0.03/0.12	% Problem  : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.03/0.13	% Command  : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 240 THM
0.13/0.34	% Computer : n029.cluster.edu
0.13/0.34	% Model    : x86_64 x86_64
0.13/0.34	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.13/0.34	% Memory   : 8042.1875MB
0.13/0.34	% OS       : Linux 3.10.0-693.el7.x86_64
0.13/0.34	% CPULimit : 1920
0.13/0.34	% WCLimit  : 240
0.13/0.34	% DateTime : Sat Sep  6 03:33:23 EDT 2025
0.13/0.34	% CPUTime  : 
0.20/0.49	%----Proving TH0
0.79/1.01	--- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 72s...
0.79/1.01	% SZS status Theorem
0.79/1.01	% SZS output start Proof
0.79/1.01	(
0.79/1.01	(declare-type tptp.a ())
0.79/1.01	(define @t1 () (@var "Xy" tptp.a))
0.79/1.01	(define @t2 () (@var "Xx" tptp.a))
0.79/1.01	(define @t3 () (@var "Xr" (-> tptp.a tptp.a Bool)))
0.79/1.01	(define @t4 () (_ (_ @t3 @t2) @t1))
0.79/1.01	(define @t5 () (@list @t2 @t1))
0.79/1.01	(define @t6 () (exists @t5 @t4))
0.79/1.01	(define @t7 () (lambda @t5 @t1))
0.79/1.01	(define @t8 () (@var "Xp" (-> (-> tptp.a tptp.a tptp.a) tptp.a)))
0.79/1.01	(define @t9 () (_ @t8 @t7))
0.79/1.01	(define @t10 () (lambda @t5 @t2))
0.79/1.01	(define @t11 () (_ @t8 @t10))
0.79/1.01	(define @t12 () (_ (_ @t3 @t11) @t9))
0.79/1.01	(define @t13 () (@list @t8))
0.79/1.01	(define @t14 () (exists @t13 @t12))
0.79/1.01	(define @t15 () (= @t14 @t6))
0.79/1.01	(define @t16 () (@list @t3))
0.79/1.01	(define @t17 () (forall @t16 @t15))
0.79/1.01	(define @t18 () (not @t17))
0.79/1.01	(define @t19 () (_ @t3 @t2 @t1))
0.79/1.01	(define @t20 () (not @t4))
0.79/1.01	(define @t21 () (forall @t5 @t20))
0.79/1.01	(define @t22 () (not @t21))
0.79/1.01	(define @t23 () (_ @t8 @t7))
0.79/1.01	(define @t24 () (_ @t8 @t10))
0.79/1.01	(define @t25 () (_ @t3 @t24 @t23))
0.79/1.01	(define @t26 () (not @t12))
0.79/1.01	(define @t27 () (forall @t13 @t26))
0.79/1.01	(define @t28 () (not @t27))
0.79/1.01	(define @t29 () (@quantifiers_skolemize (forall @t16 (= (not (forall @t13 (not @t25))) (not (forall @t5 (not @t19))))) 0))
0.79/1.01	(define @t30 () (forall @t5 (not (_ @t29 @t2 @t1))))
0.79/1.01	(define @t31 () (forall @t13 (not (_ @t29 @t24 @t23))))
0.79/1.01	(define @t32 () (not @t30))
0.79/1.01	(define @t33 () (not @t31))
0.79/1.01	(define @t34 () (= @t33 @t32))
0.79/1.01	(define @t35 () (not @t32))
0.79/1.01	(define @t36 () (not @t33))
0.79/1.01	(define @t37 () (@purify @t7))
0.79/1.01	(define @t38 () (@quantifiers_skolemize @t31 0))
0.79/1.01	(define @t39 () (_ @t38 @t37))
0.79/1.01	(define @t40 () (@purify @t10))
0.79/1.01	(define @t41 () (_ @t38 @t40))
0.79/1.01	(define @t42 () (_ @t29 @t41 @t39))
0.79/1.01	(define @t43 () (_ @t38 @t7))
0.79/1.01	(define @t44 () (_ @t38 @t10))
0.79/1.01	(define @t45 () (_ @t29 @t44 @t43))
0.79/1.01	(define @t46 () (not (not @t45)))
0.79/1.01	(define @t47 () (@quantifiers_skolemize @t30 1))
0.79/1.01	(define @t48 () (@quantifiers_skolemize @t30 0))
0.79/1.01	(define @t49 () (_ @t29 @t48 @t47))
0.79/1.01	(define @t50 () (not @t49))
0.79/1.01	(define @t51 () (not @t50))
0.79/1.01	(define @t52 () (@list true))
0.79/1.01	(define @t53 () (forall @t5 (= @t2 @t1)))
0.79/1.01	(define @t54 () (= @t41 @t47))
0.79/1.01	(define @t55 () (= @t41 @t48))
0.79/1.01	(define @t56 () (_ @t29 @t44 @t44))
0.79/1.01	(define @t57 () (not @t56))
0.79/1.01	(define @t58 () (lambda (@list (@var "BOUND_VARIABLE_7497" (-> tptp.a tptp.a tptp.a))) @t44))
0.79/1.01	(define @t59 () (_ @t58 @t7))
0.79/1.01	(define @t60 () (_ @t58 @t10))
0.79/1.01	(define @t61 () (_ @t29 @t60 @t59))
0.79/1.01	(define @t62 () (not @t61))
0.79/1.01	(define @t63 () (@list false))
0.79/1.01	(define @t64 () (@list @t31))
0.79/1.01	(define @t65 () (_ @t29 @t41 @t41))
0.79/1.01	(define @t66 () (not @t55))
0.79/1.01	(define @t67 () (not @t54))
0.79/1.01	(define @t68 () (not @t65))
0.79/1.01	(define @t69 () (and @t68 @t55 @t54 @t49))
0.79/1.01	(define @t70 () (forall @t5 (= @t1 @t2)))
0.79/1.01	(define @t71 () (= @t37 @t40))
0.79/1.01	(define @t72 () (=> @t71 @t70))
0.79/1.01	(define @t73 () (@const 0 tptp.a))
0.79/1.01	(define @t74 () (= @t10 @t7))
0.79/1.01	(define @t75 () (ite @t74 @t73 @t48))
0.79/1.01	(define @t76 () (@purify @t75))
0.79/1.01	(define @t77 () (= @t48 @t76))
0.79/1.01	(define @t78 () (= @t73 @t76))
0.79/1.01	(define @t79 () (= @t75 @t48))
0.79/1.01	(define @t80 () (= @t75 @t73))
0.79/1.01	(define @t81 () (@list @t71))
0.79/1.01	(define @t82 () (@const 1 tptp.a))
0.79/1.01	(define @t83 () (ite @t74 @t82 @t76))
0.79/1.01	(define @t84 () (@purify @t83))
0.79/1.01	(define @t85 () (= @t76 @t84))
0.79/1.01	(define @t86 () (= @t82 @t84))
0.79/1.01	(define @t87 () (ite @t74 @t82 @t75))
0.79/1.01	(define @t88 () (= @t83 @t76))
0.79/1.01	(define @t89 () (= @t83 @t82))
0.79/1.01	(define @t90 () (ite @t74 @t39 @t47))
0.79/1.01	(define @t91 () (@purify @t90))
0.79/1.01	(define @t92 () (= @t47 @t91))
0.79/1.01	(define @t93 () (= @t39 @t91))
0.79/1.01	(define @t94 () (ite @t74 @t43 @t47))
0.79/1.01	(define @t95 () (= @t90 @t47))
0.79/1.01	(define @t96 () (= @t90 @t39))
0.79/1.01	(define @t97 () (ite @t74 @t91 @t84))
0.79/1.01	(define @t98 () (@purify @t97))
0.79/1.01	(define @t99 () (_ @t29 @t97 @t91))
0.79/1.01	(define @t100 () (not @t99))
0.79/1.01	(define @t101 () (ite @t74 @t84 @t39))
0.79/1.01	(define @t102 () (ite (= @t7 @t7) @t91 @t101))
0.79/1.01	(define @t103 () (@var "BOUND_VARIABLE_102870" (-> tptp.a tptp.a tptp.a)))
0.79/1.01	(define @t104 () (lambda (@list @t103) (ite (= @t7 @t103) @t91 (ite (= @t10 @t103) @t84 @t39))))
0.79/1.01	(define @t105 () (_ @t104 @t7))
0.79/1.01	(define @t106 () (ite (= @t10 @t10) @t84 @t39))
0.79/1.01	(define @t107 () (ite (= @t7 @t10) @t91 @t106))
0.79/1.01	(define @t108 () (_ @t104 @t10))
0.79/1.01	(define @t109 () (_ @t29 @t108 @t105))
0.79/1.01	(define @t110 () (not @t109))
0.79/1.01	(define @t111 () (= @t84 @t98))
0.79/1.01	(define @t112 () (= @t91 @t98))
0.79/1.01	(define @t113 () (= @t97 @t84))
0.79/1.01	(define @t114 () (= @t97 @t91))
0.79/1.01	(define @t115 () (not @t111))
0.79/1.01	(define @t116 () (_ @t29 @t98 @t91))
0.79/1.01	(define @t117 () (not @t92))
0.79/1.01	(define @t118 () (not @t85))
0.79/1.01	(define @t119 () (not @t77))
0.79/1.01	(define @t120 () (not @t116))
0.79/1.01	(define @t121 () (and @t49 @t77 @t85 @t111 @t92 @t120))
0.79/1.01	(assume @p1 @t18)
0.79/1.01	(assume @p2 true)
0.79/1.01	(step @p3 :rule refl :args (@t19))
0.79/1.01	(step @p4 :rule refl :args (@t4))
0.79/1.01	(step @p5 :rule cong :premises (@p4 @p3) :args ((= @t4 @t19)))
0.79/1.01	(step @p6 :rule symm :premises (@p5))
0.79/1.01	(step @p7 :rule eq_resolve :premises (@p4 @p6))
0.79/1.01	(step @p8 :rule cong :premises (@p7) :args (@t20))
0.79/1.01	(step @p9 :rule cong :premises (@p8) :args (@t21))
0.79/1.01	(step @p10 :rule cong :premises (@p9) :args (@t22))
0.79/1.01	(step @p11 :rule exists-elim :args ((= @t6 @t22)))
0.79/1.01	(step @p12 :rule trans :premises (@p11 @p10))
0.79/1.01	(step @p13 :rule refl :args ((_ @t3 @t11 @t9)))
0.79/1.01	(step @p14 :rule refl :args (@t23))
0.79/1.01	(step @p15 :rule refl :args (@t24))
0.79/1.01	(step @p16 :rule cong :premises (@p15 @p14) :args (@t25))
0.79/1.01	(step @p17 :rule trans :premises (@p16 @p13))
0.79/1.01	(step @p18 :rule refl :args (@t3))
0.79/1.01	(step @p19 :rule ho_cong :premises (@p18 @p15))
0.79/1.01	(step @p20 :rule ho_cong :premises (@p19 @p14))
0.79/1.01	(step @p21 :rule cong :premises (@p20 @p17) :args ((= (_ (_ @t3 @t24) @t23) @t25)))
0.79/1.01	(step @p22 :rule symm :premises (@p21))
0.79/1.01	(step @p23 :rule refl :args (@t12))
0.79/1.01	(step @p24 :rule eq_resolve :premises (@p23 @p22))
0.79/1.01	(step @p25 :rule refl :args (@t9))
0.79/1.01	(step @p26 :rule cong :premises (@p25 @p14) :args ((= @t9 @t23)))
0.79/1.01	(step @p27 :rule symm :premises (@p26))
0.79/1.01	(step @p28 :rule eq_resolve :premises (@p25 @p27))
0.79/1.01	(step @p29 :rule refl :args (@t11))
0.79/1.01	(step @p30 :rule cong :premises (@p29 @p15) :args ((= @t11 @t24)))
0.79/1.01	(step @p31 :rule symm :premises (@p30))
0.79/1.01	(step @p32 :rule eq_resolve :premises (@p29 @p31))
0.79/1.01	(step @p33 :rule ho_cong :premises (@p18 @p32))
0.79/1.01	(step @p34 :rule ho_cong :premises (@p33 @p28))
0.79/1.01	(step @p35 :rule trans :premises (@p34 @p24))
0.79/1.01	(step @p36 :rule cong :premises (@p35) :args (@t26))
0.79/1.01	(step @p37 :rule cong :premises (@p36) :args (@t27))
0.79/1.01	(step @p38 :rule cong :premises (@p37) :args (@t28))
0.79/1.01	(step @p39 :rule exists-elim :args ((= @t14 @t28)))
0.79/1.01	(step @p40 :rule trans :premises (@p39 @p38))
0.79/1.01	(step @p41 :rule cong :premises (@p40 @p12) :args (@t15))
0.79/1.01	(step @p42 :rule cong :premises (@p41) :args (@t17))
0.79/1.01	(step @p43 :rule cong :premises (@p42) :args (@t18))
0.79/1.01	(step @p44 :rule eq_resolve :premises (@p1 @p43))
0.79/1.01	(step @p45 :rule skolemize :premises (@p44))
0.79/1.01	(step @p46 :rule bool-double-not-elim :args (@t30))
0.79/1.01	(step @p47 :rule bool-double-not-elim :args (@t31))
0.79/1.01	(step @p48 :rule refl :args (@t34))
0.79/1.01	(step @p49 :rule nary_cong :premises (@p48 @p47 @p46) :args ((or @t34 @t36 @t35)))
0.79/1.01	(step @p50 :rule cnf_equiv_neg2 :args (@t34))
0.79/1.01	(step @p51 :rule eq_resolve :premises (@p50 @p49))
0.79/1.01	(step @p52 :rule reordering :premises (@p51) :args ((or @t31 @t30 @t34)))
0.79/1.01	(step @p53 :rule refl :args (@t42))
0.79/1.01	(step @p54 :rule nary_cong :premises (@p47 @p53) :args ((or @t36 @t42)))
0.79/1.01	(step @p55 :rule eq-refl :args (@t7))
0.79/1.01	(step @p56 :rule skolem_intro :args (@t37))
0.79/1.01	(step @p57 :rule refl :args (@t7))
0.79/1.01	(step @p58 :rule cong :premises (@p57 @p56) :args ((= @t7 @t37)))
0.79/1.01	(step @p59 :rule trans :premises (@p58 @p55))
0.79/1.01	(step @p60 :rule true_elim :premises (@p59))
0.79/1.01	(step @p61 :rule cong :premises (@p60) :args (@t43))
0.79/1.01	(step @p62 :rule eq-refl :args (@t10))
0.79/1.01	(step @p63 :rule skolem_intro :args (@t40))
0.79/1.01	(step @p64 :rule refl :args (@t10))
0.79/1.01	(step @p65 :rule cong :premises (@p64 @p63) :args ((= @t10 @t40)))
0.79/1.01	(step @p66 :rule trans :premises (@p65 @p62))
0.79/1.01	(step @p67 :rule true_elim :premises (@p66))
0.79/1.01	(step @p68 :rule cong :premises (@p67) :args (@t44))
0.79/1.01	(step @p69 :rule cong :premises (@p68 @p61) :args (@t45))
0.79/1.01	(step @p70 :rule refl :args (@t33))
0.79/1.01	(step @p71 :rule cong :premises (@p70 @p69) :args ((=> @t33 @t45)))
0.79/1.01	(step @p72 :rule bool-double-not-elim :args (@t45))
0.79/1.01	(step @p73 :rule cong :premises (@p70 @p72) :args ((=> @t33 @t46)))
0.79/1.01	(step @p74 :rule trans :premises (@p73 @p71))
0.79/1.01	(assume-push @p356 @t33)
0.79/1.01	(step @p76 :rule skolemize :premises (@p356))
0.79/1.01	(step-pop @p356 :rule scope :premises (@p76))
0.79/1.01	(step @p77 :rule process_scope :premises (@p356) :args (@t46))
0.79/1.01	(step @p79 :rule eq_resolve :premises (@p77 @p74))
0.79/1.01	(step @p80 :rule implies_elim :premises (@p79))
0.79/1.01	(step @p81 :rule eq_resolve :premises (@p80 @p54))
0.79/1.01	(assume-push @p358 @t30)
0.79/1.01	(step @p83 :rule instantiate :premises (@p358) :args ((@list @t41 @t39)))
0.79/1.01	(step-pop @p358 :rule scope :premises (@p83))
0.79/1.01	(step @p84 :rule process_scope :premises (@p358) :args ((not @t42)))
0.79/1.01	(step @p86 :rule implies_elim :premises (@p84))
0.79/1.01	(step @p87 :rule chain_resolution :premises (@p86 @p81 @p52 @p45) :args ((@list false false true) (@list @t42 @t30 @t34)))
0.79/1.01	(step @p88 :rule factoring :premises (@p87))
0.79/1.01	(step @p89 :rule cnf_equiv_neg1 :args (@t34))
0.79/1.01	(step @p90 :rule reordering :premises (@p89) :args ((or @t33 @t32 @t34)))
0.79/1.01	(step @p91 :rule chain_resolution :premises (@p90 @p88 @p45) :args ((@list false true) (@list @t31 @t34)))
0.79/1.01	(step @p92 :rule refl :args (@t49))
0.79/1.01	(step @p93 :rule nary_cong :premises (@p46 @p92) :args ((or @t35 @t49)))
0.79/1.01	(step @p94 :rule bool-double-not-elim :args (@t49))
0.79/1.01	(step @p95 :rule refl :args (@t32))
0.79/1.01	(step @p96 :rule cong :premises (@p95 @p94) :args ((=> @t32 @t51)))
0.79/1.01	(assume-push @p360 @t32)
0.79/1.01	(step @p98 :rule skolemize :premises (@p360))
0.79/1.01	(step-pop @p360 :rule scope :premises (@p98))
0.79/1.01	(step @p99 :rule process_scope :premises (@p360) :args (@t51))
0.79/1.01	(step @p101 :rule eq_resolve :premises (@p99 @p96))
0.79/1.01	(step @p102 :rule implies_elim :premises (@p101))
0.79/1.01	(step @p103 :rule eq_resolve :premises (@p102 @p93))
0.79/1.01	(step @p104 :rule chain_resolution :premises (@p103 @p91) :args (@t52 (@list @t30)))
0.79/1.01	(assume-push @p362 @t53)
0.79/1.01	(step @p106 :rule instantiate :premises (@p362) :args ((@list @t41 @t47)))
0.79/1.01	(step-pop @p362 :rule scope :premises (@p106))
0.79/1.01	(step @p107 :rule process_scope :premises (@p362) :args (@t54))
0.79/1.01	(step @p109 :rule implies_elim :premises (@p107))
0.79/1.01	(assume-push @p364 @t53)
0.79/1.01	(step @p111 :rule instantiate :premises (@p364) :args ((@list @t41 @t48)))
0.79/1.01	(step-pop @p364 :rule scope :premises (@p111))
0.79/1.01	(step @p112 :rule process_scope :premises (@p364) :args (@t55))
0.79/1.01	(step @p114 :rule implies_elim :premises (@p112))
0.79/1.01	(step @p115 :rule cong :premises (@p68 @p68) :args (@t56))
0.79/1.01	(step @p116 :rule cong :premises (@p115) :args (@t57))
0.79/1.01	(step @p117 :rule refl :args (@t31))
0.79/1.01	(step @p118 :rule cong :premises (@p117 @p116) :args ((=> @t31 @t57)))
0.79/1.01	(step @p119 :rule beta-reduce :args ((= @t59 @t44)))
0.79/1.01	(step @p120 :rule beta-reduce :args ((= @t60 @t44)))
0.79/1.01	(step @p121 :rule cong :premises (@p120 @p119) :args (@t61))
0.79/1.01	(step @p122 :rule cong :premises (@p121) :args (@t62))
0.79/1.01	(step @p123 :rule cong :premises (@p117 @p122) :args ((=> @t31 @t62)))
0.79/1.01	(assume-push @p366 @t31)
0.79/1.01	(step @p125 :rule instantiate :premises (@p366) :args ((@list @t58)))
0.79/1.01	(step-pop @p366 :rule scope :premises (@p125))
0.79/1.01	(step @p126 :rule process_scope :premises (@p366) :args (@t62))
0.79/1.01	(step @p128 :rule eq_resolve :premises (@p126 @p123))
0.79/1.01	(step @p129 :rule eq_resolve :premises (@p128 @p118))
0.79/1.01	(step @p130 :rule implies_elim :premises (@p129))
0.79/1.01	(step @p131 :rule chain_resolution :premises (@p130 @p88) :args (@t63 @t64))
0.79/1.01	(step @p132 :rule bool-double-not-elim :args (@t65))
0.79/1.01	(step @p133 :rule refl :args (@t66))
0.79/1.01	(step @p134 :rule refl :args (@t67))
0.79/1.01	(step @p135 :rule refl :args (@t50))
0.79/1.01	(step @p136 :rule nary_cong :premises (@p135 @p134 @p133 @p132) :args ((or @t50 @t67 @t66 (not @t68))))
0.79/1.01	(assume-push @p368 @t68)
0.79/1.01	(assume-push @p369 @t55)
0.79/1.01	(assume-push @p370 @t54)
0.79/1.01	(assume-push @p371 @t49)
0.79/1.01	(step @p141 :rule evaluate :args ((= true false)))
0.79/1.01	(step @p142 :rule false_intro :premises (@p368))
0.79/1.01	(step @p143 :rule symm :premises (@p370))
0.79/1.01	(step @p144 :rule symm :premises (@p369))
0.79/1.01	(step @p145 :rule cong :premises (@p144 @p143) :args (@t49))
0.79/1.01	(step @p146 :rule true_intro :premises (@p371))
0.79/1.01	(step @p147 :rule symm :premises (@p146))
0.79/1.01	(step @p148 :rule trans :premises (@p147 @p145 @p142))
0.79/1.01	(step @p149 false :rule eq_resolve :premises (@p148 @p141))
0.79/1.01	(step-pop @p371 :rule scope :premises (@p149))
0.79/1.01	(step-pop @p372 :rule scope :premises (@p371))
0.79/1.01	(step-pop @p373 :rule scope :premises (@p372))
0.79/1.01	(step-pop @p374 :rule scope :premises (@p373))
0.79/1.01	(step @p150 :rule process_scope :premises (@p374) :args (false))
0.79/1.01	(assume-push @p376 @t49)
0.79/1.01	(assume-push @p377 @t54)
0.79/1.01	(assume-push @p378 @t55)
0.79/1.01	(assume-push @p379 @t68)
0.79/1.01	(step @p159 :rule and_intro :premises (@p379 @p378 @p377 @p376))
0.79/1.01	(step-pop @p379 :rule scope :premises (@p159))
0.79/1.01	(step-pop @p380 :rule scope :premises (@p379))
0.79/1.01	(step-pop @p381 :rule scope :premises (@p380))
0.79/1.01	(step-pop @p382 :rule scope :premises (@p381))
0.79/1.01	(step @p160 :rule process_scope :premises (@p382) :args (@t69))
0.79/1.01	(step @p165 :rule implies_elim :premises (@p160))
0.79/1.01	(step @p166 :rule resolution :premises (@p165 @p150) :args (true @t69))
0.79/1.01	(step @p167 :rule not_and :premises (@p166))
0.79/1.01	(step @p168 :rule eq_resolve :premises (@p167 @p136))
0.79/1.01	(step @p169 :rule chain_resolution :premises (@p168 @p131 @p104 @p114 @p109) :args ((@list true false false false) (@list @t65 @t49 @t55 @t54)))
0.79/1.01	(step @p170 :rule factoring :premises (@p169))
0.79/1.01	(step @p171 :rule eq-symm :args (@t1 @t2))
0.79/1.01	(step @p172 :rule cong :premises (@p171) :args (@t70))
0.79/1.01	(step @p173 :rule refl :args (@t71))
0.79/1.01	(step @p174 :rule cong :premises (@p173 @p172) :args (@t72))
0.79/1.01	; WARNING: add trust step for TRUST
0.79/1.01	; trust TRUST THEORY_LEMMA
0.79/1.01	(step @p175 :rule trust :premises () :args (@t72))
0.79/1.01	(step @p176 :rule eq_resolve :premises (@p175 @p174))
0.79/1.01	(step @p177 :rule implies_elim :premises (@p176))
0.79/1.01	(step @p178 :rule chain_resolution :premises (@p177 @p170) :args (@t52 (@list @t53)))
0.79/1.01	(step @p179 :rule refl :args (@t77))
0.79/1.01	(step @p180 :rule refl :args (@t78))
0.79/1.01	(step @p181 :rule eq-symm :args (@t40 @t37))
0.79/1.01	(step @p182 :rule cong :premises (@p67 @p60) :args (@t74))
0.79/1.01	(step @p183 :rule trans :premises (@p182 @p181))
0.79/1.01	(step @p184 :rule cong :premises (@p183 @p180 @p179) :args ((ite @t74 @t78 @t77)))
0.79/1.01	(step @p185 :rule eq-symm :args (@t76 @t48))
0.79/1.01	(step @p186 :rule eq-symm :args (@t76 @t73))
0.79/1.01	(step @p187 :rule refl :args (@t74))
0.79/1.01	(step @p188 :rule cong :premises (@p187 @p186 @p185) :args ((ite @t74 (= @t76 @t73) (= @t76 @t48))))
0.79/1.01	(step @p189 :rule trans :premises (@p188 @p184))
0.79/1.01	(step @p190 :rule refl :args (@t48))
0.79/1.01	(step @p191 :rule eq-refl :args (@t75))
0.79/1.01	(step @p192 :rule skolem_intro :args (@t76))
0.79/1.01	(step @p193 :rule refl :args (@t75))
0.79/1.01	(step @p194 :rule cong :premises (@p193 @p192) :args ((= @t75 @t76)))
0.79/1.01	(step @p195 :rule trans :premises (@p194 @p191))
0.79/1.01	(step @p196 :rule true_elim :premises (@p195))
0.79/1.01	(step @p197 :rule cong :premises (@p196 @p190) :args (@t79))
0.79/1.01	(step @p198 :rule refl :args (@t73))
0.79/1.01	(step @p199 :rule cong :premises (@p196 @p198) :args (@t80))
0.79/1.01	(step @p200 :rule cong :premises (@p187 @p199 @p197) :args ((ite @t74 @t80 @t79)))
0.79/1.01	(step @p201 :rule ite_eq :args (@t75))
0.79/1.01	(step @p202 :rule eq_resolve :premises (@p201 @p200))
0.79/1.01	(step @p203 :rule eq_resolve :premises (@p202 @p189))
0.79/1.01	(step @p204 :rule ite_elim2 :premises (@p203))
0.79/1.01	(step @p205 :rule chain_resolution :premises (@p204 @p178) :args (@t52 @t81))
0.79/1.01	(step @p206 :rule refl :args (@t85))
0.79/1.01	(step @p207 :rule refl :args (@t86))
0.79/1.01	(step @p208 :rule cong :premises (@p183 @p207 @p206) :args ((ite @t74 @t86 @t85)))
0.79/1.01	(step @p209 :rule eq-symm :args (@t84 @t76))
0.79/1.01	(step @p210 :rule eq-symm :args (@t84 @t82))
0.79/1.01	(step @p211 :rule cong :premises (@p187 @p210 @p209) :args ((ite @t74 (= @t84 @t82) (= @t84 @t76))))
0.79/1.01	(step @p212 :rule trans :premises (@p211 @p208))
0.79/1.01	(step @p213 :rule refl :args (@t76))
0.79/1.01	(step @p214 :rule eq-refl :args (@t87))
0.79/1.01	(step @p215 :rule refl :args (@t82))
0.79/1.01	(step @p216 :rule cong :premises (@p187 @p215 @p192) :args (@t83))
0.79/1.01	(step @p217 :rule skolem_intro :args (@t84))
0.79/1.01	(step @p218 :rule trans :premises (@p217 @p216))
0.79/1.01	(step @p219 :rule cong :premises (@p216 @p218) :args ((= @t83 @t84)))
0.79/1.01	(step @p220 :rule trans :premises (@p219 @p214))
0.79/1.01	(step @p221 :rule true_elim :premises (@p220))
0.79/1.01	(step @p222 :rule cong :premises (@p221 @p213) :args (@t88))
0.79/1.01	(step @p223 :rule cong :premises (@p221 @p215) :args (@t89))
0.79/1.01	(step @p224 :rule cong :premises (@p187 @p223 @p222) :args ((ite @t74 @t89 @t88)))
0.79/1.01	(step @p225 :rule ite_eq :args (@t83))
0.79/1.01	(step @p226 :rule eq_resolve :premises (@p225 @p224))
0.79/1.01	(step @p227 :rule eq_resolve :premises (@p226 @p212))
0.79/1.01	(step @p228 :rule ite_elim2 :premises (@p227))
0.79/1.01	(step @p229 :rule chain_resolution :premises (@p228 @p178) :args (@t52 @t81))
0.79/1.01	(step @p230 :rule refl :args (@t92))
0.79/1.01	(step @p231 :rule refl :args (@t93))
0.79/1.01	(step @p232 :rule cong :premises (@p183 @p231 @p230) :args ((ite @t74 @t93 @t92)))
0.79/1.01	(step @p233 :rule eq-symm :args (@t91 @t47))
0.79/1.01	(step @p234 :rule eq-symm :args (@t91 @t39))
0.79/1.01	(step @p235 :rule cong :premises (@p187 @p234 @p233) :args ((ite @t74 (= @t91 @t39) (= @t91 @t47))))
0.79/1.01	(step @p236 :rule trans :premises (@p235 @p232))
0.79/1.01	(step @p237 :rule refl :args (@t47))
0.79/1.01	(step @p238 :rule eq-refl :args (@t94))
0.79/1.01	(step @p239 :rule cong :premises (@p56) :args (@t39))
0.79/1.01	(step @p240 :rule cong :premises (@p187 @p239 @p237) :args (@t90))
0.79/1.01	(step @p241 :rule skolem_intro :args (@t91))
0.79/1.01	(step @p242 :rule trans :premises (@p241 @p240))
0.79/1.01	(step @p243 :rule cong :premises (@p240 @p242) :args ((= @t90 @t91)))
0.79/1.01	(step @p244 :rule trans :premises (@p243 @p238))
0.79/1.01	(step @p245 :rule true_elim :premises (@p244))
0.79/1.01	(step @p246 :rule cong :premises (@p245 @p237) :args (@t95))
0.79/1.01	(step @p247 :rule refl :args (@t39))
0.79/1.01	(step @p248 :rule cong :premises (@p245 @p247) :args (@t96))
0.79/1.01	(step @p249 :rule cong :premises (@p187 @p248 @p246) :args ((ite @t74 @t96 @t95)))
0.79/1.01	(step @p250 :rule ite_eq :args (@t90))
0.79/1.01	(step @p251 :rule eq_resolve :premises (@p250 @p249))
0.79/1.01	(step @p252 :rule eq_resolve :premises (@p251 @p236))
0.79/1.01	(step @p253 :rule ite_elim2 :premises (@p252))
0.79/1.01	(step @p254 :rule chain_resolution :premises (@p253 @p178) :args (@t52 @t81))
0.79/1.01	(step @p255 :rule refl :args (@t91))
0.79/1.01	(step @p256 :rule eq-refl :args ((ite @t74 @t94 @t87)))
0.79/1.01	(step @p257 :rule cong :premises (@p187 @p242 @p218) :args (@t97))
0.79/1.01	(step @p258 :rule skolem_intro :args (@t98))
0.79/1.01	(step @p259 :rule trans :premises (@p258 @p257))
0.79/1.01	(step @p260 :rule cong :premises (@p257 @p259) :args ((= @t97 @t98)))
0.79/1.01	(step @p261 :rule trans :premises (@p260 @p256))
0.79/1.01	(step @p262 :rule true_elim :premises (@p261))
0.79/1.01	(step @p263 :rule cong :premises (@p262 @p255) :args (@t99))
0.79/1.01	(step @p264 :rule cong :premises (@p263) :args (@t100))
0.79/1.01	(step @p265 :rule cong :premises (@p117 @p264) :args ((=> @t31 @t100)))
0.79/1.01	(step @p266 :rule ite-true-cond :args (@t91 @t101))
0.79/1.01	(step @p267 :rule refl :args (@t101))
0.79/1.01	(step @p268 :rule cong :premises (@p55 @p255 @p267) :args (@t102))
0.79/1.01	(step @p269 :rule trans :premises (@p268 @p266))
0.79/1.01	(step @p270 :rule beta-reduce :args ((= @t105 @t102)))
0.79/1.01	(step @p271 :rule trans :premises (@p270 @p269))
0.79/1.01	(step @p272 :rule ite-true-cond :args (@t84 @t39))
0.79/1.01	(step @p273 :rule refl :args (@t84))
0.79/1.01	(step @p274 :rule cong :premises (@p62 @p273 @p247) :args (@t106))
0.79/1.01	(step @p275 :rule trans :premises (@p274 @p272))
0.79/1.01	(step @p276 :rule eq-symm :args (@t7 @t10))
0.79/1.01	(step @p277 :rule cong :premises (@p276 @p255 @p275) :args (@t107))
0.79/1.01	(step @p278 :rule beta-reduce :args ((= @t108 @t107)))
0.79/1.01	(step @p279 :rule trans :premises (@p278 @p277))
0.79/1.01	(step @p280 :rule cong :premises (@p279 @p271) :args (@t109))
0.79/1.01	(step @p281 :rule cong :premises (@p280) :args (@t110))
0.79/1.01	(step @p282 :rule cong :premises (@p117 @p281) :args ((=> @t31 @t110)))
0.79/1.01	(assume-push @p384 @t31)
0.79/1.01	(step @p284 :rule instantiate :premises (@p384) :args ((@list @t104)))
0.79/1.01	(step-pop @p384 :rule scope :premises (@p284))
0.79/1.01	(step @p285 :rule process_scope :premises (@p384) :args (@t110))
0.79/1.01	(step @p287 :rule eq_resolve :premises (@p285 @p282))
0.79/1.01	(step @p288 :rule eq_resolve :premises (@p287 @p265))
0.79/1.01	(step @p289 :rule implies_elim :premises (@p288))
0.79/1.01	(step @p290 :rule chain_resolution :premises (@p289 @p88) :args (@t63 @t64))
0.79/1.01	(step @p291 :rule refl :args (@t111))
0.79/1.01	(step @p292 :rule refl :args (@t112))
0.79/1.01	(step @p293 :rule cong :premises (@p183 @p292 @p291) :args ((ite @t74 @t112 @t111)))
0.79/1.01	(step @p294 :rule eq-symm :args (@t98 @t84))
0.79/1.01	(step @p295 :rule eq-symm :args (@t98 @t91))
0.79/1.01	(step @p296 :rule cong :premises (@p187 @p295 @p294) :args ((ite @t74 (= @t98 @t91) (= @t98 @t84))))
0.79/1.01	(step @p297 :rule trans :premises (@p296 @p293))
0.79/1.01	(step @p298 :rule cong :premises (@p262 @p273) :args (@t113))
0.79/1.01	(step @p299 :rule cong :premises (@p262 @p255) :args (@t114))
0.79/1.01	(step @p300 :rule cong :premises (@p187 @p299 @p298) :args ((ite @t74 @t114 @t113)))
0.79/1.01	(step @p301 :rule ite_eq :args (@t97))
0.79/1.01	(step @p302 :rule eq_resolve :premises (@p301 @p300))
0.79/1.01	(step @p303 :rule eq_resolve :premises (@p302 @p297))
0.79/1.01	(step @p304 :rule ite_elim2 :premises (@p303))
0.79/1.01	(step @p305 :rule chain_resolution :premises (@p304 @p178) :args (@t52 @t81))
0.79/1.01	(step @p306 :rule refl :args (@t115))
0.79/1.01	(step @p307 :rule bool-double-not-elim :args (@t116))
0.79/1.01	(step @p308 :rule refl :args (@t117))
0.79/1.01	(step @p309 :rule refl :args (@t118))
0.79/1.01	(step @p310 :rule refl :args (@t119))
0.79/1.01	(step @p311 :rule nary_cong :premises (@p135 @p310 @p309 @p308 @p307 @p306) :args ((or @t50 @t119 @t118 @t117 (not @t120) @t115)))
0.79/1.01	(assume-push @p386 @t49)
0.79/1.01	(assume-push @p387 @t77)
0.79/1.01	(assume-push @p388 @t85)
0.79/1.01	(assume-push @p389 @t111)
0.79/1.01	(assume-push @p390 @t92)
0.79/1.01	(assume-push @p391 @t120)
0.79/1.01	(step @p318 :rule evaluate :args ((= false true)))
0.79/1.01	(step @p319 :rule true_intro :premises (@p386))
0.79/1.01	(step @p320 :rule symm :premises (@p390))
0.79/1.01	(step @p321 :rule symm :premises (@p387))
0.79/1.01	(step @p322 :rule symm :premises (@p388))
0.79/1.01	(step @p323 :rule symm :premises (@p389))
0.79/1.01	(step @p324 :rule trans :premises (@p323 @p322 @p321))
0.79/1.01	(step @p325 :rule cong :premises (@p324 @p320) :args (@t116))
0.79/1.01	(step @p326 :rule false_intro :premises (@p391))
0.79/1.01	(step @p327 :rule symm :premises (@p326))
0.79/1.01	(step @p328 :rule trans :premises (@p327 @p325 @p319))
0.79/1.01	(step @p329 false :rule eq_resolve :premises (@p328 @p318))
0.79/1.01	(step-pop @p391 :rule scope :premises (@p329))
0.79/1.01	(step-pop @p392 :rule scope :premises (@p391))
0.79/1.01	(step-pop @p393 :rule scope :premises (@p392))
0.79/1.01	(step-pop @p394 :rule scope :premises (@p393))
0.79/1.01	(step-pop @p395 :rule scope :premises (@p394))
0.79/1.01	(step-pop @p396 :rule scope :premises (@p395))
0.79/1.01	(step @p330 :rule process_scope :premises (@p396) :args (false))
0.79/1.01	(assume-push @p398 @t49)
0.79/1.01	(assume-push @p399 @t77)
0.79/1.01	(assume-push @p400 @t85)
0.79/1.01	(assume-push @p401 @t92)
0.79/1.01	(assume-push @p402 @t120)
0.79/1.01	(assume-push @p403 @t111)
0.79/1.01	(step @p343 :rule and_intro :premises (@p398 @p399 @p400 @p403 @p401 @p402))
0.79/1.01	(step-pop @p403 :rule scope :premises (@p343))
0.79/1.01	(step-pop @p404 :rule scope :premises (@p403))
0.79/1.01	(step-pop @p405 :rule scope :premises (@p404))
0.79/1.01	(step-pop @p406 :rule scope :premises (@p405))
0.79/1.01	(step-pop @p407 :rule scope :premises (@p406))
0.79/1.01	(step-pop @p408 :rule scope :premises (@p407))
0.79/1.01	(step @p344 :rule process_scope :premises (@p408) :args (@t121))
0.79/1.01	(step @p351 :rule implies_elim :premises (@p344))
0.79/1.01	(step @p352 :rule resolution :premises (@p351 @p330) :args (true @t121))
0.79/1.01	(step @p353 :rule not_and :premises (@p352))
0.79/1.01	(step @p354 :rule eq_resolve :premises (@p353 @p311))
0.79/1.01	(step @p355 false :rule chain_resolution :premises (@p354 @p305 @p290 @p254 @p229 @p205 @p104) :args ((@list false true false false false false) (@list @t111 @t116 @t92 @t85 @t77 @t49)))
0.79/1.01	)
0.79/1.01	% SZS output end Proof
0.79/1.01	% cvc5 exiting
0.79/1.02	EOF