%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYO011^1 : 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 : n025.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 09:11:46 AM UTC 2026 % Result : Theorem 0.51s 0.71s % Output : Proof 0.51s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SYO011^1 : TPTP v9.2.1. Released v3.7.0. % 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 : n025.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 : Tue Jun 2 23:51:31 EDT 2026 % 0.17/0.34 % CPUTime : % 0.30/0.49 %----Proving TH0 % 0.51/0.71 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.51/0.71 % SZS status Theorem % 0.51/0.71 % SZS output start Proof % 0.51/0.71 ( % 0.51/0.71 (declare-sort $$unsorted 0) % 0.51/0.71 (declare-const tptp.p (-> (-> $$unsorted $$unsorted) Bool)) % 0.51/0.71 (declare-const tptp.f (-> $$unsorted $$unsorted)) % 0.51/0.71 (define tptp.leibeq () (let ((_let_1 (@var "V" $$unsorted))) (let ((_let_2 (@var "Q" (-> $$unsorted Bool)))) (let ((_let_3 (@var "U" $$unsorted))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (=> (_ _let_2 _let_3) (_ _let_2 _let_1)))))))) % 0.51/0.71 (define @t1 () (_ tptp.p tptp.f)) % 0.51/0.71 (define @t2 () (@var "X" $$unsorted)) % 0.51/0.71 (define @t3 () (@list @t2)) % 0.51/0.71 (define @t4 () (lambda @t3 @t2)) % 0.51/0.71 (define @t5 () (_ tptp.p @t4)) % 0.51/0.71 (define @t6 () (_ tptp.f @t2)) % 0.51/0.71 (define @t7 () (forall @t3 (_ (_ tptp.leibeq @t6) @t2))) % 0.51/0.71 (define @t8 () (and @t7 @t5)) % 0.51/0.71 (define @t9 () (=> @t8 @t1)) % 0.51/0.71 (define @t10 () (not @t9)) % 0.51/0.71 (define @t11 () (@var "V" $$unsorted)) % 0.51/0.71 (define @t12 () (@var "Q" (-> $$unsorted Bool))) % 0.51/0.71 (define @t13 () (_ @t12 @t11)) % 0.51/0.71 (define @t14 () (@var "U" $$unsorted)) % 0.51/0.71 (define @t15 () (_ @t12 @t14)) % 0.51/0.71 (define @t16 () (@list @t12)) % 0.51/0.71 (define @t17 () (forall @t16 (=> @t15 @t13))) % 0.51/0.71 (define @t18 () (@list @t14 @t11)) % 0.51/0.71 (define @t19 () (lambda @t18 @t17)) % 0.51/0.71 (define @t20 () (tptp.p tptp.f)) % 0.51/0.71 (define @t21 () (@purify @t4)) % 0.51/0.71 (define @t22 () (tptp.p @t21)) % 0.51/0.71 (define @t23 () (_ tptp.p @t21)) % 0.51/0.71 (define @t24 () (tptp.f @t2)) % 0.51/0.71 (define @t25 () (not (_ @t12 @t24))) % 0.51/0.71 (define @t26 () (or @t25 (_ @t12 @t2))) % 0.51/0.71 (define @t27 () (forall (@list @t2 @t12) @t26)) % 0.51/0.71 (define @t28 () (and @t27 @t5)) % 0.51/0.71 (define @t29 () (=> @t28 @t1)) % 0.51/0.71 (define @t30 () (forall @t16 @t26)) % 0.51/0.71 (define @t31 () (_ @t12 @t11)) % 0.51/0.71 (define @t32 () (@list @t11)) % 0.51/0.71 (define @t33 () (_ @t12 @t6)) % 0.51/0.71 (define @t34 () (not @t33)) % 0.51/0.71 (define @t35 () (or @t34 @t31)) % 0.51/0.71 (define @t36 () (forall @t16 @t35)) % 0.51/0.71 (define @t37 () (lambda @t32 @t36)) % 0.51/0.71 (define @t38 () (_ @t12 @t14)) % 0.51/0.71 (define @t39 () (_ (lambda @t18 (forall @t16 (or (not @t38) @t31))) @t6)) % 0.51/0.71 (define @t40 () (forall @t3 (_ @t39 @t2))) % 0.51/0.71 (define @t41 () (and @t40 @t5)) % 0.51/0.71 (define @t42 () (=> @t41 @t1)) % 0.51/0.71 (define @t43 () (not @t15)) % 0.51/0.71 (define @t44 () (or @t43 @t13)) % 0.51/0.71 (define @t45 () (= tptp.f @t21)) % 0.51/0.71 (define @t46 () (not @t45)) % 0.51/0.71 (define @t47 () (not @t22)) % 0.51/0.71 (define @t48 () (not @t20)) % 0.51/0.71 (define @t49 () (and @t48 @t45 @t22)) % 0.51/0.71 (define @t50 () (@list true false)) % 0.51/0.71 (define @t51 () (@const 0 $$unsorted)) % 0.51/0.71 (define @t52 () (tptp.f @t51)) % 0.51/0.71 (define @t53 () (_ @t4 @t51)) % 0.51/0.71 (define @t54 () (_ @t21 @t51)) % 0.51/0.71 (define @t55 () (= @t52 @t54)) % 0.51/0.71 (define @t56 () (not @t55)) % 0.51/0.71 (define @t57 () (or @t45 @t56)) % 0.51/0.71 (define @t58 () (= @t51 @t52)) % 0.51/0.71 (define @t59 () (_ tptp.f @t51)) % 0.51/0.71 (define @t60 () (= @t59 @t52)) % 0.51/0.71 (define @t61 () (= @t51 @t59)) % 0.51/0.71 (define @t62 () (= @t52 @t59)) % 0.51/0.71 (define @t63 () (not @t62)) % 0.51/0.71 (define @t64 () (or @t63 @t61)) % 0.51/0.71 (define @t65 () (@var "BOUND_VARIABLE_43646" $$unsorted)) % 0.51/0.71 (define @t66 () (lambda (@list @t65) (= @t59 @t65))) % 0.51/0.71 (define @t67 () (_ @t66 @t51)) % 0.51/0.71 (define @t68 () (_ @t66 @t52)) % 0.51/0.71 (define @t69 () (not @t68)) % 0.51/0.71 (define @t70 () (or @t69 @t67)) % 0.51/0.71 (assume @p1 @t10) % 0.51/0.71 (assume @p2 true) % 0.51/0.71 (step @p3 (= tptp.leibeq @t19) :rule refl :args (@t19)) % 0.51/0.71 (step @p4 :rule refl :args (@t20)) % 0.51/0.71 (step @p5 :rule refl :args (@t1)) % 0.51/0.71 (step @p6 :rule cong :premises (@p5 @p4) :args ((= @t1 @t20))) % 0.51/0.71 (step @p7 :rule symm :premises (@p6)) % 0.51/0.71 (step @p8 :rule eq_resolve :premises (@p5 @p7)) % 0.51/0.71 (step @p9 :rule refl :args (@t22)) % 0.51/0.71 (step @p10 :rule refl :args (@t23)) % 0.51/0.71 (step @p11 :rule cong :premises (@p10 @p9) :args ((= @t23 @t22))) % 0.51/0.71 (step @p12 :rule symm :premises (@p11)) % 0.51/0.71 (step @p13 :rule eq_resolve :premises (@p10 @p12)) % 0.51/0.71 (step @p14 :rule eq-refl :args (@t4)) % 0.51/0.71 (step @p15 :rule skolem_intro :args (@t21)) % 0.51/0.71 (step @p16 :rule refl :args (@t4)) % 0.51/0.71 (step @p17 :rule cong :premises (@p16 @p15) :args ((= @t4 @t21))) % 0.51/0.71 (step @p18 :rule trans :premises (@p17 @p14)) % 0.51/0.71 (step @p19 :rule true_elim :premises (@p18)) % 0.51/0.71 (step @p20 :rule refl :args (tptp.p)) % 0.51/0.71 (step @p21 :rule ho_cong :premises (@p20 @p19)) % 0.51/0.71 (step @p22 :rule trans :premises (@p21 @p13)) % 0.51/0.71 (step @p23 :rule refl :args (@t27)) % 0.51/0.71 (step @p24 :rule nary_cong :premises (@p23 @p22) :args (@t28)) % 0.51/0.71 (step @p25 :rule cong :premises (@p24 @p8) :args (@t29)) % 0.51/0.71 (step @p26 :rule cong :premises (@p25) :args ((not @t29))) % 0.51/0.71 (step @p27 :rule refl :args (@t1)) % 0.51/0.71 (step @p28 :rule refl :args (@t5)) % 0.51/0.71 (step @p29 :rule quant-merge-prenex :args ((= (forall @t3 @t30) @t27))) % 0.51/0.71 (step @p30 :rule beta-reduce :args ((= (_ (lambda @t32 (forall @t16 (or @t25 @t31))) @t2) @t30))) % 0.51/0.71 (step @p31 :rule refl :args (@t2)) % 0.51/0.71 (step @p32 :rule refl :args (@t31)) % 0.51/0.71 (step @p33 :rule refl :args (@t24)) % 0.51/0.71 (step @p34 :rule refl :args (@t6)) % 0.51/0.71 (step @p35 :rule cong :premises (@p34 @p33) :args ((= @t6 @t24))) % 0.51/0.71 (step @p36 :rule symm :premises (@p35)) % 0.51/0.71 (step @p37 :rule eq_resolve :premises (@p34 @p36)) % 0.51/0.71 (step @p38 :rule cong :premises (@p37) :args (@t33)) % 0.51/0.71 (step @p39 :rule cong :premises (@p38) :args (@t34)) % 0.51/0.71 (step @p40 :rule nary_cong :premises (@p39 @p32) :args (@t35)) % 0.51/0.71 (step @p41 :rule cong :premises (@p40) :args (@t36)) % 0.51/0.71 (step @p42 :rule cong :premises (@p41) :args (@t37)) % 0.51/0.71 (step @p43 :rule beta-reduce :args ((= @t39 @t37))) % 0.51/0.71 (step @p44 :rule trans :premises (@p43 @p42)) % 0.51/0.71 (step @p45 :rule ho_cong :premises (@p44 @p31)) % 0.51/0.71 (step @p46 :rule trans :premises (@p45 @p30)) % 0.51/0.71 (step @p47 :rule cong :premises (@p46) :args (@t40)) % 0.51/0.71 (step @p48 :rule trans :premises (@p47 @p29)) % 0.51/0.71 (step @p49 :rule nary_cong :premises (@p48 @p28) :args (@t41)) % 0.51/0.71 (step @p50 :rule cong :premises (@p49 @p27) :args (@t42)) % 0.51/0.71 (step @p51 :rule cong :premises (@p50) :args ((not @t42))) % 0.51/0.71 (step @p52 :rule refl :args (@t6)) % 0.51/0.71 (step @p53 :rule refl :args (@t31)) % 0.51/0.71 (step @p54 :rule refl :args (@t13)) % 0.51/0.71 (step @p55 :rule cong :premises (@p54 @p53) :args ((= @t13 @t31))) % 0.51/0.71 (step @p56 :rule symm :premises (@p55)) % 0.51/0.71 (step @p57 :rule eq_resolve :premises (@p54 @p56)) % 0.51/0.71 (step @p58 :rule refl :args (@t38)) % 0.51/0.71 (step @p59 :rule refl :args (@t15)) % 0.51/0.71 (step @p60 :rule cong :premises (@p59 @p58) :args ((= @t15 @t38))) % 0.51/0.71 (step @p61 :rule symm :premises (@p60)) % 0.51/0.71 (step @p62 :rule eq_resolve :premises (@p59 @p61)) % 0.51/0.71 (step @p63 :rule cong :premises (@p62) :args (@t43)) % 0.51/0.71 (step @p64 :rule nary_cong :premises (@p63 @p57) :args (@t44)) % 0.51/0.71 (step @p65 :rule cong :premises (@p64) :args ((forall @t16 @t44))) % 0.51/0.71 (step @p66 :rule bool-impl-elim :args (@t15 @t13)) % 0.51/0.71 (step @p67 :rule cong :premises (@p66) :args (@t17)) % 0.51/0.71 (step @p68 :rule trans :premises (@p67 @p65)) % 0.51/0.71 (step @p69 :rule cong :premises (@p68) :args (@t19)) % 0.51/0.71 (step @p70 :rule trans :premises (@p3 @p69)) % 0.51/0.71 (step @p71 :rule ho_cong :premises (@p70 @p52)) % 0.51/0.71 (step @p72 :rule ho_cong :premises (@p71 @p31)) % 0.51/0.71 (step @p73 :rule cong :premises (@p72) :args (@t7)) % 0.51/0.71 (step @p74 :rule nary_cong :premises (@p73 @p28) :args (@t8)) % 0.51/0.71 (step @p75 :rule cong :premises (@p74 @p27) :args (@t9)) % 0.51/0.71 (step @p76 :rule cong :premises (@p75) :args (@t10)) % 0.51/0.71 (step @p77 :rule trans :premises (@p76 @p51)) % 0.51/0.71 (step @p78 :rule trans :premises (@p77 @p26)) % 0.51/0.71 (step @p79 :rule eq_resolve :premises (@p1 @p78)) % 0.51/0.71 (step @p80 :rule not_implies_elim1 :premises (@p79)) % 0.51/0.71 (step @p81 :rule and_elim :premises (@p80) :args (0)) % 0.51/0.71 (step @p82 :rule and_elim :premises (@p80) :args (1)) % 0.51/0.71 (step @p83 :rule not_implies_elim2 :premises (@p79)) % 0.51/0.71 (step @p84 :rule refl :args (@t46)) % 0.51/0.71 (step @p85 :rule bool-double-not-elim :args (@t20)) % 0.51/0.71 (step @p86 :rule refl :args (@t47)) % 0.51/0.71 (step @p87 :rule nary_cong :premises (@p86 @p85 @p84) :args ((or @t47 (not @t48) @t46))) % 0.51/0.71 (assume-push @p170 @t48) % 0.51/0.71 (assume-push @p171 @t45) % 0.51/0.71 (assume-push @p172 @t22) % 0.51/0.71 (step @p91 :rule evaluate :args ((= true false))) % 0.51/0.71 (step @p92 :rule false_intro :premises (@p83)) % 0.51/0.71 (step @p93 :rule symm :premises (@p171)) % 0.51/0.71 (step @p94 :rule cong :premises (@p93) :args (@t22)) % 0.51/0.71 (step @p95 :rule true_intro :premises (@p82)) % 0.51/0.71 (step @p96 :rule symm :premises (@p95)) % 0.51/0.71 (step @p97 :rule trans :premises (@p96 @p94 @p92)) % 0.51/0.71 (step @p98 false :rule eq_resolve :premises (@p97 @p91)) % 0.51/0.71 (step-pop @p173 :rule scope :premises (@p98)) % 0.51/0.71 (step-pop @p174 :rule scope :premises (@p173)) % 0.51/0.71 (step-pop @p175 :rule scope :premises (@p174)) % 0.51/0.71 (step @p99 :rule process_scope :premises (@p175) :args (false)) % 0.51/0.71 (assume-push @p176 @t22) % 0.51/0.71 (assume-push @p177 @t48) % 0.51/0.71 (assume-push @p178 @t45) % 0.51/0.71 (step @p106 :rule and_intro :premises (@p83 @p178 @p82)) % 0.51/0.71 (step-pop @p179 :rule scope :premises (@p106)) % 0.51/0.71 (step-pop @p180 :rule scope :premises (@p179)) % 0.51/0.71 (step-pop @p181 :rule scope :premises (@p180)) % 0.51/0.71 (step @p107 :rule process_scope :premises (@p181) :args (@t49)) % 0.51/0.71 (step @p111 :rule implies_elim :premises (@p107)) % 0.51/0.71 (step @p112 :rule resolution :premises (@p111 @p99) :args (true @t49)) % 0.51/0.71 (step @p113 :rule not_and :premises (@p112)) % 0.51/0.71 (step @p114 :rule eq_resolve :premises (@p113 @p87)) % 0.51/0.71 (step @p115 :rule reordering :premises (@p114) :args ((or @t20 @t47 @t46))) % 0.51/0.71 (step @p116 :rule chain_m_resolution :premises (@p115 @p83 @p82) :args (@t46 @t50 (@list @t20 @t22))) % 0.51/0.71 (step @p117 :rule eq-symm :args (@t52 @t51)) % 0.51/0.71 (step @p118 :rule eq-refl :args (@t51)) % 0.51/0.71 (step @p119 :rule beta-reduce :args ((= @t53 @t51))) % 0.51/0.71 (step @p120 :rule refl :args (@t51)) % 0.51/0.71 (step @p121 :rule cong :premises (@p120 @p119) :args ((= @t51 @t53))) % 0.51/0.71 (step @p122 :rule trans :premises (@p121 @p118)) % 0.51/0.71 (step @p123 :rule ho_cong :premises (@p15 @p120)) % 0.51/0.71 (step @p124 :rule cong :premises (@p120 @p123) :args ((= @t51 @t54))) % 0.51/0.71 (step @p125 :rule eq-symm :args (@t54 @t51)) % 0.51/0.71 (step @p126 :rule trans :premises (@p125 @p124 @p122)) % 0.51/0.71 (step @p127 :rule true_elim :premises (@p126)) % 0.51/0.71 (step @p128 :rule refl :args (@t52)) % 0.51/0.71 (step @p129 :rule cong :premises (@p128 @p127) :args (@t55)) % 0.51/0.71 (step @p130 :rule trans :premises (@p129 @p117)) % 0.51/0.71 (step @p131 :rule cong :premises (@p130) :args (@t56)) % 0.51/0.71 (step @p132 :rule refl :args (@t45)) % 0.51/0.71 (step @p133 :rule nary_cong :premises (@p132 @p131) :args (@t57)) % 0.51/0.71 ; WARNING: add trust step for TRUST % 0.51/0.71 ; trust TRUST THEORY_LEMMA % 0.51/0.71 (step @p134 :rule trust :premises () :args (@t57)) % 0.51/0.71 (step @p135 :rule eq_resolve :premises (@p134 @p133)) % 0.51/0.71 (step @p136 :rule chain_m_resolution :premises (@p135 @p116) :args ((not @t58) (@list true) (@list @t45))) % 0.51/0.71 (step @p137 :rule aci_norm :args ((= (or false @t58) @t58))) % 0.51/0.71 (step @p138 :rule refl :args (@t52)) % 0.51/0.71 (step @p139 :rule refl :args (@t59)) % 0.51/0.71 (step @p140 :rule cong :premises (@p139 @p138) :args (@t60)) % 0.51/0.71 (step @p141 :rule symm :premises (@p140)) % 0.51/0.71 (step @p142 :rule eq_resolve :premises (@p139 @p141)) % 0.51/0.71 (step @p143 :rule cong :premises (@p120 @p142) :args (@t61)) % 0.51/0.71 (step @p144 :rule evaluate :args ((not true))) % 0.51/0.71 (step @p145 :rule eq-refl :args (@t52)) % 0.51/0.71 (step @p146 :rule cong :premises (@p128 @p142) :args (@t62)) % 0.51/0.71 (step @p147 :rule trans :premises (@p146 @p145)) % 0.51/0.71 (step @p148 :rule cong :premises (@p147) :args (@t63)) % 0.51/0.71 (step @p149 :rule trans :premises (@p148 @p144)) % 0.51/0.71 (step @p150 :rule nary_cong :premises (@p149 @p143) :args (@t64)) % 0.51/0.71 (step @p151 :rule trans :premises (@p150 @p137)) % 0.51/0.71 (step @p152 :rule cong :premises (@p23 @p151) :args ((=> @t27 @t64))) % 0.51/0.71 (step @p153 :rule eq-symm :args (@t59 @t51)) % 0.51/0.71 (step @p154 :rule beta-reduce :args ((= @t67 (= @t59 @t51)))) % 0.51/0.71 (step @p155 :rule trans :premises (@p154 @p153)) % 0.51/0.71 (step @p156 :rule eq-symm :args (@t59 @t52)) % 0.51/0.71 (step @p157 :rule beta-reduce :args ((= @t68 @t60))) % 0.51/0.71 (step @p158 :rule trans :premises (@p157 @p156)) % 0.51/0.71 (step @p159 :rule cong :premises (@p158) :args (@t69)) % 0.51/0.71 (step @p160 :rule nary_cong :premises (@p159 @p155) :args (@t70)) % 0.51/0.71 (step @p161 :rule cong :premises (@p23 @p160) :args ((=> @t27 @t70))) % 0.51/0.71 (assume-push @p182 @t27) % 0.51/0.71 (step @p163 :rule instantiate :premises (@p81) :args ((@list @t51 @t66))) % 0.51/0.71 (step-pop @p183 :rule scope :premises (@p163)) % 0.51/0.71 (step @p164 :rule process_scope :premises (@p183) :args (@t70)) % 0.51/0.71 (step @p166 :rule eq_resolve :premises (@p164 @p161)) % 0.51/0.71 (step @p167 :rule eq_resolve :premises (@p166 @p152)) % 0.51/0.71 (step @p168 :rule implies_elim :premises (@p167)) % 0.51/0.71 (step @p169 false :rule chain_m_resolution :premises (@p168 @p136 @p81) :args (false @t50 (@list @t58 @t27))) % 0.51/0.71 ) % 0.51/0.71 % SZS output end Proof % 0.51/0.71 % cvc5 exiting %------------------------------------------------------------------------------