%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET677+3 : TPTP v9.2.1. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n013.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 08:48:25 AM UTC 2026 % Result : Theorem 0.44s 0.64s % Output : Proof 0.44s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET677+3 : TPTP v9.2.1. Released v2.2.0. % 0.00/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n013.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 16:07:30 EDT 2026 % 0.17/0.34 % CPUTime : % 0.30/0.49 %----Proving TF0_NAR, FOF, or CNF % 0.44/0.64 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.44/0.64 % SZS status Theorem % 0.44/0.64 % SZS output start Proof % 0.44/0.64 ( % 0.44/0.64 (declare-sort $$unsorted 0) % 0.44/0.64 (declare-const tptp.power_set (-> $$unsorted $$unsorted)) % 0.44/0.64 (declare-const tptp.subset_type (-> $$unsorted $$unsorted)) % 0.44/0.64 (declare-const tptp.cross_product (-> $$unsorted $$unsorted $$unsorted)) % 0.44/0.64 (declare-const tptp.range (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.44/0.64 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 0.44/0.64 (declare-const tptp.domain (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.44/0.64 (declare-const tptp.identity_relation_of (-> $$unsorted $$unsorted)) % 0.44/0.64 (declare-const tptp.member (-> $$unsorted $$unsorted Bool)) % 0.44/0.64 (declare-const tptp.member_type (-> $$unsorted $$unsorted)) % 0.44/0.64 (declare-const tptp.relation_like (-> $$unsorted Bool)) % 0.44/0.64 (declare-const tptp.relation_type (-> $$unsorted $$unsorted $$unsorted)) % 0.44/0.64 (declare-const tptp.ilf_type (-> $$unsorted $$unsorted Bool)) % 0.44/0.64 (declare-const tptp.set_type $$unsorted) % 0.44/0.64 (declare-const tptp.empty (-> $$unsorted Bool)) % 0.44/0.64 (declare-const tptp.domain_of (-> $$unsorted $$unsorted)) % 0.44/0.64 (declare-const tptp.ordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.44/0.64 (declare-const tptp.range_of (-> $$unsorted $$unsorted)) % 0.44/0.64 (declare-const tptp.binary_relation_type $$unsorted) % 0.44/0.64 (declare-const tptp.identity_relation_of_type (-> $$unsorted $$unsorted)) % 0.44/0.64 (define @t1 () (@var "D" $$unsorted)) % 0.44/0.64 (define @t2 () (@var "B" $$unsorted)) % 0.44/0.64 (define @t3 () (@var "C" $$unsorted)) % 0.44/0.64 (define @t4 () (and (= @t3 (tptp.domain @t3 @t2 @t1)) (tptp.subset @t3 (tptp.range @t3 @t2 @t1)))) % 0.44/0.64 (define @t5 () (tptp.identity_relation_of @t3)) % 0.44/0.64 (define @t6 () (tptp.subset @t5 @t1)) % 0.44/0.64 (define @t7 () (=> @t6 @t4)) % 0.44/0.64 (define @t8 () (tptp.relation_type @t3 @t2)) % 0.44/0.64 (define @t9 () (tptp.ilf_type @t1 @t8)) % 0.44/0.64 (define @t10 () (@list @t1)) % 0.44/0.64 (define @t11 () (forall @t10 (=> @t9 @t7))) % 0.44/0.64 (define @t12 () (tptp.ilf_type @t3 tptp.set_type)) % 0.44/0.64 (define @t13 () (=> @t12 @t11)) % 0.44/0.64 (define @t14 () (@list @t3)) % 0.44/0.64 (define @t15 () (forall @t14 @t13)) % 0.44/0.64 (define @t16 () (tptp.ilf_type @t2 tptp.set_type)) % 0.44/0.64 (define @t17 () (=> @t16 @t15)) % 0.44/0.64 (define @t18 () (@list @t2)) % 0.44/0.64 (define @t19 () (forall @t18 @t17)) % 0.44/0.64 (define @t20 () (tptp.range @t2 @t3 @t1)) % 0.44/0.64 (define @t21 () (tptp.domain @t2 @t3 @t1)) % 0.44/0.64 (define @t22 () (and (tptp.subset @t3 @t21) (= @t3 @t20))) % 0.44/0.64 (define @t23 () (=> @t6 @t22)) % 0.44/0.64 (define @t24 () (tptp.relation_type @t2 @t3)) % 0.44/0.64 (define @t25 () (tptp.ilf_type @t1 @t24)) % 0.44/0.64 (define @t26 () (forall @t10 (=> @t25 @t23))) % 0.44/0.64 (define @t27 () (=> @t12 @t26)) % 0.44/0.64 (define @t28 () (forall @t14 @t27)) % 0.44/0.64 (define @t29 () (=> @t16 @t28)) % 0.44/0.64 (define @t30 () (forall @t18 @t29)) % 0.44/0.64 (define @t31 () (tptp.member @t3 @t2)) % 0.44/0.64 (define @t32 () (tptp.identity_relation_of @t2)) % 0.44/0.64 (define @t33 () (tptp.ilf_type @t1 tptp.set_type)) % 0.44/0.64 (define @t34 () (tptp.relation_type @t2 @t2)) % 0.44/0.64 (define @t35 () (tptp.identity_relation_of_type @t2)) % 0.44/0.64 (define @t36 () (tptp.ilf_type @t3 @t35)) % 0.44/0.64 (define @t37 () (= @t36 (tptp.ilf_type @t3 @t34))) % 0.44/0.64 (define @t38 () (forall @t14 (=> @t12 @t37))) % 0.44/0.64 (define @t39 () (=> @t16 @t38)) % 0.44/0.64 (define @t40 () (forall @t18 @t39)) % 0.44/0.64 (define @t41 () (@var "E" $$unsorted)) % 0.44/0.64 (define @t42 () (tptp.ordered_pair @t1 @t41)) % 0.44/0.64 (define @t43 () (tptp.ilf_type @t41 tptp.set_type)) % 0.44/0.64 (define @t44 () (@list @t41)) % 0.44/0.64 (define @t45 () (tptp.subset @t2 @t3)) % 0.44/0.64 (define @t46 () (tptp.ilf_type @t2 tptp.binary_relation_type)) % 0.44/0.64 (define @t47 () (tptp.relation_like @t2)) % 0.44/0.64 (define @t48 () (tptp.cross_product @t2 @t3)) % 0.44/0.64 (define @t49 () (tptp.subset_type @t48)) % 0.44/0.64 (define @t50 () (tptp.ilf_type @t1 @t49)) % 0.44/0.64 (define @t51 () (tptp.power_set @t2)) % 0.44/0.64 (define @t52 () (tptp.subset_type @t2)) % 0.44/0.64 (define @t53 () (tptp.ilf_type @t3 @t52)) % 0.44/0.64 (define @t54 () (forall @t10 (=> @t33 (=> (tptp.member @t1 @t2) (tptp.member @t1 @t3))))) % 0.44/0.64 (define @t55 () (tptp.subset @t2 @t2)) % 0.44/0.64 (define @t56 () (tptp.empty @t2)) % 0.44/0.64 (define @t57 () (and (= @t2 (tptp.domain @t2 @t2 @t3)) (= @t2 (tptp.range @t2 @t2 @t3)))) % 0.44/0.64 (define @t58 () (tptp.subset @t32 @t3)) % 0.44/0.64 (define @t59 () (=> @t58 @t57)) % 0.44/0.64 (define @t60 () (forall @t14 (=> @t36 @t59))) % 0.44/0.64 (define @t61 () (=> @t16 @t60)) % 0.44/0.64 (define @t62 () (forall @t18 @t61)) % 0.44/0.64 (define @t63 () (not @t62)) % 0.44/0.64 (define @t64 () (@var "BOUND_VARIABLE_8486" $$unsorted)) % 0.44/0.64 (define @t65 () (and (= @t2 (tptp.domain @t2 @t2 @t64)) (= @t2 (tptp.range @t2 @t2 @t64)))) % 0.44/0.64 (define @t66 () (not (tptp.subset @t32 @t64))) % 0.44/0.64 (define @t67 () (not (tptp.ilf_type @t64 @t35))) % 0.44/0.64 (define @t68 () (not @t16)) % 0.44/0.64 (define @t69 () (or @t68 @t67 @t66 @t65)) % 0.44/0.64 (define @t70 () (or @t67 @t66 @t65)) % 0.44/0.64 (define @t71 () (or @t68 @t70)) % 0.44/0.64 (define @t72 () (@list @t2 @t64)) % 0.44/0.64 (define @t73 () (forall @t72 @t71)) % 0.44/0.64 (define @t74 () (@list @t64)) % 0.44/0.64 (define @t75 () (forall @t74 @t71)) % 0.44/0.64 (define @t76 () (forall @t74 @t70)) % 0.44/0.64 (define @t77 () (@list @t3)) % 0.44/0.64 (define @t78 () (or @t68 @t76)) % 0.44/0.64 (define @t79 () (not @t58)) % 0.44/0.64 (define @t80 () (not @t36)) % 0.44/0.64 (define @t81 () (or @t80 @t79 @t57)) % 0.44/0.64 (define @t82 () (forall @t14 @t81)) % 0.44/0.64 (define @t83 () (forall @t72 @t69)) % 0.44/0.64 (define @t84 () (@quantifiers_skolemize @t83 1)) % 0.44/0.64 (define @t85 () (@quantifiers_skolemize @t83 0)) % 0.44/0.64 (define @t86 () (tptp.range @t85 @t85 @t84)) % 0.44/0.64 (define @t87 () (= @t85 @t86)) % 0.44/0.64 (define @t88 () (tptp.domain @t85 @t85 @t84)) % 0.44/0.64 (define @t89 () (= @t85 @t88)) % 0.44/0.64 (define @t90 () (and @t89 @t87)) % 0.44/0.64 (define @t91 () (tptp.subset (tptp.identity_relation_of @t85) @t84)) % 0.44/0.64 (define @t92 () (not @t91)) % 0.44/0.64 (define @t93 () (tptp.ilf_type @t84 (tptp.identity_relation_of_type @t85))) % 0.44/0.64 (define @t94 () (not @t93)) % 0.44/0.64 (define @t95 () (tptp.ilf_type @t85 tptp.set_type)) % 0.44/0.64 (define @t96 () (not @t95)) % 0.44/0.64 (define @t97 () (or @t96 @t94 @t92 @t90)) % 0.44/0.64 (define @t98 () (@list true)) % 0.44/0.64 (define @t99 () (@list @t97)) % 0.44/0.64 (define @t100 () (@var "BOUND_VARIABLE_7734" $$unsorted)) % 0.44/0.64 (define @t101 () (@var "BOUND_VARIABLE_7732" $$unsorted)) % 0.44/0.64 (define @t102 () (and (= @t101 (tptp.domain @t101 @t2 @t100)) (tptp.subset @t101 (tptp.range @t101 @t2 @t100)))) % 0.44/0.64 (define @t103 () (not (tptp.subset (tptp.identity_relation_of @t101) @t100))) % 0.44/0.64 (define @t104 () (not (tptp.ilf_type @t100 (tptp.relation_type @t101 @t2)))) % 0.44/0.64 (define @t105 () (not (tptp.ilf_type @t101 tptp.set_type))) % 0.44/0.64 (define @t106 () (or @t105 @t104 @t103 @t102)) % 0.44/0.64 (define @t107 () (or @t68 @t106)) % 0.44/0.64 (define @t108 () (forall (@list @t2 @t101 @t100) @t107)) % 0.44/0.64 (define @t109 () (@list @t101 @t100)) % 0.44/0.64 (define @t110 () (forall @t109 @t107)) % 0.44/0.64 (define @t111 () (forall @t109 @t106)) % 0.44/0.64 (define @t112 () (@var "BOUND_VARIABLE_7710" $$unsorted)) % 0.44/0.64 (define @t113 () (or @t68 @t111)) % 0.44/0.64 (define @t114 () (and (= @t3 (tptp.domain @t3 @t2 @t112)) (tptp.subset @t3 (tptp.range @t3 @t2 @t112)))) % 0.44/0.64 (define @t115 () (not (tptp.subset @t5 @t112))) % 0.44/0.64 (define @t116 () (not (tptp.ilf_type @t112 @t8))) % 0.44/0.64 (define @t117 () (not @t12)) % 0.44/0.64 (define @t118 () (or @t117 @t116 @t115 @t114)) % 0.44/0.64 (define @t119 () (@list @t3 @t112)) % 0.44/0.64 (define @t120 () (forall @t119 @t118)) % 0.44/0.64 (define @t121 () (or @t116 @t115 @t114)) % 0.44/0.64 (define @t122 () (or @t117 @t121)) % 0.44/0.64 (define @t123 () (forall @t119 @t122)) % 0.44/0.64 (define @t124 () (@list @t112)) % 0.44/0.64 (define @t125 () (forall @t124 @t122)) % 0.44/0.64 (define @t126 () (forall @t124 @t121)) % 0.44/0.64 (define @t127 () (@list @t1)) % 0.44/0.64 (define @t128 () (or @t117 @t126)) % 0.44/0.64 (define @t129 () (not @t6)) % 0.44/0.64 (define @t130 () (not @t9)) % 0.44/0.64 (define @t131 () (or @t130 @t129 @t4)) % 0.44/0.64 (define @t132 () (forall @t10 @t131)) % 0.44/0.64 (define @t133 () (@list @t85 @t85 @t84)) % 0.44/0.64 (define @t134 () (@var "BOUND_VARIABLE_7865" $$unsorted)) % 0.44/0.64 (define @t135 () (= (tptp.ilf_type @t134 @t35) (tptp.ilf_type @t134 @t34))) % 0.44/0.64 (define @t136 () (not (tptp.ilf_type @t134 tptp.set_type))) % 0.44/0.64 (define @t137 () (or @t136 @t135)) % 0.44/0.64 (define @t138 () (or @t68 @t137)) % 0.44/0.64 (define @t139 () (forall (@list @t2 @t134) @t138)) % 0.44/0.64 (define @t140 () (@list @t134)) % 0.44/0.64 (define @t141 () (forall @t140 @t138)) % 0.44/0.64 (define @t142 () (forall @t140 @t137)) % 0.44/0.64 (define @t143 () (or @t68 @t142)) % 0.44/0.64 (define @t144 () (forall @t14 (or @t117 @t37))) % 0.44/0.64 (define @t145 () (tptp.ilf_type @t84 (tptp.relation_type @t85 @t85))) % 0.44/0.64 (define @t146 () (= @t93 @t145)) % 0.44/0.64 (define @t147 () (tptp.ilf_type @t84 tptp.set_type)) % 0.44/0.64 (define @t148 () (not @t147)) % 0.44/0.64 (define @t149 () (or @t96 @t148 @t146)) % 0.44/0.64 (define @t150 () (and @t89 (tptp.subset @t85 @t86))) % 0.44/0.64 (define @t151 () (not @t145)) % 0.44/0.64 (define @t152 () (or @t96 @t96 @t151 @t92 @t150)) % 0.44/0.64 (define @t153 () (@list false false false false)) % 0.44/0.64 (define @t154 () (@list false)) % 0.44/0.64 (define @t155 () (@var "BOUND_VARIABLE_7787" $$unsorted)) % 0.44/0.64 (define @t156 () (@var "BOUND_VARIABLE_7785" $$unsorted)) % 0.44/0.64 (define @t157 () (and (tptp.subset @t156 (tptp.domain @t2 @t156 @t155)) (= @t156 (tptp.range @t2 @t156 @t155)))) % 0.44/0.64 (define @t158 () (not (tptp.subset (tptp.identity_relation_of @t156) @t155))) % 0.44/0.64 (define @t159 () (not (tptp.ilf_type @t155 (tptp.relation_type @t2 @t156)))) % 0.44/0.64 (define @t160 () (not (tptp.ilf_type @t156 tptp.set_type))) % 0.44/0.64 (define @t161 () (or @t160 @t159 @t158 @t157)) % 0.44/0.64 (define @t162 () (or @t68 @t161)) % 0.44/0.64 (define @t163 () (forall (@list @t2 @t156 @t155) @t162)) % 0.44/0.64 (define @t164 () (@list @t156 @t155)) % 0.44/0.64 (define @t165 () (forall @t164 @t162)) % 0.44/0.64 (define @t166 () (forall @t164 @t161)) % 0.44/0.64 (define @t167 () (@var "BOUND_VARIABLE_7764" $$unsorted)) % 0.44/0.64 (define @t168 () (or @t68 @t166)) % 0.44/0.64 (define @t169 () (and (tptp.subset @t3 (tptp.domain @t2 @t3 @t167)) (= @t3 (tptp.range @t2 @t3 @t167)))) % 0.44/0.64 (define @t170 () (not (tptp.subset @t5 @t167))) % 0.44/0.64 (define @t171 () (not (tptp.ilf_type @t167 @t24))) % 0.44/0.64 (define @t172 () (or @t117 @t171 @t170 @t169)) % 0.44/0.64 (define @t173 () (@list @t3 @t167)) % 0.44/0.64 (define @t174 () (forall @t173 @t172)) % 0.44/0.64 (define @t175 () (or @t171 @t170 @t169)) % 0.44/0.64 (define @t176 () (or @t117 @t175)) % 0.44/0.64 (define @t177 () (forall @t173 @t176)) % 0.44/0.64 (define @t178 () (@list @t167)) % 0.44/0.64 (define @t179 () (forall @t178 @t176)) % 0.44/0.64 (define @t180 () (forall @t178 @t175)) % 0.44/0.64 (define @t181 () (or @t117 @t180)) % 0.44/0.64 (define @t182 () (not @t25)) % 0.44/0.64 (define @t183 () (or @t182 @t129 @t22)) % 0.44/0.64 (define @t184 () (forall @t10 @t183)) % 0.44/0.64 (define @t185 () (and (tptp.subset @t85 @t88) @t87)) % 0.44/0.64 (define @t186 () (or @t96 @t96 @t151 @t92 @t185)) % 0.44/0.64 (assume @p1 @t19) % 0.44/0.64 (assume @p2 @t30) % 0.44/0.64 (assume @p3 (forall @t18 (=> @t16 (forall @t14 (=> @t12 (forall @t10 (=> @t33 (= (tptp.member (tptp.ordered_pair @t3 @t1) @t32) (and @t31 (= @t3 @t1)))))))))) % 0.44/0.64 (assume @p4 (forall @t18 (=> @t16 (tptp.ilf_type @t32 tptp.binary_relation_type)))) % 0.44/0.64 (assume @p5 @t40) % 0.44/0.64 (assume @p6 (forall @t18 (=> @t16 (exists @t14 @t36)))) % 0.44/0.64 (assume @p7 (forall @t18 (=> @t46 (forall @t14 (=> (tptp.ilf_type @t3 tptp.binary_relation_type) (= @t45 (forall @t10 (=> @t33 (forall @t44 (=> @t43 (=> (tptp.member @t42 @t2) (tptp.member @t42 @t3)))))))))))) % 0.44/0.64 (assume @p8 (forall @t18 (=> @t16 (forall @t14 (=> @t12 (= (= @t2 @t3) (and @t45 (tptp.subset @t3 @t2)))))))) % 0.44/0.64 (assume @p9 (forall @t18 (=> @t46 (tptp.ilf_type (tptp.domain_of @t2) tptp.set_type)))) % 0.44/0.64 (assume @p10 (forall @t18 (=> @t46 (tptp.ilf_type (tptp.range_of @t2) tptp.set_type)))) % 0.44/0.64 (assume @p11 (forall @t18 (=> @t16 (forall @t14 (=> @t12 (tptp.ilf_type (tptp.ordered_pair @t2 @t3) tptp.set_type)))))) % 0.44/0.64 (assume @p12 (forall @t18 (=> @t16 (= @t46 (and @t47 @t16))))) % 0.44/0.64 (assume @p13 (exists @t18 @t46)) % 0.44/0.64 (assume @p14 (forall @t18 (=> @t16 (forall @t14 (=> @t12 (and (forall @t10 (=> @t50 @t25)) (forall @t44 (=> (tptp.ilf_type @t41 @t24) (tptp.ilf_type @t41 @t49))))))))) % 0.44/0.64 (assume @p15 (forall @t18 (=> @t16 (forall @t14 (=> @t12 (exists @t10 @t9)))))) % 0.44/0.64 (assume @p16 (forall @t18 (=> @t16 (forall @t14 (=> @t12 (= @t53 (tptp.ilf_type @t3 (tptp.member_type @t51)))))))) % 0.44/0.64 (assume @p17 (forall @t18 (=> @t16 (exists @t14 @t53)))) % 0.44/0.64 (assume @p18 (forall @t18 (=> @t16 (forall @t14 (=> @t12 (= @t45 @t54)))))) % 0.44/0.64 (assume @p19 (forall @t18 (=> @t16 @t55))) % 0.44/0.64 (assume @p20 (forall @t18 (=> @t46 @t55))) % 0.44/0.64 (assume @p21 (forall @t18 (=> @t16 (forall @t14 (=> @t12 (tptp.ilf_type @t48 tptp.set_type)))))) % 0.44/0.64 (assume @p22 (forall @t18 (=> @t16 (forall @t14 (=> @t12 (= (tptp.member @t2 (tptp.power_set @t3)) @t54)))))) % 0.44/0.64 (assume @p23 (forall @t18 (=> @t16 (and (not (tptp.empty @t51)) (tptp.ilf_type @t51 tptp.set_type))))) % 0.44/0.64 (assume @p24 (forall @t18 (=> @t16 (forall @t14 (=> (and (not (tptp.empty @t3)) @t12) (= (tptp.ilf_type @t2 (tptp.member_type @t3)) (tptp.member @t2 @t3))))))) % 0.44/0.64 (assume @p25 (forall @t18 (=> (and (not @t56) @t16) (exists @t14 (tptp.ilf_type @t3 (tptp.member_type @t2)))))) % 0.44/0.64 (assume @p26 (forall @t18 (=> @t16 (= @t47 (forall @t14 (=> @t12 (=> @t31 (exists @t10 (and @t33 (exists @t44 (and @t43 (= @t3 @t42)))))))))))) % 0.44/0.64 (assume @p27 (forall @t18 (=> @t16 (forall @t14 (=> @t12 (forall @t10 (=> @t50 (tptp.relation_like @t1)))))))) % 0.44/0.64 (assume @p28 (forall @t18 (=> @t16 (= @t56 (forall @t14 (=> @t12 (not @t31))))))) % 0.44/0.64 (assume @p29 (forall @t18 (=> (and @t56 @t16) @t47))) % 0.44/0.64 (assume @p30 (forall @t18 (=> @t16 (forall @t14 (=> @t12 (forall @t10 (=> @t25 (= @t21 (tptp.domain_of @t1))))))))) % 0.44/0.64 (assume @p31 (forall @t18 (=> @t16 (forall @t14 (=> @t12 (forall @t10 (=> @t25 (tptp.ilf_type @t21 @t52)))))))) % 0.44/0.64 (assume @p32 (forall @t18 (=> @t16 (forall @t14 (=> @t12 (forall @t10 (=> @t25 (= @t20 (tptp.range_of @t1))))))))) % 0.44/0.64 (assume @p33 (forall @t18 (=> @t16 (forall @t14 (=> @t12 (forall @t10 (=> @t25 (tptp.ilf_type @t20 (tptp.subset_type @t3))))))))) % 0.44/0.64 (assume @p34 (forall @t18 @t16)) % 0.44/0.64 (assume @p35 @t63) % 0.44/0.64 (assume @p36 true) % 0.44/0.64 (step @p37 :rule aci_norm :args ((= @t71 @t69))) % 0.44/0.64 (step @p38 :rule cong :premises (@p37) :args (@t73)) % 0.44/0.64 (step @p39 :rule quant-merge-prenex :args ((= (forall @t18 @t75) @t73))) % 0.44/0.64 (step @p40 :rule alpha_equiv :args (@t76 (@list @t64) @t77)) % 0.44/0.64 (step @p41 :rule refl :args (@t68)) % 0.44/0.64 (step @p42 :rule nary_cong :premises (@p41 @p40) :args (@t78)) % 0.44/0.64 (step @p43 :rule quant-miniscope-or :args ((= @t75 @t78))) % 0.44/0.64 (step @p44 :rule trans :premises (@p43 @p42)) % 0.44/0.64 (step @p45 :rule symm :premises (@p44)) % 0.44/0.64 (step @p46 :rule cong :premises (@p45) :args ((forall @t18 (or @t68 @t82)))) % 0.44/0.64 (step @p47 :rule trans :premises (@p46 @p39)) % 0.44/0.64 (step @p48 :rule trans :premises (@p47 @p38)) % 0.44/0.64 (step @p49 :rule bool-impl-elim :args (@t16 @t82)) % 0.44/0.64 (step @p50 :rule cong :premises (@p49) :args ((forall @t18 (=> @t16 @t82)))) % 0.44/0.64 (step @p51 :rule trans :premises (@p50 @p48)) % 0.44/0.64 (step @p52 :rule aci_norm :args ((= (or @t80 (or @t79 @t57)) @t81))) % 0.44/0.64 (step @p53 :rule bool-impl-elim :args (@t58 @t57)) % 0.44/0.64 (step @p54 :rule refl :args (@t80)) % 0.44/0.64 (step @p55 :rule nary_cong :premises (@p54 @p53) :args ((or @t80 @t59))) % 0.44/0.64 (step @p56 :rule trans :premises (@p55 @p52)) % 0.44/0.64 (step @p57 :rule bool-impl-elim :args (@t36 @t59)) % 0.44/0.64 (step @p58 :rule trans :premises (@p57 @p56)) % 0.44/0.64 (step @p59 :rule cong :premises (@p58) :args (@t60)) % 0.44/0.64 (step @p60 :rule refl :args (@t16)) % 0.44/0.64 (step @p61 :rule cong :premises (@p60 @p59) :args (@t61)) % 0.44/0.64 (step @p62 :rule cong :premises (@p61) :args (@t62)) % 0.44/0.64 (step @p63 :rule trans :premises (@p62 @p51)) % 0.44/0.64 (step @p64 :rule cong :premises (@p63) :args (@t63)) % 0.44/0.64 (step @p65 :rule eq_resolve :premises (@p35 @p64)) % 0.44/0.64 (step @p66 :rule skolemize :premises (@p65)) % 0.44/0.64 (step @p67 :rule cnf_or_neg :args (@t97 3)) % 0.44/0.64 (step @p68 :rule chain_m_resolution :premises (@p67 @p66) :args ((not @t90) @t98 @t99)) % 0.44/0.64 (step @p69 :rule aci_norm :args ((= @t107 (or @t68 @t105 @t104 @t103 @t102)))) % 0.44/0.64 (step @p70 :rule cong :premises (@p69) :args (@t108)) % 0.44/0.64 (step @p71 :rule quant-merge-prenex :args ((= (forall @t18 @t110) @t108))) % 0.44/0.64 (step @p72 :rule alpha_equiv :args (@t111 (@list @t101 @t100) (@list @t3 @t112))) % 0.44/0.64 (step @p73 :rule nary_cong :premises (@p41 @p72) :args (@t113)) % 0.44/0.64 (step @p74 :rule quant-miniscope-or :args ((= @t110 @t113))) % 0.44/0.64 (step @p75 :rule trans :premises (@p74 @p73)) % 0.44/0.64 (step @p76 :rule symm :premises (@p75)) % 0.44/0.64 (step @p77 :rule cong :premises (@p76) :args ((forall @t18 (or @t68 @t120)))) % 0.44/0.64 (step @p78 :rule trans :premises (@p77 @p71)) % 0.44/0.64 (step @p79 :rule trans :premises (@p78 @p70)) % 0.44/0.64 (step @p80 :rule bool-impl-elim :args (@t16 @t120)) % 0.44/0.64 (step @p81 :rule cong :premises (@p80) :args ((forall @t18 (=> @t16 @t120)))) % 0.44/0.64 (step @p82 :rule trans :premises (@p81 @p79)) % 0.44/0.64 (step @p83 :rule aci_norm :args ((= @t122 @t118))) % 0.44/0.64 (step @p84 :rule cong :premises (@p83) :args (@t123)) % 0.44/0.64 (step @p85 :rule quant-merge-prenex :args ((= (forall @t14 @t125) @t123))) % 0.44/0.64 (step @p86 :rule alpha_equiv :args (@t126 (@list @t112) @t127)) % 0.44/0.64 (step @p87 :rule refl :args (@t117)) % 0.44/0.64 (step @p88 :rule nary_cong :premises (@p87 @p86) :args (@t128)) % 0.44/0.64 (step @p89 :rule quant-miniscope-or :args ((= @t125 @t128))) % 0.44/0.64 (step @p90 :rule trans :premises (@p89 @p88)) % 0.44/0.64 (step @p91 :rule symm :premises (@p90)) % 0.44/0.64 (step @p92 :rule cong :premises (@p91) :args ((forall @t14 (or @t117 @t132)))) % 0.44/0.64 (step @p93 :rule trans :premises (@p92 @p85)) % 0.44/0.64 (step @p94 :rule trans :premises (@p93 @p84)) % 0.44/0.64 (step @p95 :rule bool-impl-elim :args (@t12 @t132)) % 0.44/0.64 (step @p96 :rule cong :premises (@p95) :args ((forall @t14 (=> @t12 @t132)))) % 0.44/0.64 (step @p97 :rule trans :premises (@p96 @p94)) % 0.44/0.64 (step @p98 :rule aci_norm :args ((= (or @t130 (or @t129 @t4)) @t131))) % 0.44/0.64 (step @p99 :rule bool-impl-elim :args (@t6 @t4)) % 0.44/0.64 (step @p100 :rule refl :args (@t130)) % 0.44/0.64 (step @p101 :rule nary_cong :premises (@p100 @p99) :args ((or @t130 @t7))) % 0.44/0.64 (step @p102 :rule trans :premises (@p101 @p98)) % 0.44/0.64 (step @p103 :rule bool-impl-elim :args (@t9 @t7)) % 0.44/0.64 (step @p104 :rule trans :premises (@p103 @p102)) % 0.44/0.64 (step @p105 :rule cong :premises (@p104) :args (@t11)) % 0.44/0.64 (step @p106 :rule refl :args (@t12)) % 0.44/0.64 (step @p107 :rule cong :premises (@p106 @p105) :args (@t13)) % 0.44/0.64 (step @p108 :rule cong :premises (@p107) :args (@t15)) % 0.44/0.64 (step @p109 :rule trans :premises (@p108 @p97)) % 0.44/0.64 (step @p110 :rule cong :premises (@p60 @p109) :args (@t17)) % 0.44/0.64 (step @p111 :rule cong :premises (@p110) :args (@t19)) % 0.44/0.64 (step @p112 :rule trans :premises (@p111 @p82)) % 0.44/0.64 (step @p113 :rule eq_resolve :premises (@p1 @p112)) % 0.44/0.64 (step @p114 :rule instantiate :premises (@p113) :args (@t133)) % 0.44/0.64 (step @p115 :rule aci_norm :args ((= @t138 (or @t68 @t136 @t135)))) % 0.44/0.64 (step @p116 :rule cong :premises (@p115) :args (@t139)) % 0.44/0.64 (step @p117 :rule quant-merge-prenex :args ((= (forall @t18 @t141) @t139))) % 0.44/0.64 (step @p118 :rule alpha_equiv :args (@t142 (@list @t134) @t77)) % 0.44/0.64 (step @p119 :rule nary_cong :premises (@p41 @p118) :args (@t143)) % 0.44/0.64 (step @p120 :rule quant-miniscope-or :args ((= @t141 @t143))) % 0.44/0.64 (step @p121 :rule trans :premises (@p120 @p119)) % 0.44/0.64 (step @p122 :rule symm :premises (@p121)) % 0.44/0.64 (step @p123 :rule cong :premises (@p122) :args ((forall @t18 (or @t68 @t144)))) % 0.44/0.64 (step @p124 :rule trans :premises (@p123 @p117)) % 0.44/0.64 (step @p125 :rule trans :premises (@p124 @p116)) % 0.44/0.64 (step @p126 :rule bool-impl-elim :args (@t16 @t144)) % 0.44/0.64 (step @p127 :rule cong :premises (@p126) :args ((forall @t18 (=> @t16 @t144)))) % 0.44/0.64 (step @p128 :rule trans :premises (@p127 @p125)) % 0.44/0.64 (step @p129 :rule bool-impl-elim :args (@t12 @t37)) % 0.44/0.64 (step @p130 :rule cong :premises (@p129) :args (@t38)) % 0.44/0.64 (step @p131 :rule cong :premises (@p60 @p130) :args (@t39)) % 0.44/0.64 (step @p132 :rule cong :premises (@p131) :args (@t40)) % 0.44/0.64 (step @p133 :rule trans :premises (@p132 @p128)) % 0.44/0.64 (step @p134 :rule eq_resolve :premises (@p5 @p133)) % 0.44/0.64 (step @p135 :rule instantiate :premises (@p134) :args ((@list @t85 @t84))) % 0.44/0.64 (step @p136 :rule instantiate :premises (@p34) :args ((@list @t84))) % 0.44/0.64 (step @p137 :rule bool-double-not-elim :args (@t95)) % 0.44/0.64 (step @p138 :rule refl :args (@t97)) % 0.44/0.64 (step @p139 :rule nary_cong :premises (@p138 @p137) :args ((or @t97 (not @t96)))) % 0.44/0.64 (step @p140 :rule cnf_or_neg :args (@t97 0)) % 0.44/0.64 (step @p141 :rule eq_resolve :premises (@p140 @p139)) % 0.44/0.64 (step @p142 :rule reordering :premises (@p141) :args ((or @t95 @t97))) % 0.44/0.64 (step @p143 :rule chain_m_resolution :premises (@p142 @p66) :args (@t95 @t98 @t99)) % 0.44/0.64 (step @p144 :rule cnf_or_pos :args (@t149)) % 0.44/0.64 (step @p145 :rule reordering :premises (@p144) :args ((or @t96 @t148 @t146 (not @t149)))) % 0.44/0.64 (step @p146 :rule chain_m_resolution :premises (@p145 @p143 @p136 @p135) :args (@t146 (@list false false false) (@list @t95 @t147 @t149))) % 0.44/0.64 (step @p147 :rule bool-double-not-elim :args (@t93)) % 0.44/0.64 (step @p148 :rule nary_cong :premises (@p138 @p147) :args ((or @t97 (not @t94)))) % 0.44/0.64 (step @p149 :rule cnf_or_neg :args (@t97 1)) % 0.44/0.64 (step @p150 :rule eq_resolve :premises (@p149 @p148)) % 0.44/0.64 (step @p151 :rule reordering :premises (@p150) :args ((or @t93 @t97))) % 0.44/0.64 (step @p152 :rule chain_m_resolution :premises (@p151 @p66) :args (@t93 @t98 @t99)) % 0.44/0.64 (step @p153 :rule cnf_equiv_pos1 :args (@t146)) % 0.44/0.64 (step @p154 :rule reordering :premises (@p153) :args ((or @t94 @t145 (not @t146)))) % 0.44/0.64 (step @p155 :rule chain_m_resolution :premises (@p154 @p152 @p146) :args (@t145 (@list false false) (@list @t93 @t146))) % 0.44/0.64 (step @p156 :rule bool-double-not-elim :args (@t91)) % 0.44/0.64 (step @p157 :rule nary_cong :premises (@p138 @p156) :args ((or @t97 (not @t92)))) % 0.44/0.64 (step @p158 :rule cnf_or_neg :args (@t97 2)) % 0.44/0.64 (step @p159 :rule eq_resolve :premises (@p158 @p157)) % 0.44/0.64 (step @p160 :rule reordering :premises (@p159) :args ((or @t91 @t97))) % 0.44/0.64 (step @p161 :rule chain_m_resolution :premises (@p160 @p66) :args (@t91 @t98 @t99)) % 0.44/0.64 (step @p162 :rule cnf_or_pos :args (@t152)) % 0.44/0.64 (step @p163 :rule factoring :premises (@p162)) % 0.44/0.64 (step @p164 :rule reordering :premises (@p163) :args ((or @t96 @t92 @t151 @t150 (not @t152)))) % 0.44/0.64 (step @p165 :rule chain_m_resolution :premises (@p164 @p143 @p161 @p155 @p114) :args (@t150 @t153 (@list @t95 @t91 @t145 @t152))) % 0.44/0.64 (step @p166 :rule cnf_and_pos :args (@t150 0)) % 0.44/0.64 (step @p167 :rule reordering :premises (@p166) :args ((or @t89 (not @t150)))) % 0.44/0.64 (step @p168 :rule chain_m_resolution :premises (@p167 @p165) :args (@t89 @t154 (@list @t150))) % 0.44/0.64 (step @p169 :rule aci_norm :args ((= @t162 (or @t68 @t160 @t159 @t158 @t157)))) % 0.44/0.64 (step @p170 :rule cong :premises (@p169) :args (@t163)) % 0.44/0.64 (step @p171 :rule quant-merge-prenex :args ((= (forall @t18 @t165) @t163))) % 0.44/0.64 (step @p172 :rule alpha_equiv :args (@t166 (@list @t156 @t155) (@list @t3 @t167))) % 0.44/0.64 (step @p173 :rule nary_cong :premises (@p41 @p172) :args (@t168)) % 0.44/0.64 (step @p174 :rule quant-miniscope-or :args ((= @t165 @t168))) % 0.44/0.64 (step @p175 :rule trans :premises (@p174 @p173)) % 0.44/0.64 (step @p176 :rule symm :premises (@p175)) % 0.44/0.64 (step @p177 :rule cong :premises (@p176) :args ((forall @t18 (or @t68 @t174)))) % 0.44/0.64 (step @p178 :rule trans :premises (@p177 @p171)) % 0.44/0.64 (step @p179 :rule trans :premises (@p178 @p170)) % 0.44/0.64 (step @p180 :rule bool-impl-elim :args (@t16 @t174)) % 0.44/0.64 (step @p181 :rule cong :premises (@p180) :args ((forall @t18 (=> @t16 @t174)))) % 0.44/0.64 (step @p182 :rule trans :premises (@p181 @p179)) % 0.44/0.64 (step @p183 :rule aci_norm :args ((= @t176 @t172))) % 0.44/0.64 (step @p184 :rule cong :premises (@p183) :args (@t177)) % 0.44/0.64 (step @p185 :rule quant-merge-prenex :args ((= (forall @t14 @t179) @t177))) % 0.44/0.64 (step @p186 :rule alpha_equiv :args (@t180 (@list @t167) @t127)) % 0.44/0.64 (step @p187 :rule nary_cong :premises (@p87 @p186) :args (@t181)) % 0.44/0.64 (step @p188 :rule quant-miniscope-or :args ((= @t179 @t181))) % 0.44/0.64 (step @p189 :rule trans :premises (@p188 @p187)) % 0.44/0.64 (step @p190 :rule symm :premises (@p189)) % 0.44/0.64 (step @p191 :rule cong :premises (@p190) :args ((forall @t14 (or @t117 @t184)))) % 0.44/0.64 (step @p192 :rule trans :premises (@p191 @p185)) % 0.44/0.64 (step @p193 :rule trans :premises (@p192 @p184)) % 0.44/0.64 (step @p194 :rule bool-impl-elim :args (@t12 @t184)) % 0.44/0.64 (step @p195 :rule cong :premises (@p194) :args ((forall @t14 (=> @t12 @t184)))) % 0.44/0.64 (step @p196 :rule trans :premises (@p195 @p193)) % 0.44/0.64 (step @p197 :rule aci_norm :args ((= (or @t182 (or @t129 @t22)) @t183))) % 0.44/0.64 (step @p198 :rule bool-impl-elim :args (@t6 @t22)) % 0.44/0.64 (step @p199 :rule refl :args (@t182)) % 0.44/0.64 (step @p200 :rule nary_cong :premises (@p199 @p198) :args ((or @t182 @t23))) % 0.44/0.64 (step @p201 :rule trans :premises (@p200 @p197)) % 0.44/0.64 (step @p202 :rule bool-impl-elim :args (@t25 @t23)) % 0.44/0.64 (step @p203 :rule trans :premises (@p202 @p201)) % 0.44/0.64 (step @p204 :rule cong :premises (@p203) :args (@t26)) % 0.44/0.64 (step @p205 :rule cong :premises (@p106 @p204) :args (@t27)) % 0.44/0.64 (step @p206 :rule cong :premises (@p205) :args (@t28)) % 0.44/0.64 (step @p207 :rule trans :premises (@p206 @p196)) % 0.44/0.64 (step @p208 :rule cong :premises (@p60 @p207) :args (@t29)) % 0.44/0.64 (step @p209 :rule cong :premises (@p208) :args (@t30)) % 0.44/0.64 (step @p210 :rule trans :premises (@p209 @p182)) % 0.44/0.64 (step @p211 :rule eq_resolve :premises (@p2 @p210)) % 0.44/0.64 (step @p212 :rule instantiate :premises (@p211) :args (@t133)) % 0.44/0.64 (step @p213 :rule cnf_or_pos :args (@t186)) % 0.44/0.64 (step @p214 :rule factoring :premises (@p213)) % 0.44/0.64 (step @p215 :rule reordering :premises (@p214) :args ((or @t96 @t92 @t151 @t185 (not @t186)))) % 0.44/0.64 (step @p216 :rule chain_m_resolution :premises (@p215 @p143 @p161 @p155 @p212) :args (@t185 @t153 (@list @t95 @t91 @t145 @t186))) % 0.44/0.64 (step @p217 :rule cnf_and_pos :args (@t185 1)) % 0.44/0.64 (step @p218 :rule reordering :premises (@p217) :args ((or @t87 (not @t185)))) % 0.44/0.64 (step @p219 :rule chain_m_resolution :premises (@p218 @p216) :args (@t87 @t154 (@list @t185))) % 0.44/0.64 (step @p220 :rule cnf_and_neg :args (@t90)) % 0.44/0.64 (step @p221 false :rule chain_m_resolution :premises (@p220 @p219 @p168 @p68) :args (false (@list false false true) (@list @t87 @t89 @t90))) % 0.44/0.64 ) % 0.44/0.64 % SZS output end Proof % 0.44/0.64 % cvc5 exiting %------------------------------------------------------------------------------