%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SEU364+2 : TPTP v8.2.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : do_cvc5 %s %d

% Computer : n029.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 May 29 17:49:27 EDT 2024

% Result   : Theorem 0.61s 1.06s
% Output   : Proof 0.61s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.19  % Problem    : SEU364+2 : TPTP v8.2.0. Released v3.3.0.
% 0.11/0.20  % Command    : do_cvc5 %s %d
% 0.21/0.41  % Computer : n029.cluster.edu
% 0.21/0.41  % Model    : x86_64 x86_64
% 0.21/0.41  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.21/0.41  % Memory   : 8042.1875MB
% 0.21/0.41  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.21/0.41  % CPULimit   : 300
% 0.21/0.41  % WCLimit    : 300
% 0.21/0.41  % DateTime   : Mon May 27 10:56:39 EDT 2024
% 0.21/0.42  % CPUTime    : 
% 0.61/0.76  %----Proving TF0_NAR, FOF, or CNF
% 0.61/1.06  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.61/1.06  % SZS status Theorem for /export/starexec/sandbox/tmp/tmp.8bIpux7RGx/cvc5---1.0.5_21118.smt2
% 0.61/1.06  % SZS output start Proof for /export/starexec/sandbox/tmp/tmp.8bIpux7RGx/cvc5---1.0.5_21118.smt2
% 0.61/1.06  (assume a0 (forall ((A $$unsorted)) (=> (tptp.rel_str A) (=> (tptp.strict_rel_str A) (= A (tptp.rel_str_of (tptp.the_carrier A) (tptp.the_InternalRel A)))))))
% 0.61/1.06  (assume a1 (forall ((A $$unsorted)) (=> (tptp.latt_str A) (=> (tptp.strict_latt_str A) (= A (tptp.latt_str_of (tptp.the_carrier A) (tptp.the_L_join A) (tptp.the_L_meet A)))))))
% 0.61/1.06  (assume a2 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (not (tptp.in B A)))))
% 0.61/1.06  (assume a3 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.proper_subset A B) (not (tptp.proper_subset B A)))))
% 0.61/1.06  (assume a4 (forall ((A $$unsorted)) (=> (tptp.v1_membered A) (forall ((B $$unsorted)) (=> (tptp.element B A) (tptp.v1_xcmplx_0 B))))))
% 0.61/1.06  (assume a5 (forall ((A $$unsorted)) (=> (tptp.v2_membered A) (forall ((B $$unsorted)) (=> (tptp.element B A) (and (tptp.v1_xcmplx_0 B) (tptp.v1_xreal_0 B)))))))
% 0.61/1.06  (assume a6 (forall ((A $$unsorted)) (=> (tptp.v3_membered A) (forall ((B $$unsorted)) (=> (tptp.element B A) (and (tptp.v1_xcmplx_0 B) (tptp.v1_xreal_0 B) (tptp.v1_rat_1 B)))))))
% 0.61/1.06  (assume a7 (forall ((A $$unsorted)) (=> (tptp.v4_membered A) (forall ((B $$unsorted)) (=> (tptp.element B A) (and (tptp.v1_xcmplx_0 B) (tptp.v1_xreal_0 B) (tptp.v1_int_1 B) (tptp.v1_rat_1 B)))))))
% 0.61/1.06  (assume a8 (forall ((A $$unsorted)) (=> (tptp.v5_membered A) (forall ((B $$unsorted)) (=> (tptp.element B A) (and (tptp.v1_xcmplx_0 B) (tptp.natural B) (tptp.v1_xreal_0 B) (tptp.v1_int_1 B) (tptp.v1_rat_1 B)))))))
% 0.61/1.06  (assume a9 (forall ((A $$unsorted)) (=> (tptp.empty A) (and (tptp.v1_membered A) (tptp.v2_membered A) (tptp.v3_membered A) (tptp.v4_membered A) (tptp.v5_membered A)))))
% 0.61/1.06  (assume a10 (forall ((A $$unsorted)) (=> (tptp.v1_membered A) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.powerset A)) (tptp.v1_membered B))))))
% 0.61/1.06  (assume a11 (forall ((A $$unsorted)) (=> (tptp.v2_membered A) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.powerset A)) (and (tptp.v1_membered B) (tptp.v2_membered B)))))))
% 0.61/1.06  (assume a12 (forall ((A $$unsorted)) (=> (tptp.v3_membered A) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.powerset A)) (and (tptp.v1_membered B) (tptp.v2_membered B) (tptp.v3_membered B)))))))
% 0.61/1.06  (assume a13 (forall ((A $$unsorted)) (=> (tptp.v4_membered A) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.powerset A)) (and (tptp.v1_membered B) (tptp.v2_membered B) (tptp.v3_membered B) (tptp.v4_membered B)))))))
% 0.61/1.06  (assume a14 (forall ((A $$unsorted)) (=> (tptp.ordinal A) (forall ((B $$unsorted)) (=> (tptp.element B A) (and (tptp.epsilon_transitive B) (tptp.epsilon_connected B) (tptp.ordinal B)))))))
% 0.61/1.06  (assume a15 (forall ((A $$unsorted)) (=> (tptp.empty A) (tptp.finite A))))
% 0.61/1.06  (assume a16 (forall ((A $$unsorted)) (=> (tptp.preboolean A) (and (tptp.cup_closed A) (tptp.diff_closed A)))))
% 0.61/1.06  (assume a17 (forall ((A $$unsorted)) (=> (tptp.empty A) (tptp.function A))))
% 0.61/1.06  (assume a18 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.relation_of2 C A B) (=> (and (tptp.function C) (tptp.v1_partfun1 C A B)) (and (tptp.function C) (tptp.quasi_total C A B))))))
% 0.61/1.06  (assume a19 (forall ((A $$unsorted)) (=> (tptp.latt_str A) (=> (and (not (tptp.empty_carrier A)) (tptp.lattice A)) (and (not (tptp.empty_carrier A)) (tptp.join_commutative A) (tptp.join_associative A) (tptp.meet_commutative A) (tptp.meet_associative A) (tptp.meet_absorbing A) (tptp.join_absorbing A))))))
% 0.61/1.06  (assume a20 (forall ((A $$unsorted)) (=> (tptp.v5_membered A) (tptp.v4_membered A))))
% 0.61/1.06  (assume a21 (forall ((A $$unsorted)) (=> (tptp.ordinal A) (and (tptp.epsilon_transitive A) (tptp.epsilon_connected A)))))
% 0.61/1.06  (assume a22 (forall ((A $$unsorted)) (=> (and (tptp.relation A) (tptp.symmetric A) (tptp.transitive A)) (and (tptp.relation A) (tptp.reflexive A)))))
% 0.61/1.06  (assume a23 (forall ((A $$unsorted)) (=> (tptp.empty A) (tptp.relation A))))
% 0.61/1.06  (assume a24 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.element C (tptp.powerset (tptp.cartesian_product2 A B))) (tptp.relation C))))
% 0.61/1.06  (assume a25 (forall ((A $$unsorted)) (=> (tptp.v5_membered A) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.powerset A)) (and (tptp.v1_membered B) (tptp.v2_membered B) (tptp.v3_membered B) (tptp.v4_membered B) (tptp.v5_membered B)))))))
% 0.61/1.06  (assume a26 (forall ((A $$unsorted)) (=> (and (tptp.empty A) (tptp.ordinal A)) (and (tptp.epsilon_transitive A) (tptp.epsilon_connected A) (tptp.ordinal A) (tptp.natural A)))))
% 0.61/1.06  (assume a27 (forall ((A $$unsorted)) (=> (tptp.finite A) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.powerset A)) (tptp.finite B))))))
% 0.61/1.06  (assume a28 (forall ((A $$unsorted)) (=> (and (tptp.cup_closed A) (tptp.diff_closed A)) (tptp.preboolean A))))
% 0.61/1.06  (assume a29 (forall ((A $$unsorted)) (=> (and (tptp.relation A) (tptp.empty A) (tptp.function A)) (and (tptp.relation A) (tptp.function A) (tptp.one_to_one A)))))
% 0.61/1.06  (assume a30 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.relation_of2 C A B) (=> (and (tptp.function C) (tptp.quasi_total C A B) (tptp.bijective C A B)) (and (tptp.function C) (tptp.one_to_one C) (tptp.quasi_total C A B) (tptp.onto C A B))))))
% 0.61/1.06  (assume a31 (forall ((A $$unsorted)) (=> (tptp.latt_str A) (=> (and (not (tptp.empty_carrier A)) (tptp.join_commutative A) (tptp.join_associative A) (tptp.meet_commutative A) (tptp.meet_associative A) (tptp.meet_absorbing A) (tptp.join_absorbing A)) (and (not (tptp.empty_carrier A)) (tptp.lattice A))))))
% 0.61/1.06  (assume a32 (forall ((A $$unsorted)) (=> (tptp.v4_membered A) (tptp.v3_membered A))))
% 0.61/1.06  (assume a33 (forall ((A $$unsorted)) (=> (and (tptp.epsilon_transitive A) (tptp.epsilon_connected A)) (tptp.ordinal A))))
% 0.61/1.06  (assume a34 (forall ((A $$unsorted)) (=> (tptp.element A tptp.omega) (and (tptp.epsilon_transitive A) (tptp.epsilon_connected A) (tptp.ordinal A) (tptp.natural A)))))
% 0.61/1.06  (assume a35 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.relation_of2 C A B) (=> (and (tptp.function C) (tptp.one_to_one C) (tptp.quasi_total C A B) (tptp.onto C A B)) (and (tptp.function C) (tptp.quasi_total C A B) (tptp.bijective C A B))))))
% 0.61/1.06  (assume a36 (forall ((A $$unsorted)) (=> (tptp.v3_membered A) (tptp.v2_membered A))))
% 0.61/1.06  (assume a37 (forall ((A $$unsorted)) (=> (tptp.empty A) (and (tptp.epsilon_transitive A) (tptp.epsilon_connected A) (tptp.ordinal A)))))
% 0.61/1.06  (assume a38 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation_of2 B A A) (=> (and (tptp.function B) (tptp.v1_partfun1 B A A) (tptp.reflexive B) (tptp.quasi_total B A A)) (and (tptp.function B) (tptp.one_to_one B) (tptp.quasi_total B A A) (tptp.onto B A A) (tptp.bijective B A A))))))
% 0.61/1.06  (assume a39 (forall ((A $$unsorted)) (=> (tptp.v2_membered A) (tptp.v1_membered A))))
% 0.61/1.06  (assume a40 (forall ((A $$unsorted) (B $$unsorted)) (=> (not (tptp.empty B)) (forall ((C $$unsorted)) (=> (tptp.relation_of2 C A B) (=> (and (tptp.function C) (tptp.quasi_total C A B)) (and (tptp.function C) (tptp.v1_partfun1 C A B) (tptp.quasi_total C A B))))))))
% 0.61/1.06  (assume a41 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.empty A)) (not (tptp.empty B))) (forall ((C $$unsorted)) (=> (tptp.relation_of2 C A B) (=> (and (tptp.function C) (tptp.quasi_total C A B)) (and (tptp.function C) (not (tptp.empty C)) (tptp.v1_partfun1 C A B) (tptp.quasi_total C A B))))))))
% 0.61/1.06  (assume a42 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.unordered_pair A B) (tptp.unordered_pair B A))))
% 0.61/1.06  (assume a43 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_union2 A B) (tptp.set_union2 B A))))
% 0.61/1.06  (assume a44 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.join_commutative A) (tptp.join_semilatt_str A) (tptp.element B (tptp.the_carrier A)) (tptp.element C (tptp.the_carrier A))) (= (tptp.join_commut A B C) (tptp.join_commut A C B)))))
% 0.61/1.06  (assume a45 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_intersection2 A B) (tptp.set_intersection2 B A))))
% 0.61/1.06  (assume a46 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.meet_commutative A) (tptp.meet_semilatt_str A) (tptp.element B (tptp.the_carrier A)) (tptp.element C (tptp.the_carrier A))) (= (tptp.meet_commut A B C) (tptp.meet_commut A C B)))))
% 0.61/1.06  (assume a47 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.element B (tptp.powerset A)) (tptp.element C (tptp.powerset A))) (= (tptp.subset_union2 A B C) (tptp.subset_union2 A C B)))))
% 0.61/1.06  (assume a48 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.element B (tptp.powerset A)) (tptp.element C (tptp.powerset A))) (= (tptp.subset_intersection2 A B C) (tptp.subset_intersection2 A C B)))))
% 0.61/1.06  (assume a49 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.ordinal A) (tptp.ordinal B)) (or (tptp.ordinal_subset A B) (tptp.ordinal_subset B A)))))
% 0.61/1.06  (assume a50 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (= (= B (tptp.identity_relation A)) (forall ((C $$unsorted) (D $$unsorted)) (= (tptp.in (tptp.ordered_pair C D) B) (and (tptp.in C A) (= C D))))))))
% 0.61/1.06  (assume a51 (forall ((A $$unsorted) (B $$unsorted)) (= (= A B) (and (tptp.subset A B) (tptp.subset B A)))))
% 0.61/1.06  (assume a52 (forall ((A $$unsorted)) (=> (tptp.rel_str A) (forall ((B $$unsorted) (C $$unsorted)) (=> (tptp.element C (tptp.the_carrier A)) (=> (tptp.ex_inf_of_relstr_set A B) (= (= C (tptp.meet_on_relstr A B)) (and (tptp.relstr_element_smaller A B C) (forall ((D $$unsorted)) (=> (tptp.element D (tptp.the_carrier A)) (=> (tptp.relstr_element_smaller A B D) (tptp.related A D C))))))))))))
% 0.61/1.06  (assume a53 (forall ((A $$unsorted)) (=> (tptp.one_sorted_str A) (= (tptp.identity_on_carrier A) (tptp.identity_as_relation_of (tptp.the_carrier A))))))
% 0.61/1.06  (assume a54 (forall ((A $$unsorted)) (=> (tptp.relation A) (forall ((B $$unsorted) (C $$unsorted)) (=> (tptp.relation C) (= (= C (tptp.relation_dom_restriction A B)) (forall ((D $$unsorted) (E $$unsorted)) (= (tptp.in (tptp.ordered_pair D E) C) (and (tptp.in D B) (tptp.in (tptp.ordered_pair D E) A))))))))))
% 0.61/1.06  (assume a55 (forall ((A $$unsorted)) (=> (tptp.rel_str A) (= (tptp.bottom_of_relstr A) (tptp.join_on_relstr A tptp.empty_set)))))
% 0.61/1.06  (assume a56 (forall ((A $$unsorted)) (=> (and (tptp.relation A) (tptp.function A)) (forall ((B $$unsorted) (C $$unsorted)) (= (= C (tptp.relation_image A B)) (forall ((D $$unsorted)) (= (tptp.in D C) (exists ((E $$unsorted)) (and (tptp.in E (tptp.relation_dom A)) (tptp.in E B) (= D (tptp.apply A E)))))))))))
% 0.61/1.06  (assume a57 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (forall ((C $$unsorted)) (=> (tptp.relation C) (= (= C (tptp.relation_rng_restriction A B)) (forall ((D $$unsorted) (E $$unsorted)) (= (tptp.in (tptp.ordered_pair D E) C) (and (tptp.in E A) (tptp.in (tptp.ordered_pair D E) B))))))))))
% 0.61/1.06  (assume a58 (forall ((A $$unsorted)) (=> (tptp.relation A) (= (tptp.antisymmetric A) (tptp.is_antisymmetric_in A (tptp.relation_field A))))))
% 0.61/1.06  (assume a59 (forall ((A $$unsorted)) (=> (and (tptp.relation A) (tptp.function A)) (forall ((B $$unsorted) (C $$unsorted)) (= (= C (tptp.relation_inverse_image A B)) (forall ((D $$unsorted)) (= (tptp.in D C) (and (tptp.in D (tptp.relation_dom A)) (tptp.in (tptp.apply A D) B)))))))))
% 0.61/1.06  (assume a60 (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.meet_semilatt_str A)) (= (tptp.lower_bounded_semilattstr A) (exists ((B $$unsorted)) (and (tptp.element B (tptp.the_carrier A)) (forall ((C $$unsorted)) (=> (tptp.element C (tptp.the_carrier A)) (and (= (tptp.meet A B C) B) (= (tptp.meet A C B) B))))))))))
% 0.61/1.06  (assume a61 (forall ((A $$unsorted)) (=> (tptp.top_str A) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.powerset (tptp.the_carrier A))) (forall ((C $$unsorted)) (=> (tptp.element C (tptp.powerset (tptp.the_carrier A))) (= (= C (tptp.topstr_closure A B)) (forall ((D $$unsorted)) (=> (tptp.in D (tptp.the_carrier A)) (= (tptp.in D C) (forall ((E $$unsorted)) (=> (tptp.element E (tptp.powerset (tptp.the_carrier A))) (not (and (tptp.open_subset E A) (tptp.in D E) (tptp.disjoint B E))))))))))))))))
% 0.61/1.06  (assume a62 (forall ((A $$unsorted)) (=> (tptp.relation A) (forall ((B $$unsorted) (C $$unsorted)) (= (= C (tptp.relation_image A B)) (forall ((D $$unsorted)) (= (tptp.in D C) (exists ((E $$unsorted)) (and (tptp.in (tptp.ordered_pair E D) A) (tptp.in E B))))))))))
% 0.61/1.06  (assume a63 (forall ((A $$unsorted)) (=> (tptp.rel_str A) (forall ((B $$unsorted)) (=> (tptp.rel_str B) (= (tptp.subrelstr B A) (and (tptp.subset (tptp.the_carrier B) (tptp.the_carrier A)) (tptp.subset (tptp.the_InternalRel B) (tptp.the_InternalRel A)))))))))
% 0.61/1.06  (assume a64 (forall ((A $$unsorted)) (=> (tptp.relation A) (forall ((B $$unsorted) (C $$unsorted)) (= (= C (tptp.relation_inverse_image A B)) (forall ((D $$unsorted)) (= (tptp.in D C) (exists ((E $$unsorted)) (and (tptp.in (tptp.ordered_pair D E) A) (tptp.in E B))))))))))
% 0.61/1.06  (assume a65 (forall ((A $$unsorted)) (=> (tptp.relation A) (= (tptp.connected A) (tptp.is_connected_in A (tptp.relation_field A))))))
% 0.61/1.06  (assume a66 (forall ((A $$unsorted)) (=> (tptp.rel_str A) (forall ((B $$unsorted)) (=> (tptp.subrelstr B A) (= (tptp.full_subrelstr B A) (= (tptp.the_InternalRel B) (tptp.relation_restriction_as_relation_of (tptp.the_InternalRel A) (tptp.the_carrier B)))))))))
% 0.61/1.06  (assume a67 (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.latt_str A)) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.the_carrier A)) (forall ((C $$unsorted)) (= (tptp.latt_set_smaller A B C) (forall ((D $$unsorted)) (=> (tptp.element D (tptp.the_carrier A)) (=> (tptp.in D C) (tptp.below A B D)))))))))))
% 0.61/1.06  (assume a68 (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.meet_semilatt_str A)) (=> (tptp.lower_bounded_semilattstr A) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.the_carrier A)) (= (= B (tptp.bottom_of_semilattstr A)) (forall ((C $$unsorted)) (=> (tptp.element C (tptp.the_carrier A)) (and (= (tptp.meet A B C) B) (= (tptp.meet A C B) B)))))))))))
% 0.61/1.06  (assume a69 (forall ((A $$unsorted)) (=> (tptp.relation A) (= (tptp.transitive A) (tptp.is_transitive_in A (tptp.relation_field A))))))
% 0.61/1.06  (assume a70 (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.latt_str A)) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.the_carrier A)) (forall ((C $$unsorted)) (= (tptp.latt_element_smaller A B C) (forall ((D $$unsorted)) (=> (tptp.element D (tptp.the_carrier A)) (=> (tptp.in D C) (tptp.below A D B)))))))))))
% 0.61/1.06  (assume a71 (forall ((A $$unsorted)) (=> (and (tptp.relation A) (tptp.function A)) (forall ((B $$unsorted) (C $$unsorted)) (= (tptp.apply_binary A B C) (tptp.apply A (tptp.ordered_pair B C)))))))
% 0.61/1.06  (assume a72 (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.topological_space A) (tptp.top_str A)) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.the_carrier A)) (forall ((C $$unsorted)) (=> (tptp.element C (tptp.powerset (tptp.the_carrier A))) (= (tptp.point_neighbourhood C A B) (tptp.in B (tptp.interior A C))))))))))
% 0.61/1.06  (assume a73 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (= (= D (tptp.unordered_triple A B C)) (forall ((E $$unsorted)) (= (tptp.in E D) (not (and (not (= E A)) (not (= E B)) (not (= E C)))))))))
% 0.61/1.06  (assume a74 (forall ((A $$unsorted)) (= (tptp.finite A) (exists ((B $$unsorted)) (and (tptp.relation B) (tptp.function B) (= (tptp.relation_rng B) A) (tptp.in (tptp.relation_dom B) tptp.omega))))))
% 0.61/1.06  (assume a75 (forall ((A $$unsorted)) (= (tptp.function A) (forall ((B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (tptp.in (tptp.ordered_pair B C) A) (tptp.in (tptp.ordered_pair B D) A)) (= C D))))))
% 0.61/1.06  (assume a76 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.relation_of2_as_subset C A B) (and (=> (=> (= B tptp.empty_set) (= A tptp.empty_set)) (= (tptp.quasi_total C A B) (= A (tptp.relation_dom_as_subset A B C)))) (=> (= B tptp.empty_set) (or (= A tptp.empty_set) (= (tptp.quasi_total C A B) (= C tptp.empty_set))))))))
% 0.61/1.06  (assume a77 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.strict_latt_str B) (tptp.latt_str B)) (= (= B (tptp.boole_lattice A)) (and (= (tptp.the_carrier B) (tptp.powerset A)) (forall ((C $$unsorted)) (=> (tptp.element C (tptp.powerset A)) (forall ((D $$unsorted)) (=> (tptp.element D (tptp.powerset A)) (and (= (tptp.apply_binary (tptp.the_L_join B) C D) (tptp.subset_union2 A C D)) (= (tptp.apply_binary (tptp.the_L_meet B) C D) (tptp.subset_intersection2 A C D))))))))))))
% 0.61/1.06  (assume a78 (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.join_semilatt_str A)) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.the_carrier A)) (forall ((C $$unsorted)) (=> (tptp.element C (tptp.the_carrier A)) (= (tptp.join A B C) (tptp.apply_binary_as_element (tptp.the_carrier A) (tptp.the_carrier A) (tptp.the_carrier A) (tptp.the_L_join A) B C)))))))))
% 0.61/1.06  (assume a79 (forall ((A $$unsorted)) (=> (exists ((B $$unsorted) (C $$unsorted)) (= A (tptp.ordered_pair B C))) (forall ((B $$unsorted)) (= (= B (tptp.pair_first A)) (forall ((C $$unsorted) (D $$unsorted)) (=> (= A (tptp.ordered_pair C D)) (= B C))))))))
% 0.61/1.06  (assume a80 (forall ((A $$unsorted)) (= (tptp.succ A) (tptp.set_union2 A (tptp.singleton A)))))
% 0.61/1.06  (assume a81 (forall ((A $$unsorted)) (=> (tptp.top_str A) (= (tptp.topological_space A) (and (tptp.in (tptp.the_carrier A) (tptp.the_topology A)) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.powerset (tptp.powerset (tptp.the_carrier A)))) (=> (tptp.subset B (tptp.the_topology A)) (tptp.in (tptp.union_of_subsets (tptp.the_carrier A) B) (tptp.the_topology A))))) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.powerset (tptp.the_carrier A))) (forall ((C $$unsorted)) (=> (tptp.element C (tptp.powerset (tptp.the_carrier A))) (=> (and (tptp.in B (tptp.the_topology A)) (tptp.in C (tptp.the_topology A))) (tptp.in (tptp.subset_intersection2 (tptp.the_carrier A) B C) (tptp.the_topology A))))))))))))
% 0.61/1.06  (assume a82 (forall ((A $$unsorted)) (= (tptp.relation A) (forall ((B $$unsorted)) (not (and (tptp.in B A) (forall ((C $$unsorted) (D $$unsorted)) (not (= B (tptp.ordered_pair C D))))))))))
% 0.61/1.06  (assume a83 (forall ((A $$unsorted)) (=> (tptp.relation A) (forall ((B $$unsorted)) (= (tptp.is_reflexive_in A B) (forall ((C $$unsorted)) (=> (tptp.in C B) (tptp.in (tptp.ordered_pair C C) A))))))))
% 0.61/1.06  (assume a84 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.relation_of2 C A B) (tptp.subset C (tptp.cartesian_product2 A B)))))
% 0.61/1.06  (assume a85 (forall ((A $$unsorted) (B $$unsorted)) (and (=> (not (= A tptp.empty_set)) (= (= B (tptp.set_meet A)) (forall ((C $$unsorted)) (= (tptp.in C B) (forall ((D $$unsorted)) (=> (tptp.in D A) (tptp.in C D))))))) (=> (= A tptp.empty_set) (= (= B (tptp.set_meet A)) (= B tptp.empty_set))))))
% 0.61/1.06  (assume a86 (forall ((A $$unsorted)) (=> (tptp.one_sorted_str A) (= (tptp.empty_carrier A) (tptp.empty (tptp.the_carrier A))))))
% 0.61/1.06  (assume a87 (forall ((A $$unsorted) (B $$unsorted)) (= (= B (tptp.singleton A)) (forall ((C $$unsorted)) (= (tptp.in C B) (= C A))))))
% 0.61/1.06  (assume a88 (forall ((A $$unsorted)) (=> (tptp.top_str A) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.powerset (tptp.the_carrier A))) (= (tptp.interior A B) (tptp.subset_complement (tptp.the_carrier A) (tptp.topstr_closure A (tptp.subset_complement (tptp.the_carrier A) B)))))))))
% 0.61/1.06  (assume a89 (forall ((A $$unsorted)) (=> (tptp.top_str A) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.powerset (tptp.powerset (tptp.the_carrier A)))) (= (tptp.open_subsets B A) (forall ((C $$unsorted)) (=> (tptp.element C (tptp.powerset (tptp.the_carrier A))) (=> (tptp.in C B) (tptp.open_subset C A))))))))))
% 0.61/1.06  (assume a90 (forall ((A $$unsorted)) (=> (tptp.relation A) (forall ((B $$unsorted) (C $$unsorted)) (= (= C (tptp.fiber A B)) (forall ((D $$unsorted)) (= (tptp.in D C) (and (not (= D B)) (tptp.in (tptp.ordered_pair D B) A)))))))))
% 0.61/1.06  (assume a91 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (= (= B (tptp.inclusion_relation A)) (and (= (tptp.relation_field B) A) (forall ((C $$unsorted) (D $$unsorted)) (=> (and (tptp.in C A) (tptp.in D A)) (= (tptp.in (tptp.ordered_pair C D) B) (tptp.subset C D)))))))))
% 0.61/1.06  (assume a92 (forall ((A $$unsorted)) (= (= A tptp.empty_set) (forall ((B $$unsorted)) (not (tptp.in B A))))))
% 0.61/1.06  (assume a93 (forall ((A $$unsorted) (B $$unsorted)) (= (= B (tptp.powerset A)) (forall ((C $$unsorted)) (= (tptp.in C B) (tptp.subset C A))))))
% 0.61/1.06  (assume a94 (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.latt_str A)) (=> (and (not (tptp.empty_carrier A)) (tptp.lattice A) (tptp.complete_latt_str A) (tptp.latt_str A)) (forall ((B $$unsorted) (C $$unsorted)) (=> (tptp.element C (tptp.the_carrier A)) (= (= C (tptp.join_of_latt_set A B)) (and (tptp.latt_element_smaller A C B) (forall ((D $$unsorted)) (=> (tptp.element D (tptp.the_carrier A)) (=> (tptp.latt_element_smaller A D B) (tptp.below A C D))))))))))))
% 0.61/1.06  (assume a95 (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.latt_str A)) (forall ((B $$unsorted)) (= (tptp.meet_of_latt_set A B) (tptp.join_of_latt_set A (tptp.a_2_2_lattice3 A B)))))))
% 0.61/1.06  (assume a96 (forall ((A $$unsorted)) (= (tptp.centered A) (and (not (= A tptp.empty_set)) (forall ((B $$unsorted)) (not (and (not (= B tptp.empty_set)) (tptp.subset B A) (tptp.finite B) (= (tptp.set_meet B) tptp.empty_set))))))))
% 0.61/1.06  (assume a97 (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.lattice A) (tptp.latt_str A)) (= (tptp.poset_of_lattice A) (tptp.rel_str_of (tptp.the_carrier A) (tptp.k2_lattice3 A))))))
% 0.61/1.06  (assume a98 (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.meet_semilatt_str A)) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.the_carrier A)) (forall ((C $$unsorted)) (=> (tptp.element C (tptp.the_carrier A)) (= (tptp.meet A B C) (tptp.apply_binary_as_element (tptp.the_carrier A) (tptp.the_carrier A) (tptp.the_carrier A) (tptp.the_L_meet A) B C)))))))))
% 0.61/1.06  (assume a99 (forall ((A $$unsorted)) (=> (exists ((B $$unsorted) (C $$unsorted)) (= A (tptp.ordered_pair B C))) (forall ((B $$unsorted)) (= (= B (tptp.pair_second A)) (forall ((C $$unsorted) (D $$unsorted)) (=> (= A (tptp.ordered_pair C D)) (= B D))))))))
% 0.61/1.06  (assume a100 (forall ((A $$unsorted)) (= (tptp.epsilon_transitive A) (forall ((B $$unsorted)) (=> (tptp.in B A) (tptp.subset B A))))))
% 0.61/1.06  (assume a101 (forall ((A $$unsorted)) (=> (tptp.one_sorted_str A) (= (tptp.empty_carrier_subset A) tptp.empty_set))))
% 0.61/1.06  (assume a102 (forall ((A $$unsorted)) (=> (tptp.relation A) (forall ((B $$unsorted)) (=> (tptp.relation B) (= (= A B) (forall ((C $$unsorted) (D $$unsorted)) (= (tptp.in (tptp.ordered_pair C D) A) (tptp.in (tptp.ordered_pair C D) B)))))))))
% 0.61/1.06  (assume a103 (forall ((A $$unsorted) (B $$unsorted)) (and (=> (not (tptp.empty A)) (= (tptp.element B A) (tptp.in B A))) (=> (tptp.empty A) (= (tptp.element B A) (tptp.empty B))))))
% 0.61/1.06  (assume a104 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (= C (tptp.unordered_pair A B)) (forall ((D $$unsorted)) (= (tptp.in D C) (or (= D A) (= D B)))))))
% 0.61/1.06  (assume a105 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element B A) (= (tptp.proper_element B A) (not (= B (tptp.union A)))))))
% 0.61/1.06  (assume a106 (forall ((A $$unsorted)) (=> (tptp.top_str A) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.powerset (tptp.powerset (tptp.the_carrier A)))) (= (tptp.closed_subsets B A) (forall ((C $$unsorted)) (=> (tptp.element C (tptp.powerset (tptp.the_carrier A))) (=> (tptp.in C B) (tptp.closed_subset C A))))))))))
% 0.61/1.06  (assume a107 (forall ((A $$unsorted)) (=> (tptp.relation A) (= (tptp.well_founded_relation A) (forall ((B $$unsorted)) (not (and (tptp.subset B (tptp.relation_field A)) (not (= B tptp.empty_set)) (forall ((C $$unsorted)) (not (and (tptp.in C B) (tptp.disjoint (tptp.fiber A C) B)))))))))))
% 0.61/1.06  (assume a108 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (= C (tptp.set_union2 A B)) (forall ((D $$unsorted)) (= (tptp.in D C) (or (tptp.in D A) (tptp.in D B)))))))
% 0.61/1.06  (assume a109 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (= C (tptp.cartesian_product2 A B)) (forall ((D $$unsorted)) (= (tptp.in D C) (exists ((E $$unsorted) (F $$unsorted)) (and (tptp.in E A) (tptp.in F B) (= D (tptp.ordered_pair E F)))))))))
% 0.61/1.06  (assume a110 (forall ((A $$unsorted)) (=> (tptp.top_str A) (= (tptp.compact_top_space A) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.powerset (tptp.powerset (tptp.the_carrier A)))) (not (and (tptp.is_a_cover_of_carrier A B) (tptp.open_subsets B A) (forall ((C $$unsorted)) (=> (tptp.element C (tptp.powerset (tptp.powerset (tptp.the_carrier A)))) (not (and (tptp.subset C B) (tptp.is_a_cover_of_carrier A C) (tptp.finite C)))))))))))))
% 0.61/1.06  (assume a111 (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.lattice A) (tptp.latt_str A)) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.the_carrier A)) (= (tptp.cast_to_el_of_LattPOSet A B) B))))))
% 0.61/1.06  (assume a112 (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.join_semilatt_str A)) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.the_carrier A)) (forall ((C $$unsorted)) (=> (tptp.element C (tptp.the_carrier A)) (= (tptp.below A B C) (= (tptp.join A B C) C)))))))))
% 0.61/1.06  (assume a113 (forall ((A $$unsorted)) (= (tptp.epsilon_connected A) (forall ((B $$unsorted) (C $$unsorted)) (not (and (tptp.in B A) (tptp.in C A) (not (tptp.in B C)) (not (= B C)) (not (tptp.in C B))))))))
% 0.61/1.06  (assume a114 (forall ((A $$unsorted)) (=> (tptp.one_sorted_str A) (= (tptp.cast_as_carrier_subset A) (tptp.the_carrier A)))))
% 0.61/1.06  (assume a115 (forall ((A $$unsorted)) (=> (tptp.relation A) (forall ((B $$unsorted)) (=> (tptp.relation B) (= (tptp.subset A B) (forall ((C $$unsorted) (D $$unsorted)) (=> (tptp.in (tptp.ordered_pair C D) A) (tptp.in (tptp.ordered_pair C D) B)))))))))
% 0.61/1.06  (assume a116 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset A B) (forall ((C $$unsorted)) (=> (tptp.in C A) (tptp.in C B))))))
% 0.61/1.06  (assume a117 (forall ((A $$unsorted)) (=> (tptp.relation A) (forall ((B $$unsorted)) (= (tptp.is_well_founded_in A B) (forall ((C $$unsorted)) (not (and (tptp.subset C B) (not (= C tptp.empty_set)) (forall ((D $$unsorted)) (not (and (tptp.in D C) (tptp.disjoint (tptp.fiber A D) C))))))))))))
% 0.61/1.06  (assume a118 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (= C (tptp.set_intersection2 A B)) (forall ((D $$unsorted)) (= (tptp.in D C) (and (tptp.in D A) (tptp.in D B)))))))
% 0.61/1.06  (assume a119 (forall ((A $$unsorted)) (=> (and (tptp.relation A) (tptp.function A)) (forall ((B $$unsorted) (C $$unsorted)) (and (=> (tptp.in B (tptp.relation_dom A)) (= (= C (tptp.apply A B)) (tptp.in (tptp.ordered_pair B C) A))) (=> (not (tptp.in B (tptp.relation_dom A))) (= (= C (tptp.apply A B)) (= C tptp.empty_set))))))))
% 0.61/1.06  (assume a120 (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.lattice A) (tptp.latt_str A)) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.the_carrier (tptp.poset_of_lattice A))) (= (tptp.cast_to_el_of_lattice A B) B))))))
% 0.61/1.06  (assume a121 (forall ((A $$unsorted)) (= (tptp.ordinal A) (and (tptp.epsilon_transitive A) (tptp.epsilon_connected A)))))
% 0.61/1.06  (assume a122 (forall ((A $$unsorted)) (=> (tptp.relation A) (forall ((B $$unsorted)) (= (= B (tptp.relation_dom A)) (forall ((C $$unsorted)) (= (tptp.in C B) (exists ((D $$unsorted)) (tptp.in (tptp.ordered_pair C D) A)))))))))
% 0.61/1.06  (assume a123 (forall ((A $$unsorted)) (=> (tptp.relation A) (forall ((B $$unsorted)) (= (tptp.is_antisymmetric_in A B) (forall ((C $$unsorted) (D $$unsorted)) (=> (and (tptp.in C B) (tptp.in D B) (tptp.in (tptp.ordered_pair C D) A) (tptp.in (tptp.ordered_pair D C) A)) (= C D))))))))
% 0.61/1.06  (assume a124 (forall ((A $$unsorted)) (= (tptp.cast_to_subset A) A)))
% 0.61/1.06  (assume a125 (forall ((A $$unsorted) (B $$unsorted)) (= (= B (tptp.union A)) (forall ((C $$unsorted)) (= (tptp.in C B) (exists ((D $$unsorted)) (and (tptp.in C D) (tptp.in D A))))))))
% 0.61/1.06  (assume a126 (forall ((A $$unsorted)) (=> (tptp.relation A) (= (tptp.well_ordering A) (and (tptp.reflexive A) (tptp.transitive A) (tptp.antisymmetric A) (tptp.connected A) (tptp.well_founded_relation A))))))
% 0.61/1.06  (assume a127 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.equipotent A B) (exists ((C $$unsorted)) (and (tptp.relation C) (tptp.function C) (tptp.one_to_one C) (= (tptp.relation_dom C) A) (= (tptp.relation_rng C) B))))))
% 0.61/1.06  (assume a128 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (= C (tptp.set_difference A B)) (forall ((D $$unsorted)) (= (tptp.in D C) (and (tptp.in D A) (not (tptp.in D B))))))))
% 0.61/1.06  (assume a129 (forall ((A $$unsorted)) (=> (tptp.rel_str A) (= (tptp.lower_bounded_relstr A) (exists ((B $$unsorted)) (and (tptp.element B (tptp.the_carrier A)) (tptp.relstr_element_smaller A (tptp.the_carrier A) B)))))))
% 0.61/1.06  (assume a130 (forall ((A $$unsorted)) (=> (and (tptp.relation A) (tptp.function A)) (forall ((B $$unsorted)) (= (= B (tptp.relation_rng A)) (forall ((C $$unsorted)) (= (tptp.in C B) (exists ((D $$unsorted)) (and (tptp.in D (tptp.relation_dom A)) (= C (tptp.apply A D)))))))))))
% 0.61/1.06  (assume a131 (forall ((A $$unsorted)) (=> (tptp.rel_str A) (= (tptp.transitive_relstr A) (tptp.is_transitive_in (tptp.the_InternalRel A) (tptp.the_carrier A))))))
% 0.61/1.06  (assume a132 (forall ((A $$unsorted)) (= (= A tptp.omega) (and (tptp.in tptp.empty_set A) (tptp.being_limit_ordinal A) (tptp.ordinal A) (forall ((B $$unsorted)) (=> (tptp.ordinal B) (=> (and (tptp.in tptp.empty_set B) (tptp.being_limit_ordinal B)) (tptp.subset A B))))))))
% 0.61/1.06  (assume a133 (forall ((A $$unsorted)) (=> (tptp.top_str A) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.powerset (tptp.the_carrier A))) (= (tptp.open_subset B A) (tptp.in B (tptp.the_topology A))))))))
% 0.61/1.06  (assume a134 (forall ((A $$unsorted)) (=> (tptp.relation A) (forall ((B $$unsorted)) (= (= B (tptp.relation_rng A)) (forall ((C $$unsorted)) (= (tptp.in C B) (exists ((D $$unsorted)) (tptp.in (tptp.ordered_pair D C) A)))))))))
% 0.61/1.06  (assume a135 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element B (tptp.powerset A)) (= (tptp.subset_complement A B) (tptp.set_difference A B)))))
% 0.61/1.06  (assume a136 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.ordered_pair A B) (tptp.unordered_pair (tptp.unordered_pair A B) (tptp.singleton A)))))
% 0.61/1.06  (assume a137 (forall ((A $$unsorted)) (=> (tptp.relation A) (forall ((B $$unsorted)) (= (tptp.well_orders A B) (and (tptp.is_reflexive_in A B) (tptp.is_transitive_in A B) (tptp.is_antisymmetric_in A B) (tptp.is_connected_in A B) (tptp.is_well_founded_in A B)))))))
% 0.61/1.06  (assume a138 (forall ((A $$unsorted)) (=> (tptp.rel_str A) (= (tptp.antisymmetric_relstr A) (tptp.is_antisymmetric_in (tptp.the_InternalRel A) (tptp.the_carrier A))))))
% 0.61/1.06  (assume a139 (forall ((A $$unsorted)) (= (tptp.being_limit_ordinal A) (= A (tptp.union A)))))
% 0.61/1.06  (assume a140 (forall ((A $$unsorted)) (=> (tptp.top_str A) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.powerset (tptp.the_carrier A))) (= (tptp.closed_subset B A) (tptp.open_subset (tptp.subset_difference (tptp.the_carrier A) (tptp.cast_as_carrier_subset A) B) A)))))))
% 0.61/1.06  (assume a141 (forall ((A $$unsorted)) (=> (tptp.relation A) (= (tptp.relation_field A) (tptp.set_union2 (tptp.relation_dom A) (tptp.relation_rng A))))))
% 0.61/1.06  (assume a142 (forall ((A $$unsorted)) (=> (tptp.relation A) (forall ((B $$unsorted)) (= (tptp.is_connected_in A B) (forall ((C $$unsorted) (D $$unsorted)) (not (and (tptp.in C B) (tptp.in D B) (not (= C D)) (not (tptp.in (tptp.ordered_pair C D) A)) (not (tptp.in (tptp.ordered_pair D C) A))))))))))
% 0.61/1.06  (assume a143 (forall ((A $$unsorted)) (=> (tptp.relation A) (forall ((B $$unsorted)) (= (tptp.relation_restriction A B) (tptp.set_intersection2 A (tptp.cartesian_product2 B B)))))))
% 0.61/1.06  (assume a144 (forall ((A $$unsorted)) (=> (tptp.relation A) (forall ((B $$unsorted)) (=> (tptp.relation B) (= (= B (tptp.relation_inverse A)) (forall ((C $$unsorted) (D $$unsorted)) (= (tptp.in (tptp.ordered_pair C D) B) (tptp.in (tptp.ordered_pair D C) A)))))))))
% 0.61/1.06  (assume a145 (forall ((A $$unsorted)) (=> (tptp.relation A) (forall ((B $$unsorted)) (=> (tptp.relation B) (forall ((C $$unsorted)) (=> (and (tptp.relation C) (tptp.function C)) (= (tptp.relation_isomorphism A B C) (and (= (tptp.relation_dom C) (tptp.relation_field A)) (= (tptp.relation_rng C) (tptp.relation_field B)) (tptp.one_to_one C) (forall ((D $$unsorted) (E $$unsorted)) (= (tptp.in (tptp.ordered_pair D E) A) (and (tptp.in D (tptp.relation_field A)) (tptp.in E (tptp.relation_field A)) (tptp.in (tptp.ordered_pair (tptp.apply C D) (tptp.apply C E)) B)))))))))))))
% 0.61/1.06  (assume a146 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.disjoint A B) (= (tptp.set_intersection2 A B) tptp.empty_set))))
% 0.61/1.06  (assume a147 (forall ((A $$unsorted)) (=> (tptp.rel_str A) (forall ((B $$unsorted)) (= (tptp.ex_sup_of_relstr_set A B) (exists ((C $$unsorted)) (and (tptp.element C (tptp.the_carrier A)) (tptp.relstr_set_smaller A B C) (forall ((D $$unsorted)) (=> (tptp.element D (tptp.the_carrier A)) (=> (tptp.relstr_set_smaller A B D) (tptp.related A C D)))) (forall ((D $$unsorted)) (=> (tptp.element D (tptp.the_carrier A)) (=> (and (tptp.relstr_set_smaller A B D) (forall ((E $$unsorted)) (=> (tptp.element E (tptp.the_carrier A)) (=> (tptp.relstr_set_smaller A B E) (tptp.related A D E))))) (= D C)))))))))))
% 0.61/1.06  (assume a148 (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.lattice A) (tptp.latt_str A)) (= (tptp.relation_of_lattice A) (tptp.a_1_0_filter_1 A)))))
% 0.61/1.06  (assume a149 (forall ((A $$unsorted)) (=> (and (tptp.relation A) (tptp.function A)) (= (tptp.one_to_one A) (forall ((B $$unsorted) (C $$unsorted)) (=> (and (tptp.in B (tptp.relation_dom A)) (tptp.in C (tptp.relation_dom A)) (= (tptp.apply A B) (tptp.apply A C))) (= B C)))))))
% 0.61/1.06  (assume a150 (forall ((A $$unsorted)) (=> (tptp.rel_str A) (forall ((B $$unsorted) (C $$unsorted)) (=> (tptp.element C (tptp.the_carrier A)) (= (tptp.relstr_element_smaller A B C) (forall ((D $$unsorted)) (=> (tptp.element D (tptp.the_carrier A)) (=> (tptp.in D B) (tptp.related A C D))))))))))
% 0.61/1.06  (assume a151 (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.latt_str A)) (= (tptp.meet_absorbing A) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.the_carrier A)) (forall ((C $$unsorted)) (=> (tptp.element C (tptp.the_carrier A)) (= (tptp.join A (tptp.meet A B C) C) C)))))))))
% 0.61/1.06  (assume a152 (forall ((A $$unsorted)) (=> (tptp.one_sorted_str A) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.powerset (tptp.powerset (tptp.the_carrier A)))) (= (tptp.is_a_cover_of_carrier A B) (= (tptp.cast_as_carrier_subset A) (tptp.union_of_subsets (tptp.the_carrier A) B))))))))
% 0.61/1.06  (assume a153 (forall ((A $$unsorted)) (=> (tptp.relation A) (forall ((B $$unsorted)) (=> (tptp.relation B) (forall ((C $$unsorted)) (=> (tptp.relation C) (= (= C (tptp.relation_composition A B)) (forall ((D $$unsorted) (E $$unsorted)) (= (tptp.in (tptp.ordered_pair D E) C) (exists ((F $$unsorted)) (and (tptp.in (tptp.ordered_pair D F) A) (tptp.in (tptp.ordered_pair F E) B)))))))))))))
% 0.61/1.06  (assume a154 (forall ((A $$unsorted)) (=> (tptp.relation A) (forall ((B $$unsorted)) (= (tptp.is_transitive_in A B) (forall ((C $$unsorted) (D $$unsorted) (E $$unsorted)) (=> (and (tptp.in C B) (tptp.in D B) (tptp.in E B) (tptp.in (tptp.ordered_pair C D) A) (tptp.in (tptp.ordered_pair D E) A)) (tptp.in (tptp.ordered_pair C E) A))))))))
% 0.61/1.06  (assume a155 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element B (tptp.powerset (tptp.powerset A))) (forall ((C $$unsorted)) (=> (tptp.element C (tptp.powerset (tptp.powerset A))) (= (= C (tptp.complements_of_subsets A B)) (forall ((D $$unsorted)) (=> (tptp.element D (tptp.powerset A)) (= (tptp.in D C) (tptp.in (tptp.subset_complement A D) B))))))))))
% 0.61/1.06  (assume a156 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.proper_subset A B) (and (tptp.subset A B) (not (= A B))))))
% 0.61/1.06  (assume a157 (forall ((A $$unsorted)) (=> (tptp.rel_str A) (forall ((B $$unsorted)) (= (tptp.ex_inf_of_relstr_set A B) (exists ((C $$unsorted)) (and (tptp.element C (tptp.the_carrier A)) (tptp.relstr_element_smaller A B C) (forall ((D $$unsorted)) (=> (tptp.element D (tptp.the_carrier A)) (=> (tptp.relstr_element_smaller A B D) (tptp.related A D C)))) (forall ((D $$unsorted)) (=> (tptp.element D (tptp.the_carrier A)) (=> (and (tptp.relstr_element_smaller A B D) (forall ((E $$unsorted)) (=> (tptp.element E (tptp.the_carrier A)) (=> (tptp.relstr_element_smaller A B E) (tptp.related A E D))))) (= D C)))))))))))
% 0.61/1.06  (assume a158 (forall ((A $$unsorted)) (=> (and (tptp.relation A) (tptp.function A)) (=> (tptp.one_to_one A) (= (tptp.function_inverse A) (tptp.relation_inverse A))))))
% 0.61/1.06  (assume a159 (forall ((A $$unsorted)) (=> (tptp.rel_str A) (forall ((B $$unsorted) (C $$unsorted)) (=> (tptp.element C (tptp.the_carrier A)) (= (tptp.relstr_set_smaller A B C) (forall ((D $$unsorted)) (=> (tptp.element D (tptp.the_carrier A)) (=> (tptp.in D B) (tptp.related A D C))))))))))
% 0.61/1.06  (assume a160 (forall ((A $$unsorted)) (=> (tptp.rel_str A) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.the_carrier A)) (forall ((C $$unsorted)) (=> (tptp.element C (tptp.the_carrier A)) (= (tptp.related A B C) (tptp.in (tptp.ordered_pair B C) (tptp.the_InternalRel A))))))))))
% 0.61/1.06  (assume a161 (forall ((A $$unsorted)) (=> (tptp.relation A) (= (tptp.reflexive A) (tptp.is_reflexive_in A (tptp.relation_field A))))))
% 0.61/1.06  (assume a162 (forall ((A $$unsorted)) (=> (tptp.rel_str A) (forall ((B $$unsorted) (C $$unsorted)) (=> (tptp.element C (tptp.the_carrier A)) (=> (tptp.ex_sup_of_relstr_set A B) (= (= C (tptp.join_on_relstr A B)) (and (tptp.relstr_set_smaller A B C) (forall ((D $$unsorted)) (=> (tptp.element D (tptp.the_carrier A)) (=> (tptp.relstr_set_smaller A B D) (tptp.related A C D))))))))))))
% 0.61/1.06  (assume a163 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation_of2 B A A) (and (tptp.strict_rel_str (tptp.rel_str_of A B)) (tptp.rel_str (tptp.rel_str_of A B))))))
% 0.61/1.06  (assume a164 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.function B) (tptp.quasi_total B (tptp.cartesian_product2 A A) A) (tptp.relation_of2 B (tptp.cartesian_product2 A A) A) (tptp.function C) (tptp.quasi_total C (tptp.cartesian_product2 A A) A) (tptp.relation_of2 C (tptp.cartesian_product2 A A) A)) (and (tptp.strict_latt_str (tptp.latt_str_of A B C)) (tptp.latt_str (tptp.latt_str_of A B C))))))
% 0.61/1.06  (assume a165 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.lattice A) (tptp.latt_str A) (not (tptp.empty_carrier B)) (tptp.lattice B) (tptp.latt_str B) (tptp.element C (tptp.the_carrier A)) (tptp.element D (tptp.the_carrier B))) (tptp.element (tptp.k10_filter_1 A B C D) (tptp.the_carrier (tptp.k8_filter_1 A B))))))
% 0.61/1.06  (assume a166 true)
% 0.61/1.06  (assume a167 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.latt_str A)) (tptp.element (tptp.join_of_latt_set A B) (tptp.the_carrier A)))))
% 0.61/1.06  (assume a168 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.latt_str A)) (tptp.element (tptp.meet_of_latt_set A B) (tptp.the_carrier A)))))
% 0.61/1.06  (assume a169 true)
% 0.61/1.06  (assume a170 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (not (tptp.empty A)) (not (tptp.empty B)) (tptp.element C A) (tptp.element D B)) (tptp.element (tptp.ordered_pair_as_product_element A B C D) (tptp.cartesian_product2 A B)))))
% 0.61/1.06  (assume a171 true)
% 0.61/1.06  (assume a172 true)
% 0.61/1.06  (assume a173 (forall ((A $$unsorted)) (and (tptp.strict_latt_str (tptp.boole_lattice A)) (tptp.latt_str (tptp.boole_lattice A)))))
% 0.61/1.06  (assume a174 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.join_semilatt_str A) (tptp.element B (tptp.the_carrier A)) (tptp.element C (tptp.the_carrier A))) (tptp.element (tptp.join A B C) (tptp.the_carrier A)))))
% 0.61/1.06  (assume a175 true)
% 0.61/1.06  (assume a176 true)
% 0.61/1.06  (assume a177 (forall ((A $$unsorted)) (tptp.element (tptp.k1_pcomps_1 A) (tptp.powerset (tptp.powerset A)))))
% 0.61/1.06  (assume a178 (forall ((A $$unsorted)) (=> (tptp.one_sorted_str A) (tptp.element (tptp.empty_carrier_subset A) (tptp.powerset (tptp.the_carrier A))))))
% 0.61/1.06  (assume a179 true)
% 0.61/1.06  (assume a180 true)
% 0.61/1.06  (assume a181 true)
% 0.61/1.06  (assume a182 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation A) (tptp.relation_of2_as_subset (tptp.relation_restriction_as_relation_of A B) B B))))
% 0.61/1.06  (assume a183 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.top_str A) (tptp.element B (tptp.powerset (tptp.the_carrier A)))) (tptp.element (tptp.interior A B) (tptp.powerset (tptp.the_carrier A))))))
% 0.61/1.06  (assume a184 true)
% 0.61/1.06  (assume a185 (forall ((A $$unsorted)) (tptp.relation (tptp.inclusion_relation A))))
% 0.61/1.06  (assume a186 true)
% 0.61/1.06  (assume a187 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.rel_str A) (tptp.element (tptp.join_on_relstr A B) (tptp.the_carrier A)))))
% 0.61/1.06  (assume a188 true)
% 0.61/1.06  (assume a189 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted) (F $$unsorted)) (=> (and (not (tptp.empty A)) (not (tptp.empty B)) (tptp.function D) (tptp.quasi_total D (tptp.cartesian_product2 A B) C) (tptp.relation_of2 D (tptp.cartesian_product2 A B) C) (tptp.element E A) (tptp.element F B)) (tptp.element (tptp.apply_binary_as_element A B C D E F) C))))
% 0.61/1.06  (assume a190 (forall ((A $$unsorted)) (=> (and (tptp.relation A) (tptp.function A)) (and (tptp.relation (tptp.function_inverse A)) (tptp.function (tptp.function_inverse A))))))
% 0.61/1.06  (assume a191 (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.lattice A) (tptp.latt_str A)) (and (tptp.reflexive (tptp.k2_lattice3 A)) (tptp.antisymmetric (tptp.k2_lattice3 A)) (tptp.transitive (tptp.k2_lattice3 A)) (tptp.v1_partfun1 (tptp.k2_lattice3 A) (tptp.the_carrier A) (tptp.the_carrier A)) (tptp.relation_of2_as_subset (tptp.k2_lattice3 A) (tptp.the_carrier A) (tptp.the_carrier A))))))
% 0.61/1.06  (assume a192 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.meet_semilatt_str A) (tptp.element B (tptp.the_carrier A)) (tptp.element C (tptp.the_carrier A))) (tptp.element (tptp.meet A B C) (tptp.the_carrier A)))))
% 0.61/1.06  (assume a193 true)
% 0.61/1.06  (assume a194 (forall ((A $$unsorted)) (=> (tptp.one_sorted_str A) (tptp.element (tptp.cast_as_carrier_subset A) (tptp.powerset (tptp.the_carrier A))))))
% 0.61/1.06  (assume a195 true)
% 0.61/1.06  (assume a196 (forall ((A $$unsorted)) (tptp.element (tptp.cast_to_subset A) (tptp.powerset A))))
% 0.61/1.06  (assume a197 true)
% 0.61/1.06  (assume a198 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation A) (tptp.relation (tptp.relation_restriction A B)))))
% 0.61/1.06  (assume a199 true)
% 0.61/1.06  (assume a200 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.rel_str A) (tptp.element (tptp.meet_on_relstr A B) (tptp.the_carrier A)))))
% 0.61/1.06  (assume a201 true)
% 0.61/1.06  (assume a202 (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.lattice A) (tptp.latt_str A)) (and (tptp.strict_rel_str (tptp.poset_of_lattice A)) (tptp.reflexive_relstr (tptp.poset_of_lattice A)) (tptp.transitive_relstr (tptp.poset_of_lattice A)) (tptp.antisymmetric_relstr (tptp.poset_of_lattice A)) (tptp.rel_str (tptp.poset_of_lattice A))))))
% 0.61/1.06  (assume a203 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.join_commutative A) (tptp.join_semilatt_str A) (tptp.element B (tptp.the_carrier A)) (tptp.element C (tptp.the_carrier A))) (tptp.element (tptp.join_commut A B C) (tptp.the_carrier A)))))
% 0.61/1.06  (assume a204 true)
% 0.61/1.06  (assume a205 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element B (tptp.powerset A)) (tptp.element (tptp.subset_complement A B) (tptp.powerset A)))))
% 0.61/1.06  (assume a206 true)
% 0.61/1.06  (assume a207 true)
% 0.61/1.06  (assume a208 (forall ((A $$unsorted)) (=> (tptp.rel_str A) (tptp.element (tptp.bottom_of_relstr A) (tptp.the_carrier A)))))
% 0.61/1.06  (assume a209 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.lattice A) (tptp.latt_str A) (tptp.element B (tptp.the_carrier A))) (tptp.element (tptp.cast_to_el_of_LattPOSet A B) (tptp.the_carrier (tptp.poset_of_lattice A))))))
% 0.61/1.06  (assume a210 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.meet_commutative A) (tptp.meet_semilatt_str A) (tptp.element B (tptp.the_carrier A)) (tptp.element C (tptp.the_carrier A))) (tptp.element (tptp.meet_commut A B C) (tptp.the_carrier A)))))
% 0.61/1.06  (assume a211 (forall ((A $$unsorted)) (=> (tptp.relation A) (tptp.relation (tptp.relation_inverse A)))))
% 0.61/1.06  (assume a212 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.relation_of2 C A B) (tptp.element (tptp.relation_dom_as_subset A B C) (tptp.powerset A)))))
% 0.61/1.06  (assume a213 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.element B (tptp.powerset A)) (tptp.element C (tptp.powerset A))) (tptp.element (tptp.subset_union2 A B C) (tptp.powerset A)))))
% 0.61/1.06  (assume a214 true)
% 0.61/1.06  (assume a215 true)
% 0.61/1.06  (assume a216 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.lattice A) (tptp.latt_str A) (tptp.element B (tptp.the_carrier (tptp.poset_of_lattice A)))) (tptp.element (tptp.cast_to_el_of_lattice A B) (tptp.the_carrier A)))))
% 0.61/1.06  (assume a217 (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.meet_semilatt_str A)) (tptp.element (tptp.bottom_of_semilattstr A) (tptp.the_carrier A)))))
% 0.61/1.06  (assume a218 true)
% 0.61/1.06  (assume a219 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.relation A) (tptp.relation B)) (tptp.relation (tptp.relation_composition A B)))))
% 0.61/1.06  (assume a220 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.relation_of2 C A B) (tptp.element (tptp.relation_rng_as_subset A B C) (tptp.powerset B)))))
% 0.61/1.06  (assume a221 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element B (tptp.powerset (tptp.powerset A))) (tptp.element (tptp.union_of_subsets A B) (tptp.powerset A)))))
% 0.61/1.06  (assume a222 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.element B (tptp.powerset A)) (tptp.element C (tptp.powerset A))) (tptp.element (tptp.subset_intersection2 A B C) (tptp.powerset A)))))
% 0.61/1.06  (assume a223 (forall ((A $$unsorted)) (and (tptp.v1_partfun1 (tptp.identity_as_relation_of A) A A) (tptp.relation_of2_as_subset (tptp.identity_as_relation_of A) A A))))
% 0.61/1.06  (assume a224 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.top_str A) (tptp.element B (tptp.powerset (tptp.the_carrier A)))) (tptp.element (tptp.topstr_closure A B) (tptp.powerset (tptp.the_carrier A))))))
% 0.61/1.06  (assume a225 (forall ((A $$unsorted)) (tptp.relation (tptp.identity_relation A))))
% 0.61/1.06  (assume a226 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element B (tptp.powerset (tptp.powerset A))) (tptp.element (tptp.meet_of_subsets A B) (tptp.powerset A)))))
% 0.61/1.06  (assume a227 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.element B (tptp.powerset A)) (tptp.element C (tptp.powerset A))) (tptp.element (tptp.subset_difference A B C) (tptp.powerset A)))))
% 0.61/1.06  (assume a228 (forall ((A $$unsorted)) (=> (tptp.one_sorted_str A) (and (tptp.function (tptp.identity_on_carrier A)) (tptp.quasi_total (tptp.identity_on_carrier A) (tptp.the_carrier A) (tptp.the_carrier A)) (tptp.relation_of2_as_subset (tptp.identity_on_carrier A) (tptp.the_carrier A) (tptp.the_carrier A))))))
% 0.61/1.06  (assume a229 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation A) (tptp.relation (tptp.relation_dom_restriction A B)))))
% 0.61/1.06  (assume a230 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element B (tptp.powerset (tptp.powerset A))) (tptp.element (tptp.complements_of_subsets A B) (tptp.powerset (tptp.powerset A))))))
% 0.61/1.06  (assume a231 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.latt_str A) (not (tptp.empty_carrier B)) (tptp.latt_str B)) (and (tptp.strict_latt_str (tptp.k8_filter_1 A B)) (tptp.latt_str (tptp.k8_filter_1 A B))))))
% 0.61/1.06  (assume a232 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (not (tptp.empty A)) (tptp.function C) (tptp.quasi_total C A B) (tptp.relation_of2 C A B) (tptp.element D A)) (tptp.element (tptp.apply_as_element A B C D) B))))
% 0.61/1.06  (assume a233 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (tptp.relation (tptp.relation_rng_restriction A B)))))
% 0.61/1.06  (assume a234 (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.lattice A) (tptp.latt_str A)) (tptp.relation (tptp.relation_of_lattice A)))))
% 0.61/1.06  (assume a235 true)
% 0.61/1.06  (assume a236 (forall ((A $$unsorted)) (=> (tptp.meet_semilatt_str A) (tptp.one_sorted_str A))))
% 0.61/1.06  (assume a237 (forall ((A $$unsorted)) (=> (tptp.rel_str A) (tptp.one_sorted_str A))))
% 0.61/1.06  (assume a238 (forall ((A $$unsorted)) (=> (tptp.top_str A) (tptp.one_sorted_str A))))
% 0.61/1.06  (assume a239 true)
% 0.61/1.06  (assume a240 (forall ((A $$unsorted)) (=> (tptp.join_semilatt_str A) (tptp.one_sorted_str A))))
% 0.61/1.06  (assume a241 (forall ((A $$unsorted)) (=> (tptp.latt_str A) (and (tptp.meet_semilatt_str A) (tptp.join_semilatt_str A)))))
% 0.61/1.06  (assume a242 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.topological_space A) (tptp.top_str A) (tptp.element B (tptp.the_carrier A))) (forall ((C $$unsorted)) (=> (tptp.point_neighbourhood C A B) (tptp.element C (tptp.powerset (tptp.the_carrier A))))))))
% 0.61/1.06  (assume a243 true)
% 0.61/1.06  (assume a244 true)
% 0.61/1.06  (assume a245 (forall ((A $$unsorted)) (=> (tptp.rel_str A) (forall ((B $$unsorted)) (=> (tptp.subrelstr B A) (tptp.rel_str B))))))
% 0.61/1.06  (assume a246 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.relation_of2_as_subset C A B) (tptp.element C (tptp.powerset (tptp.cartesian_product2 A B))))))
% 0.61/1.06  (assume a247 (forall ((A $$unsorted)) (=> (tptp.meet_semilatt_str A) (and (tptp.function (tptp.the_L_meet A)) (tptp.quasi_total (tptp.the_L_meet A) (tptp.cartesian_product2 (tptp.the_carrier A) (tptp.the_carrier A)) (tptp.the_carrier A)) (tptp.relation_of2_as_subset (tptp.the_L_meet A) (tptp.cartesian_product2 (tptp.the_carrier A) (tptp.the_carrier A)) (tptp.the_carrier A))))))
% 0.61/1.06  (assume a248 (forall ((A $$unsorted)) (=> (tptp.rel_str A) (tptp.relation_of2_as_subset (tptp.the_InternalRel A) (tptp.the_carrier A) (tptp.the_carrier A)))))
% 0.61/1.06  (assume a249 (forall ((A $$unsorted)) (=> (tptp.top_str A) (tptp.element (tptp.the_topology A) (tptp.powerset (tptp.powerset (tptp.the_carrier A)))))))
% 0.61/1.06  (assume a250 true)
% 0.61/1.06  (assume a251 (forall ((A $$unsorted)) (=> (tptp.join_semilatt_str A) (and (tptp.function (tptp.the_L_join A)) (tptp.quasi_total (tptp.the_L_join A) (tptp.cartesian_product2 (tptp.the_carrier A) (tptp.the_carrier A)) (tptp.the_carrier A)) (tptp.relation_of2_as_subset (tptp.the_L_join A) (tptp.cartesian_product2 (tptp.the_carrier A) (tptp.the_carrier A)) (tptp.the_carrier A))))))
% 0.61/1.06  (assume a252 (exists ((A $$unsorted)) (tptp.meet_semilatt_str A)))
% 0.61/1.06  (assume a253 (exists ((A $$unsorted)) (tptp.rel_str A)))
% 0.61/1.06  (assume a254 (exists ((A $$unsorted)) (tptp.top_str A)))
% 0.61/1.06  (assume a255 (exists ((A $$unsorted)) (tptp.one_sorted_str A)))
% 0.61/1.06  (assume a256 (exists ((A $$unsorted)) (tptp.join_semilatt_str A)))
% 0.61/1.06  (assume a257 (exists ((A $$unsorted)) (tptp.latt_str A)))
% 0.61/1.06  (assume a258 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.topological_space A) (tptp.top_str A) (tptp.element B (tptp.the_carrier A))) (exists ((C $$unsorted)) (tptp.point_neighbourhood C A B)))))
% 0.61/1.06  (assume a259 (forall ((A $$unsorted) (B $$unsorted)) (exists ((C $$unsorted)) (tptp.relation_of2 C A B))))
% 0.61/1.06  (assume a260 (forall ((A $$unsorted)) (exists ((B $$unsorted)) (tptp.element B A))))
% 0.61/1.06  (assume a261 (forall ((A $$unsorted)) (=> (tptp.rel_str A) (exists ((B $$unsorted)) (tptp.subrelstr B A)))))
% 0.61/1.06  (assume a262 (forall ((A $$unsorted) (B $$unsorted)) (exists ((C $$unsorted)) (tptp.relation_of2_as_subset C A B))))
% 0.61/1.06  (assume a263 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.finite B) (tptp.finite (tptp.set_intersection2 A B)))))
% 0.61/1.06  (assume a264 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.empty A) (tptp.relation B)) (and (tptp.empty (tptp.relation_composition B A)) (tptp.relation (tptp.relation_composition B A))))))
% 0.61/1.06  (assume a265 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.finite A) (tptp.finite (tptp.set_intersection2 A B)))))
% 0.61/1.06  (assume a266 (forall ((A $$unsorted)) (=> (tptp.empty A) (and (tptp.empty (tptp.relation_inverse A)) (tptp.relation (tptp.relation_inverse A))))))
% 0.61/1.06  (assume a267 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.finite A) (tptp.finite (tptp.set_difference A B)))))
% 0.61/1.06  (assume a268 (and (tptp.empty tptp.empty_set) (tptp.relation tptp.empty_set) (tptp.relation_empty_yielding tptp.empty_set)))
% 0.61/1.06  (assume a269 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.relation A) (tptp.function A) (tptp.finite B)) (tptp.finite (tptp.relation_image A B)))))
% 0.61/1.06  (assume a270 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.relation A) (tptp.relation_empty_yielding A)) (and (tptp.relation (tptp.relation_dom_restriction A B)) (tptp.relation_empty_yielding (tptp.relation_dom_restriction A B))))))
% 0.61/1.06  (assume a271 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.finite A) (tptp.finite B)) (tptp.finite (tptp.cartesian_product2 A B)))))
% 0.61/1.06  (assume a272 (forall ((A $$unsorted)) (and (not (tptp.empty (tptp.singleton A))) (tptp.finite (tptp.singleton A)))))
% 0.61/1.06  (assume a273 (forall ((A $$unsorted)) (and (not (tptp.empty (tptp.powerset A))) (tptp.cup_closed (tptp.powerset A)) (tptp.diff_closed (tptp.powerset A)) (tptp.preboolean (tptp.powerset A)))))
% 0.61/1.06  (assume a274 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.relation A) (tptp.function A) (tptp.relation B) (tptp.function B)) (and (tptp.relation (tptp.relation_composition A B)) (tptp.function (tptp.relation_composition A B))))))
% 0.61/1.06  (assume a275 (forall ((A $$unsorted)) (and (not (tptp.empty_carrier (tptp.boole_lattice A))) (tptp.strict_latt_str (tptp.boole_lattice A)))))
% 0.61/1.06  (assume a276 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.empty A)) (tptp.relation_of2 B A A)) (and (not (tptp.empty_carrier (tptp.rel_str_of A B))) (tptp.strict_rel_str (tptp.rel_str_of A B))))))
% 0.61/1.06  (assume a277 (forall ((A $$unsorted)) (not (tptp.empty (tptp.succ A)))))
% 0.61/1.06  (assume a278 (and (tptp.epsilon_transitive tptp.omega) (tptp.epsilon_connected tptp.omega) (tptp.ordinal tptp.omega) (not (tptp.empty tptp.omega))))
% 0.61/1.06  (assume a279 (forall ((A $$unsorted)) (=> (tptp.one_sorted_str A) (and (tptp.empty (tptp.empty_carrier_subset A)) (tptp.v1_membered (tptp.empty_carrier_subset A)) (tptp.v2_membered (tptp.empty_carrier_subset A)) (tptp.v3_membered (tptp.empty_carrier_subset A)) (tptp.v4_membered (tptp.empty_carrier_subset A)) (tptp.v5_membered (tptp.empty_carrier_subset A))))))
% 0.61/1.06  (assume a280 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.relation A) (tptp.relation B)) (tptp.relation (tptp.set_intersection2 A B)))))
% 0.61/1.06  (assume a281 (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.one_sorted_str A)) (not (tptp.empty (tptp.the_carrier A))))))
% 0.61/1.06  (assume a282 (forall ((A $$unsorted)) (not (tptp.empty (tptp.powerset A)))))
% 0.61/1.06  (assume a283 (tptp.empty tptp.empty_set))
% 0.61/1.06  (assume a284 (forall ((A $$unsorted) (B $$unsorted)) (not (tptp.empty (tptp.ordered_pair A B)))))
% 0.61/1.06  (assume a285 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.v1_membered A) (tptp.v1_membered (tptp.set_intersection2 A B)))))
% 0.61/1.06  (assume a286 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.v1_membered A) (tptp.v1_membered (tptp.set_intersection2 B A)))))
% 0.61/1.06  (assume a287 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.v2_membered A) (and (tptp.v1_membered (tptp.set_intersection2 A B)) (tptp.v2_membered (tptp.set_intersection2 A B))))))
% 0.61/1.06  (assume a288 (forall ((A $$unsorted)) (=> (and (tptp.ordinal A) (tptp.natural A)) (and (not (tptp.empty (tptp.succ A))) (tptp.epsilon_transitive (tptp.succ A)) (tptp.epsilon_connected (tptp.succ A)) (tptp.ordinal (tptp.succ A)) (tptp.natural (tptp.succ A))))))
% 0.61/1.06  (assume a289 (forall ((A $$unsorted)) (and (tptp.relation (tptp.identity_relation A)) (tptp.function (tptp.identity_relation A)))))
% 0.61/1.06  (assume a290 (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.join_commutative A) (tptp.join_semilatt_str A)) (and (tptp.relation (tptp.the_L_join A)) (tptp.function (tptp.the_L_join A)) (tptp.quasi_total (tptp.the_L_join A) (tptp.cartesian_product2 (tptp.the_carrier A) (tptp.the_carrier A)) (tptp.the_carrier A)) (tptp.v1_binop_1 (tptp.the_L_join A) (tptp.the_carrier A)) (tptp.v1_partfun1 (tptp.the_L_join A) (tptp.cartesian_product2 (tptp.the_carrier A) (tptp.the_carrier A)) (tptp.the_carrier A))))))
% 0.61/1.06  (assume a291 (forall ((A $$unsorted)) (and (not (tptp.empty_carrier (tptp.boole_lattice A))) (tptp.strict_latt_str (tptp.boole_lattice A)) (tptp.join_commutative (tptp.boole_lattice A)) (tptp.join_associative (tptp.boole_lattice A)) (tptp.meet_commutative (tptp.boole_lattice A)) (tptp.meet_associative (tptp.boole_lattice A)) (tptp.meet_absorbing (tptp.boole_lattice A)) (tptp.join_absorbing (tptp.boole_lattice A)) (tptp.lattice (tptp.boole_lattice A)))))
% 0.61/1.06  (assume a292 (forall ((A $$unsorted)) (=> (and (tptp.reflexive_relstr A) (tptp.transitive_relstr A) (tptp.antisymmetric_relstr A) (tptp.rel_str A)) (and (tptp.relation (tptp.the_InternalRel A)) (tptp.reflexive (tptp.the_InternalRel A)) (tptp.antisymmetric (tptp.the_InternalRel A)) (tptp.transitive (tptp.the_InternalRel A)) (tptp.v1_partfun1 (tptp.the_InternalRel A) (tptp.the_carrier A) (tptp.the_carrier A))))))
% 0.61/1.06  (assume a293 (and (tptp.relation tptp.empty_set) (tptp.relation_empty_yielding tptp.empty_set) (tptp.function tptp.empty_set) (tptp.one_to_one tptp.empty_set) (tptp.empty tptp.empty_set) (tptp.epsilon_transitive tptp.empty_set) (tptp.epsilon_connected tptp.empty_set) (tptp.ordinal tptp.empty_set)))
% 0.61/1.06  (assume a294 (forall ((A $$unsorted)) (and (tptp.relation (tptp.identity_relation A)) (tptp.function (tptp.identity_relation A)) (tptp.reflexive (tptp.identity_relation A)) (tptp.symmetric (tptp.identity_relation A)) (tptp.antisymmetric (tptp.identity_relation A)) (tptp.transitive (tptp.identity_relation A)))))
% 0.61/1.06  (assume a295 (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.one_sorted_str A)) (not (tptp.empty (tptp.cast_as_carrier_subset A))))))
% 0.61/1.06  (assume a296 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.relation A) (tptp.relation B)) (tptp.relation (tptp.set_union2 A B)))))
% 0.61/1.06  (assume a297 (forall ((A $$unsorted)) (not (tptp.empty (tptp.singleton A)))))
% 0.61/1.06  (assume a298 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.topological_space A) (tptp.top_str A) (tptp.element B (tptp.powerset (tptp.the_carrier A)))) (tptp.closed_subset (tptp.topstr_closure A B) A))))
% 0.61/1.06  (assume a299 (forall ((A $$unsorted) (B $$unsorted)) (=> (not (tptp.empty A)) (not (tptp.empty (tptp.set_union2 A B))))))
% 0.61/1.06  (assume a300 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.v2_membered A) (and (tptp.v1_membered (tptp.set_intersection2 B A)) (tptp.v2_membered (tptp.set_intersection2 B A))))))
% 0.61/1.06  (assume a301 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.v3_membered A) (and (tptp.v1_membered (tptp.set_intersection2 A B)) (tptp.v2_membered (tptp.set_intersection2 A B)) (tptp.v3_membered (tptp.set_intersection2 A B))))))
% 0.61/1.06  (assume a302 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.v3_membered A) (and (tptp.v1_membered (tptp.set_intersection2 B A)) (tptp.v2_membered (tptp.set_intersection2 B A)) (tptp.v3_membered (tptp.set_intersection2 B A))))))
% 0.61/1.06  (assume a303 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.v4_membered A) (and (tptp.v1_membered (tptp.set_intersection2 A B)) (tptp.v2_membered (tptp.set_intersection2 A B)) (tptp.v3_membered (tptp.set_intersection2 A B)) (tptp.v4_membered (tptp.set_intersection2 A B))))))
% 0.61/1.06  (assume a304 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.v4_membered A) (and (tptp.v1_membered (tptp.set_intersection2 B A)) (tptp.v2_membered (tptp.set_intersection2 B A)) (tptp.v3_membered (tptp.set_intersection2 B A)) (tptp.v4_membered (tptp.set_intersection2 B A))))))
% 0.61/1.06  (assume a305 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.v5_membered A) (and (tptp.v1_membered (tptp.set_intersection2 A B)) (tptp.v2_membered (tptp.set_intersection2 A B)) (tptp.v3_membered (tptp.set_intersection2 A B)) (tptp.v4_membered (tptp.set_intersection2 A B)) (tptp.v5_membered (tptp.set_intersection2 A B))))))
% 0.61/1.06  (assume a306 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.v5_membered A) (and (tptp.v1_membered (tptp.set_intersection2 B A)) (tptp.v2_membered (tptp.set_intersection2 B A)) (tptp.v3_membered (tptp.set_intersection2 B A)) (tptp.v4_membered (tptp.set_intersection2 B A)) (tptp.v5_membered (tptp.set_intersection2 B A))))))
% 0.61/1.06  (assume a307 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.v1_membered A) (tptp.v1_membered (tptp.set_difference A B)))))
% 0.61/1.06  (assume a308 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.v2_membered A) (and (tptp.v1_membered (tptp.set_difference A B)) (tptp.v2_membered (tptp.set_difference A B))))))
% 0.61/1.06  (assume a309 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.v3_membered A) (and (tptp.v1_membered (tptp.set_difference A B)) (tptp.v2_membered (tptp.set_difference A B)) (tptp.v3_membered (tptp.set_difference A B))))))
% 0.61/1.06  (assume a310 (forall ((A $$unsorted)) (=> (and (tptp.relation A) (tptp.function A) (tptp.one_to_one A)) (and (tptp.relation (tptp.relation_inverse A)) (tptp.function (tptp.relation_inverse A))))))
% 0.61/1.06  (assume a311 (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.join_associative A) (tptp.join_semilatt_str A)) (and (tptp.relation (tptp.the_L_join A)) (tptp.function (tptp.the_L_join A)) (tptp.quasi_total (tptp.the_L_join A) (tptp.cartesian_product2 (tptp.the_carrier A) (tptp.the_carrier A)) (tptp.the_carrier A)) (tptp.v2_binop_1 (tptp.the_L_join A) (tptp.the_carrier A)) (tptp.v1_partfun1 (tptp.the_L_join A) (tptp.cartesian_product2 (tptp.the_carrier A) (tptp.the_carrier A)) (tptp.the_carrier A))))))
% 0.61/1.06  (assume a312 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.empty A)) (tptp.function B) (tptp.quasi_total B (tptp.cartesian_product2 A A) A) (tptp.relation_of2 B (tptp.cartesian_product2 A A) A) (tptp.function C) (tptp.quasi_total C (tptp.cartesian_product2 A A) A) (tptp.relation_of2 C (tptp.cartesian_product2 A A) A)) (and (not (tptp.empty_carrier (tptp.latt_str_of A B C))) (tptp.strict_latt_str (tptp.latt_str_of A B C))))))
% 0.61/1.06  (assume a313 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.reflexive B) (tptp.antisymmetric B) (tptp.transitive B) (tptp.v1_partfun1 B A A) (tptp.relation_of2 B A A)) (and (tptp.strict_rel_str (tptp.rel_str_of A B)) (tptp.reflexive_relstr (tptp.rel_str_of A B)) (tptp.transitive_relstr (tptp.rel_str_of A B)) (tptp.antisymmetric_relstr (tptp.rel_str_of A B))))))
% 0.61/1.06  (assume a314 (forall ((A $$unsorted)) (=> (tptp.ordinal A) (and (not (tptp.empty (tptp.succ A))) (tptp.epsilon_transitive (tptp.succ A)) (tptp.epsilon_connected (tptp.succ A)) (tptp.ordinal (tptp.succ A))))))
% 0.61/1.06  (assume a315 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.relation A) (tptp.relation B)) (tptp.relation (tptp.set_difference A B)))))
% 0.61/1.06  (assume a316 (forall ((A $$unsorted) (B $$unsorted)) (not (tptp.empty (tptp.unordered_pair A B)))))
% 0.61/1.06  (assume a317 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.topological_space A) (tptp.top_str A) (tptp.closed_subset B A) (tptp.element B (tptp.powerset (tptp.the_carrier A)))) (tptp.open_subset (tptp.subset_complement (tptp.the_carrier A) B) A))))
% 0.61/1.06  (assume a318 (forall ((A $$unsorted) (B $$unsorted)) (=> (not (tptp.empty A)) (not (tptp.empty (tptp.set_union2 B A))))))
% 0.61/1.06  (assume a319 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.v4_membered A) (and (tptp.v1_membered (tptp.set_difference A B)) (tptp.v2_membered (tptp.set_difference A B)) (tptp.v3_membered (tptp.set_difference A B)) (tptp.v4_membered (tptp.set_difference A B))))))
% 0.61/1.06  (assume a320 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.v5_membered A) (and (tptp.v1_membered (tptp.set_difference A B)) (tptp.v2_membered (tptp.set_difference A B)) (tptp.v3_membered (tptp.set_difference A B)) (tptp.v4_membered (tptp.set_difference A B)) (tptp.v5_membered (tptp.set_difference A B))))))
% 0.61/1.06  (assume a321 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.relation A) (tptp.function A)) (and (tptp.relation (tptp.relation_dom_restriction A B)) (tptp.function (tptp.relation_dom_restriction A B))))))
% 0.61/1.06  (assume a322 (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.meet_commutative A) (tptp.meet_semilatt_str A)) (and (tptp.relation (tptp.the_L_meet A)) (tptp.function (tptp.the_L_meet A)) (tptp.quasi_total (tptp.the_L_meet A) (tptp.cartesian_product2 (tptp.the_carrier A) (tptp.the_carrier A)) (tptp.the_carrier A)) (tptp.v1_binop_1 (tptp.the_L_meet A) (tptp.the_carrier A)) (tptp.v1_partfun1 (tptp.the_L_meet A) (tptp.cartesian_product2 (tptp.the_carrier A) (tptp.the_carrier A)) (tptp.the_carrier A))))))
% 0.61/1.06  (assume a323 (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.lattice A) (tptp.latt_str A)) (and (not (tptp.empty_carrier (tptp.poset_of_lattice A))) (tptp.strict_rel_str (tptp.poset_of_lattice A)) (tptp.reflexive_relstr (tptp.poset_of_lattice A)) (tptp.transitive_relstr (tptp.poset_of_lattice A)) (tptp.antisymmetric_relstr (tptp.poset_of_lattice A))))))
% 0.61/1.06  (assume a324 (forall ((A $$unsorted)) (=> (tptp.ordinal A) (and (tptp.epsilon_transitive (tptp.union A)) (tptp.epsilon_connected (tptp.union A)) (tptp.ordinal (tptp.union A))))))
% 0.61/1.06  (assume a325 (and (tptp.empty tptp.empty_set) (tptp.relation tptp.empty_set)))
% 0.61/1.06  (assume a326 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.empty A)) (not (tptp.empty B))) (not (tptp.empty (tptp.cartesian_product2 A B))))))
% 0.61/1.06  (assume a327 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.topological_space A) (tptp.top_str A) (tptp.open_subset B A) (tptp.element B (tptp.powerset (tptp.the_carrier A)))) (tptp.closed_subset (tptp.subset_complement (tptp.the_carrier A) B) A))))
% 0.61/1.06  (assume a328 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.relation B) (tptp.function B)) (and (tptp.relation (tptp.relation_rng_restriction A B)) (tptp.function (tptp.relation_rng_restriction A B))))))
% 0.61/1.06  (assume a329 (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.meet_associative A) (tptp.meet_semilatt_str A)) (and (tptp.relation (tptp.the_L_meet A)) (tptp.function (tptp.the_L_meet A)) (tptp.quasi_total (tptp.the_L_meet A) (tptp.cartesian_product2 (tptp.the_carrier A) (tptp.the_carrier A)) (tptp.the_carrier A)) (tptp.v2_binop_1 (tptp.the_L_meet A) (tptp.the_carrier A)) (tptp.v1_partfun1 (tptp.the_L_meet A) (tptp.cartesian_product2 (tptp.the_carrier A) (tptp.the_carrier A)) (tptp.the_carrier A))))))
% 0.61/1.06  (assume a330 (forall ((A $$unsorted)) (=> (and (tptp.topological_space A) (tptp.top_str A)) (tptp.closed_subset (tptp.cast_as_carrier_subset A) A))))
% 0.61/1.06  (assume a331 (forall ((A $$unsorted)) (=> (and (not (tptp.empty A)) (tptp.relation A)) (not (tptp.empty (tptp.relation_dom A))))))
% 0.61/1.06  (assume a332 (and (tptp.empty tptp.empty_set) (tptp.v1_membered tptp.empty_set) (tptp.v2_membered tptp.empty_set) (tptp.v3_membered tptp.empty_set) (tptp.v4_membered tptp.empty_set) (tptp.v5_membered tptp.empty_set)))
% 0.61/1.06  (assume a333 (forall ((A $$unsorted)) (=> (and (not (tptp.empty A)) (tptp.relation A)) (not (tptp.empty (tptp.relation_rng A))))))
% 0.61/1.06  (assume a334 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.topological_space A) (tptp.top_str A) (tptp.element B (tptp.powerset (tptp.the_carrier A)))) (tptp.open_subset (tptp.interior A B) A))))
% 0.61/1.06  (assume a335 (forall ((A $$unsorted)) (=> (tptp.empty A) (and (tptp.empty (tptp.relation_dom A)) (tptp.relation (tptp.relation_dom A))))))
% 0.61/1.06  (assume a336 (forall ((A $$unsorted)) (=> (tptp.empty A) (and (tptp.empty (tptp.relation_rng A)) (tptp.relation (tptp.relation_rng A))))))
% 0.61/1.06  (assume a337 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.finite A) (tptp.finite B)) (tptp.finite (tptp.set_union2 A B)))))
% 0.61/1.06  (assume a338 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.empty A) (tptp.relation B)) (and (tptp.empty (tptp.relation_composition A B)) (tptp.relation (tptp.relation_composition A B))))))
% 0.61/1.06  (assume a339 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.empty_carrier B)) (tptp.lattice B) (tptp.latt_str B)) (= (tptp.in A (tptp.a_1_0_filter_1 B)) (exists ((C $$unsorted) (D $$unsorted)) (and (tptp.element C (tptp.the_carrier B)) (tptp.element D (tptp.the_carrier B)) (= A (tptp.ordered_pair_as_product_element (tptp.the_carrier B) (tptp.the_carrier B) C D)) (tptp.below_refl B C D)))))))
% 0.61/1.06  (assume a340 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.empty_carrier B)) (tptp.latt_str B)) (= (tptp.in A (tptp.a_2_2_lattice3 B C)) (exists ((D $$unsorted)) (and (tptp.element D (tptp.the_carrier B)) (= A D) (tptp.latt_set_smaller B D C)))))))
% 0.61/1.06  (assume a341 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.empty_carrier B)) (tptp.lattice B) (tptp.complete_latt_str B) (tptp.latt_str B)) (= (tptp.in A (tptp.a_2_3_lattice3 B C)) (exists ((D $$unsorted)) (and (tptp.element D (tptp.the_carrier B)) (= A D) (tptp.latt_set_smaller B D C)))))))
% 0.61/1.06  (assume a342 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation_of2 B A A) (forall ((C $$unsorted) (D $$unsorted)) (=> (= (tptp.rel_str_of A B) (tptp.rel_str_of C D)) (and (= A C) (= B D)))))))
% 0.61/1.06  (assume a343 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.function B) (tptp.quasi_total B (tptp.cartesian_product2 A A) A) (tptp.relation_of2 B (tptp.cartesian_product2 A A) A) (tptp.function C) (tptp.quasi_total C (tptp.cartesian_product2 A A) A) (tptp.relation_of2 C (tptp.cartesian_product2 A A) A)) (forall ((D $$unsorted) (E $$unsorted) (F $$unsorted)) (=> (= (tptp.latt_str_of A B C) (tptp.latt_str_of D E F)) (and (= A D) (= B E) (= C F)))))))
% 0.61/1.06  (assume a344 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_union2 A A) A)))
% 0.61/1.06  (assume a345 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_intersection2 A A) A)))
% 0.61/1.06  (assume a346 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.element B (tptp.powerset A)) (tptp.element C (tptp.powerset A))) (= (tptp.subset_union2 A B B) B))))
% 0.61/1.06  (assume a347 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.element B (tptp.powerset A)) (tptp.element C (tptp.powerset A))) (= (tptp.subset_intersection2 A B B) B))))
% 0.61/1.06  (assume a348 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element B (tptp.powerset A)) (= (tptp.subset_complement A (tptp.subset_complement A B)) B))))
% 0.61/1.06  (assume a349 (forall ((A $$unsorted)) (=> (tptp.relation A) (= (tptp.relation_inverse (tptp.relation_inverse A)) A))))
% 0.61/1.06  (assume a350 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element B (tptp.powerset (tptp.powerset A))) (= (tptp.complements_of_subsets A (tptp.complements_of_subsets A B)) B))))
% 0.61/1.06  (assume a351 (forall ((A $$unsorted) (B $$unsorted)) (not (tptp.proper_subset A A))))
% 0.61/1.06  (assume a352 (forall ((A $$unsorted)) (=> (tptp.relation A) (= (tptp.reflexive A) (forall ((B $$unsorted)) (=> (tptp.in B (tptp.relation_field A)) (tptp.in (tptp.ordered_pair B B) A)))))))
% 0.61/1.06  (assume a353 (forall ((A $$unsorted)) (not (= (tptp.singleton A) tptp.empty_set))))
% 0.61/1.06  (assume a354 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (= (tptp.set_union2 (tptp.singleton A) B) B))))
% 0.61/1.06  (assume a355 (forall ((A $$unsorted) (B $$unsorted)) (not (and (tptp.disjoint (tptp.singleton A) B) (tptp.in A B)))))
% 0.61/1.06  (assume a356 (forall ((A $$unsorted) (B $$unsorted)) (=> (not (tptp.in A B)) (tptp.disjoint (tptp.singleton A) B))))
% 0.61/1.06  (assume a357 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (tptp.subset (tptp.relation_dom (tptp.relation_rng_restriction A B)) (tptp.relation_dom B)))))
% 0.61/1.06  (assume a358 (forall ((A $$unsorted)) (=> (tptp.relation A) (= (tptp.transitive A) (forall ((B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (tptp.in (tptp.ordered_pair B C) A) (tptp.in (tptp.ordered_pair C D) A)) (tptp.in (tptp.ordered_pair B D) A)))))))
% 0.61/1.06  (assume a359 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset (tptp.singleton A) B) (tptp.in A B))))
% 0.61/1.06  (assume a360 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (not (and (tptp.well_ordering B) (tptp.equipotent A (tptp.relation_field B)) (forall ((C $$unsorted)) (=> (tptp.relation C) (not (tptp.well_orders C A)))))))))
% 0.61/1.06  (assume a361 (forall ((A $$unsorted) (B $$unsorted)) (= (= (tptp.set_difference A B) tptp.empty_set) (tptp.subset A B))))
% 0.61/1.06  (assume a362 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element B (tptp.powerset A)) (forall ((C $$unsorted)) (=> (tptp.in C B) (tptp.in C A))))))
% 0.61/1.06  (assume a363 (forall ((A $$unsorted)) (=> (tptp.relation A) (= (tptp.antisymmetric A) (forall ((B $$unsorted) (C $$unsorted)) (=> (and (tptp.in (tptp.ordered_pair B C) A) (tptp.in (tptp.ordered_pair C B) A)) (= B C)))))))
% 0.61/1.06  (assume a364 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.subset A B) (or (tptp.in C A) (tptp.subset A (tptp.set_difference B (tptp.singleton C)))))))
% 0.61/1.06  (assume a365 (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.one_sorted_str A)) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.powerset (tptp.the_carrier A))) (forall ((C $$unsorted)) (=> (tptp.element C (tptp.the_carrier A)) (= (tptp.in C (tptp.subset_complement (tptp.the_carrier A) B)) (not (tptp.in C B))))))))))
% 0.61/1.06  (assume a366 (forall ((A $$unsorted)) (=> (tptp.relation A) (= (tptp.connected A) (forall ((B $$unsorted) (C $$unsorted)) (not (and (tptp.in B (tptp.relation_field A)) (tptp.in C (tptp.relation_field A)) (not (= B C)) (not (tptp.in (tptp.ordered_pair B C) A)) (not (tptp.in (tptp.ordered_pair C B) A)))))))))
% 0.61/1.06  (assume a367 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset A (tptp.singleton B)) (or (= A tptp.empty_set) (= A (tptp.singleton B))))))
% 0.61/1.06  (assume a368 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (tptp.subset A (tptp.union B)))))
% 0.61/1.06  (assume a369 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (= (tptp.in (tptp.ordered_pair A B) (tptp.cartesian_product2 C D)) (and (tptp.in A C) (tptp.in B D)))))
% 0.61/1.06  (assume a370 (forall ((A $$unsorted) (B $$unsorted)) (=> (forall ((C $$unsorted)) (=> (tptp.in C A) (tptp.in C B))) (tptp.element A (tptp.powerset B)))))
% 0.61/1.06  (assume a371 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.relation C) (tptp.function C)) (= (tptp.in B (tptp.relation_dom (tptp.relation_dom_restriction C A))) (and (tptp.in B (tptp.relation_dom C)) (tptp.in B A))))))
% 0.61/1.06  (assume a372 (exists ((A $$unsorted)) (and (not (tptp.empty A)) (tptp.epsilon_transitive A) (tptp.epsilon_connected A) (tptp.ordinal A) (tptp.natural A))))
% 0.61/1.06  (assume a373 (exists ((A $$unsorted)) (and (not (tptp.empty A)) (tptp.finite A))))
% 0.61/1.06  (assume a374 (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.function A))))
% 0.61/1.06  (assume a375 (forall ((A $$unsorted) (B $$unsorted)) (exists ((C $$unsorted)) (and (tptp.relation_of2 C A B) (tptp.relation C) (tptp.function C) (tptp.quasi_total C A B)))))
% 0.61/1.06  (assume a376 (exists ((A $$unsorted)) (and (not (tptp.empty A)) (tptp.v1_membered A) (tptp.v2_membered A) (tptp.v3_membered A) (tptp.v4_membered A) (tptp.v5_membered A))))
% 0.61/1.06  (assume a377 (exists ((A $$unsorted)) (and (tptp.rel_str A) (tptp.strict_rel_str A))))
% 0.61/1.06  (assume a378 (exists ((A $$unsorted)) (and (tptp.epsilon_transitive A) (tptp.epsilon_connected A) (tptp.ordinal A))))
% 0.61/1.06  (assume a379 (exists ((A $$unsorted)) (and (tptp.epsilon_transitive A) (tptp.epsilon_connected A) (tptp.ordinal A) (tptp.being_limit_ordinal A))))
% 0.61/1.06  (assume a380 (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.function A) (tptp.one_to_one A) (tptp.empty A))))
% 0.61/1.06  (assume a381 (exists ((A $$unsorted)) (and (tptp.empty A) (tptp.relation A))))
% 0.61/1.06  (assume a382 (forall ((A $$unsorted)) (=> (not (tptp.empty A)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset A)) (not (tptp.empty B)))))))
% 0.61/1.06  (assume a383 (forall ((A $$unsorted)) (=> (and (tptp.topological_space A) (tptp.top_str A)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset (tptp.the_carrier A))) (tptp.open_subset B A))))))
% 0.61/1.06  (assume a384 (exists ((A $$unsorted)) (tptp.empty A)))
% 0.61/1.06  (assume a385 (forall ((A $$unsorted)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset A)) (tptp.empty B) (tptp.relation B) (tptp.function B) (tptp.one_to_one B) (tptp.epsilon_transitive B) (tptp.epsilon_connected B) (tptp.ordinal B) (tptp.natural B) (tptp.finite B)))))
% 0.61/1.06  (assume a386 (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.empty A) (tptp.function A))))
% 0.61/1.06  (assume a387 (forall ((A $$unsorted)) (exists ((B $$unsorted)) (and (tptp.relation_of2 B A A) (tptp.relation B) (tptp.function B) (tptp.one_to_one B) (tptp.quasi_total B A A) (tptp.onto B A A) (tptp.bijective B A A)))))
% 0.61/1.06  (assume a388 (exists ((A $$unsorted)) (and (tptp.rel_str A) (not (tptp.empty_carrier A)) (tptp.strict_rel_str A) (tptp.reflexive_relstr A) (tptp.transitive_relstr A) (tptp.antisymmetric_relstr A))))
% 0.61/1.06  (assume a389 (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.function A) (tptp.one_to_one A) (tptp.empty A) (tptp.epsilon_transitive A) (tptp.epsilon_connected A) (tptp.ordinal A))))
% 0.61/1.06  (assume a390 (forall ((A $$unsorted) (B $$unsorted)) (exists ((C $$unsorted)) (and (tptp.relation_of2 C A B) (tptp.relation C) (tptp.function C)))))
% 0.61/1.06  (assume a391 (exists ((A $$unsorted)) (and (not (tptp.empty A)) (tptp.relation A))))
% 0.61/1.06  (assume a392 (forall ((A $$unsorted)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset A)) (tptp.empty B)))))
% 0.61/1.06  (assume a393 (forall ((A $$unsorted)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset A)) (not (tptp.proper_element B (tptp.powerset A)))))))
% 0.61/1.06  (assume a394 (forall ((A $$unsorted)) (=> (and (tptp.topological_space A) (tptp.top_str A)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset (tptp.the_carrier A))) (tptp.open_subset B A) (tptp.closed_subset B A))))))
% 0.61/1.06  (assume a395 (exists ((A $$unsorted)) (not (tptp.empty A))))
% 0.61/1.06  (assume a396 (forall ((A $$unsorted)) (=> (not (tptp.empty A)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset A)) (not (tptp.empty B)) (tptp.finite B))))))
% 0.61/1.06  (assume a397 (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.function A) (tptp.one_to_one A))))
% 0.61/1.06  (assume a398 (exists ((A $$unsorted)) (and (tptp.latt_str A) (tptp.strict_latt_str A))))
% 0.61/1.06  (assume a399 (exists ((A $$unsorted)) (and (not (tptp.empty A)) (tptp.epsilon_transitive A) (tptp.epsilon_connected A) (tptp.ordinal A))))
% 0.61/1.06  (assume a400 (forall ((A $$unsorted)) (exists ((B $$unsorted)) (and (tptp.relation_of2 B A A) (tptp.relation B) (tptp.reflexive B) (tptp.symmetric B) (tptp.antisymmetric B) (tptp.transitive B) (tptp.v1_partfun1 B A A)))))
% 0.61/1.06  (assume a401 (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.relation_empty_yielding A))))
% 0.61/1.06  (assume a402 (exists ((A $$unsorted)) (and (tptp.one_sorted_str A) (not (tptp.empty_carrier A)))))
% 0.61/1.06  (assume a403 (forall ((A $$unsorted)) (=> (not (tptp.empty A)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset A)) (not (tptp.empty B)) (tptp.finite B))))))
% 0.61/1.06  (assume a404 (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.relation_empty_yielding A) (tptp.function A))))
% 0.61/1.06  (assume a405 (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.one_sorted_str A)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset (tptp.the_carrier A))) (not (tptp.empty B)))))))
% 0.61/1.06  (assume a406 (exists ((A $$unsorted)) (and (tptp.latt_str A) (not (tptp.empty_carrier A)) (tptp.strict_latt_str A))))
% 0.61/1.06  (assume a407 (forall ((A $$unsorted)) (=> (and (tptp.topological_space A) (tptp.top_str A)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset (tptp.the_carrier A))) (tptp.closed_subset B A))))))
% 0.61/1.06  (assume a408 (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.topological_space A) (tptp.top_str A)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset (tptp.the_carrier A))) (not (tptp.empty B)) (tptp.closed_subset B A))))))
% 0.61/1.06  (assume a409 (exists ((A $$unsorted)) (and (tptp.latt_str A) (not (tptp.empty_carrier A)) (tptp.strict_latt_str A) (tptp.join_commutative A) (tptp.join_associative A) (tptp.meet_commutative A) (tptp.meet_associative A) (tptp.meet_absorbing A) (tptp.join_absorbing A) (tptp.lattice A))))
% 0.61/1.06  (assume a410 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.lattice A) (tptp.latt_str A) (not (tptp.empty_carrier B)) (tptp.lattice B) (tptp.latt_str B) (tptp.element C (tptp.the_carrier A)) (tptp.element D (tptp.the_carrier B))) (= (tptp.k10_filter_1 A B C D) (tptp.ordered_pair C D)))))
% 0.61/1.06  (assume a411 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (not (tptp.empty A)) (not (tptp.empty B)) (tptp.element C A) (tptp.element D B)) (= (tptp.ordered_pair_as_product_element A B C D) (tptp.ordered_pair C D)))))
% 0.61/1.06  (assume a412 (forall ((A $$unsorted)) (= (tptp.k1_pcomps_1 A) (tptp.powerset A))))
% 0.61/1.06  (assume a413 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation A) (= (tptp.relation_restriction_as_relation_of A B) (tptp.relation_restriction A B)))))
% 0.61/1.06  (assume a414 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted) (F $$unsorted)) (=> (and (not (tptp.empty A)) (not (tptp.empty B)) (tptp.function D) (tptp.quasi_total D (tptp.cartesian_product2 A B) C) (tptp.relation_of2 D (tptp.cartesian_product2 A B) C) (tptp.element E A) (tptp.element F B)) (= (tptp.apply_binary_as_element A B C D E F) (tptp.apply_binary D E F)))))
% 0.61/1.06  (assume a415 (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.lattice A) (tptp.latt_str A)) (= (tptp.k2_lattice3 A) (tptp.relation_of_lattice A)))))
% 0.61/1.06  (assume a416 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.join_commutative A) (tptp.join_semilatt_str A) (tptp.element B (tptp.the_carrier A)) (tptp.element C (tptp.the_carrier A))) (= (tptp.join_commut A B C) (tptp.join A B C)))))
% 0.61/1.06  (assume a417 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.meet_commutative A) (tptp.meet_semilatt_str A) (tptp.element B (tptp.the_carrier A)) (tptp.element C (tptp.the_carrier A))) (= (tptp.meet_commut A B C) (tptp.meet A B C)))))
% 0.61/1.06  (assume a418 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.relation_of2 C A B) (= (tptp.relation_dom_as_subset A B C) (tptp.relation_dom C)))))
% 0.61/1.06  (assume a419 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.element B (tptp.powerset A)) (tptp.element C (tptp.powerset A))) (= (tptp.subset_union2 A B C) (tptp.set_union2 B C)))))
% 0.61/1.06  (assume a420 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.relation_of2 C A B) (= (tptp.relation_rng_as_subset A B C) (tptp.relation_rng C)))))
% 0.61/1.06  (assume a421 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element B (tptp.powerset (tptp.powerset A))) (= (tptp.union_of_subsets A B) (tptp.union B)))))
% 0.61/1.06  (assume a422 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.element B (tptp.powerset A)) (tptp.element C (tptp.powerset A))) (= (tptp.subset_intersection2 A B C) (tptp.set_intersection2 B C)))))
% 0.61/1.06  (assume a423 (forall ((A $$unsorted)) (= (tptp.identity_as_relation_of A) (tptp.identity_relation A))))
% 0.61/1.06  (assume a424 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element B (tptp.powerset (tptp.powerset A))) (= (tptp.meet_of_subsets A B) (tptp.set_meet B)))))
% 0.61/1.06  (assume a425 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.element B (tptp.powerset A)) (tptp.element C (tptp.powerset A))) (= (tptp.subset_difference A B C) (tptp.set_difference B C)))))
% 0.61/1.06  (assume a426 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (not (tptp.empty A)) (tptp.function C) (tptp.quasi_total C A B) (tptp.relation_of2 C A B) (tptp.element D A)) (= (tptp.apply_as_element A B C D) (tptp.apply C D)))))
% 0.61/1.06  (assume a427 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.relation_of2_as_subset C A B) (tptp.relation_of2 C A B))))
% 0.61/1.06  (assume a428 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.ordinal A) (tptp.ordinal B)) (= (tptp.ordinal_subset A B) (tptp.subset A B)))))
% 0.61/1.06  (assume a429 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.equipotent A B) (tptp.are_equipotent A B))))
% 0.61/1.06  (assume a430 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.meet_commutative A) (tptp.meet_absorbing A) (tptp.join_absorbing A) (tptp.latt_str A) (tptp.element B (tptp.the_carrier A)) (tptp.element C (tptp.the_carrier A))) (= (tptp.below_refl A B C) (tptp.below A B C)))))
% 0.61/1.06  (assume a431 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.reflexive_relstr A) (tptp.rel_str A) (tptp.element B (tptp.the_carrier A)) (tptp.element C (tptp.the_carrier A))) (= (tptp.related_reflexive A B C) (tptp.related A B C)))))
% 0.61/1.06  (assume a432 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.ordinal A) (tptp.ordinal B)) (tptp.ordinal_subset A A))))
% 0.61/1.06  (assume a433 (forall ((A $$unsorted) (B $$unsorted)) (tptp.subset A A)))
% 0.61/1.06  (assume a434 (forall ((A $$unsorted) (B $$unsorted)) (tptp.equipotent A A)))
% 0.61/1.06  (assume a435 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.meet_commutative A) (tptp.meet_absorbing A) (tptp.join_absorbing A) (tptp.latt_str A) (tptp.element B (tptp.the_carrier A)) (tptp.element C (tptp.the_carrier A))) (tptp.below_refl A B B))))
% 0.61/1.06  (assume a436 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.reflexive_relstr A) (tptp.rel_str A) (tptp.element B (tptp.the_carrier A)) (tptp.element C (tptp.the_carrier A))) (tptp.related_reflexive A B B))))
% 0.61/1.06  (assume a437 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.empty A)) (tptp.relation B)) (=> (forall ((C $$unsorted) (D $$unsorted) (E $$unsorted)) (=> (and (tptp.in C A) (exists ((F $$unsorted)) (and (= C F) (tptp.in D F) (forall ((G $$unsorted)) (=> (tptp.in G F) (tptp.in (tptp.ordered_pair D G) B))))) (tptp.in C A) (exists ((H $$unsorted)) (and (= C H) (tptp.in E H) (forall ((I $$unsorted)) (=> (tptp.in I H) (tptp.in (tptp.ordered_pair E I) B)))))) (= D E))) (exists ((C $$unsorted)) (and (tptp.relation C) (tptp.function C) (forall ((D $$unsorted) (E $$unsorted)) (= (tptp.in (tptp.ordered_pair D E) C) (and (tptp.in D A) (tptp.in D A) (exists ((J $$unsorted)) (and (= D J) (tptp.in E J) (forall ((K $$unsorted)) (=> (tptp.in K J) (tptp.in (tptp.ordered_pair E K) B))))))))))))))
% 0.61/1.06  (assume a438 (forall ((A $$unsorted)) (=> (forall ((B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (tptp.in B A) (= C (tptp.singleton B)) (tptp.in B A) (= D (tptp.singleton B))) (= C D))) (exists ((B $$unsorted)) (and (tptp.relation B) (tptp.function B) (forall ((C $$unsorted) (D $$unsorted)) (= (tptp.in (tptp.ordered_pair C D) B) (and (tptp.in C A) (tptp.in C A) (= D (tptp.singleton C))))))))))
% 0.61/1.06  (assume a439 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.one_sorted_str A) (tptp.element B (tptp.powerset (tptp.powerset (tptp.the_carrier A))))) (=> (forall ((C $$unsorted) (D $$unsorted) (E $$unsorted)) (=> (and (tptp.in C (tptp.complements_of_subsets (tptp.the_carrier A) B)) (forall ((F $$unsorted)) (=> (tptp.element F (tptp.powerset (tptp.the_carrier A))) (=> (= F C) (= D (tptp.subset_complement (tptp.the_carrier A) F))))) (tptp.in C (tptp.complements_of_subsets (tptp.the_carrier A) B)) (forall ((G $$unsorted)) (=> (tptp.element G (tptp.powerset (tptp.the_carrier A))) (=> (= G C) (= E (tptp.subset_complement (tptp.the_carrier A) G)))))) (= D E))) (exists ((C $$unsorted)) (and (tptp.relation C) (tptp.function C) (forall ((D $$unsorted) (E $$unsorted)) (= (tptp.in (tptp.ordered_pair D E) C) (and (tptp.in D (tptp.complements_of_subsets (tptp.the_carrier A) B)) (tptp.in D (tptp.complements_of_subsets (tptp.the_carrier A) B)) (forall ((H $$unsorted)) (=> (tptp.element H (tptp.powerset (tptp.the_carrier A))) (=> (= H D) (= E (tptp.subset_complement (tptp.the_carrier A) H))))))))))))))
% 0.61/1.06  (assume a440 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.one_sorted_str A) (tptp.element B (tptp.powerset (tptp.powerset (tptp.the_carrier A))))) (=> (forall ((C $$unsorted) (D $$unsorted) (E $$unsorted)) (=> (and (tptp.in C B) (forall ((F $$unsorted)) (=> (tptp.element F (tptp.powerset (tptp.the_carrier A))) (=> (= F C) (= D (tptp.subset_complement (tptp.the_carrier A) F))))) (tptp.in C B) (forall ((G $$unsorted)) (=> (tptp.element G (tptp.powerset (tptp.the_carrier A))) (=> (= G C) (= E (tptp.subset_complement (tptp.the_carrier A) G)))))) (= D E))) (exists ((C $$unsorted)) (and (tptp.relation C) (tptp.function C) (forall ((D $$unsorted) (E $$unsorted)) (= (tptp.in (tptp.ordered_pair D E) C) (and (tptp.in D B) (tptp.in D B) (forall ((H $$unsorted)) (=> (tptp.element H (tptp.powerset (tptp.the_carrier A))) (=> (= H D) (= E (tptp.subset_complement (tptp.the_carrier A) H))))))))))))))
% 0.61/1.06  (assume a441 (forall ((A $$unsorted)) (=> (exists ((B $$unsorted)) (and (tptp.ordinal B) (tptp.in B A))) (exists ((B $$unsorted)) (and (tptp.ordinal B) (tptp.in B A) (forall ((C $$unsorted)) (=> (tptp.ordinal C) (=> (tptp.in C A) (tptp.ordinal_subset B C)))))))))
% 0.61/1.06  (assume a442 (=> (and (=> (tptp.in tptp.empty_set tptp.omega) (forall ((A $$unsorted)) (=> (tptp.element A (tptp.powerset (tptp.powerset tptp.empty_set))) (not (and (not (= A tptp.empty_set)) (forall ((B $$unsorted)) (not (and (tptp.in B A) (forall ((C $$unsorted)) (=> (and (tptp.in C A) (tptp.subset B C)) (= C B))))))))))) (forall ((D $$unsorted)) (=> (tptp.ordinal D) (=> (=> (tptp.in D tptp.omega) (forall ((E $$unsorted)) (=> (tptp.element E (tptp.powerset (tptp.powerset D))) (not (and (not (= E tptp.empty_set)) (forall ((F $$unsorted)) (not (and (tptp.in F E) (forall ((G $$unsorted)) (=> (and (tptp.in G E) (tptp.subset F G)) (= G F))))))))))) (=> (tptp.in (tptp.succ D) tptp.omega) (forall ((H $$unsorted)) (=> (tptp.element H (tptp.powerset (tptp.powerset (tptp.succ D)))) (not (and (not (= H tptp.empty_set)) (forall ((I $$unsorted)) (not (and (tptp.in I H) (forall ((J $$unsorted)) (=> (and (tptp.in J H) (tptp.subset I J)) (= J I)))))))))))))) (forall ((D $$unsorted)) (=> (tptp.ordinal D) (=> (and (tptp.being_limit_ordinal D) (forall ((K $$unsorted)) (=> (tptp.ordinal K) (=> (tptp.in K D) (=> (tptp.in K tptp.omega) (forall ((L $$unsorted)) (=> (tptp.element L (tptp.powerset (tptp.powerset K))) (not (and (not (= L tptp.empty_set)) (forall ((M $$unsorted)) (not (and (tptp.in M L) (forall ((N $$unsorted)) (=> (and (tptp.in N L) (tptp.subset M N)) (= N M))))))))))))))) (or (= D tptp.empty_set) (=> (tptp.in D tptp.omega) (forall ((O $$unsorted)) (=> (tptp.element O (tptp.powerset (tptp.powerset D))) (not (and (not (= O tptp.empty_set)) (forall ((P $$unsorted)) (not (and (tptp.in P O) (forall ((Q $$unsorted)) (=> (and (tptp.in Q O) (tptp.subset P Q)) (= Q P)))))))))))))))) (forall ((D $$unsorted)) (=> (tptp.ordinal D) (=> (tptp.in D tptp.omega) (forall ((R $$unsorted)) (=> (tptp.element R (tptp.powerset (tptp.powerset D))) (not (and (not (= R tptp.empty_set)) (forall ((S $$unsorted)) (not (and (tptp.in S R) (forall ((T $$unsorted)) (=> (and (tptp.in T R) (tptp.subset S T)) (= T S)))))))))))))))
% 0.61/1.06  (assume a443 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.relation B) (tptp.relation C) (tptp.function C)) (exists ((D $$unsorted)) (and (tptp.relation D) (forall ((E $$unsorted) (F $$unsorted)) (= (tptp.in (tptp.ordered_pair E F) D) (and (tptp.in E A) (tptp.in F A) (tptp.in (tptp.ordered_pair (tptp.apply C E) (tptp.apply C F)) B)))))))))
% 0.61/1.06  (assume a444 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.empty A)) (tptp.relation B)) (=> (forall ((C $$unsorted) (D $$unsorted) (E $$unsorted)) (=> (and (tptp.in C A) (exists ((F $$unsorted)) (and (= C F) (tptp.in D F) (forall ((G $$unsorted)) (=> (tptp.in G F) (tptp.in (tptp.ordered_pair D G) B))))) (tptp.in C A) (exists ((H $$unsorted)) (and (= C H) (tptp.in E H) (forall ((I $$unsorted)) (=> (tptp.in I H) (tptp.in (tptp.ordered_pair E I) B)))))) (= D E))) (exists ((C $$unsorted)) (forall ((D $$unsorted)) (= (tptp.in D C) (exists ((E $$unsorted)) (and (tptp.in E A) (tptp.in E A) (exists ((J $$unsorted)) (and (= E J) (tptp.in D J) (forall ((K $$unsorted)) (=> (tptp.in K J) (tptp.in (tptp.ordered_pair D K) B))))))))))))))
% 0.61/1.06  (assume a445 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.empty A)) (tptp.relation B)) (forall ((C $$unsorted)) (=> (forall ((D $$unsorted) (E $$unsorted) (F $$unsorted)) (=> (and (= D E) (exists ((G $$unsorted) (H $$unsorted)) (and (= (tptp.ordered_pair G H) E) (tptp.in G A) (exists ((I $$unsorted)) (and (= G I) (tptp.in H I) (forall ((J $$unsorted)) (=> (tptp.in J I) (tptp.in (tptp.ordered_pair H J) B))))))) (= D F) (exists ((K $$unsorted) (L $$unsorted)) (and (= (tptp.ordered_pair K L) F) (tptp.in K A) (exists ((M $$unsorted)) (and (= K M) (tptp.in L M) (forall ((N $$unsorted)) (=> (tptp.in N M) (tptp.in (tptp.ordered_pair L N) B)))))))) (= E F))) (exists ((D $$unsorted)) (forall ((E $$unsorted)) (= (tptp.in E D) (exists ((F $$unsorted)) (and (tptp.in F (tptp.cartesian_product2 A C)) (= F E) (exists ((O $$unsorted) (P $$unsorted)) (and (= (tptp.ordered_pair O P) E) (tptp.in O A) (exists ((Q $$unsorted)) (and (= O Q) (tptp.in P Q) (forall ((R $$unsorted)) (=> (tptp.in R Q) (tptp.in (tptp.ordered_pair P R) B)))))))))))))))))
% 0.61/1.06  (assume a446 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.transitive_relstr A) (tptp.rel_str A) (tptp.element B (tptp.powerset (tptp.the_carrier A))) (tptp.finite C) (tptp.element C (tptp.powerset B))) (=> (forall ((D $$unsorted) (E $$unsorted) (F $$unsorted)) (=> (and (= D E) (exists ((G $$unsorted)) (and (= G E) (exists ((H $$unsorted)) (and (tptp.element H (tptp.the_carrier A)) (tptp.in H B) (tptp.relstr_set_smaller A G H))))) (= D F) (exists ((I $$unsorted)) (and (= I F) (exists ((J $$unsorted)) (and (tptp.element J (tptp.the_carrier A)) (tptp.in J B) (tptp.relstr_set_smaller A I J)))))) (= E F))) (exists ((D $$unsorted)) (forall ((E $$unsorted)) (= (tptp.in E D) (exists ((F $$unsorted)) (and (tptp.in F (tptp.powerset C)) (= F E) (exists ((K $$unsorted)) (and (= K E) (exists ((L $$unsorted)) (and (tptp.element L (tptp.the_carrier A)) (tptp.in L B) (tptp.relstr_set_smaller A K L))))))))))))))
% 0.61/1.06  (assume a447 (forall ((A $$unsorted)) (=> (forall ((B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (tptp.in B A) (= C (tptp.singleton B)) (tptp.in B A) (= D (tptp.singleton B))) (= C D))) (exists ((B $$unsorted)) (forall ((C $$unsorted)) (= (tptp.in C B) (exists ((D $$unsorted)) (and (tptp.in D A) (tptp.in D A) (= C (tptp.singleton D))))))))))
% 0.61/1.06  (assume a448 (forall ((A $$unsorted) (B $$unsorted)) (=> (forall ((C $$unsorted) (D $$unsorted) (E $$unsorted)) (=> (and (= C D) (exists ((F $$unsorted) (G $$unsorted)) (and (= (tptp.ordered_pair F G) D) (tptp.in F A) (= G (tptp.singleton F)))) (= C E) (exists ((H $$unsorted) (I $$unsorted)) (and (= (tptp.ordered_pair H I) E) (tptp.in H A) (= I (tptp.singleton H))))) (= D E))) (exists ((C $$unsorted)) (forall ((D $$unsorted)) (= (tptp.in D C) (exists ((E $$unsorted)) (and (tptp.in E (tptp.cartesian_product2 A B)) (= E D) (exists ((J $$unsorted) (K $$unsorted)) (and (= (tptp.ordered_pair J K) D) (tptp.in J A) (= K (tptp.singleton J))))))))))))
% 0.61/1.06  (assume a449 (forall ((A $$unsorted)) (=> (tptp.ordinal A) (=> (forall ((B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (= B C) (exists ((E $$unsorted)) (and (tptp.ordinal E) (= C E) (=> (tptp.in E tptp.omega) (forall ((F $$unsorted)) (=> (tptp.element F (tptp.powerset (tptp.powerset E))) (not (and (not (= F tptp.empty_set)) (forall ((G $$unsorted)) (not (and (tptp.in G F) (forall ((H $$unsorted)) (=> (and (tptp.in H F) (tptp.subset G H)) (= H G))))))))))))) (= B D) (exists ((I $$unsorted)) (and (tptp.ordinal I) (= D I) (=> (tptp.in I tptp.omega) (forall ((J $$unsorted)) (=> (tptp.element J (tptp.powerset (tptp.powerset I))) (not (and (not (= J tptp.empty_set)) (forall ((K $$unsorted)) (not (and (tptp.in K J) (forall ((L $$unsorted)) (=> (and (tptp.in L J) (tptp.subset K L)) (= L K)))))))))))))) (= C D))) (exists ((B $$unsorted)) (forall ((C $$unsorted)) (= (tptp.in C B) (exists ((D $$unsorted)) (and (tptp.in D (tptp.succ A)) (= D C) (exists ((M $$unsorted)) (and (tptp.ordinal M) (= C M) (=> (tptp.in M tptp.omega) (forall ((N $$unsorted)) (=> (tptp.element N (tptp.powerset (tptp.powerset M))) (not (and (not (= N tptp.empty_set)) (forall ((O $$unsorted)) (not (and (tptp.in O N) (forall ((P $$unsorted)) (=> (and (tptp.in P N) (tptp.subset O P)) (= P O))))))))))))))))))))))
% 0.61/1.06  (assume a450 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.topological_space A) (tptp.top_str A) (tptp.element B (tptp.powerset (tptp.the_carrier A)))) (=> (forall ((C $$unsorted) (D $$unsorted) (E $$unsorted)) (=> (and (= C D) (exists ((F $$unsorted)) (and (tptp.element F (tptp.powerset (tptp.the_carrier A))) (= F D) (tptp.closed_subset F A) (tptp.subset B D))) (= C E) (exists ((G $$unsorted)) (and (tptp.element G (tptp.powerset (tptp.the_carrier A))) (= G E) (tptp.closed_subset G A) (tptp.subset B E)))) (= D E))) (exists ((C $$unsorted)) (forall ((D $$unsorted)) (= (tptp.in D C) (exists ((E $$unsorted)) (and (tptp.in E (tptp.powerset (tptp.the_carrier A))) (= E D) (exists ((H $$unsorted)) (and (tptp.element H (tptp.powerset (tptp.the_carrier A))) (= H D) (tptp.closed_subset H A) (tptp.subset B D))))))))))))
% 0.61/1.06  (assume a451 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.topological_space A) (tptp.top_str A) (tptp.element B (tptp.powerset (tptp.powerset (tptp.the_carrier A))))) (=> (forall ((C $$unsorted) (D $$unsorted) (E $$unsorted)) (=> (and (= C D) (tptp.in (tptp.set_difference (tptp.cast_as_carrier_subset A) D) B) (= C E) (tptp.in (tptp.set_difference (tptp.cast_as_carrier_subset A) E) B)) (= D E))) (exists ((C $$unsorted)) (forall ((D $$unsorted)) (= (tptp.in D C) (exists ((E $$unsorted)) (and (tptp.in E (tptp.powerset (tptp.the_carrier A))) (= E D) (tptp.in (tptp.set_difference (tptp.cast_as_carrier_subset A) D) B))))))))))
% 0.61/1.06  (assume a452 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.ordinal A) (tptp.element B (tptp.powerset (tptp.powerset (tptp.succ A))))) (=> (forall ((C $$unsorted) (D $$unsorted) (E $$unsorted)) (=> (and (= C D) (exists ((F $$unsorted)) (and (tptp.in F B) (= D (tptp.set_difference F (tptp.singleton A))))) (= C E) (exists ((G $$unsorted)) (and (tptp.in G B) (= E (tptp.set_difference G (tptp.singleton A)))))) (= D E))) (exists ((C $$unsorted)) (forall ((D $$unsorted)) (= (tptp.in D C) (exists ((E $$unsorted)) (and (tptp.in E (tptp.powerset A)) (= E D) (exists ((H $$unsorted)) (and (tptp.in H B) (= D (tptp.set_difference H (tptp.singleton A))))))))))))))
% 0.61/1.06  (assume a453 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.one_sorted_str A) (tptp.element B (tptp.powerset (tptp.powerset (tptp.the_carrier A))))) (=> (forall ((C $$unsorted) (D $$unsorted) (E $$unsorted)) (=> (and (tptp.in C (tptp.complements_of_subsets (tptp.the_carrier A) B)) (forall ((F $$unsorted)) (=> (tptp.element F (tptp.powerset (tptp.the_carrier A))) (=> (= F C) (= D (tptp.subset_complement (tptp.the_carrier A) F))))) (tptp.in C (tptp.complements_of_subsets (tptp.the_carrier A) B)) (forall ((G $$unsorted)) (=> (tptp.element G (tptp.powerset (tptp.the_carrier A))) (=> (= G C) (= E (tptp.subset_complement (tptp.the_carrier A) G)))))) (= D E))) (exists ((C $$unsorted)) (forall ((D $$unsorted)) (= (tptp.in D C) (exists ((E $$unsorted)) (and (tptp.in E (tptp.complements_of_subsets (tptp.the_carrier A) B)) (tptp.in E (tptp.complements_of_subsets (tptp.the_carrier A) B)) (forall ((H $$unsorted)) (=> (tptp.element H (tptp.powerset (tptp.the_carrier A))) (=> (= H E) (= D (tptp.subset_complement (tptp.the_carrier A) H))))))))))))))
% 0.61/1.06  (assume a454 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.one_sorted_str A) (tptp.element B (tptp.powerset (tptp.powerset (tptp.the_carrier A))))) (forall ((C $$unsorted)) (=> (forall ((D $$unsorted) (E $$unsorted) (F $$unsorted)) (=> (and (= D E) (exists ((G $$unsorted) (H $$unsorted)) (and (= (tptp.ordered_pair G H) E) (tptp.in G (tptp.complements_of_subsets (tptp.the_carrier A) B)) (forall ((I $$unsorted)) (=> (tptp.element I (tptp.powerset (tptp.the_carrier A))) (=> (= I G) (= H (tptp.subset_complement (tptp.the_carrier A) I))))))) (= D F) (exists ((J $$unsorted) (K $$unsorted)) (and (= (tptp.ordered_pair J K) F) (tptp.in J (tptp.complements_of_subsets (tptp.the_carrier A) B)) (forall ((L $$unsorted)) (=> (tptp.element L (tptp.powerset (tptp.the_carrier A))) (=> (= L J) (= K (tptp.subset_complement (tptp.the_carrier A) L)))))))) (= E F))) (exists ((D $$unsorted)) (forall ((E $$unsorted)) (= (tptp.in E D) (exists ((F $$unsorted)) (and (tptp.in F (tptp.cartesian_product2 (tptp.complements_of_subsets (tptp.the_carrier A) B) C)) (= F E) (exists ((M $$unsorted) (N $$unsorted)) (and (= (tptp.ordered_pair M N) E) (tptp.in M (tptp.complements_of_subsets (tptp.the_carrier A) B)) (forall ((O $$unsorted)) (=> (tptp.element O (tptp.powerset (tptp.the_carrier A))) (=> (= O M) (= N (tptp.subset_complement (tptp.the_carrier A) O)))))))))))))))))
% 0.61/1.06  (assume a455 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.one_sorted_str A) (tptp.element B (tptp.powerset (tptp.powerset (tptp.the_carrier A))))) (=> (forall ((C $$unsorted) (D $$unsorted) (E $$unsorted)) (=> (and (tptp.in C B) (forall ((F $$unsorted)) (=> (tptp.element F (tptp.powerset (tptp.the_carrier A))) (=> (= F C) (= D (tptp.subset_complement (tptp.the_carrier A) F))))) (tptp.in C B) (forall ((G $$unsorted)) (=> (tptp.element G (tptp.powerset (tptp.the_carrier A))) (=> (= G C) (= E (tptp.subset_complement (tptp.the_carrier A) G)))))) (= D E))) (exists ((C $$unsorted)) (forall ((D $$unsorted)) (= (tptp.in D C) (exists ((E $$unsorted)) (and (tptp.in E B) (tptp.in E B) (forall ((H $$unsorted)) (=> (tptp.element H (tptp.powerset (tptp.the_carrier A))) (=> (= H E) (= D (tptp.subset_complement (tptp.the_carrier A) H))))))))))))))
% 0.61/1.06  (assume a456 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.one_sorted_str A) (tptp.element B (tptp.powerset (tptp.powerset (tptp.the_carrier A))))) (forall ((C $$unsorted)) (=> (forall ((D $$unsorted) (E $$unsorted) (F $$unsorted)) (=> (and (= D E) (exists ((G $$unsorted) (H $$unsorted)) (and (= (tptp.ordered_pair G H) E) (tptp.in G B) (forall ((I $$unsorted)) (=> (tptp.element I (tptp.powerset (tptp.the_carrier A))) (=> (= I G) (= H (tptp.subset_complement (tptp.the_carrier A) I))))))) (= D F) (exists ((J $$unsorted) (K $$unsorted)) (and (= (tptp.ordered_pair J K) F) (tptp.in J B) (forall ((L $$unsorted)) (=> (tptp.element L (tptp.powerset (tptp.the_carrier A))) (=> (= L J) (= K (tptp.subset_complement (tptp.the_carrier A) L)))))))) (= E F))) (exists ((D $$unsorted)) (forall ((E $$unsorted)) (= (tptp.in E D) (exists ((F $$unsorted)) (and (tptp.in F (tptp.cartesian_product2 B C)) (= F E) (exists ((M $$unsorted) (N $$unsorted)) (and (= (tptp.ordered_pair M N) E) (tptp.in M B) (forall ((O $$unsorted)) (=> (tptp.element O (tptp.powerset (tptp.the_carrier A))) (=> (= O M) (= N (tptp.subset_complement (tptp.the_carrier A) O)))))))))))))))))
% 0.61/1.06  (assume a457 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.relation B) (tptp.relation C) (tptp.function C)) (=> (forall ((D $$unsorted) (E $$unsorted) (F $$unsorted)) (=> (and (= D E) (exists ((G $$unsorted) (H $$unsorted)) (and (= E (tptp.ordered_pair G H)) (tptp.in (tptp.ordered_pair (tptp.apply C G) (tptp.apply C H)) B))) (= D F) (exists ((I $$unsorted) (J $$unsorted)) (and (= F (tptp.ordered_pair I J)) (tptp.in (tptp.ordered_pair (tptp.apply C I) (tptp.apply C J)) B)))) (= E F))) (exists ((D $$unsorted)) (forall ((E $$unsorted)) (= (tptp.in E D) (exists ((F $$unsorted)) (and (tptp.in F (tptp.cartesian_product2 A A)) (= F E) (exists ((K $$unsorted) (L $$unsorted)) (and (= E (tptp.ordered_pair K L)) (tptp.in (tptp.ordered_pair (tptp.apply C K) (tptp.apply C L)) B))))))))))))
% 0.61/1.06  (assume a458 (forall ((A $$unsorted)) (=> (forall ((B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (= B C) (tptp.ordinal C) (= B D) (tptp.ordinal D)) (= C D))) (exists ((B $$unsorted)) (forall ((C $$unsorted)) (= (tptp.in C B) (exists ((D $$unsorted)) (and (tptp.in D A) (= D C) (tptp.ordinal C)))))))))
% 0.61/1.06  (assume a459 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.element B (tptp.powerset (tptp.powerset A))) (tptp.relation C) (tptp.function C)) (=> (forall ((D $$unsorted) (E $$unsorted) (F $$unsorted)) (=> (and (= D E) (tptp.in (tptp.relation_image C E) B) (= D F) (tptp.in (tptp.relation_image C F) B)) (= E F))) (exists ((D $$unsorted)) (forall ((E $$unsorted)) (= (tptp.in E D) (exists ((F $$unsorted)) (and (tptp.in F (tptp.powerset (tptp.relation_dom C))) (= F E) (tptp.in (tptp.relation_image C E) B))))))))))
% 0.61/1.06  (assume a460 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.ordinal B) (=> (forall ((C $$unsorted) (D $$unsorted) (E $$unsorted)) (=> (and (= C D) (exists ((F $$unsorted)) (and (tptp.ordinal F) (= D F) (tptp.in F A))) (= C E) (exists ((G $$unsorted)) (and (tptp.ordinal G) (= E G) (tptp.in G A)))) (= D E))) (exists ((C $$unsorted)) (forall ((D $$unsorted)) (= (tptp.in D C) (exists ((E $$unsorted)) (and (tptp.in E (tptp.succ B)) (= E D) (exists ((H $$unsorted)) (and (tptp.ordinal H) (= D H) (tptp.in H A))))))))))))
% 0.61/1.06  (assume a461 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.empty A)) (tptp.relation B)) (forall ((C $$unsorted)) (exists ((D $$unsorted)) (forall ((E $$unsorted)) (= (tptp.in E D) (and (tptp.in E (tptp.cartesian_product2 A C)) (exists ((F $$unsorted) (G $$unsorted)) (and (= (tptp.ordered_pair F G) E) (tptp.in F A) (exists ((H $$unsorted)) (and (= F H) (tptp.in G H) (forall ((I $$unsorted)) (=> (tptp.in I H) (tptp.in (tptp.ordered_pair G I) B)))))))))))))))
% 0.61/1.06  (assume a462 (not (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.transitive_relstr A) (tptp.rel_str A) (tptp.element B (tptp.powerset (tptp.the_carrier A))) (tptp.finite C) (tptp.element C (tptp.powerset B))) (exists ((D $$unsorted)) (forall ((E $$unsorted)) (= (tptp.in E D) (and (tptp.in E (tptp.powerset C)) (exists ((F $$unsorted)) (and (= F E) (exists ((G $$unsorted)) (and (tptp.element G (tptp.the_carrier A)) (tptp.in G B) (tptp.relstr_set_smaller A F G)))))))))))))
% 0.61/1.06  (assume a463 (forall ((A $$unsorted) (B $$unsorted)) (exists ((C $$unsorted)) (forall ((D $$unsorted)) (= (tptp.in D C) (and (tptp.in D (tptp.cartesian_product2 A B)) (exists ((E $$unsorted) (F $$unsorted)) (and (= (tptp.ordered_pair E F) D) (tptp.in E A) (= F (tptp.singleton E))))))))))
% 0.61/1.06  (assume a464 (forall ((A $$unsorted)) (=> (tptp.ordinal A) (exists ((B $$unsorted)) (forall ((C $$unsorted)) (= (tptp.in C B) (and (tptp.in C (tptp.succ A)) (exists ((D $$unsorted)) (and (tptp.ordinal D) (= C D) (=> (tptp.in D tptp.omega) (forall ((E $$unsorted)) (=> (tptp.element E (tptp.powerset (tptp.powerset D))) (not (and (not (= E tptp.empty_set)) (forall ((F $$unsorted)) (not (and (tptp.in F E) (forall ((G $$unsorted)) (=> (and (tptp.in G E) (tptp.subset F G)) (= G F))))))))))))))))))))
% 0.61/1.06  (assume a465 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.topological_space A) (tptp.top_str A) (tptp.element B (tptp.powerset (tptp.the_carrier A)))) (exists ((C $$unsorted)) (forall ((D $$unsorted)) (= (tptp.in D C) (and (tptp.in D (tptp.powerset (tptp.the_carrier A))) (exists ((E $$unsorted)) (and (tptp.element E (tptp.powerset (tptp.the_carrier A))) (= E D) (tptp.closed_subset E A) (tptp.subset B D))))))))))
% 0.61/1.06  (assume a466 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.topological_space A) (tptp.top_str A) (tptp.element B (tptp.powerset (tptp.powerset (tptp.the_carrier A))))) (exists ((C $$unsorted)) (forall ((D $$unsorted)) (= (tptp.in D C) (and (tptp.in D (tptp.powerset (tptp.the_carrier A))) (tptp.in (tptp.set_difference (tptp.cast_as_carrier_subset A) D) B))))))))
% 0.61/1.06  (assume a467 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.ordinal A) (tptp.element B (tptp.powerset (tptp.powerset (tptp.succ A))))) (exists ((C $$unsorted)) (forall ((D $$unsorted)) (= (tptp.in D C) (and (tptp.in D (tptp.powerset A)) (exists ((E $$unsorted)) (and (tptp.in E B) (= D (tptp.set_difference E (tptp.singleton A))))))))))))
% 0.61/1.06  (assume a468 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.one_sorted_str A) (tptp.element B (tptp.powerset (tptp.powerset (tptp.the_carrier A))))) (forall ((C $$unsorted)) (exists ((D $$unsorted)) (forall ((E $$unsorted)) (= (tptp.in E D) (and (tptp.in E (tptp.cartesian_product2 (tptp.complements_of_subsets (tptp.the_carrier A) B) C)) (exists ((F $$unsorted) (G $$unsorted)) (and (= (tptp.ordered_pair F G) E) (tptp.in F (tptp.complements_of_subsets (tptp.the_carrier A) B)) (forall ((H $$unsorted)) (=> (tptp.element H (tptp.powerset (tptp.the_carrier A))) (=> (= H F) (= G (tptp.subset_complement (tptp.the_carrier A) H)))))))))))))))
% 0.61/1.06  (assume a469 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.one_sorted_str A) (tptp.element B (tptp.powerset (tptp.powerset (tptp.the_carrier A))))) (forall ((C $$unsorted)) (exists ((D $$unsorted)) (forall ((E $$unsorted)) (= (tptp.in E D) (and (tptp.in E (tptp.cartesian_product2 B C)) (exists ((F $$unsorted) (G $$unsorted)) (and (= (tptp.ordered_pair F G) E) (tptp.in F B) (forall ((H $$unsorted)) (=> (tptp.element H (tptp.powerset (tptp.the_carrier A))) (=> (= H F) (= G (tptp.subset_complement (tptp.the_carrier A) H)))))))))))))))
% 0.61/1.06  (assume a470 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.relation B) (tptp.relation C) (tptp.function C)) (exists ((D $$unsorted)) (forall ((E $$unsorted)) (= (tptp.in E D) (and (tptp.in E (tptp.cartesian_product2 A A)) (exists ((F $$unsorted) (G $$unsorted)) (and (= E (tptp.ordered_pair F G)) (tptp.in (tptp.ordered_pair (tptp.apply C F) (tptp.apply C G)) B))))))))))
% 0.61/1.06  (assume a471 (forall ((A $$unsorted)) (exists ((B $$unsorted)) (forall ((C $$unsorted)) (= (tptp.in C B) (and (tptp.in C A) (tptp.ordinal C)))))))
% 0.61/1.06  (assume a472 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.element B (tptp.powerset (tptp.powerset A))) (tptp.relation C) (tptp.function C)) (exists ((D $$unsorted)) (forall ((E $$unsorted)) (= (tptp.in E D) (and (tptp.in E (tptp.powerset (tptp.relation_dom C))) (tptp.in (tptp.relation_image C E) B))))))))
% 0.61/1.06  (assume a473 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.ordinal B) (exists ((C $$unsorted)) (forall ((D $$unsorted)) (= (tptp.in D C) (and (tptp.in D (tptp.succ B)) (exists ((E $$unsorted)) (and (tptp.ordinal E) (= D E) (tptp.in E A))))))))))
% 0.61/1.06  (assume a474 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.empty A)) (tptp.relation B)) (=> (and (forall ((C $$unsorted) (D $$unsorted) (E $$unsorted)) (=> (and (tptp.in C A) (exists ((F $$unsorted)) (and (= C F) (tptp.in D F) (forall ((G $$unsorted)) (=> (tptp.in G F) (tptp.in (tptp.ordered_pair D G) B))))) (exists ((H $$unsorted)) (and (= C H) (tptp.in E H) (forall ((I $$unsorted)) (=> (tptp.in I H) (tptp.in (tptp.ordered_pair E I) B)))))) (= D E))) (forall ((C $$unsorted)) (not (and (tptp.in C A) (forall ((D $$unsorted)) (not (exists ((J $$unsorted)) (and (= C J) (tptp.in D J) (forall ((K $$unsorted)) (=> (tptp.in K J) (tptp.in (tptp.ordered_pair D K) B))))))))))) (exists ((C $$unsorted)) (and (tptp.relation C) (tptp.function C) (= (tptp.relation_dom C) A) (forall ((D $$unsorted)) (=> (tptp.in D A) (exists ((L $$unsorted)) (and (= D L) (tptp.in (tptp.apply C D) L) (forall ((M $$unsorted)) (=> (tptp.in M L) (tptp.in (tptp.ordered_pair (tptp.apply C D) M) B)))))))))))))
% 0.61/1.06  (assume a475 (forall ((A $$unsorted)) (=> (and (forall ((B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (tptp.in B A) (= C (tptp.singleton B)) (= D (tptp.singleton B))) (= C D))) (forall ((B $$unsorted)) (not (and (tptp.in B A) (forall ((C $$unsorted)) (not (= C (tptp.singleton B)))))))) (exists ((B $$unsorted)) (and (tptp.relation B) (tptp.function B) (= (tptp.relation_dom B) A) (forall ((C $$unsorted)) (=> (tptp.in C A) (= (tptp.apply B C) (tptp.singleton C)))))))))
% 0.61/1.06  (assume a476 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.one_sorted_str A) (tptp.element B (tptp.powerset (tptp.powerset (tptp.the_carrier A))))) (=> (and (forall ((C $$unsorted) (D $$unsorted) (E $$unsorted)) (=> (and (tptp.in C (tptp.complements_of_subsets (tptp.the_carrier A) B)) (forall ((F $$unsorted)) (=> (tptp.element F (tptp.powerset (tptp.the_carrier A))) (=> (= F C) (= D (tptp.subset_complement (tptp.the_carrier A) F))))) (forall ((G $$unsorted)) (=> (tptp.element G (tptp.powerset (tptp.the_carrier A))) (=> (= G C) (= E (tptp.subset_complement (tptp.the_carrier A) G)))))) (= D E))) (forall ((C $$unsorted)) (not (and (tptp.in C (tptp.complements_of_subsets (tptp.the_carrier A) B)) (forall ((D $$unsorted)) (not (forall ((H $$unsorted)) (=> (tptp.element H (tptp.powerset (tptp.the_carrier A))) (=> (= H C) (= D (tptp.subset_complement (tptp.the_carrier A) H))))))))))) (exists ((C $$unsorted)) (and (tptp.relation C) (tptp.function C) (= (tptp.relation_dom C) (tptp.complements_of_subsets (tptp.the_carrier A) B)) (forall ((D $$unsorted)) (=> (tptp.in D (tptp.complements_of_subsets (tptp.the_carrier A) B)) (forall ((I $$unsorted)) (=> (tptp.element I (tptp.powerset (tptp.the_carrier A))) (=> (= I D) (= (tptp.apply C D) (tptp.subset_complement (tptp.the_carrier A) I)))))))))))))
% 0.61/1.06  (assume a477 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.one_sorted_str A) (tptp.element B (tptp.powerset (tptp.powerset (tptp.the_carrier A))))) (=> (and (forall ((C $$unsorted) (D $$unsorted) (E $$unsorted)) (=> (and (tptp.in C B) (forall ((F $$unsorted)) (=> (tptp.element F (tptp.powerset (tptp.the_carrier A))) (=> (= F C) (= D (tptp.subset_complement (tptp.the_carrier A) F))))) (forall ((G $$unsorted)) (=> (tptp.element G (tptp.powerset (tptp.the_carrier A))) (=> (= G C) (= E (tptp.subset_complement (tptp.the_carrier A) G)))))) (= D E))) (forall ((C $$unsorted)) (not (and (tptp.in C B) (forall ((D $$unsorted)) (not (forall ((H $$unsorted)) (=> (tptp.element H (tptp.powerset (tptp.the_carrier A))) (=> (= H C) (= D (tptp.subset_complement (tptp.the_carrier A) H))))))))))) (exists ((C $$unsorted)) (and (tptp.relation C) (tptp.function C) (= (tptp.relation_dom C) B) (forall ((D $$unsorted)) (=> (tptp.in D B) (forall ((I $$unsorted)) (=> (tptp.element I (tptp.powerset (tptp.the_carrier A))) (=> (= I D) (= (tptp.apply C D) (tptp.subset_complement (tptp.the_carrier A) I)))))))))))))
% 0.61/1.06  (assume a478 (=> (forall ((A $$unsorted)) (=> (tptp.ordinal A) (=> (forall ((B $$unsorted)) (=> (tptp.ordinal B) (=> (tptp.in B A) (=> (tptp.in B tptp.omega) (forall ((C $$unsorted)) (=> (tptp.element C (tptp.powerset (tptp.powerset B))) (not (and (not (= C tptp.empty_set)) (forall ((D $$unsorted)) (not (and (tptp.in D C) (forall ((E $$unsorted)) (=> (and (tptp.in E C) (tptp.subset D E)) (= E D)))))))))))))) (=> (tptp.in A tptp.omega) (forall ((F $$unsorted)) (=> (tptp.element F (tptp.powerset (tptp.powerset A))) (not (and (not (= F tptp.empty_set)) (forall ((G $$unsorted)) (not (and (tptp.in G F) (forall ((H $$unsorted)) (=> (and (tptp.in H F) (tptp.subset G H)) (= H G)))))))))))))) (forall ((A $$unsorted)) (=> (tptp.ordinal A) (=> (tptp.in A tptp.omega) (forall ((I $$unsorted)) (=> (tptp.element I (tptp.powerset (tptp.powerset A))) (not (and (not (= I tptp.empty_set)) (forall ((J $$unsorted)) (not (and (tptp.in J I) (forall ((K $$unsorted)) (=> (and (tptp.in K I) (tptp.subset J K)) (= K J)))))))))))))))
% 0.61/1.06  (assume a479 (forall ((A $$unsorted)) (exists ((B $$unsorted)) (and (tptp.relation B) (tptp.function B) (= (tptp.relation_dom B) A) (forall ((C $$unsorted)) (=> (tptp.in C A) (= (tptp.apply B C) (tptp.singleton C))))))))
% 0.61/1.06  (assume a480 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.topological_space A) (tptp.top_str A) (tptp.element B (tptp.powerset (tptp.the_carrier A)))) (exists ((C $$unsorted)) (and (tptp.element C (tptp.powerset (tptp.powerset (tptp.the_carrier A)))) (forall ((D $$unsorted)) (=> (tptp.element D (tptp.powerset (tptp.the_carrier A))) (= (tptp.in D C) (exists ((E $$unsorted)) (and (tptp.element E (tptp.powerset (tptp.the_carrier A))) (= E D) (tptp.closed_subset E A) (tptp.subset B D)))))))))))
% 0.61/1.06  (assume a481 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.topological_space A) (tptp.top_str A) (tptp.element B (tptp.powerset (tptp.powerset (tptp.the_carrier A))))) (exists ((C $$unsorted)) (and (tptp.element C (tptp.powerset (tptp.powerset (tptp.the_carrier A)))) (forall ((D $$unsorted)) (=> (tptp.element D (tptp.powerset (tptp.the_carrier A))) (= (tptp.in D C) (tptp.in (tptp.set_difference (tptp.cast_as_carrier_subset A) D) B)))))))))
% 0.61/1.06  (assume a482 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.disjoint A B) (tptp.disjoint B A))))
% 0.61/1.06  (assume a483 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.equipotent A B) (tptp.equipotent B A))))
% 0.61/1.06  (assume a484 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (= (tptp.in (tptp.ordered_pair A B) (tptp.cartesian_product2 C D)) (and (tptp.in A C) (tptp.in B D)))))
% 0.61/1.06  (assume a485 (forall ((A $$unsorted)) (tptp.in A (tptp.succ A))))
% 0.61/1.06  (assume a486 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element B (tptp.powerset (tptp.powerset A))) (and (not (and (not (= B tptp.empty_set)) (= (tptp.complements_of_subsets A B) tptp.empty_set))) (not (and (not (= (tptp.complements_of_subsets A B) tptp.empty_set)) (= B tptp.empty_set)))))))
% 0.61/1.06  (assume a487 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (not (and (= (tptp.unordered_pair A B) (tptp.unordered_pair C D)) (not (= A C)) (not (= A D))))))
% 0.61/1.06  (assume a488 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.relation C) (= (tptp.in A (tptp.relation_rng (tptp.relation_rng_restriction B C))) (and (tptp.in A B) (tptp.in A (tptp.relation_rng C)))))))
% 0.61/1.06  (assume a489 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (tptp.subset (tptp.relation_rng (tptp.relation_rng_restriction A B)) A))))
% 0.61/1.06  (assume a490 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (tptp.subset (tptp.relation_rng_restriction A B) B))))
% 0.61/1.06  (assume a491 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (tptp.subset (tptp.relation_rng (tptp.relation_rng_restriction A B)) (tptp.relation_rng B)))))
% 0.61/1.06  (assume a492 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.subset A B) (and (tptp.subset (tptp.cartesian_product2 A C) (tptp.cartesian_product2 B C)) (tptp.subset (tptp.cartesian_product2 C A) (tptp.cartesian_product2 C B))))))
% 0.61/1.06  (assume a493 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (= (tptp.relation_rng (tptp.relation_rng_restriction A B)) (tptp.set_intersection2 (tptp.relation_rng B) A)))))
% 0.61/1.06  (assume a494 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (tptp.subset A B) (tptp.subset C D)) (tptp.subset (tptp.cartesian_product2 A C) (tptp.cartesian_product2 B D)))))
% 0.61/1.06  (assume a495 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element B (tptp.powerset (tptp.powerset A))) (=> (not (= B tptp.empty_set)) (= (tptp.meet_of_subsets A (tptp.complements_of_subsets A B)) (tptp.subset_complement A (tptp.union_of_subsets A B)))))))
% 0.61/1.06  (assume a496 (forall ((A $$unsorted)) (=> (tptp.one_sorted_str A) (= (tptp.cast_as_carrier_subset A) (tptp.the_carrier A)))))
% 0.61/1.06  (assume a497 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.relation_of2_as_subset C A B) (and (tptp.subset (tptp.relation_dom C) A) (tptp.subset (tptp.relation_rng C) B)))))
% 0.61/1.06  (assume a498 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element B (tptp.powerset (tptp.powerset A))) (=> (not (= B tptp.empty_set)) (= (tptp.union_of_subsets A (tptp.complements_of_subsets A B)) (tptp.subset_complement A (tptp.meet_of_subsets A B)))))))
% 0.61/1.06  (assume a499 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.subset A B) (= (tptp.set_union2 A B) B))))
% 0.61/1.06  (assume a500 (forall ((A $$unsorted)) (exists ((B $$unsorted)) (and (tptp.in A B) (forall ((C $$unsorted) (D $$unsorted)) (=> (and (tptp.in C B) (tptp.subset D C)) (tptp.in D B))) (forall ((C $$unsorted)) (=> (tptp.in C B) (tptp.in (tptp.powerset C) B))) (forall ((C $$unsorted)) (not (and (tptp.subset C B) (not (tptp.are_equipotent C B)) (not (tptp.in C B)))))))))
% 0.61/1.06  (assume a501 (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.topological_space A) (tptp.top_str A)) (= (tptp.compact_top_space A) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.powerset (tptp.powerset (tptp.the_carrier A)))) (not (and (tptp.centered B) (tptp.closed_subsets B A) (= (tptp.meet_of_subsets (tptp.the_carrier A) B) tptp.empty_set)))))))))
% 0.61/1.07  (assume a502 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.subset A B) (tptp.finite B)) (tptp.finite A))))
% 0.61/1.07  (assume a503 (forall ((A $$unsorted)) (=> (tptp.one_sorted_str A) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.powerset (tptp.powerset (tptp.the_carrier A)))) (= (tptp.finite (tptp.complements_of_subsets (tptp.the_carrier A) B)) (tptp.finite B)))))))
% 0.61/1.07  (assume a504 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.relation C) (= (tptp.relation_dom_restriction (tptp.relation_rng_restriction A C) B) (tptp.relation_rng_restriction A (tptp.relation_dom_restriction C B))))))
% 0.61/1.07  (assume a505 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.relation C) (= (tptp.in A (tptp.relation_image C B)) (exists ((D $$unsorted)) (and (tptp.in D (tptp.relation_dom C)) (tptp.in (tptp.ordered_pair D A) C) (tptp.in D B)))))))
% 0.61/1.07  (assume a506 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (tptp.subset (tptp.relation_image B A) (tptp.relation_rng B)))))
% 0.61/1.07  (assume a507 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.relation B) (tptp.function B)) (tptp.subset (tptp.relation_image B (tptp.relation_inverse_image B A)) A))))
% 0.61/1.07  (assume a508 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (= (tptp.relation_image B A) (tptp.relation_image B (tptp.set_intersection2 (tptp.relation_dom B) A))))))
% 0.61/1.07  (assume a509 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (=> (tptp.subset A (tptp.relation_dom B)) (tptp.subset A (tptp.relation_inverse_image B (tptp.relation_image B A)))))))
% 0.61/1.07  (assume a510 (forall ((A $$unsorted)) (=> (tptp.relation A) (= (tptp.relation_image A (tptp.relation_dom A)) (tptp.relation_rng A)))))
% 0.61/1.07  (assume a511 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.relation B) (tptp.function B)) (=> (tptp.subset A (tptp.relation_rng B)) (= (tptp.relation_image B (tptp.relation_inverse_image B A)) A)))))
% 0.61/1.07  (assume a512 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (tptp.relation_of2_as_subset D C A) (=> (tptp.subset (tptp.relation_rng D) B) (tptp.relation_of2_as_subset D C B)))))
% 0.61/1.07  (assume a513 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.finite A) (tptp.finite (tptp.set_intersection2 A B)))))
% 0.61/1.07  (assume a514 (forall ((A $$unsorted)) (=> (tptp.one_sorted_str A) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.powerset (tptp.the_carrier A))) (= (tptp.subset_intersection2 (tptp.the_carrier A) B (tptp.cast_as_carrier_subset A)) B))))))
% 0.61/1.07  (assume a515 (forall ((A $$unsorted)) (=> (and (tptp.antisymmetric_relstr A) (tptp.rel_str A)) (forall ((B $$unsorted)) (= (tptp.ex_sup_of_relstr_set A B) (exists ((C $$unsorted)) (and (tptp.element C (tptp.the_carrier A)) (tptp.relstr_set_smaller A B C) (forall ((D $$unsorted)) (=> (tptp.element D (tptp.the_carrier A)) (=> (tptp.relstr_set_smaller A B D) (tptp.related A C D)))))))))))
% 0.61/1.07  (assume a516 (forall ((A $$unsorted)) (=> (tptp.relation A) (forall ((B $$unsorted)) (=> (tptp.relation B) (= (tptp.relation_rng (tptp.relation_composition A B)) (tptp.relation_image B (tptp.relation_rng A))))))))
% 0.61/1.07  (assume a517 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.relation C) (= (tptp.in A (tptp.relation_inverse_image C B)) (exists ((D $$unsorted)) (and (tptp.in D (tptp.relation_rng C)) (tptp.in (tptp.ordered_pair A D) C) (tptp.in D B)))))))
% 0.61/1.07  (assume a518 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (tptp.subset (tptp.relation_inverse_image B A) (tptp.relation_dom B)))))
% 0.61/1.07  (assume a519 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (tptp.relation_of2_as_subset D C A) (=> (tptp.subset A B) (tptp.relation_of2_as_subset D C B)))))
% 0.61/1.07  (assume a520 (forall ((A $$unsorted)) (=> (tptp.top_str A) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.powerset (tptp.powerset (tptp.the_carrier A)))) (= (tptp.closed_subsets B A) (tptp.open_subsets (tptp.complements_of_subsets (tptp.the_carrier A) B) A)))))))
% 0.61/1.07  (assume a521 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.relation C) (= (tptp.in A (tptp.relation_restriction C B)) (and (tptp.in A C) (tptp.in A (tptp.cartesian_product2 B B)))))))
% 0.61/1.07  (assume a522 (forall ((A $$unsorted)) (=> (and (tptp.antisymmetric_relstr A) (tptp.rel_str A)) (forall ((B $$unsorted)) (= (tptp.ex_inf_of_relstr_set A B) (exists ((C $$unsorted)) (and (tptp.element C (tptp.the_carrier A)) (tptp.relstr_element_smaller A B C) (forall ((D $$unsorted)) (=> (tptp.element D (tptp.the_carrier A)) (=> (tptp.relstr_element_smaller A B D) (tptp.related A D C)))))))))))
% 0.61/1.07  (assume a523 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (not (and (not (= A tptp.empty_set)) (tptp.subset A (tptp.relation_rng B)) (= (tptp.relation_inverse_image B A) tptp.empty_set))))))
% 0.61/1.07  (assume a524 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.relation C) (=> (tptp.subset A B) (tptp.subset (tptp.relation_inverse_image C A) (tptp.relation_inverse_image C B))))))
% 0.61/1.07  (assume a525 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.relation B) (tptp.function B)) (=> (tptp.finite A) (tptp.finite (tptp.relation_image B A))))))
% 0.61/1.07  (assume a526 (forall ((A $$unsorted)) (=> (tptp.one_sorted_str A) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.powerset (tptp.the_carrier A))) (= (tptp.subset_complement (tptp.the_carrier A) B) (tptp.subset_difference (tptp.the_carrier A) (tptp.cast_as_carrier_subset A) B)))))))
% 0.61/1.07  (assume a527 (forall ((A $$unsorted)) (=> (tptp.top_str A) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.powerset (tptp.powerset (tptp.the_carrier A)))) (= (tptp.open_subsets B A) (tptp.closed_subsets (tptp.complements_of_subsets (tptp.the_carrier A) B) A)))))))
% 0.61/1.07  (assume a528 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (= (tptp.relation_restriction B A) (tptp.relation_dom_restriction (tptp.relation_rng_restriction A B) A)))))
% 0.61/1.07  (assume a529 (forall ((A $$unsorted) (B $$unsorted)) (tptp.subset (tptp.set_intersection2 A B) A)))
% 0.61/1.07  (assume a530 (forall ((A $$unsorted)) (=> (tptp.finite A) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.powerset (tptp.powerset A))) (not (and (not (= B tptp.empty_set)) (forall ((C $$unsorted)) (not (and (tptp.in C B) (forall ((D $$unsorted)) (=> (and (tptp.in D B) (tptp.subset C D)) (= D C)))))))))))))
% 0.61/1.07  (assume a531 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (= (tptp.relation_restriction B A) (tptp.relation_rng_restriction A (tptp.relation_dom_restriction B A))))))
% 0.61/1.07  (assume a532 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.relation C) (=> (tptp.in A (tptp.relation_field (tptp.relation_restriction C B))) (and (tptp.in A (tptp.relation_field C)) (tptp.in A B))))))
% 0.61/1.07  (assume a533 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.subset A B) (tptp.subset A C)) (tptp.subset A (tptp.set_intersection2 B C)))))
% 0.61/1.07  (assume a534 (forall ((A $$unsorted)) (= (tptp.set_union2 A tptp.empty_set) A)))
% 0.61/1.07  (assume a535 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element B (tptp.the_carrier (tptp.boole_lattice A))) (forall ((C $$unsorted)) (=> (tptp.element C (tptp.the_carrier (tptp.boole_lattice A))) (and (= (tptp.join (tptp.boole_lattice A) B C) (tptp.set_union2 B C)) (= (tptp.meet (tptp.boole_lattice A) B C) (tptp.set_intersection2 B C))))))))
% 0.61/1.07  (assume a536 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (tptp.element A B))))
% 0.61/1.07  (assume a537 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.subset A B) (tptp.subset B C)) (tptp.subset A C))))
% 0.61/1.07  (assume a538 (= (tptp.powerset tptp.empty_set) (tptp.singleton tptp.empty_set)))
% 0.61/1.07  (assume a539 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.relation C) (=> (tptp.in (tptp.ordered_pair A B) C) (and (tptp.in A (tptp.relation_dom C)) (tptp.in B (tptp.relation_rng C)))))))
% 0.61/1.07  (assume a540 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (and (tptp.subset (tptp.relation_field (tptp.relation_restriction B A)) (tptp.relation_field B)) (tptp.subset (tptp.relation_field (tptp.relation_restriction B A)) A)))))
% 0.61/1.07  (assume a541 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.relation B) (tptp.function B)) (forall ((C $$unsorted)) (=> (and (tptp.relation C) (tptp.function C)) (= (tptp.in A (tptp.relation_dom (tptp.relation_composition C B))) (and (tptp.in A (tptp.relation_dom C)) (tptp.in (tptp.apply C A) (tptp.relation_dom B)))))))))
% 0.61/1.07  (assume a542 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (tptp.function D) (tptp.quasi_total D A B) (tptp.relation_of2_as_subset D A B)) (forall ((E $$unsorted)) (=> (and (tptp.relation E) (tptp.function E)) (=> (tptp.in C A) (or (= B tptp.empty_set) (= (tptp.apply (tptp.relation_composition D E) C) (tptp.apply E (tptp.apply D C))))))))))
% 0.61/1.07  (assume a543 (forall ((A $$unsorted)) (=> (tptp.epsilon_transitive A) (forall ((B $$unsorted)) (=> (tptp.ordinal B) (=> (tptp.proper_subset A B) (tptp.in A B)))))))
% 0.61/1.07  (assume a544 (forall ((A $$unsorted)) (=> (tptp.relation A) (tptp.subset A (tptp.cartesian_product2 (tptp.relation_dom A) (tptp.relation_rng A))))))
% 0.61/1.07  (assume a545 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.relation C) (tptp.subset (tptp.fiber (tptp.relation_restriction C A) B) (tptp.fiber C B)))))
% 0.61/1.07  (assume a546 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.relation B) (tptp.function B)) (forall ((C $$unsorted)) (=> (and (tptp.relation C) (tptp.function C)) (=> (tptp.in A (tptp.relation_dom (tptp.relation_composition C B))) (= (tptp.apply (tptp.relation_composition C B) A) (tptp.apply B (tptp.apply C A)))))))))
% 0.61/1.07  (assume a547 (forall ((A $$unsorted)) (=> (tptp.one_sorted_str A) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.powerset (tptp.the_carrier A))) (= (tptp.subset_difference (tptp.the_carrier A) (tptp.cast_as_carrier_subset A) (tptp.subset_difference (tptp.the_carrier A) (tptp.cast_as_carrier_subset A) B)) B))))))
% 0.61/1.07  (assume a548 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.relation_of2_as_subset C B A) (= (forall ((D $$unsorted)) (not (and (tptp.in D B) (forall ((E $$unsorted)) (not (tptp.in (tptp.ordered_pair D E) C)))))) (= (tptp.relation_dom_as_subset B A C) B)))))
% 0.61/1.07  (assume a549 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (=> (tptp.reflexive B) (tptp.reflexive (tptp.relation_restriction B A))))))
% 0.61/1.07  (assume a550 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.relation B) (tptp.function B)) (forall ((C $$unsorted)) (=> (and (tptp.relation C) (tptp.function C)) (=> (tptp.in A (tptp.relation_dom B)) (= (tptp.apply (tptp.relation_composition B C) A) (tptp.apply C (tptp.apply B A)))))))))
% 0.61/1.07  (assume a551 (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.meet_commutative A) (tptp.meet_absorbing A) (tptp.latt_str A)) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.the_carrier A)) (forall ((C $$unsorted)) (=> (tptp.element C (tptp.the_carrier A)) (tptp.below A (tptp.meet_commut A B C) B))))))))
% 0.61/1.07  (assume a552 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.ordinal B) (=> (tptp.in A B) (tptp.ordinal A)))))
% 0.61/1.07  (assume a553 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.relation_of2_as_subset C A B) (= (forall ((D $$unsorted)) (not (and (tptp.in D B) (forall ((E $$unsorted)) (not (tptp.in (tptp.ordered_pair E D) C)))))) (= (tptp.relation_rng_as_subset A B C) B)))))
% 0.61/1.07  (assume a554 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (=> (tptp.connected B) (tptp.connected (tptp.relation_restriction B A))))))
% 0.61/1.07  (assume a555 (forall ((A $$unsorted)) (=> (tptp.ordinal A) (forall ((B $$unsorted)) (=> (tptp.ordinal B) (not (and (not (tptp.in A B)) (not (= A B)) (not (tptp.in B A)))))))))
% 0.61/1.07  (assume a556 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (=> (tptp.transitive B) (tptp.transitive (tptp.relation_restriction B A))))))
% 0.61/1.07  (assume a557 (forall ((A $$unsorted)) (=> (and (tptp.antisymmetric_relstr A) (tptp.rel_str A)) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.the_carrier A)) (forall ((C $$unsorted)) (=> (tptp.element C (tptp.the_carrier A)) (=> (and (tptp.related A B C) (tptp.related A C B)) (= B C)))))))))
% 0.61/1.07  (assume a558 (forall ((A $$unsorted)) (=> (tptp.relation A) (forall ((B $$unsorted)) (=> (tptp.relation B) (=> (tptp.subset A B) (and (tptp.subset (tptp.relation_dom A) (tptp.relation_dom B)) (tptp.subset (tptp.relation_rng A) (tptp.relation_rng B)))))))))
% 0.61/1.07  (assume a559 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (=> (tptp.antisymmetric B) (tptp.antisymmetric (tptp.relation_restriction B A))))))
% 0.61/1.07  (assume a560 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (=> (tptp.well_orders B A) (and (= (tptp.relation_field (tptp.relation_restriction B A)) A) (tptp.well_ordering (tptp.relation_restriction B A)))))))
% 0.61/1.07  (assume a561 (forall ((A $$unsorted)) (=> (and (tptp.relation A) (tptp.function A)) (=> (tptp.finite (tptp.relation_dom A)) (tptp.finite (tptp.relation_rng A))))))
% 0.61/1.07  (assume a562 (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.join_commutative A) (tptp.join_semilatt_str A)) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.the_carrier A)) (forall ((C $$unsorted)) (=> (tptp.element C (tptp.the_carrier A)) (=> (and (tptp.below A B C) (tptp.below A C B)) (= B C)))))))))
% 0.61/1.07  (assume a563 (forall ((A $$unsorted)) (=> (and (tptp.transitive_relstr A) (tptp.rel_str A)) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.the_carrier A)) (forall ((C $$unsorted)) (=> (tptp.element C (tptp.the_carrier A)) (forall ((D $$unsorted)) (=> (tptp.element D (tptp.the_carrier A)) (=> (and (tptp.related A B C) (tptp.related A C D)) (tptp.related A B D)))))))))))
% 0.61/1.07  (assume a564 (forall ((A $$unsorted)) (exists ((B $$unsorted)) (and (tptp.relation B) (tptp.well_orders B A)))))
% 0.61/1.07  (assume a565 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.subset A B) (tptp.subset (tptp.set_intersection2 A C) (tptp.set_intersection2 B C)))))
% 0.61/1.07  (assume a566 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.empty_carrier B)) (tptp.lattice B) (tptp.latt_str B)) (forall ((C $$unsorted)) (=> (tptp.element C (tptp.the_carrier B)) (= (tptp.latt_set_smaller B C A) (tptp.relstr_element_smaller (tptp.poset_of_lattice B) A (tptp.cast_to_el_of_LattPOSet B C))))))))
% 0.61/1.07  (assume a567 (forall ((A $$unsorted)) (=> (not (tptp.empty A)) (not (and (forall ((B $$unsorted)) (not (and (tptp.in B A) (= B tptp.empty_set)))) (forall ((B $$unsorted)) (=> (and (tptp.relation B) (tptp.function B)) (not (and (= (tptp.relation_dom B) A) (forall ((C $$unsorted)) (=> (tptp.in C A) (tptp.in (tptp.apply B C) C))))))))))))
% 0.61/1.07  (assume a568 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.subset A B) (= (tptp.set_intersection2 A B) A))))
% 0.61/1.07  (assume a569 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.empty_carrier B)) (tptp.lattice B) (tptp.latt_str B)) (forall ((C $$unsorted)) (=> (tptp.element C (tptp.the_carrier (tptp.poset_of_lattice B))) (= (tptp.relstr_element_smaller (tptp.poset_of_lattice B) A C) (tptp.latt_set_smaller B (tptp.cast_to_el_of_lattice B C) A)))))))
% 0.61/1.07  (assume a570 (forall ((A $$unsorted)) (=> (tptp.top_str A) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.powerset (tptp.the_carrier A))) (= (tptp.closed_subset B A) (tptp.open_subset (tptp.subset_complement (tptp.the_carrier A) B) A)))))))
% 0.61/1.07  (assume a571 (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.lattice A) (tptp.complete_latt_str A) (tptp.latt_str A)) (forall ((B $$unsorted)) (and (= (tptp.join_of_latt_set A B) (tptp.join_on_relstr (tptp.poset_of_lattice A) B)) (= (tptp.meet_of_latt_set A B) (tptp.meet_on_relstr (tptp.poset_of_lattice A) B)))))))
% 0.61/1.07  (assume a572 (forall ((A $$unsorted)) (= (tptp.set_intersection2 A tptp.empty_set) tptp.empty_set)))
% 0.61/1.07  (assume a573 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element B (tptp.the_carrier (tptp.boole_lattice A))) (forall ((C $$unsorted)) (=> (tptp.element C (tptp.the_carrier (tptp.boole_lattice A))) (= (tptp.below (tptp.boole_lattice A) B C) (tptp.subset B C)))))))
% 0.61/1.07  (assume a574 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element A B) (or (tptp.empty B) (tptp.in A B)))))
% 0.61/1.07  (assume a575 (forall ((A $$unsorted) (B $$unsorted)) (=> (forall ((C $$unsorted)) (= (tptp.in C A) (tptp.in C B))) (= A B))))
% 0.61/1.07  (assume a576 (forall ((A $$unsorted)) (tptp.reflexive (tptp.inclusion_relation A))))
% 0.61/1.07  (assume a577 (forall ((A $$unsorted)) (tptp.subset tptp.empty_set A)))
% 0.61/1.07  (assume a578 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.empty_carrier B)) (tptp.lattice B) (tptp.latt_str B)) (forall ((C $$unsorted)) (=> (tptp.element C (tptp.the_carrier B)) (= (tptp.latt_element_smaller B C A) (tptp.relstr_set_smaller (tptp.poset_of_lattice B) A (tptp.cast_to_el_of_LattPOSet B C))))))))
% 0.61/1.07  (assume a579 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.relation C) (=> (tptp.in (tptp.ordered_pair A B) C) (and (tptp.in A (tptp.relation_field C)) (tptp.in B (tptp.relation_field C)))))))
% 0.61/1.07  (assume a580 (forall ((A $$unsorted)) (=> (tptp.top_str A) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.powerset (tptp.the_carrier A))) (= (tptp.open_subset B A) (tptp.closed_subset (tptp.subset_complement (tptp.the_carrier A) B) A)))))))
% 0.61/1.07  (assume a581 (forall ((A $$unsorted)) (=> (and (tptp.antisymmetric_relstr A) (tptp.rel_str A)) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.the_carrier A)) (forall ((C $$unsorted)) (and (=> (and (= B (tptp.join_on_relstr A C)) (tptp.ex_sup_of_relstr_set A C)) (and (tptp.relstr_set_smaller A C B) (forall ((D $$unsorted)) (=> (tptp.element D (tptp.the_carrier A)) (=> (tptp.relstr_set_smaller A C D) (tptp.related A B D)))))) (=> (and (tptp.relstr_set_smaller A C B) (forall ((D $$unsorted)) (=> (tptp.element D (tptp.the_carrier A)) (=> (tptp.relstr_set_smaller A C D) (tptp.related A B D))))) (and (= B (tptp.join_on_relstr A C)) (tptp.ex_sup_of_relstr_set A C))))))))))
% 0.61/1.07  (assume a582 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.empty_carrier B)) (tptp.lattice B) (tptp.latt_str B)) (forall ((C $$unsorted)) (=> (tptp.element C (tptp.the_carrier (tptp.poset_of_lattice B))) (= (tptp.relstr_set_smaller (tptp.poset_of_lattice B) A C) (tptp.latt_element_smaller B (tptp.cast_to_el_of_lattice B C) A)))))))
% 0.61/1.07  (assume a583 (forall ((A $$unsorted)) (=> (forall ((B $$unsorted)) (=> (tptp.in B A) (and (tptp.ordinal B) (tptp.subset B A)))) (tptp.ordinal A))))
% 0.61/1.07  (assume a584 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (=> (tptp.well_founded_relation B) (tptp.well_founded_relation (tptp.relation_restriction B A))))))
% 0.61/1.07  (assume a585 (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.lattice A) (tptp.latt_str A)) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.the_carrier A)) (forall ((C $$unsorted)) (=> (tptp.element C (tptp.the_carrier A)) (= (tptp.in (tptp.ordered_pair_as_product_element (tptp.the_carrier A) (tptp.the_carrier A) B C) (tptp.relation_of_lattice A)) (tptp.below_refl A B C)))))))))
% 0.61/1.07  (assume a586 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.ordinal B) (not (and (tptp.subset A B) (not (= A tptp.empty_set)) (forall ((C $$unsorted)) (=> (tptp.ordinal C) (not (and (tptp.in C A) (forall ((D $$unsorted)) (=> (tptp.ordinal D) (=> (tptp.in D A) (tptp.ordinal_subset C D)))))))))))))
% 0.61/1.07  (assume a587 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (=> (tptp.well_ordering B) (tptp.well_ordering (tptp.relation_restriction B A))))))
% 0.61/1.07  (assume a588 (forall ((A $$unsorted)) (=> (tptp.ordinal A) (forall ((B $$unsorted)) (=> (tptp.ordinal B) (= (tptp.in A B) (tptp.ordinal_subset (tptp.succ A) B)))))))
% 0.61/1.07  (assume a589 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.subset A B) (tptp.subset (tptp.set_difference A C) (tptp.set_difference B C)))))
% 0.61/1.07  (assume a590 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (= (tptp.ordered_pair A B) (tptp.ordered_pair C D)) (and (= A C) (= B D)))))
% 0.61/1.07  (assume a591 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.relation B) (tptp.function B)) (= (= B (tptp.identity_relation A)) (and (= (tptp.relation_dom B) A) (forall ((C $$unsorted)) (=> (tptp.in C A) (= (tptp.apply B C) C))))))))
% 0.61/1.07  (assume a592 (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.lattice A) (tptp.complete_latt_str A) (tptp.latt_str A)) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.the_carrier A)) (forall ((C $$unsorted)) (= (= B (tptp.meet_of_latt_set A C)) (and (tptp.latt_set_smaller A B C) (forall ((D $$unsorted)) (=> (tptp.element D (tptp.the_carrier A)) (=> (tptp.latt_set_smaller A D C) (tptp.below_refl A D B))))))))))))
% 0.61/1.07  (assume a593 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in B A) (= (tptp.apply (tptp.identity_relation A) B) B))))
% 0.61/1.07  (assume a594 (forall ((A $$unsorted) (B $$unsorted)) (tptp.subset (tptp.set_difference A B) A)))
% 0.61/1.07  (assume a595 (forall ((A $$unsorted)) (=> (tptp.relation A) (and (= (tptp.relation_rng A) (tptp.relation_dom (tptp.relation_inverse A))) (= (tptp.relation_dom A) (tptp.relation_rng (tptp.relation_inverse A)))))))
% 0.61/1.07  (assume a596 (forall ((A $$unsorted) (B $$unsorted)) (= (= (tptp.set_difference A B) tptp.empty_set) (tptp.subset A B))))
% 0.61/1.07  (assume a597 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset (tptp.singleton A) B) (tptp.in A B))))
% 0.61/1.07  (assume a598 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.subset (tptp.unordered_pair A B) C) (and (tptp.in A C) (tptp.in B C)))))
% 0.61/1.07  (assume a599 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (=> (and (tptp.well_ordering B) (tptp.subset A (tptp.relation_field B))) (= (tptp.relation_field (tptp.relation_restriction B A)) A)))))
% 0.61/1.07  (assume a600 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_union2 A (tptp.set_difference B A)) (tptp.set_union2 A B))))
% 0.61/1.07  (assume a601 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset A (tptp.singleton B)) (or (= A tptp.empty_set) (= A (tptp.singleton B))))))
% 0.61/1.07  (assume a602 (forall ((A $$unsorted)) (= (tptp.set_difference A tptp.empty_set) A)))
% 0.61/1.07  (assume a603 (forall ((A $$unsorted)) (and (tptp.lower_bounded_semilattstr (tptp.boole_lattice A)) (= (tptp.bottom_of_semilattstr (tptp.boole_lattice A)) tptp.empty_set))))
% 0.61/1.07  (assume a604 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (not (and (tptp.in A B) (tptp.in B C) (tptp.in C A)))))
% 0.61/1.07  (assume a605 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.element A (tptp.powerset B)) (tptp.subset A B))))
% 0.61/1.07  (assume a606 (forall ((A $$unsorted)) (tptp.transitive (tptp.inclusion_relation A))))
% 0.61/1.07  (assume a607 (forall ((A $$unsorted) (B $$unsorted)) (and (not (and (not (tptp.disjoint A B)) (forall ((C $$unsorted)) (not (and (tptp.in C A) (tptp.in C B)))))) (not (and (exists ((C $$unsorted)) (and (tptp.in C A) (tptp.in C B))) (tptp.disjoint A B))))))
% 0.61/1.07  (assume a608 (forall ((A $$unsorted)) (=> (tptp.subset A tptp.empty_set) (= A tptp.empty_set))))
% 0.61/1.07  (assume a609 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_difference (tptp.set_union2 A B) B) (tptp.set_difference A B))))
% 0.61/1.07  (assume a610 (forall ((A $$unsorted)) (=> (tptp.ordinal A) (= (tptp.being_limit_ordinal A) (forall ((B $$unsorted)) (=> (tptp.ordinal B) (=> (tptp.in B A) (tptp.in (tptp.succ B) A))))))))
% 0.61/1.07  (assume a611 (forall ((A $$unsorted)) (=> (tptp.ordinal A) (and (not (and (not (tptp.being_limit_ordinal A)) (forall ((B $$unsorted)) (=> (tptp.ordinal B) (not (= A (tptp.succ B))))))) (not (and (exists ((B $$unsorted)) (and (tptp.ordinal B) (= A (tptp.succ B)))) (tptp.being_limit_ordinal A)))))))
% 0.61/1.07  (assume a612 (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.antisymmetric_relstr A) (tptp.lower_bounded_relstr A) (tptp.rel_str A)) (and (tptp.ex_sup_of_relstr_set A tptp.empty_set) (tptp.ex_inf_of_relstr_set A (tptp.the_carrier A))))))
% 0.61/1.07  (assume a613 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element B (tptp.powerset A)) (forall ((C $$unsorted)) (=> (tptp.element C (tptp.powerset A)) (= (tptp.disjoint B C) (tptp.subset B (tptp.subset_complement A C))))))))
% 0.61/1.07  (assume a614 (forall ((A $$unsorted)) (=> (and (tptp.topological_space A) (tptp.top_str A)) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.powerset (tptp.powerset (tptp.the_carrier A)))) (=> (forall ((C $$unsorted)) (=> (tptp.element C (tptp.powerset (tptp.the_carrier A))) (=> (tptp.in C B) (tptp.closed_subset C A)))) (tptp.closed_subset (tptp.meet_of_subsets (tptp.the_carrier A) B) A)))))))
% 0.61/1.07  (assume a615 (forall ((A $$unsorted)) (=> (tptp.relation A) (forall ((B $$unsorted)) (=> (tptp.relation B) (tptp.subset (tptp.relation_dom (tptp.relation_composition A B)) (tptp.relation_dom A)))))))
% 0.61/1.07  (assume a616 (forall ((A $$unsorted)) (=> (tptp.top_str A) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.powerset (tptp.the_carrier A))) (tptp.subset (tptp.interior A B) B))))))
% 0.61/1.07  (assume a617 (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.antisymmetric_relstr A) (tptp.lower_bounded_relstr A) (tptp.rel_str A)) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.the_carrier A)) (tptp.related A (tptp.bottom_of_relstr A) B))))))
% 0.61/1.07  (assume a618 (forall ((A $$unsorted)) (=> (tptp.top_str A) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.powerset (tptp.the_carrier A))) (forall ((C $$unsorted)) (=> (tptp.in C (tptp.the_carrier A)) (= (tptp.in C (tptp.topstr_closure A B)) (forall ((D $$unsorted)) (=> (tptp.element D (tptp.powerset (tptp.the_carrier A))) (=> (and (tptp.closed_subset D A) (tptp.subset B D)) (tptp.in C D))))))))))))
% 0.61/1.07  (assume a619 (forall ((A $$unsorted)) (=> (tptp.relation A) (forall ((B $$unsorted)) (=> (tptp.relation B) (tptp.subset (tptp.relation_rng (tptp.relation_composition A B)) (tptp.relation_rng B)))))))
% 0.61/1.07  (assume a620 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.subset A B) (= B (tptp.set_union2 A (tptp.set_difference B A))))))
% 0.61/1.07  (assume a621 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (tptp.function D) (tptp.quasi_total D A B) (tptp.relation_of2_as_subset D A B)) (=> (not (= B tptp.empty_set)) (forall ((E $$unsorted)) (= (tptp.in E (tptp.relation_inverse_image D C)) (and (tptp.in E A) (tptp.in (tptp.apply D E) C))))))))
% 0.61/1.07  (assume a622 (forall ((A $$unsorted)) (=> (and (tptp.topological_space A) (tptp.top_str A)) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.powerset (tptp.the_carrier A))) (exists ((C $$unsorted)) (and (tptp.element C (tptp.powerset (tptp.powerset (tptp.the_carrier A)))) (forall ((D $$unsorted)) (=> (tptp.element D (tptp.powerset (tptp.the_carrier A))) (= (tptp.in D C) (and (tptp.closed_subset D A) (tptp.subset B D))))) (= (tptp.topstr_closure A B) (tptp.meet_of_subsets (tptp.the_carrier A) C)))))))))
% 0.61/1.07  (assume a623 (forall ((A $$unsorted)) (=> (tptp.relation A) (forall ((B $$unsorted)) (=> (tptp.relation B) (=> (tptp.subset (tptp.relation_rng A) (tptp.relation_dom B)) (= (tptp.relation_dom (tptp.relation_composition A B)) (tptp.relation_dom A))))))))
% 0.61/1.07  (assume a624 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element B (tptp.powerset (tptp.powerset A))) (not (and (not (= B tptp.empty_set)) (= (tptp.complements_of_subsets A B) tptp.empty_set))))))
% 0.61/1.07  (assume a625 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (= (tptp.set_union2 (tptp.singleton A) B) B))))
% 0.61/1.07  (assume a626 (forall ((A $$unsorted)) (=> (tptp.relation A) (forall ((B $$unsorted)) (=> (tptp.relation B) (=> (tptp.subset (tptp.relation_dom A) (tptp.relation_rng B)) (= (tptp.relation_rng (tptp.relation_composition B A)) (tptp.relation_rng A))))))))
% 0.61/1.07  (assume a627 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element B (tptp.powerset (tptp.powerset A))) (=> (not (= B tptp.empty_set)) (= (tptp.subset_difference A (tptp.cast_to_subset A) (tptp.union_of_subsets A B)) (tptp.meet_of_subsets A (tptp.complements_of_subsets A B)))))))
% 0.61/1.07  (assume a628 (forall ((A $$unsorted)) (=> (tptp.top_str A) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.powerset (tptp.the_carrier A))) (tptp.subset B (tptp.topstr_closure A B)))))))
% 0.61/1.07  (assume a629 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element B (tptp.powerset (tptp.powerset A))) (=> (not (= B tptp.empty_set)) (= (tptp.union_of_subsets A (tptp.complements_of_subsets A B)) (tptp.subset_difference A (tptp.cast_to_subset A) (tptp.meet_of_subsets A B)))))))
% 0.61/1.07  (assume a630 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_difference A (tptp.set_difference A B)) (tptp.set_intersection2 A B))))
% 0.61/1.07  (assume a631 (forall ((A $$unsorted)) (=> (tptp.relation A) (forall ((B $$unsorted)) (=> (tptp.relation B) (forall ((C $$unsorted)) (=> (and (tptp.relation C) (tptp.function C)) (=> (tptp.relation_isomorphism A B C) (tptp.relation_isomorphism B A (tptp.function_inverse C))))))))))
% 0.61/1.07  (assume a632 (forall ((A $$unsorted)) (= (tptp.set_difference tptp.empty_set A) tptp.empty_set)))
% 0.61/1.07  (assume a633 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.in A B) (tptp.element B (tptp.powerset C))) (tptp.element A C))))
% 0.61/1.07  (assume a634 (forall ((A $$unsorted)) (=> (tptp.ordinal A) (tptp.connected (tptp.inclusion_relation A)))))
% 0.61/1.07  (assume a635 (forall ((A $$unsorted) (B $$unsorted)) (and (not (and (not (tptp.disjoint A B)) (forall ((C $$unsorted)) (not (tptp.in C (tptp.set_intersection2 A B)))))) (not (and (exists ((C $$unsorted)) (tptp.in C (tptp.set_intersection2 A B))) (tptp.disjoint A B))))))
% 0.61/1.07  (assume a636 (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.lattice A) (tptp.complete_latt_str A) (tptp.latt_str A)) (and (not (tptp.empty_carrier A)) (tptp.lattice A) (tptp.lower_bounded_semilattstr A) (tptp.latt_str A) (= (tptp.bottom_of_semilattstr A) (tptp.join_of_latt_set A tptp.empty_set))))))
% 0.61/1.07  (assume a637 (forall ((A $$unsorted)) (=> (not (= A tptp.empty_set)) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.powerset A)) (forall ((C $$unsorted)) (=> (tptp.element C A) (=> (not (tptp.in C B)) (tptp.in C (tptp.subset_complement A B))))))))))
% 0.61/1.07  (assume a638 (forall ((A $$unsorted)) (=> (and (tptp.topological_space A) (tptp.top_str A)) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.powerset (tptp.the_carrier A))) (tptp.open_subset (tptp.interior A B) A))))))
% 0.61/1.07  (assume a639 (forall ((A $$unsorted)) (=> (tptp.top_str A) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.powerset (tptp.the_carrier A))) (and (=> (tptp.closed_subset B A) (= (tptp.topstr_closure A B) B)) (=> (and (tptp.topological_space A) (= (tptp.topstr_closure A B) B)) (tptp.closed_subset B A))))))))
% 0.61/1.07  (assume a640 (forall ((A $$unsorted)) (=> (tptp.relation A) (forall ((B $$unsorted)) (=> (tptp.relation B) (forall ((C $$unsorted)) (=> (and (tptp.relation C) (tptp.function C)) (=> (tptp.relation_isomorphism A B C) (and (=> (tptp.reflexive A) (tptp.reflexive B)) (=> (tptp.transitive A) (tptp.transitive B)) (=> (tptp.connected A) (tptp.connected B)) (=> (tptp.antisymmetric A) (tptp.antisymmetric B)) (=> (tptp.well_founded_relation A) (tptp.well_founded_relation B)))))))))))
% 0.61/1.07  (assume a641 (forall ((A $$unsorted)) (=> (and (tptp.relation A) (tptp.function A)) (=> (tptp.one_to_one A) (forall ((B $$unsorted)) (=> (and (tptp.relation B) (tptp.function B)) (= (= B (tptp.function_inverse A)) (and (= (tptp.relation_dom B) (tptp.relation_rng A)) (forall ((C $$unsorted) (D $$unsorted)) (and (=> (and (tptp.in C (tptp.relation_rng A)) (= D (tptp.apply B C))) (and (tptp.in D (tptp.relation_dom A)) (= C (tptp.apply A D)))) (=> (and (tptp.in D (tptp.relation_dom A)) (= C (tptp.apply A D))) (and (tptp.in C (tptp.relation_rng A)) (= D (tptp.apply B C))))))))))))))
% 0.61/1.07  (assume a642 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.element C (tptp.powerset A)) (not (and (tptp.in B (tptp.subset_complement A C)) (tptp.in B C))))))
% 0.61/1.07  (assume a643 (forall ((A $$unsorted)) (=> (tptp.relation A) (forall ((B $$unsorted)) (=> (tptp.relation B) (forall ((C $$unsorted)) (=> (and (tptp.relation C) (tptp.function C)) (=> (and (tptp.well_ordering A) (tptp.relation_isomorphism A B C)) (tptp.well_ordering B)))))))))
% 0.61/1.07  (assume a644 (forall ((A $$unsorted)) (=> (and (tptp.relation A) (tptp.function A)) (=> (tptp.one_to_one A) (and (= (tptp.relation_rng A) (tptp.relation_dom (tptp.function_inverse A))) (= (tptp.relation_dom A) (tptp.relation_rng (tptp.function_inverse A))))))))
% 0.61/1.07  (assume a645 (forall ((A $$unsorted)) (=> (and (tptp.topological_space A) (tptp.top_str A)) (forall ((B $$unsorted)) (=> (tptp.top_str B) (forall ((C $$unsorted)) (=> (tptp.element C (tptp.powerset (tptp.the_carrier A))) (forall ((D $$unsorted)) (=> (tptp.element D (tptp.powerset (tptp.the_carrier B))) (and (=> (tptp.open_subset D B) (= (tptp.interior B D) D)) (=> (= (tptp.interior A C) C) (tptp.open_subset C A))))))))))))
% 0.61/1.07  (assume a646 (forall ((A $$unsorted)) (=> (tptp.relation A) (=> (forall ((B $$unsorted) (C $$unsorted)) (not (tptp.in (tptp.ordered_pair B C) A))) (= A tptp.empty_set)))))
% 0.61/1.07  (assume a647 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.relation B) (tptp.function B)) (=> (and (tptp.one_to_one B) (tptp.in A (tptp.relation_rng B))) (and (= A (tptp.apply B (tptp.apply (tptp.function_inverse B) A))) (= A (tptp.apply (tptp.relation_composition (tptp.function_inverse B) B) A)))))))
% 0.61/1.07  (assume a648 (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.topological_space A) (tptp.top_str A)) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.powerset (tptp.the_carrier A))) (forall ((C $$unsorted)) (=> (tptp.element C (tptp.the_carrier A)) (=> (and (tptp.open_subset B A) (tptp.in C B)) (tptp.point_neighbourhood B A C)))))))))
% 0.61/1.07  (assume a649 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (not (and (tptp.in A B) (tptp.element B (tptp.powerset C)) (tptp.empty C)))))
% 0.61/1.07  (assume a650 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element B (tptp.powerset A)) (= (tptp.proper_element B (tptp.powerset A)) (not (= B A))))))
% 0.61/1.07  (assume a651 (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.one_sorted_str A)) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.powerset (tptp.powerset (tptp.the_carrier A)))) (not (and (tptp.is_a_cover_of_carrier A B) (= B tptp.empty_set))))))))
% 0.61/1.07  (assume a652 (forall ((A $$unsorted)) (=> (tptp.relation A) (= (tptp.well_founded_relation A) (tptp.is_well_founded_in A (tptp.relation_field A))))))
% 0.61/1.07  (assume a653 (forall ((A $$unsorted)) (tptp.antisymmetric (tptp.inclusion_relation A))))
% 0.61/1.07  (assume a654 (and (= (tptp.relation_dom tptp.empty_set) tptp.empty_set) (= (tptp.relation_rng tptp.empty_set) tptp.empty_set)))
% 0.61/1.07  (assume a655 (forall ((A $$unsorted) (B $$unsorted)) (not (and (tptp.subset A B) (tptp.proper_subset B A)))))
% 0.61/1.07  (assume a656 (forall ((A $$unsorted)) (=> (tptp.rel_str A) (forall ((B $$unsorted)) (=> (tptp.subrelstr B A) (forall ((C $$unsorted)) (=> (tptp.element C (tptp.the_carrier A)) (forall ((D $$unsorted)) (=> (tptp.element D (tptp.the_carrier A)) (forall ((E $$unsorted)) (=> (tptp.element E (tptp.the_carrier B)) (forall ((F $$unsorted)) (=> (tptp.element F (tptp.the_carrier B)) (=> (and (= E C) (= F D) (tptp.related B E F)) (tptp.related A C D)))))))))))))))
% 0.61/1.07  (assume a657 (forall ((A $$unsorted)) (=> (tptp.rel_str A) (forall ((B $$unsorted)) (=> (and (tptp.full_subrelstr B A) (tptp.subrelstr B A)) (forall ((C $$unsorted)) (=> (tptp.element C (tptp.the_carrier A)) (forall ((D $$unsorted)) (=> (tptp.element D (tptp.the_carrier A)) (forall ((E $$unsorted)) (=> (tptp.element E (tptp.the_carrier B)) (forall ((F $$unsorted)) (=> (tptp.element F (tptp.the_carrier B)) (=> (and (= E C) (= F D) (tptp.related A C D) (tptp.in E (tptp.the_carrier B)) (tptp.in F (tptp.the_carrier B))) (tptp.related B E F)))))))))))))))
% 0.61/1.07  (assume a658 (forall ((A $$unsorted)) (=> (and (tptp.relation A) (tptp.function A)) (=> (tptp.one_to_one A) (tptp.one_to_one (tptp.function_inverse A))))))
% 0.61/1.07  (assume a659 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.subset A B) (tptp.disjoint B C)) (tptp.disjoint A C))))
% 0.61/1.07  (assume a660 (forall ((A $$unsorted)) (=> (tptp.relation A) (=> (or (= (tptp.relation_dom A) tptp.empty_set) (= (tptp.relation_rng A) tptp.empty_set)) (= A tptp.empty_set)))))
% 0.61/1.07  (assume a661 (forall ((A $$unsorted)) (=> (tptp.relation A) (= (= (tptp.relation_dom A) tptp.empty_set) (= (tptp.relation_rng A) tptp.empty_set)))))
% 0.61/1.07  (assume a662 (forall ((A $$unsorted) (B $$unsorted)) (= (= (tptp.set_difference A (tptp.singleton B)) A) (not (tptp.in B A)))))
% 0.61/1.07  (assume a663 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.relation B) (tptp.function B)) (forall ((C $$unsorted)) (=> (and (tptp.relation C) (tptp.function C)) (= (= B (tptp.relation_dom_restriction C A)) (and (= (tptp.relation_dom B) (tptp.set_intersection2 (tptp.relation_dom C) A)) (forall ((D $$unsorted)) (=> (tptp.in D (tptp.relation_dom B)) (= (tptp.apply B D) (tptp.apply C D)))))))))))
% 0.61/1.07  (assume a664 (forall ((A $$unsorted)) (= (tptp.unordered_pair A A) (tptp.singleton A))))
% 0.61/1.07  (assume a665 (forall ((A $$unsorted)) (=> (tptp.empty A) (= A tptp.empty_set))))
% 0.61/1.07  (assume a666 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (tptp.function D) (tptp.quasi_total D A B) (tptp.relation_of2_as_subset D A B)) (=> (tptp.in C A) (or (= B tptp.empty_set) (tptp.in (tptp.apply D C) (tptp.relation_rng D)))))))
% 0.61/1.07  (assume a667 (forall ((A $$unsorted)) (=> (tptp.ordinal A) (tptp.well_founded_relation (tptp.inclusion_relation A)))))
% 0.61/1.07  (assume a668 (forall ((A $$unsorted)) (=> (tptp.rel_str A) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.the_carrier A)) (and (tptp.relstr_set_smaller A tptp.empty_set B) (tptp.relstr_element_smaller A tptp.empty_set B)))))))
% 0.61/1.07  (assume a669 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.subset (tptp.singleton A) (tptp.singleton B)) (= A B))))
% 0.61/1.07  (assume a670 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.relation C) (tptp.function C)) (=> (tptp.in B (tptp.relation_dom (tptp.relation_dom_restriction C A))) (= (tptp.apply (tptp.relation_dom_restriction C A) B) (tptp.apply C B))))))
% 0.61/1.07  (assume a671 (forall ((A $$unsorted)) (and (= (tptp.relation_dom (tptp.identity_relation A)) A) (= (tptp.relation_rng (tptp.identity_relation A)) A))))
% 0.61/1.07  (assume a672 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.relation C) (tptp.function C)) (=> (tptp.in B A) (= (tptp.apply (tptp.relation_dom_restriction C A) B) (tptp.apply C B))))))
% 0.61/1.07  (assume a673 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (tptp.relation D) (= (tptp.in (tptp.ordered_pair A B) (tptp.relation_composition (tptp.identity_relation C) D)) (and (tptp.in A C) (tptp.in (tptp.ordered_pair A B) D))))))
% 0.61/1.07  (assume a674 (forall ((A $$unsorted) (B $$unsorted)) (not (and (tptp.in A B) (tptp.empty B)))))
% 0.61/1.07  (assume a675 (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.lattice A) (tptp.latt_str A)) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.the_carrier A)) (forall ((C $$unsorted)) (=> (tptp.element C (tptp.the_carrier A)) (= (tptp.below_refl A B C) (tptp.related_reflexive (tptp.poset_of_lattice A) (tptp.cast_to_el_of_LattPOSet A B) (tptp.cast_to_el_of_LattPOSet A C))))))))))
% 0.61/1.07  (assume a676 (forall ((A $$unsorted) (B $$unsorted)) (and (= (tptp.pair_first (tptp.ordered_pair A B)) A) (= (tptp.pair_second (tptp.ordered_pair A B)) B))))
% 0.61/1.07  (assume a677 (forall ((A $$unsorted) (B $$unsorted)) (not (and (tptp.in A B) (forall ((C $$unsorted)) (not (and (tptp.in C B) (forall ((D $$unsorted)) (not (and (tptp.in D B) (tptp.in D C)))))))))))
% 0.61/1.07  (assume a678 (forall ((A $$unsorted)) (=> (tptp.ordinal A) (tptp.well_ordering (tptp.inclusion_relation A)))))
% 0.61/1.07  (assume a679 (forall ((A $$unsorted) (B $$unsorted)) (tptp.subset A (tptp.set_union2 A B))))
% 0.61/1.07  (assume a680 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.disjoint A B) (= (tptp.set_difference A B) A))))
% 0.61/1.07  (assume a681 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.relation C) (= (tptp.in A (tptp.relation_dom (tptp.relation_dom_restriction C B))) (and (tptp.in A B) (tptp.in A (tptp.relation_dom C)))))))
% 0.61/1.07  (assume a682 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (tptp.subset (tptp.relation_dom_restriction B A) B))))
% 0.61/1.07  (assume a683 (forall ((A $$unsorted) (B $$unsorted)) (not (and (tptp.empty A) (not (= A B)) (tptp.empty B)))))
% 0.61/1.07  (assume a684 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.relation C) (tptp.function C)) (= (tptp.in (tptp.ordered_pair A B) C) (and (tptp.in A (tptp.relation_dom C)) (= B (tptp.apply C A)))))))
% 0.61/1.07  (assume a685 (forall ((A $$unsorted)) (=> (tptp.relation A) (= (tptp.well_orders A (tptp.relation_field A)) (tptp.well_ordering A)))))
% 0.61/1.07  (assume a686 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.subset A B) (tptp.subset C B)) (tptp.subset (tptp.set_union2 A C) B))))
% 0.61/1.07  (assume a687 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (= (tptp.singleton A) (tptp.unordered_pair B C)) (= A B))))
% 0.61/1.07  (assume a688 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (= (tptp.relation_dom (tptp.relation_dom_restriction B A)) (tptp.set_intersection2 (tptp.relation_dom B) A)))))
% 0.61/1.07  (assume a689 (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.one_sorted_str A)) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.the_carrier A)) (= (tptp.apply_as_element (tptp.the_carrier A) (tptp.the_carrier A) (tptp.identity_on_carrier A) B) B))))))
% 0.61/1.07  (assume a690 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (tptp.subset A (tptp.union B)))))
% 0.61/1.07  (assume a691 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (= (tptp.relation_dom_restriction B A) (tptp.relation_composition (tptp.identity_relation A) B)))))
% 0.61/1.07  (assume a692 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (tptp.subset (tptp.relation_rng (tptp.relation_dom_restriction B A)) (tptp.relation_rng B)))))
% 0.61/1.07  (assume a693 (forall ((A $$unsorted)) (= (tptp.union (tptp.powerset A)) A)))
% 0.61/1.07  (assume a694 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (tptp.function D) (tptp.quasi_total D A B) (tptp.relation_of2_as_subset D A B)) (=> (tptp.subset B C) (or (and (= B tptp.empty_set) (not (= A tptp.empty_set))) (and (tptp.function D) (tptp.quasi_total D A C) (tptp.relation_of2_as_subset D A C)))))))
% 0.61/1.07  (assume a695 (forall ((A $$unsorted)) (exists ((B $$unsorted)) (and (tptp.in A B) (forall ((C $$unsorted) (D $$unsorted)) (=> (and (tptp.in C B) (tptp.subset D C)) (tptp.in D B))) (forall ((C $$unsorted)) (not (and (tptp.in C B) (forall ((D $$unsorted)) (not (and (tptp.in D B) (forall ((E $$unsorted)) (=> (tptp.subset E C) (tptp.in E D))))))))) (forall ((C $$unsorted)) (not (and (tptp.subset C B) (not (tptp.are_equipotent C B)) (not (tptp.in C B)))))))))
% 0.61/1.07  (assume a696 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (= (tptp.singleton A) (tptp.unordered_pair B C)) (= B C))))
% 0.61/1.07  (assume a697 true)
% 0.61/1.07  (step t1 (cl (not (= (not (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.transitive_relstr A) (tptp.rel_str A) (tptp.element B (tptp.powerset (tptp.the_carrier A))) (tptp.finite C) (tptp.element C (tptp.powerset B))) (exists ((D $$unsorted)) (forall ((E $$unsorted)) (= (tptp.in E D) (and (tptp.in E (tptp.powerset C)) (exists ((F $$unsorted)) (and (= F E) (exists ((G $$unsorted)) (and (tptp.element G (tptp.the_carrier A)) (tptp.in G B) (tptp.relstr_set_smaller A F G)))))))))))) (not (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (tptp.empty_carrier A) (not (tptp.transitive_relstr A)) (not (tptp.rel_str A)) (not (tptp.element B (tptp.powerset (tptp.the_carrier A)))) (not (tptp.finite C)) (not (tptp.element C (tptp.powerset B))) (not (forall ((D $$unsorted)) (not (forall ((E $$unsorted)) (= (tptp.in E D) (and (tptp.in E (tptp.powerset C)) (not (forall ((BOUND_VARIABLE_20150 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_20150 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_20150 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_20150)))))))))))))))) (not (not (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.transitive_relstr A) (tptp.rel_str A) (tptp.element B (tptp.powerset (tptp.the_carrier A))) (tptp.finite C) (tptp.element C (tptp.powerset B))) (exists ((D $$unsorted)) (forall ((E $$unsorted)) (= (tptp.in E D) (and (tptp.in E (tptp.powerset C)) (exists ((F $$unsorted)) (and (= F E) (exists ((G $$unsorted)) (and (tptp.element G (tptp.the_carrier A)) (tptp.in G B) (tptp.relstr_set_smaller A F G))))))))))))) (not (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (tptp.empty_carrier A) (not (tptp.transitive_relstr A)) (not (tptp.rel_str A)) (not (tptp.element B (tptp.powerset (tptp.the_carrier A)))) (not (tptp.finite C)) (not (tptp.element C (tptp.powerset B))) (not (forall ((D $$unsorted)) (not (forall ((E $$unsorted)) (= (tptp.in E D) (and (tptp.in E (tptp.powerset C)) (not (forall ((BOUND_VARIABLE_20150 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_20150 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_20150 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_20150))))))))))))))) :rule equiv_pos2)
% 0.61/1.07  (anchor :step t2 :args ((A $$unsorted) (:= A A) (B $$unsorted) (:= B B) (C $$unsorted) (:= C C)))
% 0.61/1.07  (step t2.t1 (cl (= A A)) :rule refl)
% 0.61/1.07  (step t2.t2 (cl (= B B)) :rule refl)
% 0.61/1.07  (step t2.t3 (cl (= C C)) :rule refl)
% 0.61/1.07  (step t2.t4 (cl (= (and (not (tptp.empty_carrier A)) (tptp.transitive_relstr A) (tptp.rel_str A) (tptp.element B (tptp.powerset (tptp.the_carrier A))) (tptp.finite C) (tptp.element C (tptp.powerset B))) (and (not (tptp.empty_carrier A)) (tptp.transitive_relstr A) (tptp.rel_str A) (tptp.element B (tptp.powerset (tptp.the_carrier A))) (tptp.finite C) (tptp.element C (tptp.powerset B))))) :rule refl)
% 0.61/1.07  (anchor :step t2.t5 :args ((D $$unsorted) (:= D D)))
% 0.61/1.07  (step t2.t5.t1 (cl (= D D)) :rule refl)
% 0.61/1.07  (anchor :step t2.t5.t2 :args ((E $$unsorted) (:= E E)))
% 0.61/1.07  (step t2.t5.t2.t1 (cl (= E E)) :rule refl)
% 0.61/1.07  (step t2.t5.t2.t2 (cl (= (tptp.in E D) (tptp.in E D))) :rule refl)
% 0.61/1.07  (step t2.t5.t2.t3 (cl (= (tptp.in E (tptp.powerset C)) (tptp.in E (tptp.powerset C)))) :rule refl)
% 0.61/1.07  (anchor :step t2.t5.t2.t4 :args ((F $$unsorted) (:= F F)))
% 0.61/1.07  (step t2.t5.t2.t4.t1 (cl (= F F)) :rule refl)
% 0.61/1.07  (step t2.t5.t2.t4.t2 (cl (= (= F E) (= E F))) :rule all_simplify)
% 0.61/1.07  (step t2.t5.t2.t4.t3 (cl (= (exists ((G $$unsorted)) (and (tptp.element G (tptp.the_carrier A)) (tptp.in G B) (tptp.relstr_set_smaller A F G))) (not (forall ((G $$unsorted)) (not (and (tptp.element G (tptp.the_carrier A)) (tptp.in G B) (tptp.relstr_set_smaller A F G))))))) :rule all_simplify)
% 0.61/1.07  (step t2.t5.t2.t4.t4 (cl (= (forall ((G $$unsorted)) (not (and (tptp.element G (tptp.the_carrier A)) (tptp.in G B) (tptp.relstr_set_smaller A F G)))) (forall ((G $$unsorted)) (or (not (tptp.element G (tptp.the_carrier A))) (not (tptp.in G B)) (not (tptp.relstr_set_smaller A F G)))))) :rule all_simplify)
% 0.61/1.07  (step t2.t5.t2.t4.t5 (cl (= (not (forall ((G $$unsorted)) (not (and (tptp.element G (tptp.the_carrier A)) (tptp.in G B) (tptp.relstr_set_smaller A F G))))) (not (forall ((G $$unsorted)) (or (not (tptp.element G (tptp.the_carrier A))) (not (tptp.in G B)) (not (tptp.relstr_set_smaller A F G))))))) :rule cong :premises (t2.t5.t2.t4.t4))
% 0.61/1.07  (step t2.t5.t2.t4.t6 (cl (= (exists ((G $$unsorted)) (and (tptp.element G (tptp.the_carrier A)) (tptp.in G B) (tptp.relstr_set_smaller A F G))) (not (forall ((G $$unsorted)) (or (not (tptp.element G (tptp.the_carrier A))) (not (tptp.in G B)) (not (tptp.relstr_set_smaller A F G))))))) :rule trans :premises (t2.t5.t2.t4.t3 t2.t5.t2.t4.t5))
% 0.61/1.07  (step t2.t5.t2.t4.t7 (cl (= (and (= F E) (exists ((G $$unsorted)) (and (tptp.element G (tptp.the_carrier A)) (tptp.in G B) (tptp.relstr_set_smaller A F G)))) (and (= E F) (not (forall ((G $$unsorted)) (or (not (tptp.element G (tptp.the_carrier A))) (not (tptp.in G B)) (not (tptp.relstr_set_smaller A F G)))))))) :rule cong :premises (t2.t5.t2.t4.t2 t2.t5.t2.t4.t6))
% 0.61/1.07  (step t2.t5.t2.t4 (cl (= (exists ((F $$unsorted)) (and (= F E) (exists ((G $$unsorted)) (and (tptp.element G (tptp.the_carrier A)) (tptp.in G B) (tptp.relstr_set_smaller A F G))))) (exists ((F $$unsorted)) (and (= E F) (not (forall ((G $$unsorted)) (or (not (tptp.element G (tptp.the_carrier A))) (not (tptp.in G B)) (not (tptp.relstr_set_smaller A F G))))))))) :rule bind)
% 0.61/1.07  (step t2.t5.t2.t5 (cl (= (exists ((F $$unsorted)) (and (= E F) (not (forall ((G $$unsorted)) (or (not (tptp.element G (tptp.the_carrier A))) (not (tptp.in G B)) (not (tptp.relstr_set_smaller A F G))))))) (not (forall ((F $$unsorted)) (not (and (= E F) (not (forall ((G $$unsorted)) (or (not (tptp.element G (tptp.the_carrier A))) (not (tptp.in G B)) (not (tptp.relstr_set_smaller A F G))))))))))) :rule all_simplify)
% 0.61/1.07  (step t2.t5.t2.t6 (cl (= (forall ((F $$unsorted)) (not (and (= E F) (not (forall ((G $$unsorted)) (or (not (tptp.element G (tptp.the_carrier A))) (not (tptp.in G B)) (not (tptp.relstr_set_smaller A F G)))))))) (forall ((F $$unsorted)) (or (not (= E F)) (forall ((G $$unsorted)) (or (not (tptp.element G (tptp.the_carrier A))) (not (tptp.in G B)) (not (tptp.relstr_set_smaller A F G)))))))) :rule all_simplify)
% 0.61/1.07  (step t2.t5.t2.t7 (cl (= (forall ((F $$unsorted)) (or (not (= E F)) (forall ((G $$unsorted)) (or (not (tptp.element G (tptp.the_carrier A))) (not (tptp.in G B)) (not (tptp.relstr_set_smaller A F G)))))) (forall ((F $$unsorted) (BOUND_VARIABLE_20150 $$unsorted)) (or (not (= E F)) (or (not (tptp.element BOUND_VARIABLE_20150 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_20150 B)) (not (tptp.relstr_set_smaller A F BOUND_VARIABLE_20150))))))) :rule all_simplify)
% 0.61/1.07  (anchor :step t2.t5.t2.t8 :args ((F $$unsorted) (:= F F) (BOUND_VARIABLE_20150 $$unsorted) (:= BOUND_VARIABLE_20150 BOUND_VARIABLE_20150)))
% 0.61/1.07  (step t2.t5.t2.t8.t1 (cl (= F F)) :rule refl)
% 0.61/1.07  (step t2.t5.t2.t8.t2 (cl (= BOUND_VARIABLE_20150 BOUND_VARIABLE_20150)) :rule refl)
% 0.61/1.07  (step t2.t5.t2.t8.t3 (cl (= (or (not (= E F)) (or (not (tptp.element BOUND_VARIABLE_20150 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_20150 B)) (not (tptp.relstr_set_smaller A F BOUND_VARIABLE_20150)))) (or (not (= E F)) (not (tptp.element BOUND_VARIABLE_20150 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_20150 B)) (not (tptp.relstr_set_smaller A F BOUND_VARIABLE_20150))))) :rule all_simplify)
% 0.61/1.07  (step t2.t5.t2.t8 (cl (= (forall ((F $$unsorted) (BOUND_VARIABLE_20150 $$unsorted)) (or (not (= E F)) (or (not (tptp.element BOUND_VARIABLE_20150 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_20150 B)) (not (tptp.relstr_set_smaller A F BOUND_VARIABLE_20150))))) (forall ((F $$unsorted) (BOUND_VARIABLE_20150 $$unsorted)) (or (not (= E F)) (not (tptp.element BOUND_VARIABLE_20150 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_20150 B)) (not (tptp.relstr_set_smaller A F BOUND_VARIABLE_20150)))))) :rule bind)
% 0.61/1.07  (step t2.t5.t2.t9 (cl (= (forall ((F $$unsorted) (BOUND_VARIABLE_20150 $$unsorted)) (or (not (= E F)) (not (tptp.element BOUND_VARIABLE_20150 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_20150 B)) (not (tptp.relstr_set_smaller A F BOUND_VARIABLE_20150)))) (forall ((BOUND_VARIABLE_20150 $$unsorted)) (or (not (= E E)) (not (tptp.element BOUND_VARIABLE_20150 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_20150 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_20150)))))) :rule all_simplify)
% 0.61/1.07  (anchor :step t2.t5.t2.t10 :args ((BOUND_VARIABLE_20150 $$unsorted) (:= BOUND_VARIABLE_20150 BOUND_VARIABLE_20150)))
% 0.61/1.07  (step t2.t5.t2.t10.t1 (cl (= BOUND_VARIABLE_20150 BOUND_VARIABLE_20150)) :rule refl)
% 0.61/1.07  (step t2.t5.t2.t10.t2 (cl (= (= E E) true)) :rule all_simplify)
% 0.61/1.07  (step t2.t5.t2.t10.t3 (cl (= (not (= E E)) (not true))) :rule cong :premises (t2.t5.t2.t10.t2))
% 0.61/1.07  (step t2.t5.t2.t10.t4 (cl (= (not true) false)) :rule all_simplify)
% 0.61/1.07  (step t2.t5.t2.t10.t5 (cl (= (not (= E E)) false)) :rule trans :premises (t2.t5.t2.t10.t3 t2.t5.t2.t10.t4))
% 0.61/1.07  (step t2.t5.t2.t10.t6 (cl (= (not (tptp.element BOUND_VARIABLE_20150 (tptp.the_carrier A))) (not (tptp.element BOUND_VARIABLE_20150 (tptp.the_carrier A))))) :rule refl)
% 0.61/1.07  (step t2.t5.t2.t10.t7 (cl (= (not (tptp.in BOUND_VARIABLE_20150 B)) (not (tptp.in BOUND_VARIABLE_20150 B)))) :rule refl)
% 0.61/1.07  (step t2.t5.t2.t10.t8 (cl (= (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_20150)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_20150)))) :rule refl)
% 0.61/1.07  (step t2.t5.t2.t10.t9 (cl (= (or (not (= E E)) (not (tptp.element BOUND_VARIABLE_20150 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_20150 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_20150))) (or false (not (tptp.element BOUND_VARIABLE_20150 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_20150 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_20150))))) :rule cong :premises (t2.t5.t2.t10.t5 t2.t5.t2.t10.t6 t2.t5.t2.t10.t7 t2.t5.t2.t10.t8))
% 0.61/1.07  (step t2.t5.t2.t10.t10 (cl (= (or false (not (tptp.element BOUND_VARIABLE_20150 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_20150 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_20150))) (or (not (tptp.element BOUND_VARIABLE_20150 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_20150 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_20150))))) :rule all_simplify)
% 0.61/1.07  (step t2.t5.t2.t10.t11 (cl (= (or (not (= E E)) (not (tptp.element BOUND_VARIABLE_20150 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_20150 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_20150))) (or (not (tptp.element BOUND_VARIABLE_20150 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_20150 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_20150))))) :rule trans :premises (t2.t5.t2.t10.t9 t2.t5.t2.t10.t10))
% 0.61/1.07  (step t2.t5.t2.t10 (cl (= (forall ((BOUND_VARIABLE_20150 $$unsorted)) (or (not (= E E)) (not (tptp.element BOUND_VARIABLE_20150 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_20150 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_20150)))) (forall ((BOUND_VARIABLE_20150 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_20150 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_20150 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_20150)))))) :rule bind)
% 0.61/1.07  (step t2.t5.t2.t11 (cl (= (forall ((F $$unsorted) (BOUND_VARIABLE_20150 $$unsorted)) (or (not (= E F)) (not (tptp.element BOUND_VARIABLE_20150 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_20150 B)) (not (tptp.relstr_set_smaller A F BOUND_VARIABLE_20150)))) (forall ((BOUND_VARIABLE_20150 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_20150 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_20150 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_20150)))))) :rule trans :premises (t2.t5.t2.t9 t2.t5.t2.t10))
% 0.61/1.07  (step t2.t5.t2.t12 (cl (= (forall ((F $$unsorted) (BOUND_VARIABLE_20150 $$unsorted)) (or (not (= E F)) (or (not (tptp.element BOUND_VARIABLE_20150 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_20150 B)) (not (tptp.relstr_set_smaller A F BOUND_VARIABLE_20150))))) (forall ((BOUND_VARIABLE_20150 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_20150 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_20150 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_20150)))))) :rule trans :premises (t2.t5.t2.t8 t2.t5.t2.t11))
% 0.61/1.07  (step t2.t5.t2.t13 (cl (= (forall ((F $$unsorted)) (or (not (= E F)) (forall ((G $$unsorted)) (or (not (tptp.element G (tptp.the_carrier A))) (not (tptp.in G B)) (not (tptp.relstr_set_smaller A F G)))))) (forall ((BOUND_VARIABLE_20150 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_20150 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_20150 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_20150)))))) :rule trans :premises (t2.t5.t2.t7 t2.t5.t2.t12))
% 0.61/1.07  (step t2.t5.t2.t14 (cl (= (forall ((F $$unsorted)) (not (and (= E F) (not (forall ((G $$unsorted)) (or (not (tptp.element G (tptp.the_carrier A))) (not (tptp.in G B)) (not (tptp.relstr_set_smaller A F G)))))))) (forall ((BOUND_VARIABLE_20150 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_20150 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_20150 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_20150)))))) :rule trans :premises (t2.t5.t2.t6 t2.t5.t2.t13))
% 0.61/1.07  (step t2.t5.t2.t15 (cl (= (not (forall ((F $$unsorted)) (not (and (= E F) (not (forall ((G $$unsorted)) (or (not (tptp.element G (tptp.the_carrier A))) (not (tptp.in G B)) (not (tptp.relstr_set_smaller A F G))))))))) (not (forall ((BOUND_VARIABLE_20150 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_20150 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_20150 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_20150))))))) :rule cong :premises (t2.t5.t2.t14))
% 0.61/1.07  (step t2.t5.t2.t16 (cl (= (exists ((F $$unsorted)) (and (= E F) (not (forall ((G $$unsorted)) (or (not (tptp.element G (tptp.the_carrier A))) (not (tptp.in G B)) (not (tptp.relstr_set_smaller A F G))))))) (not (forall ((BOUND_VARIABLE_20150 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_20150 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_20150 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_20150))))))) :rule trans :premises (t2.t5.t2.t5 t2.t5.t2.t15))
% 0.61/1.07  (step t2.t5.t2.t17 (cl (= (exists ((F $$unsorted)) (and (= F E) (exists ((G $$unsorted)) (and (tptp.element G (tptp.the_carrier A)) (tptp.in G B) (tptp.relstr_set_smaller A F G))))) (not (forall ((BOUND_VARIABLE_20150 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_20150 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_20150 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_20150))))))) :rule trans :premises (t2.t5.t2.t4 t2.t5.t2.t16))
% 0.61/1.07  (step t2.t5.t2.t18 (cl (= (and (tptp.in E (tptp.powerset C)) (exists ((F $$unsorted)) (and (= F E) (exists ((G $$unsorted)) (and (tptp.element G (tptp.the_carrier A)) (tptp.in G B) (tptp.relstr_set_smaller A F G)))))) (and (tptp.in E (tptp.powerset C)) (not (forall ((BOUND_VARIABLE_20150 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_20150 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_20150 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_20150)))))))) :rule cong :premises (t2.t5.t2.t3 t2.t5.t2.t17))
% 0.61/1.07  (step t2.t5.t2.t19 (cl (= (= (tptp.in E D) (and (tptp.in E (tptp.powerset C)) (exists ((F $$unsorted)) (and (= F E) (exists ((G $$unsorted)) (and (tptp.element G (tptp.the_carrier A)) (tptp.in G B) (tptp.relstr_set_smaller A F G))))))) (= (tptp.in E D) (and (tptp.in E (tptp.powerset C)) (not (forall ((BOUND_VARIABLE_20150 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_20150 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_20150 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_20150))))))))) :rule cong :premises (t2.t5.t2.t2 t2.t5.t2.t18))
% 0.61/1.07  (step t2.t5.t2 (cl (= (forall ((E $$unsorted)) (= (tptp.in E D) (and (tptp.in E (tptp.powerset C)) (exists ((F $$unsorted)) (and (= F E) (exists ((G $$unsorted)) (and (tptp.element G (tptp.the_carrier A)) (tptp.in G B) (tptp.relstr_set_smaller A F G)))))))) (forall ((E $$unsorted)) (= (tptp.in E D) (and (tptp.in E (tptp.powerset C)) (not (forall ((BOUND_VARIABLE_20150 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_20150 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_20150 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_20150)))))))))) :rule bind)
% 0.61/1.07  (step t2.t5 (cl (= (exists ((D $$unsorted)) (forall ((E $$unsorted)) (= (tptp.in E D) (and (tptp.in E (tptp.powerset C)) (exists ((F $$unsorted)) (and (= F E) (exists ((G $$unsorted)) (and (tptp.element G (tptp.the_carrier A)) (tptp.in G B) (tptp.relstr_set_smaller A F G))))))))) (exists ((D $$unsorted)) (forall ((E $$unsorted)) (= (tptp.in E D) (and (tptp.in E (tptp.powerset C)) (not (forall ((BOUND_VARIABLE_20150 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_20150 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_20150 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_20150))))))))))) :rule bind)
% 0.61/1.07  (step t2.t6 (cl (= (exists ((D $$unsorted)) (forall ((E $$unsorted)) (= (tptp.in E D) (and (tptp.in E (tptp.powerset C)) (not (forall ((BOUND_VARIABLE_20150 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_20150 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_20150 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_20150))))))))) (not (forall ((D $$unsorted)) (not (forall ((E $$unsorted)) (= (tptp.in E D) (and (tptp.in E (tptp.powerset C)) (not (forall ((BOUND_VARIABLE_20150 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_20150 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_20150 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_20150))))))))))))) :rule all_simplify)
% 0.61/1.07  (step t2.t7 (cl (= (exists ((D $$unsorted)) (forall ((E $$unsorted)) (= (tptp.in E D) (and (tptp.in E (tptp.powerset C)) (exists ((F $$unsorted)) (and (= F E) (exists ((G $$unsorted)) (and (tptp.element G (tptp.the_carrier A)) (tptp.in G B) (tptp.relstr_set_smaller A F G))))))))) (not (forall ((D $$unsorted)) (not (forall ((E $$unsorted)) (= (tptp.in E D) (and (tptp.in E (tptp.powerset C)) (not (forall ((BOUND_VARIABLE_20150 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_20150 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_20150 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_20150))))))))))))) :rule trans :premises (t2.t5 t2.t6))
% 0.61/1.07  (step t2.t8 (cl (= (=> (and (not (tptp.empty_carrier A)) (tptp.transitive_relstr A) (tptp.rel_str A) (tptp.element B (tptp.powerset (tptp.the_carrier A))) (tptp.finite C) (tptp.element C (tptp.powerset B))) (exists ((D $$unsorted)) (forall ((E $$unsorted)) (= (tptp.in E D) (and (tptp.in E (tptp.powerset C)) (exists ((F $$unsorted)) (and (= F E) (exists ((G $$unsorted)) (and (tptp.element G (tptp.the_carrier A)) (tptp.in G B) (tptp.relstr_set_smaller A F G)))))))))) (=> (and (not (tptp.empty_carrier A)) (tptp.transitive_relstr A) (tptp.rel_str A) (tptp.element B (tptp.powerset (tptp.the_carrier A))) (tptp.finite C) (tptp.element C (tptp.powerset B))) (not (forall ((D $$unsorted)) (not (forall ((E $$unsorted)) (= (tptp.in E D) (and (tptp.in E (tptp.powerset C)) (not (forall ((BOUND_VARIABLE_20150 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_20150 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_20150 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_20150)))))))))))))) :rule cong :premises (t2.t4 t2.t7))
% 0.61/1.07  (step t2 (cl (= (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.transitive_relstr A) (tptp.rel_str A) (tptp.element B (tptp.powerset (tptp.the_carrier A))) (tptp.finite C) (tptp.element C (tptp.powerset B))) (exists ((D $$unsorted)) (forall ((E $$unsorted)) (= (tptp.in E D) (and (tptp.in E (tptp.powerset C)) (exists ((F $$unsorted)) (and (= F E) (exists ((G $$unsorted)) (and (tptp.element G (tptp.the_carrier A)) (tptp.in G B) (tptp.relstr_set_smaller A F G))))))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.transitive_relstr A) (tptp.rel_str A) (tptp.element B (tptp.powerset (tptp.the_carrier A))) (tptp.finite C) (tptp.element C (tptp.powerset B))) (not (forall ((D $$unsorted)) (not (forall ((E $$unsorted)) (= (tptp.in E D) (and (tptp.in E (tptp.powerset C)) (not (forall ((BOUND_VARIABLE_20150 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_20150 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_20150 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_20150))))))))))))))) :rule bind)
% 0.61/1.07  (step t3 (cl (= (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.transitive_relstr A) (tptp.rel_str A) (tptp.element B (tptp.powerset (tptp.the_carrier A))) (tptp.finite C) (tptp.element C (tptp.powerset B))) (not (forall ((D $$unsorted)) (not (forall ((E $$unsorted)) (= (tptp.in E D) (and (tptp.in E (tptp.powerset C)) (not (forall ((BOUND_VARIABLE_20150 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_20150 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_20150 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_20150))))))))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (tptp.empty_carrier A) (not (tptp.transitive_relstr A)) (not (tptp.rel_str A)) (not (tptp.element B (tptp.powerset (tptp.the_carrier A)))) (not (tptp.finite C)) (not (tptp.element C (tptp.powerset B))) (not (forall ((D $$unsorted)) (not (forall ((E $$unsorted)) (= (tptp.in E D) (and (tptp.in E (tptp.powerset C)) (not (forall ((BOUND_VARIABLE_20150 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_20150 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_20150 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_20150))))))))))))))) :rule all_simplify)
% 0.61/1.07  (step t4 (cl (= (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.transitive_relstr A) (tptp.rel_str A) (tptp.element B (tptp.powerset (tptp.the_carrier A))) (tptp.finite C) (tptp.element C (tptp.powerset B))) (exists ((D $$unsorted)) (forall ((E $$unsorted)) (= (tptp.in E D) (and (tptp.in E (tptp.powerset C)) (exists ((F $$unsorted)) (and (= F E) (exists ((G $$unsorted)) (and (tptp.element G (tptp.the_carrier A)) (tptp.in G B) (tptp.relstr_set_smaller A F G))))))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (tptp.empty_carrier A) (not (tptp.transitive_relstr A)) (not (tptp.rel_str A)) (not (tptp.element B (tptp.powerset (tptp.the_carrier A)))) (not (tptp.finite C)) (not (tptp.element C (tptp.powerset B))) (not (forall ((D $$unsorted)) (not (forall ((E $$unsorted)) (= (tptp.in E D) (and (tptp.in E (tptp.powerset C)) (not (forall ((BOUND_VARIABLE_20150 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_20150 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_20150 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_20150))))))))))))))) :rule trans :premises (t2 t3))
% 0.61/1.07  (step t5 (cl (= (not (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.transitive_relstr A) (tptp.rel_str A) (tptp.element B (tptp.powerset (tptp.the_carrier A))) (tptp.finite C) (tptp.element C (tptp.powerset B))) (exists ((D $$unsorted)) (forall ((E $$unsorted)) (= (tptp.in E D) (and (tptp.in E (tptp.powerset C)) (exists ((F $$unsorted)) (and (= F E) (exists ((G $$unsorted)) (and (tptp.element G (tptp.the_carrier A)) (tptp.in G B) (tptp.relstr_set_smaller A F G)))))))))))) (not (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (tptp.empty_carrier A) (not (tptp.transitive_relstr A)) (not (tptp.rel_str A)) (not (tptp.element B (tptp.powerset (tptp.the_carrier A)))) (not (tptp.finite C)) (not (tptp.element C (tptp.powerset B))) (not (forall ((D $$unsorted)) (not (forall ((E $$unsorted)) (= (tptp.in E D) (and (tptp.in E (tptp.powerset C)) (not (forall ((BOUND_VARIABLE_20150 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_20150 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_20150 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_20150)))))))))))))))) :rule cong :premises (t4))
% 0.61/1.07  (step t6 (cl (not (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (tptp.empty_carrier A) (not (tptp.transitive_relstr A)) (not (tptp.rel_str A)) (not (tptp.element B (tptp.powerset (tptp.the_carrier A)))) (not (tptp.finite C)) (not (tptp.element C (tptp.powerset B))) (not (forall ((D $$unsorted)) (not (forall ((E $$unsorted)) (= (tptp.in E D) (and (tptp.in E (tptp.powerset C)) (not (forall ((BOUND_VARIABLE_20150 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_20150 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_20150 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_20150))))))))))))))) :rule resolution :premises (t1 t5 a462))
% 0.61/1.07  (step t7 (cl (= (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (tptp.empty_carrier A) (not (tptp.transitive_relstr A)) (not (tptp.rel_str A)) (not (tptp.element B (tptp.powerset (tptp.the_carrier A)))) (not (tptp.finite C)) (not (tptp.element C (tptp.powerset B))) (not (forall ((D $$unsorted)) (not (forall ((E $$unsorted)) (= (tptp.in E D) (and (not (forall ((BOUND_VARIABLE_18324 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_18324 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18324 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_18324))))) (tptp.in E (tptp.powerset C)))))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (tptp.empty_carrier A) (not (tptp.transitive_relstr A)) (not (tptp.rel_str A)) (not (tptp.element B (tptp.powerset (tptp.the_carrier A)))) (not (tptp.finite C)) (not (tptp.element C (tptp.powerset B))) (not (forall ((D $$unsorted)) (not (forall ((E $$unsorted)) (= (tptp.in E D) (and (not (forall ((BOUND_VARIABLE_20150 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_20150 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_20150 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_20150))))) (tptp.in E (tptp.powerset C)))))))))))) :rule hole :args ((forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (tptp.empty_carrier A) (not (tptp.transitive_relstr A)) (not (tptp.rel_str A)) (not (tptp.element B (tptp.powerset (tptp.the_carrier A)))) (not (tptp.finite C)) (not (tptp.element C (tptp.powerset B))) (not (forall ((D $$unsorted)) (not (forall ((E $$unsorted)) (= (tptp.in E D) (and (not (forall ((BOUND_VARIABLE_18324 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_18324 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18324 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_18324))))) (tptp.in E (tptp.powerset C)))))))))) (= A A) (= B B) (= C C) (= D D) (= E E) (= BOUND_VARIABLE_18324 BOUND_VARIABLE_20150)))
% 0.61/1.07  (step t8 (cl (= (= (= (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (tptp.empty_carrier A) (not (tptp.transitive_relstr A)) (not (tptp.rel_str A)) (not (tptp.element B (tptp.powerset (tptp.the_carrier A)))) (not (tptp.finite C)) (not (tptp.element C (tptp.powerset B))) (not (forall ((D $$unsorted)) (not (forall ((E $$unsorted)) (= (tptp.in E D) (and (not (forall ((BOUND_VARIABLE_20150 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_20150 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_20150 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_20150))))) (tptp.in E (tptp.powerset C)))))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (tptp.empty_carrier A) (not (tptp.transitive_relstr A)) (not (tptp.rel_str A)) (not (tptp.element B (tptp.powerset (tptp.the_carrier A)))) (not (tptp.finite C)) (not (tptp.element C (tptp.powerset B))) (not (forall ((D $$unsorted)) (not (forall ((E $$unsorted)) (= (tptp.in E D) (and (tptp.in E (tptp.powerset C)) (not (forall ((BOUND_VARIABLE_20150 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_20150 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_20150 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_20150)))))))))))))) true) (= (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (tptp.empty_carrier A) (not (tptp.transitive_relstr A)) (not (tptp.rel_str A)) (not (tptp.element B (tptp.powerset (tptp.the_carrier A)))) (not (tptp.finite C)) (not (tptp.element C (tptp.powerset B))) (not (forall ((D $$unsorted)) (not (forall ((E $$unsorted)) (= (tptp.in E D) (and (not (forall ((BOUND_VARIABLE_20150 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_20150 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_20150 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_20150))))) (tptp.in E (tptp.powerset C)))))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (tptp.empty_carrier A) (not (tptp.transitive_relstr A)) (not (tptp.rel_str A)) (not (tptp.element B (tptp.powerset (tptp.the_carrier A)))) (not (tptp.finite C)) (not (tptp.element C (tptp.powerset B))) (not (forall ((D $$unsorted)) (not (forall ((E $$unsorted)) (= (tptp.in E D) (and (tptp.in E (tptp.powerset C)) (not (forall ((BOUND_VARIABLE_20150 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_20150 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_20150 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_20150)))))))))))))))) :rule equiv_simplify)
% 0.61/1.07  (step t9 (cl (not (= (= (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (tptp.empty_carrier A) (not (tptp.transitive_relstr A)) (not (tptp.rel_str A)) (not (tptp.element B (tptp.powerset (tptp.the_carrier A)))) (not (tptp.finite C)) (not (tptp.element C (tptp.powerset B))) (not (forall ((D $$unsorted)) (not (forall ((E $$unsorted)) (= (tptp.in E D) (and (not (forall ((BOUND_VARIABLE_20150 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_20150 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_20150 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_20150))))) (tptp.in E (tptp.powerset C)))))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (tptp.empty_carrier A) (not (tptp.transitive_relstr A)) (not (tptp.rel_str A)) (not (tptp.element B (tptp.powerset (tptp.the_carrier A)))) (not (tptp.finite C)) (not (tptp.element C (tptp.powerset B))) (not (forall ((D $$unsorted)) (not (forall ((E $$unsorted)) (= (tptp.in E D) (and (tptp.in E (tptp.powerset C)) (not (forall ((BOUND_VARIABLE_20150 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_20150 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_20150 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_20150)))))))))))))) true)) (= (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (tptp.empty_carrier A) (not (tptp.transitive_relstr A)) (not (tptp.rel_str A)) (not (tptp.element B (tptp.powerset (tptp.the_carrier A)))) (not (tptp.finite C)) (not (tptp.element C (tptp.powerset B))) (not (forall ((D $$unsorted)) (not (forall ((E $$unsorted)) (= (tptp.in E D) (and (not (forall ((BOUND_VARIABLE_20150 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_20150 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_20150 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_20150))))) (tptp.in E (tptp.powerset C)))))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (tptp.empty_carrier A) (not (tptp.transitive_relstr A)) (not (tptp.rel_str A)) (not (tptp.element B (tptp.powerset (tptp.the_carrier A)))) (not (tptp.finite C)) (not (tptp.element C (tptp.powerset B))) (not (forall ((D $$unsorted)) (not (forall ((E $$unsorted)) (= (tptp.in E D) (and (tptp.in E (tptp.powerset C)) (not (forall ((BOUND_VARIABLE_20150 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_20150 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_20150 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_20150))))))))))))))) :rule equiv1 :premises (t8))
% 0.61/1.07  (step t10 (cl (= (= (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (tptp.empty_carrier A) (not (tptp.transitive_relstr A)) (not (tptp.rel_str A)) (not (tptp.element B (tptp.powerset (tptp.the_carrier A)))) (not (tptp.finite C)) (not (tptp.element C (tptp.powerset B))) (not (forall ((D $$unsorted)) (not (forall ((E $$unsorted)) (= (tptp.in E D) (and (not (forall ((BOUND_VARIABLE_20150 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_20150 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_20150 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_20150))))) (tptp.in E (tptp.powerset C)))))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (tptp.empty_carrier A) (not (tptp.transitive_relstr A)) (not (tptp.rel_str A)) (not (tptp.element B (tptp.powerset (tptp.the_carrier A)))) (not (tptp.finite C)) (not (tptp.element C (tptp.powerset B))) (not (forall ((D $$unsorted)) (not (forall ((E $$unsorted)) (= (tptp.in E D) (and (tptp.in E (tptp.powerset C)) (not (forall ((BOUND_VARIABLE_20150 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_20150 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_20150 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_20150)))))))))))))) true)) :rule hole :args ((= (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (tptp.empty_carrier A) (not (tptp.transitive_relstr A)) (not (tptp.rel_str A)) (not (tptp.element B (tptp.powerset (tptp.the_carrier A)))) (not (tptp.finite C)) (not (tptp.element C (tptp.powerset B))) (not (forall ((D $$unsorted)) (not (forall ((E $$unsorted)) (= (tptp.in E D) (and (not (forall ((BOUND_VARIABLE_20150 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_20150 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_20150 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_20150))))) (tptp.in E (tptp.powerset C)))))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (tptp.empty_carrier A) (not (tptp.transitive_relstr A)) (not (tptp.rel_str A)) (not (tptp.element B (tptp.powerset (tptp.the_carrier A)))) (not (tptp.finite C)) (not (tptp.element C (tptp.powerset B))) (not (forall ((D $$unsorted)) (not (forall ((E $$unsorted)) (= (tptp.in E D) (and (tptp.in E (tptp.powerset C)) (not (forall ((BOUND_VARIABLE_20150 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_20150 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_20150 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_20150)))))))))))))) 1))
% 0.61/1.07  (step t11 (cl (= (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (tptp.empty_carrier A) (not (tptp.transitive_relstr A)) (not (tptp.rel_str A)) (not (tptp.element B (tptp.powerset (tptp.the_carrier A)))) (not (tptp.finite C)) (not (tptp.element C (tptp.powerset B))) (not (forall ((D $$unsorted)) (not (forall ((E $$unsorted)) (= (tptp.in E D) (and (not (forall ((BOUND_VARIABLE_20150 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_20150 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_20150 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_20150))))) (tptp.in E (tptp.powerset C)))))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (tptp.empty_carrier A) (not (tptp.transitive_relstr A)) (not (tptp.rel_str A)) (not (tptp.element B (tptp.powerset (tptp.the_carrier A)))) (not (tptp.finite C)) (not (tptp.element C (tptp.powerset B))) (not (forall ((D $$unsorted)) (not (forall ((E $$unsorted)) (= (tptp.in E D) (and (tptp.in E (tptp.powerset C)) (not (forall ((BOUND_VARIABLE_20150 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_20150 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_20150 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_20150))))))))))))))) :rule resolution :premises (t9 t10))
% 0.61/1.07  (step t12 (cl (= (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (tptp.empty_carrier A) (not (tptp.transitive_relstr A)) (not (tptp.rel_str A)) (not (tptp.element B (tptp.powerset (tptp.the_carrier A)))) (not (tptp.finite C)) (not (tptp.element C (tptp.powerset B))) (not (forall ((D $$unsorted)) (not (forall ((E $$unsorted)) (= (tptp.in E D) (and (not (forall ((BOUND_VARIABLE_18324 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_18324 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18324 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_18324))))) (tptp.in E (tptp.powerset C)))))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (tptp.empty_carrier A) (not (tptp.transitive_relstr A)) (not (tptp.rel_str A)) (not (tptp.element B (tptp.powerset (tptp.the_carrier A)))) (not (tptp.finite C)) (not (tptp.element C (tptp.powerset B))) (not (forall ((D $$unsorted)) (not (forall ((E $$unsorted)) (= (tptp.in E D) (and (tptp.in E (tptp.powerset C)) (not (forall ((BOUND_VARIABLE_20150 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_20150 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_20150 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_20150))))))))))))))) :rule trans :premises (t7 t11))
% 0.61/1.07  (step t13 (cl (not (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (tptp.empty_carrier A) (not (tptp.transitive_relstr A)) (not (tptp.rel_str A)) (not (tptp.element B (tptp.powerset (tptp.the_carrier A)))) (not (tptp.finite C)) (not (tptp.element C (tptp.powerset B))) (not (forall ((D $$unsorted)) (not (forall ((E $$unsorted)) (= (tptp.in E D) (and (not (forall ((BOUND_VARIABLE_18324 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_18324 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18324 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_18324))))) (tptp.in E (tptp.powerset C))))))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (tptp.empty_carrier A) (not (tptp.transitive_relstr A)) (not (tptp.rel_str A)) (not (tptp.element B (tptp.powerset (tptp.the_carrier A)))) (not (tptp.finite C)) (not (tptp.element C (tptp.powerset B))) (not (forall ((D $$unsorted)) (not (forall ((E $$unsorted)) (= (tptp.in E D) (and (tptp.in E (tptp.powerset C)) (not (forall ((BOUND_VARIABLE_20150 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_20150 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_20150 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_20150)))))))))))))) :rule equiv1 :premises (t12))
% 0.61/1.07  (step t14 (cl (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (tptp.empty_carrier A) (not (tptp.transitive_relstr A)) (not (tptp.rel_str A)) (not (tptp.element B (tptp.powerset (tptp.the_carrier A)))) (not (tptp.finite C)) (not (tptp.element C (tptp.powerset B))) (not (forall ((D $$unsorted)) (not (forall ((E $$unsorted)) (= (tptp.in E D) (and (tptp.in E (tptp.powerset C)) (not (forall ((BOUND_VARIABLE_20150 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_20150 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_20150 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_20150))))))))))))) (not (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (tptp.empty_carrier A) (not (tptp.transitive_relstr A)) (not (tptp.rel_str A)) (not (tptp.element B (tptp.powerset (tptp.the_carrier A)))) (not (tptp.finite C)) (not (tptp.element C (tptp.powerset B))) (not (forall ((D $$unsorted)) (not (forall ((E $$unsorted)) (= (tptp.in E D) (and (not (forall ((BOUND_VARIABLE_18324 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_18324 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18324 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_18324))))) (tptp.in E (tptp.powerset C)))))))))))) :rule reordering :premises (t13))
% 0.61/1.07  (step t15 (cl (not (= (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.transitive_relstr A) (tptp.rel_str A) (tptp.element B (tptp.powerset (tptp.the_carrier A))) (tptp.finite C) (tptp.element C (tptp.powerset B))) (=> (forall ((D $$unsorted) (E $$unsorted) (F $$unsorted)) (=> (and (= D E) (exists ((G $$unsorted)) (and (= G E) (exists ((H $$unsorted)) (and (tptp.element H (tptp.the_carrier A)) (tptp.in H B) (tptp.relstr_set_smaller A G H))))) (= D F) (exists ((I $$unsorted)) (and (= I F) (exists ((J $$unsorted)) (and (tptp.element J (tptp.the_carrier A)) (tptp.in J B) (tptp.relstr_set_smaller A I J)))))) (= E F))) (exists ((D $$unsorted)) (forall ((E $$unsorted)) (= (tptp.in E D) (exists ((F $$unsorted)) (and (tptp.in F (tptp.powerset C)) (= F E) (exists ((K $$unsorted)) (and (= K E) (exists ((L $$unsorted)) (and (tptp.element L (tptp.the_carrier A)) (tptp.in L B) (tptp.relstr_set_smaller A K L))))))))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (tptp.empty_carrier A) (not (tptp.transitive_relstr A)) (not (tptp.rel_str A)) (not (tptp.element B (tptp.powerset (tptp.the_carrier A)))) (not (tptp.finite C)) (not (tptp.element C (tptp.powerset B))) (not (forall ((D $$unsorted)) (not (forall ((E $$unsorted)) (= (tptp.in E D) (and (not (forall ((BOUND_VARIABLE_18324 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_18324 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18324 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_18324))))) (tptp.in E (tptp.powerset C)))))))))))) (not (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.transitive_relstr A) (tptp.rel_str A) (tptp.element B (tptp.powerset (tptp.the_carrier A))) (tptp.finite C) (tptp.element C (tptp.powerset B))) (=> (forall ((D $$unsorted) (E $$unsorted) (F $$unsorted)) (=> (and (= D E) (exists ((G $$unsorted)) (and (= G E) (exists ((H $$unsorted)) (and (tptp.element H (tptp.the_carrier A)) (tptp.in H B) (tptp.relstr_set_smaller A G H))))) (= D F) (exists ((I $$unsorted)) (and (= I F) (exists ((J $$unsorted)) (and (tptp.element J (tptp.the_carrier A)) (tptp.in J B) (tptp.relstr_set_smaller A I J)))))) (= E F))) (exists ((D $$unsorted)) (forall ((E $$unsorted)) (= (tptp.in E D) (exists ((F $$unsorted)) (and (tptp.in F (tptp.powerset C)) (= F E) (exists ((K $$unsorted)) (and (= K E) (exists ((L $$unsorted)) (and (tptp.element L (tptp.the_carrier A)) (tptp.in L B) (tptp.relstr_set_smaller A K L)))))))))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (tptp.empty_carrier A) (not (tptp.transitive_relstr A)) (not (tptp.rel_str A)) (not (tptp.element B (tptp.powerset (tptp.the_carrier A)))) (not (tptp.finite C)) (not (tptp.element C (tptp.powerset B))) (not (forall ((D $$unsorted)) (not (forall ((E $$unsorted)) (= (tptp.in E D) (and (not (forall ((BOUND_VARIABLE_18324 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_18324 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18324 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_18324))))) (tptp.in E (tptp.powerset C))))))))))) :rule equiv_pos2)
% 0.61/1.07  (anchor :step t16 :args ((A $$unsorted) (:= A A) (B $$unsorted) (:= B B) (C $$unsorted) (:= C C)))
% 0.61/1.07  (step t16.t1 (cl (= A A)) :rule refl)
% 0.61/1.07  (step t16.t2 (cl (= B B)) :rule refl)
% 0.61/1.07  (step t16.t3 (cl (= C C)) :rule refl)
% 0.61/1.07  (step t16.t4 (cl (= (and (not (tptp.empty_carrier A)) (tptp.transitive_relstr A) (tptp.rel_str A) (tptp.element B (tptp.powerset (tptp.the_carrier A))) (tptp.finite C) (tptp.element C (tptp.powerset B))) (and (not (tptp.empty_carrier A)) (tptp.transitive_relstr A) (tptp.rel_str A) (tptp.element B (tptp.powerset (tptp.the_carrier A))) (tptp.finite C) (tptp.element C (tptp.powerset B))))) :rule refl)
% 0.61/1.07  (anchor :step t16.t5 :args ((D $$unsorted) (:= D D) (E $$unsorted) (:= E E) (F $$unsorted) (:= F F)))
% 0.61/1.07  (step t16.t5.t1 (cl (= D D)) :rule refl)
% 0.61/1.07  (step t16.t5.t2 (cl (= E E)) :rule refl)
% 0.61/1.07  (step t16.t5.t3 (cl (= F F)) :rule refl)
% 0.61/1.07  (step t16.t5.t4 (cl (= (= D E) (= D E))) :rule refl)
% 0.61/1.07  (anchor :step t16.t5.t5 :args ((G $$unsorted) (:= G G)))
% 0.61/1.07  (step t16.t5.t5.t1 (cl (= G G)) :rule refl)
% 0.61/1.07  (step t16.t5.t5.t2 (cl (= (= G E) (= E G))) :rule all_simplify)
% 0.61/1.07  (step t16.t5.t5.t3 (cl (= (exists ((H $$unsorted)) (and (tptp.element H (tptp.the_carrier A)) (tptp.in H B) (tptp.relstr_set_smaller A G H))) (not (forall ((H $$unsorted)) (not (and (tptp.element H (tptp.the_carrier A)) (tptp.in H B) (tptp.relstr_set_smaller A G H))))))) :rule all_simplify)
% 0.61/1.07  (step t16.t5.t5.t4 (cl (= (forall ((H $$unsorted)) (not (and (tptp.element H (tptp.the_carrier A)) (tptp.in H B) (tptp.relstr_set_smaller A G H)))) (forall ((H $$unsorted)) (or (not (tptp.element H (tptp.the_carrier A))) (not (tptp.in H B)) (not (tptp.relstr_set_smaller A G H)))))) :rule all_simplify)
% 0.61/1.07  (step t16.t5.t5.t5 (cl (= (not (forall ((H $$unsorted)) (not (and (tptp.element H (tptp.the_carrier A)) (tptp.in H B) (tptp.relstr_set_smaller A G H))))) (not (forall ((H $$unsorted)) (or (not (tptp.element H (tptp.the_carrier A))) (not (tptp.in H B)) (not (tptp.relstr_set_smaller A G H))))))) :rule cong :premises (t16.t5.t5.t4))
% 0.61/1.07  (step t16.t5.t5.t6 (cl (= (exists ((H $$unsorted)) (and (tptp.element H (tptp.the_carrier A)) (tptp.in H B) (tptp.relstr_set_smaller A G H))) (not (forall ((H $$unsorted)) (or (not (tptp.element H (tptp.the_carrier A))) (not (tptp.in H B)) (not (tptp.relstr_set_smaller A G H))))))) :rule trans :premises (t16.t5.t5.t3 t16.t5.t5.t5))
% 0.61/1.07  (step t16.t5.t5.t7 (cl (= (and (= G E) (exists ((H $$unsorted)) (and (tptp.element H (tptp.the_carrier A)) (tptp.in H B) (tptp.relstr_set_smaller A G H)))) (and (= E G) (not (forall ((H $$unsorted)) (or (not (tptp.element H (tptp.the_carrier A))) (not (tptp.in H B)) (not (tptp.relstr_set_smaller A G H)))))))) :rule cong :premises (t16.t5.t5.t2 t16.t5.t5.t6))
% 0.61/1.07  (step t16.t5.t5 (cl (= (exists ((G $$unsorted)) (and (= G E) (exists ((H $$unsorted)) (and (tptp.element H (tptp.the_carrier A)) (tptp.in H B) (tptp.relstr_set_smaller A G H))))) (exists ((G $$unsorted)) (and (= E G) (not (forall ((H $$unsorted)) (or (not (tptp.element H (tptp.the_carrier A))) (not (tptp.in H B)) (not (tptp.relstr_set_smaller A G H))))))))) :rule bind)
% 0.61/1.07  (step t16.t5.t6 (cl (= (exists ((G $$unsorted)) (and (= E G) (not (forall ((H $$unsorted)) (or (not (tptp.element H (tptp.the_carrier A))) (not (tptp.in H B)) (not (tptp.relstr_set_smaller A G H))))))) (not (forall ((G $$unsorted)) (not (and (= E G) (not (forall ((H $$unsorted)) (or (not (tptp.element H (tptp.the_carrier A))) (not (tptp.in H B)) (not (tptp.relstr_set_smaller A G H))))))))))) :rule all_simplify)
% 0.61/1.07  (step t16.t5.t7 (cl (= (forall ((G $$unsorted)) (not (and (= E G) (not (forall ((H $$unsorted)) (or (not (tptp.element H (tptp.the_carrier A))) (not (tptp.in H B)) (not (tptp.relstr_set_smaller A G H)))))))) (forall ((G $$unsorted)) (or (not (= E G)) (forall ((H $$unsorted)) (or (not (tptp.element H (tptp.the_carrier A))) (not (tptp.in H B)) (not (tptp.relstr_set_smaller A G H)))))))) :rule all_simplify)
% 0.61/1.07  (step t16.t5.t8 (cl (= (forall ((G $$unsorted)) (or (not (= E G)) (forall ((H $$unsorted)) (or (not (tptp.element H (tptp.the_carrier A))) (not (tptp.in H B)) (not (tptp.relstr_set_smaller A G H)))))) (forall ((G $$unsorted) (BOUND_VARIABLE_18196 $$unsorted)) (or (not (= E G)) (or (not (tptp.element BOUND_VARIABLE_18196 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18196 B)) (not (tptp.relstr_set_smaller A G BOUND_VARIABLE_18196))))))) :rule all_simplify)
% 0.61/1.07  (anchor :step t16.t5.t9 :args ((G $$unsorted) (:= G G) (BOUND_VARIABLE_18196 $$unsorted) (:= BOUND_VARIABLE_18196 BOUND_VARIABLE_18196)))
% 0.61/1.07  (step t16.t5.t9.t1 (cl (= G G)) :rule refl)
% 0.61/1.07  (step t16.t5.t9.t2 (cl (= BOUND_VARIABLE_18196 BOUND_VARIABLE_18196)) :rule refl)
% 0.61/1.07  (step t16.t5.t9.t3 (cl (= (or (not (= E G)) (or (not (tptp.element BOUND_VARIABLE_18196 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18196 B)) (not (tptp.relstr_set_smaller A G BOUND_VARIABLE_18196)))) (or (not (= E G)) (not (tptp.element BOUND_VARIABLE_18196 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18196 B)) (not (tptp.relstr_set_smaller A G BOUND_VARIABLE_18196))))) :rule all_simplify)
% 0.61/1.07  (step t16.t5.t9 (cl (= (forall ((G $$unsorted) (BOUND_VARIABLE_18196 $$unsorted)) (or (not (= E G)) (or (not (tptp.element BOUND_VARIABLE_18196 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18196 B)) (not (tptp.relstr_set_smaller A G BOUND_VARIABLE_18196))))) (forall ((G $$unsorted) (BOUND_VARIABLE_18196 $$unsorted)) (or (not (= E G)) (not (tptp.element BOUND_VARIABLE_18196 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18196 B)) (not (tptp.relstr_set_smaller A G BOUND_VARIABLE_18196)))))) :rule bind)
% 0.61/1.07  (step t16.t5.t10 (cl (= (forall ((G $$unsorted) (BOUND_VARIABLE_18196 $$unsorted)) (or (not (= E G)) (not (tptp.element BOUND_VARIABLE_18196 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18196 B)) (not (tptp.relstr_set_smaller A G BOUND_VARIABLE_18196)))) (forall ((BOUND_VARIABLE_18196 $$unsorted)) (or (not (= E E)) (not (tptp.element BOUND_VARIABLE_18196 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18196 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_18196)))))) :rule all_simplify)
% 0.61/1.07  (anchor :step t16.t5.t11 :args ((BOUND_VARIABLE_18196 $$unsorted) (:= BOUND_VARIABLE_18196 BOUND_VARIABLE_18196)))
% 0.61/1.07  (step t16.t5.t11.t1 (cl (= BOUND_VARIABLE_18196 BOUND_VARIABLE_18196)) :rule refl)
% 0.61/1.07  (step t16.t5.t11.t2 (cl (= (= E E) true)) :rule all_simplify)
% 0.61/1.07  (step t16.t5.t11.t3 (cl (= (not (= E E)) (not true))) :rule cong :premises (t16.t5.t11.t2))
% 0.61/1.07  (step t16.t5.t11.t4 (cl (= (not true) false)) :rule all_simplify)
% 0.61/1.07  (step t16.t5.t11.t5 (cl (= (not (= E E)) false)) :rule trans :premises (t16.t5.t11.t3 t16.t5.t11.t4))
% 0.61/1.07  (step t16.t5.t11.t6 (cl (= (not (tptp.element BOUND_VARIABLE_18196 (tptp.the_carrier A))) (not (tptp.element BOUND_VARIABLE_18196 (tptp.the_carrier A))))) :rule refl)
% 0.61/1.07  (step t16.t5.t11.t7 (cl (= (not (tptp.in BOUND_VARIABLE_18196 B)) (not (tptp.in BOUND_VARIABLE_18196 B)))) :rule refl)
% 0.61/1.07  (step t16.t5.t11.t8 (cl (= (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_18196)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_18196)))) :rule refl)
% 0.61/1.07  (step t16.t5.t11.t9 (cl (= (or (not (= E E)) (not (tptp.element BOUND_VARIABLE_18196 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18196 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_18196))) (or false (not (tptp.element BOUND_VARIABLE_18196 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18196 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_18196))))) :rule cong :premises (t16.t5.t11.t5 t16.t5.t11.t6 t16.t5.t11.t7 t16.t5.t11.t8))
% 0.61/1.07  (step t16.t5.t11.t10 (cl (= (or false (not (tptp.element BOUND_VARIABLE_18196 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18196 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_18196))) (or (not (tptp.element BOUND_VARIABLE_18196 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18196 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_18196))))) :rule all_simplify)
% 0.61/1.07  (step t16.t5.t11.t11 (cl (= (or (not (= E E)) (not (tptp.element BOUND_VARIABLE_18196 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18196 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_18196))) (or (not (tptp.element BOUND_VARIABLE_18196 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18196 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_18196))))) :rule trans :premises (t16.t5.t11.t9 t16.t5.t11.t10))
% 0.61/1.07  (step t16.t5.t11 (cl (= (forall ((BOUND_VARIABLE_18196 $$unsorted)) (or (not (= E E)) (not (tptp.element BOUND_VARIABLE_18196 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18196 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_18196)))) (forall ((BOUND_VARIABLE_18196 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_18196 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18196 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_18196)))))) :rule bind)
% 0.61/1.07  (step t16.t5.t12 (cl (= (forall ((G $$unsorted) (BOUND_VARIABLE_18196 $$unsorted)) (or (not (= E G)) (not (tptp.element BOUND_VARIABLE_18196 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18196 B)) (not (tptp.relstr_set_smaller A G BOUND_VARIABLE_18196)))) (forall ((BOUND_VARIABLE_18196 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_18196 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18196 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_18196)))))) :rule trans :premises (t16.t5.t10 t16.t5.t11))
% 0.61/1.07  (step t16.t5.t13 (cl (= (forall ((G $$unsorted) (BOUND_VARIABLE_18196 $$unsorted)) (or (not (= E G)) (or (not (tptp.element BOUND_VARIABLE_18196 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18196 B)) (not (tptp.relstr_set_smaller A G BOUND_VARIABLE_18196))))) (forall ((BOUND_VARIABLE_18196 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_18196 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18196 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_18196)))))) :rule trans :premises (t16.t5.t9 t16.t5.t12))
% 0.61/1.07  (step t16.t5.t14 (cl (= (forall ((G $$unsorted)) (or (not (= E G)) (forall ((H $$unsorted)) (or (not (tptp.element H (tptp.the_carrier A))) (not (tptp.in H B)) (not (tptp.relstr_set_smaller A G H)))))) (forall ((BOUND_VARIABLE_18196 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_18196 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18196 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_18196)))))) :rule trans :premises (t16.t5.t8 t16.t5.t13))
% 0.61/1.07  (step t16.t5.t15 (cl (= (forall ((G $$unsorted)) (not (and (= E G) (not (forall ((H $$unsorted)) (or (not (tptp.element H (tptp.the_carrier A))) (not (tptp.in H B)) (not (tptp.relstr_set_smaller A G H)))))))) (forall ((BOUND_VARIABLE_18196 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_18196 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18196 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_18196)))))) :rule trans :premises (t16.t5.t7 t16.t5.t14))
% 0.61/1.07  (step t16.t5.t16 (cl (= (not (forall ((G $$unsorted)) (not (and (= E G) (not (forall ((H $$unsorted)) (or (not (tptp.element H (tptp.the_carrier A))) (not (tptp.in H B)) (not (tptp.relstr_set_smaller A G H))))))))) (not (forall ((BOUND_VARIABLE_18196 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_18196 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18196 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_18196))))))) :rule cong :premises (t16.t5.t15))
% 0.61/1.07  (step t16.t5.t17 (cl (= (exists ((G $$unsorted)) (and (= E G) (not (forall ((H $$unsorted)) (or (not (tptp.element H (tptp.the_carrier A))) (not (tptp.in H B)) (not (tptp.relstr_set_smaller A G H))))))) (not (forall ((BOUND_VARIABLE_18196 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_18196 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18196 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_18196))))))) :rule trans :premises (t16.t5.t6 t16.t5.t16))
% 0.61/1.07  (step t16.t5.t18 (cl (= (exists ((G $$unsorted)) (and (= G E) (exists ((H $$unsorted)) (and (tptp.element H (tptp.the_carrier A)) (tptp.in H B) (tptp.relstr_set_smaller A G H))))) (not (forall ((BOUND_VARIABLE_18196 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_18196 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18196 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_18196))))))) :rule trans :premises (t16.t5.t5 t16.t5.t17))
% 0.61/1.07  (step t16.t5.t19 (cl (= (= D F) (= D F))) :rule refl)
% 0.61/1.07  (anchor :step t16.t5.t20 :args ((I $$unsorted) (:= I I)))
% 0.61/1.07  (step t16.t5.t20.t1 (cl (= I I)) :rule refl)
% 0.61/1.07  (step t16.t5.t20.t2 (cl (= (= I F) (= F I))) :rule all_simplify)
% 0.61/1.07  (step t16.t5.t20.t3 (cl (= (exists ((J $$unsorted)) (and (tptp.element J (tptp.the_carrier A)) (tptp.in J B) (tptp.relstr_set_smaller A I J))) (not (forall ((J $$unsorted)) (not (and (tptp.element J (tptp.the_carrier A)) (tptp.in J B) (tptp.relstr_set_smaller A I J))))))) :rule all_simplify)
% 0.61/1.07  (step t16.t5.t20.t4 (cl (= (forall ((J $$unsorted)) (not (and (tptp.element J (tptp.the_carrier A)) (tptp.in J B) (tptp.relstr_set_smaller A I J)))) (forall ((J $$unsorted)) (or (not (tptp.element J (tptp.the_carrier A))) (not (tptp.in J B)) (not (tptp.relstr_set_smaller A I J)))))) :rule all_simplify)
% 0.61/1.07  (step t16.t5.t20.t5 (cl (= (not (forall ((J $$unsorted)) (not (and (tptp.element J (tptp.the_carrier A)) (tptp.in J B) (tptp.relstr_set_smaller A I J))))) (not (forall ((J $$unsorted)) (or (not (tptp.element J (tptp.the_carrier A))) (not (tptp.in J B)) (not (tptp.relstr_set_smaller A I J))))))) :rule cong :premises (t16.t5.t20.t4))
% 0.61/1.07  (step t16.t5.t20.t6 (cl (= (exists ((J $$unsorted)) (and (tptp.element J (tptp.the_carrier A)) (tptp.in J B) (tptp.relstr_set_smaller A I J))) (not (forall ((J $$unsorted)) (or (not (tptp.element J (tptp.the_carrier A))) (not (tptp.in J B)) (not (tptp.relstr_set_smaller A I J))))))) :rule trans :premises (t16.t5.t20.t3 t16.t5.t20.t5))
% 0.61/1.07  (step t16.t5.t20.t7 (cl (= (and (= I F) (exists ((J $$unsorted)) (and (tptp.element J (tptp.the_carrier A)) (tptp.in J B) (tptp.relstr_set_smaller A I J)))) (and (= F I) (not (forall ((J $$unsorted)) (or (not (tptp.element J (tptp.the_carrier A))) (not (tptp.in J B)) (not (tptp.relstr_set_smaller A I J)))))))) :rule cong :premises (t16.t5.t20.t2 t16.t5.t20.t6))
% 0.61/1.07  (step t16.t5.t20 (cl (= (exists ((I $$unsorted)) (and (= I F) (exists ((J $$unsorted)) (and (tptp.element J (tptp.the_carrier A)) (tptp.in J B) (tptp.relstr_set_smaller A I J))))) (exists ((I $$unsorted)) (and (= F I) (not (forall ((J $$unsorted)) (or (not (tptp.element J (tptp.the_carrier A))) (not (tptp.in J B)) (not (tptp.relstr_set_smaller A I J))))))))) :rule bind)
% 0.61/1.07  (step t16.t5.t21 (cl (= (exists ((I $$unsorted)) (and (= F I) (not (forall ((J $$unsorted)) (or (not (tptp.element J (tptp.the_carrier A))) (not (tptp.in J B)) (not (tptp.relstr_set_smaller A I J))))))) (not (forall ((I $$unsorted)) (not (and (= F I) (not (forall ((J $$unsorted)) (or (not (tptp.element J (tptp.the_carrier A))) (not (tptp.in J B)) (not (tptp.relstr_set_smaller A I J))))))))))) :rule all_simplify)
% 0.61/1.07  (step t16.t5.t22 (cl (= (forall ((I $$unsorted)) (not (and (= F I) (not (forall ((J $$unsorted)) (or (not (tptp.element J (tptp.the_carrier A))) (not (tptp.in J B)) (not (tptp.relstr_set_smaller A I J)))))))) (forall ((I $$unsorted)) (or (not (= F I)) (forall ((J $$unsorted)) (or (not (tptp.element J (tptp.the_carrier A))) (not (tptp.in J B)) (not (tptp.relstr_set_smaller A I J)))))))) :rule all_simplify)
% 0.61/1.07  (step t16.t5.t23 (cl (= (forall ((I $$unsorted)) (or (not (= F I)) (forall ((J $$unsorted)) (or (not (tptp.element J (tptp.the_carrier A))) (not (tptp.in J B)) (not (tptp.relstr_set_smaller A I J)))))) (forall ((I $$unsorted) (BOUND_VARIABLE_18239 $$unsorted)) (or (not (= F I)) (or (not (tptp.element BOUND_VARIABLE_18239 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18239 B)) (not (tptp.relstr_set_smaller A I BOUND_VARIABLE_18239))))))) :rule all_simplify)
% 0.61/1.07  (anchor :step t16.t5.t24 :args ((I $$unsorted) (:= I I) (BOUND_VARIABLE_18239 $$unsorted) (:= BOUND_VARIABLE_18239 BOUND_VARIABLE_18239)))
% 0.61/1.07  (step t16.t5.t24.t1 (cl (= I I)) :rule refl)
% 0.61/1.07  (step t16.t5.t24.t2 (cl (= BOUND_VARIABLE_18239 BOUND_VARIABLE_18239)) :rule refl)
% 0.61/1.07  (step t16.t5.t24.t3 (cl (= (or (not (= F I)) (or (not (tptp.element BOUND_VARIABLE_18239 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18239 B)) (not (tptp.relstr_set_smaller A I BOUND_VARIABLE_18239)))) (or (not (= F I)) (not (tptp.element BOUND_VARIABLE_18239 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18239 B)) (not (tptp.relstr_set_smaller A I BOUND_VARIABLE_18239))))) :rule all_simplify)
% 0.61/1.07  (step t16.t5.t24 (cl (= (forall ((I $$unsorted) (BOUND_VARIABLE_18239 $$unsorted)) (or (not (= F I)) (or (not (tptp.element BOUND_VARIABLE_18239 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18239 B)) (not (tptp.relstr_set_smaller A I BOUND_VARIABLE_18239))))) (forall ((I $$unsorted) (BOUND_VARIABLE_18239 $$unsorted)) (or (not (= F I)) (not (tptp.element BOUND_VARIABLE_18239 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18239 B)) (not (tptp.relstr_set_smaller A I BOUND_VARIABLE_18239)))))) :rule bind)
% 0.61/1.07  (step t16.t5.t25 (cl (= (forall ((I $$unsorted) (BOUND_VARIABLE_18239 $$unsorted)) (or (not (= F I)) (not (tptp.element BOUND_VARIABLE_18239 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18239 B)) (not (tptp.relstr_set_smaller A I BOUND_VARIABLE_18239)))) (forall ((BOUND_VARIABLE_18239 $$unsorted)) (or (not (= F F)) (not (tptp.element BOUND_VARIABLE_18239 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18239 B)) (not (tptp.relstr_set_smaller A F BOUND_VARIABLE_18239)))))) :rule all_simplify)
% 0.61/1.07  (anchor :step t16.t5.t26 :args ((BOUND_VARIABLE_18239 $$unsorted) (:= BOUND_VARIABLE_18239 BOUND_VARIABLE_18239)))
% 0.61/1.07  (step t16.t5.t26.t1 (cl (= BOUND_VARIABLE_18239 BOUND_VARIABLE_18239)) :rule refl)
% 0.61/1.07  (step t16.t5.t26.t2 (cl (= (= F F) true)) :rule all_simplify)
% 0.61/1.07  (step t16.t5.t26.t3 (cl (= (not (= F F)) (not true))) :rule cong :premises (t16.t5.t26.t2))
% 0.61/1.07  (step t16.t5.t26.t4 (cl (= (not true) false)) :rule all_simplify)
% 0.61/1.07  (step t16.t5.t26.t5 (cl (= (not (= F F)) false)) :rule trans :premises (t16.t5.t26.t3 t16.t5.t26.t4))
% 0.61/1.07  (step t16.t5.t26.t6 (cl (= (not (tptp.element BOUND_VARIABLE_18239 (tptp.the_carrier A))) (not (tptp.element BOUND_VARIABLE_18239 (tptp.the_carrier A))))) :rule refl)
% 0.61/1.07  (step t16.t5.t26.t7 (cl (= (not (tptp.in BOUND_VARIABLE_18239 B)) (not (tptp.in BOUND_VARIABLE_18239 B)))) :rule refl)
% 0.61/1.07  (step t16.t5.t26.t8 (cl (= (not (tptp.relstr_set_smaller A F BOUND_VARIABLE_18239)) (not (tptp.relstr_set_smaller A F BOUND_VARIABLE_18239)))) :rule refl)
% 0.61/1.07  (step t16.t5.t26.t9 (cl (= (or (not (= F F)) (not (tptp.element BOUND_VARIABLE_18239 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18239 B)) (not (tptp.relstr_set_smaller A F BOUND_VARIABLE_18239))) (or false (not (tptp.element BOUND_VARIABLE_18239 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18239 B)) (not (tptp.relstr_set_smaller A F BOUND_VARIABLE_18239))))) :rule cong :premises (t16.t5.t26.t5 t16.t5.t26.t6 t16.t5.t26.t7 t16.t5.t26.t8))
% 0.61/1.07  (step t16.t5.t26.t10 (cl (= (or false (not (tptp.element BOUND_VARIABLE_18239 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18239 B)) (not (tptp.relstr_set_smaller A F BOUND_VARIABLE_18239))) (or (not (tptp.element BOUND_VARIABLE_18239 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18239 B)) (not (tptp.relstr_set_smaller A F BOUND_VARIABLE_18239))))) :rule all_simplify)
% 0.61/1.07  (step t16.t5.t26.t11 (cl (= (or (not (= F F)) (not (tptp.element BOUND_VARIABLE_18239 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18239 B)) (not (tptp.relstr_set_smaller A F BOUND_VARIABLE_18239))) (or (not (tptp.element BOUND_VARIABLE_18239 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18239 B)) (not (tptp.relstr_set_smaller A F BOUND_VARIABLE_18239))))) :rule trans :premises (t16.t5.t26.t9 t16.t5.t26.t10))
% 0.61/1.07  (step t16.t5.t26 (cl (= (forall ((BOUND_VARIABLE_18239 $$unsorted)) (or (not (= F F)) (not (tptp.element BOUND_VARIABLE_18239 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18239 B)) (not (tptp.relstr_set_smaller A F BOUND_VARIABLE_18239)))) (forall ((BOUND_VARIABLE_18239 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_18239 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18239 B)) (not (tptp.relstr_set_smaller A F BOUND_VARIABLE_18239)))))) :rule bind)
% 0.61/1.07  (step t16.t5.t27 (cl (= (forall ((I $$unsorted) (BOUND_VARIABLE_18239 $$unsorted)) (or (not (= F I)) (not (tptp.element BOUND_VARIABLE_18239 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18239 B)) (not (tptp.relstr_set_smaller A I BOUND_VARIABLE_18239)))) (forall ((BOUND_VARIABLE_18239 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_18239 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18239 B)) (not (tptp.relstr_set_smaller A F BOUND_VARIABLE_18239)))))) :rule trans :premises (t16.t5.t25 t16.t5.t26))
% 0.61/1.07  (step t16.t5.t28 (cl (= (forall ((I $$unsorted) (BOUND_VARIABLE_18239 $$unsorted)) (or (not (= F I)) (or (not (tptp.element BOUND_VARIABLE_18239 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18239 B)) (not (tptp.relstr_set_smaller A I BOUND_VARIABLE_18239))))) (forall ((BOUND_VARIABLE_18239 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_18239 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18239 B)) (not (tptp.relstr_set_smaller A F BOUND_VARIABLE_18239)))))) :rule trans :premises (t16.t5.t24 t16.t5.t27))
% 0.61/1.07  (step t16.t5.t29 (cl (= (forall ((I $$unsorted)) (or (not (= F I)) (forall ((J $$unsorted)) (or (not (tptp.element J (tptp.the_carrier A))) (not (tptp.in J B)) (not (tptp.relstr_set_smaller A I J)))))) (forall ((BOUND_VARIABLE_18239 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_18239 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18239 B)) (not (tptp.relstr_set_smaller A F BOUND_VARIABLE_18239)))))) :rule trans :premises (t16.t5.t23 t16.t5.t28))
% 0.61/1.07  (step t16.t5.t30 (cl (= (forall ((I $$unsorted)) (not (and (= F I) (not (forall ((J $$unsorted)) (or (not (tptp.element J (tptp.the_carrier A))) (not (tptp.in J B)) (not (tptp.relstr_set_smaller A I J)))))))) (forall ((BOUND_VARIABLE_18239 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_18239 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18239 B)) (not (tptp.relstr_set_smaller A F BOUND_VARIABLE_18239)))))) :rule trans :premises (t16.t5.t22 t16.t5.t29))
% 0.61/1.07  (step t16.t5.t31 (cl (= (not (forall ((I $$unsorted)) (not (and (= F I) (not (forall ((J $$unsorted)) (or (not (tptp.element J (tptp.the_carrier A))) (not (tptp.in J B)) (not (tptp.relstr_set_smaller A I J))))))))) (not (forall ((BOUND_VARIABLE_18239 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_18239 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18239 B)) (not (tptp.relstr_set_smaller A F BOUND_VARIABLE_18239))))))) :rule cong :premises (t16.t5.t30))
% 0.61/1.07  (step t16.t5.t32 (cl (= (exists ((I $$unsorted)) (and (= F I) (not (forall ((J $$unsorted)) (or (not (tptp.element J (tptp.the_carrier A))) (not (tptp.in J B)) (not (tptp.relstr_set_smaller A I J))))))) (not (forall ((BOUND_VARIABLE_18239 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_18239 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18239 B)) (not (tptp.relstr_set_smaller A F BOUND_VARIABLE_18239))))))) :rule trans :premises (t16.t5.t21 t16.t5.t31))
% 0.61/1.07  (step t16.t5.t33 (cl (= (exists ((I $$unsorted)) (and (= I F) (exists ((J $$unsorted)) (and (tptp.element J (tptp.the_carrier A)) (tptp.in J B) (tptp.relstr_set_smaller A I J))))) (not (forall ((BOUND_VARIABLE_18239 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_18239 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18239 B)) (not (tptp.relstr_set_smaller A F BOUND_VARIABLE_18239))))))) :rule trans :premises (t16.t5.t20 t16.t5.t32))
% 0.61/1.07  (step t16.t5.t34 (cl (= (and (= D E) (exists ((G $$unsorted)) (and (= G E) (exists ((H $$unsorted)) (and (tptp.element H (tptp.the_carrier A)) (tptp.in H B) (tptp.relstr_set_smaller A G H))))) (= D F) (exists ((I $$unsorted)) (and (= I F) (exists ((J $$unsorted)) (and (tptp.element J (tptp.the_carrier A)) (tptp.in J B) (tptp.relstr_set_smaller A I J)))))) (and (= D E) (not (forall ((BOUND_VARIABLE_18196 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_18196 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18196 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_18196))))) (= D F) (not (forall ((BOUND_VARIABLE_18239 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_18239 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18239 B)) (not (tptp.relstr_set_smaller A F BOUND_VARIABLE_18239)))))))) :rule cong :premises (t16.t5.t4 t16.t5.t18 t16.t5.t19 t16.t5.t33))
% 0.61/1.07  (step t16.t5.t35 (cl (= (= E F) (= E F))) :rule refl)
% 0.61/1.07  (step t16.t5.t36 (cl (= (=> (and (= D E) (exists ((G $$unsorted)) (and (= G E) (exists ((H $$unsorted)) (and (tptp.element H (tptp.the_carrier A)) (tptp.in H B) (tptp.relstr_set_smaller A G H))))) (= D F) (exists ((I $$unsorted)) (and (= I F) (exists ((J $$unsorted)) (and (tptp.element J (tptp.the_carrier A)) (tptp.in J B) (tptp.relstr_set_smaller A I J)))))) (= E F)) (=> (and (= D E) (not (forall ((BOUND_VARIABLE_18196 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_18196 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18196 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_18196))))) (= D F) (not (forall ((BOUND_VARIABLE_18239 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_18239 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18239 B)) (not (tptp.relstr_set_smaller A F BOUND_VARIABLE_18239)))))) (= E F)))) :rule cong :premises (t16.t5.t34 t16.t5.t35))
% 0.61/1.07  (step t16.t5 (cl (= (forall ((D $$unsorted) (E $$unsorted) (F $$unsorted)) (=> (and (= D E) (exists ((G $$unsorted)) (and (= G E) (exists ((H $$unsorted)) (and (tptp.element H (tptp.the_carrier A)) (tptp.in H B) (tptp.relstr_set_smaller A G H))))) (= D F) (exists ((I $$unsorted)) (and (= I F) (exists ((J $$unsorted)) (and (tptp.element J (tptp.the_carrier A)) (tptp.in J B) (tptp.relstr_set_smaller A I J)))))) (= E F))) (forall ((D $$unsorted) (E $$unsorted) (F $$unsorted)) (=> (and (= D E) (not (forall ((BOUND_VARIABLE_18196 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_18196 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18196 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_18196))))) (= D F) (not (forall ((BOUND_VARIABLE_18239 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_18239 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18239 B)) (not (tptp.relstr_set_smaller A F BOUND_VARIABLE_18239)))))) (= E F))))) :rule bind)
% 0.61/1.07  (step t16.t6 (cl (= (forall ((D $$unsorted) (E $$unsorted) (F $$unsorted)) (=> (and (= D E) (not (forall ((BOUND_VARIABLE_18196 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_18196 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18196 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_18196))))) (= D F) (not (forall ((BOUND_VARIABLE_18239 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_18239 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18239 B)) (not (tptp.relstr_set_smaller A F BOUND_VARIABLE_18239)))))) (= E F))) (forall ((D $$unsorted) (E $$unsorted) (F $$unsorted)) (or (not (= D E)) (forall ((BOUND_VARIABLE_18196 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_18196 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18196 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_18196)))) (not (= D F)) (forall ((BOUND_VARIABLE_18239 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_18239 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18239 B)) (not (tptp.relstr_set_smaller A F BOUND_VARIABLE_18239)))) (= E F))))) :rule all_simplify)
% 0.61/1.07  (step t16.t7 (cl (= (forall ((D $$unsorted) (E $$unsorted) (F $$unsorted)) (or (not (= D E)) (forall ((BOUND_VARIABLE_18196 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_18196 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18196 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_18196)))) (not (= D F)) (forall ((BOUND_VARIABLE_18239 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_18239 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18239 B)) (not (tptp.relstr_set_smaller A F BOUND_VARIABLE_18239)))) (= E F))) (forall ((D $$unsorted) (E $$unsorted) (F $$unsorted) (BOUND_VARIABLE_18282 $$unsorted) (BOUND_VARIABLE_18273 $$unsorted)) (or (not (= D E)) (or (not (tptp.element BOUND_VARIABLE_18273 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18273 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_18273))) (not (= D F)) (or (not (tptp.element BOUND_VARIABLE_18282 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18282 B)) (not (tptp.relstr_set_smaller A F BOUND_VARIABLE_18282))) (= E F))))) :rule all_simplify)
% 0.61/1.07  (anchor :step t16.t8 :args ((D $$unsorted) (:= D D) (E $$unsorted) (:= E E) (F $$unsorted) (:= F F) (BOUND_VARIABLE_18282 $$unsorted) (:= BOUND_VARIABLE_18282 BOUND_VARIABLE_18282) (BOUND_VARIABLE_18273 $$unsorted) (:= BOUND_VARIABLE_18273 BOUND_VARIABLE_18273)))
% 0.61/1.07  (step t16.t8.t1 (cl (= D D)) :rule refl)
% 0.61/1.07  (step t16.t8.t2 (cl (= E E)) :rule refl)
% 0.61/1.07  (step t16.t8.t3 (cl (= F F)) :rule refl)
% 0.61/1.07  (step t16.t8.t4 (cl (= BOUND_VARIABLE_18282 BOUND_VARIABLE_18282)) :rule refl)
% 0.61/1.07  (step t16.t8.t5 (cl (= BOUND_VARIABLE_18273 BOUND_VARIABLE_18273)) :rule refl)
% 0.61/1.07  (step t16.t8.t6 (cl (= (or (not (= D E)) (or (not (tptp.element BOUND_VARIABLE_18273 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18273 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_18273))) (not (= D F)) (or (not (tptp.element BOUND_VARIABLE_18282 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18282 B)) (not (tptp.relstr_set_smaller A F BOUND_VARIABLE_18282))) (= E F)) (or (not (= D E)) (not (= D F)) (= E F) (not (tptp.element BOUND_VARIABLE_18273 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18273 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_18273)) (not (tptp.element BOUND_VARIABLE_18282 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18282 B)) (not (tptp.relstr_set_smaller A F BOUND_VARIABLE_18282))))) :rule all_simplify)
% 0.61/1.07  (step t16.t8 (cl (= (forall ((D $$unsorted) (E $$unsorted) (F $$unsorted) (BOUND_VARIABLE_18282 $$unsorted) (BOUND_VARIABLE_18273 $$unsorted)) (or (not (= D E)) (or (not (tptp.element BOUND_VARIABLE_18273 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18273 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_18273))) (not (= D F)) (or (not (tptp.element BOUND_VARIABLE_18282 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18282 B)) (not (tptp.relstr_set_smaller A F BOUND_VARIABLE_18282))) (= E F))) (forall ((D $$unsorted) (E $$unsorted) (F $$unsorted) (BOUND_VARIABLE_18282 $$unsorted) (BOUND_VARIABLE_18273 $$unsorted)) (or (not (= D E)) (not (= D F)) (= E F) (not (tptp.element BOUND_VARIABLE_18273 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18273 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_18273)) (not (tptp.element BOUND_VARIABLE_18282 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18282 B)) (not (tptp.relstr_set_smaller A F BOUND_VARIABLE_18282)))))) :rule bind)
% 0.61/1.07  (step t16.t9 (cl (= (forall ((D $$unsorted) (E $$unsorted) (F $$unsorted) (BOUND_VARIABLE_18282 $$unsorted) (BOUND_VARIABLE_18273 $$unsorted)) (or (not (= D E)) (not (= D F)) (= E F) (not (tptp.element BOUND_VARIABLE_18273 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18273 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_18273)) (not (tptp.element BOUND_VARIABLE_18282 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18282 B)) (not (tptp.relstr_set_smaller A F BOUND_VARIABLE_18282)))) (forall ((F $$unsorted) (BOUND_VARIABLE_18282 $$unsorted) (BOUND_VARIABLE_18273 $$unsorted)) (or (not (= F F)) (not (= F F)) (= F F) (not (tptp.element BOUND_VARIABLE_18273 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18273 B)) (not (tptp.relstr_set_smaller A F BOUND_VARIABLE_18273)) (not (tptp.element BOUND_VARIABLE_18282 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18282 B)) (not (tptp.relstr_set_smaller A F BOUND_VARIABLE_18282)))))) :rule all_simplify)
% 0.61/1.07  (anchor :step t16.t10 :args ((F $$unsorted) (:= F F) (BOUND_VARIABLE_18282 $$unsorted) (:= BOUND_VARIABLE_18282 BOUND_VARIABLE_18282) (BOUND_VARIABLE_18273 $$unsorted) (:= BOUND_VARIABLE_18273 BOUND_VARIABLE_18273)))
% 0.61/1.07  (step t16.t10.t1 (cl (= F F)) :rule refl)
% 0.61/1.07  (step t16.t10.t2 (cl (= BOUND_VARIABLE_18282 BOUND_VARIABLE_18282)) :rule refl)
% 0.61/1.07  (step t16.t10.t3 (cl (= BOUND_VARIABLE_18273 BOUND_VARIABLE_18273)) :rule refl)
% 0.61/1.07  (step t16.t10.t4 (cl (= (= F F) true)) :rule all_simplify)
% 0.61/1.07  (step t16.t10.t5 (cl (= (not (= F F)) (not true))) :rule cong :premises (t16.t10.t4))
% 0.61/1.07  (step t16.t10.t6 (cl (= (not true) false)) :rule all_simplify)
% 0.61/1.07  (step t16.t10.t7 (cl (= (not (= F F)) false)) :rule trans :premises (t16.t10.t5 t16.t10.t6))
% 0.61/1.07  (step t16.t10.t8 (cl (= (not (tptp.element BOUND_VARIABLE_18273 (tptp.the_carrier A))) (not (tptp.element BOUND_VARIABLE_18273 (tptp.the_carrier A))))) :rule refl)
% 0.61/1.07  (step t16.t10.t9 (cl (= (not (tptp.in BOUND_VARIABLE_18273 B)) (not (tptp.in BOUND_VARIABLE_18273 B)))) :rule refl)
% 0.61/1.07  (step t16.t10.t10 (cl (= (not (tptp.relstr_set_smaller A F BOUND_VARIABLE_18273)) (not (tptp.relstr_set_smaller A F BOUND_VARIABLE_18273)))) :rule refl)
% 0.61/1.07  (step t16.t10.t11 (cl (= (not (tptp.element BOUND_VARIABLE_18282 (tptp.the_carrier A))) (not (tptp.element BOUND_VARIABLE_18282 (tptp.the_carrier A))))) :rule refl)
% 0.61/1.07  (step t16.t10.t12 (cl (= (not (tptp.in BOUND_VARIABLE_18282 B)) (not (tptp.in BOUND_VARIABLE_18282 B)))) :rule refl)
% 0.61/1.07  (step t16.t10.t13 (cl (= (not (tptp.relstr_set_smaller A F BOUND_VARIABLE_18282)) (not (tptp.relstr_set_smaller A F BOUND_VARIABLE_18282)))) :rule refl)
% 0.61/1.07  (step t16.t10.t14 (cl (= (or (not (= F F)) (not (= F F)) (= F F) (not (tptp.element BOUND_VARIABLE_18273 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18273 B)) (not (tptp.relstr_set_smaller A F BOUND_VARIABLE_18273)) (not (tptp.element BOUND_VARIABLE_18282 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18282 B)) (not (tptp.relstr_set_smaller A F BOUND_VARIABLE_18282))) (or false false true (not (tptp.element BOUND_VARIABLE_18273 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18273 B)) (not (tptp.relstr_set_smaller A F BOUND_VARIABLE_18273)) (not (tptp.element BOUND_VARIABLE_18282 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18282 B)) (not (tptp.relstr_set_smaller A F BOUND_VARIABLE_18282))))) :rule cong :premises (t16.t10.t7 t16.t10.t7 t16.t10.t4 t16.t10.t8 t16.t10.t9 t16.t10.t10 t16.t10.t11 t16.t10.t12 t16.t10.t13))
% 0.61/1.07  (step t16.t10.t15 (cl (= (or false false true (not (tptp.element BOUND_VARIABLE_18273 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18273 B)) (not (tptp.relstr_set_smaller A F BOUND_VARIABLE_18273)) (not (tptp.element BOUND_VARIABLE_18282 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18282 B)) (not (tptp.relstr_set_smaller A F BOUND_VARIABLE_18282))) true)) :rule all_simplify)
% 0.61/1.07  (step t16.t10.t16 (cl (= (or (not (= F F)) (not (= F F)) (= F F) (not (tptp.element BOUND_VARIABLE_18273 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18273 B)) (not (tptp.relstr_set_smaller A F BOUND_VARIABLE_18273)) (not (tptp.element BOUND_VARIABLE_18282 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18282 B)) (not (tptp.relstr_set_smaller A F BOUND_VARIABLE_18282))) true)) :rule trans :premises (t16.t10.t14 t16.t10.t15))
% 0.61/1.07  (step t16.t10 (cl (= (forall ((F $$unsorted) (BOUND_VARIABLE_18282 $$unsorted) (BOUND_VARIABLE_18273 $$unsorted)) (or (not (= F F)) (not (= F F)) (= F F) (not (tptp.element BOUND_VARIABLE_18273 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18273 B)) (not (tptp.relstr_set_smaller A F BOUND_VARIABLE_18273)) (not (tptp.element BOUND_VARIABLE_18282 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18282 B)) (not (tptp.relstr_set_smaller A F BOUND_VARIABLE_18282)))) (forall ((F $$unsorted) (BOUND_VARIABLE_18282 $$unsorted) (BOUND_VARIABLE_18273 $$unsorted)) true))) :rule bind)
% 0.61/1.07  (step t16.t11 (cl (= (forall ((F $$unsorted) (BOUND_VARIABLE_18282 $$unsorted) (BOUND_VARIABLE_18273 $$unsorted)) true) true)) :rule all_simplify)
% 0.61/1.07  (step t16.t12 (cl (= (forall ((F $$unsorted) (BOUND_VARIABLE_18282 $$unsorted) (BOUND_VARIABLE_18273 $$unsorted)) (or (not (= F F)) (not (= F F)) (= F F) (not (tptp.element BOUND_VARIABLE_18273 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18273 B)) (not (tptp.relstr_set_smaller A F BOUND_VARIABLE_18273)) (not (tptp.element BOUND_VARIABLE_18282 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18282 B)) (not (tptp.relstr_set_smaller A F BOUND_VARIABLE_18282)))) true)) :rule trans :premises (t16.t10 t16.t11))
% 0.61/1.07  (step t16.t13 (cl (= (forall ((D $$unsorted) (E $$unsorted) (F $$unsorted) (BOUND_VARIABLE_18282 $$unsorted) (BOUND_VARIABLE_18273 $$unsorted)) (or (not (= D E)) (not (= D F)) (= E F) (not (tptp.element BOUND_VARIABLE_18273 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18273 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_18273)) (not (tptp.element BOUND_VARIABLE_18282 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18282 B)) (not (tptp.relstr_set_smaller A F BOUND_VARIABLE_18282)))) true)) :rule trans :premises (t16.t9 t16.t12))
% 0.61/1.07  (step t16.t14 (cl (= (forall ((D $$unsorted) (E $$unsorted) (F $$unsorted) (BOUND_VARIABLE_18282 $$unsorted) (BOUND_VARIABLE_18273 $$unsorted)) (or (not (= D E)) (or (not (tptp.element BOUND_VARIABLE_18273 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18273 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_18273))) (not (= D F)) (or (not (tptp.element BOUND_VARIABLE_18282 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18282 B)) (not (tptp.relstr_set_smaller A F BOUND_VARIABLE_18282))) (= E F))) true)) :rule trans :premises (t16.t8 t16.t13))
% 0.61/1.07  (step t16.t15 (cl (= (forall ((D $$unsorted) (E $$unsorted) (F $$unsorted)) (or (not (= D E)) (forall ((BOUND_VARIABLE_18196 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_18196 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18196 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_18196)))) (not (= D F)) (forall ((BOUND_VARIABLE_18239 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_18239 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18239 B)) (not (tptp.relstr_set_smaller A F BOUND_VARIABLE_18239)))) (= E F))) true)) :rule trans :premises (t16.t7 t16.t14))
% 0.61/1.07  (step t16.t16 (cl (= (forall ((D $$unsorted) (E $$unsorted) (F $$unsorted)) (=> (and (= D E) (not (forall ((BOUND_VARIABLE_18196 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_18196 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18196 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_18196))))) (= D F) (not (forall ((BOUND_VARIABLE_18239 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_18239 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18239 B)) (not (tptp.relstr_set_smaller A F BOUND_VARIABLE_18239)))))) (= E F))) true)) :rule trans :premises (t16.t6 t16.t15))
% 0.61/1.07  (step t16.t17 (cl (= (forall ((D $$unsorted) (E $$unsorted) (F $$unsorted)) (=> (and (= D E) (exists ((G $$unsorted)) (and (= G E) (exists ((H $$unsorted)) (and (tptp.element H (tptp.the_carrier A)) (tptp.in H B) (tptp.relstr_set_smaller A G H))))) (= D F) (exists ((I $$unsorted)) (and (= I F) (exists ((J $$unsorted)) (and (tptp.element J (tptp.the_carrier A)) (tptp.in J B) (tptp.relstr_set_smaller A I J)))))) (= E F))) true)) :rule trans :premises (t16.t5 t16.t16))
% 0.61/1.07  (anchor :step t16.t18 :args ((D $$unsorted) (:= D D)))
% 0.61/1.07  (step t16.t18.t1 (cl (= D D)) :rule refl)
% 0.61/1.07  (anchor :step t16.t18.t2 :args ((E $$unsorted) (:= E E)))
% 0.61/1.07  (step t16.t18.t2.t1 (cl (= E E)) :rule refl)
% 0.61/1.07  (step t16.t18.t2.t2 (cl (= (tptp.in E D) (tptp.in E D))) :rule refl)
% 0.61/1.07  (anchor :step t16.t18.t2.t3 :args ((F $$unsorted) (:= F F)))
% 0.61/1.07  (step t16.t18.t2.t3.t1 (cl (= F F)) :rule refl)
% 0.61/1.07  (step t16.t18.t2.t3.t2 (cl (= (tptp.in F (tptp.powerset C)) (tptp.in F (tptp.powerset C)))) :rule refl)
% 0.61/1.07  (step t16.t18.t2.t3.t3 (cl (= (= F E) (= E F))) :rule all_simplify)
% 0.61/1.07  (anchor :step t16.t18.t2.t3.t4 :args ((K $$unsorted) (:= K K)))
% 0.61/1.07  (step t16.t18.t2.t3.t4.t1 (cl (= K K)) :rule refl)
% 0.61/1.07  (step t16.t18.t2.t3.t4.t2 (cl (= (= K E) (= E K))) :rule all_simplify)
% 0.61/1.07  (step t16.t18.t2.t3.t4.t3 (cl (= (exists ((L $$unsorted)) (and (tptp.element L (tptp.the_carrier A)) (tptp.in L B) (tptp.relstr_set_smaller A K L))) (not (forall ((L $$unsorted)) (not (and (tptp.element L (tptp.the_carrier A)) (tptp.in L B) (tptp.relstr_set_smaller A K L))))))) :rule all_simplify)
% 0.61/1.07  (step t16.t18.t2.t3.t4.t4 (cl (= (forall ((L $$unsorted)) (not (and (tptp.element L (tptp.the_carrier A)) (tptp.in L B) (tptp.relstr_set_smaller A K L)))) (forall ((L $$unsorted)) (or (not (tptp.element L (tptp.the_carrier A))) (not (tptp.in L B)) (not (tptp.relstr_set_smaller A K L)))))) :rule all_simplify)
% 0.61/1.07  (step t16.t18.t2.t3.t4.t5 (cl (= (not (forall ((L $$unsorted)) (not (and (tptp.element L (tptp.the_carrier A)) (tptp.in L B) (tptp.relstr_set_smaller A K L))))) (not (forall ((L $$unsorted)) (or (not (tptp.element L (tptp.the_carrier A))) (not (tptp.in L B)) (not (tptp.relstr_set_smaller A K L))))))) :rule cong :premises (t16.t18.t2.t3.t4.t4))
% 0.61/1.07  (step t16.t18.t2.t3.t4.t6 (cl (= (exists ((L $$unsorted)) (and (tptp.element L (tptp.the_carrier A)) (tptp.in L B) (tptp.relstr_set_smaller A K L))) (not (forall ((L $$unsorted)) (or (not (tptp.element L (tptp.the_carrier A))) (not (tptp.in L B)) (not (tptp.relstr_set_smaller A K L))))))) :rule trans :premises (t16.t18.t2.t3.t4.t3 t16.t18.t2.t3.t4.t5))
% 0.61/1.07  (step t16.t18.t2.t3.t4.t7 (cl (= (and (= K E) (exists ((L $$unsorted)) (and (tptp.element L (tptp.the_carrier A)) (tptp.in L B) (tptp.relstr_set_smaller A K L)))) (and (= E K) (not (forall ((L $$unsorted)) (or (not (tptp.element L (tptp.the_carrier A))) (not (tptp.in L B)) (not (tptp.relstr_set_smaller A K L)))))))) :rule cong :premises (t16.t18.t2.t3.t4.t2 t16.t18.t2.t3.t4.t6))
% 0.61/1.07  (step t16.t18.t2.t3.t4 (cl (= (exists ((K $$unsorted)) (and (= K E) (exists ((L $$unsorted)) (and (tptp.element L (tptp.the_carrier A)) (tptp.in L B) (tptp.relstr_set_smaller A K L))))) (exists ((K $$unsorted)) (and (= E K) (not (forall ((L $$unsorted)) (or (not (tptp.element L (tptp.the_carrier A))) (not (tptp.in L B)) (not (tptp.relstr_set_smaller A K L))))))))) :rule bind)
% 0.61/1.07  (step t16.t18.t2.t3.t5 (cl (= (exists ((K $$unsorted)) (and (= E K) (not (forall ((L $$unsorted)) (or (not (tptp.element L (tptp.the_carrier A))) (not (tptp.in L B)) (not (tptp.relstr_set_smaller A K L))))))) (not (forall ((K $$unsorted)) (not (and (= E K) (not (forall ((L $$unsorted)) (or (not (tptp.element L (tptp.the_carrier A))) (not (tptp.in L B)) (not (tptp.relstr_set_smaller A K L))))))))))) :rule all_simplify)
% 0.61/1.07  (step t16.t18.t2.t3.t6 (cl (= (forall ((K $$unsorted)) (not (and (= E K) (not (forall ((L $$unsorted)) (or (not (tptp.element L (tptp.the_carrier A))) (not (tptp.in L B)) (not (tptp.relstr_set_smaller A K L)))))))) (forall ((K $$unsorted)) (or (not (= E K)) (forall ((L $$unsorted)) (or (not (tptp.element L (tptp.the_carrier A))) (not (tptp.in L B)) (not (tptp.relstr_set_smaller A K L)))))))) :rule all_simplify)
% 0.61/1.07  (step t16.t18.t2.t3.t7 (cl (= (forall ((K $$unsorted)) (or (not (= E K)) (forall ((L $$unsorted)) (or (not (tptp.element L (tptp.the_carrier A))) (not (tptp.in L B)) (not (tptp.relstr_set_smaller A K L)))))) (forall ((K $$unsorted) (BOUND_VARIABLE_18324 $$unsorted)) (or (not (= E K)) (or (not (tptp.element BOUND_VARIABLE_18324 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18324 B)) (not (tptp.relstr_set_smaller A K BOUND_VARIABLE_18324))))))) :rule all_simplify)
% 0.61/1.07  (anchor :step t16.t18.t2.t3.t8 :args ((K $$unsorted) (:= K K) (BOUND_VARIABLE_18324 $$unsorted) (:= BOUND_VARIABLE_18324 BOUND_VARIABLE_18324)))
% 0.61/1.07  (step t16.t18.t2.t3.t8.t1 (cl (= K K)) :rule refl)
% 0.61/1.07  (step t16.t18.t2.t3.t8.t2 (cl (= BOUND_VARIABLE_18324 BOUND_VARIABLE_18324)) :rule refl)
% 0.61/1.07  (step t16.t18.t2.t3.t8.t3 (cl (= (or (not (= E K)) (or (not (tptp.element BOUND_VARIABLE_18324 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18324 B)) (not (tptp.relstr_set_smaller A K BOUND_VARIABLE_18324)))) (or (not (= E K)) (not (tptp.element BOUND_VARIABLE_18324 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18324 B)) (not (tptp.relstr_set_smaller A K BOUND_VARIABLE_18324))))) :rule all_simplify)
% 0.61/1.07  (step t16.t18.t2.t3.t8 (cl (= (forall ((K $$unsorted) (BOUND_VARIABLE_18324 $$unsorted)) (or (not (= E K)) (or (not (tptp.element BOUND_VARIABLE_18324 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18324 B)) (not (tptp.relstr_set_smaller A K BOUND_VARIABLE_18324))))) (forall ((K $$unsorted) (BOUND_VARIABLE_18324 $$unsorted)) (or (not (= E K)) (not (tptp.element BOUND_VARIABLE_18324 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18324 B)) (not (tptp.relstr_set_smaller A K BOUND_VARIABLE_18324)))))) :rule bind)
% 0.61/1.07  (step t16.t18.t2.t3.t9 (cl (= (forall ((K $$unsorted) (BOUND_VARIABLE_18324 $$unsorted)) (or (not (= E K)) (not (tptp.element BOUND_VARIABLE_18324 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18324 B)) (not (tptp.relstr_set_smaller A K BOUND_VARIABLE_18324)))) (forall ((BOUND_VARIABLE_18324 $$unsorted)) (or (not (= E E)) (not (tptp.element BOUND_VARIABLE_18324 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18324 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_18324)))))) :rule all_simplify)
% 0.61/1.07  (anchor :step t16.t18.t2.t3.t10 :args ((BOUND_VARIABLE_18324 $$unsorted) (:= BOUND_VARIABLE_18324 BOUND_VARIABLE_18324)))
% 0.61/1.07  (step t16.t18.t2.t3.t10.t1 (cl (= BOUND_VARIABLE_18324 BOUND_VARIABLE_18324)) :rule refl)
% 0.61/1.07  (step t16.t18.t2.t3.t10.t2 (cl (= (= E E) true)) :rule all_simplify)
% 0.61/1.07  (step t16.t18.t2.t3.t10.t3 (cl (= (not (= E E)) (not true))) :rule cong :premises (t16.t18.t2.t3.t10.t2))
% 0.61/1.07  (step t16.t18.t2.t3.t10.t4 (cl (= (not true) false)) :rule all_simplify)
% 0.61/1.07  (step t16.t18.t2.t3.t10.t5 (cl (= (not (= E E)) false)) :rule trans :premises (t16.t18.t2.t3.t10.t3 t16.t18.t2.t3.t10.t4))
% 0.61/1.07  (step t16.t18.t2.t3.t10.t6 (cl (= (not (tptp.element BOUND_VARIABLE_18324 (tptp.the_carrier A))) (not (tptp.element BOUND_VARIABLE_18324 (tptp.the_carrier A))))) :rule refl)
% 0.61/1.07  (step t16.t18.t2.t3.t10.t7 (cl (= (not (tptp.in BOUND_VARIABLE_18324 B)) (not (tptp.in BOUND_VARIABLE_18324 B)))) :rule refl)
% 0.61/1.07  (step t16.t18.t2.t3.t10.t8 (cl (= (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_18324)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_18324)))) :rule refl)
% 0.61/1.07  (step t16.t18.t2.t3.t10.t9 (cl (= (or (not (= E E)) (not (tptp.element BOUND_VARIABLE_18324 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18324 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_18324))) (or false (not (tptp.element BOUND_VARIABLE_18324 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18324 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_18324))))) :rule cong :premises (t16.t18.t2.t3.t10.t5 t16.t18.t2.t3.t10.t6 t16.t18.t2.t3.t10.t7 t16.t18.t2.t3.t10.t8))
% 0.61/1.07  (step t16.t18.t2.t3.t10.t10 (cl (= (or false (not (tptp.element BOUND_VARIABLE_18324 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18324 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_18324))) (or (not (tptp.element BOUND_VARIABLE_18324 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18324 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_18324))))) :rule all_simplify)
% 0.61/1.07  (step t16.t18.t2.t3.t10.t11 (cl (= (or (not (= E E)) (not (tptp.element BOUND_VARIABLE_18324 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18324 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_18324))) (or (not (tptp.element BOUND_VARIABLE_18324 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18324 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_18324))))) :rule trans :premises (t16.t18.t2.t3.t10.t9 t16.t18.t2.t3.t10.t10))
% 0.61/1.07  (step t16.t18.t2.t3.t10 (cl (= (forall ((BOUND_VARIABLE_18324 $$unsorted)) (or (not (= E E)) (not (tptp.element BOUND_VARIABLE_18324 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18324 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_18324)))) (forall ((BOUND_VARIABLE_18324 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_18324 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18324 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_18324)))))) :rule bind)
% 0.61/1.07  (step t16.t18.t2.t3.t11 (cl (= (forall ((K $$unsorted) (BOUND_VARIABLE_18324 $$unsorted)) (or (not (= E K)) (not (tptp.element BOUND_VARIABLE_18324 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18324 B)) (not (tptp.relstr_set_smaller A K BOUND_VARIABLE_18324)))) (forall ((BOUND_VARIABLE_18324 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_18324 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18324 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_18324)))))) :rule trans :premises (t16.t18.t2.t3.t9 t16.t18.t2.t3.t10))
% 0.61/1.07  (step t16.t18.t2.t3.t12 (cl (= (forall ((K $$unsorted) (BOUND_VARIABLE_18324 $$unsorted)) (or (not (= E K)) (or (not (tptp.element BOUND_VARIABLE_18324 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18324 B)) (not (tptp.relstr_set_smaller A K BOUND_VARIABLE_18324))))) (forall ((BOUND_VARIABLE_18324 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_18324 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18324 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_18324)))))) :rule trans :premises (t16.t18.t2.t3.t8 t16.t18.t2.t3.t11))
% 0.61/1.07  (step t16.t18.t2.t3.t13 (cl (= (forall ((K $$unsorted)) (or (not (= E K)) (forall ((L $$unsorted)) (or (not (tptp.element L (tptp.the_carrier A))) (not (tptp.in L B)) (not (tptp.relstr_set_smaller A K L)))))) (forall ((BOUND_VARIABLE_18324 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_18324 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18324 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_18324)))))) :rule trans :premises (t16.t18.t2.t3.t7 t16.t18.t2.t3.t12))
% 0.61/1.07  (step t16.t18.t2.t3.t14 (cl (= (forall ((K $$unsorted)) (not (and (= E K) (not (forall ((L $$unsorted)) (or (not (tptp.element L (tptp.the_carrier A))) (not (tptp.in L B)) (not (tptp.relstr_set_smaller A K L)))))))) (forall ((BOUND_VARIABLE_18324 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_18324 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18324 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_18324)))))) :rule trans :premises (t16.t18.t2.t3.t6 t16.t18.t2.t3.t13))
% 0.61/1.07  (step t16.t18.t2.t3.t15 (cl (= (not (forall ((K $$unsorted)) (not (and (= E K) (not (forall ((L $$unsorted)) (or (not (tptp.element L (tptp.the_carrier A))) (not (tptp.in L B)) (not (tptp.relstr_set_smaller A K L))))))))) (not (forall ((BOUND_VARIABLE_18324 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_18324 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18324 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_18324))))))) :rule cong :premises (t16.t18.t2.t3.t14))
% 0.61/1.07  (step t16.t18.t2.t3.t16 (cl (= (exists ((K $$unsorted)) (and (= E K) (not (forall ((L $$unsorted)) (or (not (tptp.element L (tptp.the_carrier A))) (not (tptp.in L B)) (not (tptp.relstr_set_smaller A K L))))))) (not (forall ((BOUND_VARIABLE_18324 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_18324 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18324 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_18324))))))) :rule trans :premises (t16.t18.t2.t3.t5 t16.t18.t2.t3.t15))
% 0.61/1.07  (step t16.t18.t2.t3.t17 (cl (= (exists ((K $$unsorted)) (and (= K E) (exists ((L $$unsorted)) (and (tptp.element L (tptp.the_carrier A)) (tptp.in L B) (tptp.relstr_set_smaller A K L))))) (not (forall ((BOUND_VARIABLE_18324 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_18324 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18324 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_18324))))))) :rule trans :premises (t16.t18.t2.t3.t4 t16.t18.t2.t3.t16))
% 0.61/1.07  (step t16.t18.t2.t3.t18 (cl (= (and (tptp.in F (tptp.powerset C)) (= F E) (exists ((K $$unsorted)) (and (= K E) (exists ((L $$unsorted)) (and (tptp.element L (tptp.the_carrier A)) (tptp.in L B) (tptp.relstr_set_smaller A K L)))))) (and (tptp.in F (tptp.powerset C)) (= E F) (not (forall ((BOUND_VARIABLE_18324 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_18324 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18324 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_18324)))))))) :rule cong :premises (t16.t18.t2.t3.t2 t16.t18.t2.t3.t3 t16.t18.t2.t3.t17))
% 0.61/1.07  (step t16.t18.t2.t3 (cl (= (exists ((F $$unsorted)) (and (tptp.in F (tptp.powerset C)) (= F E) (exists ((K $$unsorted)) (and (= K E) (exists ((L $$unsorted)) (and (tptp.element L (tptp.the_carrier A)) (tptp.in L B) (tptp.relstr_set_smaller A K L))))))) (exists ((F $$unsorted)) (and (tptp.in F (tptp.powerset C)) (= E F) (not (forall ((BOUND_VARIABLE_18324 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_18324 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18324 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_18324))))))))) :rule bind)
% 0.61/1.07  (step t16.t18.t2.t4 (cl (= (exists ((F $$unsorted)) (and (tptp.in F (tptp.powerset C)) (= E F) (not (forall ((BOUND_VARIABLE_18324 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_18324 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18324 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_18324))))))) (not (forall ((F $$unsorted)) (not (and (tptp.in F (tptp.powerset C)) (= E F) (not (forall ((BOUND_VARIABLE_18324 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_18324 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18324 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_18324))))))))))) :rule all_simplify)
% 0.61/1.07  (step t16.t18.t2.t5 (cl (= (forall ((F $$unsorted)) (not (and (tptp.in F (tptp.powerset C)) (= E F) (not (forall ((BOUND_VARIABLE_18324 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_18324 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18324 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_18324)))))))) (forall ((F $$unsorted)) (or (not (tptp.in F (tptp.powerset C))) (not (= E F)) (forall ((BOUND_VARIABLE_18324 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_18324 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18324 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_18324)))))))) :rule all_simplify)
% 0.61/1.07  (step t16.t18.t2.t6 (cl (= (forall ((F $$unsorted)) (or (not (tptp.in F (tptp.powerset C))) (not (= E F)) (forall ((BOUND_VARIABLE_18324 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_18324 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18324 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_18324)))))) (or (forall ((BOUND_VARIABLE_18324 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_18324 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18324 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_18324)))) (forall ((F $$unsorted)) (or (not (tptp.in F (tptp.powerset C))) (not (= E F))))))) :rule all_simplify)
% 0.61/1.07  (step t16.t18.t2.t7 (cl (= (forall ((BOUND_VARIABLE_18324 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_18324 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18324 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_18324)))) (forall ((BOUND_VARIABLE_18324 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_18324 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18324 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_18324)))))) :rule refl)
% 0.61/1.07  (step t16.t18.t2.t8 (cl (= (forall ((F $$unsorted)) (or (not (tptp.in F (tptp.powerset C))) (not (= E F)))) (or (not (tptp.in E (tptp.powerset C))) (not (= E E))))) :rule all_simplify)
% 0.61/1.07  (step t16.t18.t2.t9 (cl (= (not (tptp.in E (tptp.powerset C))) (not (tptp.in E (tptp.powerset C))))) :rule refl)
% 0.61/1.07  (step t16.t18.t2.t10 (cl (= (= E E) true)) :rule all_simplify)
% 0.61/1.07  (step t16.t18.t2.t11 (cl (= (not (= E E)) (not true))) :rule cong :premises (t16.t18.t2.t10))
% 0.61/1.07  (step t16.t18.t2.t12 (cl (= (not true) false)) :rule all_simplify)
% 0.61/1.07  (step t16.t18.t2.t13 (cl (= (not (= E E)) false)) :rule trans :premises (t16.t18.t2.t11 t16.t18.t2.t12))
% 0.61/1.07  (step t16.t18.t2.t14 (cl (= (or (not (tptp.in E (tptp.powerset C))) (not (= E E))) (or (not (tptp.in E (tptp.powerset C))) false))) :rule cong :premises (t16.t18.t2.t9 t16.t18.t2.t13))
% 0.61/1.07  (step t16.t18.t2.t15 (cl (= (or (not (tptp.in E (tptp.powerset C))) false) (not (tptp.in E (tptp.powerset C))))) :rule all_simplify)
% 0.61/1.07  (step t16.t18.t2.t16 (cl (= (or (not (tptp.in E (tptp.powerset C))) (not (= E E))) (not (tptp.in E (tptp.powerset C))))) :rule trans :premises (t16.t18.t2.t14 t16.t18.t2.t15))
% 0.61/1.07  (step t16.t18.t2.t17 (cl (= (forall ((F $$unsorted)) (or (not (tptp.in F (tptp.powerset C))) (not (= E F)))) (not (tptp.in E (tptp.powerset C))))) :rule trans :premises (t16.t18.t2.t8 t16.t18.t2.t16))
% 0.61/1.07  (step t16.t18.t2.t18 (cl (= (or (forall ((BOUND_VARIABLE_18324 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_18324 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18324 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_18324)))) (forall ((F $$unsorted)) (or (not (tptp.in F (tptp.powerset C))) (not (= E F))))) (or (forall ((BOUND_VARIABLE_18324 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_18324 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18324 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_18324)))) (not (tptp.in E (tptp.powerset C)))))) :rule cong :premises (t16.t18.t2.t7 t16.t18.t2.t17))
% 0.61/1.07  (step t16.t18.t2.t19 (cl (= (forall ((F $$unsorted)) (or (not (tptp.in F (tptp.powerset C))) (not (= E F)) (forall ((BOUND_VARIABLE_18324 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_18324 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18324 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_18324)))))) (or (forall ((BOUND_VARIABLE_18324 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_18324 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18324 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_18324)))) (not (tptp.in E (tptp.powerset C)))))) :rule trans :premises (t16.t18.t2.t6 t16.t18.t2.t18))
% 0.61/1.07  (step t16.t18.t2.t20 (cl (= (forall ((F $$unsorted)) (not (and (tptp.in F (tptp.powerset C)) (= E F) (not (forall ((BOUND_VARIABLE_18324 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_18324 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18324 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_18324)))))))) (or (forall ((BOUND_VARIABLE_18324 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_18324 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18324 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_18324)))) (not (tptp.in E (tptp.powerset C)))))) :rule trans :premises (t16.t18.t2.t5 t16.t18.t2.t19))
% 0.61/1.07  (step t16.t18.t2.t21 (cl (= (not (forall ((F $$unsorted)) (not (and (tptp.in F (tptp.powerset C)) (= E F) (not (forall ((BOUND_VARIABLE_18324 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_18324 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18324 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_18324))))))))) (not (or (forall ((BOUND_VARIABLE_18324 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_18324 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18324 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_18324)))) (not (tptp.in E (tptp.powerset C))))))) :rule cong :premises (t16.t18.t2.t20))
% 0.61/1.07  (step t16.t18.t2.t22 (cl (= (exists ((F $$unsorted)) (and (tptp.in F (tptp.powerset C)) (= E F) (not (forall ((BOUND_VARIABLE_18324 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_18324 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18324 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_18324))))))) (not (or (forall ((BOUND_VARIABLE_18324 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_18324 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18324 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_18324)))) (not (tptp.in E (tptp.powerset C))))))) :rule trans :premises (t16.t18.t2.t4 t16.t18.t2.t21))
% 0.61/1.07  (step t16.t18.t2.t23 (cl (= (exists ((F $$unsorted)) (and (tptp.in F (tptp.powerset C)) (= F E) (exists ((K $$unsorted)) (and (= K E) (exists ((L $$unsorted)) (and (tptp.element L (tptp.the_carrier A)) (tptp.in L B) (tptp.relstr_set_smaller A K L))))))) (not (or (forall ((BOUND_VARIABLE_18324 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_18324 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18324 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_18324)))) (not (tptp.in E (tptp.powerset C))))))) :rule trans :premises (t16.t18.t2.t3 t16.t18.t2.t22))
% 0.61/1.07  (step t16.t18.t2.t24 (cl (= (= (tptp.in E D) (exists ((F $$unsorted)) (and (tptp.in F (tptp.powerset C)) (= F E) (exists ((K $$unsorted)) (and (= K E) (exists ((L $$unsorted)) (and (tptp.element L (tptp.the_carrier A)) (tptp.in L B) (tptp.relstr_set_smaller A K L)))))))) (= (tptp.in E D) (not (or (forall ((BOUND_VARIABLE_18324 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_18324 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18324 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_18324)))) (not (tptp.in E (tptp.powerset C)))))))) :rule cong :premises (t16.t18.t2.t2 t16.t18.t2.t23))
% 0.61/1.07  (step t16.t18.t2 (cl (= (forall ((E $$unsorted)) (= (tptp.in E D) (exists ((F $$unsorted)) (and (tptp.in F (tptp.powerset C)) (= F E) (exists ((K $$unsorted)) (and (= K E) (exists ((L $$unsorted)) (and (tptp.element L (tptp.the_carrier A)) (tptp.in L B) (tptp.relstr_set_smaller A K L))))))))) (forall ((E $$unsorted)) (= (tptp.in E D) (not (or (forall ((BOUND_VARIABLE_18324 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_18324 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18324 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_18324)))) (not (tptp.in E (tptp.powerset C))))))))) :rule bind)
% 0.61/1.07  (step t16.t18.t3 (cl (= (forall ((E $$unsorted)) (= (tptp.in E D) (not (or (forall ((BOUND_VARIABLE_18324 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_18324 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18324 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_18324)))) (not (tptp.in E (tptp.powerset C))))))) (forall ((E $$unsorted)) (= (tptp.in E D) (and (not (forall ((BOUND_VARIABLE_18324 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_18324 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18324 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_18324))))) (tptp.in E (tptp.powerset C))))))) :rule all_simplify)
% 0.61/1.07  (step t16.t18.t4 (cl (= (forall ((E $$unsorted)) (= (tptp.in E D) (exists ((F $$unsorted)) (and (tptp.in F (tptp.powerset C)) (= F E) (exists ((K $$unsorted)) (and (= K E) (exists ((L $$unsorted)) (and (tptp.element L (tptp.the_carrier A)) (tptp.in L B) (tptp.relstr_set_smaller A K L))))))))) (forall ((E $$unsorted)) (= (tptp.in E D) (and (not (forall ((BOUND_VARIABLE_18324 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_18324 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18324 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_18324))))) (tptp.in E (tptp.powerset C))))))) :rule trans :premises (t16.t18.t2 t16.t18.t3))
% 0.61/1.07  (step t16.t18 (cl (= (exists ((D $$unsorted)) (forall ((E $$unsorted)) (= (tptp.in E D) (exists ((F $$unsorted)) (and (tptp.in F (tptp.powerset C)) (= F E) (exists ((K $$unsorted)) (and (= K E) (exists ((L $$unsorted)) (and (tptp.element L (tptp.the_carrier A)) (tptp.in L B) (tptp.relstr_set_smaller A K L)))))))))) (exists ((D $$unsorted)) (forall ((E $$unsorted)) (= (tptp.in E D) (and (not (forall ((BOUND_VARIABLE_18324 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_18324 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18324 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_18324))))) (tptp.in E (tptp.powerset C)))))))) :rule bind)
% 0.61/1.07  (step t16.t19 (cl (= (exists ((D $$unsorted)) (forall ((E $$unsorted)) (= (tptp.in E D) (and (not (forall ((BOUND_VARIABLE_18324 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_18324 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18324 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_18324))))) (tptp.in E (tptp.powerset C)))))) (not (forall ((D $$unsorted)) (not (forall ((E $$unsorted)) (= (tptp.in E D) (and (not (forall ((BOUND_VARIABLE_18324 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_18324 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18324 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_18324))))) (tptp.in E (tptp.powerset C)))))))))) :rule all_simplify)
% 0.61/1.07  (step t16.t20 (cl (= (exists ((D $$unsorted)) (forall ((E $$unsorted)) (= (tptp.in E D) (exists ((F $$unsorted)) (and (tptp.in F (tptp.powerset C)) (= F E) (exists ((K $$unsorted)) (and (= K E) (exists ((L $$unsorted)) (and (tptp.element L (tptp.the_carrier A)) (tptp.in L B) (tptp.relstr_set_smaller A K L)))))))))) (not (forall ((D $$unsorted)) (not (forall ((E $$unsorted)) (= (tptp.in E D) (and (not (forall ((BOUND_VARIABLE_18324 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_18324 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18324 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_18324))))) (tptp.in E (tptp.powerset C)))))))))) :rule trans :premises (t16.t18 t16.t19))
% 0.61/1.07  (step t16.t21 (cl (= (=> (forall ((D $$unsorted) (E $$unsorted) (F $$unsorted)) (=> (and (= D E) (exists ((G $$unsorted)) (and (= G E) (exists ((H $$unsorted)) (and (tptp.element H (tptp.the_carrier A)) (tptp.in H B) (tptp.relstr_set_smaller A G H))))) (= D F) (exists ((I $$unsorted)) (and (= I F) (exists ((J $$unsorted)) (and (tptp.element J (tptp.the_carrier A)) (tptp.in J B) (tptp.relstr_set_smaller A I J)))))) (= E F))) (exists ((D $$unsorted)) (forall ((E $$unsorted)) (= (tptp.in E D) (exists ((F $$unsorted)) (and (tptp.in F (tptp.powerset C)) (= F E) (exists ((K $$unsorted)) (and (= K E) (exists ((L $$unsorted)) (and (tptp.element L (tptp.the_carrier A)) (tptp.in L B) (tptp.relstr_set_smaller A K L))))))))))) (=> true (not (forall ((D $$unsorted)) (not (forall ((E $$unsorted)) (= (tptp.in E D) (and (not (forall ((BOUND_VARIABLE_18324 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_18324 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18324 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_18324))))) (tptp.in E (tptp.powerset C))))))))))) :rule cong :premises (t16.t17 t16.t20))
% 0.61/1.07  (step t16.t22 (cl (= (=> true (not (forall ((D $$unsorted)) (not (forall ((E $$unsorted)) (= (tptp.in E D) (and (not (forall ((BOUND_VARIABLE_18324 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_18324 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18324 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_18324))))) (tptp.in E (tptp.powerset C))))))))) (not (forall ((D $$unsorted)) (not (forall ((E $$unsorted)) (= (tptp.in E D) (and (not (forall ((BOUND_VARIABLE_18324 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_18324 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18324 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_18324))))) (tptp.in E (tptp.powerset C)))))))))) :rule all_simplify)
% 0.61/1.07  (step t16.t23 (cl (= (=> (forall ((D $$unsorted) (E $$unsorted) (F $$unsorted)) (=> (and (= D E) (exists ((G $$unsorted)) (and (= G E) (exists ((H $$unsorted)) (and (tptp.element H (tptp.the_carrier A)) (tptp.in H B) (tptp.relstr_set_smaller A G H))))) (= D F) (exists ((I $$unsorted)) (and (= I F) (exists ((J $$unsorted)) (and (tptp.element J (tptp.the_carrier A)) (tptp.in J B) (tptp.relstr_set_smaller A I J)))))) (= E F))) (exists ((D $$unsorted)) (forall ((E $$unsorted)) (= (tptp.in E D) (exists ((F $$unsorted)) (and (tptp.in F (tptp.powerset C)) (= F E) (exists ((K $$unsorted)) (and (= K E) (exists ((L $$unsorted)) (and (tptp.element L (tptp.the_carrier A)) (tptp.in L B) (tptp.relstr_set_smaller A K L))))))))))) (not (forall ((D $$unsorted)) (not (forall ((E $$unsorted)) (= (tptp.in E D) (and (not (forall ((BOUND_VARIABLE_18324 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_18324 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18324 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_18324))))) (tptp.in E (tptp.powerset C)))))))))) :rule trans :premises (t16.t21 t16.t22))
% 0.61/1.07  (step t16.t24 (cl (= (=> (and (not (tptp.empty_carrier A)) (tptp.transitive_relstr A) (tptp.rel_str A) (tptp.element B (tptp.powerset (tptp.the_carrier A))) (tptp.finite C) (tptp.element C (tptp.powerset B))) (=> (forall ((D $$unsorted) (E $$unsorted) (F $$unsorted)) (=> (and (= D E) (exists ((G $$unsorted)) (and (= G E) (exists ((H $$unsorted)) (and (tptp.element H (tptp.the_carrier A)) (tptp.in H B) (tptp.relstr_set_smaller A G H))))) (= D F) (exists ((I $$unsorted)) (and (= I F) (exists ((J $$unsorted)) (and (tptp.element J (tptp.the_carrier A)) (tptp.in J B) (tptp.relstr_set_smaller A I J)))))) (= E F))) (exists ((D $$unsorted)) (forall ((E $$unsorted)) (= (tptp.in E D) (exists ((F $$unsorted)) (and (tptp.in F (tptp.powerset C)) (= F E) (exists ((K $$unsorted)) (and (= K E) (exists ((L $$unsorted)) (and (tptp.element L (tptp.the_carrier A)) (tptp.in L B) (tptp.relstr_set_smaller A K L)))))))))))) (=> (and (not (tptp.empty_carrier A)) (tptp.transitive_relstr A) (tptp.rel_str A) (tptp.element B (tptp.powerset (tptp.the_carrier A))) (tptp.finite C) (tptp.element C (tptp.powerset B))) (not (forall ((D $$unsorted)) (not (forall ((E $$unsorted)) (= (tptp.in E D) (and (not (forall ((BOUND_VARIABLE_18324 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_18324 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18324 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_18324))))) (tptp.in E (tptp.powerset C))))))))))) :rule cong :premises (t16.t4 t16.t23))
% 0.61/1.07  (step t16 (cl (= (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.transitive_relstr A) (tptp.rel_str A) (tptp.element B (tptp.powerset (tptp.the_carrier A))) (tptp.finite C) (tptp.element C (tptp.powerset B))) (=> (forall ((D $$unsorted) (E $$unsorted) (F $$unsorted)) (=> (and (= D E) (exists ((G $$unsorted)) (and (= G E) (exists ((H $$unsorted)) (and (tptp.element H (tptp.the_carrier A)) (tptp.in H B) (tptp.relstr_set_smaller A G H))))) (= D F) (exists ((I $$unsorted)) (and (= I F) (exists ((J $$unsorted)) (and (tptp.element J (tptp.the_carrier A)) (tptp.in J B) (tptp.relstr_set_smaller A I J)))))) (= E F))) (exists ((D $$unsorted)) (forall ((E $$unsorted)) (= (tptp.in E D) (exists ((F $$unsorted)) (and (tptp.in F (tptp.powerset C)) (= F E) (exists ((K $$unsorted)) (and (= K E) (exists ((L $$unsorted)) (and (tptp.element L (tptp.the_carrier A)) (tptp.in L B) (tptp.relstr_set_smaller A K L))))))))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.transitive_relstr A) (tptp.rel_str A) (tptp.element B (tptp.powerset (tptp.the_carrier A))) (tptp.finite C) (tptp.element C (tptp.powerset B))) (not (forall ((D $$unsorted)) (not (forall ((E $$unsorted)) (= (tptp.in E D) (and (not (forall ((BOUND_VARIABLE_18324 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_18324 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18324 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_18324))))) (tptp.in E (tptp.powerset C)))))))))))) :rule bind)
% 0.61/1.07  (step t17 (cl (= (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.transitive_relstr A) (tptp.rel_str A) (tptp.element B (tptp.powerset (tptp.the_carrier A))) (tptp.finite C) (tptp.element C (tptp.powerset B))) (not (forall ((D $$unsorted)) (not (forall ((E $$unsorted)) (= (tptp.in E D) (and (not (forall ((BOUND_VARIABLE_18324 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_18324 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18324 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_18324))))) (tptp.in E (tptp.powerset C)))))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (tptp.empty_carrier A) (not (tptp.transitive_relstr A)) (not (tptp.rel_str A)) (not (tptp.element B (tptp.powerset (tptp.the_carrier A)))) (not (tptp.finite C)) (not (tptp.element C (tptp.powerset B))) (not (forall ((D $$unsorted)) (not (forall ((E $$unsorted)) (= (tptp.in E D) (and (not (forall ((BOUND_VARIABLE_18324 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_18324 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18324 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_18324))))) (tptp.in E (tptp.powerset C)))))))))))) :rule all_simplify)
% 0.61/1.07  (step t18 (cl (= (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.transitive_relstr A) (tptp.rel_str A) (tptp.element B (tptp.powerset (tptp.the_carrier A))) (tptp.finite C) (tptp.element C (tptp.powerset B))) (=> (forall ((D $$unsorted) (E $$unsorted) (F $$unsorted)) (=> (and (= D E) (exists ((G $$unsorted)) (and (= G E) (exists ((H $$unsorted)) (and (tptp.element H (tptp.the_carrier A)) (tptp.in H B) (tptp.relstr_set_smaller A G H))))) (= D F) (exists ((I $$unsorted)) (and (= I F) (exists ((J $$unsorted)) (and (tptp.element J (tptp.the_carrier A)) (tptp.in J B) (tptp.relstr_set_smaller A I J)))))) (= E F))) (exists ((D $$unsorted)) (forall ((E $$unsorted)) (= (tptp.in E D) (exists ((F $$unsorted)) (and (tptp.in F (tptp.powerset C)) (= F E) (exists ((K $$unsorted)) (and (= K E) (exists ((L $$unsorted)) (and (tptp.element L (tptp.the_carrier A)) (tptp.in L B) (tptp.relstr_set_smaller A K L))))))))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (tptp.empty_carrier A) (not (tptp.transitive_relstr A)) (not (tptp.rel_str A)) (not (tptp.element B (tptp.powerset (tptp.the_carrier A)))) (not (tptp.finite C)) (not (tptp.element C (tptp.powerset B))) (not (forall ((D $$unsorted)) (not (forall ((E $$unsorted)) (= (tptp.in E D) (and (not (forall ((BOUND_VARIABLE_18324 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_18324 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18324 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_18324))))) (tptp.in E (tptp.powerset C)))))))))))) :rule trans :premises (t16 t17))
% 0.61/1.07  (step t19 (cl (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (tptp.empty_carrier A) (not (tptp.transitive_relstr A)) (not (tptp.rel_str A)) (not (tptp.element B (tptp.powerset (tptp.the_carrier A)))) (not (tptp.finite C)) (not (tptp.element C (tptp.powerset B))) (not (forall ((D $$unsorted)) (not (forall ((E $$unsorted)) (= (tptp.in E D) (and (not (forall ((BOUND_VARIABLE_18324 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_18324 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_18324 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_18324))))) (tptp.in E (tptp.powerset C))))))))))) :rule resolution :premises (t15 t18 a446))
% 0.61/1.07  (step t20 (cl (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (tptp.empty_carrier A) (not (tptp.transitive_relstr A)) (not (tptp.rel_str A)) (not (tptp.element B (tptp.powerset (tptp.the_carrier A)))) (not (tptp.finite C)) (not (tptp.element C (tptp.powerset B))) (not (forall ((D $$unsorted)) (not (forall ((E $$unsorted)) (= (tptp.in E D) (and (tptp.in E (tptp.powerset C)) (not (forall ((BOUND_VARIABLE_20150 $$unsorted)) (or (not (tptp.element BOUND_VARIABLE_20150 (tptp.the_carrier A))) (not (tptp.in BOUND_VARIABLE_20150 B)) (not (tptp.relstr_set_smaller A E BOUND_VARIABLE_20150)))))))))))))) :rule resolution :premises (t14 t19))
% 0.61/1.07  (step t21 (cl) :rule resolution :premises (t6 t20))
% 0.61/1.07  
% 0.61/1.07  % SZS output end Proof for /export/starexec/sandbox/tmp/tmp.8bIpux7RGx/cvc5---1.0.5_21118.smt2
% 0.61/1.07  % cvc5---1.0.5 exiting
% 0.61/1.07  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------