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cvc5---1.3.4.THM-Prf.s

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%------------------------------------------------------------------------------
% File     : cvc5---1.3.4
% Problem  : SEV140^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM

% Computer : n004.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 08:55:30 AM UTC 2026

% Result   : Theorem 0.47s 0.65s
% Output   : Proof 0.47s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SEV140^5 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.13  % Command  : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.18/0.34  % Computer : n004.cluster.edu
% 0.18/0.34  % Model    : x86_64 x86_64
% 0.18/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.34  % Memory   : 8042.1875MB
% 0.18/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.18/0.34  % CPULimit : 300
% 0.18/0.34  % WCLimit  : 300
% 0.18/0.34  % DateTime : Tue Jun  2 18:15:07 EDT 2026
% 0.18/0.34  % CPUTime  : 
% 0.30/0.49  %----Proving TH0
% 0.47/0.65  --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s...
% 0.47/0.65  % SZS status Theorem
% 0.47/0.65  % SZS output start Proof
% 0.47/0.65  (
% 0.47/0.65  (declare-sort tptp.a 0)
% 0.47/0.65  (define @t1 () (@var "Xy" tptp.a))
% 0.47/0.65  (define @t2 () (@var "Xx" tptp.a))
% 0.47/0.65  (define @t3 () (@var "Xp1" (-> tptp.a tptp.a Bool)))
% 0.47/0.65  (define @t4 () (_ (_ @t3 @t2) @t1))
% 0.47/0.65  (define @t5 () (@var "Xz" tptp.a))
% 0.47/0.65  (define @t6 () (@var "Xx0" tptp.a))
% 0.47/0.65  (define @t7 () (_ @t3 @t6))
% 0.47/0.65  (define @t8 () (_ @t7 @t5))
% 0.47/0.65  (define @t9 () (@var "Xy0" tptp.a))
% 0.47/0.65  (define @t10 () (_ (_ @t3 @t9) @t5))
% 0.47/0.65  (define @t11 () (_ @t7 @t9))
% 0.47/0.65  (define @t12 () (and @t11 @t10))
% 0.47/0.65  (define @t13 () (@list @t6 @t9 @t5))
% 0.47/0.65  (define @t14 () (forall @t13 (=> @t12 @t8)))
% 0.47/0.65  (define @t15 () (@var "S" (-> tptp.a tptp.a Bool)))
% 0.47/0.65  (define @t16 () (_ (_ @t15 @t6) @t9))
% 0.47/0.65  (define @t17 () (@var "R" (-> tptp.a tptp.a Bool)))
% 0.47/0.65  (define @t18 () (_ (_ @t17 @t6) @t9))
% 0.47/0.65  (define @t19 () (or @t18 @t16))
% 0.47/0.65  (define @t20 () (@list @t6 @t9))
% 0.47/0.65  (define @t21 () (forall @t20 (=> @t19 @t11)))
% 0.47/0.65  (define @t22 () (and @t21 @t14))
% 0.47/0.65  (define @t23 () (=> @t22 @t4))
% 0.47/0.65  (define @t24 () (@list @t3))
% 0.47/0.65  (define @t25 () (forall @t24 @t23))
% 0.47/0.65  (define @t26 () (@var "Xp10" (-> tptp.a tptp.a Bool)))
% 0.47/0.65  (define @t27 () (_ (_ @t26 @t6) @t9))
% 0.47/0.65  (define @t28 () (@var "Xx1" tptp.a))
% 0.47/0.65  (define @t29 () (_ @t26 @t28))
% 0.47/0.65  (define @t30 () (_ @t29 @t5))
% 0.47/0.65  (define @t31 () (@var "Xy1" tptp.a))
% 0.47/0.65  (define @t32 () (_ (_ @t26 @t31) @t5))
% 0.47/0.65  (define @t33 () (_ @t29 @t31))
% 0.47/0.65  (define @t34 () (and @t33 @t32))
% 0.47/0.65  (define @t35 () (@list @t28 @t31 @t5))
% 0.47/0.65  (define @t36 () (forall @t35 (=> @t34 @t30)))
% 0.47/0.65  (define @t37 () (_ (_ @t15 @t28) @t31))
% 0.47/0.65  (define @t38 () (@list @t28 @t31))
% 0.47/0.65  (define @t39 () (forall @t38 (=> @t37 @t33)))
% 0.47/0.65  (define @t40 () (and @t39 @t36))
% 0.47/0.65  (define @t41 () (=> @t40 @t27))
% 0.47/0.65  (define @t42 () (@list @t26))
% 0.47/0.65  (define @t43 () (forall @t42 @t41))
% 0.47/0.65  (define @t44 () (_ (_ @t17 @t28) @t31))
% 0.47/0.65  (define @t45 () (forall @t38 (=> @t44 @t33)))
% 0.47/0.65  (define @t46 () (and @t45 @t36))
% 0.47/0.65  (define @t47 () (=> @t46 @t27))
% 0.47/0.65  (define @t48 () (forall @t42 @t47))
% 0.47/0.65  (define @t49 () (or @t48 @t43))
% 0.47/0.65  (define @t50 () (=> @t49 @t11))
% 0.47/0.65  (define @t51 () (forall @t20 @t50))
% 0.47/0.65  (define @t52 () (and @t51 @t14))
% 0.47/0.65  (define @t53 () (=> @t52 @t4))
% 0.47/0.65  (define @t54 () (forall @t24 @t53))
% 0.47/0.65  (define @t55 () (=> @t54 @t25))
% 0.47/0.65  (define @t56 () (@list @t17 @t15 @t2 @t1))
% 0.47/0.65  (define @t57 () (forall @t56 @t55))
% 0.47/0.65  (define @t58 () (not @t57))
% 0.47/0.65  (define @t59 () (@var "BOUND_VARIABLE_7593" (-> tptp.a tptp.a Bool)))
% 0.47/0.65  (define @t60 () (_ @t59 @t2 @t1))
% 0.47/0.65  (define @t61 () (_ @t59 @t6 @t9))
% 0.47/0.65  (define @t62 () (not (forall @t13 (or (not @t61) (not (_ @t59 @t9 @t5)) (_ @t59 @t6 @t5)))))
% 0.47/0.65  (define @t63 () (_ @t15 @t6 @t9))
% 0.47/0.65  (define @t64 () (_ @t17 @t6 @t9))
% 0.47/0.65  (define @t65 () (and (not @t64) (not @t63)))
% 0.47/0.65  (define @t66 () (not (forall @t20 (or @t65 @t61))))
% 0.47/0.65  (define @t67 () (_ @t3 @t2 @t1))
% 0.47/0.65  (define @t68 () (_ @t3 @t6 @t5))
% 0.47/0.65  (define @t69 () (_ @t3 @t9 @t5))
% 0.47/0.65  (define @t70 () (_ @t3 @t6 @t9))
% 0.47/0.65  (define @t71 () (forall @t13 (or (not @t70) (not @t69) @t68)))
% 0.47/0.65  (define @t72 () (not @t71))
% 0.47/0.65  (define @t73 () (_ @t26 @t6 @t9))
% 0.47/0.65  (define @t74 () (_ @t26 @t28 @t5))
% 0.47/0.65  (define @t75 () (_ @t26 @t31 @t5))
% 0.47/0.65  (define @t76 () (_ @t26 @t28 @t31))
% 0.47/0.65  (define @t77 () (forall @t35 (or (not @t76) (not @t75) @t74)))
% 0.47/0.65  (define @t78 () (not @t77))
% 0.47/0.65  (define @t79 () (_ @t15 @t28 @t31))
% 0.47/0.65  (define @t80 () (forall @t38 (or (not @t79) @t76)))
% 0.47/0.65  (define @t81 () (not @t80))
% 0.47/0.65  (define @t82 () (forall @t42 (or @t81 @t78 @t73)))
% 0.47/0.65  (define @t83 () (_ @t17 @t28 @t31))
% 0.47/0.65  (define @t84 () (forall @t38 (or (not @t83) @t76)))
% 0.47/0.65  (define @t85 () (not @t84))
% 0.47/0.65  (define @t86 () (forall @t42 (or @t85 @t78 @t73)))
% 0.47/0.65  (define @t87 () (and (not @t86) (not @t82)))
% 0.47/0.65  (define @t88 () (forall @t20 (or @t87 @t70)))
% 0.47/0.65  (define @t89 () (not @t88))
% 0.47/0.65  (define @t90 () (forall @t24 (or @t89 @t72 @t67)))
% 0.47/0.65  (define @t91 () (not @t90))
% 0.47/0.65  (define @t92 () (or @t91 @t66 @t62 @t60))
% 0.47/0.65  (define @t93 () (or @t66 @t62 @t60))
% 0.47/0.65  (define @t94 () (or @t91 @t93))
% 0.47/0.65  (define @t95 () (@list @t17 @t15 @t2 @t1 @t59))
% 0.47/0.65  (define @t96 () (forall @t95 @t94))
% 0.47/0.65  (define @t97 () (@list @t59))
% 0.47/0.65  (define @t98 () (forall @t97 @t94))
% 0.47/0.65  (define @t99 () (forall @t97 @t93))
% 0.47/0.65  (define @t100 () (or @t91 @t99))
% 0.47/0.65  (define @t101 () (forall @t20 (or @t65 @t70)))
% 0.47/0.65  (define @t102 () (not @t101))
% 0.47/0.65  (define @t103 () (forall @t24 (or @t102 @t72 @t67)))
% 0.47/0.65  (define @t104 () (or @t102 @t72 @t4))
% 0.47/0.65  (define @t105 () (and @t101 @t71))
% 0.47/0.65  (define @t106 () (not @t10))
% 0.47/0.65  (define @t107 () (not @t11))
% 0.47/0.65  (define @t108 () (or @t107 @t106 @t8))
% 0.47/0.65  (define @t109 () (not @t16))
% 0.47/0.65  (define @t110 () (not @t18))
% 0.47/0.65  (define @t111 () (and @t110 @t109))
% 0.47/0.65  (define @t112 () (or @t111 @t11))
% 0.47/0.65  (define @t113 () (or @t89 @t72 @t4))
% 0.47/0.65  (define @t114 () (and @t88 @t71))
% 0.47/0.65  (define @t115 () (or @t87 @t11))
% 0.47/0.65  (define @t116 () (or @t86 @t82))
% 0.47/0.65  (define @t117 () (or @t81 @t78 @t27))
% 0.47/0.65  (define @t118 () (and @t80 @t77))
% 0.47/0.65  (define @t119 () (not @t32))
% 0.47/0.65  (define @t120 () (not @t33))
% 0.47/0.65  (define @t121 () (or @t120 @t119 @t30))
% 0.47/0.65  (define @t122 () (not @t37))
% 0.47/0.65  (define @t123 () (or @t122 @t33))
% 0.47/0.65  (define @t124 () (or @t85 @t78 @t27))
% 0.47/0.65  (define @t125 () (and @t84 @t77))
% 0.47/0.65  (define @t126 () (not @t44))
% 0.47/0.65  (define @t127 () (or @t126 @t33))
% 0.47/0.65  (define @t128 () (forall @t95 @t92))
% 0.47/0.65  (define @t129 () (@quantifiers_skolemize @t128 3))
% 0.47/0.65  (define @t130 () (@quantifiers_skolemize @t128 2))
% 0.47/0.65  (define @t131 () (@quantifiers_skolemize @t128 1))
% 0.47/0.65  (define @t132 () (not (_ @t131 @t28 @t31)))
% 0.47/0.65  (define @t133 () (not (forall @t38 (or @t132 @t76))))
% 0.47/0.65  (define @t134 () (@quantifiers_skolemize @t128 0))
% 0.47/0.65  (define @t135 () (not (_ @t134 @t28 @t31)))
% 0.47/0.65  (define @t136 () (not (forall @t38 (or @t135 @t76))))
% 0.47/0.65  (define @t137 () (and (not (forall @t42 (or @t136 @t78 @t73))) (not (forall @t42 (or @t133 @t78 @t73)))))
% 0.47/0.65  (define @t138 () (forall @t24 (or (not (forall @t20 (or @t137 @t70))) @t72 (_ @t3 @t130 @t129))))
% 0.47/0.65  (define @t139 () (@quantifiers_skolemize @t128 4))
% 0.47/0.65  (define @t140 () (_ @t139 @t130 @t129))
% 0.47/0.65  (define @t141 () (_ @t139 @t6 @t9))
% 0.47/0.65  (define @t142 () (forall @t13 (or (not @t141) (not (_ @t139 @t9 @t5)) (_ @t139 @t6 @t5))))
% 0.47/0.65  (define @t143 () (not @t142))
% 0.47/0.65  (define @t144 () (forall @t20 (or (and (not (_ @t134 @t6 @t9)) (not (_ @t131 @t6 @t9))) @t141)))
% 0.47/0.65  (define @t145 () (not @t144))
% 0.47/0.65  (define @t146 () (not @t138))
% 0.47/0.65  (define @t147 () (or @t146 @t145 @t143 @t140))
% 0.47/0.65  (define @t148 () (@list true))
% 0.47/0.65  (define @t149 () (@list @t147))
% 0.47/0.65  (define @t150 () (@list @t139))
% 0.47/0.65  (define @t151 () (forall @t20 (or @t137 @t141)))
% 0.47/0.65  (define @t152 () (not @t151))
% 0.47/0.65  (define @t153 () (or @t152 @t143 @t140))
% 0.47/0.65  (define @t154 () (@quantifiers_skolemize @t151 1))
% 0.47/0.65  (define @t155 () (@quantifiers_skolemize @t151 0))
% 0.47/0.65  (define @t156 () (_ @t139 @t155 @t154))
% 0.47/0.65  (define @t157 () (_ @t26 @t155 @t154))
% 0.47/0.65  (define @t158 () (forall @t42 (or @t133 @t78 @t157)))
% 0.47/0.65  (define @t159 () (not @t158))
% 0.47/0.65  (define @t160 () (forall @t42 (or @t136 @t78 @t157)))
% 0.47/0.65  (define @t161 () (not @t160))
% 0.47/0.65  (define @t162 () (and @t161 @t159))
% 0.47/0.65  (define @t163 () (or @t162 @t156))
% 0.47/0.65  (define @t164 () (@list @t163))
% 0.47/0.65  (define @t165 () (@var "BOUND_VARIABLE_8889" tptp.a))
% 0.47/0.65  (define @t166 () (@var "BOUND_VARIABLE_8887" tptp.a))
% 0.47/0.65  (define @t167 () (@var "BOUND_VARIABLE_8888" tptp.a))
% 0.47/0.65  (define @t168 () (@list @t166 @t167 @t165))
% 0.47/0.65  (define @t169 () (_ @t139 @t28 @t31))
% 0.47/0.65  (define @t170 () (forall @t35 (or (not @t169) (not (_ @t139 @t31 @t5)) (_ @t139 @t28 @t5))))
% 0.47/0.65  (define @t171 () (@list false))
% 0.47/0.65  (define @t172 () (forall @t38 (or @t135 @t169)))
% 0.47/0.65  (define @t173 () (@quantifiers_skolemize @t172 1))
% 0.47/0.65  (define @t174 () (@quantifiers_skolemize @t172 0))
% 0.47/0.65  (define @t175 () (_ @t134 @t174 @t173))
% 0.47/0.65  (define @t176 () (_ @t139 @t174 @t173))
% 0.47/0.65  (define @t177 () (not @t175))
% 0.47/0.65  (define @t178 () (or @t177 @t176))
% 0.47/0.65  (define @t179 () (and @t177 (not (_ @t131 @t174 @t173))))
% 0.47/0.65  (define @t180 () (or @t179 @t176))
% 0.47/0.65  (define @t181 () (not @t178))
% 0.47/0.65  (define @t182 () (not @t172))
% 0.47/0.65  (define @t183 () (not @t170))
% 0.47/0.65  (define @t184 () (or @t182 @t183 @t156))
% 0.47/0.65  (define @t185 () (not @t184))
% 0.47/0.65  (define @t186 () (@list true false false))
% 0.47/0.65  (define @t187 () (forall @t38 (or @t132 @t169)))
% 0.47/0.65  (define @t188 () (not @t187))
% 0.47/0.65  (define @t189 () (or @t188 @t183 @t156))
% 0.47/0.65  (define @t190 () (@quantifiers_skolemize @t187 1))
% 0.47/0.65  (define @t191 () (@quantifiers_skolemize @t187 0))
% 0.47/0.65  (define @t192 () (_ @t139 @t191 @t190))
% 0.47/0.65  (define @t193 () (_ @t131 @t191 @t190))
% 0.47/0.65  (define @t194 () (not @t193))
% 0.47/0.65  (define @t195 () (or @t194 @t192))
% 0.47/0.65  (define @t196 () (not @t195))
% 0.47/0.65  (define @t197 () (@list @t195))
% 0.47/0.65  (define @t198 () (and (not (_ @t134 @t191 @t190)) @t194))
% 0.47/0.65  (define @t199 () (not @t198))
% 0.47/0.65  (define @t200 () (or @t198 @t192))
% 0.47/0.65  (assume @p1 @t58)
% 0.47/0.65  (assume @p2 true)
% 0.47/0.65  (step @p3 :rule aci_norm :args ((= @t94 @t92)))
% 0.47/0.65  (step @p4 :rule cong :premises (@p3) :args (@t96))
% 0.47/0.65  (step @p5 :rule quant-merge-prenex :args ((= (forall @t56 @t98) @t96)))
% 0.47/0.65  (step @p6 :rule alpha_equiv :args (@t99 (@list @t59) (@list @t3)))
% 0.47/0.65  (step @p7 :rule refl :args (@t91))
% 0.47/0.65  (step @p8 :rule nary_cong :premises (@p7 @p6) :args (@t100))
% 0.47/0.65  (step @p9 :rule quant-miniscope-or :args ((= @t98 @t100)))
% 0.47/0.65  (step @p10 :rule trans :premises (@p9 @p8))
% 0.47/0.65  (step @p11 :rule symm :premises (@p10))
% 0.47/0.65  (step @p12 :rule cong :premises (@p11) :args ((forall @t56 (or @t91 @t103))))
% 0.47/0.65  (step @p13 :rule trans :premises (@p12 @p5))
% 0.47/0.65  (step @p14 :rule trans :premises (@p13 @p4))
% 0.47/0.65  (step @p15 :rule bool-impl-elim :args (@t90 @t103))
% 0.47/0.65  (step @p16 :rule cong :premises (@p15) :args ((forall @t56 (=> @t90 @t103))))
% 0.47/0.65  (step @p17 :rule trans :premises (@p16 @p14))
% 0.47/0.65  (step @p18 :rule refl :args (@t67))
% 0.47/0.65  (step @p19 :rule refl :args (@t4))
% 0.47/0.65  (step @p20 :rule cong :premises (@p19 @p18) :args ((= @t4 @t67)))
% 0.47/0.65  (step @p21 :rule symm :premises (@p20))
% 0.47/0.65  (step @p22 :rule eq_resolve :premises (@p19 @p21))
% 0.47/0.65  (step @p23 :rule refl :args (@t72))
% 0.47/0.65  (step @p24 :rule refl :args (@t102))
% 0.47/0.65  (step @p25 :rule nary_cong :premises (@p24 @p23 @p22) :args (@t104))
% 0.47/0.65  (step @p26 :rule cong :premises (@p25) :args ((forall @t24 @t104)))
% 0.47/0.65  (step @p27 :rule aci_norm :args ((= (or (or @t102 @t72) @t4) @t104)))
% 0.47/0.65  (step @p28 :rule bool-and-de-morgan :args (@t101 @t71 true))
% 0.47/0.65  (step @p29 :rule nary_cong :premises (@p28 @p19) :args ((or (not @t105) @t4)))
% 0.47/0.65  (step @p30 :rule trans :premises (@p29 @p27))
% 0.47/0.65  (step @p31 :rule bool-impl-elim :args (@t105 @t4))
% 0.47/0.65  (step @p32 :rule trans :premises (@p31 @p30))
% 0.47/0.65  (step @p33 :rule cong :premises (@p32) :args ((forall @t24 (=> @t105 @t4))))
% 0.47/0.65  (step @p34 :rule trans :premises (@p33 @p26))
% 0.47/0.65  (step @p35 :rule refl :args (@t4))
% 0.47/0.65  (step @p36 :rule refl :args (@t68))
% 0.47/0.65  (step @p37 :rule refl :args (@t8))
% 0.47/0.65  (step @p38 :rule cong :premises (@p37 @p36) :args ((= @t8 @t68)))
% 0.47/0.65  (step @p39 :rule symm :premises (@p38))
% 0.47/0.65  (step @p40 :rule eq_resolve :premises (@p37 @p39))
% 0.47/0.65  (step @p41 :rule refl :args (@t69))
% 0.47/0.65  (step @p42 :rule refl :args (@t10))
% 0.47/0.65  (step @p43 :rule cong :premises (@p42 @p41) :args ((= @t10 @t69)))
% 0.47/0.65  (step @p44 :rule symm :premises (@p43))
% 0.47/0.65  (step @p45 :rule eq_resolve :premises (@p42 @p44))
% 0.47/0.65  (step @p46 :rule cong :premises (@p45) :args (@t106))
% 0.47/0.65  (step @p47 :rule refl :args (@t70))
% 0.47/0.65  (step @p48 :rule refl :args (@t11))
% 0.47/0.65  (step @p49 :rule cong :premises (@p48 @p47) :args ((= @t11 @t70)))
% 0.47/0.65  (step @p50 :rule symm :premises (@p49))
% 0.47/0.65  (step @p51 :rule eq_resolve :premises (@p48 @p50))
% 0.47/0.65  (step @p52 :rule cong :premises (@p51) :args (@t107))
% 0.47/0.65  (step @p53 :rule nary_cong :premises (@p52 @p46 @p40) :args (@t108))
% 0.47/0.65  (step @p54 :rule cong :premises (@p53) :args ((forall @t13 @t108)))
% 0.47/0.65  (step @p55 :rule aci_norm :args ((= (or (or @t107 @t106) @t8) @t108)))
% 0.47/0.65  (step @p56 :rule bool-and-de-morgan :args (@t11 @t10 true))
% 0.47/0.65  (step @p57 :rule nary_cong :premises (@p56 @p37) :args ((or (not @t12) @t8)))
% 0.47/0.65  (step @p58 :rule trans :premises (@p57 @p55))
% 0.47/0.65  (step @p59 :rule bool-impl-elim :args (@t12 @t8))
% 0.47/0.65  (step @p60 :rule trans :premises (@p59 @p58))
% 0.47/0.65  (step @p61 :rule cong :premises (@p60) :args (@t14))
% 0.47/0.65  (step @p62 :rule trans :premises (@p61 @p54))
% 0.47/0.65  (step @p63 :rule refl :args (@t63))
% 0.47/0.65  (step @p64 :rule refl :args (@t16))
% 0.47/0.65  (step @p65 :rule cong :premises (@p64 @p63) :args ((= @t16 @t63)))
% 0.47/0.65  (step @p66 :rule symm :premises (@p65))
% 0.47/0.65  (step @p67 :rule eq_resolve :premises (@p64 @p66))
% 0.47/0.65  (step @p68 :rule cong :premises (@p67) :args (@t109))
% 0.47/0.65  (step @p69 :rule refl :args (@t64))
% 0.47/0.65  (step @p70 :rule refl :args (@t18))
% 0.47/0.65  (step @p71 :rule cong :premises (@p70 @p69) :args ((= @t18 @t64)))
% 0.47/0.65  (step @p72 :rule symm :premises (@p71))
% 0.47/0.65  (step @p73 :rule eq_resolve :premises (@p70 @p72))
% 0.47/0.65  (step @p74 :rule cong :premises (@p73) :args (@t110))
% 0.47/0.65  (step @p75 :rule nary_cong :premises (@p74 @p68) :args (@t111))
% 0.47/0.65  (step @p76 :rule nary_cong :premises (@p75 @p51) :args (@t112))
% 0.47/0.65  (step @p77 :rule cong :premises (@p76) :args ((forall @t20 @t112)))
% 0.47/0.65  (step @p78 :rule bool-or-de-morgan :args (@t18 @t16 false))
% 0.47/0.65  (step @p79 :rule nary_cong :premises (@p78 @p48) :args ((or (not @t19) @t11)))
% 0.47/0.65  (step @p80 :rule bool-impl-elim :args (@t19 @t11))
% 0.47/0.65  (step @p81 :rule trans :premises (@p80 @p79))
% 0.47/0.65  (step @p82 :rule cong :premises (@p81) :args (@t21))
% 0.47/0.65  (step @p83 :rule trans :premises (@p82 @p77))
% 0.47/0.65  (step @p84 :rule nary_cong :premises (@p83 @p62) :args (@t22))
% 0.47/0.65  (step @p85 :rule cong :premises (@p84 @p35) :args (@t23))
% 0.47/0.65  (step @p86 :rule cong :premises (@p85) :args (@t25))
% 0.47/0.65  (step @p87 :rule trans :premises (@p86 @p34))
% 0.47/0.65  (step @p88 :rule refl :args (@t89))
% 0.47/0.65  (step @p89 :rule nary_cong :premises (@p88 @p23 @p22) :args (@t113))
% 0.47/0.65  (step @p90 :rule cong :premises (@p89) :args ((forall @t24 @t113)))
% 0.47/0.65  (step @p91 :rule aci_norm :args ((= (or (or @t89 @t72) @t4) @t113)))
% 0.47/0.65  (step @p92 :rule bool-and-de-morgan :args (@t88 @t71 true))
% 0.47/0.65  (step @p93 :rule nary_cong :premises (@p92 @p19) :args ((or (not @t114) @t4)))
% 0.47/0.65  (step @p94 :rule trans :premises (@p93 @p91))
% 0.47/0.65  (step @p95 :rule bool-impl-elim :args (@t114 @t4))
% 0.47/0.65  (step @p96 :rule trans :premises (@p95 @p94))
% 0.47/0.65  (step @p97 :rule cong :premises (@p96) :args ((forall @t24 (=> @t114 @t4))))
% 0.47/0.65  (step @p98 :rule trans :premises (@p97 @p90))
% 0.47/0.65  (step @p99 :rule refl :args (@t87))
% 0.47/0.65  (step @p100 :rule nary_cong :premises (@p99 @p51) :args (@t115))
% 0.47/0.65  (step @p101 :rule cong :premises (@p100) :args ((forall @t20 @t115)))
% 0.47/0.65  (step @p102 :rule bool-or-de-morgan :args (@t86 @t82 false))
% 0.47/0.65  (step @p103 :rule nary_cong :premises (@p102 @p48) :args ((or (not @t116) @t11)))
% 0.47/0.65  (step @p104 :rule bool-impl-elim :args (@t116 @t11))
% 0.47/0.65  (step @p105 :rule trans :premises (@p104 @p103))
% 0.47/0.65  (step @p106 :rule cong :premises (@p105) :args ((forall @t20 (=> @t116 @t11))))
% 0.47/0.65  (step @p107 :rule trans :premises (@p106 @p101))
% 0.47/0.65  (step @p108 :rule refl :args (@t11))
% 0.47/0.65  (step @p109 :rule refl :args (@t73))
% 0.47/0.65  (step @p110 :rule refl :args (@t27))
% 0.47/0.65  (step @p111 :rule cong :premises (@p110 @p109) :args ((= @t27 @t73)))
% 0.47/0.65  (step @p112 :rule symm :premises (@p111))
% 0.47/0.65  (step @p113 :rule eq_resolve :premises (@p110 @p112))
% 0.47/0.65  (step @p114 :rule refl :args (@t78))
% 0.47/0.65  (step @p115 :rule refl :args (@t81))
% 0.47/0.65  (step @p116 :rule nary_cong :premises (@p115 @p114 @p113) :args (@t117))
% 0.47/0.65  (step @p117 :rule cong :premises (@p116) :args ((forall @t42 @t117)))
% 0.47/0.65  (step @p118 :rule aci_norm :args ((= (or (or @t81 @t78) @t27) @t117)))
% 0.47/0.65  (step @p119 :rule bool-and-de-morgan :args (@t80 @t77 true))
% 0.47/0.65  (step @p120 :rule nary_cong :premises (@p119 @p110) :args ((or (not @t118) @t27)))
% 0.47/0.65  (step @p121 :rule trans :premises (@p120 @p118))
% 0.47/0.65  (step @p122 :rule bool-impl-elim :args (@t118 @t27))
% 0.47/0.65  (step @p123 :rule trans :premises (@p122 @p121))
% 0.47/0.65  (step @p124 :rule cong :premises (@p123) :args ((forall @t42 (=> @t118 @t27))))
% 0.47/0.65  (step @p125 :rule trans :premises (@p124 @p117))
% 0.47/0.65  (step @p126 :rule refl :args (@t27))
% 0.47/0.65  (step @p127 :rule refl :args (@t74))
% 0.47/0.65  (step @p128 :rule refl :args (@t30))
% 0.47/0.65  (step @p129 :rule cong :premises (@p128 @p127) :args ((= @t30 @t74)))
% 0.47/0.65  (step @p130 :rule symm :premises (@p129))
% 0.47/0.65  (step @p131 :rule eq_resolve :premises (@p128 @p130))
% 0.47/0.65  (step @p132 :rule refl :args (@t75))
% 0.47/0.65  (step @p133 :rule refl :args (@t32))
% 0.47/0.65  (step @p134 :rule cong :premises (@p133 @p132) :args ((= @t32 @t75)))
% 0.47/0.65  (step @p135 :rule symm :premises (@p134))
% 0.47/0.65  (step @p136 :rule eq_resolve :premises (@p133 @p135))
% 0.47/0.65  (step @p137 :rule cong :premises (@p136) :args (@t119))
% 0.47/0.65  (step @p138 :rule refl :args (@t76))
% 0.47/0.65  (step @p139 :rule refl :args (@t33))
% 0.47/0.65  (step @p140 :rule cong :premises (@p139 @p138) :args ((= @t33 @t76)))
% 0.47/0.65  (step @p141 :rule symm :premises (@p140))
% 0.47/0.65  (step @p142 :rule eq_resolve :premises (@p139 @p141))
% 0.47/0.65  (step @p143 :rule cong :premises (@p142) :args (@t120))
% 0.47/0.65  (step @p144 :rule nary_cong :premises (@p143 @p137 @p131) :args (@t121))
% 0.47/0.65  (step @p145 :rule cong :premises (@p144) :args ((forall @t35 @t121)))
% 0.47/0.65  (step @p146 :rule aci_norm :args ((= (or (or @t120 @t119) @t30) @t121)))
% 0.47/0.65  (step @p147 :rule bool-and-de-morgan :args (@t33 @t32 true))
% 0.47/0.65  (step @p148 :rule nary_cong :premises (@p147 @p128) :args ((or (not @t34) @t30)))
% 0.47/0.65  (step @p149 :rule trans :premises (@p148 @p146))
% 0.47/0.65  (step @p150 :rule bool-impl-elim :args (@t34 @t30))
% 0.47/0.65  (step @p151 :rule trans :premises (@p150 @p149))
% 0.47/0.65  (step @p152 :rule cong :premises (@p151) :args (@t36))
% 0.47/0.65  (step @p153 :rule trans :premises (@p152 @p145))
% 0.47/0.65  (step @p154 :rule refl :args (@t79))
% 0.47/0.65  (step @p155 :rule refl :args (@t37))
% 0.47/0.65  (step @p156 :rule cong :premises (@p155 @p154) :args ((= @t37 @t79)))
% 0.47/0.65  (step @p157 :rule symm :premises (@p156))
% 0.47/0.65  (step @p158 :rule eq_resolve :premises (@p155 @p157))
% 0.47/0.65  (step @p159 :rule cong :premises (@p158) :args (@t122))
% 0.47/0.65  (step @p160 :rule nary_cong :premises (@p159 @p142) :args (@t123))
% 0.47/0.65  (step @p161 :rule cong :premises (@p160) :args ((forall @t38 @t123)))
% 0.47/0.65  (step @p162 :rule bool-impl-elim :args (@t37 @t33))
% 0.47/0.65  (step @p163 :rule cong :premises (@p162) :args (@t39))
% 0.47/0.65  (step @p164 :rule trans :premises (@p163 @p161))
% 0.47/0.65  (step @p165 :rule nary_cong :premises (@p164 @p153) :args (@t40))
% 0.47/0.65  (step @p166 :rule cong :premises (@p165 @p126) :args (@t41))
% 0.47/0.65  (step @p167 :rule cong :premises (@p166) :args (@t43))
% 0.47/0.65  (step @p168 :rule trans :premises (@p167 @p125))
% 0.47/0.65  (step @p169 :rule refl :args (@t85))
% 0.47/0.65  (step @p170 :rule nary_cong :premises (@p169 @p114 @p113) :args (@t124))
% 0.47/0.65  (step @p171 :rule cong :premises (@p170) :args ((forall @t42 @t124)))
% 0.47/0.65  (step @p172 :rule aci_norm :args ((= (or (or @t85 @t78) @t27) @t124)))
% 0.47/0.65  (step @p173 :rule bool-and-de-morgan :args (@t84 @t77 true))
% 0.47/0.65  (step @p174 :rule nary_cong :premises (@p173 @p110) :args ((or (not @t125) @t27)))
% 0.47/0.65  (step @p175 :rule trans :premises (@p174 @p172))
% 0.47/0.65  (step @p176 :rule bool-impl-elim :args (@t125 @t27))
% 0.47/0.65  (step @p177 :rule trans :premises (@p176 @p175))
% 0.47/0.65  (step @p178 :rule cong :premises (@p177) :args ((forall @t42 (=> @t125 @t27))))
% 0.47/0.65  (step @p179 :rule trans :premises (@p178 @p171))
% 0.47/0.65  (step @p180 :rule refl :args (@t83))
% 0.47/0.65  (step @p181 :rule refl :args (@t44))
% 0.47/0.65  (step @p182 :rule cong :premises (@p181 @p180) :args ((= @t44 @t83)))
% 0.47/0.65  (step @p183 :rule symm :premises (@p182))
% 0.47/0.65  (step @p184 :rule eq_resolve :premises (@p181 @p183))
% 0.47/0.65  (step @p185 :rule cong :premises (@p184) :args (@t126))
% 0.47/0.65  (step @p186 :rule nary_cong :premises (@p185 @p142) :args (@t127))
% 0.47/0.65  (step @p187 :rule cong :premises (@p186) :args ((forall @t38 @t127)))
% 0.47/0.65  (step @p188 :rule bool-impl-elim :args (@t44 @t33))
% 0.47/0.65  (step @p189 :rule cong :premises (@p188) :args (@t45))
% 0.47/0.65  (step @p190 :rule trans :premises (@p189 @p187))
% 0.47/0.65  (step @p191 :rule nary_cong :premises (@p190 @p153) :args (@t46))
% 0.47/0.65  (step @p192 :rule cong :premises (@p191 @p126) :args (@t47))
% 0.47/0.65  (step @p193 :rule cong :premises (@p192) :args (@t48))
% 0.47/0.65  (step @p194 :rule trans :premises (@p193 @p179))
% 0.47/0.65  (step @p195 :rule nary_cong :premises (@p194 @p168) :args (@t49))
% 0.47/0.65  (step @p196 :rule cong :premises (@p195 @p108) :args (@t50))
% 0.47/0.65  (step @p197 :rule cong :premises (@p196) :args (@t51))
% 0.47/0.65  (step @p198 :rule trans :premises (@p197 @p107))
% 0.47/0.65  (step @p199 :rule nary_cong :premises (@p198 @p62) :args (@t52))
% 0.47/0.65  (step @p200 :rule cong :premises (@p199 @p35) :args (@t53))
% 0.47/0.65  (step @p201 :rule cong :premises (@p200) :args (@t54))
% 0.47/0.65  (step @p202 :rule trans :premises (@p201 @p98))
% 0.47/0.65  (step @p203 :rule cong :premises (@p202 @p87) :args (@t55))
% 0.47/0.65  (step @p204 :rule cong :premises (@p203) :args (@t57))
% 0.47/0.65  (step @p205 :rule trans :premises (@p204 @p17))
% 0.47/0.65  (step @p206 :rule cong :premises (@p205) :args (@t58))
% 0.47/0.65  (step @p207 :rule eq_resolve :premises (@p1 @p206))
% 0.47/0.65  (step @p208 :rule skolemize :premises (@p207))
% 0.47/0.65  (step @p209 :rule bool-double-not-elim :args (@t138))
% 0.47/0.65  (step @p210 :rule refl :args (@t147))
% 0.47/0.65  (step @p211 :rule nary_cong :premises (@p210 @p209) :args ((or @t147 (not @t146))))
% 0.47/0.65  (step @p212 :rule cnf_or_neg :args (@t147 0))
% 0.47/0.65  (step @p213 :rule eq_resolve :premises (@p212 @p211))
% 0.47/0.65  (step @p214 :rule reordering :premises (@p213) :args ((or @t138 @t147)))
% 0.47/0.65  (step @p215 :rule chain_m_resolution :premises (@p214 @p208) :args (@t138 @t148 @t149))
% 0.47/0.65  (step @p216 :rule instantiate :premises (@p215) :args (@t150))
% 0.47/0.65  (step @p217 :rule cnf_or_neg :args (@t147 3))
% 0.47/0.65  (step @p218 :rule chain_m_resolution :premises (@p217 @p208) :args ((not @t140) @t148 @t149))
% 0.47/0.65  (step @p219 :rule bool-double-not-elim :args (@t142))
% 0.47/0.65  (step @p220 :rule nary_cong :premises (@p210 @p219) :args ((or @t147 (not @t143))))
% 0.47/0.65  (step @p221 :rule cnf_or_neg :args (@t147 2))
% 0.47/0.65  (step @p222 :rule eq_resolve :premises (@p221 @p220))
% 0.47/0.65  (step @p223 :rule reordering :premises (@p222) :args ((or @t142 @t147)))
% 0.47/0.65  (step @p224 :rule chain_m_resolution :premises (@p223 @p208) :args (@t142 @t148 @t149))
% 0.47/0.65  (step @p225 :rule cnf_or_pos :args (@t153))
% 0.47/0.65  (step @p226 :rule reordering :premises (@p225) :args ((or @t143 @t140 @t152 (not @t153))))
% 0.47/0.65  (step @p227 :rule chain_m_resolution :premises (@p226 @p224 @p218 @p216) :args (@t152 (@list false true false) (@list @t142 @t140 @t153)))
% 0.47/0.65  (step @p228 :rule skolemize :premises (@p227))
% 0.47/0.65  (step @p229 :rule cnf_or_neg :args (@t163 0))
% 0.47/0.65  (step @p230 :rule chain_m_resolution :premises (@p229 @p228) :args ((not @t162) @t148 @t164))
% 0.47/0.65  (step @p231 :rule alpha_equiv :args ((forall (@list @t166 @t167 @t165) (or (not (_ @t139 @t166 @t167)) (not (_ @t139 @t167 @t165)) (_ @t139 @t166 @t165))) @t168 (@list @t28 @t31 @t5)))
% 0.47/0.65  (step @p232 :rule alpha_equiv :args (@t142 (@list @t6 @t9 @t5) @t168))
% 0.47/0.65  (step @p233 :rule trans :premises (@p232 @p231))
% 0.47/0.65  (step @p234 :rule equiv_elim1 :premises (@p233))
% 0.47/0.65  (step @p235 :rule chain_m_resolution :premises (@p234 @p224) :args (@t170 @t171 (@list @t142)))
% 0.47/0.65  (step @p236 :rule bool-double-not-elim :args (@t175))
% 0.47/0.65  (step @p237 :rule refl :args (@t178))
% 0.47/0.65  (step @p238 :rule nary_cong :premises (@p237 @p236) :args ((or @t178 (not @t177))))
% 0.47/0.65  (step @p239 :rule cnf_or_neg :args (@t178 0))
% 0.47/0.65  (step @p240 :rule eq_resolve :premises (@p239 @p238))
% 0.47/0.65  (step @p241 :rule reordering :premises (@p240) :args ((or @t175 @t178)))
% 0.47/0.65  (step @p242 :rule cnf_or_neg :args (@t178 1))
% 0.47/0.65  (step @p243 :rule cnf_and_pos :args (@t179 0))
% 0.47/0.65  (step @p244 :rule reordering :premises (@p243) :args ((or @t177 (not @t179))))
% 0.47/0.65  (step @p245 :rule bool-double-not-elim :args (@t144))
% 0.47/0.65  (step @p246 :rule nary_cong :premises (@p210 @p245) :args ((or @t147 (not @t145))))
% 0.47/0.65  (step @p247 :rule cnf_or_neg :args (@t147 1))
% 0.47/0.65  (step @p248 :rule eq_resolve :premises (@p247 @p246))
% 0.47/0.65  (step @p249 :rule reordering :premises (@p248) :args ((or @t144 @t147)))
% 0.47/0.65  (step @p250 :rule chain_m_resolution :premises (@p249 @p208) :args (@t144 @t148 @t149))
% 0.47/0.65  (step @p251 :rule instantiate :premises (@p250) :args ((@list @t174 @t173)))
% 0.47/0.65  (step @p252 :rule cnf_or_pos :args (@t180))
% 0.47/0.65  (step @p253 :rule reordering :premises (@p252) :args ((or @t176 @t179 (not @t180))))
% 0.47/0.65  (step @p254 :rule chain_m_resolution :premises (@p253 @p251 @p244 @p242 @p241) :args (@t178 (@list false true true false) (@list @t180 @t179 @t176 @t175)))
% 0.47/0.65  (step @p255 :rule refl :args (@t181))
% 0.47/0.65  (step @p256 :rule bool-double-not-elim :args (@t172))
% 0.47/0.65  (step @p257 :rule nary_cong :premises (@p256 @p255) :args ((or (not @t182) @t181)))
% 0.47/0.65  (assume-push @p319 @t182)
% 0.47/0.65  (step @p259 :rule skolemize :premises (@p319))
% 0.47/0.65  (step-pop @p320 :rule scope :premises (@p259))
% 0.47/0.65  (step @p260 :rule process_scope :premises (@p320) :args (@t181))
% 0.47/0.65  (step @p262 :rule implies_elim :premises (@p260))
% 0.47/0.65  (step @p263 :rule eq_resolve :premises (@p262 @p257))
% 0.47/0.65  (step @p264 :rule chain_m_resolution :premises (@p263 @p254) :args (@t172 @t171 (@list @t178)))
% 0.47/0.65  (step @p265 :rule cnf_or_neg :args (@t163 1))
% 0.47/0.65  (step @p266 :rule chain_m_resolution :premises (@p265 @p228) :args ((not @t156) @t148 @t164))
% 0.47/0.65  (step @p267 :rule cnf_or_pos :args (@t184))
% 0.47/0.65  (step @p268 :rule reordering :premises (@p267) :args ((or @t156 @t182 @t183 @t185)))
% 0.47/0.65  (step @p269 :rule chain_m_resolution :premises (@p268 @p266 @p264 @p235) :args (@t185 @t186 (@list @t156 @t172 @t170)))
% 0.47/0.65  (assume-push @p321 @t160)
% 0.47/0.65  (step @p271 :rule instantiate :premises (@p321) :args (@t150))
% 0.47/0.65  (step-pop @p322 :rule scope :premises (@p271))
% 0.47/0.65  (step @p272 :rule process_scope :premises (@p322) :args (@t184))
% 0.47/0.65  (step @p274 :rule implies_elim :premises (@p272))
% 0.47/0.65  (step @p275 :rule chain_m_resolution :premises (@p274 @p269) :args (@t161 @t148 (@list @t184)))
% 0.47/0.65  (step @p276 :rule bool-double-not-elim :args (@t158))
% 0.47/0.65  (step @p277 :rule bool-double-not-elim :args (@t160))
% 0.47/0.65  (step @p278 :rule refl :args (@t162))
% 0.47/0.65  (step @p279 :rule nary_cong :premises (@p278 @p277 @p276) :args ((or @t162 (not @t161) (not @t159))))
% 0.47/0.65  (step @p280 :rule cnf_and_neg :args (@t162))
% 0.47/0.65  (step @p281 :rule eq_resolve :premises (@p280 @p279))
% 0.47/0.65  (step @p282 :rule reordering :premises (@p281) :args ((or @t160 @t158 @t162)))
% 0.47/0.65  (step @p283 :rule chain_m_resolution :premises (@p282 @p275 @p230) :args (@t158 (@list true true) (@list @t160 @t162)))
% 0.47/0.65  (assume-push @p323 @t158)
% 0.47/0.65  (step @p285 :rule instantiate :premises (@p323) :args (@t150))
% 0.47/0.65  (step-pop @p324 :rule scope :premises (@p285))
% 0.47/0.65  (step @p286 :rule process_scope :premises (@p324) :args (@t189))
% 0.47/0.65  (step @p288 :rule implies_elim :premises (@p286))
% 0.47/0.65  (step @p289 :rule chain_m_resolution :premises (@p288 @p283) :args (@t189 @t171 (@list @t158)))
% 0.47/0.65  (step @p290 :rule cnf_or_pos :args (@t189))
% 0.47/0.65  (step @p291 :rule reordering :premises (@p290) :args ((or @t156 @t183 @t188 (not @t189))))
% 0.47/0.65  (step @p292 :rule chain_m_resolution :premises (@p291 @p266 @p235 @p289) :args (@t188 @t186 (@list @t156 @t170 @t189)))
% 0.47/0.65  (step @p293 :rule refl :args (@t196))
% 0.47/0.65  (step @p294 :rule bool-double-not-elim :args (@t187))
% 0.47/0.65  (step @p295 :rule nary_cong :premises (@p294 @p293) :args ((or (not @t188) @t196)))
% 0.47/0.65  (assume-push @p325 @t188)
% 0.47/0.65  (step @p297 :rule skolemize :premises (@p325))
% 0.47/0.65  (step-pop @p326 :rule scope :premises (@p297))
% 0.47/0.65  (step @p298 :rule process_scope :premises (@p326) :args (@t196))
% 0.47/0.65  (step @p300 :rule implies_elim :premises (@p298))
% 0.47/0.65  (step @p301 :rule eq_resolve :premises (@p300 @p295))
% 0.47/0.65  (step @p302 :rule chain_m_resolution :premises (@p301 @p292) :args (@t196 @t148 (@list @t187)))
% 0.47/0.65  (step @p303 :rule cnf_or_neg :args (@t195 1))
% 0.47/0.65  (step @p304 :rule chain_m_resolution :premises (@p303 @p302) :args ((not @t192) @t148 @t197))
% 0.47/0.65  (step @p305 :rule bool-double-not-elim :args (@t193))
% 0.47/0.65  (step @p306 :rule refl :args (@t195))
% 0.47/0.65  (step @p307 :rule nary_cong :premises (@p306 @p305) :args ((or @t195 (not @t194))))
% 0.47/0.65  (step @p308 :rule cnf_or_neg :args (@t195 0))
% 0.47/0.65  (step @p309 :rule eq_resolve :premises (@p308 @p307))
% 0.47/0.65  (step @p310 :rule reordering :premises (@p309) :args ((or @t193 @t195)))
% 0.47/0.65  (step @p311 :rule chain_m_resolution :premises (@p310 @p302) :args (@t193 @t148 @t197))
% 0.47/0.65  (step @p312 :rule cnf_and_pos :args (@t198 1))
% 0.47/0.65  (step @p313 :rule reordering :premises (@p312) :args ((or @t194 @t199)))
% 0.47/0.65  (step @p314 :rule chain_m_resolution :premises (@p313 @p311) :args (@t199 @t171 (@list @t193)))
% 0.47/0.65  (step @p315 :rule instantiate :premises (@p250) :args ((@list @t191 @t190)))
% 0.47/0.65  (step @p316 :rule cnf_or_pos :args (@t200))
% 0.47/0.65  (step @p317 :rule reordering :premises (@p316) :args ((or @t192 @t198 (not @t200))))
% 0.47/0.65  (step @p318 false :rule chain_m_resolution :premises (@p317 @p315 @p314 @p304) :args (false (@list false true true) (@list @t200 @t198 @t192)))
% 0.47/0.65  )
% 0.47/0.65  % SZS output end Proof
% 0.47/0.65  % cvc5 exiting
%------------------------------------------------------------------------------