TSTP Solution File: SEU281+2 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SEU281+2 : TPTP v8.2.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : do_cvc5 %s %d
% Computer : n007.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 17:49:05 EDT 2024
% Result : Theorem 0.46s 0.78s
% Output : Proof 0.46s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.16 % Problem : SEU281+2 : TPTP v8.2.0. Released v3.3.0.
% 0.06/0.17 % Command : do_cvc5 %s %d
% 0.17/0.38 % Computer : n007.cluster.edu
% 0.17/0.38 % Model : x86_64 x86_64
% 0.17/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.38 % Memory : 8042.1875MB
% 0.17/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.38 % CPULimit : 300
% 0.17/0.38 % WCLimit : 300
% 0.17/0.38 % DateTime : Mon May 27 08:36:54 EDT 2024
% 0.17/0.38 % CPUTime :
% 0.40/0.61 %----Proving TF0_NAR, FOF, or CNF
% 0.46/0.78 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.46/0.78 % SZS status Theorem for /export/starexec/sandbox/tmp/tmp.v0C41eryKi/cvc5---1.0.5_13750.smt2
% 0.46/0.78 % SZS output start Proof for /export/starexec/sandbox/tmp/tmp.v0C41eryKi/cvc5---1.0.5_13750.smt2
% 0.46/0.78 (assume a0 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (not (tptp.in B A)))))
% 0.46/0.78 (assume a1 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.proper_subset A B) (not (tptp.proper_subset B A)))))
% 0.46/0.78 (assume a2 (forall ((A $$unsorted)) (=> (tptp.empty A) (tptp.function A))))
% 0.46/0.78 (assume a3 (forall ((A $$unsorted)) (=> (tptp.ordinal A) (and (tptp.epsilon_transitive A) (tptp.epsilon_connected A)))))
% 0.46/0.78 (assume a4 (forall ((A $$unsorted)) (=> (tptp.empty A) (tptp.relation A))))
% 0.46/0.78 (assume a5 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.element C (tptp.powerset (tptp.cartesian_product2 A B))) (tptp.relation C))))
% 0.46/0.78 (assume a6 (forall ((A $$unsorted)) (=> (and (tptp.relation A) (tptp.empty A) (tptp.function A)) (and (tptp.relation A) (tptp.function A) (tptp.one_to_one A)))))
% 0.46/0.78 (assume a7 (forall ((A $$unsorted)) (=> (and (tptp.epsilon_transitive A) (tptp.epsilon_connected A)) (tptp.ordinal A))))
% 0.46/0.78 (assume a8 (forall ((A $$unsorted)) (=> (tptp.empty A) (and (tptp.epsilon_transitive A) (tptp.epsilon_connected A) (tptp.ordinal A)))))
% 0.46/0.78 (assume a9 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.unordered_pair A B) (tptp.unordered_pair B A))))
% 0.46/0.78 (assume a10 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_union2 A B) (tptp.set_union2 B A))))
% 0.46/0.78 (assume a11 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_intersection2 A B) (tptp.set_intersection2 B A))))
% 0.46/0.78 (assume a12 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.ordinal A) (tptp.ordinal B)) (or (tptp.ordinal_subset A B) (tptp.ordinal_subset B A)))))
% 0.46/0.78 (assume a13 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (= (= B (tptp.identity_relation A)) (forall ((C $$unsorted) (D $$unsorted)) (= (tptp.in (tptp.ordered_pair C D) B) (and (tptp.in C A) (= C D))))))))
% 0.46/0.78 (assume a14 (forall ((A $$unsorted) (B $$unsorted)) (= (= A B) (and (tptp.subset A B) (tptp.subset B A)))))
% 0.46/0.78 (assume a15 (forall ((A $$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))))))))))
% 0.46/0.78 (assume a16 (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 $$unsorted)) (and (tptp.in E (tptp.relation_dom A)) (tptp.in E B) (= D (tptp.apply A E)))))))))))
% 0.46/0.78 (assume a17 (forall ((A $$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))))))))))
% 0.46/0.78 (assume a18 (forall ((A $$unsorted)) (=> (tptp.relation A) (= (tptp.antisymmetric A) (tptp.is_antisymmetric_in A (tptp.relation_field A))))))
% 0.46/0.78 (assume a19 (forall ((A $$unsorted)) (=> (and (tptp.relation A) (tptp.function A)) (forall ((B $$unsorted) (C $$unsorted)) (= (= C (tptp.relation_inverse_image A B)) (forall ((D $$unsorted)) (= (tptp.in D C) (and (tptp.in D (tptp.relation_dom A)) (tptp.in (tptp.apply A D) B)))))))))
% 0.46/0.78 (assume a20 (forall ((A $$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))))))))))
% 0.46/0.78 (assume a21 (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 $$unsorted)) (and (tptp.in (tptp.ordered_pair D E) A) (tptp.in E B))))))))))
% 0.46/0.78 (assume a22 (forall ((A $$unsorted)) (=> (tptp.relation A) (= (tptp.connected A) (tptp.is_connected_in A (tptp.relation_field A))))))
% 0.46/0.78 (assume a23 (forall ((A $$unsorted)) (=> (tptp.relation A) (= (tptp.transitive A) (tptp.is_transitive_in A (tptp.relation_field A))))))
% 0.46/0.78 (assume a24 (forall ((A $$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)))))))))
% 0.46/0.78 (assume a25 (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))))))))
% 0.46/0.78 (assume a26 (forall ((A $$unsorted)) (= (tptp.succ A) (tptp.set_union2 A (tptp.singleton A)))))
% 0.46/0.78 (assume a27 (forall ((A $$unsorted)) (= (tptp.relation A) (forall ((B $$unsorted)) (not (and (tptp.in B A) (forall ((C $$unsorted) (D $$unsorted)) (not (= B (tptp.ordered_pair C D))))))))))
% 0.46/0.78 (assume a28 (forall ((A $$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))))))))
% 0.46/0.78 (assume a29 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.relation_of2 C A B) (tptp.subset C (tptp.cartesian_product2 A B)))))
% 0.46/0.78 (assume a30 (forall ((A $$unsorted) (B $$unsorted)) (and (=> (not (= A tptp.empty_set)) (= (= B (tptp.set_meet A)) (forall ((C $$unsorted)) (= (tptp.in C B) (forall ((D $$unsorted)) (=> (tptp.in D A) (tptp.in C D))))))) (=> (= A tptp.empty_set) (= (= B (tptp.set_meet A)) (= B tptp.empty_set))))))
% 0.46/0.78 (assume a31 (forall ((A $$unsorted) (B $$unsorted)) (= (= B (tptp.singleton A)) (forall ((C $$unsorted)) (= (tptp.in C B) (= C A))))))
% 0.46/0.78 (assume a32 (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)))))))))
% 0.46/0.78 (assume a33 (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)))))))))
% 0.46/0.78 (assume a34 (forall ((A $$unsorted)) (= (= A tptp.empty_set) (forall ((B $$unsorted)) (not (tptp.in B A))))))
% 0.46/0.78 (assume a35 (forall ((A $$unsorted) (B $$unsorted)) (= (= B (tptp.powerset A)) (forall ((C $$unsorted)) (= (tptp.in C B) (tptp.subset C A))))))
% 0.46/0.78 (assume a36 (forall ((A $$unsorted)) (=> (exists ((B $$unsorted) (C $$unsorted)) (= A (tptp.ordered_pair B C))) (forall ((B $$unsorted)) (= (= B (tptp.pair_second A)) (forall ((C $$unsorted) (D $$unsorted)) (=> (= A (tptp.ordered_pair C D)) (= B D))))))))
% 0.46/0.78 (assume a37 (forall ((A $$unsorted)) (= (tptp.epsilon_transitive A) (forall ((B $$unsorted)) (=> (tptp.in B A) (tptp.subset B A))))))
% 0.46/0.78 (assume a38 (forall ((A $$unsorted)) (=> (tptp.relation A) (forall ((B $$unsorted)) (=> (tptp.relation B) (= (= A B) (forall ((C $$unsorted) (D $$unsorted)) (= (tptp.in (tptp.ordered_pair C D) A) (tptp.in (tptp.ordered_pair C D) B)))))))))
% 0.46/0.78 (assume a39 (forall ((A $$unsorted) (B $$unsorted)) (and (=> (not (tptp.empty A)) (= (tptp.element B A) (tptp.in B A))) (=> (tptp.empty A) (= (tptp.element B A) (tptp.empty B))))))
% 0.46/0.78 (assume a40 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (= C (tptp.unordered_pair A B)) (forall ((D $$unsorted)) (= (tptp.in D C) (or (= D A) (= D B)))))))
% 0.46/0.78 (assume a41 (forall ((A $$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)))))))))))
% 0.46/0.78 (assume a42 (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)))))))
% 0.46/0.78 (assume a43 (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)))))))))
% 0.46/0.78 (assume a44 (forall ((A $$unsorted)) (= (tptp.epsilon_connected A) (forall ((B $$unsorted) (C $$unsorted)) (not (and (tptp.in B A) (tptp.in C A) (not (tptp.in B C)) (not (= B C)) (not (tptp.in C B))))))))
% 0.46/0.78 (assume a45 (forall ((A $$unsorted)) (=> (tptp.relation A) (forall ((B $$unsorted)) (=> (tptp.relation B) (= (tptp.subset A B) (forall ((C $$unsorted) (D $$unsorted)) (=> (tptp.in (tptp.ordered_pair C D) A) (tptp.in (tptp.ordered_pair C D) B)))))))))
% 0.46/0.78 (assume a46 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset A B) (forall ((C $$unsorted)) (=> (tptp.in C A) (tptp.in C B))))))
% 0.46/0.78 (assume a47 (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))))))))))))
% 0.46/0.78 (assume a48 (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)))))))
% 0.46/0.78 (assume a49 (forall ((A $$unsorted)) (=> (and (tptp.relation A) (tptp.function A)) (forall ((B $$unsorted) (C $$unsorted)) (and (=> (tptp.in B (tptp.relation_dom A)) (= (= C (tptp.apply A B)) (tptp.in (tptp.ordered_pair B C) A))) (=> (not (tptp.in B (tptp.relation_dom A))) (= (= C (tptp.apply A B)) (= C tptp.empty_set))))))))
% 0.46/0.78 (assume a50 (forall ((A $$unsorted)) (= (tptp.ordinal A) (and (tptp.epsilon_transitive A) (tptp.epsilon_connected A)))))
% 0.46/0.78 (assume a51 (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)))))))))
% 0.46/0.78 (assume a52 (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))))))))
% 0.46/0.78 (assume a53 (forall ((A $$unsorted)) (= (tptp.cast_to_subset A) A)))
% 0.46/0.78 (assume a54 (forall ((A $$unsorted) (B $$unsorted)) (= (= B (tptp.union A)) (forall ((C $$unsorted)) (= (tptp.in C B) (exists ((D $$unsorted)) (and (tptp.in C D) (tptp.in D A))))))))
% 0.46/0.78 (assume a55 (forall ((A $$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))))))
% 0.46/0.78 (assume a56 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.equipotent A B) (exists ((C $$unsorted)) (and (tptp.relation C) (tptp.function C) (tptp.one_to_one C) (= (tptp.relation_dom C) A) (= (tptp.relation_rng C) B))))))
% 0.46/0.78 (assume a57 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (= C (tptp.set_difference A B)) (forall ((D $$unsorted)) (= (tptp.in D C) (and (tptp.in D A) (not (tptp.in D B))))))))
% 0.46/0.78 (assume a58 (forall ((A $$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 $$unsorted)) (and (tptp.in D (tptp.relation_dom A)) (= C (tptp.apply A D)))))))))))
% 0.46/0.78 (assume a59 (forall ((A $$unsorted)) (=> (tptp.relation A) (forall ((B $$unsorted)) (= (= B (tptp.relation_rng A)) (forall ((C $$unsorted)) (= (tptp.in C B) (exists ((D $$unsorted)) (tptp.in (tptp.ordered_pair D C) A)))))))))
% 0.46/0.78 (assume a60 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element B (tptp.powerset A)) (= (tptp.subset_complement A B) (tptp.set_difference A B)))))
% 0.46/0.78 (assume a61 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.ordered_pair A B) (tptp.unordered_pair (tptp.unordered_pair A B) (tptp.singleton A)))))
% 0.46/0.78 (assume a62 (forall ((A $$unsorted)) (=> (tptp.relation A) (forall ((B $$unsorted)) (= (tptp.well_orders A B) (and (tptp.is_reflexive_in A B) (tptp.is_transitive_in A B) (tptp.is_antisymmetric_in A B) (tptp.is_connected_in A B) (tptp.is_well_founded_in A B)))))))
% 0.46/0.78 (assume a63 (forall ((A $$unsorted)) (= (tptp.being_limit_ordinal A) (= A (tptp.union A)))))
% 0.46/0.78 (assume a64 (forall ((A $$unsorted)) (=> (tptp.relation A) (= (tptp.relation_field A) (tptp.set_union2 (tptp.relation_dom A) (tptp.relation_rng A))))))
% 0.46/0.78 (assume a65 (forall ((A $$unsorted)) (=> (tptp.relation A) (forall ((B $$unsorted)) (= (tptp.is_connected_in A B) (forall ((C $$unsorted) (D $$unsorted)) (not (and (tptp.in C B) (tptp.in D B) (not (= C D)) (not (tptp.in (tptp.ordered_pair C D) A)) (not (tptp.in (tptp.ordered_pair D C) A))))))))))
% 0.46/0.78 (assume a66 (forall ((A $$unsorted)) (=> (tptp.relation A) (forall ((B $$unsorted)) (= (tptp.relation_restriction A B) (tptp.set_intersection2 A (tptp.cartesian_product2 B B)))))))
% 0.46/0.78 (assume a67 (forall ((A $$unsorted)) (=> (tptp.relation A) (forall ((B $$unsorted)) (=> (tptp.relation B) (= (= B (tptp.relation_inverse A)) (forall ((C $$unsorted) (D $$unsorted)) (= (tptp.in (tptp.ordered_pair C D) B) (tptp.in (tptp.ordered_pair D C) A)))))))))
% 0.46/0.78 (assume a68 (forall ((A $$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)))))))))))))
% 0.46/0.78 (assume a69 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.disjoint A B) (= (tptp.set_intersection2 A B) tptp.empty_set))))
% 0.46/0.78 (assume a70 (forall ((A $$unsorted)) (=> (and (tptp.relation A) (tptp.function A)) (= (tptp.one_to_one A) (forall ((B $$unsorted) (C $$unsorted)) (=> (and (tptp.in B (tptp.relation_dom A)) (tptp.in C (tptp.relation_dom A)) (= (tptp.apply A B) (tptp.apply A C))) (= B C)))))))
% 0.46/0.78 (assume a71 (forall ((A $$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 $$unsorted)) (and (tptp.in (tptp.ordered_pair D F) A) (tptp.in (tptp.ordered_pair F E) B)))))))))))))
% 0.46/0.78 (assume a72 (forall ((A $$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))))))))
% 0.46/0.78 (assume a73 (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))))))))))
% 0.46/0.78 (assume a74 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.proper_subset A B) (and (tptp.subset A B) (not (= A B))))))
% 0.46/0.78 (assume a75 (forall ((A $$unsorted)) (=> (and (tptp.relation A) (tptp.function A)) (=> (tptp.one_to_one A) (= (tptp.function_inverse A) (tptp.relation_inverse A))))))
% 0.46/0.78 (assume a76 (forall ((A $$unsorted)) (=> (tptp.relation A) (= (tptp.reflexive A) (tptp.is_reflexive_in A (tptp.relation_field A))))))
% 0.46/0.78 (assume a77 true)
% 0.46/0.78 (assume a78 true)
% 0.46/0.78 (assume a79 true)
% 0.46/0.78 (assume a80 true)
% 0.46/0.78 (assume a81 true)
% 0.46/0.78 (assume a82 true)
% 0.46/0.78 (assume a83 true)
% 0.46/0.78 (assume a84 true)
% 0.46/0.78 (assume a85 true)
% 0.46/0.78 (assume a86 (forall ((A $$unsorted)) (tptp.relation (tptp.inclusion_relation A))))
% 0.46/0.78 (assume a87 true)
% 0.46/0.78 (assume a88 true)
% 0.46/0.78 (assume a89 (forall ((A $$unsorted)) (=> (and (tptp.relation A) (tptp.function A)) (and (tptp.relation (tptp.function_inverse A)) (tptp.function (tptp.function_inverse A))))))
% 0.46/0.78 (assume a90 true)
% 0.46/0.78 (assume a91 true)
% 0.46/0.78 (assume a92 (forall ((A $$unsorted)) (tptp.element (tptp.cast_to_subset A) (tptp.powerset A))))
% 0.46/0.78 (assume a93 true)
% 0.46/0.78 (assume a94 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation A) (tptp.relation (tptp.relation_restriction A B)))))
% 0.46/0.78 (assume a95 true)
% 0.46/0.78 (assume a96 true)
% 0.46/0.78 (assume a97 true)
% 0.46/0.78 (assume a98 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element B (tptp.powerset A)) (tptp.element (tptp.subset_complement A B) (tptp.powerset A)))))
% 0.46/0.78 (assume a99 true)
% 0.46/0.78 (assume a100 true)
% 0.46/0.78 (assume a101 (forall ((A $$unsorted)) (=> (tptp.relation A) (tptp.relation (tptp.relation_inverse A)))))
% 0.46/0.78 (assume a102 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.relation_of2 C A B) (tptp.element (tptp.relation_dom_as_subset A B C) (tptp.powerset A)))))
% 0.46/0.78 (assume a103 true)
% 0.46/0.78 (assume a104 true)
% 0.46/0.78 (assume a105 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.relation A) (tptp.relation B)) (tptp.relation (tptp.relation_composition A B)))))
% 0.46/0.78 (assume a106 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.relation_of2 C A B) (tptp.element (tptp.relation_rng_as_subset A B C) (tptp.powerset B)))))
% 0.46/0.78 (assume a107 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element B (tptp.powerset (tptp.powerset A))) (tptp.element (tptp.union_of_subsets A B) (tptp.powerset A)))))
% 0.46/0.78 (assume a108 (forall ((A $$unsorted)) (tptp.relation (tptp.identity_relation A))))
% 0.46/0.78 (assume a109 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element B (tptp.powerset (tptp.powerset A))) (tptp.element (tptp.meet_of_subsets A B) (tptp.powerset A)))))
% 0.46/0.78 (assume a110 (forall ((A $$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)))))
% 0.46/0.78 (assume a111 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation A) (tptp.relation (tptp.relation_dom_restriction A B)))))
% 0.46/0.78 (assume a112 (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))))))
% 0.46/0.78 (assume a113 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (tptp.relation (tptp.relation_rng_restriction A B)))))
% 0.46/0.78 (assume a114 true)
% 0.46/0.78 (assume a115 true)
% 0.46/0.78 (assume a116 true)
% 0.46/0.78 (assume a117 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.relation_of2_as_subset C A B) (tptp.element C (tptp.powerset (tptp.cartesian_product2 A B))))))
% 0.46/0.78 (assume a118 (forall ((A $$unsorted) (B $$unsorted)) (exists ((C $$unsorted)) (tptp.relation_of2 C A B))))
% 0.46/0.78 (assume a119 (forall ((A $$unsorted)) (exists ((B $$unsorted)) (tptp.element B A))))
% 0.46/0.78 (assume a120 (forall ((A $$unsorted) (B $$unsorted)) (exists ((C $$unsorted)) (tptp.relation_of2_as_subset C A B))))
% 0.46/0.78 (assume a121 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.empty A) (tptp.relation B)) (and (tptp.empty (tptp.relation_composition B A)) (tptp.relation (tptp.relation_composition B A))))))
% 0.46/0.78 (assume a122 (forall ((A $$unsorted)) (=> (tptp.empty A) (and (tptp.empty (tptp.relation_inverse A)) (tptp.relation (tptp.relation_inverse A))))))
% 0.46/0.78 (assume a123 (and (tptp.empty tptp.empty_set) (tptp.relation tptp.empty_set) (tptp.relation_empty_yielding tptp.empty_set)))
% 0.46/0.78 (assume a124 (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))))))
% 0.46/0.78 (assume a125 (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))))))
% 0.46/0.78 (assume a126 (forall ((A $$unsorted)) (not (tptp.empty (tptp.succ A)))))
% 0.46/0.78 (assume a127 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.relation A) (tptp.relation B)) (tptp.relation (tptp.set_intersection2 A B)))))
% 0.46/0.78 (assume a128 (forall ((A $$unsorted)) (not (tptp.empty (tptp.powerset A)))))
% 0.46/0.78 (assume a129 (tptp.empty tptp.empty_set))
% 0.46/0.78 (assume a130 (forall ((A $$unsorted) (B $$unsorted)) (not (tptp.empty (tptp.ordered_pair A B)))))
% 0.46/0.78 (assume a131 (forall ((A $$unsorted)) (and (tptp.relation (tptp.identity_relation A)) (tptp.function (tptp.identity_relation A)))))
% 0.46/0.78 (assume a132 (and (tptp.relation tptp.empty_set) (tptp.relation_empty_yielding tptp.empty_set) (tptp.function tptp.empty_set) (tptp.one_to_one tptp.empty_set) (tptp.empty tptp.empty_set) (tptp.epsilon_transitive tptp.empty_set) (tptp.epsilon_connected tptp.empty_set) (tptp.ordinal tptp.empty_set)))
% 0.46/0.78 (assume a133 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.relation A) (tptp.relation B)) (tptp.relation (tptp.set_union2 A B)))))
% 0.46/0.78 (assume a134 (forall ((A $$unsorted)) (not (tptp.empty (tptp.singleton A)))))
% 0.46/0.78 (assume a135 (forall ((A $$unsorted) (B $$unsorted)) (=> (not (tptp.empty A)) (not (tptp.empty (tptp.set_union2 A B))))))
% 0.46/0.78 (assume a136 (forall ((A $$unsorted)) (=> (and (tptp.relation A) (tptp.function A) (tptp.one_to_one A)) (and (tptp.relation (tptp.relation_inverse A)) (tptp.function (tptp.relation_inverse A))))))
% 0.46/0.78 (assume a137 (forall ((A $$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))))))
% 0.46/0.78 (assume a138 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.relation A) (tptp.relation B)) (tptp.relation (tptp.set_difference A B)))))
% 0.46/0.78 (assume a139 (forall ((A $$unsorted) (B $$unsorted)) (not (tptp.empty (tptp.unordered_pair A B)))))
% 0.46/0.78 (assume a140 (forall ((A $$unsorted) (B $$unsorted)) (=> (not (tptp.empty A)) (not (tptp.empty (tptp.set_union2 B A))))))
% 0.46/0.78 (assume a141 (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))))))
% 0.46/0.78 (assume a142 (forall ((A $$unsorted)) (=> (tptp.ordinal A) (and (tptp.epsilon_transitive (tptp.union A)) (tptp.epsilon_connected (tptp.union A)) (tptp.ordinal (tptp.union A))))))
% 0.46/0.78 (assume a143 (and (tptp.empty tptp.empty_set) (tptp.relation tptp.empty_set)))
% 0.46/0.78 (assume a144 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.empty A)) (not (tptp.empty B))) (not (tptp.empty (tptp.cartesian_product2 A B))))))
% 0.46/0.78 (assume a145 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.relation B) (tptp.function B)) (and (tptp.relation (tptp.relation_rng_restriction A B)) (tptp.function (tptp.relation_rng_restriction A B))))))
% 0.46/0.78 (assume a146 (forall ((A $$unsorted)) (=> (and (not (tptp.empty A)) (tptp.relation A)) (not (tptp.empty (tptp.relation_dom A))))))
% 0.46/0.78 (assume a147 (forall ((A $$unsorted)) (=> (and (not (tptp.empty A)) (tptp.relation A)) (not (tptp.empty (tptp.relation_rng A))))))
% 0.46/0.78 (assume a148 (forall ((A $$unsorted)) (=> (tptp.empty A) (and (tptp.empty (tptp.relation_dom A)) (tptp.relation (tptp.relation_dom A))))))
% 0.46/0.78 (assume a149 (forall ((A $$unsorted)) (=> (tptp.empty A) (and (tptp.empty (tptp.relation_rng A)) (tptp.relation (tptp.relation_rng A))))))
% 0.46/0.78 (assume a150 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.empty A) (tptp.relation B)) (and (tptp.empty (tptp.relation_composition A B)) (tptp.relation (tptp.relation_composition A B))))))
% 0.46/0.78 (assume a151 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_union2 A A) A)))
% 0.46/0.78 (assume a152 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_intersection2 A A) A)))
% 0.46/0.78 (assume a153 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element B (tptp.powerset A)) (= (tptp.subset_complement A (tptp.subset_complement A B)) B))))
% 0.46/0.78 (assume a154 (forall ((A $$unsorted)) (=> (tptp.relation A) (= (tptp.relation_inverse (tptp.relation_inverse A)) A))))
% 0.46/0.78 (assume a155 (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))))
% 0.46/0.78 (assume a156 (forall ((A $$unsorted) (B $$unsorted)) (not (tptp.proper_subset A A))))
% 0.46/0.78 (assume a157 (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)))))))
% 0.46/0.78 (assume a158 (forall ((A $$unsorted)) (not (= (tptp.singleton A) tptp.empty_set))))
% 0.46/0.78 (assume a159 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (= (tptp.set_union2 (tptp.singleton A) B) B))))
% 0.46/0.78 (assume a160 (forall ((A $$unsorted) (B $$unsorted)) (not (and (tptp.disjoint (tptp.singleton A) B) (tptp.in A B)))))
% 0.46/0.78 (assume a161 (forall ((A $$unsorted) (B $$unsorted)) (=> (not (tptp.in A B)) (tptp.disjoint (tptp.singleton A) B))))
% 0.46/0.78 (assume a162 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (tptp.subset (tptp.relation_dom (tptp.relation_rng_restriction A B)) (tptp.relation_dom B)))))
% 0.46/0.78 (assume a163 (forall ((A $$unsorted)) (=> (tptp.relation A) (= (tptp.transitive A) (forall ((B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (tptp.in (tptp.ordered_pair B C) A) (tptp.in (tptp.ordered_pair C D) A)) (tptp.in (tptp.ordered_pair B D) A)))))))
% 0.46/0.78 (assume a164 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset (tptp.singleton A) B) (tptp.in A B))))
% 0.46/0.78 (assume a165 (forall ((A $$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)))))))))
% 0.46/0.78 (assume a166 (forall ((A $$unsorted) (B $$unsorted)) (= (= (tptp.set_difference A B) tptp.empty_set) (tptp.subset A B))))
% 0.46/0.78 (assume a167 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element B (tptp.powerset A)) (forall ((C $$unsorted)) (=> (tptp.in C B) (tptp.in C A))))))
% 0.46/0.78 (assume a168 (forall ((A $$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)))))))
% 0.46/0.78 (assume a169 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.subset A B) (or (tptp.in C A) (tptp.subset A (tptp.set_difference B (tptp.singleton C)))))))
% 0.46/0.78 (assume a170 (forall ((A $$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)))))))))
% 0.46/0.78 (assume a171 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset A (tptp.singleton B)) (or (= A tptp.empty_set) (= A (tptp.singleton B))))))
% 0.46/0.78 (assume a172 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (tptp.subset A (tptp.union B)))))
% 0.46/0.78 (assume a173 (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)))))
% 0.46/0.78 (assume a174 (forall ((A $$unsorted) (B $$unsorted)) (=> (forall ((C $$unsorted)) (=> (tptp.in C A) (tptp.in C B))) (tptp.element A (tptp.powerset B)))))
% 0.46/0.78 (assume a175 (forall ((A $$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))))))
% 0.46/0.78 (assume a176 (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.function A))))
% 0.46/0.78 (assume a177 (exists ((A $$unsorted)) (and (tptp.epsilon_transitive A) (tptp.epsilon_connected A) (tptp.ordinal A))))
% 0.46/0.78 (assume a178 (exists ((A $$unsorted)) (and (tptp.empty A) (tptp.relation A))))
% 0.46/0.78 (assume a179 (forall ((A $$unsorted)) (=> (not (tptp.empty A)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset A)) (not (tptp.empty B)))))))
% 0.46/0.78 (assume a180 (exists ((A $$unsorted)) (tptp.empty A)))
% 0.46/0.78 (assume a181 (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.empty A) (tptp.function A))))
% 0.46/0.78 (assume a182 (exists ((A $$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))))
% 0.46/0.78 (assume a183 (exists ((A $$unsorted)) (and (not (tptp.empty A)) (tptp.relation A))))
% 0.46/0.78 (assume a184 (forall ((A $$unsorted)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset A)) (tptp.empty B)))))
% 0.46/0.78 (assume a185 (exists ((A $$unsorted)) (not (tptp.empty A))))
% 0.46/0.78 (assume a186 (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.function A) (tptp.one_to_one A))))
% 0.46/0.78 (assume a187 (exists ((A $$unsorted)) (and (not (tptp.empty A)) (tptp.epsilon_transitive A) (tptp.epsilon_connected A) (tptp.ordinal A))))
% 0.46/0.78 (assume a188 (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.relation_empty_yielding A))))
% 0.46/0.78 (assume a189 (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.relation_empty_yielding A) (tptp.function A))))
% 0.46/0.78 (assume a190 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.relation_of2 C A B) (= (tptp.relation_dom_as_subset A B C) (tptp.relation_dom C)))))
% 0.46/0.78 (assume a191 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.relation_of2 C A B) (= (tptp.relation_rng_as_subset A B C) (tptp.relation_rng C)))))
% 0.46/0.78 (assume a192 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element B (tptp.powerset (tptp.powerset A))) (= (tptp.union_of_subsets A B) (tptp.union B)))))
% 0.46/0.78 (assume a193 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element B (tptp.powerset (tptp.powerset A))) (= (tptp.meet_of_subsets A B) (tptp.set_meet B)))))
% 0.46/0.78 (assume a194 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.element B (tptp.powerset A)) (tptp.element C (tptp.powerset A))) (= (tptp.subset_difference A B C) (tptp.set_difference B C)))))
% 0.46/0.78 (assume a195 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.relation_of2_as_subset C A B) (tptp.relation_of2 C A B))))
% 0.46/0.78 (assume a196 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.ordinal A) (tptp.ordinal B)) (= (tptp.ordinal_subset A B) (tptp.subset A B)))))
% 0.46/0.78 (assume a197 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.equipotent A B) (tptp.are_equipotent A B))))
% 0.46/0.78 (assume a198 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.ordinal A) (tptp.ordinal B)) (tptp.ordinal_subset A A))))
% 0.46/0.78 (assume a199 (forall ((A $$unsorted) (B $$unsorted)) (tptp.subset A A)))
% 0.46/0.78 (assume a200 (forall ((A $$unsorted) (B $$unsorted)) (tptp.equipotent A A)))
% 0.46/0.78 (assume a201 (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)))))))))
% 0.46/0.78 (assume a202 (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)))))))))
% 0.46/0.78 (assume a203 (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))))))))))))
% 0.46/0.78 (assume a204 (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 $$unsorted)) (and (= E (tptp.ordered_pair K L)) (tptp.in (tptp.ordered_pair (tptp.apply C K) (tptp.apply C L)) B))))))))))))
% 0.46/0.78 (assume a205 (forall ((A $$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)))))))))
% 0.46/0.78 (assume a206 (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 $$unsorted)) (and (tptp.ordinal H) (= D H) (tptp.in H A))))))))))))
% 0.46/0.78 (assume a207 (not (forall ((A $$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 $$unsorted)) (and (= (tptp.ordered_pair E F) D) (tptp.in E A) (= F (tptp.singleton E)))))))))))
% 0.46/0.78 (assume a208 (forall ((A $$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))))))))))
% 0.46/0.78 (assume a209 (forall ((A $$unsorted)) (exists ((B $$unsorted)) (forall ((C $$unsorted)) (= (tptp.in C B) (and (tptp.in C A) (tptp.ordinal C)))))))
% 0.46/0.78 (assume a210 (forall ((A $$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))))))))))
% 0.46/0.78 (assume a211 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.disjoint A B) (tptp.disjoint B A))))
% 0.46/0.78 (assume a212 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.equipotent A B) (tptp.equipotent B A))))
% 0.46/0.78 (assume a213 (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)))))
% 0.46/0.78 (assume a214 (forall ((A $$unsorted)) (tptp.in A (tptp.succ A))))
% 0.46/0.78 (assume a215 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (not (and (= (tptp.unordered_pair A B) (tptp.unordered_pair C D)) (not (= A C)) (not (= A D))))))
% 0.46/0.78 (assume a216 (forall ((A $$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)))))))
% 0.46/0.78 (assume a217 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (tptp.subset (tptp.relation_rng (tptp.relation_rng_restriction A B)) A))))
% 0.46/0.78 (assume a218 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (tptp.subset (tptp.relation_rng_restriction A B) B))))
% 0.46/0.78 (assume a219 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (tptp.subset (tptp.relation_rng (tptp.relation_rng_restriction A B)) (tptp.relation_rng B)))))
% 0.46/0.78 (assume a220 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.subset A B) (and (tptp.subset (tptp.cartesian_product2 A C) (tptp.cartesian_product2 B C)) (tptp.subset (tptp.cartesian_product2 C A) (tptp.cartesian_product2 C B))))))
% 0.46/0.78 (assume a221 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (= (tptp.relation_rng (tptp.relation_rng_restriction A B)) (tptp.set_intersection2 (tptp.relation_rng B) A)))))
% 0.46/0.78 (assume a222 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (tptp.subset A B) (tptp.subset C D)) (tptp.subset (tptp.cartesian_product2 A C) (tptp.cartesian_product2 B D)))))
% 0.46/0.78 (assume a223 (forall ((A $$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)))))
% 0.46/0.78 (assume a224 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.subset A B) (= (tptp.set_union2 A B) B))))
% 0.46/0.78 (assume a225 (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)))))))))
% 0.46/0.78 (assume a226 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.relation C) (= (tptp.relation_dom_restriction (tptp.relation_rng_restriction A C) B) (tptp.relation_rng_restriction A (tptp.relation_dom_restriction C B))))))
% 0.46/0.78 (assume a227 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.relation C) (= (tptp.in A (tptp.relation_image C B)) (exists ((D $$unsorted)) (and (tptp.in D (tptp.relation_dom C)) (tptp.in (tptp.ordered_pair D A) C) (tptp.in D B)))))))
% 0.46/0.78 (assume a228 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (tptp.subset (tptp.relation_image B A) (tptp.relation_rng B)))))
% 0.46/0.78 (assume a229 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.relation B) (tptp.function B)) (tptp.subset (tptp.relation_image B (tptp.relation_inverse_image B A)) A))))
% 0.46/0.78 (assume a230 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (= (tptp.relation_image B A) (tptp.relation_image B (tptp.set_intersection2 (tptp.relation_dom B) A))))))
% 0.46/0.78 (assume a231 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (=> (tptp.subset A (tptp.relation_dom B)) (tptp.subset A (tptp.relation_inverse_image B (tptp.relation_image B A)))))))
% 0.46/0.78 (assume a232 (forall ((A $$unsorted)) (=> (tptp.relation A) (= (tptp.relation_image A (tptp.relation_dom A)) (tptp.relation_rng A)))))
% 0.46/0.78 (assume a233 (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)))))
% 0.46/0.78 (assume a234 (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)))))
% 0.46/0.78 (assume a235 (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))))))))
% 0.46/0.78 (assume a236 (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)))))))
% 0.46/0.78 (assume a237 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (tptp.subset (tptp.relation_inverse_image B A) (tptp.relation_dom B)))))
% 0.46/0.78 (assume a238 (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)))))
% 0.46/0.78 (assume a239 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.relation C) (= (tptp.in A (tptp.relation_restriction C B)) (and (tptp.in A C) (tptp.in A (tptp.cartesian_product2 B B)))))))
% 0.46/0.78 (assume a240 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (not (and (not (= A tptp.empty_set)) (tptp.subset A (tptp.relation_rng B)) (= (tptp.relation_inverse_image B A) tptp.empty_set))))))
% 0.46/0.78 (assume a241 (forall ((A $$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))))))
% 0.46/0.78 (assume a242 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (= (tptp.relation_restriction B A) (tptp.relation_dom_restriction (tptp.relation_rng_restriction A B) A)))))
% 0.46/0.78 (assume a243 (forall ((A $$unsorted) (B $$unsorted)) (tptp.subset (tptp.set_intersection2 A B) A)))
% 0.46/0.78 (assume a244 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (= (tptp.relation_restriction B A) (tptp.relation_rng_restriction A (tptp.relation_dom_restriction B A))))))
% 0.46/0.78 (assume a245 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.relation C) (=> (tptp.in A (tptp.relation_field (tptp.relation_restriction C B))) (and (tptp.in A (tptp.relation_field C)) (tptp.in A B))))))
% 0.46/0.78 (assume a246 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.subset A B) (tptp.subset A C)) (tptp.subset A (tptp.set_intersection2 B C)))))
% 0.46/0.78 (assume a247 (forall ((A $$unsorted)) (= (tptp.set_union2 A tptp.empty_set) A)))
% 0.46/0.78 (assume a248 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (tptp.element A B))))
% 0.46/0.78 (assume a249 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.subset A B) (tptp.subset B C)) (tptp.subset A C))))
% 0.46/0.78 (assume a250 (= (tptp.powerset tptp.empty_set) (tptp.singleton tptp.empty_set)))
% 0.46/0.78 (assume a251 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.relation C) (=> (tptp.in (tptp.ordered_pair A B) C) (and (tptp.in A (tptp.relation_dom C)) (tptp.in B (tptp.relation_rng C)))))))
% 0.46/0.78 (assume a252 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (and (tptp.subset (tptp.relation_field (tptp.relation_restriction B A)) (tptp.relation_field B)) (tptp.subset (tptp.relation_field (tptp.relation_restriction B A)) A)))))
% 0.46/0.78 (assume a253 (forall ((A $$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)))))))))
% 0.46/0.78 (assume a254 (forall ((A $$unsorted)) (=> (tptp.epsilon_transitive A) (forall ((B $$unsorted)) (=> (tptp.ordinal B) (=> (tptp.proper_subset A B) (tptp.in A B)))))))
% 0.46/0.78 (assume a255 (forall ((A $$unsorted)) (=> (tptp.relation A) (tptp.subset A (tptp.cartesian_product2 (tptp.relation_dom A) (tptp.relation_rng A))))))
% 0.46/0.78 (assume a256 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.relation C) (tptp.subset (tptp.fiber (tptp.relation_restriction C A) B) (tptp.fiber C B)))))
% 0.46/0.78 (assume a257 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.relation B) (tptp.function B)) (forall ((C $$unsorted)) (=> (and (tptp.relation C) (tptp.function C)) (=> (tptp.in A (tptp.relation_dom (tptp.relation_composition C B))) (= (tptp.apply (tptp.relation_composition C B) A) (tptp.apply B (tptp.apply C A)))))))))
% 0.46/0.78 (assume a258 (forall ((A $$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)))))
% 0.46/0.78 (assume a259 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (=> (tptp.reflexive B) (tptp.reflexive (tptp.relation_restriction B A))))))
% 0.46/0.78 (assume a260 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.relation B) (tptp.function B)) (forall ((C $$unsorted)) (=> (and (tptp.relation C) (tptp.function C)) (=> (tptp.in A (tptp.relation_dom B)) (= (tptp.apply (tptp.relation_composition B C) A) (tptp.apply C (tptp.apply B A)))))))))
% 0.46/0.78 (assume a261 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.ordinal B) (=> (tptp.in A B) (tptp.ordinal A)))))
% 0.46/0.78 (assume a262 (forall ((A $$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)))))
% 0.46/0.78 (assume a263 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (=> (tptp.connected B) (tptp.connected (tptp.relation_restriction B A))))))
% 0.46/0.78 (assume a264 (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)))))))))
% 0.46/0.78 (assume a265 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (=> (tptp.transitive B) (tptp.transitive (tptp.relation_restriction B A))))))
% 0.46/0.78 (assume a266 (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)))))))))
% 0.46/0.78 (assume a267 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (=> (tptp.antisymmetric B) (tptp.antisymmetric (tptp.relation_restriction B A))))))
% 0.46/0.78 (assume a268 (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)))))))
% 0.46/0.78 (assume a269 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.subset A B) (tptp.subset (tptp.set_intersection2 A C) (tptp.set_intersection2 B C)))))
% 0.46/0.78 (assume a270 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.subset A B) (= (tptp.set_intersection2 A B) A))))
% 0.46/0.78 (assume a271 (forall ((A $$unsorted)) (= (tptp.set_intersection2 A tptp.empty_set) tptp.empty_set)))
% 0.46/0.78 (assume a272 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element A B) (or (tptp.empty B) (tptp.in A B)))))
% 0.46/0.78 (assume a273 (forall ((A $$unsorted) (B $$unsorted)) (=> (forall ((C $$unsorted)) (= (tptp.in C A) (tptp.in C B))) (= A B))))
% 0.46/0.78 (assume a274 (forall ((A $$unsorted)) (tptp.reflexive (tptp.inclusion_relation A))))
% 0.46/0.78 (assume a275 (forall ((A $$unsorted)) (tptp.subset tptp.empty_set A)))
% 0.46/0.78 (assume a276 (forall ((A $$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)))))))
% 0.46/0.78 (assume a277 (forall ((A $$unsorted)) (=> (forall ((B $$unsorted)) (=> (tptp.in B A) (and (tptp.ordinal B) (tptp.subset B A)))) (tptp.ordinal A))))
% 0.46/0.78 (assume a278 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (=> (tptp.well_founded_relation B) (tptp.well_founded_relation (tptp.relation_restriction B A))))))
% 0.46/0.78 (assume a279 (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)))))))))))))
% 0.46/0.78 (assume a280 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (=> (tptp.well_ordering B) (tptp.well_ordering (tptp.relation_restriction B A))))))
% 0.46/0.78 (assume a281 (forall ((A $$unsorted)) (=> (tptp.ordinal A) (forall ((B $$unsorted)) (=> (tptp.ordinal B) (= (tptp.in A B) (tptp.ordinal_subset (tptp.succ A) B)))))))
% 0.46/0.78 (assume a282 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.subset A B) (tptp.subset (tptp.set_difference A C) (tptp.set_difference B C)))))
% 0.46/0.78 (assume a283 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (= (tptp.ordered_pair A B) (tptp.ordered_pair C D)) (and (= A C) (= B D)))))
% 0.46/0.78 (assume a284 (forall ((A $$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))))))))
% 0.46/0.78 (assume a285 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in B A) (= (tptp.apply (tptp.identity_relation A) B) B))))
% 0.46/0.78 (assume a286 (forall ((A $$unsorted) (B $$unsorted)) (tptp.subset (tptp.set_difference A B) A)))
% 0.46/0.78 (assume a287 (forall ((A $$unsorted)) (=> (tptp.relation A) (and (= (tptp.relation_rng A) (tptp.relation_dom (tptp.relation_inverse A))) (= (tptp.relation_dom A) (tptp.relation_rng (tptp.relation_inverse A)))))))
% 0.46/0.78 (assume a288 (forall ((A $$unsorted) (B $$unsorted)) (= (= (tptp.set_difference A B) tptp.empty_set) (tptp.subset A B))))
% 0.46/0.78 (assume a289 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset (tptp.singleton A) B) (tptp.in A B))))
% 0.46/0.78 (assume a290 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.subset (tptp.unordered_pair A B) C) (and (tptp.in A C) (tptp.in B C)))))
% 0.46/0.78 (assume a291 (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)))))
% 0.46/0.78 (assume a292 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_union2 A (tptp.set_difference B A)) (tptp.set_union2 A B))))
% 0.46/0.78 (assume a293 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset A (tptp.singleton B)) (or (= A tptp.empty_set) (= A (tptp.singleton B))))))
% 0.46/0.78 (assume a294 (forall ((A $$unsorted)) (= (tptp.set_difference A tptp.empty_set) A)))
% 0.46/0.78 (assume a295 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (not (and (tptp.in A B) (tptp.in B C) (tptp.in C A)))))
% 0.46/0.78 (assume a296 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.element A (tptp.powerset B)) (tptp.subset A B))))
% 0.46/0.78 (assume a297 (forall ((A $$unsorted)) (tptp.transitive (tptp.inclusion_relation A))))
% 0.46/0.78 (assume a298 (forall ((A $$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 $$unsorted)) (and (tptp.in C A) (tptp.in C B))) (tptp.disjoint A B))))))
% 0.46/0.78 (assume a299 (forall ((A $$unsorted)) (=> (tptp.subset A tptp.empty_set) (= A tptp.empty_set))))
% 0.46/0.78 (assume a300 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_difference (tptp.set_union2 A B) B) (tptp.set_difference A B))))
% 0.46/0.78 (assume a301 (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))))))))
% 0.46/0.78 (assume a302 (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 $$unsorted)) (and (tptp.ordinal B) (= A (tptp.succ B)))) (tptp.being_limit_ordinal A)))))))
% 0.46/0.78 (assume a303 (forall ((A $$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))))))))
% 0.46/0.78 (assume a304 (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)))))))
% 0.46/0.78 (assume a305 (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)))))))
% 0.46/0.78 (assume a306 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.subset A B) (= B (tptp.set_union2 A (tptp.set_difference B A))))))
% 0.46/0.78 (assume a307 (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))))))))
% 0.46/0.78 (assume a308 (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))))))
% 0.46/0.78 (assume a309 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (= (tptp.set_union2 (tptp.singleton A) B) B))))
% 0.46/0.78 (assume a310 (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))))))))
% 0.46/0.78 (assume a311 (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)))))))
% 0.46/0.78 (assume a312 (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)))))))
% 0.46/0.78 (assume a313 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_difference A (tptp.set_difference A B)) (tptp.set_intersection2 A B))))
% 0.46/0.78 (assume a314 (forall ((A $$unsorted)) (=> (tptp.relation A) (forall ((B $$unsorted)) (=> (tptp.relation B) (forall ((C $$unsorted)) (=> (and (tptp.relation C) (tptp.function C)) (=> (tptp.relation_isomorphism A B C) (tptp.relation_isomorphism B A (tptp.function_inverse C))))))))))
% 0.46/0.78 (assume a315 (forall ((A $$unsorted)) (= (tptp.set_difference tptp.empty_set A) tptp.empty_set)))
% 0.46/0.78 (assume a316 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.in A B) (tptp.element B (tptp.powerset C))) (tptp.element A C))))
% 0.46/0.78 (assume a317 (forall ((A $$unsorted)) (=> (tptp.ordinal A) (tptp.connected (tptp.inclusion_relation A)))))
% 0.46/0.78 (assume a318 (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))))))
% 0.46/0.78 (assume a319 (forall ((A $$unsorted)) (=> (not (= A tptp.empty_set)) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.powerset A)) (forall ((C $$unsorted)) (=> (tptp.element C A) (=> (not (tptp.in C B)) (tptp.in C (tptp.subset_complement A B))))))))))
% 0.46/0.78 (assume a320 (forall ((A $$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)))))))))))
% 0.46/0.78 (assume a321 (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))))))))))))))
% 0.46/0.78 (assume a322 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.element C (tptp.powerset A)) (not (and (tptp.in B (tptp.subset_complement A C)) (tptp.in B C))))))
% 0.46/0.78 (assume a323 (forall ((A $$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)))))))))
% 0.46/0.78 (assume a324 (forall ((A $$unsorted)) (=> (and (tptp.relation A) (tptp.function A)) (=> (tptp.one_to_one A) (and (= (tptp.relation_rng A) (tptp.relation_dom (tptp.function_inverse A))) (= (tptp.relation_dom A) (tptp.relation_rng (tptp.function_inverse A))))))))
% 0.46/0.78 (assume a325 (forall ((A $$unsorted)) (=> (tptp.relation A) (=> (forall ((B $$unsorted) (C $$unsorted)) (not (tptp.in (tptp.ordered_pair B C) A))) (= A tptp.empty_set)))))
% 0.46/0.78 (assume a326 (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)))))))
% 0.46/0.78 (assume a327 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (not (and (tptp.in A B) (tptp.element B (tptp.powerset C)) (tptp.empty C)))))
% 0.46/0.78 (assume a328 (forall ((A $$unsorted)) (=> (tptp.relation A) (= (tptp.well_founded_relation A) (tptp.is_well_founded_in A (tptp.relation_field A))))))
% 0.46/0.78 (assume a329 (forall ((A $$unsorted)) (tptp.antisymmetric (tptp.inclusion_relation A))))
% 0.46/0.78 (assume a330 (and (= (tptp.relation_dom tptp.empty_set) tptp.empty_set) (= (tptp.relation_rng tptp.empty_set) tptp.empty_set)))
% 0.46/0.78 (assume a331 (forall ((A $$unsorted) (B $$unsorted)) (not (and (tptp.subset A B) (tptp.proper_subset B A)))))
% 0.46/0.78 (assume a332 (forall ((A $$unsorted)) (=> (and (tptp.relation A) (tptp.function A)) (=> (tptp.one_to_one A) (tptp.one_to_one (tptp.function_inverse A))))))
% 0.46/0.78 (assume a333 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.subset A B) (tptp.disjoint B C)) (tptp.disjoint A C))))
% 0.46/0.78 (assume a334 (forall ((A $$unsorted)) (=> (tptp.relation A) (=> (or (= (tptp.relation_dom A) tptp.empty_set) (= (tptp.relation_rng A) tptp.empty_set)) (= A tptp.empty_set)))))
% 0.46/0.78 (assume a335 (forall ((A $$unsorted)) (=> (tptp.relation A) (= (= (tptp.relation_dom A) tptp.empty_set) (= (tptp.relation_rng A) tptp.empty_set)))))
% 0.46/0.78 (assume a336 (forall ((A $$unsorted) (B $$unsorted)) (= (= (tptp.set_difference A (tptp.singleton B)) A) (not (tptp.in B A)))))
% 0.46/0.78 (assume a337 (forall ((A $$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 $$unsorted)) (=> (tptp.in D (tptp.relation_dom B)) (= (tptp.apply B D) (tptp.apply C D)))))))))))
% 0.46/0.78 (assume a338 (forall ((A $$unsorted)) (= (tptp.unordered_pair A A) (tptp.singleton A))))
% 0.46/0.78 (assume a339 (forall ((A $$unsorted)) (=> (tptp.empty A) (= A tptp.empty_set))))
% 0.46/0.78 (assume a340 (forall ((A $$unsorted)) (=> (tptp.ordinal A) (tptp.well_founded_relation (tptp.inclusion_relation A)))))
% 0.46/0.78 (assume a341 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.subset (tptp.singleton A) (tptp.singleton B)) (= A B))))
% 0.46/0.78 (assume a342 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.relation C) (tptp.function C)) (=> (tptp.in B (tptp.relation_dom (tptp.relation_dom_restriction C A))) (= (tptp.apply (tptp.relation_dom_restriction C A) B) (tptp.apply C B))))))
% 0.46/0.78 (assume a343 (forall ((A $$unsorted)) (and (= (tptp.relation_dom (tptp.identity_relation A)) A) (= (tptp.relation_rng (tptp.identity_relation A)) A))))
% 0.46/0.78 (assume a344 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.relation C) (tptp.function C)) (=> (tptp.in B A) (= (tptp.apply (tptp.relation_dom_restriction C A) B) (tptp.apply C B))))))
% 0.46/0.78 (assume a345 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (tptp.relation D) (= (tptp.in (tptp.ordered_pair A B) (tptp.relation_composition (tptp.identity_relation C) D)) (and (tptp.in A C) (tptp.in (tptp.ordered_pair A B) D))))))
% 0.46/0.78 (assume a346 (forall ((A $$unsorted) (B $$unsorted)) (not (and (tptp.in A B) (tptp.empty B)))))
% 0.46/0.78 (assume a347 (forall ((A $$unsorted) (B $$unsorted)) (and (= (tptp.pair_first (tptp.ordered_pair A B)) A) (= (tptp.pair_second (tptp.ordered_pair A B)) B))))
% 0.46/0.78 (assume a348 (forall ((A $$unsorted) (B $$unsorted)) (not (and (tptp.in A B) (forall ((C $$unsorted)) (not (and (tptp.in C B) (forall ((D $$unsorted)) (not (and (tptp.in D B) (tptp.in D C)))))))))))
% 0.46/0.78 (assume a349 (forall ((A $$unsorted)) (=> (tptp.ordinal A) (tptp.well_ordering (tptp.inclusion_relation A)))))
% 0.46/0.78 (assume a350 (forall ((A $$unsorted) (B $$unsorted)) (tptp.subset A (tptp.set_union2 A B))))
% 0.46/0.78 (assume a351 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.disjoint A B) (= (tptp.set_difference A B) A))))
% 0.46/0.78 (assume a352 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.relation C) (= (tptp.in A (tptp.relation_dom (tptp.relation_dom_restriction C B))) (and (tptp.in A B) (tptp.in A (tptp.relation_dom C)))))))
% 0.46/0.78 (assume a353 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (tptp.subset (tptp.relation_dom_restriction B A) B))))
% 0.46/0.78 (assume a354 (forall ((A $$unsorted) (B $$unsorted)) (not (and (tptp.empty A) (not (= A B)) (tptp.empty B)))))
% 0.46/0.78 (assume a355 (forall ((A $$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)))))))
% 0.46/0.78 (assume a356 (forall ((A $$unsorted)) (=> (tptp.relation A) (= (tptp.well_orders A (tptp.relation_field A)) (tptp.well_ordering A)))))
% 0.46/0.78 (assume a357 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.subset A B) (tptp.subset C B)) (tptp.subset (tptp.set_union2 A C) B))))
% 0.46/0.78 (assume a358 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (= (tptp.singleton A) (tptp.unordered_pair B C)) (= A B))))
% 0.46/0.78 (assume a359 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (= (tptp.relation_dom (tptp.relation_dom_restriction B A)) (tptp.set_intersection2 (tptp.relation_dom B) A)))))
% 0.46/0.78 (assume a360 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (tptp.subset A (tptp.union B)))))
% 0.46/0.78 (assume a361 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (= (tptp.relation_dom_restriction B A) (tptp.relation_composition (tptp.identity_relation A) B)))))
% 0.46/0.78 (assume a362 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (tptp.subset (tptp.relation_rng (tptp.relation_dom_restriction B A)) (tptp.relation_rng B)))))
% 0.46/0.78 (assume a363 (forall ((A $$unsorted)) (= (tptp.union (tptp.powerset A)) A)))
% 0.46/0.78 (assume a364 (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)))))))))
% 0.46/0.78 (assume a365 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (= (tptp.singleton A) (tptp.unordered_pair B C)) (= B C))))
% 0.46/0.78 (assume a366 true)
% 0.46/0.78 (step t1 (cl (not (= (not (forall ((A $$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 $$unsorted)) (and (= (tptp.ordered_pair E F) D) (tptp.in E A) (= F (tptp.singleton E)))))))))) (not (forall ((A $$unsorted) (B $$unsorted)) (not (forall ((C $$unsorted)) (not (forall ((D $$unsorted)) (= (tptp.in D C) (and (tptp.in D (tptp.cartesian_product2 A B)) (not (forall ((E $$unsorted)) (or (not (= D (tptp.ordered_pair E (tptp.singleton E)))) (not (tptp.in E A))))))))))))))) (not (not (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))))))))))) (not (forall ((A $$unsorted) (B $$unsorted)) (not (forall ((C $$unsorted)) (not (forall ((D $$unsorted)) (= (tptp.in D C) (and (tptp.in D (tptp.cartesian_product2 A B)) (not (forall ((E $$unsorted)) (or (not (= D (tptp.ordered_pair E (tptp.singleton E)))) (not (tptp.in E A)))))))))))))) :rule equiv_pos2)
% 0.46/0.78 (anchor :step t2 :args ((A $$unsorted) (:= A A) (B $$unsorted) (:= B B)))
% 0.46/0.78 (step t2.t1 (cl (= A A)) :rule refl)
% 0.46/0.78 (step t2.t2 (cl (= B B)) :rule refl)
% 0.46/0.78 (anchor :step t2.t3 :args ((C $$unsorted) (:= C C)))
% 0.46/0.78 (step t2.t3.t1 (cl (= C C)) :rule refl)
% 0.46/0.78 (anchor :step t2.t3.t2 :args ((D $$unsorted) (:= D D)))
% 0.46/0.78 (step t2.t3.t2.t1 (cl (= D D)) :rule refl)
% 0.46/0.78 (step t2.t3.t2.t2 (cl (= (tptp.in D C) (tptp.in D C))) :rule refl)
% 0.46/0.78 (step t2.t3.t2.t3 (cl (= (tptp.in D (tptp.cartesian_product2 A B)) (tptp.in D (tptp.cartesian_product2 A B)))) :rule refl)
% 0.46/0.78 (anchor :step t2.t3.t2.t4 :args ((E $$unsorted) (:= E E) (F $$unsorted) (:= F F)))
% 0.46/0.78 (step t2.t3.t2.t4.t1 (cl (= E E)) :rule refl)
% 0.46/0.78 (step t2.t3.t2.t4.t2 (cl (= F F)) :rule refl)
% 0.46/0.78 (step t2.t3.t2.t4.t3 (cl (= (= (tptp.ordered_pair E F) D) (= D (tptp.ordered_pair E F)))) :rule all_simplify)
% 0.46/0.78 (step t2.t3.t2.t4.t4 (cl (= (tptp.in E A) (tptp.in E A))) :rule refl)
% 0.46/0.78 (step t2.t3.t2.t4.t5 (cl (= (= F (tptp.singleton E)) (= F (tptp.singleton E)))) :rule refl)
% 0.46/0.78 (step t2.t3.t2.t4.t6 (cl (= (and (= (tptp.ordered_pair E F) D) (tptp.in E A) (= F (tptp.singleton E))) (and (= D (tptp.ordered_pair E F)) (tptp.in E A) (= F (tptp.singleton E))))) :rule cong :premises (t2.t3.t2.t4.t3 t2.t3.t2.t4.t4 t2.t3.t2.t4.t5))
% 0.46/0.78 (step t2.t3.t2.t4 (cl (= (exists ((E $$unsorted) (F $$unsorted)) (and (= (tptp.ordered_pair E F) D) (tptp.in E A) (= F (tptp.singleton E)))) (exists ((E $$unsorted) (F $$unsorted)) (and (= D (tptp.ordered_pair E F)) (tptp.in E A) (= F (tptp.singleton E)))))) :rule bind)
% 0.46/0.78 (step t2.t3.t2.t5 (cl (= (exists ((E $$unsorted) (F $$unsorted)) (and (= D (tptp.ordered_pair E F)) (tptp.in E A) (= F (tptp.singleton E)))) (not (forall ((E $$unsorted) (F $$unsorted)) (not (and (= D (tptp.ordered_pair E F)) (tptp.in E A) (= F (tptp.singleton E)))))))) :rule all_simplify)
% 0.46/0.78 (step t2.t3.t2.t6 (cl (= (forall ((E $$unsorted) (F $$unsorted)) (not (and (= D (tptp.ordered_pair E F)) (tptp.in E A) (= F (tptp.singleton E))))) (forall ((E $$unsorted) (F $$unsorted)) (or (not (= D (tptp.ordered_pair E F))) (not (tptp.in E A)) (not (= F (tptp.singleton E))))))) :rule all_simplify)
% 0.46/0.78 (step t2.t3.t2.t7 (cl (= (forall ((E $$unsorted) (F $$unsorted)) (or (not (= D (tptp.ordered_pair E F))) (not (tptp.in E A)) (not (= F (tptp.singleton E))))) (forall ((E $$unsorted)) (or (not (= D (tptp.ordered_pair E (tptp.singleton E)))) (not (tptp.in E A)) (not (= (tptp.singleton E) (tptp.singleton E))))))) :rule all_simplify)
% 0.46/0.78 (anchor :step t2.t3.t2.t8 :args ((E $$unsorted) (:= E E)))
% 0.46/0.78 (step t2.t3.t2.t8.t1 (cl (= E E)) :rule refl)
% 0.46/0.78 (step t2.t3.t2.t8.t2 (cl (= (not (= D (tptp.ordered_pair E (tptp.singleton E)))) (not (= D (tptp.ordered_pair E (tptp.singleton E)))))) :rule refl)
% 0.46/0.78 (step t2.t3.t2.t8.t3 (cl (= (not (tptp.in E A)) (not (tptp.in E A)))) :rule refl)
% 0.46/0.78 (step t2.t3.t2.t8.t4 (cl (= (= (tptp.singleton E) (tptp.singleton E)) true)) :rule all_simplify)
% 0.46/0.78 (step t2.t3.t2.t8.t5 (cl (= (not (= (tptp.singleton E) (tptp.singleton E))) (not true))) :rule cong :premises (t2.t3.t2.t8.t4))
% 0.46/0.78 (step t2.t3.t2.t8.t6 (cl (= (not true) false)) :rule all_simplify)
% 0.46/0.78 (step t2.t3.t2.t8.t7 (cl (= (not (= (tptp.singleton E) (tptp.singleton E))) false)) :rule trans :premises (t2.t3.t2.t8.t5 t2.t3.t2.t8.t6))
% 0.46/0.78 (step t2.t3.t2.t8.t8 (cl (= (or (not (= D (tptp.ordered_pair E (tptp.singleton E)))) (not (tptp.in E A)) (not (= (tptp.singleton E) (tptp.singleton E)))) (or (not (= D (tptp.ordered_pair E (tptp.singleton E)))) (not (tptp.in E A)) false))) :rule cong :premises (t2.t3.t2.t8.t2 t2.t3.t2.t8.t3 t2.t3.t2.t8.t7))
% 0.46/0.78 (step t2.t3.t2.t8.t9 (cl (= (or (not (= D (tptp.ordered_pair E (tptp.singleton E)))) (not (tptp.in E A)) false) (or (not (= D (tptp.ordered_pair E (tptp.singleton E)))) (not (tptp.in E A))))) :rule all_simplify)
% 0.46/0.78 (step t2.t3.t2.t8.t10 (cl (= (or (not (= D (tptp.ordered_pair E (tptp.singleton E)))) (not (tptp.in E A)) (not (= (tptp.singleton E) (tptp.singleton E)))) (or (not (= D (tptp.ordered_pair E (tptp.singleton E)))) (not (tptp.in E A))))) :rule trans :premises (t2.t3.t2.t8.t8 t2.t3.t2.t8.t9))
% 0.46/0.78 (step t2.t3.t2.t8 (cl (= (forall ((E $$unsorted)) (or (not (= D (tptp.ordered_pair E (tptp.singleton E)))) (not (tptp.in E A)) (not (= (tptp.singleton E) (tptp.singleton E))))) (forall ((E $$unsorted)) (or (not (= D (tptp.ordered_pair E (tptp.singleton E)))) (not (tptp.in E A)))))) :rule bind)
% 0.46/0.78 (step t2.t3.t2.t9 (cl (= (forall ((E $$unsorted) (F $$unsorted)) (or (not (= D (tptp.ordered_pair E F))) (not (tptp.in E A)) (not (= F (tptp.singleton E))))) (forall ((E $$unsorted)) (or (not (= D (tptp.ordered_pair E (tptp.singleton E)))) (not (tptp.in E A)))))) :rule trans :premises (t2.t3.t2.t7 t2.t3.t2.t8))
% 0.46/0.78 (step t2.t3.t2.t10 (cl (= (forall ((E $$unsorted) (F $$unsorted)) (not (and (= D (tptp.ordered_pair E F)) (tptp.in E A) (= F (tptp.singleton E))))) (forall ((E $$unsorted)) (or (not (= D (tptp.ordered_pair E (tptp.singleton E)))) (not (tptp.in E A)))))) :rule trans :premises (t2.t3.t2.t6 t2.t3.t2.t9))
% 0.46/0.78 (step t2.t3.t2.t11 (cl (= (not (forall ((E $$unsorted) (F $$unsorted)) (not (and (= D (tptp.ordered_pair E F)) (tptp.in E A) (= F (tptp.singleton E)))))) (not (forall ((E $$unsorted)) (or (not (= D (tptp.ordered_pair E (tptp.singleton E)))) (not (tptp.in E A))))))) :rule cong :premises (t2.t3.t2.t10))
% 0.46/0.78 (step t2.t3.t2.t12 (cl (= (exists ((E $$unsorted) (F $$unsorted)) (and (= D (tptp.ordered_pair E F)) (tptp.in E A) (= F (tptp.singleton E)))) (not (forall ((E $$unsorted)) (or (not (= D (tptp.ordered_pair E (tptp.singleton E)))) (not (tptp.in E A))))))) :rule trans :premises (t2.t3.t2.t5 t2.t3.t2.t11))
% 0.46/0.78 (step t2.t3.t2.t13 (cl (= (exists ((E $$unsorted) (F $$unsorted)) (and (= (tptp.ordered_pair E F) D) (tptp.in E A) (= F (tptp.singleton E)))) (not (forall ((E $$unsorted)) (or (not (= D (tptp.ordered_pair E (tptp.singleton E)))) (not (tptp.in E A))))))) :rule trans :premises (t2.t3.t2.t4 t2.t3.t2.t12))
% 0.46/0.78 (step t2.t3.t2.t14 (cl (= (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))))) (and (tptp.in D (tptp.cartesian_product2 A B)) (not (forall ((E $$unsorted)) (or (not (= D (tptp.ordered_pair E (tptp.singleton E)))) (not (tptp.in E A)))))))) :rule cong :premises (t2.t3.t2.t3 t2.t3.t2.t13))
% 0.46/0.78 (step t2.t3.t2.t15 (cl (= (= (tptp.in D C) (and (tptp.in D (tptp.cartesian_product2 A B)) (exists ((E $$unsorted) (F $$unsorted)) (and (= (tptp.ordered_pair E F) D) (tptp.in E A) (= F (tptp.singleton E)))))) (= (tptp.in D C) (and (tptp.in D (tptp.cartesian_product2 A B)) (not (forall ((E $$unsorted)) (or (not (= D (tptp.ordered_pair E (tptp.singleton E)))) (not (tptp.in E A))))))))) :rule cong :premises (t2.t3.t2.t2 t2.t3.t2.t14))
% 0.46/0.78 (step t2.t3.t2 (cl (= (forall ((D $$unsorted)) (= (tptp.in D C) (and (tptp.in D (tptp.cartesian_product2 A B)) (exists ((E $$unsorted) (F $$unsorted)) (and (= (tptp.ordered_pair E F) D) (tptp.in E A) (= F (tptp.singleton E))))))) (forall ((D $$unsorted)) (= (tptp.in D C) (and (tptp.in D (tptp.cartesian_product2 A B)) (not (forall ((E $$unsorted)) (or (not (= D (tptp.ordered_pair E (tptp.singleton E)))) (not (tptp.in E A)))))))))) :rule bind)
% 0.46/0.78 (step t2.t3 (cl (= (exists ((C $$unsorted)) (forall ((D $$unsorted)) (= (tptp.in D C) (and (tptp.in D (tptp.cartesian_product2 A B)) (exists ((E $$unsorted) (F $$unsorted)) (and (= (tptp.ordered_pair E F) D) (tptp.in E A) (= F (tptp.singleton E)))))))) (exists ((C $$unsorted)) (forall ((D $$unsorted)) (= (tptp.in D C) (and (tptp.in D (tptp.cartesian_product2 A B)) (not (forall ((E $$unsorted)) (or (not (= D (tptp.ordered_pair E (tptp.singleton E)))) (not (tptp.in E A))))))))))) :rule bind)
% 0.46/0.78 (step t2.t4 (cl (= (exists ((C $$unsorted)) (forall ((D $$unsorted)) (= (tptp.in D C) (and (tptp.in D (tptp.cartesian_product2 A B)) (not (forall ((E $$unsorted)) (or (not (= D (tptp.ordered_pair E (tptp.singleton E)))) (not (tptp.in E A))))))))) (not (forall ((C $$unsorted)) (not (forall ((D $$unsorted)) (= (tptp.in D C) (and (tptp.in D (tptp.cartesian_product2 A B)) (not (forall ((E $$unsorted)) (or (not (= D (tptp.ordered_pair E (tptp.singleton E)))) (not (tptp.in E A))))))))))))) :rule all_simplify)
% 0.46/0.78 (step t2.t5 (cl (= (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)))))))) (not (forall ((C $$unsorted)) (not (forall ((D $$unsorted)) (= (tptp.in D C) (and (tptp.in D (tptp.cartesian_product2 A B)) (not (forall ((E $$unsorted)) (or (not (= D (tptp.ordered_pair E (tptp.singleton E)))) (not (tptp.in E A))))))))))))) :rule trans :premises (t2.t3 t2.t4))
% 0.46/0.78 (step t2 (cl (= (forall ((A $$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 $$unsorted)) (and (= (tptp.ordered_pair E F) D) (tptp.in E A) (= F (tptp.singleton E))))))))) (forall ((A $$unsorted) (B $$unsorted)) (not (forall ((C $$unsorted)) (not (forall ((D $$unsorted)) (= (tptp.in D C) (and (tptp.in D (tptp.cartesian_product2 A B)) (not (forall ((E $$unsorted)) (or (not (= D (tptp.ordered_pair E (tptp.singleton E)))) (not (tptp.in E A)))))))))))))) :rule bind)
% 0.46/0.78 (step t3 (cl (= (not (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)))))))))) (not (forall ((A $$unsorted) (B $$unsorted)) (not (forall ((C $$unsorted)) (not (forall ((D $$unsorted)) (= (tptp.in D C) (and (tptp.in D (tptp.cartesian_product2 A B)) (not (forall ((E $$unsorted)) (or (not (= D (tptp.ordered_pair E (tptp.singleton E)))) (not (tptp.in E A))))))))))))))) :rule cong :premises (t2))
% 0.46/0.78 (step t4 (cl (not (forall ((A $$unsorted) (B $$unsorted)) (not (forall ((C $$unsorted)) (not (forall ((D $$unsorted)) (= (tptp.in D C) (and (tptp.in D (tptp.cartesian_product2 A B)) (not (forall ((E $$unsorted)) (or (not (= D (tptp.ordered_pair E (tptp.singleton E)))) (not (tptp.in E A)))))))))))))) :rule resolution :premises (t1 t3 a207))
% 0.46/0.78 (step t5 (cl (= (forall ((A $$unsorted) (B $$unsorted)) (not (forall ((C $$unsorted)) (not (forall ((D $$unsorted)) (= (tptp.in D C) (and (not (forall ((J $$unsorted)) (or (not (= D (tptp.ordered_pair J (tptp.singleton J)))) (not (tptp.in J A))))) (tptp.in D (tptp.cartesian_product2 A B))))))))) (forall ((A $$unsorted) (B $$unsorted)) (not (forall ((C $$unsorted)) (not (forall ((D $$unsorted)) (= (tptp.in D C) (and (not (forall ((E $$unsorted)) (or (not (= D (tptp.ordered_pair E (tptp.singleton E)))) (not (tptp.in E A))))) (tptp.in D (tptp.cartesian_product2 A B))))))))))) :rule hole :args ((forall ((A $$unsorted) (B $$unsorted)) (not (forall ((C $$unsorted)) (not (forall ((D $$unsorted)) (= (tptp.in D C) (and (not (forall ((J $$unsorted)) (or (not (= D (tptp.ordered_pair J (tptp.singleton J)))) (not (tptp.in J A))))) (tptp.in D (tptp.cartesian_product2 A B))))))))) (= C C) (= D D) (= J E) (= A A) (= B B)))
% 0.46/0.78 (step t6 (cl (= (= (= (forall ((A $$unsorted) (B $$unsorted)) (not (forall ((C $$unsorted)) (not (forall ((D $$unsorted)) (= (tptp.in D C) (and (not (forall ((E $$unsorted)) (or (not (= D (tptp.ordered_pair E (tptp.singleton E)))) (not (tptp.in E A))))) (tptp.in D (tptp.cartesian_product2 A B))))))))) (forall ((A $$unsorted) (B $$unsorted)) (not (forall ((C $$unsorted)) (not (forall ((D $$unsorted)) (= (tptp.in D C) (and (tptp.in D (tptp.cartesian_product2 A B)) (not (forall ((E $$unsorted)) (or (not (= D (tptp.ordered_pair E (tptp.singleton E)))) (not (tptp.in E A))))))))))))) true) (= (forall ((A $$unsorted) (B $$unsorted)) (not (forall ((C $$unsorted)) (not (forall ((D $$unsorted)) (= (tptp.in D C) (and (not (forall ((E $$unsorted)) (or (not (= D (tptp.ordered_pair E (tptp.singleton E)))) (not (tptp.in E A))))) (tptp.in D (tptp.cartesian_product2 A B))))))))) (forall ((A $$unsorted) (B $$unsorted)) (not (forall ((C $$unsorted)) (not (forall ((D $$unsorted)) (= (tptp.in D C) (and (tptp.in D (tptp.cartesian_product2 A B)) (not (forall ((E $$unsorted)) (or (not (= D (tptp.ordered_pair E (tptp.singleton E)))) (not (tptp.in E A))))))))))))))) :rule equiv_simplify)
% 0.46/0.78 (step t7 (cl (not (= (= (forall ((A $$unsorted) (B $$unsorted)) (not (forall ((C $$unsorted)) (not (forall ((D $$unsorted)) (= (tptp.in D C) (and (not (forall ((E $$unsorted)) (or (not (= D (tptp.ordered_pair E (tptp.singleton E)))) (not (tptp.in E A))))) (tptp.in D (tptp.cartesian_product2 A B))))))))) (forall ((A $$unsorted) (B $$unsorted)) (not (forall ((C $$unsorted)) (not (forall ((D $$unsorted)) (= (tptp.in D C) (and (tptp.in D (tptp.cartesian_product2 A B)) (not (forall ((E $$unsorted)) (or (not (= D (tptp.ordered_pair E (tptp.singleton E)))) (not (tptp.in E A))))))))))))) true)) (= (forall ((A $$unsorted) (B $$unsorted)) (not (forall ((C $$unsorted)) (not (forall ((D $$unsorted)) (= (tptp.in D C) (and (not (forall ((E $$unsorted)) (or (not (= D (tptp.ordered_pair E (tptp.singleton E)))) (not (tptp.in E A))))) (tptp.in D (tptp.cartesian_product2 A B))))))))) (forall ((A $$unsorted) (B $$unsorted)) (not (forall ((C $$unsorted)) (not (forall ((D $$unsorted)) (= (tptp.in D C) (and (tptp.in D (tptp.cartesian_product2 A B)) (not (forall ((E $$unsorted)) (or (not (= D (tptp.ordered_pair E (tptp.singleton E)))) (not (tptp.in E A)))))))))))))) :rule equiv1 :premises (t6))
% 0.46/0.78 (step t8 (cl (= (= (forall ((A $$unsorted) (B $$unsorted)) (not (forall ((C $$unsorted)) (not (forall ((D $$unsorted)) (= (tptp.in D C) (and (not (forall ((E $$unsorted)) (or (not (= D (tptp.ordered_pair E (tptp.singleton E)))) (not (tptp.in E A))))) (tptp.in D (tptp.cartesian_product2 A B))))))))) (forall ((A $$unsorted) (B $$unsorted)) (not (forall ((C $$unsorted)) (not (forall ((D $$unsorted)) (= (tptp.in D C) (and (tptp.in D (tptp.cartesian_product2 A B)) (not (forall ((E $$unsorted)) (or (not (= D (tptp.ordered_pair E (tptp.singleton E)))) (not (tptp.in E A))))))))))))) true)) :rule hole :args ((= (forall ((A $$unsorted) (B $$unsorted)) (not (forall ((C $$unsorted)) (not (forall ((D $$unsorted)) (= (tptp.in D C) (and (not (forall ((E $$unsorted)) (or (not (= D (tptp.ordered_pair E (tptp.singleton E)))) (not (tptp.in E A))))) (tptp.in D (tptp.cartesian_product2 A B))))))))) (forall ((A $$unsorted) (B $$unsorted)) (not (forall ((C $$unsorted)) (not (forall ((D $$unsorted)) (= (tptp.in D C) (and (tptp.in D (tptp.cartesian_product2 A B)) (not (forall ((E $$unsorted)) (or (not (= D (tptp.ordered_pair E (tptp.singleton E)))) (not (tptp.in E A))))))))))))) 1))
% 0.46/0.78 (step t9 (cl (= (forall ((A $$unsorted) (B $$unsorted)) (not (forall ((C $$unsorted)) (not (forall ((D $$unsorted)) (= (tptp.in D C) (and (not (forall ((E $$unsorted)) (or (not (= D (tptp.ordered_pair E (tptp.singleton E)))) (not (tptp.in E A))))) (tptp.in D (tptp.cartesian_product2 A B))))))))) (forall ((A $$unsorted) (B $$unsorted)) (not (forall ((C $$unsorted)) (not (forall ((D $$unsorted)) (= (tptp.in D C) (and (tptp.in D (tptp.cartesian_product2 A B)) (not (forall ((E $$unsorted)) (or (not (= D (tptp.ordered_pair E (tptp.singleton E)))) (not (tptp.in E A)))))))))))))) :rule resolution :premises (t7 t8))
% 0.46/0.78 (step t10 (cl (= (forall ((A $$unsorted) (B $$unsorted)) (not (forall ((C $$unsorted)) (not (forall ((D $$unsorted)) (= (tptp.in D C) (and (not (forall ((J $$unsorted)) (or (not (= D (tptp.ordered_pair J (tptp.singleton J)))) (not (tptp.in J A))))) (tptp.in D (tptp.cartesian_product2 A B))))))))) (forall ((A $$unsorted) (B $$unsorted)) (not (forall ((C $$unsorted)) (not (forall ((D $$unsorted)) (= (tptp.in D C) (and (tptp.in D (tptp.cartesian_product2 A B)) (not (forall ((E $$unsorted)) (or (not (= D (tptp.ordered_pair E (tptp.singleton E)))) (not (tptp.in E A)))))))))))))) :rule trans :premises (t5 t9))
% 0.46/0.78 (step t11 (cl (not (forall ((A $$unsorted) (B $$unsorted)) (not (forall ((C $$unsorted)) (not (forall ((D $$unsorted)) (= (tptp.in D C) (and (not (forall ((J $$unsorted)) (or (not (= D (tptp.ordered_pair J (tptp.singleton J)))) (not (tptp.in J A))))) (tptp.in D (tptp.cartesian_product2 A B)))))))))) (forall ((A $$unsorted) (B $$unsorted)) (not (forall ((C $$unsorted)) (not (forall ((D $$unsorted)) (= (tptp.in D C) (and (tptp.in D (tptp.cartesian_product2 A B)) (not (forall ((E $$unsorted)) (or (not (= D (tptp.ordered_pair E (tptp.singleton E)))) (not (tptp.in E A))))))))))))) :rule equiv1 :premises (t10))
% 0.46/0.78 (step t12 (cl (forall ((A $$unsorted) (B $$unsorted)) (not (forall ((C $$unsorted)) (not (forall ((D $$unsorted)) (= (tptp.in D C) (and (tptp.in D (tptp.cartesian_product2 A B)) (not (forall ((E $$unsorted)) (or (not (= D (tptp.ordered_pair E (tptp.singleton E)))) (not (tptp.in E A)))))))))))) (not (forall ((A $$unsorted) (B $$unsorted)) (not (forall ((C $$unsorted)) (not (forall ((D $$unsorted)) (= (tptp.in D C) (and (not (forall ((J $$unsorted)) (or (not (= D (tptp.ordered_pair J (tptp.singleton J)))) (not (tptp.in J A))))) (tptp.in D (tptp.cartesian_product2 A B))))))))))) :rule reordering :premises (t11))
% 0.46/0.78 (step t13 (cl (not (= (forall ((A $$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 $$unsorted)) (and (= (tptp.ordered_pair J K) D) (tptp.in J A) (= K (tptp.singleton J))))))))))) (forall ((A $$unsorted) (B $$unsorted)) (not (forall ((C $$unsorted)) (not (forall ((D $$unsorted)) (= (tptp.in D C) (and (not (forall ((J $$unsorted)) (or (not (= D (tptp.ordered_pair J (tptp.singleton J)))) (not (tptp.in J A))))) (tptp.in D (tptp.cartesian_product2 A B))))))))))) (not (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)))))))))))) (forall ((A $$unsorted) (B $$unsorted)) (not (forall ((C $$unsorted)) (not (forall ((D $$unsorted)) (= (tptp.in D C) (and (not (forall ((J $$unsorted)) (or (not (= D (tptp.ordered_pair J (tptp.singleton J)))) (not (tptp.in J A))))) (tptp.in D (tptp.cartesian_product2 A B)))))))))) :rule equiv_pos2)
% 0.46/0.78 (anchor :step t14 :args ((A $$unsorted) (:= A A) (B $$unsorted) (:= B B)))
% 0.46/0.78 (step t14.t1 (cl (= A A)) :rule refl)
% 0.46/0.78 (step t14.t2 (cl (= B B)) :rule refl)
% 0.46/0.78 (anchor :step t14.t3 :args ((C $$unsorted) (:= C C) (D $$unsorted) (:= D D) (E $$unsorted) (:= E E)))
% 0.46/0.78 (step t14.t3.t1 (cl (= C C)) :rule refl)
% 0.46/0.78 (step t14.t3.t2 (cl (= D D)) :rule refl)
% 0.46/0.78 (step t14.t3.t3 (cl (= E E)) :rule refl)
% 0.46/0.78 (step t14.t3.t4 (cl (= (= C D) (= C D))) :rule refl)
% 0.46/0.78 (anchor :step t14.t3.t5 :args ((F $$unsorted) (:= F F) (G $$unsorted) (:= G G)))
% 0.46/0.78 (step t14.t3.t5.t1 (cl (= F F)) :rule refl)
% 0.46/0.78 (step t14.t3.t5.t2 (cl (= G G)) :rule refl)
% 0.46/0.78 (step t14.t3.t5.t3 (cl (= (= (tptp.ordered_pair F G) D) (= D (tptp.ordered_pair F G)))) :rule all_simplify)
% 0.46/0.78 (step t14.t3.t5.t4 (cl (= (tptp.in F A) (tptp.in F A))) :rule refl)
% 0.46/0.78 (step t14.t3.t5.t5 (cl (= (= G (tptp.singleton F)) (= G (tptp.singleton F)))) :rule refl)
% 0.46/0.78 (step t14.t3.t5.t6 (cl (= (and (= (tptp.ordered_pair F G) D) (tptp.in F A) (= G (tptp.singleton F))) (and (= D (tptp.ordered_pair F G)) (tptp.in F A) (= G (tptp.singleton F))))) :rule cong :premises (t14.t3.t5.t3 t14.t3.t5.t4 t14.t3.t5.t5))
% 0.46/0.78 (step t14.t3.t5 (cl (= (exists ((F $$unsorted) (G $$unsorted)) (and (= (tptp.ordered_pair F G) D) (tptp.in F A) (= G (tptp.singleton F)))) (exists ((F $$unsorted) (G $$unsorted)) (and (= D (tptp.ordered_pair F G)) (tptp.in F A) (= G (tptp.singleton F)))))) :rule bind)
% 0.46/0.78 (step t14.t3.t6 (cl (= (exists ((F $$unsorted) (G $$unsorted)) (and (= D (tptp.ordered_pair F G)) (tptp.in F A) (= G (tptp.singleton F)))) (not (forall ((F $$unsorted) (G $$unsorted)) (not (and (= D (tptp.ordered_pair F G)) (tptp.in F A) (= G (tptp.singleton F)))))))) :rule all_simplify)
% 0.46/0.78 (step t14.t3.t7 (cl (= (forall ((F $$unsorted) (G $$unsorted)) (not (and (= D (tptp.ordered_pair F G)) (tptp.in F A) (= G (tptp.singleton F))))) (forall ((F $$unsorted) (G $$unsorted)) (or (not (= D (tptp.ordered_pair F G))) (not (tptp.in F A)) (not (= G (tptp.singleton F))))))) :rule all_simplify)
% 0.46/0.78 (step t14.t3.t8 (cl (= (forall ((F $$unsorted) (G $$unsorted)) (or (not (= D (tptp.ordered_pair F G))) (not (tptp.in F A)) (not (= G (tptp.singleton F))))) (forall ((F $$unsorted)) (or (not (= D (tptp.ordered_pair F (tptp.singleton F)))) (not (tptp.in F A)) (not (= (tptp.singleton F) (tptp.singleton F))))))) :rule all_simplify)
% 0.46/0.78 (anchor :step t14.t3.t9 :args ((F $$unsorted) (:= F F)))
% 0.46/0.78 (step t14.t3.t9.t1 (cl (= F F)) :rule refl)
% 0.46/0.78 (step t14.t3.t9.t2 (cl (= (not (= D (tptp.ordered_pair F (tptp.singleton F)))) (not (= D (tptp.ordered_pair F (tptp.singleton F)))))) :rule refl)
% 0.46/0.78 (step t14.t3.t9.t3 (cl (= (not (tptp.in F A)) (not (tptp.in F A)))) :rule refl)
% 0.46/0.78 (step t14.t3.t9.t4 (cl (= (= (tptp.singleton F) (tptp.singleton F)) true)) :rule all_simplify)
% 0.46/0.78 (step t14.t3.t9.t5 (cl (= (not (= (tptp.singleton F) (tptp.singleton F))) (not true))) :rule cong :premises (t14.t3.t9.t4))
% 0.46/0.78 (step t14.t3.t9.t6 (cl (= (not true) false)) :rule all_simplify)
% 0.46/0.78 (step t14.t3.t9.t7 (cl (= (not (= (tptp.singleton F) (tptp.singleton F))) false)) :rule trans :premises (t14.t3.t9.t5 t14.t3.t9.t6))
% 0.46/0.78 (step t14.t3.t9.t8 (cl (= (or (not (= D (tptp.ordered_pair F (tptp.singleton F)))) (not (tptp.in F A)) (not (= (tptp.singleton F) (tptp.singleton F)))) (or (not (= D (tptp.ordered_pair F (tptp.singleton F)))) (not (tptp.in F A)) false))) :rule cong :premises (t14.t3.t9.t2 t14.t3.t9.t3 t14.t3.t9.t7))
% 0.46/0.78 (step t14.t3.t9.t9 (cl (= (or (not (= D (tptp.ordered_pair F (tptp.singleton F)))) (not (tptp.in F A)) false) (or (not (= D (tptp.ordered_pair F (tptp.singleton F)))) (not (tptp.in F A))))) :rule all_simplify)
% 0.46/0.78 (step t14.t3.t9.t10 (cl (= (or (not (= D (tptp.ordered_pair F (tptp.singleton F)))) (not (tptp.in F A)) (not (= (tptp.singleton F) (tptp.singleton F)))) (or (not (= D (tptp.ordered_pair F (tptp.singleton F)))) (not (tptp.in F A))))) :rule trans :premises (t14.t3.t9.t8 t14.t3.t9.t9))
% 0.46/0.78 (step t14.t3.t9 (cl (= (forall ((F $$unsorted)) (or (not (= D (tptp.ordered_pair F (tptp.singleton F)))) (not (tptp.in F A)) (not (= (tptp.singleton F) (tptp.singleton F))))) (forall ((F $$unsorted)) (or (not (= D (tptp.ordered_pair F (tptp.singleton F)))) (not (tptp.in F A)))))) :rule bind)
% 0.46/0.78 (step t14.t3.t10 (cl (= (forall ((F $$unsorted) (G $$unsorted)) (or (not (= D (tptp.ordered_pair F G))) (not (tptp.in F A)) (not (= G (tptp.singleton F))))) (forall ((F $$unsorted)) (or (not (= D (tptp.ordered_pair F (tptp.singleton F)))) (not (tptp.in F A)))))) :rule trans :premises (t14.t3.t8 t14.t3.t9))
% 0.46/0.78 (step t14.t3.t11 (cl (= (forall ((F $$unsorted) (G $$unsorted)) (not (and (= D (tptp.ordered_pair F G)) (tptp.in F A) (= G (tptp.singleton F))))) (forall ((F $$unsorted)) (or (not (= D (tptp.ordered_pair F (tptp.singleton F)))) (not (tptp.in F A)))))) :rule trans :premises (t14.t3.t7 t14.t3.t10))
% 0.46/0.78 (step t14.t3.t12 (cl (= (not (forall ((F $$unsorted) (G $$unsorted)) (not (and (= D (tptp.ordered_pair F G)) (tptp.in F A) (= G (tptp.singleton F)))))) (not (forall ((F $$unsorted)) (or (not (= D (tptp.ordered_pair F (tptp.singleton F)))) (not (tptp.in F A))))))) :rule cong :premises (t14.t3.t11))
% 0.46/0.78 (step t14.t3.t13 (cl (= (exists ((F $$unsorted) (G $$unsorted)) (and (= D (tptp.ordered_pair F G)) (tptp.in F A) (= G (tptp.singleton F)))) (not (forall ((F $$unsorted)) (or (not (= D (tptp.ordered_pair F (tptp.singleton F)))) (not (tptp.in F A))))))) :rule trans :premises (t14.t3.t6 t14.t3.t12))
% 0.46/0.78 (step t14.t3.t14 (cl (= (exists ((F $$unsorted) (G $$unsorted)) (and (= (tptp.ordered_pair F G) D) (tptp.in F A) (= G (tptp.singleton F)))) (not (forall ((F $$unsorted)) (or (not (= D (tptp.ordered_pair F (tptp.singleton F)))) (not (tptp.in F A))))))) :rule trans :premises (t14.t3.t5 t14.t3.t13))
% 0.46/0.78 (step t14.t3.t15 (cl (= (= C E) (= C E))) :rule refl)
% 0.46/0.78 (anchor :step t14.t3.t16 :args ((H $$unsorted) (:= H H) (I $$unsorted) (:= I I)))
% 0.46/0.78 (step t14.t3.t16.t1 (cl (= H H)) :rule refl)
% 0.46/0.78 (step t14.t3.t16.t2 (cl (= I I)) :rule refl)
% 0.46/0.78 (step t14.t3.t16.t3 (cl (= (= (tptp.ordered_pair H I) E) (= E (tptp.ordered_pair H I)))) :rule all_simplify)
% 0.46/0.78 (step t14.t3.t16.t4 (cl (= (tptp.in H A) (tptp.in H A))) :rule refl)
% 0.46/0.78 (step t14.t3.t16.t5 (cl (= (= I (tptp.singleton H)) (= I (tptp.singleton H)))) :rule refl)
% 0.46/0.78 (step t14.t3.t16.t6 (cl (= (and (= (tptp.ordered_pair H I) E) (tptp.in H A) (= I (tptp.singleton H))) (and (= E (tptp.ordered_pair H I)) (tptp.in H A) (= I (tptp.singleton H))))) :rule cong :premises (t14.t3.t16.t3 t14.t3.t16.t4 t14.t3.t16.t5))
% 0.46/0.78 (step t14.t3.t16 (cl (= (exists ((H $$unsorted) (I $$unsorted)) (and (= (tptp.ordered_pair H I) E) (tptp.in H A) (= I (tptp.singleton H)))) (exists ((H $$unsorted) (I $$unsorted)) (and (= E (tptp.ordered_pair H I)) (tptp.in H A) (= I (tptp.singleton H)))))) :rule bind)
% 0.46/0.78 (step t14.t3.t17 (cl (= (exists ((H $$unsorted) (I $$unsorted)) (and (= E (tptp.ordered_pair H I)) (tptp.in H A) (= I (tptp.singleton H)))) (not (forall ((H $$unsorted) (I $$unsorted)) (not (and (= E (tptp.ordered_pair H I)) (tptp.in H A) (= I (tptp.singleton H)))))))) :rule all_simplify)
% 0.46/0.78 (step t14.t3.t18 (cl (= (forall ((H $$unsorted) (I $$unsorted)) (not (and (= E (tptp.ordered_pair H I)) (tptp.in H A) (= I (tptp.singleton H))))) (forall ((H $$unsorted) (I $$unsorted)) (or (not (= E (tptp.ordered_pair H I))) (not (tptp.in H A)) (not (= I (tptp.singleton H))))))) :rule all_simplify)
% 0.46/0.78 (step t14.t3.t19 (cl (= (forall ((H $$unsorted) (I $$unsorted)) (or (not (= E (tptp.ordered_pair H I))) (not (tptp.in H A)) (not (= I (tptp.singleton H))))) (forall ((H $$unsorted)) (or (not (= E (tptp.ordered_pair H (tptp.singleton H)))) (not (tptp.in H A)) (not (= (tptp.singleton H) (tptp.singleton H))))))) :rule all_simplify)
% 0.46/0.78 (anchor :step t14.t3.t20 :args ((H $$unsorted) (:= H H)))
% 0.46/0.78 (step t14.t3.t20.t1 (cl (= H H)) :rule refl)
% 0.46/0.78 (step t14.t3.t20.t2 (cl (= (not (= E (tptp.ordered_pair H (tptp.singleton H)))) (not (= E (tptp.ordered_pair H (tptp.singleton H)))))) :rule refl)
% 0.46/0.78 (step t14.t3.t20.t3 (cl (= (not (tptp.in H A)) (not (tptp.in H A)))) :rule refl)
% 0.46/0.78 (step t14.t3.t20.t4 (cl (= (= (tptp.singleton H) (tptp.singleton H)) true)) :rule all_simplify)
% 0.46/0.78 (step t14.t3.t20.t5 (cl (= (not (= (tptp.singleton H) (tptp.singleton H))) (not true))) :rule cong :premises (t14.t3.t20.t4))
% 0.46/0.78 (step t14.t3.t20.t6 (cl (= (not true) false)) :rule all_simplify)
% 0.46/0.78 (step t14.t3.t20.t7 (cl (= (not (= (tptp.singleton H) (tptp.singleton H))) false)) :rule trans :premises (t14.t3.t20.t5 t14.t3.t20.t6))
% 0.46/0.78 (step t14.t3.t20.t8 (cl (= (or (not (= E (tptp.ordered_pair H (tptp.singleton H)))) (not (tptp.in H A)) (not (= (tptp.singleton H) (tptp.singleton H)))) (or (not (= E (tptp.ordered_pair H (tptp.singleton H)))) (not (tptp.in H A)) false))) :rule cong :premises (t14.t3.t20.t2 t14.t3.t20.t3 t14.t3.t20.t7))
% 0.46/0.78 (step t14.t3.t20.t9 (cl (= (or (not (= E (tptp.ordered_pair H (tptp.singleton H)))) (not (tptp.in H A)) false) (or (not (= E (tptp.ordered_pair H (tptp.singleton H)))) (not (tptp.in H A))))) :rule all_simplify)
% 0.46/0.78 (step t14.t3.t20.t10 (cl (= (or (not (= E (tptp.ordered_pair H (tptp.singleton H)))) (not (tptp.in H A)) (not (= (tptp.singleton H) (tptp.singleton H)))) (or (not (= E (tptp.ordered_pair H (tptp.singleton H)))) (not (tptp.in H A))))) :rule trans :premises (t14.t3.t20.t8 t14.t3.t20.t9))
% 0.46/0.78 (step t14.t3.t20 (cl (= (forall ((H $$unsorted)) (or (not (= E (tptp.ordered_pair H (tptp.singleton H)))) (not (tptp.in H A)) (not (= (tptp.singleton H) (tptp.singleton H))))) (forall ((H $$unsorted)) (or (not (= E (tptp.ordered_pair H (tptp.singleton H)))) (not (tptp.in H A)))))) :rule bind)
% 0.46/0.78 (step t14.t3.t21 (cl (= (forall ((H $$unsorted) (I $$unsorted)) (or (not (= E (tptp.ordered_pair H I))) (not (tptp.in H A)) (not (= I (tptp.singleton H))))) (forall ((H $$unsorted)) (or (not (= E (tptp.ordered_pair H (tptp.singleton H)))) (not (tptp.in H A)))))) :rule trans :premises (t14.t3.t19 t14.t3.t20))
% 0.46/0.78 (step t14.t3.t22 (cl (= (forall ((H $$unsorted) (I $$unsorted)) (not (and (= E (tptp.ordered_pair H I)) (tptp.in H A) (= I (tptp.singleton H))))) (forall ((H $$unsorted)) (or (not (= E (tptp.ordered_pair H (tptp.singleton H)))) (not (tptp.in H A)))))) :rule trans :premises (t14.t3.t18 t14.t3.t21))
% 0.46/0.78 (step t14.t3.t23 (cl (= (not (forall ((H $$unsorted) (I $$unsorted)) (not (and (= E (tptp.ordered_pair H I)) (tptp.in H A) (= I (tptp.singleton H)))))) (not (forall ((H $$unsorted)) (or (not (= E (tptp.ordered_pair H (tptp.singleton H)))) (not (tptp.in H A))))))) :rule cong :premises (t14.t3.t22))
% 0.46/0.78 (step t14.t3.t24 (cl (= (exists ((H $$unsorted) (I $$unsorted)) (and (= E (tptp.ordered_pair H I)) (tptp.in H A) (= I (tptp.singleton H)))) (not (forall ((H $$unsorted)) (or (not (= E (tptp.ordered_pair H (tptp.singleton H)))) (not (tptp.in H A))))))) :rule trans :premises (t14.t3.t17 t14.t3.t23))
% 0.46/0.78 (step t14.t3.t25 (cl (= (exists ((H $$unsorted) (I $$unsorted)) (and (= (tptp.ordered_pair H I) E) (tptp.in H A) (= I (tptp.singleton H)))) (not (forall ((H $$unsorted)) (or (not (= E (tptp.ordered_pair H (tptp.singleton H)))) (not (tptp.in H A))))))) :rule trans :premises (t14.t3.t16 t14.t3.t24))
% 0.46/0.78 (step t14.t3.t26 (cl (= (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))))) (and (= C D) (not (forall ((F $$unsorted)) (or (not (= D (tptp.ordered_pair F (tptp.singleton F)))) (not (tptp.in F A))))) (= C E) (not (forall ((H $$unsorted)) (or (not (= E (tptp.ordered_pair H (tptp.singleton H)))) (not (tptp.in H A)))))))) :rule cong :premises (t14.t3.t4 t14.t3.t14 t14.t3.t15 t14.t3.t25))
% 0.46/0.78 (step t14.t3.t27 (cl (= (= D E) (= D E))) :rule refl)
% 0.46/0.78 (step t14.t3.t28 (cl (= (=> (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)) (=> (and (= C D) (not (forall ((F $$unsorted)) (or (not (= D (tptp.ordered_pair F (tptp.singleton F)))) (not (tptp.in F A))))) (= C E) (not (forall ((H $$unsorted)) (or (not (= E (tptp.ordered_pair H (tptp.singleton H)))) (not (tptp.in H A)))))) (= D E)))) :rule cong :premises (t14.t3.t26 t14.t3.t27))
% 0.46/0.78 (step t14.t3 (cl (= (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 $$unsorted)) (and (= (tptp.ordered_pair H I) E) (tptp.in H A) (= I (tptp.singleton H))))) (= D E))) (forall ((C $$unsorted) (D $$unsorted) (E $$unsorted)) (=> (and (= C D) (not (forall ((F $$unsorted)) (or (not (= D (tptp.ordered_pair F (tptp.singleton F)))) (not (tptp.in F A))))) (= C E) (not (forall ((H $$unsorted)) (or (not (= E (tptp.ordered_pair H (tptp.singleton H)))) (not (tptp.in H A)))))) (= D E))))) :rule bind)
% 0.46/0.78 (step t14.t4 (cl (= (forall ((C $$unsorted) (D $$unsorted) (E $$unsorted)) (=> (and (= C D) (not (forall ((F $$unsorted)) (or (not (= D (tptp.ordered_pair F (tptp.singleton F)))) (not (tptp.in F A))))) (= C E) (not (forall ((H $$unsorted)) (or (not (= E (tptp.ordered_pair H (tptp.singleton H)))) (not (tptp.in H A)))))) (= D E))) (forall ((C $$unsorted) (D $$unsorted) (E $$unsorted)) (or (not (= C D)) (forall ((F $$unsorted)) (or (not (= D (tptp.ordered_pair F (tptp.singleton F)))) (not (tptp.in F A)))) (not (= C E)) (forall ((H $$unsorted)) (or (not (= E (tptp.ordered_pair H (tptp.singleton H)))) (not (tptp.in H A)))) (= D E))))) :rule all_simplify)
% 0.46/0.78 (step t14.t5 (cl (= (forall ((C $$unsorted) (D $$unsorted) (E $$unsorted)) (or (not (= C D)) (forall ((F $$unsorted)) (or (not (= D (tptp.ordered_pair F (tptp.singleton F)))) (not (tptp.in F A)))) (not (= C E)) (forall ((H $$unsorted)) (or (not (= E (tptp.ordered_pair H (tptp.singleton H)))) (not (tptp.in H A)))) (= D E))) (forall ((C $$unsorted) (D $$unsorted) (E $$unsorted) (BOUND_VARIABLE_7141 $$unsorted) (BOUND_VARIABLE_7132 $$unsorted)) (or (not (= C D)) (or (not (= D (tptp.ordered_pair BOUND_VARIABLE_7132 (tptp.singleton BOUND_VARIABLE_7132)))) (not (tptp.in BOUND_VARIABLE_7132 A))) (not (= C E)) (or (not (= E (tptp.ordered_pair BOUND_VARIABLE_7141 (tptp.singleton BOUND_VARIABLE_7141)))) (not (tptp.in BOUND_VARIABLE_7141 A))) (= D E))))) :rule all_simplify)
% 0.46/0.78 (anchor :step t14.t6 :args ((C $$unsorted) (:= C C) (D $$unsorted) (:= D D) (E $$unsorted) (:= E E) (BOUND_VARIABLE_7141 $$unsorted) (:= BOUND_VARIABLE_7141 BOUND_VARIABLE_7141) (BOUND_VARIABLE_7132 $$unsorted) (:= BOUND_VARIABLE_7132 BOUND_VARIABLE_7132)))
% 0.46/0.78 (step t14.t6.t1 (cl (= C C)) :rule refl)
% 0.46/0.78 (step t14.t6.t2 (cl (= D D)) :rule refl)
% 0.46/0.78 (step t14.t6.t3 (cl (= E E)) :rule refl)
% 0.46/0.78 (step t14.t6.t4 (cl (= BOUND_VARIABLE_7141 BOUND_VARIABLE_7141)) :rule refl)
% 0.46/0.78 (step t14.t6.t5 (cl (= BOUND_VARIABLE_7132 BOUND_VARIABLE_7132)) :rule refl)
% 0.46/0.78 (step t14.t6.t6 (cl (= (or (not (= C D)) (or (not (= D (tptp.ordered_pair BOUND_VARIABLE_7132 (tptp.singleton BOUND_VARIABLE_7132)))) (not (tptp.in BOUND_VARIABLE_7132 A))) (not (= C E)) (or (not (= E (tptp.ordered_pair BOUND_VARIABLE_7141 (tptp.singleton BOUND_VARIABLE_7141)))) (not (tptp.in BOUND_VARIABLE_7141 A))) (= D E)) (or (not (= C D)) (not (= C E)) (= D E) (not (= D (tptp.ordered_pair BOUND_VARIABLE_7132 (tptp.singleton BOUND_VARIABLE_7132)))) (not (tptp.in BOUND_VARIABLE_7132 A)) (not (= E (tptp.ordered_pair BOUND_VARIABLE_7141 (tptp.singleton BOUND_VARIABLE_7141)))) (not (tptp.in BOUND_VARIABLE_7141 A))))) :rule all_simplify)
% 0.46/0.78 (step t14.t6 (cl (= (forall ((C $$unsorted) (D $$unsorted) (E $$unsorted) (BOUND_VARIABLE_7141 $$unsorted) (BOUND_VARIABLE_7132 $$unsorted)) (or (not (= C D)) (or (not (= D (tptp.ordered_pair BOUND_VARIABLE_7132 (tptp.singleton BOUND_VARIABLE_7132)))) (not (tptp.in BOUND_VARIABLE_7132 A))) (not (= C E)) (or (not (= E (tptp.ordered_pair BOUND_VARIABLE_7141 (tptp.singleton BOUND_VARIABLE_7141)))) (not (tptp.in BOUND_VARIABLE_7141 A))) (= D E))) (forall ((C $$unsorted) (D $$unsorted) (E $$unsorted) (BOUND_VARIABLE_7141 $$unsorted) (BOUND_VARIABLE_7132 $$unsorted)) (or (not (= C D)) (not (= C E)) (= D E) (not (= D (tptp.ordered_pair BOUND_VARIABLE_7132 (tptp.singleton BOUND_VARIABLE_7132)))) (not (tptp.in BOUND_VARIABLE_7132 A)) (not (= E (tptp.ordered_pair BOUND_VARIABLE_7141 (tptp.singleton BOUND_VARIABLE_7141)))) (not (tptp.in BOUND_VARIABLE_7141 A)))))) :rule bind)
% 0.46/0.78 (step t14.t7 (cl (= (forall ((C $$unsorted) (D $$unsorted) (E $$unsorted) (BOUND_VARIABLE_7141 $$unsorted) (BOUND_VARIABLE_7132 $$unsorted)) (or (not (= C D)) (not (= C E)) (= D E) (not (= D (tptp.ordered_pair BOUND_VARIABLE_7132 (tptp.singleton BOUND_VARIABLE_7132)))) (not (tptp.in BOUND_VARIABLE_7132 A)) (not (= E (tptp.ordered_pair BOUND_VARIABLE_7141 (tptp.singleton BOUND_VARIABLE_7141)))) (not (tptp.in BOUND_VARIABLE_7141 A)))) (forall ((BOUND_VARIABLE_7141 $$unsorted) (BOUND_VARIABLE_7132 $$unsorted)) (or (not (= (tptp.ordered_pair BOUND_VARIABLE_7132 (tptp.singleton BOUND_VARIABLE_7132)) (tptp.ordered_pair BOUND_VARIABLE_7132 (tptp.singleton BOUND_VARIABLE_7132)))) (not (= (tptp.ordered_pair BOUND_VARIABLE_7132 (tptp.singleton BOUND_VARIABLE_7132)) (tptp.ordered_pair BOUND_VARIABLE_7132 (tptp.singleton BOUND_VARIABLE_7132)))) (= (tptp.ordered_pair BOUND_VARIABLE_7132 (tptp.singleton BOUND_VARIABLE_7132)) (tptp.ordered_pair BOUND_VARIABLE_7132 (tptp.singleton BOUND_VARIABLE_7132))) (not (= (tptp.ordered_pair BOUND_VARIABLE_7132 (tptp.singleton BOUND_VARIABLE_7132)) (tptp.ordered_pair BOUND_VARIABLE_7132 (tptp.singleton BOUND_VARIABLE_7132)))) (not (tptp.in BOUND_VARIABLE_7132 A)) (not (= (tptp.ordered_pair BOUND_VARIABLE_7132 (tptp.singleton BOUND_VARIABLE_7132)) (tptp.ordered_pair BOUND_VARIABLE_7141 (tptp.singleton BOUND_VARIABLE_7141)))) (not (tptp.in BOUND_VARIABLE_7141 A)))))) :rule all_simplify)
% 0.46/0.78 (anchor :step t14.t8 :args ((BOUND_VARIABLE_7141 $$unsorted) (:= BOUND_VARIABLE_7141 BOUND_VARIABLE_7141) (BOUND_VARIABLE_7132 $$unsorted) (:= BOUND_VARIABLE_7132 BOUND_VARIABLE_7132)))
% 0.46/0.78 (step t14.t8.t1 (cl (= BOUND_VARIABLE_7141 BOUND_VARIABLE_7141)) :rule refl)
% 0.46/0.78 (step t14.t8.t2 (cl (= BOUND_VARIABLE_7132 BOUND_VARIABLE_7132)) :rule refl)
% 0.46/0.78 (step t14.t8.t3 (cl (= (= (tptp.ordered_pair BOUND_VARIABLE_7132 (tptp.singleton BOUND_VARIABLE_7132)) (tptp.ordered_pair BOUND_VARIABLE_7132 (tptp.singleton BOUND_VARIABLE_7132))) true)) :rule all_simplify)
% 0.46/0.78 (step t14.t8.t4 (cl (= (not (= (tptp.ordered_pair BOUND_VARIABLE_7132 (tptp.singleton BOUND_VARIABLE_7132)) (tptp.ordered_pair BOUND_VARIABLE_7132 (tptp.singleton BOUND_VARIABLE_7132)))) (not true))) :rule cong :premises (t14.t8.t3))
% 0.46/0.78 (step t14.t8.t5 (cl (= (not true) false)) :rule all_simplify)
% 0.46/0.78 (step t14.t8.t6 (cl (= (not (= (tptp.ordered_pair BOUND_VARIABLE_7132 (tptp.singleton BOUND_VARIABLE_7132)) (tptp.ordered_pair BOUND_VARIABLE_7132 (tptp.singleton BOUND_VARIABLE_7132)))) false)) :rule trans :premises (t14.t8.t4 t14.t8.t5))
% 0.46/0.78 (step t14.t8.t7 (cl (= (not (tptp.in BOUND_VARIABLE_7132 A)) (not (tptp.in BOUND_VARIABLE_7132 A)))) :rule refl)
% 0.46/0.78 (step t14.t8.t8 (cl (= (not (= (tptp.ordered_pair BOUND_VARIABLE_7132 (tptp.singleton BOUND_VARIABLE_7132)) (tptp.ordered_pair BOUND_VARIABLE_7141 (tptp.singleton BOUND_VARIABLE_7141)))) (not (= (tptp.ordered_pair BOUND_VARIABLE_7132 (tptp.singleton BOUND_VARIABLE_7132)) (tptp.ordered_pair BOUND_VARIABLE_7141 (tptp.singleton BOUND_VARIABLE_7141)))))) :rule refl)
% 0.46/0.78 (step t14.t8.t9 (cl (= (not (tptp.in BOUND_VARIABLE_7141 A)) (not (tptp.in BOUND_VARIABLE_7141 A)))) :rule refl)
% 0.46/0.78 (step t14.t8.t10 (cl (= (or (not (= (tptp.ordered_pair BOUND_VARIABLE_7132 (tptp.singleton BOUND_VARIABLE_7132)) (tptp.ordered_pair BOUND_VARIABLE_7132 (tptp.singleton BOUND_VARIABLE_7132)))) (not (= (tptp.ordered_pair BOUND_VARIABLE_7132 (tptp.singleton BOUND_VARIABLE_7132)) (tptp.ordered_pair BOUND_VARIABLE_7132 (tptp.singleton BOUND_VARIABLE_7132)))) (= (tptp.ordered_pair BOUND_VARIABLE_7132 (tptp.singleton BOUND_VARIABLE_7132)) (tptp.ordered_pair BOUND_VARIABLE_7132 (tptp.singleton BOUND_VARIABLE_7132))) (not (= (tptp.ordered_pair BOUND_VARIABLE_7132 (tptp.singleton BOUND_VARIABLE_7132)) (tptp.ordered_pair BOUND_VARIABLE_7132 (tptp.singleton BOUND_VARIABLE_7132)))) (not (tptp.in BOUND_VARIABLE_7132 A)) (not (= (tptp.ordered_pair BOUND_VARIABLE_7132 (tptp.singleton BOUND_VARIABLE_7132)) (tptp.ordered_pair BOUND_VARIABLE_7141 (tptp.singleton BOUND_VARIABLE_7141)))) (not (tptp.in BOUND_VARIABLE_7141 A))) (or false false true false (not (tptp.in BOUND_VARIABLE_7132 A)) (not (= (tptp.ordered_pair BOUND_VARIABLE_7132 (tptp.singleton BOUND_VARIABLE_7132)) (tptp.ordered_pair BOUND_VARIABLE_7141 (tptp.singleton BOUND_VARIABLE_7141)))) (not (tptp.in BOUND_VARIABLE_7141 A))))) :rule cong :premises (t14.t8.t6 t14.t8.t6 t14.t8.t3 t14.t8.t6 t14.t8.t7 t14.t8.t8 t14.t8.t9))
% 0.46/0.78 (step t14.t8.t11 (cl (= (or false false true false (not (tptp.in BOUND_VARIABLE_7132 A)) (not (= (tptp.ordered_pair BOUND_VARIABLE_7132 (tptp.singleton BOUND_VARIABLE_7132)) (tptp.ordered_pair BOUND_VARIABLE_7141 (tptp.singleton BOUND_VARIABLE_7141)))) (not (tptp.in BOUND_VARIABLE_7141 A))) true)) :rule all_simplify)
% 0.46/0.78 (step t14.t8.t12 (cl (= (or (not (= (tptp.ordered_pair BOUND_VARIABLE_7132 (tptp.singleton BOUND_VARIABLE_7132)) (tptp.ordered_pair BOUND_VARIABLE_7132 (tptp.singleton BOUND_VARIABLE_7132)))) (not (= (tptp.ordered_pair BOUND_VARIABLE_7132 (tptp.singleton BOUND_VARIABLE_7132)) (tptp.ordered_pair BOUND_VARIABLE_7132 (tptp.singleton BOUND_VARIABLE_7132)))) (= (tptp.ordered_pair BOUND_VARIABLE_7132 (tptp.singleton BOUND_VARIABLE_7132)) (tptp.ordered_pair BOUND_VARIABLE_7132 (tptp.singleton BOUND_VARIABLE_7132))) (not (= (tptp.ordered_pair BOUND_VARIABLE_7132 (tptp.singleton BOUND_VARIABLE_7132)) (tptp.ordered_pair BOUND_VARIABLE_7132 (tptp.singleton BOUND_VARIABLE_7132)))) (not (tptp.in BOUND_VARIABLE_7132 A)) (not (= (tptp.ordered_pair BOUND_VARIABLE_7132 (tptp.singleton BOUND_VARIABLE_7132)) (tptp.ordered_pair BOUND_VARIABLE_7141 (tptp.singleton BOUND_VARIABLE_7141)))) (not (tptp.in BOUND_VARIABLE_7141 A))) true)) :rule trans :premises (t14.t8.t10 t14.t8.t11))
% 0.46/0.78 (step t14.t8 (cl (= (forall ((BOUND_VARIABLE_7141 $$unsorted) (BOUND_VARIABLE_7132 $$unsorted)) (or (not (= (tptp.ordered_pair BOUND_VARIABLE_7132 (tptp.singleton BOUND_VARIABLE_7132)) (tptp.ordered_pair BOUND_VARIABLE_7132 (tptp.singleton BOUND_VARIABLE_7132)))) (not (= (tptp.ordered_pair BOUND_VARIABLE_7132 (tptp.singleton BOUND_VARIABLE_7132)) (tptp.ordered_pair BOUND_VARIABLE_7132 (tptp.singleton BOUND_VARIABLE_7132)))) (= (tptp.ordered_pair BOUND_VARIABLE_7132 (tptp.singleton BOUND_VARIABLE_7132)) (tptp.ordered_pair BOUND_VARIABLE_7132 (tptp.singleton BOUND_VARIABLE_7132))) (not (= (tptp.ordered_pair BOUND_VARIABLE_7132 (tptp.singleton BOUND_VARIABLE_7132)) (tptp.ordered_pair BOUND_VARIABLE_7132 (tptp.singleton BOUND_VARIABLE_7132)))) (not (tptp.in BOUND_VARIABLE_7132 A)) (not (= (tptp.ordered_pair BOUND_VARIABLE_7132 (tptp.singleton BOUND_VARIABLE_7132)) (tptp.ordered_pair BOUND_VARIABLE_7141 (tptp.singleton BOUND_VARIABLE_7141)))) (not (tptp.in BOUND_VARIABLE_7141 A)))) (forall ((BOUND_VARIABLE_7141 $$unsorted) (BOUND_VARIABLE_7132 $$unsorted)) true))) :rule bind)
% 0.46/0.78 (step t14.t9 (cl (= (forall ((BOUND_VARIABLE_7141 $$unsorted) (BOUND_VARIABLE_7132 $$unsorted)) true) true)) :rule all_simplify)
% 0.46/0.78 (step t14.t10 (cl (= (forall ((BOUND_VARIABLE_7141 $$unsorted) (BOUND_VARIABLE_7132 $$unsorted)) (or (not (= (tptp.ordered_pair BOUND_VARIABLE_7132 (tptp.singleton BOUND_VARIABLE_7132)) (tptp.ordered_pair BOUND_VARIABLE_7132 (tptp.singleton BOUND_VARIABLE_7132)))) (not (= (tptp.ordered_pair BOUND_VARIABLE_7132 (tptp.singleton BOUND_VARIABLE_7132)) (tptp.ordered_pair BOUND_VARIABLE_7132 (tptp.singleton BOUND_VARIABLE_7132)))) (= (tptp.ordered_pair BOUND_VARIABLE_7132 (tptp.singleton BOUND_VARIABLE_7132)) (tptp.ordered_pair BOUND_VARIABLE_7132 (tptp.singleton BOUND_VARIABLE_7132))) (not (= (tptp.ordered_pair BOUND_VARIABLE_7132 (tptp.singleton BOUND_VARIABLE_7132)) (tptp.ordered_pair BOUND_VARIABLE_7132 (tptp.singleton BOUND_VARIABLE_7132)))) (not (tptp.in BOUND_VARIABLE_7132 A)) (not (= (tptp.ordered_pair BOUND_VARIABLE_7132 (tptp.singleton BOUND_VARIABLE_7132)) (tptp.ordered_pair BOUND_VARIABLE_7141 (tptp.singleton BOUND_VARIABLE_7141)))) (not (tptp.in BOUND_VARIABLE_7141 A)))) true)) :rule trans :premises (t14.t8 t14.t9))
% 0.46/0.78 (step t14.t11 (cl (= (forall ((C $$unsorted) (D $$unsorted) (E $$unsorted) (BOUND_VARIABLE_7141 $$unsorted) (BOUND_VARIABLE_7132 $$unsorted)) (or (not (= C D)) (not (= C E)) (= D E) (not (= D (tptp.ordered_pair BOUND_VARIABLE_7132 (tptp.singleton BOUND_VARIABLE_7132)))) (not (tptp.in BOUND_VARIABLE_7132 A)) (not (= E (tptp.ordered_pair BOUND_VARIABLE_7141 (tptp.singleton BOUND_VARIABLE_7141)))) (not (tptp.in BOUND_VARIABLE_7141 A)))) true)) :rule trans :premises (t14.t7 t14.t10))
% 0.46/0.78 (step t14.t12 (cl (= (forall ((C $$unsorted) (D $$unsorted) (E $$unsorted) (BOUND_VARIABLE_7141 $$unsorted) (BOUND_VARIABLE_7132 $$unsorted)) (or (not (= C D)) (or (not (= D (tptp.ordered_pair BOUND_VARIABLE_7132 (tptp.singleton BOUND_VARIABLE_7132)))) (not (tptp.in BOUND_VARIABLE_7132 A))) (not (= C E)) (or (not (= E (tptp.ordered_pair BOUND_VARIABLE_7141 (tptp.singleton BOUND_VARIABLE_7141)))) (not (tptp.in BOUND_VARIABLE_7141 A))) (= D E))) true)) :rule trans :premises (t14.t6 t14.t11))
% 0.46/0.78 (step t14.t13 (cl (= (forall ((C $$unsorted) (D $$unsorted) (E $$unsorted)) (or (not (= C D)) (forall ((F $$unsorted)) (or (not (= D (tptp.ordered_pair F (tptp.singleton F)))) (not (tptp.in F A)))) (not (= C E)) (forall ((H $$unsorted)) (or (not (= E (tptp.ordered_pair H (tptp.singleton H)))) (not (tptp.in H A)))) (= D E))) true)) :rule trans :premises (t14.t5 t14.t12))
% 0.46/0.78 (step t14.t14 (cl (= (forall ((C $$unsorted) (D $$unsorted) (E $$unsorted)) (=> (and (= C D) (not (forall ((F $$unsorted)) (or (not (= D (tptp.ordered_pair F (tptp.singleton F)))) (not (tptp.in F A))))) (= C E) (not (forall ((H $$unsorted)) (or (not (= E (tptp.ordered_pair H (tptp.singleton H)))) (not (tptp.in H A)))))) (= D E))) true)) :rule trans :premises (t14.t4 t14.t13))
% 0.46/0.78 (step t14.t15 (cl (= (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 $$unsorted)) (and (= (tptp.ordered_pair H I) E) (tptp.in H A) (= I (tptp.singleton H))))) (= D E))) true)) :rule trans :premises (t14.t3 t14.t14))
% 0.46/0.78 (anchor :step t14.t16 :args ((C $$unsorted) (:= C C)))
% 0.46/0.78 (step t14.t16.t1 (cl (= C C)) :rule refl)
% 0.46/0.78 (anchor :step t14.t16.t2 :args ((D $$unsorted) (:= D D)))
% 0.46/0.78 (step t14.t16.t2.t1 (cl (= D D)) :rule refl)
% 0.46/0.78 (step t14.t16.t2.t2 (cl (= (tptp.in D C) (tptp.in D C))) :rule refl)
% 0.46/0.78 (anchor :step t14.t16.t2.t3 :args ((E $$unsorted) (:= E E)))
% 0.46/0.78 (step t14.t16.t2.t3.t1 (cl (= E E)) :rule refl)
% 0.46/0.78 (step t14.t16.t2.t3.t2 (cl (= (tptp.in E (tptp.cartesian_product2 A B)) (tptp.in E (tptp.cartesian_product2 A B)))) :rule refl)
% 0.46/0.78 (step t14.t16.t2.t3.t3 (cl (= (= E D) (= D E))) :rule all_simplify)
% 0.46/0.78 (anchor :step t14.t16.t2.t3.t4 :args ((J $$unsorted) (:= J J) (K $$unsorted) (:= K K)))
% 0.46/0.78 (step t14.t16.t2.t3.t4.t1 (cl (= J J)) :rule refl)
% 0.46/0.78 (step t14.t16.t2.t3.t4.t2 (cl (= K K)) :rule refl)
% 0.46/0.78 (step t14.t16.t2.t3.t4.t3 (cl (= (= (tptp.ordered_pair J K) D) (= D (tptp.ordered_pair J K)))) :rule all_simplify)
% 0.46/0.78 (step t14.t16.t2.t3.t4.t4 (cl (= (tptp.in J A) (tptp.in J A))) :rule refl)
% 0.46/0.78 (step t14.t16.t2.t3.t4.t5 (cl (= (= K (tptp.singleton J)) (= K (tptp.singleton J)))) :rule refl)
% 0.46/0.78 (step t14.t16.t2.t3.t4.t6 (cl (= (and (= (tptp.ordered_pair J K) D) (tptp.in J A) (= K (tptp.singleton J))) (and (= D (tptp.ordered_pair J K)) (tptp.in J A) (= K (tptp.singleton J))))) :rule cong :premises (t14.t16.t2.t3.t4.t3 t14.t16.t2.t3.t4.t4 t14.t16.t2.t3.t4.t5))
% 0.46/0.78 (step t14.t16.t2.t3.t4 (cl (= (exists ((J $$unsorted) (K $$unsorted)) (and (= (tptp.ordered_pair J K) D) (tptp.in J A) (= K (tptp.singleton J)))) (exists ((J $$unsorted) (K $$unsorted)) (and (= D (tptp.ordered_pair J K)) (tptp.in J A) (= K (tptp.singleton J)))))) :rule bind)
% 0.46/0.78 (step t14.t16.t2.t3.t5 (cl (= (exists ((J $$unsorted) (K $$unsorted)) (and (= D (tptp.ordered_pair J K)) (tptp.in J A) (= K (tptp.singleton J)))) (not (forall ((J $$unsorted) (K $$unsorted)) (not (and (= D (tptp.ordered_pair J K)) (tptp.in J A) (= K (tptp.singleton J)))))))) :rule all_simplify)
% 0.46/0.78 (step t14.t16.t2.t3.t6 (cl (= (forall ((J $$unsorted) (K $$unsorted)) (not (and (= D (tptp.ordered_pair J K)) (tptp.in J A) (= K (tptp.singleton J))))) (forall ((J $$unsorted) (K $$unsorted)) (or (not (= D (tptp.ordered_pair J K))) (not (tptp.in J A)) (not (= K (tptp.singleton J))))))) :rule all_simplify)
% 0.46/0.78 (step t14.t16.t2.t3.t7 (cl (= (forall ((J $$unsorted) (K $$unsorted)) (or (not (= D (tptp.ordered_pair J K))) (not (tptp.in J A)) (not (= K (tptp.singleton J))))) (forall ((J $$unsorted)) (or (not (= D (tptp.ordered_pair J (tptp.singleton J)))) (not (tptp.in J A)) (not (= (tptp.singleton J) (tptp.singleton J))))))) :rule all_simplify)
% 0.46/0.78 (anchor :step t14.t16.t2.t3.t8 :args ((J $$unsorted) (:= J J)))
% 0.46/0.78 (step t14.t16.t2.t3.t8.t1 (cl (= J J)) :rule refl)
% 0.46/0.78 (step t14.t16.t2.t3.t8.t2 (cl (= (not (= D (tptp.ordered_pair J (tptp.singleton J)))) (not (= D (tptp.ordered_pair J (tptp.singleton J)))))) :rule refl)
% 0.46/0.78 (step t14.t16.t2.t3.t8.t3 (cl (= (not (tptp.in J A)) (not (tptp.in J A)))) :rule refl)
% 0.46/0.78 (step t14.t16.t2.t3.t8.t4 (cl (= (= (tptp.singleton J) (tptp.singleton J)) true)) :rule all_simplify)
% 0.46/0.78 (step t14.t16.t2.t3.t8.t5 (cl (= (not (= (tptp.singleton J) (tptp.singleton J))) (not true))) :rule cong :premises (t14.t16.t2.t3.t8.t4))
% 0.46/0.78 (step t14.t16.t2.t3.t8.t6 (cl (= (not true) false)) :rule all_simplify)
% 0.46/0.78 (step t14.t16.t2.t3.t8.t7 (cl (= (not (= (tptp.singleton J) (tptp.singleton J))) false)) :rule trans :premises (t14.t16.t2.t3.t8.t5 t14.t16.t2.t3.t8.t6))
% 0.46/0.78 (step t14.t16.t2.t3.t8.t8 (cl (= (or (not (= D (tptp.ordered_pair J (tptp.singleton J)))) (not (tptp.in J A)) (not (= (tptp.singleton J) (tptp.singleton J)))) (or (not (= D (tptp.ordered_pair J (tptp.singleton J)))) (not (tptp.in J A)) false))) :rule cong :premises (t14.t16.t2.t3.t8.t2 t14.t16.t2.t3.t8.t3 t14.t16.t2.t3.t8.t7))
% 0.46/0.78 (step t14.t16.t2.t3.t8.t9 (cl (= (or (not (= D (tptp.ordered_pair J (tptp.singleton J)))) (not (tptp.in J A)) false) (or (not (= D (tptp.ordered_pair J (tptp.singleton J)))) (not (tptp.in J A))))) :rule all_simplify)
% 0.46/0.78 (step t14.t16.t2.t3.t8.t10 (cl (= (or (not (= D (tptp.ordered_pair J (tptp.singleton J)))) (not (tptp.in J A)) (not (= (tptp.singleton J) (tptp.singleton J)))) (or (not (= D (tptp.ordered_pair J (tptp.singleton J)))) (not (tptp.in J A))))) :rule trans :premises (t14.t16.t2.t3.t8.t8 t14.t16.t2.t3.t8.t9))
% 0.46/0.78 (step t14.t16.t2.t3.t8 (cl (= (forall ((J $$unsorted)) (or (not (= D (tptp.ordered_pair J (tptp.singleton J)))) (not (tptp.in J A)) (not (= (tptp.singleton J) (tptp.singleton J))))) (forall ((J $$unsorted)) (or (not (= D (tptp.ordered_pair J (tptp.singleton J)))) (not (tptp.in J A)))))) :rule bind)
% 0.46/0.78 (step t14.t16.t2.t3.t9 (cl (= (forall ((J $$unsorted) (K $$unsorted)) (or (not (= D (tptp.ordered_pair J K))) (not (tptp.in J A)) (not (= K (tptp.singleton J))))) (forall ((J $$unsorted)) (or (not (= D (tptp.ordered_pair J (tptp.singleton J)))) (not (tptp.in J A)))))) :rule trans :premises (t14.t16.t2.t3.t7 t14.t16.t2.t3.t8))
% 0.46/0.78 (step t14.t16.t2.t3.t10 (cl (= (forall ((J $$unsorted) (K $$unsorted)) (not (and (= D (tptp.ordered_pair J K)) (tptp.in J A) (= K (tptp.singleton J))))) (forall ((J $$unsorted)) (or (not (= D (tptp.ordered_pair J (tptp.singleton J)))) (not (tptp.in J A)))))) :rule trans :premises (t14.t16.t2.t3.t6 t14.t16.t2.t3.t9))
% 0.46/0.78 (step t14.t16.t2.t3.t11 (cl (= (not (forall ((J $$unsorted) (K $$unsorted)) (not (and (= D (tptp.ordered_pair J K)) (tptp.in J A) (= K (tptp.singleton J)))))) (not (forall ((J $$unsorted)) (or (not (= D (tptp.ordered_pair J (tptp.singleton J)))) (not (tptp.in J A))))))) :rule cong :premises (t14.t16.t2.t3.t10))
% 0.46/0.78 (step t14.t16.t2.t3.t12 (cl (= (exists ((J $$unsorted) (K $$unsorted)) (and (= D (tptp.ordered_pair J K)) (tptp.in J A) (= K (tptp.singleton J)))) (not (forall ((J $$unsorted)) (or (not (= D (tptp.ordered_pair J (tptp.singleton J)))) (not (tptp.in J A))))))) :rule trans :premises (t14.t16.t2.t3.t5 t14.t16.t2.t3.t11))
% 0.46/0.78 (step t14.t16.t2.t3.t13 (cl (= (exists ((J $$unsorted) (K $$unsorted)) (and (= (tptp.ordered_pair J K) D) (tptp.in J A) (= K (tptp.singleton J)))) (not (forall ((J $$unsorted)) (or (not (= D (tptp.ordered_pair J (tptp.singleton J)))) (not (tptp.in J A))))))) :rule trans :premises (t14.t16.t2.t3.t4 t14.t16.t2.t3.t12))
% 0.46/0.78 (step t14.t16.t2.t3.t14 (cl (= (and (tptp.in E (tptp.cartesian_product2 A B)) (= E D) (exists ((J $$unsorted) (K $$unsorted)) (and (= (tptp.ordered_pair J K) D) (tptp.in J A) (= K (tptp.singleton J))))) (and (tptp.in E (tptp.cartesian_product2 A B)) (= D E) (not (forall ((J $$unsorted)) (or (not (= D (tptp.ordered_pair J (tptp.singleton J)))) (not (tptp.in J A)))))))) :rule cong :premises (t14.t16.t2.t3.t2 t14.t16.t2.t3.t3 t14.t16.t2.t3.t13))
% 0.46/0.78 (step t14.t16.t2.t3 (cl (= (exists ((E $$unsorted)) (and (tptp.in E (tptp.cartesian_product2 A B)) (= E D) (exists ((J $$unsorted) (K $$unsorted)) (and (= (tptp.ordered_pair J K) D) (tptp.in J A) (= K (tptp.singleton J)))))) (exists ((E $$unsorted)) (and (tptp.in E (tptp.cartesian_product2 A B)) (= D E) (not (forall ((J $$unsorted)) (or (not (= D (tptp.ordered_pair J (tptp.singleton J)))) (not (tptp.in J A))))))))) :rule bind)
% 0.46/0.78 (step t14.t16.t2.t4 (cl (= (exists ((E $$unsorted)) (and (tptp.in E (tptp.cartesian_product2 A B)) (= D E) (not (forall ((J $$unsorted)) (or (not (= D (tptp.ordered_pair J (tptp.singleton J)))) (not (tptp.in J A))))))) (not (forall ((E $$unsorted)) (not (and (tptp.in E (tptp.cartesian_product2 A B)) (= D E) (not (forall ((J $$unsorted)) (or (not (= D (tptp.ordered_pair J (tptp.singleton J)))) (not (tptp.in J A))))))))))) :rule all_simplify)
% 0.46/0.78 (step t14.t16.t2.t5 (cl (= (forall ((E $$unsorted)) (not (and (tptp.in E (tptp.cartesian_product2 A B)) (= D E) (not (forall ((J $$unsorted)) (or (not (= D (tptp.ordered_pair J (tptp.singleton J)))) (not (tptp.in J A)))))))) (forall ((E $$unsorted)) (or (not (tptp.in E (tptp.cartesian_product2 A B))) (not (= D E)) (forall ((J $$unsorted)) (or (not (= D (tptp.ordered_pair J (tptp.singleton J)))) (not (tptp.in J A)))))))) :rule all_simplify)
% 0.46/0.78 (step t14.t16.t2.t6 (cl (= (forall ((E $$unsorted)) (or (not (tptp.in E (tptp.cartesian_product2 A B))) (not (= D E)) (forall ((J $$unsorted)) (or (not (= D (tptp.ordered_pair J (tptp.singleton J)))) (not (tptp.in J A)))))) (or (forall ((J $$unsorted)) (or (not (= D (tptp.ordered_pair J (tptp.singleton J)))) (not (tptp.in J A)))) (forall ((E $$unsorted)) (or (not (tptp.in E (tptp.cartesian_product2 A B))) (not (= D E))))))) :rule all_simplify)
% 0.46/0.78 (step t14.t16.t2.t7 (cl (= (forall ((J $$unsorted)) (or (not (= D (tptp.ordered_pair J (tptp.singleton J)))) (not (tptp.in J A)))) (forall ((J $$unsorted)) (or (not (= D (tptp.ordered_pair J (tptp.singleton J)))) (not (tptp.in J A)))))) :rule refl)
% 0.46/0.78 (step t14.t16.t2.t8 (cl (= (forall ((E $$unsorted)) (or (not (tptp.in E (tptp.cartesian_product2 A B))) (not (= D E)))) (or (not (tptp.in D (tptp.cartesian_product2 A B))) (not (= D D))))) :rule all_simplify)
% 0.46/0.78 (step t14.t16.t2.t9 (cl (= (not (tptp.in D (tptp.cartesian_product2 A B))) (not (tptp.in D (tptp.cartesian_product2 A B))))) :rule refl)
% 0.46/0.78 (step t14.t16.t2.t10 (cl (= (= D D) true)) :rule all_simplify)
% 0.46/0.78 (step t14.t16.t2.t11 (cl (= (not (= D D)) (not true))) :rule cong :premises (t14.t16.t2.t10))
% 0.46/0.78 (step t14.t16.t2.t12 (cl (= (not true) false)) :rule all_simplify)
% 0.46/0.78 (step t14.t16.t2.t13 (cl (= (not (= D D)) false)) :rule trans :premises (t14.t16.t2.t11 t14.t16.t2.t12))
% 0.46/0.78 (step t14.t16.t2.t14 (cl (= (or (not (tptp.in D (tptp.cartesian_product2 A B))) (not (= D D))) (or (not (tptp.in D (tptp.cartesian_product2 A B))) false))) :rule cong :premises (t14.t16.t2.t9 t14.t16.t2.t13))
% 0.46/0.78 (step t14.t16.t2.t15 (cl (= (or (not (tptp.in D (tptp.cartesian_product2 A B))) false) (not (tptp.in D (tptp.cartesian_product2 A B))))) :rule all_simplify)
% 0.46/0.78 (step t14.t16.t2.t16 (cl (= (or (not (tptp.in D (tptp.cartesian_product2 A B))) (not (= D D))) (not (tptp.in D (tptp.cartesian_product2 A B))))) :rule trans :premises (t14.t16.t2.t14 t14.t16.t2.t15))
% 0.46/0.78 (step t14.t16.t2.t17 (cl (= (forall ((E $$unsorted)) (or (not (tptp.in E (tptp.cartesian_product2 A B))) (not (= D E)))) (not (tptp.in D (tptp.cartesian_product2 A B))))) :rule trans :premises (t14.t16.t2.t8 t14.t16.t2.t16))
% 0.46/0.78 (step t14.t16.t2.t18 (cl (= (or (forall ((J $$unsorted)) (or (not (= D (tptp.ordered_pair J (tptp.singleton J)))) (not (tptp.in J A)))) (forall ((E $$unsorted)) (or (not (tptp.in E (tptp.cartesian_product2 A B))) (not (= D E))))) (or (forall ((J $$unsorted)) (or (not (= D (tptp.ordered_pair J (tptp.singleton J)))) (not (tptp.in J A)))) (not (tptp.in D (tptp.cartesian_product2 A B)))))) :rule cong :premises (t14.t16.t2.t7 t14.t16.t2.t17))
% 0.46/0.78 (step t14.t16.t2.t19 (cl (= (forall ((E $$unsorted)) (or (not (tptp.in E (tptp.cartesian_product2 A B))) (not (= D E)) (forall ((J $$unsorted)) (or (not (= D (tptp.ordered_pair J (tptp.singleton J)))) (not (tptp.in J A)))))) (or (forall ((J $$unsorted)) (or (not (= D (tptp.ordered_pair J (tptp.singleton J)))) (not (tptp.in J A)))) (not (tptp.in D (tptp.cartesian_product2 A B)))))) :rule trans :premises (t14.t16.t2.t6 t14.t16.t2.t18))
% 0.46/0.78 (step t14.t16.t2.t20 (cl (= (forall ((E $$unsorted)) (not (and (tptp.in E (tptp.cartesian_product2 A B)) (= D E) (not (forall ((J $$unsorted)) (or (not (= D (tptp.ordered_pair J (tptp.singleton J)))) (not (tptp.in J A)))))))) (or (forall ((J $$unsorted)) (or (not (= D (tptp.ordered_pair J (tptp.singleton J)))) (not (tptp.in J A)))) (not (tptp.in D (tptp.cartesian_product2 A B)))))) :rule trans :premises (t14.t16.t2.t5 t14.t16.t2.t19))
% 0.46/0.78 (step t14.t16.t2.t21 (cl (= (not (forall ((E $$unsorted)) (not (and (tptp.in E (tptp.cartesian_product2 A B)) (= D E) (not (forall ((J $$unsorted)) (or (not (= D (tptp.ordered_pair J (tptp.singleton J)))) (not (tptp.in J A))))))))) (not (or (forall ((J $$unsorted)) (or (not (= D (tptp.ordered_pair J (tptp.singleton J)))) (not (tptp.in J A)))) (not (tptp.in D (tptp.cartesian_product2 A B))))))) :rule cong :premises (t14.t16.t2.t20))
% 0.46/0.78 (step t14.t16.t2.t22 (cl (= (exists ((E $$unsorted)) (and (tptp.in E (tptp.cartesian_product2 A B)) (= D E) (not (forall ((J $$unsorted)) (or (not (= D (tptp.ordered_pair J (tptp.singleton J)))) (not (tptp.in J A))))))) (not (or (forall ((J $$unsorted)) (or (not (= D (tptp.ordered_pair J (tptp.singleton J)))) (not (tptp.in J A)))) (not (tptp.in D (tptp.cartesian_product2 A B))))))) :rule trans :premises (t14.t16.t2.t4 t14.t16.t2.t21))
% 0.46/0.78 (step t14.t16.t2.t23 (cl (= (exists ((E $$unsorted)) (and (tptp.in E (tptp.cartesian_product2 A B)) (= E D) (exists ((J $$unsorted) (K $$unsorted)) (and (= (tptp.ordered_pair J K) D) (tptp.in J A) (= K (tptp.singleton J)))))) (not (or (forall ((J $$unsorted)) (or (not (= D (tptp.ordered_pair J (tptp.singleton J)))) (not (tptp.in J A)))) (not (tptp.in D (tptp.cartesian_product2 A B))))))) :rule trans :premises (t14.t16.t2.t3 t14.t16.t2.t22))
% 0.46/0.78 (step t14.t16.t2.t24 (cl (= (= (tptp.in D C) (exists ((E $$unsorted)) (and (tptp.in E (tptp.cartesian_product2 A B)) (= E D) (exists ((J $$unsorted) (K $$unsorted)) (and (= (tptp.ordered_pair J K) D) (tptp.in J A) (= K (tptp.singleton J))))))) (= (tptp.in D C) (not (or (forall ((J $$unsorted)) (or (not (= D (tptp.ordered_pair J (tptp.singleton J)))) (not (tptp.in J A)))) (not (tptp.in D (tptp.cartesian_product2 A B)))))))) :rule cong :premises (t14.t16.t2.t2 t14.t16.t2.t23))
% 0.46/0.78 (step t14.t16.t2 (cl (= (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)))))))) (forall ((D $$unsorted)) (= (tptp.in D C) (not (or (forall ((J $$unsorted)) (or (not (= D (tptp.ordered_pair J (tptp.singleton J)))) (not (tptp.in J A)))) (not (tptp.in D (tptp.cartesian_product2 A B))))))))) :rule bind)
% 0.46/0.78 (step t14.t16.t3 (cl (= (forall ((D $$unsorted)) (= (tptp.in D C) (not (or (forall ((J $$unsorted)) (or (not (= D (tptp.ordered_pair J (tptp.singleton J)))) (not (tptp.in J A)))) (not (tptp.in D (tptp.cartesian_product2 A B))))))) (forall ((D $$unsorted)) (= (tptp.in D C) (and (not (forall ((J $$unsorted)) (or (not (= D (tptp.ordered_pair J (tptp.singleton J)))) (not (tptp.in J A))))) (tptp.in D (tptp.cartesian_product2 A B))))))) :rule all_simplify)
% 0.46/0.78 (step t14.t16.t4 (cl (= (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)))))))) (forall ((D $$unsorted)) (= (tptp.in D C) (and (not (forall ((J $$unsorted)) (or (not (= D (tptp.ordered_pair J (tptp.singleton J)))) (not (tptp.in J A))))) (tptp.in D (tptp.cartesian_product2 A B))))))) :rule trans :premises (t14.t16.t2 t14.t16.t3))
% 0.46/0.78 (step t14.t16 (cl (= (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 $$unsorted)) (and (= (tptp.ordered_pair J K) D) (tptp.in J A) (= K (tptp.singleton J))))))))) (exists ((C $$unsorted)) (forall ((D $$unsorted)) (= (tptp.in D C) (and (not (forall ((J $$unsorted)) (or (not (= D (tptp.ordered_pair J (tptp.singleton J)))) (not (tptp.in J A))))) (tptp.in D (tptp.cartesian_product2 A B)))))))) :rule bind)
% 0.46/0.78 (step t14.t17 (cl (= (exists ((C $$unsorted)) (forall ((D $$unsorted)) (= (tptp.in D C) (and (not (forall ((J $$unsorted)) (or (not (= D (tptp.ordered_pair J (tptp.singleton J)))) (not (tptp.in J A))))) (tptp.in D (tptp.cartesian_product2 A B)))))) (not (forall ((C $$unsorted)) (not (forall ((D $$unsorted)) (= (tptp.in D C) (and (not (forall ((J $$unsorted)) (or (not (= D (tptp.ordered_pair J (tptp.singleton J)))) (not (tptp.in J A))))) (tptp.in D (tptp.cartesian_product2 A B)))))))))) :rule all_simplify)
% 0.46/0.78 (step t14.t18 (cl (= (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 $$unsorted)) (and (= (tptp.ordered_pair J K) D) (tptp.in J A) (= K (tptp.singleton J))))))))) (not (forall ((C $$unsorted)) (not (forall ((D $$unsorted)) (= (tptp.in D C) (and (not (forall ((J $$unsorted)) (or (not (= D (tptp.ordered_pair J (tptp.singleton J)))) (not (tptp.in J A))))) (tptp.in D (tptp.cartesian_product2 A B)))))))))) :rule trans :premises (t14.t16 t14.t17))
% 0.46/0.78 (step t14.t19 (cl (= (=> (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)))))))))) (=> true (not (forall ((C $$unsorted)) (not (forall ((D $$unsorted)) (= (tptp.in D C) (and (not (forall ((J $$unsorted)) (or (not (= D (tptp.ordered_pair J (tptp.singleton J)))) (not (tptp.in J A))))) (tptp.in D (tptp.cartesian_product2 A B))))))))))) :rule cong :premises (t14.t15 t14.t18))
% 0.46/0.78 (step t14.t20 (cl (= (=> true (not (forall ((C $$unsorted)) (not (forall ((D $$unsorted)) (= (tptp.in D C) (and (not (forall ((J $$unsorted)) (or (not (= D (tptp.ordered_pair J (tptp.singleton J)))) (not (tptp.in J A))))) (tptp.in D (tptp.cartesian_product2 A B))))))))) (not (forall ((C $$unsorted)) (not (forall ((D $$unsorted)) (= (tptp.in D C) (and (not (forall ((J $$unsorted)) (or (not (= D (tptp.ordered_pair J (tptp.singleton J)))) (not (tptp.in J A))))) (tptp.in D (tptp.cartesian_product2 A B)))))))))) :rule all_simplify)
% 0.46/0.78 (step t14.t21 (cl (= (=> (forall ((C $$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 $$unsorted)) (and (= (tptp.ordered_pair J K) D) (tptp.in J A) (= K (tptp.singleton J)))))))))) (not (forall ((C $$unsorted)) (not (forall ((D $$unsorted)) (= (tptp.in D C) (and (not (forall ((J $$unsorted)) (or (not (= D (tptp.ordered_pair J (tptp.singleton J)))) (not (tptp.in J A))))) (tptp.in D (tptp.cartesian_product2 A B)))))))))) :rule trans :premises (t14.t19 t14.t20))
% 0.46/0.78 (step t14 (cl (= (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))))))))))) (forall ((A $$unsorted) (B $$unsorted)) (not (forall ((C $$unsorted)) (not (forall ((D $$unsorted)) (= (tptp.in D C) (and (not (forall ((J $$unsorted)) (or (not (= D (tptp.ordered_pair J (tptp.singleton J)))) (not (tptp.in J A))))) (tptp.in D (tptp.cartesian_product2 A B))))))))))) :rule bind)
% 0.46/0.78 (step t15 (cl (forall ((A $$unsorted) (B $$unsorted)) (not (forall ((C $$unsorted)) (not (forall ((D $$unsorted)) (= (tptp.in D C) (and (not (forall ((J $$unsorted)) (or (not (= D (tptp.ordered_pair J (tptp.singleton J)))) (not (tptp.in J A))))) (tptp.in D (tptp.cartesian_product2 A B)))))))))) :rule resolution :premises (t13 t14 a203))
% 0.46/0.78 (step t16 (cl (forall ((A $$unsorted) (B $$unsorted)) (not (forall ((C $$unsorted)) (not (forall ((D $$unsorted)) (= (tptp.in D C) (and (tptp.in D (tptp.cartesian_product2 A B)) (not (forall ((E $$unsorted)) (or (not (= D (tptp.ordered_pair E (tptp.singleton E)))) (not (tptp.in E A))))))))))))) :rule resolution :premises (t12 t15))
% 0.46/0.78 (step t17 (cl) :rule resolution :premises (t4 t16))
% 0.46/0.78
% 0.46/0.78 % SZS output end Proof for /export/starexec/sandbox/tmp/tmp.v0C41eryKi/cvc5---1.0.5_13750.smt2
% 0.46/0.78 % cvc5---1.0.5 exiting
% 0.46/0.79 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------