%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYO540^1 : TPTP v9.2.1. Released v5.2.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n024.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 09:13:05 AM UTC 2026 % Result : Theorem 0.16s 0.40s % Output : Proof 0.16s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.06 % Problem : SYO540^1 : TPTP v9.2.1. Released v5.2.0. % 0.00/0.07 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.08/0.25 % Computer : n024.cluster.edu % 0.08/0.25 % Model : x86_64 x86_64 % 0.08/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.08/0.25 % Memory : 8042.1875MB % 0.08/0.25 % OS : Linux 3.10.0-693.el7.x86_64 % 0.08/0.25 % CPULimit : 300 % 0.08/0.25 % WCLimit : 300 % 0.08/0.25 % DateTime : Tue Jun 2 19:19:45 EDT 2026 % 0.08/0.25 % CPUTime : % 0.16/0.33 %----Proving TH0 % 0.16/0.40 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.16/0.40 % SZS status Theorem % 0.16/0.40 % SZS output start Proof % 0.16/0.40 ( % 0.16/0.40 (declare-sort $$unsorted 0) % 0.16/0.40 (declare-const tptp.eps (-> (-> $$unsorted Bool) $$unsorted)) % 0.16/0.40 (define tptp.if () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "Z" $$unsorted))) (let ((_let_3 (@var "B" Bool))) (let ((_let_4 (@var "X" $$unsorted))) (lambda (@list _let_3 _let_4 _let_1) (_ tptp.eps (lambda (@list _let_2) (or (and _let_3 (= _let_2 _let_4)) (and (not _let_3) (= _let_2 _let_1))))))))))) % 0.16/0.40 (define @t1 () (@var "P" (-> $$unsorted Bool))) % 0.16/0.40 (define @t2 () (_ tptp.eps @t1)) % 0.16/0.40 (define @t3 () (_ @t1 @t2)) % 0.16/0.40 (define @t4 () (@var "X" $$unsorted)) % 0.16/0.40 (define @t5 () (_ @t1 @t4)) % 0.16/0.40 (define @t6 () (@list @t4)) % 0.16/0.40 (define @t7 () (exists @t6 @t5)) % 0.16/0.40 (define @t8 () (=> @t7 @t3)) % 0.16/0.40 (define @t9 () (@list @t1)) % 0.16/0.40 (define @t10 () (forall @t9 @t8)) % 0.16/0.40 (define @t11 () (@var "B" Bool)) % 0.16/0.40 (define @t12 () (= (_ (_ (_ tptp.if @t11) @t4) @t4) @t4)) % 0.16/0.40 (define @t13 () (@list @t11 @t4)) % 0.16/0.40 (define @t14 () (forall @t13 @t12)) % 0.16/0.40 (define @t15 () (not @t14)) % 0.16/0.40 (define @t16 () (@var "Y" $$unsorted)) % 0.16/0.40 (define @t17 () (@var "Z" $$unsorted)) % 0.16/0.40 (define @t18 () (not @t11)) % 0.16/0.40 (define @t19 () (and @t18 (= @t17 @t16))) % 0.16/0.40 (define @t20 () (and @t11 (= @t17 @t4))) % 0.16/0.40 (define @t21 () (or @t20 @t19)) % 0.16/0.40 (define @t22 () (@list @t17)) % 0.16/0.40 (define @t23 () (lambda @t22 @t21)) % 0.16/0.40 (define @t24 () (@list @t11 @t4 @t16)) % 0.16/0.40 (define @t25 () (lambda @t24 (_ tptp.eps @t23))) % 0.16/0.40 (define @t26 () (= @t4 @t17)) % 0.16/0.40 (define @t27 () (and @t11 @t26)) % 0.16/0.40 (define @t28 () (lambda @t22 (or @t27 (and @t18 @t26)))) % 0.16/0.40 (define @t29 () (tptp.eps @t28)) % 0.16/0.40 (define @t30 () (_ tptp.eps @t28)) % 0.16/0.40 (define @t31 () (= @t4 @t30)) % 0.16/0.40 (define @t32 () (_ tptp.eps (lambda @t22 (or @t27 (and @t18 (= @t16 @t17)))))) % 0.16/0.40 (define @t33 () (lambda (@list @t16) @t32)) % 0.16/0.40 (define @t34 () (lambda (@list @t4 @t16) @t32)) % 0.16/0.40 (define @t35 () (_ (lambda @t24 @t32) @t11)) % 0.16/0.40 (define @t36 () (= (_ (_ @t35 @t4) @t4) @t4)) % 0.16/0.40 (define @t37 () (forall @t13 @t36)) % 0.16/0.40 (define @t38 () (forall @t13 (= @t4 @t29))) % 0.16/0.40 (define @t39 () (@quantifiers_skolemize @t38 1)) % 0.16/0.40 (define @t40 () (= @t17 @t39)) % 0.16/0.40 (define @t41 () (@quantifiers_skolemize @t38 0)) % 0.16/0.40 (define @t42 () (not @t41)) % 0.16/0.40 (define @t43 () (lambda @t22 (or (and @t41 @t40) (and @t42 @t40)))) % 0.16/0.40 (define @t44 () (@purify @t43)) % 0.16/0.40 (define @t45 () (= @t39 (tptp.eps @t44))) % 0.16/0.40 (define @t46 () (not @t45)) % 0.16/0.40 (define @t47 () (not @t38)) % 0.16/0.40 (define @t48 () (tptp.eps @t43)) % 0.16/0.40 (define @t49 () (= @t39 @t48)) % 0.16/0.40 (define @t50 () (not @t49)) % 0.16/0.40 (define @t51 () (= @t39 @t17)) % 0.16/0.40 (define @t52 () (and @t42 @t51)) % 0.16/0.40 (define @t53 () (and @t41 @t51)) % 0.16/0.40 (define @t54 () (or @t53 @t52)) % 0.16/0.40 (define @t55 () (lambda @t22 @t54)) % 0.16/0.40 (define @t56 () (tptp.eps @t55)) % 0.16/0.40 (define @t57 () (= @t39 @t56)) % 0.16/0.40 (define @t58 () (not @t57)) % 0.16/0.40 (define @t59 () (@list true)) % 0.16/0.40 (define @t60 () (tptp.eps @t1)) % 0.16/0.40 (define @t61 () (_ @t1 @t60)) % 0.16/0.40 (define @t62 () (@var "BOUND_VARIABLE_7476" $$unsorted)) % 0.16/0.40 (define @t63 () (not (_ @t1 @t62))) % 0.16/0.40 (define @t64 () (or @t63 @t61)) % 0.16/0.40 (define @t65 () (forall (@list @t1 @t62) @t64)) % 0.16/0.40 (define @t66 () (@list @t62)) % 0.16/0.40 (define @t67 () (forall @t66 @t64)) % 0.16/0.40 (define @t68 () (forall @t66 @t63)) % 0.16/0.40 (define @t69 () (or @t68 @t61)) % 0.16/0.40 (define @t70 () (_ @t1 @t4)) % 0.16/0.40 (define @t71 () (forall @t6 (not @t70))) % 0.16/0.40 (define @t72 () (or @t71 @t3)) % 0.16/0.40 (define @t73 () (not @t71)) % 0.16/0.40 (define @t74 () (not @t5)) % 0.16/0.40 (define @t75 () (forall @t6 @t74)) % 0.16/0.40 (define @t76 () (not @t75)) % 0.16/0.40 (define @t77 () (@var "BOUND_VARIABLE_14751" $$unsorted)) % 0.16/0.40 (define @t78 () (@list @t77)) % 0.16/0.40 (define @t79 () (lambda @t78 (= @t39 @t77))) % 0.16/0.40 (define @t80 () (@purify @t79)) % 0.16/0.40 (define @t81 () (tptp.eps @t79)) % 0.16/0.40 (define @t82 () (= @t39 @t81)) % 0.16/0.40 (define @t83 () (lambda @t78 (= @t77 @t39))) % 0.16/0.40 (define @t84 () (tptp.eps @t83)) % 0.16/0.40 (define @t85 () (_ @t83 @t84)) % 0.16/0.40 (define @t86 () (_ @t83 @t39)) % 0.16/0.40 (define @t87 () (not @t86)) % 0.16/0.40 (define @t88 () (or @t87 @t85)) % 0.16/0.40 (define @t89 () (tptp.eps @t80)) % 0.16/0.40 (define @t90 () (= @t39 @t89)) % 0.16/0.40 (define @t91 () (= @t44 @t80)) % 0.16/0.40 (define @t92 () (and @t90 @t91)) % 0.16/0.40 (define @t93 () (not @t91)) % 0.16/0.40 (define @t94 () (@const 0 $$unsorted)) % 0.16/0.40 (define @t95 () (= @t39 @t94)) % 0.16/0.40 (define @t96 () (and @t42 @t95)) % 0.16/0.40 (define @t97 () (and @t41 @t95)) % 0.16/0.40 (define @t98 () (or @t97 @t96)) % 0.16/0.40 (define @t99 () (= (_ @t79 @t94) @t95)) % 0.16/0.40 (define @t100 () (_ @t80 @t94)) % 0.16/0.40 (define @t101 () (= @t94 @t39)) % 0.16/0.40 (define @t102 () (and @t42 @t101)) % 0.16/0.40 (define @t103 () (and @t41 @t101)) % 0.16/0.40 (define @t104 () (or @t103 @t102)) % 0.16/0.40 (define @t105 () (_ @t43 @t94)) % 0.16/0.40 (define @t106 () (_ @t44 @t94)) % 0.16/0.40 (define @t107 () (= @t106 @t100)) % 0.16/0.40 (define @t108 () (not @t107)) % 0.16/0.40 (define @t109 () (or @t91 @t108)) % 0.16/0.40 (define @t110 () (= @t95 @t98)) % 0.16/0.40 (define @t111 () (not @t95)) % 0.16/0.40 (define @t112 () (not @t97)) % 0.16/0.40 (define @t113 () (@list @t95)) % 0.16/0.40 (define @t114 () (not @t96)) % 0.16/0.40 (assume @p1 @t10) % 0.16/0.40 (assume @p2 @t15) % 0.16/0.40 (assume @p3 true) % 0.16/0.40 (step @p4 (= tptp.if @t25) :rule refl :args (@t25)) % 0.16/0.40 (step @p5 :rule refl :args (@t29)) % 0.16/0.40 (step @p6 :rule refl :args (@t30)) % 0.16/0.40 (step @p7 :rule cong :premises (@p6 @p5) :args ((= @t30 @t29))) % 0.16/0.40 (step @p8 :rule symm :premises (@p7)) % 0.16/0.40 (step @p9 :rule eq_resolve :premises (@p6 @p8)) % 0.16/0.40 (step @p10 :rule refl :args (@t4)) % 0.16/0.40 (step @p11 :rule cong :premises (@p10 @p9) :args (@t31)) % 0.16/0.40 (step @p12 :rule cong :premises (@p11) :args ((forall @t13 @t31))) % 0.16/0.40 (step @p13 :rule eq-symm :args (@t30 @t4)) % 0.16/0.40 (step @p14 :rule refl :args (@t4)) % 0.16/0.40 (step @p15 :rule beta-reduce :args ((= (_ @t33 @t4) @t30))) % 0.16/0.40 (step @p16 :rule beta-reduce :args ((= (_ @t34 @t4) @t33))) % 0.16/0.40 (step @p17 :rule beta-reduce :args ((= @t35 @t34))) % 0.16/0.40 (step @p18 :rule ho_cong :premises (@p17 @p14)) % 0.16/0.40 (step @p19 :rule trans :premises (@p18 @p16)) % 0.16/0.40 (step @p20 :rule ho_cong :premises (@p19 @p14)) % 0.16/0.40 (step @p21 :rule trans :premises (@p20 @p15)) % 0.16/0.40 (step @p22 :rule cong :premises (@p21 @p14) :args (@t36)) % 0.16/0.40 (step @p23 :rule trans :premises (@p22 @p13)) % 0.16/0.40 (step @p24 :rule cong :premises (@p23) :args (@t37)) % 0.16/0.40 (step @p25 :rule trans :premises (@p24 @p12)) % 0.16/0.40 (step @p26 :rule cong :premises (@p25) :args ((not @t37))) % 0.16/0.40 (step @p27 :rule refl :args (@t11)) % 0.16/0.40 (step @p28 :rule eq-symm :args (@t17 @t16)) % 0.16/0.40 (step @p29 :rule refl :args (@t18)) % 0.16/0.40 (step @p30 :rule nary_cong :premises (@p29 @p28) :args (@t19)) % 0.16/0.40 (step @p31 :rule eq-symm :args (@t17 @t4)) % 0.16/0.40 (step @p32 :rule nary_cong :premises (@p27 @p31) :args (@t20)) % 0.16/0.40 (step @p33 :rule nary_cong :premises (@p32 @p30) :args (@t21)) % 0.16/0.40 (step @p34 :rule cong :premises (@p33) :args (@t23)) % 0.16/0.40 (step @p35 :rule refl :args (tptp.eps)) % 0.16/0.40 (step @p36 :rule ho_cong :premises (@p35 @p34)) % 0.16/0.40 (step @p37 :rule cong :premises (@p36) :args (@t25)) % 0.16/0.40 (step @p38 :rule trans :premises (@p4 @p37)) % 0.16/0.40 (step @p39 :rule ho_cong :premises (@p38 @p27)) % 0.16/0.40 (step @p40 :rule ho_cong :premises (@p39 @p14)) % 0.16/0.40 (step @p41 :rule ho_cong :premises (@p40 @p14)) % 0.16/0.40 (step @p42 :rule cong :premises (@p41 @p14) :args (@t12)) % 0.16/0.40 (step @p43 :rule cong :premises (@p42) :args (@t14)) % 0.16/0.40 (step @p44 :rule cong :premises (@p43) :args (@t15)) % 0.16/0.40 (step @p45 :rule trans :premises (@p44 @p26)) % 0.16/0.40 (step @p46 :rule eq_resolve :premises (@p2 @p45)) % 0.16/0.40 (step @p47 :rule refl :args (@t46)) % 0.16/0.40 (step @p48 :rule bool-double-not-elim :args (@t38)) % 0.16/0.40 (step @p49 :rule nary_cong :premises (@p48 @p47) :args ((or (not @t47) @t46))) % 0.16/0.40 (step @p50 :rule eq-refl :args (@t43)) % 0.16/0.40 (step @p51 :rule skolem_intro :args (@t44)) % 0.16/0.40 (step @p52 :rule refl :args (@t43)) % 0.16/0.40 (step @p53 :rule cong :premises (@p52 @p51) :args ((= @t43 @t44))) % 0.16/0.40 (step @p54 :rule trans :premises (@p53 @p50)) % 0.16/0.40 (step @p55 :rule true_elim :premises (@p54)) % 0.16/0.40 (step @p56 :rule cong :premises (@p55) :args (@t48)) % 0.16/0.40 (step @p57 :rule refl :args (@t39)) % 0.16/0.40 (step @p58 :rule cong :premises (@p57 @p56) :args (@t49)) % 0.16/0.40 (step @p59 :rule cong :premises (@p58) :args (@t50)) % 0.16/0.40 (step @p60 :rule refl :args (@t47)) % 0.16/0.40 (step @p61 :rule cong :premises (@p60 @p59) :args ((=> @t47 @t50))) % 0.16/0.40 (step @p62 :rule eq-symm :args (@t39 @t17)) % 0.16/0.40 (step @p63 :rule refl :args (@t42)) % 0.16/0.40 (step @p64 :rule nary_cong :premises (@p63 @p62) :args (@t52)) % 0.16/0.40 (step @p65 :rule refl :args (@t41)) % 0.16/0.40 (step @p66 :rule nary_cong :premises (@p65 @p62) :args (@t53)) % 0.16/0.40 (step @p67 :rule nary_cong :premises (@p66 @p64) :args (@t54)) % 0.16/0.40 (step @p68 :rule cong :premises (@p67) :args (@t55)) % 0.16/0.40 (step @p69 :rule cong :premises (@p68) :args (@t56)) % 0.16/0.40 (step @p70 :rule cong :premises (@p57 @p69) :args (@t57)) % 0.16/0.40 (step @p71 :rule cong :premises (@p70) :args (@t58)) % 0.16/0.40 (step @p72 :rule cong :premises (@p60 @p71) :args ((=> @t47 @t58))) % 0.16/0.40 (step @p73 :rule trans :premises (@p72 @p61)) % 0.16/0.40 (assume-push @p246 @t47) % 0.16/0.40 (step @p75 :rule skolemize :premises (@p46)) % 0.16/0.40 (step-pop @p247 :rule scope :premises (@p75)) % 0.16/0.40 (step @p76 :rule process_scope :premises (@p247) :args (@t58)) % 0.16/0.40 (step @p78 :rule eq_resolve :premises (@p76 @p73)) % 0.16/0.40 (step @p79 :rule implies_elim :premises (@p78)) % 0.16/0.40 (step @p80 :rule eq_resolve :premises (@p79 @p49)) % 0.16/0.40 (step @p81 :rule chain_m_resolution :premises (@p80 @p46) :args (@t46 @t59 (@list @t38))) % 0.16/0.40 (step @p82 :rule quant-merge-prenex :args ((= (forall @t9 @t67) @t65))) % 0.16/0.40 (step @p83 :rule refl :args (@t61)) % 0.16/0.40 (step @p84 :rule alpha_equiv :args (@t68 (@list @t62) (@list @t4))) % 0.16/0.40 (step @p85 :rule nary_cong :premises (@p84 @p83) :args (@t69)) % 0.16/0.40 (step @p86 :rule quant-miniscope-or :args ((= @t67 @t69))) % 0.16/0.40 (step @p87 :rule trans :premises (@p86 @p85)) % 0.16/0.40 (step @p88 :rule symm :premises (@p87)) % 0.16/0.40 (step @p89 :rule cong :premises (@p88) :args ((forall @t9 (or @t71 @t61)))) % 0.16/0.40 (step @p90 :rule trans :premises (@p89 @p82)) % 0.16/0.40 (step @p91 :rule refl :args ((_ @t1 @t2))) % 0.16/0.40 (step @p92 :rule refl :args (@t60)) % 0.16/0.40 (step @p93 :rule cong :premises (@p92) :args (@t61)) % 0.16/0.40 (step @p94 :rule trans :premises (@p93 @p91)) % 0.16/0.40 (step @p95 :rule refl :args (@t1)) % 0.16/0.40 (step @p96 :rule ho_cong :premises (@p95 @p92)) % 0.16/0.40 (step @p97 :rule cong :premises (@p96 @p94) :args ((= (_ @t1 @t60) @t61))) % 0.16/0.40 (step @p98 :rule symm :premises (@p97)) % 0.16/0.40 (step @p99 :rule refl :args (@t3)) % 0.16/0.40 (step @p100 :rule eq_resolve :premises (@p99 @p98)) % 0.16/0.40 (step @p101 :rule refl :args (@t2)) % 0.16/0.40 (step @p102 :rule cong :premises (@p101 @p92) :args ((= @t2 @t60))) % 0.16/0.40 (step @p103 :rule symm :premises (@p102)) % 0.16/0.40 (step @p104 :rule eq_resolve :premises (@p101 @p103)) % 0.16/0.40 (step @p105 :rule ho_cong :premises (@p95 @p104)) % 0.16/0.40 (step @p106 :rule trans :premises (@p105 @p100)) % 0.16/0.40 (step @p107 :rule refl :args (@t71)) % 0.16/0.40 (step @p108 :rule nary_cong :premises (@p107 @p106) :args (@t72)) % 0.16/0.40 (step @p109 :rule cong :premises (@p108) :args ((forall @t9 @t72))) % 0.16/0.40 (step @p110 :rule trans :premises (@p109 @p90)) % 0.16/0.40 (step @p111 :rule bool-double-not-elim :args (@t71)) % 0.16/0.40 (step @p112 :rule nary_cong :premises (@p111 @p99) :args ((or (not @t73) @t3))) % 0.16/0.40 (step @p113 :rule bool-impl-elim :args (@t73 @t3)) % 0.16/0.40 (step @p114 :rule trans :premises (@p113 @p112)) % 0.16/0.40 (step @p115 :rule cong :premises (@p114) :args ((forall @t9 (=> @t73 @t3)))) % 0.16/0.40 (step @p116 :rule trans :premises (@p115 @p110)) % 0.16/0.40 (step @p117 :rule refl :args (@t3)) % 0.16/0.40 (step @p118 :rule refl :args (@t70)) % 0.16/0.40 (step @p119 :rule refl :args (@t5)) % 0.16/0.40 (step @p120 :rule cong :premises (@p119 @p118) :args ((= @t5 @t70))) % 0.16/0.40 (step @p121 :rule symm :premises (@p120)) % 0.16/0.40 (step @p122 :rule eq_resolve :premises (@p119 @p121)) % 0.16/0.40 (step @p123 :rule cong :premises (@p122) :args (@t74)) % 0.16/0.40 (step @p124 :rule cong :premises (@p123) :args (@t75)) % 0.16/0.40 (step @p125 :rule cong :premises (@p124) :args (@t76)) % 0.16/0.40 (step @p126 :rule exists-elim :args ((= @t7 @t76))) % 0.16/0.40 (step @p127 :rule trans :premises (@p126 @p125)) % 0.16/0.40 (step @p128 :rule cong :premises (@p127 @p117) :args (@t8)) % 0.16/0.40 (step @p129 :rule cong :premises (@p128) :args (@t10)) % 0.16/0.40 (step @p130 :rule trans :premises (@p129 @p116)) % 0.16/0.40 (step @p131 :rule eq_resolve :premises (@p1 @p130)) % 0.16/0.40 (step @p132 :rule eq-refl :args (@t79)) % 0.16/0.40 (step @p133 :rule skolem_intro :args (@t80)) % 0.16/0.40 (step @p134 :rule refl :args (@t79)) % 0.16/0.40 (step @p135 :rule cong :premises (@p134 @p133) :args ((= @t79 @t80))) % 0.16/0.40 (step @p136 :rule trans :premises (@p135 @p132)) % 0.16/0.40 (step @p137 :rule true_elim :premises (@p136)) % 0.16/0.40 (step @p138 :rule cong :premises (@p137) :args (@t81)) % 0.16/0.40 (step @p139 :rule cong :premises (@p57 @p138) :args (@t82)) % 0.16/0.40 (step @p140 :rule refl :args (@t65)) % 0.16/0.40 (step @p141 :rule cong :premises (@p140 @p139) :args ((=> @t65 @t82))) % 0.16/0.40 (step @p142 :rule aci_norm :args ((= (or false @t82) @t82))) % 0.16/0.40 (step @p143 :rule eq-symm :args (@t81 @t39)) % 0.16/0.40 (step @p144 :rule beta-reduce :args ((= (_ @t83 @t81) (= @t81 @t39)))) % 0.16/0.40 (step @p145 :rule trans :premises (@p144 @p143)) % 0.16/0.40 (step @p146 :rule eq-symm :args (@t77 @t39)) % 0.16/0.40 (step @p147 :rule cong :premises (@p146) :args (@t83)) % 0.16/0.40 (step @p148 :rule cong :premises (@p147) :args (@t84)) % 0.16/0.40 (step @p149 :rule cong :premises (@p148) :args (@t85)) % 0.16/0.40 (step @p150 :rule trans :premises (@p149 @p145)) % 0.16/0.40 (step @p151 :rule evaluate :args ((not true))) % 0.16/0.40 (step @p152 :rule eq-refl :args (@t39)) % 0.16/0.40 (step @p153 :rule beta-reduce :args ((= @t86 (= @t39 @t39)))) % 0.16/0.40 (step @p154 :rule trans :premises (@p153 @p152)) % 0.16/0.40 (step @p155 :rule cong :premises (@p154) :args (@t87)) % 0.16/0.40 (step @p156 :rule trans :premises (@p155 @p151)) % 0.16/0.40 (step @p157 :rule nary_cong :premises (@p156 @p150) :args (@t88)) % 0.16/0.40 (step @p158 :rule trans :premises (@p157 @p142)) % 0.16/0.40 (step @p159 :rule cong :premises (@p140 @p158) :args ((=> @t65 @t88))) % 0.16/0.40 (assume-push @p248 @t65) % 0.16/0.40 (step @p161 :rule instantiate :premises (@p131) :args ((@list @t83 @t39))) % 0.16/0.40 (step-pop @p249 :rule scope :premises (@p161)) % 0.16/0.40 (step @p162 :rule process_scope :premises (@p249) :args (@t88)) % 0.16/0.40 (step @p164 :rule eq_resolve :premises (@p162 @p159)) % 0.16/0.40 (step @p165 :rule eq_resolve :premises (@p164 @p141)) % 0.16/0.40 (step @p166 :rule implies_elim :premises (@p165)) % 0.16/0.40 (step @p167 :rule chain_m_resolution :premises (@p166 @p131) :args (@t90 (@list false) (@list @t65))) % 0.16/0.40 (assume-push @p250 @t90) % 0.16/0.40 (assume-push @p251 @t91) % 0.16/0.40 (assume-push @p252 @t91) % 0.16/0.40 (assume-push @p253 @t90) % 0.16/0.40 (step @p172 :rule symm :premises (@p251)) % 0.16/0.40 (step @p173 :rule cong :premises (@p172) :args (@t89)) % 0.16/0.40 (step @p174 :rule trans :premises (@p167 @p173)) % 0.16/0.40 (step-pop @p254 :rule scope :premises (@p174)) % 0.16/0.40 (step-pop @p255 :rule scope :premises (@p254)) % 0.16/0.40 (step @p175 :rule process_scope :premises (@p255) :args (@t45)) % 0.16/0.40 (step @p178 :rule and_intro :premises (@p251 @p167)) % 0.16/0.40 (step @p179 :rule modus_ponens :premises (@p178 @p175)) % 0.16/0.40 (step-pop @p256 :rule scope :premises (@p179)) % 0.16/0.40 (step-pop @p257 :rule scope :premises (@p256)) % 0.16/0.40 (step @p180 :rule process_scope :premises (@p257) :args (@t45)) % 0.16/0.40 (step @p183 :rule implies_elim :premises (@p180)) % 0.16/0.40 (step @p184 :rule cnf_and_neg :args (@t92)) % 0.16/0.40 (step @p185 :rule resolution :premises (@p184 @p183) :args (true @t92)) % 0.16/0.40 (step @p186 :rule reordering :premises (@p185) :args ((or @t45 (not @t90) @t93))) % 0.16/0.40 (step @p187 :rule chain_m_resolution :premises (@p186 @p167 @p81) :args (@t93 (@list false true) (@list @t90 @t45))) % 0.16/0.40 (step @p188 :rule eq-symm :args (@t98 @t95)) % 0.16/0.40 (step @p189 :rule eq-refl :args (@t95)) % 0.16/0.40 (step @p190 :rule refl :args (@t95)) % 0.16/0.40 (step @p191 :rule beta-reduce :args (@t99)) % 0.16/0.40 (step @p192 :rule cong :premises (@p191 @p190) :args (@t99)) % 0.16/0.40 (step @p193 :rule trans :premises (@p192 @p189)) % 0.16/0.40 (step @p194 :rule refl :args (@t94)) % 0.16/0.40 (step @p195 :rule ho_cong :premises (@p133 @p194)) % 0.16/0.40 (step @p196 :rule cong :premises (@p195 @p190) :args ((= @t100 @t95))) % 0.16/0.40 (step @p197 :rule trans :premises (@p196 @p193)) % 0.16/0.40 (step @p198 :rule true_elim :premises (@p197)) % 0.16/0.40 (step @p199 :rule eq-refl :args (@t98)) % 0.16/0.40 (step @p200 :rule refl :args (@t98)) % 0.16/0.40 (step @p201 :rule eq-symm :args (@t94 @t39)) % 0.16/0.40 (step @p202 :rule nary_cong :premises (@p63 @p201) :args (@t102)) % 0.16/0.40 (step @p203 :rule nary_cong :premises (@p65 @p201) :args (@t103)) % 0.16/0.40 (step @p204 :rule nary_cong :premises (@p203 @p202) :args (@t104)) % 0.16/0.40 (step @p205 :rule beta-reduce :args ((= @t105 @t104))) % 0.16/0.40 (step @p206 :rule trans :premises (@p205 @p204)) % 0.16/0.40 (step @p207 :rule cong :premises (@p206 @p200) :args ((= @t105 @t98))) % 0.16/0.40 (step @p208 :rule trans :premises (@p207 @p199)) % 0.16/0.40 (step @p209 :rule ho_cong :premises (@p51 @p194)) % 0.16/0.40 (step @p210 :rule cong :premises (@p209 @p200) :args ((= @t106 @t98))) % 0.16/0.40 (step @p211 :rule trans :premises (@p210 @p208)) % 0.16/0.40 (step @p212 :rule true_elim :premises (@p211)) % 0.16/0.40 (step @p213 :rule cong :premises (@p212 @p198) :args (@t107)) % 0.16/0.40 (step @p214 :rule trans :premises (@p213 @p188)) % 0.16/0.40 (step @p215 :rule cong :premises (@p214) :args (@t108)) % 0.16/0.40 (step @p216 :rule refl :args (@t91)) % 0.16/0.40 (step @p217 :rule nary_cong :premises (@p216 @p215) :args (@t109)) % 0.16/0.40 ; WARNING: add trust step for TRUST % 0.16/0.40 ; trust TRUST THEORY_LEMMA % 0.16/0.40 (step @p218 :rule trust :premises () :args (@t109)) % 0.16/0.40 (step @p219 :rule eq_resolve :premises (@p218 @p217)) % 0.16/0.40 (step @p220 :rule chain_m_resolution :premises (@p219 @p187) :args ((not @t110) @t59 (@list @t91))) % 0.16/0.40 (step @p221 :rule cnf_equiv_neg2 :args (@t110)) % 0.16/0.40 (step @p222 :rule cnf_or_neg :args (@t98 0)) % 0.16/0.40 (step @p223 :rule cnf_or_neg :args (@t98 1)) % 0.16/0.40 (step @p224 :rule cnf_and_neg :args (@t97)) % 0.16/0.40 (step @p225 :rule reordering :premises (@p224) :args ((or @t42 @t97 @t111))) % 0.16/0.40 (step @p226 :rule refl :args (@t111)) % 0.16/0.40 (step @p227 :rule bool-double-not-elim :args (@t41)) % 0.16/0.40 (step @p228 :rule refl :args (@t96)) % 0.16/0.40 (step @p229 :rule nary_cong :premises (@p228 @p227 @p226) :args ((or @t96 (not @t42) @t111))) % 0.16/0.40 (step @p230 :rule cnf_and_neg :args (@t96)) % 0.16/0.40 (step @p231 :rule eq_resolve :premises (@p230 @p229)) % 0.16/0.40 (step @p232 :rule reordering :premises (@p231) :args ((or @t41 @t96 @t111))) % 0.16/0.40 (step @p233 :rule chain_m_resolution :premises (@p232 @p225 @p223 @p222 @p221 @p220) :args (@t111 (@list true true true true true) (@list @t41 @t96 @t97 @t98 @t110))) % 0.16/0.40 (step @p234 :rule cnf_and_pos :args (@t97 1)) % 0.16/0.40 (step @p235 :rule reordering :premises (@p234) :args ((or @t95 @t112))) % 0.16/0.40 (step @p236 :rule chain_m_resolution :premises (@p235 @p233) :args (@t112 @t59 @t113)) % 0.16/0.40 (step @p237 :rule cnf_and_pos :args (@t96 1)) % 0.16/0.40 (step @p238 :rule reordering :premises (@p237) :args ((or @t95 @t114))) % 0.16/0.40 (step @p239 :rule chain_m_resolution :premises (@p238 @p233) :args (@t114 @t59 @t113)) % 0.16/0.40 (step @p240 :rule cnf_equiv_neg1 :args (@t110)) % 0.16/0.40 (step @p241 :rule reordering :premises (@p240) :args ((or @t95 @t98 @t110))) % 0.16/0.40 (step @p242 :rule chain_m_resolution :premises (@p241 @p233 @p220) :args (@t98 (@list true true) (@list @t95 @t110))) % 0.16/0.40 (step @p243 :rule cnf_or_pos :args (@t98)) % 0.16/0.40 (step @p244 :rule reordering :premises (@p243) :args ((or @t97 @t96 (not @t98)))) % 0.16/0.40 (step @p245 false :rule chain_m_resolution :premises (@p244 @p242 @p239 @p236) :args (false (@list false true true) (@list @t98 @t96 @t97))) % 0.16/0.40 ) % 0.16/0.40 % SZS output end Proof % 0.16/0.40 % cvc5 exiting %------------------------------------------------------------------------------