%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU049+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n017.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 02:55:08 PM UTC 2026
% Result : Theorem 18.51s 3.26s
% Output : CNFRefutation 18.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 31
% Syntax : Number of formulae : 4681 ( 255 unt; 0 def)
% Number of atoms : 11368 (4727 equ)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 11841 (5154 ~;6586 |; 75 &)
% ( 9 <=>; 16 =>; 0 <=; 1 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 17 ( 5 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 : 22 ( 22 usr; 9 con; 0-3 aty)
% Number of variables : 5555 ( 0 sgn5528 !; 27 ?;5322 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( in(X0,X1)
=> ~ in(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f2,axiom,
! [X0] :
( empty(X0)
=> function(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_funct_1) ).
fof(f3,axiom,
! [X0] :
( empty(X0)
=> relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relat_1) ).
fof(f5,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ! [X1,X2] :
( X2 = relation_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( X3 = apply(X0,X4)
& in(X4,X1)
& in(X4,relation_dom(X0)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d12_funct_1) ).
fof(f6,axiom,
! [X0,X1] :
( X1 = singleton(X0)
<=> ! [X2] :
( in(X2,X1)
<=> X2 = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
fof(f7,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f9,axiom,
! [X0] : ~ empty(powerset(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(f10,axiom,
empty(empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(f11,axiom,
! [X0] : ~ empty(singleton(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_subset_1) ).
fof(f12,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_relat_1) ).
fof(f13,axiom,
! [X0] :
( ( relation(X0)
& ~ empty(X0) )
=> ~ empty(relation_dom(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_relat_1) ).
fof(f14,axiom,
! [X0] :
( empty(X0)
=> ( relation(relation_dom(X0))
& empty(relation_dom(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc7_relat_1) ).
fof(f15,axiom,
? [X0] :
( function(X0)
& relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_funct_1) ).
fof(f16,axiom,
? [X0] :
( relation(X0)
& empty(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_relat_1) ).
fof(f17,axiom,
! [X0] :
( ~ empty(X0)
=> ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_subset_1) ).
fof(f18,axiom,
? [X0] : empty(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(f19,axiom,
? [X0] :
( function(X0)
& empty(X0)
& relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_funct_1) ).
fof(f20,axiom,
? [X0] :
( relation(X0)
& ~ empty(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_relat_1) ).
fof(f21,axiom,
! [X0] :
? [X1] :
( empty(X1)
& element(X1,powerset(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).
fof(f22,axiom,
? [X0] : ~ empty(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f26,conjecture,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ( in(X0,relation_dom(X1))
=> relation_image(X1,singleton(X0)) = singleton(apply(X1,X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t117_funct_1) ).
fof(f27,negated_conjecture,
~ ! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ( in(X0,relation_dom(X1))
=> relation_image(X1,singleton(X0)) = singleton(apply(X1,X0)) ) ),
inference(negated_conjecture,[status(cth)],[f26]) ).
fof(f28,axiom,
! [X0,X1] :
( in(X0,X1)
=> element(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
fof(f29,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(f30,axiom,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
<=> in(X2,X1) )
=> X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tarski) ).
fof(f32,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X2))
& in(X0,X1) )
=> element(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
fof(f33,axiom,
! [X0,X1,X2] :
~ ( empty(X2)
& element(X1,powerset(X2))
& in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
fof(f34,axiom,
! [X0] :
( empty(X0)
=> X0 = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(f35,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(f36,axiom,
! [X0,X1] :
~ ( empty(X1)
& X0 != X1
& empty(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
fof(f37,plain,
? [X0,X1] :
( function(X1)
& relation(X1)
& in(X0,relation_dom(X1))
& relation_image(X1,singleton(X0)) != singleton(apply(X1,X0)) ),
inference(ennf_transformation,[],[f27]) ).
fof(f38,plain,
? [X0,X1] :
( function(X1)
& relation(X1)
& in(X0,relation_dom(X1))
& relation_image(X1,singleton(X0)) != singleton(apply(X1,X0)) ),
inference(flattening,[],[f37]) ).
fof(f39,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(ennf_transformation,[],[f36]) ).
fof(f40,plain,
! [X0] :
( ~ empty(X0)
| X0 = empty_set ),
inference(ennf_transformation,[],[f34]) ).
fof(f41,plain,
! [X0,X1] :
( ? [X2] :
( in(X2,X0)
<~> in(X2,X1) )
| X0 = X1 ),
inference(ennf_transformation,[],[f30]) ).
fof(f42,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( X2 = relation_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( X3 = apply(X0,X4)
& in(X4,X1)
& in(X4,relation_dom(X0)) ) ) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f43,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( X2 = relation_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( X3 = apply(X0,X4)
& in(X4,X1)
& in(X4,relation_dom(X0)) ) ) ) ),
inference(flattening,[],[f42]) ).
fof(f44,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f35]) ).
fof(f45,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(ennf_transformation,[],[f29]) ).
fof(f46,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(flattening,[],[f45]) ).
fof(f47,plain,
! [X0,X1] :
( ~ in(X0,X1)
| element(X0,X1) ),
inference(ennf_transformation,[],[f28]) ).
fof(f48,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ in(X1,X0) ),
inference(ennf_transformation,[],[f1]) ).
fof(f49,plain,
! [X0] :
( ~ empty(X0)
| ( relation(relation_dom(X0))
& empty(relation_dom(X0)) ) ),
inference(ennf_transformation,[],[f14]) ).
fof(f50,plain,
! [X0] :
( ~ relation(X0)
| empty(X0)
| ~ empty(relation_dom(X0)) ),
inference(ennf_transformation,[],[f13]) ).
fof(f51,plain,
! [X0] :
( ~ relation(X0)
| empty(X0)
| ~ empty(relation_dom(X0)) ),
inference(flattening,[],[f50]) ).
fof(f52,plain,
! [X0] :
( ~ empty(X0)
| function(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f53,plain,
! [X0] :
( ~ empty(X0)
| relation(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f54,plain,
! [X0,X1,X2] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f33]) ).
fof(f55,plain,
! [X0,X1,X2] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(ennf_transformation,[],[f32]) ).
fof(f56,plain,
! [X0,X1,X2] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(flattening,[],[f55]) ).
fof(f57,plain,
! [X0] :
( empty(X0)
| ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) ) ),
inference(ennf_transformation,[],[f17]) ).
fof(f58,plain,
( function(sK1)
& relation(sK1)
& in(sK0,relation_dom(sK1))
& relation_image(sK1,singleton(sK0)) != singleton(apply(sK1,sK0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f38]) ).
fof(f59,plain,
! [X0,X1] :
( ? [X2] :
( ( in(X2,X0)
| in(X2,X1) )
& ( ~ in(X2,X0)
| ~ in(X2,X1) ) )
| X0 = X1 ),
inference(nnf_transformation,[],[f41]) ).
fof(f60,plain,
! [X0,X1] :
( ( ( in(sK2(X0,X1),X0)
| in(sK2(X0,X1),X1) )
& ( ~ in(sK2(X0,X1),X0)
| ~ in(sK2(X0,X1),X1) ) )
| X0 = X1 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X2,sK2(X0,X1))],[f59]) ).
fof(f61,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( ( relation_image(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| ? [X4] :
( X3 = apply(X0,X4)
& in(X4,X1)
& in(X4,relation_dom(X0)) ) )
& ( ! [X4] :
( apply(X0,X4) != X3
| ~ in(X4,X1)
| ~ in(X4,relation_dom(X0)) )
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ? [X4] :
( X3 = apply(X0,X4)
& in(X4,X1)
& in(X4,relation_dom(X0)) ) )
& ( ~ in(X3,X2)
| ! [X4] :
( apply(X0,X4) != X3
| ~ in(X4,X1)
| ~ in(X4,relation_dom(X0)) ) ) )
| X2 = relation_image(X0,X1) ) ) ),
inference(nnf_transformation,[],[f43]) ).
fof(f62,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( ( relation_image(X0,X1) != X2
| ! [X6] :
( ( ~ in(X6,X2)
| ? [X8] :
( apply(X0,X8) = X6
& in(X8,X1)
& in(X8,relation_dom(X0)) ) )
& ( ! [X7] :
( apply(X0,X7) != X6
| ~ in(X7,X1)
| ~ in(X7,relation_dom(X0)) )
| in(X6,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ? [X5] :
( apply(X0,X5) = X3
& in(X5,X1)
& in(X5,relation_dom(X0)) ) )
& ( ~ in(X3,X2)
| ! [X4] :
( apply(X0,X4) != X3
| ~ in(X4,X1)
| ~ in(X4,relation_dom(X0)) ) ) )
| X2 = relation_image(X0,X1) ) ) ),
inference(rectify,[],[f61]) ).
fof(f63,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( ( relation_image(X0,X1) != X2
| ! [X6] :
( ( ~ in(X6,X2)
| ( apply(X0,sK5(X0,X1,X6)) = X6
& in(sK5(X0,X1,X6),X1)
& in(sK5(X0,X1,X6),relation_dom(X0)) ) )
& ( ! [X7] :
( apply(X0,X7) != X6
| ~ in(X7,X1)
| ~ in(X7,relation_dom(X0)) )
| in(X6,X2) ) ) )
& ( ( ( in(sK3(X0,X1,X2),X2)
| ( sK3(X0,X1,X2) = apply(X0,sK4(X0,X1,X2))
& in(sK4(X0,X1,X2),X1)
& in(sK4(X0,X1,X2),relation_dom(X0)) ) )
& ( ~ in(sK3(X0,X1,X2),X2)
| ! [X4] :
( apply(X0,X4) != sK3(X0,X1,X2)
| ~ in(X4,X1)
| ~ in(X4,relation_dom(X0)) ) ) )
| X2 = relation_image(X0,X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5]),skolemize(X3,sK3(X0,X1,X2)),skolemize(X5,sK4(X0,X1,X2)),skolemize(X8,sK5(X0,X1,X6))],[f62]) ).
fof(f64,plain,
( function(sK6)
& empty(sK6)
& relation(sK6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X0,sK6)],[f19]) ).
fof(f65,plain,
( function(sK7)
& relation(sK7) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X0,sK7)],[f15]) ).
fof(f66,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,[],[f6]) ).
fof(f67,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,[],[f66]) ).
fof(f68,plain,
! [X0,X1] :
( ( singleton(X0) != X1
| ! [X3] :
( ( ~ in(X3,X1)
| X0 = X3 )
& ( X0 != X3
| in(X3,X1) ) ) )
& ( ( ( in(sK8(X0,X1),X1)
| sK8(X0,X1) = X0 )
& ( ~ in(sK8(X0,X1),X1)
| sK8(X0,X1) != X0 ) )
| X1 = singleton(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(X2,sK8(X0,X1))],[f67]) ).
fof(f69,plain,
( relation(sK9)
& ~ empty(sK9) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(X0,sK9)],[f20]) ).
fof(f70,plain,
( relation(sK10)
& empty(sK10) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(X0,sK10)],[f16]) ).
fof(f71,plain,
~ empty(sK11),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(X0,sK11)],[f22]) ).
fof(f72,plain,
empty(sK12),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(X0,sK12)],[f18]) ).
fof(f73,plain,
! [X0] :
( empty(sK13(X0))
& element(sK13(X0),powerset(X0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(X1,sK13(X0))],[f21]) ).
fof(f74,plain,
! [X0] :
( empty(X0)
| ( ~ empty(sK14(X0))
& element(sK14(X0),powerset(X0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(X1,sK14(X0))],[f57]) ).
fof(f75,plain,
! [X0] : element(sK15(X0),X0),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(X1,sK15(X0))],[f7]) ).
fof(f76,plain,
function(sK1),
inference(cnf_transformation,[],[f58]) ).
fof(f77,plain,
relation(sK1),
inference(cnf_transformation,[],[f58]) ).
fof(f78,plain,
in(sK0,relation_dom(sK1)),
inference(cnf_transformation,[],[f58]) ).
fof(f79,plain,
relation_image(sK1,singleton(sK0)) != singleton(apply(sK1,sK0)),
inference(cnf_transformation,[],[f58]) ).
fof(f80,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(cnf_transformation,[],[f39]) ).
fof(f81,plain,
! [X0] :
( ~ empty(X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f40]) ).
fof(f82,plain,
! [X0,X1] :
( in(sK2(X0,X1),X0)
| in(sK2(X0,X1),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f60]) ).
fof(f83,plain,
! [X0,X1] :
( ~ in(sK2(X0,X1),X0)
| ~ in(sK2(X0,X1),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f60]) ).
fof(f84,plain,
! [X2,X0,X1,X6] :
( ~ function(X0)
| ~ relation(X0)
| relation_image(X0,X1) != X2
| ~ in(X6,X2)
| apply(X0,sK5(X0,X1,X6)) = X6 ),
inference(cnf_transformation,[],[f63]) ).
fof(f85,plain,
! [X2,X0,X1,X6] :
( ~ function(X0)
| ~ relation(X0)
| relation_image(X0,X1) != X2
| ~ in(X6,X2)
| in(sK5(X0,X1,X6),X1) ),
inference(cnf_transformation,[],[f63]) ).
fof(f86,plain,
! [X2,X0,X1,X6] :
( ~ function(X0)
| ~ relation(X0)
| relation_image(X0,X1) != X2
| ~ in(X6,X2)
| in(sK5(X0,X1,X6),relation_dom(X0)) ),
inference(cnf_transformation,[],[f63]) ).
fof(f87,plain,
! [X2,X0,X1,X6,X7] :
( ~ function(X0)
| ~ relation(X0)
| relation_image(X0,X1) != X2
| apply(X0,X7) != X6
| ~ in(X7,X1)
| ~ in(X7,relation_dom(X0))
| in(X6,X2) ),
inference(cnf_transformation,[],[f63]) ).
fof(f88,plain,
! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| in(sK3(X0,X1,X2),X2)
| sK3(X0,X1,X2) = apply(X0,sK4(X0,X1,X2))
| relation_image(X0,X1) = X2 ),
inference(cnf_transformation,[],[f63]) ).
fof(f89,plain,
! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| in(sK3(X0,X1,X2),X2)
| in(sK4(X0,X1,X2),X1)
| relation_image(X0,X1) = X2 ),
inference(cnf_transformation,[],[f63]) ).
fof(f90,plain,
! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| in(sK3(X0,X1,X2),X2)
| in(sK4(X0,X1,X2),relation_dom(X0))
| relation_image(X0,X1) = X2 ),
inference(cnf_transformation,[],[f63]) ).
fof(f91,plain,
! [X2,X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(sK3(X0,X1,X2),X2)
| apply(X0,X4) != sK3(X0,X1,X2)
| ~ in(X4,X1)
| ~ in(X4,relation_dom(X0))
| relation_image(X0,X1) = X2 ),
inference(cnf_transformation,[],[f63]) ).
fof(f92,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f44]) ).
fof(f93,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(cnf_transformation,[],[f46]) ).
fof(f94,plain,
! [X0,X1] :
( ~ in(X0,X1)
| element(X0,X1) ),
inference(cnf_transformation,[],[f47]) ).
fof(f95,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ in(X1,X0) ),
inference(cnf_transformation,[],[f48]) ).
fof(f96,plain,
! [X0] :
( ~ empty(X0)
| relation(relation_dom(X0)) ),
inference(cnf_transformation,[],[f49]) ).
fof(f97,plain,
! [X0] :
( ~ empty(X0)
| empty(relation_dom(X0)) ),
inference(cnf_transformation,[],[f49]) ).
fof(f98,plain,
! [X0] :
( ~ relation(X0)
| empty(X0)
| ~ empty(relation_dom(X0)) ),
inference(cnf_transformation,[],[f51]) ).
fof(f99,plain,
function(sK6),
inference(cnf_transformation,[],[f64]) ).
fof(f100,plain,
empty(sK6),
inference(cnf_transformation,[],[f64]) ).
fof(f101,plain,
relation(sK6),
inference(cnf_transformation,[],[f64]) ).
fof(f102,plain,
function(sK7),
inference(cnf_transformation,[],[f65]) ).
fof(f103,plain,
relation(sK7),
inference(cnf_transformation,[],[f65]) ).
fof(f104,plain,
! [X0] :
( ~ empty(X0)
| function(X0) ),
inference(cnf_transformation,[],[f52]) ).
fof(f105,plain,
! [X0] : ~ empty(singleton(X0)),
inference(cnf_transformation,[],[f11]) ).
fof(f106,plain,
! [X3,X0,X1] :
( singleton(X0) != X1
| ~ in(X3,X1)
| X0 = X3 ),
inference(cnf_transformation,[],[f68]) ).
fof(f107,plain,
! [X3,X0,X1] :
( singleton(X0) != X1
| X0 != X3
| in(X3,X1) ),
inference(cnf_transformation,[],[f68]) ).
fof(f108,plain,
! [X0,X1] :
( in(sK8(X0,X1),X1)
| sK8(X0,X1) = X0
| singleton(X0) = X1 ),
inference(cnf_transformation,[],[f68]) ).
fof(f109,plain,
! [X0,X1] :
( ~ in(sK8(X0,X1),X1)
| sK8(X0,X1) != X0
| singleton(X0) = X1 ),
inference(cnf_transformation,[],[f68]) ).
fof(f110,plain,
relation(sK9),
inference(cnf_transformation,[],[f69]) ).
fof(f111,plain,
~ empty(sK9),
inference(cnf_transformation,[],[f69]) ).
fof(f112,plain,
relation(sK10),
inference(cnf_transformation,[],[f70]) ).
fof(f113,plain,
empty(sK10),
inference(cnf_transformation,[],[f70]) ).
fof(f114,plain,
! [X0] :
( ~ empty(X0)
| relation(X0) ),
inference(cnf_transformation,[],[f53]) ).
fof(f115,plain,
~ empty(sK11),
inference(cnf_transformation,[],[f71]) ).
fof(f116,plain,
empty(sK12),
inference(cnf_transformation,[],[f72]) ).
fof(f117,plain,
relation(empty_set),
inference(cnf_transformation,[],[f12]) ).
fof(f119,plain,
empty(empty_set),
inference(cnf_transformation,[],[f10]) ).
fof(f120,plain,
! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f54]) ).
fof(f121,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(cnf_transformation,[],[f56]) ).
fof(f122,plain,
! [X0] : empty(sK13(X0)),
inference(cnf_transformation,[],[f73]) ).
fof(f123,plain,
! [X0] : element(sK13(X0),powerset(X0)),
inference(cnf_transformation,[],[f73]) ).
fof(f124,plain,
! [X0] :
( empty(X0)
| ~ empty(sK14(X0)) ),
inference(cnf_transformation,[],[f74]) ).
fof(f125,plain,
! [X0] :
( empty(X0)
| element(sK14(X0),powerset(X0)) ),
inference(cnf_transformation,[],[f74]) ).
fof(f126,plain,
! [X0] : element(sK15(X0),X0),
inference(cnf_transformation,[],[f75]) ).
fof(f127,plain,
! [X0] : ~ empty(powerset(X0)),
inference(cnf_transformation,[],[f9]) ).
fof(f128,plain,
! [X2,X0,X1,X7] :
( ~ function(X0)
| ~ relation(X0)
| relation_image(X0,X1) != X2
| ~ in(X7,X1)
| ~ in(X7,relation_dom(X0))
| in(apply(X0,X7),X2) ),
inference(equality_resolution,[],[f87]) ).
fof(f129,plain,
! [X0,X1,X7] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X7,X1)
| ~ in(X7,relation_dom(X0))
| in(apply(X0,X7),relation_image(X0,X1)) ),
inference(equality_resolution,[],[f128]) ).
fof(f130,plain,
! [X0,X1,X6] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X6,relation_image(X0,X1))
| in(sK5(X0,X1,X6),relation_dom(X0)) ),
inference(equality_resolution,[],[f86]) ).
fof(f131,plain,
! [X0,X1,X6] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X6,relation_image(X0,X1))
| in(sK5(X0,X1,X6),X1) ),
inference(equality_resolution,[],[f85]) ).
fof(f132,plain,
! [X0,X1,X6] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X6,relation_image(X0,X1))
| apply(X0,sK5(X0,X1,X6)) = X6 ),
inference(equality_resolution,[],[f84]) ).
fof(f133,plain,
! [X3,X1] :
( singleton(X3) != X1
| in(X3,X1) ),
inference(equality_resolution,[],[f107]) ).
fof(f134,plain,
! [X3] : in(X3,singleton(X3)),
inference(equality_resolution,[],[f133]) ).
fof(f135,plain,
! [X3,X0] :
( ~ in(X3,singleton(X0))
| X0 = X3 ),
inference(equality_resolution,[],[f106]) ).
tcf(c_49,negated_conjecture,
singleton(apply(sK1,sK0)) != relation_image(sK1,singleton(sK0)),
inference(cnf_transformation,[],[f79]) ).
tcf(c_50,negated_conjecture,
in(sK0,relation_dom(sK1)),
inference(cnf_transformation,[],[f78]) ).
tcf(c_51,negated_conjecture,
relation(sK1),
inference(cnf_transformation,[],[f77]) ).
tcf(c_52,negated_conjecture,
function(sK1),
inference(cnf_transformation,[],[f76]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f80]) ).
tcf(c_54,plain,
! [X0: $i] :
( ( X0 = empty_set )
| ~ empty(X0) ),
inference(cnf_transformation,[],[f81]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ in(sK2(X0,X1),X1)
| ~ in(sK2(X0,X1),X0) ),
inference(cnf_transformation,[],[f83]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,X1),X1)
| in(sK2(X0,X1),X0)
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f82]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0)
| ~ in(X3,X1)
| ~ in(X3,relation_dom(X0))
| ~ in(sK3(X0,X1,X2),X2)
| ( sK3(X0,X1,X2) != apply(X0,X3) ) ),
inference(cnf_transformation,[],[f91]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(X0,X1,X2),X2)
| in(sK4(X0,X1,X2),relation_dom(X0))
| ( relation_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f90]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK4(X0,X1,X2),X1)
| in(sK3(X0,X1,X2),X2)
| ( relation_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f89]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(X0,X1,X2),X2)
| ( relation_image(X0,X1) = X2 )
| ( apply(X0,sK4(X0,X1,X2)) = sK3(X0,X1,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f88]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X1,X0),relation_image(X1,X2))
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,X2)
| ~ in(X0,relation_dom(X1)) ),
inference(cnf_transformation,[],[f129]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(X1,X2,X0),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,X2)) ),
inference(cnf_transformation,[],[f130]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(X1,X2,X0),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,X2)) ),
inference(cnf_transformation,[],[f131]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(X1,sK5(X1,X2,X0)) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,X2)) ),
inference(cnf_transformation,[],[f132]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f92]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f93]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f94]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f95]) ).
tcf(c_69,plain,
! [X0: $i] :
( empty(relation_dom(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f97]) ).
tcf(c_70,plain,
! [X0: $i] :
( relation(relation_dom(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f96]) ).
tcf(c_71,plain,
! [X0: $i] :
( empty(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(cnf_transformation,[],[f98]) ).
tcf(c_72,plain,
relation(sK6),
inference(cnf_transformation,[],[f101]) ).
tcf(c_73,plain,
empty(sK6),
inference(cnf_transformation,[],[f100]) ).
tcf(c_74,plain,
function(sK6),
inference(cnf_transformation,[],[f99]) ).
tcf(c_75,plain,
relation(sK7),
inference(cnf_transformation,[],[f103]) ).
tcf(c_76,plain,
function(sK7),
inference(cnf_transformation,[],[f102]) ).
tcf(c_77,plain,
! [X0: $i] :
( function(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f104]) ).
tcf(c_78,plain,
! [X0: $i] : ~ empty(singleton(X0)),
inference(cnf_transformation,[],[f105]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i] :
( ( singleton(X0) = X1 )
| ~ in(sK8(X0,X1),X1)
| ( sK8(X0,X1) != X0 ) ),
inference(cnf_transformation,[],[f109]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i] :
( in(sK8(X0,X1),X1)
| ( singleton(X0) = X1 )
| ( sK8(X0,X1) = X0 ) ),
inference(cnf_transformation,[],[f108]) ).
tcf(c_81,plain,
! [X0: $i] : in(X0,singleton(X0)),
inference(cnf_transformation,[],[f134]) ).
tcf(c_82,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ in(X0,singleton(X1)) ),
inference(cnf_transformation,[],[f135]) ).
tcf(c_83,plain,
~ empty(sK9),
inference(cnf_transformation,[],[f111]) ).
tcf(c_84,plain,
relation(sK9),
inference(cnf_transformation,[],[f110]) ).
tcf(c_85,plain,
empty(sK10),
inference(cnf_transformation,[],[f113]) ).
tcf(c_86,plain,
relation(sK10),
inference(cnf_transformation,[],[f112]) ).
tcf(c_87,plain,
! [X0: $i] :
( relation(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f114]) ).
tcf(c_88,plain,
~ empty(sK11),
inference(cnf_transformation,[],[f115]) ).
tcf(c_89,plain,
empty(sK12),
inference(cnf_transformation,[],[f116]) ).
tcf(c_91,plain,
relation(empty_set),
inference(cnf_transformation,[],[f117]) ).
tcf(c_92,plain,
empty(empty_set),
inference(cnf_transformation,[],[f119]) ).
tcf(c_93,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(X1)
| ~ in(X2,X0)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f120]) ).
tcf(c_94,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X2,X1)
| ~ in(X2,X0)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f121]) ).
tcf(c_95,plain,
! [X0: $i] : element(sK13(X0),powerset(X0)),
inference(cnf_transformation,[],[f123]) ).
tcf(c_96,plain,
! [X0: $i] : empty(sK13(X0)),
inference(cnf_transformation,[],[f122]) ).
tcf(c_97,plain,
! [X0: $i] :
( empty(X0)
| element(sK14(X0),powerset(X0)) ),
inference(cnf_transformation,[],[f125]) ).
tcf(c_98,plain,
! [X0: $i] :
( empty(X0)
| ~ empty(sK14(X0)) ),
inference(cnf_transformation,[],[f124]) ).
tcf(c_99,plain,
! [X0: $i] : element(sK15(X0),X0),
inference(cnf_transformation,[],[f126]) ).
tcf(c_100,plain,
! [X0: $i] : ~ empty(powerset(X0)),
inference(cnf_transformation,[],[f127]) ).
tcf(c_4390,plain,
! [X0: $i,X1: $i] :
( ( singleton(X0) = singleton(X1) )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_4397,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| ~ empty(X1)
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_4983,plain,
function(sK10),
inference(superposition,[status(thm)],[c_85,c_77]) ).
tcf(c_4984,plain,
function(sK12),
inference(superposition,[status(thm)],[c_89,c_77]) ).
tcf(c_4985,plain,
function(empty_set),
inference(superposition,[status(thm)],[c_92,c_77]) ).
tcf(c_4986,plain,
! [X0: $i] : function(sK13(X0)),
inference(superposition,[status(thm)],[c_96,c_77]) ).
tcf(c_4994,plain,
relation(sK12),
inference(superposition,[status(thm)],[c_89,c_87]) ).
tcf(c_4996,plain,
! [X0: $i] : relation(sK13(X0)),
inference(superposition,[status(thm)],[c_96,c_87]) ).
tcf(c_5003,plain,
! [X0: $i] :
( function(relation_dom(X0))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_77]) ).
tcf(c_5023,plain,
! [X0: $i] :
( ( relation_dom(X0) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_54]) ).
tcf(c_5024,plain,
empty_set = sK6,
inference(superposition,[status(thm)],[c_73,c_54]) ).
tcf(c_5025,plain,
empty_set = sK10,
inference(superposition,[status(thm)],[c_85,c_54]) ).
tcf(c_5026,plain,
empty_set = sK12,
inference(superposition,[status(thm)],[c_89,c_54]) ).
tcf(c_5028,plain,
! [X0: $i] : sK13(X0) = empty_set,
inference(superposition,[status(thm)],[c_96,c_54]) ).
tcf(c_5042,plain,
! [X0: $i] : element(empty_set,powerset(X0)),
inference(demodulation,[status(thm)],[c_95,c_5028]) ).
tcf(c_5061,plain,
~ empty(relation_dom(sK1)),
inference(superposition,[status(thm)],[c_50,c_65]) ).
tcf(c_5062,plain,
! [X0: $i,X1: $i] :
( in(sK2(X1,X0),X1)
| ( X0 = X1 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_56,c_65]) ).
tcf(c_5063,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,X1),X1)
| ( X0 = X1 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_56,c_65]) ).
tcf(c_5075,plain,
element(sK0,relation_dom(sK1)),
inference(superposition,[status(thm)],[c_50,c_67]) ).
tcf(c_5076,plain,
! [X0: $i,X1: $i] :
( element(sK2(X0,X1),X1)
| in(sK2(X0,X1),X0)
| ( X0 = X1 ) ),
inference(superposition,[status(thm)],[c_56,c_67]) ).
tcf(c_5077,plain,
! [X0: $i,X1: $i] :
( element(sK2(X0,X1),X0)
| in(sK2(X0,X1),X1)
| ( X0 = X1 ) ),
inference(superposition,[status(thm)],[c_56,c_67]) ).
tcf(c_5078,plain,
! [X0: $i] : element(X0,singleton(X0)),
inference(superposition,[status(thm)],[c_81,c_67]) ).
tcf(c_5094,plain,
~ in(relation_dom(sK1),sK0),
inference(superposition,[status(thm)],[c_50,c_68]) ).
tcf(c_5095,plain,
! [X0: $i,X1: $i] :
( in(sK2(X1,X0),X1)
| ( X0 = X1 )
| ~ in(X0,sK2(X1,X0)) ),
inference(superposition,[status(thm)],[c_56,c_68]) ).
tcf(c_5096,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,X1),X1)
| ( X0 = X1 )
| ~ in(X0,sK2(X0,X1)) ),
inference(superposition,[status(thm)],[c_56,c_68]) ).
tcf(c_5097,plain,
! [X0: $i] : ~ in(singleton(X0),X0),
inference(superposition,[status(thm)],[c_81,c_68]) ).
tcf(c_5105,plain,
~ empty(sK1),
inference(superposition,[status(thm)],[c_69,c_5061]) ).
tcf(c_5110,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(X0)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_5023]) ).
tcf(c_5111,plain,
relation_dom(empty_set) = empty_set,
inference(superposition,[status(thm)],[c_92,c_5023]) ).
tcf(c_5123,plain,
! [X0: $i] :
( empty(X0)
| empty(powerset(X0))
| in(sK14(X0),powerset(X0)) ),
inference(superposition,[status(thm)],[c_97,c_66]) ).
tcf(c_5124,plain,
! [X0: $i] :
( empty(X0)
| in(sK15(X0),X0) ),
inference(superposition,[status(thm)],[c_99,c_66]) ).
tcf(c_5125,plain,
! [X0: $i] :
( empty(powerset(X0))
| in(empty_set,powerset(X0)) ),
inference(superposition,[status(thm)],[c_5042,c_66]) ).
tcf(c_5130,plain,
! [X0: $i] : in(empty_set,powerset(X0)),
inference(forward_subsumption_resolution,[status(thm)],[c_5125,c_100]) ).
tcf(c_5131,plain,
! [X0: $i] :
( empty(X0)
| in(sK14(X0),powerset(X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5123,c_100]) ).
tcf(c_5137,plain,
! [X0: $i] : ~ in(powerset(X0),empty_set),
inference(superposition,[status(thm)],[c_5130,c_68]) ).
tcf(c_5145,plain,
! [X0: $i] :
( empty(X0)
| ~ in(X0,sK15(X0)) ),
inference(superposition,[status(thm)],[c_5124,c_68]) ).
tcf(c_5169,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,singleton(X1)),X0)
| ( singleton(X1) = X0 )
| ( sK2(X0,singleton(X1)) = X1 ) ),
inference(superposition,[status(thm)],[c_56,c_82]) ).
tcf(c_5170,plain,
! [X0: $i,X1: $i] :
( in(sK2(singleton(X0),X1),X1)
| ( singleton(X0) = X1 )
| ( sK2(singleton(X0),X1) = X0 ) ),
inference(superposition,[status(thm)],[c_56,c_82]) ).
tcf(c_5172,plain,
! [X0: $i] :
( empty(singleton(X0))
| ( sK15(singleton(X0)) = X0 ) ),
inference(superposition,[status(thm)],[c_5124,c_82]) ).
tcf(c_5173,plain,
! [X0: $i] : sK15(singleton(X0)) = X0,
inference(forward_subsumption_resolution,[status(thm)],[c_5172,c_78]) ).
tcf(c_5189,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(X0) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_53]) ).
tcf(c_5201,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ in(X0,sK15(powerset(X1))) ),
inference(superposition,[status(thm)],[c_99,c_93]) ).
tcf(c_5202,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ in(X0,empty_set) ),
inference(superposition,[status(thm)],[c_5042,c_93]) ).
tcf(c_5213,plain,
! [X0: $i] :
( empty(X0)
| ~ in(powerset(X0),sK14(X0)) ),
inference(superposition,[status(thm)],[c_5131,c_68]) ).
tcf(c_5228,plain,
! [X0: $i,X1: $i] :
( in(sK2(X1,empty_set),X1)
| ( X1 = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_56,c_5202]) ).
tcf(c_5229,plain,
! [X0: $i,X1: $i] :
( in(sK2(empty_set,X1),X1)
| ( X1 = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_56,c_5202]) ).
tcf(c_5245,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_5110]) ).
tcf(c_5246,plain,
relation_dom(relation_dom(empty_set)) = empty_set,
inference(superposition,[status(thm)],[c_92,c_5110]) ).
tcf(c_5254,plain,
! [X0: $i,X1: $i] :
( in(sK2(X1,sK15(powerset(X0))),X1)
| ( sK15(powerset(X0)) = X1 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_56,c_5201]) ).
tcf(c_5255,plain,
! [X0: $i,X1: $i] :
( in(sK2(sK15(powerset(X0)),X1),X1)
| ( sK15(powerset(X0)) = X1 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_56,c_5201]) ).
tcf(c_5256,plain,
! [X0: $i] :
( empty(sK15(powerset(X0)))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5124,c_5201]) ).
tcf(c_5269,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_5110]) ).
tcf(c_5270,plain,
! [X0: $i,X1: $i] :
( ( sK15(powerset(X0)) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_53]) ).
tcf(c_5271,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_5023]) ).
tcf(c_5272,plain,
! [X0: $i] :
( ( sK15(powerset(X0)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_54]) ).
tcf(c_5273,plain,
! [X0: $i] :
( relation(sK15(powerset(X0)))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_87]) ).
tcf(c_5274,plain,
! [X0: $i] :
( function(sK15(powerset(X0)))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_77]) ).
tcf(c_5300,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_5272]) ).
tcf(c_5301,plain,
sK15(powerset(empty_set)) = empty_set,
inference(superposition,[status(thm)],[c_92,c_5272]) ).
tcf(c_5302,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_5272]) ).
tcf(c_5308,plain,
( empty(powerset(empty_set))
| in(empty_set,powerset(empty_set)) ),
inference(superposition,[status(thm)],[c_5301,c_5124]) ).
tcf(c_5309,plain,
element(empty_set,powerset(empty_set)),
inference(superposition,[status(thm)],[c_5301,c_99]) ).
tcf(c_5310,plain,
! [X0: $i] :
( ~ empty(empty_set)
| ~ in(X0,empty_set) ),
inference(superposition,[status(thm)],[c_5301,c_5201]) ).
tcf(c_5314,plain,
! [X0: $i] : ~ in(X0,empty_set),
inference(forward_subsumption_resolution,[status(thm)],[c_5310,c_92]) ).
tcf(c_5328,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| element(X0,X1)
| ~ in(X0,sK14(X1)) ),
inference(superposition,[status(thm)],[c_97,c_94]) ).
tcf(c_5329,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| ~ in(X0,sK15(powerset(X1))) ),
inference(superposition,[status(thm)],[c_99,c_94]) ).
tcf(c_5344,plain,
! [X0: $i,X1: $i] :
( ( singleton(X1) = X0 )
| ( sK8(X1,X0) = X1 )
| ~ in(X0,sK8(X1,X0)) ),
inference(superposition,[status(thm)],[c_80,c_68]) ).
tcf(c_5345,plain,
! [X0: $i,X1: $i] :
( element(sK8(X0,X1),X1)
| ( singleton(X0) = X1 )
| ( sK8(X0,X1) = X0 ) ),
inference(superposition,[status(thm)],[c_80,c_67]) ).
tcf(c_5346,plain,
! [X0: $i,X1: $i] :
( ( singleton(X1) = X0 )
| ( sK8(X1,X0) = X1 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_80,c_65]) ).
tcf(c_5347,plain,
! [X0: $i,X1: $i] :
( ( singleton(X0) = singleton(X1) )
| ( sK8(X0,singleton(X1)) = X1 )
| ( sK8(X0,singleton(X1)) = X0 ) ),
inference(superposition,[status(thm)],[c_80,c_82]) ).
tcf(c_5348,plain,
! [X0: $i,X1: $i] :
( ( sK15(powerset(X0)) = singleton(X1) )
| ( sK8(X1,sK15(powerset(X0))) = X1 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_80,c_5201]) ).
tcf(c_5375,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ function(X1)
| ~ relation(X1)
| ~ in(X2,relation_image(X1,X0))
| ~ in(X0,sK5(X1,X0,X2)) ),
inference(superposition,[status(thm)],[c_63,c_68]) ).
tcf(c_5376,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK5(X1,X2,X0),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_63,c_67]) ).
tcf(c_5377,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(X2)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_63,c_65]) ).
tcf(c_5378,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK5(X1,singleton(X2),X0) = X2 )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,singleton(X2))) ),
inference(superposition,[status(thm)],[c_63,c_82]) ).
tcf(c_5379,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(X2)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,sK15(powerset(X2)))) ),
inference(superposition,[status(thm)],[c_63,c_5201]) ).
tcf(c_5409,plain,
! [X0: $i] :
( in(sK2(X0,empty_set),X0)
| ( X0 = empty_set ) ),
inference(superposition,[status(thm)],[c_56,c_5314]) ).
tcf(c_5410,plain,
! [X0: $i] :
( in(sK2(empty_set,X0),X0)
| ( X0 = empty_set ) ),
inference(superposition,[status(thm)],[c_56,c_5314]) ).
tcf(c_5411,plain,
! [X0: $i,X1: $i] :
( ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,empty_set)) ),
inference(superposition,[status(thm)],[c_63,c_5314]) ).
tcf(c_5412,plain,
! [X0: $i] :
( ( singleton(X0) = empty_set )
| ( sK8(X0,empty_set) = X0 ) ),
inference(superposition,[status(thm)],[c_80,c_5314]) ).
tcf(c_5432,plain,
! [X0: $i,X1: $i] :
( element(sK2(X1,sK15(powerset(X0))),X0)
| in(sK2(X1,sK15(powerset(X0))),X1)
| ( sK15(powerset(X0)) = X1 ) ),
inference(superposition,[status(thm)],[c_56,c_5329]) ).
tcf(c_5433,plain,
! [X0: $i,X1: $i] :
( element(sK2(sK15(powerset(X0)),X1),X0)
| in(sK2(sK15(powerset(X0)),X1),X1)
| ( sK15(powerset(X0)) = X1 ) ),
inference(superposition,[status(thm)],[c_56,c_5329]) ).
tcf(c_5434,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK5(X1,sK15(powerset(X2)),X0),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,sK15(powerset(X2)))) ),
inference(superposition,[status(thm)],[c_63,c_5329]) ).
tcf(c_5435,plain,
! [X0: $i,X1: $i] :
( element(sK8(X0,sK15(powerset(X1))),X1)
| ( sK15(powerset(X1)) = singleton(X0) )
| ( sK8(X0,sK15(powerset(X1))) = X0 ) ),
inference(superposition,[status(thm)],[c_80,c_5329]) ).
tcf(c_5436,plain,
! [X0: $i] :
( empty(sK15(powerset(X0)))
| element(sK15(sK15(powerset(X0))),X0) ),
inference(superposition,[status(thm)],[c_5124,c_5329]) ).
tcf(c_5467,plain,
! [X0: $i] :
( ( X0 = empty_set )
| ~ in(X0,sK2(X0,empty_set)) ),
inference(superposition,[status(thm)],[c_5409,c_68]) ).
tcf(c_5468,plain,
! [X0: $i] :
( element(sK2(X0,empty_set),X0)
| ( X0 = empty_set ) ),
inference(superposition,[status(thm)],[c_5409,c_67]) ).
tcf(c_5470,plain,
! [X0: $i] :
( ( singleton(X0) = empty_set )
| ( sK2(singleton(X0),empty_set) = X0 ) ),
inference(superposition,[status(thm)],[c_5409,c_82]) ).
tcf(c_5471,plain,
! [X0: $i] :
( element(sK2(sK15(powerset(X0)),empty_set),X0)
| ( sK15(powerset(X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_5409,c_5329]) ).
tcf(c_5495,plain,
! [X0: $i] :
( ( X0 = empty_set )
| ~ in(sK2(empty_set,X0),empty_set) ),
inference(superposition,[status(thm)],[c_5410,c_55]) ).
tcf(c_5496,plain,
! [X0: $i] :
( ( X0 = empty_set )
| ~ in(X0,sK2(empty_set,X0)) ),
inference(superposition,[status(thm)],[c_5410,c_68]) ).
tcf(c_5497,plain,
! [X0: $i] :
( element(sK2(empty_set,X0),X0)
| ( X0 = empty_set ) ),
inference(superposition,[status(thm)],[c_5410,c_67]) ).
tcf(c_5499,plain,
! [X0: $i] :
( ( singleton(X0) = empty_set )
| ( sK2(empty_set,singleton(X0)) = X0 ) ),
inference(superposition,[status(thm)],[c_5410,c_82]) ).
tcf(c_5500,plain,
! [X0: $i] :
( element(sK2(empty_set,sK15(powerset(X0))),X0)
| ( sK15(powerset(X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_5410,c_5329]) ).
tcf(c_5520,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| ( powerset(X1) = empty_set )
| ~ in(X0,sK2(powerset(X1),empty_set)) ),
inference(superposition,[status(thm)],[c_5468,c_94]) ).
tcf(c_5521,plain,
! [X0: $i,X1: $i] :
( ( powerset(X1) = empty_set )
| ~ empty(X1)
| ~ in(X0,sK2(powerset(X1),empty_set)) ),
inference(superposition,[status(thm)],[c_5468,c_93]) ).
tcf(c_5538,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| ( powerset(X1) = empty_set )
| ~ in(X0,sK2(empty_set,powerset(X1))) ),
inference(superposition,[status(thm)],[c_5497,c_94]) ).
tcf(c_5539,plain,
! [X0: $i,X1: $i] :
( ( powerset(X1) = empty_set )
| ~ empty(X1)
| ~ in(X0,sK2(empty_set,powerset(X1))) ),
inference(superposition,[status(thm)],[c_5497,c_93]) ).
tcf(c_5555,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_5245]) ).
tcf(c_5556,plain,
relation_dom(relation_dom(relation_dom(empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_5245]) ).
tcf(c_5557,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_5245]) ).
tcf(c_5567,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_5271]) ).
tcf(c_5568,plain,
relation_dom(sK15(powerset(empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_5271]) ).
tcf(c_5569,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_5271]) ).
tcf(c_5581,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_5300]) ).
tcf(c_5582,plain,
sK15(powerset(relation_dom(empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_5300]) ).
tcf(c_5583,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_5300]) ).
tcf(c_5595,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| element(sK2(X1,sK14(X0)),X0)
| in(sK2(X1,sK14(X0)),X1)
| ( sK14(X0) = X1 ) ),
inference(superposition,[status(thm)],[c_56,c_5328]) ).
tcf(c_5596,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| element(sK2(sK14(X0),X1),X0)
| in(sK2(sK14(X0),X1),X1)
| ( sK14(X0) = X1 ) ),
inference(superposition,[status(thm)],[c_56,c_5328]) ).
tcf(c_5597,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X2)
| element(sK5(X1,sK14(X2),X0),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,sK14(X2))) ),
inference(superposition,[status(thm)],[c_63,c_5328]) ).
tcf(c_5598,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| element(sK8(X0,sK14(X1)),X1)
| ( singleton(X0) = sK14(X1) )
| ( sK8(X0,sK14(X1)) = X0 ) ),
inference(superposition,[status(thm)],[c_80,c_5328]) ).
tcf(c_5599,plain,
! [X0: $i] :
( empty(X0)
| empty(sK14(X0))
| element(sK15(sK14(X0)),X0) ),
inference(superposition,[status(thm)],[c_5124,c_5328]) ).
tcf(c_5600,plain,
! [X0: $i] :
( empty(X0)
| element(sK2(sK14(X0),empty_set),X0)
| ( sK14(X0) = empty_set ) ),
inference(superposition,[status(thm)],[c_5409,c_5328]) ).
tcf(c_5601,plain,
! [X0: $i] :
( empty(X0)
| element(sK2(empty_set,sK14(X0)),X0)
| ( sK14(X0) = empty_set ) ),
inference(superposition,[status(thm)],[c_5410,c_5328]) ).
tcf(c_5647,plain,
( element(sK15(empty_set),empty_set)
| empty(sK15(powerset(empty_set))) ),
inference(superposition,[status(thm)],[c_5301,c_5436]) ).
tcf(c_5648,plain,
! [X0: $i] :
( empty(X0)
| empty(sK15(powerset(X0)))
| in(sK15(sK15(powerset(X0))),X0) ),
inference(superposition,[status(thm)],[c_5436,c_66]) ).
tcf(c_5649,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| empty(sK15(powerset(powerset(X1))))
| ~ in(X0,sK15(sK15(powerset(powerset(X1))))) ),
inference(superposition,[status(thm)],[c_5436,c_94]) ).
tcf(c_5650,plain,
! [X0: $i,X1: $i] :
( empty(sK15(powerset(powerset(X1))))
| ~ empty(X1)
| ~ in(X0,sK15(sK15(powerset(powerset(X1))))) ),
inference(superposition,[status(thm)],[c_5436,c_93]) ).
tcf(c_5651,plain,
( empty(empty_set)
| element(sK15(empty_set),empty_set) ),
inference(light_normalisation,[status(thm)],[c_5647,c_5301]) ).
tcf(c_5677,plain,
! [X0: $i,X1: $i] :
( ( singleton(X0) = singleton(X1) )
| ( sK8(X1,singleton(X0)) = X1 )
| ~ in(sK8(X1,singleton(X0)),singleton(X0))
| ( X0 != X1 ) ),
inference(superposition,[status(thm)],[c_5347,c_79]) ).
tcf(c_5678,plain,
! [X0: $i,X1: $i] :
( in(X1,singleton(X1))
| ( singleton(X0) = singleton(X1) )
| ( sK8(X0,singleton(X1)) = X0 ) ),
inference(superposition,[status(thm)],[c_5347,c_80]) ).
tcf(c_5680,plain,
! [X0: $i,X1: $i] :
( ( singleton(X0) = singleton(X1) )
| ( sK8(X0,singleton(X1)) = X1 )
| ~ in(sK8(X0,singleton(X1)),singleton(X1)) ),
inference(superposition,[status(thm)],[c_5347,c_79]) ).
tcf(c_5683,plain,
! [X0: $i,X1: $i] :
( ( singleton(X0) = singleton(X1) )
| ( sK8(X1,singleton(X0)) = X0 )
| ( X0 != X1 ) ),
inference(equality_factoring,[status(thm)],[c_5347]) ).
tcf(c_5684,plain,
! [X0: $i,X1: $i] :
( ( singleton(X0) = singleton(X1) )
| ( sK8(X0,singleton(X1)) = X0 )
| ( X0 != X1 ) ),
inference(equality_factoring,[status(thm)],[c_5347]) ).
tcf(c_5714,plain,
! [X0: $i,X1: $i] :
( in(sK5(empty_set,X1,X0),empty_set)
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ in(X0,relation_image(empty_set,X1)) ),
inference(superposition,[status(thm)],[c_5111,c_62]) ).
tcf(c_5715,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X2,relation_image(X0,X1))
| ~ in(relation_dom(X0),sK5(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_62,c_68]) ).
tcf(c_5716,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK5(X1,X2,X0),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_62,c_67]) ).
tcf(c_5717,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ function(X1)
| ~ relation(X1)
| ~ empty(relation_dom(X1))
| ~ in(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_62,c_65]) ).
tcf(c_5722,plain,
! [X0: $i,X1: $i] : ~ in(X0,relation_image(empty_set,X1)),
inference(forward_subsumption_resolution,[status(thm)],[c_5714,c_5314,c_4985,c_91]) ).
tcf(c_5749,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X2,relation_image(X0,X1)),X2)
| ( relation_image(X0,X1) = X2 )
| ( apply(X0,sK5(X0,X1,sK2(X2,relation_image(X0,X1)))) = sK2(X2,relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_56,c_64]) ).
tcf(c_5750,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(relation_image(X0,X1),X2),X2)
| ( relation_image(X0,X1) = X2 )
| ( apply(X0,sK5(X0,X1,sK2(relation_image(X0,X1),X2))) = sK2(relation_image(X0,X1),X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_56,c_64]) ).
tcf(c_5751,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( apply(X2,sK5(X2,X3,sK5(X1,relation_image(X2,X3),X0))) = sK5(X1,relation_image(X2,X3),X0) )
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,relation_image(X2,X3))) ),
inference(superposition,[status(thm)],[c_63,c_64]) ).
tcf(c_5752,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X0,X1) = singleton(X2) )
| ( sK8(X2,relation_image(X0,X1)) = X2 )
| ( apply(X0,sK5(X0,X1,sK8(X2,relation_image(X0,X1)))) = sK8(X2,relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_80,c_64]) ).
tcf(c_5753,plain,
! [X0: $i,X1: $i] :
( empty(relation_image(X0,X1))
| ( apply(X0,sK5(X0,X1,sK15(relation_image(X0,X1)))) = sK15(relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_5124,c_64]) ).
tcf(c_5754,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X0,X1) = empty_set )
| ( apply(X0,sK5(X0,X1,sK2(relation_image(X0,X1),empty_set))) = sK2(relation_image(X0,X1),empty_set) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_5409,c_64]) ).
tcf(c_5755,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X0,X1) = empty_set )
| ( apply(X0,sK5(X0,X1,sK2(empty_set,relation_image(X0,X1)))) = sK2(empty_set,relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_5410,c_64]) ).
tcf(c_5799,plain,
! [X0: $i] :
( empty(X0)
| ~ empty(empty_set)
| ( X0 != empty_set ) ),
inference(instantiation,[status(thm)],[c_4397]) ).
tcf(c_5812,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(X1,sK5(X1,X2,apply(X1,X0))) = apply(X1,X0) )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,X2)
| ~ in(X0,relation_dom(X1)) ),
inference(superposition,[status(thm)],[c_61,c_64]) ).
tcf(c_5813,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X2,X1)
| ~ in(X2,relation_dom(X0))
| ~ in(relation_image(X0,X1),apply(X0,X2)) ),
inference(superposition,[status(thm)],[c_61,c_68]) ).
tcf(c_5814,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(apply(X1,X0),relation_image(X1,X2))
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,X2)
| ~ in(X0,relation_dom(X1)) ),
inference(superposition,[status(thm)],[c_61,c_67]) ).
tcf(c_5815,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ function(X1)
| ~ relation(X1)
| ~ in(X0,X2)
| ~ empty(relation_image(X1,X2))
| ~ in(X0,relation_dom(X1)) ),
inference(superposition,[status(thm)],[c_61,c_65]) ).
tcf(c_5846,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK3(X0,relation_image(X1,X2),X3),X3)
| ( relation_image(X0,relation_image(X1,X2)) = X3 )
| ( apply(X1,sK5(X1,X2,sK4(X0,relation_image(X1,X2),X3))) = sK4(X0,relation_image(X1,X2),X3) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_59,c_64]) ).
tcf(c_5847,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(X1,X0,X2),X2)
| ( relation_image(X1,X0) = X2 )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,sK4(X1,X0,X2)) ),
inference(superposition,[status(thm)],[c_59,c_68]) ).
tcf(c_5848,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK4(X0,X1,X2),X1)
| in(sK3(X0,X1,X2),X2)
| ( relation_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_59,c_67]) ).
tcf(c_5849,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(X0,X1,X2),X2)
| ( relation_image(X0,X1) = X2 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_59,c_65]) ).
tcf(c_5850,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(X0,singleton(X1),X2),X2)
| ( relation_image(X0,singleton(X1)) = X2 )
| ( sK4(X0,singleton(X1),X2) = X1 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_59,c_82]) ).
tcf(c_5851,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X1)
| element(sK4(X0,sK14(X1),X2),X1)
| in(sK3(X0,sK14(X1),X2),X2)
| ( relation_image(X0,sK14(X1)) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_59,c_5328]) ).
tcf(c_5852,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK4(X0,sK15(powerset(X1)),X2),X1)
| in(sK3(X0,sK15(powerset(X1)),X2),X2)
| ( relation_image(X0,sK15(powerset(X1))) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_59,c_5329]) ).
tcf(c_5853,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(X0,sK15(powerset(X1)),X2),X2)
| ( relation_image(X0,sK15(powerset(X1))) = X2 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_59,c_5201]) ).
tcf(c_5854,plain,
! [X0: $i,X1: $i] :
( in(sK3(X0,empty_set,X1),X1)
| ( relation_image(X0,empty_set) = X1 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_59,c_5314]) ).
tcf(c_5855,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK4(X0,X3,relation_image(X1,X2)),X3)
| ( relation_image(X0,X3) = relation_image(X1,X2) )
| ( apply(X1,sK5(X1,X2,sK3(X0,X3,relation_image(X1,X2)))) = sK3(X0,X3,relation_image(X1,X2)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_59,c_64]) ).
tcf(c_5856,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK4(X1,X2,X0),X2)
| ( relation_image(X1,X2) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,sK3(X1,X2,X0)) ),
inference(superposition,[status(thm)],[c_59,c_68]) ).
tcf(c_5857,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK3(X0,X1,X2),X2)
| in(sK4(X0,X1,X2),X1)
| ( relation_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_59,c_67]) ).
tcf(c_5858,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK4(X0,X2,X1),X2)
| ( relation_image(X0,X2) = X1 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_59,c_65]) ).
tcf(c_5859,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK4(X0,X1,singleton(X2)),X1)
| ( relation_image(X0,X1) = singleton(X2) )
| ( sK3(X0,X1,singleton(X2)) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_59,c_82]) ).
tcf(c_5860,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X2)
| element(sK3(X0,X1,sK14(X2)),X2)
| in(sK4(X0,X1,sK14(X2)),X1)
| ( relation_image(X0,X1) = sK14(X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_59,c_5328]) ).
tcf(c_5861,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK3(X0,X1,sK15(powerset(X2))),X2)
| in(sK4(X0,X1,sK15(powerset(X2))),X1)
| ( relation_image(X0,X1) = sK15(powerset(X2)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_59,c_5329]) ).
tcf(c_5862,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK4(X0,X2,sK15(powerset(X1))),X2)
| ( relation_image(X0,X2) = sK15(powerset(X1)) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_59,c_5201]) ).
tcf(c_5863,plain,
! [X0: $i,X1: $i] :
( in(sK4(X0,X1,empty_set),X1)
| ( relation_image(X0,X1) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_59,c_5314]) ).
tcf(c_5992,plain,
! [X0: $i,X1: $i] :
( in(sK2(X1,relation_image(empty_set,X0)),X1)
| ( relation_image(empty_set,X0) = X1 ) ),
inference(superposition,[status(thm)],[c_56,c_5722]) ).
tcf(c_5993,plain,
! [X0: $i,X1: $i] :
( in(sK2(relation_image(empty_set,X0),X1),X1)
| ( relation_image(empty_set,X0) = X1 ) ),
inference(superposition,[status(thm)],[c_56,c_5722]) ).
tcf(c_5994,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK4(X0,X1,relation_image(empty_set,X2)),X1)
| ( relation_image(X0,X1) = relation_image(empty_set,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_59,c_5722]) ).
tcf(c_5995,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(X0,relation_image(empty_set,X1),X2),X2)
| ( relation_image(X0,relation_image(empty_set,X1)) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_59,c_5722]) ).
tcf(c_5996,plain,
! [X0: $i,X1: $i] :
( ~ function(empty_set)
| ~ relation(empty_set)
| ~ in(X0,X1)
| ~ in(X0,relation_dom(empty_set)) ),
inference(superposition,[status(thm)],[c_61,c_5722]) ).
tcf(c_5997,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,relation_image(empty_set,X2))) ),
inference(superposition,[status(thm)],[c_63,c_5722]) ).
tcf(c_5998,plain,
! [X0: $i,X1: $i] :
( ( relation_image(empty_set,X1) = singleton(X0) )
| ( sK8(X0,relation_image(empty_set,X1)) = X0 ) ),
inference(superposition,[status(thm)],[c_80,c_5722]) ).
tcf(c_5999,plain,
! [X0: $i] : empty(relation_image(empty_set,X0)),
inference(superposition,[status(thm)],[c_5124,c_5722]) ).
tcf(c_6000,plain,
! [X0: $i] : relation_image(empty_set,X0) = empty_set,
inference(superposition,[status(thm)],[c_5409,c_5722]) ).
tcf(c_6011,plain,
! [X0: $i,X1: $i] :
( ~ function(empty_set)
| ~ relation(empty_set)
| ~ in(X0,empty_set)
| ~ in(X0,X1) ),
inference(light_normalisation,[status(thm)],[c_5996,c_5111]) ).
tcf(c_6041,plain,
! [X0: $i,X1: $i] :
( in(apply(empty_set,X0),empty_set)
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ in(X0,X1)
| ~ in(X0,relation_dom(empty_set)) ),
inference(superposition,[status(thm)],[c_6000,c_61]) ).
tcf(c_6043,plain,
! [X0: $i,X1: $i] :
( in(apply(empty_set,X0),empty_set)
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ in(X0,empty_set)
| ~ in(X0,X1) ),
inference(light_normalisation,[status(thm)],[c_6041,c_5111]) ).
tcf(c_6048,plain,
! [X0: $i] :
( empty(X0)
| element(sK15(sK14(X0)),X0) ),
inference(global_subsumption_just,[status(thm)],[c_5599,c_98,c_5599]) ).
tcf(c_6055,plain,
! [X0: $i] :
( empty(X0)
| in(sK15(sK14(X0)),X0) ),
inference(superposition,[status(thm)],[c_6048,c_66]) ).
tcf(c_6056,plain,
! [X0: $i,X1: $i] :
( empty(powerset(X1))
| element(X0,X1)
| ~ in(X0,sK15(sK14(powerset(X1)))) ),
inference(superposition,[status(thm)],[c_6048,c_94]) ).
tcf(c_6057,plain,
! [X0: $i,X1: $i] :
( empty(powerset(X1))
| ~ empty(X1)
| ~ in(X0,sK15(sK14(powerset(X1)))) ),
inference(superposition,[status(thm)],[c_6048,c_93]) ).
tcf(c_6060,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ in(X0,sK15(sK14(powerset(X1)))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6057,c_100]) ).
tcf(c_6063,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| ~ in(X0,sK15(sK14(powerset(X1)))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6056,c_100]) ).
tcf(c_6090,plain,
! [X0: $i,X1: $i] :
( empty(relation_image(X0,X1))
| ( apply(X0,sK5(X0,X1,sK15(sK14(relation_image(X0,X1))))) = sK15(sK14(relation_image(X0,X1))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6055,c_64]) ).
tcf(c_6091,plain,
! [X0: $i] :
( empty(X0)
| ~ in(X0,sK15(sK14(X0))) ),
inference(superposition,[status(thm)],[c_6055,c_68]) ).
tcf(c_6094,plain,
! [X0: $i] :
( empty(singleton(X0))
| ( sK15(sK14(singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_6055,c_82]) ).
tcf(c_6095,plain,
! [X0: $i] :
( empty(X0)
| empty(sK14(X0))
| element(sK15(sK14(sK14(X0))),X0) ),
inference(superposition,[status(thm)],[c_6055,c_5328]) ).
tcf(c_6096,plain,
! [X0: $i] :
( empty(sK15(powerset(X0)))
| element(sK15(sK14(sK15(powerset(X0)))),X0) ),
inference(superposition,[status(thm)],[c_6055,c_5329]) ).
tcf(c_6101,plain,
! [X0: $i] : sK15(sK14(singleton(X0))) = X0,
inference(forward_subsumption_resolution,[status(thm)],[c_6094,c_78]) ).
tcf(c_6116,plain,
! [X0: $i] :
( empty(sK14(singleton(X0)))
| ~ in(sK14(singleton(X0)),X0) ),
inference(superposition,[status(thm)],[c_6101,c_5145]) ).
tcf(c_6117,plain,
! [X0: $i] :
( empty(sK14(singleton(X0)))
| in(X0,sK14(singleton(X0))) ),
inference(superposition,[status(thm)],[c_6101,c_5124]) ).
tcf(c_6118,plain,
! [X0: $i] : element(X0,sK14(singleton(X0))),
inference(superposition,[status(thm)],[c_6101,c_99]) ).
tcf(c_6146,plain,
! [X0: $i,X1: $i] :
( in(sK2(X1,sK15(sK14(powerset(X0)))),X1)
| ( sK15(sK14(powerset(X0))) = X1 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_56,c_6060]) ).
tcf(c_6147,plain,
! [X0: $i,X1: $i] :
( in(sK2(sK15(sK14(powerset(X0))),X1),X1)
| ( sK15(sK14(powerset(X0))) = X1 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_56,c_6060]) ).
tcf(c_6148,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK4(X0,X2,sK15(sK14(powerset(X1)))),X2)
| ( sK15(sK14(powerset(X1))) = relation_image(X0,X2) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_59,c_6060]) ).
tcf(c_6149,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(X0,sK15(sK14(powerset(X1))),X2),X2)
| ( relation_image(X0,sK15(sK14(powerset(X1)))) = X2 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_59,c_6060]) ).
tcf(c_6150,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(X2)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,sK15(sK14(powerset(X2))))) ),
inference(superposition,[status(thm)],[c_63,c_6060]) ).
tcf(c_6151,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK14(powerset(X0))) = singleton(X1) )
| ( sK8(X1,sK15(sK14(powerset(X0)))) = X1 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_80,c_6060]) ).
tcf(c_6153,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5409,c_6060]) ).
tcf(c_6155,plain,
! [X0: $i] :
( empty(sK15(sK14(powerset(X0))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6055,c_6060]) ).
tcf(c_6187,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(sK14(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_5300]) ).
tcf(c_6188,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(sK14(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_5271]) ).
tcf(c_6189,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_5245]) ).
tcf(c_6190,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_5272]) ).
tcf(c_6191,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_5110]) ).
tcf(c_6192,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK14(powerset(X0))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_53]) ).
tcf(c_6193,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_5023]) ).
tcf(c_6195,plain,
! [X0: $i] :
( relation(sK15(sK14(powerset(X0))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_87]) ).
tcf(c_6196,plain,
! [X0: $i] :
( function(sK15(sK14(powerset(X0))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_77]) ).
tcf(c_6247,plain,
! [X0: $i] :
( ( singleton(X0) = empty_set )
| ~ in(sK8(X0,empty_set),empty_set) ),
inference(superposition,[status(thm)],[c_5412,c_79]) ).
tcf(c_6259,plain,
! [X0: $i,X1: $i] :
( in(sK4(empty_set,X0,X1),empty_set)
| in(sK3(empty_set,X0,X1),X1)
| ( relation_image(empty_set,X0) = X1 )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_5111,c_58]) ).
tcf(c_6260,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK4(X0,X3,relation_image(X1,X2)),relation_dom(X0))
| ( relation_image(X0,X3) = relation_image(X1,X2) )
| ( apply(X1,sK5(X1,X2,sK3(X0,X3,relation_image(X1,X2)))) = sK3(X0,X3,relation_image(X1,X2)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_58,c_64]) ).
tcf(c_6261,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK4(X1,X2,X0),relation_dom(X1))
| ( relation_image(X1,X2) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,sK3(X1,X2,X0)) ),
inference(superposition,[status(thm)],[c_58,c_68]) ).
tcf(c_6262,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK3(X0,X1,X2),X2)
| in(sK4(X0,X1,X2),relation_dom(X0))
| ( relation_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_58,c_67]) ).
tcf(c_6263,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK4(X0,X2,X1),relation_dom(X0))
| ( relation_image(X0,X2) = X1 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_58,c_65]) ).
tcf(c_6264,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK4(X0,X1,singleton(X2)),relation_dom(X0))
| ( relation_image(X0,X1) = singleton(X2) )
| ( sK3(X0,X1,singleton(X2)) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_58,c_82]) ).
tcf(c_6265,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X2)
| element(sK3(X0,X1,sK14(X2)),X2)
| in(sK4(X0,X1,sK14(X2)),relation_dom(X0))
| ( relation_image(X0,X1) = sK14(X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_58,c_5328]) ).
tcf(c_6266,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK3(X0,X1,sK15(powerset(X2))),X2)
| in(sK4(X0,X1,sK15(powerset(X2))),relation_dom(X0))
| ( relation_image(X0,X1) = sK15(powerset(X2)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_58,c_5329]) ).
tcf(c_6267,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK4(X0,X2,sK15(powerset(X1))),relation_dom(X0))
| ( relation_image(X0,X2) = sK15(powerset(X1)) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_58,c_5201]) ).
tcf(c_6268,plain,
! [X0: $i,X1: $i] :
( in(sK4(X0,X1,empty_set),relation_dom(X0))
| ( relation_image(X0,X1) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_58,c_5314]) ).
tcf(c_6269,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK4(X0,X2,sK15(sK14(powerset(X1)))),relation_dom(X0))
| ( sK15(sK14(powerset(X1))) = relation_image(X0,X2) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_58,c_6060]) ).
tcf(c_6270,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(X0,X1,X2),X2)
| ( relation_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0)
| ~ in(relation_dom(X0),sK4(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_58,c_68]) ).
tcf(c_6271,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(X0,X1,X2),X2)
| element(sK4(X0,X1,X2),relation_dom(X0))
| ( relation_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_58,c_67]) ).
tcf(c_6272,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(X0,X1,X2),X2)
| ( relation_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_58,c_65]) ).
tcf(c_6287,plain,
! [X0: $i,X1: $i] :
( in(sK4(empty_set,X1,X0),empty_set)
| in(sK3(empty_set,X1,X0),X0)
| ( X0 = empty_set )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(light_normalisation,[status(thm)],[c_6259,c_6000]) ).
tcf(c_6288,plain,
! [X0: $i,X1: $i] :
( in(sK3(empty_set,X1,X0),X0)
| ( X0 = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6287,c_5314,c_4985,c_91]) ).
tcf(c_6385,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(X0,X3) = relation_image(X1,X2) )
| ( apply(X0,sK4(X0,X3,relation_image(X1,X2))) = sK3(X0,X3,relation_image(X1,X2)) )
| ( apply(X1,sK5(X1,X2,sK3(X0,X3,relation_image(X1,X2)))) = sK3(X0,X3,relation_image(X1,X2)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_60,c_64]) ).
tcf(c_6386,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X1,X2) = X0 )
| ( apply(X1,sK4(X1,X2,X0)) = sK3(X1,X2,X0) )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,sK3(X1,X2,X0)) ),
inference(superposition,[status(thm)],[c_60,c_68]) ).
tcf(c_6387,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK3(X0,X1,X2),X2)
| ( relation_image(X0,X1) = X2 )
| ( apply(X0,sK4(X0,X1,X2)) = sK3(X0,X1,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_60,c_67]) ).
tcf(c_6388,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X0,X2) = X1 )
| ( apply(X0,sK4(X0,X2,X1)) = sK3(X0,X2,X1) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_60,c_65]) ).
tcf(c_6389,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X0,X1) = singleton(X2) )
| ( sK3(X0,X1,singleton(X2)) = X2 )
| ( apply(X0,sK4(X0,X1,singleton(X2))) = sK3(X0,X1,singleton(X2)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_60,c_82]) ).
tcf(c_6390,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X2)
| element(sK3(X0,X1,sK14(X2)),X2)
| ( relation_image(X0,X1) = sK14(X2) )
| ( apply(X0,sK4(X0,X1,sK14(X2))) = sK3(X0,X1,sK14(X2)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_60,c_5328]) ).
tcf(c_6391,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK3(X0,X1,sK15(powerset(X2))),X2)
| ( relation_image(X0,X1) = sK15(powerset(X2)) )
| ( apply(X0,sK4(X0,X1,sK15(powerset(X2)))) = sK3(X0,X1,sK15(powerset(X2))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_60,c_5329]) ).
tcf(c_6392,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X0,X2) = sK15(powerset(X1)) )
| ( apply(X0,sK4(X0,X2,sK15(powerset(X1)))) = sK3(X0,X2,sK15(powerset(X1))) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_60,c_5201]) ).
tcf(c_6393,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X0,X1) = empty_set )
| ( apply(X0,sK4(X0,X1,empty_set)) = sK3(X0,X1,empty_set) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_60,c_5314]) ).
tcf(c_6394,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK15(sK14(powerset(X1))) = relation_image(X0,X2) )
| ( apply(X0,sK4(X0,X2,sK15(sK14(powerset(X1))))) = sK3(X0,X2,sK15(sK14(powerset(X1)))) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_60,c_6060]) ).
tcf(c_6596,plain,
! [X0: $i,X1: $i] :
( element(sK2(X1,sK15(sK14(powerset(X0)))),X0)
| in(sK2(X1,sK15(sK14(powerset(X0)))),X1)
| ( sK15(sK14(powerset(X0))) = X1 ) ),
inference(superposition,[status(thm)],[c_56,c_6063]) ).
tcf(c_6597,plain,
! [X0: $i,X1: $i] :
( element(sK2(sK15(sK14(powerset(X0))),X1),X0)
| in(sK2(sK15(sK14(powerset(X0))),X1),X1)
| ( sK15(sK14(powerset(X0))) = X1 ) ),
inference(superposition,[status(thm)],[c_56,c_6063]) ).
tcf(c_6598,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK3(X0,X1,sK15(sK14(powerset(X2)))),X2)
| ( sK15(sK14(powerset(X2))) = relation_image(X0,X1) )
| ( apply(X0,sK4(X0,X1,sK15(sK14(powerset(X2))))) = sK3(X0,X1,sK15(sK14(powerset(X2)))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_60,c_6063]) ).
tcf(c_6599,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK3(X0,X2,sK15(sK14(powerset(X1)))),X1)
| in(sK4(X0,X2,sK15(sK14(powerset(X1)))),relation_dom(X0))
| ( sK15(sK14(powerset(X1))) = relation_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_58,c_6063]) ).
tcf(c_6600,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK3(X0,X2,sK15(sK14(powerset(X1)))),X1)
| in(sK4(X0,X2,sK15(sK14(powerset(X1)))),X2)
| ( sK15(sK14(powerset(X1))) = relation_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_59,c_6063]) ).
tcf(c_6601,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK4(X0,sK15(sK14(powerset(X1))),X2),X1)
| in(sK3(X0,sK15(sK14(powerset(X1))),X2),X2)
| ( relation_image(X0,sK15(sK14(powerset(X1)))) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_59,c_6063]) ).
tcf(c_6602,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK5(X1,sK15(sK14(powerset(X2))),X0),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,sK15(sK14(powerset(X2))))) ),
inference(superposition,[status(thm)],[c_63,c_6063]) ).
tcf(c_6603,plain,
! [X0: $i,X1: $i] :
( element(sK8(X0,sK15(sK14(powerset(X1)))),X1)
| ( sK15(sK14(powerset(X1))) = singleton(X0) )
| ( sK8(X0,sK15(sK14(powerset(X1)))) = X0 ) ),
inference(superposition,[status(thm)],[c_80,c_6063]) ).
tcf(c_6604,plain,
! [X0: $i] :
( empty(sK15(sK14(powerset(X0))))
| element(sK15(sK15(sK14(powerset(X0)))),X0) ),
inference(superposition,[status(thm)],[c_5124,c_6063]) ).
tcf(c_6605,plain,
! [X0: $i] :
( element(sK2(sK15(sK14(powerset(X0))),empty_set),X0)
| ( sK15(sK14(powerset(X0))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5409,c_6063]) ).
tcf(c_6606,plain,
! [X0: $i] :
( element(sK2(empty_set,sK15(sK14(powerset(X0)))),X0)
| ( sK15(sK14(powerset(X0))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5410,c_6063]) ).
tcf(c_6607,plain,
! [X0: $i] :
( empty(sK15(sK14(powerset(X0))))
| element(sK15(sK14(sK15(sK14(powerset(X0))))),X0) ),
inference(superposition,[status(thm)],[c_6055,c_6063]) ).
tcf(c_6678,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_6153]) ).
tcf(c_6679,plain,
sK15(sK14(powerset(empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_6153]) ).
tcf(c_6680,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_6153]) ).
tcf(c_6681,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(sK14(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_6153]) ).
tcf(c_6696,plain,
( empty(sK14(powerset(empty_set)))
| ~ in(sK14(powerset(empty_set)),empty_set) ),
inference(superposition,[status(thm)],[c_6679,c_5145]) ).
tcf(c_6697,plain,
( empty(sK14(powerset(empty_set)))
| in(empty_set,sK14(powerset(empty_set))) ),
inference(superposition,[status(thm)],[c_6679,c_5124]) ).
tcf(c_6698,plain,
element(empty_set,sK14(powerset(empty_set))),
inference(superposition,[status(thm)],[c_6679,c_99]) ).
tcf(c_6699,plain,
( empty(powerset(empty_set))
| ~ in(powerset(empty_set),empty_set) ),
inference(superposition,[status(thm)],[c_6679,c_6091]) ).
tcf(c_6701,plain,
( empty(powerset(empty_set))
| element(empty_set,powerset(empty_set)) ),
inference(superposition,[status(thm)],[c_6679,c_6048]) ).
tcf(c_6717,plain,
( empty(powerset(empty_set))
| element(empty_set,powerset(empty_set))
| empty(sK14(powerset(empty_set))) ),
inference(superposition,[status(thm)],[c_6697,c_5328]) ).
tcf(c_6722,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X0,X1) = empty_set )
| ( apply(X0,sK5(X0,X1,sK3(empty_set,X2,relation_image(X0,X1)))) = sK3(empty_set,X2,relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6288,c_64]) ).
tcf(c_6723,plain,
! [X0: $i,X1: $i] :
( ( X0 = empty_set )
| ~ in(X0,sK3(empty_set,X1,X0)) ),
inference(superposition,[status(thm)],[c_6288,c_68]) ).
tcf(c_6724,plain,
! [X0: $i,X1: $i] :
( element(sK3(empty_set,X1,X0),X0)
| ( X0 = empty_set ) ),
inference(superposition,[status(thm)],[c_6288,c_67]) ).
tcf(c_6726,plain,
! [X0: $i,X1: $i] :
( ( singleton(X1) = empty_set )
| ( sK3(empty_set,X0,singleton(X1)) = X1 ) ),
inference(superposition,[status(thm)],[c_6288,c_82]) ).
tcf(c_6727,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| element(sK3(empty_set,X1,sK14(X0)),X0)
| ( sK14(X0) = empty_set ) ),
inference(superposition,[status(thm)],[c_6288,c_5328]) ).
tcf(c_6728,plain,
! [X0: $i,X1: $i] :
( element(sK3(empty_set,X1,sK15(powerset(X0))),X0)
| ( sK15(powerset(X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_6288,c_5329]) ).
tcf(c_6731,plain,
! [X0: $i,X1: $i] :
( element(sK3(empty_set,X1,sK15(sK14(powerset(X0)))),X0)
| ( sK15(sK14(powerset(X0))) = empty_set ) ),
inference(superposition,[status(thm)],[c_6288,c_6063]) ).
tcf(c_6777,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,X2)
| ( powerset(X2) = empty_set )
| ~ in(X0,sK3(empty_set,X1,powerset(X2))) ),
inference(superposition,[status(thm)],[c_6724,c_94]) ).
tcf(c_6778,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( powerset(X2) = empty_set )
| ~ empty(X2)
| ~ in(X0,sK3(empty_set,X1,powerset(X2))) ),
inference(superposition,[status(thm)],[c_6724,c_93]) ).
tcf(c_6795,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(X0)) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_5189]) ).
tcf(c_6796,plain,
! [X0: $i] :
( ( relation_dom(empty_set) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_92,c_5189]) ).
tcf(c_6797,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK15(powerset(X0))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_5189]) ).
tcf(c_6798,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK15(sK14(powerset(X0)))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_5189]) ).
tcf(c_6830,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_5269]) ).
tcf(c_6831,plain,
relation_dom(relation_dom(sK15(powerset(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_5269]) ).
tcf(c_6832,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(sK15(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_5269]) ).
tcf(c_6833,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_5269]) ).
tcf(c_6854,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_5302]) ).
tcf(c_6855,plain,
sK15(powerset(sK15(powerset(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_5302]) ).
tcf(c_6856,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(sK15(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_5302]) ).
tcf(c_6857,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(sK15(sK14(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_5302]) ).
tcf(c_6871,plain,
! [X0: $i] :
( in(X0,empty_set)
| in(sK2(singleton(X0),empty_set),singleton(X0))
| ( singleton(X0) = empty_set ) ),
inference(superposition,[status(thm)],[c_5470,c_56]) ).
tcf(c_6877,plain,
! [X0: $i] :
( in(sK2(singleton(X0),empty_set),singleton(X0))
| ( singleton(X0) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6871,c_5314]) ).
tcf(c_6885,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_5555]) ).
tcf(c_6886,plain,
relation_dom(relation_dom(relation_dom(relation_dom(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_5555]) ).
tcf(c_6887,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_5555]) ).
tcf(c_6888,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_5555]) ).
tcf(c_6903,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_5567]) ).
tcf(c_6904,plain,
relation_dom(sK15(powerset(relation_dom(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_5567]) ).
tcf(c_6905,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(sK15(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_5567]) ).
tcf(c_6906,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(sK15(sK14(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_5567]) ).
tcf(c_6936,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_5581]) ).
tcf(c_6937,plain,
sK15(powerset(relation_dom(relation_dom(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_5581]) ).
tcf(c_6938,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(sK15(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_5581]) ).
tcf(c_6939,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(sK15(sK14(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_5581]) ).
tcf(c_6951,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_6678]) ).
tcf(c_6952,plain,
sK15(sK14(powerset(relation_dom(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_6678]) ).
tcf(c_6953,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(sK15(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_6678]) ).
tcf(c_6954,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(sK15(sK14(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_6678]) ).
tcf(c_6991,plain,
! [X0: $i] :
( empty(X0)
| element(sK15(sK14(sK14(X0))),X0) ),
inference(global_subsumption_just,[status(thm)],[c_6095,c_98,c_6095]) ).
tcf(c_6998,plain,
! [X0: $i] :
( empty(X0)
| in(sK15(sK14(sK14(X0))),X0) ),
inference(superposition,[status(thm)],[c_6991,c_66]) ).
tcf(c_6999,plain,
! [X0: $i,X1: $i] :
( empty(powerset(X1))
| element(X0,X1)
| ~ in(X0,sK15(sK14(sK14(powerset(X1))))) ),
inference(superposition,[status(thm)],[c_6991,c_94]) ).
tcf(c_7000,plain,
! [X0: $i,X1: $i] :
( empty(powerset(X1))
| ~ empty(X1)
| ~ in(X0,sK15(sK14(sK14(powerset(X1))))) ),
inference(superposition,[status(thm)],[c_6991,c_93]) ).
tcf(c_7003,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ in(X0,sK15(sK14(sK14(powerset(X1))))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7000,c_100]) ).
tcf(c_7006,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| ~ in(X0,sK15(sK14(sK14(powerset(X1))))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6999,c_100]) ).
tcf(c_7040,plain,
! [X0: $i,X1: $i] :
( empty(relation_image(X0,X1))
| ( apply(X0,sK5(X0,X1,sK15(sK14(sK14(relation_image(X0,X1)))))) = sK15(sK14(sK14(relation_image(X0,X1)))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6998,c_64]) ).
tcf(c_7041,plain,
! [X0: $i] :
( empty(X0)
| ~ in(X0,sK15(sK14(sK14(X0)))) ),
inference(superposition,[status(thm)],[c_6998,c_68]) ).
tcf(c_7044,plain,
! [X0: $i] :
( empty(singleton(X0))
| ( sK15(sK14(sK14(singleton(X0)))) = X0 ) ),
inference(superposition,[status(thm)],[c_6998,c_82]) ).
tcf(c_7045,plain,
! [X0: $i] :
( empty(X0)
| empty(sK14(X0))
| element(sK15(sK14(sK14(sK14(X0)))),X0) ),
inference(superposition,[status(thm)],[c_6998,c_5328]) ).
tcf(c_7046,plain,
! [X0: $i] :
( empty(sK15(powerset(X0)))
| element(sK15(sK14(sK14(sK15(powerset(X0))))),X0) ),
inference(superposition,[status(thm)],[c_6998,c_5329]) ).
tcf(c_7049,plain,
! [X0: $i] :
( empty(sK15(sK14(powerset(X0))))
| element(sK15(sK14(sK14(sK15(sK14(powerset(X0)))))),X0) ),
inference(superposition,[status(thm)],[c_6998,c_6063]) ).
tcf(c_7053,plain,
! [X0: $i] : sK15(sK14(sK14(singleton(X0)))) = X0,
inference(forward_subsumption_resolution,[status(thm)],[c_7044,c_78]) ).
tcf(c_7071,plain,
! [X0: $i] :
( empty(sK14(sK14(singleton(X0))))
| ~ in(sK14(sK14(singleton(X0))),X0) ),
inference(superposition,[status(thm)],[c_7053,c_5145]) ).
tcf(c_7072,plain,
! [X0: $i] :
( empty(sK14(sK14(singleton(X0))))
| in(X0,sK14(sK14(singleton(X0)))) ),
inference(superposition,[status(thm)],[c_7053,c_5124]) ).
tcf(c_7073,plain,
! [X0: $i] : element(X0,sK14(sK14(singleton(X0)))),
inference(superposition,[status(thm)],[c_7053,c_99]) ).
tcf(c_7107,plain,
( empty(sK15(powerset(empty_set)))
| element(sK15(sK14(empty_set)),empty_set) ),
inference(superposition,[status(thm)],[c_5301,c_6096]) ).
tcf(c_7108,plain,
! [X0: $i] :
( empty(X0)
| empty(sK15(powerset(X0)))
| in(sK15(sK14(sK15(powerset(X0)))),X0) ),
inference(superposition,[status(thm)],[c_6096,c_66]) ).
tcf(c_7109,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| empty(sK15(powerset(powerset(X1))))
| ~ in(X0,sK15(sK14(sK15(powerset(powerset(X1)))))) ),
inference(superposition,[status(thm)],[c_6096,c_94]) ).
tcf(c_7110,plain,
! [X0: $i,X1: $i] :
( empty(sK15(powerset(powerset(X1))))
| ~ empty(X1)
| ~ in(X0,sK15(sK14(sK15(powerset(powerset(X1)))))) ),
inference(superposition,[status(thm)],[c_6096,c_93]) ).
tcf(c_7111,plain,
( empty(empty_set)
| element(sK15(sK14(empty_set)),empty_set) ),
inference(light_normalisation,[status(thm)],[c_7107,c_5301]) ).
tcf(c_7140,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_6193]) ).
tcf(c_7141,plain,
relation_dom(sK15(sK14(powerset(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_6193]) ).
tcf(c_7142,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(sK15(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_6193]) ).
tcf(c_7143,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_6193]) ).
tcf(c_7159,plain,
! [X0: $i,X1: $i] :
( in(sK2(X1,sK15(sK14(sK14(powerset(X0))))),X1)
| ( sK15(sK14(sK14(powerset(X0)))) = X1 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_56,c_7003]) ).
tcf(c_7160,plain,
! [X0: $i,X1: $i] :
( in(sK2(sK15(sK14(sK14(powerset(X0)))),X1),X1)
| ( sK15(sK14(sK14(powerset(X0)))) = X1 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_56,c_7003]) ).
tcf(c_7161,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK15(sK14(sK14(powerset(X1)))) = relation_image(X0,X2) )
| ( apply(X0,sK4(X0,X2,sK15(sK14(sK14(powerset(X1)))))) = sK3(X0,X2,sK15(sK14(sK14(powerset(X1))))) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_60,c_7003]) ).
tcf(c_7162,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK4(X0,X2,sK15(sK14(sK14(powerset(X1))))),relation_dom(X0))
| ( sK15(sK14(sK14(powerset(X1)))) = relation_image(X0,X2) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_58,c_7003]) ).
tcf(c_7163,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK4(X0,X2,sK15(sK14(sK14(powerset(X1))))),X2)
| ( sK15(sK14(sK14(powerset(X1)))) = relation_image(X0,X2) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_59,c_7003]) ).
tcf(c_7164,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(X0,sK15(sK14(sK14(powerset(X1)))),X2),X2)
| ( relation_image(X0,sK15(sK14(sK14(powerset(X1))))) = X2 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_59,c_7003]) ).
tcf(c_7165,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(X2)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,sK15(sK14(sK14(powerset(X2)))))) ),
inference(superposition,[status(thm)],[c_63,c_7003]) ).
tcf(c_7166,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK14(sK14(powerset(X0)))) = singleton(X1) )
| ( sK8(X1,sK15(sK14(sK14(powerset(X0))))) = X1 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_80,c_7003]) ).
tcf(c_7171,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6288,c_7003]) ).
tcf(c_7172,plain,
! [X0: $i] :
( empty(sK15(sK14(sK14(powerset(X0)))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6998,c_7003]) ).
tcf(c_7241,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_6193]) ).
tcf(c_7242,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(sK15(sK14(sK14(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_6678]) ).
tcf(c_7243,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(sK15(sK14(sK14(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_5581]) ).
tcf(c_7244,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(sK15(sK14(sK14(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_5567]) ).
tcf(c_7245,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_5555]) ).
tcf(c_7246,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(sK15(sK14(sK14(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_5302]) ).
tcf(c_7247,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_5269]) ).
tcf(c_7248,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK15(sK14(sK14(powerset(X0))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_5189]) ).
tcf(c_7249,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_6153]) ).
tcf(c_7250,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(sK14(sK14(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_5300]) ).
tcf(c_7251,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_5271]) ).
tcf(c_7252,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_5245]) ).
tcf(c_7253,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(sK14(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_5272]) ).
tcf(c_7254,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(sK14(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_5110]) ).
tcf(c_7255,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK14(sK14(powerset(X0)))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_53]) ).
tcf(c_7256,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_5023]) ).
tcf(c_7258,plain,
! [X0: $i] :
( relation(sK15(sK14(sK14(powerset(X0)))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_87]) ).
tcf(c_7259,plain,
! [X0: $i] :
( function(sK15(sK14(sK14(powerset(X0)))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_77]) ).
tcf(c_7387,plain,
! [X0: $i] :
( in(X0,empty_set)
| in(sK2(empty_set,singleton(X0)),singleton(X0))
| ( singleton(X0) = empty_set ) ),
inference(superposition,[status(thm)],[c_5499,c_56]) ).
tcf(c_7389,plain,
! [X0: $i] :
( ( singleton(X0) = empty_set )
| ~ in(X0,singleton(X0))
| ~ in(sK2(empty_set,singleton(X0)),empty_set) ),
inference(superposition,[status(thm)],[c_5499,c_55]) ).
tcf(c_7394,plain,
! [X0: $i] :
( in(sK2(empty_set,singleton(X0)),singleton(X0))
| ( singleton(X0) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7387,c_5314]) ).
tcf(c_7402,plain,
! [X0: $i,X1: $i] :
( element(sK2(X1,sK15(sK14(sK14(powerset(X0))))),X0)
| in(sK2(X1,sK15(sK14(sK14(powerset(X0))))),X1)
| ( sK15(sK14(sK14(powerset(X0)))) = X1 ) ),
inference(superposition,[status(thm)],[c_56,c_7006]) ).
tcf(c_7403,plain,
! [X0: $i,X1: $i] :
( element(sK2(sK15(sK14(sK14(powerset(X0)))),X1),X0)
| in(sK2(sK15(sK14(sK14(powerset(X0)))),X1),X1)
| ( sK15(sK14(sK14(powerset(X0)))) = X1 ) ),
inference(superposition,[status(thm)],[c_56,c_7006]) ).
tcf(c_7404,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK3(X0,X1,sK15(sK14(sK14(powerset(X2))))),X2)
| ( sK15(sK14(sK14(powerset(X2)))) = relation_image(X0,X1) )
| ( apply(X0,sK4(X0,X1,sK15(sK14(sK14(powerset(X2)))))) = sK3(X0,X1,sK15(sK14(sK14(powerset(X2))))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_60,c_7006]) ).
tcf(c_7405,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK3(X0,X2,sK15(sK14(sK14(powerset(X1))))),X1)
| in(sK4(X0,X2,sK15(sK14(sK14(powerset(X1))))),relation_dom(X0))
| ( sK15(sK14(sK14(powerset(X1)))) = relation_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_58,c_7006]) ).
tcf(c_7406,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK3(X0,X2,sK15(sK14(sK14(powerset(X1))))),X1)
| in(sK4(X0,X2,sK15(sK14(sK14(powerset(X1))))),X2)
| ( sK15(sK14(sK14(powerset(X1)))) = relation_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_59,c_7006]) ).
tcf(c_7407,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK4(X0,sK15(sK14(sK14(powerset(X1)))),X2),X1)
| in(sK3(X0,sK15(sK14(sK14(powerset(X1)))),X2),X2)
| ( relation_image(X0,sK15(sK14(sK14(powerset(X1))))) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_59,c_7006]) ).
tcf(c_7408,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK5(X1,sK15(sK14(sK14(powerset(X2)))),X0),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,sK15(sK14(sK14(powerset(X2)))))) ),
inference(superposition,[status(thm)],[c_63,c_7006]) ).
tcf(c_7409,plain,
! [X0: $i,X1: $i] :
( element(sK8(X0,sK15(sK14(sK14(powerset(X1))))),X1)
| ( sK15(sK14(sK14(powerset(X1)))) = singleton(X0) )
| ( sK8(X0,sK15(sK14(sK14(powerset(X1))))) = X0 ) ),
inference(superposition,[status(thm)],[c_80,c_7006]) ).
tcf(c_7410,plain,
! [X0: $i] :
( empty(sK15(sK14(sK14(powerset(X0)))))
| element(sK15(sK15(sK14(sK14(powerset(X0))))),X0) ),
inference(superposition,[status(thm)],[c_5124,c_7006]) ).
tcf(c_7411,plain,
! [X0: $i] :
( element(sK2(sK15(sK14(sK14(powerset(X0)))),empty_set),X0)
| ( sK15(sK14(sK14(powerset(X0)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5409,c_7006]) ).
tcf(c_7412,plain,
! [X0: $i] :
( element(sK2(empty_set,sK15(sK14(sK14(powerset(X0))))),X0)
| ( sK15(sK14(sK14(powerset(X0)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5410,c_7006]) ).
tcf(c_7413,plain,
! [X0: $i] :
( empty(sK15(sK14(sK14(powerset(X0)))))
| element(sK15(sK14(sK15(sK14(sK14(powerset(X0)))))),X0) ),
inference(superposition,[status(thm)],[c_6055,c_7006]) ).
tcf(c_7414,plain,
! [X0: $i,X1: $i] :
( element(sK3(empty_set,X1,sK15(sK14(sK14(powerset(X0))))),X0)
| ( sK15(sK14(sK14(powerset(X0)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_6288,c_7006]) ).
tcf(c_7415,plain,
! [X0: $i] :
( empty(sK15(sK14(sK14(powerset(X0)))))
| element(sK15(sK14(sK14(sK15(sK14(sK14(powerset(X0))))))),X0) ),
inference(superposition,[status(thm)],[c_6998,c_7006]) ).
tcf(c_7507,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X0,X2) = X1 )
| ( apply(X0,sK5(X0,X2,sK2(relation_image(X0,X2),X1))) = sK2(relation_image(X0,X2),X1) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_5062,c_64]) ).
tcf(c_7508,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ empty(X1)
| ~ in(X0,sK2(X0,X1)) ),
inference(superposition,[status(thm)],[c_5062,c_68]) ).
tcf(c_7509,plain,
! [X0: $i,X1: $i] :
( element(sK2(X1,X0),X1)
| ( X0 = X1 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5062,c_67]) ).
tcf(c_7511,plain,
! [X0: $i,X1: $i] :
( ( singleton(X1) = X0 )
| ( sK2(singleton(X1),X0) = X1 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5062,c_82]) ).
tcf(c_7512,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| element(sK2(sK14(X1),X0),X1)
| ( sK14(X1) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5062,c_5328]) ).
tcf(c_7513,plain,
! [X0: $i,X1: $i] :
( element(sK2(sK15(powerset(X1)),X0),X1)
| ( sK15(powerset(X1)) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5062,c_5329]) ).
tcf(c_7514,plain,
! [X0: $i,X1: $i] :
( ( sK15(powerset(X1)) = X0 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5062,c_5201]) ).
tcf(c_7516,plain,
! [X0: $i,X1: $i] :
( element(sK2(sK15(sK14(powerset(X1))),X0),X1)
| ( sK15(sK14(powerset(X1))) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5062,c_6063]) ).
tcf(c_7517,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK14(powerset(X1))) = X0 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5062,c_6060]) ).
tcf(c_7518,plain,
! [X0: $i,X1: $i] :
( element(sK2(sK15(sK14(sK14(powerset(X1)))),X0),X1)
| ( sK15(sK14(sK14(powerset(X1)))) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5062,c_7006]) ).
tcf(c_7519,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK14(sK14(powerset(X1)))) = X0 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5062,c_7003]) ).
tcf(c_7568,plain,
! [X0: $i] :
( empty(singleton(X0))
| ~ empty(empty_set)
| ( singleton(X0) != empty_set ) ),
inference(instantiation,[status(thm)],[c_5799]) ).
tcf(c_7584,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ empty(X0)
| ~ in(sK2(X0,X1),X0) ),
inference(superposition,[status(thm)],[c_5063,c_55]) ).
tcf(c_7585,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X0,X2) = X1 )
| ( apply(X0,sK5(X0,X2,sK2(X1,relation_image(X0,X2)))) = sK2(X1,relation_image(X0,X2)) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_5063,c_64]) ).
tcf(c_7586,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ empty(X1)
| ~ in(X0,sK2(X1,X0)) ),
inference(superposition,[status(thm)],[c_5063,c_68]) ).
tcf(c_7587,plain,
! [X0: $i,X1: $i] :
( element(sK2(X0,X1),X1)
| ( X0 = X1 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5063,c_67]) ).
tcf(c_7589,plain,
! [X0: $i,X1: $i] :
( ( singleton(X1) = X0 )
| ( sK2(X0,singleton(X1)) = X1 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5063,c_82]) ).
tcf(c_7590,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| element(sK2(X0,sK14(X1)),X1)
| ( sK14(X1) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5063,c_5328]) ).
tcf(c_7591,plain,
! [X0: $i,X1: $i] :
( element(sK2(X0,sK15(powerset(X1))),X1)
| ( sK15(powerset(X1)) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5063,c_5329]) ).
tcf(c_7594,plain,
! [X0: $i,X1: $i] :
( element(sK2(X0,sK15(sK14(powerset(X1)))),X1)
| ( sK15(sK14(powerset(X1))) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5063,c_6063]) ).
tcf(c_7596,plain,
! [X0: $i,X1: $i] :
( element(sK2(X0,sK15(sK14(sK14(powerset(X1))))),X1)
| ( sK15(sK14(sK14(powerset(X1)))) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5063,c_7006]) ).
tcf(c_7682,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_7171]) ).
tcf(c_7683,plain,
sK15(sK14(sK14(powerset(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_7171]) ).
tcf(c_7684,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(sK15(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_7171]) ).
tcf(c_7685,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(sK15(sK14(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_7171]) ).
tcf(c_7686,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_7171]) ).
tcf(c_7707,plain,
( empty(sK14(sK14(powerset(empty_set))))
| ~ in(sK14(sK14(powerset(empty_set))),empty_set) ),
inference(superposition,[status(thm)],[c_7683,c_5145]) ).
tcf(c_7708,plain,
( empty(sK14(sK14(powerset(empty_set))))
| in(empty_set,sK14(sK14(powerset(empty_set)))) ),
inference(superposition,[status(thm)],[c_7683,c_5124]) ).
tcf(c_7709,plain,
element(empty_set,sK14(sK14(powerset(empty_set)))),
inference(superposition,[status(thm)],[c_7683,c_99]) ).
tcf(c_7738,plain,
! [X0: $i,X1: $i] :
( ( sK15(powerset(relation_dom(X0))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_5270]) ).
tcf(c_7739,plain,
! [X0: $i] :
( ( sK15(powerset(empty_set)) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_92,c_5270]) ).
tcf(c_7740,plain,
! [X0: $i,X1: $i] :
( ( sK15(powerset(sK15(powerset(X0)))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_5270]) ).
tcf(c_7741,plain,
! [X0: $i,X1: $i] :
( ( sK15(powerset(sK15(sK14(powerset(X0))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_5270]) ).
tcf(c_7742,plain,
! [X0: $i,X1: $i] :
( ( sK15(powerset(sK15(sK14(sK14(powerset(X0)))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_5270]) ).
tcf(c_7763,plain,
! [X0: $i,X1: $i] :
( in(sK2(X1,relation_image(X0,empty_set)),X1)
| ( relation_image(X0,empty_set) = X1 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_56,c_5411]) ).
tcf(c_7764,plain,
! [X0: $i,X1: $i] :
( in(sK2(relation_image(X0,empty_set),X1),X1)
| ( relation_image(X0,empty_set) = X1 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_56,c_5411]) ).
tcf(c_7765,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X0,X2) = relation_image(X1,empty_set) )
| ( apply(X0,sK4(X0,X2,relation_image(X1,empty_set))) = sK3(X0,X2,relation_image(X1,empty_set)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_60,c_5411]) ).
tcf(c_7766,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK4(X0,X2,relation_image(X1,empty_set)),relation_dom(X0))
| ( relation_image(X0,X2) = relation_image(X1,empty_set) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_58,c_5411]) ).
tcf(c_7767,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK4(X0,X2,relation_image(X1,empty_set)),X2)
| ( relation_image(X0,X2) = relation_image(X1,empty_set) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_59,c_5411]) ).
tcf(c_7768,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(X0,relation_image(X1,empty_set),X2),X2)
| ( relation_image(X0,relation_image(X1,empty_set)) = X2 )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_59,c_5411]) ).
tcf(c_7770,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,relation_image(X2,empty_set))) ),
inference(superposition,[status(thm)],[c_63,c_5411]) ).
tcf(c_7771,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X0,empty_set) = singleton(X1) )
| ( sK8(X1,relation_image(X0,empty_set)) = X1 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_80,c_5411]) ).
tcf(c_7772,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X0,empty_set) = X1 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_5062,c_5411]) ).
tcf(c_7777,plain,
! [X0: $i] :
( ( relation_image(X0,empty_set) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6288,c_5411]) ).
tcf(c_7778,plain,
! [X0: $i] :
( empty(relation_image(X0,empty_set))
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6998,c_5411]) ).
tcf(c_7917,plain,
! [X0: $i,X1: $i] :
( ( sK15(powerset(relation_image(X0,empty_set))) = X1 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_5270]) ).
tcf(c_7918,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(relation_image(X0,empty_set))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_7171]) ).
tcf(c_7919,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(relation_image(X0,empty_set))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_6193]) ).
tcf(c_7920,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(relation_image(X0,empty_set))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_6678]) ).
tcf(c_7921,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(relation_image(X0,empty_set))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_5581]) ).
tcf(c_7922,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(relation_image(X0,empty_set))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_5567]) ).
tcf(c_7923,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_image(X0,empty_set))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_5555]) ).
tcf(c_7924,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(relation_image(X0,empty_set))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_5302]) ).
tcf(c_7925,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(relation_image(X0,empty_set))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_5269]) ).
tcf(c_7926,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_image(X0,empty_set)) = X1 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_5189]) ).
tcf(c_7927,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_image(X0,empty_set)))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_6153]) ).
tcf(c_7928,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_image(X0,empty_set)))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_5300]) ).
tcf(c_7929,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_image(X0,empty_set)))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_5271]) ).
tcf(c_7930,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_image(X0,empty_set)))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_5245]) ).
tcf(c_7931,plain,
! [X0: $i] :
( ( sK15(powerset(relation_image(X0,empty_set))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_5272]) ).
tcf(c_7932,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_image(X0,empty_set))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_5110]) ).
tcf(c_7934,plain,
! [X0: $i] :
( ( relation_dom(relation_image(X0,empty_set)) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_5023]) ).
tcf(c_7936,plain,
! [X0: $i] :
( relation(relation_image(X0,empty_set))
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_87]) ).
tcf(c_7937,plain,
! [X0: $i] :
( function(relation_image(X0,empty_set))
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_77]) ).
tcf(c_8076,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(powerset(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_5557]) ).
tcf(c_8077,plain,
relation_dom(relation_dom(relation_dom(sK15(powerset(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_5557]) ).
tcf(c_8078,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_5557]) ).
tcf(c_8079,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_5557]) ).
tcf(c_8080,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_5557]) ).
tcf(c_8081,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(powerset(relation_image(X0,empty_set)))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_5557]) ).
tcf(c_8095,plain,
! [X0: $i,X1: $i] :
( ( singleton(X0) = singleton(X1) )
| ( X0 != X1 ) ),
inference(global_subsumption_just,[status(thm)],[c_5683,c_4390]) ).
tcf(c_8102,plain,
! [X0: $i] :
( in(sK15(sK15(powerset(X0))),X0)
| empty(sK15(powerset(X0))) ),
inference(global_subsumption_just,[status(thm)],[c_5648,c_5256,c_5648]) ).
tcf(c_8103,plain,
! [X0: $i] :
( empty(sK15(powerset(X0)))
| in(sK15(sK15(powerset(X0))),X0) ),
inference(renaming,[status(thm)],[c_8102]) ).
tcf(c_8109,plain,
( empty(sK15(powerset(empty_set)))
| in(sK15(empty_set),empty_set) ),
inference(superposition,[status(thm)],[c_5301,c_8103]) ).
tcf(c_8110,plain,
! [X0: $i,X1: $i] :
( empty(sK15(powerset(relation_image(X0,X1))))
| ( apply(X0,sK5(X0,X1,sK15(sK15(powerset(relation_image(X0,X1)))))) = sK15(sK15(powerset(relation_image(X0,X1)))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8103,c_64]) ).
tcf(c_8111,plain,
! [X0: $i] :
( empty(sK15(powerset(X0)))
| ~ in(X0,sK15(sK15(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_8103,c_68]) ).
tcf(c_8114,plain,
! [X0: $i] :
( empty(sK15(powerset(singleton(X0))))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 ) ),
inference(superposition,[status(thm)],[c_8103,c_82]) ).
tcf(c_8115,plain,
! [X0: $i] :
( empty(X0)
| empty(sK15(powerset(sK14(X0))))
| element(sK15(sK15(powerset(sK14(X0)))),X0) ),
inference(superposition,[status(thm)],[c_8103,c_5328]) ).
tcf(c_8116,plain,
! [X0: $i] :
( empty(sK15(powerset(sK15(powerset(X0)))))
| element(sK15(sK15(powerset(sK15(powerset(X0))))),X0) ),
inference(superposition,[status(thm)],[c_8103,c_5329]) ).
tcf(c_8117,plain,
! [X0: $i] :
( empty(sK15(powerset(sK15(powerset(X0)))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8103,c_5201]) ).
tcf(c_8118,plain,
empty(sK15(powerset(empty_set))),
inference(superposition,[status(thm)],[c_8103,c_5314]) ).
tcf(c_8119,plain,
! [X0: $i] :
( empty(sK15(powerset(relation_image(X0,empty_set))))
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8103,c_5411]) ).
tcf(c_8120,plain,
! [X0: $i] :
( empty(sK15(powerset(sK15(sK14(powerset(X0))))))
| element(sK15(sK15(powerset(sK15(sK14(powerset(X0)))))),X0) ),
inference(superposition,[status(thm)],[c_8103,c_6063]) ).
tcf(c_8121,plain,
! [X0: $i] :
( empty(sK15(powerset(sK15(sK14(powerset(X0))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8103,c_6060]) ).
tcf(c_8122,plain,
! [X0: $i] :
( empty(sK15(powerset(sK15(sK14(sK14(powerset(X0)))))))
| element(sK15(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))),X0) ),
inference(superposition,[status(thm)],[c_8103,c_7006]) ).
tcf(c_8123,plain,
! [X0: $i] :
( empty(sK15(powerset(sK15(sK14(sK14(powerset(X0)))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8103,c_7003]) ).
tcf(c_8125,plain,
( empty(empty_set)
| in(sK15(empty_set),empty_set) ),
inference(light_normalisation,[status(thm)],[c_8109,c_5301]) ).
tcf(c_8201,plain,
( empty(sK15(powerset(empty_set)))
| ~ in(empty_set,sK15(empty_set)) ),
inference(superposition,[status(thm)],[c_5301,c_8111]) ).
tcf(c_8202,plain,
( empty(empty_set)
| ~ in(empty_set,sK15(empty_set)) ),
inference(light_normalisation,[status(thm)],[c_8201,c_5301]) ).
tcf(c_8209,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(X0))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_6795]) ).
tcf(c_8210,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(empty_set)) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_92,c_6795]) ).
tcf(c_8211,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK15(powerset(X0)))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_6795]) ).
tcf(c_8212,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK15(sK14(powerset(X0))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_6795]) ).
tcf(c_8213,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK15(sK14(sK14(powerset(X0)))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_6795]) ).
tcf(c_8214,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_image(X0,empty_set))) = X1 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_6795]) ).
tcf(c_8236,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(relation_dom(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_6830]) ).
tcf(c_8237,plain,
relation_dom(relation_dom(sK15(powerset(relation_dom(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_6830]) ).
tcf(c_8238,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_6830]) ).
tcf(c_8239,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(sK14(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_6830]) ).
tcf(c_8240,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(sK14(sK14(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_6830]) ).
tcf(c_8241,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(relation_dom(relation_image(X0,empty_set)))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_6830]) ).
tcf(c_8285,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(powerset(sK15(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_6830]) ).
tcf(c_8286,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK15(powerset(sK15(powerset(X0)))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_6795]) ).
tcf(c_8287,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(powerset(sK15(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_5557]) ).
tcf(c_8288,plain,
! [X0: $i,X1: $i] :
( ( sK15(powerset(sK15(powerset(sK15(powerset(X0)))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_5270]) ).
tcf(c_8289,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(sK15(powerset(sK15(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_7171]) ).
tcf(c_8290,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(sK15(powerset(sK15(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_6193]) ).
tcf(c_8291,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(sK15(powerset(sK15(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_6678]) ).
tcf(c_8292,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(sK15(powerset(sK15(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_5581]) ).
tcf(c_8293,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(sK15(powerset(sK15(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_5567]) ).
tcf(c_8294,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_5555]) ).
tcf(c_8295,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(sK15(powerset(sK15(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_5302]) ).
tcf(c_8296,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(sK15(powerset(sK15(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_5269]) ).
tcf(c_8297,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK15(powerset(sK15(powerset(X0))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_5189]) ).
tcf(c_8298,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(powerset(sK15(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_6153]) ).
tcf(c_8299,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(powerset(sK15(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_5300]) ).
tcf(c_8300,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(powerset(sK15(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_5271]) ).
tcf(c_8307,plain,
! [X0: $i] :
( relation(sK15(powerset(sK15(powerset(X0)))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_87]) ).
tcf(c_8308,plain,
! [X0: $i] :
( function(sK15(powerset(sK15(powerset(X0)))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_77]) ).
tcf(c_8405,plain,
( empty(sK15(powerset(empty_set)))
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_6679,c_8121]) ).
tcf(c_8406,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_6830]) ).
tcf(c_8407,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(X0))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_6795]) ).
tcf(c_8408,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_5557]) ).
tcf(c_8409,plain,
! [X0: $i,X1: $i] :
( ( sK15(powerset(sK15(powerset(sK15(sK14(powerset(X0))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_5270]) ).
tcf(c_8410,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(sK15(powerset(sK15(sK14(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_7171]) ).
tcf(c_8411,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(sK15(powerset(sK15(sK14(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_6193]) ).
tcf(c_8412,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(sK15(powerset(sK15(sK14(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_6678]) ).
tcf(c_8413,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_5581]) ).
tcf(c_8414,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_5567]) ).
tcf(c_8415,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_5555]) ).
tcf(c_8416,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(sK15(powerset(sK15(sK14(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_5302]) ).
tcf(c_8417,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_5269]) ).
tcf(c_8418,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK15(powerset(sK15(sK14(powerset(X0)))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_5189]) ).
tcf(c_8419,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(powerset(sK15(sK14(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_6153]) ).
tcf(c_8420,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_5300]) ).
tcf(c_8421,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_5271]) ).
tcf(c_8428,plain,
! [X0: $i] :
( relation(sK15(powerset(sK15(sK14(powerset(X0))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_87]) ).
tcf(c_8429,plain,
! [X0: $i] :
( function(sK15(powerset(sK15(sK14(powerset(X0))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_77]) ).
tcf(c_8541,plain,
( relation(sK15(powerset(empty_set)))
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_6679,c_8428]) ).
tcf(c_8542,plain,
( relation(empty_set)
| ~ empty(empty_set) ),
inference(light_normalisation,[status(thm)],[c_8541,c_5301]) ).
tcf(c_8547,plain,
( function(sK15(powerset(empty_set)))
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_6679,c_8429]) ).
tcf(c_8548,plain,
( function(empty_set)
| ~ empty(empty_set) ),
inference(light_normalisation,[status(thm)],[c_8547,c_5301]) ).
tcf(c_8554,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_6830]) ).
tcf(c_8555,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(powerset(X0)))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_6795]) ).
tcf(c_8556,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_5557]) ).
tcf(c_8557,plain,
! [X0: $i,X1: $i] :
( ( sK15(powerset(sK15(powerset(sK15(sK14(sK14(powerset(X0)))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_5270]) ).
tcf(c_8558,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(sK15(powerset(sK15(sK14(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_7171]) ).
tcf(c_8559,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(sK15(powerset(sK15(sK14(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_6193]) ).
tcf(c_8560,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_6678]) ).
tcf(c_8561,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_5581]) ).
tcf(c_8562,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_5567]) ).
tcf(c_8563,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_5555]) ).
tcf(c_8564,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(sK15(powerset(sK15(sK14(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_5302]) ).
tcf(c_8565,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_5269]) ).
tcf(c_8566,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_5189]) ).
tcf(c_8567,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_6153]) ).
tcf(c_8568,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_5300]) ).
tcf(c_8569,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_5271]) ).
tcf(c_8576,plain,
! [X0: $i] :
( relation(sK15(powerset(sK15(sK14(sK14(powerset(X0)))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_87]) ).
tcf(c_8577,plain,
! [X0: $i] :
( function(sK15(powerset(sK15(sK14(sK14(powerset(X0)))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_77]) ).
tcf(c_8667,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(powerset(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_5569]) ).
tcf(c_8668,plain,
relation_dom(sK15(powerset(sK15(powerset(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_5569]) ).
tcf(c_8672,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(powerset(relation_image(X0,empty_set)))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_5569]) ).
tcf(c_8673,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(powerset(sK15(powerset(sK15(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_5569]) ).
tcf(c_8674,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(powerset(sK15(powerset(sK15(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_5569]) ).
tcf(c_8675,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(powerset(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_5569]) ).
tcf(c_8705,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(powerset(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_5583]) ).
tcf(c_8706,plain,
sK15(powerset(relation_dom(sK15(powerset(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_5583]) ).
tcf(c_8710,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(powerset(relation_image(X0,empty_set)))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_5583]) ).
tcf(c_8711,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(powerset(sK15(powerset(sK15(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_5583]) ).
tcf(c_8712,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_5583]) ).
tcf(c_8713,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_5583]) ).
tcf(c_8743,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(powerset(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_6190]) ).
tcf(c_8744,plain,
sK15(powerset(sK15(sK14(powerset(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_6190]) ).
tcf(c_8745,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(powerset(sK15(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_6190]) ).
tcf(c_8746,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(powerset(sK15(sK14(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_6190]) ).
tcf(c_8747,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_6190]) ).
tcf(c_8748,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(powerset(relation_image(X0,empty_set)))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_6190]) ).
tcf(c_8749,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(powerset(sK15(powerset(sK15(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_6190]) ).
tcf(c_8750,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(powerset(sK15(powerset(sK15(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_6190]) ).
tcf(c_8751,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(powerset(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_6190]) ).
tcf(c_8821,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(relation_dom(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_6854]) ).
tcf(c_8822,plain,
sK15(powerset(sK15(powerset(relation_dom(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_6854]) ).
tcf(c_8823,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(relation_dom(sK15(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_6854]) ).
tcf(c_8824,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(relation_dom(sK15(sK14(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_6854]) ).
tcf(c_8825,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(relation_dom(sK15(sK14(sK14(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_6854]) ).
tcf(c_8826,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(relation_dom(relation_image(X0,empty_set)))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_6854]) ).
tcf(c_8827,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(relation_dom(sK15(powerset(sK15(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_6854]) ).
tcf(c_8828,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_6854]) ).
tcf(c_8829,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_6854]) ).
tcf(c_8858,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_6885]) ).
tcf(c_8859,plain,
relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_6885]) ).
tcf(c_8860,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_6885]) ).
tcf(c_8861,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_6885]) ).
tcf(c_8862,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_6885]) ).
tcf(c_8863,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_image(X0,empty_set)))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_6885]) ).
tcf(c_8864,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_6885]) ).
tcf(c_8865,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_6885]) ).
tcf(c_8866,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_6885]) ).
tcf(c_8933,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(relation_dom(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_6903]) ).
tcf(c_8934,plain,
relation_dom(sK15(powerset(relation_dom(relation_dom(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_6903]) ).
tcf(c_8935,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_6903]) ).
tcf(c_8936,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(sK14(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_6903]) ).
tcf(c_8937,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(sK14(sK14(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_6903]) ).
tcf(c_8938,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(relation_dom(relation_image(X0,empty_set)))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_6903]) ).
tcf(c_8939,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(powerset(sK15(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_6903]) ).
tcf(c_8940,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_6903]) ).
tcf(c_8941,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_6903]) ).
tcf(c_8993,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(relation_dom(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_6936]) ).
tcf(c_8994,plain,
sK15(powerset(relation_dom(relation_dom(relation_dom(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_6936]) ).
tcf(c_8995,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(relation_dom(sK15(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_6936]) ).
tcf(c_8996,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_6936]) ).
tcf(c_8997,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_6936]) ).
tcf(c_8998,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(relation_dom(relation_image(X0,empty_set)))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_6936]) ).
tcf(c_8999,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_6936]) ).
tcf(c_9000,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_6936]) ).
tcf(c_9001,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_6936]) ).
tcf(c_9025,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(powerset(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_6191]) ).
tcf(c_9026,plain,
relation_dom(relation_dom(sK15(sK14(powerset(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_6191]) ).
tcf(c_9027,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(powerset(sK15(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_6191]) ).
tcf(c_9028,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_6191]) ).
tcf(c_9029,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_6191]) ).
tcf(c_9030,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(powerset(relation_image(X0,empty_set)))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_6191]) ).
tcf(c_9031,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(powerset(sK15(powerset(sK15(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_6191]) ).
tcf(c_9032,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(powerset(sK15(powerset(sK15(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_6191]) ).
tcf(c_9033,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(powerset(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_6191]) ).
tcf(c_9087,plain,
( element(sK15(empty_set),empty_set)
| empty(sK15(sK14(powerset(empty_set)))) ),
inference(superposition,[status(thm)],[c_6679,c_6604]) ).
tcf(c_9088,plain,
! [X0: $i] :
( empty(X0)
| empty(sK15(sK14(powerset(X0))))
| in(sK15(sK15(sK14(powerset(X0)))),X0) ),
inference(superposition,[status(thm)],[c_6604,c_66]) ).
tcf(c_9089,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| empty(sK15(sK14(powerset(powerset(X1)))))
| ~ in(X0,sK15(sK15(sK14(powerset(powerset(X1)))))) ),
inference(superposition,[status(thm)],[c_6604,c_94]) ).
tcf(c_9090,plain,
! [X0: $i,X1: $i] :
( empty(sK15(sK14(powerset(powerset(X1)))))
| ~ empty(X1)
| ~ in(X0,sK15(sK15(sK14(powerset(powerset(X1)))))) ),
inference(superposition,[status(thm)],[c_6604,c_93]) ).
tcf(c_9107,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(powerset(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_6680]) ).
tcf(c_9108,plain,
sK15(sK14(powerset(sK15(powerset(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_6680]) ).
tcf(c_9112,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(powerset(relation_image(X0,empty_set)))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_6680]) ).
tcf(c_9113,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(powerset(sK15(powerset(sK15(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_6680]) ).
tcf(c_9114,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(powerset(sK15(powerset(sK15(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_6680]) ).
tcf(c_9115,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(powerset(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_6680]) ).
tcf(c_9146,plain,
! [X0: $i] : in(sK2(singleton(X0),empty_set),singleton(X0)),
inference(global_subsumption_just,[status(thm)],[c_6877,c_92,c_78,c_6877,c_7568]) ).
tcf(c_9150,plain,
! [X0: $i] : ~ in(singleton(X0),sK2(singleton(X0),empty_set)),
inference(superposition,[status(thm)],[c_9146,c_68]) ).
tcf(c_9151,plain,
! [X0: $i] : element(sK2(singleton(X0),empty_set),singleton(X0)),
inference(superposition,[status(thm)],[c_9146,c_67]) ).
tcf(c_9153,plain,
! [X0: $i] : sK2(singleton(X0),empty_set) = X0,
inference(superposition,[status(thm)],[c_9146,c_82]) ).
tcf(c_9211,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(relation_dom(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_6951]) ).
tcf(c_9212,plain,
sK15(sK14(powerset(relation_dom(relation_dom(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_6951]) ).
tcf(c_9213,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(relation_dom(sK15(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_6951]) ).
tcf(c_9214,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(relation_dom(sK15(sK14(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_6951]) ).
tcf(c_9215,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(relation_dom(sK15(sK14(sK14(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_6951]) ).
tcf(c_9216,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(relation_dom(relation_image(X0,empty_set)))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_6951]) ).
tcf(c_9217,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(relation_dom(sK15(powerset(sK15(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_6951]) ).
tcf(c_9218,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_6951]) ).
tcf(c_9219,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_6951]) ).
tcf(c_9239,plain,
! [X0: $i] :
( empty(X0)
| element(sK15(sK14(sK14(sK14(X0)))),X0) ),
inference(global_subsumption_just,[status(thm)],[c_7045,c_98,c_7045]) ).
tcf(c_9246,plain,
! [X0: $i] :
( empty(X0)
| in(sK15(sK14(sK14(sK14(X0)))),X0) ),
inference(superposition,[status(thm)],[c_9239,c_66]) ).
tcf(c_9247,plain,
! [X0: $i,X1: $i] :
( empty(powerset(X1))
| element(X0,X1)
| ~ in(X0,sK15(sK14(sK14(sK14(powerset(X1)))))) ),
inference(superposition,[status(thm)],[c_9239,c_94]) ).
tcf(c_9248,plain,
! [X0: $i,X1: $i] :
( empty(powerset(X1))
| ~ empty(X1)
| ~ in(X0,sK15(sK14(sK14(sK14(powerset(X1)))))) ),
inference(superposition,[status(thm)],[c_9239,c_93]) ).
tcf(c_9251,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ in(X0,sK15(sK14(sK14(sK14(powerset(X1)))))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9248,c_100]) ).
tcf(c_9254,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| ~ in(X0,sK15(sK14(sK14(sK14(powerset(X1)))))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9247,c_100]) ).
tcf(c_9263,plain,
! [X0: $i,X1: $i] :
( empty(relation_image(X0,X1))
| ( apply(X0,sK5(X0,X1,sK15(sK14(sK14(sK14(relation_image(X0,X1))))))) = sK15(sK14(sK14(sK14(relation_image(X0,X1))))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_9246,c_64]) ).
tcf(c_9264,plain,
! [X0: $i] :
( empty(X0)
| ~ in(X0,sK15(sK14(sK14(sK14(X0))))) ),
inference(superposition,[status(thm)],[c_9246,c_68]) ).
tcf(c_9267,plain,
! [X0: $i] :
( empty(singleton(X0))
| ( sK15(sK14(sK14(sK14(singleton(X0))))) = X0 ) ),
inference(superposition,[status(thm)],[c_9246,c_82]) ).
tcf(c_9268,plain,
! [X0: $i] :
( empty(X0)
| empty(sK14(X0))
| element(sK15(sK14(sK14(sK14(sK14(X0))))),X0) ),
inference(superposition,[status(thm)],[c_9246,c_5328]) ).
tcf(c_9269,plain,
! [X0: $i] :
( empty(sK15(powerset(X0)))
| element(sK15(sK14(sK14(sK14(sK15(powerset(X0)))))),X0) ),
inference(superposition,[status(thm)],[c_9246,c_5329]) ).
tcf(c_9273,plain,
! [X0: $i] :
( empty(sK15(sK14(powerset(X0))))
| element(sK15(sK14(sK14(sK14(sK15(sK14(powerset(X0))))))),X0) ),
inference(superposition,[status(thm)],[c_9246,c_6063]) ).
tcf(c_9275,plain,
! [X0: $i] :
( empty(sK15(sK14(sK14(powerset(X0)))))
| element(sK15(sK14(sK14(sK14(sK15(sK14(sK14(powerset(X0)))))))),X0) ),
inference(superposition,[status(thm)],[c_9246,c_7006]) ).
tcf(c_9279,plain,
! [X0: $i] : sK15(sK14(sK14(sK14(singleton(X0))))) = X0,
inference(forward_subsumption_resolution,[status(thm)],[c_9267,c_78]) ).
tcf(c_9360,plain,
! [X0: $i] :
( empty(sK14(sK14(sK14(singleton(X0)))))
| ~ in(sK14(sK14(sK14(singleton(X0)))),X0) ),
inference(superposition,[status(thm)],[c_9279,c_5145]) ).
tcf(c_9361,plain,
! [X0: $i] :
( empty(sK14(sK14(sK14(singleton(X0)))))
| in(X0,sK14(sK14(sK14(singleton(X0))))) ),
inference(superposition,[status(thm)],[c_9279,c_5124]) ).
tcf(c_9362,plain,
! [X0: $i] : element(X0,sK14(sK14(sK14(singleton(X0))))),
inference(superposition,[status(thm)],[c_9279,c_99]) ).
tcf(c_9411,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(relation_dom(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_7140]) ).
tcf(c_9412,plain,
relation_dom(sK15(sK14(powerset(relation_dom(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_7140]) ).
tcf(c_9413,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(relation_dom(sK15(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_7140]) ).
tcf(c_9414,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(relation_dom(sK15(sK14(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_7140]) ).
tcf(c_9415,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(relation_dom(sK15(sK14(sK14(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_7140]) ).
tcf(c_9416,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(relation_dom(relation_image(X0,empty_set)))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_7140]) ).
tcf(c_9417,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(relation_dom(sK15(powerset(sK15(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_7140]) ).
tcf(c_9418,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(relation_dom(sK15(powerset(sK15(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_7140]) ).
tcf(c_9419,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_7140]) ).
tcf(c_9448,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,X1)
| ( powerset(X1) = X2 )
| ~ empty(X2)
| ~ in(X0,sK2(powerset(X1),X2)) ),
inference(superposition,[status(thm)],[c_7509,c_94]) ).
tcf(c_9449,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( powerset(X1) = X2 )
| ~ empty(X2)
| ~ empty(X1)
| ~ in(X0,sK2(powerset(X1),X2)) ),
inference(superposition,[status(thm)],[c_7509,c_93]) ).
tcf(c_9467,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,X2)
| ( powerset(X2) = X1 )
| ~ empty(X1)
| ~ in(X0,sK2(X1,powerset(X2))) ),
inference(superposition,[status(thm)],[c_7587,c_94]) ).
tcf(c_9468,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( powerset(X2) = X1 )
| ~ empty(X2)
| ~ empty(X1)
| ~ in(X0,sK2(X1,powerset(X2))) ),
inference(superposition,[status(thm)],[c_7587,c_93]) ).
tcf(c_9481,plain,
( empty(sK15(powerset(empty_set)))
| element(sK15(sK14(sK14(empty_set))),empty_set) ),
inference(superposition,[status(thm)],[c_5301,c_7046]) ).
tcf(c_9482,plain,
! [X0: $i] :
( empty(X0)
| empty(sK15(powerset(X0)))
| in(sK15(sK14(sK14(sK15(powerset(X0))))),X0) ),
inference(superposition,[status(thm)],[c_7046,c_66]) ).
tcf(c_9483,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| empty(sK15(powerset(powerset(X1))))
| ~ in(X0,sK15(sK14(sK14(sK15(powerset(powerset(X1))))))) ),
inference(superposition,[status(thm)],[c_7046,c_94]) ).
tcf(c_9484,plain,
! [X0: $i,X1: $i] :
( empty(sK15(powerset(powerset(X1))))
| ~ empty(X1)
| ~ in(X0,sK15(sK14(sK14(sK15(powerset(powerset(X1))))))) ),
inference(superposition,[status(thm)],[c_7046,c_93]) ).
tcf(c_9485,plain,
( empty(empty_set)
| element(sK15(sK14(sK14(empty_set))),empty_set) ),
inference(light_normalisation,[status(thm)],[c_9481,c_5301]) ).
tcf(c_9505,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(powerset(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_7256]) ).
tcf(c_9506,plain,
relation_dom(sK15(sK14(sK14(powerset(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_7256]) ).
tcf(c_9507,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(powerset(sK15(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_7256]) ).
tcf(c_9508,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(powerset(sK15(sK14(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_7256]) ).
tcf(c_9509,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(powerset(sK15(sK14(sK14(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_7256]) ).
tcf(c_9510,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(powerset(relation_image(X0,empty_set)))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_7256]) ).
tcf(c_9511,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(powerset(sK15(powerset(sK15(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_7256]) ).
tcf(c_9512,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(powerset(sK15(powerset(sK15(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_7256]) ).
tcf(c_9513,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(powerset(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_7256]) ).
tcf(c_9556,plain,
! [X0: $i] : in(sK2(empty_set,singleton(X0)),singleton(X0)),
inference(global_subsumption_just,[status(thm)],[c_7394,c_92,c_78,c_7394,c_7568]) ).
tcf(c_9560,plain,
! [X0: $i] :
( ( singleton(X0) = empty_set )
| ~ in(sK2(empty_set,singleton(X0)),empty_set) ),
inference(superposition,[status(thm)],[c_9556,c_55]) ).
tcf(c_9561,plain,
! [X0: $i] : ~ in(singleton(X0),sK2(empty_set,singleton(X0))),
inference(superposition,[status(thm)],[c_9556,c_68]) ).
tcf(c_9562,plain,
! [X0: $i] : element(sK2(empty_set,singleton(X0)),singleton(X0)),
inference(superposition,[status(thm)],[c_9556,c_67]) ).
tcf(c_9564,plain,
! [X0: $i] : sK2(empty_set,singleton(X0)) = X0,
inference(superposition,[status(thm)],[c_9556,c_82]) ).
tcf(c_9586,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(relation_dom(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_7682]) ).
tcf(c_9587,plain,
sK15(sK14(sK14(powerset(relation_dom(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_7682]) ).
tcf(c_9588,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(relation_dom(sK15(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_7682]) ).
tcf(c_9589,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(relation_dom(sK15(sK14(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_7682]) ).
tcf(c_9590,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(relation_dom(sK15(sK14(sK14(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_7682]) ).
tcf(c_9591,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(relation_dom(relation_image(X0,empty_set)))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_7682]) ).
tcf(c_9592,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(relation_dom(sK15(powerset(sK15(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_7682]) ).
tcf(c_9593,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(relation_dom(sK15(powerset(sK15(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_7682]) ).
tcf(c_9594,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_7682]) ).
tcf(c_9654,plain,
( ( relation_image(sK1,empty_set) = empty_set )
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_52,c_7777]) ).
tcf(c_9655,plain,
( ( relation_image(sK7,empty_set) = empty_set )
| ~ relation(sK7) ),
inference(superposition,[status(thm)],[c_76,c_7777]) ).
tcf(c_9656,plain,
! [X0: $i] :
( ( relation_image(relation_dom(X0),empty_set) = empty_set )
| ~ empty(X0)
| ~ relation(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_5003,c_7777]) ).
tcf(c_9657,plain,
( ( relation_image(empty_set,empty_set) = empty_set )
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_4985,c_7777]) ).
tcf(c_9658,plain,
! [X0: $i] :
( ( relation_image(sK15(powerset(X0)),empty_set) = empty_set )
| ~ empty(X0)
| ~ relation(sK15(powerset(X0))) ),
inference(superposition,[status(thm)],[c_5274,c_7777]) ).
tcf(c_9659,plain,
! [X0: $i] :
( ( relation_image(sK15(sK14(powerset(X0))),empty_set) = empty_set )
| ~ empty(X0)
| ~ relation(sK15(sK14(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_6196,c_7777]) ).
tcf(c_9660,plain,
! [X0: $i] :
( ( relation_image(sK15(sK14(sK14(powerset(X0)))),empty_set) = empty_set )
| ~ empty(X0)
| ~ relation(sK15(sK14(sK14(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_7259,c_7777]) ).
tcf(c_9661,plain,
! [X0: $i] :
( ( relation_image(relation_image(X0,empty_set),empty_set) = empty_set )
| ~ function(X0)
| ~ relation(X0)
| ~ relation(relation_image(X0,empty_set)) ),
inference(superposition,[status(thm)],[c_7937,c_7777]) ).
tcf(c_9662,plain,
! [X0: $i] :
( ( relation_image(sK15(powerset(sK15(powerset(X0)))),empty_set) = empty_set )
| ~ empty(X0)
| ~ relation(sK15(powerset(sK15(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_8308,c_7777]) ).
tcf(c_9663,plain,
! [X0: $i] :
( ( relation_image(sK15(powerset(sK15(sK14(powerset(X0))))),empty_set) = empty_set )
| ~ empty(X0)
| ~ relation(sK15(powerset(sK15(sK14(powerset(X0)))))) ),
inference(superposition,[status(thm)],[c_8429,c_7777]) ).
tcf(c_9664,plain,
! [X0: $i] :
( ( relation_image(sK15(powerset(sK15(sK14(sK14(powerset(X0)))))),empty_set) = empty_set )
| ~ empty(X0)
| ~ relation(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))) ),
inference(superposition,[status(thm)],[c_8577,c_7777]) ).
tcf(c_9665,plain,
relation_image(sK7,empty_set) = empty_set,
inference(forward_subsumption_resolution,[status(thm)],[c_9655,c_75]) ).
tcf(c_9666,plain,
relation_image(sK1,empty_set) = empty_set,
inference(forward_subsumption_resolution,[status(thm)],[c_9654,c_51]) ).
tcf(c_9838,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( singleton(X1) = empty_set )
| ( relation_image(empty_set,X2) = singleton(X1) )
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ in(X0,X2)
| ~ in(X0,relation_dom(empty_set))
| ~ in(sK3(empty_set,X2,singleton(X1)),singleton(X1))
| ( apply(empty_set,X0) != X1 ) ),
inference(superposition,[status(thm)],[c_6726,c_57]) ).
tcf(c_9839,plain,
! [X0: $i,X1: $i] :
( in(X1,singleton(X1))
| ( singleton(X1) = empty_set )
| ( relation_image(empty_set,X0) = singleton(X1) )
| ( apply(empty_set,sK4(empty_set,X0,singleton(X1))) = sK3(empty_set,X0,singleton(X1)) )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_6726,c_60]) ).
tcf(c_9840,plain,
! [X0: $i,X1: $i] :
( in(X1,singleton(X1))
| in(sK4(empty_set,X0,singleton(X1)),relation_dom(empty_set))
| ( singleton(X1) = empty_set )
| ( relation_image(empty_set,X0) = singleton(X1) )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_6726,c_58]) ).
tcf(c_9841,plain,
! [X0: $i,X1: $i] :
( in(X1,singleton(X1))
| in(sK4(empty_set,X0,singleton(X1)),X0)
| ( singleton(X1) = empty_set )
| ( relation_image(empty_set,X0) = singleton(X1) )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_6726,c_59]) ).
tcf(c_9845,plain,
! [X0: $i,X1: $i] :
( in(X0,singleton(X0))
| in(sK4(empty_set,X1,singleton(X0)),X1)
| ( singleton(X0) = empty_set )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(light_normalisation,[status(thm)],[c_9841,c_6000]) ).
tcf(c_9846,plain,
! [X0: $i,X1: $i] :
( in(X0,singleton(X0))
| in(sK4(empty_set,X1,singleton(X0)),empty_set)
| ( singleton(X0) = empty_set )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(light_normalisation,[status(thm)],[c_9840,c_5111,c_6000]) ).
tcf(c_9847,plain,
! [X0: $i,X1: $i] :
( in(X1,singleton(X1))
| ( singleton(X1) = empty_set )
| ( apply(empty_set,sK4(empty_set,X0,singleton(X1))) = sK3(empty_set,X0,singleton(X1)) )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(light_normalisation,[status(thm)],[c_9839,c_6000]) ).
tcf(c_9848,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( singleton(X1) = empty_set )
| ( relation_image(empty_set,X2) = singleton(X1) )
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ in(X0,empty_set)
| ~ in(X0,X2)
| ~ in(sK3(empty_set,X2,singleton(X1)),singleton(X1))
| ( apply(empty_set,X0) != X1 ) ),
inference(light_normalisation,[status(thm)],[c_9838,c_5111]) ).
tcf(c_9854,plain,
! [X0: $i,X1: $i] :
( in(sK2(X1,sK15(sK14(sK14(sK14(powerset(X0)))))),X1)
| ( sK15(sK14(sK14(sK14(powerset(X0))))) = X1 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_56,c_9251]) ).
tcf(c_9855,plain,
! [X0: $i,X1: $i] :
( in(sK2(sK15(sK14(sK14(sK14(powerset(X0))))),X1),X1)
| ( sK15(sK14(sK14(sK14(powerset(X0))))) = X1 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_56,c_9251]) ).
tcf(c_9856,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK15(sK14(sK14(sK14(powerset(X1))))) = relation_image(X0,X2) )
| ( apply(X0,sK4(X0,X2,sK15(sK14(sK14(sK14(powerset(X1))))))) = sK3(X0,X2,sK15(sK14(sK14(sK14(powerset(X1)))))) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_60,c_9251]) ).
tcf(c_9857,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK4(X0,X2,sK15(sK14(sK14(sK14(powerset(X1)))))),relation_dom(X0))
| ( sK15(sK14(sK14(sK14(powerset(X1))))) = relation_image(X0,X2) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_58,c_9251]) ).
tcf(c_9858,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK4(X0,X2,sK15(sK14(sK14(sK14(powerset(X1)))))),X2)
| ( sK15(sK14(sK14(sK14(powerset(X1))))) = relation_image(X0,X2) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_59,c_9251]) ).
tcf(c_9859,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(X0,sK15(sK14(sK14(sK14(powerset(X1))))),X2),X2)
| ( relation_image(X0,sK15(sK14(sK14(sK14(powerset(X1)))))) = X2 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_59,c_9251]) ).
tcf(c_9860,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(X2)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,sK15(sK14(sK14(sK14(powerset(X2))))))) ),
inference(superposition,[status(thm)],[c_63,c_9251]) ).
tcf(c_9861,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK14(sK14(sK14(powerset(X0))))) = singleton(X1) )
| ( sK8(X1,sK15(sK14(sK14(sK14(powerset(X0)))))) = X1 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_80,c_9251]) ).
tcf(c_9862,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK14(sK14(sK14(powerset(X1))))) = X0 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5062,c_9251]) ).
tcf(c_9866,plain,
! [X0: $i] :
( empty(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8103,c_9251]) ).
tcf(c_9868,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6288,c_9251]) ).
tcf(c_9869,plain,
! [X0: $i] :
( empty(sK15(sK14(sK14(sK14(powerset(X0))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6998,c_9251]) ).
tcf(c_10008,plain,
! [X0: $i,X1: $i] :
( element(sK2(X0,sK15(sK14(sK14(sK14(powerset(X1)))))),X1)
| ( sK15(sK14(sK14(sK14(powerset(X1))))) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5063,c_9254]) ).
tcf(c_10009,plain,
! [X0: $i,X1: $i] :
( element(sK2(X1,sK15(sK14(sK14(sK14(powerset(X0)))))),X0)
| in(sK2(X1,sK15(sK14(sK14(sK14(powerset(X0)))))),X1)
| ( sK15(sK14(sK14(sK14(powerset(X0))))) = X1 ) ),
inference(superposition,[status(thm)],[c_56,c_9254]) ).
tcf(c_10010,plain,
! [X0: $i,X1: $i] :
( element(sK2(sK15(sK14(sK14(sK14(powerset(X0))))),X1),X0)
| in(sK2(sK15(sK14(sK14(sK14(powerset(X0))))),X1),X1)
| ( sK15(sK14(sK14(sK14(powerset(X0))))) = X1 ) ),
inference(superposition,[status(thm)],[c_56,c_9254]) ).
tcf(c_10011,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK3(X0,X1,sK15(sK14(sK14(sK14(powerset(X2)))))),X2)
| ( sK15(sK14(sK14(sK14(powerset(X2))))) = relation_image(X0,X1) )
| ( apply(X0,sK4(X0,X1,sK15(sK14(sK14(sK14(powerset(X2))))))) = sK3(X0,X1,sK15(sK14(sK14(sK14(powerset(X2)))))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_60,c_9254]) ).
tcf(c_10012,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK3(X0,X2,sK15(sK14(sK14(sK14(powerset(X1)))))),X1)
| in(sK4(X0,X2,sK15(sK14(sK14(sK14(powerset(X1)))))),relation_dom(X0))
| ( sK15(sK14(sK14(sK14(powerset(X1))))) = relation_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_58,c_9254]) ).
tcf(c_10013,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK3(X0,X2,sK15(sK14(sK14(sK14(powerset(X1)))))),X1)
| in(sK4(X0,X2,sK15(sK14(sK14(sK14(powerset(X1)))))),X2)
| ( sK15(sK14(sK14(sK14(powerset(X1))))) = relation_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_59,c_9254]) ).
tcf(c_10014,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK4(X0,sK15(sK14(sK14(sK14(powerset(X1))))),X2),X1)
| in(sK3(X0,sK15(sK14(sK14(sK14(powerset(X1))))),X2),X2)
| ( relation_image(X0,sK15(sK14(sK14(sK14(powerset(X1)))))) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_59,c_9254]) ).
tcf(c_10015,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK5(X1,sK15(sK14(sK14(sK14(powerset(X2))))),X0),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,sK15(sK14(sK14(sK14(powerset(X2))))))) ),
inference(superposition,[status(thm)],[c_63,c_9254]) ).
tcf(c_10016,plain,
! [X0: $i,X1: $i] :
( element(sK8(X0,sK15(sK14(sK14(sK14(powerset(X1)))))),X1)
| ( sK15(sK14(sK14(sK14(powerset(X1))))) = singleton(X0) )
| ( sK8(X0,sK15(sK14(sK14(sK14(powerset(X1)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_80,c_9254]) ).
tcf(c_10017,plain,
! [X0: $i,X1: $i] :
( element(sK2(sK15(sK14(sK14(sK14(powerset(X1))))),X0),X1)
| ( sK15(sK14(sK14(sK14(powerset(X1))))) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5062,c_9254]) ).
tcf(c_10018,plain,
! [X0: $i] :
( empty(sK15(sK14(sK14(sK14(powerset(X0))))))
| element(sK15(sK15(sK14(sK14(sK14(powerset(X0)))))),X0) ),
inference(superposition,[status(thm)],[c_5124,c_9254]) ).
tcf(c_10019,plain,
! [X0: $i] :
( element(sK2(sK15(sK14(sK14(sK14(powerset(X0))))),empty_set),X0)
| ( sK15(sK14(sK14(sK14(powerset(X0))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5409,c_9254]) ).
tcf(c_10020,plain,
! [X0: $i] :
( element(sK2(empty_set,sK15(sK14(sK14(sK14(powerset(X0)))))),X0)
| ( sK15(sK14(sK14(sK14(powerset(X0))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5410,c_9254]) ).
tcf(c_10021,plain,
! [X0: $i] :
( empty(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))
| element(sK15(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))),X0) ),
inference(superposition,[status(thm)],[c_8103,c_9254]) ).
tcf(c_10022,plain,
! [X0: $i] :
( empty(sK15(sK14(sK14(sK14(powerset(X0))))))
| element(sK15(sK14(sK15(sK14(sK14(sK14(powerset(X0))))))),X0) ),
inference(superposition,[status(thm)],[c_6055,c_9254]) ).
tcf(c_10023,plain,
! [X0: $i,X1: $i] :
( element(sK3(empty_set,X1,sK15(sK14(sK14(sK14(powerset(X0)))))),X0)
| ( sK15(sK14(sK14(sK14(powerset(X0))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_6288,c_9254]) ).
tcf(c_10024,plain,
! [X0: $i] :
( empty(sK15(sK14(sK14(sK14(powerset(X0))))))
| element(sK15(sK14(sK14(sK15(sK14(sK14(sK14(powerset(X0)))))))),X0) ),
inference(superposition,[status(thm)],[c_6998,c_9254]) ).
tcf(c_10025,plain,
! [X0: $i] :
( empty(sK15(sK14(sK14(sK14(powerset(X0))))))
| element(sK15(sK14(sK14(sK14(sK15(sK14(sK14(sK14(powerset(X0))))))))),X0) ),
inference(superposition,[status(thm)],[c_9246,c_9254]) ).
tcf(c_10103,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(relation_dom(sK15(sK14(sK14(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_7682]) ).
tcf(c_10104,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_7256]) ).
tcf(c_10105,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(relation_dom(sK15(sK14(sK14(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_7140]) ).
tcf(c_10106,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(relation_dom(sK15(sK14(sK14(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_6951]) ).
tcf(c_10107,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_6680]) ).
tcf(c_10108,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_6191]) ).
tcf(c_10109,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_6936]) ).
tcf(c_10110,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(sK14(sK14(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_6903]) ).
tcf(c_10111,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_6885]) ).
tcf(c_10112,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(relation_dom(sK15(sK14(sK14(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_6854]) ).
tcf(c_10113,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_6190]) ).
tcf(c_10114,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_5583]) ).
tcf(c_10115,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_5569]) ).
tcf(c_10116,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(sK14(sK14(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_6830]) ).
tcf(c_10117,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK15(sK14(sK14(sK14(powerset(X0))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_6795]) ).
tcf(c_10118,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_5557]) ).
tcf(c_10119,plain,
! [X0: $i,X1: $i] :
( ( sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_5270]) ).
tcf(c_10120,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_7171]) ).
tcf(c_10121,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_6193]) ).
tcf(c_10122,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(sK15(sK14(sK14(sK14(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_6678]) ).
tcf(c_10123,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(sK15(sK14(sK14(sK14(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_5581]) ).
tcf(c_10124,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(sK15(sK14(sK14(sK14(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_5567]) ).
tcf(c_10125,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(sK14(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_5555]) ).
tcf(c_10126,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_5302]) ).
tcf(c_10127,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_5269]) ).
tcf(c_10128,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK15(sK14(sK14(sK14(powerset(X0)))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_5189]) ).
tcf(c_10129,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_6153]) ).
tcf(c_10130,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(sK14(sK14(sK14(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_5300]) ).
tcf(c_10131,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_5271]) ).
tcf(c_10132,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(sK14(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_5245]) ).
tcf(c_10133,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_5272]) ).
tcf(c_10134,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(sK14(sK14(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_5110]) ).
tcf(c_10135,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK14(sK14(sK14(powerset(X0))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_53]) ).
tcf(c_10136,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(sK14(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_5023]) ).
tcf(c_10138,plain,
! [X0: $i] :
( relation(sK15(sK14(sK14(sK14(powerset(X0))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_87]) ).
tcf(c_10139,plain,
! [X0: $i] :
( function(sK15(sK14(sK14(sK14(powerset(X0))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_77]) ).
tcf(c_10327,plain,
! [X0: $i] :
( ( relation_image(sK15(sK14(sK14(sK14(powerset(X0))))),empty_set) = empty_set )
| ~ empty(X0)
| ~ relation(sK15(sK14(sK14(sK14(powerset(X0)))))) ),
inference(superposition,[status(thm)],[c_10139,c_7777]) ).
tcf(c_10337,plain,
( empty(sK15(powerset(empty_set)))
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_6000,c_8119]) ).
tcf(c_10338,plain,
( empty(sK15(powerset(empty_set)))
| ~ function(sK1)
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_9666,c_8119]) ).
tcf(c_10339,plain,
( empty(sK15(powerset(empty_set)))
| ~ function(sK7)
| ~ relation(sK7) ),
inference(superposition,[status(thm)],[c_9665,c_8119]) ).
tcf(c_10340,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(relation_dom(sK15(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_7682]) ).
tcf(c_10341,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(powerset(sK15(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_7256]) ).
tcf(c_10342,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(relation_dom(sK15(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_7140]) ).
tcf(c_10343,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(relation_dom(sK15(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_6951]) ).
tcf(c_10344,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(powerset(sK15(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_6680]) ).
tcf(c_10345,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(powerset(sK15(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_6191]) ).
tcf(c_10346,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(relation_dom(sK15(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_6936]) ).
tcf(c_10347,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_6903]) ).
tcf(c_10348,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_6885]) ).
tcf(c_10349,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(relation_dom(sK15(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_6854]) ).
tcf(c_10350,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(powerset(sK15(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_6190]) ).
tcf(c_10351,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(powerset(sK15(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_5583]) ).
tcf(c_10352,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(powerset(sK15(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_5569]) ).
tcf(c_10353,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_6830]) ).
tcf(c_10354,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK15(powerset(relation_image(X0,empty_set))))) = X1 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_6795]) ).
tcf(c_10355,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_5557]) ).
tcf(c_10356,plain,
! [X0: $i,X1: $i] :
( ( sK15(powerset(sK15(powerset(relation_image(X0,empty_set))))) = X1 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_5270]) ).
tcf(c_10357,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(sK15(powerset(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_7171]) ).
tcf(c_10358,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(sK15(powerset(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_6193]) ).
tcf(c_10359,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(sK15(powerset(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_6678]) ).
tcf(c_10360,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(sK15(powerset(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_5581]) ).
tcf(c_10361,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(sK15(powerset(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_5567]) ).
tcf(c_10362,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_5555]) ).
tcf(c_10363,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(sK15(powerset(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_5302]) ).
tcf(c_10364,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(sK15(powerset(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_5269]) ).
tcf(c_10365,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK15(powerset(relation_image(X0,empty_set)))) = X1 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_5189]) ).
tcf(c_10375,plain,
! [X0: $i] :
( relation(sK15(powerset(relation_image(X0,empty_set))))
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_87]) ).
tcf(c_10376,plain,
! [X0: $i] :
( function(sK15(powerset(relation_image(X0,empty_set))))
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_77]) ).
tcf(c_10377,plain,
( empty(empty_set)
| ~ function(sK7)
| ~ relation(sK7) ),
inference(light_normalisation,[status(thm)],[c_10339,c_5301]) ).
tcf(c_10378,plain,
( empty(empty_set)
| ~ function(sK1)
| ~ relation(sK1) ),
inference(light_normalisation,[status(thm)],[c_10338,c_5301]) ).
tcf(c_10379,plain,
( empty(empty_set)
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(light_normalisation,[status(thm)],[c_10337,c_5301]) ).
tcf(c_10713,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_7682]) ).
tcf(c_10714,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(powerset(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_7256]) ).
tcf(c_10715,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_7140]) ).
tcf(c_10716,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_6951]) ).
tcf(c_10717,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(powerset(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_6680]) ).
tcf(c_10718,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(powerset(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_6191]) ).
tcf(c_10719,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_6936]) ).
tcf(c_10720,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_6903]) ).
tcf(c_10721,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_6885]) ).
tcf(c_10722,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_6854]) ).
tcf(c_10723,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(powerset(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_6190]) ).
tcf(c_10724,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_5583]) ).
tcf(c_10725,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(powerset(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_5569]) ).
tcf(c_10726,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_6830]) ).
tcf(c_10727,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_6795]) ).
tcf(c_10728,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_5557]) ).
tcf(c_10729,plain,
! [X0: $i,X1: $i] :
( ( sK15(powerset(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_5270]) ).
tcf(c_10730,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_7171]) ).
tcf(c_10731,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_6193]) ).
tcf(c_10732,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_6678]) ).
tcf(c_10733,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_5581]) ).
tcf(c_10734,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_5567]) ).
tcf(c_10735,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_5555]) ).
tcf(c_10736,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_5302]) ).
tcf(c_10737,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_5269]) ).
tcf(c_10738,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_5189]) ).
tcf(c_10748,plain,
! [X0: $i] :
( relation(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_87]) ).
tcf(c_10749,plain,
! [X0: $i] :
( function(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_77]) ).
tcf(c_10887,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(powerset(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_9868]) ).
tcf(c_10888,plain,
sK15(sK14(sK14(sK14(powerset(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_9868]) ).
tcf(c_10889,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(powerset(sK15(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_9868]) ).
tcf(c_10890,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(powerset(sK15(sK14(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_9868]) ).
tcf(c_10891,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(powerset(sK15(sK14(sK14(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_9868]) ).
tcf(c_10892,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(powerset(relation_image(X0,empty_set)))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_9868]) ).
tcf(c_10893,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(powerset(sK15(powerset(sK15(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_9868]) ).
tcf(c_10894,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(powerset(sK15(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_9868]) ).
tcf(c_10895,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(powerset(sK15(powerset(sK15(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_9868]) ).
tcf(c_10896,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(powerset(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_9868]) ).
tcf(c_10897,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_9868]) ).
tcf(c_10898,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(powerset(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_9868]) ).
tcf(c_10950,plain,
( empty(sK14(sK14(sK14(powerset(empty_set)))))
| ~ in(sK14(sK14(sK14(powerset(empty_set)))),empty_set) ),
inference(superposition,[status(thm)],[c_10888,c_5145]) ).
tcf(c_10951,plain,
( empty(sK14(sK14(sK14(powerset(empty_set)))))
| in(empty_set,sK14(sK14(sK14(powerset(empty_set))))) ),
inference(superposition,[status(thm)],[c_10888,c_5124]) ).
tcf(c_10952,plain,
element(empty_set,sK14(sK14(sK14(powerset(empty_set))))),
inference(superposition,[status(thm)],[c_10888,c_99]) ).
tcf(c_10977,plain,
( relation(sK15(powerset(empty_set)))
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_6000,c_10375]) ).
tcf(c_10978,plain,
( relation(sK15(powerset(empty_set)))
| ~ function(sK1)
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_9666,c_10375]) ).
tcf(c_10979,plain,
( relation(sK15(powerset(empty_set)))
| ~ function(sK7)
| ~ relation(sK7) ),
inference(superposition,[status(thm)],[c_9665,c_10375]) ).
tcf(c_10980,plain,
( relation(empty_set)
| ~ function(sK7)
| ~ relation(sK7) ),
inference(light_normalisation,[status(thm)],[c_10979,c_5301]) ).
tcf(c_10981,plain,
( relation(empty_set)
| ~ function(sK1)
| ~ relation(sK1) ),
inference(light_normalisation,[status(thm)],[c_10978,c_5301]) ).
tcf(c_10989,plain,
( function(sK15(powerset(empty_set)))
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_6000,c_10376]) ).
tcf(c_10990,plain,
( function(sK15(powerset(empty_set)))
| ~ function(sK1)
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_9666,c_10376]) ).
tcf(c_10991,plain,
( function(sK15(powerset(empty_set)))
| ~ function(sK7)
| ~ relation(sK7) ),
inference(superposition,[status(thm)],[c_9665,c_10376]) ).
tcf(c_10992,plain,
! [X0: $i] :
( ( relation_image(sK15(powerset(relation_image(X0,empty_set))),empty_set) = empty_set )
| ~ function(X0)
| ~ relation(X0)
| ~ relation(sK15(powerset(relation_image(X0,empty_set)))) ),
inference(superposition,[status(thm)],[c_10376,c_7777]) ).
tcf(c_10993,plain,
( function(empty_set)
| ~ function(sK7)
| ~ relation(sK7) ),
inference(light_normalisation,[status(thm)],[c_10991,c_5301]) ).
tcf(c_10994,plain,
( function(empty_set)
| ~ function(sK1)
| ~ relation(sK1) ),
inference(light_normalisation,[status(thm)],[c_10990,c_5301]) ).
tcf(c_11020,plain,
! [X0: $i] :
( ( relation_image(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))),empty_set) = empty_set )
| ~ empty(X0)
| ~ relation(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))) ),
inference(superposition,[status(thm)],[c_10749,c_7777]) ).
tcf(c_11032,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X0,X1) = singleton(X2) )
| ( sK2(relation_image(X0,X1),singleton(X2)) = X2 )
| ( apply(X0,sK5(X0,X1,sK2(relation_image(X0,X1),singleton(X2)))) = sK2(relation_image(X0,X1),singleton(X2)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_5169,c_64]) ).
tcf(c_11033,plain,
! [X0: $i,X1: $i] :
( ( singleton(X1) = X0 )
| ( sK2(X0,singleton(X1)) = X1 )
| ~ in(X0,sK2(X0,singleton(X1))) ),
inference(superposition,[status(thm)],[c_5169,c_68]) ).
tcf(c_11034,plain,
! [X0: $i,X1: $i] :
( element(sK2(X0,singleton(X1)),X0)
| ( singleton(X1) = X0 )
| ( sK2(X0,singleton(X1)) = X1 ) ),
inference(superposition,[status(thm)],[c_5169,c_67]) ).
tcf(c_11036,plain,
! [X0: $i,X1: $i] :
( ( singleton(X0) = singleton(X1) )
| ( sK2(singleton(X0),singleton(X1)) = X1 )
| ( sK2(singleton(X0),singleton(X1)) = X0 ) ),
inference(superposition,[status(thm)],[c_5169,c_82]) ).
tcf(c_11037,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| element(sK2(sK14(X0),singleton(X1)),X0)
| ( singleton(X1) = sK14(X0) )
| ( sK2(sK14(X0),singleton(X1)) = X1 ) ),
inference(superposition,[status(thm)],[c_5169,c_5328]) ).
tcf(c_11038,plain,
! [X0: $i,X1: $i] :
( element(sK2(sK15(powerset(X0)),singleton(X1)),X0)
| ( sK15(powerset(X0)) = singleton(X1) )
| ( sK2(sK15(powerset(X0)),singleton(X1)) = X1 ) ),
inference(superposition,[status(thm)],[c_5169,c_5329]) ).
tcf(c_11039,plain,
! [X0: $i,X1: $i] :
( ( sK15(powerset(X0)) = singleton(X1) )
| ( sK2(sK15(powerset(X0)),singleton(X1)) = X1 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5169,c_5201]) ).
tcf(c_11041,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X0,empty_set) = singleton(X1) )
| ( sK2(relation_image(X0,empty_set),singleton(X1)) = X1 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_5169,c_5411]) ).
tcf(c_11042,plain,
! [X0: $i,X1: $i] :
( element(sK2(sK15(sK14(powerset(X0))),singleton(X1)),X0)
| ( sK15(sK14(powerset(X0))) = singleton(X1) )
| ( sK2(sK15(sK14(powerset(X0))),singleton(X1)) = X1 ) ),
inference(superposition,[status(thm)],[c_5169,c_6063]) ).
tcf(c_11043,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK14(powerset(X0))) = singleton(X1) )
| ( sK2(sK15(sK14(powerset(X0))),singleton(X1)) = X1 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5169,c_6060]) ).
tcf(c_11044,plain,
! [X0: $i,X1: $i] :
( element(sK2(sK15(sK14(sK14(powerset(X0)))),singleton(X1)),X0)
| ( sK15(sK14(sK14(powerset(X0)))) = singleton(X1) )
| ( sK2(sK15(sK14(sK14(powerset(X0)))),singleton(X1)) = X1 ) ),
inference(superposition,[status(thm)],[c_5169,c_7006]) ).
tcf(c_11045,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK14(sK14(powerset(X0)))) = singleton(X1) )
| ( sK2(sK15(sK14(sK14(powerset(X0)))),singleton(X1)) = X1 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5169,c_7003]) ).
tcf(c_11046,plain,
! [X0: $i,X1: $i] :
( element(sK2(sK15(sK14(sK14(sK14(powerset(X0))))),singleton(X1)),X0)
| ( sK15(sK14(sK14(sK14(powerset(X0))))) = singleton(X1) )
| ( sK2(sK15(sK14(sK14(sK14(powerset(X0))))),singleton(X1)) = X1 ) ),
inference(superposition,[status(thm)],[c_5169,c_9254]) ).
tcf(c_11047,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK14(sK14(sK14(powerset(X0))))) = singleton(X1) )
| ( sK2(sK15(sK14(sK14(sK14(powerset(X0))))),singleton(X1)) = X1 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5169,c_9251]) ).
tcf(c_11182,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK14(powerset(relation_dom(X0)))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_6192]) ).
tcf(c_11183,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(empty_set))) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_92,c_6192]) ).
tcf(c_11184,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK14(powerset(sK15(powerset(X0))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_6192]) ).
tcf(c_11185,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK14(powerset(sK15(sK14(powerset(X0)))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_6192]) ).
tcf(c_11186,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_6192]) ).
tcf(c_11187,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK14(powerset(relation_image(X0,empty_set)))) = X1 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_6192]) ).
tcf(c_11188,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK14(powerset(sK15(powerset(sK15(powerset(X0))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_6192]) ).
tcf(c_11189,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK14(powerset(sK15(powerset(relation_image(X0,empty_set)))))) = X1 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_6192]) ).
tcf(c_11190,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK14(powerset(sK15(powerset(sK15(sK14(powerset(X0)))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_6192]) ).
tcf(c_11191,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK14(powerset(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_6192]) ).
tcf(c_11192,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_6192]) ).
tcf(c_11193,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK14(powerset(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_6192]) ).
tcf(c_11239,plain,
! [X0: $i] :
( in(sK15(sK14(sK15(powerset(X0)))),X0)
| empty(sK15(powerset(X0))) ),
inference(global_subsumption_just,[status(thm)],[c_7108,c_5256,c_7108]) ).
tcf(c_11240,plain,
! [X0: $i] :
( empty(sK15(powerset(X0)))
| in(sK15(sK14(sK15(powerset(X0)))),X0) ),
inference(renaming,[status(thm)],[c_11239]) ).
tcf(c_11246,plain,
( empty(sK15(powerset(empty_set)))
| in(sK15(sK14(empty_set)),empty_set) ),
inference(superposition,[status(thm)],[c_5301,c_11240]) ).
tcf(c_11247,plain,
! [X0: $i,X1: $i] :
( empty(sK15(powerset(relation_image(X0,X1))))
| ( apply(X0,sK5(X0,X1,sK15(sK14(sK15(powerset(relation_image(X0,X1))))))) = sK15(sK14(sK15(powerset(relation_image(X0,X1))))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_11240,c_64]) ).
tcf(c_11248,plain,
! [X0: $i] :
( empty(sK15(powerset(X0)))
| ~ in(X0,sK15(sK14(sK15(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_11240,c_68]) ).
tcf(c_11251,plain,
! [X0: $i] :
( empty(sK15(powerset(singleton(X0))))
| ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 ) ),
inference(superposition,[status(thm)],[c_11240,c_82]) ).
tcf(c_11252,plain,
! [X0: $i] :
( empty(X0)
| empty(sK15(powerset(sK14(X0))))
| element(sK15(sK14(sK15(powerset(sK14(X0))))),X0) ),
inference(superposition,[status(thm)],[c_11240,c_5328]) ).
tcf(c_11253,plain,
! [X0: $i] :
( empty(sK15(powerset(sK15(powerset(X0)))))
| element(sK15(sK14(sK15(powerset(sK15(powerset(X0)))))),X0) ),
inference(superposition,[status(thm)],[c_11240,c_5329]) ).
tcf(c_11257,plain,
! [X0: $i] :
( empty(sK15(powerset(sK15(sK14(powerset(X0))))))
| element(sK15(sK14(sK15(powerset(sK15(sK14(powerset(X0))))))),X0) ),
inference(superposition,[status(thm)],[c_11240,c_6063]) ).
tcf(c_11259,plain,
! [X0: $i] :
( empty(sK15(powerset(sK15(sK14(sK14(powerset(X0)))))))
| element(sK15(sK14(sK15(powerset(sK15(sK14(sK14(powerset(X0)))))))),X0) ),
inference(superposition,[status(thm)],[c_11240,c_7006]) ).
tcf(c_11261,plain,
! [X0: $i] :
( empty(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))
| element(sK15(sK14(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))),X0) ),
inference(superposition,[status(thm)],[c_11240,c_9254]) ).
tcf(c_11263,plain,
( empty(empty_set)
| in(sK15(sK14(empty_set)),empty_set) ),
inference(light_normalisation,[status(thm)],[c_11246,c_5301]) ).
tcf(c_11299,plain,
( empty(sK15(powerset(empty_set)))
| ~ in(empty_set,sK15(sK14(empty_set))) ),
inference(superposition,[status(thm)],[c_5301,c_11248]) ).
tcf(c_11300,plain,
( empty(empty_set)
| ~ in(empty_set,sK15(sK14(empty_set))) ),
inference(light_normalisation,[status(thm)],[c_11299,c_5301]) ).
tcf(c_11315,plain,
! [X0: $i] :
( empty(X0)
| in(sK2(sK15(powerset(X0)),empty_set),X0)
| ( sK15(powerset(X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_5471,c_66]) ).
tcf(c_11316,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| ( sK15(powerset(powerset(X1))) = empty_set )
| ~ in(X0,sK2(sK15(powerset(powerset(X1))),empty_set)) ),
inference(superposition,[status(thm)],[c_5471,c_94]) ).
tcf(c_11317,plain,
! [X0: $i,X1: $i] :
( ( sK15(powerset(powerset(X1))) = empty_set )
| ~ empty(X1)
| ~ in(X0,sK2(sK15(powerset(powerset(X1))),empty_set)) ),
inference(superposition,[status(thm)],[c_5471,c_93]) ).
tcf(c_11343,plain,
! [X0: $i] :
( empty(X0)
| in(sK2(empty_set,sK15(powerset(X0))),X0)
| ( sK15(powerset(X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_5500,c_66]) ).
tcf(c_11344,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| ( sK15(powerset(powerset(X1))) = empty_set )
| ~ in(X0,sK2(empty_set,sK15(powerset(powerset(X1))))) ),
inference(superposition,[status(thm)],[c_5500,c_94]) ).
tcf(c_11345,plain,
! [X0: $i,X1: $i] :
( ( sK15(powerset(powerset(X1))) = empty_set )
| ~ empty(X1)
| ~ in(X0,sK2(empty_set,sK15(powerset(powerset(X1))))) ),
inference(superposition,[status(thm)],[c_5500,c_93]) ).
tcf(c_11363,plain,
! [X0: $i] :
( empty(X0)
| in(sK2(sK14(X0),empty_set),X0)
| ( sK14(X0) = empty_set ) ),
inference(superposition,[status(thm)],[c_5600,c_66]) ).
tcf(c_11364,plain,
! [X0: $i,X1: $i] :
( empty(powerset(X1))
| element(X0,X1)
| ( sK14(powerset(X1)) = empty_set )
| ~ in(X0,sK2(sK14(powerset(X1)),empty_set)) ),
inference(superposition,[status(thm)],[c_5600,c_94]) ).
tcf(c_11365,plain,
! [X0: $i,X1: $i] :
( empty(powerset(X1))
| ( sK14(powerset(X1)) = empty_set )
| ~ empty(X1)
| ~ in(X0,sK2(sK14(powerset(X1)),empty_set)) ),
inference(superposition,[status(thm)],[c_5600,c_93]) ).
tcf(c_11369,plain,
! [X0: $i,X1: $i] :
( ( sK14(powerset(X1)) = empty_set )
| ~ empty(X1)
| ~ in(X0,sK2(sK14(powerset(X1)),empty_set)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11365,c_100]) ).
tcf(c_11373,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| ( sK14(powerset(X1)) = empty_set )
| ~ in(X0,sK2(sK14(powerset(X1)),empty_set)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11364,c_100]) ).
tcf(c_11418,plain,
! [X0: $i] :
( empty(X0)
| in(sK2(empty_set,sK14(X0)),X0)
| ( sK14(X0) = empty_set ) ),
inference(superposition,[status(thm)],[c_5601,c_66]) ).
tcf(c_11419,plain,
! [X0: $i,X1: $i] :
( empty(powerset(X1))
| element(X0,X1)
| ( sK14(powerset(X1)) = empty_set )
| ~ in(X0,sK2(empty_set,sK14(powerset(X1)))) ),
inference(superposition,[status(thm)],[c_5601,c_94]) ).
tcf(c_11420,plain,
! [X0: $i,X1: $i] :
( empty(powerset(X1))
| ( sK14(powerset(X1)) = empty_set )
| ~ empty(X1)
| ~ in(X0,sK2(empty_set,sK14(powerset(X1)))) ),
inference(superposition,[status(thm)],[c_5601,c_93]) ).
tcf(c_11424,plain,
! [X0: $i,X1: $i] :
( ( sK14(powerset(X1)) = empty_set )
| ~ empty(X1)
| ~ in(X0,sK2(empty_set,sK14(powerset(X1)))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11420,c_100]) ).
tcf(c_11428,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| ( sK14(powerset(X1)) = empty_set )
| ~ in(X0,sK2(empty_set,sK14(powerset(X1)))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11419,c_100]) ).
tcf(c_11438,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(sK14(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_6187]) ).
tcf(c_11439,plain,
sK15(powerset(relation_dom(sK15(sK14(powerset(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_6187]) ).
tcf(c_11440,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_6187]) ).
tcf(c_11441,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_6187]) ).
tcf(c_11442,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_6187]) ).
tcf(c_11443,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(sK14(powerset(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_6187]) ).
tcf(c_11444,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(powerset(sK15(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_6187]) ).
tcf(c_11445,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_6187]) ).
tcf(c_11446,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(powerset(sK15(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_6187]) ).
tcf(c_11447,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(powerset(sK15(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_6187]) ).
tcf(c_11448,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_6187]) ).
tcf(c_11449,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_6187]) ).
tcf(c_11491,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(sK14(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_6188]) ).
tcf(c_11492,plain,
relation_dom(sK15(powerset(sK15(sK14(powerset(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_6188]) ).
tcf(c_11493,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_6188]) ).
tcf(c_11494,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(sK14(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_6188]) ).
tcf(c_11495,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_6188]) ).
tcf(c_11496,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(sK14(powerset(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_6188]) ).
tcf(c_11497,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(powerset(sK15(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_6188]) ).
tcf(c_11498,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_6188]) ).
tcf(c_11499,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(powerset(sK15(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_6188]) ).
tcf(c_11500,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(powerset(sK15(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_6188]) ).
tcf(c_11501,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_6188]) ).
tcf(c_11502,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_6188]) ).
tcf(c_11550,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_6189]) ).
tcf(c_11551,plain,
relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_6189]) ).
tcf(c_11552,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_6189]) ).
tcf(c_11553,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_6189]) ).
tcf(c_11554,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_6189]) ).
tcf(c_11555,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_6189]) ).
tcf(c_11556,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(powerset(sK15(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_6189]) ).
tcf(c_11557,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_6189]) ).
tcf(c_11558,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(powerset(sK15(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_6189]) ).
tcf(c_11559,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(powerset(sK15(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_6189]) ).
tcf(c_11560,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_6189]) ).
tcf(c_11561,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_6189]) ).
tcf(c_11642,plain,
( element(sK15(sK14(empty_set)),empty_set)
| empty(sK15(sK14(powerset(empty_set)))) ),
inference(superposition,[status(thm)],[c_6679,c_6607]) ).
tcf(c_11643,plain,
! [X0: $i] :
( empty(X0)
| empty(sK15(sK14(powerset(X0))))
| in(sK15(sK14(sK15(sK14(powerset(X0))))),X0) ),
inference(superposition,[status(thm)],[c_6607,c_66]) ).
tcf(c_11644,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| empty(sK15(sK14(powerset(powerset(X1)))))
| ~ in(X0,sK15(sK14(sK15(sK14(powerset(powerset(X1))))))) ),
inference(superposition,[status(thm)],[c_6607,c_94]) ).
tcf(c_11645,plain,
! [X0: $i,X1: $i] :
( empty(sK15(sK14(powerset(powerset(X1)))))
| ~ empty(X1)
| ~ in(X0,sK15(sK14(sK15(sK14(powerset(powerset(X1))))))) ),
inference(superposition,[status(thm)],[c_6607,c_93]) ).
tcf(c_11666,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(sK14(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_6681]) ).
tcf(c_11667,plain,
sK15(sK14(powerset(sK15(sK14(powerset(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_6681]) ).
tcf(c_11668,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(sK14(powerset(sK15(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_6681]) ).
tcf(c_11669,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(sK14(powerset(sK15(sK14(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_6681]) ).
tcf(c_11670,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_6681]) ).
tcf(c_11671,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(sK14(powerset(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_6681]) ).
tcf(c_11672,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(sK14(powerset(sK15(powerset(sK15(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_6681]) ).
tcf(c_11673,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(sK14(powerset(sK15(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_6681]) ).
tcf(c_11674,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(sK14(powerset(sK15(powerset(sK15(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_6681]) ).
tcf(c_11675,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(sK14(powerset(sK15(powerset(sK15(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_6681]) ).
tcf(c_11676,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_6681]) ).
tcf(c_11677,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(sK14(powerset(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_6681]) ).
tcf(c_11746,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK15(powerset(relation_dom(X0)))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_6797]) ).
tcf(c_11747,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(empty_set))) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_92,c_6797]) ).
tcf(c_11752,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK15(powerset(sK15(powerset(sK15(powerset(X0))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_6797]) ).
tcf(c_11753,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK15(powerset(sK15(powerset(relation_image(X0,empty_set)))))) = X1 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_6797]) ).
tcf(c_11754,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(powerset(X0)))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_6797]) ).
tcf(c_11755,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_6797]) ).
tcf(c_11757,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_6797]) ).
tcf(c_11782,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(sK15(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_6832]) ).
tcf(c_11783,plain,
relation_dom(relation_dom(sK15(powerset(sK15(powerset(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_6832]) ).
tcf(c_11788,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(sK15(powerset(sK15(powerset(sK15(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_6832]) ).
tcf(c_11789,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(sK15(powerset(sK15(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_6832]) ).
tcf(c_11790,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(sK15(powerset(sK15(powerset(sK15(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_6832]) ).
tcf(c_11791,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(sK15(powerset(sK15(powerset(sK15(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_6832]) ).
tcf(c_11793,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(sK15(powerset(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_6832]) ).
tcf(c_11908,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(sK15(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_6856]) ).
tcf(c_11909,plain,
sK15(powerset(sK15(powerset(sK15(powerset(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_6856]) ).
tcf(c_11914,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(sK15(powerset(sK15(powerset(sK15(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_6856]) ).
tcf(c_11915,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(sK15(powerset(sK15(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_6856]) ).
tcf(c_11916,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(sK15(powerset(sK15(powerset(sK15(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_6856]) ).
tcf(c_11917,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(sK15(powerset(sK15(powerset(sK15(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_6856]) ).
tcf(c_11919,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(sK15(powerset(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_6856]) ).
tcf(c_11943,plain,
! [X0: $i,X1: $i] :
( ( singleton(X0) = singleton(X1) )
| ( sK2(singleton(X0),singleton(X1)) = X0 )
| ~ empty(singleton(X1))
| ~ in(singleton(X0),X1) ),
inference(superposition,[status(thm)],[c_11036,c_7508]) ).
tcf(c_11946,plain,
! [X0: $i,X1: $i] :
( in(sK2(singleton(X0),singleton(X1)),singleton(X1))
| ( singleton(X0) = singleton(X1) )
| ( sK2(singleton(X0),singleton(X1)) = X0 )
| ~ in(singleton(X0),X1) ),
inference(superposition,[status(thm)],[c_11036,c_5096]) ).
tcf(c_11947,plain,
! [X0: $i,X1: $i] :
( in(X1,singleton(X0))
| in(sK2(singleton(X0),singleton(X1)),singleton(X1))
| ( singleton(X0) = singleton(X1) )
| ( sK2(singleton(X0),singleton(X1)) = X0 ) ),
inference(superposition,[status(thm)],[c_11036,c_56]) ).
tcf(c_11948,plain,
! [X0: $i,X1: $i] :
( in(X1,singleton(X1))
| in(sK2(singleton(X0),singleton(X1)),singleton(X0))
| ( singleton(X0) = singleton(X1) )
| ( sK2(singleton(X0),singleton(X1)) = X0 ) ),
inference(superposition,[status(thm)],[c_11036,c_56]) ).
tcf(c_11949,plain,
! [X0: $i,X1: $i] :
( ( singleton(X0) = singleton(X1) )
| ( sK2(singleton(X0),singleton(X1)) = X0 )
| ~ in(X1,singleton(X1))
| ~ in(sK2(singleton(X0),singleton(X1)),singleton(X0)) ),
inference(superposition,[status(thm)],[c_11036,c_55]) ).
tcf(c_11960,plain,
! [X0: $i,X1: $i] :
( in(X0,singleton(X1))
| in(sK2(singleton(X0),singleton(X1)),singleton(X0))
| ( singleton(X0) = singleton(X1) )
| ( sK2(singleton(X0),singleton(X1)) = X1 ) ),
inference(superposition,[status(thm)],[c_11036,c_56]) ).
tcf(c_11961,plain,
! [X0: $i,X1: $i] :
( ( singleton(X0) = singleton(X1) )
| ( sK2(singleton(X0),singleton(X1)) = X1 )
| ~ in(X0,singleton(X1))
| ~ in(sK2(singleton(X0),singleton(X1)),singleton(X0)) ),
inference(superposition,[status(thm)],[c_11036,c_55]) ).
tcf(c_11964,plain,
! [X0: $i,X1: $i] :
( in(sK2(singleton(X1),singleton(X0)),singleton(X1))
| ( singleton(X0) = singleton(X1) )
| ( sK2(singleton(X1),singleton(X0)) = X0 )
| ~ in(singleton(X0),X1) ),
inference(superposition,[status(thm)],[c_11036,c_5095]) ).
tcf(c_11967,plain,
! [X0: $i,X1: $i] :
( ( singleton(X0) = singleton(X1) )
| ( sK2(singleton(X1),singleton(X0)) = X0 )
| ( X0 != X1 ) ),
inference(equality_factoring,[status(thm)],[c_11036]) ).
tcf(c_11968,plain,
! [X0: $i,X1: $i] :
( ( singleton(X0) = singleton(X1) )
| ( sK2(singleton(X0),singleton(X1)) = X0 )
| ( X0 != X1 ) ),
inference(equality_factoring,[status(thm)],[c_11036]) ).
tcf(c_11995,plain,
! [X0: $i,X1: $i] :
( ( singleton(X0) = singleton(X1) )
| ( sK2(singleton(X0),singleton(X1)) = X0 )
| ~ in(sK2(singleton(X0),singleton(X1)),singleton(X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11949,c_81]) ).
tcf(c_12007,plain,
! [X0: $i,X1: $i] :
( ( singleton(X0) = singleton(X1) )
| ( sK2(singleton(X1),singleton(X0)) = X0 )
| ~ empty(singleton(X1))
| ~ in(singleton(X0),X1) ),
inference(superposition,[status(thm)],[c_11036,c_7586]) ).
tcf(c_12042,plain,
! [X0: $i,X1: $i] :
( ( sK15(powerset(relation_dom(relation_dom(X0)))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_7738]) ).
tcf(c_12043,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(empty_set))) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_92,c_7738]) ).
tcf(c_12044,plain,
! [X0: $i,X1: $i] :
( ( sK15(powerset(relation_dom(sK15(powerset(X0))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_7738]) ).
tcf(c_12045,plain,
! [X0: $i,X1: $i] :
( ( sK15(powerset(relation_dom(sK15(sK14(powerset(X0)))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_7738]) ).
tcf(c_12046,plain,
! [X0: $i,X1: $i] :
( ( sK15(powerset(relation_dom(sK15(sK14(sK14(powerset(X0))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_7738]) ).
tcf(c_12047,plain,
! [X0: $i,X1: $i] :
( ( sK15(powerset(relation_dom(relation_image(X0,empty_set)))) = X1 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_7738]) ).
tcf(c_12048,plain,
! [X0: $i,X1: $i] :
( ( sK15(powerset(relation_dom(sK15(powerset(sK15(powerset(X0))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_7738]) ).
tcf(c_12049,plain,
! [X0: $i,X1: $i] :
( ( sK15(powerset(relation_dom(sK15(powerset(relation_image(X0,empty_set)))))) = X1 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_7738]) ).
tcf(c_12050,plain,
! [X0: $i,X1: $i] :
( ( sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(powerset(X0)))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_7738]) ).
tcf(c_12051,plain,
! [X0: $i,X1: $i] :
( ( sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_7738]) ).
tcf(c_12052,plain,
! [X0: $i,X1: $i] :
( ( sK15(powerset(relation_dom(sK15(sK14(sK14(sK14(powerset(X0)))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_7738]) ).
tcf(c_12053,plain,
! [X0: $i,X1: $i] :
( ( sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_7738]) ).
tcf(c_12094,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(powerset(relation_dom(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_8076]) ).
tcf(c_12095,plain,
relation_dom(relation_dom(relation_dom(sK15(powerset(relation_dom(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_8076]) ).
tcf(c_12096,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_8076]) ).
tcf(c_12097,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(sK14(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_8076]) ).
tcf(c_12098,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(sK14(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_8076]) ).
tcf(c_12099,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(powerset(relation_dom(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_8076]) ).
tcf(c_12100,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(powerset(sK15(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_8076]) ).
tcf(c_12101,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_8076]) ).
tcf(c_12102,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_8076]) ).
tcf(c_12103,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_8076]) ).
tcf(c_12104,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(sK14(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_8076]) ).
tcf(c_12105,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_8076]) ).
tcf(c_12137,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_6887]) ).
tcf(c_12138,plain,
relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_6887]) ).
tcf(c_12143,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(powerset(sK15(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_6887]) ).
tcf(c_12144,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_6887]) ).
tcf(c_12145,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_6887]) ).
tcf(c_12146,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_6887]) ).
tcf(c_12148,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_6887]) ).
tcf(c_12185,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(sK15(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_6905]) ).
tcf(c_12186,plain,
relation_dom(sK15(powerset(relation_dom(sK15(powerset(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_6905]) ).
tcf(c_12191,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(sK15(powerset(sK15(powerset(sK15(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_6905]) ).
tcf(c_12192,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(sK15(powerset(sK15(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_6905]) ).
tcf(c_12193,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_6905]) ).
tcf(c_12194,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_6905]) ).
tcf(c_12196,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_6905]) ).
tcf(c_12288,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(sK15(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_6938]) ).
tcf(c_12289,plain,
sK15(powerset(relation_dom(relation_dom(sK15(powerset(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_6938]) ).
tcf(c_12294,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(sK15(powerset(sK15(powerset(sK15(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_6938]) ).
tcf(c_12295,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(sK15(powerset(sK15(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_6938]) ).
tcf(c_12296,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_6938]) ).
tcf(c_12297,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_6938]) ).
tcf(c_12299,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_6938]) ).
tcf(c_12319,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(sK15(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_6953]) ).
tcf(c_12320,plain,
sK15(sK14(powerset(relation_dom(sK15(powerset(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_6953]) ).
tcf(c_12325,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(sK15(powerset(sK15(powerset(sK15(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_6953]) ).
tcf(c_12326,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(sK15(powerset(sK15(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_6953]) ).
tcf(c_12327,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_6953]) ).
tcf(c_12328,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_6953]) ).
tcf(c_12330,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_6953]) ).
tcf(c_12362,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(sK15(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_7142]) ).
tcf(c_12363,plain,
relation_dom(sK15(sK14(powerset(sK15(powerset(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_7142]) ).
tcf(c_12368,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(sK15(powerset(sK15(powerset(sK15(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_7142]) ).
tcf(c_12369,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(sK15(powerset(sK15(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_7142]) ).
tcf(c_12370,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(sK15(powerset(sK15(powerset(sK15(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_7142]) ).
tcf(c_12371,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(sK15(powerset(sK15(powerset(sK15(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_7142]) ).
tcf(c_12373,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(sK15(powerset(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_7142]) ).
tcf(c_12393,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(sK14(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_7253]) ).
tcf(c_12394,plain,
sK15(powerset(sK15(sK14(sK14(powerset(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_7253]) ).
tcf(c_12395,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(sK14(powerset(sK15(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_7253]) ).
tcf(c_12396,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(sK14(powerset(sK15(sK14(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_7253]) ).
tcf(c_12397,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_7253]) ).
tcf(c_12398,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(sK14(powerset(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_7253]) ).
tcf(c_12399,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(sK14(powerset(sK15(powerset(sK15(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_7253]) ).
tcf(c_12400,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(sK14(powerset(sK15(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_7253]) ).
tcf(c_12401,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(sK14(powerset(sK15(powerset(sK15(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_7253]) ).
tcf(c_12402,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(sK14(powerset(sK15(powerset(sK15(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_7253]) ).
tcf(c_12403,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_7253]) ).
tcf(c_12404,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(sK14(powerset(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_7253]) ).
tcf(c_12496,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(sK14(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_7254]) ).
tcf(c_12497,plain,
relation_dom(relation_dom(sK15(sK14(sK14(powerset(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_7254]) ).
tcf(c_12498,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(sK14(powerset(sK15(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_7254]) ).
tcf(c_12499,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(sK14(powerset(sK15(sK14(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_7254]) ).
tcf(c_12500,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_7254]) ).
tcf(c_12501,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(sK14(powerset(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_7254]) ).
tcf(c_12502,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(sK14(powerset(sK15(powerset(sK15(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_7254]) ).
tcf(c_12503,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(sK14(powerset(sK15(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_7254]) ).
tcf(c_12504,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(sK14(powerset(sK15(powerset(sK15(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_7254]) ).
tcf(c_12505,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(sK14(powerset(sK15(powerset(sK15(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_7254]) ).
tcf(c_12506,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_7254]) ).
tcf(c_12507,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(sK14(powerset(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_7254]) ).
tcf(c_12539,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(sK15(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_7684]) ).
tcf(c_12540,plain,
sK15(sK14(sK14(powerset(sK15(powerset(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_7684]) ).
tcf(c_12545,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(sK15(powerset(sK15(powerset(sK15(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_7684]) ).
tcf(c_12546,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(sK15(powerset(sK15(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_7684]) ).
tcf(c_12547,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(sK15(powerset(sK15(powerset(sK15(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_7684]) ).
tcf(c_12548,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(sK15(powerset(sK15(powerset(sK15(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_7684]) ).
tcf(c_12550,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(sK15(powerset(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_7684]) ).
tcf(c_12572,plain,
( ( relation_dom(relation_image(sK1,empty_set)) = empty_set )
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_52,c_7934]) ).
tcf(c_12573,plain,
( ( relation_dom(relation_image(sK7,empty_set)) = empty_set )
| ~ relation(sK7) ),
inference(superposition,[status(thm)],[c_76,c_7934]) ).
tcf(c_12574,plain,
! [X0: $i] :
( ( relation_dom(relation_image(relation_dom(X0),empty_set)) = empty_set )
| ~ empty(X0)
| ~ relation(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_5003,c_7934]) ).
tcf(c_12575,plain,
( ( relation_dom(relation_image(empty_set,empty_set)) = empty_set )
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_4985,c_7934]) ).
tcf(c_12576,plain,
! [X0: $i] :
( ( relation_dom(relation_image(sK15(powerset(X0)),empty_set)) = empty_set )
| ~ empty(X0)
| ~ relation(sK15(powerset(X0))) ),
inference(superposition,[status(thm)],[c_5274,c_7934]) ).
tcf(c_12577,plain,
! [X0: $i] :
( ( relation_dom(relation_image(sK15(sK14(powerset(X0))),empty_set)) = empty_set )
| ~ empty(X0)
| ~ relation(sK15(sK14(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_6196,c_7934]) ).
tcf(c_12578,plain,
! [X0: $i] :
( ( relation_dom(relation_image(sK15(sK14(sK14(powerset(X0)))),empty_set)) = empty_set )
| ~ empty(X0)
| ~ relation(sK15(sK14(sK14(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_7259,c_7934]) ).
tcf(c_12579,plain,
! [X0: $i] :
( ( relation_dom(relation_image(relation_image(X0,empty_set),empty_set)) = empty_set )
| ~ function(X0)
| ~ relation(X0)
| ~ relation(relation_image(X0,empty_set)) ),
inference(superposition,[status(thm)],[c_7937,c_7934]) ).
tcf(c_12580,plain,
! [X0: $i] :
( ( relation_dom(relation_image(sK15(powerset(sK15(powerset(X0)))),empty_set)) = empty_set )
| ~ empty(X0)
| ~ relation(sK15(powerset(sK15(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_8308,c_7934]) ).
tcf(c_12581,plain,
! [X0: $i] :
( ( relation_dom(relation_image(sK15(powerset(sK15(sK14(powerset(X0))))),empty_set)) = empty_set )
| ~ empty(X0)
| ~ relation(sK15(powerset(sK15(sK14(powerset(X0)))))) ),
inference(superposition,[status(thm)],[c_8429,c_7934]) ).
tcf(c_12582,plain,
! [X0: $i] :
( ( relation_dom(relation_image(sK15(powerset(sK15(sK14(sK14(powerset(X0)))))),empty_set)) = empty_set )
| ~ empty(X0)
| ~ relation(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))) ),
inference(superposition,[status(thm)],[c_8577,c_7934]) ).
tcf(c_12583,plain,
! [X0: $i] :
( ( relation_dom(relation_image(sK15(sK14(sK14(sK14(powerset(X0))))),empty_set)) = empty_set )
| ~ empty(X0)
| ~ relation(sK15(sK14(sK14(sK14(powerset(X0)))))) ),
inference(superposition,[status(thm)],[c_10139,c_7934]) ).
tcf(c_12584,plain,
! [X0: $i] :
( ( relation_dom(relation_image(sK15(powerset(relation_image(X0,empty_set))),empty_set)) = empty_set )
| ~ function(X0)
| ~ relation(X0)
| ~ relation(sK15(powerset(relation_image(X0,empty_set)))) ),
inference(superposition,[status(thm)],[c_10376,c_7934]) ).
tcf(c_12585,plain,
! [X0: $i] :
( ( relation_dom(relation_image(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))),empty_set)) = empty_set )
| ~ empty(X0)
| ~ relation(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))) ),
inference(superposition,[status(thm)],[c_10749,c_7934]) ).
tcf(c_12586,plain,
relation_dom(relation_image(empty_set,empty_set)) = empty_set,
inference(forward_subsumption_resolution,[status(thm)],[c_12575,c_91]) ).
tcf(c_12705,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( sK15(sK14(sK14(powerset(sK15(powerset(sK15(powerset(singleton(X0))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_7684]) ).
tcf(c_12706,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( relation_dom(relation_dom(sK15(sK14(sK14(powerset(sK15(powerset(singleton(X0))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_7254]) ).
tcf(c_12707,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( sK15(powerset(sK15(sK14(sK14(powerset(sK15(powerset(singleton(X0))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_7253]) ).
tcf(c_12708,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( relation_dom(sK15(sK14(powerset(sK15(powerset(sK15(powerset(singleton(X0))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_7142]) ).
tcf(c_12709,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( sK15(sK14(powerset(relation_dom(sK15(powerset(sK15(powerset(singleton(X0))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_6953]) ).
tcf(c_12710,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( sK15(powerset(relation_dom(relation_dom(sK15(powerset(sK15(powerset(singleton(X0))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_6938]) ).
tcf(c_12711,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( relation_dom(sK15(powerset(relation_dom(sK15(powerset(sK15(powerset(singleton(X0))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_6905]) ).
tcf(c_12712,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(powerset(singleton(X0))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_6887]) ).
tcf(c_12713,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( relation_dom(relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(powerset(singleton(X0))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_8076]) ).
tcf(c_12714,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK15(powerset(singleton(X1)))) = X1 )
| ( sK15(powerset(relation_dom(sK15(powerset(singleton(X1)))))) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8114,c_7738]) ).
tcf(c_12715,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( sK15(powerset(sK15(powerset(sK15(powerset(sK15(powerset(singleton(X0))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_6856]) ).
tcf(c_12716,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( relation_dom(relation_dom(sK15(powerset(sK15(powerset(sK15(powerset(singleton(X0))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_6832]) ).
tcf(c_12717,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK15(powerset(singleton(X1)))) = X1 )
| ( relation_dom(sK15(powerset(sK15(powerset(singleton(X1)))))) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8114,c_6797]) ).
tcf(c_12718,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( sK15(sK14(powerset(sK15(sK14(powerset(sK15(powerset(singleton(X0))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_6681]) ).
tcf(c_12719,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(powerset(singleton(X0))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_6189]) ).
tcf(c_12720,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(powerset(singleton(X0))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_6188]) ).
tcf(c_12721,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(powerset(singleton(X0))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_6187]) ).
tcf(c_12722,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK15(powerset(singleton(X1)))) = X1 )
| ( sK15(sK14(powerset(sK15(powerset(singleton(X1)))))) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8114,c_6192]) ).
tcf(c_12723,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( sK15(sK14(sK14(sK14(powerset(sK15(powerset(singleton(X0)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_9868]) ).
tcf(c_12724,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( sK15(sK14(sK14(powerset(relation_dom(sK15(powerset(singleton(X0)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_7682]) ).
tcf(c_12725,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( relation_dom(sK15(sK14(sK14(powerset(sK15(powerset(singleton(X0)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_7256]) ).
tcf(c_12726,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( relation_dom(sK15(sK14(powerset(relation_dom(sK15(powerset(singleton(X0)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_7140]) ).
tcf(c_12727,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( sK15(sK14(powerset(relation_dom(relation_dom(sK15(powerset(singleton(X0)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_6951]) ).
tcf(c_12728,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( sK15(sK14(powerset(sK15(powerset(sK15(powerset(singleton(X0)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_6680]) ).
tcf(c_12729,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( relation_dom(relation_dom(sK15(sK14(powerset(sK15(powerset(singleton(X0)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_6191]) ).
tcf(c_12730,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( sK15(powerset(relation_dom(relation_dom(relation_dom(sK15(powerset(singleton(X0)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_6936]) ).
tcf(c_12731,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(powerset(singleton(X0)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_6903]) ).
tcf(c_12732,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(singleton(X0)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_6885]) ).
tcf(c_12733,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( sK15(powerset(sK15(powerset(relation_dom(sK15(powerset(singleton(X0)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_6854]) ).
tcf(c_12734,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( sK15(powerset(sK15(sK14(powerset(sK15(powerset(singleton(X0)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_6190]) ).
tcf(c_12735,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( sK15(powerset(relation_dom(sK15(powerset(sK15(powerset(singleton(X0)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_5583]) ).
tcf(c_12736,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( relation_dom(sK15(powerset(sK15(powerset(sK15(powerset(singleton(X0)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_5569]) ).
tcf(c_12737,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(powerset(singleton(X0)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_6830]) ).
tcf(c_12738,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK15(powerset(singleton(X1)))) = X1 )
| ( relation_dom(relation_dom(sK15(powerset(singleton(X1))))) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8114,c_6795]) ).
tcf(c_12739,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(powerset(singleton(X0)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_5557]) ).
tcf(c_12740,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK15(powerset(singleton(X1)))) = X1 )
| ( sK15(powerset(sK15(powerset(singleton(X1))))) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8114,c_5270]) ).
tcf(c_12741,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( sK15(sK14(sK14(powerset(sK15(powerset(singleton(X0))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_7171]) ).
tcf(c_12742,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( relation_dom(sK15(sK14(powerset(sK15(powerset(singleton(X0))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_6193]) ).
tcf(c_12743,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( sK15(sK14(powerset(relation_dom(sK15(powerset(singleton(X0))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_6678]) ).
tcf(c_12744,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( sK15(powerset(relation_dom(relation_dom(sK15(powerset(singleton(X0))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_5581]) ).
tcf(c_12745,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( relation_dom(sK15(powerset(relation_dom(sK15(powerset(singleton(X0))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_5567]) ).
tcf(c_12746,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(singleton(X0))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_5555]) ).
tcf(c_12747,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( sK15(powerset(sK15(powerset(sK15(powerset(singleton(X0))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_5302]) ).
tcf(c_12748,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( relation_dom(relation_dom(sK15(powerset(sK15(powerset(singleton(X0))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_5269]) ).
tcf(c_12749,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK15(powerset(singleton(X1)))) = X1 )
| ( relation_dom(sK15(powerset(singleton(X1)))) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8114,c_5189]) ).
tcf(c_12750,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( sK15(sK14(powerset(sK15(powerset(singleton(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_6153]) ).
tcf(c_12751,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( sK15(powerset(relation_dom(sK15(powerset(singleton(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_5300]) ).
tcf(c_12752,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( relation_dom(sK15(powerset(sK15(powerset(singleton(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_5271]) ).
tcf(c_12753,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( relation_dom(relation_dom(relation_dom(sK15(powerset(singleton(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_5245]) ).
tcf(c_12754,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( sK15(powerset(sK15(powerset(singleton(X0))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_5272]) ).
tcf(c_12755,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( relation_dom(relation_dom(sK15(powerset(singleton(X0))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_5110]) ).
tcf(c_12756,plain,
! [X0: $i,X1: $i] :
( ( sK15(powerset(singleton(X1))) = X0 )
| ( sK15(sK15(powerset(singleton(X1)))) = X1 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8114,c_53]) ).
tcf(c_12757,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( relation_dom(sK15(powerset(singleton(X0)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_5023]) ).
tcf(c_12758,plain,
! [X0: $i] :
( ( sK15(powerset(singleton(X0))) = empty_set )
| ( sK15(sK15(powerset(singleton(X0)))) = X0 ) ),
inference(superposition,[status(thm)],[c_8114,c_54]) ).
tcf(c_12759,plain,
! [X0: $i] :
( relation(sK15(powerset(singleton(X0))))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 ) ),
inference(superposition,[status(thm)],[c_8114,c_87]) ).
tcf(c_12760,plain,
! [X0: $i] :
( function(sK15(powerset(singleton(X0))))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 ) ),
inference(superposition,[status(thm)],[c_8114,c_77]) ).
tcf(c_13072,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(X0)))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_8209]) ).
tcf(c_13073,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(empty_set))) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_92,c_8209]) ).
tcf(c_13074,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(powerset(X0))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_8209]) ).
tcf(c_13075,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(X0)))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_8209]) ).
tcf(c_13076,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(powerset(X0))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_8209]) ).
tcf(c_13077,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_image(X0,empty_set)))) = X1 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_8209]) ).
tcf(c_13078,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK15(powerset(singleton(X1)))) = X1 )
| ( relation_dom(relation_dom(relation_dom(sK15(powerset(singleton(X1)))))) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8114,c_8209]) ).
tcf(c_13079,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(powerset(X0))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_8209]) ).
tcf(c_13080,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(powerset(relation_image(X0,empty_set)))))) = X1 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_8209]) ).
tcf(c_13081,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(X0)))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_8209]) ).
tcf(c_13082,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_8209]) ).
tcf(c_13083,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(sK14(powerset(X0)))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_8209]) ).
tcf(c_13084,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_8209]) ).
tcf(c_13155,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(relation_dom(relation_dom(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_8236]) ).
tcf(c_13156,plain,
relation_dom(relation_dom(sK15(powerset(relation_dom(relation_dom(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_8236]) ).
tcf(c_13157,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_8236]) ).
tcf(c_13158,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(sK14(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_8236]) ).
tcf(c_13159,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(sK14(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_8236]) ).
tcf(c_13160,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(relation_dom(relation_dom(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_8236]) ).
tcf(c_13161,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( relation_dom(relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(powerset(singleton(X0))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_8236]) ).
tcf(c_13162,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(powerset(sK15(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_8236]) ).
tcf(c_13163,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_8236]) ).
tcf(c_13164,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_8236]) ).
tcf(c_13165,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_8236]) ).
tcf(c_13166,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(sK14(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_8236]) ).
tcf(c_13167,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_8236]) ).
tcf(c_13215,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(powerset(relation_dom(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_8667]) ).
tcf(c_13216,plain,
relation_dom(sK15(powerset(sK15(powerset(relation_dom(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_8667]) ).
tcf(c_13217,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(powerset(relation_dom(sK15(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_8667]) ).
tcf(c_13218,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(powerset(relation_dom(sK15(sK14(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_8667]) ).
tcf(c_13219,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(powerset(relation_dom(sK15(sK14(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_8667]) ).
tcf(c_13220,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(powerset(relation_dom(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_8667]) ).
tcf(c_13221,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( relation_dom(sK15(powerset(sK15(powerset(relation_dom(sK15(powerset(singleton(X0))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_8667]) ).
tcf(c_13222,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(powerset(relation_dom(sK15(powerset(sK15(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_8667]) ).
tcf(c_13223,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(powerset(relation_dom(sK15(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_8667]) ).
tcf(c_13224,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_8667]) ).
tcf(c_13225,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_8667]) ).
tcf(c_13226,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(powerset(relation_dom(sK15(sK14(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_8667]) ).
tcf(c_13227,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_8667]) ).
tcf(c_13342,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(powerset(relation_dom(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_8705]) ).
tcf(c_13343,plain,
sK15(powerset(relation_dom(sK15(powerset(relation_dom(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_8705]) ).
tcf(c_13344,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(powerset(relation_dom(sK15(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_8705]) ).
tcf(c_13345,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(powerset(relation_dom(sK15(sK14(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_8705]) ).
tcf(c_13346,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(powerset(relation_dom(sK15(sK14(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_8705]) ).
tcf(c_13347,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(powerset(relation_dom(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_8705]) ).
tcf(c_13348,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( sK15(powerset(relation_dom(sK15(powerset(relation_dom(sK15(powerset(singleton(X0))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_8705]) ).
tcf(c_13349,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(powerset(relation_dom(sK15(powerset(sK15(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_8705]) ).
tcf(c_13350,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(powerset(relation_dom(sK15(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_8705]) ).
tcf(c_13351,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_8705]) ).
tcf(c_13352,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_8705]) ).
tcf(c_13353,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(powerset(relation_dom(sK15(sK14(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_8705]) ).
tcf(c_13354,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_8705]) ).
tcf(c_13409,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(powerset(relation_dom(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_8743]) ).
tcf(c_13410,plain,
sK15(powerset(sK15(sK14(powerset(relation_dom(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_8743]) ).
tcf(c_13411,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(powerset(relation_dom(sK15(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_8743]) ).
tcf(c_13412,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(powerset(relation_dom(sK15(sK14(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_8743]) ).
tcf(c_13413,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(powerset(relation_dom(sK15(sK14(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_8743]) ).
tcf(c_13414,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(powerset(relation_dom(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_8743]) ).
tcf(c_13415,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( sK15(powerset(sK15(sK14(powerset(relation_dom(sK15(powerset(singleton(X0))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_8743]) ).
tcf(c_13416,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(powerset(relation_dom(sK15(powerset(sK15(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_8743]) ).
tcf(c_13417,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(powerset(relation_dom(sK15(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_8743]) ).
tcf(c_13418,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(powerset(relation_dom(sK15(powerset(sK15(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_8743]) ).
tcf(c_13419,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_8743]) ).
tcf(c_13420,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(powerset(relation_dom(sK15(sK14(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_8743]) ).
tcf(c_13421,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_8743]) ).
tcf(c_13471,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(relation_dom(relation_dom(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_8821]) ).
tcf(c_13472,plain,
sK15(powerset(sK15(powerset(relation_dom(relation_dom(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_8821]) ).
tcf(c_13473,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(relation_dom(relation_dom(sK15(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_8821]) ).
tcf(c_13474,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(relation_dom(relation_dom(sK15(sK14(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_8821]) ).
tcf(c_13475,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(relation_dom(relation_dom(sK15(sK14(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_8821]) ).
tcf(c_13476,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(relation_dom(relation_dom(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_8821]) ).
tcf(c_13477,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( sK15(powerset(sK15(powerset(relation_dom(relation_dom(sK15(powerset(singleton(X0))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_8821]) ).
tcf(c_13478,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(relation_dom(relation_dom(sK15(powerset(sK15(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_8821]) ).
tcf(c_13479,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(relation_dom(relation_dom(sK15(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_8821]) ).
tcf(c_13480,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_8821]) ).
tcf(c_13481,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_8821]) ).
tcf(c_13482,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(relation_dom(relation_dom(sK15(sK14(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_8821]) ).
tcf(c_13483,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_8821]) ).
tcf(c_13554,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_8858]) ).
tcf(c_13555,plain,
relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_8858]) ).
tcf(c_13556,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_8858]) ).
tcf(c_13557,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_8858]) ).
tcf(c_13558,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_8858]) ).
tcf(c_13559,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_8858]) ).
tcf(c_13560,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(singleton(X0))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_8858]) ).
tcf(c_13561,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_8858]) ).
tcf(c_13562,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_8858]) ).
tcf(c_13563,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_8858]) ).
tcf(c_13564,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_8858]) ).
tcf(c_13565,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_8858]) ).
tcf(c_13566,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_8858]) ).
tcf(c_13650,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(relation_dom(relation_dom(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_8933]) ).
tcf(c_13651,plain,
relation_dom(sK15(powerset(relation_dom(relation_dom(relation_dom(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_8933]) ).
tcf(c_13652,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(relation_dom(relation_dom(sK15(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_8933]) ).
tcf(c_13653,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_8933]) ).
tcf(c_13654,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_8933]) ).
tcf(c_13655,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(relation_dom(relation_dom(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_8933]) ).
tcf(c_13656,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( relation_dom(sK15(powerset(relation_dom(relation_dom(relation_dom(sK15(powerset(singleton(X0))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_8933]) ).
tcf(c_13657,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_8933]) ).
tcf(c_13658,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(relation_dom(relation_dom(sK15(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_8933]) ).
tcf(c_13659,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_8933]) ).
tcf(c_13660,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_8933]) ).
tcf(c_13661,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_8933]) ).
tcf(c_13662,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_8933]) ).
tcf(c_13746,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_8993]) ).
tcf(c_13747,plain,
sK15(powerset(relation_dom(relation_dom(relation_dom(relation_dom(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_8993]) ).
tcf(c_13748,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_8993]) ).
tcf(c_13749,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_8993]) ).
tcf(c_13750,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_8993]) ).
tcf(c_13751,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(relation_dom(relation_dom(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_8993]) ).
tcf(c_13752,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( sK15(powerset(relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(singleton(X0))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_8993]) ).
tcf(c_13753,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_8993]) ).
tcf(c_13754,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_8993]) ).
tcf(c_13755,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_8993]) ).
tcf(c_13756,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_8993]) ).
tcf(c_13757,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_8993]) ).
tcf(c_13758,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_8993]) ).
tcf(c_13820,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(powerset(relation_dom(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_9025]) ).
tcf(c_13821,plain,
relation_dom(relation_dom(sK15(sK14(powerset(relation_dom(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_9025]) ).
tcf(c_13822,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(powerset(relation_dom(sK15(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_9025]) ).
tcf(c_13823,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(powerset(relation_dom(sK15(sK14(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_9025]) ).
tcf(c_13824,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(powerset(relation_dom(sK15(sK14(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_9025]) ).
tcf(c_13825,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(powerset(relation_dom(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_9025]) ).
tcf(c_13826,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( relation_dom(relation_dom(sK15(sK14(powerset(relation_dom(sK15(powerset(singleton(X0))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_9025]) ).
tcf(c_13827,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(powerset(relation_dom(sK15(powerset(sK15(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_9025]) ).
tcf(c_13828,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(powerset(relation_dom(sK15(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_9025]) ).
tcf(c_13829,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(powerset(relation_dom(sK15(powerset(sK15(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_9025]) ).
tcf(c_13830,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_9025]) ).
tcf(c_13831,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(powerset(relation_dom(sK15(sK14(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_9025]) ).
tcf(c_13832,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_9025]) ).
tcf(c_13924,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(powerset(relation_dom(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_9107]) ).
tcf(c_13925,plain,
sK15(sK14(powerset(sK15(powerset(relation_dom(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_9107]) ).
tcf(c_13926,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(powerset(relation_dom(sK15(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_9107]) ).
tcf(c_13927,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(powerset(relation_dom(sK15(sK14(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_9107]) ).
tcf(c_13928,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(powerset(relation_dom(sK15(sK14(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_9107]) ).
tcf(c_13929,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(powerset(relation_dom(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_9107]) ).
tcf(c_13930,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( sK15(sK14(powerset(sK15(powerset(relation_dom(sK15(powerset(singleton(X0))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_9107]) ).
tcf(c_13931,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(powerset(relation_dom(sK15(powerset(sK15(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_9107]) ).
tcf(c_13932,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(powerset(relation_dom(sK15(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_9107]) ).
tcf(c_13933,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_9107]) ).
tcf(c_13934,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_9107]) ).
tcf(c_13935,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(powerset(relation_dom(sK15(sK14(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_9107]) ).
tcf(c_13936,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_9107]) ).
tcf(c_14000,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(relation_dom(relation_dom(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_9211]) ).
tcf(c_14001,plain,
sK15(sK14(powerset(relation_dom(relation_dom(relation_dom(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_9211]) ).
tcf(c_14002,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(relation_dom(relation_dom(sK15(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_9211]) ).
tcf(c_14003,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_9211]) ).
tcf(c_14004,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_9211]) ).
tcf(c_14005,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(relation_dom(relation_dom(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_9211]) ).
tcf(c_14006,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( sK15(sK14(powerset(relation_dom(relation_dom(relation_dom(sK15(powerset(singleton(X0))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_9211]) ).
tcf(c_14007,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_9211]) ).
tcf(c_14008,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(relation_dom(relation_dom(sK15(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_9211]) ).
tcf(c_14009,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_9211]) ).
tcf(c_14010,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_9211]) ).
tcf(c_14011,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_9211]) ).
tcf(c_14012,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_9211]) ).
tcf(c_14073,plain,
! [X0: $i] :
( empty(X0)
| element(sK15(sK14(sK14(sK14(sK14(X0))))),X0) ),
inference(global_subsumption_just,[status(thm)],[c_9268,c_98,c_9268]) ).
tcf(c_14080,plain,
! [X0: $i] :
( empty(X0)
| in(sK15(sK14(sK14(sK14(sK14(X0))))),X0) ),
inference(superposition,[status(thm)],[c_14073,c_66]) ).
tcf(c_14081,plain,
! [X0: $i,X1: $i] :
( empty(powerset(X1))
| element(X0,X1)
| ~ in(X0,sK15(sK14(sK14(sK14(sK14(powerset(X1))))))) ),
inference(superposition,[status(thm)],[c_14073,c_94]) ).
tcf(c_14082,plain,
! [X0: $i,X1: $i] :
( empty(powerset(X1))
| ~ empty(X1)
| ~ in(X0,sK15(sK14(sK14(sK14(sK14(powerset(X1))))))) ),
inference(superposition,[status(thm)],[c_14073,c_93]) ).
tcf(c_14085,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ in(X0,sK15(sK14(sK14(sK14(sK14(powerset(X1))))))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14082,c_100]) ).
tcf(c_14088,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| ~ in(X0,sK15(sK14(sK14(sK14(sK14(powerset(X1))))))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14081,c_100]) ).
tcf(c_14097,plain,
! [X0: $i,X1: $i] :
( empty(relation_image(X0,X1))
| ( apply(X0,sK5(X0,X1,sK15(sK14(sK14(sK14(sK14(relation_image(X0,X1)))))))) = sK15(sK14(sK14(sK14(sK14(relation_image(X0,X1)))))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_14080,c_64]) ).
tcf(c_14098,plain,
! [X0: $i] :
( empty(X0)
| ~ in(X0,sK15(sK14(sK14(sK14(sK14(X0)))))) ),
inference(superposition,[status(thm)],[c_14080,c_68]) ).
tcf(c_14101,plain,
! [X0: $i] :
( empty(singleton(X0))
| ( sK15(sK14(sK14(sK14(sK14(singleton(X0)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_14080,c_82]) ).
tcf(c_14102,plain,
! [X0: $i] :
( empty(X0)
| empty(sK14(X0))
| element(sK15(sK14(sK14(sK14(sK14(sK14(X0)))))),X0) ),
inference(superposition,[status(thm)],[c_14080,c_5328]) ).
tcf(c_14103,plain,
! [X0: $i] :
( empty(sK15(powerset(X0)))
| element(sK15(sK14(sK14(sK14(sK14(sK15(powerset(X0))))))),X0) ),
inference(superposition,[status(thm)],[c_14080,c_5329]) ).
tcf(c_14107,plain,
! [X0: $i] :
( empty(sK15(sK14(powerset(X0))))
| element(sK15(sK14(sK14(sK14(sK14(sK15(sK14(powerset(X0)))))))),X0) ),
inference(superposition,[status(thm)],[c_14080,c_6063]) ).
tcf(c_14109,plain,
! [X0: $i] :
( empty(sK15(sK14(sK14(powerset(X0)))))
| element(sK15(sK14(sK14(sK14(sK14(sK15(sK14(sK14(powerset(X0))))))))),X0) ),
inference(superposition,[status(thm)],[c_14080,c_7006]) ).
tcf(c_14111,plain,
! [X0: $i] :
( empty(sK15(sK14(sK14(sK14(powerset(X0))))))
| element(sK15(sK14(sK14(sK14(sK14(sK15(sK14(sK14(sK14(powerset(X0)))))))))),X0) ),
inference(superposition,[status(thm)],[c_14080,c_9254]) ).
tcf(c_14115,plain,
! [X0: $i] : sK15(sK14(sK14(sK14(sK14(singleton(X0)))))) = X0,
inference(forward_subsumption_resolution,[status(thm)],[c_14101,c_78]) ).
tcf(c_14151,plain,
! [X0: $i] :
( empty(sK14(sK14(sK14(sK14(singleton(X0))))))
| ~ in(sK14(sK14(sK14(sK14(singleton(X0))))),X0) ),
inference(superposition,[status(thm)],[c_14115,c_5145]) ).
tcf(c_14152,plain,
! [X0: $i] :
( empty(sK14(sK14(sK14(sK14(singleton(X0))))))
| in(X0,sK14(sK14(sK14(sK14(singleton(X0)))))) ),
inference(superposition,[status(thm)],[c_14115,c_5124]) ).
tcf(c_14153,plain,
! [X0: $i] : element(X0,sK14(sK14(sK14(sK14(singleton(X0)))))),
inference(superposition,[status(thm)],[c_14115,c_99]) ).
tcf(c_14212,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(relation_dom(relation_dom(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_9411]) ).
tcf(c_14213,plain,
relation_dom(sK15(sK14(powerset(relation_dom(relation_dom(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_9411]) ).
tcf(c_14214,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(relation_dom(relation_dom(sK15(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_9411]) ).
tcf(c_14215,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(relation_dom(relation_dom(sK15(sK14(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_9411]) ).
tcf(c_14216,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(relation_dom(relation_dom(sK15(sK14(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_9411]) ).
tcf(c_14217,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(relation_dom(relation_dom(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_9411]) ).
tcf(c_14218,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( relation_dom(sK15(sK14(powerset(relation_dom(relation_dom(sK15(powerset(singleton(X0))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_9411]) ).
tcf(c_14219,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(relation_dom(relation_dom(sK15(powerset(sK15(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_9411]) ).
tcf(c_14220,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(relation_dom(relation_dom(sK15(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_9411]) ).
tcf(c_14221,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_9411]) ).
tcf(c_14222,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_9411]) ).
tcf(c_14223,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(relation_dom(relation_dom(sK15(sK14(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_9411]) ).
tcf(c_14224,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_9411]) ).
tcf(c_14260,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(powerset(relation_dom(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_9505]) ).
tcf(c_14261,plain,
relation_dom(sK15(sK14(sK14(powerset(relation_dom(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_9505]) ).
tcf(c_14262,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(powerset(relation_dom(sK15(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_9505]) ).
tcf(c_14263,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(powerset(relation_dom(sK15(sK14(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_9505]) ).
tcf(c_14264,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(powerset(relation_dom(sK15(sK14(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_9505]) ).
tcf(c_14265,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(powerset(relation_dom(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_9505]) ).
tcf(c_14266,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( relation_dom(sK15(sK14(sK14(powerset(relation_dom(sK15(powerset(singleton(X0))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_9505]) ).
tcf(c_14267,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(powerset(relation_dom(sK15(powerset(sK15(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_9505]) ).
tcf(c_14268,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(powerset(relation_dom(sK15(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_9505]) ).
tcf(c_14269,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(powerset(relation_dom(sK15(powerset(sK15(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_9505]) ).
tcf(c_14270,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_9505]) ).
tcf(c_14271,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(powerset(relation_dom(sK15(sK14(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_9505]) ).
tcf(c_14272,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_9505]) ).
tcf(c_14357,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(relation_dom(relation_dom(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_9586]) ).
tcf(c_14358,plain,
sK15(sK14(sK14(powerset(relation_dom(relation_dom(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_9586]) ).
tcf(c_14359,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(relation_dom(relation_dom(sK15(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_9586]) ).
tcf(c_14360,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(relation_dom(relation_dom(sK15(sK14(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_9586]) ).
tcf(c_14361,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(relation_dom(relation_dom(sK15(sK14(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_9586]) ).
tcf(c_14362,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(relation_dom(relation_dom(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_9586]) ).
tcf(c_14363,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( sK15(sK14(sK14(powerset(relation_dom(relation_dom(sK15(powerset(singleton(X0))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_9586]) ).
tcf(c_14364,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(relation_dom(relation_dom(sK15(powerset(sK15(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_9586]) ).
tcf(c_14365,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(relation_dom(relation_dom(sK15(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_9586]) ).
tcf(c_14366,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_9586]) ).
tcf(c_14367,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_9586]) ).
tcf(c_14368,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(relation_dom(relation_dom(sK15(sK14(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_9586]) ).
tcf(c_14369,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_9586]) ).
tcf(c_14463,plain,
( empty(sK15(powerset(empty_set)))
| element(sK15(sK14(sK14(sK14(empty_set)))),empty_set) ),
inference(superposition,[status(thm)],[c_5301,c_9269]) ).
tcf(c_14464,plain,
! [X0: $i] :
( empty(X0)
| empty(sK15(powerset(X0)))
| in(sK15(sK14(sK14(sK14(sK15(powerset(X0)))))),X0) ),
inference(superposition,[status(thm)],[c_9269,c_66]) ).
tcf(c_14465,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| empty(sK15(powerset(powerset(X1))))
| ~ in(X0,sK15(sK14(sK14(sK14(sK15(powerset(powerset(X1)))))))) ),
inference(superposition,[status(thm)],[c_9269,c_94]) ).
tcf(c_14466,plain,
! [X0: $i,X1: $i] :
( empty(sK15(powerset(powerset(X1))))
| ~ empty(X1)
| ~ in(X0,sK15(sK14(sK14(sK14(sK15(powerset(powerset(X1)))))))) ),
inference(superposition,[status(thm)],[c_9269,c_93]) ).
tcf(c_14467,plain,
( empty(empty_set)
| element(sK15(sK14(sK14(sK14(empty_set)))),empty_set) ),
inference(light_normalisation,[status(thm)],[c_14463,c_5301]) ).
tcf(c_14491,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(sK14(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_10136]) ).
tcf(c_14492,plain,
relation_dom(sK15(sK14(sK14(sK14(powerset(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_10136]) ).
tcf(c_14493,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(sK14(powerset(sK15(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_10136]) ).
tcf(c_14494,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(sK14(powerset(sK15(sK14(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_10136]) ).
tcf(c_14495,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_10136]) ).
tcf(c_14496,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(sK14(powerset(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_10136]) ).
tcf(c_14497,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( relation_dom(sK15(sK14(sK14(sK14(powerset(sK15(powerset(singleton(X0))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_10136]) ).
tcf(c_14498,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(sK14(powerset(sK15(powerset(sK15(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_10136]) ).
tcf(c_14499,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(sK14(powerset(sK15(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_10136]) ).
tcf(c_14500,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(sK14(powerset(sK15(powerset(sK15(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_10136]) ).
tcf(c_14501,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(sK14(powerset(sK15(powerset(sK15(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_10136]) ).
tcf(c_14502,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_10136]) ).
tcf(c_14503,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(sK14(powerset(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_10136]) ).
tcf(c_14554,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(powerset(relation_dom(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_10887]) ).
tcf(c_14555,plain,
sK15(sK14(sK14(sK14(powerset(relation_dom(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_10887]) ).
tcf(c_14556,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(powerset(relation_dom(sK15(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_10887]) ).
tcf(c_14557,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(powerset(relation_dom(sK15(sK14(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_10887]) ).
tcf(c_14558,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(powerset(relation_dom(sK15(sK14(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_10887]) ).
tcf(c_14559,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(powerset(relation_dom(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_10887]) ).
tcf(c_14560,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( sK15(sK14(sK14(sK14(powerset(relation_dom(sK15(powerset(singleton(X0))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_10887]) ).
tcf(c_14561,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(powerset(relation_dom(sK15(powerset(sK15(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_10887]) ).
tcf(c_14562,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(powerset(relation_dom(sK15(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_10887]) ).
tcf(c_14563,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(powerset(relation_dom(sK15(powerset(sK15(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_10887]) ).
tcf(c_14564,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_10887]) ).
tcf(c_14565,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(powerset(relation_dom(sK15(sK14(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_10887]) ).
tcf(c_14566,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_10887]) ).
tcf(c_14629,plain,
! [X0: $i,X1: $i] :
( empty(relation_image(X0,X1))
| ( sK14(relation_image(X0,X1)) = empty_set )
| ( apply(X0,sK5(X0,X1,sK2(sK14(relation_image(X0,X1)),empty_set))) = sK2(sK14(relation_image(X0,X1)),empty_set) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_11363,c_64]) ).
tcf(c_14630,plain,
! [X0: $i] :
( empty(X0)
| ( sK14(X0) = empty_set )
| ~ in(X0,sK2(sK14(X0),empty_set)) ),
inference(superposition,[status(thm)],[c_11363,c_68]) ).
tcf(c_14633,plain,
! [X0: $i] :
( empty(singleton(X0))
| ( sK14(singleton(X0)) = empty_set )
| ( sK2(sK14(singleton(X0)),empty_set) = X0 ) ),
inference(superposition,[status(thm)],[c_11363,c_82]) ).
tcf(c_14634,plain,
! [X0: $i] :
( empty(X0)
| empty(sK14(X0))
| element(sK2(sK14(sK14(X0)),empty_set),X0)
| ( sK14(sK14(X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_11363,c_5328]) ).
tcf(c_14635,plain,
! [X0: $i] :
( empty(sK15(powerset(X0)))
| element(sK2(sK14(sK15(powerset(X0))),empty_set),X0)
| ( sK14(sK15(powerset(X0))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11363,c_5329]) ).
tcf(c_14636,plain,
! [X0: $i] :
( empty(sK15(powerset(X0)))
| ( sK14(sK15(powerset(X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11363,c_5201]) ).
tcf(c_14638,plain,
! [X0: $i] :
( empty(relation_image(X0,empty_set))
| ( sK14(relation_image(X0,empty_set)) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_11363,c_5411]) ).
tcf(c_14639,plain,
! [X0: $i] :
( empty(sK15(sK14(powerset(X0))))
| element(sK2(sK14(sK15(sK14(powerset(X0)))),empty_set),X0)
| ( sK14(sK15(sK14(powerset(X0)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11363,c_6063]) ).
tcf(c_14640,plain,
! [X0: $i] :
( empty(sK15(sK14(powerset(X0))))
| ( sK14(sK15(sK14(powerset(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11363,c_6060]) ).
tcf(c_14641,plain,
! [X0: $i] :
( empty(sK15(sK14(sK14(powerset(X0)))))
| element(sK2(sK14(sK15(sK14(sK14(powerset(X0))))),empty_set),X0)
| ( sK14(sK15(sK14(sK14(powerset(X0))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11363,c_7006]) ).
tcf(c_14642,plain,
! [X0: $i] :
( empty(sK15(sK14(sK14(powerset(X0)))))
| ( sK14(sK15(sK14(sK14(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11363,c_7003]) ).
tcf(c_14643,plain,
! [X0: $i] :
( empty(sK15(sK14(sK14(sK14(powerset(X0))))))
| element(sK2(sK14(sK15(sK14(sK14(sK14(powerset(X0)))))),empty_set),X0)
| ( sK14(sK15(sK14(sK14(sK14(powerset(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11363,c_9254]) ).
tcf(c_14644,plain,
! [X0: $i] :
( empty(sK15(sK14(sK14(sK14(powerset(X0))))))
| ( sK14(sK15(sK14(sK14(sK14(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11363,c_9251]) ).
tcf(c_14658,plain,
! [X0: $i] :
( ( sK14(singleton(X0)) = empty_set )
| ( sK2(sK14(singleton(X0)),empty_set) = X0 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14633,c_78]) ).
tcf(c_14763,plain,
! [X0: $i,X1: $i] :
( empty(relation_image(X0,X1))
| ( sK14(relation_image(X0,X1)) = empty_set )
| ( apply(X0,sK5(X0,X1,sK2(empty_set,sK14(relation_image(X0,X1))))) = sK2(empty_set,sK14(relation_image(X0,X1))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_11418,c_64]) ).
tcf(c_14764,plain,
! [X0: $i] :
( empty(X0)
| ( sK14(X0) = empty_set )
| ~ in(X0,sK2(empty_set,sK14(X0))) ),
inference(superposition,[status(thm)],[c_11418,c_68]) ).
tcf(c_14767,plain,
! [X0: $i] :
( empty(singleton(X0))
| ( sK14(singleton(X0)) = empty_set )
| ( sK2(empty_set,sK14(singleton(X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_11418,c_82]) ).
tcf(c_14768,plain,
! [X0: $i] :
( empty(X0)
| empty(sK14(X0))
| element(sK2(empty_set,sK14(sK14(X0))),X0)
| ( sK14(sK14(X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_11418,c_5328]) ).
tcf(c_14769,plain,
! [X0: $i] :
( empty(sK15(powerset(X0)))
| element(sK2(empty_set,sK14(sK15(powerset(X0)))),X0)
| ( sK14(sK15(powerset(X0))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11418,c_5329]) ).
tcf(c_14773,plain,
! [X0: $i] :
( empty(sK15(sK14(powerset(X0))))
| element(sK2(empty_set,sK14(sK15(sK14(powerset(X0))))),X0)
| ( sK14(sK15(sK14(powerset(X0)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11418,c_6063]) ).
tcf(c_14775,plain,
! [X0: $i] :
( empty(sK15(sK14(sK14(powerset(X0)))))
| element(sK2(empty_set,sK14(sK15(sK14(sK14(powerset(X0)))))),X0)
| ( sK14(sK15(sK14(sK14(powerset(X0))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11418,c_7006]) ).
tcf(c_14777,plain,
! [X0: $i] :
( empty(sK15(sK14(sK14(sK14(powerset(X0))))))
| element(sK2(empty_set,sK14(sK15(sK14(sK14(sK14(powerset(X0))))))),X0)
| ( sK14(sK15(sK14(sK14(sK14(powerset(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11418,c_9254]) ).
tcf(c_14782,plain,
! [X0: $i] :
( ( sK14(singleton(X0)) = empty_set )
| ( sK2(empty_set,sK14(singleton(X0))) = X0 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14767,c_78]) ).
tcf(c_14838,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( relation_dom(relation_image(sK15(powerset(singleton(X0))),empty_set)) = empty_set )
| ~ relation(sK15(powerset(singleton(X0)))) ),
inference(superposition,[status(thm)],[c_12760,c_7934]) ).
tcf(c_14839,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( relation_image(sK15(powerset(singleton(X0))),empty_set) = empty_set )
| ~ relation(sK15(powerset(singleton(X0)))) ),
inference(superposition,[status(thm)],[c_12760,c_7777]) ).
tcf(c_14853,plain,
! [X0: $i,X1: $i] :
( in(sK2(X1,sK15(sK14(sK14(sK14(sK14(powerset(X0))))))),X1)
| ( sK15(sK14(sK14(sK14(sK14(powerset(X0)))))) = X1 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_56,c_14085]) ).
tcf(c_14854,plain,
! [X0: $i,X1: $i] :
( in(sK2(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))),X1),X1)
| ( sK15(sK14(sK14(sK14(sK14(powerset(X0)))))) = X1 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_56,c_14085]) ).
tcf(c_14855,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK15(sK14(sK14(sK14(sK14(powerset(X1)))))) = relation_image(X0,X2) )
| ( apply(X0,sK4(X0,X2,sK15(sK14(sK14(sK14(sK14(powerset(X1)))))))) = sK3(X0,X2,sK15(sK14(sK14(sK14(sK14(powerset(X1))))))) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_60,c_14085]) ).
tcf(c_14856,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK4(X0,X2,sK15(sK14(sK14(sK14(sK14(powerset(X1))))))),relation_dom(X0))
| ( sK15(sK14(sK14(sK14(sK14(powerset(X1)))))) = relation_image(X0,X2) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_58,c_14085]) ).
tcf(c_14857,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK4(X0,X2,sK15(sK14(sK14(sK14(sK14(powerset(X1))))))),X2)
| ( sK15(sK14(sK14(sK14(sK14(powerset(X1)))))) = relation_image(X0,X2) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_59,c_14085]) ).
tcf(c_14858,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(X0,sK15(sK14(sK14(sK14(sK14(powerset(X1)))))),X2),X2)
| ( relation_image(X0,sK15(sK14(sK14(sK14(sK14(powerset(X1))))))) = X2 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_59,c_14085]) ).
tcf(c_14859,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(X2)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,sK15(sK14(sK14(sK14(sK14(powerset(X2)))))))) ),
inference(superposition,[status(thm)],[c_63,c_14085]) ).
tcf(c_14860,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK14(sK14(sK14(sK14(powerset(X0)))))) = singleton(X1) )
| ( sK8(X1,sK15(sK14(sK14(sK14(sK14(powerset(X0))))))) = X1 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_80,c_14085]) ).
tcf(c_14861,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK14(sK14(sK14(sK14(powerset(X1)))))) = X0 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5062,c_14085]) ).
tcf(c_14863,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK14(sK14(sK14(sK14(powerset(X0)))))) = singleton(X1) )
| ( sK2(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))),singleton(X1)) = X1 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5169,c_14085]) ).
tcf(c_14868,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(sK14(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6288,c_14085]) ).
tcf(c_14870,plain,
! [X0: $i] :
( empty(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11240,c_14085]) ).
tcf(c_14872,plain,
! [X0: $i] :
( empty(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))
| ( sK14(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11363,c_14085]) ).
tcf(c_14874,plain,
! [X0: $i] :
( empty(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14080,c_14085]) ).
tcf(c_14927,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(powerset(relation_dom(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_10887]) ).
tcf(c_14928,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_10136]) ).
tcf(c_14929,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(relation_dom(relation_dom(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_9586]) ).
tcf(c_14930,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(powerset(relation_dom(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_9505]) ).
tcf(c_14931,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(relation_dom(relation_dom(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_9411]) ).
tcf(c_14932,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_9211]) ).
tcf(c_14933,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(powerset(relation_dom(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_9107]) ).
tcf(c_14934,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(powerset(relation_dom(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_9025]) ).
tcf(c_14935,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_8993]) ).
tcf(c_14936,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_8933]) ).
tcf(c_14937,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_8858]) ).
tcf(c_14938,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(relation_dom(relation_dom(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_8821]) ).
tcf(c_14939,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(powerset(relation_dom(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_8743]) ).
tcf(c_14940,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(powerset(relation_dom(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_8705]) ).
tcf(c_14941,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(powerset(relation_dom(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_8667]) ).
tcf(c_14942,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_8236]) ).
tcf(c_14943,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_8209]) ).
tcf(c_14944,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_7684]) ).
tcf(c_14945,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_7254]) ).
tcf(c_14946,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_7253]) ).
tcf(c_14947,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_7142]) ).
tcf(c_14948,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_6953]) ).
tcf(c_14949,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_6938]) ).
tcf(c_14950,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_6905]) ).
tcf(c_14951,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_6887]) ).
tcf(c_14952,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_8076]) ).
tcf(c_14953,plain,
! [X0: $i,X1: $i] :
( ( sK15(powerset(relation_dom(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_7738]) ).
tcf(c_14954,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_6856]) ).
tcf(c_14955,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_6832]) ).
tcf(c_14956,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_6797]) ).
tcf(c_14957,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_6681]) ).
tcf(c_14958,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_6189]) ).
tcf(c_14959,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_6188]) ).
tcf(c_14960,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_6187]) ).
tcf(c_14961,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_6192]) ).
tcf(c_14962,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_9868]) ).
tcf(c_14963,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(relation_dom(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_7682]) ).
tcf(c_14964,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_7256]) ).
tcf(c_14965,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(relation_dom(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_7140]) ).
tcf(c_14966,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(relation_dom(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_6951]) ).
tcf(c_14967,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_6680]) ).
tcf(c_14968,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_6191]) ).
tcf(c_14969,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_6936]) ).
tcf(c_14970,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_6903]) ).
tcf(c_14971,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_6885]) ).
tcf(c_14972,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(relation_dom(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_6854]) ).
tcf(c_14973,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_6190]) ).
tcf(c_14974,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_5583]) ).
tcf(c_14975,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_5569]) ).
tcf(c_14976,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_6830]) ).
tcf(c_14977,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_6795]) ).
tcf(c_14978,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_5557]) ).
tcf(c_14979,plain,
! [X0: $i,X1: $i] :
( ( sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_5270]) ).
tcf(c_14980,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_7171]) ).
tcf(c_14981,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_6193]) ).
tcf(c_14982,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_6678]) ).
tcf(c_14983,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_5581]) ).
tcf(c_14984,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_5567]) ).
tcf(c_14985,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_5555]) ).
tcf(c_14986,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_5302]) ).
tcf(c_14987,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_5269]) ).
tcf(c_14988,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_5189]) ).
tcf(c_14989,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_6153]) ).
tcf(c_14990,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_5300]) ).
tcf(c_14991,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_5271]) ).
tcf(c_14992,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_5245]) ).
tcf(c_14993,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_5272]) ).
tcf(c_14994,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_5110]) ).
tcf(c_14995,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK14(sK14(sK14(sK14(powerset(X0)))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_53]) ).
tcf(c_14996,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_5023]) ).
tcf(c_14998,plain,
! [X0: $i] :
( relation(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_87]) ).
tcf(c_14999,plain,
! [X0: $i] :
( function(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_77]) ).
tcf(c_15337,plain,
! [X0: $i] :
( empty(sK14(sK14(powerset(sK15(powerset(sK15(powerset(singleton(X0)))))))))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ~ in(sK14(sK14(powerset(sK15(powerset(sK15(powerset(singleton(X0)))))))),empty_set) ),
inference(superposition,[status(thm)],[c_12705,c_5145]) ).
tcf(c_15338,plain,
! [X0: $i] :
( empty(sK14(sK14(powerset(sK15(powerset(sK15(powerset(singleton(X0)))))))))
| in(empty_set,sK14(sK14(powerset(sK15(powerset(sK15(powerset(singleton(X0)))))))))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 ) ),
inference(superposition,[status(thm)],[c_12705,c_5124]) ).
tcf(c_15339,plain,
! [X0: $i] :
( element(empty_set,sK14(sK14(powerset(sK15(powerset(sK15(powerset(singleton(X0)))))))))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 ) ),
inference(superposition,[status(thm)],[c_12705,c_99]) ).
tcf(c_15340,plain,
! [X0: $i] :
( empty(sK14(powerset(sK15(powerset(sK15(powerset(singleton(X0))))))))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ~ in(sK14(powerset(sK15(powerset(sK15(powerset(singleton(X0))))))),empty_set) ),
inference(superposition,[status(thm)],[c_12705,c_6091]) ).
tcf(c_15341,plain,
! [X0: $i] :
( empty(sK14(powerset(sK15(powerset(sK15(powerset(singleton(X0))))))))
| in(empty_set,sK14(powerset(sK15(powerset(sK15(powerset(singleton(X0))))))))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 ) ),
inference(superposition,[status(thm)],[c_12705,c_6055]) ).
tcf(c_15342,plain,
! [X0: $i] :
( empty(sK14(powerset(sK15(powerset(sK15(powerset(singleton(X0))))))))
| element(empty_set,sK14(powerset(sK15(powerset(sK15(powerset(singleton(X0))))))))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 ) ),
inference(superposition,[status(thm)],[c_12705,c_6048]) ).
tcf(c_15343,plain,
! [X0: $i] :
( empty(powerset(sK15(powerset(sK15(powerset(singleton(X0)))))))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ~ in(powerset(sK15(powerset(sK15(powerset(singleton(X0)))))),empty_set) ),
inference(superposition,[status(thm)],[c_12705,c_7041]) ).
tcf(c_15344,plain,
! [X0: $i] :
( empty(powerset(sK15(powerset(sK15(powerset(singleton(X0)))))))
| in(empty_set,powerset(sK15(powerset(sK15(powerset(singleton(X0)))))))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 ) ),
inference(superposition,[status(thm)],[c_12705,c_6998]) ).
tcf(c_15345,plain,
! [X0: $i] :
( empty(powerset(sK15(powerset(sK15(powerset(singleton(X0)))))))
| element(empty_set,powerset(sK15(powerset(sK15(powerset(singleton(X0)))))))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 ) ),
inference(superposition,[status(thm)],[c_12705,c_6991]) ).
tcf(c_15346,plain,
! [X0: $i] :
( function(sK15(powerset(empty_set)))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ~ empty(sK15(powerset(sK15(powerset(singleton(X0)))))) ),
inference(superposition,[status(thm)],[c_12705,c_8577]) ).
tcf(c_15347,plain,
! [X0: $i] :
( relation(sK15(powerset(empty_set)))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ~ empty(sK15(powerset(sK15(powerset(singleton(X0)))))) ),
inference(superposition,[status(thm)],[c_12705,c_8576]) ).
tcf(c_15348,plain,
! [X0: $i] :
( empty(sK15(powerset(empty_set)))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ~ empty(sK15(powerset(sK15(powerset(singleton(X0)))))) ),
inference(superposition,[status(thm)],[c_12705,c_8123]) ).
tcf(c_15353,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ~ in(X1,empty_set)
| ~ empty(sK15(powerset(sK15(powerset(singleton(X0)))))) ),
inference(superposition,[status(thm)],[c_12705,c_7003]) ).
tcf(c_15356,plain,
! [X0: $i] :
( empty(empty_set)
| ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ~ empty(sK15(powerset(sK15(powerset(singleton(X0)))))) ),
inference(light_normalisation,[status(thm)],[c_15348,c_5301]) ).
tcf(c_15357,plain,
! [X0: $i] :
( relation(empty_set)
| ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ~ empty(sK15(powerset(sK15(powerset(singleton(X0)))))) ),
inference(light_normalisation,[status(thm)],[c_15347,c_5301]) ).
tcf(c_15358,plain,
! [X0: $i] :
( function(empty_set)
| ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ~ empty(sK15(powerset(sK15(powerset(singleton(X0)))))) ),
inference(light_normalisation,[status(thm)],[c_15346,c_5301]) ).
tcf(c_15376,plain,
! [X0: $i] :
( ( relation_dom(relation_image(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))),empty_set)) = empty_set )
| ~ empty(X0)
| ~ relation(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))) ),
inference(superposition,[status(thm)],[c_14999,c_7934]) ).
tcf(c_15377,plain,
! [X0: $i] :
( ( relation_image(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))),empty_set) = empty_set )
| ~ empty(X0)
| ~ relation(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))) ),
inference(superposition,[status(thm)],[c_14999,c_7777]) ).
tcf(c_15388,plain,
! [X0: $i,X1: $i] :
( element(sK2(X0,sK15(sK14(sK14(sK14(sK14(powerset(X1))))))),X1)
| ( sK15(sK14(sK14(sK14(sK14(powerset(X1)))))) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5063,c_14088]) ).
tcf(c_15389,plain,
! [X0: $i,X1: $i] :
( element(sK2(X1,sK15(sK14(sK14(sK14(sK14(powerset(X0))))))),X0)
| in(sK2(X1,sK15(sK14(sK14(sK14(sK14(powerset(X0))))))),X1)
| ( sK15(sK14(sK14(sK14(sK14(powerset(X0)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_56,c_14088]) ).
tcf(c_15390,plain,
! [X0: $i,X1: $i] :
( element(sK2(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))),X1),X0)
| in(sK2(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))),X1),X1)
| ( sK15(sK14(sK14(sK14(sK14(powerset(X0)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_56,c_14088]) ).
tcf(c_15391,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK3(X0,X1,sK15(sK14(sK14(sK14(sK14(powerset(X2))))))),X2)
| ( sK15(sK14(sK14(sK14(sK14(powerset(X2)))))) = relation_image(X0,X1) )
| ( apply(X0,sK4(X0,X1,sK15(sK14(sK14(sK14(sK14(powerset(X2)))))))) = sK3(X0,X1,sK15(sK14(sK14(sK14(sK14(powerset(X2))))))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_60,c_14088]) ).
tcf(c_15392,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK3(X0,X2,sK15(sK14(sK14(sK14(sK14(powerset(X1))))))),X1)
| in(sK4(X0,X2,sK15(sK14(sK14(sK14(sK14(powerset(X1))))))),relation_dom(X0))
| ( sK15(sK14(sK14(sK14(sK14(powerset(X1)))))) = relation_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_58,c_14088]) ).
tcf(c_15393,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK3(X0,X2,sK15(sK14(sK14(sK14(sK14(powerset(X1))))))),X1)
| in(sK4(X0,X2,sK15(sK14(sK14(sK14(sK14(powerset(X1))))))),X2)
| ( sK15(sK14(sK14(sK14(sK14(powerset(X1)))))) = relation_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_59,c_14088]) ).
tcf(c_15394,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK4(X0,sK15(sK14(sK14(sK14(sK14(powerset(X1)))))),X2),X1)
| in(sK3(X0,sK15(sK14(sK14(sK14(sK14(powerset(X1)))))),X2),X2)
| ( relation_image(X0,sK15(sK14(sK14(sK14(sK14(powerset(X1))))))) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_59,c_14088]) ).
tcf(c_15395,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK5(X1,sK15(sK14(sK14(sK14(sK14(powerset(X2)))))),X0),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,sK15(sK14(sK14(sK14(sK14(powerset(X2)))))))) ),
inference(superposition,[status(thm)],[c_63,c_14088]) ).
tcf(c_15396,plain,
! [X0: $i,X1: $i] :
( element(sK8(X0,sK15(sK14(sK14(sK14(sK14(powerset(X1))))))),X1)
| ( sK15(sK14(sK14(sK14(sK14(powerset(X1)))))) = singleton(X0) )
| ( sK8(X0,sK15(sK14(sK14(sK14(sK14(powerset(X1))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_80,c_14088]) ).
tcf(c_15397,plain,
! [X0: $i,X1: $i] :
( element(sK2(sK15(sK14(sK14(sK14(sK14(powerset(X1)))))),X0),X1)
| ( sK15(sK14(sK14(sK14(sK14(powerset(X1)))))) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5062,c_14088]) ).
tcf(c_15398,plain,
! [X0: $i] :
( empty(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))
| element(sK15(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))),X0) ),
inference(superposition,[status(thm)],[c_5124,c_14088]) ).
tcf(c_15399,plain,
! [X0: $i,X1: $i] :
( element(sK2(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))),singleton(X1)),X0)
| ( sK15(sK14(sK14(sK14(sK14(powerset(X0)))))) = singleton(X1) )
| ( sK2(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))),singleton(X1)) = X1 ) ),
inference(superposition,[status(thm)],[c_5169,c_14088]) ).
tcf(c_15400,plain,
! [X0: $i] :
( element(sK2(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))),empty_set),X0)
| ( sK15(sK14(sK14(sK14(sK14(powerset(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5409,c_14088]) ).
tcf(c_15401,plain,
! [X0: $i] :
( element(sK2(empty_set,sK15(sK14(sK14(sK14(sK14(powerset(X0))))))),X0)
| ( sK15(sK14(sK14(sK14(sK14(powerset(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5410,c_14088]) ).
tcf(c_15402,plain,
! [X0: $i] :
( empty(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))
| element(sK15(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))),X0) ),
inference(superposition,[status(thm)],[c_8103,c_14088]) ).
tcf(c_15403,plain,
! [X0: $i] :
( empty(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))
| element(sK15(sK14(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))),X0) ),
inference(superposition,[status(thm)],[c_6055,c_14088]) ).
tcf(c_15404,plain,
! [X0: $i,X1: $i] :
( element(sK3(empty_set,X1,sK15(sK14(sK14(sK14(sK14(powerset(X0))))))),X0)
| ( sK15(sK14(sK14(sK14(sK14(powerset(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_6288,c_14088]) ).
tcf(c_15405,plain,
! [X0: $i] :
( empty(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))
| element(sK15(sK14(sK14(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))),X0) ),
inference(superposition,[status(thm)],[c_6998,c_14088]) ).
tcf(c_15406,plain,
! [X0: $i] :
( empty(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))
| element(sK15(sK14(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))),X0) ),
inference(superposition,[status(thm)],[c_11240,c_14088]) ).
tcf(c_15407,plain,
! [X0: $i] :
( empty(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))
| element(sK15(sK14(sK14(sK14(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))),X0) ),
inference(superposition,[status(thm)],[c_9246,c_14088]) ).
tcf(c_15408,plain,
! [X0: $i] :
( empty(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))
| element(sK2(sK14(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))),empty_set),X0)
| ( sK14(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11363,c_14088]) ).
tcf(c_15409,plain,
! [X0: $i] :
( empty(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))
| element(sK2(empty_set,sK14(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))),X0)
| ( sK14(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11418,c_14088]) ).
tcf(c_15410,plain,
! [X0: $i] :
( empty(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))
| element(sK15(sK14(sK14(sK14(sK14(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))),X0) ),
inference(superposition,[status(thm)],[c_14080,c_14088]) ).
tcf(c_15581,plain,
! [X0: $i,X1: $i] :
( element(X0,singleton(X1))
| in(sK2(singleton(X0),singleton(X1)),singleton(X0))
| ( singleton(X0) = singleton(X1) )
| ( sK2(singleton(X0),singleton(X1)) = X1 ) ),
inference(superposition,[status(thm)],[c_11036,c_5076]) ).
tcf(c_15582,plain,
! [X0: $i,X1: $i] :
( element(X1,singleton(X1))
| in(sK2(singleton(X0),singleton(X1)),singleton(X0))
| ( singleton(X0) = singleton(X1) )
| ( sK2(singleton(X0),singleton(X1)) = X0 ) ),
inference(superposition,[status(thm)],[c_11036,c_5076]) ).
tcf(c_15584,plain,
! [X0: $i] :
( in(X0,empty_set)
| element(sK2(empty_set,singleton(X0)),singleton(X0))
| ( singleton(X0) = empty_set ) ),
inference(superposition,[status(thm)],[c_9564,c_5076]) ).
tcf(c_15586,plain,
! [X0: $i,X1: $i] :
( in(X1,singleton(X0))
| element(sK2(singleton(X0),singleton(X1)),singleton(X1))
| ( singleton(X0) = singleton(X1) )
| ( sK2(singleton(X0),singleton(X1)) = X0 ) ),
inference(superposition,[status(thm)],[c_11036,c_5076]) ).
tcf(c_15588,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,X2)
| in(sK2(X1,powerset(X2)),X1)
| ( powerset(X2) = X1 )
| ~ in(X0,sK2(X1,powerset(X2))) ),
inference(superposition,[status(thm)],[c_5076,c_94]) ).
tcf(c_15589,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,powerset(X2)),X1)
| ( powerset(X2) = X1 )
| ~ empty(X2)
| ~ in(X0,sK2(X1,powerset(X2))) ),
inference(superposition,[status(thm)],[c_5076,c_93]) ).
tcf(c_15591,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(relation_image(X0,X1),X2),X2)
| ( relation_image(X0,X1) = X2 )
| ( apply(X0,sK5(X0,X1,sK2(relation_image(X0,X1),X2))) = sK2(relation_image(X0,X1),X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_5076,c_64]) ).
tcf(c_15592,plain,
! [X0: $i,X1: $i] :
( element(sK2(X0,X1),X1)
| ( X0 = X1 )
| ~ in(X0,sK2(X0,X1)) ),
inference(superposition,[status(thm)],[c_5076,c_68]) ).
tcf(c_15593,plain,
! [X0: $i,X1: $i] :
( element(sK2(X0,X1),X1)
| element(sK2(X0,X1),X0)
| ( X0 = X1 ) ),
inference(superposition,[status(thm)],[c_5076,c_67]) ).
tcf(c_15595,plain,
! [X0: $i,X1: $i] :
( element(sK2(singleton(X0),X1),X1)
| ( singleton(X0) = X1 )
| ( sK2(singleton(X0),X1) = X0 ) ),
inference(superposition,[status(thm)],[c_5076,c_82]) ).
tcf(c_15596,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| element(sK2(sK14(X0),X1),X1)
| element(sK2(sK14(X0),X1),X0)
| ( sK14(X0) = X1 ) ),
inference(superposition,[status(thm)],[c_5076,c_5328]) ).
tcf(c_15597,plain,
! [X0: $i,X1: $i] :
( element(sK2(sK15(powerset(X0)),X1),X1)
| element(sK2(sK15(powerset(X0)),X1),X0)
| ( sK15(powerset(X0)) = X1 ) ),
inference(superposition,[status(thm)],[c_5076,c_5329]) ).
tcf(c_15598,plain,
! [X0: $i,X1: $i] :
( element(sK2(sK15(powerset(X0)),X1),X1)
| ( sK15(powerset(X0)) = X1 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5076,c_5201]) ).
tcf(c_15600,plain,
! [X0: $i,X1: $i] :
( element(sK2(relation_image(X0,empty_set),X1),X1)
| ( relation_image(X0,empty_set) = X1 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_5076,c_5411]) ).
tcf(c_15601,plain,
! [X0: $i,X1: $i] :
( element(sK2(sK15(sK14(powerset(X0))),X1),X1)
| element(sK2(sK15(sK14(powerset(X0))),X1),X0)
| ( sK15(sK14(powerset(X0))) = X1 ) ),
inference(superposition,[status(thm)],[c_5076,c_6063]) ).
tcf(c_15602,plain,
! [X0: $i,X1: $i] :
( element(sK2(sK15(sK14(powerset(X0))),X1),X1)
| ( sK15(sK14(powerset(X0))) = X1 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5076,c_6060]) ).
tcf(c_15603,plain,
! [X0: $i,X1: $i] :
( element(sK2(sK15(sK14(sK14(powerset(X0)))),X1),X1)
| element(sK2(sK15(sK14(sK14(powerset(X0)))),X1),X0)
| ( sK15(sK14(sK14(powerset(X0)))) = X1 ) ),
inference(superposition,[status(thm)],[c_5076,c_7006]) ).
tcf(c_15604,plain,
! [X0: $i,X1: $i] :
( element(sK2(sK15(sK14(sK14(powerset(X0)))),X1),X1)
| ( sK15(sK14(sK14(powerset(X0)))) = X1 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5076,c_7003]) ).
tcf(c_15605,plain,
! [X0: $i,X1: $i] :
( element(sK2(sK15(sK14(sK14(sK14(powerset(X0))))),X1),X1)
| element(sK2(sK15(sK14(sK14(sK14(powerset(X0))))),X1),X0)
| ( sK15(sK14(sK14(sK14(powerset(X0))))) = X1 ) ),
inference(superposition,[status(thm)],[c_5076,c_9254]) ).
tcf(c_15606,plain,
! [X0: $i,X1: $i] :
( element(sK2(sK15(sK14(sK14(sK14(powerset(X0))))),X1),X1)
| ( sK15(sK14(sK14(sK14(powerset(X0))))) = X1 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5076,c_9251]) ).
tcf(c_15607,plain,
! [X0: $i,X1: $i] :
( element(sK2(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))),X1),X1)
| element(sK2(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))),X1),X0)
| ( sK15(sK14(sK14(sK14(sK14(powerset(X0)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_5076,c_14088]) ).
tcf(c_15608,plain,
! [X0: $i,X1: $i] :
( element(sK2(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))),X1),X1)
| ( sK15(sK14(sK14(sK14(sK14(powerset(X0)))))) = X1 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5076,c_14085]) ).
tcf(c_15615,plain,
! [X0: $i] :
( in(X0,empty_set)
| element(X0,singleton(X0))
| ( singleton(X0) = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_15584,c_9564]) ).
tcf(c_15718,plain,
! [X0: $i,X1: $i] :
( element(X1,singleton(X0))
| in(sK2(singleton(X0),singleton(X1)),singleton(X1))
| ( singleton(X0) = singleton(X1) )
| ( sK2(singleton(X0),singleton(X1)) = X0 ) ),
inference(superposition,[status(thm)],[c_11036,c_5077]) ).
tcf(c_15719,plain,
! [X0: $i] :
( in(X0,empty_set)
| element(sK2(singleton(X0),empty_set),singleton(X0))
| ( singleton(X0) = empty_set ) ),
inference(superposition,[status(thm)],[c_9153,c_5077]) ).
tcf(c_15721,plain,
! [X0: $i,X1: $i] :
( in(X0,singleton(X1))
| element(sK2(singleton(X0),singleton(X1)),singleton(X0))
| ( singleton(X0) = singleton(X1) )
| ( sK2(singleton(X0),singleton(X1)) = X1 ) ),
inference(superposition,[status(thm)],[c_11036,c_5077]) ).
tcf(c_15722,plain,
! [X0: $i,X1: $i] :
( in(X1,singleton(X1))
| element(sK2(singleton(X0),singleton(X1)),singleton(X0))
| ( singleton(X0) = singleton(X1) )
| ( sK2(singleton(X0),singleton(X1)) = X0 ) ),
inference(superposition,[status(thm)],[c_11036,c_5077]) ).
tcf(c_15724,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,X1)
| in(sK2(powerset(X1),X2),X2)
| ( powerset(X1) = X2 )
| ~ in(X0,sK2(powerset(X1),X2)) ),
inference(superposition,[status(thm)],[c_5077,c_94]) ).
tcf(c_15725,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(powerset(X1),X2),X2)
| ( powerset(X1) = X2 )
| ~ empty(X1)
| ~ in(X0,sK2(powerset(X1),X2)) ),
inference(superposition,[status(thm)],[c_5077,c_93]) ).
tcf(c_15726,plain,
! [X0: $i,X1: $i] :
( element(sK2(X0,X1),X0)
| ( X0 = X1 )
| ~ in(sK2(X0,X1),X0) ),
inference(superposition,[status(thm)],[c_5077,c_55]) ).
tcf(c_15727,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X2,relation_image(X0,X1)),X2)
| ( relation_image(X0,X1) = X2 )
| ( apply(X0,sK5(X0,X1,sK2(X2,relation_image(X0,X1)))) = sK2(X2,relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_5077,c_64]) ).
tcf(c_15728,plain,
! [X0: $i,X1: $i] :
( element(sK2(X1,X0),X1)
| ( X0 = X1 )
| ~ in(X0,sK2(X1,X0)) ),
inference(superposition,[status(thm)],[c_5077,c_68]) ).
tcf(c_15732,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| element(sK2(X1,sK14(X0)),X1)
| element(sK2(X1,sK14(X0)),X0)
| ( sK14(X0) = X1 ) ),
inference(superposition,[status(thm)],[c_5077,c_5328]) ).
tcf(c_15733,plain,
! [X0: $i,X1: $i] :
( element(sK2(X1,sK15(powerset(X0))),X1)
| element(sK2(X1,sK15(powerset(X0))),X0)
| ( sK15(powerset(X0)) = X1 ) ),
inference(superposition,[status(thm)],[c_5077,c_5329]) ).
tcf(c_15734,plain,
! [X0: $i,X1: $i] :
( element(sK2(X1,sK15(powerset(X0))),X1)
| ( sK15(powerset(X0)) = X1 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5077,c_5201]) ).
tcf(c_15736,plain,
! [X0: $i,X1: $i] :
( element(sK2(X1,relation_image(X0,empty_set)),X1)
| ( relation_image(X0,empty_set) = X1 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_5077,c_5411]) ).
tcf(c_15737,plain,
! [X0: $i,X1: $i] :
( element(sK2(X1,sK15(sK14(powerset(X0)))),X1)
| element(sK2(X1,sK15(sK14(powerset(X0)))),X0)
| ( sK15(sK14(powerset(X0))) = X1 ) ),
inference(superposition,[status(thm)],[c_5077,c_6063]) ).
tcf(c_15738,plain,
! [X0: $i,X1: $i] :
( element(sK2(X1,sK15(sK14(powerset(X0)))),X1)
| ( sK15(sK14(powerset(X0))) = X1 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5077,c_6060]) ).
tcf(c_15739,plain,
! [X0: $i,X1: $i] :
( element(sK2(X1,sK15(sK14(sK14(powerset(X0))))),X1)
| element(sK2(X1,sK15(sK14(sK14(powerset(X0))))),X0)
| ( sK15(sK14(sK14(powerset(X0)))) = X1 ) ),
inference(superposition,[status(thm)],[c_5077,c_7006]) ).
tcf(c_15740,plain,
! [X0: $i,X1: $i] :
( element(sK2(X1,sK15(sK14(sK14(powerset(X0))))),X1)
| ( sK15(sK14(sK14(powerset(X0)))) = X1 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5077,c_7003]) ).
tcf(c_15741,plain,
! [X0: $i,X1: $i] :
( element(sK2(X1,sK15(sK14(sK14(sK14(powerset(X0)))))),X1)
| element(sK2(X1,sK15(sK14(sK14(sK14(powerset(X0)))))),X0)
| ( sK15(sK14(sK14(sK14(powerset(X0))))) = X1 ) ),
inference(superposition,[status(thm)],[c_5077,c_9254]) ).
tcf(c_15742,plain,
! [X0: $i,X1: $i] :
( element(sK2(X1,sK15(sK14(sK14(sK14(powerset(X0)))))),X1)
| ( sK15(sK14(sK14(sK14(powerset(X0))))) = X1 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5077,c_9251]) ).
tcf(c_15743,plain,
! [X0: $i,X1: $i] :
( element(sK2(X1,sK15(sK14(sK14(sK14(sK14(powerset(X0))))))),X1)
| element(sK2(X1,sK15(sK14(sK14(sK14(sK14(powerset(X0))))))),X0)
| ( sK15(sK14(sK14(sK14(sK14(powerset(X0)))))) = X1 ) ),
inference(superposition,[status(thm)],[c_5077,c_14088]) ).
tcf(c_15744,plain,
! [X0: $i,X1: $i] :
( element(sK2(X1,sK15(sK14(sK14(sK14(sK14(powerset(X0))))))),X1)
| ( sK15(sK14(sK14(sK14(sK14(powerset(X0)))))) = X1 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5077,c_14085]) ).
tcf(c_15859,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(sK14(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_14868]) ).
tcf(c_15860,plain,
sK15(sK14(sK14(sK14(sK14(powerset(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_14868]) ).
tcf(c_15861,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(sK14(powerset(sK15(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_14868]) ).
tcf(c_15862,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(sK14(powerset(sK15(sK14(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_14868]) ).
tcf(c_15863,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_14868]) ).
tcf(c_15864,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(sK14(powerset(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_14868]) ).
tcf(c_15865,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( sK15(sK14(sK14(sK14(sK14(powerset(sK15(powerset(singleton(X0))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_14868]) ).
tcf(c_15866,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(sK14(powerset(sK15(powerset(sK15(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_14868]) ).
tcf(c_15867,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(sK14(powerset(sK15(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_14868]) ).
tcf(c_15868,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(sK14(powerset(sK15(powerset(sK15(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_14868]) ).
tcf(c_15869,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(sK14(powerset(sK15(powerset(sK15(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_14868]) ).
tcf(c_15870,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_14868]) ).
tcf(c_15871,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(sK14(powerset(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_14868]) ).
tcf(c_15872,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_14868]) ).
tcf(c_15965,plain,
( empty(sK14(sK14(sK14(sK14(powerset(empty_set))))))
| ~ in(sK14(sK14(sK14(sK14(powerset(empty_set))))),empty_set) ),
inference(superposition,[status(thm)],[c_15860,c_5145]) ).
tcf(c_15966,plain,
( empty(sK14(sK14(sK14(sK14(powerset(empty_set))))))
| in(empty_set,sK14(sK14(sK14(sK14(powerset(empty_set)))))) ),
inference(superposition,[status(thm)],[c_15860,c_5124]) ).
tcf(c_15967,plain,
element(empty_set,sK14(sK14(sK14(sK14(powerset(empty_set)))))),
inference(superposition,[status(thm)],[c_15860,c_99]) ).
tcf(c_15993,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(sK14(powerset(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_14868]) ).
tcf(c_15994,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_10887]) ).
tcf(c_15995,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(sK14(powerset(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_10136]) ).
tcf(c_15996,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_9586]) ).
tcf(c_15997,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_9505]) ).
tcf(c_15998,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_9411]) ).
tcf(c_15999,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_9211]) ).
tcf(c_16000,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_9107]) ).
tcf(c_16001,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_9025]) ).
tcf(c_16002,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_8993]) ).
tcf(c_16003,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_8933]) ).
tcf(c_16004,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_8858]) ).
tcf(c_16005,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_8821]) ).
tcf(c_16006,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_8743]) ).
tcf(c_16007,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_8705]) ).
tcf(c_16008,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_8667]) ).
tcf(c_16009,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_8236]) ).
tcf(c_16010,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_8209]) ).
tcf(c_16011,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(sK15(powerset(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_7684]) ).
tcf(c_16012,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(sK14(powerset(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_7254]) ).
tcf(c_16013,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(sK14(powerset(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_7253]) ).
tcf(c_16014,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(sK15(powerset(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_7142]) ).
tcf(c_16015,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_6953]) ).
tcf(c_16016,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_6938]) ).
tcf(c_16017,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_6905]) ).
tcf(c_16018,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_6887]) ).
tcf(c_16019,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_8076]) ).
tcf(c_16020,plain,
! [X0: $i,X1: $i] :
( ( sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_7738]) ).
tcf(c_16021,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(sK15(powerset(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_6856]) ).
tcf(c_16022,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(sK15(powerset(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_6832]) ).
tcf(c_16023,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_6797]) ).
tcf(c_16024,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(sK14(powerset(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_6681]) ).
tcf(c_16025,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_6189]) ).
tcf(c_16026,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_6188]) ).
tcf(c_16027,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_6187]) ).
tcf(c_16028,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK14(powerset(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_6192]) ).
tcf(c_16029,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(powerset(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_9868]) ).
tcf(c_16030,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_7682]) ).
tcf(c_16031,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(powerset(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_7256]) ).
tcf(c_16032,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_7140]) ).
tcf(c_16033,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_6951]) ).
tcf(c_16034,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(powerset(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_6680]) ).
tcf(c_16035,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(powerset(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_6191]) ).
tcf(c_16036,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_6936]) ).
tcf(c_16037,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_6903]) ).
tcf(c_16038,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_6885]) ).
tcf(c_16039,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_6854]) ).
tcf(c_16040,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(powerset(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_6190]) ).
tcf(c_16041,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_5583]) ).
tcf(c_16042,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(powerset(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_5569]) ).
tcf(c_16043,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_6830]) ).
tcf(c_16044,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_6795]) ).
tcf(c_16045,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_5557]) ).
tcf(c_16046,plain,
! [X0: $i,X1: $i] :
( ( sK15(powerset(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_5270]) ).
tcf(c_16065,plain,
! [X0: $i] :
( relation(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_87]) ).
tcf(c_16066,plain,
! [X0: $i] :
( function(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_77]) ).
tcf(c_16306,plain,
! [X0: $i] :
( ( relation_dom(relation_image(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))),empty_set)) = empty_set )
| ~ empty(X0)
| ~ relation(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))) ),
inference(superposition,[status(thm)],[c_16066,c_7934]) ).
tcf(c_16307,plain,
! [X0: $i] :
( ( relation_image(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))),empty_set) = empty_set )
| ~ empty(X0)
| ~ relation(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))) ),
inference(superposition,[status(thm)],[c_16066,c_7777]) ).
tcf(c_16345,plain,
! [X0: $i,X1: $i] :
( ( singleton(X1) = relation_dom(X0) )
| ( sK8(X1,relation_dom(X0)) = X1 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_5346]) ).
tcf(c_16351,plain,
! [X0: $i,X1: $i] :
( ( sK15(powerset(singleton(X1))) = singleton(X0) )
| ( sK15(sK15(powerset(singleton(X1)))) = X1 )
| ( sK8(X0,sK15(powerset(singleton(X1)))) = X0 ) ),
inference(superposition,[status(thm)],[c_8114,c_5346]) ).
tcf(c_16352,plain,
! [X0: $i,X1: $i] :
( ( sK15(powerset(sK15(powerset(X0)))) = singleton(X1) )
| ( sK8(X1,sK15(powerset(sK15(powerset(X0))))) = X1 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_5346]) ).
tcf(c_16353,plain,
! [X0: $i,X1: $i] :
( ( sK15(powerset(relation_image(X0,empty_set))) = singleton(X1) )
| ( sK8(X1,sK15(powerset(relation_image(X0,empty_set)))) = X1 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_5346]) ).
tcf(c_16354,plain,
! [X0: $i,X1: $i] :
( ( sK15(powerset(sK15(sK14(powerset(X0))))) = singleton(X1) )
| ( sK8(X1,sK15(powerset(sK15(sK14(powerset(X0)))))) = X1 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_5346]) ).
tcf(c_16355,plain,
! [X0: $i,X1: $i] :
( ( sK15(powerset(sK15(sK14(sK14(powerset(X0)))))) = singleton(X1) )
| ( sK8(X1,sK15(powerset(sK15(sK14(sK14(powerset(X0))))))) = X1 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_5346]) ).
tcf(c_16357,plain,
! [X0: $i,X1: $i] :
( ( sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))) = singleton(X1) )
| ( sK8(X1,sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))) = X1 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_5346]) ).
tcf(c_16359,plain,
! [X0: $i,X1: $i] :
( ( sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))) = singleton(X1) )
| ( sK8(X1,sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))) = X1 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_5346]) ).
tcf(c_16394,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| in(sK3(empty_set,X1,sK14(X0)),X0)
| ( sK14(X0) = empty_set ) ),
inference(superposition,[status(thm)],[c_6727,c_66]) ).
tcf(c_16395,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(powerset(X2))
| element(X0,X2)
| ( sK14(powerset(X2)) = empty_set )
| ~ in(X0,sK3(empty_set,X1,sK14(powerset(X2)))) ),
inference(superposition,[status(thm)],[c_6727,c_94]) ).
tcf(c_16396,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(powerset(X2))
| ( sK14(powerset(X2)) = empty_set )
| ~ empty(X2)
| ~ in(X0,sK3(empty_set,X1,sK14(powerset(X2)))) ),
inference(superposition,[status(thm)],[c_6727,c_93]) ).
tcf(c_16400,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK14(powerset(X2)) = empty_set )
| ~ empty(X2)
| ~ in(X0,sK3(empty_set,X1,sK14(powerset(X2)))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16396,c_100]) ).
tcf(c_16404,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,X2)
| ( sK14(powerset(X2)) = empty_set )
| ~ in(X0,sK3(empty_set,X1,sK14(powerset(X2)))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16395,c_100]) ).
tcf(c_16431,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| in(sK3(empty_set,X1,sK15(powerset(X0))),X0)
| ( sK15(powerset(X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_6728,c_66]) ).
tcf(c_16432,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,X2)
| ( sK15(powerset(powerset(X2))) = empty_set )
| ~ in(X0,sK3(empty_set,X1,sK15(powerset(powerset(X2))))) ),
inference(superposition,[status(thm)],[c_6728,c_94]) ).
tcf(c_16433,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK15(powerset(powerset(X2))) = empty_set )
| ~ empty(X2)
| ~ in(X0,sK3(empty_set,X1,sK15(powerset(powerset(X2))))) ),
inference(superposition,[status(thm)],[c_6728,c_93]) ).
tcf(c_16451,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK15(sK14(powerset(relation_dom(X0))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_6798]) ).
tcf(c_16452,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(empty_set)))) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_92,c_6798]) ).
tcf(c_16453,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK15(sK14(powerset(sK15(powerset(X0)))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_6798]) ).
tcf(c_16454,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(X0))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_6798]) ).
tcf(c_16455,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_6798]) ).
tcf(c_16456,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK15(sK14(powerset(relation_image(X0,empty_set))))) = X1 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_6798]) ).
tcf(c_16457,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK15(powerset(singleton(X1)))) = X1 )
| ( relation_dom(sK15(sK14(powerset(sK15(powerset(singleton(X1))))))) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8114,c_6798]) ).
tcf(c_16458,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK15(sK14(powerset(sK15(powerset(sK15(powerset(X0)))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_6798]) ).
tcf(c_16459,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK15(sK14(powerset(sK15(powerset(relation_image(X0,empty_set))))))) = X1 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_6798]) ).
tcf(c_16460,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK15(sK14(powerset(sK15(powerset(sK15(sK14(powerset(X0))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_6798]) ).
tcf(c_16461,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK15(sK14(powerset(sK15(powerset(sK15(sK14(sK14(powerset(X0)))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_6798]) ).
tcf(c_16462,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_6798]) ).
tcf(c_16463,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK15(sK14(powerset(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_6798]) ).
tcf(c_16464,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_6798]) ).
tcf(c_16465,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK15(sK14(powerset(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_6798]) ).
tcf(c_16621,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_6833]) ).
tcf(c_16622,plain,
relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(empty_set))))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_6833]) ).
tcf(c_16623,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_6833]) ).
tcf(c_16624,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_6833]) ).
tcf(c_16625,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_6833]) ).
tcf(c_16626,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_6833]) ).
tcf(c_16627,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_6833]) ).
tcf(c_16628,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(powerset(sK15(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_6833]) ).
tcf(c_16629,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_6833]) ).
tcf(c_16630,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(powerset(sK15(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_6833]) ).
tcf(c_16631,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_6833]) ).
tcf(c_16632,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_6833]) ).
tcf(c_16633,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_6833]) ).
tcf(c_16634,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_6833]) ).
tcf(c_16635,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_6833]) ).
tcf(c_16674,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK4(relation_dom(sK15(sK14(sK14(powerset(sK15(powerset(singleton(X0)))))))),X1,X2),empty_set)
| in(sK3(relation_dom(sK15(sK14(sK14(powerset(sK15(powerset(singleton(X0)))))))),X1,X2),X2)
| ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( relation_image(relation_dom(sK15(sK14(sK14(powerset(sK15(powerset(singleton(X0)))))))),X1) = X2 )
| ~ function(relation_dom(sK15(sK14(sK14(powerset(sK15(powerset(singleton(X0)))))))))
| ~ relation(relation_dom(sK15(sK14(sK14(powerset(sK15(powerset(singleton(X0))))))))) ),
inference(superposition,[status(thm)],[c_12706,c_58]) ).
tcf(c_16675,plain,
! [X0: $i] :
( empty(relation_dom(sK15(sK14(sK14(powerset(sK15(powerset(singleton(X0)))))))))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ~ empty(empty_set)
| ~ relation(relation_dom(sK15(sK14(sK14(powerset(sK15(powerset(singleton(X0))))))))) ),
inference(superposition,[status(thm)],[c_12706,c_71]) ).
tcf(c_16679,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(relation_dom(sK15(sK14(sK14(powerset(sK15(powerset(singleton(X1)))))))),X2,X0),empty_set)
| ( sK15(sK15(powerset(singleton(X1)))) = X1 )
| ~ function(relation_dom(sK15(sK14(sK14(powerset(sK15(powerset(singleton(X1)))))))))
| ~ relation(relation_dom(sK15(sK14(sK14(powerset(sK15(powerset(singleton(X1)))))))))
| ~ in(X0,relation_image(relation_dom(sK15(sK14(sK14(powerset(sK15(powerset(singleton(X1)))))))),X2)) ),
inference(superposition,[status(thm)],[c_12706,c_62]) ).
tcf(c_16680,plain,
! [X0: $i] :
( empty(relation_dom(sK15(sK14(sK14(powerset(sK15(powerset(singleton(X0)))))))))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ~ relation(relation_dom(sK15(sK14(sK14(powerset(sK15(powerset(singleton(X0))))))))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16675,c_92]) ).
tcf(c_16684,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK15(sK15(powerset(singleton(X1)))) = X1 )
| ~ function(relation_dom(sK15(sK14(sK14(powerset(sK15(powerset(singleton(X1)))))))))
| ~ relation(relation_dom(sK15(sK14(sK14(powerset(sK15(powerset(singleton(X1)))))))))
| ~ in(X0,relation_image(relation_dom(sK15(sK14(sK14(powerset(sK15(powerset(singleton(X1)))))))),X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16679,c_5314]) ).
tcf(c_16689,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(relation_dom(sK15(sK14(sK14(powerset(sK15(powerset(singleton(X0)))))))),X1,X2),X2)
| ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( relation_image(relation_dom(sK15(sK14(sK14(powerset(sK15(powerset(singleton(X0)))))))),X1) = X2 )
| ~ function(relation_dom(sK15(sK14(sK14(powerset(sK15(powerset(singleton(X0)))))))))
| ~ relation(relation_dom(sK15(sK14(sK14(powerset(sK15(powerset(singleton(X0))))))))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16674,c_5314]) ).
tcf(c_16738,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK14(sK14(powerset(relation_dom(X0))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_7255]) ).
tcf(c_16739,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(empty_set)))) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_92,c_7255]) ).
tcf(c_16740,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK14(sK14(powerset(sK15(powerset(X0)))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_7255]) ).
tcf(c_16741,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK14(sK14(powerset(sK15(sK14(powerset(X0))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_7255]) ).
tcf(c_16742,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK14(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_7255]) ).
tcf(c_16743,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK14(sK14(powerset(relation_image(X0,empty_set))))) = X1 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_7255]) ).
tcf(c_16744,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK15(powerset(singleton(X1)))) = X1 )
| ( sK15(sK14(sK14(powerset(sK15(powerset(singleton(X1))))))) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8114,c_7255]) ).
tcf(c_16745,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK14(sK14(powerset(sK15(powerset(sK15(powerset(X0)))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_7255]) ).
tcf(c_16746,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK14(sK14(powerset(sK15(powerset(relation_image(X0,empty_set))))))) = X1 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_7255]) ).
tcf(c_16747,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK14(sK14(powerset(sK15(powerset(sK15(sK14(powerset(X0))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_7255]) ).
tcf(c_16748,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK14(sK14(powerset(sK15(powerset(sK15(sK14(sK14(powerset(X0)))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_7255]) ).
tcf(c_16749,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK14(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_7255]) ).
tcf(c_16750,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK14(sK14(powerset(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_7255]) ).
tcf(c_16751,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK14(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_7255]) ).
tcf(c_16752,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK14(sK14(powerset(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_7255]) ).
tcf(c_16896,plain,
! [X0: $i] :
( in(sK15(sK15(sK14(powerset(X0)))),X0)
| empty(sK15(sK14(powerset(X0)))) ),
inference(global_subsumption_just,[status(thm)],[c_9088,c_6155,c_9088]) ).
tcf(c_16897,plain,
! [X0: $i] :
( empty(sK15(sK14(powerset(X0))))
| in(sK15(sK15(sK14(powerset(X0)))),X0) ),
inference(renaming,[status(thm)],[c_16896]) ).
tcf(c_16903,plain,
( in(sK15(empty_set),empty_set)
| empty(sK15(sK14(powerset(empty_set)))) ),
inference(superposition,[status(thm)],[c_6679,c_16897]) ).
tcf(c_16904,plain,
! [X0: $i,X1: $i] :
( empty(sK15(sK14(powerset(relation_image(X0,X1)))))
| ( apply(X0,sK5(X0,X1,sK15(sK15(sK14(powerset(relation_image(X0,X1))))))) = sK15(sK15(sK14(powerset(relation_image(X0,X1))))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16897,c_64]) ).
tcf(c_16905,plain,
! [X0: $i] :
( empty(sK15(sK14(powerset(X0))))
| ~ in(X0,sK15(sK15(sK14(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_16897,c_68]) ).
tcf(c_16908,plain,
! [X0: $i] :
( empty(sK15(sK14(powerset(singleton(X0)))))
| ( sK15(sK15(sK14(powerset(singleton(X0))))) = X0 ) ),
inference(superposition,[status(thm)],[c_16897,c_82]) ).
tcf(c_16909,plain,
! [X0: $i] :
( empty(X0)
| empty(sK15(sK14(powerset(sK14(X0)))))
| element(sK15(sK15(sK14(powerset(sK14(X0))))),X0) ),
inference(superposition,[status(thm)],[c_16897,c_5328]) ).
tcf(c_16910,plain,
! [X0: $i] :
( empty(sK15(sK14(powerset(sK15(powerset(X0))))))
| element(sK15(sK15(sK14(powerset(sK15(powerset(X0)))))),X0) ),
inference(superposition,[status(thm)],[c_16897,c_5329]) ).
tcf(c_16911,plain,
! [X0: $i] :
( empty(sK15(sK14(powerset(sK15(powerset(X0))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16897,c_5201]) ).
tcf(c_16912,plain,
empty(sK15(sK14(powerset(empty_set)))),
inference(superposition,[status(thm)],[c_16897,c_5314]) ).
tcf(c_16913,plain,
! [X0: $i] :
( empty(sK15(sK14(powerset(relation_image(X0,empty_set)))))
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16897,c_5411]) ).
tcf(c_16914,plain,
! [X0: $i] :
( empty(sK15(sK14(powerset(sK15(sK14(powerset(X0)))))))
| element(sK15(sK15(sK14(powerset(sK15(sK14(powerset(X0))))))),X0) ),
inference(superposition,[status(thm)],[c_16897,c_6063]) ).
tcf(c_16915,plain,
! [X0: $i] :
( empty(sK15(sK14(powerset(sK15(sK14(powerset(X0)))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16897,c_6060]) ).
tcf(c_16916,plain,
! [X0: $i] :
( empty(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0))))))))
| element(sK15(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))),X0) ),
inference(superposition,[status(thm)],[c_16897,c_7006]) ).
tcf(c_16917,plain,
! [X0: $i] :
( empty(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0))))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16897,c_7003]) ).
tcf(c_16918,plain,
! [X0: $i] :
( empty(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))
| element(sK15(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))),X0) ),
inference(superposition,[status(thm)],[c_16897,c_9254]) ).
tcf(c_16919,plain,
! [X0: $i] :
( empty(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16897,c_9251]) ).
tcf(c_16920,plain,
! [X0: $i] :
( empty(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))
| element(sK15(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))),X0) ),
inference(superposition,[status(thm)],[c_16897,c_14088]) ).
tcf(c_16921,plain,
! [X0: $i] :
( empty(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16897,c_14085]) ).
tcf(c_17028,plain,
( empty(sK15(sK14(powerset(empty_set))))
| ~ in(empty_set,sK15(empty_set)) ),
inference(superposition,[status(thm)],[c_6679,c_16905]) ).
tcf(c_17030,plain,
! [X0: $i] :
( in(sK15(sK14(sK14(sK15(powerset(X0))))),X0)
| empty(sK15(powerset(X0))) ),
inference(global_subsumption_just,[status(thm)],[c_9482,c_5256,c_9482]) ).
tcf(c_17031,plain,
! [X0: $i] :
( empty(sK15(powerset(X0)))
| in(sK15(sK14(sK14(sK15(powerset(X0))))),X0) ),
inference(renaming,[status(thm)],[c_17030]) ).
tcf(c_17037,plain,
( empty(sK15(powerset(empty_set)))
| in(sK15(sK14(sK14(empty_set))),empty_set) ),
inference(superposition,[status(thm)],[c_5301,c_17031]) ).
tcf(c_17038,plain,
! [X0: $i,X1: $i] :
( empty(sK15(powerset(relation_image(X0,X1))))
| ( apply(X0,sK5(X0,X1,sK15(sK14(sK14(sK15(powerset(relation_image(X0,X1)))))))) = sK15(sK14(sK14(sK15(powerset(relation_image(X0,X1)))))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17031,c_64]) ).
tcf(c_17039,plain,
! [X0: $i] :
( empty(sK15(powerset(X0)))
| ~ in(X0,sK15(sK14(sK14(sK15(powerset(X0)))))) ),
inference(superposition,[status(thm)],[c_17031,c_68]) ).
tcf(c_17042,plain,
! [X0: $i] :
( empty(sK15(powerset(singleton(X0))))
| ( sK15(sK14(sK14(sK15(powerset(singleton(X0)))))) = X0 ) ),
inference(superposition,[status(thm)],[c_17031,c_82]) ).
tcf(c_17043,plain,
! [X0: $i] :
( empty(X0)
| empty(sK15(powerset(sK14(X0))))
| element(sK15(sK14(sK14(sK15(powerset(sK14(X0)))))),X0) ),
inference(superposition,[status(thm)],[c_17031,c_5328]) ).
tcf(c_17044,plain,
! [X0: $i] :
( empty(sK15(powerset(sK15(powerset(X0)))))
| element(sK15(sK14(sK14(sK15(powerset(sK15(powerset(X0))))))),X0) ),
inference(superposition,[status(thm)],[c_17031,c_5329]) ).
tcf(c_17048,plain,
! [X0: $i] :
( empty(sK15(powerset(sK15(sK14(powerset(X0))))))
| element(sK15(sK14(sK14(sK15(powerset(sK15(sK14(powerset(X0)))))))),X0) ),
inference(superposition,[status(thm)],[c_17031,c_6063]) ).
tcf(c_17050,plain,
! [X0: $i] :
( empty(sK15(powerset(sK15(sK14(sK14(powerset(X0)))))))
| element(sK15(sK14(sK14(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))))),X0) ),
inference(superposition,[status(thm)],[c_17031,c_7006]) ).
tcf(c_17052,plain,
! [X0: $i] :
( empty(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))
| element(sK15(sK14(sK14(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))),X0) ),
inference(superposition,[status(thm)],[c_17031,c_9254]) ).
tcf(c_17054,plain,
! [X0: $i] :
( empty(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))
| element(sK15(sK14(sK14(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))),X0) ),
inference(superposition,[status(thm)],[c_17031,c_14088]) ).
tcf(c_17056,plain,
( empty(empty_set)
| in(sK15(sK14(sK14(empty_set))),empty_set) ),
inference(light_normalisation,[status(thm)],[c_17037,c_5301]) ).
tcf(c_17091,plain,
( empty(sK15(sK14(powerset(empty_set))))
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_5301,c_16911]) ).
tcf(c_17092,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK14(sK14(powerset(sK15(sK14(powerset(sK15(powerset(X0))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_7255]) ).
tcf(c_17093,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(sK14(powerset(sK15(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_6833]) ).
tcf(c_17094,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(sK15(powerset(X0))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_6798]) ).
tcf(c_17095,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK14(powerset(sK15(powerset(X0))))) = singleton(X1) )
| ( sK8(X1,sK15(sK14(powerset(sK15(powerset(X0)))))) = X1 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_5346]) ).
tcf(c_17096,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(sK14(powerset(sK15(sK14(powerset(sK15(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_14868]) ).
tcf(c_17097,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(powerset(relation_dom(sK15(sK14(powerset(sK15(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_10887]) ).
tcf(c_17098,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(sK14(powerset(sK15(sK14(powerset(sK15(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_10136]) ).
tcf(c_17099,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(relation_dom(relation_dom(sK15(sK14(powerset(sK15(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_9586]) ).
tcf(c_17100,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(powerset(relation_dom(sK15(sK14(powerset(sK15(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_9505]) ).
tcf(c_17101,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(relation_dom(relation_dom(sK15(sK14(powerset(sK15(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_9411]) ).
tcf(c_17102,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_9211]) ).
tcf(c_17103,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_9107]) ).
tcf(c_17104,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(powerset(relation_dom(sK15(sK14(powerset(sK15(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_9025]) ).
tcf(c_17105,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_8993]) ).
tcf(c_17106,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_8933]) ).
tcf(c_17107,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_8858]) ).
tcf(c_17108,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(relation_dom(relation_dom(sK15(sK14(powerset(sK15(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_8821]) ).
tcf(c_17109,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(powerset(relation_dom(sK15(sK14(powerset(sK15(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_8743]) ).
tcf(c_17110,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_8705]) ).
tcf(c_17111,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_8667]) ).
tcf(c_17112,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(sK14(powerset(sK15(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_8236]) ).
tcf(c_17113,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(powerset(X0)))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_8209]) ).
tcf(c_17114,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(sK15(powerset(sK15(sK14(powerset(sK15(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_7684]) ).
tcf(c_17115,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(sK14(powerset(sK15(sK14(powerset(sK15(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_7254]) ).
tcf(c_17116,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(sK14(powerset(sK15(sK14(powerset(sK15(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_7253]) ).
tcf(c_17117,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(sK15(powerset(sK15(sK14(powerset(sK15(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_7142]) ).
tcf(c_17118,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_6953]) ).
tcf(c_17119,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_6938]) ).
tcf(c_17120,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_6905]) ).
tcf(c_17121,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_6887]) ).
tcf(c_17122,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_8076]) ).
tcf(c_17123,plain,
! [X0: $i,X1: $i] :
( ( sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(powerset(X0)))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_7738]) ).
tcf(c_17124,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(sK15(powerset(sK15(sK14(powerset(sK15(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_6856]) ).
tcf(c_17125,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(powerset(sK15(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_6832]) ).
tcf(c_17126,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(powerset(X0)))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_6797]) ).
tcf(c_17127,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(sK14(powerset(sK15(sK14(powerset(sK15(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_6681]) ).
tcf(c_17128,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(sK15(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_6189]) ).
tcf(c_17129,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(sK14(powerset(sK15(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_6188]) ).
tcf(c_17130,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(sK15(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_6187]) ).
tcf(c_17131,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK14(powerset(sK15(sK14(powerset(sK15(powerset(X0)))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_6192]) ).
tcf(c_17132,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(powerset(sK15(sK14(powerset(sK15(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_9868]) ).
tcf(c_17133,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(relation_dom(sK15(sK14(powerset(sK15(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_7682]) ).
tcf(c_17134,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(powerset(sK15(sK14(powerset(sK15(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_7256]) ).
tcf(c_17135,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(relation_dom(sK15(sK14(powerset(sK15(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_7140]) ).
tcf(c_17136,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(relation_dom(sK15(sK14(powerset(sK15(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_6951]) ).
tcf(c_17137,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(powerset(sK15(sK14(powerset(sK15(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_6680]) ).
tcf(c_17138,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(sK15(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_6191]) ).
tcf(c_17139,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_6936]) ).
tcf(c_17140,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(sK14(powerset(sK15(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_6903]) ).
tcf(c_17141,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_6885]) ).
tcf(c_17142,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_6854]) ).
tcf(c_17143,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(powerset(sK15(sK14(powerset(sK15(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_6190]) ).
tcf(c_17144,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_5583]) ).
tcf(c_17145,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(powerset(sK15(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_5569]) ).
tcf(c_17146,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_6830]) ).
tcf(c_17147,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK15(sK14(powerset(sK15(powerset(X0))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_6795]) ).
tcf(c_17148,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_5557]) ).
tcf(c_17149,plain,
! [X0: $i,X1: $i] :
( ( sK15(powerset(sK15(sK14(powerset(sK15(powerset(X0))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_5270]) ).
tcf(c_17150,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(sK15(sK14(powerset(sK15(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_7171]) ).
tcf(c_17151,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(sK15(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_6193]) ).
tcf(c_17152,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(sK15(sK14(powerset(sK15(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_6678]) ).
tcf(c_17153,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(sK15(sK14(powerset(sK15(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_5581]) ).
tcf(c_17154,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_5567]) ).
tcf(c_17155,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_5555]) ).
tcf(c_17156,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(sK15(sK14(powerset(sK15(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_5302]) ).
tcf(c_17168,plain,
! [X0: $i] :
( relation(sK15(sK14(powerset(sK15(powerset(X0))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_87]) ).
tcf(c_17169,plain,
! [X0: $i] :
( function(sK15(sK14(powerset(sK15(powerset(X0))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_77]) ).
tcf(c_17438,plain,
( relation(sK15(sK14(powerset(empty_set))))
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_5301,c_17168]) ).
tcf(c_17444,plain,
( function(sK15(sK14(powerset(empty_set))))
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_5301,c_17169]) ).
tcf(c_17445,plain,
! [X0: $i] :
( ( relation_dom(relation_image(sK15(sK14(powerset(sK15(powerset(X0))))),empty_set)) = empty_set )
| ~ empty(X0)
| ~ relation(sK15(sK14(powerset(sK15(powerset(X0)))))) ),
inference(superposition,[status(thm)],[c_17169,c_7934]) ).
tcf(c_17446,plain,
! [X0: $i] :
( ( relation_image(sK15(sK14(powerset(sK15(powerset(X0))))),empty_set) = empty_set )
| ~ empty(X0)
| ~ relation(sK15(sK14(powerset(sK15(powerset(X0)))))) ),
inference(superposition,[status(thm)],[c_17169,c_7777]) ).
tcf(c_17459,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK14(sK14(powerset(sK15(sK14(powerset(sK15(sK14(powerset(X0)))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_7255]) ).
tcf(c_17460,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(sK14(powerset(sK15(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_6833]) ).
tcf(c_17461,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(sK15(sK14(powerset(X0)))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_6798]) ).
tcf(c_17462,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK14(powerset(sK15(sK14(powerset(X0)))))) = singleton(X1) )
| ( sK8(X1,sK15(sK14(powerset(sK15(sK14(powerset(X0))))))) = X1 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_5346]) ).
tcf(c_17463,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(sK14(powerset(sK15(sK14(powerset(sK15(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_14868]) ).
tcf(c_17464,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_10887]) ).
tcf(c_17465,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(sK14(powerset(sK15(sK14(powerset(sK15(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_10136]) ).
tcf(c_17466,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_9586]) ).
tcf(c_17467,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_9505]) ).
tcf(c_17468,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_9411]) ).
tcf(c_17469,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_9211]) ).
tcf(c_17470,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_9107]) ).
tcf(c_17471,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_9025]) ).
tcf(c_17472,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_8993]) ).
tcf(c_17473,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_8933]) ).
tcf(c_17474,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_8858]) ).
tcf(c_17475,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_8821]) ).
tcf(c_17476,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_8743]) ).
tcf(c_17477,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_8705]) ).
tcf(c_17478,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_8667]) ).
tcf(c_17479,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_8236]) ).
tcf(c_17480,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(X0))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_8209]) ).
tcf(c_17481,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(sK15(powerset(sK15(sK14(powerset(sK15(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_7684]) ).
tcf(c_17482,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(sK14(powerset(sK15(sK14(powerset(sK15(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_7254]) ).
tcf(c_17483,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(sK14(powerset(sK15(sK14(powerset(sK15(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_7253]) ).
tcf(c_17484,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(sK15(powerset(sK15(sK14(powerset(sK15(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_7142]) ).
tcf(c_17485,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_6953]) ).
tcf(c_17486,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_6938]) ).
tcf(c_17487,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_6905]) ).
tcf(c_17488,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_6887]) ).
tcf(c_17489,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_8076]) ).
tcf(c_17490,plain,
! [X0: $i,X1: $i] :
( ( sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(X0))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_7738]) ).
tcf(c_17491,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(sK15(powerset(sK15(sK14(powerset(sK15(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_6856]) ).
tcf(c_17492,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(powerset(sK15(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_6832]) ).
tcf(c_17493,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(sK14(powerset(X0))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_6797]) ).
tcf(c_17494,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(sK14(powerset(sK15(sK14(powerset(sK15(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_6681]) ).
tcf(c_17495,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(sK15(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_6189]) ).
tcf(c_17496,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(sK14(powerset(sK15(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_6188]) ).
tcf(c_17497,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(sK15(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_6187]) ).
tcf(c_17498,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK14(powerset(sK15(sK14(powerset(sK15(sK14(powerset(X0))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_6192]) ).
tcf(c_17499,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(powerset(sK15(sK14(powerset(sK15(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_9868]) ).
tcf(c_17500,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_7682]) ).
tcf(c_17501,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(powerset(sK15(sK14(powerset(sK15(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_7256]) ).
tcf(c_17502,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_7140]) ).
tcf(c_17503,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_6951]) ).
tcf(c_17504,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(powerset(sK15(sK14(powerset(sK15(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_6680]) ).
tcf(c_17505,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(sK15(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_6191]) ).
tcf(c_17506,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_6936]) ).
tcf(c_17507,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_6903]) ).
tcf(c_17508,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_6885]) ).
tcf(c_17509,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_6854]) ).
tcf(c_17510,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(powerset(sK15(sK14(powerset(sK15(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_6190]) ).
tcf(c_17511,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_5583]) ).
tcf(c_17512,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(powerset(sK15(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_5569]) ).
tcf(c_17513,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_6830]) ).
tcf(c_17514,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(X0)))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_6795]) ).
tcf(c_17515,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_5557]) ).
tcf(c_17516,plain,
! [X0: $i,X1: $i] :
( ( sK15(powerset(sK15(sK14(powerset(sK15(sK14(powerset(X0)))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_5270]) ).
tcf(c_17517,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(sK15(sK14(powerset(sK15(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_7171]) ).
tcf(c_17518,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(sK15(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_6193]) ).
tcf(c_17519,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_6678]) ).
tcf(c_17520,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_5581]) ).
tcf(c_17521,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_5567]) ).
tcf(c_17522,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_5555]) ).
tcf(c_17523,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(sK15(sK14(powerset(sK15(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_5302]) ).
tcf(c_17535,plain,
! [X0: $i] :
( relation(sK15(sK14(powerset(sK15(sK14(powerset(X0)))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_87]) ).
tcf(c_17536,plain,
! [X0: $i] :
( function(sK15(sK14(powerset(sK15(sK14(powerset(X0)))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_77]) ).
tcf(c_17934,plain,
! [X0: $i] :
( ( relation_dom(relation_image(sK15(sK14(powerset(sK15(sK14(powerset(X0)))))),empty_set)) = empty_set )
| ~ empty(X0)
| ~ relation(sK15(sK14(powerset(sK15(sK14(powerset(X0))))))) ),
inference(superposition,[status(thm)],[c_17536,c_7934]) ).
tcf(c_17935,plain,
! [X0: $i] :
( ( relation_image(sK15(sK14(powerset(sK15(sK14(powerset(X0)))))),empty_set) = empty_set )
| ~ empty(X0)
| ~ relation(sK15(sK14(powerset(sK15(sK14(powerset(X0))))))) ),
inference(superposition,[status(thm)],[c_17536,c_7777]) ).
tcf(c_17947,plain,
! [X0: $i] :
( empty(sK15(sK14(powerset(empty_set))))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ~ empty(sK15(powerset(sK15(powerset(singleton(X0)))))) ),
inference(superposition,[status(thm)],[c_12705,c_16917]) ).
tcf(c_17948,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK14(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0))))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_7255]) ).
tcf(c_17949,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_6833]) ).
tcf(c_17950,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0))))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_6798]) ).
tcf(c_17951,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0))))))) = singleton(X1) )
| ( sK8(X1,sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))) = X1 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_5346]) ).
tcf(c_17952,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_14868]) ).
tcf(c_17953,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_10887]) ).
tcf(c_17954,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_10136]) ).
tcf(c_17955,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_9586]) ).
tcf(c_17956,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_9505]) ).
tcf(c_17957,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_9411]) ).
tcf(c_17958,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_9211]) ).
tcf(c_17959,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_9107]) ).
tcf(c_17960,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_9025]) ).
tcf(c_17961,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_8993]) ).
tcf(c_17962,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_8933]) ).
tcf(c_17963,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_8858]) ).
tcf(c_17964,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_8821]) ).
tcf(c_17965,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_8743]) ).
tcf(c_17966,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_8705]) ).
tcf(c_17967,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_8667]) ).
tcf(c_17968,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_8236]) ).
tcf(c_17969,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_8209]) ).
tcf(c_17970,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_7684]) ).
tcf(c_17971,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_7254]) ).
tcf(c_17972,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_7253]) ).
tcf(c_17973,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_7142]) ).
tcf(c_17974,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_6953]) ).
tcf(c_17975,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_6938]) ).
tcf(c_17976,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_6905]) ).
tcf(c_17977,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_6887]) ).
tcf(c_17978,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_8076]) ).
tcf(c_17979,plain,
! [X0: $i,X1: $i] :
( ( sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_7738]) ).
tcf(c_17980,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_6856]) ).
tcf(c_17981,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_6832]) ).
tcf(c_17982,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_6797]) ).
tcf(c_17983,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_6681]) ).
tcf(c_17984,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_6189]) ).
tcf(c_17985,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_6188]) ).
tcf(c_17986,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_6187]) ).
tcf(c_17987,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_6192]) ).
tcf(c_17988,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_9868]) ).
tcf(c_17989,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_7682]) ).
tcf(c_17990,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_7256]) ).
tcf(c_17991,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_7140]) ).
tcf(c_17992,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_6951]) ).
tcf(c_17993,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_6680]) ).
tcf(c_17994,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_6191]) ).
tcf(c_17995,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_6936]) ).
tcf(c_17996,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_6903]) ).
tcf(c_17997,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_6885]) ).
tcf(c_17998,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_6854]) ).
tcf(c_17999,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_6190]) ).
tcf(c_18000,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_5583]) ).
tcf(c_18001,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_5569]) ).
tcf(c_18002,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_6830]) ).
tcf(c_18003,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_6795]) ).
tcf(c_18004,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_5557]) ).
tcf(c_18005,plain,
! [X0: $i,X1: $i] :
( ( sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_5270]) ).
tcf(c_18006,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_7171]) ).
tcf(c_18007,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_6193]) ).
tcf(c_18008,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_6678]) ).
tcf(c_18009,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_5581]) ).
tcf(c_18010,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_5567]) ).
tcf(c_18011,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_5555]) ).
tcf(c_18012,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_5302]) ).
tcf(c_18024,plain,
! [X0: $i] :
( relation(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0))))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_87]) ).
tcf(c_18025,plain,
! [X0: $i] :
( function(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0))))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_77]) ).
tcf(c_18392,plain,
! [X0: $i] :
( relation(sK15(sK14(powerset(empty_set))))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ~ empty(sK15(powerset(sK15(powerset(singleton(X0)))))) ),
inference(superposition,[status(thm)],[c_12705,c_18024]) ).
tcf(c_18399,plain,
! [X0: $i] :
( function(sK15(sK14(powerset(empty_set))))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ~ empty(sK15(powerset(sK15(powerset(singleton(X0)))))) ),
inference(superposition,[status(thm)],[c_12705,c_18025]) ).
tcf(c_18400,plain,
! [X0: $i] :
( ( relation_dom(relation_image(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0))))))),empty_set)) = empty_set )
| ~ empty(X0)
| ~ relation(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))) ),
inference(superposition,[status(thm)],[c_18025,c_7934]) ).
tcf(c_18401,plain,
! [X0: $i] :
( ( relation_image(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0))))))),empty_set) = empty_set )
| ~ empty(X0)
| ~ relation(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))) ),
inference(superposition,[status(thm)],[c_18025,c_7777]) ).
tcf(c_18415,plain,
( empty(sK15(sK14(powerset(empty_set))))
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_6000,c_16913]) ).
tcf(c_18416,plain,
( empty(sK15(sK14(powerset(empty_set))))
| ~ function(sK1)
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_9666,c_16913]) ).
tcf(c_18417,plain,
( empty(sK15(sK14(powerset(empty_set))))
| ~ function(sK7)
| ~ relation(sK7) ),
inference(superposition,[status(thm)],[c_9665,c_16913]) ).
tcf(c_18418,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK14(sK14(powerset(sK15(sK14(powerset(relation_image(X0,empty_set)))))))) = X1 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_7255]) ).
tcf(c_18419,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(sK14(powerset(relation_image(X0,empty_set))))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_6833]) ).
tcf(c_18420,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(relation_image(X0,empty_set)))))))) = X1 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_6798]) ).
tcf(c_18421,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK14(powerset(relation_image(X0,empty_set)))) = singleton(X1) )
| ( sK8(X1,sK15(sK14(powerset(relation_image(X0,empty_set))))) = X1 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_5346]) ).
tcf(c_18422,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(sK14(powerset(sK15(sK14(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_14868]) ).
tcf(c_18423,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(powerset(relation_dom(sK15(sK14(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_10887]) ).
tcf(c_18424,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(sK14(powerset(sK15(sK14(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_10136]) ).
tcf(c_18425,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(relation_dom(relation_dom(sK15(sK14(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_9586]) ).
tcf(c_18426,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(powerset(relation_dom(sK15(sK14(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_9505]) ).
tcf(c_18427,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(relation_dom(relation_dom(sK15(sK14(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_9411]) ).
tcf(c_18428,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_9211]) ).
tcf(c_18429,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(powerset(relation_dom(sK15(sK14(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_9107]) ).
tcf(c_18430,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(powerset(relation_dom(sK15(sK14(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_9025]) ).
tcf(c_18431,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_8993]) ).
tcf(c_18432,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_8933]) ).
tcf(c_18433,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_8858]) ).
tcf(c_18434,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(relation_dom(relation_dom(sK15(sK14(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_8821]) ).
tcf(c_18435,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(powerset(relation_dom(sK15(sK14(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_8743]) ).
tcf(c_18436,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(powerset(relation_dom(sK15(sK14(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_8705]) ).
tcf(c_18437,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(powerset(relation_dom(sK15(sK14(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_8667]) ).
tcf(c_18438,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(sK14(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_8236]) ).
tcf(c_18439,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(relation_image(X0,empty_set))))))) = X1 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_8209]) ).
tcf(c_18440,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(sK15(powerset(sK15(sK14(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_7684]) ).
tcf(c_18441,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(sK14(powerset(sK15(sK14(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_7254]) ).
tcf(c_18442,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(sK14(powerset(sK15(sK14(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_7253]) ).
tcf(c_18443,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(sK15(powerset(sK15(sK14(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_7142]) ).
tcf(c_18444,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(sK15(powerset(sK15(sK14(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_6953]) ).
tcf(c_18445,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_6938]) ).
tcf(c_18446,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_6905]) ).
tcf(c_18447,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_6887]) ).
tcf(c_18448,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(sK14(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_8076]) ).
tcf(c_18449,plain,
! [X0: $i,X1: $i] :
( ( sK15(powerset(relation_dom(sK15(sK14(powerset(relation_image(X0,empty_set))))))) = X1 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_7738]) ).
tcf(c_18450,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(sK15(powerset(sK15(sK14(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_6856]) ).
tcf(c_18451,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_6832]) ).
tcf(c_18452,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK15(powerset(sK15(sK14(powerset(relation_image(X0,empty_set))))))) = X1 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_6797]) ).
tcf(c_18453,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(sK14(powerset(sK15(sK14(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_6681]) ).
tcf(c_18454,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_6189]) ).
tcf(c_18455,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(sK14(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_6188]) ).
tcf(c_18456,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_6187]) ).
tcf(c_18457,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK14(powerset(sK15(sK14(powerset(relation_image(X0,empty_set))))))) = X1 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_6192]) ).
tcf(c_18458,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(powerset(sK15(sK14(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_9868]) ).
tcf(c_18459,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(relation_dom(sK15(sK14(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_7682]) ).
tcf(c_18460,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(powerset(sK15(sK14(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_7256]) ).
tcf(c_18461,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(relation_dom(sK15(sK14(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_7140]) ).
tcf(c_18462,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(relation_dom(sK15(sK14(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_6951]) ).
tcf(c_18463,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(powerset(sK15(sK14(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_6680]) ).
tcf(c_18464,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_6191]) ).
tcf(c_18465,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_6936]) ).
tcf(c_18466,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(sK14(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_6903]) ).
tcf(c_18467,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_6885]) ).
tcf(c_18468,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(relation_dom(sK15(sK14(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_6854]) ).
tcf(c_18469,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(powerset(sK15(sK14(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_6190]) ).
tcf(c_18470,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_5583]) ).
tcf(c_18471,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_5569]) ).
tcf(c_18472,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(sK14(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_6830]) ).
tcf(c_18473,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK15(sK14(powerset(relation_image(X0,empty_set)))))) = X1 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_6795]) ).
tcf(c_18474,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_5557]) ).
tcf(c_18475,plain,
! [X0: $i,X1: $i] :
( ( sK15(powerset(sK15(sK14(powerset(relation_image(X0,empty_set)))))) = X1 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_5270]) ).
tcf(c_18476,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(sK15(sK14(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_7171]) ).
tcf(c_18477,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_6193]) ).
tcf(c_18478,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(sK15(sK14(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_6678]) ).
tcf(c_18479,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(sK15(sK14(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_5581]) ).
tcf(c_18480,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(sK15(sK14(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_5567]) ).
tcf(c_18481,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_5555]) ).
tcf(c_18482,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(sK15(sK14(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_5302]) ).
tcf(c_18494,plain,
! [X0: $i] :
( relation(sK15(sK14(powerset(relation_image(X0,empty_set)))))
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_87]) ).
tcf(c_18495,plain,
! [X0: $i] :
( function(sK15(sK14(powerset(relation_image(X0,empty_set)))))
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_77]) ).
tcf(c_18959,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK14(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_7255]) ).
tcf(c_18960,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_6833]) ).
tcf(c_18961,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_6798]) ).
tcf(c_18962,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))) = singleton(X1) )
| ( sK8(X1,sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))) = X1 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_5346]) ).
tcf(c_18963,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_14868]) ).
tcf(c_18964,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_10887]) ).
tcf(c_18965,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_10136]) ).
tcf(c_18966,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_9586]) ).
tcf(c_18967,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_9505]) ).
tcf(c_18968,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_9411]) ).
tcf(c_18969,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_9211]) ).
tcf(c_18970,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_9107]) ).
tcf(c_18971,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_9025]) ).
tcf(c_18972,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_8993]) ).
tcf(c_18973,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_8933]) ).
tcf(c_18974,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_8858]) ).
tcf(c_18975,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_8821]) ).
tcf(c_18976,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_8743]) ).
tcf(c_18977,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_8705]) ).
tcf(c_18978,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_8667]) ).
tcf(c_18979,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_8236]) ).
tcf(c_18980,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_8209]) ).
tcf(c_18981,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_7684]) ).
tcf(c_18982,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_7254]) ).
tcf(c_18983,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_7253]) ).
tcf(c_18984,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_7142]) ).
tcf(c_18985,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_6953]) ).
tcf(c_18986,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_6938]) ).
tcf(c_18987,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_6905]) ).
tcf(c_18988,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_6887]) ).
tcf(c_18989,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_8076]) ).
tcf(c_18990,plain,
! [X0: $i,X1: $i] :
( ( sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_7738]) ).
tcf(c_18991,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_6856]) ).
tcf(c_18992,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_6832]) ).
tcf(c_18993,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_6797]) ).
tcf(c_18994,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_6681]) ).
tcf(c_18995,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_6189]) ).
tcf(c_18996,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_6188]) ).
tcf(c_18997,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_6187]) ).
tcf(c_18998,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_6192]) ).
tcf(c_18999,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_9868]) ).
tcf(c_19000,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_7682]) ).
tcf(c_19001,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_7256]) ).
tcf(c_19002,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_7140]) ).
tcf(c_19003,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_6951]) ).
tcf(c_19004,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_6680]) ).
tcf(c_19005,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_6191]) ).
tcf(c_19006,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_6936]) ).
tcf(c_19007,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_6903]) ).
tcf(c_19008,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_6885]) ).
tcf(c_19009,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_6854]) ).
tcf(c_19010,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_6190]) ).
tcf(c_19011,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_5583]) ).
tcf(c_19012,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_5569]) ).
tcf(c_19013,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_6830]) ).
tcf(c_19014,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_6795]) ).
tcf(c_19015,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_5557]) ).
tcf(c_19016,plain,
! [X0: $i,X1: $i] :
( ( sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_5270]) ).
tcf(c_19017,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_7171]) ).
tcf(c_19018,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_6193]) ).
tcf(c_19019,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_6678]) ).
tcf(c_19020,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_5581]) ).
tcf(c_19021,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_5567]) ).
tcf(c_19022,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_5555]) ).
tcf(c_19023,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_5302]) ).
tcf(c_19035,plain,
! [X0: $i] :
( relation(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_87]) ).
tcf(c_19036,plain,
! [X0: $i] :
( function(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_77]) ).
tcf(c_19406,plain,
( empty(sK15(powerset(empty_set)))
| ~ in(empty_set,sK15(sK14(sK14(empty_set)))) ),
inference(superposition,[status(thm)],[c_5301,c_17039]) ).
tcf(c_19407,plain,
( empty(empty_set)
| ~ in(empty_set,sK15(sK14(sK14(empty_set)))) ),
inference(light_normalisation,[status(thm)],[c_19406,c_5301]) ).
tcf(c_19412,plain,
! [X0: $i] :
( empty(powerset(sK15(sK14(sK14(powerset(sK15(powerset(singleton(X0)))))))))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ~ in(powerset(sK15(sK14(sK14(powerset(sK15(powerset(singleton(X0)))))))),empty_set) ),
inference(superposition,[status(thm)],[c_12707,c_5145]) ).
tcf(c_19413,plain,
! [X0: $i] :
( empty(powerset(sK15(sK14(sK14(powerset(sK15(powerset(singleton(X0)))))))))
| in(empty_set,powerset(sK15(sK14(sK14(powerset(sK15(powerset(singleton(X0)))))))))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 ) ),
inference(superposition,[status(thm)],[c_12707,c_5124]) ).
tcf(c_19414,plain,
! [X0: $i] :
( element(empty_set,powerset(sK15(sK14(sK14(powerset(sK15(powerset(singleton(X0)))))))))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 ) ),
inference(superposition,[status(thm)],[c_12707,c_99]) ).
tcf(c_19416,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ~ in(X1,empty_set)
| ~ empty(sK15(sK14(sK14(powerset(sK15(powerset(singleton(X0)))))))) ),
inference(superposition,[status(thm)],[c_12707,c_5201]) ).
tcf(c_19417,plain,
! [X0: $i] :
( empty(sK15(powerset(sK15(sK14(sK14(powerset(sK15(powerset(singleton(X0))))))))))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ~ in(sK15(sK14(sK14(powerset(sK15(powerset(singleton(X0))))))),sK15(sK14(sK14(empty_set)))) ),
inference(superposition,[status(thm)],[c_12707,c_17039]) ).
tcf(c_19418,plain,
! [X0: $i] :
( function(sK15(sK14(powerset(empty_set))))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ~ empty(sK15(sK14(sK14(powerset(sK15(powerset(singleton(X0)))))))) ),
inference(superposition,[status(thm)],[c_12707,c_17169]) ).
tcf(c_19419,plain,
! [X0: $i] :
( relation(sK15(sK14(powerset(empty_set))))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ~ empty(sK15(sK14(sK14(powerset(sK15(powerset(singleton(X0)))))))) ),
inference(superposition,[status(thm)],[c_12707,c_17168]) ).
tcf(c_19420,plain,
! [X0: $i] :
( empty(sK15(sK14(powerset(empty_set))))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ~ empty(sK15(sK14(sK14(powerset(sK15(powerset(singleton(X0)))))))) ),
inference(superposition,[status(thm)],[c_12707,c_16911]) ).
tcf(c_19421,plain,
! [X0: $i] :
( empty(sK15(powerset(sK15(sK14(sK14(powerset(sK15(powerset(singleton(X0))))))))))
| in(sK15(sK14(sK14(empty_set))),sK15(sK14(sK14(powerset(sK15(powerset(singleton(X0))))))))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 ) ),
inference(superposition,[status(thm)],[c_12707,c_17031]) ).
tcf(c_19423,plain,
! [X0: $i] :
( empty(sK15(powerset(sK15(sK14(sK14(powerset(sK15(powerset(singleton(X0))))))))))
| element(sK15(sK14(sK14(sK14(empty_set)))),sK15(sK14(sK14(powerset(sK15(powerset(singleton(X0))))))))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 ) ),
inference(superposition,[status(thm)],[c_12707,c_9269]) ).
tcf(c_19426,plain,
! [X0: $i] :
( empty(sK15(powerset(sK15(sK14(sK14(powerset(sK15(powerset(singleton(X0))))))))))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ~ in(sK15(sK14(sK14(powerset(sK15(powerset(singleton(X0))))))),sK15(sK14(empty_set))) ),
inference(superposition,[status(thm)],[c_12707,c_11248]) ).
tcf(c_19427,plain,
! [X0: $i] :
( empty(sK15(powerset(sK15(sK14(sK14(powerset(sK15(powerset(singleton(X0))))))))))
| in(sK15(sK14(empty_set)),sK15(sK14(sK14(powerset(sK15(powerset(singleton(X0))))))))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 ) ),
inference(superposition,[status(thm)],[c_12707,c_11240]) ).
tcf(c_19428,plain,
! [X0: $i] :
( empty(sK15(powerset(sK15(sK14(sK14(powerset(sK15(powerset(singleton(X0))))))))))
| element(sK15(sK14(sK14(empty_set))),sK15(sK14(sK14(powerset(sK15(powerset(singleton(X0))))))))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 ) ),
inference(superposition,[status(thm)],[c_12707,c_7046]) ).
tcf(c_19429,plain,
! [X0: $i] :
( function(sK15(powerset(empty_set)))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ~ empty(sK15(sK14(sK14(powerset(sK15(powerset(singleton(X0)))))))) ),
inference(superposition,[status(thm)],[c_12707,c_8308]) ).
tcf(c_19430,plain,
! [X0: $i] :
( relation(sK15(powerset(empty_set)))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ~ empty(sK15(sK14(sK14(powerset(sK15(powerset(singleton(X0)))))))) ),
inference(superposition,[status(thm)],[c_12707,c_8307]) ).
tcf(c_19431,plain,
! [X0: $i] :
( empty(sK15(powerset(empty_set)))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ~ empty(sK15(sK14(sK14(powerset(sK15(powerset(singleton(X0)))))))) ),
inference(superposition,[status(thm)],[c_12707,c_8117]) ).
tcf(c_19432,plain,
! [X0: $i] :
( empty(sK15(powerset(sK15(sK14(sK14(powerset(sK15(powerset(singleton(X0))))))))))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ~ in(sK15(sK14(sK14(powerset(sK15(powerset(singleton(X0))))))),sK15(empty_set)) ),
inference(superposition,[status(thm)],[c_12707,c_8111]) ).
tcf(c_19433,plain,
! [X0: $i] :
( empty(sK15(powerset(sK15(sK14(sK14(powerset(sK15(powerset(singleton(X0))))))))))
| in(sK15(empty_set),sK15(sK14(sK14(powerset(sK15(powerset(singleton(X0))))))))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 ) ),
inference(superposition,[status(thm)],[c_12707,c_8103]) ).
tcf(c_19434,plain,
! [X0: $i] :
( empty(sK15(powerset(sK15(sK14(sK14(powerset(sK15(powerset(singleton(X0))))))))))
| element(sK15(sK14(empty_set)),sK15(sK14(sK14(powerset(sK15(powerset(singleton(X0))))))))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 ) ),
inference(superposition,[status(thm)],[c_12707,c_6096]) ).
tcf(c_19435,plain,
! [X0: $i] :
( element(sK15(empty_set),sK15(sK14(sK14(powerset(sK15(powerset(singleton(X0))))))))
| empty(sK15(powerset(sK15(sK14(sK14(powerset(sK15(powerset(singleton(X0))))))))))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 ) ),
inference(superposition,[status(thm)],[c_12707,c_5436]) ).
tcf(c_19442,plain,
! [X0: $i] :
( empty(empty_set)
| ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ~ empty(sK15(sK14(sK14(powerset(sK15(powerset(singleton(X0)))))))) ),
inference(light_normalisation,[status(thm)],[c_19431,c_5301]) ).
tcf(c_19443,plain,
! [X0: $i] :
( relation(empty_set)
| ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ~ empty(sK15(sK14(sK14(powerset(sK15(powerset(singleton(X0)))))))) ),
inference(light_normalisation,[status(thm)],[c_19430,c_5301]) ).
tcf(c_19444,plain,
! [X0: $i] :
( function(empty_set)
| ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ~ empty(sK15(sK14(sK14(powerset(sK15(powerset(singleton(X0)))))))) ),
inference(light_normalisation,[status(thm)],[c_19429,c_5301]) ).
tcf(c_19508,plain,
( relation(sK15(sK14(powerset(empty_set))))
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_6000,c_18494]) ).
tcf(c_19509,plain,
( relation(sK15(sK14(powerset(empty_set))))
| ~ function(sK1)
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_9666,c_18494]) ).
tcf(c_19510,plain,
( relation(sK15(sK14(powerset(empty_set))))
| ~ function(sK7)
| ~ relation(sK7) ),
inference(superposition,[status(thm)],[c_9665,c_18494]) ).
tcf(c_19520,plain,
( function(sK15(sK14(powerset(empty_set))))
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_6000,c_18495]) ).
tcf(c_19521,plain,
( function(sK15(sK14(powerset(empty_set))))
| ~ function(sK1)
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_9666,c_18495]) ).
tcf(c_19522,plain,
( function(sK15(sK14(powerset(empty_set))))
| ~ function(sK7)
| ~ relation(sK7) ),
inference(superposition,[status(thm)],[c_9665,c_18495]) ).
tcf(c_19523,plain,
! [X0: $i] :
( ( relation_dom(relation_image(sK15(sK14(powerset(relation_image(X0,empty_set)))),empty_set)) = empty_set )
| ~ function(X0)
| ~ relation(X0)
| ~ relation(sK15(sK14(powerset(relation_image(X0,empty_set))))) ),
inference(superposition,[status(thm)],[c_18495,c_7934]) ).
tcf(c_19524,plain,
! [X0: $i] :
( ( relation_image(sK15(sK14(powerset(relation_image(X0,empty_set)))),empty_set) = empty_set )
| ~ function(X0)
| ~ relation(X0)
| ~ relation(sK15(sK14(powerset(relation_image(X0,empty_set))))) ),
inference(superposition,[status(thm)],[c_18495,c_7777]) ).
tcf(c_19548,plain,
! [X0: $i] :
( ( relation_dom(relation_image(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))),empty_set)) = empty_set )
| ~ empty(X0)
| ~ relation(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))) ),
inference(superposition,[status(thm)],[c_19036,c_7934]) ).
tcf(c_19549,plain,
! [X0: $i] :
( ( relation_image(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))),empty_set) = empty_set )
| ~ empty(X0)
| ~ relation(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))) ),
inference(superposition,[status(thm)],[c_19036,c_7777]) ).
tcf(c_19560,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(sK15(sK14(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_6857]) ).
tcf(c_19561,plain,
sK15(powerset(sK15(powerset(sK15(sK14(powerset(empty_set))))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_6857]) ).
tcf(c_19566,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( sK15(powerset(sK15(powerset(sK15(sK14(powerset(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_6857]) ).
tcf(c_19567,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(sK15(sK14(powerset(sK15(powerset(sK15(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_6857]) ).
tcf(c_19568,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(sK15(sK14(powerset(sK15(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_6857]) ).
tcf(c_19569,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(sK15(sK14(powerset(sK15(powerset(sK15(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_6857]) ).
tcf(c_19570,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(sK15(sK14(powerset(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_6857]) ).
tcf(c_19572,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(sK15(sK14(powerset(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_6857]) ).
tcf(c_19573,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_6857]) ).
tcf(c_19574,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(sK15(sK14(powerset(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_6857]) ).
tcf(c_19575,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(sK15(sK14(powerset(sK15(sK14(powerset(sK15(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_6857]) ).
tcf(c_19576,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(sK15(sK14(powerset(sK15(sK14(powerset(relation_image(X0,empty_set))))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_6857]) ).
tcf(c_19577,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(sK15(sK14(powerset(sK15(sK14(powerset(sK15(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_6857]) ).
tcf(c_19578,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(sK15(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_6857]) ).
tcf(c_19579,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(sK15(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_6857]) ).
tcf(c_19681,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_6888]) ).
tcf(c_19682,plain,
relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(empty_set))))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_6888]) ).
tcf(c_19687,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_6888]) ).
tcf(c_19688,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(powerset(sK15(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_6888]) ).
tcf(c_19689,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_6888]) ).
tcf(c_19690,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(powerset(sK15(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_6888]) ).
tcf(c_19691,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_6888]) ).
tcf(c_19693,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_6888]) ).
tcf(c_19694,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_6888]) ).
tcf(c_19695,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_6888]) ).
tcf(c_19696,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(sK15(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_6888]) ).
tcf(c_19697,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(relation_image(X0,empty_set))))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_6888]) ).
tcf(c_19698,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(sK15(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_6888]) ).
tcf(c_19699,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_6888]) ).
tcf(c_19700,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_6888]) ).
tcf(c_19739,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(sK15(sK14(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_6906]) ).
tcf(c_19740,plain,
relation_dom(sK15(powerset(relation_dom(sK15(sK14(powerset(empty_set))))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_6906]) ).
tcf(c_19745,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( relation_dom(sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_6906]) ).
tcf(c_19746,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(powerset(sK15(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_6906]) ).
tcf(c_19747,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_6906]) ).
tcf(c_19748,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(powerset(sK15(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_6906]) ).
tcf(c_19749,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_6906]) ).
tcf(c_19751,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_6906]) ).
tcf(c_19752,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_6906]) ).
tcf(c_19753,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_6906]) ).
tcf(c_19754,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(sK15(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_6906]) ).
tcf(c_19755,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(relation_image(X0,empty_set))))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_6906]) ).
tcf(c_19756,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(sK15(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_6906]) ).
tcf(c_19757,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_6906]) ).
tcf(c_19758,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_6906]) ).
tcf(c_19797,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(sK15(sK14(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_6939]) ).
tcf(c_19798,plain,
sK15(powerset(relation_dom(relation_dom(sK15(sK14(powerset(empty_set))))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_6939]) ).
tcf(c_19803,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( sK15(powerset(relation_dom(relation_dom(sK15(sK14(powerset(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_6939]) ).
tcf(c_19804,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(sK15(sK14(powerset(sK15(powerset(sK15(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_6939]) ).
tcf(c_19805,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(sK15(sK14(powerset(sK15(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_6939]) ).
tcf(c_19806,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(sK15(sK14(powerset(sK15(powerset(sK15(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_6939]) ).
tcf(c_19807,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(sK15(sK14(powerset(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_6939]) ).
tcf(c_19809,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(sK15(sK14(powerset(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_6939]) ).
tcf(c_19810,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_6939]) ).
tcf(c_19811,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(sK15(sK14(powerset(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_6939]) ).
tcf(c_19812,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(sK15(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_6939]) ).
tcf(c_19813,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(relation_image(X0,empty_set))))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_6939]) ).
tcf(c_19814,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(sK15(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_6939]) ).
tcf(c_19815,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_6939]) ).
tcf(c_19816,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_6939]) ).
tcf(c_19878,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(sK15(sK14(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_6954]) ).
tcf(c_19879,plain,
sK15(sK14(powerset(relation_dom(sK15(sK14(powerset(empty_set))))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_6954]) ).
tcf(c_19884,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( sK15(sK14(powerset(relation_dom(sK15(sK14(powerset(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_6954]) ).
tcf(c_19885,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(sK15(sK14(powerset(sK15(powerset(sK15(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_6954]) ).
tcf(c_19886,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(sK15(sK14(powerset(sK15(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_6954]) ).
tcf(c_19887,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(sK15(sK14(powerset(sK15(powerset(sK15(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_6954]) ).
tcf(c_19888,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(sK15(sK14(powerset(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_6954]) ).
tcf(c_19890,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(sK15(sK14(powerset(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_6954]) ).
tcf(c_19891,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_6954]) ).
tcf(c_19892,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(sK15(sK14(powerset(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_6954]) ).
tcf(c_19893,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(sK15(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_6954]) ).
tcf(c_19894,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(relation_image(X0,empty_set))))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_6954]) ).
tcf(c_19895,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(sK15(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_6954]) ).
tcf(c_19896,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_6954]) ).
tcf(c_19897,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_6954]) ).
tcf(c_19990,plain,
( empty(sK15(sK14(powerset(empty_set))))
| element(sK15(sK14(sK14(empty_set))),empty_set) ),
inference(superposition,[status(thm)],[c_6679,c_7049]) ).
tcf(c_19991,plain,
! [X0: $i] :
( empty(X0)
| empty(sK15(sK14(powerset(X0))))
| in(sK15(sK14(sK14(sK15(sK14(powerset(X0)))))),X0) ),
inference(superposition,[status(thm)],[c_7049,c_66]) ).
tcf(c_19992,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| empty(sK15(sK14(powerset(powerset(X1)))))
| ~ in(X0,sK15(sK14(sK14(sK15(sK14(powerset(powerset(X1)))))))) ),
inference(superposition,[status(thm)],[c_7049,c_94]) ).
tcf(c_19993,plain,
! [X0: $i,X1: $i] :
( empty(sK15(sK14(powerset(powerset(X1)))))
| ~ empty(X1)
| ~ in(X0,sK15(sK14(sK14(sK15(sK14(powerset(powerset(X1)))))))) ),
inference(superposition,[status(thm)],[c_7049,c_93]) ).
tcf(c_20010,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_7143]) ).
tcf(c_20011,plain,
relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(empty_set))))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_7143]) ).
tcf(c_20016,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_7143]) ).
tcf(c_20017,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(sK15(powerset(sK15(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_7143]) ).
tcf(c_20018,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(sK15(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_7143]) ).
tcf(c_20019,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(sK15(powerset(sK15(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_7143]) ).
tcf(c_20020,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_7143]) ).
tcf(c_20022,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_7143]) ).
tcf(c_20023,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_7143]) ).
tcf(c_20024,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_7143]) ).
tcf(c_20025,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(sK15(sK14(powerset(sK15(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_7143]) ).
tcf(c_20026,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(sK15(sK14(powerset(relation_image(X0,empty_set))))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_7143]) ).
tcf(c_20027,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(sK15(sK14(powerset(sK15(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_7143]) ).
tcf(c_20028,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_7143]) ).
tcf(c_20029,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_7143]) ).
tcf(c_20099,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(sK14(sK14(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_7249]) ).
tcf(c_20100,plain,
sK15(sK14(powerset(sK15(sK14(sK14(powerset(empty_set))))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_7249]) ).
tcf(c_20101,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(sK14(sK14(powerset(sK15(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_7249]) ).
tcf(c_20102,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(sK14(sK14(powerset(sK15(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_7249]) ).
tcf(c_20103,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(sK14(sK14(powerset(sK15(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_7249]) ).
tcf(c_20104,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(sK14(sK14(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_7249]) ).
tcf(c_20105,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( sK15(sK14(powerset(sK15(sK14(sK14(powerset(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_7249]) ).
tcf(c_20106,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(sK14(sK14(powerset(sK15(powerset(sK15(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_7249]) ).
tcf(c_20107,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(sK14(sK14(powerset(sK15(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_7249]) ).
tcf(c_20108,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(sK14(sK14(powerset(sK15(powerset(sK15(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_7249]) ).
tcf(c_20109,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(sK14(sK14(powerset(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_7249]) ).
tcf(c_20110,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(sK14(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_7249]) ).
tcf(c_20111,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(sK14(sK14(powerset(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_7249]) ).
tcf(c_20112,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(sK14(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_7249]) ).
tcf(c_20113,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(sK14(sK14(powerset(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_7249]) ).
tcf(c_20114,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(sK14(sK14(powerset(sK15(sK14(powerset(sK15(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_7249]) ).
tcf(c_20115,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(sK14(sK14(powerset(sK15(sK14(powerset(relation_image(X0,empty_set))))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_7249]) ).
tcf(c_20116,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(sK14(sK14(powerset(sK15(sK14(powerset(sK15(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_7249]) ).
tcf(c_20117,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(sK14(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_7249]) ).
tcf(c_20118,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(sK14(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_7249]) ).
tcf(c_20254,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(sK14(sK14(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_7250]) ).
tcf(c_20255,plain,
sK15(powerset(relation_dom(sK15(sK14(sK14(powerset(empty_set))))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_7250]) ).
tcf(c_20256,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(sK14(sK14(powerset(sK15(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_7250]) ).
tcf(c_20257,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(sK14(sK14(powerset(sK15(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_7250]) ).
tcf(c_20258,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(sK14(sK14(powerset(sK15(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_7250]) ).
tcf(c_20259,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(sK14(sK14(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_7250]) ).
tcf(c_20260,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( sK15(powerset(relation_dom(sK15(sK14(sK14(powerset(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_7250]) ).
tcf(c_20261,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(sK14(sK14(powerset(sK15(powerset(sK15(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_7250]) ).
tcf(c_20262,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(sK14(sK14(powerset(sK15(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_7250]) ).
tcf(c_20263,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(sK14(sK14(powerset(sK15(powerset(sK15(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_7250]) ).
tcf(c_20264,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(sK14(sK14(powerset(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_7250]) ).
tcf(c_20265,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(sK14(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_7250]) ).
tcf(c_20266,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(sK14(sK14(powerset(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_7250]) ).
tcf(c_20267,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(sK14(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_7250]) ).
tcf(c_20268,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(sK14(sK14(powerset(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_7250]) ).
tcf(c_20269,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(sK14(sK14(powerset(sK15(sK14(powerset(sK15(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_7250]) ).
tcf(c_20270,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(sK14(sK14(powerset(sK15(sK14(powerset(relation_image(X0,empty_set))))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_7250]) ).
tcf(c_20271,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(sK14(sK14(powerset(sK15(sK14(powerset(sK15(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_7250]) ).
tcf(c_20272,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(sK14(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_7250]) ).
tcf(c_20273,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(sK14(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_7250]) ).
tcf(c_20362,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(sK14(sK14(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_7251]) ).
tcf(c_20363,plain,
relation_dom(sK15(powerset(sK15(sK14(sK14(powerset(empty_set))))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_7251]) ).
tcf(c_20364,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(sK14(sK14(powerset(sK15(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_7251]) ).
tcf(c_20365,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(sK14(sK14(powerset(sK15(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_7251]) ).
tcf(c_20366,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(sK14(sK14(powerset(sK15(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_7251]) ).
tcf(c_20367,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(sK14(sK14(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_7251]) ).
tcf(c_20368,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( relation_dom(sK15(powerset(sK15(sK14(sK14(powerset(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_7251]) ).
tcf(c_20369,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(sK14(sK14(powerset(sK15(powerset(sK15(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_7251]) ).
tcf(c_20370,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(sK14(sK14(powerset(sK15(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_7251]) ).
tcf(c_20371,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(sK14(sK14(powerset(sK15(powerset(sK15(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_7251]) ).
tcf(c_20372,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(sK14(sK14(powerset(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_7251]) ).
tcf(c_20373,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(sK14(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_7251]) ).
tcf(c_20374,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(sK14(sK14(powerset(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_7251]) ).
tcf(c_20375,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(sK14(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_7251]) ).
tcf(c_20376,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(sK14(sK14(powerset(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_7251]) ).
tcf(c_20377,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(sK14(sK14(powerset(sK15(sK14(powerset(sK15(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_7251]) ).
tcf(c_20378,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(sK14(sK14(powerset(sK15(sK14(powerset(relation_image(X0,empty_set))))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_7251]) ).
tcf(c_20379,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(sK14(sK14(powerset(sK15(sK14(powerset(sK15(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_7251]) ).
tcf(c_20380,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(sK14(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_7251]) ).
tcf(c_20381,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(sK14(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_7251]) ).
tcf(c_20525,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_7252]) ).
tcf(c_20526,plain,
relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(powerset(empty_set))))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_7252]) ).
tcf(c_20527,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(powerset(sK15(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_7252]) ).
tcf(c_20528,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(powerset(sK15(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_7252]) ).
tcf(c_20529,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(powerset(sK15(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_7252]) ).
tcf(c_20530,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_7252]) ).
tcf(c_20531,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(powerset(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_7252]) ).
tcf(c_20532,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(powerset(sK15(powerset(sK15(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_7252]) ).
tcf(c_20533,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(powerset(sK15(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_7252]) ).
tcf(c_20534,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(powerset(sK15(powerset(sK15(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_7252]) ).
tcf(c_20535,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(powerset(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_7252]) ).
tcf(c_20536,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_7252]) ).
tcf(c_20537,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(powerset(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_7252]) ).
tcf(c_20538,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_7252]) ).
tcf(c_20539,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(powerset(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_7252]) ).
tcf(c_20540,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(powerset(sK15(sK14(powerset(sK15(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_7252]) ).
tcf(c_20541,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(powerset(sK15(sK14(powerset(relation_image(X0,empty_set))))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_7252]) ).
tcf(c_20542,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(powerset(sK15(sK14(powerset(sK15(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_7252]) ).
tcf(c_20543,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_7252]) ).
tcf(c_20544,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_7252]) ).
tcf(c_20643,plain,
( element(sK15(empty_set),empty_set)
| empty(sK15(sK14(sK14(powerset(empty_set))))) ),
inference(superposition,[status(thm)],[c_7683,c_7410]) ).
tcf(c_20644,plain,
! [X0: $i] :
( element(sK15(empty_set),sK15(powerset(sK15(powerset(singleton(X0))))))
| empty(sK15(sK14(sK14(powerset(sK15(powerset(sK15(powerset(singleton(X0))))))))))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 ) ),
inference(superposition,[status(thm)],[c_12705,c_7410]) ).
tcf(c_20645,plain,
! [X0: $i] :
( empty(X0)
| empty(sK15(sK14(sK14(powerset(X0)))))
| in(sK15(sK15(sK14(sK14(powerset(X0))))),X0) ),
inference(superposition,[status(thm)],[c_7410,c_66]) ).
tcf(c_20646,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| empty(sK15(sK14(sK14(powerset(powerset(X1))))))
| ~ in(X0,sK15(sK15(sK14(sK14(powerset(powerset(X1))))))) ),
inference(superposition,[status(thm)],[c_7410,c_94]) ).
tcf(c_20647,plain,
! [X0: $i,X1: $i] :
( empty(sK15(sK14(sK14(powerset(powerset(X1))))))
| ~ empty(X1)
| ~ in(X0,sK15(sK15(sK14(sK14(powerset(powerset(X1))))))) ),
inference(superposition,[status(thm)],[c_7410,c_93]) ).
tcf(c_20668,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK4(sK15(sK14(powerset(sK15(powerset(sK15(powerset(singleton(X0)))))))),X1,X2),empty_set)
| in(sK3(sK15(sK14(powerset(sK15(powerset(sK15(powerset(singleton(X0)))))))),X1,X2),X2)
| ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( relation_image(sK15(sK14(powerset(sK15(powerset(sK15(powerset(singleton(X0)))))))),X1) = X2 )
| ~ function(sK15(sK14(powerset(sK15(powerset(sK15(powerset(singleton(X0)))))))))
| ~ relation(sK15(sK14(powerset(sK15(powerset(sK15(powerset(singleton(X0))))))))) ),
inference(superposition,[status(thm)],[c_12708,c_58]) ).
tcf(c_20669,plain,
! [X0: $i] :
( empty(sK15(sK14(powerset(sK15(powerset(sK15(powerset(singleton(X0)))))))))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ~ empty(empty_set)
| ~ relation(sK15(sK14(powerset(sK15(powerset(sK15(powerset(singleton(X0))))))))) ),
inference(superposition,[status(thm)],[c_12708,c_71]) ).
tcf(c_20673,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(sK15(sK14(powerset(sK15(powerset(sK15(powerset(singleton(X1)))))))),X2,X0),empty_set)
| ( sK15(sK15(powerset(singleton(X1)))) = X1 )
| ~ function(sK15(sK14(powerset(sK15(powerset(sK15(powerset(singleton(X1)))))))))
| ~ relation(sK15(sK14(powerset(sK15(powerset(sK15(powerset(singleton(X1)))))))))
| ~ in(X0,relation_image(sK15(sK14(powerset(sK15(powerset(sK15(powerset(singleton(X1)))))))),X2)) ),
inference(superposition,[status(thm)],[c_12708,c_62]) ).
tcf(c_20674,plain,
! [X0: $i] :
( empty(sK15(sK14(powerset(sK15(powerset(sK15(powerset(singleton(X0)))))))))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ~ relation(sK15(sK14(powerset(sK15(powerset(sK15(powerset(singleton(X0))))))))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_20669,c_92]) ).
tcf(c_20678,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK15(sK15(powerset(singleton(X1)))) = X1 )
| ~ function(sK15(sK14(powerset(sK15(powerset(sK15(powerset(singleton(X1)))))))))
| ~ relation(sK15(sK14(powerset(sK15(powerset(sK15(powerset(singleton(X1)))))))))
| ~ in(X0,relation_image(sK15(sK14(powerset(sK15(powerset(sK15(powerset(singleton(X1)))))))),X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_20673,c_5314]) ).
tcf(c_20683,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(sK15(sK14(powerset(sK15(powerset(sK15(powerset(singleton(X0)))))))),X1,X2),X2)
| ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( relation_image(sK15(sK14(powerset(sK15(powerset(sK15(powerset(singleton(X0)))))))),X1) = X2 )
| ~ function(sK15(sK14(powerset(sK15(powerset(sK15(powerset(singleton(X0)))))))))
| ~ relation(sK15(sK14(powerset(sK15(powerset(sK15(powerset(singleton(X0))))))))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_20668,c_5314]) ).
tcf(c_20728,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK14(powerset(relation_dom(relation_dom(X0))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_11182]) ).
tcf(c_20729,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(empty_set)))) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_92,c_11182]) ).
tcf(c_20730,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK14(powerset(relation_dom(sK15(powerset(X0)))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_11182]) ).
tcf(c_20731,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK14(powerset(relation_dom(sK15(sK14(powerset(X0))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_11182]) ).
tcf(c_20732,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK14(powerset(relation_dom(sK15(sK14(sK14(powerset(X0)))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_11182]) ).
tcf(c_20733,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK14(powerset(relation_dom(relation_image(X0,empty_set))))) = X1 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_11182]) ).
tcf(c_20734,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK15(powerset(singleton(X1)))) = X1 )
| ( sK15(sK14(powerset(relation_dom(sK15(powerset(singleton(X1))))))) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8114,c_11182]) ).
tcf(c_20735,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK14(powerset(relation_dom(sK15(powerset(sK15(powerset(X0)))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_11182]) ).
tcf(c_20736,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK14(powerset(relation_dom(sK15(powerset(relation_image(X0,empty_set))))))) = X1 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_11182]) ).
tcf(c_20737,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK14(powerset(relation_dom(sK15(powerset(sK15(sK14(powerset(X0))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_11182]) ).
tcf(c_20738,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK14(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(powerset(X0)))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_11182]) ).
tcf(c_20739,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK14(powerset(relation_dom(sK15(sK14(sK14(sK14(powerset(X0))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_11182]) ).
tcf(c_20740,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK14(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_11182]) ).
tcf(c_20741,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK14(powerset(relation_dom(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_11182]) ).
tcf(c_20742,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK14(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_11182]) ).
tcf(c_20743,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK14(powerset(relation_dom(sK15(sK14(powerset(sK15(powerset(X0))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_11182]) ).
tcf(c_20744,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK14(powerset(relation_dom(sK15(sK14(powerset(relation_image(X0,empty_set)))))))) = X1 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_11182]) ).
tcf(c_20745,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK14(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(X0)))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_11182]) ).
tcf(c_20746,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK14(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0))))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_11182]) ).
tcf(c_20747,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK14(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_11182]) ).
tcf(c_20813,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X1))))) = X1 )
| ( sK15(sK14(powerset(relation_dom(sK15(powerset(singleton(X1))))))) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11251,c_11182]) ).
tcf(c_20814,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(powerset(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_7252]) ).
tcf(c_20815,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( relation_dom(sK15(powerset(sK15(sK14(sK14(powerset(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_7251]) ).
tcf(c_20816,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( sK15(powerset(relation_dom(sK15(sK14(sK14(powerset(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_7250]) ).
tcf(c_20817,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( sK15(sK14(powerset(sK15(sK14(sK14(powerset(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_7249]) ).
tcf(c_20818,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_7143]) ).
tcf(c_20819,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( sK15(sK14(powerset(relation_dom(sK15(sK14(powerset(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_6954]) ).
tcf(c_20820,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( sK15(powerset(relation_dom(relation_dom(sK15(sK14(powerset(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_6939]) ).
tcf(c_20821,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( relation_dom(sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_6906]) ).
tcf(c_20822,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_6888]) ).
tcf(c_20823,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( sK15(powerset(sK15(powerset(sK15(sK14(powerset(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_6857]) ).
tcf(c_20824,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X1))))) = X1 )
| ( sK15(sK14(sK14(powerset(sK15(powerset(singleton(X1))))))) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11251,c_7255]) ).
tcf(c_20825,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_6833]) ).
tcf(c_20826,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X1))))) = X1 )
| ( relation_dom(sK15(sK14(powerset(sK15(powerset(singleton(X1))))))) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11251,c_6798]) ).
tcf(c_20827,plain,
! [X0: $i,X1: $i] :
( ( sK15(powerset(singleton(X1))) = singleton(X0) )
| ( sK15(sK14(sK15(powerset(singleton(X1))))) = X1 )
| ( sK8(X0,sK15(powerset(singleton(X1)))) = X0 ) ),
inference(superposition,[status(thm)],[c_11251,c_5346]) ).
tcf(c_20828,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( sK15(sK14(sK14(sK14(sK14(powerset(sK15(powerset(singleton(X0))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_14868]) ).
tcf(c_20829,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( sK15(sK14(sK14(sK14(powerset(relation_dom(sK15(powerset(singleton(X0))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_10887]) ).
tcf(c_20830,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( relation_dom(sK15(sK14(sK14(sK14(powerset(sK15(powerset(singleton(X0))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_10136]) ).
tcf(c_20831,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( sK15(sK14(sK14(powerset(relation_dom(relation_dom(sK15(powerset(singleton(X0))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_9586]) ).
tcf(c_20832,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( relation_dom(sK15(sK14(sK14(powerset(relation_dom(sK15(powerset(singleton(X0))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_9505]) ).
tcf(c_20833,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( relation_dom(sK15(sK14(powerset(relation_dom(relation_dom(sK15(powerset(singleton(X0))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_9411]) ).
tcf(c_20834,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( sK15(sK14(powerset(relation_dom(relation_dom(relation_dom(sK15(powerset(singleton(X0))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_9211]) ).
tcf(c_20835,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( sK15(sK14(powerset(sK15(powerset(relation_dom(sK15(powerset(singleton(X0))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_9107]) ).
tcf(c_20836,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( relation_dom(relation_dom(sK15(sK14(powerset(relation_dom(sK15(powerset(singleton(X0))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_9025]) ).
tcf(c_20837,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( sK15(powerset(relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(singleton(X0))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_8993]) ).
tcf(c_20838,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( relation_dom(sK15(powerset(relation_dom(relation_dom(relation_dom(sK15(powerset(singleton(X0))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_8933]) ).
tcf(c_20839,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(singleton(X0))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_8858]) ).
tcf(c_20840,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( sK15(powerset(sK15(powerset(relation_dom(relation_dom(sK15(powerset(singleton(X0))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_8821]) ).
tcf(c_20841,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( sK15(powerset(sK15(sK14(powerset(relation_dom(sK15(powerset(singleton(X0))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_8743]) ).
tcf(c_20842,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( sK15(powerset(relation_dom(sK15(powerset(relation_dom(sK15(powerset(singleton(X0))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_8705]) ).
tcf(c_20843,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( relation_dom(sK15(powerset(sK15(powerset(relation_dom(sK15(powerset(singleton(X0))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_8667]) ).
tcf(c_20844,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( relation_dom(relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(powerset(singleton(X0))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_8236]) ).
tcf(c_20845,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X1))))) = X1 )
| ( relation_dom(relation_dom(relation_dom(sK15(powerset(singleton(X1)))))) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11251,c_8209]) ).
tcf(c_20846,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( sK15(sK14(sK14(powerset(sK15(powerset(sK15(powerset(singleton(X0))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_7684]) ).
tcf(c_20847,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( relation_dom(relation_dom(sK15(sK14(sK14(powerset(sK15(powerset(singleton(X0))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_7254]) ).
tcf(c_20848,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( sK15(powerset(sK15(sK14(sK14(powerset(sK15(powerset(singleton(X0))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_7253]) ).
tcf(c_20849,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( relation_dom(sK15(sK14(powerset(sK15(powerset(sK15(powerset(singleton(X0))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_7142]) ).
tcf(c_20850,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( sK15(sK14(powerset(relation_dom(sK15(powerset(sK15(powerset(singleton(X0))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_6953]) ).
tcf(c_20851,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( sK15(powerset(relation_dom(relation_dom(sK15(powerset(sK15(powerset(singleton(X0))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_6938]) ).
tcf(c_20852,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( relation_dom(sK15(powerset(relation_dom(sK15(powerset(sK15(powerset(singleton(X0))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_6905]) ).
tcf(c_20853,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(powerset(singleton(X0))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_6887]) ).
tcf(c_20854,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( relation_dom(relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(powerset(singleton(X0))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_8076]) ).
tcf(c_20855,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X1))))) = X1 )
| ( sK15(powerset(relation_dom(sK15(powerset(singleton(X1)))))) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11251,c_7738]) ).
tcf(c_20856,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( sK15(powerset(sK15(powerset(sK15(powerset(sK15(powerset(singleton(X0))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_6856]) ).
tcf(c_20857,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( relation_dom(relation_dom(sK15(powerset(sK15(powerset(sK15(powerset(singleton(X0))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_6832]) ).
tcf(c_20858,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X1))))) = X1 )
| ( relation_dom(sK15(powerset(sK15(powerset(singleton(X1)))))) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11251,c_6797]) ).
tcf(c_20859,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( sK15(sK14(powerset(sK15(sK14(powerset(sK15(powerset(singleton(X0))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_6681]) ).
tcf(c_20860,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(powerset(singleton(X0))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_6189]) ).
tcf(c_20861,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(powerset(singleton(X0))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_6188]) ).
tcf(c_20862,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(powerset(singleton(X0))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_6187]) ).
tcf(c_20863,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X1))))) = X1 )
| ( sK15(sK14(powerset(sK15(powerset(singleton(X1)))))) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11251,c_6192]) ).
tcf(c_20864,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( sK15(sK14(sK14(sK14(powerset(sK15(powerset(singleton(X0)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_9868]) ).
tcf(c_20865,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( sK15(sK14(sK14(powerset(relation_dom(sK15(powerset(singleton(X0)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_7682]) ).
tcf(c_20866,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( relation_dom(sK15(sK14(sK14(powerset(sK15(powerset(singleton(X0)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_7256]) ).
tcf(c_20867,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( relation_dom(sK15(sK14(powerset(relation_dom(sK15(powerset(singleton(X0)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_7140]) ).
tcf(c_20868,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( sK15(sK14(powerset(relation_dom(relation_dom(sK15(powerset(singleton(X0)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_6951]) ).
tcf(c_20869,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( sK15(sK14(powerset(sK15(powerset(sK15(powerset(singleton(X0)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_6680]) ).
tcf(c_20870,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( relation_dom(relation_dom(sK15(sK14(powerset(sK15(powerset(singleton(X0)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_6191]) ).
tcf(c_20871,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( sK15(powerset(relation_dom(relation_dom(relation_dom(sK15(powerset(singleton(X0)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_6936]) ).
tcf(c_20872,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(powerset(singleton(X0)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_6903]) ).
tcf(c_20873,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(singleton(X0)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_6885]) ).
tcf(c_20874,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( sK15(powerset(sK15(powerset(relation_dom(sK15(powerset(singleton(X0)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_6854]) ).
tcf(c_20875,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( sK15(powerset(sK15(sK14(powerset(sK15(powerset(singleton(X0)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_6190]) ).
tcf(c_20876,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( sK15(powerset(relation_dom(sK15(powerset(sK15(powerset(singleton(X0)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_5583]) ).
tcf(c_20877,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( relation_dom(sK15(powerset(sK15(powerset(sK15(powerset(singleton(X0)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_5569]) ).
tcf(c_20878,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(powerset(singleton(X0)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_6830]) ).
tcf(c_20879,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X1))))) = X1 )
| ( relation_dom(relation_dom(sK15(powerset(singleton(X1))))) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11251,c_6795]) ).
tcf(c_20880,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(powerset(singleton(X0)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_5557]) ).
tcf(c_20881,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X1))))) = X1 )
| ( sK15(powerset(sK15(powerset(singleton(X1))))) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11251,c_5270]) ).
tcf(c_20882,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( sK15(sK14(sK14(powerset(sK15(powerset(singleton(X0))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_7171]) ).
tcf(c_20883,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( relation_dom(sK15(sK14(powerset(sK15(powerset(singleton(X0))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_6193]) ).
tcf(c_20884,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( sK15(sK14(powerset(relation_dom(sK15(powerset(singleton(X0))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_6678]) ).
tcf(c_20885,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( sK15(powerset(relation_dom(relation_dom(sK15(powerset(singleton(X0))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_5581]) ).
tcf(c_20886,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( relation_dom(sK15(powerset(relation_dom(sK15(powerset(singleton(X0))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_5567]) ).
tcf(c_20887,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(singleton(X0))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_5555]) ).
tcf(c_20888,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( sK15(powerset(sK15(powerset(sK15(powerset(singleton(X0))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_5302]) ).
tcf(c_20889,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( relation_dom(relation_dom(sK15(powerset(sK15(powerset(singleton(X0))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_5269]) ).
tcf(c_20890,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK15(powerset(singleton(X1)))) = X0 )
| ( sK15(sK14(sK15(powerset(singleton(X1))))) = X1 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11251,c_5189]) ).
tcf(c_20891,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( sK15(sK14(powerset(sK15(powerset(singleton(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_6153]) ).
tcf(c_20892,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( sK15(powerset(relation_dom(sK15(powerset(singleton(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_5300]) ).
tcf(c_20893,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( relation_dom(sK15(powerset(sK15(powerset(singleton(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_5271]) ).
tcf(c_20894,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( relation_dom(relation_dom(relation_dom(sK15(powerset(singleton(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_5245]) ).
tcf(c_20895,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( sK15(powerset(sK15(powerset(singleton(X0))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_5272]) ).
tcf(c_20896,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( relation_dom(relation_dom(sK15(powerset(singleton(X0))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_5110]) ).
tcf(c_20897,plain,
! [X0: $i,X1: $i] :
( ( sK15(powerset(singleton(X1))) = X0 )
| ( sK15(sK14(sK15(powerset(singleton(X1))))) = X1 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11251,c_53]) ).
tcf(c_20898,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(singleton(X0)))) = empty_set )
| ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 ) ),
inference(superposition,[status(thm)],[c_11251,c_5023]) ).
tcf(c_20899,plain,
! [X0: $i] :
( ( sK15(powerset(singleton(X0))) = empty_set )
| ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 ) ),
inference(superposition,[status(thm)],[c_11251,c_54]) ).
tcf(c_20900,plain,
! [X0: $i] :
( relation(sK15(powerset(singleton(X0))))
| ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 ) ),
inference(superposition,[status(thm)],[c_11251,c_87]) ).
tcf(c_20901,plain,
! [X0: $i] :
( function(sK15(powerset(singleton(X0))))
| ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 ) ),
inference(superposition,[status(thm)],[c_11251,c_77]) ).
tcf(c_21405,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(sK14(powerset(relation_dom(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_11438]) ).
tcf(c_21406,plain,
sK15(powerset(relation_dom(sK15(sK14(powerset(relation_dom(empty_set))))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_11438]) ).
tcf(c_21407,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(sK14(powerset(relation_dom(sK15(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_11438]) ).
tcf(c_21408,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(sK14(powerset(relation_dom(sK15(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_11438]) ).
tcf(c_21409,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(sK14(powerset(relation_dom(sK15(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_11438]) ).
tcf(c_21410,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(sK14(powerset(relation_dom(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_11438]) ).
tcf(c_21411,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( sK15(powerset(relation_dom(sK15(sK14(powerset(relation_dom(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_11438]) ).
tcf(c_21412,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( sK15(powerset(relation_dom(sK15(sK14(powerset(relation_dom(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_11438]) ).
tcf(c_21413,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(sK14(powerset(relation_dom(sK15(powerset(sK15(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_11438]) ).
tcf(c_21414,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(sK14(powerset(relation_dom(sK15(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_11438]) ).
tcf(c_21415,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(sK14(powerset(relation_dom(sK15(powerset(sK15(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_11438]) ).
tcf(c_21416,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(sK14(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_11438]) ).
tcf(c_21417,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(sK14(powerset(relation_dom(sK15(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_11438]) ).
tcf(c_21418,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(sK14(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_11438]) ).
tcf(c_21419,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(sK14(powerset(relation_dom(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_11438]) ).
tcf(c_21420,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(sK14(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_11438]) ).
tcf(c_21421,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(sK14(powerset(relation_dom(sK15(sK14(powerset(sK15(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_11438]) ).
tcf(c_21422,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(sK14(powerset(relation_dom(sK15(sK14(powerset(relation_image(X0,empty_set))))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_11438]) ).
tcf(c_21423,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(sK14(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_11438]) ).
tcf(c_21424,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(sK14(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_11438]) ).
tcf(c_21425,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(sK14(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_11438]) ).
tcf(c_21510,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(sK14(powerset(relation_dom(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_11491]) ).
tcf(c_21511,plain,
relation_dom(sK15(powerset(sK15(sK14(powerset(relation_dom(empty_set))))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_11491]) ).
tcf(c_21512,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(sK14(powerset(relation_dom(sK15(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_11491]) ).
tcf(c_21513,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(sK14(powerset(relation_dom(sK15(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_11491]) ).
tcf(c_21514,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(sK14(powerset(relation_dom(sK15(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_11491]) ).
tcf(c_21515,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(sK14(powerset(relation_dom(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_11491]) ).
tcf(c_21516,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( relation_dom(sK15(powerset(sK15(sK14(powerset(relation_dom(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_11491]) ).
tcf(c_21517,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( relation_dom(sK15(powerset(sK15(sK14(powerset(relation_dom(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_11491]) ).
tcf(c_21518,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(sK14(powerset(relation_dom(sK15(powerset(sK15(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_11491]) ).
tcf(c_21519,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(sK14(powerset(relation_dom(sK15(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_11491]) ).
tcf(c_21520,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(sK14(powerset(relation_dom(sK15(powerset(sK15(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_11491]) ).
tcf(c_21521,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(sK14(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_11491]) ).
tcf(c_21522,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(sK14(powerset(relation_dom(sK15(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_11491]) ).
tcf(c_21523,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(sK14(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_11491]) ).
tcf(c_21524,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(sK14(powerset(relation_dom(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_11491]) ).
tcf(c_21525,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(sK14(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_11491]) ).
tcf(c_21526,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(sK14(powerset(relation_dom(sK15(sK14(powerset(sK15(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_11491]) ).
tcf(c_21527,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(sK14(powerset(relation_dom(sK15(sK14(powerset(relation_image(X0,empty_set))))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_11491]) ).
tcf(c_21528,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(sK14(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_11491]) ).
tcf(c_21529,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(sK14(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_11491]) ).
tcf(c_21530,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(sK14(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_11491]) ).
tcf(c_21651,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(sK15(sK14(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_7685]) ).
tcf(c_21652,plain,
sK15(sK14(sK14(powerset(sK15(sK14(powerset(empty_set))))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_7685]) ).
tcf(c_21657,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( sK15(sK14(sK14(powerset(sK15(sK14(powerset(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_7685]) ).
tcf(c_21658,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( sK15(sK14(sK14(powerset(sK15(sK14(powerset(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_7685]) ).
tcf(c_21659,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(sK15(sK14(powerset(sK15(powerset(sK15(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_7685]) ).
tcf(c_21660,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(sK15(sK14(powerset(sK15(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_7685]) ).
tcf(c_21661,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(sK15(sK14(powerset(sK15(powerset(sK15(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_7685]) ).
tcf(c_21662,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(sK15(sK14(powerset(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_7685]) ).
tcf(c_21664,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(sK15(sK14(powerset(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_7685]) ).
tcf(c_21665,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_7685]) ).
tcf(c_21666,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(sK15(sK14(powerset(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_7685]) ).
tcf(c_21667,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(sK15(sK14(powerset(sK15(sK14(powerset(sK15(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_7685]) ).
tcf(c_21668,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(sK15(sK14(powerset(sK15(sK14(powerset(relation_image(X0,empty_set))))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_7685]) ).
tcf(c_21669,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(sK15(sK14(powerset(sK15(sK14(powerset(sK15(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_7685]) ).
tcf(c_21670,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(sK15(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_7685]) ).
tcf(c_21671,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(sK15(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_7685]) ).
tcf(c_21749,plain,
! [X0: $i,X1: $i] :
( ( sK15(powerset(sK15(powerset(relation_dom(X0))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_7740]) ).
tcf(c_21750,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(empty_set)))) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_92,c_7740]) ).
tcf(c_21755,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X1))))) = X1 )
| ( sK15(powerset(sK15(powerset(sK15(powerset(singleton(X1))))))) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11251,c_7740]) ).
tcf(c_21756,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK15(powerset(singleton(X1)))) = X1 )
| ( sK15(powerset(sK15(powerset(sK15(powerset(singleton(X1))))))) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8114,c_7740]) ).
tcf(c_21757,plain,
! [X0: $i,X1: $i] :
( ( sK15(powerset(sK15(powerset(sK15(powerset(sK15(powerset(X0)))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_7740]) ).
tcf(c_21758,plain,
! [X0: $i,X1: $i] :
( ( sK15(powerset(sK15(powerset(sK15(powerset(relation_image(X0,empty_set))))))) = X1 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_7740]) ).
tcf(c_21759,plain,
! [X0: $i,X1: $i] :
( ( sK15(powerset(sK15(powerset(sK15(powerset(sK15(sK14(powerset(X0))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_7740]) ).
tcf(c_21760,plain,
! [X0: $i,X1: $i] :
( ( sK15(powerset(sK15(powerset(sK15(powerset(sK15(sK14(sK14(powerset(X0)))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_7740]) ).
tcf(c_21762,plain,
! [X0: $i,X1: $i] :
( ( sK15(powerset(sK15(powerset(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_7740]) ).
tcf(c_21764,plain,
! [X0: $i,X1: $i] :
( ( sK15(powerset(sK15(powerset(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_7740]) ).
tcf(c_21765,plain,
! [X0: $i,X1: $i] :
( ( sK15(powerset(sK15(powerset(sK15(sK14(powerset(sK15(powerset(X0))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_7740]) ).
tcf(c_21766,plain,
! [X0: $i,X1: $i] :
( ( sK15(powerset(sK15(powerset(sK15(sK14(powerset(relation_image(X0,empty_set)))))))) = X1 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_7740]) ).
tcf(c_21767,plain,
! [X0: $i,X1: $i] :
( ( sK15(powerset(sK15(powerset(sK15(sK14(powerset(sK15(sK14(powerset(X0)))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_7740]) ).
tcf(c_21768,plain,
! [X0: $i,X1: $i] :
( ( sK15(powerset(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0))))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_7740]) ).
tcf(c_21769,plain,
! [X0: $i,X1: $i] :
( ( sK15(powerset(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_7740]) ).
tcf(c_21843,plain,
( ( sK15(powerset(relation_image(sK1,empty_set))) = empty_set )
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_52,c_7931]) ).
tcf(c_21844,plain,
( ( sK15(powerset(relation_image(sK7,empty_set))) = empty_set )
| ~ relation(sK7) ),
inference(superposition,[status(thm)],[c_76,c_7931]) ).
tcf(c_21845,plain,
! [X0: $i] :
( ( sK15(powerset(relation_image(relation_dom(X0),empty_set))) = empty_set )
| ~ empty(X0)
| ~ relation(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_5003,c_7931]) ).
tcf(c_21846,plain,
( ( sK15(powerset(relation_image(empty_set,empty_set))) = empty_set )
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_4985,c_7931]) ).
tcf(c_21847,plain,
! [X0: $i] :
( ( sK15(powerset(relation_image(sK15(powerset(X0)),empty_set))) = empty_set )
| ~ empty(X0)
| ~ relation(sK15(powerset(X0))) ),
inference(superposition,[status(thm)],[c_5274,c_7931]) ).
tcf(c_21848,plain,
! [X0: $i] :
( ( sK15(powerset(relation_image(sK15(sK14(powerset(X0))),empty_set))) = empty_set )
| ~ empty(X0)
| ~ relation(sK15(sK14(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_6196,c_7931]) ).
tcf(c_21849,plain,
! [X0: $i] :
( ( sK15(powerset(relation_image(sK15(sK14(sK14(powerset(X0)))),empty_set))) = empty_set )
| ~ empty(X0)
| ~ relation(sK15(sK14(sK14(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_7259,c_7931]) ).
tcf(c_21850,plain,
! [X0: $i] :
( ( sK15(powerset(relation_image(relation_image(X0,empty_set),empty_set))) = empty_set )
| ~ function(X0)
| ~ relation(X0)
| ~ relation(relation_image(X0,empty_set)) ),
inference(superposition,[status(thm)],[c_7937,c_7931]) ).
tcf(c_21851,plain,
! [X0: $i] :
( ( sK15(powerset(relation_image(sK15(powerset(sK15(powerset(X0)))),empty_set))) = empty_set )
| ~ empty(X0)
| ~ relation(sK15(powerset(sK15(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_8308,c_7931]) ).
tcf(c_21852,plain,
! [X0: $i] :
( ( sK15(powerset(relation_image(sK15(powerset(sK15(sK14(powerset(X0))))),empty_set))) = empty_set )
| ~ empty(X0)
| ~ relation(sK15(powerset(sK15(sK14(powerset(X0)))))) ),
inference(superposition,[status(thm)],[c_8429,c_7931]) ).
tcf(c_21853,plain,
! [X0: $i] :
( ( sK15(powerset(relation_image(sK15(powerset(sK15(sK14(sK14(powerset(X0)))))),empty_set))) = empty_set )
| ~ empty(X0)
| ~ relation(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))) ),
inference(superposition,[status(thm)],[c_8577,c_7931]) ).
tcf(c_21854,plain,
! [X0: $i] :
( ( sK15(powerset(relation_image(sK15(sK14(sK14(sK14(powerset(X0))))),empty_set))) = empty_set )
| ~ empty(X0)
| ~ relation(sK15(sK14(sK14(sK14(powerset(X0)))))) ),
inference(superposition,[status(thm)],[c_10139,c_7931]) ).
tcf(c_21855,plain,
! [X0: $i] :
( ( sK15(powerset(relation_image(sK15(powerset(relation_image(X0,empty_set))),empty_set))) = empty_set )
| ~ function(X0)
| ~ relation(X0)
| ~ relation(sK15(powerset(relation_image(X0,empty_set)))) ),
inference(superposition,[status(thm)],[c_10376,c_7931]) ).
tcf(c_21856,plain,
! [X0: $i] :
( ( sK15(powerset(relation_image(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))),empty_set))) = empty_set )
| ~ empty(X0)
| ~ relation(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))) ),
inference(superposition,[status(thm)],[c_10749,c_7931]) ).
tcf(c_21857,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( sK15(powerset(relation_image(sK15(powerset(singleton(X0))),empty_set))) = empty_set )
| ~ relation(sK15(powerset(singleton(X0)))) ),
inference(superposition,[status(thm)],[c_12760,c_7931]) ).
tcf(c_21858,plain,
! [X0: $i] :
( ( sK15(powerset(relation_image(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))),empty_set))) = empty_set )
| ~ empty(X0)
| ~ relation(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))) ),
inference(superposition,[status(thm)],[c_14999,c_7931]) ).
tcf(c_21859,plain,
! [X0: $i] :
( ( sK15(powerset(relation_image(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))),empty_set))) = empty_set )
| ~ empty(X0)
| ~ relation(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))) ),
inference(superposition,[status(thm)],[c_16066,c_7931]) ).
tcf(c_21860,plain,
! [X0: $i] :
( ( sK15(powerset(relation_image(sK15(sK14(powerset(sK15(powerset(X0))))),empty_set))) = empty_set )
| ~ empty(X0)
| ~ relation(sK15(sK14(powerset(sK15(powerset(X0)))))) ),
inference(superposition,[status(thm)],[c_17169,c_7931]) ).
tcf(c_21861,plain,
! [X0: $i] :
( ( sK15(powerset(relation_image(sK15(sK14(powerset(sK15(sK14(powerset(X0)))))),empty_set))) = empty_set )
| ~ empty(X0)
| ~ relation(sK15(sK14(powerset(sK15(sK14(powerset(X0))))))) ),
inference(superposition,[status(thm)],[c_17536,c_7931]) ).
tcf(c_21862,plain,
! [X0: $i] :
( ( sK15(powerset(relation_image(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0))))))),empty_set))) = empty_set )
| ~ empty(X0)
| ~ relation(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))) ),
inference(superposition,[status(thm)],[c_18025,c_7931]) ).
tcf(c_21863,plain,
! [X0: $i] :
( ( sK15(powerset(relation_image(sK15(sK14(powerset(relation_image(X0,empty_set)))),empty_set))) = empty_set )
| ~ function(X0)
| ~ relation(X0)
| ~ relation(sK15(sK14(powerset(relation_image(X0,empty_set))))) ),
inference(superposition,[status(thm)],[c_18495,c_7931]) ).
tcf(c_21864,plain,
! [X0: $i] :
( ( sK15(powerset(relation_image(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))),empty_set))) = empty_set )
| ~ empty(X0)
| ~ relation(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))) ),
inference(superposition,[status(thm)],[c_19036,c_7931]) ).
tcf(c_21865,plain,
sK15(powerset(relation_image(empty_set,empty_set))) = empty_set,
inference(forward_subsumption_resolution,[status(thm)],[c_21846,c_91]) ).
tcf(c_22069,plain,
( ( relation_dom(relation_dom(relation_image(sK1,empty_set))) = empty_set )
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_52,c_7932]) ).
tcf(c_22070,plain,
( ( relation_dom(relation_dom(relation_image(sK7,empty_set))) = empty_set )
| ~ relation(sK7) ),
inference(superposition,[status(thm)],[c_76,c_7932]) ).
tcf(c_22071,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_image(relation_dom(X0),empty_set))) = empty_set )
| ~ empty(X0)
| ~ relation(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_5003,c_7932]) ).
tcf(c_22072,plain,
( ( relation_dom(relation_dom(relation_image(empty_set,empty_set))) = empty_set )
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_4985,c_7932]) ).
tcf(c_22073,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_image(sK15(powerset(X0)),empty_set))) = empty_set )
| ~ empty(X0)
| ~ relation(sK15(powerset(X0))) ),
inference(superposition,[status(thm)],[c_5274,c_7932]) ).
tcf(c_22074,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_image(sK15(sK14(powerset(X0))),empty_set))) = empty_set )
| ~ empty(X0)
| ~ relation(sK15(sK14(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_6196,c_7932]) ).
tcf(c_22075,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_image(sK15(sK14(sK14(powerset(X0)))),empty_set))) = empty_set )
| ~ empty(X0)
| ~ relation(sK15(sK14(sK14(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_7259,c_7932]) ).
tcf(c_22076,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_image(relation_image(X0,empty_set),empty_set))) = empty_set )
| ~ function(X0)
| ~ relation(X0)
| ~ relation(relation_image(X0,empty_set)) ),
inference(superposition,[status(thm)],[c_7937,c_7932]) ).
tcf(c_22077,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_image(sK15(powerset(sK15(powerset(X0)))),empty_set))) = empty_set )
| ~ empty(X0)
| ~ relation(sK15(powerset(sK15(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_8308,c_7932]) ).
tcf(c_22078,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_image(sK15(powerset(sK15(sK14(powerset(X0))))),empty_set))) = empty_set )
| ~ empty(X0)
| ~ relation(sK15(powerset(sK15(sK14(powerset(X0)))))) ),
inference(superposition,[status(thm)],[c_8429,c_7932]) ).
tcf(c_22079,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_image(sK15(powerset(sK15(sK14(sK14(powerset(X0)))))),empty_set))) = empty_set )
| ~ empty(X0)
| ~ relation(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))) ),
inference(superposition,[status(thm)],[c_8577,c_7932]) ).
tcf(c_22080,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_image(sK15(sK14(sK14(sK14(powerset(X0))))),empty_set))) = empty_set )
| ~ empty(X0)
| ~ relation(sK15(sK14(sK14(sK14(powerset(X0)))))) ),
inference(superposition,[status(thm)],[c_10139,c_7932]) ).
tcf(c_22081,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_image(sK15(powerset(relation_image(X0,empty_set))),empty_set))) = empty_set )
| ~ function(X0)
| ~ relation(X0)
| ~ relation(sK15(powerset(relation_image(X0,empty_set)))) ),
inference(superposition,[status(thm)],[c_10376,c_7932]) ).
tcf(c_22082,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_image(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))),empty_set))) = empty_set )
| ~ empty(X0)
| ~ relation(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))) ),
inference(superposition,[status(thm)],[c_10749,c_7932]) ).
tcf(c_22083,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( relation_dom(relation_dom(relation_image(sK15(powerset(singleton(X0))),empty_set))) = empty_set )
| ~ relation(sK15(powerset(singleton(X0)))) ),
inference(superposition,[status(thm)],[c_12760,c_7932]) ).
tcf(c_22084,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_image(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))),empty_set))) = empty_set )
| ~ empty(X0)
| ~ relation(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))) ),
inference(superposition,[status(thm)],[c_14999,c_7932]) ).
tcf(c_22085,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_image(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))),empty_set))) = empty_set )
| ~ empty(X0)
| ~ relation(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))) ),
inference(superposition,[status(thm)],[c_16066,c_7932]) ).
tcf(c_22086,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_image(sK15(sK14(powerset(sK15(powerset(X0))))),empty_set))) = empty_set )
| ~ empty(X0)
| ~ relation(sK15(sK14(powerset(sK15(powerset(X0)))))) ),
inference(superposition,[status(thm)],[c_17169,c_7932]) ).
tcf(c_22087,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_image(sK15(sK14(powerset(sK15(sK14(powerset(X0)))))),empty_set))) = empty_set )
| ~ empty(X0)
| ~ relation(sK15(sK14(powerset(sK15(sK14(powerset(X0))))))) ),
inference(superposition,[status(thm)],[c_17536,c_7932]) ).
tcf(c_22088,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_image(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0))))))),empty_set))) = empty_set )
| ~ empty(X0)
| ~ relation(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))) ),
inference(superposition,[status(thm)],[c_18025,c_7932]) ).
tcf(c_22089,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_image(sK15(sK14(powerset(relation_image(X0,empty_set)))),empty_set))) = empty_set )
| ~ function(X0)
| ~ relation(X0)
| ~ relation(sK15(sK14(powerset(relation_image(X0,empty_set))))) ),
inference(superposition,[status(thm)],[c_18495,c_7932]) ).
tcf(c_22090,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_image(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))),empty_set))) = empty_set )
| ~ empty(X0)
| ~ relation(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))) ),
inference(superposition,[status(thm)],[c_19036,c_7932]) ).
tcf(c_22091,plain,
relation_dom(relation_dom(relation_image(empty_set,empty_set))) = empty_set,
inference(forward_subsumption_resolution,[status(thm)],[c_22072,c_91]) ).
tcf(c_22261,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_8078]) ).
tcf(c_22262,plain,
relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(powerset(empty_set))))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_8078]) ).
tcf(c_22267,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(powerset(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_8078]) ).
tcf(c_22268,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(powerset(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_8078]) ).
tcf(c_22269,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(powerset(sK15(powerset(sK15(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_8078]) ).
tcf(c_22270,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(powerset(sK15(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_8078]) ).
tcf(c_22271,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(powerset(sK15(powerset(sK15(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_8078]) ).
tcf(c_22272,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(powerset(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_8078]) ).
tcf(c_22274,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(powerset(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_8078]) ).
tcf(c_22276,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(powerset(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_8078]) ).
tcf(c_22277,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(powerset(sK15(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_8078]) ).
tcf(c_22278,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(powerset(relation_image(X0,empty_set))))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_8078]) ).
tcf(c_22279,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(powerset(sK15(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_8078]) ).
tcf(c_22280,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_8078]) ).
tcf(c_22281,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_8078]) ).
tcf(c_22362,plain,
! [X0: $i] :
( empty(X0)
| empty(sK15(powerset(sK14(X0))))
| in(sK15(sK15(powerset(sK14(X0)))),X0) ),
inference(superposition,[status(thm)],[c_8115,c_66]) ).
tcf(c_22363,plain,
! [X0: $i,X1: $i] :
( empty(powerset(X1))
| element(X0,X1)
| empty(sK15(powerset(sK14(powerset(X1)))))
| ~ in(X0,sK15(sK15(powerset(sK14(powerset(X1)))))) ),
inference(superposition,[status(thm)],[c_8115,c_94]) ).
tcf(c_22364,plain,
! [X0: $i,X1: $i] :
( empty(powerset(X1))
| empty(sK15(powerset(sK14(powerset(X1)))))
| ~ empty(X1)
| ~ in(X0,sK15(sK15(powerset(sK14(powerset(X1)))))) ),
inference(superposition,[status(thm)],[c_8115,c_93]) ).
tcf(c_22368,plain,
! [X0: $i,X1: $i] :
( empty(sK15(powerset(sK14(powerset(X1)))))
| ~ empty(X1)
| ~ in(X0,sK15(sK15(powerset(sK14(powerset(X1)))))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_22364,c_100]) ).
tcf(c_22372,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| empty(sK15(powerset(sK14(powerset(X1)))))
| ~ in(X0,sK15(sK15(powerset(sK14(powerset(X1)))))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_22363,c_100]) ).
tcf(c_22382,plain,
( element(sK15(empty_set),empty_set)
| empty(sK15(powerset(sK15(powerset(empty_set))))) ),
inference(superposition,[status(thm)],[c_5301,c_8116]) ).
tcf(c_22383,plain,
! [X0: $i] :
( element(sK15(sK15(powerset(empty_set))),sK15(sK14(sK14(powerset(sK15(powerset(singleton(X0))))))))
| empty(sK15(powerset(sK15(powerset(sK15(sK14(sK14(powerset(sK15(powerset(singleton(X0))))))))))))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 ) ),
inference(superposition,[status(thm)],[c_12707,c_8116]) ).
tcf(c_22384,plain,
! [X0: $i] :
( empty(X0)
| empty(sK15(powerset(sK15(powerset(X0)))))
| in(sK15(sK15(powerset(sK15(powerset(X0))))),X0) ),
inference(superposition,[status(thm)],[c_8116,c_66]) ).
tcf(c_22385,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| empty(sK15(powerset(sK15(powerset(powerset(X1))))))
| ~ in(X0,sK15(sK15(powerset(sK15(powerset(powerset(X1))))))) ),
inference(superposition,[status(thm)],[c_8116,c_94]) ).
tcf(c_22386,plain,
! [X0: $i,X1: $i] :
( empty(sK15(powerset(sK15(powerset(powerset(X1))))))
| ~ empty(X1)
| ~ in(X0,sK15(sK15(powerset(sK15(powerset(powerset(X1))))))) ),
inference(superposition,[status(thm)],[c_8116,c_93]) ).
tcf(c_22397,plain,
! [X0: $i] :
( element(sK15(empty_set),sK15(sK14(sK14(powerset(sK15(powerset(singleton(X0))))))))
| empty(sK15(powerset(sK15(powerset(sK15(sK14(sK14(powerset(sK15(powerset(singleton(X0))))))))))))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 ) ),
inference(light_normalisation,[status(thm)],[c_22383,c_5301]) ).
tcf(c_22458,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK15(powerset(relation_dom(X0))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_8211]) ).
tcf(c_22459,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(empty_set)))) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_92,c_8211]) ).
tcf(c_22464,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X1))))) = X1 )
| ( relation_dom(relation_dom(sK15(powerset(sK15(powerset(singleton(X1))))))) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11251,c_8211]) ).
tcf(c_22465,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK15(powerset(singleton(X1)))) = X1 )
| ( relation_dom(relation_dom(sK15(powerset(sK15(powerset(singleton(X1))))))) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8114,c_8211]) ).
tcf(c_22466,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK15(powerset(sK15(powerset(sK15(powerset(X0)))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_8211]) ).
tcf(c_22467,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK15(powerset(sK15(powerset(relation_image(X0,empty_set))))))) = X1 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_8211]) ).
tcf(c_22468,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(powerset(X0))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_8211]) ).
tcf(c_22469,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(sK14(powerset(X0)))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_8211]) ).
tcf(c_22471,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_8211]) ).
tcf(c_22473,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_8211]) ).
tcf(c_22474,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(powerset(X0))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_8211]) ).
tcf(c_22475,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(relation_image(X0,empty_set)))))))) = X1 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_8211]) ).
tcf(c_22476,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(sK14(powerset(X0)))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_8211]) ).
tcf(c_22477,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0))))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_8211]) ).
tcf(c_22478,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_8211]) ).
tcf(c_22679,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_8238]) ).
tcf(c_22680,plain,
relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(powerset(empty_set))))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_8238]) ).
tcf(c_22685,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(powerset(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_8238]) ).
tcf(c_22686,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(powerset(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_8238]) ).
tcf(c_22687,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(powerset(sK15(powerset(sK15(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_8238]) ).
tcf(c_22688,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(powerset(sK15(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_8238]) ).
tcf(c_22689,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_8238]) ).
tcf(c_22690,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_8238]) ).
tcf(c_22692,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_8238]) ).
tcf(c_22694,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_8238]) ).
tcf(c_22695,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_8238]) ).
tcf(c_22696,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(powerset(relation_image(X0,empty_set))))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_8238]) ).
tcf(c_22697,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_8238]) ).
tcf(c_22698,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_8238]) ).
tcf(c_22699,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_8238]) ).
tcf(c_22842,plain,
! [X0: $i] :
( empty(sK14(powerset(relation_dom(sK15(powerset(sK15(powerset(singleton(X0)))))))))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ~ in(sK14(powerset(relation_dom(sK15(powerset(sK15(powerset(singleton(X0)))))))),empty_set) ),
inference(superposition,[status(thm)],[c_12709,c_5145]) ).
tcf(c_22843,plain,
! [X0: $i] :
( empty(sK14(powerset(relation_dom(sK15(powerset(sK15(powerset(singleton(X0)))))))))
| in(empty_set,sK14(powerset(relation_dom(sK15(powerset(sK15(powerset(singleton(X0)))))))))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 ) ),
inference(superposition,[status(thm)],[c_12709,c_5124]) ).
tcf(c_22844,plain,
! [X0: $i] :
( element(empty_set,sK14(powerset(relation_dom(sK15(powerset(sK15(powerset(singleton(X0)))))))))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 ) ),
inference(superposition,[status(thm)],[c_12709,c_99]) ).
tcf(c_22845,plain,
! [X0: $i] :
( empty(powerset(relation_dom(sK15(powerset(sK15(powerset(singleton(X0))))))))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ~ in(powerset(relation_dom(sK15(powerset(sK15(powerset(singleton(X0))))))),empty_set) ),
inference(superposition,[status(thm)],[c_12709,c_6091]) ).
tcf(c_22846,plain,
! [X0: $i] :
( empty(powerset(relation_dom(sK15(powerset(sK15(powerset(singleton(X0))))))))
| in(empty_set,powerset(relation_dom(sK15(powerset(sK15(powerset(singleton(X0))))))))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 ) ),
inference(superposition,[status(thm)],[c_12709,c_6055]) ).
tcf(c_22847,plain,
! [X0: $i] :
( empty(powerset(relation_dom(sK15(powerset(sK15(powerset(singleton(X0))))))))
| element(empty_set,powerset(relation_dom(sK15(powerset(sK15(powerset(singleton(X0))))))))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 ) ),
inference(superposition,[status(thm)],[c_12709,c_6048]) ).
tcf(c_22848,plain,
! [X0: $i] :
( empty(sK15(sK14(powerset(relation_dom(sK15(powerset(sK15(powerset(singleton(X0))))))))))
| element(sK15(sK14(sK14(empty_set))),relation_dom(sK15(powerset(sK15(powerset(singleton(X0)))))))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 ) ),
inference(superposition,[status(thm)],[c_12709,c_7049]) ).
tcf(c_22849,plain,
! [X0: $i] :
( function(sK15(sK14(powerset(empty_set))))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ~ empty(relation_dom(sK15(powerset(sK15(powerset(singleton(X0))))))) ),
inference(superposition,[status(thm)],[c_12709,c_17536]) ).
tcf(c_22850,plain,
! [X0: $i] :
( relation(sK15(sK14(powerset(empty_set))))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ~ empty(relation_dom(sK15(powerset(sK15(powerset(singleton(X0))))))) ),
inference(superposition,[status(thm)],[c_12709,c_17535]) ).
tcf(c_22851,plain,
! [X0: $i] :
( empty(sK15(sK14(powerset(empty_set))))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ~ empty(relation_dom(sK15(powerset(sK15(powerset(singleton(X0))))))) ),
inference(superposition,[status(thm)],[c_12709,c_16915]) ).
tcf(c_22852,plain,
! [X0: $i] :
( empty(sK15(sK14(powerset(relation_dom(sK15(powerset(sK15(powerset(singleton(X0))))))))))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ~ in(relation_dom(sK15(powerset(sK15(powerset(singleton(X0)))))),sK15(empty_set)) ),
inference(superposition,[status(thm)],[c_12709,c_16905]) ).
tcf(c_22853,plain,
! [X0: $i] :
( in(sK15(empty_set),relation_dom(sK15(powerset(sK15(powerset(singleton(X0)))))))
| empty(sK15(sK14(powerset(relation_dom(sK15(powerset(sK15(powerset(singleton(X0))))))))))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 ) ),
inference(superposition,[status(thm)],[c_12709,c_16897]) ).
tcf(c_22854,plain,
! [X0: $i] :
( element(sK15(sK14(empty_set)),relation_dom(sK15(powerset(sK15(powerset(singleton(X0)))))))
| empty(sK15(sK14(powerset(relation_dom(sK15(powerset(sK15(powerset(singleton(X0))))))))))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 ) ),
inference(superposition,[status(thm)],[c_12709,c_6607]) ).
tcf(c_22855,plain,
! [X0: $i] :
( element(sK15(empty_set),relation_dom(sK15(powerset(sK15(powerset(singleton(X0)))))))
| empty(sK15(sK14(powerset(relation_dom(sK15(powerset(sK15(powerset(singleton(X0))))))))))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 ) ),
inference(superposition,[status(thm)],[c_12709,c_6604]) ).
tcf(c_22856,plain,
! [X0: $i] :
( function(sK15(powerset(empty_set)))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ~ empty(relation_dom(sK15(powerset(sK15(powerset(singleton(X0))))))) ),
inference(superposition,[status(thm)],[c_12709,c_8429]) ).
tcf(c_22857,plain,
! [X0: $i] :
( relation(sK15(powerset(empty_set)))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ~ empty(relation_dom(sK15(powerset(sK15(powerset(singleton(X0))))))) ),
inference(superposition,[status(thm)],[c_12709,c_8428]) ).
tcf(c_22858,plain,
! [X0: $i] :
( empty(sK15(powerset(empty_set)))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ~ empty(relation_dom(sK15(powerset(sK15(powerset(singleton(X0))))))) ),
inference(superposition,[status(thm)],[c_12709,c_8121]) ).
tcf(c_22863,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ~ in(X1,empty_set)
| ~ empty(relation_dom(sK15(powerset(sK15(powerset(singleton(X0))))))) ),
inference(superposition,[status(thm)],[c_12709,c_6060]) ).
tcf(c_22866,plain,
! [X0: $i] :
( empty(empty_set)
| ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ~ empty(relation_dom(sK15(powerset(sK15(powerset(singleton(X0))))))) ),
inference(light_normalisation,[status(thm)],[c_22858,c_5301]) ).
tcf(c_22867,plain,
! [X0: $i] :
( relation(empty_set)
| ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ~ empty(relation_dom(sK15(powerset(sK15(powerset(singleton(X0))))))) ),
inference(light_normalisation,[status(thm)],[c_22857,c_5301]) ).
tcf(c_22868,plain,
! [X0: $i] :
( function(empty_set)
| ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ~ empty(relation_dom(sK15(powerset(sK15(powerset(singleton(X0))))))) ),
inference(light_normalisation,[status(thm)],[c_22856,c_5301]) ).
tcf(c_22917,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(relation_dom(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_11550]) ).
tcf(c_22918,plain,
relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(relation_dom(empty_set))))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_11550]) ).
tcf(c_22919,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(relation_dom(sK15(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_11550]) ).
tcf(c_22920,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(relation_dom(sK15(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_11550]) ).
tcf(c_22921,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(relation_dom(sK15(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_11550]) ).
tcf(c_22922,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(relation_dom(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_11550]) ).
tcf(c_22923,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(relation_dom(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_11550]) ).
tcf(c_22924,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(relation_dom(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_11550]) ).
tcf(c_22925,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(relation_dom(sK15(powerset(sK15(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_11550]) ).
tcf(c_22926,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(relation_dom(sK15(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_11550]) ).
tcf(c_22927,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(relation_dom(sK15(powerset(sK15(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_11550]) ).
tcf(c_22928,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_11550]) ).
tcf(c_22929,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(relation_dom(sK15(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_11550]) ).
tcf(c_22930,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_11550]) ).
tcf(c_22931,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(relation_dom(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_11550]) ).
tcf(c_22932,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_11550]) ).
tcf(c_22933,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(relation_dom(sK15(sK14(powerset(sK15(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_11550]) ).
tcf(c_22934,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(relation_dom(sK15(sK14(powerset(relation_image(X0,empty_set))))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_11550]) ).
tcf(c_22935,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_11550]) ).
tcf(c_22936,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_11550]) ).
tcf(c_22937,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_11550]) ).
tcf(c_23101,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(sK14(powerset(relation_dom(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_11666]) ).
tcf(c_23102,plain,
sK15(sK14(powerset(sK15(sK14(powerset(relation_dom(empty_set))))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_11666]) ).
tcf(c_23103,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(sK14(powerset(relation_dom(sK15(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_11666]) ).
tcf(c_23104,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(sK14(powerset(relation_dom(sK15(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_11666]) ).
tcf(c_23105,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(sK14(powerset(relation_dom(sK15(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_11666]) ).
tcf(c_23106,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(sK14(powerset(relation_dom(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_11666]) ).
tcf(c_23107,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( sK15(sK14(powerset(sK15(sK14(powerset(relation_dom(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_11666]) ).
tcf(c_23108,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( sK15(sK14(powerset(sK15(sK14(powerset(relation_dom(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_11666]) ).
tcf(c_23109,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(sK14(powerset(relation_dom(sK15(powerset(sK15(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_11666]) ).
tcf(c_23110,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(sK14(powerset(relation_dom(sK15(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_11666]) ).
tcf(c_23111,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(sK14(powerset(relation_dom(sK15(powerset(sK15(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_11666]) ).
tcf(c_23112,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(sK14(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_11666]) ).
tcf(c_23113,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(sK14(powerset(relation_dom(sK15(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_11666]) ).
tcf(c_23114,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(sK14(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_11666]) ).
tcf(c_23115,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(sK14(powerset(relation_dom(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_11666]) ).
tcf(c_23116,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(sK14(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_11666]) ).
tcf(c_23117,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(sK14(powerset(relation_dom(sK15(sK14(powerset(sK15(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_11666]) ).
tcf(c_23118,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(sK14(powerset(relation_dom(sK15(sK14(powerset(relation_image(X0,empty_set))))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_11666]) ).
tcf(c_23119,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(sK14(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_11666]) ).
tcf(c_23120,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(sK14(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_11666]) ).
tcf(c_23121,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(sK14(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_11666]) ).
tcf(c_23269,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK15(powerset(relation_dom(relation_dom(X0))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_11746]) ).
tcf(c_23270,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(empty_set)))) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_92,c_11746]) ).
tcf(c_23271,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK15(powerset(relation_dom(sK15(powerset(X0)))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_11746]) ).
tcf(c_23272,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK15(powerset(relation_dom(sK15(sK14(powerset(X0))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_11746]) ).
tcf(c_23273,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK15(powerset(relation_dom(sK15(sK14(sK14(powerset(X0)))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_11746]) ).
tcf(c_23274,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK15(powerset(relation_dom(relation_image(X0,empty_set))))) = X1 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_11746]) ).
tcf(c_23275,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X1))))) = X1 )
| ( relation_dom(sK15(powerset(relation_dom(sK15(powerset(singleton(X1))))))) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11251,c_11746]) ).
tcf(c_23276,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK15(powerset(singleton(X1)))) = X1 )
| ( relation_dom(sK15(powerset(relation_dom(sK15(powerset(singleton(X1))))))) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8114,c_11746]) ).
tcf(c_23277,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK15(powerset(relation_dom(sK15(powerset(sK15(powerset(X0)))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_11746]) ).
tcf(c_23278,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK15(powerset(relation_dom(sK15(powerset(relation_image(X0,empty_set))))))) = X1 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_11746]) ).
tcf(c_23279,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(powerset(X0))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_11746]) ).
tcf(c_23280,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(powerset(X0)))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_11746]) ).
tcf(c_23281,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK15(powerset(relation_dom(sK15(sK14(sK14(sK14(powerset(X0))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_11746]) ).
tcf(c_23282,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_11746]) ).
tcf(c_23283,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK15(powerset(relation_dom(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_11746]) ).
tcf(c_23284,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_11746]) ).
tcf(c_23285,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(powerset(X0))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_11746]) ).
tcf(c_23286,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK15(powerset(relation_dom(sK15(sK14(powerset(relation_image(X0,empty_set)))))))) = X1 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_11746]) ).
tcf(c_23287,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(X0)))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_11746]) ).
tcf(c_23288,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0))))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_11746]) ).
tcf(c_23289,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_11746]) ).
tcf(c_23508,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(sK15(powerset(relation_dom(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_11782]) ).
tcf(c_23509,plain,
relation_dom(relation_dom(sK15(powerset(sK15(powerset(relation_dom(empty_set))))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_11782]) ).
tcf(c_23510,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(sK15(powerset(relation_dom(sK15(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_11782]) ).
tcf(c_23511,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(sK15(powerset(relation_dom(sK15(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_11782]) ).
tcf(c_23512,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(sK15(powerset(relation_dom(sK15(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_11782]) ).
tcf(c_23513,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(sK15(powerset(relation_dom(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_11782]) ).
tcf(c_23514,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( relation_dom(relation_dom(sK15(powerset(sK15(powerset(relation_dom(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_11782]) ).
tcf(c_23515,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( relation_dom(relation_dom(sK15(powerset(sK15(powerset(relation_dom(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_11782]) ).
tcf(c_23516,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(sK15(powerset(relation_dom(sK15(powerset(sK15(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_11782]) ).
tcf(c_23517,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(sK15(powerset(relation_dom(sK15(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_11782]) ).
tcf(c_23518,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_11782]) ).
tcf(c_23519,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_11782]) ).
tcf(c_23520,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(sK15(powerset(relation_dom(sK15(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_11782]) ).
tcf(c_23521,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_11782]) ).
tcf(c_23522,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(sK15(powerset(relation_dom(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_11782]) ).
tcf(c_23523,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_11782]) ).
tcf(c_23524,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_11782]) ).
tcf(c_23525,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(sK15(powerset(relation_dom(sK15(sK14(powerset(relation_image(X0,empty_set))))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_11782]) ).
tcf(c_23526,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_11782]) ).
tcf(c_23527,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_11782]) ).
tcf(c_23528,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_11782]) ).
tcf(c_23633,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(powerset(sK15(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_8298]) ).
tcf(c_23634,plain,
sK15(sK14(powerset(sK15(powerset(sK15(powerset(empty_set))))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_8298]) ).
tcf(c_23639,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( sK15(sK14(powerset(sK15(powerset(sK15(powerset(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_8298]) ).
tcf(c_23640,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( sK15(sK14(powerset(sK15(powerset(sK15(powerset(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_8298]) ).
tcf(c_23641,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(powerset(sK15(powerset(sK15(powerset(sK15(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_8298]) ).
tcf(c_23642,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(powerset(sK15(powerset(sK15(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_8298]) ).
tcf(c_23643,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(powerset(sK15(powerset(sK15(powerset(sK15(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_8298]) ).
tcf(c_23644,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(powerset(sK15(powerset(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_8298]) ).
tcf(c_23646,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(powerset(sK15(powerset(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_8298]) ).
tcf(c_23648,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(powerset(sK15(powerset(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_8298]) ).
tcf(c_23649,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(powerset(sK15(powerset(sK15(sK14(powerset(sK15(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_8298]) ).
tcf(c_23650,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(powerset(sK15(powerset(sK15(sK14(powerset(relation_image(X0,empty_set))))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_8298]) ).
tcf(c_23651,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(powerset(sK15(powerset(sK15(sK14(powerset(sK15(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_8298]) ).
tcf(c_23652,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(powerset(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_8298]) ).
tcf(c_23653,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(powerset(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_8298]) ).
tcf(c_23738,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(powerset(sK15(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_8299]) ).
tcf(c_23739,plain,
sK15(powerset(relation_dom(sK15(powerset(sK15(powerset(empty_set))))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_8299]) ).
tcf(c_23744,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( sK15(powerset(relation_dom(sK15(powerset(sK15(powerset(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_8299]) ).
tcf(c_23745,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( sK15(powerset(relation_dom(sK15(powerset(sK15(powerset(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_8299]) ).
tcf(c_23746,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(powerset(sK15(powerset(sK15(powerset(sK15(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_8299]) ).
tcf(c_23747,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(powerset(sK15(powerset(sK15(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_8299]) ).
tcf(c_23748,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(powerset(sK15(powerset(sK15(powerset(sK15(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_8299]) ).
tcf(c_23749,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(powerset(sK15(powerset(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_8299]) ).
tcf(c_23751,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(powerset(sK15(powerset(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_8299]) ).
tcf(c_23753,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(powerset(sK15(powerset(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_8299]) ).
tcf(c_23754,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(powerset(sK15(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_8299]) ).
tcf(c_23755,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(powerset(relation_image(X0,empty_set))))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_8299]) ).
tcf(c_23756,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(powerset(sK15(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_8299]) ).
tcf(c_23757,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_8299]) ).
tcf(c_23758,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_8299]) ).
tcf(c_23838,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(powerset(sK15(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_8300]) ).
tcf(c_23839,plain,
relation_dom(sK15(powerset(sK15(powerset(sK15(powerset(empty_set))))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_8300]) ).
tcf(c_23844,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( relation_dom(sK15(powerset(sK15(powerset(sK15(powerset(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_8300]) ).
tcf(c_23845,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( relation_dom(sK15(powerset(sK15(powerset(sK15(powerset(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_8300]) ).
tcf(c_23846,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(powerset(sK15(powerset(sK15(powerset(sK15(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_8300]) ).
tcf(c_23847,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(powerset(sK15(powerset(sK15(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_8300]) ).
tcf(c_23848,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(powerset(sK15(powerset(sK15(powerset(sK15(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_8300]) ).
tcf(c_23849,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(powerset(sK15(powerset(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_8300]) ).
tcf(c_23851,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(powerset(sK15(powerset(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_8300]) ).
tcf(c_23853,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(powerset(sK15(powerset(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_8300]) ).
tcf(c_23854,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(powerset(sK15(powerset(sK15(sK14(powerset(sK15(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_8300]) ).
tcf(c_23855,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(powerset(sK15(powerset(sK15(sK14(powerset(relation_image(X0,empty_set))))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_8300]) ).
tcf(c_23856,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(powerset(sK15(powerset(sK15(sK14(powerset(sK15(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_8300]) ).
tcf(c_23857,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(powerset(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_8300]) ).
tcf(c_23858,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(powerset(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_8300]) ).
tcf(c_27193,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(powerset(sK15(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_8745]) ).
tcf(c_27194,plain,
sK15(powerset(sK15(sK14(powerset(sK15(powerset(empty_set))))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_8745]) ).
tcf(c_27199,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( sK15(powerset(sK15(sK14(powerset(sK15(powerset(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_8745]) ).
tcf(c_27200,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( sK15(powerset(sK15(sK14(powerset(sK15(powerset(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_8745]) ).
tcf(c_27201,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(powerset(sK15(powerset(sK15(powerset(sK15(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_8745]) ).
tcf(c_27202,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(powerset(sK15(powerset(sK15(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_8745]) ).
tcf(c_27203,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(powerset(sK15(powerset(sK15(powerset(sK15(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_8745]) ).
tcf(c_27204,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(powerset(sK15(powerset(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_8745]) ).
tcf(c_27206,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(powerset(sK15(powerset(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_8745]) ).
tcf(c_27208,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(powerset(sK15(powerset(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_8745]) ).
tcf(c_27209,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(powerset(sK15(powerset(sK15(sK14(powerset(sK15(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_8745]) ).
tcf(c_27210,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(powerset(sK15(powerset(sK15(sK14(powerset(relation_image(X0,empty_set))))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_8745]) ).
tcf(c_27211,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(powerset(sK15(powerset(sK15(sK14(powerset(sK15(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_8745]) ).
tcf(c_27212,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(powerset(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_8745]) ).
tcf(c_27213,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(powerset(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_8745]) ).
tcf(c_27383,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(relation_dom(sK15(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_8823]) ).
tcf(c_27384,plain,
sK15(powerset(sK15(powerset(relation_dom(sK15(powerset(empty_set))))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_8823]) ).
tcf(c_27389,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( sK15(powerset(sK15(powerset(relation_dom(sK15(powerset(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_8823]) ).
tcf(c_27390,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( sK15(powerset(sK15(powerset(relation_dom(sK15(powerset(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_8823]) ).
tcf(c_27391,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(relation_dom(sK15(powerset(sK15(powerset(sK15(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_8823]) ).
tcf(c_27392,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(relation_dom(sK15(powerset(sK15(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_8823]) ).
tcf(c_27393,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_8823]) ).
tcf(c_27394,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_8823]) ).
tcf(c_27396,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_8823]) ).
tcf(c_27398,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_8823]) ).
tcf(c_27399,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_8823]) ).
tcf(c_27400,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(powerset(relation_image(X0,empty_set))))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_8823]) ).
tcf(c_27401,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_8823]) ).
tcf(c_27402,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_8823]) ).
tcf(c_27403,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_8823]) ).
tcf(c_27443,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_8860]) ).
tcf(c_27444,plain,
relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(empty_set))))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_8860]) ).
tcf(c_27449,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_8860]) ).
tcf(c_27450,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_8860]) ).
tcf(c_27451,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(powerset(sK15(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_8860]) ).
tcf(c_27452,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_8860]) ).
tcf(c_27453,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_8860]) ).
tcf(c_27454,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_8860]) ).
tcf(c_27456,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_8860]) ).
tcf(c_27458,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_8860]) ).
tcf(c_27459,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_8860]) ).
tcf(c_27460,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(relation_image(X0,empty_set))))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_8860]) ).
tcf(c_27461,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_8860]) ).
tcf(c_27462,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_8860]) ).
tcf(c_27463,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_8860]) ).
tcf(c_27503,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_8935]) ).
tcf(c_27504,plain,
relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(powerset(empty_set))))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_8935]) ).
tcf(c_27509,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(powerset(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_8935]) ).
tcf(c_27510,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(powerset(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_8935]) ).
tcf(c_27511,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(powerset(sK15(powerset(sK15(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_8935]) ).
tcf(c_27512,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(powerset(sK15(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_8935]) ).
tcf(c_27513,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_8935]) ).
tcf(c_27514,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_8935]) ).
tcf(c_27516,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_8935]) ).
tcf(c_27518,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_8935]) ).
tcf(c_27519,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_8935]) ).
tcf(c_27520,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(relation_image(X0,empty_set))))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_8935]) ).
tcf(c_27521,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_8935]) ).
tcf(c_27522,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_8935]) ).
tcf(c_27523,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_8935]) ).
tcf(c_27563,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(relation_dom(sK15(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_8995]) ).
tcf(c_27564,plain,
sK15(powerset(relation_dom(relation_dom(relation_dom(sK15(powerset(empty_set))))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_8995]) ).
tcf(c_27569,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( sK15(powerset(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_8995]) ).
tcf(c_27570,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( sK15(powerset(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_8995]) ).
tcf(c_27571,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(powerset(sK15(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_8995]) ).
tcf(c_27572,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_8995]) ).
tcf(c_27573,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_8995]) ).
tcf(c_27574,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_8995]) ).
tcf(c_27576,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_8995]) ).
tcf(c_27578,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_8995]) ).
tcf(c_27579,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_8995]) ).
tcf(c_27580,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(relation_image(X0,empty_set))))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_8995]) ).
tcf(c_27581,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_8995]) ).
tcf(c_27582,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_8995]) ).
tcf(c_27583,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_8995]) ).
tcf(c_27652,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(powerset(sK15(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_9027]) ).
tcf(c_27653,plain,
relation_dom(relation_dom(sK15(sK14(powerset(sK15(powerset(empty_set))))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_9027]) ).
tcf(c_27658,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( relation_dom(relation_dom(sK15(sK14(powerset(sK15(powerset(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_9027]) ).
tcf(c_27659,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( relation_dom(relation_dom(sK15(sK14(powerset(sK15(powerset(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_9027]) ).
tcf(c_27660,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(powerset(sK15(powerset(sK15(powerset(sK15(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_9027]) ).
tcf(c_27661,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(powerset(sK15(powerset(sK15(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_9027]) ).
tcf(c_27662,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(powerset(sK15(powerset(sK15(powerset(sK15(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_9027]) ).
tcf(c_27663,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(powerset(sK15(powerset(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_9027]) ).
tcf(c_27665,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(powerset(sK15(powerset(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_9027]) ).
tcf(c_27667,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(powerset(sK15(powerset(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_9027]) ).
tcf(c_27668,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(powerset(sK15(powerset(sK15(sK14(powerset(sK15(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_9027]) ).
tcf(c_27669,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(powerset(sK15(powerset(sK15(sK14(powerset(relation_image(X0,empty_set))))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_9027]) ).
tcf(c_27670,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(powerset(sK15(powerset(sK15(sK14(powerset(sK15(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_9027]) ).
tcf(c_27671,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(powerset(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_9027]) ).
tcf(c_27672,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(powerset(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_9027]) ).
tcf(c_27729,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(relation_dom(sK15(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_9213]) ).
tcf(c_27730,plain,
sK15(sK14(powerset(relation_dom(relation_dom(sK15(powerset(empty_set))))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_9213]) ).
tcf(c_27735,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( sK15(sK14(powerset(relation_dom(relation_dom(sK15(powerset(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_9213]) ).
tcf(c_27736,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( sK15(sK14(powerset(relation_dom(relation_dom(sK15(powerset(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_9213]) ).
tcf(c_27737,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(relation_dom(sK15(powerset(sK15(powerset(sK15(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_9213]) ).
tcf(c_27738,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(relation_dom(sK15(powerset(sK15(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_9213]) ).
tcf(c_27739,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_9213]) ).
tcf(c_27740,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_9213]) ).
tcf(c_27742,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_9213]) ).
tcf(c_27744,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_9213]) ).
tcf(c_27745,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_9213]) ).
tcf(c_27746,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(relation_image(X0,empty_set))))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_9213]) ).
tcf(c_27747,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_9213]) ).
tcf(c_27748,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_9213]) ).
tcf(c_27749,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_9213]) ).
tcf(c_27912,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(relation_dom(sK15(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_9413]) ).
tcf(c_27913,plain,
relation_dom(sK15(sK14(powerset(relation_dom(sK15(powerset(empty_set))))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_9413]) ).
tcf(c_27918,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( relation_dom(sK15(sK14(powerset(relation_dom(sK15(powerset(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_9413]) ).
tcf(c_27919,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( relation_dom(sK15(sK14(powerset(relation_dom(sK15(powerset(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_9413]) ).
tcf(c_27920,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(relation_dom(sK15(powerset(sK15(powerset(sK15(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_9413]) ).
tcf(c_27921,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(relation_dom(sK15(powerset(sK15(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_9413]) ).
tcf(c_27922,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_9413]) ).
tcf(c_27923,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_9413]) ).
tcf(c_27925,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_9413]) ).
tcf(c_27927,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_9413]) ).
tcf(c_27928,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_9413]) ).
tcf(c_27929,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(relation_dom(sK15(powerset(sK15(sK14(powerset(relation_image(X0,empty_set))))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_9413]) ).
tcf(c_27930,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_9413]) ).
tcf(c_27931,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_9413]) ).
tcf(c_27932,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_9413]) ).
tcf(c_28015,plain,
! [X0: $i] :
( empty(powerset(relation_dom(relation_dom(sK15(powerset(sK15(powerset(singleton(X0)))))))))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ~ in(powerset(relation_dom(relation_dom(sK15(powerset(sK15(powerset(singleton(X0)))))))),empty_set) ),
inference(superposition,[status(thm)],[c_12710,c_5145]) ).
tcf(c_28016,plain,
! [X0: $i] :
( empty(powerset(relation_dom(relation_dom(sK15(powerset(sK15(powerset(singleton(X0)))))))))
| in(empty_set,powerset(relation_dom(relation_dom(sK15(powerset(sK15(powerset(singleton(X0)))))))))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 ) ),
inference(superposition,[status(thm)],[c_12710,c_5124]) ).
tcf(c_28017,plain,
! [X0: $i] :
( element(empty_set,powerset(relation_dom(relation_dom(sK15(powerset(sK15(powerset(singleton(X0)))))))))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 ) ),
inference(superposition,[status(thm)],[c_12710,c_99]) ).
tcf(c_28019,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ~ in(X1,empty_set)
| ~ empty(relation_dom(relation_dom(sK15(powerset(sK15(powerset(singleton(X0)))))))) ),
inference(superposition,[status(thm)],[c_12710,c_5201]) ).
tcf(c_28020,plain,
! [X0: $i] :
( element(sK15(sK15(powerset(empty_set))),relation_dom(relation_dom(sK15(powerset(sK15(powerset(singleton(X0))))))))
| empty(sK15(powerset(sK15(powerset(relation_dom(relation_dom(sK15(powerset(sK15(powerset(singleton(X0))))))))))))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 ) ),
inference(superposition,[status(thm)],[c_12710,c_8116]) ).
tcf(c_28021,plain,
! [X0: $i] :
( empty(sK15(powerset(relation_dom(relation_dom(sK15(powerset(sK15(powerset(singleton(X0))))))))))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ~ in(relation_dom(relation_dom(sK15(powerset(sK15(powerset(singleton(X0))))))),sK15(sK14(sK14(empty_set)))) ),
inference(superposition,[status(thm)],[c_12710,c_17039]) ).
tcf(c_28022,plain,
! [X0: $i] :
( function(sK15(sK14(powerset(empty_set))))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ~ empty(relation_dom(relation_dom(sK15(powerset(sK15(powerset(singleton(X0)))))))) ),
inference(superposition,[status(thm)],[c_12710,c_17169]) ).
tcf(c_28023,plain,
! [X0: $i] :
( relation(sK15(sK14(powerset(empty_set))))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ~ empty(relation_dom(relation_dom(sK15(powerset(sK15(powerset(singleton(X0)))))))) ),
inference(superposition,[status(thm)],[c_12710,c_17168]) ).
tcf(c_28024,plain,
! [X0: $i] :
( empty(sK15(sK14(powerset(empty_set))))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ~ empty(relation_dom(relation_dom(sK15(powerset(sK15(powerset(singleton(X0)))))))) ),
inference(superposition,[status(thm)],[c_12710,c_16911]) ).
tcf(c_28025,plain,
! [X0: $i] :
( empty(sK15(powerset(relation_dom(relation_dom(sK15(powerset(sK15(powerset(singleton(X0))))))))))
| in(sK15(sK14(sK14(empty_set))),relation_dom(relation_dom(sK15(powerset(sK15(powerset(singleton(X0))))))))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 ) ),
inference(superposition,[status(thm)],[c_12710,c_17031]) ).
tcf(c_28027,plain,
! [X0: $i] :
( empty(sK15(powerset(relation_dom(relation_dom(sK15(powerset(sK15(powerset(singleton(X0))))))))))
| element(sK15(sK14(sK14(sK14(empty_set)))),relation_dom(relation_dom(sK15(powerset(sK15(powerset(singleton(X0))))))))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 ) ),
inference(superposition,[status(thm)],[c_12710,c_9269]) ).
tcf(c_28030,plain,
! [X0: $i] :
( empty(sK15(powerset(relation_dom(relation_dom(sK15(powerset(sK15(powerset(singleton(X0))))))))))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ~ in(relation_dom(relation_dom(sK15(powerset(sK15(powerset(singleton(X0))))))),sK15(sK14(empty_set))) ),
inference(superposition,[status(thm)],[c_12710,c_11248]) ).
tcf(c_28031,plain,
! [X0: $i] :
( empty(sK15(powerset(relation_dom(relation_dom(sK15(powerset(sK15(powerset(singleton(X0))))))))))
| in(sK15(sK14(empty_set)),relation_dom(relation_dom(sK15(powerset(sK15(powerset(singleton(X0))))))))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 ) ),
inference(superposition,[status(thm)],[c_12710,c_11240]) ).
tcf(c_28032,plain,
! [X0: $i] :
( empty(sK15(powerset(relation_dom(relation_dom(sK15(powerset(sK15(powerset(singleton(X0))))))))))
| element(sK15(sK14(sK14(empty_set))),relation_dom(relation_dom(sK15(powerset(sK15(powerset(singleton(X0))))))))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 ) ),
inference(superposition,[status(thm)],[c_12710,c_7046]) ).
tcf(c_28033,plain,
! [X0: $i] :
( function(sK15(powerset(empty_set)))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ~ empty(relation_dom(relation_dom(sK15(powerset(sK15(powerset(singleton(X0)))))))) ),
inference(superposition,[status(thm)],[c_12710,c_8308]) ).
tcf(c_28034,plain,
! [X0: $i] :
( relation(sK15(powerset(empty_set)))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ~ empty(relation_dom(relation_dom(sK15(powerset(sK15(powerset(singleton(X0)))))))) ),
inference(superposition,[status(thm)],[c_12710,c_8307]) ).
tcf(c_28035,plain,
! [X0: $i] :
( empty(sK15(powerset(empty_set)))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ~ empty(relation_dom(relation_dom(sK15(powerset(sK15(powerset(singleton(X0)))))))) ),
inference(superposition,[status(thm)],[c_12710,c_8117]) ).
tcf(c_28036,plain,
! [X0: $i] :
( empty(sK15(powerset(relation_dom(relation_dom(sK15(powerset(sK15(powerset(singleton(X0))))))))))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ~ in(relation_dom(relation_dom(sK15(powerset(sK15(powerset(singleton(X0))))))),sK15(empty_set)) ),
inference(superposition,[status(thm)],[c_12710,c_8111]) ).
tcf(c_28037,plain,
! [X0: $i] :
( empty(sK15(powerset(relation_dom(relation_dom(sK15(powerset(sK15(powerset(singleton(X0))))))))))
| in(sK15(empty_set),relation_dom(relation_dom(sK15(powerset(sK15(powerset(singleton(X0))))))))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 ) ),
inference(superposition,[status(thm)],[c_12710,c_8103]) ).
tcf(c_28038,plain,
! [X0: $i] :
( empty(sK15(powerset(relation_dom(relation_dom(sK15(powerset(sK15(powerset(singleton(X0))))))))))
| element(sK15(sK14(empty_set)),relation_dom(relation_dom(sK15(powerset(sK15(powerset(singleton(X0))))))))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 ) ),
inference(superposition,[status(thm)],[c_12710,c_6096]) ).
tcf(c_28039,plain,
! [X0: $i] :
( element(sK15(empty_set),relation_dom(relation_dom(sK15(powerset(sK15(powerset(singleton(X0))))))))
| empty(sK15(powerset(relation_dom(relation_dom(sK15(powerset(sK15(powerset(singleton(X0))))))))))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 ) ),
inference(superposition,[status(thm)],[c_12710,c_5436]) ).
tcf(c_28043,plain,
! [X0: $i] :
( empty(empty_set)
| ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ~ empty(relation_dom(relation_dom(sK15(powerset(sK15(powerset(singleton(X0)))))))) ),
inference(light_normalisation,[status(thm)],[c_28035,c_5301]) ).
tcf(c_28044,plain,
! [X0: $i] :
( relation(empty_set)
| ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ~ empty(relation_dom(relation_dom(sK15(powerset(sK15(powerset(singleton(X0)))))))) ),
inference(light_normalisation,[status(thm)],[c_28034,c_5301]) ).
tcf(c_28045,plain,
! [X0: $i] :
( function(empty_set)
| ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ~ empty(relation_dom(relation_dom(sK15(powerset(sK15(powerset(singleton(X0)))))))) ),
inference(light_normalisation,[status(thm)],[c_28033,c_5301]) ).
tcf(c_28079,plain,
! [X0: $i] :
( element(sK15(empty_set),relation_dom(relation_dom(sK15(powerset(sK15(powerset(singleton(X0))))))))
| empty(sK15(powerset(sK15(powerset(relation_dom(relation_dom(sK15(powerset(sK15(powerset(singleton(X0))))))))))))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 ) ),
inference(light_normalisation,[status(thm)],[c_28020,c_5301]) ).
tcf(c_28193,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(sK15(powerset(relation_dom(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_11908]) ).
tcf(c_28194,plain,
sK15(powerset(sK15(powerset(sK15(powerset(relation_dom(empty_set))))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_11908]) ).
tcf(c_28195,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(sK15(powerset(relation_dom(sK15(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_11908]) ).
tcf(c_28196,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(sK15(powerset(relation_dom(sK15(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_11908]) ).
tcf(c_28197,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(sK15(powerset(relation_dom(sK15(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_11908]) ).
tcf(c_28198,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(sK15(powerset(relation_dom(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_11908]) ).
tcf(c_28199,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( sK15(powerset(sK15(powerset(sK15(powerset(relation_dom(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_11908]) ).
tcf(c_28200,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( sK15(powerset(sK15(powerset(sK15(powerset(relation_dom(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_11908]) ).
tcf(c_28201,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(sK15(powerset(relation_dom(sK15(powerset(sK15(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_11908]) ).
tcf(c_28202,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(sK15(powerset(relation_dom(sK15(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_11908]) ).
tcf(c_28203,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_11908]) ).
tcf(c_28204,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_11908]) ).
tcf(c_28205,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(sK15(powerset(relation_dom(sK15(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_11908]) ).
tcf(c_28206,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_11908]) ).
tcf(c_28207,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(sK15(powerset(relation_dom(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_11908]) ).
tcf(c_28208,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_11908]) ).
tcf(c_28209,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_11908]) ).
tcf(c_28210,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(sK15(powerset(relation_dom(sK15(sK14(powerset(relation_image(X0,empty_set))))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_11908]) ).
tcf(c_28211,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_11908]) ).
tcf(c_28212,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_11908]) ).
tcf(c_28213,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_11908]) ).
tcf(c_28381,plain,
! [X0: $i,X1: $i] :
( ( sK15(powerset(relation_dom(relation_dom(relation_dom(X0))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_12042]) ).
tcf(c_28382,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(empty_set)))) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_92,c_12042]) ).
tcf(c_28383,plain,
! [X0: $i,X1: $i] :
( ( sK15(powerset(relation_dom(relation_dom(sK15(powerset(X0)))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_12042]) ).
tcf(c_28384,plain,
! [X0: $i,X1: $i] :
( ( sK15(powerset(relation_dom(relation_dom(sK15(sK14(powerset(X0))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_12042]) ).
tcf(c_28385,plain,
! [X0: $i,X1: $i] :
( ( sK15(powerset(relation_dom(relation_dom(sK15(sK14(sK14(powerset(X0)))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_12042]) ).
tcf(c_28386,plain,
! [X0: $i,X1: $i] :
( ( sK15(powerset(relation_dom(relation_dom(relation_image(X0,empty_set))))) = X1 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_12042]) ).
tcf(c_28387,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X1))))) = X1 )
| ( sK15(powerset(relation_dom(relation_dom(sK15(powerset(singleton(X1))))))) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11251,c_12042]) ).
tcf(c_28388,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK15(powerset(singleton(X1)))) = X1 )
| ( sK15(powerset(relation_dom(relation_dom(sK15(powerset(singleton(X1))))))) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8114,c_12042]) ).
tcf(c_28389,plain,
! [X0: $i,X1: $i] :
( ( sK15(powerset(relation_dom(relation_dom(sK15(powerset(sK15(powerset(X0)))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_12042]) ).
tcf(c_28390,plain,
! [X0: $i,X1: $i] :
( ( sK15(powerset(relation_dom(relation_dom(sK15(powerset(relation_image(X0,empty_set))))))) = X1 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_12042]) ).
tcf(c_28391,plain,
! [X0: $i,X1: $i] :
( ( sK15(powerset(relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(X0))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_12042]) ).
tcf(c_28392,plain,
! [X0: $i,X1: $i] :
( ( sK15(powerset(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(powerset(X0)))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_12042]) ).
tcf(c_28393,plain,
! [X0: $i,X1: $i] :
( ( sK15(powerset(relation_dom(relation_dom(sK15(sK14(sK14(sK14(powerset(X0))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_12042]) ).
tcf(c_28394,plain,
! [X0: $i,X1: $i] :
( ( sK15(powerset(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_12042]) ).
tcf(c_28395,plain,
! [X0: $i,X1: $i] :
( ( sK15(powerset(relation_dom(relation_dom(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_12042]) ).
tcf(c_28396,plain,
! [X0: $i,X1: $i] :
( ( sK15(powerset(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_12042]) ).
tcf(c_28397,plain,
! [X0: $i,X1: $i] :
( ( sK15(powerset(relation_dom(relation_dom(sK15(sK14(powerset(sK15(powerset(X0))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_12042]) ).
tcf(c_28398,plain,
! [X0: $i,X1: $i] :
( ( sK15(powerset(relation_dom(relation_dom(sK15(sK14(powerset(relation_image(X0,empty_set)))))))) = X1 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_12042]) ).
tcf(c_28399,plain,
! [X0: $i,X1: $i] :
( ( sK15(powerset(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(X0)))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_12042]) ).
tcf(c_28400,plain,
! [X0: $i,X1: $i] :
( ( sK15(powerset(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0))))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_12042]) ).
tcf(c_28401,plain,
! [X0: $i,X1: $i] :
( ( sK15(powerset(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_12042]) ).
tcf(c_28640,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(powerset(relation_dom(relation_dom(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_12094]) ).
tcf(c_28641,plain,
relation_dom(relation_dom(relation_dom(sK15(powerset(relation_dom(relation_dom(empty_set))))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_12094]) ).
tcf(c_28642,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_12094]) ).
tcf(c_28643,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_12094]) ).
tcf(c_28644,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_12094]) ).
tcf(c_28645,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(powerset(relation_dom(relation_dom(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_12094]) ).
tcf(c_28646,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( relation_dom(relation_dom(relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_12094]) ).
tcf(c_28647,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( relation_dom(relation_dom(relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_12094]) ).
tcf(c_28648,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(powerset(sK15(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_12094]) ).
tcf(c_28649,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_12094]) ).
tcf(c_28650,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_12094]) ).
tcf(c_28651,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_12094]) ).
tcf(c_28652,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_12094]) ).
tcf(c_28653,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_12094]) ).
tcf(c_28654,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_12094]) ).
tcf(c_28655,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_12094]) ).
tcf(c_28656,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(sK14(powerset(sK15(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_12094]) ).
tcf(c_28657,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(sK14(powerset(relation_image(X0,empty_set))))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_12094]) ).
tcf(c_28658,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_12094]) ).
tcf(c_28659,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_12094]) ).
tcf(c_28660,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_12094]) ).
tcf(c_28744,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(relation_dom(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_12137]) ).
tcf(c_28745,plain,
relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(relation_dom(empty_set))))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_12137]) ).
tcf(c_28746,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_12137]) ).
tcf(c_28747,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_12137]) ).
tcf(c_28748,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_12137]) ).
tcf(c_28749,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(relation_dom(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_12137]) ).
tcf(c_28750,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_12137]) ).
tcf(c_28751,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_12137]) ).
tcf(c_28752,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(powerset(sK15(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_12137]) ).
tcf(c_28753,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_12137]) ).
tcf(c_28754,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_12137]) ).
tcf(c_28755,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_12137]) ).
tcf(c_28756,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_12137]) ).
tcf(c_28757,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_12137]) ).
tcf(c_28758,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_12137]) ).
tcf(c_28759,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_12137]) ).
tcf(c_28760,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_12137]) ).
tcf(c_28761,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(sK14(powerset(relation_image(X0,empty_set))))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_12137]) ).
tcf(c_28762,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_12137]) ).
tcf(c_28763,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_12137]) ).
tcf(c_28764,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_12137]) ).
tcf(c_28881,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(powerset(sK15(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_9507]) ).
tcf(c_28882,plain,
relation_dom(sK15(sK14(sK14(powerset(sK15(powerset(empty_set))))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_9507]) ).
tcf(c_28887,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( relation_dom(sK15(sK14(sK14(powerset(sK15(powerset(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_9507]) ).
tcf(c_28888,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( relation_dom(sK15(sK14(sK14(powerset(sK15(powerset(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_9507]) ).
tcf(c_28889,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(powerset(sK15(powerset(sK15(powerset(sK15(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_9507]) ).
tcf(c_28890,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(powerset(sK15(powerset(sK15(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_9507]) ).
tcf(c_28891,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(powerset(sK15(powerset(sK15(powerset(sK15(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_9507]) ).
tcf(c_28892,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(powerset(sK15(powerset(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_9507]) ).
tcf(c_28894,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(powerset(sK15(powerset(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_9507]) ).
tcf(c_28896,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(powerset(sK15(powerset(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_9507]) ).
tcf(c_28897,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(powerset(sK15(powerset(sK15(sK14(powerset(sK15(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_9507]) ).
tcf(c_28898,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(powerset(sK15(powerset(sK15(sK14(powerset(relation_image(X0,empty_set))))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_9507]) ).
tcf(c_28899,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(powerset(sK15(powerset(sK15(sK14(powerset(sK15(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_9507]) ).
tcf(c_28900,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(powerset(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_9507]) ).
tcf(c_28901,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(powerset(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_9507]) ).
tcf(c_29075,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(relation_dom(sK15(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_9588]) ).
tcf(c_29076,plain,
sK15(sK14(sK14(powerset(relation_dom(sK15(powerset(empty_set))))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_9588]) ).
tcf(c_29081,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( sK15(sK14(sK14(powerset(relation_dom(sK15(powerset(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_9588]) ).
tcf(c_29082,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( sK15(sK14(sK14(powerset(relation_dom(sK15(powerset(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_9588]) ).
tcf(c_29083,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(relation_dom(sK15(powerset(sK15(powerset(sK15(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_9588]) ).
tcf(c_29084,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(relation_dom(sK15(powerset(sK15(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_9588]) ).
tcf(c_29085,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_9588]) ).
tcf(c_29086,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_9588]) ).
tcf(c_29088,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_9588]) ).
tcf(c_29090,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_9588]) ).
tcf(c_29091,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_9588]) ).
tcf(c_29092,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(relation_dom(sK15(powerset(sK15(sK14(powerset(relation_image(X0,empty_set))))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_9588]) ).
tcf(c_29093,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_9588]) ).
tcf(c_29094,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_9588]) ).
tcf(c_29095,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_9588]) ).
tcf(c_29163,plain,
! [X0: $i] :
( ( relation_image(relation_dom(X0),empty_set) = empty_set )
| ~ empty(X0) ),
inference(global_subsumption_just,[status(thm)],[c_9656,c_70,c_9656]) ).
tcf(c_29169,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(X0)),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_29163]) ).
tcf(c_29170,plain,
relation_image(relation_dom(empty_set),empty_set) = empty_set,
inference(superposition,[status(thm)],[c_92,c_29163]) ).
tcf(c_29171,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(powerset(X0))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_29163]) ).
tcf(c_29172,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(sK14(powerset(X0)))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_29163]) ).
tcf(c_29173,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(sK14(sK14(powerset(X0))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_29163]) ).
tcf(c_29174,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_image(X0,empty_set)),empty_set) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_29163]) ).
tcf(c_29175,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( relation_image(relation_dom(sK15(powerset(singleton(X0)))),empty_set) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_29163]) ).
tcf(c_29176,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( relation_image(relation_dom(sK15(powerset(singleton(X0)))),empty_set) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_29163]) ).
tcf(c_29177,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(powerset(sK15(powerset(X0))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_29163]) ).
tcf(c_29178,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(powerset(relation_image(X0,empty_set)))),empty_set) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_29163]) ).
tcf(c_29179,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(powerset(sK15(sK14(powerset(X0)))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_29163]) ).
tcf(c_29180,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_29163]) ).
tcf(c_29181,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(sK14(sK14(sK14(powerset(X0)))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_29163]) ).
tcf(c_29182,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_29163]) ).
tcf(c_29183,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_29163]) ).
tcf(c_29184,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_29163]) ).
tcf(c_29185,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(sK14(powerset(sK15(powerset(X0)))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_29163]) ).
tcf(c_29186,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(sK14(powerset(relation_image(X0,empty_set))))),empty_set) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_29163]) ).
tcf(c_29187,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(X0))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_29163]) ).
tcf(c_29188,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_29163]) ).
tcf(c_29189,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_29163]) ).
tcf(c_29190,plain,
relation_image(empty_set,empty_set) = empty_set,
inference(light_normalisation,[status(thm)],[c_29170,c_5111]) ).
tcf(c_29266,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(relation_dom(X0))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_29169]) ).
tcf(c_29267,plain,
relation_image(relation_dom(relation_dom(empty_set)),empty_set) = empty_set,
inference(superposition,[status(thm)],[c_92,c_29169]) ).
tcf(c_29268,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(sK15(powerset(X0)))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_29169]) ).
tcf(c_29269,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(sK15(sK14(powerset(X0))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_29169]) ).
tcf(c_29270,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(sK15(sK14(sK14(powerset(X0)))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_29169]) ).
tcf(c_29271,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(relation_image(X0,empty_set))),empty_set) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_29169]) ).
tcf(c_29272,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( relation_image(relation_dom(relation_dom(sK15(powerset(singleton(X0))))),empty_set) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_29169]) ).
tcf(c_29273,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( relation_image(relation_dom(relation_dom(sK15(powerset(singleton(X0))))),empty_set) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_29169]) ).
tcf(c_29274,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(sK15(powerset(sK15(powerset(X0)))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_29169]) ).
tcf(c_29275,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(sK15(powerset(relation_image(X0,empty_set))))),empty_set) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_29169]) ).
tcf(c_29276,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(X0))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_29169]) ).
tcf(c_29277,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(powerset(X0)))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_29169]) ).
tcf(c_29278,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(sK15(sK14(sK14(sK14(powerset(X0))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_29169]) ).
tcf(c_29279,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_29169]) ).
tcf(c_29280,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_29169]) ).
tcf(c_29281,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_29169]) ).
tcf(c_29282,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(sK15(sK14(powerset(sK15(powerset(X0))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_29169]) ).
tcf(c_29283,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(sK15(sK14(powerset(relation_image(X0,empty_set)))))),empty_set) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_29169]) ).
tcf(c_29284,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(X0)))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_29169]) ).
tcf(c_29285,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_29169]) ).
tcf(c_29286,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_29169]) ).
tcf(c_29402,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(powerset(relation_dom(X0)))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_29171]) ).
tcf(c_29403,plain,
relation_image(relation_dom(sK15(powerset(empty_set))),empty_set) = empty_set,
inference(superposition,[status(thm)],[c_92,c_29171]) ).
tcf(c_29408,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( relation_image(relation_dom(sK15(powerset(sK15(powerset(singleton(X0)))))),empty_set) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_29171]) ).
tcf(c_29409,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( relation_image(relation_dom(sK15(powerset(sK15(powerset(singleton(X0)))))),empty_set) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_29171]) ).
tcf(c_29410,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(powerset(sK15(powerset(sK15(powerset(X0))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_29171]) ).
tcf(c_29411,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(powerset(sK15(powerset(relation_image(X0,empty_set)))))),empty_set) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_29171]) ).
tcf(c_29412,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(powerset(X0)))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_29171]) ).
tcf(c_29413,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_29171]) ).
tcf(c_29415,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_29171]) ).
tcf(c_29417,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_29171]) ).
tcf(c_29418,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(powerset(X0)))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_29171]) ).
tcf(c_29419,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(powerset(sK15(sK14(powerset(relation_image(X0,empty_set))))))),empty_set) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_29171]) ).
tcf(c_29420,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(sK14(powerset(X0))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_29171]) ).
tcf(c_29421,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_29171]) ).
tcf(c_29422,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_29171]) ).
tcf(c_29462,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(relation_dom(relation_dom(X0)))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_29266]) ).
tcf(c_29463,plain,
relation_image(relation_dom(relation_dom(relation_dom(empty_set))),empty_set) = empty_set,
inference(superposition,[status(thm)],[c_92,c_29266]) ).
tcf(c_29464,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(relation_dom(sK15(powerset(X0))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_29266]) ).
tcf(c_29465,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(X0)))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_29266]) ).
tcf(c_29466,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(powerset(X0))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_29266]) ).
tcf(c_29467,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(relation_dom(relation_image(X0,empty_set)))),empty_set) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_29266]) ).
tcf(c_29468,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( relation_image(relation_dom(relation_dom(relation_dom(sK15(powerset(singleton(X0)))))),empty_set) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_29266]) ).
tcf(c_29469,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( relation_image(relation_dom(relation_dom(relation_dom(sK15(powerset(singleton(X0)))))),empty_set) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_29266]) ).
tcf(c_29470,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(powerset(X0))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_29266]) ).
tcf(c_29471,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(relation_dom(sK15(powerset(relation_image(X0,empty_set)))))),empty_set) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_29266]) ).
tcf(c_29472,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(X0)))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_29266]) ).
tcf(c_29473,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_29266]) ).
tcf(c_29474,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(sK14(powerset(X0)))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_29266]) ).
tcf(c_29475,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_29266]) ).
tcf(c_29476,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_29266]) ).
tcf(c_29477,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_29266]) ).
tcf(c_29478,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(powerset(X0)))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_29266]) ).
tcf(c_29479,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(relation_image(X0,empty_set))))))),empty_set) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_29266]) ).
tcf(c_29480,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(X0))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_29266]) ).
tcf(c_29481,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_29266]) ).
tcf(c_29482,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_29266]) ).
tcf(c_29547,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(sK14(powerset(relation_dom(X0))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_29172]) ).
tcf(c_29548,plain,
relation_image(relation_dom(sK15(sK14(powerset(empty_set)))),empty_set) = empty_set,
inference(superposition,[status(thm)],[c_92,c_29172]) ).
tcf(c_29553,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( relation_image(relation_dom(sK15(sK14(powerset(sK15(powerset(singleton(X0))))))),empty_set) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_29172]) ).
tcf(c_29554,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( relation_image(relation_dom(sK15(sK14(powerset(sK15(powerset(singleton(X0))))))),empty_set) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_29172]) ).
tcf(c_29555,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(sK14(powerset(sK15(powerset(sK15(powerset(X0)))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_29172]) ).
tcf(c_29556,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(sK14(powerset(sK15(powerset(relation_image(X0,empty_set))))))),empty_set) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_29172]) ).
tcf(c_29557,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(sK14(powerset(sK15(powerset(sK15(sK14(powerset(X0))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_29172]) ).
tcf(c_29558,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(sK14(powerset(sK15(powerset(sK15(sK14(sK14(powerset(X0)))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_29172]) ).
tcf(c_29560,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(sK14(powerset(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_29172]) ).
tcf(c_29561,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_29172]) ).
tcf(c_29562,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(sK14(powerset(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_29172]) ).
tcf(c_29563,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(sK15(powerset(X0))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_29172]) ).
tcf(c_29564,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(relation_image(X0,empty_set)))))))),empty_set) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_29172]) ).
tcf(c_29565,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(sK15(sK14(powerset(X0)))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_29172]) ).
tcf(c_29566,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0))))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_29172]) ).
tcf(c_29567,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_29172]) ).
tcf(c_29627,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(sK15(powerset(relation_dom(X0))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_29268]) ).
tcf(c_29628,plain,
relation_image(relation_dom(relation_dom(sK15(powerset(empty_set)))),empty_set) = empty_set,
inference(superposition,[status(thm)],[c_92,c_29268]) ).
tcf(c_29633,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( relation_image(relation_dom(relation_dom(sK15(powerset(sK15(powerset(singleton(X0))))))),empty_set) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_29268]) ).
tcf(c_29634,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( relation_image(relation_dom(relation_dom(sK15(powerset(sK15(powerset(singleton(X0))))))),empty_set) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_29268]) ).
tcf(c_29635,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(sK15(powerset(sK15(powerset(sK15(powerset(X0)))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_29268]) ).
tcf(c_29636,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(sK15(powerset(sK15(powerset(relation_image(X0,empty_set))))))),empty_set) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_29268]) ).
tcf(c_29637,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(powerset(X0))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_29268]) ).
tcf(c_29638,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(sK14(powerset(X0)))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_29268]) ).
tcf(c_29640,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_29268]) ).
tcf(c_29642,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_29268]) ).
tcf(c_29643,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(powerset(X0))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_29268]) ).
tcf(c_29644,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(relation_image(X0,empty_set)))))))),empty_set) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_29268]) ).
tcf(c_29645,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(sK14(powerset(X0)))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_29268]) ).
tcf(c_29646,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0))))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_29268]) ).
tcf(c_29647,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_29268]) ).
tcf(c_29735,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(powerset(relation_dom(relation_dom(X0))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_29402]) ).
tcf(c_29736,plain,
relation_image(relation_dom(sK15(powerset(relation_dom(empty_set)))),empty_set) = empty_set,
inference(superposition,[status(thm)],[c_92,c_29402]) ).
tcf(c_29737,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(powerset(relation_dom(sK15(powerset(X0)))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_29402]) ).
tcf(c_29738,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(powerset(relation_dom(sK15(sK14(powerset(X0))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_29402]) ).
tcf(c_29739,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(powerset(relation_dom(sK15(sK14(sK14(powerset(X0)))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_29402]) ).
tcf(c_29740,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(powerset(relation_dom(relation_image(X0,empty_set))))),empty_set) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_29402]) ).
tcf(c_29741,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( relation_image(relation_dom(sK15(powerset(relation_dom(sK15(powerset(singleton(X0))))))),empty_set) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_29402]) ).
tcf(c_29742,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( relation_image(relation_dom(sK15(powerset(relation_dom(sK15(powerset(singleton(X0))))))),empty_set) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_29402]) ).
tcf(c_29743,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(powerset(relation_dom(sK15(powerset(sK15(powerset(X0)))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_29402]) ).
tcf(c_29744,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(powerset(relation_dom(sK15(powerset(relation_image(X0,empty_set))))))),empty_set) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_29402]) ).
tcf(c_29745,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(powerset(X0))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_29402]) ).
tcf(c_29746,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(powerset(X0)))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_29402]) ).
tcf(c_29747,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(powerset(relation_dom(sK15(sK14(sK14(sK14(powerset(X0))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_29402]) ).
tcf(c_29748,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_29402]) ).
tcf(c_29749,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(powerset(relation_dom(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_29402]) ).
tcf(c_29750,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_29402]) ).
tcf(c_29751,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(powerset(X0))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_29402]) ).
tcf(c_29752,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(powerset(relation_dom(sK15(sK14(powerset(relation_image(X0,empty_set)))))))),empty_set) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_29402]) ).
tcf(c_29753,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(X0)))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_29402]) ).
tcf(c_29754,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0))))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_29402]) ).
tcf(c_29755,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_29402]) ).
tcf(c_29833,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(X0))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_29462]) ).
tcf(c_29834,plain,
relation_image(relation_dom(relation_dom(relation_dom(relation_dom(empty_set)))),empty_set) = empty_set,
inference(superposition,[status(thm)],[c_92,c_29462]) ).
tcf(c_29835,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(X0)))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_29462]) ).
tcf(c_29836,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(X0))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_29462]) ).
tcf(c_29837,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(powerset(X0)))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_29462]) ).
tcf(c_29838,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(relation_dom(relation_dom(relation_image(X0,empty_set))))),empty_set) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_29462]) ).
tcf(c_29839,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( relation_image(relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(singleton(X0))))))),empty_set) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_29462]) ).
tcf(c_29840,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( relation_image(relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(singleton(X0))))))),empty_set) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_29462]) ).
tcf(c_29841,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(powerset(X0)))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_29462]) ).
tcf(c_29842,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(relation_image(X0,empty_set))))))),empty_set) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_29462]) ).
tcf(c_29843,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(X0))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_29462]) ).
tcf(c_29844,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(powerset(X0)))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_29462]) ).
tcf(c_29845,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(sK14(powerset(X0))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_29462]) ).
tcf(c_29846,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_29462]) ).
tcf(c_29847,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_29462]) ).
tcf(c_29848,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_29462]) ).
tcf(c_29849,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(powerset(X0))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_29462]) ).
tcf(c_29850,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(relation_image(X0,empty_set)))))))),empty_set) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_29462]) ).
tcf(c_29851,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(X0)))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_29462]) ).
tcf(c_29852,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0))))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_29462]) ).
tcf(c_29853,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_29462]) ).
tcf(c_29968,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(sK14(sK14(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_10133]) ).
tcf(c_29969,plain,
sK15(powerset(sK15(sK14(sK14(sK14(powerset(empty_set))))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_10133]) ).
tcf(c_29970,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(sK14(sK14(powerset(sK15(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_10133]) ).
tcf(c_29971,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(sK14(sK14(powerset(sK15(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_10133]) ).
tcf(c_29972,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(sK14(sK14(powerset(sK15(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_10133]) ).
tcf(c_29973,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(sK14(sK14(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_10133]) ).
tcf(c_29974,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( sK15(powerset(sK15(sK14(sK14(sK14(powerset(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_10133]) ).
tcf(c_29975,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( sK15(powerset(sK15(sK14(sK14(sK14(powerset(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_10133]) ).
tcf(c_29976,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(sK14(sK14(powerset(sK15(powerset(sK15(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_10133]) ).
tcf(c_29977,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(sK14(sK14(powerset(sK15(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_10133]) ).
tcf(c_29978,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(sK14(sK14(powerset(sK15(powerset(sK15(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_10133]) ).
tcf(c_29979,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(sK14(sK14(powerset(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_10133]) ).
tcf(c_29980,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(sK14(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_10133]) ).
tcf(c_29981,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(sK14(sK14(powerset(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_10133]) ).
tcf(c_29982,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(sK14(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_10133]) ).
tcf(c_29983,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(sK14(sK14(powerset(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_10133]) ).
tcf(c_29984,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(sK14(sK14(powerset(sK15(sK14(powerset(sK15(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_10133]) ).
tcf(c_29985,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(sK14(sK14(powerset(sK15(sK14(powerset(relation_image(X0,empty_set))))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_10133]) ).
tcf(c_29986,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(sK14(sK14(powerset(sK15(sK14(powerset(sK15(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_10133]) ).
tcf(c_29987,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(sK14(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_10133]) ).
tcf(c_29988,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(sK14(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_10133]) ).
tcf(c_30153,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(sK14(sK14(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_10134]) ).
tcf(c_30154,plain,
relation_dom(relation_dom(sK15(sK14(sK14(sK14(powerset(empty_set))))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_10134]) ).
tcf(c_30155,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(sK14(sK14(powerset(sK15(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_10134]) ).
tcf(c_30156,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(sK14(sK14(powerset(sK15(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_10134]) ).
tcf(c_30157,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(sK14(sK14(powerset(sK15(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_10134]) ).
tcf(c_30158,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(sK14(sK14(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_10134]) ).
tcf(c_30159,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( relation_dom(relation_dom(sK15(sK14(sK14(sK14(powerset(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_10134]) ).
tcf(c_30160,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( relation_dom(relation_dom(sK15(sK14(sK14(sK14(powerset(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_10134]) ).
tcf(c_30161,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(sK14(sK14(powerset(sK15(powerset(sK15(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_10134]) ).
tcf(c_30162,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(sK14(sK14(powerset(sK15(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_10134]) ).
tcf(c_30163,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(sK14(sK14(powerset(sK15(powerset(sK15(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_10134]) ).
tcf(c_30164,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(sK14(sK14(powerset(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_10134]) ).
tcf(c_30165,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(sK14(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_10134]) ).
tcf(c_30166,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(sK14(sK14(powerset(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_10134]) ).
tcf(c_30167,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(sK14(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_10134]) ).
tcf(c_30168,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(sK14(sK14(powerset(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_10134]) ).
tcf(c_30169,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(sK14(sK14(powerset(sK15(sK14(powerset(sK15(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_10134]) ).
tcf(c_30170,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(sK14(sK14(powerset(sK15(sK14(powerset(relation_image(X0,empty_set))))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_10134]) ).
tcf(c_30171,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(sK14(sK14(powerset(sK15(sK14(powerset(sK15(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_10134]) ).
tcf(c_30172,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(sK14(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_10134]) ).
tcf(c_30173,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(sK14(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_10134]) ).
tcf(c_30402,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK4(sK15(powerset(relation_dom(sK15(powerset(sK15(powerset(singleton(X0)))))))),X1,X2),empty_set)
| in(sK3(sK15(powerset(relation_dom(sK15(powerset(sK15(powerset(singleton(X0)))))))),X1,X2),X2)
| ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( relation_image(sK15(powerset(relation_dom(sK15(powerset(sK15(powerset(singleton(X0)))))))),X1) = X2 )
| ~ function(sK15(powerset(relation_dom(sK15(powerset(sK15(powerset(singleton(X0)))))))))
| ~ relation(sK15(powerset(relation_dom(sK15(powerset(sK15(powerset(singleton(X0))))))))) ),
inference(superposition,[status(thm)],[c_12711,c_58]) ).
tcf(c_30403,plain,
! [X0: $i] :
( empty(sK15(powerset(relation_dom(sK15(powerset(sK15(powerset(singleton(X0)))))))))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ~ empty(empty_set)
| ~ relation(sK15(powerset(relation_dom(sK15(powerset(sK15(powerset(singleton(X0))))))))) ),
inference(superposition,[status(thm)],[c_12711,c_71]) ).
tcf(c_30407,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(sK15(powerset(relation_dom(sK15(powerset(sK15(powerset(singleton(X1)))))))),X2,X0),empty_set)
| ( sK15(sK15(powerset(singleton(X1)))) = X1 )
| ~ function(sK15(powerset(relation_dom(sK15(powerset(sK15(powerset(singleton(X1)))))))))
| ~ relation(sK15(powerset(relation_dom(sK15(powerset(sK15(powerset(singleton(X1)))))))))
| ~ in(X0,relation_image(sK15(powerset(relation_dom(sK15(powerset(sK15(powerset(singleton(X1)))))))),X2)) ),
inference(superposition,[status(thm)],[c_12711,c_62]) ).
tcf(c_30408,plain,
! [X0: $i] :
( empty(sK15(powerset(relation_dom(sK15(powerset(sK15(powerset(singleton(X0)))))))))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ~ relation(sK15(powerset(relation_dom(sK15(powerset(sK15(powerset(singleton(X0))))))))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_30403,c_92]) ).
tcf(c_30412,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK15(sK15(powerset(singleton(X1)))) = X1 )
| ~ function(sK15(powerset(relation_dom(sK15(powerset(sK15(powerset(singleton(X1)))))))))
| ~ relation(sK15(powerset(relation_dom(sK15(powerset(sK15(powerset(singleton(X1)))))))))
| ~ in(X0,relation_image(sK15(powerset(relation_dom(sK15(powerset(sK15(powerset(singleton(X1)))))))),X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_30407,c_5314]) ).
tcf(c_30417,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(sK15(powerset(relation_dom(sK15(powerset(sK15(powerset(singleton(X0)))))))),X1,X2),X2)
| ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( relation_image(sK15(powerset(relation_dom(sK15(powerset(sK15(powerset(singleton(X0)))))))),X1) = X2 )
| ~ function(sK15(powerset(relation_dom(sK15(powerset(sK15(powerset(singleton(X0)))))))))
| ~ relation(sK15(powerset(relation_dom(sK15(powerset(sK15(powerset(singleton(X0))))))))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_30402,c_5314]) ).
tcf(c_30440,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(sK15(powerset(relation_dom(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_12185]) ).
tcf(c_30441,plain,
relation_dom(sK15(powerset(relation_dom(sK15(powerset(relation_dom(empty_set))))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_12185]) ).
tcf(c_30442,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(sK15(powerset(relation_dom(sK15(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_12185]) ).
tcf(c_30443,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(sK15(powerset(relation_dom(sK15(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_12185]) ).
tcf(c_30444,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(sK15(powerset(relation_dom(sK15(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_12185]) ).
tcf(c_30445,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(sK15(powerset(relation_dom(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_12185]) ).
tcf(c_30446,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( relation_dom(sK15(powerset(relation_dom(sK15(powerset(relation_dom(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_12185]) ).
tcf(c_30447,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( relation_dom(sK15(powerset(relation_dom(sK15(powerset(relation_dom(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_12185]) ).
tcf(c_30448,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(sK15(powerset(relation_dom(sK15(powerset(sK15(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_12185]) ).
tcf(c_30449,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(sK15(powerset(relation_dom(sK15(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_12185]) ).
tcf(c_30450,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_12185]) ).
tcf(c_30451,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_12185]) ).
tcf(c_30452,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(sK15(powerset(relation_dom(sK15(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_12185]) ).
tcf(c_30453,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_12185]) ).
tcf(c_30454,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(sK15(powerset(relation_dom(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_12185]) ).
tcf(c_30455,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_12185]) ).
tcf(c_30456,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_12185]) ).
tcf(c_30457,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(sK15(powerset(relation_dom(sK15(sK14(powerset(relation_image(X0,empty_set))))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_12185]) ).
tcf(c_30458,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_12185]) ).
tcf(c_30459,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_12185]) ).
tcf(c_30460,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_12185]) ).
tcf(c_30544,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(sK15(powerset(relation_dom(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_12288]) ).
tcf(c_30545,plain,
sK15(powerset(relation_dom(relation_dom(sK15(powerset(relation_dom(empty_set))))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_12288]) ).
tcf(c_30546,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_12288]) ).
tcf(c_30547,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_12288]) ).
tcf(c_30548,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_12288]) ).
tcf(c_30549,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(sK15(powerset(relation_dom(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_12288]) ).
tcf(c_30550,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( sK15(powerset(relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_12288]) ).
tcf(c_30551,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( sK15(powerset(relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_12288]) ).
tcf(c_30552,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(powerset(sK15(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_12288]) ).
tcf(c_30553,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_12288]) ).
tcf(c_30554,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_12288]) ).
tcf(c_30555,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_12288]) ).
tcf(c_30556,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_12288]) ).
tcf(c_30557,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_12288]) ).
tcf(c_30558,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_12288]) ).
tcf(c_30559,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_12288]) ).
tcf(c_30560,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_12288]) ).
tcf(c_30561,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(sK14(powerset(relation_image(X0,empty_set))))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_12288]) ).
tcf(c_30562,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_12288]) ).
tcf(c_30563,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_12288]) ).
tcf(c_30564,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_12288]) ).
tcf(c_30744,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(sK15(powerset(relation_dom(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_12319]) ).
tcf(c_30745,plain,
sK15(sK14(powerset(relation_dom(sK15(powerset(relation_dom(empty_set))))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_12319]) ).
tcf(c_30746,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(sK15(powerset(relation_dom(sK15(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_12319]) ).
tcf(c_30747,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(sK15(powerset(relation_dom(sK15(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_12319]) ).
tcf(c_30748,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(sK15(powerset(relation_dom(sK15(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_12319]) ).
tcf(c_30749,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(sK15(powerset(relation_dom(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_12319]) ).
tcf(c_30750,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( sK15(sK14(powerset(relation_dom(sK15(powerset(relation_dom(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_12319]) ).
tcf(c_30751,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( sK15(sK14(powerset(relation_dom(sK15(powerset(relation_dom(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_12319]) ).
tcf(c_30752,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(sK15(powerset(relation_dom(sK15(powerset(sK15(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_12319]) ).
tcf(c_30753,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(sK15(powerset(relation_dom(sK15(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_12319]) ).
tcf(c_30754,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_12319]) ).
tcf(c_30755,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_12319]) ).
tcf(c_30756,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(sK15(powerset(relation_dom(sK15(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_12319]) ).
tcf(c_30757,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_12319]) ).
tcf(c_30758,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(sK15(powerset(relation_dom(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_12319]) ).
tcf(c_30759,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_12319]) ).
tcf(c_30760,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_12319]) ).
tcf(c_30761,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(sK15(powerset(relation_dom(sK15(sK14(powerset(relation_image(X0,empty_set))))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_12319]) ).
tcf(c_30762,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_12319]) ).
tcf(c_30763,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_12319]) ).
tcf(c_30764,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_12319]) ).
tcf(c_30924,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(sK15(powerset(relation_dom(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_12362]) ).
tcf(c_30925,plain,
relation_dom(sK15(sK14(powerset(sK15(powerset(relation_dom(empty_set))))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_12362]) ).
tcf(c_30926,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(sK15(powerset(relation_dom(sK15(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_12362]) ).
tcf(c_30927,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(sK15(powerset(relation_dom(sK15(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_12362]) ).
tcf(c_30928,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(sK15(powerset(relation_dom(sK15(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_12362]) ).
tcf(c_30929,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(sK15(powerset(relation_dom(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_12362]) ).
tcf(c_30930,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( relation_dom(sK15(sK14(powerset(sK15(powerset(relation_dom(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_12362]) ).
tcf(c_30931,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( relation_dom(sK15(sK14(powerset(sK15(powerset(relation_dom(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_12362]) ).
tcf(c_30932,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(sK15(powerset(relation_dom(sK15(powerset(sK15(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_12362]) ).
tcf(c_30933,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(sK15(powerset(relation_dom(sK15(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_12362]) ).
tcf(c_30934,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_12362]) ).
tcf(c_30935,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_12362]) ).
tcf(c_30936,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(sK15(powerset(relation_dom(sK15(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_12362]) ).
tcf(c_30937,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_12362]) ).
tcf(c_30938,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(sK15(powerset(relation_dom(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_12362]) ).
tcf(c_30939,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_12362]) ).
tcf(c_30940,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_12362]) ).
tcf(c_30941,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(sK15(powerset(relation_dom(sK15(sK14(powerset(relation_image(X0,empty_set))))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_12362]) ).
tcf(c_30942,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_12362]) ).
tcf(c_30943,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_12362]) ).
tcf(c_30944,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_12362]) ).
tcf(c_31070,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(powerset(sK15(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_10889]) ).
tcf(c_31071,plain,
sK15(sK14(sK14(sK14(powerset(sK15(powerset(empty_set))))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_10889]) ).
tcf(c_31076,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( sK15(sK14(sK14(sK14(powerset(sK15(powerset(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_10889]) ).
tcf(c_31077,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( sK15(sK14(sK14(sK14(powerset(sK15(powerset(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_10889]) ).
tcf(c_31078,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(powerset(sK15(powerset(sK15(powerset(sK15(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_10889]) ).
tcf(c_31079,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(powerset(sK15(powerset(sK15(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_10889]) ).
tcf(c_31080,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(powerset(sK15(powerset(sK15(powerset(sK15(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_10889]) ).
tcf(c_31081,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(powerset(sK15(powerset(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_10889]) ).
tcf(c_31083,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(powerset(sK15(powerset(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_10889]) ).
tcf(c_31085,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(powerset(sK15(powerset(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_10889]) ).
tcf(c_31086,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(powerset(sK15(powerset(sK15(sK14(powerset(sK15(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_10889]) ).
tcf(c_31087,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(powerset(sK15(powerset(sK15(sK14(powerset(relation_image(X0,empty_set))))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_10889]) ).
tcf(c_31088,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(powerset(sK15(powerset(sK15(sK14(powerset(sK15(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_10889]) ).
tcf(c_31089,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(powerset(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_10889]) ).
tcf(c_31090,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(powerset(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_10889]) ).
tcf(c_31130,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(sK14(powerset(relation_dom(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_12393]) ).
tcf(c_31131,plain,
sK15(powerset(sK15(sK14(sK14(powerset(relation_dom(empty_set))))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_12393]) ).
tcf(c_31132,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(sK14(powerset(relation_dom(sK15(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_12393]) ).
tcf(c_31133,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(sK14(powerset(relation_dom(sK15(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_12393]) ).
tcf(c_31134,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(sK14(powerset(relation_dom(sK15(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_12393]) ).
tcf(c_31135,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(sK14(powerset(relation_dom(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_12393]) ).
tcf(c_31136,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( sK15(powerset(sK15(sK14(sK14(powerset(relation_dom(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_12393]) ).
tcf(c_31137,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( sK15(powerset(sK15(sK14(sK14(powerset(relation_dom(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_12393]) ).
tcf(c_31138,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(sK14(powerset(relation_dom(sK15(powerset(sK15(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_12393]) ).
tcf(c_31139,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(sK14(powerset(relation_dom(sK15(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_12393]) ).
tcf(c_31140,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(sK14(powerset(relation_dom(sK15(powerset(sK15(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_12393]) ).
tcf(c_31141,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(sK14(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_12393]) ).
tcf(c_31142,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(sK14(powerset(relation_dom(sK15(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_12393]) ).
tcf(c_31143,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(sK14(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_12393]) ).
tcf(c_31144,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(sK14(powerset(relation_dom(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_12393]) ).
tcf(c_31145,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(sK14(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_12393]) ).
tcf(c_31146,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(sK14(powerset(relation_dom(sK15(sK14(powerset(sK15(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_12393]) ).
tcf(c_31147,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(sK14(powerset(relation_dom(sK15(sK14(powerset(relation_image(X0,empty_set))))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_12393]) ).
tcf(c_31148,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(sK14(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_12393]) ).
tcf(c_31149,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(sK14(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_12393]) ).
tcf(c_31150,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(sK14(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_12393]) ).
tcf(c_31284,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(sK14(powerset(relation_dom(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_12496]) ).
tcf(c_31285,plain,
relation_dom(relation_dom(sK15(sK14(sK14(powerset(relation_dom(empty_set))))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_12496]) ).
tcf(c_31286,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(sK14(powerset(relation_dom(sK15(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_12496]) ).
tcf(c_31287,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(sK14(powerset(relation_dom(sK15(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_12496]) ).
tcf(c_31288,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(sK14(powerset(relation_dom(sK15(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_12496]) ).
tcf(c_31289,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(sK14(powerset(relation_dom(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_12496]) ).
tcf(c_31290,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( relation_dom(relation_dom(sK15(sK14(sK14(powerset(relation_dom(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_12496]) ).
tcf(c_31291,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( relation_dom(relation_dom(sK15(sK14(sK14(powerset(relation_dom(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_12496]) ).
tcf(c_31292,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(sK14(powerset(relation_dom(sK15(powerset(sK15(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_12496]) ).
tcf(c_31293,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(sK14(powerset(relation_dom(sK15(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_12496]) ).
tcf(c_31294,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(sK14(powerset(relation_dom(sK15(powerset(sK15(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_12496]) ).
tcf(c_31295,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(sK14(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_12496]) ).
tcf(c_31296,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(sK14(powerset(relation_dom(sK15(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_12496]) ).
tcf(c_31297,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(sK14(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_12496]) ).
tcf(c_31298,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(sK14(powerset(relation_dom(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_12496]) ).
tcf(c_31299,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(sK14(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_12496]) ).
tcf(c_31300,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(sK14(powerset(relation_dom(sK15(sK14(powerset(sK15(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_12496]) ).
tcf(c_31301,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(sK14(powerset(relation_dom(sK15(sK14(powerset(relation_image(X0,empty_set))))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_12496]) ).
tcf(c_31302,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(sK14(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_12496]) ).
tcf(c_31303,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(sK14(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_12496]) ).
tcf(c_31304,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(sK14(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_12496]) ).
tcf(c_31508,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(sK15(powerset(relation_dom(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_12539]) ).
tcf(c_31509,plain,
sK15(sK14(sK14(powerset(sK15(powerset(relation_dom(empty_set))))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_12539]) ).
tcf(c_31510,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(sK15(powerset(relation_dom(sK15(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_12539]) ).
tcf(c_31511,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(sK15(powerset(relation_dom(sK15(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_12539]) ).
tcf(c_31512,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(sK15(powerset(relation_dom(sK15(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_12539]) ).
tcf(c_31513,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(sK15(powerset(relation_dom(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_12539]) ).
tcf(c_31514,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( sK15(sK14(sK14(powerset(sK15(powerset(relation_dom(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_12539]) ).
tcf(c_31515,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( sK15(sK14(sK14(powerset(sK15(powerset(relation_dom(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_12539]) ).
tcf(c_31516,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(sK15(powerset(relation_dom(sK15(powerset(sK15(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_12539]) ).
tcf(c_31517,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(sK15(powerset(relation_dom(sK15(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_12539]) ).
tcf(c_31518,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_12539]) ).
tcf(c_31519,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_12539]) ).
tcf(c_31520,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(sK15(powerset(relation_dom(sK15(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_12539]) ).
tcf(c_31521,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_12539]) ).
tcf(c_31522,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(sK15(powerset(relation_dom(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_12539]) ).
tcf(c_31523,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_12539]) ).
tcf(c_31524,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_12539]) ).
tcf(c_31525,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(sK15(powerset(relation_dom(sK15(sK14(powerset(relation_image(X0,empty_set))))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_12539]) ).
tcf(c_31526,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_12539]) ).
tcf(c_31527,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_12539]) ).
tcf(c_31528,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_12539]) ).
tcf(c_31599,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(X0))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_13072]) ).
tcf(c_31600,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(empty_set)))) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_92,c_13072]) ).
tcf(c_31601,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(X0)))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_13072]) ).
tcf(c_31602,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(X0))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_13072]) ).
tcf(c_31603,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(powerset(X0)))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_13072]) ).
tcf(c_31604,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_image(X0,empty_set))))) = X1 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_13072]) ).
tcf(c_31605,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X1))))) = X1 )
| ( relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(singleton(X1))))))) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11251,c_13072]) ).
tcf(c_31606,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK15(powerset(singleton(X1)))) = X1 )
| ( relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(singleton(X1))))))) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8114,c_13072]) ).
tcf(c_31607,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(powerset(X0)))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_13072]) ).
tcf(c_31608,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(relation_image(X0,empty_set))))))) = X1 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_13072]) ).
tcf(c_31609,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(X0))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_13072]) ).
tcf(c_31610,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(powerset(X0)))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_13072]) ).
tcf(c_31611,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(sK14(powerset(X0))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_13072]) ).
tcf(c_31612,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_13072]) ).
tcf(c_31613,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_13072]) ).
tcf(c_31614,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_13072]) ).
tcf(c_31615,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(powerset(X0))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_13072]) ).
tcf(c_31616,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(relation_image(X0,empty_set)))))))) = X1 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_13072]) ).
tcf(c_31617,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(X0)))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_13072]) ).
tcf(c_31618,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0))))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_13072]) ).
tcf(c_31619,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_13072]) ).
tcf(c_31754,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(relation_dom(relation_dom(relation_dom(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_13155]) ).
tcf(c_31755,plain,
relation_dom(relation_dom(sK15(powerset(relation_dom(relation_dom(relation_dom(empty_set))))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_13155]) ).
tcf(c_31756,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(relation_dom(relation_dom(relation_dom(sK15(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_13155]) ).
tcf(c_31757,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_13155]) ).
tcf(c_31758,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_13155]) ).
tcf(c_31759,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(relation_dom(relation_dom(relation_dom(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_13155]) ).
tcf(c_31760,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( relation_dom(relation_dom(sK15(powerset(relation_dom(relation_dom(relation_dom(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_13155]) ).
tcf(c_31761,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( relation_dom(relation_dom(sK15(powerset(relation_dom(relation_dom(relation_dom(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_13155]) ).
tcf(c_31762,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_13155]) ).
tcf(c_31763,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(relation_dom(relation_dom(relation_dom(sK15(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_13155]) ).
tcf(c_31764,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_13155]) ).
tcf(c_31765,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_13155]) ).
tcf(c_31766,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_13155]) ).
tcf(c_31767,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_13155]) ).
tcf(c_31768,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_13155]) ).
tcf(c_31769,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_13155]) ).
tcf(c_31770,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_13155]) ).
tcf(c_31771,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(relation_image(X0,empty_set))))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_13155]) ).
tcf(c_31772,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_13155]) ).
tcf(c_31773,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_13155]) ).
tcf(c_31774,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_13155]) ).
tcf(c_31900,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(powerset(relation_dom(relation_dom(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_13215]) ).
tcf(c_31901,plain,
relation_dom(sK15(powerset(sK15(powerset(relation_dom(relation_dom(empty_set))))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_13215]) ).
tcf(c_31902,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(powerset(relation_dom(relation_dom(sK15(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_13215]) ).
tcf(c_31903,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(powerset(relation_dom(relation_dom(sK15(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_13215]) ).
tcf(c_31904,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(powerset(relation_dom(relation_dom(sK15(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_13215]) ).
tcf(c_31905,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(powerset(relation_dom(relation_dom(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_13215]) ).
tcf(c_31906,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( relation_dom(sK15(powerset(sK15(powerset(relation_dom(relation_dom(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_13215]) ).
tcf(c_31907,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( relation_dom(sK15(powerset(sK15(powerset(relation_dom(relation_dom(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_13215]) ).
tcf(c_31908,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(powerset(relation_dom(relation_dom(sK15(powerset(sK15(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_13215]) ).
tcf(c_31909,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(powerset(relation_dom(relation_dom(sK15(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_13215]) ).
tcf(c_31910,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(powerset(relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_13215]) ).
tcf(c_31911,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(powerset(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_13215]) ).
tcf(c_31912,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(powerset(relation_dom(relation_dom(sK15(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_13215]) ).
tcf(c_31913,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(powerset(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_13215]) ).
tcf(c_31914,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(powerset(relation_dom(relation_dom(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_13215]) ).
tcf(c_31915,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(powerset(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_13215]) ).
tcf(c_31916,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(powerset(relation_dom(relation_dom(sK15(sK14(powerset(sK15(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_13215]) ).
tcf(c_31917,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(powerset(relation_dom(relation_dom(sK15(sK14(powerset(relation_image(X0,empty_set))))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_13215]) ).
tcf(c_31918,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(powerset(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_13215]) ).
tcf(c_31919,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(powerset(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_13215]) ).
tcf(c_31920,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(powerset(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_13215]) ).
tcf(c_32086,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(powerset(relation_dom(relation_dom(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_13342]) ).
tcf(c_32087,plain,
sK15(powerset(relation_dom(sK15(powerset(relation_dom(relation_dom(empty_set))))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_13342]) ).
tcf(c_32088,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_13342]) ).
tcf(c_32089,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_13342]) ).
tcf(c_32090,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_13342]) ).
tcf(c_32091,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(powerset(relation_dom(relation_dom(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_13342]) ).
tcf(c_32092,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( sK15(powerset(relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_13342]) ).
tcf(c_32093,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( sK15(powerset(relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_13342]) ).
tcf(c_32094,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(powerset(sK15(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_13342]) ).
tcf(c_32095,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_13342]) ).
tcf(c_32096,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_13342]) ).
tcf(c_32097,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_13342]) ).
tcf(c_32098,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_13342]) ).
tcf(c_32099,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_13342]) ).
tcf(c_32100,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_13342]) ).
tcf(c_32101,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_13342]) ).
tcf(c_32102,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(sK14(powerset(sK15(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_13342]) ).
tcf(c_32103,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(sK14(powerset(relation_image(X0,empty_set))))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_13342]) ).
tcf(c_32104,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_13342]) ).
tcf(c_32105,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_13342]) ).
tcf(c_32106,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_13342]) ).
tcf(c_32198,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(powerset(relation_dom(relation_dom(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_13409]) ).
tcf(c_32199,plain,
sK15(powerset(sK15(sK14(powerset(relation_dom(relation_dom(empty_set))))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_13409]) ).
tcf(c_32200,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(powerset(relation_dom(relation_dom(sK15(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_13409]) ).
tcf(c_32201,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(powerset(relation_dom(relation_dom(sK15(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_13409]) ).
tcf(c_32202,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(powerset(relation_dom(relation_dom(sK15(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_13409]) ).
tcf(c_32203,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(powerset(relation_dom(relation_dom(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_13409]) ).
tcf(c_32204,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( sK15(powerset(sK15(sK14(powerset(relation_dom(relation_dom(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_13409]) ).
tcf(c_32205,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( sK15(powerset(sK15(sK14(powerset(relation_dom(relation_dom(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_13409]) ).
tcf(c_32206,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(powerset(relation_dom(relation_dom(sK15(powerset(sK15(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_13409]) ).
tcf(c_32207,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(powerset(relation_dom(relation_dom(sK15(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_13409]) ).
tcf(c_32208,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(powerset(relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_13409]) ).
tcf(c_32209,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(powerset(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_13409]) ).
tcf(c_32210,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(powerset(relation_dom(relation_dom(sK15(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_13409]) ).
tcf(c_32211,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(powerset(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_13409]) ).
tcf(c_32212,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(powerset(relation_dom(relation_dom(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_13409]) ).
tcf(c_32213,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(powerset(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_13409]) ).
tcf(c_32214,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(powerset(relation_dom(relation_dom(sK15(sK14(powerset(sK15(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_13409]) ).
tcf(c_32215,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(powerset(relation_dom(relation_dom(sK15(sK14(powerset(relation_image(X0,empty_set))))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_13409]) ).
tcf(c_32216,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(powerset(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_13409]) ).
tcf(c_32217,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(powerset(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_13409]) ).
tcf(c_32218,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(powerset(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_13409]) ).
tcf(c_32500,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(relation_dom(relation_dom(relation_dom(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_13471]) ).
tcf(c_32501,plain,
sK15(powerset(sK15(powerset(relation_dom(relation_dom(relation_dom(empty_set))))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_13471]) ).
tcf(c_32502,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(relation_dom(relation_dom(relation_dom(sK15(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_13471]) ).
tcf(c_32503,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_13471]) ).
tcf(c_32504,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_13471]) ).
tcf(c_32505,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(relation_dom(relation_dom(relation_dom(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_13471]) ).
tcf(c_32506,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( sK15(powerset(sK15(powerset(relation_dom(relation_dom(relation_dom(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_13471]) ).
tcf(c_32507,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( sK15(powerset(sK15(powerset(relation_dom(relation_dom(relation_dom(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_13471]) ).
tcf(c_32508,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_13471]) ).
tcf(c_32509,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(relation_dom(relation_dom(relation_dom(sK15(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_13471]) ).
tcf(c_32510,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_13471]) ).
tcf(c_32511,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_13471]) ).
tcf(c_32512,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_13471]) ).
tcf(c_32513,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_13471]) ).
tcf(c_32514,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_13471]) ).
tcf(c_32515,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_13471]) ).
tcf(c_32516,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_13471]) ).
tcf(c_32517,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(relation_image(X0,empty_set))))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_13471]) ).
tcf(c_32518,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_13471]) ).
tcf(c_32519,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_13471]) ).
tcf(c_32520,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_13471]) ).
tcf(c_32678,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_13554]) ).
tcf(c_32679,plain,
relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(empty_set))))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_13554]) ).
tcf(c_32680,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_13554]) ).
tcf(c_32681,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_13554]) ).
tcf(c_32682,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_13554]) ).
tcf(c_32683,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_13554]) ).
tcf(c_32684,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_13554]) ).
tcf(c_32685,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_13554]) ).
tcf(c_32686,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_13554]) ).
tcf(c_32687,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_13554]) ).
tcf(c_32688,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_13554]) ).
tcf(c_32689,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_13554]) ).
tcf(c_32690,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_13554]) ).
tcf(c_32691,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_13554]) ).
tcf(c_32692,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_13554]) ).
tcf(c_32693,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_13554]) ).
tcf(c_32694,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_13554]) ).
tcf(c_32695,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(relation_image(X0,empty_set))))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_13554]) ).
tcf(c_32696,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_13554]) ).
tcf(c_32697,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_13554]) ).
tcf(c_32698,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_13554]) ).
tcf(c_32804,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_13650]) ).
tcf(c_32805,plain,
relation_dom(sK15(powerset(relation_dom(relation_dom(relation_dom(relation_dom(empty_set))))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_13650]) ).
tcf(c_32806,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_13650]) ).
tcf(c_32807,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_13650]) ).
tcf(c_32808,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_13650]) ).
tcf(c_32809,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(relation_dom(relation_dom(relation_dom(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_13650]) ).
tcf(c_32810,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( relation_dom(sK15(powerset(relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_13650]) ).
tcf(c_32811,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( relation_dom(sK15(powerset(relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_13650]) ).
tcf(c_32812,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_13650]) ).
tcf(c_32813,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_13650]) ).
tcf(c_32814,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_13650]) ).
tcf(c_32815,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_13650]) ).
tcf(c_32816,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_13650]) ).
tcf(c_32817,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_13650]) ).
tcf(c_32818,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_13650]) ).
tcf(c_32819,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_13650]) ).
tcf(c_32820,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_13650]) ).
tcf(c_32821,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(relation_image(X0,empty_set))))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_13650]) ).
tcf(c_32822,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_13650]) ).
tcf(c_32823,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_13650]) ).
tcf(c_32824,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_13650]) ).
tcf(c_32994,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK4(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(powerset(singleton(X0)))))))),X1,X2),empty_set)
| in(sK3(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(powerset(singleton(X0)))))))),X1,X2),X2)
| ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( relation_image(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(powerset(singleton(X0)))))))),X1) = X2 )
| ~ function(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(powerset(singleton(X0)))))))))
| ~ relation(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(powerset(singleton(X0))))))))) ),
inference(superposition,[status(thm)],[c_12712,c_58]) ).
tcf(c_32995,plain,
! [X0: $i] :
( empty(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(powerset(singleton(X0)))))))))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ~ empty(empty_set)
| ~ relation(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(powerset(singleton(X0))))))))) ),
inference(superposition,[status(thm)],[c_12712,c_71]) ).
tcf(c_32999,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(powerset(singleton(X1)))))))),X2,X0),empty_set)
| ( sK15(sK15(powerset(singleton(X1)))) = X1 )
| ~ function(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(powerset(singleton(X1)))))))))
| ~ relation(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(powerset(singleton(X1)))))))))
| ~ in(X0,relation_image(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(powerset(singleton(X1)))))))),X2)) ),
inference(superposition,[status(thm)],[c_12712,c_62]) ).
tcf(c_33000,plain,
! [X0: $i] :
( empty(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(powerset(singleton(X0)))))))))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ~ relation(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(powerset(singleton(X0))))))))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_32995,c_92]) ).
tcf(c_33004,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK15(sK15(powerset(singleton(X1)))) = X1 )
| ~ function(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(powerset(singleton(X1)))))))))
| ~ relation(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(powerset(singleton(X1)))))))))
| ~ in(X0,relation_image(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(powerset(singleton(X1)))))))),X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_32999,c_5314]) ).
tcf(c_33009,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(powerset(singleton(X0)))))))),X1,X2),X2)
| ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( relation_image(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(powerset(singleton(X0)))))))),X1) = X2 )
| ~ function(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(powerset(singleton(X0)))))))))
| ~ relation(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(powerset(singleton(X0))))))))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_32994,c_5314]) ).
tcf(c_33022,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_13746]) ).
tcf(c_33023,plain,
sK15(powerset(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(empty_set))))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_13746]) ).
tcf(c_33024,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_13746]) ).
tcf(c_33025,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_13746]) ).
tcf(c_33026,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_13746]) ).
tcf(c_33027,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_13746]) ).
tcf(c_33028,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( sK15(powerset(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_13746]) ).
tcf(c_33029,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( sK15(powerset(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_13746]) ).
tcf(c_33030,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_13746]) ).
tcf(c_33031,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_13746]) ).
tcf(c_33032,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_13746]) ).
tcf(c_33033,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_13746]) ).
tcf(c_33034,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_13746]) ).
tcf(c_33035,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_13746]) ).
tcf(c_33036,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_13746]) ).
tcf(c_33037,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_13746]) ).
tcf(c_33038,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_13746]) ).
tcf(c_33039,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(relation_image(X0,empty_set))))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_13746]) ).
tcf(c_33040,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_13746]) ).
tcf(c_33041,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_13746]) ).
tcf(c_33042,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_13746]) ).
tcf(c_33230,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(powerset(relation_dom(relation_dom(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_13820]) ).
tcf(c_33231,plain,
relation_dom(relation_dom(sK15(sK14(powerset(relation_dom(relation_dom(empty_set))))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_13820]) ).
tcf(c_33232,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(powerset(relation_dom(relation_dom(sK15(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_13820]) ).
tcf(c_33233,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(powerset(relation_dom(relation_dom(sK15(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_13820]) ).
tcf(c_33234,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(powerset(relation_dom(relation_dom(sK15(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_13820]) ).
tcf(c_33235,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(powerset(relation_dom(relation_dom(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_13820]) ).
tcf(c_33236,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( relation_dom(relation_dom(sK15(sK14(powerset(relation_dom(relation_dom(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_13820]) ).
tcf(c_33237,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( relation_dom(relation_dom(sK15(sK14(powerset(relation_dom(relation_dom(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_13820]) ).
tcf(c_33238,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(powerset(relation_dom(relation_dom(sK15(powerset(sK15(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_13820]) ).
tcf(c_33239,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(powerset(relation_dom(relation_dom(sK15(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_13820]) ).
tcf(c_33240,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(powerset(relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_13820]) ).
tcf(c_33241,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(powerset(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_13820]) ).
tcf(c_33242,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(powerset(relation_dom(relation_dom(sK15(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_13820]) ).
tcf(c_33243,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(powerset(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_13820]) ).
tcf(c_33244,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(powerset(relation_dom(relation_dom(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_13820]) ).
tcf(c_33245,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(powerset(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_13820]) ).
tcf(c_33246,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(powerset(relation_dom(relation_dom(sK15(sK14(powerset(sK15(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_13820]) ).
tcf(c_33247,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(powerset(relation_dom(relation_dom(sK15(sK14(powerset(relation_image(X0,empty_set))))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_13820]) ).
tcf(c_33248,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(powerset(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_13820]) ).
tcf(c_33249,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(powerset(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_13820]) ).
tcf(c_33250,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(powerset(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_13820]) ).
tcf(c_33406,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(powerset(relation_dom(relation_dom(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_13924]) ).
tcf(c_33407,plain,
sK15(sK14(powerset(sK15(powerset(relation_dom(relation_dom(empty_set))))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_13924]) ).
tcf(c_33408,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(powerset(relation_dom(relation_dom(sK15(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_13924]) ).
tcf(c_33409,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(powerset(relation_dom(relation_dom(sK15(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_13924]) ).
tcf(c_33410,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(powerset(relation_dom(relation_dom(sK15(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_13924]) ).
tcf(c_33411,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(powerset(relation_dom(relation_dom(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_13924]) ).
tcf(c_33412,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( sK15(sK14(powerset(sK15(powerset(relation_dom(relation_dom(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_13924]) ).
tcf(c_33413,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( sK15(sK14(powerset(sK15(powerset(relation_dom(relation_dom(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_13924]) ).
tcf(c_33414,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(powerset(relation_dom(relation_dom(sK15(powerset(sK15(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_13924]) ).
tcf(c_33415,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(powerset(relation_dom(relation_dom(sK15(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_13924]) ).
tcf(c_33416,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(powerset(relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_13924]) ).
tcf(c_33417,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(powerset(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_13924]) ).
tcf(c_33418,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(powerset(relation_dom(relation_dom(sK15(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_13924]) ).
tcf(c_33419,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(powerset(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_13924]) ).
tcf(c_33420,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(powerset(relation_dom(relation_dom(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_13924]) ).
tcf(c_33421,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(powerset(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_13924]) ).
tcf(c_33422,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(powerset(relation_dom(relation_dom(sK15(sK14(powerset(sK15(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_13924]) ).
tcf(c_33423,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(powerset(relation_dom(relation_dom(sK15(sK14(powerset(relation_image(X0,empty_set))))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_13924]) ).
tcf(c_33424,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(powerset(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_13924]) ).
tcf(c_33425,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(powerset(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_13924]) ).
tcf(c_33426,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(powerset(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_13924]) ).
tcf(c_33517,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_14000]) ).
tcf(c_33518,plain,
sK15(sK14(powerset(relation_dom(relation_dom(relation_dom(relation_dom(empty_set))))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_14000]) ).
tcf(c_33519,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_14000]) ).
tcf(c_33520,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_14000]) ).
tcf(c_33521,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_14000]) ).
tcf(c_33522,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(relation_dom(relation_dom(relation_dom(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_14000]) ).
tcf(c_33523,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( sK15(sK14(powerset(relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_14000]) ).
tcf(c_33524,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( sK15(sK14(powerset(relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_14000]) ).
tcf(c_33525,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_14000]) ).
tcf(c_33526,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_14000]) ).
tcf(c_33527,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_14000]) ).
tcf(c_33528,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_14000]) ).
tcf(c_33529,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_14000]) ).
tcf(c_33530,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_14000]) ).
tcf(c_33531,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_14000]) ).
tcf(c_33532,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_14000]) ).
tcf(c_33533,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_14000]) ).
tcf(c_33534,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(relation_image(X0,empty_set))))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_14000]) ).
tcf(c_33535,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_14000]) ).
tcf(c_33536,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_14000]) ).
tcf(c_33537,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_14000]) ).
tcf(c_33683,plain,
! [X0: $i] :
( empty(X0)
| element(sK15(sK14(sK14(sK14(sK14(sK14(X0)))))),X0) ),
inference(global_subsumption_just,[status(thm)],[c_14102,c_98,c_14102]) ).
tcf(c_33690,plain,
! [X0: $i] :
( empty(X0)
| in(sK15(sK14(sK14(sK14(sK14(sK14(X0)))))),X0) ),
inference(superposition,[status(thm)],[c_33683,c_66]) ).
tcf(c_33691,plain,
! [X0: $i,X1: $i] :
( empty(powerset(X1))
| element(X0,X1)
| ~ in(X0,sK15(sK14(sK14(sK14(sK14(sK14(powerset(X1)))))))) ),
inference(superposition,[status(thm)],[c_33683,c_94]) ).
tcf(c_33692,plain,
! [X0: $i,X1: $i] :
( empty(powerset(X1))
| ~ empty(X1)
| ~ in(X0,sK15(sK14(sK14(sK14(sK14(sK14(powerset(X1)))))))) ),
inference(superposition,[status(thm)],[c_33683,c_93]) ).
tcf(c_33695,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ in(X0,sK15(sK14(sK14(sK14(sK14(sK14(powerset(X1)))))))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_33692,c_100]) ).
tcf(c_33698,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| ~ in(X0,sK15(sK14(sK14(sK14(sK14(sK14(powerset(X1)))))))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_33691,c_100]) ).
tcf(c_33774,plain,
! [X0: $i,X1: $i] :
( empty(relation_image(X0,X1))
| ( apply(X0,sK5(X0,X1,sK15(sK14(sK14(sK14(sK14(sK14(relation_image(X0,X1))))))))) = sK15(sK14(sK14(sK14(sK14(sK14(relation_image(X0,X1))))))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_33690,c_64]) ).
tcf(c_33775,plain,
! [X0: $i] :
( empty(X0)
| ~ in(X0,sK15(sK14(sK14(sK14(sK14(sK14(X0))))))) ),
inference(superposition,[status(thm)],[c_33690,c_68]) ).
tcf(c_33778,plain,
! [X0: $i] :
( empty(singleton(X0))
| ( sK15(sK14(sK14(sK14(sK14(sK14(singleton(X0))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_33690,c_82]) ).
tcf(c_33779,plain,
! [X0: $i] :
( empty(X0)
| empty(sK14(X0))
| element(sK15(sK14(sK14(sK14(sK14(sK14(sK14(X0))))))),X0) ),
inference(superposition,[status(thm)],[c_33690,c_5328]) ).
tcf(c_33780,plain,
! [X0: $i] :
( empty(sK15(powerset(X0)))
| element(sK15(sK14(sK14(sK14(sK14(sK14(sK15(powerset(X0)))))))),X0) ),
inference(superposition,[status(thm)],[c_33690,c_5329]) ).
tcf(c_33784,plain,
! [X0: $i] :
( empty(sK15(sK14(powerset(X0))))
| element(sK15(sK14(sK14(sK14(sK14(sK14(sK15(sK14(powerset(X0))))))))),X0) ),
inference(superposition,[status(thm)],[c_33690,c_6063]) ).
tcf(c_33786,plain,
! [X0: $i] :
( empty(sK15(sK14(sK14(powerset(X0)))))
| element(sK15(sK14(sK14(sK14(sK14(sK14(sK15(sK14(sK14(powerset(X0)))))))))),X0) ),
inference(superposition,[status(thm)],[c_33690,c_7006]) ).
tcf(c_33788,plain,
! [X0: $i] :
( empty(sK15(sK14(sK14(sK14(powerset(X0))))))
| element(sK15(sK14(sK14(sK14(sK14(sK14(sK15(sK14(sK14(sK14(powerset(X0))))))))))),X0) ),
inference(superposition,[status(thm)],[c_33690,c_9254]) ).
tcf(c_33790,plain,
! [X0: $i] :
( empty(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))
| element(sK15(sK14(sK14(sK14(sK14(sK14(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))),X0) ),
inference(superposition,[status(thm)],[c_33690,c_14088]) ).
tcf(c_33794,plain,
! [X0: $i] : sK15(sK14(sK14(sK14(sK14(sK14(singleton(X0))))))) = X0,
inference(forward_subsumption_resolution,[status(thm)],[c_33778,c_78]) ).
tcf(c_33821,plain,
! [X0: $i] :
( empty(sK14(sK14(sK14(sK14(sK14(singleton(X0)))))))
| ~ in(sK14(sK14(sK14(sK14(sK14(singleton(X0)))))),X0) ),
inference(superposition,[status(thm)],[c_33794,c_5145]) ).
tcf(c_33822,plain,
! [X0: $i] :
( empty(sK14(sK14(sK14(sK14(sK14(singleton(X0)))))))
| in(X0,sK14(sK14(sK14(sK14(sK14(singleton(X0))))))) ),
inference(superposition,[status(thm)],[c_33794,c_5124]) ).
tcf(c_33823,plain,
! [X0: $i] : element(X0,sK14(sK14(sK14(sK14(sK14(singleton(X0))))))),
inference(superposition,[status(thm)],[c_33794,c_99]) ).
tcf(c_33855,plain,
( empty(sK15(powerset(empty_set)))
| element(sK15(sK14(sK14(sK14(sK14(empty_set))))),empty_set) ),
inference(superposition,[status(thm)],[c_5301,c_14103]) ).
tcf(c_33856,plain,
! [X0: $i] :
( empty(sK15(powerset(sK15(sK14(sK14(powerset(sK15(powerset(singleton(X0))))))))))
| element(sK15(sK14(sK14(sK14(sK14(empty_set))))),sK15(sK14(sK14(powerset(sK15(powerset(singleton(X0))))))))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 ) ),
inference(superposition,[status(thm)],[c_12707,c_14103]) ).
tcf(c_33857,plain,
! [X0: $i] :
( empty(sK15(powerset(relation_dom(relation_dom(sK15(powerset(sK15(powerset(singleton(X0))))))))))
| element(sK15(sK14(sK14(sK14(sK14(empty_set))))),relation_dom(relation_dom(sK15(powerset(sK15(powerset(singleton(X0))))))))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 ) ),
inference(superposition,[status(thm)],[c_12710,c_14103]) ).
tcf(c_33858,plain,
! [X0: $i] :
( empty(X0)
| empty(sK15(powerset(X0)))
| in(sK15(sK14(sK14(sK14(sK14(sK15(powerset(X0))))))),X0) ),
inference(superposition,[status(thm)],[c_14103,c_66]) ).
tcf(c_33859,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| empty(sK15(powerset(powerset(X1))))
| ~ in(X0,sK15(sK14(sK14(sK14(sK14(sK15(powerset(powerset(X1))))))))) ),
inference(superposition,[status(thm)],[c_14103,c_94]) ).
tcf(c_33860,plain,
! [X0: $i,X1: $i] :
( empty(sK15(powerset(powerset(X1))))
| ~ empty(X1)
| ~ in(X0,sK15(sK14(sK14(sK14(sK14(sK15(powerset(powerset(X1))))))))) ),
inference(superposition,[status(thm)],[c_14103,c_93]) ).
tcf(c_33861,plain,
( empty(empty_set)
| element(sK15(sK14(sK14(sK14(sK14(empty_set))))),empty_set) ),
inference(light_normalisation,[status(thm)],[c_33855,c_5301]) ).
tcf(c_33944,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(relation_dom(relation_dom(relation_dom(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_14212]) ).
tcf(c_33945,plain,
relation_dom(sK15(sK14(powerset(relation_dom(relation_dom(relation_dom(empty_set))))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_14212]) ).
tcf(c_33946,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(relation_dom(relation_dom(relation_dom(sK15(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_14212]) ).
tcf(c_33947,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_14212]) ).
tcf(c_33948,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_14212]) ).
tcf(c_33949,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(relation_dom(relation_dom(relation_dom(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_14212]) ).
tcf(c_33950,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( relation_dom(sK15(sK14(powerset(relation_dom(relation_dom(relation_dom(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_14212]) ).
tcf(c_33951,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( relation_dom(sK15(sK14(powerset(relation_dom(relation_dom(relation_dom(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_14212]) ).
tcf(c_33952,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_14212]) ).
tcf(c_33953,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(relation_dom(relation_dom(relation_dom(sK15(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_14212]) ).
tcf(c_33954,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_14212]) ).
tcf(c_33955,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_14212]) ).
tcf(c_33956,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_14212]) ).
tcf(c_33957,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_14212]) ).
tcf(c_33958,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_14212]) ).
tcf(c_33959,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_14212]) ).
tcf(c_33960,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_14212]) ).
tcf(c_33961,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(relation_image(X0,empty_set))))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_14212]) ).
tcf(c_33962,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_14212]) ).
tcf(c_33963,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_14212]) ).
tcf(c_33964,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_14212]) ).
tcf(c_34069,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(powerset(relation_dom(relation_dom(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_14260]) ).
tcf(c_34070,plain,
relation_dom(sK15(sK14(sK14(powerset(relation_dom(relation_dom(empty_set))))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_14260]) ).
tcf(c_34071,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(powerset(relation_dom(relation_dom(sK15(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_14260]) ).
tcf(c_34072,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(powerset(relation_dom(relation_dom(sK15(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_14260]) ).
tcf(c_34073,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(powerset(relation_dom(relation_dom(sK15(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_14260]) ).
tcf(c_34074,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(powerset(relation_dom(relation_dom(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_14260]) ).
tcf(c_34075,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( relation_dom(sK15(sK14(sK14(powerset(relation_dom(relation_dom(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_14260]) ).
tcf(c_34076,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( relation_dom(sK15(sK14(sK14(powerset(relation_dom(relation_dom(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_14260]) ).
tcf(c_34077,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(powerset(relation_dom(relation_dom(sK15(powerset(sK15(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_14260]) ).
tcf(c_34078,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(powerset(relation_dom(relation_dom(sK15(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_14260]) ).
tcf(c_34079,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(powerset(relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_14260]) ).
tcf(c_34080,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(powerset(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_14260]) ).
tcf(c_34081,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(powerset(relation_dom(relation_dom(sK15(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_14260]) ).
tcf(c_34082,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(powerset(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_14260]) ).
tcf(c_34083,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(powerset(relation_dom(relation_dom(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_14260]) ).
tcf(c_34084,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(powerset(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_14260]) ).
tcf(c_34085,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(powerset(relation_dom(relation_dom(sK15(sK14(powerset(sK15(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_14260]) ).
tcf(c_34086,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(powerset(relation_dom(relation_dom(sK15(sK14(powerset(relation_image(X0,empty_set))))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_14260]) ).
tcf(c_34087,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(powerset(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_14260]) ).
tcf(c_34088,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(powerset(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_14260]) ).
tcf(c_34089,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(powerset(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_14260]) ).
tcf(c_34263,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(relation_dom(relation_dom(relation_dom(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_14357]) ).
tcf(c_34264,plain,
sK15(sK14(sK14(powerset(relation_dom(relation_dom(relation_dom(empty_set))))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_14357]) ).
tcf(c_34265,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(relation_dom(relation_dom(relation_dom(sK15(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_14357]) ).
tcf(c_34266,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_14357]) ).
tcf(c_34267,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_14357]) ).
tcf(c_34268,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(relation_dom(relation_dom(relation_dom(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_14357]) ).
tcf(c_34269,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( sK15(sK14(sK14(powerset(relation_dom(relation_dom(relation_dom(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_14357]) ).
tcf(c_34270,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( sK15(sK14(sK14(powerset(relation_dom(relation_dom(relation_dom(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_14357]) ).
tcf(c_34271,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_14357]) ).
tcf(c_34272,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(relation_dom(relation_dom(relation_dom(sK15(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_14357]) ).
tcf(c_34273,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_14357]) ).
tcf(c_34274,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_14357]) ).
tcf(c_34275,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_14357]) ).
tcf(c_34276,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_14357]) ).
tcf(c_34277,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_14357]) ).
tcf(c_34278,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_14357]) ).
tcf(c_34279,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_14357]) ).
tcf(c_34280,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(relation_image(X0,empty_set))))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_14357]) ).
tcf(c_34281,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_14357]) ).
tcf(c_34282,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_14357]) ).
tcf(c_34283,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_14357]) ).
tcf(c_34375,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(sK14(powerset(relation_dom(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_14491]) ).
tcf(c_34376,plain,
relation_dom(sK15(sK14(sK14(sK14(powerset(relation_dom(empty_set))))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_14491]) ).
tcf(c_34377,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(sK14(powerset(relation_dom(sK15(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_14491]) ).
tcf(c_34378,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(sK14(powerset(relation_dom(sK15(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_14491]) ).
tcf(c_34379,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(sK14(powerset(relation_dom(sK15(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_14491]) ).
tcf(c_34380,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(sK14(powerset(relation_dom(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_14491]) ).
tcf(c_34381,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( relation_dom(sK15(sK14(sK14(sK14(powerset(relation_dom(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_14491]) ).
tcf(c_34382,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( relation_dom(sK15(sK14(sK14(sK14(powerset(relation_dom(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_14491]) ).
tcf(c_34383,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(sK14(powerset(relation_dom(sK15(powerset(sK15(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_14491]) ).
tcf(c_34384,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(sK14(powerset(relation_dom(sK15(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_14491]) ).
tcf(c_34385,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(sK14(powerset(relation_dom(sK15(powerset(sK15(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_14491]) ).
tcf(c_34386,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(sK14(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_14491]) ).
tcf(c_34387,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(sK14(powerset(relation_dom(sK15(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_14491]) ).
tcf(c_34388,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(sK14(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_14491]) ).
tcf(c_34389,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(sK14(powerset(relation_dom(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_14491]) ).
tcf(c_34390,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(sK14(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_14491]) ).
tcf(c_34391,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(sK14(powerset(relation_dom(sK15(sK14(powerset(sK15(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_14491]) ).
tcf(c_34392,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(sK14(powerset(relation_dom(sK15(sK14(powerset(relation_image(X0,empty_set))))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_14491]) ).
tcf(c_34393,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(sK14(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_14491]) ).
tcf(c_34394,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(sK14(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_14491]) ).
tcf(c_34395,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(sK14(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_14491]) ).
tcf(c_34487,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(powerset(relation_dom(relation_dom(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_14554]) ).
tcf(c_34488,plain,
sK15(sK14(sK14(sK14(powerset(relation_dom(relation_dom(empty_set))))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_14554]) ).
tcf(c_34489,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(powerset(relation_dom(relation_dom(sK15(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_14554]) ).
tcf(c_34490,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(powerset(relation_dom(relation_dom(sK15(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_14554]) ).
tcf(c_34491,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(powerset(relation_dom(relation_dom(sK15(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_14554]) ).
tcf(c_34492,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(powerset(relation_dom(relation_dom(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_14554]) ).
tcf(c_34493,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( sK15(sK14(sK14(sK14(powerset(relation_dom(relation_dom(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_14554]) ).
tcf(c_34494,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( sK15(sK14(sK14(sK14(powerset(relation_dom(relation_dom(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_14554]) ).
tcf(c_34495,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(powerset(relation_dom(relation_dom(sK15(powerset(sK15(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_14554]) ).
tcf(c_34496,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(powerset(relation_dom(relation_dom(sK15(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_14554]) ).
tcf(c_34497,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(powerset(relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_14554]) ).
tcf(c_34498,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(powerset(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_14554]) ).
tcf(c_34499,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(powerset(relation_dom(relation_dom(sK15(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_14554]) ).
tcf(c_34500,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(powerset(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_14554]) ).
tcf(c_34501,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(powerset(relation_dom(relation_dom(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_14554]) ).
tcf(c_34502,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(powerset(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_14554]) ).
tcf(c_34503,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(powerset(relation_dom(relation_dom(sK15(sK14(powerset(sK15(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_14554]) ).
tcf(c_34504,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(powerset(relation_dom(relation_dom(sK15(sK14(powerset(relation_image(X0,empty_set))))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_14554]) ).
tcf(c_34505,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(powerset(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_14554]) ).
tcf(c_34506,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(powerset(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_14554]) ).
tcf(c_34507,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(powerset(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_14554]) ).
tcf(c_34647,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK4(relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(powerset(singleton(X0)))))))),X1,X2),empty_set)
| in(sK3(relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(powerset(singleton(X0)))))))),X1,X2),X2)
| ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( relation_image(relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(powerset(singleton(X0)))))))),X1) = X2 )
| ~ function(relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(powerset(singleton(X0)))))))))
| ~ relation(relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(powerset(singleton(X0))))))))) ),
inference(superposition,[status(thm)],[c_12713,c_58]) ).
tcf(c_34648,plain,
! [X0: $i] :
( empty(relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(powerset(singleton(X0)))))))))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ~ empty(empty_set)
| ~ relation(relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(powerset(singleton(X0))))))))) ),
inference(superposition,[status(thm)],[c_12713,c_71]) ).
tcf(c_34652,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(powerset(singleton(X1)))))))),X2,X0),empty_set)
| ( sK15(sK15(powerset(singleton(X1)))) = X1 )
| ~ function(relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(powerset(singleton(X1)))))))))
| ~ relation(relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(powerset(singleton(X1)))))))))
| ~ in(X0,relation_image(relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(powerset(singleton(X1)))))))),X2)) ),
inference(superposition,[status(thm)],[c_12713,c_62]) ).
tcf(c_34653,plain,
! [X0: $i] :
( empty(relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(powerset(singleton(X0)))))))))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ~ relation(relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(powerset(singleton(X0))))))))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_34648,c_92]) ).
tcf(c_34657,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK15(sK15(powerset(singleton(X1)))) = X1 )
| ~ function(relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(powerset(singleton(X1)))))))))
| ~ relation(relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(powerset(singleton(X1)))))))))
| ~ in(X0,relation_image(relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(powerset(singleton(X1)))))))),X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_34652,c_5314]) ).
tcf(c_34662,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(powerset(singleton(X0)))))))),X1,X2),X2)
| ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( relation_image(relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(powerset(singleton(X0)))))))),X1) = X2 )
| ~ function(relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(powerset(singleton(X0)))))))))
| ~ relation(relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(powerset(singleton(X0))))))))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_34647,c_5314]) ).
tcf(c_34675,plain,
! [X0: $i] :
( in(X0,empty_set)
| element(sK2(sK14(singleton(X0)),empty_set),sK14(singleton(X0)))
| ( sK14(singleton(X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_14658,c_5077]) ).
tcf(c_34677,plain,
! [X0: $i] :
( in(X0,sK14(singleton(X0)))
| element(sK2(sK14(singleton(X0)),empty_set),empty_set)
| ( sK14(singleton(X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_14658,c_5076]) ).
tcf(c_34679,plain,
! [X0: $i] :
( ( sK14(singleton(X0)) = empty_set )
| ~ empty(empty_set)
| ~ in(sK14(singleton(X0)),X0) ),
inference(superposition,[status(thm)],[c_14658,c_7508]) ).
tcf(c_34681,plain,
! [X0: $i] :
( in(X0,empty_set)
| ( sK14(singleton(X0)) = empty_set )
| ~ empty(sK14(singleton(X0))) ),
inference(superposition,[status(thm)],[c_14658,c_5063]) ).
tcf(c_34683,plain,
! [X0: $i] :
( in(X0,sK14(singleton(X0)))
| in(sK2(sK14(singleton(X0)),empty_set),empty_set)
| ( sK14(singleton(X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_14658,c_56]) ).
tcf(c_34684,plain,
! [X0: $i] :
( in(X0,empty_set)
| in(sK2(sK14(singleton(X0)),empty_set),sK14(singleton(X0)))
| ( sK14(singleton(X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_14658,c_56]) ).
tcf(c_34686,plain,
! [X0: $i] :
( ( sK14(singleton(X0)) = empty_set )
| ~ in(empty_set,X0)
| ~ empty(sK14(singleton(X0))) ),
inference(superposition,[status(thm)],[c_14658,c_7586]) ).
tcf(c_34690,plain,
! [X0: $i] :
( ( sK14(singleton(X0)) = empty_set )
| ~ in(sK14(singleton(X0)),X0) ),
inference(superposition,[status(thm)],[c_14658,c_5467]) ).
tcf(c_34692,plain,
! [X0: $i] :
( in(X0,sK14(singleton(X0)))
| ( sK14(singleton(X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_14658,c_5409]) ).
tcf(c_34700,plain,
! [X0: $i] :
( ( sK14(singleton(X0)) = empty_set )
| ~ empty(sK14(singleton(X0))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_34681,c_5314]) ).
tcf(c_34707,plain,
! [X0: $i] :
( in(sK2(sK14(singleton(X0)),empty_set),sK14(singleton(X0)))
| ( sK14(singleton(X0)) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_34684,c_5314]) ).
tcf(c_34714,plain,
! [X0: $i] :
( element(sK2(sK14(singleton(X0)),empty_set),sK14(singleton(X0)))
| ( sK14(singleton(X0)) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_34675,c_5314]) ).
tcf(c_34794,plain,
! [X0: $i] :
( in(X0,sK14(singleton(X0)))
| element(sK2(empty_set,sK14(singleton(X0))),empty_set)
| ( sK14(singleton(X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_14782,c_5077]) ).
tcf(c_34796,plain,
! [X0: $i] :
( in(X0,empty_set)
| element(sK2(empty_set,sK14(singleton(X0))),sK14(singleton(X0)))
| ( sK14(singleton(X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_14782,c_5076]) ).
tcf(c_34802,plain,
! [X0: $i] :
( in(X0,empty_set)
| in(sK2(empty_set,sK14(singleton(X0))),sK14(singleton(X0)))
| ( sK14(singleton(X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_14782,c_56]) ).
tcf(c_34803,plain,
! [X0: $i] :
( in(X0,sK14(singleton(X0)))
| in(sK2(empty_set,sK14(singleton(X0))),empty_set)
| ( sK14(singleton(X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_14782,c_56]) ).
tcf(c_34804,plain,
! [X0: $i] :
( ( sK14(singleton(X0)) = empty_set )
| ~ in(X0,sK14(singleton(X0)))
| ~ in(sK2(empty_set,sK14(singleton(X0))),empty_set) ),
inference(superposition,[status(thm)],[c_14782,c_55]) ).
tcf(c_34816,plain,
! [X0: $i] :
( in(sK2(empty_set,sK14(singleton(X0))),sK14(singleton(X0)))
| ( sK14(singleton(X0)) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_34802,c_5314]) ).
tcf(c_34819,plain,
! [X0: $i] :
( element(sK2(empty_set,sK14(singleton(X0))),sK14(singleton(X0)))
| ( sK14(singleton(X0)) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_34796,c_5314]) ).
tcf(c_34833,plain,
! [X0: $i] :
( element(X0,empty_set)
| element(sK2(singleton(X0),empty_set),singleton(X0))
| ( singleton(X0) = empty_set ) ),
inference(superposition,[status(thm)],[c_9153,c_15593]) ).
tcf(c_34835,plain,
! [X0: $i,X1: $i] :
( element(X0,singleton(X1))
| element(sK2(singleton(X0),singleton(X1)),singleton(X0))
| ( singleton(X0) = singleton(X1) )
| ( sK2(singleton(X0),singleton(X1)) = X1 ) ),
inference(superposition,[status(thm)],[c_11036,c_15593]) ).
tcf(c_34836,plain,
! [X0: $i,X1: $i] :
( element(X1,singleton(X1))
| element(sK2(singleton(X0),singleton(X1)),singleton(X0))
| ( singleton(X0) = singleton(X1) )
| ( sK2(singleton(X0),singleton(X1)) = X0 ) ),
inference(superposition,[status(thm)],[c_11036,c_15593]) ).
tcf(c_34840,plain,
! [X0: $i] :
( element(X0,empty_set)
| element(sK2(empty_set,singleton(X0)),singleton(X0))
| ( singleton(X0) = empty_set ) ),
inference(superposition,[status(thm)],[c_9564,c_15593]) ).
tcf(c_34842,plain,
! [X0: $i,X1: $i] :
( element(X1,singleton(X0))
| element(sK2(singleton(X0),singleton(X1)),singleton(X1))
| ( singleton(X0) = singleton(X1) )
| ( sK2(singleton(X0),singleton(X1)) = X0 ) ),
inference(superposition,[status(thm)],[c_11036,c_15593]) ).
tcf(c_34846,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,X2)
| element(sK2(X1,powerset(X2)),X1)
| ( powerset(X2) = X1 )
| ~ in(X0,sK2(X1,powerset(X2))) ),
inference(superposition,[status(thm)],[c_15593,c_94]) ).
tcf(c_34847,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X1,powerset(X2)),X1)
| ( powerset(X2) = X1 )
| ~ empty(X2)
| ~ in(X0,sK2(X1,powerset(X2))) ),
inference(superposition,[status(thm)],[c_15593,c_93]) ).
tcf(c_34849,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,X1)
| element(sK2(powerset(X1),X2),X2)
| ( powerset(X1) = X2 )
| ~ in(X0,sK2(powerset(X1),X2)) ),
inference(superposition,[status(thm)],[c_15593,c_94]) ).
tcf(c_34850,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(powerset(X1),X2),X2)
| ( powerset(X1) = X2 )
| ~ empty(X1)
| ~ in(X0,sK2(powerset(X1),X2)) ),
inference(superposition,[status(thm)],[c_15593,c_93]) ).
tcf(c_34853,plain,
! [X0: $i] :
( element(X0,empty_set)
| element(X0,singleton(X0))
| ( singleton(X0) = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_34840,c_9564]) ).
tcf(c_34899,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(sK14(sK14(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_14996]) ).
tcf(c_34900,plain,
relation_dom(sK15(sK14(sK14(sK14(sK14(powerset(empty_set))))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_14996]) ).
tcf(c_34901,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(sK14(sK14(powerset(sK15(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_14996]) ).
tcf(c_34902,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(sK14(sK14(powerset(sK15(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_14996]) ).
tcf(c_34903,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(sK14(sK14(powerset(sK15(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_14996]) ).
tcf(c_34904,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(sK14(sK14(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_14996]) ).
tcf(c_34905,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( relation_dom(sK15(sK14(sK14(sK14(sK14(powerset(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_14996]) ).
tcf(c_34906,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( relation_dom(sK15(sK14(sK14(sK14(sK14(powerset(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_14996]) ).
tcf(c_34907,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(sK14(sK14(powerset(sK15(powerset(sK15(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_14996]) ).
tcf(c_34908,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(sK14(sK14(powerset(sK15(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_14996]) ).
tcf(c_34909,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(sK14(sK14(powerset(sK15(powerset(sK15(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_14996]) ).
tcf(c_34910,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(sK14(sK14(powerset(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_14996]) ).
tcf(c_34911,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(sK14(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_14996]) ).
tcf(c_34912,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(sK14(sK14(powerset(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_14996]) ).
tcf(c_34913,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(sK14(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_14996]) ).
tcf(c_34914,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(sK14(sK14(powerset(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_14996]) ).
tcf(c_34915,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(sK14(sK14(powerset(sK15(sK14(powerset(sK15(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_14996]) ).
tcf(c_34916,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(sK14(sK14(powerset(sK15(sK14(powerset(relation_image(X0,empty_set))))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_14996]) ).
tcf(c_34917,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(sK14(sK14(powerset(sK15(sK14(powerset(sK15(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_14996]) ).
tcf(c_34918,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(sK14(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_14996]) ).
tcf(c_34919,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(sK14(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_14996]) ).
tcf(c_35243,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(sK14(powerset(relation_dom(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_15859]) ).
tcf(c_35244,plain,
sK15(sK14(sK14(sK14(sK14(powerset(relation_dom(empty_set))))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_15859]) ).
tcf(c_35245,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(sK14(powerset(relation_dom(sK15(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_15859]) ).
tcf(c_35246,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(sK14(powerset(relation_dom(sK15(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_15859]) ).
tcf(c_35247,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(sK14(powerset(relation_dom(sK15(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_15859]) ).
tcf(c_35248,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(sK14(powerset(relation_dom(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_15859]) ).
tcf(c_35249,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( sK15(sK14(sK14(sK14(sK14(powerset(relation_dom(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_15859]) ).
tcf(c_35250,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( sK15(sK14(sK14(sK14(sK14(powerset(relation_dom(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_15859]) ).
tcf(c_35251,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(sK14(powerset(relation_dom(sK15(powerset(sK15(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_15859]) ).
tcf(c_35252,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(sK14(powerset(relation_dom(sK15(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_15859]) ).
tcf(c_35253,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(sK14(powerset(relation_dom(sK15(powerset(sK15(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_15859]) ).
tcf(c_35254,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(sK14(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_15859]) ).
tcf(c_35255,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(sK14(powerset(relation_dom(sK15(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_15859]) ).
tcf(c_35256,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(sK14(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_15859]) ).
tcf(c_35257,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(sK14(powerset(relation_dom(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_15859]) ).
tcf(c_35258,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(sK14(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_15859]) ).
tcf(c_35259,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(sK14(powerset(relation_dom(sK15(sK14(powerset(sK15(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_15859]) ).
tcf(c_35260,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(sK14(powerset(relation_dom(sK15(sK14(powerset(relation_image(X0,empty_set))))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_15859]) ).
tcf(c_35261,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(sK14(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_15859]) ).
tcf(c_35262,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(sK14(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_15859]) ).
tcf(c_35263,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(sK14(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_15859]) ).
tcf(c_35351,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(relation_image(X0,X1))
| ( sK14(relation_image(X0,X1)) = empty_set )
| ( apply(X0,sK5(X0,X1,sK3(empty_set,X2,sK14(relation_image(X0,X1))))) = sK3(empty_set,X2,sK14(relation_image(X0,X1))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16394,c_64]) ).
tcf(c_35352,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| ( sK14(X0) = empty_set )
| ~ in(X0,sK3(empty_set,X1,sK14(X0))) ),
inference(superposition,[status(thm)],[c_16394,c_68]) ).
tcf(c_35355,plain,
! [X0: $i,X1: $i] :
( empty(singleton(X1))
| ( sK14(singleton(X1)) = empty_set )
| ( sK3(empty_set,X0,sK14(singleton(X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_16394,c_82]) ).
tcf(c_35356,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| empty(sK14(X0))
| element(sK3(empty_set,X1,sK14(sK14(X0))),X0)
| ( sK14(sK14(X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_16394,c_5328]) ).
tcf(c_35357,plain,
! [X0: $i,X1: $i] :
( empty(sK15(powerset(X0)))
| element(sK3(empty_set,X1,sK14(sK15(powerset(X0)))),X0)
| ( sK14(sK15(powerset(X0))) = empty_set ) ),
inference(superposition,[status(thm)],[c_16394,c_5329]) ).
tcf(c_35361,plain,
! [X0: $i,X1: $i] :
( empty(sK15(sK14(powerset(X0))))
| element(sK3(empty_set,X1,sK14(sK15(sK14(powerset(X0))))),X0)
| ( sK14(sK15(sK14(powerset(X0)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_16394,c_6063]) ).
tcf(c_35363,plain,
! [X0: $i,X1: $i] :
( empty(sK15(sK14(sK14(powerset(X0)))))
| element(sK3(empty_set,X1,sK14(sK15(sK14(sK14(powerset(X0)))))),X0)
| ( sK14(sK15(sK14(sK14(powerset(X0))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_16394,c_7006]) ).
tcf(c_35365,plain,
! [X0: $i,X1: $i] :
( empty(sK15(sK14(sK14(sK14(powerset(X0))))))
| element(sK3(empty_set,X1,sK14(sK15(sK14(sK14(sK14(powerset(X0))))))),X0)
| ( sK14(sK15(sK14(sK14(sK14(powerset(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_16394,c_9254]) ).
tcf(c_35367,plain,
! [X0: $i,X1: $i] :
( empty(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))
| element(sK3(empty_set,X1,sK14(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))),X0)
| ( sK14(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_16394,c_14088]) ).
tcf(c_35372,plain,
! [X0: $i,X1: $i] :
( ( sK14(singleton(X1)) = empty_set )
| ( sK3(empty_set,X0,sK14(singleton(X1))) = X1 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_35355,c_78]) ).
tcf(c_35464,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(sK14(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_15859]) ).
tcf(c_35465,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(sK14(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_14996]) ).
tcf(c_35466,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(powerset(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_14554]) ).
tcf(c_35467,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(sK14(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_14491]) ).
tcf(c_35468,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_14357]) ).
tcf(c_35469,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(powerset(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_14260]) ).
tcf(c_35470,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_14212]) ).
tcf(c_35471,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_14000]) ).
tcf(c_35472,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(powerset(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_13924]) ).
tcf(c_35473,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(powerset(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_13820]) ).
tcf(c_35474,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_13746]) ).
tcf(c_35475,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_13650]) ).
tcf(c_35476,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_13554]) ).
tcf(c_35477,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_13471]) ).
tcf(c_35478,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(powerset(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_13409]) ).
tcf(c_35479,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_13342]) ).
tcf(c_35480,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(powerset(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_13215]) ).
tcf(c_35481,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_13155]) ).
tcf(c_35482,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_13072]) ).
tcf(c_35483,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_12539]) ).
tcf(c_35484,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(sK14(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_12496]) ).
tcf(c_35485,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(sK14(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_12393]) ).
tcf(c_35486,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(powerset(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_10889]) ).
tcf(c_35487,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_12362]) ).
tcf(c_35488,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_12319]) ).
tcf(c_35489,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_12288]) ).
tcf(c_35490,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_12185]) ).
tcf(c_35491,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(sK14(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_10134]) ).
tcf(c_35492,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(sK14(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_10133]) ).
tcf(c_35493,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_29462]) ).
tcf(c_35494,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_29402]) ).
tcf(c_35495,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_29268]) ).
tcf(c_35496,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_29172]) ).
tcf(c_35497,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_29266]) ).
tcf(c_35498,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_29171]) ).
tcf(c_35499,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_29169]) ).
tcf(c_35501,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_9588]) ).
tcf(c_35502,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(powerset(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_9507]) ).
tcf(c_35503,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_12137]) ).
tcf(c_35504,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_12094]) ).
tcf(c_35505,plain,
! [X0: $i,X1: $i] :
( ( sK15(powerset(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_12042]) ).
tcf(c_35506,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_11908]) ).
tcf(c_35507,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_9413]) ).
tcf(c_35508,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_9213]) ).
tcf(c_35509,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(powerset(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_9027]) ).
tcf(c_35510,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_8995]) ).
tcf(c_35511,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_8935]) ).
tcf(c_35512,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_8860]) ).
tcf(c_35513,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_8823]) ).
tcf(c_35514,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(powerset(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_8745]) ).
tcf(c_35515,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(powerset(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_8300]) ).
tcf(c_35516,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_8299]) ).
tcf(c_35517,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(powerset(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_8298]) ).
tcf(c_35518,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_11782]) ).
tcf(c_35519,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_11746]) ).
tcf(c_35520,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(sK14(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_11666]) ).
tcf(c_35521,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_11550]) ).
tcf(c_35522,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_8238]) ).
tcf(c_35523,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_8211]) ).
tcf(c_35524,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_8078]) ).
tcf(c_35525,plain,
! [X0: $i,X1: $i] :
( ( sK15(powerset(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_7740]) ).
tcf(c_35526,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(sK15(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_7685]) ).
tcf(c_35527,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(sK14(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_11491]) ).
tcf(c_35528,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(sK14(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_11438]) ).
tcf(c_35529,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK14(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_11182]) ).
tcf(c_35530,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_7252]) ).
tcf(c_35531,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(sK14(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_7251]) ).
tcf(c_35532,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(sK14(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_7250]) ).
tcf(c_35533,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(sK14(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_7249]) ).
tcf(c_35534,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_7143]) ).
tcf(c_35535,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_6954]) ).
tcf(c_35536,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_6939]) ).
tcf(c_35537,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_6906]) ).
tcf(c_35538,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_6888]) ).
tcf(c_35539,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(sK15(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_6857]) ).
tcf(c_35540,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK14(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_7255]) ).
tcf(c_35541,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_6833]) ).
tcf(c_35542,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_6798]) ).
tcf(c_35543,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))) = singleton(X1) )
| ( sK8(X1,sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))) = X1 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_5346]) ).
tcf(c_35544,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_14868]) ).
tcf(c_35545,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_10887]) ).
tcf(c_35546,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_10136]) ).
tcf(c_35547,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_9586]) ).
tcf(c_35548,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_9505]) ).
tcf(c_35549,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_9411]) ).
tcf(c_35550,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_9211]) ).
tcf(c_35551,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_9107]) ).
tcf(c_35552,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_9025]) ).
tcf(c_35553,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_8993]) ).
tcf(c_35554,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_8933]) ).
tcf(c_35555,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_8858]) ).
tcf(c_35556,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_8821]) ).
tcf(c_35557,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_8743]) ).
tcf(c_35558,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_8705]) ).
tcf(c_35559,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_8667]) ).
tcf(c_35560,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_8236]) ).
tcf(c_35561,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_8209]) ).
tcf(c_35562,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_7684]) ).
tcf(c_35563,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_7254]) ).
tcf(c_35564,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_7253]) ).
tcf(c_35565,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_7142]) ).
tcf(c_35566,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_6953]) ).
tcf(c_35567,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_6938]) ).
tcf(c_35568,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_6905]) ).
tcf(c_35569,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_6887]) ).
tcf(c_35570,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_8076]) ).
tcf(c_35571,plain,
! [X0: $i,X1: $i] :
( ( sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_7738]) ).
tcf(c_35572,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_6856]) ).
tcf(c_35573,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_6832]) ).
tcf(c_35574,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_6797]) ).
tcf(c_35575,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_6681]) ).
tcf(c_35576,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_6189]) ).
tcf(c_35577,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_6188]) ).
tcf(c_35578,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_6187]) ).
tcf(c_35579,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_6192]) ).
tcf(c_35580,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_9868]) ).
tcf(c_35581,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_7682]) ).
tcf(c_35582,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_7256]) ).
tcf(c_35583,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_7140]) ).
tcf(c_35584,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_6951]) ).
tcf(c_35585,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_6680]) ).
tcf(c_35586,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_6191]) ).
tcf(c_35587,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_6936]) ).
tcf(c_35588,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_6903]) ).
tcf(c_35589,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_6885]) ).
tcf(c_35590,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_6854]) ).
tcf(c_35591,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_6190]) ).
tcf(c_35592,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_5583]) ).
tcf(c_35593,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_5569]) ).
tcf(c_35594,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_6830]) ).
tcf(c_35595,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_6795]) ).
tcf(c_35596,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_5557]) ).
tcf(c_35597,plain,
! [X0: $i,X1: $i] :
( ( sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_5270]) ).
tcf(c_35616,plain,
! [X0: $i] :
( relation(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_87]) ).
tcf(c_35617,plain,
! [X0: $i] :
( function(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_77]) ).
tcf(c_36214,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( relation_dom(relation_dom(relation_image(sK15(powerset(singleton(X0))),empty_set))) = empty_set )
| ~ relation(sK15(powerset(singleton(X0)))) ),
inference(superposition,[status(thm)],[c_20901,c_7932]) ).
tcf(c_36215,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( sK15(powerset(relation_image(sK15(powerset(singleton(X0))),empty_set))) = empty_set )
| ~ relation(sK15(powerset(singleton(X0)))) ),
inference(superposition,[status(thm)],[c_20901,c_7931]) ).
tcf(c_36216,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( relation_dom(relation_image(sK15(powerset(singleton(X0))),empty_set)) = empty_set )
| ~ relation(sK15(powerset(singleton(X0)))) ),
inference(superposition,[status(thm)],[c_20901,c_7934]) ).
tcf(c_36217,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( relation_image(sK15(powerset(singleton(X0))),empty_set) = empty_set )
| ~ relation(sK15(powerset(singleton(X0)))) ),
inference(superposition,[status(thm)],[c_20901,c_7777]) ).
tcf(c_36240,plain,
! [X0: $i,X1: $i] :
( empty(relation_image(X0,X1))
| empty(sK15(powerset(sK14(relation_image(X0,X1)))))
| ( apply(X0,sK5(X0,X1,sK15(sK15(powerset(sK14(relation_image(X0,X1))))))) = sK15(sK15(powerset(sK14(relation_image(X0,X1))))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_22362,c_64]) ).
tcf(c_36241,plain,
! [X0: $i] :
( empty(X0)
| empty(sK15(powerset(sK14(X0))))
| ~ in(X0,sK15(sK15(powerset(sK14(X0))))) ),
inference(superposition,[status(thm)],[c_22362,c_68]) ).
tcf(c_36244,plain,
! [X0: $i] :
( empty(singleton(X0))
| empty(sK15(powerset(sK14(singleton(X0)))))
| ( sK15(sK15(powerset(sK14(singleton(X0))))) = X0 ) ),
inference(superposition,[status(thm)],[c_22362,c_82]) ).
tcf(c_36245,plain,
! [X0: $i] :
( empty(X0)
| empty(sK14(X0))
| empty(sK15(powerset(sK14(sK14(X0)))))
| element(sK15(sK15(powerset(sK14(sK14(X0))))),X0) ),
inference(superposition,[status(thm)],[c_22362,c_5328]) ).
tcf(c_36246,plain,
! [X0: $i] :
( empty(sK15(powerset(X0)))
| empty(sK15(powerset(sK14(sK15(powerset(X0))))))
| element(sK15(sK15(powerset(sK14(sK15(powerset(X0)))))),X0) ),
inference(superposition,[status(thm)],[c_22362,c_5329]) ).
tcf(c_36247,plain,
! [X0: $i] :
( empty(sK15(powerset(X0)))
| empty(sK15(powerset(sK14(sK15(powerset(X0))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_22362,c_5201]) ).
tcf(c_36249,plain,
! [X0: $i] :
( empty(relation_image(X0,empty_set))
| empty(sK15(powerset(sK14(relation_image(X0,empty_set)))))
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_22362,c_5411]) ).
tcf(c_36250,plain,
! [X0: $i] :
( empty(sK15(sK14(powerset(X0))))
| empty(sK15(powerset(sK14(sK15(sK14(powerset(X0)))))))
| element(sK15(sK15(powerset(sK14(sK15(sK14(powerset(X0))))))),X0) ),
inference(superposition,[status(thm)],[c_22362,c_6063]) ).
tcf(c_36251,plain,
! [X0: $i] :
( empty(sK15(sK14(powerset(X0))))
| empty(sK15(powerset(sK14(sK15(sK14(powerset(X0)))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_22362,c_6060]) ).
tcf(c_36252,plain,
! [X0: $i] :
( empty(sK15(sK14(sK14(powerset(X0)))))
| empty(sK15(powerset(sK14(sK15(sK14(sK14(powerset(X0))))))))
| element(sK15(sK15(powerset(sK14(sK15(sK14(sK14(powerset(X0)))))))),X0) ),
inference(superposition,[status(thm)],[c_22362,c_7006]) ).
tcf(c_36253,plain,
! [X0: $i] :
( empty(sK15(sK14(sK14(powerset(X0)))))
| empty(sK15(powerset(sK14(sK15(sK14(sK14(powerset(X0))))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_22362,c_7003]) ).
tcf(c_36254,plain,
! [X0: $i] :
( empty(sK15(sK14(sK14(sK14(powerset(X0))))))
| empty(sK15(powerset(sK14(sK15(sK14(sK14(sK14(powerset(X0)))))))))
| element(sK15(sK15(powerset(sK14(sK15(sK14(sK14(sK14(powerset(X0))))))))),X0) ),
inference(superposition,[status(thm)],[c_22362,c_9254]) ).
tcf(c_36255,plain,
! [X0: $i] :
( empty(sK15(sK14(sK14(sK14(powerset(X0))))))
| empty(sK15(powerset(sK14(sK15(sK14(sK14(sK14(powerset(X0)))))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_22362,c_9251]) ).
tcf(c_36256,plain,
! [X0: $i] :
( empty(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))
| empty(sK15(powerset(sK14(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))
| element(sK15(sK15(powerset(sK14(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))),X0) ),
inference(superposition,[status(thm)],[c_22362,c_14088]) ).
tcf(c_36257,plain,
! [X0: $i] :
( empty(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))
| empty(sK15(powerset(sK14(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_22362,c_14085]) ).
tcf(c_36274,plain,
! [X0: $i] :
( empty(sK15(powerset(sK14(singleton(X0)))))
| ( sK15(sK15(powerset(sK14(singleton(X0))))) = X0 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_36244,c_78]) ).
tcf(c_36320,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(sK14(sK14(powerset(relation_dom(X0)))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_29173]) ).
tcf(c_36321,plain,
relation_image(relation_dom(sK15(sK14(sK14(powerset(empty_set))))),empty_set) = empty_set,
inference(superposition,[status(thm)],[c_92,c_29173]) ).
tcf(c_36322,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(sK14(sK14(powerset(sK15(powerset(X0))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_29173]) ).
tcf(c_36323,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(sK14(sK14(powerset(sK15(sK14(powerset(X0)))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_29173]) ).
tcf(c_36324,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(sK14(sK14(powerset(sK15(sK14(sK14(powerset(X0))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_29173]) ).
tcf(c_36325,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(sK14(sK14(powerset(relation_image(X0,empty_set)))))),empty_set) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_29173]) ).
tcf(c_36326,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( relation_image(relation_dom(sK15(sK14(sK14(powerset(sK15(powerset(singleton(X0)))))))),empty_set) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_29173]) ).
tcf(c_36327,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( relation_image(relation_dom(sK15(sK14(sK14(powerset(sK15(powerset(singleton(X0)))))))),empty_set) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_29173]) ).
tcf(c_36328,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(sK14(sK14(powerset(sK15(powerset(sK15(powerset(X0))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_29173]) ).
tcf(c_36329,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(sK14(sK14(powerset(sK15(powerset(relation_image(X0,empty_set)))))))),empty_set) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_29173]) ).
tcf(c_36330,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(sK14(sK14(powerset(sK15(powerset(sK15(sK14(powerset(X0)))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_29173]) ).
tcf(c_36331,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(sK14(sK14(powerset(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_29173]) ).
tcf(c_36332,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(sK14(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_29173]) ).
tcf(c_36333,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(sK14(sK14(powerset(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_29173]) ).
tcf(c_36334,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(sK14(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_29173]) ).
tcf(c_36335,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(sK14(sK14(powerset(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_29173]) ).
tcf(c_36336,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(sK14(sK14(powerset(sK15(sK14(powerset(sK15(powerset(X0)))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_29173]) ).
tcf(c_36337,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(sK14(sK14(powerset(sK15(sK14(powerset(relation_image(X0,empty_set))))))))),empty_set) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_29173]) ).
tcf(c_36338,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(sK14(sK14(powerset(sK15(sK14(powerset(sK15(sK14(powerset(X0))))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_29173]) ).
tcf(c_36339,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(sK14(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_29173]) ).
tcf(c_36340,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(sK14(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_29173]) ).
tcf(c_36341,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(sK14(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_29173]) ).
tcf(c_36435,plain,
! [X0: $i] :
( empty(powerset(sK15(powerset(sK15(powerset(sK15(powerset(singleton(X0)))))))))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ~ in(powerset(sK15(powerset(sK15(powerset(sK15(powerset(singleton(X0)))))))),empty_set) ),
inference(superposition,[status(thm)],[c_12715,c_5145]) ).
tcf(c_36436,plain,
! [X0: $i] :
( empty(powerset(sK15(powerset(sK15(powerset(sK15(powerset(singleton(X0)))))))))
| in(empty_set,powerset(sK15(powerset(sK15(powerset(sK15(powerset(singleton(X0)))))))))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 ) ),
inference(superposition,[status(thm)],[c_12715,c_5124]) ).
tcf(c_36437,plain,
! [X0: $i] :
( element(empty_set,powerset(sK15(powerset(sK15(powerset(sK15(powerset(singleton(X0)))))))))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 ) ),
inference(superposition,[status(thm)],[c_12715,c_99]) ).
tcf(c_36439,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ~ in(X1,empty_set)
| ~ empty(sK15(powerset(sK15(powerset(sK15(powerset(singleton(X0)))))))) ),
inference(superposition,[status(thm)],[c_12715,c_5201]) ).
tcf(c_36440,plain,
! [X0: $i] :
( empty(sK15(powerset(sK15(powerset(sK15(powerset(sK15(powerset(singleton(X0))))))))))
| element(sK15(sK14(sK14(sK14(sK14(empty_set))))),sK15(powerset(sK15(powerset(sK15(powerset(singleton(X0))))))))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 ) ),
inference(superposition,[status(thm)],[c_12715,c_14103]) ).
tcf(c_36441,plain,
! [X0: $i] :
( element(sK15(sK15(powerset(empty_set))),sK15(powerset(sK15(powerset(sK15(powerset(singleton(X0))))))))
| empty(sK15(powerset(sK15(powerset(sK15(powerset(sK15(powerset(sK15(powerset(singleton(X0))))))))))))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 ) ),
inference(superposition,[status(thm)],[c_12715,c_8116]) ).
tcf(c_36442,plain,
! [X0: $i] :
( empty(sK15(powerset(sK15(powerset(sK15(powerset(sK15(powerset(singleton(X0))))))))))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ~ in(sK15(powerset(sK15(powerset(sK15(powerset(singleton(X0))))))),sK15(sK14(sK14(empty_set)))) ),
inference(superposition,[status(thm)],[c_12715,c_17039]) ).
tcf(c_36443,plain,
! [X0: $i] :
( function(sK15(sK14(powerset(empty_set))))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ~ empty(sK15(powerset(sK15(powerset(sK15(powerset(singleton(X0)))))))) ),
inference(superposition,[status(thm)],[c_12715,c_17169]) ).
tcf(c_36444,plain,
! [X0: $i] :
( relation(sK15(sK14(powerset(empty_set))))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ~ empty(sK15(powerset(sK15(powerset(sK15(powerset(singleton(X0)))))))) ),
inference(superposition,[status(thm)],[c_12715,c_17168]) ).
tcf(c_36445,plain,
! [X0: $i] :
( empty(sK15(sK14(powerset(empty_set))))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ~ empty(sK15(powerset(sK15(powerset(sK15(powerset(singleton(X0)))))))) ),
inference(superposition,[status(thm)],[c_12715,c_16911]) ).
tcf(c_36446,plain,
! [X0: $i] :
( empty(sK15(powerset(sK15(powerset(sK15(powerset(sK15(powerset(singleton(X0))))))))))
| in(sK15(sK14(sK14(empty_set))),sK15(powerset(sK15(powerset(sK15(powerset(singleton(X0))))))))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 ) ),
inference(superposition,[status(thm)],[c_12715,c_17031]) ).
tcf(c_36448,plain,
! [X0: $i] :
( empty(sK15(powerset(sK15(powerset(sK15(powerset(sK15(powerset(singleton(X0))))))))))
| element(sK15(sK14(sK14(sK14(empty_set)))),sK15(powerset(sK15(powerset(sK15(powerset(singleton(X0))))))))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 ) ),
inference(superposition,[status(thm)],[c_12715,c_9269]) ).
tcf(c_36451,plain,
! [X0: $i] :
( empty(sK15(powerset(sK15(powerset(sK15(powerset(sK15(powerset(singleton(X0))))))))))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ~ in(sK15(powerset(sK15(powerset(sK15(powerset(singleton(X0))))))),sK15(sK14(empty_set))) ),
inference(superposition,[status(thm)],[c_12715,c_11248]) ).
tcf(c_36452,plain,
! [X0: $i] :
( empty(sK15(powerset(sK15(powerset(sK15(powerset(sK15(powerset(singleton(X0))))))))))
| in(sK15(sK14(empty_set)),sK15(powerset(sK15(powerset(sK15(powerset(singleton(X0))))))))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 ) ),
inference(superposition,[status(thm)],[c_12715,c_11240]) ).
tcf(c_36453,plain,
! [X0: $i] :
( empty(sK15(powerset(sK15(powerset(sK15(powerset(sK15(powerset(singleton(X0))))))))))
| element(sK15(sK14(sK14(empty_set))),sK15(powerset(sK15(powerset(sK15(powerset(singleton(X0))))))))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 ) ),
inference(superposition,[status(thm)],[c_12715,c_7046]) ).
tcf(c_36454,plain,
! [X0: $i] :
( function(sK15(powerset(empty_set)))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ~ empty(sK15(powerset(sK15(powerset(sK15(powerset(singleton(X0)))))))) ),
inference(superposition,[status(thm)],[c_12715,c_8308]) ).
tcf(c_36455,plain,
! [X0: $i] :
( relation(sK15(powerset(empty_set)))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ~ empty(sK15(powerset(sK15(powerset(sK15(powerset(singleton(X0)))))))) ),
inference(superposition,[status(thm)],[c_12715,c_8307]) ).
tcf(c_36456,plain,
! [X0: $i] :
( empty(sK15(powerset(empty_set)))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ~ empty(sK15(powerset(sK15(powerset(sK15(powerset(singleton(X0)))))))) ),
inference(superposition,[status(thm)],[c_12715,c_8117]) ).
tcf(c_36457,plain,
! [X0: $i] :
( empty(sK15(powerset(sK15(powerset(sK15(powerset(sK15(powerset(singleton(X0))))))))))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ~ in(sK15(powerset(sK15(powerset(sK15(powerset(singleton(X0))))))),sK15(empty_set)) ),
inference(superposition,[status(thm)],[c_12715,c_8111]) ).
tcf(c_36458,plain,
! [X0: $i] :
( empty(sK15(powerset(sK15(powerset(sK15(powerset(sK15(powerset(singleton(X0))))))))))
| in(sK15(empty_set),sK15(powerset(sK15(powerset(sK15(powerset(singleton(X0))))))))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 ) ),
inference(superposition,[status(thm)],[c_12715,c_8103]) ).
tcf(c_36459,plain,
! [X0: $i] :
( empty(sK15(powerset(sK15(powerset(sK15(powerset(sK15(powerset(singleton(X0))))))))))
| element(sK15(sK14(empty_set)),sK15(powerset(sK15(powerset(sK15(powerset(singleton(X0))))))))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 ) ),
inference(superposition,[status(thm)],[c_12715,c_6096]) ).
tcf(c_36460,plain,
! [X0: $i] :
( element(sK15(empty_set),sK15(powerset(sK15(powerset(sK15(powerset(singleton(X0))))))))
| empty(sK15(powerset(sK15(powerset(sK15(powerset(sK15(powerset(singleton(X0))))))))))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 ) ),
inference(superposition,[status(thm)],[c_12715,c_5436]) ).
tcf(c_36464,plain,
! [X0: $i] :
( element(sK15(empty_set),sK15(powerset(sK15(powerset(singleton(X0))))))
| empty(sK15(powerset(sK15(powerset(sK15(powerset(sK15(powerset(singleton(X0))))))))))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 ) ),
inference(superposition,[status(thm)],[c_12715,c_8116]) ).
tcf(c_36468,plain,
! [X0: $i] :
( empty(empty_set)
| ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ~ empty(sK15(powerset(sK15(powerset(sK15(powerset(singleton(X0)))))))) ),
inference(light_normalisation,[status(thm)],[c_36456,c_5301]) ).
tcf(c_36469,plain,
! [X0: $i] :
( relation(empty_set)
| ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ~ empty(sK15(powerset(sK15(powerset(sK15(powerset(singleton(X0)))))))) ),
inference(light_normalisation,[status(thm)],[c_36455,c_5301]) ).
tcf(c_36470,plain,
! [X0: $i] :
( function(empty_set)
| ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ~ empty(sK15(powerset(sK15(powerset(sK15(powerset(singleton(X0)))))))) ),
inference(light_normalisation,[status(thm)],[c_36454,c_5301]) ).
tcf(c_36507,plain,
! [X0: $i] :
( element(sK15(empty_set),sK15(powerset(sK15(powerset(sK15(powerset(singleton(X0))))))))
| empty(sK15(powerset(sK15(powerset(sK15(powerset(sK15(powerset(sK15(powerset(singleton(X0))))))))))))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 ) ),
inference(light_normalisation,[status(thm)],[c_36441,c_5301]) ).
tcf(c_36569,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(sK14(powerset(relation_dom(relation_dom(X0)))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_29547]) ).
tcf(c_36570,plain,
relation_image(relation_dom(sK15(sK14(powerset(relation_dom(empty_set))))),empty_set) = empty_set,
inference(superposition,[status(thm)],[c_92,c_29547]) ).
tcf(c_36571,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(sK14(powerset(relation_dom(sK15(powerset(X0))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_29547]) ).
tcf(c_36572,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(sK14(powerset(relation_dom(sK15(sK14(powerset(X0)))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_29547]) ).
tcf(c_36573,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(sK14(powerset(relation_dom(sK15(sK14(sK14(powerset(X0))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_29547]) ).
tcf(c_36574,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(sK14(powerset(relation_dom(relation_image(X0,empty_set)))))),empty_set) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_29547]) ).
tcf(c_36575,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( relation_image(relation_dom(sK15(sK14(powerset(relation_dom(sK15(powerset(singleton(X0)))))))),empty_set) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_29547]) ).
tcf(c_36576,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( relation_image(relation_dom(sK15(sK14(powerset(relation_dom(sK15(powerset(singleton(X0)))))))),empty_set) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_29547]) ).
tcf(c_36577,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(sK14(powerset(relation_dom(sK15(powerset(sK15(powerset(X0))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_29547]) ).
tcf(c_36578,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(sK14(powerset(relation_dom(sK15(powerset(relation_image(X0,empty_set)))))))),empty_set) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_29547]) ).
tcf(c_36579,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(sK14(powerset(relation_dom(sK15(powerset(sK15(sK14(powerset(X0)))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_29547]) ).
tcf(c_36580,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(sK14(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_29547]) ).
tcf(c_36581,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(sK14(powerset(relation_dom(sK15(sK14(sK14(sK14(powerset(X0)))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_29547]) ).
tcf(c_36582,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(sK14(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_29547]) ).
tcf(c_36583,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(sK14(powerset(relation_dom(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_29547]) ).
tcf(c_36584,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(sK14(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_29547]) ).
tcf(c_36585,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(sK14(powerset(relation_dom(sK15(sK14(powerset(sK15(powerset(X0)))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_29547]) ).
tcf(c_36586,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(sK14(powerset(relation_dom(sK15(sK14(powerset(relation_image(X0,empty_set))))))))),empty_set) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_29547]) ).
tcf(c_36587,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(sK14(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(X0))))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_29547]) ).
tcf(c_36588,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(sK14(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_29547]) ).
tcf(c_36589,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(sK14(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_29547]) ).
tcf(c_36590,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(sK14(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_29547]) ).
tcf(c_36780,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(sK15(powerset(relation_dom(relation_dom(X0)))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_29627]) ).
tcf(c_36781,plain,
relation_image(relation_dom(relation_dom(sK15(powerset(relation_dom(empty_set))))),empty_set) = empty_set,
inference(superposition,[status(thm)],[c_92,c_29627]) ).
tcf(c_36782,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(powerset(X0))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_29627]) ).
tcf(c_36783,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(sK14(powerset(X0)))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_29627]) ).
tcf(c_36784,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(sK14(sK14(powerset(X0))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_29627]) ).
tcf(c_36785,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(sK15(powerset(relation_dom(relation_image(X0,empty_set)))))),empty_set) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_29627]) ).
tcf(c_36786,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( relation_image(relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(powerset(singleton(X0)))))))),empty_set) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_29627]) ).
tcf(c_36787,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( relation_image(relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(powerset(singleton(X0)))))))),empty_set) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_29627]) ).
tcf(c_36788,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(powerset(sK15(powerset(X0))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_29627]) ).
tcf(c_36789,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(powerset(relation_image(X0,empty_set)))))))),empty_set) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_29627]) ).
tcf(c_36790,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(powerset(X0)))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_29627]) ).
tcf(c_36791,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_29627]) ).
tcf(c_36792,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(sK14(sK14(sK14(powerset(X0)))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_29627]) ).
tcf(c_36793,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_29627]) ).
tcf(c_36794,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_29627]) ).
tcf(c_36795,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_29627]) ).
tcf(c_36796,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(powerset(X0)))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_29627]) ).
tcf(c_36797,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(sK14(powerset(relation_image(X0,empty_set))))))))),empty_set) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_29627]) ).
tcf(c_36798,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(X0))))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_29627]) ).
tcf(c_36799,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_29627]) ).
tcf(c_36800,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_29627]) ).
tcf(c_36801,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_29627]) ).
tcf(c_36965,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(powerset(relation_dom(relation_dom(relation_dom(X0)))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_29735]) ).
tcf(c_36966,plain,
relation_image(relation_dom(sK15(powerset(relation_dom(relation_dom(empty_set))))),empty_set) = empty_set,
inference(superposition,[status(thm)],[c_92,c_29735]) ).
tcf(c_36967,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(powerset(X0))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_29735]) ).
tcf(c_36968,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(sK14(powerset(X0)))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_29735]) ).
tcf(c_36969,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(sK14(sK14(powerset(X0))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_29735]) ).
tcf(c_36970,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(powerset(relation_dom(relation_dom(relation_image(X0,empty_set)))))),empty_set) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_29735]) ).
tcf(c_36971,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( relation_image(relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(powerset(singleton(X0)))))))),empty_set) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_29735]) ).
tcf(c_36972,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( relation_image(relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(powerset(singleton(X0)))))))),empty_set) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_29735]) ).
tcf(c_36973,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(powerset(sK15(powerset(X0))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_29735]) ).
tcf(c_36974,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(powerset(relation_image(X0,empty_set)))))))),empty_set) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_29735]) ).
tcf(c_36975,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(X0)))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_29735]) ).
tcf(c_36976,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_29735]) ).
tcf(c_36977,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(sK14(sK14(sK14(powerset(X0)))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_29735]) ).
tcf(c_36978,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_29735]) ).
tcf(c_36979,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_29735]) ).
tcf(c_36980,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_29735]) ).
tcf(c_36981,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(sK14(powerset(sK15(powerset(X0)))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_29735]) ).
tcf(c_36982,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(sK14(powerset(relation_image(X0,empty_set))))))))),empty_set) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_29735]) ).
tcf(c_36983,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(X0))))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_29735]) ).
tcf(c_36984,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_29735]) ).
tcf(c_36985,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_29735]) ).
tcf(c_36986,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_29735]) ).
tcf(c_37080,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(X0)))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_29833]) ).
tcf(c_37081,plain,
relation_image(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(empty_set))))),empty_set) = empty_set,
inference(superposition,[status(thm)],[c_92,c_29833]) ).
tcf(c_37082,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(X0))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_29833]) ).
tcf(c_37083,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(X0)))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_29833]) ).
tcf(c_37084,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(powerset(X0))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_29833]) ).
tcf(c_37085,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_image(X0,empty_set)))))),empty_set) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_29833]) ).
tcf(c_37086,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( relation_image(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(singleton(X0)))))))),empty_set) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_29833]) ).
tcf(c_37087,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( relation_image(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(singleton(X0)))))))),empty_set) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_29833]) ).
tcf(c_37088,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(powerset(X0))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_29833]) ).
tcf(c_37089,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(relation_image(X0,empty_set)))))))),empty_set) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_29833]) ).
tcf(c_37090,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(X0)))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_29833]) ).
tcf(c_37091,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_29833]) ).
tcf(c_37092,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(sK14(powerset(X0)))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_29833]) ).
tcf(c_37093,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_29833]) ).
tcf(c_37094,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_29833]) ).
tcf(c_37095,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_29833]) ).
tcf(c_37096,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(powerset(X0)))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_29833]) ).
tcf(c_37097,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(relation_image(X0,empty_set))))))))),empty_set) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_29833]) ).
tcf(c_37098,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(X0))))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_29833]) ).
tcf(c_37099,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_29833]) ).
tcf(c_37100,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_29833]) ).
tcf(c_37101,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_29833]) ).
tcf(c_37318,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(powerset(sK15(powerset(relation_dom(X0)))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_29177]) ).
tcf(c_37319,plain,
relation_image(relation_dom(sK15(powerset(sK15(powerset(empty_set))))),empty_set) = empty_set,
inference(superposition,[status(thm)],[c_92,c_29177]) ).
tcf(c_37324,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( relation_image(relation_dom(sK15(powerset(sK15(powerset(sK15(powerset(singleton(X0)))))))),empty_set) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_29177]) ).
tcf(c_37325,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( relation_image(relation_dom(sK15(powerset(sK15(powerset(sK15(powerset(singleton(X0)))))))),empty_set) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_29177]) ).
tcf(c_37326,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(powerset(sK15(powerset(sK15(powerset(sK15(powerset(X0))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_29177]) ).
tcf(c_37327,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(powerset(sK15(powerset(sK15(powerset(relation_image(X0,empty_set)))))))),empty_set) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_29177]) ).
tcf(c_37328,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(powerset(sK15(powerset(sK15(powerset(sK15(sK14(powerset(X0)))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_29177]) ).
tcf(c_37329,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(powerset(sK15(powerset(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_29177]) ).
tcf(c_37331,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(powerset(sK15(powerset(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_29177]) ).
tcf(c_37333,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(powerset(sK15(powerset(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_29177]) ).
tcf(c_37334,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(powerset(sK15(powerset(X0)))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_29177]) ).
tcf(c_37335,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(powerset(relation_image(X0,empty_set))))))))),empty_set) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_29177]) ).
tcf(c_37336,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(powerset(sK15(sK14(powerset(X0))))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_29177]) ).
tcf(c_37337,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_29177]) ).
tcf(c_37338,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_29177]) ).
tcf(c_37339,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_29177]) ).
tcf(c_37465,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(sK15(sK14(powerset(relation_dom(X0)))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_29269]) ).
tcf(c_37466,plain,
relation_image(relation_dom(relation_dom(sK15(sK14(powerset(empty_set))))),empty_set) = empty_set,
inference(superposition,[status(thm)],[c_92,c_29269]) ).
tcf(c_37471,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( relation_image(relation_dom(relation_dom(sK15(sK14(powerset(sK15(powerset(singleton(X0)))))))),empty_set) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_29269]) ).
tcf(c_37472,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( relation_image(relation_dom(relation_dom(sK15(sK14(powerset(sK15(powerset(singleton(X0)))))))),empty_set) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_29269]) ).
tcf(c_37473,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(sK15(sK14(powerset(sK15(powerset(sK15(powerset(X0))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_29269]) ).
tcf(c_37474,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(sK15(sK14(powerset(sK15(powerset(relation_image(X0,empty_set)))))))),empty_set) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_29269]) ).
tcf(c_37475,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(sK15(sK14(powerset(sK15(powerset(sK15(sK14(powerset(X0)))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_29269]) ).
tcf(c_37476,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(sK15(sK14(powerset(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_29269]) ).
tcf(c_37478,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(sK15(sK14(powerset(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_29269]) ).
tcf(c_37480,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(sK15(sK14(powerset(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_29269]) ).
tcf(c_37481,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(sK15(powerset(X0)))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_29269]) ).
tcf(c_37482,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(relation_image(X0,empty_set))))))))),empty_set) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_29269]) ).
tcf(c_37483,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(sK15(sK14(powerset(X0))))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_29269]) ).
tcf(c_37484,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_29269]) ).
tcf(c_37485,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_29269]) ).
tcf(c_37486,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_29269]) ).
tcf(c_37528,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(relation_dom(sK15(powerset(relation_dom(X0)))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_29464]) ).
tcf(c_37529,plain,
relation_image(relation_dom(relation_dom(relation_dom(sK15(powerset(empty_set))))),empty_set) = empty_set,
inference(superposition,[status(thm)],[c_92,c_29464]) ).
tcf(c_37534,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( relation_image(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(powerset(singleton(X0)))))))),empty_set) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_29464]) ).
tcf(c_37535,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( relation_image(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(powerset(singleton(X0)))))))),empty_set) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_29464]) ).
tcf(c_37536,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(powerset(sK15(powerset(X0))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_29464]) ).
tcf(c_37537,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(powerset(relation_image(X0,empty_set)))))))),empty_set) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_29464]) ).
tcf(c_37538,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(powerset(X0)))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_29464]) ).
tcf(c_37539,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_29464]) ).
tcf(c_37541,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_29464]) ).
tcf(c_37543,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_29464]) ).
tcf(c_37544,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(powerset(X0)))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_29464]) ).
tcf(c_37545,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(relation_image(X0,empty_set))))))))),empty_set) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_29464]) ).
tcf(c_37546,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(sK14(powerset(X0))))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_29464]) ).
tcf(c_37547,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_29464]) ).
tcf(c_37548,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_29464]) ).
tcf(c_37549,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_29464]) ).
tcf(c_37591,plain,
! [X0: $i,X1: $i] :
( element(sK2(X1,sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))),X1)
| ( sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))) = X1 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5077,c_33695]) ).
tcf(c_37593,plain,
! [X0: $i,X1: $i] :
( in(sK2(X1,sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))),X1)
| ( sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))) = X1 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_56,c_33695]) ).
tcf(c_37594,plain,
! [X0: $i,X1: $i] :
( element(sK2(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))),X1),X1)
| ( sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))) = X1 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5076,c_33695]) ).
tcf(c_37595,plain,
! [X0: $i,X1: $i] :
( in(sK2(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))),X1),X1)
| ( sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))) = X1 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_56,c_33695]) ).
tcf(c_37596,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK15(sK14(sK14(sK14(sK14(sK14(powerset(X1))))))) = relation_image(X0,X2) )
| ( apply(X0,sK4(X0,X2,sK15(sK14(sK14(sK14(sK14(sK14(powerset(X1))))))))) = sK3(X0,X2,sK15(sK14(sK14(sK14(sK14(sK14(powerset(X1)))))))) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_60,c_33695]) ).
tcf(c_37597,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK4(X0,X2,sK15(sK14(sK14(sK14(sK14(sK14(powerset(X1)))))))),relation_dom(X0))
| ( sK15(sK14(sK14(sK14(sK14(sK14(powerset(X1))))))) = relation_image(X0,X2) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_58,c_33695]) ).
tcf(c_37598,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK4(X0,X2,sK15(sK14(sK14(sK14(sK14(sK14(powerset(X1)))))))),X2)
| ( sK15(sK14(sK14(sK14(sK14(sK14(powerset(X1))))))) = relation_image(X0,X2) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_59,c_33695]) ).
tcf(c_37599,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(X0,sK15(sK14(sK14(sK14(sK14(sK14(powerset(X1))))))),X2),X2)
| ( relation_image(X0,sK15(sK14(sK14(sK14(sK14(sK14(powerset(X1)))))))) = X2 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_59,c_33695]) ).
tcf(c_37600,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(X2)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,sK15(sK14(sK14(sK14(sK14(sK14(powerset(X2))))))))) ),
inference(superposition,[status(thm)],[c_63,c_33695]) ).
tcf(c_37601,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))) = singleton(X1) )
| ( sK8(X1,sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))) = X1 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_80,c_33695]) ).
tcf(c_37602,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK14(sK14(sK14(sK14(sK14(powerset(X1))))))) = X0 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5062,c_33695]) ).
tcf(c_37604,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))) = singleton(X1) )
| ( sK2(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))),singleton(X1)) = X1 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5169,c_33695]) ).
tcf(c_37609,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6288,c_33695]) ).
tcf(c_37612,plain,
! [X0: $i] :
( empty(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16897,c_33695]) ).
tcf(c_37614,plain,
! [X0: $i] :
( empty(sK15(powerset(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17031,c_33695]) ).
tcf(c_37618,plain,
! [X0: $i] :
( empty(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))))
| ( sK14(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16394,c_33695]) ).
tcf(c_37619,plain,
! [X0: $i] :
( empty(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))))
| empty(sK15(powerset(sK14(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_22362,c_33695]) ).
tcf(c_37620,plain,
! [X0: $i] :
( empty(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_33690,c_33695]) ).
tcf(c_37684,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_29464]) ).
tcf(c_37685,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_29269]) ).
tcf(c_37686,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_29177]) ).
tcf(c_37687,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_29833]) ).
tcf(c_37688,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_29735]) ).
tcf(c_37689,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_29627]) ).
tcf(c_37690,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(sK14(powerset(relation_dom(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_29547]) ).
tcf(c_37691,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(sK14(sK14(powerset(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_29173]) ).
tcf(c_37692,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(sK14(powerset(relation_dom(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_15859]) ).
tcf(c_37693,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(sK14(sK14(powerset(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_14996]) ).
tcf(c_37694,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(powerset(relation_dom(relation_dom(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_14554]) ).
tcf(c_37695,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(sK14(powerset(relation_dom(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_14491]) ).
tcf(c_37696,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_14357]) ).
tcf(c_37697,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(powerset(relation_dom(relation_dom(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_14260]) ).
tcf(c_37698,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_14212]) ).
tcf(c_37699,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_14000]) ).
tcf(c_37700,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(powerset(relation_dom(relation_dom(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_13924]) ).
tcf(c_37701,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(powerset(relation_dom(relation_dom(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_13820]) ).
tcf(c_37702,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_13746]) ).
tcf(c_37703,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_13650]) ).
tcf(c_37704,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_13554]) ).
tcf(c_37705,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_13471]) ).
tcf(c_37706,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(powerset(relation_dom(relation_dom(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_13409]) ).
tcf(c_37707,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_13342]) ).
tcf(c_37708,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(powerset(relation_dom(relation_dom(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_13215]) ).
tcf(c_37709,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_13155]) ).
tcf(c_37710,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_13072]) ).
tcf(c_37711,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(sK15(powerset(relation_dom(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_12539]) ).
tcf(c_37712,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(sK14(powerset(relation_dom(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_12496]) ).
tcf(c_37713,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(sK14(powerset(relation_dom(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_12393]) ).
tcf(c_37714,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(powerset(sK15(powerset(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_10889]) ).
tcf(c_37715,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(sK15(powerset(relation_dom(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_12362]) ).
tcf(c_37716,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(sK15(powerset(relation_dom(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_12319]) ).
tcf(c_37717,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_12288]) ).
tcf(c_37718,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(sK15(powerset(relation_dom(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_12185]) ).
tcf(c_37719,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(sK14(sK14(powerset(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_10134]) ).
tcf(c_37720,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(sK14(sK14(powerset(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_10133]) ).
tcf(c_37721,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_29462]) ).
tcf(c_37722,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(powerset(relation_dom(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_29402]) ).
tcf(c_37723,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_29268]) ).
tcf(c_37724,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_29172]) ).
tcf(c_37725,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_29266]) ).
tcf(c_37726,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_29171]) ).
tcf(c_37727,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_29169]) ).
tcf(c_37728,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_29163]) ).
tcf(c_37729,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_9588]) ).
tcf(c_37730,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(powerset(sK15(powerset(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_9507]) ).
tcf(c_37731,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_12137]) ).
tcf(c_37732,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_12094]) ).
tcf(c_37733,plain,
! [X0: $i,X1: $i] :
( ( sK15(powerset(relation_dom(relation_dom(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_12042]) ).
tcf(c_37734,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(sK15(powerset(relation_dom(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_11908]) ).
tcf(c_37735,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_9413]) ).
tcf(c_37736,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_9213]) ).
tcf(c_37737,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(powerset(sK15(powerset(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_9027]) ).
tcf(c_37738,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_8995]) ).
tcf(c_37739,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_8935]) ).
tcf(c_37740,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_8860]) ).
tcf(c_37741,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_8823]) ).
tcf(c_37742,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(powerset(sK15(powerset(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_8745]) ).
tcf(c_37743,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(powerset(sK15(powerset(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_8300]) ).
tcf(c_37744,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_8299]) ).
tcf(c_37745,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(powerset(sK15(powerset(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_8298]) ).
tcf(c_37746,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(sK15(powerset(relation_dom(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_11782]) ).
tcf(c_37747,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK15(powerset(relation_dom(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_11746]) ).
tcf(c_37748,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(sK14(powerset(relation_dom(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_11666]) ).
tcf(c_37749,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(relation_dom(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_11550]) ).
tcf(c_37750,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_8238]) ).
tcf(c_37751,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_8211]) ).
tcf(c_37752,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_8078]) ).
tcf(c_37753,plain,
! [X0: $i,X1: $i] :
( ( sK15(powerset(sK15(powerset(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_7740]) ).
tcf(c_37754,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_7685]) ).
tcf(c_37755,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(sK14(powerset(relation_dom(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_11491]) ).
tcf(c_37756,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(sK14(powerset(relation_dom(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_11438]) ).
tcf(c_37757,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK14(powerset(relation_dom(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_11182]) ).
tcf(c_37758,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(powerset(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_7252]) ).
tcf(c_37759,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(sK14(sK14(powerset(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_7251]) ).
tcf(c_37760,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(sK14(sK14(powerset(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_7250]) ).
tcf(c_37761,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(sK14(sK14(powerset(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_7249]) ).
tcf(c_37762,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_7143]) ).
tcf(c_37763,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_6954]) ).
tcf(c_37764,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_6939]) ).
tcf(c_37765,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_6906]) ).
tcf(c_37766,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_6888]) ).
tcf(c_37767,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_6857]) ).
tcf(c_37768,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK14(sK14(powerset(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_7255]) ).
tcf(c_37769,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_6833]) ).
tcf(c_37770,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_6798]) ).
tcf(c_37772,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(sK14(powerset(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_14868]) ).
tcf(c_37773,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(powerset(relation_dom(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_10887]) ).
tcf(c_37774,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(sK14(powerset(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_10136]) ).
tcf(c_37775,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(relation_dom(relation_dom(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_9586]) ).
tcf(c_37776,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(powerset(relation_dom(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_9505]) ).
tcf(c_37777,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(relation_dom(relation_dom(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_9411]) ).
tcf(c_37778,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_9211]) ).
tcf(c_37779,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(powerset(relation_dom(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_9107]) ).
tcf(c_37780,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(powerset(relation_dom(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_9025]) ).
tcf(c_37781,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_8993]) ).
tcf(c_37782,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_8933]) ).
tcf(c_37783,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_8858]) ).
tcf(c_37784,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(relation_dom(relation_dom(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_8821]) ).
tcf(c_37785,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(powerset(relation_dom(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_8743]) ).
tcf(c_37786,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(powerset(relation_dom(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_8705]) ).
tcf(c_37787,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(powerset(relation_dom(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_8667]) ).
tcf(c_37788,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_8236]) ).
tcf(c_37789,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_8209]) ).
tcf(c_37790,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(sK15(powerset(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_7684]) ).
tcf(c_37791,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(sK14(powerset(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_7254]) ).
tcf(c_37792,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(sK14(powerset(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_7253]) ).
tcf(c_37793,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(sK15(powerset(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_7142]) ).
tcf(c_37794,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_6953]) ).
tcf(c_37795,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_6938]) ).
tcf(c_37796,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_6905]) ).
tcf(c_37797,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_6887]) ).
tcf(c_37798,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_8076]) ).
tcf(c_37799,plain,
! [X0: $i,X1: $i] :
( ( sK15(powerset(relation_dom(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_7738]) ).
tcf(c_37800,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(sK15(powerset(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_6856]) ).
tcf(c_37801,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_6832]) ).
tcf(c_37802,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_6797]) ).
tcf(c_37803,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_6681]) ).
tcf(c_37804,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_6189]) ).
tcf(c_37805,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_6188]) ).
tcf(c_37806,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_6187]) ).
tcf(c_37807,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_6192]) ).
tcf(c_37808,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(powerset(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_9868]) ).
tcf(c_37809,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(relation_dom(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_7682]) ).
tcf(c_37810,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(powerset(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_7256]) ).
tcf(c_37811,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(relation_dom(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_7140]) ).
tcf(c_37812,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(relation_dom(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_6951]) ).
tcf(c_37813,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(powerset(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_6680]) ).
tcf(c_37814,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_6191]) ).
tcf(c_37815,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_6936]) ).
tcf(c_37816,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(relation_dom(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_6903]) ).
tcf(c_37817,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_6885]) ).
tcf(c_37818,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(relation_dom(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_6854]) ).
tcf(c_37819,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_6190]) ).
tcf(c_37820,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_5583]) ).
tcf(c_37821,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(powerset(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_5569]) ).
tcf(c_37822,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(relation_dom(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_6830]) ).
tcf(c_37823,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_6795]) ).
tcf(c_37824,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_5557]) ).
tcf(c_37825,plain,
! [X0: $i,X1: $i] :
( ( sK15(powerset(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_5270]) ).
tcf(c_37826,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(powerset(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_7171]) ).
tcf(c_37827,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_6193]) ).
tcf(c_37828,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(relation_dom(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_6678]) ).
tcf(c_37829,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(relation_dom(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_5581]) ).
tcf(c_37830,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(relation_dom(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_5567]) ).
tcf(c_37831,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_5555]) ).
tcf(c_37832,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(powerset(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_5302]) ).
tcf(c_37833,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_5269]) ).
tcf(c_37834,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_5189]) ).
tcf(c_37835,plain,
! [X0: $i] :
( ( sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_6153]) ).
tcf(c_37836,plain,
! [X0: $i] :
( ( sK15(powerset(relation_dom(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_5300]) ).
tcf(c_37837,plain,
! [X0: $i] :
( ( relation_dom(sK15(powerset(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_5271]) ).
tcf(c_37838,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_5245]) ).
tcf(c_37839,plain,
! [X0: $i] :
( ( sK15(powerset(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_5272]) ).
tcf(c_37840,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_5110]) ).
tcf(c_37841,plain,
! [X0: $i,X1: $i] :
( ( sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_53]) ).
tcf(c_37842,plain,
! [X0: $i] :
( ( relation_dom(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_5023]) ).
tcf(c_37844,plain,
! [X0: $i] :
( relation(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_87]) ).
tcf(c_37845,plain,
! [X0: $i] :
( function(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_77]) ).
tcf(c_38534,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_image(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))),empty_set))) = empty_set )
| ~ empty(X0)
| ~ relation(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))) ),
inference(superposition,[status(thm)],[c_37845,c_7932]) ).
tcf(c_38535,plain,
! [X0: $i] :
( ( sK15(powerset(relation_image(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))),empty_set))) = empty_set )
| ~ empty(X0)
| ~ relation(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))) ),
inference(superposition,[status(thm)],[c_37845,c_7931]) ).
tcf(c_38536,plain,
! [X0: $i] :
( ( relation_dom(relation_image(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))),empty_set)) = empty_set )
| ~ empty(X0)
| ~ relation(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))) ),
inference(superposition,[status(thm)],[c_37845,c_7934]) ).
tcf(c_38537,plain,
! [X0: $i] :
( ( relation_image(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))),empty_set) = empty_set )
| ~ empty(X0)
| ~ relation(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))) ),
inference(superposition,[status(thm)],[c_37845,c_7777]) ).
tcf(c_38574,plain,
! [X0: $i,X1: $i] :
( element(sK2(X1,sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))),X1)
| element(sK2(X1,sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))),X0)
| ( sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))) = X1 ) ),
inference(superposition,[status(thm)],[c_5077,c_33698]) ).
tcf(c_38575,plain,
! [X0: $i,X1: $i] :
( element(sK2(X0,sK15(sK14(sK14(sK14(sK14(sK14(powerset(X1)))))))),X1)
| ( sK15(sK14(sK14(sK14(sK14(sK14(powerset(X1))))))) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5063,c_33698]) ).
tcf(c_38576,plain,
! [X0: $i,X1: $i] :
( element(sK2(X1,sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))),X0)
| in(sK2(X1,sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))),X1)
| ( sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))) = X1 ) ),
inference(superposition,[status(thm)],[c_56,c_33698]) ).
tcf(c_38577,plain,
! [X0: $i,X1: $i] :
( element(sK2(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))),X1),X1)
| element(sK2(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))),X1),X0)
| ( sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))) = X1 ) ),
inference(superposition,[status(thm)],[c_5076,c_33698]) ).
tcf(c_38578,plain,
! [X0: $i,X1: $i] :
( element(sK2(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))),X1),X0)
| in(sK2(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))),X1),X1)
| ( sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))) = X1 ) ),
inference(superposition,[status(thm)],[c_56,c_33698]) ).
tcf(c_38579,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK3(X0,X1,sK15(sK14(sK14(sK14(sK14(sK14(powerset(X2)))))))),X2)
| ( sK15(sK14(sK14(sK14(sK14(sK14(powerset(X2))))))) = relation_image(X0,X1) )
| ( apply(X0,sK4(X0,X1,sK15(sK14(sK14(sK14(sK14(sK14(powerset(X2))))))))) = sK3(X0,X1,sK15(sK14(sK14(sK14(sK14(sK14(powerset(X2)))))))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_60,c_33698]) ).
tcf(c_38580,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK3(X0,X2,sK15(sK14(sK14(sK14(sK14(sK14(powerset(X1)))))))),X1)
| in(sK4(X0,X2,sK15(sK14(sK14(sK14(sK14(sK14(powerset(X1)))))))),relation_dom(X0))
| ( sK15(sK14(sK14(sK14(sK14(sK14(powerset(X1))))))) = relation_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_58,c_33698]) ).
tcf(c_38581,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK3(X0,X2,sK15(sK14(sK14(sK14(sK14(sK14(powerset(X1)))))))),X1)
| in(sK4(X0,X2,sK15(sK14(sK14(sK14(sK14(sK14(powerset(X1)))))))),X2)
| ( sK15(sK14(sK14(sK14(sK14(sK14(powerset(X1))))))) = relation_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_59,c_33698]) ).
tcf(c_38582,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK4(X0,sK15(sK14(sK14(sK14(sK14(sK14(powerset(X1))))))),X2),X1)
| in(sK3(X0,sK15(sK14(sK14(sK14(sK14(sK14(powerset(X1))))))),X2),X2)
| ( relation_image(X0,sK15(sK14(sK14(sK14(sK14(sK14(powerset(X1)))))))) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_59,c_33698]) ).
tcf(c_38583,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK5(X1,sK15(sK14(sK14(sK14(sK14(sK14(powerset(X2))))))),X0),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,sK15(sK14(sK14(sK14(sK14(sK14(powerset(X2))))))))) ),
inference(superposition,[status(thm)],[c_63,c_33698]) ).
tcf(c_38584,plain,
! [X0: $i,X1: $i] :
( element(sK8(X0,sK15(sK14(sK14(sK14(sK14(sK14(powerset(X1)))))))),X1)
| ( sK15(sK14(sK14(sK14(sK14(sK14(powerset(X1))))))) = singleton(X0) )
| ( sK8(X0,sK15(sK14(sK14(sK14(sK14(sK14(powerset(X1)))))))) = X0 ) ),
inference(superposition,[status(thm)],[c_80,c_33698]) ).
tcf(c_38585,plain,
! [X0: $i,X1: $i] :
( element(sK2(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X1))))))),X0),X1)
| ( sK15(sK14(sK14(sK14(sK14(sK14(powerset(X1))))))) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5062,c_33698]) ).
tcf(c_38586,plain,
! [X0: $i] :
( empty(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))))
| element(sK15(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))),X0) ),
inference(superposition,[status(thm)],[c_5124,c_33698]) ).
tcf(c_38587,plain,
! [X0: $i,X1: $i] :
( element(sK2(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))),singleton(X1)),X0)
| ( sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))) = singleton(X1) )
| ( sK2(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))),singleton(X1)) = X1 ) ),
inference(superposition,[status(thm)],[c_5169,c_33698]) ).
tcf(c_38588,plain,
! [X0: $i] :
( element(sK2(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))),empty_set),X0)
| ( sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5409,c_33698]) ).
tcf(c_38589,plain,
! [X0: $i] :
( element(sK2(empty_set,sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))),X0)
| ( sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5410,c_33698]) ).
tcf(c_38590,plain,
! [X0: $i] :
( empty(sK15(powerset(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))))))
| element(sK15(sK15(powerset(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))))),X0) ),
inference(superposition,[status(thm)],[c_8103,c_33698]) ).
tcf(c_38591,plain,
! [X0: $i] :
( empty(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))))
| element(sK15(sK14(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))))),X0) ),
inference(superposition,[status(thm)],[c_6055,c_33698]) ).
tcf(c_38592,plain,
! [X0: $i,X1: $i] :
( element(sK3(empty_set,X1,sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))),X0)
| ( sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_6288,c_33698]) ).
tcf(c_38593,plain,
! [X0: $i] :
( empty(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))))
| element(sK15(sK14(sK14(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))))),X0) ),
inference(superposition,[status(thm)],[c_6998,c_33698]) ).
tcf(c_38594,plain,
! [X0: $i] :
( empty(sK15(powerset(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))))))
| element(sK15(sK14(sK15(powerset(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))))))),X0) ),
inference(superposition,[status(thm)],[c_11240,c_33698]) ).
tcf(c_38595,plain,
! [X0: $i] :
( empty(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))))))
| element(sK15(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))))))),X0) ),
inference(superposition,[status(thm)],[c_16897,c_33698]) ).
tcf(c_38596,plain,
! [X0: $i] :
( empty(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))))
| element(sK15(sK14(sK14(sK14(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))))))),X0) ),
inference(superposition,[status(thm)],[c_9246,c_33698]) ).
tcf(c_38597,plain,
! [X0: $i] :
( empty(sK15(powerset(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))))))
| element(sK15(sK14(sK14(sK15(powerset(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))))))),X0) ),
inference(superposition,[status(thm)],[c_17031,c_33698]) ).
tcf(c_38598,plain,
! [X0: $i] :
( empty(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))))
| element(sK2(sK14(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))),empty_set),X0)
| ( sK14(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11363,c_33698]) ).
tcf(c_38599,plain,
! [X0: $i] :
( empty(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))))
| element(sK2(empty_set,sK14(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))))),X0)
| ( sK14(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11418,c_33698]) ).
tcf(c_38600,plain,
! [X0: $i] :
( empty(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))))
| element(sK15(sK14(sK14(sK14(sK14(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))))))),X0) ),
inference(superposition,[status(thm)],[c_14080,c_33698]) ).
tcf(c_38601,plain,
! [X0: $i,X1: $i] :
( empty(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))))
| element(sK3(empty_set,X1,sK14(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))))),X0)
| ( sK14(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_16394,c_33698]) ).
tcf(c_38602,plain,
! [X0: $i] :
( empty(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))))
| empty(sK15(powerset(sK14(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))))))
| element(sK15(sK15(powerset(sK14(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))))))),X0) ),
inference(superposition,[status(thm)],[c_22362,c_33698]) ).
tcf(c_38603,plain,
! [X0: $i] :
( empty(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))))
| element(sK15(sK14(sK14(sK14(sK14(sK14(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0))))))))))))),X0) ),
inference(superposition,[status(thm)],[c_33690,c_33698]) ).
tcf(c_38768,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_image(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))),empty_set))) = empty_set )
| ~ empty(X0)
| ~ relation(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))) ),
inference(superposition,[status(thm)],[c_35617,c_7932]) ).
tcf(c_38769,plain,
! [X0: $i] :
( ( sK15(powerset(relation_image(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))),empty_set))) = empty_set )
| ~ empty(X0)
| ~ relation(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))) ),
inference(superposition,[status(thm)],[c_35617,c_7931]) ).
tcf(c_38770,plain,
! [X0: $i] :
( ( relation_dom(relation_image(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))),empty_set)) = empty_set )
| ~ empty(X0)
| ~ relation(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))) ),
inference(superposition,[status(thm)],[c_35617,c_7934]) ).
tcf(c_38771,plain,
! [X0: $i] :
( ( relation_image(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))),empty_set) = empty_set )
| ~ empty(X0)
| ~ relation(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))) ),
inference(superposition,[status(thm)],[c_35617,c_7777]) ).
tcf(c_38790,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(sK14(sK14(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_37609]) ).
tcf(c_38791,plain,
sK15(sK14(sK14(sK14(sK14(sK14(powerset(empty_set))))))) = empty_set,
inference(superposition,[status(thm)],[c_92,c_37609]) ).
tcf(c_38792,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(sK14(sK14(powerset(sK15(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5256,c_37609]) ).
tcf(c_38793,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(sK14(sK14(powerset(sK15(sK14(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6155,c_37609]) ).
tcf(c_38794,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(sK14(sK14(powerset(sK15(sK14(sK14(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7172,c_37609]) ).
tcf(c_38795,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(sK14(sK14(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7778,c_37609]) ).
tcf(c_38796,plain,
! [X0: $i] :
( ( sK15(sK14(sK15(powerset(singleton(X0))))) = X0 )
| ( sK15(sK14(sK14(sK14(sK14(sK14(powerset(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11251,c_37609]) ).
tcf(c_38797,plain,
! [X0: $i] :
( ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( sK15(sK14(sK14(sK14(sK14(sK14(powerset(sK15(powerset(singleton(X0)))))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8114,c_37609]) ).
tcf(c_38798,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(sK14(sK14(powerset(sK15(powerset(sK15(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8117,c_37609]) ).
tcf(c_38799,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(sK14(sK14(powerset(sK15(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8119,c_37609]) ).
tcf(c_38800,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(sK14(sK14(powerset(sK15(powerset(sK15(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8121,c_37609]) ).
tcf(c_38801,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(sK14(sK14(powerset(sK15(powerset(sK15(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8123,c_37609]) ).
tcf(c_38802,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(sK14(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9869,c_37609]) ).
tcf(c_38803,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(sK14(sK14(powerset(sK15(powerset(sK15(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9866,c_37609]) ).
tcf(c_38804,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(sK14(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14874,c_37609]) ).
tcf(c_38805,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(sK14(sK14(powerset(sK15(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14870,c_37609]) ).
tcf(c_38806,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(sK14(sK14(powerset(sK15(sK14(powerset(sK15(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16911,c_37609]) ).
tcf(c_38807,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(sK14(sK14(powerset(sK15(sK14(powerset(relation_image(X0,empty_set))))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16913,c_37609]) ).
tcf(c_38808,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(sK14(sK14(powerset(sK15(sK14(powerset(sK15(sK14(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16915,c_37609]) ).
tcf(c_38809,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(sK14(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16917,c_37609]) ).
tcf(c_38810,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(sK14(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(powerset(X0))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16919,c_37609]) ).
tcf(c_38811,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(sK14(sK14(powerset(sK15(sK14(powerset(sK15(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16921,c_37609]) ).
tcf(c_38812,plain,
! [X0: $i] :
( ( sK15(sK14(sK14(sK14(sK14(sK14(powerset(sK15(sK14(sK14(sK14(sK14(sK14(powerset(X0)))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37620,c_37609]) ).
tcf(c_39001,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK4(relation_dom(sK15(powerset(sK15(powerset(sK15(powerset(singleton(X0)))))))),X1,X2),empty_set)
| in(sK3(relation_dom(sK15(powerset(sK15(powerset(sK15(powerset(singleton(X0)))))))),X1,X2),X2)
| ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( relation_image(relation_dom(sK15(powerset(sK15(powerset(sK15(powerset(singleton(X0)))))))),X1) = X2 )
| ~ function(relation_dom(sK15(powerset(sK15(powerset(sK15(powerset(singleton(X0)))))))))
| ~ relation(relation_dom(sK15(powerset(sK15(powerset(sK15(powerset(singleton(X0))))))))) ),
inference(superposition,[status(thm)],[c_12716,c_58]) ).
tcf(c_39002,plain,
! [X0: $i] :
( empty(relation_dom(sK15(powerset(sK15(powerset(sK15(powerset(singleton(X0)))))))))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ~ empty(empty_set)
| ~ relation(relation_dom(sK15(powerset(sK15(powerset(sK15(powerset(singleton(X0))))))))) ),
inference(superposition,[status(thm)],[c_12716,c_71]) ).
tcf(c_39006,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(relation_dom(sK15(powerset(sK15(powerset(sK15(powerset(singleton(X1)))))))),X2,X0),empty_set)
| ( sK15(sK15(powerset(singleton(X1)))) = X1 )
| ~ function(relation_dom(sK15(powerset(sK15(powerset(sK15(powerset(singleton(X1)))))))))
| ~ relation(relation_dom(sK15(powerset(sK15(powerset(sK15(powerset(singleton(X1)))))))))
| ~ in(X0,relation_image(relation_dom(sK15(powerset(sK15(powerset(sK15(powerset(singleton(X1)))))))),X2)) ),
inference(superposition,[status(thm)],[c_12716,c_62]) ).
tcf(c_39007,plain,
! [X0: $i] :
( empty(relation_dom(sK15(powerset(sK15(powerset(sK15(powerset(singleton(X0)))))))))
| ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ~ relation(relation_dom(sK15(powerset(sK15(powerset(sK15(powerset(singleton(X0))))))))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_39002,c_92]) ).
tcf(c_39011,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK15(sK15(powerset(singleton(X1)))) = X1 )
| ~ function(relation_dom(sK15(powerset(sK15(powerset(sK15(powerset(singleton(X1)))))))))
| ~ relation(relation_dom(sK15(powerset(sK15(powerset(sK15(powerset(singleton(X1)))))))))
| ~ in(X0,relation_image(relation_dom(sK15(powerset(sK15(powerset(sK15(powerset(singleton(X1)))))))),X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_39006,c_5314]) ).
tcf(c_39016,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(relation_dom(sK15(powerset(sK15(powerset(sK15(powerset(singleton(X0)))))))),X1,X2),X2)
| ( sK15(sK15(powerset(singleton(X0)))) = X0 )
| ( relation_image(relation_dom(sK15(powerset(sK15(powerset(sK15(powerset(singleton(X0)))))))),X1) = X2 )
| ~ function(relation_dom(sK15(powerset(sK15(powerset(sK15(powerset(singleton(X0)))))))))
| ~ relation(relation_dom(sK15(powerset(sK15(powerset(sK15(powerset(singleton(X0))))))))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_39001,c_5314]) ).
tcf(c_39025,plain,
( empty(sK14(sK14(sK14(sK14(sK14(powerset(empty_set)))))))
| ~ in(sK14(sK14(sK14(sK14(sK14(powerset(empty_set)))))),empty_set) ),
inference(superposition,[status(thm)],[c_38791,c_5145]) ).
tcf(c_39026,plain,
( empty(sK14(sK14(sK14(sK14(sK14(powerset(empty_set)))))))
| in(empty_set,sK14(sK14(sK14(sK14(sK14(powerset(empty_set))))))) ),
inference(superposition,[status(thm)],[c_38791,c_5124]) ).
tcf(c_39027,plain,
element(empty_set,sK14(sK14(sK14(sK14(sK14(powerset(empty_set))))))),
inference(superposition,[status(thm)],[c_38791,c_99]) ).
tcf(c_39059,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X2,relation_image(X0,X1)),X2)
| ( relation_image(X0,X1) = X2 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_5077,c_5377]) ).
tcf(c_39061,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X2,relation_image(X0,X1)),X2)
| ( relation_image(X0,X1) = X2 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_56,c_5377]) ).
tcf(c_39062,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(relation_image(X0,X1),X2),X2)
| ( relation_image(X0,X1) = X2 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_5076,c_5377]) ).
tcf(c_39063,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(relation_image(X0,X1),X2),X2)
| ( relation_image(X0,X1) = X2 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_56,c_5377]) ).
tcf(c_39064,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(X0,X3) = relation_image(X1,X2) )
| ( apply(X0,sK4(X0,X3,relation_image(X1,X2))) = sK3(X0,X3,relation_image(X1,X2)) )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_60,c_5377]) ).
tcf(c_39065,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK4(X0,X3,relation_image(X1,X2)),relation_dom(X0))
| ( relation_image(X0,X3) = relation_image(X1,X2) )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_58,c_5377]) ).
tcf(c_39066,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK4(X0,X3,relation_image(X1,X2)),X3)
| ( relation_image(X0,X3) = relation_image(X1,X2) )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_59,c_5377]) ).
tcf(c_39067,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK3(X0,relation_image(X1,X2),X3),X3)
| ( relation_image(X0,relation_image(X1,X2)) = X3 )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_59,c_5377]) ).
tcf(c_39068,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(X2)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,X2)
| ~ in(X0,relation_dom(X1)) ),
inference(superposition,[status(thm)],[c_61,c_5377]) ).
tcf(c_39069,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ empty(X3)
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,relation_image(X2,X3))) ),
inference(superposition,[status(thm)],[c_63,c_5377]) ).
tcf(c_39070,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X0,X1) = singleton(X2) )
| ( sK8(X2,relation_image(X0,X1)) = X2 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_80,c_5377]) ).
tcf(c_39071,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X0,X2) = X1 )
| ~ empty(X2)
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_5062,c_5377]) ).
tcf(c_39073,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X0,X1) = singleton(X2) )
| ( sK2(relation_image(X0,X1),singleton(X2)) = X2 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_5169,c_5377]) ).
tcf(c_39078,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X0,X1) = empty_set )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6288,c_5377]) ).
tcf(c_39081,plain,
! [X0: $i,X1: $i] :
( empty(sK15(sK14(powerset(relation_image(X0,X1)))))
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16897,c_5377]) ).
tcf(c_39083,plain,
! [X0: $i,X1: $i] :
( empty(sK15(powerset(relation_image(X0,X1))))
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17031,c_5377]) ).
tcf(c_39087,plain,
! [X0: $i,X1: $i] :
( empty(relation_image(X0,X1))
| ( sK14(relation_image(X0,X1)) = empty_set )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16394,c_5377]) ).
tcf(c_39088,plain,
! [X0: $i,X1: $i] :
( empty(relation_image(X0,X1))
| empty(sK15(powerset(sK14(relation_image(X0,X1)))))
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_22362,c_5377]) ).
tcf(c_39089,plain,
! [X0: $i,X1: $i] :
( empty(relation_image(X0,X1))
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_33690,c_5377]) ).
tcf(c_39233,plain,
! [X0: $i,X1: $i] :
( element(sK2(X1,sK2(powerset(X0),empty_set)),X1)
| element(sK2(X1,sK2(powerset(X0),empty_set)),X0)
| ( powerset(X0) = empty_set )
| ( sK2(powerset(X0),empty_set) = X1 ) ),
inference(superposition,[status(thm)],[c_5077,c_5520]) ).
tcf(c_39234,plain,
! [X0: $i,X1: $i] :
( element(sK2(X0,sK2(powerset(X1),empty_set)),X1)
| ( powerset(X1) = empty_set )
| ( sK2(powerset(X1),empty_set) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5063,c_5520]) ).
tcf(c_39235,plain,
! [X0: $i,X1: $i] :
( element(sK2(X1,sK2(powerset(X0),empty_set)),X0)
| in(sK2(X1,sK2(powerset(X0),empty_set)),X1)
| ( powerset(X0) = empty_set )
| ( sK2(powerset(X0),empty_set) = X1 ) ),
inference(superposition,[status(thm)],[c_56,c_5520]) ).
tcf(c_39236,plain,
! [X0: $i,X1: $i] :
( element(sK2(sK2(powerset(X0),empty_set),X1),X1)
| element(sK2(sK2(powerset(X0),empty_set),X1),X0)
| ( powerset(X0) = empty_set )
| ( sK2(powerset(X0),empty_set) = X1 ) ),
inference(superposition,[status(thm)],[c_5076,c_5520]) ).
tcf(c_39237,plain,
! [X0: $i,X1: $i] :
( element(sK2(sK2(powerset(X0),empty_set),X1),X0)
| in(sK2(sK2(powerset(X0),empty_set),X1),X1)
| ( powerset(X0) = empty_set )
| ( sK2(powerset(X0),empty_set) = X1 ) ),
inference(superposition,[status(thm)],[c_56,c_5520]) ).
tcf(c_39238,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK3(X0,X1,sK2(powerset(X2),empty_set)),X2)
| ( powerset(X2) = empty_set )
| ( sK2(powerset(X2),empty_set) = relation_image(X0,X1) )
| ( apply(X0,sK4(X0,X1,sK2(powerset(X2),empty_set))) = sK3(X0,X1,sK2(powerset(X2),empty_set)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_60,c_5520]) ).
tcf(c_39239,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK3(X0,X2,sK2(powerset(X1),empty_set)),X1)
| in(sK4(X0,X2,sK2(powerset(X1),empty_set)),relation_dom(X0))
| ( powerset(X1) = empty_set )
| ( sK2(powerset(X1),empty_set) = relation_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_58,c_5520]) ).
tcf(c_39240,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK3(X0,X2,sK2(powerset(X1),empty_set)),X1)
| in(sK4(X0,X2,sK2(powerset(X1),empty_set)),X2)
| ( powerset(X1) = empty_set )
| ( sK2(powerset(X1),empty_set) = relation_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_59,c_5520]) ).
tcf(c_39241,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK4(X0,sK2(powerset(X1),empty_set),X2),X1)
| in(sK3(X0,sK2(powerset(X1),empty_set),X2),X2)
| ( powerset(X1) = empty_set )
| ( relation_image(X0,sK2(powerset(X1),empty_set)) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_59,c_5520]) ).
tcf(c_39242,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK5(X1,sK2(powerset(X2),empty_set),X0),X2)
| ( powerset(X2) = empty_set )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,sK2(powerset(X2),empty_set))) ),
inference(superposition,[status(thm)],[c_63,c_5520]) ).
tcf(c_39243,plain,
! [X0: $i,X1: $i] :
( element(sK8(X0,sK2(powerset(X1),empty_set)),X1)
| ( powerset(X1) = empty_set )
| ( sK2(powerset(X1),empty_set) = singleton(X0) )
| ( sK8(X0,sK2(powerset(X1),empty_set)) = X0 ) ),
inference(superposition,[status(thm)],[c_80,c_5520]) ).
tcf(c_39244,plain,
! [X0: $i,X1: $i] :
( element(sK2(sK2(powerset(X1),empty_set),X0),X1)
| ( powerset(X1) = empty_set )
| ( sK2(powerset(X1),empty_set) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5062,c_5520]) ).
tcf(c_39245,plain,
! [X0: $i] :
( empty(sK2(powerset(X0),empty_set))
| element(sK15(sK2(powerset(X0),empty_set)),X0)
| ( powerset(X0) = empty_set ) ),
inference(superposition,[status(thm)],[c_5124,c_5520]) ).
tcf(c_39246,plain,
! [X0: $i,X1: $i] :
( element(sK2(sK2(powerset(X0),empty_set),singleton(X1)),X0)
| ( powerset(X0) = empty_set )
| ( sK2(powerset(X0),empty_set) = singleton(X1) )
| ( sK2(sK2(powerset(X0),empty_set),singleton(X1)) = X1 ) ),
inference(superposition,[status(thm)],[c_5169,c_5520]) ).
tcf(c_39247,plain,
! [X0: $i] :
( element(sK2(sK2(powerset(X0),empty_set),empty_set),X0)
| ( powerset(X0) = empty_set )
| ( sK2(powerset(X0),empty_set) = empty_set ) ),
inference(superposition,[status(thm)],[c_5409,c_5520]) ).
tcf(c_39248,plain,
! [X0: $i] :
( element(sK2(empty_set,sK2(powerset(X0),empty_set)),X0)
| ( powerset(X0) = empty_set )
| ( sK2(powerset(X0),empty_set) = empty_set ) ),
inference(superposition,[status(thm)],[c_5410,c_5520]) ).
tcf(c_39249,plain,
! [X0: $i] :
( empty(sK15(powerset(sK2(powerset(X0),empty_set))))
| element(sK15(sK15(powerset(sK2(powerset(X0),empty_set)))),X0)
| ( powerset(X0) = empty_set ) ),
inference(superposition,[status(thm)],[c_8103,c_5520]) ).
tcf(c_39250,plain,
! [X0: $i] :
( empty(sK2(powerset(X0),empty_set))
| element(sK15(sK14(sK2(powerset(X0),empty_set))),X0)
| ( powerset(X0) = empty_set ) ),
inference(superposition,[status(thm)],[c_6055,c_5520]) ).
tcf(c_39251,plain,
! [X0: $i,X1: $i] :
( element(sK3(empty_set,X1,sK2(powerset(X0),empty_set)),X0)
| ( powerset(X0) = empty_set )
| ( sK2(powerset(X0),empty_set) = empty_set ) ),
inference(superposition,[status(thm)],[c_6288,c_5520]) ).
tcf(c_39252,plain,
! [X0: $i] :
( empty(sK2(powerset(X0),empty_set))
| element(sK15(sK14(sK14(sK2(powerset(X0),empty_set)))),X0)
| ( powerset(X0) = empty_set ) ),
inference(superposition,[status(thm)],[c_6998,c_5520]) ).
tcf(c_39253,plain,
! [X0: $i] :
( empty(sK15(powerset(sK2(powerset(X0),empty_set))))
| element(sK15(sK14(sK15(powerset(sK2(powerset(X0),empty_set))))),X0)
| ( powerset(X0) = empty_set ) ),
inference(superposition,[status(thm)],[c_11240,c_5520]) ).
tcf(c_39254,plain,
! [X0: $i] :
( empty(sK15(sK14(powerset(sK2(powerset(X0),empty_set)))))
| element(sK15(sK15(sK14(powerset(sK2(powerset(X0),empty_set))))),X0)
| ( powerset(X0) = empty_set ) ),
inference(superposition,[status(thm)],[c_16897,c_5520]) ).
tcf(c_39255,plain,
! [X0: $i] :
( empty(sK2(powerset(X0),empty_set))
| element(sK15(sK14(sK14(sK14(sK2(powerset(X0),empty_set))))),X0)
| ( powerset(X0) = empty_set ) ),
inference(superposition,[status(thm)],[c_9246,c_5520]) ).
tcf(c_39256,plain,
! [X0: $i] :
( empty(sK15(powerset(sK2(powerset(X0),empty_set))))
| element(sK15(sK14(sK14(sK15(powerset(sK2(powerset(X0),empty_set)))))),X0)
| ( powerset(X0) = empty_set ) ),
inference(superposition,[status(thm)],[c_17031,c_5520]) ).
tcf(c_39257,plain,
! [X0: $i] :
( empty(sK2(powerset(X0),empty_set))
| element(sK2(sK14(sK2(powerset(X0),empty_set)),empty_set),X0)
| ( powerset(X0) = empty_set )
| ( sK14(sK2(powerset(X0),empty_set)) = empty_set ) ),
inference(superposition,[status(thm)],[c_11363,c_5520]) ).
tcf(c_39258,plain,
! [X0: $i] :
( empty(sK2(powerset(X0),empty_set))
| element(sK2(empty_set,sK14(sK2(powerset(X0),empty_set))),X0)
| ( powerset(X0) = empty_set )
| ( sK14(sK2(powerset(X0),empty_set)) = empty_set ) ),
inference(superposition,[status(thm)],[c_11418,c_5520]) ).
tcf(c_39259,plain,
! [X0: $i] :
( empty(sK2(powerset(X0),empty_set))
| element(sK15(sK14(sK14(sK14(sK14(sK2(powerset(X0),empty_set)))))),X0)
| ( powerset(X0) = empty_set ) ),
inference(superposition,[status(thm)],[c_14080,c_5520]) ).
tcf(c_39260,plain,
! [X0: $i,X1: $i] :
( empty(sK2(powerset(X0),empty_set))
| element(sK3(empty_set,X1,sK14(sK2(powerset(X0),empty_set))),X0)
| ( powerset(X0) = empty_set )
| ( sK14(sK2(powerset(X0),empty_set)) = empty_set ) ),
inference(superposition,[status(thm)],[c_16394,c_5520]) ).
tcf(c_39261,plain,
! [X0: $i] :
( empty(sK2(powerset(X0),empty_set))
| empty(sK15(powerset(sK14(sK2(powerset(X0),empty_set)))))
| element(sK15(sK15(powerset(sK14(sK2(powerset(X0),empty_set))))),X0)
| ( powerset(X0) = empty_set ) ),
inference(superposition,[status(thm)],[c_22362,c_5520]) ).
tcf(c_39262,plain,
! [X0: $i] :
( empty(sK2(powerset(X0),empty_set))
| element(sK15(sK14(sK14(sK14(sK14(sK14(sK2(powerset(X0),empty_set))))))),X0)
| ( powerset(X0) = empty_set ) ),
inference(superposition,[status(thm)],[c_33690,c_5520]) ).
tcf(c_39531,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_39262,c_39261,c_39260,c_39259,c_39258,c_39257,c_39256,c_39255,c_39254,c_39253,c_39252,c_39251,c_39250,c_39249,c_39248,c_39247,c_39246,c_39245,c_39244,c_39243,c_39242,c_39241,c_39240,c_39239,c_39238,c_39237,c_39236,c_39235,c_39234,c_39233,c_39088,c_39087,c_39081,c_39027,c_39026,c_39025,c_39016,c_39011,c_39007,c_39006,c_39002,c_39001,c_38812,c_38811,c_38810,c_38809,c_38808,c_38807,c_38806,c_38805,c_38804,c_38803,c_38802,c_38801,c_38800,c_38799,c_38798,c_38797,c_38796,c_38795,c_38794,c_38793,c_38792,c_38791,c_38790,c_38771,c_38770,c_38769,c_38768,c_38603,c_38602,c_38601,c_38600,c_38599,c_38598,c_38597,c_38596,c_38595,c_38594,c_38593,c_38592,c_38591,c_38590,c_38589,c_38588,c_38587,c_38586,c_38585,c_38584,c_38583,c_38582,c_38581,c_38580,c_38579,c_38578,c_38577,c_38576,c_38575,c_38574,c_38537,c_38536,c_38535,c_38534,c_37845,c_37844,c_37842,c_37841,c_37840,c_37839,c_37838,c_37837,c_37836,c_37835,c_37834,c_37833,c_37832,c_37831,c_37830,c_37829,c_37828,c_37827,c_37826,c_37825,c_37824,c_37823,c_37822,c_37821,c_37820,c_37819,c_37818,c_37817,c_37816,c_37815,c_37814,c_37813,c_37812,c_37811,c_37810,c_37809,c_37808,c_37807,c_37806,c_37805,c_37804,c_37803,c_37802,c_37801,c_37800,c_37799,c_37798,c_37797,c_37796,c_37795,c_37794,c_37793,c_37792,c_37791,c_37790,c_37789,c_37788,c_37787,c_37786,c_37785,c_37784,c_37783,c_37782,c_37781,c_37780,c_37779,c_37778,c_37777,c_37776,c_37775,c_37774,c_37773,c_37772,c_37770,c_37769,c_37768,c_37767,c_37766,c_37765,c_37764,c_37763,c_37762,c_37761,c_37760,c_37759,c_37758,c_37757,c_37756,c_37755,c_37754,c_37753,c_37752,c_37751,c_37750,c_37749,c_37748,c_37747,c_37746,c_37745,c_37744,c_37743,c_37742,c_37741,c_37740,c_37739,c_37738,c_37737,c_37736,c_37735,c_37734,c_37733,c_37732,c_37731,c_37730,c_37729,c_37728,c_37727,c_37726,c_37725,c_37724,c_37723,c_37722,c_37721,c_37720,c_37719,c_37718,c_37717,c_37716,c_37715,c_37714,c_37713,c_37712,c_37711,c_37710,c_37709,c_37708,c_37707,c_37706,c_37705,c_37704,c_37703,c_37702,c_37701,c_37700,c_37699,c_37698,c_37697,c_37696,c_37695,c_37694,c_37693,c_37692,c_37691,c_37690,c_37689,c_37688,c_37687,c_37686,c_37685,c_37684,c_37619,c_37618,c_37612,c_37614,c_37609,c_37604,c_37620,c_37601,c_37600,c_37599,c_37598,c_37597,c_37596,c_37595,c_37594,c_37593,c_37602,c_37591,c_37549,c_37548,c_37547,c_37546,c_37545,c_37544,c_37543,c_37541,c_37539,c_37538,c_37537,c_37536,c_37535,c_37534,c_37529,c_37528,c_37486,c_37485,c_37484,c_37483,c_37482,c_37481,c_37480,c_37478,c_37476,c_37475,c_37474,c_37473,c_37472,c_37471,c_37466,c_37465,c_37339,c_37338,c_37337,c_37336,c_37335,c_37334,c_37333,c_37331,c_37329,c_37328,c_37327,c_37326,c_37325,c_37324,c_37319,c_37318,c_37101,c_37100,c_37099,c_37098,c_37097,c_37096,c_37095,c_37094,c_37093,c_37092,c_37091,c_37090,c_37089,c_37088,c_37087,c_37086,c_37085,c_37084,c_37083,c_37082,c_37081,c_37080,c_36986,c_36985,c_36984,c_36983,c_36982,c_36981,c_36980,c_36979,c_36978,c_36977,c_36976,c_36975,c_36974,c_36973,c_36972,c_36971,c_36970,c_36969,c_36968,c_36967,c_36966,c_36965,c_36801,c_36800,c_36799,c_36798,c_36797,c_36796,c_36795,c_36794,c_36793,c_36792,c_36791,c_36790,c_36789,c_36788,c_36787,c_36786,c_36785,c_36784,c_36783,c_36782,c_36781,c_36780,c_36590,c_36589,c_36588,c_36587,c_36586,c_36585,c_36584,c_36583,c_36582,c_36581,c_36580,c_36579,c_36578,c_36577,c_36576,c_36575,c_36574,c_36573,c_36572,c_36571,c_36570,c_36569,c_36507,c_36464,c_36468,c_36469,c_36470,c_36460,c_36459,c_36458,c_36457,c_36456,c_36455,c_36454,c_36453,c_36452,c_36451,c_36448,c_36446,c_36445,c_36444,c_36443,c_36442,c_36441,c_36440,c_36439,c_36437,c_36436,c_36435,c_36341,c_36340,c_36339,c_36338,c_36337,c_36336,c_36335,c_36334,c_36333,c_36332,c_36331,c_36330,c_36329,c_36328,c_36327,c_36326,c_36325,c_36324,c_36323,c_36322,c_36321,c_36320,c_36274,c_36257,c_36256,c_36255,c_36254,c_36253,c_36252,c_36251,c_36250,c_36249,c_36247,c_36246,c_36245,c_36244,c_36241,c_36240,c_36217,c_36216,c_36215,c_36214,c_35617,c_35616,c_35597,c_35596,c_35595,c_35594,c_35593,c_35592,c_35591,c_35590,c_35589,c_35588,c_35587,c_35586,c_35585,c_35584,c_35583,c_35582,c_35581,c_35580,c_35579,c_35578,c_35577,c_35576,c_35575,c_35574,c_35573,c_35572,c_35571,c_35570,c_35569,c_35568,c_35567,c_35566,c_35565,c_35564,c_35563,c_35562,c_35561,c_35560,c_35559,c_35558,c_35557,c_35556,c_35555,c_35554,c_35553,c_35552,c_35551,c_35550,c_35549,c_35548,c_35547,c_35546,c_35545,c_35544,c_35543,c_35542,c_35541,c_35540,c_35539,c_35538,c_35537,c_35536,c_35535,c_35534,c_35533,c_35532,c_35531,c_35530,c_35529,c_35528,c_35527,c_35526,c_35525,c_35524,c_35523,c_35522,c_35521,c_35520,c_35519,c_35518,c_35517,c_35516,c_35515,c_35514,c_35513,c_35512,c_35511,c_35510,c_35509,c_35508,c_35507,c_35506,c_35505,c_35504,c_35503,c_35502,c_35501,c_35499,c_35498,c_35497,c_35496,c_35495,c_35494,c_35493,c_35492,c_35491,c_35490,c_35489,c_35488,c_35487,c_35486,c_35485,c_35484,c_35483,c_35482,c_35481,c_35480,c_35479,c_35478,c_35477,c_35476,c_35475,c_35474,c_35473,c_35472,c_35471,c_35470,c_35469,c_35468,c_35467,c_35466,c_35465,c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c_5201,c_5189,c_5173,c_5172,c_5170,c_5169,c_5145,c_5137,c_5131,c_5130,c_5125,c_5124,c_5123,c_5111,c_5110,c_5105,c_5097,c_5096,c_5095,c_5094,c_5078,c_5077,c_5076,c_5075,c_5063,c_5062,c_5061,c_5042,c_5028,c_5026,c_5025,c_5024,c_5023,c_5003,c_4996,c_4994,c_4986,c_4985,c_4984,c_4983,c_8095,c_100,c_99,c_98,c_97,c_96,c_95,c_94,c_93,c_91,c_92,c_89,c_88,c_87,c_86,c_85,c_84,c_83,c_82,c_81,c_80,c_79,c_78,c_77,c_76,c_75,c_74,c_73,c_72,c_71,c_70,c_69,c_68,c_67,c_66,c_65,c_64,c_63,c_62,c_61,c_60,c_59,c_58,c_57,c_56,c_55,c_54,c_53,c_52,c_51,c_50,c_49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU049+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n017.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 12:34:01 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 18.51/3.26 % SZS status Started for theBenchmark.p
% 18.51/3.26 % SZS status Theorem for theBenchmark.p
% 18.51/3.26
% 18.51/3.26 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 18.51/3.26
% 18.51/3.26 % ------ iProver source info
% 18.51/3.26
% 18.51/3.26 % git: date: 2026-07-19 20:42:38 +0200
% 18.51/3.26 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 18.51/3.26 % git: non_committed_changes: false
% 18.51/3.26
% 18.51/3.26 % ------ Parsing...
% 18.51/3.26 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 18.51/3.26
% 18.51/3.26 % ------ Preprocessing... sup_sim: 0 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 %
% 18.51/3.26
% 18.51/3.26 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 18.51/3.26
% 18.51/3.26 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 18.51/3.26 % ------ Proving...
% 18.51/3.26 % ------ Problem Properties
% 18.51/3.26
% 18.51/3.26 %
% 18.51/3.26 % clauses 51
% 18.51/3.26 % conjectures 4
% 18.51/3.26 % EPR 23
% 18.51/3.26 % Horn 44
% 18.51/3.26 % unary 23
% 18.51/3.26 % binary 11
% 18.51/3.26 % lits 111
% 18.51/3.26 % lits eq 17
% 18.51/3.26 % fd_pure 0
% 18.51/3.26 % fd_pseudo 0
% 18.51/3.26 % fd_cond 1
% 18.51/3.26 % fd_pseudo_cond 9
% 18.51/3.26 % AC symbols 0
% 18.51/3.26
% 18.51/3.26 % ------ Schedule dynamic 5 is on
% 18.51/3.26
% 18.51/3.26 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 18.51/3.26
% 18.51/3.26
% 18.51/3.26 % ------
% 18.51/3.26 % Current options:
% 18.51/3.26 % ------
% 18.51/3.26
% 18.51/3.26
% 18.51/3.26 %
% 18.51/3.26
% 18.51/3.26 % ------ Proving...
% 18.51/3.26 %
% 18.51/3.26
% 18.51/3.26 % SZS status Theorem for theBenchmark.p
% 18.51/3.26
% 18.51/3.26 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 18.93/3.37
% 18.93/3.37
%------------------------------------------------------------------------------