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cvc5---1.3.4.THM-Prf.s

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%------------------------------------------------------------------------------
% File     : cvc5---1.3.4
% Problem  : SEU290+1 : TPTP v9.2.1. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM

% Computer : n006.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 08:51:15 AM UTC 2026

% Result   : Theorem 33.87s 34.14s
% Output   : Proof 33.87s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SEU290+1 : TPTP v9.2.1. Released v3.3.0.
% 0.12/0.13  % Command  : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.16/0.35  % Computer : n006.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 16:52:49 EDT 2026
% 0.16/0.35  % CPUTime  : 
% 0.30/0.51  %----Proving TF0_NAR, FOF, or CNF
% 33.87/34.14  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15...
% 33.87/34.14  --- Run --no-e-matching --full-saturate-quant at 6...
% 33.87/34.14  --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 6...
% 33.87/34.14  --- Run --finite-model-find --uf-ss=no-minimal at 6...
% 33.87/34.14  --- Run --multi-trigger-when-single --full-saturate-quant at 30...
% 33.87/34.14  % SZS status Theorem
% 33.87/34.14  % SZS output start Proof
% 33.87/34.14  (
% 33.87/34.14  (declare-sort $$unsorted 0)
% 33.87/34.14  (declare-const tptp.relation_of2 (-> $$unsorted $$unsorted $$unsorted Bool))
% 33.87/34.14  (declare-const tptp.relation_rng (-> $$unsorted $$unsorted))
% 33.87/34.14  (declare-const tptp.function (-> $$unsorted Bool))
% 33.87/34.14  (declare-const tptp.powerset (-> $$unsorted $$unsorted))
% 33.87/34.14  (declare-const tptp.empty (-> $$unsorted Bool))
% 33.87/34.14  (declare-const tptp.relation (-> $$unsorted Bool))
% 33.87/34.14  (declare-const tptp.quasi_total (-> $$unsorted $$unsorted $$unsorted Bool))
% 33.87/34.14  (declare-const tptp.cartesian_product2 (-> $$unsorted $$unsorted $$unsorted))
% 33.87/34.14  (declare-const tptp.subset (-> $$unsorted $$unsorted Bool))
% 33.87/34.14  (declare-const tptp.element (-> $$unsorted $$unsorted Bool))
% 33.87/34.14  (declare-const tptp.in (-> $$unsorted $$unsorted Bool))
% 33.87/34.14  (declare-const tptp.apply (-> $$unsorted $$unsorted $$unsorted))
% 33.87/34.14  (declare-const tptp.relation_dom (-> $$unsorted $$unsorted))
% 33.87/34.14  (declare-const tptp.one_to_one (-> $$unsorted Bool))
% 33.87/34.14  (declare-const tptp.relation_empty_yielding (-> $$unsorted Bool))
% 33.87/34.14  (declare-const tptp.empty_set $$unsorted)
% 33.87/34.14  (declare-const tptp.relation_dom_as_subset (-> $$unsorted $$unsorted $$unsorted $$unsorted))
% 33.87/34.14  (declare-const tptp.relation_of2_as_subset (-> $$unsorted $$unsorted $$unsorted Bool))
% 33.87/34.14  (define @t1 () (@var "A" $$unsorted))
% 33.87/34.14  (define @t2 () (@var "B" $$unsorted))
% 33.87/34.14  (define @t3 () (tptp.in @t1 @t2))
% 33.87/34.14  (define @t4 () (@list @t1 @t2))
% 33.87/34.14  (define @t5 () (tptp.function @t1))
% 33.87/34.14  (define @t6 () (tptp.empty @t1))
% 33.87/34.14  (define @t7 () (@list @t1))
% 33.87/34.14  (define @t8 () (tptp.relation @t1))
% 33.87/34.14  (define @t9 () (@var "C" $$unsorted))
% 33.87/34.14  (define @t10 () (tptp.relation @t9))
% 33.87/34.14  (define @t11 () (tptp.cartesian_product2 @t1 @t2))
% 33.87/34.14  (define @t12 () (tptp.element @t9 (tptp.powerset @t11)))
% 33.87/34.14  (define @t13 () (@list @t1 @t2 @t9))
% 33.87/34.14  (define @t14 () (forall @t13 (=> @t12 @t10)))
% 33.87/34.14  (define @t15 () (tptp.one_to_one @t1))
% 33.87/34.14  (define @t16 () (and @t8 @t5 @t15))
% 33.87/34.14  (define @t17 () (and @t8 @t6 @t5))
% 33.87/34.14  (define @t18 () (tptp.quasi_total @t9 @t1 @t2))
% 33.87/34.14  (define @t19 () (= @t18 (= @t9 tptp.empty_set)))
% 33.87/34.14  (define @t20 () (= @t1 tptp.empty_set))
% 33.87/34.14  (define @t21 () (or @t20 @t19))
% 33.87/34.14  (define @t22 () (= @t2 tptp.empty_set))
% 33.87/34.14  (define @t23 () (tptp.relation_dom_as_subset @t1 @t2 @t9))
% 33.87/34.14  (define @t24 () (= @t18 (= @t1 @t23)))
% 33.87/34.14  (define @t25 () (=> @t22 @t20))
% 33.87/34.14  (define @t26 () (and (=> @t25 @t24) (=> @t22 @t21)))
% 33.87/34.14  (define @t27 () (tptp.relation_of2_as_subset @t9 @t1 @t2))
% 33.87/34.14  (define @t28 () (forall @t13 (=> @t27 @t26)))
% 33.87/34.14  (define @t29 () (@var "D" $$unsorted))
% 33.87/34.14  (define @t30 () (= @t9 (tptp.apply @t1 @t29)))
% 33.87/34.14  (define @t31 () (tptp.relation_dom @t1))
% 33.87/34.14  (define @t32 () (tptp.in @t29 @t31))
% 33.87/34.14  (define @t33 () (and @t32 @t30))
% 33.87/34.14  (define @t34 () (@list @t29))
% 33.87/34.14  (define @t35 () (exists @t34 @t33))
% 33.87/34.14  (define @t36 () (tptp.in @t9 @t2))
% 33.87/34.14  (define @t37 () (= @t36 @t35))
% 33.87/34.14  (define @t38 () (@list @t9))
% 33.87/34.14  (define @t39 () (forall @t38 @t37))
% 33.87/34.14  (define @t40 () (tptp.relation_rng @t1))
% 33.87/34.14  (define @t41 () (= @t2 @t40))
% 33.87/34.14  (define @t42 () (= @t41 @t39))
% 33.87/34.14  (define @t43 () (@list @t2))
% 33.87/34.14  (define @t44 () (forall @t43 @t42))
% 33.87/34.14  (define @t45 () (and @t8 @t5))
% 33.87/34.14  (define @t46 () (=> @t45 @t44))
% 33.87/34.14  (define @t47 () (forall @t7 @t46))
% 33.87/34.14  (define @t48 () (tptp.powerset @t1))
% 33.87/34.14  (define @t49 () (tptp.relation_of2 @t9 @t1 @t2))
% 33.87/34.14  (define @t50 () (forall @t13 (=> @t27 @t12)))
% 33.87/34.14  (define @t51 () (tptp.relation tptp.empty_set))
% 33.87/34.14  (define @t52 () (tptp.empty tptp.empty_set))
% 33.87/34.14  (define @t53 () (tptp.empty @t2))
% 33.87/34.14  (define @t54 () (not @t53))
% 33.87/34.14  (define @t55 () (not @t6))
% 33.87/34.14  (define @t56 () (tptp.empty @t31))
% 33.87/34.14  (define @t57 () (and @t55 @t8))
% 33.87/34.14  (define @t58 () (tptp.empty @t40))
% 33.87/34.14  (define @t59 () (tptp.function @t9))
% 33.87/34.14  (define @t60 () (tptp.element @t2 @t48))
% 33.87/34.14  (define @t61 () (tptp.relation_empty_yielding @t1))
% 33.87/34.14  (define @t62 () (= @t23 (tptp.relation_dom @t9)))
% 33.87/34.14  (define @t63 () (forall @t13 (=> @t49 @t62)))
% 33.87/34.14  (define @t64 () (tptp.element @t1 @t2))
% 33.87/34.14  (define @t65 () (tptp.element @t2 (tptp.powerset @t9)))
% 33.87/34.14  (define @t66 () (tptp.in (tptp.apply @t29 @t9) (tptp.relation_rng @t29)))
% 33.87/34.14  (define @t67 () (or @t22 @t66))
% 33.87/34.14  (define @t68 () (tptp.in @t9 @t1))
% 33.87/34.14  (define @t69 () (=> @t68 @t67))
% 33.87/34.14  (define @t70 () (tptp.relation_of2_as_subset @t29 @t1 @t2))
% 33.87/34.14  (define @t71 () (tptp.quasi_total @t29 @t1 @t2))
% 33.87/34.14  (define @t72 () (tptp.function @t29))
% 33.87/34.14  (define @t73 () (and @t72 @t71 @t70))
% 33.87/34.14  (define @t74 () (@list @t1 @t2 @t9 @t29))
% 33.87/34.14  (define @t75 () (forall @t74 (=> @t73 @t69)))
% 33.87/34.14  (define @t76 () (not @t75))
% 33.87/34.14  (define @t77 () (@var "BOUND_VARIABLE_7676" $$unsorted))
% 33.87/34.14  (define @t78 () (tptp.in @t9 @t77))
% 33.87/34.14  (define @t79 () (not (forall @t34 (or (not @t32) (not @t30)))))
% 33.87/34.14  (define @t80 () (forall @t38 (= @t78 @t79)))
% 33.87/34.14  (define @t81 () (= (= @t77 @t40) @t80))
% 33.87/34.14  (define @t82 () (not @t5))
% 33.87/34.14  (define @t83 () (not @t8))
% 33.87/34.14  (define @t84 () (or @t83 @t82 @t81))
% 33.87/34.14  (define @t85 () (@list @t1 @t77))
% 33.87/34.14  (define @t86 () (forall @t85 @t84))
% 33.87/34.14  (define @t87 () (@list @t77))
% 33.87/34.14  (define @t88 () (forall @t87 @t84))
% 33.87/34.14  (define @t89 () (forall @t87 @t81))
% 33.87/34.14  (define @t90 () (or @t83 @t82 @t89))
% 33.87/34.14  (define @t91 () (forall @t43 (= @t41 (forall @t38 (= @t36 @t79)))))
% 33.87/34.14  (define @t92 () (or @t83 @t82 @t91))
% 33.87/34.14  (define @t93 () (forall @t34 (not @t33)))
% 33.87/34.14  (define @t94 () (not @t93))
% 33.87/34.14  (define @t95 () (not @t68))
% 33.87/34.14  (define @t96 () (not @t70))
% 33.87/34.14  (define @t97 () (not @t71))
% 33.87/34.14  (define @t98 () (not @t72))
% 33.87/34.14  (define @t99 () (or @t98 @t97 @t96 @t95 @t22 @t66))
% 33.87/34.14  (define @t100 () (forall @t74 @t99))
% 33.87/34.14  (define @t101 () (@quantifiers_skolemize @t100 3))
% 33.87/34.14  (define @t102 () (tptp.relation_rng @t101))
% 33.87/34.14  (define @t103 () (tptp.apply @t101 @t29))
% 33.87/34.14  (define @t104 () (tptp.relation_dom @t101))
% 33.87/34.14  (define @t105 () (not (tptp.in @t29 @t104)))
% 33.87/34.14  (define @t106 () (forall @t38 (= (not (forall @t34 (or @t105 (not (= @t9 @t103))))) (tptp.in @t9 @t102))))
% 33.87/34.14  (define @t107 () (= (= @t102 @t102) @t106))
% 33.87/34.14  (define @t108 () (tptp.function @t101))
% 33.87/34.14  (define @t109 () (not @t108))
% 33.87/34.14  (define @t110 () (tptp.relation @t101))
% 33.87/34.14  (define @t111 () (not @t110))
% 33.87/34.14  (define @t112 () (or @t111 @t109 @t107))
% 33.87/34.14  (define @t113 () (forall @t85 (or @t83 @t82 (= (= @t40 @t77) (forall @t38 (= @t79 @t78))))))
% 33.87/34.14  (define @t114 () (or @t111 @t109 @t106))
% 33.87/34.14  (define @t115 () (@list false))
% 33.87/34.14  (define @t116 () (@quantifiers_skolemize @t100 1))
% 33.87/34.14  (define @t117 () (@quantifiers_skolemize @t100 0))
% 33.87/34.14  (define @t118 () (@list @t117 @t116 @t101))
% 33.87/34.14  (define @t119 () (or @t95 @t22 @t66))
% 33.87/34.14  (define @t120 () (or @t98 @t97 @t96))
% 33.87/34.14  (define @t121 () (@quantifiers_skolemize @t100 2))
% 33.87/34.14  (define @t122 () (tptp.apply @t101 @t121))
% 33.87/34.14  (define @t123 () (tptp.in @t122 @t102))
% 33.87/34.14  (define @t124 () (= tptp.empty_set @t116))
% 33.87/34.14  (define @t125 () (tptp.in @t121 @t117))
% 33.87/34.14  (define @t126 () (not @t125))
% 33.87/34.14  (define @t127 () (tptp.relation_of2_as_subset @t101 @t117 @t116))
% 33.87/34.14  (define @t128 () (not @t127))
% 33.87/34.14  (define @t129 () (tptp.quasi_total @t101 @t117 @t116))
% 33.87/34.14  (define @t130 () (not @t129))
% 33.87/34.14  (define @t131 () (or @t109 @t130 @t128 @t126 @t124 @t123))
% 33.87/34.14  (define @t132 () (not @t131))
% 33.87/34.14  (define @t133 () (not @t100))
% 33.87/34.14  (define @t134 () (= @t116 tptp.empty_set))
% 33.87/34.14  (define @t135 () (or @t109 @t130 @t128 @t126 @t134 @t123))
% 33.87/34.14  (define @t136 () (not @t135))
% 33.87/34.14  (define @t137 () (@list true))
% 33.87/34.14  (define @t138 () (@list @t131))
% 33.87/34.14  (define @t139 () (tptp.element @t101 (tptp.powerset (tptp.cartesian_product2 @t117 @t116))))
% 33.87/34.14  (define @t140 () (or @t128 @t139))
% 33.87/34.14  (define @t141 () (@list false false))
% 33.87/34.14  (define @t142 () (not @t139))
% 33.87/34.14  (define @t143 () (or @t142 @t110))
% 33.87/34.14  (define @t144 () (forall @t34 (or @t105 (not (= @t122 @t103)))))
% 33.87/34.14  (define @t145 () (not @t144))
% 33.87/34.14  (define @t146 () (= @t145 @t123))
% 33.87/34.14  (define @t147 () (= @t123 @t145))
% 33.87/34.14  (define @t148 () (not @t147))
% 33.87/34.14  (define @t149 () (@list true false))
% 33.87/34.14  (define @t150 () (not (tptp.in @t121 @t104)))
% 33.87/34.14  (define @t151 () (not (= @t122 @t122)))
% 33.87/34.14  (define @t152 () (or @t150 @t151))
% 33.87/34.14  (define @t153 () (tptp.relation_of2 @t101 @t117 @t116))
% 33.87/34.14  (define @t154 () (= @t127 @t153))
% 33.87/34.14  (define @t155 () (tptp.relation_dom_as_subset @t117 @t116 @t101))
% 33.87/34.14  (define @t156 () (= @t155 @t104))
% 33.87/34.14  (define @t157 () (not @t153))
% 33.87/34.14  (define @t158 () (or @t157 @t156))
% 33.87/34.14  (define @t159 () (not @t22))
% 33.87/34.14  (define @t160 () (or @t159 @t20 @t19))
% 33.87/34.14  (define @t161 () (not @t27))
% 33.87/34.14  (define @t162 () (= @t129 (= @t101 tptp.empty_set)))
% 33.87/34.14  (define @t163 () (not @t134))
% 33.87/34.14  (define @t164 () (= @t117 tptp.empty_set))
% 33.87/34.14  (define @t165 () (or @t163 @t164 @t162))
% 33.87/34.14  (define @t166 () (= @t117 @t155))
% 33.87/34.14  (define @t167 () (= @t129 @t166))
% 33.87/34.14  (define @t168 () (not @t164))
% 33.87/34.14  (define @t169 () (and @t134 @t168))
% 33.87/34.14  (define @t170 () (or @t169 @t167))
% 33.87/34.14  (define @t171 () (and @t170 @t165))
% 33.87/34.14  (define @t172 () (or @t128 @t171))
% 33.87/34.14  (define @t173 () (forall @t13 (or @t161 (and (or (and @t22 (not @t20)) @t24) @t160))))
% 33.87/34.14  (define @t174 () (= tptp.empty_set @t117))
% 33.87/34.14  (define @t175 () (not @t124))
% 33.87/34.14  (define @t176 () (and @t124 (not @t174)))
% 33.87/34.14  (define @t177 () (or @t176 @t167))
% 33.87/34.14  (define @t178 () (and @t177 (or @t175 @t174 (= @t129 (= tptp.empty_set @t101)))))
% 33.87/34.14  (define @t179 () (or @t128 @t178))
% 33.87/34.14  (define @t180 () (not @t176))
% 33.87/34.14  (assume @p1 (forall @t4 (=> @t3 (not (tptp.in @t2 @t1)))))
% 33.87/34.14  (assume @p2 (forall @t7 (=> @t6 @t5)))
% 33.87/34.14  (assume @p3 (forall @t7 (=> @t6 @t8)))
% 33.87/34.14  (assume @p4 @t14)
% 33.87/34.14  (assume @p5 (forall @t7 (=> @t17 @t16)))
% 33.87/34.14  (assume @p6 @t28)
% 33.87/34.14  (assume @p7 @t47)
% 33.87/34.14  (assume @p8 true)
% 33.87/34.14  (assume @p9 (forall @t13 (=> @t49 (tptp.element @t23 @t48))))
% 33.87/34.14  (assume @p10 @t50)
% 33.87/34.14  (assume @p11 (forall @t4 (exists @t38 @t49)))
% 33.87/34.14  (assume @p12 (forall @t7 (exists @t43 (tptp.element @t2 @t1))))
% 33.87/34.14  (assume @p13 (forall @t4 (exists @t38 @t27)))
% 33.87/34.14  (assume @p14 (and @t52 @t51 (tptp.relation_empty_yielding tptp.empty_set)))
% 33.87/34.14  (assume @p15 (forall @t7 (not (tptp.empty @t48))))
% 33.87/34.14  (assume @p16 @t52)
% 33.87/34.14  (assume @p17 (and @t52 @t51))
% 33.87/34.14  (assume @p18 (forall @t4 (=> (and @t55 @t54) (not (tptp.empty @t11)))))
% 33.87/34.14  (assume @p19 (forall @t7 (=> @t57 (not @t56))))
% 33.87/34.14  (assume @p20 (forall @t7 (=> @t57 (not @t58))))
% 33.87/34.14  (assume @p21 (forall @t7 (=> @t6 (and @t56 (tptp.relation @t31)))))
% 33.87/34.14  (assume @p22 (forall @t7 (=> @t6 (and @t58 (tptp.relation @t40)))))
% 33.87/34.14  (assume @p23 (exists @t7 @t45))
% 33.87/34.14  (assume @p24 (forall @t4 (exists @t38 (and @t49 @t10 @t59 @t18))))
% 33.87/34.14  (assume @p25 (exists @t7 (and @t8 @t5 @t15 @t6)))
% 33.87/34.14  (assume @p26 (exists @t7 (and @t6 @t8)))
% 33.87/34.14  (assume @p27 (forall @t7 (=> @t55 (exists @t43 (and @t60 @t54)))))
% 33.87/34.14  (assume @p28 (exists @t7 @t6))
% 33.87/34.14  (assume @p29 (exists @t7 @t17))
% 33.87/34.14  (assume @p30 (forall @t4 (exists @t38 (and @t49 @t10 @t59))))
% 33.87/34.14  (assume @p31 (exists @t7 @t57))
% 33.87/34.14  (assume @p32 (forall @t7 (exists @t43 (and @t60 @t53))))
% 33.87/34.14  (assume @p33 (exists @t7 @t55))
% 33.87/34.14  (assume @p34 (exists @t7 @t16))
% 33.87/34.14  (assume @p35 (exists @t7 (and @t8 @t61)))
% 33.87/34.14  (assume @p36 (exists @t7 (and @t8 @t61 @t5)))
% 33.87/34.14  (assume @p37 @t63)
% 33.87/34.14  (assume @p38 (forall @t13 (= @t27 @t49)))
% 33.87/34.14  (assume @p39 (forall @t4 (tptp.subset @t1 @t1)))
% 33.87/34.14  (assume @p40 (forall @t4 (=> @t3 @t64)))
% 33.87/34.14  (assume @p41 (forall @t4 (=> @t64 (or @t53 @t3))))
% 33.87/34.14  (assume @p42 (forall @t4 (= (tptp.element @t1 (tptp.powerset @t2)) (tptp.subset @t1 @t2))))
% 33.87/34.14  (assume @p43 (forall @t13 (=> (and @t3 @t65) (tptp.element @t1 @t9))))
% 33.87/34.14  (assume @p44 (forall @t13 (not (and @t3 @t65 (tptp.empty @t9)))))
% 33.87/34.14  (assume @p45 (forall @t7 (=> @t6 @t20)))
% 33.87/34.14  (assume @p46 @t76)
% 33.87/34.14  (assume @p47 (forall @t4 (not (and @t3 @t53))))
% 33.87/34.14  (assume @p48 (forall @t4 (not (and @t6 (not (= @t1 @t2)) @t53))))
% 33.87/34.14  (step @p49 :rule evaluate :args ((= true false)))
% 33.87/34.14  (step @p50 :rule eq-symm :args (@t78 @t79))
% 33.87/34.14  (step @p51 :rule cong :premises (@p50) :args (@t80))
% 33.87/34.14  (step @p52 :rule eq-symm :args (@t77 @t40))
% 33.87/34.14  (step @p53 :rule cong :premises (@p52 @p51) :args (@t81))
% 33.87/34.14  (step @p54 :rule refl :args (@t82))
% 33.87/34.14  (step @p55 :rule refl :args (@t83))
% 33.87/34.14  (step @p56 :rule nary_cong :premises (@p55 @p54 @p53) :args (@t84))
% 33.87/34.14  (step @p57 :rule cong :premises (@p56) :args (@t86))
% 33.87/34.14  (step @p58 :rule quant-merge-prenex :args ((= (forall @t7 @t88) @t86)))
% 33.87/34.14  (step @p59 :rule alpha_equiv :args (@t89 (@list @t77) (@list @t2)))
% 33.87/34.14  (step @p60 :rule refl :args (@t82))
% 33.87/34.14  (step @p61 :rule refl :args (@t83))
% 33.87/34.14  (step @p62 :rule nary_cong :premises (@p61 @p60 @p59) :args (@t90))
% 33.87/34.14  (step @p63 :rule quant-miniscope-or :args ((= @t88 @t90)))
% 33.87/34.14  (step @p64 :rule trans :premises (@p63 @p62))
% 33.87/34.14  (step @p65 :rule symm :premises (@p64))
% 33.87/34.14  (step @p66 :rule cong :premises (@p65) :args ((forall @t7 @t92)))
% 33.87/34.14  (step @p67 :rule trans :premises (@p66 @p58))
% 33.87/34.14  (step @p68 :rule trans :premises (@p67 @p57))
% 33.87/34.14  (step @p69 :rule aci_norm :args ((= (or (or @t83 @t82) @t91) @t92)))
% 33.87/34.14  (step @p70 :rule refl :args (@t91))
% 33.87/34.14  (step @p71 :rule bool-and-de-morgan :args (@t8 @t5 true))
% 33.87/34.14  (step @p72 :rule nary_cong :premises (@p71 @p70) :args ((or (not @t45) @t91)))
% 33.87/34.14  (step @p73 :rule trans :premises (@p72 @p69))
% 33.87/34.14  (step @p74 :rule bool-impl-elim :args (@t45 @t91))
% 33.87/34.14  (step @p75 :rule trans :premises (@p74 @p73))
% 33.87/34.14  (step @p76 :rule cong :premises (@p75) :args ((forall @t7 (=> @t45 @t91))))
% 33.87/34.14  (step @p77 :rule trans :premises (@p76 @p68))
% 33.87/34.14  (step @p78 :rule bool-and-de-morgan :args (@t32 @t30 true))
% 33.87/34.14  (step @p79 :rule cong :premises (@p78) :args (@t93))
% 33.87/34.14  (step @p80 :rule cong :premises (@p79) :args (@t94))
% 33.87/34.14  (step @p81 :rule exists-elim :args ((= @t35 @t94)))
% 33.87/34.14  (step @p82 :rule trans :premises (@p81 @p80))
% 33.87/34.14  (step @p83 :rule refl :args (@t36))
% 33.87/34.14  (step @p84 :rule cong :premises (@p83 @p82) :args (@t37))
% 33.87/34.14  (step @p85 :rule cong :premises (@p84) :args (@t39))
% 33.87/34.14  (step @p86 :rule refl :args (@t41))
% 33.87/34.14  (step @p87 :rule cong :premises (@p86 @p85) :args (@t42))
% 33.87/34.14  (step @p88 :rule cong :premises (@p87) :args (@t44))
% 33.87/34.14  (step @p89 :rule refl :args (@t45))
% 33.87/34.14  (step @p90 :rule cong :premises (@p89 @p88) :args (@t46))
% 33.87/34.14  (step @p91 :rule cong :premises (@p90) :args (@t47))
% 33.87/34.14  (step @p92 :rule trans :premises (@p91 @p77))
% 33.87/34.14  (step @p93 :rule eq_resolve :premises (@p7 @p92))
% 33.87/34.14  (step @p94 :rule bool-eq-true :args (@t106))
% 33.87/34.14  (step @p95 :rule eq-symm :args (true @t106))
% 33.87/34.14  (step @p96 :rule trans :premises (@p95 @p94))
% 33.87/34.14  (step @p97 :rule refl :args (@t106))
% 33.87/34.14  (step @p98 :rule eq-refl :args (@t102))
% 33.87/34.14  (step @p99 :rule cong :premises (@p98 @p97) :args (@t107))
% 33.87/34.14  (step @p100 :rule trans :premises (@p99 @p96))
% 33.87/34.14  (step @p101 :rule refl :args (@t109))
% 33.87/34.14  (step @p102 :rule refl :args (@t111))
% 33.87/34.14  (step @p103 :rule nary_cong :premises (@p102 @p101 @p100) :args (@t112))
% 33.87/34.14  (step @p104 :rule refl :args (@t113))
% 33.87/34.14  (step @p105 :rule cong :premises (@p104 @p103) :args ((=> @t113 @t112)))
% 33.87/34.14  (assume-push @p300 @t113)
% 33.87/34.14  (step @p107 :rule instantiate :premises (@p93) :args ((@list @t101 @t102)))
% 33.87/34.14  (step-pop @p301 :rule scope :premises (@p107))
% 33.87/34.14  (step @p108 :rule process_scope :premises (@p301) :args (@t112))
% 33.87/34.14  (step @p110 :rule eq_resolve :premises (@p108 @p105))
% 33.87/34.14  (step @p111 :rule implies_elim :premises (@p110))
% 33.87/34.14  (step @p112 :rule chain_m_resolution :premises (@p111 @p93) :args (@t114 @t115 (@list @t113)))
% 33.87/34.14  (step @p113 :rule bool-impl-elim :args (@t12 @t10))
% 33.87/34.14  (step @p114 :rule cong :premises (@p113) :args (@t14))
% 33.87/34.14  (step @p115 :rule eq_resolve :premises (@p4 @p114))
% 33.87/34.14  (step @p116 :rule instantiate :premises (@p115) :args (@t118))
% 33.87/34.14  (step @p117 :rule bool-impl-elim :args (@t27 @t12))
% 33.87/34.14  (step @p118 :rule cong :premises (@p117) :args (@t50))
% 33.87/34.14  (step @p119 :rule eq_resolve :premises (@p10 @p118))
% 33.87/34.14  (step @p120 :rule instantiate :premises (@p119) :args (@t118))
% 33.87/34.14  (step @p121 :rule aci_norm :args ((= (or @t120 @t119) @t99)))
% 33.87/34.14  (step @p122 :rule aci_norm :args ((= (or @t95 @t67) @t119)))
% 33.87/34.14  (step @p123 :rule bool-impl-elim :args (@t68 @t67))
% 33.87/34.14  (step @p124 :rule trans :premises (@p123 @p122))
% 33.87/34.14  (step @p125 :rule aci_norm :args ((= (or @t98 (or @t97 @t96)) @t120)))
% 33.87/34.14  (step @p126 :rule bool-and-de-morgan :args (@t71 @t70 true))
% 33.87/34.14  (step @p127 :rule refl :args (@t98))
% 33.87/34.14  (step @p128 :rule nary_cong :premises (@p127 @p126) :args ((or @t98 (not (and @t71 @t70)))))
% 33.87/34.14  (step @p129 :rule bool-and-de-morgan :args (@t72 @t71 (and @t70)))
% 33.87/34.14  (step @p130 :rule trans :premises (@p129 @p128))
% 33.87/34.14  (step @p131 :rule trans :premises (@p130 @p125))
% 33.87/34.14  (step @p132 :rule nary_cong :premises (@p131 @p124) :args ((or (not @t73) @t69)))
% 33.87/34.14  (step @p133 :rule trans :premises (@p132 @p121))
% 33.87/34.14  (step @p134 :rule bool-impl-elim :args (@t73 @t69))
% 33.87/34.14  (step @p135 :rule trans :premises (@p134 @p133))
% 33.87/34.14  (step @p136 :rule cong :premises (@p135) :args (@t75))
% 33.87/34.14  (step @p137 :rule cong :premises (@p136) :args (@t76))
% 33.87/34.14  (step @p138 :rule eq_resolve :premises (@p46 @p137))
% 33.87/34.14  (step @p139 :rule refl :args (@t132))
% 33.87/34.14  (step @p140 :rule bool-double-not-elim :args (@t100))
% 33.87/34.14  (step @p141 :rule nary_cong :premises (@p140 @p139) :args ((or (not @t133) @t132)))
% 33.87/34.14  (step @p142 :rule refl :args (@t123))
% 33.87/34.14  (step @p143 :rule eq-symm :args (@t116 tptp.empty_set))
% 33.87/34.14  (step @p144 :rule refl :args (@t126))
% 33.87/34.14  (step @p145 :rule refl :args (@t128))
% 33.87/34.14  (step @p146 :rule refl :args (@t130))
% 33.87/34.14  (step @p147 :rule nary_cong :premises (@p101 @p146 @p145 @p144 @p143 @p142) :args (@t135))
% 33.87/34.14  (step @p148 :rule cong :premises (@p147) :args (@t136))
% 33.87/34.14  (step @p149 :rule refl :args (@t133))
% 33.87/34.14  (step @p150 :rule cong :premises (@p149 @p148) :args ((=> @t133 @t136)))
% 33.87/34.14  (assume-push @p302 @t133)
% 33.87/34.14  (step @p152 :rule skolemize :premises (@p138))
% 33.87/34.14  (step-pop @p303 :rule scope :premises (@p152))
% 33.87/34.14  (step @p153 :rule process_scope :premises (@p303) :args (@t136))
% 33.87/34.14  (step @p155 :rule eq_resolve :premises (@p153 @p150))
% 33.87/34.14  (step @p156 :rule implies_elim :premises (@p155))
% 33.87/34.14  (step @p157 :rule eq_resolve :premises (@p156 @p141))
% 33.87/34.14  (step @p158 :rule chain_m_resolution :premises (@p157 @p138) :args (@t132 @t137 (@list @t100)))
% 33.87/34.14  (step @p159 :rule bool-double-not-elim :args (@t127))
% 33.87/34.14  (step @p160 :rule refl :args (@t131))
% 33.87/34.14  (step @p161 :rule nary_cong :premises (@p160 @p159) :args ((or @t131 (not @t128))))
% 33.87/34.14  (step @p162 :rule cnf_or_neg :args (@t131 2))
% 33.87/34.14  (step @p163 :rule eq_resolve :premises (@p162 @p161))
% 33.87/34.14  (step @p164 :rule reordering :premises (@p163) :args ((or @t127 @t131)))
% 33.87/34.14  (step @p165 :rule chain_m_resolution :premises (@p164 @p158) :args (@t127 @t137 @t138))
% 33.87/34.14  (step @p166 :rule cnf_or_pos :args (@t140))
% 33.87/34.14  (step @p167 :rule reordering :premises (@p166) :args ((or @t128 @t139 (not @t140))))
% 33.87/34.14  (step @p168 :rule chain_m_resolution :premises (@p167 @p165 @p120) :args (@t139 @t141 (@list @t127 @t140)))
% 33.87/34.14  (step @p169 :rule cnf_or_pos :args (@t143))
% 33.87/34.14  (step @p170 :rule reordering :premises (@p169) :args ((or @t110 @t142 (not @t143))))
% 33.87/34.14  (step @p171 :rule chain_m_resolution :premises (@p170 @p168 @p116) :args (@t110 @t141 (@list @t139 @t143)))
% 33.87/34.14  (step @p172 :rule bool-double-not-elim :args (@t108))
% 33.87/34.14  (step @p173 :rule nary_cong :premises (@p160 @p172) :args ((or @t131 (not @t109))))
% 33.87/34.14  (step @p174 :rule cnf_or_neg :args (@t131 0))
% 33.87/34.14  (step @p175 :rule eq_resolve :premises (@p174 @p173))
% 33.87/34.14  (step @p176 :rule reordering :premises (@p175) :args ((or @t108 @t131)))
% 33.87/34.14  (step @p177 :rule chain_m_resolution :premises (@p176 @p158) :args (@t108 @t137 @t138))
% 33.87/34.14  (step @p178 :rule cnf_or_pos :args (@t114))
% 33.87/34.14  (step @p179 :rule reordering :premises (@p178) :args ((or @t109 @t111 @t106 (not @t114))))
% 33.87/34.14  (step @p180 :rule chain_m_resolution :premises (@p179 @p177 @p171 @p112) :args (@t106 (@list false false false) (@list @t108 @t110 @t114)))
% 33.87/34.14  (step @p181 :rule eq-symm :args (@t145 @t123))
% 33.87/34.14  (step @p182 :rule cong :premises (@p97 @p181) :args ((=> @t106 @t146)))
% 33.87/34.14  (assume-push @p304 @t106)
% 33.87/34.14  (step @p184 :rule instantiate :premises (@p180) :args ((@list @t122)))
% 33.87/34.14  (step-pop @p305 :rule scope :premises (@p184))
% 33.87/34.14  (step @p185 :rule process_scope :premises (@p305) :args (@t146))
% 33.87/34.14  (step @p187 :rule eq_resolve :premises (@p185 @p182))
% 33.87/34.14  (step @p188 :rule implies_elim :premises (@p187))
% 33.87/34.14  (step @p189 :rule chain_m_resolution :premises (@p188 @p180) :args (@t147 @t115 (@list @t106)))
% 33.87/34.14  (step @p190 :rule cnf_or_neg :args (@t131 5))
% 33.87/34.14  (step @p191 :rule chain_m_resolution :premises (@p190 @p158) :args ((not @t123) @t137 @t138))
% 33.87/34.14  (step @p192 :rule bool-double-not-elim :args (@t144))
% 33.87/34.14  (step @p193 :rule refl :args (@t148))
% 33.87/34.14  (step @p194 :rule nary_cong :premises (@p193 @p142 @p192) :args ((or @t148 @t123 (not @t145))))
% 33.87/34.14  (step @p195 :rule cnf_equiv_pos2 :args (@t147))
% 33.87/34.14  (step @p196 :rule eq_resolve :premises (@p195 @p194))
% 33.87/34.14  (step @p197 :rule reordering :premises (@p196) :args ((or @t123 @t144 @t148)))
% 33.87/34.14  (step @p198 :rule chain_m_resolution :premises (@p197 @p191 @p189) :args (@t144 @t149 (@list @t123 @t147)))
% 33.87/34.14  (step @p199 :rule aci_norm :args ((= (or @t150 false) @t150)))
% 33.87/34.14  (step @p200 :rule evaluate :args ((not true)))
% 33.87/34.14  (step @p201 :rule eq-refl :args (@t122))
% 33.87/34.14  (step @p202 :rule cong :premises (@p201) :args (@t151))
% 33.87/34.14  (step @p203 :rule trans :premises (@p202 @p200))
% 33.87/34.14  (step @p204 :rule refl :args (@t150))
% 33.87/34.14  (step @p205 :rule nary_cong :premises (@p204 @p203) :args (@t152))
% 33.87/34.14  (step @p206 :rule trans :premises (@p205 @p199))
% 33.87/34.14  (step @p207 :rule refl :args (@t144))
% 33.87/34.14  (step @p208 :rule cong :premises (@p207 @p206) :args ((=> @t144 @t152)))
% 33.87/34.14  (assume-push @p306 @t144)
% 33.87/34.14  (step @p210 :rule instantiate :premises (@p198) :args ((@list @t121)))
% 33.87/34.14  (step-pop @p307 :rule scope :premises (@p210))
% 33.87/34.14  (step @p211 :rule process_scope :premises (@p307) :args (@t152))
% 33.87/34.14  (step @p213 :rule eq_resolve :premises (@p211 @p208))
% 33.87/34.14  (step @p214 :rule implies_elim :premises (@p213))
% 33.87/34.14  (step @p215 :rule chain_m_resolution :premises (@p214 @p198) :args (@t150 @t115 (@list @t144)))
% 33.87/34.14  (step @p216 :rule false_intro :premises (@p215))
% 33.87/34.14  (step @p217 :rule bool-impl-elim :args (@t49 @t62))
% 33.87/34.14  (step @p218 :rule cong :premises (@p217) :args (@t63))
% 33.87/34.14  (step @p219 :rule eq_resolve :premises (@p37 @p218))
% 33.87/34.14  (step @p220 :rule instantiate :premises (@p219) :args (@t118))
% 33.87/34.14  (step @p221 :rule instantiate :premises (@p38) :args (@t118))
% 33.87/34.14  (step @p222 :rule cnf_equiv_pos1 :args (@t154))
% 33.87/34.14  (step @p223 :rule reordering :premises (@p222) :args ((or @t128 @t153 (not @t154))))
% 33.87/34.14  (step @p224 :rule chain_m_resolution :premises (@p223 @p165 @p221) :args (@t153 @t141 (@list @t127 @t154)))
% 33.87/34.14  (step @p225 :rule cnf_or_pos :args (@t158))
% 33.87/34.14  (step @p226 :rule reordering :premises (@p225) :args ((or @t157 @t156 (not @t158))))
% 33.87/34.14  (step @p227 :rule chain_m_resolution :premises (@p226 @p224 @p220) :args (@t156 @t141 (@list @t153 @t158)))
% 33.87/34.14  (step @p228 :rule aci_norm :args ((= (or @t159 @t21) @t160)))
% 33.87/34.14  (step @p229 :rule bool-impl-elim :args (@t22 @t21))
% 33.87/34.14  (step @p230 :rule trans :premises (@p229 @p228))
% 33.87/34.14  (step @p231 :rule refl :args (@t24))
% 33.87/34.14  (step @p232 :rule bool-implies-de-morgan :args (@t22 @t20))
% 33.87/34.14  (step @p233 :rule nary_cong :premises (@p232 @p231) :args ((or (not @t25) @t24)))
% 33.87/34.14  (step @p234 :rule bool-impl-elim :args (@t25 @t24))
% 33.87/34.14  (step @p235 :rule trans :premises (@p234 @p233))
% 33.87/34.14  (step @p236 :rule nary_cong :premises (@p235 @p230) :args (@t26))
% 33.87/34.14  (step @p237 :rule refl :args (@t161))
% 33.87/34.14  (step @p238 :rule nary_cong :premises (@p237 @p236) :args ((or @t161 @t26)))
% 33.87/34.14  (step @p239 :rule bool-impl-elim :args (@t27 @t26))
% 33.87/34.14  (step @p240 :rule trans :premises (@p239 @p238))
% 33.87/34.14  (step @p241 :rule cong :premises (@p240) :args (@t28))
% 33.87/34.14  (step @p242 :rule eq_resolve :premises (@p6 @p241))
% 33.87/34.14  (step @p243 :rule eq-symm :args (@t101 tptp.empty_set))
% 33.87/34.14  (step @p244 :rule refl :args (@t129))
% 33.87/34.14  (step @p245 :rule cong :premises (@p244 @p243) :args (@t162))
% 33.87/34.14  (step @p246 :rule eq-symm :args (@t117 tptp.empty_set))
% 33.87/34.14  (step @p247 :rule cong :premises (@p143) :args (@t163))
% 33.87/34.14  (step @p248 :rule nary_cong :premises (@p247 @p246 @p245) :args (@t165))
% 33.87/34.14  (step @p249 :rule refl :args (@t167))
% 33.87/34.14  (step @p250 :rule cong :premises (@p246) :args (@t168))
% 33.87/34.14  (step @p251 :rule nary_cong :premises (@p143 @p250) :args (@t169))
% 33.87/34.14  (step @p252 :rule nary_cong :premises (@p251 @p249) :args (@t170))
% 33.87/34.14  (step @p253 :rule nary_cong :premises (@p252 @p248) :args (@t171))
% 33.87/34.14  (step @p254 :rule nary_cong :premises (@p145 @p253) :args (@t172))
% 33.87/34.14  (step @p255 :rule refl :args (@t173))
% 33.87/34.14  (step @p256 :rule cong :premises (@p255 @p254) :args ((=> @t173 @t172)))
% 33.87/34.14  (assume-push @p308 @t173)
% 33.87/34.14  (step @p258 :rule instantiate :premises (@p242) :args (@t118))
% 33.87/34.14  (step-pop @p309 :rule scope :premises (@p258))
% 33.87/34.14  (step @p259 :rule process_scope :premises (@p309) :args (@t172))
% 33.87/34.14  (step @p261 :rule eq_resolve :premises (@p259 @p256))
% 33.87/34.14  (step @p262 :rule implies_elim :premises (@p261))
% 33.87/34.14  (step @p263 :rule chain_m_resolution :premises (@p262 @p242) :args (@t179 @t115 (@list @t173)))
% 33.87/34.14  (step @p264 :rule cnf_or_pos :args (@t179))
% 33.87/34.14  (step @p265 :rule reordering :premises (@p264) :args ((or @t128 @t178 (not @t179))))
% 33.87/34.14  (step @p266 :rule chain_m_resolution :premises (@p265 @p165 @p263) :args (@t178 @t141 (@list @t127 @t179)))
% 33.87/34.14  (step @p267 :rule cnf_and_pos :args (@t178 0))
% 33.87/34.14  (step @p268 :rule reordering :premises (@p267) :args ((or @t177 (not @t178))))
% 33.87/34.14  (step @p269 :rule chain_m_resolution :premises (@p268 @p266) :args (@t177 @t115 (@list @t178)))
% 33.87/34.14  (step @p270 :rule cnf_or_neg :args (@t131 4))
% 33.87/34.14  (step @p271 :rule chain_m_resolution :premises (@p270 @p158) :args (@t175 @t137 @t138))
% 33.87/34.14  (step @p272 :rule cnf_and_pos :args (@t176 0))
% 33.87/34.14  (step @p273 :rule reordering :premises (@p272) :args ((or @t124 @t180)))
% 33.87/34.14  (step @p274 :rule chain_m_resolution :premises (@p273 @p271) :args (@t180 @t137 (@list @t124)))
% 33.87/34.14  (step @p275 :rule cnf_or_pos :args (@t177))
% 33.87/34.14  (step @p276 :rule reordering :premises (@p275) :args ((or @t167 @t176 (not @t177))))
% 33.87/34.14  (step @p277 :rule chain_m_resolution :premises (@p276 @p274 @p269) :args (@t167 @t149 (@list @t176 @t177)))
% 33.87/34.14  (step @p278 :rule bool-double-not-elim :args (@t129))
% 33.87/34.14  (step @p279 :rule nary_cong :premises (@p160 @p278) :args ((or @t131 (not @t130))))
% 33.87/34.14  (step @p280 :rule cnf_or_neg :args (@t131 1))
% 33.87/34.14  (step @p281 :rule eq_resolve :premises (@p280 @p279))
% 33.87/34.14  (step @p282 :rule reordering :premises (@p281) :args ((or @t129 @t131)))
% 33.87/34.14  (step @p283 :rule chain_m_resolution :premises (@p282 @p158) :args (@t129 @t137 @t138))
% 33.87/34.14  (step @p284 :rule cnf_equiv_pos1 :args (@t167))
% 33.87/34.14  (step @p285 :rule reordering :premises (@p284) :args ((or @t130 @t166 (not @t167))))
% 33.87/34.14  (step @p286 :rule chain_m_resolution :premises (@p285 @p283 @p277) :args (@t166 @t141 (@list @t129 @t167)))
% 33.87/34.14  (step @p287 :rule trans :premises (@p286 @p227))
% 33.87/34.14  (step @p288 :rule refl :args (@t121))
% 33.87/34.14  (step @p289 :rule cong :premises (@p288 @p287) :args (@t125))
% 33.87/34.14  (step @p290 :rule bool-double-not-elim :args (@t125))
% 33.87/34.14  (step @p291 :rule nary_cong :premises (@p160 @p290) :args ((or @t131 (not @t126))))
% 33.87/34.14  (step @p292 :rule cnf_or_neg :args (@t131 3))
% 33.87/34.14  (step @p293 :rule eq_resolve :premises (@p292 @p291))
% 33.87/34.14  (step @p294 :rule reordering :premises (@p293) :args ((or @t125 @t131)))
% 33.87/34.14  (step @p295 :rule chain_m_resolution :premises (@p294 @p158) :args (@t125 @t137 @t138))
% 33.87/34.14  (step @p296 :rule true_intro :premises (@p295))
% 33.87/34.14  (step @p297 :rule symm :premises (@p296))
% 33.87/34.14  (step @p298 :rule trans :premises (@p297 @p289 @p216))
% 33.87/34.14  (step @p299 false :rule eq_resolve :premises (@p298 @p49))
% 33.87/34.14  )
% 33.87/34.14  % SZS output end Proof
% 33.87/34.14  % cvc5 exiting
%------------------------------------------------------------------------------