%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYO354^5 : 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 : n005.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 09:12:29 AM UTC 2026 % Result : Theorem 0.39s 0.62s % Output : Proof 0.39s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SYO354^5 : TPTP v9.2.1. Released v4.0.0. % 0.13/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n005.cluster.edu % 0.17/0.34 % Model : x86_64 x86_64 % 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.34 % Memory : 8042.1875MB % 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.34 % CPULimit : 300 % 0.17/0.34 % WCLimit : 300 % 0.17/0.34 % DateTime : Wed Jun 3 00:05:33 EDT 2026 % 0.17/0.35 % CPUTime : % 0.30/0.49 %----Proving TH0 % 0.39/0.62 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.39/0.62 % SZS status Theorem % 0.39/0.62 % SZS output start Proof % 0.39/0.62 ( % 0.39/0.62 (declare-sort $$unsorted 0) % 0.39/0.62 (declare-const tptp.m (-> $$unsorted $$unsorted)) % 0.39/0.62 (declare-const tptp.n (-> $$unsorted $$unsorted)) % 0.39/0.62 (define @t1 () (@var "X" $$unsorted)) % 0.39/0.62 (define @t2 () (_ tptp.n @t1)) % 0.39/0.62 (define @t3 () (@list @t1)) % 0.39/0.62 (define @t4 () (lambda @t3 @t2)) % 0.39/0.62 (define @t5 () (@var "Q" (-> (-> $$unsorted $$unsorted) Bool))) % 0.39/0.62 (define @t6 () (_ @t5 @t4)) % 0.39/0.62 (define @t7 () (_ tptp.m @t1)) % 0.39/0.62 (define @t8 () (lambda @t3 @t7)) % 0.39/0.62 (define @t9 () (_ @t5 @t8)) % 0.39/0.62 (define @t10 () (@list @t5)) % 0.39/0.62 (define @t11 () (forall @t10 (=> @t9 @t6))) % 0.39/0.62 (define @t12 () (@var "P" (-> $$unsorted Bool))) % 0.39/0.62 (define @t13 () (_ @t12 @t2)) % 0.39/0.62 (define @t14 () (_ @t12 @t7)) % 0.39/0.62 (define @t15 () (@list @t1 @t12)) % 0.39/0.62 (define @t16 () (forall @t15 (=> @t14 @t13))) % 0.39/0.62 (define @t17 () (=> @t16 @t11)) % 0.39/0.62 (define @t18 () (not @t17)) % 0.39/0.62 (define @t19 () (tptp.n @t1)) % 0.39/0.62 (define @t20 () (lambda @t3 @t19)) % 0.39/0.62 (define @t21 () (_ @t5 @t20)) % 0.39/0.62 (define @t22 () (tptp.m @t1)) % 0.39/0.62 (define @t23 () (lambda @t3 @t22)) % 0.39/0.62 (define @t24 () (_ @t5 @t23)) % 0.39/0.62 (define @t25 () (not @t24)) % 0.39/0.62 (define @t26 () (or @t25 @t21)) % 0.39/0.62 (define @t27 () (not @t9)) % 0.39/0.62 (define @t28 () (or @t27 @t6)) % 0.39/0.62 (define @t29 () (_ @t12 @t19)) % 0.39/0.62 (define @t30 () (_ @t12 @t22)) % 0.39/0.62 (define @t31 () (not @t14)) % 0.39/0.62 (define @t32 () (or @t31 @t13)) % 0.39/0.62 (define @t33 () (@quantifiers_skolemize (forall @t10 (or (not (_ @t5 tptp.m)) (_ @t5 tptp.n))) 0)) % 0.39/0.62 (define @t34 () (_ @t33 tptp.n)) % 0.39/0.62 (define @t35 () (_ @t33 tptp.m)) % 0.39/0.62 (define @t36 () (not @t35)) % 0.39/0.62 (define @t37 () (or @t36 @t34)) % 0.39/0.62 (define @t38 () (not @t34)) % 0.39/0.62 (define @t39 () (@list true)) % 0.39/0.62 (define @t40 () (@list @t37)) % 0.39/0.62 (define @t41 () (= tptp.n tptp.m)) % 0.39/0.62 (define @t42 () (not @t41)) % 0.39/0.62 (define @t43 () (and @t38 @t41 @t35)) % 0.39/0.62 (define @t44 () (@const 0 $$unsorted)) % 0.39/0.62 (define @t45 () (tptp.m @t44)) % 0.39/0.62 (define @t46 () (tptp.n @t44)) % 0.39/0.62 (define @t47 () (= @t46 @t45)) % 0.39/0.62 (define @t48 () (not @t47)) % 0.39/0.62 (define @t49 () (_ tptp.m @t44)) % 0.39/0.62 (define @t50 () (= @t49 @t45)) % 0.39/0.62 (define @t51 () (= @t46 @t49)) % 0.39/0.62 (define @t52 () (= @t45 @t49)) % 0.39/0.62 (define @t53 () (not @t52)) % 0.39/0.62 (define @t54 () (or @t53 @t51)) % 0.39/0.62 (define @t55 () (forall @t15 (or (not @t30) @t29))) % 0.39/0.62 (define @t56 () (@var "BOUND_VARIABLE_14760" $$unsorted)) % 0.39/0.62 (define @t57 () (lambda (@list @t56) (= @t49 @t56))) % 0.39/0.62 (define @t58 () (_ @t57 @t46)) % 0.39/0.62 (define @t59 () (_ @t57 @t45)) % 0.39/0.62 (define @t60 () (not @t59)) % 0.39/0.62 (define @t61 () (or @t60 @t58)) % 0.39/0.62 (assume @p1 @t18) % 0.39/0.62 (assume @p2 true) % 0.39/0.62 (step @p3 :rule lambda-elim :args ((= @t20 tptp.n))) % 0.39/0.62 (step @p4 :rule cong :premises (@p3) :args (@t21)) % 0.39/0.62 (step @p5 :rule lambda-elim :args ((= @t23 tptp.m))) % 0.39/0.62 (step @p6 :rule cong :premises (@p5) :args (@t24)) % 0.39/0.62 (step @p7 :rule cong :premises (@p6) :args (@t25)) % 0.39/0.62 (step @p8 :rule nary_cong :premises (@p7 @p4) :args (@t26)) % 0.39/0.62 (step @p9 :rule cong :premises (@p8) :args ((forall @t10 @t26))) % 0.39/0.62 (step @p10 :rule refl :args ((_ @t5 @t4))) % 0.39/0.62 (step @p11 :rule refl :args (@t19)) % 0.39/0.62 (step @p12 :rule cong :premises (@p11) :args (@t20)) % 0.39/0.62 (step @p13 :rule cong :premises (@p12) :args (@t21)) % 0.39/0.62 (step @p14 :rule trans :premises (@p13 @p10)) % 0.39/0.62 (step @p15 :rule refl :args (@t5)) % 0.39/0.62 (step @p16 :rule ho_cong :premises (@p15 @p12)) % 0.39/0.62 (step @p17 :rule cong :premises (@p16 @p14) :args ((= (_ @t5 @t20) @t21))) % 0.39/0.62 (step @p18 :rule symm :premises (@p17)) % 0.39/0.62 (step @p19 :rule refl :args (@t6)) % 0.39/0.62 (step @p20 :rule eq_resolve :premises (@p19 @p18)) % 0.39/0.62 (step @p21 :rule refl :args (@t2)) % 0.39/0.62 (step @p22 :rule cong :premises (@p21 @p11) :args ((= @t2 @t19))) % 0.39/0.62 (step @p23 :rule symm :premises (@p22)) % 0.39/0.62 (step @p24 :rule eq_resolve :premises (@p21 @p23)) % 0.39/0.62 (step @p25 :rule cong :premises (@p24) :args (@t4)) % 0.39/0.62 (step @p26 :rule ho_cong :premises (@p15 @p25)) % 0.39/0.62 (step @p27 :rule trans :premises (@p26 @p20)) % 0.39/0.62 (step @p28 :rule refl :args ((_ @t5 @t8))) % 0.39/0.62 (step @p29 :rule refl :args (@t22)) % 0.39/0.62 (step @p30 :rule cong :premises (@p29) :args (@t23)) % 0.39/0.62 (step @p31 :rule cong :premises (@p30) :args (@t24)) % 0.39/0.62 (step @p32 :rule trans :premises (@p31 @p28)) % 0.39/0.62 (step @p33 :rule ho_cong :premises (@p15 @p30)) % 0.39/0.62 (step @p34 :rule cong :premises (@p33 @p32) :args ((= (_ @t5 @t23) @t24))) % 0.39/0.62 (step @p35 :rule symm :premises (@p34)) % 0.39/0.62 (step @p36 :rule refl :args (@t9)) % 0.39/0.62 (step @p37 :rule eq_resolve :premises (@p36 @p35)) % 0.39/0.62 (step @p38 :rule refl :args (@t7)) % 0.39/0.62 (step @p39 :rule cong :premises (@p38 @p29) :args ((= @t7 @t22))) % 0.39/0.62 (step @p40 :rule symm :premises (@p39)) % 0.39/0.62 (step @p41 :rule eq_resolve :premises (@p38 @p40)) % 0.39/0.62 (step @p42 :rule cong :premises (@p41) :args (@t8)) % 0.39/0.62 (step @p43 :rule ho_cong :premises (@p15 @p42)) % 0.39/0.62 (step @p44 :rule trans :premises (@p43 @p37)) % 0.39/0.62 (step @p45 :rule cong :premises (@p44) :args (@t27)) % 0.39/0.62 (step @p46 :rule nary_cong :premises (@p45 @p27) :args (@t28)) % 0.39/0.62 (step @p47 :rule cong :premises (@p46) :args ((forall @t10 @t28))) % 0.39/0.62 (step @p48 :rule trans :premises (@p47 @p9)) % 0.39/0.62 (step @p49 :rule bool-impl-elim :args (@t9 @t6)) % 0.39/0.62 (step @p50 :rule cong :premises (@p49) :args (@t11)) % 0.39/0.62 (step @p51 :rule trans :premises (@p50 @p48)) % 0.39/0.62 (step @p52 :rule refl :args ((_ @t12 @t2))) % 0.39/0.62 (step @p53 :rule cong :premises (@p11) :args (@t29)) % 0.39/0.62 (step @p54 :rule trans :premises (@p53 @p52)) % 0.39/0.62 (step @p55 :rule refl :args (@t12)) % 0.39/0.62 (step @p56 :rule ho_cong :premises (@p55 @p11)) % 0.39/0.62 (step @p57 :rule cong :premises (@p56 @p54) :args ((= (_ @t12 @t19) @t29))) % 0.39/0.62 (step @p58 :rule symm :premises (@p57)) % 0.39/0.62 (step @p59 :rule refl :args (@t13)) % 0.39/0.62 (step @p60 :rule eq_resolve :premises (@p59 @p58)) % 0.39/0.62 (step @p61 :rule ho_cong :premises (@p55 @p24)) % 0.39/0.62 (step @p62 :rule trans :premises (@p61 @p60)) % 0.39/0.62 (step @p63 :rule refl :args ((_ @t12 @t7))) % 0.39/0.62 (step @p64 :rule cong :premises (@p29) :args (@t30)) % 0.39/0.62 (step @p65 :rule trans :premises (@p64 @p63)) % 0.39/0.62 (step @p66 :rule ho_cong :premises (@p55 @p29)) % 0.39/0.62 (step @p67 :rule cong :premises (@p66 @p65) :args ((= (_ @t12 @t22) @t30))) % 0.39/0.62 (step @p68 :rule symm :premises (@p67)) % 0.39/0.62 (step @p69 :rule refl :args (@t14)) % 0.39/0.62 (step @p70 :rule eq_resolve :premises (@p69 @p68)) % 0.39/0.62 (step @p71 :rule ho_cong :premises (@p55 @p41)) % 0.39/0.62 (step @p72 :rule trans :premises (@p71 @p70)) % 0.39/0.62 (step @p73 :rule cong :premises (@p72) :args (@t31)) % 0.39/0.62 (step @p74 :rule nary_cong :premises (@p73 @p62) :args (@t32)) % 0.39/0.62 (step @p75 :rule cong :premises (@p74) :args ((forall @t15 @t32))) % 0.39/0.62 (step @p76 :rule bool-impl-elim :args (@t14 @t13)) % 0.39/0.62 (step @p77 :rule cong :premises (@p76) :args (@t16)) % 0.39/0.62 (step @p78 :rule trans :premises (@p77 @p75)) % 0.39/0.62 (step @p79 :rule cong :premises (@p78 @p51) :args (@t17)) % 0.39/0.62 (step @p80 :rule cong :premises (@p79) :args (@t18)) % 0.39/0.62 (step @p81 :rule eq_resolve :premises (@p1 @p80)) % 0.39/0.62 (step @p82 :rule not_implies_elim1 :premises (@p81)) % 0.39/0.62 (step @p83 :rule not_implies_elim2 :premises (@p81)) % 0.39/0.62 (step @p84 :rule skolemize :premises (@p83)) % 0.39/0.62 (step @p85 :rule cnf_or_neg :args (@t37 1)) % 0.39/0.62 (step @p86 :rule chain_m_resolution :premises (@p85 @p84) :args (@t38 @t39 @t40)) % 0.39/0.62 (step @p87 :rule bool-double-not-elim :args (@t35)) % 0.39/0.62 (step @p88 :rule refl :args (@t37)) % 0.39/0.62 (step @p89 :rule nary_cong :premises (@p88 @p87) :args ((or @t37 (not @t36)))) % 0.39/0.62 (step @p90 :rule cnf_or_neg :args (@t37 0)) % 0.39/0.62 (step @p91 :rule eq_resolve :premises (@p90 @p89)) % 0.39/0.62 (step @p92 :rule reordering :premises (@p91) :args ((or @t35 @t37))) % 0.39/0.62 (step @p93 :rule chain_m_resolution :premises (@p92 @p84) :args (@t35 @t39 @t40)) % 0.39/0.62 (step @p94 :rule refl :args (@t42)) % 0.39/0.62 (step @p95 :rule bool-double-not-elim :args (@t34)) % 0.39/0.62 (step @p96 :rule refl :args (@t36)) % 0.39/0.62 (step @p97 :rule nary_cong :premises (@p96 @p95 @p94) :args ((or @t36 (not @t38) @t42))) % 0.39/0.62 (assume-push @p164 @t38) % 0.39/0.62 (assume-push @p165 @t41) % 0.39/0.62 (assume-push @p166 @t35) % 0.39/0.62 (step @p101 :rule evaluate :args ((= true false))) % 0.39/0.62 (step @p102 :rule false_intro :premises (@p86)) % 0.39/0.62 (step @p103 :rule symm :premises (@p165)) % 0.39/0.62 (step @p104 :rule cong :premises (@p103) :args (@t35)) % 0.39/0.62 (step @p105 :rule true_intro :premises (@p93)) % 0.39/0.62 (step @p106 :rule symm :premises (@p105)) % 0.39/0.62 (step @p107 :rule trans :premises (@p106 @p104 @p102)) % 0.39/0.62 (step @p108 false :rule eq_resolve :premises (@p107 @p101)) % 0.39/0.62 (step-pop @p167 :rule scope :premises (@p108)) % 0.39/0.62 (step-pop @p168 :rule scope :premises (@p167)) % 0.39/0.62 (step-pop @p169 :rule scope :premises (@p168)) % 0.39/0.62 (step @p109 :rule process_scope :premises (@p169) :args (false)) % 0.39/0.62 (assume-push @p170 @t35) % 0.39/0.62 (assume-push @p171 @t38) % 0.39/0.62 (assume-push @p172 @t41) % 0.39/0.62 (step @p116 :rule and_intro :premises (@p86 @p172 @p93)) % 0.39/0.62 (step-pop @p173 :rule scope :premises (@p116)) % 0.39/0.62 (step-pop @p174 :rule scope :premises (@p173)) % 0.39/0.62 (step-pop @p175 :rule scope :premises (@p174)) % 0.39/0.62 (step @p117 :rule process_scope :premises (@p175) :args (@t43)) % 0.39/0.62 (step @p121 :rule implies_elim :premises (@p117)) % 0.39/0.62 (step @p122 :rule resolution :premises (@p121 @p109) :args (true @t43)) % 0.39/0.62 (step @p123 :rule not_and :premises (@p122)) % 0.39/0.62 (step @p124 :rule eq_resolve :premises (@p123 @p97)) % 0.39/0.62 (step @p125 :rule chain_m_resolution :premises (@p124 @p93 @p86) :args (@t42 (@list false true) (@list @t35 @t34))) % 0.39/0.62 ; WARNING: add trust step for TRUST % 0.39/0.62 ; trust TRUST THEORY_LEMMA % 0.39/0.62 (step @p126 :rule trust :premises () :args ((or @t41 @t48))) % 0.39/0.62 (step @p127 :rule chain_m_resolution :premises (@p126 @p125) :args (@t48 @t39 (@list @t41))) % 0.39/0.62 (step @p128 :rule aci_norm :args ((= (or false @t47) @t47))) % 0.39/0.62 (step @p129 :rule refl :args (@t45)) % 0.39/0.62 (step @p130 :rule refl :args (@t49)) % 0.39/0.62 (step @p131 :rule cong :premises (@p130 @p129) :args (@t50)) % 0.39/0.62 (step @p132 :rule symm :premises (@p131)) % 0.39/0.62 (step @p133 :rule eq_resolve :premises (@p130 @p132)) % 0.39/0.62 (step @p134 :rule refl :args (@t46)) % 0.39/0.62 (step @p135 :rule cong :premises (@p134 @p133) :args (@t51)) % 0.39/0.62 (step @p136 :rule evaluate :args ((not true))) % 0.39/0.62 (step @p137 :rule eq-refl :args (@t45)) % 0.39/0.62 (step @p138 :rule refl :args (@t45)) % 0.39/0.62 (step @p139 :rule cong :premises (@p138 @p133) :args (@t52)) % 0.39/0.62 (step @p140 :rule trans :premises (@p139 @p137)) % 0.39/0.62 (step @p141 :rule cong :premises (@p140) :args (@t53)) % 0.39/0.62 (step @p142 :rule trans :premises (@p141 @p136)) % 0.39/0.62 (step @p143 :rule nary_cong :premises (@p142 @p135) :args (@t54)) % 0.39/0.62 (step @p144 :rule trans :premises (@p143 @p128)) % 0.39/0.62 (step @p145 :rule refl :args (@t55)) % 0.39/0.62 (step @p146 :rule cong :premises (@p145 @p144) :args ((=> @t55 @t54))) % 0.39/0.62 (step @p147 :rule eq-symm :args (@t49 @t46)) % 0.39/0.62 (step @p148 :rule beta-reduce :args ((= @t58 (= @t49 @t46)))) % 0.39/0.62 (step @p149 :rule trans :premises (@p148 @p147)) % 0.39/0.62 (step @p150 :rule eq-symm :args (@t49 @t45)) % 0.39/0.62 (step @p151 :rule beta-reduce :args ((= @t59 @t50))) % 0.39/0.62 (step @p152 :rule trans :premises (@p151 @p150)) % 0.39/0.62 (step @p153 :rule cong :premises (@p152) :args (@t60)) % 0.39/0.62 (step @p154 :rule nary_cong :premises (@p153 @p149) :args (@t61)) % 0.39/0.62 (step @p155 :rule cong :premises (@p145 @p154) :args ((=> @t55 @t61))) % 0.39/0.62 (assume-push @p176 @t55) % 0.39/0.62 (step @p157 :rule instantiate :premises (@p82) :args ((@list @t44 @t57))) % 0.39/0.62 (step-pop @p177 :rule scope :premises (@p157)) % 0.39/0.62 (step @p158 :rule process_scope :premises (@p177) :args (@t61)) % 0.39/0.62 (step @p160 :rule eq_resolve :premises (@p158 @p155)) % 0.39/0.62 (step @p161 :rule eq_resolve :premises (@p160 @p146)) % 0.39/0.62 (step @p162 :rule implies_elim :premises (@p161)) % 0.39/0.62 (step @p163 false :rule chain_m_resolution :premises (@p162 @p127 @p82) :args (false (@list true false) (@list @t47 @t55))) % 0.39/0.62 ) % 0.39/0.62 % SZS output end Proof % 0.39/0.62 % cvc5 exiting %------------------------------------------------------------------------------