 @p81) :args (@t60)) % 0.39/0.63 (step @p89 :rule trans :premises (@p88 @p78)) % 0.39/0.63 (step @p90 :rule refl :args (@t49)) % 0.39/0.63 (step @p91 :rule cong :premises (@p90 @p89) :args ((=> @t49 @t60))) % 0.39/0.63 (assume-push @p113 @t49) % 0.39/0.63 (step @p93 :rule instantiate :premises (@p77) :args ((@list @t56))) % 0.39/0.63 (step-pop @p114 :rule scope :premises (@p93)) % 0.39/0.63 (step @p94 :rule process_scope :premises (@p114) :args (@t60)) % 0.39/0.63 (step @p96 :rule eq_resolve :premises (@p94 @p91)) % 0.39/0.63 (step @p97 :rule implies_elim :premises (@p96)) % 0.39/0.63 (step @p98 :rule chain_m_resolution :premises (@p97 @p77) :args (@t54 (@list false) (@list @t49))) % 0.39/0.63 (step @p99 :rule symm :premises (@p98)) % 0.39/0.63 (step @p100 :rule refl :args (@t44)) % 0.39/0.63 (step @p101 :rule ho_cong :premises (@p100 @p99)) % 0.39/0.63 (step @p102 :rule refl :args (@t47)) % 0.39/0.63 (step @p103 :rule bool-double-not-elim :args (@t47)) % 0.39/0.63 (step @p104 :rule nary_cong :premises (@p72 @p103) :args ((or @t51 (not @t48)))) % 0.39/0.63 (step @p105 :rule cnf_or_neg :args (@t51 1)) % 0.39/0.63 (step @p106 :rule eq_resolve :premises (@p105 @p104)) % 0.39/0.63 (step @p107 :rule reordering :premises (@p106) :args ((or @t47 @t51))) % 0.39/0.63 (step @p108 :rule chain_m_resolution :premises (@p107 @p65) :args (@t47 @t52 @t53)) % 0.39/0.63 (step @p109 :rule true_intro :premises (@p108)) % 0.39/0.63 (step @p110 :rule symm :premises (@p109)) % 0.39/0.63 (step @p111 :rule trans :premises (@p110 @p102 @p101 @p70 @p68)) % 0.39/0.63 (step @p112 false :rule eq_resolve :premises (@p111 @p4)) % 0.39/0.63 ) % 0.39/0.63 % SZS output end Proof % 0.39/0.63 % cvc5 exiting %------------------------------------------------------------------------------