0.05/0.12	% Problem  : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.05/0.13	% Command  : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 240 THM
0.13/0.35	% Computer : n029.cluster.edu
0.13/0.35	% Model    : x86_64 x86_64
0.13/0.35	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.13/0.35	% Memory   : 8042.1875MB
0.13/0.35	% OS       : Linux 3.10.0-693.el7.x86_64
0.13/0.35	% CPULimit : 1920
0.13/0.35	% WCLimit  : 240
0.13/0.35	% DateTime : Sat Sep  6 01:11:52 EDT 2025
0.13/0.35	% CPUTime  : 
0.20/0.51	%----Proving TH0
0.38/0.58	--- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 72s...
0.38/0.58	% SZS status Theorem
0.38/0.58	% SZS output start Proof
0.38/0.58	(
0.38/0.58	(declare-type $$unsorted ())
0.38/0.58	(define tptp.in () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "M" (-> $$unsorted Bool)))) (lambda (@list _let_1 _let_2) (_ _let_2 _let_1)))))
0.38/0.58	(define tptp.is_a () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "M" (-> $$unsorted Bool)))) (lambda (@list _let_1 _let_2) (_ _let_2 _let_1)))))
0.38/0.58	(define tptp.emptyset () (lambda (@list (@var "X" $$unsorted)) false))
0.38/0.58	(define tptp.unord_pair () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "U" $$unsorted))) (let ((_let_3 (@var "X" $$unsorted))) (lambda (@list _let_3 _let_1 _let_2) (or (= _let_2 _let_3) (= _let_2 _let_1)))))))
0.38/0.58	(define tptp.singleton () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "U" $$unsorted))) (lambda (@list _let_1 _let_2) (= _let_2 _let_1)))))
0.38/0.58	(define tptp.union () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ _let_3 _let_1) (_ _let_2 _let_1)))))))
0.38/0.58	(define tptp.excl_union () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (_ _let_2 _let_1))) (let ((_let_4 (@var "X" (-> $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_1))) (lambda (@list _let_4 _let_2 _let_1) (or (and _let_5 (not _let_3)) (and (not _let_5) _let_3)))))))))
0.38/0.58	(define tptp.intersection () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (and (_ _let_3 _let_1) (_ _let_2 _let_1)))))))
0.38/0.58	(define tptp.setminus () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (and (_ _let_3 _let_1) (not (_ _let_2 _let_1))))))))
0.38/0.58	(define tptp.complement () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (not (_ _let_2 _let_1))))))
0.38/0.58	(define tptp.disjoint () (let ((_let_1 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_2 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (= (_ (_ tptp.intersection _let_2) _let_1) tptp.emptyset)))))
0.38/0.58	(define tptp.subset () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2) (forall (@list _let_1) (=> (_ _let_3 _let_1) (_ _let_2 _let_1))))))))
0.38/0.58	(define tptp.meets () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2) (exists (@list _let_1) (and (_ _let_3 _let_1) (_ _let_2 _let_1))))))))
0.38/0.58	(define tptp.misses () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2) (not (exists (@list _let_1) (and (_ _let_3 _let_1) (_ _let_2 _let_1)))))))))
0.38/0.58	(define @t1 () (@var "Z" (-> $$unsorted Bool)))
0.38/0.58	(define @t2 () (@var "X" (-> $$unsorted Bool)))
0.38/0.58	(define @t3 () (_ tptp.setminus @t2))
0.38/0.58	(define @t4 () (@var "Y" (-> $$unsorted Bool)))
0.38/0.58	(define @t5 () (= (_ @t3 (_ (_ tptp.union @t4) @t1)) (_ (_ tptp.intersection (_ @t3 @t4)) (_ @t3 @t1))))
0.38/0.58	(define @t6 () (@list @t2 @t4 @t1))
0.38/0.58	(define @t7 () (forall @t6 @t5))
0.38/0.58	(define @t8 () (not @t7))
0.38/0.58	(define @t9 () (@var "X" $$unsorted))
0.38/0.58	(define @t10 () (@var "M" (-> $$unsorted Bool)))
0.38/0.58	(define @t11 () (lambda (@list @t9 @t10) (_ @t10 @t9)))
0.38/0.58	(define @t12 () (lambda (@list @t9) false))
0.38/0.58	(define @t13 () (@var "Y" $$unsorted))
0.38/0.58	(define @t14 () (@var "U" $$unsorted))
0.38/0.58	(define @t15 () (= @t14 @t9))
0.38/0.58	(define @t16 () (lambda (@list @t9 @t13 @t14) (or @t15 (= @t14 @t13))))
0.38/0.58	(define @t17 () (lambda (@list @t9 @t14) @t15))
0.38/0.58	(define @t18 () (_ @t4 @t14))
0.38/0.58	(define @t19 () (_ @t2 @t14))
0.38/0.58	(define @t20 () (@list @t2 @t4 @t14))
0.38/0.58	(define @t21 () (lambda @t20 (or @t19 @t18)))
0.38/0.58	(define @t22 () (not @t19))
0.38/0.58	(define @t23 () (not @t18))
0.38/0.58	(define @t24 () (and @t19 @t23))
0.38/0.58	(define @t25 () (lambda @t20 (or @t24 (and @t22 @t18))))
0.38/0.58	(define @t26 () (and @t19 @t18))
0.38/0.58	(define @t27 () (lambda @t20 @t26))
0.38/0.58	(define @t28 () (lambda @t20 @t24))
0.38/0.58	(define @t29 () (lambda (@list @t2 @t14) @t22))
0.38/0.58	(define @t30 () (@list @t2 @t4))
0.38/0.58	(define @t31 () (lambda @t30 (= (_ (_ tptp.intersection @t2) @t4) tptp.emptyset)))
0.38/0.58	(define @t32 () (@list @t14))
0.38/0.58	(define @t33 () (lambda @t30 (forall @t32 (=> @t19 @t18))))
0.38/0.58	(define @t34 () (exists @t32 @t26))
0.38/0.58	(define @t35 () (lambda @t30 @t34))
0.38/0.58	(define @t36 () (lambda @t30 (not @t34)))
0.38/0.58	(define @t37 () (_ @t1 @t14))
0.38/0.58	(define @t38 () (_ @t1 @t14))
0.38/0.58	(define @t39 () (not @t38))
0.38/0.58	(define @t40 () (_ @t4 @t14))
0.38/0.58	(define @t41 () (_ @t2 @t14))
0.38/0.58	(define @t42 () (and @t19 @t23 @t39))
0.38/0.58	(define @t43 () (lambda @t32 @t42))
0.38/0.58	(define @t44 () (or @t18 @t38))
0.38/0.58	(define @t45 () (not @t44))
0.38/0.58	(define @t46 () (and @t19 @t45))
0.38/0.58	(define @t47 () (lambda @t32 @t46))
0.38/0.58	(define @t48 () (= @t47 @t43))
0.38/0.58	(define @t49 () (and @t19 @t39))
0.38/0.58	(define @t50 () (lambda @t32 @t49))
0.38/0.58	(define @t51 () (_ @t50 @t14))
0.38/0.58	(define @t52 () (and @t51 @t19 @t23))
0.38/0.58	(define @t53 () (lambda @t32 @t52))
0.38/0.58	(define @t54 () (@var "BOUND_VARIABLE_7529" (-> $$unsorted Bool)))
0.38/0.58	(define @t55 () (_ @t54 @t14))
0.38/0.58	(define @t56 () (and @t55 @t19 @t23))
0.38/0.58	(define @t57 () (@list @t54 @t14))
0.38/0.58	(define @t58 () (lambda (@list @t4 @t14) @t24))
0.38/0.58	(define @t59 () (_ @t28 @t2))
0.38/0.58	(define @t60 () (lambda @t32 @t24))
0.38/0.58	(define @t61 () (_ @t60 @t14))
0.38/0.58	(define @t62 () (and @t61 @t55))
0.38/0.58	(define @t63 () (lambda @t57 @t62))
0.38/0.58	(define @t64 () (@list @t4))
0.38/0.58	(define @t65 () (lambda @t32 @t44))
0.38/0.58	(define @t66 () (_ @t65 @t14))
0.38/0.58	(define @t67 () (not @t66))
0.38/0.58	(define @t68 () (and @t19 @t67))
0.38/0.58	(define @t69 () (lambda @t32 @t68))
0.38/0.58	(define @t70 () (@var "BOUND_VARIABLE_7502" (-> $$unsorted Bool)))
0.38/0.58	(define @t71 () (_ @t70 @t14))
0.38/0.58	(define @t72 () (lambda (@list @t70 @t14) (or @t18 @t71)))
0.38/0.58	(define @t73 () (= (_ @t59 (_ (_ @t21 @t4) @t1)) (_ (_ @t27 (_ @t59 @t4)) (_ @t59 @t1))))
0.38/0.58	(define @t74 () (forall @t6 @t73))
0.38/0.58	(define @t75 () (forall @t6 (= (lambda @t32 (and @t41 (not (or @t40 @t37)))) (lambda @t32 (and @t41 (not @t40) (not @t37))))))
0.38/0.58	(define @t76 () (@quantifiers_skolemize @t75 2))
0.38/0.58	(define @t77 () (_ @t76 @t14))
0.38/0.58	(define @t78 () (@quantifiers_skolemize @t75 1))
0.38/0.58	(define @t79 () (_ @t78 @t14))
0.38/0.58	(define @t80 () (@quantifiers_skolemize @t75 0))
0.38/0.58	(define @t81 () (_ @t80 @t14))
0.38/0.58	(define @t82 () (lambda @t32 (and @t81 (not (or @t79 @t77)))))
0.38/0.58	(define @t83 () (@purify @t82))
0.38/0.58	(define @t84 () (lambda @t32 (and @t81 (not @t79) (not @t77))))
0.38/0.58	(define @t85 () (@purify @t84))
0.38/0.58	(define @t86 () (= @t85 @t83))
0.38/0.58	(define @t87 () (not @t86))
0.38/0.58	(define @t88 () (not @t75))
0.38/0.58	(define @t89 () (= @t82 @t84))
0.38/0.58	(define @t90 () (not @t89))
0.38/0.58	(define @t91 () (@list true))
0.38/0.58	(define @t92 () (@const 0 $$unsorted))
0.38/0.58	(define @t93 () (_ @t76 @t92))
0.38/0.58	(define @t94 () (not @t93))
0.38/0.58	(define @t95 () (_ @t78 @t92))
0.38/0.58	(define @t96 () (not @t95))
0.38/0.58	(define @t97 () (_ @t80 @t92))
0.38/0.58	(define @t98 () (and @t97 @t96 @t94))
0.38/0.58	(define @t99 () (or @t95 @t93))
0.38/0.58	(define @t100 () (not @t99))
0.38/0.58	(define @t101 () (and @t97 @t100))
0.38/0.58	(define @t102 () (= (_ @t82 @t92) @t101))
0.38/0.58	(define @t103 () (_ @t83 @t92))
0.38/0.58	(define @t104 () (= (_ @t84 @t92) @t98))
0.38/0.58	(define @t105 () (_ @t85 @t92))
0.38/0.58	(define @t106 () (= @t105 @t103))
0.38/0.58	(define @t107 () (not @t106))
0.38/0.58	(define @t108 () (or @t86 @t107))
0.38/0.58	(define @t109 () (not @t98))
0.38/0.58	(define @t110 () (not @t101))
0.38/0.58	(define @t111 () (= @t101 @t98))
0.38/0.58	(define @t112 () (@list true true true false))
0.38/0.58	(define @t113 () (@list @t111 @t101 @t98 @t99))
0.38/0.58	(define @t114 () (not @t97))
0.38/0.58	(define @t115 () (@list @t97))
0.38/0.58	(assume @p1 @t8)
0.38/0.58	(assume @p2 true)
0.38/0.58	(step @p3 (= tptp.in @t11) :rule refl :args (@t11))
0.38/0.58	(step @p4 (= tptp.is_a @t11) :rule refl :args (@t11))
0.38/0.58	(step @p5 (= tptp.emptyset @t12) :rule refl :args (@t12))
0.38/0.58	(step @p6 (= tptp.unord_pair @t16) :rule refl :args (@t16))
0.38/0.58	(step @p7 (= tptp.singleton @t17) :rule refl :args (@t17))
0.38/0.58	(step @p8 (= tptp.union @t21) :rule refl :args (@t21))
0.38/0.58	(step @p9 (= tptp.excl_union @t25) :rule refl :args (@t25))
0.38/0.58	(step @p10 (= tptp.intersection @t27) :rule refl :args (@t27))
0.38/0.58	(step @p11 (= tptp.setminus @t28) :rule refl :args (@t28))
0.38/0.58	(step @p12 (= tptp.complement @t29) :rule refl :args (@t29))
0.38/0.58	(step @p13 (= tptp.disjoint @t31) :rule refl :args (@t31))
0.38/0.58	(step @p14 (= tptp.subset @t33) :rule refl :args (@t33))
0.38/0.58	(step @p15 (= tptp.meets @t35) :rule refl :args (@t35))
0.38/0.58	(step @p16 (= tptp.misses @t36) :rule refl :args (@t36))
0.38/0.58	(step @p17 :rule refl :args (@t37))
0.38/0.58	(step @p18 :rule refl :args (@t38))
0.38/0.58	(step @p19 :rule cong :premises (@p18 @p17) :args ((= @t38 @t37)))
0.38/0.58	(step @p20 :rule symm :premises (@p19))
0.38/0.58	(step @p21 :rule eq_resolve :premises (@p18 @p20))
0.38/0.58	(step @p22 :rule cong :premises (@p21) :args (@t39))
0.38/0.58	(step @p23 :rule refl :args (@t40))
0.38/0.58	(step @p24 :rule refl :args (@t18))
0.38/0.58	(step @p25 :rule cong :premises (@p24 @p23) :args ((= @t18 @t40)))
0.38/0.58	(step @p26 :rule symm :premises (@p25))
0.38/0.58	(step @p27 :rule eq_resolve :premises (@p24 @p26))
0.38/0.58	(step @p28 :rule cong :premises (@p27) :args (@t23))
0.38/0.58	(step @p29 :rule refl :args (@t41))
0.38/0.58	(step @p30 :rule refl :args (@t19))
0.38/0.58	(step @p31 :rule cong :premises (@p30 @p29) :args ((= @t19 @t41)))
0.38/0.58	(step @p32 :rule symm :premises (@p31))
0.38/0.58	(step @p33 :rule eq_resolve :premises (@p30 @p32))
0.38/0.58	(step @p34 :rule nary_cong :premises (@p33 @p28 @p22) :args (@t42))
0.38/0.58	(step @p35 :rule cong :premises (@p34) :args (@t43))
0.38/0.58	(step @p36 :rule nary_cong :premises (@p27 @p21) :args (@t44))
0.38/0.58	(step @p37 :rule cong :premises (@p36) :args (@t45))
0.38/0.58	(step @p38 :rule nary_cong :premises (@p33 @p37) :args (@t46))
0.38/0.58	(step @p39 :rule cong :premises (@p38) :args (@t47))
0.38/0.58	(step @p40 :rule cong :premises (@p39 @p35) :args (@t48))
0.38/0.58	(step @p41 :rule cong :premises (@p40) :args ((forall @t6 @t48)))
0.38/0.58	(step @p42 :rule aci_norm :args ((= (and @t49 @t19 @t23) @t42)))
0.38/0.58	(step @p43 :rule refl :args (@t23))
0.38/0.58	(step @p44 :rule refl :args (@t19))
0.38/0.58	(step @p45 :rule beta-reduce :args ((= @t51 @t49)))
0.38/0.58	(step @p46 :rule nary_cong :premises (@p45 @p44 @p43) :args (@t52))
0.38/0.58	(step @p47 :rule trans :premises (@p46 @p42))
0.38/0.58	(step @p48 :rule cong :premises (@p47) :args (@t53))
0.38/0.58	(step @p49 :rule beta-reduce :args ((= (_ (lambda @t57 @t56) @t50) @t53)))
0.38/0.58	(step @p50 :rule trans :premises (@p49 @p48))
0.38/0.58	(step @p51 :rule beta-reduce :args ((= (_ @t58 @t1) @t50)))
0.38/0.58	(step @p52 :rule refl :args (@t1))
0.38/0.58	(step @p53 :rule beta-reduce :args ((= @t59 @t58)))
0.38/0.58	(step @p54 :rule ho_cong :premises (@p53 @p52))
0.38/0.58	(step @p55 :rule trans :premises (@p54 @p51))
0.38/0.58	(step @p56 :rule aci_norm :args ((= (and @t24 @t55) @t56)))
0.38/0.58	(step @p57 :rule refl :args (@t55))
0.38/0.58	(step @p58 :rule beta-reduce :args ((= @t61 @t24)))
0.38/0.58	(step @p59 :rule nary_cong :premises (@p58 @p57) :args (@t62))
0.38/0.58	(step @p60 :rule trans :premises (@p59 @p56))
0.38/0.58	(step @p61 :rule cong :premises (@p60) :args (@t63))
0.38/0.58	(step @p62 :rule beta-reduce :args ((= (_ (lambda (@list @t2 @t54 @t14) (and @t19 @t55)) @t60) @t63)))
0.38/0.58	(step @p63 :rule trans :premises (@p62 @p61))
0.38/0.58	(step @p64 :rule refl :args (@t60))
0.38/0.58	(step @p65 :rule alpha_equiv :args (@t27 @t64 (@list @t54)))
0.38/0.58	(step @p66 :rule ho_cong :premises (@p65 @p64))
0.38/0.58	(step @p67 :rule trans :premises (@p66 @p63))
0.38/0.58	(step @p68 :rule beta-reduce :args ((= (_ @t58 @t4) @t60)))
0.38/0.58	(step @p69 :rule refl :args (@t4))
0.38/0.58	(step @p70 :rule ho_cong :premises (@p53 @p69))
0.38/0.58	(step @p71 :rule trans :premises (@p70 @p68))
0.38/0.58	(step @p72 :rule refl :args (@t27))
0.38/0.58	(step @p73 :rule ho_cong :premises (@p72 @p71))
0.38/0.58	(step @p74 :rule trans :premises (@p73 @p67))
0.38/0.58	(step @p75 :rule ho_cong :premises (@p74 @p55))
0.38/0.58	(step @p76 :rule trans :premises (@p75 @p50))
0.38/0.58	(step @p77 :rule beta-reduce :args ((= @t66 @t44)))
0.38/0.58	(step @p78 :rule cong :premises (@p77) :args (@t67))
0.38/0.58	(step @p79 :rule nary_cong :premises (@p44 @p78) :args (@t68))
0.38/0.58	(step @p80 :rule cong :premises (@p79) :args (@t69))
0.38/0.58	(step @p81 :rule beta-reduce :args ((= (_ @t58 @t65) @t69)))
0.38/0.58	(step @p82 :rule trans :premises (@p81 @p80))
0.38/0.58	(step @p83 :rule beta-reduce :args ((= (_ @t72 @t1) @t65)))
0.38/0.58	(step @p84 :rule beta-reduce :args ((= (_ (lambda (@list @t2 @t70 @t14) (or @t19 @t71)) @t4) @t72)))
0.38/0.58	(step @p85 :rule refl :args (@t4))
0.38/0.58	(step @p86 :rule alpha_equiv :args (@t21 @t64 (@list @t70)))
0.38/0.58	(step @p87 :rule ho_cong :premises (@p86 @p85))
0.38/0.58	(step @p88 :rule trans :premises (@p87 @p84))
0.38/0.58	(step @p89 :rule ho_cong :premises (@p88 @p52))
0.38/0.58	(step @p90 :rule trans :premises (@p89 @p83))
0.38/0.58	(step @p91 :rule ho_cong :premises (@p53 @p90))
0.38/0.58	(step @p92 :rule trans :premises (@p91 @p82))
0.38/0.58	(step @p93 :rule cong :premises (@p92 @p76) :args (@t73))
0.38/0.58	(step @p94 :rule cong :premises (@p93) :args (@t74))
0.38/0.58	(step @p95 :rule trans :premises (@p94 @p41))
0.38/0.58	(step @p96 :rule cong :premises (@p95) :args ((not @t74)))
0.38/0.58	(step @p97 :rule refl :args (@t2))
0.38/0.58	(step @p98 :rule ho_cong :premises (@p11 @p97))
0.38/0.58	(step @p99 :rule ho_cong :premises (@p98 @p52))
0.38/0.58	(step @p100 :rule ho_cong :premises (@p98 @p69))
0.38/0.58	(step @p101 :rule ho_cong :premises (@p10 @p100))
0.38/0.58	(step @p102 :rule ho_cong :premises (@p101 @p99))
0.38/0.58	(step @p103 :rule ho_cong :premises (@p8 @p69))
0.38/0.58	(step @p104 :rule ho_cong :premises (@p103 @p52))
0.38/0.58	(step @p105 :rule ho_cong :premises (@p98 @p104))
0.38/0.58	(step @p106 :rule cong :premises (@p105 @p102) :args (@t5))
0.38/0.58	(step @p107 :rule cong :premises (@p106) :args (@t7))
0.38/0.58	(step @p108 :rule cong :premises (@p107) :args (@t8))
0.38/0.58	(step @p109 :rule trans :premises (@p108 @p96))
0.38/0.58	(step @p110 :rule eq_resolve :premises (@p1 @p109))
0.38/0.58	(step @p111 :rule refl :args (@t87))
0.38/0.58	(step @p112 :rule bool-double-not-elim :args (@t75))
0.38/0.58	(step @p113 :rule nary_cong :premises (@p112 @p111) :args ((or (not @t88) @t87)))
0.38/0.58	(step @p114 :rule eq-symm :args (@t83 @t85))
0.38/0.58	(step @p115 :rule eq-refl :args (@t84))
0.38/0.58	(step @p116 :rule skolem_intro :args (@t85))
0.38/0.58	(step @p117 :rule refl :args (@t84))
0.38/0.58	(step @p118 :rule cong :premises (@p117 @p116) :args ((= @t84 @t85)))
0.38/0.58	(step @p119 :rule trans :premises (@p118 @p115))
0.38/0.58	(step @p120 :rule true_elim :premises (@p119))
0.38/0.58	(step @p121 :rule eq-refl :args (@t82))
0.38/0.58	(step @p122 :rule skolem_intro :args (@t83))
0.38/0.58	(step @p123 :rule refl :args (@t82))
0.38/0.58	(step @p124 :rule cong :premises (@p123 @p122) :args ((= @t82 @t83)))
0.38/0.58	(step @p125 :rule trans :premises (@p124 @p121))
0.38/0.58	(step @p126 :rule true_elim :premises (@p125))
0.38/0.58	(step @p127 :rule cong :premises (@p126 @p120) :args (@t89))
0.38/0.58	(step @p128 :rule trans :premises (@p127 @p114))
0.38/0.58	(step @p129 :rule cong :premises (@p128) :args (@t90))
0.38/0.58	(step @p130 :rule refl :args (@t88))
0.38/0.58	(step @p131 :rule cong :premises (@p130 @p129) :args ((=> @t88 @t90)))
0.38/0.58	(assume-push @p208 @t88)
0.38/0.58	(step @p133 :rule skolemize :premises (@p110))
0.38/0.58	(step-pop @p208 :rule scope :premises (@p133))
0.38/0.58	(step @p134 :rule process_scope :premises (@p208) :args (@t90))
0.38/0.58	(step @p136 :rule eq_resolve :premises (@p134 @p131))
0.38/0.58	(step @p137 :rule implies_elim :premises (@p136))
0.38/0.58	(step @p138 :rule eq_resolve :premises (@p137 @p113))
0.38/0.58	(step @p139 :rule chain_resolution :premises (@p138 @p110) :args (@t91 (@list @t75)))
0.38/0.58	(step @p140 :rule eq-symm :args (@t98 @t101))
0.38/0.58	(step @p141 :rule eq-refl :args (@t101))
0.38/0.58	(step @p142 :rule refl :args (@t101))
0.38/0.58	(step @p143 :rule beta-reduce :args (@t102))
0.38/0.58	(step @p144 :rule cong :premises (@p143 @p142) :args (@t102))
0.38/0.58	(step @p145 :rule trans :premises (@p144 @p141))
0.38/0.58	(step @p146 :rule refl :args (@t92))
0.38/0.58	(step @p147 :rule ho_cong :premises (@p122 @p146))
0.38/0.58	(step @p148 :rule cong :premises (@p147 @p142) :args ((= @t103 @t101)))
0.38/0.58	(step @p149 :rule trans :premises (@p148 @p145))
0.38/0.58	(step @p150 :rule true_elim :premises (@p149))
0.38/0.58	(step @p151 :rule eq-refl :args (@t98))
0.38/0.58	(step @p152 :rule refl :args (@t98))
0.38/0.58	(step @p153 :rule beta-reduce :args (@t104))
0.38/0.58	(step @p154 :rule cong :premises (@p153 @p152) :args (@t104))
0.38/0.58	(step @p155 :rule trans :premises (@p154 @p151))
0.38/0.58	(step @p156 :rule ho_cong :premises (@p116 @p146))
0.38/0.58	(step @p157 :rule cong :premises (@p156 @p152) :args ((= @t105 @t98)))
0.38/0.58	(step @p158 :rule trans :premises (@p157 @p155))
0.38/0.58	(step @p159 :rule true_elim :premises (@p158))
0.38/0.58	(step @p160 :rule cong :premises (@p159 @p150) :args (@t106))
0.38/0.58	(step @p161 :rule trans :premises (@p160 @p140))
0.38/0.58	(step @p162 :rule cong :premises (@p161) :args (@t107))
0.38/0.58	(step @p163 :rule refl :args (@t86))
0.38/0.58	(step @p164 :rule nary_cong :premises (@p163 @p162) :args (@t108))
0.38/0.58	; WARNING: add trust step for TRUST
0.38/0.58	; trust TRUST THEORY_LEMMA
0.38/0.58	(step @p165 :rule trust :premises () :args (@t108))
0.38/0.58	(step @p166 :rule eq_resolve :premises (@p165 @p164))
0.38/0.58	(step @p167 :rule chain_resolution :premises (@p166 @p139) :args (@t91 (@list @t86)))
0.38/0.58	(step @p168 :rule cnf_or_neg :args (@t99 1))
0.38/0.58	(step @p169 :rule cnf_and_pos :args (@t98 2))
0.38/0.58	(step @p170 :rule reordering :premises (@p169) :args ((or @t94 @t109)))
0.38/0.58	(step @p171 :rule cnf_and_pos :args (@t101 1))
0.38/0.58	(step @p172 :rule reordering :premises (@p171) :args ((or @t100 @t110)))
0.38/0.58	(step @p173 :rule cnf_equiv_neg1 :args (@t111))
0.38/0.58	(step @p174 :rule reordering :premises (@p173) :args ((or @t101 @t98 @t111)))
0.38/0.58	(step @p175 :rule chain_resolution :premises (@p174 @p167 @p172 @p170 @p168) :args (@t112 @t113))
0.38/0.58	(step @p176 :rule factoring :premises (@p175))
0.38/0.58	(step @p177 :rule cnf_or_neg :args (@t99 0))
0.38/0.58	(step @p178 :rule cnf_and_pos :args (@t98 1))
0.38/0.58	(step @p179 :rule reordering :premises (@p178) :args ((or @t96 @t109)))
0.38/0.58	(step @p180 :rule chain_resolution :premises (@p174 @p167 @p172 @p179 @p177) :args (@t112 @t113))
0.38/0.58	(step @p181 :rule factoring :premises (@p180))
0.38/0.58	(step @p182 :rule cnf_or_pos :args (@t99))
0.38/0.58	(step @p183 :rule reordering :premises (@p182) :args ((or @t95 @t93 @t100)))
0.38/0.59	(step @p184 :rule bool-double-not-elim :args (@t93))
0.38/0.59	(step @p185 :rule bool-double-not-elim :args (@t95))
0.38/0.59	(step @p186 :rule refl :args (@t114))
0.38/0.59	(step @p187 :rule nary_cong :premises (@p152 @p186 @p185 @p184) :args ((or @t98 @t114 (not @t96) (not @t94))))
0.38/0.59	(step @p188 :rule cnf_and_neg :args (@t98))
0.38/0.59	(step @p189 :rule eq_resolve :premises (@p188 @p187))
0.38/0.59	(step @p190 :rule reordering :premises (@p189) :args ((or @t95 @t93 @t98 @t114)))
0.38/0.59	(step @p191 :rule bool-double-not-elim :args (@t99))
0.38/0.59	(step @p192 :rule nary_cong :premises (@p142 @p186 @p191) :args ((or @t101 @t114 (not @t100))))
0.38/0.59	(step @p193 :rule cnf_and_neg :args (@t101))
0.38/0.59	(step @p194 :rule eq_resolve :premises (@p193 @p192))
0.38/0.59	(step @p195 :rule reordering :premises (@p194) :args ((or @t99 @t101 @t114)))
0.38/0.59	(step @p196 :rule cnf_equiv_neg2 :args (@t111))
0.38/0.59	(step @p197 :rule chain_resolution :premises (@p196 @p167 @p195 @p190 @p183) :args ((@list true false false true) @t113))
0.38/0.59	(step @p198 :rule factoring :premises (@p197))
0.38/0.59	(step @p199 :rule reordering :premises (@p198) :args ((or @t95 @t93 @t114)))
0.38/0.59	(step @p200 :rule chain_resolution :premises (@p199 @p181 @p176) :args ((@list true true) (@list @t95 @t93)))
0.38/0.59	(step @p201 :rule cnf_and_pos :args (@t101 0))
0.38/0.59	(step @p202 :rule reordering :premises (@p201) :args ((or @t97 @t110)))
0.38/0.59	(step @p203 :rule chain_resolution :premises (@p202 @p200) :args (@t91 @t115))
0.38/0.59	(step @p204 :rule cnf_and_pos :args (@t98 0))
0.38/0.59	(step @p205 :rule reordering :premises (@p204) :args ((or @t97 @t109)))
0.38/0.59	(step @p206 :rule chain_resolution :premises (@p205 @p200) :args (@t91 @t115))
0.38/0.59	(step @p207 false :rule chain_resolution :premises (@p174 @p206 @p203 @p167) :args ((@list true true true) (@list @t98 @t101 @t111)))
0.38/0.59	)
0.38/0.59	% SZS output end Proof
0.38/0.59	% cvc5 exiting
0.38/0.59	EOF