%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYO042^2 : TPTP v9.2.1. Released v4.1.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n003.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 09:11:51 AM UTC 2026 % Result : Theorem 0.28s 0.54s % Output : Proof 0.28s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : SYO042^2 : TPTP v9.2.1. Released v4.1.0. % 0.12/0.14 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.35 % Computer : n003.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 23:52:14 EDT 2026 % 0.17/0.35 % CPUTime : % 0.28/0.49 %----Proving TH0 % 0.28/0.54 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.28/0.54 % SZS status Theorem % 0.28/0.54 % SZS output start Proof % 0.28/0.54 ( % 0.28/0.54 (declare-const tptp.y Bool) % 0.28/0.54 (declare-const tptp.x Bool) % 0.28/0.54 (declare-const tptp.g (-> Bool Bool)) % 0.28/0.54 (declare-const tptp.p (-> (-> Bool Bool) Bool)) % 0.28/0.54 (define @t1 () (@var "_lvar_0" Bool)) % 0.28/0.54 (define @t2 () (lambda (@list @t1) (not @t1))) % 0.28/0.54 (define @t3 () (not (_ tptp.p @t2))) % 0.28/0.54 (define @t4 () (_ tptp.p tptp.g)) % 0.28/0.54 (define @t5 () (_ tptp.g tptp.y)) % 0.28/0.54 (define @t6 () (_ tptp.g tptp.x)) % 0.28/0.54 (define @t7 () (= tptp.x tptp.y)) % 0.28/0.54 (define @t8 () (not @t7)) % 0.28/0.54 (define @t9 () (and @t8 (= @t6 tptp.y) (= @t5 tptp.x) @t4 @t3)) % 0.28/0.54 (define @t10 () (@var "BOUND_VARIABLE_7452" Bool)) % 0.28/0.54 (define @t11 () (= @t10 true)) % 0.28/0.54 (define @t12 () (@list @t10)) % 0.28/0.54 (define @t13 () (lambda @t12 (ite @t11 false true))) % 0.28/0.54 (define @t14 () (@purify @t13)) % 0.28/0.54 (define @t15 () (tptp.p @t14)) % 0.28/0.54 (define @t16 () (_ tptp.p @t14)) % 0.28/0.54 (define @t17 () (not @t11)) % 0.28/0.54 (define @t18 () (not (_ tptp.p @t13))) % 0.28/0.54 (define @t19 () (tptp.p tptp.g)) % 0.28/0.54 (define @t20 () (@purify @t6)) % 0.28/0.54 (define @t21 () (tptp.g @t20)) % 0.28/0.54 (define @t22 () (_ tptp.g @t20)) % 0.28/0.54 (define @t23 () (= @t6 @t20)) % 0.28/0.54 (define @t24 () (= tptp.x (_ tptp.g @t6))) % 0.28/0.54 (define @t25 () (@purify tptp.x)) % 0.28/0.54 (define @t26 () (tptp.g @t25)) % 0.28/0.54 (define @t27 () (_ tptp.g @t25)) % 0.28/0.54 (define @t28 () (= tptp.x @t6)) % 0.28/0.54 (define @t29 () (not @t28)) % 0.28/0.54 (define @t30 () (and @t29 @t24 @t4 @t18)) % 0.28/0.54 (define @t31 () (= tptp.x @t5)) % 0.28/0.54 (define @t32 () (= tptp.y @t6)) % 0.28/0.54 (define @t33 () (not tptp.x)) % 0.28/0.54 (define @t34 () (not @t20)) % 0.28/0.54 (define @t35 () (= tptp.g @t14)) % 0.28/0.54 (define @t36 () (not @t35)) % 0.28/0.54 (define @t37 () (not @t19)) % 0.28/0.54 (define @t38 () (not @t15)) % 0.28/0.54 (define @t39 () (and @t19 @t35 @t38)) % 0.28/0.54 (define @t40 () (@const 0 Bool)) % 0.28/0.54 (define @t41 () (@purify @t40)) % 0.28/0.54 (define @t42 () (tptp.g @t41)) % 0.28/0.54 (define @t43 () (not @t41)) % 0.28/0.54 (define @t44 () (not @t40)) % 0.28/0.54 (define @t45 () (= @t40 true)) % 0.28/0.54 (define @t46 () (not @t45)) % 0.28/0.54 (define @t47 () (_ @t13 @t40)) % 0.28/0.54 (define @t48 () (_ @t14 @t40)) % 0.28/0.54 (define @t49 () (tptp.g @t40)) % 0.28/0.54 (define @t50 () (= @t49 @t48)) % 0.28/0.54 (define @t51 () (not @t50)) % 0.28/0.54 (define @t52 () (or @t35 @t51)) % 0.28/0.54 (define @t53 () (= @t43 @t42)) % 0.28/0.54 (define @t54 () (@list true)) % 0.28/0.54 (define @t55 () (not @t42)) % 0.28/0.54 (define @t56 () (not @t43)) % 0.28/0.54 (define @t57 () (not @t21)) % 0.28/0.54 (define @t58 () (and @t21 @t34 @t43)) % 0.28/0.54 (define @t59 () (not @t25)) % 0.28/0.54 (define @t60 () (not @t26)) % 0.28/0.54 (define @t61 () (and @t25 @t60 @t41)) % 0.28/0.54 (define @t62 () (@list tptp.x)) % 0.28/0.54 (define @t63 () (and @t26 @t59 @t43)) % 0.28/0.54 (define @t64 () (and @t20 @t57 @t41)) % 0.28/0.54 (assume @p1 (not (not @t9))) % 0.28/0.54 (assume @p2 true) % 0.28/0.54 (step @p3 :rule refl :args (@t15)) % 0.28/0.54 (step @p4 :rule refl :args (@t16)) % 0.28/0.54 (step @p5 :rule cong :premises (@p4 @p3) :args ((= @t16 @t15))) % 0.28/0.54 (step @p6 :rule symm :premises (@p5)) % 0.28/0.54 (step @p7 :rule eq_resolve :premises (@p4 @p6)) % 0.28/0.54 (step @p8 :rule eq-refl :args (@t13)) % 0.28/0.54 (step @p9 :rule refl :args (@t13)) % 0.28/0.54 (step @p10 :rule symm :premises (@p9)) % 0.28/0.54 (step @p11 :rule bool-eq-true :args (@t10)) % 0.28/0.54 (step @p12 :rule cong :premises (@p11) :args (@t17)) % 0.28/0.54 (step @p13 :rule bool-eq-false :args (@t11)) % 0.28/0.54 (step @p14 :rule trans :premises (@p13 @p12)) % 0.28/0.54 (step @p15 :rule evaluate :args ((not true))) % 0.28/0.54 (step @p16 :rule ite-neg-branch :premises (@p15) :args (@t11 false true)) % 0.28/0.54 (step @p17 :rule trans :premises (@p16 @p14)) % 0.28/0.54 (step @p18 :rule symm :premises (@p17)) % 0.28/0.54 (step @p19 :rule cong :premises (@p18) :args ((lambda @t12 (not @t10)))) % 0.28/0.54 (step @p20 :rule trans :premises (@p19 @p10)) % 0.28/0.54 (step @p21 :rule bool-eq-true :args (@t10)) % 0.28/0.54 (step @p22 :rule cong :premises (@p21) :args (@t17)) % 0.28/0.54 (step @p23 :rule aci_norm :args ((= (and @t17 true) @t17))) % 0.28/0.54 (step @p24 :rule ite-then-false :args (@t11 true)) % 0.28/0.54 (step @p25 :rule trans :premises (@p24 @p23)) % 0.28/0.54 (step @p26 :rule trans :premises (@p25 @p22)) % 0.28/0.54 (step @p27 :rule cong :premises (@p26) :args (@t13)) % 0.28/0.54 (step @p28 :rule trans :premises (@p27 @p20)) % 0.28/0.54 (step @p29 :rule refl :args (@t13)) % 0.28/0.54 (step @p30 :rule cong :premises (@p29 @p28) :args ((= @t13 @t13))) % 0.28/0.54 (step @p31 :rule trans :premises (@p30 @p8)) % 0.28/0.54 (step @p32 :rule skolem_intro :args (@t14)) % 0.28/0.54 (step @p33 :rule cong :premises (@p29 @p32) :args ((= @t13 @t14))) % 0.28/0.54 (step @p34 :rule trans :premises (@p33 @p31)) % 0.28/0.54 (step @p35 :rule true_elim :premises (@p34)) % 0.28/0.54 (step @p36 :rule refl :args (tptp.p)) % 0.28/0.54 (step @p37 :rule ho_cong :premises (@p36 @p35)) % 0.28/0.54 (step @p38 :rule trans :premises (@p37 @p7)) % 0.28/0.54 (step @p39 :rule cong :premises (@p38) :args (@t18)) % 0.28/0.54 (step @p40 :rule refl :args (@t19)) % 0.28/0.54 (step @p41 :rule refl :args (@t4)) % 0.28/0.54 (step @p42 :rule cong :premises (@p41 @p40) :args ((= @t4 @t19))) % 0.28/0.54 (step @p43 :rule symm :premises (@p42)) % 0.28/0.54 (step @p44 :rule eq_resolve :premises (@p41 @p43)) % 0.28/0.54 (step @p45 :rule refl :args (@t21)) % 0.28/0.54 (step @p46 :rule refl :args (@t22)) % 0.28/0.54 (step @p47 :rule cong :premises (@p46 @p45) :args ((= @t22 @t21))) % 0.28/0.54 (step @p48 :rule symm :premises (@p47)) % 0.28/0.54 (step @p49 :rule eq_resolve :premises (@p46 @p48)) % 0.28/0.54 (step @p50 :rule eq-refl :args (@t6)) % 0.28/0.54 (step @p51 :rule skolem_intro :args (@t20)) % 0.28/0.54 (step @p52 :rule refl :args (@t6)) % 0.28/0.54 (step @p53 :rule cong :premises (@p52 @p51) :args (@t23)) % 0.28/0.54 (step @p54 :rule trans :premises (@p53 @p50)) % 0.28/0.54 (step @p55 :rule true_elim :premises (@p54)) % 0.28/0.54 (step @p56 :rule refl :args (tptp.g)) % 0.28/0.54 (step @p57 :rule ho_cong :premises (@p56 @p55)) % 0.28/0.54 (step @p58 :rule trans :premises (@p57 @p49)) % 0.28/0.54 (step @p59 :rule refl :args (tptp.x)) % 0.28/0.54 (step @p60 :rule cong :premises (@p59 @p58) :args (@t24)) % 0.28/0.54 (step @p61 :rule refl :args (@t26)) % 0.28/0.54 (step @p62 :rule refl :args (@t27)) % 0.28/0.54 (step @p63 :rule cong :premises (@p62 @p61) :args ((= @t27 @t26))) % 0.28/0.54 (step @p64 :rule symm :premises (@p63)) % 0.28/0.54 (step @p65 :rule eq_resolve :premises (@p62 @p64)) % 0.28/0.54 (step @p66 :rule eq-refl :args (tptp.x)) % 0.28/0.54 (step @p67 :rule skolem_intro :args (@t25)) % 0.28/0.54 (step @p68 :rule cong :premises (@p59 @p67) :args ((= tptp.x @t25))) % 0.28/0.54 (step @p69 :rule trans :premises (@p68 @p66)) % 0.28/0.54 (step @p70 :rule true_elim :premises (@p69)) % 0.28/0.54 (step @p71 :rule ho_cong :premises (@p56 @p70)) % 0.28/0.54 (step @p72 :rule trans :premises (@p71 @p65)) % 0.28/0.54 (step @p73 :rule cong :premises (@p59 @p72) :args (@t28)) % 0.28/0.54 (step @p74 :rule cong :premises (@p73) :args (@t29)) % 0.28/0.54 (step @p75 :rule nary_cong :premises (@p74 @p60 @p44 @p39) :args (@t30)) % 0.28/0.54 (step @p76 :rule aci_norm :args ((= (and @t29 true @t24 @t4 @t18) @t30))) % 0.28/0.54 (step @p77 :rule refl :args (@t18)) % 0.28/0.54 (step @p78 :rule refl :args (@t4)) % 0.28/0.54 (step @p79 :rule refl :args (@t24)) % 0.28/0.54 (step @p80 :rule refl :args (@t29)) % 0.28/0.54 (step @p81 :rule nary_cong :premises (@p80 @p50 @p79 @p78 @p77) :args ((and @t29 (= @t6 @t6) @t24 @t4 @t18))) % 0.28/0.54 (step @p82 :rule trans :premises (@p81 @p76)) % 0.28/0.54 (step @p83 :rule alpha_equiv :args (@t2 (@list @t1) (@list @t10))) % 0.28/0.54 (step @p84 :rule trans :premises (@p83 @p19)) % 0.28/0.54 (step @p85 :rule trans :premises (@p84 @p10)) % 0.28/0.54 (step @p86 :rule ho_cong :premises (@p36 @p85)) % 0.28/0.54 (step @p87 :rule cong :premises (@p86) :args (@t3)) % 0.28/0.54 (step @p88 :rule eq-symm :args (@t5 tptp.x)) % 0.28/0.54 (step @p89 :rule eq-symm :args (@t6 tptp.y)) % 0.28/0.54 (step @p90 :rule refl :args (@t8)) % 0.28/0.54 (step @p91 :rule nary_cong :premises (@p90 @p89 @p88 @p78 @p87) :args (@t9)) % 0.28/0.54 (step @p92 :rule bool-double-not-elim :args (@t9)) % 0.28/0.54 (step @p93 :rule trans :premises (@p92 @p91)) % 0.28/0.54 (step @p94 :rule eq_resolve :premises (@p1 @p93)) % 0.28/0.54 (step @p95 :rule and_elim :premises (@p94) :args (1)) % 0.28/0.54 (step @p96 :rule ho_cong :premises (@p56 @p95)) % 0.28/0.54 (step @p97 :rule cong :premises (@p59 @p96) :args (@t31)) % 0.28/0.54 (step @p98 :rule cong :premises (@p95 @p52) :args (@t32)) % 0.28/0.54 (step @p99 :rule cong :premises (@p59 @p95) :args (@t7)) % 0.28/0.54 (step @p100 :rule cong :premises (@p99) :args (@t8)) % 0.28/0.54 (step @p101 :rule nary_cong :premises (@p100 @p98 @p97 @p78 @p77) :args ((and @t8 @t32 @t31 @t4 @t18))) % 0.28/0.54 (step @p102 :rule trans :premises (@p101 @p82)) % 0.28/0.54 (step @p103 :rule trans :premises (@p93 @p102 @p75)) % 0.28/0.54 (step @p104 :rule eq_resolve :premises (@p1 @p103)) % 0.28/0.54 (step @p105 :rule and_elim :premises (@p104) :args (0)) % 0.28/0.54 (step @p106 :rule not_equiv_elim2 :premises (@p105)) % 0.28/0.54 (step @p107 :rule and_elim :premises (@p104) :args (1)) % 0.28/0.54 (step @p108 :rule equiv_elim1 :premises (@p107)) % 0.28/0.54 (step @p109 :rule reordering :premises (@p108) :args ((or @t21 @t33))) % 0.28/0.54 (step @p110 :rule equiv_elim1 :premises (@p70)) % 0.28/0.54 (step @p111 :rule reordering :premises (@p110) :args ((or @t25 @t33))) % 0.28/0.54 (step @p112 :rule eq-symm :args (@t26 @t20)) % 0.28/0.54 (step @p113 :rule refl :args (@t20)) % 0.28/0.54 (step @p114 :rule cong :premises (@p72 @p113) :args (@t23)) % 0.28/0.54 (step @p115 :rule trans :premises (@p114 @p112)) % 0.28/0.54 (step @p116 :rule eq-symm :args (@t20 @t6)) % 0.28/0.54 (step @p117 :rule trans :premises (@p116 @p115)) % 0.28/0.54 (step @p118 :rule eq_resolve :premises (@p51 @p117)) % 0.28/0.54 (step @p119 :rule equiv_elim1 :premises (@p118)) % 0.28/0.54 (step @p120 :rule reordering :premises (@p119) :args ((or @t26 @t34))) % 0.28/0.54 (step @p121 :rule and_elim :premises (@p104) :args (2)) % 0.28/0.54 (step @p122 :rule and_elim :premises (@p104) :args (3)) % 0.28/0.54 (step @p123 :rule refl :args (@t36)) % 0.28/0.54 (step @p124 :rule refl :args (@t37)) % 0.28/0.54 (step @p125 :rule bool-double-not-elim :args (@t15)) % 0.28/0.54 (step @p126 :rule nary_cong :premises (@p125 @p124 @p123) :args ((or (not @t38) @t37 @t36))) % 0.28/0.54 (assume-push @p344 @t19) % 0.28/0.54 (assume-push @p345 @t35) % 0.28/0.54 (assume-push @p346 @t38) % 0.28/0.54 (step @p130 :rule evaluate :args ((= false true))) % 0.28/0.54 (step @p131 :rule true_intro :premises (@p121)) % 0.28/0.54 (step @p132 :rule symm :premises (@p345)) % 0.28/0.54 (step @p133 :rule cong :premises (@p132) :args (@t15)) % 0.28/0.54 (step @p134 :rule false_intro :premises (@p122)) % 0.28/0.54 (step @p135 :rule symm :premises (@p134)) % 0.28/0.54 (step @p136 :rule trans :premises (@p135 @p133 @p131)) % 0.28/0.54 (step @p137 false :rule eq_resolve :premises (@p136 @p130)) % 0.28/0.54 (step-pop @p347 :rule scope :premises (@p137)) % 0.28/0.54 (step-pop @p348 :rule scope :premises (@p347)) % 0.28/0.54 (step-pop @p349 :rule scope :premises (@p348)) % 0.28/0.54 (step @p138 :rule process_scope :premises (@p349) :args (false)) % 0.28/0.54 (assume-push @p350 @t38) % 0.28/0.54 (assume-push @p351 @t19) % 0.28/0.54 (assume-push @p352 @t35) % 0.28/0.54 (step @p145 :rule and_intro :premises (@p121 @p352 @p122)) % 0.28/0.54 (step-pop @p353 :rule scope :premises (@p145)) % 0.28/0.54 (step-pop @p354 :rule scope :premises (@p353)) % 0.28/0.54 (step-pop @p355 :rule scope :premises (@p354)) % 0.28/0.54 (step @p146 :rule process_scope :premises (@p355) :args (@t39)) % 0.28/0.54 (step @p150 :rule implies_elim :premises (@p146)) % 0.28/0.54 (step @p151 :rule resolution :premises (@p150 @p138) :args (true @t39)) % 0.28/0.54 (step @p152 :rule not_and :premises (@p151)) % 0.28/0.54 (step @p153 :rule eq_resolve :premises (@p152 @p126)) % 0.28/0.54 (step @p154 :rule chain_m_resolution :premises (@p153 @p122 @p121) :args (@t36 (@list true false) (@list @t15 @t19))) % 0.28/0.54 (step @p155 :rule eq-symm :args (@t42 @t43)) % 0.28/0.54 (step @p156 :rule eq-refl :args (@t44)) % 0.28/0.54 (step @p157 :rule bool-eq-true :args (@t40)) % 0.28/0.54 (step @p158 :rule cong :premises (@p157) :args (@t46)) % 0.28/0.54 (step @p159 :rule aci_norm :args ((= (and @t46 true) @t46))) % 0.28/0.54 (step @p160 :rule ite-then-false :args (@t45 true)) % 0.28/0.54 (step @p161 :rule trans :premises (@p160 @p159)) % 0.28/0.54 (step @p162 :rule trans :premises (@p161 @p158)) % 0.28/0.54 (step @p163 :rule beta-reduce :args ((= @t47 (ite @t45 false true)))) % 0.28/0.54 (step @p164 :rule trans :premises (@p163 @p162)) % 0.28/0.54 (step @p165 :rule refl :args (@t44)) % 0.28/0.54 (step @p166 :rule cong :premises (@p165 @p164) :args ((= @t44 @t47))) % 0.28/0.54 (step @p167 :rule trans :premises (@p166 @p156)) % 0.28/0.54 (step @p168 :rule eq-symm :args (@t47 @t44)) % 0.28/0.54 (step @p169 :rule trans :premises (@p168 @p167)) % 0.28/0.54 (step @p170 :rule skolem_intro :args (@t41)) % 0.28/0.54 (step @p171 :rule cong :premises (@p170) :args (@t43)) % 0.28/0.54 (step @p172 :rule ho_cong :premises (@p32 @p170)) % 0.28/0.54 (step @p173 :rule cong :premises (@p172 @p171) :args ((= (_ @t14 @t41) @t43))) % 0.28/0.54 (step @p174 :rule trans :premises (@p173 @p169)) % 0.28/0.54 (step @p175 :rule true_elim :premises (@p174)) % 0.28/0.54 (step @p176 :rule eq-refl :args (@t40)) % 0.28/0.54 (step @p177 :rule refl :args (@t40)) % 0.28/0.54 (step @p178 :rule cong :premises (@p177 @p170) :args ((= @t40 @t41))) % 0.28/0.54 (step @p179 :rule trans :premises (@p178 @p176)) % 0.28/0.54 (step @p180 :rule true_elim :premises (@p179)) % 0.28/0.54 (step @p181 :rule cong :premises (@p180) :args (@t48)) % 0.28/0.54 (step @p182 :rule trans :premises (@p181 @p175)) % 0.28/0.54 (step @p183 :rule cong :premises (@p180) :args (@t49)) % 0.28/0.54 (step @p184 :rule cong :premises (@p183 @p182) :args (@t50)) % 0.28/0.54 (step @p185 :rule trans :premises (@p184 @p155)) % 0.28/0.54 (step @p186 :rule cong :premises (@p185) :args (@t51)) % 0.28/0.54 (step @p187 :rule refl :args (@t35)) % 0.28/0.54 (step @p188 :rule nary_cong :premises (@p187 @p186) :args (@t52)) % 0.28/0.54 ; WARNING: add trust step for TRUST % 0.28/0.54 ; trust TRUST THEORY_LEMMA % 0.28/0.54 (step @p189 :rule trust :premises () :args (@t52)) % 0.28/0.54 (step @p190 :rule eq_resolve :premises (@p189 @p188)) % 0.28/0.54 (step @p191 :rule chain_m_resolution :premises (@p190 @p154) :args ((not @t53) @t54 (@list @t35))) % 0.28/0.54 (step @p192 :rule refl :args (@t55)) % 0.28/0.54 (step @p193 :rule bool-double-not-elim :args (@t41)) % 0.28/0.54 (step @p194 :rule refl :args (@t53)) % 0.28/0.54 (step @p195 :rule nary_cong :premises (@p194 @p193 @p192) :args ((or @t53 @t56 @t55))) % 0.28/0.54 (step @p196 :rule cnf_equiv_neg2 :args (@t53)) % 0.28/0.54 (step @p197 :rule eq_resolve :premises (@p196 @p195)) % 0.28/0.54 (step @p198 :rule reordering :premises (@p197) :args ((or @t41 @t53 @t55))) % 0.28/0.54 (step @p199 :rule refl :args (@t42)) % 0.28/0.54 (step @p200 :rule bool-double-not-elim :args (@t20)) % 0.28/0.54 (step @p201 :rule refl :args (@t57)) % 0.28/0.54 (step @p202 :rule nary_cong :premises (@p201 @p200 @p193 @p199) :args ((or @t57 (not @t34) @t56 @t42))) % 0.28/0.54 (assume-push @p356 @t21) % 0.28/0.54 (assume-push @p357 @t34) % 0.28/0.54 (assume-push @p358 @t43) % 0.28/0.54 (assume-push @p359 @t21) % 0.28/0.54 (assume-push @p360 @t34) % 0.28/0.54 (assume-push @p361 @t43) % 0.28/0.54 (step @p209 :rule true_intro :premises (@p356)) % 0.28/0.54 (step @p210 :rule false_intro :premises (@p357)) % 0.28/0.54 (step @p211 :rule symm :premises (@p210)) % 0.28/0.54 (step @p212 :rule false_intro :premises (@p358)) % 0.28/0.54 (step @p213 :rule trans :premises (@p212 @p211)) % 0.28/0.54 (step @p214 :rule cong :premises (@p213) :args (@t42)) % 0.28/0.54 (step @p215 :rule trans :premises (@p214 @p209)) % 0.28/0.54 (step @p216 :rule true_elim :premises (@p215)) % 0.28/0.54 (step-pop @p362 :rule scope :premises (@p216)) % 0.28/0.54 (step-pop @p363 :rule scope :premises (@p362)) % 0.28/0.54 (step-pop @p364 :rule scope :premises (@p363)) % 0.28/0.54 (step @p217 :rule process_scope :premises (@p364) :args (@t42)) % 0.28/0.54 (step @p221 :rule and_intro :premises (@p356 @p357 @p358)) % 0.28/0.54 (step @p222 :rule modus_ponens :premises (@p221 @p217)) % 0.28/0.54 (step-pop @p365 :rule scope :premises (@p222)) % 0.28/0.54 (step-pop @p366 :rule scope :premises (@p365)) % 0.28/0.54 (step-pop @p367 :rule scope :premises (@p366)) % 0.28/0.54 (step @p223 :rule process_scope :premises (@p367) :args (@t42)) % 0.28/0.54 (step @p227 :rule implies_elim :premises (@p223)) % 0.28/0.54 (step @p228 :rule cnf_and_neg :args (@t58)) % 0.28/0.54 (step @p229 :rule resolution :premises (@p228 @p227) :args (true @t58)) % 0.28/0.54 (step @p230 :rule eq_resolve :premises (@p229 @p202)) % 0.28/0.54 (step @p231 :rule reordering :premises (@p230) :args ((or @t20 @t57 @t41 @t42))) % 0.28/0.54 (step @p232 :rule chain_m_resolution :premises (@p231 @p198 @p191) :args ((or @t20 @t57 @t41) (@list true true) (@list @t42 @t53))) % 0.28/0.54 (step @p233 :rule cnf_equiv_neg1 :args (@t53)) % 0.28/0.54 (step @p234 :rule reordering :premises (@p233) :args ((or @t43 @t42 @t53))) % 0.28/0.54 (step @p235 :rule refl :args (@t43)) % 0.28/0.54 (step @p236 :rule bool-double-not-elim :args (@t26)) % 0.28/0.54 (step @p237 :rule refl :args (@t59)) % 0.28/0.54 (step @p238 :rule nary_cong :premises (@p237 @p236 @p235 @p192) :args ((or @t59 (not @t60) @t43 @t55))) % 0.28/0.54 (assume-push @p368 @t25) % 0.28/0.54 (assume-push @p369 @t60) % 0.28/0.54 (assume-push @p370 @t41) % 0.28/0.54 (assume-push @p371 @t60) % 0.28/0.54 (assume-push @p372 @t25) % 0.28/0.54 (assume-push @p373 @t41) % 0.28/0.54 (step @p245 :rule false_intro :premises (@p369)) % 0.28/0.54 (step @p246 :rule true_intro :premises (@p368)) % 0.28/0.54 (step @p247 :rule symm :premises (@p246)) % 0.28/0.54 (step @p248 :rule true_intro :premises (@p370)) % 0.28/0.54 (step @p249 :rule trans :premises (@p248 @p247)) % 0.28/0.54 (step @p250 :rule cong :premises (@p249) :args (@t42)) % 0.28/0.54 (step @p251 :rule trans :premises (@p250 @p245)) % 0.28/0.54 (step @p252 :rule false_elim :premises (@p251)) % 0.28/0.54 (step-pop @p374 :rule scope :premises (@p252)) % 0.28/0.54 (step-pop @p375 :rule scope :premises (@p374)) % 0.28/0.54 (step-pop @p376 :rule scope :premises (@p375)) % 0.28/0.54 (step @p253 :rule process_scope :premises (@p376) :args (@t55)) % 0.28/0.54 (step @p257 :rule and_intro :premises (@p369 @p368 @p370)) % 0.28/0.54 (step @p258 :rule modus_ponens :premises (@p257 @p253)) % 0.28/0.54 (step-pop @p377 :rule scope :premises (@p258)) % 0.28/0.54 (step-pop @p378 :rule scope :premises (@p377)) % 0.28/0.54 (step-pop @p379 :rule scope :premises (@p378)) % 0.28/0.54 (step @p259 :rule process_scope :premises (@p379) :args (@t55)) % 0.28/0.54 (step @p263 :rule implies_elim :premises (@p259)) % 0.28/0.54 (step @p264 :rule cnf_and_neg :args (@t61)) % 0.28/0.54 (step @p265 :rule resolution :premises (@p264 @p263) :args (true @t61)) % 0.28/0.54 (step @p266 :rule eq_resolve :premises (@p265 @p238)) % 0.28/0.54 (step @p267 :rule reordering :premises (@p266) :args ((or @t26 @t59 @t43 @t55))) % 0.28/0.54 (step @p268 :rule chain_m_resolution :premises (@p267 @p234 @p191 @p232 @p120 @p111 @p109 @p106) :args (@t33 (@list false true false true false false true) (@list @t42 @t53 @t41 @t20 @t25 @t21 @t26))) % 0.28/0.54 (step @p269 :rule equiv_elim2 :premises (@p107)) % 0.28/0.54 (step @p270 :rule chain_m_resolution :premises (@p269 @p268) :args (@t57 @t54 @t62)) % 0.28/0.54 (step @p271 :rule not_equiv_elim1 :premises (@p105)) % 0.28/0.54 (step @p272 :rule chain_m_resolution :premises (@p271 @p268) :args (@t26 @t54 @t62)) % 0.28/0.54 (step @p273 :rule equiv_elim2 :premises (@p118)) % 0.28/0.54 (step @p274 :rule chain_m_resolution :premises (@p273 @p272) :args (@t20 (@list false) (@list @t26))) % 0.28/0.54 (step @p275 :rule equiv_elim2 :premises (@p70)) % 0.28/0.54 (step @p276 :rule chain_m_resolution :premises (@p275 @p268) :args (@t59 @t54 @t62)) % 0.28/0.54 (step @p277 :rule bool-double-not-elim :args (@t25)) % 0.28/0.54 (step @p278 :rule refl :args (@t60)) % 0.28/0.54 (step @p279 :rule nary_cong :premises (@p278 @p277 @p193 @p199) :args ((or @t60 (not @t59) @t56 @t42))) % 0.28/0.54 (assume-push @p380 @t26) % 0.28/0.54 (assume-push @p381 @t59) % 0.28/0.54 (assume-push @p382 @t43) % 0.28/0.54 (assume-push @p383 @t26) % 0.28/0.54 (assume-push @p384 @t59) % 0.28/0.54 (assume-push @p385 @t43) % 0.28/0.54 (step @p286 :rule true_intro :premises (@p380)) % 0.28/0.54 (step @p287 :rule false_intro :premises (@p381)) % 0.28/0.54 (step @p288 :rule symm :premises (@p287)) % 0.28/0.54 (step @p289 :rule false_intro :premises (@p382)) % 0.28/0.54 (step @p290 :rule trans :premises (@p289 @p288)) % 0.28/0.54 (step @p291 :rule cong :premises (@p290) :args (@t42)) % 0.28/0.54 (step @p292 :rule trans :premises (@p291 @p286)) % 0.28/0.54 (step @p293 :rule true_elim :premises (@p292)) % 0.28/0.54 (step-pop @p386 :rule scope :premises (@p293)) % 0.28/0.54 (step-pop @p387 :rule scope :premises (@p386)) % 0.28/0.54 (step-pop @p388 :rule scope :premises (@p387)) % 0.28/0.54 (step @p294 :rule process_scope :premises (@p388) :args (@t42)) % 0.28/0.54 (step @p298 :rule and_intro :premises (@p380 @p381 @p382)) % 0.28/0.54 (step @p299 :rule modus_ponens :premises (@p298 @p294)) % 0.28/0.54 (step-pop @p389 :rule scope :premises (@p299)) % 0.28/0.54 (step-pop @p390 :rule scope :premises (@p389)) % 0.28/0.54 (step-pop @p391 :rule scope :premises (@p390)) % 0.28/0.54 (step @p300 :rule process_scope :premises (@p391) :args (@t42)) % 0.28/0.54 (step @p304 :rule implies_elim :premises (@p300)) % 0.28/0.54 (step @p305 :rule cnf_and_neg :args (@t63)) % 0.28/0.54 (step @p306 :rule resolution :premises (@p305 @p304) :args (true @t63)) % 0.28/0.54 (step @p307 :rule eq_resolve :premises (@p306 @p279)) % 0.28/0.54 (step @p308 :rule reordering :premises (@p307) :args ((or @t25 @t60 @t41 @t42))) % 0.28/0.54 (step @p309 :rule chain_m_resolution :premises (@p308 @p276 @p272 @p198 @p191) :args (@t41 (@list true false true true) (@list @t25 @t26 @t42 @t53))) % 0.28/0.54 (step @p310 :rule chain_m_resolution :premises (@p234 @p309 @p191) :args (@t42 (@list false true) (@list @t41 @t53))) % 0.28/0.54 (step @p311 :rule bool-double-not-elim :args (@t21)) % 0.28/0.54 (step @p312 :rule refl :args (@t34)) % 0.28/0.54 (step @p313 :rule nary_cong :premises (@p312 @p311 @p235 @p192) :args ((or @t34 (not @t57) @t43 @t55))) % 0.28/0.54 (assume-push @p392 @t20) % 0.28/0.54 (assume-push @p393 @t57) % 0.28/0.54 (assume-push @p394 @t41) % 0.28/0.54 (assume-push @p395 @t57) % 0.28/0.54 (assume-push @p396 @t20) % 0.28/0.54 (assume-push @p397 @t41) % 0.28/0.54 (step @p320 :rule false_intro :premises (@p393)) % 0.28/0.54 (step @p321 :rule true_intro :premises (@p392)) % 0.28/0.54 (step @p322 :rule symm :premises (@p321)) % 0.28/0.54 (step @p323 :rule true_intro :premises (@p394)) % 0.28/0.54 (step @p324 :rule trans :premises (@p323 @p322)) % 0.28/0.54 (step @p325 :rule cong :premises (@p324) :args (@t42)) % 0.28/0.54 (step @p326 :rule trans :premises (@p325 @p320)) % 0.28/0.54 (step @p327 :rule false_elim :premises (@p326)) % 0.28/0.54 (step-pop @p398 :rule scope :premises (@p327)) % 0.28/0.54 (step-pop @p399 :rule scope :premises (@p398)) % 0.28/0.54 (step-pop @p400 :rule scope :premises (@p399)) % 0.28/0.54 (step @p328 :rule process_scope :premises (@p400) :args (@t55)) % 0.28/0.54 (step @p332 :rule and_intro :premises (@p393 @p392 @p394)) % 0.28/0.54 (step @p333 :rule modus_ponens :premises (@p332 @p328)) % 0.28/0.54 (step-pop @p401 :rule scope :premises (@p333)) % 0.28/0.54 (step-pop @p402 :rule scope :premises (@p401)) % 0.28/0.54 (step-pop @p403 :rule scope :premises (@p402)) % 0.28/0.54 (step @p334 :rule process_scope :premises (@p403) :args (@t55)) % 0.28/0.54 (step @p338 :rule implies_elim :premises (@p334)) % 0.28/0.54 (step @p339 :rule cnf_and_neg :args (@t64)) % 0.28/0.54 (step @p340 :rule resolution :premises (@p339 @p338) :args (true @t64)) % 0.28/0.54 (step @p341 :rule eq_resolve :premises (@p340 @p313)) % 0.28/0.54 (step @p342 :rule reordering :premises (@p341) :args ((or @t21 @t34 @t43 @t55))) % 0.28/0.54 (step @p343 false :rule chain_m_resolution :premises (@p342 @p310 @p309 @p274 @p270) :args (false (@list false false false true) (@list @t42 @t41 @t20 @t21))) % 0.28/0.54 ) % 0.28/0.54 % SZS output end Proof % 0.28/0.54 % cvc5 exiting %------------------------------------------------------------------------------