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cvc5---1.3.4.THM-Prf.s

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%------------------------------------------------------------------------------
% File     : cvc5---1.3.4
% Problem  : SET623^3 : TPTP v9.2.1. Released v3.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM

% Computer : n001.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 08:48:16 AM UTC 2026

% Result   : Theorem 0.39s 0.58s
% Output   : Proof 0.39s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SET623^3 : TPTP v9.2.1. Released v3.6.0.
% 0.13/0.13  % Command  : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/0.35  % Computer : n001.cluster.edu
% 0.16/0.35  % Model    : x86_64 x86_64
% 0.16/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35  % Memory   : 8042.1875MB
% 0.16/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.35  % CPULimit : 300
% 0.16/0.35  % WCLimit  : 300
% 0.16/0.35  % DateTime : Tue Jun  2 16:05:50 EDT 2026
% 0.16/0.35  % CPUTime  : 
% 0.28/0.50  %----Proving TH0
% 0.39/0.58  --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s...
% 0.39/0.58  % SZS status Theorem
% 0.39/0.58  % SZS output start Proof
% 0.39/0.58  (
% 0.39/0.58  (declare-sort $$unsorted 0)
% 0.39/0.58  (define tptp.in () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "M" (-> $$unsorted Bool)))) (lambda (@list _let_1 _let_2) (_ _let_2 _let_1)))))
% 0.39/0.58  (define tptp.is_a () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "M" (-> $$unsorted Bool)))) (lambda (@list _let_1 _let_2) (_ _let_2 _let_1)))))
% 0.39/0.58  (define tptp.emptyset () (lambda (@list (@var "X" $$unsorted)) false))
% 0.39/0.58  (define tptp.unord_pair () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "U" $$unsorted))) (let ((_let_3 (@var "X" $$unsorted))) (lambda (@list _let_3 _let_1 _let_2) (or (= _let_2 _let_3) (= _let_2 _let_1)))))))
% 0.39/0.58  (define tptp.singleton () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "U" $$unsorted))) (lambda (@list _let_1 _let_2) (= _let_2 _let_1)))))
% 0.39/0.58  (define tptp.union () (let ((_let_1 (@var "U" $$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)))))))
% 0.39/0.58  (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" (-> $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_1))) (lambda (@list _let_4 _let_2 _let_1) (or (and _let_5 (not _let_3)) (and (not _let_5) _let_3)))))))))
% 0.39/0.58  (define tptp.intersection () (let ((_let_1 (@var "U" $$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)))))))
% 0.39/0.58  (define tptp.setminus () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (and (_ _let_3 _let_1) (not (_ _let_2 _let_1))))))))
% 0.39/0.58  (define tptp.complement () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (not (_ _let_2 _let_1))))))
% 0.39/0.58  (define tptp.disjoint () (let ((_let_1 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_2 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (= (_ (_ tptp.intersection _let_2) _let_1) tptp.emptyset)))))
% 0.39/0.58  (define tptp.subset () (let ((_let_1 (@var "U" $$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))))))))
% 0.39/0.58  (define tptp.meets () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2) (exists (@list _let_1) (and (_ _let_3 _let_1) (_ _let_2 _let_1))))))))
% 0.39/0.58  (define tptp.misses () (let ((_let_1 (@var "U" $$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)))))))))
% 0.39/0.58  (define @t1 () (@var "Z" (-> $$unsorted Bool)))
% 0.39/0.58  (define @t2 () (@var "Y" (-> $$unsorted Bool)))
% 0.39/0.58  (define @t3 () (@var "X" (-> $$unsorted Bool)))
% 0.39/0.58  (define @t4 () (_ tptp.excl_union @t3))
% 0.39/0.58  (define @t5 () (= (_ (_ tptp.excl_union (_ @t4 @t2)) @t1) (_ @t4 (_ (_ tptp.excl_union @t2) @t1))))
% 0.39/0.58  (define @t6 () (@list @t3 @t2 @t1))
% 0.39/0.58  (define @t7 () (forall @t6 @t5))
% 0.39/0.58  (define @t8 () (not @t7))
% 0.39/0.58  (define @t9 () (@var "X" $$unsorted))
% 0.39/0.58  (define @t10 () (@var "M" (-> $$unsorted Bool)))
% 0.39/0.58  (define @t11 () (lambda (@list @t9 @t10) (_ @t10 @t9)))
% 0.39/0.58  (define @t12 () (lambda (@list @t9) false))
% 0.39/0.58  (define @t13 () (@var "Y" $$unsorted))
% 0.39/0.58  (define @t14 () (@var "U" $$unsorted))
% 0.39/0.58  (define @t15 () (= @t14 @t9))
% 0.39/0.58  (define @t16 () (lambda (@list @t9 @t13 @t14) (or @t15 (= @t14 @t13))))
% 0.39/0.58  (define @t17 () (lambda (@list @t9 @t14) @t15))
% 0.39/0.58  (define @t18 () (_ @t2 @t14))
% 0.39/0.58  (define @t19 () (_ @t3 @t14))
% 0.39/0.58  (define @t20 () (@list @t3 @t2 @t14))
% 0.39/0.58  (define @t21 () (lambda @t20 (or @t19 @t18)))
% 0.39/0.58  (define @t22 () (not @t19))
% 0.39/0.58  (define @t23 () (and @t22 @t18))
% 0.39/0.58  (define @t24 () (not @t18))
% 0.39/0.58  (define @t25 () (and @t19 @t24))
% 0.39/0.58  (define @t26 () (or @t25 @t23))
% 0.39/0.58  (define @t27 () (lambda @t20 @t26))
% 0.39/0.58  (define @t28 () (and @t19 @t18))
% 0.39/0.58  (define @t29 () (lambda @t20 @t28))
% 0.39/0.58  (define @t30 () (lambda @t20 @t25))
% 0.39/0.58  (define @t31 () (lambda (@list @t3 @t14) @t22))
% 0.39/0.58  (define @t32 () (@list @t3 @t2))
% 0.39/0.58  (define @t33 () (lambda @t32 (= (_ (_ tptp.intersection @t3) @t2) tptp.emptyset)))
% 0.39/0.58  (define @t34 () (@list @t14))
% 0.39/0.58  (define @t35 () (lambda @t32 (forall @t34 (=> @t19 @t18))))
% 0.39/0.58  (define @t36 () (exists @t34 @t28))
% 0.39/0.58  (define @t37 () (lambda @t32 @t36))
% 0.39/0.58  (define @t38 () (lambda @t32 (not @t36)))
% 0.39/0.58  (define @t39 () (@const 0 $$unsorted))
% 0.39/0.58  (define @t40 () (_ @t1 @t14))
% 0.39/0.58  (define @t41 () (_ @t2 @t14))
% 0.39/0.58  (define @t42 () (not @t41))
% 0.39/0.58  (define @t43 () (not @t40))
% 0.39/0.58  (define @t44 () (or (and @t41 @t43) (and @t42 @t40)))
% 0.39/0.58  (define @t45 () (_ @t3 @t14))
% 0.39/0.58  (define @t46 () (not @t45))
% 0.39/0.58  (define @t47 () (or (and @t45 @t42) (and @t46 @t41)))
% 0.39/0.58  (define @t48 () (forall @t6 (= (lambda @t34 (or (and @t47 @t43) (and (not @t47) @t40))) (lambda @t34 (or (and @t45 (not @t44)) (and @t46 @t44))))))
% 0.39/0.58  (define @t49 () (@quantifiers_skolemize @t48 1))
% 0.39/0.58  (define @t50 () (_ @t49 @t39))
% 0.39/0.58  (define @t51 () (@quantifiers_skolemize @t48 0))
% 0.39/0.58  (define @t52 () (_ @t51 @t39))
% 0.39/0.58  (define @t53 () (not @t52))
% 0.39/0.58  (define @t54 () (and @t53 @t50))
% 0.39/0.58  (define @t55 () (not @t54))
% 0.39/0.58  (define @t56 () (@quantifiers_skolemize @t48 2))
% 0.39/0.58  (define @t57 () (_ @t56 @t39))
% 0.39/0.58  (define @t58 () (not @t50))
% 0.39/0.58  (define @t59 () (and @t58 @t57))
% 0.39/0.58  (define @t60 () (not @t57))
% 0.39/0.58  (define @t61 () (and @t50 @t60))
% 0.39/0.58  (define @t62 () (or @t61 @t59))
% 0.39/0.58  (define @t63 () (and @t53 @t62))
% 0.39/0.58  (define @t64 () (not @t63))
% 0.39/0.58  (define @t65 () (and @t52 @t58))
% 0.39/0.58  (define @t66 () (not @t58))
% 0.39/0.58  (define @t67 () (not @t61))
% 0.39/0.58  (define @t68 () (or @t65 @t54))
% 0.39/0.58  (define @t69 () (not @t68))
% 0.39/0.58  (define @t70 () (and @t69 @t57))
% 0.39/0.58  (define @t71 () (not @t70))
% 0.39/0.58  (define @t72 () (and @t68 @t60))
% 0.39/0.58  (define @t73 () (not @t60))
% 0.39/0.58  (define @t74 () (not @t59))
% 0.39/0.58  (define @t75 () (or @t72 @t70))
% 0.39/0.58  (define @t76 () (not @t62))
% 0.39/0.58  (define @t77 () (_ @t1 @t14))
% 0.39/0.58  (define @t78 () (and @t24 @t77))
% 0.39/0.58  (define @t79 () (not @t77))
% 0.39/0.58  (define @t80 () (and @t18 @t79))
% 0.39/0.58  (define @t81 () (or @t80 @t78))
% 0.39/0.58  (define @t82 () (and @t22 @t81))
% 0.39/0.58  (define @t83 () (not @t81))
% 0.39/0.58  (define @t84 () (and @t19 @t83))
% 0.39/0.58  (define @t85 () (or @t84 @t82))
% 0.39/0.58  (define @t86 () (lambda @t34 @t85))
% 0.39/0.58  (define @t87 () (not @t26))
% 0.39/0.58  (define @t88 () (and @t87 @t77))
% 0.39/0.58  (define @t89 () (and @t26 @t79))
% 0.39/0.58  (define @t90 () (or @t89 @t88))
% 0.39/0.58  (define @t91 () (lambda @t34 @t90))
% 0.39/0.58  (define @t92 () (= @t91 @t86))
% 0.39/0.58  (define @t93 () (lambda @t34 @t81))
% 0.39/0.58  (define @t94 () (_ @t93 @t14))
% 0.39/0.58  (define @t95 () (and @t22 @t94))
% 0.39/0.58  (define @t96 () (not @t94))
% 0.39/0.58  (define @t97 () (and @t19 @t96))
% 0.39/0.58  (define @t98 () (or @t97 @t95))
% 0.39/0.58  (define @t99 () (lambda @t34 @t98))
% 0.39/0.58  (define @t100 () (lambda (@list @t2 @t14) @t26))
% 0.39/0.58  (define @t101 () (@var "BOUND_VARIABLE_7671" (-> $$unsorted Bool)))
% 0.39/0.58  (define @t102 () (_ @t101 @t14))
% 0.39/0.58  (define @t103 () (not @t102))
% 0.39/0.58  (define @t104 () (lambda (@list @t101 @t14) (or (and @t18 @t103) (and @t24 @t102))))
% 0.39/0.58  (define @t105 () (@list @t2))
% 0.39/0.58  (define @t106 () (_ @t27 @t3))
% 0.39/0.58  (define @t107 () (@var "BOUND_VARIABLE_7640" (-> $$unsorted Bool)))
% 0.39/0.58  (define @t108 () (_ @t107 @t14))
% 0.39/0.58  (define @t109 () (not @t108))
% 0.39/0.58  (define @t110 () (@list @t107 @t14))
% 0.39/0.58  (define @t111 () (lambda @t34 @t26))
% 0.39/0.58  (define @t112 () (_ @t111 @t14))
% 0.39/0.58  (define @t113 () (not @t112))
% 0.39/0.58  (define @t114 () (and @t113 @t108))
% 0.39/0.58  (define @t115 () (and @t112 @t109))
% 0.39/0.58  (define @t116 () (or @t115 @t114))
% 0.39/0.58  (define @t117 () (lambda @t110 @t116))
% 0.39/0.58  (define @t118 () (= (_ (_ @t27 (_ @t106 @t2)) @t1) (_ @t106 (_ (_ @t27 @t2) @t1))))
% 0.39/0.58  (define @t119 () (forall @t6 @t118))
% 0.39/0.58  (define @t120 () (_ @t56 @t14))
% 0.39/0.58  (define @t121 () (_ @t49 @t14))
% 0.39/0.58  (define @t122 () (_ @t51 @t14))
% 0.39/0.58  (define @t123 () (not @t122))
% 0.39/0.58  (define @t124 () (not @t121))
% 0.39/0.58  (define @t125 () (or (and @t122 @t124) (and @t123 @t121)))
% 0.39/0.58  (define @t126 () (not @t120))
% 0.39/0.58  (define @t127 () (lambda @t34 (or (and @t125 @t126) (and (not @t125) @t120))))
% 0.39/0.58  (define @t128 () (@purify @t127))
% 0.39/0.58  (define @t129 () (or (and @t121 @t126) (and @t124 @t120)))
% 0.39/0.58  (define @t130 () (lambda @t34 (or (and @t122 (not @t129)) (and @t123 @t129))))
% 0.39/0.58  (define @t131 () (@purify @t130))
% 0.39/0.58  (define @t132 () (= @t131 @t128))
% 0.39/0.58  (define @t133 () (not @t132))
% 0.39/0.58  (define @t134 () (not @t48))
% 0.39/0.58  (define @t135 () (= @t127 @t130))
% 0.39/0.58  (define @t136 () (not @t135))
% 0.39/0.58  (define @t137 () (@list true))
% 0.39/0.58  (define @t138 () (and @t52 @t76))
% 0.39/0.58  (define @t139 () (or @t138 @t63))
% 0.39/0.58  (define @t140 () (= (_ @t127 @t39) @t75))
% 0.39/0.58  (define @t141 () (_ @t128 @t39))
% 0.39/0.58  (define @t142 () (= (_ @t130 @t39) @t139))
% 0.39/0.58  (define @t143 () (_ @t131 @t39))
% 0.39/0.58  (define @t144 () (= @t143 @t141))
% 0.39/0.58  (define @t145 () (not @t144))
% 0.39/0.58  (define @t146 () (or @t132 @t145))
% 0.39/0.58  (define @t147 () (= @t75 @t139))
% 0.39/0.58  (define @t148 () (not @t72))
% 0.39/0.58  (define @t149 () (not @t75))
% 0.39/0.58  (define @t150 () (not @t138))
% 0.39/0.58  (define @t151 () (not @t65))
% 0.39/0.58  (define @t152 () (@list @t52))
% 0.39/0.58  (define @t153 () (not @t53))
% 0.39/0.58  (define @t154 () (@list @t50))
% 0.39/0.58  (define @t155 () (@list true true))
% 0.39/0.58  (define @t156 () (@list @t57))
% 0.39/0.58  (assume @p1 @t8)
% 0.39/0.58  (assume @p2 true)
% 0.39/0.58  (step @p3 (= tptp.in @t11) :rule refl :args (@t11))
% 0.39/0.58  (step @p4 (= tptp.is_a @t11) :rule refl :args (@t11))
% 0.39/0.58  (step @p5 (= tptp.emptyset @t12) :rule refl :args (@t12))
% 0.39/0.58  (step @p6 (= tptp.unord_pair @t16) :rule refl :args (@t16))
% 0.39/0.58  (step @p7 (= tptp.singleton @t17) :rule refl :args (@t17))
% 0.39/0.58  (step @p8 (= tptp.union @t21) :rule refl :args (@t21))
% 0.39/0.58  (step @p9 (= tptp.excl_union @t27) :rule refl :args (@t27))
% 0.39/0.58  (step @p10 (= tptp.intersection @t29) :rule refl :args (@t29))
% 0.39/0.58  (step @p11 (= tptp.setminus @t30) :rule refl :args (@t30))
% 0.39/0.58  (step @p12 (= tptp.complement @t31) :rule refl :args (@t31))
% 0.39/0.58  (step @p13 (= tptp.disjoint @t33) :rule refl :args (@t33))
% 0.39/0.58  (step @p14 (= tptp.subset @t35) :rule refl :args (@t35))
% 0.39/0.58  (step @p15 (= tptp.meets @t37) :rule refl :args (@t37))
% 0.39/0.58  (step @p16 (= tptp.misses @t38) :rule refl :args (@t38))
% 0.39/0.58  (step @p17 :rule cnf_and_pos :args (@t54 0))
% 0.39/0.58  (step @p18 :rule reordering :premises (@p17) :args ((or @t53 @t55)))
% 0.39/0.58  (step @p19 :rule cnf_and_pos :args (@t63 0))
% 0.39/0.58  (step @p20 :rule reordering :premises (@p19) :args ((or @t53 @t64)))
% 0.39/0.58  (step @p21 :rule bool-double-not-elim :args (@t50))
% 0.39/0.58  (step @p22 :rule refl :args (@t53))
% 0.39/0.58  (step @p23 :rule refl :args (@t65))
% 0.39/0.58  (step @p24 :rule nary_cong :premises (@p23 @p22 @p21) :args ((or @t65 @t53 @t66)))
% 0.39/0.58  (step @p25 :rule cnf_and_neg :args (@t65))
% 0.39/0.58  (step @p26 :rule eq_resolve :premises (@p25 @p24))
% 0.39/0.58  (step @p27 :rule reordering :premises (@p26) :args ((or @t50 @t65 @t53)))
% 0.39/0.58  (step @p28 :rule cnf_and_pos :args (@t61 0))
% 0.39/0.58  (step @p29 :rule reordering :premises (@p28) :args ((or @t50 @t67)))
% 0.39/0.58  (step @p30 :rule cnf_or_neg :args (@t68 0))
% 0.39/0.58  (step @p31 :rule cnf_and_pos :args (@t70 0))
% 0.39/0.58  (step @p32 :rule reordering :premises (@p31) :args ((or @t69 @t71)))
% 0.39/0.58  (step @p33 :rule bool-double-not-elim :args (@t57))
% 0.39/0.58  (step @p34 :rule refl :args (@t69))
% 0.39/0.58  (step @p35 :rule refl :args (@t72))
% 0.39/0.58  (step @p36 :rule nary_cong :premises (@p35 @p34 @p33) :args ((or @t72 @t69 @t73)))
% 0.39/0.58  (step @p37 :rule cnf_and_neg :args (@t72))
% 0.39/0.58  (step @p38 :rule eq_resolve :premises (@p37 @p36))
% 0.39/0.58  (step @p39 :rule reordering :premises (@p38) :args ((or @t57 @t72 @t69)))
% 0.39/0.58  (step @p40 :rule cnf_and_pos :args (@t59 1))
% 0.39/0.58  (step @p41 :rule reordering :premises (@p40) :args ((or @t57 @t74)))
% 0.39/0.58  (step @p42 :rule cnf_or_neg :args (@t75 0))
% 0.39/0.58  (step @p43 :rule cnf_or_pos :args (@t62))
% 0.39/0.58  (step @p44 :rule reordering :premises (@p43) :args ((or @t61 @t59 @t76)))
% 0.39/0.58  (step @p45 :rule refl :args (@t40))
% 0.39/0.58  (step @p46 :rule refl :args (@t77))
% 0.39/0.58  (step @p47 :rule cong :premises (@p46 @p45) :args ((= @t77 @t40)))
% 0.39/0.58  (step @p48 :rule symm :premises (@p47))
% 0.39/0.58  (step @p49 :rule eq_resolve :premises (@p46 @p48))
% 0.39/0.58  (step @p50 :rule refl :args (@t41))
% 0.39/0.58  (step @p51 :rule refl :args (@t18))
% 0.39/0.58  (step @p52 :rule cong :premises (@p51 @p50) :args ((= @t18 @t41)))
% 0.39/0.58  (step @p53 :rule symm :premises (@p52))
% 0.39/0.58  (step @p54 :rule eq_resolve :premises (@p51 @p53))
% 0.39/0.58  (step @p55 :rule cong :premises (@p54) :args (@t24))
% 0.39/0.58  (step @p56 :rule nary_cong :premises (@p55 @p49) :args (@t78))
% 0.39/0.58  (step @p57 :rule cong :premises (@p49) :args (@t79))
% 0.39/0.58  (step @p58 :rule nary_cong :premises (@p54 @p57) :args (@t80))
% 0.39/0.58  (step @p59 :rule nary_cong :premises (@p58 @p56) :args (@t81))
% 0.39/0.58  (step @p60 :rule refl :args (@t45))
% 0.39/0.58  (step @p61 :rule refl :args (@t19))
% 0.39/0.58  (step @p62 :rule cong :premises (@p61 @p60) :args ((= @t19 @t45)))
% 0.39/0.58  (step @p63 :rule symm :premises (@p62))
% 0.39/0.58  (step @p64 :rule eq_resolve :premises (@p61 @p63))
% 0.39/0.58  (step @p65 :rule cong :premises (@p64) :args (@t22))
% 0.39/0.58  (step @p66 :rule nary_cong :premises (@p65 @p59) :args (@t82))
% 0.39/0.58  (step @p67 :rule cong :premises (@p59) :args (@t83))
% 0.39/0.58  (step @p68 :rule nary_cong :premises (@p64 @p67) :args (@t84))
% 0.39/0.58  (step @p69 :rule nary_cong :premises (@p68 @p66) :args (@t85))
% 0.39/0.58  (step @p70 :rule cong :premises (@p69) :args (@t86))
% 0.39/0.58  (step @p71 :rule nary_cong :premises (@p65 @p54) :args (@t23))
% 0.39/0.58  (step @p72 :rule nary_cong :premises (@p64 @p55) :args (@t25))
% 0.39/0.58  (step @p73 :rule nary_cong :premises (@p72 @p71) :args (@t26))
% 0.39/0.58  (step @p74 :rule cong :premises (@p73) :args (@t87))
% 0.39/0.58  (step @p75 :rule nary_cong :premises (@p74 @p49) :args (@t88))
% 0.39/0.58  (step @p76 :rule nary_cong :premises (@p73 @p57) :args (@t89))
% 0.39/0.58  (step @p77 :rule nary_cong :premises (@p76 @p75) :args (@t90))
% 0.39/0.58  (step @p78 :rule cong :premises (@p77) :args (@t91))
% 0.39/0.58  (step @p79 :rule cong :premises (@p78 @p70) :args (@t92))
% 0.39/0.58  (step @p80 :rule cong :premises (@p79) :args ((forall @t6 @t92)))
% 0.39/0.58  (step @p81 :rule beta-reduce :args ((= @t94 @t81)))
% 0.39/0.58  (step @p82 :rule refl :args (@t22))
% 0.39/0.58  (step @p83 :rule nary_cong :premises (@p82 @p81) :args (@t95))
% 0.39/0.58  (step @p84 :rule cong :premises (@p81) :args (@t96))
% 0.39/0.58  (step @p85 :rule refl :args (@t19))
% 0.39/0.58  (step @p86 :rule nary_cong :premises (@p85 @p84) :args (@t97))
% 0.39/0.58  (step @p87 :rule nary_cong :premises (@p86 @p83) :args (@t98))
% 0.39/0.58  (step @p88 :rule cong :premises (@p87) :args (@t99))
% 0.39/0.58  (step @p89 :rule beta-reduce :args ((= (_ @t100 @t93) @t99)))
% 0.39/0.58  (step @p90 :rule trans :premises (@p89 @p88))
% 0.39/0.58  (step @p91 :rule beta-reduce :args ((= (_ @t104 @t1) @t93)))
% 0.39/0.58  (step @p92 :rule refl :args (@t1))
% 0.39/0.58  (step @p93 :rule beta-reduce :args ((= (_ (lambda (@list @t3 @t101 @t14) (or (and @t19 @t103) (and @t22 @t102))) @t2) @t104)))
% 0.39/0.58  (step @p94 :rule refl :args (@t2))
% 0.39/0.58  (step @p95 :rule alpha_equiv :args (@t27 @t105 (@list @t101)))
% 0.39/0.58  (step @p96 :rule ho_cong :premises (@p95 @p94))
% 0.39/0.58  (step @p97 :rule trans :premises (@p96 @p93))
% 0.39/0.58  (step @p98 :rule ho_cong :premises (@p97 @p92))
% 0.39/0.58  (step @p99 :rule trans :premises (@p98 @p91))
% 0.39/0.58  (step @p100 :rule beta-reduce :args ((= @t106 @t100)))
% 0.39/0.58  (step @p101 :rule ho_cong :premises (@p100 @p99))
% 0.39/0.58  (step @p102 :rule trans :premises (@p101 @p90))
% 0.39/0.58  (step @p103 :rule beta-reduce :args ((= (_ (lambda @t110 (or (and @t26 @t109) (and @t87 @t108))) @t1) @t91)))
% 0.39/0.58  (step @p104 :rule refl :args (@t108))
% 0.39/0.58  (step @p105 :rule beta-reduce :args ((= @t112 @t26)))
% 0.39/0.58  (step @p106 :rule cong :premises (@p105) :args (@t113))
% 0.39/0.58  (step @p107 :rule nary_cong :premises (@p106 @p104) :args (@t114))
% 0.39/0.58  (step @p108 :rule refl :args (@t109))
% 0.39/0.58  (step @p109 :rule nary_cong :premises (@p105 @p108) :args (@t115))
% 0.39/0.58  (step @p110 :rule nary_cong :premises (@p109 @p107) :args (@t116))
% 0.39/0.58  (step @p111 :rule cong :premises (@p110) :args (@t117))
% 0.39/0.58  (step @p112 :rule beta-reduce :args ((= (_ (lambda (@list @t3 @t107 @t14) (or (and @t19 @t109) (and @t22 @t108))) @t111) @t117)))
% 0.39/0.58  (step @p113 :rule trans :premises (@p112 @p111))
% 0.39/0.58  (step @p114 :rule refl :args (@t111))
% 0.39/0.58  (step @p115 :rule alpha_equiv :args (@t27 @t105 (@list @t107)))
% 0.39/0.58  (step @p116 :rule ho_cong :premises (@p115 @p114))
% 0.39/0.58  (step @p117 :rule trans :premises (@p116 @p113))
% 0.39/0.58  (step @p118 :rule beta-reduce :args ((= (_ @t100 @t2) @t111)))
% 0.39/0.58  (step @p119 :rule refl :args (@t2))
% 0.39/0.58  (step @p120 :rule ho_cong :premises (@p100 @p119))
% 0.39/0.58  (step @p121 :rule trans :premises (@p120 @p118))
% 0.39/0.58  (step @p122 :rule refl :args (@t27))
% 0.39/0.58  (step @p123 :rule ho_cong :premises (@p122 @p121))
% 0.39/0.58  (step @p124 :rule trans :premises (@p123 @p117))
% 0.39/0.58  (step @p125 :rule ho_cong :premises (@p124 @p92))
% 0.39/0.58  (step @p126 :rule trans :premises (@p125 @p103))
% 0.39/0.58  (step @p127 :rule cong :premises (@p126 @p102) :args (@t118))
% 0.39/0.58  (step @p128 :rule cong :premises (@p127) :args (@t119))
% 0.39/0.58  (step @p129 :rule trans :premises (@p128 @p80))
% 0.39/0.58  (step @p130 :rule cong :premises (@p129) :args ((not @t119)))
% 0.39/0.58  (step @p131 :rule ho_cong :premises (@p9 @p119))
% 0.39/0.58  (step @p132 :rule ho_cong :premises (@p131 @p92))
% 0.39/0.58  (step @p133 :rule refl :args (@t3))
% 0.39/0.58  (step @p134 :rule ho_cong :premises (@p9 @p133))
% 0.39/0.59  (step @p135 :rule ho_cong :premises (@p134 @p132))
% 0.39/0.59  (step @p136 :rule ho_cong :premises (@p134 @p119))
% 0.39/0.59  (step @p137 :rule ho_cong :premises (@p9 @p136))
% 0.39/0.59  (step @p138 :rule ho_cong :premises (@p137 @p92))
% 0.39/0.59  (step @p139 :rule cong :premises (@p138 @p135) :args (@t5))
% 0.39/0.59  (step @p140 :rule cong :premises (@p139) :args (@t7))
% 0.39/0.59  (step @p141 :rule cong :premises (@p140) :args (@t8))
% 0.39/0.59  (step @p142 :rule trans :premises (@p141 @p130))
% 0.39/0.59  (step @p143 :rule eq_resolve :premises (@p1 @p142))
% 0.39/0.59  (step @p144 :rule refl :args (@t133))
% 0.39/0.59  (step @p145 :rule bool-double-not-elim :args (@t48))
% 0.39/0.59  (step @p146 :rule nary_cong :premises (@p145 @p144) :args ((or (not @t134) @t133)))
% 0.39/0.59  (step @p147 :rule eq-symm :args (@t128 @t131))
% 0.39/0.59  (step @p148 :rule eq-refl :args (@t130))
% 0.39/0.59  (step @p149 :rule skolem_intro :args (@t131))
% 0.39/0.59  (step @p150 :rule refl :args (@t130))
% 0.39/0.59  (step @p151 :rule cong :premises (@p150 @p149) :args ((= @t130 @t131)))
% 0.39/0.59  (step @p152 :rule trans :premises (@p151 @p148))
% 0.39/0.59  (step @p153 :rule true_elim :premises (@p152))
% 0.39/0.59  (step @p154 :rule eq-refl :args (@t127))
% 0.39/0.59  (step @p155 :rule skolem_intro :args (@t128))
% 0.39/0.59  (step @p156 :rule refl :args (@t127))
% 0.39/0.59  (step @p157 :rule cong :premises (@p156 @p155) :args ((= @t127 @t128)))
% 0.39/0.59  (step @p158 :rule trans :premises (@p157 @p154))
% 0.39/0.59  (step @p159 :rule true_elim :premises (@p158))
% 0.39/0.59  (step @p160 :rule cong :premises (@p159 @p153) :args (@t135))
% 0.39/0.59  (step @p161 :rule trans :premises (@p160 @p147))
% 0.39/0.59  (step @p162 :rule cong :premises (@p161) :args (@t136))
% 0.39/0.59  (step @p163 :rule refl :args (@t134))
% 0.39/0.59  (step @p164 :rule cong :premises (@p163 @p162) :args ((=> @t134 @t136)))
% 0.39/0.59  (assume-push @p294 @t134)
% 0.39/0.59  (step @p166 :rule skolemize :premises (@p143))
% 0.39/0.59  (step-pop @p295 :rule scope :premises (@p166))
% 0.39/0.59  (step @p167 :rule process_scope :premises (@p295) :args (@t136))
% 0.39/0.59  (step @p169 :rule eq_resolve :premises (@p167 @p164))
% 0.39/0.59  (step @p170 :rule implies_elim :premises (@p169))
% 0.39/0.59  (step @p171 :rule eq_resolve :premises (@p170 @p146))
% 0.39/0.59  (step @p172 :rule chain_m_resolution :premises (@p171 @p143) :args (@t133 @t137 (@list @t48)))
% 0.39/0.59  (step @p173 :rule eq-symm :args (@t139 @t75))
% 0.39/0.59  (step @p174 :rule eq-refl :args (@t75))
% 0.39/0.59  (step @p175 :rule refl :args (@t75))
% 0.39/0.59  (step @p176 :rule beta-reduce :args (@t140))
% 0.39/0.59  (step @p177 :rule cong :premises (@p176 @p175) :args (@t140))
% 0.39/0.59  (step @p178 :rule trans :premises (@p177 @p174))
% 0.39/0.59  (step @p179 :rule refl :args (@t39))
% 0.39/0.59  (step @p180 :rule ho_cong :premises (@p155 @p179))
% 0.39/0.59  (step @p181 :rule cong :premises (@p180 @p175) :args ((= @t141 @t75)))
% 0.39/0.59  (step @p182 :rule trans :premises (@p181 @p178))
% 0.39/0.59  (step @p183 :rule true_elim :premises (@p182))
% 0.39/0.59  (step @p184 :rule eq-refl :args (@t139))
% 0.39/0.59  (step @p185 :rule refl :args (@t139))
% 0.39/0.59  (step @p186 :rule beta-reduce :args (@t142))
% 0.39/0.59  (step @p187 :rule cong :premises (@p186 @p185) :args (@t142))
% 0.39/0.59  (step @p188 :rule trans :premises (@p187 @p184))
% 0.39/0.59  (step @p189 :rule ho_cong :premises (@p149 @p179))
% 0.39/0.59  (step @p190 :rule cong :premises (@p189 @p185) :args ((= @t143 @t139)))
% 0.39/0.59  (step @p191 :rule trans :premises (@p190 @p188))
% 0.39/0.59  (step @p192 :rule true_elim :premises (@p191))
% 0.39/0.59  (step @p193 :rule cong :premises (@p192 @p183) :args (@t144))
% 0.39/0.59  (step @p194 :rule trans :premises (@p193 @p173))
% 0.39/0.59  (step @p195 :rule cong :premises (@p194) :args (@t145))
% 0.39/0.59  (step @p196 :rule refl :args (@t132))
% 0.39/0.59  (step @p197 :rule nary_cong :premises (@p196 @p195) :args (@t146))
% 0.39/0.59  ; WARNING: add trust step for TRUST
% 0.39/0.59  ; trust TRUST THEORY_LEMMA
% 0.39/0.59  (step @p198 :rule trust :premises () :args (@t146))
% 0.39/0.59  (step @p199 :rule eq_resolve :premises (@p198 @p197))
% 0.39/0.59  (step @p200 :rule chain_m_resolution :premises (@p199 @p172) :args ((not @t147) @t137 (@list @t132)))
% 0.39/0.59  (step @p201 :rule cnf_equiv_neg2 :args (@t147))
% 0.39/0.59  (step @p202 :rule bool-double-not-elim :args (@t62))
% 0.39/0.59  (step @p203 :rule refl :args (@t138))
% 0.39/0.59  (step @p204 :rule nary_cong :premises (@p203 @p22 @p202) :args ((or @t138 @t53 (not @t76))))
% 0.39/0.59  (step @p205 :rule cnf_and_neg :args (@t138))
% 0.39/0.59  (step @p206 :rule eq_resolve :premises (@p205 @p204))
% 0.39/0.59  (step @p207 :rule reordering :premises (@p206) :args ((or @t53 @t62 @t138)))
% 0.39/0.59  (step @p208 :rule cnf_or_neg :args (@t139 0))
% 0.39/0.59  (step @p209 :rule chain_m_resolution :premises (@p208 @p207 @p201 @p200 @p44 @p42 @p41 @p39) :args ((or @t53 @t57 @t69 @t61) (@list false true true true false true false) (@list @t138 @t139 @t147 @t62 @t75 @t59 @t72)))
% 0.39/0.59  (step @p210 :rule cnf_and_pos :args (@t72 1))
% 0.39/0.59  (step @p211 :rule reordering :premises (@p210) :args ((or @t60 @t148)))
% 0.39/0.59  (step @p212 :rule refl :args (@t60))
% 0.39/0.59  (step @p213 :rule refl :args (@t59))
% 0.39/0.59  (step @p214 :rule nary_cong :premises (@p213 @p21 @p212) :args ((or @t59 @t66 @t60)))
% 0.39/0.59  (step @p215 :rule cnf_and_neg :args (@t59))
% 0.39/0.59  (step @p216 :rule eq_resolve :premises (@p215 @p214))
% 0.39/0.59  (step @p217 :rule reordering :premises (@p216) :args ((or @t50 @t60 @t59)))
% 0.39/0.59  (step @p218 :rule cnf_or_pos :args (@t75))
% 0.39/0.59  (step @p219 :rule reordering :premises (@p218) :args ((or @t72 @t70 @t149)))
% 0.39/0.59  (step @p220 :rule cnf_or_neg :args (@t62 1))
% 0.39/0.59  (step @p221 :rule cnf_equiv_neg1 :args (@t147))
% 0.39/0.59  (step @p222 :rule reordering :premises (@p221) :args ((or @t75 @t139 @t147)))
% 0.39/0.59  (step @p223 :rule cnf_and_pos :args (@t138 1))
% 0.39/0.59  (step @p224 :rule reordering :premises (@p223) :args ((or @t76 @t150)))
% 0.39/0.59  (step @p225 :rule cnf_or_pos :args (@t139))
% 0.39/0.59  (step @p226 :rule reordering :premises (@p225) :args ((or @t138 @t63 (not @t139))))
% 0.39/0.59  (step @p227 :rule chain_m_resolution :premises (@p226 @p224 @p222 @p200 @p220 @p219 @p217 @p211 @p209 @p32 @p30 @p29 @p27 @p20) :args ((or @t50 @t53) (@list true false true false true false true false true false true false true) (@list @t138 @t139 @t147 @t62 @t75 @t59 @t72 @t57 @t70 @t68 @t61 @t65 @t63)))
% 0.39/0.59  (step @p228 :rule cnf_and_pos :args (@t65 1))
% 0.39/0.59  (step @p229 :rule reordering :premises (@p228) :args ((or @t58 @t151)))
% 0.39/0.59  (step @p230 :rule cnf_or_pos :args (@t68))
% 0.39/0.59  (step @p231 :rule reordering :premises (@p230) :args ((or @t65 @t54 @t69)))
% 0.39/0.59  (step @p232 :rule cnf_and_pos :args (@t72 0))
% 0.39/0.59  (step @p233 :rule reordering :premises (@p232) :args ((or @t68 @t148)))
% 0.39/0.59  (step @p234 :rule cnf_and_pos :args (@t59 0))
% 0.39/0.59  (step @p235 :rule reordering :premises (@p234) :args ((or @t58 @t74)))
% 0.39/0.59  (step @p236 :rule bool-double-not-elim :args (@t68))
% 0.39/0.59  (step @p237 :rule refl :args (@t70))
% 0.39/0.59  (step @p238 :rule nary_cong :premises (@p237 @p236 @p212) :args ((or @t70 (not @t69) @t60)))
% 0.39/0.59  (step @p239 :rule cnf_and_neg :args (@t70))
% 0.39/0.59  (step @p240 :rule eq_resolve :premises (@p239 @p238))
% 0.39/0.59  (step @p241 :rule reordering :premises (@p240) :args ((or @t68 @t60 @t70)))
% 0.39/0.59  (step @p242 :rule cnf_and_pos :args (@t61 1))
% 0.39/0.59  (step @p243 :rule reordering :premises (@p242) :args ((or @t60 @t67)))
% 0.39/0.59  (step @p244 :rule cnf_or_neg :args (@t75 1))
% 0.39/0.59  (step @p245 :rule chain_m_resolution :premises (@p208 @p207 @p201 @p200 @p44 @p244 @p243 @p241 @p231 @p18 @p229 @p235 @p227) :args ((or @t53 @t60) (@list false true true true false true false true true true true false) (@list @t138 @t139 @t147 @t62 @t75 @t61 @t70 @t68 @t54 @t65 @t59 @t50)))
% 0.39/0.59  (step @p246 :rule cnf_and_pos :args (@t70 1))
% 0.39/0.59  (step @p247 :rule reordering :premises (@p246) :args ((or @t57 @t71)))
% 0.39/0.59  (step @p248 :rule refl :args (@t58))
% 0.39/0.59  (step @p249 :rule refl :args (@t61))
% 0.39/0.59  (step @p250 :rule nary_cong :premises (@p249 @p248 @p33) :args ((or @t61 @t58 @t73)))
% 0.39/0.59  (step @p251 :rule cnf_and_neg :args (@t61))
% 0.39/0.59  (step @p252 :rule eq_resolve :premises (@p251 @p250))
% 0.39/0.59  (step @p253 :rule reordering :premises (@p252) :args ((or @t58 @t57 @t61)))
% 0.39/0.59  (step @p254 :rule cnf_or_neg :args (@t62 0))
% 0.39/0.59  (step @p255 :rule chain_m_resolution :premises (@p226 @p224 @p222 @p200 @p254 @p219 @p253 @p247 @p245 @p233 @p231 @p229 @p227 @p20 @p18) :args (@t53 (@list true false true false true false true true true true true false true true) (@list @t138 @t139 @t147 @t62 @t75 @t61 @t70 @t57 @t72 @t68 @t65 @t50 @t63 @t54)))
% 0.39/0.59  (step @p256 :rule cnf_and_pos :args (@t138 0))
% 0.39/0.59  (step @p257 :rule reordering :premises (@p256) :args ((or @t52 @t150)))
% 0.39/0.59  (step @p258 :rule chain_m_resolution :premises (@p257 @p255) :args (@t150 @t137 @t152))
% 0.39/0.59  (step @p259 :rule bool-double-not-elim :args (@t52))
% 0.39/0.59  (step @p260 :rule refl :args (@t54))
% 0.39/0.59  (step @p261 :rule nary_cong :premises (@p260 @p259 @p248) :args ((or @t54 @t153 @t58)))
% 0.39/0.59  (step @p262 :rule cnf_and_neg :args (@t54))
% 0.39/0.59  (step @p263 :rule eq_resolve :premises (@p262 @p261))
% 0.39/0.59  (step @p264 :rule reordering :premises (@p263) :args ((or @t52 @t58 @t54)))
% 0.39/0.59  (step @p265 :rule cnf_or_neg :args (@t68 1))
% 0.39/0.59  (step @p266 :rule refl :args (@t76))
% 0.39/0.59  (step @p267 :rule refl :args (@t63))
% 0.39/0.59  (step @p268 :rule nary_cong :premises (@p267 @p259 @p266) :args ((or @t63 @t153 @t76)))
% 0.39/0.59  (step @p269 :rule cnf_and_neg :args (@t63))
% 0.39/0.59  (step @p270 :rule eq_resolve :premises (@p269 @p268))
% 0.39/0.59  (step @p271 :rule reordering :premises (@p270) :args ((or @t52 @t76 @t63)))
% 0.39/0.59  (step @p272 :rule cnf_or_neg :args (@t139 1))
% 0.39/0.59  (step @p273 :rule chain_m_resolution :premises (@p272 @p271 @p255 @p201 @p200 @p254 @p42 @p253 @p39 @p265 @p264 @p255) :args ((or @t58 @t57) (@list false true true true false false false false false false true) (@list @t63 @t52 @t139 @t147 @t62 @t75 @t61 @t72 @t68 @t54 @t52)))
% 0.39/0.59  (step @p274 :rule cnf_and_pos :args (@t63 1))
% 0.39/0.59  (step @p275 :rule reordering :premises (@p274) :args ((or @t62 @t64)))
% 0.39/0.59  (step @p276 :rule chain_m_resolution :premises (@p226 @p258 @p275 @p222 @p200 @p44 @p219 @p243 @p211 @p273 @p32 @p265 @p235 @p264 @p255) :args (@t58 (@list true true false true true true true true false true false true false true) (@list @t138 @t63 @t139 @t147 @t62 @t75 @t61 @t72 @t57 @t70 @t68 @t59 @t54 @t52)))
% 0.39/0.59  (step @p277 :rule cnf_and_pos :args (@t54 1))
% 0.39/0.59  (step @p278 :rule reordering :premises (@p277) :args ((or @t50 @t55)))
% 0.39/0.59  (step @p279 :rule chain_m_resolution :premises (@p278 @p276) :args (@t55 @t137 @t154))
% 0.39/0.59  (step @p280 :rule cnf_and_pos :args (@t65 0))
% 0.39/0.59  (step @p281 :rule reordering :premises (@p280) :args ((or @t52 @t151)))
% 0.39/0.59  (step @p282 :rule chain_m_resolution :premises (@p281 @p255) :args (@t151 @t137 @t152))
% 0.39/0.59  (step @p283 :rule chain_m_resolution :premises (@p231 @p282 @p279) :args (@t69 @t155 (@list @t65 @t54)))
% 0.39/0.59  (step @p284 :rule chain_m_resolution :premises (@p272 @p271 @p255 @p201 @p200 @p220 @p244 @p217 @p276 @p241 @p283) :args (@t60 (@list false true true true false false false true false true) (@list @t63 @t52 @t139 @t147 @t62 @t75 @t59 @t50 @t70 @t68)))
% 0.39/0.59  (step @p285 :rule chain_m_resolution :premises (@p247 @p284) :args (@t71 @t137 @t156))
% 0.39/0.59  (step @p286 :rule chain_m_resolution :premises (@p233 @p283) :args (@t148 @t137 (@list @t68)))
% 0.39/0.59  (step @p287 :rule chain_m_resolution :premises (@p219 @p286 @p285) :args (@t149 @t155 (@list @t72 @t70)))
% 0.39/0.59  (step @p288 :rule chain_m_resolution :premises (@p222 @p287 @p200) :args (@t139 @t155 (@list @t75 @t147)))
% 0.39/0.59  (step @p289 :rule chain_m_resolution :premises (@p41 @p284) :args (@t74 @t137 @t156))
% 0.39/0.59  (step @p290 :rule chain_m_resolution :premises (@p29 @p276) :args (@t67 @t137 @t154))
% 0.39/0.59  (step @p291 :rule chain_m_resolution :premises (@p44 @p290 @p289) :args (@t76 @t155 (@list @t61 @t59)))
% 0.39/0.59  (step @p292 :rule chain_m_resolution :premises (@p275 @p291) :args (@t64 @t137 (@list @t62)))
% 0.39/0.59  (step @p293 false :rule chain_m_resolution :premises (@p226 @p292 @p288 @p258) :args (false (@list true false true) (@list @t63 @t139 @t138)))
% 0.39/0.59  )
% 0.39/0.59  % SZS output end Proof
% 0.39/0.59  % cvc5 exiting
%------------------------------------------------------------------------------