%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU822^2 : 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 : n007.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 0.37s 0.61s % Output : Proof 0.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU822^2 : 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 % 0.16/0.34 % Computer : n007.cluster.edu % 0.16/0.34 % Model : x86_64 x86_64 % 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.34 % Memory : 8042.1875MB % 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.34 % CPULimit : 300 % 0.16/0.34 % WCLimit : 300 % 0.16/0.34 % DateTime : Tue Jun 2 17:53:41 EDT 2026 % 0.16/0.34 % CPUTime : % 0.28/0.49 %----Proving TH0 % 0.37/0.61 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.37/0.61 % SZS status Theorem % 0.37/0.61 % SZS output start Proof % 0.37/0.61 ( % 0.37/0.61 (declare-sort $$unsorted 0) % 0.37/0.61 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 0.37/0.61 (declare-const tptp.nonempty (-> $$unsorted Bool)) % 0.37/0.61 (declare-const tptp.powerset (-> $$unsorted $$unsorted)) % 0.37/0.61 (declare-const tptp.transitiveset (-> $$unsorted Bool)) % 0.37/0.61 (declare-const tptp.ordinalIrrefl Bool) % 0.37/0.61 (define tptp.stricttotalorderedByIn () (let ((_let_1 (@var "X" $$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" $$unsorted))) (let ((_let_12 (_ tptp.in _let_11))) (lambda (@list _let_3) (and (forall (@list _let_11) (=> (_ _let_12 _let_3) (forall _let_5 (=> _let_4 (forall _let_10 (=> _let_9 (=> (and (_ _let_12 _let_1) _let_8) (_ _let_12 _let_6)))))))) (forall _let_5 (=> _let_4 (forall _let_10 (=> _let_9 (or (= _let_1 _let_6) _let_8 (_ _let_7 _let_1)))))) (forall _let_5 (=> _let_4 (not (_ _let_2 _let_1))))))))))))))))))) % 0.37/0.61 (define tptp.wellorderedByIn () (let ((_let_1 (@var "Y" $$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" $$unsorted))) (lambda (@list _let_5) (and (_ tptp.stricttotalorderedByIn _let_5) (forall (@list _let_4) (=> (_ (_ tptp.in _let_4) (_ tptp.powerset _let_5)) (=> (_ tptp.nonempty _let_4) (exists (@list _let_2) (and (_ _let_3 _let_4) (forall (@list _let_1) (=> (_ (_ tptp.in _let_1) _let_4) (or (= _let_2 _let_1) (_ _let_3 _let_1))))))))))))))))) % 0.37/0.61 (define tptp.ordinal () (let ((_let_1 (@var "Xx" $$unsorted))) (lambda (@list _let_1) (and (_ tptp.transitiveset _let_1) (_ tptp.wellorderedByIn _let_1))))) % 0.37/0.61 (define @t1 () (@var "A" $$unsorted)) % 0.37/0.61 (define @t2 () (_ tptp.in @t1)) % 0.37/0.61 (define @t3 () (_ @t2 @t1)) % 0.37/0.61 (define @t4 () (not @t3)) % 0.37/0.61 (define @t5 () (@var "X" $$unsorted)) % 0.37/0.61 (define @t6 () (_ @t2 @t5)) % 0.37/0.61 (define @t7 () (@list @t1)) % 0.37/0.61 (define @t8 () (forall @t7 (=> @t6 @t4))) % 0.37/0.61 (define @t9 () (_ tptp.ordinal @t5)) % 0.37/0.61 (define @t10 () (=> @t9 @t8)) % 0.37/0.61 (define @t11 () (@list @t5)) % 0.37/0.61 (define @t12 () (forall @t11 @t10)) % 0.37/0.61 (define @t13 () (= tptp.ordinalIrrefl @t12)) % 0.37/0.61 (define @t14 () (_ tptp.in @t5)) % 0.37/0.61 (define @t15 () (_ @t14 @t5)) % 0.37/0.61 (define @t16 () (not @t15)) % 0.37/0.61 (define @t17 () (=> @t9 @t16)) % 0.37/0.61 (define @t18 () (forall @t11 @t17)) % 0.37/0.61 (define @t19 () (=> tptp.ordinalIrrefl @t18)) % 0.37/0.61 (define @t20 () (not @t19)) % 0.37/0.61 (define @t21 () (_ @t14 @t1)) % 0.37/0.61 (define @t22 () (forall @t11 (=> @t21 @t16))) % 0.37/0.61 (define @t23 () (@var "Y" $$unsorted)) % 0.37/0.61 (define @t24 () (_ tptp.in @t23)) % 0.37/0.61 (define @t25 () (_ @t24 @t5)) % 0.37/0.61 (define @t26 () (_ @t14 @t23)) % 0.37/0.61 (define @t27 () (= @t5 @t23)) % 0.37/0.61 (define @t28 () (or @t27 @t26 @t25)) % 0.37/0.61 (define @t29 () (_ @t24 @t1)) % 0.37/0.61 (define @t30 () (@list @t23)) % 0.37/0.61 (define @t31 () (forall @t30 (=> @t29 @t28))) % 0.37/0.61 (define @t32 () (=> @t21 @t31)) % 0.37/0.61 (define @t33 () (forall @t11 @t32)) % 0.37/0.61 (define @t34 () (@var "Xx" $$unsorted)) % 0.37/0.61 (define @t35 () (_ tptp.in @t34)) % 0.37/0.61 (define @t36 () (_ @t35 @t23)) % 0.37/0.61 (define @t37 () (_ @t35 @t5)) % 0.37/0.61 (define @t38 () (and @t37 @t26)) % 0.37/0.61 (define @t39 () (=> @t38 @t36)) % 0.37/0.61 (define @t40 () (forall @t30 (=> @t29 @t39))) % 0.37/0.61 (define @t41 () (=> @t21 @t40)) % 0.37/0.61 (define @t42 () (forall @t11 @t41)) % 0.37/0.61 (define @t43 () (_ @t35 @t1)) % 0.37/0.61 (define @t44 () (=> @t43 @t42)) % 0.37/0.61 (define @t45 () (@list @t34)) % 0.37/0.61 (define @t46 () (forall @t45 @t44)) % 0.37/0.61 (define @t47 () (and @t46 @t33 @t22)) % 0.37/0.61 (define @t48 () (lambda @t7 @t47)) % 0.37/0.61 (define @t49 () (= @t34 @t23)) % 0.37/0.61 (define @t50 () (or @t49 @t36)) % 0.37/0.61 (define @t51 () (forall @t30 (=> @t25 @t50))) % 0.37/0.61 (define @t52 () (and @t37 @t51)) % 0.37/0.61 (define @t53 () (exists @t45 @t52)) % 0.37/0.61 (define @t54 () (_ tptp.nonempty @t5)) % 0.37/0.61 (define @t55 () (=> @t54 @t53)) % 0.37/0.61 (define @t56 () (_ tptp.powerset @t1)) % 0.37/0.61 (define @t57 () (_ @t14 @t56)) % 0.37/0.61 (define @t58 () (=> @t57 @t55)) % 0.37/0.61 (define @t59 () (forall @t11 @t58)) % 0.37/0.61 (define @t60 () (and (_ tptp.stricttotalorderedByIn @t1) @t59)) % 0.37/0.61 (define @t61 () (lambda @t7 @t60)) % 0.37/0.61 (define @t62 () (_ tptp.transitiveset @t34)) % 0.37/0.61 (define @t63 () (and @t62 (_ tptp.wellorderedByIn @t34))) % 0.37/0.61 (define @t64 () (lambda @t45 @t63)) % 0.37/0.61 (define @t65 () (tptp.in @t5 @t5)) % 0.37/0.61 (define @t66 () (not @t65)) % 0.37/0.61 (define @t67 () (@var "BOUND_VARIABLE_7736" $$unsorted)) % 0.37/0.61 (define @t68 () (not (tptp.in @t67 @t67))) % 0.37/0.61 (define @t69 () (@list @t67)) % 0.37/0.61 (define @t70 () (forall @t69 (or (not (tptp.in @t67 @t5)) @t68))) % 0.37/0.61 (define @t71 () (not @t70)) % 0.37/0.61 (define @t72 () (@var "BOUND_VARIABLE_7745" $$unsorted)) % 0.37/0.61 (define @t73 () (@var "BOUND_VARIABLE_7534" $$unsorted)) % 0.37/0.61 (define @t74 () (tptp.in @t73 @t72)) % 0.37/0.61 (define @t75 () (tptp.in @t72 @t73)) % 0.37/0.61 (define @t76 () (= @t73 @t72)) % 0.37/0.61 (define @t77 () (tptp.in @t73 @t5)) % 0.37/0.61 (define @t78 () (@list @t72 @t73)) % 0.37/0.61 (define @t79 () (forall @t78 (or (not (tptp.in @t72 @t5)) (not @t77) @t76 @t75 @t74))) % 0.37/0.61 (define @t80 () (not @t79)) % 0.37/0.61 (define @t81 () (@var "BOUND_VARIABLE_7506" $$unsorted)) % 0.37/0.61 (define @t82 () (@var "BOUND_VARIABLE_7633" $$unsorted)) % 0.37/0.61 (define @t83 () (tptp.in @t82 @t81)) % 0.37/0.61 (define @t84 () (@var "BOUND_VARIABLE_7504" $$unsorted)) % 0.37/0.61 (define @t85 () (not (tptp.in @t84 @t81))) % 0.37/0.61 (define @t86 () (not (tptp.in @t82 @t84))) % 0.37/0.61 (define @t87 () (@list @t82 @t84 @t81)) % 0.37/0.61 (define @t88 () (forall @t87 (or (not (tptp.in @t82 @t5)) (not (tptp.in @t84 @t5)) @t86 (not (tptp.in @t81 @t5)) @t85 @t83))) % 0.37/0.61 (define @t89 () (not @t88)) % 0.37/0.61 (define @t90 () (@var "BOUND_VARIABLE_7643" $$unsorted)) % 0.37/0.61 (define @t91 () (tptp.in @t90 @t23)) % 0.37/0.61 (define @t92 () (= @t23 @t90)) % 0.37/0.61 (define @t93 () (@var "BOUND_VARIABLE_7755" $$unsorted)) % 0.37/0.61 (define @t94 () (@list @t90)) % 0.37/0.61 (define @t95 () (not (forall @t94 (or (not (tptp.in @t90 @t93)) (not (forall @t30 (or (not (tptp.in @t23 @t93)) @t92 @t91))))))) % 0.37/0.61 (define @t96 () (not (tptp.nonempty @t93))) % 0.37/0.61 (define @t97 () (@list @t93)) % 0.37/0.61 (define @t98 () (forall @t97 (or (not (tptp.in @t93 (tptp.powerset @t5))) @t96 @t95))) % 0.37/0.61 (define @t99 () (not @t98)) % 0.37/0.61 (define @t100 () (tptp.transitiveset @t5)) % 0.37/0.61 (define @t101 () (not @t100)) % 0.37/0.61 (define @t102 () (forall @t11 (or @t101 @t99 @t89 @t80 @t71 @t66))) % 0.37/0.61 (define @t103 () (@var "BOUND_VARIABLE_7832" $$unsorted)) % 0.37/0.61 (define @t104 () (not (tptp.in @t103 @t103))) % 0.37/0.61 (define @t105 () (not (tptp.in @t103 @t5))) % 0.37/0.61 (define @t106 () (or @t105 @t104)) % 0.37/0.61 (define @t107 () (or @t101 @t99 @t89 @t80 @t71 @t106)) % 0.37/0.61 (define @t108 () (forall (@list @t5 @t103) @t107)) % 0.37/0.61 (define @t109 () (@list @t103)) % 0.37/0.61 (define @t110 () (forall @t109 @t107)) % 0.37/0.61 (define @t111 () (forall @t109 @t106)) % 0.37/0.61 (define @t112 () (or @t101 @t99 @t89 @t80 @t71 @t111)) % 0.37/0.61 (define @t113 () (tptp.in @t1 @t1)) % 0.37/0.61 (define @t114 () (tptp.in @t1 @t5)) % 0.37/0.61 (define @t115 () (forall @t7 (or (not @t114) (not @t113)))) % 0.37/0.61 (define @t116 () (_ tptp.transitiveset @t5)) % 0.37/0.61 (define @t117 () (not @t116)) % 0.37/0.61 (define @t118 () (or @t117 @t99 @t89 @t80 @t71 @t115)) % 0.37/0.61 (define @t119 () (or @t117 @t99 @t89 @t80 @t71)) % 0.37/0.61 (define @t120 () (and @t116 @t98 @t88 @t79 @t70)) % 0.37/0.61 (define @t121 () (not @t120)) % 0.37/0.61 (define @t122 () (not @t6)) % 0.37/0.61 (define @t123 () (or @t122 @t4)) % 0.37/0.61 (define @t124 () (forall @t69 (or (not (tptp.in @t67 @t34)) @t68))) % 0.37/0.61 (define @t125 () (not (tptp.in @t73 @t34))) % 0.37/0.61 (define @t126 () (not (tptp.in @t72 @t34))) % 0.37/0.61 (define @t127 () (forall @t87 (or (not (tptp.in @t82 @t34)) (not (tptp.in @t84 @t34)) @t86 (not (tptp.in @t81 @t34)) @t85 @t83))) % 0.37/0.61 (define @t128 () (tptp.powerset @t34)) % 0.37/0.61 (define @t129 () (forall @t97 (or (not (tptp.in @t93 @t128)) @t96 @t95))) % 0.37/0.61 (define @t130 () (or @t126 @t125 (= @t72 @t73) @t75 @t74)) % 0.37/0.61 (define @t131 () (forall @t78 @t130)) % 0.37/0.61 (define @t132 () (and @t62 @t129 @t127 @t131 @t124)) % 0.37/0.61 (define @t133 () (not (tptp.in @t5 @t34))) % 0.37/0.61 (define @t134 () (forall @t11 (or @t133 @t66))) % 0.37/0.61 (define @t135 () (@list @t5)) % 0.37/0.61 (define @t136 () (tptp.in @t5 @t73)) % 0.37/0.61 (define @t137 () (= @t5 @t73)) % 0.37/0.61 (define @t138 () (@list @t5 @t73)) % 0.37/0.61 (define @t139 () (forall @t138 (or @t133 @t125 @t137 @t136 @t77))) % 0.37/0.61 (define @t140 () (tptp.in @t23 @t5)) % 0.37/0.61 (define @t141 () (not @t140)) % 0.37/0.61 (define @t142 () (not (tptp.in @t90 @t5))) % 0.37/0.61 (define @t143 () (not (forall @t94 (or @t142 (not (forall @t30 (or @t141 @t92 @t91))))))) % 0.37/0.61 (define @t144 () (tptp.nonempty @t5)) % 0.37/0.61 (define @t145 () (not @t144)) % 0.37/0.61 (define @t146 () (forall @t11 (or (not (tptp.in @t5 @t128)) @t145 @t143))) % 0.37/0.61 (define @t147 () (and @t62 @t146 @t127 @t139 @t134)) % 0.37/0.61 (define @t148 () (lambda @t45 @t147)) % 0.37/0.61 (define @t149 () (_ @t148 @t5)) % 0.37/0.61 (define @t150 () (=> @t149 @t8)) % 0.37/0.61 (define @t151 () (forall @t11 @t150)) % 0.37/0.61 (define @t152 () (and @t146 @t127 @t139 @t134)) % 0.37/0.61 (define @t153 () (tptp.in @t5 @t1)) % 0.37/0.61 (define @t154 () (not @t153)) % 0.37/0.61 (define @t155 () (forall @t11 (or @t154 @t66))) % 0.37/0.61 (define @t156 () (not (tptp.in @t73 @t1))) % 0.37/0.61 (define @t157 () (or @t154 @t156 @t137 @t136 @t77)) % 0.37/0.61 (define @t158 () (forall @t138 @t157)) % 0.37/0.61 (define @t159 () (not (tptp.in @t81 @t1))) % 0.37/0.61 (define @t160 () (not (tptp.in @t84 @t1))) % 0.37/0.61 (define @t161 () (forall @t87 (or (not (tptp.in @t82 @t1)) @t160 @t86 @t159 @t85 @t83))) % 0.37/0.61 (define @t162 () (tptp.powerset @t1)) % 0.37/0.61 (define @t163 () (tptp.in @t5 @t162)) % 0.37/0.61 (define @t164 () (not @t163)) % 0.37/0.61 (define @t165 () (or @t141 (= @t90 @t23) @t91)) % 0.37/0.61 (define @t166 () (forall @t30 @t165)) % 0.37/0.61 (define @t167 () (not @t166)) % 0.37/0.61 (define @t168 () (or @t142 @t167)) % 0.37/0.61 (define @t169 () (forall @t94 @t168)) % 0.37/0.61 (define @t170 () (not @t169)) % 0.37/0.61 (define @t171 () (or @t164 @t145 @t170)) % 0.37/0.61 (define @t172 () (forall @t11 @t171)) % 0.37/0.61 (define @t173 () (and @t172 @t161 @t158 @t155)) % 0.37/0.61 (define @t174 () (tptp.in @t34 @t81)) % 0.37/0.61 (define @t175 () (not (tptp.in @t34 @t84))) % 0.37/0.61 (define @t176 () (tptp.in @t34 @t1)) % 0.37/0.61 (define @t177 () (not @t176)) % 0.37/0.61 (define @t178 () (or @t177 @t160 @t175 @t159 @t85 @t174)) % 0.37/0.61 (define @t179 () (@list @t34 @t84 @t81)) % 0.37/0.61 (define @t180 () (forall @t179 @t178)) % 0.37/0.61 (define @t181 () (@list @t34)) % 0.37/0.61 (define @t182 () (tptp.in @t34 @t23)) % 0.37/0.61 (define @t183 () (forall @t30 (or @t141 @t49 @t182))) % 0.37/0.61 (define @t184 () (not @t183)) % 0.37/0.61 (define @t185 () (tptp.in @t34 @t5)) % 0.37/0.61 (define @t186 () (not @t185)) % 0.37/0.61 (define @t187 () (forall @t45 (or @t186 @t184))) % 0.37/0.61 (define @t188 () (not @t187)) % 0.37/0.61 (define @t189 () (or @t164 @t145 @t188)) % 0.37/0.61 (define @t190 () (forall @t11 @t189)) % 0.37/0.61 (define @t191 () (and @t190 @t180 @t158 @t155)) % 0.37/0.61 (define @t192 () (lambda @t7 @t191)) % 0.37/0.61 (define @t193 () (and @t180 @t158 @t155)) % 0.37/0.61 (define @t194 () (not @t54)) % 0.37/0.61 (define @t195 () (not @t57)) % 0.37/0.61 (define @t196 () (or @t195 @t194 @t188)) % 0.37/0.61 (define @t197 () (=> @t54 @t188)) % 0.37/0.61 (define @t198 () (not @t37)) % 0.37/0.61 (define @t199 () (or @t198 @t184)) % 0.37/0.61 (define @t200 () (and @t37 @t183)) % 0.37/0.61 (define @t201 () (forall @t45 (not @t200))) % 0.37/0.61 (define @t202 () (not @t201)) % 0.37/0.61 (define @t203 () (not @t25)) % 0.37/0.61 (define @t204 () (or @t203 @t49 @t36)) % 0.37/0.61 (define @t205 () (_ (lambda @t7 @t193) @t1)) % 0.37/0.61 (define @t206 () (not @t21)) % 0.37/0.61 (define @t207 () (or @t206 @t16)) % 0.37/0.61 (define @t208 () (or @t156 @t137 @t136 @t77)) % 0.37/0.61 (define @t209 () (or @t154 @t208)) % 0.37/0.61 (define @t210 () (forall @t138 @t209)) % 0.37/0.61 (define @t211 () (@list @t73)) % 0.37/0.61 (define @t212 () (forall @t211 @t209)) % 0.37/0.61 (define @t213 () (forall @t211 @t208)) % 0.37/0.61 (define @t214 () (@list @t23)) % 0.37/0.61 (define @t215 () (or @t154 @t213)) % 0.37/0.61 (define @t216 () (tptp.in @t5 @t23)) % 0.37/0.61 (define @t217 () (tptp.in @t23 @t1)) % 0.37/0.61 (define @t218 () (not @t217)) % 0.37/0.61 (define @t219 () (forall @t30 (or @t218 @t27 @t216 @t140))) % 0.37/0.61 (define @t220 () (or @t206 @t219)) % 0.37/0.61 (define @t221 () (not @t29)) % 0.37/0.61 (define @t222 () (or @t221 @t27 @t26 @t25)) % 0.37/0.61 (define @t223 () (or @t160 @t175 @t159 @t85 @t174)) % 0.37/0.61 (define @t224 () (or @t177 @t223)) % 0.37/0.61 (define @t225 () (forall @t179 @t224)) % 0.37/0.61 (define @t226 () (@list @t84 @t81)) % 0.37/0.61 (define @t227 () (forall @t226 @t224)) % 0.37/0.61 (define @t228 () (forall @t226 @t223)) % 0.37/0.61 (define @t229 () (@var "BOUND_VARIABLE_7482" $$unsorted)) % 0.37/0.61 (define @t230 () (or @t177 @t228)) % 0.37/0.61 (define @t231 () (tptp.in @t34 @t229)) % 0.37/0.61 (define @t232 () (not (tptp.in @t5 @t229))) % 0.37/0.61 (define @t233 () (not (tptp.in @t229 @t1))) % 0.37/0.61 (define @t234 () (or @t154 @t186 @t233 @t232 @t231)) % 0.37/0.61 (define @t235 () (@list @t5 @t229)) % 0.37/0.61 (define @t236 () (forall @t235 @t234)) % 0.37/0.61 (define @t237 () (not @t43)) % 0.37/0.61 (define @t238 () (or @t237 @t236)) % 0.37/0.61 (define @t239 () (or @t233 @t232 @t231)) % 0.37/0.61 (define @t240 () (or @t154 @t186 @t239)) % 0.37/0.61 (define @t241 () (forall @t235 @t240)) % 0.37/0.61 (define @t242 () (@list @t229)) % 0.37/0.61 (define @t243 () (forall @t242 @t240)) % 0.37/0.61 (define @t244 () (forall @t242 @t239)) % 0.37/0.61 (define @t245 () (or @t154 @t186 @t244)) % 0.37/0.61 (define @t246 () (forall @t30 (or @t218 (not @t216) @t182))) % 0.37/0.61 (define @t247 () (or @t206 @t198 @t246)) % 0.37/0.61 (define @t248 () (or @t198 @t246)) % 0.37/0.61 (define @t249 () (not @t26)) % 0.37/0.61 (define @t250 () (or @t221 @t249 @t36)) % 0.37/0.61 (define @t251 () (forall @t30 @t250)) % 0.37/0.61 (define @t252 () (or @t198 @t251)) % 0.37/0.61 (define @t253 () (or @t198 @t250)) % 0.37/0.61 (define @t254 () (or @t221 @t198 @t249 @t36)) % 0.37/0.61 (define @t255 () (or @t198 @t249 @t36)) % 0.37/0.61 (define @t256 () (=> tptp.ordinalIrrefl @t102)) % 0.37/0.61 (define @t257 () (or @t117 @t99 @t89 @t80 @t71 @t16)) % 0.37/0.61 (define @t258 () (=> @t149 @t16)) % 0.37/0.61 (define @t259 () (forall @t11 @t258)) % 0.37/0.61 (define @t260 () (=> tptp.ordinalIrrefl @t259)) % 0.37/0.61 (define @t261 () (@quantifiers_skolemize @t102 0)) % 0.37/0.61 (define @t262 () (forall @t69 (or (not (tptp.in @t67 @t261)) @t68))) % 0.37/0.61 (define @t263 () (tptp.in @t261 @t261)) % 0.37/0.61 (define @t264 () (not @t263)) % 0.37/0.61 (define @t265 () (not @t262)) % 0.37/0.61 (define @t266 () (or (not (tptp.transitiveset @t261)) (not (forall @t97 (or (not (tptp.in @t93 (tptp.powerset @t261))) @t96 @t95))) (not (forall @t87 (or (not (tptp.in @t82 @t261)) (not (tptp.in @t84 @t261)) @t86 (not (tptp.in @t81 @t261)) @t85 @t83))) (not (forall @t78 (or (not (tptp.in @t72 @t261)) (not (tptp.in @t73 @t261)) @t76 @t75 @t74))) @t265 @t264)) % 0.37/0.61 (define @t267 () (@list true)) % 0.37/0.61 (define @t268 () (@list @t266)) % 0.37/0.61 (define @t269 () (or @t264 @t264)) % 0.37/0.61 (assume @p1 @t13) % 0.37/0.61 (assume @p2 @t20) % 0.37/0.61 (assume @p3 true) % 0.37/0.61 (step @p4 (= tptp.stricttotalorderedByIn @t48) :rule refl :args (@t48)) % 0.37/0.61 (step @p5 (= tptp.wellorderedByIn @t61) :rule refl :args (@t61)) % 0.37/0.61 (step @p6 (= tptp.ordinal @t64) :rule refl :args (@t64)) % 0.37/0.61 (step @p7 :rule refl :args (@t102)) % 0.37/0.61 (step @p8 :rule aci_norm :args ((= @t107 (or @t101 @t99 @t89 @t80 @t71 @t105 @t104)))) % 0.37/0.61 (step @p9 :rule cong :premises (@p8) :args (@t108)) % 0.37/0.61 (step @p10 :rule quant-merge-prenex :args ((= (forall @t11 @t110) @t108))) % 0.37/0.61 (step @p11 :rule alpha_equiv :args (@t111 (@list @t103) (@list @t1))) % 0.37/0.61 (step @p12 :rule refl :args (@t71)) % 0.37/0.61 (step @p13 :rule refl :args (@t80)) % 0.37/0.61 (step @p14 :rule refl :args (@t89)) % 0.37/0.61 (step @p15 :rule refl :args (@t99)) % 0.37/0.61 (step @p16 :rule refl :args (@t101)) % 0.37/0.61 (step @p17 :rule nary_cong :premises (@p16 @p15 @p14 @p13 @p12 @p11) :args (@t112)) % 0.37/0.61 (step @p18 :rule quant-miniscope-or :args ((= @t110 @t112))) % 0.37/0.61 (step @p19 :rule trans :premises (@p18 @p17)) % 0.37/0.61 (step @p20 :rule symm :premises (@p19)) % 0.37/0.61 (step @p21 :rule cong :premises (@p20) :args ((forall @t11 (or @t101 @t99 @t89 @t80 @t71 @t115)))) % 0.37/0.61 (step @p22 :rule trans :premises (@p21 @p10)) % 0.37/0.61 (step @p23 :rule trans :premises (@p22 @p9)) % 0.37/0.61 (step @p24 :rule refl :args (@t115)) % 0.37/0.61 (step @p25 :rule refl :args (@t100)) % 0.37/0.61 (step @p26 :rule refl :args (@t116)) % 0.37/0.61 (step @p27 :rule cong :premises (@p26 @p25) :args ((= @t116 @t100))) % 0.37/0.61 (step @p28 :rule symm :premises (@p27)) % 0.37/0.61 (step @p29 :rule eq_resolve :premises (@p26 @p28)) % 0.37/0.61 (step @p30 :rule cong :premises (@p29) :args (@t117)) % 0.37/0.61 (step @p31 :rule nary_cong :premises (@p30 @p15 @p14 @p13 @p12 @p24) :args (@t118)) % 0.37/0.61 (step @p32 :rule cong :premises (@p31) :args ((forall @t11 @t118))) % 0.37/0.61 (step @p33 :rule trans :premises (@p32 @p23)) % 0.37/0.61 (step @p34 :rule aci_norm :args ((= (or @t119 @t115) @t118))) % 0.37/0.61 (step @p35 :rule aci_norm :args ((= (or @t117 (or @t99 (or @t89 (or @t80 @t71)))) @t119))) % 0.37/0.61 (step @p36 :rule bool-and-de-morgan :args (@t79 @t70 true)) % 0.37/0.61 (step @p37 :rule nary_cong :premises (@p14 @p36) :args ((or @t89 (not (and @t79 @t70))))) % 0.37/0.61 (step @p38 :rule bool-and-de-morgan :args (@t88 @t79 (and @t70))) % 0.37/0.61 (step @p39 :rule trans :premises (@p38 @p37)) % 0.37/0.61 (step @p40 :rule nary_cong :premises (@p15 @p39) :args ((or @t99 (not (and @t88 @t79 @t70))))) % 0.37/0.61 (step @p41 :rule bool-and-de-morgan :args (@t98 @t88 (and @t79 @t70))) % 0.37/0.61 (step @p42 :rule trans :premises (@p41 @p40)) % 0.37/0.61 (step @p43 :rule refl :args (@t117)) % 0.37/0.61 (step @p44 :rule nary_cong :premises (@p43 @p42) :args ((or @t117 (not (and @t98 @t88 @t79 @t70))))) % 0.37/0.61 (step @p45 :rule bool-and-de-morgan :args (@t116 @t98 (and @t88 @t79 @t70))) % 0.37/0.61 (step @p46 :rule trans :premises (@p45 @p44)) % 0.37/0.61 (step @p47 :rule trans :premises (@p46 @p35)) % 0.37/0.61 (step @p48 :rule nary_cong :premises (@p47 @p24) :args ((or @t121 @t115))) % 0.37/0.61 (step @p49 :rule trans :premises (@p48 @p34)) % 0.37/0.61 (step @p50 :rule bool-impl-elim :args (@t120 @t115)) % 0.37/0.61 (step @p51 :rule trans :premises (@p50 @p49)) % 0.37/0.61 (step @p52 :rule cong :premises (@p51) :args ((forall @t11 (=> @t120 @t115)))) % 0.37/0.61 (step @p53 :rule trans :premises (@p52 @p33)) % 0.37/0.61 (step @p54 :rule refl :args (@t113)) % 0.37/0.61 (step @p55 :rule refl :args (@t3)) % 0.37/0.61 (step @p56 :rule cong :premises (@p55 @p54) :args ((= @t3 @t113))) % 0.37/0.61 (step @p57 :rule symm :premises (@p56)) % 0.37/0.61 (step @p58 :rule eq_resolve :premises (@p55 @p57)) % 0.37/0.61 (step @p59 :rule cong :premises (@p58) :args (@t4)) % 0.37/0.61 (step @p60 :rule refl :args (@t114)) % 0.37/0.61 (step @p61 :rule refl :args (@t6)) % 0.37/0.61 (step @p62 :rule cong :premises (@p61 @p60) :args ((= @t6 @t114))) % 0.37/0.61 (step @p63 :rule symm :premises (@p62)) % 0.37/0.61 (step @p64 :rule eq_resolve :premises (@p61 @p63)) % 0.37/0.61 (step @p65 :rule cong :premises (@p64) :args (@t122)) % 0.37/0.61 (step @p66 :rule nary_cong :premises (@p65 @p59) :args (@t123)) % 0.37/0.61 (step @p67 :rule cong :premises (@p66) :args ((forall @t7 @t123))) % 0.37/0.61 (step @p68 :rule bool-impl-elim :args (@t6 @t4)) % 0.37/0.61 (step @p69 :rule cong :premises (@p68) :args (@t8)) % 0.37/0.61 (step @p70 :rule trans :premises (@p69 @p67)) % 0.37/0.61 (step @p71 :rule beta-reduce :args ((= (_ (lambda @t45 (and @t62 @t129 @t127 (forall @t78 (or @t126 @t125 @t76 @t75 @t74)) @t124)) @t5) @t120))) % 0.37/0.61 (step @p72 :rule refl :args (@t5)) % 0.37/0.61 (step @p73 :rule refl :args (@t124)) % 0.37/0.61 (step @p74 :rule refl :args (@t74)) % 0.37/0.61 (step @p75 :rule refl :args (@t75)) % 0.37/0.61 (step @p76 :rule eq-symm :args (@t72 @t73)) % 0.37/0.61 (step @p77 :rule refl :args (@t125)) % 0.37/0.61 (step @p78 :rule refl :args (@t126)) % 0.37/0.61 (step @p79 :rule nary_cong :premises (@p78 @p77 @p76 @p75 @p74) :args (@t130)) % 0.37/0.61 (step @p80 :rule cong :premises (@p79) :args (@t131)) % 0.37/0.61 (step @p81 :rule refl :args (@t127)) % 0.37/0.61 (step @p82 :rule refl :args (@t129)) % 0.37/0.61 (step @p83 :rule refl :args (@t62)) % 0.37/0.61 (step @p84 :rule nary_cong :premises (@p83 @p82 @p81 @p80 @p73) :args (@t132)) % 0.37/0.61 (step @p85 :rule cong :premises (@p84) :args ((lambda @t45 @t132))) % 0.37/0.61 (step @p86 :rule ho_cong :premises (@p85 @p72)) % 0.37/0.61 (step @p87 :rule trans :premises (@p86 @p71)) % 0.37/0.61 (step @p88 :rule refl :args (@t5)) % 0.37/0.61 (step @p89 :rule alpha_equiv :args (@t134 @t135 (@list @t67))) % 0.37/0.61 (step @p90 :rule alpha_equiv :args (@t139 @t135 (@list @t72))) % 0.37/0.61 (step @p91 :rule refl :args (@t127)) % 0.37/0.61 (step @p92 :rule alpha_equiv :args (@t146 @t135 (@list @t93))) % 0.37/0.61 (step @p93 :rule refl :args (@t62)) % 0.37/0.61 (step @p94 :rule nary_cong :premises (@p93 @p92 @p91 @p90 @p89) :args (@t147)) % 0.37/0.61 (step @p95 :rule cong :premises (@p94) :args (@t148)) % 0.37/0.61 (step @p96 :rule ho_cong :premises (@p95 @p88)) % 0.37/0.61 (step @p97 :rule trans :premises (@p96 @p87)) % 0.37/0.61 (step @p98 :rule cong :premises (@p97 @p70) :args (@t150)) % 0.37/0.61 (step @p99 :rule cong :premises (@p98) :args (@t151)) % 0.37/0.61 (step @p100 :rule trans :premises (@p99 @p53)) % 0.37/0.61 (step @p101 :rule refl :args (tptp.ordinalIrrefl)) % 0.37/0.61 (step @p102 :rule cong :premises (@p101 @p100) :args ((= tptp.ordinalIrrefl @t151))) % 0.37/0.61 (step @p103 :rule refl :args (@t8)) % 0.37/0.61 (step @p104 :rule aci_norm :args ((= (and @t62 @t152) @t147))) % 0.37/0.61 (step @p105 :rule beta-reduce :args ((= (_ (lambda @t7 (and (forall @t11 (or @t164 @t145 @t143)) @t161 @t158 @t155)) @t34) @t152))) % 0.37/0.61 (step @p106 :rule refl :args (@t34)) % 0.37/0.61 (step @p107 :rule refl :args (@t155)) % 0.37/0.61 (step @p108 :rule refl :args (@t158)) % 0.37/0.61 (step @p109 :rule refl :args (@t161)) % 0.37/0.61 (step @p110 :rule refl :args (@t91)) % 0.37/0.61 (step @p111 :rule eq-symm :args (@t90 @t23)) % 0.37/0.61 (step @p112 :rule refl :args (@t141)) % 0.37/0.61 (step @p113 :rule nary_cong :premises (@p112 @p111 @p110) :args (@t165)) % 0.37/0.61 (step @p114 :rule cong :premises (@p113) :args (@t166)) % 0.37/0.61 (step @p115 :rule cong :premises (@p114) :args (@t167)) % 0.37/0.61 (step @p116 :rule refl :args (@t142)) % 0.37/0.61 (step @p117 :rule nary_cong :premises (@p116 @p115) :args (@t168)) % 0.37/0.61 (step @p118 :rule cong :premises (@p117) :args (@t169)) % 0.37/0.61 (step @p119 :rule cong :premises (@p118) :args (@t170)) % 0.37/0.61 (step @p120 :rule refl :args (@t145)) % 0.37/0.61 (step @p121 :rule refl :args (@t164)) % 0.37/0.61 (step @p122 :rule nary_cong :premises (@p121 @p120 @p119) :args (@t171)) % 0.37/0.61 (step @p123 :rule cong :premises (@p122) :args (@t172)) % 0.37/0.61 (step @p124 :rule nary_cong :premises (@p123 @p109 @p108 @p107) :args (@t173)) % 0.37/0.61 (step @p125 :rule cong :premises (@p124) :args ((lambda @t7 @t173))) % 0.37/0.61 (step @p126 :rule ho_cong :premises (@p125 @p106)) % 0.37/0.61 (step @p127 :rule trans :premises (@p126 @p105)) % 0.37/0.61 (step @p128 :rule refl :args (@t34)) % 0.37/0.61 (step @p129 :rule refl :args (@t155)) % 0.37/0.61 (step @p130 :rule refl :args (@t158)) % 0.37/0.61 (step @p131 :rule alpha_equiv :args (@t180 @t181 (@list @t82))) % 0.37/0.61 (step @p132 :rule alpha_equiv :args (@t187 @t181 (@list @t90))) % 0.37/0.61 (step @p133 :rule cong :premises (@p132) :args (@t188)) % 0.37/0.61 (step @p134 :rule refl :args (@t145)) % 0.37/0.61 (step @p135 :rule refl :args (@t164)) % 0.37/0.61 (step @p136 :rule nary_cong :premises (@p135 @p134 @p133) :args (@t189)) % 0.37/0.61 (step @p137 :rule cong :premises (@p136) :args (@t190)) % 0.37/0.61 (step @p138 :rule nary_cong :premises (@p137 @p131 @p130 @p129) :args (@t191)) % 0.37/0.61 (step @p139 :rule cong :premises (@p138) :args (@t192)) % 0.37/0.61 (step @p140 :rule ho_cong :premises (@p139 @p128)) % 0.37/0.61 (step @p141 :rule trans :premises (@p140 @p127)) % 0.37/0.61 (step @p142 :rule nary_cong :premises (@p83 @p141) :args ((and @t62 (_ @t192 @t34)))) % 0.37/0.61 (step @p143 :rule trans :premises (@p142 @p104)) % 0.37/0.61 (step @p144 :rule aci_norm :args ((= (and @t193 @t190) @t191))) % 0.37/0.61 (step @p145 :rule refl :args (@t188)) % 0.37/0.61 (step @p146 :rule refl :args (@t144)) % 0.37/0.61 (step @p147 :rule refl :args (@t54)) % 0.37/0.61 (step @p148 :rule cong :premises (@p147 @p146) :args ((= @t54 @t144))) % 0.37/0.61 (step @p149 :rule symm :premises (@p148)) % 0.37/0.61 (step @p150 :rule eq_resolve :premises (@p147 @p149)) % 0.37/0.61 (step @p151 :rule cong :premises (@p150) :args (@t194)) % 0.37/0.61 (step @p152 :rule refl :args ((tptp.in @t5 @t56))) % 0.37/0.61 (step @p153 :rule refl :args (@t162)) % 0.37/0.61 (step @p154 :rule cong :premises (@p88 @p153) :args (@t163)) % 0.37/0.61 (step @p155 :rule trans :premises (@p154 @p152)) % 0.37/0.61 (step @p156 :rule refl :args (@t14)) % 0.37/0.61 (step @p157 :rule ho_cong :premises (@p156 @p153)) % 0.37/0.61 (step @p158 :rule cong :premises (@p157 @p155) :args ((= (_ @t14 @t162) @t163))) % 0.37/0.61 (step @p159 :rule symm :premises (@p158)) % 0.37/0.61 (step @p160 :rule refl :args (@t57)) % 0.37/0.61 (step @p161 :rule eq_resolve :premises (@p160 @p159)) % 0.37/0.61 (step @p162 :rule refl :args (@t56)) % 0.37/0.61 (step @p163 :rule cong :premises (@p162 @p153) :args ((= @t56 @t162))) % 0.37/0.61 (step @p164 :rule symm :premises (@p163)) % 0.37/0.61 (step @p165 :rule eq_resolve :premises (@p162 @p164)) % 0.37/0.61 (step @p166 :rule ho_cong :premises (@p156 @p165)) % 0.37/0.61 (step @p167 :rule trans :premises (@p166 @p161)) % 0.37/0.61 (step @p168 :rule cong :premises (@p167) :args (@t195)) % 0.37/0.61 (step @p169 :rule nary_cong :premises (@p168 @p151 @p145) :args (@t196)) % 0.37/0.61 (step @p170 :rule cong :premises (@p169) :args ((forall @t11 @t196))) % 0.37/0.61 (step @p171 :rule aci_norm :args ((= (or @t195 (or @t194 @t188)) @t196))) % 0.37/0.61 (step @p172 :rule bool-impl-elim :args (@t54 @t188)) % 0.37/0.61 (step @p173 :rule refl :args (@t195)) % 0.37/0.61 (step @p174 :rule nary_cong :premises (@p173 @p172) :args ((or @t195 @t197))) % 0.37/0.61 (step @p175 :rule trans :premises (@p174 @p171)) % 0.37/0.61 (step @p176 :rule bool-impl-elim :args (@t57 @t197)) % 0.37/0.61 (step @p177 :rule 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% 0.37/0.61 (step-pop @p435 :rule scope :premises (@p428)) % 0.37/0.61 (step @p429 :rule process_scope :premises (@p435) :args (@t269)) % 0.37/0.61 (step @p431 :rule eq_resolve :premises (@p429 @p426)) % 0.37/0.61 (step @p432 :rule implies_elim :premises (@p431)) % 0.37/0.61 (step @p433 false :rule chain_m_resolution :premises (@p432 @p423 @p417) :args (false (@list false false) (@list @t263 @t262))) % 0.37/0.61 ) % 0.37/0.61 % SZS output end Proof % 0.37/0.61 % cvc5 exiting %------------------------------------------------------------------------------