%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYN551+2 : TPTP v9.2.1. Bugfixed v3.1.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n016.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 09:09:22 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 : SYN551+2 : TPTP v9.2.1. Bugfixed v3.1.0. % 0.13/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n016.cluster.edu % 0.16/0.34 % Model : x86_64 x86_64 % 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.34 % Memory : 8042.1875MB % 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.34 % CPULimit : 300 % 0.16/0.34 % WCLimit : 300 % 0.16/0.34 % DateTime : Tue Jun 2 23:32:39 EDT 2026 % 0.16/0.35 % CPUTime : % 0.26/0.50 %----Proving TF0_NAR, FOF, or CNF % 0.51/0.71 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 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 $$unsorted 0) % 0.51/0.71 (declare-const tptp.g (-> $$unsorted $$unsorted)) % 0.51/0.71 (declare-const tptp.f (-> $$unsorted $$unsorted)) % 0.51/0.71 (define @t1 () (@var "Y" $$unsorted)) % 0.51/0.71 (define @t2 () (@var "X" $$unsorted)) % 0.51/0.71 (define @t3 () (= @t2 @t1)) % 0.51/0.71 (define @t4 () (= @t1 (tptp.g (tptp.f @t1)))) % 0.51/0.71 (define @t5 () (@list @t1)) % 0.51/0.71 (define @t6 () (forall @t5 (= @t4 @t3))) % 0.51/0.71 (define @t7 () (@list @t2)) % 0.51/0.71 (define @t8 () (exists @t7 @t6)) % 0.51/0.71 (define @t9 () (= @t1 (tptp.f (tptp.g @t1)))) % 0.51/0.71 (define @t10 () (forall @t5 (= @t9 @t3))) % 0.51/0.71 (define @t11 () (exists @t7 @t10)) % 0.51/0.71 (define @t12 () (= @t11 @t8)) % 0.51/0.71 (define @t13 () (not @t12)) % 0.51/0.71 (define @t14 () (forall @t5 (= @t3 @t4))) % 0.51/0.71 (define @t15 () (forall @t7 (not @t14))) % 0.51/0.71 (define @t16 () (forall @t7 (not @t10))) % 0.51/0.71 (define @t17 () (not @t15)) % 0.51/0.71 (define @t18 () (not @t17)) % 0.51/0.71 (define @t19 () (not @t16)) % 0.51/0.71 (define @t20 () (not @t19)) % 0.51/0.71 (define @t21 () (@quantifiers_skolemize @t16 0)) % 0.51/0.71 (define @t22 () (forall @t5 (= @t9 (= @t1 @t21)))) % 0.51/0.71 (define @t23 () (= @t9 (= @t21 @t1))) % 0.51/0.71 (define @t24 () (forall @t5 @t23)) % 0.51/0.71 (define @t25 () (not (not @t24))) % 0.51/0.71 (define @t26 () (tptp.g @t21)) % 0.51/0.71 (define @t27 () (tptp.f @t26)) % 0.51/0.71 (define @t28 () (= @t21 @t27)) % 0.51/0.71 (define @t29 () (= @t28 (= @t21 @t21))) % 0.51/0.71 (define @t30 () (= @t26 @t1)) % 0.51/0.71 (define @t31 () (forall @t5 (= @t30 @t4))) % 0.51/0.71 (define @t32 () (not @t31)) % 0.51/0.71 (define @t33 () (forall @t5 (= @t4 (= @t1 @t26)))) % 0.51/0.71 (define @t34 () (@quantifiers_skolemize @t33 0)) % 0.51/0.71 (define @t35 () (= @t26 @t34)) % 0.51/0.71 (define @t36 () (tptp.f @t34)) % 0.51/0.71 (define @t37 () (tptp.g @t36)) % 0.51/0.71 (define @t38 () (= @t34 @t37)) % 0.51/0.71 (define @t39 () (= @t38 @t35)) % 0.51/0.71 (define @t40 () (not @t39)) % 0.51/0.71 (define @t41 () (not @t33)) % 0.51/0.71 (define @t42 () (= @t38 (= @t34 @t26))) % 0.51/0.71 (define @t43 () (not @t42)) % 0.51/0.71 (define @t44 () (= @t36 (tptp.f @t37))) % 0.51/0.71 (define @t45 () (= @t44 (= @t36 @t21))) % 0.51/0.71 (define @t46 () (= @t21 @t36)) % 0.51/0.71 (define @t47 () (and @t38 @t46)) % 0.51/0.71 (define @t48 () (not @t46)) % 0.51/0.71 (define @t49 () (@list false)) % 0.51/0.71 (define @t50 () (and @t35 @t46)) % 0.51/0.71 (define @t51 () (= @t44 @t46)) % 0.51/0.71 (define @t52 () (and @t28 @t35)) % 0.51/0.71 (define @t53 () (@list @t16)) % 0.51/0.71 (define @t54 () (@quantifiers_skolemize @t15 0)) % 0.51/0.71 (define @t55 () (forall @t5 (= @t4 (= @t1 @t54)))) % 0.51/0.71 (define @t56 () (= @t54 @t1)) % 0.51/0.71 (define @t57 () (forall @t5 (= @t56 @t4))) % 0.51/0.71 (define @t58 () (not (not @t57))) % 0.51/0.71 (define @t59 () (@list true)) % 0.51/0.71 (define @t60 () (tptp.f @t54)) % 0.51/0.71 (define @t61 () (tptp.g @t60)) % 0.51/0.71 (define @t62 () (= @t54 @t61)) % 0.51/0.71 (define @t63 () (= @t62 (= @t54 @t54))) % 0.51/0.71 (define @t64 () (@list @t55)) % 0.51/0.71 (define @t65 () (= @t9 (= @t60 @t1))) % 0.51/0.71 (define @t66 () (forall @t5 @t65)) % 0.51/0.71 (define @t67 () (not @t66)) % 0.51/0.71 (define @t68 () (forall @t5 (= @t9 (= @t1 @t60)))) % 0.51/0.71 (define @t69 () (not @t68)) % 0.51/0.71 (define @t70 () (@quantifiers_skolemize @t68 0)) % 0.51/0.71 (define @t71 () (= @t60 @t70)) % 0.51/0.71 (define @t72 () (tptp.g @t70)) % 0.51/0.71 (define @t73 () (tptp.f @t72)) % 0.51/0.71 (define @t74 () (= @t70 @t73)) % 0.51/0.71 (define @t75 () (= @t74 @t71)) % 0.51/0.71 (define @t76 () (not @t75)) % 0.51/0.71 (define @t77 () (= @t74 (= @t70 @t60))) % 0.51/0.71 (define @t78 () (not @t77)) % 0.51/0.71 (define @t79 () (= @t72 (tptp.g @t73))) % 0.51/0.71 (define @t80 () (= @t72 @t54)) % 0.51/0.71 (define @t81 () (= @t79 @t80)) % 0.51/0.71 (define @t82 () (= @t54 @t72)) % 0.51/0.71 (define @t83 () (= @t82 @t79)) % 0.51/0.71 (define @t84 () (and @t74 @t82)) % 0.51/0.71 (define @t85 () (not @t74)) % 0.51/0.71 (define @t86 () (and @t62 @t71)) % 0.51/0.71 (assume @p1 @t13) % 0.51/0.71 (assume @p2 true) % 0.51/0.71 (step @p3 :rule bool-double-not-elim :args (@t15)) % 0.51/0.71 (step @p4 :rule bool-double-not-elim :args (@t16)) % 0.51/0.71 (step @p5 :rule nary_cong :premises (@p4 @p3) :args ((or @t20 @t18))) % 0.51/0.71 (step @p6 :rule exists-elim :args ((= (exists @t7 @t14) @t17))) % 0.51/0.71 (step @p7 :rule eq-symm :args (@t4 @t3)) % 0.51/0.71 (step @p8 :rule cong :premises (@p7) :args (@t6)) % 0.51/0.71 (step @p9 :rule cong :premises (@p8) :args (@t8)) % 0.51/0.71 (step @p10 :rule trans :premises (@p9 @p6)) % 0.51/0.71 (step @p11 :rule exists-elim :args ((= @t11 @t19))) % 0.51/0.71 (step @p12 :rule cong :premises (@p11 @p10) :args (@t12)) % 0.51/0.71 (step @p13 :rule cong :premises (@p12) :args (@t13)) % 0.51/0.71 (step @p14 :rule eq_resolve :premises (@p1 @p13)) % 0.51/0.71 (step @p15 :rule not_equiv_elim2 :premises (@p14)) % 0.51/0.71 (step @p16 :rule eq_resolve :premises (@p15 @p5)) % 0.51/0.71 (step @p17 :rule refl :args (@t22)) % 0.51/0.71 (step @p18 :rule nary_cong :premises (@p4 @p17) :args ((or @t20 @t22))) % 0.51/0.71 (step @p19 :rule eq-symm :args (@t21 @t1)) % 0.51/0.71 (step @p20 :rule refl :args (@t9)) % 0.51/0.71 (step @p21 :rule cong :premises (@p20 @p19) :args (@t23)) % 0.51/0.71 (step @p22 :rule cong :premises (@p21) :args (@t24)) % 0.51/0.71 (step @p23 :rule bool-double-not-elim :args (@t24)) % 0.51/0.71 (step @p24 :rule trans :premises (@p23 @p22)) % 0.51/0.71 (step @p25 :rule refl :args (@t19)) % 0.51/0.71 (step @p26 :rule cong :premises (@p25 @p24) :args ((=> @t19 @t25))) % 0.51/0.71 (assume-push @p293 @t19) % 0.51/0.71 (step @p28 :rule skolemize :premises (@p293)) % 0.51/0.71 (step-pop @p294 :rule scope :premises (@p28)) % 0.51/0.71 (step @p29 :rule process_scope :premises (@p294) :args (@t25)) % 0.51/0.71 (step @p31 :rule eq_resolve :premises (@p29 @p26)) % 0.51/0.71 (step @p32 :rule implies_elim :premises (@p31)) % 0.51/0.71 (step @p33 :rule eq_resolve :premises (@p32 @p18)) % 0.51/0.71 (step @p34 :rule bool-eq-true :args (@t28)) % 0.51/0.71 (step @p35 :rule eq-refl :args (@t21)) % 0.51/0.71 (step @p36 :rule refl :args (@t28)) % 0.51/0.71 (step @p37 :rule cong :premises (@p36 @p35) :args (@t29)) % 0.51/0.71 (step @p38 :rule trans :premises (@p37 @p34)) % 0.51/0.71 (step @p39 :rule cong :premises (@p17 @p38) :args ((=> @t22 @t29))) % 0.51/0.71 (assume-push @p295 @t22) % 0.51/0.71 (step @p41 :rule instantiate :premises (@p295) :args ((@list @t21))) % 0.51/0.71 (step-pop @p296 :rule scope :premises (@p41)) % 0.51/0.71 (step @p42 :rule process_scope :premises (@p296) :args (@t29)) % 0.51/0.71 (step @p44 :rule eq_resolve :premises (@p42 @p39)) % 0.51/0.71 (step @p45 :rule implies_elim :premises (@p44)) % 0.51/0.71 (step @p46 :rule eq-symm :args (@t26 @t1)) % 0.51/0.71 (step @p47 :rule refl :args (@t4)) % 0.51/0.71 (step @p48 :rule cong :premises (@p47 @p46) :args ((= @t4 @t30))) % 0.51/0.71 (step @p49 :rule eq-symm :args (@t30 @t4)) % 0.51/0.71 (step @p50 :rule trans :premises (@p49 @p48)) % 0.51/0.71 (step @p51 :rule cong :premises (@p50) :args (@t31)) % 0.51/0.71 (step @p52 :rule cong :premises (@p51) :args (@t32)) % 0.51/0.71 (step @p53 :rule refl :args (@t15)) % 0.51/0.71 (step @p54 :rule cong :premises (@p53 @p52) :args ((=> @t15 @t32))) % 0.51/0.71 (assume-push @p297 @t15) % 0.51/0.71 (step @p56 :rule instantiate :premises (@p297) :args ((@list @t26))) % 0.51/0.71 (step-pop @p298 :rule scope :premises (@p56)) % 0.51/0.71 (step @p57 :rule process_scope :premises (@p298) :args (@t32)) % 0.51/0.71 (step @p59 :rule eq_resolve :premises (@p57 @p54)) % 0.51/0.71 (step @p60 :rule implies_elim :premises (@p59)) % 0.51/0.71 (step @p61 :rule refl :args (@t40)) % 0.51/0.71 (step @p62 :rule bool-double-not-elim :args (@t33)) % 0.51/0.71 (step @p63 :rule nary_cong :premises (@p62 @p61) :args ((or (not @t41) @t40))) % 0.51/0.71 (step @p64 :rule eq-symm :args (@t34 @t26)) % 0.51/0.71 (step @p65 :rule refl :args (@t38)) % 0.51/0.71 (step @p66 :rule cong :premises (@p65 @p64) :args (@t42)) % 0.51/0.71 (step @p67 :rule cong :premises (@p66) :args (@t43)) % 0.51/0.71 (step @p68 :rule refl :args (@t41)) % 0.51/0.71 (step @p69 :rule cong :premises (@p68 @p67) :args ((=> @t41 @t43))) % 0.51/0.71 (assume-push @p299 @t41) % 0.51/0.71 (step @p71 :rule skolemize :premises (@p299)) % 0.51/0.71 (step-pop @p300 :rule scope :premises (@p71)) % 0.51/0.71 (step @p72 :rule process_scope :premises (@p300) :args (@t43)) % 0.51/0.71 (step @p74 :rule eq_resolve :premises (@p72 @p69)) % 0.51/0.71 (step @p75 :rule implies_elim :premises (@p74)) % 0.51/0.71 (step @p76 :rule eq_resolve :premises (@p75 @p63)) % 0.51/0.71 (step @p77 :rule eq-symm :args (@t36 @t21)) % 0.51/0.71 (step @p78 :rule refl :args (@t44)) % 0.51/0.71 (step @p79 :rule cong :premises (@p78 @p77) :args (@t45)) % 0.51/0.71 (step @p80 :rule cong :premises (@p17 @p79) :args ((=> @t22 @t45))) % 0.51/0.71 (assume-push @p301 @t22) % 0.51/0.71 (step @p82 :rule instantiate :premises (@p301) :args ((@list @t36))) % 0.51/0.71 (step-pop @p302 :rule scope :premises (@p82)) % 0.51/0.71 (step @p83 :rule process_scope :premises (@p302) :args (@t45)) % 0.51/0.71 (step @p85 :rule eq_resolve :premises (@p83 @p80)) % 0.51/0.71 (step @p86 :rule implies_elim :premises (@p85)) % 0.51/0.71 (step @p87 :rule cnf_equiv_neg1 :args (@t39)) % 0.51/0.71 (step @p88 :rule reordering :premises (@p87) :args ((or @t38 @t35 @t39))) % 0.51/0.71 (assume-push @p303 @t38) % 0.51/0.71 (assume-push @p304 @t46) % 0.51/0.71 (assume-push @p305 @t38) % 0.51/0.71 (assume-push @p306 @t46) % 0.51/0.71 (step @p93 :rule symm :premises (@p303)) % 0.51/0.71 (step @p94 :rule cong :premises (@p304) :args (@t26)) % 0.51/0.71 (step @p95 :rule trans :premises (@p94 @p93)) % 0.51/0.71 (step-pop @p307 :rule scope :premises (@p95)) % 0.51/0.71 (step-pop @p308 :rule scope :premises (@p307)) % 0.51/0.71 (step @p96 :rule process_scope :premises (@p308) :args (@t35)) % 0.51/0.71 (step @p99 :rule and_intro :premises (@p303 @p304)) % 0.51/0.71 (step @p100 :rule modus_ponens :premises (@p99 @p96)) % 0.51/0.71 (step-pop @p309 :rule scope :premises (@p100)) % 0.51/0.71 (step-pop @p310 :rule scope :premises (@p309)) % 0.51/0.71 (step @p101 :rule process_scope :premises (@p310) :args (@t35)) % 0.51/0.71 (step @p104 :rule implies_elim :premises (@p101)) % 0.51/0.71 (step @p105 :rule cnf_and_neg :args (@t47)) % 0.51/0.71 (step @p106 :rule resolution :premises (@p105 @p104) :args (true @t47)) % 0.51/0.71 (step @p107 :rule reordering :premises (@p106) :args ((or @t35 (not @t38) @t48))) % 0.51/0.71 (step @p108 :rule chain_m_resolution :premises (@p107 @p88) :args ((or @t35 @t39 @t48) @t49 (@list @t38))) % 0.51/0.71 (step @p109 :rule cnf_equiv_neg2 :args (@t39)) % 0.51/0.71 (assume-push @p311 @t35) % 0.51/0.71 (assume-push @p312 @t46) % 0.51/0.71 (assume-push @p313 @t46) % 0.51/0.71 (assume-push @p314 @t35) % 0.51/0.71 (step @p114 :rule cong :premises (@p312) :args (@t26)) % 0.51/0.71 (step @p115 :rule symm :premises (@p311)) % 0.51/0.71 (step @p116 :rule trans :premises (@p115 @p114)) % 0.51/0.71 (step-pop @p315 :rule scope :premises (@p116)) % 0.51/0.71 (step-pop @p316 :rule scope :premises (@p315)) % 0.51/0.71 (step @p117 :rule process_scope :premises (@p316) :args (@t38)) % 0.51/0.71 (step @p120 :rule and_intro :premises (@p312 @p311)) % 0.51/0.71 (step @p121 :rule modus_ponens :premises (@p120 @p117)) % 0.51/0.71 (step-pop @p317 :rule scope :premises (@p121)) % 0.51/0.71 (step-pop @p318 :rule scope :premises (@p317)) % 0.51/0.71 (step @p122 :rule process_scope :premises (@p318) :args (@t38)) % 0.51/0.71 (step @p125 :rule implies_elim :premises (@p122)) % 0.51/0.71 (step @p126 :rule cnf_and_neg :args (@t50)) % 0.51/0.71 (step @p127 :rule resolution :premises (@p126 @p125) :args (true @t50)) % 0.51/0.71 (step @p128 :rule reordering :premises (@p127) :args ((or @t38 (not @t35) @t48))) % 0.51/0.71 (step @p129 :rule chain_m_resolution :premises (@p128 @p109 @p108) :args ((or @t39 @t48) (@list true false) (@list @t38 @t35))) % 0.51/0.71 (step @p130 :rule cnf_equiv_pos1 :args (@t51)) % 0.51/0.71 (step @p131 :rule reordering :premises (@p130) :args ((or @t46 (not @t44) (not @t51)))) % 0.51/0.71 (assume-push @p319 @t28) % 0.51/0.71 (assume-push @p320 @t35) % 0.51/0.71 (assume-push @p321 @t35) % 0.51/0.71 (assume-push @p322 @t28) % 0.51/0.71 (step @p136 :rule cong :premises (@p320) :args (@t27)) % 0.51/0.71 (step @p137 :rule trans :premises (@p319 @p136)) % 0.51/0.71 (step-pop @p323 :rule scope :premises (@p137)) % 0.51/0.71 (step-pop @p324 :rule scope :premises (@p323)) % 0.51/0.71 (step @p138 :rule process_scope :premises (@p324) :args (@t46)) % 0.51/0.71 (step @p141 :rule and_intro :premises (@p320 @p319)) % 0.51/0.71 (step @p142 :rule modus_ponens :premises (@p141 @p138)) % 0.51/0.71 (step-pop @p325 :rule scope :premises (@p142)) % 0.51/0.71 (step-pop @p326 :rule scope :premises (@p325)) % 0.51/0.71 (step @p143 :rule process_scope :premises (@p326) :args (@t46)) % 0.51/0.71 (step @p146 :rule implies_elim :premises (@p143)) % 0.51/0.71 (step @p147 :rule cnf_and_neg :args (@t52)) % 0.51/0.71 (step @p148 :rule resolution :premises (@p147 @p146) :args (true @t52)) % 0.51/0.71 (assume-push @p327 @t38) % 0.51/0.71 (assume-push @p328 @t38) % 0.51/0.71 (step @p151 :rule cong :premises (@p327) :args (@t36)) % 0.51/0.71 (step-pop @p329 :rule scope :premises (@p151)) % 0.51/0.71 (step @p152 :rule process_scope :premises (@p329) :args (@t44)) % 0.51/0.71 (step @p154 :rule modus_ponens :premises (@p327 @p152)) % 0.51/0.71 (step-pop @p330 :rule scope :premises (@p154)) % 0.51/0.71 (step @p155 :rule process_scope :premises (@p330) :args (@t44)) % 0.51/0.71 (step @p157 :rule implies_elim :premises (@p155)) % 0.51/0.71 (step @p158 :rule chain_m_resolution :premises (@p157 @p88 @p148 @p131 @p129 @p86 @p76 @p60 @p45 @p33 @p16) :args (@t16 (@list false true true true false true true false false false) (@list @t38 @t35 @t44 @t46 @t51 @t39 @t33 @t28 @t22 @t15))) % 0.51/0.71 (step @p159 :rule not_equiv_elim1 :premises (@p14)) % 0.51/0.71 (step @p160 :rule chain_m_resolution :premises (@p159 @p158) :args (@t17 @t49 @t53)) % 0.51/0.71 (step @p161 :rule refl :args (@t55)) % 0.51/0.71 (step @p162 :rule nary_cong :premises (@p3 @p161) :args ((or @t18 @t55))) % 0.51/0.71 (step @p163 :rule eq-symm :args (@t54 @t1)) % 0.51/0.71 (step @p164 :rule cong :premises (@p47 @p163) :args ((= @t4 @t56))) % 0.51/0.71 (step @p165 :rule eq-symm :args (@t56 @t4)) % 0.51/0.71 (step @p166 :rule trans :premises (@p165 @p164)) % 0.51/0.71 (step @p167 :rule cong :premises (@p166) :args (@t57)) % 0.51/0.71 (step @p168 :rule bool-double-not-elim :args (@t57)) % 0.51/0.71 (step @p169 :rule trans :premises (@p168 @p167)) % 0.51/0.71 (step @p170 :rule refl :args (@t17)) % 0.51/0.71 (step @p171 :rule cong :premises (@p170 @p169) :args ((=> @t17 @t58))) % 0.51/0.71 (assume-push @p331 @t17) % 0.51/0.71 (step @p173 :rule skolemize :premises (@p331)) % 0.51/0.71 (step-pop @p332 :rule scope :premises (@p173)) % 0.51/0.71 (step @p174 :rule process_scope :premises (@p332) :args (@t58)) % 0.51/0.71 (step @p176 :rule eq_resolve :premises (@p174 @p171)) % 0.51/0.71 (step @p177 :rule implies_elim :premises (@p176)) % 0.51/0.71 (step @p178 :rule eq_resolve :premises (@p177 @p162)) % 0.51/0.71 (step @p179 :rule chain_m_resolution :premises (@p178 @p160) :args (@t55 @t59 (@list @t15))) % 0.51/0.71 (step @p180 :rule bool-eq-true :args (@t62)) % 0.51/0.71 (step @p181 :rule eq-refl :args (@t54)) % 0.51/0.71 (step @p182 :rule refl :args (@t62)) % 0.51/0.71 (step @p183 :rule cong :premises (@p182 @p181) :args (@t63)) % 0.51/0.71 (step @p184 :rule trans :premises (@p183 @p180)) % 0.51/0.71 (step @p185 :rule cong :premises (@p161 @p184) :args ((=> @t55 @t63))) % 0.51/0.71 (assume-push @p333 @t55) % 0.51/0.71 (step @p187 :rule instantiate :premises (@p333) :args ((@list @t54))) % 0.51/0.71 (step-pop @p334 :rule scope :premises (@p187)) % 0.51/0.71 (step @p188 :rule process_scope :premises (@p334) :args (@t63)) % 0.51/0.71 (step @p190 :rule eq_resolve :premises (@p188 @p185)) % 0.51/0.71 (step @p191 :rule implies_elim :premises (@p190)) % 0.51/0.71 (step @p192 :rule chain_m_resolution :premises (@p191 @p179) :args (@t62 @t49 @t64)) % 0.51/0.71 (step @p193 :rule eq-symm :args (@t60 @t1)) % 0.51/0.71 (step @p194 :rule cong :premises (@p20 @p193) :args (@t65)) % 0.51/0.71 (step @p195 :rule cong :premises (@p194) :args (@t66)) % 0.51/0.71 (step @p196 :rule cong :premises (@p195) :args (@t67)) % 0.51/0.71 (step @p197 :rule refl :args (@t16)) % 0.51/0.71 (step @p198 :rule cong :premises (@p197 @p196) :args ((=> @t16 @t67))) % 0.51/0.71 (assume-push @p335 @t16) % 0.51/0.71 (step @p200 :rule instantiate :premises (@p335) :args ((@list @t60))) % 0.51/0.71 (step-pop @p336 :rule scope :premises (@p200)) % 0.51/0.71 (step @p201 :rule process_scope :premises (@p336) :args (@t67)) % 0.51/0.71 (step @p203 :rule eq_resolve :premises (@p201 @p198)) % 0.51/0.71 (step @p204 :rule implies_elim :premises (@p203)) % 0.51/0.71 (step @p205 :rule chain_m_resolution :premises (@p204 @p158) :args (@t69 @t49 @t53)) % 0.51/0.71 (step @p206 :rule refl :args (@t76)) % 0.51/0.71 (step @p207 :rule bool-double-not-elim :args (@t68)) % 0.51/0.71 (step @p208 :rule nary_cong :premises (@p207 @p206) :args ((or (not @t69) @t76))) % 0.51/0.71 (step @p209 :rule eq-symm :args (@t70 @t60)) % 0.51/0.71 (step @p210 :rule refl :args (@t74)) % 0.51/0.71 (step @p211 :rule cong :premises (@p210 @p209) :args (@t77)) % 0.51/0.71 (step @p212 :rule cong :premises (@p211) :args (@t78)) % 0.51/0.71 (step @p213 :rule refl :args (@t69)) % 0.51/0.71 (step @p214 :rule cong :premises (@p213 @p212) :args ((=> @t69 @t78))) % 0.51/0.71 (assume-push @p337 @t69) % 0.51/0.71 (step @p216 :rule skolemize :premises (@p337)) % 0.51/0.71 (step-pop @p338 :rule scope :premises (@p216)) % 0.51/0.71 (step @p217 :rule process_scope :premises (@p338) :args (@t78)) % 0.51/0.71 (step @p219 :rule eq_resolve :premises (@p217 @p214)) % 0.51/0.71 (step @p220 :rule implies_elim :premises (@p219)) % 0.51/0.71 (step @p221 :rule eq_resolve :premises (@p220 @p208)) % 0.51/0.71 (step @p222 :rule chain_m_resolution :premises (@p221 @p205) :args (@t76 @t59 (@list @t68))) % 0.51/0.71 (step @p223 :rule cnf_equiv_neg2 :args (@t75)) % 0.51/0.71 (assume-push @p339 @t74) % 0.51/0.71 (assume-push @p340 @t74) % 0.51/0.71 (step @p226 :rule cong :premises (@p339) :args (@t72)) % 0.51/0.71 (step-pop @p341 :rule scope :premises (@p226)) % 0.51/0.71 (step @p227 :rule process_scope :premises (@p341) :args (@t79)) % 0.51/0.71 (step @p229 :rule modus_ponens :premises (@p339 @p227)) % 0.51/0.71 (step-pop @p342 :rule scope :premises (@p229)) % 0.51/0.71 (step @p230 :rule process_scope :premises (@p342) :args (@t79)) % 0.51/0.71 (step @p232 :rule implies_elim :premises (@p230)) % 0.51/0.71 (step @p233 :rule refl :args (@t79)) % 0.51/0.71 (step @p234 :rule eq-symm :args (@t72 @t54)) % 0.51/0.71 (step @p235 :rule cong :premises (@p234 @p233) :args ((= @t80 @t79))) % 0.51/0.71 (step @p236 :rule eq-symm :args (@t79 @t80)) % 0.51/0.71 (step @p237 :rule trans :premises (@p236 @p235)) % 0.51/0.71 (step @p238 :rule cong :premises (@p161 @p237) :args ((=> @t55 @t81))) % 0.51/0.71 (assume-push @p343 @t55) % 0.51/0.71 (step @p240 :rule instantiate :premises (@p343) :args ((@list @t72))) % 0.51/0.71 (step-pop @p344 :rule scope :premises (@p240)) % 0.51/0.71 (step @p241 :rule process_scope :premises (@p344) :args (@t81)) % 0.51/0.71 (step @p243 :rule eq_resolve :premises (@p241 @p238)) % 0.51/0.71 (step @p244 :rule implies_elim :premises (@p243)) % 0.51/0.71 (step @p245 :rule chain_m_resolution :premises (@p244 @p179) :args (@t83 @t49 @t64)) % 0.51/0.71 (step @p246 :rule cnf_equiv_pos2 :args (@t83)) % 0.51/0.71 (step @p247 :rule reordering :premises (@p246) :args ((or @t82 (not @t79) (not @t83)))) % 0.51/0.71 (assume-push @p345 @t74) % 0.51/0.71 (assume-push @p346 @t82) % 0.51/0.71 (assume-push @p347 @t74) % 0.51/0.71 (assume-push @p348 @t82) % 0.51/0.71 (step @p252 :rule symm :premises (@p345)) % 0.51/0.71 (step @p253 :rule cong :premises (@p346) :args (@t60)) % 0.51/0.71 (step @p254 :rule trans :premises (@p253 @p252)) % 0.51/0.71 (step-pop @p349 :rule scope :premises (@p254)) % 0.51/0.71 (step-pop @p350 :rule scope :premises (@p349)) % 0.51/0.71 (step @p255 :rule process_scope :premises (@p350) :args (@t71)) % 0.51/0.71 (step @p258 :rule and_intro :premises (@p345 @p346)) % 0.51/0.71 (step @p259 :rule modus_ponens :premises (@p258 @p255)) % 0.51/0.71 (step-pop @p351 :rule scope :premises (@p259)) % 0.51/0.71 (step-pop @p352 :rule scope :premises (@p351)) % 0.51/0.71 (step @p260 :rule process_scope :premises (@p352) :args (@t71)) % 0.51/0.71 (step @p263 :rule implies_elim :premises (@p260)) % 0.51/0.71 (step @p264 :rule cnf_and_neg :args (@t84)) % 0.51/0.71 (step @p265 :rule resolution :premises (@p264 @p263) :args (true @t84)) % 0.51/0.71 (step @p266 :rule reordering :premises (@p265) :args ((or @t71 @t85 (not @t82)))) % 0.51/0.71 (step @p267 :rule chain_m_resolution :premises (@p266 @p247 @p245 @p232 @p223 @p222) :args (@t85 (@list false false false true true) (@list @t82 @t83 @t79 @t71 @t75))) % 0.51/0.71 (step @p268 :rule cnf_equiv_neg1 :args (@t75)) % 0.51/0.71 (step @p269 :rule reordering :premises (@p268) :args ((or @t74 @t71 @t75))) % 0.51/0.71 (step @p270 :rule chain_m_resolution :premises (@p269 @p267 @p222) :args (@t71 (@list true true) (@list @t74 @t75))) % 0.51/0.71 (assume-push @p353 @t62) % 0.51/0.71 (assume-push @p354 @t71) % 0.51/0.71 (assume-push @p355 @t71) % 0.51/0.71 (assume-push @p356 @t62) % 0.51/0.71 (step @p275 :rule cong :premises (@p354) :args (@t61)) % 0.51/0.71 (step @p276 :rule trans :premises (@p353 @p275)) % 0.51/0.71 (step @p277 :rule cong :premises (@p276) :args (@t60)) % 0.51/0.71 (step @p278 :rule symm :premises (@p354)) % 0.51/0.71 (step @p279 :rule trans :premises (@p278 @p277)) % 0.51/0.71 (step-pop @p357 :rule scope :premises (@p279)) % 0.51/0.71 (step-pop @p358 :rule scope :premises (@p357)) % 0.51/0.71 (step @p280 :rule process_scope :premises (@p358) :args (@t74)) % 0.51/0.71 (step @p283 :rule and_intro :premises (@p354 @p353)) % 0.51/0.71 (step @p284 :rule modus_ponens :premises (@p283 @p280)) % 0.51/0.71 (step-pop @p359 :rule scope :premises (@p284)) % 0.51/0.71 (step-pop @p360 :rule scope :premises (@p359)) % 0.51/0.71 (step @p285 :rule process_scope :premises (@p360) :args (@t74)) % 0.51/0.71 (step @p288 :rule implies_elim :premises (@p285)) % 0.51/0.71 (step @p289 :rule cnf_and_neg :args (@t86)) % 0.51/0.71 (step @p290 :rule resolution :premises (@p289 @p288) :args (true @t86)) % 0.51/0.71 (step @p291 :rule reordering :premises (@p290) :args ((or (not @t62) @t74 (not @t71)))) % 0.51/0.71 (step @p292 false :rule chain_m_resolution :premises (@p291 @p270 @p267 @p192) :args (false (@list false true false) (@list @t71 @t74 @t62))) % 0.51/0.71 ) % 0.51/0.71 % SZS output end Proof % 0.51/0.71 % cvc5 exiting %------------------------------------------------------------------------------