%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU387+1 : TPTP v9.2.1. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n022.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 08:51:35 AM UTC 2026 % Result : Theorem 0.36s 0.70s % Output : Proof 0.36s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU387+1 : TPTP v9.2.1. Released v3.3.0. % 0.12/0.14 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.16/0.35 % Computer : n022.cluster.edu % 0.16/0.35 % Model : x86_64 x86_64 % 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.35 % Memory : 8042.1875MB % 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.35 % CPULimit : 300 % 0.16/0.35 % WCLimit : 300 % 0.16/0.35 % DateTime : Tue Jun 2 17:06:38 EDT 2026 % 0.16/0.35 % CPUTime : % 0.28/0.52 %----Proving TF0_NAR, FOF, or CNF % 0.36/0.70 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.36/0.70 % SZS status Theorem % 0.36/0.70 % SZS output start Proof % 0.36/0.70 ( % 0.36/0.70 (declare-sort $$unsorted 0) % 0.36/0.70 (declare-const tptp.proper_element (-> $$unsorted $$unsorted Bool)) % 0.36/0.70 (declare-const tptp.relation_empty_yielding (-> $$unsorted Bool)) % 0.36/0.70 (declare-const tptp.empty_set $$unsorted) % 0.36/0.70 (declare-const tptp.one_sorted_str (-> $$unsorted Bool)) % 0.36/0.70 (declare-const tptp.bounded_relstr (-> $$unsorted Bool)) % 0.36/0.70 (declare-const tptp.reflexive_relstr (-> $$unsorted Bool)) % 0.36/0.70 (declare-const tptp.empty_carrier (-> $$unsorted Bool)) % 0.36/0.70 (declare-const tptp.relation (-> $$unsorted Bool)) % 0.36/0.70 (declare-const tptp.upper_relstr_subset (-> $$unsorted $$unsorted Bool)) % 0.36/0.70 (declare-const tptp.distributive_relstr (-> $$unsorted Bool)) % 0.36/0.70 (declare-const tptp.up_complete_relstr (-> $$unsorted Bool)) % 0.36/0.70 (declare-const tptp.trivial_carrier (-> $$unsorted Bool)) % 0.36/0.70 (declare-const tptp.filtered_subset (-> $$unsorted $$unsorted Bool)) % 0.36/0.70 (declare-const tptp.v1_yellow_3 (-> $$unsorted Bool)) % 0.36/0.70 (declare-const tptp.complete_relstr (-> $$unsorted Bool)) % 0.36/0.70 (declare-const tptp.relation_of2 (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.36/0.70 (declare-const tptp.rel_str (-> $$unsorted Bool)) % 0.36/0.70 (declare-const tptp.empty (-> $$unsorted Bool)) % 0.36/0.70 (declare-const tptp.strict_rel_str (-> $$unsorted Bool)) % 0.36/0.70 (declare-const tptp.rel_str_of (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.70 (declare-const tptp.lower_bounded_relstr (-> $$unsorted Bool)) % 0.36/0.70 (declare-const tptp.the_InternalRel (-> $$unsorted $$unsorted)) % 0.36/0.70 (declare-const tptp.bottom_of_relstr (-> $$unsorted $$unsorted)) % 0.36/0.70 (declare-const tptp.upper_bounded_relstr (-> $$unsorted Bool)) % 0.36/0.70 (declare-const tptp.with_infima_relstr (-> $$unsorted Bool)) % 0.36/0.70 (declare-const tptp.relation_of2_as_subset (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.36/0.70 (declare-const tptp.with_suprema_relstr (-> $$unsorted Bool)) % 0.36/0.70 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 0.36/0.70 (declare-const tptp.antisymmetric_relstr (-> $$unsorted Bool)) % 0.36/0.70 (declare-const tptp.transitive_relstr (-> $$unsorted Bool)) % 0.36/0.70 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 0.36/0.70 (declare-const tptp.finite (-> $$unsorted Bool)) % 0.36/0.70 (declare-const tptp.heyting_relstr (-> $$unsorted Bool)) % 0.36/0.70 (declare-const tptp.join_complete_relstr (-> $$unsorted Bool)) % 0.36/0.70 (declare-const tptp.cartesian_product2 (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.70 (declare-const tptp.complemented_relstr (-> $$unsorted Bool)) % 0.36/0.70 (declare-const tptp.powerset (-> $$unsorted $$unsorted)) % 0.36/0.70 (declare-const tptp.boolean_relstr (-> $$unsorted Bool)) % 0.36/0.70 (declare-const tptp.element (-> $$unsorted $$unsorted Bool)) % 0.36/0.70 (declare-const tptp.directed_relstr (-> $$unsorted Bool)) % 0.36/0.70 (declare-const tptp.connected_relstr (-> $$unsorted Bool)) % 0.36/0.70 (declare-const tptp.the_carrier (-> $$unsorted $$unsorted)) % 0.36/0.70 (declare-const tptp.boole_POSet (-> $$unsorted $$unsorted)) % 0.36/0.70 (define @t1 () (@var "A" $$unsorted)) % 0.36/0.70 (define @t2 () (tptp.the_InternalRel @t1)) % 0.36/0.70 (define @t3 () (tptp.the_carrier @t1)) % 0.36/0.70 (define @t4 () (tptp.strict_rel_str @t1)) % 0.36/0.70 (define @t5 () (tptp.rel_str @t1)) % 0.36/0.70 (define @t6 () (@list @t1)) % 0.36/0.70 (define @t7 () (@var "B" $$unsorted)) % 0.36/0.70 (define @t8 () (tptp.in @t1 @t7)) % 0.36/0.70 (define @t9 () (@list @t1 @t7)) % 0.36/0.70 (define @t10 () (tptp.join_complete_relstr @t1)) % 0.36/0.70 (define @t11 () (tptp.up_complete_relstr @t1)) % 0.36/0.70 (define @t12 () (tptp.reflexive_relstr @t1)) % 0.36/0.70 (define @t13 () (tptp.empty_carrier @t1)) % 0.36/0.70 (define @t14 () (not @t13)) % 0.36/0.70 (define @t15 () (tptp.complete_relstr @t1)) % 0.36/0.70 (define @t16 () (tptp.lower_bounded_relstr @t1)) % 0.36/0.70 (define @t17 () (tptp.bounded_relstr @t1)) % 0.36/0.70 (define @t18 () (tptp.upper_bounded_relstr @t1)) % 0.36/0.70 (define @t19 () (tptp.with_infima_relstr @t1)) % 0.36/0.70 (define @t20 () (tptp.with_suprema_relstr @t1)) % 0.36/0.70 (define @t21 () (tptp.antisymmetric_relstr @t1)) % 0.36/0.70 (define @t22 () (tptp.transitive_relstr @t1)) % 0.36/0.70 (define @t23 () (tptp.finite @t1)) % 0.36/0.70 (define @t24 () (tptp.empty @t1)) % 0.36/0.70 (define @t25 () (tptp.relation @t1)) % 0.36/0.70 (define @t26 () (@var "C" $$unsorted)) % 0.36/0.70 (define @t27 () (tptp.cartesian_product2 @t1 @t7)) % 0.36/0.70 (define @t28 () (tptp.element @t26 (tptp.powerset @t27))) % 0.36/0.70 (define @t29 () (@list @t1 @t7 @t26)) % 0.36/0.70 (define @t30 () (and @t14 @t15)) % 0.36/0.70 (define @t31 () (tptp.finite @t7)) % 0.36/0.70 (define @t32 () (tptp.powerset @t1)) % 0.36/0.70 (define @t33 () (tptp.element @t7 @t32)) % 0.36/0.70 (define @t34 () (@list @t7)) % 0.36/0.70 (define @t35 () (tptp.trivial_carrier @t1)) % 0.36/0.70 (define @t36 () (and @t14 @t12 @t35)) % 0.36/0.70 (define @t37 () (and @t16 @t18)) % 0.36/0.70 (define @t38 () (tptp.connected_relstr @t1)) % 0.36/0.70 (define @t39 () (tptp.rel_str_of @t1 @t7)) % 0.36/0.70 (define @t40 () (tptp.relation_of2 @t7 @t1 @t1)) % 0.36/0.70 (define @t41 () (tptp.bottom_of_relstr @t1)) % 0.36/0.70 (define @t42 () (tptp.boole_POSet @t1)) % 0.36/0.70 (define @t43 () (tptp.rel_str @t42)) % 0.36/0.70 (define @t44 () (tptp.strict_rel_str @t42)) % 0.36/0.70 (define @t45 () (forall @t6 (and @t44 @t43))) % 0.36/0.70 (define @t46 () (tptp.one_sorted_str @t1)) % 0.36/0.70 (define @t47 () (tptp.relation_of2_as_subset @t26 @t1 @t7)) % 0.36/0.70 (define @t48 () (tptp.relation_of2 @t26 @t1 @t7)) % 0.36/0.70 (define @t49 () (@list @t26)) % 0.36/0.70 (define @t50 () (tptp.relation tptp.empty_set)) % 0.36/0.70 (define @t51 () (tptp.empty tptp.empty_set)) % 0.36/0.70 (define @t52 () (and @t14 @t46)) % 0.36/0.70 (define @t53 () (tptp.complete_relstr @t42)) % 0.36/0.70 (define @t54 () (tptp.with_infima_relstr @t42)) % 0.36/0.70 (define @t55 () (tptp.with_suprema_relstr @t42)) % 0.36/0.70 (define @t56 () (tptp.boolean_relstr @t42)) % 0.36/0.70 (define @t57 () (tptp.complemented_relstr @t42)) % 0.36/0.70 (define @t58 () (tptp.heyting_relstr @t42)) % 0.36/0.70 (define @t59 () (tptp.distributive_relstr @t42)) % 0.36/0.70 (define @t60 () (not (tptp.v1_yellow_3 @t42))) % 0.36/0.70 (define @t61 () (tptp.join_complete_relstr @t42)) % 0.36/0.70 (define @t62 () (tptp.up_complete_relstr @t42)) % 0.36/0.70 (define @t63 () (tptp.bounded_relstr @t42)) % 0.36/0.70 (define @t64 () (tptp.upper_bounded_relstr @t42)) % 0.36/0.70 (define @t65 () (tptp.lower_bounded_relstr @t42)) % 0.36/0.70 (define @t66 () (tptp.antisymmetric_relstr @t42)) % 0.36/0.70 (define @t67 () (tptp.transitive_relstr @t42)) % 0.36/0.70 (define @t68 () (tptp.reflexive_relstr @t42)) % 0.36/0.70 (define @t69 () (not (tptp.empty_carrier @t42))) % 0.36/0.70 (define @t70 () (forall @t6 (and @t69 @t44 @t68 @t67 @t66 @t65 @t64 @t63 @t62 @t61 @t60 @t59 @t58 @t57 @t56 @t55 @t54 @t53))) % 0.36/0.70 (define @t71 () (not @t24)) % 0.36/0.70 (define @t72 () (tptp.empty @t7)) % 0.36/0.70 (define @t73 () (not @t72)) % 0.36/0.70 (define @t74 () (@var "D" $$unsorted)) % 0.36/0.70 (define @t75 () (tptp.upper_relstr_subset @t7 @t1)) % 0.36/0.70 (define @t76 () (tptp.filtered_subset @t7 @t1)) % 0.36/0.70 (define @t77 () (tptp.powerset @t3)) % 0.36/0.70 (define @t78 () (tptp.element @t7 @t77)) % 0.36/0.70 (define @t79 () (not @t35)) % 0.36/0.70 (define @t80 () (tptp.proper_element @t7 @t77)) % 0.36/0.70 (define @t81 () (tptp.bottom_of_relstr @t42)) % 0.36/0.70 (define @t82 () (forall @t6 (= @t81 tptp.empty_set))) % 0.36/0.70 (define @t83 () (tptp.element @t1 @t7)) % 0.36/0.70 (define @t84 () (tptp.empty @t26)) % 0.36/0.70 (define @t85 () (tptp.in @t26 @t7)) % 0.36/0.70 (define @t86 () (forall @t49 (not (and @t85 @t84)))) % 0.36/0.70 (define @t87 () (tptp.powerset (tptp.the_carrier @t42))) % 0.36/0.70 (define @t88 () (tptp.element @t7 @t87)) % 0.36/0.70 (define @t89 () (tptp.proper_element @t7 @t87)) % 0.36/0.70 (define @t90 () (tptp.upper_relstr_subset @t7 @t42)) % 0.36/0.70 (define @t91 () (tptp.filtered_subset @t7 @t42)) % 0.36/0.70 (define @t92 () (and @t73 @t91 @t90 @t89 @t88)) % 0.36/0.70 (define @t93 () (=> @t92 @t86)) % 0.36/0.70 (define @t94 () (forall @t34 @t93)) % 0.36/0.70 (define @t95 () (=> @t71 @t94)) % 0.36/0.70 (define @t96 () (forall @t6 @t95)) % 0.36/0.70 (define @t97 () (not @t96)) % 0.36/0.70 (define @t98 () (tptp.element @t7 (tptp.powerset @t26))) % 0.36/0.70 (define @t99 () (= @t1 tptp.empty_set)) % 0.36/0.70 (define @t100 () (forall @t6 (=> @t24 @t99))) % 0.36/0.70 (define @t101 () (= @t80 (not (tptp.in @t41 @t7)))) % 0.36/0.70 (define @t102 () (and @t73 @t76 @t75 @t78)) % 0.36/0.70 (define @t103 () (forall @t34 (=> @t102 @t101))) % 0.36/0.70 (define @t104 () (and @t14 @t12 @t22 @t21 @t16 @t5)) % 0.36/0.70 (define @t105 () (=> @t104 @t103)) % 0.36/0.70 (define @t106 () (forall @t6 @t105)) % 0.36/0.70 (define @t107 () (@var "BOUND_VARIABLE_8592" $$unsorted)) % 0.36/0.70 (define @t108 () (not (tptp.empty @t107))) % 0.36/0.70 (define @t109 () (@var "BOUND_VARIABLE_8590" $$unsorted)) % 0.36/0.70 (define @t110 () (not (tptp.in @t107 @t109))) % 0.36/0.70 (define @t111 () (not (tptp.element @t109 @t87))) % 0.36/0.70 (define @t112 () (not (tptp.proper_element @t109 @t87))) % 0.36/0.70 (define @t113 () (not (tptp.upper_relstr_subset @t109 @t42))) % 0.36/0.70 (define @t114 () (not (tptp.filtered_subset @t109 @t42))) % 0.36/0.70 (define @t115 () (tptp.empty @t109)) % 0.36/0.70 (define @t116 () (or @t24 @t115 @t114 @t113 @t112 @t111 @t110 @t108)) % 0.36/0.70 (define @t117 () (or @t115 @t114 @t113 @t112 @t111 @t110 @t108)) % 0.36/0.70 (define @t118 () (or @t24 @t117)) % 0.36/0.70 (define @t119 () (@list @t1 @t109 @t107)) % 0.36/0.70 (define @t120 () (forall @t119 @t118)) % 0.36/0.70 (define @t121 () (@list @t109 @t107)) % 0.36/0.70 (define @t122 () (forall @t121 @t118)) % 0.36/0.70 (define @t123 () (forall @t121 @t117)) % 0.36/0.70 (define @t124 () (@var "BOUND_VARIABLE_8574" $$unsorted)) % 0.36/0.70 (define @t125 () (or @t24 @t123)) % 0.36/0.70 (define @t126 () (not (tptp.empty @t124))) % 0.36/0.70 (define @t127 () (not (tptp.in @t124 @t7))) % 0.36/0.70 (define @t128 () (not @t88)) % 0.36/0.70 (define @t129 () (not @t89)) % 0.36/0.70 (define @t130 () (not @t90)) % 0.36/0.70 (define @t131 () (not @t91)) % 0.36/0.70 (define @t132 () (or @t72 @t131 @t130 @t129 @t128 @t127 @t126)) % 0.36/0.70 (define @t133 () (@list @t7 @t124)) % 0.36/0.70 (define @t134 () (forall @t133 @t132)) % 0.36/0.70 (define @t135 () (or @t127 @t126)) % 0.36/0.70 (define @t136 () (or @t72 @t131 @t130 @t129 @t128 @t135)) % 0.36/0.70 (define @t137 () (forall @t133 @t136)) % 0.36/0.70 (define @t138 () (@list @t124)) % 0.36/0.70 (define @t139 () (forall @t138 @t136)) % 0.36/0.70 (define @t140 () (forall @t138 @t135)) % 0.36/0.70 (define @t141 () (or @t72 @t131 @t130 @t129 @t128 @t140)) % 0.36/0.70 (define @t142 () (forall @t49 (or (not @t85) (not @t84)))) % 0.36/0.70 (define @t143 () (or @t72 @t131 @t130 @t129 @t128 @t142)) % 0.36/0.70 (define @t144 () (not @t73)) % 0.36/0.70 (define @t145 () (or @t144 @t131 @t130 @t129 @t128)) % 0.36/0.70 (define @t146 () (forall @t119 @t116)) % 0.36/0.70 (define @t147 () (@quantifiers_skolemize @t146 1)) % 0.36/0.70 (define @t148 () (@quantifiers_skolemize @t146 2)) % 0.36/0.70 (define @t149 () (tptp.in @t148 @t147)) % 0.36/0.70 (define @t150 () (tptp.empty @t148)) % 0.36/0.70 (define @t151 () (not @t150)) % 0.36/0.70 (define @t152 () (not @t149)) % 0.36/0.70 (define @t153 () (@quantifiers_skolemize @t146 0)) % 0.36/0.70 (define @t154 () (tptp.boole_POSet @t153)) % 0.36/0.70 (define @t155 () (tptp.powerset (tptp.the_carrier @t154))) % 0.36/0.70 (define @t156 () (tptp.element @t147 @t155)) % 0.36/0.70 (define @t157 () (not @t156)) % 0.36/0.70 (define @t158 () (tptp.proper_element @t147 @t155)) % 0.36/0.70 (define @t159 () (not @t158)) % 0.36/0.70 (define @t160 () (tptp.upper_relstr_subset @t147 @t154)) % 0.36/0.70 (define @t161 () (not @t160)) % 0.36/0.70 (define @t162 () (tptp.filtered_subset @t147 @t154)) % 0.36/0.70 (define @t163 () (not @t162)) % 0.36/0.70 (define @t164 () (tptp.empty @t147)) % 0.36/0.70 (define @t165 () (or (tptp.empty @t153) @t164 @t163 @t161 @t159 @t157 @t152 @t151)) % 0.36/0.70 (define @t166 () (@list true)) % 0.36/0.70 (define @t167 () (@list @t165)) % 0.36/0.70 (define @t168 () (@list @t153)) % 0.36/0.70 (define @t169 () (or @t151 (= @t148 tptp.empty_set))) % 0.36/0.70 (define @t170 () (forall @t6 (or @t71 @t99))) % 0.36/0.70 (define @t171 () (= tptp.empty_set @t148)) % 0.36/0.70 (define @t172 () (or @t151 @t171)) % 0.36/0.70 (define @t173 () (@list false false)) % 0.36/0.70 (define @t174 () (@var "BOUND_VARIABLE_8643" $$unsorted)) % 0.36/0.70 (define @t175 () (= (tptp.proper_element @t174 @t77) (not (tptp.in @t41 @t174)))) % 0.36/0.70 (define @t176 () (not (tptp.element @t174 @t77))) % 0.36/0.70 (define @t177 () (not (tptp.upper_relstr_subset @t174 @t1))) % 0.36/0.70 (define @t178 () (not (tptp.filtered_subset @t174 @t1))) % 0.36/0.70 (define @t179 () (tptp.empty @t174)) % 0.36/0.70 (define @t180 () (not @t5)) % 0.36/0.70 (define @t181 () (not @t16)) % 0.36/0.70 (define @t182 () (not @t21)) % 0.36/0.70 (define @t183 () (not @t22)) % 0.36/0.70 (define @t184 () (not @t12)) % 0.36/0.70 (define @t185 () (or @t179 @t178 @t177 @t176 @t175)) % 0.36/0.70 (define @t186 () (or @t13 @t184 @t183 @t182 @t181 @t180 @t185)) % 0.36/0.70 (define @t187 () (forall (@list @t1 @t174) @t186)) % 0.36/0.70 (define @t188 () (@list @t174)) % 0.36/0.70 (define @t189 () (forall @t188 @t186)) % 0.36/0.70 (define @t190 () (forall @t188 @t185)) % 0.36/0.70 (define @t191 () (or @t13 @t184 @t183 @t182 @t181 @t180 @t190)) % 0.36/0.70 (define @t192 () (not @t78)) % 0.36/0.70 (define @t193 () (not @t75)) % 0.36/0.70 (define @t194 () (not @t76)) % 0.36/0.70 (define @t195 () (or @t72 @t194 @t193 @t192 @t101)) % 0.36/0.70 (define @t196 () (forall @t34 @t195)) % 0.36/0.70 (define @t197 () (or @t13 @t184 @t183 @t182 @t181 @t180 @t196)) % 0.36/0.70 (define @t198 () (not @t14)) % 0.36/0.70 (define @t199 () (or @t198 @t184 @t183 @t182 @t181 @t180)) % 0.36/0.70 (define @t200 () (or @t144 @t194 @t193 @t192)) % 0.36/0.70 (define @t201 () (forall @t6 @t53)) % 0.36/0.70 (define @t202 () (@list @t1)) % 0.36/0.70 (define @t203 () (forall @t6 @t54)) % 0.36/0.70 (define @t204 () (forall @t6 @t55)) % 0.36/0.70 (define @t205 () (forall @t6 @t56)) % 0.36/0.70 (define @t206 () (forall @t6 @t57)) % 0.36/0.70 (define @t207 () (forall @t6 @t58)) % 0.36/0.70 (define @t208 () (forall @t6 @t59)) % 0.36/0.70 (define @t209 () (forall @t6 @t60)) % 0.36/0.70 (define @t210 () (forall @t6 @t61)) % 0.36/0.70 (define @t211 () (forall @t6 @t62)) % 0.36/0.70 (define @t212 () (forall @t6 @t63)) % 0.36/0.70 (define @t213 () (forall @t6 @t64)) % 0.36/0.70 (define @t214 () (forall @t6 @t65)) % 0.36/0.70 (define @t215 () (forall @t6 @t66)) % 0.36/0.70 (define @t216 () (forall @t6 @t67)) % 0.36/0.70 (define @t217 () (forall @t6 @t68)) % 0.36/0.70 (define @t218 () (forall @t6 @t44)) % 0.36/0.70 (define @t219 () (forall @t6 @t69)) % 0.36/0.70 (define @t220 () (and @t219 @t218 @t217 @t216 @t215 @t214 @t213 @t212 @t211 @t210 @t209 @t208 @t207 @t206 @t205 @t204 @t203 @t201)) % 0.36/0.70 (define @t221 () (forall @t6 @t43)) % 0.36/0.70 (define @t222 () (and @t218 @t221)) % 0.36/0.70 (define @t223 () (tptp.bottom_of_relstr @t154)) % 0.36/0.70 (define @t224 () (tptp.in @t223 @t147)) % 0.36/0.70 (define @t225 () (not @t224)) % 0.36/0.70 (define @t226 () (= @t158 @t225)) % 0.36/0.70 (define @t227 () (tptp.rel_str @t154)) % 0.36/0.70 (define @t228 () (not @t227)) % 0.36/0.70 (define @t229 () (tptp.lower_bounded_relstr @t154)) % 0.36/0.70 (define @t230 () (not @t229)) % 0.36/0.70 (define @t231 () (tptp.antisymmetric_relstr @t154)) % 0.36/0.70 (define @t232 () (not @t231)) % 0.36/0.70 (define @t233 () (tptp.transitive_relstr @t154)) % 0.36/0.70 (define @t234 () (not @t233)) % 0.36/0.70 (define @t235 () (tptp.reflexive_relstr @t154)) % 0.36/0.70 (define @t236 () (not @t235)) % 0.36/0.70 (define @t237 () (tptp.empty_carrier @t154)) % 0.36/0.70 (define @t238 () (or @t237 @t236 @t234 @t232 @t230 @t228 @t164 @t163 @t161 @t157 @t226)) % 0.36/0.70 (define @t239 () (= tptp.empty_set @t223)) % 0.36/0.70 (define @t240 () (and @t149 @t239 @t171)) % 0.36/0.70 (assume @p1 (forall @t6 (=> @t5 (=> @t4 (= @t1 (tptp.rel_str_of @t3 @t2)))))) % 0.36/0.70 (assume @p2 (forall @t9 (=> @t8 (not (tptp.in @t7 @t1))))) % 0.36/0.70 (assume @p3 (forall @t6 (=> @t5 (=> (and @t14 @t12 @t15) (and @t14 @t12 @t11 @t10))))) % 0.36/0.70 (assume @p4 (forall @t6 (=> @t5 (=> (and @t14 @t12 @t10) (and @t14 @t12 @t16))))) % 0.36/0.70 (assume @p5 (forall @t6 (=> @t5 (=> (and @t14 @t12 @t22 @t21 @t20 @t16 @t11) (and @t14 @t12 @t22 @t21 @t20 @t19 @t15 @t16 @t18 @t17))))) % 0.36/0.70 (assume @p6 (forall @t6 (=> @t5 (=> (and @t14 @t12 @t21 @t10) (and @t14 @t12 @t21 @t19))))) % 0.36/0.70 (assume @p7 (forall @t6 (=> @t5 (=> (and @t14 @t12 @t21 @t18 @t10) (and @t14 @t12 @t21 @t20 @t18))))) % 0.36/0.70 (assume @p8 (forall @t6 (=> @t24 @t23))) % 0.36/0.70 (assume @p9 (forall @t6 (=> @t5 (=> @t20 @t14)))) % 0.36/0.70 (assume @p10 (forall @t6 (=> @t24 @t25))) % 0.36/0.70 (assume @p11 (forall @t29 (=> @t28 (tptp.relation @t26)))) % 0.36/0.70 (assume @p12 (forall @t6 (=> @t5 (=> @t30 (and @t14 @t20 @t19))))) % 0.36/0.70 (assume @p13 (forall @t6 (=> @t23 (forall @t34 (=> @t33 @t31))))) % 0.36/0.70 (assume @p14 (forall @t6 (=> @t5 (=> @t19 @t14)))) % 0.36/0.70 (assume @p15 (forall @t6 (=> @t5 (=> @t36 (and @t14 @t12 @t22 @t21 @t15))))) % 0.36/0.70 (assume @p16 (forall @t6 (=> @t5 (=> @t30 (and @t14 @t17))))) % 0.36/0.70 (assume @p17 (forall @t6 (=> @t5 (=> @t17 @t37)))) % 0.36/0.70 (assume @p18 (forall @t6 (=> @t5 (=> @t36 (and @t14 @t12 @t38))))) % 0.36/0.70 (assume @p19 (forall @t6 (=> @t5 (=> @t37 @t17)))) % 0.36/0.70 (assume @p20 (forall @t6 (=> @t5 (=> (and @t12 @t20 @t11) (and @t14 @t12 @t20 @t18))))) % 0.36/0.70 (assume @p21 (forall @t9 (=> @t40 (and (tptp.strict_rel_str @t39) (tptp.rel_str @t39))))) % 0.36/0.70 (assume @p22 true) % 0.36/0.70 (assume @p23 (forall @t6 (=> @t5 (tptp.element @t41 @t3)))) % 0.36/0.70 (assume @p24 @t45) % 0.36/0.70 (assume @p25 (forall @t6 (=> @t5 @t46))) % 0.36/0.70 (assume @p26 (forall @t29 (=> @t47 @t28))) % 0.36/0.70 (assume @p27 (forall @t6 (=> @t5 (tptp.relation_of2_as_subset @t2 @t3 @t3)))) % 0.36/0.70 (assume @p28 (exists @t6 @t5)) % 0.36/0.70 (assume @p29 (exists @t6 @t46)) % 0.36/0.70 (assume @p30 (forall @t9 (exists @t49 @t48))) % 0.36/0.70 (assume @p31 (forall @t6 (exists @t34 (tptp.element @t7 @t1)))) % 0.36/0.70 (assume @p32 (forall @t9 (exists @t49 @t47))) % 0.36/0.70 (assume @p33 (and @t51 @t50 (tptp.relation_empty_yielding tptp.empty_set))) % 0.36/0.70 (assume @p34 (forall @t9 (=> (and @t23 @t31) (tptp.finite @t27)))) % 0.36/0.70 (assume @p35 (forall @t6 (=> @t52 (not (tptp.empty @t3))))) % 0.36/0.70 (assume @p36 (forall @t6 (not (tptp.empty @t32)))) % 0.36/0.70 (assume @p37 @t70) % 0.36/0.70 (assume @p38 (forall @t6 (=> @t71 (and @t69 (not (tptp.trivial_carrier @t42)) @t44 @t68 @t67 @t66 @t65 @t64 @t63 @t62 @t61 @t60 @t59 @t58 @t57 @t56 @t55 @t54 @t53)))) % 0.36/0.70 (assume @p39 (and @t51 @t50)) % 0.36/0.70 (assume @p40 (forall @t9 (=> (and @t71 @t73) (not (tptp.empty @t27))))) % 0.36/0.70 (assume @p41 (forall @t6 (and @t69 @t44 @t68 @t67 @t66))) % 0.36/0.70 (assume @p42 (forall @t6 (and @t69 @t44 @t68 @t67 @t66 @t65 @t64 @t63 @t55 @t54 @t53))) % 0.36/0.70 (assume @p43 (forall @t6 (and @t69 @t44 @t68 @t67 @t66 @t65 @t64 @t63 (tptp.directed_relstr @t42) @t62 @t61 @t60 @t55 @t54 @t53))) % 0.36/0.70 (assume @p44 (forall @t9 (=> @t40 (forall (@list @t26 @t74) (=> (= @t39 (tptp.rel_str_of @t26 @t74)) (and (= @t1 @t26) (= @t7 @t74))))))) % 0.36/0.70 (assume @p45 (forall @t6 (=> (and @t14 @t12 @t22 @t5) (exists @t34 (and @t78 @t73 @t76 @t75))))) % 0.36/0.70 (assume @p46 (exists @t6 (and @t5 @t14 @t12 @t22 @t21 @t38))) % 0.36/0.70 (assume @p47 (exists @t6 (and @t5 @t14 @t4 @t12 @t22 @t21 @t20 @t19 @t15 @t16 @t18 @t17 @t11 @t10))) % 0.36/0.70 (assume @p48 (exists @t6 (and @t71 @t23))) % 0.36/0.70 (assume @p49 (exists @t6 (and @t5 @t14 @t4 @t12 @t22 @t21 @t15))) % 0.36/0.70 (assume @p50 (exists @t6 (and @t24 @t25))) % 0.36/0.70 (assume @p51 (forall @t6 (=> @t71 (exists @t34 (and @t33 @t73))))) % 0.36/0.70 (assume @p52 (exists @t6 (and @t5 @t14 @t79 @t4 @t12 @t22 @t21 @t16 @t18 @t17 (not (tptp.v1_yellow_3 @t1)) (tptp.distributive_relstr @t1) (tptp.heyting_relstr @t1) (tptp.complemented_relstr @t1) (tptp.boolean_relstr @t1) @t20 @t19))) % 0.36/0.70 (assume @p53 (exists @t6 (and @t5 @t14 @t4 @t12 @t22 @t21 @t20 @t19 @t15 @t35))) % 0.36/0.70 (assume @p54 (exists @t6 (and @t5 @t14 @t4 @t12 @t22 @t21 @t20 @t19 @t15))) % 0.36/0.70 (assume @p55 (exists @t6 (and @t71 @t25))) % 0.36/0.70 (assume @p56 (forall @t6 (exists @t34 (and @t33 @t72)))) % 0.36/0.70 (assume @p57 (forall @t6 (exists @t34 (and (tptp.element @t7 (tptp.powerset @t32)) @t73 @t31)))) % 0.36/0.70 (assume @p58 (exists @t6 (and @t5 @t14 @t12 @t22 @t21 @t20 @t19 @t15 @t16 @t18 @t17))) % 0.36/0.70 (assume @p59 (forall @t6 (=> @t71 (exists @t34 (and @t33 @t73 @t31))))) % 0.36/0.70 (assume @p60 (exists @t6 (and @t25 (tptp.relation_empty_yielding @t1)))) % 0.36/0.70 (assume @p61 (exists @t6 (and @t46 @t14))) % 0.36/0.70 (assume @p62 (forall @t6 (=> @t46 (exists @t34 (and (tptp.element @t7 (tptp.powerset @t77)) @t73 @t31))))) % 0.36/0.70 (assume @p63 (forall @t6 (=> (and @t14 @t79 @t12 @t22 @t21 @t18 @t5) (exists @t34 (and @t78 @t73 @t80 @t76 @t75))))) % 0.36/0.70 (assume @p64 (exists @t6 (and @t5 @t14 @t4 @t22 (tptp.directed_relstr @t1)))) % 0.36/0.70 (assume @p65 (forall @t6 (=> @t52 (exists @t34 (and @t78 @t73))))) % 0.36/0.70 (assume @p66 (forall @t29 (= @t47 @t48))) % 0.36/0.70 (assume @p67 (forall @t9 (tptp.subset @t1 @t1))) % 0.36/0.70 (assume @p68 @t82) % 0.36/0.70 (assume @p69 (forall @t9 (=> @t8 @t83))) % 0.36/0.70 (assume @p70 (forall @t9 (=> @t83 (or @t72 @t8)))) % 0.36/0.70 (assume @p71 @t97) % 0.36/0.70 (assume @p72 (forall @t9 (= (tptp.element @t1 (tptp.powerset @t7)) (tptp.subset @t1 @t7)))) % 0.36/0.70 (assume @p73 (forall @t29 (=> (and @t8 @t98) (tptp.element @t1 @t26)))) % 0.36/0.70 (assume @p74 (forall @t29 (not (and @t8 @t98 @t84)))) % 0.36/0.70 (assume @p75 @t100) % 0.36/0.70 (assume @p76 (forall @t9 (not (and @t8 @t72)))) % 0.36/0.70 (assume @p77 (forall @t9 (not (and @t24 (not (= @t1 @t7)) @t72)))) % 0.36/0.70 (assume @p78 @t106) % 0.36/0.70 (step @p79 :rule aci_norm :args ((= @t118 @t116))) % 0.36/0.70 (step @p80 :rule cong :premises (@p79) :args (@t120)) % 0.36/0.70 (step @p81 :rule quant-merge-prenex :args ((= (forall @t6 @t122) @t120))) % 0.36/0.70 (step @p82 :rule alpha_equiv :args (@t123 (@list @t109 @t107) (@list @t7 @t124))) % 0.36/0.70 (step @p83 :rule refl :args (@t24)) % 0.36/0.70 (step @p84 :rule nary_cong :premises (@p83 @p82) :args (@t125)) % 0.36/0.70 (step @p85 :rule quant-miniscope-or :args ((= @t122 @t125))) % 0.36/0.70 (step @p86 :rule trans :premises (@p85 @p84)) % 0.36/0.70 (step @p87 :rule symm :premises (@p86)) % 0.36/0.70 (step @p88 :rule cong :premises (@p87) :args ((forall @t6 (or @t24 @t134)))) % 0.36/0.70 (step @p89 :rule trans :premises (@p88 @p81)) % 0.36/0.70 (step @p90 :rule trans :premises (@p89 @p80)) % 0.36/0.70 (step @p91 :rule refl :args (@t134)) % 0.36/0.70 (step @p92 :rule bool-double-not-elim :args (@t24)) % 0.36/0.70 (step @p93 :rule nary_cong :premises (@p92 @p91) :args ((or (not @t71) @t134))) % 0.36/0.70 (step @p94 :rule bool-impl-elim :args (@t71 @t134)) % 0.36/0.70 (step @p95 :rule trans :premises (@p94 @p93)) % 0.36/0.70 (step @p96 :rule cong :premises (@p95) :args ((forall @t6 (=> @t71 @t134)))) % 0.36/0.70 (step @p97 :rule trans :premises (@p96 @p90)) % 0.36/0.70 (step @p98 :rule aci_norm :args ((= @t136 @t132))) % 0.36/0.70 (step @p99 :rule cong :premises (@p98) :args (@t137)) % 0.36/0.70 (step @p100 :rule quant-merge-prenex :args ((= (forall @t34 @t139) @t137))) % 0.36/0.70 (step @p101 :rule alpha_equiv :args (@t140 (@list @t124) (@list @t26))) % 0.36/0.70 (step @p102 :rule refl :args (@t128)) % 0.36/0.70 (step @p103 :rule refl :args (@t129)) % 0.36/0.70 (step @p104 :rule refl :args (@t130)) % 0.36/0.70 (step @p105 :rule refl :args (@t131)) % 0.36/0.70 (step @p106 :rule refl :args (@t72)) % 0.36/0.70 (step @p107 :rule nary_cong :premises (@p106 @p105 @p104 @p103 @p102 @p101) :args (@t141)) % 0.36/0.70 (step @p108 :rule quant-miniscope-or :args ((= @t139 @t141))) % 0.36/0.70 (step @p109 :rule trans :premises (@p108 @p107)) % 0.36/0.70 (step @p110 :rule symm :premises (@p109)) % 0.36/0.70 (step @p111 :rule cong :premises (@p110) :args ((forall @t34 @t143))) % 0.36/0.70 (step @p112 :rule trans :premises (@p111 @p100)) % 0.36/0.70 (step @p113 :rule trans :premises (@p112 @p99)) % 0.36/0.70 (step @p114 :rule aci_norm :args ((= (or (or @t72 @t131 @t130 @t129 @t128) @t142) @t143))) % 0.36/0.70 (step @p115 :rule refl :args (@t142)) % 0.36/0.70 (step @p116 :rule bool-double-not-elim :args (@t72)) % 0.36/0.70 (step @p117 :rule nary_cong :premises (@p116 @p105 @p104 @p103 @p102) :args (@t145)) % 0.36/0.70 (step @p118 :rule aci_norm :args ((= (or @t144 (or @t131 (or @t130 (or @t129 @t128)))) @t145))) % 0.36/0.70 (step @p119 :rule trans :premises (@p118 @p117)) % 0.36/0.70 (step @p120 :rule bool-and-de-morgan :args (@t89 @t88 true)) % 0.36/0.70 (step @p121 :rule nary_cong :premises (@p104 @p120) :args ((or @t130 (not (and @t89 @t88))))) % 0.36/0.70 (step @p122 :rule bool-and-de-morgan :args (@t90 @t89 (and @t88))) % 0.36/0.70 (step @p123 :rule trans :premises (@p122 @p121)) % 0.36/0.70 (step @p124 :rule nary_cong :premises (@p105 @p123) :args ((or @t131 (not (and @t90 @t89 @t88))))) % 0.36/0.70 (step @p125 :rule bool-and-de-morgan :args (@t91 @t90 (and @t89 @t88))) % 0.36/0.70 (step @p126 :rule trans :premises (@p125 @p124)) % 0.36/0.70 (step @p127 :rule refl :args (@t144)) % 0.36/0.70 (step @p128 :rule nary_cong :premises (@p127 @p126) :args ((or @t144 (not (and @t91 @t90 @t89 @t88))))) % 0.36/0.70 (step @p129 :rule bool-and-de-morgan :args (@t73 @t91 (and @t90 @t89 @t88))) % 0.36/0.70 (step @p130 :rule trans :premises (@p129 @p128)) % 0.36/0.70 (step @p131 :rule trans :premises (@p130 @p119)) % 0.36/0.70 (step @p132 :rule nary_cong :premises (@p131 @p115) :args ((or (not @t92) @t142))) % 0.36/0.70 (step @p133 :rule trans :premises (@p132 @p114)) % 0.36/0.70 (step @p134 :rule bool-impl-elim :args (@t92 @t142)) % 0.36/0.70 (step @p135 :rule trans :premises (@p134 @p133)) % 0.36/0.70 (step @p136 :rule cong :premises (@p135) :args ((forall @t34 (=> @t92 @t142)))) % 0.36/0.70 (step @p137 :rule trans :premises (@p136 @p113)) % 0.36/0.70 (step @p138 :rule bool-and-de-morgan :args (@t85 @t84 true)) % 0.36/0.70 (step @p139 :rule cong :premises (@p138) :args (@t86)) % 0.36/0.70 (step @p140 :rule refl :args (@t92)) % 0.36/0.70 (step @p141 :rule cong :premises (@p140 @p139) :args (@t93)) % 0.36/0.70 (step @p142 :rule cong :premises (@p141) :args (@t94)) % 0.36/0.70 (step @p143 :rule trans :premises (@p142 @p137)) % 0.36/0.70 (step @p144 :rule refl :args (@t71)) % 0.36/0.70 (step @p145 :rule cong :premises (@p144 @p143) :args (@t95)) % 0.36/0.70 (step @p146 :rule cong :premises (@p145) :args (@t96)) % 0.36/0.70 (step @p147 :rule trans :premises (@p146 @p97)) % 0.36/0.70 (step @p148 :rule cong :premises (@p147) :args (@t97)) % 0.36/0.70 (step @p149 :rule eq_resolve :premises (@p71 @p148)) % 0.36/0.70 (step @p150 :rule skolemize :premises (@p149)) % 0.36/0.70 (step @p151 :rule bool-double-not-elim :args (@t149)) % 0.36/0.70 (step @p152 :rule refl :args (@t165)) % 0.36/0.70 (step @p153 :rule nary_cong :premises (@p152 @p151) :args ((or @t165 (not @t152)))) % 0.36/0.70 (step @p154 :rule cnf_or_neg :args (@t165 6)) % 0.36/0.70 (step @p155 :rule eq_resolve :premises (@p154 @p153)) % 0.36/0.70 (step @p156 :rule reordering :premises (@p155) :args ((or @t149 @t165))) % 0.36/0.70 (step @p157 :rule chain_m_resolution 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:premises (@p345) :args ((or @t152 @t224 (not @t239) (not @t171)))) % 0.36/0.70 (step @p347 false :rule chain_m_resolution :premises (@p346 @p328 @p185 @p161 @p157) :args (false (@list true false false false) (@list @t224 @t171 @t239 @t149))) % 0.36/0.70 ) % 0.36/0.70 % SZS output end Proof % 0.36/0.70 % cvc5 exiting %------------------------------------------------------------------------------