%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU821^2 : 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 : n004.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Jun 3 08:53:22 AM UTC 2026 % Result : Theorem 0.39s 0.61s % Output : Proof 0.39s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU821^2 : TPTP v9.2.1. Released v3.7.0. % 0.13/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n004.cluster.edu % 0.17/0.34 % Model : x86_64 x86_64 % 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.34 % Memory : 8042.1875MB % 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.34 % CPULimit : 300 % 0.17/0.34 % WCLimit : 300 % 0.17/0.34 % DateTime : Tue Jun 2 17:54:37 EDT 2026 % 0.17/0.34 % CPUTime : % 0.27/0.49 %----Proving TH0 % 0.39/0.61 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.39/0.61 % SZS status Theorem % 0.39/0.61 % SZS output start Proof % 0.39/0.61 ( % 0.39/0.61 (declare-sort $$unsorted 0) % 0.39/0.61 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 0.39/0.61 (declare-const tptp.nonempty (-> $$unsorted Bool)) % 0.39/0.61 (declare-const tptp.powerset (-> $$unsorted $$unsorted)) % 0.39/0.61 (declare-const tptp.transitiveset (-> $$unsorted Bool)) % 0.39/0.61 (define tptp.stricttotalorderedByIn () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (_ tptp.in _let_1))) (let ((_let_3 (@var "A" $$unsorted))) (let ((_let_4 (_ _let_2 _let_3))) (let ((_let_5 (@list _let_1))) (let ((_let_6 (@var "Y" $$unsorted))) (let ((_let_7 (_ tptp.in _let_6))) (let ((_let_8 (_ _let_2 _let_6))) (let ((_let_9 (_ _let_7 _let_3))) (let ((_let_10 (@list _let_6))) (let ((_let_11 (@var "Xx" $$unsorted))) (let ((_let_12 (_ tptp.in _let_11))) (lambda (@list _let_3) (and (forall (@list _let_11) (=> (_ _let_12 _let_3) (forall _let_5 (=> _let_4 (forall _let_10 (=> _let_9 (=> (and (_ _let_12 _let_1) _let_8) (_ _let_12 _let_6)))))))) (forall _let_5 (=> _let_4 (forall _let_10 (=> _let_9 (or (= _let_1 _let_6) _let_8 (_ _let_7 _let_1)))))) (forall _let_5 (=> _let_4 (not (_ _let_2 _let_1))))))))))))))))))) % 0.39/0.61 (define tptp.wellorderedByIn () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "Xx" $$unsorted))) (let ((_let_3 (_ tptp.in _let_2))) (let ((_let_4 (@var "X" $$unsorted))) (let ((_let_5 (@var "A" $$unsorted))) (lambda (@list _let_5) (and (_ tptp.stricttotalorderedByIn _let_5) (forall (@list _let_4) (=> (_ (_ tptp.in _let_4) (_ tptp.powerset _let_5)) (=> (_ tptp.nonempty _let_4) (exists (@list _let_2) (and (_ _let_3 _let_4) (forall (@list _let_1) (=> (_ (_ tptp.in _let_1) _let_4) (or (= _let_2 _let_1) (_ _let_3 _let_1))))))))))))))))) % 0.39/0.61 (define tptp.ordinal () (let ((_let_1 (@var "Xx" $$unsorted))) (lambda (@list _let_1) (and (_ tptp.transitiveset _let_1) (_ tptp.wellorderedByIn _let_1))))) % 0.39/0.61 (define @t1 () (@var "A" $$unsorted)) % 0.39/0.61 (define @t2 () (_ tptp.in @t1)) % 0.39/0.61 (define @t3 () (_ @t2 @t1)) % 0.39/0.61 (define @t4 () (not @t3)) % 0.39/0.61 (define @t5 () (@var "X" $$unsorted)) % 0.39/0.61 (define @t6 () (_ @t2 @t5)) % 0.39/0.61 (define @t7 () (@list @t1)) % 0.39/0.61 (define @t8 () (forall @t7 (=> @t6 @t4))) % 0.39/0.61 (define @t9 () (=> (_ tptp.ordinal @t5) @t8)) % 0.39/0.61 (define @t10 () (@list @t5)) % 0.39/0.61 (define @t11 () (forall @t10 @t9)) % 0.39/0.61 (define @t12 () (not @t11)) % 0.39/0.61 (define @t13 () (_ tptp.in @t5)) % 0.39/0.61 (define @t14 () (_ @t13 @t5)) % 0.39/0.61 (define @t15 () (not @t14)) % 0.39/0.61 (define @t16 () (_ @t13 @t1)) % 0.39/0.61 (define @t17 () (forall @t10 (=> @t16 @t15))) % 0.39/0.61 (define @t18 () (@var "Y" $$unsorted)) % 0.39/0.61 (define @t19 () (_ tptp.in @t18)) % 0.39/0.61 (define @t20 () (_ @t19 @t5)) % 0.39/0.61 (define @t21 () (_ @t13 @t18)) % 0.39/0.61 (define @t22 () (= @t5 @t18)) % 0.39/0.61 (define @t23 () (or @t22 @t21 @t20)) % 0.39/0.61 (define @t24 () (_ @t19 @t1)) % 0.39/0.61 (define @t25 () (@list @t18)) % 0.39/0.61 (define @t26 () (forall @t25 (=> @t24 @t23))) % 0.39/0.61 (define @t27 () (=> @t16 @t26)) % 0.39/0.61 (define @t28 () (forall @t10 @t27)) % 0.39/0.61 (define @t29 () (@var "Xx" $$unsorted)) % 0.39/0.61 (define @t30 () (_ tptp.in @t29)) % 0.39/0.61 (define @t31 () (_ @t30 @t18)) % 0.39/0.61 (define @t32 () (_ @t30 @t5)) % 0.39/0.61 (define @t33 () (and @t32 @t21)) % 0.39/0.61 (define @t34 () (=> @t33 @t31)) % 0.39/0.61 (define @t35 () (forall @t25 (=> @t24 @t34))) % 0.39/0.61 (define @t36 () (=> @t16 @t35)) % 0.39/0.61 (define @t37 () (forall @t10 @t36)) % 0.39/0.61 (define @t38 () (_ @t30 @t1)) % 0.39/0.61 (define @t39 () (=> @t38 @t37)) % 0.39/0.61 (define @t40 () (@list @t29)) % 0.39/0.61 (define @t41 () (forall @t40 @t39)) % 0.39/0.61 (define @t42 () (and @t41 @t28 @t17)) % 0.39/0.61 (define @t43 () (lambda @t7 @t42)) % 0.39/0.61 (define @t44 () (= @t29 @t18)) % 0.39/0.61 (define @t45 () (or @t44 @t31)) % 0.39/0.61 (define @t46 () (forall @t25 (=> @t20 @t45))) % 0.39/0.61 (define @t47 () (and @t32 @t46)) % 0.39/0.61 (define @t48 () (exists @t40 @t47)) % 0.39/0.61 (define @t49 () (_ tptp.nonempty @t5)) % 0.39/0.61 (define @t50 () (=> @t49 @t48)) % 0.39/0.61 (define @t51 () (_ tptp.powerset @t1)) % 0.39/0.61 (define @t52 () (_ @t13 @t51)) % 0.39/0.61 (define @t53 () (=> @t52 @t50)) % 0.39/0.61 (define @t54 () (forall @t10 @t53)) % 0.39/0.61 (define @t55 () (and (_ tptp.stricttotalorderedByIn @t1) @t54)) % 0.39/0.61 (define @t56 () (lambda @t7 @t55)) % 0.39/0.61 (define @t57 () (_ tptp.transitiveset @t29)) % 0.39/0.61 (define @t58 () (and @t57 (_ tptp.wellorderedByIn @t29))) % 0.39/0.61 (define @t59 () (lambda @t40 @t58)) % 0.39/0.61 (define @t60 () (@var "BOUND_VARIABLE_7827" $$unsorted)) % 0.39/0.61 (define @t61 () (not (tptp.in @t60 @t60))) % 0.39/0.61 (define @t62 () (not (tptp.in @t60 @t5))) % 0.39/0.61 (define @t63 () (@var "BOUND_VARIABLE_7731" $$unsorted)) % 0.39/0.61 (define @t64 () (not (tptp.in @t63 @t63))) % 0.39/0.61 (define @t65 () (@list @t63)) % 0.39/0.61 (define @t66 () (forall @t65 (or (not (tptp.in @t63 @t5)) @t64))) % 0.39/0.61 (define @t67 () (not @t66)) % 0.39/0.61 (define @t68 () (@var "BOUND_VARIABLE_7740" $$unsorted)) % 0.39/0.61 (define @t69 () (@var "BOUND_VARIABLE_7534" $$unsorted)) % 0.39/0.61 (define @t70 () (tptp.in @t69 @t68)) % 0.39/0.61 (define @t71 () (tptp.in @t68 @t69)) % 0.39/0.61 (define @t72 () (= @t69 @t68)) % 0.39/0.61 (define @t73 () (tptp.in @t69 @t5)) % 0.39/0.61 (define @t74 () (@list @t68 @t69)) % 0.39/0.61 (define @t75 () (forall @t74 (or (not (tptp.in @t68 @t5)) (not @t73) @t72 @t71 @t70))) % 0.39/0.61 (define @t76 () (not @t75)) % 0.39/0.61 (define @t77 () (@var "BOUND_VARIABLE_7506" $$unsorted)) % 0.39/0.61 (define @t78 () (@var "BOUND_VARIABLE_7633" $$unsorted)) % 0.39/0.61 (define @t79 () (tptp.in @t78 @t77)) % 0.39/0.61 (define @t80 () (@var "BOUND_VARIABLE_7504" $$unsorted)) % 0.39/0.61 (define @t81 () (not (tptp.in @t80 @t77))) % 0.39/0.61 (define @t82 () (not (tptp.in @t78 @t80))) % 0.39/0.61 (define @t83 () (@list @t78 @t80 @t77)) % 0.39/0.61 (define @t84 () (forall @t83 (or (not (tptp.in @t78 @t5)) (not (tptp.in @t80 @t5)) @t82 (not (tptp.in @t77 @t5)) @t81 @t79))) % 0.39/0.61 (define @t85 () (not @t84)) % 0.39/0.61 (define @t86 () (@var "BOUND_VARIABLE_7643" $$unsorted)) % 0.39/0.61 (define @t87 () (tptp.in @t86 @t18)) % 0.39/0.61 (define @t88 () (= @t18 @t86)) % 0.39/0.61 (define @t89 () (@var "BOUND_VARIABLE_7750" $$unsorted)) % 0.39/0.61 (define @t90 () (@list @t86)) % 0.39/0.61 (define @t91 () (not (forall @t90 (or (not (tptp.in @t86 @t89)) (not (forall @t25 (or (not (tptp.in @t18 @t89)) @t88 @t87))))))) % 0.39/0.61 (define @t92 () (not (tptp.nonempty @t89))) % 0.39/0.61 (define @t93 () (@list @t89)) % 0.39/0.61 (define @t94 () (forall @t93 (or (not (tptp.in @t89 (tptp.powerset @t5))) @t92 @t91))) % 0.39/0.61 (define @t95 () (not @t94)) % 0.39/0.61 (define @t96 () (tptp.transitiveset @t5)) % 0.39/0.61 (define @t97 () (not @t96)) % 0.39/0.61 (define @t98 () (or @t97 @t95 @t85 @t76 @t67 @t62 @t61)) % 0.39/0.61 (define @t99 () (or @t62 @t61)) % 0.39/0.61 (define @t100 () (or @t97 @t95 @t85 @t76 @t67 @t99)) % 0.39/0.61 (define @t101 () (@list @t5 @t60)) % 0.39/0.61 (define @t102 () (forall @t101 @t100)) % 0.39/0.61 (define @t103 () (@list @t60)) % 0.39/0.61 (define @t104 () (forall @t103 @t100)) % 0.39/0.61 (define @t105 () (forall @t103 @t99)) % 0.39/0.61 (define @t106 () (or @t97 @t95 @t85 @t76 @t67 @t105)) % 0.39/0.61 (define @t107 () (tptp.in @t1 @t1)) % 0.39/0.61 (define @t108 () (tptp.in @t1 @t5)) % 0.39/0.61 (define @t109 () (forall @t7 (or (not @t108) (not @t107)))) % 0.39/0.61 (define @t110 () (_ tptp.transitiveset @t5)) % 0.39/0.61 (define @t111 () (not @t110)) % 0.39/0.61 (define @t112 () (or @t111 @t95 @t85 @t76 @t67 @t109)) % 0.39/0.61 (define @t113 () (or @t111 @t95 @t85 @t76 @t67)) % 0.39/0.61 (define @t114 () (and @t110 @t94 @t84 @t75 @t66)) % 0.39/0.61 (define @t115 () (not @t6)) % 0.39/0.61 (define @t116 () (or @t115 @t4)) % 0.39/0.61 (define @t117 () (forall @t65 (or (not (tptp.in @t63 @t29)) @t64))) % 0.39/0.61 (define @t118 () (not (tptp.in @t69 @t29))) % 0.39/0.61 (define @t119 () (not (tptp.in @t68 @t29))) % 0.39/0.61 (define @t120 () (forall @t83 (or (not (tptp.in @t78 @t29)) (not (tptp.in @t80 @t29)) @t82 (not (tptp.in @t77 @t29)) @t81 @t79))) % 0.39/0.61 (define @t121 () (tptp.powerset @t29)) % 0.39/0.61 (define @t122 () (forall @t93 (or (not (tptp.in @t89 @t121)) @t92 @t91))) % 0.39/0.61 (define @t123 () (or @t119 @t118 (= @t68 @t69) @t71 @t70)) % 0.39/0.61 (define @t124 () (forall @t74 @t123)) % 0.39/0.61 (define @t125 () (and @t57 @t122 @t120 @t124 @t117)) % 0.39/0.61 (define @t126 () (tptp.in @t5 @t5)) % 0.39/0.61 (define @t127 () (not @t126)) % 0.39/0.61 (define @t128 () (not (tptp.in @t5 @t29))) % 0.39/0.61 (define @t129 () (forall @t10 (or @t128 @t127))) % 0.39/0.61 (define @t130 () (@list @t5)) % 0.39/0.61 (define @t131 () (tptp.in @t5 @t69)) % 0.39/0.61 (define @t132 () (= @t5 @t69)) % 0.39/0.61 (define @t133 () (@list @t5 @t69)) % 0.39/0.61 (define @t134 () (forall @t133 (or @t128 @t118 @t132 @t131 @t73))) % 0.39/0.61 (define @t135 () (tptp.in @t18 @t5)) % 0.39/0.61 (define @t136 () (not @t135)) % 0.39/0.61 (define @t137 () (not (tptp.in @t86 @t5))) % 0.39/0.61 (define @t138 () (not (forall @t90 (or @t137 (not (forall @t25 (or @t136 @t88 @t87))))))) % 0.39/0.61 (define @t139 () (tptp.nonempty @t5)) % 0.39/0.61 (define @t140 () (not @t139)) % 0.39/0.61 (define @t141 () (forall @t10 (or (not (tptp.in @t5 @t121)) @t140 @t138))) % 0.39/0.61 (define @t142 () (and @t57 @t141 @t120 @t134 @t129)) % 0.39/0.61 (define @t143 () (lambda @t40 @t142)) % 0.39/0.61 (define @t144 () (=> (_ @t143 @t5) @t8)) % 0.39/0.61 (define @t145 () (forall @t10 @t144)) % 0.39/0.61 (define @t146 () (and @t141 @t120 @t134 @t129)) % 0.39/0.61 (define @t147 () (tptp.in @t5 @t1)) % 0.39/0.61 (define @t148 () (not @t147)) % 0.39/0.61 (define @t149 () (forall @t10 (or @t148 @t127))) % 0.39/0.61 (define @t150 () (not (tptp.in @t69 @t1))) % 0.39/0.61 (define @t151 () (or @t148 @t150 @t132 @t131 @t73)) % 0.39/0.61 (define @t152 () (forall @t133 @t151)) % 0.39/0.61 (define @t153 () (not (tptp.in @t77 @t1))) % 0.39/0.61 (define @t154 () (not (tptp.in @t80 @t1))) % 0.39/0.61 (define @t155 () (forall @t83 (or (not (tptp.in @t78 @t1)) @t154 @t82 @t153 @t81 @t79))) % 0.39/0.61 (define @t156 () (tptp.powerset @t1)) % 0.39/0.61 (define @t157 () (tptp.in @t5 @t156)) % 0.39/0.61 (define @t158 () (not @t157)) % 0.39/0.61 (define @t159 () (or @t136 (= @t86 @t18) @t87)) % 0.39/0.61 (define @t160 () (forall @t25 @t159)) % 0.39/0.61 (define @t161 () (not @t160)) % 0.39/0.61 (define @t162 () (or @t137 @t161)) % 0.39/0.61 (define @t163 () (forall @t90 @t162)) % 0.39/0.61 (define @t164 () (not @t163)) % 0.39/0.61 (define @t165 () (or @t158 @t140 @t164)) % 0.39/0.61 (define @t166 () (forall @t10 @t165)) % 0.39/0.61 (define @t167 () (and @t166 @t155 @t152 @t149)) % 0.39/0.61 (define @t168 () (tptp.in @t29 @t77)) % 0.39/0.61 (define @t169 () (not (tptp.in @t29 @t80))) % 0.39/0.61 (define @t170 () (tptp.in @t29 @t1)) % 0.39/0.61 (define @t171 () (not @t170)) % 0.39/0.61 (define @t172 () (or @t171 @t154 @t169 @t153 @t81 @t168)) % 0.39/0.61 (define @t173 () (@list @t29 @t80 @t77)) % 0.39/0.61 (define @t174 () (forall @t173 @t172)) % 0.39/0.61 (define @t175 () (@list @t29)) % 0.39/0.61 (define @t176 () (tptp.in @t29 @t18)) % 0.39/0.61 (define @t177 () (forall @t25 (or @t136 @t44 @t176))) % 0.39/0.61 (define @t178 () (not @t177)) % 0.39/0.61 (define @t179 () (tptp.in @t29 @t5)) % 0.39/0.61 (define @t180 () (not @t179)) % 0.39/0.61 (define @t181 () (forall @t40 (or @t180 @t178))) % 0.39/0.61 (define @t182 () (not @t181)) % 0.39/0.61 (define @t183 () (or @t158 @t140 @t182)) % 0.39/0.61 (define @t184 () (forall @t10 @t183)) % 0.39/0.61 (define @t185 () (and @t184 @t174 @t152 @t149)) % 0.39/0.61 (define @t186 () (lambda @t7 @t185)) % 0.39/0.61 (define @t187 () (and @t174 @t152 @t149)) % 0.39/0.61 (define @t188 () (not @t49)) % 0.39/0.61 (define @t189 () (not @t52)) % 0.39/0.61 (define @t190 () (or @t189 @t188 @t182)) % 0.39/0.61 (define @t191 () (=> @t49 @t182)) % 0.39/0.61 (define @t192 () (not @t32)) % 0.39/0.61 (define @t193 () (or @t192 @t178)) % 0.39/0.61 (define @t194 () (and @t32 @t177)) % 0.39/0.61 (define @t195 () (forall @t40 (not @t194))) % 0.39/0.61 (define @t196 () (not @t195)) % 0.39/0.61 (define @t197 () (not @t20)) % 0.39/0.61 (define @t198 () (or @t197 @t44 @t31)) % 0.39/0.61 (define @t199 () (_ (lambda @t7 @t187) @t1)) % 0.39/0.61 (define @t200 () (not @t16)) % 0.39/0.61 (define @t201 () (or @t200 @t15)) % 0.39/0.61 (define @t202 () (or @t150 @t132 @t131 @t73)) % 0.39/0.61 (define @t203 () (or @t148 @t202)) % 0.39/0.61 (define @t204 () (forall @t133 @t203)) % 0.39/0.61 (define @t205 () (@list @t69)) % 0.39/0.61 (define @t206 () (forall @t205 @t203)) % 0.39/0.61 (define @t207 () (forall @t205 @t202)) % 0.39/0.61 (define @t208 () (@list @t18)) % 0.39/0.61 (define @t209 () (or @t148 @t207)) % 0.39/0.61 (define @t210 () (tptp.in @t5 @t18)) % 0.39/0.61 (define @t211 () (tptp.in @t18 @t1)) % 0.39/0.61 (define @t212 () (not @t211)) % 0.39/0.61 (define @t213 () (forall @t25 (or @t212 @t22 @t210 @t135))) % 0.39/0.61 (define @t214 () (or @t200 @t213)) % 0.39/0.61 (define @t215 () (not @t24)) % 0.39/0.61 (define @t216 () (or @t215 @t22 @t21 @t20)) % 0.39/0.61 (define @t217 () (or @t154 @t169 @t153 @t81 @t168)) % 0.39/0.61 (define @t218 () (or @t171 @t217)) % 0.39/0.61 (define @t219 () (forall @t173 @t218)) % 0.39/0.61 (define @t220 () (@list @t80 @t77)) % 0.39/0.61 (define @t221 () (forall @t220 @t218)) % 0.39/0.61 (define @t222 () (forall @t220 @t217)) % 0.39/0.61 (define @t223 () (@var "BOUND_VARIABLE_7482" $$unsorted)) % 0.39/0.61 (define @t224 () (or @t171 @t222)) % 0.39/0.61 (define @t225 () (tptp.in @t29 @t223)) % 0.39/0.61 (define @t226 () (not (tptp.in @t5 @t223))) % 0.39/0.61 (define @t227 () (not (tptp.in @t223 @t1))) % 0.39/0.61 (define @t228 () (or @t148 @t180 @t227 @t226 @t225)) % 0.39/0.61 (define @t229 () (@list @t5 @t223)) % 0.39/0.61 (define @t230 () (forall @t229 @t228)) % 0.39/0.61 (define @t231 () (not @t38)) % 0.39/0.61 (define @t232 () (or @t231 @t230)) % 0.39/0.61 (define @t233 () (or @t227 @t226 @t225)) % 0.39/0.61 (define @t234 () (or @t148 @t180 @t233)) % 0.39/0.61 (define @t235 () (forall @t229 @t234)) % 0.39/0.61 (define @t236 () (@list @t223)) % 0.39/0.61 (define @t237 () (forall @t236 @t234)) % 0.39/0.61 (define @t238 () (forall @t236 @t233)) % 0.39/0.61 (define @t239 () (or @t148 @t180 @t238)) % 0.39/0.61 (define @t240 () (forall @t25 (or @t212 (not @t210) @t176))) % 0.39/0.61 (define @t241 () (or @t200 @t192 @t240)) % 0.39/0.61 (define @t242 () (or @t192 @t240)) % 0.39/0.61 (define @t243 () (not @t21)) % 0.39/0.61 (define @t244 () (or @t215 @t243 @t31)) % 0.39/0.61 (define @t245 () (forall @t25 @t244)) % 0.39/0.61 (define @t246 () (or @t192 @t245)) % 0.39/0.61 (define @t247 () (or @t192 @t244)) % 0.39/0.61 (define @t248 () (or @t215 @t192 @t243 @t31)) % 0.39/0.61 (define @t249 () (or @t192 @t243 @t31)) % 0.39/0.61 (define @t250 () (forall @t101 @t98)) % 0.39/0.61 (define @t251 () (@quantifiers_skolemize @t250 0)) % 0.39/0.61 (define @t252 () (forall @t65 (or (not (tptp.in @t63 @t251)) @t64))) % 0.39/0.61 (define @t253 () (@quantifiers_skolemize @t250 1)) % 0.39/0.61 (define @t254 () (tptp.in @t253 @t253)) % 0.39/0.61 (define @t255 () (not @t254)) % 0.39/0.61 (define @t256 () (tptp.in @t253 @t251)) % 0.39/0.61 (define @t257 () (not @t256)) % 0.39/0.61 (define @t258 () (not @t252)) % 0.39/0.61 (define @t259 () (or (not (tptp.transitiveset @t251)) (not (forall @t93 (or (not (tptp.in @t89 (tptp.powerset @t251))) @t92 @t91))) (not (forall @t83 (or (not (tptp.in @t78 @t251)) (not (tptp.in @t80 @t251)) @t82 (not (tptp.in @t77 @t251)) @t81 @t79))) (not (forall @t74 (or (not (tptp.in @t68 @t251)) (not (tptp.in @t69 @t251)) @t72 @t71 @t70))) @t258 @t257 @t255)) % 0.39/0.61 (define @t260 () (@list true)) % 0.39/0.61 (define @t261 () (@list @t259)) % 0.39/0.61 (define @t262 () (or @t257 @t255)) % 0.39/0.61 (define @t263 () (not @t262)) % 0.39/0.61 (assume @p1 @t12) % 0.39/0.61 (assume @p2 true) % 0.39/0.61 (step @p3 (= tptp.stricttotalorderedByIn @t43) :rule refl :args (@t43)) % 0.39/0.61 (step @p4 (= tptp.wellorderedByIn @t56) :rule refl :args (@t56)) % 0.39/0.61 (step @p5 (= tptp.ordinal @t59) :rule refl :args (@t59)) % 0.39/0.61 (step @p6 :rule aci_norm :args ((= @t100 @t98))) % 0.39/0.61 (step @p7 :rule cong :premises (@p6) :args (@t102)) % 0.39/0.61 (step @p8 :rule quant-merge-prenex :args ((= (forall @t10 @t104) @t102))) % 0.39/0.61 (step @p9 :rule alpha_equiv :args (@t105 (@list @t60) (@list @t1))) % 0.39/0.61 (step @p10 :rule refl :args (@t67)) % 0.39/0.61 (step @p11 :rule refl :args (@t76)) % 0.39/0.61 (step @p12 :rule refl :args (@t85)) % 0.39/0.61 (step @p13 :rule refl :args (@t95)) % 0.39/0.61 (step @p14 :rule refl :args (@t97)) % 0.39/0.61 (step @p15 :rule nary_cong :premises (@p14 @p13 @p12 @p11 @p10 @p9) :args (@t106)) % 0.39/0.61 (step @p16 :rule quant-miniscope-or :args ((= @t104 @t106))) % 0.39/0.61 (step @p17 :rule trans :premises (@p16 @p15)) % 0.39/0.61 (step @p18 :rule symm :premises (@p17)) % 0.39/0.61 (step @p19 :rule cong :premises (@p18) :args ((forall @t10 (or @t97 @t95 @t85 @t76 @t67 @t109)))) % 0.39/0.61 (step @p20 :rule trans :premises (@p19 @p8)) % 0.39/0.61 (step @p21 :rule trans :premises (@p20 @p7)) % 0.39/0.61 (step @p22 :rule refl :args (@t109)) % 0.39/0.61 (step @p23 :rule refl :args (@t96)) % 0.39/0.61 (step @p24 :rule refl :args (@t110)) % 0.39/0.61 (step @p25 :rule cong :premises (@p24 @p23) :args ((= @t110 @t96))) % 0.39/0.61 (step @p26 :rule symm :premises (@p25)) % 0.39/0.61 (step @p27 :rule eq_resolve :premises (@p24 @p26)) % 0.39/0.61 (step @p28 :rule cong :premises (@p27) :args (@t111)) % 0.39/0.61 (step @p29 :rule nary_cong :premises (@p28 @p13 @p12 @p11 @p10 @p22) :args (@t112)) % 0.39/0.61 (step @p30 :rule cong :premises (@p29) :args ((forall @t10 @t112))) % 0.39/0.61 (step @p31 :rule trans :premises (@p30 @p21)) % 0.39/0.61 (step @p32 :rule aci_norm :args ((= (or @t113 @t109) @t112))) % 0.39/0.61 (step @p33 :rule aci_norm :args ((= (or @t111 (or @t95 (or @t85 (or @t76 @t67)))) @t113))) % 0.39/0.61 (step @p34 :rule bool-and-de-morgan :args (@t75 @t66 true)) % 0.39/0.61 (step @p35 :rule nary_cong :premises (@p12 @p34) :args ((or @t85 (not (and @t75 @t66))))) % 0.39/0.61 (step @p36 :rule bool-and-de-morgan :args (@t84 @t75 (and @t66))) % 0.39/0.61 (step @p37 :rule trans :premises (@p36 @p35)) % 0.39/0.61 (step @p38 :rule nary_cong :premises (@p13 @p37) :args ((or @t95 (not (and @t84 @t75 @t66))))) % 0.39/0.61 (step @p39 :rule bool-and-de-morgan :args (@t94 @t84 (and @t75 @t66))) % 0.39/0.61 (step @p40 :rule trans :premises (@p39 @p38)) % 0.39/0.61 (step @p41 :rule refl :args (@t111)) % 0.39/0.61 (step @p42 :rule nary_cong :premises (@p41 @p40) :args ((or @t111 (not (and @t94 @t84 @t75 @t66))))) % 0.39/0.61 (step @p43 :rule bool-and-de-morgan :args (@t110 @t94 (and @t84 @t75 @t66))) % 0.39/0.61 (step @p44 :rule trans :premises (@p43 @p42)) % 0.39/0.61 (step @p45 :rule trans :premises (@p44 @p33)) % 0.39/0.61 (step @p46 :rule nary_cong :premises (@p45 @p22) :args ((or (not @t114) @t109))) % 0.39/0.61 (step @p47 :rule trans :premises (@p46 @p32)) % 0.39/0.61 (step @p48 :rule bool-impl-elim :args (@t114 @t109)) % 0.39/0.61 (step @p49 :rule trans :premises (@p48 @p47)) % 0.39/0.61 (step @p50 :rule cong :premises (@p49) :args ((forall @t10 (=> @t114 @t109)))) % 0.39/0.61 (step @p51 :rule trans :premises (@p50 @p31)) % 0.39/0.61 (step @p52 :rule refl :args (@t107)) % 0.39/0.61 (step @p53 :rule refl :args (@t3)) % 0.39/0.61 (step @p54 :rule cong :premises (@p53 @p52) :args ((= @t3 @t107))) % 0.39/0.61 (step @p55 :rule symm :premises (@p54)) % 0.39/0.61 (step @p56 :rule eq_resolve :premises (@p53 @p55)) % 0.39/0.61 (step @p57 :rule cong :premises (@p56) :args (@t4)) % 0.39/0.61 (step @p58 :rule refl :args (@t108)) % 0.39/0.61 (step @p59 :rule refl :args (@t6)) % 0.39/0.61 (step @p60 :rule cong :premises (@p59 @p58) :args ((= @t6 @t108))) % 0.39/0.61 (step @p61 :rule symm :premises (@p60)) % 0.39/0.61 (step @p62 :rule eq_resolve :premises (@p59 @p61)) % 0.39/0.61 (step @p63 :rule cong :premises (@p62) :args (@t115)) % 0.39/0.61 (step @p64 :rule nary_cong :premises (@p63 @p57) :args (@t116)) % 0.39/0.61 (step @p65 :rule cong :premises (@p64) :args ((forall @t7 @t116))) % 0.39/0.61 (step @p66 :rule bool-impl-elim :args (@t6 @t4)) % 0.39/0.61 (step @p67 :rule cong :premises (@p66) :args (@t8)) % 0.39/0.61 (step @p68 :rule trans :premises (@p67 @p65)) % 0.39/0.61 (step @p69 :rule beta-reduce :args ((= (_ (lambda @t40 (and @t57 @t122 @t120 (forall @t74 (or @t119 @t118 @t72 @t71 @t70)) @t117)) @t5) @t114))) % 0.39/0.61 (step @p70 :rule refl :args (@t5)) % 0.39/0.61 (step @p71 :rule refl :args (@t117)) % 0.39/0.61 (step @p72 :rule refl :args (@t70)) % 0.39/0.61 (step @p73 :rule refl :args (@t71)) % 0.39/0.61 (step @p74 :rule eq-symm :args (@t68 @t69)) % 0.39/0.61 (step @p75 :rule refl :args (@t118)) % 0.39/0.61 (step @p76 :rule refl :args (@t119)) % 0.39/0.61 (step @p77 :rule nary_cong :premises (@p76 @p75 @p74 @p73 @p72) :args (@t123)) % 0.39/0.61 (step @p78 :rule cong :premises (@p77) :args (@t124)) % 0.39/0.61 (step @p79 :rule refl :args (@t120)) % 0.39/0.61 (step @p80 :rule refl :args (@t122)) % 0.39/0.61 (step @p81 :rule refl :args (@t57)) % 0.39/0.61 (step @p82 :rule nary_cong :premises (@p81 @p80 @p79 @p78 @p71) :args (@t125)) % 0.39/0.61 (step @p83 :rule cong :premises (@p82) :args ((lambda @t40 @t125))) % 0.39/0.61 (step @p84 :rule ho_cong :premises (@p83 @p70)) % 0.39/0.61 (step @p85 :rule trans :premises (@p84 @p69)) % 0.39/0.61 (step @p86 :rule refl :args (@t5)) % 0.39/0.61 (step @p87 :rule alpha_equiv :args (@t129 @t130 (@list @t63))) % 0.39/0.61 (step @p88 :rule alpha_equiv :args (@t134 @t130 (@list @t68))) % 0.39/0.61 (step @p89 :rule refl :args (@t120)) % 0.39/0.61 (step @p90 :rule alpha_equiv :args (@t141 @t130 (@list @t89))) % 0.39/0.61 (step @p91 :rule refl :args (@t57)) % 0.39/0.61 (step @p92 :rule nary_cong :premises (@p91 @p90 @p89 @p88 @p87) :args (@t142)) % 0.39/0.61 (step @p93 :rule cong :premises (@p92) :args (@t143)) % 0.39/0.61 (step @p94 :rule ho_cong :premises (@p93 @p86)) % 0.39/0.61 (step @p95 :rule trans :premises (@p94 @p85)) % 0.39/0.61 (step @p96 :rule cong :premises (@p95 @p68) :args (@t144)) % 0.39/0.61 (step @p97 :rule cong :premises (@p96) :args (@t145)) % 0.39/0.61 (step @p98 :rule trans :premises (@p97 @p51)) % 0.39/0.61 (step @p99 :rule cong :premises (@p98) :args ((not @t145))) % 0.39/0.61 (step @p100 :rule refl :args (@t8)) % 0.39/0.61 (step @p101 :rule aci_norm :args ((= (and @t57 @t146) @t142))) % 0.39/0.61 (step @p102 :rule beta-reduce :args ((= (_ (lambda @t7 (and (forall @t10 (or @t158 @t140 @t138)) @t155 @t152 @t149)) @t29) @t146))) % 0.39/0.61 (step @p103 :rule refl :args (@t29)) % 0.39/0.61 (step @p104 :rule refl :args (@t149)) % 0.39/0.61 (step @p105 :rule refl :args (@t152)) % 0.39/0.61 (step @p106 :rule refl :args (@t155)) % 0.39/0.61 (step @p107 :rule refl :args (@t87)) % 0.39/0.61 (step @p108 :rule eq-symm :args (@t86 @t18)) % 0.39/0.61 (step @p109 :rule refl :args (@t136)) % 0.39/0.61 (step @p110 :rule nary_cong :premises (@p109 @p108 @p107) :args (@t159)) % 0.39/0.61 (step @p111 :rule cong :premises (@p110) :args (@t160)) % 0.39/0.61 (step @p112 :rule cong :premises (@p111) :args (@t161)) % 0.39/0.61 (step @p113 :rule refl :args (@t137)) % 0.39/0.61 (step @p114 :rule nary_cong :premises (@p113 @p112) :args (@t162)) % 0.39/0.61 (step @p115 :rule cong :premises (@p114) :args (@t163)) % 0.39/0.61 (step @p116 :rule cong :premises (@p115) :args (@t164)) % 0.39/0.61 (step @p117 :rule refl :args (@t140)) % 0.39/0.61 (step @p118 :rule refl :args (@t158)) % 0.39/0.61 (step @p119 :rule nary_cong :premises (@p118 @p117 @p116) :args (@t165)) % 0.39/0.61 (step @p120 :rule cong :premises (@p119) :args (@t166)) % 0.39/0.61 (step @p121 :rule nary_cong :premises (@p120 @p106 @p105 @p104) :args (@t167)) % 0.39/0.61 (step @p122 :rule cong :premises (@p121) :args ((lambda @t7 @t167))) % 0.39/0.61 (step @p123 :rule ho_cong :premises (@p122 @p103)) % 0.39/0.61 (step @p124 :rule trans :premises (@p123 @p102)) % 0.39/0.61 (step @p125 :rule refl :args (@t29)) % 0.39/0.61 (step @p126 :rule refl :args (@t149)) % 0.39/0.61 (step @p127 :rule refl :args (@t152)) % 0.39/0.61 (step @p128 :rule alpha_equiv :args (@t174 @t175 (@list @t78))) % 0.39/0.61 (step @p129 :rule alpha_equiv :args (@t181 @t175 (@list @t86))) % 0.39/0.61 (step @p130 :rule cong :premises (@p129) :args (@t182)) % 0.39/0.61 (step @p131 :rule refl :args (@t140)) % 0.39/0.61 (step @p132 :rule refl :args (@t158)) % 0.39/0.61 (step @p133 :rule nary_cong :premises (@p132 @p131 @p130) :args (@t183)) % 0.39/0.61 (step @p134 :rule cong :premises (@p133) :args (@t184)) % 0.39/0.61 (step @p135 :rule nary_cong :premises (@p134 @p128 @p127 @p126) :args (@t185)) % 0.39/0.61 (step @p136 :rule cong :premises (@p135) :args (@t186)) % 0.39/0.61 (step @p137 :rule ho_cong :premises (@p136 @p125)) % 0.39/0.61 (step @p138 :rule trans :premises (@p137 @p124)) % 0.39/0.61 (step @p139 :rule nary_cong :premises (@p81 @p138) :args ((and @t57 (_ @t186 @t29)))) % 0.39/0.61 (step @p140 :rule trans :premises (@p139 @p101)) % 0.39/0.61 (step @p141 :rule aci_norm :args ((= (and @t187 @t184) @t185))) % 0.39/0.61 (step @p142 :rule refl :args (@t182)) % 0.39/0.61 (step @p143 :rule refl :args (@t139)) % 0.39/0.61 (step @p144 :rule refl :args (@t49)) % 0.39/0.61 (step @p145 :rule cong :premises (@p144 @p143) :args ((= @t49 @t139))) % 0.39/0.61 (step @p146 :rule symm :premises (@p145)) % 0.39/0.61 (step @p147 :rule eq_resolve :premises (@p144 @p146)) % 0.39/0.61 (step @p148 :rule cong :premises (@p147) :args (@t188)) % 0.39/0.61 (step @p149 :rule refl :args ((tptp.in @t5 @t51))) % 0.39/0.61 (step @p150 :rule refl :args (@t156)) % 0.39/0.61 (step @p151 :rule cong :premises (@p86 @p150) :args (@t157)) % 0.39/0.61 (step @p152 :rule trans :premises (@p151 @p149)) % 0.39/0.61 (step @p153 :rule refl :args (@t13)) % 0.39/0.61 (step @p154 :rule ho_cong :premises (@p153 @p150)) % 0.39/0.61 (step @p155 :rule cong :premises (@p154 @p152) :args ((= (_ @t13 @t156) @t157))) % 0.39/0.61 (step @p156 :rule symm :premises (@p155)) % 0.39/0.61 (step @p157 :rule refl :args (@t52)) % 0.39/0.61 (step @p158 :rule eq_resolve :premises (@p157 @p156)) % 0.39/0.61 (step @p159 :rule refl :args (@t51)) % 0.39/0.61 (step @p160 :rule cong :premises (@p159 @p150) :args ((= @t51 @t156))) % 0.39/0.61 (step @p161 :rule symm :premises (@p160)) % 0.39/0.61 (step @p162 :rule eq_resolve :premises (@p159 @p161)) % 0.39/0.61 (step @p163 :rule ho_cong :premises (@p153 @p162)) % 0.39/0.61 (step @p164 :rule trans :premises (@p163 @p158)) % 0.39/0.61 (step @p165 :rule cong :premises (@p164) :args (@t189)) % 0.39/0.61 (step @p166 :rule nary_cong :premises (@p165 @p148 @p142) :args (@t190)) % 0.39/0.61 (step @p167 :rule cong :premises (@p166) :args ((forall @t10 @t190))) % 0.39/0.61 (step @p168 :rule aci_norm :args ((= (or @t189 (or @t188 @t182)) @t190))) % 0.39/0.61 (step @p169 :rule bool-impl-elim :args (@t49 @t182)) % 0.39/0.61 (step @p170 :rule refl :args (@t189)) % 0.39/0.61 (step @p171 :rule nary_cong :premises (@p170 @p169) :args ((or @t189 @t191))) % 0.39/0.61 (step @p172 :rule trans :premises (@p171 @p168)) % 0.39/0.61 (step @p173 :rule bool-impl-elim :args (@t52 @t191)) % 0.39/0.61 (step @p174 :rule trans :premises (@p173 @p172)) % 0.39/0.61 (step @p175 :rule cong :premises (@p174) :args ((forall @t10 (=> @t52 @t191)))) % 0.39/0.61 (step @p176 :rule trans :premises (@p175 @p167)) % 0.39/0.61 (step @p177 :rule refl :args (@t178)) % 0.39/0.61 (step @p178 :rule refl :args (@t179)) % 0.39/0.61 (step @p179 :rule refl :args (@t32)) % 0.39/0.61 (step @p180 :rule cong :premises (@p179 @p178) :args ((= @t32 @t179))) % 0.39/0.61 (step @p181 :rule symm :premises (@p180)) % 0.39/0.61 (step @p182 :rule eq_resolve :premises (@p179 @p181)) % 0.39/0.61 (step @p183 :rule cong :premises (@p182) :args (@t192)) % 0.39/0.61 (step @p184 :rule nary_cong :premises (@p183 @p177) :args (@t193)) % 0.39/0.61 (step @p185 :rule cong :premises (@p184) :args ((forall @t40 @t193))) % 0.39/0.61 (step @p186 :rule bool-and-de-morgan :args (@t32 @t177 true)) % 0.39/0.61 (step @p187 :rule cong :premises (@p186) :args (@t195)) % 0.39/0.61 (step @p188 :rule trans :premises (@p187 @p185)) % 0.39/0.61 (step @p189 :rule cong :premises (@p188) :args (@t196)) % 0.39/0.61 (step @p190 :rule exists-elim :args ((= (exists @t40 @t194) @t196))) % 0.39/0.61 (step @p191 :rule trans :premises (@p190 @p189)) % 0.39/0.61 (step @p192 :rule refl :args (@t176)) % 0.39/0.61 (step @p193 :rule refl :args (@t31)) % 0.39/0.61 (step @p194 :rule cong :premises (@p193 @p192) :args ((= @t31 @t176))) % 0.39/0.61 (step @p195 :rule symm :premises (@p194)) % 0.39/0.61 (step @p196 :rule eq_resolve :premises (@p193 @p195)) % 0.39/0.61 (step @p197 :rule refl :args (@t44)) % 0.39/0.61 (step @p198 :rule refl :args (@t135)) % 0.39/0.61 (step @p199 :rule refl :args (@t20)) % 0.39/0.61 (step @p200 :rule cong :premises (@p199 @p198) :args ((= @t20 @t135))) % 0.39/0.61 (step @p201 :rule symm :premises (@p200)) % 0.39/0.61 (step @p202 :rule eq_resolve :premises (@p199 @p201)) % 0.39/0.61 (step @p203 :rule cong :premises (@p202) :args (@t197)) % 0.39/0.61 (step @p204 :rule nary_cong :premises (@p203 @p197 @p196) :args (@t198)) % 0.39/0.61 (step @p205 :rule cong :premises (@p204) :args ((forall @t25 @t198))) % 0.39/0.61 (step @p206 :rule aci_norm :args ((= (or @t197 @t45) @t198))) % 0.39/0.61 (step @p207 :rule bool-impl-elim :args (@t20 @t45)) % 0.39/0.61 (step @p208 :rule trans :premises (@p207 @p206)) % 0.39/0.61 (step @p209 :rule cong :premises (@p208) :args (@t46)) % 0.39/0.61 (step @p210 :rule trans :premises (@p209 @p205)) % 0.39/0.61 (step @p211 :rule refl :args (@t32)) % 0.39/0.61 (step @p212 :rule nary_cong :premises (@p211 @p210) :args (@t47)) % 0.39/0.61 (step @p213 :rule cong :premises (@p212) :args (@t48)) % 0.39/0.61 (step @p214 :rule trans :premises (@p213 @p191)) % 0.39/0.61 (step @p215 :rule refl :args (@t49)) % 0.39/0.61 (step @p216 :rule cong :premises (@p215 @p214) :args (@t50)) % 0.39/0.61 (step @p217 :rule refl :args (@t52)) % 0.39/0.61 (step @p218 :rule cong :premises (@p217 @p216) :args (@t53)) % 0.39/0.61 (step @p219 :rule cong :premises (@p218) :args (@t54)) % 0.39/0.61 (step @p220 :rule trans :premises (@p219 @p176)) % 0.39/0.61 (step @p221 :rule beta-reduce :args ((= @t199 @t187))) % 0.39/0.61 (step @p222 :rule nary_cong :premises (@p221 @p220) :args ((and @t199 @t54))) % 0.39/0.61 (step @p223 :rule trans :premises (@p222 @p141)) % 0.39/0.61 (step @p224 :rule refl :args (@t54)) % 0.39/0.61 (step @p225 :rule refl :args (@t1)) % 0.39/0.61 (step @p226 :rule refl :args (@t126)) % 0.39/0.61 (step @p227 :rule refl :args (@t14)) % 0.39/0.61 (step @p228 :rule cong :premises (@p227 @p226) :args ((= @t14 @t126))) % 0.39/0.61 (step @p229 :rule symm :premises (@p228)) % 0.39/0.61 (step @p230 :rule eq_resolve :premises (@p227 @p229)) % 0.39/0.61 (step @p231 :rule cong :premises (@p230) :args (@t15)) % 0.39/0.61 (step @p232 :rule refl :args (@t147)) % 0.39/0.61 (step @p233 :rule refl :args (@t16)) % 0.39/0.61 (step @p234 :rule cong :premises (@p233 @p232) :args ((= @t16 @t147))) % 0.39/0.61 (step @p235 :rule symm :premises (@p234)) % 0.39/0.61 (step @p236 :rule eq_resolve :premises (@p233 @p235)) % 0.39/0.61 (step @p237 :rule cong :premises (@p236) :args (@t200)) % 0.39/0.61 (step @p238 :rule nary_cong :premises (@p237 @p231) :args (@t201)) % 0.39/0.61 (step @p239 :rule cong :premises (@p238) :args ((forall @t10 @t201))) % 0.39/0.61 (step @p240 :rule bool-impl-elim :args (@t16 @t15)) % 0.39/0.61 (step @p241 :rule cong :premises (@p240) :args (@t17)) % 0.39/0.61 (step @p242 :rule trans :premises (@p241 @p239)) % 0.39/0.61 (step @p243 :rule aci_norm :args ((= @t203 @t151))) % 0.39/0.61 (step @p244 :rule cong :premises (@p243) :args (@t204)) % 0.39/0.61 (step @p245 :rule quant-merge-prenex :args ((= (forall @t10 @t206) @t204))) % 0.39/0.61 (step @p246 :rule alpha_equiv :args (@t207 (@list @t69) @t208)) % 0.39/0.61 (step @p247 :rule refl :args (@t148)) % 0.39/0.61 (step @p248 :rule nary_cong :premises (@p247 @p246) :args (@t209)) % 0.39/0.61 (step @p249 :rule quant-miniscope-or :args ((= @t206 @t209))) % 0.39/0.61 (step @p250 :rule trans :premises (@p249 @p248)) % 0.39/0.61 (step @p251 :rule symm :premises (@p250)) % 0.39/0.61 (step @p252 :rule cong :premises (@p251) :args ((forall @t10 (or @t148 @t213)))) % 0.39/0.61 (step @p253 :rule trans :premises (@p252 @p245)) % 0.39/0.61 (step @p254 :rule trans :premises (@p253 @p244)) % 0.39/0.61 (step @p255 :rule refl :args (@t213)) % 0.39/0.61 (step @p256 :rule nary_cong :premises (@p237 @p255) :args (@t214)) % 0.39/0.61 (step @p257 :rule cong :premises (@p256) :args ((forall @t10 @t214))) % 0.39/0.61 (step @p258 :rule trans :premises (@p257 @p254)) % 0.39/0.61 (step @p259 :rule bool-impl-elim :args (@t16 @t213)) % 0.39/0.61 (step @p260 :rule cong :premises (@p259) :args ((forall @t10 (=> @t16 @t213)))) % 0.39/0.61 (step @p261 :rule trans :premises (@p260 @p258)) % 0.39/0.61 (step @p262 :rule refl :args (@t210)) % 0.39/0.61 (step @p263 :rule refl :args (@t21)) % 0.39/0.61 (step @p264 :rule cong :premises (@p263 @p262) :args ((= @t21 @t210))) % 0.39/0.61 (step @p265 :rule symm :premises (@p264)) % 0.39/0.61 (step @p266 :rule eq_resolve :premises (@p263 @p265)) % 0.39/0.61 (step @p267 :rule refl :args (@t22)) % 0.39/0.61 (step @p268 :rule refl :args (@t211)) % 0.39/0.61 (step @p269 :rule refl :args (@t24)) % 0.39/0.61 (step @p270 :rule cong :premises (@p269 @p268) :args ((= @t24 @t211))) % 0.39/0.61 (step @p271 :rule symm :premises (@p270)) % 0.39/0.61 (step @p272 :rule eq_resolve :premises (@p269 @p271)) % 0.39/0.61 (step @p273 :rule cong :premises (@p272) :args (@t215)) % 0.39/0.61 (step @p274 :rule nary_cong :premises (@p273 @p267 @p266 @p202) :args (@t216)) % 0.39/0.61 (step @p275 :rule cong :premises (@p274) :args ((forall @t25 @t216))) % 0.39/0.61 (step @p276 :rule aci_norm :args ((= (or @t215 @t23) @t216))) % 0.39/0.61 (step @p277 :rule bool-impl-elim :args (@t24 @t23)) % 0.39/0.61 (step @p278 :rule trans :premises (@p277 @p276)) % 0.39/0.61 (step @p279 :rule cong :premises (@p278) :args (@t26)) % 0.39/0.61 (step @p280 :rule trans :premises (@p279 @p275)) % 0.39/0.61 (step @p281 :rule refl :args (@t16)) % 0.39/0.61 (step @p282 :rule cong :premises (@p281 @p280) :args (@t27)) % 0.39/0.61 (step @p283 :rule cong :premises (@p282) :args (@t28)) % 0.39/0.61 (step @p284 :rule trans :premises (@p283 @p261)) % 0.39/0.61 (step @p285 :rule aci_norm :args ((= @t218 @t172))) % 0.39/0.61 (step @p286 :rule cong :premises (@p285) :args (@t219)) % 0.39/0.61 (step @p287 :rule quant-merge-prenex :args ((= (forall @t40 @t221) @t219))) % 0.39/0.61 (step @p288 :rule alpha_equiv :args (@t222 (@list @t80 @t77) (@list @t5 @t223))) % 0.39/0.61 (step @p289 :rule refl :args (@t171)) % 0.39/0.61 (step @p290 :rule nary_cong :premises (@p289 @p288) :args (@t224)) % 0.39/0.61 (step @p291 :rule quant-miniscope-or :args ((= @t221 @t224))) % 0.39/0.61 (step @p292 :rule trans :premises (@p291 @p290)) % 0.39/0.61 (step @p293 :rule symm :premises (@p292)) % 0.39/0.61 (step @p294 :rule cong :premises (@p293) :args ((forall @t40 (or @t171 @t230)))) % 0.39/0.61 (step @p295 :rule trans :premises (@p294 @p287)) % 0.39/0.61 (step @p296 :rule trans :premises (@p295 @p286)) % 0.39/0.61 (step @p297 :rule refl :args (@t230)) % 0.39/0.61 (step @p298 :rule refl :args (@t170)) % 0.39/0.61 (step @p299 :rule refl :args (@t38)) % 0.39/0.61 (step @p300 :rule cong :premises (@p299 @p298) :args ((= @t38 @t170))) % 0.39/0.61 (step @p301 :rule symm :premises (@p300)) % 0.39/0.61 (step @p302 :rule eq_resolve :premises (@p299 @p301)) % 0.39/0.61 (step @p303 :rule cong :premises (@p302) :args (@t231)) % 0.39/0.61 (step @p304 :rule nary_cong :premises (@p303 @p297) :args (@t232)) % 0.39/0.61 (step @p305 :rule cong :premises (@p304) :args ((forall @t40 @t232))) % 0.39/0.61 (step @p306 :rule trans :premises (@p305 @p296)) % 0.39/0.61 (step @p307 :rule bool-impl-elim :args (@t38 @t230)) % 0.39/0.61 (step @p308 :rule cong :premises (@p307) :args ((forall @t40 (=> @t38 @t230)))) % 0.39/0.61 (step @p309 :rule trans :premises (@p308 @p306)) % 0.39/0.61 (step @p310 :rule aci_norm :args ((= @t234 @t228))) % 0.39/0.61 (step @p311 :rule cong :premises (@p310) :args (@t235)) % 0.39/0.61 (step @p312 :rule quant-merge-prenex :args ((= (forall @t10 @t237) @t235))) % 0.39/0.61 (step @p313 :rule alpha_equiv :args (@t238 (@list @t223) @t208)) % 0.39/0.61 (step @p314 :rule refl :args (@t180)) % 0.39/0.61 (step @p315 :rule nary_cong :premises (@p247 @p314 @p313) :args (@t239)) % 0.39/0.61 (step @p316 :rule quant-miniscope-or :args ((= @t237 @t239))) % 0.39/0.61 (step @p317 :rule trans :premises (@p316 @p315)) % 0.39/0.61 (step @p318 :rule symm :premises (@p317)) % 0.39/0.61 (step @p319 :rule cong :premises (@p318) :args ((forall @t10 (or @t148 @t180 @t240)))) % 0.39/0.61 (step @p320 :rule trans :premises (@p319 @p312)) % 0.39/0.61 (step @p321 :rule trans :premises (@p320 @p311)) % 0.39/0.61 (step @p322 :rule refl :args (@t240)) % 0.39/0.61 (step @p323 :rule nary_cong :premises (@p237 @p183 @p322) :args (@t241)) % 0.39/0.61 (step @p324 :rule cong :premises (@p323) :args ((forall @t10 @t241))) % 0.39/0.61 (step @p325 :rule trans :premises (@p324 @p321)) % 0.39/0.61 (step @p326 :rule aci_norm :args ((= (or @t200 @t242) @t241))) % 0.39/0.61 (step @p327 :rule bool-impl-elim :args (@t16 @t242)) % 0.39/0.61 (step @p328 :rule trans :premises (@p327 @p326)) % 0.39/0.61 (step @p329 :rule cong :premises (@p328) :args ((forall @t10 (=> @t16 @t242)))) % 0.39/0.61 (step @p330 :rule trans :premises (@p329 @p325)) % 0.39/0.61 (step @p331 :rule cong :premises (@p266) :args (@t243)) % 0.39/0.61 (step @p332 :rule nary_cong :premises (@p273 @p331 @p196) :args (@t244)) % 0.39/0.61 (step @p333 :rule cong :premises (@p332) :args (@t245)) % 0.39/0.61 (step @p334 :rule refl :args (@t192)) % 0.39/0.61 (step @p335 :rule nary_cong :premises (@p334 @p333) :args (@t246)) % 0.39/0.61 (step @p336 :rule quant-miniscope-or :args ((= (forall @t25 @t247) @t246))) % 0.39/0.61 (step @p337 :rule aci_norm :args ((= @t248 @t247))) % 0.39/0.61 (step @p338 :rule cong :premises (@p337) :args ((forall @t25 @t248))) % 0.39/0.61 (step @p339 :rule trans :premises (@p338 @p336)) % 0.39/0.61 (step @p340 :rule trans :premises (@p339 @p335)) % 0.39/0.61 (step @p341 :rule aci_norm :args ((= (or @t215 @t249) @t248))) % 0.39/0.61 (step @p342 :rule aci_norm :args ((= (or (or @t192 @t243) @t31) @t249))) % 0.39/0.61 (step @p343 :rule bool-and-de-morgan :args (@t32 @t21 true)) % 0.39/0.61 (step @p344 :rule nary_cong :premises (@p343 @p193) :args ((or (not @t33) @t31))) % 0.39/0.61 (step @p345 :rule trans :premises (@p344 @p342)) % 0.39/0.61 (step @p346 :rule bool-impl-elim :args (@t33 @t31)) % 0.39/0.61 (step @p347 :rule trans :premises (@p346 @p345)) % 0.39/0.61 (step @p348 :rule refl :args (@t215)) % 0.39/0.61 (step @p349 :rule nary_cong :premises (@p348 @p347) :args ((or @t215 @t34))) % 0.39/0.61 (step @p350 :rule trans :premises (@p349 @p341)) % 0.39/0.61 (step @p351 :rule bool-impl-elim :args (@t24 @t34)) % 0.39/0.61 (step @p352 :rule trans :premises (@p351 @p350)) % 0.39/0.61 (step @p353 :rule cong :premises (@p352) :args (@t35)) % 0.39/0.61 (step @p354 :rule trans :premises (@p353 @p340)) % 0.39/0.61 (step @p355 :rule cong :premises (@p281 @p354) :args (@t36)) % 0.39/0.61 (step @p356 :rule cong :premises (@p355) :args (@t37)) % 0.39/0.61 (step @p357 :rule trans :premises (@p356 @p330)) % 0.39/0.61 (step @p358 :rule refl :args (@t38)) % 0.39/0.61 (step @p359 :rule cong :premises (@p358 @p357) :args (@t39)) % 0.39/0.61 (step @p360 :rule cong :premises (@p359) :args (@t41)) % 0.39/0.61 (step @p361 :rule trans :premises (@p360 @p309)) % 0.39/0.61 (step @p362 :rule nary_cong :premises (@p361 @p284 @p242) :args (@t42)) % 0.39/0.61 (step @p363 :rule cong :premises (@p362) :args (@t43)) % 0.39/0.61 (step @p364 :rule trans :premises (@p3 @p363)) % 0.39/0.61 (step @p365 :rule ho_cong :premises (@p364 @p225)) % 0.39/0.61 (step @p366 :rule nary_cong :premises (@p365 @p224) :args (@t55)) % 0.39/0.61 (step @p367 :rule trans :premises (@p366 @p223)) % 0.39/0.61 (step @p368 :rule cong :premises (@p367) :args (@t56)) % 0.39/0.61 (step @p369 :rule trans :premises (@p4 @p368)) % 0.39/0.61 (step @p370 :rule ho_cong :premises (@p369 @p103)) % 0.39/0.61 (step @p371 :rule nary_cong :premises (@p81 @p370) :args (@t58)) % 0.39/0.61 (step @p372 :rule trans :premises (@p371 @p140)) % 0.39/0.61 (step @p373 :rule cong :premises (@p372) :args (@t59)) % 0.39/0.61 (step @p374 :rule trans :premises (@p5 @p373)) % 0.39/0.61 (step @p375 :rule ho_cong :premises (@p374 @p70)) % 0.39/0.61 (step @p376 :rule cong :premises (@p375 @p100) :args (@t9)) % 0.39/0.61 (step @p377 :rule cong :premises (@p376) :args (@t11)) % 0.39/0.61 (step @p378 :rule cong :premises (@p377) :args (@t12)) % 0.39/0.61 (step @p379 :rule trans :premises (@p378 @p99)) % 0.39/0.61 (step @p380 :rule eq_resolve :premises (@p1 @p379)) % 0.39/0.61 (step @p381 :rule skolemize :premises (@p380)) % 0.39/0.61 (step @p382 :rule bool-double-not-elim :args (@t252)) % 0.39/0.61 (step @p383 :rule refl :args (@t259)) % 0.39/0.61 (step @p384 :rule nary_cong :premises (@p383 @p382) :args ((or @t259 (not @t258)))) % 0.39/0.61 (step @p385 :rule cnf_or_neg :args (@t259 4)) % 0.39/0.61 (step @p386 :rule eq_resolve :premises (@p385 @p384)) % 0.39/0.61 (step @p387 :rule reordering :premises (@p386) :args ((or @t252 @t259))) % 0.39/0.61 (step @p388 :rule chain_m_resolution :premises (@p387 @p381) :args (@t252 @t260 @t261)) % 0.39/0.61 (step @p389 :rule bool-double-not-elim :args (@t254)) % 0.39/0.61 (step @p390 :rule nary_cong :premises (@p383 @p389) :args ((or @t259 (not @t255)))) % 0.39/0.61 (step @p391 :rule cnf_or_neg :args (@t259 6)) % 0.39/0.61 (step @p392 :rule eq_resolve :premises (@p391 @p390)) % 0.39/0.61 (step @p393 :rule reordering :premises (@p392) :args ((or @t254 @t259))) % 0.39/0.61 (step @p394 :rule chain_m_resolution :premises (@p393 @p381) :args (@t254 @t260 @t261)) % 0.39/0.61 (step @p395 :rule bool-double-not-elim :args (@t256)) % 0.39/0.61 (step @p396 :rule nary_cong :premises (@p383 @p395) :args ((or @t259 (not @t257)))) % 0.39/0.61 (step @p397 :rule cnf_or_neg :args (@t259 5)) % 0.39/0.61 (step @p398 :rule eq_resolve :premises (@p397 @p396)) % 0.39/0.61 (step @p399 :rule reordering :premises (@p398) :args ((or @t256 @t259))) % 0.39/0.61 (step @p400 :rule chain_m_resolution :premises (@p399 @p381) :args (@t256 @t260 @t261)) % 0.39/0.61 (step @p401 :rule cnf_or_pos :args (@t262)) % 0.39/0.61 (step @p402 :rule reordering :premises (@p401) :args ((or @t257 @t255 @t263))) % 0.39/0.61 (step @p403 :rule chain_m_resolution :premises (@p402 @p400 @p394) :args (@t263 (@list false false) (@list @t256 @t254))) % 0.39/0.61 (assume-push @p410 @t252) % 0.39/0.61 (step @p405 :rule instantiate :premises (@p388) :args ((@list @t253))) % 0.39/0.61 (step-pop @p411 :rule scope :premises (@p405)) % 0.39/0.61 (step @p406 :rule process_scope :premises (@p411) :args (@t262)) % 0.39/0.61 (step @p408 :rule implies_elim :premises (@p406)) % 0.39/0.61 (step @p409 false :rule chain_m_resolution :premises (@p408 @p403 @p388) :args (false (@list true false) (@list @t262 @t252))) % 0.39/0.61 ) % 0.39/0.61 % SZS output end Proof % 0.39/0.61 % cvc5 exiting %------------------------------------------------------------------------------