%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYO238^5 : TPTP v9.2.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n027.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 09:12:17 AM UTC 2026 % Result : Theorem 0.30s 0.56s % Output : Proof 0.30s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SYO238^5 : TPTP v9.2.1. Released v4.0.0. % 0.12/0.14 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n027.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 : Wed Jun 3 00:01:36 EDT 2026 % 0.16/0.35 % CPUTime : % 0.30/0.49 %----Proving TH0 % 0.30/0.56 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.30/0.56 % SZS status Theorem % 0.30/0.56 % SZS output start Proof % 0.30/0.56 ( % 0.30/0.56 (declare-sort $$unsorted 0) % 0.30/0.56 (declare-const tptp.f (-> $$unsorted $$unsorted)) % 0.30/0.56 (declare-const tptp.cP (-> $$unsorted Bool)) % 0.30/0.56 (declare-const tptp.x $$unsorted) % 0.30/0.56 (declare-const tptp.cB Bool) % 0.30/0.56 (define @t1 () (_ tptp.cP tptp.x)) % 0.30/0.56 (define @t2 () (=> @t1 tptp.cB)) % 0.30/0.56 (define @t3 () (@var "Xx0" $$unsorted)) % 0.30/0.56 (define @t4 () (@list @t3)) % 0.30/0.56 (define @t5 () (lambda @t4 @t3)) % 0.30/0.56 (define @t6 () (_ tptp.f @t3)) % 0.30/0.56 (define @t7 () (lambda @t4 (_ tptp.f @t6))) % 0.30/0.56 (define @t8 () (= @t7 @t5)) % 0.30/0.56 (define @t9 () (=> @t8 tptp.cB)) % 0.30/0.56 (define @t10 () (=> @t9 @t2)) % 0.30/0.56 (define @t11 () (forall @t4 (= @t6 @t3))) % 0.30/0.56 (define @t12 () (=> (=> true @t11) @t10)) % 0.30/0.56 (define @t13 () (not @t12)) % 0.30/0.56 (define @t14 () (tptp.cP tptp.x)) % 0.30/0.56 (define @t15 () (not @t1)) % 0.30/0.56 (define @t16 () (@purify @t7)) % 0.30/0.56 (define @t17 () (@purify @t5)) % 0.30/0.56 (define @t18 () (not @t8)) % 0.30/0.56 (define @t19 () (=> @t18 @t15)) % 0.30/0.56 (define @t20 () (tptp.f @t3)) % 0.30/0.56 (define @t21 () (forall @t4 (= @t3 @t20))) % 0.30/0.56 (define @t22 () (=> @t21 @t19)) % 0.30/0.56 (define @t23 () (=> (=> @t8 false) (=> @t1 false))) % 0.30/0.56 (define @t24 () (=> @t21 @t23)) % 0.30/0.56 (define @t25 () (= @t3 @t6)) % 0.30/0.56 (define @t26 () (=> @t21 @t10)) % 0.30/0.56 (define @t27 () (@const 0 $$unsorted)) % 0.30/0.56 (define @t28 () (_ tptp.f @t27)) % 0.30/0.56 (define @t29 () (tptp.f @t27)) % 0.30/0.56 (define @t30 () (tptp.f @t29)) % 0.30/0.56 (define @t31 () (_ tptp.f @t28)) % 0.30/0.56 (define @t32 () (= (_ @t7 @t27) @t31)) % 0.30/0.56 (define @t33 () (_ @t16 @t27)) % 0.30/0.56 (define @t34 () (_ @t5 @t27)) % 0.30/0.56 (define @t35 () (_ @t17 @t27)) % 0.30/0.56 (define @t36 () (= @t35 @t33)) % 0.30/0.56 (define @t37 () (not @t36)) % 0.30/0.56 (define @t38 () (= @t17 @t16)) % 0.30/0.56 (define @t39 () (or @t38 @t37)) % 0.30/0.56 (define @t40 () (= @t27 @t30)) % 0.30/0.56 (define @t41 () (not @t40)) % 0.30/0.56 (define @t42 () (= @t29 @t30)) % 0.30/0.56 (define @t43 () (not @t42)) % 0.30/0.56 (define @t44 () (= @t27 @t29)) % 0.30/0.56 (define @t45 () (not @t44)) % 0.30/0.56 (define @t46 () (and @t41 @t44)) % 0.30/0.56 (assume @p1 @t13) % 0.30/0.56 (assume @p2 true) % 0.30/0.56 (step @p3 :rule refl :args (@t14)) % 0.30/0.56 (step @p4 :rule refl :args (@t1)) % 0.30/0.56 (step @p5 :rule cong :premises (@p4 @p3) :args ((= @t1 @t14))) % 0.30/0.56 (step @p6 :rule symm :premises (@p5)) % 0.30/0.56 (step @p7 :rule eq_resolve :premises (@p4 @p6)) % 0.30/0.56 (step @p8 :rule cong :premises (@p7) :args (@t15)) % 0.30/0.56 (step @p9 :rule eq-symm :args (@t16 @t17)) % 0.30/0.56 (step @p10 :rule eq-refl :args (@t5)) % 0.30/0.56 (step @p11 :rule skolem_intro :args (@t17)) % 0.30/0.56 (step @p12 :rule refl :args (@t5)) % 0.30/0.56 (step @p13 :rule cong :premises (@p12 @p11) :args ((= @t5 @t17))) % 0.30/0.56 (step @p14 :rule trans :premises (@p13 @p10)) % 0.30/0.56 (step @p15 :rule true_elim :premises (@p14)) % 0.30/0.56 (step @p16 :rule eq-refl :args (@t7)) % 0.30/0.56 (step @p17 :rule skolem_intro :args (@t16)) % 0.30/0.56 (step @p18 :rule refl :args (@t7)) % 0.30/0.56 (step @p19 :rule cong :premises (@p18 @p17) :args ((= @t7 @t16))) % 0.30/0.56 (step @p20 :rule trans :premises (@p19 @p16)) % 0.30/0.56 (step @p21 :rule true_elim :premises (@p20)) % 0.30/0.56 (step @p22 :rule cong :premises (@p21 @p15) :args (@t8)) % 0.30/0.56 (step @p23 :rule trans :premises (@p22 @p9)) % 0.30/0.56 (step @p24 :rule cong :premises (@p23) :args (@t18)) % 0.30/0.56 (step @p25 :rule cong :premises (@p24 @p8) :args (@t19)) % 0.30/0.56 (step @p26 :rule refl :args (@t21)) % 0.30/0.56 (step @p27 :rule cong :premises (@p26 @p25) :args (@t22)) % 0.30/0.56 (step @p28 :rule cong :premises (@p27) :args ((not @t22))) % 0.30/0.56 (step @p29 :rule bool-impl-false1 :args (@t1)) % 0.30/0.56 (step @p30 :rule bool-impl-false1 :args (@t8)) % 0.30/0.56 (step @p31 :rule cong :premises (@p30 @p29) :args (@t23)) % 0.30/0.56 (step @p32 :rule cong :premises (@p26 @p31) :args (@t24)) % 0.30/0.56 (step @p33 :rule cong :premises (@p32) :args ((not @t24))) % 0.30/0.56 (step @p34 :rule bool-eq-false :args (tptp.cB)) % 0.30/0.56 (step @p35 :rule symm :premises (@p34)) % 0.30/0.56 (step @p36 :rule refl :args (@t10)) % 0.30/0.56 (step @p37 :rule refl :args (@t20)) % 0.30/0.56 (step @p38 :rule refl :args (@t6)) % 0.30/0.56 (step @p39 :rule cong :premises (@p38 @p37) :args ((= @t6 @t20))) % 0.30/0.56 (step @p40 :rule symm :premises (@p39)) % 0.30/0.56 (step @p41 :rule eq_resolve :premises (@p38 @p40)) % 0.30/0.56 (step @p42 :rule refl :args (@t3)) % 0.30/0.56 (step @p43 :rule cong :premises (@p42 @p41) :args (@t25)) % 0.30/0.56 (step @p44 :rule cong :premises (@p43) :args ((forall @t4 @t25))) % 0.30/0.56 (step @p45 :rule eq-symm :args (@t6 @t3)) % 0.30/0.56 (step @p46 :rule cong :premises (@p45) :args (@t11)) % 0.30/0.56 (step @p47 :rule trans :premises (@p46 @p44)) % 0.30/0.56 (step @p48 :rule bool-impl-true2 :args (@t11)) % 0.30/0.56 (step @p49 :rule trans :premises (@p48 @p47)) % 0.30/0.56 (step @p50 :rule cong :premises (@p49 @p36) :args (@t12)) % 0.30/0.56 (step @p51 :rule cong :premises (@p50) :args (@t13)) % 0.30/0.56 (step @p52 :rule eq_resolve :premises (@p1 @p51)) % 0.30/0.56 (step @p53 :rule not_implies_elim2 :premises (@p52)) % 0.30/0.56 (step @p54 :rule not_implies_elim2 :premises (@p53)) % 0.30/0.56 (step @p55 :rule not_implies_elim2 :premises (@p54)) % 0.30/0.56 (step @p56 :rule eq_resolve :premises (@p55 @p35)) % 0.30/0.56 (step @p57 :rule refl :args (@t1)) % 0.30/0.56 (step @p58 :rule cong :premises (@p57 @p56) :args (@t2)) % 0.30/0.56 (step @p59 :rule refl :args (@t8)) % 0.30/0.56 (step @p60 :rule cong :premises (@p59 @p56) :args (@t9)) % 0.30/0.56 (step @p61 :rule cong :premises (@p60 @p58) :args (@t10)) % 0.30/0.56 (step @p62 :rule cong :premises (@p26 @p61) :args (@t26)) % 0.30/0.56 (step @p63 :rule cong :premises (@p62) :args ((not @t26))) % 0.30/0.56 (step @p64 :rule trans :premises (@p63 @p33)) % 0.30/0.56 (step @p65 :rule trans :premises (@p51 @p64 @p28)) % 0.30/0.56 (step @p66 :rule eq_resolve :premises (@p1 @p65)) % 0.30/0.56 (step @p67 :rule not_implies_elim2 :premises (@p66)) % 0.30/0.56 (step @p68 :rule not_implies_elim1 :premises (@p67)) % 0.30/0.56 (step @p69 :rule refl :args ((tptp.f @t28))) % 0.30/0.56 (step @p70 :rule refl :args (@t29)) % 0.30/0.56 (step @p71 :rule cong :premises (@p70) :args (@t30)) % 0.30/0.56 (step @p72 :rule trans :premises (@p71 @p69)) % 0.30/0.56 (step @p73 :rule refl :args (tptp.f)) % 0.30/0.56 (step @p74 :rule ho_cong :premises (@p73 @p70)) % 0.30/0.56 (step @p75 :rule cong :premises (@p74 @p72) :args ((= (_ tptp.f @t29) @t30))) % 0.30/0.56 (step @p76 :rule symm :premises (@p75)) % 0.30/0.56 (step @p77 :rule refl :args (@t31)) % 0.30/0.56 (step @p78 :rule eq_resolve :premises (@p77 @p76)) % 0.30/0.56 (step @p79 :rule refl :args (@t28)) % 0.30/0.56 (step @p80 :rule cong :premises (@p79 @p70) :args ((= @t28 @t29))) % 0.30/0.56 (step @p81 :rule symm :premises (@p80)) % 0.30/0.56 (step @p82 :rule eq_resolve :premises (@p79 @p81)) % 0.30/0.56 (step @p83 :rule refl :args (tptp.f)) % 0.30/0.56 (step @p84 :rule ho_cong :premises (@p83 @p82)) % 0.30/0.56 (step @p85 :rule trans :premises (@p84 @p78)) % 0.30/0.56 (step @p86 :rule eq-refl :args (@t31)) % 0.30/0.56 (step @p87 :rule refl :args (@t31)) % 0.30/0.56 (step @p88 :rule beta-reduce :args (@t32)) % 0.30/0.56 (step @p89 :rule cong :premises (@p88 @p87) :args (@t32)) % 0.30/0.56 (step @p90 :rule trans :premises (@p89 @p86)) % 0.30/0.56 (step @p91 :rule refl :args (@t27)) % 0.30/0.56 (step @p92 :rule ho_cong :premises (@p17 @p91)) % 0.30/0.56 (step @p93 :rule cong :premises (@p92 @p87) :args ((= @t33 @t31))) % 0.30/0.56 (step @p94 :rule trans :premises (@p93 @p90)) % 0.30/0.56 (step @p95 :rule true_elim :premises (@p94)) % 0.30/0.56 (step @p96 :rule trans :premises (@p95 @p85)) % 0.30/0.56 (step @p97 :rule eq-refl :args (@t27)) % 0.30/0.56 (step @p98 :rule beta-reduce :args ((= @t34 @t27))) % 0.30/0.56 (step @p99 :rule cong :premises (@p91 @p98) :args ((= @t27 @t34))) % 0.30/0.56 (step @p100 :rule trans :premises (@p99 @p97)) % 0.30/0.56 (step @p101 :rule ho_cong :premises (@p11 @p91)) % 0.30/0.56 (step @p102 :rule cong :premises (@p91 @p101) :args ((= @t27 @t35))) % 0.30/0.56 (step @p103 :rule eq-symm :args (@t35 @t27)) % 0.30/0.56 (step @p104 :rule trans :premises (@p103 @p102 @p100)) % 0.30/0.56 (step @p105 :rule true_elim :premises (@p104)) % 0.30/0.56 (step @p106 :rule cong :premises (@p105 @p96) :args (@t36)) % 0.30/0.56 (step @p107 :rule cong :premises (@p106) :args (@t37)) % 0.30/0.56 (step @p108 :rule refl :args (@t38)) % 0.30/0.56 (step @p109 :rule nary_cong :premises (@p108 @p107) :args (@t39)) % 0.30/0.56 ; WARNING: add trust step for TRUST % 0.30/0.56 ; trust TRUST THEORY_LEMMA % 0.30/0.56 (step @p110 :rule trust :premises () :args (@t39)) % 0.30/0.56 (step @p111 :rule eq_resolve :premises (@p110 @p109)) % 0.30/0.56 (step @p112 :rule chain_m_resolution :premises (@p111 @p68) :args (@t41 (@list true) (@list @t38))) % 0.30/0.56 (step @p113 :rule not_implies_elim1 :premises (@p66)) % 0.30/0.56 (step @p114 :rule instantiate :premises (@p113) :args ((@list @t27))) % 0.30/0.56 (step @p115 :rule instantiate :premises (@p113) :args ((@list @t29))) % 0.30/0.56 (step @p116 :rule refl :args (@t43)) % 0.30/0.56 (step @p117 :rule refl :args (@t45)) % 0.30/0.56 (step @p118 :rule bool-double-not-elim :args (@t40)) % 0.30/0.56 (step @p119 :rule nary_cong :premises (@p118 @p117 @p116) :args ((or (not @t41) @t45 @t43))) % 0.30/0.56 (assume-push @p136 @t41) % 0.30/0.56 (assume-push @p137 @t44) % 0.30/0.56 (step @p122 :rule false_intro :premises (@p112)) % 0.30/0.56 (step @p123 :rule refl :args (@t30)) % 0.30/0.56 (step @p124 :rule symm :premises (@p114)) % 0.30/0.56 (step @p125 :rule cong :premises (@p124 @p123) :args (@t42)) % 0.30/0.56 (step @p126 :rule trans :premises (@p125 @p122)) % 0.30/0.56 (step @p127 :rule false_elim :premises (@p126)) % 0.30/0.56 (step-pop @p138 :rule scope :premises (@p127)) % 0.30/0.56 (step-pop @p139 :rule scope :premises (@p138)) % 0.30/0.56 (step @p128 :rule process_scope :premises (@p139) :args (@t43)) % 0.30/0.56 (step @p131 :rule implies_elim :premises (@p128)) % 0.30/0.56 (step @p132 :rule cnf_and_neg :args (@t46)) % 0.30/0.56 (step @p133 :rule resolution :premises (@p132 @p131) :args (true @t46)) % 0.30/0.56 (step @p134 :rule eq_resolve :premises (@p133 @p119)) % 0.30/0.56 (step @p135 false :rule chain_m_resolution :premises (@p134 @p115 @p114 @p112) :args (false (@list false false true) (@list @t42 @t44 @t40))) % 0.30/0.56 ) % 0.30/0.56 % SZS output end Proof % 0.30/0.56 % cvc5 exiting %------------------------------------------------------------------------------