%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU708^2 : 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 : n020.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 08:52:49 AM UTC 2026 % Result : Theorem 201.83s 202.20s % Output : Proof 201.83s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU708^2 : TPTP v9.2.1. Released v3.7.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.15/0.34 % Computer : n020.cluster.edu % 0.15/0.34 % Model : x86_64 x86_64 % 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.34 % Memory : 8042.1875MB % 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.34 % CPULimit : 300 % 0.15/0.34 % WCLimit : 300 % 0.15/0.34 % DateTime : Tue Jun 2 17:48:10 EDT 2026 % 0.15/0.34 % CPUTime : % 0.32/0.49 %----Proving TH0 % 201.83/202.20 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 201.83/202.20 --- 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 30s... % 201.83/202.20 --- 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 30s... % 201.83/202.20 --- Run --ho-elim --full-saturate-quant at 18s... % 201.83/202.20 --- Run --ho-elim --no-e-matching --full-saturate-quant at 12s... % 201.83/202.20 --- Run --ho-elim --no-e-matching --enum-inst-sum --full-saturate-quant at 12s... % 201.83/202.20 --- Run --ho-elim --finite-model-find --uf-ss=no-minimal at 9s... % 201.83/202.20 --- Run --no-ho-matching --finite-model-find --uf-ss=no-minimal at 6s... % 201.83/202.20 % SZS status Theorem % 201.83/202.20 % SZS output start Proof % 201.83/202.20 ( % 201.83/202.20 (declare-sort $$unsorted 0) % 201.83/202.20 (declare-const tptp.dsetconstr (-> $$unsorted (-> $$unsorted Bool) $$unsorted)) % 201.83/202.20 (declare-const tptp.setunion (-> $$unsorted $$unsorted)) % 201.83/202.20 (declare-const tptp.theeq Bool) % 201.83/202.20 (declare-const tptp.ifSingleton Bool) % 201.83/202.20 (declare-const tptp.singleton (-> $$unsorted Bool)) % 201.83/202.20 (declare-const tptp.iffalseProp1 Bool) % 201.83/202.20 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 201.83/202.20 (define tptp.if () (let ((_let_1 (@var "Xy" $$unsorted))) (let ((_let_2 (@var "Xz" $$unsorted))) (let ((_let_3 (@var "Xphi" Bool))) (let ((_let_4 (@var "Xx" $$unsorted))) (let ((_let_5 (@var "A" $$unsorted))) (lambda (@list _let_5 _let_3 _let_4 _let_1) (_ tptp.setunion (_ (_ tptp.dsetconstr _let_5) (lambda (@list _let_2) (or (and _let_3 (= _let_2 _let_4)) (and (not _let_3) (= _let_2 _let_1))))))))))))) % 201.83/202.20 (define @t1 () (@var "Xy" $$unsorted)) % 201.83/202.20 (define @t2 () (@var "Xz" $$unsorted)) % 201.83/202.20 (define @t3 () (@var "Xphi" Bool)) % 201.83/202.20 (define @t4 () (not @t3)) % 201.83/202.20 (define @t5 () (and @t4 (= @t2 @t1))) % 201.83/202.20 (define @t6 () (@var "Xx" $$unsorted)) % 201.83/202.20 (define @t7 () (and @t3 (= @t2 @t6))) % 201.83/202.20 (define @t8 () (or @t7 @t5)) % 201.83/202.20 (define @t9 () (@list @t2)) % 201.83/202.20 (define @t10 () (lambda @t9 @t8)) % 201.83/202.20 (define @t11 () (@var "A" $$unsorted)) % 201.83/202.20 (define @t12 () (_ tptp.dsetconstr @t11)) % 201.83/202.20 (define @t13 () (_ @t12 @t10)) % 201.83/202.20 (define @t14 () (_ tptp.in @t1)) % 201.83/202.20 (define @t15 () (=> @t4 (_ @t14 @t13))) % 201.83/202.20 (define @t16 () (_ @t14 @t11)) % 201.83/202.20 (define @t17 () (=> @t16 @t15)) % 201.83/202.20 (define @t18 () (@list @t1)) % 201.83/202.20 (define @t19 () (forall @t18 @t17)) % 201.83/202.20 (define @t20 () (_ tptp.in @t6)) % 201.83/202.20 (define @t21 () (_ @t20 @t11)) % 201.83/202.20 (define @t22 () (=> @t21 @t19)) % 201.83/202.20 (define @t23 () (@list @t11 @t3 @t6)) % 201.83/202.20 (define @t24 () (forall @t23 @t22)) % 201.83/202.20 (define @t25 () (= tptp.iffalseProp1 @t24)) % 201.83/202.20 (define @t26 () (=> @t16 (_ tptp.singleton @t13))) % 201.83/202.20 (define @t27 () (forall @t18 @t26)) % 201.83/202.20 (define @t28 () (=> @t21 @t27)) % 201.83/202.20 (define @t29 () (forall @t23 @t28)) % 201.83/202.20 (define @t30 () (= tptp.ifSingleton @t29)) % 201.83/202.20 (define @t31 () (@var "X" $$unsorted)) % 201.83/202.20 (define @t32 () (_ tptp.setunion @t31)) % 201.83/202.20 (define @t33 () (_ @t20 @t31)) % 201.83/202.20 (define @t34 () (=> @t33 (= @t32 @t6))) % 201.83/202.20 (define @t35 () (@list @t6)) % 201.83/202.20 (define @t36 () (forall @t35 @t34)) % 201.83/202.20 (define @t37 () (_ tptp.singleton @t31)) % 201.83/202.20 (define @t38 () (=> @t37 @t36)) % 201.83/202.20 (define @t39 () (@list @t31)) % 201.83/202.20 (define @t40 () (forall @t39 @t38)) % 201.83/202.20 (define @t41 () (= tptp.theeq @t40)) % 201.83/202.20 (define @t42 () (= (_ (_ (_ (_ tptp.if @t11) @t3) @t6) @t1) @t1)) % 201.83/202.20 (define @t43 () (=> @t4 @t42)) % 201.83/202.20 (define @t44 () (=> @t16 @t43)) % 201.83/202.20 (define @t45 () (forall @t18 @t44)) % 201.83/202.20 (define @t46 () (=> @t21 @t45)) % 201.83/202.20 (define @t47 () (forall @t23 @t46)) % 201.83/202.20 (define @t48 () (=> tptp.theeq @t47)) % 201.83/202.20 (define @t49 () (=> tptp.ifSingleton @t48)) % 201.83/202.20 (define @t50 () (=> tptp.iffalseProp1 @t49)) % 201.83/202.20 (define @t51 () (not @t50)) % 201.83/202.20 (define @t52 () (@list @t11 @t3 @t6 @t1)) % 201.83/202.20 (define @t53 () (lambda @t52 (_ tptp.setunion @t13))) % 201.83/202.20 (define @t54 () (@var "BOUND_VARIABLE_7696" $$unsorted)) % 201.83/202.20 (define @t55 () (= @t2 @t54)) % 201.83/202.20 (define @t56 () (not (tptp.in @t54 @t11))) % 201.83/202.20 (define @t57 () (tptp.in @t6 @t11)) % 201.83/202.20 (define @t58 () (not @t57)) % 201.83/202.20 (define @t59 () (@list @t11 @t6 @t54)) % 201.83/202.20 (define @t60 () (forall @t59 (or @t58 @t56 (= @t54 (tptp.setunion (tptp.dsetconstr @t11 (lambda @t9 @t55))))))) % 201.83/202.20 (define @t61 () (@var "BOUND_VARIABLE_7641" $$unsorted)) % 201.83/202.20 (define @t62 () (tptp.setunion @t31)) % 201.83/202.20 (define @t63 () (not (tptp.in @t61 @t31))) % 201.83/202.20 (define @t64 () (tptp.singleton @t31)) % 201.83/202.20 (define @t65 () (not @t64)) % 201.83/202.20 (define @t66 () (= @t61 @t62)) % 201.83/202.20 (define @t67 () (or @t65 @t63 @t66)) % 201.83/202.20 (define @t68 () (or @t63 @t66)) % 201.83/202.20 (define @t69 () (or @t65 @t68)) % 201.83/202.20 (define @t70 () (@list @t31 @t61)) % 201.83/202.20 (define @t71 () (forall @t70 @t69)) % 201.83/202.20 (define @t72 () (@list @t61)) % 201.83/202.20 (define @t73 () (forall @t72 @t69)) % 201.83/202.20 (define @t74 () (forall @t72 @t68)) % 201.83/202.20 (define @t75 () (or @t65 @t74)) % 201.83/202.20 (define @t76 () (tptp.in @t6 @t31)) % 201.83/202.20 (define @t77 () (forall @t35 (or (not @t76) (= @t6 @t62)))) % 201.83/202.20 (define @t78 () (not @t37)) % 201.83/202.20 (define @t79 () (or @t78 @t77)) % 201.83/202.20 (define @t80 () (= @t6 @t32)) % 201.83/202.20 (define @t81 () (not @t33)) % 201.83/202.20 (define @t82 () (or @t81 @t80)) % 201.83/202.20 (define @t83 () (=> tptp.theeq @t60)) % 201.83/202.20 (define @t84 () (@var "BOUND_VARIABLE_7588" $$unsorted)) % 201.83/202.20 (define @t85 () (and @t4 (= @t84 @t2))) % 201.83/202.20 (define @t86 () (= @t6 @t2)) % 201.83/202.20 (define @t87 () (and @t3 @t86)) % 201.83/202.20 (define @t88 () (or @t87 @t85)) % 201.83/202.20 (define @t89 () (lambda @t9 @t88)) % 201.83/202.20 (define @t90 () (tptp.dsetconstr @t11 @t89)) % 201.83/202.20 (define @t91 () (tptp.singleton @t90)) % 201.83/202.20 (define @t92 () (not (tptp.in @t84 @t11))) % 201.83/202.20 (define @t93 () (or @t58 @t92 @t91)) % 201.83/202.20 (define @t94 () (or @t92 @t91)) % 201.83/202.20 (define @t95 () (or @t58 @t94)) % 201.83/202.20 (define @t96 () (@list @t11 @t3 @t6 @t84)) % 201.83/202.20 (define @t97 () (forall @t96 @t95)) % 201.83/202.20 (define @t98 () (@list @t84)) % 201.83/202.20 (define @t99 () (forall @t98 @t95)) % 201.83/202.20 (define @t100 () (forall @t98 @t94)) % 201.83/202.20 (define @t101 () (@list @t1)) % 201.83/202.20 (define @t102 () (or @t58 @t100)) % 201.83/202.20 (define @t103 () (lambda @t9 (or @t87 (and @t4 (= @t1 @t2))))) % 201.83/202.20 (define @t104 () (tptp.dsetconstr @t11 @t103)) % 201.83/202.20 (define @t105 () (tptp.singleton @t104)) % 201.83/202.20 (define @t106 () (tptp.in @t1 @t11)) % 201.83/202.20 (define @t107 () (not @t106)) % 201.83/202.20 (define @t108 () (forall @t18 (or @t107 @t105))) % 201.83/202.20 (define @t109 () (not @t21)) % 201.83/202.20 (define @t110 () (or @t109 @t108)) % 201.83/202.20 (define @t111 () (_ @t12 @t103)) % 201.83/202.20 (define @t112 () (_ tptp.singleton @t111)) % 201.83/202.20 (define @t113 () (not @t16)) % 201.83/202.20 (define @t114 () (or @t113 @t112)) % 201.83/202.20 (define @t115 () (=> tptp.ifSingleton @t83)) % 201.83/202.20 (define @t116 () (@var "BOUND_VARIABLE_7531" $$unsorted)) % 201.83/202.20 (define @t117 () (= @t2 @t116)) % 201.83/202.20 (define @t118 () (not false)) % 201.83/202.20 (define @t119 () (and @t118 @t117)) % 201.83/202.20 (define @t120 () (and false @t86)) % 201.83/202.20 (define @t121 () (or @t120 @t119)) % 201.83/202.20 (define @t122 () (lambda @t9 @t121)) % 201.83/202.20 (define @t123 () (tptp.dsetconstr @t11 @t122)) % 201.83/202.20 (define @t124 () (tptp.in @t116 @t123)) % 201.83/202.20 (define @t125 () (not (tptp.in @t116 @t11))) % 201.83/202.20 (define @t126 () (or @t58 @t125 @t124)) % 201.83/202.20 (define @t127 () (or @t58 false @t125 @t124)) % 201.83/202.20 (define @t128 () (@list @t11 @t6 @t116)) % 201.83/202.20 (define @t129 () (tptp.in @t116 (tptp.dsetconstr @t11 (lambda @t9 (or @t87 (and @t4 @t117)))))) % 201.83/202.20 (define @t130 () (not (= @t3 false))) % 201.83/202.20 (define @t131 () (@list @t3)) % 201.83/202.20 (define @t132 () (not @t4)) % 201.83/202.20 (define @t133 () (or @t3 @t58 @t3 @t125 @t129)) % 201.83/202.20 (define @t134 () (or @t58 @t3 @t125 @t129)) % 201.83/202.20 (define @t135 () (forall @t131 @t134)) % 201.83/202.20 (define @t136 () (forall @t128 @t135)) % 201.83/202.20 (define @t137 () (forall (@list @t11 @t6 @t116 @t3) @t134)) % 201.83/202.20 (define @t138 () (@list @t11 @t3 @t6 @t116)) % 201.83/202.20 (define @t139 () (and @t4 (= @t116 @t2))) % 201.83/202.20 (define @t140 () (or @t87 @t139)) % 201.83/202.20 (define @t141 () (lambda @t9 @t140)) % 201.83/202.20 (define @t142 () (tptp.dsetconstr @t11 @t141)) % 201.83/202.20 (define @t143 () (tptp.in @t116 @t142)) % 201.83/202.20 (define @t144 () (or @t58 @t3 @t125 @t143)) % 201.83/202.20 (define @t145 () (or @t125 @t143)) % 201.83/202.20 (define @t146 () (or @t58 @t3 @t145)) % 201.83/202.20 (define @t147 () (forall @t138 @t146)) % 201.83/202.20 (define @t148 () (@list @t116)) % 201.83/202.20 (define @t149 () (forall @t148 @t146)) % 201.83/202.20 (define @t150 () (forall @t148 @t145)) % 201.83/202.20 (define @t151 () (or @t58 @t3 @t150)) % 201.83/202.20 (define @t152 () (tptp.in @t1 @t104)) % 201.83/202.20 (define @t153 () (forall @t18 (or @t107 @t152))) % 201.83/202.20 (define @t154 () (or @t109 @t3 @t153)) % 201.83/202.20 (define @t155 () (or @t3 @t153)) % 201.83/202.20 (define @t156 () (_ @t14 @t111)) % 201.83/202.20 (define @t157 () (or @t113 @t156)) % 201.83/202.20 (define @t158 () (forall @t18 @t157)) % 201.83/202.20 (define @t159 () (or @t3 @t158)) % 201.83/202.20 (define @t160 () (or @t3 @t157)) % 201.83/202.20 (define @t161 () (or @t113 @t3 @t156)) % 201.83/202.20 (define @t162 () (=> @t4 @t156)) % 201.83/202.20 (define @t163 () (=> tptp.iffalseProp1 @t115)) % 201.83/202.20 (define @t164 () (and @t118 @t55)) % 201.83/202.20 (define @t165 () (or @t120 @t164)) % 201.83/202.20 (define @t166 () (lambda @t9 @t165)) % 201.83/202.20 (define @t167 () (tptp.dsetconstr @t11 @t166)) % 201.83/202.20 (define @t168 () (tptp.setunion @t167)) % 201.83/202.20 (define @t169 () (= @t54 @t168)) % 201.83/202.20 (define @t170 () (or @t58 @t56 @t169)) % 201.83/202.20 (define @t171 () (or @t58 false @t56 @t169)) % 201.83/202.20 (define @t172 () (= @t54 (tptp.setunion (tptp.dsetconstr @t11 (lambda @t9 (or @t87 (and @t4 @t55))))))) % 201.83/202.20 (define @t173 () (or @t3 @t58 @t3 @t56 @t172)) % 201.83/202.20 (define @t174 () (or @t58 @t3 @t56 @t172)) % 201.83/202.20 (define @t175 () (forall @t131 @t174)) % 201.83/202.20 (define @t176 () (forall @t59 @t175)) % 201.83/202.20 (define @t177 () (forall (@list @t11 @t6 @t54 @t3) @t174)) % 201.83/202.20 (define @t178 () (@list @t11 @t3 @t6 @t54)) % 201.83/202.20 (define @t179 () (and @t4 (= @t54 @t2))) % 201.83/202.20 (define @t180 () (or @t87 @t179)) % 201.83/202.20 (define @t181 () (lambda @t9 @t180)) % 201.83/202.20 (define @t182 () (tptp.dsetconstr @t11 @t181)) % 201.83/202.20 (define @t183 () (tptp.setunion @t182)) % 201.83/202.20 (define @t184 () (= @t54 @t183)) % 201.83/202.20 (define @t185 () (or @t58 @t3 @t56 @t184)) % 201.83/202.20 (define @t186 () (or @t56 @t184)) % 201.83/202.20 (define @t187 () (or @t58 @t3 @t186)) % 201.83/202.20 (define @t188 () (forall @t178 @t187)) % 201.83/202.20 (define @t189 () (@list @t54)) % 201.83/202.20 (define @t190 () (forall @t189 @t187)) % 201.83/202.20 (define @t191 () (forall @t189 @t186)) % 201.83/202.20 (define @t192 () (or @t58 @t3 @t191)) % 201.83/202.20 (define @t193 () (tptp.setunion @t104)) % 201.83/202.20 (define @t194 () (forall @t18 (or @t107 (= @t1 @t193)))) % 201.83/202.20 (define @t195 () (or @t109 @t3 @t194)) % 201.83/202.20 (define @t196 () (or @t3 @t194)) % 201.83/202.20 (define @t197 () (_ tptp.setunion @t111)) % 201.83/202.20 (define @t198 () (= @t1 @t197)) % 201.83/202.20 (define @t199 () (or @t113 @t198)) % 201.83/202.20 (define @t200 () (forall @t18 @t199)) % 201.83/202.20 (define @t201 () (or @t3 @t200)) % 201.83/202.20 (define @t202 () (or @t3 @t199)) % 201.83/202.20 (define @t203 () (or @t113 @t3 @t198)) % 201.83/202.20 (define @t204 () (=> @t4 @t198)) % 201.83/202.20 (define @t205 () (lambda @t18 @t197)) % 201.83/202.20 (define @t206 () (lambda (@list @t6 @t1) @t197)) % 201.83/202.20 (define @t207 () (lambda (@list @t3 @t6 @t1) @t197)) % 201.83/202.20 (define @t208 () (_ (lambda @t52 @t197) @t11)) % 201.83/202.20 (define @t209 () (= (_ (_ (_ @t208 @t3) @t6) @t1) @t1)) % 201.83/202.20 (define @t210 () (=> @t4 @t209)) % 201.83/202.20 (define @t211 () (=> @t16 @t210)) % 201.83/202.20 (define @t212 () (forall @t18 @t211)) % 201.83/202.20 (define @t213 () (=> @t21 @t212)) % 201.83/202.20 (define @t214 () (forall @t23 @t213)) % 201.83/202.20 (define @t215 () (=> tptp.theeq @t214)) % 201.83/202.20 (define @t216 () (=> tptp.ifSingleton @t215)) % 201.83/202.20 (define @t217 () (=> tptp.iffalseProp1 @t216)) % 201.83/202.20 (define @t218 () (@quantifiers_skolemize @t60 2)) % 201.83/202.20 (define @t219 () (= @t2 @t218)) % 201.83/202.20 (define @t220 () (lambda @t9 @t219)) % 201.83/202.20 (define @t221 () (@purify @t220)) % 201.83/202.20 (define @t222 () (@quantifiers_skolemize @t60 0)) % 201.83/202.20 (define @t223 () (tptp.dsetconstr @t222 @t220)) % 201.83/202.20 (define @t224 () (tptp.singleton @t223)) % 201.83/202.20 (define @t225 () (tptp.in @t218 @t222)) % 201.83/202.20 (define @t226 () (not @t225)) % 201.83/202.20 (define @t227 () (or @t226 @t226 @t224)) % 201.83/202.20 (define @t228 () (forall @t96 (or @t58 @t92 (tptp.singleton (tptp.dsetconstr @t11 (lambda @t9 (or @t87 (and @t4 (= @t2 @t84))))))))) % 201.83/202.20 (define @t229 () (and @t118 @t219)) % 201.83/202.20 (define @t230 () (and false (= @t218 @t2))) % 201.83/202.20 (define @t231 () (or @t230 @t229)) % 201.83/202.20 (define @t232 () (lambda @t9 @t231)) % 201.83/202.20 (define @t233 () (tptp.dsetconstr @t222 @t232)) % 201.83/202.20 (define @t234 () (tptp.singleton @t233)) % 201.83/202.20 (define @t235 () (or @t226 @t226 @t234)) % 201.83/202.20 (define @t236 () (tptp.dsetconstr @t222 @t221)) % 201.83/202.20 (define @t237 () (tptp.singleton @t236)) % 201.83/202.20 (define @t238 () (or @t226 @t226 @t237)) % 201.83/202.20 (define @t239 () (@list false)) % 201.83/202.20 (define @t240 () (tptp.setunion @t236)) % 201.83/202.20 (define @t241 () (= @t218 @t240)) % 201.83/202.20 (define @t242 () (not (tptp.in (@quantifiers_skolemize @t60 1) @t222))) % 201.83/202.20 (define @t243 () (or @t242 @t226 @t241)) % 201.83/202.20 (define @t244 () (not @t243)) % 201.83/202.20 (define @t245 () (not @t60)) % 201.83/202.20 (define @t246 () (tptp.setunion @t223)) % 201.83/202.20 (define @t247 () (= @t218 @t246)) % 201.83/202.20 (define @t248 () (or @t242 @t226 @t247)) % 201.83/202.20 (define @t249 () (not @t248)) % 201.83/202.20 (define @t250 () (@list true)) % 201.83/202.20 (define @t251 () (@list @t243)) % 201.83/202.20 (define @t252 () (@list false false)) % 201.83/202.20 (define @t253 () (tptp.in @t218 @t223)) % 201.83/202.20 (define @t254 () (or @t226 @t226 @t253)) % 201.83/202.20 (define @t255 () (forall @t128 (or @t58 @t125 (tptp.in @t116 (tptp.dsetconstr @t11 (lambda @t9 @t117)))))) % 201.83/202.20 (define @t256 () (tptp.in @t218 @t236)) % 201.83/202.20 (define @t257 () (or @t226 @t226 @t256)) % 201.83/202.20 (define @t258 () (not @t256)) % 201.83/202.20 (define @t259 () (not @t237)) % 201.83/202.20 (define @t260 () (or @t259 @t258 @t241)) % 201.83/202.20 (define @t261 () (not @t260)) % 201.83/202.20 (define @t262 () (or @t259 @t258 (= @t240 @t218))) % 201.83/202.20 (define @t263 () (forall @t70 (or @t65 @t63 (= @t62 @t61)))) % 201.83/202.20 (assume @p1 @t25) % 201.83/202.20 (assume @p2 @t30) % 201.83/202.20 (assume @p3 @t41) % 201.83/202.20 (assume @p4 @t51) % 201.83/202.20 (assume @p5 true) % 201.83/202.20 (step @p6 (= tptp.if @t53) :rule refl :args (@t53)) % 201.83/202.20 (step @p7 :rule refl :args (@t60)) % 201.83/202.20 (step @p8 :rule eq-symm :args (@t61 @t62)) % 201.83/202.20 (step @p9 :rule refl :args (@t63)) % 201.83/202.20 (step @p10 :rule refl :args (@t65)) % 201.83/202.20 (step @p11 :rule nary_cong :premises (@p10 @p9 @p8) :args (@t67)) % 201.83/202.20 (step @p12 :rule aci_norm :args ((= @t69 @t67))) % 201.83/202.20 (step @p13 :rule trans :premises (@p12 @p11)) % 201.83/202.20 (step @p14 :rule cong :premises (@p13) :args (@t71)) % 201.83/202.20 (step @p15 :rule quant-merge-prenex :args ((= (forall @t39 @t73) @t71))) % 201.83/202.20 (step @p16 :rule alpha_equiv :args (@t74 (@list @t61) (@list @t6))) % 201.83/202.20 (step @p17 :rule refl :args (@t65)) % 201.83/202.20 (step @p18 :rule nary_cong :premises (@p17 @p16) :args (@t75)) % 201.83/202.20 (step @p19 :rule quant-miniscope-or :args ((= @t73 @t75))) % 201.83/202.20 (step @p20 :rule trans :premises (@p19 @p18)) % 201.83/202.20 (step @p21 :rule symm :premises (@p20)) % 201.83/202.20 (step @p22 :rule cong :premises (@p21) :args ((forall @t39 (or @t65 @t77)))) % 201.83/202.20 (step @p23 :rule trans :premises (@p22 @p15)) % 201.83/202.20 (step @p24 :rule trans :premises (@p23 @p14)) % 201.83/202.20 (step @p25 :rule refl :args (@t77)) % 201.83/202.20 (step @p26 :rule refl :args (@t64)) % 201.83/202.20 (step @p27 :rule refl :args (@t37)) % 201.83/202.20 (step @p28 :rule cong :premises (@p27 @p26) :args ((= @t37 @t64))) % 201.83/202.20 (step @p29 :rule symm :premises (@p28)) % 201.83/202.20 (step @p30 :rule eq_resolve :premises (@p27 @p29)) % 201.83/202.20 (step @p31 :rule cong :premises (@p30) :args (@t78)) % 201.83/202.20 (step @p32 :rule nary_cong :premises (@p31 @p25) :args (@t79)) % 201.83/202.20 (step @p33 :rule cong :premises (@p32) :args ((forall @t39 @t79))) % 201.83/202.20 (step @p34 :rule trans :premises (@p33 @p24)) % 201.83/202.20 (step @p35 :rule bool-impl-elim :args (@t37 @t77)) % 201.83/202.20 (step @p36 :rule cong :premises (@p35) :args ((forall @t39 (=> @t37 @t77)))) % 201.83/202.20 (step @p37 :rule trans :premises (@p36 @p34)) % 201.83/202.20 (step @p38 :rule refl :args (@t62)) % 201.83/202.20 (step @p39 :rule refl :args (@t32)) % 201.83/202.20 (step @p40 :rule cong :premises (@p39 @p38) :args ((= @t32 @t62))) % 201.83/202.20 (step @p41 :rule symm :premises (@p40)) % 201.83/202.20 (step @p42 :rule eq_resolve :premises (@p39 @p41)) % 201.83/202.20 (step @p43 :rule refl :args (@t6)) % 201.83/202.20 (step @p44 :rule cong :premises (@p43 @p42) :args (@t80)) % 201.83/202.20 (step @p45 :rule refl :args (@t76)) % 201.83/202.20 (step @p46 :rule refl :args (@t33)) % 201.83/202.20 (step @p47 :rule cong :premises (@p46 @p45) :args ((= @t33 @t76))) % 201.83/202.20 (step @p48 :rule symm :premises (@p47)) % 201.83/202.20 (step @p49 :rule eq_resolve :premises (@p46 @p48)) % 201.83/202.20 (step @p50 :rule cong :premises (@p49) :args (@t81)) % 201.83/202.20 (step @p51 :rule nary_cong :premises (@p50 @p44) :args (@t82)) % 201.83/202.20 (step @p52 :rule cong :premises (@p51) :args ((forall @t35 @t82))) % 201.83/202.20 (step @p53 :rule bool-impl-elim :args (@t33 @t80)) % 201.83/202.20 (step @p54 :rule cong :premises (@p53) :args ((forall @t35 (=> @t33 @t80)))) % 201.83/202.20 (step @p55 :rule trans :premises (@p54 @p52)) % 201.83/202.20 (step @p56 :rule eq-symm :args (@t32 @t6)) % 201.83/202.20 (step @p57 :rule refl :args (@t33)) % 201.83/202.20 (step @p58 :rule cong :premises (@p57 @p56) :args (@t34)) % 201.83/202.20 (step @p59 :rule cong :premises (@p58) :args (@t36)) % 201.83/202.20 (step @p60 :rule trans :premises (@p59 @p55)) % 201.83/202.20 (step @p61 :rule refl :args (@t37)) % 201.83/202.20 (step @p62 :rule cong :premises (@p61 @p60) :args (@t38)) % 201.83/202.20 (step @p63 :rule cong :premises (@p62) :args (@t40)) % 201.83/202.20 (step @p64 :rule trans :premises (@p63 @p37)) % 201.83/202.20 (step @p65 :rule refl :args (tptp.theeq)) % 201.83/202.20 (step @p66 :rule cong :premises (@p65 @p64) :args (@t41)) % 201.83/202.20 (step @p67 :rule eq_resolve :premises (@p3 @p66)) % 201.83/202.20 (step @p68 :rule cong :premises (@p67 @p7) :args (@t83)) % 201.83/202.20 (step @p69 :rule eq-symm :args (@t84 @t2)) % 201.83/202.20 (step @p70 :rule refl :args (@t4)) % 201.83/202.20 (step @p71 :rule nary_cong :premises (@p70 @p69) :args (@t85)) % 201.83/202.20 (step @p72 :rule refl :args (@t87)) % 201.83/202.20 (step @p73 :rule nary_cong :premises (@p72 @p71) :args (@t88)) % 201.83/202.20 (step @p74 :rule cong :premises (@p73) :args (@t89)) % 201.83/202.20 (step @p75 :rule refl :args (@t11)) % 201.83/202.20 (step @p76 :rule cong :premises (@p75 @p74) :args (@t90)) % 201.83/202.20 (step @p77 :rule cong :premises (@p76) :args (@t91)) % 201.83/202.20 (step @p78 :rule refl :args (@t92)) % 201.83/202.20 (step @p79 :rule refl :args (@t58)) % 201.83/202.20 (step @p80 :rule nary_cong :premises (@p79 @p78 @p77) :args (@t93)) % 201.83/202.20 (step @p81 :rule aci_norm :args ((= @t95 @t93))) % 201.83/202.20 (step @p82 :rule trans :premises (@p81 @p80)) % 201.83/202.20 (step @p83 :rule cong :premises (@p82) :args (@t97)) % 201.83/202.20 (step @p84 :rule quant-merge-prenex :args ((= (forall @t23 @t99) @t97))) % 201.83/202.20 (step @p85 :rule alpha_equiv :args (@t100 (@list @t84) @t101)) % 201.83/202.20 (step @p86 :rule refl :args (@t58)) % 201.83/202.20 (step @p87 :rule nary_cong :premises (@p86 @p85) :args (@t102)) % 201.83/202.20 (step @p88 :rule quant-miniscope-or :args ((= @t99 @t102))) % 201.83/202.20 (step @p89 :rule trans :premises (@p88 @p87)) % 201.83/202.20 (step @p90 :rule symm :premises (@p89)) % 201.83/202.20 (step @p91 :rule cong :premises (@p90) :args ((forall @t23 (or @t58 @t108)))) % 201.83/202.20 (step @p92 :rule trans :premises (@p91 @p84)) % 201.83/202.20 (step @p93 :rule trans :premises (@p92 @p83)) % 201.83/202.20 (step @p94 :rule refl :args (@t108)) % 201.83/202.20 (step @p95 :rule refl :args (@t57)) % 201.83/202.20 (step @p96 :rule refl :args (@t21)) % 201.83/202.20 (step @p97 :rule cong :premises (@p96 @p95) :args ((= @t21 @t57))) % 201.83/202.20 (step @p98 :rule symm :premises (@p97)) % 201.83/202.20 (step @p99 :rule eq_resolve :premises (@p96 @p98)) % 201.83/202.20 (step @p100 :rule cong :premises (@p99) :args (@t109)) % 201.83/202.20 (step @p101 :rule nary_cong :premises (@p100 @p94) :args (@t110)) % 201.83/202.20 (step @p102 :rule cong :premises (@p101) :args ((forall @t23 @t110))) % 201.83/202.20 (step @p103 :rule trans :premises (@p102 @p93)) % 201.83/202.20 (step @p104 :rule bool-impl-elim :args (@t21 @t108)) % 201.83/202.20 (step @p105 :rule cong :premises (@p104) :args ((forall @t23 (=> @t21 @t108)))) % 201.83/202.20 (step @p106 :rule trans :premises (@p105 @p103)) % 201.83/202.20 (step @p107 :rule refl :args ((tptp.singleton @t111))) % 201.83/202.20 (step @p108 :rule refl :args (@t104)) % 201.83/202.20 (step @p109 :rule cong :premises (@p108) :args (@t105)) % 201.83/202.20 (step @p110 :rule trans :premises (@p109 @p107)) % 201.83/202.20 (step @p111 :rule refl :args (tptp.singleton)) % 201.83/202.20 (step @p112 :rule ho_cong :premises (@p111 @p108)) % 201.83/202.20 (step @p113 :rule cong :premises (@p112 @p110) :args ((= (_ tptp.singleton @t104) @t105))) % 201.83/202.20 (step @p114 :rule symm :premises (@p113)) % 201.83/202.20 (step @p115 :rule refl :args (@t112)) % 201.83/202.20 (step @p116 :rule eq_resolve :premises (@p115 @p114)) % 201.83/202.20 (step @p117 :rule refl :args (@t111)) % 201.83/202.20 (step @p118 :rule cong :premises (@p117 @p108) :args ((= @t111 @t104))) % 201.83/202.20 (step @p119 :rule symm :premises (@p118)) % 201.83/202.20 (step @p120 :rule eq_resolve :premises (@p117 @p119)) % 201.83/202.20 (step @p121 :rule ho_cong :premises (@p111 @p120)) % 201.83/202.20 (step @p122 :rule trans :premises (@p121 @p116)) % 201.83/202.20 (step @p123 :rule refl :args (@t106)) % 201.83/202.20 (step @p124 :rule refl :args (@t16)) % 201.83/202.20 (step @p125 :rule cong :premises (@p124 @p123) :args ((= @t16 @t106))) % 201.83/202.20 (step @p126 :rule symm :premises (@p125)) % 201.83/202.20 (step @p127 :rule eq_resolve :premises (@p124 @p126)) % 201.83/202.20 (step @p128 :rule cong :premises (@p127) :args (@t113)) % 201.83/202.20 (step @p129 :rule nary_cong :premises (@p128 @p122) :args (@t114)) % 201.83/202.20 (step @p130 :rule cong :premises (@p129) :args ((forall @t18 @t114))) % 201.83/202.20 (step @p131 :rule bool-impl-elim :args (@t16 @t112)) % 201.83/202.20 (step @p132 :rule cong :premises (@p131) :args ((forall @t18 (=> @t16 @t112)))) % 201.83/202.20 (step @p133 :rule trans :premises (@p132 @p130)) % 201.83/202.20 (step @p134 :rule eq-symm :args (@t2 @t1)) % 201.83/202.20 (step @p135 :rule nary_cong :premises (@p70 @p134) :args (@t5)) % 201.83/202.20 (step @p136 :rule eq-symm :args (@t2 @t6)) % 201.83/202.20 (step @p137 :rule refl :args (@t3)) % 201.83/202.20 (step @p138 :rule nary_cong :premises (@p137 @p136) :args (@t7)) % 201.83/202.20 (step @p139 :rule nary_cong :premises (@p138 @p135) :args (@t8)) % 201.83/202.20 (step @p140 :rule cong :premises (@p139) :args (@t10)) % 201.83/202.20 (step @p141 :rule refl :args (@t12)) % 201.83/202.20 (step @p142 :rule ho_cong :premises (@p141 @p140)) % 201.83/202.20 (step @p143 :rule refl :args (tptp.singleton)) % 201.83/202.20 (step @p144 :rule ho_cong :premises (@p143 @p142)) % 201.83/202.20 (step @p145 :rule refl :args (@t16)) % 201.83/202.20 (step @p146 :rule cong :premises (@p145 @p144) :args (@t26)) % 201.83/202.20 (step @p147 :rule cong :premises (@p146) :args (@t27)) % 201.83/202.20 (step @p148 :rule trans :premises (@p147 @p133)) % 201.83/202.20 (step @p149 :rule refl :args (@t21)) % 201.83/202.20 (step @p150 :rule cong :premises (@p149 @p148) :args (@t28)) % 201.83/202.20 (step @p151 :rule cong :premises (@p150) :args (@t29)) % 201.83/202.20 (step @p152 :rule trans :premises (@p151 @p106)) % 201.83/202.20 (step @p153 :rule refl :args (tptp.ifSingleton)) % 201.83/202.20 (step @p154 :rule cong :premises (@p153 @p152) :args (@t30)) % 201.83/202.20 (step @p155 :rule eq_resolve :premises (@p2 @p154)) % 201.83/202.20 (step @p156 :rule cong :premises (@p155 @p68) :args (@t115)) % 201.83/202.20 (step @p157 :rule aci_norm :args ((= (or false @t117) @t117))) % 201.83/202.20 (step @p158 :rule aci_norm :args ((= (and true @t117) @t117))) % 201.83/202.20 (step @p159 :rule refl :args (@t117)) % 201.83/202.20 (step @p160 :rule evaluate :args (@t118)) % 201.83/202.20 (step @p161 :rule nary_cong :premises (@p160 @p159) :args (@t119)) % 201.83/202.20 (step @p162 :rule trans :premises (@p161 @p158)) % 201.83/202.20 (step @p163 :rule absorb :args ((= @t120 false))) % 201.83/202.20 (step @p164 :rule nary_cong :premises (@p163 @p162) :args (@t121)) % 201.83/202.20 (step @p165 :rule trans :premises (@p164 @p157)) % 201.83/202.20 (step @p166 :rule cong :premises (@p165) :args (@t122)) % 201.83/202.20 (step @p167 :rule cong :premises (@p75 @p166) :args (@t123)) % 201.83/202.20 (step @p168 :rule refl :args (@t116)) % 201.83/202.20 (step @p169 :rule cong :premises (@p168 @p167) :args (@t124)) % 201.83/202.20 (step @p170 :rule refl :args (@t125)) % 201.83/202.20 (step @p171 :rule nary_cong :premises (@p79 @p170 @p169) :args (@t126)) % 201.83/202.20 (step @p172 :rule aci_norm :args ((= @t127 @t126))) % 201.83/202.20 (step @p173 :rule trans :premises (@p172 @p171)) % 201.83/202.20 (step @p174 :rule cong :premises (@p173) :args ((forall @t128 @t127))) % 201.83/202.20 (step @p175 :rule quant-var-elim-eq :args ((= (forall @t131 (or @t130 @t58 @t3 @t125 @t129)) @t127))) % 201.83/202.20 (step @p176 :rule refl :args (@t129)) % 201.83/202.20 (step @p177 :rule refl :args (@t125)) % 201.83/202.20 (step @p178 :rule refl :args (@t3)) % 201.83/202.20 (step @p179 :rule bool-eq-false :args (@t3)) % 201.83/202.20 (step @p180 :rule symm :premises (@p179)) % 201.83/202.20 (step @p181 :rule cong :premises (@p180) :args (@t132)) % 201.83/202.20 (step @p182 :rule bool-double-not-elim :args (@t3)) % 201.83/202.20 (step @p183 :rule symm :premises (@p182)) % 201.83/202.20 (step @p184 :rule trans :premises (@p183 @p181)) % 201.83/202.20 (step @p185 :rule nary_cong :premises (@p184 @p86 @p178 @p177 @p176) :args (@t133)) % 201.83/202.20 (step @p186 :rule aci_norm :args ((= @t134 @t133))) % 201.83/202.20 (step @p187 :rule trans :premises (@p186 @p185)) % 201.83/202.20 (step @p188 :rule cong :premises (@p187) :args (@t135)) % 201.83/202.20 (step @p189 :rule trans :premises (@p188 @p175)) % 201.83/202.20 (step @p190 :rule cong :premises (@p189) :args (@t136)) % 201.83/202.20 (step @p191 :rule quant-merge-prenex :args ((= @t136 @t137))) % 201.83/202.20 (step @p192 :rule symm :premises (@p191)) % 201.83/202.20 (step @p193 :rule quant_var_reordering :args ((= (forall @t138 @t134) @t137))) % 201.83/202.20 (step @p194 :rule trans :premises (@p193 @p192 @p190)) % 201.83/202.20 (step @p195 :rule trans :premises (@p194 @p174)) % 201.83/202.20 (step @p196 :rule eq-symm :args (@t116 @t2)) % 201.83/202.20 (step @p197 :rule nary_cong :premises (@p70 @p196) :args (@t139)) % 201.83/202.20 (step @p198 :rule nary_cong :premises (@p72 @p197) :args (@t140)) % 201.83/202.20 (step @p199 :rule cong :premises (@p198) :args (@t141)) % 201.83/202.20 (step @p200 :rule cong :premises (@p75 @p199) :args (@t142)) % 201.83/202.20 (step @p201 :rule cong :premises (@p168 @p200) :args (@t143)) % 201.83/202.20 (step @p202 :rule nary_cong :premises (@p79 @p137 @p170 @p201) :args (@t144)) % 201.83/202.20 (step @p203 :rule aci_norm :args ((= @t146 @t144))) % 201.83/202.20 (step @p204 :rule trans :premises (@p203 @p202)) % 201.83/202.20 (step @p205 :rule cong :premises (@p204) :args (@t147)) % 201.83/202.20 (step @p206 :rule trans :premises (@p205 @p195)) % 201.83/202.20 (step @p207 :rule quant-merge-prenex :args ((= (forall @t23 @t149) @t147))) % 201.83/202.20 (step @p208 :rule alpha_equiv :args (@t150 (@list @t116) @t101)) % 201.83/202.20 (step @p209 :rule nary_cong :premises (@p86 @p178 @p208) :args (@t151)) % 201.83/202.20 (step @p210 :rule quant-miniscope-or :args ((= @t149 @t151))) % 201.83/202.20 (step @p211 :rule trans :premises (@p210 @p209)) % 201.83/202.20 (step @p212 :rule symm :premises (@p211)) % 201.83/202.20 (step @p213 :rule cong :premises (@p212) :args ((forall @t23 (or @t58 @t3 @t153)))) % 201.83/202.20 (step @p214 :rule trans :premises (@p213 @p207)) % 201.83/202.20 (step @p215 :rule trans :premises (@p214 @p206)) % 201.83/202.20 (step @p216 :rule refl :args (@t153)) % 201.83/202.20 (step @p217 :rule nary_cong :premises (@p100 @p178 @p216) :args (@t154)) % 201.83/202.20 (step @p218 :rule cong :premises (@p217) :args ((forall @t23 @t154))) % 201.83/202.20 (step @p219 :rule trans :premises (@p218 @p215)) % 201.83/202.20 (step @p220 :rule aci_norm :args ((= (or @t109 @t155) @t154))) % 201.83/202.20 (step @p221 :rule bool-impl-elim :args (@t21 @t155)) % 201.83/202.20 (step @p222 :rule trans :premises (@p221 @p220)) % 201.83/202.20 (step @p223 :rule cong :premises (@p222) :args ((forall @t23 (=> @t21 @t155)))) % 201.83/202.20 (step @p224 :rule trans :premises (@p223 @p219)) % 201.83/202.20 (step @p225 :rule refl :args ((tptp.in @t1 @t111))) % 201.83/202.20 (step @p226 :rule refl :args (@t1)) % 201.83/202.20 (step @p227 :rule cong :premises (@p226 @p108) :args (@t152)) % 201.83/202.20 (step @p228 :rule trans :premises (@p227 @p225)) % 201.83/202.20 (step @p229 :rule refl :args (@t14)) % 201.83/202.20 (step @p230 :rule ho_cong :premises (@p229 @p108)) % 201.83/202.20 (step @p231 :rule cong :premises (@p230 @p228) :args ((= (_ @t14 @t104) @t152))) % 201.83/202.20 (step @p232 :rule symm :premises (@p231)) % 201.83/202.20 (step @p233 :rule refl :args (@t156)) % 201.83/202.20 (step @p234 :rule eq_resolve :premises (@p233 @p232)) % 201.83/202.20 (step @p235 :rule ho_cong :premises (@p229 @p120)) % 201.83/202.20 (step @p236 :rule trans :premises (@p235 @p234)) % 201.83/202.20 (step @p237 :rule nary_cong :premises (@p128 @p236) :args (@t157)) % 201.83/202.20 (step @p238 :rule cong :premises (@p237) :args (@t158)) % 201.83/202.20 (step @p239 :rule nary_cong :premises (@p137 @p238) :args (@t159)) % 201.83/202.20 (step @p240 :rule quant-miniscope-or :args ((= (forall @t18 @t160) @t159))) % 201.83/202.20 (step @p241 :rule aci_norm :args ((= @t161 @t160))) % 201.83/202.20 (step @p242 :rule cong :premises (@p241) :args ((forall @t18 @t161))) % 201.83/202.20 (step @p243 :rule trans :premises (@p242 @p240)) % 201.83/202.20 (step @p244 :rule trans :premises (@p243 @p239)) % 201.83/202.20 (step @p245 :rule aci_norm :args ((= (or @t113 (or @t3 @t156)) @t161))) % 201.83/202.20 (step @p246 :rule nary_cong :premises (@p182 @p233) :args ((or @t132 @t156))) % 201.83/202.20 (step @p247 :rule bool-impl-elim :args (@t4 @t156)) % 201.83/202.20 (step @p248 :rule trans :premises (@p247 @p246)) % 201.83/202.20 (step @p249 :rule refl :args (@t113)) % 201.83/202.20 (step @p250 :rule nary_cong :premises (@p249 @p248) :args ((or @t113 @t162))) % 201.83/202.20 (step @p251 :rule trans :premises (@p250 @p245)) % 201.83/202.20 (step @p252 :rule bool-impl-elim :args (@t16 @t162)) % 201.83/202.20 (step @p253 :rule trans :premises (@p252 @p251)) % 201.83/202.20 (step @p254 :rule cong :premises (@p253) :args ((forall @t18 (=> @t16 @t162)))) % 201.83/202.20 (step @p255 :rule trans :premises (@p254 @p244)) % 201.83/202.20 (step @p256 :rule refl :args (@t14)) % 201.83/202.20 (step @p257 :rule ho_cong :premises (@p256 @p142)) % 201.83/202.20 (step @p258 :rule cong :premises (@p70 @p257) :args (@t15)) % 201.83/202.20 (step @p259 :rule cong :premises (@p145 @p258) :args (@t17)) % 201.83/202.20 (step @p260 :rule cong :premises (@p259) :args (@t19)) % 201.83/202.20 (step @p261 :rule trans :premises (@p260 @p255)) % 201.83/202.20 (step @p262 :rule cong :premises (@p149 @p261) :args (@t22)) % 201.83/202.20 (step @p263 :rule cong :premises (@p262) :args (@t24)) % 201.83/202.20 (step @p264 :rule trans :premises (@p263 @p224)) % 201.83/202.20 (step @p265 :rule refl :args (tptp.iffalseProp1)) % 201.83/202.20 (step @p266 :rule cong :premises (@p265 @p264) :args (@t25)) % 201.83/202.20 (step @p267 :rule eq_resolve :premises (@p1 @p266)) % 201.83/202.20 (step @p268 :rule cong :premises (@p267 @p156) :args (@t163)) % 201.83/202.20 (step @p269 :rule cong :premises (@p268) :args ((not @t163))) % 201.83/202.20 (step @p270 :rule aci_norm :args ((= (or false @t55) @t55))) % 201.83/202.20 (step @p271 :rule aci_norm :args ((= (and true @t55) @t55))) % 201.83/202.20 (step @p272 :rule refl :args (@t55)) % 201.83/202.20 (step @p273 :rule nary_cong :premises (@p160 @p272) :args (@t164)) % 201.83/202.20 (step @p274 :rule trans :premises (@p273 @p271)) % 201.83/202.20 (step @p275 :rule nary_cong :premises (@p163 @p274) :args (@t165)) % 201.83/202.20 (step @p276 :rule trans :premises (@p275 @p270)) % 201.83/202.20 (step @p277 :rule cong :premises (@p276) :args (@t166)) % 201.83/202.20 (step @p278 :rule cong :premises (@p75 @p277) :args (@t167)) % 201.83/202.20 (step @p279 :rule cong :premises (@p278) :args (@t168)) % 201.83/202.20 (step @p280 :rule refl :args (@t54)) % 201.83/202.20 (step @p281 :rule cong :premises (@p280 @p279) :args (@t169)) % 201.83/202.20 (step @p282 :rule refl :args (@t56)) % 201.83/202.20 (step @p283 :rule nary_cong :premises (@p79 @p282 @p281) :args (@t170)) % 201.83/202.20 (step @p284 :rule aci_norm :args ((= @t171 @t170))) % 201.83/202.20 (step @p285 :rule trans :premises (@p284 @p283)) % 201.83/202.20 (step @p286 :rule cong :premises (@p285) :args ((forall @t59 @t171))) % 201.83/202.20 (step @p287 :rule quant-var-elim-eq :args ((= (forall @t131 (or @t130 @t58 @t3 @t56 @t172)) @t171))) % 201.83/202.20 (step @p288 :rule refl :args (@t172)) % 201.83/202.20 (step @p289 :rule refl :args (@t56)) % 201.83/202.20 (step @p290 :rule nary_cong :premises (@p184 @p86 @p178 @p289 @p288) :args (@t173)) % 201.83/202.20 (step @p291 :rule aci_norm :args ((= @t174 @t173))) % 201.83/202.20 (step @p292 :rule trans :premises (@p291 @p290)) % 201.83/202.20 (step @p293 :rule cong :premises (@p292) :args (@t175)) % 201.83/202.20 (step @p294 :rule trans :premises (@p293 @p287)) % 201.83/202.20 (step @p295 :rule cong :premises (@p294) :args (@t176)) % 201.83/202.20 (step @p296 :rule quant-merge-prenex :args ((= @t176 @t177))) % 201.83/202.20 (step @p297 :rule symm :premises (@p296)) % 201.83/202.20 (step @p298 :rule quant_var_reordering :args ((= (forall @t178 @t174) @t177))) % 201.83/202.20 (step @p299 :rule trans :premises (@p298 @p297 @p295)) % 201.83/202.20 (step @p300 :rule trans :premises (@p299 @p286)) % 201.83/202.20 (step @p301 :rule eq-symm :args (@t54 @t2)) % 201.83/202.20 (step @p302 :rule nary_cong :premises (@p70 @p301) :args (@t179)) % 201.83/202.20 (step @p303 :rule nary_cong :premises (@p72 @p302) :args (@t180)) % 201.83/202.20 (step @p304 :rule cong :premises (@p303) :args (@t181)) % 201.83/202.20 (step @p305 :rule cong :premises (@p75 @p304) :args (@t182)) % 201.83/202.20 (step @p306 :rule cong :premises (@p305) :args (@t183)) % 201.83/202.20 (step @p307 :rule cong :premises (@p280 @p306) :args (@t184)) % 201.83/202.20 (step @p308 :rule nary_cong :premises (@p79 @p137 @p282 @p307) :args (@t185)) % 201.83/202.20 (step @p309 :rule aci_norm :args ((= @t187 @t185))) % 201.83/202.20 (step @p310 :rule trans :premises (@p309 @p308)) % 201.83/202.20 (step @p311 :rule cong :premises (@p310) :args (@t188)) % 201.83/202.20 (step @p312 :rule trans :premises (@p311 @p300)) % 201.83/202.20 (step @p313 :rule quant-merge-prenex :args ((= (forall @t23 @t190) @t188))) % 201.83/202.20 (step @p314 :rule alpha_equiv :args (@t191 (@list @t54) @t101)) % 201.83/202.20 (step @p315 :rule nary_cong :premises (@p86 @p178 @p314) :args (@t192)) % 201.83/202.20 (step @p316 :rule quant-miniscope-or :args ((= @t190 @t192))) % 201.83/202.20 (step @p317 :rule trans :premises (@p316 @p315)) % 201.83/202.20 (step @p318 :rule symm :premises (@p317)) % 201.83/202.20 (step @p319 :rule cong :premises (@p318) :args ((forall @t23 (or @t58 @t3 @t194)))) % 201.83/202.20 (step @p320 :rule trans :premises (@p319 @p313)) % 201.83/202.20 (step @p321 :rule trans :premises (@p320 @p312)) % 201.83/202.20 (step @p322 :rule refl :args (@t194)) % 201.83/202.20 (step @p323 :rule nary_cong :premises (@p100 @p178 @p322) :args (@t195)) % 201.83/202.20 (step @p324 :rule cong :premises (@p323) :args ((forall @t23 @t195))) % 201.83/202.20 (step @p325 :rule trans :premises (@p324 @p321)) % 201.83/202.20 (step @p326 :rule aci_norm :args ((= (or @t109 @t196) @t195))) % 201.83/202.20 (step @p327 :rule bool-impl-elim :args (@t21 @t196)) % 201.83/202.20 (step @p328 :rule trans :premises (@p327 @p326)) % 201.83/202.20 (step @p329 :rule cong :premises (@p328) :args ((forall @t23 (=> @t21 @t196)))) % 201.83/202.20 (step @p330 :rule trans :premises (@p329 @p325)) % 201.83/202.20 (step @p331 :rule refl :args ((tptp.setunion @t111))) % 201.83/202.20 (step @p332 :rule cong :premises (@p108) :args (@t193)) % 201.83/202.20 (step @p333 :rule trans :premises (@p332 @p331)) % 201.83/202.20 (step @p334 :rule refl :args (tptp.setunion)) % 201.83/202.20 (step @p335 :rule ho_cong :premises (@p334 @p108)) % 201.83/202.20 (step @p336 :rule cong :premises (@p335 @p333) :args ((= (_ tptp.setunion @t104) @t193))) % 201.83/202.20 (step @p337 :rule symm :premises (@p336)) % 201.83/202.20 (step @p338 :rule refl :args (@t197)) % 201.83/202.20 (step @p339 :rule eq_resolve :premises (@p338 @p337)) % 201.83/202.20 (step @p340 :rule ho_cong :premises (@p334 @p120)) % 201.83/202.20 (step @p341 :rule trans :premises (@p340 @p339)) % 201.83/202.20 (step @p342 :rule cong :premises (@p226 @p341) :args (@t198)) % 201.83/202.20 (step @p343 :rule nary_cong :premises (@p128 @p342) :args (@t199)) % 201.83/202.20 (step @p344 :rule cong :premises (@p343) :args (@t200)) % 201.83/202.20 (step @p345 :rule nary_cong :premises (@p137 @p344) :args (@t201)) % 201.83/202.20 (step @p346 :rule quant-miniscope-or :args ((= (forall @t18 @t202) @t201))) % 201.83/202.20 (step @p347 :rule aci_norm :args ((= @t203 @t202))) % 201.83/202.20 (step @p348 :rule cong :premises (@p347) :args ((forall @t18 @t203))) % 201.83/202.20 (step @p349 :rule trans :premises (@p348 @p346)) % 201.83/202.20 (step @p350 :rule trans :premises (@p349 @p345)) % 201.83/202.20 (step @p351 :rule aci_norm :args ((= (or @t113 (or @t3 @t198)) @t203))) % 201.83/202.20 (step @p352 :rule refl :args (@t198)) % 201.83/202.20 (step @p353 :rule nary_cong :premises (@p182 @p352) :args ((or @t132 @t198))) % 201.83/202.20 (step @p354 :rule bool-impl-elim :args (@t4 @t198)) % 201.83/202.20 (step @p355 :rule trans :premises (@p354 @p353)) % 201.83/202.20 (step @p356 :rule nary_cong :premises (@p249 @p355) :args ((or @t113 @t204))) % 201.83/202.20 (step @p357 :rule trans :premises (@p356 @p351)) % 201.83/202.20 (step @p358 :rule bool-impl-elim :args (@t16 @t204)) % 201.83/202.20 (step @p359 :rule trans :premises (@p358 @p357)) % 201.83/202.20 (step @p360 :rule cong :premises (@p359) :args ((forall @t18 (=> @t16 @t204)))) % 201.83/202.20 (step @p361 :rule trans :premises (@p360 @p350)) % 201.83/202.20 (step @p362 :rule eq-symm :args (@t197 @t1)) % 201.83/202.20 (step @p363 :rule refl :args (@t1)) % 201.83/202.20 (step @p364 :rule beta-reduce :args ((= (_ @t205 @t1) @t197))) % 201.83/202.20 (step @p365 :rule beta-reduce :args ((= (_ @t206 @t6) @t205))) % 201.83/202.20 (step @p366 :rule refl :args (@t6)) % 201.83/202.20 (step @p367 :rule beta-reduce :args ((= (_ @t207 @t3) @t206))) % 201.83/202.20 (step @p368 :rule beta-reduce :args ((= @t208 @t207))) % 201.83/202.20 (step @p369 :rule ho_cong :premises (@p368 @p137)) % 201.83/202.20 (step @p370 :rule trans :premises (@p369 @p367)) % 201.83/202.20 (step @p371 :rule ho_cong :premises (@p370 @p366)) % 201.83/202.20 (step @p372 :rule trans :premises (@p371 @p365)) % 201.83/202.20 (step @p373 :rule ho_cong :premises (@p372 @p363)) % 201.83/202.20 (step @p374 :rule trans :premises (@p373 @p364)) % 201.83/202.20 (step @p375 :rule cong :premises (@p374 @p363) :args (@t209)) % 201.83/202.20 (step @p376 :rule trans :premises (@p375 @p362)) % 201.83/202.20 (step @p377 :rule cong :premises (@p70 @p376) :args (@t210)) % 201.83/202.20 (step @p378 :rule cong :premises (@p145 @p377) :args (@t211)) % 201.83/202.20 (step @p379 :rule cong :premises (@p378) :args (@t212)) % 201.83/202.20 (step @p380 :rule trans :premises (@p379 @p361)) % 201.83/202.20 (step @p381 :rule cong :premises (@p149 @p380) :args (@t213)) % 201.83/202.20 (step @p382 :rule cong :premises (@p381) :args (@t214)) % 201.83/202.20 (step @p383 :rule trans :premises (@p382 @p330)) % 201.83/202.20 (step @p384 :rule cong :premises (@p65 @p383) :args (@t215)) % 201.83/202.20 (step @p385 :rule cong :premises (@p153 @p384) :args (@t216)) % 201.83/202.20 (step @p386 :rule cong :premises (@p265 @p385) :args (@t217)) % 201.83/202.20 (step @p387 :rule cong :premises (@p386) :args ((not @t217))) % 201.83/202.20 (step @p388 :rule refl :args (tptp.setunion)) % 201.83/202.20 (step @p389 :rule ho_cong :premises (@p388 @p142)) % 201.83/202.20 (step @p390 :rule cong :premises (@p389) :args (@t53)) % 201.83/202.20 (step @p391 :rule trans :premises (@p6 @p390)) % 201.83/202.20 (step @p392 :rule ho_cong :premises (@p391 @p75)) % 201.83/202.20 (step @p393 :rule ho_cong :premises (@p392 @p137)) % 201.83/202.20 (step @p394 :rule ho_cong :premises (@p393 @p366)) % 201.83/202.20 (step @p395 :rule ho_cong :premises (@p394 @p363)) % 201.83/202.20 (step @p396 :rule cong :premises (@p395 @p363) :args (@t42)) % 201.83/202.20 (step @p397 :rule cong :premises (@p70 @p396) :args (@t43)) % 201.83/202.20 (step @p398 :rule cong :premises (@p145 @p397) :args (@t44)) % 201.83/202.20 (step @p399 :rule cong :premises (@p398) :args (@t45)) % 201.83/202.20 (step @p400 :rule cong :premises (@p149 @p399) :args (@t46)) % 201.83/202.20 (step @p401 :rule cong :premises (@p400) :args (@t47)) % 201.83/202.20 (step @p402 :rule cong :premises (@p65 @p401) :args (@t48)) % 201.83/202.20 (step @p403 :rule cong :premises (@p153 @p402) :args (@t49)) % 201.83/202.20 (step @p404 :rule cong :premises (@p265 @p403) :args (@t50)) % 201.83/202.20 (step @p405 :rule cong :premises (@p404) :args (@t51)) % 201.83/202.20 (step @p406 :rule trans :premises (@p405 @p387)) % 201.83/202.20 (step @p407 :rule trans :premises (@p406 @p269)) % 201.83/202.20 (step @p408 :rule eq_resolve :premises (@p4 @p407)) % 201.83/202.20 (step @p409 :rule not_implies_elim2 :premises (@p408)) % 201.83/202.20 (step @p410 :rule not_implies_elim2 :premises (@p409)) % 201.83/202.20 (step @p411 :rule not_implies_elim1 :premises (@p410)) % 201.83/202.20 (step @p412 :rule not_implies_elim1 :premises (@p409)) % 201.83/202.20 (step @p413 :rule eq-refl :args (@t220)) % 201.83/202.20 (step @p414 :rule skolem_intro :args (@t221)) % 201.83/202.20 (step @p415 :rule refl :args (@t220)) % 201.83/202.20 (step @p416 :rule cong :premises (@p415 @p414) :args ((= @t220 @t221))) % 201.83/202.20 (step @p417 :rule trans :premises (@p416 @p413)) % 201.83/202.20 (step @p418 :rule true_elim :premises (@p417)) % 201.83/202.20 (step @p419 :rule refl :args (@t222)) % 201.83/202.20 (step @p420 :rule cong :premises (@p419 @p418) :args (@t223)) % 201.83/202.20 (step @p421 :rule cong :premises (@p420) :args (@t224)) % 201.83/202.20 (step @p422 :rule refl :args (@t226)) % 201.83/202.20 (step @p423 :rule nary_cong :premises (@p422 @p422 @p421) :args (@t227)) % 201.83/202.20 (step @p424 :rule refl :args (@t228)) % 201.83/202.20 (step @p425 :rule cong :premises (@p424 @p423) :args ((=> @t228 @t227))) % 201.83/202.20 (step @p426 :rule aci_norm :args ((= (or false @t219) @t219))) % 201.83/202.20 (step @p427 :rule aci_norm :args ((= (and true @t219) @t219))) % 201.83/202.20 (step @p428 :rule refl :args (@t219)) % 201.83/202.20 (step @p429 :rule nary_cong :premises (@p160 @p428) :args (@t229)) % 201.83/202.20 (step @p430 :rule trans :premises (@p429 @p427)) % 201.83/202.20 (step @p431 :rule absorb :args ((= @t230 false))) % 201.83/202.20 (step @p432 :rule nary_cong :premises (@p431 @p430) :args (@t231)) % 201.83/202.20 (step @p433 :rule trans :premises (@p432 @p426)) % 201.83/202.20 (step @p434 :rule cong :premises (@p433) :args (@t232)) % 201.83/202.20 (step @p435 :rule cong :premises (@p419 @p434) :args (@t233)) % 201.83/202.20 (step @p436 :rule cong :premises (@p435) :args (@t234)) % 201.83/202.20 (step @p437 :rule nary_cong :premises (@p422 @p422 @p436) :args (@t235)) % 201.83/202.20 (step @p438 :rule cong :premises (@p424 @p437) :args ((=> @t228 @t235))) % 201.83/202.20 (assume-push @p512 @t228) % 201.83/202.20 (step @p440 :rule instantiate :premises (@p412) :args ((@list @t222 false @t218 @t218))) % 201.83/202.20 (step-pop @p513 :rule scope :premises (@p440)) % 201.83/202.20 (step @p441 :rule process_scope :premises (@p513) :args (@t235)) % 201.83/202.20 (step @p443 :rule eq_resolve :premises (@p441 @p438)) % 201.83/202.20 (step @p444 :rule eq_resolve :premises (@p443 @p425)) % 201.83/202.20 (step @p445 :rule implies_elim :premises (@p444)) % 201.83/202.20 (step @p446 :rule chain_m_resolution :premises (@p445 @p412) :args (@t238 @t239 (@list @t228))) % 201.83/202.20 (step @p447 :rule not_implies_elim2 :premises (@p410)) % 201.83/202.20 (step @p448 :rule refl :args (@t244)) % 201.83/202.20 (step @p449 :rule bool-double-not-elim :args (@t60)) % 201.83/202.20 (step @p450 :rule nary_cong :premises (@p449 @p448) :args ((or (not @t245) @t244))) % 201.83/202.20 (step @p451 :rule cong :premises (@p420) :args (@t246)) % 201.83/202.20 (step @p452 :rule refl :args (@t218)) % 201.83/202.20 (step @p453 :rule cong :premises (@p452 @p451) :args (@t247)) % 201.83/202.20 (step @p454 :rule refl :args (@t242)) % 201.83/202.20 (step @p455 :rule nary_cong :premises (@p454 @p422 @p453) :args (@t248)) % 201.83/202.20 (step @p456 :rule cong :premises (@p455) :args (@t249)) % 201.83/202.20 (step @p457 :rule refl :args (@t245)) % 201.83/202.20 (step @p458 :rule cong :premises (@p457 @p456) :args ((=> @t245 @t249))) % 201.83/202.20 (assume-push @p514 @t245) % 201.83/202.20 (step @p460 :rule skolemize :premises (@p447)) % 201.83/202.20 (step-pop @p515 :rule scope :premises (@p460)) % 201.83/202.20 (step @p461 :rule process_scope :premises (@p515) :args (@t249)) % 201.83/202.20 (step @p463 :rule eq_resolve :premises (@p461 @p458)) % 201.83/202.20 (step @p464 :rule implies_elim :premises (@p463)) % 201.83/202.20 (step @p465 :rule eq_resolve :premises (@p464 @p450)) % 201.83/202.20 (step @p466 :rule chain_m_resolution :premises (@p465 @p447) :args (@t244 @t250 (@list @t60))) % 201.83/202.20 (step @p467 :rule bool-double-not-elim :args (@t225)) % 201.83/202.20 (step @p468 :rule refl :args (@t243)) % 201.83/202.20 (step @p469 :rule nary_cong :premises (@p468 @p467) :args ((or @t243 (not @t226)))) % 201.83/202.20 (step @p470 :rule cnf_or_neg :args (@t243 1)) % 201.83/202.20 (step @p471 :rule eq_resolve :premises (@p470 @p469)) % 201.83/202.20 (step @p472 :rule reordering :premises (@p471) :args ((or @t225 @t243))) % 201.83/202.20 (step @p473 :rule chain_m_resolution :premises (@p472 @p466) :args (@t225 @t250 @t251)) % 201.83/202.20 (step @p474 :rule cnf_or_pos :args (@t238)) % 201.83/202.20 (step @p475 :rule factoring :premises (@p474)) % 201.83/202.20 (step @p476 :rule reordering :premises (@p475) :args ((or @t226 @t237 (not @t238)))) % 201.83/202.20 (step @p477 :rule chain_m_resolution :premises (@p476 @p473 @p446) :args (@t237 @t252 (@list @t225 @t238))) % 201.83/202.20 (step @p478 :rule not_implies_elim1 :premises (@p408)) % 201.83/202.20 (step @p479 :rule cong :premises (@p452 @p420) :args (@t253)) % 201.83/202.20 (step @p480 :rule nary_cong :premises (@p422 @p422 @p479) :args (@t254)) % 201.83/202.20 (step @p481 :rule refl :args (@t255)) % 201.83/202.20 (step @p482 :rule cong :premises (@p481 @p480) :args ((=> @t255 @t254))) % 201.83/202.20 (assume-push @p516 @t255) % 201.83/202.20 (step @p484 :rule instantiate :premises (@p478) :args ((@list @t222 @t218 @t218))) % 201.83/202.20 (step-pop @p517 :rule scope :premises (@p484)) % 201.83/202.20 (step @p485 :rule process_scope :premises (@p517) :args (@t254)) % 201.83/202.20 (step @p487 :rule eq_resolve :premises (@p485 @p482)) % 201.83/202.20 (step @p488 :rule implies_elim :premises (@p487)) % 201.83/202.20 (step @p489 :rule chain_m_resolution :premises (@p488 @p478) :args (@t257 @t239 (@list @t255))) % 201.83/202.20 (step @p490 :rule cnf_or_pos :args (@t257)) % 201.83/202.20 (step @p491 :rule factoring :premises (@p490)) % 201.83/202.20 (step @p492 :rule reordering :premises (@p491) :args ((or @t226 @t256 (not @t257)))) % 201.83/202.20 (step @p493 :rule chain_m_resolution :premises (@p492 @p473 @p489) :args (@t256 @t252 (@list @t225 @t257))) % 201.83/202.20 (step @p494 :rule cnf_or_neg :args (@t243 2)) % 201.83/202.20 (step @p495 :rule chain_m_resolution :premises (@p494 @p466) :args ((not @t241) @t250 @t251)) % 201.83/202.20 (step @p496 :rule cnf_or_pos :args (@t260)) % 201.83/202.20 (step @p497 :rule reordering :premises (@p496) :args ((or @t241 @t258 @t259 @t261))) % 201.83/202.20 (step @p498 :rule chain_m_resolution :premises (@p497 @p495 @p493 @p477) :args (@t261 (@list true false false) (@list @t241 @t256 @t237))) % 201.83/202.20 (step @p499 :rule eq-symm :args (@t240 @t218)) % 201.83/202.20 (step @p500 :rule refl :args (@t258)) % 201.83/202.20 (step @p501 :rule refl :args (@t259)) % 201.83/202.20 (step @p502 :rule nary_cong :premises (@p501 @p500 @p499) :args (@t262)) % 201.83/202.20 (step @p503 :rule refl :args (@t263)) % 201.83/202.20 (step @p504 :rule cong :premises (@p503 @p502) :args ((=> @t263 @t262))) % 201.83/202.20 (assume-push @p518 @t263) % 201.83/202.20 (step @p506 :rule instantiate :premises (@p411) :args ((@list @t236 @t218))) % 201.83/202.20 (step-pop @p519 :rule scope :premises (@p506)) % 201.83/202.20 (step @p507 :rule process_scope :premises (@p519) :args (@t262)) % 201.83/202.20 (step @p509 :rule eq_resolve :premises (@p507 @p504)) % 201.83/202.20 (step @p510 :rule implies_elim :premises (@p509)) % 201.83/202.20 (step @p511 false :rule chain_m_resolution :premises (@p510 @p498 @p411) :args (false (@list true false) (@list @t260 @t263))) % 201.83/202.20 ) % 201.83/202.20 % SZS output end Proof % 201.83/202.20 % cvc5 exiting %------------------------------------------------------------------------------