%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SET038-3 : TPTP v8.2.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : do_cvc5 %s %d

% Computer : n024.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 17:43:49 EDT 2024

% Result   : Unsatisfiable 26.45s 26.70s
% Output   : Proof 26.53s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.15  % Problem    : SET038-3 : TPTP v8.2.0. Released v1.0.0.
% 0.13/0.16  % Command    : do_cvc5 %s %d
% 0.15/0.37  % Computer : n024.cluster.edu
% 0.15/0.37  % Model    : x86_64 x86_64
% 0.15/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37  % Memory   : 8042.1875MB
% 0.15/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37  % CPULimit   : 300
% 0.15/0.37  % WCLimit    : 300
% 0.15/0.37  % DateTime   : Tue May 28 08:31:39 EDT 2024
% 0.15/0.37  % CPUTime    : 
% 0.21/0.54  %----Proving TF0_NAR, FOF, or CNF
% 0.37/0.54  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 10.48/10.68  --- Run --no-e-matching --full-saturate-quant at 5...
% 15.55/15.75  --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 20.59/20.80  --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 25.62/25.84  --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 26.45/26.70  % SZS status Unsatisfiable for /export/starexec/sandbox2/tmp/tmp.Se1txPSMwZ/cvc5---1.0.5_21104.smt2
% 26.45/26.70  % SZS output start Proof for /export/starexec/sandbox2/tmp/tmp.Se1txPSMwZ/cvc5---1.0.5_21104.smt2
% 26.53/26.72  (assume a0 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X Y)) (tptp.little_set X))))
% 26.53/26.72  (assume a1 (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.little_set (tptp.f1 X Y)) (= X Y))))
% 26.53/26.72  (assume a2 (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.member (tptp.f1 X Y) X) (tptp.member (tptp.f1 X Y) Y) (= X Y))))
% 26.53/26.72  (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))))
% 26.53/26.72  (assume a4 (forall ((U $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member U (tptp.non_ordered_pair X Y))) (= U X) (= U Y))))
% 26.53/26.72  (assume a5 (forall ((U $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (tptp.member U (tptp.non_ordered_pair X Y)) (not (tptp.little_set U)) (not (= U X)))))
% 26.53/26.72  (assume a6 (forall ((U $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (tptp.member U (tptp.non_ordered_pair X Y)) (not (tptp.little_set U)) (not (= U Y)))))
% 26.53/26.72  (assume a7 (forall ((X $$unsorted) (Y $$unsorted)) (tptp.little_set (tptp.non_ordered_pair X Y))))
% 26.53/26.72  (assume a8 (forall ((X $$unsorted)) (= (tptp.singleton_set X) (tptp.non_ordered_pair X X))))
% 26.53/26.72  (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)))))
% 26.53/26.72  (assume a10 (forall ((X $$unsorted)) (or (not (tptp.ordered_pair_predicate X)) (tptp.little_set (tptp.f2 X)))))
% 26.53/26.72  (assume a11 (forall ((X $$unsorted)) (or (not (tptp.ordered_pair_predicate X)) (tptp.little_set (tptp.f3 X)))))
% 26.53/26.72  (assume a12 (forall ((X $$unsorted)) (or (not (tptp.ordered_pair_predicate X)) (= X (tptp.ordered_pair (tptp.f2 X) (tptp.f3 X))))))
% 26.53/26.72  (assume a13 (forall ((X $$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))))))
% 26.53/26.72  (assume a14 (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.first X))) (tptp.little_set (tptp.f4 Z X)))))
% 26.53/26.72  (assume a15 (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.first X))) (tptp.little_set (tptp.f5 Z X)))))
% 26.53/26.72  (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))))))
% 26.53/26.72  (assume a17 (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.first X))) (tptp.member Z (tptp.f4 Z X)))))
% 26.53/26.72  (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)))))
% 26.53/26.72  (assume a19 (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.second X))) (tptp.little_set (tptp.f6 Z X)))))
% 26.53/26.72  (assume a20 (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.second X))) (tptp.little_set (tptp.f7 Z X)))))
% 26.53/26.72  (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))))))
% 26.53/26.72  (assume a22 (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.second X))) (tptp.member Z (tptp.f7 Z X)))))
% 26.53/26.72  (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)))))
% 26.53/26.72  (assume a24 (forall ((Z $$unsorted)) (or (not (tptp.member Z tptp.estin)) (tptp.ordered_pair_predicate Z))))
% 26.53/26.72  (assume a25 (forall ((Z $$unsorted)) (or (not (tptp.member Z tptp.estin)) (tptp.member (tptp.first Z) (tptp.second Z)))))
% 26.53/26.72  (assume a26 (forall ((Z $$unsorted)) (or (tptp.member Z tptp.estin) (not (tptp.little_set Z)) (not (tptp.ordered_pair_predicate Z)) (not (tptp.member (tptp.first Z) (tptp.second Z))))))
% 26.53/26.72  (assume a27 (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.intersection X Y))) (tptp.member Z X))))
% 26.53/26.72  (assume a28 (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.intersection X Y))) (tptp.member Z Y))))
% 26.53/26.72  (assume a29 (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (tptp.member Z (tptp.intersection X Y)) (not (tptp.member Z X)) (not (tptp.member Z Y)))))
% 26.53/26.72  (assume a30 (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.complement X))) (not (tptp.member Z X)))))
% 26.53/26.72  (assume a31 (forall ((Z $$unsorted) (X $$unsorted)) (or (tptp.member Z (tptp.complement X)) (not (tptp.little_set Z)) (tptp.member Z X))))
% 26.53/26.72  (assume a32 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.union X Y) (tptp.complement (tptp.intersection (tptp.complement X) (tptp.complement Y))))))
% 26.53/26.72  (assume a33 (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.domain_of X))) (tptp.ordered_pair_predicate (tptp.f8 Z X)))))
% 26.53/26.72  (assume a34 (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.domain_of X))) (tptp.member (tptp.f8 Z X) X))))
% 26.53/26.72  (assume a35 (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.domain_of X))) (= Z (tptp.first (tptp.f8 Z X))))))
% 26.53/26.72  (assume a36 (forall ((Z $$unsorted) (X $$unsorted) (Xp $$unsorted)) (or (tptp.member Z (tptp.domain_of X)) (not (tptp.little_set Z)) (not (tptp.ordered_pair_predicate Xp)) (not (tptp.member Xp X)) (not (= Z (tptp.first Xp))))))
% 26.53/26.72  (assume a37 (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.cross_product X Y))) (tptp.ordered_pair_predicate Z))))
% 26.53/26.72  (assume a38 (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.cross_product X Y))) (tptp.member (tptp.first Z) X))))
% 26.53/26.72  (assume a39 (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.cross_product X Y))) (tptp.member (tptp.second Z) Y))))
% 26.53/26.72  (assume a40 (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (tptp.member Z (tptp.cross_product X Y)) (not (tptp.little_set Z)) (not (tptp.ordered_pair_predicate Z)) (not (tptp.member (tptp.first Z) X)) (not (tptp.member (tptp.second Z) Y)))))
% 26.53/26.72  (assume a41 (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.converse X))) (tptp.ordered_pair_predicate Z))))
% 26.53/26.72  (assume a42 (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.converse X))) (tptp.member (tptp.ordered_pair (tptp.second Z) (tptp.first Z)) X))))
% 26.53/26.72  (assume a43 (forall ((Z $$unsorted) (X $$unsorted)) (or (tptp.member Z (tptp.converse X)) (not (tptp.little_set Z)) (not (tptp.ordered_pair_predicate Z)) (not (tptp.member (tptp.ordered_pair (tptp.second Z) (tptp.first Z)) X)))))
% 26.53/26.72  (assume a44 (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.rotate_right X))) (tptp.little_set (tptp.f9 Z X)))))
% 26.53/26.72  (assume a45 (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.rotate_right X))) (tptp.little_set (tptp.f10 Z X)))))
% 26.53/26.72  (assume a46 (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.rotate_right X))) (tptp.little_set (tptp.f11 Z X)))))
% 26.53/26.72  (assume a47 (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.rotate_right X))) (= Z (tptp.ordered_pair (tptp.f9 Z X) (tptp.ordered_pair (tptp.f10 Z X) (tptp.f11 Z X)))))))
% 26.53/26.72  (assume a48 (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.rotate_right X))) (tptp.member (tptp.ordered_pair (tptp.f10 Z X) (tptp.ordered_pair (tptp.f11 Z X) (tptp.f9 Z X))) X))))
% 26.53/26.72  (assume a49 (forall ((Z $$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)))))
% 26.53/26.72  (assume a50 (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.flip_range_of X))) (tptp.little_set (tptp.f12 Z X)))))
% 26.53/26.72  (assume a51 (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.flip_range_of X))) (tptp.little_set (tptp.f13 Z X)))))
% 26.53/26.72  (assume a52 (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.flip_range_of X))) (tptp.little_set (tptp.f14 Z X)))))
% 26.53/26.72  (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)))))))
% 26.53/26.72  (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))))
% 26.53/26.72  (assume a55 (forall ((Z $$unsorted) (X $$unsorted) (U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (tptp.member Z (tptp.flip_range_of X)) (not (tptp.little_set Z)) (not (tptp.little_set U)) (not (tptp.little_set V)) (not (tptp.little_set W)) (not (= Z (tptp.ordered_pair U (tptp.ordered_pair V W)))) (not (tptp.member (tptp.ordered_pair U (tptp.ordered_pair W V)) X)))))
% 26.53/26.72  (assume a56 (forall ((X $$unsorted)) (= (tptp.successor X) (tptp.union X (tptp.singleton_set X)))))
% 26.53/26.72  (assume a57 (forall ((Z $$unsorted)) (not (tptp.member Z tptp.empty_set))))
% 26.53/26.72  (assume a58 (forall ((Z $$unsorted)) (or (tptp.member Z tptp.universal_set) (not (tptp.little_set Z)))))
% 26.53/26.72  (assume a59 (tptp.little_set tptp.infinity))
% 26.53/26.72  (assume a60 (tptp.member tptp.empty_set tptp.infinity))
% 26.53/26.72  (assume a61 (forall ((X $$unsorted)) (or (not (tptp.member X tptp.infinity)) (tptp.member (tptp.successor X) tptp.infinity))))
% 26.53/26.72  (assume a62 (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.sigma X))) (tptp.member (tptp.f16 Z X) X))))
% 26.53/26.72  (assume a63 (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.sigma X))) (tptp.member Z (tptp.f16 Z X)))))
% 26.53/26.72  (assume a64 (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (tptp.member Z (tptp.sigma X)) (not (tptp.member Y X)) (not (tptp.member Z Y)))))
% 26.53/26.72  (assume a65 (forall ((U $$unsorted)) (or (not (tptp.little_set U)) (tptp.little_set (tptp.sigma U)))))
% 26.53/26.72  (assume a66 (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (not (tptp.subset X Y)) (not (tptp.member U X)) (tptp.member U Y))))
% 26.53/26.72  (assume a67 (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.subset X Y) (tptp.member (tptp.f17 X Y) X))))
% 26.53/26.72  (assume a68 (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.subset X Y) (not (tptp.member (tptp.f17 X Y) Y)))))
% 26.53/26.72  (assume a69 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.proper_subset X Y)) (tptp.subset X Y))))
% 26.53/26.72  (assume a70 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.proper_subset X Y)) (not (= X Y)))))
% 26.53/26.72  (assume a71 (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.proper_subset X Y) (not (tptp.subset X Y)) (= X Y))))
% 26.53/26.72  (assume a72 (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.powerset X))) (tptp.subset Z X))))
% 26.53/26.72  (assume a73 (forall ((Z $$unsorted) (X $$unsorted)) (or (tptp.member Z (tptp.powerset X)) (not (tptp.little_set Z)) (not (tptp.subset Z X)))))
% 26.53/26.72  (assume a74 (forall ((U $$unsorted)) (or (not (tptp.little_set U)) (tptp.little_set (tptp.powerset U)))))
% 26.53/26.72  (assume a75 (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.relation Z)) (not (tptp.member X Z)) (tptp.ordered_pair_predicate X))))
% 26.53/26.72  (assume a76 (forall ((Z $$unsorted)) (or (tptp.relation Z) (tptp.member (tptp.f18 Z) Z))))
% 26.53/26.72  (assume a77 (forall ((Z $$unsorted)) (or (tptp.relation Z) (not (tptp.ordered_pair_predicate (tptp.f18 Z))))))
% 26.53/26.72  (assume a78 (forall ((X $$unsorted) (U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.single_valued_set X)) (not (tptp.little_set U)) (not (tptp.little_set V)) (not (tptp.little_set W)) (not (tptp.member (tptp.ordered_pair U V) X)) (not (tptp.member (tptp.ordered_pair U W) X)) (= V W))))
% 26.53/26.72  (assume a79 (forall ((X $$unsorted)) (or (tptp.single_valued_set X) (tptp.little_set (tptp.f19 X)))))
% 26.53/26.72  (assume a80 (forall ((X $$unsorted)) (or (tptp.single_valued_set X) (tptp.little_set (tptp.f20 X)))))
% 26.53/26.72  (assume a81 (forall ((X $$unsorted)) (or (tptp.single_valued_set X) (tptp.little_set (tptp.f21 X)))))
% 26.53/26.72  (assume a82 (forall ((X $$unsorted)) (or (tptp.single_valued_set X) (tptp.member (tptp.ordered_pair (tptp.f19 X) (tptp.f20 X)) X))))
% 26.53/26.72  (assume a83 (forall ((X $$unsorted)) (or (tptp.single_valued_set X) (tptp.member (tptp.ordered_pair (tptp.f19 X) (tptp.f21 X)) X))))
% 26.53/26.72  (assume a84 (forall ((X $$unsorted)) (or (tptp.single_valued_set X) (not (= (tptp.f20 X) (tptp.f21 X))))))
% 26.53/26.72  (assume a85 (forall ((Xf $$unsorted)) (or (not (tptp.function Xf)) (tptp.relation Xf))))
% 26.53/26.72  (assume a86 (forall ((Xf $$unsorted)) (or (not (tptp.function Xf)) (tptp.single_valued_set Xf))))
% 26.53/26.72  (assume a87 (forall ((Xf $$unsorted)) (or (tptp.function Xf) (not (tptp.relation Xf)) (not (tptp.single_valued_set Xf)))))
% 26.53/26.72  (assume a88 (forall ((Z $$unsorted) (X $$unsorted) (Xf $$unsorted)) (or (not (tptp.member Z (tptp.image X Xf))) (tptp.ordered_pair_predicate (tptp.f22 Z X Xf)))))
% 26.53/26.72  (assume a89 (forall ((Z $$unsorted) (X $$unsorted) (Xf $$unsorted)) (or (not (tptp.member Z (tptp.image X Xf))) (tptp.member (tptp.f22 Z X Xf) Xf))))
% 26.53/26.72  (assume a90 (forall ((Z $$unsorted) (X $$unsorted) (Xf $$unsorted)) (or (not (tptp.member Z (tptp.image X Xf))) (tptp.member (tptp.first (tptp.f22 Z X Xf)) X))))
% 26.53/26.72  (assume a91 (forall ((Z $$unsorted) (X $$unsorted) (Xf $$unsorted)) (or (not (tptp.member Z (tptp.image X Xf))) (= (tptp.second (tptp.f22 Z X Xf)) Z))))
% 26.53/26.72  (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)))))
% 26.53/26.72  (assume a93 (forall ((X $$unsorted) (Xf $$unsorted)) (or (not (tptp.little_set X)) (not (tptp.function Xf)) (tptp.little_set (tptp.image X Xf)))))
% 26.53/26.72  (assume a94 (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (not (tptp.disjoint X Y)) (not (tptp.member U X)) (not (tptp.member U Y)))))
% 26.53/26.72  (assume a95 (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.disjoint X Y) (tptp.member (tptp.f23 X Y) X))))
% 26.53/26.72  (assume a96 (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.disjoint X Y) (tptp.member (tptp.f23 X Y) Y))))
% 26.53/26.72  (assume a97 (forall ((X $$unsorted)) (or (= X tptp.empty_set) (tptp.member (tptp.f24 X) X))))
% 26.53/26.72  (assume a98 (forall ((X $$unsorted)) (or (= X tptp.empty_set) (tptp.disjoint (tptp.f24 X) X))))
% 26.53/26.72  (assume a99 (tptp.function tptp.f25))
% 26.53/26.72  (assume a100 (forall ((X $$unsorted)) (or (not (tptp.little_set X)) (= X tptp.empty_set) (tptp.member (tptp.f26 X) X))))
% 26.53/26.72  (assume a101 (forall ((X $$unsorted)) (or (not (tptp.little_set X)) (= X tptp.empty_set) (tptp.member (tptp.ordered_pair X (tptp.f26 X)) tptp.f25))))
% 26.53/26.72  (assume a102 (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.range_of X))) (tptp.ordered_pair_predicate (tptp.f27 Z X)))))
% 26.53/26.72  (assume a103 (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.range_of X))) (tptp.member (tptp.f27 Z X) X))))
% 26.53/26.72  (assume a104 (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.range_of X))) (= Z (tptp.second (tptp.f27 Z X))))))
% 26.53/26.72  (assume a105 (forall ((Z $$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))))))
% 26.53/26.72  (assume a106 (forall ((Z $$unsorted)) (or (not (tptp.member Z tptp.identity_relation)) (tptp.ordered_pair_predicate Z))))
% 26.53/26.72  (assume a107 (forall ((Z $$unsorted)) (or (not (tptp.member Z tptp.identity_relation)) (= (tptp.first Z) (tptp.second Z)))))
% 26.53/26.72  (assume a108 (forall ((Z $$unsorted)) (or (tptp.member Z tptp.identity_relation) (not (tptp.little_set Z)) (not (tptp.ordered_pair_predicate Z)) (not (= (tptp.first Z) (tptp.second Z))))))
% 26.53/26.72  (assume a109 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.restrict X Y) (tptp.intersection X (tptp.cross_product Y tptp.universal_set)))))
% 26.53/26.72  (assume a110 (forall ((Xf $$unsorted)) (or (not (tptp.one_to_one_function Xf)) (tptp.function Xf))))
% 26.53/26.72  (assume a111 (forall ((Xf $$unsorted)) (or (not (tptp.one_to_one_function Xf)) (tptp.function (tptp.converse Xf)))))
% 26.53/26.72  (assume a112 (forall ((Xf $$unsorted)) (or (tptp.one_to_one_function Xf) (not (tptp.function Xf)) (not (tptp.function (tptp.converse Xf))))))
% 26.53/26.72  (assume a113 (forall ((Z $$unsorted) (Xf $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.apply Xf Y))) (tptp.ordered_pair_predicate (tptp.f28 Z Xf Y)))))
% 26.53/26.72  (assume a114 (forall ((Z $$unsorted) (Xf $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.apply Xf Y))) (tptp.member (tptp.f28 Z Xf Y) Xf))))
% 26.53/26.72  (assume a115 (forall ((Z $$unsorted) (Xf $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.apply Xf Y))) (= (tptp.first (tptp.f28 Z Xf Y)) Y))))
% 26.53/26.72  (assume a116 (forall ((Z $$unsorted) (Xf $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.apply Xf Y))) (tptp.member Z (tptp.second (tptp.f28 Z Xf Y))))))
% 26.53/26.72  (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))))))
% 26.53/26.72  (assume a118 (forall ((Xf $$unsorted) (X $$unsorted) (Y $$unsorted)) (= (tptp.apply_to_two_arguments Xf X Y) (tptp.apply Xf (tptp.ordered_pair X Y)))))
% 26.53/26.72  (assume a119 (forall ((Xf $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.maps Xf X Y)) (tptp.function Xf))))
% 26.53/26.72  (assume a120 (forall ((Xf $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.maps Xf X Y)) (= (tptp.domain_of Xf) X))))
% 26.53/26.72  (assume a121 (forall ((Xf $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.maps Xf X Y)) (tptp.subset (tptp.range_of Xf) Y))))
% 26.53/26.72  (assume a122 (forall ((Xf $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (tptp.maps Xf X Y) (not (tptp.function Xf)) (not (= (tptp.domain_of Xf) X)) (not (tptp.subset (tptp.range_of Xf) Y)))))
% 26.53/26.72  (assume a123 (forall ((Xs $$unsorted) (Xf $$unsorted)) (or (not (tptp.closed Xs Xf)) (tptp.little_set Xs))))
% 26.53/26.72  (assume a124 (forall ((Xs $$unsorted) (Xf $$unsorted)) (or (not (tptp.closed Xs Xf)) (tptp.little_set Xf))))
% 26.53/26.72  (assume a125 (forall ((Xs $$unsorted) (Xf $$unsorted)) (or (not (tptp.closed Xs Xf)) (tptp.maps Xf (tptp.cross_product Xs Xs) Xs))))
% 26.53/26.72  (assume a126 (forall ((Xs $$unsorted) (Xf $$unsorted)) (or (tptp.closed Xs Xf) (not (tptp.little_set Xs)) (not (tptp.little_set Xf)) (not (tptp.maps Xf (tptp.cross_product Xs Xs) Xs)))))
% 26.53/26.72  (assume a127 (forall ((Z $$unsorted) (Xf $$unsorted) (Xg $$unsorted)) (or (not (tptp.member Z (tptp.compose Xf Xg))) (tptp.little_set (tptp.f29 Z Xf Xg)))))
% 26.53/26.72  (assume a128 (forall ((Z $$unsorted) (Xf $$unsorted) (Xg $$unsorted)) (or (not (tptp.member Z (tptp.compose Xf Xg))) (tptp.little_set (tptp.f30 Z Xf Xg)))))
% 26.53/26.72  (assume a129 (forall ((Z $$unsorted) (Xf $$unsorted) (Xg $$unsorted)) (or (not (tptp.member Z (tptp.compose Xf Xg))) (tptp.little_set (tptp.f31 Z Xf Xg)))))
% 26.53/26.72  (assume a130 (forall ((Z $$unsorted) (Xf $$unsorted) (Xg $$unsorted)) (or (not (tptp.member Z (tptp.compose Xf Xg))) (= Z (tptp.ordered_pair (tptp.f29 Z Xf Xg) (tptp.f30 Z Xf Xg))))))
% 26.53/26.72  (assume a131 (forall ((Z $$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))))
% 26.53/26.72  (assume a132 (forall ((Z $$unsorted) (Xf $$unsorted) (Xg $$unsorted)) (or (not (tptp.member Z (tptp.compose Xf Xg))) (tptp.member (tptp.ordered_pair (tptp.f31 Z Xf Xg) (tptp.f30 Z Xf Xg)) Xg))))
% 26.53/26.72  (assume a133 (forall ((Z $$unsorted) (Xf $$unsorted) (Xg $$unsorted) (X $$unsorted) (Y $$unsorted) (W $$unsorted)) (or (tptp.member Z (tptp.compose Xf Xg)) (not (tptp.little_set Z)) (not (tptp.little_set X)) (not (tptp.little_set Y)) (not (tptp.little_set W)) (not (= Z (tptp.ordered_pair X Y))) (not (tptp.member (tptp.ordered_pair X W) Xf)) (not (tptp.member (tptp.ordered_pair W Y) Xg)))))
% 26.53/26.72  (assume a134 (forall ((Xh $$unsorted) (Xs1 $$unsorted) (Xf1 $$unsorted) (Xs2 $$unsorted) (Xf2 $$unsorted)) (or (not (tptp.homomorphism Xh Xs1 Xf1 Xs2 Xf2)) (tptp.closed Xs1 Xf1))))
% 26.53/26.72  (assume a135 (forall ((Xh $$unsorted) (Xs1 $$unsorted) (Xf1 $$unsorted) (Xs2 $$unsorted) (Xf2 $$unsorted)) (or (not (tptp.homomorphism Xh Xs1 Xf1 Xs2 Xf2)) (tptp.closed Xs2 Xf2))))
% 26.53/26.72  (assume a136 (forall ((Xh $$unsorted) (Xs1 $$unsorted) (Xf1 $$unsorted) (Xs2 $$unsorted) (Xf2 $$unsorted)) (or (not (tptp.homomorphism Xh Xs1 Xf1 Xs2 Xf2)) (tptp.maps Xh Xs1 Xs2))))
% 26.53/26.72  (assume a137 (forall ((Xh $$unsorted) (Xs1 $$unsorted) (Xf1 $$unsorted) (Xs2 $$unsorted) (Xf2 $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.homomorphism Xh Xs1 Xf1 Xs2 Xf2)) (not (tptp.member X Xs1)) (not (tptp.member Y Xs1)) (= (tptp.apply Xh (tptp.apply_to_two_arguments Xf1 X Y)) (tptp.apply_to_two_arguments Xf2 (tptp.apply Xh X) (tptp.apply Xh Y))))))
% 26.53/26.72  (assume a138 (forall ((Xh $$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))))
% 26.53/26.72  (assume a139 (forall ((Xh $$unsorted) (Xs1 $$unsorted) (Xf1 $$unsorted) (Xs2 $$unsorted) (Xf2 $$unsorted)) (or (tptp.homomorphism Xh Xs1 Xf1 Xs2 Xf2) (not (tptp.closed Xs1 Xf1)) (not (tptp.closed Xs2 Xf2)) (not (tptp.maps Xh Xs1 Xs2)) (tptp.member (tptp.f33 Xh Xs1 Xf1 Xs2 Xf2) Xs1))))
% 26.53/26.72  (assume a140 (forall ((Xh $$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))))))))
% 26.53/26.72  (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))))
% 26.53/26.72  (assume a142 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.little_set X)) (not (tptp.little_set Y)) (not (= (tptp.non_ordered_pair Z X) (tptp.non_ordered_pair Z Y))) (= X Y))))
% 26.53/26.72  (assume a143 (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (not (tptp.little_set X)) (not (tptp.little_set Y)) (not (tptp.little_set U)) (not (tptp.little_set V)) (not (= (tptp.ordered_pair X Y) (tptp.ordered_pair U V))) (= Y V))))
% 26.53/26.72  (assume a144 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.subset X Y)) (not (tptp.subset Y X)) (= X Y))))
% 26.53/26.72  (assume a145 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.little_set X)) (not (tptp.little_set Y)) (= (tptp.first (tptp.ordered_pair X Y)) X))))
% 26.53/26.72  (assume a146 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.little_set X)) (not (tptp.little_set Y)) (= (tptp.second (tptp.ordered_pair X Y)) Y))))
% 26.53/26.72  (assume a147 (forall ((X $$unsorted)) (or (not (tptp.ordered_pair_predicate X)) (tptp.little_set (tptp.first X)))))
% 26.53/26.72  (assume a148 (forall ((X $$unsorted)) (or (not (tptp.ordered_pair_predicate X)) (tptp.little_set (tptp.second X)))))
% 26.53/26.72  (assume a149 (forall ((X $$unsorted)) (or (not (tptp.little_set X)) (tptp.member X (tptp.singleton_set X)))))
% 26.53/26.72  (assume a150 (forall ((X $$unsorted) (Y $$unsorted)) (tptp.little_set (tptp.ordered_pair X Y))))
% 26.53/26.72  (assume a151 (forall ((X $$unsorted)) (or (not (tptp.ordered_pair_predicate X)) (tptp.little_set X))))
% 26.53/26.72  (assume a152 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.subset X Y)) (not (tptp.subset Y Z)) (tptp.subset X Z))))
% 26.53/26.72  (assume a153 (forall ((Xf $$unsorted) (Y $$unsorted)) (tptp.subset (tptp.apply Xf Y) (tptp.sigma (tptp.image (tptp.singleton_set Y) Xf)))))
% 26.53/26.72  (assume a154 (forall ((Y $$unsorted) (Xf $$unsorted)) (tptp.subset (tptp.image (tptp.singleton_set Y) Xf) (tptp.apply Xf Y))))
% 26.53/26.72  (assume a155 (forall ((Y $$unsorted) (X $$unsorted)) (or (not (tptp.function Y)) (tptp.little_set (tptp.apply Y X)))))
% 26.53/26.72  (assume a156 (forall ((Y $$unsorted) (X $$unsorted)) (tptp.relation (tptp.compose Y X))))
% 26.53/26.72  (assume a157 (forall ((Y $$unsorted) (X $$unsorted)) (tptp.subset (tptp.range_of (tptp.compose Y X)) (tptp.range_of Y))))
% 26.53/26.72  (assume a158 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.subset (tptp.range_of X) (tptp.domain_of Y))) (= (tptp.domain_of X) (tptp.domain_of (tptp.compose Y X))))))
% 26.53/26.72  (assume a159 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.function X)) (not (tptp.function Y)) (tptp.function (tptp.compose Y X)))))
% 26.53/26.72  (assume a160 (forall ((Xf $$unsorted) (U $$unsorted) (V $$unsorted) (Xg $$unsorted) (W $$unsorted)) (or (not (tptp.maps Xf U V)) (not (tptp.maps Xg V W)) (tptp.maps (tptp.compose Xg Xf) U W))))
% 26.53/26.72  (assume a161 (forall ((X $$unsorted) (Y $$unsorted) (Xf $$unsorted)) (or (not (tptp.little_set X)) (not (tptp.little_set Y)) (not (tptp.function Xf)) (not (tptp.member (tptp.ordered_pair X Y) Xf)) (= (tptp.apply Xf X) Y))))
% 26.53/26.72  (assume a162 (forall ((Xf $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.function Xf)) (not (tptp.member X (tptp.domain_of Xf))) (not (= (tptp.apply Xf X) Y)) (tptp.member (tptp.ordered_pair X Y) Xf))))
% 26.53/26.72  (assume a163 (tptp.maps tptp.a_function tptp.a_domain tptp.a_range))
% 26.53/26.72  (assume a164 (tptp.member tptp.a tptp.a_domain))
% 26.53/26.72  (assume a165 (not (tptp.member (tptp.apply tptp.a_function tptp.a) tptp.a_range)))
% 26.53/26.72  (step t1 (cl (not (or (tptp.member (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)) (not (tptp.little_set (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))))) (not (tptp.ordered_pair_predicate (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)))) (not (tptp.member (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)) tptp.a_function)))) (tptp.member (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)) (not (tptp.little_set (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))))) (not (tptp.ordered_pair_predicate (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)))) (not (tptp.member (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)) tptp.a_function))) :rule or_pos)
% 26.53/26.72  (step t2 (cl (not (tptp.member (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)) tptp.a_function)) (not (tptp.ordered_pair_predicate (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)))) (tptp.member (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)) (not (tptp.little_set (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))))) (not (or (tptp.member (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)) (not (tptp.little_set (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))))) (not (tptp.ordered_pair_predicate (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)))) (not (tptp.member (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)) tptp.a_function))))) :rule reordering :premises (t1))
% 26.53/26.72  (step t3 (cl (not (= (or (not (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))))) (not (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))))) (not (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)))) (not (tptp.member (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)))) (or (not (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))))) (not (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))))) (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)) (not (tptp.member (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)))))) (not (or (not (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))))) (not (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))))) (not (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)))) (not (tptp.member (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function))))) (or (not (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))))) (not (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))))) (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)) (not (tptp.member (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function))))) :rule equiv_pos2)
% 26.53/26.72  (step t4 (cl (= (not (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))))) (not (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))))))) :rule refl)
% 26.53/26.72  (step t5 (cl (= (not (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))))) (not (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))))))) :rule refl)
% 26.53/26.72  (step t6 (cl (= (= (= (not (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)))) (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function))) true) (= (not (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)))) (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function))))) :rule equiv_simplify)
% 26.53/26.72  (step t7 (cl (not (= (= (not (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)))) (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function))) true)) (= (not (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)))) (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)))) :rule equiv1 :premises (t6))
% 26.53/26.72  (step t8 (cl (= (= (not (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)))) (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function))) (= (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)) (not (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function))))))) :rule all_simplify)
% 26.53/26.72  (step t9 (cl (= (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)) (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)))) :rule refl)
% 26.53/26.72  (step t10 (cl (= (not (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)))) (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)))) :rule all_simplify)
% 26.53/26.72  (step t11 (cl (= (= (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)) (not (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function))))) (= (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)) (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function))))) :rule cong :premises (t9 t10))
% 26.53/26.72  (step t12 (cl (= (= (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)) (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function))) true)) :rule all_simplify)
% 26.53/26.72  (step t13 (cl (= (= (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)) (not (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function))))) true)) :rule trans :premises (t11 t12))
% 26.53/26.72  (step t14 (cl (= (= (not (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)))) (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function))) true)) :rule trans :premises (t8 t13))
% 26.53/26.72  (step t15 (cl (= (not (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)))) (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)))) :rule resolution :premises (t7 t14))
% 26.53/26.72  (step t16 (cl (= (not (tptp.member (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function))) (not (tptp.member (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function))))) :rule refl)
% 26.53/26.72  (step t17 (cl (= (or (not (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))))) (not (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))))) (not (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)))) (not (tptp.member (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)))) (or (not (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))))) (not (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))))) (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)) (not (tptp.member (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)))))) :rule cong :premises (t4 t5 t15 t16))
% 26.53/26.72  (step t18 (cl (and (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)))) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a)))) (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)))) (not (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))))) (not (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))))) (not (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function))))) :rule and_neg)
% 26.53/26.72  (step t19 (cl (=> (and (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)))) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a)))) (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)))) (not (tptp.member (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)))) (and (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)))) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a)))) (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function))))) :rule implies_neg1)
% 26.53/26.72  (anchor :step t20)
% 26.53/26.72  (assume t20.a0 (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)))))
% 26.53/26.72  (assume t20.a1 (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a)))))
% 26.53/26.72  (assume t20.a2 (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function))))
% 26.53/26.72  (step t20.t1 (cl (=> (and (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function))) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a)))) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))))) (not (tptp.member (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)))) (and (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function))) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a)))) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)))))) :rule implies_neg1)
% 26.53/26.72  (anchor :step t20.t2)
% 26.53/26.72  (assume t20.t2.a0 (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function))))
% 26.53/26.72  (assume t20.t2.a1 (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a)))))
% 26.53/26.72  (assume t20.t2.a2 (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)))))
% 26.53/26.72  (step t20.t2.t1 (cl (= (= (tptp.member (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)) false) (not (tptp.member (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function))))) :rule equiv_simplify)
% 26.53/26.72  (step t20.t2.t2 (cl (not (= (tptp.member (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)) false)) (not (tptp.member (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)))) :rule equiv1 :premises (t20.t2.t1))
% 26.53/26.72  (step t20.t2.t3 (cl (= (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))) (tptp.apply tptp.a_function tptp.a))) :rule symm :premises (t20.t2.a2))
% 26.53/26.72  (step t20.t2.t4 (cl (= (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.apply tptp.a_function tptp.a))) :rule symm :premises (t20.t2.a1))
% 26.53/26.72  (step t20.t2.t5 (cl (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))))) :rule symm :premises (t20.t2.t4))
% 26.53/26.72  (step t20.t2.t6 (cl (= (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))))) :rule trans :premises (t20.t2.t3 t20.t2.t5))
% 26.53/26.72  (step t20.t2.t7 (cl (= (tptp.range_of tptp.a_function) (tptp.range_of tptp.a_function))) :rule refl)
% 26.53/26.72  (step t20.t2.t8 (cl (= (tptp.member (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)) (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)))) :rule cong :premises (t20.t2.t6 t20.t2.t7))
% 26.53/26.72  (step t20.t2.t9 (cl (= (= (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)) false) (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function))))) :rule equiv_simplify)
% 26.53/26.72  (step t20.t2.t10 (cl (= (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)) false) (not (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function))))) :rule equiv2 :premises (t20.t2.t9))
% 26.53/26.72  (step t20.t2.t11 (cl (not (not (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function))))) (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function))) :rule not_not)
% 26.53/26.72  (step t20.t2.t12 (cl (= (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)) false) (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function))) :rule resolution :premises (t20.t2.t10 t20.t2.t11))
% 26.53/26.72  (step t20.t2.t13 (cl (= (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)) false)) :rule resolution :premises (t20.t2.t12 t20.t2.a0))
% 26.53/26.72  (step t20.t2.t14 (cl (= (tptp.member (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)) false)) :rule trans :premises (t20.t2.t8 t20.t2.t13))
% 26.53/26.72  (step t20.t2.t15 (cl (not (tptp.member (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)))) :rule resolution :premises (t20.t2.t2 t20.t2.t14))
% 26.53/26.72  (step t20.t2 (cl (not (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)))) (not (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))))) (not (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))))) (not (tptp.member (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)))) :rule subproof :discharge (t20.t2.a0 t20.t2.a1 t20.t2.a2))
% 26.53/26.72  (step t20.t3 (cl (not (and (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function))) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a)))) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)))))) (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)))) :rule and_pos)
% 26.53/26.72  (step t20.t4 (cl (not (and (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function))) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a)))) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)))))) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))))) :rule and_pos)
% 26.53/26.72  (step t20.t5 (cl (not (and (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function))) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a)))) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)))))) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))))) :rule and_pos)
% 26.53/26.72  (step t20.t6 (cl (not (tptp.member (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function))) (not (and (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function))) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a)))) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)))))) (not (and (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function))) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a)))) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)))))) (not (and (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function))) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a)))) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))))))) :rule resolution :premises (t20.t2 t20.t3 t20.t4 t20.t5))
% 26.53/26.72  (step t20.t7 (cl (not (and (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function))) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a)))) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)))))) (not (and (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function))) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a)))) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)))))) (not (and (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function))) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a)))) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)))))) (not (tptp.member (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)))) :rule reordering :premises (t20.t6))
% 26.53/26.72  (step t20.t8 (cl (not (and (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function))) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a)))) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)))))) (not (tptp.member (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)))) :rule contraction :premises (t20.t7))
% 26.53/26.72  (step t20.t9 (cl (=> (and (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function))) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a)))) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))))) (not (tptp.member (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)))) (not (tptp.member (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)))) :rule resolution :premises (t20.t1 t20.t8))
% 26.53/26.72  (step t20.t10 (cl (=> (and (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function))) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a)))) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))))) (not (tptp.member (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)))) (not (not (tptp.member (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function))))) :rule implies_neg2)
% 26.53/26.72  (step t20.t11 (cl (=> (and (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function))) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a)))) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))))) (not (tptp.member (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)))) (=> (and (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function))) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a)))) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))))) (not (tptp.member (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function))))) :rule resolution :premises (t20.t9 t20.t10))
% 26.53/26.72  (step t20.t12 (cl (=> (and (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function))) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a)))) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))))) (not (tptp.member (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function))))) :rule contraction :premises (t20.t11))
% 26.53/26.72  (step t20.t13 (cl (not (and (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function))) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a)))) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)))))) (not (tptp.member (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)))) :rule implies :premises (t20.t12))
% 26.53/26.72  (step t20.t14 (cl (and (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function))) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a)))) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))))) (not (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)))) (not (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))))) (not (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)))))) :rule and_neg)
% 26.53/26.72  (step t20.t15 (cl (and (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function))) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a)))) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)))))) :rule resolution :premises (t20.t14 t20.a2 t20.a1 t20.a0))
% 26.53/26.72  (step t20.t16 (cl (not (tptp.member (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)))) :rule resolution :premises (t20.t13 t20.t15))
% 26.53/26.72  (step t20 (cl (not (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))))) (not (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))))) (not (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)))) (not (tptp.member (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)))) :rule subproof :discharge (t20.a0 t20.a1 t20.a2))
% 26.53/26.72  (step t21 (cl (not (and (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)))) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a)))) (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function))))) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))))) :rule and_pos)
% 26.53/26.72  (step t22 (cl (not (and (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)))) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a)))) (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function))))) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))))) :rule and_pos)
% 26.53/26.72  (step t23 (cl (not (and (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)))) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a)))) (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function))))) (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)))) :rule and_pos)
% 26.53/26.72  (step t24 (cl (not (tptp.member (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function))) (not (and (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)))) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a)))) (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function))))) (not (and (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)))) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a)))) (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function))))) (not (and (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)))) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a)))) (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)))))) :rule resolution :premises (t20 t21 t22 t23))
% 26.53/26.72  (step t25 (cl (not (and (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)))) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a)))) (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function))))) (not (and (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)))) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a)))) (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function))))) (not (and (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)))) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a)))) (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function))))) (not (tptp.member (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)))) :rule reordering :premises (t24))
% 26.53/26.72  (step t26 (cl (not (and (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)))) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a)))) (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function))))) (not (tptp.member (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)))) :rule contraction :premises (t25))
% 26.53/26.72  (step t27 (cl (=> (and (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)))) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a)))) (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)))) (not (tptp.member (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)))) (not (tptp.member (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)))) :rule resolution :premises (t19 t26))
% 26.53/26.72  (step t28 (cl (=> (and (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)))) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a)))) (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)))) (not (tptp.member (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)))) (not (not (tptp.member (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function))))) :rule implies_neg2)
% 26.53/26.72  (step t29 (cl (=> (and (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)))) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a)))) (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)))) (not (tptp.member (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)))) (=> (and (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)))) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a)))) (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)))) (not (tptp.member (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function))))) :rule resolution :premises (t27 t28))
% 26.53/26.72  (step t30 (cl (=> (and (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)))) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a)))) (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)))) (not (tptp.member (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function))))) :rule contraction :premises (t29))
% 26.53/26.72  (step t31 (cl (not (and (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)))) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a)))) (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function))))) (not (tptp.member (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)))) :rule implies :premises (t30))
% 26.53/26.72  (step t32 (cl (not (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))))) (not (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))))) (not (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)))) (not (tptp.member (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)))) :rule resolution :premises (t18 t31))
% 26.53/26.72  (step t33 (cl (or (not (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))))) (not (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))))) (not (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)))) (not (tptp.member (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)))) (not (not (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))))))) :rule or_neg)
% 26.53/26.72  (step t34 (cl (or (not (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))))) (not (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))))) (not (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)))) (not (tptp.member (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)))) (not (not (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))))))) :rule or_neg)
% 26.53/26.72  (step t35 (cl (or (not (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))))) (not (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))))) (not (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)))) (not (tptp.member (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)))) (not (not (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)))))) :rule or_neg)
% 26.53/26.72  (step t36 (cl (or (not (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))))) (not (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))))) (not (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)))) (not (tptp.member (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)))) (not (not (tptp.member (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function))))) :rule or_neg)
% 26.53/26.72  (step t37 (cl (or (not (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))))) (not (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))))) (not (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)))) (not (tptp.member (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)))) (or (not (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))))) (not (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))))) (not (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)))) (not (tptp.member (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)))) (or (not (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))))) (not (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))))) (not (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)))) (not (tptp.member (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)))) (or (not (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))))) (not (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))))) (not (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)))) (not (tptp.member (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function))))) :rule resolution :premises (t32 t33 t34 t35 t36))
% 26.53/26.72  (step t38 (cl (or (not (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))))) (not (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))))) (not (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)))) (not (tptp.member (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function))))) :rule contraction :premises (t37))
% 26.53/26.72  (step t39 (cl (or (not (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))))) (not (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))))) (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)) (not (tptp.member (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function))))) :rule resolution :premises (t3 t17 t38))
% 26.53/26.72  (step t40 (cl (not (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))))) (not (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))))) (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)) (not (tptp.member (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)))) :rule or :premises (t39))
% 26.53/26.72  (step t41 (cl (not (or (not (tptp.little_set tptp.a)) (not (tptp.little_set (tptp.apply tptp.a_function tptp.a))) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)))))) (not (tptp.little_set tptp.a)) (not (tptp.little_set (tptp.apply tptp.a_function tptp.a))) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))))) :rule or_pos)
% 26.53/26.72  (step t42 (cl (not (tptp.little_set tptp.a)) (not (tptp.little_set (tptp.apply tptp.a_function tptp.a))) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)))) (not (or (not (tptp.little_set tptp.a)) (not (tptp.little_set (tptp.apply tptp.a_function tptp.a))) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))))))) :rule reordering :premises (t41))
% 26.53/26.72  (step t43 (cl (not (or (not (tptp.member tptp.a tptp.a_domain)) (tptp.little_set tptp.a))) (not (tptp.member tptp.a tptp.a_domain)) (tptp.little_set tptp.a)) :rule or_pos)
% 26.53/26.72  (step t44 (cl (not (tptp.member tptp.a tptp.a_domain)) (tptp.little_set tptp.a) (not (or (not (tptp.member tptp.a tptp.a_domain)) (tptp.little_set tptp.a)))) :rule reordering :premises (t43))
% 26.53/26.72  (step t45 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X Y)) (tptp.little_set X))) (or (not (tptp.member tptp.a tptp.a_domain)) (tptp.little_set tptp.a))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X Y)) (tptp.little_set X)))) :rule implies_neg1)
% 26.53/26.72  (anchor :step t46)
% 26.53/26.72  (assume t46.a0 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X Y)) (tptp.little_set X))))
% 26.53/26.72  (step t46.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X Y)) (tptp.little_set X)))) (or (not (tptp.member tptp.a tptp.a_domain)) (tptp.little_set tptp.a)))) :rule forall_inst :args ((:= X tptp.a) (:= Y tptp.a_domain)))
% 26.53/26.72  (step t46.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X Y)) (tptp.little_set X)))) (or (not (tptp.member tptp.a tptp.a_domain)) (tptp.little_set tptp.a))) :rule or :premises (t46.t1))
% 26.53/26.72  (step t46.t3 (cl (or (not (tptp.member tptp.a tptp.a_domain)) (tptp.little_set tptp.a))) :rule resolution :premises (t46.t2 t46.a0))
% 26.53/26.72  (step t46 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X Y)) (tptp.little_set X)))) (or (not (tptp.member tptp.a tptp.a_domain)) (tptp.little_set tptp.a))) :rule subproof :discharge (t46.a0))
% 26.53/26.72  (step t47 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X Y)) (tptp.little_set X))) (or (not (tptp.member tptp.a tptp.a_domain)) (tptp.little_set tptp.a))) (or (not (tptp.member tptp.a tptp.a_domain)) (tptp.little_set tptp.a))) :rule resolution :premises (t45 t46))
% 26.53/26.72  (step t48 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X Y)) (tptp.little_set X))) (or (not (tptp.member tptp.a tptp.a_domain)) (tptp.little_set tptp.a))) (not (or (not (tptp.member tptp.a tptp.a_domain)) (tptp.little_set tptp.a)))) :rule implies_neg2)
% 26.53/26.72  (step t49 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X Y)) (tptp.little_set X))) (or (not (tptp.member tptp.a tptp.a_domain)) (tptp.little_set tptp.a))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X Y)) (tptp.little_set X))) (or (not (tptp.member tptp.a tptp.a_domain)) (tptp.little_set tptp.a)))) :rule resolution :premises (t47 t48))
% 26.53/26.72  (step t50 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X Y)) (tptp.little_set X))) (or (not (tptp.member tptp.a tptp.a_domain)) (tptp.little_set tptp.a)))) :rule contraction :premises (t49))
% 26.53/26.72  (step t51 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X Y)) (tptp.little_set X)))) (or (not (tptp.member tptp.a tptp.a_domain)) (tptp.little_set tptp.a))) :rule implies :premises (t50))
% 26.53/26.72  (step t52 (cl (or (not (tptp.member tptp.a tptp.a_domain)) (tptp.little_set tptp.a))) :rule resolution :premises (t51 a0))
% 26.53/26.72  (step t53 (cl (tptp.little_set tptp.a)) :rule resolution :premises (t44 a164 t52))
% 26.53/26.72  (step t54 (cl (not (or (not (tptp.function tptp.a_function)) (tptp.little_set (tptp.apply tptp.a_function tptp.a)))) (not (tptp.function tptp.a_function)) (tptp.little_set (tptp.apply tptp.a_function tptp.a))) :rule or_pos)
% 26.53/26.72  (step t55 (cl (not (tptp.function tptp.a_function)) (tptp.little_set (tptp.apply tptp.a_function tptp.a)) (not (or (not (tptp.function tptp.a_function)) (tptp.little_set (tptp.apply tptp.a_function tptp.a))))) :rule reordering :premises (t54))
% 26.53/26.72  (step t56 (cl (not (or (not (tptp.maps tptp.a_function tptp.a_domain tptp.a_range)) (tptp.function tptp.a_function))) (not (tptp.maps tptp.a_function tptp.a_domain tptp.a_range)) (tptp.function tptp.a_function)) :rule or_pos)
% 26.53/26.72  (step t57 (cl (not (tptp.maps tptp.a_function tptp.a_domain tptp.a_range)) (tptp.function tptp.a_function) (not (or (not (tptp.maps tptp.a_function tptp.a_domain tptp.a_range)) (tptp.function tptp.a_function)))) :rule reordering :premises (t56))
% 26.53/26.72  (step t58 (cl (=> (forall ((Xf $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.maps Xf X Y)) (tptp.function Xf))) (or (not (tptp.maps tptp.a_function tptp.a_domain tptp.a_range)) (tptp.function tptp.a_function))) (forall ((Xf $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.maps Xf X Y)) (tptp.function Xf)))) :rule implies_neg1)
% 26.53/26.72  (anchor :step t59)
% 26.53/26.72  (assume t59.a0 (forall ((Xf $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.maps Xf X Y)) (tptp.function Xf))))
% 26.53/26.72  (step t59.t1 (cl (or (not (forall ((Xf $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.maps Xf X Y)) (tptp.function Xf)))) (or (not (tptp.maps tptp.a_function tptp.a_domain tptp.a_range)) (tptp.function tptp.a_function)))) :rule forall_inst :args ((:= Xf tptp.a_function) (:= X tptp.a_domain) (:= Y tptp.a_range)))
% 26.53/26.72  (step t59.t2 (cl (not (forall ((Xf $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.maps Xf X Y)) (tptp.function Xf)))) (or (not (tptp.maps tptp.a_function tptp.a_domain tptp.a_range)) (tptp.function tptp.a_function))) :rule or :premises (t59.t1))
% 26.53/26.72  (step t59.t3 (cl (or (not (tptp.maps tptp.a_function tptp.a_domain tptp.a_range)) (tptp.function tptp.a_function))) :rule resolution :premises (t59.t2 t59.a0))
% 26.53/26.72  (step t59 (cl (not (forall ((Xf $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.maps Xf X Y)) (tptp.function Xf)))) (or (not (tptp.maps tptp.a_function tptp.a_domain tptp.a_range)) (tptp.function tptp.a_function))) :rule subproof :discharge (t59.a0))
% 26.53/26.72  (step t60 (cl (=> (forall ((Xf $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.maps Xf X Y)) (tptp.function Xf))) (or (not (tptp.maps tptp.a_function tptp.a_domain tptp.a_range)) (tptp.function tptp.a_function))) (or (not (tptp.maps tptp.a_function tptp.a_domain tptp.a_range)) (tptp.function tptp.a_function))) :rule resolution :premises (t58 t59))
% 26.53/26.72  (step t61 (cl (=> (forall ((Xf $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.maps Xf X Y)) (tptp.function Xf))) (or (not (tptp.maps tptp.a_function tptp.a_domain tptp.a_range)) (tptp.function tptp.a_function))) (not (or (not (tptp.maps tptp.a_function tptp.a_domain tptp.a_range)) (tptp.function tptp.a_function)))) :rule implies_neg2)
% 26.53/26.72  (step t62 (cl (=> (forall ((Xf $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.maps Xf X Y)) (tptp.function Xf))) (or (not (tptp.maps tptp.a_function tptp.a_domain tptp.a_range)) (tptp.function tptp.a_function))) (=> (forall ((Xf $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.maps Xf X Y)) (tptp.function Xf))) (or (not (tptp.maps tptp.a_function tptp.a_domain tptp.a_range)) (tptp.function tptp.a_function)))) :rule resolution :premises (t60 t61))
% 26.53/26.72  (step t63 (cl (=> (forall ((Xf $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.maps Xf X Y)) (tptp.function Xf))) (or (not (tptp.maps tptp.a_function tptp.a_domain tptp.a_range)) (tptp.function tptp.a_function)))) :rule contraction :premises (t62))
% 26.53/26.72  (step t64 (cl (not (forall ((Xf $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.maps Xf X Y)) (tptp.function Xf)))) (or (not (tptp.maps tptp.a_function tptp.a_domain tptp.a_range)) (tptp.function tptp.a_function))) :rule implies :premises (t63))
% 26.53/26.72  (step t65 (cl (or (not (tptp.maps tptp.a_function tptp.a_domain tptp.a_range)) (tptp.function tptp.a_function))) :rule resolution :premises (t64 a119))
% 26.53/26.72  (step t66 (cl (tptp.function tptp.a_function)) :rule resolution :premises (t57 a163 t65))
% 26.53/26.72  (step t67 (cl (=> (forall ((Y $$unsorted) (X $$unsorted)) (or (not (tptp.function Y)) (tptp.little_set (tptp.apply Y X)))) (or (not (tptp.function tptp.a_function)) (tptp.little_set (tptp.apply tptp.a_function tptp.a)))) (forall ((Y $$unsorted) (X $$unsorted)) (or (not (tptp.function Y)) (tptp.little_set (tptp.apply Y X))))) :rule implies_neg1)
% 26.53/26.72  (anchor :step t68)
% 26.53/26.72  (assume t68.a0 (forall ((Y $$unsorted) (X $$unsorted)) (or (not (tptp.function Y)) (tptp.little_set (tptp.apply Y X)))))
% 26.53/26.72  (step t68.t1 (cl (or (not (forall ((Y $$unsorted) (X $$unsorted)) (or (not (tptp.function Y)) (tptp.little_set (tptp.apply Y X))))) (or (not (tptp.function tptp.a_function)) (tptp.little_set (tptp.apply tptp.a_function tptp.a))))) :rule forall_inst :args ((:= Y tptp.a_function) (:= X tptp.a)))
% 26.53/26.72  (step t68.t2 (cl (not (forall ((Y $$unsorted) (X $$unsorted)) (or (not (tptp.function Y)) (tptp.little_set (tptp.apply Y X))))) (or (not (tptp.function tptp.a_function)) (tptp.little_set (tptp.apply tptp.a_function tptp.a)))) :rule or :premises (t68.t1))
% 26.53/26.72  (step t68.t3 (cl (or (not (tptp.function tptp.a_function)) (tptp.little_set (tptp.apply tptp.a_function tptp.a)))) :rule resolution :premises (t68.t2 t68.a0))
% 26.53/26.72  (step t68 (cl (not (forall ((Y $$unsorted) (X $$unsorted)) (or (not (tptp.function Y)) (tptp.little_set (tptp.apply Y X))))) (or (not (tptp.function tptp.a_function)) (tptp.little_set (tptp.apply tptp.a_function tptp.a)))) :rule subproof :discharge (t68.a0))
% 26.53/26.72  (step t69 (cl (=> (forall ((Y $$unsorted) (X $$unsorted)) (or (not (tptp.function Y)) (tptp.little_set (tptp.apply Y X)))) (or (not (tptp.function tptp.a_function)) (tptp.little_set (tptp.apply tptp.a_function tptp.a)))) (or (not (tptp.function tptp.a_function)) (tptp.little_set (tptp.apply tptp.a_function tptp.a)))) :rule resolution :premises (t67 t68))
% 26.53/26.72  (step t70 (cl (=> (forall ((Y $$unsorted) (X $$unsorted)) (or (not (tptp.function Y)) (tptp.little_set (tptp.apply Y X)))) (or (not (tptp.function tptp.a_function)) (tptp.little_set (tptp.apply tptp.a_function tptp.a)))) (not (or (not (tptp.function tptp.a_function)) (tptp.little_set (tptp.apply tptp.a_function tptp.a))))) :rule implies_neg2)
% 26.53/26.72  (step t71 (cl (=> (forall ((Y $$unsorted) (X $$unsorted)) (or (not (tptp.function Y)) (tptp.little_set (tptp.apply Y X)))) (or (not (tptp.function tptp.a_function)) (tptp.little_set (tptp.apply tptp.a_function tptp.a)))) (=> (forall ((Y $$unsorted) (X $$unsorted)) (or (not (tptp.function Y)) (tptp.little_set (tptp.apply Y X)))) (or (not (tptp.function tptp.a_function)) (tptp.little_set (tptp.apply tptp.a_function tptp.a))))) :rule resolution :premises (t69 t70))
% 26.53/26.72  (step t72 (cl (=> (forall ((Y $$unsorted) (X $$unsorted)) (or (not (tptp.function Y)) (tptp.little_set (tptp.apply Y X)))) (or (not (tptp.function tptp.a_function)) (tptp.little_set (tptp.apply tptp.a_function tptp.a))))) :rule contraction :premises (t71))
% 26.53/26.72  (step t73 (cl (not (forall ((Y $$unsorted) (X $$unsorted)) (or (not (tptp.function Y)) (tptp.little_set (tptp.apply Y X))))) (or (not (tptp.function tptp.a_function)) (tptp.little_set (tptp.apply tptp.a_function tptp.a)))) :rule implies :premises (t72))
% 26.53/26.72  (step t74 (cl (or (not (tptp.function tptp.a_function)) (tptp.little_set (tptp.apply tptp.a_function tptp.a)))) :rule resolution :premises (t73 a155))
% 26.53/26.72  (step t75 (cl (tptp.little_set (tptp.apply tptp.a_function tptp.a))) :rule resolution :premises (t55 t66 t74))
% 26.53/26.72  (step t76 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.little_set X)) (not (tptp.little_set Y)) (= Y (tptp.second (tptp.ordered_pair X Y))))) (or (not (tptp.little_set tptp.a)) (not (tptp.little_set (tptp.apply tptp.a_function tptp.a))) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)))))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.little_set X)) (not (tptp.little_set Y)) (= Y (tptp.second (tptp.ordered_pair X Y)))))) :rule implies_neg1)
% 26.53/26.72  (anchor :step t77)
% 26.53/26.72  (assume t77.a0 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.little_set X)) (not (tptp.little_set Y)) (= Y (tptp.second (tptp.ordered_pair X Y))))))
% 26.53/26.72  (step t77.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.little_set X)) (not (tptp.little_set Y)) (= Y (tptp.second (tptp.ordered_pair X Y)))))) (or (not (tptp.little_set tptp.a)) (not (tptp.little_set (tptp.apply tptp.a_function tptp.a))) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))))))) :rule forall_inst :args ((:= X tptp.a) (:= Y (tptp.apply tptp.a_function tptp.a))))
% 26.53/26.72  (step t77.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.little_set X)) (not (tptp.little_set Y)) (= Y (tptp.second (tptp.ordered_pair X Y)))))) (or (not (tptp.little_set tptp.a)) (not (tptp.little_set (tptp.apply tptp.a_function tptp.a))) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)))))) :rule or :premises (t77.t1))
% 26.53/26.72  (step t77.t3 (cl (or (not (tptp.little_set tptp.a)) (not (tptp.little_set (tptp.apply tptp.a_function tptp.a))) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)))))) :rule resolution :premises (t77.t2 t77.a0))
% 26.53/26.72  (step t77 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.little_set X)) (not (tptp.little_set Y)) (= Y (tptp.second (tptp.ordered_pair X Y)))))) (or (not (tptp.little_set tptp.a)) (not (tptp.little_set (tptp.apply tptp.a_function tptp.a))) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)))))) :rule subproof :discharge (t77.a0))
% 26.53/26.72  (step t78 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.little_set X)) (not (tptp.little_set Y)) (= Y (tptp.second (tptp.ordered_pair X Y))))) (or (not (tptp.little_set tptp.a)) (not (tptp.little_set (tptp.apply tptp.a_function tptp.a))) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)))))) (or (not (tptp.little_set tptp.a)) (not (tptp.little_set (tptp.apply tptp.a_function tptp.a))) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)))))) :rule resolution :premises (t76 t77))
% 26.53/26.72  (step t79 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.little_set X)) (not (tptp.little_set Y)) (= Y (tptp.second (tptp.ordered_pair X Y))))) (or (not (tptp.little_set tptp.a)) (not (tptp.little_set (tptp.apply tptp.a_function tptp.a))) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)))))) (not (or (not (tptp.little_set tptp.a)) (not (tptp.little_set (tptp.apply tptp.a_function tptp.a))) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))))))) :rule implies_neg2)
% 26.53/26.72  (step t80 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.little_set X)) (not (tptp.little_set Y)) (= Y (tptp.second (tptp.ordered_pair X Y))))) (or (not (tptp.little_set tptp.a)) (not (tptp.little_set (tptp.apply tptp.a_function tptp.a))) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.little_set X)) (not (tptp.little_set Y)) (= Y (tptp.second (tptp.ordered_pair X Y))))) (or (not (tptp.little_set tptp.a)) (not (tptp.little_set (tptp.apply tptp.a_function tptp.a))) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))))))) :rule resolution :premises (t78 t79))
% 26.53/26.72  (step t81 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.little_set X)) (not (tptp.little_set Y)) (= Y (tptp.second (tptp.ordered_pair X Y))))) (or (not (tptp.little_set tptp.a)) (not (tptp.little_set (tptp.apply tptp.a_function tptp.a))) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))))))) :rule contraction :premises (t80))
% 26.53/26.72  (step t82 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.little_set X)) (not (tptp.little_set Y)) (= Y (tptp.second (tptp.ordered_pair X Y)))))) (or (not (tptp.little_set tptp.a)) (not (tptp.little_set (tptp.apply tptp.a_function tptp.a))) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)))))) :rule implies :premises (t81))
% 26.53/26.72  (step t83 (cl (not (= (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.little_set X)) (not (tptp.little_set Y)) (= (tptp.second (tptp.ordered_pair X Y)) Y))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.little_set X)) (not (tptp.little_set Y)) (= Y (tptp.second (tptp.ordered_pair X Y))))))) (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.little_set X)) (not (tptp.little_set Y)) (= (tptp.second (tptp.ordered_pair X Y)) Y)))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.little_set X)) (not (tptp.little_set Y)) (= Y (tptp.second (tptp.ordered_pair X Y)))))) :rule equiv_pos2)
% 26.53/26.72  (anchor :step t84 :args ((X $$unsorted) (:= X X) (Y $$unsorted) (:= Y Y)))
% 26.53/26.72  (step t84.t1 (cl (= X X)) :rule refl)
% 26.53/26.72  (step t84.t2 (cl (= Y Y)) :rule refl)
% 26.53/26.72  (step t84.t3 (cl (= (not (tptp.little_set X)) (not (tptp.little_set X)))) :rule refl)
% 26.53/26.72  (step t84.t4 (cl (= (not (tptp.little_set Y)) (not (tptp.little_set Y)))) :rule refl)
% 26.53/26.72  (step t84.t5 (cl (= (= (tptp.second (tptp.ordered_pair X Y)) Y) (= Y (tptp.second (tptp.ordered_pair X Y))))) :rule all_simplify)
% 26.53/26.72  (step t84.t6 (cl (= (or (not (tptp.little_set X)) (not (tptp.little_set Y)) (= (tptp.second (tptp.ordered_pair X Y)) Y)) (or (not (tptp.little_set X)) (not (tptp.little_set Y)) (= Y (tptp.second (tptp.ordered_pair X Y)))))) :rule cong :premises (t84.t3 t84.t4 t84.t5))
% 26.53/26.72  (step t84 (cl (= (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.little_set X)) (not (tptp.little_set Y)) (= (tptp.second (tptp.ordered_pair X Y)) Y))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.little_set X)) (not (tptp.little_set Y)) (= Y (tptp.second (tptp.ordered_pair X Y))))))) :rule bind)
% 26.53/26.72  (step t85 (cl (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.little_set X)) (not (tptp.little_set Y)) (= Y (tptp.second (tptp.ordered_pair X Y)))))) :rule resolution :premises (t83 t84 a146))
% 26.53/26.72  (step t86 (cl (or (not (tptp.little_set tptp.a)) (not (tptp.little_set (tptp.apply tptp.a_function tptp.a))) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)))))) :rule resolution :premises (t82 t85))
% 26.53/26.72  (step t87 (cl (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))))) :rule resolution :premises (t42 t53 t75 t86))
% 26.53/26.72  (step t88 (cl (not (or (not (tptp.little_set (tptp.apply tptp.a_function tptp.a))) (not (tptp.little_set (tptp.apply tptp.a_function tptp.a))) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a)))))) (not (tptp.little_set (tptp.apply tptp.a_function tptp.a))) (not (tptp.little_set (tptp.apply tptp.a_function tptp.a))) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))))) :rule or_pos)
% 26.53/26.72  (step t89 (cl (not (or (not (tptp.little_set (tptp.apply tptp.a_function tptp.a))) (not (tptp.little_set (tptp.apply tptp.a_function tptp.a))) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a)))))) (not (tptp.little_set (tptp.apply tptp.a_function tptp.a))) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))))) :rule contraction :premises (t88))
% 26.53/26.72  (step t90 (cl (not (tptp.little_set (tptp.apply tptp.a_function tptp.a))) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a)))) (not (or (not (tptp.little_set (tptp.apply tptp.a_function tptp.a))) (not (tptp.little_set (tptp.apply tptp.a_function tptp.a))) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))))))) :rule reordering :premises (t89))
% 26.53/26.72  (step t91 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.little_set X)) (not (tptp.little_set Y)) (= Y (tptp.second (tptp.ordered_pair X Y))))) (or (not (tptp.little_set (tptp.apply tptp.a_function tptp.a))) (not (tptp.little_set (tptp.apply tptp.a_function tptp.a))) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a)))))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.little_set X)) (not (tptp.little_set Y)) (= Y (tptp.second (tptp.ordered_pair X Y)))))) :rule implies_neg1)
% 26.53/26.72  (anchor :step t92)
% 26.53/26.72  (assume t92.a0 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.little_set X)) (not (tptp.little_set Y)) (= Y (tptp.second (tptp.ordered_pair X Y))))))
% 26.53/26.72  (step t92.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.little_set X)) (not (tptp.little_set Y)) (= Y (tptp.second (tptp.ordered_pair X Y)))))) (or (not (tptp.little_set (tptp.apply tptp.a_function tptp.a))) (not (tptp.little_set (tptp.apply tptp.a_function tptp.a))) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))))))) :rule forall_inst :args ((:= X (tptp.apply tptp.a_function tptp.a)) (:= Y (tptp.apply tptp.a_function tptp.a))))
% 26.53/26.72  (step t92.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.little_set X)) (not (tptp.little_set Y)) (= Y (tptp.second (tptp.ordered_pair X Y)))))) (or (not (tptp.little_set (tptp.apply tptp.a_function tptp.a))) (not (tptp.little_set (tptp.apply tptp.a_function tptp.a))) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a)))))) :rule or :premises (t92.t1))
% 26.53/26.72  (step t92.t3 (cl (or (not (tptp.little_set (tptp.apply tptp.a_function tptp.a))) (not (tptp.little_set (tptp.apply tptp.a_function tptp.a))) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a)))))) :rule resolution :premises (t92.t2 t92.a0))
% 26.53/26.72  (step t92 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.little_set X)) (not (tptp.little_set Y)) (= Y (tptp.second (tptp.ordered_pair X Y)))))) (or (not (tptp.little_set (tptp.apply tptp.a_function tptp.a))) (not (tptp.little_set (tptp.apply tptp.a_function tptp.a))) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a)))))) :rule subproof :discharge (t92.a0))
% 26.53/26.72  (step t93 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.little_set X)) (not (tptp.little_set Y)) (= Y (tptp.second (tptp.ordered_pair X Y))))) (or (not (tptp.little_set (tptp.apply tptp.a_function tptp.a))) (not (tptp.little_set (tptp.apply tptp.a_function tptp.a))) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a)))))) (or (not (tptp.little_set (tptp.apply tptp.a_function tptp.a))) (not (tptp.little_set (tptp.apply tptp.a_function tptp.a))) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a)))))) :rule resolution :premises (t91 t92))
% 26.53/26.72  (step t94 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.little_set X)) (not (tptp.little_set Y)) (= Y (tptp.second (tptp.ordered_pair X Y))))) (or (not (tptp.little_set (tptp.apply tptp.a_function tptp.a))) (not (tptp.little_set (tptp.apply tptp.a_function tptp.a))) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a)))))) (not (or (not (tptp.little_set (tptp.apply tptp.a_function tptp.a))) (not (tptp.little_set (tptp.apply tptp.a_function tptp.a))) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))))))) :rule implies_neg2)
% 26.53/26.72  (step t95 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.little_set X)) (not (tptp.little_set Y)) (= Y (tptp.second (tptp.ordered_pair X Y))))) (or (not (tptp.little_set (tptp.apply tptp.a_function tptp.a))) (not (tptp.little_set (tptp.apply tptp.a_function tptp.a))) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a)))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.little_set X)) (not (tptp.little_set Y)) (= Y (tptp.second (tptp.ordered_pair X Y))))) (or (not (tptp.little_set (tptp.apply tptp.a_function tptp.a))) (not (tptp.little_set (tptp.apply tptp.a_function tptp.a))) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))))))) :rule resolution :premises (t93 t94))
% 26.53/26.72  (step t96 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.little_set X)) (not (tptp.little_set Y)) (= Y (tptp.second (tptp.ordered_pair X Y))))) (or (not (tptp.little_set (tptp.apply tptp.a_function tptp.a))) (not (tptp.little_set (tptp.apply tptp.a_function tptp.a))) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))))))) :rule contraction :premises (t95))
% 26.53/26.72  (step t97 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.little_set X)) (not (tptp.little_set Y)) (= Y (tptp.second (tptp.ordered_pair X Y)))))) (or (not (tptp.little_set (tptp.apply tptp.a_function tptp.a))) (not (tptp.little_set (tptp.apply tptp.a_function tptp.a))) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a)))))) :rule implies :premises (t96))
% 26.53/26.72  (step t98 (cl (or (not (tptp.little_set (tptp.apply tptp.a_function tptp.a))) (not (tptp.little_set (tptp.apply tptp.a_function tptp.a))) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a)))))) :rule resolution :premises (t97 t85))
% 26.53/26.72  (step t99 (cl (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))))) :rule resolution :premises (t90 t75 t98))
% 26.53/26.72  (step t100 (cl (not (or (not (tptp.subset (tptp.range_of tptp.a_function) tptp.a_range)) (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function))) (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) tptp.a_range))) (not (tptp.subset (tptp.range_of tptp.a_function) tptp.a_range)) (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function))) (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) tptp.a_range)) :rule or_pos)
% 26.53/26.72  (step t101 (cl (not (tptp.subset (tptp.range_of tptp.a_function) tptp.a_range)) (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function))) (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) tptp.a_range) (not (or (not (tptp.subset (tptp.range_of tptp.a_function) tptp.a_range)) (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function))) (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) tptp.a_range)))) :rule reordering :premises (t100))
% 26.53/26.72  (step t102 (cl (not (or (not (tptp.maps tptp.a_function tptp.a_domain tptp.a_range)) (tptp.subset (tptp.range_of tptp.a_function) tptp.a_range))) (not (tptp.maps tptp.a_function tptp.a_domain tptp.a_range)) (tptp.subset (tptp.range_of tptp.a_function) tptp.a_range)) :rule or_pos)
% 26.53/26.72  (step t103 (cl (not (tptp.maps tptp.a_function tptp.a_domain tptp.a_range)) (tptp.subset (tptp.range_of tptp.a_function) tptp.a_range) (not (or (not (tptp.maps tptp.a_function tptp.a_domain tptp.a_range)) (tptp.subset (tptp.range_of tptp.a_function) tptp.a_range)))) :rule reordering :premises (t102))
% 26.53/26.72  (step t104 (cl (=> (forall ((Xf $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.maps Xf X Y)) (tptp.subset (tptp.range_of Xf) Y))) (or (not (tptp.maps tptp.a_function tptp.a_domain tptp.a_range)) (tptp.subset (tptp.range_of tptp.a_function) tptp.a_range))) (forall ((Xf $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.maps Xf X Y)) (tptp.subset (tptp.range_of Xf) Y)))) :rule implies_neg1)
% 26.53/26.72  (anchor :step t105)
% 26.53/26.72  (assume t105.a0 (forall ((Xf $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.maps Xf X Y)) (tptp.subset (tptp.range_of Xf) Y))))
% 26.53/26.72  (step t105.t1 (cl (or (not (forall ((Xf $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.maps Xf X Y)) (tptp.subset (tptp.range_of Xf) Y)))) (or (not (tptp.maps tptp.a_function tptp.a_domain tptp.a_range)) (tptp.subset (tptp.range_of tptp.a_function) tptp.a_range)))) :rule forall_inst :args ((:= Xf tptp.a_function) (:= X tptp.a_domain) (:= Y tptp.a_range)))
% 26.53/26.72  (step t105.t2 (cl (not (forall ((Xf $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.maps Xf X Y)) (tptp.subset (tptp.range_of Xf) Y)))) (or (not (tptp.maps tptp.a_function tptp.a_domain tptp.a_range)) (tptp.subset (tptp.range_of tptp.a_function) tptp.a_range))) :rule or :premises (t105.t1))
% 26.53/26.72  (step t105.t3 (cl (or (not (tptp.maps tptp.a_function tptp.a_domain tptp.a_range)) (tptp.subset (tptp.range_of tptp.a_function) tptp.a_range))) :rule resolution :premises (t105.t2 t105.a0))
% 26.53/26.72  (step t105 (cl (not (forall ((Xf $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.maps Xf X Y)) (tptp.subset (tptp.range_of Xf) Y)))) (or (not (tptp.maps tptp.a_function tptp.a_domain tptp.a_range)) (tptp.subset (tptp.range_of tptp.a_function) tptp.a_range))) :rule subproof :discharge (t105.a0))
% 26.53/26.72  (step t106 (cl (=> (forall ((Xf $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.maps Xf X Y)) (tptp.subset (tptp.range_of Xf) Y))) (or (not (tptp.maps tptp.a_function tptp.a_domain tptp.a_range)) (tptp.subset (tptp.range_of tptp.a_function) tptp.a_range))) (or (not (tptp.maps tptp.a_function tptp.a_domain tptp.a_range)) (tptp.subset (tptp.range_of tptp.a_function) tptp.a_range))) :rule resolution :premises (t104 t105))
% 26.53/26.72  (step t107 (cl (=> (forall ((Xf $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.maps Xf X Y)) (tptp.subset (tptp.range_of Xf) Y))) (or (not (tptp.maps tptp.a_function tptp.a_domain tptp.a_range)) (tptp.subset (tptp.range_of tptp.a_function) tptp.a_range))) (not (or (not (tptp.maps tptp.a_function tptp.a_domain tptp.a_range)) (tptp.subset (tptp.range_of tptp.a_function) tptp.a_range)))) :rule implies_neg2)
% 26.53/26.72  (step t108 (cl (=> (forall ((Xf $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.maps Xf X Y)) (tptp.subset (tptp.range_of Xf) Y))) (or (not (tptp.maps tptp.a_function tptp.a_domain tptp.a_range)) (tptp.subset (tptp.range_of tptp.a_function) tptp.a_range))) (=> (forall ((Xf $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.maps Xf X Y)) (tptp.subset (tptp.range_of Xf) Y))) (or (not (tptp.maps tptp.a_function tptp.a_domain tptp.a_range)) (tptp.subset (tptp.range_of tptp.a_function) tptp.a_range)))) :rule resolution :premises (t106 t107))
% 26.53/26.72  (step t109 (cl (=> (forall ((Xf $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.maps Xf X Y)) (tptp.subset (tptp.range_of Xf) Y))) (or (not (tptp.maps tptp.a_function tptp.a_domain tptp.a_range)) (tptp.subset (tptp.range_of tptp.a_function) tptp.a_range)))) :rule contraction :premises (t108))
% 26.53/26.72  (step t110 (cl (not (forall ((Xf $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.maps Xf X Y)) (tptp.subset (tptp.range_of Xf) Y)))) (or (not (tptp.maps tptp.a_function tptp.a_domain tptp.a_range)) (tptp.subset (tptp.range_of tptp.a_function) tptp.a_range))) :rule implies :premises (t109))
% 26.53/26.72  (step t111 (cl (or (not (tptp.maps tptp.a_function tptp.a_domain tptp.a_range)) (tptp.subset (tptp.range_of tptp.a_function) tptp.a_range))) :rule resolution :premises (t110 a121))
% 26.53/26.72  (step t112 (cl (tptp.subset (tptp.range_of tptp.a_function) tptp.a_range)) :rule resolution :premises (t103 a163 t111))
% 26.53/26.72  (step t113 (cl (not (= (or (not (not (tptp.member (tptp.apply tptp.a_function tptp.a) tptp.a_range))) (not (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))))) (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) tptp.a_range))) (or (tptp.member (tptp.apply tptp.a_function tptp.a) tptp.a_range) (not (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))))) (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) tptp.a_range))))) (not (or (not (not (tptp.member (tptp.apply tptp.a_function tptp.a) tptp.a_range))) (not (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))))) (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) tptp.a_range)))) (or (tptp.member (tptp.apply tptp.a_function tptp.a) tptp.a_range) (not (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))))) (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) tptp.a_range)))) :rule equiv_pos2)
% 26.53/26.72  (step t114 (cl (= (= (= (not (not (tptp.member (tptp.apply tptp.a_function tptp.a) tptp.a_range))) (tptp.member (tptp.apply tptp.a_function tptp.a) tptp.a_range)) true) (= (not (not (tptp.member (tptp.apply tptp.a_function tptp.a) tptp.a_range))) (tptp.member (tptp.apply tptp.a_function tptp.a) tptp.a_range)))) :rule equiv_simplify)
% 26.53/26.72  (step t115 (cl (not (= (= (not (not (tptp.member (tptp.apply tptp.a_function tptp.a) tptp.a_range))) (tptp.member (tptp.apply tptp.a_function tptp.a) tptp.a_range)) true)) (= (not (not (tptp.member (tptp.apply tptp.a_function tptp.a) tptp.a_range))) (tptp.member (tptp.apply tptp.a_function tptp.a) tptp.a_range))) :rule equiv1 :premises (t114))
% 26.53/26.72  (step t116 (cl (= (= (not (not (tptp.member (tptp.apply tptp.a_function tptp.a) tptp.a_range))) (tptp.member (tptp.apply tptp.a_function tptp.a) tptp.a_range)) (= (tptp.member (tptp.apply tptp.a_function tptp.a) tptp.a_range) (not (not (tptp.member (tptp.apply tptp.a_function tptp.a) tptp.a_range)))))) :rule all_simplify)
% 26.53/26.72  (step t117 (cl (= (tptp.member (tptp.apply tptp.a_function tptp.a) tptp.a_range) (tptp.member (tptp.apply tptp.a_function tptp.a) tptp.a_range))) :rule refl)
% 26.53/26.72  (step t118 (cl (= (not (not (tptp.member (tptp.apply tptp.a_function tptp.a) tptp.a_range))) (tptp.member (tptp.apply tptp.a_function tptp.a) tptp.a_range))) :rule all_simplify)
% 26.53/26.72  (step t119 (cl (= (= (tptp.member (tptp.apply tptp.a_function tptp.a) tptp.a_range) (not (not (tptp.member (tptp.apply tptp.a_function tptp.a) tptp.a_range)))) (= (tptp.member (tptp.apply tptp.a_function tptp.a) tptp.a_range) (tptp.member (tptp.apply tptp.a_function tptp.a) tptp.a_range)))) :rule cong :premises (t117 t118))
% 26.53/26.72  (step t120 (cl (= (= (tptp.member (tptp.apply tptp.a_function tptp.a) tptp.a_range) (tptp.member (tptp.apply tptp.a_function tptp.a) tptp.a_range)) true)) :rule all_simplify)
% 26.53/26.72  (step t121 (cl (= (= (tptp.member (tptp.apply tptp.a_function tptp.a) tptp.a_range) (not (not (tptp.member (tptp.apply tptp.a_function tptp.a) tptp.a_range)))) true)) :rule trans :premises (t119 t120))
% 26.53/26.72  (step t122 (cl (= (= (not (not (tptp.member (tptp.apply tptp.a_function tptp.a) tptp.a_range))) (tptp.member (tptp.apply tptp.a_function tptp.a) tptp.a_range)) true)) :rule trans :premises (t116 t121))
% 26.53/26.72  (step t123 (cl (= (not (not (tptp.member (tptp.apply tptp.a_function tptp.a) tptp.a_range))) (tptp.member (tptp.apply tptp.a_function tptp.a) tptp.a_range))) :rule resolution :premises (t115 t122))
% 26.53/26.72  (step t124 (cl (= (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) tptp.a_range)) (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) tptp.a_range)))) :rule refl)
% 26.53/26.72  (step t125 (cl (= (or (not (not (tptp.member (tptp.apply tptp.a_function tptp.a) tptp.a_range))) (not (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))))) (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) tptp.a_range))) (or (tptp.member (tptp.apply tptp.a_function tptp.a) tptp.a_range) (not (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))))) (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) tptp.a_range))))) :rule cong :premises (t123 t5 t124))
% 26.53/26.72  (step t126 (cl (and (not (tptp.member (tptp.apply tptp.a_function tptp.a) tptp.a_range)) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))))) (not (not (tptp.member (tptp.apply tptp.a_function tptp.a) tptp.a_range))) (not (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a)))))) :rule and_neg)
% 26.53/26.72  (step t127 (cl (=> (and (not (tptp.member (tptp.apply tptp.a_function tptp.a) tptp.a_range)) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))))) (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) tptp.a_range))) (and (not (tptp.member (tptp.apply tptp.a_function tptp.a) tptp.a_range)) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a)))))) :rule implies_neg1)
% 26.53/26.72  (anchor :step t128)
% 26.53/26.72  (assume t128.a0 (not (tptp.member (tptp.apply tptp.a_function tptp.a) tptp.a_range)))
% 26.53/26.72  (assume t128.a1 (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a)))))
% 26.53/26.72  (step t128.t1 (cl (=> (and (not (tptp.member (tptp.apply tptp.a_function tptp.a) tptp.a_range)) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))))) (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) tptp.a_range))) (and (not (tptp.member (tptp.apply tptp.a_function tptp.a) tptp.a_range)) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a)))))) :rule implies_neg1)
% 26.53/26.72  (anchor :step t128.t2)
% 26.53/26.72  (assume t128.t2.a0 (not (tptp.member (tptp.apply tptp.a_function tptp.a) tptp.a_range)))
% 26.53/26.72  (assume t128.t2.a1 (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a)))))
% 26.53/26.72  (step t128.t2.t1 (cl (= (= (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) tptp.a_range) false) (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) tptp.a_range)))) :rule equiv_simplify)
% 26.53/26.72  (step t128.t2.t2 (cl (not (= (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) tptp.a_range) false)) (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) tptp.a_range))) :rule equiv1 :premises (t128.t2.t1))
% 26.53/26.72  (step t128.t2.t3 (cl (= (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.apply tptp.a_function tptp.a))) :rule symm :premises (t128.t2.a1))
% 26.53/26.72  (step t128.t2.t4 (cl (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))))) :rule symm :premises (t128.t2.t3))
% 26.53/26.72  (step t128.t2.t5 (cl (= (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.apply tptp.a_function tptp.a))) :rule symm :premises (t128.t2.t4))
% 26.53/26.72  (step t128.t2.t6 (cl (= tptp.a_range tptp.a_range)) :rule refl)
% 26.53/26.72  (step t128.t2.t7 (cl (= (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) tptp.a_range) (tptp.member (tptp.apply tptp.a_function tptp.a) tptp.a_range))) :rule cong :premises (t128.t2.t5 t128.t2.t6))
% 26.53/26.72  (step t128.t2.t8 (cl (= (= (tptp.member (tptp.apply tptp.a_function tptp.a) tptp.a_range) false) (not (tptp.member (tptp.apply tptp.a_function tptp.a) tptp.a_range)))) :rule equiv_simplify)
% 26.53/26.72  (step t128.t2.t9 (cl (= (tptp.member (tptp.apply tptp.a_function tptp.a) tptp.a_range) false) (not (not (tptp.member (tptp.apply tptp.a_function tptp.a) tptp.a_range)))) :rule equiv2 :premises (t128.t2.t8))
% 26.53/26.72  (step t128.t2.t10 (cl (not (not (not (tptp.member (tptp.apply tptp.a_function tptp.a) tptp.a_range)))) (tptp.member (tptp.apply tptp.a_function tptp.a) tptp.a_range)) :rule not_not)
% 26.53/26.72  (step t128.t2.t11 (cl (= (tptp.member (tptp.apply tptp.a_function tptp.a) tptp.a_range) false) (tptp.member (tptp.apply tptp.a_function tptp.a) tptp.a_range)) :rule resolution :premises (t128.t2.t9 t128.t2.t10))
% 26.53/26.72  (step t128.t2.t12 (cl (= (tptp.member (tptp.apply tptp.a_function tptp.a) tptp.a_range) false)) :rule resolution :premises (t128.t2.t11 t128.t2.a0))
% 26.53/26.72  (step t128.t2.t13 (cl (= (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) tptp.a_range) false)) :rule trans :premises (t128.t2.t7 t128.t2.t12))
% 26.53/26.72  (step t128.t2.t14 (cl (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) tptp.a_range))) :rule resolution :premises (t128.t2.t2 t128.t2.t13))
% 26.53/26.72  (step t128.t2 (cl (not (not (tptp.member (tptp.apply tptp.a_function tptp.a) tptp.a_range))) (not (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))))) (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) tptp.a_range))) :rule subproof :discharge (t128.t2.a0 t128.t2.a1))
% 26.53/26.72  (step t128.t3 (cl (not (and (not (tptp.member (tptp.apply tptp.a_function tptp.a) tptp.a_range)) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a)))))) (not (tptp.member (tptp.apply tptp.a_function tptp.a) tptp.a_range))) :rule and_pos)
% 26.53/26.72  (step t128.t4 (cl (not (and (not (tptp.member (tptp.apply tptp.a_function tptp.a) tptp.a_range)) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a)))))) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))))) :rule and_pos)
% 26.53/26.72  (step t128.t5 (cl (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) tptp.a_range)) (not (and (not (tptp.member (tptp.apply tptp.a_function tptp.a) tptp.a_range)) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a)))))) (not (and (not (tptp.member (tptp.apply tptp.a_function tptp.a) tptp.a_range)) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))))))) :rule resolution :premises (t128.t2 t128.t3 t128.t4))
% 26.53/26.72  (step t128.t6 (cl (not (and (not (tptp.member (tptp.apply tptp.a_function tptp.a) tptp.a_range)) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a)))))) (not (and (not (tptp.member (tptp.apply tptp.a_function tptp.a) tptp.a_range)) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a)))))) (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) tptp.a_range))) :rule reordering :premises (t128.t5))
% 26.53/26.72  (step t128.t7 (cl (not (and (not (tptp.member (tptp.apply tptp.a_function tptp.a) tptp.a_range)) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a)))))) (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) tptp.a_range))) :rule contraction :premises (t128.t6))
% 26.53/26.72  (step t128.t8 (cl (=> (and (not (tptp.member (tptp.apply tptp.a_function tptp.a) tptp.a_range)) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))))) (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) tptp.a_range))) (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) tptp.a_range))) :rule resolution :premises (t128.t1 t128.t7))
% 26.53/26.72  (step t128.t9 (cl (=> (and (not (tptp.member (tptp.apply tptp.a_function tptp.a) tptp.a_range)) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))))) (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) tptp.a_range))) (not (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) tptp.a_range)))) :rule implies_neg2)
% 26.53/26.72  (step t128.t10 (cl (=> (and (not (tptp.member (tptp.apply tptp.a_function tptp.a) tptp.a_range)) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))))) (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) tptp.a_range))) (=> (and (not (tptp.member (tptp.apply tptp.a_function tptp.a) tptp.a_range)) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))))) (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) tptp.a_range)))) :rule resolution :premises (t128.t8 t128.t9))
% 26.53/26.72  (step t128.t11 (cl (=> (and (not (tptp.member (tptp.apply tptp.a_function tptp.a) tptp.a_range)) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))))) (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) tptp.a_range)))) :rule contraction :premises (t128.t10))
% 26.53/26.72  (step t128.t12 (cl (not (and (not (tptp.member (tptp.apply tptp.a_function tptp.a) tptp.a_range)) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a)))))) (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) tptp.a_range))) :rule implies :premises (t128.t11))
% 26.53/26.72  (step t128.t13 (cl (and (not (tptp.member (tptp.apply tptp.a_function tptp.a) tptp.a_range)) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))))) (not (not (tptp.member (tptp.apply tptp.a_function tptp.a) tptp.a_range))) (not (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a)))))) :rule and_neg)
% 26.53/26.72  (step t128.t14 (cl (and (not (tptp.member (tptp.apply tptp.a_function tptp.a) tptp.a_range)) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a)))))) :rule resolution :premises (t128.t13 t128.a0 t128.a1))
% 26.53/26.72  (step t128.t15 (cl (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) tptp.a_range))) :rule resolution :premises (t128.t12 t128.t14))
% 26.53/26.72  (step t128 (cl (not (not (tptp.member (tptp.apply tptp.a_function tptp.a) tptp.a_range))) (not (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))))) (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) tptp.a_range))) :rule subproof :discharge (t128.a0 t128.a1))
% 26.53/26.72  (step t129 (cl (not (and (not (tptp.member (tptp.apply tptp.a_function tptp.a) tptp.a_range)) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a)))))) (not (tptp.member (tptp.apply tptp.a_function tptp.a) tptp.a_range))) :rule and_pos)
% 26.53/26.72  (step t130 (cl (not (and (not (tptp.member (tptp.apply tptp.a_function tptp.a) tptp.a_range)) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a)))))) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))))) :rule and_pos)
% 26.53/26.72  (step t131 (cl (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) tptp.a_range)) (not (and (not (tptp.member (tptp.apply tptp.a_function tptp.a) tptp.a_range)) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a)))))) (not (and (not (tptp.member (tptp.apply tptp.a_function tptp.a) tptp.a_range)) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))))))) :rule resolution :premises (t128 t129 t130))
% 26.53/26.72  (step t132 (cl (not (and (not (tptp.member (tptp.apply tptp.a_function tptp.a) tptp.a_range)) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a)))))) (not (and (not (tptp.member (tptp.apply tptp.a_function tptp.a) tptp.a_range)) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a)))))) (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) tptp.a_range))) :rule reordering :premises (t131))
% 26.53/26.72  (step t133 (cl (not (and (not (tptp.member (tptp.apply tptp.a_function tptp.a) tptp.a_range)) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a)))))) (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) tptp.a_range))) :rule contraction :premises (t132))
% 26.53/26.72  (step t134 (cl (=> (and (not (tptp.member (tptp.apply tptp.a_function tptp.a) tptp.a_range)) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))))) (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) tptp.a_range))) (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) tptp.a_range))) :rule resolution :premises (t127 t133))
% 26.53/26.72  (step t135 (cl (=> (and (not (tptp.member (tptp.apply tptp.a_function tptp.a) tptp.a_range)) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))))) (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) tptp.a_range))) (not (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) tptp.a_range)))) :rule implies_neg2)
% 26.53/26.72  (step t136 (cl (=> (and (not (tptp.member (tptp.apply tptp.a_function tptp.a) tptp.a_range)) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))))) (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) tptp.a_range))) (=> (and (not (tptp.member (tptp.apply tptp.a_function tptp.a) tptp.a_range)) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))))) (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) tptp.a_range)))) :rule resolution :premises (t134 t135))
% 26.53/26.72  (step t137 (cl (=> (and (not (tptp.member (tptp.apply tptp.a_function tptp.a) tptp.a_range)) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))))) (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) tptp.a_range)))) :rule contraction :premises (t136))
% 26.53/26.72  (step t138 (cl (not (and (not (tptp.member (tptp.apply tptp.a_function tptp.a) tptp.a_range)) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a)))))) (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) tptp.a_range))) :rule implies :premises (t137))
% 26.53/26.72  (step t139 (cl (not (not (tptp.member (tptp.apply tptp.a_function tptp.a) tptp.a_range))) (not (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))))) (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) tptp.a_range))) :rule resolution :premises (t126 t138))
% 26.53/26.72  (step t140 (cl (or (not (not (tptp.member (tptp.apply tptp.a_function tptp.a) tptp.a_range))) (not (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))))) (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) tptp.a_range))) (not (not (not (tptp.member (tptp.apply tptp.a_function tptp.a) tptp.a_range))))) :rule or_neg)
% 26.53/26.72  (step t141 (cl (or (not (not (tptp.member (tptp.apply tptp.a_function tptp.a) tptp.a_range))) (not (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))))) (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) tptp.a_range))) (not (not (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))))))) :rule or_neg)
% 26.53/26.72  (step t142 (cl (or (not (not (tptp.member (tptp.apply tptp.a_function tptp.a) tptp.a_range))) (not (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))))) (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) tptp.a_range))) (not (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) tptp.a_range)))) :rule or_neg)
% 26.53/26.72  (step t143 (cl (or (not (not (tptp.member (tptp.apply tptp.a_function tptp.a) tptp.a_range))) (not (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))))) (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) tptp.a_range))) (or (not (not (tptp.member (tptp.apply tptp.a_function tptp.a) tptp.a_range))) (not (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))))) (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) tptp.a_range))) (or (not (not (tptp.member (tptp.apply tptp.a_function tptp.a) tptp.a_range))) (not (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))))) (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) tptp.a_range)))) :rule resolution :premises (t139 t140 t141 t142))
% 26.53/26.72  (step t144 (cl (or (not (not (tptp.member (tptp.apply tptp.a_function tptp.a) tptp.a_range))) (not (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))))) (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) tptp.a_range)))) :rule contraction :premises (t143))
% 26.53/26.72  (step t145 (cl (or (tptp.member (tptp.apply tptp.a_function tptp.a) tptp.a_range) (not (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))))) (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) tptp.a_range)))) :rule resolution :premises (t113 t125 t144))
% 26.53/26.72  (step t146 (cl (tptp.member (tptp.apply tptp.a_function tptp.a) tptp.a_range) (not (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))))) (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) tptp.a_range))) :rule or :premises (t145))
% 26.53/26.72  (step t147 (cl (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) tptp.a_range))) :rule resolution :premises (t146 a165 t99))
% 26.53/26.72  (step t148 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (not (tptp.subset X Y)) (not (tptp.member U X)) (tptp.member U Y))) (or (not (tptp.subset (tptp.range_of tptp.a_function) tptp.a_range)) (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function))) (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) tptp.a_range))) (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (not (tptp.subset X Y)) (not (tptp.member U X)) (tptp.member U Y)))) :rule implies_neg1)
% 26.53/26.72  (anchor :step t149)
% 26.53/26.72  (assume t149.a0 (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (not (tptp.subset X Y)) (not (tptp.member U X)) (tptp.member U Y))))
% 26.53/26.72  (step t149.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (not (tptp.subset X Y)) (not (tptp.member U X)) (tptp.member U Y)))) (or (not (tptp.subset (tptp.range_of tptp.a_function) tptp.a_range)) (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function))) (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) tptp.a_range)))) :rule forall_inst :args ((:= X (tptp.range_of tptp.a_function)) (:= Y tptp.a_range) (:= U (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))))))
% 26.53/26.72  (step t149.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (not (tptp.subset X Y)) (not (tptp.member U X)) (tptp.member U Y)))) (or (not (tptp.subset (tptp.range_of tptp.a_function) tptp.a_range)) (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function))) (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) tptp.a_range))) :rule or :premises (t149.t1))
% 26.53/26.72  (step t149.t3 (cl (or (not (tptp.subset (tptp.range_of tptp.a_function) tptp.a_range)) (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function))) (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) tptp.a_range))) :rule resolution :premises (t149.t2 t149.a0))
% 26.53/26.72  (step t149 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (not (tptp.subset X Y)) (not (tptp.member U X)) (tptp.member U Y)))) (or (not (tptp.subset (tptp.range_of tptp.a_function) tptp.a_range)) (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function))) (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) tptp.a_range))) :rule subproof :discharge (t149.a0))
% 26.53/26.72  (step t150 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (not (tptp.subset X Y)) (not (tptp.member U X)) (tptp.member U Y))) (or (not (tptp.subset (tptp.range_of tptp.a_function) tptp.a_range)) (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function))) (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) tptp.a_range))) (or (not (tptp.subset (tptp.range_of tptp.a_function) tptp.a_range)) (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function))) (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) tptp.a_range))) :rule resolution :premises (t148 t149))
% 26.53/26.72  (step t151 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (not (tptp.subset X Y)) (not (tptp.member U X)) (tptp.member U Y))) (or (not (tptp.subset (tptp.range_of tptp.a_function) tptp.a_range)) (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function))) (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) tptp.a_range))) (not (or (not (tptp.subset (tptp.range_of tptp.a_function) tptp.a_range)) (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function))) (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) tptp.a_range)))) :rule implies_neg2)
% 26.53/26.72  (step t152 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (not (tptp.subset X Y)) (not (tptp.member U X)) (tptp.member U Y))) (or (not (tptp.subset (tptp.range_of tptp.a_function) tptp.a_range)) (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function))) (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) tptp.a_range))) (=> (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (not (tptp.subset X Y)) (not (tptp.member U X)) (tptp.member U Y))) (or (not (tptp.subset (tptp.range_of tptp.a_function) tptp.a_range)) (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function))) (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) tptp.a_range)))) :rule resolution :premises (t150 t151))
% 26.53/26.72  (step t153 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (not (tptp.subset X Y)) (not (tptp.member U X)) (tptp.member U Y))) (or (not (tptp.subset (tptp.range_of tptp.a_function) tptp.a_range)) (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function))) (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) tptp.a_range)))) :rule contraction :premises (t152))
% 26.53/26.72  (step t154 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (not (tptp.subset X Y)) (not (tptp.member U X)) (tptp.member U Y)))) (or (not (tptp.subset (tptp.range_of tptp.a_function) tptp.a_range)) (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function))) (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) tptp.a_range))) :rule implies :premises (t153))
% 26.53/26.72  (step t155 (cl (or (not (tptp.subset (tptp.range_of tptp.a_function) tptp.a_range)) (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function))) (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) tptp.a_range))) :rule resolution :premises (t154 a66))
% 26.53/26.72  (step t156 (cl (not (tptp.member (tptp.second (tptp.ordered_pair (tptp.apply tptp.a_function tptp.a) (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)))) :rule resolution :premises (t101 t112 t147 t155))
% 26.53/26.72  (step t157 (cl (not (tptp.member (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)))) :rule resolution :premises (t40 t87 t99 t156))
% 26.53/26.72  (step t158 (cl (and (tptp.little_set (tptp.apply tptp.a_function tptp.a)) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))))) (not (tptp.little_set (tptp.apply tptp.a_function tptp.a))) (not (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)))))) :rule and_neg)
% 26.53/26.72  (step t159 (cl (=> (and (tptp.little_set (tptp.apply tptp.a_function tptp.a)) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))))) (tptp.little_set (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))))) (and (tptp.little_set (tptp.apply tptp.a_function tptp.a)) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)))))) :rule implies_neg1)
% 26.53/26.72  (anchor :step t160)
% 26.53/26.72  (assume t160.a0 (tptp.little_set (tptp.apply tptp.a_function tptp.a)))
% 26.53/26.72  (assume t160.a1 (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)))))
% 26.53/26.72  (step t160.t1 (cl (=> (and (tptp.little_set (tptp.apply tptp.a_function tptp.a)) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))))) (tptp.little_set (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))))) (and (tptp.little_set (tptp.apply tptp.a_function tptp.a)) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)))))) :rule implies_neg1)
% 26.53/26.72  (anchor :step t160.t2)
% 26.53/26.72  (assume t160.t2.a0 (tptp.little_set (tptp.apply tptp.a_function tptp.a)))
% 26.53/26.72  (assume t160.t2.a1 (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)))))
% 26.53/26.72  (step t160.t2.t1 (cl (= (= (tptp.little_set (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)))) true) (tptp.little_set (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)))))) :rule equiv_simplify)
% 26.53/26.72  (step t160.t2.t2 (cl (not (= (tptp.little_set (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)))) true)) (tptp.little_set (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))))) :rule equiv1 :premises (t160.t2.t1))
% 26.53/26.72  (step t160.t2.t3 (cl (= (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))) (tptp.apply tptp.a_function tptp.a))) :rule symm :premises (t160.t2.a1))
% 26.53/26.72  (step t160.t2.t4 (cl (= (tptp.little_set (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)))) (tptp.little_set (tptp.apply tptp.a_function tptp.a)))) :rule cong :premises (t160.t2.t3))
% 26.53/26.72  (step t160.t2.t5 (cl (= (= (tptp.little_set (tptp.apply tptp.a_function tptp.a)) true) (tptp.little_set (tptp.apply tptp.a_function tptp.a)))) :rule equiv_simplify)
% 26.53/26.72  (step t160.t2.t6 (cl (= (tptp.little_set (tptp.apply tptp.a_function tptp.a)) true) (not (tptp.little_set (tptp.apply tptp.a_function tptp.a)))) :rule equiv2 :premises (t160.t2.t5))
% 26.53/26.72  (step t160.t2.t7 (cl (= (tptp.little_set (tptp.apply tptp.a_function tptp.a)) true)) :rule resolution :premises (t160.t2.t6 t160.t2.a0))
% 26.53/26.72  (step t160.t2.t8 (cl (= (tptp.little_set (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)))) true)) :rule trans :premises (t160.t2.t4 t160.t2.t7))
% 26.53/26.72  (step t160.t2.t9 (cl (tptp.little_set (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))))) :rule resolution :premises (t160.t2.t2 t160.t2.t8))
% 26.53/26.72  (step t160.t2 (cl (not (tptp.little_set (tptp.apply tptp.a_function tptp.a))) (not (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))))) (tptp.little_set (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))))) :rule subproof :discharge (t160.t2.a0 t160.t2.a1))
% 26.53/26.72  (step t160.t3 (cl (not (and (tptp.little_set (tptp.apply tptp.a_function tptp.a)) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)))))) (tptp.little_set (tptp.apply tptp.a_function tptp.a))) :rule and_pos)
% 26.53/26.72  (step t160.t4 (cl (not (and (tptp.little_set (tptp.apply tptp.a_function tptp.a)) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)))))) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))))) :rule and_pos)
% 26.53/26.72  (step t160.t5 (cl (tptp.little_set (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)))) (not (and (tptp.little_set (tptp.apply tptp.a_function tptp.a)) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)))))) (not (and (tptp.little_set (tptp.apply tptp.a_function tptp.a)) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))))))) :rule resolution :premises (t160.t2 t160.t3 t160.t4))
% 26.53/26.72  (step t160.t6 (cl (not (and (tptp.little_set (tptp.apply tptp.a_function tptp.a)) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)))))) (not (and (tptp.little_set (tptp.apply tptp.a_function tptp.a)) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)))))) (tptp.little_set (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))))) :rule reordering :premises (t160.t5))
% 26.53/26.72  (step t160.t7 (cl (not (and (tptp.little_set (tptp.apply tptp.a_function tptp.a)) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)))))) (tptp.little_set (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))))) :rule contraction :premises (t160.t6))
% 26.53/26.72  (step t160.t8 (cl (=> (and (tptp.little_set (tptp.apply tptp.a_function tptp.a)) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))))) (tptp.little_set (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))))) (tptp.little_set (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))))) :rule resolution :premises (t160.t1 t160.t7))
% 26.53/26.72  (step t160.t9 (cl (=> (and (tptp.little_set (tptp.apply tptp.a_function tptp.a)) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))))) (tptp.little_set (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))))) (not (tptp.little_set (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)))))) :rule implies_neg2)
% 26.53/26.72  (step t160.t10 (cl (=> (and (tptp.little_set (tptp.apply tptp.a_function tptp.a)) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))))) (tptp.little_set (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))))) (=> (and (tptp.little_set (tptp.apply tptp.a_function tptp.a)) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))))) (tptp.little_set (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)))))) :rule resolution :premises (t160.t8 t160.t9))
% 26.53/26.72  (step t160.t11 (cl (=> (and (tptp.little_set (tptp.apply tptp.a_function tptp.a)) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))))) (tptp.little_set (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)))))) :rule contraction :premises (t160.t10))
% 26.53/26.72  (step t160.t12 (cl (not (and (tptp.little_set (tptp.apply tptp.a_function tptp.a)) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)))))) (tptp.little_set (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))))) :rule implies :premises (t160.t11))
% 26.53/26.72  (step t160.t13 (cl (and (tptp.little_set (tptp.apply tptp.a_function tptp.a)) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))))) (not (tptp.little_set (tptp.apply tptp.a_function tptp.a))) (not (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)))))) :rule and_neg)
% 26.53/26.72  (step t160.t14 (cl (and (tptp.little_set (tptp.apply tptp.a_function tptp.a)) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)))))) :rule resolution :premises (t160.t13 t160.a0 t160.a1))
% 26.53/26.72  (step t160.t15 (cl (tptp.little_set (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))))) :rule resolution :premises (t160.t12 t160.t14))
% 26.53/26.72  (step t160 (cl (not (tptp.little_set (tptp.apply tptp.a_function tptp.a))) (not (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))))) (tptp.little_set (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))))) :rule subproof :discharge (t160.a0 t160.a1))
% 26.53/26.72  (step t161 (cl (not (and (tptp.little_set (tptp.apply tptp.a_function tptp.a)) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)))))) (tptp.little_set (tptp.apply tptp.a_function tptp.a))) :rule and_pos)
% 26.53/26.72  (step t162 (cl (not (and (tptp.little_set (tptp.apply tptp.a_function tptp.a)) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)))))) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))))) :rule and_pos)
% 26.53/26.72  (step t163 (cl (tptp.little_set (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)))) (not (and (tptp.little_set (tptp.apply tptp.a_function tptp.a)) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)))))) (not (and (tptp.little_set (tptp.apply tptp.a_function tptp.a)) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))))))) :rule resolution :premises (t160 t161 t162))
% 26.53/26.72  (step t164 (cl (not (and (tptp.little_set (tptp.apply tptp.a_function tptp.a)) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)))))) (not (and (tptp.little_set (tptp.apply tptp.a_function tptp.a)) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)))))) (tptp.little_set (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))))) :rule reordering :premises (t163))
% 26.53/26.72  (step t165 (cl (not (and (tptp.little_set (tptp.apply tptp.a_function tptp.a)) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)))))) (tptp.little_set (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))))) :rule contraction :premises (t164))
% 26.53/26.72  (step t166 (cl (=> (and (tptp.little_set (tptp.apply tptp.a_function tptp.a)) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))))) (tptp.little_set (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))))) (tptp.little_set (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))))) :rule resolution :premises (t159 t165))
% 26.53/26.72  (step t167 (cl (=> (and (tptp.little_set (tptp.apply tptp.a_function tptp.a)) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))))) (tptp.little_set (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))))) (not (tptp.little_set (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)))))) :rule implies_neg2)
% 26.53/26.72  (step t168 (cl (=> (and (tptp.little_set (tptp.apply tptp.a_function tptp.a)) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))))) (tptp.little_set (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))))) (=> (and (tptp.little_set (tptp.apply tptp.a_function tptp.a)) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))))) (tptp.little_set (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)))))) :rule resolution :premises (t166 t167))
% 26.53/26.72  (step t169 (cl (=> (and (tptp.little_set (tptp.apply tptp.a_function tptp.a)) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))))) (tptp.little_set (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)))))) :rule contraction :premises (t168))
% 26.53/26.72  (step t170 (cl (not (and (tptp.little_set (tptp.apply tptp.a_function tptp.a)) (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)))))) (tptp.little_set (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))))) :rule implies :premises (t169))
% 26.53/26.72  (step t171 (cl (not (tptp.little_set (tptp.apply tptp.a_function tptp.a))) (not (= (tptp.apply tptp.a_function tptp.a) (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))))) (tptp.little_set (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))))) :rule resolution :premises (t158 t170))
% 26.53/26.72  (step t172 (cl (tptp.little_set (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))))) :rule resolution :premises (t171 t75 t87))
% 26.53/26.72  (step t173 (cl (=> (forall ((X $$unsorted) (Xp $$unsorted)) (or (tptp.member (tptp.second Xp) (tptp.range_of X)) (not (tptp.little_set (tptp.second Xp))) (not (tptp.ordered_pair_predicate Xp)) (not (tptp.member Xp X)))) (or (tptp.member (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)) (not (tptp.little_set (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))))) (not (tptp.ordered_pair_predicate (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)))) (not (tptp.member (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)) tptp.a_function)))) (forall ((X $$unsorted) (Xp $$unsorted)) (or (tptp.member (tptp.second Xp) (tptp.range_of X)) (not (tptp.little_set (tptp.second Xp))) (not (tptp.ordered_pair_predicate Xp)) (not (tptp.member Xp X))))) :rule implies_neg1)
% 26.53/26.72  (anchor :step t174)
% 26.53/26.72  (assume t174.a0 (forall ((X $$unsorted) (Xp $$unsorted)) (or (tptp.member (tptp.second Xp) (tptp.range_of X)) (not (tptp.little_set (tptp.second Xp))) (not (tptp.ordered_pair_predicate Xp)) (not (tptp.member Xp X)))))
% 26.53/26.72  (step t174.t1 (cl (or (not (forall ((X $$unsorted) (Xp $$unsorted)) (or (tptp.member (tptp.second Xp) (tptp.range_of X)) (not (tptp.little_set (tptp.second Xp))) (not (tptp.ordered_pair_predicate Xp)) (not (tptp.member Xp X))))) (or (tptp.member (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)) (not (tptp.little_set (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))))) (not (tptp.ordered_pair_predicate (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)))) (not (tptp.member (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)) tptp.a_function))))) :rule forall_inst :args ((:= X tptp.a_function) (:= Xp (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)))))
% 26.53/26.72  (step t174.t2 (cl (not (forall ((X $$unsorted) (Xp $$unsorted)) (or (tptp.member (tptp.second Xp) (tptp.range_of X)) (not (tptp.little_set (tptp.second Xp))) (not (tptp.ordered_pair_predicate Xp)) (not (tptp.member Xp X))))) (or (tptp.member (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)) (not (tptp.little_set (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))))) (not (tptp.ordered_pair_predicate (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)))) (not (tptp.member (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)) tptp.a_function)))) :rule or :premises (t174.t1))
% 26.53/26.72  (step t174.t3 (cl (or (tptp.member (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)) (not (tptp.little_set (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))))) (not (tptp.ordered_pair_predicate (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)))) (not (tptp.member (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)) tptp.a_function)))) :rule resolution :premises (t174.t2 t174.a0))
% 26.53/26.72  (step t174 (cl (not (forall ((X $$unsorted) (Xp $$unsorted)) (or (tptp.member (tptp.second Xp) (tptp.range_of X)) (not (tptp.little_set (tptp.second Xp))) (not (tptp.ordered_pair_predicate Xp)) (not (tptp.member Xp X))))) (or (tptp.member (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)) (not (tptp.little_set (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))))) (not (tptp.ordered_pair_predicate (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)))) (not (tptp.member (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)) tptp.a_function)))) :rule subproof :discharge (t174.a0))
% 26.53/26.72  (step t175 (cl (=> (forall ((X $$unsorted) (Xp $$unsorted)) (or (tptp.member (tptp.second Xp) (tptp.range_of X)) (not (tptp.little_set (tptp.second Xp))) (not (tptp.ordered_pair_predicate Xp)) (not (tptp.member Xp X)))) (or (tptp.member (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)) (not (tptp.little_set (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))))) (not (tptp.ordered_pair_predicate (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)))) (not (tptp.member (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)) tptp.a_function)))) (or (tptp.member (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)) (not (tptp.little_set (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))))) (not (tptp.ordered_pair_predicate (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)))) (not (tptp.member (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)) tptp.a_function)))) :rule resolution :premises (t173 t174))
% 26.53/26.72  (step t176 (cl (=> (forall ((X $$unsorted) (Xp $$unsorted)) (or (tptp.member (tptp.second Xp) (tptp.range_of X)) (not (tptp.little_set (tptp.second Xp))) (not (tptp.ordered_pair_predicate Xp)) (not (tptp.member Xp X)))) (or (tptp.member (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)) (not (tptp.little_set (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))))) (not (tptp.ordered_pair_predicate (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)))) (not (tptp.member (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)) tptp.a_function)))) (not (or (tptp.member (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)) (not (tptp.little_set (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))))) (not (tptp.ordered_pair_predicate (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)))) (not (tptp.member (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)) tptp.a_function))))) :rule implies_neg2)
% 26.53/26.72  (step t177 (cl (=> (forall ((X $$unsorted) (Xp $$unsorted)) (or (tptp.member (tptp.second Xp) (tptp.range_of X)) (not (tptp.little_set (tptp.second Xp))) (not (tptp.ordered_pair_predicate Xp)) (not (tptp.member Xp X)))) (or (tptp.member (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)) (not (tptp.little_set (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))))) (not (tptp.ordered_pair_predicate (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)))) (not (tptp.member (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)) tptp.a_function)))) (=> (forall ((X $$unsorted) (Xp $$unsorted)) (or (tptp.member (tptp.second Xp) (tptp.range_of X)) (not (tptp.little_set (tptp.second Xp))) (not (tptp.ordered_pair_predicate Xp)) (not (tptp.member Xp X)))) (or (tptp.member (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)) (not (tptp.little_set (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))))) (not (tptp.ordered_pair_predicate (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)))) (not (tptp.member (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)) tptp.a_function))))) :rule resolution :premises (t175 t176))
% 26.53/26.72  (step t178 (cl (=> (forall ((X $$unsorted) (Xp $$unsorted)) (or (tptp.member (tptp.second Xp) (tptp.range_of X)) (not (tptp.little_set (tptp.second Xp))) (not (tptp.ordered_pair_predicate Xp)) (not (tptp.member Xp X)))) (or (tptp.member (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)) (not (tptp.little_set (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))))) (not (tptp.ordered_pair_predicate (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)))) (not (tptp.member (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)) tptp.a_function))))) :rule contraction :premises (t177))
% 26.53/26.72  (step t179 (cl (not (forall ((X $$unsorted) (Xp $$unsorted)) (or (tptp.member (tptp.second Xp) (tptp.range_of X)) (not (tptp.little_set (tptp.second Xp))) (not (tptp.ordered_pair_predicate Xp)) (not (tptp.member Xp X))))) (or (tptp.member (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)) (not (tptp.little_set (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))))) (not (tptp.ordered_pair_predicate (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)))) (not (tptp.member (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)) tptp.a_function)))) :rule implies :premises (t178))
% 26.53/26.72  (step t180 (cl (not (= (forall ((Z $$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))))) (forall ((X $$unsorted) (Xp $$unsorted)) (or (tptp.member (tptp.second Xp) (tptp.range_of X)) (not (tptp.little_set (tptp.second Xp))) (not (tptp.ordered_pair_predicate Xp)) (not (tptp.member Xp X)))))) (not (forall ((Z $$unsorted) (X $$unsorted) (Xp $$unsorted)) (or (tptp.member Z (tptp.range_of X)) (not (tptp.little_set Z)) (not (tptp.ordered_pair_predicate Xp)) (not (tptp.member Xp X)) (not (= Z (tptp.second Xp)))))) (forall ((X $$unsorted) (Xp $$unsorted)) (or (tptp.member (tptp.second Xp) (tptp.range_of X)) (not (tptp.little_set (tptp.second Xp))) (not (tptp.ordered_pair_predicate Xp)) (not (tptp.member Xp X))))) :rule equiv_pos2)
% 26.53/26.72  (step t181 (cl (= (forall ((Z $$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))))) (forall ((X $$unsorted) (Xp $$unsorted)) (or (tptp.member (tptp.second Xp) (tptp.range_of X)) (not (tptp.little_set (tptp.second Xp))) (not (tptp.ordered_pair_predicate Xp)) (not (tptp.member Xp X)) (not (= (tptp.second Xp) (tptp.second Xp))))))) :rule all_simplify)
% 26.53/26.72  (anchor :step t182 :args ((X $$unsorted) (:= X X) (Xp $$unsorted) (:= Xp Xp)))
% 26.53/26.72  (step t182.t1 (cl (= X X)) :rule refl)
% 26.53/26.72  (step t182.t2 (cl (= Xp Xp)) :rule refl)
% 26.53/26.72  (step t182.t3 (cl (= (tptp.member (tptp.second Xp) (tptp.range_of X)) (tptp.member (tptp.second Xp) (tptp.range_of X)))) :rule refl)
% 26.53/26.72  (step t182.t4 (cl (= (not (tptp.little_set (tptp.second Xp))) (not (tptp.little_set (tptp.second Xp))))) :rule refl)
% 26.53/26.72  (step t182.t5 (cl (= (not (tptp.ordered_pair_predicate Xp)) (not (tptp.ordered_pair_predicate Xp)))) :rule refl)
% 26.53/26.72  (step t182.t6 (cl (= (not (tptp.member Xp X)) (not (tptp.member Xp X)))) :rule refl)
% 26.53/26.72  (step t182.t7 (cl (= (= (tptp.second Xp) (tptp.second Xp)) true)) :rule all_simplify)
% 26.53/26.72  (step t182.t8 (cl (= (not (= (tptp.second Xp) (tptp.second Xp))) (not true))) :rule cong :premises (t182.t7))
% 26.53/26.72  (step t182.t9 (cl (= (not true) false)) :rule all_simplify)
% 26.53/26.72  (step t182.t10 (cl (= (not (= (tptp.second Xp) (tptp.second Xp))) false)) :rule trans :premises (t182.t8 t182.t9))
% 26.53/26.72  (step t182.t11 (cl (= (or (tptp.member (tptp.second Xp) (tptp.range_of X)) (not (tptp.little_set (tptp.second Xp))) (not (tptp.ordered_pair_predicate Xp)) (not (tptp.member Xp X)) (not (= (tptp.second Xp) (tptp.second Xp)))) (or (tptp.member (tptp.second Xp) (tptp.range_of X)) (not (tptp.little_set (tptp.second Xp))) (not (tptp.ordered_pair_predicate Xp)) (not (tptp.member Xp X)) false))) :rule cong :premises (t182.t3 t182.t4 t182.t5 t182.t6 t182.t10))
% 26.53/26.72  (step t182.t12 (cl (= (or (tptp.member (tptp.second Xp) (tptp.range_of X)) (not (tptp.little_set (tptp.second Xp))) (not (tptp.ordered_pair_predicate Xp)) (not (tptp.member Xp X)) false) (or (tptp.member (tptp.second Xp) (tptp.range_of X)) (not (tptp.little_set (tptp.second Xp))) (not (tptp.ordered_pair_predicate Xp)) (not (tptp.member Xp X))))) :rule all_simplify)
% 26.53/26.72  (step t182.t13 (cl (= (or (tptp.member (tptp.second Xp) (tptp.range_of X)) (not (tptp.little_set (tptp.second Xp))) (not (tptp.ordered_pair_predicate Xp)) (not (tptp.member Xp X)) (not (= (tptp.second Xp) (tptp.second Xp)))) (or (tptp.member (tptp.second Xp) (tptp.range_of X)) (not (tptp.little_set (tptp.second Xp))) (not (tptp.ordered_pair_predicate Xp)) (not (tptp.member Xp X))))) :rule trans :premises (t182.t11 t182.t12))
% 26.53/26.72  (step t182 (cl (= (forall ((X $$unsorted) (Xp $$unsorted)) (or (tptp.member (tptp.second Xp) (tptp.range_of X)) (not (tptp.little_set (tptp.second Xp))) (not (tptp.ordered_pair_predicate Xp)) (not (tptp.member Xp X)) (not (= (tptp.second Xp) (tptp.second Xp))))) (forall ((X $$unsorted) (Xp $$unsorted)) (or (tptp.member (tptp.second Xp) (tptp.range_of X)) (not (tptp.little_set (tptp.second Xp))) (not (tptp.ordered_pair_predicate Xp)) (not (tptp.member Xp X)))))) :rule bind)
% 26.53/26.72  (step t183 (cl (= (forall ((Z $$unsorted) (X $$unsorted) (Xp $$unsorted)) (or (tptp.member Z (tptp.range_of X)) (not (tptp.little_set Z)) (not (tptp.ordered_pair_predicate Xp)) (not (tptp.member Xp X)) (not (= Z (tptp.second Xp))))) (forall ((X $$unsorted) (Xp $$unsorted)) (or (tptp.member (tptp.second Xp) (tptp.range_of X)) (not (tptp.little_set (tptp.second Xp))) (not (tptp.ordered_pair_predicate Xp)) (not (tptp.member Xp X)))))) :rule trans :premises (t181 t182))
% 26.53/26.72  (step t184 (cl (forall ((X $$unsorted) (Xp $$unsorted)) (or (tptp.member (tptp.second Xp) (tptp.range_of X)) (not (tptp.little_set (tptp.second Xp))) (not (tptp.ordered_pair_predicate Xp)) (not (tptp.member Xp X))))) :rule resolution :premises (t180 t183 a105))
% 26.53/26.72  (step t185 (cl (or (tptp.member (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))) (tptp.range_of tptp.a_function)) (not (tptp.little_set (tptp.second (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))))) (not (tptp.ordered_pair_predicate (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)))) (not (tptp.member (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)) tptp.a_function)))) :rule resolution :premises (t179 t184))
% 26.53/26.72  (step t186 (cl (not (or (tptp.ordered_pair_predicate (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))) (not (tptp.little_set tptp.a)) (not (tptp.little_set (tptp.apply tptp.a_function tptp.a))))) (tptp.ordered_pair_predicate (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))) (not (tptp.little_set tptp.a)) (not (tptp.little_set (tptp.apply tptp.a_function tptp.a)))) :rule or_pos)
% 26.53/26.72  (step t187 (cl (not (tptp.little_set tptp.a)) (not (tptp.little_set (tptp.apply tptp.a_function tptp.a))) (tptp.ordered_pair_predicate (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))) (not (or (tptp.ordered_pair_predicate (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))) (not (tptp.little_set tptp.a)) (not (tptp.little_set (tptp.apply tptp.a_function tptp.a)))))) :rule reordering :premises (t186))
% 26.53/26.72  (step t188 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted)) (or (tptp.ordered_pair_predicate (tptp.ordered_pair Y Z)) (not (tptp.little_set Y)) (not (tptp.little_set Z)))) (or (tptp.ordered_pair_predicate (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))) (not (tptp.little_set tptp.a)) (not (tptp.little_set (tptp.apply tptp.a_function tptp.a))))) (forall ((Y $$unsorted) (Z $$unsorted)) (or (tptp.ordered_pair_predicate (tptp.ordered_pair Y Z)) (not (tptp.little_set Y)) (not (tptp.little_set Z))))) :rule implies_neg1)
% 26.53/26.72  (anchor :step t189)
% 26.53/26.72  (assume t189.a0 (forall ((Y $$unsorted) (Z $$unsorted)) (or (tptp.ordered_pair_predicate (tptp.ordered_pair Y Z)) (not (tptp.little_set Y)) (not (tptp.little_set Z)))))
% 26.53/26.72  (step t189.t1 (cl (or (not (forall ((Y $$unsorted) (Z $$unsorted)) (or (tptp.ordered_pair_predicate (tptp.ordered_pair Y Z)) (not (tptp.little_set Y)) (not (tptp.little_set Z))))) (or (tptp.ordered_pair_predicate (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))) (not (tptp.little_set tptp.a)) (not (tptp.little_set (tptp.apply tptp.a_function tptp.a)))))) :rule forall_inst :args ((:= Y tptp.a) (:= Z (tptp.apply tptp.a_function tptp.a))))
% 26.53/26.72  (step t189.t2 (cl (not (forall ((Y $$unsorted) (Z $$unsorted)) (or (tptp.ordered_pair_predicate (tptp.ordered_pair Y Z)) (not (tptp.little_set Y)) (not (tptp.little_set Z))))) (or (tptp.ordered_pair_predicate (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))) (not (tptp.little_set tptp.a)) (not (tptp.little_set (tptp.apply tptp.a_function tptp.a))))) :rule or :premises (t189.t1))
% 26.53/26.72  (step t189.t3 (cl (or (tptp.ordered_pair_predicate (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))) (not (tptp.little_set tptp.a)) (not (tptp.little_set (tptp.apply tptp.a_function tptp.a))))) :rule resolution :premises (t189.t2 t189.a0))
% 26.53/26.72  (step t189 (cl (not (forall ((Y $$unsorted) (Z $$unsorted)) (or (tptp.ordered_pair_predicate (tptp.ordered_pair Y Z)) (not (tptp.little_set Y)) (not (tptp.little_set Z))))) (or (tptp.ordered_pair_predicate (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))) (not (tptp.little_set tptp.a)) (not (tptp.little_set (tptp.apply tptp.a_function tptp.a))))) :rule subproof :discharge (t189.a0))
% 26.53/26.72  (step t190 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted)) (or (tptp.ordered_pair_predicate (tptp.ordered_pair Y Z)) (not (tptp.little_set Y)) (not (tptp.little_set Z)))) (or (tptp.ordered_pair_predicate (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))) (not (tptp.little_set tptp.a)) (not (tptp.little_set (tptp.apply tptp.a_function tptp.a))))) (or (tptp.ordered_pair_predicate (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))) (not (tptp.little_set tptp.a)) (not (tptp.little_set (tptp.apply tptp.a_function tptp.a))))) :rule resolution :premises (t188 t189))
% 26.53/26.72  (step t191 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted)) (or (tptp.ordered_pair_predicate (tptp.ordered_pair Y Z)) (not (tptp.little_set Y)) (not (tptp.little_set Z)))) (or (tptp.ordered_pair_predicate (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))) (not (tptp.little_set tptp.a)) (not (tptp.little_set (tptp.apply tptp.a_function tptp.a))))) (not (or (tptp.ordered_pair_predicate (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))) (not (tptp.little_set tptp.a)) (not (tptp.little_set (tptp.apply tptp.a_function tptp.a)))))) :rule implies_neg2)
% 26.53/26.72  (step t192 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted)) (or (tptp.ordered_pair_predicate (tptp.ordered_pair Y Z)) (not (tptp.little_set Y)) (not (tptp.little_set Z)))) (or (tptp.ordered_pair_predicate (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))) (not (tptp.little_set tptp.a)) (not (tptp.little_set (tptp.apply tptp.a_function tptp.a))))) (=> (forall ((Y $$unsorted) (Z $$unsorted)) (or (tptp.ordered_pair_predicate (tptp.ordered_pair Y Z)) (not (tptp.little_set Y)) (not (tptp.little_set Z)))) (or (tptp.ordered_pair_predicate (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))) (not (tptp.little_set tptp.a)) (not (tptp.little_set (tptp.apply tptp.a_function tptp.a)))))) :rule resolution :premises (t190 t191))
% 26.53/26.72  (step t193 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted)) (or (tptp.ordered_pair_predicate (tptp.ordered_pair Y Z)) (not (tptp.little_set Y)) (not (tptp.little_set Z)))) (or (tptp.ordered_pair_predicate (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))) (not (tptp.little_set tptp.a)) (not (tptp.little_set (tptp.apply tptp.a_function tptp.a)))))) :rule contraction :premises (t192))
% 26.53/26.72  (step t194 (cl (not (forall ((Y $$unsorted) (Z $$unsorted)) (or (tptp.ordered_pair_predicate (tptp.ordered_pair Y Z)) (not (tptp.little_set Y)) (not (tptp.little_set Z))))) (or (tptp.ordered_pair_predicate (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))) (not (tptp.little_set tptp.a)) (not (tptp.little_set (tptp.apply tptp.a_function tptp.a))))) :rule implies :premises (t193))
% 26.53/26.72  (step t195 (cl (not (= (forall ((X $$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))))) (forall ((Y $$unsorted) (Z $$unsorted)) (or (tptp.ordered_pair_predicate (tptp.ordered_pair Y Z)) (not (tptp.little_set Y)) (not (tptp.little_set Z)))))) (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (tptp.ordered_pair_predicate X) (not (tptp.little_set Y)) (not (tptp.little_set Z)) (not (= X (tptp.ordered_pair Y Z)))))) (forall ((Y $$unsorted) (Z $$unsorted)) (or (tptp.ordered_pair_predicate (tptp.ordered_pair Y Z)) (not (tptp.little_set Y)) (not (tptp.little_set Z))))) :rule equiv_pos2)
% 26.53/26.72  (step t196 (cl (= (forall ((X $$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))))) (forall ((Y $$unsorted) (Z $$unsorted)) (or (tptp.ordered_pair_predicate (tptp.ordered_pair Y Z)) (not (tptp.little_set Y)) (not (tptp.little_set Z)) (not (= (tptp.ordered_pair Y Z) (tptp.ordered_pair Y Z))))))) :rule all_simplify)
% 26.53/26.72  (anchor :step t197 :args ((Y $$unsorted) (:= Y Y) (Z $$unsorted) (:= Z Z)))
% 26.53/26.72  (step t197.t1 (cl (= Y Y)) :rule refl)
% 26.53/26.72  (step t197.t2 (cl (= Z Z)) :rule refl)
% 26.53/26.72  (step t197.t3 (cl (= (tptp.ordered_pair_predicate (tptp.ordered_pair Y Z)) (tptp.ordered_pair_predicate (tptp.ordered_pair Y Z)))) :rule refl)
% 26.53/26.72  (step t197.t4 (cl (= (not (tptp.little_set Y)) (not (tptp.little_set Y)))) :rule refl)
% 26.53/26.72  (step t197.t5 (cl (= (not (tptp.little_set Z)) (not (tptp.little_set Z)))) :rule refl)
% 26.53/26.72  (step t197.t6 (cl (= (= (tptp.ordered_pair Y Z) (tptp.ordered_pair Y Z)) true)) :rule all_simplify)
% 26.53/26.72  (step t197.t7 (cl (= (not (= (tptp.ordered_pair Y Z) (tptp.ordered_pair Y Z))) (not true))) :rule cong :premises (t197.t6))
% 26.53/26.72  (step t197.t8 (cl (= (not true) false)) :rule all_simplify)
% 26.53/26.72  (step t197.t9 (cl (= (not (= (tptp.ordered_pair Y Z) (tptp.ordered_pair Y Z))) false)) :rule trans :premises (t197.t7 t197.t8))
% 26.53/26.72  (step t197.t10 (cl (= (or (tptp.ordered_pair_predicate (tptp.ordered_pair Y Z)) (not (tptp.little_set Y)) (not (tptp.little_set Z)) (not (= (tptp.ordered_pair Y Z) (tptp.ordered_pair Y Z)))) (or (tptp.ordered_pair_predicate (tptp.ordered_pair Y Z)) (not (tptp.little_set Y)) (not (tptp.little_set Z)) false))) :rule cong :premises (t197.t3 t197.t4 t197.t5 t197.t9))
% 26.53/26.72  (step t197.t11 (cl (= (or (tptp.ordered_pair_predicate (tptp.ordered_pair Y Z)) (not (tptp.little_set Y)) (not (tptp.little_set Z)) false) (or (tptp.ordered_pair_predicate (tptp.ordered_pair Y Z)) (not (tptp.little_set Y)) (not (tptp.little_set Z))))) :rule all_simplify)
% 26.53/26.72  (step t197.t12 (cl (= (or (tptp.ordered_pair_predicate (tptp.ordered_pair Y Z)) (not (tptp.little_set Y)) (not (tptp.little_set Z)) (not (= (tptp.ordered_pair Y Z) (tptp.ordered_pair Y Z)))) (or (tptp.ordered_pair_predicate (tptp.ordered_pair Y Z)) (not (tptp.little_set Y)) (not (tptp.little_set Z))))) :rule trans :premises (t197.t10 t197.t11))
% 26.53/26.72  (step t197 (cl (= (forall ((Y $$unsorted) (Z $$unsorted)) (or (tptp.ordered_pair_predicate (tptp.ordered_pair Y Z)) (not (tptp.little_set Y)) (not (tptp.little_set Z)) (not (= (tptp.ordered_pair Y Z) (tptp.ordered_pair Y Z))))) (forall ((Y $$unsorted) (Z $$unsorted)) (or (tptp.ordered_pair_predicate (tptp.ordered_pair Y Z)) (not (tptp.little_set Y)) (not (tptp.little_set Z)))))) :rule bind)
% 26.53/26.72  (step t198 (cl (= (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (tptp.ordered_pair_predicate X) (not (tptp.little_set Y)) (not (tptp.little_set Z)) (not (= X (tptp.ordered_pair Y Z))))) (forall ((Y $$unsorted) (Z $$unsorted)) (or (tptp.ordered_pair_predicate (tptp.ordered_pair Y Z)) (not (tptp.little_set Y)) (not (tptp.little_set Z)))))) :rule trans :premises (t196 t197))
% 26.53/26.72  (step t199 (cl (forall ((Y $$unsorted) (Z $$unsorted)) (or (tptp.ordered_pair_predicate (tptp.ordered_pair Y Z)) (not (tptp.little_set Y)) (not (tptp.little_set Z))))) :rule resolution :premises (t195 t198 a13))
% 26.53/26.72  (step t200 (cl (or (tptp.ordered_pair_predicate (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a))) (not (tptp.little_set tptp.a)) (not (tptp.little_set (tptp.apply tptp.a_function tptp.a))))) :rule resolution :premises (t194 t199))
% 26.53/26.72  (step t201 (cl (tptp.ordered_pair_predicate (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)))) :rule resolution :premises (t187 t53 t75 t200))
% 26.53/26.72  (step t202 (cl (not (or (not (tptp.function tptp.a_function)) (not (tptp.member tptp.a (tptp.domain_of tptp.a_function))) (tptp.member (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)) tptp.a_function))) (not (tptp.function tptp.a_function)) (not (tptp.member tptp.a (tptp.domain_of tptp.a_function))) (tptp.member (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)) tptp.a_function)) :rule or_pos)
% 26.53/26.72  (step t203 (cl (not (tptp.function tptp.a_function)) (not (tptp.member tptp.a (tptp.domain_of tptp.a_function))) (tptp.member (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)) tptp.a_function) (not (or (not (tptp.function tptp.a_function)) (not (tptp.member tptp.a (tptp.domain_of tptp.a_function))) (tptp.member (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)) tptp.a_function)))) :rule reordering :premises (t202))
% 26.53/26.72  (step t204 (cl (and (tptp.member tptp.a tptp.a_domain) (= tptp.a_domain (tptp.domain_of tptp.a_function))) (not (tptp.member tptp.a tptp.a_domain)) (not (= tptp.a_domain (tptp.domain_of tptp.a_function)))) :rule and_neg)
% 26.53/26.72  (step t205 (cl (=> (and (tptp.member tptp.a tptp.a_domain) (= tptp.a_domain (tptp.domain_of tptp.a_function))) (tptp.member tptp.a (tptp.domain_of tptp.a_function))) (and (tptp.member tptp.a tptp.a_domain) (= tptp.a_domain (tptp.domain_of tptp.a_function)))) :rule implies_neg1)
% 26.53/26.72  (anchor :step t206)
% 26.53/26.72  (assume t206.a0 (tptp.member tptp.a tptp.a_domain))
% 26.53/26.72  (assume t206.a1 (= tptp.a_domain (tptp.domain_of tptp.a_function)))
% 26.53/26.72  (step t206.t1 (cl (=> (and (tptp.member tptp.a tptp.a_domain) (= tptp.a_domain (tptp.domain_of tptp.a_function))) (tptp.member tptp.a (tptp.domain_of tptp.a_function))) (and (tptp.member tptp.a tptp.a_domain) (= tptp.a_domain (tptp.domain_of tptp.a_function)))) :rule implies_neg1)
% 26.53/26.72  (anchor :step t206.t2)
% 26.53/26.72  (assume t206.t2.a0 (tptp.member tptp.a tptp.a_domain))
% 26.53/26.72  (assume t206.t2.a1 (= tptp.a_domain (tptp.domain_of tptp.a_function)))
% 26.53/26.72  (step t206.t2.t1 (cl (= (= (tptp.member tptp.a (tptp.domain_of tptp.a_function)) true) (tptp.member tptp.a (tptp.domain_of tptp.a_function)))) :rule equiv_simplify)
% 26.53/26.72  (step t206.t2.t2 (cl (not (= (tptp.member tptp.a (tptp.domain_of tptp.a_function)) true)) (tptp.member tptp.a (tptp.domain_of tptp.a_function))) :rule equiv1 :premises (t206.t2.t1))
% 26.53/26.72  (step t206.t2.t3 (cl (= tptp.a tptp.a)) :rule refl)
% 26.53/26.72  (step t206.t2.t4 (cl (= (tptp.domain_of tptp.a_function) tptp.a_domain)) :rule symm :premises (t206.t2.a1))
% 26.53/26.72  (step t206.t2.t5 (cl (= (tptp.member tptp.a (tptp.domain_of tptp.a_function)) (tptp.member tptp.a tptp.a_domain))) :rule cong :premises (t206.t2.t3 t206.t2.t4))
% 26.53/26.72  (step t206.t2.t6 (cl (= (= (tptp.member tptp.a tptp.a_domain) true) (tptp.member tptp.a tptp.a_domain))) :rule equiv_simplify)
% 26.53/26.72  (step t206.t2.t7 (cl (= (tptp.member tptp.a tptp.a_domain) true) (not (tptp.member tptp.a tptp.a_domain))) :rule equiv2 :premises (t206.t2.t6))
% 26.53/26.72  (step t206.t2.t8 (cl (= (tptp.member tptp.a tptp.a_domain) true)) :rule resolution :premises (t206.t2.t7 t206.t2.a0))
% 26.53/26.72  (step t206.t2.t9 (cl (= (tptp.member tptp.a (tptp.domain_of tptp.a_function)) true)) :rule trans :premises (t206.t2.t5 t206.t2.t8))
% 26.53/26.72  (step t206.t2.t10 (cl (tptp.member tptp.a (tptp.domain_of tptp.a_function))) :rule resolution :premises (t206.t2.t2 t206.t2.t9))
% 26.53/26.72  (step t206.t2 (cl (not (tptp.member tptp.a tptp.a_domain)) (not (= tptp.a_domain (tptp.domain_of tptp.a_function))) (tptp.member tptp.a (tptp.domain_of tptp.a_function))) :rule subproof :discharge (t206.t2.a0 t206.t2.a1))
% 26.53/26.72  (step t206.t3 (cl (not (and (tptp.member tptp.a tptp.a_domain) (= tptp.a_domain (tptp.domain_of tptp.a_function)))) (tptp.member tptp.a tptp.a_domain)) :rule and_pos)
% 26.53/26.72  (step t206.t4 (cl (not (and (tptp.member tptp.a tptp.a_domain) (= tptp.a_domain (tptp.domain_of tptp.a_function)))) (= tptp.a_domain (tptp.domain_of tptp.a_function))) :rule and_pos)
% 26.53/26.72  (step t206.t5 (cl (tptp.member tptp.a (tptp.domain_of tptp.a_function)) (not (and (tptp.member tptp.a tptp.a_domain) (= tptp.a_domain (tptp.domain_of tptp.a_function)))) (not (and (tptp.member tptp.a tptp.a_domain) (= tptp.a_domain (tptp.domain_of tptp.a_function))))) :rule resolution :premises (t206.t2 t206.t3 t206.t4))
% 26.53/26.72  (step t206.t6 (cl (not (and (tptp.member tptp.a tptp.a_domain) (= tptp.a_domain (tptp.domain_of tptp.a_function)))) (not (and (tptp.member tptp.a tptp.a_domain) (= tptp.a_domain (tptp.domain_of tptp.a_function)))) (tptp.member tptp.a (tptp.domain_of tptp.a_function))) :rule reordering :premises (t206.t5))
% 26.53/26.72  (step t206.t7 (cl (not (and (tptp.member tptp.a tptp.a_domain) (= tptp.a_domain (tptp.domain_of tptp.a_function)))) (tptp.member tptp.a (tptp.domain_of tptp.a_function))) :rule contraction :premises (t206.t6))
% 26.53/26.72  (step t206.t8 (cl (=> (and (tptp.member tptp.a tptp.a_domain) (= tptp.a_domain (tptp.domain_of tptp.a_function))) (tptp.member tptp.a (tptp.domain_of tptp.a_function))) (tptp.member tptp.a (tptp.domain_of tptp.a_function))) :rule resolution :premises (t206.t1 t206.t7))
% 26.53/26.72  (step t206.t9 (cl (=> (and (tptp.member tptp.a tptp.a_domain) (= tptp.a_domain (tptp.domain_of tptp.a_function))) (tptp.member tptp.a (tptp.domain_of tptp.a_function))) (not (tptp.member tptp.a (tptp.domain_of tptp.a_function)))) :rule implies_neg2)
% 26.53/26.72  (step t206.t10 (cl (=> (and (tptp.member tptp.a tptp.a_domain) (= tptp.a_domain (tptp.domain_of tptp.a_function))) (tptp.member tptp.a (tptp.domain_of tptp.a_function))) (=> (and (tptp.member tptp.a tptp.a_domain) (= tptp.a_domain (tptp.domain_of tptp.a_function))) (tptp.member tptp.a (tptp.domain_of tptp.a_function)))) :rule resolution :premises (t206.t8 t206.t9))
% 26.53/26.72  (step t206.t11 (cl (=> (and (tptp.member tptp.a tptp.a_domain) (= tptp.a_domain (tptp.domain_of tptp.a_function))) (tptp.member tptp.a (tptp.domain_of tptp.a_function)))) :rule contraction :premises (t206.t10))
% 26.53/26.72  (step t206.t12 (cl (not (and (tptp.member tptp.a tptp.a_domain) (= tptp.a_domain (tptp.domain_of tptp.a_function)))) (tptp.member tptp.a (tptp.domain_of tptp.a_function))) :rule implies :premises (t206.t11))
% 26.53/26.72  (step t206.t13 (cl (and (tptp.member tptp.a tptp.a_domain) (= tptp.a_domain (tptp.domain_of tptp.a_function))) (not (tptp.member tptp.a tptp.a_domain)) (not (= tptp.a_domain (tptp.domain_of tptp.a_function)))) :rule and_neg)
% 26.53/26.72  (step t206.t14 (cl (and (tptp.member tptp.a tptp.a_domain) (= tptp.a_domain (tptp.domain_of tptp.a_function)))) :rule resolution :premises (t206.t13 t206.a0 t206.a1))
% 26.53/26.72  (step t206.t15 (cl (tptp.member tptp.a (tptp.domain_of tptp.a_function))) :rule resolution :premises (t206.t12 t206.t14))
% 26.53/26.72  (step t206 (cl (not (tptp.member tptp.a tptp.a_domain)) (not (= tptp.a_domain (tptp.domain_of tptp.a_function))) (tptp.member tptp.a (tptp.domain_of tptp.a_function))) :rule subproof :discharge (t206.a0 t206.a1))
% 26.53/26.72  (step t207 (cl (not (and (tptp.member tptp.a tptp.a_domain) (= tptp.a_domain (tptp.domain_of tptp.a_function)))) (tptp.member tptp.a tptp.a_domain)) :rule and_pos)
% 26.53/26.72  (step t208 (cl (not (and (tptp.member tptp.a tptp.a_domain) (= tptp.a_domain (tptp.domain_of tptp.a_function)))) (= tptp.a_domain (tptp.domain_of tptp.a_function))) :rule and_pos)
% 26.53/26.72  (step t209 (cl (tptp.member tptp.a (tptp.domain_of tptp.a_function)) (not (and (tptp.member tptp.a tptp.a_domain) (= tptp.a_domain (tptp.domain_of tptp.a_function)))) (not (and (tptp.member tptp.a tptp.a_domain) (= tptp.a_domain (tptp.domain_of tptp.a_function))))) :rule resolution :premises (t206 t207 t208))
% 26.53/26.72  (step t210 (cl (not (and (tptp.member tptp.a tptp.a_domain) (= tptp.a_domain (tptp.domain_of tptp.a_function)))) (not (and (tptp.member tptp.a tptp.a_domain) (= tptp.a_domain (tptp.domain_of tptp.a_function)))) (tptp.member tptp.a (tptp.domain_of tptp.a_function))) :rule reordering :premises (t209))
% 26.53/26.72  (step t211 (cl (not (and (tptp.member tptp.a tptp.a_domain) (= tptp.a_domain (tptp.domain_of tptp.a_function)))) (tptp.member tptp.a (tptp.domain_of tptp.a_function))) :rule contraction :premises (t210))
% 26.53/26.72  (step t212 (cl (=> (and (tptp.member tptp.a tptp.a_domain) (= tptp.a_domain (tptp.domain_of tptp.a_function))) (tptp.member tptp.a (tptp.domain_of tptp.a_function))) (tptp.member tptp.a (tptp.domain_of tptp.a_function))) :rule resolution :premises (t205 t211))
% 26.53/26.72  (step t213 (cl (=> (and (tptp.member tptp.a tptp.a_domain) (= tptp.a_domain (tptp.domain_of tptp.a_function))) (tptp.member tptp.a (tptp.domain_of tptp.a_function))) (not (tptp.member tptp.a (tptp.domain_of tptp.a_function)))) :rule implies_neg2)
% 26.53/26.72  (step t214 (cl (=> (and (tptp.member tptp.a tptp.a_domain) (= tptp.a_domain (tptp.domain_of tptp.a_function))) (tptp.member tptp.a (tptp.domain_of tptp.a_function))) (=> (and (tptp.member tptp.a tptp.a_domain) (= tptp.a_domain (tptp.domain_of tptp.a_function))) (tptp.member tptp.a (tptp.domain_of tptp.a_function)))) :rule resolution :premises (t212 t213))
% 26.53/26.72  (step t215 (cl (=> (and (tptp.member tptp.a tptp.a_domain) (= tptp.a_domain (tptp.domain_of tptp.a_function))) (tptp.member tptp.a (tptp.domain_of tptp.a_function)))) :rule contraction :premises (t214))
% 26.53/26.72  (step t216 (cl (not (and (tptp.member tptp.a tptp.a_domain) (= tptp.a_domain (tptp.domain_of tptp.a_function)))) (tptp.member tptp.a (tptp.domain_of tptp.a_function))) :rule implies :premises (t215))
% 26.53/26.72  (step t217 (cl (not (tptp.member tptp.a tptp.a_domain)) (not (= tptp.a_domain (tptp.domain_of tptp.a_function))) (tptp.member tptp.a (tptp.domain_of tptp.a_function))) :rule resolution :premises (t204 t216))
% 26.53/26.72  (step t218 (cl (not (tptp.member tptp.a tptp.a_domain)) (tptp.member tptp.a (tptp.domain_of tptp.a_function)) (not (= tptp.a_domain (tptp.domain_of tptp.a_function)))) :rule reordering :premises (t217))
% 26.53/26.72  (step t219 (cl (not (or (not (tptp.maps tptp.a_function tptp.a_domain tptp.a_range)) (= tptp.a_domain (tptp.domain_of tptp.a_function)))) (not (tptp.maps tptp.a_function tptp.a_domain tptp.a_range)) (= tptp.a_domain (tptp.domain_of tptp.a_function))) :rule or_pos)
% 26.53/26.72  (step t220 (cl (not (tptp.maps tptp.a_function tptp.a_domain tptp.a_range)) (= tptp.a_domain (tptp.domain_of tptp.a_function)) (not (or (not (tptp.maps tptp.a_function tptp.a_domain tptp.a_range)) (= tptp.a_domain (tptp.domain_of tptp.a_function))))) :rule reordering :premises (t219))
% 26.53/26.72  (step t221 (cl (=> (forall ((Xf $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.maps Xf X Y)) (= X (tptp.domain_of Xf)))) (or (not (tptp.maps tptp.a_function tptp.a_domain tptp.a_range)) (= tptp.a_domain (tptp.domain_of tptp.a_function)))) (forall ((Xf $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.maps Xf X Y)) (= X (tptp.domain_of Xf))))) :rule implies_neg1)
% 26.53/26.72  (anchor :step t222)
% 26.53/26.72  (assume t222.a0 (forall ((Xf $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.maps Xf X Y)) (= X (tptp.domain_of Xf)))))
% 26.53/26.72  (step t222.t1 (cl (or (not (forall ((Xf $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.maps Xf X Y)) (= X (tptp.domain_of Xf))))) (or (not (tptp.maps tptp.a_function tptp.a_domain tptp.a_range)) (= tptp.a_domain (tptp.domain_of tptp.a_function))))) :rule forall_inst :args ((:= Xf tptp.a_function) (:= X tptp.a_domain) (:= Y tptp.a_range)))
% 26.53/26.72  (step t222.t2 (cl (not (forall ((Xf $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.maps Xf X Y)) (= X (tptp.domain_of Xf))))) (or (not (tptp.maps tptp.a_function tptp.a_domain tptp.a_range)) (= tptp.a_domain (tptp.domain_of tptp.a_function)))) :rule or :premises (t222.t1))
% 26.53/26.72  (step t222.t3 (cl (or (not (tptp.maps tptp.a_function tptp.a_domain tptp.a_range)) (= tptp.a_domain (tptp.domain_of tptp.a_function)))) :rule resolution :premises (t222.t2 t222.a0))
% 26.53/26.72  (step t222 (cl (not (forall ((Xf $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.maps Xf X Y)) (= X (tptp.domain_of Xf))))) (or (not (tptp.maps tptp.a_function tptp.a_domain tptp.a_range)) (= tptp.a_domain (tptp.domain_of tptp.a_function)))) :rule subproof :discharge (t222.a0))
% 26.53/26.72  (step t223 (cl (=> (forall ((Xf $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.maps Xf X Y)) (= X (tptp.domain_of Xf)))) (or (not (tptp.maps tptp.a_function tptp.a_domain tptp.a_range)) (= tptp.a_domain (tptp.domain_of tptp.a_function)))) (or (not (tptp.maps tptp.a_function tptp.a_domain tptp.a_range)) (= tptp.a_domain (tptp.domain_of tptp.a_function)))) :rule resolution :premises (t221 t222))
% 26.53/26.72  (step t224 (cl (=> (forall ((Xf $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.maps Xf X Y)) (= X (tptp.domain_of Xf)))) (or (not (tptp.maps tptp.a_function tptp.a_domain tptp.a_range)) (= tptp.a_domain (tptp.domain_of tptp.a_function)))) (not (or (not (tptp.maps tptp.a_function tptp.a_domain tptp.a_range)) (= tptp.a_domain (tptp.domain_of tptp.a_function))))) :rule implies_neg2)
% 26.53/26.72  (step t225 (cl (=> (forall ((Xf $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.maps Xf X Y)) (= X (tptp.domain_of Xf)))) (or (not (tptp.maps tptp.a_function tptp.a_domain tptp.a_range)) (= tptp.a_domain (tptp.domain_of tptp.a_function)))) (=> (forall ((Xf $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.maps Xf X Y)) (= X (tptp.domain_of Xf)))) (or (not (tptp.maps tptp.a_function tptp.a_domain tptp.a_range)) (= tptp.a_domain (tptp.domain_of tptp.a_function))))) :rule resolution :premises (t223 t224))
% 26.53/26.72  (step t226 (cl (=> (forall ((Xf $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.maps Xf X Y)) (= X (tptp.domain_of Xf)))) (or (not (tptp.maps tptp.a_function tptp.a_domain tptp.a_range)) (= tptp.a_domain (tptp.domain_of tptp.a_function))))) :rule contraction :premises (t225))
% 26.53/26.72  (step t227 (cl (not (forall ((Xf $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.maps Xf X Y)) (= X (tptp.domain_of Xf))))) (or (not (tptp.maps tptp.a_function tptp.a_domain tptp.a_range)) (= tptp.a_domain (tptp.domain_of tptp.a_function)))) :rule implies :premises (t226))
% 26.53/26.72  (step t228 (cl (not (= (forall ((Xf $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.maps Xf X Y)) (= (tptp.domain_of Xf) X))) (forall ((Xf $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.maps Xf X Y)) (= X (tptp.domain_of Xf)))))) (not (forall ((Xf $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.maps Xf X Y)) (= (tptp.domain_of Xf) X)))) (forall ((Xf $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.maps Xf X Y)) (= X (tptp.domain_of Xf))))) :rule equiv_pos2)
% 26.53/26.72  (anchor :step t229 :args ((Xf $$unsorted) (:= Xf Xf) (X $$unsorted) (:= X X) (Y $$unsorted) (:= Y Y)))
% 26.53/26.72  (step t229.t1 (cl (= Xf Xf)) :rule refl)
% 26.53/26.72  (step t229.t2 (cl (= X X)) :rule refl)
% 26.53/26.72  (step t229.t3 (cl (= Y Y)) :rule refl)
% 26.53/26.72  (step t229.t4 (cl (= (not (tptp.maps Xf X Y)) (not (tptp.maps Xf X Y)))) :rule refl)
% 26.53/26.72  (step t229.t5 (cl (= (= (tptp.domain_of Xf) X) (= X (tptp.domain_of Xf)))) :rule all_simplify)
% 26.53/26.72  (step t229.t6 (cl (= (or (not (tptp.maps Xf X Y)) (= (tptp.domain_of Xf) X)) (or (not (tptp.maps Xf X Y)) (= X (tptp.domain_of Xf))))) :rule cong :premises (t229.t4 t229.t5))
% 26.53/26.72  (step t229 (cl (= (forall ((Xf $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.maps Xf X Y)) (= (tptp.domain_of Xf) X))) (forall ((Xf $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.maps Xf X Y)) (= X (tptp.domain_of Xf)))))) :rule bind)
% 26.53/26.72  (step t230 (cl (forall ((Xf $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.maps Xf X Y)) (= X (tptp.domain_of Xf))))) :rule resolution :premises (t228 t229 a120))
% 26.53/26.72  (step t231 (cl (or (not (tptp.maps tptp.a_function tptp.a_domain tptp.a_range)) (= tptp.a_domain (tptp.domain_of tptp.a_function)))) :rule resolution :premises (t227 t230))
% 26.53/26.72  (step t232 (cl (= tptp.a_domain (tptp.domain_of tptp.a_function))) :rule resolution :premises (t220 a163 t231))
% 26.53/26.72  (step t233 (cl (tptp.member tptp.a (tptp.domain_of tptp.a_function))) :rule resolution :premises (t218 a164 t232))
% 26.53/26.72  (step t234 (cl (=> (forall ((Xf $$unsorted) (X $$unsorted)) (or (not (tptp.function Xf)) (not (tptp.member X (tptp.domain_of Xf))) (tptp.member (tptp.ordered_pair X (tptp.apply Xf X)) Xf))) (or (not (tptp.function tptp.a_function)) (not (tptp.member tptp.a (tptp.domain_of tptp.a_function))) (tptp.member (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)) tptp.a_function))) (forall ((Xf $$unsorted) (X $$unsorted)) (or (not (tptp.function Xf)) (not (tptp.member X (tptp.domain_of Xf))) (tptp.member (tptp.ordered_pair X (tptp.apply Xf X)) Xf)))) :rule implies_neg1)
% 26.53/26.72  (anchor :step t235)
% 26.53/26.72  (assume t235.a0 (forall ((Xf $$unsorted) (X $$unsorted)) (or (not (tptp.function Xf)) (not (tptp.member X (tptp.domain_of Xf))) (tptp.member (tptp.ordered_pair X (tptp.apply Xf X)) Xf))))
% 26.53/26.72  (step t235.t1 (cl (or (not (forall ((Xf $$unsorted) (X $$unsorted)) (or (not (tptp.function Xf)) (not (tptp.member X (tptp.domain_of Xf))) (tptp.member (tptp.ordered_pair X (tptp.apply Xf X)) Xf)))) (or (not (tptp.function tptp.a_function)) (not (tptp.member tptp.a (tptp.domain_of tptp.a_function))) (tptp.member (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)) tptp.a_function)))) :rule forall_inst :args ((:= Xf tptp.a_function) (:= X tptp.a)))
% 26.53/26.72  (step t235.t2 (cl (not (forall ((Xf $$unsorted) (X $$unsorted)) (or (not (tptp.function Xf)) (not (tptp.member X (tptp.domain_of Xf))) (tptp.member (tptp.ordered_pair X (tptp.apply Xf X)) Xf)))) (or (not (tptp.function tptp.a_function)) (not (tptp.member tptp.a (tptp.domain_of tptp.a_function))) (tptp.member (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)) tptp.a_function))) :rule or :premises (t235.t1))
% 26.53/26.72  (step t235.t3 (cl (or (not (tptp.function tptp.a_function)) (not (tptp.member tptp.a (tptp.domain_of tptp.a_function))) (tptp.member (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)) tptp.a_function))) :rule resolution :premises (t235.t2 t235.a0))
% 26.53/26.72  (step t235 (cl (not (forall ((Xf $$unsorted) (X $$unsorted)) (or (not (tptp.function Xf)) (not (tptp.member X (tptp.domain_of Xf))) (tptp.member (tptp.ordered_pair X (tptp.apply Xf X)) Xf)))) (or (not (tptp.function tptp.a_function)) (not (tptp.member tptp.a (tptp.domain_of tptp.a_function))) (tptp.member (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)) tptp.a_function))) :rule subproof :discharge (t235.a0))
% 26.53/26.72  (step t236 (cl (=> (forall ((Xf $$unsorted) (X $$unsorted)) (or (not (tptp.function Xf)) (not (tptp.member X (tptp.domain_of Xf))) (tptp.member (tptp.ordered_pair X (tptp.apply Xf X)) Xf))) (or (not (tptp.function tptp.a_function)) (not (tptp.member tptp.a (tptp.domain_of tptp.a_function))) (tptp.member (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)) tptp.a_function))) (or (not (tptp.function tptp.a_function)) (not (tptp.member tptp.a (tptp.domain_of tptp.a_function))) (tptp.member (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)) tptp.a_function))) :rule resolution :premises (t234 t235))
% 26.53/26.72  (step t237 (cl (=> (forall ((Xf $$unsorted) (X $$unsorted)) (or (not (tptp.function Xf)) (not (tptp.member X (tptp.domain_of Xf))) (tptp.member (tptp.ordered_pair X (tptp.apply Xf X)) Xf))) (or (not (tptp.function tptp.a_function)) (not (tptp.member tptp.a (tptp.domain_of tptp.a_function))) (tptp.member (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)) tptp.a_function))) (not (or (not (tptp.function tptp.a_function)) (not (tptp.member tptp.a (tptp.domain_of tptp.a_function))) (tptp.member (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)) tptp.a_function)))) :rule implies_neg2)
% 26.53/26.72  (step t238 (cl (=> (forall ((Xf $$unsorted) (X $$unsorted)) (or (not (tptp.function Xf)) (not (tptp.member X (tptp.domain_of Xf))) (tptp.member (tptp.ordered_pair X (tptp.apply Xf X)) Xf))) (or (not (tptp.function tptp.a_function)) (not (tptp.member tptp.a (tptp.domain_of tptp.a_function))) (tptp.member (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)) tptp.a_function))) (=> (forall ((Xf $$unsorted) (X $$unsorted)) (or (not (tptp.function Xf)) (not (tptp.member X (tptp.domain_of Xf))) (tptp.member (tptp.ordered_pair X (tptp.apply Xf X)) Xf))) (or (not (tptp.function tptp.a_function)) (not (tptp.member tptp.a (tptp.domain_of tptp.a_function))) (tptp.member (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)) tptp.a_function)))) :rule resolution :premises (t236 t237))
% 26.53/26.72  (step t239 (cl (=> (forall ((Xf $$unsorted) (X $$unsorted)) (or (not (tptp.function Xf)) (not (tptp.member X (tptp.domain_of Xf))) (tptp.member (tptp.ordered_pair X (tptp.apply Xf X)) Xf))) (or (not (tptp.function tptp.a_function)) (not (tptp.member tptp.a (tptp.domain_of tptp.a_function))) (tptp.member (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)) tptp.a_function)))) :rule contraction :premises (t238))
% 26.53/26.72  (step t240 (cl (not (forall ((Xf $$unsorted) (X $$unsorted)) (or (not (tptp.function Xf)) (not (tptp.member X (tptp.domain_of Xf))) (tptp.member (tptp.ordered_pair X (tptp.apply Xf X)) Xf)))) (or (not (tptp.function tptp.a_function)) (not (tptp.member tptp.a (tptp.domain_of tptp.a_function))) (tptp.member (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)) tptp.a_function))) :rule implies :premises (t239))
% 26.53/26.72  (step t241 (cl (not (= (forall ((Xf $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.function Xf)) (not (tptp.member X (tptp.domain_of Xf))) (not (= (tptp.apply Xf X) Y)) (tptp.member (tptp.ordered_pair X Y) Xf))) (forall ((Xf $$unsorted) (X $$unsorted)) (or (not (tptp.function Xf)) (not (tptp.member X (tptp.domain_of Xf))) (tptp.member (tptp.ordered_pair X (tptp.apply Xf X)) Xf))))) (not (forall ((Xf $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.function Xf)) (not (tptp.member X (tptp.domain_of Xf))) (not (= (tptp.apply Xf X) Y)) (tptp.member (tptp.ordered_pair X Y) Xf)))) (forall ((Xf $$unsorted) (X $$unsorted)) (or (not (tptp.function Xf)) (not (tptp.member X (tptp.domain_of Xf))) (tptp.member (tptp.ordered_pair X (tptp.apply Xf X)) Xf)))) :rule equiv_pos2)
% 26.53/26.72  (anchor :step t242 :args ((Xf $$unsorted) (:= Xf Xf) (X $$unsorted) (:= X X) (Y $$unsorted) (:= Y Y)))
% 26.53/26.72  (step t242.t1 (cl (= Xf Xf)) :rule refl)
% 26.53/26.72  (step t242.t2 (cl (= X X)) :rule refl)
% 26.53/26.72  (step t242.t3 (cl (= Y Y)) :rule refl)
% 26.53/26.72  (step t242.t4 (cl (= (not (tptp.function Xf)) (not (tptp.function Xf)))) :rule refl)
% 26.53/26.72  (step t242.t5 (cl (= (not (tptp.member X (tptp.domain_of Xf))) (not (tptp.member X (tptp.domain_of Xf))))) :rule refl)
% 26.53/26.72  (step t242.t6 (cl (= (= (tptp.apply Xf X) Y) (= Y (tptp.apply Xf X)))) :rule all_simplify)
% 26.53/26.72  (step t242.t7 (cl (= (not (= (tptp.apply Xf X) Y)) (not (= Y (tptp.apply Xf X))))) :rule cong :premises (t242.t6))
% 26.53/26.72  (step t242.t8 (cl (= (tptp.member (tptp.ordered_pair X Y) Xf) (tptp.member (tptp.ordered_pair X Y) Xf))) :rule refl)
% 26.53/26.72  (step t242.t9 (cl (= (or (not (tptp.function Xf)) (not (tptp.member X (tptp.domain_of Xf))) (not (= (tptp.apply Xf X) Y)) (tptp.member (tptp.ordered_pair X Y) Xf)) (or (not (tptp.function Xf)) (not (tptp.member X (tptp.domain_of Xf))) (not (= Y (tptp.apply Xf X))) (tptp.member (tptp.ordered_pair X Y) Xf)))) :rule cong :premises (t242.t4 t242.t5 t242.t7 t242.t8))
% 26.53/26.72  (step t242 (cl (= (forall ((Xf $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.function Xf)) (not (tptp.member X (tptp.domain_of Xf))) (not (= (tptp.apply Xf X) Y)) (tptp.member (tptp.ordered_pair X Y) Xf))) (forall ((Xf $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.function Xf)) (not (tptp.member X (tptp.domain_of Xf))) (not (= Y (tptp.apply Xf X))) (tptp.member (tptp.ordered_pair X Y) Xf))))) :rule bind)
% 26.53/26.72  (step t243 (cl (= (forall ((Xf $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.function Xf)) (not (tptp.member X (tptp.domain_of Xf))) (not (= Y (tptp.apply Xf X))) (tptp.member (tptp.ordered_pair X Y) Xf))) (forall ((Xf $$unsorted) (X $$unsorted)) (or (not (tptp.function Xf)) (not (tptp.member X (tptp.domain_of Xf))) (not (= (tptp.apply Xf X) (tptp.apply Xf X))) (tptp.member (tptp.ordered_pair X (tptp.apply Xf X)) Xf))))) :rule all_simplify)
% 26.53/26.72  (anchor :step t244 :args ((Xf $$unsorted) (:= Xf Xf) (X $$unsorted) (:= X X)))
% 26.53/26.72  (step t244.t1 (cl (= Xf Xf)) :rule refl)
% 26.53/26.72  (step t244.t2 (cl (= X X)) :rule refl)
% 26.53/26.72  (step t244.t3 (cl (= (not (tptp.function Xf)) (not (tptp.function Xf)))) :rule refl)
% 26.53/26.72  (step t244.t4 (cl (= (not (tptp.member X (tptp.domain_of Xf))) (not (tptp.member X (tptp.domain_of Xf))))) :rule refl)
% 26.53/26.72  (step t244.t5 (cl (= (= (tptp.apply Xf X) (tptp.apply Xf X)) true)) :rule all_simplify)
% 26.53/26.72  (step t244.t6 (cl (= (not (= (tptp.apply Xf X) (tptp.apply Xf X))) (not true))) :rule cong :premises (t244.t5))
% 26.53/26.72  (step t244.t7 (cl (= (not true) false)) :rule all_simplify)
% 26.53/26.72  (step t244.t8 (cl (= (not (= (tptp.apply Xf X) (tptp.apply Xf X))) false)) :rule trans :premises (t244.t6 t244.t7))
% 26.53/26.72  (step t244.t9 (cl (= (tptp.member (tptp.ordered_pair X (tptp.apply Xf X)) Xf) (tptp.member (tptp.ordered_pair X (tptp.apply Xf X)) Xf))) :rule refl)
% 26.53/26.72  (step t244.t10 (cl (= (or (not (tptp.function Xf)) (not (tptp.member X (tptp.domain_of Xf))) (not (= (tptp.apply Xf X) (tptp.apply Xf X))) (tptp.member (tptp.ordered_pair X (tptp.apply Xf X)) Xf)) (or (not (tptp.function Xf)) (not (tptp.member X (tptp.domain_of Xf))) false (tptp.member (tptp.ordered_pair X (tptp.apply Xf X)) Xf)))) :rule cong :premises (t244.t3 t244.t4 t244.t8 t244.t9))
% 26.53/26.72  (step t244.t11 (cl (= (or (not (tptp.function Xf)) (not (tptp.member X (tptp.domain_of Xf))) false (tptp.member (tptp.ordered_pair X (tptp.apply Xf X)) Xf)) (or (not (tptp.function Xf)) (not (tptp.member X (tptp.domain_of Xf))) (tptp.member (tptp.ordered_pair X (tptp.apply Xf X)) Xf)))) :rule all_simplify)
% 26.53/26.72  (step t244.t12 (cl (= (or (not (tptp.function Xf)) (not (tptp.member X (tptp.domain_of Xf))) (not (= (tptp.apply Xf X) (tptp.apply Xf X))) (tptp.member (tptp.ordered_pair X (tptp.apply Xf X)) Xf)) (or (not (tptp.function Xf)) (not (tptp.member X (tptp.domain_of Xf))) (tptp.member (tptp.ordered_pair X (tptp.apply Xf X)) Xf)))) :rule trans :premises (t244.t10 t244.t11))
% 26.53/26.72  (step t244 (cl (= (forall ((Xf $$unsorted) (X $$unsorted)) (or (not (tptp.function Xf)) (not (tptp.member X (tptp.domain_of Xf))) (not (= (tptp.apply Xf X) (tptp.apply Xf X))) (tptp.member (tptp.ordered_pair X (tptp.apply Xf X)) Xf))) (forall ((Xf $$unsorted) (X $$unsorted)) (or (not (tptp.function Xf)) (not (tptp.member X (tptp.domain_of Xf))) (tptp.member (tptp.ordered_pair X (tptp.apply Xf X)) Xf))))) :rule bind)
% 26.53/26.72  (step t245 (cl (= (forall ((Xf $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.function Xf)) (not (tptp.member X (tptp.domain_of Xf))) (not (= Y (tptp.apply Xf X))) (tptp.member (tptp.ordered_pair X Y) Xf))) (forall ((Xf $$unsorted) (X $$unsorted)) (or (not (tptp.function Xf)) (not (tptp.member X (tptp.domain_of Xf))) (tptp.member (tptp.ordered_pair X (tptp.apply Xf X)) Xf))))) :rule trans :premises (t243 t244))
% 26.53/26.72  (step t246 (cl (= (forall ((Xf $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.function Xf)) (not (tptp.member X (tptp.domain_of Xf))) (not (= (tptp.apply Xf X) Y)) (tptp.member (tptp.ordered_pair X Y) Xf))) (forall ((Xf $$unsorted) (X $$unsorted)) (or (not (tptp.function Xf)) (not (tptp.member X (tptp.domain_of Xf))) (tptp.member (tptp.ordered_pair X (tptp.apply Xf X)) Xf))))) :rule trans :premises (t242 t245))
% 26.53/26.72  (step t247 (cl (forall ((Xf $$unsorted) (X $$unsorted)) (or (not (tptp.function Xf)) (not (tptp.member X (tptp.domain_of Xf))) (tptp.member (tptp.ordered_pair X (tptp.apply Xf X)) Xf)))) :rule resolution :premises (t241 t246 a162))
% 26.53/26.72  (step t248 (cl (or (not (tptp.function tptp.a_function)) (not (tptp.member tptp.a (tptp.domain_of tptp.a_function))) (tptp.member (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)) tptp.a_function))) :rule resolution :premises (t240 t247))
% 26.53/26.72  (step t249 (cl (tptp.member (tptp.ordered_pair tptp.a (tptp.apply tptp.a_function tptp.a)) tptp.a_function)) :rule resolution :premises (t203 t66 t233 t248))
% 26.53/26.72  (step t250 (cl) :rule resolution :premises (t2 t157 t172 t185 t201 t249))
% 26.53/26.72  
% 26.53/26.72  % SZS output end Proof for /export/starexec/sandbox2/tmp/tmp.Se1txPSMwZ/cvc5---1.0.5_21104.smt2
% 26.53/26.73  % cvc5---1.0.5 exiting
% 26.53/26.73  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------