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 : n031.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 : Fri Sep  5 20:16:22 EDT 2025
0.13/0.34	% CPUTime  : 
0.19/0.49	%----Proving TH0
0.39/0.57	--- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 72s...
0.39/0.57	% SZS status Theorem
0.39/0.57	% SZS output start Proof
0.39/0.57	(
0.39/0.57	(declare-type $$unsorted ())
0.39/0.57	(define tptp.in () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "M" (-> $$unsorted Bool)))) (lambda (@list _let_1 _let_2) (_ _let_2 _let_1)))))
0.39/0.57	(define tptp.is_a () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "M" (-> $$unsorted Bool)))) (lambda (@list _let_1 _let_2) (_ _let_2 _let_1)))))
0.39/0.57	(define tptp.emptyset () (lambda (@list (@var "X" $$unsorted)) false))
0.39/0.57	(define tptp.unord_pair () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "U" $$unsorted))) (let ((_let_3 (@var "X" $$unsorted))) (lambda (@list _let_3 _let_1 _let_2) (or (= _let_2 _let_3) (= _let_2 _let_1)))))))
0.39/0.57	(define tptp.singleton () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "U" $$unsorted))) (lambda (@list _let_1 _let_2) (= _let_2 _let_1)))))
0.39/0.57	(define tptp.union () (let ((_let_1 (@var "U" $$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)))))))
0.39/0.57	(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" (-> $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_1))) (lambda (@list _let_4 _let_2 _let_1) (or (and _let_5 (not _let_3)) (and (not _let_5) _let_3)))))))))
0.39/0.57	(define tptp.intersection () (let ((_let_1 (@var "U" $$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)))))))
0.39/0.57	(define tptp.setminus () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (and (_ _let_3 _let_1) (not (_ _let_2 _let_1))))))))
0.39/0.57	(define tptp.complement () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (not (_ _let_2 _let_1))))))
0.39/0.57	(define tptp.disjoint () (let ((_let_1 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_2 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (= (_ (_ tptp.intersection _let_2) _let_1) tptp.emptyset)))))
0.39/0.57	(define tptp.subset () (let ((_let_1 (@var "U" $$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))))))))
0.39/0.57	(define tptp.meets () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2) (exists (@list _let_1) (and (_ _let_3 _let_1) (_ _let_2 _let_1))))))))
0.39/0.57	(define tptp.misses () (let ((_let_1 (@var "U" $$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)))))))))
0.39/0.57	(define @t1 () (@var "Z" (-> $$unsorted Bool)))
0.39/0.57	(define @t2 () (@var "Y" (-> $$unsorted Bool)))
0.39/0.57	(define @t3 () (@var "X" (-> $$unsorted Bool)))
0.39/0.57	(define @t4 () (_ tptp.excl_union @t3))
0.39/0.57	(define @t5 () (= (_ (_ tptp.excl_union (_ @t4 @t2)) @t1) (_ @t4 (_ (_ tptp.excl_union @t2) @t1))))
0.39/0.57	(define @t6 () (@list @t3 @t2 @t1))
0.39/0.57	(define @t7 () (forall @t6 @t5))
0.39/0.57	(define @t8 () (not @t7))
0.39/0.57	(define @t9 () (@var "X" $$unsorted))
0.39/0.57	(define @t10 () (@var "M" (-> $$unsorted Bool)))
0.39/0.57	(define @t11 () (lambda (@list @t9 @t10) (_ @t10 @t9)))
0.39/0.57	(define @t12 () (lambda (@list @t9) false))
0.39/0.57	(define @t13 () (@var "Y" $$unsorted))
0.39/0.57	(define @t14 () (@var "U" $$unsorted))
0.39/0.57	(define @t15 () (= @t14 @t9))
0.39/0.57	(define @t16 () (lambda (@list @t9 @t13 @t14) (or @t15 (= @t14 @t13))))
0.39/0.57	(define @t17 () (lambda (@list @t9 @t14) @t15))
0.39/0.57	(define @t18 () (_ @t2 @t14))
0.39/0.57	(define @t19 () (_ @t3 @t14))
0.39/0.57	(define @t20 () (@list @t3 @t2 @t14))
0.39/0.57	(define @t21 () (lambda @t20 (or @t19 @t18)))
0.39/0.57	(define @t22 () (not @t19))
0.39/0.57	(define @t23 () (and @t22 @t18))
0.39/0.57	(define @t24 () (not @t18))
0.39/0.57	(define @t25 () (and @t19 @t24))
0.39/0.57	(define @t26 () (or @t25 @t23))
0.39/0.57	(define @t27 () (lambda @t20 @t26))
0.39/0.57	(define @t28 () (and @t19 @t18))
0.39/0.57	(define @t29 () (lambda @t20 @t28))
0.39/0.57	(define @t30 () (lambda @t20 @t25))
0.39/0.57	(define @t31 () (lambda (@list @t3 @t14) @t22))
0.39/0.57	(define @t32 () (@list @t3 @t2))
0.39/0.57	(define @t33 () (lambda @t32 (= (_ (_ tptp.intersection @t3) @t2) tptp.emptyset)))
0.39/0.57	(define @t34 () (@list @t14))
0.39/0.57	(define @t35 () (lambda @t32 (forall @t34 (=> @t19 @t18))))
0.39/0.57	(define @t36 () (exists @t34 @t28))
0.39/0.57	(define @t37 () (lambda @t32 @t36))
0.39/0.57	(define @t38 () (lambda @t32 (not @t36)))
0.39/0.57	(define @t39 () (@const 0 $$unsorted))
0.39/0.57	(define @t40 () (_ @t1 @t14))
0.39/0.57	(define @t41 () (_ @t2 @t14))
0.39/0.57	(define @t42 () (not @t41))
0.39/0.57	(define @t43 () (not @t40))
0.39/0.57	(define @t44 () (or (and @t41 @t43) (and @t42 @t40)))
0.39/0.57	(define @t45 () (_ @t3 @t14))
0.39/0.57	(define @t46 () (not @t45))
0.39/0.57	(define @t47 () (or (and @t45 @t42) (and @t46 @t41)))
0.39/0.57	(define @t48 () (forall @t6 (= (lambda @t34 (or (and @t47 @t43) (and (not @t47) @t40))) (lambda @t34 (or (and @t45 (not @t44)) (and @t46 @t44))))))
0.39/0.57	(define @t49 () (@quantifiers_skolemize @t48 2))
0.39/0.57	(define @t50 () (_ @t49 @t39))
0.39/0.57	(define @t51 () (@quantifiers_skolemize @t48 1))
0.39/0.57	(define @t52 () (_ @t51 @t39))
0.39/0.57	(define @t53 () (not @t52))
0.39/0.57	(define @t54 () (and @t53 @t50))
0.39/0.57	(define @t55 () (not @t50))
0.39/0.57	(define @t56 () (and @t52 @t55))
0.39/0.57	(define @t57 () (or @t56 @t54))
0.39/0.57	(define @t58 () (@quantifiers_skolemize @t48 0))
0.39/0.57	(define @t59 () (_ @t58 @t39))
0.39/0.57	(define @t60 () (not @t59))
0.39/0.57	(define @t61 () (and @t60 @t57))
0.39/0.57	(define @t62 () (not @t61))
0.39/0.57	(define @t63 () (and @t59 @t53))
0.39/0.57	(define @t64 () (not @t53))
0.39/0.57	(define @t65 () (not @t56))
0.39/0.57	(define @t66 () (and @t60 @t52))
0.39/0.57	(define @t67 () (or @t63 @t66))
0.39/0.57	(define @t68 () (not @t67))
0.39/0.57	(define @t69 () (and @t68 @t50))
0.39/0.57	(define @t70 () (not @t69))
0.39/0.57	(define @t71 () (and @t67 @t55))
0.39/0.57	(define @t72 () (not @t55))
0.39/0.57	(define @t73 () (not @t54))
0.39/0.57	(define @t74 () (or @t71 @t69))
0.39/0.57	(define @t75 () (not @t57))
0.39/0.57	(define @t76 () (_ @t1 @t14))
0.39/0.57	(define @t77 () (and @t24 @t76))
0.39/0.57	(define @t78 () (not @t76))
0.39/0.57	(define @t79 () (and @t18 @t78))
0.39/0.57	(define @t80 () (or @t79 @t77))
0.39/0.57	(define @t81 () (and @t22 @t80))
0.39/0.57	(define @t82 () (not @t80))
0.39/0.57	(define @t83 () (and @t19 @t82))
0.39/0.57	(define @t84 () (or @t83 @t81))
0.39/0.57	(define @t85 () (lambda @t34 @t84))
0.39/0.57	(define @t86 () (not @t26))
0.39/0.57	(define @t87 () (and @t86 @t76))
0.39/0.57	(define @t88 () (and @t26 @t78))
0.39/0.57	(define @t89 () (or @t88 @t87))
0.39/0.57	(define @t90 () (lambda @t34 @t89))
0.39/0.57	(define @t91 () (= @t90 @t85))
0.39/0.57	(define @t92 () (lambda @t34 @t80))
0.39/0.57	(define @t93 () (_ @t92 @t14))
0.39/0.57	(define @t94 () (and @t22 @t93))
0.39/0.57	(define @t95 () (not @t93))
0.39/0.57	(define @t96 () (and @t19 @t95))
0.39/0.57	(define @t97 () (or @t96 @t94))
0.39/0.57	(define @t98 () (lambda @t34 @t97))
0.39/0.57	(define @t99 () (lambda (@list @t2 @t14) @t26))
0.39/0.57	(define @t100 () (@var "BOUND_VARIABLE_7533" (-> $$unsorted Bool)))
0.39/0.57	(define @t101 () (_ @t100 @t14))
0.39/0.57	(define @t102 () (not @t101))
0.39/0.57	(define @t103 () (lambda (@list @t100 @t14) (or (and @t18 @t102) (and @t24 @t101))))
0.39/0.57	(define @t104 () (@list @t2))
0.39/0.57	(define @t105 () (_ @t27 @t3))
0.39/0.57	(define @t106 () (@var "BOUND_VARIABLE_7502" (-> $$unsorted Bool)))
0.39/0.57	(define @t107 () (_ @t106 @t14))
0.39/0.57	(define @t108 () (not @t107))
0.39/0.57	(define @t109 () (@list @t106 @t14))
0.39/0.57	(define @t110 () (lambda @t34 @t26))
0.39/0.57	(define @t111 () (_ @t110 @t14))
0.39/0.57	(define @t112 () (not @t111))
0.39/0.57	(define @t113 () (and @t112 @t107))
0.39/0.57	(define @t114 () (and @t111 @t108))
0.39/0.57	(define @t115 () (or @t114 @t113))
0.39/0.57	(define @t116 () (lambda @t109 @t115))
0.39/0.57	(define @t117 () (= (_ (_ @t27 (_ @t105 @t2)) @t1) (_ @t105 (_ (_ @t27 @t2) @t1))))
0.39/0.57	(define @t118 () (forall @t6 @t117))
0.39/0.57	(define @t119 () (_ @t49 @t14))
0.39/0.57	(define @t120 () (_ @t51 @t14))
0.39/0.57	(define @t121 () (_ @t58 @t14))
0.39/0.57	(define @t122 () (not @t121))
0.39/0.57	(define @t123 () (not @t120))
0.39/0.57	(define @t124 () (or (and @t121 @t123) (and @t122 @t120)))
0.39/0.57	(define @t125 () (not @t119))
0.39/0.57	(define @t126 () (lambda @t34 (or (and @t124 @t125) (and (not @t124) @t119))))
0.39/0.57	(define @t127 () (@purify @t126))
0.39/0.57	(define @t128 () (or (and @t120 @t125) (and @t123 @t119)))
0.39/0.57	(define @t129 () (lambda @t34 (or (and @t121 (not @t128)) (and @t122 @t128))))
0.39/0.57	(define @t130 () (@purify @t129))
0.39/0.57	(define @t131 () (= @t130 @t127))
0.39/0.57	(define @t132 () (not @t131))
0.39/0.57	(define @t133 () (not @t48))
0.39/0.57	(define @t134 () (= @t126 @t129))
0.39/0.57	(define @t135 () (not @t134))
0.39/0.57	(define @t136 () (@list true))
0.39/0.57	(define @t137 () (and @t59 @t75))
0.39/0.57	(define @t138 () (or @t137 @t61))
0.39/0.57	(define @t139 () (= (_ @t126 @t39) @t74))
0.39/0.57	(define @t140 () (_ @t127 @t39))
0.39/0.57	(define @t141 () (= (_ @t129 @t39) @t138))
0.39/0.57	(define @t142 () (_ @t130 @t39))
0.39/0.57	(define @t143 () (= @t142 @t140))
0.39/0.57	(define @t144 () (not @t143))
0.39/0.57	(define @t145 () (or @t131 @t144))
0.39/0.57	(define @t146 () (= @t74 @t138))
0.39/0.57	(define @t147 () (@list @t137 @t138 @t146 @t57 @t74 @t54 @t71))
0.39/0.57	(define @t148 () (not @t71))
0.39/0.57	(define @t149 () (not @t137))
0.39/0.57	(define @t150 () (not @t63))
0.39/0.57	(define @t151 () (not @t66))
0.39/0.57	(define @t152 () (@list false))
0.39/0.57	(define @t153 () (@list @t52))
0.39/0.57	(define @t154 () (@list @t59))
0.39/0.57	(define @t155 () (not @t60))
0.39/0.57	(define @t156 () (@list @t50))
0.39/0.57	(define @t157 () (@list true true))
0.39/0.57	(assume @p1 @t8)
0.39/0.57	(assume @p2 true)
0.39/0.57	(step @p3 (= tptp.in @t11) :rule refl :args (@t11))
0.39/0.57	(step @p4 (= tptp.is_a @t11) :rule refl :args (@t11))
0.39/0.57	(step @p5 (= tptp.emptyset @t12) :rule refl :args (@t12))
0.39/0.57	(step @p6 (= tptp.unord_pair @t16) :rule refl :args (@t16))
0.39/0.57	(step @p7 (= tptp.singleton @t17) :rule refl :args (@t17))
0.39/0.57	(step @p8 (= tptp.union @t21) :rule refl :args (@t21))
0.39/0.57	(step @p9 (= tptp.excl_union @t27) :rule refl :args (@t27))
0.39/0.57	(step @p10 (= tptp.intersection @t29) :rule refl :args (@t29))
0.39/0.57	(step @p11 (= tptp.setminus @t30) :rule refl :args (@t30))
0.39/0.57	(step @p12 (= tptp.complement @t31) :rule refl :args (@t31))
0.39/0.57	(step @p13 (= tptp.disjoint @t33) :rule refl :args (@t33))
0.39/0.57	(step @p14 (= tptp.subset @t35) :rule refl :args (@t35))
0.39/0.57	(step @p15 (= tptp.meets @t37) :rule refl :args (@t37))
0.39/0.57	(step @p16 (= tptp.misses @t38) :rule refl :args (@t38))
0.39/0.57	(step @p17 :rule cnf_and_pos :args (@t61 0))
0.39/0.57	(step @p18 :rule reordering :premises (@p17) :args ((or @t60 @t62)))
0.39/0.57	(step @p19 :rule bool-double-not-elim :args (@t52))
0.39/0.57	(step @p20 :rule refl :args (@t60))
0.39/0.57	(step @p21 :rule refl :args (@t63))
0.39/0.57	(step @p22 :rule nary_cong :premises (@p21 @p20 @p19) :args ((or @t63 @t60 @t64)))
0.39/0.57	(step @p23 :rule cnf_and_neg :args (@t63))
0.39/0.57	(step @p24 :rule eq_resolve :premises (@p23 @p22))
0.39/0.57	(step @p25 :rule reordering :premises (@p24) :args ((or @t52 @t63 @t60)))
0.39/0.57	(step @p26 :rule cnf_and_pos :args (@t56 0))
0.39/0.57	(step @p27 :rule reordering :premises (@p26) :args ((or @t52 @t65)))
0.39/0.57	(step @p28 :rule cnf_or_neg :args (@t67 0))
0.39/0.57	(step @p29 :rule cnf_and_pos :args (@t69 0))
0.39/0.57	(step @p30 :rule reordering :premises (@p29) :args ((or @t68 @t70)))
0.39/0.57	(step @p31 :rule bool-double-not-elim :args (@t50))
0.39/0.57	(step @p32 :rule refl :args (@t68))
0.39/0.57	(step @p33 :rule refl :args (@t71))
0.39/0.57	(step @p34 :rule nary_cong :premises (@p33 @p32 @p31) :args ((or @t71 @t68 @t72)))
0.39/0.57	(step @p35 :rule cnf_and_neg :args (@t71))
0.39/0.57	(step @p36 :rule eq_resolve :premises (@p35 @p34))
0.39/0.57	(step @p37 :rule reordering :premises (@p36) :args ((or @t50 @t71 @t68)))
0.39/0.57	(step @p38 :rule cnf_and_pos :args (@t54 1))
0.39/0.57	(step @p39 :rule reordering :premises (@p38) :args ((or @t50 @t73)))
0.39/0.57	(step @p40 :rule cnf_or_neg :args (@t74 0))
0.39/0.57	(step @p41 :rule cnf_or_pos :args (@t57))
0.39/0.57	(step @p42 :rule reordering :premises (@p41) :args ((or @t56 @t54 @t75)))
0.39/0.57	(step @p43 :rule refl :args (@t40))
0.39/0.57	(step @p44 :rule refl :args (@t76))
0.39/0.57	(step @p45 :rule cong :premises (@p44 @p43) :args ((= @t76 @t40)))
0.39/0.57	(step @p46 :rule symm :premises (@p45))
0.39/0.57	(step @p47 :rule eq_resolve :premises (@p44 @p46))
0.39/0.57	(step @p48 :rule refl :args (@t41))
0.39/0.57	(step @p49 :rule refl :args (@t18))
0.39/0.57	(step @p50 :rule cong :premises (@p49 @p48) :args ((= @t18 @t41)))
0.39/0.57	(step @p51 :rule symm :premises (@p50))
0.39/0.57	(step @p52 :rule eq_resolve :premises (@p49 @p51))
0.39/0.57	(step @p53 :rule cong :premises (@p52) :args (@t24))
0.39/0.57	(step @p54 :rule nary_cong :premises (@p53 @p47) :args (@t77))
0.39/0.57	(step @p55 :rule cong :premises (@p47) :args (@t78))
0.39/0.57	(step @p56 :rule nary_cong :premises (@p52 @p55) :args (@t79))
0.39/0.57	(step @p57 :rule nary_cong :premises (@p56 @p54) :args (@t80))
0.39/0.57	(step @p58 :rule refl :args (@t45))
0.39/0.57	(step @p59 :rule refl :args (@t19))
0.39/0.57	(step @p60 :rule cong :premises (@p59 @p58) :args ((= @t19 @t45)))
0.39/0.57	(step @p61 :rule symm :premises (@p60))
0.39/0.57	(step @p62 :rule eq_resolve :premises (@p59 @p61))
0.39/0.57	(step @p63 :rule cong :premises (@p62) :args (@t22))
0.39/0.57	(step @p64 :rule nary_cong :premises (@p63 @p57) :args (@t81))
0.39/0.57	(step @p65 :rule cong :premises (@p57) :args (@t82))
0.39/0.57	(step @p66 :rule nary_cong :premises (@p62 @p65) :args (@t83))
0.39/0.57	(step @p67 :rule nary_cong :premises (@p66 @p64) :args (@t84))
0.39/0.57	(step @p68 :rule cong :premises (@p67) :args (@t85))
0.39/0.57	(step @p69 :rule nary_cong :premises (@p63 @p52) :args (@t23))
0.39/0.57	(step @p70 :rule nary_cong :premises (@p62 @p53) :args (@t25))
0.39/0.57	(step @p71 :rule nary_cong :premises (@p70 @p69) :args (@t26))
0.39/0.57	(step @p72 :rule cong :premises (@p71) :args (@t86))
0.39/0.57	(step @p73 :rule nary_cong :premises (@p72 @p47) :args (@t87))
0.39/0.57	(step @p74 :rule nary_cong :premises (@p71 @p55) :args (@t88))
0.39/0.57	(step @p75 :rule nary_cong :premises (@p74 @p73) :args (@t89))
0.39/0.57	(step @p76 :rule cong :premises (@p75) :args (@t90))
0.39/0.57	(step @p77 :rule cong :premises (@p76 @p68) :args (@t91))
0.39/0.57	(step @p78 :rule cong :premises (@p77) :args ((forall @t6 @t91)))
0.39/0.57	(step @p79 :rule beta-reduce :args ((= @t93 @t80)))
0.39/0.57	(step @p80 :rule refl :args (@t22))
0.39/0.57	(step @p81 :rule nary_cong :premises (@p80 @p79) :args (@t94))
0.39/0.57	(step @p82 :rule cong :premises (@p79) :args (@t95))
0.39/0.57	(step @p83 :rule refl :args (@t19))
0.39/0.57	(step @p84 :rule nary_cong :premises (@p83 @p82) :args (@t96))
0.39/0.57	(step @p85 :rule nary_cong :premises (@p84 @p81) :args (@t97))
0.39/0.57	(step @p86 :rule cong :premises (@p85) :args (@t98))
0.39/0.57	(step @p87 :rule beta-reduce :args ((= (_ @t99 @t92) @t98)))
0.39/0.57	(step @p88 :rule trans :premises (@p87 @p86))
0.39/0.57	(step @p89 :rule beta-reduce :args ((= (_ @t103 @t1) @t92)))
0.39/0.57	(step @p90 :rule refl :args (@t1))
0.39/0.57	(step @p91 :rule beta-reduce :args ((= (_ (lambda (@list @t3 @t100 @t14) (or (and @t19 @t102) (and @t22 @t101))) @t2) @t103)))
0.39/0.57	(step @p92 :rule refl :args (@t2))
0.39/0.57	(step @p93 :rule alpha_equiv :args (@t27 @t104 (@list @t100)))
0.39/0.57	(step @p94 :rule ho_cong :premises (@p93 @p92))
0.39/0.57	(step @p95 :rule trans :premises (@p94 @p91))
0.39/0.57	(step @p96 :rule ho_cong :premises (@p95 @p90))
0.39/0.57	(step @p97 :rule trans :premises (@p96 @p89))
0.39/0.57	(step @p98 :rule beta-reduce :args ((= @t105 @t99)))
0.39/0.57	(step @p99 :rule ho_cong :premises (@p98 @p97))
0.39/0.57	(step @p100 :rule trans :premises (@p99 @p88))
0.39/0.57	(step @p101 :rule beta-reduce :args ((= (_ (lambda @t109 (or (and @t26 @t108) (and @t86 @t107))) @t1) @t90)))
0.39/0.57	(step @p102 :rule refl :args (@t107))
0.39/0.57	(step @p103 :rule beta-reduce :args ((= @t111 @t26)))
0.39/0.57	(step @p104 :rule cong :premises (@p103) :args (@t112))
0.39/0.57	(step @p105 :rule nary_cong :premises (@p104 @p102) :args (@t113))
0.39/0.57	(step @p106 :rule refl :args (@t108))
0.39/0.57	(step @p107 :rule nary_cong :premises (@p103 @p106) :args (@t114))
0.39/0.57	(step @p108 :rule nary_cong :premises (@p107 @p105) :args (@t115))
0.39/0.57	(step @p109 :rule cong :premises (@p108) :args (@t116))
0.39/0.57	(step @p110 :rule beta-reduce :args ((= (_ (lambda (@list @t3 @t106 @t14) (or (and @t19 @t108) (and @t22 @t107))) @t110) @t116)))
0.39/0.57	(step @p111 :rule trans :premises (@p110 @p109))
0.39/0.57	(step @p112 :rule refl :args (@t110))
0.39/0.57	(step @p113 :rule alpha_equiv :args (@t27 @t104 (@list @t106)))
0.39/0.57	(step @p114 :rule ho_cong :premises (@p113 @p112))
0.39/0.57	(step @p115 :rule trans :premises (@p114 @p111))
0.39/0.57	(step @p116 :rule beta-reduce :args ((= (_ @t99 @t2) @t110)))
0.39/0.57	(step @p117 :rule refl :args (@t2))
0.39/0.57	(step @p118 :rule ho_cong :premises (@p98 @p117))
0.39/0.57	(step @p119 :rule trans :premises (@p118 @p116))
0.39/0.57	(step @p120 :rule refl :args (@t27))
0.39/0.57	(step @p121 :rule ho_cong :premises (@p120 @p119))
0.39/0.57	(step @p122 :rule trans :premises (@p121 @p115))
0.39/0.57	(step @p123 :rule ho_cong :premises (@p122 @p90))
0.39/0.57	(step @p124 :rule trans :premises (@p123 @p101))
0.39/0.57	(step @p125 :rule cong :premises (@p124 @p100) :args (@t117))
0.39/0.57	(step @p126 :rule cong :premises (@p125) :args (@t118))
0.39/0.57	(step @p127 :rule trans :premises (@p126 @p78))
0.39/0.57	(step @p128 :rule cong :premises (@p127) :args ((not @t118)))
0.39/0.57	(step @p129 :rule ho_cong :premises (@p9 @p117))
0.39/0.57	(step @p130 :rule ho_cong :premises (@p129 @p90))
0.39/0.57	(step @p131 :rule refl :args (@t3))
0.39/0.57	(step @p132 :rule ho_cong :premises (@p9 @p131))
0.39/0.57	(step @p133 :rule ho_cong :premises (@p132 @p130))
0.39/0.57	(step @p134 :rule ho_cong :premises (@p132 @p117))
0.39/0.57	(step @p135 :rule ho_cong :premises (@p9 @p134))
0.39/0.57	(step @p136 :rule ho_cong :premises (@p135 @p90))
0.39/0.57	(step @p137 :rule cong :premises (@p136 @p133) :args (@t5))
0.39/0.57	(step @p138 :rule cong :premises (@p137) :args (@t7))
0.39/0.57	(step @p139 :rule cong :premises (@p138) :args (@t8))
0.39/0.57	(step @p140 :rule trans :premises (@p139 @p128))
0.39/0.57	(step @p141 :rule eq_resolve :premises (@p1 @p140))
0.39/0.57	(step @p142 :rule refl :args (@t132))
0.39/0.57	(step @p143 :rule bool-double-not-elim :args (@t48))
0.39/0.57	(step @p144 :rule nary_cong :premises (@p143 @p142) :args ((or (not @t133) @t132)))
0.39/0.57	(step @p145 :rule eq-symm :args (@t127 @t130))
0.39/0.57	(step @p146 :rule eq-refl :args (@t129))
0.39/0.57	(step @p147 :rule skolem_intro :args (@t130))
0.39/0.57	(step @p148 :rule refl :args (@t129))
0.39/0.57	(step @p149 :rule cong :premises (@p148 @p147) :args ((= @t129 @t130)))
0.39/0.57	(step @p150 :rule trans :premises (@p149 @p146))
0.39/0.57	(step @p151 :rule true_elim :premises (@p150))
0.39/0.57	(step @p152 :rule eq-refl :args (@t126))
0.39/0.57	(step @p153 :rule skolem_intro :args (@t127))
0.39/0.57	(step @p154 :rule refl :args (@t126))
0.39/0.57	(step @p155 :rule cong :premises (@p154 @p153) :args ((= @t126 @t127)))
0.39/0.57	(step @p156 :rule trans :premises (@p155 @p152))
0.39/0.57	(step @p157 :rule true_elim :premises (@p156))
0.39/0.57	(step @p158 :rule cong :premises (@p157 @p151) :args (@t134))
0.39/0.57	(step @p159 :rule trans :premises (@p158 @p145))
0.39/0.57	(step @p160 :rule cong :premises (@p159) :args (@t135))
0.39/0.57	(step @p161 :rule refl :args (@t133))
0.39/0.57	(step @p162 :rule cong :premises (@p161 @p160) :args ((=> @t133 @t135)))
0.39/0.57	(assume-push @p312 @t133)
0.39/0.57	(step @p164 :rule skolemize :premises (@p141))
0.39/0.57	(step-pop @p312 :rule scope :premises (@p164))
0.39/0.57	(step @p165 :rule process_scope :premises (@p312) :args (@t135))
0.39/0.57	(step @p167 :rule eq_resolve :premises (@p165 @p162))
0.39/0.57	(step @p168 :rule implies_elim :premises (@p167))
0.39/0.57	(step @p169 :rule eq_resolve :premises (@p168 @p144))
0.39/0.57	(step @p170 :rule chain_resolution :premises (@p169 @p141) :args (@t136 (@list @t48)))
0.39/0.57	(step @p171 :rule eq-symm :args (@t138 @t74))
0.39/0.57	(step @p172 :rule eq-refl :args (@t74))
0.39/0.57	(step @p173 :rule refl :args (@t74))
0.39/0.57	(step @p174 :rule beta-reduce :args (@t139))
0.39/0.57	(step @p175 :rule cong :premises (@p174 @p173) :args (@t139))
0.39/0.57	(step @p176 :rule trans :premises (@p175 @p172))
0.39/0.57	(step @p177 :rule refl :args (@t39))
0.39/0.57	(step @p178 :rule ho_cong :premises (@p153 @p177))
0.39/0.57	(step @p179 :rule cong :premises (@p178 @p173) :args ((= @t140 @t74)))
0.39/0.57	(step @p180 :rule trans :premises (@p179 @p176))
0.39/0.57	(step @p181 :rule true_elim :premises (@p180))
0.39/0.57	(step @p182 :rule eq-refl :args (@t138))
0.39/0.57	(step @p183 :rule refl :args (@t138))
0.39/0.57	(step @p184 :rule beta-reduce :args (@t141))
0.39/0.57	(step @p185 :rule cong :premises (@p184 @p183) :args (@t141))
0.39/0.57	(step @p186 :rule trans :premises (@p185 @p182))
0.39/0.57	(step @p187 :rule ho_cong :premises (@p147 @p177))
0.39/0.57	(step @p188 :rule cong :premises (@p187 @p183) :args ((= @t142 @t138)))
0.39/0.57	(step @p189 :rule trans :premises (@p188 @p186))
0.39/0.57	(step @p190 :rule true_elim :premises (@p189))
0.39/0.57	(step @p191 :rule cong :premises (@p190 @p181) :args (@t143))
0.39/0.57	(step @p192 :rule trans :premises (@p191 @p171))
0.39/0.57	(step @p193 :rule cong :premises (@p192) :args (@t144))
0.39/0.57	(step @p194 :rule refl :args (@t131))
0.39/0.57	(step @p195 :rule nary_cong :premises (@p194 @p193) :args (@t145))
0.39/0.57	; WARNING: add trust step for TRUST
0.39/0.57	; trust TRUST THEORY_LEMMA
0.39/0.57	(step @p196 :rule trust :premises () :args (@t145))
0.39/0.57	(step @p197 :rule eq_resolve :premises (@p196 @p195))
0.39/0.57	(step @p198 :rule chain_resolution :premises (@p197 @p170) :args (@t136 (@list @t131)))
0.39/0.57	(step @p199 :rule cnf_equiv_neg2 :args (@t146))
0.39/0.57	(step @p200 :rule bool-double-not-elim :args (@t57))
0.39/0.57	(step @p201 :rule refl :args (@t137))
0.39/0.57	(step @p202 :rule nary_cong :premises (@p201 @p20 @p200) :args ((or @t137 @t60 (not @t75))))
0.39/0.57	(step @p203 :rule cnf_and_neg :args (@t137))
0.39/0.57	(step @p204 :rule eq_resolve :premises (@p203 @p202))
0.39/0.57	(step @p205 :rule reordering :premises (@p204) :args ((or @t60 @t57 @t137)))
0.39/0.57	(step @p206 :rule cnf_or_neg :args (@t138 0))
0.39/0.57	(step @p207 :rule chain_resolution :premises (@p206 @p205 @p199 @p198 @p42 @p40 @p39 @p37) :args ((@list false true true true false true false) @t147))
0.39/0.57	(step @p208 :rule factoring :premises (@p207))
0.39/0.57	(step @p209 :rule reordering :premises (@p208) :args ((or @t60 @t50 @t68 @t56)))
0.39/0.57	(step @p210 :rule cnf_and_pos :args (@t71 1))
0.39/0.57	(step @p211 :rule reordering :premises (@p210) :args ((or @t55 @t148)))
0.39/0.57	(step @p212 :rule refl :args (@t55))
0.39/0.57	(step @p213 :rule refl :args (@t54))
0.39/0.57	(step @p214 :rule nary_cong :premises (@p213 @p19 @p212) :args ((or @t54 @t64 @t55)))
0.39/0.57	(step @p215 :rule cnf_and_neg :args (@t54))
0.39/0.57	(step @p216 :rule eq_resolve :premises (@p215 @p214))
0.39/0.57	(step @p217 :rule reordering :premises (@p216) :args ((or @t52 @t55 @t54)))
0.39/0.57	(step @p218 :rule cnf_or_pos :args (@t74))
0.39/0.57	(step @p219 :rule reordering :premises (@p218) :args ((or @t71 @t69 (not @t74))))
0.39/0.57	(step @p220 :rule cnf_or_neg :args (@t57 1))
0.39/0.57	(step @p221 :rule cnf_equiv_neg1 :args (@t146))
0.39/0.57	(step @p222 :rule reordering :premises (@p221) :args ((or @t74 @t138 @t146)))
0.39/0.57	(step @p223 :rule cnf_and_pos :args (@t137 1))
0.39/0.57	(step @p224 :rule reordering :premises (@p223) :args ((or @t75 @t149)))
0.39/0.57	(step @p225 :rule cnf_or_pos :args (@t138))
0.39/0.57	(step @p226 :rule reordering :premises (@p225) :args ((or @t137 @t61 (not @t138))))
0.39/0.57	(step @p227 :rule chain_resolution :premises (@p226 @p224 @p222 @p198 @p220 @p219 @p217 @p211) :args ((@list true false true false true false true) @t147))
0.39/0.57	(step @p228 :rule factoring :premises (@p227))
0.39/0.57	(step @p229 :rule chain_resolution :premises (@p228 @p209 @p30) :args ((@list false true) (@list @t50 @t69)))
0.39/0.57	(step @p230 :rule factoring :premises (@p229))
0.39/0.57	(step @p231 :rule chain_resolution :premises (@p230 @p28 @p27 @p25 @p18) :args ((@list false true false true) (@list @t67 @t56 @t63 @t61)))
0.39/0.57	(step @p232 :rule factoring :premises (@p231))
0.39/0.57	(step @p233 :rule cnf_and_pos :args (@t54 0))
0.39/0.57	(step @p234 :rule reordering :premises (@p233) :args ((or @t53 @t73)))
0.39/0.57	(step @p235 :rule cnf_and_pos :args (@t63 1))
0.39/0.57	(step @p236 :rule reordering :premises (@p235) :args ((or @t53 @t150)))
0.39/0.57	(step @p237 :rule cnf_and_pos :args (@t66 0))
0.39/0.57	(step @p238 :rule reordering :premises (@p237) :args ((or @t60 @t151)))
0.39/0.57	(step @p239 :rule cnf_or_pos :args (@t67))
0.39/0.57	(step @p240 :rule reordering :premises (@p239) :args ((or @t63 @t66 @t68)))
0.39/0.57	(step @p241 :rule bool-double-not-elim :args (@t67))
0.39/0.57	(step @p242 :rule refl :args (@t69))
0.39/0.57	(step @p243 :rule nary_cong :premises (@p242 @p241 @p212) :args ((or @t69 (not @t68) @t55)))
0.39/0.57	(step @p244 :rule cnf_and_neg :args (@t69))
0.39/0.57	(step @p245 :rule eq_resolve :premises (@p244 @p243))
0.39/0.57	(step @p246 :rule reordering :premises (@p245) :args ((or @t67 @t55 @t69)))
0.39/0.57	(step @p247 :rule cnf_and_pos :args (@t56 1))
0.39/0.57	(step @p248 :rule reordering :premises (@p247) :args ((or @t55 @t65)))
0.39/0.57	(step @p249 :rule cnf_or_neg :args (@t74 1))
0.39/0.57	(step @p250 :rule chain_resolution :premises (@p206 @p205 @p199 @p198 @p42 @p249 @p248 @p246 @p240 @p238 @p236 @p234) :args ((@list false true true true false true false true true true true) (@list @t137 @t138 @t146 @t57 @t74 @t56 @t69 @t67 @t66 @t63 @t54)))
0.39/0.57	(step @p251 :rule factoring :premises (@p250))
0.39/0.57	(step @p252 :rule chain_resolution :premises (@p251 @p232) :args (@t152 @t153))
0.39/0.57	(step @p253 :rule factoring :premises (@p252))
0.39/0.57	(step @p254 :rule cnf_and_pos :args (@t71 0))
0.39/0.57	(step @p255 :rule reordering :premises (@p254) :args ((or @t67 @t148)))
0.39/0.57	(step @p256 :rule cnf_and_pos :args (@t69 1))
0.39/0.57	(step @p257 :rule reordering :premises (@p256) :args ((or @t50 @t70)))
0.39/0.57	(step @p258 :rule refl :args (@t53))
0.39/0.57	(step @p259 :rule refl :args (@t56))
0.39/0.57	(step @p260 :rule nary_cong :premises (@p259 @p258 @p31) :args ((or @t56 @t53 @t72)))
0.39/0.57	(step @p261 :rule cnf_and_neg :args (@t56))
0.39/0.57	(step @p262 :rule eq_resolve :premises (@p261 @p260))
0.39/0.57	(step @p263 :rule reordering :premises (@p262) :args ((or @t53 @t50 @t56)))
0.39/0.57	(step @p264 :rule cnf_or_neg :args (@t57 0))
0.39/0.57	(step @p265 :rule chain_resolution :premises (@p226 @p224 @p222 @p198 @p264 @p219 @p263 @p257 @p255 @p240 @p236 @p18 @p238) :args ((@list true false true false true false true true true true true true) (@list @t137 @t138 @t146 @t57 @t74 @t56 @t69 @t71 @t67 @t63 @t61 @t66)))
0.39/0.57	(step @p266 :rule factoring :premises (@p265))
0.39/0.57	(step @p267 :rule chain_resolution :premises (@p266 @p253 @p232) :args ((@list true false) (@list @t50 @t52)))
0.39/0.57	(step @p268 :rule factoring :premises (@p267))
0.39/0.57	(step @p269 :rule cnf_and_pos :args (@t137 0))
0.39/0.57	(step @p270 :rule reordering :premises (@p269) :args ((or @t59 @t149)))
0.39/0.57	(step @p271 :rule chain_resolution :premises (@p270 @p268) :args (@t136 @t154))
0.39/0.57	(step @p272 :rule bool-double-not-elim :args (@t59))
0.39/0.57	(step @p273 :rule refl :args (@t66))
0.39/0.57	(step @p274 :rule nary_cong :premises (@p273 @p272 @p258) :args ((or @t66 @t155 @t53)))
0.39/0.57	(step @p275 :rule cnf_and_neg :args (@t66))
0.39/0.57	(step @p276 :rule eq_resolve :premises (@p275 @p274))
0.39/0.57	(step @p277 :rule reordering :premises (@p276) :args ((or @t59 @t53 @t66)))
0.39/0.57	(step @p278 :rule cnf_or_neg :args (@t67 1))
0.39/0.57	(step @p279 :rule refl :args (@t75))
0.39/0.57	(step @p280 :rule refl :args (@t61))
0.39/0.57	(step @p281 :rule nary_cong :premises (@p280 @p272 @p279) :args ((or @t61 @t155 @t75)))
0.39/0.57	(step @p282 :rule cnf_and_neg :args (@t61))
0.39/0.57	(step @p283 :rule eq_resolve :premises (@p282 @p281))
0.39/0.57	(step @p284 :rule reordering :premises (@p283) :args ((or @t59 @t75 @t61)))
0.39/0.57	(step @p285 :rule cnf_or_neg :args (@t138 1))
0.39/0.57	(step @p286 :rule chain_resolution :premises (@p285 @p284 @p268 @p199 @p198 @p264 @p40 @p263 @p37 @p278 @p277 @p268) :args ((@list false true true true false false false false false false true) (@list @t61 @t59 @t138 @t146 @t57 @t74 @t56 @t71 @t67 @t66 @t59)))
0.39/0.57	(step @p287 :rule factoring :premises (@p286))
0.39/0.57	(step @p288 :rule cnf_and_pos :args (@t61 1))
0.39/0.57	(step @p289 :rule reordering :premises (@p288) :args ((or @t57 @t62)))
0.39/0.57	(step @p290 :rule chain_resolution :premises (@p226 @p271 @p289 @p222 @p198 @p42 @p219 @p248 @p211 @p30 @p278 @p234 @p277 @p268) :args ((@list true true false true true true true true true false true false true) (@list @t137 @t61 @t138 @t146 @t57 @t74 @t56 @t71 @t69 @t67 @t54 @t66 @t59)))
0.39/0.57	(step @p291 :rule factoring :premises (@p290))
0.39/0.57	(step @p292 :rule chain_resolution :premises (@p291 @p287) :args (@t152 @t156))
0.39/0.57	(step @p293 :rule factoring :premises (@p292))
0.39/0.57	(step @p294 :rule cnf_and_pos :args (@t66 1))
0.39/0.57	(step @p295 :rule reordering :premises (@p294) :args ((or @t52 @t151)))
0.39/0.57	(step @p296 :rule chain_resolution :premises (@p295 @p293) :args (@t136 @t153))
0.39/0.57	(step @p297 :rule cnf_and_pos :args (@t63 0))
0.39/0.57	(step @p298 :rule reordering :premises (@p297) :args ((or @t59 @t150)))
0.39/0.57	(step @p299 :rule chain_resolution :premises (@p298 @p268) :args (@t136 @t154))
0.39/0.57	(step @p300 :rule chain_resolution :premises (@p240 @p299 @p296) :args (@t157 (@list @t63 @t66)))
0.39/0.57	(step @p301 :rule chain_resolution :premises (@p285 @p284 @p268 @p199 @p198 @p220 @p249 @p217 @p293 @p246 @p300) :args ((@list false true true true false false false true false true) (@list @t61 @t59 @t138 @t146 @t57 @t74 @t54 @t52 @t69 @t67)))
0.39/0.57	(step @p302 :rule factoring :premises (@p301))
0.39/0.57	(step @p303 :rule chain_resolution :premises (@p257 @p302) :args (@t136 @t156))
0.39/0.57	(step @p304 :rule chain_resolution :premises (@p255 @p300) :args (@t136 (@list @t67)))
0.39/0.57	(step @p305 :rule chain_resolution :premises (@p219 @p304 @p303) :args (@t157 (@list @t71 @t69)))
0.39/0.57	(step @p306 :rule chain_resolution :premises (@p222 @p305 @p198) :args (@t157 (@list @t74 @t146)))
0.39/0.57	(step @p307 :rule chain_resolution :premises (@p39 @p302) :args (@t136 @t156))
0.39/0.57	(step @p308 :rule chain_resolution :premises (@p27 @p293) :args (@t136 @t153))
0.39/0.57	(step @p309 :rule chain_resolution :premises (@p42 @p308 @p307) :args (@t157 (@list @t56 @t54)))
0.39/0.57	(step @p310 :rule chain_resolution :premises (@p289 @p309) :args (@t136 (@list @t57)))
0.39/0.57	(step @p311 false :rule chain_resolution :premises (@p226 @p310 @p306 @p271) :args ((@list true false true) (@list @t61 @t138 @t137)))
0.39/0.57	)
0.39/0.57	% SZS output end Proof
0.39/0.57	% cvc5 exiting
0.39/0.58	EOF