%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYO277^5 : 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 : n011.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 09:12:21 AM UTC 2026 % Result : Theorem 0.53s 0.73s % Output : Proof 0.53s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SYO277^5 : TPTP v9.2.1. Released v4.0.0. % 0.00/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n011.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 00:01:35 EDT 2026 % 0.17/0.34 % CPUTime : % 0.30/0.48 %----Proving TH0 % 0.53/0.73 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.53/0.73 % SZS status Theorem % 0.53/0.73 % SZS output start Proof % 0.53/0.73 ( % 0.53/0.73 (declare-sort $$unsorted 0) % 0.53/0.73 (define @t1 () (@var "Y" $$unsorted)) % 0.53/0.73 (define @t2 () (@var "X" $$unsorted)) % 0.53/0.73 (define @t3 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.53/0.73 (define @t4 () (_ (_ @t3 @t2) @t1)) % 0.53/0.73 (define @t5 () (@var "Z" $$unsorted)) % 0.53/0.73 (define @t6 () (_ (_ @t3 @t5) @t5)) % 0.53/0.73 (define @t7 () (@list @t5)) % 0.53/0.73 (define @t8 () (forall @t7 @t6)) % 0.53/0.73 (define @t9 () (=> @t8 @t4)) % 0.53/0.73 (define @t10 () (@list @t3)) % 0.53/0.73 (define @t11 () (forall @t10 @t9)) % 0.53/0.73 (define @t12 () (@var "Xq" (-> $$unsorted Bool))) % 0.53/0.73 (define @t13 () (_ @t12 @t1)) % 0.53/0.73 (define @t14 () (_ @t12 @t2)) % 0.53/0.73 (define @t15 () (@list @t12)) % 0.53/0.73 (define @t16 () (forall @t15 (=> @t14 @t13))) % 0.53/0.73 (define @t17 () (= @t16 @t11)) % 0.53/0.73 (define @t18 () (@list @t2 @t1)) % 0.53/0.73 (define @t19 () (forall @t18 @t17)) % 0.53/0.73 (define @t20 () (not @t19)) % 0.53/0.73 (define @t21 () (_ @t3 @t2 @t1)) % 0.53/0.73 (define @t22 () (_ @t3 @t5 @t5)) % 0.53/0.73 (define @t23 () (forall @t7 @t22)) % 0.53/0.73 (define @t24 () (not @t23)) % 0.53/0.73 (define @t25 () (or @t24 @t4)) % 0.53/0.73 (define @t26 () (_ @t12 @t1)) % 0.53/0.73 (define @t27 () (_ @t12 @t2)) % 0.53/0.73 (define @t28 () (not @t14)) % 0.53/0.73 (define @t29 () (or @t28 @t13)) % 0.53/0.73 (define @t30 () (forall @t18 (= (forall @t15 (or (not @t27) @t26)) (forall @t10 (or @t24 @t21))))) % 0.53/0.73 (define @t31 () (@quantifiers_skolemize @t30 1)) % 0.53/0.73 (define @t32 () (@quantifiers_skolemize @t30 0)) % 0.53/0.73 (define @t33 () (forall @t10 (or @t24 (_ @t3 @t32 @t31)))) % 0.53/0.73 (define @t34 () (forall @t15 (or (not (_ @t12 @t32)) (_ @t12 @t31)))) % 0.53/0.73 (define @t35 () (= @t34 @t33)) % 0.53/0.73 (define @t36 () (@quantifiers_skolemize @t33 0)) % 0.53/0.73 (define @t37 () (_ @t36 @t32 @t31)) % 0.53/0.73 (define @t38 () (_ @t36 @t32)) % 0.53/0.73 (define @t39 () (_ @t38 @t31)) % 0.53/0.73 (define @t40 () (_ @t36 @t32 @t32)) % 0.53/0.73 (define @t41 () (_ @t38 @t32)) % 0.53/0.73 (define @t42 () (not @t41)) % 0.53/0.73 (define @t43 () (or @t42 @t39)) % 0.53/0.73 (define @t44 () (_ @t38 @t31)) % 0.53/0.73 (define @t45 () (_ @t38 @t32)) % 0.53/0.73 (define @t46 () (not @t45)) % 0.53/0.73 (define @t47 () (or @t46 @t44)) % 0.53/0.73 (define @t48 () (forall @t7 (_ @t36 @t5 @t5))) % 0.53/0.73 (define @t49 () (not @t48)) % 0.53/0.73 (define @t50 () (or @t49 @t37)) % 0.53/0.73 (define @t51 () (not @t50)) % 0.53/0.73 (define @t52 () (not @t33)) % 0.53/0.73 (define @t53 () (not @t40)) % 0.53/0.73 (define @t54 () (or @t53 @t37)) % 0.53/0.73 (define @t55 () (not @t34)) % 0.53/0.73 (define @t56 () (@quantifiers_skolemize @t34 0)) % 0.53/0.73 (define @t57 () (_ @t56 @t31)) % 0.53/0.73 (define @t58 () (_ @t56 @t32)) % 0.53/0.73 (define @t59 () (not @t58)) % 0.53/0.73 (define @t60 () (or @t59 @t57)) % 0.53/0.73 (define @t61 () (not @t60)) % 0.53/0.73 (define @t62 () (@list true)) % 0.53/0.73 (define @t63 () (@list @t60)) % 0.53/0.73 (define @t64 () (not @t57)) % 0.53/0.73 (define @t65 () (= @t32 @t31)) % 0.53/0.73 (define @t66 () (@var "BOUND_VARIABLE_51409" $$unsorted)) % 0.53/0.73 (define @t67 () (@var "BOUND_VARIABLE_51408" $$unsorted)) % 0.53/0.73 (define @t68 () (lambda (@list @t67 @t66) (= @t67 @t66))) % 0.53/0.73 (define @t69 () (_ @t68 @t32 @t31)) % 0.53/0.73 (define @t70 () (_ @t68 @t5 @t5)) % 0.53/0.73 (define @t71 () (forall @t7 @t70)) % 0.53/0.73 (define @t72 () (not @t71)) % 0.53/0.73 (define @t73 () (or @t72 @t69)) % 0.53/0.73 (define @t74 () (not @t65)) % 0.53/0.73 (define @t75 () (and @t58 @t65 @t64)) % 0.53/0.73 (assume @p1 @t20) % 0.53/0.73 (assume @p2 true) % 0.53/0.73 (step @p3 :rule refl :args (@t21)) % 0.53/0.73 (step @p4 :rule refl :args (@t4)) % 0.53/0.73 (step @p5 :rule cong :premises (@p4 @p3) :args ((= @t4 @t21))) % 0.53/0.73 (step @p6 :rule symm :premises (@p5)) % 0.53/0.73 (step @p7 :rule eq_resolve :premises (@p4 @p6)) % 0.53/0.73 (step @p8 :rule refl :args (@t24)) % 0.53/0.73 (step @p9 :rule nary_cong :premises (@p8 @p7) :args (@t25)) % 0.53/0.73 (step @p10 :rule cong :premises (@p9) :args ((forall @t10 @t25))) % 0.53/0.73 (step @p11 :rule bool-impl-elim :args (@t23 @t4)) % 0.53/0.73 (step @p12 :rule cong :premises (@p11) :args ((forall @t10 (=> @t23 @t4)))) % 0.53/0.73 (step @p13 :rule trans :premises (@p12 @p10)) % 0.53/0.73 (step @p14 :rule refl :args (@t4)) % 0.53/0.73 (step @p15 :rule refl :args (@t22)) % 0.53/0.73 (step @p16 :rule refl :args (@t6)) % 0.53/0.73 (step @p17 :rule cong :premises (@p16 @p15) :args ((= @t6 @t22))) % 0.53/0.73 (step @p18 :rule symm :premises (@p17)) % 0.53/0.73 (step @p19 :rule eq_resolve :premises (@p16 @p18)) % 0.53/0.73 (step @p20 :rule cong :premises (@p19) :args (@t8)) % 0.53/0.73 (step @p21 :rule cong :premises (@p20 @p14) :args (@t9)) % 0.53/0.73 (step @p22 :rule cong :premises (@p21) :args (@t11)) % 0.53/0.73 (step @p23 :rule trans :premises (@p22 @p13)) % 0.53/0.73 (step @p24 :rule refl :args (@t26)) % 0.53/0.73 (step @p25 :rule refl :args (@t13)) % 0.53/0.73 (step @p26 :rule cong :premises (@p25 @p24) :args ((= @t13 @t26))) % 0.53/0.73 (step @p27 :rule symm :premises (@p26)) % 0.53/0.73 (step @p28 :rule eq_resolve :premises (@p25 @p27)) % 0.53/0.73 (step @p29 :rule refl :args (@t27)) % 0.53/0.73 (step @p30 :rule refl :args (@t14)) % 0.53/0.73 (step @p31 :rule cong :premises (@p30 @p29) :args ((= @t14 @t27))) % 0.53/0.73 (step @p32 :rule symm :premises (@p31)) % 0.53/0.73 (step @p33 :rule eq_resolve :premises (@p30 @p32)) % 0.53/0.73 (step @p34 :rule cong :premises (@p33) :args (@t28)) % 0.53/0.73 (step @p35 :rule nary_cong :premises (@p34 @p28) :args (@t29)) % 0.53/0.73 (step @p36 :rule cong :premises (@p35) :args ((forall @t15 @t29))) % 0.53/0.73 (step @p37 :rule bool-impl-elim :args (@t14 @t13)) % 0.53/0.73 (step @p38 :rule cong :premises (@p37) :args (@t16)) % 0.53/0.73 (step @p39 :rule trans :premises (@p38 @p36)) % 0.53/0.73 (step @p40 :rule cong :premises (@p39 @p23) :args (@t17)) % 0.53/0.73 (step @p41 :rule cong :premises (@p40) :args (@t19)) % 0.53/0.73 (step @p42 :rule cong :premises (@p41) :args (@t20)) % 0.53/0.73 (step @p43 :rule eq_resolve :premises (@p1 @p42)) % 0.53/0.73 (step @p44 :rule skolemize :premises (@p43)) % 0.53/0.73 (step @p45 :rule cnf_equiv_neg2 :args (@t35)) % 0.53/0.73 (step @p46 :rule refl :args (@t37)) % 0.53/0.73 (step @p47 :rule refl :args (@t39)) % 0.53/0.73 (step @p48 :rule cong :premises (@p47 @p46) :args ((= @t39 @t37))) % 0.53/0.73 (step @p49 :rule symm :premises (@p48)) % 0.53/0.73 (step @p50 :rule eq_resolve :premises (@p47 @p49)) % 0.53/0.73 (step @p51 :rule refl :args (@t40)) % 0.53/0.73 (step @p52 :rule refl :args (@t41)) % 0.53/0.73 (step @p53 :rule cong :premises (@p52 @p51) :args ((= @t41 @t40))) % 0.53/0.73 (step @p54 :rule symm :premises (@p53)) % 0.53/0.73 (step @p55 :rule eq_resolve :premises (@p52 @p54)) % 0.53/0.73 (step @p56 :rule cong :premises (@p55) :args (@t42)) % 0.53/0.73 (step @p57 :rule nary_cong :premises (@p56 @p50) :args (@t43)) % 0.53/0.73 (step @p58 :rule refl :args (@t34)) % 0.53/0.73 (step @p59 :rule cong :premises (@p58 @p57) :args ((=> @t34 @t43))) % 0.53/0.73 (step @p60 :rule refl :args (@t44)) % 0.53/0.73 (step @p61 :rule refl :args (@t45)) % 0.53/0.73 (step @p62 :rule cong :premises (@p61) :args (@t46)) % 0.53/0.73 (step @p63 :rule nary_cong :premises (@p62 @p60) :args (@t47)) % 0.53/0.73 (step @p64 :rule cong :premises (@p58 @p63) :args ((=> @t34 @t47))) % 0.53/0.73 (assume-push @p172 @t34) % 0.53/0.73 (step @p66 :rule instantiate :premises (@p172) :args ((@list @t38))) % 0.53/0.73 (step-pop @p173 :rule scope :premises (@p66)) % 0.53/0.73 (step @p67 :rule process_scope :premises (@p173) :args (@t47)) % 0.53/0.73 (step @p69 :rule eq_resolve :premises (@p67 @p64)) % 0.53/0.73 (step @p70 :rule eq_resolve :premises (@p69 @p59)) % 0.53/0.73 (step @p71 :rule implies_elim :premises (@p70)) % 0.53/0.73 (step @p72 :rule refl :args (@t51)) % 0.53/0.73 (step @p73 :rule bool-double-not-elim :args (@t33)) % 0.53/0.73 (step @p74 :rule nary_cong :premises (@p73 @p72) :args ((or (not @t52) @t51))) % 0.53/0.73 (assume-push @p174 @t52) % 0.53/0.73 (step @p76 :rule skolemize :premises (@p174)) % 0.53/0.73 (step-pop @p175 :rule scope :premises (@p76)) % 0.53/0.73 (step @p77 :rule process_scope :premises (@p175) :args (@t51)) % 0.53/0.73 (step @p79 :rule implies_elim :premises (@p77)) % 0.53/0.73 (step @p80 :rule eq_resolve :premises (@p79 @p74)) % 0.53/0.73 (step @p81 :rule bool-double-not-elim :args (@t48)) % 0.53/0.73 (step @p82 :rule refl :args (@t50)) % 0.53/0.73 (step @p83 :rule nary_cong :premises (@p82 @p81) :args ((or @t50 (not @t49)))) % 0.53/0.73 (step @p84 :rule cnf_or_neg :args (@t50 0)) % 0.53/0.73 (step @p85 :rule eq_resolve :premises (@p84 @p83)) % 0.53/0.73 (step @p86 :rule reordering :premises (@p85) :args ((or @t48 @t50))) % 0.53/0.73 (step @p87 :rule cnf_or_neg :args (@t50 1)) % 0.53/0.73 (step @p88 :rule cnf_or_pos :args (@t54)) % 0.53/0.73 (step @p89 :rule reordering :premises (@p88) :args ((or @t37 @t53 (not @t54)))) % 0.53/0.73 (assume-push @p176 @t48) % 0.53/0.73 (step @p91 :rule instantiate :premises (@p176) :args ((@list @t32))) % 0.53/0.73 (step-pop @p177 :rule scope :premises (@p91)) % 0.53/0.73 (step @p92 :rule process_scope :premises (@p177) :args (@t40)) % 0.53/0.73 (step @p94 :rule implies_elim :premises (@p92)) % 0.53/0.73 (step @p95 :rule chain_m_resolution :premises (@p94 @p89 @p87 @p86 @p80 @p71 @p45 @p44) :args (@t55 (@list true true false true false true true) (@list @t40 @t37 @t48 @t50 @t54 @t33 @t35))) % 0.53/0.73 (step @p96 :rule refl :args (@t61)) % 0.53/0.73 (step @p97 :rule bool-double-not-elim :args (@t34)) % 0.53/0.73 (step @p98 :rule nary_cong :premises (@p97 @p96) :args ((or (not @t55) @t61))) % 0.53/0.73 (assume-push @p178 @t55) % 0.53/0.73 (step @p100 :rule skolemize :premises (@p178)) % 0.53/0.73 (step-pop @p179 :rule scope :premises (@p100)) % 0.53/0.73 (step @p101 :rule process_scope :premises (@p179) :args (@t61)) % 0.53/0.73 (step @p103 :rule implies_elim :premises (@p101)) % 0.53/0.73 (step @p104 :rule eq_resolve :premises (@p103 @p98)) % 0.53/0.73 (step @p105 :rule chain_m_resolution :premises (@p104 @p95) :args (@t61 @t62 (@list @t34))) % 0.53/0.73 (step @p106 :rule bool-double-not-elim :args (@t58)) % 0.53/0.73 (step @p107 :rule refl :args (@t60)) % 0.53/0.73 (step @p108 :rule nary_cong :premises (@p107 @p106) :args ((or @t60 (not @t59)))) % 0.53/0.73 (step @p109 :rule cnf_or_neg :args (@t60 0)) % 0.53/0.73 (step @p110 :rule eq_resolve :premises (@p109 @p108)) % 0.53/0.73 (step @p111 :rule reordering :premises (@p110) :args ((or @t58 @t60))) % 0.53/0.73 (step @p112 :rule chain_m_resolution :premises (@p111 @p105) :args (@t58 @t62 @t63)) % 0.53/0.73 (step @p113 :rule cnf_or_neg :args (@t60 1)) % 0.53/0.73 (step @p114 :rule chain_m_resolution :premises (@p113 @p105) :args (@t64 @t62 @t63)) % 0.53/0.73 (step @p115 :rule cnf_equiv_neg1 :args (@t35)) % 0.53/0.73 (step @p116 :rule reordering :premises (@p115) :args ((or @t34 @t33 @t35))) % 0.53/0.73 (step @p117 :rule chain_m_resolution :premises (@p116 @p95 @p44) :args (@t33 (@list true true) (@list @t34 @t35))) % 0.53/0.73 (step @p118 :rule aci_norm :args ((= (or false @t65) @t65))) % 0.53/0.73 (step @p119 :rule beta-reduce :args ((= @t69 @t65))) % 0.53/0.73 (step @p120 :rule evaluate :args ((not true))) % 0.53/0.73 (step @p121 :rule quant-unused-vars :args ((= (forall @t7 true) true))) % 0.53/0.73 (step @p122 :rule eq-refl :args (@t5)) % 0.53/0.73 (step @p123 :rule beta-reduce :args ((= @t70 (= @t5 @t5)))) % 0.53/0.73 (step @p124 :rule trans :premises (@p123 @p122)) % 0.53/0.73 (step @p125 :rule cong :premises (@p124) :args (@t71)) % 0.53/0.73 (step @p126 :rule trans :premises (@p125 @p121)) % 0.53/0.73 (step @p127 :rule cong :premises (@p126) :args (@t72)) % 0.53/0.73 (step @p128 :rule trans :premises (@p127 @p120)) % 0.53/0.73 (step @p129 :rule nary_cong :premises (@p128 @p119) :args (@t73)) % 0.53/0.73 (step @p130 :rule trans :premises (@p129 @p118)) % 0.53/0.73 (step @p131 :rule refl :args (@t33)) % 0.53/0.73 (step @p132 :rule cong :premises (@p131 @p130) :args ((=> @t33 @t73))) % 0.53/0.73 (assume-push @p180 @t33) % 0.53/0.73 (step @p134 :rule instantiate :premises (@p180) :args ((@list @t68))) % 0.53/0.73 (step-pop @p181 :rule scope :premises (@p134)) % 0.53/0.73 (step @p135 :rule process_scope :premises (@p181) :args (@t73)) % 0.53/0.73 (step @p137 :rule eq_resolve :premises (@p135 @p132)) % 0.53/0.73 (step @p138 :rule implies_elim :premises (@p137)) % 0.53/0.73 (step @p139 :rule chain_m_resolution :premises (@p138 @p117) :args (@t65 (@list false) (@list @t33))) % 0.53/0.73 (step @p140 :rule refl :args (@t74)) % 0.53/0.73 (step @p141 :rule bool-double-not-elim :args (@t57)) % 0.53/0.73 (step @p142 :rule refl :args (@t59)) % 0.53/0.73 (step @p143 :rule nary_cong :premises (@p142 @p141 @p140) :args ((or @t59 (not @t64) @t74))) % 0.53/0.73 (assume-push @p182 @t58) % 0.53/0.73 (assume-push @p183 @t65) % 0.53/0.73 (assume-push @p184 @t64) % 0.53/0.73 (step @p147 :rule evaluate :args ((= false true))) % 0.53/0.73 (step @p148 :rule true_intro :premises (@p182)) % 0.53/0.73 (step @p149 :rule symm :premises (@p183)) % 0.53/0.73 (step @p150 :rule cong :premises (@p149) :args (@t57)) % 0.53/0.73 (step @p151 :rule false_intro :premises (@p184)) % 0.53/0.73 (step @p152 :rule symm :premises (@p151)) % 0.53/0.73 (step @p153 :rule trans :premises (@p152 @p150 @p148)) % 0.53/0.73 (step @p154 false :rule eq_resolve :premises (@p153 @p147)) % 0.53/0.73 (step-pop @p185 :rule scope :premises (@p154)) % 0.53/0.73 (step-pop @p186 :rule scope :premises (@p185)) % 0.53/0.73 (step-pop @p187 :rule scope :premises (@p186)) % 0.53/0.73 (step @p155 :rule process_scope :premises (@p187) :args (false)) % 0.53/0.73 (assume-push @p188 @t58) % 0.53/0.73 (assume-push @p189 @t64) % 0.53/0.73 (assume-push @p190 @t65) % 0.53/0.73 (step @p162 :rule and_intro :premises (@p188 @p190 @p189)) % 0.53/0.73 (step-pop @p191 :rule scope :premises (@p162)) % 0.53/0.73 (step-pop @p192 :rule scope :premises (@p191)) % 0.53/0.73 (step-pop @p193 :rule scope :premises (@p192)) % 0.53/0.73 (step @p163 :rule process_scope :premises (@p193) :args (@t75)) % 0.53/0.73 (step @p167 :rule implies_elim :premises (@p163)) % 0.53/0.73 (step @p168 :rule resolution :premises (@p167 @p155) :args (true @t75)) % 0.53/0.73 (step @p169 :rule not_and :premises (@p168)) % 0.53/0.73 (step @p170 :rule eq_resolve :premises (@p169 @p143)) % 0.53/0.73 (step @p171 false :rule chain_m_resolution :premises (@p170 @p139 @p114 @p112) :args (false (@list false true false) (@list @t65 @t57 @t58))) % 0.53/0.73 ) % 0.53/0.73 % SZS output end Proof % 0.53/0.73 % cvc5 exiting %------------------------------------------------------------------------------