%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU039+1 : TPTP v9.2.1. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n010.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 08:50:29 AM UTC 2026 % Result : Theorem 112.24s 112.97s % Output : Proof 112.24s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU039+1 : TPTP v9.2.1. Released v3.2.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n010.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 16:24:10 EDT 2026 % 0.17/0.34 % CPUTime : % 0.28/0.50 %----Proving TF0_NAR, FOF, or CNF % 112.24/112.97 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 112.24/112.97 --- Run --no-e-matching --full-saturate-quant at 6... % 112.24/112.97 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 6... % 112.24/112.97 --- Run --finite-model-find --uf-ss=no-minimal at 6... % 112.24/112.97 --- Run --multi-trigger-when-single --full-saturate-quant at 30... % 112.24/112.97 --- Run --trigger-sel=max --full-saturate-quant at 15... % 112.24/112.97 --- Run --multi-trigger-when-single --multi-trigger-priority --full-saturate-quant at 33... % 112.24/112.97 --- Run --multi-trigger-cache --full-saturate-quant at 15... % 112.24/112.97 % SZS status Theorem % 112.24/112.97 % SZS output start Proof % 112.24/112.97 ( % 112.24/112.97 (declare-sort $$unsorted 0) % 112.24/112.97 (declare-const tptp.powerset (-> $$unsorted $$unsorted)) % 112.24/112.97 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 112.24/112.97 (declare-const tptp.function (-> $$unsorted Bool)) % 112.24/112.97 (declare-const tptp.relation (-> $$unsorted Bool)) % 112.24/112.97 (declare-const tptp.one_to_one (-> $$unsorted Bool)) % 112.24/112.97 (declare-const tptp.relation_rng (-> $$unsorted $$unsorted)) % 112.24/112.97 (declare-const tptp.element (-> $$unsorted $$unsorted Bool)) % 112.24/112.97 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 112.24/112.97 (declare-const tptp.set_intersection2 (-> $$unsorted $$unsorted $$unsorted)) % 112.24/112.97 (declare-const tptp.empty (-> $$unsorted Bool)) % 112.24/112.97 (declare-const tptp.relation_dom_restriction (-> $$unsorted $$unsorted $$unsorted)) % 112.24/112.97 (declare-const tptp.relation_dom (-> $$unsorted $$unsorted)) % 112.24/112.97 (declare-const tptp.empty_set $$unsorted) % 112.24/112.97 (declare-const tptp.apply (-> $$unsorted $$unsorted $$unsorted)) % 112.24/112.97 (declare-const tptp.relation_empty_yielding (-> $$unsorted Bool)) % 112.24/112.97 (define @t1 () (@var "A" $$unsorted)) % 112.24/112.97 (define @t2 () (@var "B" $$unsorted)) % 112.24/112.97 (define @t3 () (tptp.in @t2 @t1)) % 112.24/112.97 (define @t4 () (not @t3)) % 112.24/112.97 (define @t5 () (tptp.in @t1 @t2)) % 112.24/112.97 (define @t6 () (@list @t1 @t2)) % 112.24/112.97 (define @t7 () (tptp.function @t1)) % 112.24/112.97 (define @t8 () (tptp.empty @t1)) % 112.24/112.97 (define @t9 () (@list @t1)) % 112.24/112.97 (define @t10 () (tptp.relation @t1)) % 112.24/112.97 (define @t11 () (and @t10 @t7 (tptp.one_to_one @t1))) % 112.24/112.97 (define @t12 () (and @t10 @t8 @t7)) % 112.24/112.97 (define @t13 () (tptp.set_intersection2 @t1 @t2)) % 112.24/112.97 (define @t14 () (@var "D" $$unsorted)) % 112.24/112.97 (define @t15 () (@var "C" $$unsorted)) % 112.24/112.97 (define @t16 () (@list @t14)) % 112.24/112.97 (define @t17 () (forall @t16 (= (tptp.in @t14 @t15) (and (tptp.in @t14 @t1) (tptp.in @t14 @t2))))) % 112.24/112.97 (define @t18 () (= (= @t15 @t13) @t17)) % 112.24/112.97 (define @t19 () (@list @t1 @t2 @t15)) % 112.24/112.97 (define @t20 () (forall @t19 @t18)) % 112.24/112.97 (define @t21 () (= @t15 (tptp.apply @t1 @t14))) % 112.24/112.97 (define @t22 () (tptp.relation_dom @t1)) % 112.24/112.97 (define @t23 () (tptp.in @t14 @t22)) % 112.24/112.97 (define @t24 () (and @t23 @t21)) % 112.24/112.97 (define @t25 () (exists @t16 @t24)) % 112.24/112.97 (define @t26 () (tptp.in @t15 @t2)) % 112.24/112.97 (define @t27 () (= @t26 @t25)) % 112.24/112.97 (define @t28 () (@list @t15)) % 112.24/112.97 (define @t29 () (forall @t28 @t27)) % 112.24/112.97 (define @t30 () (tptp.relation_rng @t1)) % 112.24/112.97 (define @t31 () (= @t2 @t30)) % 112.24/112.97 (define @t32 () (= @t31 @t29)) % 112.24/112.97 (define @t33 () (@list @t2)) % 112.24/112.97 (define @t34 () (forall @t33 @t32)) % 112.24/112.97 (define @t35 () (and @t10 @t7)) % 112.24/112.97 (define @t36 () (=> @t35 @t34)) % 112.24/112.97 (define @t37 () (forall @t9 @t36)) % 112.24/112.97 (define @t38 () (tptp.relation_dom_restriction @t1 @t2)) % 112.24/112.97 (define @t39 () (tptp.relation @t38)) % 112.24/112.97 (define @t40 () (forall @t6 (=> @t10 @t39))) % 112.24/112.97 (define @t41 () (tptp.relation tptp.empty_set)) % 112.24/112.97 (define @t42 () (tptp.empty tptp.empty_set)) % 112.24/112.97 (define @t43 () (and @t10 (tptp.relation_empty_yielding @t1))) % 112.24/112.97 (define @t44 () (tptp.relation @t2)) % 112.24/112.97 (define @t45 () (tptp.powerset @t1)) % 112.24/112.97 (define @t46 () (and @t39 (tptp.function @t38))) % 112.24/112.97 (define @t47 () (forall @t6 (=> @t35 @t46))) % 112.24/112.97 (define @t48 () (tptp.empty @t22)) % 112.24/112.97 (define @t49 () (not @t8)) % 112.24/112.97 (define @t50 () (and @t49 @t10)) % 112.24/112.97 (define @t51 () (tptp.empty @t30)) % 112.24/112.97 (define @t52 () (tptp.empty @t2)) % 112.24/112.97 (define @t53 () (tptp.element @t2 @t45)) % 112.24/112.97 (define @t54 () (tptp.element @t1 @t2)) % 112.24/112.97 (define @t55 () (tptp.element @t2 (tptp.powerset @t15))) % 112.24/112.97 (define @t56 () (tptp.apply @t2 @t14)) % 112.24/112.97 (define @t57 () (= @t56 (tptp.apply @t15 @t14))) % 112.24/112.97 (define @t58 () (tptp.relation_dom @t2)) % 112.24/112.97 (define @t59 () (tptp.in @t14 @t58)) % 112.24/112.97 (define @t60 () (forall @t16 (=> @t59 @t57))) % 112.24/112.97 (define @t61 () (tptp.relation_dom @t15)) % 112.24/112.97 (define @t62 () (= @t58 (tptp.set_intersection2 @t61 @t1))) % 112.24/112.97 (define @t63 () (and @t62 @t60)) % 112.24/112.97 (define @t64 () (tptp.relation_dom_restriction @t15 @t1)) % 112.24/112.97 (define @t65 () (= @t2 @t64)) % 112.24/112.97 (define @t66 () (= @t65 @t63)) % 112.24/112.97 (define @t67 () (tptp.function @t15)) % 112.24/112.97 (define @t68 () (tptp.relation @t15)) % 112.24/112.97 (define @t69 () (and @t68 @t67)) % 112.24/112.97 (define @t70 () (=> @t69 @t66)) % 112.24/112.97 (define @t71 () (forall @t28 @t70)) % 112.24/112.97 (define @t72 () (tptp.function @t2)) % 112.24/112.97 (define @t73 () (and @t44 @t72)) % 112.24/112.97 (define @t74 () (=> @t73 @t71)) % 112.24/112.97 (define @t75 () (forall @t6 @t74)) % 112.24/112.97 (define @t76 () (tptp.apply @t15 @t2)) % 112.24/112.97 (define @t77 () (= (tptp.apply @t64 @t2) @t76)) % 112.24/112.97 (define @t78 () (=> @t3 @t77)) % 112.24/112.97 (define @t79 () (forall @t19 (=> @t69 @t78))) % 112.24/112.97 (define @t80 () (tptp.in @t76 (tptp.relation_rng @t64))) % 112.24/112.97 (define @t81 () (tptp.in @t2 @t61)) % 112.24/112.97 (define @t82 () (and @t81 @t3)) % 112.24/112.97 (define @t83 () (=> @t82 @t80)) % 112.24/112.97 (define @t84 () (forall @t19 (=> @t69 @t83))) % 112.24/112.97 (define @t85 () (not @t84)) % 112.24/112.97 (define @t86 () (= @t13 @t15)) % 112.24/112.97 (define @t87 () (not @t81)) % 112.24/112.97 (define @t88 () (not @t67)) % 112.24/112.97 (define @t89 () (not @t68)) % 112.24/112.97 (define @t90 () (or @t89 @t88 @t87 @t4 @t80)) % 112.24/112.97 (define @t91 () (forall @t19 @t90)) % 112.24/112.97 (define @t92 () (@quantifiers_skolemize @t91 2)) % 112.24/112.97 (define @t93 () (tptp.relation_dom @t92)) % 112.24/112.97 (define @t94 () (@quantifiers_skolemize @t91 0)) % 112.24/112.97 (define @t95 () (tptp.set_intersection2 @t93 @t94)) % 112.24/112.97 (define @t96 () (forall @t16 (= (tptp.in @t14 @t95) (and (tptp.in @t14 @t94) (tptp.in @t14 @t93))))) % 112.24/112.97 (define @t97 () (tptp.set_intersection2 @t94 @t93)) % 112.24/112.97 (define @t98 () (= @t97 @t95)) % 112.24/112.97 (define @t99 () (forall @t19 (= @t17 @t86))) % 112.24/112.97 (define @t100 () (= @t96 @t98)) % 112.24/112.97 (define @t101 () (= @t95 @t97)) % 112.24/112.97 (define @t102 () (= @t101 @t96)) % 112.24/112.97 (define @t103 () (@list false)) % 112.24/112.97 (define @t104 () (@list false false)) % 112.24/112.97 (define @t105 () (@quantifiers_skolemize @t91 1)) % 112.24/112.97 (define @t106 () (@list @t105)) % 112.24/112.97 (define @t107 () (or @t87 @t4 @t80)) % 112.24/112.97 (define @t108 () (or @t89 @t88)) % 112.24/112.97 (define @t109 () (not @t69)) % 112.24/112.97 (define @t110 () (tptp.in @t105 @t94)) % 112.24/112.97 (define @t111 () (tptp.relation_dom_restriction @t92 @t94)) % 112.24/112.97 (define @t112 () (tptp.relation_rng @t111)) % 112.24/112.97 (define @t113 () (tptp.apply @t92 @t105)) % 112.24/112.97 (define @t114 () (tptp.in @t113 @t112)) % 112.24/112.97 (define @t115 () (not @t110)) % 112.24/112.97 (define @t116 () (tptp.in @t105 @t93)) % 112.24/112.97 (define @t117 () (not @t116)) % 112.24/112.97 (define @t118 () (tptp.function @t92)) % 112.24/112.97 (define @t119 () (not @t118)) % 112.24/112.97 (define @t120 () (tptp.relation @t92)) % 112.24/112.97 (define @t121 () (not @t120)) % 112.24/112.97 (define @t122 () (or @t121 @t119 @t117 @t115 @t114)) % 112.24/112.97 (define @t123 () (@list true)) % 112.24/112.97 (define @t124 () (@list @t122)) % 112.24/112.97 (define @t125 () (and @t110 @t116)) % 112.24/112.97 (define @t126 () (tptp.in @t105 @t95)) % 112.24/112.97 (define @t127 () (= @t126 @t125)) % 112.24/112.97 (define @t128 () (@var "BOUND_VARIABLE_7831" $$unsorted)) % 112.24/112.97 (define @t129 () (not @t59)) % 112.24/112.97 (define @t130 () (= (= @t2 (tptp.relation_dom_restriction @t128 @t1)) (and (= @t58 (tptp.set_intersection2 (tptp.relation_dom @t128) @t1)) (forall @t16 (or @t129 (= @t56 (tptp.apply @t128 @t14))))))) % 112.24/112.97 (define @t131 () (not (tptp.function @t128))) % 112.24/112.97 (define @t132 () (not (tptp.relation @t128))) % 112.24/112.97 (define @t133 () (not @t72)) % 112.24/112.97 (define @t134 () (not @t44)) % 112.24/112.97 (define @t135 () (or @t134 @t133 @t132 @t131 @t130)) % 112.24/112.97 (define @t136 () (or @t132 @t131 @t130)) % 112.24/112.97 (define @t137 () (or @t134 @t133 @t136)) % 112.24/112.97 (define @t138 () (@list @t1 @t2 @t128)) % 112.24/112.97 (define @t139 () (forall @t138 @t137)) % 112.24/112.97 (define @t140 () (@list @t128)) % 112.24/112.97 (define @t141 () (forall @t140 @t137)) % 112.24/112.97 (define @t142 () (forall @t140 @t136)) % 112.24/112.97 (define @t143 () (or @t134 @t133 @t142)) % 112.24/112.97 (define @t144 () (= @t65 (and @t62 (forall @t16 (or @t129 @t57))))) % 112.24/112.97 (define @t145 () (or @t89 @t88 @t144)) % 112.24/112.97 (define @t146 () (forall @t28 @t145)) % 112.24/112.97 (define @t147 () (or @t134 @t133 @t146)) % 112.24/112.97 (define @t148 () (tptp.apply @t111 @t14)) % 112.24/112.97 (define @t149 () (tptp.apply @t92 @t14)) % 112.24/112.97 (define @t150 () (tptp.relation_dom @t111)) % 112.24/112.97 (define @t151 () (not (tptp.in @t14 @t150))) % 112.24/112.97 (define @t152 () (= @t95 @t150)) % 112.24/112.97 (define @t153 () (and @t152 (forall @t16 (or @t151 (= @t149 @t148))))) % 112.24/112.97 (define @t154 () (or @t151 (= @t148 @t149))) % 112.24/112.97 (define @t155 () (forall @t16 @t154)) % 112.24/112.97 (define @t156 () (and (= @t150 @t95) @t155)) % 112.24/112.97 (define @t157 () (= (= @t111 @t111) @t156)) % 112.24/112.97 (define @t158 () (tptp.function @t111)) % 112.24/112.97 (define @t159 () (not @t158)) % 112.24/112.97 (define @t160 () (tptp.relation @t111)) % 112.24/112.97 (define @t161 () (not @t160)) % 112.24/112.97 (define @t162 () (or @t161 @t159 @t121 @t119 @t157)) % 112.24/112.97 (define @t163 () (forall @t138 @t135)) % 112.24/112.97 (define @t164 () (or @t161 @t159 @t121 @t119 @t153)) % 112.24/112.97 (define @t165 () (not @t7)) % 112.24/112.97 (define @t166 () (not @t10)) % 112.24/112.97 (define @t167 () (or @t166 @t165)) % 112.24/112.97 (define @t168 () (not @t35)) % 112.24/112.97 (define @t169 () (@list @t92 @t94)) % 112.24/112.97 (define @t170 () (and @t160 @t158)) % 112.24/112.97 (define @t171 () (or @t121 @t119 @t170)) % 112.24/112.97 (define @t172 () (@list false false false)) % 112.24/112.97 (define @t173 () (or @t121 @t160)) % 112.24/112.97 (define @t174 () (tptp.in @t105 @t150)) % 112.24/112.97 (define @t175 () (@var "BOUND_VARIABLE_7667" $$unsorted)) % 112.24/112.97 (define @t176 () (tptp.in @t15 @t175)) % 112.24/112.97 (define @t177 () (not (forall @t16 (or (not @t23) (not @t21))))) % 112.24/112.97 (define @t178 () (forall @t28 (= @t176 @t177))) % 112.24/112.97 (define @t179 () (= (= @t175 @t30) @t178)) % 112.24/112.97 (define @t180 () (or @t166 @t165 @t179)) % 112.24/112.97 (define @t181 () (@list @t1 @t175)) % 112.24/112.97 (define @t182 () (forall @t181 @t180)) % 112.24/112.97 (define @t183 () (@list @t175)) % 112.24/112.97 (define @t184 () (forall @t183 @t180)) % 112.24/112.97 (define @t185 () (forall @t183 @t179)) % 112.24/112.97 (define @t186 () (or @t166 @t165 @t185)) % 112.24/112.97 (define @t187 () (forall @t33 (= @t31 (forall @t28 (= @t26 @t177))))) % 112.24/112.97 (define @t188 () (or @t166 @t165 @t187)) % 112.24/112.97 (define @t189 () (forall @t16 (not @t24))) % 112.24/112.97 (define @t190 () (not @t189)) % 112.24/112.97 (define @t191 () (not (forall @t16 (or @t151 (not (= @t15 @t148)))))) % 112.24/112.97 (define @t192 () (tptp.in @t15 @t112)) % 112.24/112.97 (define @t193 () (forall @t28 (= @t192 @t191))) % 112.24/112.97 (define @t194 () (forall @t28 (= @t191 @t192))) % 112.24/112.97 (define @t195 () (= (= @t112 @t112) @t194)) % 112.24/112.97 (define @t196 () (or @t161 @t159 @t195)) % 112.24/112.97 (define @t197 () (forall @t181 (or @t166 @t165 (= (= @t30 @t175) (forall @t28 (= @t177 @t176)))))) % 112.24/112.97 (define @t198 () (or @t161 @t159 @t193)) % 112.24/112.97 (define @t199 () (forall @t16 (or @t151 (not (= @t113 @t148))))) % 112.24/112.97 (define @t200 () (not @t199)) % 112.24/112.97 (define @t201 () (= @t114 @t200)) % 112.24/112.97 (define @t202 () (not @t201)) % 112.24/112.97 (define @t203 () (or @t89 @t88 @t4 @t77)) % 112.24/112.97 (define @t204 () (tptp.apply @t111 @t105)) % 112.24/112.97 (define @t205 () (or @t121 @t119 @t115 (= @t204 @t113))) % 112.24/112.97 (define @t206 () (forall @t19 @t203)) % 112.24/112.97 (define @t207 () (= @t113 @t204)) % 112.24/112.97 (define @t208 () (or @t121 @t119 @t115 @t207)) % 112.24/112.97 (define @t209 () (not @t207)) % 112.24/112.97 (define @t210 () (not @t174)) % 112.24/112.97 (define @t211 () (or @t210 @t209)) % 112.24/112.97 (assume @p1 (forall @t6 (=> @t5 @t4))) % 112.24/112.97 (assume @p2 (forall @t9 (=> @t8 @t7))) % 112.24/112.97 (assume @p3 (forall @t9 (=> @t8 @t10))) % 112.24/112.97 (assume @p4 (forall @t9 (=> @t12 @t11))) % 112.24/112.97 (assume @p5 (forall @t6 (= @t13 (tptp.set_intersection2 @t2 @t1)))) % 112.24/112.97 (assume @p6 @t20) % 112.24/112.97 (assume @p7 @t37) % 112.24/112.97 (assume @p8 @t40) % 112.24/112.97 (assume @p9 (forall @t9 (exists @t33 (tptp.element @t2 @t1)))) % 112.24/112.97 (assume @p10 (and @t42 @t41 (tptp.relation_empty_yielding tptp.empty_set))) % 112.24/112.97 (assume @p11 (forall @t6 (=> @t43 (and @t39 (tptp.relation_empty_yielding @t38))))) % 112.24/112.97 (assume @p12 (forall @t6 (=> (and @t10 @t44) (tptp.relation @t13)))) % 112.24/112.97 (assume @p13 (forall @t9 (not (tptp.empty @t45)))) % 112.24/112.97 (assume @p14 @t42) % 112.24/112.97 (assume @p15 @t47) % 112.24/112.97 (assume @p16 (and @t42 @t41)) % 112.24/112.97 (assume @p17 (forall @t9 (=> @t50 (not @t48)))) % 112.24/112.97 (assume @p18 (forall @t9 (=> @t50 (not @t51)))) % 112.24/112.97 (assume @p19 (forall @t9 (=> @t8 (and @t48 (tptp.relation @t22))))) % 112.24/112.97 (assume @p20 (forall @t9 (=> @t8 (and @t51 (tptp.relation @t30))))) % 112.24/112.97 (assume @p21 (forall @t6 (= (tptp.set_intersection2 @t1 @t1) @t1))) % 112.24/112.97 (assume @p22 (exists @t9 @t35)) % 112.24/112.97 (assume @p23 (exists @t9 (and @t8 @t10))) % 112.24/112.97 (assume @p24 (forall @t9 (=> @t49 (exists @t33 (and @t53 (not @t52)))))) % 112.24/112.97 (assume @p25 (exists @t9 @t8)) % 112.24/112.97 (assume @p26 (exists @t9 @t12)) % 112.24/112.97 (assume @p27 (exists @t9 @t50)) % 112.24/112.97 (assume @p28 (forall @t9 (exists @t33 (and @t53 @t52)))) % 112.24/112.97 (assume @p29 (exists @t9 @t49)) % 112.24/112.97 (assume @p30 (exists @t9 @t11)) % 112.24/112.97 (assume @p31 (exists @t9 @t43)) % 112.24/112.97 (assume @p32 (forall @t6 (tptp.subset @t1 @t1))) % 112.24/112.97 (assume @p33 (forall @t6 (=> @t5 @t54))) % 112.24/112.97 (assume @p34 (forall @t9 (= (tptp.set_intersection2 @t1 tptp.empty_set) tptp.empty_set))) % 112.24/112.97 (assume @p35 (forall @t6 (=> @t54 (or @t52 @t5)))) % 112.24/112.97 (assume @p36 (forall @t6 (= (tptp.element @t1 (tptp.powerset @t2)) (tptp.subset @t1 @t2)))) % 112.24/112.97 (assume @p37 (forall @t19 (=> (and @t5 @t55) 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112.24/112.97 (step @p239 :rule symm :premises (@p238)) % 112.24/112.97 (step @p240 :rule cong :premises (@p239) :args ((forall @t9 @t188))) % 112.24/112.97 (step @p241 :rule trans :premises (@p240 @p232)) % 112.24/112.97 (step @p242 :rule trans :premises (@p241 @p231)) % 112.24/112.97 (step @p243 :rule aci_norm :args ((= (or @t167 @t187) @t188))) % 112.24/112.97 (step @p244 :rule refl :args (@t187)) % 112.24/112.97 (step @p245 :rule nary_cong :premises (@p182 @p244) :args ((or @t168 @t187))) % 112.24/112.97 (step @p246 :rule trans :premises (@p245 @p243)) % 112.24/112.97 (step @p247 :rule bool-impl-elim :args (@t35 @t187)) % 112.24/112.97 (step @p248 :rule trans :premises (@p247 @p246)) % 112.24/112.97 (step @p249 :rule cong :premises (@p248) :args ((forall @t9 (=> @t35 @t187)))) % 112.24/112.97 (step @p250 :rule trans :premises (@p249 @p242)) % 112.24/112.97 (step @p251 :rule bool-and-de-morgan :args (@t23 @t21 true)) % 112.24/112.97 (step @p252 :rule cong :premises (@p251) :args (@t189)) % 112.24/112.97 (step @p253 :rule cong :premises (@p252) :args (@t190)) % 112.24/112.97 (step @p254 :rule exists-elim :args ((= @t25 @t190))) % 112.24/112.97 (step @p255 :rule trans :premises (@p254 @p253)) % 112.24/112.97 (step @p256 :rule refl :args (@t26)) % 112.24/112.97 (step @p257 :rule cong :premises (@p256 @p255) :args (@t27)) % 112.24/112.97 (step @p258 :rule cong :premises (@p257) :args (@t29)) % 112.24/112.97 (step @p259 :rule refl :args (@t31)) % 112.24/112.97 (step @p260 :rule cong :premises (@p259 @p258) :args (@t32)) % 112.24/112.97 (step @p261 :rule cong :premises (@p260) :args (@t34)) % 112.24/112.97 (step @p262 :rule refl :args (@t35)) % 112.24/112.97 (step @p263 :rule cong :premises (@p262 @p261) :args (@t36)) % 112.24/112.97 (step @p264 :rule cong :premises (@p263) :args (@t37)) % 112.24/112.97 (step @p265 :rule trans :premises (@p264 @p250)) % 112.24/112.97 (step @p266 :rule eq_resolve :premises (@p7 @p265)) % 112.24/112.97 (step @p267 :rule bool-eq-true :args (@t193)) % 112.24/112.97 (step @p268 :rule eq-symm :args (true @t193)) % 112.24/112.97 (step @p269 :rule trans :premises (@p268 @p267)) % 112.24/112.97 (step @p270 :rule eq-symm :args (@t191 @t192)) % 112.24/112.97 (step @p271 :rule cong :premises (@p270) :args (@t194)) % 112.24/112.97 (step @p272 :rule eq-refl :args (@t112)) % 112.24/112.97 (step @p273 :rule cong :premises (@p272 @p271) :args (@t195)) % 112.24/112.97 (step @p274 :rule trans :premises (@p273 @p269)) % 112.24/112.97 (step @p275 :rule nary_cong :premises (@p169 @p168 @p274) :args (@t196)) % 112.24/112.97 (step @p276 :rule refl :args (@t197)) % 112.24/112.97 (step @p277 :rule cong :premises (@p276 @p275) :args ((=> @t197 @t196))) % 112.24/112.97 (assume-push @p334 @t197) % 112.24/112.97 (step @p279 :rule instantiate :premises (@p266) :args ((@list @t111 @t112))) % 112.24/112.97 (step-pop @p335 :rule scope :premises (@p279)) % 112.24/112.97 (step @p280 :rule process_scope :premises (@p335) :args (@t196)) % 112.24/112.97 (step @p282 :rule eq_resolve :premises (@p280 @p277)) % 112.24/112.97 (step @p283 :rule implies_elim :premises (@p282)) % 112.24/112.97 (step @p284 :rule chain_m_resolution :premises (@p283 @p266) :args (@t198 @t103 (@list @t197))) % 112.24/112.97 (step @p285 :rule cnf_or_pos :args (@t198)) % 112.24/112.97 (step @p286 :rule reordering :premises (@p285) :args ((or @t161 @t159 @t193 (not @t198)))) % 112.24/112.97 (step @p287 :rule chain_m_resolution :premises (@p286 @p214 @p207 @p284) :args (@t193 @t172 (@list @t160 @t158 @t198))) % 112.24/112.97 (step @p288 :rule instantiate :premises (@p287) :args ((@list @t113))) % 112.24/112.97 (step @p289 :rule cnf_or_neg :args (@t122 4)) % 112.24/112.97 (step @p290 :rule chain_m_resolution :premises (@p289 @p89) :args ((not @t114) @t123 @t124)) % 112.24/112.97 (step @p291 :rule bool-double-not-elim :args (@t199)) % 112.24/112.97 (step @p292 :rule refl :args (@t114)) % 112.24/112.97 (step @p293 :rule refl :args (@t202)) % 112.24/112.97 (step @p294 :rule nary_cong :premises (@p293 @p292 @p291) :args ((or @t202 @t114 (not @t200)))) % 112.24/112.97 (step @p295 :rule cnf_equiv_pos2 :args (@t201)) % 112.24/112.97 (step @p296 :rule eq_resolve :premises (@p295 @p294)) % 112.24/112.97 (step @p297 :rule reordering :premises (@p296) :args ((or @t114 @t199 @t202))) % 112.24/112.97 (step @p298 :rule chain_m_resolution :premises (@p297 @p290 @p288) :args (@t199 (@list true false) (@list @t114 @t201))) % 112.24/112.97 (step @p299 :rule instantiate :premises (@p298) :args (@t106)) % 112.24/112.97 (step @p300 :rule aci_norm :args ((= (or @t108 (or @t4 @t77)) @t203))) % 112.24/112.97 (step @p301 :rule bool-impl-elim :args (@t3 @t77)) % 112.24/112.97 (step @p302 :rule nary_cong :premises (@p81 @p301) :args ((or @t109 @t78))) % 112.24/112.97 (step @p303 :rule trans :premises (@p302 @p300)) % 112.24/112.97 (step @p304 :rule bool-impl-elim :args (@t69 @t78)) % 112.24/112.97 (step @p305 :rule trans :premises (@p304 @p303)) % 112.24/112.97 (step @p306 :rule cong :premises (@p305) :args (@t79)) % 112.24/112.97 (step @p307 :rule eq_resolve :premises (@p41 @p306)) % 112.24/112.97 (step @p308 :rule eq-symm :args (@t204 @t113)) % 112.24/112.97 (step @p309 :rule refl :args (@t115)) % 112.24/112.97 (step @p310 :rule nary_cong :premises (@p167 @p166 @p309 @p308) :args (@t205)) % 112.24/112.97 (step @p311 :rule refl :args (@t206)) % 112.24/112.97 (step @p312 :rule cong :premises (@p311 @p310) :args ((=> @t206 @t205))) % 112.24/112.97 (assume-push @p336 @t206) % 112.24/112.97 (step @p314 :rule instantiate :premises (@p307) :args ((@list @t94 @t105 @t92))) % 112.24/112.97 (step-pop @p337 :rule scope :premises (@p314)) % 112.24/112.97 (step @p315 :rule process_scope :premises (@p337) :args (@t205)) % 112.24/112.97 (step @p317 :rule eq_resolve :premises (@p315 @p312)) % 112.24/112.97 (step @p318 :rule implies_elim :premises (@p317)) % 112.24/112.97 (step @p319 :rule chain_m_resolution :premises (@p318 @p307) :args (@t208 @t103 (@list @t206))) % 112.24/112.97 (step @p320 :rule cnf_or_pos :args (@t208)) % 112.24/112.97 (step @p321 :rule reordering :premises (@p320) :args ((or @t121 @t119 @t115 @t207 (not @t208)))) % 112.24/112.97 (step @p322 :rule chain_m_resolution :premises (@p321 @p201 @p195 @p96 @p319) :args (@t207 (@list false false false false) (@list @t120 @t118 @t110 @t208))) % 112.24/112.98 (step @p323 :rule cnf_or_pos :args (@t211)) % 112.24/112.98 (step @p324 :rule reordering :premises (@p323) :args ((or @t209 @t210 (not @t211)))) % 112.24/112.98 (step @p325 :rule chain_m_resolution :premises (@p324 @p322 @p299) :args (@t210 @t104 (@list @t207 @t211))) % 112.24/112.98 (step @p326 :rule false_intro :premises (@p325)) % 112.24/112.98 (step @p327 :rule symm :premises (@p326)) % 112.24/112.98 (step @p328 :rule trans :premises (@p327 @p223 @p109)) % 112.24/112.98 (step @p329 false :rule eq_resolve :premises (@p328 @p46)) % 112.24/112.98 ) % 112.24/112.98 % SZS output end Proof % 112.24/112.98 % cvc5 exiting %------------------------------------------------------------------------------