%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU162+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 02:55:41 PM UTC 2026
% Result : Theorem 8.35s 1.82s
% Output : CNFRefutation 8.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 74
% Syntax : Number of formulae : 1940 ( 723 unt; 0 def)
% Number of atoms : 4079 (1113 equ)
% Maximal formula atoms : 18 ( 2 avg)
% Number of connectives : 4022 (1883 ~;1868 |; 212 &)
% ( 31 <=>; 26 =>; 0 <=; 2 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 33 ( 33 usr; 5 con; 0-3 aty)
% Number of variables : 4735 ( 2 sgn4682 !; 53 ?;3748 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( in(X0,X1)
=> ~ in(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f2,axiom,
! [X0,X1] :
( proper_subset(X0,X1)
=> ~ proper_subset(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_xboole_0) ).
fof(f3,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f4,axiom,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(f5,axiom,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(f6,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X1,X0)
& subset(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).
fof(f7,axiom,
! [X0,X1] :
( X1 = singleton(X0)
<=> ! [X2] :
( in(X2,X1)
<=> X2 = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
fof(f8,axiom,
! [X0] :
( X0 = empty_set
<=> ! [X1] : ~ in(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(f9,axiom,
! [X0,X1] :
( X1 = powerset(X0)
<=> ! [X2] :
( in(X2,X1)
<=> subset(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_zfmisc_1) ).
fof(f10,axiom,
! [X0,X1,X2] :
( X2 = unordered_pair(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( X3 = X1
| X3 = X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tarski) ).
fof(f11,axiom,
! [X0,X1,X2] :
( X2 = set_union2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
| in(X3,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(f12,axiom,
! [X0,X1,X2] :
( X2 = cartesian_product2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4,X5] :
( X3 = ordered_pair(X4,X5)
& in(X5,X1)
& in(X4,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_zfmisc_1) ).
fof(f13,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f14,axiom,
! [X0,X1,X2] :
( X2 = set_intersection2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
& in(X3,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(f15,axiom,
! [X0,X1] :
( X1 = union(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( in(X3,X0)
& in(X2,X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_tarski) ).
fof(f16,axiom,
! [X0,X1,X2] :
( X2 = set_difference(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( ~ in(X3,X1)
& in(X3,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_xboole_0) ).
fof(f17,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
fof(f18,axiom,
! [X0,X1] :
( disjoint(X0,X1)
<=> set_intersection2(X0,X1) = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_xboole_0) ).
fof(f19,axiom,
! [X0,X1] :
( proper_subset(X0,X1)
<=> ( X0 != X1
& subset(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_xboole_0) ).
fof(f30,axiom,
empty(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(f31,axiom,
! [X0,X1] : ~ empty(ordered_pair(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
fof(f32,axiom,
! [X0,X1] :
( ~ empty(X0)
=> ~ empty(set_union2(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_xboole_0) ).
fof(f33,axiom,
! [X0,X1] :
( ~ empty(X0)
=> ~ empty(set_union2(X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_xboole_0) ).
fof(f34,axiom,
! [X0,X1] : set_union2(X0,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
fof(f36,axiom,
! [X0,X1] : ~ proper_subset(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',irreflexivity_r2_xboole_0) ).
fof(f37,axiom,
! [X0] : singleton(X0) != empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l1_zfmisc_1) ).
fof(f39,axiom,
! [X0,X1] :
~ ( in(X0,X1)
& disjoint(singleton(X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l25_zfmisc_1) ).
fof(f40,axiom,
! [X0,X1] :
( ~ in(X0,X1)
=> disjoint(singleton(X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l28_zfmisc_1) ).
fof(f43,axiom,
! [X0,X1,X2] :
( subset(X0,X1)
=> ( subset(X0,set_difference(X1,singleton(X2)))
| in(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l3_zfmisc_1) ).
fof(f45,axiom,
! [X0,X1] :
( in(X0,X1)
=> subset(X0,union(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l50_zfmisc_1) ).
fof(f46,axiom,
! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
<=> ( in(X1,X3)
& in(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l55_zfmisc_1) ).
fof(f47,axiom,
? [X0] : empty(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(f48,axiom,
? [X0] : ~ empty(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f50,axiom,
! [X0,X1] :
( disjoint(X0,X1)
=> disjoint(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
fof(f51,axiom,
! [X0,X1,X2,X3] :
~ ( X0 != X3
& X0 != X2
& unordered_pair(X0,X1) = unordered_pair(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_zfmisc_1) ).
fof(f52,axiom,
! [X0,X1] :
( subset(X0,X1)
=> set_union2(X0,X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_xboole_1) ).
fof(f54,axiom,
! [X0,X1,X2] :
( ( subset(X0,X2)
& subset(X0,X1) )
=> subset(X0,set_intersection2(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_xboole_1) ).
fof(f55,axiom,
! [X0] : set_union2(X0,empty_set) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_boole) ).
fof(f56,axiom,
! [X0,X1,X2] :
( ( subset(X1,X2)
& subset(X0,X1) )
=> subset(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_xboole_1) ).
fof(f57,axiom,
powerset(empty_set) = singleton(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_zfmisc_1) ).
fof(f58,axiom,
! [X0,X1,X2] :
( subset(X0,X1)
=> subset(set_intersection2(X0,X2),set_intersection2(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_xboole_1) ).
fof(f59,axiom,
! [X0,X1] :
( subset(X0,X1)
=> set_intersection2(X0,X1) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_xboole_1) ).
fof(f60,axiom,
! [X0] : set_intersection2(X0,empty_set) = empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_boole) ).
fof(f61,axiom,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
<=> in(X2,X1) )
=> X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_tarski) ).
fof(f62,axiom,
! [X0] : subset(empty_set,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_xboole_1) ).
fof(f63,axiom,
! [X0,X1,X2] :
( subset(X0,X1)
=> subset(set_difference(X0,X2),set_difference(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_xboole_1) ).
fof(f64,axiom,
! [X0,X1,X2,X3] :
( ordered_pair(X0,X1) = ordered_pair(X2,X3)
=> ( X1 = X3
& X0 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_zfmisc_1) ).
fof(f65,axiom,
! [X0,X1] : subset(set_difference(X0,X1),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_xboole_1) ).
fof(f66,axiom,
! [X0,X1] :
( set_difference(X0,X1) = empty_set
<=> subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_xboole_1) ).
fof(f67,axiom,
! [X0,X1] :
( subset(singleton(X0),X1)
<=> in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_zfmisc_1) ).
fof(f68,axiom,
! [X0,X1,X2] :
( subset(unordered_pair(X0,X1),X2)
<=> ( in(X1,X2)
& in(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_zfmisc_1) ).
fof(f69,axiom,
! [X0,X1] : set_union2(X0,set_difference(X1,X0)) = set_union2(X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_xboole_1) ).
fof(f70,axiom,
! [X0,X1] :
( subset(X0,singleton(X1))
<=> ( X0 = singleton(X1)
| X0 = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_zfmisc_1) ).
fof(f71,axiom,
! [X0] : set_difference(X0,empty_set) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_boole) ).
fof(f72,axiom,
! [X0,X1] :
( ~ ( disjoint(X0,X1)
& ? [X2] :
( in(X2,X1)
& in(X2,X0) ) )
& ~ ( ! [X2] :
~ ( in(X2,X1)
& in(X2,X0) )
& ~ disjoint(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_0) ).
fof(f73,axiom,
! [X0] :
( subset(X0,empty_set)
=> X0 = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_1) ).
fof(f74,axiom,
! [X0,X1] : set_difference(set_union2(X0,X1),X1) = set_difference(X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_xboole_1) ).
fof(f76,axiom,
! [X0,X1] :
( in(X0,X1)
=> set_union2(singleton(X0),X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_zfmisc_1) ).
fof(f77,axiom,
! [X0,X1] : set_difference(X0,set_difference(X0,X1)) = set_intersection2(X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_xboole_1) ).
fof(f78,axiom,
! [X0] : set_difference(empty_set,X0) = empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_boole) ).
fof(f79,axiom,
! [X0,X1] :
( ~ ( disjoint(X0,X1)
& ? [X2] : in(X2,set_intersection2(X0,X1)) )
& ~ ( ! [X2] : ~ in(X2,set_intersection2(X0,X1))
& ~ disjoint(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_xboole_0) ).
fof(f80,axiom,
! [X0,X1] :
~ ( proper_subset(X1,X0)
& subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_xboole_1) ).
fof(f81,axiom,
! [X0,X1,X2] :
( ( disjoint(X1,X2)
& subset(X0,X1) )
=> disjoint(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_xboole_1) ).
fof(f82,conjecture,
! [X0,X1] :
( set_difference(X0,singleton(X1)) = X0
<=> ~ in(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_zfmisc_1) ).
fof(f83,negated_conjecture,
~ ! [X0,X1] :
( set_difference(X0,singleton(X1)) = X0
<=> ~ in(X1,X0) ),
inference(negated_conjecture,[status(cth)],[f82]) ).
fof(f84,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_enumset1) ).
fof(f85,axiom,
! [X0] :
( empty(X0)
=> X0 = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
fof(f86,axiom,
! [X0,X1] :
( subset(singleton(X0),singleton(X1))
=> X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_zfmisc_1) ).
fof(f87,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(f88,axiom,
! [X0,X1] : subset(X0,set_union2(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_xboole_1) ).
fof(f89,axiom,
! [X0,X1] :
( disjoint(X0,X1)
<=> set_difference(X0,X1) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t83_xboole_1) ).
fof(f90,axiom,
! [X0,X1] :
~ ( empty(X1)
& X0 != X1
& empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
fof(f91,axiom,
! [X0,X1,X2] :
( ( subset(X2,X1)
& subset(X0,X1) )
=> subset(set_union2(X0,X2),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_xboole_1) ).
fof(f92,axiom,
! [X0,X1,X2] :
( singleton(X0) = unordered_pair(X1,X2)
=> X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_zfmisc_1) ).
fof(f93,axiom,
! [X0,X1,X2] :
( singleton(X0) = unordered_pair(X1,X2)
=> X1 = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_zfmisc_1) ).
fof(f94,plain,
! [X0,X1] :
( ~ ( disjoint(X0,X1)
& ? [X3] :
( in(X3,X1)
& in(X3,X0) ) )
& ~ ( ! [X2] :
~ ( in(X2,X1)
& in(X2,X0) )
& ~ disjoint(X0,X1) ) ),
inference(rectify,[],[f72]) ).
fof(f95,plain,
! [X0,X1] :
( ~ ( disjoint(X0,X1)
& ? [X3] : in(X3,set_intersection2(X0,X1)) )
& ~ ( ! [X2] : ~ in(X2,set_intersection2(X0,X1))
& ~ disjoint(X0,X1) ) ),
inference(rectify,[],[f79]) ).
fof(f96,plain,
! [X0] : set_union2(X0,X0) = X0,
inference(rectify,[],[f34]) ).
fof(f99,plain,
! [X0] : ~ proper_subset(X0,X0),
inference(rectify,[],[f36]) ).
fof(f100,plain,
! [X0,X1] :
( ( X0 != X1
& subset(X0,X1) )
=> proper_subset(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f19]) ).
fof(f102,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ disjoint(singleton(X0),X1) ),
inference(ennf_transformation,[],[f39]) ).
fof(f103,plain,
! [X0,X1] :
( in(X0,X1)
| disjoint(singleton(X0),X1) ),
inference(ennf_transformation,[],[f40]) ).
fof(f104,plain,
! [X0,X1,X2] :
( ~ subset(X0,X1)
| subset(X0,set_difference(X1,singleton(X2)))
| in(X2,X0) ),
inference(ennf_transformation,[],[f43]) ).
fof(f105,plain,
! [X0,X1,X2] :
( ~ subset(X0,X1)
| subset(X0,set_difference(X1,singleton(X2)))
| in(X2,X0) ),
inference(flattening,[],[f104]) ).
fof(f106,plain,
! [X0,X1] :
( ~ in(X0,X1)
| subset(X0,union(X1)) ),
inference(ennf_transformation,[],[f45]) ).
fof(f107,plain,
! [X0,X1,X2,X3] :
( X0 = X3
| X0 = X2
| unordered_pair(X0,X1) != unordered_pair(X2,X3) ),
inference(ennf_transformation,[],[f51]) ).
fof(f108,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| set_union2(X0,X1) = X1 ),
inference(ennf_transformation,[],[f52]) ).
fof(f109,plain,
! [X0,X1,X2] :
( ~ subset(X0,X2)
| ~ subset(X0,X1)
| subset(X0,set_intersection2(X1,X2)) ),
inference(ennf_transformation,[],[f54]) ).
fof(f110,plain,
! [X0,X1,X2] :
( ~ subset(X0,X2)
| ~ subset(X0,X1)
| subset(X0,set_intersection2(X1,X2)) ),
inference(flattening,[],[f109]) ).
fof(f111,plain,
! [X0,X1,X2] :
( ~ subset(X1,X2)
| ~ subset(X0,X1)
| subset(X0,X2) ),
inference(ennf_transformation,[],[f56]) ).
fof(f112,plain,
! [X0,X1,X2] :
( ~ subset(X1,X2)
| ~ subset(X0,X1)
| subset(X0,X2) ),
inference(flattening,[],[f111]) ).
fof(f113,plain,
! [X0,X1,X2] :
( ~ subset(X0,X1)
| subset(set_intersection2(X0,X2),set_intersection2(X1,X2)) ),
inference(ennf_transformation,[],[f58]) ).
fof(f114,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| set_intersection2(X0,X1) = X0 ),
inference(ennf_transformation,[],[f59]) ).
fof(f115,plain,
! [X0,X1,X2] :
( ~ subset(X0,X1)
| subset(set_difference(X0,X2),set_difference(X1,X2)) ),
inference(ennf_transformation,[],[f63]) ).
fof(f116,plain,
! [X0,X1,X2,X3] :
( ordered_pair(X0,X1) != ordered_pair(X2,X3)
| ( X1 = X3
& X0 = X2 ) ),
inference(ennf_transformation,[],[f64]) ).
fof(f117,plain,
! [X0,X1] :
( ( ~ disjoint(X0,X1)
| ! [X3] :
( ~ in(X3,X1)
| ~ in(X3,X0) ) )
& ( ? [X2] :
( in(X2,X1)
& in(X2,X0) )
| disjoint(X0,X1) ) ),
inference(ennf_transformation,[],[f94]) ).
fof(f118,plain,
! [X0] :
( ~ subset(X0,empty_set)
| X0 = empty_set ),
inference(ennf_transformation,[],[f73]) ).
fof(f120,plain,
! [X0,X1] :
( ~ in(X0,X1)
| set_union2(singleton(X0),X1) = X1 ),
inference(ennf_transformation,[],[f76]) ).
fof(f121,plain,
! [X0,X1] :
( ( ~ disjoint(X0,X1)
| ! [X3] : ~ in(X3,set_intersection2(X0,X1)) )
& ( ? [X2] : in(X2,set_intersection2(X0,X1))
| disjoint(X0,X1) ) ),
inference(ennf_transformation,[],[f95]) ).
fof(f122,plain,
! [X0,X1] :
( ~ proper_subset(X1,X0)
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f80]) ).
fof(f123,plain,
! [X0,X1,X2] :
( ~ disjoint(X1,X2)
| ~ subset(X0,X1)
| disjoint(X0,X2) ),
inference(ennf_transformation,[],[f81]) ).
fof(f124,plain,
! [X0,X1,X2] :
( ~ disjoint(X1,X2)
| ~ subset(X0,X1)
| disjoint(X0,X2) ),
inference(flattening,[],[f123]) ).
fof(f125,plain,
? [X0,X1] :
( set_difference(X0,singleton(X1)) = X0
<~> ~ in(X1,X0) ),
inference(ennf_transformation,[],[f83]) ).
fof(f126,plain,
! [X0,X1] :
( ~ subset(singleton(X0),singleton(X1))
| X0 = X1 ),
inference(ennf_transformation,[],[f86]) ).
fof(f127,plain,
! [X0,X1,X2] :
( ~ subset(X2,X1)
| ~ subset(X0,X1)
| subset(set_union2(X0,X2),X1) ),
inference(ennf_transformation,[],[f91]) ).
fof(f128,plain,
! [X0,X1,X2] :
( ~ subset(X2,X1)
| ~ subset(X0,X1)
| subset(set_union2(X0,X2),X1) ),
inference(flattening,[],[f127]) ).
fof(f129,plain,
! [X0,X1,X2] :
( singleton(X0) != unordered_pair(X1,X2)
| X0 = X1 ),
inference(ennf_transformation,[],[f92]) ).
fof(f130,plain,
! [X0,X1,X2] :
( singleton(X0) != unordered_pair(X1,X2)
| X1 = X2 ),
inference(ennf_transformation,[],[f93]) ).
fof(f131,plain,
! [X0,X1] :
( ? [X2] :
( in(X2,X0)
<~> in(X2,X1) )
| X0 = X1 ),
inference(ennf_transformation,[],[f61]) ).
fof(f132,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) ),
inference(ennf_transformation,[],[f13]) ).
fof(f133,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ in(X1,X0) ),
inference(ennf_transformation,[],[f1]) ).
fof(f134,plain,
! [X0,X1] :
( ~ disjoint(X0,X1)
| disjoint(X1,X0) ),
inference(ennf_transformation,[],[f50]) ).
fof(f135,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(X0,X1)
| proper_subset(X0,X1) ),
inference(ennf_transformation,[],[f100]) ).
fof(f136,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(X0,X1)
| proper_subset(X0,X1) ),
inference(flattening,[],[f135]) ).
fof(f137,plain,
! [X0,X1] :
( ~ proper_subset(X0,X1)
| ~ proper_subset(X1,X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f138,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(ennf_transformation,[],[f90]) ).
fof(f139,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f87]) ).
fof(f140,plain,
! [X0] :
( ~ empty(X0)
| X0 = empty_set ),
inference(ennf_transformation,[],[f85]) ).
fof(f141,plain,
! [X0,X1] :
( empty(X0)
| ~ empty(set_union2(X1,X0)) ),
inference(ennf_transformation,[],[f33]) ).
fof(f142,plain,
! [X0,X1] :
( empty(X0)
| ~ empty(set_union2(X0,X1)) ),
inference(ennf_transformation,[],[f32]) ).
fof(f147,plain,
! [X0,X1,X2,X3] :
( ( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ( in(X1,X3)
& in(X0,X2) ) )
& ( ~ in(X1,X3)
| ~ in(X0,X2)
| in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(nnf_transformation,[],[f46]) ).
fof(f148,plain,
! [X0,X1,X2,X3] :
( ( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ( in(X1,X3)
& in(X0,X2) ) )
& ( ~ in(X1,X3)
| ~ in(X0,X2)
| in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(flattening,[],[f147]) ).
fof(f149,plain,
! [X0,X1] :
( ( empty_set != set_difference(X0,X1)
| subset(X0,X1) )
& ( ~ subset(X0,X1)
| set_difference(X0,X1) = empty_set ) ),
inference(nnf_transformation,[],[f66]) ).
fof(f150,plain,
! [X0,X1] :
( ( ~ subset(singleton(X0),X1)
| in(X0,X1) )
& ( ~ in(X0,X1)
| subset(singleton(X0),X1) ) ),
inference(nnf_transformation,[],[f67]) ).
fof(f151,plain,
! [X0,X1,X2] :
( ( ~ subset(unordered_pair(X0,X1),X2)
| ( in(X1,X2)
& in(X0,X2) ) )
& ( ~ in(X1,X2)
| ~ in(X0,X2)
| subset(unordered_pair(X0,X1),X2) ) ),
inference(nnf_transformation,[],[f68]) ).
fof(f152,plain,
! [X0,X1,X2] :
( ( ~ subset(unordered_pair(X0,X1),X2)
| ( in(X1,X2)
& in(X0,X2) ) )
& ( ~ in(X1,X2)
| ~ in(X0,X2)
| subset(unordered_pair(X0,X1),X2) ) ),
inference(flattening,[],[f151]) ).
fof(f153,plain,
! [X0,X1] :
( ( ~ subset(X0,singleton(X1))
| X0 = singleton(X1)
| X0 = empty_set )
& ( ( singleton(X1) != X0
& empty_set != X0 )
| subset(X0,singleton(X1)) ) ),
inference(nnf_transformation,[],[f70]) ).
fof(f154,plain,
! [X0,X1] :
( ( ~ subset(X0,singleton(X1))
| X0 = singleton(X1)
| X0 = empty_set )
& ( ( singleton(X1) != X0
& empty_set != X0 )
| subset(X0,singleton(X1)) ) ),
inference(flattening,[],[f153]) ).
fof(f155,plain,
! [X0,X1] :
( ( ~ disjoint(X0,X1)
| ! [X3] :
( ~ in(X3,X1)
| ~ in(X3,X0) ) )
& ( ( in(sK0(X0,X1),X1)
& in(sK0(X0,X1),X0) )
| disjoint(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f117]) ).
fof(f156,plain,
! [X0,X1] :
( ( ~ disjoint(X0,X1)
| ! [X3] : ~ in(X3,set_intersection2(X0,X1)) )
& ( in(sK1(X0,X1),set_intersection2(X0,X1))
| disjoint(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X2,sK1(X0,X1))],[f121]) ).
fof(f157,plain,
? [X0,X1] :
( ( set_difference(X0,singleton(X1)) = X0
| ~ in(X1,X0) )
& ( set_difference(X0,singleton(X1)) != X0
| in(X1,X0) ) ),
inference(nnf_transformation,[],[f125]) ).
fof(f158,plain,
( ( sK2 = set_difference(sK2,singleton(sK3))
| ~ in(sK3,sK2) )
& ( sK2 != set_difference(sK2,singleton(sK3))
| in(sK3,sK2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X0,sK2),skolemize(X1,sK3)],[f157]) ).
fof(f159,plain,
! [X0,X1] :
( ( ~ disjoint(X0,X1)
| set_difference(X0,X1) = X0 )
& ( set_difference(X0,X1) != X0
| disjoint(X0,X1) ) ),
inference(nnf_transformation,[],[f89]) ).
fof(f160,plain,
! [X0,X1] :
( ( singleton(X0) != X1
| ! [X2] :
( ( ~ in(X2,X1)
| X2 = X0 )
& ( X0 != X2
| in(X2,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| X2 = X0 )
& ( ~ in(X2,X1)
| X0 != X2 ) )
| X1 = singleton(X0) ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f161,plain,
! [X0,X1] :
( ( singleton(X0) != X1
| ! [X3] :
( ( ~ in(X3,X1)
| X0 = X3 )
& ( X0 != X3
| in(X3,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| X2 = X0 )
& ( ~ in(X2,X1)
| X0 != X2 ) )
| X1 = singleton(X0) ) ),
inference(rectify,[],[f160]) ).
fof(f162,plain,
! [X0,X1] :
( ( singleton(X0) != X1
| ! [X3] :
( ( ~ in(X3,X1)
| X0 = X3 )
& ( X0 != X3
| in(X3,X1) ) ) )
& ( ( ( in(sK4(X0,X1),X1)
| sK4(X0,X1) = X0 )
& ( ~ in(sK4(X0,X1),X1)
| sK4(X0,X1) != X0 ) )
| X1 = singleton(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X2,sK4(X0,X1))],[f161]) ).
fof(f163,plain,
! [X0] :
( ( empty_set != X0
| ! [X1] : ~ in(X1,X0) )
& ( ? [X1] : in(X1,X0)
| X0 = empty_set ) ),
inference(nnf_transformation,[],[f8]) ).
fof(f164,plain,
! [X0] :
( ( empty_set != X0
| ! [X2] : ~ in(X2,X0) )
& ( ? [X1] : in(X1,X0)
| X0 = empty_set ) ),
inference(rectify,[],[f163]) ).
fof(f165,plain,
! [X0] :
( ( empty_set != X0
| ! [X2] : ~ in(X2,X0) )
& ( in(sK5(X0),X0)
| X0 = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X1,sK5(X0))],[f164]) ).
fof(f166,plain,
! [X0,X1] :
( ? [X2] :
( ( in(X2,X0)
| in(X2,X1) )
& ( ~ in(X2,X0)
| ~ in(X2,X1) ) )
| X0 = X1 ),
inference(nnf_transformation,[],[f131]) ).
fof(f167,plain,
! [X0,X1] :
( ( ( in(sK6(X0,X1),X0)
| in(sK6(X0,X1),X1) )
& ( ~ in(sK6(X0,X1),X0)
| ~ in(sK6(X0,X1),X1) ) )
| X0 = X1 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X2,sK6(X0,X1))],[f166]) ).
fof(f168,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) )
& ( ? [X2] :
( in(X2,X0)
& ~ in(X2,X1) )
| subset(X0,X1) ) ),
inference(nnf_transformation,[],[f132]) ).
fof(f169,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ in(X3,X0)
| in(X3,X1) ) )
& ( ? [X2] :
( in(X2,X0)
& ~ in(X2,X1) )
| subset(X0,X1) ) ),
inference(rectify,[],[f168]) ).
fof(f170,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ in(X3,X0)
| in(X3,X1) ) )
& ( ( in(sK7(X0,X1),X0)
& ~ in(sK7(X0,X1),X1) )
| subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X2,sK7(X0,X1))],[f169]) ).
fof(f171,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| in(X3,X1)
| in(X3,X0) )
& ( ( ~ in(X3,X1)
& ~ in(X3,X0) )
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| in(X3,X1)
| in(X3,X0) )
& ( ~ in(X3,X2)
| ( ~ in(X3,X1)
& ~ in(X3,X0) ) ) )
| X2 = set_union2(X0,X1) ) ),
inference(nnf_transformation,[],[f11]) ).
fof(f172,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| in(X3,X1)
| in(X3,X0) )
& ( ( ~ in(X3,X1)
& ~ in(X3,X0) )
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| in(X3,X1)
| in(X3,X0) )
& ( ~ in(X3,X2)
| ( ~ in(X3,X1)
& ~ in(X3,X0) ) ) )
| X2 = set_union2(X0,X1) ) ),
inference(flattening,[],[f171]) ).
fof(f173,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| in(X4,X1)
| in(X4,X0) )
& ( ( ~ in(X4,X1)
& ~ in(X4,X0) )
| in(X4,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| in(X3,X1)
| in(X3,X0) )
& ( ~ in(X3,X2)
| ( ~ in(X3,X1)
& ~ in(X3,X0) ) ) )
| X2 = set_union2(X0,X1) ) ),
inference(rectify,[],[f172]) ).
fof(f174,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| in(X4,X1)
| in(X4,X0) )
& ( ( ~ in(X4,X1)
& ~ in(X4,X0) )
| in(X4,X2) ) ) )
& ( ( ( in(sK8(X0,X1,X2),X2)
| in(sK8(X0,X1,X2),X1)
| in(sK8(X0,X1,X2),X0) )
& ( ~ in(sK8(X0,X1,X2),X2)
| ( ~ in(sK8(X0,X1,X2),X1)
& ~ in(sK8(X0,X1,X2),X0) ) ) )
| X2 = set_union2(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(X3,sK8(X0,X1,X2))],[f173]) ).
fof(f175,plain,
! [X0,X1] :
( ( ~ disjoint(X0,X1)
| set_intersection2(X0,X1) = empty_set )
& ( set_intersection2(X0,X1) != empty_set
| disjoint(X0,X1) ) ),
inference(nnf_transformation,[],[f18]) ).
fof(f176,plain,
! [X0,X1] :
( ( X0 != X1
| ( subset(X1,X0)
& subset(X0,X1) ) )
& ( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f177,plain,
! [X0,X1] :
( ( X0 != X1
| ( subset(X1,X0)
& subset(X0,X1) ) )
& ( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ) ),
inference(flattening,[],[f176]) ).
fof(f178,plain,
! [X0,X1,X2] :
( ( set_difference(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| ( ~ in(X3,X1)
& in(X3,X0) ) )
& ( in(X3,X1)
| ~ in(X3,X0)
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ( ~ in(X3,X1)
& in(X3,X0) ) )
& ( ~ in(X3,X2)
| in(X3,X1)
| ~ in(X3,X0) ) )
| X2 = set_difference(X0,X1) ) ),
inference(nnf_transformation,[],[f16]) ).
fof(f179,plain,
! [X0,X1,X2] :
( ( set_difference(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| ( ~ in(X3,X1)
& in(X3,X0) ) )
& ( in(X3,X1)
| ~ in(X3,X0)
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ( ~ in(X3,X1)
& in(X3,X0) ) )
& ( ~ in(X3,X2)
| in(X3,X1)
| ~ in(X3,X0) ) )
| X2 = set_difference(X0,X1) ) ),
inference(flattening,[],[f178]) ).
fof(f180,plain,
! [X0,X1,X2] :
( ( set_difference(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| ( ~ in(X4,X1)
& in(X4,X0) ) )
& ( in(X4,X1)
| ~ in(X4,X0)
| in(X4,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ( ~ in(X3,X1)
& in(X3,X0) ) )
& ( ~ in(X3,X2)
| in(X3,X1)
| ~ in(X3,X0) ) )
| X2 = set_difference(X0,X1) ) ),
inference(rectify,[],[f179]) ).
fof(f181,plain,
! [X0,X1,X2] :
( ( set_difference(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| ( ~ in(X4,X1)
& in(X4,X0) ) )
& ( in(X4,X1)
| ~ in(X4,X0)
| in(X4,X2) ) ) )
& ( ( ( in(sK9(X0,X1,X2),X2)
| ( ~ in(sK9(X0,X1,X2),X1)
& in(sK9(X0,X1,X2),X0) ) )
& ( ~ in(sK9(X0,X1,X2),X2)
| in(sK9(X0,X1,X2),X1)
| ~ in(sK9(X0,X1,X2),X0) ) )
| X2 = set_difference(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(X3,sK9(X0,X1,X2))],[f180]) ).
fof(f182,plain,
! [X0,X1] :
( ( union(X0) != X1
| ! [X2] :
( ( ~ in(X2,X1)
| ? [X3] :
( in(X3,X0)
& in(X2,X3) ) )
& ( ! [X3] :
( ~ in(X3,X0)
| ~ in(X2,X3) )
| in(X2,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| ? [X3] :
( in(X3,X0)
& in(X2,X3) ) )
& ( ~ in(X2,X1)
| ! [X3] :
( ~ in(X3,X0)
| ~ in(X2,X3) ) ) )
| X1 = union(X0) ) ),
inference(nnf_transformation,[],[f15]) ).
fof(f183,plain,
! [X0,X1] :
( ( union(X0) != X1
| ! [X5] :
( ( ~ in(X5,X1)
| ? [X7] :
( in(X7,X0)
& in(X5,X7) ) )
& ( ! [X6] :
( ~ in(X6,X0)
| ~ in(X5,X6) )
| in(X5,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| ? [X4] :
( in(X4,X0)
& in(X2,X4) ) )
& ( ~ in(X2,X1)
| ! [X3] :
( ~ in(X3,X0)
| ~ in(X2,X3) ) ) )
| X1 = union(X0) ) ),
inference(rectify,[],[f182]) ).
fof(f184,plain,
! [X0,X1] :
( ( union(X0) != X1
| ! [X5] :
( ( ~ in(X5,X1)
| ( in(sK12(X0,X5),X0)
& in(X5,sK12(X0,X5)) ) )
& ( ! [X6] :
( ~ in(X6,X0)
| ~ in(X5,X6) )
| in(X5,X1) ) ) )
& ( ( ( in(sK10(X0,X1),X1)
| ( in(sK11(X0,X1),X0)
& in(sK10(X0,X1),sK11(X0,X1)) ) )
& ( ~ in(sK10(X0,X1),X1)
| ! [X3] :
( ~ in(X3,X0)
| ~ in(sK10(X0,X1),X3) ) ) )
| X1 = union(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11,sK12]),skolemize(X2,sK10(X0,X1)),skolemize(X4,sK11(X0,X1)),skolemize(X7,sK12(X0,X5))],[f183]) ).
fof(f185,plain,
! [X0,X1,X2] :
( ( cartesian_product2(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| ? [X4,X5] :
( X3 = ordered_pair(X4,X5)
& in(X5,X1)
& in(X4,X0) ) )
& ( ! [X4,X5] :
( ordered_pair(X4,X5) != X3
| ~ in(X5,X1)
| ~ in(X4,X0) )
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ? [X4,X5] :
( X3 = ordered_pair(X4,X5)
& in(X5,X1)
& in(X4,X0) ) )
& ( ~ in(X3,X2)
| ! [X4,X5] :
( ordered_pair(X4,X5) != X3
| ~ in(X5,X1)
| ~ in(X4,X0) ) ) )
| X2 = cartesian_product2(X0,X1) ) ),
inference(nnf_transformation,[],[f12]) ).
fof(f186,plain,
! [X0,X1,X2] :
( ( cartesian_product2(X0,X1) != X2
| ! [X8] :
( ( ~ in(X8,X2)
| ? [X11,X12] :
( ordered_pair(X11,X12) = X8
& in(X12,X1)
& in(X11,X0) ) )
& ( ! [X9,X10] :
( ordered_pair(X9,X10) != X8
| ~ in(X10,X1)
| ~ in(X9,X0) )
| in(X8,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ? [X6,X7] :
( ordered_pair(X6,X7) = X3
& in(X7,X1)
& in(X6,X0) ) )
& ( ~ in(X3,X2)
| ! [X4,X5] :
( ordered_pair(X4,X5) != X3
| ~ in(X5,X1)
| ~ in(X4,X0) ) ) )
| X2 = cartesian_product2(X0,X1) ) ),
inference(rectify,[],[f185]) ).
fof(f187,plain,
! [X0,X1,X2] :
( ( cartesian_product2(X0,X1) != X2
| ! [X8] :
( ( ~ in(X8,X2)
| ( ordered_pair(sK16(X0,X1,X8),sK17(X0,X1,X8)) = X8
& in(sK17(X0,X1,X8),X1)
& in(sK16(X0,X1,X8),X0) ) )
& ( ! [X9,X10] :
( ordered_pair(X9,X10) != X8
| ~ in(X10,X1)
| ~ in(X9,X0) )
| in(X8,X2) ) ) )
& ( ( ( in(sK13(X0,X1,X2),X2)
| ( sK13(X0,X1,X2) = ordered_pair(sK14(X0,X1,X2),sK15(X0,X1,X2))
& in(sK15(X0,X1,X2),X1)
& in(sK14(X0,X1,X2),X0) ) )
& ( ~ in(sK13(X0,X1,X2),X2)
| ! [X4,X5] :
( ordered_pair(X4,X5) != sK13(X0,X1,X2)
| ~ in(X5,X1)
| ~ in(X4,X0) ) ) )
| X2 = cartesian_product2(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13,sK14,sK15,sK16,sK17]),skolemize(X3,sK13(X0,X1,X2)),skolemize(X6,sK14(X0,X1,X2)),skolemize(X7,sK15(X0,X1,X2)),skolemize(X11,sK16(X0,X1,X8)),skolemize(X12,sK17(X0,X1,X8))],[f186]) ).
fof(f188,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| X3 = X1
| X3 = X0 )
& ( ( X1 != X3
& X0 != X3 )
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| X3 = X1
| X3 = X0 )
& ( ~ in(X3,X2)
| ( X1 != X3
& X0 != X3 ) ) )
| X2 = unordered_pair(X0,X1) ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f189,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| X3 = X1
| X3 = X0 )
& ( ( X1 != X3
& X0 != X3 )
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| X3 = X1
| X3 = X0 )
& ( ~ in(X3,X2)
| ( X1 != X3
& X0 != X3 ) ) )
| X2 = unordered_pair(X0,X1) ) ),
inference(flattening,[],[f188]) ).
fof(f190,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| X1 = X4
| X0 = X4 )
& ( ( X1 != X4
& X0 != X4 )
| in(X4,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| X3 = X1
| X3 = X0 )
& ( ~ in(X3,X2)
| ( X1 != X3
& X0 != X3 ) ) )
| X2 = unordered_pair(X0,X1) ) ),
inference(rectify,[],[f189]) ).
fof(f191,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| X1 = X4
| X0 = X4 )
& ( ( X1 != X4
& X0 != X4 )
| in(X4,X2) ) ) )
& ( ( ( in(sK18(X0,X1,X2),X2)
| sK18(X0,X1,X2) = X1
| sK18(X0,X1,X2) = X0 )
& ( ~ in(sK18(X0,X1,X2),X2)
| ( sK18(X0,X1,X2) != X1
& sK18(X0,X1,X2) != X0 ) ) )
| X2 = unordered_pair(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(X3,sK18(X0,X1,X2))],[f190]) ).
fof(f192,plain,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| ( in(X3,X1)
& in(X3,X0) ) )
& ( ~ in(X3,X1)
| ~ in(X3,X0)
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ( in(X3,X1)
& in(X3,X0) ) )
& ( ~ in(X3,X2)
| ~ in(X3,X1)
| ~ in(X3,X0) ) )
| X2 = set_intersection2(X0,X1) ) ),
inference(nnf_transformation,[],[f14]) ).
fof(f193,plain,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| ( in(X3,X1)
& in(X3,X0) ) )
& ( ~ in(X3,X1)
| ~ in(X3,X0)
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ( in(X3,X1)
& in(X3,X0) ) )
& ( ~ in(X3,X2)
| ~ in(X3,X1)
| ~ in(X3,X0) ) )
| X2 = set_intersection2(X0,X1) ) ),
inference(flattening,[],[f192]) ).
fof(f194,plain,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| ( in(X4,X1)
& in(X4,X0) ) )
& ( ~ in(X4,X1)
| ~ in(X4,X0)
| in(X4,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ( in(X3,X1)
& in(X3,X0) ) )
& ( ~ in(X3,X2)
| ~ in(X3,X1)
| ~ in(X3,X0) ) )
| X2 = set_intersection2(X0,X1) ) ),
inference(rectify,[],[f193]) ).
fof(f195,plain,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| ( in(X4,X1)
& in(X4,X0) ) )
& ( ~ in(X4,X1)
| ~ in(X4,X0)
| in(X4,X2) ) ) )
& ( ( ( in(sK19(X0,X1,X2),X2)
| ( in(sK19(X0,X1,X2),X1)
& in(sK19(X0,X1,X2),X0) ) )
& ( ~ in(sK19(X0,X1,X2),X2)
| ~ in(sK19(X0,X1,X2),X1)
| ~ in(sK19(X0,X1,X2),X0) ) )
| X2 = set_intersection2(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(X3,sK19(X0,X1,X2))],[f194]) ).
fof(f196,plain,
! [X0,X1] :
( ( powerset(X0) != X1
| ! [X2] :
( ( ~ in(X2,X1)
| subset(X2,X0) )
& ( ~ subset(X2,X0)
| in(X2,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| subset(X2,X0) )
& ( ~ in(X2,X1)
| ~ subset(X2,X0) ) )
| X1 = powerset(X0) ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f197,plain,
! [X0,X1] :
( ( powerset(X0) != X1
| ! [X3] :
( ( ~ in(X3,X1)
| subset(X3,X0) )
& ( ~ subset(X3,X0)
| in(X3,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| subset(X2,X0) )
& ( ~ in(X2,X1)
| ~ subset(X2,X0) ) )
| X1 = powerset(X0) ) ),
inference(rectify,[],[f196]) ).
fof(f198,plain,
! [X0,X1] :
( ( powerset(X0) != X1
| ! [X3] :
( ( ~ in(X3,X1)
| subset(X3,X0) )
& ( ~ subset(X3,X0)
| in(X3,X1) ) ) )
& ( ( ( in(sK20(X0,X1),X1)
| subset(sK20(X0,X1),X0) )
& ( ~ in(sK20(X0,X1),X1)
| ~ subset(sK20(X0,X1),X0) ) )
| X1 = powerset(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(X2,sK20(X0,X1))],[f197]) ).
fof(f199,plain,
~ empty(sK21),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21]),skolemize(X0,sK21)],[f48]) ).
fof(f200,plain,
empty(sK22),
inference(skolemize,[status(esa),new_symbols(skolem,[sK22]),skolemize(X0,sK22)],[f47]) ).
fof(f201,plain,
! [X0] : singleton(X0) != empty_set,
inference(cnf_transformation,[],[f37]) ).
fof(f203,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ disjoint(singleton(X0),X1) ),
inference(cnf_transformation,[],[f102]) ).
fof(f204,plain,
! [X0,X1] :
( in(X0,X1)
| disjoint(singleton(X0),X1) ),
inference(cnf_transformation,[],[f103]) ).
fof(f209,plain,
! [X2,X0,X1] :
( ~ subset(X0,X1)
| subset(X0,set_difference(X1,singleton(X2)))
| in(X2,X0) ),
inference(cnf_transformation,[],[f105]) ).
fof(f213,plain,
! [X0,X1] :
( ~ in(X0,X1)
| subset(X0,union(X1)) ),
inference(cnf_transformation,[],[f106]) ).
fof(f214,plain,
! [X2,X3,X0,X1] :
( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| in(X1,X3) ),
inference(cnf_transformation,[],[f148]) ).
fof(f215,plain,
! [X2,X3,X0,X1] :
( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| in(X0,X2) ),
inference(cnf_transformation,[],[f148]) ).
fof(f217,plain,
! [X2,X3,X0,X1] :
( X0 = X3
| X0 = X2
| unordered_pair(X0,X1) != unordered_pair(X2,X3) ),
inference(cnf_transformation,[],[f107]) ).
fof(f218,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| set_union2(X0,X1) = X1 ),
inference(cnf_transformation,[],[f108]) ).
fof(f220,plain,
! [X2,X0,X1] :
( ~ subset(X0,X2)
| ~ subset(X0,X1)
| subset(X0,set_intersection2(X1,X2)) ),
inference(cnf_transformation,[],[f110]) ).
fof(f221,plain,
! [X2,X0,X1] :
( ~ subset(X1,X2)
| ~ subset(X0,X1)
| subset(X0,X2) ),
inference(cnf_transformation,[],[f112]) ).
fof(f222,plain,
powerset(empty_set) = singleton(empty_set),
inference(cnf_transformation,[],[f57]) ).
fof(f223,plain,
! [X2,X0,X1] :
( ~ subset(X0,X1)
| subset(set_intersection2(X0,X2),set_intersection2(X1,X2)) ),
inference(cnf_transformation,[],[f113]) ).
fof(f224,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| set_intersection2(X0,X1) = X0 ),
inference(cnf_transformation,[],[f114]) ).
fof(f225,plain,
! [X0] : subset(empty_set,X0),
inference(cnf_transformation,[],[f62]) ).
fof(f226,plain,
! [X2,X0,X1] :
( ~ subset(X0,X1)
| subset(set_difference(X0,X2),set_difference(X1,X2)) ),
inference(cnf_transformation,[],[f115]) ).
fof(f227,plain,
! [X2,X3,X0,X1] :
( ordered_pair(X0,X1) != ordered_pair(X2,X3)
| X1 = X3 ),
inference(cnf_transformation,[],[f116]) ).
fof(f228,plain,
! [X2,X3,X0,X1] :
( ordered_pair(X0,X1) != ordered_pair(X2,X3)
| X0 = X2 ),
inference(cnf_transformation,[],[f116]) ).
fof(f229,plain,
! [X0,X1] : subset(set_difference(X0,X1),X0),
inference(cnf_transformation,[],[f65]) ).
fof(f230,plain,
! [X0,X1] :
( empty_set != set_difference(X0,X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f149]) ).
fof(f231,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| empty_set = set_difference(X0,X1) ),
inference(cnf_transformation,[],[f149]) ).
fof(f233,plain,
! [X0,X1] :
( ~ in(X0,X1)
| subset(singleton(X0),X1) ),
inference(cnf_transformation,[],[f150]) ).
fof(f234,plain,
! [X2,X0,X1] :
( ~ subset(unordered_pair(X0,X1),X2)
| in(X1,X2) ),
inference(cnf_transformation,[],[f152]) ).
fof(f235,plain,
! [X2,X0,X1] :
( ~ subset(unordered_pair(X0,X1),X2)
| in(X0,X2) ),
inference(cnf_transformation,[],[f152]) ).
fof(f236,plain,
! [X2,X0,X1] :
( ~ in(X1,X2)
| ~ in(X0,X2)
| subset(unordered_pair(X0,X1),X2) ),
inference(cnf_transformation,[],[f152]) ).
fof(f237,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X0,set_difference(X1,X0)),
inference(cnf_transformation,[],[f69]) ).
fof(f238,plain,
! [X0,X1] :
( ~ subset(X0,singleton(X1))
| singleton(X1) = X0
| empty_set = X0 ),
inference(cnf_transformation,[],[f154]) ).
fof(f241,plain,
! [X3,X0,X1] :
( ~ disjoint(X0,X1)
| ~ in(X3,X1)
| ~ in(X3,X0) ),
inference(cnf_transformation,[],[f155]) ).
fof(f242,plain,
! [X0,X1] :
( in(sK0(X0,X1),X1)
| disjoint(X0,X1) ),
inference(cnf_transformation,[],[f155]) ).
fof(f243,plain,
! [X0,X1] :
( in(sK0(X0,X1),X0)
| disjoint(X0,X1) ),
inference(cnf_transformation,[],[f155]) ).
fof(f244,plain,
! [X0] :
( ~ subset(X0,empty_set)
| empty_set = X0 ),
inference(cnf_transformation,[],[f118]) ).
fof(f245,plain,
! [X0,X1] : set_difference(X0,X1) = set_difference(set_union2(X0,X1),X1),
inference(cnf_transformation,[],[f74]) ).
fof(f247,plain,
! [X0,X1] :
( ~ in(X0,X1)
| set_union2(singleton(X0),X1) = X1 ),
inference(cnf_transformation,[],[f120]) ).
fof(f248,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_difference(X0,set_difference(X0,X1)),
inference(cnf_transformation,[],[f77]) ).
fof(f249,plain,
! [X3,X0,X1] :
( ~ disjoint(X0,X1)
| ~ in(X3,set_intersection2(X0,X1)) ),
inference(cnf_transformation,[],[f156]) ).
fof(f250,plain,
! [X0,X1] :
( in(sK1(X0,X1),set_intersection2(X0,X1))
| disjoint(X0,X1) ),
inference(cnf_transformation,[],[f156]) ).
fof(f251,plain,
! [X0,X1] :
( ~ proper_subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f122]) ).
fof(f252,plain,
! [X2,X0,X1] :
( ~ disjoint(X1,X2)
| ~ subset(X0,X1)
| disjoint(X0,X2) ),
inference(cnf_transformation,[],[f124]) ).
fof(f253,plain,
( sK2 = set_difference(sK2,singleton(sK3))
| ~ in(sK3,sK2) ),
inference(cnf_transformation,[],[f158]) ).
fof(f254,plain,
( sK2 != set_difference(sK2,singleton(sK3))
| in(sK3,sK2) ),
inference(cnf_transformation,[],[f158]) ).
fof(f255,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f84]) ).
fof(f256,plain,
! [X0,X1] :
( ~ subset(singleton(X0),singleton(X1))
| X0 = X1 ),
inference(cnf_transformation,[],[f126]) ).
fof(f257,plain,
! [X0,X1] : subset(X0,set_union2(X0,X1)),
inference(cnf_transformation,[],[f88]) ).
fof(f258,plain,
! [X0,X1] :
( ~ disjoint(X0,X1)
| set_difference(X0,X1) = X0 ),
inference(cnf_transformation,[],[f159]) ).
fof(f259,plain,
! [X0,X1] :
( set_difference(X0,X1) != X0
| disjoint(X0,X1) ),
inference(cnf_transformation,[],[f159]) ).
fof(f260,plain,
! [X2,X0,X1] :
( ~ subset(X2,X1)
| ~ subset(X0,X1)
| subset(set_union2(X0,X2),X1) ),
inference(cnf_transformation,[],[f128]) ).
fof(f261,plain,
! [X2,X0,X1] :
( singleton(X0) != unordered_pair(X1,X2)
| X0 = X1 ),
inference(cnf_transformation,[],[f129]) ).
fof(f262,plain,
! [X2,X0,X1] :
( singleton(X0) != unordered_pair(X1,X2)
| X1 = X2 ),
inference(cnf_transformation,[],[f130]) ).
fof(f263,plain,
! [X3,X0,X1] :
( singleton(X0) != X1
| ~ in(X3,X1)
| X0 = X3 ),
inference(cnf_transformation,[],[f162]) ).
fof(f265,plain,
! [X0,X1] :
( in(sK4(X0,X1),X1)
| sK4(X0,X1) = X0
| singleton(X0) = X1 ),
inference(cnf_transformation,[],[f162]) ).
fof(f266,plain,
! [X0,X1] :
( ~ in(sK4(X0,X1),X1)
| sK4(X0,X1) != X0
| singleton(X0) = X1 ),
inference(cnf_transformation,[],[f162]) ).
fof(f267,plain,
! [X0] : empty_set = set_difference(empty_set,X0),
inference(cnf_transformation,[],[f78]) ).
fof(f268,plain,
! [X0] : set_difference(X0,empty_set) = X0,
inference(cnf_transformation,[],[f71]) ).
fof(f269,plain,
! [X0] : empty_set = set_intersection2(X0,empty_set),
inference(cnf_transformation,[],[f60]) ).
fof(f270,plain,
! [X0] : set_union2(X0,empty_set) = X0,
inference(cnf_transformation,[],[f55]) ).
fof(f271,plain,
! [X2,X0] :
( empty_set != X0
| ~ in(X2,X0) ),
inference(cnf_transformation,[],[f165]) ).
fof(f272,plain,
! [X0] :
( in(sK5(X0),X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f165]) ).
fof(f273,plain,
! [X0,X1] :
( in(sK6(X0,X1),X0)
| in(sK6(X0,X1),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f167]) ).
fof(f274,plain,
! [X0,X1] :
( ~ in(sK6(X0,X1),X0)
| ~ in(sK6(X0,X1),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f167]) ).
fof(f275,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f170]) ).
fof(f276,plain,
! [X0,X1] :
( in(sK7(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f170]) ).
fof(f277,plain,
! [X0,X1] :
( ~ in(sK7(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f170]) ).
fof(f278,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ in(X1,X0) ),
inference(cnf_transformation,[],[f133]) ).
fof(f279,plain,
! [X0] : set_union2(X0,X0) = X0,
inference(cnf_transformation,[],[f96]) ).
fof(f280,plain,
! [X2,X0,X1,X4] :
( set_union2(X0,X1) != X2
| ~ in(X4,X2)
| in(X4,X1)
| in(X4,X0) ),
inference(cnf_transformation,[],[f174]) ).
fof(f281,plain,
! [X2,X0,X1,X4] :
( set_union2(X0,X1) != X2
| ~ in(X4,X1)
| in(X4,X2) ),
inference(cnf_transformation,[],[f174]) ).
fof(f282,plain,
! [X2,X0,X1,X4] :
( set_union2(X0,X1) != X2
| ~ in(X4,X0)
| in(X4,X2) ),
inference(cnf_transformation,[],[f174]) ).
fof(f283,plain,
! [X2,X0,X1] :
( in(sK8(X0,X1,X2),X2)
| in(sK8(X0,X1,X2),X1)
| in(sK8(X0,X1,X2),X0)
| set_union2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f174]) ).
fof(f284,plain,
! [X2,X0,X1] :
( ~ in(sK8(X0,X1,X2),X2)
| ~ in(sK8(X0,X1,X2),X1)
| set_union2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f174]) ).
fof(f285,plain,
! [X2,X0,X1] :
( ~ in(sK8(X0,X1,X2),X2)
| ~ in(sK8(X0,X1,X2),X0)
| set_union2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f174]) ).
fof(f286,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f4]) ).
fof(f287,plain,
! [X0,X1] :
( ~ disjoint(X0,X1)
| disjoint(X1,X0) ),
inference(cnf_transformation,[],[f134]) ).
fof(f288,plain,
! [X0,X1] :
( ~ disjoint(X0,X1)
| set_intersection2(X0,X1) = empty_set ),
inference(cnf_transformation,[],[f175]) ).
fof(f289,plain,
! [X0,X1] :
( set_intersection2(X0,X1) != empty_set
| disjoint(X0,X1) ),
inference(cnf_transformation,[],[f175]) ).
fof(f291,plain,
! [X0,X1] :
( X0 != X1
| subset(X1,X0) ),
inference(cnf_transformation,[],[f177]) ).
fof(f293,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f177]) ).
fof(f294,plain,
! [X2,X0,X1,X4] :
( set_difference(X0,X1) != X2
| ~ in(X4,X2)
| ~ in(X4,X1) ),
inference(cnf_transformation,[],[f181]) ).
fof(f295,plain,
! [X2,X0,X1,X4] :
( set_difference(X0,X1) != X2
| ~ in(X4,X2)
| in(X4,X0) ),
inference(cnf_transformation,[],[f181]) ).
fof(f296,plain,
! [X2,X0,X1,X4] :
( set_difference(X0,X1) != X2
| in(X4,X1)
| ~ in(X4,X0)
| in(X4,X2) ),
inference(cnf_transformation,[],[f181]) ).
fof(f297,plain,
! [X2,X0,X1] :
( in(sK9(X0,X1,X2),X2)
| ~ in(sK9(X0,X1,X2),X1)
| set_difference(X0,X1) = X2 ),
inference(cnf_transformation,[],[f181]) ).
fof(f298,plain,
! [X2,X0,X1] :
( in(sK9(X0,X1,X2),X2)
| in(sK9(X0,X1,X2),X0)
| set_difference(X0,X1) = X2 ),
inference(cnf_transformation,[],[f181]) ).
fof(f299,plain,
! [X2,X0,X1] :
( ~ in(sK9(X0,X1,X2),X2)
| in(sK9(X0,X1,X2),X1)
| ~ in(sK9(X0,X1,X2),X0)
| set_difference(X0,X1) = X2 ),
inference(cnf_transformation,[],[f181]) ).
fof(f300,plain,
! [X0,X1,X5] :
( union(X0) != X1
| ~ in(X5,X1)
| in(sK12(X0,X5),X0) ),
inference(cnf_transformation,[],[f184]) ).
fof(f301,plain,
! [X0,X1,X5] :
( union(X0) != X1
| ~ in(X5,X1)
| in(X5,sK12(X0,X5)) ),
inference(cnf_transformation,[],[f184]) ).
fof(f302,plain,
! [X0,X1,X6,X5] :
( union(X0) != X1
| ~ in(X6,X0)
| ~ in(X5,X6)
| in(X5,X1) ),
inference(cnf_transformation,[],[f184]) ).
fof(f303,plain,
! [X0,X1] :
( in(sK10(X0,X1),X1)
| in(sK11(X0,X1),X0)
| union(X0) = X1 ),
inference(cnf_transformation,[],[f184]) ).
fof(f304,plain,
! [X0,X1] :
( in(sK10(X0,X1),X1)
| in(sK10(X0,X1),sK11(X0,X1))
| union(X0) = X1 ),
inference(cnf_transformation,[],[f184]) ).
fof(f305,plain,
! [X3,X0,X1] :
( ~ in(sK10(X0,X1),X1)
| ~ in(X3,X0)
| ~ in(sK10(X0,X1),X3)
| union(X0) = X1 ),
inference(cnf_transformation,[],[f184]) ).
fof(f306,plain,
! [X2,X0,X1,X8] :
( cartesian_product2(X0,X1) != X2
| ~ in(X8,X2)
| ordered_pair(sK16(X0,X1,X8),sK17(X0,X1,X8)) = X8 ),
inference(cnf_transformation,[],[f187]) ).
fof(f307,plain,
! [X2,X0,X1,X8] :
( cartesian_product2(X0,X1) != X2
| ~ in(X8,X2)
| in(sK17(X0,X1,X8),X1) ),
inference(cnf_transformation,[],[f187]) ).
fof(f308,plain,
! [X2,X0,X1,X8] :
( cartesian_product2(X0,X1) != X2
| ~ in(X8,X2)
| in(sK16(X0,X1,X8),X0) ),
inference(cnf_transformation,[],[f187]) ).
fof(f309,plain,
! [X2,X10,X0,X1,X8,X9] :
( cartesian_product2(X0,X1) != X2
| ordered_pair(X9,X10) != X8
| ~ in(X10,X1)
| ~ in(X9,X0)
| in(X8,X2) ),
inference(cnf_transformation,[],[f187]) ).
fof(f310,plain,
! [X2,X0,X1] :
( in(sK13(X0,X1,X2),X2)
| sK13(X0,X1,X2) = ordered_pair(sK14(X0,X1,X2),sK15(X0,X1,X2))
| cartesian_product2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f187]) ).
fof(f311,plain,
! [X2,X0,X1] :
( in(sK13(X0,X1,X2),X2)
| in(sK15(X0,X1,X2),X1)
| cartesian_product2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f187]) ).
fof(f312,plain,
! [X2,X0,X1] :
( in(sK13(X0,X1,X2),X2)
| in(sK14(X0,X1,X2),X0)
| cartesian_product2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f187]) ).
fof(f313,plain,
! [X2,X0,X1,X4,X5] :
( ~ in(sK13(X0,X1,X2),X2)
| ordered_pair(X4,X5) != sK13(X0,X1,X2)
| ~ in(X5,X1)
| ~ in(X4,X0)
| cartesian_product2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f187]) ).
fof(f314,plain,
! [X0,X1] : ~ empty(ordered_pair(X0,X1)),
inference(cnf_transformation,[],[f31]) ).
fof(f315,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f17]) ).
fof(f316,plain,
! [X2,X0,X1,X4] :
( unordered_pair(X0,X1) != X2
| ~ in(X4,X2)
| X1 = X4
| X0 = X4 ),
inference(cnf_transformation,[],[f191]) ).
fof(f317,plain,
! [X2,X0,X1,X4] :
( unordered_pair(X0,X1) != X2
| X1 != X4
| in(X4,X2) ),
inference(cnf_transformation,[],[f191]) ).
fof(f318,plain,
! [X2,X0,X1,X4] :
( unordered_pair(X0,X1) != X2
| X0 != X4
| in(X4,X2) ),
inference(cnf_transformation,[],[f191]) ).
fof(f319,plain,
! [X2,X0,X1] :
( in(sK18(X0,X1,X2),X2)
| sK18(X0,X1,X2) = X1
| sK18(X0,X1,X2) = X0
| unordered_pair(X0,X1) = X2 ),
inference(cnf_transformation,[],[f191]) ).
fof(f320,plain,
! [X2,X0,X1] :
( ~ in(sK18(X0,X1,X2),X2)
| sK18(X0,X1,X2) != X1
| unordered_pair(X0,X1) = X2 ),
inference(cnf_transformation,[],[f191]) ).
fof(f321,plain,
! [X2,X0,X1] :
( ~ in(sK18(X0,X1,X2),X2)
| sK18(X0,X1,X2) != X0
| unordered_pair(X0,X1) = X2 ),
inference(cnf_transformation,[],[f191]) ).
fof(f322,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f324,plain,
! [X2,X0,X1,X4] :
( set_intersection2(X0,X1) != X2
| ~ in(X4,X2)
| in(X4,X1) ),
inference(cnf_transformation,[],[f195]) ).
fof(f326,plain,
! [X2,X0,X1,X4] :
( set_intersection2(X0,X1) != X2
| ~ in(X4,X1)
| ~ in(X4,X0)
| in(X4,X2) ),
inference(cnf_transformation,[],[f195]) ).
fof(f327,plain,
! [X2,X0,X1] :
( in(sK19(X0,X1,X2),X2)
| in(sK19(X0,X1,X2),X1)
| set_intersection2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f195]) ).
fof(f328,plain,
! [X2,X0,X1] :
( in(sK19(X0,X1,X2),X2)
| in(sK19(X0,X1,X2),X0)
| set_intersection2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f195]) ).
fof(f329,plain,
! [X2,X0,X1] :
( ~ in(sK19(X0,X1,X2),X2)
| ~ in(sK19(X0,X1,X2),X1)
| ~ in(sK19(X0,X1,X2),X0)
| set_intersection2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f195]) ).
fof(f330,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f5]) ).
fof(f331,plain,
! [X3,X0,X1] :
( powerset(X0) != X1
| ~ in(X3,X1)
| subset(X3,X0) ),
inference(cnf_transformation,[],[f198]) ).
fof(f332,plain,
! [X3,X0,X1] :
( powerset(X0) != X1
| ~ subset(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f198]) ).
fof(f333,plain,
! [X0,X1] :
( in(sK20(X0,X1),X1)
| subset(sK20(X0,X1),X0)
| powerset(X0) = X1 ),
inference(cnf_transformation,[],[f198]) ).
fof(f334,plain,
! [X0,X1] :
( ~ in(sK20(X0,X1),X1)
| ~ subset(sK20(X0,X1),X0)
| powerset(X0) = X1 ),
inference(cnf_transformation,[],[f198]) ).
fof(f335,plain,
! [X0] : ~ proper_subset(X0,X0),
inference(cnf_transformation,[],[f99]) ).
fof(f336,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(X0,X1)
| proper_subset(X0,X1) ),
inference(cnf_transformation,[],[f136]) ).
fof(f337,plain,
! [X0,X1] :
( ~ proper_subset(X0,X1)
| ~ proper_subset(X1,X0) ),
inference(cnf_transformation,[],[f137]) ).
fof(f338,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(cnf_transformation,[],[f138]) ).
fof(f339,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f139]) ).
fof(f340,plain,
! [X0] :
( ~ empty(X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f140]) ).
fof(f341,plain,
~ empty(sK21),
inference(cnf_transformation,[],[f199]) ).
fof(f342,plain,
empty(sK22),
inference(cnf_transformation,[],[f200]) ).
fof(f343,plain,
! [X0,X1] :
( empty(X0)
| ~ empty(set_union2(X1,X0)) ),
inference(cnf_transformation,[],[f141]) ).
fof(f344,plain,
! [X0,X1] :
( empty(X0)
| ~ empty(set_union2(X0,X1)) ),
inference(cnf_transformation,[],[f142]) ).
fof(f345,plain,
empty(empty_set),
inference(cnf_transformation,[],[f30]) ).
fof(f346,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),
inference(definition_unfolding,[],[f315,f255]) ).
fof(f347,plain,
! [X0] : empty_set != unordered_pair(X0,X0),
inference(definition_unfolding,[],[f201,f255]) ).
fof(f349,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ disjoint(unordered_pair(X0,X0),X1) ),
inference(definition_unfolding,[],[f203,f255]) ).
fof(f350,plain,
! [X0,X1] :
( in(X0,X1)
| disjoint(unordered_pair(X0,X0),X1) ),
inference(definition_unfolding,[],[f204,f255]) ).
fof(f353,plain,
! [X2,X0,X1] :
( ~ subset(X0,X1)
| subset(X0,set_difference(X1,unordered_pair(X2,X2)))
| in(X2,X0) ),
inference(definition_unfolding,[],[f209,f255]) ).
fof(f358,plain,
! [X2,X3,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),cartesian_product2(X2,X3))
| in(X0,X2) ),
inference(definition_unfolding,[],[f215,f346]) ).
fof(f359,plain,
! [X2,X3,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),cartesian_product2(X2,X3))
| in(X1,X3) ),
inference(definition_unfolding,[],[f214,f346]) ).
fof(f361,plain,
! [X2,X0,X1] :
( ~ subset(X0,X2)
| ~ subset(X0,X1)
| subset(X0,set_difference(X1,set_difference(X1,X2))) ),
inference(definition_unfolding,[],[f220,f248]) ).
fof(f362,plain,
powerset(empty_set) = unordered_pair(empty_set,empty_set),
inference(definition_unfolding,[],[f222,f255]) ).
fof(f363,plain,
! [X2,X0,X1] :
( ~ subset(X0,X1)
| subset(set_difference(X0,set_difference(X0,X2)),set_difference(X1,set_difference(X1,X2))) ),
inference(definition_unfolding,[],[f223,f248,f248]) ).
fof(f364,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| set_difference(X0,set_difference(X0,X1)) = X0 ),
inference(definition_unfolding,[],[f224,f248]) ).
fof(f365,plain,
! [X2,X3,X0,X1] :
( unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)) != unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2))
| X0 = X2 ),
inference(definition_unfolding,[],[f228,f346,f346]) ).
fof(f366,plain,
! [X2,X3,X0,X1] :
( unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)) != unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2))
| X1 = X3 ),
inference(definition_unfolding,[],[f227,f346,f346]) ).
fof(f367,plain,
! [X0,X1] :
( ~ in(X0,X1)
| subset(unordered_pair(X0,X0),X1) ),
inference(definition_unfolding,[],[f233,f255]) ).
fof(f371,plain,
! [X0,X1] :
( ~ subset(X0,unordered_pair(X1,X1))
| unordered_pair(X1,X1) = X0
| empty_set = X0 ),
inference(definition_unfolding,[],[f238,f255,f255]) ).
fof(f372,plain,
! [X0,X1] :
( ~ in(X0,X1)
| set_union2(unordered_pair(X0,X0),X1) = X1 ),
inference(definition_unfolding,[],[f247,f255]) ).
fof(f373,plain,
! [X0,X1] :
( in(sK1(X0,X1),set_difference(X0,set_difference(X0,X1)))
| disjoint(X0,X1) ),
inference(definition_unfolding,[],[f250,f248]) ).
fof(f374,plain,
! [X3,X0,X1] :
( ~ disjoint(X0,X1)
| ~ in(X3,set_difference(X0,set_difference(X0,X1))) ),
inference(definition_unfolding,[],[f249,f248]) ).
fof(f375,plain,
( sK2 != set_difference(sK2,unordered_pair(sK3,sK3))
| in(sK3,sK2) ),
inference(definition_unfolding,[],[f254,f255]) ).
fof(f376,plain,
( sK2 = set_difference(sK2,unordered_pair(sK3,sK3))
| ~ in(sK3,sK2) ),
inference(definition_unfolding,[],[f253,f255]) ).
fof(f377,plain,
! [X0,X1] :
( ~ subset(unordered_pair(X0,X0),unordered_pair(X1,X1))
| X0 = X1 ),
inference(definition_unfolding,[],[f256,f255,f255]) ).
fof(f378,plain,
! [X2,X0,X1] :
( unordered_pair(X0,X0) != unordered_pair(X1,X2)
| X0 = X1 ),
inference(definition_unfolding,[],[f261,f255]) ).
fof(f379,plain,
! [X2,X0,X1] :
( unordered_pair(X0,X0) != unordered_pair(X1,X2)
| X1 = X2 ),
inference(definition_unfolding,[],[f262,f255]) ).
fof(f380,plain,
! [X0,X1] :
( ~ in(sK4(X0,X1),X1)
| sK4(X0,X1) != X0
| unordered_pair(X0,X0) = X1 ),
inference(definition_unfolding,[],[f266,f255]) ).
fof(f381,plain,
! [X0,X1] :
( in(sK4(X0,X1),X1)
| sK4(X0,X1) = X0
| unordered_pair(X0,X0) = X1 ),
inference(definition_unfolding,[],[f265,f255]) ).
fof(f383,plain,
! [X3,X0,X1] :
( unordered_pair(X0,X0) != X1
| ~ in(X3,X1)
| X0 = X3 ),
inference(definition_unfolding,[],[f263,f255]) ).
fof(f384,plain,
! [X0] : empty_set = set_difference(X0,set_difference(X0,empty_set)),
inference(definition_unfolding,[],[f269,f248]) ).
fof(f385,plain,
! [X0,X1] :
( empty_set != set_difference(X0,set_difference(X0,X1))
| disjoint(X0,X1) ),
inference(definition_unfolding,[],[f289,f248]) ).
fof(f386,plain,
! [X0,X1] :
( ~ disjoint(X0,X1)
| empty_set = set_difference(X0,set_difference(X0,X1)) ),
inference(definition_unfolding,[],[f288,f248]) ).
fof(f387,plain,
! [X2,X0,X1,X4,X5] :
( ~ in(sK13(X0,X1,X2),X2)
| sK13(X0,X1,X2) != unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4))
| ~ in(X5,X1)
| ~ in(X4,X0)
| cartesian_product2(X0,X1) = X2 ),
inference(definition_unfolding,[],[f313,f346]) ).
fof(f388,plain,
! [X2,X0,X1] :
( in(sK13(X0,X1,X2),X2)
| sK13(X0,X1,X2) = unordered_pair(unordered_pair(sK14(X0,X1,X2),sK15(X0,X1,X2)),unordered_pair(sK14(X0,X1,X2),sK14(X0,X1,X2)))
| cartesian_product2(X0,X1) = X2 ),
inference(definition_unfolding,[],[f310,f346]) ).
fof(f389,plain,
! [X2,X10,X0,X1,X8,X9] :
( cartesian_product2(X0,X1) != X2
| unordered_pair(unordered_pair(X9,X10),unordered_pair(X9,X9)) != X8
| ~ in(X10,X1)
| ~ in(X9,X0)
| in(X8,X2) ),
inference(definition_unfolding,[],[f309,f346]) ).
fof(f390,plain,
! [X2,X0,X1,X8] :
( cartesian_product2(X0,X1) != X2
| ~ in(X8,X2)
| unordered_pair(unordered_pair(sK16(X0,X1,X8),sK17(X0,X1,X8)),unordered_pair(sK16(X0,X1,X8),sK16(X0,X1,X8))) = X8 ),
inference(definition_unfolding,[],[f306,f346]) ).
fof(f391,plain,
! [X0,X1] : ~ empty(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0))),
inference(definition_unfolding,[],[f314,f346]) ).
fof(f393,plain,
! [X2,X0,X1] :
( ~ in(sK19(X0,X1,X2),X2)
| ~ in(sK19(X0,X1,X2),X1)
| ~ in(sK19(X0,X1,X2),X0)
| set_difference(X0,set_difference(X0,X1)) = X2 ),
inference(definition_unfolding,[],[f329,f248]) ).
fof(f394,plain,
! [X2,X0,X1] :
( in(sK19(X0,X1,X2),X2)
| in(sK19(X0,X1,X2),X0)
| set_difference(X0,set_difference(X0,X1)) = X2 ),
inference(definition_unfolding,[],[f328,f248]) ).
fof(f395,plain,
! [X2,X0,X1] :
( in(sK19(X0,X1,X2),X2)
| in(sK19(X0,X1,X2),X1)
| set_difference(X0,set_difference(X0,X1)) = X2 ),
inference(definition_unfolding,[],[f327,f248]) ).
fof(f396,plain,
! [X2,X0,X1,X4] :
( set_difference(X0,set_difference(X0,X1)) != X2
| ~ in(X4,X1)
| ~ in(X4,X0)
| in(X4,X2) ),
inference(definition_unfolding,[],[f326,f248]) ).
fof(f398,plain,
! [X2,X0,X1,X4] :
( set_difference(X0,set_difference(X0,X1)) != X2
| ~ in(X4,X2)
| in(X4,X1) ),
inference(definition_unfolding,[],[f324,f248]) ).
fof(f399,plain,
! [X0,X1] : set_difference(X0,set_difference(X0,X1)) = set_difference(X1,set_difference(X1,X0)),
inference(definition_unfolding,[],[f330,f248,f248]) ).
fof(f406,plain,
! [X3,X0] :
( ~ in(X3,unordered_pair(X0,X0))
| X0 = X3 ),
inference(equality_resolution,[],[f383]) ).
fof(f407,plain,
! [X2] : ~ in(X2,empty_set),
inference(equality_resolution,[],[f271]) ).
fof(f408,plain,
! [X0,X1,X4] :
( ~ in(X4,X0)
| in(X4,set_union2(X0,X1)) ),
inference(equality_resolution,[],[f282]) ).
fof(f409,plain,
! [X0,X1,X4] :
( ~ in(X4,X1)
| in(X4,set_union2(X0,X1)) ),
inference(equality_resolution,[],[f281]) ).
fof(f410,plain,
! [X0,X1,X4] :
( ~ in(X4,set_union2(X0,X1))
| in(X4,X1)
| in(X4,X0) ),
inference(equality_resolution,[],[f280]) ).
fof(f412,plain,
! [X1] : subset(X1,X1),
inference(equality_resolution,[],[f291]) ).
fof(f413,plain,
! [X0,X1,X4] :
( in(X4,X1)
| ~ in(X4,X0)
| in(X4,set_difference(X0,X1)) ),
inference(equality_resolution,[],[f296]) ).
fof(f414,plain,
! [X0,X1,X4] :
( ~ in(X4,set_difference(X0,X1))
| in(X4,X0) ),
inference(equality_resolution,[],[f295]) ).
fof(f415,plain,
! [X0,X1,X4] :
( ~ in(X4,set_difference(X0,X1))
| ~ in(X4,X1) ),
inference(equality_resolution,[],[f294]) ).
fof(f416,plain,
! [X0,X6,X5] :
( ~ in(X6,X0)
| ~ in(X5,X6)
| in(X5,union(X0)) ),
inference(equality_resolution,[],[f302]) ).
fof(f417,plain,
! [X0,X5] :
( ~ in(X5,union(X0))
| in(X5,sK12(X0,X5)) ),
inference(equality_resolution,[],[f301]) ).
fof(f418,plain,
! [X0,X5] :
( ~ in(X5,union(X0))
| in(sK12(X0,X5),X0) ),
inference(equality_resolution,[],[f300]) ).
fof(f419,plain,
! [X2,X10,X0,X1,X9] :
( cartesian_product2(X0,X1) != X2
| ~ in(X10,X1)
| ~ in(X9,X0)
| in(unordered_pair(unordered_pair(X9,X10),unordered_pair(X9,X9)),X2) ),
inference(equality_resolution,[],[f389]) ).
fof(f420,plain,
! [X10,X0,X1,X9] :
( ~ in(X10,X1)
| ~ in(X9,X0)
| in(unordered_pair(unordered_pair(X9,X10),unordered_pair(X9,X9)),cartesian_product2(X0,X1)) ),
inference(equality_resolution,[],[f419]) ).
fof(f421,plain,
! [X0,X1,X8] :
( ~ in(X8,cartesian_product2(X0,X1))
| in(sK16(X0,X1,X8),X0) ),
inference(equality_resolution,[],[f308]) ).
fof(f422,plain,
! [X0,X1,X8] :
( ~ in(X8,cartesian_product2(X0,X1))
| in(sK17(X0,X1,X8),X1) ),
inference(equality_resolution,[],[f307]) ).
fof(f423,plain,
! [X0,X1,X8] :
( ~ in(X8,cartesian_product2(X0,X1))
| unordered_pair(unordered_pair(sK16(X0,X1,X8),sK17(X0,X1,X8)),unordered_pair(sK16(X0,X1,X8),sK16(X0,X1,X8))) = X8 ),
inference(equality_resolution,[],[f390]) ).
fof(f424,plain,
! [X2,X1,X4] :
( unordered_pair(X4,X1) != X2
| in(X4,X2) ),
inference(equality_resolution,[],[f318]) ).
fof(f425,plain,
! [X1,X4] : in(X4,unordered_pair(X4,X1)),
inference(equality_resolution,[],[f424]) ).
fof(f426,plain,
! [X2,X0,X4] :
( unordered_pair(X0,X4) != X2
| in(X4,X2) ),
inference(equality_resolution,[],[f317]) ).
fof(f427,plain,
! [X0,X4] : in(X4,unordered_pair(X0,X4)),
inference(equality_resolution,[],[f426]) ).
fof(f428,plain,
! [X0,X1,X4] :
( ~ in(X4,unordered_pair(X0,X1))
| X1 = X4
| X0 = X4 ),
inference(equality_resolution,[],[f316]) ).
fof(f429,plain,
! [X0,X1,X4] :
( ~ in(X4,X1)
| ~ in(X4,X0)
| in(X4,set_difference(X0,set_difference(X0,X1))) ),
inference(equality_resolution,[],[f396]) ).
fof(f431,plain,
! [X0,X1,X4] :
( ~ in(X4,set_difference(X0,set_difference(X0,X1)))
| in(X4,X1) ),
inference(equality_resolution,[],[f398]) ).
fof(f432,plain,
! [X3,X0] :
( ~ subset(X3,X0)
| in(X3,powerset(X0)) ),
inference(equality_resolution,[],[f332]) ).
fof(f433,plain,
! [X3,X0] :
( ~ in(X3,powerset(X0))
| subset(X3,X0) ),
inference(equality_resolution,[],[f331]) ).
tcf(c_49,plain,
! [X0: $i] : unordered_pair(X0,X0) != empty_set,
inference(cnf_transformation,[],[f347]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] :
( ~ in(X0,X1)
| ~ disjoint(unordered_pair(X0,X0),X1) ),
inference(cnf_transformation,[],[f349]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( in(X0,X1)
| disjoint(unordered_pair(X0,X0),X1) ),
inference(cnf_transformation,[],[f350]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,X0)
| subset(X0,set_difference(X1,unordered_pair(X2,X2)))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f353]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] :
( subset(X0,union(X1))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f213]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f358]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X1,X3)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f359]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X0 = X3 )
| ( X0 = X2 )
| ( unordered_pair(X0,X1) != unordered_pair(X2,X3) ) ),
inference(cnf_transformation,[],[f217]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] :
( ( set_union2(X0,X1) = X1 )
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f218]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,set_difference(X1,set_difference(X1,X2)))
| ~ subset(X0,X2)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f361]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f221]) ).
tcf(c_70,plain,
unordered_pair(empty_set,empty_set) = powerset(empty_set),
inference(cnf_transformation,[],[f362]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(X0,set_difference(X0,X2)),set_difference(X1,set_difference(X1,X2)))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f363]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i] :
( ( set_difference(X0,set_difference(X0,X1)) = X0 )
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f364]) ).
tcf(c_73,plain,
! [X0: $i] : subset(empty_set,X0),
inference(cnf_transformation,[],[f225]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(X0,X2),set_difference(X1,X2))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f226]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X0 = X2 )
| ( unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)) != unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)) ) ),
inference(cnf_transformation,[],[f365]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = X3 )
| ( unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)) != unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)) ) ),
inference(cnf_transformation,[],[f366]) ).
tcf(c_77,plain,
! [X0: $i,X1: $i] : subset(set_difference(X0,X1),X0),
inference(cnf_transformation,[],[f229]) ).
tcf(c_78,plain,
! [X0: $i,X1: $i] :
( ( set_difference(X0,X1) = empty_set )
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f231]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ( set_difference(X0,X1) != empty_set ) ),
inference(cnf_transformation,[],[f230]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i] :
( subset(unordered_pair(X0,X0),X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f367]) ).
tcf(c_82,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(unordered_pair(X0,X2),X1)
| ~ in(X2,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f236]) ).
tcf(c_83,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ subset(unordered_pair(X0,X1),X2) ),
inference(cnf_transformation,[],[f235]) ).
tcf(c_84,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,X2)
| ~ subset(unordered_pair(X0,X1),X2) ),
inference(cnf_transformation,[],[f234]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i] : set_union2(X0,set_difference(X1,X0)) = set_union2(X0,X1),
inference(cnf_transformation,[],[f237]) ).
tcf(c_88,plain,
! [X0: $i,X1: $i] :
( ( X0 = empty_set )
| ( unordered_pair(X1,X1) = X0 )
| ~ subset(X0,unordered_pair(X1,X1)) ),
inference(cnf_transformation,[],[f371]) ).
tcf(c_89,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| in(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f243]) ).
tcf(c_90,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| in(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f242]) ).
tcf(c_91,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ disjoint(X1,X2)
| ~ in(X0,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f241]) ).
tcf(c_92,plain,
! [X0: $i] :
( ( X0 = empty_set )
| ~ subset(X0,empty_set) ),
inference(cnf_transformation,[],[f244]) ).
tcf(c_93,plain,
! [X0: $i,X1: $i] : set_difference(set_union2(X0,X1),X1) = set_difference(X0,X1),
inference(cnf_transformation,[],[f245]) ).
tcf(c_95,plain,
! [X0: $i,X1: $i] :
( ( set_union2(unordered_pair(X0,X0),X1) = X1 )
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f372]) ).
tcf(c_96,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| in(sK1(X0,X1),set_difference(X0,set_difference(X0,X1))) ),
inference(cnf_transformation,[],[f373]) ).
tcf(c_97,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ disjoint(X1,X2)
| ~ in(X0,set_difference(X1,set_difference(X1,X2))) ),
inference(cnf_transformation,[],[f374]) ).
tcf(c_98,plain,
! [X0: $i,X1: $i] :
( ~ proper_subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f251]) ).
tcf(c_99,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(X2,X1)
| ~ subset(X2,X0)
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[],[f252]) ).
tcf(c_100,negated_conjecture,
( in(sK3,sK2)
| ( set_difference(sK2,unordered_pair(sK3,sK3)) != sK2 ) ),
inference(cnf_transformation,[],[f375]) ).
tcf(c_101,negated_conjecture,
( ( set_difference(sK2,unordered_pair(sK3,sK3)) = sK2 )
| ~ in(sK3,sK2) ),
inference(cnf_transformation,[],[f376]) ).
tcf(c_102,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ subset(unordered_pair(X0,X0),unordered_pair(X1,X1)) ),
inference(cnf_transformation,[],[f377]) ).
tcf(c_103,plain,
! [X0: $i,X1: $i] : subset(X0,set_union2(X0,X1)),
inference(cnf_transformation,[],[f257]) ).
tcf(c_104,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| ( set_difference(X0,X1) != X0 ) ),
inference(cnf_transformation,[],[f259]) ).
tcf(c_105,plain,
! [X0: $i,X1: $i] :
( ( set_difference(X0,X1) = X0 )
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[],[f258]) ).
tcf(c_106,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_union2(X0,X2),X1)
| ~ subset(X2,X1)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f260]) ).
tcf(c_107,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X1 )
| ( unordered_pair(X0,X0) != unordered_pair(X1,X2) ) ),
inference(cnf_transformation,[],[f378]) ).
tcf(c_108,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( unordered_pair(X0,X0) != unordered_pair(X1,X2) ) ),
inference(cnf_transformation,[],[f379]) ).
tcf(c_109,plain,
! [X0: $i,X1: $i] :
( ( unordered_pair(X0,X0) = X1 )
| ~ in(sK4(X0,X1),X1)
| ( sK4(X0,X1) != X0 ) ),
inference(cnf_transformation,[],[f380]) ).
tcf(c_110,plain,
! [X0: $i,X1: $i] :
( in(sK4(X0,X1),X1)
| ( sK4(X0,X1) = X0 )
| ( unordered_pair(X0,X0) = X1 ) ),
inference(cnf_transformation,[],[f381]) ).
tcf(c_112,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ in(X0,unordered_pair(X1,X1)) ),
inference(cnf_transformation,[],[f406]) ).
tcf(c_113,plain,
! [X0: $i] : set_difference(empty_set,X0) = empty_set,
inference(cnf_transformation,[],[f267]) ).
tcf(c_114,plain,
! [X0: $i] : set_difference(X0,empty_set) = X0,
inference(cnf_transformation,[],[f268]) ).
tcf(c_115,plain,
! [X0: $i] : set_difference(X0,set_difference(X0,empty_set)) = empty_set,
inference(cnf_transformation,[],[f384]) ).
tcf(c_116,plain,
! [X0: $i] : set_union2(X0,empty_set) = X0,
inference(cnf_transformation,[],[f270]) ).
tcf(c_117,plain,
! [X0: $i] :
( in(sK5(X0),X0)
| ( X0 = empty_set ) ),
inference(cnf_transformation,[],[f272]) ).
tcf(c_118,plain,
! [X0: $i] : ~ in(X0,empty_set),
inference(cnf_transformation,[],[f407]) ).
tcf(c_119,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ in(sK6(X0,X1),X1)
| ~ in(sK6(X0,X1),X0) ),
inference(cnf_transformation,[],[f274]) ).
tcf(c_120,plain,
! [X0: $i,X1: $i] :
( in(sK6(X0,X1),X1)
| in(sK6(X0,X1),X0)
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f273]) ).
tcf(c_121,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ in(sK7(X0,X1),X1) ),
inference(cnf_transformation,[],[f277]) ).
tcf(c_122,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| in(sK7(X0,X1),X0) ),
inference(cnf_transformation,[],[f276]) ).
tcf(c_123,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ subset(X1,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f275]) ).
tcf(c_124,plain,
! [X0: $i,X1: $i] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f278]) ).
tcf(c_125,plain,
! [X0: $i] : set_union2(X0,X0) = X0,
inference(cnf_transformation,[],[f279]) ).
tcf(c_126,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_union2(X0,X1) = X2 )
| ~ in(sK8(X0,X1,X2),X2)
| ~ in(sK8(X0,X1,X2),X0) ),
inference(cnf_transformation,[],[f285]) ).
tcf(c_127,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_union2(X0,X1) = X2 )
| ~ in(sK8(X0,X1,X2),X2)
| ~ in(sK8(X0,X1,X2),X1) ),
inference(cnf_transformation,[],[f284]) ).
tcf(c_128,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK8(X0,X1,X2),X2)
| in(sK8(X0,X1,X2),X1)
| in(sK8(X0,X1,X2),X0)
| ( set_union2(X0,X1) = X2 ) ),
inference(cnf_transformation,[],[f283]) ).
tcf(c_129,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,set_union2(X1,X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f408]) ).
tcf(c_130,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,set_union2(X2,X1))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f409]) ).
tcf(c_131,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| in(X0,X1)
| ~ in(X0,set_union2(X1,X2)) ),
inference(cnf_transformation,[],[f410]) ).
tcf(c_132,plain,
! [X0: $i,X1: $i] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f286]) ).
tcf(c_133,plain,
! [X0: $i,X1: $i] :
( disjoint(X1,X0)
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[],[f287]) ).
tcf(c_134,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| ( set_difference(X0,set_difference(X0,X1)) != empty_set ) ),
inference(cnf_transformation,[],[f385]) ).
tcf(c_135,plain,
! [X0: $i,X1: $i] :
( ( set_difference(X0,set_difference(X0,X1)) = empty_set )
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[],[f386]) ).
tcf(c_137,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f293]) ).
tcf(c_139,plain,
! [X0: $i] : subset(X0,X0),
inference(cnf_transformation,[],[f412]) ).
tcf(c_140,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK9(X0,X1,X2),X1)
| ( set_difference(X0,X1) = X2 )
| ~ in(sK9(X0,X1,X2),X2)
| ~ in(sK9(X0,X1,X2),X0) ),
inference(cnf_transformation,[],[f299]) ).
tcf(c_141,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK9(X0,X1,X2),X2)
| in(sK9(X0,X1,X2),X0)
| ( set_difference(X0,X1) = X2 ) ),
inference(cnf_transformation,[],[f298]) ).
tcf(c_142,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK9(X0,X1,X2),X2)
| ( set_difference(X0,X1) = X2 )
| ~ in(sK9(X0,X1,X2),X1) ),
inference(cnf_transformation,[],[f297]) ).
tcf(c_143,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| in(X0,set_difference(X1,X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f413]) ).
tcf(c_144,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X1)
| ~ in(X0,set_difference(X1,X2)) ),
inference(cnf_transformation,[],[f414]) ).
tcf(c_145,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(X0,X2)
| ~ in(X0,set_difference(X1,X2)) ),
inference(cnf_transformation,[],[f415]) ).
tcf(c_146,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( union(X0) = X1 )
| ~ in(X2,X0)
| ~ in(sK10(X0,X1),X2)
| ~ in(sK10(X0,X1),X1) ),
inference(cnf_transformation,[],[f305]) ).
tcf(c_147,plain,
! [X0: $i,X1: $i] :
( in(sK10(X0,X1),X1)
| in(sK10(X0,X1),sK11(X0,X1))
| ( union(X0) = X1 ) ),
inference(cnf_transformation,[],[f304]) ).
tcf(c_148,plain,
! [X0: $i,X1: $i] :
( in(sK11(X0,X1),X0)
| in(sK10(X0,X1),X1)
| ( union(X0) = X1 ) ),
inference(cnf_transformation,[],[f303]) ).
tcf(c_149,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,union(X2))
| ~ in(X1,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f416]) ).
tcf(c_150,plain,
! [X0: $i,X1: $i] :
( in(X0,sK12(X1,X0))
| ~ in(X0,union(X1)) ),
inference(cnf_transformation,[],[f417]) ).
tcf(c_151,plain,
! [X0: $i,X1: $i] :
( in(sK12(X1,X0),X1)
| ~ in(X0,union(X1)) ),
inference(cnf_transformation,[],[f418]) ).
tcf(c_152,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ~ in(X1,X3)
| ~ in(X0,X2)
| ~ in(sK13(X2,X3,X4),X4)
| ( unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)) != sK13(X2,X3,X4) ) ),
inference(cnf_transformation,[],[f387]) ).
tcf(c_153,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK14(X0,X1,X2),X0)
| in(sK13(X0,X1,X2),X2)
| ( cartesian_product2(X0,X1) = X2 ) ),
inference(cnf_transformation,[],[f312]) ).
tcf(c_154,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK15(X0,X1,X2),X1)
| in(sK13(X0,X1,X2),X2)
| ( cartesian_product2(X0,X1) = X2 ) ),
inference(cnf_transformation,[],[f311]) ).
tcf(c_155,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK13(X0,X1,X2),X2)
| ( cartesian_product2(X0,X1) = X2 )
| ( unordered_pair(unordered_pair(sK14(X0,X1,X2),sK15(X0,X1,X2)),unordered_pair(sK14(X0,X1,X2),sK14(X0,X1,X2))) = sK13(X0,X1,X2) ) ),
inference(cnf_transformation,[],[f388]) ).
tcf(c_156,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(X0,X2),unordered_pair(X0,X0)),cartesian_product2(X1,X3))
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f420]) ).
tcf(c_157,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK16(X1,X2,X0),X1)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(cnf_transformation,[],[f421]) ).
tcf(c_158,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK17(X1,X2,X0),X2)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(cnf_transformation,[],[f422]) ).
tcf(c_159,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( unordered_pair(unordered_pair(sK16(X1,X2,X0),sK17(X1,X2,X0)),unordered_pair(sK16(X1,X2,X0),sK16(X1,X2,X0))) = X0 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(cnf_transformation,[],[f423]) ).
tcf(c_160,plain,
! [X0: $i,X1: $i] : ~ empty(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0))),
inference(cnf_transformation,[],[f391]) ).
tcf(c_161,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( unordered_pair(X0,X1) = X2 )
| ~ in(sK18(X0,X1,X2),X2)
| ( sK18(X0,X1,X2) != X0 ) ),
inference(cnf_transformation,[],[f321]) ).
tcf(c_162,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( unordered_pair(X0,X1) = X2 )
| ~ in(sK18(X0,X1,X2),X2)
| ( sK18(X0,X1,X2) != X1 ) ),
inference(cnf_transformation,[],[f320]) ).
tcf(c_163,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK18(X0,X1,X2),X2)
| ( unordered_pair(X0,X1) = X2 )
| ( sK18(X0,X1,X2) = X1 )
| ( sK18(X0,X1,X2) = X0 ) ),
inference(cnf_transformation,[],[f319]) ).
tcf(c_164,plain,
! [X0: $i,X1: $i] : in(X0,unordered_pair(X0,X1)),
inference(cnf_transformation,[],[f425]) ).
tcf(c_165,plain,
! [X0: $i,X1: $i] : in(X0,unordered_pair(X1,X0)),
inference(cnf_transformation,[],[f427]) ).
tcf(c_166,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ( X0 = X1 )
| ~ in(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[],[f428]) ).
tcf(c_167,plain,
! [X0: $i,X1: $i] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f322]) ).
tcf(c_169,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(X0,set_difference(X0,X1)) = X2 )
| ~ in(sK19(X0,X1,X2),X2)
| ~ in(sK19(X0,X1,X2),X1)
| ~ in(sK19(X0,X1,X2),X0) ),
inference(cnf_transformation,[],[f393]) ).
tcf(c_170,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK19(X0,X1,X2),X2)
| in(sK19(X0,X1,X2),X0)
| ( set_difference(X0,set_difference(X0,X1)) = X2 ) ),
inference(cnf_transformation,[],[f394]) ).
tcf(c_171,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK19(X0,X1,X2),X2)
| in(sK19(X0,X1,X2),X1)
| ( set_difference(X0,set_difference(X0,X1)) = X2 ) ),
inference(cnf_transformation,[],[f395]) ).
tcf(c_172,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,set_difference(X1,set_difference(X1,X2)))
| ~ in(X0,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f429]) ).
tcf(c_174,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ in(X0,set_difference(X1,set_difference(X1,X2))) ),
inference(cnf_transformation,[],[f431]) ).
tcf(c_175,plain,
! [X0: $i,X1: $i] : set_difference(X0,set_difference(X0,X1)) = set_difference(X1,set_difference(X1,X0)),
inference(cnf_transformation,[],[f399]) ).
tcf(c_176,plain,
! [X0: $i,X1: $i] :
( ( powerset(X0) = X1 )
| ~ subset(sK20(X0,X1),X0)
| ~ in(sK20(X0,X1),X1) ),
inference(cnf_transformation,[],[f334]) ).
tcf(c_177,plain,
! [X0: $i,X1: $i] :
( subset(sK20(X0,X1),X0)
| in(sK20(X0,X1),X1)
| ( powerset(X0) = X1 ) ),
inference(cnf_transformation,[],[f333]) ).
tcf(c_178,plain,
! [X0: $i,X1: $i] :
( in(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f432]) ).
tcf(c_179,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ in(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f433]) ).
tcf(c_180,plain,
! [X0: $i] : ~ proper_subset(X0,X0),
inference(cnf_transformation,[],[f335]) ).
tcf(c_181,plain,
! [X0: $i,X1: $i] :
( proper_subset(X0,X1)
| ( X0 = X1 )
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f336]) ).
tcf(c_182,plain,
! [X0: $i,X1: $i] :
( ~ proper_subset(X1,X0)
| ~ proper_subset(X0,X1) ),
inference(cnf_transformation,[],[f337]) ).
tcf(c_183,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f338]) ).
tcf(c_184,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f339]) ).
tcf(c_185,plain,
! [X0: $i] :
( ( X0 = empty_set )
| ~ empty(X0) ),
inference(cnf_transformation,[],[f340]) ).
tcf(c_186,plain,
~ empty(sK21),
inference(cnf_transformation,[],[f341]) ).
tcf(c_187,plain,
empty(sK22),
inference(cnf_transformation,[],[f342]) ).
tcf(c_188,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| ~ empty(set_union2(X0,X1)) ),
inference(cnf_transformation,[],[f343]) ).
tcf(c_189,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| ~ empty(set_union2(X0,X1)) ),
inference(cnf_transformation,[],[f344]) ).
tcf(c_190,plain,
empty(empty_set),
inference(cnf_transformation,[],[f345]) ).
tcf(c_387,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( unordered_pair(unordered_pair(sK16(X1,X2,X0),sK17(X1,X2,X0)),unordered_pair(sK16(X1,X2,X0),sK16(X1,X2,X0))) = X0 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(prop_impl_just,[status(thm)],[c_159]) ).
tcf(c_1252,plain,
! [X0: $i] : set_difference(X0,X0) = empty_set,
inference(light_normalisation,[status(thm)],[c_115,c_114]) ).
tcf(c_1681,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( unordered_pair(unordered_pair(sK16(X1,X2,X0),sK16(X1,X2,X0)),unordered_pair(sK16(X1,X2,X0),sK17(X1,X2,X0))) = X0 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(demodulation,[status(thm)],[c_387,c_167]) ).
tcf(c_1706,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK13(X0,X1,X2),X2)
| ( cartesian_product2(X0,X1) = X2 )
| ( unordered_pair(unordered_pair(sK14(X0,X1,X2),sK14(X0,X1,X2)),unordered_pair(sK14(X0,X1,X2),sK15(X0,X1,X2))) = sK13(X0,X1,X2) ) ),
inference(demodulation,[status(thm)],[c_155,c_167]) ).
tcf(c_1855,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( unordered_pair(unordered_pair(sK16(X1,X2,X0),sK16(X1,X2,X0)),unordered_pair(sK16(X1,X2,X0),sK17(X1,X2,X0))) = X0 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(prop_impl_just,[status(thm)],[c_1681]) ).
tcf(c_5203,plain,
subset(empty_set,empty_set),
inference(superposition,[status(thm)],[c_113,c_77]) ).
tcf(c_5207,plain,
powerset(empty_set) != empty_set,
inference(superposition,[status(thm)],[c_70,c_49]) ).
tcf(c_5208,plain,
in(empty_set,powerset(empty_set)),
inference(superposition,[status(thm)],[c_70,c_164]) ).
tcf(c_5218,plain,
! [X0: $i,X1: $i] : ~ empty(unordered_pair(X0,X1)),
inference(superposition,[status(thm)],[c_164,c_184]) ).
tcf(c_5220,plain,
~ empty(powerset(empty_set)),
inference(superposition,[status(thm)],[c_5208,c_184]) ).
tcf(c_5228,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( cartesian_product2(X1,X2) = X0 )
| ( unordered_pair(unordered_pair(sK14(X1,X2,X0),sK14(X1,X2,X0)),unordered_pair(sK14(X1,X2,X0),sK15(X1,X2,X0))) = sK13(X1,X2,X0) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_1706,c_184]) ).
tcf(c_5229,plain,
! [X0: $i,X1: $i] :
( ( cartesian_product2(X0,X1) = empty_set )
| ( unordered_pair(unordered_pair(sK14(X0,X1,empty_set),sK14(X0,X1,empty_set)),unordered_pair(sK14(X0,X1,empty_set),sK15(X0,X1,empty_set))) = sK13(X0,X1,empty_set) ) ),
inference(superposition,[status(thm)],[c_1706,c_118]) ).
tcf(c_5240,plain,
empty_set = sK22,
inference(superposition,[status(thm)],[c_187,c_185]) ).
tcf(c_5259,plain,
! [X0: $i] :
( in(empty_set,X0)
| disjoint(powerset(empty_set),X0) ),
inference(superposition,[status(thm)],[c_70,c_52]) ).
tcf(c_5260,plain,
! [X0: $i,X1: $i] :
( in(X1,X0)
| disjoint(X0,unordered_pair(X1,X1)) ),
inference(superposition,[status(thm)],[c_52,c_133]) ).
tcf(c_5272,plain,
! [X0: $i] :
( in(empty_set,X0)
| disjoint(X0,powerset(empty_set)) ),
inference(superposition,[status(thm)],[c_5259,c_133]) ).
tcf(c_5289,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89,c_184]) ).
tcf(c_5290,plain,
! [X0: $i] : disjoint(empty_set,X0),
inference(superposition,[status(thm)],[c_89,c_118]) ).
tcf(c_5294,plain,
! [X0: $i] : disjoint(X0,empty_set),
inference(superposition,[status(thm)],[c_5290,c_133]) ).
tcf(c_5300,plain,
! [X0: $i,X1: $i] :
( disjoint(X1,X0)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5289,c_133]) ).
tcf(c_5325,plain,
! [X0: $i,X1: $i] :
( ( cartesian_product2(X0,X1) = empty_set )
| ~ empty(sK13(X0,X1,empty_set)) ),
inference(superposition,[status(thm)],[c_5229,c_5218]) ).
tcf(c_5326,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(sK14(X0,X1,empty_set),sK14(X0,X1,empty_set)),sK13(X0,X1,empty_set))
| ( cartesian_product2(X0,X1) = empty_set ) ),
inference(superposition,[status(thm)],[c_5229,c_164]) ).
tcf(c_5327,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(sK14(X0,X1,empty_set),sK15(X0,X1,empty_set)),sK13(X0,X1,empty_set))
| ( cartesian_product2(X0,X1) = empty_set ) ),
inference(superposition,[status(thm)],[c_5229,c_165]) ).
tcf(c_5341,plain,
! [X0: $i,X1: $i] :
( ~ in(X1,X0)
| ~ proper_subset(union(X0),X1) ),
inference(superposition,[status(thm)],[c_61,c_98]) ).
tcf(c_5342,plain,
! [X0: $i] : ~ proper_subset(X0,empty_set),
inference(superposition,[status(thm)],[c_73,c_98]) ).
tcf(c_5343,plain,
! [X0: $i,X1: $i] : ~ proper_subset(X0,set_difference(X0,X1)),
inference(superposition,[status(thm)],[c_77,c_98]) ).
tcf(c_5344,plain,
! [X0: $i,X1: $i] : ~ proper_subset(set_union2(X0,X1),X0),
inference(superposition,[status(thm)],[c_103,c_98]) ).
tcf(c_5360,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_122,c_184]) ).
tcf(c_5368,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| ~ in(X0,sK0(X0,X1)) ),
inference(superposition,[status(thm)],[c_89,c_124]) ).
tcf(c_5369,plain,
! [X0: $i,X1: $i] :
( disjoint(X1,X0)
| ~ in(X0,sK0(X1,X0)) ),
inference(superposition,[status(thm)],[c_90,c_124]) ).
tcf(c_5370,plain,
! [X0: $i] :
( ( X0 = empty_set )
| ~ in(X0,sK5(X0)) ),
inference(superposition,[status(thm)],[c_117,c_124]) ).
tcf(c_5371,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ in(X0,sK7(X0,X1)) ),
inference(superposition,[status(thm)],[c_122,c_124]) ).
tcf(c_5372,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( cartesian_product2(X1,X2) = X0 )
| ( unordered_pair(unordered_pair(sK14(X1,X2,X0),sK14(X1,X2,X0)),unordered_pair(sK14(X1,X2,X0),sK15(X1,X2,X0))) = sK13(X1,X2,X0) )
| ~ in(X0,sK13(X1,X2,X0)) ),
inference(superposition,[status(thm)],[c_1706,c_124]) ).
tcf(c_5373,plain,
! [X0: $i,X1: $i] : ~ in(unordered_pair(X0,X1),X0),
inference(superposition,[status(thm)],[c_164,c_124]) ).
tcf(c_5374,plain,
! [X0: $i,X1: $i] : ~ in(unordered_pair(X0,X1),X1),
inference(superposition,[status(thm)],[c_165,c_124]) ).
tcf(c_5375,plain,
~ in(powerset(empty_set),empty_set),
inference(superposition,[status(thm)],[c_5208,c_124]) ).
tcf(c_5388,plain,
~ proper_subset(empty_set,empty_set),
inference(superposition,[status(thm)],[c_113,c_5343]) ).
tcf(c_5397,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ proper_subset(X0,X1) ),
inference(superposition,[status(thm)],[c_5360,c_98]) ).
tcf(c_5402,plain,
! [X0: $i,X1: $i] :
( ( cartesian_product2(X0,X1) = empty_set )
| ~ in(sK13(X0,X1,empty_set),unordered_pair(sK14(X0,X1,empty_set),sK14(X0,X1,empty_set))) ),
inference(superposition,[status(thm)],[c_5229,c_5373]) ).
tcf(c_5407,plain,
! [X0: $i,X1: $i] :
( ( cartesian_product2(X0,X1) = empty_set )
| ~ in(sK13(X0,X1,empty_set),unordered_pair(sK14(X0,X1,empty_set),sK15(X0,X1,empty_set))) ),
inference(superposition,[status(thm)],[c_5229,c_5374]) ).
tcf(c_5422,plain,
! [X0: $i,X1: $i] : ~ proper_subset(set_union2(X0,X1),X1),
inference(superposition,[status(thm)],[c_132,c_5344]) ).
tcf(c_5425,plain,
! [X0: $i,X1: $i] : subset(X0,set_union2(X1,X0)),
inference(superposition,[status(thm)],[c_132,c_103]) ).
tcf(c_5426,plain,
! [X0: $i] : set_union2(empty_set,X0) = X0,
inference(superposition,[status(thm)],[c_132,c_116]) ).
tcf(c_5460,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(cartesian_product2(X0,X1),X2)
| ( unordered_pair(unordered_pair(sK16(X0,X1,sK0(cartesian_product2(X0,X1),X2)),sK16(X0,X1,sK0(cartesian_product2(X0,X1),X2))),unordered_pair(sK16(X0,X1,sK0(cartesian_product2(X0,X1),X2)),sK17(X0,X1,sK0(cartesian_product2(X0,X1),X2)))) = sK0(cartesian_product2(X0,X1),X2) ) ),
inference(superposition,[status(thm)],[c_89,c_1855]) ).
tcf(c_5461,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(X2,cartesian_product2(X0,X1))
| ( unordered_pair(unordered_pair(sK16(X0,X1,sK0(X2,cartesian_product2(X0,X1))),sK16(X0,X1,sK0(X2,cartesian_product2(X0,X1)))),unordered_pair(sK16(X0,X1,sK0(X2,cartesian_product2(X0,X1))),sK17(X0,X1,sK0(X2,cartesian_product2(X0,X1))))) = sK0(X2,cartesian_product2(X0,X1)) ) ),
inference(superposition,[status(thm)],[c_90,c_1855]) ).
tcf(c_5462,plain,
! [X0: $i,X1: $i] :
( ( cartesian_product2(X0,X1) = empty_set )
| ( unordered_pair(unordered_pair(sK16(X0,X1,sK5(cartesian_product2(X0,X1))),sK16(X0,X1,sK5(cartesian_product2(X0,X1)))),unordered_pair(sK16(X0,X1,sK5(cartesian_product2(X0,X1))),sK17(X0,X1,sK5(cartesian_product2(X0,X1))))) = sK5(cartesian_product2(X0,X1)) ) ),
inference(superposition,[status(thm)],[c_117,c_1855]) ).
tcf(c_5463,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(cartesian_product2(X0,X1),X2)
| ( unordered_pair(unordered_pair(sK16(X0,X1,sK7(cartesian_product2(X0,X1),X2)),sK16(X0,X1,sK7(cartesian_product2(X0,X1),X2))),unordered_pair(sK16(X0,X1,sK7(cartesian_product2(X0,X1),X2)),sK17(X0,X1,sK7(cartesian_product2(X0,X1),X2)))) = sK7(cartesian_product2(X0,X1),X2) ) ),
inference(superposition,[status(thm)],[c_122,c_1855]) ).
tcf(c_5464,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( cartesian_product2(X0,X1) = cartesian_product2(X2,X3) )
| ( unordered_pair(unordered_pair(sK14(X2,X3,cartesian_product2(X0,X1)),sK14(X2,X3,cartesian_product2(X0,X1))),unordered_pair(sK14(X2,X3,cartesian_product2(X0,X1)),sK15(X2,X3,cartesian_product2(X0,X1)))) = sK13(X2,X3,cartesian_product2(X0,X1)) )
| ( unordered_pair(unordered_pair(sK16(X0,X1,sK13(X2,X3,cartesian_product2(X0,X1))),sK16(X0,X1,sK13(X2,X3,cartesian_product2(X0,X1)))),unordered_pair(sK16(X0,X1,sK13(X2,X3,cartesian_product2(X0,X1))),sK17(X0,X1,sK13(X2,X3,cartesian_product2(X0,X1))))) = sK13(X2,X3,cartesian_product2(X0,X1)) ) ),
inference(superposition,[status(thm)],[c_1706,c_1855]) ).
tcf(c_5485,plain,
! [X0: $i,X1: $i] :
( ~ subset(X1,X0)
| ~ in(powerset(X0),X1) ),
inference(superposition,[status(thm)],[c_178,c_124]) ).
tcf(c_5486,plain,
! [X0: $i,X1: $i] :
( ~ empty(powerset(X1))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_178,c_184]) ).
tcf(c_5487,plain,
! [X0: $i,X1: $i] : ~ subset(unordered_pair(powerset(X0),X1),X0),
inference(superposition,[status(thm)],[c_178,c_5373]) ).
tcf(c_5488,plain,
! [X0: $i,X1: $i] : ~ subset(unordered_pair(X0,powerset(X1)),X1),
inference(superposition,[status(thm)],[c_178,c_5374]) ).
tcf(c_5500,plain,
! [X0: $i,X1: $i] :
( disjoint(powerset(X0),X1)
| subset(sK0(powerset(X0),X1),X0) ),
inference(superposition,[status(thm)],[c_89,c_179]) ).
tcf(c_5501,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,powerset(X1))
| subset(sK0(X0,powerset(X1)),X1) ),
inference(superposition,[status(thm)],[c_90,c_179]) ).
tcf(c_5502,plain,
! [X0: $i] :
( subset(sK5(powerset(X0)),X0)
| ( powerset(X0) = empty_set ) ),
inference(superposition,[status(thm)],[c_117,c_179]) ).
tcf(c_5503,plain,
! [X0: $i,X1: $i] :
( subset(powerset(X0),X1)
| subset(sK7(powerset(X0),X1),X0) ),
inference(superposition,[status(thm)],[c_122,c_179]) ).
tcf(c_5504,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK13(X0,X1,powerset(X2)),X2)
| ( cartesian_product2(X0,X1) = powerset(X2) )
| ( unordered_pair(unordered_pair(sK14(X0,X1,powerset(X2)),sK14(X0,X1,powerset(X2))),unordered_pair(sK14(X0,X1,powerset(X2)),sK15(X0,X1,powerset(X2)))) = sK13(X0,X1,powerset(X2)) ) ),
inference(superposition,[status(thm)],[c_1706,c_179]) ).
tcf(c_5531,plain,
! [X0: $i] :
( subset(powerset(empty_set),X0)
| ~ in(empty_set,X0) ),
inference(superposition,[status(thm)],[c_70,c_80]) ).
tcf(c_5532,plain,
! [X0: $i,X1: $i] :
( ~ in(X1,X0)
| ~ proper_subset(X0,unordered_pair(X1,X1)) ),
inference(superposition,[status(thm)],[c_80,c_98]) ).
tcf(c_5538,plain,
! [X0: $i] : ~ in(powerset(X0),X0),
inference(superposition,[status(thm)],[c_80,c_5487]) ).
tcf(c_5539,plain,
! [X0: $i,X1: $i] : ~ empty(unordered_pair(powerset(X0),X1)),
inference(superposition,[status(thm)],[c_5360,c_5487]) ).
tcf(c_5540,plain,
! [X0: $i,X1: $i] : ~ in(unordered_pair(powerset(union(X0)),X1),X0),
inference(superposition,[status(thm)],[c_61,c_5487]) ).
tcf(c_5545,plain,
! [X0: $i] : ~ subset(powerset(powerset(X0)),X0),
inference(superposition,[status(thm)],[c_178,c_5538]) ).
tcf(c_5547,plain,
! [X0: $i] : ~ empty(powerset(powerset(X0))),
inference(superposition,[status(thm)],[c_5360,c_5545]) ).
tcf(c_5548,plain,
! [X0: $i] : ~ in(powerset(powerset(union(X0))),X0),
inference(superposition,[status(thm)],[c_61,c_5545]) ).
tcf(c_5552,plain,
! [X0: $i,X1: $i] : ~ empty(unordered_pair(X0,powerset(X1))),
inference(superposition,[status(thm)],[c_5360,c_5488]) ).
tcf(c_5553,plain,
! [X0: $i,X1: $i] : ~ in(unordered_pair(X0,powerset(union(X1))),X1),
inference(superposition,[status(thm)],[c_61,c_5488]) ).
tcf(c_5557,plain,
! [X0: $i] : ~ subset(powerset(powerset(union(powerset(X0)))),X0),
inference(superposition,[status(thm)],[c_178,c_5548]) ).
tcf(c_5575,plain,
! [X0: $i] : ~ empty(powerset(X0)),
inference(superposition,[status(thm)],[c_139,c_5486]) ).
tcf(c_5581,plain,
! [X0: $i] :
( ~ in(empty_set,X0)
| ~ proper_subset(X0,powerset(empty_set)) ),
inference(superposition,[status(thm)],[c_5531,c_98]) ).
tcf(c_5582,plain,
( ( powerset(empty_set) = empty_set )
| ~ in(empty_set,empty_set) ),
inference(superposition,[status(thm)],[c_5531,c_92]) ).
tcf(c_5585,plain,
! [X0: $i,X1: $i] : ~ subset(unordered_pair(powerset(union(powerset(X0))),X1),X0),
inference(superposition,[status(thm)],[c_178,c_5540]) ).
tcf(c_5589,plain,
! [X0: $i,X1: $i] : ~ subset(unordered_pair(X0,powerset(union(powerset(X1)))),X1),
inference(superposition,[status(thm)],[c_178,c_5553]) ).
tcf(c_5597,plain,
! [X0: $i,X1: $i] :
( ( cartesian_product2(X0,X1) = empty_set )
| ~ in(sK5(cartesian_product2(X0,X1)),unordered_pair(sK16(X0,X1,sK5(cartesian_product2(X0,X1))),sK17(X0,X1,sK5(cartesian_product2(X0,X1))))) ),
inference(superposition,[status(thm)],[c_5462,c_5374]) ).
tcf(c_5598,plain,
! [X0: $i,X1: $i] :
( ( cartesian_product2(X0,X1) = empty_set )
| ~ in(sK5(cartesian_product2(X0,X1)),unordered_pair(sK16(X0,X1,sK5(cartesian_product2(X0,X1))),sK16(X0,X1,sK5(cartesian_product2(X0,X1))))) ),
inference(superposition,[status(thm)],[c_5462,c_5373]) ).
tcf(c_5599,plain,
! [X0: $i,X1: $i] :
( ( cartesian_product2(X0,X1) = empty_set )
| ~ empty(sK5(cartesian_product2(X0,X1))) ),
inference(superposition,[status(thm)],[c_5462,c_5218]) ).
tcf(c_5600,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(sK16(X0,X1,sK5(cartesian_product2(X0,X1))),sK16(X0,X1,sK5(cartesian_product2(X0,X1)))),sK5(cartesian_product2(X0,X1)))
| ( cartesian_product2(X0,X1) = empty_set ) ),
inference(superposition,[status(thm)],[c_5462,c_164]) ).
tcf(c_5601,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(sK16(X0,X1,sK5(cartesian_product2(X0,X1))),sK17(X0,X1,sK5(cartesian_product2(X0,X1)))),sK5(cartesian_product2(X0,X1)))
| ( cartesian_product2(X0,X1) = empty_set ) ),
inference(superposition,[status(thm)],[c_5462,c_165]) ).
tcf(c_5623,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,union(X2))
| ~ in(unordered_pair(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_61,c_83]) ).
tcf(c_5624,plain,
! [X0: $i,X1: $i,X2: $i] : in(X0,set_union2(unordered_pair(X0,X1),X2)),
inference(superposition,[status(thm)],[c_103,c_83]) ).
tcf(c_5626,plain,
! [X0: $i,X1: $i,X2: $i] : in(X0,set_union2(X1,unordered_pair(X0,X2))),
inference(superposition,[status(thm)],[c_5425,c_83]) ).
tcf(c_5628,plain,
! [X0: $i] :
( in(empty_set,X0)
| ~ subset(powerset(empty_set),X0) ),
inference(superposition,[status(thm)],[c_70,c_83]) ).
tcf(c_5630,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(sK14(X0,X1,empty_set),sK14(X0,X1,empty_set)),X2)
| ( cartesian_product2(X0,X1) = empty_set )
| ~ subset(sK13(X0,X1,empty_set),X2) ),
inference(superposition,[status(thm)],[c_5229,c_83]) ).
tcf(c_5631,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(sK16(X0,X1,sK5(cartesian_product2(X0,X1))),sK16(X0,X1,sK5(cartesian_product2(X0,X1)))),X2)
| ( cartesian_product2(X0,X1) = empty_set )
| ~ subset(sK5(cartesian_product2(X0,X1)),X2) ),
inference(superposition,[status(thm)],[c_5462,c_83]) ).
tcf(c_5653,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,union(X2))
| ~ in(unordered_pair(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_61,c_84]) ).
tcf(c_5654,plain,
! [X0: $i,X1: $i,X2: $i] : in(X0,set_union2(unordered_pair(X1,X0),X2)),
inference(superposition,[status(thm)],[c_103,c_84]) ).
tcf(c_5656,plain,
! [X0: $i,X1: $i,X2: $i] : in(X0,set_union2(X1,unordered_pair(X2,X0))),
inference(superposition,[status(thm)],[c_5425,c_84]) ).
tcf(c_5660,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(sK14(X0,X1,empty_set),sK15(X0,X1,empty_set)),X2)
| ( cartesian_product2(X0,X1) = empty_set )
| ~ subset(sK13(X0,X1,empty_set),X2) ),
inference(superposition,[status(thm)],[c_5229,c_84]) ).
tcf(c_5661,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(sK16(X0,X1,sK5(cartesian_product2(X0,X1))),sK17(X0,X1,sK5(cartesian_product2(X0,X1)))),X2)
| ( cartesian_product2(X0,X1) = empty_set )
| ~ subset(sK5(cartesian_product2(X0,X1)),X2) ),
inference(superposition,[status(thm)],[c_5462,c_84]) ).
tcf(c_5677,plain,
! [X0: $i,X1: $i] :
( subset(X0,powerset(X1))
| ~ subset(sK7(X0,powerset(X1)),X1) ),
inference(superposition,[status(thm)],[c_178,c_121]) ).
tcf(c_5690,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(X2,X0)
| ~ in(set_union2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_129,c_124]) ).
tcf(c_5691,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(X2,X0)
| ~ empty(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_129,c_184]) ).
tcf(c_5692,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,set_union2(X1,X2))
| ~ in(sK7(X0,set_union2(X1,X2)),X1) ),
inference(superposition,[status(thm)],[c_129,c_121]) ).
tcf(c_5693,plain,
! [X0: $i,X1: $i,X2: $i] : ~ in(unordered_pair(set_union2(X0,X1),X2),X0),
inference(superposition,[status(thm)],[c_129,c_5373]) ).
tcf(c_5694,plain,
! [X0: $i,X1: $i,X2: $i] : ~ in(unordered_pair(X0,set_union2(X1,X2)),X1),
inference(superposition,[status(thm)],[c_129,c_5374]) ).
tcf(c_5695,plain,
! [X0: $i,X1: $i] : ~ in(powerset(set_union2(X0,X1)),X0),
inference(superposition,[status(thm)],[c_129,c_5538]) ).
tcf(c_5696,plain,
! [X0: $i,X1: $i,X2: $i] : ~ in(unordered_pair(powerset(union(set_union2(X0,X1))),X2),X0),
inference(superposition,[status(thm)],[c_129,c_5540]) ).
tcf(c_5697,plain,
! [X0: $i,X1: $i] : ~ in(powerset(powerset(union(set_union2(X0,X1)))),X0),
inference(superposition,[status(thm)],[c_129,c_5548]) ).
tcf(c_5698,plain,
! [X0: $i,X1: $i,X2: $i] : ~ in(unordered_pair(X0,powerset(union(set_union2(X1,X2)))),X1),
inference(superposition,[status(thm)],[c_129,c_5553]) ).
tcf(c_5716,plain,
! [X0: $i] : in(empty_set,set_union2(powerset(empty_set),X0)),
inference(superposition,[status(thm)],[c_70,c_5624]) ).
tcf(c_5718,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(sK14(X0,X1,empty_set),sK14(X0,X1,empty_set)),set_union2(sK13(X0,X1,empty_set),X2))
| ( cartesian_product2(X0,X1) = empty_set ) ),
inference(superposition,[status(thm)],[c_5229,c_5624]) ).
tcf(c_5719,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(sK16(X0,X1,sK5(cartesian_product2(X0,X1))),sK16(X0,X1,sK5(cartesian_product2(X0,X1)))),set_union2(sK5(cartesian_product2(X0,X1)),X2))
| ( cartesian_product2(X0,X1) = empty_set ) ),
inference(superposition,[status(thm)],[c_5462,c_5624]) ).
tcf(c_5720,plain,
! [X0: $i,X1: $i,X2: $i] : ~ in(set_union2(unordered_pair(X0,X1),X2),X0),
inference(superposition,[status(thm)],[c_5624,c_124]) ).
tcf(c_5721,plain,
! [X0: $i,X1: $i,X2: $i] : ~ empty(set_union2(unordered_pair(X0,X1),X2)),
inference(superposition,[status(thm)],[c_5624,c_184]) ).
tcf(c_5734,plain,
! [X0: $i] : in(empty_set,set_union2(X0,powerset(empty_set))),
inference(superposition,[status(thm)],[c_132,c_5716]) ).
tcf(c_5735,plain,
! [X0: $i] : ~ in(set_union2(powerset(empty_set),X0),empty_set),
inference(superposition,[status(thm)],[c_5716,c_124]) ).
tcf(c_5736,plain,
! [X0: $i] : ~ empty(set_union2(powerset(empty_set),X0)),
inference(superposition,[status(thm)],[c_5716,c_184]) ).
tcf(c_5743,plain,
! [X0: $i] : ~ in(set_union2(X0,powerset(empty_set)),empty_set),
inference(superposition,[status(thm)],[c_5734,c_124]) ).
tcf(c_5744,plain,
! [X0: $i] : ~ empty(set_union2(X0,powerset(empty_set))),
inference(superposition,[status(thm)],[c_5734,c_184]) ).
tcf(c_5761,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(sK14(X0,X1,empty_set),sK14(X0,X1,empty_set)),set_union2(X2,sK13(X0,X1,empty_set)))
| ( cartesian_product2(X0,X1) = empty_set ) ),
inference(superposition,[status(thm)],[c_5229,c_5626]) ).
tcf(c_5762,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(sK16(X0,X1,sK5(cartesian_product2(X0,X1))),sK16(X0,X1,sK5(cartesian_product2(X0,X1)))),set_union2(X2,sK5(cartesian_product2(X0,X1))))
| ( cartesian_product2(X0,X1) = empty_set ) ),
inference(superposition,[status(thm)],[c_5462,c_5626]) ).
tcf(c_5763,plain,
! [X0: $i,X1: $i,X2: $i] : ~ in(set_union2(X0,unordered_pair(X1,X2)),X1),
inference(superposition,[status(thm)],[c_5626,c_124]) ).
tcf(c_5764,plain,
! [X0: $i,X1: $i,X2: $i] : ~ empty(set_union2(X0,unordered_pair(X1,X2))),
inference(superposition,[status(thm)],[c_5626,c_184]) ).
tcf(c_5780,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(sK14(X0,X1,empty_set),sK15(X0,X1,empty_set)),set_union2(sK13(X0,X1,empty_set),X2))
| ( cartesian_product2(X0,X1) = empty_set ) ),
inference(superposition,[status(thm)],[c_5229,c_5654]) ).
tcf(c_5781,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(sK16(X0,X1,sK5(cartesian_product2(X0,X1))),sK17(X0,X1,sK5(cartesian_product2(X0,X1)))),set_union2(sK5(cartesian_product2(X0,X1)),X2))
| ( cartesian_product2(X0,X1) = empty_set ) ),
inference(superposition,[status(thm)],[c_5462,c_5654]) ).
tcf(c_5782,plain,
! [X0: $i,X1: $i,X2: $i] : ~ in(set_union2(unordered_pair(X0,X1),X2),X1),
inference(superposition,[status(thm)],[c_5654,c_124]) ).
tcf(c_5797,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(sK14(X0,X1,empty_set),sK15(X0,X1,empty_set)),set_union2(X2,sK13(X0,X1,empty_set)))
| ( cartesian_product2(X0,X1) = empty_set ) ),
inference(superposition,[status(thm)],[c_5229,c_5656]) ).
tcf(c_5798,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(sK16(X0,X1,sK5(cartesian_product2(X0,X1))),sK17(X0,X1,sK5(cartesian_product2(X0,X1)))),set_union2(X2,sK5(cartesian_product2(X0,X1))))
| ( cartesian_product2(X0,X1) = empty_set ) ),
inference(superposition,[status(thm)],[c_5462,c_5656]) ).
tcf(c_5799,plain,
! [X0: $i,X1: $i,X2: $i] : ~ in(set_union2(X0,unordered_pair(X1,X2)),X2),
inference(superposition,[status(thm)],[c_5656,c_124]) ).
tcf(c_5807,plain,
! [X0: $i,X1: $i,X2: $i] : ~ in(powerset(set_union2(set_union2(X0,X1),X2)),X0),
inference(superposition,[status(thm)],[c_129,c_5695]) ).
tcf(c_5808,plain,
! [X0: $i,X1: $i] : ~ subset(powerset(set_union2(powerset(X0),X1)),X0),
inference(superposition,[status(thm)],[c_178,c_5695]) ).
tcf(c_5812,plain,
! [X0: $i,X1: $i] : ~ in(powerset(set_union2(X0,X1)),X1),
inference(superposition,[status(thm)],[c_132,c_5695]) ).
tcf(c_5813,plain,
! [X0: $i] : ~ in(powerset(X0),empty_set),
inference(superposition,[status(thm)],[c_5426,c_5695]) ).
tcf(c_5823,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( cartesian_product2(X0,X1) = empty_set )
| ~ empty(set_union2(sK13(X0,X1,empty_set),X2)) ),
inference(superposition,[status(thm)],[c_5229,c_5721]) ).
tcf(c_5824,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( cartesian_product2(X0,X1) = empty_set )
| ~ empty(set_union2(sK5(cartesian_product2(X0,X1)),X2)) ),
inference(superposition,[status(thm)],[c_5462,c_5721]) ).
tcf(c_5838,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( cartesian_product2(X1,X2) = empty_set )
| ~ empty(set_union2(X0,sK13(X1,X2,empty_set))) ),
inference(superposition,[status(thm)],[c_5229,c_5764]) ).
tcf(c_5839,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( cartesian_product2(X1,X2) = empty_set )
| ~ empty(set_union2(X0,sK5(cartesian_product2(X1,X2)))) ),
inference(superposition,[status(thm)],[c_5462,c_5764]) ).
tcf(c_5849,plain,
! [X0: $i,X1: $i,X2: $i] : ~ in(powerset(set_union2(X0,set_union2(X1,X2))),X1),
inference(superposition,[status(thm)],[c_129,c_5812]) ).
tcf(c_5850,plain,
! [X0: $i,X1: $i] : ~ subset(powerset(set_union2(X0,powerset(X1))),X1),
inference(superposition,[status(thm)],[c_178,c_5812]) ).
tcf(c_5866,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X0,X1) = cartesian_product2(X2,X3) )
| ( unordered_pair(unordered_pair(sK14(X0,X1,cartesian_product2(X2,X3)),sK14(X0,X1,cartesian_product2(X2,X3))),unordered_pair(sK14(X0,X1,cartesian_product2(X2,X3)),sK15(X0,X1,cartesian_product2(X2,X3)))) = sK13(X0,X1,cartesian_product2(X2,X3)) )
| ~ empty(set_union2(sK13(X0,X1,cartesian_product2(X2,X3)),X4)) ),
inference(superposition,[status(thm)],[c_5464,c_5721]) ).
tcf(c_5867,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(unordered_pair(sK16(X2,X3,sK13(X0,X1,cartesian_product2(X2,X3))),sK16(X2,X3,sK13(X0,X1,cartesian_product2(X2,X3)))),set_union2(sK13(X0,X1,cartesian_product2(X2,X3)),X4))
| ( cartesian_product2(X0,X1) = cartesian_product2(X2,X3) )
| ( unordered_pair(unordered_pair(sK14(X0,X1,cartesian_product2(X2,X3)),sK14(X0,X1,cartesian_product2(X2,X3))),unordered_pair(sK14(X0,X1,cartesian_product2(X2,X3)),sK15(X0,X1,cartesian_product2(X2,X3)))) = sK13(X0,X1,cartesian_product2(X2,X3)) ) ),
inference(superposition,[status(thm)],[c_5464,c_5624]) ).
tcf(c_5868,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(unordered_pair(sK16(X2,X3,sK13(X0,X1,cartesian_product2(X2,X3))),sK17(X2,X3,sK13(X0,X1,cartesian_product2(X2,X3)))),X4)
| ( cartesian_product2(X0,X1) = cartesian_product2(X2,X3) )
| ( unordered_pair(unordered_pair(sK14(X0,X1,cartesian_product2(X2,X3)),sK14(X0,X1,cartesian_product2(X2,X3))),unordered_pair(sK14(X0,X1,cartesian_product2(X2,X3)),sK15(X0,X1,cartesian_product2(X2,X3)))) = sK13(X0,X1,cartesian_product2(X2,X3)) )
| ~ subset(sK13(X0,X1,cartesian_product2(X2,X3)),X4) ),
inference(superposition,[status(thm)],[c_5464,c_84]) ).
tcf(c_5869,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(unordered_pair(sK16(X2,X3,sK13(X0,X1,cartesian_product2(X2,X3))),sK16(X2,X3,sK13(X0,X1,cartesian_product2(X2,X3)))),X4)
| ( cartesian_product2(X0,X1) = cartesian_product2(X2,X3) )
| ( unordered_pair(unordered_pair(sK14(X0,X1,cartesian_product2(X2,X3)),sK14(X0,X1,cartesian_product2(X2,X3))),unordered_pair(sK14(X0,X1,cartesian_product2(X2,X3)),sK15(X0,X1,cartesian_product2(X2,X3)))) = sK13(X0,X1,cartesian_product2(X2,X3)) )
| ~ subset(sK13(X0,X1,cartesian_product2(X2,X3)),X4) ),
inference(superposition,[status(thm)],[c_5464,c_83]) ).
tcf(c_5870,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( cartesian_product2(X0,X1) = cartesian_product2(X2,X3) )
| ( unordered_pair(unordered_pair(sK14(X0,X1,cartesian_product2(X2,X3)),sK14(X0,X1,cartesian_product2(X2,X3))),unordered_pair(sK14(X0,X1,cartesian_product2(X2,X3)),sK15(X0,X1,cartesian_product2(X2,X3)))) = sK13(X0,X1,cartesian_product2(X2,X3)) )
| ~ in(sK13(X0,X1,cartesian_product2(X2,X3)),unordered_pair(sK16(X2,X3,sK13(X0,X1,cartesian_product2(X2,X3))),sK17(X2,X3,sK13(X0,X1,cartesian_product2(X2,X3))))) ),
inference(superposition,[status(thm)],[c_5464,c_5374]) ).
tcf(c_5871,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( cartesian_product2(X0,X1) = cartesian_product2(X2,X3) )
| ( unordered_pair(unordered_pair(sK14(X0,X1,cartesian_product2(X2,X3)),sK14(X0,X1,cartesian_product2(X2,X3))),unordered_pair(sK14(X0,X1,cartesian_product2(X2,X3)),sK15(X0,X1,cartesian_product2(X2,X3)))) = sK13(X0,X1,cartesian_product2(X2,X3)) )
| ~ in(sK13(X0,X1,cartesian_product2(X2,X3)),unordered_pair(sK16(X2,X3,sK13(X0,X1,cartesian_product2(X2,X3))),sK16(X2,X3,sK13(X0,X1,cartesian_product2(X2,X3))))) ),
inference(superposition,[status(thm)],[c_5464,c_5373]) ).
tcf(c_5872,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( cartesian_product2(X0,X1) = cartesian_product2(X2,X3) )
| ( unordered_pair(unordered_pair(sK14(X0,X1,cartesian_product2(X2,X3)),sK14(X0,X1,cartesian_product2(X2,X3))),unordered_pair(sK14(X0,X1,cartesian_product2(X2,X3)),sK15(X0,X1,cartesian_product2(X2,X3)))) = sK13(X0,X1,cartesian_product2(X2,X3)) )
| ~ empty(sK13(X0,X1,cartesian_product2(X2,X3))) ),
inference(superposition,[status(thm)],[c_5464,c_5218]) ).
tcf(c_5873,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(sK16(X2,X3,sK13(X0,X1,cartesian_product2(X2,X3))),sK16(X2,X3,sK13(X0,X1,cartesian_product2(X2,X3)))),sK13(X0,X1,cartesian_product2(X2,X3)))
| ( cartesian_product2(X0,X1) = cartesian_product2(X2,X3) )
| ( unordered_pair(unordered_pair(sK14(X0,X1,cartesian_product2(X2,X3)),sK14(X0,X1,cartesian_product2(X2,X3))),unordered_pair(sK14(X0,X1,cartesian_product2(X2,X3)),sK15(X0,X1,cartesian_product2(X2,X3)))) = sK13(X0,X1,cartesian_product2(X2,X3)) ) ),
inference(superposition,[status(thm)],[c_5464,c_164]) ).
tcf(c_5874,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(unordered_pair(sK16(X2,X3,sK13(X0,X1,cartesian_product2(X2,X3))),sK16(X2,X3,sK13(X0,X1,cartesian_product2(X2,X3)))),set_union2(X4,sK13(X0,X1,cartesian_product2(X2,X3))))
| ( cartesian_product2(X0,X1) = cartesian_product2(X2,X3) )
| ( unordered_pair(unordered_pair(sK14(X0,X1,cartesian_product2(X2,X3)),sK14(X0,X1,cartesian_product2(X2,X3))),unordered_pair(sK14(X0,X1,cartesian_product2(X2,X3)),sK15(X0,X1,cartesian_product2(X2,X3)))) = sK13(X0,X1,cartesian_product2(X2,X3)) ) ),
inference(superposition,[status(thm)],[c_5464,c_5626]) ).
tcf(c_5875,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X1,X2) = cartesian_product2(X3,X4) )
| ( unordered_pair(unordered_pair(sK14(X1,X2,cartesian_product2(X3,X4)),sK14(X1,X2,cartesian_product2(X3,X4))),unordered_pair(sK14(X1,X2,cartesian_product2(X3,X4)),sK15(X1,X2,cartesian_product2(X3,X4)))) = sK13(X1,X2,cartesian_product2(X3,X4)) )
| ~ empty(set_union2(X0,sK13(X1,X2,cartesian_product2(X3,X4)))) ),
inference(superposition,[status(thm)],[c_5464,c_5764]) ).
tcf(c_5876,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(unordered_pair(sK16(X2,X3,sK13(X0,X1,cartesian_product2(X2,X3))),sK17(X2,X3,sK13(X0,X1,cartesian_product2(X2,X3)))),set_union2(sK13(X0,X1,cartesian_product2(X2,X3)),X4))
| ( cartesian_product2(X0,X1) = cartesian_product2(X2,X3) )
| ( unordered_pair(unordered_pair(sK14(X0,X1,cartesian_product2(X2,X3)),sK14(X0,X1,cartesian_product2(X2,X3))),unordered_pair(sK14(X0,X1,cartesian_product2(X2,X3)),sK15(X0,X1,cartesian_product2(X2,X3)))) = sK13(X0,X1,cartesian_product2(X2,X3)) ) ),
inference(superposition,[status(thm)],[c_5464,c_5654]) ).
tcf(c_5877,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(sK16(X2,X3,sK13(X0,X1,cartesian_product2(X2,X3))),sK17(X2,X3,sK13(X0,X1,cartesian_product2(X2,X3)))),sK13(X0,X1,cartesian_product2(X2,X3)))
| ( cartesian_product2(X0,X1) = cartesian_product2(X2,X3) )
| ( unordered_pair(unordered_pair(sK14(X0,X1,cartesian_product2(X2,X3)),sK14(X0,X1,cartesian_product2(X2,X3))),unordered_pair(sK14(X0,X1,cartesian_product2(X2,X3)),sK15(X0,X1,cartesian_product2(X2,X3)))) = sK13(X0,X1,cartesian_product2(X2,X3)) ) ),
inference(superposition,[status(thm)],[c_5464,c_165]) ).
tcf(c_5878,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(unordered_pair(sK16(X2,X3,sK13(X0,X1,cartesian_product2(X2,X3))),sK17(X2,X3,sK13(X0,X1,cartesian_product2(X2,X3)))),set_union2(X4,sK13(X0,X1,cartesian_product2(X2,X3))))
| ( cartesian_product2(X0,X1) = cartesian_product2(X2,X3) )
| ( unordered_pair(unordered_pair(sK14(X0,X1,cartesian_product2(X2,X3)),sK14(X0,X1,cartesian_product2(X2,X3))),unordered_pair(sK14(X0,X1,cartesian_product2(X2,X3)),sK15(X0,X1,cartesian_product2(X2,X3)))) = sK13(X0,X1,cartesian_product2(X2,X3)) ) ),
inference(superposition,[status(thm)],[c_5464,c_5656]) ).
tcf(c_5953,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(X2,X1)
| ~ in(set_union2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_130,c_124]) ).
tcf(c_5954,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(X2,X1)
| ~ empty(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_130,c_184]) ).
tcf(c_5955,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,set_union2(X1,X2))
| ~ in(sK7(X0,set_union2(X1,X2)),X2) ),
inference(superposition,[status(thm)],[c_130,c_121]) ).
tcf(c_5956,plain,
! [X0: $i,X1: $i,X2: $i] : ~ in(unordered_pair(set_union2(X0,X1),X2),X1),
inference(superposition,[status(thm)],[c_130,c_5373]) ).
tcf(c_5957,plain,
! [X0: $i,X1: $i,X2: $i] : ~ in(unordered_pair(X0,set_union2(X1,X2)),X2),
inference(superposition,[status(thm)],[c_130,c_5374]) ).
tcf(c_5959,plain,
! [X0: $i,X1: $i,X2: $i] : ~ in(unordered_pair(powerset(union(set_union2(X0,X1))),X2),X1),
inference(superposition,[status(thm)],[c_130,c_5540]) ).
tcf(c_5960,plain,
! [X0: $i,X1: $i] : ~ in(powerset(powerset(union(set_union2(X0,X1)))),X1),
inference(superposition,[status(thm)],[c_130,c_5548]) ).
tcf(c_5961,plain,
! [X0: $i,X1: $i,X2: $i] : ~ in(unordered_pair(X0,powerset(union(set_union2(X1,X2)))),X2),
inference(superposition,[status(thm)],[c_130,c_5553]) ).
tcf(c_5962,plain,
! [X0: $i,X1: $i,X2: $i] : ~ in(powerset(set_union2(set_union2(X0,X1),X2)),X1),
inference(superposition,[status(thm)],[c_130,c_5695]) ).
tcf(c_5963,plain,
! [X0: $i,X1: $i,X2: $i] : ~ in(powerset(set_union2(X0,set_union2(X1,X2))),X2),
inference(superposition,[status(thm)],[c_130,c_5812]) ).
tcf(c_5983,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(set_difference(X0,X1),X2)
| in(sK0(set_difference(X0,X1),X2),X0) ),
inference(superposition,[status(thm)],[c_89,c_144]) ).
tcf(c_5984,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(X0,set_difference(X1,X2))
| in(sK0(X0,set_difference(X1,X2)),X1) ),
inference(superposition,[status(thm)],[c_90,c_144]) ).
tcf(c_5985,plain,
! [X0: $i,X1: $i] :
( in(sK5(set_difference(X0,X1)),X0)
| ( set_difference(X0,X1) = empty_set ) ),
inference(superposition,[status(thm)],[c_117,c_144]) ).
tcf(c_5986,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(X0,X1),X2)
| in(sK7(set_difference(X0,X1),X2),X0) ),
inference(superposition,[status(thm)],[c_122,c_144]) ).
tcf(c_5987,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK13(X0,X1,set_difference(X2,X3)),X2)
| ( set_difference(X2,X3) = cartesian_product2(X0,X1) )
| ( unordered_pair(unordered_pair(sK14(X0,X1,set_difference(X2,X3)),sK14(X0,X1,set_difference(X2,X3))),unordered_pair(sK14(X0,X1,set_difference(X2,X3)),sK15(X0,X1,set_difference(X2,X3)))) = sK13(X0,X1,set_difference(X2,X3)) ) ),
inference(superposition,[status(thm)],[c_1706,c_144]) ).
tcf(c_6014,plain,
! [X0: $i,X1: $i] :
( ~ in(X0,X1)
| ~ empty(unordered_pair(X0,X0)) ),
inference(superposition,[status(thm)],[c_5289,c_51]) ).
tcf(c_6017,plain,
! [X0: $i,X1: $i] :
( in(X1,unordered_pair(X0,X0))
| ~ in(X0,unordered_pair(X1,X1)) ),
inference(superposition,[status(thm)],[c_5260,c_51]) ).
tcf(c_6018,plain,
! [X0: $i] :
( in(empty_set,unordered_pair(X0,X0))
| ~ in(X0,powerset(empty_set)) ),
inference(superposition,[status(thm)],[c_5272,c_51]) ).
tcf(c_6019,plain,
! [X0: $i] :
( ~ in(empty_set,X0)
| ~ disjoint(powerset(empty_set),X0) ),
inference(superposition,[status(thm)],[c_70,c_51]) ).
tcf(c_6030,plain,
! [X0: $i] : ~ empty(powerset(powerset(union(powerset(X0))))),
inference(superposition,[status(thm)],[c_5360,c_5557]) ).
tcf(c_6031,plain,
! [X0: $i] : ~ in(powerset(powerset(union(powerset(union(X0))))),X0),
inference(superposition,[status(thm)],[c_61,c_5557]) ).
tcf(c_6039,plain,
! [X0: $i] :
( in(empty_set,X0)
| ~ empty(powerset(empty_set)) ),
inference(superposition,[status(thm)],[c_5360,c_5628]) ).
tcf(c_6040,plain,
! [X0: $i] :
( in(empty_set,union(X0))
| ~ in(powerset(empty_set),X0) ),
inference(superposition,[status(thm)],[c_61,c_5628]) ).
tcf(c_6048,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : ~ in(unordered_pair(set_union2(set_union2(X0,X1),X2),X3),X0),
inference(superposition,[status(thm)],[c_129,c_5693]) ).
tcf(c_6049,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : ~ in(unordered_pair(set_union2(set_union2(X0,X1),X2),X3),X1),
inference(superposition,[status(thm)],[c_130,c_5693]) ).
tcf(c_6050,plain,
! [X0: $i,X1: $i,X2: $i] : ~ subset(unordered_pair(set_union2(powerset(X0),X1),X2),X0),
inference(superposition,[status(thm)],[c_178,c_5693]) ).
tcf(c_6057,plain,
! [X0: $i,X1: $i] : ~ in(unordered_pair(X0,X1),empty_set),
inference(superposition,[status(thm)],[c_5426,c_5693]) ).
tcf(c_6063,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : ~ in(unordered_pair(X0,set_union2(set_union2(X1,X2),X3)),X1),
inference(superposition,[status(thm)],[c_129,c_5694]) ).
tcf(c_6064,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : ~ in(unordered_pair(X0,set_union2(set_union2(X1,X2),X3)),X2),
inference(superposition,[status(thm)],[c_130,c_5694]) ).
tcf(c_6065,plain,
! [X0: $i,X1: $i,X2: $i] : ~ subset(unordered_pair(X0,set_union2(powerset(X1),X2)),X1),
inference(superposition,[status(thm)],[c_178,c_5694]) ).
tcf(c_6079,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : ~ in(set_union2(unordered_pair(set_union2(X0,X1),X2),X3),X0),
inference(superposition,[status(thm)],[c_129,c_5720]) ).
tcf(c_6080,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : ~ in(set_union2(unordered_pair(set_union2(X0,X1),X2),X3),X1),
inference(superposition,[status(thm)],[c_130,c_5720]) ).
tcf(c_6081,plain,
! [X0: $i,X1: $i,X2: $i] : ~ subset(set_union2(unordered_pair(powerset(X0),X1),X2),X0),
inference(superposition,[status(thm)],[c_178,c_5720]) ).
tcf(c_6089,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( cartesian_product2(X0,X1) = empty_set )
| ~ in(set_union2(sK13(X0,X1,empty_set),X2),unordered_pair(sK14(X0,X1,empty_set),sK14(X0,X1,empty_set))) ),
inference(superposition,[status(thm)],[c_5229,c_5720]) ).
tcf(c_6090,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( cartesian_product2(X0,X1) = empty_set )
| ~ in(set_union2(sK5(cartesian_product2(X0,X1)),X2),unordered_pair(sK16(X0,X1,sK5(cartesian_product2(X0,X1))),sK16(X0,X1,sK5(cartesian_product2(X0,X1))))) ),
inference(superposition,[status(thm)],[c_5462,c_5720]) ).
tcf(c_6091,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X0,X1) = cartesian_product2(X2,X3) )
| ( unordered_pair(unordered_pair(sK14(X0,X1,cartesian_product2(X2,X3)),sK14(X0,X1,cartesian_product2(X2,X3))),unordered_pair(sK14(X0,X1,cartesian_product2(X2,X3)),sK15(X0,X1,cartesian_product2(X2,X3)))) = sK13(X0,X1,cartesian_product2(X2,X3)) )
| ~ in(set_union2(sK13(X0,X1,cartesian_product2(X2,X3)),X4),unordered_pair(sK16(X2,X3,sK13(X0,X1,cartesian_product2(X2,X3))),sK16(X2,X3,sK13(X0,X1,cartesian_product2(X2,X3))))) ),
inference(superposition,[status(thm)],[c_5464,c_5720]) ).
tcf(c_6110,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : ~ in(set_union2(X0,unordered_pair(set_union2(X1,X2),X3)),X1),
inference(superposition,[status(thm)],[c_129,c_5763]) ).
tcf(c_6111,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : ~ in(set_union2(X0,unordered_pair(set_union2(X1,X2),X3)),X2),
inference(superposition,[status(thm)],[c_130,c_5763]) ).
tcf(c_6112,plain,
! [X0: $i,X1: $i,X2: $i] : ~ subset(set_union2(X0,unordered_pair(powerset(X1),X2)),X1),
inference(superposition,[status(thm)],[c_178,c_5763]) ).
tcf(c_6120,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( cartesian_product2(X1,X2) = empty_set )
| ~ in(set_union2(X0,sK13(X1,X2,empty_set)),unordered_pair(sK14(X1,X2,empty_set),sK14(X1,X2,empty_set))) ),
inference(superposition,[status(thm)],[c_5229,c_5763]) ).
tcf(c_6121,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( cartesian_product2(X1,X2) = empty_set )
| ~ in(set_union2(X0,sK5(cartesian_product2(X1,X2))),unordered_pair(sK16(X1,X2,sK5(cartesian_product2(X1,X2))),sK16(X1,X2,sK5(cartesian_product2(X1,X2))))) ),
inference(superposition,[status(thm)],[c_5462,c_5763]) ).
tcf(c_6122,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X1,X2) = cartesian_product2(X3,X4) )
| ( unordered_pair(unordered_pair(sK14(X1,X2,cartesian_product2(X3,X4)),sK14(X1,X2,cartesian_product2(X3,X4))),unordered_pair(sK14(X1,X2,cartesian_product2(X3,X4)),sK15(X1,X2,cartesian_product2(X3,X4)))) = sK13(X1,X2,cartesian_product2(X3,X4)) )
| ~ in(set_union2(X0,sK13(X1,X2,cartesian_product2(X3,X4))),unordered_pair(sK16(X3,X4,sK13(X1,X2,cartesian_product2(X3,X4))),sK16(X3,X4,sK13(X1,X2,cartesian_product2(X3,X4))))) ),
inference(superposition,[status(thm)],[c_5464,c_5763]) ).
tcf(c_6138,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : ~ in(set_union2(unordered_pair(X0,set_union2(X1,X2)),X3),X1),
inference(superposition,[status(thm)],[c_129,c_5782]) ).
tcf(c_6139,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : ~ in(set_union2(unordered_pair(X0,set_union2(X1,X2)),X3),X2),
inference(superposition,[status(thm)],[c_130,c_5782]) ).
tcf(c_6140,plain,
! [X0: $i,X1: $i,X2: $i] : ~ subset(set_union2(unordered_pair(X0,powerset(X1)),X2),X1),
inference(superposition,[status(thm)],[c_178,c_5782]) ).
tcf(c_6148,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( cartesian_product2(X0,X1) = empty_set )
| ~ in(set_union2(sK13(X0,X1,empty_set),X2),unordered_pair(sK14(X0,X1,empty_set),sK15(X0,X1,empty_set))) ),
inference(superposition,[status(thm)],[c_5229,c_5782]) ).
tcf(c_6149,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( cartesian_product2(X0,X1) = empty_set )
| ~ in(set_union2(sK5(cartesian_product2(X0,X1)),X2),unordered_pair(sK16(X0,X1,sK5(cartesian_product2(X0,X1))),sK17(X0,X1,sK5(cartesian_product2(X0,X1))))) ),
inference(superposition,[status(thm)],[c_5462,c_5782]) ).
tcf(c_6150,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X0,X1) = cartesian_product2(X2,X3) )
| ( unordered_pair(unordered_pair(sK14(X0,X1,cartesian_product2(X2,X3)),sK14(X0,X1,cartesian_product2(X2,X3))),unordered_pair(sK14(X0,X1,cartesian_product2(X2,X3)),sK15(X0,X1,cartesian_product2(X2,X3)))) = sK13(X0,X1,cartesian_product2(X2,X3)) )
| ~ in(set_union2(sK13(X0,X1,cartesian_product2(X2,X3)),X4),unordered_pair(sK16(X2,X3,sK13(X0,X1,cartesian_product2(X2,X3))),sK17(X2,X3,sK13(X0,X1,cartesian_product2(X2,X3))))) ),
inference(superposition,[status(thm)],[c_5464,c_5782]) ).
tcf(c_6171,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : ~ in(set_union2(X0,unordered_pair(X1,set_union2(X2,X3))),X2),
inference(superposition,[status(thm)],[c_129,c_5799]) ).
tcf(c_6172,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : ~ in(set_union2(X0,unordered_pair(X1,set_union2(X2,X3))),X3),
inference(superposition,[status(thm)],[c_130,c_5799]) ).
tcf(c_6173,plain,
! [X0: $i,X1: $i,X2: $i] : ~ subset(set_union2(X0,unordered_pair(X1,powerset(X2))),X2),
inference(superposition,[status(thm)],[c_178,c_5799]) ).
tcf(c_6181,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( cartesian_product2(X1,X2) = empty_set )
| ~ in(set_union2(X0,sK13(X1,X2,empty_set)),unordered_pair(sK14(X1,X2,empty_set),sK15(X1,X2,empty_set))) ),
inference(superposition,[status(thm)],[c_5229,c_5799]) ).
tcf(c_6182,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( cartesian_product2(X1,X2) = empty_set )
| ~ in(set_union2(X0,sK5(cartesian_product2(X1,X2))),unordered_pair(sK16(X1,X2,sK5(cartesian_product2(X1,X2))),sK17(X1,X2,sK5(cartesian_product2(X1,X2))))) ),
inference(superposition,[status(thm)],[c_5462,c_5799]) ).
tcf(c_6183,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X1,X2) = cartesian_product2(X3,X4) )
| ( unordered_pair(unordered_pair(sK14(X1,X2,cartesian_product2(X3,X4)),sK14(X1,X2,cartesian_product2(X3,X4))),unordered_pair(sK14(X1,X2,cartesian_product2(X3,X4)),sK15(X1,X2,cartesian_product2(X3,X4)))) = sK13(X1,X2,cartesian_product2(X3,X4)) )
| ~ in(set_union2(X0,sK13(X1,X2,cartesian_product2(X3,X4))),unordered_pair(sK16(X3,X4,sK13(X1,X2,cartesian_product2(X3,X4))),sK17(X3,X4,sK13(X1,X2,cartesian_product2(X3,X4))))) ),
inference(superposition,[status(thm)],[c_5464,c_5799]) ).
tcf(c_6201,plain,
! [X0: $i,X1: $i] : ~ empty(powerset(set_union2(powerset(X0),X1))),
inference(superposition,[status(thm)],[c_5360,c_5808]) ).
tcf(c_6202,plain,
! [X0: $i,X1: $i] : ~ in(powerset(set_union2(powerset(union(X0)),X1)),X0),
inference(superposition,[status(thm)],[c_61,c_5808]) ).
tcf(c_6208,plain,
! [X0: $i,X1: $i] : ~ empty(powerset(set_union2(X0,powerset(X1)))),
inference(superposition,[status(thm)],[c_5360,c_5850]) ).
tcf(c_6209,plain,
! [X0: $i,X1: $i] : ~ in(powerset(set_union2(X0,powerset(union(X1)))),X1),
inference(superposition,[status(thm)],[c_61,c_5850]) ).
tcf(c_6215,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : ~ in(unordered_pair(set_union2(X0,set_union2(X1,X2)),X3),X1),
inference(superposition,[status(thm)],[c_129,c_5956]) ).
tcf(c_6216,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : ~ in(unordered_pair(set_union2(X0,set_union2(X1,X2)),X3),X2),
inference(superposition,[status(thm)],[c_130,c_5956]) ).
tcf(c_6217,plain,
! [X0: $i,X1: $i,X2: $i] : ~ subset(unordered_pair(set_union2(X0,powerset(X1)),X2),X1),
inference(superposition,[status(thm)],[c_178,c_5956]) ).
tcf(c_6230,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : ~ in(unordered_pair(X0,set_union2(X1,set_union2(X2,X3))),X2),
inference(superposition,[status(thm)],[c_129,c_5957]) ).
tcf(c_6231,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : ~ in(unordered_pair(X0,set_union2(X1,set_union2(X2,X3))),X3),
inference(superposition,[status(thm)],[c_130,c_5957]) ).
tcf(c_6232,plain,
! [X0: $i,X1: $i,X2: $i] : ~ subset(unordered_pair(X0,set_union2(X1,powerset(X2))),X2),
inference(superposition,[status(thm)],[c_178,c_5957]) ).
tcf(c_6261,plain,
! [X0: $i,X1: $i] :
( ( set_union2(X0,X1) = X1 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5360,c_66]) ).
tcf(c_6262,plain,
! [X0: $i,X1: $i] :
( ( set_union2(X0,union(X1)) = union(X1) )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_61,c_66]) ).
tcf(c_6264,plain,
! [X0: $i,X1: $i] : set_union2(set_difference(X0,X1),X0) = X0,
inference(superposition,[status(thm)],[c_77,c_66]) ).
tcf(c_6265,plain,
! [X0: $i,X1: $i] : set_union2(X0,set_union2(X0,X1)) = set_union2(X0,X1),
inference(superposition,[status(thm)],[c_103,c_66]) ).
tcf(c_6267,plain,
! [X0: $i,X1: $i] : set_union2(X0,set_union2(X1,X0)) = set_union2(X1,X0),
inference(superposition,[status(thm)],[c_5425,c_66]) ).
tcf(c_6268,plain,
! [X0: $i] :
( ( set_union2(powerset(empty_set),X0) = X0 )
| ~ in(empty_set,X0) ),
inference(superposition,[status(thm)],[c_5531,c_66]) ).
tcf(c_6286,plain,
! [X0: $i,X1: $i] :
( ( set_difference(unordered_pair(X0,X0),X1) = empty_set )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_80,c_78]) ).
tcf(c_6287,plain,
! [X0: $i,X1: $i] :
( ( set_difference(X0,X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5360,c_78]) ).
tcf(c_6288,plain,
! [X0: $i,X1: $i] :
( ( set_difference(X0,union(X1)) = empty_set )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_61,c_78]) ).
tcf(c_6290,plain,
! [X0: $i,X1: $i] : set_difference(set_difference(X0,X1),X0) = empty_set,
inference(superposition,[status(thm)],[c_77,c_78]) ).
tcf(c_6291,plain,
! [X0: $i,X1: $i] : set_difference(X0,set_union2(X0,X1)) = empty_set,
inference(superposition,[status(thm)],[c_103,c_78]) ).
tcf(c_6293,plain,
! [X0: $i,X1: $i] : set_difference(X0,set_union2(X1,X0)) = empty_set,
inference(superposition,[status(thm)],[c_5425,c_78]) ).
tcf(c_6294,plain,
! [X0: $i] :
( ( set_difference(powerset(empty_set),X0) = empty_set )
| ~ in(empty_set,X0) ),
inference(superposition,[status(thm)],[c_5531,c_78]) ).
tcf(c_6315,plain,
! [X0: $i] :
( subset(X0,empty_set)
| ( X0 != empty_set ) ),
inference(superposition,[status(thm)],[c_114,c_79]) ).
tcf(c_6320,plain,
! [X0: $i] : set_union2(X0,X0) = set_union2(X0,empty_set),
inference(superposition,[status(thm)],[c_1252,c_85]) ).
tcf(c_6321,plain,
! [X0: $i,X1: $i,X2: $i] : ~ in(unordered_pair(set_union2(X0,X1),X2),set_difference(X1,X0)),
inference(superposition,[status(thm)],[c_85,c_5956]) ).
tcf(c_6323,plain,
! [X0: $i,X1: $i] : ~ in(powerset(set_union2(X0,X1)),set_difference(X1,X0)),
inference(superposition,[status(thm)],[c_85,c_5812]) ).
tcf(c_6325,plain,
! [X0: $i,X1: $i] : ~ proper_subset(set_union2(X0,X1),set_difference(X1,X0)),
inference(superposition,[status(thm)],[c_85,c_5422]) ).
tcf(c_6328,plain,
! [X0: $i,X1: $i] :
( empty(set_difference(X1,X0))
| ~ empty(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_85,c_188]) ).
tcf(c_6330,plain,
! [X0: $i,X1: $i,X2: $i] : ~ in(unordered_pair(X0,set_union2(X1,X2)),set_difference(X2,X1)),
inference(superposition,[status(thm)],[c_85,c_5957]) ).
tcf(c_6333,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,set_union2(X2,X1))
| ~ in(X0,set_difference(X1,X2)) ),
inference(superposition,[status(thm)],[c_85,c_130]) ).
tcf(c_6334,plain,
! [X0: $i,X1: $i] : subset(set_difference(X0,X1),set_union2(X1,X0)),
inference(superposition,[status(thm)],[c_85,c_5425]) ).
tcf(c_6335,plain,
! [X0: $i] : set_union2(empty_set,X0) = set_difference(X0,empty_set),
inference(superposition,[status(thm)],[c_85,c_5426]) ).
tcf(c_6365,plain,
! [X0: $i] : subset(empty_set,set_union2(X0,empty_set)),
inference(superposition,[status(thm)],[c_113,c_6334]) ).
tcf(c_6366,plain,
! [X0: $i] : subset(X0,set_union2(empty_set,X0)),
inference(superposition,[status(thm)],[c_114,c_6334]) ).
tcf(c_6367,plain,
! [X0: $i] : subset(empty_set,set_union2(X0,X0)),
inference(superposition,[status(thm)],[c_1252,c_6334]) ).
tcf(c_6369,plain,
! [X0: $i,X1: $i] : subset(set_difference(set_difference(X0,X1),X1),set_union2(X1,X0)),
inference(superposition,[status(thm)],[c_85,c_6334]) ).
tcf(c_6370,plain,
! [X0: $i] : subset(set_difference(empty_set,X0),X0),
inference(superposition,[status(thm)],[c_116,c_6334]) ).
tcf(c_6371,plain,
! [X0: $i] : subset(set_difference(X0,X0),X0),
inference(superposition,[status(thm)],[c_125,c_6334]) ).
tcf(c_6372,plain,
! [X0: $i,X1: $i] : subset(set_difference(X0,X1),set_union2(X0,X1)),
inference(superposition,[status(thm)],[c_132,c_6334]) ).
tcf(c_6373,plain,
! [X0: $i] : subset(set_difference(X0,empty_set),X0),
inference(superposition,[status(thm)],[c_5426,c_6334]) ).
tcf(c_6374,plain,
! [X0: $i,X1: $i] : set_difference(set_difference(X0,X1),set_union2(X1,X0)) = empty_set,
inference(superposition,[status(thm)],[c_6334,c_78]) ).
tcf(c_6375,plain,
! [X0: $i,X1: $i] : set_union2(set_difference(X0,X1),set_union2(X1,X0)) = set_union2(X1,X0),
inference(superposition,[status(thm)],[c_6334,c_66]) ).
tcf(c_6392,plain,
! [X0: $i] : subset(empty_set,set_union2(empty_set,X0)),
inference(superposition,[status(thm)],[c_113,c_6372]) ).
tcf(c_6393,plain,
! [X0: $i] : subset(X0,set_union2(X0,empty_set)),
inference(superposition,[status(thm)],[c_114,c_6372]) ).
tcf(c_6396,plain,
! [X0: $i,X1: $i] : subset(set_difference(X0,set_difference(X1,X0)),set_union2(X0,X1)),
inference(superposition,[status(thm)],[c_85,c_6372]) ).
tcf(c_6401,plain,
! [X0: $i,X1: $i] : set_difference(set_difference(X0,X1),set_union2(X0,X1)) = empty_set,
inference(superposition,[status(thm)],[c_6372,c_78]) ).
tcf(c_6402,plain,
! [X0: $i,X1: $i] : set_union2(set_difference(X0,X1),set_union2(X0,X1)) = set_union2(X0,X1),
inference(superposition,[status(thm)],[c_6372,c_66]) ).
tcf(c_6403,plain,
! [X0: $i,X1: $i] : ~ proper_subset(set_union2(X0,X1),set_difference(X0,X1)),
inference(superposition,[status(thm)],[c_6372,c_98]) ).
tcf(c_6409,plain,
! [X0: $i,X1: $i] : set_union2(X0,set_difference(X0,X1)) = X0,
inference(demodulation,[status(thm)],[c_6264,c_132]) ).
tcf(c_6412,plain,
set_union2(empty_set,empty_set) = empty_set,
inference(superposition,[status(thm)],[c_113,c_6409]) ).
tcf(c_6415,plain,
! [X0: $i,X1: $i] : subset(set_difference(X0,set_difference(X0,X1)),X0),
inference(superposition,[status(thm)],[c_6409,c_6372]) ).
tcf(c_6416,plain,
! [X0: $i,X1: $i,X2: $i] : ~ in(unordered_pair(X0,X1),set_difference(X0,X2)),
inference(superposition,[status(thm)],[c_6409,c_5956]) ).
tcf(c_6418,plain,
! [X0: $i,X1: $i] : ~ in(powerset(X0),set_difference(X0,X1)),
inference(superposition,[status(thm)],[c_6409,c_5812]) ).
tcf(c_6423,plain,
! [X0: $i,X1: $i] :
( empty(set_difference(X0,X1))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6409,c_188]) ).
tcf(c_6426,plain,
! [X0: $i,X1: $i,X2: $i] : ~ in(unordered_pair(X0,X1),set_difference(X1,X2)),
inference(superposition,[status(thm)],[c_6409,c_5957]) ).
tcf(c_6430,plain,
! [X0: $i,X1: $i] : subset(set_difference(set_difference(X0,X1),X0),X0),
inference(superposition,[status(thm)],[c_6409,c_6334]) ).
tcf(c_6466,plain,
set_difference(empty_set,empty_set) = empty_set,
inference(superposition,[status(thm)],[c_113,c_6290]) ).
tcf(c_6469,plain,
! [X0: $i,X1: $i] : set_difference(empty_set,set_difference(X0,X1)) = empty_set,
inference(superposition,[status(thm)],[c_6290,c_6290]) ).
tcf(c_6472,plain,
! [X0: $i,X1: $i] : ~ in(powerset(set_difference(X0,X1)),empty_set),
inference(superposition,[status(thm)],[c_6290,c_6418]) ).
tcf(c_6473,plain,
! [X0: $i,X1: $i] : set_union2(set_difference(X0,X1),empty_set) = set_difference(X0,X1),
inference(superposition,[status(thm)],[c_6290,c_6409]) ).
tcf(c_6474,plain,
! [X0: $i,X1: $i] : subset(empty_set,set_union2(set_difference(X0,X1),X0)),
inference(superposition,[status(thm)],[c_6290,c_6372]) ).
tcf(c_6475,plain,
! [X0: $i,X1: $i] : subset(empty_set,set_union2(X0,set_difference(X0,X1))),
inference(superposition,[status(thm)],[c_6290,c_6334]) ).
tcf(c_6477,plain,
! [X0: $i,X1: $i] : ~ proper_subset(set_difference(X0,X1),empty_set),
inference(superposition,[status(thm)],[c_6290,c_5343]) ).
tcf(c_6478,plain,
! [X0: $i,X1: $i] : subset(empty_set,set_difference(X0,X1)),
inference(superposition,[status(thm)],[c_6290,c_77]) ).
tcf(c_6480,plain,
! [X0: $i,X1: $i] : set_union2(X0,set_difference(X0,X1)) = set_union2(X0,empty_set),
inference(superposition,[status(thm)],[c_6290,c_85]) ).
tcf(c_6495,plain,
! [X0: $i,X1: $i] : subset(empty_set,set_union2(X0,set_union2(X0,X1))),
inference(superposition,[status(thm)],[c_6291,c_6372]) ).
tcf(c_6496,plain,
! [X0: $i,X1: $i] : subset(empty_set,set_union2(set_union2(X0,X1),X0)),
inference(superposition,[status(thm)],[c_6291,c_6334]) ).
tcf(c_6501,plain,
! [X0: $i,X1: $i] : set_union2(set_union2(X0,X1),X0) = set_union2(set_union2(X0,X1),empty_set),
inference(superposition,[status(thm)],[c_6291,c_85]) ).
tcf(c_6502,plain,
! [X0: $i,X1: $i] : subset(empty_set,set_union2(X0,X1)),
inference(light_normalisation,[status(thm)],[c_6495,c_6265]) ).
tcf(c_6515,plain,
! [X0: $i,X1: $i] : subset(empty_set,set_union2(X0,set_union2(X1,X0))),
inference(superposition,[status(thm)],[c_6293,c_6372]) ).
tcf(c_6516,plain,
! [X0: $i,X1: $i] : subset(empty_set,set_union2(set_union2(X0,X1),X1)),
inference(superposition,[status(thm)],[c_6293,c_6334]) ).
tcf(c_6521,plain,
! [X0: $i,X1: $i] : set_union2(set_union2(X0,X1),X1) = set_union2(set_union2(X0,X1),empty_set),
inference(superposition,[status(thm)],[c_6293,c_85]) ).
tcf(c_6529,plain,
! [X0: $i,X1: $i] : ~ proper_subset(set_union2(X0,X1),set_difference(set_difference(X1,X0),X0)),
inference(superposition,[status(thm)],[c_85,c_6325]) ).
tcf(c_6530,plain,
! [X0: $i] : ~ proper_subset(X0,set_difference(empty_set,X0)),
inference(superposition,[status(thm)],[c_116,c_6325]) ).
tcf(c_6531,plain,
! [X0: $i] : ~ proper_subset(X0,set_difference(X0,X0)),
inference(superposition,[status(thm)],[c_125,c_6325]) ).
tcf(c_6533,plain,
! [X0: $i] : ~ proper_subset(X0,set_difference(X0,empty_set)),
inference(superposition,[status(thm)],[c_5426,c_6325]) ).
tcf(c_6534,plain,
! [X0: $i,X1: $i] : ~ proper_subset(X0,set_difference(set_difference(X0,X1),X0)),
inference(superposition,[status(thm)],[c_6409,c_6325]) ).
tcf(c_6535,plain,
! [X0: $i] : ~ proper_subset(set_union2(X0,empty_set),empty_set),
inference(superposition,[status(thm)],[c_113,c_6325]) ).
tcf(c_6536,plain,
! [X0: $i] : ~ proper_subset(set_union2(empty_set,X0),X0),
inference(superposition,[status(thm)],[c_114,c_6325]) ).
tcf(c_6537,plain,
! [X0: $i] : ~ proper_subset(set_union2(X0,X0),empty_set),
inference(superposition,[status(thm)],[c_1252,c_6325]) ).
tcf(c_6538,plain,
! [X0: $i,X1: $i] : ~ proper_subset(set_union2(X0,set_difference(X0,X1)),empty_set),
inference(superposition,[status(thm)],[c_6290,c_6325]) ).
tcf(c_6539,plain,
! [X0: $i,X1: $i] : ~ proper_subset(set_union2(set_union2(X0,X1),X0),empty_set),
inference(superposition,[status(thm)],[c_6291,c_6325]) ).
tcf(c_6540,plain,
! [X0: $i,X1: $i] : ~ proper_subset(set_union2(set_union2(X0,X1),X1),empty_set),
inference(superposition,[status(thm)],[c_6293,c_6325]) ).
tcf(c_6551,plain,
! [X0: $i,X1: $i] : ~ proper_subset(set_union2(X0,X1),set_difference(X0,set_difference(X1,X0))),
inference(superposition,[status(thm)],[c_85,c_6403]) ).
tcf(c_6556,plain,
! [X0: $i,X1: $i] : ~ proper_subset(X0,set_difference(X0,set_difference(X0,X1))),
inference(superposition,[status(thm)],[c_6409,c_6403]) ).
tcf(c_6557,plain,
! [X0: $i] : ~ proper_subset(set_union2(empty_set,X0),empty_set),
inference(superposition,[status(thm)],[c_113,c_6403]) ).
tcf(c_6558,plain,
! [X0: $i] : ~ proper_subset(set_union2(X0,empty_set),X0),
inference(superposition,[status(thm)],[c_114,c_6403]) ).
tcf(c_6560,plain,
! [X0: $i,X1: $i] : ~ proper_subset(set_union2(set_difference(X0,X1),X0),empty_set),
inference(superposition,[status(thm)],[c_6290,c_6403]) ).
tcf(c_6561,plain,
! [X0: $i,X1: $i] : ~ proper_subset(set_union2(X0,set_union2(X0,X1)),empty_set),
inference(superposition,[status(thm)],[c_6291,c_6403]) ).
tcf(c_6562,plain,
! [X0: $i,X1: $i] : ~ proper_subset(set_union2(X0,set_union2(X1,X0)),empty_set),
inference(superposition,[status(thm)],[c_6293,c_6403]) ).
tcf(c_6565,plain,
! [X0: $i,X1: $i] : ~ proper_subset(set_union2(X0,X1),empty_set),
inference(light_normalisation,[status(thm)],[c_6562,c_6267]) ).
tcf(c_6569,plain,
! [X0: $i] : ~ in(powerset(empty_set),set_difference(empty_set,X0)),
inference(superposition,[status(thm)],[c_70,c_6416]) ).
tcf(c_6571,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( cartesian_product2(X0,X1) = empty_set )
| ~ in(sK13(X0,X1,empty_set),set_difference(unordered_pair(sK14(X0,X1,empty_set),sK14(X0,X1,empty_set)),X2)) ),
inference(superposition,[status(thm)],[c_5229,c_6416]) ).
tcf(c_6572,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( cartesian_product2(X0,X1) = empty_set )
| ~ in(sK5(cartesian_product2(X0,X1)),set_difference(unordered_pair(sK16(X0,X1,sK5(cartesian_product2(X0,X1))),sK16(X0,X1,sK5(cartesian_product2(X0,X1)))),X2)) ),
inference(superposition,[status(thm)],[c_5462,c_6416]) ).
tcf(c_6573,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X0,X1) = cartesian_product2(X2,X3) )
| ( unordered_pair(unordered_pair(sK14(X0,X1,cartesian_product2(X2,X3)),sK14(X0,X1,cartesian_product2(X2,X3))),unordered_pair(sK14(X0,X1,cartesian_product2(X2,X3)),sK15(X0,X1,cartesian_product2(X2,X3)))) = sK13(X0,X1,cartesian_product2(X2,X3)) )
| ~ in(sK13(X0,X1,cartesian_product2(X2,X3)),set_difference(unordered_pair(sK16(X2,X3,sK13(X0,X1,cartesian_product2(X2,X3))),sK16(X2,X3,sK13(X0,X1,cartesian_product2(X2,X3)))),X4)) ),
inference(superposition,[status(thm)],[c_5464,c_6416]) ).
tcf(c_6574,plain,
! [X0: $i] : ~ in(unordered_pair(empty_set,X0),empty_set),
inference(superposition,[status(thm)],[c_113,c_6416]) ).
tcf(c_6577,plain,
! [X0: $i,X1: $i,X2: $i] : ~ in(unordered_pair(set_difference(X0,X1),X2),empty_set),
inference(superposition,[status(thm)],[c_6290,c_6416]) ).
tcf(c_6595,plain,
! [X0: $i] : set_difference(empty_set,set_union2(X0,empty_set)) = empty_set,
inference(superposition,[status(thm)],[c_113,c_6374]) ).
tcf(c_6596,plain,
! [X0: $i] : set_difference(X0,set_union2(empty_set,X0)) = empty_set,
inference(superposition,[status(thm)],[c_114,c_6374]) ).
tcf(c_6597,plain,
! [X0: $i] : set_difference(empty_set,set_union2(X0,X0)) = empty_set,
inference(superposition,[status(thm)],[c_1252,c_6374]) ).
tcf(c_6598,plain,
! [X0: $i,X1: $i] : set_difference(empty_set,set_union2(X0,set_difference(X0,X1))) = empty_set,
inference(superposition,[status(thm)],[c_6290,c_6374]) ).
tcf(c_6599,plain,
! [X0: $i,X1: $i] : set_difference(empty_set,set_union2(set_union2(X0,X1),X0)) = empty_set,
inference(superposition,[status(thm)],[c_6291,c_6374]) ).
tcf(c_6600,plain,
! [X0: $i,X1: $i] : set_difference(empty_set,set_union2(set_union2(X0,X1),X1)) = empty_set,
inference(superposition,[status(thm)],[c_6293,c_6374]) ).
tcf(c_6603,plain,
! [X0: $i,X1: $i] : set_difference(set_difference(set_difference(X0,X1),X1),set_union2(X1,X0)) = empty_set,
inference(superposition,[status(thm)],[c_85,c_6374]) ).
tcf(c_6604,plain,
! [X0: $i] : set_difference(set_difference(empty_set,X0),X0) = empty_set,
inference(superposition,[status(thm)],[c_116,c_6374]) ).
tcf(c_6605,plain,
! [X0: $i] : set_difference(set_difference(X0,X0),X0) = empty_set,
inference(superposition,[status(thm)],[c_125,c_6374]) ).
tcf(c_6607,plain,
! [X0: $i] : set_difference(set_difference(X0,empty_set),X0) = empty_set,
inference(superposition,[status(thm)],[c_5426,c_6374]) ).
tcf(c_6608,plain,
! [X0: $i,X1: $i] : set_difference(set_difference(set_difference(X0,X1),X0),X0) = empty_set,
inference(superposition,[status(thm)],[c_6409,c_6374]) ).
tcf(c_6609,plain,
! [X0: $i,X1: $i] : set_difference(empty_set,set_union2(set_union2(X0,X1),set_difference(X1,X0))) = empty_set,
inference(superposition,[status(thm)],[c_6374,c_6374]) ).
tcf(c_6610,plain,
! [X0: $i,X1: $i] : ~ proper_subset(set_union2(set_difference(X0,X1),set_union2(X1,X0)),empty_set),
inference(superposition,[status(thm)],[c_6374,c_6403]) ).
tcf(c_6615,plain,
! [X0: $i,X1: $i] : subset(empty_set,set_union2(set_difference(X0,X1),set_union2(X1,X0))),
inference(superposition,[status(thm)],[c_6374,c_6372]) ).
tcf(c_6616,plain,
! [X0: $i,X1: $i] : subset(empty_set,set_union2(set_union2(X0,X1),set_difference(X1,X0))),
inference(superposition,[status(thm)],[c_6374,c_6334]) ).
tcf(c_6622,plain,
! [X0: $i,X1: $i] : ~ proper_subset(set_union2(set_union2(X0,X1),set_difference(X1,X0)),empty_set),
inference(superposition,[status(thm)],[c_6374,c_6325]) ).
tcf(c_6623,plain,
! [X0: $i,X1: $i] : set_union2(set_union2(X0,X1),set_difference(X1,X0)) = set_union2(set_union2(X0,X1),empty_set),
inference(superposition,[status(thm)],[c_6374,c_85]) ).
tcf(c_6643,plain,
! [X0: $i,X1: $i] : set_difference(set_union2(X0,X1),set_difference(X1,X0)) = set_difference(X0,set_difference(X1,X0)),
inference(superposition,[status(thm)],[c_85,c_93]) ).
tcf(c_6644,plain,
! [X0: $i,X1: $i] : set_difference(set_union2(X0,X1),X0) = set_difference(X1,X0),
inference(superposition,[status(thm)],[c_132,c_93]) ).
tcf(c_6645,plain,
! [X0: $i] : set_difference(X0,X0) = set_difference(empty_set,X0),
inference(superposition,[status(thm)],[c_5426,c_93]) ).
tcf(c_6646,plain,
! [X0: $i,X1: $i] : set_difference(set_difference(X0,X1),set_union2(X1,set_union2(X0,X1))) = empty_set,
inference(superposition,[status(thm)],[c_93,c_6374]) ).
tcf(c_6647,plain,
! [X0: $i,X1: $i] : ~ proper_subset(set_union2(set_union2(X0,X1),X1),set_difference(X0,X1)),
inference(superposition,[status(thm)],[c_93,c_6403]) ).
tcf(c_6649,plain,
! [X0: $i,X1: $i] :
( empty(set_difference(X0,X1))
| ~ empty(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_93,c_6423]) ).
tcf(c_6650,plain,
! [X0: $i,X1: $i] : ~ in(powerset(set_union2(X0,X1)),set_difference(X0,X1)),
inference(superposition,[status(thm)],[c_93,c_6418]) ).
tcf(c_6651,plain,
! [X0: $i,X1: $i] : set_union2(set_union2(X0,X1),set_difference(X0,X1)) = set_union2(X0,X1),
inference(superposition,[status(thm)],[c_93,c_6409]) ).
tcf(c_6652,plain,
! [X0: $i,X1: $i] : subset(set_difference(X0,X1),set_union2(set_union2(X0,X1),X1)),
inference(superposition,[status(thm)],[c_93,c_6372]) ).
tcf(c_6653,plain,
! [X0: $i,X1: $i] : subset(set_difference(X0,X1),set_union2(X1,set_union2(X0,X1))),
inference(superposition,[status(thm)],[c_93,c_6334]) ).
tcf(c_6654,plain,
! [X0: $i,X1: $i] :
( subset(set_union2(X0,X1),X1)
| ( set_difference(X0,X1) != empty_set ) ),
inference(superposition,[status(thm)],[c_93,c_79]) ).
tcf(c_6657,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,set_union2(X1,X2))
| ~ in(X0,set_difference(X1,X2)) ),
inference(superposition,[status(thm)],[c_93,c_144]) ).
tcf(c_6658,plain,
! [X0: $i,X1: $i,X2: $i] : ~ in(unordered_pair(set_union2(X0,X1),X2),set_difference(X0,X1)),
inference(superposition,[status(thm)],[c_93,c_6416]) ).
tcf(c_6659,plain,
! [X0: $i,X1: $i] : ~ proper_subset(set_union2(X0,set_union2(X1,X0)),set_difference(X1,X0)),
inference(superposition,[status(thm)],[c_93,c_6325]) ).
tcf(c_6660,plain,
! [X0: $i,X1: $i] : set_union2(X0,set_union2(X1,X0)) = set_union2(X0,set_difference(X1,X0)),
inference(superposition,[status(thm)],[c_93,c_85]) ).
tcf(c_6661,plain,
! [X0: $i] : set_union2(X0,empty_set) = set_difference(X0,empty_set),
inference(superposition,[status(thm)],[c_93,c_114]) ).
tcf(c_6692,plain,
! [X0: $i,X1: $i] :
( disjoint(set_union2(X0,X1),X1)
| ( set_union2(X0,X1) != set_difference(X0,X1) ) ),
inference(superposition,[status(thm)],[c_93,c_104]) ).
tcf(c_6695,plain,
! [X0: $i] :
( disjoint(X0,X0)
| ( X0 != empty_set ) ),
inference(superposition,[status(thm)],[c_1252,c_104]) ).
tcf(c_6696,plain,
! [X0: $i,X1: $i] :
( disjoint(set_difference(X0,X1),X0)
| ( set_difference(X0,X1) != empty_set ) ),
inference(superposition,[status(thm)],[c_6290,c_104]) ).
tcf(c_6697,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,set_union2(X0,X1))
| ( X0 != empty_set ) ),
inference(superposition,[status(thm)],[c_6291,c_104]) ).
tcf(c_6698,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,set_union2(X1,X0))
| ( X0 != empty_set ) ),
inference(superposition,[status(thm)],[c_6293,c_104]) ).
tcf(c_6699,plain,
! [X0: $i,X1: $i] :
( disjoint(set_difference(X0,X1),set_union2(X1,X0))
| ( set_difference(X0,X1) != empty_set ) ),
inference(superposition,[status(thm)],[c_6374,c_104]) ).
tcf(c_6736,plain,
! [X0: $i,X1: $i] :
( in(X0,X1)
| ( set_difference(unordered_pair(X0,X0),X1) = unordered_pair(X0,X0) ) ),
inference(superposition,[status(thm)],[c_52,c_105]) ).
tcf(c_6737,plain,
! [X0: $i,X1: $i] :
( ( set_difference(X0,X1) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5289,c_105]) ).
tcf(c_6738,plain,
! [X0: $i,X1: $i] :
( ( set_difference(X1,X0) = X1 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5300,c_105]) ).
tcf(c_6741,plain,
! [X0: $i] :
( in(empty_set,X0)
| ( set_difference(powerset(empty_set),X0) = powerset(empty_set) ) ),
inference(superposition,[status(thm)],[c_5259,c_105]) ).
tcf(c_6742,plain,
! [X0: $i,X1: $i] :
( in(X1,X0)
| ( set_difference(X0,unordered_pair(X1,X1)) = X0 ) ),
inference(superposition,[status(thm)],[c_5260,c_105]) ).
tcf(c_6743,plain,
! [X0: $i] :
( in(empty_set,X0)
| ( set_difference(X0,powerset(empty_set)) = X0 ) ),
inference(superposition,[status(thm)],[c_5272,c_105]) ).
tcf(c_6764,plain,
! [X0: $i,X1: $i] :
( disjoint(unordered_pair(X0,X0),X1)
| ( sK0(unordered_pair(X0,X0),X1) = X0 ) ),
inference(superposition,[status(thm)],[c_89,c_112]) ).
tcf(c_6765,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,unordered_pair(X1,X1))
| ( sK0(X0,unordered_pair(X1,X1)) = X1 ) ),
inference(superposition,[status(thm)],[c_90,c_112]) ).
tcf(c_6766,plain,
! [X0: $i] :
( ( unordered_pair(X0,X0) = empty_set )
| ( sK5(unordered_pair(X0,X0)) = X0 ) ),
inference(superposition,[status(thm)],[c_117,c_112]) ).
tcf(c_6767,plain,
! [X0: $i,X1: $i] :
( subset(unordered_pair(X0,X0),X1)
| ( sK7(unordered_pair(X0,X0),X1) = X0 ) ),
inference(superposition,[status(thm)],[c_122,c_112]) ).
tcf(c_6768,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( unordered_pair(X2,X2) = cartesian_product2(X0,X1) )
| ( sK13(X0,X1,unordered_pair(X2,X2)) = X2 )
| ( unordered_pair(unordered_pair(sK14(X0,X1,unordered_pair(X2,X2)),sK14(X0,X1,unordered_pair(X2,X2))),unordered_pair(sK14(X0,X1,unordered_pair(X2,X2)),sK15(X0,X1,unordered_pair(X2,X2)))) = sK13(X0,X1,unordered_pair(X2,X2)) ) ),
inference(superposition,[status(thm)],[c_1706,c_112]) ).
tcf(c_6771,plain,
! [X0: $i] :
( ( X0 = empty_set )
| ~ in(X0,powerset(empty_set)) ),
inference(superposition,[status(thm)],[c_70,c_112]) ).
tcf(c_6776,plain,
! [X0: $i] : sK5(unordered_pair(X0,X0)) = X0,
inference(forward_subsumption_resolution,[status(thm)],[c_6766,c_49]) ).
tcf(c_6843,plain,
sK5(powerset(empty_set)) = empty_set,
inference(superposition,[status(thm)],[c_70,c_6776]) ).
tcf(c_6844,plain,
! [X0: $i] :
( in(X0,unordered_pair(X0,X0))
| ( unordered_pair(X0,X0) = empty_set ) ),
inference(superposition,[status(thm)],[c_6776,c_117]) ).
tcf(c_6849,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( cartesian_product2(X0,X1) = empty_set )
| ~ in(sK13(X0,X1,empty_set),set_difference(unordered_pair(sK14(X0,X1,empty_set),sK15(X0,X1,empty_set)),X2)) ),
inference(superposition,[status(thm)],[c_5229,c_6426]) ).
tcf(c_6850,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( cartesian_product2(X0,X1) = empty_set )
| ~ in(sK5(cartesian_product2(X0,X1)),set_difference(unordered_pair(sK16(X0,X1,sK5(cartesian_product2(X0,X1))),sK17(X0,X1,sK5(cartesian_product2(X0,X1)))),X2)) ),
inference(superposition,[status(thm)],[c_5462,c_6426]) ).
tcf(c_6851,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X0,X1) = cartesian_product2(X2,X3) )
| ( unordered_pair(unordered_pair(sK14(X0,X1,cartesian_product2(X2,X3)),sK14(X0,X1,cartesian_product2(X2,X3))),unordered_pair(sK14(X0,X1,cartesian_product2(X2,X3)),sK15(X0,X1,cartesian_product2(X2,X3)))) = sK13(X0,X1,cartesian_product2(X2,X3)) )
| ~ in(sK13(X0,X1,cartesian_product2(X2,X3)),set_difference(unordered_pair(sK16(X2,X3,sK13(X0,X1,cartesian_product2(X2,X3))),sK17(X2,X3,sK13(X0,X1,cartesian_product2(X2,X3)))),X4)) ),
inference(superposition,[status(thm)],[c_5464,c_6426]) ).
tcf(c_6852,plain,
! [X0: $i,X1: $i,X2: $i] : ~ in(unordered_pair(X0,set_union2(X1,X2)),set_difference(X1,X2)),
inference(superposition,[status(thm)],[c_93,c_6426]) ).
tcf(c_6853,plain,
! [X0: $i] : ~ in(unordered_pair(X0,empty_set),empty_set),
inference(superposition,[status(thm)],[c_113,c_6426]) ).
tcf(c_6859,plain,
! [X0: $i,X1: $i,X2: $i] : ~ in(unordered_pair(X0,set_difference(X1,X2)),empty_set),
inference(superposition,[status(thm)],[c_6374,c_6426]) ).
tcf(c_6874,plain,
disjoint(empty_set,empty_set),
inference(equality_resolution,[status(thm)],[c_6695]) ).
tcf(c_6891,plain,
( ( powerset(empty_set) = empty_set )
| ~ in(powerset(empty_set),empty_set) ),
inference(superposition,[status(thm)],[c_6843,c_5370]) ).
tcf(c_6892,plain,
! [X0: $i] :
( ( unordered_pair(X0,X0) = empty_set )
| ~ in(unordered_pair(X0,X0),X0) ),
inference(superposition,[status(thm)],[c_6776,c_5370]) ).
tcf(c_6901,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(powerset(X2),X0)
| ~ subset(set_union2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_129,c_5485]) ).
tcf(c_6902,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(powerset(X2),X1)
| ~ subset(set_union2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_130,c_5485]) ).
tcf(c_6905,plain,
! [X0: $i,X1: $i] :
( ~ subset(powerset(X1),X0)
| ~ subset(powerset(X0),X1) ),
inference(superposition,[status(thm)],[c_178,c_5485]) ).
tcf(c_6921,plain,
! [X0: $i] : ~ in(powerset(union(powerset(X0))),X0),
inference(superposition,[status(thm)],[c_80,c_5585]) ).
tcf(c_6922,plain,
! [X0: $i,X1: $i] : ~ empty(unordered_pair(powerset(union(powerset(X0))),X1)),
inference(superposition,[status(thm)],[c_5360,c_5585]) ).
tcf(c_6923,plain,
! [X0: $i,X1: $i] : ~ in(unordered_pair(powerset(union(powerset(union(X0)))),X1),X0),
inference(superposition,[status(thm)],[c_61,c_5585]) ).
tcf(c_6928,plain,
! [X0: $i,X1: $i] : set_union2(set_difference(X0,X1),set_union2(X1,set_union2(X0,X1))) = set_union2(X1,set_union2(X0,X1)),
inference(superposition,[status(thm)],[c_93,c_6375]) ).
tcf(c_6929,plain,
! [X0: $i] : set_union2(empty_set,set_union2(X0,empty_set)) = set_union2(X0,empty_set),
inference(superposition,[status(thm)],[c_113,c_6375]) ).
tcf(c_6930,plain,
! [X0: $i] : set_union2(X0,set_union2(empty_set,X0)) = set_union2(empty_set,X0),
inference(superposition,[status(thm)],[c_114,c_6375]) ).
tcf(c_6931,plain,
! [X0: $i] : set_union2(empty_set,set_union2(X0,X0)) = set_union2(X0,X0),
inference(superposition,[status(thm)],[c_1252,c_6375]) ).
tcf(c_6932,plain,
! [X0: $i,X1: $i] : set_union2(empty_set,set_union2(X0,set_difference(X0,X1))) = set_union2(X0,set_difference(X0,X1)),
inference(superposition,[status(thm)],[c_6290,c_6375]) ).
tcf(c_6933,plain,
! [X0: $i,X1: $i] : set_union2(empty_set,set_union2(set_union2(X0,X1),X0)) = set_union2(set_union2(X0,X1),X0),
inference(superposition,[status(thm)],[c_6291,c_6375]) ).
tcf(c_6934,plain,
! [X0: $i,X1: $i] : set_union2(empty_set,set_union2(set_union2(X0,X1),X1)) = set_union2(set_union2(X0,X1),X1),
inference(superposition,[status(thm)],[c_6293,c_6375]) ).
tcf(c_6935,plain,
! [X0: $i,X1: $i] : set_union2(empty_set,set_union2(set_union2(X0,X1),set_difference(X1,X0))) = set_union2(set_union2(X0,X1),set_difference(X1,X0)),
inference(superposition,[status(thm)],[c_6374,c_6375]) ).
tcf(c_6937,plain,
! [X0: $i,X1: $i] : set_union2(set_difference(set_difference(X0,X1),X1),set_union2(X1,X0)) = set_union2(X1,X0),
inference(superposition,[status(thm)],[c_85,c_6375]) ).
tcf(c_6938,plain,
! [X0: $i] : set_union2(set_difference(empty_set,X0),X0) = X0,
inference(superposition,[status(thm)],[c_116,c_6375]) ).
tcf(c_6939,plain,
! [X0: $i] : set_union2(set_difference(X0,X0),X0) = X0,
inference(superposition,[status(thm)],[c_125,c_6375]) ).
tcf(c_6941,plain,
! [X0: $i] : set_union2(set_difference(X0,empty_set),X0) = X0,
inference(superposition,[status(thm)],[c_5426,c_6375]) ).
tcf(c_6943,plain,
! [X0: $i,X1: $i] : set_union2(set_difference(set_difference(X0,X1),X0),X0) = X0,
inference(superposition,[status(thm)],[c_6409,c_6375]) ).
tcf(c_6944,plain,
! [X0: $i,X1: $i] : set_difference(set_union2(X0,X1),set_union2(X0,X1)) = set_difference(set_difference(X1,X0),set_union2(X0,X1)),
inference(superposition,[status(thm)],[c_6375,c_93]) ).
tcf(c_6945,plain,
! [X0: $i,X1: $i] : ~ proper_subset(set_union2(X0,X1),set_difference(set_difference(X1,X0),set_union2(X0,X1))),
inference(superposition,[status(thm)],[c_6375,c_6403]) ).
tcf(c_6946,plain,
! [X0: $i,X1: $i] : ~ proper_subset(set_union2(X0,X1),set_difference(set_union2(X0,X1),set_difference(X1,X0))),
inference(superposition,[status(thm)],[c_6375,c_6325]) ).
tcf(c_6948,plain,
! [X0: $i,X1: $i] : subset(set_difference(set_difference(X0,X1),set_union2(X1,X0)),set_union2(X1,X0)),
inference(superposition,[status(thm)],[c_6375,c_6372]) ).
tcf(c_6949,plain,
! [X0: $i,X1: $i,X2: $i] : ~ in(unordered_pair(set_union2(X0,X1),X2),set_union2(X0,X1)),
inference(superposition,[status(thm)],[c_6375,c_5956]) ).
tcf(c_6951,plain,
! [X0: $i,X1: $i] : ~ in(powerset(set_union2(X0,X1)),set_union2(X0,X1)),
inference(superposition,[status(thm)],[c_6375,c_5812]) ).
tcf(c_6953,plain,
! [X0: $i,X1: $i] : ~ proper_subset(set_union2(X0,X1),set_union2(X0,X1)),
inference(superposition,[status(thm)],[c_6375,c_5422]) ).
tcf(c_6958,plain,
! [X0: $i,X1: $i,X2: $i] : ~ in(unordered_pair(X0,set_union2(X1,X2)),set_union2(X1,X2)),
inference(superposition,[status(thm)],[c_6375,c_5957]) ).
tcf(c_6962,plain,
! [X0: $i,X1: $i] : set_union2(set_difference(set_union2(X0,X1),set_difference(X1,X0)),set_union2(X0,X1)) = set_union2(X0,X1),
inference(superposition,[status(thm)],[c_6375,c_6375]) ).
tcf(c_6963,plain,
! [X0: $i,X1: $i] : set_difference(set_difference(set_union2(X0,X1),set_difference(X1,X0)),set_union2(X0,X1)) = empty_set,
inference(superposition,[status(thm)],[c_6375,c_6374]) ).
tcf(c_6964,plain,
! [X0: $i,X1: $i] : set_difference(set_union2(X0,X1),set_union2(X0,X1)) = empty_set,
inference(superposition,[status(thm)],[c_6375,c_6293]) ).
tcf(c_6965,plain,
! [X0: $i,X1: $i] : subset(set_difference(set_union2(X0,X1),set_difference(X1,X0)),set_union2(X0,X1)),
inference(superposition,[status(thm)],[c_6375,c_6334]) ).
tcf(c_6966,plain,
! [X0: $i,X1: $i] : subset(set_union2(X0,X1),set_union2(X0,X1)),
inference(superposition,[status(thm)],[c_6375,c_5425]) ).
tcf(c_6977,plain,
! [X0: $i,X1: $i] : set_difference(set_difference(X0,set_difference(X1,X0)),set_union2(X0,X1)) = empty_set,
inference(light_normalisation,[status(thm)],[c_6963,c_6643]) ).
tcf(c_6979,plain,
! [X0: $i,X1: $i] : set_union2(set_difference(X0,set_difference(X1,X0)),set_union2(X0,X1)) = set_union2(X0,X1),
inference(light_normalisation,[status(thm)],[c_6962,c_6643]) ).
tcf(c_6980,plain,
! [X0: $i,X1: $i] : set_union2(empty_set,set_union2(set_union2(X0,X1),empty_set)) = set_union2(set_union2(X0,X1),empty_set),
inference(light_normalisation,[status(thm)],[c_6935,c_6623]) ).
tcf(c_6991,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(set_difference(X0,X1),X2)
| ~ in(sK0(set_difference(X0,X1),X2),X1) ),
inference(superposition,[status(thm)],[c_89,c_145]) ).
tcf(c_6992,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(X0,set_difference(X1,X2))
| ~ in(sK0(X0,set_difference(X1,X2)),X2) ),
inference(superposition,[status(thm)],[c_90,c_145]) ).
tcf(c_6993,plain,
! [X0: $i,X1: $i] :
( ( set_difference(X0,X1) = empty_set )
| ~ in(sK5(set_difference(X0,X1)),X1) ),
inference(superposition,[status(thm)],[c_117,c_145]) ).
tcf(c_6994,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(X0,X1),X2)
| ~ in(sK7(set_difference(X0,X1),X2),X1) ),
inference(superposition,[status(thm)],[c_122,c_145]) ).
tcf(c_6995,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_difference(X2,X3) = cartesian_product2(X0,X1) )
| ( unordered_pair(unordered_pair(sK14(X0,X1,set_difference(X2,X3)),sK14(X0,X1,set_difference(X2,X3))),unordered_pair(sK14(X0,X1,set_difference(X2,X3)),sK15(X0,X1,set_difference(X2,X3)))) = sK13(X0,X1,set_difference(X2,X3)) )
| ~ in(sK13(X0,X1,set_difference(X2,X3)),X3) ),
inference(superposition,[status(thm)],[c_1706,c_145]) ).
tcf(c_7022,plain,
! [X0: $i,X1: $i] :
( ~ in(X1,union(X0))
| ~ in(sK12(X0,X1),X1) ),
inference(superposition,[status(thm)],[c_150,c_124]) ).
tcf(c_7023,plain,
! [X0: $i,X1: $i] :
( ~ empty(sK12(X1,X0))
| ~ in(X0,union(X1)) ),
inference(superposition,[status(thm)],[c_150,c_184]) ).
tcf(c_7024,plain,
! [X0: $i,X1: $i] :
( ~ in(powerset(X1),union(X0))
| ~ subset(sK12(X0,powerset(X1)),X1) ),
inference(superposition,[status(thm)],[c_150,c_5485]) ).
tcf(c_7038,plain,
! [X0: $i,X1: $i] :
( ~ in(X1,union(X0))
| ~ in(X0,sK12(X0,X1)) ),
inference(superposition,[status(thm)],[c_151,c_124]) ).
tcf(c_7039,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ in(X0,union(X1)) ),
inference(superposition,[status(thm)],[c_151,c_184]) ).
tcf(c_7040,plain,
! [X0: $i,X1: $i] :
( ( sK12(unordered_pair(X1,X1),X0) = X1 )
| ~ in(X0,union(unordered_pair(X1,X1))) ),
inference(superposition,[status(thm)],[c_151,c_112]) ).
tcf(c_7041,plain,
! [X0: $i] : ~ in(X0,union(empty_set)),
inference(superposition,[status(thm)],[c_151,c_118]) ).
tcf(c_7042,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(X2,union(set_difference(X0,X1)))
| ~ in(sK12(set_difference(X0,X1),X2),X1) ),
inference(superposition,[status(thm)],[c_151,c_145]) ).
tcf(c_7043,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(set_difference(X1,X2),X0),X1)
| ~ in(X0,union(set_difference(X1,X2))) ),
inference(superposition,[status(thm)],[c_151,c_144]) ).
tcf(c_7044,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( unordered_pair(unordered_pair(sK16(X1,X2,sK12(cartesian_product2(X1,X2),X0)),sK16(X1,X2,sK12(cartesian_product2(X1,X2),X0))),unordered_pair(sK16(X1,X2,sK12(cartesian_product2(X1,X2),X0)),sK17(X1,X2,sK12(cartesian_product2(X1,X2),X0)))) = sK12(cartesian_product2(X1,X2),X0) )
| ~ in(X0,union(cartesian_product2(X1,X2))) ),
inference(superposition,[status(thm)],[c_151,c_1855]) ).
tcf(c_7045,plain,
! [X0: $i,X1: $i] :
( subset(sK12(powerset(X1),X0),X1)
| ~ in(X0,union(powerset(X1))) ),
inference(superposition,[status(thm)],[c_151,c_179]) ).
tcf(c_7073,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(X0,X2) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6423,c_183]) ).
tcf(c_7077,plain,
! [X0: $i] : disjoint(union(empty_set),X0),
inference(superposition,[status(thm)],[c_89,c_7041]) ).
tcf(c_7078,plain,
! [X0: $i] : disjoint(X0,union(empty_set)),
inference(superposition,[status(thm)],[c_90,c_7041]) ).
tcf(c_7079,plain,
union(empty_set) = empty_set,
inference(superposition,[status(thm)],[c_117,c_7041]) ).
tcf(c_7080,plain,
! [X0: $i] : subset(union(empty_set),X0),
inference(superposition,[status(thm)],[c_122,c_7041]) ).
tcf(c_7081,plain,
! [X0: $i] : ~ in(X0,union(union(empty_set))),
inference(superposition,[status(thm)],[c_151,c_7041]) ).
tcf(c_7082,plain,
! [X0: $i,X1: $i] :
( ( cartesian_product2(X0,X1) = union(empty_set) )
| ( unordered_pair(unordered_pair(sK14(X0,X1,union(empty_set)),sK14(X0,X1,union(empty_set))),unordered_pair(sK14(X0,X1,union(empty_set)),sK15(X0,X1,union(empty_set)))) = sK13(X0,X1,union(empty_set)) ) ),
inference(superposition,[status(thm)],[c_1706,c_7041]) ).
tcf(c_7094,plain,
! [X0: $i] : ~ in(unordered_pair(X0,powerset(empty_set)),empty_set),
inference(superposition,[status(thm)],[c_7079,c_5553]) ).
tcf(c_7097,plain,
! [X0: $i] : ~ in(unordered_pair(powerset(empty_set),X0),empty_set),
inference(superposition,[status(thm)],[c_7079,c_5540]) ).
tcf(c_7098,plain,
~ in(powerset(powerset(empty_set)),empty_set),
inference(superposition,[status(thm)],[c_7079,c_5548]) ).
tcf(c_7100,plain,
! [X0: $i,X1: $i] : ~ in(powerset(union(powerset(set_union2(X0,X1)))),X0),
inference(superposition,[status(thm)],[c_129,c_6921]) ).
tcf(c_7101,plain,
! [X0: $i,X1: $i] : ~ in(powerset(union(powerset(set_union2(X0,X1)))),X1),
inference(superposition,[status(thm)],[c_130,c_6921]) ).
tcf(c_7102,plain,
! [X0: $i] : ~ subset(powerset(union(powerset(powerset(X0)))),X0),
inference(superposition,[status(thm)],[c_178,c_6921]) ).
tcf(c_7109,plain,
! [X0: $i,X1: $i] :
( disjoint(union(X0),X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89,c_7039]) ).
tcf(c_7110,plain,
! [X0: $i,X1: $i] :
( disjoint(X1,union(X0))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_90,c_7039]) ).
tcf(c_7111,plain,
! [X0: $i] :
( ( union(X0) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_117,c_7039]) ).
tcf(c_7112,plain,
! [X0: $i,X1: $i] :
( subset(union(X0),X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_122,c_7039]) ).
tcf(c_7113,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ in(X0,union(union(X1))) ),
inference(superposition,[status(thm)],[c_151,c_7039]) ).
tcf(c_7114,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( cartesian_product2(X1,X2) = union(X0) )
| ( unordered_pair(unordered_pair(sK14(X1,X2,union(X0)),sK14(X1,X2,union(X0))),unordered_pair(sK14(X1,X2,union(X0)),sK15(X1,X2,union(X0)))) = sK13(X1,X2,union(X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_1706,c_7039]) ).
tcf(c_7140,plain,
! [X0: $i,X1: $i] :
( ( set_difference(union(X0),X1) = union(X0) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7109,c_105]) ).
tcf(c_7151,plain,
! [X0: $i,X1: $i] :
( ( set_difference(X1,union(X0)) = X1 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7110,c_105]) ).
tcf(c_7161,plain,
! [X0: $i,X1: $i] :
( ( set_difference(union(X0),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7112,c_78]) ).
tcf(c_7162,plain,
! [X0: $i,X1: $i] :
( ( set_union2(union(X0),X1) = X1 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7112,c_66]) ).
tcf(c_7163,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ proper_subset(X0,union(X1)) ),
inference(superposition,[status(thm)],[c_7112,c_98]) ).
tcf(c_7177,plain,
! [X0: $i] : ~ empty(powerset(union(powerset(powerset(X0))))),
inference(superposition,[status(thm)],[c_5360,c_7102]) ).
tcf(c_7178,plain,
! [X0: $i] : ~ in(powerset(union(powerset(powerset(union(X0))))),X0),
inference(superposition,[status(thm)],[c_61,c_7102]) ).
tcf(c_7180,plain,
! [X0: $i,X1: $i] : set_difference(set_difference(X0,X1),set_union2(set_union2(X0,X1),X1)) = empty_set,
inference(superposition,[status(thm)],[c_93,c_6401]) ).
tcf(c_7181,plain,
! [X0: $i] : set_difference(empty_set,set_union2(empty_set,X0)) = empty_set,
inference(superposition,[status(thm)],[c_113,c_6401]) ).
tcf(c_7182,plain,
! [X0: $i] : set_difference(X0,set_union2(X0,empty_set)) = empty_set,
inference(superposition,[status(thm)],[c_114,c_6401]) ).
tcf(c_7184,plain,
! [X0: $i,X1: $i] : set_difference(empty_set,set_union2(set_difference(X0,X1),X0)) = empty_set,
inference(superposition,[status(thm)],[c_6290,c_6401]) ).
tcf(c_7185,plain,
! [X0: $i,X1: $i] : set_difference(empty_set,set_union2(X0,set_union2(X0,X1))) = empty_set,
inference(superposition,[status(thm)],[c_6291,c_6401]) ).
tcf(c_7186,plain,
! [X0: $i,X1: $i] : set_difference(empty_set,set_union2(X0,set_union2(X1,X0))) = empty_set,
inference(superposition,[status(thm)],[c_6293,c_6401]) ).
tcf(c_7187,plain,
! [X0: $i,X1: $i] : set_difference(empty_set,set_union2(set_difference(X0,X1),set_union2(X1,X0))) = empty_set,
inference(superposition,[status(thm)],[c_6374,c_6401]) ).
tcf(c_7195,plain,
! [X0: $i,X1: $i] : set_difference(set_difference(set_difference(X0,X1),set_union2(X1,X0)),set_union2(X1,X0)) = empty_set,
inference(superposition,[status(thm)],[c_6375,c_6401]) ).
tcf(c_7196,plain,
! [X0: $i,X1: $i] : set_difference(set_difference(X0,set_difference(X0,X1)),X0) = empty_set,
inference(superposition,[status(thm)],[c_6409,c_6401]) ).
tcf(c_7197,plain,
! [X0: $i,X1: $i] : set_difference(empty_set,set_union2(set_difference(X0,X1),set_union2(X0,X1))) = empty_set,
inference(superposition,[status(thm)],[c_6401,c_6401]) ).
tcf(c_7198,plain,
! [X0: $i,X1: $i] : set_union2(empty_set,set_union2(set_union2(X0,X1),set_difference(X0,X1))) = set_union2(set_union2(X0,X1),set_difference(X0,X1)),
inference(superposition,[status(thm)],[c_6401,c_6375]) ).
tcf(c_7199,plain,
! [X0: $i,X1: $i] :
( disjoint(set_difference(X0,X1),set_union2(X0,X1))
| ( set_difference(X0,X1) != empty_set ) ),
inference(superposition,[status(thm)],[c_6401,c_104]) ).
tcf(c_7200,plain,
! [X0: $i,X1: $i] : set_difference(empty_set,set_union2(set_union2(X0,X1),set_difference(X0,X1))) = empty_set,
inference(superposition,[status(thm)],[c_6401,c_6374]) ).
tcf(c_7201,plain,
! [X0: $i,X1: $i] : ~ proper_subset(set_union2(set_difference(X0,X1),set_union2(X0,X1)),empty_set),
inference(superposition,[status(thm)],[c_6401,c_6403]) ).
tcf(c_7206,plain,
! [X0: $i,X1: $i] : subset(empty_set,set_union2(set_difference(X0,X1),set_union2(X0,X1))),
inference(superposition,[status(thm)],[c_6401,c_6372]) ).
tcf(c_7207,plain,
! [X0: $i,X1: $i] : subset(empty_set,set_union2(set_union2(X0,X1),set_difference(X0,X1))),
inference(superposition,[status(thm)],[c_6401,c_6334]) ).
tcf(c_7215,plain,
! [X0: $i,X1: $i] : ~ proper_subset(set_union2(set_union2(X0,X1),set_difference(X0,X1)),empty_set),
inference(superposition,[status(thm)],[c_6401,c_6325]) ).
tcf(c_7216,plain,
! [X0: $i,X1: $i] : set_union2(set_union2(X0,X1),set_difference(X0,X1)) = set_union2(set_union2(X0,X1),empty_set),
inference(superposition,[status(thm)],[c_6401,c_85]) ).
tcf(c_7223,plain,
! [X0: $i,X1: $i] : set_difference(empty_set,set_union2(X0,X1)) = empty_set,
inference(light_normalisation,[status(thm)],[c_7186,c_6267]) ).
tcf(c_7228,plain,
! [X0: $i,X1: $i] : set_union2(set_union2(X0,X1),empty_set) = set_union2(X0,X1),
inference(light_normalisation,[status(thm)],[c_7216,c_6651]) ).
tcf(c_7232,plain,
! [X0: $i,X1: $i] : set_union2(empty_set,set_union2(X0,X1)) = set_union2(X0,X1),
inference(light_normalisation,[status(thm)],[c_7198,c_6651]) ).
tcf(c_7243,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(unordered_pair(X0,X0),X2)
| ~ subset(X1,X2)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_80,c_69]) ).
tcf(c_7244,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X2,X1)
| ~ empty(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_5360,c_69]) ).
tcf(c_7245,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X2,X1)
| ~ in(X2,X0)
| ~ subset(union(X0),X1) ),
inference(superposition,[status(thm)],[c_61,c_69]) ).
tcf(c_7246,plain,
! [X0: $i,X1: $i] :
( subset(empty_set,X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_73,c_69]) ).
tcf(c_7247,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(X0,X2),X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_77,c_69]) ).
tcf(c_7248,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,X2)
| ~ subset(set_union2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_103,c_69]) ).
tcf(c_7250,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X1,X2)
| ~ subset(set_union2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_5425,c_69]) ).
tcf(c_7251,plain,
! [X0: $i,X1: $i] :
( subset(powerset(empty_set),X1)
| ~ in(empty_set,X0)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_5531,c_69]) ).
tcf(c_7252,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(X1,X0),X2)
| ~ subset(set_union2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_6334,c_69]) ).
tcf(c_7253,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(X0,X1),X2)
| ~ subset(set_union2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_6372,c_69]) ).
tcf(c_7254,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(union(X2),X1)
| ~ empty(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_7112,c_69]) ).
tcf(c_7296,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(X0,X1),set_difference(X2,X1))
| ~ subset(set_union2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_93,c_74]) ).
tcf(c_7297,plain,
! [X0: $i,X1: $i] :
( subset(empty_set,set_difference(X0,X1))
| ~ subset(empty_set,X0) ),
inference(superposition,[status(thm)],[c_113,c_74]) ).
tcf(c_7298,plain,
! [X0: $i,X1: $i] :
( subset(X0,set_difference(X1,empty_set))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_114,c_74]) ).
tcf(c_7299,plain,
! [X0: $i,X1: $i] :
( subset(empty_set,set_difference(X1,X0))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_1252,c_74]) ).
tcf(c_7300,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(empty_set,set_difference(X2,X0))
| ~ subset(set_difference(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_6290,c_74]) ).
tcf(c_7301,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(empty_set,set_difference(X1,set_union2(X0,X2)))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_6291,c_74]) ).
tcf(c_7302,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(empty_set,set_difference(X1,set_union2(X2,X0)))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_6293,c_74]) ).
tcf(c_7303,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(empty_set,set_difference(X2,set_union2(X1,X0)))
| ~ subset(set_difference(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_6374,c_74]) ).
tcf(c_7304,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(empty_set,set_difference(X2,set_union2(X0,X1)))
| ~ subset(set_difference(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_6401,c_74]) ).
tcf(c_7305,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(X0,X2),set_difference(X1,X2))
| ~ subset(X0,set_union2(X1,X2)) ),
inference(superposition,[status(thm)],[c_93,c_74]) ).
tcf(c_7306,plain,
! [X0: $i,X1: $i] :
( subset(set_difference(X0,X1),empty_set)
| ~ subset(X0,empty_set) ),
inference(superposition,[status(thm)],[c_113,c_74]) ).
tcf(c_7307,plain,
! [X0: $i,X1: $i] :
( subset(set_difference(X0,empty_set),X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_114,c_74]) ).
tcf(c_7308,plain,
! [X0: $i,X1: $i] :
( subset(set_difference(X0,X1),empty_set)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_1252,c_74]) ).
tcf(c_7309,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(X0,X1),empty_set)
| ~ subset(X0,set_difference(X1,X2)) ),
inference(superposition,[status(thm)],[c_6290,c_74]) ).
tcf(c_7310,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(X0,set_union2(X1,X2)),empty_set)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_6291,c_74]) ).
tcf(c_7311,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(X0,set_union2(X2,X1)),empty_set)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_6293,c_74]) ).
tcf(c_7312,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(X0,set_union2(X2,X1)),empty_set)
| ~ subset(X0,set_difference(X1,X2)) ),
inference(superposition,[status(thm)],[c_6374,c_74]) ).
tcf(c_7313,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(X0,set_union2(X1,X2)),empty_set)
| ~ subset(X0,set_difference(X1,X2)) ),
inference(superposition,[status(thm)],[c_6401,c_74]) ).
tcf(c_7314,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(set_difference(X3,X1),X2)
| ~ subset(X3,X0)
| ~ subset(set_difference(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_74,c_69]) ).
tcf(c_7315,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(set_difference(X0,X2),set_difference(X1,X2)) = empty_set )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_74,c_78]) ).
tcf(c_7316,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_union2(set_difference(X0,X2),set_difference(X1,X2)) = set_difference(X1,X2) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_74,c_66]) ).
tcf(c_7317,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ subset(X2,X0)
| ~ proper_subset(set_difference(X0,X1),set_difference(X2,X1)) ),
inference(superposition,[status(thm)],[c_74,c_98]) ).
tcf(c_7396,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(X0,X2)
| in(X1,X2)
| ~ subset(X0,unordered_pair(X1,X1)) ),
inference(superposition,[status(thm)],[c_52,c_99]) ).
tcf(c_7397,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(X0,X2)
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_5289,c_99]) ).
tcf(c_7398,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(X0,X2)
| ~ empty(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_5300,c_99]) ).
tcf(c_7399,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| ~ subset(X0,empty_set) ),
inference(superposition,[status(thm)],[c_5290,c_99]) ).
tcf(c_7401,plain,
! [X0: $i,X1: $i] :
( in(empty_set,X1)
| disjoint(X0,X1)
| ~ subset(X0,powerset(empty_set)) ),
inference(superposition,[status(thm)],[c_5259,c_99]) ).
tcf(c_7402,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,X1)
| disjoint(X0,unordered_pair(X2,X2))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_5260,c_99]) ).
tcf(c_7403,plain,
! [X0: $i,X1: $i] :
( in(empty_set,X1)
| disjoint(X0,powerset(empty_set))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_5272,c_99]) ).
tcf(c_7404,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(X0,X2)
| ~ empty(X1)
| ~ subset(X0,union(X1)) ),
inference(superposition,[status(thm)],[c_7109,c_99]) ).
tcf(c_7405,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(X0,union(X2))
| ~ empty(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_7110,c_99]) ).
tcf(c_7438,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(X0,X2)
| in(sK0(X0,X2),X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_89,c_123]) ).
tcf(c_7439,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(X2,X0)
| in(sK0(X2,X0),X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_90,c_123]) ).
tcf(c_7440,plain,
! [X0: $i,X1: $i] :
( in(sK5(X0),X1)
| ( X0 = empty_set )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_117,c_123]) ).
tcf(c_7441,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,X2)
| in(sK7(X0,X2),X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_122,c_123]) ).
tcf(c_7442,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,X2)
| ~ in(X3,X0)
| ~ subset(set_union2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_129,c_123]) ).
tcf(c_7443,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,X2)
| ~ in(X3,X1)
| ~ subset(set_union2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_130,c_123]) ).
tcf(c_7444,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,X2)
| ~ in(X1,union(X0))
| ~ subset(sK12(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_150,c_123]) ).
tcf(c_7445,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(X1,X0),X2)
| ~ subset(X1,X2)
| ~ in(X0,union(X1)) ),
inference(superposition,[status(thm)],[c_151,c_123]) ).
tcf(c_7446,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK13(X2,X3,X0),X1)
| ( cartesian_product2(X2,X3) = X0 )
| ( unordered_pair(unordered_pair(sK14(X2,X3,X0),sK14(X2,X3,X0)),unordered_pair(sK14(X2,X3,X0),sK15(X2,X3,X0))) = sK13(X2,X3,X0) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_1706,c_123]) ).
tcf(c_7449,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,X1)
| ~ subset(X2,X0)
| ~ subset(powerset(X0),X1) ),
inference(superposition,[status(thm)],[c_178,c_123]) ).
tcf(c_7452,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,X3)
| ~ subset(set_union2(unordered_pair(X0,X1),X2),X3) ),
inference(superposition,[status(thm)],[c_5624,c_123]) ).
tcf(c_7453,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X1,X3)
| ~ subset(set_union2(X0,unordered_pair(X1,X2)),X3) ),
inference(superposition,[status(thm)],[c_5626,c_123]) ).
tcf(c_7454,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X1,X3)
| ~ subset(set_union2(unordered_pair(X0,X1),X2),X3) ),
inference(superposition,[status(thm)],[c_5654,c_123]) ).
tcf(c_7455,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X2,X3)
| ~ subset(set_union2(X0,unordered_pair(X1,X2)),X3) ),
inference(superposition,[status(thm)],[c_5656,c_123]) ).
tcf(c_7456,plain,
! [X0: $i,X1: $i] :
( in(empty_set,X1)
| ~ subset(set_union2(powerset(empty_set),X0),X1) ),
inference(superposition,[status(thm)],[c_5716,c_123]) ).
tcf(c_7457,plain,
! [X0: $i,X1: $i] :
( in(empty_set,X1)
| ~ subset(set_union2(X0,powerset(empty_set)),X1) ),
inference(superposition,[status(thm)],[c_5734,c_123]) ).
tcf(c_7521,plain,
! [X0: $i,X1: $i] : disjoint(set_difference(empty_set,X0),X1),
inference(superposition,[status(thm)],[c_77,c_7399]) ).
tcf(c_7523,plain,
! [X0: $i] :
( disjoint(powerset(empty_set),X0)
| ~ in(empty_set,empty_set) ),
inference(superposition,[status(thm)],[c_5531,c_7399]) ).
tcf(c_7531,plain,
! [X0: $i,X1: $i] :
( ( union(set_difference(X0,X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6423,c_7111]) ).
tcf(c_7545,plain,
! [X0: $i,X1: $i] : ~ empty(unordered_pair(X0,powerset(union(powerset(X1))))),
inference(superposition,[status(thm)],[c_5360,c_5589]) ).
tcf(c_7546,plain,
! [X0: $i,X1: $i] : ~ in(unordered_pair(X0,powerset(union(powerset(union(X1))))),X1),
inference(superposition,[status(thm)],[c_61,c_5589]) ).
tcf(c_7560,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(set_union2(X2,X1))
| ~ in(X0,set_difference(X1,X2)) ),
inference(superposition,[status(thm)],[c_6375,c_5691]) ).
tcf(c_7565,plain,
! [X0: $i,X1: $i,X2: $i] : ~ in(powerset(powerset(union(set_union2(set_union2(X0,X1),X2)))),X0),
inference(superposition,[status(thm)],[c_129,c_5697]) ).
tcf(c_7566,plain,
! [X0: $i,X1: $i,X2: $i] : ~ in(powerset(powerset(union(set_union2(set_union2(X0,X1),X2)))),X1),
inference(superposition,[status(thm)],[c_130,c_5697]) ).
tcf(c_7567,plain,
! [X0: $i,X1: $i] : ~ subset(powerset(powerset(union(set_union2(powerset(X0),X1)))),X0),
inference(superposition,[status(thm)],[c_178,c_5697]) ).
tcf(c_7573,plain,
! [X0: $i] : ~ in(powerset(powerset(union(X0))),empty_set),
inference(superposition,[status(thm)],[c_5426,c_5697]) ).
tcf(c_7574,plain,
! [X0: $i,X1: $i] : ~ in(powerset(powerset(union(set_union2(X0,X1)))),set_difference(X1,X0)),
inference(superposition,[status(thm)],[c_6375,c_5697]) ).
tcf(c_7582,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : ~ in(powerset(set_union2(set_union2(set_union2(X0,X1),X2),X3)),X0),
inference(superposition,[status(thm)],[c_129,c_5807]) ).
tcf(c_7583,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : ~ in(powerset(set_union2(set_union2(set_union2(X0,X1),X2),X3)),X1),
inference(superposition,[status(thm)],[c_130,c_5807]) ).
tcf(c_7584,plain,
! [X0: $i,X1: $i,X2: $i] : ~ subset(powerset(set_union2(set_union2(powerset(X0),X1),X2)),X0),
inference(superposition,[status(thm)],[c_178,c_5807]) ).
tcf(c_7596,plain,
! [X0: $i,X1: $i] : ~ in(powerset(set_union2(X0,X1)),empty_set),
inference(superposition,[status(thm)],[c_5426,c_5807]) ).
tcf(c_7597,plain,
! [X0: $i,X1: $i,X2: $i] : ~ in(powerset(set_union2(set_union2(X0,X1),X2)),set_difference(X1,X0)),
inference(superposition,[status(thm)],[c_6375,c_5807]) ).
tcf(c_7620,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : ~ in(powerset(set_union2(X0,set_union2(set_union2(X1,X2),X3))),X1),
inference(superposition,[status(thm)],[c_129,c_5849]) ).
tcf(c_7621,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : ~ in(powerset(set_union2(X0,set_union2(set_union2(X1,X2),X3))),X2),
inference(superposition,[status(thm)],[c_130,c_5849]) ).
tcf(c_7622,plain,
! [X0: $i,X1: $i,X2: $i] : ~ subset(powerset(set_union2(X0,set_union2(powerset(X1),X2))),X1),
inference(superposition,[status(thm)],[c_178,c_5849]) ).
tcf(c_7634,plain,
! [X0: $i,X1: $i,X2: $i] : ~ in(powerset(set_union2(X0,set_union2(X1,X2))),set_difference(X2,X1)),
inference(superposition,[status(thm)],[c_6375,c_5849]) ).
tcf(c_7655,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(set_union2(X1,X2))
| ~ in(X0,set_union2(X1,X2)) ),
inference(superposition,[status(thm)],[c_6375,c_5954]) ).
tcf(c_7656,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(X1)
| ~ in(X0,set_difference(X1,X2)) ),
inference(superposition,[status(thm)],[c_6409,c_5954]) ).
tcf(c_7673,plain,
! [X0: $i,X1: $i,X2: $i] : ~ in(powerset(powerset(union(set_union2(X0,set_union2(X1,X2))))),X1),
inference(superposition,[status(thm)],[c_129,c_5960]) ).
tcf(c_7674,plain,
! [X0: $i,X1: $i,X2: $i] : ~ in(powerset(powerset(union(set_union2(X0,set_union2(X1,X2))))),X2),
inference(superposition,[status(thm)],[c_130,c_5960]) ).
tcf(c_7675,plain,
! [X0: $i,X1: $i] : ~ subset(powerset(powerset(union(set_union2(X0,powerset(X1))))),X1),
inference(superposition,[status(thm)],[c_178,c_5960]) ).
tcf(c_7682,plain,
! [X0: $i,X1: $i] : ~ in(powerset(powerset(union(set_union2(X0,X1)))),set_union2(X0,X1)),
inference(superposition,[status(thm)],[c_6375,c_5960]) ).
tcf(c_7683,plain,
! [X0: $i,X1: $i] : ~ in(powerset(powerset(union(X0))),set_difference(X0,X1)),
inference(superposition,[status(thm)],[c_6409,c_5960]) ).
tcf(c_7689,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : ~ in(powerset(set_union2(set_union2(X0,set_union2(X1,X2)),X3)),X1),
inference(superposition,[status(thm)],[c_129,c_5962]) ).
tcf(c_7690,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : ~ in(powerset(set_union2(set_union2(X0,set_union2(X1,X2)),X3)),X2),
inference(superposition,[status(thm)],[c_130,c_5962]) ).
tcf(c_7691,plain,
! [X0: $i,X1: $i,X2: $i] : ~ subset(powerset(set_union2(set_union2(X0,powerset(X1)),X2)),X1),
inference(superposition,[status(thm)],[c_178,c_5962]) ).
tcf(c_7704,plain,
! [X0: $i,X1: $i,X2: $i] : ~ in(powerset(set_union2(set_union2(X0,X1),X2)),set_union2(X0,X1)),
inference(superposition,[status(thm)],[c_6375,c_5962]) ).
tcf(c_7705,plain,
! [X0: $i,X1: $i,X2: $i] : ~ in(powerset(set_union2(X0,X1)),set_difference(X0,X2)),
inference(superposition,[status(thm)],[c_6409,c_5962]) ).
tcf(c_7720,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : ~ in(powerset(set_union2(X0,set_union2(X1,set_union2(X2,X3)))),X2),
inference(superposition,[status(thm)],[c_129,c_5963]) ).
tcf(c_7721,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : ~ in(powerset(set_union2(X0,set_union2(X1,set_union2(X2,X3)))),X3),
inference(superposition,[status(thm)],[c_130,c_5963]) ).
tcf(c_7722,plain,
! [X0: $i,X1: $i,X2: $i] : ~ subset(powerset(set_union2(X0,set_union2(X1,powerset(X2)))),X2),
inference(superposition,[status(thm)],[c_178,c_5963]) ).
tcf(c_7734,plain,
! [X0: $i,X1: $i,X2: $i] : ~ in(powerset(set_union2(X0,set_union2(X1,X2))),set_union2(X1,X2)),
inference(superposition,[status(thm)],[c_6375,c_5963]) ).
tcf(c_7735,plain,
! [X0: $i,X1: $i,X2: $i] : ~ in(powerset(set_union2(X0,X1)),set_difference(X1,X2)),
inference(superposition,[status(thm)],[c_6409,c_5963]) ).
tcf(c_7749,plain,
! [X0: $i,X1: $i] : set_union2(set_difference(X0,X1),set_union2(set_union2(X0,X1),X1)) = set_union2(set_union2(X0,X1),X1),
inference(superposition,[status(thm)],[c_93,c_6402]) ).
tcf(c_7750,plain,
! [X0: $i] : set_union2(empty_set,set_union2(empty_set,X0)) = set_union2(empty_set,X0),
inference(superposition,[status(thm)],[c_113,c_6402]) ).
tcf(c_7751,plain,
! [X0: $i] : set_union2(X0,set_union2(X0,empty_set)) = set_union2(X0,empty_set),
inference(superposition,[status(thm)],[c_114,c_6402]) ).
tcf(c_7753,plain,
! [X0: $i,X1: $i] : set_union2(empty_set,set_union2(set_difference(X0,X1),X0)) = set_union2(set_difference(X0,X1),X0),
inference(superposition,[status(thm)],[c_6290,c_6402]) ).
tcf(c_7754,plain,
! [X0: $i,X1: $i] : set_union2(empty_set,set_union2(X0,set_union2(X0,X1))) = set_union2(X0,set_union2(X0,X1)),
inference(superposition,[status(thm)],[c_6291,c_6402]) ).
tcf(c_7755,plain,
! [X0: $i,X1: $i] : set_union2(empty_set,set_union2(X0,set_union2(X1,X0))) = set_union2(X0,set_union2(X1,X0)),
inference(superposition,[status(thm)],[c_6293,c_6402]) ).
tcf(c_7756,plain,
! [X0: $i,X1: $i] : set_union2(empty_set,set_union2(set_difference(X0,X1),set_union2(X1,X0))) = set_union2(set_difference(X0,X1),set_union2(X1,X0)),
inference(superposition,[status(thm)],[c_6374,c_6402]) ).
tcf(c_7757,plain,
! [X0: $i,X1: $i] : set_union2(empty_set,set_union2(set_difference(X0,X1),set_union2(X0,X1))) = set_union2(set_difference(X0,X1),set_union2(X0,X1)),
inference(superposition,[status(thm)],[c_6401,c_6402]) ).
tcf(c_7764,plain,
! [X0: $i,X1: $i] : set_union2(set_difference(set_difference(X0,X1),set_union2(X1,X0)),set_union2(X1,X0)) = set_union2(X1,X0),
inference(superposition,[status(thm)],[c_6375,c_6402]) ).
tcf(c_7766,plain,
! [X0: $i,X1: $i] : set_union2(set_difference(X0,set_difference(X0,X1)),X0) = X0,
inference(superposition,[status(thm)],[c_6409,c_6402]) ).
tcf(c_7767,plain,
! [X0: $i,X1: $i] : set_union2(set_difference(set_difference(X0,X1),set_union2(X0,X1)),set_union2(X0,X1)) = set_union2(X0,X1),
inference(superposition,[status(thm)],[c_6402,c_6402]) ).
tcf(c_7771,plain,
! [X0: $i,X1: $i,X2: $i] : ~ in(powerset(set_union2(set_union2(X0,X1),X2)),set_difference(X0,X1)),
inference(superposition,[status(thm)],[c_6402,c_5807]) ).
tcf(c_7772,plain,
! [X0: $i,X1: $i] : ~ in(powerset(powerset(union(set_union2(X0,X1)))),set_difference(X0,X1)),
inference(superposition,[status(thm)],[c_6402,c_5697]) ).
tcf(c_7773,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(set_union2(X1,X2))
| ~ in(X0,set_difference(X1,X2)) ),
inference(superposition,[status(thm)],[c_6402,c_5691]) ).
tcf(c_7774,plain,
! [X0: $i,X1: $i] : set_difference(set_difference(set_difference(X0,X1),set_union2(X0,X1)),set_union2(X0,X1)) = empty_set,
inference(superposition,[status(thm)],[c_6402,c_6401]) ).
tcf(c_7775,plain,
! [X0: $i,X1: $i] : set_difference(set_union2(X0,X1),set_union2(X0,X1)) = set_difference(set_difference(X0,X1),set_union2(X0,X1)),
inference(superposition,[status(thm)],[c_6402,c_93]) ).
tcf(c_7776,plain,
! [X0: $i,X1: $i] : ~ proper_subset(set_union2(X0,X1),set_difference(set_difference(X0,X1),set_union2(X0,X1))),
inference(superposition,[status(thm)],[c_6402,c_6403]) ).
tcf(c_7777,plain,
! [X0: $i,X1: $i] : ~ proper_subset(set_union2(X0,X1),set_difference(set_union2(X0,X1),set_difference(X0,X1))),
inference(superposition,[status(thm)],[c_6402,c_6325]) ).
tcf(c_7779,plain,
! [X0: $i,X1: $i] : subset(set_difference(set_difference(X0,X1),set_union2(X0,X1)),set_union2(X0,X1)),
inference(superposition,[status(thm)],[c_6402,c_6372]) ).
tcf(c_7790,plain,
! [X0: $i,X1: $i,X2: $i] : ~ in(powerset(set_union2(X0,set_union2(X1,X2))),set_difference(X1,X2)),
inference(superposition,[status(thm)],[c_6402,c_5849]) ).
tcf(c_7795,plain,
! [X0: $i,X1: $i] : set_union2(set_difference(set_union2(X0,X1),set_difference(X0,X1)),set_union2(X0,X1)) = set_union2(X0,X1),
inference(superposition,[status(thm)],[c_6402,c_6375]) ).
tcf(c_7796,plain,
! [X0: $i,X1: $i] : set_difference(set_difference(set_union2(X0,X1),set_difference(X0,X1)),set_union2(X0,X1)) = empty_set,
inference(superposition,[status(thm)],[c_6402,c_6374]) ).
tcf(c_7798,plain,
! [X0: $i,X1: $i] : subset(set_difference(set_union2(X0,X1),set_difference(X0,X1)),set_union2(X0,X1)),
inference(superposition,[status(thm)],[c_6402,c_6334]) ).
tcf(c_7851,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(set_difference(X0,set_difference(X0,X1)),X2)
| in(sK0(set_difference(X0,set_difference(X0,X1)),X2),X1) ),
inference(superposition,[status(thm)],[c_89,c_174]) ).
tcf(c_7852,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(X0,set_difference(X1,set_difference(X1,X2)))
| in(sK0(X0,set_difference(X1,set_difference(X1,X2))),X2) ),
inference(superposition,[status(thm)],[c_90,c_174]) ).
tcf(c_7853,plain,
! [X0: $i,X1: $i] :
( in(sK5(set_difference(X0,set_difference(X0,X1))),X1)
| ( set_difference(X0,set_difference(X0,X1)) = empty_set ) ),
inference(superposition,[status(thm)],[c_117,c_174]) ).
tcf(c_7854,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(X0,set_difference(X0,X1)),X2)
| in(sK7(set_difference(X0,set_difference(X0,X1)),X2),X1) ),
inference(superposition,[status(thm)],[c_122,c_174]) ).
tcf(c_7855,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(set_difference(X1,set_difference(X1,X2)),X0),X2)
| ~ in(X0,union(set_difference(X1,set_difference(X1,X2)))) ),
inference(superposition,[status(thm)],[c_151,c_174]) ).
tcf(c_7856,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK13(X0,X1,set_difference(X2,set_difference(X2,X3))),X3)
| ( set_difference(X2,set_difference(X2,X3)) = cartesian_product2(X0,X1) )
| ( unordered_pair(unordered_pair(sK14(X0,X1,set_difference(X2,set_difference(X2,X3))),sK14(X0,X1,set_difference(X2,set_difference(X2,X3)))),unordered_pair(sK14(X0,X1,set_difference(X2,set_difference(X2,X3))),sK15(X0,X1,set_difference(X2,set_difference(X2,X3))))) = sK13(X0,X1,set_difference(X2,set_difference(X2,X3))) ) ),
inference(superposition,[status(thm)],[c_1706,c_174]) ).
tcf(c_7858,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ in(X0,set_difference(set_union2(X1,X2),set_difference(X1,X2))) ),
inference(superposition,[status(thm)],[c_93,c_174]) ).
tcf(c_7860,plain,
! [X0: $i,X1: $i] :
( in(X0,empty_set)
| ~ in(X0,set_difference(X1,X1)) ),
inference(superposition,[status(thm)],[c_114,c_174]) ).
tcf(c_7861,plain,
! [X0: $i,X1: $i] :
( in(X0,X1)
| ~ in(X0,set_difference(X1,empty_set)) ),
inference(superposition,[status(thm)],[c_1252,c_174]) ).
tcf(c_7862,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X1)
| ~ in(X0,set_difference(set_difference(X1,X2),empty_set)) ),
inference(superposition,[status(thm)],[c_6290,c_174]) ).
tcf(c_7863,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,set_union2(X1,X2))
| ~ in(X0,set_difference(X1,empty_set)) ),
inference(superposition,[status(thm)],[c_6291,c_174]) ).
tcf(c_7864,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,set_union2(X2,X1))
| ~ in(X0,set_difference(X1,empty_set)) ),
inference(superposition,[status(thm)],[c_6293,c_174]) ).
tcf(c_7865,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,set_union2(X2,X1))
| ~ in(X0,set_difference(set_difference(X1,X2),empty_set)) ),
inference(superposition,[status(thm)],[c_6374,c_174]) ).
tcf(c_7866,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,set_union2(X1,X2))
| ~ in(X0,set_difference(set_difference(X1,X2),empty_set)) ),
inference(superposition,[status(thm)],[c_6401,c_174]) ).
tcf(c_7869,plain,
! [X0: $i,X1: $i] : ~ in(X0,set_difference(X1,X1)),
inference(forward_subsumption_resolution,[status(thm)],[c_7860,c_118]) ).
tcf(c_7944,plain,
! [X0: $i,X1: $i] :
( proper_subset(unordered_pair(X0,X0),X1)
| ( unordered_pair(X0,X0) = X1 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_80,c_181]) ).
tcf(c_7945,plain,
! [X0: $i,X1: $i] :
( proper_subset(X0,X1)
| ( X0 = X1 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5360,c_181]) ).
tcf(c_7946,plain,
! [X0: $i,X1: $i] :
( proper_subset(X0,union(X1))
| ( union(X1) = X0 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_61,c_181]) ).
tcf(c_7947,plain,
! [X0: $i] :
( proper_subset(empty_set,X0)
| ( X0 = empty_set ) ),
inference(superposition,[status(thm)],[c_73,c_181]) ).
tcf(c_7948,plain,
! [X0: $i,X1: $i,X2: $i] :
( proper_subset(set_difference(X0,X2),set_difference(X1,X2))
| ( set_difference(X0,X2) = set_difference(X1,X2) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_74,c_181]) ).
tcf(c_7949,plain,
! [X0: $i,X1: $i] :
( proper_subset(set_difference(X0,X1),X0)
| ( set_difference(X0,X1) = X0 ) ),
inference(superposition,[status(thm)],[c_77,c_181]) ).
tcf(c_7950,plain,
! [X0: $i,X1: $i] :
( proper_subset(X0,set_union2(X0,X1))
| ( set_union2(X0,X1) = X0 ) ),
inference(superposition,[status(thm)],[c_103,c_181]) ).
tcf(c_7952,plain,
! [X0: $i,X1: $i] :
( proper_subset(X1,set_union2(X0,X1))
| ( set_union2(X0,X1) = X1 ) ),
inference(superposition,[status(thm)],[c_5425,c_181]) ).
tcf(c_7953,plain,
! [X0: $i] :
( proper_subset(powerset(empty_set),X0)
| ( powerset(empty_set) = X0 )
| ~ in(empty_set,X0) ),
inference(superposition,[status(thm)],[c_5531,c_181]) ).
tcf(c_7954,plain,
! [X0: $i,X1: $i] :
( proper_subset(set_difference(X1,X0),set_union2(X0,X1))
| ( set_union2(X0,X1) = set_difference(X1,X0) ) ),
inference(superposition,[status(thm)],[c_6334,c_181]) ).
tcf(c_7955,plain,
! [X0: $i,X1: $i] :
( proper_subset(set_difference(X0,X1),set_union2(X0,X1))
| ( set_union2(X0,X1) = set_difference(X0,X1) ) ),
inference(superposition,[status(thm)],[c_6372,c_181]) ).
tcf(c_7956,plain,
! [X0: $i,X1: $i] :
( proper_subset(union(X0),X1)
| ( union(X0) = X1 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7112,c_181]) ).
tcf(c_8047,plain,
! [X0: $i,X1: $i] :
( ( set_difference(unordered_pair(X0,X0),set_difference(unordered_pair(X0,X0),X1)) = unordered_pair(X0,X0) )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_80,c_72]) ).
tcf(c_8048,plain,
! [X0: $i,X1: $i] :
( ( set_difference(X0,set_difference(X0,X1)) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5360,c_72]) ).
tcf(c_8049,plain,
! [X0: $i,X1: $i] :
( ( set_difference(X0,set_difference(X0,union(X1))) = X0 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_61,c_72]) ).
tcf(c_8050,plain,
! [X0: $i] : set_difference(empty_set,set_difference(empty_set,X0)) = empty_set,
inference(superposition,[status(thm)],[c_73,c_72]) ).
tcf(c_8051,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(set_difference(X0,X2),set_difference(set_difference(X0,X2),set_difference(X1,X2))) = set_difference(X0,X2) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_74,c_72]) ).
tcf(c_8052,plain,
! [X0: $i,X1: $i] : set_difference(set_difference(X0,X1),set_difference(set_difference(X0,X1),X0)) = set_difference(X0,X1),
inference(superposition,[status(thm)],[c_77,c_72]) ).
tcf(c_8053,plain,
! [X0: $i,X1: $i] : set_difference(X0,set_difference(X0,set_union2(X0,X1))) = X0,
inference(superposition,[status(thm)],[c_103,c_72]) ).
tcf(c_8054,plain,
! [X0: $i] : set_difference(X0,set_difference(X0,X0)) = X0,
inference(superposition,[status(thm)],[c_139,c_72]) ).
tcf(c_8055,plain,
! [X0: $i,X1: $i] : set_difference(X0,set_difference(X0,set_union2(X1,X0))) = X0,
inference(superposition,[status(thm)],[c_5425,c_72]) ).
tcf(c_8056,plain,
! [X0: $i] :
( ( set_difference(powerset(empty_set),set_difference(powerset(empty_set),X0)) = powerset(empty_set) )
| ~ in(empty_set,X0) ),
inference(superposition,[status(thm)],[c_5531,c_72]) ).
tcf(c_8057,plain,
! [X0: $i,X1: $i] : set_difference(set_difference(X0,X1),set_difference(set_difference(X0,X1),set_union2(X1,X0))) = set_difference(X0,X1),
inference(superposition,[status(thm)],[c_6334,c_72]) ).
tcf(c_8058,plain,
! [X0: $i,X1: $i] : set_difference(set_difference(X0,X1),set_difference(set_difference(X0,X1),set_union2(X0,X1))) = set_difference(X0,X1),
inference(superposition,[status(thm)],[c_6372,c_72]) ).
tcf(c_8059,plain,
! [X0: $i,X1: $i] :
( ( set_difference(union(X0),set_difference(union(X0),X1)) = union(X0) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7112,c_72]) ).
tcf(c_8070,plain,
! [X0: $i,X1: $i] : set_difference(set_difference(X0,X1),empty_set) = set_difference(X0,X1),
inference(light_normalisation,[status(thm)],[c_8052,c_6290]) ).
tcf(c_8101,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(X0,X1)
| ~ disjoint(X0,X2)
| ~ in(sK0(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_89,c_91]) ).
tcf(c_8102,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(X0,X1)
| ~ disjoint(X1,X2)
| ~ in(sK0(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_90,c_91]) ).
tcf(c_8103,plain,
! [X0: $i,X1: $i] :
( ( X0 = empty_set )
| ~ disjoint(X0,X1)
| ~ in(sK5(X0),X1) ),
inference(superposition,[status(thm)],[c_117,c_91]) ).
tcf(c_8104,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,X1)
| ~ disjoint(X0,X2)
| ~ in(sK7(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_122,c_91]) ).
tcf(c_8105,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ in(X3,X2)
| ~ in(X3,X0)
| ~ disjoint(set_union2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_129,c_91]) ).
tcf(c_8106,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ in(X3,X2)
| ~ in(X3,X1)
| ~ disjoint(set_union2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_130,c_91]) ).
tcf(c_8107,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(X1,X2)
| ~ in(X1,union(X0))
| ~ disjoint(sK12(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_150,c_91]) ).
tcf(c_8108,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ disjoint(X0,X2)
| ~ in(X1,union(X0))
| ~ in(sK12(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_151,c_91]) ).
tcf(c_8109,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( cartesian_product2(X0,X1) = X2 )
| ( unordered_pair(unordered_pair(sK14(X0,X1,X2),sK14(X0,X1,X2)),unordered_pair(sK14(X0,X1,X2),sK15(X0,X1,X2))) = sK13(X0,X1,X2) )
| ~ disjoint(X2,X3)
| ~ in(sK13(X0,X1,X2),X3) ),
inference(superposition,[status(thm)],[c_1706,c_91]) ).
tcf(c_8110,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(X0,X2)
| ~ disjoint(unordered_pair(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_164,c_91]) ).
tcf(c_8111,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(X1,X2)
| ~ disjoint(unordered_pair(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_165,c_91]) ).
tcf(c_8112,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ subset(X2,X0)
| ~ in(X2,X1)
| ~ disjoint(powerset(X0),X1) ),
inference(superposition,[status(thm)],[c_178,c_91]) ).
tcf(c_8114,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( cartesian_product2(X0,X1) = empty_set )
| ~ disjoint(sK13(X0,X1,empty_set),X2)
| ~ in(unordered_pair(sK14(X0,X1,empty_set),sK14(X0,X1,empty_set)),X2) ),
inference(superposition,[status(thm)],[c_5326,c_91]) ).
tcf(c_8115,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ in(X0,X3)
| ~ disjoint(set_union2(unordered_pair(X0,X1),X2),X3) ),
inference(superposition,[status(thm)],[c_5624,c_91]) ).
tcf(c_8116,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ in(X1,X3)
| ~ disjoint(set_union2(X0,unordered_pair(X1,X2)),X3) ),
inference(superposition,[status(thm)],[c_5626,c_91]) ).
tcf(c_8117,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ in(X1,X3)
| ~ disjoint(set_union2(unordered_pair(X0,X1),X2),X3) ),
inference(superposition,[status(thm)],[c_5654,c_91]) ).
tcf(c_8118,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ in(X2,X3)
| ~ disjoint(set_union2(X0,unordered_pair(X1,X2)),X3) ),
inference(superposition,[status(thm)],[c_5656,c_91]) ).
tcf(c_8119,plain,
! [X0: $i,X1: $i] :
( ~ in(empty_set,X1)
| ~ disjoint(set_union2(powerset(empty_set),X0),X1) ),
inference(superposition,[status(thm)],[c_5716,c_91]) ).
tcf(c_8120,plain,
! [X0: $i,X1: $i] :
( ~ in(empty_set,X1)
| ~ disjoint(set_union2(X0,powerset(empty_set)),X1) ),
inference(superposition,[status(thm)],[c_5734,c_91]) ).
tcf(c_8261,plain,
! [X0: $i] :
( ~ empty(powerset(empty_set))
| ~ in(empty_set,X0) ),
inference(superposition,[status(thm)],[c_5289,c_6019]) ).
tcf(c_8262,plain,
! [X0: $i] :
( ~ empty(X0)
| ~ in(empty_set,X0) ),
inference(superposition,[status(thm)],[c_5300,c_6019]) ).
tcf(c_8263,plain,
~ in(empty_set,empty_set),
inference(superposition,[status(thm)],[c_5294,c_6019]) ).
tcf(c_8265,plain,
! [X0: $i] :
( in(X0,powerset(empty_set))
| ~ in(empty_set,unordered_pair(X0,X0)) ),
inference(superposition,[status(thm)],[c_5260,c_6019]) ).
tcf(c_8267,plain,
! [X0: $i] :
( ~ empty(X0)
| ~ in(empty_set,union(X0)) ),
inference(superposition,[status(thm)],[c_7110,c_6019]) ).
tcf(c_8274,plain,
! [X0: $i,X1: $i] : ~ in(powerset(powerset(union(powerset(union(set_union2(X0,X1)))))),X0),
inference(superposition,[status(thm)],[c_129,c_6031]) ).
tcf(c_8275,plain,
! [X0: $i,X1: $i] : ~ in(powerset(powerset(union(powerset(union(set_union2(X0,X1)))))),X1),
inference(superposition,[status(thm)],[c_130,c_6031]) ).
tcf(c_8276,plain,
! [X0: $i] : ~ subset(powerset(powerset(union(powerset(union(powerset(X0)))))),X0),
inference(superposition,[status(thm)],[c_178,c_6031]) ).
tcf(c_8277,plain,
~ in(powerset(powerset(union(powerset(empty_set)))),empty_set),
inference(superposition,[status(thm)],[c_7079,c_6031]) ).
tcf(c_8284,plain,
! [X0: $i,X1: $i] :
( in(empty_set,union(set_union2(X0,X1)))
| ~ in(powerset(empty_set),X0) ),
inference(superposition,[status(thm)],[c_129,c_6040]) ).
tcf(c_8285,plain,
! [X0: $i,X1: $i] :
( in(empty_set,union(set_union2(X1,X0)))
| ~ in(powerset(empty_set),X0) ),
inference(superposition,[status(thm)],[c_130,c_6040]) ).
tcf(c_8286,plain,
! [X0: $i] :
( in(empty_set,union(sK12(X0,powerset(empty_set))))
| ~ in(powerset(empty_set),union(X0)) ),
inference(superposition,[status(thm)],[c_150,c_6040]) ).
tcf(c_8287,plain,
! [X0: $i] : in(empty_set,union(unordered_pair(powerset(empty_set),X0))),
inference(superposition,[status(thm)],[c_164,c_6040]) ).
tcf(c_8288,plain,
! [X0: $i] : in(empty_set,union(unordered_pair(X0,powerset(empty_set)))),
inference(superposition,[status(thm)],[c_165,c_6040]) ).
tcf(c_8289,plain,
! [X0: $i] :
( in(empty_set,union(powerset(X0)))
| ~ subset(powerset(empty_set),X0) ),
inference(superposition,[status(thm)],[c_178,c_6040]) ).
tcf(c_8290,plain,
! [X0: $i,X1: $i] : in(empty_set,union(set_union2(unordered_pair(powerset(empty_set),X0),X1))),
inference(superposition,[status(thm)],[c_5624,c_6040]) ).
tcf(c_8291,plain,
! [X0: $i,X1: $i] : in(empty_set,union(set_union2(X0,unordered_pair(powerset(empty_set),X1)))),
inference(superposition,[status(thm)],[c_5626,c_6040]) ).
tcf(c_8292,plain,
! [X0: $i,X1: $i] : in(empty_set,union(set_union2(unordered_pair(X0,powerset(empty_set)),X1))),
inference(superposition,[status(thm)],[c_5654,c_6040]) ).
tcf(c_8293,plain,
! [X0: $i,X1: $i] : in(empty_set,union(set_union2(X0,unordered_pair(X1,powerset(empty_set))))),
inference(superposition,[status(thm)],[c_5656,c_6040]) ).
tcf(c_8339,plain,
! [X0: $i,X1: $i] :
( ~ in(empty_set,X1)
| ~ disjoint(union(unordered_pair(powerset(empty_set),X0)),X1) ),
inference(superposition,[status(thm)],[c_8287,c_91]) ).
tcf(c_8340,plain,
! [X0: $i,X1: $i] :
( in(empty_set,X1)
| ~ subset(union(unordered_pair(powerset(empty_set),X0)),X1) ),
inference(superposition,[status(thm)],[c_8287,c_123]) ).
tcf(c_8341,plain,
! [X0: $i] : ~ in(union(unordered_pair(powerset(empty_set),X0)),empty_set),
inference(superposition,[status(thm)],[c_8287,c_124]) ).
tcf(c_8342,plain,
! [X0: $i] : ~ empty(union(unordered_pair(powerset(empty_set),X0))),
inference(superposition,[status(thm)],[c_8287,c_184]) ).
tcf(c_8343,plain,
! [X0: $i] : ~ empty(unordered_pair(powerset(empty_set),X0)),
inference(superposition,[status(thm)],[c_8287,c_7039]) ).
tcf(c_8352,plain,
! [X0: $i,X1: $i] :
( ~ in(empty_set,X1)
| ~ disjoint(union(unordered_pair(X0,powerset(empty_set))),X1) ),
inference(superposition,[status(thm)],[c_8288,c_91]) ).
tcf(c_8353,plain,
! [X0: $i,X1: $i] :
( in(empty_set,X1)
| ~ subset(union(unordered_pair(X0,powerset(empty_set))),X1) ),
inference(superposition,[status(thm)],[c_8288,c_123]) ).
tcf(c_8354,plain,
! [X0: $i] : ~ in(union(unordered_pair(X0,powerset(empty_set))),empty_set),
inference(superposition,[status(thm)],[c_8288,c_124]) ).
tcf(c_8355,plain,
! [X0: $i] : ~ empty(union(unordered_pair(X0,powerset(empty_set)))),
inference(superposition,[status(thm)],[c_8288,c_184]) ).
tcf(c_8356,plain,
! [X0: $i] : ~ empty(unordered_pair(X0,powerset(empty_set))),
inference(superposition,[status(thm)],[c_8288,c_7039]) ).
tcf(c_8404,plain,
! [X0: $i,X1: $i] : ~ in(set_union2(powerset(X0),X1),X0),
inference(superposition,[status(thm)],[c_80,c_6050]) ).
tcf(c_8405,plain,
! [X0: $i,X1: $i,X2: $i] : ~ empty(unordered_pair(set_union2(powerset(X0),X1),X2)),
inference(superposition,[status(thm)],[c_5360,c_6050]) ).
tcf(c_8406,plain,
! [X0: $i,X1: $i,X2: $i] : ~ in(unordered_pair(set_union2(powerset(union(X0)),X1),X2),X0),
inference(superposition,[status(thm)],[c_61,c_6050]) ).
tcf(c_8417,plain,
! [X0: $i] : set_difference(set_difference(X0,empty_set),set_union2(empty_set,X0)) = empty_set,
inference(superposition,[status(thm)],[c_114,c_6603]) ).
tcf(c_8419,plain,
! [X0: $i,X1: $i] : set_difference(set_difference(set_difference(X0,X1),X1),set_union2(X1,set_union2(X0,X1))) = empty_set,
inference(superposition,[status(thm)],[c_93,c_6603]) ).
tcf(c_8422,plain,
! [X0: $i] : set_difference(set_difference(empty_set,X0),set_union2(X0,X0)) = empty_set,
inference(superposition,[status(thm)],[c_1252,c_6603]) ).
tcf(c_8423,plain,
! [X0: $i,X1: $i] : set_difference(set_difference(empty_set,X0),set_union2(X0,set_difference(X0,X1))) = empty_set,
inference(superposition,[status(thm)],[c_6290,c_6603]) ).
tcf(c_8424,plain,
! [X0: $i,X1: $i] : set_difference(set_difference(empty_set,set_union2(X0,X1)),set_union2(set_union2(X0,X1),X0)) = empty_set,
inference(superposition,[status(thm)],[c_6291,c_6603]) ).
tcf(c_8425,plain,
! [X0: $i,X1: $i] : set_difference(set_difference(empty_set,set_union2(X0,X1)),set_union2(set_union2(X0,X1),X1)) = empty_set,
inference(superposition,[status(thm)],[c_6293,c_6603]) ).
tcf(c_8426,plain,
! [X0: $i,X1: $i] : set_difference(set_difference(empty_set,set_union2(X0,X1)),set_union2(set_union2(X0,X1),set_difference(X1,X0))) = empty_set,
inference(superposition,[status(thm)],[c_6374,c_6603]) ).
tcf(c_8427,plain,
! [X0: $i,X1: $i] : set_difference(set_difference(empty_set,set_union2(X0,X1)),set_union2(set_union2(X0,X1),set_difference(X0,X1))) = empty_set,
inference(superposition,[status(thm)],[c_6401,c_6603]) ).
tcf(c_8430,plain,
! [X0: $i,X1: $i] : set_difference(set_difference(set_difference(set_difference(X0,X1),X1),X1),set_union2(X1,X0)) = empty_set,
inference(superposition,[status(thm)],[c_85,c_6603]) ).
tcf(c_8431,plain,
! [X0: $i] : set_difference(set_difference(set_difference(empty_set,X0),X0),X0) = empty_set,
inference(superposition,[status(thm)],[c_116,c_6603]) ).
tcf(c_8432,plain,
! [X0: $i] : set_difference(set_difference(set_difference(X0,X0),X0),X0) = empty_set,
inference(superposition,[status(thm)],[c_125,c_6603]) ).
tcf(c_8433,plain,
! [X0: $i,X1: $i] : set_difference(set_difference(set_difference(X0,X1),X1),set_union2(X0,X1)) = empty_set,
inference(superposition,[status(thm)],[c_132,c_6603]) ).
tcf(c_8434,plain,
! [X0: $i] : set_difference(set_difference(set_difference(X0,empty_set),empty_set),X0) = empty_set,
inference(superposition,[status(thm)],[c_5426,c_6603]) ).
tcf(c_8435,plain,
! [X0: $i,X1: $i] : set_difference(set_difference(set_difference(set_union2(X0,X1),set_difference(X1,X0)),set_difference(X1,X0)),set_union2(X0,X1)) = empty_set,
inference(superposition,[status(thm)],[c_6375,c_6603]) ).
tcf(c_8436,plain,
! [X0: $i,X1: $i] : set_difference(set_difference(set_difference(set_union2(X0,X1),set_difference(X0,X1)),set_difference(X0,X1)),set_union2(X0,X1)) = empty_set,
inference(superposition,[status(thm)],[c_6402,c_6603]) ).
tcf(c_8437,plain,
! [X0: $i,X1: $i] : set_difference(set_difference(set_difference(set_difference(X0,X1),X0),X0),X0) = empty_set,
inference(superposition,[status(thm)],[c_6409,c_6603]) ).
tcf(c_8438,plain,
! [X0: $i,X1: $i] : set_difference(set_difference(empty_set,set_union2(X0,X1)),set_union2(set_union2(X0,X1),set_difference(set_difference(X1,X0),X0))) = empty_set,
inference(superposition,[status(thm)],[c_6603,c_6603]) ).
tcf(c_8439,plain,
! [X0: $i,X1: $i] : set_union2(empty_set,set_union2(set_difference(set_difference(X0,X1),X1),set_union2(X1,X0))) = set_union2(set_difference(set_difference(X0,X1),X1),set_union2(X1,X0)),
inference(superposition,[status(thm)],[c_6603,c_6402]) ).
tcf(c_8440,plain,
! [X0: $i,X1: $i] : set_difference(empty_set,set_union2(set_difference(set_difference(X0,X1),X1),set_union2(X1,X0))) = empty_set,
inference(superposition,[status(thm)],[c_6603,c_6401]) ).
tcf(c_8441,plain,
! [X0: $i,X1: $i] : set_union2(empty_set,set_union2(set_union2(X0,X1),set_difference(set_difference(X1,X0),X0))) = set_union2(set_union2(X0,X1),set_difference(set_difference(X1,X0),X0)),
inference(superposition,[status(thm)],[c_6603,c_6375]) ).
tcf(c_8442,plain,
! [X0: $i,X1: $i] :
( disjoint(set_difference(set_difference(X0,X1),X1),set_union2(X1,X0))
| ( set_difference(set_difference(X0,X1),X1) != empty_set ) ),
inference(superposition,[status(thm)],[c_6603,c_104]) ).
tcf(c_8443,plain,
! [X0: $i,X1: $i] : set_difference(empty_set,set_union2(set_union2(X0,X1),set_difference(set_difference(X1,X0),X0))) = empty_set,
inference(superposition,[status(thm)],[c_6603,c_6374]) ).
tcf(c_8444,plain,
! [X0: $i,X1: $i] : ~ proper_subset(set_union2(set_difference(set_difference(X0,X1),X1),set_union2(X1,X0)),empty_set),
inference(superposition,[status(thm)],[c_6603,c_6403]) ).
tcf(c_8445,plain,
! [X0: $i,X1: $i] : set_difference(empty_set,set_difference(set_difference(X0,X1),X1)) = empty_set,
inference(superposition,[status(thm)],[c_6603,c_6290]) ).
tcf(c_8447,plain,
! [X0: $i,X1: $i] : ~ in(powerset(set_difference(set_difference(X0,X1),X1)),empty_set),
inference(superposition,[status(thm)],[c_6603,c_6418]) ).
tcf(c_8448,plain,
! [X0: $i,X1: $i] : set_union2(set_difference(set_difference(X0,X1),X1),empty_set) = set_difference(set_difference(X0,X1),X1),
inference(superposition,[status(thm)],[c_6603,c_6409]) ).
tcf(c_8449,plain,
! [X0: $i,X1: $i] : subset(empty_set,set_union2(set_difference(set_difference(X0,X1),X1),set_union2(X1,X0))),
inference(superposition,[status(thm)],[c_6603,c_6372]) ).
tcf(c_8450,plain,
! [X0: $i,X1: $i] : subset(empty_set,set_union2(set_union2(X0,X1),set_difference(set_difference(X1,X0),X0))),
inference(superposition,[status(thm)],[c_6603,c_6334]) ).
tcf(c_8452,plain,
! [X0: $i,X1: $i] : ~ proper_subset(set_difference(set_difference(X0,X1),X1),empty_set),
inference(superposition,[status(thm)],[c_6603,c_5343]) ).
tcf(c_8453,plain,
! [X0: $i,X1: $i] : subset(empty_set,set_difference(set_difference(X0,X1),X1)),
inference(superposition,[status(thm)],[c_6603,c_77]) ).
tcf(c_8454,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,set_union2(X2,X1))
| ~ in(X0,set_difference(set_difference(set_difference(X1,X2),X2),empty_set)) ),
inference(superposition,[status(thm)],[c_6603,c_174]) ).
tcf(c_8455,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(X0,set_union2(X2,X1)),empty_set)
| ~ subset(X0,set_difference(set_difference(X1,X2),X2)) ),
inference(superposition,[status(thm)],[c_6603,c_74]) ).
tcf(c_8457,plain,
! [X0: $i,X1: $i,X2: $i] : ~ in(unordered_pair(X0,set_difference(set_difference(X1,X2),X2)),empty_set),
inference(superposition,[status(thm)],[c_6603,c_6426]) ).
tcf(c_8459,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(empty_set,set_difference(X2,set_union2(X1,X0)))
| ~ subset(set_difference(set_difference(X0,X1),X1),X2) ),
inference(superposition,[status(thm)],[c_6603,c_74]) ).
tcf(c_8460,plain,
! [X0: $i,X1: $i,X2: $i] : ~ in(unordered_pair(set_difference(set_difference(X0,X1),X1),X2),empty_set),
inference(superposition,[status(thm)],[c_6603,c_6416]) ).
tcf(c_8461,plain,
! [X0: $i,X1: $i] : ~ proper_subset(set_union2(set_union2(X0,X1),set_difference(set_difference(X1,X0),X0)),empty_set),
inference(superposition,[status(thm)],[c_6603,c_6325]) ).
tcf(c_8462,plain,
! [X0: $i,X1: $i] : set_union2(set_union2(X0,X1),set_difference(set_difference(X1,X0),X0)) = set_union2(set_union2(X0,X1),empty_set),
inference(superposition,[status(thm)],[c_6603,c_85]) ).
tcf(c_8477,plain,
! [X0: $i,X1: $i] : set_difference(set_difference(empty_set,set_union2(X0,X1)),set_union2(X0,X1)) = empty_set,
inference(light_normalisation,[status(thm)],[c_8427,c_6651]) ).
tcf(c_8478,plain,
! [X0: $i,X1: $i] : set_difference(set_difference(empty_set,set_union2(X0,X1)),set_union2(set_union2(X0,X1),empty_set)) = empty_set,
inference(light_normalisation,[status(thm)],[c_8426,c_6623]) ).
tcf(c_8481,plain,
! [X0: $i,X1: $i] : set_difference(set_difference(set_difference(X0,set_difference(X1,X0)),set_difference(X1,X0)),set_union2(X0,X1)) = empty_set,
inference(light_normalisation,[status(thm)],[c_8435,c_6643]) ).
tcf(c_8528,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| ( set_union2(unordered_pair(sK0(X0,X1),sK0(X0,X1)),X0) = X0 ) ),
inference(superposition,[status(thm)],[c_89,c_95]) ).
tcf(c_8529,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| ( set_union2(unordered_pair(sK0(X0,X1),sK0(X0,X1)),X1) = X1 ) ),
inference(superposition,[status(thm)],[c_90,c_95]) ).
tcf(c_8530,plain,
! [X0: $i] :
( ( X0 = empty_set )
| ( set_union2(unordered_pair(sK5(X0),sK5(X0)),X0) = X0 ) ),
inference(superposition,[status(thm)],[c_117,c_95]) ).
tcf(c_8531,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ( set_union2(unordered_pair(sK7(X0,X1),sK7(X0,X1)),X0) = X0 ) ),
inference(superposition,[status(thm)],[c_122,c_95]) ).
tcf(c_8532,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_union2(unordered_pair(X0,X0),set_union2(X1,X2)) = set_union2(X1,X2) )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_129,c_95]) ).
tcf(c_8533,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_union2(unordered_pair(X0,X0),set_union2(X2,X1)) = set_union2(X2,X1) )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_130,c_95]) ).
tcf(c_8534,plain,
! [X0: $i,X1: $i] :
( ( set_union2(unordered_pair(X0,X0),sK12(X1,X0)) = sK12(X1,X0) )
| ~ in(X0,union(X1)) ),
inference(superposition,[status(thm)],[c_150,c_95]) ).
tcf(c_8535,plain,
! [X0: $i,X1: $i] :
( ( set_union2(unordered_pair(sK12(X1,X0),sK12(X1,X0)),X1) = X1 )
| ~ in(X0,union(X1)) ),
inference(superposition,[status(thm)],[c_151,c_95]) ).
tcf(c_8536,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( cartesian_product2(X0,X1) = X2 )
| ( set_union2(unordered_pair(sK13(X0,X1,X2),sK13(X0,X1,X2)),X2) = X2 )
| ( unordered_pair(unordered_pair(sK14(X0,X1,X2),sK14(X0,X1,X2)),unordered_pair(sK14(X0,X1,X2),sK15(X0,X1,X2))) = sK13(X0,X1,X2) ) ),
inference(superposition,[status(thm)],[c_1706,c_95]) ).
tcf(c_8537,plain,
! [X0: $i,X1: $i] : set_union2(unordered_pair(X0,X0),unordered_pair(X0,X1)) = unordered_pair(X0,X1),
inference(superposition,[status(thm)],[c_164,c_95]) ).
tcf(c_8538,plain,
! [X0: $i,X1: $i] : set_union2(unordered_pair(X0,X0),unordered_pair(X1,X0)) = unordered_pair(X1,X0),
inference(superposition,[status(thm)],[c_165,c_95]) ).
tcf(c_8539,plain,
! [X0: $i,X1: $i] :
( ( set_union2(unordered_pair(X0,X0),powerset(X1)) = powerset(X1) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_178,c_95]) ).
tcf(c_8540,plain,
set_union2(unordered_pair(empty_set,empty_set),powerset(empty_set)) = powerset(empty_set),
inference(superposition,[status(thm)],[c_5208,c_95]) ).
tcf(c_8541,plain,
! [X0: $i,X1: $i] :
( ( cartesian_product2(X0,X1) = empty_set )
| ( set_union2(unordered_pair(unordered_pair(sK14(X0,X1,empty_set),sK14(X0,X1,empty_set)),unordered_pair(sK14(X0,X1,empty_set),sK14(X0,X1,empty_set))),sK13(X0,X1,empty_set)) = sK13(X0,X1,empty_set) ) ),
inference(superposition,[status(thm)],[c_5326,c_95]) ).
tcf(c_8542,plain,
! [X0: $i,X1: $i,X2: $i] : set_union2(unordered_pair(X0,X0),set_union2(unordered_pair(X0,X1),X2)) = set_union2(unordered_pair(X0,X1),X2),
inference(superposition,[status(thm)],[c_5624,c_95]) ).
tcf(c_8543,plain,
! [X0: $i,X1: $i,X2: $i] : set_union2(unordered_pair(X0,X0),set_union2(X1,unordered_pair(X0,X2))) = set_union2(X1,unordered_pair(X0,X2)),
inference(superposition,[status(thm)],[c_5626,c_95]) ).
tcf(c_8544,plain,
! [X0: $i,X1: $i,X2: $i] : set_union2(unordered_pair(X0,X0),set_union2(unordered_pair(X1,X0),X2)) = set_union2(unordered_pair(X1,X0),X2),
inference(superposition,[status(thm)],[c_5654,c_95]) ).
tcf(c_8545,plain,
! [X0: $i,X1: $i,X2: $i] : set_union2(unordered_pair(X0,X0),set_union2(X1,unordered_pair(X2,X0))) = set_union2(X1,unordered_pair(X2,X0)),
inference(superposition,[status(thm)],[c_5656,c_95]) ).
tcf(c_8546,plain,
! [X0: $i] : set_union2(unordered_pair(empty_set,empty_set),set_union2(powerset(empty_set),X0)) = set_union2(powerset(empty_set),X0),
inference(superposition,[status(thm)],[c_5716,c_95]) ).
tcf(c_8547,plain,
! [X0: $i] : set_union2(unordered_pair(empty_set,empty_set),set_union2(X0,powerset(empty_set))) = set_union2(X0,powerset(empty_set)),
inference(superposition,[status(thm)],[c_5734,c_95]) ).
tcf(c_8548,plain,
! [X0: $i] : set_union2(unordered_pair(empty_set,empty_set),union(unordered_pair(powerset(empty_set),X0))) = union(unordered_pair(powerset(empty_set),X0)),
inference(superposition,[status(thm)],[c_8287,c_95]) ).
tcf(c_8549,plain,
! [X0: $i] : set_union2(unordered_pair(empty_set,empty_set),union(unordered_pair(X0,powerset(empty_set)))) = union(unordered_pair(X0,powerset(empty_set))),
inference(superposition,[status(thm)],[c_8288,c_95]) ).
tcf(c_8550,plain,
set_union2(powerset(empty_set),powerset(empty_set)) = powerset(empty_set),
inference(light_normalisation,[status(thm)],[c_8540,c_70]) ).
tcf(c_8551,plain,
! [X0: $i] : set_union2(powerset(empty_set),set_union2(X0,powerset(empty_set))) = set_union2(X0,powerset(empty_set)),
inference(light_normalisation,[status(thm)],[c_8547,c_70]) ).
tcf(c_8552,plain,
! [X0: $i] : set_union2(powerset(empty_set),set_union2(powerset(empty_set),X0)) = set_union2(powerset(empty_set),X0),
inference(light_normalisation,[status(thm)],[c_8546,c_70]) ).
tcf(c_8563,plain,
! [X0: $i] : set_union2(powerset(empty_set),union(unordered_pair(X0,powerset(empty_set)))) = union(unordered_pair(X0,powerset(empty_set))),
inference(light_normalisation,[status(thm)],[c_8549,c_70]) ).
tcf(c_8564,plain,
! [X0: $i] : set_union2(powerset(empty_set),union(unordered_pair(powerset(empty_set),X0))) = union(unordered_pair(powerset(empty_set),X0)),
inference(light_normalisation,[status(thm)],[c_8548,c_70]) ).
tcf(c_8613,plain,
! [X0: $i,X1: $i] :
( disjoint(set_union2(X0,X1),X1)
| in(sK1(set_union2(X0,X1),X1),set_difference(set_union2(X0,X1),set_difference(X0,X1))) ),
inference(superposition,[status(thm)],[c_93,c_96]) ).
tcf(c_8616,plain,
! [X0: $i] :
( disjoint(X0,X0)
| in(sK1(X0,X0),set_difference(X0,empty_set)) ),
inference(superposition,[status(thm)],[c_1252,c_96]) ).
tcf(c_8617,plain,
! [X0: $i,X1: $i] :
( disjoint(set_difference(X0,X1),X0)
| in(sK1(set_difference(X0,X1),X0),set_difference(set_difference(X0,X1),empty_set)) ),
inference(superposition,[status(thm)],[c_6290,c_96]) ).
tcf(c_8618,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,set_union2(X0,X1))
| in(sK1(X0,set_union2(X0,X1)),set_difference(X0,empty_set)) ),
inference(superposition,[status(thm)],[c_6291,c_96]) ).
tcf(c_8619,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,set_union2(X1,X0))
| in(sK1(X0,set_union2(X1,X0)),set_difference(X0,empty_set)) ),
inference(superposition,[status(thm)],[c_6293,c_96]) ).
tcf(c_8620,plain,
! [X0: $i,X1: $i] :
( disjoint(set_difference(X0,X1),set_union2(X1,X0))
| in(sK1(set_difference(X0,X1),set_union2(X1,X0)),set_difference(set_difference(X0,X1),empty_set)) ),
inference(superposition,[status(thm)],[c_6374,c_96]) ).
tcf(c_8621,plain,
! [X0: $i,X1: $i] :
( disjoint(set_difference(X0,X1),set_union2(X0,X1))
| in(sK1(set_difference(X0,X1),set_union2(X0,X1)),set_difference(set_difference(X0,X1),empty_set)) ),
inference(superposition,[status(thm)],[c_6401,c_96]) ).
tcf(c_8622,plain,
! [X0: $i,X1: $i] :
( disjoint(set_difference(set_difference(X0,X1),X1),set_union2(X1,X0))
| in(sK1(set_difference(set_difference(X0,X1),X1),set_union2(X1,X0)),set_difference(set_difference(set_difference(X0,X1),X1),empty_set)) ),
inference(superposition,[status(thm)],[c_6603,c_96]) ).
tcf(c_8623,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| ( set_union2(unordered_pair(sK1(X0,X1),sK1(X0,X1)),set_difference(X0,set_difference(X0,X1))) = set_difference(X0,set_difference(X0,X1)) ) ),
inference(superposition,[status(thm)],[c_96,c_95]) ).
tcf(c_8624,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(X0,X1)
| ~ in(sK1(X0,X1),X2)
| ~ disjoint(set_difference(X0,set_difference(X0,X1)),X2) ),
inference(superposition,[status(thm)],[c_96,c_91]) ).
tcf(c_8625,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(X0,X1)
| in(sK1(X0,X1),X2)
| ~ subset(set_difference(X0,set_difference(X0,X1)),X2) ),
inference(superposition,[status(thm)],[c_96,c_123]) ).
tcf(c_8626,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| ~ in(set_difference(X0,set_difference(X0,X1)),sK1(X0,X1)) ),
inference(superposition,[status(thm)],[c_96,c_124]) ).
tcf(c_8627,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| ~ empty(set_difference(X0,set_difference(X0,X1))) ),
inference(superposition,[status(thm)],[c_96,c_184]) ).
tcf(c_8628,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| in(sK1(X0,X1),X1) ),
inference(superposition,[status(thm)],[c_96,c_174]) ).
tcf(c_8629,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| ~ in(sK1(X0,X1),set_difference(X0,X1)) ),
inference(superposition,[status(thm)],[c_96,c_145]) ).
tcf(c_8630,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| in(sK1(X0,X1),X0) ),
inference(superposition,[status(thm)],[c_96,c_144]) ).
tcf(c_8637,plain,
! [X0: $i] :
( disjoint(X0,X0)
| in(sK1(X0,X0),X0) ),
inference(light_normalisation,[status(thm)],[c_8616,c_114]) ).
tcf(c_8644,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,set_union2(X1,X0))
| in(sK1(X0,set_union2(X1,X0)),X0) ),
inference(light_normalisation,[status(thm)],[c_8619,c_114]) ).
tcf(c_8647,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,set_union2(X0,X1))
| in(sK1(X0,set_union2(X0,X1)),X0) ),
inference(light_normalisation,[status(thm)],[c_8618,c_114]) ).
tcf(c_8725,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(set_difference(X0,set_difference(X0,X1)),X2)
| ~ disjoint(X0,X1) ),
inference(superposition,[status(thm)],[c_89,c_97]) ).
tcf(c_8726,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(X2,set_difference(X0,set_difference(X0,X1)))
| ~ disjoint(X0,X1) ),
inference(superposition,[status(thm)],[c_90,c_97]) ).
tcf(c_8729,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(X0,set_difference(X0,X1)),X2)
| ~ disjoint(X0,X1) ),
inference(superposition,[status(thm)],[c_122,c_97]) ).
tcf(c_8730,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ disjoint(X1,X2)
| ~ in(X0,union(set_difference(X1,set_difference(X1,X2)))) ),
inference(superposition,[status(thm)],[c_151,c_97]) ).
tcf(c_8731,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_difference(X0,set_difference(X0,X1)) = cartesian_product2(X2,X3) )
| ( unordered_pair(unordered_pair(sK14(X2,X3,set_difference(X0,set_difference(X0,X1))),sK14(X2,X3,set_difference(X0,set_difference(X0,X1)))),unordered_pair(sK14(X2,X3,set_difference(X0,set_difference(X0,X1))),sK15(X2,X3,set_difference(X0,set_difference(X0,X1))))) = sK13(X2,X3,set_difference(X0,set_difference(X0,X1))) )
| ~ disjoint(X0,X1) ),
inference(superposition,[status(thm)],[c_1706,c_97]) ).
tcf(c_8733,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ disjoint(set_union2(X1,X2),X2)
| ~ in(X0,set_difference(set_union2(X1,X2),set_difference(X1,X2))) ),
inference(superposition,[status(thm)],[c_93,c_97]) ).
tcf(c_8734,plain,
! [X0: $i,X1: $i] :
( ~ disjoint(empty_set,X1)
| ~ in(X0,set_difference(empty_set,empty_set)) ),
inference(superposition,[status(thm)],[c_113,c_97]) ).
tcf(c_8735,plain,
! [X0: $i,X1: $i] :
( ~ disjoint(X1,empty_set)
| ~ in(X0,set_difference(X1,X1)) ),
inference(superposition,[status(thm)],[c_114,c_97]) ).
tcf(c_8736,plain,
! [X0: $i,X1: $i] :
( ~ disjoint(X1,X1)
| ~ in(X0,set_difference(X1,empty_set)) ),
inference(superposition,[status(thm)],[c_1252,c_97]) ).
tcf(c_8737,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ disjoint(set_difference(X1,X2),X1)
| ~ in(X0,set_difference(set_difference(X1,X2),empty_set)) ),
inference(superposition,[status(thm)],[c_6290,c_97]) ).
tcf(c_8738,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(X2,set_difference(X0,empty_set))
| ~ disjoint(X0,set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_6291,c_97]) ).
tcf(c_8739,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(X2,set_difference(X0,empty_set))
| ~ disjoint(X0,set_union2(X1,X0)) ),
inference(superposition,[status(thm)],[c_6293,c_97]) ).
tcf(c_8740,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(X2,set_difference(set_difference(X0,X1),empty_set))
| ~ disjoint(set_difference(X0,X1),set_union2(X1,X0)) ),
inference(superposition,[status(thm)],[c_6374,c_97]) ).
tcf(c_8741,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(X2,set_difference(set_difference(X0,X1),empty_set))
| ~ disjoint(set_difference(X0,X1),set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_6401,c_97]) ).
tcf(c_8742,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(X2,set_difference(set_difference(set_difference(X0,X1),X1),empty_set))
| ~ disjoint(set_difference(set_difference(X0,X1),X1),set_union2(X1,X0)) ),
inference(superposition,[status(thm)],[c_6603,c_97]) ).
tcf(c_8746,plain,
! [X0: $i] : ~ in(X0,set_difference(empty_set,empty_set)),
inference(forward_subsumption_resolution,[status(thm)],[c_8734,c_5290]) ).
tcf(c_8753,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(X2,X0)
| ~ disjoint(X0,set_union2(X1,X0)) ),
inference(light_normalisation,[status(thm)],[c_8739,c_114]) ).
tcf(c_8756,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(X2,X0)
| ~ disjoint(X0,set_union2(X0,X1)) ),
inference(light_normalisation,[status(thm)],[c_8738,c_114]) ).
tcf(c_8848,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ empty(unordered_pair(X0,X0)) ),
inference(superposition,[status(thm)],[c_5360,c_102]) ).
tcf(c_8850,plain,
! [X0: $i] :
( ( X0 = empty_set )
| ~ subset(powerset(empty_set),unordered_pair(X0,X0)) ),
inference(superposition,[status(thm)],[c_70,c_102]) ).
tcf(c_8851,plain,
! [X0: $i] :
( ( X0 = empty_set )
| ~ subset(unordered_pair(X0,X0),powerset(empty_set)) ),
inference(superposition,[status(thm)],[c_70,c_102]) ).
tcf(c_8857,plain,
! [X0: $i,X1: $i,X2: $i] : ~ in(set_union2(powerset(set_union2(X0,X1)),X2),X0),
inference(superposition,[status(thm)],[c_129,c_8404]) ).
tcf(c_8858,plain,
! [X0: $i,X1: $i,X2: $i] : ~ in(set_union2(powerset(set_union2(X0,X1)),X2),X1),
inference(superposition,[status(thm)],[c_130,c_8404]) ).
tcf(c_8859,plain,
! [X0: $i,X1: $i] : ~ subset(set_union2(powerset(powerset(X0)),X1),X0),
inference(superposition,[status(thm)],[c_178,c_8404]) ).
tcf(c_8864,plain,
! [X0: $i,X1: $i] : ~ in(set_union2(X0,powerset(X1)),X1),
inference(superposition,[status(thm)],[c_132,c_8404]) ).
tcf(c_8901,plain,
! [X0: $i,X1: $i,X2: $i] : ~ in(set_union2(X0,powerset(set_union2(X1,X2))),X1),
inference(superposition,[status(thm)],[c_129,c_8864]) ).
tcf(c_8902,plain,
! [X0: $i,X1: $i,X2: $i] : ~ in(set_union2(X0,powerset(set_union2(X1,X2))),X2),
inference(superposition,[status(thm)],[c_130,c_8864]) ).
tcf(c_8903,plain,
! [X0: $i,X1: $i] : ~ subset(set_union2(X0,powerset(powerset(X1))),X1),
inference(superposition,[status(thm)],[c_178,c_8864]) ).
tcf(c_8914,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| ( set_union2(unordered_pair(sK1(X0,X1),sK1(X0,X1)),X1) = X1 ) ),
inference(superposition,[status(thm)],[c_8628,c_95]) ).
tcf(c_8915,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(X0,X1)
| ~ disjoint(X1,X2)
| ~ in(sK1(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_8628,c_91]) ).
tcf(c_8916,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(X2,X0)
| in(sK1(X2,X0),X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_8628,c_123]) ).
tcf(c_8917,plain,
! [X0: $i,X1: $i] :
( disjoint(X1,X0)
| ~ in(X0,sK1(X1,X0)) ),
inference(superposition,[status(thm)],[c_8628,c_124]) ).
tcf(c_8920,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(X0,set_difference(X1,set_difference(X1,X2)))
| in(sK1(X0,set_difference(X1,set_difference(X1,X2))),X2) ),
inference(superposition,[status(thm)],[c_8628,c_174]) ).
tcf(c_8921,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,unordered_pair(X1,X1))
| ( sK1(X0,unordered_pair(X1,X1)) = X1 ) ),
inference(superposition,[status(thm)],[c_8628,c_112]) ).
tcf(c_8923,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(X0,set_difference(X1,X2))
| ~ in(sK1(X0,set_difference(X1,X2)),X2) ),
inference(superposition,[status(thm)],[c_8628,c_145]) ).
tcf(c_8924,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(X0,set_difference(X1,X2))
| in(sK1(X0,set_difference(X1,X2)),X1) ),
inference(superposition,[status(thm)],[c_8628,c_144]) ).
tcf(c_8926,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(X2,cartesian_product2(X0,X1))
| ( unordered_pair(unordered_pair(sK16(X0,X1,sK1(X2,cartesian_product2(X0,X1))),sK16(X0,X1,sK1(X2,cartesian_product2(X0,X1)))),unordered_pair(sK16(X0,X1,sK1(X2,cartesian_product2(X0,X1))),sK17(X0,X1,sK1(X2,cartesian_product2(X0,X1))))) = sK1(X2,cartesian_product2(X0,X1)) ) ),
inference(superposition,[status(thm)],[c_8628,c_1855]) ).
tcf(c_8927,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,powerset(X1))
| subset(sK1(X0,powerset(X1)),X1) ),
inference(superposition,[status(thm)],[c_8628,c_179]) ).
tcf(c_8982,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| ( set_union2(unordered_pair(sK1(X0,X1),sK1(X0,X1)),X0) = X0 ) ),
inference(superposition,[status(thm)],[c_8630,c_95]) ).
tcf(c_8983,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(X0,X1)
| ~ disjoint(X0,X2)
| ~ in(sK1(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_8630,c_91]) ).
tcf(c_8984,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(X0,X2)
| in(sK1(X0,X2),X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_8630,c_123]) ).
tcf(c_8985,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| ~ in(X0,sK1(X0,X1)) ),
inference(superposition,[status(thm)],[c_8630,c_124]) ).
tcf(c_8988,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(set_difference(X0,set_difference(X0,X1)),X2)
| in(sK1(set_difference(X0,set_difference(X0,X1)),X2),X1) ),
inference(superposition,[status(thm)],[c_8630,c_174]) ).
tcf(c_8989,plain,
! [X0: $i,X1: $i] :
( disjoint(unordered_pair(X0,X0),X1)
| ( sK1(unordered_pair(X0,X0),X1) = X0 ) ),
inference(superposition,[status(thm)],[c_8630,c_112]) ).
tcf(c_8991,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(set_difference(X0,X1),X2)
| ~ in(sK1(set_difference(X0,X1),X2),X1) ),
inference(superposition,[status(thm)],[c_8630,c_145]) ).
tcf(c_8992,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(set_difference(X0,X1),X2)
| in(sK1(set_difference(X0,X1),X2),X0) ),
inference(superposition,[status(thm)],[c_8630,c_144]) ).
tcf(c_8994,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(cartesian_product2(X0,X1),X2)
| ( unordered_pair(unordered_pair(sK16(X0,X1,sK1(cartesian_product2(X0,X1),X2)),sK16(X0,X1,sK1(cartesian_product2(X0,X1),X2))),unordered_pair(sK16(X0,X1,sK1(cartesian_product2(X0,X1),X2)),sK17(X0,X1,sK1(cartesian_product2(X0,X1),X2)))) = sK1(cartesian_product2(X0,X1),X2) ) ),
inference(superposition,[status(thm)],[c_8630,c_1855]) ).
tcf(c_8995,plain,
! [X0: $i,X1: $i] :
( disjoint(powerset(X0),X1)
| subset(sK1(powerset(X0),X1),X0) ),
inference(superposition,[status(thm)],[c_8630,c_179]) ).
tcf(c_9024,plain,
! [X0: $i,X1: $i] : ~ empty(set_union2(powerset(powerset(X0)),X1)),
inference(superposition,[status(thm)],[c_5360,c_8859]) ).
tcf(c_9025,plain,
! [X0: $i,X1: $i] : ~ in(set_union2(powerset(powerset(union(X0))),X1),X0),
inference(superposition,[status(thm)],[c_61,c_8859]) ).
tcf(c_9038,plain,
! [X0: $i,X1: $i] : ~ empty(set_union2(X0,powerset(powerset(X1)))),
inference(superposition,[status(thm)],[c_132,c_9024]) ).
tcf(c_9076,plain,
! [X0: $i,X1: $i] : ~ in(set_union2(X0,powerset(powerset(union(X1)))),X1),
inference(superposition,[status(thm)],[c_61,c_8903]) ).
tcf(c_9083,plain,
! [X0: $i,X1: $i,X2: $i] : ~ empty(unordered_pair(X0,set_union2(powerset(X1),X2))),
inference(superposition,[status(thm)],[c_5360,c_6065]) ).
tcf(c_9084,plain,
! [X0: $i,X1: $i,X2: $i] : ~ in(unordered_pair(X0,set_union2(powerset(union(X1)),X2)),X1),
inference(superposition,[status(thm)],[c_61,c_6065]) ).
tcf(c_9094,plain,
! [X0: $i,X1: $i,X2: $i] : ~ empty(set_union2(unordered_pair(powerset(X0),X1),X2)),
inference(superposition,[status(thm)],[c_5360,c_6081]) ).
tcf(c_9095,plain,
! [X0: $i,X1: $i,X2: $i] : ~ in(set_union2(unordered_pair(powerset(union(X0)),X1),X2),X0),
inference(superposition,[status(thm)],[c_61,c_6081]) ).
tcf(c_9111,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(set_union2(X0,X1),X2)
| in(sK0(set_union2(X0,X1),X2),X1)
| in(sK0(set_union2(X0,X1),X2),X0) ),
inference(superposition,[status(thm)],[c_89,c_131]) ).
tcf(c_9112,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(X0,set_union2(X1,X2))
| in(sK0(X0,set_union2(X1,X2)),X2)
| in(sK0(X0,set_union2(X1,X2)),X1) ),
inference(superposition,[status(thm)],[c_90,c_131]) ).
tcf(c_9113,plain,
! [X0: $i,X1: $i] :
( in(sK5(set_union2(X0,X1)),X1)
| in(sK5(set_union2(X0,X1)),X0)
| ( set_union2(X0,X1) = empty_set ) ),
inference(superposition,[status(thm)],[c_117,c_131]) ).
tcf(c_9114,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_union2(X0,X1),X2)
| in(sK7(set_union2(X0,X1),X2),X1)
| in(sK7(set_union2(X0,X1),X2),X0) ),
inference(superposition,[status(thm)],[c_122,c_131]) ).
tcf(c_9117,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(set_union2(X1,X2),X0),X2)
| in(sK12(set_union2(X1,X2),X0),X1)
| ~ in(X0,union(set_union2(X1,X2))) ),
inference(superposition,[status(thm)],[c_151,c_131]) ).
tcf(c_9118,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK13(X0,X1,set_union2(X2,X3)),X3)
| in(sK13(X0,X1,set_union2(X2,X3)),X2)
| ( set_union2(X2,X3) = cartesian_product2(X0,X1) )
| ( unordered_pair(unordered_pair(sK14(X0,X1,set_union2(X2,X3)),sK14(X0,X1,set_union2(X2,X3))),unordered_pair(sK14(X0,X1,set_union2(X2,X3)),sK15(X0,X1,set_union2(X2,X3)))) = sK13(X0,X1,set_union2(X2,X3)) ) ),
inference(superposition,[status(thm)],[c_1706,c_131]) ).
tcf(c_9125,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(X0,set_union2(X1,X2))
| in(sK1(X0,set_union2(X1,X2)),X2)
| in(sK1(X0,set_union2(X1,X2)),X1) ),
inference(superposition,[status(thm)],[c_8628,c_131]) ).
tcf(c_9126,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(set_union2(X0,X1),X2)
| in(sK1(set_union2(X0,X1),X2),X1)
| in(sK1(set_union2(X0,X1),X2),X0) ),
inference(superposition,[status(thm)],[c_8630,c_131]) ).
tcf(c_9128,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X1)
| in(X0,set_difference(X2,X1))
| ~ in(X0,set_union2(X1,X2)) ),
inference(superposition,[status(thm)],[c_85,c_131]) ).
tcf(c_9180,plain,
! [X0: $i,X1: $i] :
( disjoint(set_union2(X0,X1),X1)
| ( set_difference(set_union2(X0,X1),set_difference(X0,X1)) != empty_set ) ),
inference(superposition,[status(thm)],[c_93,c_134]) ).
tcf(c_9183,plain,
! [X0: $i] :
( disjoint(X0,X0)
| ( set_difference(X0,empty_set) != empty_set ) ),
inference(superposition,[status(thm)],[c_1252,c_134]) ).
tcf(c_9184,plain,
! [X0: $i,X1: $i] :
( disjoint(set_difference(X0,X1),X0)
| ( set_difference(set_difference(X0,X1),empty_set) != empty_set ) ),
inference(superposition,[status(thm)],[c_6290,c_134]) ).
tcf(c_9185,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,set_union2(X0,X1))
| ( set_difference(X0,empty_set) != empty_set ) ),
inference(superposition,[status(thm)],[c_6291,c_134]) ).
tcf(c_9186,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,set_union2(X1,X0))
| ( set_difference(X0,empty_set) != empty_set ) ),
inference(superposition,[status(thm)],[c_6293,c_134]) ).
tcf(c_9187,plain,
! [X0: $i,X1: $i] :
( disjoint(set_difference(X0,X1),set_union2(X1,X0))
| ( set_difference(set_difference(X0,X1),empty_set) != empty_set ) ),
inference(superposition,[status(thm)],[c_6374,c_134]) ).
tcf(c_9188,plain,
! [X0: $i,X1: $i] :
( disjoint(set_difference(X0,X1),set_union2(X0,X1))
| ( set_difference(set_difference(X0,X1),empty_set) != empty_set ) ),
inference(superposition,[status(thm)],[c_6401,c_134]) ).
tcf(c_9189,plain,
! [X0: $i,X1: $i] :
( disjoint(set_difference(set_difference(X0,X1),X1),set_union2(X1,X0))
| ( set_difference(set_difference(set_difference(X0,X1),X1),empty_set) != empty_set ) ),
inference(superposition,[status(thm)],[c_6603,c_134]) ).
tcf(c_9227,plain,
! [X0: $i,X1: $i] :
( in(X0,X1)
| ( set_difference(unordered_pair(X0,X0),set_difference(unordered_pair(X0,X0),X1)) = empty_set ) ),
inference(superposition,[status(thm)],[c_52,c_135]) ).
tcf(c_9228,plain,
! [X0: $i,X1: $i] :
( ( set_difference(X0,set_difference(X0,X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5289,c_135]) ).
tcf(c_9229,plain,
! [X0: $i,X1: $i] :
( ( set_difference(X1,set_difference(X1,X0)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5300,c_135]) ).
tcf(c_9231,plain,
! [X0: $i] : set_difference(X0,set_difference(X0,empty_set)) = empty_set,
inference(superposition,[status(thm)],[c_5294,c_135]) ).
tcf(c_9232,plain,
! [X0: $i] :
( in(empty_set,X0)
| ( set_difference(powerset(empty_set),set_difference(powerset(empty_set),X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_5259,c_135]) ).
tcf(c_9233,plain,
! [X0: $i,X1: $i] :
( in(X1,X0)
| ( set_difference(X0,set_difference(X0,unordered_pair(X1,X1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5260,c_135]) ).
tcf(c_9234,plain,
! [X0: $i] :
( in(empty_set,X0)
| ( set_difference(X0,set_difference(X0,powerset(empty_set))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5272,c_135]) ).
tcf(c_9235,plain,
! [X0: $i,X1: $i] :
( ( set_difference(union(X0),set_difference(union(X0),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7109,c_135]) ).
tcf(c_9236,plain,
! [X0: $i,X1: $i] :
( ( set_difference(X1,set_difference(X1,union(X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7110,c_135]) ).
tcf(c_9299,plain,
! [X0: $i,X1: $i] :
( ( unordered_pair(X1,X1) = X0 )
| ~ in(X1,X0)
| ~ subset(X0,unordered_pair(X1,X1)) ),
inference(superposition,[status(thm)],[c_80,c_137]) ).
tcf(c_9300,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_5360,c_137]) ).
tcf(c_9301,plain,
! [X0: $i,X1: $i] :
( ( union(X0) = X1 )
| ~ in(X1,X0)
| ~ subset(union(X0),X1) ),
inference(superposition,[status(thm)],[c_61,c_137]) ).
tcf(c_9303,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(X0,X1) = set_difference(X2,X1) )
| ~ subset(X2,X0)
| ~ subset(set_difference(X0,X1),set_difference(X2,X1)) ),
inference(superposition,[status(thm)],[c_74,c_137]) ).
tcf(c_9304,plain,
! [X0: $i,X1: $i] :
( ( set_difference(X0,X1) = X0 )
| ~ subset(X0,set_difference(X0,X1)) ),
inference(superposition,[status(thm)],[c_77,c_137]) ).
tcf(c_9305,plain,
! [X0: $i,X1: $i] :
( ( set_union2(X0,X1) = X0 )
| ~ subset(set_union2(X0,X1),X0) ),
inference(superposition,[status(thm)],[c_103,c_137]) ).
tcf(c_9307,plain,
! [X0: $i,X1: $i] :
( ( set_union2(X0,X1) = X1 )
| ~ subset(set_union2(X0,X1),X1) ),
inference(superposition,[status(thm)],[c_5425,c_137]) ).
tcf(c_9308,plain,
! [X0: $i] :
( ( powerset(empty_set) = X0 )
| ~ in(empty_set,X0)
| ~ subset(X0,powerset(empty_set)) ),
inference(superposition,[status(thm)],[c_5531,c_137]) ).
tcf(c_9309,plain,
! [X0: $i,X1: $i] :
( ( set_union2(X0,X1) = set_difference(X1,X0) )
| ~ subset(set_union2(X0,X1),set_difference(X1,X0)) ),
inference(superposition,[status(thm)],[c_6334,c_137]) ).
tcf(c_9310,plain,
! [X0: $i,X1: $i] :
( ( set_union2(X0,X1) = set_difference(X0,X1) )
| ~ subset(set_union2(X0,X1),set_difference(X0,X1)) ),
inference(superposition,[status(thm)],[c_6372,c_137]) ).
tcf(c_9311,plain,
! [X0: $i,X1: $i] :
( ( union(X1) = X0 )
| ~ empty(X1)
| ~ subset(X0,union(X1)) ),
inference(superposition,[status(thm)],[c_7112,c_137]) ).
tcf(c_9342,plain,
! [X0: $i,X1: $i,X2: $i] : ~ empty(set_union2(X0,unordered_pair(powerset(X1),X2))),
inference(superposition,[status(thm)],[c_5360,c_6112]) ).
tcf(c_9343,plain,
! [X0: $i,X1: $i,X2: $i] : ~ in(set_union2(X0,unordered_pair(powerset(union(X1)),X2)),X1),
inference(superposition,[status(thm)],[c_61,c_6112]) ).
tcf(c_9351,plain,
! [X0: $i,X1: $i,X2: $i] : ~ empty(set_union2(unordered_pair(X0,powerset(X1)),X2)),
inference(superposition,[status(thm)],[c_5360,c_6140]) ).
tcf(c_9352,plain,
! [X0: $i,X1: $i,X2: $i] : ~ in(set_union2(unordered_pair(X0,powerset(union(X1))),X2),X1),
inference(superposition,[status(thm)],[c_61,c_6140]) ).
tcf(c_9362,plain,
! [X0: $i,X1: $i,X2: $i] : ~ empty(set_union2(X0,unordered_pair(X1,powerset(X2)))),
inference(superposition,[status(thm)],[c_5360,c_6173]) ).
tcf(c_9363,plain,
! [X0: $i,X1: $i,X2: $i] : ~ in(set_union2(X0,unordered_pair(X1,powerset(union(X2)))),X2),
inference(superposition,[status(thm)],[c_61,c_6173]) ).
tcf(c_9371,plain,
! [X0: $i,X1: $i,X2: $i] : ~ in(powerset(set_union2(powerset(union(set_union2(X0,X1))),X2)),X0),
inference(superposition,[status(thm)],[c_129,c_6202]) ).
tcf(c_9372,plain,
! [X0: $i,X1: $i,X2: $i] : ~ in(powerset(set_union2(powerset(union(set_union2(X0,X1))),X2)),X1),
inference(superposition,[status(thm)],[c_130,c_6202]) ).
tcf(c_9373,plain,
! [X0: $i,X1: $i] : ~ subset(powerset(set_union2(powerset(union(powerset(X0))),X1)),X0),
inference(superposition,[status(thm)],[c_178,c_6202]) ).
tcf(c_9380,plain,
! [X0: $i] : ~ in(powerset(set_union2(powerset(empty_set),X0)),empty_set),
inference(superposition,[status(thm)],[c_7079,c_6202]) ).
tcf(c_9389,plain,
! [X0: $i,X1: $i,X2: $i] : ~ in(powerset(set_union2(X0,powerset(union(set_union2(X1,X2))))),X1),
inference(superposition,[status(thm)],[c_129,c_6209]) ).
tcf(c_9390,plain,
! [X0: $i,X1: $i,X2: $i] : ~ in(powerset(set_union2(X0,powerset(union(set_union2(X1,X2))))),X2),
inference(superposition,[status(thm)],[c_130,c_6209]) ).
tcf(c_9391,plain,
! [X0: $i,X1: $i] : ~ subset(powerset(set_union2(X0,powerset(union(powerset(X1))))),X1),
inference(superposition,[status(thm)],[c_178,c_6209]) ).
tcf(c_9396,plain,
! [X0: $i] : ~ in(powerset(set_union2(X0,powerset(empty_set))),empty_set),
inference(superposition,[status(thm)],[c_7079,c_6209]) ).
tcf(c_9406,plain,
! [X0: $i,X1: $i,X2: $i] : ~ empty(unordered_pair(set_union2(X0,powerset(X1)),X2)),
inference(superposition,[status(thm)],[c_5360,c_6217]) ).
tcf(c_9407,plain,
! [X0: $i,X1: $i,X2: $i] : ~ in(unordered_pair(set_union2(X0,powerset(union(X1))),X2),X1),
inference(superposition,[status(thm)],[c_61,c_6217]) ).
tcf(c_9461,plain,
! [X0: $i,X1: $i,X2: $i] : ~ empty(unordered_pair(X0,set_union2(X1,powerset(X2)))),
inference(superposition,[status(thm)],[c_5360,c_6232]) ).
tcf(c_9462,plain,
! [X0: $i,X1: $i,X2: $i] : ~ in(unordered_pair(X0,set_union2(X1,powerset(union(X2)))),X2),
inference(superposition,[status(thm)],[c_61,c_6232]) ).
tcf(c_9475,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_union2(set_difference(X0,X1),X2) = X2 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6423,c_6261]) ).
tcf(c_9483,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(set_difference(X0,X1),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6423,c_6287]) ).
tcf(c_9487,plain,
! [X0: $i,X1: $i] : ~ in(powerset(set_union2(X0,X1)),set_difference(set_difference(X1,X0),X0)),
inference(superposition,[status(thm)],[c_85,c_6323]) ).
tcf(c_9488,plain,
! [X0: $i] : ~ in(powerset(X0),set_difference(empty_set,X0)),
inference(superposition,[status(thm)],[c_116,c_6323]) ).
tcf(c_9489,plain,
! [X0: $i] : ~ in(powerset(X0),set_difference(X0,X0)),
inference(superposition,[status(thm)],[c_125,c_6323]) ).
tcf(c_9491,plain,
! [X0: $i] : ~ in(powerset(X0),set_difference(X0,empty_set)),
inference(superposition,[status(thm)],[c_5426,c_6323]) ).
tcf(c_9492,plain,
! [X0: $i,X1: $i] : ~ in(powerset(set_union2(X0,X1)),set_difference(set_union2(X0,X1),set_difference(X1,X0))),
inference(superposition,[status(thm)],[c_6375,c_6323]) ).
tcf(c_9493,plain,
! [X0: $i,X1: $i] : ~ in(powerset(set_union2(X0,X1)),set_difference(set_union2(X0,X1),set_difference(X0,X1))),
inference(superposition,[status(thm)],[c_6402,c_6323]) ).
tcf(c_9494,plain,
! [X0: $i,X1: $i] : ~ in(powerset(X0),set_difference(set_difference(X0,X1),X0)),
inference(superposition,[status(thm)],[c_6409,c_6323]) ).
tcf(c_9495,plain,
! [X0: $i,X1: $i] : ~ in(powerset(set_union2(X0,set_union2(X1,X0))),set_difference(X1,X0)),
inference(superposition,[status(thm)],[c_93,c_6323]) ).
tcf(c_9496,plain,
! [X0: $i] : ~ in(powerset(set_union2(X0,empty_set)),empty_set),
inference(superposition,[status(thm)],[c_113,c_6323]) ).
tcf(c_9497,plain,
! [X0: $i] : ~ in(powerset(set_union2(empty_set,X0)),X0),
inference(superposition,[status(thm)],[c_114,c_6323]) ).
tcf(c_9498,plain,
! [X0: $i] : ~ in(powerset(set_union2(X0,X0)),empty_set),
inference(superposition,[status(thm)],[c_1252,c_6323]) ).
tcf(c_9499,plain,
! [X0: $i,X1: $i] : ~ in(powerset(set_union2(X0,set_difference(X0,X1))),empty_set),
inference(superposition,[status(thm)],[c_6290,c_6323]) ).
tcf(c_9500,plain,
! [X0: $i,X1: $i] : ~ in(powerset(set_union2(set_union2(X0,X1),X0)),empty_set),
inference(superposition,[status(thm)],[c_6291,c_6323]) ).
tcf(c_9501,plain,
! [X0: $i,X1: $i] : ~ in(powerset(set_union2(set_union2(X0,X1),X1)),empty_set),
inference(superposition,[status(thm)],[c_6293,c_6323]) ).
tcf(c_9502,plain,
! [X0: $i,X1: $i] : ~ in(powerset(set_union2(set_union2(X0,X1),set_difference(X1,X0))),empty_set),
inference(superposition,[status(thm)],[c_6374,c_6323]) ).
tcf(c_9503,plain,
! [X0: $i,X1: $i] : ~ in(powerset(set_union2(set_union2(X0,X1),set_difference(X0,X1))),empty_set),
inference(superposition,[status(thm)],[c_6401,c_6323]) ).
tcf(c_9504,plain,
! [X0: $i,X1: $i] : ~ in(powerset(set_union2(set_union2(X0,X1),set_difference(set_difference(X1,X0),X0))),empty_set),
inference(superposition,[status(thm)],[c_6603,c_6323]) ).
tcf(c_9515,plain,
! [X0: $i,X1: $i] : ~ in(powerset(set_union2(set_union2(X0,X1),empty_set)),empty_set),
inference(light_normalisation,[status(thm)],[c_9504,c_8462]) ).
tcf(c_9516,plain,
! [X0: $i,X1: $i] : ~ in(powerset(set_union2(X0,X1)),set_difference(X0,set_difference(X1,X0))),
inference(light_normalisation,[status(thm)],[c_9492,c_6643]) ).
tcf(c_9524,plain,
! [X0: $i,X1: $i] :
( empty(set_difference(set_difference(X1,X0),X0))
| ~ empty(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_85,c_6328]) ).
tcf(c_9525,plain,
! [X0: $i] :
( empty(set_difference(empty_set,X0))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_116,c_6328]) ).
tcf(c_9526,plain,
! [X0: $i] :
( empty(set_difference(X0,X0))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_125,c_6328]) ).
tcf(c_9528,plain,
! [X0: $i] :
( empty(set_difference(X0,empty_set))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5426,c_6328]) ).
tcf(c_9529,plain,
! [X0: $i,X1: $i] :
( empty(set_difference(set_union2(X0,X1),set_difference(X1,X0)))
| ~ empty(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_6375,c_6328]) ).
tcf(c_9530,plain,
! [X0: $i,X1: $i] :
( empty(set_difference(set_union2(X0,X1),set_difference(X0,X1)))
| ~ empty(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_6402,c_6328]) ).
tcf(c_9531,plain,
! [X0: $i,X1: $i] :
( empty(set_difference(set_difference(X0,X1),X0))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6409,c_6328]) ).
tcf(c_9533,plain,
! [X0: $i] :
( empty(empty_set)
| ~ empty(X0) ),
inference(light_normalisation,[status(thm)],[c_9526,c_1252]) ).
tcf(c_9540,plain,
! [X0: $i,X1: $i] :
( empty(set_difference(X0,set_difference(X1,X0)))
| ~ empty(set_union2(X0,X1)) ),
inference(light_normalisation,[status(thm)],[c_9529,c_6643]) ).
tcf(c_9549,plain,
! [X0: $i] : subset(set_difference(X0,empty_set),set_union2(empty_set,X0)),
inference(superposition,[status(thm)],[c_114,c_6369]) ).
tcf(c_9551,plain,
! [X0: $i,X1: $i] : subset(set_difference(set_difference(X0,X1),X1),set_union2(X1,set_union2(X0,X1))),
inference(superposition,[status(thm)],[c_93,c_6369]) ).
tcf(c_9554,plain,
! [X0: $i] : subset(set_difference(empty_set,X0),set_union2(X0,X0)),
inference(superposition,[status(thm)],[c_1252,c_6369]) ).
tcf(c_9555,plain,
! [X0: $i,X1: $i] : subset(set_difference(empty_set,X0),set_union2(X0,set_difference(X0,X1))),
inference(superposition,[status(thm)],[c_6290,c_6369]) ).
tcf(c_9556,plain,
! [X0: $i,X1: $i] : subset(set_difference(empty_set,set_union2(X0,X1)),set_union2(set_union2(X0,X1),X0)),
inference(superposition,[status(thm)],[c_6291,c_6369]) ).
tcf(c_9557,plain,
! [X0: $i,X1: $i] : subset(set_difference(empty_set,set_union2(X0,X1)),set_union2(set_union2(X0,X1),X1)),
inference(superposition,[status(thm)],[c_6293,c_6369]) ).
tcf(c_9558,plain,
! [X0: $i,X1: $i] : subset(set_difference(empty_set,set_union2(X0,X1)),set_union2(set_union2(X0,X1),set_difference(X1,X0))),
inference(superposition,[status(thm)],[c_6374,c_6369]) ).
tcf(c_9559,plain,
! [X0: $i,X1: $i] : subset(set_difference(empty_set,set_union2(X0,X1)),set_union2(set_union2(X0,X1),set_difference(X0,X1))),
inference(superposition,[status(thm)],[c_6401,c_6369]) ).
tcf(c_9560,plain,
! [X0: $i,X1: $i] : subset(set_difference(empty_set,set_union2(X0,X1)),set_union2(set_union2(X0,X1),set_difference(set_difference(X1,X0),X0))),
inference(superposition,[status(thm)],[c_6603,c_6369]) ).
tcf(c_9562,plain,
! [X0: $i,X1: $i] : subset(set_difference(set_difference(set_difference(X0,X1),X1),X1),set_union2(X1,X0)),
inference(superposition,[status(thm)],[c_85,c_6369]) ).
tcf(c_9563,plain,
! [X0: $i] : subset(set_difference(set_difference(empty_set,X0),X0),X0),
inference(superposition,[status(thm)],[c_116,c_6369]) ).
tcf(c_9564,plain,
! [X0: $i] : subset(set_difference(set_difference(X0,X0),X0),X0),
inference(superposition,[status(thm)],[c_125,c_6369]) ).
tcf(c_9565,plain,
! [X0: $i,X1: $i] : subset(set_difference(set_difference(X0,X1),X1),set_union2(X0,X1)),
inference(superposition,[status(thm)],[c_132,c_6369]) ).
tcf(c_9566,plain,
! [X0: $i] : subset(set_difference(set_difference(X0,empty_set),empty_set),X0),
inference(superposition,[status(thm)],[c_5426,c_6369]) ).
tcf(c_9567,plain,
! [X0: $i,X1: $i] : subset(set_difference(set_difference(set_union2(X0,X1),set_difference(X1,X0)),set_difference(X1,X0)),set_union2(X0,X1)),
inference(superposition,[status(thm)],[c_6375,c_6369]) ).
tcf(c_9568,plain,
! [X0: $i,X1: $i] : subset(set_difference(set_difference(set_union2(X0,X1),set_difference(X0,X1)),set_difference(X0,X1)),set_union2(X0,X1)),
inference(superposition,[status(thm)],[c_6402,c_6369]) ).
tcf(c_9569,plain,
! [X0: $i,X1: $i] : subset(set_difference(set_difference(set_difference(X0,X1),X0),X0),X0),
inference(superposition,[status(thm)],[c_6409,c_6369]) ).
tcf(c_9570,plain,
! [X0: $i,X1: $i] :
( ( set_difference(set_difference(X1,X0),X0) = set_union2(X0,X1) )
| ~ subset(set_union2(X0,X1),set_difference(set_difference(X1,X0),X0)) ),
inference(superposition,[status(thm)],[c_6369,c_137]) ).
tcf(c_9571,plain,
! [X0: $i,X1: $i] : set_difference(set_difference(set_difference(X0,X1),X1),set_difference(set_difference(set_difference(X0,X1),X1),set_union2(X1,X0))) = set_difference(set_difference(X0,X1),X1),
inference(superposition,[status(thm)],[c_6369,c_72]) ).
tcf(c_9572,plain,
! [X0: $i,X1: $i] :
( proper_subset(set_difference(set_difference(X0,X1),X1),set_union2(X1,X0))
| ( set_difference(set_difference(X0,X1),X1) = set_union2(X1,X0) ) ),
inference(superposition,[status(thm)],[c_6369,c_181]) ).
tcf(c_9573,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(set_difference(X1,X0),X0),X2)
| ~ subset(set_union2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_6369,c_69]) ).
tcf(c_9586,plain,
! [X0: $i,X1: $i] : subset(set_difference(empty_set,set_union2(X0,X1)),set_union2(X0,X1)),
inference(light_normalisation,[status(thm)],[c_9559,c_6651]) ).
tcf(c_9587,plain,
! [X0: $i,X1: $i] : subset(set_difference(set_difference(X0,set_difference(X1,X0)),set_difference(X1,X0)),set_union2(X0,X1)),
inference(light_normalisation,[status(thm)],[c_9567,c_6643]) ).
tcf(c_9588,plain,
! [X0: $i,X1: $i] : subset(set_difference(empty_set,set_union2(X0,X1)),set_union2(set_union2(X0,X1),empty_set)),
inference(light_normalisation,[status(thm)],[c_9560,c_8462]) ).
tcf(c_9593,plain,
! [X0: $i,X1: $i] : set_difference(set_difference(set_difference(X0,X1),X1),empty_set) = set_difference(set_difference(X0,X1),X1),
inference(light_normalisation,[status(thm)],[c_9571,c_6603]) ).
tcf(c_9650,plain,
! [X0: $i,X1: $i] : set_difference(set_union2(X0,X1),set_difference(set_difference(X1,X0),X0)) = set_difference(X0,set_difference(set_difference(X1,X0),X0)),
inference(superposition,[status(thm)],[c_85,c_6643]) ).
tcf(c_9651,plain,
! [X0: $i,X1: $i] : set_difference(set_union2(X0,X1),set_difference(X0,X1)) = set_difference(X1,set_difference(X0,X1)),
inference(superposition,[status(thm)],[c_132,c_6643]) ).
tcf(c_9652,plain,
! [X0: $i] : set_difference(X0,set_difference(X0,empty_set)) = set_difference(empty_set,set_difference(X0,empty_set)),
inference(superposition,[status(thm)],[c_5426,c_6643]) ).
tcf(c_9653,plain,
! [X0: $i,X1: $i] : set_difference(set_union2(X0,X1),set_difference(set_union2(X0,X1),set_difference(X1,X0))) = set_difference(set_difference(X1,X0),set_difference(set_union2(X0,X1),set_difference(X1,X0))),
inference(superposition,[status(thm)],[c_6375,c_6643]) ).
tcf(c_9654,plain,
! [X0: $i,X1: $i] : set_difference(set_union2(X0,X1),set_difference(set_union2(X0,X1),set_difference(X0,X1))) = set_difference(set_difference(X0,X1),set_difference(set_union2(X0,X1),set_difference(X0,X1))),
inference(superposition,[status(thm)],[c_6402,c_6643]) ).
tcf(c_9655,plain,
! [X0: $i,X1: $i] : set_difference(set_union2(X0,set_union2(X1,X0)),set_difference(X1,X0)) = set_difference(X0,set_difference(X1,X0)),
inference(superposition,[status(thm)],[c_93,c_6643]) ).
tcf(c_9656,plain,
! [X0: $i] : set_difference(set_union2(X0,empty_set),empty_set) = set_difference(X0,empty_set),
inference(superposition,[status(thm)],[c_113,c_6643]) ).
tcf(c_9657,plain,
! [X0: $i] : set_difference(set_union2(empty_set,X0),X0) = set_difference(empty_set,X0),
inference(superposition,[status(thm)],[c_114,c_6643]) ).
tcf(c_9658,plain,
! [X0: $i] : set_difference(set_union2(X0,X0),empty_set) = set_difference(X0,empty_set),
inference(superposition,[status(thm)],[c_1252,c_6643]) ).
tcf(c_9659,plain,
! [X0: $i,X1: $i] : set_difference(set_union2(X0,set_difference(X0,X1)),empty_set) = set_difference(X0,empty_set),
inference(superposition,[status(thm)],[c_6290,c_6643]) ).
tcf(c_9660,plain,
! [X0: $i,X1: $i] : set_difference(set_union2(set_union2(X0,X1),X0),empty_set) = set_difference(set_union2(X0,X1),empty_set),
inference(superposition,[status(thm)],[c_6291,c_6643]) ).
tcf(c_9661,plain,
! [X0: $i,X1: $i] : set_difference(set_union2(set_union2(X0,X1),X1),empty_set) = set_difference(set_union2(X0,X1),empty_set),
inference(superposition,[status(thm)],[c_6293,c_6643]) ).
tcf(c_9662,plain,
! [X0: $i,X1: $i] : set_difference(set_union2(set_union2(X0,X1),set_difference(X1,X0)),empty_set) = set_difference(set_union2(X0,X1),empty_set),
inference(superposition,[status(thm)],[c_6374,c_6643]) ).
tcf(c_9663,plain,
! [X0: $i,X1: $i] : set_difference(set_union2(set_union2(X0,X1),set_difference(X0,X1)),empty_set) = set_difference(set_union2(X0,X1),empty_set),
inference(superposition,[status(thm)],[c_6401,c_6643]) ).
tcf(c_9664,plain,
! [X0: $i,X1: $i] : set_difference(set_union2(set_union2(X0,X1),set_difference(set_difference(X1,X0),X0)),empty_set) = set_difference(set_union2(X0,X1),empty_set),
inference(superposition,[status(thm)],[c_6603,c_6643]) ).
tcf(c_9666,plain,
! [X0: $i,X1: $i] : subset(set_difference(set_difference(X0,set_difference(X1,X0)),set_difference(X1,X0)),set_union2(set_difference(X1,X0),set_union2(X0,X1))),
inference(superposition,[status(thm)],[c_6643,c_6369]) ).
tcf(c_9667,plain,
! [X0: $i,X1: $i] :
( disjoint(set_union2(X0,X1),set_difference(X1,X0))
| ( set_difference(set_union2(X0,X1),set_difference(X0,set_difference(X1,X0))) != empty_set ) ),
inference(superposition,[status(thm)],[c_6643,c_134]) ).
tcf(c_9668,plain,
! [X0: $i,X1: $i] :
( disjoint(set_union2(X0,X1),set_difference(X1,X0))
| in(sK1(set_union2(X0,X1),set_difference(X1,X0)),set_difference(set_union2(X0,X1),set_difference(X0,set_difference(X1,X0)))) ),
inference(superposition,[status(thm)],[c_6643,c_96]) ).
tcf(c_9669,plain,
! [X0: $i,X1: $i] : set_difference(set_difference(set_difference(X0,set_difference(X1,X0)),set_difference(X1,X0)),set_union2(set_difference(X1,X0),set_union2(X0,X1))) = empty_set,
inference(superposition,[status(thm)],[c_6643,c_6603]) ).
tcf(c_9670,plain,
! [X0: $i,X1: $i] : set_union2(set_difference(X0,set_difference(X1,X0)),set_union2(set_union2(X0,X1),set_difference(X1,X0))) = set_union2(set_union2(X0,X1),set_difference(X1,X0)),
inference(superposition,[status(thm)],[c_6643,c_6402]) ).
tcf(c_9671,plain,
! [X0: $i,X1: $i] : set_difference(set_difference(X0,set_difference(X1,X0)),set_union2(set_union2(X0,X1),set_difference(X1,X0))) = empty_set,
inference(superposition,[status(thm)],[c_6643,c_6401]) ).
tcf(c_9672,plain,
! [X0: $i,X1: $i] : set_union2(set_difference(X0,set_difference(X1,X0)),set_union2(set_difference(X1,X0),set_union2(X0,X1))) = set_union2(set_difference(X1,X0),set_union2(X0,X1)),
inference(superposition,[status(thm)],[c_6643,c_6375]) ).
tcf(c_9673,plain,
! [X0: $i,X1: $i] :
( disjoint(set_union2(X0,X1),set_difference(X1,X0))
| ( set_difference(X0,set_difference(X1,X0)) != set_union2(X0,X1) ) ),
inference(superposition,[status(thm)],[c_6643,c_104]) ).
tcf(c_9674,plain,
! [X0: $i,X1: $i] : set_difference(set_difference(X0,set_difference(X1,X0)),set_union2(set_difference(X1,X0),set_union2(X0,X1))) = empty_set,
inference(superposition,[status(thm)],[c_6643,c_6374]) ).
tcf(c_9675,plain,
! [X0: $i,X1: $i] : ~ proper_subset(set_union2(set_union2(X0,X1),set_difference(X1,X0)),set_difference(X0,set_difference(X1,X0))),
inference(superposition,[status(thm)],[c_6643,c_6403]) ).
tcf(c_9679,plain,
! [X0: $i,X1: $i] : set_union2(set_union2(X0,X1),set_difference(X0,set_difference(X1,X0))) = set_union2(X0,X1),
inference(superposition,[status(thm)],[c_6643,c_6409]) ).
tcf(c_9680,plain,
! [X0: $i,X1: $i] : subset(set_difference(X0,set_difference(X1,X0)),set_union2(set_union2(X0,X1),set_difference(X1,X0))),
inference(superposition,[status(thm)],[c_6643,c_6372]) ).
tcf(c_9681,plain,
! [X0: $i,X1: $i] : subset(set_difference(X0,set_difference(X1,X0)),set_union2(set_difference(X1,X0),set_union2(X0,X1))),
inference(superposition,[status(thm)],[c_6643,c_6334]) ).
tcf(c_9682,plain,
! [X0: $i,X1: $i] :
( subset(set_union2(X0,X1),set_difference(X1,X0))
| ( set_difference(X0,set_difference(X1,X0)) != empty_set ) ),
inference(superposition,[status(thm)],[c_6643,c_79]) ).
tcf(c_9685,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ disjoint(set_union2(X1,X2),set_difference(X2,X1))
| ~ in(X0,set_difference(set_union2(X1,X2),set_difference(X1,set_difference(X2,X1)))) ),
inference(superposition,[status(thm)],[c_6643,c_97]) ).
tcf(c_9686,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,set_difference(X2,X1))
| ~ in(X0,set_difference(set_union2(X1,X2),set_difference(X1,set_difference(X2,X1)))) ),
inference(superposition,[status(thm)],[c_6643,c_174]) ).
tcf(c_9687,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(X0,set_difference(X2,X1)),set_difference(X1,set_difference(X2,X1)))
| ~ subset(X0,set_union2(X1,X2)) ),
inference(superposition,[status(thm)],[c_6643,c_74]) ).
tcf(c_9688,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(X0,set_difference(X2,X1))
| ~ in(X0,set_difference(X1,set_difference(X2,X1))) ),
inference(superposition,[status(thm)],[c_6643,c_145]) ).
tcf(c_9689,plain,
! [X0: $i,X1: $i,X2: $i] : ~ in(unordered_pair(X0,set_union2(X1,X2)),set_difference(X1,set_difference(X2,X1))),
inference(superposition,[status(thm)],[c_6643,c_6426]) ).
tcf(c_9690,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,set_union2(X1,X2))
| ~ in(X0,set_difference(X1,set_difference(X2,X1))) ),
inference(superposition,[status(thm)],[c_6643,c_144]) ).
tcf(c_9691,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(X0,set_difference(X1,X0)),set_difference(X2,set_difference(X1,X0)))
| ~ subset(set_union2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_6643,c_74]) ).
tcf(c_9692,plain,
! [X0: $i,X1: $i,X2: $i] : ~ in(unordered_pair(set_union2(X0,X1),X2),set_difference(X0,set_difference(X1,X0))),
inference(superposition,[status(thm)],[c_6643,c_6416]) ).
tcf(c_9693,plain,
! [X0: $i,X1: $i] : set_difference(set_union2(set_difference(X0,X1),set_union2(X1,X0)),set_difference(X1,set_difference(X0,X1))) = set_difference(set_difference(X0,X1),set_difference(X1,set_difference(X0,X1))),
inference(superposition,[status(thm)],[c_6643,c_6643]) ).
tcf(c_9694,plain,
! [X0: $i,X1: $i] : ~ in(powerset(set_union2(set_difference(X0,X1),set_union2(X1,X0))),set_difference(X1,set_difference(X0,X1))),
inference(superposition,[status(thm)],[c_6643,c_6323]) ).
tcf(c_9695,plain,
! [X0: $i,X1: $i] : ~ proper_subset(set_union2(set_difference(X0,X1),set_union2(X1,X0)),set_difference(X1,set_difference(X0,X1))),
inference(superposition,[status(thm)],[c_6643,c_6325]) ).
tcf(c_9696,plain,
! [X0: $i,X1: $i] : set_union2(set_difference(X0,X1),set_difference(X1,set_difference(X0,X1))) = set_union2(set_difference(X0,X1),set_union2(X1,X0)),
inference(superposition,[status(thm)],[c_6643,c_85]) ).
tcf(c_9718,plain,
! [X0: $i,X1: $i] : set_union2(set_difference(X0,X1),set_difference(X1,set_difference(X0,X1))) = set_union2(X1,X0),
inference(light_normalisation,[status(thm)],[c_9696,c_6375]) ).
tcf(c_9721,plain,
! [X0: $i,X1: $i] : set_difference(set_union2(set_union2(X0,X1),empty_set),empty_set) = set_difference(set_union2(X0,X1),empty_set),
inference(light_normalisation,[status(thm)],[c_9664,c_8462]) ).
tcf(c_9726,plain,
! [X0: $i,X1: $i] : set_difference(set_union2(X0,X1),set_difference(X0,set_difference(X1,X0))) = set_difference(set_difference(X1,X0),set_difference(X0,set_difference(X1,X0))),
inference(light_normalisation,[status(thm)],[c_9693,c_6375]) ).
tcf(c_9830,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| in(X0,set_difference(X1,X2))
| ~ in(X0,set_union2(X1,X2)) ),
inference(superposition,[status(thm)],[c_93,c_143]) ).
tcf(c_9839,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,empty_set)
| in(X0,set_union2(X2,X1))
| ~ in(X0,set_difference(set_difference(X1,X2),X2)) ),
inference(superposition,[status(thm)],[c_6603,c_143]) ).
tcf(c_9840,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,set_difference(X2,X1))
| in(X0,set_difference(X1,set_difference(X2,X1)))
| ~ in(X0,set_union2(X1,X2)) ),
inference(superposition,[status(thm)],[c_6643,c_143]) ).
tcf(c_9841,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ( set_union2(unordered_pair(X0,X0),set_difference(X1,X2)) = set_difference(X1,X2) )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_143,c_95]) ).
tcf(c_9842,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,X1)
| ~ in(X3,X2)
| ~ in(X3,X0)
| ~ disjoint(set_difference(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_143,c_91]) ).
tcf(c_9843,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,X2)
| in(X3,X1)
| ~ in(X3,X0)
| ~ subset(set_difference(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_143,c_123]) ).
tcf(c_9844,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,X1)
| ~ in(X2,X0)
| ~ in(set_difference(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_143,c_124]) ).
tcf(c_9845,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,X1)
| ~ in(X2,X0)
| ~ empty(set_difference(X0,X1)) ),
inference(superposition,[status(thm)],[c_143,c_184]) ).
tcf(c_9846,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,set_difference(X1,X2))
| ~ disjoint(X1,X2)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_143,c_97]) ).
tcf(c_9848,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,set_difference(X1,X2))
| in(sK7(X0,set_difference(X1,X2)),X2)
| ~ in(sK7(X0,set_difference(X1,X2)),X1) ),
inference(superposition,[status(thm)],[c_143,c_121]) ).
tcf(c_9851,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(set_difference(X0,X1),X2),X1)
| ~ in(unordered_pair(set_difference(X0,X1),X2),X0) ),
inference(superposition,[status(thm)],[c_143,c_5373]) ).
tcf(c_9852,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(X0,set_difference(X1,X2)),X2)
| ~ in(unordered_pair(X0,set_difference(X1,X2)),X1) ),
inference(superposition,[status(thm)],[c_143,c_5374]) ).
tcf(c_9853,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(powerset(X2),X1)
| ~ in(powerset(X2),X0)
| ~ subset(set_difference(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_143,c_5485]) ).
tcf(c_9854,plain,
! [X0: $i,X1: $i] :
( in(powerset(set_difference(X0,X1)),X1)
| ~ in(powerset(set_difference(X0,X1)),X0) ),
inference(superposition,[status(thm)],[c_143,c_5538]) ).
tcf(c_9855,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(powerset(union(set_difference(X0,X1))),X2),X1)
| ~ in(unordered_pair(powerset(union(set_difference(X0,X1))),X2),X0) ),
inference(superposition,[status(thm)],[c_143,c_5540]) ).
tcf(c_9856,plain,
! [X0: $i,X1: $i] :
( in(powerset(powerset(union(set_difference(X0,X1)))),X1)
| ~ in(powerset(powerset(union(set_difference(X0,X1)))),X0) ),
inference(superposition,[status(thm)],[c_143,c_5548]) ).
tcf(c_9857,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(X0,powerset(union(set_difference(X1,X2)))),X2)
| ~ in(unordered_pair(X0,powerset(union(set_difference(X1,X2)))),X1) ),
inference(superposition,[status(thm)],[c_143,c_5553]) ).
tcf(c_9858,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(set_union2(set_difference(X0,X1),X2),X3),X1)
| ~ in(unordered_pair(set_union2(set_difference(X0,X1),X2),X3),X0) ),
inference(superposition,[status(thm)],[c_143,c_5693]) ).
tcf(c_9859,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(X0,set_union2(set_difference(X1,X2),X3)),X2)
| ~ in(unordered_pair(X0,set_union2(set_difference(X1,X2),X3)),X1) ),
inference(superposition,[status(thm)],[c_143,c_5694]) ).
tcf(c_9860,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(powerset(set_union2(set_difference(X0,X1),X2)),X1)
| ~ in(powerset(set_union2(set_difference(X0,X1),X2)),X0) ),
inference(superposition,[status(thm)],[c_143,c_5695]) ).
tcf(c_9861,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(powerset(powerset(union(set_union2(set_difference(X0,X1),X2)))),X1)
| ~ in(powerset(powerset(union(set_union2(set_difference(X0,X1),X2)))),X0) ),
inference(superposition,[status(thm)],[c_143,c_5697]) ).
tcf(c_9862,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(set_union2(unordered_pair(set_difference(X0,X1),X2),X3),X1)
| ~ in(set_union2(unordered_pair(set_difference(X0,X1),X2),X3),X0) ),
inference(superposition,[status(thm)],[c_143,c_5720]) ).
tcf(c_9863,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(set_union2(X0,unordered_pair(set_difference(X1,X2),X3)),X2)
| ~ in(set_union2(X0,unordered_pair(set_difference(X1,X2),X3)),X1) ),
inference(superposition,[status(thm)],[c_143,c_5763]) ).
tcf(c_9864,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(set_union2(unordered_pair(X0,set_difference(X1,X2)),X3),X2)
| ~ in(set_union2(unordered_pair(X0,set_difference(X1,X2)),X3),X1) ),
inference(superposition,[status(thm)],[c_143,c_5782]) ).
tcf(c_9865,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(set_union2(X0,unordered_pair(X1,set_difference(X2,X3))),X3)
| ~ in(set_union2(X0,unordered_pair(X1,set_difference(X2,X3))),X2) ),
inference(superposition,[status(thm)],[c_143,c_5799]) ).
tcf(c_9866,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(powerset(set_union2(set_union2(set_difference(X0,X1),X2),X3)),X1)
| ~ in(powerset(set_union2(set_union2(set_difference(X0,X1),X2),X3)),X0) ),
inference(superposition,[status(thm)],[c_143,c_5807]) ).
tcf(c_9867,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(powerset(set_union2(X0,set_difference(X1,X2))),X2)
| ~ in(powerset(set_union2(X0,set_difference(X1,X2))),X1) ),
inference(superposition,[status(thm)],[c_143,c_5812]) ).
tcf(c_9868,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(powerset(set_union2(X0,set_union2(set_difference(X1,X2),X3))),X2)
| ~ in(powerset(set_union2(X0,set_union2(set_difference(X1,X2),X3))),X1) ),
inference(superposition,[status(thm)],[c_143,c_5849]) ).
tcf(c_9869,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(set_union2(X0,set_difference(X1,X2)),X3),X2)
| ~ in(unordered_pair(set_union2(X0,set_difference(X1,X2)),X3),X1) ),
inference(superposition,[status(thm)],[c_143,c_5956]) ).
tcf(c_9870,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(X0,set_union2(X1,set_difference(X2,X3))),X3)
| ~ in(unordered_pair(X0,set_union2(X1,set_difference(X2,X3))),X2) ),
inference(superposition,[status(thm)],[c_143,c_5957]) ).
tcf(c_9871,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(powerset(powerset(union(set_union2(X0,set_difference(X1,X2))))),X2)
| ~ in(powerset(powerset(union(set_union2(X0,set_difference(X1,X2))))),X1) ),
inference(superposition,[status(thm)],[c_143,c_5960]) ).
tcf(c_9872,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(powerset(set_union2(set_union2(X0,set_difference(X1,X2)),X3)),X2)
| ~ in(powerset(set_union2(set_union2(X0,set_difference(X1,X2)),X3)),X1) ),
inference(superposition,[status(thm)],[c_143,c_5962]) ).
tcf(c_9873,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(powerset(set_union2(X0,set_union2(X1,set_difference(X2,X3)))),X3)
| ~ in(powerset(set_union2(X0,set_union2(X1,set_difference(X2,X3)))),X2) ),
inference(superposition,[status(thm)],[c_143,c_5963]) ).
tcf(c_9874,plain,
! [X0: $i,X1: $i] :
( in(powerset(powerset(union(powerset(union(set_difference(X0,X1)))))),X1)
| ~ in(powerset(powerset(union(powerset(union(set_difference(X0,X1)))))),X0) ),
inference(superposition,[status(thm)],[c_143,c_6031]) ).
tcf(c_9875,plain,
! [X0: $i,X1: $i] :
( in(powerset(empty_set),X1)
| in(empty_set,union(set_difference(X0,X1)))
| ~ in(powerset(empty_set),X0) ),
inference(superposition,[status(thm)],[c_143,c_6040]) ).
tcf(c_9876,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(powerset(set_union2(powerset(union(set_difference(X0,X1))),X2)),X1)
| ~ in(powerset(set_union2(powerset(union(set_difference(X0,X1))),X2)),X0) ),
inference(superposition,[status(thm)],[c_143,c_6202]) ).
tcf(c_9877,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(powerset(set_union2(X0,powerset(union(set_difference(X1,X2))))),X2)
| ~ in(powerset(set_union2(X0,powerset(union(set_difference(X1,X2))))),X1) ),
inference(superposition,[status(thm)],[c_143,c_6209]) ).
tcf(c_9882,plain,
! [X0: $i,X1: $i] :
( in(powerset(union(powerset(set_difference(X0,X1)))),X1)
| ~ in(powerset(union(powerset(set_difference(X0,X1)))),X0) ),
inference(superposition,[status(thm)],[c_143,c_6921]) ).
tcf(c_9883,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(set_union2(powerset(set_difference(X0,X1)),X2),X1)
| ~ in(set_union2(powerset(set_difference(X0,X1)),X2),X0) ),
inference(superposition,[status(thm)],[c_143,c_8404]) ).
tcf(c_9884,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(set_union2(X0,powerset(set_difference(X1,X2))),X2)
| ~ in(set_union2(X0,powerset(set_difference(X1,X2))),X1) ),
inference(superposition,[status(thm)],[c_143,c_8864]) ).
tcf(c_9913,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,set_union2(X2,X1))
| ~ in(X0,set_difference(set_difference(X1,X2),X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9839,c_118]) ).
tcf(c_10065,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(X0,X2)
| in(sK0(X0,X2),union(X1))
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_89,c_149]) ).
tcf(c_10066,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(X2,X0)
| in(sK0(X2,X0),union(X1))
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_90,c_149]) ).
tcf(c_10067,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(X0,X1)
| in(sK1(X0,X1),union(X2))
| ~ in(set_difference(X0,set_difference(X0,X1)),X2) ),
inference(superposition,[status(thm)],[c_96,c_149]) ).
tcf(c_10068,plain,
! [X0: $i,X1: $i] :
( in(sK5(X0),union(X1))
| ( X0 = empty_set )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_117,c_149]) ).
tcf(c_10069,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,X2)
| in(sK7(X0,X2),union(X1))
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_122,c_149]) ).
tcf(c_10070,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,union(X2))
| ~ in(X3,X0)
| ~ in(set_union2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_129,c_149]) ).
tcf(c_10071,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,union(X2))
| ~ in(X3,X1)
| ~ in(set_union2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_130,c_149]) ).
tcf(c_10072,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,X1)
| in(X3,union(X2))
| ~ in(X3,X0)
| ~ in(set_difference(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_143,c_149]) ).
tcf(c_10073,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,union(X2))
| ~ in(X1,union(X0))
| ~ in(sK12(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_150,c_149]) ).
tcf(c_10074,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(X1,X0),union(X2))
| ~ in(X1,X2)
| ~ in(X0,union(X1)) ),
inference(superposition,[status(thm)],[c_151,c_149]) ).
tcf(c_10075,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK13(X2,X3,X0),union(X1))
| ( cartesian_product2(X2,X3) = X0 )
| ( unordered_pair(unordered_pair(sK14(X2,X3,X0),sK14(X2,X3,X0)),unordered_pair(sK14(X2,X3,X0),sK15(X2,X3,X0))) = sK13(X2,X3,X0) )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1706,c_149]) ).
tcf(c_10078,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,union(X1))
| ~ subset(X2,X0)
| ~ in(powerset(X0),X1) ),
inference(superposition,[status(thm)],[c_178,c_149]) ).
tcf(c_10080,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(sK14(X0,X1,empty_set),sK14(X0,X1,empty_set)),union(X2))
| ( cartesian_product2(X0,X1) = empty_set )
| ~ in(sK13(X0,X1,empty_set),X2) ),
inference(superposition,[status(thm)],[c_5326,c_149]) ).
tcf(c_10081,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,union(X3))
| ~ in(set_union2(unordered_pair(X0,X1),X2),X3) ),
inference(superposition,[status(thm)],[c_5624,c_149]) ).
tcf(c_10082,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X1,union(X3))
| ~ in(set_union2(X0,unordered_pair(X1,X2)),X3) ),
inference(superposition,[status(thm)],[c_5626,c_149]) ).
tcf(c_10083,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X1,union(X3))
| ~ in(set_union2(unordered_pair(X0,X1),X2),X3) ),
inference(superposition,[status(thm)],[c_5654,c_149]) ).
tcf(c_10084,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X2,union(X3))
| ~ in(set_union2(X0,unordered_pair(X1,X2)),X3) ),
inference(superposition,[status(thm)],[c_5656,c_149]) ).
tcf(c_10085,plain,
! [X0: $i,X1: $i] :
( in(empty_set,union(X1))
| ~ in(set_union2(powerset(empty_set),X0),X1) ),
inference(superposition,[status(thm)],[c_5716,c_149]) ).
tcf(c_10086,plain,
! [X0: $i,X1: $i] :
( in(empty_set,union(X1))
| ~ in(set_union2(X0,powerset(empty_set)),X1) ),
inference(superposition,[status(thm)],[c_5734,c_149]) ).
tcf(c_10087,plain,
! [X0: $i,X1: $i] :
( in(empty_set,union(X1))
| ~ in(union(unordered_pair(powerset(empty_set),X0)),X1) ),
inference(superposition,[status(thm)],[c_8287,c_149]) ).
tcf(c_10088,plain,
! [X0: $i,X1: $i] :
( in(empty_set,union(X1))
| ~ in(union(unordered_pair(X0,powerset(empty_set))),X1) ),
inference(superposition,[status(thm)],[c_8288,c_149]) ).
tcf(c_10089,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(X2,X0)
| in(sK1(X2,X0),union(X1))
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_8628,c_149]) ).
tcf(c_10090,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(X0,X2)
| in(sK1(X0,X2),union(X1))
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_8630,c_149]) ).
tcf(c_10206,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK16(X1,X2,X0),union(X3))
| ~ in(X1,X3)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_157,c_149]) ).
tcf(c_10207,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_union2(unordered_pair(sK16(X1,X2,X0),sK16(X1,X2,X0)),X1) = X1 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_157,c_95]) ).
tcf(c_10208,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ disjoint(X0,X3)
| ~ in(X2,cartesian_product2(X0,X1))
| ~ in(sK16(X0,X1,X2),X3) ),
inference(superposition,[status(thm)],[c_157,c_91]) ).
tcf(c_10209,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK16(X1,X2,X0),X3)
| ~ subset(X1,X3)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_157,c_123]) ).
tcf(c_10210,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(X2,cartesian_product2(X0,X1))
| ~ in(X0,sK16(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_157,c_124]) ).
tcf(c_10211,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(X1)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_157,c_184]) ).
tcf(c_10212,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ disjoint(X1,X2)
| ~ in(X0,cartesian_product2(set_difference(X1,set_difference(X1,X2)),X3)) ),
inference(superposition,[status(thm)],[c_157,c_97]) ).
tcf(c_10213,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK16(set_difference(X1,set_difference(X1,X2)),X3,X0),X2)
| ~ in(X0,cartesian_product2(set_difference(X1,set_difference(X1,X2)),X3)) ),
inference(superposition,[status(thm)],[c_157,c_174]) ).
tcf(c_10214,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK16(unordered_pair(X1,X1),X2,X0) = X1 )
| ~ in(X0,cartesian_product2(unordered_pair(X1,X1),X2)) ),
inference(superposition,[status(thm)],[c_157,c_112]) ).
tcf(c_10215,plain,
! [X0: $i,X1: $i] : ~ in(X0,cartesian_product2(empty_set,X1)),
inference(superposition,[status(thm)],[c_157,c_118]) ).
tcf(c_10216,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK16(set_union2(X1,X2),X3,X0),X2)
| in(sK16(set_union2(X1,X2),X3,X0),X1)
| ~ in(X0,cartesian_product2(set_union2(X1,X2),X3)) ),
inference(superposition,[status(thm)],[c_157,c_131]) ).
tcf(c_10217,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ in(X3,cartesian_product2(set_difference(X0,X1),X2))
| ~ in(sK16(set_difference(X0,X1),X2,X3),X1) ),
inference(superposition,[status(thm)],[c_157,c_145]) ).
tcf(c_10218,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK16(set_difference(X1,X2),X3,X0),X1)
| ~ in(X0,cartesian_product2(set_difference(X1,X2),X3)) ),
inference(superposition,[status(thm)],[c_157,c_144]) ).
tcf(c_10219,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(X1)
| ~ in(X0,cartesian_product2(union(X1),X2)) ),
inference(superposition,[status(thm)],[c_157,c_7039]) ).
tcf(c_10220,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( unordered_pair(unordered_pair(sK16(X1,X2,sK16(cartesian_product2(X1,X2),X3,X0)),sK16(X1,X2,sK16(cartesian_product2(X1,X2),X3,X0))),unordered_pair(sK16(X1,X2,sK16(cartesian_product2(X1,X2),X3,X0)),sK17(X1,X2,sK16(cartesian_product2(X1,X2),X3,X0)))) = sK16(cartesian_product2(X1,X2),X3,X0) )
| ~ in(X0,cartesian_product2(cartesian_product2(X1,X2),X3)) ),
inference(superposition,[status(thm)],[c_157,c_1855]) ).
tcf(c_10221,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK16(powerset(X1),X2,X0),X1)
| ~ in(X0,cartesian_product2(powerset(X1),X2)) ),
inference(superposition,[status(thm)],[c_157,c_179]) ).
tcf(c_10285,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK17(X1,X2,X0),union(X3))
| ~ in(X2,X3)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_158,c_149]) ).
tcf(c_10286,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_union2(unordered_pair(sK17(X1,X2,X0),sK17(X1,X2,X0)),X2) = X2 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_158,c_95]) ).
tcf(c_10287,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ disjoint(X1,X3)
| ~ in(X2,cartesian_product2(X0,X1))
| ~ in(sK17(X0,X1,X2),X3) ),
inference(superposition,[status(thm)],[c_158,c_91]) ).
tcf(c_10288,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK17(X1,X2,X0),X3)
| ~ subset(X2,X3)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_158,c_123]) ).
tcf(c_10289,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(X2,cartesian_product2(X1,X0))
| ~ in(X0,sK17(X1,X0,X2)) ),
inference(superposition,[status(thm)],[c_158,c_124]) ).
tcf(c_10290,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(X2)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_158,c_184]) ).
tcf(c_10291,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ disjoint(X2,X3)
| ~ in(X0,cartesian_product2(X1,set_difference(X2,set_difference(X2,X3)))) ),
inference(superposition,[status(thm)],[c_158,c_97]) ).
tcf(c_10292,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK17(X1,set_difference(X2,set_difference(X2,X3)),X0),X3)
| ~ in(X0,cartesian_product2(X1,set_difference(X2,set_difference(X2,X3)))) ),
inference(superposition,[status(thm)],[c_158,c_174]) ).
tcf(c_10293,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK17(X1,unordered_pair(X2,X2),X0) = X2 )
| ~ in(X0,cartesian_product2(X1,unordered_pair(X2,X2))) ),
inference(superposition,[status(thm)],[c_158,c_112]) ).
tcf(c_10294,plain,
! [X0: $i,X1: $i] : ~ in(X0,cartesian_product2(X1,empty_set)),
inference(superposition,[status(thm)],[c_158,c_118]) ).
tcf(c_10295,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK17(X1,set_union2(X2,X3),X0),X3)
| in(sK17(X1,set_union2(X2,X3),X0),X2)
| ~ in(X0,cartesian_product2(X1,set_union2(X2,X3))) ),
inference(superposition,[status(thm)],[c_158,c_131]) ).
tcf(c_10296,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ in(X3,cartesian_product2(X0,set_difference(X1,X2)))
| ~ in(sK17(X0,set_difference(X1,X2),X3),X2) ),
inference(superposition,[status(thm)],[c_158,c_145]) ).
tcf(c_10297,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK17(X1,set_difference(X2,X3),X0),X2)
| ~ in(X0,cartesian_product2(X1,set_difference(X2,X3))) ),
inference(superposition,[status(thm)],[c_158,c_144]) ).
tcf(c_10298,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(X2)
| ~ in(X0,cartesian_product2(X1,union(X2))) ),
inference(superposition,[status(thm)],[c_158,c_7039]) ).
tcf(c_10299,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( unordered_pair(unordered_pair(sK16(X2,X3,sK17(X1,cartesian_product2(X2,X3),X0)),sK16(X2,X3,sK17(X1,cartesian_product2(X2,X3),X0))),unordered_pair(sK16(X2,X3,sK17(X1,cartesian_product2(X2,X3),X0)),sK17(X2,X3,sK17(X1,cartesian_product2(X2,X3),X0)))) = sK17(X1,cartesian_product2(X2,X3),X0) )
| ~ in(X0,cartesian_product2(X1,cartesian_product2(X2,X3))) ),
inference(superposition,[status(thm)],[c_158,c_1855]) ).
tcf(c_10300,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK17(X1,powerset(X2),X0),X2)
| ~ in(X0,cartesian_product2(X1,powerset(X2))) ),
inference(superposition,[status(thm)],[c_158,c_179]) ).
tcf(c_10381,plain,
! [X0: $i] : cartesian_product2(empty_set,X0) = empty_set,
inference(superposition,[status(thm)],[c_117,c_10215]) ).
tcf(c_10382,plain,
! [X0: $i,X1: $i] : subset(cartesian_product2(empty_set,X0),X1),
inference(superposition,[status(thm)],[c_122,c_10215]) ).
tcf(c_10383,plain,
! [X0: $i,X1: $i] : ~ in(X0,union(cartesian_product2(empty_set,X1))),
inference(superposition,[status(thm)],[c_151,c_10215]) ).
tcf(c_10384,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( cartesian_product2(X0,X1) = cartesian_product2(empty_set,X2) )
| ( unordered_pair(unordered_pair(sK14(X0,X1,cartesian_product2(empty_set,X2)),sK14(X0,X1,cartesian_product2(empty_set,X2))),unordered_pair(sK14(X0,X1,cartesian_product2(empty_set,X2)),sK15(X0,X1,cartesian_product2(empty_set,X2)))) = sK13(X0,X1,cartesian_product2(empty_set,X2)) ) ),
inference(superposition,[status(thm)],[c_1706,c_10215]) ).
tcf(c_10385,plain,
! [X0: $i,X1: $i,X2: $i] : ~ in(X0,cartesian_product2(cartesian_product2(empty_set,X1),X2)),
inference(superposition,[status(thm)],[c_157,c_10215]) ).
tcf(c_10386,plain,
! [X0: $i,X1: $i,X2: $i] : ~ in(X0,cartesian_product2(X1,cartesian_product2(empty_set,X2))),
inference(superposition,[status(thm)],[c_158,c_10215]) ).
tcf(c_10387,plain,
! [X0: $i,X1: $i] : disjoint(X0,cartesian_product2(empty_set,X1)),
inference(superposition,[status(thm)],[c_8628,c_10215]) ).
tcf(c_10388,plain,
! [X0: $i,X1: $i] : disjoint(cartesian_product2(empty_set,X0),X1),
inference(superposition,[status(thm)],[c_8630,c_10215]) ).
tcf(c_10438,plain,
! [X0: $i] : cartesian_product2(X0,empty_set) = empty_set,
inference(superposition,[status(thm)],[c_117,c_10294]) ).
tcf(c_10439,plain,
! [X0: $i,X1: $i] : subset(cartesian_product2(X0,empty_set),X1),
inference(superposition,[status(thm)],[c_122,c_10294]) ).
tcf(c_10440,plain,
! [X0: $i,X1: $i] : ~ in(X0,union(cartesian_product2(X1,empty_set))),
inference(superposition,[status(thm)],[c_151,c_10294]) ).
tcf(c_10441,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( cartesian_product2(X0,X1) = cartesian_product2(X2,empty_set) )
| ( unordered_pair(unordered_pair(sK14(X0,X1,cartesian_product2(X2,empty_set)),sK14(X0,X1,cartesian_product2(X2,empty_set))),unordered_pair(sK14(X0,X1,cartesian_product2(X2,empty_set)),sK15(X0,X1,cartesian_product2(X2,empty_set)))) = sK13(X0,X1,cartesian_product2(X2,empty_set)) ) ),
inference(superposition,[status(thm)],[c_1706,c_10294]) ).
tcf(c_10442,plain,
! [X0: $i,X1: $i,X2: $i] : ~ in(X0,cartesian_product2(cartesian_product2(X1,empty_set),X2)),
inference(superposition,[status(thm)],[c_157,c_10294]) ).
tcf(c_10443,plain,
! [X0: $i,X1: $i,X2: $i] : ~ in(X0,cartesian_product2(X1,cartesian_product2(X2,empty_set))),
inference(superposition,[status(thm)],[c_158,c_10294]) ).
tcf(c_10444,plain,
! [X0: $i,X1: $i] : disjoint(X0,cartesian_product2(X1,empty_set)),
inference(superposition,[status(thm)],[c_8628,c_10294]) ).
tcf(c_10445,plain,
! [X0: $i,X1: $i] : disjoint(cartesian_product2(X0,empty_set),X1),
inference(superposition,[status(thm)],[c_8630,c_10294]) ).
tcf(c_10452,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( cartesian_product2(X1,X2) = cartesian_product2(empty_set,X0) )
| ( unordered_pair(unordered_pair(sK14(X1,X2,cartesian_product2(empty_set,X0)),sK14(X1,X2,cartesian_product2(empty_set,X0))),unordered_pair(sK14(X1,X2,cartesian_product2(empty_set,X0)),sK15(X1,X2,cartesian_product2(empty_set,X0)))) = sK13(X1,X2,cartesian_product2(empty_set,X0)) )
| ( unordered_pair(unordered_pair(sK16(empty_set,X0,sK13(X1,X2,empty_set)),sK16(empty_set,X0,sK13(X1,X2,empty_set))),unordered_pair(sK16(empty_set,X0,sK13(X1,X2,empty_set)),sK17(empty_set,X0,sK13(X1,X2,empty_set)))) = sK13(X1,X2,empty_set) ) ),
inference(superposition,[status(thm)],[c_10381,c_5464]) ).
tcf(c_10455,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( cartesian_product2(X1,X2) = empty_set )
| ( unordered_pair(unordered_pair(sK14(X1,X2,empty_set),sK14(X1,X2,empty_set)),unordered_pair(sK14(X1,X2,empty_set),sK15(X1,X2,empty_set))) = sK13(X1,X2,empty_set) )
| ( unordered_pair(unordered_pair(sK16(empty_set,X0,sK13(X1,X2,empty_set)),sK16(empty_set,X0,sK13(X1,X2,empty_set))),unordered_pair(sK16(empty_set,X0,sK13(X1,X2,empty_set)),sK17(empty_set,X0,sK13(X1,X2,empty_set)))) = sK13(X1,X2,empty_set) ) ),
inference(light_normalisation,[status(thm)],[c_10452,c_10381]) ).
tcf(c_10459,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( cartesian_product2(X1,X2) = cartesian_product2(X0,empty_set) )
| ( unordered_pair(unordered_pair(sK14(X1,X2,cartesian_product2(X0,empty_set)),sK14(X1,X2,cartesian_product2(X0,empty_set))),unordered_pair(sK14(X1,X2,cartesian_product2(X0,empty_set)),sK15(X1,X2,cartesian_product2(X0,empty_set)))) = sK13(X1,X2,cartesian_product2(X0,empty_set)) )
| ( unordered_pair(unordered_pair(sK16(X0,empty_set,sK13(X1,X2,empty_set)),sK16(X0,empty_set,sK13(X1,X2,empty_set))),unordered_pair(sK16(X0,empty_set,sK13(X1,X2,empty_set)),sK17(X0,empty_set,sK13(X1,X2,empty_set)))) = sK13(X1,X2,empty_set) ) ),
inference(superposition,[status(thm)],[c_10438,c_5464]) ).
tcf(c_10462,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( cartesian_product2(X1,X2) = empty_set )
| ( unordered_pair(unordered_pair(sK14(X1,X2,empty_set),sK14(X1,X2,empty_set)),unordered_pair(sK14(X1,X2,empty_set),sK15(X1,X2,empty_set))) = sK13(X1,X2,empty_set) )
| ( unordered_pair(unordered_pair(sK16(X0,empty_set,sK13(X1,X2,empty_set)),sK16(X0,empty_set,sK13(X1,X2,empty_set))),unordered_pair(sK16(X0,empty_set,sK13(X1,X2,empty_set)),sK17(X0,empty_set,sK13(X1,X2,empty_set)))) = sK13(X1,X2,empty_set) ) ),
inference(light_normalisation,[status(thm)],[c_10459,c_10438]) ).
tcf(c_10470,plain,
! [X0: $i,X1: $i] : set_difference(set_union2(X0,X1),X0) = set_difference(set_difference(X1,X0),X0),
inference(superposition,[status(thm)],[c_85,c_6644]) ).
tcf(c_10473,plain,
! [X0: $i,X1: $i] : set_difference(set_difference(X0,X1),X0) = set_difference(X0,X0),
inference(superposition,[status(thm)],[c_6409,c_6644]) ).
tcf(c_10474,plain,
! [X0: $i,X1: $i] : subset(set_difference(set_difference(X0,X1),X1),set_union2(X1,set_union2(X1,X0))),
inference(superposition,[status(thm)],[c_6644,c_6369]) ).
tcf(c_10475,plain,
! [X0: $i,X1: $i] :
( disjoint(set_union2(X0,X1),X0)
| ( set_difference(set_union2(X0,X1),set_difference(X1,X0)) != empty_set ) ),
inference(superposition,[status(thm)],[c_6644,c_134]) ).
tcf(c_10476,plain,
! [X0: $i,X1: $i] :
( disjoint(set_union2(X0,X1),X0)
| in(sK1(set_union2(X0,X1),X0),set_difference(set_union2(X0,X1),set_difference(X1,X0))) ),
inference(superposition,[status(thm)],[c_6644,c_96]) ).
tcf(c_10477,plain,
! [X0: $i,X1: $i] : set_difference(set_difference(set_difference(X0,X1),X1),set_union2(X1,set_union2(X1,X0))) = empty_set,
inference(superposition,[status(thm)],[c_6644,c_6603]) ).
tcf(c_10478,plain,
! [X0: $i,X1: $i] : set_union2(set_difference(X0,X1),set_union2(set_union2(X1,X0),X1)) = set_union2(set_union2(X1,X0),X1),
inference(superposition,[status(thm)],[c_6644,c_6402]) ).
tcf(c_10479,plain,
! [X0: $i,X1: $i] : set_difference(set_difference(X0,X1),set_union2(set_union2(X1,X0),X1)) = empty_set,
inference(superposition,[status(thm)],[c_6644,c_6401]) ).
tcf(c_10480,plain,
! [X0: $i,X1: $i] : set_union2(set_difference(X0,X1),set_union2(X1,set_union2(X1,X0))) = set_union2(X1,set_union2(X1,X0)),
inference(superposition,[status(thm)],[c_6644,c_6375]) ).
tcf(c_10481,plain,
! [X0: $i,X1: $i] :
( disjoint(set_union2(X0,X1),X0)
| ( set_union2(X0,X1) != set_difference(X1,X0) ) ),
inference(superposition,[status(thm)],[c_6644,c_104]) ).
tcf(c_10482,plain,
! [X0: $i,X1: $i] : set_difference(set_difference(X0,X1),set_union2(X1,set_union2(X1,X0))) = empty_set,
inference(superposition,[status(thm)],[c_6644,c_6374]) ).
tcf(c_10483,plain,
! [X0: $i,X1: $i] : ~ proper_subset(set_union2(set_union2(X0,X1),X0),set_difference(X1,X0)),
inference(superposition,[status(thm)],[c_6644,c_6403]) ).
tcf(c_10487,plain,
! [X0: $i,X1: $i] : set_union2(set_union2(X0,X1),set_difference(X1,X0)) = set_union2(X0,X1),
inference(superposition,[status(thm)],[c_6644,c_6409]) ).
tcf(c_10488,plain,
! [X0: $i,X1: $i] : subset(set_difference(X0,X1),set_union2(set_union2(X1,X0),X1)),
inference(superposition,[status(thm)],[c_6644,c_6372]) ).
tcf(c_10489,plain,
! [X0: $i,X1: $i] : subset(set_difference(X0,X1),set_union2(X1,set_union2(X1,X0))),
inference(superposition,[status(thm)],[c_6644,c_6334]) ).
tcf(c_10490,plain,
! [X0: $i,X1: $i] :
( subset(set_union2(X1,X0),X1)
| ( set_difference(X0,X1) != empty_set ) ),
inference(superposition,[status(thm)],[c_6644,c_79]) ).
tcf(c_10494,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ disjoint(set_union2(X1,X2),X1)
| ~ in(X0,set_difference(set_union2(X1,X2),set_difference(X2,X1))) ),
inference(superposition,[status(thm)],[c_6644,c_97]) ).
tcf(c_10495,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X1)
| ~ in(X0,set_difference(set_union2(X1,X2),set_difference(X2,X1))) ),
inference(superposition,[status(thm)],[c_6644,c_174]) ).
tcf(c_10496,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(X0,X1),set_difference(X2,X1))
| ~ subset(X0,set_union2(X1,X2)) ),
inference(superposition,[status(thm)],[c_6644,c_74]) ).
tcf(c_10500,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(X1,X0),set_difference(X2,X0))
| ~ subset(set_union2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_6644,c_74]) ).
tcf(c_10502,plain,
! [X0: $i,X1: $i] : set_difference(set_union2(X0,set_union2(X0,X1)),set_difference(X1,X0)) = set_difference(X0,set_difference(X1,X0)),
inference(superposition,[status(thm)],[c_6644,c_6643]) ).
tcf(c_10503,plain,
! [X0: $i,X1: $i] : ~ in(powerset(set_union2(X0,set_union2(X0,X1))),set_difference(X1,X0)),
inference(superposition,[status(thm)],[c_6644,c_6323]) ).
tcf(c_10504,plain,
! [X0: $i,X1: $i] : ~ proper_subset(set_union2(X0,set_union2(X0,X1)),set_difference(X1,X0)),
inference(superposition,[status(thm)],[c_6644,c_6325]) ).
tcf(c_10505,plain,
! [X0: $i,X1: $i] : set_union2(X0,set_union2(X0,X1)) = set_union2(X0,set_difference(X1,X0)),
inference(superposition,[status(thm)],[c_6644,c_85]) ).
tcf(c_10513,plain,
! [X0: $i,X1: $i] : set_difference(set_difference(X0,X1),X1) = set_difference(X0,X1),
inference(light_normalisation,[status(thm)],[c_10470,c_6644]) ).
tcf(c_10525,plain,
! [X0: $i,X1: $i] :
( disjoint(set_union2(X0,X1),X0)
| ( set_difference(X0,set_difference(X1,X0)) != empty_set ) ),
inference(light_normalisation,[status(thm)],[c_10475,c_6643]) ).
tcf(c_10528,plain,
! [X0: $i,X1: $i] :
( disjoint(set_union2(X0,X1),X0)
| in(sK1(set_union2(X0,X1),X0),set_difference(X0,set_difference(X1,X0))) ),
inference(light_normalisation,[status(thm)],[c_10476,c_6643]) ).
tcf(c_10574,plain,
! [X0: $i,X1: $i] : set_difference(set_union2(X0,X1),set_difference(X0,X1)) = set_difference(X1,set_difference(X1,set_union2(X0,X1))),
inference(superposition,[status(thm)],[c_93,c_175]) ).
tcf(c_10575,plain,
! [X0: $i] : set_difference(X0,set_difference(X0,empty_set)) = set_difference(empty_set,empty_set),
inference(superposition,[status(thm)],[c_113,c_175]) ).
tcf(c_10576,plain,
! [X0: $i] : set_difference(empty_set,set_difference(empty_set,X0)) = set_difference(X0,X0),
inference(superposition,[status(thm)],[c_114,c_175]) ).
tcf(c_10577,plain,
! [X0: $i,X1: $i] : set_difference(X0,set_difference(X0,set_difference(X0,X1))) = set_difference(set_difference(X0,X1),empty_set),
inference(superposition,[status(thm)],[c_6290,c_175]) ).
tcf(c_10578,plain,
! [X0: $i,X1: $i] : set_difference(set_union2(X0,X1),set_difference(X1,X0)) = set_difference(X0,set_difference(X0,set_union2(X0,X1))),
inference(superposition,[status(thm)],[c_6644,c_175]) ).
tcf(c_10579,plain,
! [X0: $i,X1: $i] : set_difference(set_difference(X0,X1),set_difference(set_difference(X0,X1),set_union2(X1,X0))) = set_difference(set_union2(X1,X0),set_difference(X1,set_difference(X0,X1))),
inference(superposition,[status(thm)],[c_6643,c_175]) ).
tcf(c_10615,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,set_difference(X0,X1))
| ( set_difference(X0,set_difference(X1,set_difference(X1,X0))) != empty_set ) ),
inference(superposition,[status(thm)],[c_175,c_134]) ).
tcf(c_10616,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,set_difference(X0,X1))
| in(sK1(X0,set_difference(X0,X1)),set_difference(X0,set_difference(X1,set_difference(X1,X0)))) ),
inference(superposition,[status(thm)],[c_175,c_96]) ).
tcf(c_10617,plain,
! [X0: $i,X1: $i] : set_union2(set_difference(X0,set_difference(X0,X1)),set_union2(X1,set_difference(X1,X0))) = set_union2(X1,set_difference(X1,X0)),
inference(superposition,[status(thm)],[c_175,c_6402]) ).
tcf(c_10618,plain,
! [X0: $i,X1: $i] : set_difference(set_difference(X0,set_difference(X0,X1)),set_union2(X1,set_difference(X1,X0))) = empty_set,
inference(superposition,[status(thm)],[c_175,c_6401]) ).
tcf(c_10619,plain,
! [X0: $i,X1: $i] : set_union2(set_difference(X0,set_difference(X0,X1)),set_union2(set_difference(X1,X0),X1)) = set_union2(set_difference(X1,X0),X1),
inference(superposition,[status(thm)],[c_175,c_6375]) ).
tcf(c_10620,plain,
! [X0: $i,X1: $i] :
( disjoint(X1,set_difference(X1,X0))
| ( set_difference(X0,set_difference(X0,X1)) != X1 ) ),
inference(superposition,[status(thm)],[c_175,c_104]) ).
tcf(c_10621,plain,
! [X0: $i,X1: $i] : set_difference(set_difference(X0,set_difference(X0,X1)),set_union2(set_difference(X1,X0),X1)) = empty_set,
inference(superposition,[status(thm)],[c_175,c_6374]) ).
tcf(c_10622,plain,
! [X0: $i,X1: $i] : ~ proper_subset(set_union2(X0,set_difference(X0,X1)),set_difference(X1,set_difference(X1,X0))),
inference(superposition,[status(thm)],[c_175,c_6403]) ).
tcf(c_10623,plain,
! [X0: $i,X1: $i] : set_difference(set_difference(X0,set_difference(X0,X1)),X1) = empty_set,
inference(superposition,[status(thm)],[c_175,c_6290]) ).
tcf(c_10624,plain,
! [X0: $i,X1: $i] :
( empty(set_difference(X1,set_difference(X1,X0)))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_175,c_6423]) ).
tcf(c_10625,plain,
! [X0: $i,X1: $i] : ~ in(powerset(X0),set_difference(X1,set_difference(X1,X0))),
inference(superposition,[status(thm)],[c_175,c_6418]) ).
tcf(c_10626,plain,
! [X0: $i,X1: $i] : set_union2(X0,set_difference(X1,set_difference(X1,X0))) = X0,
inference(superposition,[status(thm)],[c_175,c_6409]) ).
tcf(c_10627,plain,
! [X0: $i,X1: $i] : subset(set_difference(X0,set_difference(X0,X1)),set_union2(X1,set_difference(X1,X0))),
inference(superposition,[status(thm)],[c_175,c_6372]) ).
tcf(c_10628,plain,
! [X0: $i,X1: $i] : subset(set_difference(X0,set_difference(X0,X1)),set_union2(set_difference(X1,X0),X1)),
inference(superposition,[status(thm)],[c_175,c_6334]) ).
tcf(c_10629,plain,
! [X0: $i,X1: $i] :
( subset(X1,set_difference(X1,X0))
| ( set_difference(X0,set_difference(X0,X1)) != empty_set ) ),
inference(superposition,[status(thm)],[c_175,c_79]) ).
tcf(c_10630,plain,
! [X0: $i,X1: $i] : ~ proper_subset(X0,set_difference(X1,set_difference(X1,X0))),
inference(superposition,[status(thm)],[c_175,c_5343]) ).
tcf(c_10631,plain,
! [X0: $i,X1: $i] : subset(set_difference(X0,set_difference(X0,X1)),X1),
inference(superposition,[status(thm)],[c_175,c_77]) ).
tcf(c_10632,plain,
! [X0: $i,X1: $i] :
( disjoint(X1,X0)
| ( set_difference(X0,set_difference(X0,X1)) != empty_set ) ),
inference(superposition,[status(thm)],[c_175,c_134]) ).
tcf(c_10633,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| in(sK1(X0,X1),set_difference(X1,set_difference(X1,X0))) ),
inference(superposition,[status(thm)],[c_175,c_96]) ).
tcf(c_10634,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,set_difference(X1,X2))
| in(X0,set_difference(X2,set_difference(X2,X1)))
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_175,c_143]) ).
tcf(c_10635,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ disjoint(X1,set_difference(X1,X2))
| ~ in(X0,set_difference(X1,set_difference(X2,set_difference(X2,X1)))) ),
inference(superposition,[status(thm)],[c_175,c_97]) ).
tcf(c_10636,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,set_difference(X1,X2))
| ~ in(X0,set_difference(X1,set_difference(X2,set_difference(X2,X1)))) ),
inference(superposition,[status(thm)],[c_175,c_174]) ).
tcf(c_10637,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(X0,set_difference(X1,X2)),set_difference(X2,set_difference(X2,X1)))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_175,c_74]) ).
tcf(c_10638,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(X0,set_difference(X2,X1))
| ~ in(X0,set_difference(X1,set_difference(X1,X2))) ),
inference(superposition,[status(thm)],[c_175,c_145]) ).
tcf(c_10639,plain,
! [X0: $i,X1: $i,X2: $i] : ~ in(unordered_pair(X0,X1),set_difference(X2,set_difference(X2,X1))),
inference(superposition,[status(thm)],[c_175,c_6426]) ).
tcf(c_10641,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ disjoint(X2,X1)
| ~ in(X0,set_difference(X1,set_difference(X1,X2))) ),
inference(superposition,[status(thm)],[c_175,c_97]) ).
tcf(c_10642,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X1)
| ~ in(X0,set_difference(X1,set_difference(X1,X2))) ),
inference(superposition,[status(thm)],[c_175,c_174]) ).
tcf(c_10643,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(X2,set_difference(X2,X0)),set_difference(X1,set_difference(X0,X2)))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_175,c_74]) ).
tcf(c_10644,plain,
! [X0: $i,X1: $i,X2: $i] : ~ in(unordered_pair(X0,X1),set_difference(X2,set_difference(X2,X0))),
inference(superposition,[status(thm)],[c_175,c_6416]) ).
tcf(c_10645,plain,
! [X0: $i,X1: $i] : set_difference(set_union2(set_difference(X0,X1),X0),set_difference(X1,set_difference(X1,X0))) = set_difference(set_difference(X0,X1),set_difference(X1,set_difference(X1,X0))),
inference(superposition,[status(thm)],[c_175,c_6643]) ).
tcf(c_10646,plain,
! [X0: $i,X1: $i] : ~ in(powerset(set_union2(set_difference(X0,X1),X0)),set_difference(X1,set_difference(X1,X0))),
inference(superposition,[status(thm)],[c_175,c_6323]) ).
tcf(c_10647,plain,
! [X0: $i,X1: $i] : ~ proper_subset(set_union2(set_difference(X0,X1),X0),set_difference(X1,set_difference(X1,X0))),
inference(superposition,[status(thm)],[c_175,c_6325]) ).
tcf(c_10648,plain,
! [X0: $i,X1: $i] : set_union2(set_difference(X0,X1),set_difference(X1,set_difference(X1,X0))) = set_union2(set_difference(X0,X1),X0),
inference(superposition,[status(thm)],[c_175,c_85]) ).
tcf(c_10682,plain,
! [X0: $i,X1: $i] : set_difference(X0,set_difference(X1,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_10578,c_114,c_6291,c_6643]) ).
tcf(c_10687,plain,
! [X0: $i,X1: $i] : set_difference(set_union2(X0,X1),set_difference(X0,set_difference(X1,X0))) = set_difference(set_difference(X1,X0),empty_set),
inference(light_normalisation,[status(thm)],[c_10579,c_6374]) ).
tcf(c_10688,plain,
! [X0: $i,X1: $i] : set_difference(set_union2(X0,X1),set_difference(X1,X0)) = X0,
inference(demodulation,[status(thm)],[c_6643,c_10682]) ).
tcf(c_10828,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(unordered_pair(X2,X0),X1)
| ~ in(X2,X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_167,c_82]) ).
tcf(c_10829,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK13(X0,X1,empty_set),X2)
| ( cartesian_product2(X0,X1) = empty_set )
| ~ in(unordered_pair(sK14(X0,X1,empty_set),sK15(X0,X1,empty_set)),X2)
| ~ in(unordered_pair(sK14(X0,X1,empty_set),sK14(X0,X1,empty_set)),X2) ),
inference(superposition,[status(thm)],[c_5229,c_82]) ).
tcf(c_10830,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK5(cartesian_product2(X0,X1)),X2)
| ( cartesian_product2(X0,X1) = empty_set )
| ~ in(unordered_pair(sK16(X0,X1,sK5(cartesian_product2(X0,X1))),sK17(X0,X1,sK5(cartesian_product2(X0,X1)))),X2)
| ~ in(unordered_pair(sK16(X0,X1,sK5(cartesian_product2(X0,X1))),sK16(X0,X1,sK5(cartesian_product2(X0,X1)))),X2) ),
inference(superposition,[status(thm)],[c_5462,c_82]) ).
tcf(c_10831,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subset(sK13(X2,X3,cartesian_product2(X0,X1)),X4)
| ( cartesian_product2(X0,X1) = cartesian_product2(X2,X3) )
| ( unordered_pair(unordered_pair(sK14(X2,X3,cartesian_product2(X0,X1)),sK14(X2,X3,cartesian_product2(X0,X1))),unordered_pair(sK14(X2,X3,cartesian_product2(X0,X1)),sK15(X2,X3,cartesian_product2(X0,X1)))) = sK13(X2,X3,cartesian_product2(X0,X1)) )
| ~ in(unordered_pair(sK16(X0,X1,sK13(X2,X3,cartesian_product2(X0,X1))),sK17(X0,X1,sK13(X2,X3,cartesian_product2(X0,X1)))),X4)
| ~ in(unordered_pair(sK16(X0,X1,sK13(X2,X3,cartesian_product2(X0,X1))),sK16(X0,X1,sK13(X2,X3,cartesian_product2(X0,X1)))),X4) ),
inference(superposition,[status(thm)],[c_5464,c_82]) ).
tcf(c_10832,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( unordered_pair(X1,X2) = X0 )
| ~ in(X2,X0)
| ~ in(X1,X0)
| ~ subset(X0,unordered_pair(X1,X2)) ),
inference(superposition,[status(thm)],[c_82,c_137]) ).
tcf(c_10833,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(unordered_pair(X0,X2),set_difference(unordered_pair(X0,X2),X1)) = unordered_pair(X0,X2) )
| ~ in(X2,X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_82,c_72]) ).
tcf(c_10834,plain,
! [X0: $i,X1: $i,X2: $i] :
( proper_subset(unordered_pair(X0,X2),X1)
| ( unordered_pair(X0,X2) = X1 )
| ~ in(X2,X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_82,c_181]) ).
tcf(c_10835,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(unordered_pair(X0,X2),X3)
| ~ subset(X1,X3)
| ~ in(X2,X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_82,c_69]) ).
tcf(c_10836,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(unordered_pair(X0,X2),X1) = empty_set )
| ~ in(X2,X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_82,c_78]) ).
tcf(c_10837,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_union2(unordered_pair(X0,X2),X1) = X1 )
| ~ in(X2,X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_82,c_66]) ).
tcf(c_10838,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(X2,X0)
| ~ in(X1,X0)
| ~ proper_subset(X0,unordered_pair(X1,X2)) ),
inference(superposition,[status(thm)],[c_82,c_98]) ).
tcf(c_10906,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_union2(X1,X0),X2)
| ~ subset(X1,X2)
| ~ subset(set_difference(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_85,c_106]) ).
tcf(c_10909,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_union2(X2,X0),X1)
| ~ subset(X2,X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_132,c_106]) ).
tcf(c_10914,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_union2(X1,X2) = X0 )
| ~ subset(X2,X0)
| ~ subset(X1,X0)
| ~ subset(X0,set_union2(X1,X2)) ),
inference(superposition,[status(thm)],[c_106,c_137]) ).
tcf(c_10915,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(set_union2(X0,X2),set_difference(set_union2(X0,X2),X1)) = set_union2(X0,X2) )
| ~ subset(X2,X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_106,c_72]) ).
tcf(c_10916,plain,
! [X0: $i,X1: $i,X2: $i] :
( proper_subset(set_union2(X0,X2),X1)
| ( set_union2(X0,X2) = X1 )
| ~ subset(X2,X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_106,c_181]) ).
tcf(c_10917,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(set_union2(X0,X3),X2)
| ~ subset(X3,X1)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_106,c_69]) ).
tcf(c_10918,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(set_union2(X0,X2),X1) = empty_set )
| ~ subset(X2,X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_106,c_78]) ).
tcf(c_10919,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_union2(set_union2(X0,X2),X1) = X1 )
| ~ subset(X2,X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_106,c_66]) ).
tcf(c_10920,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ subset(X2,X0)
| ~ subset(X1,X0)
| ~ proper_subset(X0,set_union2(X1,X2)) ),
inference(superposition,[status(thm)],[c_106,c_98]) ).
tcf(c_10921,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(set_union2(X0,X1),X2)
| ~ subset(X1,empty_set)
| ~ subset(X0,empty_set) ),
inference(superposition,[status(thm)],[c_106,c_7399]) ).
tcf(c_10922,plain,
! [X0: $i,X1: $i] :
( ( set_union2(X0,X1) = empty_set )
| ~ subset(X1,empty_set)
| ~ subset(X0,empty_set) ),
inference(superposition,[status(thm)],[c_106,c_92]) ).
tcf(c_11007,plain,
! [X0: $i,X1: $i] :
( ( X0 = empty_set )
| ( unordered_pair(X0,X1) != powerset(empty_set) ) ),
inference(superposition,[status(thm)],[c_70,c_107]) ).
tcf(c_11010,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ( unordered_pair(X0,X0) != unordered_pair(X1,X2) ) ),
inference(superposition,[status(thm)],[c_167,c_107]) ).
tcf(c_11011,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( cartesian_product2(X0,X1) = empty_set )
| ( unordered_pair(sK14(X0,X1,empty_set),sK14(X0,X1,empty_set)) = X2 )
| ( sK13(X0,X1,empty_set) != unordered_pair(X2,X2) ) ),
inference(superposition,[status(thm)],[c_5229,c_107]) ).
tcf(c_11012,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( cartesian_product2(X0,X1) = empty_set )
| ( unordered_pair(sK16(X0,X1,sK5(cartesian_product2(X0,X1))),sK16(X0,X1,sK5(cartesian_product2(X0,X1)))) = X2 )
| ( sK5(cartesian_product2(X0,X1)) != unordered_pair(X2,X2) ) ),
inference(superposition,[status(thm)],[c_5462,c_107]) ).
tcf(c_11013,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X0,X1) = cartesian_product2(X2,X3) )
| ( unordered_pair(sK16(X2,X3,sK13(X0,X1,cartesian_product2(X2,X3))),sK16(X2,X3,sK13(X0,X1,cartesian_product2(X2,X3)))) = X4 )
| ( unordered_pair(unordered_pair(sK14(X0,X1,cartesian_product2(X2,X3)),sK14(X0,X1,cartesian_product2(X2,X3))),unordered_pair(sK14(X0,X1,cartesian_product2(X2,X3)),sK15(X0,X1,cartesian_product2(X2,X3)))) = sK13(X0,X1,cartesian_product2(X2,X3)) )
| ( sK13(X0,X1,cartesian_product2(X2,X3)) != unordered_pair(X4,X4) ) ),
inference(superposition,[status(thm)],[c_5464,c_107]) ).
tcf(c_11035,plain,
! [X0: $i,X1: $i] : subset(set_difference(set_union2(X0,X1),set_difference(X0,X1)),X1),
inference(superposition,[status(thm)],[c_93,c_10631]) ).
tcf(c_11036,plain,
! [X0: $i] : subset(set_difference(empty_set,empty_set),X0),
inference(superposition,[status(thm)],[c_113,c_10631]) ).
tcf(c_11037,plain,
! [X0: $i] : subset(set_difference(X0,X0),empty_set),
inference(superposition,[status(thm)],[c_114,c_10631]) ).
tcf(c_11039,plain,
! [X0: $i,X1: $i] : subset(set_difference(X0,set_difference(X1,set_difference(X1,X0))),set_difference(X0,X1)),
inference(superposition,[status(thm)],[c_175,c_10631]) ).
tcf(c_11040,plain,
! [X0: $i,X1: $i] : subset(set_difference(set_difference(X0,X1),empty_set),X0),
inference(superposition,[status(thm)],[c_6290,c_10631]) ).
tcf(c_11041,plain,
! [X0: $i,X1: $i] : subset(set_difference(X0,empty_set),set_union2(X0,X1)),
inference(superposition,[status(thm)],[c_6291,c_10631]) ).
tcf(c_11042,plain,
! [X0: $i,X1: $i] : subset(set_difference(X0,empty_set),set_union2(X1,X0)),
inference(superposition,[status(thm)],[c_6293,c_10631]) ).
tcf(c_11043,plain,
! [X0: $i,X1: $i] : subset(set_difference(set_difference(X0,X1),empty_set),set_union2(X1,X0)),
inference(superposition,[status(thm)],[c_6374,c_10631]) ).
tcf(c_11044,plain,
! [X0: $i,X1: $i] : subset(set_difference(set_difference(X0,X1),empty_set),set_union2(X0,X1)),
inference(superposition,[status(thm)],[c_6401,c_10631]) ).
tcf(c_11045,plain,
! [X0: $i,X1: $i] : subset(set_difference(set_union2(X0,X1),set_difference(X1,X0)),X0),
inference(superposition,[status(thm)],[c_6644,c_10631]) ).
tcf(c_11046,plain,
! [X0: $i,X1: $i] :
( ( set_difference(X1,set_difference(X1,X0)) = X0 )
| ~ subset(X0,set_difference(X1,set_difference(X1,X0))) ),
inference(superposition,[status(thm)],[c_10631,c_137]) ).
tcf(c_11047,plain,
! [X0: $i,X1: $i] : set_difference(set_difference(X0,set_difference(X0,X1)),set_difference(set_difference(X0,set_difference(X0,X1)),X1)) = set_difference(X0,set_difference(X0,X1)),
inference(superposition,[status(thm)],[c_10631,c_72]) ).
tcf(c_11048,plain,
! [X0: $i,X1: $i] :
( proper_subset(set_difference(X0,set_difference(X0,X1)),X1)
| ( set_difference(X0,set_difference(X0,X1)) = X1 ) ),
inference(superposition,[status(thm)],[c_10631,c_181]) ).
tcf(c_11049,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(X2,set_difference(X2,X0)),X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_10631,c_69]) ).
tcf(c_11051,plain,
! [X0: $i,X1: $i] : set_union2(set_difference(X0,set_difference(X0,X1)),X1) = X1,
inference(superposition,[status(thm)],[c_10631,c_66]) ).
tcf(c_11053,plain,
! [X0: $i,X1: $i] : disjoint(set_difference(X0,set_difference(X0,empty_set)),X1),
inference(superposition,[status(thm)],[c_10631,c_7399]) ).
tcf(c_11068,plain,
! [X0: $i,X1: $i] : set_difference(set_difference(X0,set_difference(X0,X1)),empty_set) = set_difference(X0,set_difference(X0,X1)),
inference(light_normalisation,[status(thm)],[c_11047,c_10623]) ).
tcf(c_11093,plain,
! [X0: $i,X1: $i] : ~ proper_subset(X0,set_difference(set_union2(X1,X0),set_difference(X1,X0))),
inference(superposition,[status(thm)],[c_93,c_10630]) ).
tcf(c_11094,plain,
! [X0: $i] : ~ proper_subset(X0,set_difference(empty_set,empty_set)),
inference(superposition,[status(thm)],[c_113,c_10630]) ).
tcf(c_11095,plain,
! [X0: $i] : ~ proper_subset(empty_set,set_difference(X0,X0)),
inference(superposition,[status(thm)],[c_114,c_10630]) ).
tcf(c_11097,plain,
! [X0: $i,X1: $i] : ~ proper_subset(set_difference(X0,X1),set_difference(X0,set_difference(X1,set_difference(X1,X0)))),
inference(superposition,[status(thm)],[c_175,c_10630]) ).
tcf(c_11098,plain,
! [X0: $i,X1: $i] : ~ proper_subset(X0,set_difference(set_difference(X0,X1),empty_set)),
inference(superposition,[status(thm)],[c_6290,c_10630]) ).
tcf(c_11099,plain,
! [X0: $i,X1: $i] : ~ proper_subset(set_union2(X0,X1),set_difference(X0,empty_set)),
inference(superposition,[status(thm)],[c_6291,c_10630]) ).
tcf(c_11100,plain,
! [X0: $i,X1: $i] : ~ proper_subset(set_union2(X0,X1),set_difference(X1,empty_set)),
inference(superposition,[status(thm)],[c_6293,c_10630]) ).
tcf(c_11101,plain,
! [X0: $i,X1: $i] : ~ proper_subset(set_union2(X0,X1),set_difference(set_difference(X1,X0),empty_set)),
inference(superposition,[status(thm)],[c_6374,c_10630]) ).
tcf(c_11102,plain,
! [X0: $i,X1: $i] : ~ proper_subset(set_union2(X0,X1),set_difference(set_difference(X0,X1),empty_set)),
inference(superposition,[status(thm)],[c_6401,c_10630]) ).
tcf(c_11103,plain,
! [X0: $i,X1: $i] : ~ proper_subset(X0,set_difference(set_union2(X0,X1),set_difference(X1,X0))),
inference(superposition,[status(thm)],[c_6644,c_10630]) ).
tcf(c_11116,plain,
! [X0: $i,X1: $i] : set_difference(set_difference(X0,X1),set_difference(X1,set_difference(X1,X0))) = set_difference(X0,X1),
inference(superposition,[status(thm)],[c_175,c_10682]) ).
tcf(c_11122,plain,
! [X0: $i,X1: $i] : set_difference(set_union2(X0,X1),empty_set) = set_union2(X0,X1),
inference(superposition,[status(thm)],[c_6401,c_10682]) ).
tcf(c_11124,plain,
! [X0: $i,X1: $i] : subset(set_difference(X0,X0),set_difference(X1,X0)),
inference(superposition,[status(thm)],[c_10682,c_10631]) ).
tcf(c_11127,plain,
! [X0: $i,X1: $i] : set_union2(X0,set_union2(X0,set_difference(X1,X0))) = set_union2(X0,set_difference(X1,X0)),
inference(superposition,[status(thm)],[c_10682,c_6402]) ).
tcf(c_11128,plain,
! [X0: $i,X1: $i] : set_difference(X0,set_union2(X0,set_difference(X1,X0))) = empty_set,
inference(superposition,[status(thm)],[c_10682,c_6401]) ).
tcf(c_11129,plain,
! [X0: $i,X1: $i] : set_union2(X0,set_union2(set_difference(X1,X0),X0)) = set_union2(set_difference(X1,X0),X0),
inference(superposition,[status(thm)],[c_10682,c_6375]) ).
tcf(c_11130,plain,
! [X0: $i,X1: $i] : disjoint(X0,set_difference(X1,X0)),
inference(superposition,[status(thm)],[c_10682,c_104]) ).
tcf(c_11131,plain,
! [X0: $i,X1: $i] : set_difference(X0,set_union2(set_difference(X1,X0),X0)) = empty_set,
inference(superposition,[status(thm)],[c_10682,c_6374]) ).
tcf(c_11132,plain,
! [X0: $i,X1: $i] : ~ proper_subset(set_union2(X0,set_difference(X1,X0)),X0),
inference(superposition,[status(thm)],[c_10682,c_6403]) ).
tcf(c_11137,plain,
! [X0: $i,X1: $i] : subset(X0,set_union2(X0,set_difference(X1,X0))),
inference(superposition,[status(thm)],[c_10682,c_6372]) ).
tcf(c_11138,plain,
! [X0: $i,X1: $i] : subset(X0,set_union2(set_difference(X1,X0),X0)),
inference(superposition,[status(thm)],[c_10682,c_6334]) ).
tcf(c_11139,plain,
! [X0: $i,X1: $i] :
( subset(X0,set_difference(X1,X0))
| ( X0 != empty_set ) ),
inference(superposition,[status(thm)],[c_10682,c_79]) ).
tcf(c_11147,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,set_difference(X2,X1))
| ~ in(X0,set_difference(X1,X1)) ),
inference(superposition,[status(thm)],[c_10682,c_174]) ).
tcf(c_11148,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(X0,set_difference(X2,X1)),X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_10682,c_74]) ).
tcf(c_11152,plain,
! [X0: $i,X1: $i] :
( ~ disjoint(X1,X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_10682,c_97]) ).
tcf(c_11154,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,set_difference(X1,set_difference(X2,X0)))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_10682,c_74]) ).
tcf(c_11157,plain,
! [X0: $i,X1: $i] : ~ proper_subset(set_difference(X0,X1),set_difference(X1,X1)),
inference(superposition,[status(thm)],[c_10682,c_10630]) ).
tcf(c_11158,plain,
! [X0: $i,X1: $i] : ~ in(powerset(set_union2(set_difference(X0,X1),X1)),X1),
inference(superposition,[status(thm)],[c_10682,c_6323]) ).
tcf(c_11159,plain,
! [X0: $i,X1: $i] : ~ proper_subset(set_union2(set_difference(X0,X1),X1),X1),
inference(superposition,[status(thm)],[c_10682,c_6325]) ).
tcf(c_11240,plain,
! [X0: $i,X1: $i] : disjoint(set_difference(X0,X1),set_difference(X1,set_difference(X1,X0))),
inference(superposition,[status(thm)],[c_175,c_11130]) ).
tcf(c_11246,plain,
! [X0: $i,X1: $i] : disjoint(set_union2(X0,X1),empty_set),
inference(superposition,[status(thm)],[c_6401,c_11130]) ).
tcf(c_11248,plain,
! [X0: $i,X1: $i] : ~ in(X0,set_difference(X1,unordered_pair(X0,X0))),
inference(superposition,[status(thm)],[c_11130,c_51]) ).
tcf(c_11249,plain,
! [X0: $i,X1: $i] : set_difference(X0,set_difference(X0,set_difference(X1,X0))) = empty_set,
inference(superposition,[status(thm)],[c_11130,c_135]) ).
tcf(c_11250,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(X0,set_difference(X2,X1))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_11130,c_99]) ).
tcf(c_11252,plain,
! [X0: $i,X1: $i] : disjoint(set_difference(X0,X1),X1),
inference(superposition,[status(thm)],[c_11130,c_133]) ).
tcf(c_11253,plain,
! [X0: $i] : ~ in(empty_set,set_difference(X0,powerset(empty_set))),
inference(superposition,[status(thm)],[c_11130,c_6019]) ).
tcf(c_11266,plain,
! [X0: $i,X1: $i] : disjoint(set_difference(X0,set_difference(X0,X1)),set_difference(X1,X0)),
inference(superposition,[status(thm)],[c_175,c_11252]) ).
tcf(c_11272,plain,
! [X0: $i,X1: $i] : disjoint(empty_set,set_union2(X0,X1)),
inference(superposition,[status(thm)],[c_6401,c_11252]) ).
tcf(c_11274,plain,
! [X0: $i,X1: $i] : set_difference(set_difference(X0,X1),set_difference(set_difference(X0,X1),X1)) = empty_set,
inference(superposition,[status(thm)],[c_11252,c_135]) ).
tcf(c_11275,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(X0,X2)
| ~ subset(X0,set_difference(X1,X2)) ),
inference(superposition,[status(thm)],[c_11252,c_99]) ).
tcf(c_11280,plain,
! [X0: $i,X1: $i] : set_difference(set_difference(X0,X1),set_difference(X0,X1)) = empty_set,
inference(light_normalisation,[status(thm)],[c_11274,c_10513]) ).
tcf(c_11286,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( unordered_pair(X0,X1) != powerset(empty_set) ) ),
inference(superposition,[status(thm)],[c_70,c_108]) ).
tcf(c_11290,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( cartesian_product2(X0,X1) = empty_set )
| ( unordered_pair(sK14(X0,X1,empty_set),sK14(X0,X1,empty_set)) = unordered_pair(sK14(X0,X1,empty_set),sK15(X0,X1,empty_set)) )
| ( sK13(X0,X1,empty_set) != unordered_pair(X2,X2) ) ),
inference(superposition,[status(thm)],[c_5229,c_108]) ).
tcf(c_11291,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( cartesian_product2(X0,X1) = empty_set )
| ( unordered_pair(sK16(X0,X1,sK5(cartesian_product2(X0,X1))),sK16(X0,X1,sK5(cartesian_product2(X0,X1)))) = unordered_pair(sK16(X0,X1,sK5(cartesian_product2(X0,X1))),sK17(X0,X1,sK5(cartesian_product2(X0,X1)))) )
| ( sK5(cartesian_product2(X0,X1)) != unordered_pair(X2,X2) ) ),
inference(superposition,[status(thm)],[c_5462,c_108]) ).
tcf(c_11292,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X0,X1) = cartesian_product2(X2,X3) )
| ( unordered_pair(sK16(X2,X3,sK13(X0,X1,cartesian_product2(X2,X3))),sK16(X2,X3,sK13(X0,X1,cartesian_product2(X2,X3)))) = unordered_pair(sK16(X2,X3,sK13(X0,X1,cartesian_product2(X2,X3))),sK17(X2,X3,sK13(X0,X1,cartesian_product2(X2,X3)))) )
| ( unordered_pair(unordered_pair(sK14(X0,X1,cartesian_product2(X2,X3)),sK14(X0,X1,cartesian_product2(X2,X3))),unordered_pair(sK14(X0,X1,cartesian_product2(X2,X3)),sK15(X0,X1,cartesian_product2(X2,X3)))) = sK13(X0,X1,cartesian_product2(X2,X3)) )
| ( sK13(X0,X1,cartesian_product2(X2,X3)) != unordered_pair(X4,X4) ) ),
inference(superposition,[status(thm)],[c_5464,c_108]) ).
tcf(c_11312,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,X0)
| subset(X0,set_difference(X1,unordered_pair(X2,X2)))
| ~ subset(X0,set_union2(X1,unordered_pair(X2,X2))) ),
inference(superposition,[status(thm)],[c_93,c_57]) ).
tcf(c_11314,plain,
! [X0: $i,X1: $i] :
( subset(X0,empty_set)
| in(X1,X0)
| ~ subset(X0,unordered_pair(X1,X1)) ),
inference(superposition,[status(thm)],[c_1252,c_57]) ).
tcf(c_11315,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,empty_set)
| in(X1,X0)
| ~ subset(X0,set_difference(unordered_pair(X1,X1),X2)) ),
inference(superposition,[status(thm)],[c_6290,c_57]) ).
tcf(c_11316,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,X0)
| subset(X0,set_difference(X2,unordered_pair(X1,X1)))
| ~ subset(X0,set_union2(unordered_pair(X1,X1),X2)) ),
inference(superposition,[status(thm)],[c_6644,c_57]) ).
tcf(c_11317,plain,
! [X0: $i,X1: $i] :
( in(empty_set,X0)
| subset(X0,set_difference(X1,powerset(empty_set)))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_70,c_57]) ).
tcf(c_11318,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,X2)
| ( set_difference(X0,unordered_pair(X1,X1)) = X2 )
| ~ subset(X2,X0)
| ~ subset(set_difference(X0,unordered_pair(X1,X1)),X2) ),
inference(superposition,[status(thm)],[c_57,c_137]) ).
tcf(c_11319,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,X0)
| ( set_difference(X0,set_difference(X0,set_difference(X1,unordered_pair(X2,X2)))) = X0 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_72]) ).
tcf(c_11320,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,X0)
| proper_subset(X0,set_difference(X1,unordered_pair(X2,X2)))
| ( set_difference(X1,unordered_pair(X2,X2)) = X0 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_181]) ).
tcf(c_11321,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(X3,X2)
| in(X1,X3)
| ~ subset(X3,X0)
| ~ subset(set_difference(X0,unordered_pair(X1,X1)),X2) ),
inference(superposition,[status(thm)],[c_57,c_69]) ).
tcf(c_11322,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,X0)
| ( set_difference(X0,set_difference(X1,unordered_pair(X2,X2))) = empty_set )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_78]) ).
tcf(c_11323,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,X0)
| ( set_union2(X0,set_difference(X1,unordered_pair(X2,X2))) = set_difference(X1,unordered_pair(X2,X2)) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_66]) ).
tcf(c_11324,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,X2)
| ~ subset(X2,X0)
| ~ proper_subset(set_difference(X0,unordered_pair(X1,X1)),X2) ),
inference(superposition,[status(thm)],[c_57,c_98]) ).
tcf(c_11325,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,unordered_pair(X0,X1))
| in(X1,set_difference(X2,unordered_pair(X3,X3)))
| ~ subset(unordered_pair(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_57,c_84]) ).
tcf(c_11326,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,unordered_pair(X0,X1))
| in(X0,set_difference(X2,unordered_pair(X3,X3)))
| ~ subset(unordered_pair(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_57,c_83]) ).
tcf(c_11327,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,unordered_pair(powerset(set_difference(X0,unordered_pair(X1,X1))),X2))
| ~ subset(unordered_pair(powerset(set_difference(X0,unordered_pair(X1,X1))),X2),X0) ),
inference(superposition,[status(thm)],[c_57,c_5487]) ).
tcf(c_11328,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,unordered_pair(X0,powerset(set_difference(X1,unordered_pair(X2,X2)))))
| ~ subset(unordered_pair(X0,powerset(set_difference(X1,unordered_pair(X2,X2)))),X1) ),
inference(superposition,[status(thm)],[c_57,c_5488]) ).
tcf(c_11329,plain,
! [X0: $i,X1: $i] :
( in(X1,powerset(empty_set))
| in(empty_set,set_difference(X0,unordered_pair(X1,X1)))
| ~ subset(powerset(empty_set),X0) ),
inference(superposition,[status(thm)],[c_57,c_5628]) ).
tcf(c_11330,plain,
! [X0: $i,X1: $i] :
( in(X1,powerset(powerset(set_difference(X0,unordered_pair(X1,X1)))))
| ~ subset(powerset(powerset(set_difference(X0,unordered_pair(X1,X1)))),X0) ),
inference(superposition,[status(thm)],[c_57,c_5545]) ).
tcf(c_11331,plain,
! [X0: $i,X1: $i] :
( in(X1,powerset(powerset(union(powerset(set_difference(X0,unordered_pair(X1,X1)))))))
| ~ subset(powerset(powerset(union(powerset(set_difference(X0,unordered_pair(X1,X1)))))),X0) ),
inference(superposition,[status(thm)],[c_57,c_5557]) ).
tcf(c_11332,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,unordered_pair(powerset(union(powerset(set_difference(X0,unordered_pair(X1,X1))))),X2))
| ~ subset(unordered_pair(powerset(union(powerset(set_difference(X0,unordered_pair(X1,X1))))),X2),X0) ),
inference(superposition,[status(thm)],[c_57,c_5585]) ).
tcf(c_11333,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,unordered_pair(X0,powerset(union(powerset(set_difference(X1,unordered_pair(X2,X2)))))))
| ~ subset(unordered_pair(X0,powerset(union(powerset(set_difference(X1,unordered_pair(X2,X2)))))),X1) ),
inference(superposition,[status(thm)],[c_57,c_5589]) ).
tcf(c_11334,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,powerset(set_union2(powerset(set_difference(X0,unordered_pair(X1,X1))),X2)))
| ~ subset(powerset(set_union2(powerset(set_difference(X0,unordered_pair(X1,X1))),X2)),X0) ),
inference(superposition,[status(thm)],[c_57,c_5808]) ).
tcf(c_11335,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,powerset(set_union2(X0,powerset(set_difference(X1,unordered_pair(X2,X2))))))
| ~ subset(powerset(set_union2(X0,powerset(set_difference(X1,unordered_pair(X2,X2))))),X1) ),
inference(superposition,[status(thm)],[c_57,c_5850]) ).
tcf(c_11336,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X1,unordered_pair(set_union2(powerset(set_difference(X0,unordered_pair(X1,X1))),X2),X3))
| ~ subset(unordered_pair(set_union2(powerset(set_difference(X0,unordered_pair(X1,X1))),X2),X3),X0) ),
inference(superposition,[status(thm)],[c_57,c_6050]) ).
tcf(c_11337,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X2,unordered_pair(X0,set_union2(powerset(set_difference(X1,unordered_pair(X2,X2))),X3)))
| ~ subset(unordered_pair(X0,set_union2(powerset(set_difference(X1,unordered_pair(X2,X2))),X3)),X1) ),
inference(superposition,[status(thm)],[c_57,c_6065]) ).
tcf(c_11338,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X1,set_union2(unordered_pair(powerset(set_difference(X0,unordered_pair(X1,X1))),X2),X3))
| ~ subset(set_union2(unordered_pair(powerset(set_difference(X0,unordered_pair(X1,X1))),X2),X3),X0) ),
inference(superposition,[status(thm)],[c_57,c_6081]) ).
tcf(c_11339,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X2,set_union2(X0,unordered_pair(powerset(set_difference(X1,unordered_pair(X2,X2))),X3)))
| ~ subset(set_union2(X0,unordered_pair(powerset(set_difference(X1,unordered_pair(X2,X2))),X3)),X1) ),
inference(superposition,[status(thm)],[c_57,c_6112]) ).
tcf(c_11340,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X2,set_union2(unordered_pair(X0,powerset(set_difference(X1,unordered_pair(X2,X2)))),X3))
| ~ subset(set_union2(unordered_pair(X0,powerset(set_difference(X1,unordered_pair(X2,X2)))),X3),X1) ),
inference(superposition,[status(thm)],[c_57,c_6140]) ).
tcf(c_11341,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,set_union2(X0,unordered_pair(X1,powerset(set_difference(X2,unordered_pair(X3,X3))))))
| ~ subset(set_union2(X0,unordered_pair(X1,powerset(set_difference(X2,unordered_pair(X3,X3))))),X2) ),
inference(superposition,[status(thm)],[c_57,c_6173]) ).
tcf(c_11342,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X2,unordered_pair(set_union2(X0,powerset(set_difference(X1,unordered_pair(X2,X2)))),X3))
| ~ subset(unordered_pair(set_union2(X0,powerset(set_difference(X1,unordered_pair(X2,X2)))),X3),X1) ),
inference(superposition,[status(thm)],[c_57,c_6217]) ).
tcf(c_11343,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,unordered_pair(X0,set_union2(X1,powerset(set_difference(X2,unordered_pair(X3,X3))))))
| ~ subset(unordered_pair(X0,set_union2(X1,powerset(set_difference(X2,unordered_pair(X3,X3))))),X2) ),
inference(superposition,[status(thm)],[c_57,c_6232]) ).
tcf(c_11344,plain,
! [X0: $i,X1: $i] :
( in(X1,powerset(union(powerset(powerset(set_difference(X0,unordered_pair(X1,X1)))))))
| ~ subset(powerset(union(powerset(powerset(set_difference(X0,unordered_pair(X1,X1)))))),X0) ),
inference(superposition,[status(thm)],[c_57,c_7102]) ).
tcf(c_11345,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,set_union2(powerset(powerset(set_difference(X0,unordered_pair(X1,X1)))),X2))
| ~ subset(set_union2(powerset(powerset(set_difference(X0,unordered_pair(X1,X1)))),X2),X0) ),
inference(superposition,[status(thm)],[c_57,c_8859]) ).
tcf(c_11346,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,set_union2(X0,powerset(powerset(set_difference(X1,unordered_pair(X2,X2))))))
| ~ subset(set_union2(X0,powerset(powerset(set_difference(X1,unordered_pair(X2,X2))))),X1) ),
inference(superposition,[status(thm)],[c_57,c_8903]) ).
tcf(c_11542,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK6(X2,X0),X2)
| in(sK6(X2,X0),union(X1))
| ( X0 = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_120,c_149]) ).
tcf(c_11543,plain,
! [X0: $i,X1: $i] :
( in(sK6(X0,X1),X0)
| ( X0 = X1 )
| ( set_union2(unordered_pair(sK6(X0,X1),sK6(X0,X1)),X1) = X1 ) ),
inference(superposition,[status(thm)],[c_120,c_95]) ).
tcf(c_11544,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK6(X0,X1),X0)
| ( X0 = X1 )
| ~ disjoint(X1,X2)
| ~ in(sK6(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_120,c_91]) ).
tcf(c_11545,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK6(X2,X0),X2)
| in(sK6(X2,X0),X1)
| ( X0 = X2 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_120,c_123]) ).
tcf(c_11546,plain,
! [X0: $i,X1: $i] :
( in(sK6(X1,X0),X1)
| ( X0 = X1 )
| ~ in(X0,sK6(X1,X0)) ),
inference(superposition,[status(thm)],[c_120,c_124]) ).
tcf(c_11547,plain,
! [X0: $i,X1: $i] :
( in(sK6(X1,X0),X1)
| ( X0 = X1 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_120,c_184]) ).
tcf(c_11548,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK6(X2,set_difference(X0,set_difference(X0,X1))),X2)
| ( set_difference(X0,set_difference(X0,X1)) = X2 )
| ~ disjoint(X0,X1) ),
inference(superposition,[status(thm)],[c_120,c_97]) ).
tcf(c_11549,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK6(X2,set_difference(X0,set_difference(X0,X1))),X2)
| in(sK6(X2,set_difference(X0,set_difference(X0,X1))),X1)
| ( set_difference(X0,set_difference(X0,X1)) = X2 ) ),
inference(superposition,[status(thm)],[c_120,c_174]) ).
tcf(c_11550,plain,
! [X0: $i,X1: $i] :
( in(sK6(X0,unordered_pair(X1,X1)),X0)
| ( unordered_pair(X1,X1) = X0 )
| ( sK6(X0,unordered_pair(X1,X1)) = X1 ) ),
inference(superposition,[status(thm)],[c_120,c_112]) ).
tcf(c_11551,plain,
! [X0: $i] :
( in(sK6(X0,empty_set),X0)
| ( X0 = empty_set ) ),
inference(superposition,[status(thm)],[c_120,c_118]) ).
tcf(c_11552,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK6(X2,set_union2(X0,X1)),X2)
| in(sK6(X2,set_union2(X0,X1)),X1)
| in(sK6(X2,set_union2(X0,X1)),X0)
| ( set_union2(X0,X1) = X2 ) ),
inference(superposition,[status(thm)],[c_120,c_131]) ).
tcf(c_11553,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK6(X0,set_difference(X1,X2)),X0)
| ( set_difference(X1,X2) = X0 )
| ~ in(sK6(X0,set_difference(X1,X2)),X2) ),
inference(superposition,[status(thm)],[c_120,c_145]) ).
tcf(c_11554,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK6(X2,set_difference(X0,X1)),X2)
| in(sK6(X2,set_difference(X0,X1)),X0)
| ( set_difference(X0,X1) = X2 ) ),
inference(superposition,[status(thm)],[c_120,c_144]) ).
tcf(c_11555,plain,
! [X0: $i,X1: $i] :
( in(sK6(X1,union(X0)),X1)
| ( union(X0) = X1 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_120,c_7039]) ).
tcf(c_11556,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK6(X2,cartesian_product2(X0,X1)),X2)
| ( cartesian_product2(X0,X1) = X2 )
| ( unordered_pair(unordered_pair(sK16(X0,X1,sK6(X2,cartesian_product2(X0,X1))),sK16(X0,X1,sK6(X2,cartesian_product2(X0,X1)))),unordered_pair(sK16(X0,X1,sK6(X2,cartesian_product2(X0,X1))),sK17(X0,X1,sK6(X2,cartesian_product2(X0,X1))))) = sK6(X2,cartesian_product2(X0,X1)) ) ),
inference(superposition,[status(thm)],[c_120,c_1855]) ).
tcf(c_11557,plain,
! [X0: $i,X1: $i] :
( subset(sK6(X1,powerset(X0)),X0)
| in(sK6(X1,powerset(X0)),X1)
| ( powerset(X0) = X1 ) ),
inference(superposition,[status(thm)],[c_120,c_179]) ).
tcf(c_11558,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK6(X0,X2),X2)
| in(sK6(X0,X2),union(X1))
| ( X0 = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_120,c_149]) ).
tcf(c_11559,plain,
! [X0: $i,X1: $i] :
( in(sK6(X0,X1),X1)
| ( X0 = X1 )
| ( set_union2(unordered_pair(sK6(X0,X1),sK6(X0,X1)),X0) = X0 ) ),
inference(superposition,[status(thm)],[c_120,c_95]) ).
tcf(c_11560,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK6(X0,X1),X1)
| ( X0 = X1 )
| ~ disjoint(X0,X2)
| ~ in(sK6(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_120,c_91]) ).
tcf(c_11561,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK6(X0,X2),X2)
| in(sK6(X0,X2),X1)
| ( X0 = X2 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_120,c_123]) ).
tcf(c_11562,plain,
! [X0: $i,X1: $i] :
( in(sK6(X0,X1),X1)
| ( X0 = X1 )
| ~ in(X0,sK6(X0,X1)) ),
inference(superposition,[status(thm)],[c_120,c_124]) ).
tcf(c_11563,plain,
! [X0: $i,X1: $i] :
( in(sK6(X0,X1),X1)
| ( X0 = X1 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_120,c_184]) ).
tcf(c_11564,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK6(set_difference(X0,set_difference(X0,X1)),X2),X2)
| ( set_difference(X0,set_difference(X0,X1)) = X2 )
| ~ disjoint(X0,X1) ),
inference(superposition,[status(thm)],[c_120,c_97]) ).
tcf(c_11565,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK6(set_difference(X0,set_difference(X0,X1)),X2),X2)
| in(sK6(set_difference(X0,set_difference(X0,X1)),X2),X1)
| ( set_difference(X0,set_difference(X0,X1)) = X2 ) ),
inference(superposition,[status(thm)],[c_120,c_174]) ).
tcf(c_11566,plain,
! [X0: $i,X1: $i] :
( in(sK6(unordered_pair(X0,X0),X1),X1)
| ( unordered_pair(X0,X0) = X1 )
| ( sK6(unordered_pair(X0,X0),X1) = X0 ) ),
inference(superposition,[status(thm)],[c_120,c_112]) ).
tcf(c_11567,plain,
! [X0: $i] :
( in(sK6(empty_set,X0),X0)
| ( X0 = empty_set ) ),
inference(superposition,[status(thm)],[c_120,c_118]) ).
tcf(c_11568,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK6(set_union2(X0,X1),X2),X2)
| in(sK6(set_union2(X0,X1),X2),X1)
| in(sK6(set_union2(X0,X1),X2),X0)
| ( set_union2(X0,X1) = X2 ) ),
inference(superposition,[status(thm)],[c_120,c_131]) ).
tcf(c_11569,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK6(set_difference(X0,X1),X2),X2)
| ( set_difference(X0,X1) = X2 )
| ~ in(sK6(set_difference(X0,X1),X2),X1) ),
inference(superposition,[status(thm)],[c_120,c_145]) ).
tcf(c_11570,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK6(set_difference(X0,X1),X2),X2)
| in(sK6(set_difference(X0,X1),X2),X0)
| ( set_difference(X0,X1) = X2 ) ),
inference(superposition,[status(thm)],[c_120,c_144]) ).
tcf(c_11571,plain,
! [X0: $i,X1: $i] :
( in(sK6(union(X0),X1),X1)
| ( union(X0) = X1 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_120,c_7039]) ).
tcf(c_11572,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK6(cartesian_product2(X0,X1),X2),X2)
| ( cartesian_product2(X0,X1) = X2 )
| ( unordered_pair(unordered_pair(sK16(X0,X1,sK6(cartesian_product2(X0,X1),X2)),sK16(X0,X1,sK6(cartesian_product2(X0,X1),X2))),unordered_pair(sK16(X0,X1,sK6(cartesian_product2(X0,X1),X2)),sK17(X0,X1,sK6(cartesian_product2(X0,X1),X2)))) = sK6(cartesian_product2(X0,X1),X2) ) ),
inference(superposition,[status(thm)],[c_120,c_1855]) ).
tcf(c_11573,plain,
! [X0: $i,X1: $i] :
( subset(sK6(powerset(X0),X1),X0)
| in(sK6(powerset(X0),X1),X1)
| ( powerset(X0) = X1 ) ),
inference(superposition,[status(thm)],[c_120,c_179]) ).
tcf(c_11776,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(unordered_pair(X0,X1),X2)
| ( sK0(unordered_pair(X0,X1),X2) = X1 )
| ( sK0(unordered_pair(X0,X1),X2) = X0 ) ),
inference(superposition,[status(thm)],[c_89,c_166]) ).
tcf(c_11777,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(X0,unordered_pair(X1,X2))
| ( sK0(X0,unordered_pair(X1,X2)) = X2 )
| ( sK0(X0,unordered_pair(X1,X2)) = X1 ) ),
inference(superposition,[status(thm)],[c_90,c_166]) ).
tcf(c_11778,plain,
! [X0: $i,X1: $i] :
( ( unordered_pair(X0,X1) = empty_set )
| ( sK5(unordered_pair(X0,X1)) = X1 )
| ( sK5(unordered_pair(X0,X1)) = X0 ) ),
inference(superposition,[status(thm)],[c_117,c_166]) ).
tcf(c_11779,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK6(X0,unordered_pair(X1,X2)),X0)
| ( unordered_pair(X1,X2) = X0 )
| ( sK6(X0,unordered_pair(X1,X2)) = X2 )
| ( sK6(X0,unordered_pair(X1,X2)) = X1 ) ),
inference(superposition,[status(thm)],[c_120,c_166]) ).
tcf(c_11780,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK6(unordered_pair(X0,X1),X2),X2)
| ( unordered_pair(X0,X1) = X2 )
| ( sK6(unordered_pair(X0,X1),X2) = X1 )
| ( sK6(unordered_pair(X0,X1),X2) = X0 ) ),
inference(superposition,[status(thm)],[c_120,c_166]) ).
tcf(c_11781,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(unordered_pair(X0,X1),X2)
| ( sK7(unordered_pair(X0,X1),X2) = X1 )
| ( sK7(unordered_pair(X0,X1),X2) = X0 ) ),
inference(superposition,[status(thm)],[c_122,c_166]) ).
tcf(c_11782,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK12(unordered_pair(X1,X2),X0) = X2 )
| ( sK12(unordered_pair(X1,X2),X0) = X1 )
| ~ in(X0,union(unordered_pair(X1,X2))) ),
inference(superposition,[status(thm)],[c_151,c_166]) ).
tcf(c_11783,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( unordered_pair(X2,X3) = cartesian_product2(X0,X1) )
| ( sK13(X0,X1,unordered_pair(X2,X3)) = X3 )
| ( sK13(X0,X1,unordered_pair(X2,X3)) = X2 )
| ( unordered_pair(unordered_pair(sK14(X0,X1,unordered_pair(X2,X3)),sK14(X0,X1,unordered_pair(X2,X3))),unordered_pair(sK14(X0,X1,unordered_pair(X2,X3)),sK15(X0,X1,unordered_pair(X2,X3)))) = sK13(X0,X1,unordered_pair(X2,X3)) ) ),
inference(superposition,[status(thm)],[c_1706,c_166]) ).
tcf(c_11784,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK16(unordered_pair(X1,X2),X3,X0) = X2 )
| ( sK16(unordered_pair(X1,X2),X3,X0) = X1 )
| ~ in(X0,cartesian_product2(unordered_pair(X1,X2),X3)) ),
inference(superposition,[status(thm)],[c_157,c_166]) ).
tcf(c_11785,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK17(X1,unordered_pair(X2,X3),X0) = X3 )
| ( sK17(X1,unordered_pair(X2,X3),X0) = X2 )
| ~ in(X0,cartesian_product2(X1,unordered_pair(X2,X3))) ),
inference(superposition,[status(thm)],[c_158,c_166]) ).
tcf(c_11788,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(X0,unordered_pair(X1,X2))
| ( sK1(X0,unordered_pair(X1,X2)) = X2 )
| ( sK1(X0,unordered_pair(X1,X2)) = X1 ) ),
inference(superposition,[status(thm)],[c_8628,c_166]) ).
tcf(c_11789,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(unordered_pair(X0,X1),X2)
| ( sK1(unordered_pair(X0,X1),X2) = X1 )
| ( sK1(unordered_pair(X0,X1),X2) = X0 ) ),
inference(superposition,[status(thm)],[c_8630,c_166]) ).
tcf(c_11793,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( cartesian_product2(X1,X2) = empty_set )
| ( unordered_pair(sK14(X1,X2,empty_set),sK15(X1,X2,empty_set)) = X0 )
| ( unordered_pair(sK14(X1,X2,empty_set),sK14(X1,X2,empty_set)) = X0 )
| ~ in(X0,sK13(X1,X2,empty_set)) ),
inference(superposition,[status(thm)],[c_5229,c_166]) ).
tcf(c_11794,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( cartesian_product2(X1,X2) = empty_set )
| ( unordered_pair(sK16(X1,X2,sK5(cartesian_product2(X1,X2))),sK17(X1,X2,sK5(cartesian_product2(X1,X2)))) = X0 )
| ( unordered_pair(sK16(X1,X2,sK5(cartesian_product2(X1,X2))),sK16(X1,X2,sK5(cartesian_product2(X1,X2)))) = X0 )
| ~ in(X0,sK5(cartesian_product2(X1,X2))) ),
inference(superposition,[status(thm)],[c_5462,c_166]) ).
tcf(c_11795,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X1,X2) = cartesian_product2(X3,X4) )
| ( unordered_pair(sK16(X3,X4,sK13(X1,X2,cartesian_product2(X3,X4))),sK17(X3,X4,sK13(X1,X2,cartesian_product2(X3,X4)))) = X0 )
| ( unordered_pair(sK16(X3,X4,sK13(X1,X2,cartesian_product2(X3,X4))),sK16(X3,X4,sK13(X1,X2,cartesian_product2(X3,X4)))) = X0 )
| ( unordered_pair(unordered_pair(sK14(X1,X2,cartesian_product2(X3,X4)),sK14(X1,X2,cartesian_product2(X3,X4))),unordered_pair(sK14(X1,X2,cartesian_product2(X3,X4)),sK15(X1,X2,cartesian_product2(X3,X4)))) = sK13(X1,X2,cartesian_product2(X3,X4)) )
| ~ in(X0,sK13(X1,X2,cartesian_product2(X3,X4))) ),
inference(superposition,[status(thm)],[c_5464,c_166]) ).
tcf(c_11878,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| ~ disjoint(set_difference(X0,set_difference(X0,X1)),set_difference(X0,set_difference(X0,X1))) ),
inference(superposition,[status(thm)],[c_96,c_11152]) ).
tcf(c_11879,plain,
! [X0: $i] :
( ( X0 = empty_set )
| ~ disjoint(X0,X0) ),
inference(superposition,[status(thm)],[c_117,c_11152]) ).
tcf(c_11880,plain,
! [X0: $i,X1: $i] :
( in(sK6(X1,X0),X1)
| ( X0 = X1 )
| ~ disjoint(X0,X0) ),
inference(superposition,[status(thm)],[c_120,c_11152]) ).
tcf(c_11881,plain,
! [X0: $i,X1: $i] :
( in(sK6(X0,X1),X1)
| ( X0 = X1 )
| ~ disjoint(X0,X0) ),
inference(superposition,[status(thm)],[c_120,c_11152]) ).
tcf(c_11882,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ disjoint(X0,X0) ),
inference(superposition,[status(thm)],[c_122,c_11152]) ).
tcf(c_11883,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(X2,X0)
| ~ disjoint(set_union2(X0,X1),set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_129,c_11152]) ).
tcf(c_11884,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(X2,X1)
| ~ disjoint(set_union2(X0,X1),set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_130,c_11152]) ).
tcf(c_11885,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,X1)
| ~ in(X2,X0)
| ~ disjoint(set_difference(X0,X1),set_difference(X0,X1)) ),
inference(superposition,[status(thm)],[c_143,c_11152]) ).
tcf(c_11886,plain,
! [X0: $i,X1: $i] :
( ~ in(X1,union(X0))
| ~ disjoint(sK12(X0,X1),sK12(X0,X1)) ),
inference(superposition,[status(thm)],[c_150,c_11152]) ).
tcf(c_11887,plain,
! [X0: $i,X1: $i] :
( ~ disjoint(X1,X1)
| ~ in(X0,union(X1)) ),
inference(superposition,[status(thm)],[c_151,c_11152]) ).
tcf(c_11888,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( cartesian_product2(X1,X2) = X0 )
| ( unordered_pair(unordered_pair(sK14(X1,X2,X0),sK14(X1,X2,X0)),unordered_pair(sK14(X1,X2,X0),sK15(X1,X2,X0))) = sK13(X1,X2,X0) )
| ~ disjoint(X0,X0) ),
inference(superposition,[status(thm)],[c_1706,c_11152]) ).
tcf(c_11889,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ disjoint(X1,X1)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_157,c_11152]) ).
tcf(c_11890,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ disjoint(X2,X2)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_158,c_11152]) ).
tcf(c_11891,plain,
! [X0: $i,X1: $i] : ~ disjoint(unordered_pair(X0,X1),unordered_pair(X0,X1)),
inference(superposition,[status(thm)],[c_164,c_11152]) ).
tcf(c_11893,plain,
! [X0: $i,X1: $i] :
( ~ subset(X1,X0)
| ~ disjoint(powerset(X0),powerset(X0)) ),
inference(superposition,[status(thm)],[c_178,c_11152]) ).
tcf(c_11894,plain,
~ disjoint(powerset(empty_set),powerset(empty_set)),
inference(superposition,[status(thm)],[c_5208,c_11152]) ).
tcf(c_11895,plain,
! [X0: $i,X1: $i] :
( ( cartesian_product2(X0,X1) = empty_set )
| ~ disjoint(sK13(X0,X1,empty_set),sK13(X0,X1,empty_set)) ),
inference(superposition,[status(thm)],[c_5326,c_11152]) ).
tcf(c_11898,plain,
! [X0: $i,X1: $i,X2: $i] : ~ disjoint(set_union2(unordered_pair(X0,X1),X2),set_union2(unordered_pair(X0,X1),X2)),
inference(superposition,[status(thm)],[c_5654,c_11152]) ).
tcf(c_11899,plain,
! [X0: $i,X1: $i,X2: $i] : ~ disjoint(set_union2(X0,unordered_pair(X1,X2)),set_union2(X0,unordered_pair(X1,X2))),
inference(superposition,[status(thm)],[c_5656,c_11152]) ).
tcf(c_11900,plain,
! [X0: $i] : ~ disjoint(set_union2(powerset(empty_set),X0),set_union2(powerset(empty_set),X0)),
inference(superposition,[status(thm)],[c_5716,c_11152]) ).
tcf(c_11901,plain,
! [X0: $i] : ~ disjoint(set_union2(X0,powerset(empty_set)),set_union2(X0,powerset(empty_set))),
inference(superposition,[status(thm)],[c_5734,c_11152]) ).
tcf(c_11902,plain,
! [X0: $i] : ~ disjoint(union(unordered_pair(powerset(empty_set),X0)),union(unordered_pair(powerset(empty_set),X0))),
inference(superposition,[status(thm)],[c_8287,c_11152]) ).
tcf(c_11903,plain,
! [X0: $i] : ~ disjoint(union(unordered_pair(X0,powerset(empty_set))),union(unordered_pair(X0,powerset(empty_set)))),
inference(superposition,[status(thm)],[c_8288,c_11152]) ).
tcf(c_11904,plain,
! [X0: $i,X1: $i] :
( disjoint(X1,X0)
| ~ disjoint(X0,X0) ),
inference(superposition,[status(thm)],[c_8628,c_11152]) ).
tcf(c_11905,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| ~ disjoint(X0,X0) ),
inference(superposition,[status(thm)],[c_8630,c_11152]) ).
tcf(c_12031,plain,
! [X0: $i,X1: $i] :
( subset(unordered_pair(X0,X0),X1)
| in(X0,unordered_pair(X0,X0)) ),
inference(superposition,[status(thm)],[c_5260,c_11882]) ).
tcf(c_12045,plain,
! [X0: $i,X1: $i] :
( disjoint(X1,unordered_pair(X0,X0))
| in(X0,unordered_pair(X0,X0)) ),
inference(superposition,[status(thm)],[c_5260,c_11904]) ).
tcf(c_12059,plain,
! [X0: $i,X1: $i] :
( disjoint(unordered_pair(X0,X0),X1)
| in(X0,unordered_pair(X0,X0)) ),
inference(superposition,[status(thm)],[c_5260,c_11905]) ).
tcf(c_12064,plain,
! [X0: $i,X1: $i] :
( in(X0,unordered_pair(X0,X0))
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_143,c_11248]) ).
tcf(c_12088,plain,
! [X0: $i] : in(X0,unordered_pair(X0,X0)),
inference(superposition,[status(thm)],[c_5260,c_11891]) ).
tcf(c_12099,plain,
! [X0: $i,X1: $i] :
( ( cartesian_product2(X0,X1) = empty_set )
| ~ disjoint(sK5(cartesian_product2(X0,X1)),sK5(cartesian_product2(X0,X1))) ),
inference(superposition,[status(thm)],[c_5462,c_11891]) ).
tcf(c_12100,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( cartesian_product2(X0,X1) = cartesian_product2(X2,X3) )
| ( unordered_pair(unordered_pair(sK14(X0,X1,cartesian_product2(X2,X3)),sK14(X0,X1,cartesian_product2(X2,X3))),unordered_pair(sK14(X0,X1,cartesian_product2(X2,X3)),sK15(X0,X1,cartesian_product2(X2,X3)))) = sK13(X0,X1,cartesian_product2(X2,X3)) )
| ~ disjoint(sK13(X0,X1,cartesian_product2(X2,X3)),sK13(X0,X1,cartesian_product2(X2,X3))) ),
inference(superposition,[status(thm)],[c_5464,c_11891]) ).
tcf(c_12110,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,X2)
| ~ in(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,X1)),cartesian_product2(X2,X3)) ),
inference(superposition,[status(thm)],[c_167,c_63]) ).
tcf(c_12113,plain,
! [X0: $i,X1: $i] :
( in(empty_set,X0)
| ~ in(unordered_pair(powerset(empty_set),powerset(empty_set)),cartesian_product2(X0,X1)) ),
inference(superposition,[status(thm)],[c_70,c_63]) ).
tcf(c_12114,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X1,X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X1,X1)),cartesian_product2(X2,X3)) ),
inference(superposition,[status(thm)],[c_167,c_63]) ).
tcf(c_12115,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(sK14(X0,X1,empty_set),sK14(X0,X1,empty_set)),X2)
| ( cartesian_product2(X0,X1) = empty_set )
| ~ in(unordered_pair(sK13(X0,X1,empty_set),unordered_pair(unordered_pair(sK14(X0,X1,empty_set),sK14(X0,X1,empty_set)),unordered_pair(sK14(X0,X1,empty_set),sK14(X0,X1,empty_set)))),cartesian_product2(X2,X3)) ),
inference(superposition,[status(thm)],[c_5229,c_63]) ).
tcf(c_12116,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(sK16(X0,X1,sK5(cartesian_product2(X0,X1))),sK16(X0,X1,sK5(cartesian_product2(X0,X1)))),X2)
| ( cartesian_product2(X0,X1) = empty_set )
| ~ in(unordered_pair(sK5(cartesian_product2(X0,X1)),unordered_pair(unordered_pair(sK16(X0,X1,sK5(cartesian_product2(X0,X1))),sK16(X0,X1,sK5(cartesian_product2(X0,X1)))),unordered_pair(sK16(X0,X1,sK5(cartesian_product2(X0,X1))),sK16(X0,X1,sK5(cartesian_product2(X0,X1)))))),cartesian_product2(X2,X3)) ),
inference(superposition,[status(thm)],[c_5462,c_63]) ).
tcf(c_12117,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(unordered_pair(sK16(X2,X3,sK13(X0,X1,cartesian_product2(X2,X3))),sK16(X2,X3,sK13(X0,X1,cartesian_product2(X2,X3)))),X4)
| ( cartesian_product2(X0,X1) = cartesian_product2(X2,X3) )
| ( unordered_pair(unordered_pair(sK14(X0,X1,cartesian_product2(X2,X3)),sK14(X0,X1,cartesian_product2(X2,X3))),unordered_pair(sK14(X0,X1,cartesian_product2(X2,X3)),sK15(X0,X1,cartesian_product2(X2,X3)))) = sK13(X0,X1,cartesian_product2(X2,X3)) )
| ~ in(unordered_pair(sK13(X0,X1,cartesian_product2(X2,X3)),unordered_pair(unordered_pair(sK16(X2,X3,sK13(X0,X1,cartesian_product2(X2,X3))),sK16(X2,X3,sK13(X0,X1,cartesian_product2(X2,X3)))),unordered_pair(sK16(X2,X3,sK13(X0,X1,cartesian_product2(X2,X3))),sK16(X2,X3,sK13(X0,X1,cartesian_product2(X2,X3)))))),cartesian_product2(X4,X5)) ),
inference(superposition,[status(thm)],[c_5464,c_63]) ).
tcf(c_12118,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(empty_set,X1)
| ~ in(unordered_pair(unordered_pair(empty_set,X0),powerset(empty_set)),cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_70,c_63]) ).
tcf(c_12119,plain,
! [X0: $i,X1: $i] :
( in(X0,empty_set)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),empty_set) ),
inference(superposition,[status(thm)],[c_10381,c_63]) ).
tcf(c_12120,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),empty_set) ),
inference(superposition,[status(thm)],[c_10438,c_63]) ).
tcf(c_12145,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X1,X3)
| ~ in(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,X1)),cartesian_product2(X2,X3)) ),
inference(superposition,[status(thm)],[c_167,c_64]) ).
tcf(c_12148,plain,
! [X0: $i,X1: $i] :
( in(empty_set,X1)
| ~ in(unordered_pair(powerset(empty_set),powerset(empty_set)),cartesian_product2(X0,X1)) ),
inference(superposition,[status(thm)],[c_70,c_64]) ).
tcf(c_12149,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,X3)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X1,X1)),cartesian_product2(X2,X3)) ),
inference(superposition,[status(thm)],[c_167,c_64]) ).
tcf(c_12150,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(sK14(X0,X1,empty_set),sK15(X0,X1,empty_set)),X3)
| ( cartesian_product2(X0,X1) = empty_set )
| ~ in(unordered_pair(sK13(X0,X1,empty_set),unordered_pair(unordered_pair(sK14(X0,X1,empty_set),sK14(X0,X1,empty_set)),unordered_pair(sK14(X0,X1,empty_set),sK14(X0,X1,empty_set)))),cartesian_product2(X2,X3)) ),
inference(superposition,[status(thm)],[c_5229,c_64]) ).
tcf(c_12151,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(sK16(X0,X1,sK5(cartesian_product2(X0,X1))),sK17(X0,X1,sK5(cartesian_product2(X0,X1)))),X3)
| ( cartesian_product2(X0,X1) = empty_set )
| ~ in(unordered_pair(sK5(cartesian_product2(X0,X1)),unordered_pair(unordered_pair(sK16(X0,X1,sK5(cartesian_product2(X0,X1))),sK16(X0,X1,sK5(cartesian_product2(X0,X1)))),unordered_pair(sK16(X0,X1,sK5(cartesian_product2(X0,X1))),sK16(X0,X1,sK5(cartesian_product2(X0,X1)))))),cartesian_product2(X2,X3)) ),
inference(superposition,[status(thm)],[c_5462,c_64]) ).
tcf(c_12152,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(unordered_pair(sK16(X2,X3,sK13(X0,X1,cartesian_product2(X2,X3))),sK17(X2,X3,sK13(X0,X1,cartesian_product2(X2,X3)))),X5)
| ( cartesian_product2(X0,X1) = cartesian_product2(X2,X3) )
| ( unordered_pair(unordered_pair(sK14(X0,X1,cartesian_product2(X2,X3)),sK14(X0,X1,cartesian_product2(X2,X3))),unordered_pair(sK14(X0,X1,cartesian_product2(X2,X3)),sK15(X0,X1,cartesian_product2(X2,X3)))) = sK13(X0,X1,cartesian_product2(X2,X3)) )
| ~ in(unordered_pair(sK13(X0,X1,cartesian_product2(X2,X3)),unordered_pair(unordered_pair(sK16(X2,X3,sK13(X0,X1,cartesian_product2(X2,X3))),sK16(X2,X3,sK13(X0,X1,cartesian_product2(X2,X3)))),unordered_pair(sK16(X2,X3,sK13(X0,X1,cartesian_product2(X2,X3))),sK16(X2,X3,sK13(X0,X1,cartesian_product2(X2,X3)))))),cartesian_product2(X4,X5)) ),
inference(superposition,[status(thm)],[c_5464,c_64]) ).
tcf(c_12153,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ in(unordered_pair(unordered_pair(empty_set,X0),powerset(empty_set)),cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_70,c_64]) ).
tcf(c_12154,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),empty_set) ),
inference(superposition,[status(thm)],[c_10381,c_64]) ).
tcf(c_12155,plain,
! [X0: $i,X1: $i] :
( in(X1,empty_set)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),empty_set) ),
inference(superposition,[status(thm)],[c_10438,c_64]) ).
tcf(c_12198,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,set_difference(X2,set_difference(X2,X1)))
| ~ subset(X0,X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_175,c_68]) ).
tcf(c_12201,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,set_difference(set_union2(X1,X2),set_difference(X1,X2)))
| ~ subset(X0,X2)
| ~ subset(X0,set_union2(X1,X2)) ),
inference(superposition,[status(thm)],[c_93,c_68]) ).
tcf(c_12202,plain,
! [X0: $i,X1: $i] :
( subset(X0,set_difference(empty_set,empty_set))
| ~ subset(X0,empty_set)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_113,c_68]) ).
tcf(c_12203,plain,
! [X0: $i,X1: $i] :
( subset(X0,set_difference(X1,X1))
| ~ subset(X0,empty_set)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_114,c_68]) ).
tcf(c_12205,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,set_difference(X1,set_difference(X2,set_difference(X2,X1))))
| ~ subset(X0,X1)
| ~ subset(X0,set_difference(X1,X2)) ),
inference(superposition,[status(thm)],[c_175,c_68]) ).
tcf(c_12206,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,set_difference(set_difference(X1,X2),empty_set))
| ~ subset(X0,X1)
| ~ subset(X0,set_difference(X1,X2)) ),
inference(superposition,[status(thm)],[c_6290,c_68]) ).
tcf(c_12208,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,set_difference(X2,empty_set))
| ~ subset(X0,X2)
| ~ subset(X0,set_union2(X1,X2)) ),
inference(superposition,[status(thm)],[c_6293,c_68]) ).
tcf(c_12209,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,set_difference(set_difference(X2,X1),empty_set))
| ~ subset(X0,set_difference(X2,X1))
| ~ subset(X0,set_union2(X1,X2)) ),
inference(superposition,[status(thm)],[c_6374,c_68]) ).
tcf(c_12210,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,set_difference(X2,X2))
| ~ subset(X0,X2)
| ~ subset(X0,set_difference(X1,X2)) ),
inference(superposition,[status(thm)],[c_10682,c_68]) ).
tcf(c_12211,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,set_difference(set_difference(X1,X2),empty_set))
| ~ subset(X0,set_difference(X1,X2))
| ~ subset(X0,set_union2(X1,X2)) ),
inference(superposition,[status(thm)],[c_6401,c_68]) ).
tcf(c_12212,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,set_difference(set_union2(X1,X2),set_difference(X2,X1)))
| ~ subset(X0,X1)
| ~ subset(X0,set_union2(X1,X2)) ),
inference(superposition,[status(thm)],[c_6644,c_68]) ).
tcf(c_12213,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(X0,set_difference(X0,X1)) = X2 )
| ~ subset(X2,X1)
| ~ subset(X2,X0)
| ~ subset(set_difference(X0,set_difference(X0,X1)),X2) ),
inference(superposition,[status(thm)],[c_68,c_137]) ).
tcf(c_12214,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(X0,set_difference(X0,set_difference(X1,set_difference(X1,X2)))) = X0 )
| ~ subset(X0,X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_68,c_72]) ).
tcf(c_12215,plain,
! [X0: $i,X1: $i,X2: $i] :
( proper_subset(X0,set_difference(X1,set_difference(X1,X2)))
| ( set_difference(X1,set_difference(X1,X2)) = X0 )
| ~ subset(X0,X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_68,c_181]) ).
tcf(c_12216,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(X3,X2)
| ~ subset(X3,X1)
| ~ subset(X3,X0)
| ~ subset(set_difference(X0,set_difference(X0,X1)),X2) ),
inference(superposition,[status(thm)],[c_68,c_69]) ).
tcf(c_12217,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(X0,set_difference(X1,set_difference(X1,X2))) = empty_set )
| ~ subset(X0,X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_68,c_78]) ).
tcf(c_12218,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_union2(X0,set_difference(X1,set_difference(X1,X2))) = set_difference(X1,set_difference(X1,X2)) )
| ~ subset(X0,X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_68,c_66]) ).
tcf(c_12219,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ subset(X2,X1)
| ~ subset(X2,X0)
| ~ proper_subset(set_difference(X0,set_difference(X0,X1)),X2) ),
inference(superposition,[status(thm)],[c_68,c_98]) ).
tcf(c_12220,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X1,set_difference(X2,set_difference(X2,X3)))
| ~ subset(unordered_pair(X0,X1),X3)
| ~ subset(unordered_pair(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_68,c_84]) ).
tcf(c_12221,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,set_difference(X2,set_difference(X2,X3)))
| ~ subset(unordered_pair(X0,X1),X3)
| ~ subset(unordered_pair(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_68,c_83]) ).
tcf(c_12222,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ subset(unordered_pair(powerset(set_difference(X0,set_difference(X0,X1))),X2),X1)
| ~ subset(unordered_pair(powerset(set_difference(X0,set_difference(X0,X1))),X2),X0) ),
inference(superposition,[status(thm)],[c_68,c_5487]) ).
tcf(c_12223,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ subset(unordered_pair(X0,powerset(set_difference(X1,set_difference(X1,X2)))),X2)
| ~ subset(unordered_pair(X0,powerset(set_difference(X1,set_difference(X1,X2)))),X1) ),
inference(superposition,[status(thm)],[c_68,c_5488]) ).
tcf(c_12224,plain,
! [X0: $i,X1: $i] :
( in(empty_set,set_difference(X0,set_difference(X0,X1)))
| ~ subset(powerset(empty_set),X1)
| ~ subset(powerset(empty_set),X0) ),
inference(superposition,[status(thm)],[c_68,c_5628]) ).
tcf(c_12225,plain,
! [X0: $i,X1: $i] :
( ~ subset(powerset(powerset(set_difference(X0,set_difference(X0,X1)))),X1)
| ~ subset(powerset(powerset(set_difference(X0,set_difference(X0,X1)))),X0) ),
inference(superposition,[status(thm)],[c_68,c_5545]) ).
tcf(c_12226,plain,
! [X0: $i,X1: $i] :
( ~ subset(powerset(powerset(union(powerset(set_difference(X0,set_difference(X0,X1)))))),X1)
| ~ subset(powerset(powerset(union(powerset(set_difference(X0,set_difference(X0,X1)))))),X0) ),
inference(superposition,[status(thm)],[c_68,c_5557]) ).
tcf(c_12227,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ subset(unordered_pair(powerset(union(powerset(set_difference(X0,set_difference(X0,X1))))),X2),X1)
| ~ subset(unordered_pair(powerset(union(powerset(set_difference(X0,set_difference(X0,X1))))),X2),X0) ),
inference(superposition,[status(thm)],[c_68,c_5585]) ).
tcf(c_12228,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ subset(unordered_pair(X0,powerset(union(powerset(set_difference(X1,set_difference(X1,X2)))))),X2)
| ~ subset(unordered_pair(X0,powerset(union(powerset(set_difference(X1,set_difference(X1,X2)))))),X1) ),
inference(superposition,[status(thm)],[c_68,c_5589]) ).
tcf(c_12229,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ subset(powerset(set_union2(powerset(set_difference(X0,set_difference(X0,X1))),X2)),X1)
| ~ subset(powerset(set_union2(powerset(set_difference(X0,set_difference(X0,X1))),X2)),X0) ),
inference(superposition,[status(thm)],[c_68,c_5808]) ).
tcf(c_12230,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ subset(powerset(set_union2(X0,powerset(set_difference(X1,set_difference(X1,X2))))),X2)
| ~ subset(powerset(set_union2(X0,powerset(set_difference(X1,set_difference(X1,X2))))),X1) ),
inference(superposition,[status(thm)],[c_68,c_5850]) ).
tcf(c_12231,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ subset(unordered_pair(set_union2(powerset(set_difference(X0,set_difference(X0,X1))),X2),X3),X1)
| ~ subset(unordered_pair(set_union2(powerset(set_difference(X0,set_difference(X0,X1))),X2),X3),X0) ),
inference(superposition,[status(thm)],[c_68,c_6050]) ).
tcf(c_12232,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ subset(unordered_pair(X0,set_union2(powerset(set_difference(X1,set_difference(X1,X2))),X3)),X2)
| ~ subset(unordered_pair(X0,set_union2(powerset(set_difference(X1,set_difference(X1,X2))),X3)),X1) ),
inference(superposition,[status(thm)],[c_68,c_6065]) ).
tcf(c_12233,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ subset(set_union2(unordered_pair(powerset(set_difference(X0,set_difference(X0,X1))),X2),X3),X1)
| ~ subset(set_union2(unordered_pair(powerset(set_difference(X0,set_difference(X0,X1))),X2),X3),X0) ),
inference(superposition,[status(thm)],[c_68,c_6081]) ).
tcf(c_12234,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ subset(set_union2(X0,unordered_pair(powerset(set_difference(X1,set_difference(X1,X2))),X3)),X2)
| ~ subset(set_union2(X0,unordered_pair(powerset(set_difference(X1,set_difference(X1,X2))),X3)),X1) ),
inference(superposition,[status(thm)],[c_68,c_6112]) ).
tcf(c_12235,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ subset(set_union2(unordered_pair(X0,powerset(set_difference(X1,set_difference(X1,X2)))),X3),X2)
| ~ subset(set_union2(unordered_pair(X0,powerset(set_difference(X1,set_difference(X1,X2)))),X3),X1) ),
inference(superposition,[status(thm)],[c_68,c_6140]) ).
tcf(c_12236,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ subset(set_union2(X0,unordered_pair(X1,powerset(set_difference(X2,set_difference(X2,X3))))),X3)
| ~ subset(set_union2(X0,unordered_pair(X1,powerset(set_difference(X2,set_difference(X2,X3))))),X2) ),
inference(superposition,[status(thm)],[c_68,c_6173]) ).
tcf(c_12237,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ subset(unordered_pair(set_union2(X0,powerset(set_difference(X1,set_difference(X1,X2)))),X3),X2)
| ~ subset(unordered_pair(set_union2(X0,powerset(set_difference(X1,set_difference(X1,X2)))),X3),X1) ),
inference(superposition,[status(thm)],[c_68,c_6217]) ).
tcf(c_12238,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ subset(unordered_pair(X0,set_union2(X1,powerset(set_difference(X2,set_difference(X2,X3))))),X3)
| ~ subset(unordered_pair(X0,set_union2(X1,powerset(set_difference(X2,set_difference(X2,X3))))),X2) ),
inference(superposition,[status(thm)],[c_68,c_6232]) ).
tcf(c_12239,plain,
! [X0: $i,X1: $i] :
( ~ subset(powerset(union(powerset(powerset(set_difference(X0,set_difference(X0,X1)))))),X1)
| ~ subset(powerset(union(powerset(powerset(set_difference(X0,set_difference(X0,X1)))))),X0) ),
inference(superposition,[status(thm)],[c_68,c_7102]) ).
tcf(c_12240,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ subset(set_union2(powerset(powerset(set_difference(X0,set_difference(X0,X1)))),X2),X1)
| ~ subset(set_union2(powerset(powerset(set_difference(X0,set_difference(X0,X1)))),X2),X0) ),
inference(superposition,[status(thm)],[c_68,c_8859]) ).
tcf(c_12241,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ subset(set_union2(X0,powerset(powerset(set_difference(X1,set_difference(X1,X2))))),X2)
| ~ subset(set_union2(X0,powerset(powerset(set_difference(X1,set_difference(X1,X2))))),X1) ),
inference(superposition,[status(thm)],[c_68,c_8903]) ).
tcf(c_12466,plain,
! [X0: $i,X1: $i] :
( subset(empty_set,set_difference(X0,set_difference(X0,X1)))
| ~ subset(empty_set,X0) ),
inference(superposition,[status(thm)],[c_113,c_71]) ).
tcf(c_12467,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(X2,set_difference(X2,X0)),set_difference(X1,set_difference(X1,X2)))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_175,c_71]) ).
tcf(c_12468,plain,
! [X0: $i,X1: $i] :
( subset(X0,set_difference(X1,set_difference(X1,X0)))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_10682,c_71]) ).
tcf(c_12470,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(set_union2(X0,X1),set_difference(X0,X1)),set_difference(X2,set_difference(X2,X1)))
| ~ subset(set_union2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_93,c_71]) ).
tcf(c_12471,plain,
! [X0: $i,X1: $i] :
( subset(set_difference(empty_set,empty_set),set_difference(X0,set_difference(X0,X1)))
| ~ subset(empty_set,X0) ),
inference(superposition,[status(thm)],[c_113,c_71]) ).
tcf(c_12472,plain,
! [X0: $i,X1: $i] :
( subset(set_difference(X0,X0),set_difference(X1,set_difference(X1,empty_set)))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_114,c_71]) ).
tcf(c_12473,plain,
! [X0: $i,X1: $i] :
( subset(set_difference(X0,empty_set),set_difference(X1,set_difference(X1,X0)))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_1252,c_71]) ).
tcf(c_12474,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(X0,set_difference(X2,set_difference(X2,X0))),set_difference(X1,set_difference(X1,set_difference(X0,X2))))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_175,c_71]) ).
tcf(c_12475,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(set_difference(X0,X1),empty_set),set_difference(X2,set_difference(X2,X0)))
| ~ subset(set_difference(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_6290,c_71]) ).
tcf(c_12476,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(X0,empty_set),set_difference(X1,set_difference(X1,set_union2(X0,X2))))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_6291,c_71]) ).
tcf(c_12477,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(X0,empty_set),set_difference(X1,set_difference(X1,set_union2(X2,X0))))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_6293,c_71]) ).
tcf(c_12478,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(set_difference(X0,X1),empty_set),set_difference(X2,set_difference(X2,set_union2(X1,X0))))
| ~ subset(set_difference(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_6374,c_71]) ).
tcf(c_12479,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(X0,X0),set_difference(X1,set_difference(X1,set_difference(X2,X0))))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_10682,c_71]) ).
tcf(c_12480,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(set_difference(X0,X1),empty_set),set_difference(X2,set_difference(X2,set_union2(X0,X1))))
| ~ subset(set_difference(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_6401,c_71]) ).
tcf(c_12481,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(set_union2(X0,X1),set_difference(X1,X0)),set_difference(X2,set_difference(X2,X0)))
| ~ subset(set_union2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_6644,c_71]) ).
tcf(c_12483,plain,
! [X0: $i,X1: $i] :
( subset(set_difference(X0,set_difference(X0,X1)),empty_set)
| ~ subset(X0,empty_set) ),
inference(superposition,[status(thm)],[c_113,c_71]) ).
tcf(c_12484,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(X0,set_difference(X0,X2)),set_difference(X2,set_difference(X2,X1)))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_175,c_71]) ).
tcf(c_12487,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(X0,set_difference(X0,X2)),set_difference(set_union2(X1,X2),set_difference(X1,X2)))
| ~ subset(X0,set_union2(X1,X2)) ),
inference(superposition,[status(thm)],[c_93,c_71]) ).
tcf(c_12488,plain,
! [X0: $i,X1: $i] :
( subset(set_difference(X0,set_difference(X0,X1)),set_difference(empty_set,empty_set))
| ~ subset(X0,empty_set) ),
inference(superposition,[status(thm)],[c_113,c_71]) ).
tcf(c_12489,plain,
! [X0: $i,X1: $i] :
( subset(set_difference(X0,set_difference(X0,empty_set)),set_difference(X1,X1))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_114,c_71]) ).
tcf(c_12490,plain,
! [X0: $i,X1: $i] :
( subset(set_difference(X0,set_difference(X0,X1)),set_difference(X1,empty_set))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_1252,c_71]) ).
tcf(c_12491,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(X0,set_difference(X0,set_difference(X1,X2))),set_difference(X1,set_difference(X2,set_difference(X2,X1))))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_175,c_71]) ).
tcf(c_12492,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(X0,set_difference(X0,X1)),set_difference(set_difference(X1,X2),empty_set))
| ~ subset(X0,set_difference(X1,X2)) ),
inference(superposition,[status(thm)],[c_6290,c_71]) ).
tcf(c_12493,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(X0,set_difference(X0,set_union2(X1,X2))),set_difference(X1,empty_set))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_6291,c_71]) ).
tcf(c_12494,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(X0,set_difference(X0,set_union2(X2,X1))),set_difference(X1,empty_set))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_6293,c_71]) ).
tcf(c_12495,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(X0,set_difference(X0,set_union2(X2,X1))),set_difference(set_difference(X1,X2),empty_set))
| ~ subset(X0,set_difference(X1,X2)) ),
inference(superposition,[status(thm)],[c_6374,c_71]) ).
tcf(c_12496,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(X0,set_difference(X0,set_difference(X2,X1))),set_difference(X1,X1))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_10682,c_71]) ).
tcf(c_12497,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(X0,set_difference(X0,set_union2(X1,X2))),set_difference(set_difference(X1,X2),empty_set))
| ~ subset(X0,set_difference(X1,X2)) ),
inference(superposition,[status(thm)],[c_6401,c_71]) ).
tcf(c_12498,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(X0,set_difference(X0,X1)),set_difference(set_union2(X1,X2),set_difference(X2,X1)))
| ~ subset(X0,set_union2(X1,X2)) ),
inference(superposition,[status(thm)],[c_6644,c_71]) ).
tcf(c_12499,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(X0,set_difference(X0,X1)) = set_difference(X2,set_difference(X2,X1)) )
| ~ subset(X2,X0)
| ~ subset(set_difference(X0,set_difference(X0,X1)),set_difference(X2,set_difference(X2,X1))) ),
inference(superposition,[status(thm)],[c_71,c_137]) ).
tcf(c_12500,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(set_difference(X0,set_difference(X0,X2)),set_difference(set_difference(X0,set_difference(X0,X2)),set_difference(X1,set_difference(X1,X2)))) = set_difference(X0,set_difference(X0,X2)) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_71,c_72]) ).
tcf(c_12501,plain,
! [X0: $i,X1: $i,X2: $i] :
( proper_subset(set_difference(X0,set_difference(X0,X2)),set_difference(X1,set_difference(X1,X2)))
| ( set_difference(X0,set_difference(X0,X2)) = set_difference(X1,set_difference(X1,X2)) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_71,c_181]) ).
tcf(c_12502,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(set_difference(X3,set_difference(X3,X1)),X2)
| ~ subset(X3,X0)
| ~ subset(set_difference(X0,set_difference(X0,X1)),X2) ),
inference(superposition,[status(thm)],[c_71,c_69]) ).
tcf(c_12503,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(set_difference(X0,set_difference(X0,X2)),set_difference(X1,set_difference(X1,X2))) = empty_set )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_71,c_78]) ).
tcf(c_12504,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_union2(set_difference(X0,set_difference(X0,X2)),set_difference(X1,set_difference(X1,X2))) = set_difference(X1,set_difference(X1,X2)) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_71,c_66]) ).
tcf(c_12505,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ subset(X2,X0)
| ~ proper_subset(set_difference(X0,set_difference(X0,X1)),set_difference(X2,set_difference(X2,X1))) ),
inference(superposition,[status(thm)],[c_71,c_98]) ).
tcf(c_12512,plain,
! [X0: $i,X1: $i] :
( subset(empty_set,set_difference(X1,X1))
| ~ subset(X0,X1) ),
inference(light_normalisation,[status(thm)],[c_12489,c_114,c_1252]) ).
tcf(c_12516,plain,
! [X0: $i,X1: $i] :
( subset(empty_set,set_difference(X1,set_difference(X1,empty_set)))
| ~ subset(X0,X1) ),
inference(light_normalisation,[status(thm)],[c_12472,c_1252]) ).
tcf(c_12517,plain,
! [X0: $i,X1: $i] : subset(set_difference(empty_set,empty_set),set_difference(X0,set_difference(X0,X1))),
inference(forward_subsumption_resolution,[status(thm)],[c_12471,c_73]) ).
tcf(c_12526,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(empty_set,set_difference(X1,set_difference(X1,set_difference(X2,X0))))
| ~ subset(X0,X1) ),
inference(light_normalisation,[status(thm)],[c_12479,c_1252]) ).
tcf(c_12527,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,set_difference(X1,set_difference(X1,set_union2(X2,X0))))
| ~ subset(X0,X1) ),
inference(light_normalisation,[status(thm)],[c_12477,c_114]) ).
tcf(c_12530,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,set_difference(X1,set_difference(X1,set_union2(X0,X2))))
| ~ subset(X0,X1) ),
inference(light_normalisation,[status(thm)],[c_12476,c_114]) ).
tcf(c_12556,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,set_difference(X2,set_difference(X2,X0)))
| ~ subset(set_union2(X0,X1),X2) ),
inference(light_normalisation,[status(thm)],[c_12481,c_10688]) ).
tcf(c_12565,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(X1,set_difference(X0,X1)),set_difference(X2,set_difference(X2,X1)))
| ~ subset(set_union2(X0,X1),X2) ),
inference(light_normalisation,[status(thm)],[c_12470,c_9651]) ).
tcf(c_12762,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_12565,c_12556,c_12530,c_12527,c_12526,c_12517,c_12516,c_12512,c_12505,c_12504,c_12503,c_12502,c_12501,c_12500,c_12499,c_12498,c_12497,c_12496,c_12495,c_12494,c_12493,c_12492,c_12490,c_12489,c_12488,c_12487,c_12491,c_12483,c_12484,c_12481,c_12480,c_12479,c_12478,c_12477,c_12476,c_12475,c_12473,c_12472,c_12471,c_12470,c_12474,c_12468,c_12466,c_12467,c_12241,c_12240,c_12239,c_12238,c_12237,c_12236,c_12235,c_12234,c_12233,c_12232,c_12231,c_12230,c_12229,c_12228,c_12227,c_12226,c_12225,c_12224,c_12223,c_12222,c_12221,c_12220,c_12219,c_12218,c_12217,c_12216,c_12215,c_12214,c_12213,c_12212,c_12211,c_12210,c_12209,c_12208,c_12206,c_12203,c_12202,c_12201,c_12205,c_12198,c_12155,c_12154,c_12153,c_12152,c_12151,c_12150,c_12148,c_12149,c_12145,c_12120,c_12119,c_12118,c_12117,c_12116,c_12115,c_12113,c_12114,c_12110,c_12100,c_12099,c_12064,c_12059,c_12045,c_12031,c_11903,c_11902,c_11901,c_11900,c_11899,c_11898,c_11895,c_11894,c_11893,c_11891,c_11890,c_11889,c_11888,c_11887,c_11886,c_11885,c_11884,c_11883,c_11882,c_11881,c_11880,c_11879,c_11878,c_11904,c_11905,c_11795,c_11794,c_11793,c_11789,c_11788,c_11785,c_11784,c_11783,c_11782,c_11781,c_11780,c_11779,c_11778,c_11777,c_11776,c_11573,c_11572,c_11571,c_11570,c_11569,c_11568,c_11567,c_11566,c_11565,c_11564,c_11563,c_11562,c_11561,c_11560,c_11559,c_11558,c_11557,c_11556,c_11555,c_11554,c_11553,c_11552,c_11551,c_11550,c_11549,c_11548,c_11547,c_11546,c_11545,c_11544,c_11543,c_11542,c_11346,c_11345,c_11344,c_11343,c_11342,c_11341,c_11340,c_11339,c_11338,c_11337,c_11336,c_11335,c_11334,c_11333,c_11332,c_11331,c_11330,c_11329,c_11328,c_11327,c_11326,c_11325,c_11324,c_11323,c_11322,c_11321,c_11320,c_11319,c_11318,c_11317,c_11316,c_11315,c_11314,c_11312,c_11292,c_11291,c_11290,c_11286,c_11280,c_11275,c_11274,c_11272,c_11266,c_11253,c_11250,c_11249,c_11248,c_11252,c_11246,c_11240,c_11159,c_11158,c_11157,c_11154,c_11152,c_11148,c_11147,c_11139,c_11138,c_11137,c_11132,c_11131,c_11130,c_11129,c_11128,c_11127,c_11124,c_11122,c_11116,c_11103,c_11102,c_11101,c_11100,c_11099,c_11098,c_11095,c_11094,c_11093,c_11097,c_11068,c_11053,c_11051,c_11049,c_11048,c_11047,c_11046,c_11045,c_11044,c_11043,c_11042,c_11041,c_11040,c_11037,c_11036,c_11035,c_11039,c_11013,c_11012,c_11011,c_11010,c_11007,c_10922,c_10921,c_10920,c_10919,c_10918,c_10917,c_10916,c_10915,c_10914,c_10906,c_10909,c_10838,c_10837,c_10836,c_10835,c_10834,c_10833,c_10832,c_10831,c_10830,c_10829,c_10828,c_10688,c_10687,c_10682,c_10648,c_10647,c_10646,c_10645,c_10644,c_10643,c_10641,c_10639,c_10638,c_10637,c_10636,c_10635,c_10634,c_10633,c_10632,c_10631,c_10630,c_10629,c_10628,c_10627,c_10626,c_10625,c_10624,c_10623,c_10622,c_10621,c_10620,c_10619,c_10618,c_10617,c_10616,c_10615,c_10579,c_10578,c_10577,c_10576,c_10575,c_10574,c_10528,c_10525,c_10513,c_10505,c_10504,c_10503,c_10502,c_10500,c_10496,c_10495,c_10494,c_10490,c_10489,c_10488,c_10487,c_10483,c_10482,c_10481,c_10480,c_10479,c_10478,c_10477,c_10476,c_10475,c_10474,c_10473,c_10470,c_10462,c_10459,c_10455,c_10452,c_10443,c_10442,c_10441,c_10440,c_10439,c_10438,c_10444,c_10445,c_10386,c_10385,c_10384,c_10383,c_10382,c_10381,c_10387,c_10388,c_10300,c_10299,c_10298,c_10297,c_10296,c_10295,c_10294,c_10293,c_10292,c_10291,c_10290,c_10289,c_10288,c_10287,c_10286,c_10285,c_10221,c_10220,c_10219,c_10218,c_10217,c_10216,c_10215,c_10214,c_10213,c_10212,c_10211,c_10210,c_10209,c_10208,c_10207,c_10206,c_10090,c_10089,c_10088,c_10087,c_10086,c_10085,c_10084,c_10083,c_10082,c_10081,c_10080,c_10078,c_10075,c_10074,c_10073,c_10072,c_10071,c_10070,c_10069,c_10068,c_10067,c_10066,c_10065,c_9913,c_9884,c_9883,c_9882,c_9877,c_9876,c_9875,c_9874,c_9873,c_9872,c_9871,c_9870,c_9869,c_9868,c_9867,c_9866,c_9865,c_9864,c_9863,c_9862,c_9861,c_9860,c_9859,c_9858,c_9857,c_9856,c_9855,c_9854,c_9853,c_9852,c_9851,c_9848,c_9846,c_9845,c_9844,c_9843,c_9842,c_9841,c_9840,c_9839,c_9830,c_9726,c_9721,c_9718,c_9696,c_9695,c_9694,c_9692,c_9691,c_9690,c_9689,c_9688,c_9687,c_9686,c_9685,c_9682,c_9681,c_9680,c_9679,c_9675,c_9674,c_9673,c_9672,c_9671,c_9670,c_9669,c_9668,c_9667,c_9666,c_9693,c_9664,c_9663,c_9662,c_9661,c_9660,c_9659,c_9658,c_9657,c_9656,c_9655,c_9654,c_9653,c_9652,c_9650,c_9651,c_9593,c_9588,c_9587,c_9586,c_9573,c_9572,c_9571,c_9570,c_9569,c_9568,c_9567,c_9566,c_9564,c_9563,c_9562,c_9565,c_9560,c_9559,c_9558,c_9557,c_9556,c_9555,c_9554,c_9551,c_9549,c_9540,c_9533,c_9531,c_9530,c_9529,c_9528,c_9526,c_9525,c_9524,c_9516,c_9515,c_9504,c_9503,c_9502,c_9501,c_9500,c_9499,c_9498,c_9497,c_9496,c_9495,c_9494,c_9493,c_9492,c_9491,c_9489,c_9488,c_9487,c_9483,c_9475,c_9462,c_9461,c_9407,c_9406,c_9396,c_9391,c_9390,c_9389,c_9380,c_9373,c_9372,c_9371,c_9363,c_9362,c_9352,c_9351,c_9343,c_9342,c_9311,c_9310,c_9309,c_9308,c_9307,c_9305,c_9304,c_9303,c_9301,c_9300,c_9299,c_9236,c_9235,c_9234,c_9233,c_9232,c_9229,c_9228,c_9227,c_9189,c_9188,c_9187,c_9186,c_9185,c_9184,c_9183,c_9180,c_9128,c_9126,c_9125,c_9118,c_9117,c_9114,c_9113,c_9112,c_9111,c_9095,c_9094,c_9084,c_9083,c_9076,c_9038,c_9025,c_9024,c_8995,c_8994,c_8992,c_8991,c_8989,c_8988,c_8985,c_8984,c_8983,c_8982,c_8927,c_8926,c_8924,c_8923,c_8921,c_8920,c_8917,c_8916,c_8915,c_8914,c_8903,c_8902,c_8901,c_8864,c_8859,c_8858,c_8857,c_8851,c_8850,c_8848,c_8756,c_8753,c_8746,c_8742,c_8741,c_8740,c_8739,c_8738,c_8737,c_8736,c_8735,c_8734,c_8733,c_8731,c_8730,c_8729,c_8726,c_8725,c_8647,c_8644,c_8637,c_8630,c_8629,c_8628,c_8627,c_8626,c_8625,c_8624,c_8623,c_8622,c_8621,c_8620,c_8619,c_8618,c_8617,c_8616,c_8613,c_8564,c_8563,c_8552,c_8551,c_8550,c_8549,c_8548,c_8547,c_8546,c_8545,c_8544,c_8543,c_8542,c_8541,c_8540,c_8539,c_8538,c_8537,c_8536,c_8535,c_8534,c_8533,c_8532,c_8531,c_8530,c_8529,c_8528,c_8481,c_8478,c_8477,c_8462,c_8461,c_8460,c_8459,c_8457,c_8455,c_8454,c_8453,c_8452,c_8450,c_8449,c_8448,c_8447,c_8445,c_8444,c_8443,c_8442,c_8441,c_8440,c_8439,c_8437,c_8436,c_8435,c_8434,c_8432,c_8431,c_8430,c_8433,c_8438,c_8427,c_8426,c_8425,c_8424,c_8423,c_8422,c_8419,c_8417,c_8406,c_8405,c_8404,c_8356,c_8355,c_8354,c_8353,c_8352,c_8343,c_8342,c_8341,c_8340,c_8339,c_8293,c_8292,c_8291,c_8290,c_8289,c_8288,c_8287,c_8286,c_8285,c_8284,c_8277,c_8276,c_8275,c_8274,c_8267,c_8265,c_8262,c_8261,c_8120,c_8119,c_8118,c_8117,c_8116,c_8115,c_8114,c_8112,c_8111,c_8110,c_8109,c_8108,c_8107,c_8106,c_8105,c_8104,c_8103,c_8102,c_8101,c_8070,c_8059,c_8058,c_8057,c_8056,c_8055,c_8053,c_8052,c_8051,c_8050,c_8049,c_8048,c_8047,c_7956,c_7955,c_7954,c_7953,c_7952,c_7950,c_7949,c_7948,c_7947,c_7946,c_7945,c_7944,c_7869,c_7866,c_7865,c_7864,c_7863,c_7862,c_7861,c_7860,c_7858,c_7856,c_7855,c_7854,c_7853,c_7852,c_7851,c_7798,c_7796,c_7795,c_7790,c_7779,c_7777,c_7776,c_7775,c_7774,c_7773,c_7772,c_7771,c_7766,c_7767,c_7764,c_7757,c_7756,c_7755,c_7754,c_7753,c_7751,c_7750,c_7749,c_7735,c_7734,c_7722,c_7721,c_7720,c_7705,c_7704,c_7691,c_7690,c_7689,c_7683,c_7682,c_7675,c_7674,c_7673,c_7656,c_7655,c_7634,c_7622,c_7621,c_7620,c_7597,c_7596,c_7584,c_7583,c_7582,c_7574,c_7573,c_7567,c_7566,c_7565,c_7560,c_7546,c_7545,c_7531,c_7523,c_7521,c_7457,c_7456,c_7455,c_7454,c_7453,c_7452,c_7449,c_7446,c_7445,c_7444,c_7443,c_7442,c_7441,c_7440,c_7439,c_7438,c_7405,c_7404,c_7403,c_7402,c_7401,c_7399,c_7398,c_7397,c_7396,c_7317,c_7316,c_7315,c_7314,c_7313,c_7312,c_7311,c_7310,c_7309,c_7308,c_7307,c_7306,c_7305,c_7304,c_7303,c_7302,c_7301,c_7300,c_7299,c_7298,c_7297,c_7296,c_7254,c_7253,c_7252,c_7251,c_7250,c_7248,c_7247,c_7246,c_7245,c_7244,c_7243,c_7232,c_7228,c_7223,c_7216,c_7215,c_7207,c_7206,c_7201,c_7200,c_7199,c_7198,c_7196,c_7195,c_7197,c_7187,c_7186,c_7185,c_7184,c_7182,c_7181,c_7180,c_7178,c_7177,c_7163,c_7162,c_7161,c_7151,c_7140,c_7114,c_7113,c_7112,c_7111,c_7110,c_7109,c_7102,c_7101,c_7100,c_7098,c_7097,c_7094,c_7082,c_7081,c_7080,c_7079,c_7078,c_7077,c_7073,c_7045,c_7044,c_7043,c_7042,c_7041,c_7040,c_7039,c_7038,c_7024,c_7023,c_7022,c_6995,c_6994,c_6993,c_6992,c_6991,c_6980,c_6979,c_6977,c_6966,c_6965,c_6964,c_6963,c_6958,c_6953,c_6951,c_6949,c_6948,c_6946,c_6945,c_6944,c_6943,c_6962,c_6941,c_6939,c_6938,c_6937,c_6935,c_6934,c_6933,c_6932,c_6931,c_6930,c_6929,c_6928,c_6923,c_6922,c_6921,c_6905,c_6902,c_6901,c_6892,c_6891,c_6859,c_6853,c_6852,c_6851,c_6850,c_6849,c_6844,c_6843,c_6776,c_6771,c_6768,c_6767,c_6766,c_6765,c_6764,c_6743,c_6742,c_6741,c_6738,c_6737,c_6736,c_6699,c_6698,c_6697,c_6696,c_6695,c_6692,c_6660,c_6659,c_6658,c_6657,c_6654,c_6653,c_6652,c_6651,c_6650,c_6649,c_6647,c_6646,c_6645,c_6643,c_6644,c_6661,c_6623,c_6622,c_6616,c_6615,c_6610,c_6608,c_6607,c_6605,c_6604,c_6603,c_6609,c_6600,c_6599,c_6598,c_6597,c_6596,c_6595,c_6577,c_6574,c_6573,c_6572,c_6571,c_6569,c_6565,c_6562,c_6561,c_6560,c_6558,c_6557,c_6556,c_6551,c_6540,c_6539,c_6538,c_6537,c_6536,c_6535,c_6534,c_6533,c_6531,c_6530,c_6529,c_6521,c_6516,c_6515,c_6502,c_6501,c_6496,c_6495,c_6480,c_6478,c_6477,c_6475,c_6474,c_6473,c_6472,c_6469,c_6430,c_6426,c_6423,c_6418,c_6416,c_6409,c_6403,c_6402,c_6401,c_6396,c_6393,c_6392,c_6375,c_6374,c_6373,c_6371,c_6370,c_6369,c_6372,c_6367,c_6366,c_6365,c_6334,c_6333,c_6330,c_6328,c_6325,c_6323,c_6321,c_6320,c_6335,c_6315,c_6294,c_6293,c_6291,c_6290,c_6288,c_6287,c_6286,c_6268,c_6267,c_6265,c_6264,c_6262,c_6261,c_6232,c_6231,c_6230,c_6217,c_6216,c_6215,c_6209,c_6208,c_6202,c_6201,c_6183,c_6182,c_6181,c_6173,c_6172,c_6171,c_6150,c_6149,c_6148,c_6140,c_6139,c_6138,c_6122,c_6121,c_6120,c_6112,c_6111,c_6110,c_6091,c_6090,c_6089,c_6081,c_6080,c_6079,c_6065,c_6064,c_6063,c_6057,c_6050,c_6049,c_6048,c_6040,c_6039,c_6031,c_6030,c_6019,c_6018,c_6017,c_6014,c_5987,c_5986,c_5985,c_5984,c_5983,c_5963,c_5962,c_5961,c_5960,c_5959,c_5957,c_5956,c_5955,c_5954,c_5953,c_5878,c_5877,c_5876,c_5875,c_5874,c_5873,c_5872,c_5871,c_5870,c_5869,c_5868,c_5867,c_5866,c_5850,c_5849,c_5839,c_5838,c_5824,c_5823,c_5813,c_5812,c_5808,c_5807,c_5799,c_5798,c_5797,c_5782,c_5781,c_5780,c_5764,c_5763,c_5762,c_5761,c_5744,c_5743,c_5736,c_5735,c_5734,c_5721,c_5720,c_5719,c_5718,c_5716,c_5698,c_5697,c_5696,c_5695,c_5694,c_5693,c_5692,c_5691,c_5690,c_5677,c_5661,c_5660,c_5656,c_5654,c_5653,c_5631,c_5630,c_5628,c_5626,c_5624,c_5623,c_5601,c_5600,c_5599,c_5598,c_5597,c_5589,c_5585,c_5582,c_5581,c_5575,c_5557,c_5553,c_5552,c_5548,c_5547,c_5545,c_5540,c_5539,c_5538,c_5532,c_5531,c_5504,c_5503,c_5502,c_5501,c_5500,c_5488,c_5487,c_5486,c_5485,c_5464,c_5463,c_5462,c_5461,c_5460,c_5425,c_5422,c_5426,c_5407,c_5402,c_5397,c_5375,c_5374,c_5373,c_5372,c_5371,c_5370,c_5369,c_5368,c_5360,c_5344,c_5343,c_5342,c_5341,c_5327,c_5326,c_5325,c_5300,c_5294,c_6874,c_5290,c_5289,c_5272,c_5260,c_5259,c_5240,c_5229,c_5228,c_5220,c_5218,c_5208,c_5207,c_1706,c_1855,c_1252,c_6466,c_6412,c_8263,c_5388,c_5203,c_190,c_189,c_188,c_187,c_186,c_185,c_184,c_183,c_182,c_181,c_180,c_179,c_178,c_177,c_176,c_175,c_174,c_10642,c_172,c_171,c_170,c_169,c_8054,c_167,c_166,c_165,c_164,c_163,c_162,c_161,c_160,c_158,c_157,c_154,c_153,c_152,c_151,c_150,c_149,c_148,c_147,c_146,c_145,c_144,c_143,c_142,c_141,c_140,c_137,c_139,c_135,c_134,c_133,c_132,c_131,c_130,c_129,c_128,c_127,c_126,c_125,c_124,c_123,c_122,c_121,c_120,c_119,c_118,c_117,c_116,c_9231,c_114,c_113,c_112,c_12088,c_110,c_109,c_108,c_107,c_106,c_105,c_104,c_103,c_102,c_101,c_100,c_99,c_98,c_97,c_96,c_93,c_92,c_91,c_90,c_89,c_85,c_84,c_83,c_82,c_77,c_76,c_75,c_74,c_73,c_72,c_71,c_70,c_69,c_68,c_6415,c_66,c_65,c_64,c_63,c_156,c_61,c_88,c_57,c_79,c_78,c_80,c_52,c_51,c_95,c_49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU162+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.07 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.18/0.45 % Computer : n006.cluster.edu
% 0.18/0.45 % Model : x86_64 x86_64
% 0.18/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.45 % Memory : 8046.5625MB
% 0.18/0.45 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Thu Sep 24 12:59:26 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.18/0.49 Running first-order theorem proving
% 0.18/0.49 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.23/0.50
% 0.23/0.50 % ======== iProver multi-core TPTP/SMT =========
% 0.23/0.50
% 0.23/0.50 % Detected problem language: tptp
% 0.23/0.52 % Proving...
% 8.35/1.82 % SZS status Started for theBenchmark.p
% 8.35/1.82 % SZS status Theorem for theBenchmark.p
% 8.35/1.82
% 8.35/1.82 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 8.35/1.82
% 8.35/1.82 % ------ iProver source info
% 8.35/1.82
% 8.35/1.82 % git: date: 2026-07-19 20:42:38 +0200
% 8.35/1.82 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 8.35/1.82 % git: non_committed_changes: false
% 8.35/1.82
% 8.35/1.82 % ------ Parsing...
% 8.35/1.82 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 8.35/1.82
% 8.35/1.82 % ------ Preprocessing... sup_sim: 6 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 8.35/1.82
% 8.35/1.82 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 8.35/1.82
% 8.35/1.82 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 8.35/1.82 % ------ Proving...
% 8.35/1.82 % ------ Problem Properties
% 8.35/1.82
% 8.35/1.82 %
% 8.35/1.82 % clauses 123
% 8.35/1.82 % conjectures 2
% 8.35/1.82 % EPR 21
% 8.35/1.82 % Horn 95
% 8.35/1.82 % unary 24
% 8.35/1.82 % binary 55
% 8.35/1.82 % lits 273
% 8.35/1.82 % lits eq 80
% 8.35/1.82 % fd_pure 0
% 8.35/1.82 % fd_pseudo 0
% 8.35/1.82 % fd_cond 3
% 8.35/1.82 % fd_pseudo_cond 35
% 8.35/1.82 % AC symbols 0
% 8.35/1.82
% 8.35/1.82 % ------ Schedule dynamic 5 is on
% 8.35/1.82
% 8.35/1.82 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 8.35/1.82
% 8.35/1.82
% 8.35/1.82 % ------
% 8.35/1.82 % Current options:
% 8.35/1.82 % ------
% 8.35/1.82
% 8.35/1.82
% 8.35/1.82 %
% 8.35/1.82
% 8.35/1.82 % ------ Proving...
% 8.35/1.82 %
% 8.35/1.82
% 8.35/1.82 % SZS status Theorem for theBenchmark.p
% 8.35/1.82
% 8.35/1.82 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 8.35/1.84
% 8.35/1.84
%------------------------------------------------------------------------------