%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SET025-3 : TPTP v8.2.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : do_cvc5 %s %d

% Computer : n023.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 17:43:44 EDT 2024

% Result   : Unsatisfiable 0.43s 0.63s
% Output   : Proof 0.45s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.14  % Problem    : SET025-3 : TPTP v8.2.0. Released v1.0.0.
% 0.07/0.15  % Command    : do_cvc5 %s %d
% 0.14/0.36  % Computer : n023.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit   : 300
% 0.14/0.36  % WCLimit    : 300
% 0.14/0.36  % DateTime   : Tue May 28 10:10:24 EDT 2024
% 0.14/0.36  % CPUTime    : 
% 0.21/0.53  %----Proving TF0_NAR, FOF, or CNF
% 0.21/0.54  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.43/0.63  % SZS status Unsatisfiable for /export/starexec/sandbox/tmp/tmp.Xu6wv0wdyL/cvc5---1.0.5_3669.smt2
% 0.43/0.63  % SZS output start Proof for /export/starexec/sandbox/tmp/tmp.Xu6wv0wdyL/cvc5---1.0.5_3669.smt2
% 0.45/0.64  (assume a0 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X Y)) (tptp.little_set X))))
% 0.45/0.64  (assume a1 (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.little_set (tptp.f1 X Y)) (= X Y))))
% 0.45/0.64  (assume a2 (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.member (tptp.f1 X Y) X) (tptp.member (tptp.f1 X Y) Y) (= X Y))))
% 0.45/0.64  (assume a3 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.f1 X Y) X)) (not (tptp.member (tptp.f1 X Y) Y)) (= X Y))))
% 0.45/0.64  (assume a4 (forall ((U $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member U (tptp.non_ordered_pair X Y))) (= U X) (= U Y))))
% 0.45/0.64  (assume a5 (forall ((U $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (tptp.member U (tptp.non_ordered_pair X Y)) (not (tptp.little_set U)) (not (= U X)))))
% 0.45/0.64  (assume a6 (forall ((U $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (tptp.member U (tptp.non_ordered_pair X Y)) (not (tptp.little_set U)) (not (= U Y)))))
% 0.45/0.64  (assume a7 (forall ((X $$unsorted) (Y $$unsorted)) (tptp.little_set (tptp.non_ordered_pair X Y))))
% 0.45/0.64  (assume a8 (forall ((X $$unsorted)) (= (tptp.singleton_set X) (tptp.non_ordered_pair X X))))
% 0.45/0.64  (assume a9 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.ordered_pair X Y) (tptp.non_ordered_pair (tptp.singleton_set X) (tptp.non_ordered_pair X Y)))))
% 0.45/0.64  (assume a10 (forall ((X $$unsorted)) (or (not (tptp.ordered_pair_predicate X)) (tptp.little_set (tptp.f2 X)))))
% 0.45/0.64  (assume a11 (forall ((X $$unsorted)) (or (not (tptp.ordered_pair_predicate X)) (tptp.little_set (tptp.f3 X)))))
% 0.45/0.64  (assume a12 (forall ((X $$unsorted)) (or (not (tptp.ordered_pair_predicate X)) (= X (tptp.ordered_pair (tptp.f2 X) (tptp.f3 X))))))
% 0.45/0.64  (assume a13 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (tptp.ordered_pair_predicate X) (not (tptp.little_set Y)) (not (tptp.little_set Z)) (not (= X (tptp.ordered_pair Y Z))))))
% 0.45/0.64  (assume a14 (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.first X))) (tptp.little_set (tptp.f4 Z X)))))
% 0.45/0.64  (assume a15 (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.first X))) (tptp.little_set (tptp.f5 Z X)))))
% 0.45/0.64  (assume a16 (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.first X))) (= X (tptp.ordered_pair (tptp.f4 Z X) (tptp.f5 Z X))))))
% 0.45/0.64  (assume a17 (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.first X))) (tptp.member Z (tptp.f4 Z X)))))
% 0.45/0.64  (assume a18 (forall ((Z $$unsorted) (X $$unsorted) (U $$unsorted) (V $$unsorted)) (or (tptp.member Z (tptp.first X)) (not (tptp.little_set U)) (not (tptp.little_set V)) (not (= X (tptp.ordered_pair U V))) (not (tptp.member Z U)))))
% 0.45/0.64  (assume a19 (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.second X))) (tptp.little_set (tptp.f6 Z X)))))
% 0.45/0.64  (assume a20 (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.second X))) (tptp.little_set (tptp.f7 Z X)))))
% 0.45/0.64  (assume a21 (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.second X))) (= X (tptp.ordered_pair (tptp.f6 Z X) (tptp.f7 Z X))))))
% 0.45/0.64  (assume a22 (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.second X))) (tptp.member Z (tptp.f7 Z X)))))
% 0.45/0.64  (assume a23 (forall ((Z $$unsorted) (X $$unsorted) (U $$unsorted) (V $$unsorted)) (or (tptp.member Z (tptp.second X)) (not (tptp.little_set U)) (not (tptp.little_set V)) (not (= X (tptp.ordered_pair U V))) (not (tptp.member Z V)))))
% 0.45/0.64  (assume a24 (forall ((Z $$unsorted)) (or (not (tptp.member Z tptp.estin)) (tptp.ordered_pair_predicate Z))))
% 0.45/0.64  (assume a25 (forall ((Z $$unsorted)) (or (not (tptp.member Z tptp.estin)) (tptp.member (tptp.first Z) (tptp.second Z)))))
% 0.45/0.64  (assume a26 (forall ((Z $$unsorted)) (or (tptp.member Z tptp.estin) (not (tptp.little_set Z)) (not (tptp.ordered_pair_predicate Z)) (not (tptp.member (tptp.first Z) (tptp.second Z))))))
% 0.45/0.64  (assume a27 (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.intersection X Y))) (tptp.member Z X))))
% 0.45/0.64  (assume a28 (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.intersection X Y))) (tptp.member Z Y))))
% 0.45/0.64  (assume a29 (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (tptp.member Z (tptp.intersection X Y)) (not (tptp.member Z X)) (not (tptp.member Z Y)))))
% 0.45/0.64  (assume a30 (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.complement X))) (not (tptp.member Z X)))))
% 0.45/0.64  (assume a31 (forall ((Z $$unsorted) (X $$unsorted)) (or (tptp.member Z (tptp.complement X)) (not (tptp.little_set Z)) (tptp.member Z X))))
% 0.45/0.64  (assume a32 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.union X Y) (tptp.complement (tptp.intersection (tptp.complement X) (tptp.complement Y))))))
% 0.45/0.64  (assume a33 (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.domain_of X))) (tptp.ordered_pair_predicate (tptp.f8 Z X)))))
% 0.45/0.64  (assume a34 (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.domain_of X))) (tptp.member (tptp.f8 Z X) X))))
% 0.45/0.64  (assume a35 (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.domain_of X))) (= Z (tptp.first (tptp.f8 Z X))))))
% 0.45/0.64  (assume a36 (forall ((Z $$unsorted) (X $$unsorted) (Xp $$unsorted)) (or (tptp.member Z (tptp.domain_of X)) (not (tptp.little_set Z)) (not (tptp.ordered_pair_predicate Xp)) (not (tptp.member Xp X)) (not (= Z (tptp.first Xp))))))
% 0.45/0.64  (assume a37 (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.cross_product X Y))) (tptp.ordered_pair_predicate Z))))
% 0.45/0.64  (assume a38 (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.cross_product X Y))) (tptp.member (tptp.first Z) X))))
% 0.45/0.64  (assume a39 (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.cross_product X Y))) (tptp.member (tptp.second Z) Y))))
% 0.45/0.64  (assume a40 (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (tptp.member Z (tptp.cross_product X Y)) (not (tptp.little_set Z)) (not (tptp.ordered_pair_predicate Z)) (not (tptp.member (tptp.first Z) X)) (not (tptp.member (tptp.second Z) Y)))))
% 0.45/0.64  (assume a41 (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.converse X))) (tptp.ordered_pair_predicate Z))))
% 0.45/0.64  (assume a42 (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.converse X))) (tptp.member (tptp.ordered_pair (tptp.second Z) (tptp.first Z)) X))))
% 0.45/0.64  (assume a43 (forall ((Z $$unsorted) (X $$unsorted)) (or (tptp.member Z (tptp.converse X)) (not (tptp.little_set Z)) (not (tptp.ordered_pair_predicate Z)) (not (tptp.member (tptp.ordered_pair (tptp.second Z) (tptp.first Z)) X)))))
% 0.45/0.64  (assume a44 (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.rotate_right X))) (tptp.little_set (tptp.f9 Z X)))))
% 0.45/0.64  (assume a45 (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.rotate_right X))) (tptp.little_set (tptp.f10 Z X)))))
% 0.45/0.64  (assume a46 (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.rotate_right X))) (tptp.little_set (tptp.f11 Z X)))))
% 0.45/0.64  (assume a47 (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.rotate_right X))) (= Z (tptp.ordered_pair (tptp.f9 Z X) (tptp.ordered_pair (tptp.f10 Z X) (tptp.f11 Z X)))))))
% 0.45/0.64  (assume a48 (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.rotate_right X))) (tptp.member (tptp.ordered_pair (tptp.f10 Z X) (tptp.ordered_pair (tptp.f11 Z X) (tptp.f9 Z X))) X))))
% 0.45/0.64  (assume a49 (forall ((Z $$unsorted) (X $$unsorted) (U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (tptp.member Z (tptp.rotate_right X)) (not (tptp.little_set Z)) (not (tptp.little_set U)) (not (tptp.little_set V)) (not (tptp.little_set W)) (not (= Z (tptp.ordered_pair U (tptp.ordered_pair V W)))) (not (tptp.member (tptp.ordered_pair V (tptp.ordered_pair W U)) X)))))
% 0.45/0.64  (assume a50 (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.flip_range_of X))) (tptp.little_set (tptp.f12 Z X)))))
% 0.45/0.64  (assume a51 (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.flip_range_of X))) (tptp.little_set (tptp.f13 Z X)))))
% 0.45/0.64  (assume a52 (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.flip_range_of X))) (tptp.little_set (tptp.f14 Z X)))))
% 0.45/0.64  (assume a53 (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.flip_range_of X))) (= Z (tptp.ordered_pair (tptp.f12 Z X) (tptp.ordered_pair (tptp.f13 Z X) (tptp.f14 Z X)))))))
% 0.45/0.64  (assume a54 (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.flip_range_of X))) (tptp.member (tptp.ordered_pair (tptp.f12 Z X) (tptp.ordered_pair (tptp.f14 Z X) (tptp.f13 Z X))) X))))
% 0.45/0.64  (assume a55 (forall ((Z $$unsorted) (X $$unsorted) (U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (tptp.member Z (tptp.flip_range_of X)) (not (tptp.little_set Z)) (not (tptp.little_set U)) (not (tptp.little_set V)) (not (tptp.little_set W)) (not (= Z (tptp.ordered_pair U (tptp.ordered_pair V W)))) (not (tptp.member (tptp.ordered_pair U (tptp.ordered_pair W V)) X)))))
% 0.45/0.64  (assume a56 (forall ((X $$unsorted)) (= (tptp.successor X) (tptp.union X (tptp.singleton_set X)))))
% 0.45/0.64  (assume a57 (forall ((Z $$unsorted)) (not (tptp.member Z tptp.empty_set))))
% 0.45/0.64  (assume a58 (forall ((Z $$unsorted)) (or (tptp.member Z tptp.universal_set) (not (tptp.little_set Z)))))
% 0.45/0.64  (assume a59 (tptp.little_set tptp.infinity))
% 0.45/0.64  (assume a60 (tptp.member tptp.empty_set tptp.infinity))
% 0.45/0.64  (assume a61 (forall ((X $$unsorted)) (or (not (tptp.member X tptp.infinity)) (tptp.member (tptp.successor X) tptp.infinity))))
% 0.45/0.64  (assume a62 (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.sigma X))) (tptp.member (tptp.f16 Z X) X))))
% 0.45/0.64  (assume a63 (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.sigma X))) (tptp.member Z (tptp.f16 Z X)))))
% 0.45/0.64  (assume a64 (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (tptp.member Z (tptp.sigma X)) (not (tptp.member Y X)) (not (tptp.member Z Y)))))
% 0.45/0.64  (assume a65 (forall ((U $$unsorted)) (or (not (tptp.little_set U)) (tptp.little_set (tptp.sigma U)))))
% 0.45/0.64  (assume a66 (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (not (tptp.subset X Y)) (not (tptp.member U X)) (tptp.member U Y))))
% 0.45/0.64  (assume a67 (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.subset X Y) (tptp.member (tptp.f17 X Y) X))))
% 0.45/0.64  (assume a68 (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.subset X Y) (not (tptp.member (tptp.f17 X Y) Y)))))
% 0.45/0.64  (assume a69 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.proper_subset X Y)) (tptp.subset X Y))))
% 0.45/0.64  (assume a70 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.proper_subset X Y)) (not (= X Y)))))
% 0.45/0.64  (assume a71 (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.proper_subset X Y) (not (tptp.subset X Y)) (= X Y))))
% 0.45/0.64  (assume a72 (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.powerset X))) (tptp.subset Z X))))
% 0.45/0.64  (assume a73 (forall ((Z $$unsorted) (X $$unsorted)) (or (tptp.member Z (tptp.powerset X)) (not (tptp.little_set Z)) (not (tptp.subset Z X)))))
% 0.45/0.64  (assume a74 (forall ((U $$unsorted)) (or (not (tptp.little_set U)) (tptp.little_set (tptp.powerset U)))))
% 0.45/0.64  (assume a75 (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.relation Z)) (not (tptp.member X Z)) (tptp.ordered_pair_predicate X))))
% 0.45/0.64  (assume a76 (forall ((Z $$unsorted)) (or (tptp.relation Z) (tptp.member (tptp.f18 Z) Z))))
% 0.45/0.64  (assume a77 (forall ((Z $$unsorted)) (or (tptp.relation Z) (not (tptp.ordered_pair_predicate (tptp.f18 Z))))))
% 0.45/0.64  (assume a78 (forall ((X $$unsorted) (U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.single_valued_set X)) (not (tptp.little_set U)) (not (tptp.little_set V)) (not (tptp.little_set W)) (not (tptp.member (tptp.ordered_pair U V) X)) (not (tptp.member (tptp.ordered_pair U W) X)) (= V W))))
% 0.45/0.64  (assume a79 (forall ((X $$unsorted)) (or (tptp.single_valued_set X) (tptp.little_set (tptp.f19 X)))))
% 0.45/0.64  (assume a80 (forall ((X $$unsorted)) (or (tptp.single_valued_set X) (tptp.little_set (tptp.f20 X)))))
% 0.45/0.64  (assume a81 (forall ((X $$unsorted)) (or (tptp.single_valued_set X) (tptp.little_set (tptp.f21 X)))))
% 0.45/0.64  (assume a82 (forall ((X $$unsorted)) (or (tptp.single_valued_set X) (tptp.member (tptp.ordered_pair (tptp.f19 X) (tptp.f20 X)) X))))
% 0.45/0.64  (assume a83 (forall ((X $$unsorted)) (or (tptp.single_valued_set X) (tptp.member (tptp.ordered_pair (tptp.f19 X) (tptp.f21 X)) X))))
% 0.45/0.64  (assume a84 (forall ((X $$unsorted)) (or (tptp.single_valued_set X) (not (= (tptp.f20 X) (tptp.f21 X))))))
% 0.45/0.64  (assume a85 (forall ((Xf $$unsorted)) (or (not (tptp.function Xf)) (tptp.relation Xf))))
% 0.45/0.64  (assume a86 (forall ((Xf $$unsorted)) (or (not (tptp.function Xf)) (tptp.single_valued_set Xf))))
% 0.45/0.64  (assume a87 (forall ((Xf $$unsorted)) (or (tptp.function Xf) (not (tptp.relation Xf)) (not (tptp.single_valued_set Xf)))))
% 0.45/0.64  (assume a88 (forall ((Z $$unsorted) (X $$unsorted) (Xf $$unsorted)) (or (not (tptp.member Z (tptp.image X Xf))) (tptp.ordered_pair_predicate (tptp.f22 Z X Xf)))))
% 0.45/0.64  (assume a89 (forall ((Z $$unsorted) (X $$unsorted) (Xf $$unsorted)) (or (not (tptp.member Z (tptp.image X Xf))) (tptp.member (tptp.f22 Z X Xf) Xf))))
% 0.45/0.64  (assume a90 (forall ((Z $$unsorted) (X $$unsorted) (Xf $$unsorted)) (or (not (tptp.member Z (tptp.image X Xf))) (tptp.member (tptp.first (tptp.f22 Z X Xf)) X))))
% 0.45/0.64  (assume a91 (forall ((Z $$unsorted) (X $$unsorted) (Xf $$unsorted)) (or (not (tptp.member Z (tptp.image X Xf))) (= (tptp.second (tptp.f22 Z X Xf)) Z))))
% 0.45/0.64  (assume a92 (forall ((Z $$unsorted) (X $$unsorted) (Xf $$unsorted) (Y $$unsorted)) (or (tptp.member Z (tptp.image X Xf)) (not (tptp.little_set Z)) (not (tptp.ordered_pair_predicate Y)) (not (tptp.member Y Xf)) (not (tptp.member (tptp.first Y) X)) (not (= (tptp.second Y) Z)))))
% 0.45/0.64  (assume a93 (forall ((X $$unsorted) (Xf $$unsorted)) (or (not (tptp.little_set X)) (not (tptp.function Xf)) (tptp.little_set (tptp.image X Xf)))))
% 0.45/0.64  (assume a94 (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (not (tptp.disjoint X Y)) (not (tptp.member U X)) (not (tptp.member U Y)))))
% 0.45/0.64  (assume a95 (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.disjoint X Y) (tptp.member (tptp.f23 X Y) X))))
% 0.45/0.64  (assume a96 (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.disjoint X Y) (tptp.member (tptp.f23 X Y) Y))))
% 0.45/0.64  (assume a97 (forall ((X $$unsorted)) (or (= X tptp.empty_set) (tptp.member (tptp.f24 X) X))))
% 0.45/0.64  (assume a98 (forall ((X $$unsorted)) (or (= X tptp.empty_set) (tptp.disjoint (tptp.f24 X) X))))
% 0.45/0.64  (assume a99 (tptp.function tptp.f25))
% 0.45/0.64  (assume a100 (forall ((X $$unsorted)) (or (not (tptp.little_set X)) (= X tptp.empty_set) (tptp.member (tptp.f26 X) X))))
% 0.45/0.64  (assume a101 (forall ((X $$unsorted)) (or (not (tptp.little_set X)) (= X tptp.empty_set) (tptp.member (tptp.ordered_pair X (tptp.f26 X)) tptp.f25))))
% 0.45/0.64  (assume a102 (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.range_of X))) (tptp.ordered_pair_predicate (tptp.f27 Z X)))))
% 0.45/0.64  (assume a103 (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.range_of X))) (tptp.member (tptp.f27 Z X) X))))
% 0.45/0.64  (assume a104 (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.range_of X))) (= Z (tptp.second (tptp.f27 Z X))))))
% 0.45/0.64  (assume a105 (forall ((Z $$unsorted) (X $$unsorted) (Xp $$unsorted)) (or (tptp.member Z (tptp.range_of X)) (not (tptp.little_set Z)) (not (tptp.ordered_pair_predicate Xp)) (not (tptp.member Xp X)) (not (= Z (tptp.second Xp))))))
% 0.45/0.64  (assume a106 (forall ((Z $$unsorted)) (or (not (tptp.member Z tptp.identity_relation)) (tptp.ordered_pair_predicate Z))))
% 0.45/0.64  (assume a107 (forall ((Z $$unsorted)) (or (not (tptp.member Z tptp.identity_relation)) (= (tptp.first Z) (tptp.second Z)))))
% 0.45/0.64  (assume a108 (forall ((Z $$unsorted)) (or (tptp.member Z tptp.identity_relation) (not (tptp.little_set Z)) (not (tptp.ordered_pair_predicate Z)) (not (= (tptp.first Z) (tptp.second Z))))))
% 0.45/0.64  (assume a109 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.restrict X Y) (tptp.intersection X (tptp.cross_product Y tptp.universal_set)))))
% 0.45/0.64  (assume a110 (forall ((Xf $$unsorted)) (or (not (tptp.one_to_one_function Xf)) (tptp.function Xf))))
% 0.45/0.64  (assume a111 (forall ((Xf $$unsorted)) (or (not (tptp.one_to_one_function Xf)) (tptp.function (tptp.converse Xf)))))
% 0.45/0.64  (assume a112 (forall ((Xf $$unsorted)) (or (tptp.one_to_one_function Xf) (not (tptp.function Xf)) (not (tptp.function (tptp.converse Xf))))))
% 0.45/0.64  (assume a113 (forall ((Z $$unsorted) (Xf $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.apply Xf Y))) (tptp.ordered_pair_predicate (tptp.f28 Z Xf Y)))))
% 0.45/0.64  (assume a114 (forall ((Z $$unsorted) (Xf $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.apply Xf Y))) (tptp.member (tptp.f28 Z Xf Y) Xf))))
% 0.45/0.64  (assume a115 (forall ((Z $$unsorted) (Xf $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.apply Xf Y))) (= (tptp.first (tptp.f28 Z Xf Y)) Y))))
% 0.45/0.64  (assume a116 (forall ((Z $$unsorted) (Xf $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.apply Xf Y))) (tptp.member Z (tptp.second (tptp.f28 Z Xf Y))))))
% 0.45/0.64  (assume a117 (forall ((Z $$unsorted) (Xf $$unsorted) (Y $$unsorted) (W $$unsorted)) (or (tptp.member Z (tptp.apply Xf Y)) (not (tptp.ordered_pair_predicate W)) (not (tptp.member W Xf)) (not (= (tptp.first W) Y)) (not (tptp.member Z (tptp.second W))))))
% 0.45/0.64  (assume a118 (forall ((Xf $$unsorted) (X $$unsorted) (Y $$unsorted)) (= (tptp.apply_to_two_arguments Xf X Y) (tptp.apply Xf (tptp.ordered_pair X Y)))))
% 0.45/0.64  (assume a119 (forall ((Xf $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.maps Xf X Y)) (tptp.function Xf))))
% 0.45/0.64  (assume a120 (forall ((Xf $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.maps Xf X Y)) (= (tptp.domain_of Xf) X))))
% 0.45/0.64  (assume a121 (forall ((Xf $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.maps Xf X Y)) (tptp.subset (tptp.range_of Xf) Y))))
% 0.45/0.64  (assume a122 (forall ((Xf $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (tptp.maps Xf X Y) (not (tptp.function Xf)) (not (= (tptp.domain_of Xf) X)) (not (tptp.subset (tptp.range_of Xf) Y)))))
% 0.45/0.64  (assume a123 (forall ((Xs $$unsorted) (Xf $$unsorted)) (or (not (tptp.closed Xs Xf)) (tptp.little_set Xs))))
% 0.45/0.64  (assume a124 (forall ((Xs $$unsorted) (Xf $$unsorted)) (or (not (tptp.closed Xs Xf)) (tptp.little_set Xf))))
% 0.45/0.64  (assume a125 (forall ((Xs $$unsorted) (Xf $$unsorted)) (or (not (tptp.closed Xs Xf)) (tptp.maps Xf (tptp.cross_product Xs Xs) Xs))))
% 0.45/0.64  (assume a126 (forall ((Xs $$unsorted) (Xf $$unsorted)) (or (tptp.closed Xs Xf) (not (tptp.little_set Xs)) (not (tptp.little_set Xf)) (not (tptp.maps Xf (tptp.cross_product Xs Xs) Xs)))))
% 0.45/0.64  (assume a127 (forall ((Z $$unsorted) (Xf $$unsorted) (Xg $$unsorted)) (or (not (tptp.member Z (tptp.compose Xf Xg))) (tptp.little_set (tptp.f29 Z Xf Xg)))))
% 0.45/0.64  (assume a128 (forall ((Z $$unsorted) (Xf $$unsorted) (Xg $$unsorted)) (or (not (tptp.member Z (tptp.compose Xf Xg))) (tptp.little_set (tptp.f30 Z Xf Xg)))))
% 0.45/0.64  (assume a129 (forall ((Z $$unsorted) (Xf $$unsorted) (Xg $$unsorted)) (or (not (tptp.member Z (tptp.compose Xf Xg))) (tptp.little_set (tptp.f31 Z Xf Xg)))))
% 0.45/0.64  (assume a130 (forall ((Z $$unsorted) (Xf $$unsorted) (Xg $$unsorted)) (or (not (tptp.member Z (tptp.compose Xf Xg))) (= Z (tptp.ordered_pair (tptp.f29 Z Xf Xg) (tptp.f30 Z Xf Xg))))))
% 0.45/0.64  (assume a131 (forall ((Z $$unsorted) (Xf $$unsorted) (Xg $$unsorted)) (or (not (tptp.member Z (tptp.compose Xf Xg))) (tptp.member (tptp.ordered_pair (tptp.f29 Z Xf Xg) (tptp.f31 Z Xf Xg)) Xf))))
% 0.45/0.64  (assume a132 (forall ((Z $$unsorted) (Xf $$unsorted) (Xg $$unsorted)) (or (not (tptp.member Z (tptp.compose Xf Xg))) (tptp.member (tptp.ordered_pair (tptp.f31 Z Xf Xg) (tptp.f30 Z Xf Xg)) Xg))))
% 0.45/0.64  (assume a133 (forall ((Z $$unsorted) (Xf $$unsorted) (Xg $$unsorted) (X $$unsorted) (Y $$unsorted) (W $$unsorted)) (or (tptp.member Z (tptp.compose Xf Xg)) (not (tptp.little_set Z)) (not (tptp.little_set X)) (not (tptp.little_set Y)) (not (tptp.little_set W)) (not (= Z (tptp.ordered_pair X Y))) (not (tptp.member (tptp.ordered_pair X W) Xf)) (not (tptp.member (tptp.ordered_pair W Y) Xg)))))
% 0.45/0.64  (assume a134 (forall ((Xh $$unsorted) (Xs1 $$unsorted) (Xf1 $$unsorted) (Xs2 $$unsorted) (Xf2 $$unsorted)) (or (not (tptp.homomorphism Xh Xs1 Xf1 Xs2 Xf2)) (tptp.closed Xs1 Xf1))))
% 0.45/0.64  (assume a135 (forall ((Xh $$unsorted) (Xs1 $$unsorted) (Xf1 $$unsorted) (Xs2 $$unsorted) (Xf2 $$unsorted)) (or (not (tptp.homomorphism Xh Xs1 Xf1 Xs2 Xf2)) (tptp.closed Xs2 Xf2))))
% 0.45/0.64  (assume a136 (forall ((Xh $$unsorted) (Xs1 $$unsorted) (Xf1 $$unsorted) (Xs2 $$unsorted) (Xf2 $$unsorted)) (or (not (tptp.homomorphism Xh Xs1 Xf1 Xs2 Xf2)) (tptp.maps Xh Xs1 Xs2))))
% 0.45/0.64  (assume a137 (forall ((Xh $$unsorted) (Xs1 $$unsorted) (Xf1 $$unsorted) (Xs2 $$unsorted) (Xf2 $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.homomorphism Xh Xs1 Xf1 Xs2 Xf2)) (not (tptp.member X Xs1)) (not (tptp.member Y Xs1)) (= (tptp.apply Xh (tptp.apply_to_two_arguments Xf1 X Y)) (tptp.apply_to_two_arguments Xf2 (tptp.apply Xh X) (tptp.apply Xh Y))))))
% 0.45/0.64  (assume a138 (forall ((Xh $$unsorted) (Xs1 $$unsorted) (Xf1 $$unsorted) (Xs2 $$unsorted) (Xf2 $$unsorted)) (or (tptp.homomorphism Xh Xs1 Xf1 Xs2 Xf2) (not (tptp.closed Xs1 Xf1)) (not (tptp.closed Xs2 Xf2)) (not (tptp.maps Xh Xs1 Xs2)) (tptp.member (tptp.f32 Xh Xs1 Xf1 Xs2 Xf2) Xs1))))
% 0.45/0.64  (assume a139 (forall ((Xh $$unsorted) (Xs1 $$unsorted) (Xf1 $$unsorted) (Xs2 $$unsorted) (Xf2 $$unsorted)) (or (tptp.homomorphism Xh Xs1 Xf1 Xs2 Xf2) (not (tptp.closed Xs1 Xf1)) (not (tptp.closed Xs2 Xf2)) (not (tptp.maps Xh Xs1 Xs2)) (tptp.member (tptp.f33 Xh Xs1 Xf1 Xs2 Xf2) Xs1))))
% 0.45/0.64  (assume a140 (forall ((Xh $$unsorted) (Xs1 $$unsorted) (Xf1 $$unsorted) (Xs2 $$unsorted) (Xf2 $$unsorted)) (or (tptp.homomorphism Xh Xs1 Xf1 Xs2 Xf2) (not (tptp.closed Xs1 Xf1)) (not (tptp.closed Xs2 Xf2)) (not (tptp.maps Xh Xs1 Xs2)) (not (= (tptp.apply Xh (tptp.apply_to_two_arguments Xf1 (tptp.f32 Xh Xs1 Xf1 Xs2 Xf2) (tptp.f33 Xh Xs1 Xf1 Xs2 Xf2))) (tptp.apply_to_two_arguments Xf2 (tptp.apply Xh (tptp.f32 Xh Xs1 Xf1 Xs2 Xf2)) (tptp.apply Xh (tptp.f33 Xh Xs1 Xf1 Xs2 Xf2))))))))
% 0.45/0.64  (assume a141 (forall ((X $$unsorted) (U $$unsorted) (Y $$unsorted) (V $$unsorted)) (or (not (tptp.little_set X)) (not (tptp.little_set U)) (not (= (tptp.ordered_pair X Y) (tptp.ordered_pair U V))) (= X U))))
% 0.45/0.64  (assume a142 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.little_set X)) (not (tptp.little_set Y)) (not (= (tptp.non_ordered_pair Z X) (tptp.non_ordered_pair Z Y))) (= X Y))))
% 0.45/0.64  (assume a143 (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (not (tptp.little_set X)) (not (tptp.little_set Y)) (not (tptp.little_set U)) (not (tptp.little_set V)) (not (= (tptp.ordered_pair X Y) (tptp.ordered_pair U V))) (= Y V))))
% 0.45/0.64  (assume a144 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.subset X Y)) (not (tptp.subset Y X)) (= X Y))))
% 0.45/0.64  (assume a145 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.little_set X)) (not (tptp.little_set Y)) (= (tptp.first (tptp.ordered_pair X Y)) X))))
% 0.45/0.64  (assume a146 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.little_set X)) (not (tptp.little_set Y)) (= (tptp.second (tptp.ordered_pair X Y)) Y))))
% 0.45/0.64  (assume a147 (forall ((X $$unsorted)) (or (not (tptp.ordered_pair_predicate X)) (tptp.little_set (tptp.first X)))))
% 0.45/0.64  (assume a148 (forall ((X $$unsorted)) (or (not (tptp.ordered_pair_predicate X)) (tptp.little_set (tptp.second X)))))
% 0.45/0.64  (assume a149 (forall ((X $$unsorted)) (or (not (tptp.little_set X)) (tptp.member X (tptp.singleton_set X)))))
% 0.45/0.64  (assume a150 (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b))))
% 0.45/0.64  (step t1 (cl (not (= (or (not (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b)))) (not (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b)))) (not (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))))) (or (tptp.little_set (tptp.ordered_pair tptp.a tptp.b)) (not (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b)))) (not (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))))))) (not (or (not (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b)))) (not (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b)))) (not (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b)))))) (or (tptp.little_set (tptp.ordered_pair tptp.a tptp.b)) (not (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b)))) (not (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b)))))) :rule equiv_pos2)
% 0.45/0.64  (step t2 (cl (= (= (= (not (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b)))) (tptp.little_set (tptp.ordered_pair tptp.a tptp.b))) true) (= (not (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b)))) (tptp.little_set (tptp.ordered_pair tptp.a tptp.b))))) :rule equiv_simplify)
% 0.45/0.64  (step t3 (cl (not (= (= (not (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b)))) (tptp.little_set (tptp.ordered_pair tptp.a tptp.b))) true)) (= (not (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b)))) (tptp.little_set (tptp.ordered_pair tptp.a tptp.b)))) :rule equiv1 :premises (t2))
% 0.45/0.64  (step t4 (cl (= (= (not (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b)))) (tptp.little_set (tptp.ordered_pair tptp.a tptp.b))) (= (tptp.little_set (tptp.ordered_pair tptp.a tptp.b)) (not (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b))))))) :rule all_simplify)
% 0.45/0.64  (step t5 (cl (= (tptp.little_set (tptp.ordered_pair tptp.a tptp.b)) (tptp.little_set (tptp.ordered_pair tptp.a tptp.b)))) :rule refl)
% 0.45/0.64  (step t6 (cl (= (not (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b)))) (tptp.little_set (tptp.ordered_pair tptp.a tptp.b)))) :rule all_simplify)
% 0.45/0.64  (step t7 (cl (= (= (tptp.little_set (tptp.ordered_pair tptp.a tptp.b)) (not (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b))))) (= (tptp.little_set (tptp.ordered_pair tptp.a tptp.b)) (tptp.little_set (tptp.ordered_pair tptp.a tptp.b))))) :rule cong :premises (t5 t6))
% 0.45/0.64  (step t8 (cl (= (= (tptp.little_set (tptp.ordered_pair tptp.a tptp.b)) (tptp.little_set (tptp.ordered_pair tptp.a tptp.b))) true)) :rule all_simplify)
% 0.45/0.64  (step t9 (cl (= (= (tptp.little_set (tptp.ordered_pair tptp.a tptp.b)) (not (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b))))) true)) :rule trans :premises (t7 t8))
% 0.45/0.64  (step t10 (cl (= (= (not (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b)))) (tptp.little_set (tptp.ordered_pair tptp.a tptp.b))) true)) :rule trans :premises (t4 t9))
% 0.45/0.64  (step t11 (cl (= (not (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b)))) (tptp.little_set (tptp.ordered_pair tptp.a tptp.b)))) :rule resolution :premises (t3 t10))
% 0.45/0.64  (step t12 (cl (= (not (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b)))) (not (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b)))))) :rule refl)
% 0.45/0.64  (step t13 (cl (= (not (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b)))) (not (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b)))))) :rule refl)
% 0.45/0.64  (step t14 (cl (= (or (not (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b)))) (not (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b)))) (not (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))))) (or (tptp.little_set (tptp.ordered_pair tptp.a tptp.b)) (not (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b)))) (not (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))))))) :rule cong :premises (t11 t12 t13))
% 0.45/0.64  (step t15 (cl (not (= (=> (and (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b))) (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b)))) (and (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b))))) (not (and (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b))) (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))))))) (not (=> (and (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b))) (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b)))) (and (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b)))))) (not (and (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b))) (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b)))))) :rule equiv_pos2)
% 0.45/0.64  (step t16 (cl (= (and (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b))) (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b)))) (and (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b))) (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b)))))) :rule refl)
% 0.45/0.64  (step t17 (cl (= (= (and (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b)))) false) (not (and (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b))))))) :rule equiv_simplify)
% 0.45/0.64  (step t18 (cl (= (and (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b)))) false) (not (not (and (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b))))))) :rule equiv2 :premises (t17))
% 0.45/0.64  (step t19 (cl (not (not (not (and (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b))))))) (and (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b))))) :rule not_not)
% 0.45/0.64  (step t20 (cl (= (and (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b)))) false) (and (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b))))) :rule resolution :premises (t18 t19))
% 0.45/0.64  (step t21 (cl (=> (and (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b)))) false) (and (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b))))) :rule implies_neg1)
% 0.45/0.64  (anchor :step t22)
% 0.45/0.64  (assume t22.a0 (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))))
% 0.45/0.64  (assume t22.a1 (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))))
% 0.45/0.64  (assume t22.a2 (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b))))
% 0.45/0.64  (step t22.t1 (cl (not (= (= false true) false)) (not (= false true)) false) :rule equiv_pos2)
% 0.45/0.64  (step t22.t2 (cl (= (= false true) false)) :rule all_simplify)
% 0.45/0.64  (step t22.t3 (cl (= (= (tptp.little_set (tptp.ordered_pair tptp.a tptp.b)) false) (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b))))) :rule equiv_simplify)
% 0.45/0.64  (step t22.t4 (cl (= (tptp.little_set (tptp.ordered_pair tptp.a tptp.b)) false) (not (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b))))) :rule equiv2 :premises (t22.t3))
% 0.45/0.64  (step t22.t5 (cl (not (not (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b))))) (tptp.little_set (tptp.ordered_pair tptp.a tptp.b))) :rule not_not)
% 0.45/0.64  (step t22.t6 (cl (= (tptp.little_set (tptp.ordered_pair tptp.a tptp.b)) false) (tptp.little_set (tptp.ordered_pair tptp.a tptp.b))) :rule resolution :premises (t22.t4 t22.t5))
% 0.45/0.64  (step t22.t7 (cl (= (tptp.little_set (tptp.ordered_pair tptp.a tptp.b)) false)) :rule resolution :premises (t22.t6 t22.a2))
% 0.45/0.64  (step t22.t8 (cl (= false (tptp.little_set (tptp.ordered_pair tptp.a tptp.b)))) :rule symm :premises (t22.t7))
% 0.45/0.64  (step t22.t9 (cl (= (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b)) (tptp.ordered_pair tptp.a tptp.b))) :rule symm :premises (t22.a1))
% 0.45/0.64  (step t22.t10 (cl (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b)))) :rule symm :premises (t22.t9))
% 0.45/0.64  (step t22.t11 (cl (= (tptp.little_set (tptp.ordered_pair tptp.a tptp.b)) (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))))) :rule cong :premises (t22.t10))
% 0.45/0.64  (step t22.t12 (cl (= (= (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) true) (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))))) :rule equiv_simplify)
% 0.45/0.64  (step t22.t13 (cl (= (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) true) (not (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))))) :rule equiv2 :premises (t22.t12))
% 0.45/0.64  (step t22.t14 (cl (= (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) true)) :rule resolution :premises (t22.t13 t22.a0))
% 0.45/0.64  (step t22.t15 (cl (= false true)) :rule trans :premises (t22.t8 t22.t11 t22.t14))
% 0.45/0.64  (step t22.t16 (cl false) :rule resolution :premises (t22.t1 t22.t2 t22.t15))
% 0.45/0.64  (step t22 (cl (not (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b)))) (not (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b)))) (not (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b)))) false) :rule subproof :discharge (t22.a0 t22.a1 t22.a2))
% 0.45/0.64  (step t23 (cl (not (and (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b))))) (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b)))) :rule and_pos)
% 0.45/0.64  (step t24 (cl (not (and (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b))))) (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b)))) :rule and_pos)
% 0.45/0.64  (step t25 (cl (not (and (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b))))) (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b)))) :rule and_pos)
% 0.45/0.64  (step t26 (cl false (not (and (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b))))) (not (and (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b))))) (not (and (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b)))))) :rule resolution :premises (t22 t23 t24 t25))
% 0.45/0.64  (step t27 (cl (not (and (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b))))) (not (and (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b))))) (not (and (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b))))) false) :rule reordering :premises (t26))
% 0.45/0.64  (step t28 (cl (not (and (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b))))) false) :rule contraction :premises (t27))
% 0.45/0.64  (step t29 (cl (=> (and (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b)))) false) false) :rule resolution :premises (t21 t28))
% 0.45/0.64  (step t30 (cl (=> (and (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b)))) false) (not false)) :rule implies_neg2)
% 0.45/0.64  (step t31 (cl (=> (and (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b)))) false) (=> (and (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b)))) false)) :rule resolution :premises (t29 t30))
% 0.45/0.64  (step t32 (cl (=> (and (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b)))) false)) :rule contraction :premises (t31))
% 0.45/0.64  (step t33 (cl (= (=> (and (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b)))) false) (not (and (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b))))))) :rule implies_simplify)
% 0.45/0.64  (step t34 (cl (not (=> (and (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b)))) false)) (not (and (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b)))))) :rule equiv1 :premises (t33))
% 0.45/0.64  (step t35 (cl (not (and (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b)))))) :rule resolution :premises (t32 t34))
% 0.45/0.64  (step t36 (cl (= (and (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b)))) false)) :rule resolution :premises (t20 t35))
% 0.45/0.64  (step t37 (cl (= (=> (and (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b))) (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b)))) (and (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b))))) (=> (and (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b))) (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b)))) false))) :rule cong :premises (t16 t36))
% 0.45/0.64  (step t38 (cl (= (=> (and (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b))) (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b)))) false) (not (and (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b))) (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))))))) :rule all_simplify)
% 0.45/0.64  (step t39 (cl (= (=> (and (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b))) (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b)))) (and (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b))))) (not (and (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b))) (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))))))) :rule trans :premises (t37 t38))
% 0.45/0.64  (step t40 (cl (=> (and (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b))) (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b)))) (and (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b))))) (and (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b))) (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))))) :rule implies_neg1)
% 0.45/0.64  (anchor :step t41)
% 0.45/0.64  (assume t41.a0 (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b))))
% 0.45/0.64  (assume t41.a1 (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))))
% 0.45/0.64  (assume t41.a2 (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))))
% 0.45/0.64  (step t41.t1 (cl (and (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b)))) (not (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b)))) (not (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b)))) (not (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b))))) :rule and_neg)
% 0.45/0.64  (step t41.t2 (cl (and (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b))))) :rule resolution :premises (t41.t1 t41.a2 t41.a1 t41.a0))
% 0.45/0.64  (step t41 (cl (not (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b)))) (not (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b)))) (not (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b)))) (and (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b))))) :rule subproof :discharge (t41.a0 t41.a1 t41.a2))
% 0.45/0.64  (step t42 (cl (not (and (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b))) (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))))) (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b)))) :rule and_pos)
% 0.45/0.64  (step t43 (cl (not (and (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b))) (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))))) (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b)))) :rule and_pos)
% 0.45/0.64  (step t44 (cl (not (and (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b))) (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))))) (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b)))) :rule and_pos)
% 0.45/0.64  (step t45 (cl (and (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b)))) (not (and (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b))) (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))))) (not (and (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b))) (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))))) (not (and (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b))) (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b)))))) :rule resolution :premises (t41 t42 t43 t44))
% 0.45/0.64  (step t46 (cl (not (and (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b))) (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))))) (not (and (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b))) (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))))) (not (and (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b))) (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))))) (and (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b))))) :rule reordering :premises (t45))
% 0.45/0.64  (step t47 (cl (not (and (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b))) (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))))) (and (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b))))) :rule contraction :premises (t46))
% 0.45/0.64  (step t48 (cl (=> (and (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b))) (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b)))) (and (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b))))) (and (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b))))) :rule resolution :premises (t40 t47))
% 0.45/0.64  (step t49 (cl (=> (and (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b))) (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b)))) (and (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b))))) (not (and (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b)))))) :rule implies_neg2)
% 0.45/0.64  (step t50 (cl (=> (and (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b))) (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b)))) (and (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b))))) (=> (and (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b))) (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b)))) (and (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b)))))) :rule resolution :premises (t48 t49))
% 0.45/0.64  (step t51 (cl (=> (and (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b))) (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b)))) (and (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b)))))) :rule contraction :premises (t50))
% 0.45/0.64  (step t52 (cl (not (and (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b))) (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))) (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b)))))) :rule resolution :premises (t15 t39 t51))
% 0.45/0.64  (step t53 (cl (not (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b)))) (not (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b)))) (not (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))))) :rule not_and :premises (t52))
% 0.45/0.64  (step t54 (cl (or (not (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b)))) (not (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b)))) (not (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))))) (not (not (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b)))))) :rule or_neg)
% 0.45/0.64  (step t55 (cl (or (not (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b)))) (not (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b)))) (not (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))))) (not (not (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b)))))) :rule or_neg)
% 0.45/0.64  (step t56 (cl (or (not (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b)))) (not (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b)))) (not (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))))) (not (not (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b)))))) :rule or_neg)
% 0.45/0.64  (step t57 (cl (or (not (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b)))) (not (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b)))) (not (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))))) (or (not (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b)))) (not (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b)))) (not (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))))) (or (not (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b)))) (not (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b)))) (not (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b)))))) :rule resolution :premises (t53 t54 t55 t56))
% 0.45/0.64  (step t58 (cl (or (not (not (tptp.little_set (tptp.ordered_pair tptp.a tptp.b)))) (not (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b)))) (not (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b)))))) :rule contraction :premises (t57))
% 0.45/0.64  (step t59 (cl (or (tptp.little_set (tptp.ordered_pair tptp.a tptp.b)) (not (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b)))) (not (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b)))))) :rule resolution :premises (t1 t14 t58))
% 0.45/0.64  (step t60 (cl (tptp.little_set (tptp.ordered_pair tptp.a tptp.b)) (not (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b)))) (not (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))))) :rule or :premises (t59))
% 0.45/0.64  (step t61 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (tptp.little_set (tptp.non_ordered_pair X Y))) (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b)))) (forall ((X $$unsorted) (Y $$unsorted)) (tptp.little_set (tptp.non_ordered_pair X Y)))) :rule implies_neg1)
% 0.45/0.64  (anchor :step t62)
% 0.45/0.64  (assume t62.a0 (forall ((X $$unsorted) (Y $$unsorted)) (tptp.little_set (tptp.non_ordered_pair X Y))))
% 0.45/0.64  (step t62.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (tptp.little_set (tptp.non_ordered_pair X Y)))) (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))))) :rule forall_inst :args ((:= X (tptp.singleton_set tptp.a)) (:= Y (tptp.non_ordered_pair tptp.a tptp.b))))
% 0.45/0.64  (step t62.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (tptp.little_set (tptp.non_ordered_pair X Y)))) (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b)))) :rule or :premises (t62.t1))
% 0.45/0.64  (step t62.t3 (cl (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b)))) :rule resolution :premises (t62.t2 t62.a0))
% 0.45/0.64  (step t62 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (tptp.little_set (tptp.non_ordered_pair X Y)))) (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b)))) :rule subproof :discharge (t62.a0))
% 0.45/0.64  (step t63 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (tptp.little_set (tptp.non_ordered_pair X Y))) (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b)))) (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b)))) :rule resolution :premises (t61 t62))
% 0.45/0.64  (step t64 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (tptp.little_set (tptp.non_ordered_pair X Y))) (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b)))) (not (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))))) :rule implies_neg2)
% 0.45/0.64  (step t65 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (tptp.little_set (tptp.non_ordered_pair X Y))) (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (tptp.little_set (tptp.non_ordered_pair X Y))) (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))))) :rule resolution :premises (t63 t64))
% 0.45/0.64  (step t66 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (tptp.little_set (tptp.non_ordered_pair X Y))) (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))))) :rule contraction :premises (t65))
% 0.45/0.64  (step t67 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (tptp.little_set (tptp.non_ordered_pair X Y)))) (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b)))) :rule implies :premises (t66))
% 0.45/0.64  (step t68 (cl (tptp.little_set (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b)))) :rule resolution :premises (t67 a7))
% 0.45/0.64  (step t69 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.ordered_pair X Y) (tptp.non_ordered_pair (tptp.singleton_set X) (tptp.non_ordered_pair X Y)))) (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b)))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.ordered_pair X Y) (tptp.non_ordered_pair (tptp.singleton_set X) (tptp.non_ordered_pair X Y))))) :rule implies_neg1)
% 0.45/0.64  (anchor :step t70)
% 0.45/0.64  (assume t70.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.ordered_pair X Y) (tptp.non_ordered_pair (tptp.singleton_set X) (tptp.non_ordered_pair X Y)))))
% 0.45/0.64  (step t70.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.ordered_pair X Y) (tptp.non_ordered_pair (tptp.singleton_set X) (tptp.non_ordered_pair X Y))))) (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))))) :rule forall_inst :args ((:= X tptp.a) (:= Y tptp.b)))
% 0.45/0.64  (step t70.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.ordered_pair X Y) (tptp.non_ordered_pair (tptp.singleton_set X) (tptp.non_ordered_pair X Y))))) (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b)))) :rule or :premises (t70.t1))
% 0.45/0.64  (step t70.t3 (cl (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b)))) :rule resolution :premises (t70.t2 t70.a0))
% 0.45/0.64  (step t70 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.ordered_pair X Y) (tptp.non_ordered_pair (tptp.singleton_set X) (tptp.non_ordered_pair X Y))))) (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b)))) :rule subproof :discharge (t70.a0))
% 0.45/0.64  (step t71 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.ordered_pair X Y) (tptp.non_ordered_pair (tptp.singleton_set X) (tptp.non_ordered_pair X Y)))) (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b)))) (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b)))) :rule resolution :premises (t69 t70))
% 0.45/0.64  (step t72 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.ordered_pair X Y) (tptp.non_ordered_pair (tptp.singleton_set X) (tptp.non_ordered_pair X Y)))) (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b)))) (not (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))))) :rule implies_neg2)
% 0.45/0.64  (step t73 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.ordered_pair X Y) (tptp.non_ordered_pair (tptp.singleton_set X) (tptp.non_ordered_pair X Y)))) (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.ordered_pair X Y) (tptp.non_ordered_pair (tptp.singleton_set X) (tptp.non_ordered_pair X Y)))) (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))))) :rule resolution :premises (t71 t72))
% 0.45/0.64  (step t74 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.ordered_pair X Y) (tptp.non_ordered_pair (tptp.singleton_set X) (tptp.non_ordered_pair X Y)))) (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b))))) :rule contraction :premises (t73))
% 0.45/0.64  (step t75 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.ordered_pair X Y) (tptp.non_ordered_pair (tptp.singleton_set X) (tptp.non_ordered_pair X Y))))) (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b)))) :rule implies :premises (t74))
% 0.45/0.64  (step t76 (cl (= (tptp.ordered_pair tptp.a tptp.b) (tptp.non_ordered_pair (tptp.singleton_set tptp.a) (tptp.non_ordered_pair tptp.a tptp.b)))) :rule resolution :premises (t75 a9))
% 0.45/0.64  (step t77 (cl) :rule resolution :premises (t60 t68 t76 a150))
% 0.45/0.64  
% 0.45/0.64  % SZS output end Proof for /export/starexec/sandbox/tmp/tmp.Xu6wv0wdyL/cvc5---1.0.5_3669.smt2
% 0.45/0.65  % cvc5---1.0.5 exiting
% 0.45/0.65  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------