%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SET103-6 : TPTP v8.2.0. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : do_cvc5 %s %d

% Computer : n006.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 17:44:12 EDT 2024

% Result   : Unsatisfiable 30.43s 30.63s
% Output   : Proof 30.43s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem    : SET103-6 : TPTP v8.2.0. Bugfixed v2.1.0.
% 0.12/0.14  % Command    : do_cvc5 %s %d
% 0.15/0.35  % Computer : n006.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit   : 300
% 0.15/0.35  % WCLimit    : 300
% 0.15/0.35  % DateTime   : Tue May 28 09:21:39 EDT 2024
% 0.15/0.35  % CPUTime    : 
% 0.21/0.51  %----Proving TF0_NAR, FOF, or CNF
% 0.21/0.52  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 10.44/10.69  --- Run --no-e-matching --full-saturate-quant at 5...
% 15.53/15.73  --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 20.54/20.78  --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 25.61/25.82  --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 30.43/30.63  % SZS status Unsatisfiable for /export/starexec/sandbox/tmp/tmp.GbxorQhN9e/cvc5---1.0.5_18319.smt2
% 30.43/30.63  % SZS output start Proof for /export/starexec/sandbox/tmp/tmp.GbxorQhN9e/cvc5---1.0.5_18319.smt2
% 30.43/30.65  (assume a0 (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (not (tptp.subclass X Y)) (not (tptp.member U X)) (tptp.member U Y))))
% 30.43/30.65  (assume a1 (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.member (tptp.not_subclass_element X Y) X) (tptp.subclass X Y))))
% 30.43/30.65  (assume a2 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.not_subclass_element X Y) Y)) (tptp.subclass X Y))))
% 30.43/30.65  (assume a3 (forall ((X $$unsorted)) (tptp.subclass X tptp.universal_class)))
% 30.43/30.65  (assume a4 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= X Y)) (tptp.subclass X Y))))
% 30.43/30.65  (assume a5 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= X Y)) (tptp.subclass Y X))))
% 30.43/30.65  (assume a6 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.subclass X Y)) (not (tptp.subclass Y X)) (= X Y))))
% 30.43/30.65  (assume a7 (forall ((U $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member U (tptp.unordered_pair X Y))) (= U X) (= U Y))))
% 30.43/30.65  (assume a8 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (tptp.member X (tptp.unordered_pair X Y)))))
% 30.43/30.65  (assume a9 (forall ((Y $$unsorted) (X $$unsorted)) (or (not (tptp.member Y tptp.universal_class)) (tptp.member Y (tptp.unordered_pair X Y)))))
% 30.43/30.65  (assume a10 (forall ((X $$unsorted) (Y $$unsorted)) (tptp.member (tptp.unordered_pair X Y) tptp.universal_class)))
% 30.43/30.65  (assume a11 (forall ((X $$unsorted)) (= (tptp.unordered_pair X X) (tptp.singleton X))))
% 30.43/30.65  (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))))
% 30.43/30.65  (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))))
% 30.43/30.65  (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))))
% 30.43/30.65  (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)))))
% 30.43/30.65  (assume a16 (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.cross_product X Y))) (= (tptp.ordered_pair (tptp.first Z) (tptp.second Z)) Z))))
% 30.43/30.65  (assume a17 (tptp.subclass tptp.element_relation (tptp.cross_product tptp.universal_class tptp.universal_class)))
% 30.43/30.65  (assume a18 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.ordered_pair X Y) tptp.element_relation)) (tptp.member X Y))))
% 30.43/30.65  (assume a19 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.ordered_pair X Y) (tptp.cross_product tptp.universal_class tptp.universal_class))) (not (tptp.member X Y)) (tptp.member (tptp.ordered_pair X Y) tptp.element_relation))))
% 30.43/30.65  (assume a20 (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.intersection X Y))) (tptp.member Z X))))
% 30.43/30.65  (assume a21 (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.intersection X Y))) (tptp.member Z Y))))
% 30.43/30.65  (assume a22 (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z X)) (not (tptp.member Z Y)) (tptp.member Z (tptp.intersection X Y)))))
% 30.43/30.65  (assume a23 (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.complement X))) (not (tptp.member Z X)))))
% 30.43/30.65  (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))))
% 30.43/30.65  (assume a25 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.complement (tptp.intersection (tptp.complement X) (tptp.complement Y))) (tptp.union X Y))))
% 30.43/30.65  (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))))
% 30.43/30.65  (assume a27 (forall ((Xr $$unsorted) (X $$unsorted) (Y $$unsorted)) (= (tptp.intersection Xr (tptp.cross_product X Y)) (tptp.restrict Xr X Y))))
% 30.43/30.65  (assume a28 (forall ((X $$unsorted) (Y $$unsorted) (Xr $$unsorted)) (= (tptp.intersection (tptp.cross_product X Y) Xr) (tptp.restrict Xr X Y))))
% 30.43/30.65  (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))))))
% 30.43/30.65  (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)))))
% 30.43/30.65  (assume a31 (forall ((X $$unsorted)) (tptp.subclass (tptp.rotate X) (tptp.cross_product (tptp.cross_product tptp.universal_class tptp.universal_class) tptp.universal_class))))
% 30.43/30.65  (assume a32 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (or (not (tptp.member (tptp.ordered_pair (tptp.ordered_pair U V) W) (tptp.rotate X))) (tptp.member (tptp.ordered_pair (tptp.ordered_pair V W) U) X))))
% 30.43/30.65  (assume a33 (forall ((V $$unsorted) (W $$unsorted) (U $$unsorted) (X $$unsorted)) (or (not (tptp.member (tptp.ordered_pair (tptp.ordered_pair V W) U) X)) (not (tptp.member (tptp.ordered_pair (tptp.ordered_pair U V) W) (tptp.cross_product (tptp.cross_product tptp.universal_class tptp.universal_class) tptp.universal_class))) (tptp.member (tptp.ordered_pair (tptp.ordered_pair U V) W) (tptp.rotate X)))))
% 30.43/30.65  (assume a34 (forall ((X $$unsorted)) (tptp.subclass (tptp.flip X) (tptp.cross_product (tptp.cross_product tptp.universal_class tptp.universal_class) tptp.universal_class))))
% 30.43/30.65  (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))))
% 30.43/30.65  (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)))))
% 30.43/30.65  (assume a37 (forall ((Y $$unsorted)) (= (tptp.domain_of (tptp.flip (tptp.cross_product Y tptp.universal_class))) (tptp.inverse Y))))
% 30.43/30.65  (assume a38 (forall ((Z $$unsorted)) (= (tptp.domain_of (tptp.inverse Z)) (tptp.range_of Z))))
% 30.43/30.65  (assume a39 (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (= (tptp.first (tptp.not_subclass_element (tptp.restrict Z X (tptp.singleton Y)) tptp.null_class)) (tptp.domain Z X Y))))
% 30.43/30.65  (assume a40 (forall ((Z $$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))))
% 30.43/30.65  (assume a41 (forall ((Xr $$unsorted) (X $$unsorted)) (= (tptp.range_of (tptp.restrict Xr X tptp.universal_class)) (tptp.image Xr X))))
% 30.43/30.65  (assume a42 (forall ((X $$unsorted)) (= (tptp.union X (tptp.singleton X)) (tptp.successor X))))
% 30.43/30.65  (assume a43 (tptp.subclass tptp.successor_relation (tptp.cross_product tptp.universal_class tptp.universal_class)))
% 30.43/30.65  (assume a44 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.ordered_pair X Y) tptp.successor_relation)) (= (tptp.successor X) Y))))
% 30.43/30.65  (assume a45 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= (tptp.successor X) Y)) (not (tptp.member (tptp.ordered_pair X Y) (tptp.cross_product tptp.universal_class tptp.universal_class))) (tptp.member (tptp.ordered_pair X Y) tptp.successor_relation))))
% 30.43/30.65  (assume a46 (forall ((X $$unsorted)) (or (not (tptp.inductive X)) (tptp.member tptp.null_class X))))
% 30.43/30.65  (assume a47 (forall ((X $$unsorted)) (or (not (tptp.inductive X)) (tptp.subclass (tptp.image tptp.successor_relation X) X))))
% 30.43/30.65  (assume a48 (forall ((X $$unsorted)) (or (not (tptp.member tptp.null_class X)) (not (tptp.subclass (tptp.image tptp.successor_relation X) X)) (tptp.inductive X))))
% 30.43/30.65  (assume a49 (tptp.inductive tptp.omega))
% 30.43/30.65  (assume a50 (forall ((Y $$unsorted)) (or (not (tptp.inductive Y)) (tptp.subclass tptp.omega Y))))
% 30.43/30.65  (assume a51 (tptp.member tptp.omega tptp.universal_class))
% 30.43/30.65  (assume a52 (forall ((X $$unsorted)) (= (tptp.domain_of (tptp.restrict tptp.element_relation tptp.universal_class X)) (tptp.sum_class X))))
% 30.43/30.65  (assume a53 (forall ((X $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (tptp.member (tptp.sum_class X) tptp.universal_class))))
% 30.43/30.65  (assume a54 (forall ((X $$unsorted)) (= (tptp.complement (tptp.image tptp.element_relation (tptp.complement X))) (tptp.power_class X))))
% 30.43/30.65  (assume a55 (forall ((U $$unsorted)) (or (not (tptp.member U tptp.universal_class)) (tptp.member (tptp.power_class U) tptp.universal_class))))
% 30.43/30.65  (assume a56 (forall ((Yr $$unsorted) (Xr $$unsorted)) (tptp.subclass (tptp.compose Yr Xr) (tptp.cross_product tptp.universal_class tptp.universal_class))))
% 30.43/30.65  (assume a57 (forall ((Y $$unsorted) (Z $$unsorted) (Yr $$unsorted) (Xr $$unsorted)) (or (not (tptp.member (tptp.ordered_pair Y Z) (tptp.compose Yr Xr))) (tptp.member Z (tptp.image Yr (tptp.image Xr (tptp.singleton Y)))))))
% 30.43/30.65  (assume a58 (forall ((Z $$unsorted) (Yr $$unsorted) (Xr $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.image Yr (tptp.image Xr (tptp.singleton Y))))) (not (tptp.member (tptp.ordered_pair Y Z) (tptp.cross_product tptp.universal_class tptp.universal_class))) (tptp.member (tptp.ordered_pair Y Z) (tptp.compose Yr Xr)))))
% 30.43/30.65  (assume a59 (forall ((X $$unsorted)) (or (not (tptp.single_valued_class X)) (tptp.subclass (tptp.compose X (tptp.inverse X)) tptp.identity_relation))))
% 30.43/30.65  (assume a60 (forall ((X $$unsorted)) (or (not (tptp.subclass (tptp.compose X (tptp.inverse X)) tptp.identity_relation)) (tptp.single_valued_class X))))
% 30.43/30.65  (assume a61 (forall ((Xf $$unsorted)) (or (not (tptp.function Xf)) (tptp.subclass Xf (tptp.cross_product tptp.universal_class tptp.universal_class)))))
% 30.43/30.65  (assume a62 (forall ((Xf $$unsorted)) (or (not (tptp.function Xf)) (tptp.subclass (tptp.compose Xf (tptp.inverse Xf)) tptp.identity_relation))))
% 30.43/30.65  (assume a63 (forall ((Xf $$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))))
% 30.43/30.65  (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))))
% 30.43/30.65  (assume a65 (forall ((X $$unsorted)) (or (= X tptp.null_class) (tptp.member (tptp.regular X) X))))
% 30.43/30.65  (assume a66 (forall ((X $$unsorted)) (or (= X tptp.null_class) (= (tptp.intersection X (tptp.regular X)) tptp.null_class))))
% 30.43/30.65  (assume a67 (forall ((Xf $$unsorted) (Y $$unsorted)) (= (tptp.sum_class (tptp.image Xf (tptp.singleton Y))) (tptp.apply Xf Y))))
% 30.43/30.65  (assume a68 (tptp.function tptp.choice))
% 30.43/30.65  (assume a69 (forall ((Y $$unsorted)) (or (not (tptp.member Y tptp.universal_class)) (= Y tptp.null_class) (tptp.member (tptp.apply tptp.choice Y) Y))))
% 30.43/30.65  (assume a70 (forall ((Xf $$unsorted)) (or (not (tptp.one_to_one Xf)) (tptp.function Xf))))
% 30.43/30.65  (assume a71 (forall ((Xf $$unsorted)) (or (not (tptp.one_to_one Xf)) (tptp.function (tptp.inverse Xf)))))
% 30.43/30.65  (assume a72 (forall ((Xf $$unsorted)) (or (not (tptp.function (tptp.inverse Xf))) (not (tptp.function Xf)) (tptp.one_to_one Xf))))
% 30.43/30.65  (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))
% 30.43/30.65  (assume a74 (= (tptp.intersection (tptp.inverse tptp.subset_relation) tptp.subset_relation) tptp.identity_relation))
% 30.43/30.65  (assume a75 (forall ((Xr $$unsorted)) (= (tptp.complement (tptp.domain_of (tptp.intersection Xr tptp.identity_relation))) (tptp.diagonalise Xr))))
% 30.43/30.65  (assume a76 (forall ((X $$unsorted)) (= (tptp.intersection (tptp.domain_of X) (tptp.diagonalise (tptp.compose (tptp.inverse tptp.element_relation) X))) (tptp.cantor X))))
% 30.43/30.65  (assume a77 (forall ((Xf $$unsorted)) (or (not (tptp.operation Xf)) (tptp.function Xf))))
% 30.43/30.65  (assume a78 (forall ((Xf $$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)))))
% 30.43/30.65  (assume a79 (forall ((Xf $$unsorted)) (or (not (tptp.operation Xf)) (tptp.subclass (tptp.range_of Xf) (tptp.domain_of (tptp.domain_of Xf))))))
% 30.43/30.65  (assume a80 (forall ((Xf $$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))))
% 30.43/30.65  (assume a81 (forall ((Xh $$unsorted) (Xf1 $$unsorted) (Xf2 $$unsorted)) (or (not (tptp.compatible Xh Xf1 Xf2)) (tptp.function Xh))))
% 30.43/30.65  (assume a82 (forall ((Xh $$unsorted) (Xf1 $$unsorted) (Xf2 $$unsorted)) (or (not (tptp.compatible Xh Xf1 Xf2)) (= (tptp.domain_of (tptp.domain_of Xf1)) (tptp.domain_of Xh)))))
% 30.43/30.65  (assume a83 (forall ((Xh $$unsorted) (Xf1 $$unsorted) (Xf2 $$unsorted)) (or (not (tptp.compatible Xh Xf1 Xf2)) (tptp.subclass (tptp.range_of Xh) (tptp.domain_of (tptp.domain_of Xf2))))))
% 30.43/30.65  (assume a84 (forall ((Xh $$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))))
% 30.43/30.65  (assume a85 (forall ((Xh $$unsorted) (Xf1 $$unsorted) (Xf2 $$unsorted)) (or (not (tptp.homomorphism Xh Xf1 Xf2)) (tptp.operation Xf1))))
% 30.43/30.65  (assume a86 (forall ((Xh $$unsorted) (Xf1 $$unsorted) (Xf2 $$unsorted)) (or (not (tptp.homomorphism Xh Xf1 Xf2)) (tptp.operation Xf2))))
% 30.43/30.65  (assume a87 (forall ((Xh $$unsorted) (Xf1 $$unsorted) (Xf2 $$unsorted)) (or (not (tptp.homomorphism Xh Xf1 Xf2)) (tptp.compatible Xh Xf1 Xf2))))
% 30.43/30.65  (assume a88 (forall ((Xh $$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)))))))
% 30.43/30.65  (assume a89 (forall ((Xf1 $$unsorted) (Xf2 $$unsorted) (Xh $$unsorted)) (or (not (tptp.operation Xf1)) (not (tptp.operation Xf2)) (not (tptp.compatible Xh Xf1 Xf2)) (tptp.member (tptp.ordered_pair (tptp.not_homomorphism1 Xh Xf1 Xf2) (tptp.not_homomorphism2 Xh Xf1 Xf2)) (tptp.domain_of Xf1)) (tptp.homomorphism Xh Xf1 Xf2))))
% 30.43/30.65  (assume a90 (forall ((Xf1 $$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))))
% 30.43/30.65  (assume a91 (not (= (tptp.unordered_pair (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.null_class)) (tptp.ordered_pair tptp.x tptp.y))))
% 30.43/30.65  (assume a92 (not (tptp.member tptp.y tptp.universal_class)))
% 30.43/30.65  (step t1 (cl (and (= (tptp.ordered_pair tptp.x tptp.y) (tptp.unordered_pair (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x (tptp.singleton tptp.y)))) (= tptp.null_class (tptp.singleton tptp.y))) (not (= (tptp.ordered_pair tptp.x tptp.y) (tptp.unordered_pair (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x (tptp.singleton tptp.y))))) (not (= tptp.null_class (tptp.singleton tptp.y)))) :rule and_neg)
% 30.43/30.65  (step t2 (cl (=> (and (= (tptp.ordered_pair tptp.x tptp.y) (tptp.unordered_pair (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x (tptp.singleton tptp.y)))) (= tptp.null_class (tptp.singleton tptp.y))) (= (tptp.unordered_pair (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.null_class)) (tptp.ordered_pair tptp.x tptp.y))) (and (= (tptp.ordered_pair tptp.x tptp.y) (tptp.unordered_pair (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x (tptp.singleton tptp.y)))) (= tptp.null_class (tptp.singleton tptp.y)))) :rule implies_neg1)
% 30.43/30.65  (anchor :step t3)
% 30.43/30.65  (assume t3.a0 (= (tptp.ordered_pair tptp.x tptp.y) (tptp.unordered_pair (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x (tptp.singleton tptp.y)))))
% 30.43/30.65  (assume t3.a1 (= tptp.null_class (tptp.singleton tptp.y)))
% 30.43/30.65  (step t3.t1 (cl (=> (and (= (tptp.ordered_pair tptp.x tptp.y) (tptp.unordered_pair (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x (tptp.singleton tptp.y)))) (= tptp.null_class (tptp.singleton tptp.y))) (= (tptp.unordered_pair (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.null_class)) (tptp.ordered_pair tptp.x tptp.y))) (and (= (tptp.ordered_pair tptp.x tptp.y) (tptp.unordered_pair (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x (tptp.singleton tptp.y)))) (= tptp.null_class (tptp.singleton tptp.y)))) :rule implies_neg1)
% 30.43/30.65  (anchor :step t3.t2)
% 30.43/30.65  (assume t3.t2.a0 (= (tptp.ordered_pair tptp.x tptp.y) (tptp.unordered_pair (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x (tptp.singleton tptp.y)))))
% 30.43/30.65  (assume t3.t2.a1 (= tptp.null_class (tptp.singleton tptp.y)))
% 30.43/30.65  (step t3.t2.t1 (cl (= (tptp.singleton tptp.x) (tptp.singleton tptp.x))) :rule refl)
% 30.43/30.65  (step t3.t2.t2 (cl (= tptp.x tptp.x)) :rule refl)
% 30.43/30.65  (step t3.t2.t3 (cl (= (tptp.singleton tptp.y) tptp.null_class)) :rule symm :premises (t3.t2.a1))
% 30.43/30.65  (step t3.t2.t4 (cl (= tptp.null_class (tptp.singleton tptp.y))) :rule symm :premises (t3.t2.t3))
% 30.43/30.65  (step t3.t2.t5 (cl (= (tptp.unordered_pair tptp.x tptp.null_class) (tptp.unordered_pair tptp.x (tptp.singleton tptp.y)))) :rule cong :premises (t3.t2.t2 t3.t2.t4))
% 30.43/30.65  (step t3.t2.t6 (cl (= (tptp.unordered_pair (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.null_class)) (tptp.unordered_pair (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x (tptp.singleton tptp.y))))) :rule cong :premises (t3.t2.t1 t3.t2.t5))
% 30.43/30.65  (step t3.t2.t7 (cl (= (tptp.unordered_pair (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x (tptp.singleton tptp.y))) (tptp.ordered_pair tptp.x tptp.y))) :rule symm :premises (t3.t2.a0))
% 30.43/30.65  (step t3.t2.t8 (cl (= (tptp.unordered_pair (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.null_class)) (tptp.ordered_pair tptp.x tptp.y))) :rule trans :premises (t3.t2.t6 t3.t2.t7))
% 30.43/30.65  (step t3.t2 (cl (not (= (tptp.ordered_pair tptp.x tptp.y) (tptp.unordered_pair (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x (tptp.singleton tptp.y))))) (not (= tptp.null_class (tptp.singleton tptp.y))) (= (tptp.unordered_pair (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.null_class)) (tptp.ordered_pair tptp.x tptp.y))) :rule subproof :discharge (t3.t2.a0 t3.t2.a1))
% 30.43/30.65  (step t3.t3 (cl (not (and (= (tptp.ordered_pair tptp.x tptp.y) (tptp.unordered_pair (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x (tptp.singleton tptp.y)))) (= tptp.null_class (tptp.singleton tptp.y)))) (= (tptp.ordered_pair tptp.x tptp.y) (tptp.unordered_pair (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x (tptp.singleton tptp.y))))) :rule and_pos)
% 30.43/30.65  (step t3.t4 (cl (not (and (= (tptp.ordered_pair tptp.x tptp.y) (tptp.unordered_pair (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x (tptp.singleton tptp.y)))) (= tptp.null_class (tptp.singleton tptp.y)))) (= tptp.null_class (tptp.singleton tptp.y))) :rule and_pos)
% 30.43/30.65  (step t3.t5 (cl (= (tptp.unordered_pair (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.null_class)) (tptp.ordered_pair tptp.x tptp.y)) (not (and (= (tptp.ordered_pair tptp.x tptp.y) (tptp.unordered_pair (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x (tptp.singleton tptp.y)))) (= tptp.null_class (tptp.singleton tptp.y)))) (not (and (= (tptp.ordered_pair tptp.x tptp.y) (tptp.unordered_pair (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x (tptp.singleton tptp.y)))) (= tptp.null_class (tptp.singleton tptp.y))))) :rule resolution :premises (t3.t2 t3.t3 t3.t4))
% 30.43/30.65  (step t3.t6 (cl (not (and (= (tptp.ordered_pair tptp.x tptp.y) (tptp.unordered_pair (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x (tptp.singleton tptp.y)))) (= tptp.null_class (tptp.singleton tptp.y)))) (not (and (= (tptp.ordered_pair tptp.x tptp.y) (tptp.unordered_pair (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x (tptp.singleton tptp.y)))) (= tptp.null_class (tptp.singleton tptp.y)))) (= (tptp.unordered_pair (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.null_class)) (tptp.ordered_pair tptp.x tptp.y))) :rule reordering :premises (t3.t5))
% 30.43/30.65  (step t3.t7 (cl (not (and (= (tptp.ordered_pair tptp.x tptp.y) (tptp.unordered_pair (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x (tptp.singleton tptp.y)))) (= tptp.null_class (tptp.singleton tptp.y)))) (= (tptp.unordered_pair (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.null_class)) (tptp.ordered_pair tptp.x tptp.y))) :rule contraction :premises (t3.t6))
% 30.43/30.65  (step t3.t8 (cl (=> (and (= (tptp.ordered_pair tptp.x tptp.y) (tptp.unordered_pair (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x (tptp.singleton tptp.y)))) (= tptp.null_class (tptp.singleton tptp.y))) (= (tptp.unordered_pair (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.null_class)) (tptp.ordered_pair tptp.x tptp.y))) (= (tptp.unordered_pair (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.null_class)) (tptp.ordered_pair tptp.x tptp.y))) :rule resolution :premises (t3.t1 t3.t7))
% 30.43/30.65  (step t3.t9 (cl (=> (and (= (tptp.ordered_pair tptp.x tptp.y) (tptp.unordered_pair (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x (tptp.singleton tptp.y)))) (= tptp.null_class (tptp.singleton tptp.y))) (= (tptp.unordered_pair (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.null_class)) (tptp.ordered_pair tptp.x tptp.y))) (not (= (tptp.unordered_pair (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.null_class)) (tptp.ordered_pair tptp.x tptp.y)))) :rule implies_neg2)
% 30.43/30.65  (step t3.t10 (cl (=> (and (= (tptp.ordered_pair tptp.x tptp.y) (tptp.unordered_pair (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x (tptp.singleton tptp.y)))) (= tptp.null_class (tptp.singleton tptp.y))) (= (tptp.unordered_pair (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.null_class)) (tptp.ordered_pair tptp.x tptp.y))) (=> (and (= (tptp.ordered_pair tptp.x tptp.y) (tptp.unordered_pair (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x (tptp.singleton tptp.y)))) (= tptp.null_class (tptp.singleton tptp.y))) (= (tptp.unordered_pair (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.null_class)) (tptp.ordered_pair tptp.x tptp.y)))) :rule resolution :premises (t3.t8 t3.t9))
% 30.43/30.65  (step t3.t11 (cl (=> (and (= (tptp.ordered_pair tptp.x tptp.y) (tptp.unordered_pair (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x (tptp.singleton tptp.y)))) (= tptp.null_class (tptp.singleton tptp.y))) (= (tptp.unordered_pair (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.null_class)) (tptp.ordered_pair tptp.x tptp.y)))) :rule contraction :premises (t3.t10))
% 30.43/30.65  (step t3.t12 (cl (not (and (= (tptp.ordered_pair tptp.x tptp.y) (tptp.unordered_pair (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x (tptp.singleton tptp.y)))) (= tptp.null_class (tptp.singleton tptp.y)))) (= (tptp.unordered_pair (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.null_class)) (tptp.ordered_pair tptp.x tptp.y))) :rule implies :premises (t3.t11))
% 30.43/30.65  (step t3.t13 (cl (and (= (tptp.ordered_pair tptp.x tptp.y) (tptp.unordered_pair (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x (tptp.singleton tptp.y)))) (= tptp.null_class (tptp.singleton tptp.y))) (not (= (tptp.ordered_pair tptp.x tptp.y) (tptp.unordered_pair (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x (tptp.singleton tptp.y))))) (not (= tptp.null_class (tptp.singleton tptp.y)))) :rule and_neg)
% 30.43/30.65  (step t3.t14 (cl (and (= (tptp.ordered_pair tptp.x tptp.y) (tptp.unordered_pair (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x (tptp.singleton tptp.y)))) (= tptp.null_class (tptp.singleton tptp.y)))) :rule resolution :premises (t3.t13 t3.a0 t3.a1))
% 30.43/30.65  (step t3.t15 (cl (= (tptp.unordered_pair (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.null_class)) (tptp.ordered_pair tptp.x tptp.y))) :rule resolution :premises (t3.t12 t3.t14))
% 30.43/30.65  (step t3 (cl (not (= (tptp.ordered_pair tptp.x tptp.y) (tptp.unordered_pair (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x (tptp.singleton tptp.y))))) (not (= tptp.null_class (tptp.singleton tptp.y))) (= (tptp.unordered_pair (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.null_class)) (tptp.ordered_pair tptp.x tptp.y))) :rule subproof :discharge (t3.a0 t3.a1))
% 30.43/30.65  (step t4 (cl (not (and (= (tptp.ordered_pair tptp.x tptp.y) (tptp.unordered_pair (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x (tptp.singleton tptp.y)))) (= tptp.null_class (tptp.singleton tptp.y)))) (= (tptp.ordered_pair tptp.x tptp.y) (tptp.unordered_pair (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x (tptp.singleton tptp.y))))) :rule and_pos)
% 30.43/30.65  (step t5 (cl (not (and (= (tptp.ordered_pair tptp.x tptp.y) (tptp.unordered_pair (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x (tptp.singleton tptp.y)))) (= tptp.null_class (tptp.singleton tptp.y)))) (= tptp.null_class (tptp.singleton tptp.y))) :rule and_pos)
% 30.43/30.65  (step t6 (cl (= (tptp.unordered_pair (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.null_class)) (tptp.ordered_pair tptp.x tptp.y)) (not (and (= (tptp.ordered_pair tptp.x tptp.y) (tptp.unordered_pair (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x (tptp.singleton tptp.y)))) (= tptp.null_class (tptp.singleton tptp.y)))) (not (and (= (tptp.ordered_pair tptp.x tptp.y) (tptp.unordered_pair (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x (tptp.singleton tptp.y)))) (= tptp.null_class (tptp.singleton tptp.y))))) :rule resolution :premises (t3 t4 t5))
% 30.43/30.65  (step t7 (cl (not (and (= (tptp.ordered_pair tptp.x tptp.y) (tptp.unordered_pair (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x (tptp.singleton tptp.y)))) (= tptp.null_class (tptp.singleton tptp.y)))) (not (and (= (tptp.ordered_pair tptp.x tptp.y) (tptp.unordered_pair (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x (tptp.singleton tptp.y)))) (= tptp.null_class (tptp.singleton tptp.y)))) (= (tptp.unordered_pair (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.null_class)) (tptp.ordered_pair tptp.x tptp.y))) :rule reordering :premises (t6))
% 30.43/30.65  (step t8 (cl (not (and (= (tptp.ordered_pair tptp.x tptp.y) (tptp.unordered_pair (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x (tptp.singleton tptp.y)))) (= tptp.null_class (tptp.singleton tptp.y)))) (= (tptp.unordered_pair (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.null_class)) (tptp.ordered_pair tptp.x tptp.y))) :rule contraction :premises (t7))
% 30.43/30.65  (step t9 (cl (=> (and (= (tptp.ordered_pair tptp.x tptp.y) (tptp.unordered_pair (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x (tptp.singleton tptp.y)))) (= tptp.null_class (tptp.singleton tptp.y))) (= (tptp.unordered_pair (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.null_class)) (tptp.ordered_pair tptp.x tptp.y))) (= (tptp.unordered_pair (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.null_class)) (tptp.ordered_pair tptp.x tptp.y))) :rule resolution :premises (t2 t8))
% 30.43/30.65  (step t10 (cl (=> (and (= (tptp.ordered_pair tptp.x tptp.y) (tptp.unordered_pair (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x (tptp.singleton tptp.y)))) (= tptp.null_class (tptp.singleton tptp.y))) (= (tptp.unordered_pair (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.null_class)) (tptp.ordered_pair tptp.x tptp.y))) (not (= (tptp.unordered_pair (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.null_class)) (tptp.ordered_pair tptp.x tptp.y)))) :rule implies_neg2)
% 30.43/30.65  (step t11 (cl (=> (and (= (tptp.ordered_pair tptp.x tptp.y) (tptp.unordered_pair (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x (tptp.singleton tptp.y)))) (= tptp.null_class (tptp.singleton tptp.y))) (= (tptp.unordered_pair (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.null_class)) (tptp.ordered_pair tptp.x tptp.y))) (=> (and (= (tptp.ordered_pair tptp.x tptp.y) (tptp.unordered_pair (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x (tptp.singleton tptp.y)))) (= tptp.null_class (tptp.singleton tptp.y))) (= (tptp.unordered_pair (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.null_class)) (tptp.ordered_pair tptp.x tptp.y)))) :rule resolution :premises (t9 t10))
% 30.43/30.65  (step t12 (cl (=> (and (= (tptp.ordered_pair tptp.x tptp.y) (tptp.unordered_pair (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x (tptp.singleton tptp.y)))) (= tptp.null_class (tptp.singleton tptp.y))) (= (tptp.unordered_pair (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.null_class)) (tptp.ordered_pair tptp.x tptp.y)))) :rule contraction :premises (t11))
% 30.43/30.65  (step t13 (cl (not (and (= (tptp.ordered_pair tptp.x tptp.y) (tptp.unordered_pair (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x (tptp.singleton tptp.y)))) (= tptp.null_class (tptp.singleton tptp.y)))) (= (tptp.unordered_pair (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.null_class)) (tptp.ordered_pair tptp.x tptp.y))) :rule implies :premises (t12))
% 30.43/30.65  (step t14 (cl (not (= (tptp.ordered_pair tptp.x tptp.y) (tptp.unordered_pair (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x (tptp.singleton tptp.y))))) (not (= tptp.null_class (tptp.singleton tptp.y))) (= (tptp.unordered_pair (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.null_class)) (tptp.ordered_pair tptp.x tptp.y))) :rule resolution :premises (t1 t13))
% 30.43/30.65  (step t15 (cl (= (tptp.unordered_pair (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x tptp.null_class)) (tptp.ordered_pair tptp.x tptp.y)) (not (= (tptp.ordered_pair tptp.x tptp.y) (tptp.unordered_pair (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x (tptp.singleton tptp.y))))) (not (= tptp.null_class (tptp.singleton tptp.y)))) :rule reordering :premises (t14))
% 30.43/30.65  (step t16 (cl (not (or (not (tptp.member (tptp.singleton tptp.y) tptp.universal_class)) (= tptp.null_class (tptp.singleton tptp.y)) (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.singleton tptp.y)))) (not (tptp.member (tptp.singleton tptp.y) tptp.universal_class)) (= tptp.null_class (tptp.singleton tptp.y)) (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.singleton tptp.y))) :rule or_pos)
% 30.43/30.65  (step t17 (cl (not (tptp.member (tptp.singleton tptp.y) tptp.universal_class)) (= tptp.null_class (tptp.singleton tptp.y)) (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.singleton tptp.y)) (not (or (not (tptp.member (tptp.singleton tptp.y) tptp.universal_class)) (= tptp.null_class (tptp.singleton tptp.y)) (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.singleton tptp.y))))) :rule reordering :premises (t16))
% 30.43/30.65  (step t18 (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)
% 30.43/30.65  (step t19 (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)
% 30.43/30.65  (anchor :step t20)
% 30.43/30.65  (assume t20.a0 (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)))
% 30.43/30.65  (assume t20.a1 (tptp.member (tptp.unordered_pair tptp.y tptp.y) tptp.universal_class))
% 30.43/30.65  (step t20.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)
% 30.43/30.65  (anchor :step t20.t2)
% 30.43/30.65  (assume t20.t2.a0 (tptp.member (tptp.unordered_pair tptp.y tptp.y) tptp.universal_class))
% 30.43/30.65  (assume t20.t2.a1 (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)))
% 30.43/30.65  (step t20.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)
% 30.43/30.65  (step t20.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 (t20.t2.t1))
% 30.43/30.65  (step t20.t2.t3 (cl (= (tptp.unordered_pair tptp.y tptp.y) (tptp.singleton tptp.y))) :rule symm :premises (t20.t2.a1))
% 30.43/30.65  (step t20.t2.t4 (cl (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y))) :rule symm :premises (t20.t2.t3))
% 30.43/30.65  (step t20.t2.t5 (cl (= tptp.universal_class tptp.universal_class)) :rule refl)
% 30.43/30.65  (step t20.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 (t20.t2.t4 t20.t2.t5))
% 30.43/30.65  (step t20.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)
% 30.43/30.65  (step t20.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 (t20.t2.t7))
% 30.43/30.65  (step t20.t2.t9 (cl (= (tptp.member (tptp.unordered_pair tptp.y tptp.y) tptp.universal_class) true)) :rule resolution :premises (t20.t2.t8 t20.t2.a0))
% 30.43/30.65  (step t20.t2.t10 (cl (= (tptp.member (tptp.singleton tptp.y) tptp.universal_class) true)) :rule trans :premises (t20.t2.t6 t20.t2.t9))
% 30.43/30.65  (step t20.t2.t11 (cl (tptp.member (tptp.singleton tptp.y) tptp.universal_class)) :rule resolution :premises (t20.t2.t2 t20.t2.t10))
% 30.43/30.65  (step t20.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 (t20.t2.a0 t20.t2.a1))
% 30.43/30.65  (step t20.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)
% 30.43/30.65  (step t20.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)
% 30.43/30.65  (step t20.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 (t20.t2 t20.t3 t20.t4))
% 30.43/30.65  (step t20.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 (t20.t5))
% 30.43/30.65  (step t20.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 (t20.t6))
% 30.43/30.65  (step t20.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 (t20.t1 t20.t7))
% 30.43/30.65  (step t20.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)
% 30.43/30.65  (step t20.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 (t20.t8 t20.t9))
% 30.43/30.65  (step t20.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 (t20.t10))
% 30.43/30.65  (step t20.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 (t20.t11))
% 30.43/30.65  (step t20.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)
% 30.43/30.65  (step t20.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 (t20.t13 t20.a1 t20.a0))
% 30.43/30.65  (step t20.t15 (cl (tptp.member (tptp.singleton tptp.y) tptp.universal_class)) :rule resolution :premises (t20.t12 t20.t14))
% 30.43/30.65  (step t20 (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 (t20.a0 t20.a1))
% 30.43/30.65  (step t21 (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)
% 30.43/30.65  (step t22 (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)
% 30.43/30.65  (step t23 (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 (t20 t21 t22))
% 30.43/30.65  (step t24 (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 (t23))
% 30.43/30.65  (step t25 (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 (t24))
% 30.43/30.65  (step t26 (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 (t19 t25))
% 30.43/30.65  (step t27 (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)
% 30.43/30.65  (step t28 (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 (t26 t27))
% 30.43/30.65  (step t29 (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 (t28))
% 30.43/30.65  (step t30 (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 (t29))
% 30.43/30.65  (step t31 (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 (t18 t30))
% 30.43/30.65  (step t32 (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 (t31))
% 30.43/30.65  (step t33 (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)
% 30.43/30.65  (step t34 (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)
% 30.43/30.65  (step t35 (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)
% 30.43/30.65  (step t36 (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 (t34 t35))
% 30.43/30.65  (step t37 (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)
% 30.43/30.65  (anchor :step t38)
% 30.43/30.65  (assume t38.a0 (forall ((X $$unsorted)) (= (tptp.unordered_pair X X) (tptp.singleton X))))
% 30.43/30.65  (step t38.t1 (cl (or (not (forall ((X $$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)))
% 30.43/30.65  (step t38.t2 (cl (not (forall ((X $$unsorted)) (= (tptp.unordered_pair X X) (tptp.singleton X)))) (= (tptp.unordered_pair tptp.y tptp.y) (tptp.singleton tptp.y))) :rule or :premises (t38.t1))
% 30.43/30.65  (step t38.t3 (cl (= (tptp.unordered_pair tptp.y tptp.y) (tptp.singleton tptp.y))) :rule resolution :premises (t38.t2 t38.a0))
% 30.43/30.65  (step t38 (cl (not (forall ((X $$unsorted)) (= (tptp.unordered_pair X X) (tptp.singleton X)))) (= (tptp.unordered_pair tptp.y tptp.y) (tptp.singleton tptp.y))) :rule subproof :discharge (t38.a0))
% 30.43/30.65  (step t39 (cl (=> (forall ((X $$unsorted)) (= (tptp.unordered_pair X X) (tptp.singleton X))) (= (tptp.unordered_pair tptp.y tptp.y) (tptp.singleton tptp.y))) (= (tptp.unordered_pair tptp.y tptp.y) (tptp.singleton tptp.y))) :rule resolution :premises (t37 t38))
% 30.43/30.65  (step t40 (cl (=> (forall ((X $$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)
% 30.43/30.65  (step t41 (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 (t39 t40))
% 30.43/30.65  (step t42 (cl (=> (forall ((X $$unsorted)) (= (tptp.unordered_pair X X) (tptp.singleton X))) (= (tptp.unordered_pair tptp.y tptp.y) (tptp.singleton tptp.y)))) :rule contraction :premises (t41))
% 30.43/30.65  (step t43 (cl (=> (forall ((X $$unsorted)) (= (tptp.unordered_pair X X) (tptp.singleton X))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)))) :rule resolution :premises (t33 t36 t42))
% 30.43/30.65  (step t44 (cl (not (forall ((X $$unsorted)) (= (tptp.unordered_pair X X) (tptp.singleton X)))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y))) :rule implies :premises (t43))
% 30.43/30.65  (step t45 (cl (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y))) :rule resolution :premises (t44 a11))
% 30.43/30.65  (step t46 (cl (=> (forall ((X $$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 $$unsorted)) (tptp.member (tptp.unordered_pair X Y) tptp.universal_class))) :rule implies_neg1)
% 30.43/30.65  (anchor :step t47)
% 30.43/30.65  (assume t47.a0 (forall ((X $$unsorted) (Y $$unsorted)) (tptp.member (tptp.unordered_pair X Y) tptp.universal_class)))
% 30.43/30.65  (step t47.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (tptp.member (tptp.unordered_pair X Y) tptp.universal_class))) (tptp.member (tptp.unordered_pair tptp.y tptp.y) tptp.universal_class))) :rule forall_inst :args ((:= X tptp.y) (:= Y tptp.y)))
% 30.43/30.65  (step t47.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (tptp.member (tptp.unordered_pair X Y) tptp.universal_class))) (tptp.member (tptp.unordered_pair tptp.y tptp.y) tptp.universal_class)) :rule or :premises (t47.t1))
% 30.43/30.65  (step t47.t3 (cl (tptp.member (tptp.unordered_pair tptp.y tptp.y) tptp.universal_class)) :rule resolution :premises (t47.t2 t47.a0))
% 30.43/30.65  (step t47 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (tptp.member (tptp.unordered_pair X Y) tptp.universal_class))) (tptp.member (tptp.unordered_pair tptp.y tptp.y) tptp.universal_class)) :rule subproof :discharge (t47.a0))
% 30.43/30.65  (step t48 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (tptp.member (tptp.unordered_pair X Y) tptp.universal_class)) (tptp.member (tptp.unordered_pair tptp.y tptp.y) tptp.universal_class)) (tptp.member (tptp.unordered_pair tptp.y tptp.y) tptp.universal_class)) :rule resolution :premises (t46 t47))
% 30.43/30.65  (step t49 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (tptp.member (tptp.unordered_pair X Y) tptp.universal_class)) (tptp.member (tptp.unordered_pair tptp.y tptp.y) tptp.universal_class)) (not (tptp.member (tptp.unordered_pair tptp.y tptp.y) tptp.universal_class))) :rule implies_neg2)
% 30.43/30.65  (step t50 (cl (=> (forall ((X $$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 $$unsorted)) (tptp.member (tptp.unordered_pair X Y) tptp.universal_class)) (tptp.member (tptp.unordered_pair tptp.y tptp.y) tptp.universal_class))) :rule resolution :premises (t48 t49))
% 30.43/30.65  (step t51 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (tptp.member (tptp.unordered_pair X Y) tptp.universal_class)) (tptp.member (tptp.unordered_pair tptp.y tptp.y) tptp.universal_class))) :rule contraction :premises (t50))
% 30.43/30.65  (step t52 (cl (not (forall ((X $$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 (t51))
% 30.43/30.65  (step t53 (cl (tptp.member (tptp.unordered_pair tptp.y tptp.y) tptp.universal_class)) :rule resolution :premises (t52 a10))
% 30.43/30.65  (step t54 (cl (tptp.member (tptp.singleton tptp.y) tptp.universal_class)) :rule resolution :premises (t32 t45 t53))
% 30.43/30.65  (step t55 (cl (not (= (or (not (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y))) (not (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y)))) (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.singleton tptp.y)))) (or (not (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y))) (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y)) (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.singleton tptp.y)))))) (not (or (not (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y))) (not (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y)))) (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.singleton tptp.y))))) (or (not (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y))) (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y)) (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.singleton tptp.y))))) :rule equiv_pos2)
% 30.43/30.65  (step t56 (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)
% 30.43/30.65  (step t57 (cl (= (= (= (not (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y)))) (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y))) true) (= (not (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y)))) (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y))))) :rule equiv_simplify)
% 30.43/30.65  (step t58 (cl (not (= (= (not (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y)))) (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y))) true)) (= (not (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y)))) (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y)))) :rule equiv1 :premises (t57))
% 30.43/30.65  (step t59 (cl (= (= (not (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y)))) (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y))) (= (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y)) (not (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y))))))) :rule all_simplify)
% 30.43/30.65  (step t60 (cl (= (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y)) (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y)))) :rule refl)
% 30.43/30.65  (step t61 (cl (= (not (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y)))) (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y)))) :rule all_simplify)
% 30.43/30.65  (step t62 (cl (= (= (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y)) (not (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y))))) (= (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y)) (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y))))) :rule cong :premises (t60 t61))
% 30.43/30.65  (step t63 (cl (= (= (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y)) (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y))) true)) :rule all_simplify)
% 30.43/30.65  (step t64 (cl (= (= (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y)) (not (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y))))) true)) :rule trans :premises (t62 t63))
% 30.43/30.65  (step t65 (cl (= (= (not (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y)))) (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y))) true)) :rule trans :premises (t59 t64))
% 30.43/30.65  (step t66 (cl (= (not (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y)))) (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y)))) :rule resolution :premises (t58 t65))
% 30.43/30.65  (step t67 (cl (= (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.singleton tptp.y))) (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.singleton tptp.y))))) :rule refl)
% 30.43/30.65  (step t68 (cl (= (or (not (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y))) (not (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y)))) (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.singleton tptp.y)))) (or (not (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y))) (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y)) (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.singleton tptp.y)))))) :rule cong :premises (t56 t66 t67))
% 30.43/30.65  (step t69 (cl (and (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y)))) (not (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y))) (not (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y))))) :rule and_neg)
% 30.43/30.65  (step t70 (cl (=> (and (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y)))) (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.singleton tptp.y)))) (and (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y))))) :rule implies_neg1)
% 30.43/30.65  (anchor :step t71)
% 30.43/30.65  (assume t71.a0 (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)))
% 30.43/30.65  (assume t71.a1 (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y))))
% 30.43/30.65  (step t71.t1 (cl (=> (and (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y))) (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.singleton tptp.y)))) (and (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)))) :rule implies_neg1)
% 30.43/30.65  (anchor :step t71.t2)
% 30.43/30.65  (assume t71.t2.a0 (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y))))
% 30.43/30.65  (assume t71.t2.a1 (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)))
% 30.43/30.65  (step t71.t2.t1 (cl (= (= (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.singleton tptp.y)) false) (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.singleton tptp.y))))) :rule equiv_simplify)
% 30.43/30.65  (step t71.t2.t2 (cl (not (= (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.singleton tptp.y)) false)) (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.singleton tptp.y)))) :rule equiv1 :premises (t71.t2.t1))
% 30.43/30.65  (step t71.t2.t3 (cl (= (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.apply tptp.choice (tptp.singleton tptp.y)))) :rule refl)
% 30.43/30.65  (step t71.t2.t4 (cl (= (tptp.unordered_pair tptp.y tptp.y) (tptp.singleton tptp.y))) :rule symm :premises (t71.t2.a1))
% 30.43/30.65  (step t71.t2.t5 (cl (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y))) :rule symm :premises (t71.t2.t4))
% 30.43/30.65  (step t71.t2.t6 (cl (= (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.singleton tptp.y)) (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y)))) :rule cong :premises (t71.t2.t3 t71.t2.t5))
% 30.43/30.65  (step t71.t2.t7 (cl (= (= (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y)) false) (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y))))) :rule equiv_simplify)
% 30.43/30.65  (step t71.t2.t8 (cl (= (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y)) false) (not (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y))))) :rule equiv2 :premises (t71.t2.t7))
% 30.43/30.65  (step t71.t2.t9 (cl (not (not (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y))))) (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y))) :rule not_not)
% 30.43/30.65  (step t71.t2.t10 (cl (= (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y)) false) (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y))) :rule resolution :premises (t71.t2.t8 t71.t2.t9))
% 30.43/30.65  (step t71.t2.t11 (cl (= (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y)) false)) :rule resolution :premises (t71.t2.t10 t71.t2.a0))
% 30.43/30.65  (step t71.t2.t12 (cl (= (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.singleton tptp.y)) false)) :rule trans :premises (t71.t2.t6 t71.t2.t11))
% 30.43/30.65  (step t71.t2.t13 (cl (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.singleton tptp.y)))) :rule resolution :premises (t71.t2.t2 t71.t2.t12))
% 30.43/30.65  (step t71.t2 (cl (not (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y)))) (not (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y))) (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.singleton tptp.y)))) :rule subproof :discharge (t71.t2.a0 t71.t2.a1))
% 30.43/30.65  (step t71.t3 (cl (not (and (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)))) (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y)))) :rule and_pos)
% 30.43/30.65  (step t71.t4 (cl (not (and (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y))) (= (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)
% 30.43/30.65  (step t71.t5 (cl (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.singleton tptp.y))) (not (and (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)))) (not (and (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y))))) :rule resolution :premises (t71.t2 t71.t3 t71.t4))
% 30.43/30.65  (step t71.t6 (cl (not (and (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)))) (not (and (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)))) (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.singleton tptp.y)))) :rule reordering :premises (t71.t5))
% 30.43/30.65  (step t71.t7 (cl (not (and (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)))) (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.singleton tptp.y)))) :rule contraction :premises (t71.t6))
% 30.43/30.65  (step t71.t8 (cl (=> (and (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y))) (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.singleton tptp.y)))) (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.singleton tptp.y)))) :rule resolution :premises (t71.t1 t71.t7))
% 30.43/30.65  (step t71.t9 (cl (=> (and (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y))) (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.singleton tptp.y)))) (not (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.singleton tptp.y))))) :rule implies_neg2)
% 30.43/30.65  (step t71.t10 (cl (=> (and (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y))) (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.singleton tptp.y)))) (=> (and (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y))) (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.singleton tptp.y))))) :rule resolution :premises (t71.t8 t71.t9))
% 30.43/30.65  (step t71.t11 (cl (=> (and (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y))) (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.singleton tptp.y))))) :rule contraction :premises (t71.t10))
% 30.43/30.65  (step t71.t12 (cl (not (and (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)))) (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.singleton tptp.y)))) :rule implies :premises (t71.t11))
% 30.43/30.65  (step t71.t13 (cl (and (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y))) (not (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y)))) (not (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)))) :rule and_neg)
% 30.43/30.65  (step t71.t14 (cl (and (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y))) (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)))) :rule resolution :premises (t71.t13 t71.a1 t71.a0))
% 30.43/30.65  (step t71.t15 (cl (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.singleton tptp.y)))) :rule resolution :premises (t71.t12 t71.t14))
% 30.43/30.65  (step t71 (cl (not (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y))) (not (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y)))) (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.singleton tptp.y)))) :rule subproof :discharge (t71.a0 t71.a1))
% 30.43/30.65  (step t72 (cl (not (and (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (not (tptp.member (tptp.apply tptp.choice (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)
% 30.43/30.65  (step t73 (cl (not (and (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y))))) (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y)))) :rule and_pos)
% 30.43/30.65  (step t74 (cl (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.singleton tptp.y))) (not (and (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y))))) (not (and (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y)))))) :rule resolution :premises (t71 t72 t73))
% 30.43/30.65  (step t75 (cl (not (and (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y))))) (not (and (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y))))) (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.singleton tptp.y)))) :rule reordering :premises (t74))
% 30.43/30.65  (step t76 (cl (not (and (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y))))) (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.singleton tptp.y)))) :rule contraction :premises (t75))
% 30.43/30.65  (step t77 (cl (=> (and (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y)))) (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.singleton tptp.y)))) (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.singleton tptp.y)))) :rule resolution :premises (t70 t76))
% 30.43/30.65  (step t78 (cl (=> (and (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y)))) (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.singleton tptp.y)))) (not (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.singleton tptp.y))))) :rule implies_neg2)
% 30.43/30.65  (step t79 (cl (=> (and (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y)))) (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.singleton tptp.y)))) (=> (and (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y)))) (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.singleton tptp.y))))) :rule resolution :premises (t77 t78))
% 30.43/30.65  (step t80 (cl (=> (and (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y)))) (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.singleton tptp.y))))) :rule contraction :premises (t79))
% 30.43/30.65  (step t81 (cl (not (and (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y)) (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y))))) (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.singleton tptp.y)))) :rule implies :premises (t80))
% 30.43/30.65  (step t82 (cl (not (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y))) (not (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y)))) (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.singleton tptp.y)))) :rule resolution :premises (t69 t81))
% 30.43/30.65  (step t83 (cl (or (not (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y))) (not (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y)))) (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.singleton tptp.y)))) (not (not (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y))))) :rule or_neg)
% 30.43/30.65  (step t84 (cl (or (not (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y))) (not (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y)))) (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.singleton tptp.y)))) (not (not (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y)))))) :rule or_neg)
% 30.43/30.65  (step t85 (cl (or (not (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y))) (not (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y)))) (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.singleton tptp.y)))) (not (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.singleton tptp.y))))) :rule or_neg)
% 30.43/30.65  (step t86 (cl (or (not (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y))) (not (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y)))) (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.singleton tptp.y)))) (or (not (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y))) (not (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y)))) (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.singleton tptp.y)))) (or (not (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y))) (not (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y)))) (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.singleton tptp.y))))) :rule resolution :premises (t82 t83 t84 t85))
% 30.43/30.65  (step t87 (cl (or (not (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y))) (not (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y)))) (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.singleton tptp.y))))) :rule contraction :premises (t86))
% 30.43/30.65  (step t88 (cl (or (not (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y))) (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y)) (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.singleton tptp.y))))) :rule resolution :premises (t55 t68 t87))
% 30.43/30.65  (step t89 (cl (not (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y))) (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y)) (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.singleton tptp.y)))) :rule or :premises (t88))
% 30.43/30.65  (step t90 (cl (not (= (tptp.singleton tptp.y) (tptp.unordered_pair tptp.y tptp.y))) (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.singleton tptp.y))) (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y))) :rule reordering :premises (t89))
% 30.43/30.65  (step t91 (cl (not (or (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y))) (= tptp.y (tptp.apply tptp.choice (tptp.singleton tptp.y))) (= tptp.y (tptp.apply tptp.choice (tptp.singleton tptp.y))))) (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y))) (= tptp.y (tptp.apply tptp.choice (tptp.singleton tptp.y))) (= tptp.y (tptp.apply tptp.choice (tptp.singleton tptp.y)))) :rule or_pos)
% 30.43/30.65  (step t92 (cl (not (or (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y))) (= tptp.y (tptp.apply tptp.choice (tptp.singleton tptp.y))) (= tptp.y (tptp.apply tptp.choice (tptp.singleton tptp.y))))) (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y))) (= tptp.y (tptp.apply tptp.choice (tptp.singleton tptp.y)))) :rule contraction :premises (t91))
% 30.43/30.65  (step t93 (cl (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y))) (= tptp.y (tptp.apply tptp.choice (tptp.singleton tptp.y))) (not (or (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y))) (= tptp.y (tptp.apply tptp.choice (tptp.singleton tptp.y))) (= tptp.y (tptp.apply tptp.choice (tptp.singleton tptp.y)))))) :rule reordering :premises (t92))
% 30.43/30.65  (step t94 (cl (not (= (or (not (not (tptp.member tptp.y tptp.universal_class))) (not (= tptp.y (tptp.apply tptp.choice (tptp.singleton tptp.y)))) (not (= (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))))) (not (tptp.member (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))) tptp.universal_class))) (or (tptp.member tptp.y tptp.universal_class) (not (= tptp.y (tptp.apply tptp.choice (tptp.singleton tptp.y)))) (not (= (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))))) (not (tptp.member (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))) tptp.universal_class))))) (not (or (not (not (tptp.member tptp.y tptp.universal_class))) (not (= tptp.y (tptp.apply tptp.choice (tptp.singleton tptp.y)))) (not (= (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))))) (not (tptp.member (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))) tptp.universal_class)))) (or (tptp.member tptp.y tptp.universal_class) (not (= tptp.y (tptp.apply tptp.choice (tptp.singleton tptp.y)))) (not (= (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))))) (not (tptp.member (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))) tptp.universal_class)))) :rule equiv_pos2)
% 30.43/30.65  (step t95 (cl (= (= (= (not (not (tptp.member tptp.y tptp.universal_class))) (tptp.member tptp.y tptp.universal_class)) true) (= (not (not (tptp.member tptp.y tptp.universal_class))) (tptp.member tptp.y tptp.universal_class)))) :rule equiv_simplify)
% 30.43/30.65  (step t96 (cl (not (= (= (not (not (tptp.member tptp.y tptp.universal_class))) (tptp.member tptp.y tptp.universal_class)) true)) (= (not (not (tptp.member tptp.y tptp.universal_class))) (tptp.member tptp.y tptp.universal_class))) :rule equiv1 :premises (t95))
% 30.43/30.65  (step t97 (cl (= (= (not (not (tptp.member tptp.y tptp.universal_class))) (tptp.member tptp.y tptp.universal_class)) (= (tptp.member tptp.y tptp.universal_class) (not (not (tptp.member tptp.y tptp.universal_class)))))) :rule all_simplify)
% 30.43/30.65  (step t98 (cl (= (tptp.member tptp.y tptp.universal_class) (tptp.member tptp.y tptp.universal_class))) :rule refl)
% 30.43/30.65  (step t99 (cl (= (not (not (tptp.member tptp.y tptp.universal_class))) (tptp.member tptp.y tptp.universal_class))) :rule all_simplify)
% 30.43/30.65  (step t100 (cl (= (= (tptp.member tptp.y tptp.universal_class) (not (not (tptp.member tptp.y tptp.universal_class)))) (= (tptp.member tptp.y tptp.universal_class) (tptp.member tptp.y tptp.universal_class)))) :rule cong :premises (t98 t99))
% 30.43/30.65  (step t101 (cl (= (= (tptp.member tptp.y tptp.universal_class) (tptp.member tptp.y tptp.universal_class)) true)) :rule all_simplify)
% 30.43/30.65  (step t102 (cl (= (= (tptp.member tptp.y tptp.universal_class) (not (not (tptp.member tptp.y tptp.universal_class)))) true)) :rule trans :premises (t100 t101))
% 30.43/30.65  (step t103 (cl (= (= (not (not (tptp.member tptp.y tptp.universal_class))) (tptp.member tptp.y tptp.universal_class)) true)) :rule trans :premises (t97 t102))
% 30.43/30.65  (step t104 (cl (= (not (not (tptp.member tptp.y tptp.universal_class))) (tptp.member tptp.y tptp.universal_class))) :rule resolution :premises (t96 t103))
% 30.43/30.65  (step t105 (cl (= (not (= tptp.y (tptp.apply tptp.choice (tptp.singleton tptp.y)))) (not (= tptp.y (tptp.apply tptp.choice (tptp.singleton tptp.y)))))) :rule refl)
% 30.43/30.65  (step t106 (cl (= (not (= (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))))) (not (= (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))))))) :rule refl)
% 30.43/30.65  (step t107 (cl (= (not (tptp.member (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))) tptp.universal_class)) (not (tptp.member (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))) tptp.universal_class)))) :rule refl)
% 30.43/30.65  (step t108 (cl (= (or (not (not (tptp.member tptp.y tptp.universal_class))) (not (= tptp.y (tptp.apply tptp.choice (tptp.singleton tptp.y)))) (not (= (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))))) (not (tptp.member (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))) tptp.universal_class))) (or (tptp.member tptp.y tptp.universal_class) (not (= tptp.y (tptp.apply tptp.choice (tptp.singleton tptp.y)))) (not (= (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))))) (not (tptp.member (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))) tptp.universal_class))))) :rule cong :premises (t104 t105 t106 t107))
% 30.43/30.65  (step t109 (cl (=> (and (not (tptp.member tptp.y tptp.universal_class)) (= tptp.y (tptp.apply tptp.choice (tptp.singleton tptp.y))) (= (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y))))) (tptp.member (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))) tptp.universal_class)) false) (and (not (tptp.member tptp.y tptp.universal_class)) (= tptp.y (tptp.apply tptp.choice (tptp.singleton tptp.y))) (= (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y))))) (tptp.member (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))) tptp.universal_class))) :rule implies_neg1)
% 30.43/30.65  (anchor :step t110)
% 30.43/30.65  (assume t110.a0 (not (tptp.member tptp.y tptp.universal_class)))
% 30.43/30.65  (assume t110.a1 (= tptp.y (tptp.apply tptp.choice (tptp.singleton tptp.y))))
% 30.43/30.65  (assume t110.a2 (= (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y))))))
% 30.43/30.65  (assume t110.a3 (tptp.member (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))) tptp.universal_class))
% 30.43/30.65  (step t110.t1 (cl (not (= (= true false) false)) (not (= true false)) false) :rule equiv_pos2)
% 30.43/30.65  (step t110.t2 (cl (= (= true false) false)) :rule all_simplify)
% 30.43/30.65  (step t110.t3 (cl (= (= (tptp.member (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))) tptp.universal_class) true) (tptp.member (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))) tptp.universal_class))) :rule equiv_simplify)
% 30.43/30.65  (step t110.t4 (cl (= (tptp.member (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))) tptp.universal_class) true) (not (tptp.member (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))) tptp.universal_class))) :rule equiv2 :premises (t110.t3))
% 30.43/30.65  (step t110.t5 (cl (= (tptp.member (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))) tptp.universal_class) true)) :rule resolution :premises (t110.t4 t110.a3))
% 30.43/30.65  (step t110.t6 (cl (= true (tptp.member (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))) tptp.universal_class))) :rule symm :premises (t110.t5))
% 30.43/30.65  (step t110.t7 (cl (= (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))) (tptp.apply tptp.choice (tptp.singleton tptp.y)))) :rule symm :premises (t110.a2))
% 30.43/30.65  (step t110.t8 (cl (= (tptp.apply tptp.choice (tptp.singleton tptp.y)) tptp.y)) :rule symm :premises (t110.a1))
% 30.43/30.65  (step t110.t9 (cl (= (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))) tptp.y)) :rule trans :premises (t110.t7 t110.t8))
% 30.43/30.65  (step t110.t10 (cl (= tptp.universal_class tptp.universal_class)) :rule refl)
% 30.43/30.65  (step t110.t11 (cl (= (tptp.member (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))) tptp.universal_class) (tptp.member tptp.y tptp.universal_class))) :rule cong :premises (t110.t9 t110.t10))
% 30.43/30.65  (step t110.t12 (cl (= (= (tptp.member tptp.y tptp.universal_class) false) (not (tptp.member tptp.y tptp.universal_class)))) :rule equiv_simplify)
% 30.43/30.65  (step t110.t13 (cl (= (tptp.member tptp.y tptp.universal_class) false) (not (not (tptp.member tptp.y tptp.universal_class)))) :rule equiv2 :premises (t110.t12))
% 30.43/30.65  (step t110.t14 (cl (not (not (not (tptp.member tptp.y tptp.universal_class)))) (tptp.member tptp.y tptp.universal_class)) :rule not_not)
% 30.43/30.65  (step t110.t15 (cl (= (tptp.member tptp.y tptp.universal_class) false) (tptp.member tptp.y tptp.universal_class)) :rule resolution :premises (t110.t13 t110.t14))
% 30.43/30.65  (step t110.t16 (cl (= (tptp.member tptp.y tptp.universal_class) false)) :rule resolution :premises (t110.t15 t110.a0))
% 30.43/30.65  (step t110.t17 (cl (= true false)) :rule trans :premises (t110.t6 t110.t11 t110.t16))
% 30.43/30.65  (step t110.t18 (cl false) :rule resolution :premises (t110.t1 t110.t2 t110.t17))
% 30.43/30.65  (step t110 (cl (not (not (tptp.member tptp.y tptp.universal_class))) (not (= tptp.y (tptp.apply tptp.choice (tptp.singleton tptp.y)))) (not (= (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))))) (not (tptp.member (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))) tptp.universal_class)) false) :rule subproof :discharge (t110.a0 t110.a1 t110.a2 t110.a3))
% 30.43/30.65  (step t111 (cl (not (and (not (tptp.member tptp.y tptp.universal_class)) (= tptp.y (tptp.apply tptp.choice (tptp.singleton tptp.y))) (= (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y))))) (tptp.member (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))) tptp.universal_class))) (not (tptp.member tptp.y tptp.universal_class))) :rule and_pos)
% 30.43/30.65  (step t112 (cl (not (and (not (tptp.member tptp.y tptp.universal_class)) (= tptp.y (tptp.apply tptp.choice (tptp.singleton tptp.y))) (= (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y))))) (tptp.member (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))) tptp.universal_class))) (= tptp.y (tptp.apply tptp.choice (tptp.singleton tptp.y)))) :rule and_pos)
% 30.43/30.65  (step t113 (cl (not (and (not (tptp.member tptp.y tptp.universal_class)) (= tptp.y (tptp.apply tptp.choice (tptp.singleton tptp.y))) (= (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y))))) (tptp.member (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))) tptp.universal_class))) (= (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))))) :rule and_pos)
% 30.43/30.65  (step t114 (cl (not (and (not (tptp.member tptp.y tptp.universal_class)) (= tptp.y (tptp.apply tptp.choice (tptp.singleton tptp.y))) (= (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y))))) (tptp.member (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))) tptp.universal_class))) (tptp.member (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))) tptp.universal_class)) :rule and_pos)
% 30.43/30.65  (step t115 (cl false (not (and (not (tptp.member tptp.y tptp.universal_class)) (= tptp.y (tptp.apply tptp.choice (tptp.singleton tptp.y))) (= (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y))))) (tptp.member (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))) tptp.universal_class))) (not (and (not (tptp.member tptp.y tptp.universal_class)) (= tptp.y (tptp.apply tptp.choice (tptp.singleton tptp.y))) (= (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y))))) (tptp.member (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))) tptp.universal_class))) (not (and (not (tptp.member tptp.y tptp.universal_class)) (= tptp.y (tptp.apply tptp.choice (tptp.singleton tptp.y))) (= (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y))))) (tptp.member (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))) tptp.universal_class))) (not (and (not (tptp.member tptp.y tptp.universal_class)) (= tptp.y (tptp.apply tptp.choice (tptp.singleton tptp.y))) (= (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y))))) (tptp.member (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))) tptp.universal_class)))) :rule resolution :premises (t110 t111 t112 t113 t114))
% 30.43/30.65  (step t116 (cl (not (and (not (tptp.member tptp.y tptp.universal_class)) (= tptp.y (tptp.apply tptp.choice (tptp.singleton tptp.y))) (= (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y))))) (tptp.member (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))) tptp.universal_class))) (not (and (not (tptp.member tptp.y tptp.universal_class)) (= tptp.y (tptp.apply tptp.choice (tptp.singleton tptp.y))) (= (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y))))) (tptp.member (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))) tptp.universal_class))) (not (and (not (tptp.member tptp.y tptp.universal_class)) (= tptp.y (tptp.apply tptp.choice (tptp.singleton tptp.y))) (= (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y))))) (tptp.member (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))) tptp.universal_class))) (not (and (not (tptp.member tptp.y tptp.universal_class)) (= tptp.y (tptp.apply tptp.choice (tptp.singleton tptp.y))) (= (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y))))) (tptp.member (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))) tptp.universal_class))) false) :rule reordering :premises (t115))
% 30.43/30.65  (step t117 (cl (not (and (not (tptp.member tptp.y tptp.universal_class)) (= tptp.y (tptp.apply tptp.choice (tptp.singleton tptp.y))) (= (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y))))) (tptp.member (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))) tptp.universal_class))) false) :rule contraction :premises (t116))
% 30.43/30.65  (step t118 (cl (=> (and (not (tptp.member tptp.y tptp.universal_class)) (= tptp.y (tptp.apply tptp.choice (tptp.singleton tptp.y))) (= (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y))))) (tptp.member (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))) tptp.universal_class)) false) false) :rule resolution :premises (t109 t117))
% 30.43/30.65  (step t119 (cl (=> (and (not (tptp.member tptp.y tptp.universal_class)) (= tptp.y (tptp.apply tptp.choice (tptp.singleton tptp.y))) (= (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y))))) (tptp.member (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))) tptp.universal_class)) false) (not false)) :rule implies_neg2)
% 30.43/30.65  (step t120 (cl (=> (and (not (tptp.member tptp.y tptp.universal_class)) (= tptp.y (tptp.apply tptp.choice (tptp.singleton tptp.y))) (= (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y))))) (tptp.member (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))) tptp.universal_class)) false) (=> (and (not (tptp.member tptp.y tptp.universal_class)) (= tptp.y (tptp.apply tptp.choice (tptp.singleton tptp.y))) (= (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y))))) (tptp.member (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))) tptp.universal_class)) false)) :rule resolution :premises (t118 t119))
% 30.43/30.65  (step t121 (cl (=> (and (not (tptp.member tptp.y tptp.universal_class)) (= tptp.y (tptp.apply tptp.choice (tptp.singleton tptp.y))) (= (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y))))) (tptp.member (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))) tptp.universal_class)) false)) :rule contraction :premises (t120))
% 30.43/30.65  (step t122 (cl (= (=> (and (not (tptp.member tptp.y tptp.universal_class)) (= tptp.y (tptp.apply tptp.choice (tptp.singleton tptp.y))) (= (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y))))) (tptp.member (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))) tptp.universal_class)) false) (not (and (not (tptp.member tptp.y tptp.universal_class)) (= tptp.y (tptp.apply tptp.choice (tptp.singleton tptp.y))) (= (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y))))) (tptp.member (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))) tptp.universal_class))))) :rule implies_simplify)
% 30.43/30.65  (step t123 (cl (not (=> (and (not (tptp.member tptp.y tptp.universal_class)) (= tptp.y (tptp.apply tptp.choice (tptp.singleton tptp.y))) (= (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y))))) (tptp.member (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))) tptp.universal_class)) false)) (not (and (not (tptp.member tptp.y tptp.universal_class)) (= tptp.y (tptp.apply tptp.choice (tptp.singleton tptp.y))) (= (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y))))) (tptp.member (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))) tptp.universal_class)))) :rule equiv1 :premises (t122))
% 30.43/30.65  (step t124 (cl (not (and (not (tptp.member tptp.y tptp.universal_class)) (= tptp.y (tptp.apply tptp.choice (tptp.singleton tptp.y))) (= (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y))))) (tptp.member (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))) tptp.universal_class)))) :rule resolution :premises (t121 t123))
% 30.43/30.65  (step t125 (cl (not (not (tptp.member tptp.y tptp.universal_class))) (not (= tptp.y (tptp.apply tptp.choice (tptp.singleton tptp.y)))) (not (= (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))))) (not (tptp.member (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))) tptp.universal_class))) :rule not_and :premises (t124))
% 30.43/30.65  (step t126 (cl (or (not (not (tptp.member tptp.y tptp.universal_class))) (not (= tptp.y (tptp.apply tptp.choice (tptp.singleton tptp.y)))) (not (= (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))))) (not (tptp.member (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))) tptp.universal_class))) (not (not (not (tptp.member tptp.y tptp.universal_class))))) :rule or_neg)
% 30.43/30.65  (step t127 (cl (or (not (not (tptp.member tptp.y tptp.universal_class))) (not (= tptp.y (tptp.apply tptp.choice (tptp.singleton tptp.y)))) (not (= (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))))) (not (tptp.member (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))) tptp.universal_class))) (not (not (= tptp.y (tptp.apply tptp.choice (tptp.singleton tptp.y)))))) :rule or_neg)
% 30.43/30.65  (step t128 (cl (or (not (not (tptp.member tptp.y tptp.universal_class))) (not (= tptp.y (tptp.apply tptp.choice (tptp.singleton tptp.y)))) (not (= (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))))) (not (tptp.member (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))) tptp.universal_class))) (not (not (= (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))))))) :rule or_neg)
% 30.43/30.65  (step t129 (cl (or (not (not (tptp.member tptp.y tptp.universal_class))) (not (= tptp.y (tptp.apply tptp.choice (tptp.singleton tptp.y)))) (not (= (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))))) (not (tptp.member (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))) tptp.universal_class))) (not (not (tptp.member (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))) tptp.universal_class)))) :rule or_neg)
% 30.43/30.65  (step t130 (cl (or (not (not (tptp.member tptp.y tptp.universal_class))) (not (= tptp.y (tptp.apply tptp.choice (tptp.singleton tptp.y)))) (not (= (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))))) (not (tptp.member (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))) tptp.universal_class))) (or (not (not (tptp.member tptp.y tptp.universal_class))) (not (= tptp.y (tptp.apply tptp.choice (tptp.singleton tptp.y)))) (not (= (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))))) (not (tptp.member (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))) tptp.universal_class))) (or (not (not (tptp.member tptp.y tptp.universal_class))) (not (= tptp.y (tptp.apply tptp.choice (tptp.singleton tptp.y)))) (not (= (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))))) (not (tptp.member (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))) tptp.universal_class))) (or (not (not (tptp.member tptp.y tptp.universal_class))) (not (= tptp.y (tptp.apply tptp.choice (tptp.singleton tptp.y)))) (not (= (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))))) (not (tptp.member (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))) tptp.universal_class)))) :rule resolution :premises (t125 t126 t127 t128 t129))
% 30.43/30.65  (step t131 (cl (or (not (not (tptp.member tptp.y tptp.universal_class))) (not (= tptp.y (tptp.apply tptp.choice (tptp.singleton tptp.y)))) (not (= (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))))) (not (tptp.member (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))) tptp.universal_class)))) :rule contraction :premises (t130))
% 30.43/30.65  (step t132 (cl (or (tptp.member tptp.y tptp.universal_class) (not (= tptp.y (tptp.apply tptp.choice (tptp.singleton tptp.y)))) (not (= (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))))) (not (tptp.member (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))) tptp.universal_class)))) :rule resolution :premises (t94 t108 t131))
% 30.43/30.65  (step t133 (cl (tptp.member tptp.y tptp.universal_class) (not (= tptp.y (tptp.apply tptp.choice (tptp.singleton tptp.y)))) (not (= (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))))) (not (tptp.member (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))) tptp.universal_class))) :rule or :premises (t132))
% 30.43/30.65  (step t134 (cl (not (= (=> (forall ((Xf $$unsorted) (Y $$unsorted)) (= (tptp.sum_class (tptp.image Xf (tptp.singleton Y))) (tptp.apply Xf Y))) (= (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))) (tptp.apply tptp.choice (tptp.singleton tptp.y)))) (=> (forall ((Xf $$unsorted) (Y $$unsorted)) (= (tptp.sum_class (tptp.image Xf (tptp.singleton Y))) (tptp.apply Xf Y))) (= (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))))))) (not (=> (forall ((Xf $$unsorted) (Y $$unsorted)) (= (tptp.sum_class (tptp.image Xf (tptp.singleton Y))) (tptp.apply Xf Y))) (= (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))) (tptp.apply tptp.choice (tptp.singleton tptp.y))))) (=> (forall ((Xf $$unsorted) (Y $$unsorted)) (= (tptp.sum_class (tptp.image Xf (tptp.singleton Y))) (tptp.apply Xf Y))) (= (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y))))))) :rule equiv_pos2)
% 30.43/30.65  (step t135 (cl (= (forall ((Xf $$unsorted) (Y $$unsorted)) (= (tptp.sum_class (tptp.image Xf (tptp.singleton Y))) (tptp.apply Xf Y))) (forall ((Xf $$unsorted) (Y $$unsorted)) (= (tptp.sum_class (tptp.image Xf (tptp.singleton Y))) (tptp.apply Xf Y))))) :rule refl)
% 30.43/30.65  (step t136 (cl (= (= (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))) (tptp.apply tptp.choice (tptp.singleton tptp.y))) (= (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y))))))) :rule all_simplify)
% 30.43/30.65  (step t137 (cl (= (=> (forall ((Xf $$unsorted) (Y $$unsorted)) (= (tptp.sum_class (tptp.image Xf (tptp.singleton Y))) (tptp.apply Xf Y))) (= (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))) (tptp.apply tptp.choice (tptp.singleton tptp.y)))) (=> (forall ((Xf $$unsorted) (Y $$unsorted)) (= (tptp.sum_class (tptp.image Xf (tptp.singleton Y))) (tptp.apply Xf Y))) (= (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))))))) :rule cong :premises (t135 t136))
% 30.43/30.65  (step t138 (cl (=> (forall ((Xf $$unsorted) (Y $$unsorted)) (= (tptp.sum_class (tptp.image Xf (tptp.singleton Y))) (tptp.apply Xf Y))) (= (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))) (tptp.apply tptp.choice (tptp.singleton tptp.y)))) (forall ((Xf $$unsorted) (Y $$unsorted)) (= (tptp.sum_class (tptp.image Xf (tptp.singleton Y))) (tptp.apply Xf Y)))) :rule implies_neg1)
% 30.43/30.65  (anchor :step t139)
% 30.43/30.65  (assume t139.a0 (forall ((Xf $$unsorted) (Y $$unsorted)) (= (tptp.sum_class (tptp.image Xf (tptp.singleton Y))) (tptp.apply Xf Y))))
% 30.43/30.65  (step t139.t1 (cl (or (not (forall ((Xf $$unsorted) (Y $$unsorted)) (= (tptp.sum_class (tptp.image Xf (tptp.singleton Y))) (tptp.apply Xf Y)))) (= (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))) (tptp.apply tptp.choice (tptp.singleton tptp.y))))) :rule forall_inst :args ((:= Xf tptp.choice) (:= Y (tptp.singleton tptp.y))))
% 30.43/30.65  (step t139.t2 (cl (not (forall ((Xf $$unsorted) (Y $$unsorted)) (= (tptp.sum_class (tptp.image Xf (tptp.singleton Y))) (tptp.apply Xf Y)))) (= (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))) (tptp.apply tptp.choice (tptp.singleton tptp.y)))) :rule or :premises (t139.t1))
% 30.43/30.65  (step t139.t3 (cl (= (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))) (tptp.apply tptp.choice (tptp.singleton tptp.y)))) :rule resolution :premises (t139.t2 t139.a0))
% 30.43/30.65  (step t139 (cl (not (forall ((Xf $$unsorted) (Y $$unsorted)) (= (tptp.sum_class (tptp.image Xf (tptp.singleton Y))) (tptp.apply Xf Y)))) (= (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))) (tptp.apply tptp.choice (tptp.singleton tptp.y)))) :rule subproof :discharge (t139.a0))
% 30.43/30.65  (step t140 (cl (=> (forall ((Xf $$unsorted) (Y $$unsorted)) (= (tptp.sum_class (tptp.image Xf (tptp.singleton Y))) (tptp.apply Xf Y))) (= (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))) (tptp.apply tptp.choice (tptp.singleton tptp.y)))) (= (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))) (tptp.apply tptp.choice (tptp.singleton tptp.y)))) :rule resolution :premises (t138 t139))
% 30.43/30.65  (step t141 (cl (=> (forall ((Xf $$unsorted) (Y $$unsorted)) (= (tptp.sum_class (tptp.image Xf (tptp.singleton Y))) (tptp.apply Xf Y))) (= (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))) (tptp.apply tptp.choice (tptp.singleton tptp.y)))) (not (= (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))) (tptp.apply tptp.choice (tptp.singleton tptp.y))))) :rule implies_neg2)
% 30.43/30.65  (step t142 (cl (=> (forall ((Xf $$unsorted) (Y $$unsorted)) (= (tptp.sum_class (tptp.image Xf (tptp.singleton Y))) (tptp.apply Xf Y))) (= (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))) (tptp.apply tptp.choice (tptp.singleton tptp.y)))) (=> (forall ((Xf $$unsorted) (Y $$unsorted)) (= (tptp.sum_class (tptp.image Xf (tptp.singleton Y))) (tptp.apply Xf Y))) (= (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))) (tptp.apply tptp.choice (tptp.singleton tptp.y))))) :rule resolution :premises (t140 t141))
% 30.43/30.65  (step t143 (cl (=> (forall ((Xf $$unsorted) (Y $$unsorted)) (= (tptp.sum_class (tptp.image Xf (tptp.singleton Y))) (tptp.apply Xf Y))) (= (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))) (tptp.apply tptp.choice (tptp.singleton tptp.y))))) :rule contraction :premises (t142))
% 30.43/30.65  (step t144 (cl (=> (forall ((Xf $$unsorted) (Y $$unsorted)) (= (tptp.sum_class (tptp.image Xf (tptp.singleton Y))) (tptp.apply Xf Y))) (= (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y))))))) :rule resolution :premises (t134 t137 t143))
% 30.43/30.65  (step t145 (cl (not (forall ((Xf $$unsorted) (Y $$unsorted)) (= (tptp.sum_class (tptp.image Xf (tptp.singleton Y))) (tptp.apply Xf Y)))) (= (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))))) :rule implies :premises (t144))
% 30.43/30.65  (step t146 (cl (= (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))))) :rule resolution :premises (t145 a67))
% 30.43/30.65  (step t147 (cl (not (or (not (tptp.member (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y))) tptp.universal_class)) (tptp.member (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))) tptp.universal_class))) (not (tptp.member (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y))) tptp.universal_class)) (tptp.member (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))) tptp.universal_class)) :rule or_pos)
% 30.43/30.65  (step t148 (cl (not (tptp.member (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y))) tptp.universal_class)) (tptp.member (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))) tptp.universal_class) (not (or (not (tptp.member (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y))) tptp.universal_class)) (tptp.member (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))) tptp.universal_class)))) :rule reordering :premises (t147))
% 30.43/30.65  (step t149 (cl (not (or (not (tptp.function tptp.choice)) (not (tptp.member (tptp.singleton (tptp.singleton tptp.y)) tptp.universal_class)) (tptp.member (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y))) tptp.universal_class))) (not (tptp.function tptp.choice)) (not (tptp.member (tptp.singleton (tptp.singleton tptp.y)) tptp.universal_class)) (tptp.member (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y))) tptp.universal_class)) :rule or_pos)
% 30.43/30.65  (step t150 (cl (not (tptp.function tptp.choice)) (not (tptp.member (tptp.singleton (tptp.singleton tptp.y)) tptp.universal_class)) (tptp.member (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y))) tptp.universal_class) (not (or (not (tptp.function tptp.choice)) (not (tptp.member (tptp.singleton (tptp.singleton tptp.y)) tptp.universal_class)) (tptp.member (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y))) tptp.universal_class)))) :rule reordering :premises (t149))
% 30.43/30.65  (step t151 (cl (and (= (tptp.singleton (tptp.singleton tptp.y)) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y))) (tptp.member (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y)) tptp.universal_class)) (not (= (tptp.singleton (tptp.singleton tptp.y)) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y)))) (not (tptp.member (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y)) tptp.universal_class))) :rule and_neg)
% 30.43/30.65  (step t152 (cl (=> (and (= (tptp.singleton (tptp.singleton tptp.y)) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y))) (tptp.member (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y)) tptp.universal_class)) (tptp.member (tptp.singleton (tptp.singleton tptp.y)) tptp.universal_class)) (and (= (tptp.singleton (tptp.singleton tptp.y)) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y))) (tptp.member (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y)) tptp.universal_class))) :rule implies_neg1)
% 30.43/30.65  (anchor :step t153)
% 30.43/30.65  (assume t153.a0 (= (tptp.singleton (tptp.singleton tptp.y)) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y))))
% 30.43/30.65  (assume t153.a1 (tptp.member (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y)) tptp.universal_class))
% 30.43/30.65  (step t153.t1 (cl (=> (and (tptp.member (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y)) tptp.universal_class) (= (tptp.singleton (tptp.singleton tptp.y)) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y)))) (tptp.member (tptp.singleton (tptp.singleton tptp.y)) tptp.universal_class)) (and (tptp.member (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y)) tptp.universal_class) (= (tptp.singleton (tptp.singleton tptp.y)) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y))))) :rule implies_neg1)
% 30.43/30.65  (anchor :step t153.t2)
% 30.43/30.65  (assume t153.t2.a0 (tptp.member (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y)) tptp.universal_class))
% 30.43/30.65  (assume t153.t2.a1 (= (tptp.singleton (tptp.singleton tptp.y)) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y))))
% 30.43/30.65  (step t153.t2.t1 (cl (= (= (tptp.member (tptp.singleton (tptp.singleton tptp.y)) tptp.universal_class) true) (tptp.member (tptp.singleton (tptp.singleton tptp.y)) tptp.universal_class))) :rule equiv_simplify)
% 30.43/30.65  (step t153.t2.t2 (cl (not (= (tptp.member (tptp.singleton (tptp.singleton tptp.y)) tptp.universal_class) true)) (tptp.member (tptp.singleton (tptp.singleton tptp.y)) tptp.universal_class)) :rule equiv1 :premises (t153.t2.t1))
% 30.43/30.65  (step t153.t2.t3 (cl (= (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y)) (tptp.singleton (tptp.singleton tptp.y)))) :rule symm :premises (t153.t2.a1))
% 30.43/30.65  (step t153.t2.t4 (cl (= (tptp.singleton (tptp.singleton tptp.y)) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y)))) :rule symm :premises (t153.t2.t3))
% 30.43/30.65  (step t153.t2.t5 (cl (= tptp.universal_class tptp.universal_class)) :rule refl)
% 30.43/30.65  (step t153.t2.t6 (cl (= (tptp.member (tptp.singleton (tptp.singleton tptp.y)) tptp.universal_class) (tptp.member (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y)) tptp.universal_class))) :rule cong :premises (t153.t2.t4 t153.t2.t5))
% 30.43/30.65  (step t153.t2.t7 (cl (= (= (tptp.member (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y)) tptp.universal_class) true) (tptp.member (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y)) tptp.universal_class))) :rule equiv_simplify)
% 30.43/30.65  (step t153.t2.t8 (cl (= (tptp.member (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y)) tptp.universal_class) true) (not (tptp.member (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y)) tptp.universal_class))) :rule equiv2 :premises (t153.t2.t7))
% 30.43/30.65  (step t153.t2.t9 (cl (= (tptp.member (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y)) tptp.universal_class) true)) :rule resolution :premises (t153.t2.t8 t153.t2.a0))
% 30.43/30.65  (step t153.t2.t10 (cl (= (tptp.member (tptp.singleton (tptp.singleton tptp.y)) tptp.universal_class) true)) :rule trans :premises (t153.t2.t6 t153.t2.t9))
% 30.43/30.65  (step t153.t2.t11 (cl (tptp.member (tptp.singleton (tptp.singleton tptp.y)) tptp.universal_class)) :rule resolution :premises (t153.t2.t2 t153.t2.t10))
% 30.43/30.65  (step t153.t2 (cl (not (tptp.member (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y)) tptp.universal_class)) (not (= (tptp.singleton (tptp.singleton tptp.y)) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y)))) (tptp.member (tptp.singleton (tptp.singleton tptp.y)) tptp.universal_class)) :rule subproof :discharge (t153.t2.a0 t153.t2.a1))
% 30.43/30.65  (step t153.t3 (cl (not (and (tptp.member (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y)) tptp.universal_class) (= (tptp.singleton (tptp.singleton tptp.y)) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y))))) (tptp.member (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y)) tptp.universal_class)) :rule and_pos)
% 30.43/30.65  (step t153.t4 (cl (not (and (tptp.member (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y)) tptp.universal_class) (= (tptp.singleton (tptp.singleton tptp.y)) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y))))) (= (tptp.singleton (tptp.singleton tptp.y)) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y)))) :rule and_pos)
% 30.43/30.65  (step t153.t5 (cl (tptp.member (tptp.singleton (tptp.singleton tptp.y)) tptp.universal_class) (not (and (tptp.member (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y)) tptp.universal_class) (= (tptp.singleton (tptp.singleton tptp.y)) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y))))) (not (and (tptp.member (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y)) tptp.universal_class) (= (tptp.singleton (tptp.singleton tptp.y)) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y)))))) :rule resolution :premises (t153.t2 t153.t3 t153.t4))
% 30.43/30.65  (step t153.t6 (cl (not (and (tptp.member (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y)) tptp.universal_class) (= (tptp.singleton (tptp.singleton tptp.y)) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y))))) (not (and (tptp.member (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y)) tptp.universal_class) (= (tptp.singleton (tptp.singleton tptp.y)) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y))))) (tptp.member (tptp.singleton (tptp.singleton tptp.y)) tptp.universal_class)) :rule reordering :premises (t153.t5))
% 30.43/30.65  (step t153.t7 (cl (not (and (tptp.member (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y)) tptp.universal_class) (= (tptp.singleton (tptp.singleton tptp.y)) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y))))) (tptp.member (tptp.singleton (tptp.singleton tptp.y)) tptp.universal_class)) :rule contraction :premises (t153.t6))
% 30.43/30.65  (step t153.t8 (cl (=> (and (tptp.member (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y)) tptp.universal_class) (= (tptp.singleton (tptp.singleton tptp.y)) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y)))) (tptp.member (tptp.singleton (tptp.singleton tptp.y)) tptp.universal_class)) (tptp.member (tptp.singleton (tptp.singleton tptp.y)) tptp.universal_class)) :rule resolution :premises (t153.t1 t153.t7))
% 30.43/30.65  (step t153.t9 (cl (=> (and (tptp.member (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y)) tptp.universal_class) (= (tptp.singleton (tptp.singleton tptp.y)) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y)))) (tptp.member (tptp.singleton (tptp.singleton tptp.y)) tptp.universal_class)) (not (tptp.member (tptp.singleton (tptp.singleton tptp.y)) tptp.universal_class))) :rule implies_neg2)
% 30.43/30.65  (step t153.t10 (cl (=> (and (tptp.member (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y)) tptp.universal_class) (= (tptp.singleton (tptp.singleton tptp.y)) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y)))) (tptp.member (tptp.singleton (tptp.singleton tptp.y)) tptp.universal_class)) (=> (and (tptp.member (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y)) tptp.universal_class) (= (tptp.singleton (tptp.singleton tptp.y)) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y)))) (tptp.member (tptp.singleton (tptp.singleton tptp.y)) tptp.universal_class))) :rule resolution :premises (t153.t8 t153.t9))
% 30.43/30.65  (step t153.t11 (cl (=> (and (tptp.member (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y)) tptp.universal_class) (= (tptp.singleton (tptp.singleton tptp.y)) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y)))) (tptp.member (tptp.singleton (tptp.singleton tptp.y)) tptp.universal_class))) :rule contraction :premises (t153.t10))
% 30.43/30.65  (step t153.t12 (cl (not (and (tptp.member (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y)) tptp.universal_class) (= (tptp.singleton (tptp.singleton tptp.y)) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y))))) (tptp.member (tptp.singleton (tptp.singleton tptp.y)) tptp.universal_class)) :rule implies :premises (t153.t11))
% 30.43/30.65  (step t153.t13 (cl (and (tptp.member (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y)) tptp.universal_class) (= (tptp.singleton (tptp.singleton tptp.y)) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y)))) (not (tptp.member (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y)) tptp.universal_class)) (not (= (tptp.singleton (tptp.singleton tptp.y)) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y))))) :rule and_neg)
% 30.43/30.65  (step t153.t14 (cl (and (tptp.member (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y)) tptp.universal_class) (= (tptp.singleton (tptp.singleton tptp.y)) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y))))) :rule resolution :premises (t153.t13 t153.a1 t153.a0))
% 30.43/30.65  (step t153.t15 (cl (tptp.member (tptp.singleton (tptp.singleton tptp.y)) tptp.universal_class)) :rule resolution :premises (t153.t12 t153.t14))
% 30.43/30.65  (step t153 (cl (not (= (tptp.singleton (tptp.singleton tptp.y)) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y)))) (not (tptp.member (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y)) tptp.universal_class)) (tptp.member (tptp.singleton (tptp.singleton tptp.y)) tptp.universal_class)) :rule subproof :discharge (t153.a0 t153.a1))
% 30.43/30.65  (step t154 (cl (not (and (= (tptp.singleton (tptp.singleton tptp.y)) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y))) (tptp.member (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y)) tptp.universal_class))) (= (tptp.singleton (tptp.singleton tptp.y)) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y)))) :rule and_pos)
% 30.43/30.65  (step t155 (cl (not (and (= (tptp.singleton (tptp.singleton tptp.y)) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y))) (tptp.member (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y)) tptp.universal_class))) (tptp.member (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y)) tptp.universal_class)) :rule and_pos)
% 30.43/30.65  (step t156 (cl (tptp.member (tptp.singleton (tptp.singleton tptp.y)) tptp.universal_class) (not (and (= (tptp.singleton (tptp.singleton tptp.y)) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y))) (tptp.member (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y)) tptp.universal_class))) (not (and (= (tptp.singleton (tptp.singleton tptp.y)) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y))) (tptp.member (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y)) tptp.universal_class)))) :rule resolution :premises (t153 t154 t155))
% 30.43/30.65  (step t157 (cl (not (and (= (tptp.singleton (tptp.singleton tptp.y)) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y))) (tptp.member (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y)) tptp.universal_class))) (not (and (= (tptp.singleton (tptp.singleton tptp.y)) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y))) (tptp.member (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y)) tptp.universal_class))) (tptp.member (tptp.singleton (tptp.singleton tptp.y)) tptp.universal_class)) :rule reordering :premises (t156))
% 30.43/30.65  (step t158 (cl (not (and (= (tptp.singleton (tptp.singleton tptp.y)) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y))) (tptp.member (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y)) tptp.universal_class))) (tptp.member (tptp.singleton (tptp.singleton tptp.y)) tptp.universal_class)) :rule contraction :premises (t157))
% 30.43/30.65  (step t159 (cl (=> (and (= (tptp.singleton (tptp.singleton tptp.y)) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y))) (tptp.member (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y)) tptp.universal_class)) (tptp.member (tptp.singleton (tptp.singleton tptp.y)) tptp.universal_class)) (tptp.member (tptp.singleton (tptp.singleton tptp.y)) tptp.universal_class)) :rule resolution :premises (t152 t158))
% 30.43/30.65  (step t160 (cl (=> (and (= (tptp.singleton (tptp.singleton tptp.y)) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y))) (tptp.member (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y)) tptp.universal_class)) (tptp.member (tptp.singleton (tptp.singleton tptp.y)) tptp.universal_class)) (not (tptp.member (tptp.singleton (tptp.singleton tptp.y)) tptp.universal_class))) :rule implies_neg2)
% 30.43/30.65  (step t161 (cl (=> (and (= (tptp.singleton (tptp.singleton tptp.y)) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y))) (tptp.member (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y)) tptp.universal_class)) (tptp.member (tptp.singleton (tptp.singleton tptp.y)) tptp.universal_class)) (=> (and (= (tptp.singleton (tptp.singleton tptp.y)) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y))) (tptp.member (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y)) tptp.universal_class)) (tptp.member (tptp.singleton (tptp.singleton tptp.y)) tptp.universal_class))) :rule resolution :premises (t159 t160))
% 30.43/30.65  (step t162 (cl (=> (and (= (tptp.singleton (tptp.singleton tptp.y)) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y))) (tptp.member (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y)) tptp.universal_class)) (tptp.member (tptp.singleton (tptp.singleton tptp.y)) tptp.universal_class))) :rule contraction :premises (t161))
% 30.43/30.65  (step t163 (cl (not (and (= (tptp.singleton (tptp.singleton tptp.y)) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y))) (tptp.member (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y)) tptp.universal_class))) (tptp.member (tptp.singleton (tptp.singleton tptp.y)) tptp.universal_class)) :rule implies :premises (t162))
% 30.43/30.65  (step t164 (cl (not (= (tptp.singleton (tptp.singleton tptp.y)) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y)))) (not (tptp.member (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y)) tptp.universal_class)) (tptp.member (tptp.singleton (tptp.singleton tptp.y)) tptp.universal_class)) :rule resolution :premises (t151 t163))
% 30.43/30.65  (step t165 (cl (not (= (tptp.singleton (tptp.singleton tptp.y)) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y)))) (tptp.member (tptp.singleton (tptp.singleton tptp.y)) tptp.universal_class) (not (tptp.member (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y)) tptp.universal_class))) :rule reordering :premises (t164))
% 30.43/30.65  (step t166 (cl (not (= (=> (forall ((X $$unsorted)) (= (tptp.unordered_pair X X) (tptp.singleton X))) (= (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y)) (tptp.singleton (tptp.singleton tptp.y)))) (=> (forall ((X $$unsorted)) (= (tptp.unordered_pair X X) (tptp.singleton X))) (= (tptp.singleton (tptp.singleton tptp.y)) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y)))))) (not (=> (forall ((X $$unsorted)) (= (tptp.unordered_pair X X) (tptp.singleton X))) (= (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y)) (tptp.singleton (tptp.singleton tptp.y))))) (=> (forall ((X $$unsorted)) (= (tptp.unordered_pair X X) (tptp.singleton X))) (= (tptp.singleton (tptp.singleton tptp.y)) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y))))) :rule equiv_pos2)
% 30.43/30.65  (step t167 (cl (= (= (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y)) (tptp.singleton (tptp.singleton tptp.y))) (= (tptp.singleton (tptp.singleton tptp.y)) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y))))) :rule all_simplify)
% 30.43/30.65  (step t168 (cl (= (=> (forall ((X $$unsorted)) (= (tptp.unordered_pair X X) (tptp.singleton X))) (= (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y)) (tptp.singleton (tptp.singleton tptp.y)))) (=> (forall ((X $$unsorted)) (= (tptp.unordered_pair X X) (tptp.singleton X))) (= (tptp.singleton (tptp.singleton tptp.y)) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y)))))) :rule cong :premises (t34 t167))
% 30.43/30.65  (step t169 (cl (=> (forall ((X $$unsorted)) (= (tptp.unordered_pair X X) (tptp.singleton X))) (= (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y)) (tptp.singleton (tptp.singleton tptp.y)))) (forall ((X $$unsorted)) (= (tptp.unordered_pair X X) (tptp.singleton X)))) :rule implies_neg1)
% 30.43/30.65  (anchor :step t170)
% 30.43/30.65  (assume t170.a0 (forall ((X $$unsorted)) (= (tptp.unordered_pair X X) (tptp.singleton X))))
% 30.43/30.65  (step t170.t1 (cl (or (not (forall ((X $$unsorted)) (= (tptp.unordered_pair X X) (tptp.singleton X)))) (= (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y)) (tptp.singleton (tptp.singleton tptp.y))))) :rule forall_inst :args ((:= X (tptp.singleton tptp.y))))
% 30.43/30.65  (step t170.t2 (cl (not (forall ((X $$unsorted)) (= (tptp.unordered_pair X X) (tptp.singleton X)))) (= (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y)) (tptp.singleton (tptp.singleton tptp.y)))) :rule or :premises (t170.t1))
% 30.43/30.65  (step t170.t3 (cl (= (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y)) (tptp.singleton (tptp.singleton tptp.y)))) :rule resolution :premises (t170.t2 t170.a0))
% 30.43/30.65  (step t170 (cl (not (forall ((X $$unsorted)) (= (tptp.unordered_pair X X) (tptp.singleton X)))) (= (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y)) (tptp.singleton (tptp.singleton tptp.y)))) :rule subproof :discharge (t170.a0))
% 30.43/30.65  (step t171 (cl (=> (forall ((X $$unsorted)) (= (tptp.unordered_pair X X) (tptp.singleton X))) (= (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y)) (tptp.singleton (tptp.singleton tptp.y)))) (= (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y)) (tptp.singleton (tptp.singleton tptp.y)))) :rule resolution :premises (t169 t170))
% 30.43/30.65  (step t172 (cl (=> (forall ((X $$unsorted)) (= (tptp.unordered_pair X X) (tptp.singleton X))) (= (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y)) (tptp.singleton (tptp.singleton tptp.y)))) (not (= (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y)) (tptp.singleton (tptp.singleton tptp.y))))) :rule implies_neg2)
% 30.43/30.65  (step t173 (cl (=> (forall ((X $$unsorted)) (= (tptp.unordered_pair X X) (tptp.singleton X))) (= (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y)) (tptp.singleton (tptp.singleton tptp.y)))) (=> (forall ((X $$unsorted)) (= (tptp.unordered_pair X X) (tptp.singleton X))) (= (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y)) (tptp.singleton (tptp.singleton tptp.y))))) :rule resolution :premises (t171 t172))
% 30.43/30.65  (step t174 (cl (=> (forall ((X $$unsorted)) (= (tptp.unordered_pair X X) (tptp.singleton X))) (= (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y)) (tptp.singleton (tptp.singleton tptp.y))))) :rule contraction :premises (t173))
% 30.43/30.65  (step t175 (cl (=> (forall ((X $$unsorted)) (= (tptp.unordered_pair X X) (tptp.singleton X))) (= (tptp.singleton (tptp.singleton tptp.y)) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y))))) :rule resolution :premises (t166 t168 t174))
% 30.43/30.65  (step t176 (cl (not (forall ((X $$unsorted)) (= (tptp.unordered_pair X X) (tptp.singleton X)))) (= (tptp.singleton (tptp.singleton tptp.y)) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y)))) :rule implies :premises (t175))
% 30.43/30.65  (step t177 (cl (= (tptp.singleton (tptp.singleton tptp.y)) (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y)))) :rule resolution :premises (t176 a11))
% 30.43/30.65  (step t178 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (tptp.member (tptp.unordered_pair X Y) tptp.universal_class)) (tptp.member (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y)) tptp.universal_class)) (forall ((X $$unsorted) (Y $$unsorted)) (tptp.member (tptp.unordered_pair X Y) tptp.universal_class))) :rule implies_neg1)
% 30.43/30.65  (anchor :step t179)
% 30.43/30.65  (assume t179.a0 (forall ((X $$unsorted) (Y $$unsorted)) (tptp.member (tptp.unordered_pair X Y) tptp.universal_class)))
% 30.43/30.65  (step t179.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.singleton tptp.y) (tptp.singleton tptp.y)) tptp.universal_class))) :rule forall_inst :args ((:= X (tptp.singleton tptp.y)) (:= Y (tptp.singleton tptp.y))))
% 30.43/30.65  (step t179.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (tptp.member (tptp.unordered_pair X Y) tptp.universal_class))) (tptp.member (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y)) tptp.universal_class)) :rule or :premises (t179.t1))
% 30.43/30.65  (step t179.t3 (cl (tptp.member (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y)) tptp.universal_class)) :rule resolution :premises (t179.t2 t179.a0))
% 30.43/30.65  (step t179 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (tptp.member (tptp.unordered_pair X Y) tptp.universal_class))) (tptp.member (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y)) tptp.universal_class)) :rule subproof :discharge (t179.a0))
% 30.43/30.65  (step t180 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (tptp.member (tptp.unordered_pair X Y) tptp.universal_class)) (tptp.member (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y)) tptp.universal_class)) (tptp.member (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y)) tptp.universal_class)) :rule resolution :premises (t178 t179))
% 30.43/30.65  (step t181 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (tptp.member (tptp.unordered_pair X Y) tptp.universal_class)) (tptp.member (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y)) tptp.universal_class)) (not (tptp.member (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y)) tptp.universal_class))) :rule implies_neg2)
% 30.43/30.65  (step t182 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (tptp.member (tptp.unordered_pair X Y) tptp.universal_class)) (tptp.member (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton 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.singleton tptp.y) (tptp.singleton tptp.y)) tptp.universal_class))) :rule resolution :premises (t180 t181))
% 30.43/30.65  (step t183 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (tptp.member (tptp.unordered_pair X Y) tptp.universal_class)) (tptp.member (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y)) tptp.universal_class))) :rule contraction :premises (t182))
% 30.43/30.65  (step t184 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (tptp.member (tptp.unordered_pair X Y) tptp.universal_class))) (tptp.member (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y)) tptp.universal_class)) :rule implies :premises (t183))
% 30.43/30.65  (step t185 (cl (tptp.member (tptp.unordered_pair (tptp.singleton tptp.y) (tptp.singleton tptp.y)) tptp.universal_class)) :rule resolution :premises (t184 a10))
% 30.43/30.65  (step t186 (cl (tptp.member (tptp.singleton (tptp.singleton tptp.y)) tptp.universal_class)) :rule resolution :premises (t165 t177 t185))
% 30.43/30.65  (step t187 (cl (=> (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))) (or (not (tptp.function tptp.choice)) (not (tptp.member (tptp.singleton (tptp.singleton tptp.y)) tptp.universal_class)) (tptp.member (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y))) tptp.universal_class))) (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)))) :rule implies_neg1)
% 30.43/30.65  (anchor :step t188)
% 30.43/30.65  (assume t188.a0 (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))))
% 30.43/30.65  (step t188.t1 (cl (or (not (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)))) (or (not (tptp.function tptp.choice)) (not (tptp.member (tptp.singleton (tptp.singleton tptp.y)) tptp.universal_class)) (tptp.member (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y))) tptp.universal_class)))) :rule forall_inst :args ((:= Xf tptp.choice) (:= X (tptp.singleton (tptp.singleton tptp.y)))))
% 30.43/30.65  (step t188.t2 (cl (not (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)))) (or (not (tptp.function tptp.choice)) (not (tptp.member (tptp.singleton (tptp.singleton tptp.y)) tptp.universal_class)) (tptp.member (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y))) tptp.universal_class))) :rule or :premises (t188.t1))
% 30.43/30.65  (step t188.t3 (cl (or (not (tptp.function tptp.choice)) (not (tptp.member (tptp.singleton (tptp.singleton tptp.y)) tptp.universal_class)) (tptp.member (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y))) tptp.universal_class))) :rule resolution :premises (t188.t2 t188.a0))
% 30.43/30.65  (step t188 (cl (not (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)))) (or (not (tptp.function tptp.choice)) (not (tptp.member (tptp.singleton (tptp.singleton tptp.y)) tptp.universal_class)) (tptp.member (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y))) tptp.universal_class))) :rule subproof :discharge (t188.a0))
% 30.43/30.65  (step t189 (cl (=> (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))) (or (not (tptp.function tptp.choice)) (not (tptp.member (tptp.singleton (tptp.singleton tptp.y)) tptp.universal_class)) (tptp.member (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y))) tptp.universal_class))) (or (not (tptp.function tptp.choice)) (not (tptp.member (tptp.singleton (tptp.singleton tptp.y)) tptp.universal_class)) (tptp.member (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y))) tptp.universal_class))) :rule resolution :premises (t187 t188))
% 30.43/30.65  (step t190 (cl (=> (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))) (or (not (tptp.function tptp.choice)) (not (tptp.member (tptp.singleton (tptp.singleton tptp.y)) tptp.universal_class)) (tptp.member (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y))) tptp.universal_class))) (not (or (not (tptp.function tptp.choice)) (not (tptp.member (tptp.singleton (tptp.singleton tptp.y)) tptp.universal_class)) (tptp.member (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y))) tptp.universal_class)))) :rule implies_neg2)
% 30.43/30.65  (step t191 (cl (=> (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))) (or (not (tptp.function tptp.choice)) (not (tptp.member (tptp.singleton (tptp.singleton tptp.y)) tptp.universal_class)) (tptp.member (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y))) tptp.universal_class))) (=> (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))) (or (not (tptp.function tptp.choice)) (not (tptp.member (tptp.singleton (tptp.singleton tptp.y)) tptp.universal_class)) (tptp.member (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y))) tptp.universal_class)))) :rule resolution :premises (t189 t190))
% 30.43/30.65  (step t192 (cl (=> (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))) (or (not (tptp.function tptp.choice)) (not (tptp.member (tptp.singleton (tptp.singleton tptp.y)) tptp.universal_class)) (tptp.member (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y))) tptp.universal_class)))) :rule contraction :premises (t191))
% 30.43/30.65  (step t193 (cl (not (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)))) (or (not (tptp.function tptp.choice)) (not (tptp.member (tptp.singleton (tptp.singleton tptp.y)) tptp.universal_class)) (tptp.member (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y))) tptp.universal_class))) :rule implies :premises (t192))
% 30.43/30.65  (step t194 (cl (or (not (tptp.function tptp.choice)) (not (tptp.member (tptp.singleton (tptp.singleton tptp.y)) tptp.universal_class)) (tptp.member (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y))) tptp.universal_class))) :rule resolution :premises (t193 a64))
% 30.43/30.65  (step t195 (cl (tptp.member (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y))) tptp.universal_class)) :rule resolution :premises (t150 a68 t186 t194))
% 30.43/30.65  (step t196 (cl (=> (forall ((X $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (tptp.member (tptp.sum_class X) tptp.universal_class))) (or (not (tptp.member (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y))) tptp.universal_class)) (tptp.member (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))) tptp.universal_class))) (forall ((X $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (tptp.member (tptp.sum_class X) tptp.universal_class)))) :rule implies_neg1)
% 30.43/30.65  (anchor :step t197)
% 30.43/30.65  (assume t197.a0 (forall ((X $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (tptp.member (tptp.sum_class X) tptp.universal_class))))
% 30.43/30.65  (step t197.t1 (cl (or (not (forall ((X $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (tptp.member (tptp.sum_class X) tptp.universal_class)))) (or (not (tptp.member (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y))) tptp.universal_class)) (tptp.member (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))) tptp.universal_class)))) :rule forall_inst :args ((:= X (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y))))))
% 30.43/30.65  (step t197.t2 (cl (not (forall ((X $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (tptp.member (tptp.sum_class X) tptp.universal_class)))) (or (not (tptp.member (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y))) tptp.universal_class)) (tptp.member (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))) tptp.universal_class))) :rule or :premises (t197.t1))
% 30.43/30.65  (step t197.t3 (cl (or (not (tptp.member (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y))) tptp.universal_class)) (tptp.member (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))) tptp.universal_class))) :rule resolution :premises (t197.t2 t197.a0))
% 30.43/30.65  (step t197 (cl (not (forall ((X $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (tptp.member (tptp.sum_class X) tptp.universal_class)))) (or (not (tptp.member (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y))) tptp.universal_class)) (tptp.member (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))) tptp.universal_class))) :rule subproof :discharge (t197.a0))
% 30.43/30.65  (step t198 (cl (=> (forall ((X $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (tptp.member (tptp.sum_class X) tptp.universal_class))) (or (not (tptp.member (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y))) tptp.universal_class)) (tptp.member (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))) tptp.universal_class))) (or (not (tptp.member (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y))) tptp.universal_class)) (tptp.member (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))) tptp.universal_class))) :rule resolution :premises (t196 t197))
% 30.43/30.65  (step t199 (cl (=> (forall ((X $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (tptp.member (tptp.sum_class X) tptp.universal_class))) (or (not (tptp.member (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y))) tptp.universal_class)) (tptp.member (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))) tptp.universal_class))) (not (or (not (tptp.member (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y))) tptp.universal_class)) (tptp.member (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))) tptp.universal_class)))) :rule implies_neg2)
% 30.43/30.65  (step t200 (cl (=> (forall ((X $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (tptp.member (tptp.sum_class X) tptp.universal_class))) (or (not (tptp.member (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y))) tptp.universal_class)) (tptp.member (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))) tptp.universal_class))) (=> (forall ((X $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (tptp.member (tptp.sum_class X) tptp.universal_class))) (or (not (tptp.member (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y))) tptp.universal_class)) (tptp.member (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))) tptp.universal_class)))) :rule resolution :premises (t198 t199))
% 30.43/30.65  (step t201 (cl (=> (forall ((X $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (tptp.member (tptp.sum_class X) tptp.universal_class))) (or (not (tptp.member (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y))) tptp.universal_class)) (tptp.member (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))) tptp.universal_class)))) :rule contraction :premises (t200))
% 30.43/30.65  (step t202 (cl (not (forall ((X $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (tptp.member (tptp.sum_class X) tptp.universal_class)))) (or (not (tptp.member (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y))) tptp.universal_class)) (tptp.member (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))) tptp.universal_class))) :rule implies :premises (t201))
% 30.43/30.65  (step t203 (cl (or (not (tptp.member (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y))) tptp.universal_class)) (tptp.member (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))) tptp.universal_class))) :rule resolution :premises (t202 a53))
% 30.43/30.65  (step t204 (cl (tptp.member (tptp.sum_class (tptp.image tptp.choice (tptp.singleton (tptp.singleton tptp.y)))) tptp.universal_class)) :rule resolution :premises (t148 t195 t203))
% 30.43/30.65  (step t205 (cl (not (= tptp.y (tptp.apply tptp.choice (tptp.singleton tptp.y))))) :rule resolution :premises (t133 a92 t146 t204))
% 30.43/30.65  (step t206 (cl (not (= (=> (forall ((U $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member U (tptp.unordered_pair X Y))) (= U X) (= U Y))) (or (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y))) (= (tptp.apply tptp.choice (tptp.singleton tptp.y)) tptp.y) (= (tptp.apply tptp.choice (tptp.singleton tptp.y)) tptp.y))) (=> (forall ((U $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member U (tptp.unordered_pair X Y))) (= U X) (= U Y))) (or (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y))) (= tptp.y (tptp.apply tptp.choice (tptp.singleton tptp.y))) (= tptp.y (tptp.apply tptp.choice (tptp.singleton tptp.y))))))) (not (=> (forall ((U $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member U (tptp.unordered_pair X Y))) (= U X) (= U Y))) (or (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y))) (= (tptp.apply tptp.choice (tptp.singleton tptp.y)) tptp.y) (= (tptp.apply tptp.choice (tptp.singleton tptp.y)) tptp.y)))) (=> (forall ((U $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member U (tptp.unordered_pair X Y))) (= U X) (= U Y))) (or (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y))) (= tptp.y (tptp.apply tptp.choice (tptp.singleton tptp.y))) (= tptp.y (tptp.apply tptp.choice (tptp.singleton tptp.y)))))) :rule equiv_pos2)
% 30.43/30.65  (step t207 (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)
% 30.43/30.65  (step t208 (cl (= (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y))) (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y))))) :rule refl)
% 30.43/30.65  (step t209 (cl (= (= (tptp.apply tptp.choice (tptp.singleton tptp.y)) tptp.y) (= tptp.y (tptp.apply tptp.choice (tptp.singleton tptp.y))))) :rule all_simplify)
% 30.43/30.65  (step t210 (cl (= (or (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y))) (= (tptp.apply tptp.choice (tptp.singleton tptp.y)) tptp.y) (= (tptp.apply tptp.choice (tptp.singleton tptp.y)) tptp.y)) (or (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y))) (= tptp.y (tptp.apply tptp.choice (tptp.singleton tptp.y))) (= tptp.y (tptp.apply tptp.choice (tptp.singleton tptp.y)))))) :rule cong :premises (t208 t209 t209))
% 30.43/30.65  (step t211 (cl (= (=> (forall ((U $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member U (tptp.unordered_pair X Y))) (= U X) (= U Y))) (or (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y))) (= (tptp.apply tptp.choice (tptp.singleton tptp.y)) tptp.y) (= (tptp.apply tptp.choice (tptp.singleton tptp.y)) tptp.y))) (=> (forall ((U $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member U (tptp.unordered_pair X Y))) (= U X) (= U Y))) (or (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y))) (= tptp.y (tptp.apply tptp.choice (tptp.singleton tptp.y))) (= tptp.y (tptp.apply tptp.choice (tptp.singleton tptp.y))))))) :rule cong :premises (t207 t210))
% 30.43/30.65  (step t212 (cl (=> (forall ((U $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member U (tptp.unordered_pair X Y))) (= U X) (= U Y))) (or (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y))) (= (tptp.apply tptp.choice (tptp.singleton tptp.y)) tptp.y) (= (tptp.apply tptp.choice (tptp.singleton tptp.y)) tptp.y))) (forall ((U $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member U (tptp.unordered_pair X Y))) (= U X) (= U Y)))) :rule implies_neg1)
% 30.43/30.65  (anchor :step t213)
% 30.43/30.65  (assume t213.a0 (forall ((U $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member U (tptp.unordered_pair X Y))) (= U X) (= U Y))))
% 30.43/30.65  (step t213.t1 (cl (or (not (forall ((U $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member U (tptp.unordered_pair X Y))) (= U X) (= U Y)))) (or (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y))) (= (tptp.apply tptp.choice (tptp.singleton tptp.y)) tptp.y) (= (tptp.apply tptp.choice (tptp.singleton tptp.y)) tptp.y)))) :rule forall_inst :args ((:= U (tptp.apply tptp.choice (tptp.singleton tptp.y))) (:= X tptp.y) (:= Y tptp.y)))
% 30.43/30.65  (step t213.t2 (cl (not (forall ((U $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member U (tptp.unordered_pair X Y))) (= U X) (= U Y)))) (or (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y))) (= (tptp.apply tptp.choice (tptp.singleton tptp.y)) tptp.y) (= (tptp.apply tptp.choice (tptp.singleton tptp.y)) tptp.y))) :rule or :premises (t213.t1))
% 30.43/30.65  (step t213.t3 (cl (or (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y))) (= (tptp.apply tptp.choice (tptp.singleton tptp.y)) tptp.y) (= (tptp.apply tptp.choice (tptp.singleton tptp.y)) tptp.y))) :rule resolution :premises (t213.t2 t213.a0))
% 30.43/30.65  (step t213 (cl (not (forall ((U $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member U (tptp.unordered_pair X Y))) (= U X) (= U Y)))) (or (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y))) (= (tptp.apply tptp.choice (tptp.singleton tptp.y)) tptp.y) (= (tptp.apply tptp.choice (tptp.singleton tptp.y)) tptp.y))) :rule subproof :discharge (t213.a0))
% 30.43/30.65  (step t214 (cl (=> (forall ((U $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member U (tptp.unordered_pair X Y))) (= U X) (= U Y))) (or (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y))) (= (tptp.apply tptp.choice (tptp.singleton tptp.y)) tptp.y) (= (tptp.apply tptp.choice (tptp.singleton tptp.y)) tptp.y))) (or (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y))) (= (tptp.apply tptp.choice (tptp.singleton tptp.y)) tptp.y) (= (tptp.apply tptp.choice (tptp.singleton tptp.y)) tptp.y))) :rule resolution :premises (t212 t213))
% 30.43/30.65  (step t215 (cl (=> (forall ((U $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member U (tptp.unordered_pair X Y))) (= U X) (= U Y))) (or (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y))) (= (tptp.apply tptp.choice (tptp.singleton tptp.y)) tptp.y) (= (tptp.apply tptp.choice (tptp.singleton tptp.y)) tptp.y))) (not (or (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y))) (= (tptp.apply tptp.choice (tptp.singleton tptp.y)) tptp.y) (= (tptp.apply tptp.choice (tptp.singleton tptp.y)) tptp.y)))) :rule implies_neg2)
% 30.43/30.65  (step t216 (cl (=> (forall ((U $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member U (tptp.unordered_pair X Y))) (= U X) (= U Y))) (or (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y))) (= (tptp.apply tptp.choice (tptp.singleton tptp.y)) tptp.y) (= (tptp.apply tptp.choice (tptp.singleton tptp.y)) tptp.y))) (=> (forall ((U $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member U (tptp.unordered_pair X Y))) (= U X) (= U Y))) (or (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y))) (= (tptp.apply tptp.choice (tptp.singleton tptp.y)) tptp.y) (= (tptp.apply tptp.choice (tptp.singleton tptp.y)) tptp.y)))) :rule resolution :premises (t214 t215))
% 30.43/30.65  (step t217 (cl (=> (forall ((U $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member U (tptp.unordered_pair X Y))) (= U X) (= U Y))) (or (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y))) (= (tptp.apply tptp.choice (tptp.singleton tptp.y)) tptp.y) (= (tptp.apply tptp.choice (tptp.singleton tptp.y)) tptp.y)))) :rule contraction :premises (t216))
% 30.43/30.65  (step t218 (cl (=> (forall ((U $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member U (tptp.unordered_pair X Y))) (= U X) (= U Y))) (or (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y))) (= tptp.y (tptp.apply tptp.choice (tptp.singleton tptp.y))) (= tptp.y (tptp.apply tptp.choice (tptp.singleton tptp.y)))))) :rule resolution :premises (t206 t211 t217))
% 30.43/30.65  (step t219 (cl (not (forall ((U $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member U (tptp.unordered_pair X Y))) (= U X) (= U Y)))) (or (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y))) (= tptp.y (tptp.apply tptp.choice (tptp.singleton tptp.y))) (= tptp.y (tptp.apply tptp.choice (tptp.singleton tptp.y))))) :rule implies :premises (t218))
% 30.43/30.65  (step t220 (cl (or (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y))) (= tptp.y (tptp.apply tptp.choice (tptp.singleton tptp.y))) (= tptp.y (tptp.apply tptp.choice (tptp.singleton tptp.y))))) :rule resolution :premises (t219 a7))
% 30.43/30.65  (step t221 (cl (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.unordered_pair tptp.y tptp.y)))) :rule resolution :premises (t93 t205 t220))
% 30.43/30.65  (step t222 (cl (not (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.singleton tptp.y)))) :rule resolution :premises (t90 t45 t221))
% 30.43/30.65  (step t223 (cl (=> (forall ((Y $$unsorted)) (or (not (tptp.member Y tptp.universal_class)) (= tptp.null_class Y) (tptp.member (tptp.apply tptp.choice Y) Y))) (or (not (tptp.member (tptp.singleton tptp.y) tptp.universal_class)) (= tptp.null_class (tptp.singleton tptp.y)) (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.singleton tptp.y)))) (forall ((Y $$unsorted)) (or (not (tptp.member Y tptp.universal_class)) (= tptp.null_class Y) (tptp.member (tptp.apply tptp.choice Y) Y)))) :rule implies_neg1)
% 30.43/30.65  (anchor :step t224)
% 30.43/30.65  (assume t224.a0 (forall ((Y $$unsorted)) (or (not (tptp.member Y tptp.universal_class)) (= tptp.null_class Y) (tptp.member (tptp.apply tptp.choice Y) Y))))
% 30.43/30.65  (step t224.t1 (cl (or (not (forall ((Y $$unsorted)) (or (not (tptp.member Y tptp.universal_class)) (= tptp.null_class Y) (tptp.member (tptp.apply tptp.choice Y) Y)))) (or (not (tptp.member (tptp.singleton tptp.y) tptp.universal_class)) (= tptp.null_class (tptp.singleton tptp.y)) (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.singleton tptp.y))))) :rule forall_inst :args ((:= Y (tptp.singleton tptp.y))))
% 30.43/30.65  (step t224.t2 (cl (not (forall ((Y $$unsorted)) (or (not (tptp.member Y tptp.universal_class)) (= tptp.null_class Y) (tptp.member (tptp.apply tptp.choice Y) Y)))) (or (not (tptp.member (tptp.singleton tptp.y) tptp.universal_class)) (= tptp.null_class (tptp.singleton tptp.y)) (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.singleton tptp.y)))) :rule or :premises (t224.t1))
% 30.43/30.65  (step t224.t3 (cl (or (not (tptp.member (tptp.singleton tptp.y) tptp.universal_class)) (= tptp.null_class (tptp.singleton tptp.y)) (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.singleton tptp.y)))) :rule resolution :premises (t224.t2 t224.a0))
% 30.43/30.65  (step t224 (cl (not (forall ((Y $$unsorted)) (or (not (tptp.member Y tptp.universal_class)) (= tptp.null_class Y) (tptp.member (tptp.apply tptp.choice Y) Y)))) (or (not (tptp.member (tptp.singleton tptp.y) tptp.universal_class)) (= tptp.null_class (tptp.singleton tptp.y)) (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.singleton tptp.y)))) :rule subproof :discharge (t224.a0))
% 30.43/30.65  (step t225 (cl (=> (forall ((Y $$unsorted)) (or (not (tptp.member Y tptp.universal_class)) (= tptp.null_class Y) (tptp.member (tptp.apply tptp.choice Y) Y))) (or (not (tptp.member (tptp.singleton tptp.y) tptp.universal_class)) (= tptp.null_class (tptp.singleton tptp.y)) (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.singleton tptp.y)))) (or (not (tptp.member (tptp.singleton tptp.y) tptp.universal_class)) (= tptp.null_class (tptp.singleton tptp.y)) (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.singleton tptp.y)))) :rule resolution :premises (t223 t224))
% 30.43/30.65  (step t226 (cl (=> (forall ((Y $$unsorted)) (or (not (tptp.member Y tptp.universal_class)) (= tptp.null_class Y) (tptp.member (tptp.apply tptp.choice Y) Y))) (or (not (tptp.member (tptp.singleton tptp.y) tptp.universal_class)) (= tptp.null_class (tptp.singleton tptp.y)) (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.singleton tptp.y)))) (not (or (not (tptp.member (tptp.singleton tptp.y) tptp.universal_class)) (= tptp.null_class (tptp.singleton tptp.y)) (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.singleton tptp.y))))) :rule implies_neg2)
% 30.43/30.65  (step t227 (cl (=> (forall ((Y $$unsorted)) (or (not (tptp.member Y tptp.universal_class)) (= tptp.null_class Y) (tptp.member (tptp.apply tptp.choice Y) Y))) (or (not (tptp.member (tptp.singleton tptp.y) tptp.universal_class)) (= tptp.null_class (tptp.singleton tptp.y)) (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.singleton tptp.y)))) (=> (forall ((Y $$unsorted)) (or (not (tptp.member Y tptp.universal_class)) (= tptp.null_class Y) (tptp.member (tptp.apply tptp.choice Y) Y))) (or (not (tptp.member (tptp.singleton tptp.y) tptp.universal_class)) (= tptp.null_class (tptp.singleton tptp.y)) (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.singleton tptp.y))))) :rule resolution :premises (t225 t226))
% 30.43/30.65  (step t228 (cl (=> (forall ((Y $$unsorted)) (or (not (tptp.member Y tptp.universal_class)) (= tptp.null_class Y) (tptp.member (tptp.apply tptp.choice Y) Y))) (or (not (tptp.member (tptp.singleton tptp.y) tptp.universal_class)) (= tptp.null_class (tptp.singleton tptp.y)) (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.singleton tptp.y))))) :rule contraction :premises (t227))
% 30.43/30.65  (step t229 (cl (not (forall ((Y $$unsorted)) (or (not (tptp.member Y tptp.universal_class)) (= tptp.null_class Y) (tptp.member (tptp.apply tptp.choice Y) Y)))) (or (not (tptp.member (tptp.singleton tptp.y) tptp.universal_class)) (= tptp.null_class (tptp.singleton tptp.y)) (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.singleton tptp.y)))) :rule implies :premises (t228))
% 30.43/30.65  (step t230 (cl (not (= (forall ((Y $$unsorted)) (or (not (tptp.member Y tptp.universal_class)) (= Y tptp.null_class) (tptp.member (tptp.apply tptp.choice Y) Y))) (forall ((Y $$unsorted)) (or (not (tptp.member Y tptp.universal_class)) (= tptp.null_class Y) (tptp.member (tptp.apply tptp.choice Y) Y))))) (not (forall ((Y $$unsorted)) (or (not (tptp.member Y tptp.universal_class)) (= Y tptp.null_class) (tptp.member (tptp.apply tptp.choice Y) Y)))) (forall ((Y $$unsorted)) (or (not (tptp.member Y tptp.universal_class)) (= tptp.null_class Y) (tptp.member (tptp.apply tptp.choice Y) Y)))) :rule equiv_pos2)
% 30.43/30.65  (anchor :step t231 :args ((Y $$unsorted) (:= Y Y)))
% 30.43/30.65  (step t231.t1 (cl (= Y Y)) :rule refl)
% 30.43/30.65  (step t231.t2 (cl (= (not (tptp.member Y tptp.universal_class)) (not (tptp.member Y tptp.universal_class)))) :rule refl)
% 30.43/30.65  (step t231.t3 (cl (= (= Y tptp.null_class) (= tptp.null_class Y))) :rule all_simplify)
% 30.43/30.65  (step t231.t4 (cl (= (tptp.member (tptp.apply tptp.choice Y) Y) (tptp.member (tptp.apply tptp.choice Y) Y))) :rule refl)
% 30.43/30.65  (step t231.t5 (cl (= (or (not (tptp.member Y tptp.universal_class)) (= Y tptp.null_class) (tptp.member (tptp.apply tptp.choice Y) Y)) (or (not (tptp.member Y tptp.universal_class)) (= tptp.null_class Y) (tptp.member (tptp.apply tptp.choice Y) Y)))) :rule cong :premises (t231.t2 t231.t3 t231.t4))
% 30.43/30.65  (step t231 (cl (= (forall ((Y $$unsorted)) (or (not (tptp.member Y tptp.universal_class)) (= Y tptp.null_class) (tptp.member (tptp.apply tptp.choice Y) Y))) (forall ((Y $$unsorted)) (or (not (tptp.member Y tptp.universal_class)) (= tptp.null_class Y) (tptp.member (tptp.apply tptp.choice Y) Y))))) :rule bind)
% 30.43/30.65  (step t232 (cl (forall ((Y $$unsorted)) (or (not (tptp.member Y tptp.universal_class)) (= tptp.null_class Y) (tptp.member (tptp.apply tptp.choice Y) Y)))) :rule resolution :premises (t230 t231 a69))
% 30.43/30.65  (step t233 (cl (or (not (tptp.member (tptp.singleton tptp.y) tptp.universal_class)) (= tptp.null_class (tptp.singleton tptp.y)) (tptp.member (tptp.apply tptp.choice (tptp.singleton tptp.y)) (tptp.singleton tptp.y)))) :rule resolution :premises (t229 t232))
% 30.43/30.65  (step t234 (cl (= tptp.null_class (tptp.singleton tptp.y))) :rule resolution :premises (t17 t54 t222 t233))
% 30.43/30.65  (step t235 (cl (not (= (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.unordered_pair (tptp.singleton X) (tptp.unordered_pair X (tptp.singleton Y))) (tptp.ordered_pair X Y))) (= (tptp.unordered_pair (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x (tptp.singleton tptp.y))) (tptp.ordered_pair tptp.x tptp.y))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.unordered_pair (tptp.singleton X) (tptp.unordered_pair X (tptp.singleton Y))) (tptp.ordered_pair X Y))) (= (tptp.ordered_pair tptp.x tptp.y) (tptp.unordered_pair (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x (tptp.singleton tptp.y))))))) (not (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.unordered_pair (tptp.singleton X) (tptp.unordered_pair X (tptp.singleton Y))) (tptp.ordered_pair X Y))) (= (tptp.unordered_pair (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x (tptp.singleton tptp.y))) (tptp.ordered_pair tptp.x tptp.y)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.unordered_pair (tptp.singleton X) (tptp.unordered_pair X (tptp.singleton Y))) (tptp.ordered_pair X Y))) (= (tptp.ordered_pair tptp.x tptp.y) (tptp.unordered_pair (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x (tptp.singleton tptp.y)))))) :rule equiv_pos2)
% 30.43/30.65  (step t236 (cl (= (forall ((X $$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 $$unsorted)) (= (tptp.unordered_pair (tptp.singleton X) (tptp.unordered_pair X (tptp.singleton Y))) (tptp.ordered_pair X Y))))) :rule refl)
% 30.43/30.65  (step t237 (cl (= (= (tptp.unordered_pair (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x (tptp.singleton tptp.y))) (tptp.ordered_pair tptp.x tptp.y)) (= (tptp.ordered_pair tptp.x tptp.y) (tptp.unordered_pair (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x (tptp.singleton tptp.y)))))) :rule all_simplify)
% 30.43/30.65  (step t238 (cl (= (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.unordered_pair (tptp.singleton X) (tptp.unordered_pair X (tptp.singleton Y))) (tptp.ordered_pair X Y))) (= (tptp.unordered_pair (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x (tptp.singleton tptp.y))) (tptp.ordered_pair tptp.x tptp.y))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.unordered_pair (tptp.singleton X) (tptp.unordered_pair X (tptp.singleton Y))) (tptp.ordered_pair X Y))) (= (tptp.ordered_pair tptp.x tptp.y) (tptp.unordered_pair (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x (tptp.singleton tptp.y))))))) :rule cong :premises (t236 t237))
% 30.43/30.65  (step t239 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.unordered_pair (tptp.singleton X) (tptp.unordered_pair X (tptp.singleton Y))) (tptp.ordered_pair X Y))) (= (tptp.unordered_pair (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x (tptp.singleton tptp.y))) (tptp.ordered_pair tptp.x tptp.y))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.unordered_pair (tptp.singleton X) (tptp.unordered_pair X (tptp.singleton Y))) (tptp.ordered_pair X Y)))) :rule implies_neg1)
% 30.43/30.65  (anchor :step t240)
% 30.43/30.65  (assume t240.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.unordered_pair (tptp.singleton X) (tptp.unordered_pair X (tptp.singleton Y))) (tptp.ordered_pair X Y))))
% 30.43/30.65  (step t240.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.unordered_pair (tptp.singleton X) (tptp.unordered_pair X (tptp.singleton Y))) (tptp.ordered_pair X Y)))) (= (tptp.unordered_pair (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x (tptp.singleton tptp.y))) (tptp.ordered_pair tptp.x tptp.y)))) :rule forall_inst :args ((:= X tptp.x) (:= Y tptp.y)))
% 30.43/30.65  (step t240.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.unordered_pair (tptp.singleton X) (tptp.unordered_pair X (tptp.singleton Y))) (tptp.ordered_pair X Y)))) (= (tptp.unordered_pair (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x (tptp.singleton tptp.y))) (tptp.ordered_pair tptp.x tptp.y))) :rule or :premises (t240.t1))
% 30.43/30.65  (step t240.t3 (cl (= (tptp.unordered_pair (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x (tptp.singleton tptp.y))) (tptp.ordered_pair tptp.x tptp.y))) :rule resolution :premises (t240.t2 t240.a0))
% 30.43/30.65  (step t240 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.unordered_pair (tptp.singleton X) (tptp.unordered_pair X (tptp.singleton Y))) (tptp.ordered_pair X Y)))) (= (tptp.unordered_pair (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x (tptp.singleton tptp.y))) (tptp.ordered_pair tptp.x tptp.y))) :rule subproof :discharge (t240.a0))
% 30.43/30.65  (step t241 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.unordered_pair (tptp.singleton X) (tptp.unordered_pair X (tptp.singleton Y))) (tptp.ordered_pair X Y))) (= (tptp.unordered_pair (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x (tptp.singleton tptp.y))) (tptp.ordered_pair tptp.x tptp.y))) (= (tptp.unordered_pair (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x (tptp.singleton tptp.y))) (tptp.ordered_pair tptp.x tptp.y))) :rule resolution :premises (t239 t240))
% 30.43/30.65  (step t242 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.unordered_pair (tptp.singleton X) (tptp.unordered_pair X (tptp.singleton Y))) (tptp.ordered_pair X Y))) (= (tptp.unordered_pair (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x (tptp.singleton tptp.y))) (tptp.ordered_pair tptp.x tptp.y))) (not (= (tptp.unordered_pair (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x (tptp.singleton tptp.y))) (tptp.ordered_pair tptp.x tptp.y)))) :rule implies_neg2)
% 30.43/30.65  (step t243 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.unordered_pair (tptp.singleton X) (tptp.unordered_pair X (tptp.singleton Y))) (tptp.ordered_pair X Y))) (= (tptp.unordered_pair (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x (tptp.singleton tptp.y))) (tptp.ordered_pair tptp.x tptp.y))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.unordered_pair (tptp.singleton X) (tptp.unordered_pair X (tptp.singleton Y))) (tptp.ordered_pair X Y))) (= (tptp.unordered_pair (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x (tptp.singleton tptp.y))) (tptp.ordered_pair tptp.x tptp.y)))) :rule resolution :premises (t241 t242))
% 30.43/30.65  (step t244 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.unordered_pair (tptp.singleton X) (tptp.unordered_pair X (tptp.singleton Y))) (tptp.ordered_pair X Y))) (= (tptp.unordered_pair (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x (tptp.singleton tptp.y))) (tptp.ordered_pair tptp.x tptp.y)))) :rule contraction :premises (t243))
% 30.43/30.65  (step t245 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.unordered_pair (tptp.singleton X) (tptp.unordered_pair X (tptp.singleton Y))) (tptp.ordered_pair X Y))) (= (tptp.ordered_pair tptp.x tptp.y) (tptp.unordered_pair (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x (tptp.singleton tptp.y)))))) :rule resolution :premises (t235 t238 t244))
% 30.43/30.65  (step t246 (cl (not (forall ((X $$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.x tptp.y) (tptp.unordered_pair (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x (tptp.singleton tptp.y))))) :rule implies :premises (t245))
% 30.43/30.65  (step t247 (cl (= (tptp.ordered_pair tptp.x tptp.y) (tptp.unordered_pair (tptp.singleton tptp.x) (tptp.unordered_pair tptp.x (tptp.singleton tptp.y))))) :rule resolution :premises (t246 a12))
% 30.43/30.65  (step t248 (cl) :rule resolution :premises (t15 t234 t247 a91))
% 30.43/30.65  
% 30.43/30.66  % SZS output end Proof for /export/starexec/sandbox/tmp/tmp.GbxorQhN9e/cvc5---1.0.5_18319.smt2
% 30.43/30.66  % cvc5---1.0.5 exiting
% 30.43/30.66  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------