%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU189+2 : 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 : n004.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 08:50:53 AM UTC 2026 % Result : Theorem 0.34s 0.65s % Output : Proof 0.34s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU189+2 : TPTP v9.2.1. Released v3.3.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.14/0.34 % Computer : n004.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 300 % 0.14/0.34 % DateTime : Tue Jun 2 16:34:52 EDT 2026 % 0.14/0.34 % CPUTime : % 0.29/0.51 %----Proving TF0_NAR, FOF, or CNF % 0.34/0.65 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.34/0.65 % SZS status Theorem % 0.34/0.65 % SZS output start Proof % 0.34/0.65 ( % 0.34/0.65 (declare-sort $$unsorted 0) % 0.34/0.65 (declare-const tptp.are_equipotent (-> $$unsorted $$unsorted Bool)) % 0.34/0.65 (declare-const tptp.ordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.34/0.65 (declare-const tptp.relation (-> $$unsorted Bool)) % 0.34/0.65 (declare-const tptp.empty_set $$unsorted) % 0.34/0.65 (declare-const tptp.relation_composition (-> $$unsorted $$unsorted $$unsorted)) % 0.34/0.65 (declare-const tptp.meet_of_subsets (-> $$unsorted $$unsorted $$unsorted)) % 0.34/0.65 (declare-const tptp.powerset (-> $$unsorted $$unsorted)) % 0.34/0.65 (declare-const tptp.set_union2 (-> $$unsorted $$unsorted $$unsorted)) % 0.34/0.65 (declare-const tptp.union_of_subsets (-> $$unsorted $$unsorted $$unsorted)) % 0.34/0.65 (declare-const tptp.empty (-> $$unsorted Bool)) % 0.34/0.65 (declare-const tptp.proper_subset (-> $$unsorted $$unsorted Bool)) % 0.34/0.65 (declare-const tptp.complements_of_subsets (-> $$unsorted $$unsorted $$unsorted)) % 0.34/0.65 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 0.34/0.65 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 0.34/0.65 (declare-const tptp.set_meet (-> $$unsorted $$unsorted)) % 0.34/0.65 (declare-const tptp.set_difference (-> $$unsorted $$unsorted $$unsorted)) % 0.34/0.65 (declare-const tptp.element (-> $$unsorted $$unsorted Bool)) % 0.34/0.65 (declare-const tptp.relation_rng (-> $$unsorted $$unsorted)) % 0.34/0.65 (declare-const tptp.cartesian_product2 (-> $$unsorted $$unsorted $$unsorted)) % 0.34/0.65 (declare-const tptp.relation_dom (-> $$unsorted $$unsorted)) % 0.34/0.65 (declare-const tptp.subset_difference (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.34/0.65 (declare-const tptp.cast_to_subset (-> $$unsorted $$unsorted)) % 0.34/0.65 (declare-const tptp.union (-> $$unsorted $$unsorted)) % 0.34/0.65 (declare-const tptp.disjoint (-> $$unsorted $$unsorted Bool)) % 0.34/0.65 (declare-const tptp.unordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.34/0.65 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 0.34/0.65 (declare-const tptp.subset_complement (-> $$unsorted $$unsorted $$unsorted)) % 0.34/0.65 (declare-const tptp.set_intersection2 (-> $$unsorted $$unsorted $$unsorted)) % 0.34/0.65 (declare-const tptp.relation_field (-> $$unsorted $$unsorted)) % 0.34/0.65 (declare-const tptp.relation_inverse (-> $$unsorted $$unsorted)) % 0.34/0.65 (define @t1 () (@var "A" $$unsorted)) % 0.34/0.65 (define @t2 () (@var "B" $$unsorted)) % 0.34/0.65 (define @t3 () (tptp.in @t2 @t1)) % 0.34/0.65 (define @t4 () (not @t3)) % 0.34/0.65 (define @t5 () (tptp.in @t1 @t2)) % 0.34/0.65 (define @t6 () (@list @t1 @t2)) % 0.34/0.65 (define @t7 () (tptp.proper_subset @t2 @t1)) % 0.34/0.65 (define @t8 () (tptp.proper_subset @t1 @t2)) % 0.34/0.65 (define @t9 () (tptp.relation @t1)) % 0.34/0.65 (define @t10 () (tptp.empty @t1)) % 0.34/0.65 (define @t11 () (@list @t1)) % 0.34/0.65 (define @t12 () (tptp.unordered_pair @t1 @t2)) % 0.34/0.65 (define @t13 () (tptp.set_union2 @t2 @t1)) % 0.34/0.65 (define @t14 () (tptp.set_union2 @t1 @t2)) % 0.34/0.65 (define @t15 () (tptp.set_intersection2 @t1 @t2)) % 0.34/0.65 (define @t16 () (tptp.subset @t1 @t2)) % 0.34/0.65 (define @t17 () (= @t1 @t2)) % 0.34/0.65 (define @t18 () (@var "D" $$unsorted)) % 0.34/0.65 (define @t19 () (@var "C" $$unsorted)) % 0.34/0.65 (define @t20 () (tptp.ordered_pair @t19 @t18)) % 0.34/0.65 (define @t21 () (@list @t19 @t18)) % 0.34/0.65 (define @t22 () (@list @t2)) % 0.34/0.65 (define @t23 () (= @t2 tptp.empty_set)) % 0.34/0.65 (define @t24 () (= @t2 (tptp.set_meet @t1))) % 0.34/0.65 (define @t25 () (= @t1 tptp.empty_set)) % 0.34/0.65 (define @t26 () (tptp.in @t19 @t18)) % 0.34/0.65 (define @t27 () (tptp.in @t18 @t1)) % 0.34/0.65 (define @t28 () (@list @t18)) % 0.34/0.65 (define @t29 () (tptp.in @t19 @t2)) % 0.34/0.65 (define @t30 () (@list @t19)) % 0.34/0.65 (define @t31 () (not @t25)) % 0.34/0.65 (define @t32 () (tptp.singleton @t1)) % 0.34/0.65 (define @t33 () (tptp.powerset @t1)) % 0.34/0.65 (define @t34 () (tptp.empty @t2)) % 0.34/0.65 (define @t35 () (tptp.element @t2 @t1)) % 0.34/0.65 (define @t36 () (not @t10)) % 0.34/0.65 (define @t37 () (tptp.in @t18 @t19)) % 0.34/0.65 (define @t38 () (@list @t1 @t2 @t19)) % 0.34/0.65 (define @t39 () (tptp.in @t18 @t2)) % 0.34/0.65 (define @t40 () (@var "F" $$unsorted)) % 0.34/0.65 (define @t41 () (@var "E" $$unsorted)) % 0.34/0.65 (define @t42 () (tptp.cartesian_product2 @t1 @t2)) % 0.34/0.65 (define @t43 () (tptp.in @t19 @t1)) % 0.34/0.65 (define @t44 () (forall @t30 (=> @t43 @t29))) % 0.34/0.65 (define @t45 () (tptp.relation_dom @t1)) % 0.34/0.65 (define @t46 () (tptp.cast_to_subset @t1)) % 0.34/0.65 (define @t47 () (tptp.set_difference @t1 @t2)) % 0.34/0.65 (define @t48 () (tptp.in (tptp.ordered_pair @t18 @t19) @t1)) % 0.34/0.65 (define @t49 () (tptp.relation_rng @t1)) % 0.34/0.65 (define @t50 () (tptp.subset_complement @t1 @t2)) % 0.34/0.65 (define @t51 () (tptp.element @t2 @t33)) % 0.34/0.65 (define @t52 () (tptp.ordered_pair @t1 @t2)) % 0.34/0.65 (define @t53 () (tptp.relation_inverse @t1)) % 0.34/0.65 (define @t54 () (tptp.relation @t2)) % 0.34/0.65 (define @t55 () (tptp.disjoint @t1 @t2)) % 0.34/0.65 (define @t56 () (tptp.relation_composition @t1 @t2)) % 0.34/0.65 (define @t57 () (tptp.relation @t19)) % 0.34/0.65 (define @t58 () (tptp.complements_of_subsets @t1 @t2)) % 0.34/0.65 (define @t59 () (tptp.powerset @t33)) % 0.34/0.65 (define @t60 () (tptp.element @t2 @t59)) % 0.34/0.65 (define @t61 () (not @t17)) % 0.34/0.65 (define @t62 () (and @t9 @t54)) % 0.34/0.65 (define @t63 () (tptp.union_of_subsets @t1 @t2)) % 0.34/0.65 (define @t64 () (tptp.meet_of_subsets @t1 @t2)) % 0.34/0.65 (define @t65 () (tptp.subset_difference @t1 @t2 @t19)) % 0.34/0.65 (define @t66 () (tptp.element @t19 @t33)) % 0.34/0.65 (define @t67 () (and @t51 @t66)) % 0.34/0.65 (define @t68 () (tptp.empty tptp.empty_set)) % 0.34/0.65 (define @t69 () (not @t34)) % 0.34/0.65 (define @t70 () (tptp.empty @t45)) % 0.34/0.65 (define @t71 () (and @t36 @t9)) % 0.34/0.65 (define @t72 () (tptp.empty @t49)) % 0.34/0.65 (define @t73 () (tptp.disjoint @t32 @t2)) % 0.34/0.65 (define @t74 () (tptp.singleton @t2)) % 0.34/0.65 (define @t75 () (tptp.union @t2)) % 0.34/0.65 (define @t76 () (tptp.in @t1 @t19)) % 0.34/0.65 (define @t77 () (@list @t1 @t2 @t19 @t18)) % 0.34/0.65 (define @t78 () (tptp.element @t1 (tptp.powerset @t2))) % 0.34/0.65 (define @t79 () (tptp.set_difference @t2 @t19)) % 0.34/0.65 (define @t80 () (= @t1 @t19)) % 0.34/0.65 (define @t81 () (tptp.cartesian_product2 @t1 @t19)) % 0.34/0.65 (define @t82 () (not @t29)) % 0.34/0.65 (define @t83 () (tptp.subset @t19 @t2)) % 0.34/0.65 (define @t84 () (forall @t30 (not (and @t83 (not (tptp.are_equipotent @t19 @t2)) @t82)))) % 0.34/0.65 (define @t85 () (tptp.powerset @t19)) % 0.34/0.65 (define @t86 () (forall @t21 (=> (and @t29 (tptp.subset @t18 @t19)) @t39))) % 0.34/0.65 (define @t87 () (tptp.set_intersection2 @t2 @t19)) % 0.34/0.65 (define @t88 () (tptp.subset @t1 @t19)) % 0.34/0.65 (define @t89 () (tptp.element @t1 @t2)) % 0.34/0.65 (define @t90 () (tptp.in @t52 @t19)) % 0.34/0.65 (define @t91 () (tptp.relation_rng @t2)) % 0.34/0.65 (define @t92 () (tptp.relation_dom @t2)) % 0.34/0.65 (define @t93 () (tptp.relation_field @t19)) % 0.34/0.65 (define @t94 () (tptp.in @t2 @t19)) % 0.34/0.65 (define @t95 () (tptp.set_union2 @t1 (tptp.set_difference @t2 @t1))) % 0.34/0.65 (define @t96 () (and @t43 @t29)) % 0.34/0.65 (define @t97 () (not @t55)) % 0.34/0.65 (define @t98 () (tptp.subset_complement @t1 @t19)) % 0.34/0.65 (define @t99 () (tptp.disjoint @t2 @t19)) % 0.34/0.65 (define @t100 () (tptp.relation_dom @t56)) % 0.34/0.65 (define @t101 () (not @t23)) % 0.34/0.65 (define @t102 () (tptp.element @t2 @t85)) % 0.34/0.65 (define @t103 () (tptp.in @t19 @t15)) % 0.34/0.65 (define @t104 () (tptp.relation_rng tptp.empty_set)) % 0.34/0.65 (define @t105 () (tptp.relation_dom tptp.empty_set)) % 0.34/0.65 (define @t106 () (= @t49 tptp.empty_set)) % 0.34/0.65 (define @t107 () (= @t45 tptp.empty_set)) % 0.34/0.65 (define @t108 () (or @t107 @t106)) % 0.34/0.65 (define @t109 () (=> @t108 @t25)) % 0.34/0.65 (define @t110 () (=> @t9 @t109)) % 0.34/0.65 (define @t111 () (forall @t11 @t110)) % 0.34/0.65 (define @t112 () (= @t107 @t106)) % 0.34/0.65 (define @t113 () (=> @t9 @t112)) % 0.34/0.65 (define @t114 () (forall @t11 @t113)) % 0.34/0.65 (define @t115 () (not @t114)) % 0.34/0.65 (define @t116 () (= @t32 (tptp.unordered_pair @t2 @t19))) % 0.34/0.65 (define @t117 () (= tptp.empty_set @t49)) % 0.34/0.65 (define @t118 () (= tptp.empty_set @t45)) % 0.34/0.65 (define @t119 () (= @t118 @t117)) % 0.34/0.65 (define @t120 () (not @t9)) % 0.34/0.65 (define @t121 () (@quantifiers_skolemize (forall @t11 (or @t120 @t119)) 0)) % 0.34/0.65 (define @t122 () (= tptp.empty_set (tptp.relation_rng @t121))) % 0.34/0.65 (define @t123 () (= tptp.empty_set (tptp.relation_dom @t121))) % 0.34/0.65 (define @t124 () (= @t123 @t122)) % 0.34/0.65 (define @t125 () (tptp.relation @t121)) % 0.34/0.65 (define @t126 () (not @t125)) % 0.34/0.65 (define @t127 () (or @t126 @t124)) % 0.34/0.65 (define @t128 () (@list true)) % 0.34/0.65 (define @t129 () (@list @t127)) % 0.34/0.65 (define @t130 () (not @t122)) % 0.34/0.65 (define @t131 () (not @t123)) % 0.34/0.65 (define @t132 () (and @t131 @t130)) % 0.34/0.65 (define @t133 () (not @t132)) % 0.34/0.65 (define @t134 () (and (not @t118) (not @t117))) % 0.34/0.65 (define @t135 () (or @t120 @t134 @t25)) % 0.34/0.65 (define @t136 () (or @t118 @t117)) % 0.34/0.65 (define @t137 () (=> @t136 @t25)) % 0.34/0.65 (define @t138 () (or @t126 @t132 (= @t121 tptp.empty_set))) % 0.34/0.65 (define @t139 () (forall @t11 @t135)) % 0.34/0.65 (define @t140 () (= tptp.empty_set @t121)) % 0.34/0.65 (define @t141 () (or @t126 @t132 @t140)) % 0.34/0.65 (define @t142 () (@list false)) % 0.34/0.65 (define @t143 () (= tptp.empty_set @t105)) % 0.34/0.65 (define @t144 () (and @t143 @t140)) % 0.34/0.65 (define @t145 () (not @t140)) % 0.34/0.65 (define @t146 () (@list false true false)) % 0.34/0.65 (define @t147 () (= tptp.empty_set @t104)) % 0.34/0.65 (define @t148 () (and @t147 @t140)) % 0.34/0.65 (assume @p1 (forall @t6 (=> @t5 @t4))) % 0.34/0.65 (assume @p2 (forall @t6 (=> @t8 (not @t7)))) % 0.34/0.65 (assume @p3 (forall @t11 (=> @t10 @t9))) % 0.34/0.65 (assume @p4 (forall @t6 (= @t12 (tptp.unordered_pair @t2 @t1)))) % 0.34/0.65 (assume @p5 (forall @t6 (= @t14 @t13))) % 0.34/0.65 (assume @p6 (forall @t6 (= @t15 (tptp.set_intersection2 @t2 @t1)))) % 0.34/0.65 (assume @p7 (forall @t6 (= @t17 (and @t16 (tptp.subset @t2 @t1))))) % 0.34/0.65 (assume @p8 (forall @t11 (= @t9 (forall @t22 (not (and @t3 (forall @t21 (not (= @t2 @t20))))))))) % 0.34/0.65 (assume @p9 (forall @t6 (and (=> @t31 (= @t24 (forall @t30 (= @t29 (forall @t28 (=> @t27 @t26)))))) (=> @t25 (= @t24 @t23))))) % 0.34/0.65 (assume @p10 (forall @t6 (= (= @t2 @t32) (forall @t30 (= @t29 (= @t19 @t1)))))) % 0.34/0.65 (assume @p11 (forall @t11 (= @t25 (forall @t22 @t4)))) % 0.34/0.65 (assume @p12 (forall @t6 (= (= @t2 @t33) (forall @t30 (= @t29 (tptp.subset @t19 @t1)))))) % 0.34/0.65 (assume @p13 (forall @t6 (and (=> @t36 (= @t35 @t3)) (=> @t10 (= @t35 @t34))))) % 0.34/0.65 (assume @p14 (forall @t38 (= (= @t19 @t12) (forall @t28 (= @t37 (or (= @t18 @t1) (= @t18 @t2))))))) % 0.34/0.65 (assume @p15 (forall @t38 (= (= @t19 @t14) (forall @t28 (= @t37 (or @t27 @t39)))))) % 0.34/0.65 (assume @p16 (forall @t38 (= (= @t19 @t42) (forall @t28 (= @t37 (exists (@list @t41 @t40) (and (tptp.in @t41 @t1) (tptp.in @t40 @t2) (= @t18 (tptp.ordered_pair @t41 @t40))))))))) % 0.34/0.65 (assume @p17 (forall @t6 (= @t16 @t44))) % 0.34/0.65 (assume @p18 (forall @t38 (= (= @t19 @t15) (forall @t28 (= @t37 (and @t27 @t39)))))) % 0.34/0.65 (assume @p19 (forall @t11 (=> @t9 (forall @t22 (= (= @t2 @t45) (forall @t30 (= @t29 (exists @t28 (tptp.in @t20 @t1))))))))) % 0.34/0.65 (assume @p20 (forall @t11 (= @t46 @t1))) % 0.34/0.65 (assume @p21 (forall @t6 (= (= @t2 (tptp.union @t1)) (forall @t30 (= @t29 (exists @t28 (and @t26 @t27))))))) % 0.34/0.65 (assume @p22 (forall @t38 (= (= @t19 @t47) (forall @t28 (= @t37 (and @t27 (not @t39))))))) % 0.34/0.65 (assume @p23 (forall @t11 (=> @t9 (forall @t22 (= (= @t2 @t49) (forall @t30 (= @t29 (exists @t28 @t48)))))))) % 0.34/0.65 (assume @p24 (forall @t6 (=> @t51 (= @t50 @t47)))) % 0.34/0.65 (assume @p25 (forall @t6 (= @t52 (tptp.unordered_pair @t12 @t32)))) % 0.34/0.65 (assume @p26 (forall @t11 (=> @t9 (= (tptp.relation_field @t1) (tptp.set_union2 @t45 @t49))))) % 0.34/0.65 (assume @p27 (forall @t11 (=> @t9 (forall @t22 (=> @t54 (= (= @t2 @t53) (forall @t21 (= (tptp.in @t20 @t2) @t48)))))))) % 0.34/0.65 (assume @p28 (forall @t6 (= @t55 (= @t15 tptp.empty_set)))) % 0.34/0.65 (assume @p29 (forall @t11 (=> @t9 (forall @t22 (=> @t54 (forall @t30 (=> @t57 (= (= @t19 @t56) (forall (@list @t18 @t41) (= (tptp.in (tptp.ordered_pair @t18 @t41) @t19) (exists (@list @t40) (and (tptp.in (tptp.ordered_pair @t18 @t40) @t1) (tptp.in (tptp.ordered_pair @t40 @t41) @t2))))))))))))) % 0.34/0.65 (assume @p30 (forall @t6 (=> @t60 (forall @t30 (=> (tptp.element @t19 @t59) (= (= @t19 @t58) (forall @t28 (=> (tptp.element @t18 @t33) (= @t37 (tptp.in (tptp.subset_complement @t1 @t18) @t2)))))))))) % 0.34/0.65 (assume @p31 (forall @t6 (= @t8 (and @t16 @t61)))) % 0.34/0.65 (assume @p32 true) % 0.34/0.65 (assume @p33 (forall @t11 (tptp.element @t46 @t33))) % 0.34/0.65 (assume @p34 (forall @t6 (=> @t51 (tptp.element @t50 @t33)))) % 0.34/0.65 (assume @p35 (forall @t11 (=> @t9 (tptp.relation @t53)))) % 0.34/0.65 (assume @p36 (forall @t6 (=> @t62 (tptp.relation @t56)))) % 0.34/0.65 (assume @p37 (forall @t6 (=> @t60 (tptp.element @t63 @t33)))) % 0.34/0.65 (assume @p38 (forall @t6 (=> @t60 (tptp.element @t64 @t33)))) % 0.34/0.65 (assume @p39 (forall @t38 (=> @t67 (tptp.element @t65 @t33)))) % 0.34/0.65 (assume @p40 (forall @t6 (=> @t60 (tptp.element @t58 @t59)))) % 0.34/0.65 (assume @p41 (forall @t11 (exists @t22 @t35))) % 0.34/0.65 (assume @p42 (forall @t11 (not (tptp.empty @t33)))) % 0.34/0.65 (assume @p43 @t68) % 0.34/0.65 (assume @p44 (forall @t6 (not (tptp.empty @t52)))) % 0.34/0.65 (assume @p45 (forall @t6 (=> @t62 (tptp.relation @t14)))) % 0.34/0.65 (assume @p46 (forall @t11 (not (tptp.empty @t32)))) % 0.34/0.65 (assume @p47 (forall @t6 (=> @t36 (not (tptp.empty @t14))))) % 0.34/0.65 (assume @p48 (forall @t6 (not (tptp.empty @t12)))) % 0.34/0.65 (assume @p49 (forall @t6 (=> @t36 (not (tptp.empty @t13))))) % 0.34/0.65 (assume @p50 (and @t68 (tptp.relation tptp.empty_set))) % 0.34/0.65 (assume @p51 (forall @t6 (=> (and @t36 @t69) (not (tptp.empty @t42))))) % 0.34/0.65 (assume @p52 (forall @t11 (=> @t71 (not @t70)))) % 0.34/0.65 (assume @p53 (forall @t11 (=> @t71 (not @t72)))) % 0.34/0.65 (assume @p54 (forall @t11 (=> @t10 (and @t70 (tptp.relation @t45))))) % 0.34/0.65 (assume @p55 (forall @t11 (=> @t10 (and @t72 (tptp.relation @t49))))) % 0.34/0.65 (assume @p56 (forall @t6 (= (tptp.set_union2 @t1 @t1) @t1))) % 0.34/0.65 (assume @p57 (forall @t6 (= (tptp.set_intersection2 @t1 @t1) @t1))) % 0.34/0.65 (assume @p58 (forall @t6 (=> @t51 (= (tptp.subset_complement @t1 @t50) @t2)))) % 0.34/0.65 (assume @p59 (forall @t11 (=> @t9 (= (tptp.relation_inverse @t53) @t1)))) % 0.34/0.65 (assume @p60 (forall @t6 (=> @t60 (= (tptp.complements_of_subsets @t1 @t58) @t2)))) % 0.34/0.65 (assume @p61 (forall @t6 (not (tptp.proper_subset @t1 @t1)))) % 0.34/0.65 (assume @p62 (forall @t11 (not (= @t32 tptp.empty_set)))) % 0.34/0.65 (assume @p63 (forall @t6 (=> @t5 (= (tptp.set_union2 @t32 @t2) @t2)))) % 0.34/0.65 (assume @p64 (forall @t6 (not (and @t73 @t5)))) % 0.34/0.65 (assume @p65 (forall @t6 (=> (not @t5) @t73))) % 0.34/0.65 (assume @p66 (forall @t6 (= (tptp.subset @t32 @t2) @t5))) % 0.34/0.65 (assume @p67 (forall @t6 (= (= @t47 tptp.empty_set) @t16))) % 0.34/0.65 (assume @p68 (forall @t6 (=> @t51 (forall @t30 (=> @t29 @t43))))) % 0.34/0.65 (assume @p69 (forall @t38 (=> @t16 (or @t43 (tptp.subset @t1 (tptp.set_difference @t2 (tptp.singleton @t19))))))) % 0.34/0.65 (assume @p70 (forall @t6 (= (tptp.subset @t1 @t74) (or @t25 (= @t1 @t74))))) % 0.34/0.65 (assume @p71 (forall @t6 (=> @t5 (tptp.subset @t1 @t75)))) % 0.34/0.65 (assume @p72 (forall @t77 (= (tptp.in @t52 (tptp.cartesian_product2 @t19 @t18)) (and @t76 (tptp.in @t2 @t18))))) % 0.34/0.65 (assume @p73 (forall @t6 (=> @t44 @t78))) % 0.34/0.65 (assume @p74 (exists @t11 (and @t10 @t9))) % 0.34/0.65 (assume @p75 (forall @t11 (=> @t36 (exists @t22 (and @t51 @t69))))) % 0.34/0.65 (assume @p76 (exists @t11 @t10)) % 0.34/0.65 (assume @p77 (exists @t11 @t71)) % 0.34/0.65 (assume @p78 (forall @t11 (exists @t22 (and @t51 @t34)))) % 0.34/0.65 (assume @p79 (exists @t11 @t36)) % 0.34/0.65 (assume @p80 (forall @t6 (=> @t60 (= @t63 @t75)))) % 0.34/0.65 (assume @p81 (forall @t6 (=> @t60 (= @t64 (tptp.set_meet @t2))))) % 0.34/0.65 (assume @p82 (forall @t38 (=> @t67 (= @t65 @t79)))) % 0.34/0.65 (assume @p83 (forall @t6 (tptp.subset @t1 @t1))) % 0.34/0.65 (assume @p84 (forall @t6 (=> @t55 (tptp.disjoint @t2 @t1)))) % 0.34/0.65 (assume @p85 (forall @t77 (not (and (= @t12 (tptp.unordered_pair @t19 @t18)) (not @t80) (not (= @t1 @t18)))))) % 0.34/0.65 (assume @p86 (forall @t38 (=> @t16 (and (tptp.subset @t81 (tptp.cartesian_product2 @t2 @t19)) (tptp.subset (tptp.cartesian_product2 @t19 @t1) (tptp.cartesian_product2 @t19 @t2)))))) % 0.34/0.65 (assume @p87 (forall @t77 (=> (and @t16 (tptp.subset @t19 @t18)) (tptp.subset @t81 (tptp.cartesian_product2 @t2 @t18))))) % 0.34/0.65 (assume @p88 (forall @t6 (=> @t16 (= @t14 @t2)))) % 0.34/0.65 (assume @p89 (forall @t11 (exists @t22 (and @t5 @t86 (forall @t30 (=> @t29 (tptp.in @t85 @t2))) @t84)))) % 0.34/0.65 (assume @p90 (forall @t6 (tptp.subset @t15 @t1))) % 0.34/0.65 (assume @p91 (forall @t38 (=> (and @t16 @t88) (tptp.subset @t1 @t87)))) % 0.34/0.65 (assume @p92 (forall @t11 (= (tptp.set_union2 @t1 tptp.empty_set) @t1))) % 0.34/0.65 (assume @p93 (forall @t6 (=> @t5 @t89))) % 0.34/0.65 (assume @p94 (forall @t38 (=> (and @t16 (tptp.subset @t2 @t19)) @t88))) % 0.34/0.65 (assume @p95 (= (tptp.powerset tptp.empty_set) (tptp.singleton tptp.empty_set))) % 0.34/0.65 (assume @p96 (forall @t38 (=> @t57 (=> @t90 (and (tptp.in @t1 (tptp.relation_dom @t19)) (tptp.in @t2 (tptp.relation_rng @t19))))))) % 0.34/0.65 (assume @p97 (forall @t11 (=> @t9 (tptp.subset @t1 (tptp.cartesian_product2 @t45 @t49))))) % 0.34/0.65 (assume @p98 (forall @t11 (=> @t9 (forall @t22 (=> @t54 (=> @t16 (and (tptp.subset @t45 @t92) (tptp.subset @t49 @t91)))))))) % 0.34/0.65 (assume @p99 (forall @t38 (=> @t16 (tptp.subset (tptp.set_intersection2 @t1 @t19) @t87)))) % 0.34/0.65 (assume @p100 (forall @t6 (=> @t16 (= @t15 @t1)))) % 0.34/0.65 (assume @p101 (forall @t11 (= (tptp.set_intersection2 @t1 tptp.empty_set) tptp.empty_set))) % 0.34/0.65 (assume @p102 (forall @t6 (=> @t89 (or @t34 @t5)))) % 0.34/0.65 (assume @p103 (forall @t6 (=> (forall @t30 (= @t43 @t29)) @t17))) % 0.34/0.65 (assume @p104 (forall @t11 (tptp.subset tptp.empty_set @t1))) % 0.34/0.65 (assume @p105 (forall @t38 (=> @t57 (=> @t90 (and (tptp.in @t1 @t93) (tptp.in @t2 @t93)))))) % 0.34/0.65 (assume @p106 (forall @t38 (=> @t16 (tptp.subset (tptp.set_difference @t1 @t19) @t79)))) % 0.34/0.65 (assume @p107 (forall @t77 (=> (= @t52 @t20) (and @t80 (= @t2 @t18))))) % 0.34/0.65 (assume @p108 (forall @t6 (tptp.subset @t47 @t1))) % 0.34/0.65 (assume @p109 (forall @t11 (=> @t9 (and (= @t49 (tptp.relation_dom @t53)) (= @t45 (tptp.relation_rng @t53)))))) % 0.34/0.65 (assume @p110 (forall @t38 (= (tptp.subset @t12 @t19) (and @t76 @t94)))) % 0.34/0.65 (assume @p111 (forall @t6 (= @t95 @t14))) % 0.34/0.65 (assume @p112 (forall @t11 (= (tptp.set_difference @t1 tptp.empty_set) @t1))) % 0.34/0.65 (assume @p113 (forall @t6 (= @t78 @t16))) % 0.34/0.65 (assume @p114 (forall @t6 (and (not (and @t97 (forall @t30 (not @t96)))) (not (and (exists @t30 @t96) @t55))))) % 0.34/0.65 (assume @p115 (forall @t11 (=> (tptp.subset @t1 tptp.empty_set) @t25))) % 0.34/0.65 (assume @p116 (forall @t6 (= (tptp.set_difference @t14 @t2) @t47))) % 0.34/0.65 (assume @p117 (forall @t6 (=> @t51 (forall @t30 (=> @t66 (= @t99 (tptp.subset @t2 @t98))))))) % 0.34/0.65 (assume @p118 (forall @t11 (=> @t9 (forall @t22 (=> @t54 (tptp.subset @t100 @t45)))))) % 0.34/0.65 (assume @p119 (forall @t11 (=> @t9 (forall @t22 (=> @t54 (tptp.subset (tptp.relation_rng @t56) @t91)))))) % 0.34/0.65 (assume @p120 (forall @t6 (=> @t16 (= @t2 @t95)))) % 0.34/0.65 (assume @p121 (forall @t11 (=> @t9 (forall @t22 (=> @t54 (=> (tptp.subset @t49 @t92) (= @t100 @t45))))))) % 0.34/0.65 (assume @p122 (forall @t6 (=> @t60 (not (and @t101 (= @t58 tptp.empty_set)))))) % 0.34/0.65 (assume @p123 (forall @t11 (=> @t9 (forall @t22 (=> @t54 (=> (tptp.subset @t45 @t91) (= (tptp.relation_rng (tptp.relation_composition @t2 @t1)) @t49))))))) % 0.34/0.65 (assume @p124 (forall @t6 (=> @t60 (=> @t101 (= (tptp.subset_difference @t1 @t46 @t63) (tptp.meet_of_subsets @t1 @t58)))))) % 0.34/0.65 (assume @p125 (forall @t6 (=> @t60 (=> @t101 (= (tptp.union_of_subsets @t1 @t58) (tptp.subset_difference @t1 @t46 @t64)))))) % 0.34/0.65 (assume @p126 (forall @t6 (= (tptp.set_difference @t1 @t47) @t15))) % 0.34/0.65 (assume @p127 (forall @t11 (= (tptp.set_difference tptp.empty_set @t1) tptp.empty_set))) % 0.34/0.65 (assume @p128 (forall @t38 (=> (and @t5 @t102) (tptp.element @t1 @t19)))) % 0.34/0.65 (assume @p129 (forall @t6 (and (not (and @t97 (forall @t30 (not @t103)))) (not (and (exists @t30 @t103) @t55))))) % 0.34/0.65 (assume @p130 (forall @t11 (=> @t31 (forall @t22 (=> @t51 (forall @t30 (=> (tptp.element @t19 @t1) (=> @t82 (tptp.in @t19 @t50))))))))) % 0.34/0.65 (assume @p131 (forall @t38 (=> @t66 (not (and (tptp.in @t2 @t98) @t94))))) % 0.34/0.65 (assume @p132 (forall @t11 (=> @t9 (=> (forall (@list @t2 @t19) (not (tptp.in (tptp.ordered_pair @t2 @t19) @t1))) @t25)))) % 0.34/0.65 (assume @p133 (forall @t38 (not (and @t5 @t102 (tptp.empty @t19))))) % 0.34/0.65 (assume @p134 (and (= @t105 tptp.empty_set) (= @t104 tptp.empty_set))) % 0.34/0.65 (assume @p135 (forall @t6 (not (and @t16 @t7)))) % 0.34/0.65 (assume @p136 (forall @t38 (=> (and @t16 @t99) (tptp.disjoint @t1 @t19)))) % 0.34/0.65 (assume @p137 @t111) % 0.34/0.65 (assume @p138 @t115) % 0.34/0.65 (assume @p139 (forall @t6 (= (= (tptp.set_difference @t1 @t74) @t1) @t4))) % 0.34/0.65 (assume @p140 (forall @t11 (= (tptp.unordered_pair @t1 @t1) @t32))) % 0.34/0.65 (assume @p141 (forall @t11 (=> @t10 @t25))) % 0.34/0.65 (assume @p142 (forall @t6 (=> (tptp.subset @t32 @t74) @t17))) % 0.34/0.65 (assume @p143 (forall @t6 (not (and @t5 @t34)))) % 0.34/0.65 (assume @p144 (forall @t6 (tptp.subset @t1 @t14))) % 0.34/0.65 (assume @p145 (forall @t6 (= @t55 (= @t47 @t1)))) % 0.34/0.65 (assume @p146 (forall @t6 (not (and @t10 @t61 @t34)))) % 0.34/0.65 (assume @p147 (forall @t38 (=> (and @t16 @t83) (tptp.subset (tptp.set_union2 @t1 @t19) @t2)))) % 0.34/0.65 (assume @p148 (forall @t38 (=> @t116 @t17))) % 0.34/0.65 (assume @p149 (forall @t11 (= (tptp.union @t33) @t1))) % 0.34/0.65 (assume @p150 (forall @t11 (exists @t22 (and @t5 @t86 (forall @t30 (not (and @t29 (forall @t28 (not (and @t39 (forall (@list @t41) (=> (tptp.subset @t41 @t19) (tptp.in @t41 @t18))))))))) @t84)))) % 0.34/0.65 (assume @p151 (forall @t38 (=> @t116 (= @t2 @t19)))) % 0.34/0.65 (step @p152 :rule and_elim :premises (@p134) :args (1)) % 0.34/0.65 (step @p153 :rule symm :premises (@p152)) % 0.34/0.65 (step @p154 :rule bool-impl-elim :args (@t9 @t119)) % 0.34/0.65 (step @p155 :rule cong :premises (@p154) :args ((forall @t11 (=> @t9 @t119)))) % 0.34/0.65 (step @p156 :rule eq-symm :args (@t49 tptp.empty_set)) % 0.34/0.65 (step @p157 :rule eq-symm :args (@t45 tptp.empty_set)) % 0.34/0.65 (step @p158 :rule cong :premises (@p157 @p156) :args (@t112)) % 0.34/0.65 (step @p159 :rule refl :args (@t9)) % 0.34/0.65 (step @p160 :rule cong :premises (@p159 @p158) :args (@t113)) % 0.34/0.65 (step @p161 :rule cong :premises (@p160) :args (@t114)) % 0.34/0.65 (step @p162 :rule trans :premises (@p161 @p155)) % 0.34/0.65 (step @p163 :rule cong :premises (@p162) :args (@t115)) % 0.34/0.65 (step @p164 :rule eq_resolve :premises (@p138 @p163)) % 0.34/0.65 (step @p165 :rule skolemize :premises (@p164)) % 0.34/0.65 (step @p166 :rule cnf_or_neg :args (@t127 1)) % 0.34/0.65 (step @p167 :rule chain_m_resolution :premises (@p166 @p165) :args ((not @t124) @t128 @t129)) % 0.34/0.65 (step @p168 :rule cnf_equiv_neg1 :args (@t124)) % 0.34/0.65 (step @p169 :rule reordering :premises (@p168) :args ((or @t123 @t122 @t124))) % 0.34/0.65 (step @p170 :rule cnf_and_pos :args (@t132 1)) % 0.34/0.65 (step @p171 :rule reordering :premises (@p170) :args ((or @t130 @t133))) % 0.34/0.65 (step @p172 :rule bool-double-not-elim :args (@t125)) % 0.34/0.65 (step @p173 :rule refl :args (@t127)) % 0.34/0.65 (step @p174 :rule nary_cong :premises (@p173 @p172) :args ((or @t127 (not @t126)))) % 0.34/0.65 (step @p175 :rule cnf_or_neg :args (@t127 0)) % 0.34/0.65 (step @p176 :rule eq_resolve :premises (@p175 @p174)) % 0.34/0.65 (step @p177 :rule reordering :premises (@p176) :args ((or @t125 @t127))) % 0.34/0.65 (step @p178 :rule chain_m_resolution :premises (@p177 @p165) :args (@t125 @t128 @t129)) % 0.34/0.65 (step @p179 :rule aci_norm :args ((= (or @t120 (or @t134 @t25)) @t135))) % 0.34/0.65 (step @p180 :rule refl :args (@t25)) % 0.34/0.65 (step @p181 :rule bool-or-de-morgan :args (@t118 @t117 false)) % 0.34/0.65 (step @p182 :rule nary_cong :premises (@p181 @p180) :args ((or (not @t136) @t25))) % 0.34/0.65 (step @p183 :rule bool-impl-elim :args (@t136 @t25)) % 0.34/0.65 (step @p184 :rule trans :premises (@p183 @p182)) % 0.34/0.65 (step @p185 :rule refl :args (@t120)) % 0.34/0.65 (step @p186 :rule nary_cong :premises (@p185 @p184) :args ((or @t120 @t137))) % 0.34/0.65 (step @p187 :rule trans :premises (@p186 @p179)) % 0.34/0.65 (step @p188 :rule bool-impl-elim :args (@t9 @t137)) % 0.34/0.65 (step @p189 :rule trans :premises (@p188 @p187)) % 0.34/0.65 (step @p190 :rule cong :premises (@p189) :args ((forall @t11 (=> @t9 @t137)))) % 0.34/0.65 (step @p191 :rule refl :args (@t25)) % 0.34/0.65 (step @p192 :rule nary_cong :premises (@p157 @p156) :args (@t108)) % 0.34/0.65 (step @p193 :rule cong :premises (@p192 @p191) :args (@t109)) % 0.34/0.65 (step @p194 :rule cong :premises (@p159 @p193) :args (@t110)) % 0.34/0.65 (step @p195 :rule cong :premises (@p194) :args (@t111)) % 0.34/0.65 (step @p196 :rule trans :premises (@p195 @p190)) % 0.34/0.65 (step @p197 :rule eq_resolve :premises (@p137 @p196)) % 0.34/0.65 (step @p198 :rule eq-symm :args (@t121 tptp.empty_set)) % 0.34/0.65 (step @p199 :rule refl :args (@t132)) % 0.34/0.65 (step @p200 :rule refl :args (@t126)) % 0.34/0.65 (step @p201 :rule nary_cong :premises (@p200 @p199 @p198) :args (@t138)) % 0.34/0.65 (step @p202 :rule refl :args (@t139)) % 0.34/0.65 (step @p203 :rule cong :premises (@p202 @p201) :args ((=> @t139 @t138))) % 0.34/0.65 (assume-push @p259 @t139) % 0.34/0.65 (step @p205 :rule instantiate :premises (@p197) :args ((@list @t121))) % 0.34/0.65 (step-pop @p260 :rule scope :premises (@p205)) % 0.34/0.65 (step @p206 :rule process_scope :premises (@p260) :args (@t138)) % 0.34/0.65 (step @p208 :rule eq_resolve :premises (@p206 @p203)) % 0.34/0.65 (step @p209 :rule implies_elim :premises (@p208)) % 0.34/0.65 (step @p210 :rule chain_m_resolution :premises (@p209 @p197) :args (@t141 @t142 (@list @t139))) % 0.34/0.65 (step @p211 :rule cnf_or_pos :args (@t141)) % 0.34/0.65 (step @p212 :rule reordering :premises (@p211) :args ((or @t126 @t140 @t132 (not @t141)))) % 0.34/0.65 (step @p213 :rule and_elim :premises (@p134) :args (0)) % 0.34/0.65 (step @p214 :rule symm :premises (@p213)) % 0.34/0.65 (assume-push @p261 @t143) % 0.34/0.65 (assume-push @p262 @t140) % 0.34/0.65 (assume-push @p263 @t140) % 0.34/0.65 (assume-push @p264 @t143) % 0.34/0.65 (step @p219 :rule cong :premises (@p262) :args (@t105)) % 0.34/0.65 (step @p220 :rule trans :premises (@p214 @p219)) % 0.34/0.65 (step-pop @p265 :rule scope :premises (@p220)) % 0.34/0.65 (step-pop @p266 :rule scope :premises (@p265)) % 0.34/0.65 (step @p221 :rule process_scope :premises (@p266) :args (@t123)) % 0.34/0.65 (step @p224 :rule and_intro :premises (@p262 @p214)) % 0.34/0.65 (step @p225 :rule modus_ponens :premises (@p224 @p221)) % 0.34/0.65 (step-pop @p267 :rule scope :premises (@p225)) % 0.34/0.65 (step-pop @p268 :rule scope :premises (@p267)) % 0.34/0.65 (step @p226 :rule process_scope :premises (@p268) :args (@t123)) % 0.34/0.65 (step @p229 :rule implies_elim :premises (@p226)) % 0.34/0.65 (step @p230 :rule cnf_and_neg :args (@t144)) % 0.34/0.65 (step @p231 :rule resolution :premises (@p230 @p229) :args (true @t144)) % 0.34/0.65 (step @p232 :rule reordering :premises (@p231) :args ((or (not @t143) @t123 @t145))) % 0.34/0.65 (step @p233 :rule chain_m_resolution :premises (@p232 @p214 @p212 @p210 @p178 @p171 @p169 @p167) :args (@t123 (@list false false false false true false true) (@list @t143 @t140 @t141 @t125 @t132 @t122 @t124))) % 0.34/0.65 (step @p234 :rule cnf_equiv_neg2 :args (@t124)) % 0.34/0.65 (step @p235 :rule chain_m_resolution :premises (@p234 @p167 @p233) :args (@t130 (@list true false) (@list @t124 @t123))) % 0.34/0.65 (step @p236 :rule cnf_and_pos :args (@t132 0)) % 0.34/0.65 (step @p237 :rule reordering :premises (@p236) :args ((or @t131 @t133))) % 0.34/0.65 (step @p238 :rule chain_m_resolution :premises (@p237 @p233) :args (@t133 @t142 (@list @t123))) % 0.34/0.65 (step @p239 :rule chain_m_resolution :premises (@p212 @p178 @p238 @p210) :args (@t140 @t146 (@list @t125 @t132 @t141))) % 0.34/0.65 (assume-push @p269 @t147) % 0.34/0.65 (assume-push @p270 @t140) % 0.34/0.65 (assume-push @p271 @t140) % 0.34/0.65 (assume-push @p272 @t147) % 0.34/0.65 (step @p244 :rule cong :premises (@p270) :args (@t104)) % 0.34/0.65 (step @p245 :rule trans :premises (@p153 @p244)) % 0.34/0.65 (step-pop @p273 :rule scope :premises (@p245)) % 0.34/0.65 (step-pop @p274 :rule scope :premises (@p273)) % 0.34/0.65 (step @p246 :rule process_scope :premises (@p274) :args (@t122)) % 0.34/0.65 (step @p249 :rule and_intro :premises (@p270 @p153)) % 0.34/0.65 (step @p250 :rule modus_ponens :premises (@p249 @p246)) % 0.34/0.65 (step-pop @p275 :rule scope :premises (@p250)) % 0.34/0.65 (step-pop @p276 :rule scope :premises (@p275)) % 0.34/0.65 (step @p251 :rule process_scope :premises (@p276) :args (@t122)) % 0.34/0.65 (step @p254 :rule implies_elim :premises (@p251)) % 0.34/0.65 (step @p255 :rule cnf_and_neg :args (@t148)) % 0.34/0.65 (step @p256 :rule resolution :premises (@p255 @p254) :args (true @t148)) % 0.34/0.65 (step @p257 :rule reordering :premises (@p256) :args ((or (not @t147) @t122 @t145))) % 0.34/0.65 (step @p258 false :rule chain_m_resolution :premises (@p257 @p239 @p235 @p153) :args (false @t146 (@list @t140 @t122 @t147))) % 0.34/0.65 ) % 0.34/0.65 % SZS output end Proof % 0.34/0.65 % cvc5 exiting %------------------------------------------------------------------------------