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cvc5---1.3.4.THM-Prf.s

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%------------------------------------------------------------------------------
% File     : cvc5---1.3.4
% Problem  : SEU750^2 : TPTP v9.2.1. Released v3.7.0.
% 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 08:53:01 AM UTC 2026

% Result   : Theorem 0.36s 0.60s
% Output   : Proof 0.36s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SEU750^2 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.14  % Command  : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.17/0.35  % Computer : n001.cluster.edu
% 0.17/0.35  % Model    : x86_64 x86_64
% 0.17/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.35  % Memory   : 8042.1875MB
% 0.17/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.17/0.35  % CPULimit : 300
% 0.17/0.35  % WCLimit  : 300
% 0.17/0.35  % DateTime : Tue Jun  2 17:51:20 EDT 2026
% 0.17/0.35  % CPUTime  : 
% 0.30/0.50  %----Proving TH0
% 0.36/0.60  --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s...
% 0.36/0.60  % SZS status Theorem
% 0.36/0.60  % SZS output start Proof
% 0.36/0.60  (
% 0.36/0.60  (declare-sort $$unsorted 0)
% 0.36/0.60  (declare-const tptp.binunionTIRcontra Bool)
% 0.36/0.60  (declare-const tptp.powerset (-> $$unsorted $$unsorted))
% 0.36/0.60  (declare-const tptp.binunion (-> $$unsorted $$unsorted $$unsorted))
% 0.36/0.60  (declare-const tptp.setminusER Bool)
% 0.36/0.60  (declare-const tptp.setminusI Bool)
% 0.36/0.60  (declare-const tptp.in (-> $$unsorted $$unsorted Bool))
% 0.36/0.60  (declare-const tptp.setminus (-> $$unsorted $$unsorted $$unsorted))
% 0.36/0.60  (define @t1 () (@var "B" $$unsorted))
% 0.36/0.60  (define @t2 () (@var "A" $$unsorted))
% 0.36/0.60  (define @t3 () (_ tptp.setminus @t2))
% 0.36/0.60  (define @t4 () (_ @t3 @t1))
% 0.36/0.60  (define @t5 () (@var "Xx" $$unsorted))
% 0.36/0.60  (define @t6 () (_ tptp.in @t5))
% 0.36/0.60  (define @t7 () (_ @t6 @t4))
% 0.36/0.60  (define @t8 () (_ @t6 @t1))
% 0.36/0.60  (define @t9 () (not @t8))
% 0.36/0.60  (define @t10 () (=> @t9 @t7))
% 0.36/0.60  (define @t11 () (_ @t6 @t2))
% 0.36/0.60  (define @t12 () (@list @t2 @t1 @t5))
% 0.36/0.60  (define @t13 () (forall @t12 (=> @t11 @t10)))
% 0.36/0.60  (define @t14 () (= tptp.setminusI @t13))
% 0.36/0.60  (define @t15 () (forall @t12 (=> @t7 @t9)))
% 0.36/0.60  (define @t16 () (= tptp.setminusER @t15))
% 0.36/0.60  (define @t17 () (@var "Y" $$unsorted))
% 0.36/0.60  (define @t18 () (_ @t6 @t17))
% 0.36/0.60  (define @t19 () (not @t18))
% 0.36/0.60  (define @t20 () (@var "X" $$unsorted))
% 0.36/0.60  (define @t21 () (_ (_ tptp.binunion @t20) @t17))
% 0.36/0.60  (define @t22 () (_ @t6 @t21))
% 0.36/0.60  (define @t23 () (not @t22))
% 0.36/0.60  (define @t24 () (=> @t23 @t19))
% 0.36/0.60  (define @t25 () (@list @t5))
% 0.36/0.60  (define @t26 () (forall @t25 (=> @t11 @t24)))
% 0.36/0.60  (define @t27 () (_ tptp.powerset @t2))
% 0.36/0.60  (define @t28 () (_ tptp.in @t17))
% 0.36/0.60  (define @t29 () (_ @t28 @t27))
% 0.36/0.60  (define @t30 () (=> @t29 @t26))
% 0.36/0.60  (define @t31 () (@list @t17))
% 0.36/0.60  (define @t32 () (forall @t31 @t30))
% 0.36/0.60  (define @t33 () (_ tptp.in @t20))
% 0.36/0.60  (define @t34 () (_ @t33 @t27))
% 0.36/0.60  (define @t35 () (=> @t34 @t32))
% 0.36/0.60  (define @t36 () (@list @t2 @t20))
% 0.36/0.60  (define @t37 () (forall @t36 @t35))
% 0.36/0.60  (define @t38 () (= tptp.binunionTIRcontra @t37))
% 0.36/0.60  (define @t39 () (_ @t3 @t17))
% 0.36/0.60  (define @t40 () (_ @t6 @t39))
% 0.36/0.60  (define @t41 () (_ @t3 @t21))
% 0.36/0.60  (define @t42 () (_ @t6 @t41))
% 0.36/0.60  (define @t43 () (=> @t42 @t40))
% 0.36/0.60  (define @t44 () (forall @t25 (=> @t11 @t43)))
% 0.36/0.60  (define @t45 () (=> @t29 @t44))
% 0.36/0.60  (define @t46 () (forall @t31 @t45))
% 0.36/0.60  (define @t47 () (=> @t34 @t46))
% 0.36/0.60  (define @t48 () (forall @t36 @t47))
% 0.36/0.60  (define @t49 () (=> tptp.binunionTIRcontra @t48))
% 0.36/0.60  (define @t50 () (=> tptp.setminusER @t49))
% 0.36/0.60  (define @t51 () (=> tptp.setminusI @t50))
% 0.36/0.60  (define @t52 () (not @t51))
% 0.36/0.60  (define @t53 () (@var "BOUND_VARIABLE_7600" $$unsorted))
% 0.36/0.60  (define @t54 () (@var "BOUND_VARIABLE_7602" $$unsorted))
% 0.36/0.60  (define @t55 () (tptp.in @t54 (tptp.setminus @t2 @t53)))
% 0.36/0.60  (define @t56 () (not (tptp.in @t54 (tptp.setminus @t2 (tptp.binunion @t20 @t53)))))
% 0.36/0.60  (define @t57 () (not (tptp.in @t54 @t2)))
% 0.36/0.60  (define @t58 () (tptp.powerset @t2))
% 0.36/0.60  (define @t59 () (not (tptp.in @t53 @t58)))
% 0.36/0.60  (define @t60 () (tptp.in @t20 @t58))
% 0.36/0.60  (define @t61 () (not @t60))
% 0.36/0.60  (define @t62 () (or @t61 @t59 @t57 @t56 @t55))
% 0.36/0.60  (define @t63 () (@list @t2 @t20 @t53 @t54))
% 0.36/0.60  (define @t64 () (forall @t63 @t62))
% 0.36/0.60  (define @t65 () (@var "BOUND_VARIABLE_7541" $$unsorted))
% 0.36/0.60  (define @t66 () (@var "BOUND_VARIABLE_7543" $$unsorted))
% 0.36/0.60  (define @t67 () (not (tptp.in @t66 @t65)))
% 0.36/0.60  (define @t68 () (tptp.in @t66 (tptp.binunion @t20 @t65)))
% 0.36/0.60  (define @t69 () (not (tptp.in @t66 @t2)))
% 0.36/0.60  (define @t70 () (not (tptp.in @t65 @t58)))
% 0.36/0.60  (define @t71 () (or @t61 @t70 @t69 @t68 @t67))
% 0.36/0.60  (define @t72 () (or @t70 @t69 @t68 @t67))
% 0.36/0.60  (define @t73 () (or @t61 @t72))
% 0.36/0.60  (define @t74 () (@list @t2 @t20 @t65 @t66))
% 0.36/0.60  (define @t75 () (forall @t74 @t73))
% 0.36/0.60  (define @t76 () (@list @t65 @t66))
% 0.36/0.60  (define @t77 () (forall @t76 @t73))
% 0.36/0.60  (define @t78 () (forall @t76 @t72))
% 0.36/0.60  (define @t79 () (@var "BOUND_VARIABLE_7518" $$unsorted))
% 0.36/0.60  (define @t80 () (or @t61 @t78))
% 0.36/0.60  (define @t81 () (not (tptp.in @t79 @t17)))
% 0.36/0.60  (define @t82 () (tptp.binunion @t20 @t17))
% 0.36/0.60  (define @t83 () (tptp.in @t79 @t82))
% 0.36/0.60  (define @t84 () (not (tptp.in @t79 @t2)))
% 0.36/0.60  (define @t85 () (tptp.in @t17 @t58))
% 0.36/0.60  (define @t86 () (not @t85))
% 0.36/0.60  (define @t87 () (or @t86 @t84 @t83 @t81))
% 0.36/0.60  (define @t88 () (@list @t17 @t79))
% 0.36/0.60  (define @t89 () (forall @t88 @t87))
% 0.36/0.60  (define @t90 () (not @t34))
% 0.36/0.60  (define @t91 () (or @t90 @t89))
% 0.36/0.60  (define @t92 () (or @t84 @t83 @t81))
% 0.36/0.60  (define @t93 () (or @t86 @t92))
% 0.36/0.60  (define @t94 () (forall @t88 @t93))
% 0.36/0.60  (define @t95 () (@list @t79))
% 0.36/0.60  (define @t96 () (forall @t95 @t93))
% 0.36/0.60  (define @t97 () (forall @t95 @t92))
% 0.36/0.60  (define @t98 () (@list @t5))
% 0.36/0.60  (define @t99 () (or @t86 @t97))
% 0.36/0.60  (define @t100 () (tptp.in @t5 @t17))
% 0.36/0.60  (define @t101 () (tptp.in @t5 @t82))
% 0.36/0.60  (define @t102 () (tptp.in @t5 @t2))
% 0.36/0.60  (define @t103 () (not @t102))
% 0.36/0.60  (define @t104 () (forall @t25 (or @t103 @t101 (not @t100))))
% 0.36/0.60  (define @t105 () (not @t29))
% 0.36/0.60  (define @t106 () (or @t105 @t104))
% 0.36/0.60  (define @t107 () (not @t11))
% 0.36/0.60  (define @t108 () (or @t107 @t22 @t19))
% 0.36/0.60  (define @t109 () (=> tptp.binunionTIRcontra @t64))
% 0.36/0.60  (define @t110 () (tptp.in @t5 @t1))
% 0.36/0.60  (define @t111 () (tptp.setminus @t2 @t1))
% 0.36/0.60  (define @t112 () (tptp.in @t5 @t111))
% 0.36/0.60  (define @t113 () (not @t7))
% 0.36/0.60  (define @t114 () (or @t113 @t9))
% 0.36/0.60  (define @t115 () (=> tptp.setminusER @t109))
% 0.36/0.60  (define @t116 () (or @t107 @t8 @t7))
% 0.36/0.60  (define @t117 () (=> tptp.setminusI @t115))
% 0.36/0.60  (define @t118 () (or @t59 @t57 @t56 @t55))
% 0.36/0.60  (define @t119 () (or @t61 @t118))
% 0.36/0.60  (define @t120 () (forall @t63 @t119))
% 0.36/0.60  (define @t121 () (@list @t53 @t54))
% 0.36/0.60  (define @t122 () (forall @t121 @t119))
% 0.36/0.60  (define @t123 () (forall @t121 @t118))
% 0.36/0.60  (define @t124 () (@var "BOUND_VARIABLE_7581" $$unsorted))
% 0.36/0.60  (define @t125 () (or @t61 @t123))
% 0.36/0.60  (define @t126 () (tptp.setminus @t2 @t17))
% 0.36/0.60  (define @t127 () (tptp.in @t124 @t126))
% 0.36/0.60  (define @t128 () (tptp.setminus @t2 @t82))
% 0.36/0.60  (define @t129 () (not (tptp.in @t124 @t128)))
% 0.36/0.60  (define @t130 () (not (tptp.in @t124 @t2)))
% 0.36/0.60  (define @t131 () (or @t86 @t130 @t129 @t127))
% 0.36/0.60  (define @t132 () (@list @t17 @t124))
% 0.36/0.60  (define @t133 () (forall @t132 @t131))
% 0.36/0.60  (define @t134 () (or @t90 @t133))
% 0.36/0.60  (define @t135 () (or @t130 @t129 @t127))
% 0.36/0.60  (define @t136 () (or @t86 @t135))
% 0.36/0.60  (define @t137 () (forall @t132 @t136))
% 0.36/0.60  (define @t138 () (@list @t124))
% 0.36/0.60  (define @t139 () (forall @t138 @t136))
% 0.36/0.60  (define @t140 () (forall @t138 @t135))
% 0.36/0.60  (define @t141 () (or @t86 @t140))
% 0.36/0.60  (define @t142 () (tptp.in @t5 @t126))
% 0.36/0.60  (define @t143 () (tptp.in @t5 @t128))
% 0.36/0.60  (define @t144 () (forall @t25 (or @t103 (not @t143) @t142)))
% 0.36/0.60  (define @t145 () (or @t105 @t144))
% 0.36/0.60  (define @t146 () (not @t42))
% 0.36/0.60  (define @t147 () (or @t107 @t146 @t40))
% 0.36/0.60  (define @t148 () (@quantifiers_skolemize @t64 3))
% 0.36/0.60  (define @t149 () (@quantifiers_skolemize @t64 2))
% 0.36/0.60  (define @t150 () (@quantifiers_skolemize @t64 0))
% 0.36/0.60  (define @t151 () (tptp.in @t148 (tptp.setminus @t150 @t149)))
% 0.36/0.60  (define @t152 () (@quantifiers_skolemize @t64 1))
% 0.36/0.60  (define @t153 () (tptp.binunion @t152 @t149))
% 0.36/0.60  (define @t154 () (tptp.in @t148 (tptp.setminus @t150 @t153)))
% 0.36/0.60  (define @t155 () (not @t154))
% 0.36/0.60  (define @t156 () (tptp.in @t148 @t150))
% 0.36/0.60  (define @t157 () (not @t156))
% 0.36/0.60  (define @t158 () (tptp.powerset @t150))
% 0.36/0.60  (define @t159 () (tptp.in @t149 @t158))
% 0.36/0.60  (define @t160 () (not @t159))
% 0.36/0.60  (define @t161 () (tptp.in @t152 @t158))
% 0.36/0.60  (define @t162 () (not @t161))
% 0.36/0.60  (define @t163 () (or @t162 @t160 @t157 @t155 @t151))
% 0.36/0.60  (define @t164 () (@list true))
% 0.36/0.60  (define @t165 () (@list @t163))
% 0.36/0.60  (define @t166 () (tptp.in @t148 @t149))
% 0.36/0.60  (define @t167 () (or @t157 @t166 @t151))
% 0.36/0.60  (define @t168 () (tptp.in @t148 @t153))
% 0.36/0.60  (define @t169 () (not @t168))
% 0.36/0.60  (define @t170 () (or @t155 @t169))
% 0.36/0.60  (define @t171 () (not @t166))
% 0.36/0.60  (define @t172 () (or @t162 @t160 @t157 @t168 @t171))
% 0.36/0.60  (define @t173 () (not @t172))
% 0.36/0.60  (define @t174 () (forall @t74 @t71))
% 0.36/0.60  (assume @p1 @t14)
% 0.36/0.60  (assume @p2 @t16)
% 0.36/0.60  (assume @p3 @t38)
% 0.36/0.60  (assume @p4 @t52)
% 0.36/0.60  (assume @p5 true)
% 0.36/0.60  (step @p6 :rule refl :args (@t64))
% 0.36/0.60  (step @p7 :rule aci_norm :args ((= @t73 @t71)))
% 0.36/0.60  (step @p8 :rule cong :premises (@p7) :args (@t75))
% 0.36/0.60  (step @p9 :rule quant-merge-prenex :args ((= (forall @t36 @t77) @t75)))
% 0.36/0.60  (step @p10 :rule alpha_equiv :args (@t78 (@list @t65 @t66) (@list @t17 @t79)))
% 0.36/0.60  (step @p11 :rule refl :args (@t61))
% 0.36/0.60  (step @p12 :rule nary_cong :premises (@p11 @p10) :args (@t80))
% 0.36/0.60  (step @p13 :rule quant-miniscope-or :args ((= @t77 @t80)))
% 0.36/0.60  (step @p14 :rule trans :premises (@p13 @p12))
% 0.36/0.60  (step @p15 :rule symm :premises (@p14))
% 0.36/0.60  (step @p16 :rule cong :premises (@p15) :args ((forall @t36 (or @t61 @t89))))
% 0.36/0.60  (step @p17 :rule trans :premises (@p16 @p9))
% 0.36/0.60  (step @p18 :rule trans :premises (@p17 @p8))
% 0.36/0.60  (step @p19 :rule refl :args (@t89))
% 0.36/0.60  (step @p20 :rule refl :args ((tptp.in @t20 @t27)))
% 0.36/0.60  (step @p21 :rule refl :args (@t58))
% 0.36/0.60  (step @p22 :rule refl :args (@t20))
% 0.36/0.60  (step @p23 :rule cong :premises (@p22 @p21) :args (@t60))
% 0.36/0.60  (step @p24 :rule trans :premises (@p23 @p20))
% 0.36/0.60  (step @p25 :rule refl :args (@t33))
% 0.36/0.60  (step @p26 :rule ho_cong :premises (@p25 @p21))
% 0.36/0.60  (step @p27 :rule cong :premises (@p26 @p24) :args ((= (_ @t33 @t58) @t60)))
% 0.36/0.60  (step @p28 :rule symm :premises (@p27))
% 0.36/0.60  (step @p29 :rule refl :args (@t34))
% 0.36/0.60  (step @p30 :rule eq_resolve :premises (@p29 @p28))
% 0.36/0.60  (step @p31 :rule refl :args (@t27))
% 0.36/0.60  (step @p32 :rule cong :premises (@p31 @p21) :args ((= @t27 @t58)))
% 0.36/0.60  (step @p33 :rule symm :premises (@p32))
% 0.36/0.60  (step @p34 :rule eq_resolve :premises (@p31 @p33))
% 0.36/0.60  (step @p35 :rule ho_cong :premises (@p25 @p34))
% 0.36/0.60  (step @p36 :rule trans :premises (@p35 @p30))
% 0.36/0.60  (step @p37 :rule cong :premises (@p36) :args (@t90))
% 0.36/0.60  (step @p38 :rule nary_cong :premises (@p37 @p19) :args (@t91))
% 0.36/0.60  (step @p39 :rule cong :premises (@p38) :args ((forall @t36 @t91)))
% 0.36/0.60  (step @p40 :rule trans :premises (@p39 @p18))
% 0.36/0.60  (step @p41 :rule bool-impl-elim :args (@t34 @t89))
% 0.36/0.60  (step @p42 :rule cong :premises (@p41) :args ((forall @t36 (=> @t34 @t89))))
% 0.36/0.60  (step @p43 :rule trans :premises (@p42 @p40))
% 0.36/0.60  (step @p44 :rule aci_norm :args ((= @t93 @t87)))
% 0.36/0.60  (step @p45 :rule cong :premises (@p44) :args (@t94))
% 0.36/0.60  (step @p46 :rule quant-merge-prenex :args ((= (forall @t31 @t96) @t94)))
% 0.36/0.60  (step @p47 :rule alpha_equiv :args (@t97 (@list @t79) @t98))
% 0.36/0.60  (step @p48 :rule refl :args (@t86))
% 0.36/0.60  (step @p49 :rule nary_cong :premises (@p48 @p47) :args (@t99))
% 0.36/0.60  (step @p50 :rule quant-miniscope-or :args ((= @t96 @t99)))
% 0.36/0.60  (step @p51 :rule trans :premises (@p50 @p49))
% 0.36/0.60  (step @p52 :rule symm :premises (@p51))
% 0.36/0.60  (step @p53 :rule cong :premises (@p52) :args ((forall @t31 (or @t86 @t104))))
% 0.36/0.60  (step @p54 :rule trans :premises (@p53 @p46))
% 0.36/0.60  (step @p55 :rule trans :premises (@p54 @p45))
% 0.36/0.60  (step @p56 :rule refl :args (@t104))
% 0.36/0.60  (step @p57 :rule refl :args ((tptp.in @t17 @t27)))
% 0.36/0.60  (step @p58 :rule refl :args (@t17))
% 0.36/0.60  (step @p59 :rule cong :premises (@p58 @p21) :args (@t85))
% 0.36/0.60  (step @p60 :rule trans :premises (@p59 @p57))
% 0.36/0.60  (step @p61 :rule refl :args (@t28))
% 0.36/0.60  (step @p62 :rule ho_cong :premises (@p61 @p21))
% 0.36/0.60  (step @p63 :rule cong :premises (@p62 @p60) :args ((= (_ @t28 @t58) @t85)))
% 0.36/0.60  (step @p64 :rule symm :premises (@p63))
% 0.36/0.60  (step @p65 :rule refl :args (@t29))
% 0.36/0.60  (step @p66 :rule eq_resolve :premises (@p65 @p64))
% 0.36/0.60  (step @p67 :rule ho_cong :premises (@p61 @p34))
% 0.36/0.60  (step @p68 :rule trans :premises (@p67 @p66))
% 0.36/0.60  (step @p69 :rule cong :premises (@p68) :args (@t105))
% 0.36/0.60  (step @p70 :rule nary_cong :premises (@p69 @p56) :args (@t106))
% 0.36/0.60  (step @p71 :rule cong :premises (@p70) :args ((forall @t31 @t106)))
% 0.36/0.60  (step @p72 :rule trans :premises (@p71 @p55))
% 0.36/0.60  (step @p73 :rule bool-impl-elim :args (@t29 @t104))
% 0.36/0.60  (step @p74 :rule cong :premises (@p73) :args ((forall @t31 (=> @t29 @t104))))
% 0.36/0.60  (step @p75 :rule trans :premises (@p74 @p72))
% 0.36/0.60  (step @p76 :rule refl :args (@t100))
% 0.36/0.60  (step @p77 :rule refl :args (@t18))
% 0.36/0.60  (step @p78 :rule cong :premises (@p77 @p76) :args ((= @t18 @t100)))
% 0.36/0.60  (step @p79 :rule symm :premises (@p78))
% 0.36/0.60  (step @p80 :rule eq_resolve :premises (@p77 @p79))
% 0.36/0.60  (step @p81 :rule cong :premises (@p80) :args (@t19))
% 0.36/0.60  (step @p82 :rule refl :args ((tptp.in @t5 @t21)))
% 0.36/0.60  (step @p83 :rule refl :args (@t82))
% 0.36/0.60  (step @p84 :rule refl :args (@t5))
% 0.36/0.60  (step @p85 :rule cong :premises (@p84 @p83) :args (@t101))
% 0.36/0.60  (step @p86 :rule trans :premises (@p85 @p82))
% 0.36/0.60  (step @p87 :rule refl :args (@t6))
% 0.36/0.60  (step @p88 :rule ho_cong :premises (@p87 @p83))
% 0.36/0.60  (step @p89 :rule cong :premises (@p88 @p86) :args ((= (_ @t6 @t82) @t101)))
% 0.36/0.60  (step @p90 :rule symm :premises (@p89))
% 0.36/0.60  (step @p91 :rule refl :args (@t22))
% 0.36/0.60  (step @p92 :rule eq_resolve :premises (@p91 @p90))
% 0.36/0.60  (step @p93 :rule refl :args (@t21))
% 0.36/0.60  (step @p94 :rule cong :premises (@p93 @p83) :args ((= @t21 @t82)))
% 0.36/0.60  (step @p95 :rule symm :premises (@p94))
% 0.36/0.60  (step @p96 :rule eq_resolve :premises (@p93 @p95))
% 0.36/0.60  (step @p97 :rule ho_cong :premises (@p87 @p96))
% 0.36/0.60  (step @p98 :rule trans :premises (@p97 @p92))
% 0.36/0.60  (step @p99 :rule refl :args (@t102))
% 0.36/0.60  (step @p100 :rule refl :args (@t11))
% 0.36/0.60  (step @p101 :rule cong :premises (@p100 @p99) :args ((= @t11 @t102)))
% 0.36/0.60  (step @p102 :rule symm :premises (@p101))
% 0.36/0.60  (step @p103 :rule eq_resolve :premises (@p100 @p102))
% 0.36/0.60  (step @p104 :rule cong :premises (@p103) :args (@t107))
% 0.36/0.60  (step @p105 :rule nary_cong :premises (@p104 @p98 @p81) :args (@t108))
% 0.36/0.60  (step @p106 :rule cong :premises (@p105) :args ((forall @t25 @t108)))
% 0.36/0.60  (step @p107 :rule aci_norm :args ((= (or @t107 (or @t22 @t19)) @t108)))
% 0.36/0.60  (step @p108 :rule refl :args (@t19))
% 0.36/0.60  (step @p109 :rule bool-double-not-elim :args (@t22))
% 0.36/0.60  (step @p110 :rule nary_cong :premises (@p109 @p108) :args ((or (not @t23) @t19)))
% 0.36/0.60  (step @p111 :rule bool-impl-elim :args (@t23 @t19))
% 0.36/0.60  (step @p112 :rule trans :premises (@p111 @p110))
% 0.36/0.60  (step @p113 :rule refl :args (@t107))
% 0.36/0.60  (step @p114 :rule nary_cong :premises (@p113 @p112) :args ((or @t107 @t24)))
% 0.36/0.60  (step @p115 :rule trans :premises (@p114 @p107))
% 0.36/0.60  (step @p116 :rule bool-impl-elim :args (@t11 @t24))
% 0.36/0.60  (step @p117 :rule trans :premises (@p116 @p115))
% 0.36/0.60  (step @p118 :rule cong :premises (@p117) :args (@t26))
% 0.36/0.60  (step @p119 :rule trans :premises (@p118 @p106))
% 0.36/0.60  (step @p120 :rule refl :args (@t29))
% 0.36/0.60  (step @p121 :rule cong :premises (@p120 @p119) :args (@t30))
% 0.36/0.60  (step @p122 :rule cong :premises (@p121) :args (@t32))
% 0.36/0.60  (step @p123 :rule trans :premises (@p122 @p75))
% 0.36/0.60  (step @p124 :rule refl :args (@t34))
% 0.36/0.60  (step @p125 :rule cong :premises (@p124 @p123) :args (@t35))
% 0.36/0.60  (step @p126 :rule cong :premises (@p125) :args (@t37))
% 0.36/0.60  (step @p127 :rule trans :premises (@p126 @p43))
% 0.36/0.60  (step @p128 :rule refl :args (tptp.binunionTIRcontra))
% 0.36/0.60  (step @p129 :rule cong :premises (@p128 @p127) :args (@t38))
% 0.36/0.60  (step @p130 :rule eq_resolve :premises (@p3 @p129))
% 0.36/0.60  (step @p131 :rule cong :premises (@p130 @p6) :args (@t109))
% 0.36/0.60  (step @p132 :rule refl :args (@t110))
% 0.36/0.60  (step @p133 :rule refl :args (@t8))
% 0.36/0.60  (step @p134 :rule cong :premises (@p133 @p132) :args ((= @t8 @t110)))
% 0.36/0.60  (step @p135 :rule symm :premises (@p134))
% 0.36/0.60  (step @p136 :rule eq_resolve :premises (@p133 @p135))
% 0.36/0.60  (step @p137 :rule cong :premises (@p136) :args (@t9))
% 0.36/0.60  (step @p138 :rule refl :args ((tptp.in @t5 @t4)))
% 0.36/0.60  (step @p139 :rule refl :args (@t111))
% 0.36/0.60  (step @p140 :rule cong :premises (@p84 @p139) :args (@t112))
% 0.36/0.60  (step @p141 :rule trans :premises (@p140 @p138))
% 0.36/0.60  (step @p142 :rule ho_cong :premises (@p87 @p139))
% 0.36/0.60  (step @p143 :rule cong :premises (@p142 @p141) :args ((= (_ @t6 @t111) @t112)))
% 0.36/0.60  (step @p144 :rule symm :premises (@p143))
% 0.36/0.60  (step @p145 :rule refl :args (@t7))
% 0.36/0.60  (step @p146 :rule eq_resolve :premises (@p145 @p144))
% 0.36/0.60  (step @p147 :rule refl :args (@t4))
% 0.36/0.60  (step @p148 :rule cong :premises (@p147 @p139) :args ((= @t4 @t111)))
% 0.36/0.60  (step @p149 :rule symm :premises (@p148))
% 0.36/0.60  (step @p150 :rule eq_resolve :premises (@p147 @p149))
% 0.36/0.60  (step @p151 :rule ho_cong :premises (@p87 @p150))
% 0.36/0.60  (step @p152 :rule trans :premises (@p151 @p146))
% 0.36/0.60  (step @p153 :rule cong :premises (@p152) :args (@t113))
% 0.36/0.60  (step @p154 :rule nary_cong :premises (@p153 @p137) :args (@t114))
% 0.36/0.60  (step @p155 :rule cong :premises (@p154) :args ((forall @t12 @t114)))
% 0.36/0.60  (step @p156 :rule bool-impl-elim :args (@t7 @t9))
% 0.36/0.60  (step @p157 :rule cong :premises (@p156) :args (@t15))
% 0.36/0.60  (step @p158 :rule trans :premises (@p157 @p155))
% 0.36/0.60  (step @p159 :rule refl :args (tptp.setminusER))
% 0.36/0.60  (step @p160 :rule cong :premises (@p159 @p158) :args (@t16))
% 0.36/0.60  (step @p161 :rule eq_resolve :premises (@p2 @p160))
% 0.36/0.60  (step @p162 :rule cong :premises (@p161 @p131) :args (@t115))
% 0.36/0.60  (step @p163 :rule nary_cong :premises (@p104 @p136 @p152) :args (@t116))
% 0.36/0.60  (step @p164 :rule cong :premises (@p163) :args ((forall @t12 @t116)))
% 0.36/0.60  (step @p165 :rule aci_norm :args ((= (or @t107 (or @t8 @t7)) @t116)))
% 0.36/0.60  (step @p166 :rule bool-double-not-elim :args (@t8))
% 0.36/0.60  (step @p167 :rule nary_cong :premises (@p166 @p145) :args ((or (not @t9) @t7)))
% 0.36/0.60  (step @p168 :rule bool-impl-elim :args (@t9 @t7))
% 0.36/0.60  (step @p169 :rule trans :premises (@p168 @p167))
% 0.36/0.60  (step @p170 :rule nary_cong :premises (@p113 @p169) :args ((or @t107 @t10)))
% 0.36/0.60  (step @p171 :rule trans :premises (@p170 @p165))
% 0.36/0.60  (step @p172 :rule bool-impl-elim :args (@t11 @t10))
% 0.36/0.60  (step @p173 :rule trans :premises (@p172 @p171))
% 0.36/0.60  (step @p174 :rule cong :premises (@p173) :args (@t13))
% 0.36/0.60  (step @p175 :rule trans :premises (@p174 @p164))
% 0.36/0.60  (step @p176 :rule refl :args (tptp.setminusI))
% 0.36/0.60  (step @p177 :rule cong :premises (@p176 @p175) :args (@t14))
% 0.36/0.60  (step @p178 :rule eq_resolve :premises (@p1 @p177))
% 0.36/0.60  (step @p179 :rule cong :premises (@p178 @p162) :args (@t117))
% 0.36/0.60  (step @p180 :rule cong :premises (@p179) :args ((not @t117)))
% 0.36/0.60  (step @p181 :rule aci_norm :args ((= @t119 @t62)))
% 0.36/0.60  (step @p182 :rule cong :premises (@p181) :args (@t120))
% 0.36/0.60  (step @p183 :rule quant-merge-prenex :args ((= (forall @t36 @t122) @t120)))
% 0.36/0.60  (step @p184 :rule alpha_equiv :args (@t123 (@list @t53 @t54) (@list @t17 @t124)))
% 0.36/0.60  (step @p185 :rule nary_cong :premises (@p11 @p184) :args (@t125))
% 0.36/0.60  (step @p186 :rule quant-miniscope-or :args ((= @t122 @t125)))
% 0.36/0.60  (step @p187 :rule trans :premises (@p186 @p185))
% 0.36/0.60  (step @p188 :rule symm :premises (@p187))
% 0.36/0.60  (step @p189 :rule cong :premises (@p188) :args ((forall @t36 (or @t61 @t133))))
% 0.36/0.60  (step @p190 :rule trans :premises (@p189 @p183))
% 0.36/0.60  (step @p191 :rule trans :premises (@p190 @p182))
% 0.36/0.60  (step @p192 :rule refl :args (@t133))
% 0.36/0.60  (step @p193 :rule nary_cong :premises (@p37 @p192) :args (@t134))
% 0.36/0.60  (step @p194 :rule cong :premises (@p193) :args ((forall @t36 @t134)))
% 0.36/0.60  (step @p195 :rule trans :premises (@p194 @p191))
% 0.36/0.60  (step @p196 :rule bool-impl-elim :args (@t34 @t133))
% 0.36/0.60  (step @p197 :rule cong :premises (@p196) :args ((forall @t36 (=> @t34 @t133))))
% 0.36/0.60  (step @p198 :rule trans :premises (@p197 @p195))
% 0.36/0.60  (step @p199 :rule aci_norm :args ((= @t136 @t131)))
% 0.36/0.60  (step @p200 :rule cong :premises (@p199) :args (@t137))
% 0.36/0.60  (step @p201 :rule quant-merge-prenex :args ((= (forall @t31 @t139) @t137)))
% 0.36/0.60  (step @p202 :rule alpha_equiv :args (@t140 (@list @t124) @t98))
% 0.36/0.60  (step @p203 :rule nary_cong :premises (@p48 @p202) :args (@t141))
% 0.36/0.60  (step @p204 :rule quant-miniscope-or :args ((= @t139 @t141)))
% 0.36/0.60  (step @p205 :rule trans :premises (@p204 @p203))
% 0.36/0.60  (step @p206 :rule symm :premises (@p205))
% 0.36/0.60  (step @p207 :rule cong :premises (@p206) :args ((forall @t31 (or @t86 @t144))))
% 0.36/0.60  (step @p208 :rule trans :premises (@p207 @p201))
% 0.36/0.60  (step @p209 :rule trans :premises (@p208 @p200))
% 0.36/0.60  (step @p210 :rule refl :args (@t144))
% 0.36/0.60  (step @p211 :rule nary_cong :premises (@p69 @p210) :args (@t145))
% 0.36/0.60  (step @p212 :rule cong :premises (@p211) :args ((forall @t31 @t145)))
% 0.36/0.60  (step @p213 :rule trans :premises (@p212 @p209))
% 0.36/0.60  (step @p214 :rule bool-impl-elim :args (@t29 @t144))
% 0.36/0.60  (step @p215 :rule cong :premises (@p214) :args ((forall @t31 (=> @t29 @t144))))
% 0.36/0.60  (step @p216 :rule trans :premises (@p215 @p213))
% 0.36/0.60  (step @p217 :rule refl :args ((tptp.in @t5 @t39)))
% 0.36/0.60  (step @p218 :rule refl :args (@t126))
% 0.36/0.60  (step @p219 :rule cong :premises (@p84 @p218) :args (@t142))
% 0.36/0.60  (step @p220 :rule trans :premises (@p219 @p217))
% 0.36/0.60  (step @p221 :rule ho_cong :premises (@p87 @p218))
% 0.36/0.60  (step @p222 :rule cong :premises (@p221 @p220) :args ((= (_ @t6 @t126) @t142)))
% 0.36/0.60  (step @p223 :rule symm :premises (@p222))
% 0.36/0.60  (step @p224 :rule refl :args (@t40))
% 0.36/0.60  (step @p225 :rule eq_resolve :premises (@p224 @p223))
% 0.36/0.60  (step @p226 :rule refl :args (@t39))
% 0.36/0.60  (step @p227 :rule cong :premises (@p226 @p218) :args ((= @t39 @t126)))
% 0.36/0.60  (step @p228 :rule symm :premises (@p227))
% 0.36/0.60  (step @p229 :rule eq_resolve :premises (@p226 @p228))
% 0.36/0.60  (step @p230 :rule ho_cong :premises (@p87 @p229))
% 0.36/0.60  (step @p231 :rule trans :premises (@p230 @p225))
% 0.36/0.60  (step @p232 :rule refl :args ((tptp.in @t5 @t41)))
% 0.36/0.60  (step @p233 :rule refl :args ((tptp.setminus @t2 @t21)))
% 0.36/0.60  (step @p234 :rule refl :args (@t2))
% 0.36/0.60  (step @p235 :rule cong :premises (@p234 @p83) :args (@t128))
% 0.36/0.60  (step @p236 :rule trans :premises (@p235 @p233))
% 0.36/0.60  (step @p237 :rule cong :premises (@p84 @p236) :args (@t143))
% 0.36/0.60  (step @p238 :rule trans :premises (@p237 @p232))
% 0.36/0.60  (step @p239 :rule ho_cong :premises (@p87 @p236))
% 0.36/0.60  (step @p240 :rule cong :premises (@p239 @p238) :args ((= (_ @t6 @t128) @t143)))
% 0.36/0.60  (step @p241 :rule symm :premises (@p240))
% 0.36/0.60  (step @p242 :rule refl :args (@t42))
% 0.36/0.60  (step @p243 :rule eq_resolve :premises (@p242 @p241))
% 0.36/0.60  (step @p244 :rule refl :args (@t3))
% 0.36/0.60  (step @p245 :rule ho_cong :premises (@p244 @p83))
% 0.36/0.60  (step @p246 :rule cong :premises (@p245 @p236) :args ((= (_ @t3 @t82) @t128)))
% 0.36/0.60  (step @p247 :rule symm :premises (@p246))
% 0.36/0.60  (step @p248 :rule refl :args (@t41))
% 0.36/0.60  (step @p249 :rule eq_resolve :premises (@p248 @p247))
% 0.36/0.60  (step @p250 :rule ho_cong :premises (@p244 @p96))
% 0.36/0.60  (step @p251 :rule trans :premises (@p250 @p249))
% 0.36/0.60  (step @p252 :rule ho_cong :premises (@p87 @p251))
% 0.36/0.60  (step @p253 :rule trans :premises (@p252 @p243))
% 0.36/0.60  (step @p254 :rule cong :premises (@p253) :args (@t146))
% 0.36/0.60  (step @p255 :rule nary_cong :premises (@p104 @p254 @p231) :args (@t147))
% 0.36/0.60  (step @p256 :rule cong :premises (@p255) :args ((forall @t25 @t147)))
% 0.36/0.60  (step @p257 :rule aci_norm :args ((= (or @t107 (or @t146 @t40)) @t147)))
% 0.36/0.60  (step @p258 :rule bool-impl-elim :args (@t42 @t40))
% 0.36/0.60  (step @p259 :rule nary_cong :premises (@p113 @p258) :args ((or @t107 @t43)))
% 0.36/0.60  (step @p260 :rule trans :premises (@p259 @p257))
% 0.36/0.60  (step @p261 :rule bool-impl-elim :args (@t11 @t43))
% 0.36/0.60  (step @p262 :rule trans :premises (@p261 @p260))
% 0.36/0.60  (step @p263 :rule cong :premises (@p262) :args (@t44))
% 0.36/0.60  (step @p264 :rule trans :premises (@p263 @p256))
% 0.36/0.60  (step @p265 :rule cong :premises (@p120 @p264) :args (@t45))
% 0.36/0.60  (step @p266 :rule cong :premises (@p265) :args (@t46))
% 0.36/0.60  (step @p267 :rule trans :premises (@p266 @p216))
% 0.36/0.60  (step @p268 :rule cong :premises (@p124 @p267) :args (@t47))
% 0.36/0.60  (step @p269 :rule cong :premises (@p268) :args (@t48))
% 0.36/0.60  (step @p270 :rule trans :premises (@p269 @p198))
% 0.36/0.60  (step @p271 :rule cong :premises (@p128 @p270) :args (@t49))
% 0.36/0.60  (step @p272 :rule cong :premises (@p159 @p271) :args (@t50))
% 0.36/0.60  (step @p273 :rule cong :premises (@p176 @p272) :args (@t51))
% 0.36/0.60  (step @p274 :rule cong :premises (@p273) :args (@t52))
% 0.36/0.60  (step @p275 :rule trans :premises (@p274 @p180))
% 0.36/0.60  (step @p276 :rule eq_resolve :premises (@p4 @p275))
% 0.36/0.60  (step @p277 :rule not_implies_elim2 :premises (@p276))
% 0.36/0.60  (step @p278 :rule not_implies_elim2 :premises (@p277))
% 0.36/0.60  (step @p279 :rule not_implies_elim1 :premises (@p278))
% 0.36/0.60  (step @p280 :rule not_implies_elim1 :premises (@p276))
% 0.36/0.60  (step @p281 :rule instantiate :premises (@p280) :args ((@list @t150 @t149 @t148)))
% 0.36/0.60  (step @p282 :rule not_implies_elim2 :premises (@p278))
% 0.36/0.60  (step @p283 :rule skolemize :premises (@p282))
% 0.36/0.60  (step @p284 :rule cnf_or_neg :args (@t163 4))
% 0.36/0.60  (step @p285 :rule chain_m_resolution :premises (@p284 @p283) :args ((not @t151) @t164 @t165))
% 0.36/0.60  (step @p286 :rule bool-double-not-elim :args (@t156))
% 0.36/0.60  (step @p287 :rule refl :args (@t163))
% 0.36/0.60  (step @p288 :rule nary_cong :premises (@p287 @p286) :args ((or @t163 (not @t157))))
% 0.36/0.60  (step @p289 :rule cnf_or_neg :args (@t163 2))
% 0.36/0.60  (step @p290 :rule eq_resolve :premises (@p289 @p288))
% 0.36/0.60  (step @p291 :rule reordering :premises (@p290) :args ((or @t156 @t163)))
% 0.36/0.60  (step @p292 :rule chain_m_resolution :premises (@p291 @p283) :args (@t156 @t164 @t165))
% 0.36/0.60  (step @p293 :rule cnf_or_pos :args (@t167))
% 0.36/0.60  (step @p294 :rule reordering :premises (@p293) :args ((or @t157 @t151 @t166 (not @t167))))
% 0.36/0.60  (step @p295 :rule chain_m_resolution :premises (@p294 @p292 @p285 @p281) :args (@t166 (@list false true false) (@list @t156 @t151 @t167)))
% 0.36/0.60  (step @p296 :rule not_implies_elim1 :premises (@p277))
% 0.36/0.60  (step @p297 :rule instantiate :premises (@p296) :args ((@list @t150 @t153 @t148)))
% 0.36/0.60  (step @p298 :rule bool-double-not-elim :args (@t154))
% 0.36/0.60  (step @p299 :rule nary_cong :premises (@p287 @p298) :args ((or @t163 (not @t155))))
% 0.36/0.60  (step @p300 :rule cnf_or_neg :args (@t163 3))
% 0.36/0.60  (step @p301 :rule eq_resolve :premises (@p300 @p299))
% 0.36/0.60  (step @p302 :rule reordering :premises (@p301) :args ((or @t154 @t163)))
% 0.36/0.60  (step @p303 :rule chain_m_resolution :premises (@p302 @p283) :args (@t154 @t164 @t165))
% 0.36/0.60  (step @p304 :rule cnf_or_pos :args (@t170))
% 0.36/0.60  (step @p305 :rule reordering :premises (@p304) :args ((or @t155 @t169 (not @t170))))
% 0.36/0.60  (step @p306 :rule chain_m_resolution :premises (@p305 @p303 @p297) :args (@t169 (@list false false) (@list @t154 @t170)))
% 0.36/0.60  (step @p307 :rule bool-double-not-elim :args (@t159))
% 0.36/0.60  (step @p308 :rule nary_cong :premises (@p287 @p307) :args ((or @t163 (not @t160))))
% 0.36/0.60  (step @p309 :rule cnf_or_neg :args (@t163 1))
% 0.36/0.60  (step @p310 :rule eq_resolve :premises (@p309 @p308))
% 0.36/0.60  (step @p311 :rule reordering :premises (@p310) :args ((or @t159 @t163)))
% 0.36/0.60  (step @p312 :rule chain_m_resolution :premises (@p311 @p283) :args (@t159 @t164 @t165))
% 0.36/0.60  (step @p313 :rule bool-double-not-elim :args (@t161))
% 0.36/0.60  (step @p314 :rule nary_cong :premises (@p287 @p313) :args ((or @t163 (not @t162))))
% 0.36/0.60  (step @p315 :rule cnf_or_neg :args (@t163 0))
% 0.36/0.60  (step @p316 :rule eq_resolve :premises (@p315 @p314))
% 0.36/0.60  (step @p317 :rule reordering :premises (@p316) :args ((or @t161 @t163)))
% 0.36/0.60  (step @p318 :rule chain_m_resolution :premises (@p317 @p283) :args (@t161 @t164 @t165))
% 0.36/0.60  (step @p319 :rule cnf_or_pos :args (@t172))
% 0.36/0.60  (step @p320 :rule reordering :premises (@p319) :args ((or @t162 @t160 @t157 @t168 @t171 @t173)))
% 0.36/0.60  (step @p321 :rule chain_m_resolution :premises (@p320 @p318 @p312 @p292 @p306 @p295) :args (@t173 (@list false false false true false) (@list @t161 @t159 @t156 @t168 @t166)))
% 0.36/0.60  (assume-push @p328 @t174)
% 0.36/0.60  (step @p323 :rule instantiate :premises (@p279) :args ((@list @t150 @t152 @t149 @t148)))
% 0.36/0.60  (step-pop @p329 :rule scope :premises (@p323))
% 0.36/0.60  (step @p324 :rule process_scope :premises (@p329) :args (@t172))
% 0.36/0.60  (step @p326 :rule implies_elim :premises (@p324))
% 0.36/0.60  (step @p327 false :rule chain_m_resolution :premises (@p326 @p321 @p279) :args (false (@list true false) (@list @t172 @t174)))
% 0.36/0.60  )
% 0.36/0.60  % SZS output end Proof
% 0.36/0.60  % cvc5 exiting
%------------------------------------------------------------------------------