0.04/0.12	% Problem  : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.04/0.13	% Command  : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 240 THM
0.12/0.34	% Computer : n031.cluster.edu
0.12/0.34	% Model    : x86_64 x86_64
0.12/0.34	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.12/0.34	% Memory   : 8042.1875MB
0.12/0.34	% OS       : Linux 3.10.0-693.el7.x86_64
0.12/0.34	% CPULimit : 1920
0.12/0.34	% WCLimit  : 240
0.12/0.34	% DateTime : Fri Sep  5 22:02:37 EDT 2025
0.12/0.34	% CPUTime  : 
0.20/0.49	%----Proving TH0
160.24/160.74	--- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 72s...
160.24/160.74	--- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --mbqi-enum-choice-grammar-all --no-cegqi --no-sygus-inst at 24s...
160.24/160.74	--- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-mbqi-nested-check --no-cegqi --no-sygus-inst at 24s...
160.24/160.74	--- Run --ho-elim --full-saturate-quant at 14s...
160.24/160.74	--- Run --ho-elim --no-e-matching --full-saturate-quant at 9s...
160.24/160.74	--- Run --ho-elim --no-e-matching --enum-inst-sum --full-saturate-quant at 9s...
160.24/160.74	--- Run --ho-elim --finite-model-find --uf-ss=no-minimal at 7s...
160.24/160.74	--- Run --no-ho-matching --finite-model-find --uf-ss=no-minimal at 4s...
160.24/160.74	% SZS status Theorem
160.24/160.74	% SZS output start Proof
160.24/160.74	(
160.24/160.74	(declare-type $$unsorted ())
160.24/160.74	(declare-const tptp.dsetconstr (-> $$unsorted (-> $$unsorted Bool) $$unsorted))
160.24/160.74	(declare-const tptp.setunion (-> $$unsorted $$unsorted))
160.24/160.74	(declare-const tptp.theeq Bool)
160.24/160.74	(declare-const tptp.ifSingleton Bool)
160.24/160.74	(declare-const tptp.singleton (-> $$unsorted Bool))
160.24/160.74	(declare-const tptp.iftrueProp1 Bool)
160.24/160.74	(declare-const tptp.in (-> $$unsorted $$unsorted Bool))
160.24/160.74	(define tptp.if () (let ((_let_1 (@var "Xy" $$unsorted))) (let ((_let_2 (@var "Xz" $$unsorted))) (let ((_let_3 (@var "Xphi" Bool))) (let ((_let_4 (@var "Xx" $$unsorted))) (let ((_let_5 (@var "A" $$unsorted))) (lambda (@list _let_5 _let_3 _let_4 _let_1) (_ tptp.setunion (_ (_ tptp.dsetconstr _let_5) (lambda (@list _let_2) (or (and _let_3 (= _let_2 _let_4)) (and (not _let_3) (= _let_2 _let_1)))))))))))))
160.24/160.74	(define @t1 () (@var "Xy" $$unsorted))
160.24/160.74	(define @t2 () (@var "Xz" $$unsorted))
160.24/160.74	(define @t3 () (@var "Xphi" Bool))
160.24/160.74	(define @t4 () (not @t3))
160.24/160.74	(define @t5 () (and @t4 (= @t2 @t1)))
160.24/160.74	(define @t6 () (@var "Xx" $$unsorted))
160.24/160.74	(define @t7 () (and @t3 (= @t2 @t6)))
160.24/160.74	(define @t8 () (or @t7 @t5))
160.24/160.74	(define @t9 () (@list @t2))
160.24/160.74	(define @t10 () (lambda @t9 @t8))
160.24/160.74	(define @t11 () (@var "A" $$unsorted))
160.24/160.74	(define @t12 () (_ tptp.dsetconstr @t11))
160.24/160.74	(define @t13 () (_ @t12 @t10))
160.24/160.74	(define @t14 () (_ tptp.in @t6))
160.24/160.74	(define @t15 () (=> @t3 (_ @t14 @t13)))
160.24/160.74	(define @t16 () (_ (_ tptp.in @t1) @t11))
160.24/160.74	(define @t17 () (=> @t16 @t15))
160.24/160.74	(define @t18 () (@list @t1))
160.24/160.74	(define @t19 () (forall @t18 @t17))
160.24/160.74	(define @t20 () (_ @t14 @t11))
160.24/160.74	(define @t21 () (=> @t20 @t19))
160.24/160.74	(define @t22 () (@list @t11 @t3 @t6))
160.24/160.74	(define @t23 () (forall @t22 @t21))
160.24/160.74	(define @t24 () (= tptp.iftrueProp1 @t23))
160.24/160.74	(define @t25 () (=> @t16 (_ tptp.singleton @t13)))
160.24/160.74	(define @t26 () (forall @t18 @t25))
160.24/160.74	(define @t27 () (=> @t20 @t26))
160.24/160.74	(define @t28 () (forall @t22 @t27))
160.24/160.74	(define @t29 () (= tptp.ifSingleton @t28))
160.24/160.74	(define @t30 () (@var "X" $$unsorted))
160.24/160.74	(define @t31 () (_ tptp.setunion @t30))
160.24/160.74	(define @t32 () (_ @t14 @t30))
160.24/160.74	(define @t33 () (=> @t32 (= @t31 @t6)))
160.24/160.74	(define @t34 () (@list @t6))
160.24/160.74	(define @t35 () (forall @t34 @t33))
160.24/160.74	(define @t36 () (_ tptp.singleton @t30))
160.24/160.74	(define @t37 () (=> @t36 @t35))
160.24/160.74	(define @t38 () (@list @t30))
160.24/160.74	(define @t39 () (forall @t38 @t37))
160.24/160.74	(define @t40 () (= tptp.theeq @t39))
160.24/160.74	(define @t41 () (= (_ (_ (_ (_ tptp.if @t11) @t3) @t6) @t1) @t6))
160.24/160.74	(define @t42 () (=> @t3 @t41))
160.24/160.74	(define @t43 () (=> @t16 @t42))
160.24/160.74	(define @t44 () (forall @t18 @t43))
160.24/160.74	(define @t45 () (=> @t20 @t44))
160.24/160.74	(define @t46 () (forall @t22 @t45))
160.24/160.74	(define @t47 () (=> tptp.theeq @t46))
160.24/160.74	(define @t48 () (=> tptp.ifSingleton @t47))
160.24/160.74	(define @t49 () (=> tptp.iftrueProp1 @t48))
160.24/160.74	(define @t50 () (not @t49))
160.24/160.74	(define @t51 () (@list @t11 @t3 @t6 @t1))
160.24/160.74	(define @t52 () (lambda @t51 (_ tptp.setunion @t13)))
160.24/160.74	(define @t53 () (= @t6 @t2))
160.24/160.74	(define @t54 () (tptp.dsetconstr @t11 (lambda @t9 @t53)))
160.24/160.74	(define @t55 () (= @t6 (tptp.setunion @t54)))
160.24/160.74	(define @t56 () (@var "BOUND_VARIABLE_7558" $$unsorted))
160.24/160.74	(define @t57 () (not (tptp.in @t56 @t11)))
160.24/160.74	(define @t58 () (tptp.in @t6 @t11))
160.24/160.74	(define @t59 () (not @t58))
160.24/160.74	(define @t60 () (or @t59 @t57 @t55))
160.24/160.74	(define @t61 () (@list @t11 @t6 @t56))
160.24/160.74	(define @t62 () (forall @t61 @t60))
160.24/160.74	(define @t63 () (@var "BOUND_VARIABLE_7503" $$unsorted))
160.24/160.74	(define @t64 () (tptp.setunion @t30))
160.24/160.74	(define @t65 () (not (tptp.in @t63 @t30)))
160.24/160.74	(define @t66 () (tptp.singleton @t30))
160.24/160.74	(define @t67 () (not @t66))
160.24/160.74	(define @t68 () (= @t63 @t64))
160.24/160.74	(define @t69 () (or @t67 @t65 @t68))
160.24/160.74	(define @t70 () (or @t65 @t68))
160.24/160.74	(define @t71 () (or @t67 @t70))
160.24/160.74	(define @t72 () (@list @t30 @t63))
160.24/160.74	(define @t73 () (forall @t72 @t71))
160.24/160.74	(define @t74 () (@list @t63))
160.24/160.74	(define @t75 () (forall @t74 @t71))
160.24/160.74	(define @t76 () (forall @t74 @t70))
160.24/160.74	(define @t77 () (or @t67 @t76))
160.24/160.74	(define @t78 () (tptp.in @t6 @t30))
160.24/160.74	(define @t79 () (forall @t34 (or (not @t78) (= @t6 @t64))))
160.24/160.74	(define @t80 () (not @t36))
160.24/160.74	(define @t81 () (or @t80 @t79))
160.24/160.74	(define @t82 () (= @t6 @t31))
160.24/160.74	(define @t83 () (not @t32))
160.24/160.74	(define @t84 () (or @t83 @t82))
160.24/160.74	(define @t85 () (=> tptp.theeq @t62))
160.24/160.74	(define @t86 () (@var "BOUND_VARIABLE_7450" $$unsorted))
160.24/160.74	(define @t87 () (and @t4 (= @t86 @t2)))
160.24/160.74	(define @t88 () (and @t3 @t53))
160.24/160.74	(define @t89 () (or @t88 @t87))
160.24/160.74	(define @t90 () (lambda @t9 @t89))
160.24/160.74	(define @t91 () (tptp.dsetconstr @t11 @t90))
160.24/160.74	(define @t92 () (tptp.singleton @t91))
160.24/160.74	(define @t93 () (not (tptp.in @t86 @t11)))
160.24/160.74	(define @t94 () (or @t59 @t93 @t92))
160.24/160.74	(define @t95 () (or @t93 @t92))
160.24/160.74	(define @t96 () (or @t59 @t95))
160.24/160.74	(define @t97 () (@list @t11 @t3 @t6 @t86))
160.24/160.74	(define @t98 () (forall @t97 @t96))
160.24/160.74	(define @t99 () (@list @t86))
160.24/160.74	(define @t100 () (forall @t99 @t96))
160.24/160.74	(define @t101 () (forall @t99 @t95))
160.24/160.74	(define @t102 () (@list @t1))
160.24/160.74	(define @t103 () (or @t59 @t101))
160.24/160.74	(define @t104 () (lambda @t9 (or @t88 (and @t4 (= @t1 @t2)))))
160.24/160.74	(define @t105 () (tptp.dsetconstr @t11 @t104))
160.24/160.74	(define @t106 () (tptp.singleton @t105))
160.24/160.74	(define @t107 () (tptp.in @t1 @t11))
160.24/160.74	(define @t108 () (not @t107))
160.24/160.74	(define @t109 () (forall @t18 (or @t108 @t106)))
160.24/160.74	(define @t110 () (not @t20))
160.24/160.74	(define @t111 () (or @t110 @t109))
160.24/160.74	(define @t112 () (_ @t12 @t104))
160.24/160.74	(define @t113 () (_ tptp.singleton @t112))
160.24/160.74	(define @t114 () (not @t16))
160.24/160.74	(define @t115 () (or @t114 @t113))
160.24/160.74	(define @t116 () (=> tptp.ifSingleton @t85))
160.24/160.74	(define @t117 () (tptp.in @t6 @t54))
160.24/160.74	(define @t118 () (@var "BOUND_VARIABLE_7393" $$unsorted))
160.24/160.74	(define @t119 () (not (tptp.in @t118 @t11)))
160.24/160.74	(define @t120 () (or @t59 @t119 @t117))
160.24/160.74	(define @t121 () (= @t2 @t118))
160.24/160.74	(define @t122 () (not true))
160.24/160.74	(define @t123 () (and @t122 @t121))
160.24/160.74	(define @t124 () (and true @t53))
160.24/160.74	(define @t125 () (or @t124 @t123))
160.24/160.74	(define @t126 () (lambda @t9 @t125))
160.24/160.74	(define @t127 () (tptp.dsetconstr @t11 @t126))
160.24/160.74	(define @t128 () (tptp.in @t6 @t127))
160.24/160.74	(define @t129 () (or @t59 @t122 @t119 @t128))
160.24/160.74	(define @t130 () (@list @t11 @t6 @t118))
160.24/160.74	(define @t131 () (tptp.in @t6 (tptp.dsetconstr @t11 (lambda @t9 (or @t88 (and @t4 @t121))))))
160.24/160.74	(define @t132 () (not (= @t3 true)))
160.24/160.74	(define @t133 () (@list @t3))
160.24/160.74	(define @t134 () (or @t4 @t59 @t4 @t119 @t131))
160.24/160.74	(define @t135 () (or @t59 @t4 @t119 @t131))
160.24/160.74	(define @t136 () (forall @t133 @t135))
160.24/160.74	(define @t137 () (forall @t130 @t136))
160.24/160.74	(define @t138 () (forall (@list @t11 @t6 @t118 @t3) @t135))
160.24/160.74	(define @t139 () (@list @t11 @t3 @t6 @t118))
160.24/160.74	(define @t140 () (and @t4 (= @t118 @t2)))
160.24/160.74	(define @t141 () (or @t88 @t140))
160.24/160.74	(define @t142 () (lambda @t9 @t141))
160.24/160.74	(define @t143 () (tptp.dsetconstr @t11 @t142))
160.24/160.74	(define @t144 () (tptp.in @t6 @t143))
160.24/160.74	(define @t145 () (or @t59 @t4 @t119 @t144))
160.24/160.74	(define @t146 () (or @t119 @t144))
160.24/160.74	(define @t147 () (or @t59 @t4 @t146))
160.24/160.74	(define @t148 () (forall @t139 @t147))
160.24/160.74	(define @t149 () (@list @t118))
160.24/160.74	(define @t150 () (forall @t149 @t147))
160.24/160.74	(define @t151 () (forall @t149 @t146))
160.24/160.74	(define @t152 () (or @t59 @t4 @t151))
160.24/160.74	(define @t153 () (tptp.in @t6 @t105))
160.24/160.74	(define @t154 () (forall @t18 (or @t108 @t153)))
160.24/160.74	(define @t155 () (or @t110 @t4 @t154))
160.24/160.74	(define @t156 () (or @t4 @t154))
160.24/160.74	(define @t157 () (_ @t14 @t112))
160.24/160.74	(define @t158 () (or @t114 @t157))
160.24/160.74	(define @t159 () (forall @t18 @t158))
160.24/160.74	(define @t160 () (or @t4 @t159))
160.24/160.74	(define @t161 () (or @t4 @t158))
160.24/160.74	(define @t162 () (or @t114 @t4 @t157))
160.24/160.74	(define @t163 () (=> @t3 @t157))
160.24/160.74	(define @t164 () (=> tptp.iftrueProp1 @t116))
160.24/160.74	(define @t165 () (= @t2 @t56))
160.24/160.74	(define @t166 () (and @t122 @t165))
160.24/160.74	(define @t167 () (or @t124 @t166))
160.24/160.74	(define @t168 () (lambda @t9 @t167))
160.24/160.74	(define @t169 () (tptp.dsetconstr @t11 @t168))
160.24/160.74	(define @t170 () (tptp.setunion @t169))
160.24/160.74	(define @t171 () (= @t6 @t170))
160.24/160.74	(define @t172 () (or @t59 @t122 @t57 @t171))
160.24/160.74	(define @t173 () (= @t6 (tptp.setunion (tptp.dsetconstr @t11 (lambda @t9 (or @t88 (and @t4 @t165)))))))
160.24/160.74	(define @t174 () (or @t4 @t59 @t4 @t57 @t173))
160.24/160.74	(define @t175 () (or @t59 @t4 @t57 @t173))
160.24/160.74	(define @t176 () (forall @t133 @t175))
160.24/160.74	(define @t177 () (forall @t61 @t176))
160.24/160.74	(define @t178 () (forall (@list @t11 @t6 @t56 @t3) @t175))
160.24/160.74	(define @t179 () (@list @t11 @t3 @t6 @t56))
160.24/160.74	(define @t180 () (and @t4 (= @t56 @t2)))
160.24/160.74	(define @t181 () (or @t88 @t180))
160.24/160.74	(define @t182 () (lambda @t9 @t181))
160.24/160.74	(define @t183 () (tptp.dsetconstr @t11 @t182))
160.24/160.74	(define @t184 () (tptp.setunion @t183))
160.24/160.74	(define @t185 () (= @t6 @t184))
160.24/160.74	(define @t186 () (or @t59 @t4 @t57 @t185))
160.24/160.74	(define @t187 () (or @t57 @t185))
160.24/160.74	(define @t188 () (or @t59 @t4 @t187))
160.24/160.74	(define @t189 () (forall @t179 @t188))
160.24/160.74	(define @t190 () (@list @t56))
160.24/160.74	(define @t191 () (forall @t190 @t188))
160.24/160.74	(define @t192 () (forall @t190 @t187))
160.24/160.74	(define @t193 () (or @t59 @t4 @t192))
160.24/160.74	(define @t194 () (tptp.setunion @t105))
160.24/160.74	(define @t195 () (forall @t18 (or @t108 (= @t6 @t194))))
160.24/160.74	(define @t196 () (or @t110 @t4 @t195))
160.24/160.74	(define @t197 () (or @t4 @t195))
160.24/160.74	(define @t198 () (_ tptp.setunion @t112))
160.24/160.74	(define @t199 () (= @t6 @t198))
160.24/160.74	(define @t200 () (or @t114 @t199))
160.24/160.74	(define @t201 () (forall @t18 @t200))
160.24/160.74	(define @t202 () (or @t4 @t201))
160.24/160.74	(define @t203 () (or @t4 @t200))
160.24/160.74	(define @t204 () (or @t114 @t4 @t199))
160.24/160.74	(define @t205 () (=> @t3 @t199))
160.24/160.74	(define @t206 () (lambda @t18 @t198))
160.24/160.74	(define @t207 () (lambda (@list @t6 @t1) @t198))
160.24/160.74	(define @t208 () (lambda (@list @t3 @t6 @t1) @t198))
160.24/160.74	(define @t209 () (_ (lambda @t51 @t198) @t11))
160.24/160.74	(define @t210 () (= (_ (_ (_ @t209 @t3) @t6) @t1) @t6))
160.24/160.74	(define @t211 () (=> @t3 @t210))
160.24/160.74	(define @t212 () (=> @t16 @t211))
160.24/160.74	(define @t213 () (forall @t18 @t212))
160.24/160.74	(define @t214 () (=> @t20 @t213))
160.24/160.74	(define @t215 () (forall @t22 @t214))
160.24/160.74	(define @t216 () (=> tptp.theeq @t215))
160.24/160.74	(define @t217 () (=> tptp.ifSingleton @t216))
160.24/160.74	(define @t218 () (=> tptp.iftrueProp1 @t217))
160.24/160.74	(define @t219 () (@quantifiers_skolemize @t62 1))
160.24/160.74	(define @t220 () (= @t2 @t219))
160.24/160.74	(define @t221 () (lambda @t9 @t220))
160.24/160.74	(define @t222 () (@purify @t221))
160.24/160.74	(define @t223 () (@quantifiers_skolemize @t62 0))
160.24/160.74	(define @t224 () (tptp.dsetconstr @t223 @t221))
160.24/160.74	(define @t225 () (tptp.singleton @t224))
160.24/160.74	(define @t226 () (tptp.in @t219 @t223))
160.24/160.74	(define @t227 () (not @t226))
160.24/160.74	(define @t228 () (or @t227 @t227 @t225))
160.24/160.74	(define @t229 () (forall @t97 (or @t59 @t93 (tptp.singleton (tptp.dsetconstr @t11 (lambda @t9 (or @t88 (and @t4 (= @t2 @t86)))))))))
160.24/160.74	(define @t230 () (not false))
160.24/160.74	(define @t231 () (and @t230 @t220))
160.24/160.74	(define @t232 () (= @t219 @t2))
160.24/160.74	(define @t233 () (and false @t232))
160.24/160.74	(define @t234 () (or @t233 @t231))
160.24/160.74	(define @t235 () (lambda @t9 @t234))
160.24/160.74	(define @t236 () (tptp.dsetconstr @t223 @t235))
160.24/160.74	(define @t237 () (tptp.singleton @t236))
160.24/160.74	(define @t238 () (or @t227 @t227 @t237))
160.24/160.74	(define @t239 () (@list false))
160.24/160.74	(define @t240 () (tptp.dsetconstr @t223 @t222))
160.24/160.74	(define @t241 () (tptp.setunion @t240))
160.24/160.74	(define @t242 () (= @t219 @t241))
160.24/160.74	(define @t243 () (not (tptp.in (@quantifiers_skolemize @t62 2) @t223)))
160.24/160.74	(define @t244 () (or @t227 @t243 @t242))
160.24/160.74	(define @t245 () (not @t244))
160.24/160.74	(define @t246 () (not @t62))
160.24/160.74	(define @t247 () (tptp.setunion @t224))
160.24/160.74	(define @t248 () (= @t219 @t247))
160.24/160.74	(define @t249 () (or @t227 @t243 @t248))
160.24/160.74	(define @t250 () (not @t249))
160.24/160.74	(define @t251 () (lambda @t9 @t232))
160.24/160.74	(define @t252 () (tptp.dsetconstr @t223 @t251))
160.24/160.74	(define @t253 () (tptp.setunion @t252))
160.24/160.74	(define @t254 () (= @t219 @t253))
160.24/160.74	(define @t255 () (or @t227 @t243 @t254))
160.24/160.74	(define @t256 () (not @t255))
160.24/160.74	(define @t257 () (@list true))
160.24/160.74	(define @t258 () (@list @t244))
160.24/160.74	(define @t259 () (tptp.singleton @t240))
160.24/160.74	(define @t260 () (or @t227 @t227 @t259))
160.24/160.74	(define @t261 () (@list false false))
160.24/160.74	(define @t262 () (tptp.in @t219 @t224))
160.24/160.74	(define @t263 () (or @t227 @t227 @t262))
160.24/160.74	(define @t264 () (forall @t130 @t120))
160.24/160.74	(define @t265 () (tptp.in @t219 @t252))
160.24/160.74	(define @t266 () (or @t227 @t227 @t265))
160.24/160.74	(define @t267 () (tptp.in @t219 @t240))
160.24/160.74	(define @t268 () (or @t227 @t227 @t267))
160.24/160.74	(define @t269 () (not @t267))
160.24/160.74	(define @t270 () (not @t259))
160.24/160.74	(define @t271 () (or @t270 @t269 @t242))
160.24/160.74	(define @t272 () (or @t270 @t269 (= @t241 @t219)))
160.24/160.74	(define @t273 () (forall @t72 (or @t67 @t65 (= @t64 @t63))))
160.24/160.74	(assume @p1 @t24)
160.24/160.74	(assume @p2 @t29)
160.24/160.74	(assume @p3 @t40)
160.24/160.74	(assume @p4 @t50)
160.24/160.74	(assume @p5 true)
160.24/160.74	(step @p6 (= tptp.if @t52) :rule refl :args (@t52))
160.24/160.74	(step @p7 :rule refl :args (@t62))
160.24/160.74	(step @p8 :rule eq-symm :args (@t63 @t64))
160.24/160.74	(step @p9 :rule refl :args (@t65))
160.24/160.74	(step @p10 :rule refl :args (@t67))
160.24/160.74	(step @p11 :rule nary_cong :premises (@p10 @p9 @p8) :args (@t69))
160.24/160.74	(step @p12 :rule aci_norm :args ((= @t71 @t69)))
160.24/160.74	(step @p13 :rule trans :premises (@p12 @p11))
160.24/160.74	(step @p14 :rule cong :premises (@p13) :args (@t73))
160.24/160.74	(step @p15 :rule quant-merge-prenex :args ((= (forall @t38 @t75) @t73)))
160.24/160.74	(step @p16 :rule alpha_equiv :args (@t76 (@list @t63) (@list @t6)))
160.24/160.74	(step @p17 :rule refl :args (@t67))
160.24/160.74	(step @p18 :rule nary_cong :premises (@p17 @p16) :args (@t77))
160.24/160.74	(step @p19 :rule quant-miniscope-or :args ((= @t75 @t77)))
160.24/160.74	(step @p20 :rule trans :premises (@p19 @p18))
160.24/160.74	(step @p21 :rule symm :premises (@p20))
160.24/160.74	(step @p22 :rule cong :premises (@p21) :args ((forall @t38 (or @t67 @t79))))
160.24/160.74	(step @p23 :rule trans :premises (@p22 @p15))
160.24/160.74	(step @p24 :rule trans :premises (@p23 @p14))
160.24/160.74	(step @p25 :rule refl :args (@t79))
160.24/160.74	(step @p26 :rule refl :args (@t66))
160.24/160.74	(step @p27 :rule refl :args (@t36))
160.24/160.74	(step @p28 :rule cong :premises (@p27 @p26) :args ((= @t36 @t66)))
160.24/160.74	(step @p29 :rule symm :premises (@p28))
160.24/160.74	(step @p30 :rule eq_resolve :premises (@p27 @p29))
160.24/160.74	(step @p31 :rule cong :premises (@p30) :args (@t80))
160.24/160.74	(step @p32 :rule nary_cong :premises (@p31 @p25) :args (@t81))
160.24/160.74	(step @p33 :rule cong :premises (@p32) :args ((forall @t38 @t81)))
160.24/160.74	(step @p34 :rule trans :premises (@p33 @p24))
160.24/160.74	(step @p35 :rule bool-impl-elim :args (@t36 @t79))
160.24/160.74	(step @p36 :rule cong :premises (@p35) :args ((forall @t38 (=> @t36 @t79))))
160.24/160.74	(step @p37 :rule trans :premises (@p36 @p34))
160.24/160.74	(step @p38 :rule refl :args (@t64))
160.24/160.74	(step @p39 :rule refl :args (@t31))
160.24/160.74	(step @p40 :rule cong :premises (@p39 @p38) :args ((= @t31 @t64)))
160.24/160.74	(step @p41 :rule symm :premises (@p40))
160.24/160.74	(step @p42 :rule eq_resolve :premises (@p39 @p41))
160.24/160.74	(step @p43 :rule refl :args (@t6))
160.24/160.74	(step @p44 :rule cong :premises (@p43 @p42) :args (@t82))
160.24/160.74	(step @p45 :rule refl :args (@t78))
160.24/160.74	(step @p46 :rule refl :args (@t32))
160.24/160.74	(step @p47 :rule cong :premises (@p46 @p45) :args ((= @t32 @t78)))
160.24/160.74	(step @p48 :rule symm :premises (@p47))
160.24/160.74	(step @p49 :rule eq_resolve :premises (@p46 @p48))
160.24/160.74	(step @p50 :rule cong :premises (@p49) :args (@t83))
160.24/160.74	(step @p51 :rule nary_cong :premises (@p50 @p44) :args (@t84))
160.24/160.74	(step @p52 :rule cong :premises (@p51) :args ((forall @t34 @t84)))
160.24/160.74	(step @p53 :rule bool-impl-elim :args (@t32 @t82))
160.24/160.74	(step @p54 :rule cong :premises (@p53) :args ((forall @t34 (=> @t32 @t82))))
160.24/160.74	(step @p55 :rule trans :premises (@p54 @p52))
160.24/160.74	(step @p56 :rule eq-symm :args (@t31 @t6))
160.24/160.74	(step @p57 :rule refl :args (@t32))
160.24/160.74	(step @p58 :rule cong :premises (@p57 @p56) :args (@t33))
160.24/160.74	(step @p59 :rule cong :premises (@p58) :args (@t35))
160.24/160.74	(step @p60 :rule trans :premises (@p59 @p55))
160.24/160.74	(step @p61 :rule refl :args (@t36))
160.24/160.74	(step @p62 :rule cong :premises (@p61 @p60) :args (@t37))
160.24/160.74	(step @p63 :rule cong :premises (@p62) :args (@t39))
160.24/160.74	(step @p64 :rule trans :premises (@p63 @p37))
160.24/160.74	(step @p65 :rule refl :args (tptp.theeq))
160.24/160.74	(step @p66 :rule cong :premises (@p65 @p64) :args (@t40))
160.24/160.74	(step @p67 :rule eq_resolve :premises (@p3 @p66))
160.24/160.74	(step @p68 :rule cong :premises (@p67 @p7) :args (@t85))
160.24/160.74	(step @p69 :rule eq-symm :args (@t86 @t2))
160.24/160.74	(step @p70 :rule refl :args (@t4))
160.24/160.74	(step @p71 :rule nary_cong :premises (@p70 @p69) :args (@t87))
160.24/160.74	(step @p72 :rule refl :args (@t88))
160.24/160.74	(step @p73 :rule nary_cong :premises (@p72 @p71) :args (@t89))
160.24/160.74	(step @p74 :rule cong :premises (@p73) :args (@t90))
160.24/160.74	(step @p75 :rule refl :args (@t11))
160.24/160.74	(step @p76 :rule cong :premises (@p75 @p74) :args (@t91))
160.24/160.74	(step @p77 :rule cong :premises (@p76) :args (@t92))
160.24/160.74	(step @p78 :rule refl :args (@t93))
160.24/160.74	(step @p79 :rule refl :args (@t59))
160.24/160.74	(step @p80 :rule nary_cong :premises (@p79 @p78 @p77) :args (@t94))
160.24/160.74	(step @p81 :rule aci_norm :args ((= @t96 @t94)))
160.24/160.74	(step @p82 :rule trans :premises (@p81 @p80))
160.24/160.74	(step @p83 :rule cong :premises (@p82) :args (@t98))
160.24/160.74	(step @p84 :rule quant-merge-prenex :args ((= (forall @t22 @t100) @t98)))
160.24/160.74	(step @p85 :rule alpha_equiv :args (@t101 (@list @t86) @t102))
160.24/160.74	(step @p86 :rule refl :args (@t59))
160.24/160.74	(step @p87 :rule nary_cong :premises (@p86 @p85) :args (@t103))
160.24/160.74	(step @p88 :rule quant-miniscope-or :args ((= @t100 @t103)))
160.24/160.74	(step @p89 :rule trans :premises (@p88 @p87))
160.24/160.74	(step @p90 :rule symm :premises (@p89))
160.24/160.74	(step @p91 :rule cong :premises (@p90) :args ((forall @t22 (or @t59 @t109))))
160.24/160.74	(step @p92 :rule trans :premises (@p91 @p84))
160.24/160.74	(step @p93 :rule trans :premises (@p92 @p83))
160.24/160.74	(step @p94 :rule refl :args (@t109))
160.24/160.74	(step @p95 :rule refl :args (@t58))
160.24/160.74	(step @p96 :rule refl :args (@t20))
160.24/160.74	(step @p97 :rule cong :premises (@p96 @p95) :args ((= @t20 @t58)))
160.24/160.74	(step @p98 :rule symm :premises (@p97))
160.24/160.74	(step @p99 :rule eq_resolve :premises (@p96 @p98))
160.24/160.74	(step @p100 :rule cong :premises (@p99) :args (@t110))
160.24/160.74	(step @p101 :rule nary_cong :premises (@p100 @p94) :args (@t111))
160.24/160.74	(step @p102 :rule cong :premises (@p101) :args ((forall @t22 @t111)))
160.24/160.74	(step @p103 :rule trans :premises (@p102 @p93))
160.24/160.74	(step @p104 :rule bool-impl-elim :args (@t20 @t109))
160.24/160.74	(step @p105 :rule cong :premises (@p104) :args ((forall @t22 (=> @t20 @t109))))
160.24/160.74	(step @p106 :rule trans :premises (@p105 @p103))
160.24/160.74	(step @p107 :rule refl :args ((tptp.singleton @t112)))
160.24/160.74	(step @p108 :rule refl :args (@t105))
160.24/160.74	(step @p109 :rule cong :premises (@p108) :args (@t106))
160.24/160.74	(step @p110 :rule trans :premises (@p109 @p107))
160.24/160.74	(step @p111 :rule refl :args (tptp.singleton))
160.24/160.74	(step @p112 :rule ho_cong :premises (@p111 @p108))
160.24/160.74	(step @p113 :rule cong :premises (@p112 @p110) :args ((= (_ tptp.singleton @t105) @t106)))
160.24/160.74	(step @p114 :rule symm :premises (@p113))
160.24/160.74	(step @p115 :rule refl :args (@t113))
160.24/160.74	(step @p116 :rule eq_resolve :premises (@p115 @p114))
160.24/160.74	(step @p117 :rule refl :args (@t112))
160.24/160.74	(step @p118 :rule cong :premises (@p117 @p108) :args ((= @t112 @t105)))
160.24/160.74	(step @p119 :rule symm :premises (@p118))
160.24/160.74	(step @p120 :rule eq_resolve :premises (@p117 @p119))
160.24/160.74	(step @p121 :rule ho_cong :premises (@p111 @p120))
160.24/160.74	(step @p122 :rule trans :premises (@p121 @p116))
160.24/160.74	(step @p123 :rule refl :args (@t107))
160.24/160.74	(step @p124 :rule refl :args (@t16))
160.24/160.74	(step @p125 :rule cong :premises (@p124 @p123) :args ((= @t16 @t107)))
160.24/160.74	(step @p126 :rule symm :premises (@p125))
160.24/160.74	(step @p127 :rule eq_resolve :premises (@p124 @p126))
160.24/160.74	(step @p128 :rule cong :premises (@p127) :args (@t114))
160.24/160.74	(step @p129 :rule nary_cong :premises (@p128 @p122) :args (@t115))
160.24/160.74	(step @p130 :rule cong :premises (@p129) :args ((forall @t18 @t115)))
160.24/160.74	(step @p131 :rule bool-impl-elim :args (@t16 @t113))
160.24/160.74	(step @p132 :rule cong :premises (@p131) :args ((forall @t18 (=> @t16 @t113))))
160.24/160.74	(step @p133 :rule trans :premises (@p132 @p130))
160.24/160.74	(step @p134 :rule eq-symm :args (@t2 @t1))
160.24/160.74	(step @p135 :rule nary_cong :premises (@p70 @p134) :args (@t5))
160.24/160.74	(step @p136 :rule eq-symm :args (@t2 @t6))
160.24/160.74	(step @p137 :rule refl :args (@t3))
160.24/160.74	(step @p138 :rule nary_cong :premises (@p137 @p136) :args (@t7))
160.24/160.74	(step @p139 :rule nary_cong :premises (@p138 @p135) :args (@t8))
160.24/160.74	(step @p140 :rule cong :premises (@p139) :args (@t10))
160.24/160.74	(step @p141 :rule refl :args (@t12))
160.24/160.74	(step @p142 :rule ho_cong :premises (@p141 @p140))
160.24/160.74	(step @p143 :rule refl :args (tptp.singleton))
160.24/160.74	(step @p144 :rule ho_cong :premises (@p143 @p142))
160.24/160.74	(step @p145 :rule refl :args (@t16))
160.24/160.74	(step @p146 :rule cong :premises (@p145 @p144) :args (@t25))
160.24/160.74	(step @p147 :rule cong :premises (@p146) :args (@t26))
160.24/160.74	(step @p148 :rule trans :premises (@p147 @p133))
160.24/160.74	(step @p149 :rule refl :args (@t20))
160.24/160.74	(step @p150 :rule cong :premises (@p149 @p148) :args (@t27))
160.24/160.74	(step @p151 :rule cong :premises (@p150) :args (@t28))
160.24/160.74	(step @p152 :rule trans :premises (@p151 @p106))
160.24/160.74	(step @p153 :rule refl :args (tptp.ifSingleton))
160.24/160.74	(step @p154 :rule cong :premises (@p153 @p152) :args (@t29))
160.24/160.74	(step @p155 :rule eq_resolve :premises (@p2 @p154))
160.24/160.74	(step @p156 :rule cong :premises (@p155 @p68) :args (@t116))
160.24/160.74	(step @p157 :rule aci_norm :args ((= (or @t59 false @t119 @t117) @t120)))
160.24/160.74	(step @p158 :rule aci_norm :args ((= (or @t53 false) @t53)))
160.24/160.74	(step @p159 :rule absorb :args ((= (and false @t121) false)))
160.24/160.74	(step @p160 :rule refl :args (@t121))
160.24/160.74	(step @p161 :rule evaluate :args (@t122))
160.24/160.74	(step @p162 :rule nary_cong :premises (@p161 @p160) :args (@t123))
160.24/160.74	(step @p163 :rule trans :premises (@p162 @p159))
160.24/160.74	(step @p164 :rule aci_norm :args ((= @t124 @t53)))
160.24/160.74	(step @p165 :rule nary_cong :premises (@p164 @p163) :args (@t125))
160.24/160.74	(step @p166 :rule trans :premises (@p165 @p158))
160.24/160.74	(step @p167 :rule cong :premises (@p166) :args (@t126))
160.24/160.74	(step @p168 :rule cong :premises (@p75 @p167) :args (@t127))
160.24/160.74	(step @p169 :rule refl :args (@t6))
160.24/160.74	(step @p170 :rule cong :premises (@p169 @p168) :args (@t128))
160.24/160.74	(step @p171 :rule refl :args (@t119))
160.24/160.74	(step @p172 :rule nary_cong :premises (@p79 @p161 @p171 @p170) :args (@t129))
160.24/160.74	(step @p173 :rule trans :premises (@p172 @p157))
160.24/160.74	(step @p174 :rule cong :premises (@p173) :args ((forall @t130 @t129)))
160.24/160.74	(step @p175 :rule quant-var-elim-eq :args ((= (forall @t133 (or @t132 @t59 @t4 @t119 @t131)) @t129)))
160.24/160.74	(step @p176 :rule refl :args (@t131))
160.24/160.74	(step @p177 :rule refl :args (@t119))
160.24/160.74	(step @p178 :rule refl :args (@t4))
160.24/160.74	(step @p179 :rule bool-eq-true :args (@t3))
160.24/160.74	(step @p180 :rule symm :premises (@p179))
160.24/160.74	(step @p181 :rule cong :premises (@p180) :args (@t4))
160.24/160.74	(step @p182 :rule nary_cong :premises (@p181 @p86 @p178 @p177 @p176) :args (@t134))
160.24/160.74	(step @p183 :rule aci_norm :args ((= @t135 @t134)))
160.24/160.74	(step @p184 :rule trans :premises (@p183 @p182))
160.24/160.74	(step @p185 :rule cong :premises (@p184) :args (@t136))
160.24/160.74	(step @p186 :rule trans :premises (@p185 @p175))
160.24/160.74	(step @p187 :rule cong :premises (@p186) :args (@t137))
160.24/160.74	(step @p188 :rule quant-merge-prenex :args ((= @t137 @t138)))
160.24/160.74	(step @p189 :rule symm :premises (@p188))
160.24/160.74	(step @p190 :rule quant_var_reordering :args ((= (forall @t139 @t135) @t138)))
160.24/160.74	(step @p191 :rule trans :premises (@p190 @p189 @p187))
160.24/160.74	(step @p192 :rule trans :premises (@p191 @p174))
160.24/160.74	(step @p193 :rule eq-symm :args (@t118 @t2))
160.24/160.74	(step @p194 :rule nary_cong :premises (@p70 @p193) :args (@t140))
160.24/160.74	(step @p195 :rule nary_cong :premises (@p72 @p194) :args (@t141))
160.24/160.74	(step @p196 :rule cong :premises (@p195) :args (@t142))
160.24/160.74	(step @p197 :rule cong :premises (@p75 @p196) :args (@t143))
160.24/160.74	(step @p198 :rule cong :premises (@p169 @p197) :args (@t144))
160.24/160.74	(step @p199 :rule nary_cong :premises (@p79 @p70 @p171 @p198) :args (@t145))
160.24/160.74	(step @p200 :rule aci_norm :args ((= @t147 @t145)))
160.24/160.74	(step @p201 :rule trans :premises (@p200 @p199))
160.24/160.74	(step @p202 :rule cong :premises (@p201) :args (@t148))
160.24/160.74	(step @p203 :rule trans :premises (@p202 @p192))
160.24/160.74	(step @p204 :rule quant-merge-prenex :args ((= (forall @t22 @t150) @t148)))
160.24/160.74	(step @p205 :rule alpha_equiv :args (@t151 (@list @t118) @t102))
160.24/160.74	(step @p206 :rule nary_cong :premises (@p86 @p178 @p205) :args (@t152))
160.24/160.74	(step @p207 :rule quant-miniscope-or :args ((= @t150 @t152)))
160.24/160.74	(step @p208 :rule trans :premises (@p207 @p206))
160.24/160.74	(step @p209 :rule symm :premises (@p208))
160.24/160.74	(step @p210 :rule cong :premises (@p209) :args ((forall @t22 (or @t59 @t4 @t154))))
160.24/160.74	(step @p211 :rule trans :premises (@p210 @p204))
160.24/160.74	(step @p212 :rule trans :premises (@p211 @p203))
160.24/160.74	(step @p213 :rule refl :args (@t154))
160.24/160.74	(step @p214 :rule nary_cong :premises (@p100 @p178 @p213) :args (@t155))
160.24/160.74	(step @p215 :rule cong :premises (@p214) :args ((forall @t22 @t155)))
160.24/160.74	(step @p216 :rule trans :premises (@p215 @p212))
160.24/160.74	(step @p217 :rule aci_norm :args ((= (or @t110 @t156) @t155)))
160.24/160.74	(step @p218 :rule bool-impl-elim :args (@t20 @t156))
160.24/160.74	(step @p219 :rule trans :premises (@p218 @p217))
160.24/160.74	(step @p220 :rule cong :premises (@p219) :args ((forall @t22 (=> @t20 @t156))))
160.24/160.74	(step @p221 :rule trans :premises (@p220 @p216))
160.24/160.74	(step @p222 :rule refl :args ((tptp.in @t6 @t112)))
160.24/160.74	(step @p223 :rule cong :premises (@p43 @p108) :args (@t153))
160.24/160.74	(step @p224 :rule trans :premises (@p223 @p222))
160.24/160.74	(step @p225 :rule refl :args (@t14))
160.24/160.74	(step @p226 :rule ho_cong :premises (@p225 @p108))
160.24/160.74	(step @p227 :rule cong :premises (@p226 @p224) :args ((= (_ @t14 @t105) @t153)))
160.24/160.74	(step @p228 :rule symm :premises (@p227))
160.24/160.74	(step @p229 :rule refl :args (@t157))
160.24/160.74	(step @p230 :rule eq_resolve :premises (@p229 @p228))
160.24/160.74	(step @p231 :rule ho_cong :premises (@p225 @p120))
160.24/160.74	(step @p232 :rule trans :premises (@p231 @p230))
160.24/160.74	(step @p233 :rule nary_cong :premises (@p128 @p232) :args (@t158))
160.24/160.74	(step @p234 :rule cong :premises (@p233) :args (@t159))
160.24/160.74	(step @p235 :rule nary_cong :premises (@p70 @p234) :args (@t160))
160.24/160.74	(step @p236 :rule quant-miniscope-or :args ((= (forall @t18 @t161) @t160)))
160.24/160.74	(step @p237 :rule aci_norm :args ((= @t162 @t161)))
160.24/160.74	(step @p238 :rule cong :premises (@p237) :args ((forall @t18 @t162)))
160.24/160.74	(step @p239 :rule trans :premises (@p238 @p236))
160.24/160.74	(step @p240 :rule trans :premises (@p239 @p235))
160.24/160.74	(step @p241 :rule aci_norm :args ((= (or @t114 (or @t4 @t157)) @t162)))
160.24/160.74	(step @p242 :rule bool-impl-elim :args (@t3 @t157))
160.24/160.74	(step @p243 :rule refl :args (@t114))
160.24/160.74	(step @p244 :rule nary_cong :premises (@p243 @p242) :args ((or @t114 @t163)))
160.24/160.74	(step @p245 :rule trans :premises (@p244 @p241))
160.24/160.74	(step @p246 :rule bool-impl-elim :args (@t16 @t163))
160.24/160.74	(step @p247 :rule trans :premises (@p246 @p245))
160.24/160.74	(step @p248 :rule cong :premises (@p247) :args ((forall @t18 (=> @t16 @t163))))
160.24/160.74	(step @p249 :rule trans :premises (@p248 @p240))
160.24/160.74	(step @p250 :rule refl :args (@t14))
160.24/160.74	(step @p251 :rule ho_cong :premises (@p250 @p142))
160.24/160.74	(step @p252 :rule cong :premises (@p137 @p251) :args (@t15))
160.24/160.74	(step @p253 :rule cong :premises (@p145 @p252) :args (@t17))
160.24/160.74	(step @p254 :rule cong :premises (@p253) :args (@t19))
160.24/160.74	(step @p255 :rule trans :premises (@p254 @p249))
160.24/160.74	(step @p256 :rule cong :premises (@p149 @p255) :args (@t21))
160.24/160.74	(step @p257 :rule cong :premises (@p256) :args (@t23))
160.24/160.74	(step @p258 :rule trans :premises (@p257 @p221))
160.24/160.74	(step @p259 :rule refl :args (tptp.iftrueProp1))
160.24/160.74	(step @p260 :rule cong :premises (@p259 @p258) :args (@t24))
160.24/160.74	(step @p261 :rule eq_resolve :premises (@p1 @p260))
160.24/160.74	(step @p262 :rule cong :premises (@p261 @p156) :args (@t164))
160.24/160.74	(step @p263 :rule cong :premises (@p262) :args ((not @t164)))
160.24/160.74	(step @p264 :rule aci_norm :args ((= (or @t59 false @t57 @t55) @t60)))
160.24/160.74	(step @p265 :rule absorb :args ((= (and false @t165) false)))
160.24/160.74	(step @p266 :rule refl :args (@t165))
160.24/160.74	(step @p267 :rule nary_cong :premises (@p161 @p266) :args (@t166))
160.24/160.74	(step @p268 :rule trans :premises (@p267 @p265))
160.24/160.74	(step @p269 :rule nary_cong :premises (@p164 @p268) :args (@t167))
160.24/160.74	(step @p270 :rule trans :premises (@p269 @p158))
160.24/160.74	(step @p271 :rule cong :premises (@p270) :args (@t168))
160.24/160.74	(step @p272 :rule cong :premises (@p75 @p271) :args (@t169))
160.24/160.74	(step @p273 :rule cong :premises (@p272) :args (@t170))
160.24/160.74	(step @p274 :rule cong :premises (@p169 @p273) :args (@t171))
160.24/160.74	(step @p275 :rule refl :args (@t57))
160.24/160.74	(step @p276 :rule nary_cong :premises (@p79 @p161 @p275 @p274) :args (@t172))
160.24/160.74	(step @p277 :rule trans :premises (@p276 @p264))
160.24/160.74	(step @p278 :rule cong :premises (@p277) :args ((forall @t61 @t172)))
160.24/160.74	(step @p279 :rule quant-var-elim-eq :args ((= (forall @t133 (or @t132 @t59 @t4 @t57 @t173)) @t172)))
160.24/160.74	(step @p280 :rule refl :args (@t173))
160.24/160.74	(step @p281 :rule refl :args (@t57))
160.24/160.74	(step @p282 :rule nary_cong :premises (@p181 @p86 @p178 @p281 @p280) :args (@t174))
160.24/160.74	(step @p283 :rule aci_norm :args ((= @t175 @t174)))
160.24/160.74	(step @p284 :rule trans :premises (@p283 @p282))
160.24/160.74	(step @p285 :rule cong :premises (@p284) :args (@t176))
160.24/160.74	(step @p286 :rule trans :premises (@p285 @p279))
160.24/160.74	(step @p287 :rule cong :premises (@p286) :args (@t177))
160.24/160.74	(step @p288 :rule quant-merge-prenex :args ((= @t177 @t178)))
160.24/160.74	(step @p289 :rule symm :premises (@p288))
160.24/160.74	(step @p290 :rule quant_var_reordering :args ((= (forall @t179 @t175) @t178)))
160.24/160.74	(step @p291 :rule trans :premises (@p290 @p289 @p287))
160.24/160.74	(step @p292 :rule trans :premises (@p291 @p278))
160.24/160.74	(step @p293 :rule eq-symm :args (@t56 @t2))
160.24/160.74	(step @p294 :rule nary_cong :premises (@p70 @p293) :args (@t180))
160.24/160.74	(step @p295 :rule nary_cong :premises (@p72 @p294) :args (@t181))
160.24/160.74	(step @p296 :rule cong :premises (@p295) :args (@t182))
160.24/160.74	(step @p297 :rule cong :premises (@p75 @p296) :args (@t183))
160.24/160.74	(step @p298 :rule cong :premises (@p297) :args (@t184))
160.24/160.74	(step @p299 :rule cong :premises (@p169 @p298) :args (@t185))
160.24/160.74	(step @p300 :rule nary_cong :premises (@p79 @p70 @p275 @p299) :args (@t186))
160.24/160.74	(step @p301 :rule aci_norm :args ((= @t188 @t186)))
160.24/160.74	(step @p302 :rule trans :premises (@p301 @p300))
160.24/160.74	(step @p303 :rule cong :premises (@p302) :args (@t189))
160.24/160.74	(step @p304 :rule trans :premises (@p303 @p292))
160.24/160.74	(step @p305 :rule quant-merge-prenex :args ((= (forall @t22 @t191) @t189)))
160.24/160.74	(step @p306 :rule alpha_equiv :args (@t192 (@list @t56) @t102))
160.24/160.74	(step @p307 :rule nary_cong :premises (@p86 @p178 @p306) :args (@t193))
160.24/160.74	(step @p308 :rule quant-miniscope-or :args ((= @t191 @t193)))
160.24/160.74	(step @p309 :rule trans :premises (@p308 @p307))
160.24/160.74	(step @p310 :rule symm :premises (@p309))
160.24/160.74	(step @p311 :rule cong :premises (@p310) :args ((forall @t22 (or @t59 @t4 @t195))))
160.24/160.74	(step @p312 :rule trans :premises (@p311 @p305))
160.24/160.74	(step @p313 :rule trans :premises (@p312 @p304))
160.24/160.74	(step @p314 :rule refl :args (@t195))
160.24/160.74	(step @p315 :rule nary_cong :premises (@p100 @p178 @p314) :args (@t196))
160.24/160.74	(step @p316 :rule cong :premises (@p315) :args ((forall @t22 @t196)))
160.24/160.74	(step @p317 :rule trans :premises (@p316 @p313))
160.24/160.74	(step @p318 :rule aci_norm :args ((= (or @t110 @t197) @t196)))
160.24/160.74	(step @p319 :rule bool-impl-elim :args (@t20 @t197))
160.24/160.74	(step @p320 :rule trans :premises (@p319 @p318))
160.24/160.74	(step @p321 :rule cong :premises (@p320) :args ((forall @t22 (=> @t20 @t197))))
160.24/160.74	(step @p322 :rule trans :premises (@p321 @p317))
160.24/160.74	(step @p323 :rule refl :args ((tptp.setunion @t112)))
160.24/160.74	(step @p324 :rule cong :premises (@p108) :args (@t194))
160.24/160.74	(step @p325 :rule trans :premises (@p324 @p323))
160.24/160.74	(step @p326 :rule refl :args (tptp.setunion))
160.24/160.74	(step @p327 :rule ho_cong :premises (@p326 @p108))
160.24/160.74	(step @p328 :rule cong :premises (@p327 @p325) :args ((= (_ tptp.setunion @t105) @t194)))
160.24/160.74	(step @p329 :rule symm :premises (@p328))
160.24/160.74	(step @p330 :rule refl :args (@t198))
160.24/160.74	(step @p331 :rule eq_resolve :premises (@p330 @p329))
160.24/160.74	(step @p332 :rule ho_cong :premises (@p326 @p120))
160.24/160.74	(step @p333 :rule trans :premises (@p332 @p331))
160.24/160.74	(step @p334 :rule cong :premises (@p43 @p333) :args (@t199))
160.24/160.74	(step @p335 :rule nary_cong :premises (@p128 @p334) :args (@t200))
160.24/160.74	(step @p336 :rule cong :premises (@p335) :args (@t201))
160.24/160.74	(step @p337 :rule nary_cong :premises (@p70 @p336) :args (@t202))
160.24/160.74	(step @p338 :rule quant-miniscope-or :args ((= (forall @t18 @t203) @t202)))
160.24/160.74	(step @p339 :rule aci_norm :args ((= @t204 @t203)))
160.24/160.74	(step @p340 :rule cong :premises (@p339) :args ((forall @t18 @t204)))
160.24/160.74	(step @p341 :rule trans :premises (@p340 @p338))
160.24/160.74	(step @p342 :rule trans :premises (@p341 @p337))
160.24/160.74	(step @p343 :rule aci_norm :args ((= (or @t114 (or @t4 @t199)) @t204)))
160.24/160.74	(step @p344 :rule bool-impl-elim :args (@t3 @t199))
160.24/160.74	(step @p345 :rule nary_cong :premises (@p243 @p344) :args ((or @t114 @t205)))
160.24/160.74	(step @p346 :rule trans :premises (@p345 @p343))
160.24/160.74	(step @p347 :rule bool-impl-elim :args (@t16 @t205))
160.24/160.74	(step @p348 :rule trans :premises (@p347 @p346))
160.24/160.74	(step @p349 :rule cong :premises (@p348) :args ((forall @t18 (=> @t16 @t205))))
160.24/160.74	(step @p350 :rule trans :premises (@p349 @p342))
160.24/160.74	(step @p351 :rule eq-symm :args (@t198 @t6))
160.24/160.74	(step @p352 :rule beta-reduce :args ((= (_ @t206 @t1) @t198)))
160.24/160.74	(step @p353 :rule refl :args (@t1))
160.24/160.74	(step @p354 :rule beta-reduce :args ((= (_ @t207 @t6) @t206)))
160.24/160.74	(step @p355 :rule beta-reduce :args ((= (_ @t208 @t3) @t207)))
160.24/160.74	(step @p356 :rule beta-reduce :args ((= @t209 @t208)))
160.24/160.74	(step @p357 :rule ho_cong :premises (@p356 @p137))
160.24/160.74	(step @p358 :rule trans :premises (@p357 @p355))
160.24/160.74	(step @p359 :rule ho_cong :premises (@p358 @p169))
160.24/160.74	(step @p360 :rule trans :premises (@p359 @p354))
160.24/160.74	(step @p361 :rule ho_cong :premises (@p360 @p353))
160.24/160.74	(step @p362 :rule trans :premises (@p361 @p352))
160.24/160.74	(step @p363 :rule cong :premises (@p362 @p169) :args (@t210))
160.24/160.74	(step @p364 :rule trans :premises (@p363 @p351))
160.24/160.74	(step @p365 :rule cong :premises (@p137 @p364) :args (@t211))
160.24/160.74	(step @p366 :rule cong :premises (@p145 @p365) :args (@t212))
160.24/160.74	(step @p367 :rule cong :premises (@p366) :args (@t213))
160.24/160.74	(step @p368 :rule trans :premises (@p367 @p350))
160.24/160.74	(step @p369 :rule cong :premises (@p149 @p368) :args (@t214))
160.24/160.74	(step @p370 :rule cong :premises (@p369) :args (@t215))
160.24/160.74	(step @p371 :rule trans :premises (@p370 @p322))
160.24/160.74	(step @p372 :rule cong :premises (@p65 @p371) :args (@t216))
160.24/160.74	(step @p373 :rule cong :premises (@p153 @p372) :args (@t217))
160.24/160.74	(step @p374 :rule cong :premises (@p259 @p373) :args (@t218))
160.24/160.74	(step @p375 :rule cong :premises (@p374) :args ((not @t218)))
160.24/160.74	(step @p376 :rule refl :args (tptp.setunion))
160.24/160.74	(step @p377 :rule ho_cong :premises (@p376 @p142))
160.24/160.74	(step @p378 :rule cong :premises (@p377) :args (@t52))
160.24/160.74	(step @p379 :rule trans :premises (@p6 @p378))
160.24/160.74	(step @p380 :rule ho_cong :premises (@p379 @p75))
160.24/160.74	(step @p381 :rule ho_cong :premises (@p380 @p137))
160.24/160.74	(step @p382 :rule ho_cong :premises (@p381 @p169))
160.24/160.74	(step @p383 :rule ho_cong :premises (@p382 @p353))
160.24/160.74	(step @p384 :rule cong :premises (@p383 @p169) :args (@t41))
160.24/160.74	(step @p385 :rule cong :premises (@p137 @p384) :args (@t42))
160.24/160.74	(step @p386 :rule cong :premises (@p145 @p385) :args (@t43))
160.24/160.74	(step @p387 :rule cong :premises (@p386) :args (@t44))
160.24/160.74	(step @p388 :rule cong :premises (@p149 @p387) :args (@t45))
160.24/160.74	(step @p389 :rule cong :premises (@p388) :args (@t46))
160.24/160.74	(step @p390 :rule cong :premises (@p65 @p389) :args (@t47))
160.24/160.74	(step @p391 :rule cong :premises (@p153 @p390) :args (@t48))
160.24/160.74	(step @p392 :rule cong :premises (@p259 @p391) :args (@t49))
160.24/160.74	(step @p393 :rule cong :premises (@p392) :args (@t50))
160.24/160.74	(step @p394 :rule trans :premises (@p393 @p375))
160.24/160.74	(step @p395 :rule trans :premises (@p394 @p263))
160.24/160.74	(step @p396 :rule eq_resolve :premises (@p4 @p395))
160.24/160.74	(step @p397 :rule not_implies_elim2 :premises (@p396))
160.24/160.74	(step @p398 :rule not_implies_elim2 :premises (@p397))
160.24/160.74	(step @p399 :rule not_implies_elim1 :premises (@p398))
160.24/160.74	(step @p400 :rule not_implies_elim1 :premises (@p397))
160.24/160.74	(step @p401 :rule eq-refl :args (@t221))
160.24/160.74	(step @p402 :rule skolem_intro :args (@t222))
160.24/160.74	(step @p403 :rule refl :args (@t221))
160.24/160.74	(step @p404 :rule cong :premises (@p403 @p402) :args ((= @t221 @t222)))
160.24/160.74	(step @p405 :rule trans :premises (@p404 @p401))
160.24/160.74	(step @p406 :rule true_elim :premises (@p405))
160.24/160.74	(step @p407 :rule refl :args (@t223))
160.24/160.74	(step @p408 :rule cong :premises (@p407 @p406) :args (@t224))
160.24/160.74	(step @p409 :rule cong :premises (@p408) :args (@t225))
160.24/160.74	(step @p410 :rule refl :args (@t227))
160.24/160.74	(step @p411 :rule nary_cong :premises (@p410 @p410 @p409) :args (@t228))
160.24/160.74	(step @p412 :rule refl :args (@t229))
160.24/160.74	(step @p413 :rule cong :premises (@p412 @p411) :args ((=> @t229 @t228)))
160.24/160.74	(step @p414 :rule aci_norm :args ((= (or false @t220) @t220)))
160.24/160.74	(step @p415 :rule aci_norm :args ((= (and true @t220) @t220)))
160.24/160.74	(step @p416 :rule refl :args (@t220))
160.24/160.74	(step @p417 :rule evaluate :args (@t230))
160.24/160.74	(step @p418 :rule nary_cong :premises (@p417 @p416) :args (@t231))
160.24/160.74	(step @p419 :rule trans :premises (@p418 @p415))
160.24/160.74	(step @p420 :rule absorb :args ((= @t233 false)))
160.24/160.74	(step @p421 :rule nary_cong :premises (@p420 @p419) :args (@t234))
160.24/160.74	(step @p422 :rule trans :premises (@p421 @p414))
160.24/160.74	(step @p423 :rule cong :premises (@p422) :args (@t235))
160.24/160.74	(step @p424 :rule cong :premises (@p407 @p423) :args (@t236))
160.24/160.74	(step @p425 :rule cong :premises (@p424) :args (@t237))
160.24/160.74	(step @p426 :rule nary_cong :premises (@p410 @p410 @p425) :args (@t238))
160.24/160.74	(step @p427 :rule cong :premises (@p412 @p426) :args ((=> @t229 @t238)))
160.24/160.74	(assume-push @p514 @t229)
160.24/160.74	(step @p429 :rule instantiate :premises (@p400) :args ((@list @t223 false @t219 @t219)))
160.24/160.74	(step-pop @p514 :rule scope :premises (@p429))
160.24/160.74	(step @p430 :rule process_scope :premises (@p514) :args (@t238))
160.24/160.74	(step @p432 :rule eq_resolve :premises (@p430 @p427))
160.24/160.74	(step @p433 :rule eq_resolve :premises (@p432 @p413))
160.24/160.74	(step @p434 :rule implies_elim :premises (@p433))
160.24/160.74	(step @p435 :rule chain_resolution :premises (@p434 @p400) :args (@t239 (@list @t229)))
160.24/160.74	(step @p436 :rule not_implies_elim2 :premises (@p398))
160.24/160.74	(step @p437 :rule refl :args (@t245))
160.24/160.74	(step @p438 :rule bool-double-not-elim :args (@t62))
160.24/160.74	(step @p439 :rule nary_cong :premises (@p438 @p437) :args ((or (not @t246) @t245)))
160.24/160.74	(step @p440 :rule cong :premises (@p408) :args (@t247))
160.24/160.74	(step @p441 :rule refl :args (@t219))
160.24/160.74	(step @p442 :rule cong :premises (@p441 @p440) :args (@t248))
160.24/160.74	(step @p443 :rule refl :args (@t243))
160.24/160.74	(step @p444 :rule nary_cong :premises (@p410 @p443 @p442) :args (@t249))
160.24/160.74	(step @p445 :rule cong :premises (@p444) :args (@t250))
160.24/160.74	(step @p446 :rule refl :args (@t246))
160.24/160.74	(step @p447 :rule cong :premises (@p446 @p445) :args ((=> @t246 @t250)))
160.24/160.74	(step @p448 :rule eq-symm :args (@t219 @t2))
160.24/160.74	(step @p449 :rule cong :premises (@p448) :args (@t251))
160.24/160.74	(step @p450 :rule cong :premises (@p407 @p449) :args (@t252))
160.24/160.74	(step @p451 :rule cong :premises (@p450) :args (@t253))
160.24/160.74	(step @p452 :rule cong :premises (@p441 @p451) :args (@t254))
160.24/160.74	(step @p453 :rule nary_cong :premises (@p410 @p443 @p452) :args (@t255))
160.24/160.74	(step @p454 :rule cong :premises (@p453) :args (@t256))
160.24/160.74	(step @p455 :rule cong :premises (@p446 @p454) :args ((=> @t246 @t256)))
160.24/160.74	(step @p456 :rule trans :premises (@p455 @p447))
160.24/160.74	(assume-push @p516 @t246)
160.24/160.74	(step @p458 :rule skolemize :premises (@p436))
160.24/160.74	(step-pop @p516 :rule scope :premises (@p458))
160.24/160.74	(step @p459 :rule process_scope :premises (@p516) :args (@t256))
160.24/160.74	(step @p461 :rule eq_resolve :premises (@p459 @p456))
160.24/160.74	(step @p462 :rule implies_elim :premises (@p461))
160.24/160.74	(step @p463 :rule eq_resolve :premises (@p462 @p439))
160.24/160.74	(step @p464 :rule chain_resolution :premises (@p463 @p436) :args (@t257 (@list @t62)))
160.24/160.74	(step @p465 :rule bool-double-not-elim :args (@t226))
160.24/160.74	(step @p466 :rule refl :args (@t244))
160.24/160.74	(step @p467 :rule nary_cong :premises (@p466 @p465) :args ((or @t244 (not @t227))))
160.24/160.74	(step @p468 :rule cnf_or_neg :args (@t244 0))
160.24/160.74	(step @p469 :rule eq_resolve :premises (@p468 @p467))
160.24/160.74	(step @p470 :rule reordering :premises (@p469) :args ((or @t226 @t244)))
160.24/160.74	(step @p471 :rule chain_resolution :premises (@p470 @p464) :args (@t257 @t258))
160.24/160.74	(step @p472 :rule cnf_or_pos :args (@t260))
160.24/160.74	(step @p473 :rule factoring :premises (@p472))
160.24/160.74	(step @p474 :rule reordering :premises (@p473) :args ((or @t227 @t259 (not @t260))))
160.24/160.74	(step @p475 :rule chain_resolution :premises (@p474 @p471 @p435) :args (@t261 (@list @t226 @t260)))
160.24/160.74	(step @p476 :rule not_implies_elim1 :premises (@p396))
160.24/160.74	(step @p477 :rule cong :premises (@p441 @p408) :args (@t262))
160.24/160.74	(step @p478 :rule nary_cong :premises (@p410 @p410 @p477) :args (@t263))
160.24/160.74	(step @p479 :rule refl :args (@t264))
160.24/160.74	(step @p480 :rule cong :premises (@p479 @p478) :args ((=> @t264 @t263)))
160.24/160.74	(step @p481 :rule cong :premises (@p441 @p450) :args (@t265))
160.24/160.74	(step @p482 :rule nary_cong :premises (@p410 @p410 @p481) :args (@t266))
160.24/160.74	(step @p483 :rule cong :premises (@p479 @p482) :args ((=> @t264 @t266)))
160.24/160.74	(assume-push @p518 @t264)
160.24/160.74	(step @p485 :rule instantiate :premises (@p476) :args ((@list @t223 @t219 @t219)))
160.24/160.74	(step-pop @p518 :rule scope :premises (@p485))
160.24/160.74	(step @p486 :rule process_scope :premises (@p518) :args (@t266))
160.24/160.74	(step @p488 :rule eq_resolve :premises (@p486 @p483))
160.24/160.74	(step @p489 :rule eq_resolve :premises (@p488 @p480))
160.24/160.74	(step @p490 :rule implies_elim :premises (@p489))
160.24/160.74	(step @p491 :rule chain_resolution :premises (@p490 @p476) :args (@t239 (@list @t264)))
160.24/160.74	(step @p492 :rule cnf_or_pos :args (@t268))
160.24/160.74	(step @p493 :rule factoring :premises (@p492))
160.24/160.74	(step @p494 :rule reordering :premises (@p493) :args ((or @t227 @t267 (not @t268))))
160.24/160.74	(step @p495 :rule chain_resolution :premises (@p494 @p471 @p491) :args (@t261 (@list @t226 @t268)))
160.24/160.74	(step @p496 :rule cnf_or_neg :args (@t244 2))
160.24/160.74	(step @p497 :rule chain_resolution :premises (@p496 @p464) :args (@t257 @t258))
160.24/160.74	(step @p498 :rule cnf_or_pos :args (@t271))
160.24/160.74	(step @p499 :rule reordering :premises (@p498) :args ((or @t242 @t269 @t270 (not @t271))))
160.24/160.74	(step @p500 :rule chain_resolution :premises (@p499 @p497 @p495 @p475) :args ((@list true false false) (@list @t242 @t267 @t259)))
160.24/160.74	(step @p501 :rule eq-symm :args (@t241 @t219))
160.24/160.74	(step @p502 :rule refl :args (@t269))
160.24/160.74	(step @p503 :rule refl :args (@t270))
160.24/160.74	(step @p504 :rule nary_cong :premises (@p503 @p502 @p501) :args (@t272))
160.24/160.74	(step @p505 :rule refl :args (@t273))
160.24/160.74	(step @p506 :rule cong :premises (@p505 @p504) :args ((=> @t273 @t272)))
160.24/160.74	(assume-push @p520 @t273)
160.24/160.74	(step @p508 :rule instantiate :premises (@p399) :args ((@list @t240 @t219)))
160.24/160.74	(step-pop @p520 :rule scope :premises (@p508))
160.24/160.74	(step @p509 :rule process_scope :premises (@p520) :args (@t272))
160.24/160.74	(step @p511 :rule eq_resolve :premises (@p509 @p506))
160.24/160.74	(step @p512 :rule implies_elim :premises (@p511))
160.24/160.74	(step @p513 false :rule chain_resolution :premises (@p512 @p500 @p399) :args ((@list true false) (@list @t271 @t273)))
160.24/160.74	)
160.24/160.74	% SZS output end Proof
160.24/160.74	% cvc5 exiting
160.24/160.74	EOF