%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU200+2 : TPTP v9.2.1. Released v3.3.0. % 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 08:50:56 AM UTC 2026 % Result : Theorem 0.37s 0.68s % Output : Proof 0.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU200+2 : TPTP v9.2.1. Released v3.3.0. % 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 16:37:40 EDT 2026 % 0.17/0.35 % CPUTime : % 0.31/0.53 %----Proving TF0_NAR, FOF, or CNF % 0.37/0.68 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.37/0.68 % SZS status Theorem % 0.37/0.68 % SZS output start Proof % 0.37/0.68 ( % 0.37/0.68 (declare-sort $$unsorted 0) % 0.37/0.68 (declare-const tptp.subset_difference (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.37/0.68 (declare-const tptp.union_of_subsets (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.68 (declare-const tptp.relation_dom_restriction (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.68 (declare-const tptp.cartesian_product2 (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.68 (declare-const tptp.relation_rng_restriction (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.68 (declare-const tptp.are_equipotent (-> $$unsorted $$unsorted Bool)) % 0.37/0.68 (declare-const tptp.meet_of_subsets (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.68 (declare-const tptp.relation_composition (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.68 (declare-const tptp.set_union2 (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.68 (declare-const tptp.identity_relation (-> $$unsorted $$unsorted)) % 0.37/0.68 (declare-const tptp.relation_inverse (-> $$unsorted $$unsorted)) % 0.37/0.68 (declare-const tptp.ordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.68 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 0.37/0.68 (declare-const tptp.relation_rng (-> $$unsorted $$unsorted)) % 0.37/0.68 (declare-const tptp.set_intersection2 (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.68 (declare-const tptp.relation_field (-> $$unsorted $$unsorted)) % 0.37/0.68 (declare-const tptp.unordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.68 (declare-const tptp.subset_complement (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.68 (declare-const tptp.empty_set $$unsorted) % 0.37/0.68 (declare-const tptp.empty (-> $$unsorted Bool)) % 0.37/0.68 (declare-const tptp.complements_of_subsets (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.68 (declare-const tptp.relation (-> $$unsorted Bool)) % 0.37/0.68 (declare-const tptp.proper_subset (-> $$unsorted $$unsorted Bool)) % 0.37/0.68 (declare-const tptp.relation_dom (-> $$unsorted $$unsorted)) % 0.37/0.68 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 0.37/0.68 (declare-const tptp.disjoint (-> $$unsorted $$unsorted Bool)) % 0.37/0.68 (declare-const tptp.powerset (-> $$unsorted $$unsorted)) % 0.37/0.68 (declare-const tptp.set_meet (-> $$unsorted $$unsorted)) % 0.37/0.68 (declare-const tptp.union (-> $$unsorted $$unsorted)) % 0.37/0.68 (declare-const tptp.element (-> $$unsorted $$unsorted Bool)) % 0.37/0.68 (declare-const tptp.cast_to_subset (-> $$unsorted $$unsorted)) % 0.37/0.68 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 0.37/0.68 (declare-const tptp.set_difference (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.68 (define @t1 () (@var "A" $$unsorted)) % 0.37/0.68 (define @t2 () (@var "B" $$unsorted)) % 0.37/0.68 (define @t3 () (tptp.in @t2 @t1)) % 0.37/0.68 (define @t4 () (not @t3)) % 0.37/0.68 (define @t5 () (tptp.in @t1 @t2)) % 0.37/0.68 (define @t6 () (@list @t1 @t2)) % 0.37/0.68 (define @t7 () (tptp.proper_subset @t2 @t1)) % 0.37/0.68 (define @t8 () (tptp.proper_subset @t1 @t2)) % 0.37/0.68 (define @t9 () (tptp.relation @t1)) % 0.37/0.68 (define @t10 () (tptp.empty @t1)) % 0.37/0.68 (define @t11 () (@list @t1)) % 0.37/0.68 (define @t12 () (tptp.unordered_pair @t1 @t2)) % 0.37/0.68 (define @t13 () (tptp.set_union2 @t2 @t1)) % 0.37/0.68 (define @t14 () (tptp.set_union2 @t1 @t2)) % 0.37/0.68 (define @t15 () (tptp.set_intersection2 @t1 @t2)) % 0.37/0.68 (define @t16 () (@var "D" $$unsorted)) % 0.37/0.68 (define @t17 () (@var "C" $$unsorted)) % 0.37/0.68 (define @t18 () (tptp.in @t17 @t1)) % 0.37/0.68 (define @t19 () (tptp.ordered_pair @t17 @t16)) % 0.37/0.68 (define @t20 () (tptp.in @t19 @t2)) % 0.37/0.68 (define @t21 () (@list @t17 @t16)) % 0.37/0.68 (define @t22 () (tptp.identity_relation @t1)) % 0.37/0.68 (define @t23 () (tptp.relation @t2)) % 0.37/0.68 (define @t24 () (tptp.subset @t1 @t2)) % 0.37/0.68 (define @t25 () (= @t1 @t2)) % 0.37/0.68 (define @t26 () (@var "E" $$unsorted)) % 0.37/0.68 (define @t27 () (tptp.ordered_pair @t16 @t26)) % 0.37/0.68 (define @t28 () (tptp.in @t16 @t2)) % 0.37/0.68 (define @t29 () (tptp.in @t27 @t17)) % 0.37/0.68 (define @t30 () (@list @t16 @t26)) % 0.37/0.68 (define @t31 () (tptp.relation_dom_restriction @t1 @t2)) % 0.37/0.68 (define @t32 () (tptp.relation @t17)) % 0.37/0.68 (define @t33 () (@list @t2 @t17)) % 0.37/0.68 (define @t34 () (tptp.in @t26 @t1)) % 0.37/0.68 (define @t35 () (tptp.relation_rng_restriction @t1 @t2)) % 0.37/0.68 (define @t36 () (@list @t17)) % 0.37/0.68 (define @t37 () (@list @t2)) % 0.37/0.68 (define @t38 () (= @t2 tptp.empty_set)) % 0.37/0.68 (define @t39 () (= @t2 (tptp.set_meet @t1))) % 0.37/0.68 (define @t40 () (= @t1 tptp.empty_set)) % 0.37/0.68 (define @t41 () (tptp.in @t17 @t16)) % 0.37/0.68 (define @t42 () (tptp.in @t16 @t1)) % 0.37/0.68 (define @t43 () (@list @t16)) % 0.37/0.68 (define @t44 () (tptp.in @t17 @t2)) % 0.37/0.68 (define @t45 () (not @t40)) % 0.37/0.68 (define @t46 () (tptp.singleton @t1)) % 0.37/0.68 (define @t47 () (tptp.powerset @t1)) % 0.37/0.68 (define @t48 () (tptp.in @t19 @t1)) % 0.37/0.68 (define @t49 () (tptp.empty @t2)) % 0.37/0.68 (define @t50 () (tptp.element @t2 @t1)) % 0.37/0.68 (define @t51 () (not @t10)) % 0.37/0.68 (define @t52 () (tptp.in @t16 @t17)) % 0.37/0.68 (define @t53 () (@list @t1 @t2 @t17)) % 0.37/0.68 (define @t54 () (@var "F" $$unsorted)) % 0.37/0.68 (define @t55 () (tptp.cartesian_product2 @t1 @t2)) % 0.37/0.68 (define @t56 () (forall @t36 (=> @t18 @t44))) % 0.37/0.68 (define @t57 () (tptp.relation_dom @t1)) % 0.37/0.68 (define @t58 () (tptp.cast_to_subset @t1)) % 0.37/0.68 (define @t59 () (tptp.set_difference @t1 @t2)) % 0.37/0.68 (define @t60 () (tptp.in (tptp.ordered_pair @t16 @t17) @t1)) % 0.37/0.68 (define @t61 () (tptp.relation_rng @t1)) % 0.37/0.68 (define @t62 () (tptp.subset_complement @t1 @t2)) % 0.37/0.68 (define @t63 () (tptp.element @t2 @t47)) % 0.37/0.68 (define @t64 () (tptp.ordered_pair @t1 @t2)) % 0.37/0.68 (define @t65 () (tptp.relation_inverse @t1)) % 0.37/0.68 (define @t66 () (tptp.disjoint @t1 @t2)) % 0.37/0.68 (define @t67 () (tptp.relation_composition @t1 @t2)) % 0.37/0.68 (define @t68 () (tptp.complements_of_subsets @t1 @t2)) % 0.37/0.68 (define @t69 () (tptp.powerset @t47)) % 0.37/0.68 (define @t70 () (tptp.element @t2 @t69)) % 0.37/0.68 (define @t71 () (not @t25)) % 0.37/0.68 (define @t72 () (tptp.relation @t67)) % 0.37/0.68 (define @t73 () (and @t9 @t23)) % 0.37/0.68 (define @t74 () (tptp.union_of_subsets @t1 @t2)) % 0.37/0.68 (define @t75 () (tptp.meet_of_subsets @t1 @t2)) % 0.37/0.68 (define @t76 () (tptp.subset_difference @t1 @t2 @t17)) % 0.37/0.68 (define @t77 () (tptp.element @t17 @t47)) % 0.37/0.68 (define @t78 () (and @t63 @t77)) % 0.37/0.68 (define @t79 () (tptp.relation @t35)) % 0.37/0.68 (define @t80 () (forall @t6 (=> @t23 @t79))) % 0.37/0.68 (define @t81 () (tptp.relation_composition @t2 @t1)) % 0.37/0.68 (define @t82 () (and @t10 @t23)) % 0.37/0.68 (define @t83 () (tptp.empty tptp.empty_set)) % 0.37/0.68 (define @t84 () (not @t49)) % 0.37/0.68 (define @t85 () (tptp.empty @t57)) % 0.37/0.68 (define @t86 () (and @t51 @t9)) % 0.37/0.68 (define @t87 () (tptp.empty @t61)) % 0.37/0.68 (define @t88 () (tptp.disjoint @t46 @t2)) % 0.37/0.68 (define @t89 () (tptp.singleton @t2)) % 0.37/0.68 (define @t90 () (tptp.union @t2)) % 0.37/0.68 (define @t91 () (tptp.in @t1 @t17)) % 0.37/0.68 (define @t92 () (@list @t1 @t2 @t17 @t16)) % 0.37/0.68 (define @t93 () (tptp.element @t1 (tptp.powerset @t2))) % 0.37/0.68 (define @t94 () (tptp.set_difference @t2 @t17)) % 0.37/0.68 (define @t95 () (= @t1 @t17)) % 0.37/0.68 (define @t96 () (tptp.relation_rng @t17)) % 0.37/0.68 (define @t97 () (tptp.relation_rng @t35)) % 0.37/0.68 (define @t98 () (tptp.subset @t35 @t2)) % 0.37/0.68 (define @t99 () (forall @t6 (=> @t23 @t98))) % 0.37/0.68 (define @t100 () (tptp.relation_rng @t2)) % 0.37/0.68 (define @t101 () (tptp.subset @t97 @t100)) % 0.37/0.68 (define @t102 () (forall @t6 (=> @t23 @t101))) % 0.37/0.68 (define @t103 () (not @t102)) % 0.37/0.68 (define @t104 () (tptp.cartesian_product2 @t1 @t17)) % 0.37/0.68 (define @t105 () (not @t44)) % 0.37/0.68 (define @t106 () (tptp.subset @t17 @t2)) % 0.37/0.68 (define @t107 () (forall @t36 (not (and @t106 (not (tptp.are_equipotent @t17 @t2)) @t105)))) % 0.37/0.68 (define @t108 () (tptp.powerset @t17)) % 0.37/0.68 (define @t109 () (forall @t21 (=> (and @t44 (tptp.subset @t16 @t17)) @t28))) % 0.37/0.68 (define @t110 () (tptp.set_intersection2 @t2 @t17)) % 0.37/0.68 (define @t111 () (tptp.subset @t1 @t17)) % 0.37/0.68 (define @t112 () (tptp.element @t1 @t2)) % 0.37/0.68 (define @t113 () (tptp.in @t1 (tptp.relation_dom @t17))) % 0.37/0.68 (define @t114 () (tptp.in @t64 @t17)) % 0.37/0.68 (define @t115 () (tptp.relation_dom @t2)) % 0.37/0.68 (define @t116 () (and (tptp.subset @t57 @t115) (tptp.subset @t61 @t100))) % 0.37/0.68 (define @t117 () (=> @t24 @t116)) % 0.37/0.68 (define @t118 () (forall @t37 (=> @t23 @t117))) % 0.37/0.68 (define @t119 () (=> @t9 @t118)) % 0.37/0.68 (define @t120 () (forall @t11 @t119)) % 0.37/0.68 (define @t121 () (tptp.relation_field @t17)) % 0.37/0.68 (define @t122 () (tptp.in @t2 @t17)) % 0.37/0.68 (define @t123 () (tptp.set_union2 @t1 (tptp.set_difference @t2 @t1))) % 0.37/0.68 (define @t124 () (and @t18 @t44)) % 0.37/0.68 (define @t125 () (not @t66)) % 0.37/0.68 (define @t126 () (tptp.subset_complement @t1 @t17)) % 0.37/0.68 (define @t127 () (tptp.disjoint @t2 @t17)) % 0.37/0.68 (define @t128 () (tptp.relation_dom @t67)) % 0.37/0.68 (define @t129 () (not @t38)) % 0.37/0.68 (define @t130 () (tptp.element @t2 @t108)) % 0.37/0.68 (define @t131 () (tptp.in @t17 @t15)) % 0.37/0.68 (define @t132 () (= @t61 tptp.empty_set)) % 0.37/0.68 (define @t133 () (= @t57 tptp.empty_set)) % 0.37/0.68 (define @t134 () (tptp.relation_dom_restriction @t2 @t1)) % 0.37/0.68 (define @t135 () (= @t46 (tptp.unordered_pair @t2 @t17))) % 0.37/0.68 (define @t136 () (not @t23)) % 0.37/0.68 (define @t137 () (forall @t6 (or @t136 @t101))) % 0.37/0.68 (define @t138 () (@quantifiers_skolemize @t137 1)) % 0.37/0.68 (define @t139 () (tptp.relation @t138)) % 0.37/0.68 (define @t140 () (@quantifiers_skolemize @t137 0)) % 0.37/0.68 (define @t141 () (tptp.relation_rng_restriction @t140 @t138)) % 0.37/0.68 (define @t142 () (tptp.subset (tptp.relation_rng @t141) (tptp.relation_rng @t138))) % 0.37/0.68 (define @t143 () (not @t139)) % 0.37/0.68 (define @t144 () (or @t143 @t142)) % 0.37/0.68 (define @t145 () (@list true)) % 0.37/0.68 (define @t146 () (@list @t144)) % 0.37/0.68 (define @t147 () (@var "BOUND_VARIABLE_9138" $$unsorted)) % 0.37/0.68 (define @t148 () (and (tptp.subset @t57 (tptp.relation_dom @t147)) (tptp.subset @t61 (tptp.relation_rng @t147)))) % 0.37/0.68 (define @t149 () (not (tptp.subset @t1 @t147))) % 0.37/0.68 (define @t150 () (not (tptp.relation @t147))) % 0.37/0.68 (define @t151 () (not @t9)) % 0.37/0.68 (define @t152 () (or @t150 @t149 @t148)) % 0.37/0.68 (define @t153 () (or @t151 @t152)) % 0.37/0.68 (define @t154 () (forall (@list @t1 @t147) @t153)) % 0.37/0.68 (define @t155 () (@list @t147)) % 0.37/0.68 (define @t156 () (forall @t155 @t153)) % 0.37/0.68 (define @t157 () (forall @t155 @t152)) % 0.37/0.68 (define @t158 () (or @t151 @t157)) % 0.37/0.68 (define @t159 () (not @t24)) % 0.37/0.68 (define @t160 () (or @t136 @t159 @t116)) % 0.37/0.68 (define @t161 () (forall @t37 @t160)) % 0.37/0.68 (define @t162 () (and (tptp.subset (tptp.relation_dom @t141) (tptp.relation_dom @t138)) @t142)) % 0.37/0.68 (define @t163 () (not @t162)) % 0.37/0.68 (define @t164 () (@list @t140 @t138)) % 0.37/0.68 (define @t165 () (tptp.relation @t141)) % 0.37/0.68 (define @t166 () (or @t143 @t165)) % 0.37/0.68 (define @t167 () (@list false false)) % 0.37/0.68 (define @t168 () (tptp.subset @t141 @t138)) % 0.37/0.68 (define @t169 () (or @t143 @t168)) % 0.37/0.68 (define @t170 () (not @t168)) % 0.37/0.68 (define @t171 () (not @t165)) % 0.37/0.68 (define @t172 () (or @t171 @t143 @t170 @t162)) % 0.37/0.68 (assume @p1 (forall @t6 (=> @t5 @t4))) % 0.37/0.68 (assume @p2 (forall @t6 (=> @t8 (not @t7)))) % 0.37/0.68 (assume @p3 (forall @t11 (=> @t10 @t9))) % 0.37/0.68 (assume @p4 (forall @t6 (= @t12 (tptp.unordered_pair @t2 @t1)))) % 0.37/0.68 (assume @p5 (forall @t6 (= @t14 @t13))) % 0.37/0.68 (assume @p6 (forall @t6 (= @t15 (tptp.set_intersection2 @t2 @t1)))) % 0.37/0.68 (assume @p7 (forall @t6 (=> @t23 (= (= @t2 @t22) (forall @t21 (= @t20 (and @t18 (= @t17 @t16)))))))) % 0.37/0.68 (assume @p8 (forall @t6 (= @t25 (and @t24 (tptp.subset @t2 @t1))))) % 0.37/0.68 (assume @p9 (forall @t11 (=> @t9 (forall @t33 (=> @t32 (= (= @t17 @t31) (forall @t30 (= @t29 (and @t28 (tptp.in @t27 @t1)))))))))) % 0.37/0.68 (assume @p10 (forall @t6 (=> @t23 (forall @t36 (=> @t32 (= (= @t17 @t35) (forall @t30 (= @t29 (and @t34 (tptp.in @t27 @t2)))))))))) % 0.37/0.68 (assume @p11 (forall @t11 (= @t9 (forall @t37 (not (and @t3 (forall @t21 (not (= @t2 @t19))))))))) % 0.37/0.68 (assume @p12 (forall @t6 (and (=> @t45 (= @t39 (forall @t36 (= @t44 (forall @t43 (=> @t42 @t41)))))) (=> @t40 (= @t39 @t38))))) % 0.37/0.68 (assume @p13 (forall @t6 (= (= @t2 @t46) (forall @t36 (= @t44 (= @t17 @t1)))))) % 0.37/0.68 (assume @p14 (forall @t11 (= @t40 (forall @t37 @t4)))) % 0.37/0.68 (assume @p15 (forall @t6 (= (= @t2 @t47) (forall @t36 (= @t44 (tptp.subset @t17 @t1)))))) % 0.37/0.68 (assume @p16 (forall @t11 (=> @t9 (forall @t37 (=> @t23 (= @t25 (forall @t21 (= @t48 @t20)))))))) % 0.37/0.68 (assume @p17 (forall @t6 (and (=> @t51 (= @t50 @t3)) (=> @t10 (= @t50 @t49))))) % 0.37/0.68 (assume @p18 (forall @t53 (= (= @t17 @t12) (forall @t43 (= @t52 (or (= @t16 @t1) (= @t16 @t2))))))) % 0.37/0.68 (assume @p19 (forall @t53 (= (= @t17 @t14) (forall @t43 (= @t52 (or @t42 @t28)))))) % 0.37/0.68 (assume @p20 (forall @t53 (= (= @t17 @t55) (forall @t43 (= @t52 (exists (@list @t26 @t54) (and @t34 (tptp.in @t54 @t2) (= @t16 (tptp.ordered_pair @t26 @t54))))))))) % 0.37/0.68 (assume @p21 (forall @t11 (=> @t9 (forall @t37 (=> @t23 (= @t24 (forall @t21 (=> @t48 @t20)))))))) % 0.37/0.68 (assume @p22 (forall @t6 (= @t24 @t56))) % 0.37/0.68 (assume @p23 (forall @t53 (= (= @t17 @t15) (forall @t43 (= @t52 (and @t42 @t28)))))) % 0.37/0.68 (assume @p24 (forall @t11 (=> @t9 (forall @t37 (= (= @t2 @t57) (forall @t36 (= @t44 (exists @t43 @t48)))))))) % 0.37/0.68 (assume @p25 (forall @t11 (= @t58 @t1))) % 0.37/0.68 (assume @p26 (forall @t6 (= (= @t2 (tptp.union @t1)) (forall @t36 (= @t44 (exists @t43 (and @t41 @t42))))))) % 0.37/0.68 (assume @p27 (forall @t53 (= (= @t17 @t59) (forall @t43 (= @t52 (and @t42 (not @t28))))))) % 0.37/0.68 (assume @p28 (forall @t11 (=> @t9 (forall @t37 (= (= @t2 @t61) (forall @t36 (= @t44 (exists @t43 @t60)))))))) % 0.37/0.68 (assume @p29 (forall @t6 (=> @t63 (= @t62 @t59)))) % 0.37/0.68 (assume @p30 (forall @t6 (= @t64 (tptp.unordered_pair @t12 @t46)))) % 0.37/0.68 (assume @p31 (forall @t11 (=> @t9 (= (tptp.relation_field @t1) (tptp.set_union2 @t57 @t61))))) % 0.37/0.68 (assume @p32 (forall @t11 (=> @t9 (forall @t37 (=> @t23 (= (= @t2 @t65) (forall @t21 (= @t20 @t60)))))))) % 0.37/0.68 (assume @p33 (forall @t6 (= @t66 (= @t15 tptp.empty_set)))) % 0.37/0.68 (assume @p34 (forall @t11 (=> @t9 (forall @t37 (=> @t23 (forall @t36 (=> @t32 (= (= @t17 @t67) (forall @t30 (= @t29 (exists (@list @t54) (and (tptp.in (tptp.ordered_pair @t16 @t54) @t1) (tptp.in (tptp.ordered_pair @t54 @t26) @t2))))))))))))) % 0.37/0.68 (assume @p35 (forall @t6 (=> @t70 (forall @t36 (=> (tptp.element @t17 @t69) (= (= @t17 @t68) (forall @t43 (=> (tptp.element @t16 @t47) (= @t52 (tptp.in (tptp.subset_complement @t1 @t16) @t2)))))))))) % 0.37/0.68 (assume @p36 (forall @t6 (= @t8 (and @t24 @t71)))) % 0.37/0.68 (assume @p37 true) % 0.37/0.68 (assume @p38 (forall @t11 (tptp.element @t58 @t47))) % 0.37/0.68 (assume @p39 (forall @t6 (=> @t63 (tptp.element @t62 @t47)))) % 0.37/0.68 (assume @p40 (forall @t11 (=> @t9 (tptp.relation @t65)))) % 0.37/0.68 (assume @p41 (forall @t6 (=> @t73 @t72))) % 0.37/0.68 (assume @p42 (forall @t6 (=> @t70 (tptp.element @t74 @t47)))) % 0.37/0.68 (assume @p43 (forall @t11 (tptp.relation @t22))) % 0.37/0.68 (assume @p44 (forall @t6 (=> @t70 (tptp.element @t75 @t47)))) % 0.37/0.68 (assume @p45 (forall @t53 (=> @t78 (tptp.element @t76 @t47)))) % 0.37/0.68 (assume @p46 (forall @t6 (=> @t9 (tptp.relation @t31)))) % 0.37/0.68 (assume @p47 (forall @t6 (=> @t70 (tptp.element @t68 @t69)))) % 0.37/0.68 (assume @p48 @t80) % 0.37/0.68 (assume @p49 (forall @t11 (exists @t37 @t50))) % 0.37/0.68 (assume @p50 (forall @t6 (=> @t82 (and (tptp.empty @t81) (tptp.relation @t81))))) % 0.37/0.68 (assume @p51 (forall @t6 (=> @t73 (tptp.relation @t15)))) % 0.37/0.68 (assume @p52 (forall @t11 (not (tptp.empty @t47)))) % 0.37/0.68 (assume @p53 @t83) % 0.37/0.68 (assume @p54 (forall @t6 (not (tptp.empty @t64)))) % 0.37/0.68 (assume @p55 (forall @t6 (=> @t73 (tptp.relation @t14)))) % 0.37/0.68 (assume @p56 (forall @t11 (not (tptp.empty @t46)))) % 0.37/0.68 (assume @p57 (forall @t6 (=> @t51 (not (tptp.empty @t14))))) % 0.37/0.68 (assume @p58 (forall @t6 (not (tptp.empty @t12)))) % 0.37/0.68 (assume @p59 (forall @t6 (=> @t51 (not (tptp.empty @t13))))) % 0.37/0.68 (assume @p60 (and @t83 (tptp.relation tptp.empty_set))) % 0.37/0.68 (assume @p61 (forall @t6 (=> (and @t51 @t84) (not (tptp.empty @t55))))) % 0.37/0.68 (assume @p62 (forall @t11 (=> @t86 (not @t85)))) % 0.37/0.68 (assume @p63 (forall @t11 (=> @t86 (not @t87)))) % 0.37/0.68 (assume @p64 (forall @t11 (=> @t10 (and @t85 (tptp.relation @t57))))) % 0.37/0.68 (assume @p65 (forall @t11 (=> @t10 (and @t87 (tptp.relation @t61))))) % 0.37/0.68 (assume @p66 (forall @t6 (=> @t82 (and (tptp.empty @t67) @t72)))) % 0.37/0.68 (assume @p67 (forall @t6 (= (tptp.set_union2 @t1 @t1) @t1))) % 0.37/0.68 (assume @p68 (forall @t6 (= (tptp.set_intersection2 @t1 @t1) @t1))) % 0.37/0.68 (assume @p69 (forall @t6 (=> @t63 (= (tptp.subset_complement @t1 @t62) @t2)))) % 0.37/0.68 (assume @p70 (forall @t11 (=> @t9 (= (tptp.relation_inverse @t65) @t1)))) % 0.37/0.68 (assume @p71 (forall @t6 (=> @t70 (= (tptp.complements_of_subsets @t1 @t68) @t2)))) % 0.37/0.68 (assume @p72 (forall @t6 (not (tptp.proper_subset @t1 @t1)))) % 0.37/0.68 (assume @p73 (forall @t11 (not (= @t46 tptp.empty_set)))) % 0.37/0.68 (assume @p74 (forall @t6 (=> @t5 (= (tptp.set_union2 @t46 @t2) @t2)))) % 0.37/0.68 (assume @p75 (forall @t6 (not (and @t88 @t5)))) % 0.37/0.68 (assume @p76 (forall @t6 (=> (not @t5) @t88))) % 0.37/0.68 (assume @p77 (forall @t6 (= (tptp.subset @t46 @t2) @t5))) % 0.37/0.68 (assume @p78 (forall @t6 (= (= @t59 tptp.empty_set) @t24))) % 0.37/0.68 (assume @p79 (forall @t6 (=> @t63 (forall @t36 (=> @t44 @t18))))) % 0.37/0.68 (assume @p80 (forall @t53 (=> @t24 (or @t18 (tptp.subset @t1 (tptp.set_difference @t2 (tptp.singleton @t17))))))) % 0.37/0.68 (assume @p81 (forall @t6 (= (tptp.subset @t1 @t89) (or @t40 (= @t1 @t89))))) % 0.37/0.68 (assume @p82 (forall @t6 (=> @t5 (tptp.subset @t1 @t90)))) % 0.37/0.68 (assume @p83 (forall @t92 (= (tptp.in @t64 (tptp.cartesian_product2 @t17 @t16)) (and @t91 (tptp.in @t2 @t16))))) % 0.37/0.68 (assume @p84 (forall @t6 (=> @t56 @t93))) % 0.37/0.68 (assume @p85 (exists @t11 (and @t10 @t9))) % 0.37/0.68 (assume @p86 (forall @t11 (=> @t51 (exists @t37 (and @t63 @t84))))) % 0.37/0.68 (assume @p87 (exists @t11 @t10)) % 0.37/0.68 (assume @p88 (exists @t11 @t86)) % 0.37/0.68 (assume @p89 (forall @t11 (exists @t37 (and @t63 @t49)))) % 0.37/0.68 (assume @p90 (exists @t11 @t51)) % 0.37/0.68 (assume @p91 (forall @t6 (=> @t70 (= @t74 @t90)))) % 0.37/0.68 (assume @p92 (forall @t6 (=> @t70 (= @t75 (tptp.set_meet @t2))))) % 0.37/0.68 (assume @p93 (forall @t53 (=> @t78 (= @t76 @t94)))) % 0.37/0.68 (assume @p94 (forall @t6 (tptp.subset @t1 @t1))) % 0.37/0.68 (assume @p95 (forall @t6 (=> @t66 (tptp.disjoint @t2 @t1)))) % 0.37/0.68 (assume @p96 (forall @t92 (not (and (= @t12 (tptp.unordered_pair @t17 @t16)) (not @t95) (not (= @t1 @t16)))))) % 0.37/0.68 (assume @p97 (forall @t53 (=> @t32 (= (tptp.in @t1 (tptp.relation_rng (tptp.relation_rng_restriction @t2 @t17))) (and @t5 (tptp.in @t1 @t96)))))) % 0.37/0.68 (assume @p98 (forall @t6 (=> @t23 (tptp.subset @t97 @t1)))) % 0.37/0.68 (assume @p99 @t99) % 0.37/0.68 (assume @p100 @t103) % 0.37/0.68 (assume @p101 (forall @t53 (=> @t24 (and (tptp.subset @t104 (tptp.cartesian_product2 @t2 @t17)) (tptp.subset (tptp.cartesian_product2 @t17 @t1) (tptp.cartesian_product2 @t17 @t2)))))) % 0.37/0.68 (assume @p102 (forall @t92 (=> (and @t24 (tptp.subset @t17 @t16)) (tptp.subset @t104 (tptp.cartesian_product2 @t2 @t16))))) % 0.37/0.68 (assume @p103 (forall @t6 (=> @t24 (= @t14 @t2)))) % 0.37/0.68 (assume @p104 (forall @t11 (exists @t37 (and @t5 @t109 (forall @t36 (=> @t44 (tptp.in @t108 @t2))) @t107)))) % 0.37/0.68 (assume @p105 (forall @t6 (tptp.subset @t15 @t1))) % 0.37/0.68 (assume @p106 (forall @t53 (=> (and @t24 @t111) (tptp.subset @t1 @t110)))) % 0.37/0.68 (assume @p107 (forall @t11 (= (tptp.set_union2 @t1 tptp.empty_set) @t1))) % 0.37/0.68 (assume @p108 (forall @t6 (=> @t5 @t112))) % 0.37/0.68 (assume @p109 (forall @t53 (=> (and @t24 (tptp.subset @t2 @t17)) @t111))) % 0.37/0.68 (assume @p110 (= (tptp.powerset tptp.empty_set) (tptp.singleton tptp.empty_set))) % 0.37/0.68 (assume @p111 (forall @t53 (=> @t32 (=> @t114 (and @t113 (tptp.in @t2 @t96)))))) % 0.37/0.68 (assume @p112 (forall @t11 (=> @t9 (tptp.subset @t1 (tptp.cartesian_product2 @t57 @t61))))) % 0.37/0.68 (assume @p113 @t120) % 0.37/0.68 (assume @p114 (forall @t53 (=> @t24 (tptp.subset (tptp.set_intersection2 @t1 @t17) @t110)))) % 0.37/0.68 (assume @p115 (forall @t6 (=> @t24 (= @t15 @t1)))) % 0.37/0.68 (assume @p116 (forall @t11 (= (tptp.set_intersection2 @t1 tptp.empty_set) tptp.empty_set))) % 0.37/0.68 (assume @p117 (forall @t6 (=> @t112 (or @t49 @t5)))) % 0.37/0.68 (assume @p118 (forall @t6 (=> (forall @t36 (= @t18 @t44)) @t25))) % 0.37/0.68 (assume @p119 (forall @t11 (tptp.subset tptp.empty_set @t1))) % 0.37/0.68 (assume @p120 (forall @t53 (=> @t32 (=> @t114 (and (tptp.in @t1 @t121) (tptp.in @t2 @t121)))))) % 0.37/0.68 (assume @p121 (forall @t53 (=> @t24 (tptp.subset (tptp.set_difference @t1 @t17) @t94)))) % 0.37/0.68 (assume @p122 (forall @t92 (=> (= @t64 @t19) (and @t95 (= @t2 @t16))))) % 0.37/0.68 (assume @p123 (forall @t6 (tptp.subset @t59 @t1))) % 0.37/0.68 (assume @p124 (forall @t11 (=> @t9 (and (= @t61 (tptp.relation_dom @t65)) (= @t57 (tptp.relation_rng @t65)))))) % 0.37/0.68 (assume @p125 (forall @t53 (= (tptp.subset @t12 @t17) (and @t91 @t122)))) % 0.37/0.68 (assume @p126 (forall @t6 (= @t123 @t14))) % 0.37/0.68 (assume @p127 (forall @t11 (= (tptp.set_difference @t1 tptp.empty_set) @t1))) % 0.37/0.68 (assume @p128 (forall @t6 (= @t93 @t24))) % 0.37/0.68 (assume @p129 (forall @t6 (and (not (and @t125 (forall @t36 (not @t124)))) (not (and (exists @t36 @t124) @t66))))) % 0.37/0.68 (assume @p130 (forall @t11 (=> (tptp.subset @t1 tptp.empty_set) @t40))) % 0.37/0.68 (assume @p131 (forall @t6 (= (tptp.set_difference @t14 @t2) @t59))) % 0.37/0.68 (assume @p132 (forall @t6 (=> @t63 (forall @t36 (=> @t77 (= @t127 (tptp.subset @t2 @t126))))))) % 0.37/0.68 (assume @p133 (forall @t11 (=> @t9 (forall @t37 (=> @t23 (tptp.subset @t128 @t57)))))) % 0.37/0.68 (assume @p134 (forall @t11 (=> @t9 (forall @t37 (=> @t23 (tptp.subset (tptp.relation_rng @t67) @t100)))))) % 0.37/0.68 (assume @p135 (forall @t6 (=> @t24 (= @t2 @t123)))) % 0.37/0.68 (assume @p136 (forall @t11 (=> @t9 (forall @t37 (=> @t23 (=> (tptp.subset @t61 @t115) (= @t128 @t57))))))) % 0.37/0.68 (assume @p137 (forall @t6 (=> @t70 (not (and @t129 (= @t68 tptp.empty_set)))))) % 0.37/0.68 (assume @p138 (forall @t11 (=> @t9 (forall @t37 (=> @t23 (=> (tptp.subset @t57 @t100) (= (tptp.relation_rng @t81) @t61))))))) % 0.37/0.68 (assume @p139 (forall @t6 (=> @t70 (=> @t129 (= (tptp.subset_difference @t1 @t58 @t74) (tptp.meet_of_subsets @t1 @t68)))))) % 0.37/0.68 (assume @p140 (forall @t6 (=> @t70 (=> @t129 (= (tptp.union_of_subsets @t1 @t68) (tptp.subset_difference @t1 @t58 @t75)))))) % 0.37/0.68 (assume @p141 (forall @t6 (= (tptp.set_difference @t1 @t59) @t15))) % 0.37/0.68 (assume @p142 (forall @t11 (= (tptp.set_difference tptp.empty_set @t1) tptp.empty_set))) % 0.37/0.68 (assume @p143 (forall @t53 (=> (and @t5 @t130) (tptp.element @t1 @t17)))) % 0.37/0.68 (assume @p144 (forall @t6 (and (not (and @t125 (forall @t36 (not @t131)))) (not (and (exists @t36 @t131) @t66))))) % 0.37/0.68 (assume @p145 (forall @t11 (=> @t45 (forall @t37 (=> @t63 (forall @t36 (=> (tptp.element @t17 @t1) (=> @t105 (tptp.in @t17 @t62))))))))) % 0.37/0.68 (assume @p146 (forall @t53 (=> @t77 (not (and (tptp.in @t2 @t126) @t122))))) % 0.37/0.68 (assume @p147 (forall @t11 (=> @t9 (=> (forall @t33 (not (tptp.in (tptp.ordered_pair @t2 @t17) @t1))) @t40)))) % 0.37/0.68 (assume @p148 (forall @t53 (not (and @t5 @t130 (tptp.empty @t17))))) % 0.37/0.68 (assume @p149 (and (= (tptp.relation_dom tptp.empty_set) tptp.empty_set) (= (tptp.relation_rng tptp.empty_set) tptp.empty_set))) % 0.37/0.68 (assume @p150 (forall @t6 (not (and @t24 @t7)))) % 0.37/0.68 (assume @p151 (forall @t53 (=> (and @t24 @t127) (tptp.disjoint @t1 @t17)))) % 0.37/0.68 (assume @p152 (forall @t11 (=> @t9 (=> (or @t133 @t132) @t40)))) % 0.37/0.68 (assume @p153 (forall @t11 (=> @t9 (= @t133 @t132)))) % 0.37/0.68 (assume @p154 (forall @t6 (= (= (tptp.set_difference @t1 @t89) @t1) @t4))) % 0.37/0.68 (assume @p155 (forall @t11 (= (tptp.unordered_pair @t1 @t1) @t46))) % 0.37/0.68 (assume @p156 (forall @t11 (=> @t10 @t40))) % 0.37/0.68 (assume @p157 (forall @t6 (=> (tptp.subset @t46 @t89) @t25))) % 0.37/0.68 (assume @p158 (forall @t11 (and (= (tptp.relation_dom @t22) @t1) (= (tptp.relation_rng @t22) @t1)))) % 0.37/0.68 (assume @p159 (forall @t92 (=> (tptp.relation @t16) (= (tptp.in @t64 (tptp.relation_composition (tptp.identity_relation @t17) @t16)) (and @t91 (tptp.in @t64 @t16)))))) % 0.37/0.68 (assume @p160 (forall @t6 (not (and @t5 @t49)))) % 0.37/0.68 (assume @p161 (forall @t6 (tptp.subset @t1 @t14))) % 0.37/0.68 (assume @p162 (forall @t6 (= @t66 (= @t59 @t1)))) % 0.37/0.68 (assume @p163 (forall @t53 (=> @t32 (= (tptp.in @t1 (tptp.relation_dom (tptp.relation_dom_restriction @t17 @t2))) (and @t5 @t113))))) % 0.37/0.68 (assume @p164 (forall @t6 (=> @t23 (tptp.subset @t134 @t2)))) % 0.37/0.68 (assume @p165 (forall @t6 (not (and @t10 @t71 @t49)))) % 0.37/0.68 (assume @p166 (forall @t53 (=> (and @t24 @t106) (tptp.subset (tptp.set_union2 @t1 @t17) @t2)))) % 0.37/0.68 (assume @p167 (forall @t53 (=> @t135 @t25))) % 0.37/0.68 (assume @p168 (forall @t6 (=> @t23 (= (tptp.relation_dom @t134) (tptp.set_intersection2 @t115 @t1))))) % 0.37/0.68 (assume @p169 (forall @t6 (=> @t23 (= @t134 (tptp.relation_composition @t22 @t2))))) % 0.37/0.68 (assume @p170 (forall @t6 (=> @t23 (tptp.subset (tptp.relation_rng @t134) @t100)))) % 0.37/0.68 (assume @p171 (forall @t11 (= (tptp.union @t47) @t1))) % 0.37/0.68 (assume @p172 (forall @t11 (exists @t37 (and @t5 @t109 (forall @t36 (not (and @t44 (forall @t43 (not (and @t28 (forall (@list @t26) (=> (tptp.subset @t26 @t17) (tptp.in @t26 @t16))))))))) @t107)))) % 0.37/0.68 (assume @p173 (forall @t53 (=> @t135 (= @t2 @t17)))) % 0.37/0.68 (step @p174 :rule bool-impl-elim :args (@t23 @t101)) % 0.37/0.68 (step @p175 :rule cong :premises (@p174) :args (@t102)) % 0.37/0.68 (step @p176 :rule cong :premises (@p175) :args (@t103)) % 0.37/0.68 (step @p177 :rule eq_resolve :premises (@p100 @p176)) % 0.37/0.68 (step @p178 :rule skolemize :premises (@p177)) % 0.37/0.68 (step @p179 :rule bool-double-not-elim :args (@t139)) % 0.37/0.68 (step @p180 :rule refl :args (@t144)) % 0.37/0.68 (step @p181 :rule nary_cong :premises (@p180 @p179) :args ((or @t144 (not @t143)))) % 0.37/0.68 (step @p182 :rule cnf_or_neg :args (@t144 0)) % 0.37/0.68 (step @p183 :rule eq_resolve :premises (@p182 @p181)) % 0.37/0.68 (step @p184 :rule reordering :premises (@p183) :args ((or @t139 @t144))) % 0.37/0.68 (step @p185 :rule chain_m_resolution :premises (@p184 @p178) :args (@t139 @t145 @t146)) % 0.37/0.68 (step @p186 :rule aci_norm :args ((= @t153 (or @t151 @t150 @t149 @t148)))) % 0.37/0.68 (step @p187 :rule cong :premises (@p186) :args (@t154)) % 0.37/0.68 (step @p188 :rule quant-merge-prenex :args ((= (forall @t11 @t156) @t154))) % 0.37/0.68 (step @p189 :rule alpha_equiv :args (@t157 (@list @t147) (@list @t2))) % 0.37/0.68 (step @p190 :rule refl :args (@t151)) % 0.37/0.68 (step @p191 :rule nary_cong :premises (@p190 @p189) :args (@t158)) % 0.37/0.68 (step @p192 :rule quant-miniscope-or :args ((= @t156 @t158))) % 0.37/0.68 (step @p193 :rule trans :premises (@p192 @p191)) % 0.37/0.68 (step @p194 :rule symm :premises (@p193)) % 0.37/0.68 (step @p195 :rule cong :premises (@p194) :args ((forall @t11 (or @t151 @t161)))) % 0.37/0.68 (step @p196 :rule trans :premises (@p195 @p188)) % 0.37/0.68 (step @p197 :rule trans :premises (@p196 @p187)) % 0.37/0.68 (step @p198 :rule bool-impl-elim :args (@t9 @t161)) % 0.37/0.68 (step @p199 :rule cong :premises (@p198) :args ((forall @t11 (=> @t9 @t161)))) % 0.37/0.68 (step @p200 :rule trans :premises (@p199 @p197)) % 0.37/0.68 (step @p201 :rule aci_norm :args ((= (or @t136 (or @t159 @t116)) @t160))) % 0.37/0.68 (step @p202 :rule bool-impl-elim :args (@t24 @t116)) % 0.37/0.68 (step @p203 :rule refl :args (@t136)) % 0.37/0.68 (step @p204 :rule nary_cong :premises (@p203 @p202) :args ((or @t136 @t117))) % 0.37/0.68 (step @p205 :rule trans :premises (@p204 @p201)) % 0.37/0.68 (step @p206 :rule bool-impl-elim :args (@t23 @t117)) % 0.37/0.68 (step @p207 :rule trans :premises (@p206 @p205)) % 0.37/0.68 (step @p208 :rule cong :premises (@p207) :args (@t118)) % 0.37/0.68 (step @p209 :rule refl :args (@t9)) % 0.37/0.68 (step @p210 :rule cong :premises (@p209 @p208) :args (@t119)) % 0.37/0.68 (step @p211 :rule cong :premises (@p210) :args (@t120)) % 0.37/0.68 (step @p212 :rule trans :premises (@p211 @p200)) % 0.37/0.68 (step @p213 :rule eq_resolve :premises (@p113 @p212)) % 0.37/0.68 (step @p214 :rule instantiate :premises (@p213) :args ((@list @t141 @t138))) % 0.37/0.68 (step @p215 :rule cnf_or_neg :args (@t144 1)) % 0.37/0.68 (step @p216 :rule chain_m_resolution :premises (@p215 @p178) :args ((not @t142) @t145 @t146)) % 0.37/0.68 (step @p217 :rule cnf_and_pos :args (@t162 1)) % 0.37/0.68 (step @p218 :rule reordering :premises (@p217) :args ((or @t142 @t163))) % 0.37/0.68 (step @p219 :rule chain_m_resolution :premises (@p218 @p216) :args (@t163 @t145 (@list @t142))) % 0.37/0.68 (step @p220 :rule bool-impl-elim :args (@t23 @t79)) % 0.37/0.68 (step @p221 :rule cong :premises (@p220) :args (@t80)) % 0.37/0.68 (step @p222 :rule eq_resolve :premises (@p48 @p221)) % 0.37/0.68 (step @p223 :rule instantiate :premises (@p222) :args (@t164)) % 0.37/0.68 (step @p224 :rule cnf_or_pos :args (@t166)) % 0.37/0.68 (step @p225 :rule reordering :premises (@p224) :args ((or @t143 @t165 (not @t166)))) % 0.37/0.68 (step @p226 :rule chain_m_resolution :premises (@p225 @p185 @p223) :args (@t165 @t167 (@list @t139 @t166))) % 0.37/0.68 (step @p227 :rule bool-impl-elim :args (@t23 @t98)) % 0.37/0.68 (step @p228 :rule cong :premises (@p227) :args (@t99)) % 0.37/0.68 (step @p229 :rule eq_resolve :premises (@p99 @p228)) % 0.37/0.68 (step @p230 :rule instantiate :premises (@p229) :args (@t164)) % 0.37/0.68 (step @p231 :rule cnf_or_pos :args (@t169)) % 0.37/0.68 (step @p232 :rule reordering :premises (@p231) :args ((or @t143 @t168 (not @t169)))) % 0.37/0.68 (step @p233 :rule chain_m_resolution :premises (@p232 @p185 @p230) :args (@t168 @t167 (@list @t139 @t169))) % 0.37/0.68 (step @p234 :rule cnf_or_pos :args (@t172)) % 0.37/0.68 (step @p235 :rule reordering :premises (@p234) :args ((or @t143 @t171 @t170 @t162 (not @t172)))) % 0.37/0.68 (step @p236 false :rule chain_m_resolution :premises (@p235 @p233 @p226 @p219 @p214 @p185) :args (false (@list false false true false false) (@list @t168 @t165 @t162 @t172 @t139))) % 0.37/0.68 ) % 0.37/0.68 % SZS output end Proof % 0.37/0.68 % cvc5 exiting %------------------------------------------------------------------------------