%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYO374^5 : 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 : n018.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 09:12:31 AM UTC 2026 % Result : Theorem 0.46s 0.63s % Output : Proof 0.46s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.13/0.13 % Problem : SYO374^5 : TPTP v9.2.1. Released v4.0.0. % 0.13/0.14 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.18/0.35 % Computer : n018.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 : Wed Jun 3 00:05:50 EDT 2026 % 0.18/0.35 % CPUTime : % 0.33/0.50 %----Proving TH0 % 0.46/0.63 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.46/0.63 % SZS status Theorem % 0.46/0.63 % SZS output start Proof % 0.46/0.63 ( % 0.46/0.63 (declare-sort $$unsorted 0) % 0.46/0.63 (declare-const tptp.cM (-> $$unsorted $$unsorted)) % 0.46/0.63 (declare-const tptp.cN (-> $$unsorted $$unsorted)) % 0.46/0.63 (define @t1 () (@var "Xq" (-> (-> $$unsorted $$unsorted) Bool))) % 0.46/0.63 (define @t2 () (_ @t1 tptp.cN)) % 0.46/0.63 (define @t3 () (_ @t1 tptp.cM)) % 0.46/0.63 (define @t4 () (= @t3 @t2)) % 0.46/0.63 (define @t5 () (@list @t1)) % 0.46/0.63 (define @t6 () (forall @t5 @t4)) % 0.46/0.63 (define @t7 () (@var "Xx" $$unsorted)) % 0.46/0.63 (define @t8 () (_ tptp.cN @t7)) % 0.46/0.63 (define @t9 () (@var "Xp" (-> $$unsorted Bool))) % 0.46/0.63 (define @t10 () (_ @t9 @t8)) % 0.46/0.63 (define @t11 () (_ tptp.cM @t7)) % 0.46/0.63 (define @t12 () (_ @t9 @t11)) % 0.46/0.63 (define @t13 () (= @t12 @t10)) % 0.46/0.63 (define @t14 () (@list @t7 @t9)) % 0.46/0.63 (define @t15 () (forall @t14 @t13)) % 0.46/0.63 (define @t16 () (=> @t15 @t6)) % 0.46/0.63 (define @t17 () (not @t16)) % 0.46/0.63 (define @t18 () (_ @t1 tptp.cN)) % 0.46/0.63 (define @t19 () (_ @t1 tptp.cM)) % 0.46/0.63 (define @t20 () (tptp.cN @t7)) % 0.46/0.63 (define @t21 () (_ @t9 @t20)) % 0.46/0.63 (define @t22 () (tptp.cM @t7)) % 0.46/0.63 (define @t23 () (_ @t9 @t22)) % 0.46/0.63 (define @t24 () (@const 0 $$unsorted)) % 0.46/0.63 (define @t25 () (tptp.cM @t24)) % 0.46/0.63 (define @t26 () (tptp.cN @t24)) % 0.46/0.63 (define @t27 () (= @t26 @t25)) % 0.46/0.63 (define @t28 () (_ tptp.cN @t24)) % 0.46/0.63 (define @t29 () (= @t28 @t26)) % 0.46/0.63 (define @t30 () (= @t25 @t28)) % 0.46/0.63 (define @t31 () (= @t26 @t28)) % 0.46/0.63 (define @t32 () (= @t31 @t30)) % 0.46/0.63 (define @t33 () (forall @t14 (= @t23 @t21))) % 0.46/0.63 (define @t34 () (@var "BOUND_VARIABLE_14740" $$unsorted)) % 0.46/0.63 (define @t35 () (lambda (@list @t34) (= @t28 @t34))) % 0.46/0.63 (define @t36 () (_ @t35 @t26)) % 0.46/0.63 (define @t37 () (_ @t35 @t25)) % 0.46/0.63 (define @t38 () (= @t37 @t36)) % 0.46/0.63 (define @t39 () (@list false)) % 0.46/0.63 (define @t40 () (= tptp.cN tptp.cM)) % 0.46/0.63 (define @t41 () (@quantifiers_skolemize (forall @t5 (= @t19 @t18)) 0)) % 0.46/0.63 (define @t42 () (_ @t41 tptp.cN)) % 0.46/0.63 (define @t43 () (_ @t41 tptp.cM)) % 0.46/0.63 (define @t44 () (= @t43 @t42)) % 0.46/0.63 (define @t45 () (not @t40)) % 0.46/0.63 (define @t46 () (not @t43)) % 0.46/0.63 (define @t47 () (not @t42)) % 0.46/0.63 (define @t48 () (and @t47 @t40 @t43)) % 0.46/0.63 (define @t49 () (and @t46 @t40)) % 0.46/0.63 (assume @p1 @t17) % 0.46/0.63 (assume @p2 true) % 0.46/0.63 (step @p3 :rule refl :args (@t18)) % 0.46/0.63 (step @p4 :rule refl :args (@t2)) % 0.46/0.63 (step @p5 :rule cong :premises (@p4 @p3) :args ((= @t2 @t18))) % 0.46/0.63 (step @p6 :rule symm :premises (@p5)) % 0.46/0.63 (step @p7 :rule eq_resolve :premises (@p4 @p6)) % 0.46/0.63 (step @p8 :rule refl :args (@t19)) % 0.46/0.63 (step @p9 :rule refl :args (@t3)) % 0.46/0.63 (step @p10 :rule cong :premises (@p9 @p8) :args ((= @t3 @t19))) % 0.46/0.63 (step @p11 :rule symm :premises (@p10)) % 0.46/0.63 (step @p12 :rule eq_resolve :premises (@p9 @p11)) % 0.46/0.63 (step @p13 :rule cong :premises (@p12 @p7) :args (@t4)) % 0.46/0.63 (step @p14 :rule cong :premises (@p13) :args (@t6)) % 0.46/0.63 (step @p15 :rule refl :args ((_ @t9 @t8))) % 0.46/0.63 (step @p16 :rule refl :args (@t20)) % 0.46/0.63 (step @p17 :rule cong :premises (@p16) :args (@t21)) % 0.46/0.63 (step @p18 :rule trans :premises (@p17 @p15)) % 0.46/0.63 (step @p19 :rule refl :args (@t9)) % 0.46/0.63 (step @p20 :rule ho_cong :premises (@p19 @p16)) % 0.46/0.63 (step @p21 :rule cong :premises (@p20 @p18) :args ((= (_ @t9 @t20) @t21))) % 0.46/0.63 (step @p22 :rule symm :premises (@p21)) % 0.46/0.63 (step @p23 :rule refl :args (@t10)) % 0.46/0.63 (step @p24 :rule eq_resolve :premises (@p23 @p22)) % 0.46/0.63 (step @p25 :rule refl :args (@t8)) % 0.46/0.63 (step @p26 :rule cong :premises (@p25 @p16) :args ((= @t8 @t20))) % 0.46/0.63 (step @p27 :rule symm :premises (@p26)) % 0.46/0.63 (step @p28 :rule eq_resolve :premises (@p25 @p27)) % 0.46/0.63 (step @p29 :rule ho_cong :premises (@p19 @p28)) % 0.46/0.63 (step @p30 :rule trans :premises (@p29 @p24)) % 0.46/0.63 (step @p31 :rule refl :args ((_ @t9 @t11))) % 0.46/0.63 (step @p32 :rule refl :args (@t22)) % 0.46/0.63 (step @p33 :rule cong :premises (@p32) :args (@t23)) % 0.46/0.63 (step @p34 :rule trans :premises (@p33 @p31)) % 0.46/0.63 (step @p35 :rule ho_cong :premises (@p19 @p32)) % 0.46/0.63 (step @p36 :rule cong :premises (@p35 @p34) :args ((= (_ @t9 @t22) @t23))) % 0.46/0.63 (step @p37 :rule symm :premises (@p36)) % 0.46/0.63 (step @p38 :rule refl :args (@t12)) % 0.46/0.63 (step @p39 :rule eq_resolve :premises (@p38 @p37)) % 0.46/0.63 (step @p40 :rule refl :args (@t11)) % 0.46/0.63 (step @p41 :rule cong :premises (@p40 @p32) :args ((= @t11 @t22))) % 0.46/0.63 (step @p42 :rule symm :premises (@p41)) % 0.46/0.63 (step @p43 :rule eq_resolve :premises (@p40 @p42)) % 0.46/0.63 (step @p44 :rule ho_cong :premises (@p19 @p43)) % 0.46/0.63 (step @p45 :rule trans :premises (@p44 @p39)) % 0.46/0.63 (step @p46 :rule cong :premises (@p45 @p30) :args (@t13)) % 0.46/0.63 (step @p47 :rule cong :premises (@p46) :args (@t15)) % 0.46/0.63 (step @p48 :rule cong :premises (@p47 @p14) :args (@t16)) % 0.46/0.63 (step @p49 :rule cong :premises (@p48) :args (@t17)) % 0.46/0.63 (step @p50 :rule eq_resolve :premises (@p1 @p49)) % 0.46/0.63 (step @p51 :rule not_implies_elim1 :premises (@p50)) % 0.46/0.63 (step @p52 :rule bool-eq-true :args (@t27)) % 0.46/0.63 (step @p53 :rule eq-symm :args (true @t27)) % 0.46/0.63 (step @p54 :rule trans :premises (@p53 @p52)) % 0.46/0.63 (step @p55 :rule eq-symm :args (@t25 @t26)) % 0.46/0.63 (step @p56 :rule refl :args (@t26)) % 0.46/0.63 (step @p57 :rule refl :args (@t28)) % 0.46/0.63 (step @p58 :rule cong :premises (@p57 @p56) :args (@t29)) % 0.46/0.63 (step @p59 :rule symm :premises (@p58)) % 0.46/0.63 (step @p60 :rule eq_resolve :premises (@p57 @p59)) % 0.46/0.63 (step @p61 :rule refl :args (@t25)) % 0.46/0.63 (step @p62 :rule cong :premises (@p61 @p60) :args (@t30)) % 0.46/0.63 (step @p63 :rule trans :premises (@p62 @p55)) % 0.46/0.63 (step @p64 :rule eq-refl :args (@t26)) % 0.46/0.63 (step @p65 :rule refl :args (@t26)) % 0.46/0.63 (step @p66 :rule cong :premises (@p65 @p60) :args (@t31)) % 0.46/0.63 (step @p67 :rule trans :premises (@p66 @p64)) % 0.46/0.63 (step @p68 :rule cong :premises (@p67 @p63) :args (@t32)) % 0.46/0.63 (step @p69 :rule trans :premises (@p68 @p54)) % 0.46/0.63 (step @p70 :rule refl :args (@t33)) % 0.46/0.63 (step @p71 :rule cong :premises (@p70 @p69) :args ((=> @t33 @t32))) % 0.46/0.63 (step @p72 :rule eq-symm :args (@t30 @t31)) % 0.46/0.63 (step @p73 :rule eq-symm :args (@t28 @t26)) % 0.46/0.63 (step @p74 :rule beta-reduce :args ((= @t36 @t29))) % 0.46/0.63 (step @p75 :rule trans :premises (@p74 @p73)) % 0.46/0.63 (step @p76 :rule eq-symm :args (@t28 @t25)) % 0.46/0.63 (step @p77 :rule beta-reduce :args ((= @t37 (= @t28 @t25)))) % 0.46/0.63 (step @p78 :rule trans :premises (@p77 @p76)) % 0.46/0.63 (step @p79 :rule cong :premises (@p78 @p75) :args (@t38)) % 0.46/0.63 (step @p80 :rule trans :premises (@p79 @p72)) % 0.46/0.63 (step @p81 :rule cong :premises (@p70 @p80) :args ((=> @t33 @t38))) % 0.46/0.63 (assume-push @p156 @t33) % 0.46/0.63 (step @p83 :rule instantiate :premises (@p51) :args ((@list @t24 @t35))) % 0.46/0.63 (step-pop @p157 :rule scope :premises (@p83)) % 0.46/0.63 (step @p84 :rule process_scope :premises (@p157) :args (@t38)) % 0.46/0.63 (step @p86 :rule eq_resolve :premises (@p84 @p81)) % 0.46/0.63 (step @p87 :rule eq_resolve :premises (@p86 @p71)) % 0.46/0.63 (step @p88 :rule implies_elim :premises (@p87)) % 0.46/0.63 (step @p89 :rule chain_m_resolution :premises (@p88 @p51) :args (@t27 @t39 (@list @t33))) % 0.46/0.63 ; WARNING: add trust step for TRUST % 0.46/0.63 ; trust TRUST THEORY_LEMMA % 0.46/0.63 (step @p90 :rule trust :premises () :args ((or @t40 (not @t27)))) % 0.46/0.63 (step @p91 :rule chain_m_resolution :premises (@p90 @p89) :args (@t40 @t39 (@list @t27))) % 0.46/0.63 (step @p92 :rule not_implies_elim2 :premises (@p50)) % 0.46/0.63 (step @p93 :rule skolemize :premises (@p92)) % 0.46/0.63 (step @p94 :rule cnf_equiv_neg2 :args (@t44)) % 0.46/0.63 (step @p95 :rule refl :args (@t45)) % 0.46/0.63 (step @p96 :rule bool-double-not-elim :args (@t42)) % 0.46/0.63 (step @p97 :rule refl :args (@t46)) % 0.46/0.63 (step @p98 :rule nary_cong :premises (@p97 @p96 @p95) :args ((or @t46 (not @t47) @t45))) % 0.46/0.63 (assume-push @p158 @t47) % 0.46/0.63 (assume-push @p159 @t40) % 0.46/0.63 (assume-push @p160 @t43) % 0.46/0.63 (step @p102 :rule evaluate :args ((= true false))) % 0.46/0.63 (step @p103 :rule false_intro :premises (@p158)) % 0.46/0.63 (step @p104 :rule symm :premises (@p91)) % 0.46/0.63 (step @p105 :rule cong :premises (@p104) :args (@t43)) % 0.46/0.63 (step @p106 :rule true_intro :premises (@p160)) % 0.46/0.63 (step @p107 :rule symm :premises (@p106)) % 0.46/0.63 (step @p108 :rule trans :premises (@p107 @p105 @p103)) % 0.46/0.63 (step @p109 false :rule eq_resolve :premises (@p108 @p102)) % 0.46/0.63 (step-pop @p161 :rule scope :premises (@p109)) % 0.46/0.63 (step-pop @p162 :rule scope :premises (@p161)) % 0.46/0.63 (step-pop @p163 :rule scope :premises (@p162)) % 0.46/0.63 (step @p110 :rule process_scope :premises (@p163) :args (false)) % 0.46/0.63 (assume-push @p164 @t43) % 0.46/0.63 (assume-push @p165 @t47) % 0.46/0.63 (assume-push @p166 @t40) % 0.46/0.63 (step @p117 :rule and_intro :premises (@p165 @p91 @p164)) % 0.46/0.63 (step-pop @p167 :rule scope :premises (@p117)) % 0.46/0.63 (step-pop @p168 :rule scope :premises (@p167)) % 0.46/0.63 (step-pop @p169 :rule scope :premises (@p168)) % 0.46/0.63 (step @p118 :rule process_scope :premises (@p169) :args (@t48)) % 0.46/0.63 (step @p122 :rule implies_elim :premises (@p118)) % 0.46/0.63 (step @p123 :rule resolution :premises (@p122 @p110) :args (true @t48)) % 0.46/0.63 (step @p124 :rule not_and :premises (@p123)) % 0.46/0.63 (step @p125 :rule eq_resolve :premises (@p124 @p98)) % 0.46/0.63 (step @p126 :rule reordering :premises (@p125) :args ((or @t42 @t46 @t45))) % 0.46/0.63 (step @p127 :rule chain_m_resolution :premises (@p126 @p91 @p94 @p93) :args (@t46 (@list false true true) (@list @t40 @t42 @t44))) % 0.46/0.64 (step @p128 :rule cnf_equiv_neg1 :args (@t44)) % 0.46/0.64 (step @p129 :rule reordering :premises (@p128) :args ((or @t43 @t42 @t44))) % 0.46/0.64 (step @p130 :rule chain_m_resolution :premises (@p129 @p127 @p93) :args (@t42 (@list true true) (@list @t43 @t44))) % 0.46/0.64 (step @p131 :rule refl :args (@t47)) % 0.46/0.64 (step @p132 :rule bool-double-not-elim :args (@t43)) % 0.46/0.64 (step @p133 :rule nary_cong :premises (@p132 @p95 @p131) :args ((or (not @t46) @t45 @t47))) % 0.46/0.64 (assume-push @p170 @t46) % 0.46/0.64 (assume-push @p171 @t40) % 0.46/0.64 (assume-push @p172 @t46) % 0.46/0.64 (assume-push @p173 @t40) % 0.46/0.64 (step @p138 :rule false_intro :premises (@p170)) % 0.46/0.64 (step @p139 :rule cong :premises (@p91) :args (@t42)) % 0.46/0.64 (step @p140 :rule trans :premises (@p139 @p138)) % 0.46/0.64 (step @p141 :rule false_elim :premises (@p140)) % 0.46/0.64 (step-pop @p174 :rule scope :premises (@p141)) % 0.46/0.64 (step-pop @p175 :rule scope :premises (@p174)) % 0.46/0.64 (step @p142 :rule process_scope :premises (@p175) :args (@t47)) % 0.46/0.64 (step @p145 :rule and_intro :premises (@p170 @p91)) % 0.46/0.64 (step @p146 :rule modus_ponens :premises (@p145 @p142)) % 0.46/0.64 (step-pop @p176 :rule scope :premises (@p146)) % 0.46/0.64 (step-pop @p177 :rule scope :premises (@p176)) % 0.46/0.64 (step @p147 :rule process_scope :premises (@p177) :args (@t47)) % 0.46/0.64 (step @p150 :rule implies_elim :premises (@p147)) % 0.46/0.64 (step @p151 :rule cnf_and_neg :args (@t49)) % 0.46/0.64 (step @p152 :rule resolution :premises (@p151 @p150) :args (true @t49)) % 0.46/0.64 (step @p153 :rule eq_resolve :premises (@p152 @p133)) % 0.46/0.64 (step @p154 :rule reordering :premises (@p153) :args ((or @t43 @t47 @t45))) % 0.46/0.64 (step @p155 false :rule chain_m_resolution :premises (@p154 @p130 @p127 @p91) :args (false (@list false true false) (@list @t42 @t43 @t40))) % 0.46/0.64 ) % 0.46/0.64 % SZS output end Proof % 0.46/0.64 % cvc5 exiting %------------------------------------------------------------------------------