%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SET016-6 : TPTP v8.2.0. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : do_cvc5 %s %d

% Computer : n028.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 17:43:38 EDT 2024

% Result   : Unsatisfiable 25.67s 26.00s
% Output   : Proof 25.76s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : SET016-6 : TPTP v8.2.0. Bugfixed v2.1.0.
% 0.07/0.14  % Command    : do_cvc5 %s %d
% 0.14/0.35  % Computer : n028.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Tue May 28 10:43:09 EDT 2024
% 0.14/0.35  % CPUTime    : 
% 0.20/0.52  %----Proving TF0_NAR, FOF, or CNF
% 0.36/0.52  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 10.43/10.68  --- Run --no-e-matching --full-saturate-quant at 5...
% 15.49/15.76  --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 20.56/20.83  --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 25.63/25.90  --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 25.67/26.00  % SZS status Unsatisfiable for /export/starexec/sandbox/tmp/tmp.lE0e3d0pWC/cvc5---1.0.5_11112.smt2
% 25.67/26.00  % SZS output start Proof for /export/starexec/sandbox/tmp/tmp.lE0e3d0pWC/cvc5---1.0.5_11112.smt2
% 25.76/26.02  (assume a0 (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (not (tptp.subclass X Y)) (not (tptp.member U X)) (tptp.member U Y))))
% 25.76/26.02  (assume a1 (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.member (tptp.not_subclass_element X Y) X) (tptp.subclass X Y))))
% 25.76/26.02  (assume a2 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.not_subclass_element X Y) Y)) (tptp.subclass X Y))))
% 25.76/26.02  (assume a3 (forall ((X $$unsorted)) (tptp.subclass X tptp.universal_class)))
% 25.76/26.02  (assume a4 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= X Y)) (tptp.subclass X Y))))
% 25.76/26.02  (assume a5 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= X Y)) (tptp.subclass Y X))))
% 25.76/26.02  (assume a6 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.subclass X Y)) (not (tptp.subclass Y X)) (= X Y))))
% 25.76/26.02  (assume a7 (forall ((U $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member U (tptp.unordered_pair X Y))) (= U X) (= U Y))))
% 25.76/26.02  (assume a8 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (tptp.member X (tptp.unordered_pair X Y)))))
% 25.76/26.02  (assume a9 (forall ((Y $$unsorted) (X $$unsorted)) (or (not (tptp.member Y tptp.universal_class)) (tptp.member Y (tptp.unordered_pair X Y)))))
% 25.76/26.02  (assume a10 (forall ((X $$unsorted) (Y $$unsorted)) (tptp.member (tptp.unordered_pair X Y) tptp.universal_class)))
% 25.76/26.02  (assume a11 (forall ((X $$unsorted)) (= (tptp.unordered_pair X X) (tptp.singleton X))))
% 25.76/26.02  (assume a12 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.unordered_pair (tptp.singleton X) (tptp.unordered_pair X (tptp.singleton Y))) (tptp.ordered_pair X Y))))
% 25.76/26.02  (assume a13 (forall ((U $$unsorted) (V $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.ordered_pair U V) (tptp.cross_product X Y))) (tptp.member U X))))
% 25.76/26.02  (assume a14 (forall ((U $$unsorted) (V $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.ordered_pair U V) (tptp.cross_product X Y))) (tptp.member V Y))))
% 25.76/26.02  (assume a15 (forall ((U $$unsorted) (X $$unsorted) (V $$unsorted) (Y $$unsorted)) (or (not (tptp.member U X)) (not (tptp.member V Y)) (tptp.member (tptp.ordered_pair U V) (tptp.cross_product X Y)))))
% 25.76/26.02  (assume a16 (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.cross_product X Y))) (= (tptp.ordered_pair (tptp.first Z) (tptp.second Z)) Z))))
% 25.76/26.02  (assume a17 (tptp.subclass tptp.element_relation (tptp.cross_product tptp.universal_class tptp.universal_class)))
% 25.76/26.02  (assume a18 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.ordered_pair X Y) tptp.element_relation)) (tptp.member X Y))))
% 25.76/26.02  (assume a19 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.ordered_pair X Y) (tptp.cross_product tptp.universal_class tptp.universal_class))) (not (tptp.member X Y)) (tptp.member (tptp.ordered_pair X Y) tptp.element_relation))))
% 25.76/26.02  (assume a20 (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.intersection X Y))) (tptp.member Z X))))
% 25.76/26.02  (assume a21 (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.intersection X Y))) (tptp.member Z Y))))
% 25.76/26.02  (assume a22 (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z X)) (not (tptp.member Z Y)) (tptp.member Z (tptp.intersection X Y)))))
% 25.76/26.02  (assume a23 (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.complement X))) (not (tptp.member Z X)))))
% 25.76/26.02  (assume a24 (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z tptp.universal_class)) (tptp.member Z (tptp.complement X)) (tptp.member Z X))))
% 25.76/26.02  (assume a25 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.complement (tptp.intersection (tptp.complement X) (tptp.complement Y))) (tptp.union X Y))))
% 25.76/26.02  (assume a26 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.intersection (tptp.complement (tptp.intersection X Y)) (tptp.complement (tptp.intersection (tptp.complement X) (tptp.complement Y)))) (tptp.symmetric_difference X Y))))
% 25.76/26.02  (assume a27 (forall ((Xr $$unsorted) (X $$unsorted) (Y $$unsorted)) (= (tptp.intersection Xr (tptp.cross_product X Y)) (tptp.restrict Xr X Y))))
% 25.76/26.02  (assume a28 (forall ((X $$unsorted) (Y $$unsorted) (Xr $$unsorted)) (= (tptp.intersection (tptp.cross_product X Y) Xr) (tptp.restrict Xr X Y))))
% 25.76/26.02  (assume a29 (forall ((X $$unsorted) (Z $$unsorted)) (or (not (= (tptp.restrict X (tptp.singleton Z) tptp.universal_class) tptp.null_class)) (not (tptp.member Z (tptp.domain_of X))))))
% 25.76/26.02  (assume a30 (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z tptp.universal_class)) (= (tptp.restrict X (tptp.singleton Z) tptp.universal_class) tptp.null_class) (tptp.member Z (tptp.domain_of X)))))
% 25.76/26.02  (assume a31 (forall ((X $$unsorted)) (tptp.subclass (tptp.rotate X) (tptp.cross_product (tptp.cross_product tptp.universal_class tptp.universal_class) tptp.universal_class))))
% 25.76/26.02  (assume a32 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (or (not (tptp.member (tptp.ordered_pair (tptp.ordered_pair U V) W) (tptp.rotate X))) (tptp.member (tptp.ordered_pair (tptp.ordered_pair V W) U) X))))
% 25.76/26.02  (assume a33 (forall ((V $$unsorted) (W $$unsorted) (U $$unsorted) (X $$unsorted)) (or (not (tptp.member (tptp.ordered_pair (tptp.ordered_pair V W) U) X)) (not (tptp.member (tptp.ordered_pair (tptp.ordered_pair U V) W) (tptp.cross_product (tptp.cross_product tptp.universal_class tptp.universal_class) tptp.universal_class))) (tptp.member (tptp.ordered_pair (tptp.ordered_pair U V) W) (tptp.rotate X)))))
% 25.76/26.02  (assume a34 (forall ((X $$unsorted)) (tptp.subclass (tptp.flip X) (tptp.cross_product (tptp.cross_product tptp.universal_class tptp.universal_class) tptp.universal_class))))
% 25.76/26.02  (assume a35 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (or (not (tptp.member (tptp.ordered_pair (tptp.ordered_pair U V) W) (tptp.flip X))) (tptp.member (tptp.ordered_pair (tptp.ordered_pair V U) W) X))))
% 25.76/26.02  (assume a36 (forall ((V $$unsorted) (U $$unsorted) (W $$unsorted) (X $$unsorted)) (or (not (tptp.member (tptp.ordered_pair (tptp.ordered_pair V U) W) X)) (not (tptp.member (tptp.ordered_pair (tptp.ordered_pair U V) W) (tptp.cross_product (tptp.cross_product tptp.universal_class tptp.universal_class) tptp.universal_class))) (tptp.member (tptp.ordered_pair (tptp.ordered_pair U V) W) (tptp.flip X)))))
% 25.76/26.02  (assume a37 (forall ((Y $$unsorted)) (= (tptp.domain_of (tptp.flip (tptp.cross_product Y tptp.universal_class))) (tptp.inverse Y))))
% 25.76/26.02  (assume a38 (forall ((Z $$unsorted)) (= (tptp.domain_of (tptp.inverse Z)) (tptp.range_of Z))))
% 25.76/26.02  (assume a39 (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (= (tptp.first (tptp.not_subclass_element (tptp.restrict Z X (tptp.singleton Y)) tptp.null_class)) (tptp.domain Z X Y))))
% 25.76/26.02  (assume a40 (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (= (tptp.second (tptp.not_subclass_element (tptp.restrict Z (tptp.singleton X) Y) tptp.null_class)) (tptp.range Z X Y))))
% 25.76/26.02  (assume a41 (forall ((Xr $$unsorted) (X $$unsorted)) (= (tptp.range_of (tptp.restrict Xr X tptp.universal_class)) (tptp.image Xr X))))
% 25.76/26.02  (assume a42 (forall ((X $$unsorted)) (= (tptp.union X (tptp.singleton X)) (tptp.successor X))))
% 25.76/26.02  (assume a43 (tptp.subclass tptp.successor_relation (tptp.cross_product tptp.universal_class tptp.universal_class)))
% 25.76/26.02  (assume a44 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.ordered_pair X Y) tptp.successor_relation)) (= (tptp.successor X) Y))))
% 25.76/26.02  (assume a45 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= (tptp.successor X) Y)) (not (tptp.member (tptp.ordered_pair X Y) (tptp.cross_product tptp.universal_class tptp.universal_class))) (tptp.member (tptp.ordered_pair X Y) tptp.successor_relation))))
% 25.76/26.02  (assume a46 (forall ((X $$unsorted)) (or (not (tptp.inductive X)) (tptp.member tptp.null_class X))))
% 25.76/26.02  (assume a47 (forall ((X $$unsorted)) (or (not (tptp.inductive X)) (tptp.subclass (tptp.image tptp.successor_relation X) X))))
% 25.76/26.02  (assume a48 (forall ((X $$unsorted)) (or (not (tptp.member tptp.null_class X)) (not (tptp.subclass (tptp.image tptp.successor_relation X) X)) (tptp.inductive X))))
% 25.76/26.02  (assume a49 (tptp.inductive tptp.omega))
% 25.76/26.02  (assume a50 (forall ((Y $$unsorted)) (or (not (tptp.inductive Y)) (tptp.subclass tptp.omega Y))))
% 25.76/26.02  (assume a51 (tptp.member tptp.omega tptp.universal_class))
% 25.76/26.02  (assume a52 (forall ((X $$unsorted)) (= (tptp.domain_of (tptp.restrict tptp.element_relation tptp.universal_class X)) (tptp.sum_class X))))
% 25.76/26.02  (assume a53 (forall ((X $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (tptp.member (tptp.sum_class X) tptp.universal_class))))
% 25.76/26.02  (assume a54 (forall ((X $$unsorted)) (= (tptp.complement (tptp.image tptp.element_relation (tptp.complement X))) (tptp.power_class X))))
% 25.76/26.02  (assume a55 (forall ((U $$unsorted)) (or (not (tptp.member U tptp.universal_class)) (tptp.member (tptp.power_class U) tptp.universal_class))))
% 25.76/26.02  (assume a56 (forall ((Yr $$unsorted) (Xr $$unsorted)) (tptp.subclass (tptp.compose Yr Xr) (tptp.cross_product tptp.universal_class tptp.universal_class))))
% 25.76/26.02  (assume a57 (forall ((Y $$unsorted) (Z $$unsorted) (Yr $$unsorted) (Xr $$unsorted)) (or (not (tptp.member (tptp.ordered_pair Y Z) (tptp.compose Yr Xr))) (tptp.member Z (tptp.image Yr (tptp.image Xr (tptp.singleton Y)))))))
% 25.76/26.02  (assume a58 (forall ((Z $$unsorted) (Yr $$unsorted) (Xr $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.image Yr (tptp.image Xr (tptp.singleton Y))))) (not (tptp.member (tptp.ordered_pair Y Z) (tptp.cross_product tptp.universal_class tptp.universal_class))) (tptp.member (tptp.ordered_pair Y Z) (tptp.compose Yr Xr)))))
% 25.76/26.02  (assume a59 (forall ((X $$unsorted)) (or (not (tptp.single_valued_class X)) (tptp.subclass (tptp.compose X (tptp.inverse X)) tptp.identity_relation))))
% 25.76/26.02  (assume a60 (forall ((X $$unsorted)) (or (not (tptp.subclass (tptp.compose X (tptp.inverse X)) tptp.identity_relation)) (tptp.single_valued_class X))))
% 25.76/26.02  (assume a61 (forall ((Xf $$unsorted)) (or (not (tptp.function Xf)) (tptp.subclass Xf (tptp.cross_product tptp.universal_class tptp.universal_class)))))
% 25.76/26.02  (assume a62 (forall ((Xf $$unsorted)) (or (not (tptp.function Xf)) (tptp.subclass (tptp.compose Xf (tptp.inverse Xf)) tptp.identity_relation))))
% 25.76/26.02  (assume a63 (forall ((Xf $$unsorted)) (or (not (tptp.subclass Xf (tptp.cross_product tptp.universal_class tptp.universal_class))) (not (tptp.subclass (tptp.compose Xf (tptp.inverse Xf)) tptp.identity_relation)) (tptp.function Xf))))
% 25.76/26.02  (assume a64 (forall ((Xf $$unsorted) (X $$unsorted)) (or (not (tptp.function Xf)) (not (tptp.member X tptp.universal_class)) (tptp.member (tptp.image Xf X) tptp.universal_class))))
% 25.76/26.02  (assume a65 (forall ((X $$unsorted)) (or (= X tptp.null_class) (tptp.member (tptp.regular X) X))))
% 25.76/26.02  (assume a66 (forall ((X $$unsorted)) (or (= X tptp.null_class) (= (tptp.intersection X (tptp.regular X)) tptp.null_class))))
% 25.76/26.02  (assume a67 (forall ((Xf $$unsorted) (Y $$unsorted)) (= (tptp.sum_class (tptp.image Xf (tptp.singleton Y))) (tptp.apply Xf Y))))
% 25.76/26.02  (assume a68 (tptp.function tptp.choice))
% 25.76/26.02  (assume a69 (forall ((Y $$unsorted)) (or (not (tptp.member Y tptp.universal_class)) (= Y tptp.null_class) (tptp.member (tptp.apply tptp.choice Y) Y))))
% 25.76/26.02  (assume a70 (forall ((Xf $$unsorted)) (or (not (tptp.one_to_one Xf)) (tptp.function Xf))))
% 25.76/26.02  (assume a71 (forall ((Xf $$unsorted)) (or (not (tptp.one_to_one Xf)) (tptp.function (tptp.inverse Xf)))))
% 25.76/26.02  (assume a72 (forall ((Xf $$unsorted)) (or (not (tptp.function (tptp.inverse Xf))) (not (tptp.function Xf)) (tptp.one_to_one Xf))))
% 25.76/26.02  (assume a73 (= (tptp.intersection (tptp.cross_product tptp.universal_class tptp.universal_class) (tptp.intersection (tptp.cross_product tptp.universal_class tptp.universal_class) (tptp.complement (tptp.compose (tptp.complement tptp.element_relation) (tptp.inverse tptp.element_relation))))) tptp.subset_relation))
% 25.76/26.02  (assume a74 (= (tptp.intersection (tptp.inverse tptp.subset_relation) tptp.subset_relation) tptp.identity_relation))
% 25.76/26.02  (assume a75 (forall ((Xr $$unsorted)) (= (tptp.complement (tptp.domain_of (tptp.intersection Xr tptp.identity_relation))) (tptp.diagonalise Xr))))
% 25.76/26.02  (assume a76 (forall ((X $$unsorted)) (= (tptp.intersection (tptp.domain_of X) (tptp.diagonalise (tptp.compose (tptp.inverse tptp.element_relation) X))) (tptp.cantor X))))
% 25.76/26.02  (assume a77 (forall ((Xf $$unsorted)) (or (not (tptp.operation Xf)) (tptp.function Xf))))
% 25.76/26.02  (assume a78 (forall ((Xf $$unsorted)) (or (not (tptp.operation Xf)) (= (tptp.cross_product (tptp.domain_of (tptp.domain_of Xf)) (tptp.domain_of (tptp.domain_of Xf))) (tptp.domain_of Xf)))))
% 25.76/26.02  (assume a79 (forall ((Xf $$unsorted)) (or (not (tptp.operation Xf)) (tptp.subclass (tptp.range_of Xf) (tptp.domain_of (tptp.domain_of Xf))))))
% 25.76/26.02  (assume a80 (forall ((Xf $$unsorted)) (or (not (tptp.function Xf)) (not (= (tptp.cross_product (tptp.domain_of (tptp.domain_of Xf)) (tptp.domain_of (tptp.domain_of Xf))) (tptp.domain_of Xf))) (not (tptp.subclass (tptp.range_of Xf) (tptp.domain_of (tptp.domain_of Xf)))) (tptp.operation Xf))))
% 25.76/26.02  (assume a81 (forall ((Xh $$unsorted) (Xf1 $$unsorted) (Xf2 $$unsorted)) (or (not (tptp.compatible Xh Xf1 Xf2)) (tptp.function Xh))))
% 25.76/26.02  (assume a82 (forall ((Xh $$unsorted) (Xf1 $$unsorted) (Xf2 $$unsorted)) (or (not (tptp.compatible Xh Xf1 Xf2)) (= (tptp.domain_of (tptp.domain_of Xf1)) (tptp.domain_of Xh)))))
% 25.76/26.02  (assume a83 (forall ((Xh $$unsorted) (Xf1 $$unsorted) (Xf2 $$unsorted)) (or (not (tptp.compatible Xh Xf1 Xf2)) (tptp.subclass (tptp.range_of Xh) (tptp.domain_of (tptp.domain_of Xf2))))))
% 25.76/26.02  (assume a84 (forall ((Xh $$unsorted) (Xf1 $$unsorted) (Xf2 $$unsorted)) (or (not (tptp.function Xh)) (not (= (tptp.domain_of (tptp.domain_of Xf1)) (tptp.domain_of Xh))) (not (tptp.subclass (tptp.range_of Xh) (tptp.domain_of (tptp.domain_of Xf2)))) (tptp.compatible Xh Xf1 Xf2))))
% 25.76/26.02  (assume a85 (forall ((Xh $$unsorted) (Xf1 $$unsorted) (Xf2 $$unsorted)) (or (not (tptp.homomorphism Xh Xf1 Xf2)) (tptp.operation Xf1))))
% 25.76/26.02  (assume a86 (forall ((Xh $$unsorted) (Xf1 $$unsorted) (Xf2 $$unsorted)) (or (not (tptp.homomorphism Xh Xf1 Xf2)) (tptp.operation Xf2))))
% 25.76/26.02  (assume a87 (forall ((Xh $$unsorted) (Xf1 $$unsorted) (Xf2 $$unsorted)) (or (not (tptp.homomorphism Xh Xf1 Xf2)) (tptp.compatible Xh Xf1 Xf2))))
% 25.76/26.02  (assume a88 (forall ((Xh $$unsorted) (Xf1 $$unsorted) (Xf2 $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.homomorphism Xh Xf1 Xf2)) (not (tptp.member (tptp.ordered_pair X Y) (tptp.domain_of Xf1))) (= (tptp.apply Xf2 (tptp.ordered_pair (tptp.apply Xh X) (tptp.apply Xh Y))) (tptp.apply Xh (tptp.apply Xf1 (tptp.ordered_pair X Y)))))))
% 25.76/26.02  (assume a89 (forall ((Xf1 $$unsorted) (Xf2 $$unsorted) (Xh $$unsorted)) (or (not (tptp.operation Xf1)) (not (tptp.operation Xf2)) (not (tptp.compatible Xh Xf1 Xf2)) (tptp.member (tptp.ordered_pair (tptp.not_homomorphism1 Xh Xf1 Xf2) (tptp.not_homomorphism2 Xh Xf1 Xf2)) (tptp.domain_of Xf1)) (tptp.homomorphism Xh Xf1 Xf2))))
% 25.76/26.02  (assume a90 (forall ((Xf1 $$unsorted) (Xf2 $$unsorted) (Xh $$unsorted)) (or (not (tptp.operation Xf1)) (not (tptp.operation Xf2)) (not (tptp.compatible Xh Xf1 Xf2)) (not (= (tptp.apply Xf2 (tptp.ordered_pair (tptp.apply Xh (tptp.not_homomorphism1 Xh Xf1 Xf2)) (tptp.apply Xh (tptp.not_homomorphism2 Xh Xf1 Xf2)))) (tptp.apply Xh (tptp.apply Xf1 (tptp.ordered_pair (tptp.not_homomorphism1 Xh Xf1 Xf2) (tptp.not_homomorphism2 Xh Xf1 Xf2)))))) (tptp.homomorphism Xh Xf1 Xf2))))
% 25.76/26.02  (assume a91 (= (tptp.ordered_pair tptp.w tptp.x) (tptp.ordered_pair tptp.y tptp.z)))
% 25.76/26.02  (assume a92 (tptp.member tptp.w tptp.universal_class))
% 25.76/26.02  (assume a93 (not (= tptp.w tptp.y)))
% 25.76/26.02  (step t1 (cl (not (= (or (not (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w))) (not (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y))) (not (= (tptp.singleton tptp.w) (tptp.singleton tptp.y))) (not (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y)))) (not (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)))) (or (not (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w))) (not (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y))) (not (= (tptp.singleton tptp.w) (tptp.singleton tptp.y))) (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)))))) (not (or (not (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w))) (not (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y))) (not (= (tptp.singleton tptp.w) (tptp.singleton tptp.y))) (not (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y)))) (not (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w))))) (or (not (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w))) (not (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y))) (not (= (tptp.singleton tptp.w) (tptp.singleton tptp.y))) (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w))))) :rule equiv_pos2)
% 25.76/26.02  (step t2 (cl (= (not (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w))) (not (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w))))) :rule refl)
% 25.76/26.02  (step t3 (cl (= (not (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y))) (not (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y))))) :rule refl)
% 25.76/26.02  (step t4 (cl (= (not (= (tptp.singleton tptp.w) (tptp.singleton tptp.y))) (not (= (tptp.singleton tptp.w) (tptp.singleton tptp.y))))) :rule refl)
% 25.76/26.02  (step t5 (cl (= (= (= (not (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y)))) (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) true) (= (not (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y)))) (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))))) :rule equiv_simplify)
% 25.76/26.02  (step t6 (cl (not (= (= (not (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y)))) (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) true)) (= (not (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y)))) (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y)))) :rule equiv1 :premises (t5))
% 25.76/26.02  (step t7 (cl (= (= (not (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y)))) (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (= (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y)) (not (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))))))) :rule all_simplify)
% 25.76/26.02  (step t8 (cl (= (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y)) (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y)))) :rule refl)
% 25.76/26.02  (step t9 (cl (= (not (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y)))) (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y)))) :rule all_simplify)
% 25.76/26.02  (step t10 (cl (= (= (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y)) (not (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))))) (= (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y)) (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))))) :rule cong :premises (t8 t9))
% 25.76/26.02  (step t11 (cl (= (= (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y)) (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) true)) :rule all_simplify)
% 25.76/26.02  (step t12 (cl (= (= (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y)) (not (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))))) true)) :rule trans :premises (t10 t11))
% 25.76/26.02  (step t13 (cl (= (= (not (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y)))) (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) true)) :rule trans :premises (t7 t12))
% 25.76/26.02  (step t14 (cl (= (not (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y)))) (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y)))) :rule resolution :premises (t6 t13))
% 25.76/26.02  (step t15 (cl (= (not (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w))) (not (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w))))) :rule refl)
% 25.76/26.02  (step t16 (cl (= (or (not (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w))) (not (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y))) (not (= (tptp.singleton tptp.w) (tptp.singleton tptp.y))) (not (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y)))) (not (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)))) (or (not (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w))) (not (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y))) (not (= (tptp.singleton tptp.w) (tptp.singleton tptp.y))) (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)))))) :rule cong :premises (t2 t3 t4 t14 t15))
% 25.76/26.02  (step t17 (cl (not (= (=> (and (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.singleton tptp.w) (tptp.singleton tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w))) (and (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.singleton tptp.y)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))))) (not (and (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.singleton tptp.w) (tptp.singleton tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)))))) (not (=> (and (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.singleton tptp.w) (tptp.singleton tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w))) (and (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.singleton tptp.y)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y)))))) (not (and (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.singleton tptp.w) (tptp.singleton tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w))))) :rule equiv_pos2)
% 25.76/26.02  (step t18 (cl (= (and (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.singleton tptp.w) (tptp.singleton tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w))) (and (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.singleton tptp.w) (tptp.singleton tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w))))) :rule refl)
% 25.76/26.02  (step t19 (cl (= (= (and (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.singleton tptp.y)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y)))) false) (not (and (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.singleton tptp.y)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))))))) :rule equiv_simplify)
% 25.76/26.02  (step t20 (cl (= (and (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.singleton tptp.y)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y)))) false) (not (not (and (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.singleton tptp.y)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))))))) :rule equiv2 :premises (t19))
% 25.76/26.02  (step t21 (cl (not (not (not (and (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.singleton tptp.y)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))))))) (and (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.singleton tptp.y)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))))) :rule not_not)
% 25.76/26.02  (step t22 (cl (= (and (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.singleton tptp.y)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y)))) false) (and (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.singleton tptp.y)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))))) :rule resolution :premises (t20 t21))
% 25.76/26.02  (step t23 (cl (=> (and (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.singleton tptp.y)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y)))) false) (and (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.singleton tptp.y)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))))) :rule implies_neg1)
% 25.76/26.02  (anchor :step t24)
% 25.76/26.02  (assume t24.a0 (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)))
% 25.76/26.02  (assume t24.a1 (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w)))
% 25.76/26.02  (assume t24.a2 (= (tptp.singleton tptp.w) (tptp.singleton tptp.y)))
% 25.76/26.02  (assume t24.a3 (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)))
% 25.76/26.02  (assume t24.a4 (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))))
% 25.76/26.02  (step t24.t1 (cl (not (= (= false true) false)) (not (= false true)) false) :rule equiv_pos2)
% 25.76/26.02  (step t24.t2 (cl (= (= false true) false)) :rule all_simplify)
% 25.76/26.02  (step t24.t3 (cl (= (= (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y)) false) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))))) :rule equiv_simplify)
% 25.76/26.02  (step t24.t4 (cl (= (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y)) false) (not (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))))) :rule equiv2 :premises (t24.t3))
% 25.76/26.02  (step t24.t5 (cl (not (not (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))))) (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) :rule not_not)
% 25.76/26.02  (step t24.t6 (cl (= (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y)) false) (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) :rule resolution :premises (t24.t4 t24.t5))
% 25.76/26.02  (step t24.t7 (cl (= (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y)) false)) :rule resolution :premises (t24.t6 t24.a4))
% 25.76/26.02  (step t24.t8 (cl (= false (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y)))) :rule symm :premises (t24.t7))
% 25.76/26.02  (step t24.t9 (cl (= tptp.w tptp.w)) :rule refl)
% 25.76/26.02  (step t24.t10 (cl (= (tptp.unordered_pair tptp.y tptp.y) (tptp.singleton tptp.y))) :rule symm :premises (t24.a3))
% 25.76/26.02  (step t24.t11 (cl (= (tptp.singleton tptp.y) (tptp.singleton tptp.w))) :rule symm :premises (t24.a2))
% 25.76/26.02  (step t24.t12 (cl (= (tptp.unordered_pair tptp.w tptp.w) (tptp.singleton tptp.w))) :rule symm :premises (t24.a1))
% 25.76/26.02  (step t24.t13 (cl (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w))) :rule symm :premises (t24.t12))
% 25.76/26.02  (step t24.t14 (cl (= (tptp.unordered_pair tptp.y tptp.y) (tptp.unordered_pair tptp.w tptp.w))) :rule trans :premises (t24.t10 t24.t11 t24.t13))
% 25.76/26.02  (step t24.t15 (cl (= (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y)) (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)))) :rule cong :premises (t24.t9 t24.t14))
% 25.76/26.02  (step t24.t16 (cl (= (= (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)) true) (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)))) :rule equiv_simplify)
% 25.76/26.02  (step t24.t17 (cl (= (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)) true) (not (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)))) :rule equiv2 :premises (t24.t16))
% 25.76/26.02  (step t24.t18 (cl (= (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)) true)) :rule resolution :premises (t24.t17 t24.a0))
% 25.76/26.02  (step t24.t19 (cl (= false true)) :rule trans :premises (t24.t8 t24.t15 t24.t18))
% 25.76/26.02  (step t24.t20 (cl false) :rule resolution :premises (t24.t1 t24.t2 t24.t19))
% 25.76/26.02  (step t24 (cl (not (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w))) (not (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w))) (not (= (tptp.singleton tptp.w) (tptp.singleton tptp.y))) (not (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y))) (not (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y)))) false) :rule subproof :discharge (t24.a0 t24.a1 t24.a2 t24.a3 t24.a4))
% 25.76/26.02  (step t25 (cl (not (and (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.singleton tptp.y)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))))) (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w))) :rule and_pos)
% 25.76/26.02  (step t26 (cl (not (and (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.singleton tptp.y)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))))) (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w))) :rule and_pos)
% 25.76/26.02  (step t27 (cl (not (and (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.singleton tptp.y)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))))) (= (tptp.singleton tptp.w) (tptp.singleton tptp.y))) :rule and_pos)
% 25.76/26.02  (step t28 (cl (not (and (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.singleton tptp.y)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y))) :rule and_pos)
% 25.76/26.02  (step t29 (cl (not (and (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.singleton tptp.y)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))))) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y)))) :rule and_pos)
% 25.76/26.02  (step t30 (cl false (not (and (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.singleton tptp.y)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))))) (not (and (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.singleton tptp.y)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))))) (not (and (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.singleton tptp.y)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))))) (not (and (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.singleton tptp.y)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))))) (not (and (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.singleton tptp.y)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y)))))) :rule resolution :premises (t24 t25 t26 t27 t28 t29))
% 25.76/26.02  (step t31 (cl (not (and (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.singleton tptp.y)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))))) (not (and (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.singleton tptp.y)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))))) (not (and (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.singleton tptp.y)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))))) (not (and (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.singleton tptp.y)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))))) (not (and (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.singleton tptp.y)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))))) false) :rule reordering :premises (t30))
% 25.76/26.02  (step t32 (cl (not (and (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.singleton tptp.y)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))))) false) :rule contraction :premises (t31))
% 25.76/26.02  (step t33 (cl (=> (and (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.singleton tptp.y)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y)))) false) false) :rule resolution :premises (t23 t32))
% 25.76/26.02  (step t34 (cl (=> (and (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.singleton tptp.y)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y)))) false) (not false)) :rule implies_neg2)
% 25.76/26.02  (step t35 (cl (=> (and (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.singleton tptp.y)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y)))) false) (=> (and (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.singleton tptp.y)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y)))) false)) :rule resolution :premises (t33 t34))
% 25.76/26.02  (step t36 (cl (=> (and (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.singleton tptp.y)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y)))) false)) :rule contraction :premises (t35))
% 25.76/26.02  (step t37 (cl (= (=> (and (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.singleton tptp.y)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y)))) false) (not (and (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.singleton tptp.y)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))))))) :rule implies_simplify)
% 25.76/26.02  (step t38 (cl (not (=> (and (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.singleton tptp.y)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y)))) false)) (not (and (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.singleton tptp.y)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y)))))) :rule equiv1 :premises (t37))
% 25.76/26.02  (step t39 (cl (not (and (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.singleton tptp.y)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y)))))) :rule resolution :premises (t36 t38))
% 25.76/26.02  (step t40 (cl (= (and (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.singleton tptp.y)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y)))) false)) :rule resolution :premises (t22 t39))
% 25.76/26.02  (step t41 (cl (= (=> (and (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.singleton tptp.w) (tptp.singleton tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w))) (and (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.singleton tptp.y)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))))) (=> (and (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.singleton tptp.w) (tptp.singleton tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w))) false))) :rule cong :premises (t18 t40))
% 25.76/26.02  (step t42 (cl (= (=> (and (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.singleton tptp.w) (tptp.singleton tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w))) false) (not (and (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.singleton tptp.w) (tptp.singleton tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)))))) :rule all_simplify)
% 25.76/26.02  (step t43 (cl (= (=> (and (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.singleton tptp.w) (tptp.singleton tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w))) (and (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.singleton tptp.y)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))))) (not (and (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.singleton tptp.w) (tptp.singleton tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)))))) :rule trans :premises (t41 t42))
% 25.76/26.02  (step t44 (cl (=> (and (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.singleton tptp.w) (tptp.singleton tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w))) (and (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.singleton tptp.y)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))))) (and (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.singleton tptp.w) (tptp.singleton tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)))) :rule implies_neg1)
% 25.76/26.02  (anchor :step t45)
% 25.76/26.02  (assume t45.a0 (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w)))
% 25.76/26.02  (assume t45.a1 (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)))
% 25.76/26.02  (assume t45.a2 (= (tptp.singleton tptp.w) (tptp.singleton tptp.y)))
% 25.76/26.02  (assume t45.a3 (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))))
% 25.76/26.02  (assume t45.a4 (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)))
% 25.76/26.02  (step t45.t1 (cl (and (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.singleton tptp.y)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y)))) (not (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w))) (not (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w))) (not (= (tptp.singleton tptp.w) (tptp.singleton tptp.y))) (not (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y))) (not (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))))) :rule and_neg)
% 25.76/26.02  (step t45.t2 (cl (and (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.singleton tptp.y)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))))) :rule resolution :premises (t45.t1 t45.a4 t45.a0 t45.a2 t45.a1 t45.a3))
% 25.76/26.02  (step t45 (cl (not (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w))) (not (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y))) (not (= (tptp.singleton tptp.w) (tptp.singleton tptp.y))) (not (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y)))) (not (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w))) (and (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.singleton tptp.y)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))))) :rule subproof :discharge (t45.a0 t45.a1 t45.a2 t45.a3 t45.a4))
% 25.76/26.02  (step t46 (cl (not (and (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.singleton tptp.w) (tptp.singleton tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)))) (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w))) :rule and_pos)
% 25.76/26.02  (step t47 (cl (not (and (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.singleton tptp.w) (tptp.singleton tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y))) :rule and_pos)
% 25.76/26.02  (step t48 (cl (not (and (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.singleton tptp.w) (tptp.singleton tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)))) (= (tptp.singleton tptp.w) (tptp.singleton tptp.y))) :rule and_pos)
% 25.76/26.02  (step t49 (cl (not (and (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.singleton tptp.w) (tptp.singleton tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)))) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y)))) :rule and_pos)
% 25.76/26.02  (step t50 (cl (not (and (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.singleton tptp.w) (tptp.singleton tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)))) (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w))) :rule and_pos)
% 25.76/26.02  (step t51 (cl (and (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.singleton tptp.y)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y)))) (not (and (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.singleton tptp.w) (tptp.singleton tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)))) (not (and (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.singleton tptp.w) (tptp.singleton tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)))) (not (and (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.singleton tptp.w) (tptp.singleton tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)))) (not (and (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.singleton tptp.w) (tptp.singleton tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)))) (not (and (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.singleton tptp.w) (tptp.singleton tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w))))) :rule resolution :premises (t45 t46 t47 t48 t49 t50))
% 25.76/26.02  (step t52 (cl (not (and (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.singleton tptp.w) (tptp.singleton tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)))) (not (and (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.singleton tptp.w) (tptp.singleton tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)))) (not (and (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.singleton tptp.w) (tptp.singleton tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)))) (not (and (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.singleton tptp.w) (tptp.singleton tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)))) (not (and (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.singleton tptp.w) (tptp.singleton tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)))) (and (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.singleton tptp.y)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))))) :rule reordering :premises (t51))
% 25.76/26.02  (step t53 (cl (not (and (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.singleton tptp.w) (tptp.singleton tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)))) (and (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.singleton tptp.y)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))))) :rule contraction :premises (t52))
% 25.76/26.02  (step t54 (cl (=> (and (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.singleton tptp.w) (tptp.singleton tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w))) (and (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.singleton tptp.y)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))))) (and (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.singleton tptp.y)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))))) :rule resolution :premises (t44 t53))
% 25.76/26.02  (step t55 (cl (=> (and (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.singleton tptp.w) (tptp.singleton tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w))) (and (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.singleton tptp.y)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))))) (not (and (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.singleton tptp.y)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y)))))) :rule implies_neg2)
% 25.76/26.02  (step t56 (cl (=> (and (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.singleton tptp.w) (tptp.singleton tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w))) (and (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.singleton tptp.y)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))))) (=> (and (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.singleton tptp.w) (tptp.singleton tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w))) (and (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.singleton tptp.y)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y)))))) :rule resolution :premises (t54 t55))
% 25.76/26.02  (step t57 (cl (=> (and (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.singleton tptp.w) (tptp.singleton tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w))) (and (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.w) (tptp.singleton tptp.y)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y)))))) :rule contraction :premises (t56))
% 25.76/26.02  (step t58 (cl (not (and (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.singleton tptp.w) (tptp.singleton tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w))))) :rule resolution :premises (t17 t43 t57))
% 25.76/26.02  (step t59 (cl (not (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w))) (not (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y))) (not (= (tptp.singleton tptp.w) (tptp.singleton tptp.y))) (not (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y)))) (not (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)))) :rule not_and :premises (t58))
% 25.76/26.02  (step t60 (cl (or (not (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w))) (not (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y))) (not (= (tptp.singleton tptp.w) (tptp.singleton tptp.y))) (not (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y)))) (not (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)))) (not (not (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w))))) :rule or_neg)
% 25.76/26.02  (step t61 (cl (or (not (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w))) (not (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y))) (not (= (tptp.singleton tptp.w) (tptp.singleton tptp.y))) (not (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y)))) (not (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)))) (not (not (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y))))) :rule or_neg)
% 25.76/26.02  (step t62 (cl (or (not (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w))) (not (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y))) (not (= (tptp.singleton tptp.w) (tptp.singleton tptp.y))) (not (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y)))) (not (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)))) (not (not (= (tptp.singleton tptp.w) (tptp.singleton tptp.y))))) :rule or_neg)
% 25.76/26.02  (step t63 (cl (or (not (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w))) (not (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y))) (not (= (tptp.singleton tptp.w) (tptp.singleton tptp.y))) (not (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y)))) (not (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)))) (not (not (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y)))))) :rule or_neg)
% 25.76/26.02  (step t64 (cl (or (not (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w))) (not (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y))) (not (= (tptp.singleton tptp.w) (tptp.singleton tptp.y))) (not (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y)))) (not (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)))) (not (not (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w))))) :rule or_neg)
% 25.76/26.02  (step t65 (cl (or (not (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w))) (not (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y))) (not (= (tptp.singleton tptp.w) (tptp.singleton tptp.y))) (not (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y)))) (not (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)))) (or (not (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w))) (not (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y))) (not (= (tptp.singleton tptp.w) (tptp.singleton tptp.y))) (not (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y)))) (not (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)))) (or (not (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w))) (not (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y))) (not (= (tptp.singleton tptp.w) (tptp.singleton tptp.y))) (not (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y)))) (not (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)))) (or (not (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w))) (not (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y))) (not (= (tptp.singleton tptp.w) (tptp.singleton tptp.y))) (not (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y)))) (not (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)))) (or (not (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w))) (not (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y))) (not (= (tptp.singleton tptp.w) (tptp.singleton tptp.y))) (not (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y)))) (not (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w))))) :rule resolution :premises (t59 t60 t61 t62 t63 t64))
% 25.76/26.02  (step t66 (cl (or (not (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w))) (not (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y))) (not (= (tptp.singleton tptp.w) (tptp.singleton tptp.y))) (not (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y)))) (not (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w))))) :rule contraction :premises (t65))
% 25.76/26.02  (step t67 (cl (or (not (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w))) (not (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y))) (not (= (tptp.singleton tptp.w) (tptp.singleton tptp.y))) (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w))))) :rule resolution :premises (t1 t16 t66))
% 25.76/26.02  (step t68 (cl (not (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w))) (not (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y))) (not (= (tptp.singleton tptp.w) (tptp.singleton tptp.y))) (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)))) :rule or :premises (t67))
% 25.76/26.02  (step t69 (cl (not (or (not (tptp.member tptp.w tptp.universal_class)) (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)))) (not (tptp.member tptp.w tptp.universal_class)) (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w))) :rule or_pos)
% 25.76/26.02  (step t70 (cl (not (tptp.member tptp.w tptp.universal_class)) (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)) (not (or (not (tptp.member tptp.w tptp.universal_class)) (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w))))) :rule reordering :premises (t69))
% 25.76/26.02  (step t71 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (tptp.member X (tptp.unordered_pair X Y)))) (or (not (tptp.member tptp.w tptp.universal_class)) (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (tptp.member X (tptp.unordered_pair X Y))))) :rule implies_neg1)
% 25.76/26.02  (anchor :step t72)
% 25.76/26.02  (assume t72.a0 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (tptp.member X (tptp.unordered_pair X Y)))))
% 25.76/26.02  (step t72.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (tptp.member X (tptp.unordered_pair X Y))))) (or (not (tptp.member tptp.w tptp.universal_class)) (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w))))) :rule forall_inst :args ((:= X tptp.w) (:= Y tptp.w)))
% 25.76/26.02  (step t72.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (tptp.member X (tptp.unordered_pair X Y))))) (or (not (tptp.member tptp.w tptp.universal_class)) (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)))) :rule or :premises (t72.t1))
% 25.76/26.02  (step t72.t3 (cl (or (not (tptp.member tptp.w tptp.universal_class)) (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)))) :rule resolution :premises (t72.t2 t72.a0))
% 25.76/26.02  (step t72 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (tptp.member X (tptp.unordered_pair X Y))))) (or (not (tptp.member tptp.w tptp.universal_class)) (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)))) :rule subproof :discharge (t72.a0))
% 25.76/26.02  (step t73 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (tptp.member X (tptp.unordered_pair X Y)))) (or (not (tptp.member tptp.w tptp.universal_class)) (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)))) (or (not (tptp.member tptp.w tptp.universal_class)) (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)))) :rule resolution :premises (t71 t72))
% 25.76/26.02  (step t74 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (tptp.member X (tptp.unordered_pair X Y)))) (or (not (tptp.member tptp.w tptp.universal_class)) (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)))) (not (or (not (tptp.member tptp.w tptp.universal_class)) (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w))))) :rule implies_neg2)
% 25.76/26.02  (step t75 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (tptp.member X (tptp.unordered_pair X Y)))) (or (not (tptp.member tptp.w tptp.universal_class)) (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (tptp.member X (tptp.unordered_pair X Y)))) (or (not (tptp.member tptp.w tptp.universal_class)) (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w))))) :rule resolution :premises (t73 t74))
% 25.76/26.02  (step t76 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (tptp.member X (tptp.unordered_pair X Y)))) (or (not (tptp.member tptp.w tptp.universal_class)) (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w))))) :rule contraction :premises (t75))
% 25.76/26.02  (step t77 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (tptp.member X (tptp.unordered_pair X Y))))) (or (not (tptp.member tptp.w tptp.universal_class)) (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)))) :rule implies :premises (t76))
% 25.76/26.02  (step t78 (cl (or (not (tptp.member tptp.w tptp.universal_class)) (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w)))) :rule resolution :premises (t77 a8))
% 25.76/26.02  (step t79 (cl (tptp.member tptp.w (tptp.unordered_pair tptp.w tptp.w))) :rule resolution :premises (t70 a92 t78))
% 25.76/26.02  (step t80 (cl (not (or (not (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) (= (tptp.singleton tptp.w) (tptp.singleton tptp.y)) (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y)))) (not (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) (= (tptp.singleton tptp.w) (tptp.singleton tptp.y)) (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y))) :rule or_pos)
% 25.76/26.02  (step t81 (cl (= (tptp.singleton tptp.w) (tptp.singleton tptp.y)) (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y)) (not (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) (not (or (not (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) (= (tptp.singleton tptp.w) (tptp.singleton tptp.y)) (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y))))) :rule reordering :premises (t80))
% 25.76/26.02  (step t82 (cl (not (= (or (not (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))) (not (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y))) (not (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y))) (not (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))))) (or (not (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))) (not (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y))) (not (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y))) (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))))) (not (or (not (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))) (not (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y))) (not (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y))) (not (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y)))))) (or (not (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))) (not (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y))) (not (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y))) (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y)))) :rule equiv_pos2)
% 25.76/26.02  (step t83 (cl (= (not (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))) (not (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))))) :rule refl)
% 25.76/26.02  (step t84 (cl (= (not (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y))) (not (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y))))) :rule refl)
% 25.76/26.02  (step t85 (cl (= (or (not (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))) (not (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y))) (not (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y))) (not (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))))) (or (not (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))) (not (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y))) (not (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y))) (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))))) :rule cong :premises (t83 t3 t84 t14))
% 25.76/26.02  (step t86 (cl (not (= (=> (and (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y)))) (and (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y)) (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) (not (and (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))))))) (not (=> (and (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y)))) (and (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y)) (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))))) (not (and (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y)))))) :rule equiv_pos2)
% 25.76/26.02  (step t87 (cl (= (and (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y)))) (and (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y)))))) :rule refl)
% 25.76/26.02  (step t88 (cl (= (= (and (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y)) (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))) false) (not (and (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y)) (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))))) :rule equiv_simplify)
% 25.76/26.02  (step t89 (cl (= (and (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y)) (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))) false) (not (not (and (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y)) (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))))) :rule equiv2 :premises (t88))
% 25.76/26.02  (step t90 (cl (not (not (not (and (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y)) (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))))) (and (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y)) (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) :rule not_not)
% 25.76/26.02  (step t91 (cl (= (and (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y)) (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))) false) (and (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y)) (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) :rule resolution :premises (t89 t90))
% 25.76/26.02  (step t92 (cl (=> (and (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y)) (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))) false) (and (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y)) (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) :rule implies_neg1)
% 25.76/26.02  (anchor :step t93)
% 25.76/26.02  (assume t93.a0 (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))))
% 25.76/26.02  (assume t93.a1 (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)))
% 25.76/26.02  (assume t93.a2 (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y)))
% 25.76/26.02  (assume t93.a3 (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))
% 25.76/26.02  (step t93.t1 (cl (not (= (= true false) false)) (not (= true false)) false) :rule equiv_pos2)
% 25.76/26.02  (step t93.t2 (cl (= (= true false) false)) :rule all_simplify)
% 25.76/26.02  (step t93.t3 (cl (= (= (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))) true) (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) :rule equiv_simplify)
% 25.76/26.02  (step t93.t4 (cl (= (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))) true) (not (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) :rule equiv2 :premises (t93.t3))
% 25.76/26.02  (step t93.t5 (cl (= (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))) true)) :rule resolution :premises (t93.t4 t93.a3))
% 25.76/26.02  (step t93.t6 (cl (= true (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) :rule symm :premises (t93.t5))
% 25.76/26.02  (step t93.t7 (cl (= tptp.w tptp.w)) :rule refl)
% 25.76/26.02  (step t93.t8 (cl (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))) :rule symm :premises (t93.a2))
% 25.76/26.02  (step t93.t9 (cl (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y))) :rule symm :premises (t93.t8))
% 25.76/26.02  (step t93.t10 (cl (= (tptp.unordered_pair tptp.y tptp.y) (tptp.singleton tptp.y))) :rule symm :premises (t93.a1))
% 25.76/26.02  (step t93.t11 (cl (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y))) :rule symm :premises (t93.t10))
% 25.76/26.02  (step t93.t12 (cl (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.unordered_pair tptp.y tptp.y))) :rule trans :premises (t93.t9 t93.t11))
% 25.76/26.02  (step t93.t13 (cl (= (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))) (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y)))) :rule cong :premises (t93.t7 t93.t12))
% 25.76/26.02  (step t93.t14 (cl (= (= (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y)) false) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))))) :rule equiv_simplify)
% 25.76/26.02  (step t93.t15 (cl (= (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y)) false) (not (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))))) :rule equiv2 :premises (t93.t14))
% 25.76/26.02  (step t93.t16 (cl (not (not (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))))) (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) :rule not_not)
% 25.76/26.02  (step t93.t17 (cl (= (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y)) false) (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) :rule resolution :premises (t93.t15 t93.t16))
% 25.76/26.02  (step t93.t18 (cl (= (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y)) false)) :rule resolution :premises (t93.t17 t93.a0))
% 25.76/26.02  (step t93.t19 (cl (= true false)) :rule trans :premises (t93.t6 t93.t13 t93.t18))
% 25.76/26.02  (step t93.t20 (cl false) :rule resolution :premises (t93.t1 t93.t2 t93.t19))
% 25.76/26.02  (step t93 (cl (not (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y)))) (not (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y))) (not (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y))) (not (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))) false) :rule subproof :discharge (t93.a0 t93.a1 t93.a2 t93.a3))
% 25.76/26.03  (step t94 (cl (not (and (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y)) (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y)))) :rule and_pos)
% 25.76/26.03  (step t95 (cl (not (and (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y)) (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y))) :rule and_pos)
% 25.76/26.03  (step t96 (cl (not (and (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y)) (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y))) :rule and_pos)
% 25.76/26.03  (step t97 (cl (not (and (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y)) (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))) :rule and_pos)
% 25.76/26.03  (step t98 (cl false (not (and (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y)) (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) (not (and (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y)) (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) (not (and (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y)) (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) (not (and (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y)) (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))))) :rule resolution :premises (t93 t94 t95 t96 t97))
% 25.76/26.03  (step t99 (cl (not (and (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y)) (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) (not (and (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y)) (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) (not (and (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y)) (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) (not (and (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y)) (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) false) :rule reordering :premises (t98))
% 25.76/26.03  (step t100 (cl (not (and (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y)) (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) false) :rule contraction :premises (t99))
% 25.76/26.03  (step t101 (cl (=> (and (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y)) (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))) false) false) :rule resolution :premises (t92 t100))
% 25.76/26.03  (step t102 (cl (=> (and (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y)) (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))) false) (not false)) :rule implies_neg2)
% 25.76/26.03  (step t103 (cl (=> (and (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y)) (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))) false) (=> (and (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y)) (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))) false)) :rule resolution :premises (t101 t102))
% 25.76/26.03  (step t104 (cl (=> (and (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y)) (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))) false)) :rule contraction :premises (t103))
% 25.76/26.03  (step t105 (cl (= (=> (and (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y)) (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))) false) (not (and (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y)) (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))))) :rule implies_simplify)
% 25.76/26.03  (step t106 (cl (not (=> (and (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y)) (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))) false)) (not (and (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y)) (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))))) :rule equiv1 :premises (t105))
% 25.76/26.03  (step t107 (cl (not (and (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y)) (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))))) :rule resolution :premises (t104 t106))
% 25.76/26.03  (step t108 (cl (= (and (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y)) (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))) false)) :rule resolution :premises (t91 t107))
% 25.76/26.03  (step t109 (cl (= (=> (and (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y)))) (and (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y)) (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) (=> (and (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y)))) false))) :rule cong :premises (t87 t108))
% 25.76/26.03  (step t110 (cl (= (=> (and (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y)))) false) (not (and (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))))))) :rule all_simplify)
% 25.76/26.03  (step t111 (cl (= (=> (and (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y)))) (and (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y)) (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) (not (and (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))))))) :rule trans :premises (t109 t110))
% 25.76/26.03  (step t112 (cl (=> (and (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y)))) (and (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y)) (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) (and (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))))) :rule implies_neg1)
% 25.76/26.03  (anchor :step t113)
% 25.76/26.03  (assume t113.a0 (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))
% 25.76/26.03  (assume t113.a1 (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)))
% 25.76/26.03  (assume t113.a2 (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y)))
% 25.76/26.03  (assume t113.a3 (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))))
% 25.76/26.03  (step t113.t1 (cl (and (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y)) (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))) (not (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y)))) (not (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y))) (not (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y))) (not (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) :rule and_neg)
% 25.76/26.03  (step t113.t2 (cl (and (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y)) (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) :rule resolution :premises (t113.t1 t113.a3 t113.a1 t113.a2 t113.a0))
% 25.76/26.03  (step t113 (cl (not (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))) (not (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y))) (not (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y))) (not (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y)))) (and (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y)) (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) :rule subproof :discharge (t113.a0 t113.a1 t113.a2 t113.a3))
% 25.76/26.03  (step t114 (cl (not (and (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))))) (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))) :rule and_pos)
% 25.76/26.03  (step t115 (cl (not (and (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y))) :rule and_pos)
% 25.76/26.03  (step t116 (cl (not (and (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))))) (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y))) :rule and_pos)
% 25.76/26.03  (step t117 (cl (not (and (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))))) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y)))) :rule and_pos)
% 25.76/26.03  (step t118 (cl (and (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y)) (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))) (not (and (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))))) (not (and (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))))) (not (and (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))))) (not (and (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y)))))) :rule resolution :premises (t113 t114 t115 t116 t117))
% 25.76/26.03  (step t119 (cl (not (and (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))))) (not (and (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))))) (not (and (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))))) (not (and (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))))) (and (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y)) (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) :rule reordering :premises (t118))
% 25.76/26.03  (step t120 (cl (not (and (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))))) (and (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y)) (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) :rule contraction :premises (t119))
% 25.76/26.03  (step t121 (cl (=> (and (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y)))) (and (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y)) (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) (and (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y)) (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) :rule resolution :premises (t112 t120))
% 25.76/26.03  (step t122 (cl (=> (and (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y)))) (and (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y)) (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) (not (and (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y)) (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))))) :rule implies_neg2)
% 25.76/26.03  (step t123 (cl (=> (and (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y)))) (and (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y)) (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) (=> (and (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y)))) (and (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y)) (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))))) :rule resolution :premises (t121 t122))
% 25.76/26.03  (step t124 (cl (=> (and (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y)))) (and (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y)) (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))))) :rule contraction :premises (t123))
% 25.76/26.03  (step t125 (cl (not (and (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y)) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y)))))) :rule resolution :premises (t86 t111 t124))
% 25.76/26.03  (step t126 (cl (not (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))) (not (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y))) (not (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y))) (not (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))))) :rule not_and :premises (t125))
% 25.76/26.03  (step t127 (cl (or (not (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))) (not (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y))) (not (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y))) (not (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))))) (not (not (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))))) :rule or_neg)
% 25.76/26.03  (step t128 (cl (or (not (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))) (not (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y))) (not (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y))) (not (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))))) (not (not (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y))))) :rule or_neg)
% 25.76/26.03  (step t129 (cl (or (not (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))) (not (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y))) (not (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y))) (not (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))))) (not (not (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y))))) :rule or_neg)
% 25.76/26.03  (step t130 (cl (or (not (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))) (not (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y))) (not (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y))) (not (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))))) (not (not (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y)))))) :rule or_neg)
% 25.76/26.03  (step t131 (cl (or (not (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))) (not (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y))) (not (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y))) (not (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))))) (or (not (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))) (not (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y))) (not (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y))) (not (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))))) (or (not (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))) (not (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y))) (not (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y))) (not (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))))) (or (not (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))) (not (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y))) (not (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y))) (not (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y)))))) :rule resolution :premises (t126 t127 t128 t129 t130))
% 25.76/26.03  (step t132 (cl (or (not (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))) (not (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y))) (not (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y))) (not (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y)))))) :rule contraction :premises (t131))
% 25.76/26.03  (step t133 (cl (or (not (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))) (not (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y))) (not (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y))) (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y)))) :rule resolution :premises (t82 t85 t132))
% 25.76/26.03  (step t134 (cl (not (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))) (not (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y))) (not (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y))) (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) :rule or :premises (t133))
% 25.76/26.03  (step t135 (cl (not (or (not (tptp.member tptp.w tptp.universal_class)) (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) (not (tptp.member tptp.w tptp.universal_class)) (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))) :rule or_pos)
% 25.76/26.03  (step t136 (cl (not (tptp.member tptp.w tptp.universal_class)) (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))) (not (or (not (tptp.member tptp.w tptp.universal_class)) (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))))) :rule reordering :premises (t135))
% 25.76/26.03  (step t137 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (tptp.member X (tptp.unordered_pair X Y)))) (or (not (tptp.member tptp.w tptp.universal_class)) (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (tptp.member X (tptp.unordered_pair X Y))))) :rule implies_neg1)
% 25.76/26.03  (anchor :step t138)
% 25.76/26.03  (assume t138.a0 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (tptp.member X (tptp.unordered_pair X Y)))))
% 25.76/26.03  (step t138.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (tptp.member X (tptp.unordered_pair X Y))))) (or (not (tptp.member tptp.w tptp.universal_class)) (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))))) :rule forall_inst :args ((:= X tptp.w) (:= Y (tptp.singleton tptp.x))))
% 25.76/26.03  (step t138.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (tptp.member X (tptp.unordered_pair X Y))))) (or (not (tptp.member tptp.w tptp.universal_class)) (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) :rule or :premises (t138.t1))
% 25.76/26.03  (step t138.t3 (cl (or (not (tptp.member tptp.w tptp.universal_class)) (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) :rule resolution :premises (t138.t2 t138.a0))
% 25.76/26.03  (step t138 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (tptp.member X (tptp.unordered_pair X Y))))) (or (not (tptp.member tptp.w tptp.universal_class)) (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) :rule subproof :discharge (t138.a0))
% 25.76/26.03  (step t139 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (tptp.member X (tptp.unordered_pair X Y)))) (or (not (tptp.member tptp.w tptp.universal_class)) (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) (or (not (tptp.member tptp.w tptp.universal_class)) (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) :rule resolution :premises (t137 t138))
% 25.76/26.03  (step t140 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (tptp.member X (tptp.unordered_pair X Y)))) (or (not (tptp.member tptp.w tptp.universal_class)) (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) (not (or (not (tptp.member tptp.w tptp.universal_class)) (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))))) :rule implies_neg2)
% 25.76/26.03  (step t141 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (tptp.member X (tptp.unordered_pair X Y)))) (or (not (tptp.member tptp.w tptp.universal_class)) (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (tptp.member X (tptp.unordered_pair X Y)))) (or (not (tptp.member tptp.w tptp.universal_class)) (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))))) :rule resolution :premises (t139 t140))
% 25.76/26.03  (step t142 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (tptp.member X (tptp.unordered_pair X Y)))) (or (not (tptp.member tptp.w tptp.universal_class)) (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))))) :rule contraction :premises (t141))
% 25.76/26.03  (step t143 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (tptp.member X (tptp.unordered_pair X Y))))) (or (not (tptp.member tptp.w tptp.universal_class)) (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) :rule implies :premises (t142))
% 25.76/26.03  (step t144 (cl (or (not (tptp.member tptp.w tptp.universal_class)) (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) :rule resolution :premises (t143 a8))
% 25.76/26.03  (step t145 (cl (tptp.member tptp.w (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))) :rule resolution :premises (t136 a92 t144))
% 25.76/26.03  (step t146 (cl (not (= (=> (forall ((X $$unsorted)) (= (tptp.unordered_pair X X) (tptp.singleton X))) (= (tptp.unordered_pair tptp.y tptp.y) (tptp.singleton tptp.y))) (=> (forall ((X $$unsorted)) (= (tptp.unordered_pair X X) (tptp.singleton X))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y))))) (not (=> (forall ((X $$unsorted)) (= (tptp.unordered_pair X X) (tptp.singleton X))) (= (tptp.unordered_pair tptp.y tptp.y) (tptp.singleton tptp.y)))) (=> (forall ((X $$unsorted)) (= (tptp.unordered_pair X X) (tptp.singleton X))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)))) :rule equiv_pos2)
% 25.76/26.03  (step t147 (cl (= (forall ((X $$unsorted)) (= (tptp.unordered_pair X X) (tptp.singleton X))) (forall ((X $$unsorted)) (= (tptp.unordered_pair X X) (tptp.singleton X))))) :rule refl)
% 25.76/26.03  (step t148 (cl (= (= (tptp.unordered_pair tptp.y tptp.y) (tptp.singleton tptp.y)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)))) :rule all_simplify)
% 25.76/26.03  (step t149 (cl (= (=> (forall ((X $$unsorted)) (= (tptp.unordered_pair X X) (tptp.singleton X))) (= (tptp.unordered_pair tptp.y tptp.y) (tptp.singleton tptp.y))) (=> (forall ((X $$unsorted)) (= (tptp.unordered_pair X X) (tptp.singleton X))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y))))) :rule cong :premises (t147 t148))
% 25.76/26.03  (step t150 (cl (=> (forall ((X $$unsorted)) (= (tptp.unordered_pair X X) (tptp.singleton X))) (= (tptp.unordered_pair tptp.y tptp.y) (tptp.singleton tptp.y))) (forall ((X $$unsorted)) (= (tptp.unordered_pair X X) (tptp.singleton X)))) :rule implies_neg1)
% 25.76/26.03  (anchor :step t151)
% 25.76/26.03  (assume t151.a0 (forall ((X $$unsorted)) (= (tptp.unordered_pair X X) (tptp.singleton X))))
% 25.76/26.03  (step t151.t1 (cl (or (not (forall ((X $$unsorted)) (= (tptp.unordered_pair X X) (tptp.singleton X)))) (= (tptp.unordered_pair tptp.y tptp.y) (tptp.singleton tptp.y)))) :rule forall_inst :args ((:= X tptp.y)))
% 25.76/26.03  (step t151.t2 (cl (not (forall ((X $$unsorted)) (= (tptp.unordered_pair X X) (tptp.singleton X)))) (= (tptp.unordered_pair tptp.y tptp.y) (tptp.singleton tptp.y))) :rule or :premises (t151.t1))
% 25.76/26.03  (step t151.t3 (cl (= (tptp.unordered_pair tptp.y tptp.y) (tptp.singleton tptp.y))) :rule resolution :premises (t151.t2 t151.a0))
% 25.76/26.03  (step t151 (cl (not (forall ((X $$unsorted)) (= (tptp.unordered_pair X X) (tptp.singleton X)))) (= (tptp.unordered_pair tptp.y tptp.y) (tptp.singleton tptp.y))) :rule subproof :discharge (t151.a0))
% 25.76/26.03  (step t152 (cl (=> (forall ((X $$unsorted)) (= (tptp.unordered_pair X X) (tptp.singleton X))) (= (tptp.unordered_pair tptp.y tptp.y) (tptp.singleton tptp.y))) (= (tptp.unordered_pair tptp.y tptp.y) (tptp.singleton tptp.y))) :rule resolution :premises (t150 t151))
% 25.76/26.03  (step t153 (cl (=> (forall ((X $$unsorted)) (= (tptp.unordered_pair X X) (tptp.singleton X))) (= (tptp.unordered_pair tptp.y tptp.y) (tptp.singleton tptp.y))) (not (= (tptp.unordered_pair tptp.y tptp.y) (tptp.singleton tptp.y)))) :rule implies_neg2)
% 25.76/26.03  (step t154 (cl (=> (forall ((X $$unsorted)) (= (tptp.unordered_pair X X) (tptp.singleton X))) (= (tptp.unordered_pair tptp.y tptp.y) (tptp.singleton tptp.y))) (=> (forall ((X $$unsorted)) (= (tptp.unordered_pair X X) (tptp.singleton X))) (= (tptp.unordered_pair tptp.y tptp.y) (tptp.singleton tptp.y)))) :rule resolution :premises (t152 t153))
% 25.76/26.03  (step t155 (cl (=> (forall ((X $$unsorted)) (= (tptp.unordered_pair X X) (tptp.singleton X))) (= (tptp.unordered_pair tptp.y tptp.y) (tptp.singleton tptp.y)))) :rule contraction :premises (t154))
% 25.76/26.03  (step t156 (cl (=> (forall ((X $$unsorted)) (= (tptp.unordered_pair X X) (tptp.singleton X))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)))) :rule resolution :premises (t146 t149 t155))
% 25.76/26.03  (step t157 (cl (not (forall ((X $$unsorted)) (= (tptp.unordered_pair X X) (tptp.singleton X)))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y))) :rule implies :premises (t156))
% 25.76/26.03  (step t158 (cl (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y))) :rule resolution :premises (t157 a11))
% 25.76/26.03  (step t159 (cl (not (or (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (= tptp.w tptp.y) (= tptp.w tptp.y))) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (= tptp.w tptp.y) (= tptp.w tptp.y)) :rule or_pos)
% 25.76/26.03  (step t160 (cl (not (or (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (= tptp.w tptp.y) (= tptp.w tptp.y))) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (= tptp.w tptp.y)) :rule contraction :premises (t159))
% 25.76/26.03  (step t161 (cl (= tptp.w tptp.y) (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (not (or (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (= tptp.w tptp.y) (= tptp.w tptp.y)))) :rule reordering :premises (t160))
% 25.76/26.03  (step t162 (cl (=> (forall ((U $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member U (tptp.unordered_pair X Y))) (= U X) (= U Y))) (or (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (= tptp.w tptp.y) (= tptp.w tptp.y))) (forall ((U $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member U (tptp.unordered_pair X Y))) (= U X) (= U Y)))) :rule implies_neg1)
% 25.76/26.03  (anchor :step t163)
% 25.76/26.03  (assume t163.a0 (forall ((U $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member U (tptp.unordered_pair X Y))) (= U X) (= U Y))))
% 25.76/26.03  (step t163.t1 (cl (or (not (forall ((U $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member U (tptp.unordered_pair X Y))) (= U X) (= U Y)))) (or (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (= tptp.w tptp.y) (= tptp.w tptp.y)))) :rule forall_inst :args ((:= U tptp.w) (:= X tptp.y) (:= Y tptp.y)))
% 25.76/26.03  (step t163.t2 (cl (not (forall ((U $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member U (tptp.unordered_pair X Y))) (= U X) (= U Y)))) (or (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (= tptp.w tptp.y) (= tptp.w tptp.y))) :rule or :premises (t163.t1))
% 25.76/26.03  (step t163.t3 (cl (or (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (= tptp.w tptp.y) (= tptp.w tptp.y))) :rule resolution :premises (t163.t2 t163.a0))
% 25.76/26.03  (step t163 (cl (not (forall ((U $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member U (tptp.unordered_pair X Y))) (= U X) (= U Y)))) (or (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (= tptp.w tptp.y) (= tptp.w tptp.y))) :rule subproof :discharge (t163.a0))
% 25.76/26.03  (step t164 (cl (=> (forall ((U $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member U (tptp.unordered_pair X Y))) (= U X) (= U Y))) (or (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (= tptp.w tptp.y) (= tptp.w tptp.y))) (or (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (= tptp.w tptp.y) (= tptp.w tptp.y))) :rule resolution :premises (t162 t163))
% 25.76/26.03  (step t165 (cl (=> (forall ((U $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member U (tptp.unordered_pair X Y))) (= U X) (= U Y))) (or (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (= tptp.w tptp.y) (= tptp.w tptp.y))) (not (or (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (= tptp.w tptp.y) (= tptp.w tptp.y)))) :rule implies_neg2)
% 25.76/26.03  (step t166 (cl (=> (forall ((U $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member U (tptp.unordered_pair X Y))) (= U X) (= U Y))) (or (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (= tptp.w tptp.y) (= tptp.w tptp.y))) (=> (forall ((U $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member U (tptp.unordered_pair X Y))) (= U X) (= U Y))) (or (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (= tptp.w tptp.y) (= tptp.w tptp.y)))) :rule resolution :premises (t164 t165))
% 25.76/26.03  (step t167 (cl (=> (forall ((U $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member U (tptp.unordered_pair X Y))) (= U X) (= U Y))) (or (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (= tptp.w tptp.y) (= tptp.w tptp.y)))) :rule contraction :premises (t166))
% 25.76/26.03  (step t168 (cl (not (forall ((U $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member U (tptp.unordered_pair X Y))) (= U X) (= U Y)))) (or (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (= tptp.w tptp.y) (= tptp.w tptp.y))) :rule implies :premises (t167))
% 25.76/26.03  (step t169 (cl (or (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y))) (= tptp.w tptp.y) (= tptp.w tptp.y))) :rule resolution :premises (t168 a7))
% 25.76/26.03  (step t170 (cl (not (tptp.member tptp.w (tptp.unordered_pair tptp.y tptp.y)))) :rule resolution :premises (t161 a93 t169))
% 25.76/26.03  (step t171 (cl (not (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y)))) :rule resolution :premises (t134 t145 t158 t170))
% 25.76/26.03  (step t172 (cl (and (= (tptp.ordered_pair tptp.w tptp.x) (tptp.ordered_pair tptp.y tptp.z)) (= (tptp.ordered_pair tptp.w tptp.x) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))) (= (tptp.ordered_pair tptp.y tptp.z) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))) (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z))))) (not (= (tptp.ordered_pair tptp.w tptp.x) (tptp.ordered_pair tptp.y tptp.z))) (not (= (tptp.ordered_pair tptp.w tptp.x) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) (not (= (tptp.ordered_pair tptp.y tptp.z) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z))))) (not (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))))) :rule and_neg)
% 25.76/26.03  (step t173 (cl (=> (and (= (tptp.ordered_pair tptp.w tptp.x) (tptp.ordered_pair tptp.y tptp.z)) (= (tptp.ordered_pair tptp.w tptp.x) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))) (= (tptp.ordered_pair tptp.y tptp.z) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))) (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z))))) (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) (and (= (tptp.ordered_pair tptp.w tptp.x) (tptp.ordered_pair tptp.y tptp.z)) (= (tptp.ordered_pair tptp.w tptp.x) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))) (= (tptp.ordered_pair tptp.y tptp.z) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))) (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))))) :rule implies_neg1)
% 25.76/26.03  (anchor :step t174)
% 25.76/26.03  (assume t174.a0 (= (tptp.ordered_pair tptp.w tptp.x) (tptp.ordered_pair tptp.y tptp.z)))
% 25.76/26.03  (assume t174.a1 (= (tptp.ordered_pair tptp.w tptp.x) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))))
% 25.76/26.03  (assume t174.a2 (= (tptp.ordered_pair tptp.y tptp.z) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))))
% 25.76/26.03  (assume t174.a3 (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))))
% 25.76/26.03  (step t174.t1 (cl (=> (and (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))) (= (tptp.ordered_pair tptp.y tptp.z) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))) (= (tptp.ordered_pair tptp.w tptp.x) (tptp.ordered_pair tptp.y tptp.z)) (= (tptp.ordered_pair tptp.w tptp.x) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) (and (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))) (= (tptp.ordered_pair tptp.y tptp.z) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))) (= (tptp.ordered_pair tptp.w tptp.x) (tptp.ordered_pair tptp.y tptp.z)) (= (tptp.ordered_pair tptp.w tptp.x) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))))) :rule implies_neg1)
% 25.76/26.03  (anchor :step t174.t2)
% 25.76/26.03  (assume t174.t2.a0 (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))))
% 25.76/26.03  (assume t174.t2.a1 (= (tptp.ordered_pair tptp.y tptp.z) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))))
% 25.76/26.03  (assume t174.t2.a2 (= (tptp.ordered_pair tptp.w tptp.x) (tptp.ordered_pair tptp.y tptp.z)))
% 25.76/26.03  (assume t174.t2.a3 (= (tptp.ordered_pair tptp.w tptp.x) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))))
% 25.76/26.03  (step t174.t2.t1 (cl (= (= (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))) true) (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))))) :rule equiv_simplify)
% 25.76/26.03  (step t174.t2.t2 (cl (not (= (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))) true)) (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) :rule equiv1 :premises (t174.t2.t1))
% 25.76/26.03  (step t174.t2.t3 (cl (= (tptp.singleton tptp.y) (tptp.singleton tptp.y))) :rule refl)
% 25.76/26.03  (step t174.t2.t4 (cl (= (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))) (tptp.ordered_pair tptp.w tptp.x))) :rule symm :premises (t174.t2.a3))
% 25.76/26.03  (step t174.t2.t5 (cl (= (tptp.ordered_pair tptp.y tptp.z) (tptp.ordered_pair tptp.w tptp.x))) :rule symm :premises (t174.t2.a2))
% 25.76/26.03  (step t174.t2.t6 (cl (= (tptp.ordered_pair tptp.w tptp.x) (tptp.ordered_pair tptp.y tptp.z))) :rule symm :premises (t174.t2.t5))
% 25.76/26.03  (step t174.t2.t7 (cl (= (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z))) (tptp.ordered_pair tptp.y tptp.z))) :rule symm :premises (t174.t2.a1))
% 25.76/26.03  (step t174.t2.t8 (cl (= (tptp.ordered_pair tptp.y tptp.z) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z))))) :rule symm :premises (t174.t2.t7))
% 25.76/26.03  (step t174.t2.t9 (cl (= (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z))))) :rule trans :premises (t174.t2.t4 t174.t2.t6 t174.t2.t8))
% 25.76/26.03  (step t174.t2.t10 (cl (= (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))) (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))))) :rule cong :premises (t174.t2.t3 t174.t2.t9))
% 25.76/26.03  (step t174.t2.t11 (cl (= (= (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))) true) (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))))) :rule equiv_simplify)
% 25.76/26.03  (step t174.t2.t12 (cl (= (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))) true) (not (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))))) :rule equiv2 :premises (t174.t2.t11))
% 25.76/26.03  (step t174.t2.t13 (cl (= (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))) true)) :rule resolution :premises (t174.t2.t12 t174.t2.a0))
% 25.76/26.03  (step t174.t2.t14 (cl (= (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))) true)) :rule trans :premises (t174.t2.t10 t174.t2.t13))
% 25.76/26.03  (step t174.t2.t15 (cl (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) :rule resolution :premises (t174.t2.t2 t174.t2.t14))
% 25.76/26.03  (step t174.t2 (cl (not (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z))))) (not (= (tptp.ordered_pair tptp.y tptp.z) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z))))) (not (= (tptp.ordered_pair tptp.w tptp.x) (tptp.ordered_pair tptp.y tptp.z))) (not (= (tptp.ordered_pair tptp.w tptp.x) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) :rule subproof :discharge (t174.t2.a0 t174.t2.a1 t174.t2.a2 t174.t2.a3))
% 25.76/26.03  (step t174.t3 (cl (not (and (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))) (= (tptp.ordered_pair tptp.y tptp.z) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))) (= (tptp.ordered_pair tptp.w tptp.x) (tptp.ordered_pair tptp.y tptp.z)) (= (tptp.ordered_pair tptp.w tptp.x) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))))) (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z))))) :rule and_pos)
% 25.76/26.03  (step t174.t4 (cl (not (and (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))) (= (tptp.ordered_pair tptp.y tptp.z) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))) (= (tptp.ordered_pair tptp.w tptp.x) (tptp.ordered_pair tptp.y tptp.z)) (= (tptp.ordered_pair tptp.w tptp.x) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))))) (= (tptp.ordered_pair tptp.y tptp.z) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z))))) :rule and_pos)
% 25.76/26.03  (step t174.t5 (cl (not (and (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))) (= (tptp.ordered_pair tptp.y tptp.z) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))) (= (tptp.ordered_pair tptp.w tptp.x) (tptp.ordered_pair tptp.y tptp.z)) (= (tptp.ordered_pair tptp.w tptp.x) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))))) (= (tptp.ordered_pair tptp.w tptp.x) (tptp.ordered_pair tptp.y tptp.z))) :rule and_pos)
% 25.76/26.03  (step t174.t6 (cl (not (and (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))) (= (tptp.ordered_pair tptp.y tptp.z) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))) (= (tptp.ordered_pair tptp.w tptp.x) (tptp.ordered_pair tptp.y tptp.z)) (= (tptp.ordered_pair tptp.w tptp.x) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))))) (= (tptp.ordered_pair tptp.w tptp.x) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) :rule and_pos)
% 25.76/26.03  (step t174.t7 (cl (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))) (not (and (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))) (= (tptp.ordered_pair tptp.y tptp.z) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))) (= (tptp.ordered_pair tptp.w tptp.x) (tptp.ordered_pair tptp.y tptp.z)) (= (tptp.ordered_pair tptp.w tptp.x) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))))) (not (and (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))) (= (tptp.ordered_pair tptp.y tptp.z) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))) (= (tptp.ordered_pair tptp.w tptp.x) (tptp.ordered_pair tptp.y tptp.z)) (= (tptp.ordered_pair tptp.w tptp.x) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))))) (not (and (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))) (= (tptp.ordered_pair tptp.y tptp.z) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))) (= (tptp.ordered_pair tptp.w tptp.x) (tptp.ordered_pair tptp.y tptp.z)) (= (tptp.ordered_pair tptp.w tptp.x) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))))) (not (and (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))) (= (tptp.ordered_pair tptp.y tptp.z) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))) (= (tptp.ordered_pair tptp.w tptp.x) (tptp.ordered_pair tptp.y tptp.z)) (= (tptp.ordered_pair tptp.w tptp.x) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))))) :rule resolution :premises (t174.t2 t174.t3 t174.t4 t174.t5 t174.t6))
% 25.76/26.03  (step t174.t8 (cl (not (and (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))) (= (tptp.ordered_pair tptp.y tptp.z) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))) (= (tptp.ordered_pair tptp.w tptp.x) (tptp.ordered_pair tptp.y tptp.z)) (= (tptp.ordered_pair tptp.w tptp.x) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))))) (not (and (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))) (= (tptp.ordered_pair tptp.y tptp.z) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))) (= (tptp.ordered_pair tptp.w tptp.x) (tptp.ordered_pair tptp.y tptp.z)) (= (tptp.ordered_pair tptp.w tptp.x) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))))) (not (and (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))) (= (tptp.ordered_pair tptp.y tptp.z) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))) (= (tptp.ordered_pair tptp.w tptp.x) (tptp.ordered_pair tptp.y tptp.z)) (= (tptp.ordered_pair tptp.w tptp.x) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))))) (not (and (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))) (= (tptp.ordered_pair tptp.y tptp.z) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))) (= (tptp.ordered_pair tptp.w tptp.x) (tptp.ordered_pair tptp.y tptp.z)) (= (tptp.ordered_pair tptp.w tptp.x) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))))) (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) :rule reordering :premises (t174.t7))
% 25.76/26.03  (step t174.t9 (cl (not (and (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))) (= (tptp.ordered_pair tptp.y tptp.z) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))) (= (tptp.ordered_pair tptp.w tptp.x) (tptp.ordered_pair tptp.y tptp.z)) (= (tptp.ordered_pair tptp.w tptp.x) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))))) (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) :rule contraction :premises (t174.t8))
% 25.76/26.03  (step t174.t10 (cl (=> (and (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))) (= (tptp.ordered_pair tptp.y tptp.z) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))) (= (tptp.ordered_pair tptp.w tptp.x) (tptp.ordered_pair tptp.y tptp.z)) (= (tptp.ordered_pair tptp.w tptp.x) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) :rule resolution :premises (t174.t1 t174.t9))
% 25.76/26.03  (step t174.t11 (cl (=> (and (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))) (= (tptp.ordered_pair tptp.y tptp.z) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))) (= (tptp.ordered_pair tptp.w tptp.x) (tptp.ordered_pair tptp.y tptp.z)) (= (tptp.ordered_pair tptp.w tptp.x) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) (not (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))))) :rule implies_neg2)
% 25.76/26.03  (step t174.t12 (cl (=> (and (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))) (= (tptp.ordered_pair tptp.y tptp.z) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))) (= (tptp.ordered_pair tptp.w tptp.x) (tptp.ordered_pair tptp.y tptp.z)) (= (tptp.ordered_pair tptp.w tptp.x) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) (=> (and (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))) (= (tptp.ordered_pair tptp.y tptp.z) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))) (= (tptp.ordered_pair tptp.w tptp.x) (tptp.ordered_pair tptp.y tptp.z)) (= (tptp.ordered_pair tptp.w tptp.x) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))))) :rule resolution :premises (t174.t10 t174.t11))
% 25.76/26.03  (step t174.t13 (cl (=> (and (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))) (= (tptp.ordered_pair tptp.y tptp.z) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))) (= (tptp.ordered_pair tptp.w tptp.x) (tptp.ordered_pair tptp.y tptp.z)) (= (tptp.ordered_pair tptp.w tptp.x) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))))) :rule contraction :premises (t174.t12))
% 25.76/26.03  (step t174.t14 (cl (not (and (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))) (= (tptp.ordered_pair tptp.y tptp.z) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))) (= (tptp.ordered_pair tptp.w tptp.x) (tptp.ordered_pair tptp.y tptp.z)) (= (tptp.ordered_pair tptp.w tptp.x) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))))) (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) :rule implies :premises (t174.t13))
% 25.76/26.03  (step t174.t15 (cl (and (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))) (= (tptp.ordered_pair tptp.y tptp.z) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))) (= (tptp.ordered_pair tptp.w tptp.x) (tptp.ordered_pair tptp.y tptp.z)) (= (tptp.ordered_pair tptp.w tptp.x) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) (not (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z))))) (not (= (tptp.ordered_pair tptp.y tptp.z) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z))))) (not (= (tptp.ordered_pair tptp.w tptp.x) (tptp.ordered_pair tptp.y tptp.z))) (not (= (tptp.ordered_pair tptp.w tptp.x) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))))) :rule and_neg)
% 25.76/26.03  (step t174.t16 (cl (and (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))) (= (tptp.ordered_pair tptp.y tptp.z) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))) (= (tptp.ordered_pair tptp.w tptp.x) (tptp.ordered_pair tptp.y tptp.z)) (= (tptp.ordered_pair tptp.w tptp.x) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))))) :rule resolution :premises (t174.t15 t174.a3 t174.a2 t174.a0 t174.a1))
% 25.76/26.03  (step t174.t17 (cl (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) :rule resolution :premises (t174.t14 t174.t16))
% 25.76/26.03  (step t174 (cl (not (= (tptp.ordered_pair tptp.w tptp.x) (tptp.ordered_pair tptp.y tptp.z))) (not (= (tptp.ordered_pair tptp.w tptp.x) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) (not (= (tptp.ordered_pair tptp.y tptp.z) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z))))) (not (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z))))) (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) :rule subproof :discharge (t174.a0 t174.a1 t174.a2 t174.a3))
% 25.76/26.03  (step t175 (cl (not (and (= (tptp.ordered_pair tptp.w tptp.x) (tptp.ordered_pair tptp.y tptp.z)) (= (tptp.ordered_pair tptp.w tptp.x) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))) (= (tptp.ordered_pair tptp.y tptp.z) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))) (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))))) (= (tptp.ordered_pair tptp.w tptp.x) (tptp.ordered_pair tptp.y tptp.z))) :rule and_pos)
% 25.76/26.03  (step t176 (cl (not (and (= (tptp.ordered_pair tptp.w tptp.x) (tptp.ordered_pair tptp.y tptp.z)) (= (tptp.ordered_pair tptp.w tptp.x) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))) (= (tptp.ordered_pair tptp.y tptp.z) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))) (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))))) (= (tptp.ordered_pair tptp.w tptp.x) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) :rule and_pos)
% 25.76/26.03  (step t177 (cl (not (and (= (tptp.ordered_pair tptp.w tptp.x) (tptp.ordered_pair tptp.y tptp.z)) (= (tptp.ordered_pair tptp.w tptp.x) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))) (= (tptp.ordered_pair tptp.y tptp.z) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))) (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))))) (= (tptp.ordered_pair tptp.y tptp.z) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z))))) :rule and_pos)
% 25.76/26.03  (step t178 (cl (not (and (= (tptp.ordered_pair tptp.w tptp.x) (tptp.ordered_pair tptp.y tptp.z)) (= (tptp.ordered_pair tptp.w tptp.x) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))) (= (tptp.ordered_pair tptp.y tptp.z) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))) (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))))) (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z))))) :rule and_pos)
% 25.76/26.03  (step t179 (cl (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))) (not (and (= (tptp.ordered_pair tptp.w tptp.x) (tptp.ordered_pair tptp.y tptp.z)) (= (tptp.ordered_pair tptp.w tptp.x) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))) (= (tptp.ordered_pair tptp.y tptp.z) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))) (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))))) (not (and (= (tptp.ordered_pair tptp.w tptp.x) (tptp.ordered_pair tptp.y tptp.z)) (= (tptp.ordered_pair tptp.w tptp.x) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))) (= (tptp.ordered_pair tptp.y tptp.z) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))) (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))))) (not (and (= (tptp.ordered_pair tptp.w tptp.x) (tptp.ordered_pair tptp.y tptp.z)) (= (tptp.ordered_pair tptp.w tptp.x) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))) (= (tptp.ordered_pair tptp.y tptp.z) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))) (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))))) (not (and (= (tptp.ordered_pair tptp.w tptp.x) (tptp.ordered_pair tptp.y tptp.z)) (= (tptp.ordered_pair tptp.w tptp.x) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))) (= (tptp.ordered_pair tptp.y tptp.z) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))) (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z))))))) :rule resolution :premises (t174 t175 t176 t177 t178))
% 25.76/26.03  (step t180 (cl (not (and (= (tptp.ordered_pair tptp.w tptp.x) (tptp.ordered_pair tptp.y tptp.z)) (= (tptp.ordered_pair tptp.w tptp.x) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))) (= (tptp.ordered_pair tptp.y tptp.z) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))) (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))))) (not (and (= (tptp.ordered_pair tptp.w tptp.x) (tptp.ordered_pair tptp.y tptp.z)) (= (tptp.ordered_pair tptp.w tptp.x) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))) (= (tptp.ordered_pair tptp.y tptp.z) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))) (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))))) (not (and (= (tptp.ordered_pair tptp.w tptp.x) (tptp.ordered_pair tptp.y tptp.z)) (= (tptp.ordered_pair tptp.w tptp.x) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))) (= (tptp.ordered_pair tptp.y tptp.z) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))) (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))))) (not (and (= (tptp.ordered_pair tptp.w tptp.x) (tptp.ordered_pair tptp.y tptp.z)) (= (tptp.ordered_pair tptp.w tptp.x) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))) (= (tptp.ordered_pair tptp.y tptp.z) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))) (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))))) (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) :rule reordering :premises (t179))
% 25.76/26.03  (step t181 (cl (not (and (= (tptp.ordered_pair tptp.w tptp.x) (tptp.ordered_pair tptp.y tptp.z)) (= (tptp.ordered_pair tptp.w tptp.x) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))) (= (tptp.ordered_pair tptp.y tptp.z) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))) (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))))) (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) :rule contraction :premises (t180))
% 25.76/26.03  (step t182 (cl (=> (and (= (tptp.ordered_pair tptp.w tptp.x) (tptp.ordered_pair tptp.y tptp.z)) (= (tptp.ordered_pair tptp.w tptp.x) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))) (= (tptp.ordered_pair tptp.y tptp.z) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))) (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z))))) (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) :rule resolution :premises (t173 t181))
% 25.76/26.03  (step t183 (cl (=> (and (= (tptp.ordered_pair tptp.w tptp.x) (tptp.ordered_pair tptp.y tptp.z)) (= (tptp.ordered_pair tptp.w tptp.x) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))) (= (tptp.ordered_pair tptp.y tptp.z) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))) (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z))))) (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) (not (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))))) :rule implies_neg2)
% 25.76/26.03  (step t184 (cl (=> (and (= (tptp.ordered_pair tptp.w tptp.x) (tptp.ordered_pair tptp.y tptp.z)) (= (tptp.ordered_pair tptp.w tptp.x) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))) (= (tptp.ordered_pair tptp.y tptp.z) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))) (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z))))) (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) (=> (and (= (tptp.ordered_pair tptp.w tptp.x) (tptp.ordered_pair tptp.y tptp.z)) (= (tptp.ordered_pair tptp.w tptp.x) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))) (= (tptp.ordered_pair tptp.y tptp.z) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))) (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z))))) (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))))) :rule resolution :premises (t182 t183))
% 25.76/26.03  (step t185 (cl (=> (and (= (tptp.ordered_pair tptp.w tptp.x) (tptp.ordered_pair tptp.y tptp.z)) (= (tptp.ordered_pair tptp.w tptp.x) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))) (= (tptp.ordered_pair tptp.y tptp.z) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))) (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z))))) (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))))) :rule contraction :premises (t184))
% 25.76/26.03  (step t186 (cl (not (and (= (tptp.ordered_pair tptp.w tptp.x) (tptp.ordered_pair tptp.y tptp.z)) (= (tptp.ordered_pair tptp.w tptp.x) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))) (= (tptp.ordered_pair tptp.y tptp.z) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))) (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))))) (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) :rule implies :premises (t185))
% 25.76/26.03  (step t187 (cl (not (= (tptp.ordered_pair tptp.w tptp.x) (tptp.ordered_pair tptp.y tptp.z))) (not (= (tptp.ordered_pair tptp.w tptp.x) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) (not (= (tptp.ordered_pair tptp.y tptp.z) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z))))) (not (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z))))) (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) :rule resolution :premises (t172 t186))
% 25.76/26.03  (step t188 (cl (not (= (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.unordered_pair (tptp.singleton X) (tptp.unordered_pair X (tptp.singleton Y))) (tptp.ordered_pair X Y))) (= (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))) (tptp.ordered_pair tptp.w tptp.x))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.unordered_pair (tptp.singleton X) (tptp.unordered_pair X (tptp.singleton Y))) (tptp.ordered_pair X Y))) (= (tptp.ordered_pair tptp.w tptp.x) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))))) (not (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.unordered_pair (tptp.singleton X) (tptp.unordered_pair X (tptp.singleton Y))) (tptp.ordered_pair X Y))) (= (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))) (tptp.ordered_pair tptp.w tptp.x)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.unordered_pair (tptp.singleton X) (tptp.unordered_pair X (tptp.singleton Y))) (tptp.ordered_pair X Y))) (= (tptp.ordered_pair tptp.w tptp.x) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))))) :rule equiv_pos2)
% 25.76/26.03  (step t189 (cl (= (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.unordered_pair (tptp.singleton X) (tptp.unordered_pair X (tptp.singleton Y))) (tptp.ordered_pair X Y))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.unordered_pair (tptp.singleton X) (tptp.unordered_pair X (tptp.singleton Y))) (tptp.ordered_pair X Y))))) :rule refl)
% 25.76/26.03  (step t190 (cl (= (= (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))) (tptp.ordered_pair tptp.w tptp.x)) (= (tptp.ordered_pair tptp.w tptp.x) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))))) :rule all_simplify)
% 25.76/26.03  (step t191 (cl (= (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.unordered_pair (tptp.singleton X) (tptp.unordered_pair X (tptp.singleton Y))) (tptp.ordered_pair X Y))) (= (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))) (tptp.ordered_pair tptp.w tptp.x))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.unordered_pair (tptp.singleton X) (tptp.unordered_pair X (tptp.singleton Y))) (tptp.ordered_pair X Y))) (= (tptp.ordered_pair tptp.w tptp.x) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))))) :rule cong :premises (t189 t190))
% 25.76/26.03  (step t192 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.unordered_pair (tptp.singleton X) (tptp.unordered_pair X (tptp.singleton Y))) (tptp.ordered_pair X Y))) (= (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))) (tptp.ordered_pair tptp.w tptp.x))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.unordered_pair (tptp.singleton X) (tptp.unordered_pair X (tptp.singleton Y))) (tptp.ordered_pair X Y)))) :rule implies_neg1)
% 25.76/26.03  (anchor :step t193)
% 25.76/26.03  (assume t193.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.unordered_pair (tptp.singleton X) (tptp.unordered_pair X (tptp.singleton Y))) (tptp.ordered_pair X Y))))
% 25.76/26.03  (step t193.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.unordered_pair (tptp.singleton X) (tptp.unordered_pair X (tptp.singleton Y))) (tptp.ordered_pair X Y)))) (= (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))) (tptp.ordered_pair tptp.w tptp.x)))) :rule forall_inst :args ((:= X tptp.w) (:= Y tptp.x)))
% 25.76/26.03  (step t193.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.unordered_pair (tptp.singleton X) (tptp.unordered_pair X (tptp.singleton Y))) (tptp.ordered_pair X Y)))) (= (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))) (tptp.ordered_pair tptp.w tptp.x))) :rule or :premises (t193.t1))
% 25.76/26.03  (step t193.t3 (cl (= (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))) (tptp.ordered_pair tptp.w tptp.x))) :rule resolution :premises (t193.t2 t193.a0))
% 25.76/26.03  (step t193 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.unordered_pair (tptp.singleton X) (tptp.unordered_pair X (tptp.singleton Y))) (tptp.ordered_pair X Y)))) (= (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))) (tptp.ordered_pair tptp.w tptp.x))) :rule subproof :discharge (t193.a0))
% 25.76/26.03  (step t194 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.unordered_pair (tptp.singleton X) (tptp.unordered_pair X (tptp.singleton Y))) (tptp.ordered_pair X Y))) (= (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))) (tptp.ordered_pair tptp.w tptp.x))) (= (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))) (tptp.ordered_pair tptp.w tptp.x))) :rule resolution :premises (t192 t193))
% 25.76/26.03  (step t195 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.unordered_pair (tptp.singleton X) (tptp.unordered_pair X (tptp.singleton Y))) (tptp.ordered_pair X Y))) (= (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))) (tptp.ordered_pair tptp.w tptp.x))) (not (= (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))) (tptp.ordered_pair tptp.w tptp.x)))) :rule implies_neg2)
% 25.76/26.03  (step t196 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.unordered_pair (tptp.singleton X) (tptp.unordered_pair X (tptp.singleton Y))) (tptp.ordered_pair X Y))) (= (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))) (tptp.ordered_pair tptp.w tptp.x))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.unordered_pair (tptp.singleton X) (tptp.unordered_pair X (tptp.singleton Y))) (tptp.ordered_pair X Y))) (= (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))) (tptp.ordered_pair tptp.w tptp.x)))) :rule resolution :premises (t194 t195))
% 25.76/26.03  (step t197 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.unordered_pair (tptp.singleton X) (tptp.unordered_pair X (tptp.singleton Y))) (tptp.ordered_pair X Y))) (= (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))) (tptp.ordered_pair tptp.w tptp.x)))) :rule contraction :premises (t196))
% 25.76/26.03  (step t198 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.unordered_pair (tptp.singleton X) (tptp.unordered_pair X (tptp.singleton Y))) (tptp.ordered_pair X Y))) (= (tptp.ordered_pair tptp.w tptp.x) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))))) :rule resolution :premises (t188 t191 t197))
% 25.76/26.03  (step t199 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.unordered_pair (tptp.singleton X) (tptp.unordered_pair X (tptp.singleton Y))) (tptp.ordered_pair X Y)))) (= (tptp.ordered_pair tptp.w tptp.x) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) :rule implies :premises (t198))
% 25.76/26.03  (step t200 (cl (= (tptp.ordered_pair tptp.w tptp.x) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) :rule resolution :premises (t199 a12))
% 25.76/26.03  (step t201 (cl (not (= (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.unordered_pair (tptp.singleton X) (tptp.unordered_pair X (tptp.singleton Y))) (tptp.ordered_pair X Y))) (= (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z))) (tptp.ordered_pair tptp.y tptp.z))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.unordered_pair (tptp.singleton X) (tptp.unordered_pair X (tptp.singleton Y))) (tptp.ordered_pair X Y))) (= (tptp.ordered_pair tptp.y tptp.z) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z))))))) (not (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.unordered_pair (tptp.singleton X) (tptp.unordered_pair X (tptp.singleton Y))) (tptp.ordered_pair X Y))) (= (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z))) (tptp.ordered_pair tptp.y tptp.z)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.unordered_pair (tptp.singleton X) (tptp.unordered_pair X (tptp.singleton Y))) (tptp.ordered_pair X Y))) (= (tptp.ordered_pair tptp.y tptp.z) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))))) :rule equiv_pos2)
% 25.76/26.03  (step t202 (cl (= (= (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z))) (tptp.ordered_pair tptp.y tptp.z)) (= (tptp.ordered_pair tptp.y tptp.z) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))))) :rule all_simplify)
% 25.76/26.03  (step t203 (cl (= (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.unordered_pair (tptp.singleton X) (tptp.unordered_pair X (tptp.singleton Y))) (tptp.ordered_pair X Y))) (= (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z))) (tptp.ordered_pair tptp.y tptp.z))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.unordered_pair (tptp.singleton X) (tptp.unordered_pair X (tptp.singleton Y))) (tptp.ordered_pair X Y))) (= (tptp.ordered_pair tptp.y tptp.z) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z))))))) :rule cong :premises (t189 t202))
% 25.76/26.03  (step t204 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.unordered_pair (tptp.singleton X) (tptp.unordered_pair X (tptp.singleton Y))) (tptp.ordered_pair X Y))) (= (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z))) (tptp.ordered_pair tptp.y tptp.z))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.unordered_pair (tptp.singleton X) (tptp.unordered_pair X (tptp.singleton Y))) (tptp.ordered_pair X Y)))) :rule implies_neg1)
% 25.76/26.03  (anchor :step t205)
% 25.76/26.03  (assume t205.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.unordered_pair (tptp.singleton X) (tptp.unordered_pair X (tptp.singleton Y))) (tptp.ordered_pair X Y))))
% 25.76/26.03  (step t205.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.unordered_pair (tptp.singleton X) (tptp.unordered_pair X (tptp.singleton Y))) (tptp.ordered_pair X Y)))) (= (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z))) (tptp.ordered_pair tptp.y tptp.z)))) :rule forall_inst :args ((:= X tptp.y) (:= Y tptp.z)))
% 25.76/26.03  (step t205.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.unordered_pair (tptp.singleton X) (tptp.unordered_pair X (tptp.singleton Y))) (tptp.ordered_pair X Y)))) (= (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z))) (tptp.ordered_pair tptp.y tptp.z))) :rule or :premises (t205.t1))
% 25.76/26.03  (step t205.t3 (cl (= (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z))) (tptp.ordered_pair tptp.y tptp.z))) :rule resolution :premises (t205.t2 t205.a0))
% 25.76/26.03  (step t205 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.unordered_pair (tptp.singleton X) (tptp.unordered_pair X (tptp.singleton Y))) (tptp.ordered_pair X Y)))) (= (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z))) (tptp.ordered_pair tptp.y tptp.z))) :rule subproof :discharge (t205.a0))
% 25.76/26.03  (step t206 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.unordered_pair (tptp.singleton X) (tptp.unordered_pair X (tptp.singleton Y))) (tptp.ordered_pair X Y))) (= (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z))) (tptp.ordered_pair tptp.y tptp.z))) (= (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z))) (tptp.ordered_pair tptp.y tptp.z))) :rule resolution :premises (t204 t205))
% 25.76/26.03  (step t207 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.unordered_pair (tptp.singleton X) (tptp.unordered_pair X (tptp.singleton Y))) (tptp.ordered_pair X Y))) (= (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z))) (tptp.ordered_pair tptp.y tptp.z))) (not (= (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z))) (tptp.ordered_pair tptp.y tptp.z)))) :rule implies_neg2)
% 25.76/26.03  (step t208 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.unordered_pair (tptp.singleton X) (tptp.unordered_pair X (tptp.singleton Y))) (tptp.ordered_pair X Y))) (= (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z))) (tptp.ordered_pair tptp.y tptp.z))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.unordered_pair (tptp.singleton X) (tptp.unordered_pair X (tptp.singleton Y))) (tptp.ordered_pair X Y))) (= (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z))) (tptp.ordered_pair tptp.y tptp.z)))) :rule resolution :premises (t206 t207))
% 25.76/26.03  (step t209 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.unordered_pair (tptp.singleton X) (tptp.unordered_pair X (tptp.singleton Y))) (tptp.ordered_pair X Y))) (= (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z))) (tptp.ordered_pair tptp.y tptp.z)))) :rule contraction :premises (t208))
% 25.76/26.03  (step t210 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.unordered_pair (tptp.singleton X) (tptp.unordered_pair X (tptp.singleton Y))) (tptp.ordered_pair X Y))) (= (tptp.ordered_pair tptp.y tptp.z) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))))) :rule resolution :premises (t201 t203 t209))
% 25.76/26.03  (step t211 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.unordered_pair (tptp.singleton X) (tptp.unordered_pair X (tptp.singleton Y))) (tptp.ordered_pair X Y)))) (= (tptp.ordered_pair tptp.y tptp.z) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z))))) :rule implies :premises (t210))
% 25.76/26.03  (step t212 (cl (= (tptp.ordered_pair tptp.y tptp.z) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z))))) :rule resolution :premises (t211 a12))
% 25.76/26.03  (step t213 (cl (not (or (not (tptp.member (tptp.singleton tptp.y) tptp.universal_class)) (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))))) (not (tptp.member (tptp.singleton tptp.y) tptp.universal_class)) (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z))))) :rule or_pos)
% 25.76/26.03  (step t214 (cl (not (tptp.member (tptp.singleton tptp.y) tptp.universal_class)) (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))) (not (or (not (tptp.member (tptp.singleton tptp.y) tptp.universal_class)) (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z))))))) :rule reordering :premises (t213))
% 25.76/26.03  (step t215 (cl (and (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (tptp.member (tptp.unordered_pair tptp.y tptp.y) tptp.universal_class)) (not (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y))) (not (tptp.member (tptp.unordered_pair tptp.y tptp.y) tptp.universal_class))) :rule and_neg)
% 25.76/26.03  (step t216 (cl (=> (and (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (tptp.member (tptp.unordered_pair tptp.y tptp.y) tptp.universal_class)) (tptp.member (tptp.singleton tptp.y) tptp.universal_class)) (and (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (tptp.member (tptp.unordered_pair tptp.y tptp.y) tptp.universal_class))) :rule implies_neg1)
% 25.76/26.03  (anchor :step t217)
% 25.76/26.03  (assume t217.a0 (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)))
% 25.76/26.03  (assume t217.a1 (tptp.member (tptp.unordered_pair tptp.y tptp.y) tptp.universal_class))
% 25.76/26.03  (step t217.t1 (cl (=> (and (tptp.member (tptp.unordered_pair tptp.y tptp.y) tptp.universal_class) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y))) (tptp.member (tptp.singleton tptp.y) tptp.universal_class)) (and (tptp.member (tptp.unordered_pair tptp.y tptp.y) tptp.universal_class) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)))) :rule implies_neg1)
% 25.76/26.03  (anchor :step t217.t2)
% 25.76/26.03  (assume t217.t2.a0 (tptp.member (tptp.unordered_pair tptp.y tptp.y) tptp.universal_class))
% 25.76/26.03  (assume t217.t2.a1 (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)))
% 25.76/26.03  (step t217.t2.t1 (cl (= (= (tptp.member (tptp.singleton tptp.y) tptp.universal_class) true) (tptp.member (tptp.singleton tptp.y) tptp.universal_class))) :rule equiv_simplify)
% 25.76/26.03  (step t217.t2.t2 (cl (not (= (tptp.member (tptp.singleton tptp.y) tptp.universal_class) true)) (tptp.member (tptp.singleton tptp.y) tptp.universal_class)) :rule equiv1 :premises (t217.t2.t1))
% 25.76/26.03  (step t217.t2.t3 (cl (= (tptp.unordered_pair tptp.y tptp.y) (tptp.singleton tptp.y))) :rule symm :premises (t217.t2.a1))
% 25.76/26.03  (step t217.t2.t4 (cl (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y))) :rule symm :premises (t217.t2.t3))
% 25.76/26.03  (step t217.t2.t5 (cl (= tptp.universal_class tptp.universal_class)) :rule refl)
% 25.76/26.03  (step t217.t2.t6 (cl (= (tptp.member (tptp.singleton tptp.y) tptp.universal_class) (tptp.member (tptp.unordered_pair tptp.y tptp.y) tptp.universal_class))) :rule cong :premises (t217.t2.t4 t217.t2.t5))
% 25.76/26.03  (step t217.t2.t7 (cl (= (= (tptp.member (tptp.unordered_pair tptp.y tptp.y) tptp.universal_class) true) (tptp.member (tptp.unordered_pair tptp.y tptp.y) tptp.universal_class))) :rule equiv_simplify)
% 25.76/26.03  (step t217.t2.t8 (cl (= (tptp.member (tptp.unordered_pair tptp.y tptp.y) tptp.universal_class) true) (not (tptp.member (tptp.unordered_pair tptp.y tptp.y) tptp.universal_class))) :rule equiv2 :premises (t217.t2.t7))
% 25.76/26.03  (step t217.t2.t9 (cl (= (tptp.member (tptp.unordered_pair tptp.y tptp.y) tptp.universal_class) true)) :rule resolution :premises (t217.t2.t8 t217.t2.a0))
% 25.76/26.03  (step t217.t2.t10 (cl (= (tptp.member (tptp.singleton tptp.y) tptp.universal_class) true)) :rule trans :premises (t217.t2.t6 t217.t2.t9))
% 25.76/26.03  (step t217.t2.t11 (cl (tptp.member (tptp.singleton tptp.y) tptp.universal_class)) :rule resolution :premises (t217.t2.t2 t217.t2.t10))
% 25.76/26.03  (step t217.t2 (cl (not (tptp.member (tptp.unordered_pair tptp.y tptp.y) tptp.universal_class)) (not (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y))) (tptp.member (tptp.singleton tptp.y) tptp.universal_class)) :rule subproof :discharge (t217.t2.a0 t217.t2.a1))
% 25.76/26.03  (step t217.t3 (cl (not (and (tptp.member (tptp.unordered_pair tptp.y tptp.y) tptp.universal_class) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)))) (tptp.member (tptp.unordered_pair tptp.y tptp.y) tptp.universal_class)) :rule and_pos)
% 25.76/26.03  (step t217.t4 (cl (not (and (tptp.member (tptp.unordered_pair tptp.y tptp.y) tptp.universal_class) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y))) :rule and_pos)
% 25.76/26.03  (step t217.t5 (cl (tptp.member (tptp.singleton tptp.y) tptp.universal_class) (not (and (tptp.member (tptp.unordered_pair tptp.y tptp.y) tptp.universal_class) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)))) (not (and (tptp.member (tptp.unordered_pair tptp.y tptp.y) tptp.universal_class) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y))))) :rule resolution :premises (t217.t2 t217.t3 t217.t4))
% 25.76/26.03  (step t217.t6 (cl (not (and (tptp.member (tptp.unordered_pair tptp.y tptp.y) tptp.universal_class) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)))) (not (and (tptp.member (tptp.unordered_pair tptp.y tptp.y) tptp.universal_class) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)))) (tptp.member (tptp.singleton tptp.y) tptp.universal_class)) :rule reordering :premises (t217.t5))
% 25.76/26.03  (step t217.t7 (cl (not (and (tptp.member (tptp.unordered_pair tptp.y tptp.y) tptp.universal_class) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)))) (tptp.member (tptp.singleton tptp.y) tptp.universal_class)) :rule contraction :premises (t217.t6))
% 25.76/26.03  (step t217.t8 (cl (=> (and (tptp.member (tptp.unordered_pair tptp.y tptp.y) tptp.universal_class) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y))) (tptp.member (tptp.singleton tptp.y) tptp.universal_class)) (tptp.member (tptp.singleton tptp.y) tptp.universal_class)) :rule resolution :premises (t217.t1 t217.t7))
% 25.76/26.03  (step t217.t9 (cl (=> (and (tptp.member (tptp.unordered_pair tptp.y tptp.y) tptp.universal_class) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y))) (tptp.member (tptp.singleton tptp.y) tptp.universal_class)) (not (tptp.member (tptp.singleton tptp.y) tptp.universal_class))) :rule implies_neg2)
% 25.76/26.03  (step t217.t10 (cl (=> (and (tptp.member (tptp.unordered_pair tptp.y tptp.y) tptp.universal_class) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y))) (tptp.member (tptp.singleton tptp.y) tptp.universal_class)) (=> (and (tptp.member (tptp.unordered_pair tptp.y tptp.y) tptp.universal_class) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y))) (tptp.member (tptp.singleton tptp.y) tptp.universal_class))) :rule resolution :premises (t217.t8 t217.t9))
% 25.76/26.03  (step t217.t11 (cl (=> (and (tptp.member (tptp.unordered_pair tptp.y tptp.y) tptp.universal_class) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y))) (tptp.member (tptp.singleton tptp.y) tptp.universal_class))) :rule contraction :premises (t217.t10))
% 25.76/26.03  (step t217.t12 (cl (not (and (tptp.member (tptp.unordered_pair tptp.y tptp.y) tptp.universal_class) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)))) (tptp.member (tptp.singleton tptp.y) tptp.universal_class)) :rule implies :premises (t217.t11))
% 25.76/26.03  (step t217.t13 (cl (and (tptp.member (tptp.unordered_pair tptp.y tptp.y) tptp.universal_class) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y))) (not (tptp.member (tptp.unordered_pair tptp.y tptp.y) tptp.universal_class)) (not (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)))) :rule and_neg)
% 25.76/26.03  (step t217.t14 (cl (and (tptp.member (tptp.unordered_pair tptp.y tptp.y) tptp.universal_class) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)))) :rule resolution :premises (t217.t13 t217.a1 t217.a0))
% 25.76/26.03  (step t217.t15 (cl (tptp.member (tptp.singleton tptp.y) tptp.universal_class)) :rule resolution :premises (t217.t12 t217.t14))
% 25.76/26.03  (step t217 (cl (not (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y))) (not (tptp.member (tptp.unordered_pair tptp.y tptp.y) tptp.universal_class)) (tptp.member (tptp.singleton tptp.y) tptp.universal_class)) :rule subproof :discharge (t217.a0 t217.a1))
% 25.76/26.03  (step t218 (cl (not (and (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (tptp.member (tptp.unordered_pair tptp.y tptp.y) tptp.universal_class))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y))) :rule and_pos)
% 25.76/26.03  (step t219 (cl (not (and (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (tptp.member (tptp.unordered_pair tptp.y tptp.y) tptp.universal_class))) (tptp.member (tptp.unordered_pair tptp.y tptp.y) tptp.universal_class)) :rule and_pos)
% 25.76/26.03  (step t220 (cl (tptp.member (tptp.singleton tptp.y) tptp.universal_class) (not (and (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (tptp.member (tptp.unordered_pair tptp.y tptp.y) tptp.universal_class))) (not (and (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (tptp.member (tptp.unordered_pair tptp.y tptp.y) tptp.universal_class)))) :rule resolution :premises (t217 t218 t219))
% 25.76/26.03  (step t221 (cl (not (and (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (tptp.member (tptp.unordered_pair tptp.y tptp.y) tptp.universal_class))) (not (and (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (tptp.member (tptp.unordered_pair tptp.y tptp.y) tptp.universal_class))) (tptp.member (tptp.singleton tptp.y) tptp.universal_class)) :rule reordering :premises (t220))
% 25.76/26.03  (step t222 (cl (not (and (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (tptp.member (tptp.unordered_pair tptp.y tptp.y) tptp.universal_class))) (tptp.member (tptp.singleton tptp.y) tptp.universal_class)) :rule contraction :premises (t221))
% 25.76/26.03  (step t223 (cl (=> (and (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (tptp.member (tptp.unordered_pair tptp.y tptp.y) tptp.universal_class)) (tptp.member (tptp.singleton tptp.y) tptp.universal_class)) (tptp.member (tptp.singleton tptp.y) tptp.universal_class)) :rule resolution :premises (t216 t222))
% 25.76/26.03  (step t224 (cl (=> (and (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (tptp.member (tptp.unordered_pair tptp.y tptp.y) tptp.universal_class)) (tptp.member (tptp.singleton tptp.y) tptp.universal_class)) (not (tptp.member (tptp.singleton tptp.y) tptp.universal_class))) :rule implies_neg2)
% 25.76/26.03  (step t225 (cl (=> (and (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (tptp.member (tptp.unordered_pair tptp.y tptp.y) tptp.universal_class)) (tptp.member (tptp.singleton tptp.y) tptp.universal_class)) (=> (and (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (tptp.member (tptp.unordered_pair tptp.y tptp.y) tptp.universal_class)) (tptp.member (tptp.singleton tptp.y) tptp.universal_class))) :rule resolution :premises (t223 t224))
% 25.76/26.03  (step t226 (cl (=> (and (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (tptp.member (tptp.unordered_pair tptp.y tptp.y) tptp.universal_class)) (tptp.member (tptp.singleton tptp.y) tptp.universal_class))) :rule contraction :premises (t225))
% 25.76/26.03  (step t227 (cl (not (and (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (tptp.member (tptp.unordered_pair tptp.y tptp.y) tptp.universal_class))) (tptp.member (tptp.singleton tptp.y) tptp.universal_class)) :rule implies :premises (t226))
% 25.76/26.03  (step t228 (cl (not (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y))) (not (tptp.member (tptp.unordered_pair tptp.y tptp.y) tptp.universal_class)) (tptp.member (tptp.singleton tptp.y) tptp.universal_class)) :rule resolution :premises (t215 t227))
% 25.76/26.03  (step t229 (cl (tptp.member (tptp.singleton tptp.y) tptp.universal_class) (not (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y))) (not (tptp.member (tptp.unordered_pair tptp.y tptp.y) tptp.universal_class))) :rule reordering :premises (t228))
% 25.76/26.03  (step t230 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (tptp.member (tptp.unordered_pair X Y) tptp.universal_class)) (tptp.member (tptp.unordered_pair tptp.y tptp.y) tptp.universal_class)) (forall ((X $$unsorted) (Y $$unsorted)) (tptp.member (tptp.unordered_pair X Y) tptp.universal_class))) :rule implies_neg1)
% 25.76/26.03  (anchor :step t231)
% 25.76/26.03  (assume t231.a0 (forall ((X $$unsorted) (Y $$unsorted)) (tptp.member (tptp.unordered_pair X Y) tptp.universal_class)))
% 25.76/26.03  (step t231.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (tptp.member (tptp.unordered_pair X Y) tptp.universal_class))) (tptp.member (tptp.unordered_pair tptp.y tptp.y) tptp.universal_class))) :rule forall_inst :args ((:= X tptp.y) (:= Y tptp.y)))
% 25.76/26.03  (step t231.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (tptp.member (tptp.unordered_pair X Y) tptp.universal_class))) (tptp.member (tptp.unordered_pair tptp.y tptp.y) tptp.universal_class)) :rule or :premises (t231.t1))
% 25.76/26.03  (step t231.t3 (cl (tptp.member (tptp.unordered_pair tptp.y tptp.y) tptp.universal_class)) :rule resolution :premises (t231.t2 t231.a0))
% 25.76/26.03  (step t231 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (tptp.member (tptp.unordered_pair X Y) tptp.universal_class))) (tptp.member (tptp.unordered_pair tptp.y tptp.y) tptp.universal_class)) :rule subproof :discharge (t231.a0))
% 25.76/26.03  (step t232 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (tptp.member (tptp.unordered_pair X Y) tptp.universal_class)) (tptp.member (tptp.unordered_pair tptp.y tptp.y) tptp.universal_class)) (tptp.member (tptp.unordered_pair tptp.y tptp.y) tptp.universal_class)) :rule resolution :premises (t230 t231))
% 25.76/26.03  (step t233 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (tptp.member (tptp.unordered_pair X Y) tptp.universal_class)) (tptp.member (tptp.unordered_pair tptp.y tptp.y) tptp.universal_class)) (not (tptp.member (tptp.unordered_pair tptp.y tptp.y) tptp.universal_class))) :rule implies_neg2)
% 25.76/26.03  (step t234 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (tptp.member (tptp.unordered_pair X Y) tptp.universal_class)) (tptp.member (tptp.unordered_pair tptp.y tptp.y) tptp.universal_class)) (=> (forall ((X $$unsorted) (Y $$unsorted)) (tptp.member (tptp.unordered_pair X Y) tptp.universal_class)) (tptp.member (tptp.unordered_pair tptp.y tptp.y) tptp.universal_class))) :rule resolution :premises (t232 t233))
% 25.76/26.03  (step t235 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (tptp.member (tptp.unordered_pair X Y) tptp.universal_class)) (tptp.member (tptp.unordered_pair tptp.y tptp.y) tptp.universal_class))) :rule contraction :premises (t234))
% 25.76/26.03  (step t236 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (tptp.member (tptp.unordered_pair X Y) tptp.universal_class))) (tptp.member (tptp.unordered_pair tptp.y tptp.y) tptp.universal_class)) :rule implies :premises (t235))
% 25.76/26.03  (step t237 (cl (tptp.member (tptp.unordered_pair tptp.y tptp.y) tptp.universal_class)) :rule resolution :premises (t236 a10))
% 25.76/26.03  (step t238 (cl (tptp.member (tptp.singleton tptp.y) tptp.universal_class)) :rule resolution :premises (t229 t158 t237))
% 25.76/26.03  (step t239 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (tptp.member X (tptp.unordered_pair X Y)))) (or (not (tptp.member (tptp.singleton tptp.y) tptp.universal_class)) (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (tptp.member X (tptp.unordered_pair X Y))))) :rule implies_neg1)
% 25.76/26.03  (anchor :step t240)
% 25.76/26.03  (assume t240.a0 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (tptp.member X (tptp.unordered_pair X Y)))))
% 25.76/26.03  (step t240.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (tptp.member X (tptp.unordered_pair X Y))))) (or (not (tptp.member (tptp.singleton tptp.y) tptp.universal_class)) (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z))))))) :rule forall_inst :args ((:= X (tptp.singleton tptp.y)) (:= Y (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))))
% 25.76/26.03  (step t240.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (tptp.member X (tptp.unordered_pair X Y))))) (or (not (tptp.member (tptp.singleton tptp.y) tptp.universal_class)) (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))))) :rule or :premises (t240.t1))
% 25.76/26.03  (step t240.t3 (cl (or (not (tptp.member (tptp.singleton tptp.y) tptp.universal_class)) (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))))) :rule resolution :premises (t240.t2 t240.a0))
% 25.76/26.03  (step t240 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (tptp.member X (tptp.unordered_pair X Y))))) (or (not (tptp.member (tptp.singleton tptp.y) tptp.universal_class)) (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))))) :rule subproof :discharge (t240.a0))
% 25.76/26.03  (step t241 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (tptp.member X (tptp.unordered_pair X Y)))) (or (not (tptp.member (tptp.singleton tptp.y) tptp.universal_class)) (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))))) (or (not (tptp.member (tptp.singleton tptp.y) tptp.universal_class)) (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))))) :rule resolution :premises (t239 t240))
% 25.76/26.03  (step t242 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (tptp.member X (tptp.unordered_pair X Y)))) (or (not (tptp.member (tptp.singleton tptp.y) tptp.universal_class)) (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))))) (not (or (not (tptp.member (tptp.singleton tptp.y) tptp.universal_class)) (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z))))))) :rule implies_neg2)
% 25.76/26.03  (step t243 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (tptp.member X (tptp.unordered_pair X Y)))) (or (not (tptp.member (tptp.singleton tptp.y) tptp.universal_class)) (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (tptp.member X (tptp.unordered_pair X Y)))) (or (not (tptp.member (tptp.singleton tptp.y) tptp.universal_class)) (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z))))))) :rule resolution :premises (t241 t242))
% 25.76/26.03  (step t244 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (tptp.member X (tptp.unordered_pair X Y)))) (or (not (tptp.member (tptp.singleton tptp.y) tptp.universal_class)) (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z))))))) :rule contraction :premises (t243))
% 25.76/26.03  (step t245 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (tptp.member X (tptp.unordered_pair X Y))))) (or (not (tptp.member (tptp.singleton tptp.y) tptp.universal_class)) (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))))) :rule implies :premises (t244))
% 25.76/26.03  (step t246 (cl (or (not (tptp.member (tptp.singleton tptp.y) tptp.universal_class)) (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z)))))) :rule resolution :premises (t245 a8))
% 25.76/26.03  (step t247 (cl (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y (tptp.singleton tptp.z))))) :rule resolution :premises (t214 t238 t246))
% 25.76/26.03  (step t248 (cl (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) :rule resolution :premises (t187 a91 t200 t212 t247))
% 25.76/26.03  (step t249 (cl (not (= (=> (forall ((U $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member U (tptp.unordered_pair X Y))) (= U X) (= U Y))) (or (not (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) (= (tptp.singleton tptp.y) (tptp.singleton tptp.w)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) (=> (forall ((U $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member U (tptp.unordered_pair X Y))) (= U X) (= U Y))) (or (not (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) (= (tptp.singleton tptp.w) (tptp.singleton tptp.y)) (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y)))))) (not (=> (forall ((U $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member U (tptp.unordered_pair X Y))) (= U X) (= U Y))) (or (not (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) (= (tptp.singleton tptp.y) (tptp.singleton tptp.w)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))))) (=> (forall ((U $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member U (tptp.unordered_pair X Y))) (= U X) (= U Y))) (or (not (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) (= (tptp.singleton tptp.w) (tptp.singleton tptp.y)) (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y))))) :rule equiv_pos2)
% 25.76/26.03  (step t250 (cl (= (forall ((U $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member U (tptp.unordered_pair X Y))) (= U X) (= U Y))) (forall ((U $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member U (tptp.unordered_pair X Y))) (= U X) (= U Y))))) :rule refl)
% 25.76/26.03  (step t251 (cl (= (not (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) (not (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))))) :rule refl)
% 25.76/26.03  (step t252 (cl (= (= (tptp.singleton tptp.y) (tptp.singleton tptp.w)) (= (tptp.singleton tptp.w) (tptp.singleton tptp.y)))) :rule all_simplify)
% 25.76/26.03  (step t253 (cl (= (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))) (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y)))) :rule all_simplify)
% 25.76/26.03  (step t254 (cl (= (or (not (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) (= (tptp.singleton tptp.y) (tptp.singleton tptp.w)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))) (or (not (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) (= (tptp.singleton tptp.w) (tptp.singleton tptp.y)) (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y))))) :rule cong :premises (t251 t252 t253))
% 25.76/26.03  (step t255 (cl (= (=> (forall ((U $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member U (tptp.unordered_pair X Y))) (= U X) (= U Y))) (or (not (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) (= (tptp.singleton tptp.y) (tptp.singleton tptp.w)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) (=> (forall ((U $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member U (tptp.unordered_pair X Y))) (= U X) (= U Y))) (or (not (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) (= (tptp.singleton tptp.w) (tptp.singleton tptp.y)) (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y)))))) :rule cong :premises (t250 t254))
% 25.76/26.03  (step t256 (cl (=> (forall ((U $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member U (tptp.unordered_pair X Y))) (= U X) (= U Y))) (or (not (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) (= (tptp.singleton tptp.y) (tptp.singleton tptp.w)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) (forall ((U $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member U (tptp.unordered_pair X Y))) (= U X) (= U Y)))) :rule implies_neg1)
% 25.76/26.03  (anchor :step t257)
% 25.76/26.03  (assume t257.a0 (forall ((U $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member U (tptp.unordered_pair X Y))) (= U X) (= U Y))))
% 25.76/26.03  (step t257.t1 (cl (or (not (forall ((U $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member U (tptp.unordered_pair X Y))) (= U X) (= U Y)))) (or (not (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) (= (tptp.singleton tptp.y) (tptp.singleton tptp.w)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))))) :rule forall_inst :args ((:= U (tptp.singleton tptp.y)) (:= X (tptp.singleton tptp.w)) (:= Y (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))))
% 25.76/26.03  (step t257.t2 (cl (not (forall ((U $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member U (tptp.unordered_pair X Y))) (= U X) (= U Y)))) (or (not (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) (= (tptp.singleton tptp.y) (tptp.singleton tptp.w)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) :rule or :premises (t257.t1))
% 25.76/26.03  (step t257.t3 (cl (or (not (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) (= (tptp.singleton tptp.y) (tptp.singleton tptp.w)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) :rule resolution :premises (t257.t2 t257.a0))
% 25.76/26.03  (step t257 (cl (not (forall ((U $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member U (tptp.unordered_pair X Y))) (= U X) (= U Y)))) (or (not (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) (= (tptp.singleton tptp.y) (tptp.singleton tptp.w)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) :rule subproof :discharge (t257.a0))
% 25.76/26.03  (step t258 (cl (=> (forall ((U $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member U (tptp.unordered_pair X Y))) (= U X) (= U Y))) (or (not (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) (= (tptp.singleton tptp.y) (tptp.singleton tptp.w)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) (or (not (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) (= (tptp.singleton tptp.y) (tptp.singleton tptp.w)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) :rule resolution :premises (t256 t257))
% 25.76/26.03  (step t259 (cl (=> (forall ((U $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member U (tptp.unordered_pair X Y))) (= U X) (= U Y))) (or (not (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) (= (tptp.singleton tptp.y) (tptp.singleton tptp.w)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) (not (or (not (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) (= (tptp.singleton tptp.y) (tptp.singleton tptp.w)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))))) :rule implies_neg2)
% 25.76/26.03  (step t260 (cl (=> (forall ((U $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member U (tptp.unordered_pair X Y))) (= U X) (= U Y))) (or (not (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) (= (tptp.singleton tptp.y) (tptp.singleton tptp.w)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) (=> (forall ((U $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member U (tptp.unordered_pair X Y))) (= U X) (= U Y))) (or (not (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) (= (tptp.singleton tptp.y) (tptp.singleton tptp.w)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))))) :rule resolution :premises (t258 t259))
% 25.76/26.03  (step t261 (cl (=> (forall ((U $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member U (tptp.unordered_pair X Y))) (= U X) (= U Y))) (or (not (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) (= (tptp.singleton tptp.y) (tptp.singleton tptp.w)) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)))))) :rule contraction :premises (t260))
% 25.76/26.03  (step t262 (cl (=> (forall ((U $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member U (tptp.unordered_pair X Y))) (= U X) (= U Y))) (or (not (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) (= (tptp.singleton tptp.w) (tptp.singleton tptp.y)) (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y))))) :rule resolution :premises (t249 t255 t261))
% 25.76/26.03  (step t263 (cl (not (forall ((U $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member U (tptp.unordered_pair X Y))) (= U X) (= U Y)))) (or (not (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) (= (tptp.singleton tptp.w) (tptp.singleton tptp.y)) (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y)))) :rule implies :premises (t262))
% 25.76/26.03  (step t264 (cl (or (not (tptp.member (tptp.singleton tptp.y) (tptp.unordered_pair (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w (tptp.singleton tptp.x))))) (= (tptp.singleton tptp.w) (tptp.singleton tptp.y)) (= (tptp.unordered_pair tptp.w (tptp.singleton tptp.x)) (tptp.singleton tptp.y)))) :rule resolution :premises (t263 a7))
% 25.76/26.03  (step t265 (cl (= (tptp.singleton tptp.w) (tptp.singleton tptp.y))) :rule resolution :premises (t81 t171 t248 t264))
% 25.76/26.03  (step t266 (cl (not (= (=> (forall ((X $$unsorted)) (= (tptp.unordered_pair X X) (tptp.singleton X))) (= (tptp.unordered_pair tptp.w tptp.w) (tptp.singleton tptp.w))) (=> (forall ((X $$unsorted)) (= (tptp.unordered_pair X X) (tptp.singleton X))) (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w))))) (not (=> (forall ((X $$unsorted)) (= (tptp.unordered_pair X X) (tptp.singleton X))) (= (tptp.unordered_pair tptp.w tptp.w) (tptp.singleton tptp.w)))) (=> (forall ((X $$unsorted)) (= (tptp.unordered_pair X X) (tptp.singleton X))) (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w)))) :rule equiv_pos2)
% 25.76/26.03  (step t267 (cl (= (= (tptp.unordered_pair tptp.w tptp.w) (tptp.singleton tptp.w)) (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w)))) :rule all_simplify)
% 25.76/26.03  (step t268 (cl (= (=> (forall ((X $$unsorted)) (= (tptp.unordered_pair X X) (tptp.singleton X))) (= (tptp.unordered_pair tptp.w tptp.w) (tptp.singleton tptp.w))) (=> (forall ((X $$unsorted)) (= (tptp.unordered_pair X X) (tptp.singleton X))) (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w))))) :rule cong :premises (t147 t267))
% 25.76/26.03  (step t269 (cl (=> (forall ((X $$unsorted)) (= (tptp.unordered_pair X X) (tptp.singleton X))) (= (tptp.unordered_pair tptp.w tptp.w) (tptp.singleton tptp.w))) (forall ((X $$unsorted)) (= (tptp.unordered_pair X X) (tptp.singleton X)))) :rule implies_neg1)
% 25.76/26.03  (anchor :step t270)
% 25.76/26.03  (assume t270.a0 (forall ((X $$unsorted)) (= (tptp.unordered_pair X X) (tptp.singleton X))))
% 25.76/26.03  (step t270.t1 (cl (or (not (forall ((X $$unsorted)) (= (tptp.unordered_pair X X) (tptp.singleton X)))) (= (tptp.unordered_pair tptp.w tptp.w) (tptp.singleton tptp.w)))) :rule forall_inst :args ((:= X tptp.w)))
% 25.76/26.03  (step t270.t2 (cl (not (forall ((X $$unsorted)) (= (tptp.unordered_pair X X) (tptp.singleton X)))) (= (tptp.unordered_pair tptp.w tptp.w) (tptp.singleton tptp.w))) :rule or :premises (t270.t1))
% 25.76/26.03  (step t270.t3 (cl (= (tptp.unordered_pair tptp.w tptp.w) (tptp.singleton tptp.w))) :rule resolution :premises (t270.t2 t270.a0))
% 25.76/26.03  (step t270 (cl (not (forall ((X $$unsorted)) (= (tptp.unordered_pair X X) (tptp.singleton X)))) (= (tptp.unordered_pair tptp.w tptp.w) (tptp.singleton tptp.w))) :rule subproof :discharge (t270.a0))
% 25.76/26.03  (step t271 (cl (=> (forall ((X $$unsorted)) (= (tptp.unordered_pair X X) (tptp.singleton X))) (= (tptp.unordered_pair tptp.w tptp.w) (tptp.singleton tptp.w))) (= (tptp.unordered_pair tptp.w tptp.w) (tptp.singleton tptp.w))) :rule resolution :premises (t269 t270))
% 25.76/26.03  (step t272 (cl (=> (forall ((X $$unsorted)) (= (tptp.unordered_pair X X) (tptp.singleton X))) (= (tptp.unordered_pair tptp.w tptp.w) (tptp.singleton tptp.w))) (not (= (tptp.unordered_pair tptp.w tptp.w) (tptp.singleton tptp.w)))) :rule implies_neg2)
% 25.76/26.03  (step t273 (cl (=> (forall ((X $$unsorted)) (= (tptp.unordered_pair X X) (tptp.singleton X))) (= (tptp.unordered_pair tptp.w tptp.w) (tptp.singleton tptp.w))) (=> (forall ((X $$unsorted)) (= (tptp.unordered_pair X X) (tptp.singleton X))) (= (tptp.unordered_pair tptp.w tptp.w) (tptp.singleton tptp.w)))) :rule resolution :premises (t271 t272))
% 25.76/26.03  (step t274 (cl (=> (forall ((X $$unsorted)) (= (tptp.unordered_pair X X) (tptp.singleton X))) (= (tptp.unordered_pair tptp.w tptp.w) (tptp.singleton tptp.w)))) :rule contraction :premises (t273))
% 25.76/26.03  (step t275 (cl (=> (forall ((X $$unsorted)) (= (tptp.unordered_pair X X) (tptp.singleton X))) (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w)))) :rule resolution :premises (t266 t268 t274))
% 25.76/26.03  (step t276 (cl (not (forall ((X $$unsorted)) (= (tptp.unordered_pair X X) (tptp.singleton X)))) (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w))) :rule implies :premises (t275))
% 25.76/26.03  (step t277 (cl (= (tptp.singleton tptp.w) (tptp.unordered_pair tptp.w tptp.w))) :rule resolution :premises (t276 a11))
% 25.76/26.03  (step t278 (cl) :rule resolution :premises (t68 t79 t265 t170 t158 t277))
% 25.76/26.03  
% 25.76/26.03  % SZS output end Proof for /export/starexec/sandbox/tmp/tmp.lE0e3d0pWC/cvc5---1.0.5_11112.smt2
% 25.76/26.03  % cvc5---1.0.5 exiting
% 25.76/26.03  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------