%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU924^5 : 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 : n001.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 08:53:32 AM UTC 2026 % Result : Theorem 0.34s 0.64s % Output : Proof 0.34s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU924^5 : TPTP v9.2.1. Released v4.0.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.35 % Computer : n001.cluster.edu % 0.17/0.35 % Model : x86_64 x86_64 % 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.35 % Memory : 8042.1875MB % 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.35 % CPULimit : 300 % 0.17/0.35 % WCLimit : 300 % 0.17/0.35 % DateTime : Tue Jun 2 18:01:05 EDT 2026 % 0.17/0.35 % CPUTime : % 0.27/0.51 %----Proving TH0 % 0.34/0.64 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.34/0.64 % SZS status Theorem % 0.34/0.64 % SZS output start Proof % 0.34/0.64 ( % 0.34/0.64 (declare-sort $$unsorted 0) % 0.34/0.64 (define @t1 () (@var "Xz" $$unsorted)) % 0.34/0.64 (define @t2 () (@var "Xx" $$unsorted)) % 0.34/0.64 (define @t3 () (@var "Xg" (-> $$unsorted $$unsorted))) % 0.34/0.64 (define @t4 () (_ @t3 @t2)) % 0.34/0.64 (define @t5 () (@list @t2)) % 0.34/0.64 (define @t6 () (forall @t5 (= @t4 @t1))) % 0.34/0.64 (define @t7 () (@var "Xp" (-> (-> $$unsorted $$unsorted) Bool))) % 0.34/0.64 (define @t8 () (_ @t7 @t3)) % 0.34/0.64 (define @t9 () (lambda @t5 @t1)) % 0.34/0.64 (define @t10 () (_ @t7 @t9)) % 0.34/0.64 (define @t11 () (@var "Xj" (-> $$unsorted $$unsorted))) % 0.34/0.64 (define @t12 () (_ @t7 @t11)) % 0.34/0.64 (define @t13 () (@list @t11)) % 0.34/0.64 (define @t14 () (forall @t13 (=> @t12 @t10))) % 0.34/0.64 (define @t15 () (and @t10 @t14)) % 0.34/0.64 (define @t16 () (=> @t15 @t8)) % 0.34/0.64 (define @t17 () (@list @t7)) % 0.34/0.64 (define @t18 () (forall @t17 @t16)) % 0.34/0.64 (define @t19 () (=> @t18 @t6)) % 0.34/0.64 (define @t20 () (@list @t1 @t3)) % 0.34/0.64 (define @t21 () (forall @t20 @t19)) % 0.34/0.64 (define @t22 () (not @t21)) % 0.34/0.64 (define @t23 () (@var "BOUND_VARIABLE_7468" $$unsorted)) % 0.34/0.64 (define @t24 () (= @t1 (_ @t3 @t23))) % 0.34/0.64 (define @t25 () (_ @t7 @t3)) % 0.34/0.64 (define @t26 () (_ @t7 @t11)) % 0.34/0.64 (define @t27 () (forall @t13 (not @t26))) % 0.34/0.64 (define @t28 () (not @t27)) % 0.34/0.64 (define @t29 () (_ @t7 @t9)) % 0.34/0.64 (define @t30 () (not @t29)) % 0.34/0.64 (define @t31 () (forall @t17 (or @t30 (and @t30 @t28) @t25))) % 0.34/0.64 (define @t32 () (not @t31)) % 0.34/0.64 (define @t33 () (or @t32 @t24)) % 0.34/0.64 (define @t34 () (forall (@list @t1 @t3 @t23) @t33)) % 0.34/0.64 (define @t35 () (@list @t23)) % 0.34/0.64 (define @t36 () (forall @t35 @t33)) % 0.34/0.64 (define @t37 () (forall @t35 @t24)) % 0.34/0.64 (define @t38 () (or @t32 @t37)) % 0.34/0.64 (define @t39 () (_ @t3 @t2)) % 0.34/0.64 (define @t40 () (forall @t5 (= @t1 @t39))) % 0.34/0.64 (define @t41 () (= @t1 @t4)) % 0.34/0.64 (define @t42 () (not @t10)) % 0.34/0.64 (define @t43 () (and @t42 @t28)) % 0.34/0.64 (define @t44 () (or @t42 @t43 @t8)) % 0.34/0.64 (define @t45 () (or @t10 @t27)) % 0.34/0.64 (define @t46 () (and @t10 @t45)) % 0.34/0.64 (define @t47 () (not @t12)) % 0.34/0.64 (define @t48 () (forall @t13 @t47)) % 0.34/0.64 (define @t49 () (or @t10 @t48)) % 0.34/0.64 (define @t50 () (or @t10 @t47)) % 0.34/0.64 (define @t51 () (or @t47 @t10)) % 0.34/0.64 (define @t52 () (@quantifiers_skolemize @t34 1)) % 0.34/0.64 (define @t53 () (@quantifiers_skolemize @t34 0)) % 0.34/0.64 (define @t54 () (lambda @t5 @t53)) % 0.34/0.64 (define @t55 () (not (_ @t7 @t54))) % 0.34/0.64 (define @t56 () (forall @t17 (or @t55 (and @t55 @t28) (_ @t7 @t52)))) % 0.34/0.64 (define @t57 () (_ @t52 (@quantifiers_skolemize @t34 2))) % 0.34/0.64 (define @t58 () (= @t53 @t57)) % 0.34/0.64 (define @t59 () (not @t56)) % 0.34/0.64 (define @t60 () (or @t59 @t58)) % 0.34/0.64 (define @t61 () (@list true)) % 0.34/0.64 (define @t62 () (@list @t60)) % 0.34/0.64 (define @t63 () (= @t11 @t52)) % 0.34/0.64 (define @t64 () (not (forall @t13 @t63))) % 0.34/0.64 (define @t65 () (@purify @t54)) % 0.34/0.64 (define @t66 () (= @t52 @t54)) % 0.34/0.64 (define @t67 () (and @t66 @t64)) % 0.34/0.64 (define @t68 () (or @t66 @t67)) % 0.34/0.64 (define @t69 () (not (= @t52 @t52))) % 0.34/0.64 (define @t70 () (@var "BOUND_VARIABLE_14910" (-> $$unsorted $$unsorted))) % 0.34/0.64 (define @t71 () (lambda (@list @t70) (not (= @t52 @t70)))) % 0.34/0.64 (define @t72 () (_ @t71 @t52)) % 0.34/0.64 (define @t73 () (not (= @t52 @t11))) % 0.34/0.64 (define @t74 () (_ @t71 @t11)) % 0.34/0.64 (define @t75 () (not @t74)) % 0.34/0.64 (define @t76 () (forall @t13 @t75)) % 0.34/0.64 (define @t77 () (not @t76)) % 0.34/0.64 (define @t78 () (_ @t71 @t54)) % 0.34/0.64 (define @t79 () (not @t78)) % 0.34/0.64 (define @t80 () (and @t79 @t77)) % 0.34/0.64 (define @t81 () (or @t79 @t80 @t72)) % 0.34/0.64 (define @t82 () (= @t52 @t65)) % 0.34/0.64 (define @t83 () (and @t82 @t64)) % 0.34/0.64 (define @t84 () (or @t82 @t83)) % 0.34/0.64 (define @t85 () (=> @t82 (= @t57 @t53))) % 0.34/0.64 (define @t86 () (not @t82)) % 0.34/0.64 (define @t87 () (not @t83)) % 0.34/0.64 (assume @p1 @t22) % 0.34/0.64 (assume @p2 true) % 0.34/0.64 (step @p3 :rule quant-merge-prenex :args ((= (forall @t20 @t36) @t34))) % 0.34/0.64 (step @p4 :rule alpha_equiv :args (@t37 (@list @t23) (@list @t2))) % 0.34/0.64 (step @p5 :rule refl :args (@t32)) % 0.34/0.64 (step @p6 :rule nary_cong :premises (@p5 @p4) :args (@t38)) % 0.34/0.64 (step @p7 :rule quant-miniscope-or :args ((= @t36 @t38))) % 0.34/0.64 (step @p8 :rule trans :premises (@p7 @p6)) % 0.34/0.64 (step @p9 :rule symm :premises (@p8)) % 0.34/0.64 (step @p10 :rule cong :premises (@p9) :args ((forall @t20 (or @t32 @t40)))) % 0.34/0.64 (step @p11 :rule trans :premises (@p10 @p3)) % 0.34/0.64 (step @p12 :rule bool-impl-elim :args (@t31 @t40)) % 0.34/0.64 (step @p13 :rule cong :premises (@p12) :args ((forall @t20 (=> @t31 @t40)))) % 0.34/0.64 (step @p14 :rule trans :premises (@p13 @p11)) % 0.34/0.64 (step @p15 :rule refl :args (@t39)) % 0.34/0.64 (step @p16 :rule refl :args (@t4)) % 0.34/0.64 (step @p17 :rule cong :premises (@p16 @p15) :args ((= @t4 @t39))) % 0.34/0.64 (step @p18 :rule symm :premises (@p17)) % 0.34/0.64 (step @p19 :rule eq_resolve :premises (@p16 @p18)) % 0.34/0.64 (step @p20 :rule refl :args (@t1)) % 0.34/0.64 (step @p21 :rule cong :premises (@p20 @p19) :args (@t41)) % 0.34/0.64 (step @p22 :rule cong :premises (@p21) :args ((forall @t5 @t41))) % 0.34/0.64 (step @p23 :rule eq-symm :args (@t4 @t1)) % 0.34/0.64 (step @p24 :rule cong :premises (@p23) :args (@t6)) % 0.34/0.64 (step @p25 :rule trans :premises (@p24 @p22)) % 0.34/0.64 (step @p26 :rule refl :args (@t25)) % 0.34/0.64 (step @p27 :rule refl :args (@t8)) % 0.34/0.64 (step @p28 :rule cong :premises (@p27 @p26) :args ((= @t8 @t25))) % 0.34/0.64 (step @p29 :rule symm :premises (@p28)) % 0.34/0.64 (step @p30 :rule eq_resolve :premises (@p27 @p29)) % 0.34/0.64 (step @p31 :rule refl :args (@t28)) % 0.34/0.64 (step @p32 :rule refl :args (@t29)) % 0.34/0.64 (step @p33 :rule refl :args (@t10)) % 0.34/0.64 (step @p34 :rule cong :premises (@p33 @p32) :args ((= @t10 @t29))) % 0.34/0.64 (step @p35 :rule symm :premises (@p34)) % 0.34/0.64 (step @p36 :rule eq_resolve :premises (@p33 @p35)) % 0.34/0.64 (step @p37 :rule cong :premises (@p36) :args (@t42)) % 0.34/0.64 (step @p38 :rule nary_cong :premises (@p37 @p31) :args (@t43)) % 0.34/0.64 (step @p39 :rule nary_cong :premises (@p37 @p38 @p30) :args (@t44)) % 0.34/0.64 (step @p40 :rule cong :premises (@p39) :args ((forall @t17 @t44))) % 0.34/0.64 (step @p41 :rule aci_norm :args ((= (or (or @t42 @t43) @t8) @t44))) % 0.34/0.64 (step @p42 :rule bool-or-de-morgan :args (@t10 @t27 false)) % 0.34/0.64 (step @p43 :rule refl :args (@t42)) % 0.34/0.64 (step @p44 :rule nary_cong :premises (@p43 @p42) :args ((or @t42 (not @t45)))) % 0.34/0.64 (step @p45 :rule bool-and-de-morgan :args (@t10 @t45 true)) % 0.34/0.64 (step @p46 :rule trans :premises (@p45 @p44)) % 0.34/0.64 (step @p47 :rule nary_cong :premises (@p46 @p27) :args ((or (not @t46) @t8))) % 0.34/0.64 (step @p48 :rule trans :premises (@p47 @p41)) % 0.34/0.64 (step @p49 :rule bool-impl-elim :args (@t46 @t8)) % 0.34/0.64 (step @p50 :rule trans :premises (@p49 @p48)) % 0.34/0.64 (step @p51 :rule cong :premises (@p50) :args ((forall @t17 (=> @t46 @t8)))) % 0.34/0.64 (step @p52 :rule trans :premises (@p51 @p40)) % 0.34/0.64 (step @p53 :rule refl :args (@t8)) % 0.34/0.64 (step @p54 :rule refl :args (@t26)) % 0.34/0.64 (step @p55 :rule refl :args (@t12)) % 0.34/0.64 (step @p56 :rule cong :premises (@p55 @p54) :args ((= @t12 @t26))) % 0.34/0.64 (step @p57 :rule symm :premises (@p56)) % 0.34/0.64 (step @p58 :rule eq_resolve :premises (@p55 @p57)) % 0.34/0.64 (step @p59 :rule cong :premises (@p58) :args (@t47)) % 0.34/0.64 (step @p60 :rule cong :premises (@p59) :args (@t48)) % 0.34/0.64 (step @p61 :rule refl :args (@t10)) % 0.34/0.64 (step @p62 :rule nary_cong :premises (@p61 @p60) :args (@t49)) % 0.34/0.64 (step @p63 :rule quant-miniscope-or :args ((= (forall @t13 @t50) @t49))) % 0.34/0.64 (step @p64 :rule aci_norm :args ((= @t51 @t50))) % 0.34/0.64 (step @p65 :rule cong :premises (@p64) :args ((forall @t13 @t51))) % 0.34/0.64 (step @p66 :rule trans :premises (@p65 @p63)) % 0.34/0.64 (step @p67 :rule trans :premises (@p66 @p62)) % 0.34/0.64 (step @p68 :rule bool-impl-elim :args (@t12 @t10)) % 0.34/0.64 (step @p69 :rule cong :premises (@p68) :args (@t14)) % 0.34/0.64 (step @p70 :rule trans :premises (@p69 @p67)) % 0.34/0.64 (step @p71 :rule nary_cong :premises (@p61 @p70) :args (@t15)) % 0.34/0.64 (step @p72 :rule cong :premises (@p71 @p53) :args (@t16)) % 0.34/0.64 (step @p73 :rule cong :premises (@p72) :args (@t18)) % 0.34/0.64 (step @p74 :rule trans :premises (@p73 @p52)) % 0.34/0.64 (step @p75 :rule cong :premises (@p74 @p25) :args (@t19)) % 0.34/0.64 (step @p76 :rule cong :premises (@p75) :args (@t21)) % 0.34/0.64 (step @p77 :rule trans :premises (@p76 @p14)) % 0.34/0.64 (step @p78 :rule cong :premises (@p77) :args (@t22)) % 0.34/0.64 (step @p79 :rule eq_resolve :premises (@p1 @p78)) % 0.34/0.64 (step @p80 :rule skolemize :premises (@p79)) % 0.34/0.64 (step @p81 :rule bool-double-not-elim :args (@t56)) % 0.34/0.64 (step @p82 :rule refl :args (@t60)) % 0.34/0.64 (step @p83 :rule nary_cong :premises (@p82 @p81) :args ((or @t60 (not @t59)))) % 0.34/0.64 (step @p84 :rule cnf_or_neg :args (@t60 0)) % 0.34/0.64 (step @p85 :rule eq_resolve :premises (@p84 @p83)) % 0.34/0.64 (step @p86 :rule reordering :premises (@p85) :args ((or @t56 @t60))) % 0.34/0.64 (step @p87 :rule chain_m_resolution :premises (@p86 @p80) :args (@t56 @t61 @t62)) % 0.34/0.64 (step @p88 :rule refl :args (@t64)) % 0.34/0.64 (step @p89 :rule eq-refl :args (@t54)) % 0.34/0.64 (step @p90 :rule skolem_intro :args (@t65)) % 0.34/0.64 (step @p91 :rule refl :args (@t54)) % 0.34/0.64 (step @p92 :rule cong :premises (@p91 @p90) :args ((= @t54 @t65))) % 0.34/0.64 (step @p93 :rule trans :premises (@p92 @p89)) % 0.34/0.64 (step @p94 :rule true_elim :premises (@p93)) % 0.34/0.65 (step @p95 :rule refl :args (@t52)) % 0.34/0.65 (step @p96 :rule cong :premises (@p95 @p94) :args (@t66)) % 0.34/0.65 (step @p97 :rule nary_cong :premises (@p96 @p88) :args (@t67)) % 0.34/0.65 (step @p98 :rule nary_cong :premises (@p96 @p97) :args (@t68)) % 0.34/0.65 (step @p99 :rule refl :args (@t56)) % 0.34/0.65 (step @p100 :rule cong :premises (@p99 @p98) :args ((=> @t56 @t68))) % 0.34/0.65 (step @p101 :rule aci_norm :args ((= (or @t66 @t67 false) @t68))) % 0.34/0.65 (step @p102 :rule evaluate :args ((not true))) % 0.34/0.65 (step @p103 :rule eq-refl :args (@t52)) % 0.34/0.65 (step @p104 :rule cong :premises (@p103) :args (@t69)) % 0.34/0.65 (step @p105 :rule trans :premises (@p104 @p102)) % 0.34/0.65 (step @p106 :rule beta-reduce :args ((= @t72 @t69))) % 0.34/0.65 (step @p107 :rule trans :premises (@p106 @p105)) % 0.34/0.65 (step @p108 :rule bool-double-not-elim :args (@t63)) % 0.34/0.65 (step @p109 :rule eq-symm :args (@t52 @t11)) % 0.34/0.65 (step @p110 :rule cong :premises (@p109) :args (@t73)) % 0.34/0.65 (step @p111 :rule beta-reduce :args ((= @t74 @t73))) % 0.34/0.65 (step @p112 :rule trans :premises (@p111 @p110)) % 0.34/0.65 (step @p113 :rule cong :premises (@p112) :args (@t75)) % 0.34/0.65 (step @p114 :rule trans :premises (@p113 @p108)) % 0.34/0.65 (step @p115 :rule cong :premises (@p114) :args (@t76)) % 0.34/0.65 (step @p116 :rule cong :premises (@p115) :args (@t77)) % 0.34/0.65 (step @p117 :rule bool-double-not-elim :args (@t66)) % 0.34/0.65 (step @p118 :rule beta-reduce :args ((= @t78 (not @t66)))) % 0.34/0.65 (step @p119 :rule cong :premises (@p118) :args (@t79)) % 0.34/0.65 (step @p120 :rule trans :premises (@p119 @p117)) % 0.34/0.65 (step @p121 :rule nary_cong :premises (@p120 @p116) :args (@t80)) % 0.34/0.65 (step @p122 :rule nary_cong :premises (@p120 @p121 @p107) :args (@t81)) % 0.34/0.65 (step @p123 :rule trans :premises (@p122 @p101)) % 0.34/0.65 (step @p124 :rule cong :premises (@p99 @p123) :args ((=> @t56 @t81))) % 0.34/0.65 (assume-push @p149 @t56) % 0.34/0.65 (step @p126 :rule instantiate :premises (@p87) :args ((@list @t71))) % 0.34/0.65 (step-pop @p150 :rule scope :premises (@p126)) % 0.34/0.65 (step @p127 :rule process_scope :premises (@p150) :args (@t81)) % 0.34/0.65 (step @p129 :rule eq_resolve :premises (@p127 @p124)) % 0.34/0.65 (step @p130 :rule eq_resolve :premises (@p129 @p100)) % 0.34/0.65 (step @p131 :rule implies_elim :premises (@p130)) % 0.34/0.65 (step @p132 :rule chain_m_resolution :premises (@p131 @p87) :args (@t84 (@list false) (@list @t56))) % 0.34/0.65 (step @p133 :rule cnf_or_neg :args (@t60 1)) % 0.34/0.65 (step @p134 :rule chain_m_resolution :premises (@p133 @p80) :args ((not @t58) @t61 @t62)) % 0.34/0.65 (step @p135 :rule eq-symm :args (@t57 @t53)) % 0.34/0.65 (step @p136 :rule refl :args (@t82)) % 0.34/0.65 (step @p137 :rule cong :premises (@p136 @p135) :args (@t85)) % 0.34/0.65 ; WARNING: add trust step for TRUST % 0.34/0.65 ; trust TRUST THEORY_LEMMA % 0.34/0.65 (step @p138 :rule trust :premises () :args (@t85)) % 0.34/0.65 (step @p139 :rule eq_resolve :premises (@p138 @p137)) % 0.34/0.65 (step @p140 :rule implies_elim :premises (@p139)) % 0.34/0.65 (step @p141 :rule reordering :premises (@p140) :args ((or @t58 @t86))) % 0.34/0.65 (step @p142 :rule chain_m_resolution :premises (@p141 @p134) :args (@t86 @t61 (@list @t58))) % 0.34/0.65 (step @p143 :rule cnf_and_pos :args (@t83 0)) % 0.34/0.65 (step @p144 :rule reordering :premises (@p143) :args ((or @t82 @t87))) % 0.34/0.65 (step @p145 :rule chain_m_resolution :premises (@p144 @p142) :args (@t87 @t61 (@list @t82))) % 0.34/0.65 (step @p146 :rule cnf_or_pos :args (@t84)) % 0.34/0.65 (step @p147 :rule reordering :premises (@p146) :args ((or @t82 @t83 (not @t84)))) % 0.34/0.65 (step @p148 false :rule chain_m_resolution :premises (@p147 @p145 @p142 @p132) :args (false (@list true true false) (@list @t83 @t82 @t84))) % 0.34/0.65 ) % 0.34/0.65 % SZS output end Proof % 0.34/0.65 % cvc5 exiting %------------------------------------------------------------------------------