%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU930^5 : 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 : n013.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 08:53:33 AM UTC 2026 % Result : Theorem 0.31s 0.56s % Output : Proof 0.33s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU930^5 : 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 % 0.17/0.34 % Computer : n013.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 18:00:30 EDT 2026 % 0.17/0.34 % CPUTime : % 0.31/0.48 %----Proving TH0 % 0.31/0.56 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.31/0.56 % SZS status Theorem % 0.31/0.56 % SZS output start Proof % 0.31/0.56 ( % 0.31/0.56 (declare-sort $$unsorted 0) % 0.31/0.56 (declare-const tptp.g (-> $$unsorted $$unsorted)) % 0.31/0.56 (declare-const tptp.f (-> $$unsorted $$unsorted)) % 0.31/0.56 (define @t1 () (@var "Xx" $$unsorted)) % 0.31/0.56 (define @t2 () (_ tptp.f @t1)) % 0.31/0.56 (define @t3 () (@var "Xz" $$unsorted)) % 0.31/0.56 (define @t4 () (_ tptp.g @t3)) % 0.31/0.56 (define @t5 () (=> (= @t4 @t3) (= @t3 @t1))) % 0.31/0.56 (define @t6 () (@list @t3)) % 0.31/0.56 (define @t7 () (forall @t6 @t5)) % 0.31/0.56 (define @t8 () (_ tptp.g @t1)) % 0.31/0.56 (define @t9 () (and (= @t8 @t1) @t7)) % 0.31/0.56 (define @t10 () (=> @t9 (= @t2 @t1))) % 0.31/0.56 (define @t11 () (@list @t1)) % 0.31/0.56 (define @t12 () (forall @t11 @t10)) % 0.31/0.56 (define @t13 () (_ tptp.g @t2)) % 0.31/0.56 (define @t14 () (lambda @t11 @t13)) % 0.31/0.56 (define @t15 () (_ tptp.f @t8)) % 0.31/0.56 (define @t16 () (lambda @t11 @t15)) % 0.31/0.56 (define @t17 () (= @t16 @t14)) % 0.31/0.56 (define @t18 () (=> @t17 @t12)) % 0.31/0.56 (define @t19 () (not @t18)) % 0.31/0.56 (define @t20 () (tptp.f @t1)) % 0.31/0.56 (define @t21 () (= @t1 @t3)) % 0.31/0.56 (define @t22 () (tptp.g @t3)) % 0.31/0.56 (define @t23 () (not (= @t3 @t22))) % 0.31/0.56 (define @t24 () (forall @t6 (or @t23 @t21))) % 0.31/0.56 (define @t25 () (not @t24)) % 0.31/0.56 (define @t26 () (tptp.g @t1)) % 0.31/0.56 (define @t27 () (forall @t11 (or (not (= @t1 @t26)) @t25 (= @t1 @t20)))) % 0.31/0.56 (define @t28 () (@purify @t16)) % 0.31/0.56 (define @t29 () (@purify @t14)) % 0.31/0.56 (define @t30 () (=> @t17 @t27)) % 0.31/0.56 (define @t31 () (= @t1 @t2)) % 0.31/0.56 (define @t32 () (= @t1 @t8)) % 0.31/0.56 (define @t33 () (not @t32)) % 0.31/0.56 (define @t34 () (or @t33 @t25 @t31)) % 0.31/0.56 (define @t35 () (and @t32 @t24)) % 0.31/0.56 (define @t36 () (= @t3 @t4)) % 0.31/0.56 (define @t37 () (not @t36)) % 0.31/0.56 (define @t38 () (or @t37 @t21)) % 0.31/0.56 (define @t39 () (@quantifiers_skolemize @t27 0)) % 0.31/0.56 (define @t40 () (tptp.f @t39)) % 0.31/0.56 (define @t41 () (= @t39 @t40)) % 0.31/0.56 (define @t42 () (forall @t6 (or @t23 (= @t3 @t39)))) % 0.31/0.56 (define @t43 () (not @t42)) % 0.31/0.56 (define @t44 () (tptp.g @t39)) % 0.31/0.56 (define @t45 () (= @t39 @t44)) % 0.31/0.56 (define @t46 () (not @t45)) % 0.31/0.56 (define @t47 () (or @t46 @t43 @t41)) % 0.31/0.56 (define @t48 () (not @t47)) % 0.31/0.56 (define @t49 () (not @t27)) % 0.31/0.56 (define @t50 () (or @t23 (= @t39 @t3))) % 0.31/0.56 (define @t51 () (forall @t6 @t50)) % 0.31/0.56 (define @t52 () (not @t51)) % 0.31/0.56 (define @t53 () (or @t46 @t52 @t41)) % 0.31/0.56 (define @t54 () (not @t53)) % 0.31/0.56 (define @t55 () (@list true)) % 0.31/0.56 (define @t56 () (@list @t47)) % 0.31/0.56 (define @t57 () (tptp.g @t20)) % 0.31/0.56 (define @t58 () (tptp.f @t26)) % 0.31/0.56 (define @t59 () (= @t15 @t13)) % 0.31/0.56 (define @t60 () (forall @t11 (= @t13 @t15))) % 0.31/0.56 (define @t61 () (= @t29 @t28)) % 0.31/0.56 (define @t62 () (=> @t61 @t60)) % 0.31/0.56 (define @t63 () (tptp.g @t40)) % 0.31/0.56 (define @t64 () (= @t39 @t63)) % 0.31/0.56 (define @t65 () (= @t63 (tptp.g @t63))) % 0.31/0.56 (define @t66 () (not @t65)) % 0.31/0.56 (define @t67 () (or @t66 @t64)) % 0.31/0.56 (define @t68 () (not @t67)) % 0.31/0.56 (define @t69 () (or @t66 (= @t63 @t39))) % 0.31/0.56 (assume @p1 @t19) % 0.31/0.56 (assume @p2 true) % 0.31/0.56 (step @p3 :rule refl :args (@t27)) % 0.31/0.56 (step @p4 :rule eq-symm :args (@t28 @t29)) % 0.31/0.56 (step @p5 :rule eq-refl :args (@t14)) % 0.31/0.56 (step @p6 :rule skolem_intro :args (@t29)) % 0.31/0.56 (step @p7 :rule refl :args (@t14)) % 0.31/0.56 (step @p8 :rule cong :premises (@p7 @p6) :args ((= @t14 @t29))) % 0.31/0.56 (step @p9 :rule trans :premises (@p8 @p5)) % 0.31/0.56 (step @p10 :rule true_elim :premises (@p9)) % 0.31/0.56 (step @p11 :rule eq-refl :args (@t16)) % 0.31/0.56 (step @p12 :rule skolem_intro :args (@t28)) % 0.31/0.56 (step @p13 :rule refl :args (@t16)) % 0.31/0.56 (step @p14 :rule cong :premises (@p13 @p12) :args ((= @t16 @t28))) % 0.31/0.56 (step @p15 :rule trans :premises (@p14 @p11)) % 0.31/0.56 (step @p16 :rule true_elim :premises (@p15)) % 0.31/0.56 (step @p17 :rule cong :premises (@p16 @p10) :args (@t17)) % 0.31/0.56 (step @p18 :rule trans :premises (@p17 @p4)) % 0.31/0.56 (step @p19 :rule cong :premises (@p18 @p3) :args (@t30)) % 0.31/0.56 (step @p20 :rule cong :premises (@p19) :args ((not @t30))) % 0.31/0.56 (step @p21 :rule refl :args (@t20)) % 0.31/0.56 (step @p22 :rule refl :args (@t2)) % 0.31/0.56 (step @p23 :rule cong :premises (@p22 @p21) :args ((= @t2 @t20))) % 0.31/0.56 (step @p24 :rule symm :premises (@p23)) % 0.31/0.56 (step @p25 :rule eq_resolve :premises (@p22 @p24)) % 0.31/0.56 (step @p26 :rule refl :args (@t1)) % 0.31/0.56 (step @p27 :rule cong :premises (@p26 @p25) :args (@t31)) % 0.31/0.56 (step @p28 :rule refl :args (@t25)) % 0.31/0.56 (step @p29 :rule refl :args (@t26)) % 0.31/0.56 (step @p30 :rule refl :args (@t8)) % 0.31/0.56 (step @p31 :rule cong :premises (@p30 @p29) :args ((= @t8 @t26))) % 0.31/0.56 (step @p32 :rule symm :premises (@p31)) % 0.31/0.56 (step @p33 :rule eq_resolve :premises (@p30 @p32)) % 0.31/0.56 (step @p34 :rule cong :premises (@p26 @p33) :args (@t32)) % 0.31/0.56 (step @p35 :rule cong :premises (@p34) :args (@t33)) % 0.31/0.56 (step @p36 :rule nary_cong :premises (@p35 @p28 @p27) :args (@t34)) % 0.31/0.56 (step @p37 :rule cong :premises (@p36) :args ((forall @t11 @t34))) % 0.31/0.56 (step @p38 :rule aci_norm :args ((= (or (or @t33 @t25) @t31) @t34))) % 0.31/0.56 (step @p39 :rule refl :args (@t31)) % 0.31/0.56 (step @p40 :rule bool-and-de-morgan :args (@t32 @t24 true)) % 0.31/0.56 (step @p41 :rule nary_cong :premises (@p40 @p39) :args ((or (not @t35) @t31))) % 0.31/0.56 (step @p42 :rule trans :premises (@p41 @p38)) % 0.31/0.56 (step @p43 :rule bool-impl-elim :args (@t35 @t31)) % 0.31/0.56 (step @p44 :rule trans :premises (@p43 @p42)) % 0.31/0.56 (step @p45 :rule cong :premises (@p44) :args ((forall @t11 (=> @t35 @t31)))) % 0.31/0.56 (step @p46 :rule trans :premises (@p45 @p37)) % 0.31/0.56 (step @p47 :rule eq-symm :args (@t2 @t1)) % 0.31/0.56 (step @p48 :rule refl :args (@t21)) % 0.31/0.56 (step @p49 :rule refl :args (@t22)) % 0.31/0.56 (step @p50 :rule refl :args (@t4)) % 0.31/0.56 (step @p51 :rule cong :premises (@p50 @p49) :args ((= @t4 @t22))) % 0.31/0.56 (step @p52 :rule symm :premises (@p51)) % 0.31/0.56 (step @p53 :rule eq_resolve :premises (@p50 @p52)) % 0.31/0.56 (step @p54 :rule refl :args (@t3)) % 0.31/0.56 (step @p55 :rule cong :premises (@p54 @p53) :args (@t36)) % 0.31/0.56 (step @p56 :rule cong :premises (@p55) :args (@t37)) % 0.31/0.56 (step @p57 :rule nary_cong :premises (@p56 @p48) :args (@t38)) % 0.31/0.56 (step @p58 :rule cong :premises (@p57) :args ((forall @t6 @t38))) % 0.31/0.56 (step @p59 :rule bool-impl-elim :args (@t36 @t21)) % 0.31/0.56 (step @p60 :rule cong :premises (@p59) :args ((forall @t6 (=> @t36 @t21)))) % 0.31/0.56 (step @p61 :rule trans :premises (@p60 @p58)) % 0.31/0.56 (step @p62 :rule eq-symm :args (@t3 @t1)) % 0.31/0.56 (step @p63 :rule eq-symm :args (@t4 @t3)) % 0.31/0.56 (step @p64 :rule cong :premises (@p63 @p62) :args (@t5)) % 0.31/0.56 (step @p65 :rule cong :premises (@p64) :args (@t7)) % 0.31/0.56 (step @p66 :rule trans :premises (@p65 @p61)) % 0.31/0.56 (step @p67 :rule eq-symm :args (@t8 @t1)) % 0.31/0.56 (step @p68 :rule nary_cong :premises (@p67 @p66) :args (@t9)) % 0.31/0.56 (step @p69 :rule cong :premises (@p68 @p47) :args (@t10)) % 0.31/0.56 (step @p70 :rule cong :premises (@p69) :args (@t12)) % 0.31/0.56 (step @p71 :rule trans :premises (@p70 @p46)) % 0.31/0.56 (step @p72 :rule refl :args (@t17)) % 0.31/0.56 (step @p73 :rule cong :premises (@p72 @p71) :args (@t18)) % 0.31/0.56 (step @p74 :rule cong :premises (@p73) :args (@t19)) % 0.31/0.56 (step @p75 :rule trans :premises (@p74 @p20)) % 0.31/0.56 (step @p76 :rule eq_resolve :premises (@p1 @p75)) % 0.31/0.56 (step @p77 :rule not_implies_elim2 :premises (@p76)) % 0.31/0.56 (step @p78 :rule refl :args (@t48)) % 0.31/0.56 (step @p79 :rule bool-double-not-elim :args (@t27)) % 0.31/0.56 (step @p80 :rule nary_cong :premises (@p79 @p78) :args ((or (not @t49) @t48))) % 0.31/0.56 (step @p81 :rule refl :args (@t41)) % 0.31/0.56 (step @p82 :rule eq-symm :args (@t39 @t3)) % 0.31/0.56 (step @p83 :rule refl :args (@t23)) % 0.31/0.56 (step @p84 :rule nary_cong :premises (@p83 @p82) :args (@t50)) % 0.31/0.56 (step @p85 :rule cong :premises (@p84) :args (@t51)) % 0.31/0.56 (step @p86 :rule cong :premises (@p85) :args (@t52)) % 0.31/0.56 (step @p87 :rule refl :args (@t46)) % 0.31/0.56 (step @p88 :rule nary_cong :premises (@p87 @p86 @p81) :args (@t53)) % 0.31/0.56 (step @p89 :rule cong :premises (@p88) :args (@t54)) % 0.31/0.56 (step @p90 :rule refl :args (@t49)) % 0.31/0.56 (step @p91 :rule cong :premises (@p90 @p89) :args ((=> @t49 @t54))) % 0.31/0.56 (assume-push @p177 @t49) % 0.31/0.56 (step @p93 :rule skolemize :premises (@p77)) % 0.31/0.56 (step-pop @p178 :rule scope :premises (@p93)) % 0.31/0.56 (step @p94 :rule process_scope :premises (@p178) :args (@t54)) % 0.31/0.56 (step @p96 :rule eq_resolve :premises (@p94 @p91)) % 0.31/0.56 (step @p97 :rule implies_elim :premises (@p96)) % 0.31/0.56 (step @p98 :rule eq_resolve :premises (@p97 @p80)) % 0.31/0.56 (step @p99 :rule chain_m_resolution :premises (@p98 @p77) :args (@t48 @t55 (@list @t27))) % 0.31/0.56 (step @p100 :rule bool-double-not-elim :args (@t42)) % 0.31/0.56 (step @p101 :rule refl :args (@t47)) % 0.31/0.56 (step @p102 :rule nary_cong :premises (@p101 @p100) :args ((or @t47 (not @t43)))) % 0.31/0.56 (step @p103 :rule cnf_or_neg :args (@t47 1)) % 0.31/0.56 (step @p104 :rule eq_resolve :premises (@p103 @p102)) % 0.31/0.56 (step @p105 :rule reordering :premises (@p104) :args ((or @t42 @t47))) % 0.31/0.56 (step @p106 :rule chain_m_resolution :premises (@p105 @p99) :args (@t42 @t55 @t56)) % 0.31/0.56 (step @p107 :rule cnf_or_neg :args (@t47 2)) % 0.31/0.56 (step @p108 :rule chain_m_resolution :premises (@p107 @p99) :args ((not @t41) @t55 @t56)) % 0.31/0.56 (step @p109 :rule false_intro :premises (@p108)) % 0.31/0.56 (step @p110 :rule bool-double-not-elim :args (@t45)) % 0.33/0.56 (step @p111 :rule nary_cong :premises (@p101 @p110) :args ((or @t47 (not @t46)))) % 0.33/0.56 (step @p112 :rule cnf_or_neg :args (@t47 0)) % 0.33/0.56 (step @p113 :rule eq_resolve :premises (@p112 @p111)) % 0.33/0.56 (step @p114 :rule reordering :premises (@p113) :args ((or @t45 @t47))) % 0.33/0.56 (step @p115 :rule chain_m_resolution :premises (@p114 @p99) :args (@t45 @t55 @t56)) % 0.33/0.56 (step @p116 :rule symm :premises (@p115)) % 0.33/0.56 (step @p117 :rule cong :premises (@p116) :args ((tptp.f @t44))) % 0.33/0.56 (step @p118 :rule not_implies_elim1 :premises (@p76)) % 0.33/0.56 (step @p119 :rule refl :args ((tptp.g @t2))) % 0.33/0.56 (step @p120 :rule cong :premises (@p21) :args (@t57)) % 0.33/0.56 (step @p121 :rule trans :premises (@p120 @p119)) % 0.33/0.56 (step @p122 :rule refl :args (tptp.g)) % 0.33/0.56 (step @p123 :rule ho_cong :premises (@p122 @p21)) % 0.33/0.56 (step @p124 :rule cong :premises (@p123 @p121) :args ((= (_ tptp.g @t20) @t57))) % 0.33/0.56 (step @p125 :rule symm :premises (@p124)) % 0.33/0.56 (step @p126 :rule refl :args (@t13)) % 0.33/0.56 (step @p127 :rule eq_resolve :premises (@p126 @p125)) % 0.33/0.56 (step @p128 :rule ho_cong :premises (@p122 @p25)) % 0.33/0.56 (step @p129 :rule trans :premises (@p128 @p127)) % 0.33/0.56 (step @p130 :rule refl :args ((tptp.f @t8))) % 0.33/0.56 (step @p131 :rule cong :premises (@p29) :args (@t58)) % 0.33/0.56 (step @p132 :rule trans :premises (@p131 @p130)) % 0.33/0.56 (step @p133 :rule refl :args (tptp.f)) % 0.33/0.56 (step @p134 :rule ho_cong :premises (@p133 @p29)) % 0.33/0.56 (step @p135 :rule cong :premises (@p134 @p132) :args ((= (_ tptp.f @t26) @t58))) % 0.33/0.56 (step @p136 :rule symm :premises (@p135)) % 0.33/0.56 (step @p137 :rule refl :args (@t15)) % 0.33/0.56 (step @p138 :rule eq_resolve :premises (@p137 @p136)) % 0.33/0.56 (step @p139 :rule ho_cong :premises (@p133 @p33)) % 0.33/0.56 (step @p140 :rule trans :premises (@p139 @p138)) % 0.33/0.56 (step @p141 :rule cong :premises (@p140 @p129) :args (@t59)) % 0.33/0.56 (step @p142 :rule cong :premises (@p141) :args ((forall @t11 @t59))) % 0.33/0.56 (step @p143 :rule eq-symm :args (@t13 @t15)) % 0.33/0.56 (step @p144 :rule cong :premises (@p143) :args (@t60)) % 0.33/0.56 (step @p145 :rule trans :premises (@p144 @p142)) % 0.33/0.56 (step @p146 :rule refl :args (@t61)) % 0.33/0.56 (step @p147 :rule cong :premises (@p146 @p145) :args (@t62)) % 0.33/0.56 ; WARNING: add trust step for TRUST % 0.33/0.56 ; trust TRUST THEORY_LEMMA % 0.33/0.56 (step @p148 :rule trust :premises () :args (@t62)) % 0.33/0.56 (step @p149 :rule eq_resolve :premises (@p148 @p147)) % 0.33/0.56 (step @p150 :rule implies_elim :premises (@p149)) % 0.33/0.56 (step @p151 :rule chain_m_resolution :premises (@p150 @p118) :args ((forall @t11 (= @t58 @t57)) (@list false) (@list @t61))) % 0.33/0.56 (step @p152 :rule instantiate :premises (@p151) :args ((@list @t39))) % 0.33/0.56 (step @p153 :rule symm :premises (@p152)) % 0.33/0.56 (step @p154 :rule trans :premises (@p153 @p117)) % 0.33/0.56 (step @p155 :rule refl :args (@t39)) % 0.33/0.56 (step @p156 :rule cong :premises (@p155 @p154) :args (@t64)) % 0.33/0.56 (step @p157 :rule trans :premises (@p156 @p109)) % 0.33/0.56 (step @p158 :rule false_elim :premises (@p157)) % 0.33/0.56 (step @p159 :rule cong :premises (@p115) :args (@t40)) % 0.33/0.56 (step @p160 :rule trans :premises (@p159 @p152)) % 0.33/0.56 (step @p161 :rule cong :premises (@p160) :args (@t63)) % 0.33/0.56 (step @p162 :rule cnf_or_pos :args (@t67)) % 0.33/0.56 (step @p163 :rule reordering :premises (@p162) :args ((or @t66 @t64 @t68))) % 0.33/0.56 (step @p164 :rule chain_m_resolution :premises (@p163 @p161 @p158) :args (@t68 (@list false true) (@list @t65 @t64))) % 0.33/0.56 (step @p165 :rule eq-symm :args (@t63 @t39)) % 0.33/0.56 (step @p166 :rule refl :args (@t66)) % 0.33/0.56 (step @p167 :rule nary_cong :premises (@p166 @p165) :args (@t69)) % 0.33/0.56 (step @p168 :rule refl :args (@t42)) % 0.33/0.56 (step @p169 :rule cong :premises (@p168 @p167) :args ((=> @t42 @t69))) % 0.33/0.56 (assume-push @p179 @t42) % 0.33/0.56 (step @p171 :rule instantiate :premises (@p106) :args ((@list @t63))) % 0.33/0.56 (step-pop @p180 :rule scope :premises (@p171)) % 0.33/0.56 (step @p172 :rule process_scope :premises (@p180) :args (@t69)) % 0.33/0.56 (step @p174 :rule eq_resolve :premises (@p172 @p169)) % 0.33/0.56 (step @p175 :rule implies_elim :premises (@p174)) % 0.33/0.56 (step @p176 false :rule chain_m_resolution :premises (@p175 @p164 @p106) :args (false (@list true false) (@list @t67 @t42))) % 0.33/0.56 ) % 0.33/0.56 % SZS output end Proof % 0.33/0.56 % cvc5 exiting %------------------------------------------------------------------------------