%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU081+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n016.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 02:55:20 PM UTC 2026
% Result : Theorem 34.69s 5.80s
% Output : CNFRefutation 34.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 30
% Syntax : Number of formulae : 6770 ( 380 unt; 0 def)
% Number of atoms : 18107 (8197 equ)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 19927 (8590 ~;11241 |; 72 &)
% ( 9 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 14 ( 3 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 : 21 ( 21 usr; 9 con; 0-3 aty)
% Number of variables : 8933 ( 0 sgn8909 !; 24 ?;8705 :)
% 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] : relation(identity_relation(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_relat_1) ).
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] :
( function(identity_relation(X0))
& relation(identity_relation(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_funct_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] :
( element(X1,powerset(X0))
=> relation_image(identity_relation(X0),X1) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t162_funct_1) ).
fof(f27,negated_conjecture,
~ ! [X0,X1] :
( element(X1,powerset(X0))
=> relation_image(identity_relation(X0),X1) = X1 ),
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] :
( ( function(X1)
& relation(X1) )
=> ( X1 = identity_relation(X0)
<=> ( ! [X2] :
( in(X2,X0)
=> apply(X1,X2) = X2 )
& relation_dom(X1) = X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_funct_1) ).
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] :
( element(X1,powerset(X0))
& relation_image(identity_relation(X0),X1) != X1 ),
inference(ennf_transformation,[],[f27]) ).
fof(f38,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(ennf_transformation,[],[f36]) ).
fof(f39,plain,
! [X0] :
( ~ empty(X0)
| X0 = empty_set ),
inference(ennf_transformation,[],[f34]) ).
fof(f40,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(f41,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,[],[f40]) ).
fof(f42,plain,
! [X0,X1,X2] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f33]) ).
fof(f43,plain,
! [X0,X1,X2] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(ennf_transformation,[],[f32]) ).
fof(f44,plain,
! [X0,X1,X2] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(flattening,[],[f43]) ).
fof(f45,plain,
! [X0] :
( empty(X0)
| ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) ) ),
inference(ennf_transformation,[],[f17]) ).
fof(f46,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(ennf_transformation,[],[f29]) ).
fof(f47,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(flattening,[],[f46]) ).
fof(f48,plain,
! [X0,X1] :
( ~ in(X0,X1)
| element(X0,X1) ),
inference(ennf_transformation,[],[f28]) ).
fof(f49,plain,
! [X0] :
( ~ empty(X0)
| relation(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f50,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f35]) ).
fof(f51,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ in(X1,X0) ),
inference(ennf_transformation,[],[f1]) ).
fof(f52,plain,
! [X0] :
( ~ empty(X0)
| ( relation(relation_dom(X0))
& empty(relation_dom(X0)) ) ),
inference(ennf_transformation,[],[f14]) ).
fof(f53,plain,
! [X0] :
( ~ relation(X0)
| empty(X0)
| ~ empty(relation_dom(X0)) ),
inference(ennf_transformation,[],[f13]) ).
fof(f54,plain,
! [X0] :
( ~ relation(X0)
| empty(X0)
| ~ empty(relation_dom(X0)) ),
inference(flattening,[],[f53]) ).
fof(f55,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ( X1 = identity_relation(X0)
<=> ( ! [X2] :
( ~ in(X2,X0)
| apply(X1,X2) = X2 )
& relation_dom(X1) = X0 ) ) ),
inference(ennf_transformation,[],[f30]) ).
fof(f56,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ( X1 = identity_relation(X0)
<=> ( ! [X2] :
( ~ in(X2,X0)
| apply(X1,X2) = X2 )
& relation_dom(X1) = X0 ) ) ),
inference(flattening,[],[f55]) ).
fof(f57,plain,
! [X0] :
( ~ empty(X0)
| function(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f58,plain,
( element(sK1,powerset(sK0))
& sK1 != relation_image(identity_relation(sK0),sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f37]) ).
fof(f59,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,[],[f41]) ).
fof(f60,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,[],[f59]) ).
fof(f61,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( ( relation_image(X0,X1) != X2
| ! [X6] :
( ( ~ in(X6,X2)
| ( apply(X0,sK4(X0,X1,X6)) = X6
& in(sK4(X0,X1,X6),X1)
& in(sK4(X0,X1,X6),relation_dom(X0)) ) )
& ( ! [X7] :
( apply(X0,X7) != X6
| ~ in(X7,X1)
| ~ in(X7,relation_dom(X0)) )
| in(X6,X2) ) ) )
& ( ( ( in(sK2(X0,X1,X2),X2)
| ( sK2(X0,X1,X2) = apply(X0,sK3(X0,X1,X2))
& in(sK3(X0,X1,X2),X1)
& in(sK3(X0,X1,X2),relation_dom(X0)) ) )
& ( ~ in(sK2(X0,X1,X2),X2)
| ! [X4] :
( apply(X0,X4) != sK2(X0,X1,X2)
| ~ in(X4,X1)
| ~ in(X4,relation_dom(X0)) ) ) )
| X2 = relation_image(X0,X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X3,sK2(X0,X1,X2)),skolemize(X5,sK3(X0,X1,X2)),skolemize(X8,sK4(X0,X1,X6))],[f60]) ).
fof(f62,plain,
! [X0] :
( empty(sK5(X0))
& element(sK5(X0),powerset(X0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X1,sK5(X0))],[f21]) ).
fof(f63,plain,
! [X0] :
( empty(X0)
| ( ~ empty(sK6(X0))
& element(sK6(X0),powerset(X0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X1,sK6(X0))],[f45]) ).
fof(f64,plain,
! [X0] : element(sK7(X0),X0),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X1,sK7(X0))],[f7]) ).
fof(f65,plain,
~ empty(sK8),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(X0,sK8)],[f22]) ).
fof(f66,plain,
( relation(sK9)
& ~ empty(sK9) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(X0,sK9)],[f20]) ).
fof(f67,plain,
empty(sK10),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(X0,sK10)],[f18]) ).
fof(f68,plain,
( relation(sK11)
& empty(sK11) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(X0,sK11)],[f16]) ).
fof(f69,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ( ( identity_relation(X0) != X1
| ( ! [X2] :
( ~ in(X2,X0)
| apply(X1,X2) = X2 )
& relation_dom(X1) = X0 ) )
& ( ? [X2] :
( in(X2,X0)
& apply(X1,X2) != X2 )
| relation_dom(X1) != X0
| X1 = identity_relation(X0) ) ) ),
inference(nnf_transformation,[],[f56]) ).
fof(f70,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ( ( identity_relation(X0) != X1
| ( ! [X2] :
( ~ in(X2,X0)
| apply(X1,X2) = X2 )
& relation_dom(X1) = X0 ) )
& ( ? [X2] :
( in(X2,X0)
& apply(X1,X2) != X2 )
| relation_dom(X1) != X0
| X1 = identity_relation(X0) ) ) ),
inference(flattening,[],[f69]) ).
fof(f71,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ( ( identity_relation(X0) != X1
| ( ! [X3] :
( ~ in(X3,X0)
| apply(X1,X3) = X3 )
& relation_dom(X1) = X0 ) )
& ( ? [X2] :
( in(X2,X0)
& apply(X1,X2) != X2 )
| relation_dom(X1) != X0
| X1 = identity_relation(X0) ) ) ),
inference(rectify,[],[f70]) ).
fof(f72,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ( ( identity_relation(X0) != X1
| ( ! [X3] :
( ~ in(X3,X0)
| apply(X1,X3) = X3 )
& relation_dom(X1) = X0 ) )
& ( ( in(sK12(X0,X1),X0)
& sK12(X0,X1) != apply(X1,sK12(X0,X1)) )
| relation_dom(X1) != X0
| X1 = identity_relation(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(X2,sK12(X0,X1))],[f71]) ).
fof(f73,plain,
( function(sK13)
& empty(sK13)
& relation(sK13) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(X0,sK13)],[f19]) ).
fof(f74,plain,
( function(sK14)
& relation(sK14) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(X0,sK14)],[f15]) ).
fof(f75,plain,
element(sK1,powerset(sK0)),
inference(cnf_transformation,[],[f58]) ).
fof(f76,plain,
sK1 != relation_image(identity_relation(sK0),sK1),
inference(cnf_transformation,[],[f58]) ).
fof(f77,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(cnf_transformation,[],[f38]) ).
fof(f78,plain,
! [X0] :
( ~ empty(X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f39]) ).
fof(f79,plain,
! [X2,X0,X1,X6] :
( ~ function(X0)
| ~ relation(X0)
| relation_image(X0,X1) != X2
| ~ in(X6,X2)
| apply(X0,sK4(X0,X1,X6)) = X6 ),
inference(cnf_transformation,[],[f61]) ).
fof(f80,plain,
! [X2,X0,X1,X6] :
( ~ function(X0)
| ~ relation(X0)
| relation_image(X0,X1) != X2
| ~ in(X6,X2)
| in(sK4(X0,X1,X6),X1) ),
inference(cnf_transformation,[],[f61]) ).
fof(f81,plain,
! [X2,X0,X1,X6] :
( ~ function(X0)
| ~ relation(X0)
| relation_image(X0,X1) != X2
| ~ in(X6,X2)
| in(sK4(X0,X1,X6),relation_dom(X0)) ),
inference(cnf_transformation,[],[f61]) ).
fof(f82,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,[],[f61]) ).
fof(f83,plain,
! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| in(sK2(X0,X1,X2),X2)
| sK2(X0,X1,X2) = apply(X0,sK3(X0,X1,X2))
| relation_image(X0,X1) = X2 ),
inference(cnf_transformation,[],[f61]) ).
fof(f84,plain,
! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| in(sK2(X0,X1,X2),X2)
| in(sK3(X0,X1,X2),X1)
| relation_image(X0,X1) = X2 ),
inference(cnf_transformation,[],[f61]) ).
fof(f85,plain,
! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| in(sK2(X0,X1,X2),X2)
| in(sK3(X0,X1,X2),relation_dom(X0))
| relation_image(X0,X1) = X2 ),
inference(cnf_transformation,[],[f61]) ).
fof(f86,plain,
! [X2,X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(sK2(X0,X1,X2),X2)
| apply(X0,X4) != sK2(X0,X1,X2)
| ~ in(X4,X1)
| ~ in(X4,relation_dom(X0))
| relation_image(X0,X1) = X2 ),
inference(cnf_transformation,[],[f61]) ).
fof(f87,plain,
! [X0] : function(identity_relation(X0)),
inference(cnf_transformation,[],[f11]) ).
fof(f88,plain,
! [X0] : relation(identity_relation(X0)),
inference(cnf_transformation,[],[f11]) ).
fof(f89,plain,
! [X0] : relation(identity_relation(X0)),
inference(cnf_transformation,[],[f6]) ).
fof(f90,plain,
! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f42]) ).
fof(f91,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(cnf_transformation,[],[f44]) ).
fof(f92,plain,
! [X0] : empty(sK5(X0)),
inference(cnf_transformation,[],[f62]) ).
fof(f93,plain,
! [X0] : element(sK5(X0),powerset(X0)),
inference(cnf_transformation,[],[f62]) ).
fof(f94,plain,
! [X0] :
( empty(X0)
| ~ empty(sK6(X0)) ),
inference(cnf_transformation,[],[f63]) ).
fof(f95,plain,
! [X0] :
( empty(X0)
| element(sK6(X0),powerset(X0)) ),
inference(cnf_transformation,[],[f63]) ).
fof(f96,plain,
! [X0] : ~ empty(powerset(X0)),
inference(cnf_transformation,[],[f9]) ).
fof(f97,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(cnf_transformation,[],[f47]) ).
fof(f98,plain,
! [X0,X1] :
( ~ in(X0,X1)
| element(X0,X1) ),
inference(cnf_transformation,[],[f48]) ).
fof(f99,plain,
! [X0] : element(sK7(X0),X0),
inference(cnf_transformation,[],[f64]) ).
fof(f100,plain,
~ empty(sK8),
inference(cnf_transformation,[],[f65]) ).
fof(f101,plain,
relation(sK9),
inference(cnf_transformation,[],[f66]) ).
fof(f102,plain,
~ empty(sK9),
inference(cnf_transformation,[],[f66]) ).
fof(f103,plain,
empty(sK10),
inference(cnf_transformation,[],[f67]) ).
fof(f104,plain,
relation(sK11),
inference(cnf_transformation,[],[f68]) ).
fof(f105,plain,
empty(sK11),
inference(cnf_transformation,[],[f68]) ).
fof(f106,plain,
! [X0] :
( ~ empty(X0)
| relation(X0) ),
inference(cnf_transformation,[],[f49]) ).
fof(f107,plain,
relation(empty_set),
inference(cnf_transformation,[],[f12]) ).
fof(f109,plain,
empty(empty_set),
inference(cnf_transformation,[],[f10]) ).
fof(f110,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f50]) ).
fof(f111,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ in(X1,X0) ),
inference(cnf_transformation,[],[f51]) ).
fof(f112,plain,
! [X0] :
( ~ empty(X0)
| relation(relation_dom(X0)) ),
inference(cnf_transformation,[],[f52]) ).
fof(f113,plain,
! [X0] :
( ~ empty(X0)
| empty(relation_dom(X0)) ),
inference(cnf_transformation,[],[f52]) ).
fof(f114,plain,
! [X0] :
( ~ relation(X0)
| empty(X0)
| ~ empty(relation_dom(X0)) ),
inference(cnf_transformation,[],[f54]) ).
fof(f115,plain,
! [X3,X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| identity_relation(X0) != X1
| ~ in(X3,X0)
| apply(X1,X3) = X3 ),
inference(cnf_transformation,[],[f72]) ).
fof(f116,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| identity_relation(X0) != X1
| relation_dom(X1) = X0 ),
inference(cnf_transformation,[],[f72]) ).
fof(f117,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| in(sK12(X0,X1),X0)
| relation_dom(X1) != X0
| identity_relation(X0) = X1 ),
inference(cnf_transformation,[],[f72]) ).
fof(f118,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| sK12(X0,X1) != apply(X1,sK12(X0,X1))
| relation_dom(X1) != X0
| identity_relation(X0) = X1 ),
inference(cnf_transformation,[],[f72]) ).
fof(f119,plain,
function(sK13),
inference(cnf_transformation,[],[f73]) ).
fof(f120,plain,
empty(sK13),
inference(cnf_transformation,[],[f73]) ).
fof(f121,plain,
relation(sK13),
inference(cnf_transformation,[],[f73]) ).
fof(f122,plain,
function(sK14),
inference(cnf_transformation,[],[f74]) ).
fof(f123,plain,
relation(sK14),
inference(cnf_transformation,[],[f74]) ).
fof(f124,plain,
! [X0] :
( ~ empty(X0)
| function(X0) ),
inference(cnf_transformation,[],[f57]) ).
fof(f125,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,[],[f82]) ).
fof(f126,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,[],[f125]) ).
fof(f127,plain,
! [X0,X1,X6] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X6,relation_image(X0,X1))
| in(sK4(X0,X1,X6),relation_dom(X0)) ),
inference(equality_resolution,[],[f81]) ).
fof(f128,plain,
! [X0,X1,X6] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X6,relation_image(X0,X1))
| in(sK4(X0,X1,X6),X1) ),
inference(equality_resolution,[],[f80]) ).
fof(f129,plain,
! [X0,X1,X6] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X6,relation_image(X0,X1))
| apply(X0,sK4(X0,X1,X6)) = X6 ),
inference(equality_resolution,[],[f79]) ).
fof(f130,plain,
! [X1] :
( ~ function(X1)
| ~ relation(X1)
| sK12(relation_dom(X1),X1) != apply(X1,sK12(relation_dom(X1),X1))
| identity_relation(relation_dom(X1)) = X1 ),
inference(equality_resolution,[],[f118]) ).
fof(f131,plain,
! [X1] :
( ~ function(X1)
| ~ relation(X1)
| in(sK12(relation_dom(X1),X1),relation_dom(X1))
| identity_relation(relation_dom(X1)) = X1 ),
inference(equality_resolution,[],[f117]) ).
fof(f132,plain,
! [X0] :
( ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| relation_dom(identity_relation(X0)) = X0 ),
inference(equality_resolution,[],[f116]) ).
fof(f133,plain,
! [X3,X0] :
( ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ in(X3,X0)
| apply(identity_relation(X0),X3) = X3 ),
inference(equality_resolution,[],[f115]) ).
tcf(c_49,negated_conjecture,
relation_image(identity_relation(sK0),sK1) != sK1,
inference(cnf_transformation,[],[f76]) ).
tcf(c_50,negated_conjecture,
element(sK1,powerset(sK0)),
inference(cnf_transformation,[],[f75]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f77]) ).
tcf(c_52,plain,
! [X0: $i] :
( ( X0 = empty_set )
| ~ empty(X0) ),
inference(cnf_transformation,[],[f78]) ).
tcf(c_53,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(sK2(X0,X1,X2),X2)
| ( sK2(X0,X1,X2) != apply(X0,X3) ) ),
inference(cnf_transformation,[],[f86]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,X2),X2)
| in(sK3(X0,X1,X2),relation_dom(X0))
| ( relation_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f85]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(X0,X1,X2),X1)
| in(sK2(X0,X1,X2),X2)
| ( relation_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f84]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,X2),X2)
| ( relation_image(X0,X1) = X2 )
| ( apply(X0,sK3(X0,X1,X2)) = sK2(X0,X1,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f83]) ).
tcf(c_57,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,[],[f126]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK4(X1,X2,X0),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,X2)) ),
inference(cnf_transformation,[],[f127]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK4(X1,X2,X0),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,X2)) ),
inference(cnf_transformation,[],[f128]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(X1,sK4(X1,X2,X0)) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,X2)) ),
inference(cnf_transformation,[],[f129]) ).
tcf(c_61,plain,
! [X0: $i] : relation(identity_relation(X0)),
inference(cnf_transformation,[],[f88]) ).
tcf(c_62,plain,
! [X0: $i] : function(identity_relation(X0)),
inference(cnf_transformation,[],[f87]) ).
tcf(c_63,plain,
! [X0: $i] : relation(identity_relation(X0)),
inference(cnf_transformation,[],[f89]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(X1)
| ~ in(X2,X0)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f90]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X2,X1)
| ~ in(X2,X0)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f91]) ).
tcf(c_66,plain,
! [X0: $i] : element(sK5(X0),powerset(X0)),
inference(cnf_transformation,[],[f93]) ).
tcf(c_67,plain,
! [X0: $i] : empty(sK5(X0)),
inference(cnf_transformation,[],[f92]) ).
tcf(c_68,plain,
! [X0: $i] :
( empty(X0)
| element(sK6(X0),powerset(X0)) ),
inference(cnf_transformation,[],[f95]) ).
tcf(c_69,plain,
! [X0: $i] :
( empty(X0)
| ~ empty(sK6(X0)) ),
inference(cnf_transformation,[],[f94]) ).
tcf(c_70,plain,
! [X0: $i] : ~ empty(powerset(X0)),
inference(cnf_transformation,[],[f96]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f97]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f98]) ).
tcf(c_73,plain,
! [X0: $i] : element(sK7(X0),X0),
inference(cnf_transformation,[],[f99]) ).
tcf(c_74,plain,
~ empty(sK8),
inference(cnf_transformation,[],[f100]) ).
tcf(c_75,plain,
~ empty(sK9),
inference(cnf_transformation,[],[f102]) ).
tcf(c_76,plain,
relation(sK9),
inference(cnf_transformation,[],[f101]) ).
tcf(c_77,plain,
empty(sK10),
inference(cnf_transformation,[],[f103]) ).
tcf(c_78,plain,
empty(sK11),
inference(cnf_transformation,[],[f105]) ).
tcf(c_79,plain,
relation(sK11),
inference(cnf_transformation,[],[f104]) ).
tcf(c_80,plain,
! [X0: $i] :
( relation(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f106]) ).
tcf(c_82,plain,
relation(empty_set),
inference(cnf_transformation,[],[f107]) ).
tcf(c_83,plain,
empty(empty_set),
inference(cnf_transformation,[],[f109]) ).
tcf(c_84,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f110]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f111]) ).
tcf(c_86,plain,
! [X0: $i] :
( empty(relation_dom(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f113]) ).
tcf(c_87,plain,
! [X0: $i] :
( relation(relation_dom(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f112]) ).
tcf(c_88,plain,
! [X0: $i] :
( empty(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(cnf_transformation,[],[f114]) ).
tcf(c_89,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(X0)) = X0 )
| ~ function(X0)
| ~ relation(X0)
| ( apply(X0,sK12(relation_dom(X0),X0)) != sK12(relation_dom(X0),X0) ) ),
inference(cnf_transformation,[],[f130]) ).
tcf(c_90,plain,
! [X0: $i] :
( in(sK12(relation_dom(X0),X0),relation_dom(X0))
| ( identity_relation(relation_dom(X0)) = X0 )
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f131]) ).
tcf(c_91,plain,
! [X0: $i] :
( ( relation_dom(identity_relation(X0)) = X0 )
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0)) ),
inference(cnf_transformation,[],[f132]) ).
tcf(c_92,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X1),X0) = X0 )
| ~ function(identity_relation(X1))
| ~ relation(identity_relation(X1))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f133]) ).
tcf(c_93,plain,
relation(sK13),
inference(cnf_transformation,[],[f121]) ).
tcf(c_94,plain,
empty(sK13),
inference(cnf_transformation,[],[f120]) ).
tcf(c_95,plain,
function(sK13),
inference(cnf_transformation,[],[f119]) ).
tcf(c_96,plain,
relation(sK14),
inference(cnf_transformation,[],[f123]) ).
tcf(c_97,plain,
function(sK14),
inference(cnf_transformation,[],[f122]) ).
tcf(c_98,plain,
! [X0: $i] :
( function(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f124]) ).
tcf(c_103,plain,
~ empty(powerset(empty_set)),
inference(instantiation,[status(thm)],[c_70]) ).
tcf(c_121,plain,
! [X0: $i] : relation_dom(identity_relation(X0)) = X0,
inference(global_subsumption_just,[status(thm)],[c_91,c_63,c_62,c_91]) ).
tcf(c_148,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X1),X0) = X0 )
| ~ function(identity_relation(X1))
| ~ in(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_92,c_61]) ).
tcf(c_151,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X1),X0) = X0 )
| ~ in(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_148,c_62]) ).
tcf(c_5010,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| ~ empty(X1)
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_5593,plain,
! [X0: $i] : relation(sK5(X0)),
inference(superposition,[status(thm)],[c_67,c_80]) ).
tcf(c_5594,plain,
relation(sK10),
inference(superposition,[status(thm)],[c_77,c_80]) ).
tcf(c_5607,plain,
! [X0: $i] : function(sK5(X0)),
inference(superposition,[status(thm)],[c_67,c_98]) ).
tcf(c_5608,plain,
function(sK10),
inference(superposition,[status(thm)],[c_77,c_98]) ).
tcf(c_5609,plain,
function(sK11),
inference(superposition,[status(thm)],[c_78,c_98]) ).
tcf(c_5610,plain,
function(empty_set),
inference(superposition,[status(thm)],[c_83,c_98]) ).
tcf(c_5621,plain,
! [X0: $i] :
( empty(X0)
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_121,c_86]) ).
tcf(c_5622,plain,
! [X0: $i] :
( function(relation_dom(X0))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_98]) ).
tcf(c_5633,plain,
! [X0: $i] :
( relation(X0)
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_121,c_87]) ).
tcf(c_5644,plain,
! [X0: $i] :
( function(X0)
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_121,c_5622]) ).
tcf(c_5659,plain,
! [X0: $i] : sK5(X0) = empty_set,
inference(superposition,[status(thm)],[c_67,c_52]) ).
tcf(c_5660,plain,
empty_set = sK10,
inference(superposition,[status(thm)],[c_77,c_52]) ).
tcf(c_5661,plain,
empty_set = sK11,
inference(superposition,[status(thm)],[c_78,c_52]) ).
tcf(c_5663,plain,
! [X0: $i] :
( ( relation_dom(X0) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_52]) ).
tcf(c_5664,plain,
empty_set = sK13,
inference(superposition,[status(thm)],[c_94,c_52]) ).
tcf(c_5669,plain,
! [X0: $i] : element(empty_set,powerset(X0)),
inference(demodulation,[status(thm)],[c_66,c_5659]) ).
tcf(c_5701,plain,
( empty(powerset(sK0))
| in(sK1,powerset(sK0)) ),
inference(superposition,[status(thm)],[c_50,c_71]) ).
tcf(c_5702,plain,
! [X0: $i] :
( empty(X0)
| empty(powerset(X0))
| in(sK6(X0),powerset(X0)) ),
inference(superposition,[status(thm)],[c_68,c_71]) ).
tcf(c_5703,plain,
! [X0: $i] :
( empty(X0)
| in(sK7(X0),X0) ),
inference(superposition,[status(thm)],[c_73,c_71]) ).
tcf(c_5706,plain,
in(sK1,powerset(sK0)),
inference(forward_subsumption_resolution,[status(thm)],[c_5701,c_70]) ).
tcf(c_5707,plain,
! [X0: $i] :
( empty(X0)
| in(sK6(X0),powerset(X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5702,c_70]) ).
tcf(c_5710,plain,
! [X0: $i] :
( empty(powerset(X0))
| in(empty_set,powerset(X0)) ),
inference(superposition,[status(thm)],[c_5669,c_71]) ).
tcf(c_5711,plain,
! [X0: $i] : in(empty_set,powerset(X0)),
inference(forward_subsumption_resolution,[status(thm)],[c_5710,c_70]) ).
tcf(c_5713,plain,
~ in(powerset(sK0),sK1),
inference(superposition,[status(thm)],[c_5706,c_85]) ).
tcf(c_5714,plain,
~ empty(powerset(sK0)),
inference(superposition,[status(thm)],[c_5706,c_84]) ).
tcf(c_5716,plain,
! [X0: $i] : ~ in(powerset(X0),empty_set),
inference(superposition,[status(thm)],[c_5711,c_85]) ).
tcf(c_5724,plain,
! [X0: $i] :
( empty(X0)
| ~ in(X0,sK7(X0)) ),
inference(superposition,[status(thm)],[c_5703,c_85]) ).
tcf(c_5733,plain,
! [X0: $i] :
( empty(X0)
| ~ in(powerset(X0),sK6(X0)) ),
inference(superposition,[status(thm)],[c_5707,c_85]) ).
tcf(c_5746,plain,
relation_dom(empty_set) = empty_set,
inference(superposition,[status(thm)],[c_83,c_5663]) ).
tcf(c_5747,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(X0)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_5663]) ).
tcf(c_5765,plain,
! [X0: $i] :
( empty(identity_relation(X0))
| ~ empty(X0)
| ~ relation(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_121,c_88]) ).
tcf(c_5767,plain,
! [X0: $i] :
( empty(identity_relation(X0))
| ~ empty(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5765,c_63]) ).
tcf(c_5775,plain,
! [X0: $i] :
( ( relation_dom(identity_relation(X0)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_5663]) ).
tcf(c_5776,plain,
! [X0: $i] :
( ( identity_relation(X0) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_52]) ).
tcf(c_5793,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(X0) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_51]) ).
tcf(c_5794,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(X0) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_51]) ).
tcf(c_5805,plain,
apply(identity_relation(powerset(sK0)),sK1) = sK1,
inference(superposition,[status(thm)],[c_5706,c_151]) ).
tcf(c_5806,plain,
! [X0: $i] :
( empty(X0)
| ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) ) ),
inference(superposition,[status(thm)],[c_5707,c_151]) ).
tcf(c_5807,plain,
! [X0: $i] :
( empty(X0)
| ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) ) ),
inference(superposition,[status(thm)],[c_5703,c_151]) ).
tcf(c_5808,plain,
! [X0: $i] : apply(identity_relation(powerset(X0)),empty_set) = empty_set,
inference(superposition,[status(thm)],[c_5711,c_151]) ).
tcf(c_5820,plain,
! [X0: $i] :
( ~ empty(sK0)
| ~ in(X0,sK1) ),
inference(superposition,[status(thm)],[c_50,c_64]) ).
tcf(c_5822,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ in(X0,sK7(powerset(X1))) ),
inference(superposition,[status(thm)],[c_73,c_64]) ).
tcf(c_5823,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ in(X0,empty_set) ),
inference(superposition,[status(thm)],[c_5669,c_64]) ).
tcf(c_5838,plain,
! [X0: $i] :
( element(X0,sK0)
| ~ in(X0,sK1) ),
inference(superposition,[status(thm)],[c_50,c_65]) ).
tcf(c_5839,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| element(X0,X1)
| ~ in(X0,sK6(X1)) ),
inference(superposition,[status(thm)],[c_68,c_65]) ).
tcf(c_5840,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| ~ in(X0,sK7(powerset(X1))) ),
inference(superposition,[status(thm)],[c_73,c_65]) ).
tcf(c_5841,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| ~ in(X0,empty_set) ),
inference(superposition,[status(thm)],[c_5669,c_65]) ).
tcf(c_5857,plain,
( empty(sK1)
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_5703,c_5820]) ).
tcf(c_5873,plain,
( empty(sK1)
| element(sK7(sK1),sK0) ),
inference(superposition,[status(thm)],[c_5703,c_5838]) ).
tcf(c_5880,plain,
( empty(sK0)
| empty(sK1)
| in(sK7(sK1),sK0) ),
inference(superposition,[status(thm)],[c_5873,c_71]) ).
tcf(c_5884,plain,
( in(sK7(sK1),sK0)
| empty(sK1) ),
inference(global_subsumption_just,[status(thm)],[c_5880,c_5857,c_5880]) ).
tcf(c_5885,plain,
( empty(sK1)
| in(sK7(sK1),sK0) ),
inference(renaming,[status(thm)],[c_5884]) ).
tcf(c_5890,plain,
( empty(sK1)
| ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) ) ),
inference(superposition,[status(thm)],[c_5885,c_151]) ).
tcf(c_5891,plain,
( empty(sK1)
| ~ in(sK0,sK7(sK1)) ),
inference(superposition,[status(thm)],[c_5885,c_85]) ).
tcf(c_5906,plain,
! [X0: $i] :
( ( X0 = sK1 )
| ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5890,c_51]) ).
tcf(c_5907,plain,
( ( relation_dom(sK1) = empty_set )
| ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) ) ),
inference(superposition,[status(thm)],[c_5890,c_5663]) ).
tcf(c_5908,plain,
( ( sK1 = empty_set )
| ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) ) ),
inference(superposition,[status(thm)],[c_5890,c_52]) ).
tcf(c_5909,plain,
( function(sK1)
| ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) ) ),
inference(superposition,[status(thm)],[c_5890,c_98]) ).
tcf(c_5910,plain,
( relation(sK1)
| ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) ) ),
inference(superposition,[status(thm)],[c_5890,c_80]) ).
tcf(c_5943,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(identity_relation(X2),sK4(X1,X2,X0)) = sK4(X1,X2,X0) )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_59,c_151]) ).
tcf(c_5944,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ function(X1)
| ~ relation(X1)
| ~ in(X2,relation_image(X1,X0))
| ~ in(X0,sK4(X1,X0,X2)) ),
inference(superposition,[status(thm)],[c_59,c_85]) ).
tcf(c_5945,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ function(X1)
| ~ relation(X1)
| ~ empty(X2)
| ~ in(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_59,c_84]) ).
tcf(c_5946,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK4(X1,X2,X0),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_59,c_72]) ).
tcf(c_5947,plain,
! [X0: $i,X1: $i] :
( element(sK4(X1,sK1,X0),sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,sK1)) ),
inference(superposition,[status(thm)],[c_59,c_5838]) ).
tcf(c_5948,plain,
! [X0: $i,X1: $i] :
( ~ empty(sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,sK1)) ),
inference(superposition,[status(thm)],[c_59,c_5820]) ).
tcf(c_5949,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ function(X1)
| ~ relation(X1)
| ~ empty(X2)
| ~ in(X0,relation_image(X1,empty_set)) ),
inference(superposition,[status(thm)],[c_59,c_5823]) ).
tcf(c_5992,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK4(identity_relation(X1),X2,X0),X1)
| ~ function(identity_relation(X1))
| ~ relation(identity_relation(X1))
| ~ in(X0,relation_image(identity_relation(X1),X2)) ),
inference(superposition,[status(thm)],[c_121,c_58]) ).
tcf(c_5993,plain,
! [X0: $i,X1: $i] :
( in(sK4(empty_set,X1,X0),empty_set)
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ in(X0,relation_image(empty_set,X1)) ),
inference(superposition,[status(thm)],[c_5746,c_58]) ).
tcf(c_5994,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(identity_relation(relation_dom(X1)),sK4(X1,X2,X0)) = sK4(X1,X2,X0) )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_58,c_151]) ).
tcf(c_5995,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X2,relation_image(X0,X1))
| ~ in(relation_dom(X0),sK4(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_58,c_85]) ).
tcf(c_5996,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_58,c_84]) ).
tcf(c_5997,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK4(X1,X2,X0),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_58,c_72]) ).
tcf(c_6002,plain,
! [X0: $i,X1: $i] :
( in(sK4(empty_set,X1,X0),empty_set)
| ~ in(X0,relation_image(empty_set,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5993,c_5610,c_82]) ).
tcf(c_6013,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK4(identity_relation(X1),X2,X0),X1)
| ~ in(X0,relation_image(identity_relation(X1),X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5992,c_62,c_63]) ).
tcf(c_6034,plain,
! [X0: $i] :
( in(sK12(X0,identity_relation(X0)),X0)
| ( identity_relation(relation_dom(identity_relation(X0))) = identity_relation(X0) )
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_121,c_90]) ).
tcf(c_6035,plain,
( in(sK12(empty_set,empty_set),empty_set)
| ( identity_relation(relation_dom(empty_set)) = empty_set )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_5746,c_90]) ).
tcf(c_6036,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(X0)) = X0 )
| ( apply(identity_relation(relation_dom(X0)),sK12(relation_dom(X0),X0)) = sK12(relation_dom(X0),X0) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_90,c_151]) ).
tcf(c_6037,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(X0)) = X0 )
| ~ function(X0)
| ~ relation(X0)
| ~ in(relation_dom(X0),sK12(relation_dom(X0),X0)) ),
inference(superposition,[status(thm)],[c_90,c_85]) ).
tcf(c_6038,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(X0)) = X0 )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_90,c_84]) ).
tcf(c_6039,plain,
! [X0: $i] :
( element(sK12(relation_dom(X0),X0),relation_dom(X0))
| ( identity_relation(relation_dom(X0)) = X0 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_90,c_72]) ).
tcf(c_6044,plain,
( in(sK12(empty_set,empty_set),empty_set)
| ( identity_relation(empty_set) = empty_set )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(light_normalisation,[status(thm)],[c_6035,c_5746]) ).
tcf(c_6045,plain,
( in(sK12(empty_set,empty_set),empty_set)
| ( identity_relation(empty_set) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6044,c_5610,c_82]) ).
tcf(c_6075,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( apply(X2,sK4(X2,X3,sK4(X1,relation_image(X2,X3),X0))) = sK4(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_59,c_60]) ).
tcf(c_6076,plain,
! [X0: $i,X1: $i] :
( empty(relation_image(X0,X1))
| ( apply(X0,sK4(X0,X1,sK7(relation_image(X0,X1)))) = sK7(relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_5703,c_60]) ).
tcf(c_6094,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK4(X1,empty_set,X0),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,empty_set)) ),
inference(superposition,[status(thm)],[c_59,c_5841]) ).
tcf(c_6104,plain,
identity_relation(empty_set) = empty_set,
inference(superposition,[status(thm)],[c_83,c_5776]) ).
tcf(c_6105,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(X0)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_5776]) ).
tcf(c_6106,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(X0)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_5776]) ).
tcf(c_6107,plain,
( ( identity_relation(sK1) = empty_set )
| ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) ) ),
inference(superposition,[status(thm)],[c_5890,c_5776]) ).
tcf(c_6132,plain,
relation_dom(relation_dom(empty_set)) = empty_set,
inference(superposition,[status(thm)],[c_83,c_5747]) ).
tcf(c_6133,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_5747]) ).
tcf(c_6134,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(identity_relation(X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_5747]) ).
tcf(c_6135,plain,
( ( relation_dom(relation_dom(sK1)) = empty_set )
| ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) ) ),
inference(superposition,[status(thm)],[c_5890,c_5747]) ).
tcf(c_6157,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(sK0)
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,relation_image(X2,sK1))) ),
inference(superposition,[status(thm)],[c_59,c_5948]) ).
tcf(c_6158,plain,
! [X0: $i] :
( empty(relation_image(X0,sK1))
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_5703,c_5948]) ).
tcf(c_6179,plain,
! [X0: $i,X1: $i] :
( empty(sK0)
| in(sK4(X1,sK1,X0),sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,sK1)) ),
inference(superposition,[status(thm)],[c_5947,c_71]) ).
tcf(c_6194,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_image(X0,sK1))) = empty_set )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6158,c_5747]) ).
tcf(c_6195,plain,
! [X0: $i] :
( ( identity_relation(relation_image(X0,sK1)) = empty_set )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6158,c_5776]) ).
tcf(c_6196,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X1,sK1) = X0 )
| ~ empty(sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6158,c_51]) ).
tcf(c_6197,plain,
! [X0: $i] :
( ( relation_dom(relation_image(X0,sK1)) = empty_set )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6158,c_5663]) ).
tcf(c_6198,plain,
! [X0: $i] :
( ( relation_image(X0,sK1) = empty_set )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6158,c_52]) ).
tcf(c_6199,plain,
! [X0: $i] :
( function(relation_image(X0,sK1))
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6158,c_98]) ).
tcf(c_6200,plain,
! [X0: $i] :
( relation(relation_image(X0,sK1))
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6158,c_80]) ).
tcf(c_6237,plain,
( in(sK3(identity_relation(sK0),sK1,sK1),sK1)
| in(sK2(identity_relation(sK0),sK1,sK1),sK1)
| ( relation_image(identity_relation(sK0),sK1) = sK1 )
| ~ function(identity_relation(sK0))
| ~ relation(identity_relation(sK0)) ),
inference(instantiation,[status(thm)],[c_55]) ).
tcf(c_6246,plain,
! [X0: $i,X1: $i] :
( ~ in(X0,relation_image(X1,sK1))
| ~ relation(X1)
| ~ function(X1)
| in(sK4(X1,sK1,X0),sK0) ),
inference(global_subsumption_just,[status(thm)],[c_6179,c_5948,c_6179]) ).
tcf(c_6247,plain,
! [X0: $i,X1: $i] :
( in(sK4(X1,sK1,X0),sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,sK1)) ),
inference(renaming,[status(thm)],[c_6246]) ).
tcf(c_6257,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(sK0),sK4(X1,sK1,X0)) = sK4(X1,sK1,X0) )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,sK1)) ),
inference(superposition,[status(thm)],[c_6247,c_151]) ).
tcf(c_6258,plain,
! [X0: $i,X1: $i] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X1,relation_image(X0,sK1))
| ~ in(sK0,sK4(X0,sK1,X1)) ),
inference(superposition,[status(thm)],[c_6247,c_85]) ).
tcf(c_6283,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ empty(sK0)
| ~ function(X3)
| ~ function(X2)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,relation_image(X2,relation_image(X3,sK1)))) ),
inference(superposition,[status(thm)],[c_59,c_6157]) ).
tcf(c_6284,plain,
! [X0: $i,X1: $i] :
( empty(relation_image(X0,relation_image(X1,sK1)))
| ~ empty(sK0)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_5703,c_6157]) ).
tcf(c_6330,plain,
! [X0: $i] :
( ( relation_image(identity_relation(X0),sK1) = empty_set )
| ~ empty(sK0)
| ~ relation(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_62,c_6198]) ).
tcf(c_6331,plain,
( ( relation_image(sK14,sK1) = empty_set )
| ~ relation(sK14)
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_97,c_6198]) ).
tcf(c_6332,plain,
( ( relation_image(empty_set,sK1) = empty_set )
| ~ relation(empty_set)
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_5610,c_6198]) ).
tcf(c_6333,plain,
! [X0: $i] :
( ( relation_image(relation_dom(X0),sK1) = empty_set )
| ~ empty(sK0)
| ~ empty(X0)
| ~ relation(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_5622,c_6198]) ).
tcf(c_6334,plain,
( ( relation_image(sK1,sK1) = empty_set )
| ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ~ relation(sK1)
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_5909,c_6198]) ).
tcf(c_6335,plain,
! [X0: $i] :
( ( relation_image(relation_image(X0,sK1),sK1) = empty_set )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0)
| ~ relation(relation_image(X0,sK1)) ),
inference(superposition,[status(thm)],[c_6199,c_6198]) ).
tcf(c_6336,plain,
( ( relation_image(empty_set,sK1) = empty_set )
| ~ empty(sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6332,c_82]) ).
tcf(c_6339,plain,
( ( relation_image(sK14,sK1) = empty_set )
| ~ empty(sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6331,c_96]) ).
tcf(c_6342,plain,
! [X0: $i] :
( ( relation_image(identity_relation(X0),sK1) = empty_set )
| ~ empty(sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6330,c_63]) ).
tcf(c_6361,plain,
! [X0: $i] :
( empty(powerset(X0))
| ~ empty(sK6(powerset(X0))) ),
inference(instantiation,[status(thm)],[c_69]) ).
tcf(c_6362,plain,
( empty(powerset(empty_set))
| ~ empty(sK6(powerset(empty_set))) ),
inference(instantiation,[status(thm)],[c_6361]) ).
tcf(c_6379,plain,
! [X0: $i] :
( in(sK1,relation_image(identity_relation(powerset(sK0)),X0))
| ~ in(sK1,X0)
| ~ function(identity_relation(powerset(sK0)))
| ~ relation(identity_relation(powerset(sK0)))
| ~ in(sK1,relation_dom(identity_relation(powerset(sK0)))) ),
inference(superposition,[status(thm)],[c_5805,c_57]) ).
tcf(c_6380,plain,
! [X0: $i,X1: $i] :
( in(empty_set,relation_image(identity_relation(powerset(X0)),X1))
| ~ in(empty_set,X1)
| ~ function(identity_relation(powerset(X0)))
| ~ relation(identity_relation(powerset(X0)))
| ~ in(empty_set,relation_dom(identity_relation(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_5808,c_57]) ).
tcf(c_6381,plain,
! [X0: $i] :
( in(sK7(sK1),relation_image(identity_relation(sK0),X0))
| ( relation_dom(sK1) = empty_set )
| ~ function(identity_relation(sK0))
| ~ relation(identity_relation(sK0))
| ~ in(sK7(sK1),X0)
| ~ in(sK7(sK1),relation_dom(identity_relation(sK0))) ),
inference(superposition,[status(thm)],[c_5907,c_57]) ).
tcf(c_6382,plain,
! [X0: $i] :
( in(sK7(sK1),relation_image(identity_relation(sK0),X0))
| ( sK1 = empty_set )
| ~ function(identity_relation(sK0))
| ~ relation(identity_relation(sK0))
| ~ in(sK7(sK1),X0)
| ~ in(sK7(sK1),relation_dom(identity_relation(sK0))) ),
inference(superposition,[status(thm)],[c_5908,c_57]) ).
tcf(c_6383,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(X1,sK4(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_57,c_60]) ).
tcf(c_6384,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(identity_relation(relation_image(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_57,c_151]) ).
tcf(c_6385,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_57,c_85]) ).
tcf(c_6386,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X2,X1)
| ~ in(X2,relation_dom(X0))
| ~ empty(relation_image(X0,X1)) ),
inference(superposition,[status(thm)],[c_57,c_84]) ).
tcf(c_6387,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_57,c_72]) ).
tcf(c_6388,plain,
! [X0: $i,X1: $i] :
( ~ empty(sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,sK1)
| ~ in(X0,relation_dom(X1)) ),
inference(superposition,[status(thm)],[c_57,c_5948]) ).
tcf(c_6389,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(sK0)
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(X0,relation_dom(X2))
| ~ in(X0,relation_image(X1,sK1)) ),
inference(superposition,[status(thm)],[c_57,c_6157]) ).
tcf(c_6427,plain,
! [X0: $i,X1: $i] :
( in(empty_set,relation_image(identity_relation(powerset(X0)),X1))
| ~ in(empty_set,X1)
| ~ in(empty_set,relation_dom(identity_relation(powerset(X0)))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6380,c_62,c_63]) ).
tcf(c_6431,plain,
! [X0: $i] :
( in(sK1,relation_image(identity_relation(powerset(sK0)),X0))
| ~ in(sK1,X0)
| ~ in(sK1,relation_dom(identity_relation(powerset(sK0)))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6379,c_62,c_63]) ).
tcf(c_6435,plain,
! [X0: $i] :
( in(sK7(sK1),relation_image(identity_relation(sK0),X0))
| ( sK1 = empty_set )
| ~ in(sK7(sK1),X0)
| ~ in(sK7(sK1),relation_dom(identity_relation(sK0))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6382,c_62,c_63]) ).
tcf(c_6440,plain,
! [X0: $i] :
( in(sK7(sK1),relation_image(identity_relation(sK0),X0))
| ( relation_dom(sK1) = empty_set )
| ~ in(sK7(sK1),X0)
| ~ in(sK7(sK1),relation_dom(identity_relation(sK0))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6381,c_62,c_63]) ).
tcf(c_6470,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,relation_image(X1,X2),X3),X3)
| ( relation_image(X0,relation_image(X1,X2)) = X3 )
| ( apply(X1,sK4(X1,X2,sK3(X0,relation_image(X1,X2),X3))) = sK3(X0,relation_image(X1,X2),X3) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_55,c_60]) ).
tcf(c_6471,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,X2),X2)
| ( relation_image(X0,X1) = X2 )
| ( apply(identity_relation(X1),sK3(X0,X1,X2)) = sK3(X0,X1,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_55,c_151]) ).
tcf(c_6472,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,X0,X2),X2)
| ( relation_image(X1,X0) = X2 )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,sK3(X1,X0,X2)) ),
inference(superposition,[status(thm)],[c_55,c_85]) ).
tcf(c_6473,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,X0,X2),X2)
| ( relation_image(X1,X0) = X2 )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_55,c_84]) ).
tcf(c_6474,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,X2),X2)
| element(sK3(X0,X1,X2),X1)
| ( relation_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_55,c_72]) ).
tcf(c_6475,plain,
! [X0: $i,X1: $i] :
( element(sK3(X0,sK1,X1),sK0)
| in(sK2(X0,sK1,X1),X1)
| ( relation_image(X0,sK1) = X1 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_55,c_5838]) ).
tcf(c_6476,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,sK1,X1),X1)
| ( relation_image(X0,sK1) = X1 )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_55,c_5820]) ).
tcf(c_6477,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,empty_set,X1),X1)
| element(sK3(X0,empty_set,X1),X2)
| ( relation_image(X0,empty_set) = X1 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_55,c_5841]) ).
tcf(c_6478,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,empty_set,X2),X2)
| ( relation_image(X1,empty_set) = X2 )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_55,c_5823]) ).
tcf(c_6479,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,relation_image(X1,sK1),X2),X2)
| ( relation_image(X0,relation_image(X1,sK1)) = X2 )
| ~ empty(sK0)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_55,c_5948]) ).
tcf(c_6480,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,relation_image(X1,relation_image(X2,sK1)),X3),X3)
| ( relation_image(X0,relation_image(X1,relation_image(X2,sK1))) = X3 )
| ~ empty(sK0)
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_55,c_6157]) ).
tcf(c_6481,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK3(X0,X3,relation_image(X1,X2)),X3)
| ( relation_image(X0,X3) = relation_image(X1,X2) )
| ( apply(X1,sK4(X1,X2,sK2(X0,X3,relation_image(X1,X2)))) = sK2(X0,X3,relation_image(X1,X2)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_55,c_60]) ).
tcf(c_6482,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(X0,X2,X1),X2)
| ( relation_image(X0,X2) = X1 )
| ( apply(identity_relation(X1),sK2(X0,X2,X1)) = sK2(X0,X2,X1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_55,c_151]) ).
tcf(c_6483,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(X1,X2,X0),X2)
| ( relation_image(X1,X2) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,sK2(X1,X2,X0)) ),
inference(superposition,[status(thm)],[c_55,c_85]) ).
tcf(c_6484,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(X1,X2,X0),X2)
| ( relation_image(X1,X2) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_55,c_84]) ).
tcf(c_6485,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(X0,X1,X2),X1)
| element(sK2(X0,X1,X2),X2)
| ( relation_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_55,c_72]) ).
tcf(c_6486,plain,
! [X0: $i,X1: $i] :
( element(sK2(X0,X1,sK1),sK0)
| in(sK3(X0,X1,sK1),X1)
| ( relation_image(X0,X1) = sK1 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_55,c_5838]) ).
tcf(c_6487,plain,
! [X0: $i,X1: $i] :
( in(sK3(X0,X1,sK1),X1)
| ( relation_image(X0,X1) = sK1 )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_55,c_5820]) ).
tcf(c_6488,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(X0,X1,empty_set),X1)
| element(sK2(X0,X1,empty_set),X2)
| ( relation_image(X0,X1) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_55,c_5841]) ).
tcf(c_6489,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(X1,X2,empty_set),X2)
| ( relation_image(X1,X2) = empty_set )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_55,c_5823]) ).
tcf(c_6490,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(X0,X2,relation_image(X1,sK1)),X2)
| ( relation_image(X0,X2) = relation_image(X1,sK1) )
| ~ empty(sK0)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_55,c_5948]) ).
tcf(c_6491,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK3(X0,X3,relation_image(X1,relation_image(X2,sK1))),X3)
| ( relation_image(X1,relation_image(X2,sK1)) = relation_image(X0,X3) )
| ~ empty(sK0)
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_55,c_6157]) ).
tcf(c_6638,plain,
relation(identity_relation(sK0)),
inference(instantiation,[status(thm)],[c_63]) ).
tcf(c_6687,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(identity_relation(X0),X1,X2),X0)
| in(sK2(identity_relation(X0),X1,X2),X2)
| ( relation_image(identity_relation(X0),X1) = X2 )
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_121,c_54]) ).
tcf(c_6688,plain,
! [X0: $i,X1: $i] :
( in(sK3(empty_set,X0,X1),empty_set)
| in(sK2(empty_set,X0,X1),X1)
| ( relation_image(empty_set,X0) = X1 )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_5746,c_54]) ).
tcf(c_6689,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK3(X0,X3,relation_image(X1,X2)),relation_dom(X0))
| ( relation_image(X0,X3) = relation_image(X1,X2) )
| ( apply(X1,sK4(X1,X2,sK2(X0,X3,relation_image(X1,X2)))) = sK2(X0,X3,relation_image(X1,X2)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_54,c_60]) ).
tcf(c_6690,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(X0,X2,X1),relation_dom(X0))
| ( relation_image(X0,X2) = X1 )
| ( apply(identity_relation(X1),sK2(X0,X2,X1)) = sK2(X0,X2,X1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_54,c_151]) ).
tcf(c_6691,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(X1,X2,X0),relation_dom(X1))
| ( relation_image(X1,X2) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,sK2(X1,X2,X0)) ),
inference(superposition,[status(thm)],[c_54,c_85]) ).
tcf(c_6692,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(X1,X2,X0),relation_dom(X1))
| ( relation_image(X1,X2) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_54,c_84]) ).
tcf(c_6693,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X0,X1,X2),X2)
| in(sK3(X0,X1,X2),relation_dom(X0))
| ( relation_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_54,c_72]) ).
tcf(c_6694,plain,
! [X0: $i,X1: $i] :
( element(sK2(X0,X1,sK1),sK0)
| in(sK3(X0,X1,sK1),relation_dom(X0))
| ( relation_image(X0,X1) = sK1 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_54,c_5838]) ).
tcf(c_6695,plain,
! [X0: $i,X1: $i] :
( in(sK3(X0,X1,sK1),relation_dom(X0))
| ( relation_image(X0,X1) = sK1 )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_54,c_5820]) ).
tcf(c_6696,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X0,X1,empty_set),X2)
| in(sK3(X0,X1,empty_set),relation_dom(X0))
| ( relation_image(X0,X1) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_54,c_5841]) ).
tcf(c_6697,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(X1,X2,empty_set),relation_dom(X1))
| ( relation_image(X1,X2) = empty_set )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_54,c_5823]) ).
tcf(c_6698,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(X0,X2,relation_image(X1,sK1)),relation_dom(X0))
| ( relation_image(X0,X2) = relation_image(X1,sK1) )
| ~ empty(sK0)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_54,c_5948]) ).
tcf(c_6699,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK3(X0,X3,relation_image(X1,relation_image(X2,sK1))),relation_dom(X0))
| ( relation_image(X1,relation_image(X2,sK1)) = relation_image(X0,X3) )
| ~ empty(sK0)
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_54,c_6157]) ).
tcf(c_6700,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,X2),X2)
| ( relation_image(X0,X1) = X2 )
| ( apply(identity_relation(relation_dom(X0)),sK3(X0,X1,X2)) = sK3(X0,X1,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_54,c_151]) ).
tcf(c_6701,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,X2),X2)
| ( relation_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0)
| ~ in(relation_dom(X0),sK3(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_54,c_85]) ).
tcf(c_6702,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,X2),X2)
| ( relation_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_54,c_84]) ).
tcf(c_6703,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,X2),X2)
| element(sK3(X0,X1,X2),relation_dom(X0))
| ( relation_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_54,c_72]) ).
tcf(c_6724,plain,
! [X0: $i,X1: $i] :
( in(sK3(empty_set,X0,X1),empty_set)
| in(sK2(empty_set,X0,X1),X1)
| ( relation_image(empty_set,X0) = X1 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6688,c_5610,c_82]) ).
tcf(c_6758,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(identity_relation(X0),X1,X2),X0)
| in(sK2(identity_relation(X0),X1,X2),X2)
| ( relation_image(identity_relation(X0),X1) = X2 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6687,c_62,c_63]) ).
tcf(c_6825,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(identity_relation(X0))) = identity_relation(X0) )
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ( apply(identity_relation(X0),sK12(X0,identity_relation(X0))) != sK12(X0,identity_relation(X0)) ) ),
inference(superposition,[status(thm)],[c_121,c_89]) ).
tcf(c_6826,plain,
( ( identity_relation(relation_dom(empty_set)) = empty_set )
| ~ function(empty_set)
| ~ relation(empty_set)
| ( apply(empty_set,sK12(empty_set,empty_set)) != sK12(empty_set,empty_set) ) ),
inference(superposition,[status(thm)],[c_5746,c_89]) ).
tcf(c_6833,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(X1,X2,sK7(powerset(X0))),relation_dom(X1))
| ( relation_image(X1,X2) = sK7(powerset(X0)) )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_54,c_5822]) ).
tcf(c_6834,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(X1,X2,sK7(powerset(X0))),X2)
| ( relation_image(X1,X2) = sK7(powerset(X0)) )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_55,c_5822]) ).
tcf(c_6835,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,sK7(powerset(X0)),X2),X2)
| ( relation_image(X1,sK7(powerset(X0))) = X2 )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_55,c_5822]) ).
tcf(c_6836,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ function(X1)
| ~ relation(X1)
| ~ empty(X2)
| ~ in(X0,relation_image(X1,sK7(powerset(X2)))) ),
inference(superposition,[status(thm)],[c_59,c_5822]) ).
tcf(c_6837,plain,
! [X0: $i] :
( empty(sK7(powerset(X0)))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5703,c_5822]) ).
tcf(c_6875,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(powerset(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_5747]) ).
tcf(c_6876,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_5776]) ).
tcf(c_6877,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(X0)) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_51]) ).
tcf(c_6878,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_5663]) ).
tcf(c_6879,plain,
! [X0: $i] :
( ( sK7(powerset(X0)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_52]) ).
tcf(c_6880,plain,
! [X0: $i] :
( function(sK7(powerset(X0)))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_98]) ).
tcf(c_6881,plain,
! [X0: $i] :
( relation(sK7(powerset(X0)))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_80]) ).
tcf(c_6906,plain,
! [X0: $i] :
( empty(sK6(powerset(X0)))
| ~ empty(sK6(sK6(powerset(X0)))) ),
inference(instantiation,[status(thm)],[c_69]) ).
tcf(c_6911,plain,
( empty(sK6(powerset(empty_set)))
| ~ empty(sK6(sK6(powerset(empty_set)))) ),
inference(instantiation,[status(thm)],[c_6906]) ).
tcf(c_6913,plain,
! [X0: $i,X1: $i] :
( empty(sK6(powerset(X1)))
| in(X0,sK6(powerset(X1)))
| ~ element(X0,sK6(powerset(X1))) ),
inference(instantiation,[status(thm)],[c_71]) ).
tcf(c_6914,plain,
( empty(sK6(powerset(empty_set)))
| in(empty_set,sK6(powerset(empty_set)))
| ~ element(empty_set,sK6(powerset(empty_set))) ),
inference(instantiation,[status(thm)],[c_6913]) ).
tcf(c_6919,plain,
! [X0: $i] :
( ( relation_image(sK7(powerset(X0)),sK1) = empty_set )
| ~ empty(sK0)
| ~ empty(X0)
| ~ relation(sK7(powerset(X0))) ),
inference(superposition,[status(thm)],[c_6880,c_6198]) ).
tcf(c_6939,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X1,X2) = relation_image(X0,sK1) )
| ( apply(X1,sK4(X1,X2,sK2(X0,sK1,relation_image(X1,X2)))) = sK2(X0,sK1,relation_image(X1,X2)) )
| ~ empty(sK0)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6476,c_60]) ).
tcf(c_6940,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X0,sK1) = X1 )
| ( apply(identity_relation(X1),sK2(X0,sK1,X1)) = sK2(X0,sK1,X1) )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6476,c_151]) ).
tcf(c_6941,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X1,sK1) = X0 )
| ~ empty(sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,sK2(X1,sK1,X0)) ),
inference(superposition,[status(thm)],[c_6476,c_85]) ).
tcf(c_6943,plain,
! [X0: $i,X1: $i] :
( element(sK2(X0,sK1,X1),X1)
| ( relation_image(X0,sK1) = X1 )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6476,c_72]) ).
tcf(c_6945,plain,
! [X0: $i] :
( ( relation_image(X0,sK1) = sK1 )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6476,c_5820]) ).
tcf(c_6946,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X1,sK1) = sK7(powerset(X0)) )
| ~ empty(sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6476,c_5822]) ).
tcf(c_6948,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X1,sK1) = empty_set )
| ~ empty(sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6476,c_5823]) ).
tcf(c_6949,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X0,sK1) = relation_image(X1,sK1) )
| ~ empty(sK0)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6476,c_5948]) ).
tcf(c_6950,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X1,relation_image(X2,sK1)) = relation_image(X0,sK1) )
| ~ empty(sK0)
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6476,c_6157]) ).
tcf(c_7035,plain,
function(empty_set),
inference(superposition,[status(thm)],[c_83,c_98]) ).
tcf(c_7045,plain,
! [X0: $i] :
( ( relation_image(identity_relation(X0),sK1) = sK1 )
| ~ empty(sK0)
| ~ relation(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_62,c_6945]) ).
tcf(c_7046,plain,
( ( relation_image(sK14,sK1) = sK1 )
| ~ relation(sK14)
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_97,c_6945]) ).
tcf(c_7047,plain,
( ( relation_image(empty_set,sK1) = sK1 )
| ~ relation(empty_set)
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_5610,c_6945]) ).
tcf(c_7048,plain,
! [X0: $i] :
( ( relation_image(relation_dom(X0),sK1) = sK1 )
| ~ empty(sK0)
| ~ empty(X0)
| ~ relation(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_5622,c_6945]) ).
tcf(c_7049,plain,
( ( relation_image(sK1,sK1) = sK1 )
| ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ~ relation(sK1)
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_5909,c_6945]) ).
tcf(c_7050,plain,
! [X0: $i] :
( ( relation_image(relation_image(X0,sK1),sK1) = sK1 )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0)
| ~ relation(relation_image(X0,sK1)) ),
inference(superposition,[status(thm)],[c_6199,c_6945]) ).
tcf(c_7051,plain,
! [X0: $i] :
( ( relation_image(sK7(powerset(X0)),sK1) = sK1 )
| ~ empty(sK0)
| ~ empty(X0)
| ~ relation(sK7(powerset(X0))) ),
inference(superposition,[status(thm)],[c_6880,c_6945]) ).
tcf(c_7052,plain,
( ( relation_image(empty_set,sK1) = sK1 )
| ~ empty(sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7047,c_82]) ).
tcf(c_7055,plain,
( ( relation_image(sK14,sK1) = sK1 )
| ~ empty(sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7046,c_96]) ).
tcf(c_7058,plain,
! [X0: $i] :
( ( relation_image(identity_relation(X0),sK1) = sK1 )
| ~ empty(sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7045,c_63]) ).
tcf(c_7104,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X0,relation_image(X1,X2)) = sK1 )
| ( apply(X1,sK4(X1,X2,sK3(X0,relation_image(X1,X2),sK1))) = sK3(X0,relation_image(X1,X2),sK1) )
| ~ empty(sK0)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6487,c_60]) ).
tcf(c_7105,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X0,X1) = sK1 )
| ( apply(identity_relation(X1),sK3(X0,X1,sK1)) = sK3(X0,X1,sK1) )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6487,c_151]) ).
tcf(c_7106,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X1,X0) = sK1 )
| ~ empty(sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,sK3(X1,X0,sK1)) ),
inference(superposition,[status(thm)],[c_6487,c_85]) ).
tcf(c_7107,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X1,X0) = sK1 )
| ~ empty(sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6487,c_84]) ).
tcf(c_7108,plain,
! [X0: $i,X1: $i] :
( element(sK3(X0,X1,sK1),X1)
| ( relation_image(X0,X1) = sK1 )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6487,c_72]) ).
tcf(c_7111,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X1,sK7(powerset(X0))) = sK1 )
| ~ empty(sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6487,c_5822]) ).
tcf(c_7112,plain,
! [X0: $i,X1: $i] :
( element(sK3(X0,empty_set,sK1),X1)
| ( relation_image(X0,empty_set) = sK1 )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6487,c_5841]) ).
tcf(c_7113,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X1,empty_set) = sK1 )
| ~ empty(sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6487,c_5823]) ).
tcf(c_7114,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X0,relation_image(X1,sK1)) = sK1 )
| ~ empty(sK0)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6487,c_5948]) ).
tcf(c_7115,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X0,relation_image(X1,relation_image(X2,sK1))) = sK1 )
| ~ empty(sK0)
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6487,c_6157]) ).
tcf(c_7212,plain,
! [X0: $i,X1: $i] :
( in(sK3(identity_relation(X0),X1,sK1),X0)
| ( relation_image(identity_relation(X0),X1) = sK1 )
| ~ empty(sK0)
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_121,c_6695]) ).
tcf(c_7213,plain,
! [X0: $i] :
( in(sK3(empty_set,X0,sK1),empty_set)
| ( relation_image(empty_set,X0) = sK1 )
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_5746,c_6695]) ).
tcf(c_7214,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X0,X1) = sK1 )
| ( apply(identity_relation(relation_dom(X0)),sK3(X0,X1,sK1)) = sK3(X0,X1,sK1) )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6695,c_151]) ).
tcf(c_7215,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X0,X1) = sK1 )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0)
| ~ in(relation_dom(X0),sK3(X0,X1,sK1)) ),
inference(superposition,[status(thm)],[c_6695,c_85]) ).
tcf(c_7216,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X0,X1) = sK1 )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_6695,c_84]) ).
tcf(c_7217,plain,
! [X0: $i,X1: $i] :
( element(sK3(X0,X1,sK1),relation_dom(X0))
| ( relation_image(X0,X1) = sK1 )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6695,c_72]) ).
tcf(c_7223,plain,
! [X0: $i] :
( in(sK3(empty_set,X0,sK1),empty_set)
| ( relation_image(empty_set,X0) = sK1 )
| ~ empty(sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7213,c_5610,c_82]) ).
tcf(c_7237,plain,
! [X0: $i,X1: $i] :
( in(sK3(identity_relation(X0),X1,sK1),X0)
| ( relation_image(identity_relation(X0),X1) = sK1 )
| ~ empty(sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7212,c_62,c_63]) ).
tcf(c_7276,plain,
! [X0: $i,X1: $i] :
( empty(sK0)
| in(sK3(X0,sK1,X1),sK0)
| in(sK2(X0,sK1,X1),X1)
| ( relation_image(X0,sK1) = X1 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6475,c_71]) ).
tcf(c_7277,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK3(X0,sK1,relation_image(X1,X2)),sK0)
| ( relation_image(X1,X2) = relation_image(X0,sK1) )
| ( apply(X1,sK4(X1,X2,sK2(X0,sK1,relation_image(X1,X2)))) = sK2(X0,sK1,relation_image(X1,X2)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6475,c_60]) ).
tcf(c_7278,plain,
! [X0: $i,X1: $i] :
( element(sK3(X0,sK1,X1),sK0)
| ( relation_image(X0,sK1) = X1 )
| ( apply(identity_relation(X1),sK2(X0,sK1,X1)) = sK2(X0,sK1,X1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6475,c_151]) ).
tcf(c_7279,plain,
! [X0: $i,X1: $i] :
( element(sK3(X1,sK1,X0),sK0)
| ( relation_image(X1,sK1) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,sK2(X1,sK1,X0)) ),
inference(superposition,[status(thm)],[c_6475,c_85]) ).
tcf(c_7280,plain,
! [X0: $i,X1: $i] :
( element(sK3(X1,sK1,X0),sK0)
| ( relation_image(X1,sK1) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6475,c_84]) ).
tcf(c_7281,plain,
! [X0: $i,X1: $i] :
( element(sK3(X0,sK1,X1),sK0)
| element(sK2(X0,sK1,X1),X1)
| ( relation_image(X0,sK1) = X1 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6475,c_72]) ).
tcf(c_7282,plain,
! [X0: $i] :
( element(sK3(X0,sK1,sK1),sK0)
| element(sK2(X0,sK1,sK1),sK0)
| ( relation_image(X0,sK1) = sK1 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6475,c_5838]) ).
tcf(c_7284,plain,
! [X0: $i,X1: $i] :
( element(sK3(X1,sK1,sK7(powerset(X0))),sK0)
| ( relation_image(X1,sK1) = sK7(powerset(X0)) )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6475,c_5822]) ).
tcf(c_7285,plain,
! [X0: $i,X1: $i] :
( element(sK3(X0,sK1,empty_set),sK0)
| element(sK2(X0,sK1,empty_set),X1)
| ( relation_image(X0,sK1) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6475,c_5841]) ).
tcf(c_7286,plain,
! [X0: $i,X1: $i] :
( element(sK3(X1,sK1,empty_set),sK0)
| ( relation_image(X1,sK1) = empty_set )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6475,c_5823]) ).
tcf(c_7398,plain,
! [X0: $i,X1: $i] :
( empty(sK0)
| in(sK2(X0,X1,sK1),sK0)
| in(sK3(X0,X1,sK1),X1)
| ( relation_image(X0,X1) = sK1 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6486,c_71]) ).
tcf(c_7399,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X0,relation_image(X1,X2),sK1),sK0)
| ( relation_image(X0,relation_image(X1,X2)) = sK1 )
| ( apply(X1,sK4(X1,X2,sK3(X0,relation_image(X1,X2),sK1))) = sK3(X0,relation_image(X1,X2),sK1) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6486,c_60]) ).
tcf(c_7400,plain,
! [X0: $i,X1: $i] :
( element(sK2(X0,X1,sK1),sK0)
| ( relation_image(X0,X1) = sK1 )
| ( apply(identity_relation(X1),sK3(X0,X1,sK1)) = sK3(X0,X1,sK1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6486,c_151]) ).
tcf(c_7401,plain,
! [X0: $i,X1: $i] :
( element(sK2(X1,X0,sK1),sK0)
| ( relation_image(X1,X0) = sK1 )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,sK3(X1,X0,sK1)) ),
inference(superposition,[status(thm)],[c_6486,c_85]) ).
tcf(c_7402,plain,
! [X0: $i,X1: $i] :
( element(sK2(X1,X0,sK1),sK0)
| ( relation_image(X1,X0) = sK1 )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6486,c_84]) ).
tcf(c_7403,plain,
! [X0: $i,X1: $i] :
( element(sK2(X0,X1,sK1),sK0)
| element(sK3(X0,X1,sK1),X1)
| ( relation_image(X0,X1) = sK1 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6486,c_72]) ).
tcf(c_7406,plain,
! [X0: $i,X1: $i] :
( element(sK2(X1,sK7(powerset(X0)),sK1),sK0)
| ( relation_image(X1,sK7(powerset(X0))) = sK1 )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6486,c_5822]) ).
tcf(c_7407,plain,
! [X0: $i,X1: $i] :
( element(sK2(X0,empty_set,sK1),sK0)
| element(sK3(X0,empty_set,sK1),X1)
| ( relation_image(X0,empty_set) = sK1 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6486,c_5841]) ).
tcf(c_7408,plain,
! [X0: $i,X1: $i] :
( element(sK2(X1,empty_set,sK1),sK0)
| ( relation_image(X1,empty_set) = sK1 )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6486,c_5823]) ).
tcf(c_7478,plain,
! [X0: $i] : sK5(X0) = empty_set,
inference(superposition,[status(thm)],[c_67,c_52]) ).
tcf(c_7482,plain,
! [X0: $i] :
( ( relation_dom(X0) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_52]) ).
tcf(c_7488,plain,
! [X0: $i] : element(empty_set,powerset(X0)),
inference(demodulation,[status(thm)],[c_66,c_7478]) ).
tcf(c_7519,plain,
! [X0: $i] :
( empty(X0)
| in(sK7(X0),X0) ),
inference(superposition,[status(thm)],[c_73,c_71]) ).
tcf(c_7560,plain,
relation_dom(empty_set) = empty_set,
inference(superposition,[status(thm)],[c_83,c_7482]) ).
tcf(c_7574,plain,
! [X0: $i] :
( empty(sK0)
| in(sK3(X0,sK1,sK1),sK0)
| element(sK2(X0,sK1,sK1),sK0)
| ( relation_image(X0,sK1) = sK1 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7282,c_71]) ).
tcf(c_7592,plain,
! [X0: $i,X1: $i] :
( element(sK2(identity_relation(X0),X1,sK1),sK0)
| in(sK3(identity_relation(X0),X1,sK1),X0)
| ( relation_image(identity_relation(X0),X1) = sK1 )
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_121,c_6694]) ).
tcf(c_7593,plain,
! [X0: $i] :
( in(sK3(empty_set,X0,sK1),empty_set)
| element(sK2(empty_set,X0,sK1),sK0)
| ( relation_image(empty_set,X0) = sK1 )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_5746,c_6694]) ).
tcf(c_7594,plain,
! [X0: $i,X1: $i] :
( element(sK2(X0,X1,sK1),sK0)
| ( relation_image(X0,X1) = sK1 )
| ( apply(identity_relation(relation_dom(X0)),sK3(X0,X1,sK1)) = sK3(X0,X1,sK1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6694,c_151]) ).
tcf(c_7595,plain,
! [X0: $i,X1: $i] :
( element(sK2(X0,X1,sK1),sK0)
| ( relation_image(X0,X1) = sK1 )
| ~ function(X0)
| ~ relation(X0)
| ~ in(relation_dom(X0),sK3(X0,X1,sK1)) ),
inference(superposition,[status(thm)],[c_6694,c_85]) ).
tcf(c_7596,plain,
! [X0: $i,X1: $i] :
( element(sK2(X0,X1,sK1),sK0)
| ( relation_image(X0,X1) = sK1 )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_6694,c_84]) ).
tcf(c_7597,plain,
! [X0: $i,X1: $i] :
( element(sK2(X0,X1,sK1),sK0)
| element(sK3(X0,X1,sK1),relation_dom(X0))
| ( relation_image(X0,X1) = sK1 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6694,c_72]) ).
tcf(c_7603,plain,
! [X0: $i] :
( in(sK3(empty_set,X0,sK1),empty_set)
| element(sK2(empty_set,X0,sK1),sK0)
| ( relation_image(empty_set,X0) = sK1 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7593,c_5610,c_82]) ).
tcf(c_7617,plain,
! [X0: $i,X1: $i] :
( element(sK2(identity_relation(X0),X1,sK1),sK0)
| in(sK3(identity_relation(X0),X1,sK1),X0)
| ( relation_image(identity_relation(X0),X1) = sK1 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7592,c_62,c_63]) ).
tcf(c_7684,plain,
! [X0: $i] :
( in(sK7(sK1),relation_image(identity_relation(sK0),X0))
| ( identity_relation(sK1) = empty_set )
| ~ function(identity_relation(sK0))
| ~ relation(identity_relation(sK0))
| ~ in(sK7(sK1),X0)
| ~ in(sK7(sK1),relation_dom(identity_relation(sK0))) ),
inference(superposition,[status(thm)],[c_6107,c_57]) ).
tcf(c_7685,plain,
! [X0: $i] :
( in(sK7(sK1),relation_image(identity_relation(sK0),X0))
| ( identity_relation(sK1) = empty_set )
| ~ in(sK7(sK1),X0)
| ~ in(sK7(sK1),relation_dom(identity_relation(sK0))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7684,c_62,c_63]) ).
tcf(c_7701,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(X0,X3) = relation_image(X1,X2) )
| ( apply(X0,sK3(X0,X3,relation_image(X1,X2))) = sK2(X0,X3,relation_image(X1,X2)) )
| ( apply(X1,sK4(X1,X2,sK2(X0,X3,relation_image(X1,X2)))) = sK2(X0,X3,relation_image(X1,X2)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_56,c_60]) ).
tcf(c_7702,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X0,X2) = X1 )
| ( apply(X0,sK3(X0,X2,X1)) = sK2(X0,X2,X1) )
| ( apply(identity_relation(X1),sK2(X0,X2,X1)) = sK2(X0,X2,X1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_56,c_151]) ).
tcf(c_7703,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X1,X2) = X0 )
| ( apply(X1,sK3(X1,X2,X0)) = sK2(X1,X2,X0) )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,sK2(X1,X2,X0)) ),
inference(superposition,[status(thm)],[c_56,c_85]) ).
tcf(c_7704,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X1,X2) = X0 )
| ( apply(X1,sK3(X1,X2,X0)) = sK2(X1,X2,X0) )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_56,c_84]) ).
tcf(c_7705,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X0,X1,X2),X2)
| ( relation_image(X0,X1) = X2 )
| ( apply(X0,sK3(X0,X1,X2)) = sK2(X0,X1,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_56,c_72]) ).
tcf(c_7706,plain,
! [X0: $i,X1: $i] :
( element(sK2(X0,X1,sK1),sK0)
| ( relation_image(X0,X1) = sK1 )
| ( apply(X0,sK3(X0,X1,sK1)) = sK2(X0,X1,sK1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_56,c_5838]) ).
tcf(c_7707,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X0,X1) = sK1 )
| ( apply(X0,sK3(X0,X1,sK1)) = sK2(X0,X1,sK1) )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_56,c_5820]) ).
tcf(c_7708,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X1,X2) = sK7(powerset(X0)) )
| ( apply(X1,sK3(X1,X2,sK7(powerset(X0)))) = sK2(X1,X2,sK7(powerset(X0))) )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_56,c_5822]) ).
tcf(c_7709,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X0,X1,empty_set),X2)
| ( relation_image(X0,X1) = empty_set )
| ( apply(X0,sK3(X0,X1,empty_set)) = sK2(X0,X1,empty_set) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_56,c_5841]) ).
tcf(c_7710,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X1,X2) = empty_set )
| ( apply(X1,sK3(X1,X2,empty_set)) = sK2(X1,X2,empty_set) )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_56,c_5823]) ).
tcf(c_7711,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X0,X2) = relation_image(X1,sK1) )
| ( apply(X0,sK3(X0,X2,relation_image(X1,sK1))) = sK2(X0,X2,relation_image(X1,sK1)) )
| ~ empty(sK0)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_56,c_5948]) ).
tcf(c_7712,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(X1,relation_image(X2,sK1)) = relation_image(X0,X3) )
| ( apply(X0,sK3(X0,X3,relation_image(X1,relation_image(X2,sK1)))) = sK2(X0,X3,relation_image(X1,relation_image(X2,sK1))) )
| ~ empty(sK0)
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_56,c_6157]) ).
tcf(c_7835,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X0,X1,sK7(powerset(X2))),X2)
| ( relation_image(X0,X1) = sK7(powerset(X2)) )
| ( apply(X0,sK3(X0,X1,sK7(powerset(X2)))) = sK2(X0,X1,sK7(powerset(X2))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_56,c_5840]) ).
tcf(c_7836,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X0,X1,sK7(powerset(X2))),X2)
| in(sK3(X0,X1,sK7(powerset(X2))),relation_dom(X0))
| ( relation_image(X0,X1) = sK7(powerset(X2)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_54,c_5840]) ).
tcf(c_7837,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(X0,X1,sK7(powerset(X2))),X1)
| element(sK2(X0,X1,sK7(powerset(X2))),X2)
| ( relation_image(X0,X1) = sK7(powerset(X2)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_55,c_5840]) ).
tcf(c_7838,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,sK7(powerset(X1)),X2),X2)
| element(sK3(X0,sK7(powerset(X1)),X2),X1)
| ( relation_image(X0,sK7(powerset(X1))) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_55,c_5840]) ).
tcf(c_7839,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK4(X1,sK7(powerset(X2)),X0),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,sK7(powerset(X2)))) ),
inference(superposition,[status(thm)],[c_59,c_5840]) ).
tcf(c_7840,plain,
! [X0: $i] :
( empty(sK7(powerset(X0)))
| element(sK7(sK7(powerset(X0))),X0) ),
inference(superposition,[status(thm)],[c_5703,c_5840]) ).
tcf(c_7841,plain,
! [X0: $i,X1: $i] :
( element(sK3(X0,sK1,sK7(powerset(X1))),sK0)
| element(sK2(X0,sK1,sK7(powerset(X1))),X1)
| ( relation_image(X0,sK1) = sK7(powerset(X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6475,c_5840]) ).
tcf(c_7842,plain,
! [X0: $i,X1: $i] :
( element(sK2(X0,sK1,sK7(powerset(X1))),X1)
| ( relation_image(X0,sK1) = sK7(powerset(X1)) )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6476,c_5840]) ).
tcf(c_7843,plain,
! [X0: $i,X1: $i] :
( element(sK2(X0,sK7(powerset(X1)),sK1),sK0)
| element(sK3(X0,sK7(powerset(X1)),sK1),X1)
| ( relation_image(X0,sK7(powerset(X1))) = sK1 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6486,c_5840]) ).
tcf(c_7844,plain,
! [X0: $i,X1: $i] :
( element(sK3(X0,sK7(powerset(X1)),sK1),X1)
| ( relation_image(X0,sK7(powerset(X1))) = sK1 )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6487,c_5840]) ).
tcf(c_7922,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ in(X0,empty_set) ),
inference(superposition,[status(thm)],[c_7488,c_64]) ).
tcf(c_7933,plain,
identity_relation(relation_dom(empty_set)) = empty_set,
inference(superposition,[status(thm)],[c_83,c_6105]) ).
tcf(c_7934,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_6105]) ).
tcf(c_7935,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(identity_relation(X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_6105]) ).
tcf(c_7936,plain,
( ( identity_relation(relation_dom(sK1)) = empty_set )
| ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) ) ),
inference(superposition,[status(thm)],[c_5890,c_6105]) ).
tcf(c_7937,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_image(X0,sK1))) = empty_set )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6158,c_6105]) ).
tcf(c_7938,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(powerset(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_6105]) ).
tcf(c_7961,plain,
identity_relation(identity_relation(empty_set)) = empty_set,
inference(superposition,[status(thm)],[c_83,c_6106]) ).
tcf(c_7962,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_6106]) ).
tcf(c_7963,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_6106]) ).
tcf(c_7964,plain,
( ( identity_relation(identity_relation(sK1)) = empty_set )
| ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) ) ),
inference(superposition,[status(thm)],[c_5890,c_6106]) ).
tcf(c_7965,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_image(X0,sK1))) = empty_set )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6158,c_6106]) ).
tcf(c_7966,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(powerset(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_6106]) ).
tcf(c_8004,plain,
sK7(powerset(empty_set)) = empty_set,
inference(superposition,[status(thm)],[c_83,c_6879]) ).
tcf(c_8005,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_6879]) ).
tcf(c_8006,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_6879]) ).
tcf(c_8007,plain,
( ( sK7(powerset(sK1)) = empty_set )
| ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) ) ),
inference(superposition,[status(thm)],[c_5890,c_6879]) ).
tcf(c_8008,plain,
! [X0: $i] :
( ( sK7(powerset(relation_image(X0,sK1))) = empty_set )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6158,c_6879]) ).
tcf(c_8009,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(powerset(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_6879]) ).
tcf(c_8028,plain,
! [X0: $i] :
( empty(sK1)
| ~ empty(X0)
| ( sK1 != X0 ) ),
inference(instantiation,[status(thm)],[c_5010]) ).
tcf(c_8030,plain,
( empty(sK1)
| ~ empty(empty_set)
| ( sK1 != empty_set ) ),
inference(instantiation,[status(thm)],[c_8028]) ).
tcf(c_8039,plain,
! [X0: $i] :
( element(X0,sK0)
| ~ in(X0,sK1) ),
inference(superposition,[status(thm)],[c_50,c_65]) ).
tcf(c_8062,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(X0),X1) = sK1 )
| ( apply(identity_relation(X0),sK3(identity_relation(X0),X1,sK1)) = sK2(identity_relation(X0),X1,sK1) )
| ~ empty(sK0)
| ~ relation(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_62,c_7707]) ).
tcf(c_8063,plain,
! [X0: $i] :
( ( relation_image(sK14,X0) = sK1 )
| ( apply(sK14,sK3(sK14,X0,sK1)) = sK2(sK14,X0,sK1) )
| ~ relation(sK14)
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_97,c_7707]) ).
tcf(c_8064,plain,
! [X0: $i] :
( ( relation_image(empty_set,X0) = sK1 )
| ( apply(empty_set,sK3(empty_set,X0,sK1)) = sK2(empty_set,X0,sK1) )
| ~ relation(empty_set)
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_5610,c_7707]) ).
tcf(c_8065,plain,
! [X0: $i,X1: $i] :
( ( relation_image(relation_dom(X0),X1) = sK1 )
| ( apply(relation_dom(X0),sK3(relation_dom(X0),X1,sK1)) = sK2(relation_dom(X0),X1,sK1) )
| ~ empty(sK0)
| ~ empty(X0)
| ~ relation(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_5622,c_7707]) ).
tcf(c_8066,plain,
! [X0: $i] :
( ( relation_image(sK1,X0) = sK1 )
| ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ( apply(sK1,sK3(sK1,X0,sK1)) = sK2(sK1,X0,sK1) )
| ~ relation(sK1)
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_5909,c_7707]) ).
tcf(c_8067,plain,
! [X0: $i,X1: $i] :
( ( relation_image(relation_image(X0,sK1),X1) = sK1 )
| ( apply(relation_image(X0,sK1),sK3(relation_image(X0,sK1),X1,sK1)) = sK2(relation_image(X0,sK1),X1,sK1) )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0)
| ~ relation(relation_image(X0,sK1)) ),
inference(superposition,[status(thm)],[c_6199,c_7707]) ).
tcf(c_8068,plain,
! [X0: $i,X1: $i] :
( ( relation_image(sK7(powerset(X0)),X1) = sK1 )
| ( apply(sK7(powerset(X0)),sK3(sK7(powerset(X0)),X1,sK1)) = sK2(sK7(powerset(X0)),X1,sK1) )
| ~ empty(sK0)
| ~ empty(X0)
| ~ relation(sK7(powerset(X0))) ),
inference(superposition,[status(thm)],[c_6880,c_7707]) ).
tcf(c_8069,plain,
! [X0: $i] :
( ( relation_image(empty_set,X0) = sK1 )
| ( apply(empty_set,sK3(empty_set,X0,sK1)) = sK2(empty_set,X0,sK1) )
| ~ empty(sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8064,c_82]) ).
tcf(c_8073,plain,
! [X0: $i] :
( ( relation_image(sK14,X0) = sK1 )
| ( apply(sK14,sK3(sK14,X0,sK1)) = sK2(sK14,X0,sK1) )
| ~ empty(sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8063,c_96]) ).
tcf(c_8077,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(X0),X1) = sK1 )
| ( apply(identity_relation(X0),sK3(identity_relation(X0),X1,sK1)) = sK2(identity_relation(X0),X1,sK1) )
| ~ empty(sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8062,c_63]) ).
tcf(c_8112,plain,
function(identity_relation(sK0)),
inference(instantiation,[status(thm)],[c_62]) ).
tcf(c_8123,plain,
! [X0: $i,X1: $i] :
( empty(sK0)
| in(sK2(X0,X1,sK1),sK0)
| ( relation_image(X0,X1) = sK1 )
| ( apply(X0,sK3(X0,X1,sK1)) = sK2(X0,X1,sK1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7706,c_71]) ).
tcf(c_8131,plain,
! [X0: $i] :
( ( relation_image(relation_dom(X0),sK1) = sK1 )
| ~ empty(sK0)
| ~ empty(X0) ),
inference(global_subsumption_just,[status(thm)],[c_7048,c_87,c_7048]) ).
tcf(c_8140,plain,
( ( relation_image(relation_dom(empty_set),sK1) = sK1 )
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_83,c_8131]) ).
tcf(c_8141,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_dom(X0)),sK1) = sK1 )
| ~ empty(sK0)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_8131]) ).
tcf(c_8142,plain,
! [X0: $i] :
( ( relation_image(relation_dom(identity_relation(X0)),sK1) = sK1 )
| ~ empty(sK0)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_8131]) ).
tcf(c_8143,plain,
( ( relation_image(relation_dom(sK1),sK1) = sK1 )
| ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_5890,c_8131]) ).
tcf(c_8144,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_image(X0,sK1)),sK1) = sK1 )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6158,c_8131]) ).
tcf(c_8145,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK7(powerset(X0))),sK1) = sK1 )
| ~ empty(sK0)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_8131]) ).
tcf(c_8147,plain,
! [X0: $i] :
( ( relation_image(X0,sK1) = sK1 )
| ~ empty(sK0)
| ~ empty(X0) ),
inference(light_normalisation,[status(thm)],[c_8142,c_121]) ).
tcf(c_8184,plain,
( relation(sK1)
| ~ empty(sK1) ),
inference(instantiation,[status(thm)],[c_80]) ).
tcf(c_8208,plain,
! [X0: $i] :
( ( relation_image(X0,empty_set) = sK1 )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_83,c_7107]) ).
tcf(c_8209,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X1,relation_dom(X0)) = sK1 )
| ~ empty(sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_7107]) ).
tcf(c_8210,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X1,identity_relation(X0)) = sK1 )
| ~ empty(sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_7107]) ).
tcf(c_8211,plain,
! [X0: $i] :
( ( relation_image(X0,sK1) = sK1 )
| ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_5890,c_7107]) ).
tcf(c_8212,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X1,relation_image(X0,sK1)) = sK1 )
| ~ empty(sK0)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6158,c_7107]) ).
tcf(c_8301,plain,
! [X0: $i] :
( ( relation_image(X0,empty_set) = sK1 )
| ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_5890,c_7113]) ).
tcf(c_8302,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X1,empty_set) = sK1 )
| ~ empty(sK0)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6158,c_7113]) ).
tcf(c_8316,plain,
! [X0: $i] :
( ( relation_image(sK7(powerset(X0)),sK1) = sK1 )
| ~ empty(sK0)
| ~ empty(X0) ),
inference(global_subsumption_just,[status(thm)],[c_7051,c_6881,c_7051]) ).
tcf(c_8325,plain,
( ( relation_image(sK7(powerset(empty_set)),sK1) = sK1 )
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_83,c_8316]) ).
tcf(c_8326,plain,
! [X0: $i] :
( ( relation_image(sK7(powerset(relation_dom(X0))),sK1) = sK1 )
| ~ empty(sK0)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_8316]) ).
tcf(c_8327,plain,
! [X0: $i] :
( ( relation_image(sK7(powerset(identity_relation(X0))),sK1) = sK1 )
| ~ empty(sK0)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_8316]) ).
tcf(c_8328,plain,
( ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ( relation_image(sK7(powerset(sK1)),sK1) = sK1 )
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_5890,c_8316]) ).
tcf(c_8329,plain,
! [X0: $i] :
( ( relation_image(sK7(powerset(relation_image(X0,sK1))),sK1) = sK1 )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6158,c_8316]) ).
tcf(c_8330,plain,
! [X0: $i] :
( ( relation_image(sK7(powerset(sK7(powerset(X0)))),sK1) = sK1 )
| ~ empty(sK0)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_8316]) ).
tcf(c_8356,plain,
! [X0: $i] :
( in(sK7(sK1),relation_image(identity_relation(sK0),X0))
| ( relation_dom(relation_dom(sK1)) = empty_set )
| ~ function(identity_relation(sK0))
| ~ relation(identity_relation(sK0))
| ~ in(sK7(sK1),X0)
| ~ in(sK7(sK1),relation_dom(identity_relation(sK0))) ),
inference(superposition,[status(thm)],[c_6135,c_57]) ).
tcf(c_8357,plain,
! [X0: $i] :
( in(sK7(sK1),relation_image(identity_relation(sK0),X0))
| ( relation_dom(relation_dom(sK1)) = empty_set )
| ~ in(sK7(sK1),X0)
| ~ in(sK7(sK1),relation_dom(identity_relation(sK0))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8356,c_62,c_63]) ).
tcf(c_8368,plain,
( empty(powerset(empty_set))
| in(empty_set,powerset(empty_set)) ),
inference(superposition,[status(thm)],[c_8004,c_5703]) ).
tcf(c_8369,plain,
element(empty_set,powerset(empty_set)),
inference(superposition,[status(thm)],[c_8004,c_73]) ).
tcf(c_8371,plain,
! [X0: $i] :
( ~ empty(empty_set)
| ~ in(X0,empty_set) ),
inference(superposition,[status(thm)],[c_8004,c_5822]) ).
tcf(c_8375,plain,
! [X0: $i] : ~ in(X0,empty_set),
inference(forward_subsumption_resolution,[status(thm)],[c_8371,c_83]) ).
tcf(c_8386,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X2)
| element(sK2(X0,X1,sK6(X2)),X2)
| ( relation_image(X0,X1) = sK6(X2) )
| ( apply(X0,sK3(X0,X1,sK6(X2))) = sK2(X0,X1,sK6(X2)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_56,c_5839]) ).
tcf(c_8387,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X2)
| element(sK2(X0,X1,sK6(X2)),X2)
| in(sK3(X0,X1,sK6(X2)),relation_dom(X0))
| ( relation_image(X0,X1) = sK6(X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_54,c_5839]) ).
tcf(c_8388,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X2)
| in(sK3(X0,X1,sK6(X2)),X1)
| element(sK2(X0,X1,sK6(X2)),X2)
| ( relation_image(X0,X1) = sK6(X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_55,c_5839]) ).
tcf(c_8389,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X1)
| in(sK2(X0,sK6(X1),X2),X2)
| element(sK3(X0,sK6(X1),X2),X1)
| ( relation_image(X0,sK6(X1)) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_55,c_5839]) ).
tcf(c_8390,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X2)
| element(sK4(X1,sK6(X2),X0),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,sK6(X2))) ),
inference(superposition,[status(thm)],[c_59,c_5839]) ).
tcf(c_8391,plain,
! [X0: $i] :
( empty(X0)
| empty(sK6(X0))
| element(sK7(sK6(X0)),X0) ),
inference(superposition,[status(thm)],[c_5703,c_5839]) ).
tcf(c_8392,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| element(sK3(X0,sK1,sK6(X1)),sK0)
| element(sK2(X0,sK1,sK6(X1)),X1)
| ( relation_image(X0,sK1) = sK6(X1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6475,c_5839]) ).
tcf(c_8393,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| element(sK2(X0,sK1,sK6(X1)),X1)
| ( relation_image(X0,sK1) = sK6(X1) )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6476,c_5839]) ).
tcf(c_8394,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| element(sK2(X0,sK6(X1),sK1),sK0)
| element(sK3(X0,sK6(X1),sK1),X1)
| ( relation_image(X0,sK6(X1)) = sK1 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6486,c_5839]) ).
tcf(c_8395,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| element(sK3(X0,sK6(X1),sK1),X1)
| ( relation_image(X0,sK6(X1)) = sK1 )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6487,c_5839]) ).
tcf(c_8452,plain,
! [X0: $i] : ~ in(X0,empty_set),
inference(global_subsumption_just,[status(thm)],[c_7922,c_8375]) ).
tcf(c_8508,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X0,X1) = empty_set )
| ( apply(X0,sK3(X0,X1,empty_set)) = sK2(X0,X1,empty_set) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_56,c_8375]) ).
tcf(c_8509,plain,
! [X0: $i,X1: $i] :
( in(sK3(X0,X1,empty_set),relation_dom(X0))
| ( relation_image(X0,X1) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_54,c_8375]) ).
tcf(c_8510,plain,
! [X0: $i,X1: $i] :
( in(sK3(X0,X1,empty_set),X1)
| ( relation_image(X0,X1) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_55,c_8375]) ).
tcf(c_8511,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,empty_set,X1),X1)
| ( relation_image(X0,empty_set) = X1 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_55,c_8375]) ).
tcf(c_8512,plain,
! [X0: $i,X1: $i] :
( ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,empty_set)) ),
inference(superposition,[status(thm)],[c_59,c_8375]) ).
tcf(c_8514,plain,
! [X0: $i] :
( element(sK3(X0,sK1,empty_set),sK0)
| ( relation_image(X0,sK1) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6475,c_8375]) ).
tcf(c_8516,plain,
! [X0: $i] :
( element(sK2(X0,empty_set,sK1),sK0)
| ( relation_image(X0,empty_set) = sK1 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6486,c_8375]) ).
tcf(c_8560,plain,
relation_dom(relation_dom(relation_dom(empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_6133]) ).
tcf(c_8561,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_6133]) ).
tcf(c_8562,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(identity_relation(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_6133]) ).
tcf(c_8563,plain,
( ( relation_dom(relation_dom(relation_dom(sK1))) = empty_set )
| ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) ) ),
inference(superposition,[status(thm)],[c_5890,c_6133]) ).
tcf(c_8564,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_image(X0,sK1)))) = empty_set )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6158,c_6133]) ).
tcf(c_8565,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK7(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_6133]) ).
tcf(c_8658,plain,
! [X0: $i] :
( empty(sK0)
| in(sK3(X0,sK1,empty_set),sK0)
| ( relation_image(X0,sK1) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8514,c_71]) ).
tcf(c_8673,plain,
! [X0: $i] :
( empty(sK0)
| in(sK2(X0,empty_set,sK1),sK0)
| ( relation_image(X0,empty_set) = sK1 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8516,c_71]) ).
tcf(c_8680,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X0,X1) = sK1 )
| ~ empty(sK0)
| ~ empty(relation_dom(X0))
| ~ relation(X0) ),
inference(global_subsumption_just,[status(thm)],[c_7216,c_98,c_88,c_7216]) ).
tcf(c_8681,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X0,X1) = sK1 )
| ~ empty(sK0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(renaming,[status(thm)],[c_8680]) ).
tcf(c_8691,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X0,X1) = sK1 )
| ~ empty(sK0)
| ~ relation(X0)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_8681]) ).
tcf(c_8692,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(X0),X1) = sK1 )
| ~ empty(sK0)
| ~ empty(X0)
| ~ relation(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_121,c_8681]) ).
tcf(c_8693,plain,
! [X0: $i] :
( ( relation_image(empty_set,X0) = sK1 )
| ~ relation(empty_set)
| ~ empty(empty_set)
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_5746,c_8681]) ).
tcf(c_8694,plain,
! [X0: $i] :
( ( relation_image(empty_set,X0) = sK1 )
| ~ empty(sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8693,c_82,c_83]) ).
tcf(c_8701,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(X0),X1) = sK1 )
| ~ empty(sK0)
| ~ empty(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8692,c_63]) ).
tcf(c_8721,plain,
! [X0: $i] :
( ( relation_image(X0,sK1) = sK7(powerset(empty_set)) )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_83,c_6946]) ).
tcf(c_8722,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(relation_dom(X0))) = relation_image(X1,sK1) )
| ~ empty(sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_6946]) ).
tcf(c_8723,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(identity_relation(X0))) = relation_image(X1,sK1) )
| ~ empty(sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_6946]) ).
tcf(c_8724,plain,
! [X0: $i] :
( ( relation_image(X0,sK1) = sK7(powerset(sK1)) )
| ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_5890,c_6946]) ).
tcf(c_8725,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(relation_image(X0,sK1))) = relation_image(X1,sK1) )
| ~ empty(sK0)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6158,c_6946]) ).
tcf(c_8726,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(sK7(powerset(X0)))) = relation_image(X1,sK1) )
| ~ empty(sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_6946]) ).
tcf(c_8819,plain,
! [X0: $i] :
( ( relation_image(X0,sK7(powerset(empty_set))) = sK1 )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_83,c_7111]) ).
tcf(c_8820,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X1,sK7(powerset(relation_dom(X0)))) = sK1 )
| ~ empty(sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_7111]) ).
tcf(c_8821,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X1,sK7(powerset(identity_relation(X0)))) = sK1 )
| ~ empty(sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_7111]) ).
tcf(c_8822,plain,
! [X0: $i] :
( ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ( relation_image(X0,sK7(powerset(sK1))) = sK1 )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_5890,c_7111]) ).
tcf(c_8823,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X1,sK7(powerset(relation_image(X0,sK1)))) = sK1 )
| ~ empty(sK0)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6158,c_7111]) ).
tcf(c_8824,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X1,sK7(powerset(sK7(powerset(X0))))) = sK1 )
| ~ empty(sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_7111]) ).
tcf(c_8879,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,X2)
| ( relation_image(X1,sK1) = powerset(X2) )
| ~ empty(sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,sK2(X1,sK1,powerset(X2))) ),
inference(superposition,[status(thm)],[c_6943,c_65]) ).
tcf(c_8880,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X1,sK1) = powerset(X2) )
| ~ empty(sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X2)
| ~ in(X0,sK2(X1,sK1,powerset(X2))) ),
inference(superposition,[status(thm)],[c_6943,c_64]) ).
tcf(c_8896,plain,
( ( relation_image(sK1,sK1) = sK1 )
| ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ~ empty(sK0) ),
inference(global_subsumption_just,[status(thm)],[c_7049,c_5857,c_7049,c_8184]) ).
tcf(c_8914,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,X2)
| ( relation_image(X1,powerset(X2)) = sK1 )
| ~ empty(sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,sK3(X1,powerset(X2),sK1)) ),
inference(superposition,[status(thm)],[c_7108,c_65]) ).
tcf(c_8915,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X1,powerset(X2)) = sK1 )
| ~ empty(sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X2)
| ~ in(X0,sK3(X1,powerset(X2),sK1)) ),
inference(superposition,[status(thm)],[c_7108,c_64]) ).
tcf(c_8937,plain,
! [X0: $i] :
( in(sK7(sK1),relation_image(identity_relation(sK0),X0))
| ( identity_relation(relation_dom(sK1)) = empty_set )
| ~ function(identity_relation(sK0))
| ~ relation(identity_relation(sK0))
| ~ in(sK7(sK1),X0)
| ~ in(sK7(sK1),relation_dom(identity_relation(sK0))) ),
inference(superposition,[status(thm)],[c_7936,c_57]) ).
tcf(c_8938,plain,
! [X0: $i] :
( in(sK7(sK1),relation_image(identity_relation(sK0),X0))
| ( identity_relation(relation_dom(sK1)) = empty_set )
| ~ in(sK7(sK1),X0)
| ~ in(sK7(sK1),relation_dom(identity_relation(sK0))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8937,c_62,c_63]) ).
tcf(c_8956,plain,
identity_relation(relation_dom(relation_dom(empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_7934]) ).
tcf(c_8957,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(relation_dom(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_7934]) ).
tcf(c_8958,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(identity_relation(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_7934]) ).
tcf(c_8959,plain,
( ( identity_relation(relation_dom(relation_dom(sK1))) = empty_set )
| ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) ) ),
inference(superposition,[status(thm)],[c_5890,c_7934]) ).
tcf(c_8960,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(relation_image(X0,sK1)))) = empty_set )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6158,c_7934]) ).
tcf(c_8961,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(sK7(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_7934]) ).
tcf(c_8985,plain,
! [X0: $i,X1: $i] :
( empty(sK6(sK6(powerset(X1))))
| in(X0,sK6(sK6(powerset(X1))))
| ~ element(X0,sK6(sK6(powerset(X1)))) ),
inference(instantiation,[status(thm)],[c_71]) ).
tcf(c_8986,plain,
( empty(sK6(sK6(powerset(empty_set))))
| in(empty_set,sK6(sK6(powerset(empty_set))))
| ~ element(empty_set,sK6(sK6(powerset(empty_set)))) ),
inference(instantiation,[status(thm)],[c_8985]) ).
tcf(c_8991,plain,
identity_relation(identity_relation(relation_dom(empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_7962]) ).
tcf(c_8992,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(relation_dom(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_7962]) ).
tcf(c_8993,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(identity_relation(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_7962]) ).
tcf(c_8994,plain,
( ( identity_relation(identity_relation(relation_dom(sK1))) = empty_set )
| ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) ) ),
inference(superposition,[status(thm)],[c_5890,c_7962]) ).
tcf(c_8995,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(relation_image(X0,sK1)))) = empty_set )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6158,c_7962]) ).
tcf(c_8996,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(sK7(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_7962]) ).
tcf(c_9016,plain,
sK7(powerset(relation_dom(empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_8005]) ).
tcf(c_9017,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(relation_dom(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_8005]) ).
tcf(c_9018,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(identity_relation(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_8005]) ).
tcf(c_9019,plain,
( ( sK7(powerset(relation_dom(sK1))) = empty_set )
| ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) ) ),
inference(superposition,[status(thm)],[c_5890,c_8005]) ).
tcf(c_9020,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(relation_image(X0,sK1)))) = empty_set )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6158,c_8005]) ).
tcf(c_9021,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(sK7(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_8005]) ).
tcf(c_9052,plain,
! [X0: $i,X1: $i] :
( in(sK4(empty_set,X1,X0),empty_set)
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ in(X0,relation_image(empty_set,X1)) ),
inference(superposition,[status(thm)],[c_7560,c_58]) ).
tcf(c_9061,plain,
! [X0: $i,X1: $i] : ~ in(X0,relation_image(empty_set,X1)),
inference(forward_subsumption_resolution,[status(thm)],[c_9052,c_8452,c_7035,c_82]) ).
tcf(c_9086,plain,
identity_relation(sK7(powerset(empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_6876]) ).
tcf(c_9087,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(relation_dom(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_6876]) ).
tcf(c_9088,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(identity_relation(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_6876]) ).
tcf(c_9089,plain,
( ( identity_relation(sK7(powerset(sK1))) = empty_set )
| ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) ) ),
inference(superposition,[status(thm)],[c_5890,c_6876]) ).
tcf(c_9090,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(relation_image(X0,sK1)))) = empty_set )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6158,c_6876]) ).
tcf(c_9091,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(sK7(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_6876]) ).
tcf(c_9113,plain,
relation_dom(sK7(powerset(empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_6878]) ).
tcf(c_9114,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(relation_dom(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_6878]) ).
tcf(c_9115,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(identity_relation(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_6878]) ).
tcf(c_9116,plain,
( ( relation_dom(sK7(powerset(sK1))) = empty_set )
| ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) ) ),
inference(superposition,[status(thm)],[c_5890,c_6878]) ).
tcf(c_9117,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(relation_image(X0,sK1)))) = empty_set )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6158,c_6878]) ).
tcf(c_9118,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(sK7(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_6878]) ).
tcf(c_9148,plain,
( empty(sK7(powerset(empty_set)))
| element(sK7(empty_set),empty_set) ),
inference(superposition,[status(thm)],[c_8004,c_7840]) ).
tcf(c_9149,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| empty(sK7(powerset(powerset(X1))))
| ~ in(X0,sK7(sK7(powerset(powerset(X1))))) ),
inference(superposition,[status(thm)],[c_7840,c_65]) ).
tcf(c_9150,plain,
! [X0: $i,X1: $i] :
( empty(sK7(powerset(powerset(X1))))
| ~ empty(X1)
| ~ in(X0,sK7(sK7(powerset(powerset(X1))))) ),
inference(superposition,[status(thm)],[c_7840,c_64]) ).
tcf(c_9151,plain,
! [X0: $i] :
( empty(X0)
| empty(sK7(powerset(X0)))
| in(sK7(sK7(powerset(X0))),X0) ),
inference(superposition,[status(thm)],[c_7840,c_71]) ).
tcf(c_9152,plain,
( empty(empty_set)
| element(sK7(empty_set),empty_set) ),
inference(light_normalisation,[status(thm)],[c_9148,c_8004]) ).
tcf(c_9174,plain,
! [X0: $i,X1: $i] :
( empty(sK0)
| in(sK3(X1,sK1,X0),sK0)
| ( relation_image(X1,sK1) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7280,c_71]) ).
tcf(c_9191,plain,
! [X0: $i,X1: $i] :
( empty(sK0)
| in(sK2(X1,X0,sK1),sK0)
| ( relation_image(X1,X0) = sK1 )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7402,c_71]) ).
tcf(c_9208,plain,
! [X0: $i] :
( ( relation_image(relation_image(X0,sK1),sK1) = sK1 )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(global_subsumption_just,[status(thm)],[c_7050,c_6200,c_7050]) ).
tcf(c_9219,plain,
! [X0: $i] :
( ( relation_image(relation_image(identity_relation(X0),sK1),sK1) = sK1 )
| ~ empty(sK0)
| ~ relation(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_62,c_9208]) ).
tcf(c_9220,plain,
( ( relation_image(relation_image(sK14,sK1),sK1) = sK1 )
| ~ relation(sK14)
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_97,c_9208]) ).
tcf(c_9221,plain,
( ( relation_image(relation_image(empty_set,sK1),sK1) = sK1 )
| ~ relation(empty_set)
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_5610,c_9208]) ).
tcf(c_9222,plain,
! [X0: $i] :
( ( relation_image(relation_image(relation_dom(X0),sK1),sK1) = sK1 )
| ~ empty(sK0)
| ~ empty(X0)
| ~ relation(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_5622,c_9208]) ).
tcf(c_9223,plain,
( ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ( relation_image(relation_image(sK1,sK1),sK1) = sK1 )
| ~ relation(sK1)
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_5909,c_9208]) ).
tcf(c_9224,plain,
! [X0: $i] :
( ( relation_image(relation_image(relation_image(X0,sK1),sK1),sK1) = sK1 )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0)
| ~ relation(relation_image(X0,sK1)) ),
inference(superposition,[status(thm)],[c_6199,c_9208]) ).
tcf(c_9225,plain,
! [X0: $i] :
( ( relation_image(relation_image(sK7(powerset(X0)),sK1),sK1) = sK1 )
| ~ empty(sK0)
| ~ empty(X0)
| ~ relation(sK7(powerset(X0))) ),
inference(superposition,[status(thm)],[c_6880,c_9208]) ).
tcf(c_9226,plain,
( ( relation_image(relation_image(empty_set,sK1),sK1) = sK1 )
| ~ empty(sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9221,c_82]) ).
tcf(c_9229,plain,
( ( relation_image(relation_image(sK14,sK1),sK1) = sK1 )
| ~ empty(sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9220,c_96]) ).
tcf(c_9232,plain,
! [X0: $i] :
( ( relation_image(relation_image(identity_relation(X0),sK1),sK1) = sK1 )
| ~ empty(sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9219,c_63]) ).
tcf(c_9305,plain,
! [X0: $i] :
( in(sK7(sK1),relation_image(identity_relation(sK0),X0))
| ( identity_relation(identity_relation(sK1)) = empty_set )
| ~ function(identity_relation(sK0))
| ~ relation(identity_relation(sK0))
| ~ in(sK7(sK1),X0)
| ~ in(sK7(sK1),relation_dom(identity_relation(sK0))) ),
inference(superposition,[status(thm)],[c_7964,c_57]) ).
tcf(c_9306,plain,
! [X0: $i] :
( in(sK7(sK1),relation_image(identity_relation(sK0),X0))
| ( identity_relation(identity_relation(sK1)) = empty_set )
| ~ in(sK7(sK1),X0)
| ~ in(sK7(sK1),relation_dom(identity_relation(sK0))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9305,c_62,c_63]) ).
tcf(c_9318,plain,
! [X0: $i] :
( ( relation_dom(empty_set) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_83,c_5793]) ).
tcf(c_9319,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(X0)) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_5793]) ).
tcf(c_9320,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(identity_relation(X0)) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_5793]) ).
tcf(c_9321,plain,
! [X0: $i] :
( ( relation_dom(sK1) = X0 )
| ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5890,c_5793]) ).
tcf(c_9322,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_image(X1,sK1)) = X0 )
| ~ empty(sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6158,c_5793]) ).
tcf(c_9323,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(powerset(X0))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_5793]) ).
tcf(c_9346,plain,
! [X0: $i] :
( ( identity_relation(empty_set) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_83,c_5794]) ).
tcf(c_9347,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(X0)) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_5794]) ).
tcf(c_9348,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(X0)) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_5794]) ).
tcf(c_9349,plain,
! [X0: $i] :
( ( identity_relation(sK1) = X0 )
| ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5890,c_5794]) ).
tcf(c_9350,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_image(X1,sK1)) = X0 )
| ~ empty(sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6158,c_5794]) ).
tcf(c_9351,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK7(powerset(X0))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_5794]) ).
tcf(c_9409,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(X1) = X0 )
| ( apply(identity_relation(X1),sK7(X1)) = sK7(X1) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5807,c_5794]) ).
tcf(c_9410,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(X1) = X0 )
| ( apply(identity_relation(X1),sK7(X1)) = sK7(X1) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5807,c_5793]) ).
tcf(c_9411,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(X0))) = empty_set )
| ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) ) ),
inference(superposition,[status(thm)],[c_5807,c_6878]) ).
tcf(c_9412,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(X0))) = empty_set )
| ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) ) ),
inference(superposition,[status(thm)],[c_5807,c_6876]) ).
tcf(c_9413,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(X0))) = empty_set )
| ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) ) ),
inference(superposition,[status(thm)],[c_5807,c_8005]) ).
tcf(c_9414,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(X0))) = empty_set )
| ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) ) ),
inference(superposition,[status(thm)],[c_5807,c_7962]) ).
tcf(c_9415,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(X0))) = empty_set )
| ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) ) ),
inference(superposition,[status(thm)],[c_5807,c_7934]) ).
tcf(c_9416,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X1),sK7(X1)) = sK7(X1) )
| ( relation_image(X0,sK7(powerset(X1))) = sK1 )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_5807,c_7111]) ).
tcf(c_9417,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X0,sK1) = sK7(powerset(X1)) )
| ( apply(identity_relation(X1),sK7(X1)) = sK7(X1) )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_5807,c_6946]) ).
tcf(c_9418,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(X0))) = empty_set )
| ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) ) ),
inference(superposition,[status(thm)],[c_5807,c_6133]) ).
tcf(c_9419,plain,
! [X0: $i] :
( ( relation_image(sK7(powerset(X0)),sK1) = sK1 )
| ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_5807,c_8316]) ).
tcf(c_9420,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X0,empty_set) = sK1 )
| ( apply(identity_relation(X1),sK7(X1)) = sK7(X1) )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_5807,c_7113]) ).
tcf(c_9421,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X0,X1) = sK1 )
| ( apply(identity_relation(X1),sK7(X1)) = sK7(X1) )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_5807,c_7107]) ).
tcf(c_9422,plain,
! [X0: $i] :
( ( relation_image(relation_dom(X0),sK1) = sK1 )
| ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_5807,c_8131]) ).
tcf(c_9423,plain,
! [X0: $i] :
( ( sK7(powerset(X0)) = empty_set )
| ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) ) ),
inference(superposition,[status(thm)],[c_5807,c_6879]) ).
tcf(c_9424,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(X0)) = empty_set )
| ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) ) ),
inference(superposition,[status(thm)],[c_5807,c_6106]) ).
tcf(c_9425,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(X0)) = empty_set )
| ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) ) ),
inference(superposition,[status(thm)],[c_5807,c_6105]) ).
tcf(c_9426,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(X0)) = empty_set )
| ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) ) ),
inference(superposition,[status(thm)],[c_5807,c_5747]) ).
tcf(c_9427,plain,
! [X0: $i] :
( ( identity_relation(X0) = empty_set )
| ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) ) ),
inference(superposition,[status(thm)],[c_5807,c_5776]) ).
tcf(c_9428,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( apply(identity_relation(X1),sK7(X1)) = sK7(X1) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5807,c_51]) ).
tcf(c_9429,plain,
! [X0: $i] :
( ( relation_dom(X0) = empty_set )
| ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) ) ),
inference(superposition,[status(thm)],[c_5807,c_5663]) ).
tcf(c_9430,plain,
! [X0: $i] :
( ( X0 = empty_set )
| ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) ) ),
inference(superposition,[status(thm)],[c_5807,c_52]) ).
tcf(c_9431,plain,
! [X0: $i] :
( function(X0)
| ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) ) ),
inference(superposition,[status(thm)],[c_5807,c_98]) ).
tcf(c_9432,plain,
! [X0: $i] :
( relation(X0)
| ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) ) ),
inference(superposition,[status(thm)],[c_5807,c_80]) ).
tcf(c_9433,plain,
! [X0: $i] :
( empty(X0)
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_5807,c_69]) ).
tcf(c_9434,plain,
! [X0: $i] : apply(identity_relation(powerset(X0)),sK7(powerset(X0))) = sK7(powerset(X0)),
inference(superposition,[status(thm)],[c_5807,c_70]) ).
tcf(c_9435,plain,
apply(identity_relation(sK8),sK7(sK8)) = sK7(sK8),
inference(superposition,[status(thm)],[c_5807,c_74]) ).
tcf(c_9436,plain,
apply(identity_relation(sK9),sK7(sK9)) = sK7(sK9),
inference(superposition,[status(thm)],[c_5807,c_75]) ).
tcf(c_9437,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X0,X1) = sK1 )
| ( apply(identity_relation(relation_dom(X0)),sK7(relation_dom(X0))) = sK7(relation_dom(X0)) )
| ~ empty(sK0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_5807,c_8681]) ).
tcf(c_9438,plain,
! [X0: $i] :
( empty(X0)
| ( apply(identity_relation(relation_dom(X0)),sK7(relation_dom(X0))) = sK7(relation_dom(X0)) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_5807,c_88]) ).
tcf(c_9439,plain,
! [X0: $i] :
( function(X0)
| ( apply(identity_relation(identity_relation(X0)),sK7(identity_relation(X0))) = sK7(identity_relation(X0)) ) ),
inference(superposition,[status(thm)],[c_5807,c_5644]) ).
tcf(c_9440,plain,
! [X0: $i] :
( relation(X0)
| ( apply(identity_relation(identity_relation(X0)),sK7(identity_relation(X0))) = sK7(identity_relation(X0)) ) ),
inference(superposition,[status(thm)],[c_5807,c_5633]) ).
tcf(c_9441,plain,
! [X0: $i] :
( empty(X0)
| ( apply(identity_relation(identity_relation(X0)),sK7(identity_relation(X0))) = sK7(identity_relation(X0)) ) ),
inference(superposition,[status(thm)],[c_5807,c_5621]) ).
tcf(c_9442,plain,
! [X0: $i] :
( ( relation_image(empty_set,X0) = sK1 )
| ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) ) ),
inference(superposition,[status(thm)],[c_5807,c_8694]) ).
tcf(c_9443,plain,
! [X0: $i] :
( ( relation_image(identity_relation(X0),sK1) = sK1 )
| ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) ) ),
inference(superposition,[status(thm)],[c_5807,c_7058]) ).
tcf(c_9444,plain,
( ( relation_image(sK1,sK1) = sK1 )
| ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) )
| ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) ) ),
inference(superposition,[status(thm)],[c_5807,c_8896]) ).
tcf(c_9445,plain,
! [X0: $i] :
( ( relation_image(identity_relation(X0),sK1) = empty_set )
| ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) ) ),
inference(superposition,[status(thm)],[c_5807,c_6342]) ).
tcf(c_9446,plain,
( ( relation_image(sK14,sK1) = sK1 )
| ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) ) ),
inference(superposition,[status(thm)],[c_5807,c_7055]) ).
tcf(c_9447,plain,
( ( relation_image(sK14,sK1) = empty_set )
| ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) ) ),
inference(superposition,[status(thm)],[c_5807,c_6339]) ).
tcf(c_9448,plain,
( ( relation_image(empty_set,sK1) = empty_set )
| ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) ) ),
inference(superposition,[status(thm)],[c_5807,c_6336]) ).
tcf(c_9449,plain,
( empty(sK1)
| ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) ) ),
inference(superposition,[status(thm)],[c_5807,c_5857]) ).
tcf(c_9614,plain,
! [X0: $i] : empty(relation_image(empty_set,X0)),
inference(superposition,[status(thm)],[c_7519,c_9061]) ).
tcf(c_9622,plain,
! [X0: $i] : relation_image(empty_set,X0) = empty_set,
inference(superposition,[status(thm)],[c_9614,c_52]) ).
tcf(c_9663,plain,
! [X0: $i] :
( in(sK7(sK8),relation_image(identity_relation(sK8),X0))
| ~ function(identity_relation(sK8))
| ~ relation(identity_relation(sK8))
| ~ in(sK7(sK8),X0)
| ~ in(sK7(sK8),relation_dom(identity_relation(sK8))) ),
inference(superposition,[status(thm)],[c_9435,c_57]) ).
tcf(c_9664,plain,
! [X0: $i] :
( in(sK7(sK8),relation_image(identity_relation(sK8),X0))
| ~ in(sK7(sK8),X0)
| ~ in(sK7(sK8),relation_dom(identity_relation(sK8))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9663,c_62,c_63]) ).
tcf(c_9669,plain,
! [X0: $i] :
( in(sK7(sK9),relation_image(identity_relation(sK9),X0))
| ~ function(identity_relation(sK9))
| ~ relation(identity_relation(sK9))
| ~ in(sK7(sK9),X0)
| ~ in(sK7(sK9),relation_dom(identity_relation(sK9))) ),
inference(superposition,[status(thm)],[c_9436,c_57]) ).
tcf(c_9670,plain,
! [X0: $i] :
( in(sK7(sK9),relation_image(identity_relation(sK9),X0))
| ~ in(sK7(sK9),X0)
| ~ in(sK7(sK9),relation_dom(identity_relation(sK9))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9669,c_62,c_63]) ).
tcf(c_9679,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(X0))) = empty_set )
| ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) ) ),
inference(superposition,[status(thm)],[c_5807,c_7963]) ).
tcf(c_9680,plain,
identity_relation(identity_relation(identity_relation(empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_7963]) ).
tcf(c_9681,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(relation_dom(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_7963]) ).
tcf(c_9682,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_7963]) ).
tcf(c_9683,plain,
( ( identity_relation(identity_relation(identity_relation(sK1))) = empty_set )
| ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) ) ),
inference(superposition,[status(thm)],[c_5890,c_7963]) ).
tcf(c_9684,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(relation_image(X0,sK1)))) = empty_set )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6158,c_7963]) ).
tcf(c_9685,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(sK7(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_7963]) ).
tcf(c_9745,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(X0))) = empty_set )
| ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) ) ),
inference(superposition,[status(thm)],[c_5807,c_8006]) ).
tcf(c_9746,plain,
sK7(powerset(identity_relation(empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_8006]) ).
tcf(c_9747,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(relation_dom(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_8006]) ).
tcf(c_9748,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(identity_relation(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_8006]) ).
tcf(c_9749,plain,
( ( sK7(powerset(identity_relation(sK1))) = empty_set )
| ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) ) ),
inference(superposition,[status(thm)],[c_5890,c_8006]) ).
tcf(c_9750,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(relation_image(X0,sK1)))) = empty_set )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6158,c_8006]) ).
tcf(c_9751,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(sK7(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_8006]) ).
tcf(c_9806,plain,
! [X0: $i] :
( empty(X0)
| element(sK7(sK6(X0)),X0) ),
inference(global_subsumption_just,[status(thm)],[c_8391,c_69,c_8391]) ).
tcf(c_9812,plain,
! [X0: $i,X1: $i] :
( empty(powerset(X1))
| element(X0,X1)
| ~ in(X0,sK7(sK6(powerset(X1)))) ),
inference(superposition,[status(thm)],[c_9806,c_65]) ).
tcf(c_9813,plain,
! [X0: $i,X1: $i] :
( empty(powerset(X1))
| ~ empty(X1)
| ~ in(X0,sK7(sK6(powerset(X1)))) ),
inference(superposition,[status(thm)],[c_9806,c_64]) ).
tcf(c_9814,plain,
! [X0: $i] :
( empty(X0)
| in(sK7(sK6(X0)),X0) ),
inference(superposition,[status(thm)],[c_9806,c_71]) ).
tcf(c_9817,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ in(X0,sK7(sK6(powerset(X1)))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9813,c_70]) ).
tcf(c_9820,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| ~ in(X0,sK7(sK6(powerset(X1)))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9812,c_70]) ).
tcf(c_9852,plain,
( ( sK7(powerset(identity_relation(sK1))) = empty_set )
| ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) ) ),
inference(superposition,[status(thm)],[c_9449,c_8006]) ).
tcf(c_9853,plain,
( ( identity_relation(identity_relation(identity_relation(sK1))) = empty_set )
| ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) ) ),
inference(superposition,[status(thm)],[c_9449,c_7963]) ).
tcf(c_9854,plain,
! [X0: $i] :
( ( identity_relation(sK1) = X0 )
| ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9449,c_5794]) ).
tcf(c_9855,plain,
! [X0: $i] :
( ( relation_dom(sK1) = X0 )
| ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9449,c_5793]) ).
tcf(c_9856,plain,
( ( relation_dom(sK7(powerset(sK1))) = empty_set )
| ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) ) ),
inference(superposition,[status(thm)],[c_9449,c_6878]) ).
tcf(c_9857,plain,
( ( identity_relation(sK7(powerset(sK1))) = empty_set )
| ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) ) ),
inference(superposition,[status(thm)],[c_9449,c_6876]) ).
tcf(c_9858,plain,
( ( sK7(powerset(relation_dom(sK1))) = empty_set )
| ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) ) ),
inference(superposition,[status(thm)],[c_9449,c_8005]) ).
tcf(c_9859,plain,
( ( identity_relation(identity_relation(relation_dom(sK1))) = empty_set )
| ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) ) ),
inference(superposition,[status(thm)],[c_9449,c_7962]) ).
tcf(c_9860,plain,
( ( identity_relation(relation_dom(relation_dom(sK1))) = empty_set )
| ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) ) ),
inference(superposition,[status(thm)],[c_9449,c_7934]) ).
tcf(c_9861,plain,
! [X0: $i] :
( ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) )
| ( relation_image(X0,sK7(powerset(sK1))) = sK1 )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_9449,c_7111]) ).
tcf(c_9862,plain,
! [X0: $i] :
( ( relation_image(X0,sK1) = sK7(powerset(sK1)) )
| ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_9449,c_6946]) ).
tcf(c_9863,plain,
( ( relation_dom(relation_dom(relation_dom(sK1))) = empty_set )
| ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) ) ),
inference(superposition,[status(thm)],[c_9449,c_6133]) ).
tcf(c_9864,plain,
( ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) )
| ( relation_image(sK7(powerset(sK1)),sK1) = sK1 )
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_9449,c_8316]) ).
tcf(c_9865,plain,
! [X0: $i] :
( ( relation_image(X0,empty_set) = sK1 )
| ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_9449,c_7113]) ).
tcf(c_9866,plain,
! [X0: $i] :
( ( relation_image(X0,sK1) = sK1 )
| ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_9449,c_7107]) ).
tcf(c_9867,plain,
( ( relation_image(relation_dom(sK1),sK1) = sK1 )
| ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) )
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_9449,c_8131]) ).
tcf(c_9868,plain,
( ( sK7(powerset(sK1)) = empty_set )
| ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) ) ),
inference(superposition,[status(thm)],[c_9449,c_6879]) ).
tcf(c_9869,plain,
( ( identity_relation(identity_relation(sK1)) = empty_set )
| ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) ) ),
inference(superposition,[status(thm)],[c_9449,c_6106]) ).
tcf(c_9870,plain,
( ( identity_relation(relation_dom(sK1)) = empty_set )
| ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) ) ),
inference(superposition,[status(thm)],[c_9449,c_6105]) ).
tcf(c_9871,plain,
( ( relation_dom(relation_dom(sK1)) = empty_set )
| ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) ) ),
inference(superposition,[status(thm)],[c_9449,c_5747]) ).
tcf(c_9872,plain,
( ( identity_relation(sK1) = empty_set )
| ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) ) ),
inference(superposition,[status(thm)],[c_9449,c_5776]) ).
tcf(c_9873,plain,
! [X0: $i] :
( ( X0 = sK1 )
| ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9449,c_51]) ).
tcf(c_9874,plain,
( ( relation_dom(sK1) = empty_set )
| ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) ) ),
inference(superposition,[status(thm)],[c_9449,c_5663]) ).
tcf(c_9875,plain,
( ( sK1 = empty_set )
| ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) ) ),
inference(superposition,[status(thm)],[c_9449,c_52]) ).
tcf(c_9876,plain,
( function(sK1)
| ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) ) ),
inference(superposition,[status(thm)],[c_9449,c_98]) ).
tcf(c_9877,plain,
( relation(sK1)
| ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) ) ),
inference(superposition,[status(thm)],[c_9449,c_80]) ).
tcf(c_10032,plain,
! [X0: $i,X1: $i] :
( element(sK3(identity_relation(X0),X1,sK1),X0)
| ( relation_image(identity_relation(X0),X1) = sK1 )
| ~ empty(sK0)
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_121,c_7217]) ).
tcf(c_10033,plain,
! [X0: $i] :
( element(sK3(empty_set,X0,sK1),empty_set)
| ( relation_image(empty_set,X0) = sK1 )
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_5746,c_7217]) ).
tcf(c_10036,plain,
! [X0: $i,X1: $i] :
( element(sK3(identity_relation(X0),X1,sK1),X0)
| ( relation_image(identity_relation(X0),X1) = sK1 )
| ~ empty(sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_10032,c_62,c_63]) ).
tcf(c_10056,plain,
! [X0: $i,X1: $i] :
( element(sK2(X0,X1,sK1),sK0)
| ( relation_image(X0,X1) = sK1 )
| ~ empty(relation_dom(X0))
| ~ relation(X0) ),
inference(global_subsumption_just,[status(thm)],[c_7596,c_98,c_88,c_7596]) ).
tcf(c_10057,plain,
! [X0: $i,X1: $i] :
( element(sK2(X0,X1,sK1),sK0)
| ( relation_image(X0,X1) = sK1 )
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(renaming,[status(thm)],[c_10056]) ).
tcf(c_10067,plain,
! [X0: $i,X1: $i] :
( empty(sK0)
| in(sK2(X0,X1,sK1),sK0)
| ( relation_image(X0,X1) = sK1 )
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_10057,c_71]) ).
tcf(c_10122,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(X0),sK1) = relation_image(X1,sK1) )
| ~ empty(sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_62,c_6949]) ).
tcf(c_10123,plain,
! [X0: $i] :
( ( relation_image(X0,sK1) = relation_image(sK14,sK1) )
| ~ relation(sK14)
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_97,c_6949]) ).
tcf(c_10124,plain,
! [X0: $i] :
( ( relation_image(X0,sK1) = relation_image(empty_set,sK1) )
| ~ relation(empty_set)
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_5610,c_6949]) ).
tcf(c_10125,plain,
! [X0: $i,X1: $i] :
( ( relation_image(relation_dom(X0),sK1) = relation_image(X1,sK1) )
| ~ empty(sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0)
| ~ relation(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_5622,c_6949]) ).
tcf(c_10126,plain,
! [X0: $i] :
( ( relation_image(X0,sK1) = relation_image(sK1,sK1) )
| ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ~ relation(sK1)
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_5909,c_6949]) ).
tcf(c_10127,plain,
! [X0: $i,X1: $i] :
( ( relation_image(relation_image(X0,sK1),sK1) = relation_image(X1,sK1) )
| ~ empty(sK0)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_image(X0,sK1)) ),
inference(superposition,[status(thm)],[c_6199,c_6949]) ).
tcf(c_10128,plain,
! [X0: $i,X1: $i] :
( ( relation_image(sK7(powerset(X0)),sK1) = relation_image(X1,sK1) )
| ~ empty(sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0)
| ~ relation(sK7(powerset(X0))) ),
inference(superposition,[status(thm)],[c_6880,c_6949]) ).
tcf(c_10129,plain,
! [X0: $i] :
( ( relation_image(X0,sK1) = relation_image(empty_set,sK1) )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_10124,c_82]) ).
tcf(c_10134,plain,
! [X0: $i] :
( ( relation_image(X0,sK1) = relation_image(sK14,sK1) )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_10123,c_96]) ).
tcf(c_10139,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(X1),sK1) = relation_image(X0,sK1) )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_10122,c_63]) ).
tcf(c_10193,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(X0),relation_image(X1,sK1)) = sK1 )
| ~ empty(sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_62,c_7114]) ).
tcf(c_10194,plain,
! [X0: $i] :
( ( relation_image(sK14,relation_image(X0,sK1)) = sK1 )
| ~ relation(sK14)
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_97,c_7114]) ).
tcf(c_10195,plain,
! [X0: $i] :
( ( relation_image(empty_set,relation_image(X0,sK1)) = sK1 )
| ~ relation(empty_set)
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_5610,c_7114]) ).
tcf(c_10196,plain,
! [X0: $i,X1: $i] :
( ( relation_image(relation_dom(X0),relation_image(X1,sK1)) = sK1 )
| ~ empty(sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0)
| ~ relation(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_5622,c_7114]) ).
tcf(c_10197,plain,
! [X0: $i] :
( ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ( relation_image(sK1,relation_image(X0,sK1)) = sK1 )
| ~ relation(sK1)
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_5909,c_7114]) ).
tcf(c_10198,plain,
! [X0: $i,X1: $i] :
( ( relation_image(relation_image(X0,sK1),relation_image(X1,sK1)) = sK1 )
| ~ empty(sK0)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_image(X0,sK1)) ),
inference(superposition,[status(thm)],[c_6199,c_7114]) ).
tcf(c_10199,plain,
! [X0: $i,X1: $i] :
( ( relation_image(sK7(powerset(X0)),relation_image(X1,sK1)) = sK1 )
| ~ empty(sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0)
| ~ relation(sK7(powerset(X0))) ),
inference(superposition,[status(thm)],[c_6880,c_7114]) ).
tcf(c_10200,plain,
! [X0: $i] :
( ( relation_image(empty_set,relation_image(X0,sK1)) = sK1 )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_10195,c_82]) ).
tcf(c_10205,plain,
! [X0: $i] :
( ( relation_image(sK14,relation_image(X0,sK1)) = sK1 )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_10194,c_96]) ).
tcf(c_10210,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(X1),relation_image(X0,sK1)) = sK1 )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_10193,c_63]) ).
tcf(c_10287,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(X0),X1) = sK1 )
| ~ empty(sK0)
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ in(X0,sK3(identity_relation(X0),X1,sK1)) ),
inference(superposition,[status(thm)],[c_121,c_7215]) ).
tcf(c_10288,plain,
! [X0: $i] :
( ( relation_image(empty_set,X0) = sK1 )
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ empty(sK0)
| ~ in(empty_set,sK3(empty_set,X0,sK1)) ),
inference(superposition,[status(thm)],[c_5746,c_7215]) ).
tcf(c_10290,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(X0),X1) = sK1 )
| ~ empty(sK0)
| ~ in(X0,sK3(identity_relation(X0),X1,sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_10287,c_62,c_63]) ).
tcf(c_10305,plain,
! [X0: $i,X1: $i] :
( empty(sK0)
| in(sK3(X0,sK1,X1),sK0)
| element(sK2(X0,sK1,X1),X1)
| ( relation_image(X0,sK1) = X1 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7281,c_71]) ).
tcf(c_10306,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,X2)
| element(sK3(X1,sK1,powerset(X2)),sK0)
| ( relation_image(X1,sK1) = powerset(X2) )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,sK2(X1,sK1,powerset(X2))) ),
inference(superposition,[status(thm)],[c_7281,c_65]) ).
tcf(c_10307,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK3(X1,sK1,powerset(X2)),sK0)
| ( relation_image(X1,sK1) = powerset(X2) )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X2)
| ~ in(X0,sK2(X1,sK1,powerset(X2))) ),
inference(superposition,[status(thm)],[c_7281,c_64]) ).
tcf(c_10336,plain,
! [X0: $i] :
( in(sK7(sK1),relation_image(identity_relation(sK0),X0))
| ( sK7(powerset(sK1)) = empty_set )
| ~ function(identity_relation(sK0))
| ~ relation(identity_relation(sK0))
| ~ in(sK7(sK1),X0)
| ~ in(sK7(sK1),relation_dom(identity_relation(sK0))) ),
inference(superposition,[status(thm)],[c_8007,c_57]) ).
tcf(c_10337,plain,
! [X0: $i] :
( in(sK7(sK1),relation_image(identity_relation(sK0),X0))
| ( sK7(powerset(sK1)) = empty_set )
| ~ in(sK7(sK1),X0)
| ~ in(sK7(sK1),relation_dom(identity_relation(sK0))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_10336,c_62,c_63]) ).
tcf(c_10347,plain,
! [X0: $i,X1: $i] :
( empty(relation_image(X0,X1))
| ( apply(X0,sK4(X0,X1,sK7(sK6(relation_image(X0,X1))))) = sK7(sK6(relation_image(X0,X1))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_9814,c_60]) ).
tcf(c_10348,plain,
! [X0: $i] :
( empty(X0)
| ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9814,c_151]) ).
tcf(c_10349,plain,
! [X0: $i] :
( empty(X0)
| ~ in(X0,sK7(sK6(X0))) ),
inference(superposition,[status(thm)],[c_9814,c_85]) ).
tcf(c_10352,plain,
( empty(sK1)
| element(sK7(sK6(sK1)),sK0) ),
inference(superposition,[status(thm)],[c_9814,c_5838]) ).
tcf(c_10354,plain,
! [X0: $i] :
( empty(X0)
| empty(sK6(X0))
| element(sK7(sK6(sK6(X0))),X0) ),
inference(superposition,[status(thm)],[c_9814,c_5839]) ).
tcf(c_10355,plain,
! [X0: $i] :
( empty(sK7(powerset(X0)))
| element(sK7(sK6(sK7(powerset(X0)))),X0) ),
inference(superposition,[status(thm)],[c_9814,c_5840]) ).
tcf(c_10411,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK7(sK6(powerset(X0))) = relation_image(X1,X2) )
| ( apply(X1,sK3(X1,X2,sK7(sK6(powerset(X0))))) = sK2(X1,X2,sK7(sK6(powerset(X0)))) )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_56,c_9817]) ).
tcf(c_10412,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(X1,X2,sK7(sK6(powerset(X0)))),relation_dom(X1))
| ( sK7(sK6(powerset(X0))) = relation_image(X1,X2) )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_54,c_9817]) ).
tcf(c_10413,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(X1,X2,sK7(sK6(powerset(X0)))),X2)
| ( sK7(sK6(powerset(X0))) = relation_image(X1,X2) )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_55,c_9817]) ).
tcf(c_10414,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,sK7(sK6(powerset(X0))),X2),X2)
| ( relation_image(X1,sK7(sK6(powerset(X0)))) = X2 )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_55,c_9817]) ).
tcf(c_10415,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ function(X1)
| ~ relation(X1)
| ~ empty(X2)
| ~ in(X0,relation_image(X1,sK7(sK6(powerset(X2))))) ),
inference(superposition,[status(thm)],[c_59,c_9817]) ).
tcf(c_10417,plain,
! [X0: $i,X1: $i] :
( element(sK3(X1,sK1,sK7(sK6(powerset(X0)))),sK0)
| ( sK7(sK6(powerset(X0))) = relation_image(X1,sK1) )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6475,c_9817]) ).
tcf(c_10418,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(powerset(X0))) = relation_image(X1,sK1) )
| ~ empty(sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6476,c_9817]) ).
tcf(c_10419,plain,
! [X0: $i,X1: $i] :
( element(sK2(X1,sK7(sK6(powerset(X0))),sK1),sK0)
| ( relation_image(X1,sK7(sK6(powerset(X0)))) = sK1 )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6486,c_9817]) ).
tcf(c_10420,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X1,sK7(sK6(powerset(X0)))) = sK1 )
| ~ empty(sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6487,c_9817]) ).
tcf(c_10421,plain,
! [X0: $i] :
( empty(sK7(sK6(powerset(X0))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9814,c_9817]) ).
tcf(c_10558,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X0,X1,sK7(sK6(powerset(X2)))),X2)
| ( sK7(sK6(powerset(X2))) = relation_image(X0,X1) )
| ( apply(X0,sK3(X0,X1,sK7(sK6(powerset(X2))))) = sK2(X0,X1,sK7(sK6(powerset(X2)))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_56,c_9820]) ).
tcf(c_10559,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X0,X2,sK7(sK6(powerset(X1)))),X1)
| in(sK3(X0,X2,sK7(sK6(powerset(X1)))),relation_dom(X0))
| ( sK7(sK6(powerset(X1))) = relation_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_54,c_9820]) ).
tcf(c_10560,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(X0,X2,sK7(sK6(powerset(X1)))),X2)
| element(sK2(X0,X2,sK7(sK6(powerset(X1)))),X1)
| ( sK7(sK6(powerset(X1))) = relation_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_55,c_9820]) ).
tcf(c_10561,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,sK7(sK6(powerset(X1))),X2),X2)
| element(sK3(X0,sK7(sK6(powerset(X1))),X2),X1)
| ( relation_image(X0,sK7(sK6(powerset(X1)))) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_55,c_9820]) ).
tcf(c_10562,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK4(X1,sK7(sK6(powerset(X2))),X0),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,sK7(sK6(powerset(X2))))) ),
inference(superposition,[status(thm)],[c_59,c_9820]) ).
tcf(c_10563,plain,
! [X0: $i] :
( empty(sK7(sK6(powerset(X0))))
| element(sK7(sK7(sK6(powerset(X0)))),X0) ),
inference(superposition,[status(thm)],[c_5703,c_9820]) ).
tcf(c_10564,plain,
! [X0: $i,X1: $i] :
( element(sK3(X0,sK1,sK7(sK6(powerset(X1)))),sK0)
| element(sK2(X0,sK1,sK7(sK6(powerset(X1)))),X1)
| ( sK7(sK6(powerset(X1))) = relation_image(X0,sK1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6475,c_9820]) ).
tcf(c_10565,plain,
! [X0: $i,X1: $i] :
( element(sK2(X0,sK1,sK7(sK6(powerset(X1)))),X1)
| ( sK7(sK6(powerset(X1))) = relation_image(X0,sK1) )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6476,c_9820]) ).
tcf(c_10566,plain,
! [X0: $i,X1: $i] :
( element(sK2(X0,sK7(sK6(powerset(X1))),sK1),sK0)
| element(sK3(X0,sK7(sK6(powerset(X1))),sK1),X1)
| ( relation_image(X0,sK7(sK6(powerset(X1)))) = sK1 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6486,c_9820]) ).
tcf(c_10567,plain,
! [X0: $i,X1: $i] :
( element(sK3(X0,sK7(sK6(powerset(X1))),sK1),X1)
| ( relation_image(X0,sK7(sK6(powerset(X1)))) = sK1 )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6487,c_9820]) ).
tcf(c_10568,plain,
! [X0: $i] :
( empty(sK7(sK6(powerset(X0))))
| element(sK7(sK6(sK7(sK6(powerset(X0))))),X0) ),
inference(superposition,[status(thm)],[c_9814,c_9820]) ).
tcf(c_10650,plain,
( empty(sK0)
| empty(sK1)
| in(sK7(sK6(sK1)),sK0) ),
inference(superposition,[status(thm)],[c_10352,c_71]) ).
tcf(c_10658,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(sK7(sK6(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_8006]) ).
tcf(c_10659,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(sK7(sK6(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_7963]) ).
tcf(c_10660,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK7(sK6(powerset(X0)))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_5794]) ).
tcf(c_10661,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(sK6(powerset(X0)))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_5793]) ).
tcf(c_10662,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(sK7(sK6(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_6878]) ).
tcf(c_10663,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(sK7(sK6(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_6876]) ).
tcf(c_10664,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(sK7(sK6(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_8005]) ).
tcf(c_10665,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(sK7(sK6(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_7962]) ).
tcf(c_10666,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(sK7(sK6(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_7934]) ).
tcf(c_10667,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X1,sK7(powerset(sK7(sK6(powerset(X0)))))) = sK1 )
| ~ empty(sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_7111]) ).
tcf(c_10668,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(sK7(sK6(powerset(X0))))) = relation_image(X1,sK1) )
| ~ empty(sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_6946]) ).
tcf(c_10669,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK7(sK6(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_6133]) ).
tcf(c_10670,plain,
! [X0: $i] :
( ( relation_image(sK7(powerset(sK7(sK6(powerset(X0))))),sK1) = sK1 )
| ~ empty(sK0)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_8316]) ).
tcf(c_10673,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK7(sK6(powerset(X0)))),sK1) = sK1 )
| ~ empty(sK0)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_8131]) ).
tcf(c_10674,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(sK6(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_6879]) ).
tcf(c_10675,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(sK6(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_6106]) ).
tcf(c_10676,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(sK6(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_6105]) ).
tcf(c_10677,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(sK6(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_5747]) ).
tcf(c_10678,plain,
! [X0: $i] :
( ( identity_relation(sK7(sK6(powerset(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_5776]) ).
tcf(c_10679,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(powerset(X0))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_51]) ).
tcf(c_10680,plain,
! [X0: $i] :
( ( relation_dom(sK7(sK6(powerset(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_5663]) ).
tcf(c_10681,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_52]) ).
tcf(c_10682,plain,
! [X0: $i] :
( function(sK7(sK6(powerset(X0))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_98]) ).
tcf(c_10683,plain,
! [X0: $i] :
( relation(sK7(sK6(powerset(X0))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_80]) ).
tcf(c_10825,plain,
! [X0: $i,X1: $i] :
( ( relation_image(sK7(sK6(powerset(X0))),relation_image(X1,sK1)) = sK1 )
| ~ empty(sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0)
| ~ relation(sK7(sK6(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_10682,c_7114]) ).
tcf(c_10826,plain,
! [X0: $i,X1: $i] :
( ( relation_image(sK7(sK6(powerset(X0))),sK1) = relation_image(X1,sK1) )
| ~ empty(sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0)
| ~ relation(sK7(sK6(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_10682,c_6949]) ).
tcf(c_10827,plain,
! [X0: $i] :
( ( relation_image(relation_image(sK7(sK6(powerset(X0))),sK1),sK1) = sK1 )
| ~ empty(sK0)
| ~ empty(X0)
| ~ relation(sK7(sK6(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_10682,c_9208]) ).
tcf(c_10828,plain,
! [X0: $i,X1: $i] :
( ( relation_image(sK7(sK6(powerset(X0))),X1) = sK1 )
| ( apply(sK7(sK6(powerset(X0))),sK3(sK7(sK6(powerset(X0))),X1,sK1)) = sK2(sK7(sK6(powerset(X0))),X1,sK1) )
| ~ empty(sK0)
| ~ empty(X0)
| ~ relation(sK7(sK6(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_10682,c_7707]) ).
tcf(c_10829,plain,
! [X0: $i] :
( ( relation_image(sK7(sK6(powerset(X0))),sK1) = sK1 )
| ~ empty(sK0)
| ~ empty(X0)
| ~ relation(sK7(sK6(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_10682,c_6945]) ).
tcf(c_10830,plain,
! [X0: $i] :
( ( relation_image(sK7(sK6(powerset(X0))),sK1) = empty_set )
| ~ empty(sK0)
| ~ empty(X0)
| ~ relation(sK7(sK6(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_10682,c_6198]) ).
tcf(c_11014,plain,
( in(sK7(sK6(sK1)),sK0)
| empty(sK1) ),
inference(global_subsumption_just,[status(thm)],[c_10650,c_5857,c_10650]) ).
tcf(c_11015,plain,
( empty(sK1)
| in(sK7(sK6(sK1)),sK0) ),
inference(renaming,[status(thm)],[c_11014]) ).
tcf(c_11020,plain,
( empty(sK1)
| ( apply(identity_relation(sK0),sK7(sK6(sK1))) = sK7(sK6(sK1)) ) ),
inference(superposition,[status(thm)],[c_11015,c_151]) ).
tcf(c_11021,plain,
( empty(sK1)
| ~ in(sK0,sK7(sK6(sK1))) ),
inference(superposition,[status(thm)],[c_11015,c_85]) ).
tcf(c_11038,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(powerset(X1))) = relation_image(X0,sK1) )
| ( apply(identity_relation(X1),sK7(X1)) = sK7(X1) )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_5807,c_10418]) ).
tcf(c_11039,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(empty_set))) = relation_image(X0,sK1) )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_83,c_10418]) ).
tcf(c_11040,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(powerset(relation_dom(X0)))) = relation_image(X1,sK1) )
| ~ empty(sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_10418]) ).
tcf(c_11041,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(powerset(identity_relation(X0)))) = relation_image(X1,sK1) )
| ~ empty(sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_10418]) ).
tcf(c_11042,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(sK1))) = relation_image(X0,sK1) )
| ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_9449,c_10418]) ).
tcf(c_11043,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(sK1))) = relation_image(X0,sK1) )
| ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_5890,c_10418]) ).
tcf(c_11044,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(powerset(relation_image(X0,sK1)))) = relation_image(X1,sK1) )
| ~ empty(sK0)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6158,c_10418]) ).
tcf(c_11045,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(powerset(sK7(powerset(X0))))) = relation_image(X1,sK1) )
| ~ empty(sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_10418]) ).
tcf(c_11046,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(powerset(sK7(sK6(powerset(X0)))))) = relation_image(X1,sK1) )
| ~ empty(sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_10418]) ).
tcf(c_11111,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X1),sK7(X1)) = sK7(X1) )
| ( relation_image(X0,sK7(sK6(powerset(X1)))) = sK1 )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_5807,c_10420]) ).
tcf(c_11112,plain,
! [X0: $i] :
( ( relation_image(X0,sK7(sK6(powerset(empty_set)))) = sK1 )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_83,c_10420]) ).
tcf(c_11113,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X1,sK7(sK6(powerset(relation_dom(X0))))) = sK1 )
| ~ empty(sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_10420]) ).
tcf(c_11114,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X1,sK7(sK6(powerset(identity_relation(X0))))) = sK1 )
| ~ empty(sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_10420]) ).
tcf(c_11115,plain,
! [X0: $i] :
( ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) )
| ( relation_image(X0,sK7(sK6(powerset(sK1)))) = sK1 )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_9449,c_10420]) ).
tcf(c_11116,plain,
! [X0: $i] :
( ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ( relation_image(X0,sK7(sK6(powerset(sK1)))) = sK1 )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_5890,c_10420]) ).
tcf(c_11117,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X1,sK7(sK6(powerset(relation_image(X0,sK1))))) = sK1 )
| ~ empty(sK0)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6158,c_10420]) ).
tcf(c_11118,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X1,sK7(sK6(powerset(sK7(powerset(X0)))))) = sK1 )
| ~ empty(sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_10420]) ).
tcf(c_11119,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X1,sK7(sK6(powerset(sK7(sK6(powerset(X0))))))) = sK1 )
| ~ empty(sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_10420]) ).
tcf(c_11188,plain,
! [X0: $i] :
( ( relation_image(sK7(sK6(powerset(X0))),sK1) = sK1 )
| ~ empty(sK0)
| ~ empty(X0) ),
inference(global_subsumption_just,[status(thm)],[c_10829,c_10683,c_10829]) ).
tcf(c_11197,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( relation_image(sK7(sK6(powerset(X0))),sK1) = sK1 )
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_5807,c_11188]) ).
tcf(c_11198,plain,
( ( relation_image(sK7(sK6(powerset(empty_set))),sK1) = sK1 )
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_83,c_11188]) ).
tcf(c_11199,plain,
! [X0: $i] :
( ( relation_image(sK7(sK6(powerset(relation_dom(X0)))),sK1) = sK1 )
| ~ empty(sK0)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_11188]) ).
tcf(c_11200,plain,
! [X0: $i] :
( ( relation_image(sK7(sK6(powerset(identity_relation(X0)))),sK1) = sK1 )
| ~ empty(sK0)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_11188]) ).
tcf(c_11201,plain,
( ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) )
| ( relation_image(sK7(sK6(powerset(sK1))),sK1) = sK1 )
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_9449,c_11188]) ).
tcf(c_11202,plain,
( ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ( relation_image(sK7(sK6(powerset(sK1))),sK1) = sK1 )
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_5890,c_11188]) ).
tcf(c_11203,plain,
! [X0: $i] :
( ( relation_image(sK7(sK6(powerset(relation_image(X0,sK1)))),sK1) = sK1 )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6158,c_11188]) ).
tcf(c_11204,plain,
! [X0: $i] :
( ( relation_image(sK7(sK6(powerset(sK7(powerset(X0))))),sK1) = sK1 )
| ~ empty(sK0)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_11188]) ).
tcf(c_11205,plain,
! [X0: $i] :
( ( relation_image(sK7(sK6(powerset(sK7(sK6(powerset(X0)))))),sK1) = sK1 )
| ~ empty(sK0)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_11188]) ).
tcf(c_11269,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,X2)
| element(sK2(X1,powerset(X2),sK1),sK0)
| ( relation_image(X1,powerset(X2)) = sK1 )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,sK3(X1,powerset(X2),sK1)) ),
inference(superposition,[status(thm)],[c_7403,c_65]) ).
tcf(c_11270,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X1,powerset(X2),sK1),sK0)
| ( relation_image(X1,powerset(X2)) = sK1 )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X2)
| ~ in(X0,sK3(X1,powerset(X2),sK1)) ),
inference(superposition,[status(thm)],[c_7403,c_64]) ).
tcf(c_11308,plain,
! [X0: $i] :
( element(sK3(X0,sK1,empty_set),sK0)
| ( relation_image(X0,sK1) = sK7(powerset(empty_set)) )
| ~ empty(empty_set)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8004,c_7284]) ).
tcf(c_11309,plain,
! [X0: $i,X1: $i] :
( empty(sK0)
| in(sK3(X1,sK1,sK7(powerset(X0))),sK0)
| ( relation_image(X1,sK1) = sK7(powerset(X0)) )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7284,c_71]) ).
tcf(c_11310,plain,
! [X0: $i] :
( element(sK3(X0,sK1,empty_set),sK0)
| ( relation_image(X0,sK1) = empty_set )
| ~ empty(empty_set)
| ~ function(X0)
| ~ relation(X0) ),
inference(light_normalisation,[status(thm)],[c_11308,c_8004]) ).
tcf(c_11323,plain,
! [X0: $i] :
( in(sK7(sK1),relation_image(identity_relation(sK0),X0))
| ( relation_dom(relation_dom(relation_dom(sK1))) = empty_set )
| ~ function(identity_relation(sK0))
| ~ relation(identity_relation(sK0))
| ~ in(sK7(sK1),X0)
| ~ in(sK7(sK1),relation_dom(identity_relation(sK0))) ),
inference(superposition,[status(thm)],[c_8563,c_57]) ).
tcf(c_11324,plain,
! [X0: $i] :
( in(sK7(sK1),relation_image(identity_relation(sK0),X0))
| ( relation_dom(relation_dom(relation_dom(sK1))) = empty_set )
| ~ in(sK7(sK1),X0)
| ~ in(sK7(sK1),relation_dom(identity_relation(sK0))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11323,c_62,c_63]) ).
tcf(c_11338,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(X0))) = empty_set )
| ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) ) ),
inference(superposition,[status(thm)],[c_5807,c_10681]) ).
tcf(c_11339,plain,
sK7(sK6(powerset(empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_10681]) ).
tcf(c_11340,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(relation_dom(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_10681]) ).
tcf(c_11341,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(identity_relation(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_10681]) ).
tcf(c_11342,plain,
( ( sK7(sK6(powerset(sK1))) = empty_set )
| ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) ) ),
inference(superposition,[status(thm)],[c_9449,c_10681]) ).
tcf(c_11343,plain,
( ( sK7(sK6(powerset(sK1))) = empty_set )
| ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) ) ),
inference(superposition,[status(thm)],[c_5890,c_10681]) ).
tcf(c_11344,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(relation_image(X0,sK1)))) = empty_set )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6158,c_10681]) ).
tcf(c_11345,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(sK7(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_10681]) ).
tcf(c_11346,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(sK7(sK6(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_10681]) ).
tcf(c_11390,plain,
( empty(sK6(powerset(empty_set)))
| ~ in(sK6(powerset(empty_set)),empty_set) ),
inference(superposition,[status(thm)],[c_11339,c_5724]) ).
tcf(c_11391,plain,
( empty(sK6(powerset(empty_set)))
| in(empty_set,sK6(powerset(empty_set))) ),
inference(superposition,[status(thm)],[c_11339,c_5703]) ).
tcf(c_11392,plain,
element(empty_set,sK6(powerset(empty_set))),
inference(superposition,[status(thm)],[c_11339,c_73]) ).
tcf(c_11393,plain,
( empty(powerset(empty_set))
| ~ in(powerset(empty_set),empty_set) ),
inference(superposition,[status(thm)],[c_11339,c_10349]) ).
tcf(c_11395,plain,
( empty(powerset(empty_set))
| element(empty_set,powerset(empty_set)) ),
inference(superposition,[status(thm)],[c_11339,c_9806]) ).
tcf(c_11404,plain,
in(empty_set,sK6(powerset(empty_set))),
inference(global_subsumption_just,[status(thm)],[c_11391,c_103,c_6362,c_6914,c_11392]) ).
tcf(c_11406,plain,
apply(identity_relation(sK6(powerset(empty_set))),empty_set) = empty_set,
inference(superposition,[status(thm)],[c_11404,c_151]) ).
tcf(c_11407,plain,
~ in(sK6(powerset(empty_set)),empty_set),
inference(superposition,[status(thm)],[c_11404,c_85]) ).
tcf(c_11408,plain,
~ empty(sK6(powerset(empty_set))),
inference(superposition,[status(thm)],[c_11404,c_84]) ).
tcf(c_11411,plain,
apply(identity_relation(sK6(powerset(empty_set))),sK7(sK6(powerset(empty_set)))) = sK7(sK6(powerset(empty_set))),
inference(superposition,[status(thm)],[c_5807,c_11408]) ).
tcf(c_11420,plain,
! [X0: $i] :
( in(empty_set,relation_image(identity_relation(sK6(powerset(empty_set))),X0))
| ~ in(empty_set,X0)
| ~ function(identity_relation(sK6(powerset(empty_set))))
| ~ relation(identity_relation(sK6(powerset(empty_set))))
| ~ in(empty_set,relation_dom(identity_relation(sK6(powerset(empty_set))))) ),
inference(superposition,[status(thm)],[c_11406,c_57]) ).
tcf(c_11421,plain,
! [X0: $i] :
( in(empty_set,relation_image(identity_relation(sK6(powerset(empty_set))),X0))
| ~ in(empty_set,X0)
| ~ in(empty_set,relation_dom(identity_relation(sK6(powerset(empty_set))))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11420,c_62,c_63]) ).
tcf(c_11429,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(powerset(X0)))) = empty_set )
| ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) ) ),
inference(superposition,[status(thm)],[c_5807,c_6875]) ).
tcf(c_11430,plain,
relation_dom(relation_dom(sK7(powerset(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_6875]) ).
tcf(c_11431,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(powerset(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_6875]) ).
tcf(c_11432,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(powerset(identity_relation(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_6875]) ).
tcf(c_11433,plain,
( ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) )
| ( relation_dom(relation_dom(sK7(powerset(sK1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_9449,c_6875]) ).
tcf(c_11434,plain,
( ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ( relation_dom(relation_dom(sK7(powerset(sK1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5890,c_6875]) ).
tcf(c_11435,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(powerset(relation_image(X0,sK1))))) = empty_set )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6158,c_6875]) ).
tcf(c_11436,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(powerset(sK7(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_6875]) ).
tcf(c_11437,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(powerset(sK7(sK6(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_6875]) ).
tcf(c_11514,plain,
! [X0: $i] :
( element(sK2(X0,empty_set,sK1),sK0)
| ( relation_image(X0,sK7(powerset(empty_set))) = sK1 )
| ~ empty(empty_set)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8004,c_7406]) ).
tcf(c_11515,plain,
! [X0: $i,X1: $i] :
( empty(sK0)
| in(sK2(X1,sK7(powerset(X0)),sK1),sK0)
| ( relation_image(X1,sK7(powerset(X0))) = sK1 )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7406,c_71]) ).
tcf(c_11516,plain,
! [X0: $i] :
( element(sK2(X0,empty_set,sK1),sK0)
| ( relation_image(X0,empty_set) = sK1 )
| ~ empty(empty_set)
| ~ function(X0)
| ~ relation(X0) ),
inference(light_normalisation,[status(thm)],[c_11514,c_8004]) ).
tcf(c_11535,plain,
! [X0: $i,X1: $i] :
( element(sK2(identity_relation(X0),X1,sK1),sK0)
| element(sK3(identity_relation(X0),X1,sK1),X0)
| ( relation_image(identity_relation(X0),X1) = sK1 )
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_121,c_7597]) ).
tcf(c_11536,plain,
! [X0: $i] :
( element(sK3(empty_set,X0,sK1),empty_set)
| element(sK2(empty_set,X0,sK1),sK0)
| ( relation_image(empty_set,X0) = sK1 )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_5746,c_7597]) ).
tcf(c_11538,plain,
! [X0: $i] :
( element(sK3(empty_set,X0,sK1),empty_set)
| element(sK2(empty_set,X0,sK1),sK0)
| ( relation_image(empty_set,X0) = sK1 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11536,c_5610,c_82]) ).
tcf(c_11542,plain,
! [X0: $i,X1: $i] :
( element(sK2(identity_relation(X0),X1,sK1),sK0)
| element(sK3(identity_relation(X0),X1,sK1),X0)
| ( relation_image(identity_relation(X0),X1) = sK1 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11535,c_62,c_63]) ).
tcf(c_11558,plain,
! [X0: $i] :
( element(sK2(X0,sK1,empty_set),empty_set)
| ( relation_image(X0,sK1) = sK7(powerset(empty_set)) )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8004,c_7842]) ).
tcf(c_11559,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,X2)
| ( sK7(powerset(powerset(X2))) = relation_image(X1,sK1) )
| ~ empty(sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,sK2(X1,sK1,sK7(powerset(powerset(X2))))) ),
inference(superposition,[status(thm)],[c_7842,c_65]) ).
tcf(c_11560,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK7(powerset(powerset(X2))) = relation_image(X1,sK1) )
| ~ empty(sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X2)
| ~ in(X0,sK2(X1,sK1,sK7(powerset(powerset(X2))))) ),
inference(superposition,[status(thm)],[c_7842,c_64]) ).
tcf(c_11561,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| in(sK2(X0,sK1,sK7(powerset(X1))),X1)
| ( relation_image(X0,sK1) = sK7(powerset(X1)) )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7842,c_71]) ).
tcf(c_11593,plain,
! [X0: $i] :
( element(sK3(X0,empty_set,sK1),empty_set)
| ( relation_image(X0,sK7(powerset(empty_set))) = sK1 )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8004,c_7844]) ).
tcf(c_11594,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,X2)
| ( relation_image(X1,sK7(powerset(powerset(X2)))) = sK1 )
| ~ empty(sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,sK3(X1,sK7(powerset(powerset(X2))),sK1)) ),
inference(superposition,[status(thm)],[c_7844,c_65]) ).
tcf(c_11595,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X1,sK7(powerset(powerset(X2)))) = sK1 )
| ~ empty(sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X2)
| ~ in(X0,sK3(X1,sK7(powerset(powerset(X2))),sK1)) ),
inference(superposition,[status(thm)],[c_7844,c_64]) ).
tcf(c_11596,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| in(sK3(X0,sK7(powerset(X1)),sK1),X1)
| ( relation_image(X0,sK7(powerset(X1))) = sK1 )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7844,c_71]) ).
tcf(c_11630,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(powerset(X2))
| element(X0,X2)
| ( relation_image(X1,sK1) = sK6(powerset(X2)) )
| ~ empty(sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,sK2(X1,sK1,sK6(powerset(X2)))) ),
inference(superposition,[status(thm)],[c_8393,c_65]) ).
tcf(c_11631,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(powerset(X2))
| ( relation_image(X1,sK1) = sK6(powerset(X2)) )
| ~ empty(sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X2)
| ~ in(X0,sK2(X1,sK1,sK6(powerset(X2)))) ),
inference(superposition,[status(thm)],[c_8393,c_64]) ).
tcf(c_11632,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| in(sK2(X0,sK1,sK6(X1)),X1)
| ( relation_image(X0,sK1) = sK6(X1) )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8393,c_71]) ).
tcf(c_11639,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X1,sK1) = sK6(powerset(X2)) )
| ~ empty(sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X2)
| ~ in(X0,sK2(X1,sK1,sK6(powerset(X2)))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11631,c_70]) ).
tcf(c_11646,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,X2)
| ( relation_image(X1,sK1) = sK6(powerset(X2)) )
| ~ empty(sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,sK2(X1,sK1,sK6(powerset(X2)))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11630,c_70]) ).
tcf(c_11672,plain,
! [X0: $i,X1: $i] :
( element(sK2(X0,X1,sK1),sK0)
| in(sK3(X0,X1,sK1),relation_dom(X0))
| ( relation_image(X0,X1) = sK1 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_54,c_8039]) ).
tcf(c_11795,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(powerset(X2))
| element(X0,X2)
| ( relation_image(X1,sK6(powerset(X2))) = sK1 )
| ~ empty(sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,sK3(X1,sK6(powerset(X2)),sK1)) ),
inference(superposition,[status(thm)],[c_8395,c_65]) ).
tcf(c_11796,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(powerset(X2))
| ( relation_image(X1,sK6(powerset(X2))) = sK1 )
| ~ empty(sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X2)
| ~ in(X0,sK3(X1,sK6(powerset(X2)),sK1)) ),
inference(superposition,[status(thm)],[c_8395,c_64]) ).
tcf(c_11797,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| in(sK3(X0,sK6(X1),sK1),X1)
| ( relation_image(X0,sK6(X1)) = sK1 )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8395,c_71]) ).
tcf(c_11804,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X1,sK6(powerset(X2))) = sK1 )
| ~ empty(sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X2)
| ~ in(X0,sK3(X1,sK6(powerset(X2)),sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11796,c_70]) ).
tcf(c_11811,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,X2)
| ( relation_image(X1,sK6(powerset(X2))) = sK1 )
| ~ empty(sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,sK3(X1,sK6(powerset(X2)),sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11795,c_70]) ).
tcf(c_11820,plain,
! [X0: $i,X1: $i] :
( ~ relation(X0)
| ~ function(X0)
| ( relation_image(X0,sK1) = X1 )
| in(sK2(X0,sK1,X1),X1)
| in(sK3(X0,sK1,X1),sK0) ),
inference(global_subsumption_just,[status(thm)],[c_7276,c_6476,c_7276]) ).
tcf(c_11821,plain,
! [X0: $i,X1: $i] :
( in(sK3(X0,sK1,X1),sK0)
| in(sK2(X0,sK1,X1),X1)
| ( relation_image(X0,sK1) = X1 )
| ~ function(X0)
| ~ relation(X0) ),
inference(renaming,[status(thm)],[c_11820]) ).
tcf(c_11833,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,sK1,X1),X1)
| ( relation_image(X0,sK1) = X1 )
| ( apply(identity_relation(sK0),sK3(X0,sK1,X1)) = sK3(X0,sK1,X1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_11821,c_151]) ).
tcf(c_11834,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,sK1,X1),X1)
| ( relation_image(X0,sK1) = X1 )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK0,sK3(X0,sK1,X1)) ),
inference(superposition,[status(thm)],[c_11821,c_85]) ).
tcf(c_11837,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(X0,sK1,relation_image(X1,X2)),sK0)
| ( relation_image(X1,X2) = relation_image(X0,sK1) )
| ( apply(X1,sK4(X1,X2,sK2(X0,sK1,relation_image(X1,X2)))) = sK2(X0,sK1,relation_image(X1,X2)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_11821,c_60]) ).
tcf(c_11838,plain,
! [X0: $i,X1: $i] :
( in(sK3(X0,sK1,X1),sK0)
| ( relation_image(X0,sK1) = X1 )
| ( apply(identity_relation(X1),sK2(X0,sK1,X1)) = sK2(X0,sK1,X1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_11821,c_151]) ).
tcf(c_11839,plain,
! [X0: $i,X1: $i] :
( in(sK3(X1,sK1,X0),sK0)
| ( relation_image(X1,sK1) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,sK2(X1,sK1,X0)) ),
inference(superposition,[status(thm)],[c_11821,c_85]) ).
tcf(c_11840,plain,
! [X0: $i,X1: $i] :
( in(sK3(X1,sK1,X0),sK0)
| ( relation_image(X1,sK1) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11821,c_84]) ).
tcf(c_11841,plain,
! [X0: $i,X1: $i] :
( in(sK3(X0,sK1,X1),sK0)
| element(sK2(X0,sK1,X1),X1)
| ( relation_image(X0,sK1) = X1 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_11821,c_72]) ).
tcf(c_11842,plain,
! [X0: $i] :
( in(sK3(X0,sK1,sK1),sK0)
| element(sK2(X0,sK1,sK1),sK0)
| ( relation_image(X0,sK1) = sK1 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_11821,c_5838]) ).
tcf(c_11844,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| in(sK3(X0,sK1,sK6(X1)),sK0)
| element(sK2(X0,sK1,sK6(X1)),X1)
| ( relation_image(X0,sK1) = sK6(X1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_11821,c_5839]) ).
tcf(c_11845,plain,
! [X0: $i,X1: $i] :
( in(sK3(X0,sK1,sK7(powerset(X1))),sK0)
| element(sK2(X0,sK1,sK7(powerset(X1))),X1)
| ( relation_image(X0,sK1) = sK7(powerset(X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_11821,c_5840]) ).
tcf(c_11846,plain,
! [X0: $i,X1: $i] :
( in(sK3(X1,sK1,sK7(powerset(X0))),sK0)
| ( relation_image(X1,sK1) = sK7(powerset(X0)) )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11821,c_5822]) ).
tcf(c_11847,plain,
! [X0: $i] :
( in(sK3(X0,sK1,empty_set),sK0)
| ( relation_image(X0,sK1) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_11821,c_8375]) ).
tcf(c_11850,plain,
! [X0: $i,X1: $i] :
( in(sK3(X0,sK1,sK7(sK6(powerset(X1)))),sK0)
| element(sK2(X0,sK1,sK7(sK6(powerset(X1)))),X1)
| ( sK7(sK6(powerset(X1))) = relation_image(X0,sK1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_11821,c_9820]) ).
tcf(c_11851,plain,
! [X0: $i,X1: $i] :
( in(sK3(X1,sK1,sK7(sK6(powerset(X0)))),sK0)
| ( sK7(sK6(powerset(X0))) = relation_image(X1,sK1) )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11821,c_9817]) ).
tcf(c_11940,plain,
! [X0: $i] :
( in(sK7(sK1),relation_image(identity_relation(sK0),X0))
| ( identity_relation(relation_dom(relation_dom(sK1))) = empty_set )
| ~ function(identity_relation(sK0))
| ~ relation(identity_relation(sK0))
| ~ in(sK7(sK1),X0)
| ~ in(sK7(sK1),relation_dom(identity_relation(sK0))) ),
inference(superposition,[status(thm)],[c_8959,c_57]) ).
tcf(c_11941,plain,
! [X0: $i] :
( in(sK7(sK1),relation_image(identity_relation(sK0),X0))
| ( identity_relation(relation_dom(relation_dom(sK1))) = empty_set )
| ~ in(sK7(sK1),X0)
| ~ in(sK7(sK1),relation_dom(identity_relation(sK0))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11940,c_62,c_63]) ).
tcf(c_11951,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(X0)))) = empty_set )
| ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) ) ),
inference(superposition,[status(thm)],[c_5807,c_8561]) ).
tcf(c_11952,plain,
relation_dom(relation_dom(relation_dom(relation_dom(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_8561]) ).
tcf(c_11953,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_8561]) ).
tcf(c_11954,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(identity_relation(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_8561]) ).
tcf(c_11955,plain,
( ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) )
| ( relation_dom(relation_dom(relation_dom(relation_dom(sK1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_9449,c_8561]) ).
tcf(c_11956,plain,
( ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ( relation_dom(relation_dom(relation_dom(relation_dom(sK1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5890,c_8561]) ).
tcf(c_11957,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_image(X0,sK1))))) = empty_set )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6158,c_8561]) ).
tcf(c_11958,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK7(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_8561]) ).
tcf(c_11959,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK7(sK6(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_8561]) ).
tcf(c_12025,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(relation_dom(X0)))) = empty_set )
| ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) ) ),
inference(superposition,[status(thm)],[c_5807,c_8957]) ).
tcf(c_12026,plain,
identity_relation(relation_dom(relation_dom(relation_dom(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_8957]) ).
tcf(c_12027,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(relation_dom(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_8957]) ).
tcf(c_12028,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(relation_dom(identity_relation(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_8957]) ).
tcf(c_12029,plain,
( ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) )
| ( identity_relation(relation_dom(relation_dom(relation_dom(sK1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_9449,c_8957]) ).
tcf(c_12030,plain,
( ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ( identity_relation(relation_dom(relation_dom(relation_dom(sK1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5890,c_8957]) ).
tcf(c_12031,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(relation_dom(relation_image(X0,sK1))))) = empty_set )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6158,c_8957]) ).
tcf(c_12032,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(relation_dom(sK7(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_8957]) ).
tcf(c_12033,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(relation_dom(sK7(sK6(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_8957]) ).
tcf(c_12061,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(relation_dom(X0)))) = empty_set )
| ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) ) ),
inference(superposition,[status(thm)],[c_5807,c_8992]) ).
tcf(c_12062,plain,
identity_relation(identity_relation(relation_dom(relation_dom(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_8992]) ).
tcf(c_12063,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(relation_dom(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_8992]) ).
tcf(c_12064,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(relation_dom(identity_relation(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_8992]) ).
tcf(c_12065,plain,
( ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) )
| ( identity_relation(identity_relation(relation_dom(relation_dom(sK1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_9449,c_8992]) ).
tcf(c_12066,plain,
( ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ( identity_relation(identity_relation(relation_dom(relation_dom(sK1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5890,c_8992]) ).
tcf(c_12067,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(relation_dom(relation_image(X0,sK1))))) = empty_set )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6158,c_8992]) ).
tcf(c_12068,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(relation_dom(sK7(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_8992]) ).
tcf(c_12069,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(relation_dom(sK7(sK6(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_8992]) ).
tcf(c_12097,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(relation_dom(X0)))) = empty_set )
| ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) ) ),
inference(superposition,[status(thm)],[c_5807,c_9017]) ).
tcf(c_12098,plain,
sK7(powerset(relation_dom(relation_dom(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_9017]) ).
tcf(c_12099,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(relation_dom(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_9017]) ).
tcf(c_12100,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(relation_dom(identity_relation(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_9017]) ).
tcf(c_12101,plain,
( ( sK7(powerset(relation_dom(relation_dom(sK1)))) = empty_set )
| ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) ) ),
inference(superposition,[status(thm)],[c_9449,c_9017]) ).
tcf(c_12102,plain,
( ( sK7(powerset(relation_dom(relation_dom(sK1)))) = empty_set )
| ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) ) ),
inference(superposition,[status(thm)],[c_5890,c_9017]) ).
tcf(c_12103,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(relation_dom(relation_image(X0,sK1))))) = empty_set )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6158,c_9017]) ).
tcf(c_12104,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(relation_dom(sK7(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_9017]) ).
tcf(c_12105,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(relation_dom(sK7(sK6(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_9017]) ).
tcf(c_12133,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(powerset(X0)))) = empty_set )
| ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) ) ),
inference(superposition,[status(thm)],[c_5807,c_7938]) ).
tcf(c_12134,plain,
identity_relation(relation_dom(sK7(powerset(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_7938]) ).
tcf(c_12135,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(powerset(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_7938]) ).
tcf(c_12136,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(powerset(identity_relation(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_7938]) ).
tcf(c_12137,plain,
( ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) )
| ( identity_relation(relation_dom(sK7(powerset(sK1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_9449,c_7938]) ).
tcf(c_12138,plain,
( ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ( identity_relation(relation_dom(sK7(powerset(sK1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5890,c_7938]) ).
tcf(c_12139,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(powerset(relation_image(X0,sK1))))) = empty_set )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6158,c_7938]) ).
tcf(c_12140,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(powerset(sK7(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_7938]) ).
tcf(c_12141,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(powerset(sK7(sK6(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_7938]) ).
tcf(c_12210,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(powerset(X0)))) = empty_set )
| ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) ) ),
inference(superposition,[status(thm)],[c_5807,c_7966]) ).
tcf(c_12211,plain,
identity_relation(identity_relation(sK7(powerset(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_7966]) ).
tcf(c_12212,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(powerset(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_7966]) ).
tcf(c_12213,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(powerset(identity_relation(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_7966]) ).
tcf(c_12214,plain,
( ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) )
| ( identity_relation(identity_relation(sK7(powerset(sK1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_9449,c_7966]) ).
tcf(c_12215,plain,
( ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ( identity_relation(identity_relation(sK7(powerset(sK1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5890,c_7966]) ).
tcf(c_12216,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(powerset(relation_image(X0,sK1))))) = empty_set )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6158,c_7966]) ).
tcf(c_12217,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(powerset(sK7(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_7966]) ).
tcf(c_12218,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(powerset(sK7(sK6(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_7966]) ).
tcf(c_12316,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(powerset(X0)))) = empty_set )
| ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) ) ),
inference(superposition,[status(thm)],[c_5807,c_8009]) ).
tcf(c_12317,plain,
sK7(powerset(sK7(powerset(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_8009]) ).
tcf(c_12318,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(powerset(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_8009]) ).
tcf(c_12319,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(powerset(identity_relation(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_8009]) ).
tcf(c_12320,plain,
( ( sK7(powerset(sK7(powerset(sK1)))) = empty_set )
| ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) ) ),
inference(superposition,[status(thm)],[c_9449,c_8009]) ).
tcf(c_12321,plain,
( ( sK7(powerset(sK7(powerset(sK1)))) = empty_set )
| ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) ) ),
inference(superposition,[status(thm)],[c_5890,c_8009]) ).
tcf(c_12322,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(powerset(relation_image(X0,sK1))))) = empty_set )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6158,c_8009]) ).
tcf(c_12323,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(powerset(sK7(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_8009]) ).
tcf(c_12324,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(powerset(sK7(sK6(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_8009]) ).
tcf(c_12354,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(relation_dom(X0)))) = empty_set )
| ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) ) ),
inference(superposition,[status(thm)],[c_5807,c_9087]) ).
tcf(c_12355,plain,
identity_relation(sK7(powerset(relation_dom(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_9087]) ).
tcf(c_12356,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(relation_dom(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_9087]) ).
tcf(c_12357,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(relation_dom(identity_relation(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_9087]) ).
tcf(c_12358,plain,
( ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) )
| ( identity_relation(sK7(powerset(relation_dom(sK1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_9449,c_9087]) ).
tcf(c_12359,plain,
( ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ( identity_relation(sK7(powerset(relation_dom(sK1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5890,c_9087]) ).
tcf(c_12360,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(relation_dom(relation_image(X0,sK1))))) = empty_set )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6158,c_9087]) ).
tcf(c_12361,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(relation_dom(sK7(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_9087]) ).
tcf(c_12362,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(relation_dom(sK7(sK6(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_9087]) ).
tcf(c_12479,plain,
! [X0: $i] :
( empty(sK0)
| in(sK3(X0,sK1,sK1),sK0)
| in(sK2(X0,sK1,sK1),sK0)
| ( relation_image(X0,sK1) = sK1 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_11842,c_71]) ).
tcf(c_12512,plain,
! [X0: $i,X1: $i] :
( ~ relation(X0)
| ~ function(X0)
| ( relation_image(X0,X1) = sK1 )
| in(sK3(X0,X1,sK1),X1)
| in(sK2(X0,X1,sK1),sK0) ),
inference(global_subsumption_just,[status(thm)],[c_7398,c_6487,c_7398]) ).
tcf(c_12513,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,X1,sK1),sK0)
| in(sK3(X0,X1,sK1),X1)
| ( relation_image(X0,X1) = sK1 )
| ~ function(X0)
| ~ relation(X0) ),
inference(renaming,[status(thm)],[c_12512]) ).
tcf(c_12525,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,relation_image(X1,X2),sK1),sK0)
| ( relation_image(X0,relation_image(X1,X2)) = sK1 )
| ( apply(X1,sK4(X1,X2,sK3(X0,relation_image(X1,X2),sK1))) = sK3(X0,relation_image(X1,X2),sK1) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_12513,c_60]) ).
tcf(c_12526,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,X1,sK1),sK0)
| ( relation_image(X0,X1) = sK1 )
| ( apply(identity_relation(X1),sK3(X0,X1,sK1)) = sK3(X0,X1,sK1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_12513,c_151]) ).
tcf(c_12527,plain,
! [X0: $i,X1: $i] :
( in(sK2(X1,X0,sK1),sK0)
| ( relation_image(X1,X0) = sK1 )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,sK3(X1,X0,sK1)) ),
inference(superposition,[status(thm)],[c_12513,c_85]) ).
tcf(c_12528,plain,
! [X0: $i,X1: $i] :
( in(sK2(X1,X0,sK1),sK0)
| ( relation_image(X1,X0) = sK1 )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12513,c_84]) ).
tcf(c_12529,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,X1,sK1),sK0)
| element(sK3(X0,X1,sK1),X1)
| ( relation_image(X0,X1) = sK1 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_12513,c_72]) ).
tcf(c_12530,plain,
! [X0: $i] :
( in(sK2(X0,sK1,sK1),sK0)
| element(sK3(X0,sK1,sK1),sK0)
| ( relation_image(X0,sK1) = sK1 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_12513,c_5838]) ).
tcf(c_12532,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| in(sK2(X0,sK6(X1),sK1),sK0)
| element(sK3(X0,sK6(X1),sK1),X1)
| ( relation_image(X0,sK6(X1)) = sK1 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_12513,c_5839]) ).
tcf(c_12533,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,sK7(powerset(X1)),sK1),sK0)
| element(sK3(X0,sK7(powerset(X1)),sK1),X1)
| ( relation_image(X0,sK7(powerset(X1))) = sK1 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_12513,c_5840]) ).
tcf(c_12534,plain,
! [X0: $i,X1: $i] :
( in(sK2(X1,sK7(powerset(X0)),sK1),sK0)
| ( relation_image(X1,sK7(powerset(X0))) = sK1 )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12513,c_5822]) ).
tcf(c_12535,plain,
! [X0: $i] :
( in(sK2(X0,empty_set,sK1),sK0)
| ( relation_image(X0,empty_set) = sK1 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_12513,c_8375]) ).
tcf(c_12538,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,sK7(sK6(powerset(X1))),sK1),sK0)
| element(sK3(X0,sK7(sK6(powerset(X1))),sK1),X1)
| ( relation_image(X0,sK7(sK6(powerset(X1)))) = sK1 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_12513,c_9820]) ).
tcf(c_12539,plain,
! [X0: $i,X1: $i] :
( in(sK2(X1,sK7(sK6(powerset(X0))),sK1),sK0)
| ( relation_image(X1,sK7(sK6(powerset(X0)))) = sK1 )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12513,c_9817]) ).
tcf(c_12633,plain,
! [X0: $i,X1: $i] :
( element(sK2(identity_relation(X0),X1,sK1),sK0)
| ( relation_image(identity_relation(X0),X1) = sK1 )
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ in(X0,sK3(identity_relation(X0),X1,sK1)) ),
inference(superposition,[status(thm)],[c_121,c_7595]) ).
tcf(c_12634,plain,
! [X0: $i] :
( element(sK2(empty_set,X0,sK1),sK0)
| ( relation_image(empty_set,X0) = sK1 )
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ in(empty_set,sK3(empty_set,X0,sK1)) ),
inference(superposition,[status(thm)],[c_5746,c_7595]) ).
tcf(c_12635,plain,
! [X0: $i] :
( element(sK2(empty_set,X0,sK1),sK0)
| ( relation_image(empty_set,X0) = sK1 )
| ~ in(empty_set,sK3(empty_set,X0,sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12634,c_5610,c_82]) ).
tcf(c_12639,plain,
! [X0: $i,X1: $i] :
( element(sK2(identity_relation(X0),X1,sK1),sK0)
| ( relation_image(identity_relation(X0),X1) = sK1 )
| ~ in(X0,sK3(identity_relation(X0),X1,sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12633,c_62,c_63]) ).
tcf(c_12645,plain,
! [X0: $i] :
( ~ relation(X0)
| ~ function(X0)
| ( relation_image(X0,sK1) = sK1 )
| in(sK2(X0,sK1,sK1),sK0)
| in(sK3(X0,sK1,sK1),sK0) ),
inference(global_subsumption_just,[status(thm)],[c_12479,c_6945,c_12479]) ).
tcf(c_12646,plain,
! [X0: $i] :
( in(sK3(X0,sK1,sK1),sK0)
| in(sK2(X0,sK1,sK1),sK0)
| ( relation_image(X0,sK1) = sK1 )
| ~ function(X0)
| ~ relation(X0) ),
inference(renaming,[status(thm)],[c_12645]) ).
tcf(c_12658,plain,
! [X0: $i] :
( in(sK2(X0,sK1,sK1),sK0)
| ( relation_image(X0,sK1) = sK1 )
| ( apply(identity_relation(sK0),sK3(X0,sK1,sK1)) = sK3(X0,sK1,sK1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_12646,c_151]) ).
tcf(c_12659,plain,
! [X0: $i] :
( in(sK2(X0,sK1,sK1),sK0)
| ( relation_image(X0,sK1) = sK1 )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK0,sK3(X0,sK1,sK1)) ),
inference(superposition,[status(thm)],[c_12646,c_85]) ).
tcf(c_12720,plain,
! [X0: $i] :
( element(sK3(X0,sK1,empty_set),sK0)
| ( sK7(sK6(powerset(empty_set))) = relation_image(X0,sK1) )
| ~ empty(empty_set)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_11339,c_10417]) ).
tcf(c_12734,plain,
! [X0: $i] :
( element(sK2(X0,empty_set,sK1),sK0)
| ( relation_image(X0,sK7(sK6(powerset(empty_set)))) = sK1 )
| ~ empty(empty_set)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_11339,c_10419]) ).
tcf(c_12742,plain,
! [X0: $i] :
( in(sK7(sK1),relation_image(identity_relation(sK0),X0))
| ( identity_relation(identity_relation(relation_dom(sK1))) = empty_set )
| ~ function(identity_relation(sK0))
| ~ relation(identity_relation(sK0))
| ~ in(sK7(sK1),X0)
| ~ in(sK7(sK1),relation_dom(identity_relation(sK0))) ),
inference(superposition,[status(thm)],[c_8994,c_57]) ).
tcf(c_12743,plain,
! [X0: $i] :
( in(sK7(sK1),relation_image(identity_relation(sK0),X0))
| ( identity_relation(identity_relation(relation_dom(sK1))) = empty_set )
| ~ in(sK7(sK1),X0)
| ~ in(sK7(sK1),relation_dom(identity_relation(sK0))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12742,c_62,c_63]) ).
tcf(c_12753,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(relation_dom(X0)))) = empty_set )
| ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) ) ),
inference(superposition,[status(thm)],[c_5807,c_9114]) ).
tcf(c_12754,plain,
relation_dom(sK7(powerset(relation_dom(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_9114]) ).
tcf(c_12755,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(relation_dom(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_9114]) ).
tcf(c_12756,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(relation_dom(identity_relation(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_9114]) ).
tcf(c_12757,plain,
( ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) )
| ( relation_dom(sK7(powerset(relation_dom(sK1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_9449,c_9114]) ).
tcf(c_12758,plain,
( ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ( relation_dom(sK7(powerset(relation_dom(sK1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5890,c_9114]) ).
tcf(c_12759,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(relation_dom(relation_image(X0,sK1))))) = empty_set )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6158,c_9114]) ).
tcf(c_12760,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(relation_dom(sK7(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_9114]) ).
tcf(c_12761,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(relation_dom(sK7(sK6(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_9114]) ).
tcf(c_12789,plain,
( ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) )
| ( relation_image(relation_image(sK14,sK1),sK1) = sK1 ) ),
inference(superposition,[status(thm)],[c_5807,c_9229]) ).
tcf(c_12824,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( relation_image(X0,relation_image(X1,sK1)) = sK1 )
| ~ empty(sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_9431,c_7114]) ).
tcf(c_12825,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X0,sK1) = relation_image(X1,sK1) )
| ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ~ empty(sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_9431,c_6949]) ).
tcf(c_12826,plain,
! [X0: $i] :
( ( relation_image(relation_image(X0,sK1),sK1) = sK1 )
| ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ~ empty(sK0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_9431,c_9208]) ).
tcf(c_12827,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X0,X1) = sK1 )
| ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( apply(X0,sK3(X0,X1,sK1)) = sK2(X0,X1,sK1) )
| ~ empty(sK0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_9431,c_7707]) ).
tcf(c_12828,plain,
! [X0: $i] :
( ( relation_image(X0,sK1) = sK1 )
| ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ~ empty(sK0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_9431,c_6945]) ).
tcf(c_12829,plain,
! [X0: $i] :
( ( relation_image(X0,sK1) = empty_set )
| ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ~ empty(sK0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_9431,c_6198]) ).
tcf(c_12869,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(identity_relation(X0)))) = empty_set )
| ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) ) ),
inference(superposition,[status(thm)],[c_5807,c_9088]) ).
tcf(c_12870,plain,
identity_relation(sK7(powerset(identity_relation(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_9088]) ).
tcf(c_12871,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(identity_relation(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_9088]) ).
tcf(c_12872,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(identity_relation(identity_relation(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_9088]) ).
tcf(c_12873,plain,
( ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) )
| ( identity_relation(sK7(powerset(identity_relation(sK1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_9449,c_9088]) ).
tcf(c_12874,plain,
( ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ( identity_relation(sK7(powerset(identity_relation(sK1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5890,c_9088]) ).
tcf(c_12875,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(identity_relation(relation_image(X0,sK1))))) = empty_set )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6158,c_9088]) ).
tcf(c_12876,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(identity_relation(sK7(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_9088]) ).
tcf(c_12877,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(identity_relation(sK7(sK6(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_9088]) ).
tcf(c_12907,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(identity_relation(X0)))) = empty_set )
| ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) ) ),
inference(superposition,[status(thm)],[c_5807,c_9115]) ).
tcf(c_12908,plain,
relation_dom(sK7(powerset(identity_relation(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_9115]) ).
tcf(c_12909,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(identity_relation(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_9115]) ).
tcf(c_12910,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(identity_relation(identity_relation(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_9115]) ).
tcf(c_12911,plain,
( ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) )
| ( relation_dom(sK7(powerset(identity_relation(sK1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_9449,c_9115]) ).
tcf(c_12912,plain,
( ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ( relation_dom(sK7(powerset(identity_relation(sK1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5890,c_9115]) ).
tcf(c_12913,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(identity_relation(relation_image(X0,sK1))))) = empty_set )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6158,c_9115]) ).
tcf(c_12914,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(identity_relation(sK7(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_9115]) ).
tcf(c_12915,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(identity_relation(sK7(sK6(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_9115]) ).
tcf(c_13032,plain,
( ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) )
| ( relation_image(relation_image(empty_set,sK1),sK1) = sK1 ) ),
inference(superposition,[status(thm)],[c_5807,c_9226]) ).
tcf(c_13042,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(relation_dom(X0)))) = empty_set )
| ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) ) ),
inference(superposition,[status(thm)],[c_5807,c_9681]) ).
tcf(c_13043,plain,
identity_relation(identity_relation(identity_relation(relation_dom(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_9681]) ).
tcf(c_13044,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(relation_dom(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_9681]) ).
tcf(c_13045,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(relation_dom(identity_relation(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_9681]) ).
tcf(c_13046,plain,
( ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) )
| ( identity_relation(identity_relation(identity_relation(relation_dom(sK1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_9449,c_9681]) ).
tcf(c_13047,plain,
( ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ( identity_relation(identity_relation(identity_relation(relation_dom(sK1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5890,c_9681]) ).
tcf(c_13048,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(relation_dom(relation_image(X0,sK1))))) = empty_set )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6158,c_9681]) ).
tcf(c_13049,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(relation_dom(sK7(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_9681]) ).
tcf(c_13050,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(relation_dom(sK7(sK6(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_9681]) ).
tcf(c_13094,plain,
! [X0: $i] :
( ( relation_image(X0,sK1) = sK1 )
| ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ~ empty(sK0) ),
inference(global_subsumption_just,[status(thm)],[c_12828,c_9432,c_12828]) ).
tcf(c_13102,plain,
! [X0: $i] :
( ( relation_image(X0,sK1) = sK1 )
| ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) )
| ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) ) ),
inference(superposition,[status(thm)],[c_5807,c_13094]) ).
tcf(c_13118,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,X2)
| ( sK7(sK6(powerset(powerset(X2)))) = relation_image(X1,sK1) )
| ~ empty(sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,sK2(X1,sK1,sK7(sK6(powerset(powerset(X2)))))) ),
inference(superposition,[status(thm)],[c_10565,c_65]) ).
tcf(c_13119,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK7(sK6(powerset(powerset(X2)))) = relation_image(X1,sK1) )
| ~ empty(sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X2)
| ~ in(X0,sK2(X1,sK1,sK7(sK6(powerset(powerset(X2)))))) ),
inference(superposition,[status(thm)],[c_10565,c_64]) ).
tcf(c_13120,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| in(sK2(X0,sK1,sK7(sK6(powerset(X1)))),X1)
| ( sK7(sK6(powerset(X1))) = relation_image(X0,sK1) )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_10565,c_71]) ).
tcf(c_13160,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,X2)
| ( relation_image(X1,sK7(sK6(powerset(powerset(X2))))) = sK1 )
| ~ empty(sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,sK3(X1,sK7(sK6(powerset(powerset(X2)))),sK1)) ),
inference(superposition,[status(thm)],[c_10567,c_65]) ).
tcf(c_13161,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X1,sK7(sK6(powerset(powerset(X2))))) = sK1 )
| ~ empty(sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X2)
| ~ in(X0,sK3(X1,sK7(sK6(powerset(powerset(X2)))),sK1)) ),
inference(superposition,[status(thm)],[c_10567,c_64]) ).
tcf(c_13162,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| in(sK3(X0,sK7(sK6(powerset(X1))),sK1),X1)
| ( relation_image(X0,sK7(sK6(powerset(X1)))) = sK1 )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_10567,c_71]) ).
tcf(c_13200,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X0,sK1) = X1 )
| ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( apply(identity_relation(X1),sK2(X0,sK1,X1)) = sK2(X0,sK1,X1) )
| ~ empty(sK0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_9431,c_6940]) ).
tcf(c_13201,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(X0),sK1) = X1 )
| ( apply(identity_relation(X1),sK2(identity_relation(X0),sK1,X1)) = sK2(identity_relation(X0),sK1,X1) )
| ~ empty(sK0)
| ~ relation(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_62,c_6940]) ).
tcf(c_13202,plain,
! [X0: $i] :
( ( relation_image(sK14,sK1) = X0 )
| ( apply(identity_relation(X0),sK2(sK14,sK1,X0)) = sK2(sK14,sK1,X0) )
| ~ relation(sK14)
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_97,c_6940]) ).
tcf(c_13203,plain,
! [X0: $i] :
( ( relation_image(empty_set,sK1) = X0 )
| ( apply(identity_relation(X0),sK2(empty_set,sK1,X0)) = sK2(empty_set,sK1,X0) )
| ~ relation(empty_set)
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_5610,c_6940]) ).
tcf(c_13204,plain,
! [X0: $i,X1: $i] :
( ( relation_image(relation_dom(X0),sK1) = X1 )
| ( apply(identity_relation(X1),sK2(relation_dom(X0),sK1,X1)) = sK2(relation_dom(X0),sK1,X1) )
| ~ empty(sK0)
| ~ empty(X0)
| ~ relation(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_5622,c_6940]) ).
tcf(c_13205,plain,
! [X0: $i] :
( ( relation_image(sK1,sK1) = X0 )
| ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ( apply(identity_relation(X0),sK2(sK1,sK1,X0)) = sK2(sK1,sK1,X0) )
| ~ relation(sK1)
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_5909,c_6940]) ).
tcf(c_13206,plain,
! [X0: $i,X1: $i] :
( ( relation_image(relation_image(X0,sK1),sK1) = X1 )
| ( apply(identity_relation(X1),sK2(relation_image(X0,sK1),sK1,X1)) = sK2(relation_image(X0,sK1),sK1,X1) )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0)
| ~ relation(relation_image(X0,sK1)) ),
inference(superposition,[status(thm)],[c_6199,c_6940]) ).
tcf(c_13207,plain,
! [X0: $i,X1: $i] :
( ( relation_image(sK7(powerset(X0)),sK1) = X1 )
| ( apply(identity_relation(X1),sK2(sK7(powerset(X0)),sK1,X1)) = sK2(sK7(powerset(X0)),sK1,X1) )
| ~ empty(sK0)
| ~ empty(X0)
| ~ relation(sK7(powerset(X0))) ),
inference(superposition,[status(thm)],[c_6880,c_6940]) ).
tcf(c_13208,plain,
! [X0: $i,X1: $i] :
( ( relation_image(sK7(sK6(powerset(X0))),sK1) = X1 )
| ( apply(identity_relation(X1),sK2(sK7(sK6(powerset(X0))),sK1,X1)) = sK2(sK7(sK6(powerset(X0))),sK1,X1) )
| ~ empty(sK0)
| ~ empty(X0)
| ~ relation(sK7(sK6(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_10682,c_6940]) ).
tcf(c_13209,plain,
! [X0: $i] :
( ( relation_image(empty_set,sK1) = X0 )
| ( apply(identity_relation(X0),sK2(empty_set,sK1,X0)) = sK2(empty_set,sK1,X0) )
| ~ empty(sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_13203,c_82]) ).
tcf(c_13213,plain,
! [X0: $i] :
( ( relation_image(sK14,sK1) = X0 )
| ( apply(identity_relation(X0),sK2(sK14,sK1,X0)) = sK2(sK14,sK1,X0) )
| ~ empty(sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_13202,c_96]) ).
tcf(c_13217,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(X1),sK1) = X0 )
| ( apply(identity_relation(X0),sK2(identity_relation(X1),sK1,X0)) = sK2(identity_relation(X1),sK1,X0) )
| ~ empty(sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_13201,c_63]) ).
tcf(c_13256,plain,
( ~ empty(sK1)
| ~ in(sK2(identity_relation(sK0),sK1,sK1),sK1) ),
inference(instantiation,[status(thm)],[c_84]) ).
tcf(c_13275,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X0,X1) = sK1 )
| ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( apply(identity_relation(X1),sK3(X0,X1,sK1)) = sK3(X0,X1,sK1) )
| ~ empty(sK0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_9431,c_7105]) ).
tcf(c_13276,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(X0),X1) = sK1 )
| ( apply(identity_relation(X1),sK3(identity_relation(X0),X1,sK1)) = sK3(identity_relation(X0),X1,sK1) )
| ~ empty(sK0)
| ~ relation(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_62,c_7105]) ).
tcf(c_13277,plain,
! [X0: $i] :
( ( relation_image(sK14,X0) = sK1 )
| ( apply(identity_relation(X0),sK3(sK14,X0,sK1)) = sK3(sK14,X0,sK1) )
| ~ relation(sK14)
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_97,c_7105]) ).
tcf(c_13278,plain,
! [X0: $i] :
( ( relation_image(empty_set,X0) = sK1 )
| ( apply(identity_relation(X0),sK3(empty_set,X0,sK1)) = sK3(empty_set,X0,sK1) )
| ~ relation(empty_set)
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_5610,c_7105]) ).
tcf(c_13279,plain,
! [X0: $i,X1: $i] :
( ( relation_image(relation_dom(X0),X1) = sK1 )
| ( apply(identity_relation(X1),sK3(relation_dom(X0),X1,sK1)) = sK3(relation_dom(X0),X1,sK1) )
| ~ empty(sK0)
| ~ empty(X0)
| ~ relation(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_5622,c_7105]) ).
tcf(c_13280,plain,
! [X0: $i] :
( ( relation_image(sK1,X0) = sK1 )
| ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ( apply(identity_relation(X0),sK3(sK1,X0,sK1)) = sK3(sK1,X0,sK1) )
| ~ relation(sK1)
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_5909,c_7105]) ).
tcf(c_13281,plain,
! [X0: $i,X1: $i] :
( ( relation_image(relation_image(X0,sK1),X1) = sK1 )
| ( apply(identity_relation(X1),sK3(relation_image(X0,sK1),X1,sK1)) = sK3(relation_image(X0,sK1),X1,sK1) )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0)
| ~ relation(relation_image(X0,sK1)) ),
inference(superposition,[status(thm)],[c_6199,c_7105]) ).
tcf(c_13282,plain,
! [X0: $i,X1: $i] :
( ( relation_image(sK7(powerset(X0)),X1) = sK1 )
| ( apply(identity_relation(X1),sK3(sK7(powerset(X0)),X1,sK1)) = sK3(sK7(powerset(X0)),X1,sK1) )
| ~ empty(sK0)
| ~ empty(X0)
| ~ relation(sK7(powerset(X0))) ),
inference(superposition,[status(thm)],[c_6880,c_7105]) ).
tcf(c_13283,plain,
! [X0: $i,X1: $i] :
( ( relation_image(sK7(sK6(powerset(X0))),X1) = sK1 )
| ( apply(identity_relation(X1),sK3(sK7(sK6(powerset(X0))),X1,sK1)) = sK3(sK7(sK6(powerset(X0))),X1,sK1) )
| ~ empty(sK0)
| ~ empty(X0)
| ~ relation(sK7(sK6(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_10682,c_7105]) ).
tcf(c_13284,plain,
! [X0: $i] :
( ( relation_image(empty_set,X0) = sK1 )
| ( apply(identity_relation(X0),sK3(empty_set,X0,sK1)) = sK3(empty_set,X0,sK1) )
| ~ empty(sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_13278,c_82]) ).
tcf(c_13288,plain,
! [X0: $i] :
( ( relation_image(sK14,X0) = sK1 )
| ( apply(identity_relation(X0),sK3(sK14,X0,sK1)) = sK3(sK14,X0,sK1) )
| ~ empty(sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_13277,c_96]) ).
tcf(c_13292,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(X1),X0) = sK1 )
| ( apply(identity_relation(X0),sK3(identity_relation(X1),X0,sK1)) = sK3(identity_relation(X1),X0,sK1) )
| ~ empty(sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_13276,c_63]) ).
tcf(c_13388,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X0,X1) = sK1 )
| ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( apply(identity_relation(relation_dom(X0)),sK3(X0,X1,sK1)) = sK3(X0,X1,sK1) )
| ~ empty(sK0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_9431,c_7214]) ).
tcf(c_13389,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(X0),X1) = sK1 )
| ( apply(identity_relation(relation_dom(identity_relation(X0))),sK3(identity_relation(X0),X1,sK1)) = sK3(identity_relation(X0),X1,sK1) )
| ~ empty(sK0)
| ~ relation(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_62,c_7214]) ).
tcf(c_13390,plain,
! [X0: $i] :
( ( relation_image(sK14,X0) = sK1 )
| ( apply(identity_relation(relation_dom(sK14)),sK3(sK14,X0,sK1)) = sK3(sK14,X0,sK1) )
| ~ relation(sK14)
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_97,c_7214]) ).
tcf(c_13391,plain,
! [X0: $i] :
( ( relation_image(empty_set,X0) = sK1 )
| ( apply(identity_relation(relation_dom(empty_set)),sK3(empty_set,X0,sK1)) = sK3(empty_set,X0,sK1) )
| ~ relation(empty_set)
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_5610,c_7214]) ).
tcf(c_13392,plain,
! [X0: $i,X1: $i] :
( ( relation_image(relation_dom(X0),X1) = sK1 )
| ( apply(identity_relation(relation_dom(relation_dom(X0))),sK3(relation_dom(X0),X1,sK1)) = sK3(relation_dom(X0),X1,sK1) )
| ~ empty(sK0)
| ~ empty(X0)
| ~ relation(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_5622,c_7214]) ).
tcf(c_13393,plain,
! [X0: $i] :
( ( relation_image(sK1,X0) = sK1 )
| ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ( apply(identity_relation(relation_dom(sK1)),sK3(sK1,X0,sK1)) = sK3(sK1,X0,sK1) )
| ~ relation(sK1)
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_5909,c_7214]) ).
tcf(c_13394,plain,
! [X0: $i,X1: $i] :
( ( relation_image(relation_image(X0,sK1),X1) = sK1 )
| ( apply(identity_relation(relation_dom(relation_image(X0,sK1))),sK3(relation_image(X0,sK1),X1,sK1)) = sK3(relation_image(X0,sK1),X1,sK1) )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0)
| ~ relation(relation_image(X0,sK1)) ),
inference(superposition,[status(thm)],[c_6199,c_7214]) ).
tcf(c_13395,plain,
! [X0: $i,X1: $i] :
( ( relation_image(sK7(powerset(X0)),X1) = sK1 )
| ( apply(identity_relation(relation_dom(sK7(powerset(X0)))),sK3(sK7(powerset(X0)),X1,sK1)) = sK3(sK7(powerset(X0)),X1,sK1) )
| ~ empty(sK0)
| ~ empty(X0)
| ~ relation(sK7(powerset(X0))) ),
inference(superposition,[status(thm)],[c_6880,c_7214]) ).
tcf(c_13396,plain,
! [X0: $i,X1: $i] :
( ( relation_image(sK7(sK6(powerset(X0))),X1) = sK1 )
| ( apply(identity_relation(relation_dom(sK7(sK6(powerset(X0))))),sK3(sK7(sK6(powerset(X0))),X1,sK1)) = sK3(sK7(sK6(powerset(X0))),X1,sK1) )
| ~ empty(sK0)
| ~ empty(X0)
| ~ relation(sK7(sK6(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_10682,c_7214]) ).
tcf(c_13397,plain,
! [X0: $i] :
( ( relation_image(empty_set,X0) = sK1 )
| ( apply(empty_set,sK3(empty_set,X0,sK1)) = sK3(empty_set,X0,sK1) )
| ~ relation(empty_set)
| ~ empty(sK0) ),
inference(light_normalisation,[status(thm)],[c_13391,c_5746,c_6104]) ).
tcf(c_13398,plain,
! [X0: $i] :
( ( relation_image(empty_set,X0) = sK1 )
| ( apply(empty_set,sK3(empty_set,X0,sK1)) = sK3(empty_set,X0,sK1) )
| ~ empty(sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_13397,c_82]) ).
tcf(c_13402,plain,
! [X0: $i] :
( ( relation_image(sK14,X0) = sK1 )
| ( apply(identity_relation(relation_dom(sK14)),sK3(sK14,X0,sK1)) = sK3(sK14,X0,sK1) )
| ~ empty(sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_13390,c_96]) ).
tcf(c_13406,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(X0),X1) = sK1 )
| ( apply(identity_relation(X0),sK3(identity_relation(X0),X1,sK1)) = sK3(identity_relation(X0),X1,sK1) )
| ~ empty(sK0)
| ~ relation(identity_relation(X0)) ),
inference(light_normalisation,[status(thm)],[c_13389,c_121]) ).
tcf(c_13407,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(X0),X1) = sK1 )
| ( apply(identity_relation(X0),sK3(identity_relation(X0),X1,sK1)) = sK3(identity_relation(X0),X1,sK1) )
| ~ empty(sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_13406,c_63]) ).
tcf(c_13500,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(powerset(X2))
| element(X0,X2)
| element(sK3(X1,sK1,sK6(powerset(X2))),sK0)
| ( relation_image(X1,sK1) = sK6(powerset(X2)) )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,sK2(X1,sK1,sK6(powerset(X2)))) ),
inference(superposition,[status(thm)],[c_8392,c_65]) ).
tcf(c_13501,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(powerset(X2))
| element(sK3(X1,sK1,sK6(powerset(X2))),sK0)
| ( relation_image(X1,sK1) = sK6(powerset(X2)) )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X2)
| ~ in(X0,sK2(X1,sK1,sK6(powerset(X2)))) ),
inference(superposition,[status(thm)],[c_8392,c_64]) ).
tcf(c_13502,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| element(sK3(X0,sK1,sK6(X1)),sK0)
| in(sK2(X0,sK1,sK6(X1)),X1)
| ( relation_image(X0,sK1) = sK6(X1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8392,c_71]) ).
tcf(c_13509,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK3(X1,sK1,sK6(powerset(X2))),sK0)
| ( relation_image(X1,sK1) = sK6(powerset(X2)) )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X2)
| ~ in(X0,sK2(X1,sK1,sK6(powerset(X2)))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_13501,c_70]) ).
tcf(c_13516,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,X2)
| element(sK3(X1,sK1,sK6(powerset(X2))),sK0)
| ( relation_image(X1,sK1) = sK6(powerset(X2)) )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,sK2(X1,sK1,sK6(powerset(X2)))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_13500,c_70]) ).
tcf(c_13544,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(powerset(X2))
| element(X0,X2)
| element(sK2(X1,sK6(powerset(X2)),sK1),sK0)
| ( relation_image(X1,sK6(powerset(X2))) = sK1 )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,sK3(X1,sK6(powerset(X2)),sK1)) ),
inference(superposition,[status(thm)],[c_8394,c_65]) ).
tcf(c_13545,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(powerset(X2))
| element(sK2(X1,sK6(powerset(X2)),sK1),sK0)
| ( relation_image(X1,sK6(powerset(X2))) = sK1 )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X2)
| ~ in(X0,sK3(X1,sK6(powerset(X2)),sK1)) ),
inference(superposition,[status(thm)],[c_8394,c_64]) ).
tcf(c_13546,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| element(sK2(X0,sK6(X1),sK1),sK0)
| in(sK3(X0,sK6(X1),sK1),X1)
| ( relation_image(X0,sK6(X1)) = sK1 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8394,c_71]) ).
tcf(c_13553,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X1,sK6(powerset(X2)),sK1),sK0)
| ( relation_image(X1,sK6(powerset(X2))) = sK1 )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X2)
| ~ in(X0,sK3(X1,sK6(powerset(X2)),sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_13545,c_70]) ).
tcf(c_13560,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,X2)
| element(sK2(X1,sK6(powerset(X2)),sK1),sK0)
| ( relation_image(X1,sK6(powerset(X2))) = sK1 )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,sK3(X1,sK6(powerset(X2)),sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_13544,c_70]) ).
tcf(c_13636,plain,
! [X0: $i] :
( in(sK7(sK1),relation_image(identity_relation(sK0),X0))
| ( sK7(powerset(relation_dom(sK1))) = empty_set )
| ~ function(identity_relation(sK0))
| ~ relation(identity_relation(sK0))
| ~ in(sK7(sK1),X0)
| ~ in(sK7(sK1),relation_dom(identity_relation(sK0))) ),
inference(superposition,[status(thm)],[c_9019,c_57]) ).
tcf(c_13637,plain,
! [X0: $i] :
( in(sK7(sK1),relation_image(identity_relation(sK0),X0))
| ( sK7(powerset(relation_dom(sK1))) = empty_set )
| ~ in(sK7(sK1),X0)
| ~ in(sK7(sK1),relation_dom(identity_relation(sK0))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_13636,c_62,c_63]) ).
tcf(c_13647,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(relation_dom(X0)))) = empty_set )
| ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) ) ),
inference(superposition,[status(thm)],[c_5807,c_9747]) ).
tcf(c_13648,plain,
sK7(powerset(identity_relation(relation_dom(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_9747]) ).
tcf(c_13649,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(relation_dom(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_9747]) ).
tcf(c_13650,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(relation_dom(identity_relation(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_9747]) ).
tcf(c_13651,plain,
( ( sK7(powerset(identity_relation(relation_dom(sK1)))) = empty_set )
| ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) ) ),
inference(superposition,[status(thm)],[c_9449,c_9747]) ).
tcf(c_13652,plain,
( ( sK7(powerset(identity_relation(relation_dom(sK1)))) = empty_set )
| ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) ) ),
inference(superposition,[status(thm)],[c_5890,c_9747]) ).
tcf(c_13653,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(relation_dom(relation_image(X0,sK1))))) = empty_set )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6158,c_9747]) ).
tcf(c_13654,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(relation_dom(sK7(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_9747]) ).
tcf(c_13655,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(relation_dom(sK7(sK6(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_9747]) ).
tcf(c_13712,plain,
! [X0: $i] :
( ( relation_image(sK1,X0) = sK1 )
| ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) )
| ( apply(identity_relation(relation_dom(sK1)),sK3(sK1,X0,sK1)) = sK3(sK1,X0,sK1) )
| ~ relation(sK1)
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_9876,c_7214]) ).
tcf(c_13713,plain,
! [X0: $i] :
( ( relation_image(sK1,X0) = sK1 )
| ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) )
| ( apply(identity_relation(X0),sK3(sK1,X0,sK1)) = sK3(sK1,X0,sK1) )
| ~ relation(sK1)
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_9876,c_7105]) ).
tcf(c_13714,plain,
! [X0: $i] :
( ( relation_image(sK1,sK1) = X0 )
| ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) )
| ( apply(identity_relation(X0),sK2(sK1,sK1,X0)) = sK2(sK1,sK1,X0) )
| ~ relation(sK1)
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_9876,c_6940]) ).
tcf(c_13715,plain,
! [X0: $i] :
( ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) )
| ( relation_image(sK1,relation_image(X0,sK1)) = sK1 )
| ~ relation(sK1)
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_9876,c_7114]) ).
tcf(c_13716,plain,
! [X0: $i] :
( ( relation_image(X0,sK1) = relation_image(sK1,sK1) )
| ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) )
| ~ relation(sK1)
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_9876,c_6949]) ).
tcf(c_13717,plain,
( ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) )
| ( relation_image(relation_image(sK1,sK1),sK1) = sK1 )
| ~ relation(sK1)
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_9876,c_9208]) ).
tcf(c_13718,plain,
! [X0: $i] :
( ( relation_image(sK1,X0) = sK1 )
| ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) )
| ( apply(sK1,sK3(sK1,X0,sK1)) = sK2(sK1,X0,sK1) )
| ~ relation(sK1)
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_9876,c_7707]) ).
tcf(c_13719,plain,
( ( relation_image(sK1,sK1) = sK1 )
| ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) )
| ~ relation(sK1)
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_9876,c_6945]) ).
tcf(c_13720,plain,
( ( relation_image(sK1,sK1) = empty_set )
| ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) )
| ~ relation(sK1)
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_9876,c_6198]) ).
tcf(c_13815,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(relation_dom(X0)))) = empty_set )
| ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) ) ),
inference(superposition,[status(thm)],[c_5807,c_11340]) ).
tcf(c_13816,plain,
sK7(sK6(powerset(relation_dom(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_11340]) ).
tcf(c_13817,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(relation_dom(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_11340]) ).
tcf(c_13818,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(relation_dom(identity_relation(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_11340]) ).
tcf(c_13819,plain,
( ( sK7(sK6(powerset(relation_dom(sK1)))) = empty_set )
| ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) ) ),
inference(superposition,[status(thm)],[c_9449,c_11340]) ).
tcf(c_13820,plain,
( ( sK7(sK6(powerset(relation_dom(sK1)))) = empty_set )
| ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) ) ),
inference(superposition,[status(thm)],[c_5890,c_11340]) ).
tcf(c_13821,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(relation_dom(relation_image(X0,sK1))))) = empty_set )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6158,c_11340]) ).
tcf(c_13822,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(relation_dom(sK7(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_11340]) ).
tcf(c_13823,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(relation_dom(sK7(sK6(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_11340]) ).
tcf(c_13851,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(X0)))) = empty_set )
| ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) ) ),
inference(superposition,[status(thm)],[c_5807,c_9682]) ).
tcf(c_13852,plain,
identity_relation(identity_relation(identity_relation(identity_relation(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_9682]) ).
tcf(c_13853,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_9682]) ).
tcf(c_13854,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(identity_relation(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_9682]) ).
tcf(c_13855,plain,
( ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) )
| ( identity_relation(identity_relation(identity_relation(identity_relation(sK1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_9449,c_9682]) ).
tcf(c_13856,plain,
( ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ( identity_relation(identity_relation(identity_relation(identity_relation(sK1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5890,c_9682]) ).
tcf(c_13857,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(relation_image(X0,sK1))))) = empty_set )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6158,c_9682]) ).
tcf(c_13858,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(sK7(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_9682]) ).
tcf(c_13859,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(sK7(sK6(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_9682]) ).
tcf(c_13967,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(identity_relation(X0)))) = empty_set )
| ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) ) ),
inference(superposition,[status(thm)],[c_5807,c_9748]) ).
tcf(c_13968,plain,
sK7(powerset(identity_relation(identity_relation(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_9748]) ).
tcf(c_13969,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(identity_relation(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_9748]) ).
tcf(c_13970,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(identity_relation(identity_relation(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_9748]) ).
tcf(c_13971,plain,
( ( sK7(powerset(identity_relation(identity_relation(sK1)))) = empty_set )
| ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) ) ),
inference(superposition,[status(thm)],[c_9449,c_9748]) ).
tcf(c_13972,plain,
( ( sK7(powerset(identity_relation(identity_relation(sK1)))) = empty_set )
| ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) ) ),
inference(superposition,[status(thm)],[c_5890,c_9748]) ).
tcf(c_13973,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(identity_relation(relation_image(X0,sK1))))) = empty_set )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6158,c_9748]) ).
tcf(c_13974,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(identity_relation(sK7(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_9748]) ).
tcf(c_13975,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(identity_relation(sK7(sK6(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_9748]) ).
tcf(c_14078,plain,
! [X0: $i] :
( empty(X0)
| element(sK7(sK6(sK6(X0))),X0) ),
inference(global_subsumption_just,[status(thm)],[c_10354,c_69,c_10354]) ).
tcf(c_14084,plain,
! [X0: $i,X1: $i] :
( empty(powerset(X1))
| element(X0,X1)
| ~ in(X0,sK7(sK6(sK6(powerset(X1))))) ),
inference(superposition,[status(thm)],[c_14078,c_65]) ).
tcf(c_14085,plain,
! [X0: $i,X1: $i] :
( empty(powerset(X1))
| ~ empty(X1)
| ~ in(X0,sK7(sK6(sK6(powerset(X1))))) ),
inference(superposition,[status(thm)],[c_14078,c_64]) ).
tcf(c_14086,plain,
! [X0: $i] :
( empty(X0)
| in(sK7(sK6(sK6(X0))),X0) ),
inference(superposition,[status(thm)],[c_14078,c_71]) ).
tcf(c_14089,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ in(X0,sK7(sK6(sK6(powerset(X1))))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14085,c_70]) ).
tcf(c_14092,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| ~ in(X0,sK7(sK6(sK6(powerset(X1))))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14084,c_70]) ).
tcf(c_14101,plain,
! [X0: $i,X1: $i] :
( empty(relation_image(X0,X1))
| ( apply(X0,sK4(X0,X1,sK7(sK6(sK6(relation_image(X0,X1)))))) = sK7(sK6(sK6(relation_image(X0,X1)))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_14086,c_60]) ).
tcf(c_14102,plain,
! [X0: $i] :
( empty(X0)
| ( apply(identity_relation(X0),sK7(sK6(sK6(X0)))) = sK7(sK6(sK6(X0))) ) ),
inference(superposition,[status(thm)],[c_14086,c_151]) ).
tcf(c_14103,plain,
! [X0: $i] :
( empty(X0)
| ~ in(X0,sK7(sK6(sK6(X0)))) ),
inference(superposition,[status(thm)],[c_14086,c_85]) ).
tcf(c_14106,plain,
( empty(sK1)
| element(sK7(sK6(sK6(sK1))),sK0) ),
inference(superposition,[status(thm)],[c_14086,c_5838]) ).
tcf(c_14108,plain,
! [X0: $i] :
( empty(X0)
| empty(sK6(X0))
| element(sK7(sK6(sK6(sK6(X0)))),X0) ),
inference(superposition,[status(thm)],[c_14086,c_5839]) ).
tcf(c_14109,plain,
! [X0: $i] :
( empty(sK7(powerset(X0)))
| element(sK7(sK6(sK6(sK7(powerset(X0))))),X0) ),
inference(superposition,[status(thm)],[c_14086,c_5840]) ).
tcf(c_14114,plain,
! [X0: $i] :
( empty(sK7(sK6(powerset(X0))))
| element(sK7(sK6(sK6(sK7(sK6(powerset(X0)))))),X0) ),
inference(superposition,[status(thm)],[c_14086,c_9820]) ).
tcf(c_14203,plain,
( empty(sK0)
| empty(sK1)
| in(sK7(sK6(sK6(sK1))),sK0) ),
inference(superposition,[status(thm)],[c_14106,c_71]) ).
tcf(c_14207,plain,
( in(sK7(sK6(sK6(sK1))),sK0)
| empty(sK1) ),
inference(global_subsumption_just,[status(thm)],[c_14203,c_5857,c_14203]) ).
tcf(c_14208,plain,
( empty(sK1)
| in(sK7(sK6(sK6(sK1))),sK0) ),
inference(renaming,[status(thm)],[c_14207]) ).
tcf(c_14213,plain,
( empty(sK1)
| ( apply(identity_relation(sK0),sK7(sK6(sK6(sK1)))) = sK7(sK6(sK6(sK1))) ) ),
inference(superposition,[status(thm)],[c_14208,c_151]) ).
tcf(c_14214,plain,
( empty(sK1)
| ~ in(sK0,sK7(sK6(sK6(sK1)))) ),
inference(superposition,[status(thm)],[c_14208,c_85]) ).
tcf(c_14221,plain,
( ( relation_image(sK1,sK1) = sK1 )
| ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) )
| ~ empty(sK0) ),
inference(global_subsumption_just,[status(thm)],[c_13719,c_5857,c_8184,c_13719]) ).
tcf(c_14226,plain,
( ( relation_image(sK1,sK1) = sK1 )
| ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14221,c_5807]) ).
tcf(c_14233,plain,
! [X0: $i] :
( in(sK7(sK0),relation_image(identity_relation(sK0),X0))
| ( relation_image(sK1,sK1) = sK1 )
| ~ function(identity_relation(sK0))
| ~ relation(identity_relation(sK0))
| ~ in(sK7(sK0),X0)
| ~ in(sK7(sK0),relation_dom(identity_relation(sK0))) ),
inference(superposition,[status(thm)],[c_14226,c_57]) ).
tcf(c_14234,plain,
! [X0: $i] :
( in(sK7(sK0),relation_image(identity_relation(sK0),X0))
| ( relation_image(sK1,sK1) = sK1 )
| ~ in(sK7(sK0),X0)
| ~ in(sK7(sK0),relation_dom(identity_relation(sK0))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14233,c_62,c_63]) ).
tcf(c_14250,plain,
! [X0: $i] :
( element(sK3(X0,sK1,empty_set),sK0)
| element(sK2(X0,sK1,sK7(powerset(empty_set))),empty_set)
| ( relation_image(X0,sK1) = sK7(powerset(empty_set)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8004,c_7841]) ).
tcf(c_14251,plain,
! [X0: $i] :
( element(sK2(X0,sK1,empty_set),empty_set)
| element(sK3(X0,sK1,sK7(powerset(empty_set))),sK0)
| ( relation_image(X0,sK1) = sK7(powerset(empty_set)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8004,c_7841]) ).
tcf(c_14253,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,X2)
| element(sK3(X1,sK1,sK7(powerset(powerset(X2)))),sK0)
| ( sK7(powerset(powerset(X2))) = relation_image(X1,sK1) )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,sK2(X1,sK1,sK7(powerset(powerset(X2))))) ),
inference(superposition,[status(thm)],[c_7841,c_65]) ).
tcf(c_14254,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK3(X1,sK1,sK7(powerset(powerset(X2)))),sK0)
| ( sK7(powerset(powerset(X2))) = relation_image(X1,sK1) )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X2)
| ~ in(X0,sK2(X1,sK1,sK7(powerset(powerset(X2))))) ),
inference(superposition,[status(thm)],[c_7841,c_64]) ).
tcf(c_14255,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| element(sK3(X0,sK1,sK7(powerset(X1))),sK0)
| in(sK2(X0,sK1,sK7(powerset(X1))),X1)
| ( relation_image(X0,sK1) = sK7(powerset(X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7841,c_71]) ).
tcf(c_14256,plain,
! [X0: $i] :
( element(sK3(X0,sK1,empty_set),sK0)
| element(sK2(X0,sK1,empty_set),empty_set)
| ( relation_image(X0,sK1) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(light_normalisation,[status(thm)],[c_14251,c_8004]) ).
tcf(c_14384,plain,
! [X0: $i] :
( element(sK3(X0,empty_set,sK1),empty_set)
| element(sK2(X0,sK7(powerset(empty_set)),sK1),sK0)
| ( relation_image(X0,sK7(powerset(empty_set))) = sK1 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8004,c_7843]) ).
tcf(c_14385,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,X2)
| element(sK2(X1,sK7(powerset(powerset(X2))),sK1),sK0)
| ( relation_image(X1,sK7(powerset(powerset(X2)))) = sK1 )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,sK3(X1,sK7(powerset(powerset(X2))),sK1)) ),
inference(superposition,[status(thm)],[c_7843,c_65]) ).
tcf(c_14386,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X1,sK7(powerset(powerset(X2))),sK1),sK0)
| ( relation_image(X1,sK7(powerset(powerset(X2)))) = sK1 )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X2)
| ~ in(X0,sK3(X1,sK7(powerset(powerset(X2))),sK1)) ),
inference(superposition,[status(thm)],[c_7843,c_64]) ).
tcf(c_14387,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| element(sK2(X0,sK7(powerset(X1)),sK1),sK0)
| in(sK3(X0,sK7(powerset(X1)),sK1),X1)
| ( relation_image(X0,sK7(powerset(X1))) = sK1 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7843,c_71]) ).
tcf(c_14420,plain,
! [X0: $i] :
( in(sK3(empty_set,X0,sK1),empty_set)
| element(sK2(empty_set,X0,sK1),sK0)
| ( relation_image(empty_set,X0) = sK1 )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_7560,c_11672]) ).
tcf(c_14430,plain,
! [X0: $i] :
( in(sK3(empty_set,X0,sK1),empty_set)
| element(sK2(empty_set,X0,sK1),sK0)
| ( sK1 = empty_set )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(light_normalisation,[status(thm)],[c_14420,c_9622]) ).
tcf(c_14431,plain,
! [X0: $i] :
( element(sK2(empty_set,X0,sK1),sK0)
| ( sK1 = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14430,c_8452,c_7035,c_82]) ).
tcf(c_14470,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(X0,relation_image(X1,sK1)) = relation_image(X2,X3) )
| ( apply(X2,sK4(X2,X3,sK2(X0,relation_image(X1,sK1),relation_image(X2,X3)))) = sK2(X0,relation_image(X1,sK1),relation_image(X2,X3)) )
| ~ empty(sK0)
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6479,c_60]) ).
tcf(c_14471,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X0,relation_image(X1,sK1)) = X2 )
| ( apply(identity_relation(X2),sK2(X0,relation_image(X1,sK1),X2)) = sK2(X0,relation_image(X1,sK1),X2) )
| ~ empty(sK0)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6479,c_151]) ).
tcf(c_14472,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X1,relation_image(X2,sK1)) = X0 )
| ~ empty(sK0)
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(X0,sK2(X1,relation_image(X2,sK1),X0)) ),
inference(superposition,[status(thm)],[c_6479,c_85]) ).
tcf(c_14473,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X1,relation_image(X2,sK1)) = X0 )
| ~ empty(sK0)
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6479,c_84]) ).
tcf(c_14474,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X0,relation_image(X1,sK1),X2),X2)
| ( relation_image(X0,relation_image(X1,sK1)) = X2 )
| ~ empty(sK0)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6479,c_72]) ).
tcf(c_14477,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X2)
| element(sK2(X0,relation_image(X1,sK1),sK6(X2)),X2)
| ( relation_image(X0,relation_image(X1,sK1)) = sK6(X2) )
| ~ empty(sK0)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6479,c_5839]) ).
tcf(c_14478,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X0,relation_image(X1,sK1),sK7(powerset(X2))),X2)
| ( relation_image(X0,relation_image(X1,sK1)) = sK7(powerset(X2)) )
| ~ empty(sK0)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6479,c_5840]) ).
tcf(c_14479,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X1,relation_image(X2,sK1)) = sK7(powerset(X0)) )
| ~ empty(sK0)
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6479,c_5822]) ).
tcf(c_14480,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X0,relation_image(X1,sK1)) = empty_set )
| ~ empty(sK0)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6479,c_8375]) ).
tcf(c_14481,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X0,relation_image(X1,sK1)) = relation_image(X2,sK1) )
| ~ empty(sK0)
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6479,c_5948]) ).
tcf(c_14482,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(X0,relation_image(X1,sK1)) = relation_image(X2,relation_image(X3,sK1)) )
| ~ empty(sK0)
| ~ function(X3)
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6479,c_6157]) ).
tcf(c_14483,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X0,relation_image(X1,sK1),sK7(sK6(powerset(X2)))),X2)
| ( relation_image(X0,relation_image(X1,sK1)) = sK7(sK6(powerset(X2))) )
| ~ empty(sK0)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6479,c_9820]) ).
tcf(c_14484,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X1,relation_image(X2,sK1)) = sK7(sK6(powerset(X0))) )
| ~ empty(sK0)
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6479,c_9817]) ).
tcf(c_14707,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(X0,relation_image(X2,X3)) = relation_image(X1,sK1) )
| ( apply(X2,sK4(X2,X3,sK3(X0,relation_image(X2,X3),relation_image(X1,sK1)))) = sK3(X0,relation_image(X2,X3),relation_image(X1,sK1)) )
| ~ empty(sK0)
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6490,c_60]) ).
tcf(c_14708,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X0,X2) = relation_image(X1,sK1) )
| ( apply(identity_relation(X2),sK3(X0,X2,relation_image(X1,sK1))) = sK3(X0,X2,relation_image(X1,sK1)) )
| ~ empty(sK0)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6490,c_151]) ).
tcf(c_14709,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X1,X0) = relation_image(X2,sK1) )
| ~ empty(sK0)
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(X0,sK3(X1,X0,relation_image(X2,sK1))) ),
inference(superposition,[status(thm)],[c_6490,c_85]) ).
tcf(c_14710,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X1,X0) = relation_image(X2,sK1) )
| ~ empty(sK0)
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6490,c_84]) ).
tcf(c_14711,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK3(X0,X2,relation_image(X1,sK1)),X2)
| ( relation_image(X0,X2) = relation_image(X1,sK1) )
| ~ empty(sK0)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6490,c_72]) ).
tcf(c_14714,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X2)
| element(sK3(X0,sK6(X2),relation_image(X1,sK1)),X2)
| ( relation_image(X0,sK6(X2)) = relation_image(X1,sK1) )
| ~ empty(sK0)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6490,c_5839]) ).
tcf(c_14715,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK3(X0,sK7(powerset(X2)),relation_image(X1,sK1)),X2)
| ( relation_image(X0,sK7(powerset(X2))) = relation_image(X1,sK1) )
| ~ empty(sK0)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6490,c_5840]) ).
tcf(c_14716,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X1,sK7(powerset(X0))) = relation_image(X2,sK1) )
| ~ empty(sK0)
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6490,c_5822]) ).
tcf(c_14717,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X0,empty_set) = relation_image(X1,sK1) )
| ~ empty(sK0)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6490,c_8375]) ).
tcf(c_14718,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X0,relation_image(X2,sK1)) = relation_image(X1,sK1) )
| ~ empty(sK0)
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6490,c_5948]) ).
tcf(c_14719,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(X0,relation_image(X2,relation_image(X3,sK1))) = relation_image(X1,sK1) )
| ~ empty(sK0)
| ~ function(X3)
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6490,c_6157]) ).
tcf(c_14720,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK3(X0,sK7(sK6(powerset(X2))),relation_image(X1,sK1)),X2)
| ( relation_image(X0,sK7(sK6(powerset(X2)))) = relation_image(X1,sK1) )
| ~ empty(sK0)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6490,c_9820]) ).
tcf(c_14721,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X1,sK7(sK6(powerset(X0)))) = relation_image(X2,sK1) )
| ~ empty(sK0)
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6490,c_9817]) ).
tcf(c_14851,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( relation_image(X1,relation_image(X2,sK1)) = relation_image(X0,sK1) )
| ~ empty(sK0)
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_9431,c_6950]) ).
tcf(c_14852,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X1,relation_image(X2,sK1)) = relation_image(identity_relation(X0),sK1) )
| ~ empty(sK0)
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_62,c_6950]) ).
tcf(c_14853,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X0,relation_image(X1,sK1)) = relation_image(sK14,sK1) )
| ~ relation(sK14)
| ~ empty(sK0)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_97,c_6950]) ).
tcf(c_14854,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X0,relation_image(X1,sK1)) = relation_image(empty_set,sK1) )
| ~ relation(empty_set)
| ~ empty(sK0)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_5610,c_6950]) ).
tcf(c_14855,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X1,relation_image(X2,sK1)) = relation_image(relation_dom(X0),sK1) )
| ~ empty(sK0)
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ empty(X0)
| ~ relation(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_5622,c_6950]) ).
tcf(c_14856,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) )
| ( relation_image(X0,relation_image(X1,sK1)) = relation_image(sK1,sK1) )
| ~ relation(sK1)
| ~ empty(sK0)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_9876,c_6950]) ).
tcf(c_14857,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ( relation_image(X0,relation_image(X1,sK1)) = relation_image(sK1,sK1) )
| ~ relation(sK1)
| ~ empty(sK0)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_5909,c_6950]) ).
tcf(c_14858,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X1,relation_image(X2,sK1)) = relation_image(relation_image(X0,sK1),sK1) )
| ~ empty(sK0)
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_image(X0,sK1)) ),
inference(superposition,[status(thm)],[c_6199,c_6950]) ).
tcf(c_14859,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X1,relation_image(X2,sK1)) = relation_image(sK7(powerset(X0)),sK1) )
| ~ empty(sK0)
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ empty(X0)
| ~ relation(sK7(powerset(X0))) ),
inference(superposition,[status(thm)],[c_6880,c_6950]) ).
tcf(c_14860,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK7(sK6(powerset(X0))),sK1) = relation_image(X1,relation_image(X2,sK1)) )
| ~ empty(sK0)
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ empty(X0)
| ~ relation(sK7(sK6(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_10682,c_6950]) ).
tcf(c_14861,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X0,relation_image(X1,sK1)) = relation_image(empty_set,sK1) )
| ~ empty(sK0)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14854,c_82]) ).
tcf(c_14868,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X0,relation_image(X1,sK1)) = relation_image(sK14,sK1) )
| ~ empty(sK0)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14853,c_96]) ).
tcf(c_14875,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X0,relation_image(X1,sK1)) = relation_image(identity_relation(X2),sK1) )
| ~ empty(sK0)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14852,c_63]) ).
tcf(c_15050,plain,
! [X0: $i] :
( in(sK7(sK1),relation_image(identity_relation(sK0),X0))
| ( identity_relation(sK7(powerset(sK1))) = empty_set )
| ~ function(identity_relation(sK0))
| ~ relation(identity_relation(sK0))
| ~ in(sK7(sK1),X0)
| ~ in(sK7(sK1),relation_dom(identity_relation(sK0))) ),
inference(superposition,[status(thm)],[c_9089,c_57]) ).
tcf(c_15051,plain,
! [X0: $i] :
( in(sK7(sK1),relation_image(identity_relation(sK0),X0))
| ( identity_relation(sK7(powerset(sK1))) = empty_set )
| ~ in(sK7(sK1),X0)
| ~ in(sK7(sK1),relation_dom(identity_relation(sK0))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_15050,c_62,c_63]) ).
tcf(c_15093,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK7(sK6(sK6(powerset(X0)))) = relation_image(X1,X2) )
| ( apply(X1,sK3(X1,X2,sK7(sK6(sK6(powerset(X0)))))) = sK2(X1,X2,sK7(sK6(sK6(powerset(X0))))) )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_56,c_14089]) ).
tcf(c_15094,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(X1,X2,sK7(sK6(sK6(powerset(X0))))),relation_dom(X1))
| ( sK7(sK6(sK6(powerset(X0)))) = relation_image(X1,X2) )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_54,c_14089]) ).
tcf(c_15095,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(X1,X2,sK7(sK6(sK6(powerset(X0))))),X2)
| ( sK7(sK6(sK6(powerset(X0)))) = relation_image(X1,X2) )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_55,c_14089]) ).
tcf(c_15096,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,sK7(sK6(sK6(powerset(X0)))),X2),X2)
| ( relation_image(X1,sK7(sK6(sK6(powerset(X0))))) = X2 )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_55,c_14089]) ).
tcf(c_15097,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ function(X1)
| ~ relation(X1)
| ~ empty(X2)
| ~ in(X0,relation_image(X1,sK7(sK6(sK6(powerset(X2)))))) ),
inference(superposition,[status(thm)],[c_59,c_14089]) ).
tcf(c_15099,plain,
! [X0: $i,X1: $i] :
( in(sK3(X1,sK1,sK7(sK6(sK6(powerset(X0))))),sK0)
| ( sK7(sK6(sK6(powerset(X0)))) = relation_image(X1,sK1) )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11821,c_14089]) ).
tcf(c_15100,plain,
! [X0: $i,X1: $i] :
( element(sK3(X1,sK1,sK7(sK6(sK6(powerset(X0))))),sK0)
| ( sK7(sK6(sK6(powerset(X0)))) = relation_image(X1,sK1) )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6475,c_14089]) ).
tcf(c_15101,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(sK6(powerset(X0)))) = relation_image(X1,sK1) )
| ~ empty(sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6476,c_14089]) ).
tcf(c_15102,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X1,relation_image(X2,sK1)) = sK7(sK6(sK6(powerset(X0)))) )
| ~ empty(sK0)
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6479,c_14089]) ).
tcf(c_15103,plain,
! [X0: $i,X1: $i] :
( in(sK2(X1,sK7(sK6(sK6(powerset(X0)))),sK1),sK0)
| ( relation_image(X1,sK7(sK6(sK6(powerset(X0))))) = sK1 )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12513,c_14089]) ).
tcf(c_15104,plain,
! [X0: $i,X1: $i] :
( element(sK2(X1,sK7(sK6(sK6(powerset(X0)))),sK1),sK0)
| ( relation_image(X1,sK7(sK6(sK6(powerset(X0))))) = sK1 )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6486,c_14089]) ).
tcf(c_15105,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X1,sK7(sK6(sK6(powerset(X0))))) = sK1 )
| ~ empty(sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6487,c_14089]) ).
tcf(c_15106,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X1,sK7(sK6(sK6(powerset(X0))))) = relation_image(X2,sK1) )
| ~ empty(sK0)
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6490,c_14089]) ).
tcf(c_15107,plain,
! [X0: $i] :
( empty(sK7(sK6(sK6(powerset(X0)))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9814,c_14089]) ).
tcf(c_15379,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X0,X1,sK7(sK6(sK6(powerset(X2))))),X2)
| ( sK7(sK6(sK6(powerset(X2)))) = relation_image(X0,X1) )
| ( apply(X0,sK3(X0,X1,sK7(sK6(sK6(powerset(X2)))))) = sK2(X0,X1,sK7(sK6(sK6(powerset(X2))))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_56,c_14092]) ).
tcf(c_15380,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X0,X2,sK7(sK6(sK6(powerset(X1))))),X1)
| in(sK3(X0,X2,sK7(sK6(sK6(powerset(X1))))),relation_dom(X0))
| ( sK7(sK6(sK6(powerset(X1)))) = relation_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_54,c_14092]) ).
tcf(c_15381,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(X0,X2,sK7(sK6(sK6(powerset(X1))))),X2)
| element(sK2(X0,X2,sK7(sK6(sK6(powerset(X1))))),X1)
| ( sK7(sK6(sK6(powerset(X1)))) = relation_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_55,c_14092]) ).
tcf(c_15382,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,sK7(sK6(sK6(powerset(X1)))),X2),X2)
| element(sK3(X0,sK7(sK6(sK6(powerset(X1)))),X2),X1)
| ( relation_image(X0,sK7(sK6(sK6(powerset(X1))))) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_55,c_14092]) ).
tcf(c_15383,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK4(X1,sK7(sK6(sK6(powerset(X2)))),X0),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,sK7(sK6(sK6(powerset(X2)))))) ),
inference(superposition,[status(thm)],[c_59,c_14092]) ).
tcf(c_15384,plain,
! [X0: $i] :
( empty(sK7(sK6(sK6(powerset(X0)))))
| element(sK7(sK7(sK6(sK6(powerset(X0))))),X0) ),
inference(superposition,[status(thm)],[c_5703,c_14092]) ).
tcf(c_15385,plain,
! [X0: $i,X1: $i] :
( in(sK3(X0,sK1,sK7(sK6(sK6(powerset(X1))))),sK0)
| element(sK2(X0,sK1,sK7(sK6(sK6(powerset(X1))))),X1)
| ( sK7(sK6(sK6(powerset(X1)))) = relation_image(X0,sK1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_11821,c_14092]) ).
tcf(c_15386,plain,
! [X0: $i,X1: $i] :
( element(sK3(X0,sK1,sK7(sK6(sK6(powerset(X1))))),sK0)
| element(sK2(X0,sK1,sK7(sK6(sK6(powerset(X1))))),X1)
| ( sK7(sK6(sK6(powerset(X1)))) = relation_image(X0,sK1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6475,c_14092]) ).
tcf(c_15387,plain,
! [X0: $i,X1: $i] :
( element(sK2(X0,sK1,sK7(sK6(sK6(powerset(X1))))),X1)
| ( sK7(sK6(sK6(powerset(X1)))) = relation_image(X0,sK1) )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6476,c_14092]) ).
tcf(c_15388,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X0,relation_image(X1,sK1),sK7(sK6(sK6(powerset(X2))))),X2)
| ( relation_image(X0,relation_image(X1,sK1)) = sK7(sK6(sK6(powerset(X2)))) )
| ~ empty(sK0)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6479,c_14092]) ).
tcf(c_15389,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,sK7(sK6(sK6(powerset(X1)))),sK1),sK0)
| element(sK3(X0,sK7(sK6(sK6(powerset(X1)))),sK1),X1)
| ( relation_image(X0,sK7(sK6(sK6(powerset(X1))))) = sK1 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_12513,c_14092]) ).
tcf(c_15390,plain,
! [X0: $i,X1: $i] :
( element(sK2(X0,sK7(sK6(sK6(powerset(X1)))),sK1),sK0)
| element(sK3(X0,sK7(sK6(sK6(powerset(X1)))),sK1),X1)
| ( relation_image(X0,sK7(sK6(sK6(powerset(X1))))) = sK1 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6486,c_14092]) ).
tcf(c_15391,plain,
! [X0: $i,X1: $i] :
( element(sK3(X0,sK7(sK6(sK6(powerset(X1)))),sK1),X1)
| ( relation_image(X0,sK7(sK6(sK6(powerset(X1))))) = sK1 )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6487,c_14092]) ).
tcf(c_15392,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK3(X0,sK7(sK6(sK6(powerset(X2)))),relation_image(X1,sK1)),X2)
| ( relation_image(X0,sK7(sK6(sK6(powerset(X2))))) = relation_image(X1,sK1) )
| ~ empty(sK0)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6490,c_14092]) ).
tcf(c_15393,plain,
! [X0: $i] :
( empty(sK7(sK6(sK6(powerset(X0)))))
| element(sK7(sK6(sK7(sK6(sK6(powerset(X0)))))),X0) ),
inference(superposition,[status(thm)],[c_9814,c_14092]) ).
tcf(c_15394,plain,
! [X0: $i] :
( empty(sK7(sK6(sK6(powerset(X0)))))
| element(sK7(sK6(sK6(sK7(sK6(sK6(powerset(X0))))))),X0) ),
inference(superposition,[status(thm)],[c_14086,c_14092]) ).
tcf(c_15601,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(identity_relation(sK7(sK6(sK6(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_9748]) ).
tcf(c_15602,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(sK7(sK6(sK6(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_9682]) ).
tcf(c_15603,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(relation_dom(sK7(sK6(sK6(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_11340]) ).
tcf(c_15604,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(relation_dom(sK7(sK6(sK6(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_9747]) ).
tcf(c_15605,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(relation_dom(sK7(sK6(sK6(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_9681]) ).
tcf(c_15606,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(identity_relation(sK7(sK6(sK6(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_9115]) ).
tcf(c_15607,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(identity_relation(sK7(sK6(sK6(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_9088]) ).
tcf(c_15608,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(relation_dom(sK7(sK6(sK6(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_9114]) ).
tcf(c_15609,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(relation_dom(sK7(sK6(sK6(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_9087]) ).
tcf(c_15610,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_8009]) ).
tcf(c_15611,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_7966]) ).
tcf(c_15612,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_7938]) ).
tcf(c_15613,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(relation_dom(sK7(sK6(sK6(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_9017]) ).
tcf(c_15614,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(relation_dom(sK7(sK6(sK6(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_8992]) ).
tcf(c_15615,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(relation_dom(sK7(sK6(sK6(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_8957]) ).
tcf(c_15616,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK7(sK6(sK6(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_8561]) ).
tcf(c_15617,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_6875]) ).
tcf(c_15618,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(sK7(sK6(sK6(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_10681]) ).
tcf(c_15619,plain,
! [X0: $i] :
( ( relation_image(sK7(sK6(powerset(sK7(sK6(sK6(powerset(X0))))))),sK1) = sK1 )
| ~ empty(sK0)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_11188]) ).
tcf(c_15620,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X1,sK7(sK6(powerset(sK7(sK6(sK6(powerset(X0)))))))) = sK1 )
| ~ empty(sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_10420]) ).
tcf(c_15621,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(powerset(sK7(sK6(sK6(powerset(X0))))))) = relation_image(X1,sK1) )
| ~ empty(sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_10418]) ).
tcf(c_15622,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(sK7(sK6(sK6(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_8006]) ).
tcf(c_15623,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(sK7(sK6(sK6(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_7963]) ).
tcf(c_15624,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK7(sK6(sK6(powerset(X0))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_5794]) ).
tcf(c_15625,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(sK6(sK6(powerset(X0))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_5793]) ).
tcf(c_15626,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_6878]) ).
tcf(c_15627,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(sK7(sK6(sK6(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_6876]) ).
tcf(c_15628,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(sK7(sK6(sK6(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_8005]) ).
tcf(c_15629,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(sK7(sK6(sK6(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_7962]) ).
tcf(c_15630,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(sK7(sK6(sK6(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_7934]) ).
tcf(c_15631,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X1,sK7(powerset(sK7(sK6(sK6(powerset(X0))))))) = sK1 )
| ~ empty(sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_7111]) ).
tcf(c_15632,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(sK7(sK6(sK6(powerset(X0)))))) = relation_image(X1,sK1) )
| ~ empty(sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_6946]) ).
tcf(c_15633,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK7(sK6(sK6(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_6133]) ).
tcf(c_15634,plain,
! [X0: $i] :
( ( relation_image(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))),sK1) = sK1 )
| ~ empty(sK0)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_8316]) ).
tcf(c_15637,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK7(sK6(sK6(powerset(X0))))),sK1) = sK1 )
| ~ empty(sK0)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_8131]) ).
tcf(c_15638,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(sK6(sK6(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_6879]) ).
tcf(c_15639,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(sK6(sK6(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_6106]) ).
tcf(c_15640,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(sK6(sK6(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_6105]) ).
tcf(c_15641,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(sK6(sK6(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_5747]) ).
tcf(c_15642,plain,
! [X0: $i] :
( ( identity_relation(sK7(sK6(sK6(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_5776]) ).
tcf(c_15643,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(sK6(powerset(X0)))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_51]) ).
tcf(c_15644,plain,
! [X0: $i] :
( ( relation_dom(sK7(sK6(sK6(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_5663]) ).
tcf(c_15645,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(powerset(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_52]) ).
tcf(c_15646,plain,
! [X0: $i] :
( function(sK7(sK6(sK6(powerset(X0)))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_98]) ).
tcf(c_15647,plain,
! [X0: $i] :
( relation(sK7(sK6(sK6(powerset(X0)))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_80]) ).
tcf(c_15975,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK7(sK6(sK6(powerset(X0)))),sK1) = relation_image(X1,relation_image(X2,sK1)) )
| ~ empty(sK0)
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ empty(X0)
| ~ relation(sK7(sK6(sK6(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_15646,c_6950]) ).
tcf(c_15976,plain,
! [X0: $i,X1: $i] :
( ( relation_image(sK7(sK6(sK6(powerset(X0)))),X1) = sK1 )
| ( apply(identity_relation(relation_dom(sK7(sK6(sK6(powerset(X0)))))),sK3(sK7(sK6(sK6(powerset(X0)))),X1,sK1)) = sK3(sK7(sK6(sK6(powerset(X0)))),X1,sK1) )
| ~ empty(sK0)
| ~ empty(X0)
| ~ relation(sK7(sK6(sK6(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_15646,c_7214]) ).
tcf(c_15977,plain,
! [X0: $i,X1: $i] :
( ( relation_image(sK7(sK6(sK6(powerset(X0)))),X1) = sK1 )
| ( apply(identity_relation(X1),sK3(sK7(sK6(sK6(powerset(X0)))),X1,sK1)) = sK3(sK7(sK6(sK6(powerset(X0)))),X1,sK1) )
| ~ empty(sK0)
| ~ empty(X0)
| ~ relation(sK7(sK6(sK6(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_15646,c_7105]) ).
tcf(c_15978,plain,
! [X0: $i,X1: $i] :
( ( relation_image(sK7(sK6(sK6(powerset(X0)))),sK1) = X1 )
| ( apply(identity_relation(X1),sK2(sK7(sK6(sK6(powerset(X0)))),sK1,X1)) = sK2(sK7(sK6(sK6(powerset(X0)))),sK1,X1) )
| ~ empty(sK0)
| ~ empty(X0)
| ~ relation(sK7(sK6(sK6(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_15646,c_6940]) ).
tcf(c_15979,plain,
! [X0: $i,X1: $i] :
( ( relation_image(sK7(sK6(sK6(powerset(X0)))),relation_image(X1,sK1)) = sK1 )
| ~ empty(sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0)
| ~ relation(sK7(sK6(sK6(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_15646,c_7114]) ).
tcf(c_15980,plain,
! [X0: $i,X1: $i] :
( ( relation_image(sK7(sK6(sK6(powerset(X0)))),sK1) = relation_image(X1,sK1) )
| ~ empty(sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0)
| ~ relation(sK7(sK6(sK6(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_15646,c_6949]) ).
tcf(c_15981,plain,
! [X0: $i] :
( ( relation_image(relation_image(sK7(sK6(sK6(powerset(X0)))),sK1),sK1) = sK1 )
| ~ empty(sK0)
| ~ empty(X0)
| ~ relation(sK7(sK6(sK6(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_15646,c_9208]) ).
tcf(c_15982,plain,
! [X0: $i,X1: $i] :
( ( relation_image(sK7(sK6(sK6(powerset(X0)))),X1) = sK1 )
| ( apply(sK7(sK6(sK6(powerset(X0)))),sK3(sK7(sK6(sK6(powerset(X0)))),X1,sK1)) = sK2(sK7(sK6(sK6(powerset(X0)))),X1,sK1) )
| ~ empty(sK0)
| ~ empty(X0)
| ~ relation(sK7(sK6(sK6(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_15646,c_7707]) ).
tcf(c_15983,plain,
! [X0: $i] :
( ( relation_image(sK7(sK6(sK6(powerset(X0)))),sK1) = sK1 )
| ~ empty(sK0)
| ~ empty(X0)
| ~ relation(sK7(sK6(sK6(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_15646,c_6945]) ).
tcf(c_15984,plain,
! [X0: $i] :
( ( relation_image(sK7(sK6(sK6(powerset(X0)))),sK1) = empty_set )
| ~ empty(sK0)
| ~ empty(X0)
| ~ relation(sK7(sK6(sK6(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_15646,c_6198]) ).
tcf(c_16075,plain,
( empty(sK7(powerset(empty_set)))
| element(sK7(sK6(empty_set)),empty_set) ),
inference(superposition,[status(thm)],[c_8004,c_10355]) ).
tcf(c_16076,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| empty(sK7(powerset(powerset(X1))))
| ~ in(X0,sK7(sK6(sK7(powerset(powerset(X1)))))) ),
inference(superposition,[status(thm)],[c_10355,c_65]) ).
tcf(c_16077,plain,
! [X0: $i,X1: $i] :
( empty(sK7(powerset(powerset(X1))))
| ~ empty(X1)
| ~ in(X0,sK7(sK6(sK7(powerset(powerset(X1)))))) ),
inference(superposition,[status(thm)],[c_10355,c_64]) ).
tcf(c_16078,plain,
! [X0: $i] :
( empty(X0)
| empty(sK7(powerset(X0)))
| in(sK7(sK6(sK7(powerset(X0)))),X0) ),
inference(superposition,[status(thm)],[c_10355,c_71]) ).
tcf(c_16079,plain,
( empty(empty_set)
| element(sK7(sK6(empty_set)),empty_set) ),
inference(light_normalisation,[status(thm)],[c_16075,c_8004]) ).
tcf(c_16101,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(sK6(powerset(X1)))) = relation_image(X0,sK1) )
| ( apply(identity_relation(X1),sK7(X1)) = sK7(X1) )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_5807,c_15101]) ).
tcf(c_16102,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(powerset(empty_set)))) = relation_image(X0,sK1) )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_83,c_15101]) ).
tcf(c_16103,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(sK6(powerset(relation_dom(X0))))) = relation_image(X1,sK1) )
| ~ empty(sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_15101]) ).
tcf(c_16104,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(sK6(powerset(identity_relation(X0))))) = relation_image(X1,sK1) )
| ~ empty(sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_15101]) ).
tcf(c_16105,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(powerset(sK1)))) = relation_image(X0,sK1) )
| ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_9449,c_15101]) ).
tcf(c_16106,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(powerset(sK1)))) = relation_image(X0,sK1) )
| ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_5890,c_15101]) ).
tcf(c_16107,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(sK6(powerset(relation_image(X0,sK1))))) = relation_image(X1,sK1) )
| ~ empty(sK0)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6158,c_15101]) ).
tcf(c_16108,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(sK6(powerset(sK7(powerset(X0)))))) = relation_image(X1,sK1) )
| ~ empty(sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_15101]) ).
tcf(c_16109,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(sK6(powerset(sK7(sK6(powerset(X0))))))) = relation_image(X1,sK1) )
| ~ empty(sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_15101]) ).
tcf(c_16110,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(sK6(powerset(sK7(sK6(sK6(powerset(X0)))))))) = relation_image(X1,sK1) )
| ~ empty(sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_15101]) ).
tcf(c_16228,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X1),sK7(X1)) = sK7(X1) )
| ( relation_image(X0,sK7(sK6(sK6(powerset(X1))))) = sK1 )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_5807,c_15105]) ).
tcf(c_16229,plain,
! [X0: $i] :
( ( relation_image(X0,sK7(sK6(sK6(powerset(empty_set))))) = sK1 )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_83,c_15105]) ).
tcf(c_16230,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X1,sK7(sK6(sK6(powerset(relation_dom(X0)))))) = sK1 )
| ~ empty(sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_15105]) ).
tcf(c_16231,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X1,sK7(sK6(sK6(powerset(identity_relation(X0)))))) = sK1 )
| ~ empty(sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_15105]) ).
tcf(c_16232,plain,
! [X0: $i] :
( ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) )
| ( relation_image(X0,sK7(sK6(sK6(powerset(sK1))))) = sK1 )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_9449,c_15105]) ).
tcf(c_16233,plain,
! [X0: $i] :
( ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ( relation_image(X0,sK7(sK6(sK6(powerset(sK1))))) = sK1 )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_5890,c_15105]) ).
tcf(c_16234,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X1,sK7(sK6(sK6(powerset(relation_image(X0,sK1)))))) = sK1 )
| ~ empty(sK0)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6158,c_15105]) ).
tcf(c_16235,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X1,sK7(sK6(sK6(powerset(sK7(powerset(X0))))))) = sK1 )
| ~ empty(sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_15105]) ).
tcf(c_16236,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X1,sK7(sK6(sK6(powerset(sK7(sK6(powerset(X0)))))))) = sK1 )
| ~ empty(sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_15105]) ).
tcf(c_16237,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X1,sK7(sK6(sK6(powerset(sK7(sK6(sK6(powerset(X0))))))))) = sK1 )
| ~ empty(sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_15105]) ).
tcf(c_16314,plain,
! [X0: $i] :
( ( relation_image(sK7(sK6(sK6(powerset(X0)))),sK1) = sK1 )
| ~ empty(sK0)
| ~ empty(X0) ),
inference(global_subsumption_just,[status(thm)],[c_15983,c_15647,c_15983]) ).
tcf(c_16323,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( relation_image(sK7(sK6(sK6(powerset(X0)))),sK1) = sK1 )
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_5807,c_16314]) ).
tcf(c_16324,plain,
( ( relation_image(sK7(sK6(sK6(powerset(empty_set)))),sK1) = sK1 )
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_83,c_16314]) ).
tcf(c_16325,plain,
! [X0: $i] :
( ( relation_image(sK7(sK6(sK6(powerset(relation_dom(X0))))),sK1) = sK1 )
| ~ empty(sK0)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_16314]) ).
tcf(c_16326,plain,
! [X0: $i] :
( ( relation_image(sK7(sK6(sK6(powerset(identity_relation(X0))))),sK1) = sK1 )
| ~ empty(sK0)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_16314]) ).
tcf(c_16327,plain,
( ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) )
| ( relation_image(sK7(sK6(sK6(powerset(sK1)))),sK1) = sK1 )
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_9449,c_16314]) ).
tcf(c_16328,plain,
( ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ( relation_image(sK7(sK6(sK6(powerset(sK1)))),sK1) = sK1 )
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_5890,c_16314]) ).
tcf(c_16329,plain,
! [X0: $i] :
( ( relation_image(sK7(sK6(sK6(powerset(relation_image(X0,sK1))))),sK1) = sK1 )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6158,c_16314]) ).
tcf(c_16330,plain,
! [X0: $i] :
( ( relation_image(sK7(sK6(sK6(powerset(sK7(powerset(X0)))))),sK1) = sK1 )
| ~ empty(sK0)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_16314]) ).
tcf(c_16331,plain,
! [X0: $i] :
( ( relation_image(sK7(sK6(sK6(powerset(sK7(sK6(powerset(X0))))))),sK1) = sK1 )
| ~ empty(sK0)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_16314]) ).
tcf(c_16332,plain,
! [X0: $i] :
( ( relation_image(sK7(sK6(sK6(powerset(sK7(sK6(sK6(powerset(X0)))))))),sK1) = sK1 )
| ~ empty(sK0)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_16314]) ).
tcf(c_16471,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,X2)
| ( sK7(sK6(sK6(powerset(powerset(X2))))) = relation_image(X1,sK1) )
| ~ empty(sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,sK2(X1,sK1,sK7(sK6(sK6(powerset(powerset(X2))))))) ),
inference(superposition,[status(thm)],[c_15387,c_65]) ).
tcf(c_16472,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK7(sK6(sK6(powerset(powerset(X2))))) = relation_image(X1,sK1) )
| ~ empty(sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X2)
| ~ in(X0,sK2(X1,sK1,sK7(sK6(sK6(powerset(powerset(X2))))))) ),
inference(superposition,[status(thm)],[c_15387,c_64]) ).
tcf(c_16473,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| in(sK2(X0,sK1,sK7(sK6(sK6(powerset(X1))))),X1)
| ( sK7(sK6(sK6(powerset(X1)))) = relation_image(X0,sK1) )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_15387,c_71]) ).
tcf(c_16504,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,X2)
| ( relation_image(X1,sK7(sK6(sK6(powerset(powerset(X2)))))) = sK1 )
| ~ empty(sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,sK3(X1,sK7(sK6(sK6(powerset(powerset(X2))))),sK1)) ),
inference(superposition,[status(thm)],[c_15391,c_65]) ).
tcf(c_16505,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X1,sK7(sK6(sK6(powerset(powerset(X2)))))) = sK1 )
| ~ empty(sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X2)
| ~ in(X0,sK3(X1,sK7(sK6(sK6(powerset(powerset(X2))))),sK1)) ),
inference(superposition,[status(thm)],[c_15391,c_64]) ).
tcf(c_16506,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| in(sK3(X0,sK7(sK6(sK6(powerset(X1)))),sK1),X1)
| ( relation_image(X0,sK7(sK6(sK6(powerset(X1))))) = sK1 )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_15391,c_71]) ).
tcf(c_16543,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( relation_image(X0,relation_image(X1,relation_image(X2,sK1))) = sK1 )
| ~ empty(sK0)
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_9431,c_7115]) ).
tcf(c_16544,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(identity_relation(X0),relation_image(X1,relation_image(X2,sK1))) = sK1 )
| ~ empty(sK0)
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_62,c_7115]) ).
tcf(c_16545,plain,
! [X0: $i,X1: $i] :
( ( relation_image(sK14,relation_image(X0,relation_image(X1,sK1))) = sK1 )
| ~ relation(sK14)
| ~ empty(sK0)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_97,c_7115]) ).
tcf(c_16546,plain,
! [X0: $i,X1: $i] :
( ( relation_image(empty_set,relation_image(X0,relation_image(X1,sK1))) = sK1 )
| ~ relation(empty_set)
| ~ empty(sK0)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_5610,c_7115]) ).
tcf(c_16547,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(relation_dom(X0),relation_image(X1,relation_image(X2,sK1))) = sK1 )
| ~ empty(sK0)
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ empty(X0)
| ~ relation(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_5622,c_7115]) ).
tcf(c_16548,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) )
| ( relation_image(sK1,relation_image(X0,relation_image(X1,sK1))) = sK1 )
| ~ relation(sK1)
| ~ empty(sK0)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_9876,c_7115]) ).
tcf(c_16549,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ( relation_image(sK1,relation_image(X0,relation_image(X1,sK1))) = sK1 )
| ~ relation(sK1)
| ~ empty(sK0)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_5909,c_7115]) ).
tcf(c_16550,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(relation_image(X0,sK1),relation_image(X1,relation_image(X2,sK1))) = sK1 )
| ~ empty(sK0)
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_image(X0,sK1)) ),
inference(superposition,[status(thm)],[c_6199,c_7115]) ).
tcf(c_16551,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK7(powerset(X0)),relation_image(X1,relation_image(X2,sK1))) = sK1 )
| ~ empty(sK0)
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ empty(X0)
| ~ relation(sK7(powerset(X0))) ),
inference(superposition,[status(thm)],[c_6880,c_7115]) ).
tcf(c_16552,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK7(sK6(powerset(X0))),relation_image(X1,relation_image(X2,sK1))) = sK1 )
| ~ empty(sK0)
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ empty(X0)
| ~ relation(sK7(sK6(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_10682,c_7115]) ).
tcf(c_16553,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK7(sK6(sK6(powerset(X0)))),relation_image(X1,relation_image(X2,sK1))) = sK1 )
| ~ empty(sK0)
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ empty(X0)
| ~ relation(sK7(sK6(sK6(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_15646,c_7115]) ).
tcf(c_16554,plain,
! [X0: $i,X1: $i] :
( ( relation_image(empty_set,relation_image(X0,relation_image(X1,sK1))) = sK1 )
| ~ empty(sK0)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16546,c_82]) ).
tcf(c_16561,plain,
! [X0: $i,X1: $i] :
( ( relation_image(sK14,relation_image(X0,relation_image(X1,sK1))) = sK1 )
| ~ empty(sK0)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16545,c_96]) ).
tcf(c_16568,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(identity_relation(X2),relation_image(X0,relation_image(X1,sK1))) = sK1 )
| ~ empty(sK0)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16544,c_63]) ).
tcf(c_16743,plain,
! [X0: $i] :
( in(sK7(sK1),relation_image(identity_relation(sK0),X0))
| ( relation_dom(sK7(powerset(sK1))) = empty_set )
| ~ function(identity_relation(sK0))
| ~ relation(identity_relation(sK0))
| ~ in(sK7(sK1),X0)
| ~ in(sK7(sK1),relation_dom(identity_relation(sK0))) ),
inference(superposition,[status(thm)],[c_9116,c_57]) ).
tcf(c_16744,plain,
! [X0: $i] :
( in(sK7(sK1),relation_image(identity_relation(sK0),X0))
| ( relation_dom(sK7(powerset(sK1))) = empty_set )
| ~ in(sK7(sK1),X0)
| ~ in(sK7(sK1),relation_dom(identity_relation(sK0))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16743,c_62,c_63]) ).
tcf(c_16754,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(powerset(X0)))) = empty_set )
| ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) ) ),
inference(superposition,[status(thm)],[c_5807,c_15645]) ).
tcf(c_16755,plain,
sK7(sK6(sK6(powerset(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_15645]) ).
tcf(c_16756,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(powerset(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_15645]) ).
tcf(c_16757,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(powerset(identity_relation(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_15645]) ).
tcf(c_16758,plain,
( ( sK7(sK6(sK6(powerset(sK1)))) = empty_set )
| ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) ) ),
inference(superposition,[status(thm)],[c_9449,c_15645]) ).
tcf(c_16759,plain,
( ( sK7(sK6(sK6(powerset(sK1)))) = empty_set )
| ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) ) ),
inference(superposition,[status(thm)],[c_5890,c_15645]) ).
tcf(c_16760,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(powerset(relation_image(X0,sK1))))) = empty_set )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6158,c_15645]) ).
tcf(c_16761,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(powerset(sK7(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_15645]) ).
tcf(c_16762,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(powerset(sK7(sK6(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_15645]) ).
tcf(c_16763,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(powerset(sK7(sK6(sK6(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_15645]) ).
tcf(c_16841,plain,
( empty(sK6(sK6(powerset(empty_set))))
| ~ in(sK6(sK6(powerset(empty_set))),empty_set) ),
inference(superposition,[status(thm)],[c_16755,c_5724]) ).
tcf(c_16842,plain,
( empty(sK6(sK6(powerset(empty_set))))
| in(empty_set,sK6(sK6(powerset(empty_set)))) ),
inference(superposition,[status(thm)],[c_16755,c_5703]) ).
tcf(c_16843,plain,
element(empty_set,sK6(sK6(powerset(empty_set)))),
inference(superposition,[status(thm)],[c_16755,c_73]) ).
tcf(c_16850,plain,
! [X0: $i] :
( element(sK2(X0,empty_set,sK1),sK0)
| ( relation_image(X0,sK7(sK6(sK6(powerset(empty_set))))) = sK1 )
| ~ empty(empty_set)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16755,c_15104]) ).
tcf(c_16851,plain,
! [X0: $i] :
( element(sK3(X0,sK1,empty_set),sK0)
| ( sK7(sK6(sK6(powerset(empty_set)))) = relation_image(X0,sK1) )
| ~ empty(empty_set)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16755,c_15100]) ).
tcf(c_16901,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(powerset(X0)))) = empty_set )
| ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) ) ),
inference(superposition,[status(thm)],[c_5806,c_15645]) ).
tcf(c_16902,plain,
! [X0: $i] :
( ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ( relation_image(sK7(sK6(sK6(powerset(X0)))),sK1) = sK1 )
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_5806,c_16314]) ).
tcf(c_16903,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(powerset(X1)),sK6(X1)) = sK6(X1) )
| ( relation_image(X0,sK7(sK6(sK6(powerset(X1))))) = sK1 )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_5806,c_15105]) ).
tcf(c_16904,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(sK6(powerset(X1)))) = relation_image(X0,sK1) )
| ( apply(identity_relation(powerset(X1)),sK6(X1)) = sK6(X1) )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_5806,c_15101]) ).
tcf(c_16905,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(identity_relation(X0)))) = empty_set )
| ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) ) ),
inference(superposition,[status(thm)],[c_5806,c_9748]) ).
tcf(c_16906,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(X0)))) = empty_set )
| ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) ) ),
inference(superposition,[status(thm)],[c_5806,c_9682]) ).
tcf(c_16907,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(relation_dom(X0)))) = empty_set )
| ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) ) ),
inference(superposition,[status(thm)],[c_5806,c_11340]) ).
tcf(c_16908,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(relation_dom(X0)))) = empty_set )
| ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) ) ),
inference(superposition,[status(thm)],[c_5806,c_9747]) ).
tcf(c_16909,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(relation_dom(X0)))) = empty_set )
| ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) ) ),
inference(superposition,[status(thm)],[c_5806,c_9681]) ).
tcf(c_16910,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(identity_relation(X0)))) = empty_set )
| ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) ) ),
inference(superposition,[status(thm)],[c_5806,c_9115]) ).
tcf(c_16911,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(identity_relation(X0)))) = empty_set )
| ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) ) ),
inference(superposition,[status(thm)],[c_5806,c_9088]) ).
tcf(c_16912,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(relation_dom(X0)))) = empty_set )
| ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) ) ),
inference(superposition,[status(thm)],[c_5806,c_9114]) ).
tcf(c_16913,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(relation_dom(X0)))) = empty_set )
| ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) ) ),
inference(superposition,[status(thm)],[c_5806,c_9087]) ).
tcf(c_16914,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(powerset(X0)))) = empty_set )
| ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) ) ),
inference(superposition,[status(thm)],[c_5806,c_8009]) ).
tcf(c_16915,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(powerset(X0)))) = empty_set )
| ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) ) ),
inference(superposition,[status(thm)],[c_5806,c_7966]) ).
tcf(c_16916,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(powerset(X0)))) = empty_set )
| ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) ) ),
inference(superposition,[status(thm)],[c_5806,c_7938]) ).
tcf(c_16917,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(relation_dom(X0)))) = empty_set )
| ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) ) ),
inference(superposition,[status(thm)],[c_5806,c_9017]) ).
tcf(c_16918,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(relation_dom(X0)))) = empty_set )
| ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) ) ),
inference(superposition,[status(thm)],[c_5806,c_8992]) ).
tcf(c_16919,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(relation_dom(X0)))) = empty_set )
| ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) ) ),
inference(superposition,[status(thm)],[c_5806,c_8957]) ).
tcf(c_16920,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(X0)))) = empty_set )
| ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) ) ),
inference(superposition,[status(thm)],[c_5806,c_8561]) ).
tcf(c_16921,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(powerset(X0)))) = empty_set )
| ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) ) ),
inference(superposition,[status(thm)],[c_5806,c_6875]) ).
tcf(c_16922,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(X0))) = empty_set )
| ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) ) ),
inference(superposition,[status(thm)],[c_5806,c_10681]) ).
tcf(c_16923,plain,
! [X0: $i] :
( ( relation_image(sK7(sK6(powerset(X0))),sK1) = sK1 )
| ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_5806,c_11188]) ).
tcf(c_16924,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(powerset(X1)),sK6(X1)) = sK6(X1) )
| ( relation_image(X0,sK7(sK6(powerset(X1)))) = sK1 )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_5806,c_10420]) ).
tcf(c_16925,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(powerset(X1))) = relation_image(X0,sK1) )
| ( apply(identity_relation(powerset(X1)),sK6(X1)) = sK6(X1) )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_5806,c_10418]) ).
tcf(c_16926,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(X0))) = empty_set )
| ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) ) ),
inference(superposition,[status(thm)],[c_5806,c_8006]) ).
tcf(c_16927,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(X0))) = empty_set )
| ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) ) ),
inference(superposition,[status(thm)],[c_5806,c_7963]) ).
tcf(c_16928,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(X1) = X0 )
| ( apply(identity_relation(powerset(X1)),sK6(X1)) = sK6(X1) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5806,c_5794]) ).
tcf(c_16929,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(X1) = X0 )
| ( apply(identity_relation(powerset(X1)),sK6(X1)) = sK6(X1) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5806,c_5793]) ).
tcf(c_16930,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(X0))) = empty_set )
| ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) ) ),
inference(superposition,[status(thm)],[c_5806,c_6878]) ).
tcf(c_16931,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(X0))) = empty_set )
| ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) ) ),
inference(superposition,[status(thm)],[c_5806,c_6876]) ).
tcf(c_16932,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(X0))) = empty_set )
| ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) ) ),
inference(superposition,[status(thm)],[c_5806,c_8005]) ).
tcf(c_16933,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(X0))) = empty_set )
| ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) ) ),
inference(superposition,[status(thm)],[c_5806,c_7962]) ).
tcf(c_16934,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(X0))) = empty_set )
| ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) ) ),
inference(superposition,[status(thm)],[c_5806,c_7934]) ).
tcf(c_16935,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X0,sK7(powerset(X1))) = sK1 )
| ( apply(identity_relation(powerset(X1)),sK6(X1)) = sK6(X1) )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_5806,c_7111]) ).
tcf(c_16936,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X0,sK1) = sK7(powerset(X1)) )
| ( apply(identity_relation(powerset(X1)),sK6(X1)) = sK6(X1) )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_5806,c_6946]) ).
tcf(c_16937,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(X0))) = empty_set )
| ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) ) ),
inference(superposition,[status(thm)],[c_5806,c_6133]) ).
tcf(c_16938,plain,
! [X0: $i] :
( ( relation_image(sK7(powerset(X0)),sK1) = sK1 )
| ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_5806,c_8316]) ).
tcf(c_16939,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X0,empty_set) = sK1 )
| ( apply(identity_relation(powerset(X1)),sK6(X1)) = sK6(X1) )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_5806,c_7113]) ).
tcf(c_16940,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X0,X1) = sK1 )
| ( apply(identity_relation(powerset(X1)),sK6(X1)) = sK6(X1) )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_5806,c_7107]) ).
tcf(c_16941,plain,
! [X0: $i] :
( ( relation_image(relation_dom(X0),sK1) = sK1 )
| ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_5806,c_8131]) ).
tcf(c_16942,plain,
! [X0: $i] :
( ( sK7(powerset(X0)) = empty_set )
| ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) ) ),
inference(superposition,[status(thm)],[c_5806,c_6879]) ).
tcf(c_16943,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(X0)) = empty_set )
| ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) ) ),
inference(superposition,[status(thm)],[c_5806,c_6106]) ).
tcf(c_16944,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(X0)) = empty_set )
| ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) ) ),
inference(superposition,[status(thm)],[c_5806,c_6105]) ).
tcf(c_16945,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(X0)) = empty_set )
| ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) ) ),
inference(superposition,[status(thm)],[c_5806,c_5747]) ).
tcf(c_16946,plain,
! [X0: $i] :
( ( identity_relation(X0) = empty_set )
| ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) ) ),
inference(superposition,[status(thm)],[c_5806,c_5776]) ).
tcf(c_16947,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( apply(identity_relation(powerset(X1)),sK6(X1)) = sK6(X1) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5806,c_51]) ).
tcf(c_16948,plain,
! [X0: $i] :
( ( relation_dom(X0) = empty_set )
| ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) ) ),
inference(superposition,[status(thm)],[c_5806,c_5663]) ).
tcf(c_16949,plain,
! [X0: $i] :
( ( X0 = empty_set )
| ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) ) ),
inference(superposition,[status(thm)],[c_5806,c_52]) ).
tcf(c_16950,plain,
! [X0: $i] :
( function(X0)
| ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) ) ),
inference(superposition,[status(thm)],[c_5806,c_98]) ).
tcf(c_16951,plain,
! [X0: $i] :
( relation(X0)
| ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) ) ),
inference(superposition,[status(thm)],[c_5806,c_80]) ).
tcf(c_16952,plain,
! [X0: $i] :
( empty(X0)
| ( apply(identity_relation(powerset(sK6(X0))),sK6(sK6(X0))) = sK6(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_5806,c_69]) ).
tcf(c_16953,plain,
! [X0: $i] : apply(identity_relation(powerset(powerset(X0))),sK6(powerset(X0))) = sK6(powerset(X0)),
inference(superposition,[status(thm)],[c_5806,c_70]) ).
tcf(c_16954,plain,
apply(identity_relation(powerset(sK8)),sK6(sK8)) = sK6(sK8),
inference(superposition,[status(thm)],[c_5806,c_74]) ).
tcf(c_16955,plain,
apply(identity_relation(powerset(sK9)),sK6(sK9)) = sK6(sK9),
inference(superposition,[status(thm)],[c_5806,c_75]) ).
tcf(c_16956,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X0,X1) = sK1 )
| ( apply(identity_relation(powerset(relation_dom(X0))),sK6(relation_dom(X0))) = sK6(relation_dom(X0)) )
| ~ empty(sK0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_5806,c_8681]) ).
tcf(c_16957,plain,
! [X0: $i] :
( empty(X0)
| ( apply(identity_relation(powerset(relation_dom(X0))),sK6(relation_dom(X0))) = sK6(relation_dom(X0)) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_5806,c_88]) ).
tcf(c_16958,plain,
! [X0: $i] :
( function(X0)
| ( apply(identity_relation(powerset(identity_relation(X0))),sK6(identity_relation(X0))) = sK6(identity_relation(X0)) ) ),
inference(superposition,[status(thm)],[c_5806,c_5644]) ).
tcf(c_16959,plain,
! [X0: $i] :
( relation(X0)
| ( apply(identity_relation(powerset(identity_relation(X0))),sK6(identity_relation(X0))) = sK6(identity_relation(X0)) ) ),
inference(superposition,[status(thm)],[c_5806,c_5633]) ).
tcf(c_16960,plain,
! [X0: $i] :
( empty(X0)
| ( apply(identity_relation(powerset(identity_relation(X0))),sK6(identity_relation(X0))) = sK6(identity_relation(X0)) ) ),
inference(superposition,[status(thm)],[c_5806,c_5621]) ).
tcf(c_16961,plain,
! [X0: $i] :
( ( relation_image(X0,sK1) = sK1 )
| ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0) ) ),
inference(superposition,[status(thm)],[c_5806,c_13094]) ).
tcf(c_16962,plain,
( ( relation_image(relation_image(empty_set,sK1),sK1) = sK1 )
| ( apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0) ) ),
inference(superposition,[status(thm)],[c_5806,c_9226]) ).
tcf(c_16963,plain,
( ( relation_image(relation_image(sK14,sK1),sK1) = sK1 )
| ( apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0) ) ),
inference(superposition,[status(thm)],[c_5806,c_9229]) ).
tcf(c_16964,plain,
! [X0: $i] :
( ( relation_image(empty_set,X0) = sK1 )
| ( apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0) ) ),
inference(superposition,[status(thm)],[c_5806,c_8694]) ).
tcf(c_16965,plain,
! [X0: $i] :
( ( relation_image(identity_relation(X0),sK1) = sK1 )
| ( apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0) ) ),
inference(superposition,[status(thm)],[c_5806,c_7058]) ).
tcf(c_16966,plain,
( ( relation_image(sK1,sK1) = sK1 )
| ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ( apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0) ) ),
inference(superposition,[status(thm)],[c_5806,c_8896]) ).
tcf(c_16967,plain,
! [X0: $i] :
( ( relation_image(identity_relation(X0),sK1) = empty_set )
| ( apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0) ) ),
inference(superposition,[status(thm)],[c_5806,c_6342]) ).
tcf(c_16968,plain,
( ( relation_image(sK14,sK1) = sK1 )
| ( apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0) ) ),
inference(superposition,[status(thm)],[c_5806,c_7055]) ).
tcf(c_16969,plain,
( ( relation_image(sK14,sK1) = empty_set )
| ( apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0) ) ),
inference(superposition,[status(thm)],[c_5806,c_6339]) ).
tcf(c_16970,plain,
( ( relation_image(empty_set,sK1) = empty_set )
| ( apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0) ) ),
inference(superposition,[status(thm)],[c_5806,c_6336]) ).
tcf(c_16971,plain,
( empty(sK1)
| ( apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0) ) ),
inference(superposition,[status(thm)],[c_5806,c_5857]) ).
tcf(c_16972,plain,
apply(identity_relation(powerset(sK6(powerset(empty_set)))),sK6(sK6(powerset(empty_set)))) = sK6(sK6(powerset(empty_set))),
inference(superposition,[status(thm)],[c_5806,c_11408]) ).
tcf(c_17421,plain,
! [X0: $i] :
( in(sK6(sK8),relation_image(identity_relation(powerset(sK8)),X0))
| ~ function(identity_relation(powerset(sK8)))
| ~ relation(identity_relation(powerset(sK8)))
| ~ in(sK6(sK8),X0)
| ~ in(sK6(sK8),relation_dom(identity_relation(powerset(sK8)))) ),
inference(superposition,[status(thm)],[c_16954,c_57]) ).
tcf(c_17422,plain,
! [X0: $i] :
( in(sK6(sK8),relation_image(identity_relation(powerset(sK8)),X0))
| ~ in(sK6(sK8),X0)
| ~ in(sK6(sK8),relation_dom(identity_relation(powerset(sK8)))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17421,c_62,c_63]) ).
tcf(c_17466,plain,
! [X0: $i] :
( in(sK6(sK9),relation_image(identity_relation(powerset(sK9)),X0))
| ~ function(identity_relation(powerset(sK9)))
| ~ relation(identity_relation(powerset(sK9)))
| ~ in(sK6(sK9),X0)
| ~ in(sK6(sK9),relation_dom(identity_relation(powerset(sK9)))) ),
inference(superposition,[status(thm)],[c_16955,c_57]) ).
tcf(c_17467,plain,
! [X0: $i] :
( in(sK6(sK9),relation_image(identity_relation(powerset(sK9)),X0))
| ~ in(sK6(sK9),X0)
| ~ in(sK6(sK9),relation_dom(identity_relation(powerset(sK9)))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17466,c_62,c_63]) ).
tcf(c_17476,plain,
! [X0: $i] :
( ( identity_relation(sK7(sK6(powerset(X0)))) = empty_set )
| ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) ) ),
inference(superposition,[status(thm)],[c_5806,c_10678]) ).
tcf(c_17477,plain,
! [X0: $i] :
( ( identity_relation(sK7(sK6(powerset(X0)))) = empty_set )
| ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) ) ),
inference(superposition,[status(thm)],[c_5807,c_10678]) ).
tcf(c_17478,plain,
identity_relation(sK7(sK6(powerset(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_10678]) ).
tcf(c_17479,plain,
! [X0: $i] :
( ( identity_relation(sK7(sK6(powerset(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_10678]) ).
tcf(c_17480,plain,
! [X0: $i] :
( ( identity_relation(sK7(sK6(powerset(identity_relation(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_10678]) ).
tcf(c_17481,plain,
( ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) )
| ( identity_relation(sK7(sK6(powerset(sK1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_9449,c_10678]) ).
tcf(c_17482,plain,
( ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ( identity_relation(sK7(sK6(powerset(sK1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5890,c_10678]) ).
tcf(c_17483,plain,
! [X0: $i] :
( ( identity_relation(sK7(sK6(powerset(relation_image(X0,sK1))))) = empty_set )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6158,c_10678]) ).
tcf(c_17484,plain,
! [X0: $i] :
( ( identity_relation(sK7(sK6(powerset(sK7(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_10678]) ).
tcf(c_17485,plain,
! [X0: $i] :
( ( identity_relation(sK7(sK6(powerset(sK7(sK6(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_10678]) ).
tcf(c_17486,plain,
! [X0: $i] :
( ( identity_relation(sK7(sK6(powerset(sK7(sK6(sK6(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_10678]) ).
tcf(c_17533,plain,
! [X0: $i] :
( ( relation_dom(sK7(sK6(powerset(X0)))) = empty_set )
| ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) ) ),
inference(superposition,[status(thm)],[c_5806,c_10680]) ).
tcf(c_17534,plain,
! [X0: $i] :
( ( relation_dom(sK7(sK6(powerset(X0)))) = empty_set )
| ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) ) ),
inference(superposition,[status(thm)],[c_5807,c_10680]) ).
tcf(c_17535,plain,
relation_dom(sK7(sK6(powerset(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_10680]) ).
tcf(c_17536,plain,
! [X0: $i] :
( ( relation_dom(sK7(sK6(powerset(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_10680]) ).
tcf(c_17537,plain,
! [X0: $i] :
( ( relation_dom(sK7(sK6(powerset(identity_relation(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_10680]) ).
tcf(c_17538,plain,
( ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) )
| ( relation_dom(sK7(sK6(powerset(sK1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_9449,c_10680]) ).
tcf(c_17539,plain,
( ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ( relation_dom(sK7(sK6(powerset(sK1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5890,c_10680]) ).
tcf(c_17540,plain,
! [X0: $i] :
( ( relation_dom(sK7(sK6(powerset(relation_image(X0,sK1))))) = empty_set )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6158,c_10680]) ).
tcf(c_17541,plain,
! [X0: $i] :
( ( relation_dom(sK7(sK6(powerset(sK7(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_10680]) ).
tcf(c_17542,plain,
! [X0: $i] :
( ( relation_dom(sK7(sK6(powerset(sK7(sK6(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_10680]) ).
tcf(c_17543,plain,
! [X0: $i] :
( ( relation_dom(sK7(sK6(powerset(sK7(sK6(sK6(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_10680]) ).
tcf(c_17623,plain,
( ( relation_dom(sK7(sK6(powerset(sK1)))) = empty_set )
| ( apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0) ) ),
inference(superposition,[status(thm)],[c_16971,c_10680]) ).
tcf(c_17624,plain,
( ( identity_relation(sK7(sK6(powerset(sK1)))) = empty_set )
| ( apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0) ) ),
inference(superposition,[status(thm)],[c_16971,c_10678]) ).
tcf(c_17625,plain,
( ( sK7(sK6(sK6(powerset(sK1)))) = empty_set )
| ( apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0) ) ),
inference(superposition,[status(thm)],[c_16971,c_15645]) ).
tcf(c_17626,plain,
( ( apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0) )
| ( relation_image(sK7(sK6(sK6(powerset(sK1)))),sK1) = sK1 )
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_16971,c_16314]) ).
tcf(c_17627,plain,
! [X0: $i] :
( ( apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0) )
| ( relation_image(X0,sK7(sK6(sK6(powerset(sK1))))) = sK1 )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16971,c_15105]) ).
tcf(c_17628,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(powerset(sK1)))) = relation_image(X0,sK1) )
| ( apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0) )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16971,c_15101]) ).
tcf(c_17629,plain,
( ( sK7(powerset(identity_relation(identity_relation(sK1)))) = empty_set )
| ( apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0) ) ),
inference(superposition,[status(thm)],[c_16971,c_9748]) ).
tcf(c_17630,plain,
( ( identity_relation(identity_relation(identity_relation(identity_relation(sK1)))) = empty_set )
| ( apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0) ) ),
inference(superposition,[status(thm)],[c_16971,c_9682]) ).
tcf(c_17631,plain,
( ( sK7(sK6(powerset(relation_dom(sK1)))) = empty_set )
| ( apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0) ) ),
inference(superposition,[status(thm)],[c_16971,c_11340]) ).
tcf(c_17632,plain,
( ( sK7(powerset(identity_relation(relation_dom(sK1)))) = empty_set )
| ( apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0) ) ),
inference(superposition,[status(thm)],[c_16971,c_9747]) ).
tcf(c_17633,plain,
( ( identity_relation(identity_relation(identity_relation(relation_dom(sK1)))) = empty_set )
| ( apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0) ) ),
inference(superposition,[status(thm)],[c_16971,c_9681]) ).
tcf(c_17634,plain,
( ( relation_dom(sK7(powerset(identity_relation(sK1)))) = empty_set )
| ( apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0) ) ),
inference(superposition,[status(thm)],[c_16971,c_9115]) ).
tcf(c_17635,plain,
( ( identity_relation(sK7(powerset(identity_relation(sK1)))) = empty_set )
| ( apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0) ) ),
inference(superposition,[status(thm)],[c_16971,c_9088]) ).
tcf(c_17636,plain,
( ( relation_dom(sK7(powerset(relation_dom(sK1)))) = empty_set )
| ( apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0) ) ),
inference(superposition,[status(thm)],[c_16971,c_9114]) ).
tcf(c_17637,plain,
( ( identity_relation(sK7(powerset(relation_dom(sK1)))) = empty_set )
| ( apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0) ) ),
inference(superposition,[status(thm)],[c_16971,c_9087]) ).
tcf(c_17638,plain,
( ( sK7(powerset(sK7(powerset(sK1)))) = empty_set )
| ( apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0) ) ),
inference(superposition,[status(thm)],[c_16971,c_8009]) ).
tcf(c_17639,plain,
( ( identity_relation(identity_relation(sK7(powerset(sK1)))) = empty_set )
| ( apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0) ) ),
inference(superposition,[status(thm)],[c_16971,c_7966]) ).
tcf(c_17640,plain,
( ( identity_relation(relation_dom(sK7(powerset(sK1)))) = empty_set )
| ( apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0) ) ),
inference(superposition,[status(thm)],[c_16971,c_7938]) ).
tcf(c_17641,plain,
( ( sK7(powerset(relation_dom(relation_dom(sK1)))) = empty_set )
| ( apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0) ) ),
inference(superposition,[status(thm)],[c_16971,c_9017]) ).
tcf(c_17642,plain,
( ( identity_relation(identity_relation(relation_dom(relation_dom(sK1)))) = empty_set )
| ( apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0) ) ),
inference(superposition,[status(thm)],[c_16971,c_8992]) ).
tcf(c_17643,plain,
( ( identity_relation(relation_dom(relation_dom(relation_dom(sK1)))) = empty_set )
| ( apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0) ) ),
inference(superposition,[status(thm)],[c_16971,c_8957]) ).
tcf(c_17644,plain,
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK1)))) = empty_set )
| ( apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0) ) ),
inference(superposition,[status(thm)],[c_16971,c_8561]) ).
tcf(c_17645,plain,
( ( relation_dom(relation_dom(sK7(powerset(sK1)))) = empty_set )
| ( apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0) ) ),
inference(superposition,[status(thm)],[c_16971,c_6875]) ).
tcf(c_17646,plain,
( ( sK7(sK6(powerset(sK1))) = empty_set )
| ( apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0) ) ),
inference(superposition,[status(thm)],[c_16971,c_10681]) ).
tcf(c_17647,plain,
( ( apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0) )
| ( relation_image(sK7(sK6(powerset(sK1))),sK1) = sK1 )
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_16971,c_11188]) ).
tcf(c_17648,plain,
! [X0: $i] :
( ( apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0) )
| ( relation_image(X0,sK7(sK6(powerset(sK1)))) = sK1 )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16971,c_10420]) ).
tcf(c_17649,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(sK1))) = relation_image(X0,sK1) )
| ( apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0) )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16971,c_10418]) ).
tcf(c_17650,plain,
( ( sK7(powerset(identity_relation(sK1))) = empty_set )
| ( apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0) ) ),
inference(superposition,[status(thm)],[c_16971,c_8006]) ).
tcf(c_17651,plain,
( ( identity_relation(identity_relation(identity_relation(sK1))) = empty_set )
| ( apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0) ) ),
inference(superposition,[status(thm)],[c_16971,c_7963]) ).
tcf(c_17652,plain,
! [X0: $i] :
( ( identity_relation(sK1) = X0 )
| ( apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16971,c_5794]) ).
tcf(c_17653,plain,
! [X0: $i] :
( ( relation_dom(sK1) = X0 )
| ( apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16971,c_5793]) ).
tcf(c_17654,plain,
( ( relation_dom(sK7(powerset(sK1))) = empty_set )
| ( apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0) ) ),
inference(superposition,[status(thm)],[c_16971,c_6878]) ).
tcf(c_17655,plain,
( ( identity_relation(sK7(powerset(sK1))) = empty_set )
| ( apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0) ) ),
inference(superposition,[status(thm)],[c_16971,c_6876]) ).
tcf(c_17656,plain,
( ( sK7(powerset(relation_dom(sK1))) = empty_set )
| ( apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0) ) ),
inference(superposition,[status(thm)],[c_16971,c_8005]) ).
tcf(c_17657,plain,
( ( identity_relation(identity_relation(relation_dom(sK1))) = empty_set )
| ( apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0) ) ),
inference(superposition,[status(thm)],[c_16971,c_7962]) ).
tcf(c_17658,plain,
( ( identity_relation(relation_dom(relation_dom(sK1))) = empty_set )
| ( apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0) ) ),
inference(superposition,[status(thm)],[c_16971,c_7934]) ).
tcf(c_17659,plain,
! [X0: $i] :
( ( relation_image(X0,sK7(powerset(sK1))) = sK1 )
| ( apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0) )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16971,c_7111]) ).
tcf(c_17660,plain,
! [X0: $i] :
( ( relation_image(X0,sK1) = sK7(powerset(sK1)) )
| ( apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0) )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16971,c_6946]) ).
tcf(c_17661,plain,
( ( relation_dom(relation_dom(relation_dom(sK1))) = empty_set )
| ( apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0) ) ),
inference(superposition,[status(thm)],[c_16971,c_6133]) ).
tcf(c_17662,plain,
( ( relation_image(sK7(powerset(sK1)),sK1) = sK1 )
| ( apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0) )
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_16971,c_8316]) ).
tcf(c_17663,plain,
! [X0: $i] :
( ( relation_image(X0,empty_set) = sK1 )
| ( apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0) )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16971,c_7113]) ).
tcf(c_17664,plain,
! [X0: $i] :
( ( relation_image(X0,sK1) = sK1 )
| ( apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0) )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16971,c_7107]) ).
tcf(c_17665,plain,
( ( relation_image(relation_dom(sK1),sK1) = sK1 )
| ( apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0) )
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_16971,c_8131]) ).
tcf(c_17666,plain,
( ( sK7(powerset(sK1)) = empty_set )
| ( apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0) ) ),
inference(superposition,[status(thm)],[c_16971,c_6879]) ).
tcf(c_17667,plain,
( ( identity_relation(identity_relation(sK1)) = empty_set )
| ( apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0) ) ),
inference(superposition,[status(thm)],[c_16971,c_6106]) ).
tcf(c_17668,plain,
( ( identity_relation(relation_dom(sK1)) = empty_set )
| ( apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0) ) ),
inference(superposition,[status(thm)],[c_16971,c_6105]) ).
tcf(c_17669,plain,
( ( relation_dom(relation_dom(sK1)) = empty_set )
| ( apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0) ) ),
inference(superposition,[status(thm)],[c_16971,c_5747]) ).
tcf(c_17670,plain,
( ( identity_relation(sK1) = empty_set )
| ( apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0) ) ),
inference(superposition,[status(thm)],[c_16971,c_5776]) ).
tcf(c_17671,plain,
! [X0: $i] :
( ( X0 = sK1 )
| ( apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16971,c_51]) ).
tcf(c_17672,plain,
( ( relation_dom(sK1) = empty_set )
| ( apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0) ) ),
inference(superposition,[status(thm)],[c_16971,c_5663]) ).
tcf(c_17673,plain,
( ( sK1 = empty_set )
| ( apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0) ) ),
inference(superposition,[status(thm)],[c_16971,c_52]) ).
tcf(c_17674,plain,
( function(sK1)
| ( apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0) ) ),
inference(superposition,[status(thm)],[c_16971,c_98]) ).
tcf(c_17675,plain,
( relation(sK1)
| ( apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0) ) ),
inference(superposition,[status(thm)],[c_16971,c_80]) ).
tcf(c_18176,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(identity_relation(X0),X2,relation_image(X1,sK1)),X0)
| ( relation_image(identity_relation(X0),X2) = relation_image(X1,sK1) )
| ~ empty(sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_121,c_6698]) ).
tcf(c_18177,plain,
! [X0: $i,X1: $i] :
( in(sK3(empty_set,X1,relation_image(X0,sK1)),empty_set)
| ( relation_image(X0,sK1) = relation_image(empty_set,X1) )
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_5746,c_6698]) ).
tcf(c_18178,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X0,X2) = relation_image(X1,sK1) )
| ( apply(identity_relation(relation_dom(X0)),sK3(X0,X2,relation_image(X1,sK1))) = sK3(X0,X2,relation_image(X1,sK1)) )
| ~ empty(sK0)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6698,c_151]) ).
tcf(c_18179,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X0,X1) = relation_image(X2,sK1) )
| ~ empty(sK0)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ in(relation_dom(X0),sK3(X0,X1,relation_image(X2,sK1))) ),
inference(superposition,[status(thm)],[c_6698,c_85]) ).
tcf(c_18180,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X0,X2) = relation_image(X1,sK1) )
| ~ empty(sK0)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_6698,c_84]) ).
tcf(c_18181,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK3(X0,X2,relation_image(X1,sK1)),relation_dom(X0))
| ( relation_image(X0,X2) = relation_image(X1,sK1) )
| ~ empty(sK0)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6698,c_72]) ).
tcf(c_18189,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X0,sK1) = relation_image(empty_set,X1) )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18177,c_8375,c_5610,c_82]) ).
tcf(c_18208,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(identity_relation(X1),X2,relation_image(X0,sK1)),X1)
| ( relation_image(identity_relation(X1),X2) = relation_image(X0,sK1) )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18176,c_62,c_63]) ).
tcf(c_18234,plain,
! [X0: $i,X1: $i] :
( empty(sK0)
| in(sK2(X0,X1,sK1),sK0)
| ( relation_image(X0,X1) = sK1 )
| ( apply(identity_relation(relation_dom(X0)),sK3(X0,X1,sK1)) = sK3(X0,X1,sK1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7594,c_71]) ).
tcf(c_18242,plain,
! [X0: $i,X1: $i] :
( ( relation_image(relation_dom(X0),X1) = sK1 )
| ( apply(relation_dom(X0),sK3(relation_dom(X0),X1,sK1)) = sK2(relation_dom(X0),X1,sK1) )
| ~ empty(sK0)
| ~ empty(X0) ),
inference(global_subsumption_just,[status(thm)],[c_8065,c_87,c_8065]) ).
tcf(c_18253,plain,
! [X0: $i,X1: $i] :
( ( relation_image(relation_dom(X0),X1) = sK1 )
| ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ( apply(relation_dom(X0),sK3(relation_dom(X0),X1,sK1)) = sK2(relation_dom(X0),X1,sK1) )
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_5806,c_18242]) ).
tcf(c_18254,plain,
! [X0: $i,X1: $i] :
( ( relation_image(relation_dom(X0),X1) = sK1 )
| ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( apply(relation_dom(X0),sK3(relation_dom(X0),X1,sK1)) = sK2(relation_dom(X0),X1,sK1) )
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_5807,c_18242]) ).
tcf(c_18255,plain,
! [X0: $i] :
( ( relation_image(relation_dom(empty_set),X0) = sK1 )
| ( apply(relation_dom(empty_set),sK3(relation_dom(empty_set),X0,sK1)) = sK2(relation_dom(empty_set),X0,sK1) )
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_83,c_18242]) ).
tcf(c_18256,plain,
! [X0: $i,X1: $i] :
( ( relation_image(relation_dom(relation_dom(X0)),X1) = sK1 )
| ( apply(relation_dom(relation_dom(X0)),sK3(relation_dom(relation_dom(X0)),X1,sK1)) = sK2(relation_dom(relation_dom(X0)),X1,sK1) )
| ~ empty(sK0)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_18242]) ).
tcf(c_18257,plain,
! [X0: $i,X1: $i] :
( ( relation_image(relation_dom(identity_relation(X0)),X1) = sK1 )
| ( apply(relation_dom(identity_relation(X0)),sK3(relation_dom(identity_relation(X0)),X1,sK1)) = sK2(relation_dom(identity_relation(X0)),X1,sK1) )
| ~ empty(sK0)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_18242]) ).
tcf(c_18258,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK1),X0) = sK1 )
| ( apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0) )
| ( apply(relation_dom(sK1),sK3(relation_dom(sK1),X0,sK1)) = sK2(relation_dom(sK1),X0,sK1) )
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_16971,c_18242]) ).
tcf(c_18259,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK1),X0) = sK1 )
| ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) )
| ( apply(relation_dom(sK1),sK3(relation_dom(sK1),X0,sK1)) = sK2(relation_dom(sK1),X0,sK1) )
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_9449,c_18242]) ).
tcf(c_18260,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK1),X0) = sK1 )
| ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ( apply(relation_dom(sK1),sK3(relation_dom(sK1),X0,sK1)) = sK2(relation_dom(sK1),X0,sK1) )
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_5890,c_18242]) ).
tcf(c_18261,plain,
! [X0: $i,X1: $i] :
( ( relation_image(relation_dom(relation_image(X0,sK1)),X1) = sK1 )
| ( apply(relation_dom(relation_image(X0,sK1)),sK3(relation_dom(relation_image(X0,sK1)),X1,sK1)) = sK2(relation_dom(relation_image(X0,sK1)),X1,sK1) )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6158,c_18242]) ).
tcf(c_18262,plain,
! [X0: $i,X1: $i] :
( ( relation_image(relation_dom(sK7(powerset(X0))),X1) = sK1 )
| ( apply(relation_dom(sK7(powerset(X0))),sK3(relation_dom(sK7(powerset(X0))),X1,sK1)) = sK2(relation_dom(sK7(powerset(X0))),X1,sK1) )
| ~ empty(sK0)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_18242]) ).
tcf(c_18263,plain,
! [X0: $i,X1: $i] :
( ( relation_image(relation_dom(sK7(sK6(powerset(X0)))),X1) = sK1 )
| ( apply(relation_dom(sK7(sK6(powerset(X0)))),sK3(relation_dom(sK7(sK6(powerset(X0)))),X1,sK1)) = sK2(relation_dom(sK7(sK6(powerset(X0)))),X1,sK1) )
| ~ empty(sK0)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_18242]) ).
tcf(c_18264,plain,
! [X0: $i,X1: $i] :
( ( relation_image(relation_dom(sK7(sK6(sK6(powerset(X0))))),X1) = sK1 )
| ( apply(relation_dom(sK7(sK6(sK6(powerset(X0))))),sK3(relation_dom(sK7(sK6(sK6(powerset(X0))))),X1,sK1)) = sK2(relation_dom(sK7(sK6(sK6(powerset(X0))))),X1,sK1) )
| ~ empty(sK0)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_18242]) ).
tcf(c_18266,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X0,X1) = sK1 )
| ( apply(X0,sK3(X0,X1,sK1)) = sK2(X0,X1,sK1) )
| ~ empty(sK0)
| ~ empty(X0) ),
inference(light_normalisation,[status(thm)],[c_18257,c_121]) ).
tcf(c_18358,plain,
( ( apply(empty_set,sK7(empty_set)) = sK7(empty_set) )
| ( relation_dom(sK7(powerset(empty_set))) = empty_set ) ),
inference(superposition,[status(thm)],[c_6104,c_9411]) ).
tcf(c_18359,plain,
( ( apply(identity_relation(powerset(empty_set)),empty_set) = empty_set )
| ( relation_dom(sK7(powerset(powerset(empty_set)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8004,c_9411]) ).
tcf(c_18361,plain,
( ( apply(identity_relation(sK6(sK6(powerset(empty_set)))),empty_set) = empty_set )
| ( relation_dom(sK7(powerset(sK6(sK6(powerset(empty_set)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_16755,c_9411]) ).
tcf(c_18362,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(sK7(powerset(X0))) = empty_set )
| ( relation_image(identity_relation(X0),X1) = X2 )
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),relation_dom(identity_relation(X0)))
| ~ in(sK2(identity_relation(X0),X1,X2),X2)
| ( sK2(identity_relation(X0),X1,X2) != sK7(X0) ) ),
inference(superposition,[status(thm)],[c_9411,c_53]) ).
tcf(c_18363,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0),relation_image(identity_relation(X0),X1))
| ( relation_dom(sK7(powerset(X0))) = empty_set )
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),relation_dom(identity_relation(X0))) ),
inference(superposition,[status(thm)],[c_9411,c_57]) ).
tcf(c_18367,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0),relation_image(identity_relation(X0),X1))
| ( relation_dom(sK7(powerset(X0))) = empty_set )
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),X0) ),
inference(light_normalisation,[status(thm)],[c_18363,c_121]) ).
tcf(c_18368,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0),relation_image(identity_relation(X0),X1))
| ( relation_dom(sK7(powerset(X0))) = empty_set )
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18367,c_62,c_63]) ).
tcf(c_18373,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(sK7(powerset(X0))) = empty_set )
| ( relation_image(identity_relation(X0),X1) = X2 )
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),X0)
| ~ in(sK2(identity_relation(X0),X1,X2),X2)
| ( sK2(identity_relation(X0),X1,X2) != sK7(X0) ) ),
inference(light_normalisation,[status(thm)],[c_18362,c_121]) ).
tcf(c_18374,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(sK7(powerset(X0))) = empty_set )
| ( relation_image(identity_relation(X0),X1) = X2 )
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),X0)
| ~ in(sK2(identity_relation(X0),X1,X2),X2)
| ( sK2(identity_relation(X0),X1,X2) != sK7(X0) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18373,c_62,c_63]) ).
tcf(c_18383,plain,
! [X0: $i,X1: $i] : ~ in(X0,relation_image(empty_set,X1)),
inference(global_subsumption_just,[status(thm)],[c_6002,c_9061]) ).
tcf(c_18385,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X0,X1) = relation_image(empty_set,X2) )
| ( apply(X0,sK3(X0,X1,relation_image(empty_set,X2))) = sK2(X0,X1,relation_image(empty_set,X2)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_56,c_18383]) ).
tcf(c_18386,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(X0,X1,relation_image(empty_set,X2)),relation_dom(X0))
| ( relation_image(X0,X1) = relation_image(empty_set,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_54,c_18383]) ).
tcf(c_18387,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(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_55,c_18383]) ).
tcf(c_18388,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(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_55,c_18383]) ).
tcf(c_18389,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_57,c_18383]) ).
tcf(c_18390,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_59,c_18383]) ).
tcf(c_18392,plain,
! [X0: $i,X1: $i] :
( in(sK3(X0,sK1,relation_image(empty_set,X1)),sK0)
| ( relation_image(X0,sK1) = relation_image(empty_set,X1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_11821,c_18383]) ).
tcf(c_18393,plain,
! [X0: $i,X1: $i] :
( element(sK3(X0,sK1,relation_image(empty_set,X1)),sK0)
| ( relation_image(X0,sK1) = relation_image(empty_set,X1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6475,c_18383]) ).
tcf(c_18395,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X0,relation_image(X1,sK1)) = relation_image(empty_set,X2) )
| ~ empty(sK0)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6479,c_18383]) ).
tcf(c_18396,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,relation_image(empty_set,X1),sK1),sK0)
| ( relation_image(X0,relation_image(empty_set,X1)) = sK1 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_12513,c_18383]) ).
tcf(c_18397,plain,
! [X0: $i,X1: $i] :
( element(sK2(X0,relation_image(empty_set,X1),sK1),sK0)
| ( relation_image(X0,relation_image(empty_set,X1)) = sK1 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6486,c_18383]) ).
tcf(c_18398,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X0,relation_image(empty_set,X1)) = sK1 )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6487,c_18383]) ).
tcf(c_18399,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X0,relation_image(empty_set,X2)) = relation_image(X1,sK1) )
| ~ empty(sK0)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6490,c_18383]) ).
tcf(c_18400,plain,
! [X0: $i] : empty(relation_image(empty_set,X0)),
inference(superposition,[status(thm)],[c_9814,c_18383]) ).
tcf(c_18405,plain,
! [X0: $i,X1: $i] :
( ~ function(empty_set)
| ~ relation(empty_set)
| ~ in(X0,empty_set)
| ~ in(X0,X1) ),
inference(light_normalisation,[status(thm)],[c_18389,c_5746]) ).
tcf(c_18500,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(X1)) = X0 )
| ( apply(identity_relation(powerset(X1)),sK6(X1)) = sK6(X1) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5806,c_6877]) ).
tcf(c_18501,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(X1)) = X0 )
| ( apply(identity_relation(X1),sK7(X1)) = sK7(X1) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5807,c_6877]) ).
tcf(c_18502,plain,
! [X0: $i] :
( ( sK7(powerset(empty_set)) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_83,c_6877]) ).
tcf(c_18503,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(relation_dom(X0))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_6877]) ).
tcf(c_18504,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(identity_relation(X0))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_6877]) ).
tcf(c_18505,plain,
! [X0: $i] :
( ( sK7(powerset(sK1)) = X0 )
| ( apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16971,c_6877]) ).
tcf(c_18506,plain,
! [X0: $i] :
( ( sK7(powerset(sK1)) = X0 )
| ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9449,c_6877]) ).
tcf(c_18507,plain,
! [X0: $i] :
( ( sK7(powerset(sK1)) = X0 )
| ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5890,c_6877]) ).
tcf(c_18508,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(relation_image(X1,sK1))) = X0 )
| ~ empty(sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6158,c_6877]) ).
tcf(c_18509,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(sK7(powerset(X0)))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_6877]) ).
tcf(c_18510,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(sK7(sK6(powerset(X0))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_6877]) ).
tcf(c_18511,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(sK7(sK6(sK6(powerset(X0)))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_6877]) ).
tcf(c_18601,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X0,X2) = relation_image(X1,empty_set) )
| ( apply(X0,sK3(X0,X2,relation_image(X1,empty_set))) = sK2(X0,X2,relation_image(X1,empty_set)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_56,c_8512]) ).
tcf(c_18602,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(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_54,c_8512]) ).
tcf(c_18603,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(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_55,c_8512]) ).
tcf(c_18604,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(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_55,c_8512]) ).
tcf(c_18606,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_59,c_8512]) ).
tcf(c_18608,plain,
! [X0: $i,X1: $i] :
( in(sK3(X0,sK1,relation_image(X1,empty_set)),sK0)
| ( relation_image(X0,sK1) = relation_image(X1,empty_set) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_11821,c_8512]) ).
tcf(c_18609,plain,
! [X0: $i,X1: $i] :
( element(sK3(X0,sK1,relation_image(X1,empty_set)),sK0)
| ( relation_image(X0,sK1) = relation_image(X1,empty_set) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6475,c_8512]) ).
tcf(c_18610,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X0,sK1) = relation_image(X1,empty_set) )
| ~ empty(sK0)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6476,c_8512]) ).
tcf(c_18611,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X0,relation_image(X1,sK1)) = relation_image(X2,empty_set) )
| ~ empty(sK0)
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6479,c_8512]) ).
tcf(c_18612,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,relation_image(X1,empty_set),sK1),sK0)
| ( relation_image(X0,relation_image(X1,empty_set)) = sK1 )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_12513,c_8512]) ).
tcf(c_18613,plain,
! [X0: $i,X1: $i] :
( element(sK2(X0,relation_image(X1,empty_set),sK1),sK0)
| ( relation_image(X0,relation_image(X1,empty_set)) = sK1 )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6486,c_8512]) ).
tcf(c_18614,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X0,relation_image(X1,empty_set)) = sK1 )
| ~ empty(sK0)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6487,c_8512]) ).
tcf(c_18615,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X0,relation_image(X2,empty_set)) = relation_image(X1,sK1) )
| ~ empty(sK0)
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6490,c_8512]) ).
tcf(c_18616,plain,
! [X0: $i] :
( empty(relation_image(X0,empty_set))
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_9814,c_8512]) ).
tcf(c_18731,plain,
! [X0: $i] :
( in(sK7(sK7(powerset(X0))),X0)
| empty(sK7(powerset(X0))) ),
inference(global_subsumption_just,[status(thm)],[c_9151,c_6837,c_9151]) ).
tcf(c_18732,plain,
! [X0: $i] :
( empty(sK7(powerset(X0)))
| in(sK7(sK7(powerset(X0))),X0) ),
inference(renaming,[status(thm)],[c_18731]) ).
tcf(c_18738,plain,
( in(sK7(empty_set),empty_set)
| empty(sK7(powerset(empty_set))) ),
inference(superposition,[status(thm)],[c_8004,c_18732]) ).
tcf(c_18739,plain,
! [X0: $i,X1: $i] :
( empty(sK7(powerset(relation_image(X0,X1))))
| ( apply(X0,sK4(X0,X1,sK7(sK7(powerset(relation_image(X0,X1)))))) = sK7(sK7(powerset(relation_image(X0,X1)))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18732,c_60]) ).
tcf(c_18740,plain,
! [X0: $i] :
( empty(sK7(powerset(X0)))
| ( apply(identity_relation(X0),sK7(sK7(powerset(X0)))) = sK7(sK7(powerset(X0))) ) ),
inference(superposition,[status(thm)],[c_18732,c_151]) ).
tcf(c_18741,plain,
! [X0: $i] :
( empty(sK7(powerset(X0)))
| ~ in(X0,sK7(sK7(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_18732,c_85]) ).
tcf(c_18744,plain,
! [X0: $i] : empty(sK7(powerset(relation_image(empty_set,X0)))),
inference(superposition,[status(thm)],[c_18732,c_18383]) ).
tcf(c_18745,plain,
( empty(sK7(powerset(sK1)))
| element(sK7(sK7(powerset(sK1))),sK0) ),
inference(superposition,[status(thm)],[c_18732,c_5838]) ).
tcf(c_18746,plain,
( empty(sK7(powerset(sK1)))
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_18732,c_5820]) ).
tcf(c_18747,plain,
! [X0: $i] :
( empty(X0)
| empty(sK7(powerset(sK6(X0))))
| element(sK7(sK7(powerset(sK6(X0)))),X0) ),
inference(superposition,[status(thm)],[c_18732,c_5839]) ).
tcf(c_18748,plain,
! [X0: $i] :
( empty(sK7(powerset(sK7(powerset(X0)))))
| element(sK7(sK7(powerset(sK7(powerset(X0))))),X0) ),
inference(superposition,[status(thm)],[c_18732,c_5840]) ).
tcf(c_18749,plain,
! [X0: $i] :
( empty(sK7(powerset(sK7(powerset(X0)))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18732,c_5822]) ).
tcf(c_18750,plain,
empty(sK7(powerset(empty_set))),
inference(superposition,[status(thm)],[c_18732,c_8375]) ).
tcf(c_18751,plain,
! [X0: $i] :
( empty(sK7(powerset(relation_image(X0,sK1))))
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18732,c_5948]) ).
tcf(c_18752,plain,
! [X0: $i] :
( empty(sK7(powerset(relation_image(X0,empty_set))))
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18732,c_8512]) ).
tcf(c_18753,plain,
! [X0: $i,X1: $i] :
( empty(sK7(powerset(relation_image(X0,relation_image(X1,sK1)))))
| ~ empty(sK0)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18732,c_6157]) ).
tcf(c_18754,plain,
! [X0: $i] :
( empty(sK7(powerset(sK7(sK6(powerset(X0))))))
| element(sK7(sK7(powerset(sK7(sK6(powerset(X0)))))),X0) ),
inference(superposition,[status(thm)],[c_18732,c_9820]) ).
tcf(c_18755,plain,
! [X0: $i] :
( empty(sK7(powerset(sK7(sK6(powerset(X0))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18732,c_9817]) ).
tcf(c_18756,plain,
! [X0: $i] :
( empty(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))
| element(sK7(sK7(powerset(sK7(sK6(sK6(powerset(X0))))))),X0) ),
inference(superposition,[status(thm)],[c_18732,c_14092]) ).
tcf(c_18757,plain,
! [X0: $i] :
( empty(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18732,c_14089]) ).
tcf(c_18761,plain,
( empty(empty_set)
| in(sK7(empty_set),empty_set) ),
inference(light_normalisation,[status(thm)],[c_18738,c_8004]) ).
tcf(c_18870,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(relation_image(empty_set,X1))) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18400,c_6877]) ).
tcf(c_18871,plain,
! [X0: $i,X1: $i] :
( ( relation_image(relation_dom(relation_image(empty_set,X0)),X1) = sK1 )
| ( apply(relation_dom(relation_image(empty_set,X0)),sK3(relation_dom(relation_image(empty_set,X0)),X1,sK1)) = sK2(relation_dom(relation_image(empty_set,X0)),X1,sK1) )
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_18400,c_18242]) ).
tcf(c_18872,plain,
! [X0: $i] : relation_dom(sK7(sK6(powerset(relation_image(empty_set,X0))))) = empty_set,
inference(superposition,[status(thm)],[c_18400,c_10680]) ).
tcf(c_18873,plain,
! [X0: $i] : identity_relation(sK7(sK6(powerset(relation_image(empty_set,X0))))) = empty_set,
inference(superposition,[status(thm)],[c_18400,c_10678]) ).
tcf(c_18874,plain,
! [X0: $i] : sK7(sK6(sK6(powerset(relation_image(empty_set,X0))))) = empty_set,
inference(superposition,[status(thm)],[c_18400,c_15645]) ).
tcf(c_18875,plain,
! [X0: $i] :
( ( relation_image(sK7(sK6(sK6(powerset(relation_image(empty_set,X0))))),sK1) = sK1 )
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_18400,c_16314]) ).
tcf(c_18876,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X0,sK7(sK6(sK6(powerset(relation_image(empty_set,X1)))))) = sK1 )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18400,c_15105]) ).
tcf(c_18877,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(sK6(powerset(relation_image(empty_set,X1))))) = relation_image(X0,sK1) )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18400,c_15101]) ).
tcf(c_18878,plain,
! [X0: $i] : sK7(powerset(identity_relation(identity_relation(relation_image(empty_set,X0))))) = empty_set,
inference(superposition,[status(thm)],[c_18400,c_9748]) ).
tcf(c_18879,plain,
! [X0: $i] : identity_relation(identity_relation(identity_relation(identity_relation(relation_image(empty_set,X0))))) = empty_set,
inference(superposition,[status(thm)],[c_18400,c_9682]) ).
tcf(c_18880,plain,
! [X0: $i] : sK7(sK6(powerset(relation_dom(relation_image(empty_set,X0))))) = empty_set,
inference(superposition,[status(thm)],[c_18400,c_11340]) ).
tcf(c_18881,plain,
! [X0: $i] : sK7(powerset(identity_relation(relation_dom(relation_image(empty_set,X0))))) = empty_set,
inference(superposition,[status(thm)],[c_18400,c_9747]) ).
tcf(c_18882,plain,
! [X0: $i] : identity_relation(identity_relation(identity_relation(relation_dom(relation_image(empty_set,X0))))) = empty_set,
inference(superposition,[status(thm)],[c_18400,c_9681]) ).
tcf(c_18883,plain,
! [X0: $i] : relation_dom(sK7(powerset(identity_relation(relation_image(empty_set,X0))))) = empty_set,
inference(superposition,[status(thm)],[c_18400,c_9115]) ).
tcf(c_18884,plain,
! [X0: $i] : identity_relation(sK7(powerset(identity_relation(relation_image(empty_set,X0))))) = empty_set,
inference(superposition,[status(thm)],[c_18400,c_9088]) ).
tcf(c_18885,plain,
! [X0: $i] : relation_dom(sK7(powerset(relation_dom(relation_image(empty_set,X0))))) = empty_set,
inference(superposition,[status(thm)],[c_18400,c_9114]) ).
tcf(c_18886,plain,
! [X0: $i] : identity_relation(sK7(powerset(relation_dom(relation_image(empty_set,X0))))) = empty_set,
inference(superposition,[status(thm)],[c_18400,c_9087]) ).
tcf(c_18887,plain,
! [X0: $i] : sK7(powerset(sK7(powerset(relation_image(empty_set,X0))))) = empty_set,
inference(superposition,[status(thm)],[c_18400,c_8009]) ).
tcf(c_18888,plain,
! [X0: $i] : identity_relation(identity_relation(sK7(powerset(relation_image(empty_set,X0))))) = empty_set,
inference(superposition,[status(thm)],[c_18400,c_7966]) ).
tcf(c_18889,plain,
! [X0: $i] : identity_relation(relation_dom(sK7(powerset(relation_image(empty_set,X0))))) = empty_set,
inference(superposition,[status(thm)],[c_18400,c_7938]) ).
tcf(c_18890,plain,
! [X0: $i] : sK7(powerset(relation_dom(relation_dom(relation_image(empty_set,X0))))) = empty_set,
inference(superposition,[status(thm)],[c_18400,c_9017]) ).
tcf(c_18891,plain,
! [X0: $i] : identity_relation(identity_relation(relation_dom(relation_dom(relation_image(empty_set,X0))))) = empty_set,
inference(superposition,[status(thm)],[c_18400,c_8992]) ).
tcf(c_18892,plain,
! [X0: $i] : identity_relation(relation_dom(relation_dom(relation_dom(relation_image(empty_set,X0))))) = empty_set,
inference(superposition,[status(thm)],[c_18400,c_8957]) ).
tcf(c_18893,plain,
! [X0: $i] : relation_dom(relation_dom(relation_dom(relation_dom(relation_image(empty_set,X0))))) = empty_set,
inference(superposition,[status(thm)],[c_18400,c_8561]) ).
tcf(c_18894,plain,
! [X0: $i] : relation_dom(relation_dom(sK7(powerset(relation_image(empty_set,X0))))) = empty_set,
inference(superposition,[status(thm)],[c_18400,c_6875]) ).
tcf(c_18895,plain,
! [X0: $i] : sK7(sK6(powerset(relation_image(empty_set,X0)))) = empty_set,
inference(superposition,[status(thm)],[c_18400,c_10681]) ).
tcf(c_18896,plain,
! [X0: $i] :
( ( relation_image(sK7(sK6(powerset(relation_image(empty_set,X0)))),sK1) = sK1 )
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_18400,c_11188]) ).
tcf(c_18897,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X0,sK7(sK6(powerset(relation_image(empty_set,X1))))) = sK1 )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18400,c_10420]) ).
tcf(c_18898,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(powerset(relation_image(empty_set,X1)))) = relation_image(X0,sK1) )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18400,c_10418]) ).
tcf(c_18899,plain,
! [X0: $i] : sK7(powerset(identity_relation(relation_image(empty_set,X0)))) = empty_set,
inference(superposition,[status(thm)],[c_18400,c_8006]) ).
tcf(c_18900,plain,
! [X0: $i] : identity_relation(identity_relation(identity_relation(relation_image(empty_set,X0)))) = empty_set,
inference(superposition,[status(thm)],[c_18400,c_7963]) ).
tcf(c_18901,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_image(empty_set,X1)) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18400,c_5794]) ).
tcf(c_18902,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_image(empty_set,X1)) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18400,c_5793]) ).
tcf(c_18903,plain,
! [X0: $i] : relation_dom(sK7(powerset(relation_image(empty_set,X0)))) = empty_set,
inference(superposition,[status(thm)],[c_18400,c_6878]) ).
tcf(c_18904,plain,
! [X0: $i] : identity_relation(sK7(powerset(relation_image(empty_set,X0)))) = empty_set,
inference(superposition,[status(thm)],[c_18400,c_6876]) ).
tcf(c_18905,plain,
! [X0: $i] : sK7(powerset(relation_dom(relation_image(empty_set,X0)))) = empty_set,
inference(superposition,[status(thm)],[c_18400,c_8005]) ).
tcf(c_18906,plain,
! [X0: $i] : identity_relation(identity_relation(relation_dom(relation_image(empty_set,X0)))) = empty_set,
inference(superposition,[status(thm)],[c_18400,c_7962]) ).
tcf(c_18907,plain,
! [X0: $i] : identity_relation(relation_dom(relation_dom(relation_image(empty_set,X0)))) = empty_set,
inference(superposition,[status(thm)],[c_18400,c_7934]) ).
tcf(c_18908,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X0,sK7(powerset(relation_image(empty_set,X1)))) = sK1 )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18400,c_7111]) ).
tcf(c_18909,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(relation_image(empty_set,X1))) = relation_image(X0,sK1) )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18400,c_6946]) ).
tcf(c_18910,plain,
! [X0: $i] : relation_dom(relation_dom(relation_dom(relation_image(empty_set,X0)))) = empty_set,
inference(superposition,[status(thm)],[c_18400,c_6133]) ).
tcf(c_18911,plain,
! [X0: $i] :
( ( relation_image(sK7(powerset(relation_image(empty_set,X0))),sK1) = sK1 )
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_18400,c_8316]) ).
tcf(c_18914,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_image(empty_set,X0)),sK1) = sK1 )
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_18400,c_8131]) ).
tcf(c_18915,plain,
! [X0: $i] : sK7(powerset(relation_image(empty_set,X0))) = empty_set,
inference(superposition,[status(thm)],[c_18400,c_6879]) ).
tcf(c_18916,plain,
! [X0: $i] : identity_relation(identity_relation(relation_image(empty_set,X0))) = empty_set,
inference(superposition,[status(thm)],[c_18400,c_6106]) ).
tcf(c_18917,plain,
! [X0: $i] : identity_relation(relation_dom(relation_image(empty_set,X0))) = empty_set,
inference(superposition,[status(thm)],[c_18400,c_6105]) ).
tcf(c_18918,plain,
! [X0: $i] : relation_dom(relation_dom(relation_image(empty_set,X0))) = empty_set,
inference(superposition,[status(thm)],[c_18400,c_5747]) ).
tcf(c_18919,plain,
! [X0: $i] : identity_relation(relation_image(empty_set,X0)) = empty_set,
inference(superposition,[status(thm)],[c_18400,c_5776]) ).
tcf(c_18920,plain,
! [X0: $i,X1: $i] :
( ( relation_image(empty_set,X1) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18400,c_51]) ).
tcf(c_18921,plain,
! [X0: $i] : relation_dom(relation_image(empty_set,X0)) = empty_set,
inference(superposition,[status(thm)],[c_18400,c_5663]) ).
tcf(c_18922,plain,
! [X0: $i] : relation_image(empty_set,X0) = empty_set,
inference(superposition,[status(thm)],[c_18400,c_52]) ).
tcf(c_18923,plain,
! [X0: $i] : function(relation_image(empty_set,X0)),
inference(superposition,[status(thm)],[c_18400,c_98]) ).
tcf(c_18924,plain,
! [X0: $i] : relation(relation_image(empty_set,X0)),
inference(superposition,[status(thm)],[c_18400,c_80]) ).
tcf(c_18970,plain,
( ( sK1 = empty_set )
| ~ empty(sK0) ),
inference(demodulation,[status(thm)],[c_8694,c_18922]) ).
tcf(c_19400,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(powerset(sK1)))) = X0 )
| ~ empty(sK0)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18746,c_6877]) ).
tcf(c_19401,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK7(powerset(sK1))),X0) = sK1 )
| ( apply(relation_dom(sK7(powerset(sK1))),sK3(relation_dom(sK7(powerset(sK1))),X0,sK1)) = sK2(relation_dom(sK7(powerset(sK1))),X0,sK1) )
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_18746,c_18242]) ).
tcf(c_19402,plain,
( ( relation_dom(sK7(sK6(powerset(sK7(powerset(sK1)))))) = empty_set )
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_18746,c_10680]) ).
tcf(c_19403,plain,
( ( identity_relation(sK7(sK6(powerset(sK7(powerset(sK1)))))) = empty_set )
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_18746,c_10678]) ).
tcf(c_19404,plain,
( ( sK7(sK6(sK6(powerset(sK7(powerset(sK1)))))) = empty_set )
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_18746,c_15645]) ).
tcf(c_19405,plain,
( ( relation_image(sK7(sK6(sK6(powerset(sK7(powerset(sK1)))))),sK1) = sK1 )
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_18746,c_16314]) ).
tcf(c_19406,plain,
! [X0: $i] :
( ( relation_image(X0,sK7(sK6(sK6(powerset(sK7(powerset(sK1))))))) = sK1 )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18746,c_15105]) ).
tcf(c_19407,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(powerset(sK7(powerset(sK1)))))) = relation_image(X0,sK1) )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18746,c_15101]) ).
tcf(c_19408,plain,
( ( sK7(powerset(identity_relation(identity_relation(sK7(powerset(sK1)))))) = empty_set )
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_18746,c_9748]) ).
tcf(c_19409,plain,
( ( identity_relation(identity_relation(identity_relation(identity_relation(sK7(powerset(sK1)))))) = empty_set )
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_18746,c_9682]) ).
tcf(c_19410,plain,
( ( sK7(sK6(powerset(relation_dom(sK7(powerset(sK1)))))) = empty_set )
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_18746,c_11340]) ).
tcf(c_19411,plain,
( ( sK7(powerset(identity_relation(relation_dom(sK7(powerset(sK1)))))) = empty_set )
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_18746,c_9747]) ).
tcf(c_19412,plain,
( ( identity_relation(identity_relation(identity_relation(relation_dom(sK7(powerset(sK1)))))) = empty_set )
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_18746,c_9681]) ).
tcf(c_19413,plain,
( ( relation_dom(sK7(powerset(identity_relation(sK7(powerset(sK1)))))) = empty_set )
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_18746,c_9115]) ).
tcf(c_19414,plain,
( ( identity_relation(sK7(powerset(identity_relation(sK7(powerset(sK1)))))) = empty_set )
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_18746,c_9088]) ).
tcf(c_19415,plain,
( ( relation_dom(sK7(powerset(relation_dom(sK7(powerset(sK1)))))) = empty_set )
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_18746,c_9114]) ).
tcf(c_19416,plain,
( ( identity_relation(sK7(powerset(relation_dom(sK7(powerset(sK1)))))) = empty_set )
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_18746,c_9087]) ).
tcf(c_19417,plain,
( ( sK7(powerset(sK7(powerset(sK7(powerset(sK1)))))) = empty_set )
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_18746,c_8009]) ).
tcf(c_19418,plain,
( ( identity_relation(identity_relation(sK7(powerset(sK7(powerset(sK1)))))) = empty_set )
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_18746,c_7966]) ).
tcf(c_19419,plain,
( ( identity_relation(relation_dom(sK7(powerset(sK7(powerset(sK1)))))) = empty_set )
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_18746,c_7938]) ).
tcf(c_19420,plain,
( ( sK7(powerset(relation_dom(relation_dom(sK7(powerset(sK1)))))) = empty_set )
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_18746,c_9017]) ).
tcf(c_19421,plain,
( ( identity_relation(identity_relation(relation_dom(relation_dom(sK7(powerset(sK1)))))) = empty_set )
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_18746,c_8992]) ).
tcf(c_19422,plain,
( ( identity_relation(relation_dom(relation_dom(relation_dom(sK7(powerset(sK1)))))) = empty_set )
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_18746,c_8957]) ).
tcf(c_19423,plain,
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK7(powerset(sK1)))))) = empty_set )
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_18746,c_8561]) ).
tcf(c_19424,plain,
( ( relation_dom(relation_dom(sK7(powerset(sK7(powerset(sK1)))))) = empty_set )
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_18746,c_6875]) ).
tcf(c_19425,plain,
( ( sK7(sK6(powerset(sK7(powerset(sK1))))) = empty_set )
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_18746,c_10681]) ).
tcf(c_19426,plain,
( ( relation_image(sK7(sK6(powerset(sK7(powerset(sK1))))),sK1) = sK1 )
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_18746,c_11188]) ).
tcf(c_19427,plain,
! [X0: $i] :
( ( relation_image(X0,sK7(sK6(powerset(sK7(powerset(sK1)))))) = sK1 )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18746,c_10420]) ).
tcf(c_19428,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(sK7(powerset(sK1))))) = relation_image(X0,sK1) )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18746,c_10418]) ).
tcf(c_19429,plain,
( ( sK7(powerset(identity_relation(sK7(powerset(sK1))))) = empty_set )
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_18746,c_8006]) ).
tcf(c_19430,plain,
( ( identity_relation(identity_relation(identity_relation(sK7(powerset(sK1))))) = empty_set )
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_18746,c_7963]) ).
tcf(c_19431,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(sK1))) = X0 )
| ~ empty(sK0)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18746,c_5794]) ).
tcf(c_19432,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(sK1))) = X0 )
| ~ empty(sK0)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18746,c_5793]) ).
tcf(c_19433,plain,
( ( relation_dom(sK7(powerset(sK7(powerset(sK1))))) = empty_set )
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_18746,c_6878]) ).
tcf(c_19434,plain,
( ( identity_relation(sK7(powerset(sK7(powerset(sK1))))) = empty_set )
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_18746,c_6876]) ).
tcf(c_19435,plain,
( ( sK7(powerset(relation_dom(sK7(powerset(sK1))))) = empty_set )
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_18746,c_8005]) ).
tcf(c_19436,plain,
( ( identity_relation(identity_relation(relation_dom(sK7(powerset(sK1))))) = empty_set )
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_18746,c_7962]) ).
tcf(c_19437,plain,
( ( identity_relation(relation_dom(relation_dom(sK7(powerset(sK1))))) = empty_set )
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_18746,c_7934]) ).
tcf(c_19438,plain,
! [X0: $i] :
( ( relation_image(X0,sK7(powerset(sK7(powerset(sK1))))) = sK1 )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18746,c_7111]) ).
tcf(c_19439,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(powerset(sK1)))) = relation_image(X0,sK1) )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18746,c_6946]) ).
tcf(c_19440,plain,
( ( relation_dom(relation_dom(relation_dom(sK7(powerset(sK1))))) = empty_set )
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_18746,c_6133]) ).
tcf(c_19441,plain,
( ( relation_image(sK7(powerset(sK7(powerset(sK1)))),sK1) = sK1 )
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_18746,c_8316]) ).
tcf(c_19443,plain,
! [X0: $i] :
( ( relation_image(X0,sK7(powerset(sK1))) = sK1 )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18746,c_7107]) ).
tcf(c_19444,plain,
( ( relation_image(relation_dom(sK7(powerset(sK1))),sK1) = sK1 )
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_18746,c_8131]) ).
tcf(c_19445,plain,
( ( sK7(powerset(sK7(powerset(sK1)))) = empty_set )
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_18746,c_6879]) ).
tcf(c_19446,plain,
( ( identity_relation(identity_relation(sK7(powerset(sK1)))) = empty_set )
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_18746,c_6106]) ).
tcf(c_19447,plain,
( ( identity_relation(relation_dom(sK7(powerset(sK1)))) = empty_set )
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_18746,c_6105]) ).
tcf(c_19448,plain,
( ( relation_dom(relation_dom(sK7(powerset(sK1)))) = empty_set )
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_18746,c_5747]) ).
tcf(c_19449,plain,
( ( identity_relation(sK7(powerset(sK1))) = empty_set )
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_18746,c_5776]) ).
tcf(c_19450,plain,
! [X0: $i] :
( ( sK7(powerset(sK1)) = X0 )
| ~ empty(sK0)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18746,c_51]) ).
tcf(c_19451,plain,
( ( relation_dom(sK7(powerset(sK1))) = empty_set )
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_18746,c_5663]) ).
tcf(c_19452,plain,
( ( sK7(powerset(sK1)) = empty_set )
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_18746,c_52]) ).
tcf(c_19453,plain,
( function(sK7(powerset(sK1)))
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_18746,c_98]) ).
tcf(c_19454,plain,
( relation(sK7(powerset(sK1)))
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_18746,c_80]) ).
tcf(c_19822,plain,
( empty(sK0)
| empty(sK7(powerset(sK1)))
| in(sK7(sK7(powerset(sK1))),sK0) ),
inference(superposition,[status(thm)],[c_18745,c_71]) ).
tcf(c_19866,plain,
! [X0: $i,X1: $i] :
( ( relation_image(sK7(powerset(sK1)),relation_image(X0,relation_image(X1,sK1))) = sK1 )
| ~ empty(sK0)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(sK7(powerset(sK1))) ),
inference(superposition,[status(thm)],[c_19453,c_7115]) ).
tcf(c_19867,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X0,relation_image(X1,sK1)) = relation_image(sK7(powerset(sK1)),sK1) )
| ~ empty(sK0)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(sK7(powerset(sK1))) ),
inference(superposition,[status(thm)],[c_19453,c_6950]) ).
tcf(c_19868,plain,
! [X0: $i] :
( ( relation_image(sK7(powerset(sK1)),X0) = sK1 )
| ( apply(identity_relation(relation_dom(sK7(powerset(sK1)))),sK3(sK7(powerset(sK1)),X0,sK1)) = sK3(sK7(powerset(sK1)),X0,sK1) )
| ~ empty(sK0)
| ~ relation(sK7(powerset(sK1))) ),
inference(superposition,[status(thm)],[c_19453,c_7214]) ).
tcf(c_19869,plain,
! [X0: $i] :
( ( relation_image(sK7(powerset(sK1)),X0) = sK1 )
| ( apply(identity_relation(X0),sK3(sK7(powerset(sK1)),X0,sK1)) = sK3(sK7(powerset(sK1)),X0,sK1) )
| ~ empty(sK0)
| ~ relation(sK7(powerset(sK1))) ),
inference(superposition,[status(thm)],[c_19453,c_7105]) ).
tcf(c_19870,plain,
! [X0: $i] :
( ( relation_image(sK7(powerset(sK1)),sK1) = X0 )
| ( apply(identity_relation(X0),sK2(sK7(powerset(sK1)),sK1,X0)) = sK2(sK7(powerset(sK1)),sK1,X0) )
| ~ empty(sK0)
| ~ relation(sK7(powerset(sK1))) ),
inference(superposition,[status(thm)],[c_19453,c_6940]) ).
tcf(c_19871,plain,
! [X0: $i] :
( ( relation_image(sK7(powerset(sK1)),relation_image(X0,sK1)) = sK1 )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0)
| ~ relation(sK7(powerset(sK1))) ),
inference(superposition,[status(thm)],[c_19453,c_7114]) ).
tcf(c_19872,plain,
! [X0: $i] :
( ( relation_image(sK7(powerset(sK1)),sK1) = relation_image(X0,sK1) )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0)
| ~ relation(sK7(powerset(sK1))) ),
inference(superposition,[status(thm)],[c_19453,c_6949]) ).
tcf(c_19873,plain,
( ( relation_image(relation_image(sK7(powerset(sK1)),sK1),sK1) = sK1 )
| ~ empty(sK0)
| ~ relation(sK7(powerset(sK1))) ),
inference(superposition,[status(thm)],[c_19453,c_9208]) ).
tcf(c_19874,plain,
! [X0: $i] :
( ( relation_image(sK7(powerset(sK1)),X0) = sK1 )
| ( apply(sK7(powerset(sK1)),sK3(sK7(powerset(sK1)),X0,sK1)) = sK2(sK7(powerset(sK1)),X0,sK1) )
| ~ empty(sK0)
| ~ relation(sK7(powerset(sK1))) ),
inference(superposition,[status(thm)],[c_19453,c_7707]) ).
tcf(c_19875,plain,
( ( relation_image(sK7(powerset(sK1)),sK1) = sK1 )
| ~ empty(sK0)
| ~ relation(sK7(powerset(sK1))) ),
inference(superposition,[status(thm)],[c_19453,c_6945]) ).
tcf(c_19876,plain,
( ( relation_image(sK7(powerset(sK1)),sK1) = empty_set )
| ~ empty(sK0)
| ~ relation(sK7(powerset(sK1))) ),
inference(superposition,[status(thm)],[c_19453,c_6198]) ).
tcf(c_19988,plain,
( ( apply(empty_set,sK7(empty_set)) = sK7(empty_set) )
| ( identity_relation(sK7(powerset(empty_set))) = empty_set ) ),
inference(superposition,[status(thm)],[c_6104,c_9412]) ).
tcf(c_19989,plain,
( ( apply(identity_relation(powerset(empty_set)),empty_set) = empty_set )
| ( identity_relation(sK7(powerset(powerset(empty_set)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8004,c_9412]) ).
tcf(c_19991,plain,
( ( apply(identity_relation(sK6(sK6(powerset(empty_set)))),empty_set) = empty_set )
| ( identity_relation(sK7(powerset(sK6(sK6(powerset(empty_set)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_16755,c_9412]) ).
tcf(c_19992,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(sK7(powerset(X0))) = empty_set )
| ( relation_image(identity_relation(X0),X1) = X2 )
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),relation_dom(identity_relation(X0)))
| ~ in(sK2(identity_relation(X0),X1,X2),X2)
| ( sK2(identity_relation(X0),X1,X2) != sK7(X0) ) ),
inference(superposition,[status(thm)],[c_9412,c_53]) ).
tcf(c_19993,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0),relation_image(identity_relation(X0),X1))
| ( identity_relation(sK7(powerset(X0))) = empty_set )
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),relation_dom(identity_relation(X0))) ),
inference(superposition,[status(thm)],[c_9412,c_57]) ).
tcf(c_19997,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0),relation_image(identity_relation(X0),X1))
| ( identity_relation(sK7(powerset(X0))) = empty_set )
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),X0) ),
inference(light_normalisation,[status(thm)],[c_19993,c_121]) ).
tcf(c_19998,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0),relation_image(identity_relation(X0),X1))
| ( identity_relation(sK7(powerset(X0))) = empty_set )
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_19997,c_62,c_63]) ).
tcf(c_20003,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(sK7(powerset(X0))) = empty_set )
| ( relation_image(identity_relation(X0),X1) = X2 )
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),X0)
| ~ in(sK2(identity_relation(X0),X1,X2),X2)
| ( sK2(identity_relation(X0),X1,X2) != sK7(X0) ) ),
inference(light_normalisation,[status(thm)],[c_19992,c_121]) ).
tcf(c_20004,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(sK7(powerset(X0))) = empty_set )
| ( relation_image(identity_relation(X0),X1) = X2 )
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),X0)
| ~ in(sK2(identity_relation(X0),X1,X2),X2)
| ( sK2(identity_relation(X0),X1,X2) != sK7(X0) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_20003,c_62,c_63]) ).
tcf(c_20027,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_18922,c_57]) ).
tcf(c_20029,plain,
! [X0: $i,X1: $i] :
( in(sK3(X0,X1,empty_set),relation_dom(X0))
| ( relation_image(X0,X1) = relation_image(empty_set,sK1) )
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18922,c_6698]) ).
tcf(c_20030,plain,
! [X0: $i,X1: $i] :
( in(sK3(X0,X1,empty_set),X1)
| ( relation_image(X0,X1) = relation_image(empty_set,sK1) )
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18922,c_6490]) ).
tcf(c_20031,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,empty_set,X1),X1)
| ( relation_image(X0,relation_image(empty_set,sK1)) = X1 )
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18922,c_6479]) ).
tcf(c_20039,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_20027,c_5746]) ).
tcf(c_20040,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,empty_set,X1),X1)
| ( relation_image(X0,relation_image(empty_set,sK1)) = X1 )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_20031,c_5610,c_82]) ).
tcf(c_20046,plain,
! [X0: $i,X1: $i] :
( in(sK3(X0,X1,empty_set),X1)
| ( relation_image(X0,X1) = relation_image(empty_set,sK1) )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_20030,c_5610,c_82]) ).
tcf(c_20052,plain,
! [X0: $i,X1: $i] :
( in(sK3(X0,X1,empty_set),relation_dom(X0))
| ( relation_image(X0,X1) = relation_image(empty_set,sK1) )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_20029,c_5610,c_82]) ).
tcf(c_20107,plain,
( empty(sK7(powerset(empty_set)))
| ~ in(empty_set,sK7(empty_set)) ),
inference(superposition,[status(thm)],[c_8004,c_18741]) ).
tcf(c_20108,plain,
( empty(empty_set)
| ~ in(empty_set,sK7(empty_set)) ),
inference(light_normalisation,[status(thm)],[c_20107,c_8004]) ).
tcf(c_20124,plain,
! [X0: $i] :
( ( apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0) )
| ( relation_image(relation_image(identity_relation(X0),sK1),sK1) = sK1 ) ),
inference(superposition,[status(thm)],[c_5806,c_9232]) ).
tcf(c_20125,plain,
! [X0: $i] :
( ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) )
| ( relation_image(relation_image(identity_relation(X0),sK1),sK1) = sK1 ) ),
inference(superposition,[status(thm)],[c_5807,c_9232]) ).
tcf(c_20174,plain,
( ( sK7(sK6(powerset(sK7(powerset(sK1))))) = empty_set )
| ( apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0) ) ),
inference(superposition,[status(thm)],[c_5806,c_19425]) ).
tcf(c_20175,plain,
( ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) )
| ( sK7(sK6(powerset(sK7(powerset(sK1))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_19425]) ).
tcf(c_20184,plain,
( ( sK7(powerset(identity_relation(sK7(powerset(sK1))))) = empty_set )
| ( apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0) ) ),
inference(superposition,[status(thm)],[c_5806,c_19429]) ).
tcf(c_20185,plain,
( ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) )
| ( sK7(powerset(identity_relation(sK7(powerset(sK1))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_19429]) ).
tcf(c_20194,plain,
( ( apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0) )
| ( identity_relation(identity_relation(identity_relation(sK7(powerset(sK1))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_19430]) ).
tcf(c_20195,plain,
( ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) )
| ( identity_relation(identity_relation(identity_relation(sK7(powerset(sK1))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_19430]) ).
tcf(c_20258,plain,
( ( apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0) )
| ( relation_dom(sK7(powerset(sK7(powerset(sK1))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_19433]) ).
tcf(c_20259,plain,
( ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) )
| ( relation_dom(sK7(powerset(sK7(powerset(sK1))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_19433]) ).
tcf(c_20268,plain,
( ( apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0) )
| ( identity_relation(sK7(powerset(sK7(powerset(sK1))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_19434]) ).
tcf(c_20269,plain,
( ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) )
| ( identity_relation(sK7(powerset(sK7(powerset(sK1))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_19434]) ).
tcf(c_20359,plain,
( ( sK7(powerset(relation_dom(empty_set))) = empty_set )
| ( apply(empty_set,sK7(empty_set)) = sK7(empty_set) ) ),
inference(superposition,[status(thm)],[c_6104,c_9413]) ).
tcf(c_20360,plain,
( ( sK7(powerset(relation_dom(powerset(empty_set)))) = empty_set )
| ( apply(identity_relation(powerset(empty_set)),empty_set) = empty_set ) ),
inference(superposition,[status(thm)],[c_8004,c_9413]) ).
tcf(c_20362,plain,
( ( sK7(powerset(relation_dom(sK6(sK6(powerset(empty_set)))))) = empty_set )
| ( apply(identity_relation(sK6(sK6(powerset(empty_set)))),empty_set) = empty_set ) ),
inference(superposition,[status(thm)],[c_16755,c_9413]) ).
tcf(c_20363,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK7(powerset(relation_dom(X0))) = empty_set )
| ( relation_image(identity_relation(X0),X1) = X2 )
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),relation_dom(identity_relation(X0)))
| ~ in(sK2(identity_relation(X0),X1,X2),X2)
| ( sK2(identity_relation(X0),X1,X2) != sK7(X0) ) ),
inference(superposition,[status(thm)],[c_9413,c_53]) ).
tcf(c_20364,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0),relation_image(identity_relation(X0),X1))
| ( sK7(powerset(relation_dom(X0))) = empty_set )
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),relation_dom(identity_relation(X0))) ),
inference(superposition,[status(thm)],[c_9413,c_57]) ).
tcf(c_20368,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0),relation_image(identity_relation(X0),X1))
| ( sK7(powerset(relation_dom(X0))) = empty_set )
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),X0) ),
inference(light_normalisation,[status(thm)],[c_20364,c_121]) ).
tcf(c_20369,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0),relation_image(identity_relation(X0),X1))
| ( sK7(powerset(relation_dom(X0))) = empty_set )
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_20368,c_62,c_63]) ).
tcf(c_20374,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK7(powerset(relation_dom(X0))) = empty_set )
| ( relation_image(identity_relation(X0),X1) = X2 )
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),X0)
| ~ in(sK2(identity_relation(X0),X1,X2),X2)
| ( sK2(identity_relation(X0),X1,X2) != sK7(X0) ) ),
inference(light_normalisation,[status(thm)],[c_20363,c_121]) ).
tcf(c_20375,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK7(powerset(relation_dom(X0))) = empty_set )
| ( relation_image(identity_relation(X0),X1) = X2 )
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),X0)
| ~ in(sK2(identity_relation(X0),X1,X2),X2)
| ( sK2(identity_relation(X0),X1,X2) != sK7(X0) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_20374,c_62,c_63]) ).
tcf(c_20390,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(X1)) = X0 )
| ( apply(identity_relation(powerset(X1)),sK6(X1)) = sK6(X1) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5806,c_9319]) ).
tcf(c_20391,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(X1)) = X0 )
| ( apply(identity_relation(X1),sK7(X1)) = sK7(X1) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5807,c_9319]) ).
tcf(c_20392,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(empty_set)) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_83,c_9319]) ).
tcf(c_20393,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(X0))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_9319]) ).
tcf(c_20394,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(identity_relation(X0))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_9319]) ).
tcf(c_20395,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK1)) = X0 )
| ( apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16971,c_9319]) ).
tcf(c_20396,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK1)) = X0 )
| ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9449,c_9319]) ).
tcf(c_20397,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK1)) = X0 )
| ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5890,c_9319]) ).
tcf(c_20398,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_image(X1,sK1))) = X0 )
| ~ empty(sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6158,c_9319]) ).
tcf(c_20399,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK7(powerset(X0)))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_9319]) ).
tcf(c_20400,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK7(sK6(powerset(X0))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_9319]) ).
tcf(c_20401,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK7(sK6(sK6(powerset(X0)))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_9319]) ).
tcf(c_20402,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(powerset(sK1)))) = X0 )
| ~ empty(sK0)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18746,c_9319]) ).
tcf(c_20486,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(X1)) = X0 )
| ( apply(identity_relation(powerset(X1)),sK6(X1)) = sK6(X1) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5806,c_9347]) ).
tcf(c_20487,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(X1)) = X0 )
| ( apply(identity_relation(X1),sK7(X1)) = sK7(X1) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5807,c_9347]) ).
tcf(c_20488,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(empty_set)) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_83,c_9347]) ).
tcf(c_20489,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(relation_dom(X0))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_9347]) ).
tcf(c_20490,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(identity_relation(X0))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_9347]) ).
tcf(c_20491,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK1)) = X0 )
| ( apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16971,c_9347]) ).
tcf(c_20492,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK1)) = X0 )
| ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9449,c_9347]) ).
tcf(c_20493,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK1)) = X0 )
| ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5890,c_9347]) ).
tcf(c_20494,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(relation_image(X1,sK1))) = X0 )
| ~ empty(sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6158,c_9347]) ).
tcf(c_20495,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(sK7(powerset(X0)))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_9347]) ).
tcf(c_20496,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(sK7(sK6(powerset(X0))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_9347]) ).
tcf(c_20497,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(sK7(sK6(sK6(powerset(X0)))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_9347]) ).
tcf(c_20498,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(powerset(sK1)))) = X0 )
| ~ empty(sK0)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18746,c_9347]) ).
tcf(c_20553,plain,
apply(identity_relation(powerset(empty_set)),empty_set) = empty_set,
inference(superposition,[status(thm)],[c_8004,c_9434]) ).
tcf(c_20554,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(identity_relation(powerset(X0)),X1) = X2 )
| ~ function(identity_relation(powerset(X0)))
| ~ relation(identity_relation(powerset(X0)))
| ~ in(sK7(powerset(X0)),X1)
| ~ in(sK7(powerset(X0)),relation_dom(identity_relation(powerset(X0))))
| ~ in(sK2(identity_relation(powerset(X0)),X1,X2),X2)
| ( sK2(identity_relation(powerset(X0)),X1,X2) != sK7(powerset(X0)) ) ),
inference(superposition,[status(thm)],[c_9434,c_53]) ).
tcf(c_20555,plain,
! [X0: $i,X1: $i] :
( in(sK7(powerset(X0)),relation_image(identity_relation(powerset(X0)),X1))
| ~ function(identity_relation(powerset(X0)))
| ~ relation(identity_relation(powerset(X0)))
| ~ in(sK7(powerset(X0)),X1)
| ~ in(sK7(powerset(X0)),relation_dom(identity_relation(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_9434,c_57]) ).
tcf(c_20556,plain,
! [X0: $i,X1: $i] :
( in(sK7(powerset(X0)),relation_image(identity_relation(powerset(X0)),X1))
| ~ in(sK7(powerset(X0)),X1)
| ~ in(sK7(powerset(X0)),relation_dom(identity_relation(powerset(X0)))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_20555,c_62,c_63]) ).
tcf(c_20560,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(identity_relation(powerset(X0)),X1) = X2 )
| ~ in(sK7(powerset(X0)),X1)
| ~ in(sK7(powerset(X0)),relation_dom(identity_relation(powerset(X0))))
| ~ in(sK2(identity_relation(powerset(X0)),X1,X2),X2)
| ( sK2(identity_relation(powerset(X0)),X1,X2) != sK7(powerset(X0)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_20554,c_62,c_63]) ).
tcf(c_20578,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(sK7(powerset(sK7(powerset(X0)))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_9347]) ).
tcf(c_20579,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK7(powerset(sK7(powerset(X0)))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_9319]) ).
tcf(c_20580,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(sK7(powerset(sK7(powerset(X0)))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_6877]) ).
tcf(c_20581,plain,
! [X0: $i,X1: $i] :
( ( relation_image(relation_dom(sK7(powerset(sK7(powerset(X0))))),X1) = sK1 )
| ( apply(relation_dom(sK7(powerset(sK7(powerset(X0))))),sK3(relation_dom(sK7(powerset(sK7(powerset(X0))))),X1,sK1)) = sK2(relation_dom(sK7(powerset(sK7(powerset(X0))))),X1,sK1) )
| ~ empty(sK0)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_18242]) ).
tcf(c_20582,plain,
! [X0: $i] :
( ( relation_dom(sK7(sK6(powerset(sK7(powerset(sK7(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_10680]) ).
tcf(c_20583,plain,
! [X0: $i] :
( ( identity_relation(sK7(sK6(powerset(sK7(powerset(sK7(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_10678]) ).
tcf(c_20584,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(powerset(sK7(powerset(sK7(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_15645]) ).
tcf(c_20585,plain,
! [X0: $i] :
( ( relation_image(sK7(sK6(sK6(powerset(sK7(powerset(sK7(powerset(X0)))))))),sK1) = sK1 )
| ~ empty(sK0)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_16314]) ).
tcf(c_20586,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X1,sK7(sK6(sK6(powerset(sK7(powerset(sK7(powerset(X0))))))))) = sK1 )
| ~ empty(sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_15105]) ).
tcf(c_20587,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(sK6(powerset(sK7(powerset(sK7(powerset(X0)))))))) = relation_image(X1,sK1) )
| ~ empty(sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_15101]) ).
tcf(c_20588,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(identity_relation(sK7(powerset(sK7(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_9748]) ).
tcf(c_20589,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(sK7(powerset(sK7(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_9682]) ).
tcf(c_20590,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(relation_dom(sK7(powerset(sK7(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_11340]) ).
tcf(c_20591,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(relation_dom(sK7(powerset(sK7(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_9747]) ).
tcf(c_20592,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(relation_dom(sK7(powerset(sK7(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_9681]) ).
tcf(c_20593,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(identity_relation(sK7(powerset(sK7(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_9115]) ).
tcf(c_20594,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(identity_relation(sK7(powerset(sK7(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_9088]) ).
tcf(c_20595,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(relation_dom(sK7(powerset(sK7(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_9114]) ).
tcf(c_20596,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(relation_dom(sK7(powerset(sK7(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_9087]) ).
tcf(c_20597,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(powerset(sK7(powerset(sK7(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_8009]) ).
tcf(c_20598,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(powerset(sK7(powerset(sK7(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_7966]) ).
tcf(c_20599,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(powerset(sK7(powerset(sK7(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_7938]) ).
tcf(c_20600,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(relation_dom(sK7(powerset(sK7(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_9017]) ).
tcf(c_20601,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(relation_dom(sK7(powerset(sK7(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_8992]) ).
tcf(c_20602,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(relation_dom(sK7(powerset(sK7(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_8957]) ).
tcf(c_20603,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK7(powerset(sK7(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_8561]) ).
tcf(c_20604,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(powerset(sK7(powerset(sK7(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_6875]) ).
tcf(c_20605,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(sK7(powerset(sK7(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_10681]) ).
tcf(c_20606,plain,
! [X0: $i] :
( ( relation_image(sK7(sK6(powerset(sK7(powerset(sK7(powerset(X0))))))),sK1) = sK1 )
| ~ empty(sK0)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_11188]) ).
tcf(c_20607,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X1,sK7(sK6(powerset(sK7(powerset(sK7(powerset(X0)))))))) = sK1 )
| ~ empty(sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_10420]) ).
tcf(c_20608,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(powerset(sK7(powerset(sK7(powerset(X0))))))) = relation_image(X1,sK1) )
| ~ empty(sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_10418]) ).
tcf(c_20609,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(sK7(powerset(sK7(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_8006]) ).
tcf(c_20610,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(sK7(powerset(sK7(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_7963]) ).
tcf(c_20611,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK7(powerset(sK7(powerset(X0))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_5794]) ).
tcf(c_20612,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(powerset(sK7(powerset(X0))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_5793]) ).
tcf(c_20613,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(sK7(powerset(sK7(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_6878]) ).
tcf(c_20614,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(sK7(powerset(sK7(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_6876]) ).
tcf(c_20615,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(sK7(powerset(sK7(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_8005]) ).
tcf(c_20616,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(sK7(powerset(sK7(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_7962]) ).
tcf(c_20617,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(sK7(powerset(sK7(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_7934]) ).
tcf(c_20618,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X1,sK7(powerset(sK7(powerset(sK7(powerset(X0))))))) = sK1 )
| ~ empty(sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_7111]) ).
tcf(c_20619,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(sK7(powerset(sK7(powerset(X0)))))) = relation_image(X1,sK1) )
| ~ empty(sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_6946]) ).
tcf(c_20620,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK7(powerset(sK7(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_6133]) ).
tcf(c_20621,plain,
! [X0: $i] :
( ( relation_image(sK7(powerset(sK7(powerset(sK7(powerset(X0)))))),sK1) = sK1 )
| ~ empty(sK0)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_8316]) ).
tcf(c_20624,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK7(powerset(sK7(powerset(X0))))),sK1) = sK1 )
| ~ empty(sK0)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_8131]) ).
tcf(c_20633,plain,
! [X0: $i] :
( function(sK7(powerset(sK7(powerset(X0)))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_98]) ).
tcf(c_20634,plain,
! [X0: $i] :
( relation(sK7(powerset(sK7(powerset(X0)))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_80]) ).
tcf(c_21129,plain,
( ( sK7(powerset(relation_dom(sK7(powerset(sK1))))) = empty_set )
| ( apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0) ) ),
inference(superposition,[status(thm)],[c_5806,c_19435]) ).
tcf(c_21130,plain,
( ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) )
| ( sK7(powerset(relation_dom(sK7(powerset(sK1))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_19435]) ).
tcf(c_21139,plain,
( ( apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0) )
| ( identity_relation(identity_relation(relation_dom(sK7(powerset(sK1))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_19436]) ).
tcf(c_21140,plain,
( ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) )
| ( identity_relation(identity_relation(relation_dom(sK7(powerset(sK1))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_19436]) ).
tcf(c_21149,plain,
( ( apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0) )
| ( identity_relation(relation_dom(relation_dom(sK7(powerset(sK1))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_19437]) ).
tcf(c_21150,plain,
( ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) )
| ( identity_relation(relation_dom(relation_dom(sK7(powerset(sK1))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_19437]) ).
tcf(c_21167,plain,
( ( apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0) )
| ( relation_dom(relation_dom(relation_dom(sK7(powerset(sK1))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_19440]) ).
tcf(c_21168,plain,
( ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) )
| ( relation_dom(relation_dom(relation_dom(sK7(powerset(sK1))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_19440]) ).
tcf(c_21195,plain,
( ( apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0) )
| ( relation_image(relation_dom(sK7(powerset(sK1))),sK1) = sK1 ) ),
inference(superposition,[status(thm)],[c_5806,c_19444]) ).
tcf(c_21196,plain,
( ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) )
| ( relation_image(relation_dom(sK7(powerset(sK1))),sK1) = sK1 ) ),
inference(superposition,[status(thm)],[c_5807,c_19444]) ).
tcf(c_21207,plain,
! [X0: $i] :
( ( sK7(powerset(sK1)) = X0 )
| ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_5806,c_19450]) ).
tcf(c_21208,plain,
! [X0: $i] :
( ( sK7(powerset(sK1)) = X0 )
| ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_5807,c_19450]) ).
tcf(c_21210,plain,
! [X0: $i] :
( ( sK7(powerset(sK1)) = relation_dom(X0) )
| ~ empty(sK0)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_19450]) ).
tcf(c_21211,plain,
! [X0: $i] :
( ( sK7(powerset(sK1)) = identity_relation(X0) )
| ~ empty(sK0)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_19450]) ).
tcf(c_21212,plain,
( ( sK7(powerset(sK1)) = sK1 )
| ( apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0) )
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_16971,c_19450]) ).
tcf(c_21213,plain,
( ( sK7(powerset(sK1)) = sK1 )
| ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) )
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_9449,c_19450]) ).
tcf(c_21214,plain,
( ( sK7(powerset(sK1)) = sK1 )
| ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_5890,c_19450]) ).
tcf(c_21215,plain,
! [X0: $i] :
( ( relation_image(X0,sK1) = sK7(powerset(sK1)) )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6158,c_19450]) ).
tcf(c_21216,plain,
! [X0: $i] :
( ( sK7(powerset(X0)) = sK7(powerset(sK1)) )
| ~ empty(sK0)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_19450]) ).
tcf(c_21217,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(X0))) = sK7(powerset(sK1)) )
| ~ empty(sK0)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_19450]) ).
tcf(c_21218,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(powerset(X0)))) = sK7(powerset(sK1)) )
| ~ empty(sK0)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_19450]) ).
tcf(c_21220,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(powerset(X0)))) = sK7(powerset(sK1)) )
| ~ empty(sK0)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_19450]) ).
tcf(c_21303,plain,
( in(sK7(sK7(powerset(sK1))),sK0)
| empty(sK7(powerset(sK1))) ),
inference(global_subsumption_just,[status(thm)],[c_19822,c_18746,c_19822]) ).
tcf(c_21304,plain,
( empty(sK7(powerset(sK1)))
| in(sK7(sK7(powerset(sK1))),sK0) ),
inference(renaming,[status(thm)],[c_21303]) ).
tcf(c_21309,plain,
( empty(sK7(powerset(sK1)))
| ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) ) ),
inference(superposition,[status(thm)],[c_21304,c_151]) ).
tcf(c_21310,plain,
( empty(sK7(powerset(sK1)))
| ~ in(sK0,sK7(sK7(powerset(sK1)))) ),
inference(superposition,[status(thm)],[c_21304,c_85]) ).
tcf(c_21321,plain,
( ( apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0) )
| ( relation_dom(sK7(sK6(powerset(sK7(powerset(sK1)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_19402]) ).
tcf(c_21322,plain,
( ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) )
| ( relation_dom(sK7(sK6(powerset(sK7(powerset(sK1)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_19402]) ).
tcf(c_21331,plain,
( ( apply(empty_set,sK7(empty_set)) = sK7(empty_set) )
| ( identity_relation(identity_relation(relation_dom(empty_set))) = empty_set ) ),
inference(superposition,[status(thm)],[c_6104,c_9414]) ).
tcf(c_21332,plain,
( ( apply(identity_relation(powerset(empty_set)),empty_set) = empty_set )
| ( identity_relation(identity_relation(relation_dom(powerset(empty_set)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8004,c_9414]) ).
tcf(c_21334,plain,
( ( apply(identity_relation(sK6(sK6(powerset(empty_set)))),empty_set) = empty_set )
| ( identity_relation(identity_relation(relation_dom(sK6(sK6(powerset(empty_set)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_16755,c_9414]) ).
tcf(c_21335,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(identity_relation(relation_dom(X0))) = empty_set )
| ( relation_image(identity_relation(X0),X1) = X2 )
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),relation_dom(identity_relation(X0)))
| ~ in(sK2(identity_relation(X0),X1,X2),X2)
| ( sK2(identity_relation(X0),X1,X2) != sK7(X0) ) ),
inference(superposition,[status(thm)],[c_9414,c_53]) ).
tcf(c_21336,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0),relation_image(identity_relation(X0),X1))
| ( identity_relation(identity_relation(relation_dom(X0))) = empty_set )
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),relation_dom(identity_relation(X0))) ),
inference(superposition,[status(thm)],[c_9414,c_57]) ).
tcf(c_21340,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0),relation_image(identity_relation(X0),X1))
| ( identity_relation(identity_relation(relation_dom(X0))) = empty_set )
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),X0) ),
inference(light_normalisation,[status(thm)],[c_21336,c_121]) ).
tcf(c_21341,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0),relation_image(identity_relation(X0),X1))
| ( identity_relation(identity_relation(relation_dom(X0))) = empty_set )
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_21340,c_62,c_63]) ).
tcf(c_21346,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(identity_relation(relation_dom(X0))) = empty_set )
| ( relation_image(identity_relation(X0),X1) = X2 )
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),X0)
| ~ in(sK2(identity_relation(X0),X1,X2),X2)
| ( sK2(identity_relation(X0),X1,X2) != sK7(X0) ) ),
inference(light_normalisation,[status(thm)],[c_21335,c_121]) ).
tcf(c_21347,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(identity_relation(relation_dom(X0))) = empty_set )
| ( relation_image(identity_relation(X0),X1) = X2 )
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),X0)
| ~ in(sK2(identity_relation(X0),X1,X2),X2)
| ( sK2(identity_relation(X0),X1,X2) != sK7(X0) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_21346,c_62,c_63]) ).
tcf(c_21361,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK7(powerset(sK7(powerset(X0)))),relation_image(X1,relation_image(X2,sK1))) = sK1 )
| ~ empty(sK0)
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ empty(X0)
| ~ relation(sK7(powerset(sK7(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_20633,c_7115]) ).
tcf(c_21362,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK7(powerset(sK7(powerset(X0)))),sK1) = relation_image(X1,relation_image(X2,sK1)) )
| ~ empty(sK0)
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ empty(X0)
| ~ relation(sK7(powerset(sK7(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_20633,c_6950]) ).
tcf(c_21363,plain,
! [X0: $i,X1: $i] :
( ( relation_image(sK7(powerset(sK7(powerset(X0)))),X1) = sK1 )
| ( apply(identity_relation(relation_dom(sK7(powerset(sK7(powerset(X0)))))),sK3(sK7(powerset(sK7(powerset(X0)))),X1,sK1)) = sK3(sK7(powerset(sK7(powerset(X0)))),X1,sK1) )
| ~ empty(sK0)
| ~ empty(X0)
| ~ relation(sK7(powerset(sK7(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_20633,c_7214]) ).
tcf(c_21364,plain,
! [X0: $i,X1: $i] :
( ( relation_image(sK7(powerset(sK7(powerset(X0)))),X1) = sK1 )
| ( apply(identity_relation(X1),sK3(sK7(powerset(sK7(powerset(X0)))),X1,sK1)) = sK3(sK7(powerset(sK7(powerset(X0)))),X1,sK1) )
| ~ empty(sK0)
| ~ empty(X0)
| ~ relation(sK7(powerset(sK7(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_20633,c_7105]) ).
tcf(c_21365,plain,
! [X0: $i,X1: $i] :
( ( relation_image(sK7(powerset(sK7(powerset(X0)))),sK1) = X1 )
| ( apply(identity_relation(X1),sK2(sK7(powerset(sK7(powerset(X0)))),sK1,X1)) = sK2(sK7(powerset(sK7(powerset(X0)))),sK1,X1) )
| ~ empty(sK0)
| ~ empty(X0)
| ~ relation(sK7(powerset(sK7(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_20633,c_6940]) ).
tcf(c_21366,plain,
! [X0: $i,X1: $i] :
( ( relation_image(sK7(powerset(sK7(powerset(X0)))),relation_image(X1,sK1)) = sK1 )
| ~ empty(sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0)
| ~ relation(sK7(powerset(sK7(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_20633,c_7114]) ).
tcf(c_21367,plain,
! [X0: $i,X1: $i] :
( ( relation_image(sK7(powerset(sK7(powerset(X0)))),sK1) = relation_image(X1,sK1) )
| ~ empty(sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0)
| ~ relation(sK7(powerset(sK7(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_20633,c_6949]) ).
tcf(c_21368,plain,
! [X0: $i] :
( ( relation_image(relation_image(sK7(powerset(sK7(powerset(X0)))),sK1),sK1) = sK1 )
| ~ empty(sK0)
| ~ empty(X0)
| ~ relation(sK7(powerset(sK7(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_20633,c_9208]) ).
tcf(c_21369,plain,
! [X0: $i,X1: $i] :
( ( relation_image(sK7(powerset(sK7(powerset(X0)))),X1) = sK1 )
| ( apply(sK7(powerset(sK7(powerset(X0)))),sK3(sK7(powerset(sK7(powerset(X0)))),X1,sK1)) = sK2(sK7(powerset(sK7(powerset(X0)))),X1,sK1) )
| ~ empty(sK0)
| ~ empty(X0)
| ~ relation(sK7(powerset(sK7(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_20633,c_7707]) ).
tcf(c_21371,plain,
! [X0: $i] :
( ( relation_image(sK7(powerset(sK7(powerset(X0)))),sK1) = empty_set )
| ~ empty(sK0)
| ~ empty(X0)
| ~ relation(sK7(powerset(sK7(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_20633,c_6198]) ).
tcf(c_21509,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(powerset(relation_dom(X0))))) = empty_set )
| ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) ) ),
inference(superposition,[status(thm)],[c_5806,c_11431]) ).
tcf(c_21510,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( relation_dom(relation_dom(sK7(powerset(relation_dom(X0))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_11431]) ).
tcf(c_21511,plain,
relation_dom(relation_dom(sK7(powerset(relation_dom(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_11431]) ).
tcf(c_21512,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(powerset(relation_dom(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_11431]) ).
tcf(c_21513,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(powerset(relation_dom(identity_relation(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_11431]) ).
tcf(c_21514,plain,
( ( apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0) )
| ( relation_dom(relation_dom(sK7(powerset(relation_dom(sK1))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_16971,c_11431]) ).
tcf(c_21515,plain,
( ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) )
| ( relation_dom(relation_dom(sK7(powerset(relation_dom(sK1))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_9449,c_11431]) ).
tcf(c_21516,plain,
( ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ( relation_dom(relation_dom(sK7(powerset(relation_dom(sK1))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5890,c_11431]) ).
tcf(c_21517,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(powerset(relation_dom(relation_image(X0,sK1)))))) = empty_set )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6158,c_11431]) ).
tcf(c_21518,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(powerset(relation_dom(sK7(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_11431]) ).
tcf(c_21519,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(powerset(relation_dom(sK7(sK6(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_11431]) ).
tcf(c_21520,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(powerset(relation_dom(sK7(sK6(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_11431]) ).
tcf(c_21521,plain,
( ( relation_dom(relation_dom(sK7(powerset(relation_dom(sK7(powerset(sK1))))))) = empty_set )
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_18746,c_11431]) ).
tcf(c_21522,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(powerset(relation_dom(sK7(powerset(sK7(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_11431]) ).
tcf(c_21615,plain,
( ( apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0) )
| ( identity_relation(sK7(sK6(powerset(sK7(powerset(sK1)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_19403]) ).
tcf(c_21616,plain,
( ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) )
| ( identity_relation(sK7(sK6(powerset(sK7(powerset(sK1)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_19403]) ).
tcf(c_21625,plain,
( ( apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0) )
| ( sK7(sK6(sK6(powerset(sK7(powerset(sK1)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_19404]) ).
tcf(c_21626,plain,
( ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) )
| ( sK7(sK6(sK6(powerset(sK7(powerset(sK1)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_19404]) ).
tcf(c_21635,plain,
( ( apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0) )
| ( sK7(powerset(identity_relation(identity_relation(sK7(powerset(sK1)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_19408]) ).
tcf(c_21636,plain,
( ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) )
| ( sK7(powerset(identity_relation(identity_relation(sK7(powerset(sK1)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_19408]) ).
tcf(c_21645,plain,
( ( apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0) )
| ( identity_relation(identity_relation(identity_relation(identity_relation(sK7(powerset(sK1)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_19409]) ).
tcf(c_21646,plain,
( ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) )
| ( identity_relation(identity_relation(identity_relation(identity_relation(sK7(powerset(sK1)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_19409]) ).
tcf(c_21655,plain,
( ( apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0) )
| ( sK7(sK6(powerset(relation_dom(sK7(powerset(sK1)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_19410]) ).
tcf(c_21656,plain,
( ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) )
| ( sK7(sK6(powerset(relation_dom(sK7(powerset(sK1)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_19410]) ).
tcf(c_21665,plain,
( ( apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0) )
| ( sK7(powerset(identity_relation(relation_dom(sK7(powerset(sK1)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_19411]) ).
tcf(c_21666,plain,
( ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) )
| ( sK7(powerset(identity_relation(relation_dom(sK7(powerset(sK1)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_19411]) ).
tcf(c_21685,plain,
( ( apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0) )
| ( identity_relation(identity_relation(identity_relation(relation_dom(sK7(powerset(sK1)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_19412]) ).
tcf(c_21686,plain,
( ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) )
| ( identity_relation(identity_relation(identity_relation(relation_dom(sK7(powerset(sK1)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_19412]) ).
tcf(c_21699,plain,
( ( apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0) )
| ( relation_dom(sK7(powerset(identity_relation(sK7(powerset(sK1)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_19413]) ).
tcf(c_21700,plain,
( ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) )
| ( relation_dom(sK7(powerset(identity_relation(sK7(powerset(sK1)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_19413]) ).
tcf(c_21731,plain,
( ( apply(empty_set,sK7(empty_set)) = sK7(empty_set) )
| ( identity_relation(relation_dom(relation_dom(empty_set))) = empty_set ) ),
inference(superposition,[status(thm)],[c_6104,c_9415]) ).
tcf(c_21732,plain,
( ( apply(identity_relation(powerset(empty_set)),empty_set) = empty_set )
| ( identity_relation(relation_dom(relation_dom(powerset(empty_set)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8004,c_9415]) ).
tcf(c_21734,plain,
( ( apply(identity_relation(sK6(sK6(powerset(empty_set)))),empty_set) = empty_set )
| ( identity_relation(relation_dom(relation_dom(sK6(sK6(powerset(empty_set)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_16755,c_9415]) ).
tcf(c_21735,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(relation_dom(relation_dom(X0))) = empty_set )
| ( relation_image(identity_relation(X0),X1) = X2 )
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),relation_dom(identity_relation(X0)))
| ~ in(sK2(identity_relation(X0),X1,X2),X2)
| ( sK2(identity_relation(X0),X1,X2) != sK7(X0) ) ),
inference(superposition,[status(thm)],[c_9415,c_53]) ).
tcf(c_21736,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0),relation_image(identity_relation(X0),X1))
| ( identity_relation(relation_dom(relation_dom(X0))) = empty_set )
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),relation_dom(identity_relation(X0))) ),
inference(superposition,[status(thm)],[c_9415,c_57]) ).
tcf(c_21740,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0),relation_image(identity_relation(X0),X1))
| ( identity_relation(relation_dom(relation_dom(X0))) = empty_set )
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),X0) ),
inference(light_normalisation,[status(thm)],[c_21736,c_121]) ).
tcf(c_21741,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0),relation_image(identity_relation(X0),X1))
| ( identity_relation(relation_dom(relation_dom(X0))) = empty_set )
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_21740,c_62,c_63]) ).
tcf(c_21746,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(relation_dom(relation_dom(X0))) = empty_set )
| ( relation_image(identity_relation(X0),X1) = X2 )
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),X0)
| ~ in(sK2(identity_relation(X0),X1,X2),X2)
| ( sK2(identity_relation(X0),X1,X2) != sK7(X0) ) ),
inference(light_normalisation,[status(thm)],[c_21735,c_121]) ).
tcf(c_21747,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(relation_dom(relation_dom(X0))) = empty_set )
| ( relation_image(identity_relation(X0),X1) = X2 )
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),X0)
| ~ in(sK2(identity_relation(X0),X1,X2),X2)
| ( sK2(identity_relation(X0),X1,X2) != sK7(X0) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_21746,c_62,c_63]) ).
tcf(c_21760,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(X0))))) = empty_set )
| ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) ) ),
inference(superposition,[status(thm)],[c_5806,c_11953]) ).
tcf(c_21761,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(X0))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_11953]) ).
tcf(c_21762,plain,
relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_11953]) ).
tcf(c_21763,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_86,c_11953]) ).
tcf(c_21764,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(identity_relation(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_11953]) ).
tcf(c_21765,plain,
( ( apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0) )
| ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK1))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_16971,c_11953]) ).
tcf(c_21766,plain,
( ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) )
| ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK1))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_9449,c_11953]) ).
tcf(c_21767,plain,
( ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK1))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5890,c_11953]) ).
tcf(c_21768,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_image(X0,sK1)))))) = empty_set )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6158,c_11953]) ).
tcf(c_21769,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK7(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_11953]) ).
tcf(c_21770,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK7(sK6(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_11953]) ).
tcf(c_21771,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK7(sK6(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_11953]) ).
tcf(c_21772,plain,
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK7(powerset(sK1))))))) = empty_set )
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_18746,c_11953]) ).
tcf(c_21773,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK7(powerset(sK7(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_11953]) ).
tcf(c_21911,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(relation_dom(relation_dom(X0))))) = empty_set )
| ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) ) ),
inference(superposition,[status(thm)],[c_5806,c_12027]) ).
tcf(c_21912,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( identity_relation(relation_dom(relation_dom(relation_dom(relation_dom(X0))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_12027]) ).
tcf(c_21913,plain,
identity_relation(relation_dom(relation_dom(relation_dom(relation_dom(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_12027]) ).
tcf(c_21914,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_12027]) ).
tcf(c_21915,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(relation_dom(relation_dom(identity_relation(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_12027]) ).
tcf(c_21916,plain,
( ( apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0) )
| ( identity_relation(relation_dom(relation_dom(relation_dom(relation_dom(sK1))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_16971,c_12027]) ).
tcf(c_21917,plain,
( ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) )
| ( identity_relation(relation_dom(relation_dom(relation_dom(relation_dom(sK1))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_9449,c_12027]) ).
tcf(c_21918,plain,
( ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ( identity_relation(relation_dom(relation_dom(relation_dom(relation_dom(sK1))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5890,c_12027]) ).
tcf(c_21919,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(relation_dom(relation_dom(relation_image(X0,sK1)))))) = empty_set )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6158,c_12027]) ).
tcf(c_21920,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(relation_dom(relation_dom(sK7(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_12027]) ).
tcf(c_21921,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(relation_dom(relation_dom(sK7(sK6(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_12027]) ).
tcf(c_21922,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(relation_dom(relation_dom(sK7(sK6(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_12027]) ).
tcf(c_21923,plain,
( ( identity_relation(relation_dom(relation_dom(relation_dom(relation_dom(sK7(powerset(sK1))))))) = empty_set )
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_18746,c_12027]) ).
tcf(c_21924,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(relation_dom(relation_dom(sK7(powerset(sK7(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_12027]) ).
tcf(c_22028,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(relation_dom(relation_dom(X0))))) = empty_set )
| ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) ) ),
inference(superposition,[status(thm)],[c_5806,c_12063]) ).
tcf(c_22029,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( identity_relation(identity_relation(relation_dom(relation_dom(relation_dom(X0))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_12063]) ).
tcf(c_22030,plain,
identity_relation(identity_relation(relation_dom(relation_dom(relation_dom(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_12063]) ).
tcf(c_22031,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(relation_dom(relation_dom(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_12063]) ).
tcf(c_22032,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(relation_dom(relation_dom(identity_relation(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_12063]) ).
tcf(c_22033,plain,
( ( apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0) )
| ( identity_relation(identity_relation(relation_dom(relation_dom(relation_dom(sK1))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_16971,c_12063]) ).
tcf(c_22034,plain,
( ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) )
| ( identity_relation(identity_relation(relation_dom(relation_dom(relation_dom(sK1))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_9449,c_12063]) ).
tcf(c_22035,plain,
( ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ( identity_relation(identity_relation(relation_dom(relation_dom(relation_dom(sK1))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5890,c_12063]) ).
tcf(c_22036,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(relation_dom(relation_dom(relation_image(X0,sK1)))))) = empty_set )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6158,c_12063]) ).
tcf(c_22037,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(relation_dom(relation_dom(sK7(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_12063]) ).
tcf(c_22038,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(relation_dom(relation_dom(sK7(sK6(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_12063]) ).
tcf(c_22039,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(relation_dom(relation_dom(sK7(sK6(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_12063]) ).
tcf(c_22040,plain,
( ( identity_relation(identity_relation(relation_dom(relation_dom(relation_dom(sK7(powerset(sK1))))))) = empty_set )
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_18746,c_12063]) ).
tcf(c_22041,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(relation_dom(relation_dom(sK7(powerset(sK7(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_12063]) ).
tcf(c_22118,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(relation_dom(relation_dom(X0))))) = empty_set )
| ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) ) ),
inference(superposition,[status(thm)],[c_5806,c_12099]) ).
tcf(c_22119,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( sK7(powerset(relation_dom(relation_dom(relation_dom(X0))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_12099]) ).
tcf(c_22120,plain,
sK7(powerset(relation_dom(relation_dom(relation_dom(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_12099]) ).
tcf(c_22121,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(relation_dom(relation_dom(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_12099]) ).
tcf(c_22122,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(relation_dom(relation_dom(identity_relation(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_12099]) ).
tcf(c_22123,plain,
( ( sK7(powerset(relation_dom(relation_dom(relation_dom(sK1))))) = empty_set )
| ( apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0) ) ),
inference(superposition,[status(thm)],[c_16971,c_12099]) ).
tcf(c_22124,plain,
( ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) )
| ( sK7(powerset(relation_dom(relation_dom(relation_dom(sK1))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_9449,c_12099]) ).
tcf(c_22125,plain,
( ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ( sK7(powerset(relation_dom(relation_dom(relation_dom(sK1))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5890,c_12099]) ).
tcf(c_22126,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(relation_dom(relation_dom(relation_image(X0,sK1)))))) = empty_set )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6158,c_12099]) ).
tcf(c_22127,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(relation_dom(relation_dom(sK7(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_12099]) ).
tcf(c_22128,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(relation_dom(relation_dom(sK7(sK6(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_12099]) ).
tcf(c_22129,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(relation_dom(relation_dom(sK7(sK6(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_12099]) ).
tcf(c_22130,plain,
( ( sK7(powerset(relation_dom(relation_dom(relation_dom(sK7(powerset(sK1))))))) = empty_set )
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_18746,c_12099]) ).
tcf(c_22131,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(relation_dom(relation_dom(sK7(powerset(sK7(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_12099]) ).
tcf(c_22209,plain,
( ( apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0) )
| ( identity_relation(sK7(powerset(identity_relation(sK7(powerset(sK1)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_19414]) ).
tcf(c_22210,plain,
( ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) )
| ( identity_relation(sK7(powerset(identity_relation(sK7(powerset(sK1)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_19414]) ).
tcf(c_22219,plain,
( ( apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0) )
| ( relation_dom(sK7(powerset(relation_dom(sK7(powerset(sK1)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_19415]) ).
tcf(c_22220,plain,
( ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) )
| ( relation_dom(sK7(powerset(relation_dom(sK7(powerset(sK1)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_19415]) ).
tcf(c_22229,plain,
( ( apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0) )
| ( identity_relation(sK7(powerset(relation_dom(sK7(powerset(sK1)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_19416]) ).
tcf(c_22230,plain,
( ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) )
| ( identity_relation(sK7(powerset(relation_dom(sK7(powerset(sK1)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_19416]) ).
tcf(c_22239,plain,
( ( apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0) )
| ( sK7(powerset(sK7(powerset(sK7(powerset(sK1)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_19417]) ).
tcf(c_22240,plain,
( ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) )
| ( sK7(powerset(sK7(powerset(sK7(powerset(sK1)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_19417]) ).
tcf(c_22256,plain,
( ( apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0) )
| ( identity_relation(identity_relation(sK7(powerset(sK7(powerset(sK1)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_19418]) ).
tcf(c_22257,plain,
( ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) )
| ( identity_relation(identity_relation(sK7(powerset(sK7(powerset(sK1)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_19418]) ).
tcf(c_22266,plain,
( ( apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0) )
| ( identity_relation(relation_dom(sK7(powerset(sK7(powerset(sK1)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_19419]) ).
tcf(c_22267,plain,
( ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) )
| ( identity_relation(relation_dom(sK7(powerset(sK7(powerset(sK1)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_19419]) ).
tcf(c_22276,plain,
( ( apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0) )
| ( sK7(powerset(relation_dom(relation_dom(sK7(powerset(sK1)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_19420]) ).
tcf(c_22277,plain,
( ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) )
| ( sK7(powerset(relation_dom(relation_dom(sK7(powerset(sK1)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_19420]) ).
tcf(c_22286,plain,
( ( apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0) )
| ( identity_relation(identity_relation(relation_dom(relation_dom(sK7(powerset(sK1)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_19421]) ).
tcf(c_22287,plain,
( ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) )
| ( identity_relation(identity_relation(relation_dom(relation_dom(sK7(powerset(sK1)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_19421]) ).
tcf(c_22299,plain,
( ( apply(empty_set,sK7(empty_set)) = sK7(empty_set) )
| ( relation_dom(relation_dom(relation_dom(empty_set))) = empty_set ) ),
inference(superposition,[status(thm)],[c_6104,c_9418]) ).
tcf(c_22300,plain,
( ( apply(identity_relation(powerset(empty_set)),empty_set) = empty_set )
| ( relation_dom(relation_dom(relation_dom(powerset(empty_set)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8004,c_9418]) ).
tcf(c_22302,plain,
( ( apply(identity_relation(sK6(sK6(powerset(empty_set)))),empty_set) = empty_set )
| ( relation_dom(relation_dom(relation_dom(sK6(sK6(powerset(empty_set)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_16755,c_9418]) ).
tcf(c_22303,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_dom(relation_dom(X0))) = empty_set )
| ( relation_image(identity_relation(X0),X1) = X2 )
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),relation_dom(identity_relation(X0)))
| ~ in(sK2(identity_relation(X0),X1,X2),X2)
| ( sK2(identity_relation(X0),X1,X2) != sK7(X0) ) ),
inference(superposition,[status(thm)],[c_9418,c_53]) ).
tcf(c_22304,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0),relation_image(identity_relation(X0),X1))
| ( relation_dom(relation_dom(relation_dom(X0))) = empty_set )
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),relation_dom(identity_relation(X0))) ),
inference(superposition,[status(thm)],[c_9418,c_57]) ).
tcf(c_22308,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0),relation_image(identity_relation(X0),X1))
| ( relation_dom(relation_dom(relation_dom(X0))) = empty_set )
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),X0) ),
inference(light_normalisation,[status(thm)],[c_22304,c_121]) ).
tcf(c_22309,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0),relation_image(identity_relation(X0),X1))
| ( relation_dom(relation_dom(relation_dom(X0))) = empty_set )
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_22308,c_62,c_63]) ).
tcf(c_22314,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_dom(relation_dom(X0))) = empty_set )
| ( relation_image(identity_relation(X0),X1) = X2 )
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),X0)
| ~ in(sK2(identity_relation(X0),X1,X2),X2)
| ( sK2(identity_relation(X0),X1,X2) != sK7(X0) ) ),
inference(light_normalisation,[status(thm)],[c_22303,c_121]) ).
tcf(c_22315,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_dom(relation_dom(X0))) = empty_set )
| ( relation_image(identity_relation(X0),X1) = X2 )
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),X0)
| ~ in(sK2(identity_relation(X0),X1,X2),X2)
| ( sK2(identity_relation(X0),X1,X2) != sK7(X0) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_22314,c_62,c_63]) ).
tcf(c_22335,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(powerset(relation_dom(X0))))) = empty_set )
| ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) ) ),
inference(superposition,[status(thm)],[c_5806,c_12135]) ).
tcf(c_22336,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( identity_relation(relation_dom(sK7(powerset(relation_dom(X0))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_12135]) ).
tcf(c_22337,plain,
identity_relation(relation_dom(sK7(powerset(relation_dom(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_12135]) ).
tcf(c_22338,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(powerset(relation_dom(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_12135]) ).
tcf(c_22339,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(powerset(relation_dom(identity_relation(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_12135]) ).
tcf(c_22340,plain,
( ( apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0) )
| ( identity_relation(relation_dom(sK7(powerset(relation_dom(sK1))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_16971,c_12135]) ).
tcf(c_22341,plain,
( ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) )
| ( identity_relation(relation_dom(sK7(powerset(relation_dom(sK1))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_9449,c_12135]) ).
tcf(c_22342,plain,
( ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ( identity_relation(relation_dom(sK7(powerset(relation_dom(sK1))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5890,c_12135]) ).
tcf(c_22343,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(powerset(relation_dom(relation_image(X0,sK1)))))) = empty_set )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6158,c_12135]) ).
tcf(c_22344,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(powerset(relation_dom(sK7(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_12135]) ).
tcf(c_22345,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(powerset(relation_dom(sK7(sK6(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_12135]) ).
tcf(c_22346,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(powerset(relation_dom(sK7(sK6(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_12135]) ).
tcf(c_22347,plain,
( ( identity_relation(relation_dom(sK7(powerset(relation_dom(sK7(powerset(sK1))))))) = empty_set )
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_18746,c_12135]) ).
tcf(c_22348,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(powerset(relation_dom(sK7(powerset(sK7(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_12135]) ).
tcf(c_22423,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(powerset(relation_dom(X0))))) = empty_set )
| ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) ) ),
inference(superposition,[status(thm)],[c_5806,c_12212]) ).
tcf(c_22424,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( identity_relation(identity_relation(sK7(powerset(relation_dom(X0))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_12212]) ).
tcf(c_22425,plain,
identity_relation(identity_relation(sK7(powerset(relation_dom(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_12212]) ).
tcf(c_22426,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(powerset(relation_dom(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_12212]) ).
tcf(c_22427,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(powerset(relation_dom(identity_relation(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_12212]) ).
tcf(c_22428,plain,
( ( apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0) )
| ( identity_relation(identity_relation(sK7(powerset(relation_dom(sK1))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_16971,c_12212]) ).
tcf(c_22429,plain,
( ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) )
| ( identity_relation(identity_relation(sK7(powerset(relation_dom(sK1))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_9449,c_12212]) ).
tcf(c_22430,plain,
( ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ( identity_relation(identity_relation(sK7(powerset(relation_dom(sK1))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5890,c_12212]) ).
tcf(c_22431,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(powerset(relation_dom(relation_image(X0,sK1)))))) = empty_set )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6158,c_12212]) ).
tcf(c_22432,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(powerset(relation_dom(sK7(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_12212]) ).
tcf(c_22433,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(powerset(relation_dom(sK7(sK6(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_12212]) ).
tcf(c_22434,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(powerset(relation_dom(sK7(sK6(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_12212]) ).
tcf(c_22435,plain,
( ( identity_relation(identity_relation(sK7(powerset(relation_dom(sK7(powerset(sK1))))))) = empty_set )
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_18746,c_12212]) ).
tcf(c_22436,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(powerset(relation_dom(sK7(powerset(sK7(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_12212]) ).
tcf(c_22498,plain,
( ~ empty(sK1)
| ~ in(sK3(identity_relation(sK0),sK1,sK1),sK1) ),
inference(instantiation,[status(thm)],[c_84]) ).
tcf(c_22512,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(powerset(relation_dom(X0))))) = empty_set )
| ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) ) ),
inference(superposition,[status(thm)],[c_5806,c_12318]) ).
tcf(c_22513,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( sK7(powerset(sK7(powerset(relation_dom(X0))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_12318]) ).
tcf(c_22514,plain,
sK7(powerset(sK7(powerset(relation_dom(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_12318]) ).
tcf(c_22515,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(powerset(relation_dom(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_12318]) ).
tcf(c_22516,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(powerset(relation_dom(identity_relation(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_12318]) ).
tcf(c_22517,plain,
( ( sK7(powerset(sK7(powerset(relation_dom(sK1))))) = empty_set )
| ( apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0) ) ),
inference(superposition,[status(thm)],[c_16971,c_12318]) ).
tcf(c_22518,plain,
( ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) )
| ( sK7(powerset(sK7(powerset(relation_dom(sK1))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_9449,c_12318]) ).
tcf(c_22519,plain,
( ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ( sK7(powerset(sK7(powerset(relation_dom(sK1))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5890,c_12318]) ).
tcf(c_22520,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(powerset(relation_dom(relation_image(X0,sK1)))))) = empty_set )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6158,c_12318]) ).
tcf(c_22521,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(powerset(relation_dom(sK7(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_12318]) ).
tcf(c_22522,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(powerset(relation_dom(sK7(sK6(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_12318]) ).
tcf(c_22523,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(powerset(relation_dom(sK7(sK6(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_12318]) ).
tcf(c_22524,plain,
( ( sK7(powerset(sK7(powerset(relation_dom(sK7(powerset(sK1))))))) = empty_set )
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_18746,c_12318]) ).
tcf(c_22525,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(powerset(relation_dom(sK7(powerset(sK7(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_12318]) ).
tcf(c_23161,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(relation_dom(relation_dom(X0))))) = empty_set )
| ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) ) ),
inference(superposition,[status(thm)],[c_5806,c_12356]) ).
tcf(c_23162,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( identity_relation(sK7(powerset(relation_dom(relation_dom(X0))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_12356]) ).
tcf(c_23163,plain,
identity_relation(sK7(powerset(relation_dom(relation_dom(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_12356]) ).
tcf(c_23164,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(relation_dom(relation_dom(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_12356]) ).
tcf(c_23165,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(relation_dom(relation_dom(identity_relation(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_12356]) ).
tcf(c_23166,plain,
( ( apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0) )
| ( identity_relation(sK7(powerset(relation_dom(relation_dom(sK1))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_16971,c_12356]) ).
tcf(c_23167,plain,
( ( apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0) )
| ( identity_relation(sK7(powerset(relation_dom(relation_dom(sK1))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_9449,c_12356]) ).
tcf(c_23168,plain,
( ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ( identity_relation(sK7(powerset(relation_dom(relation_dom(sK1))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5890,c_12356]) ).
tcf(c_23169,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(relation_dom(relation_dom(relation_image(X0,sK1)))))) = empty_set )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6158,c_12356]) ).
tcf(c_23170,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(relation_dom(relation_dom(sK7(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_12356]) ).
tcf(c_23171,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(relation_dom(relation_dom(sK7(sK6(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_12356]) ).
tcf(c_23172,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(relation_dom(relation_dom(sK7(sK6(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_12356]) ).
tcf(c_23173,plain,
( ( identity_relation(sK7(powerset(relation_dom(relation_dom(sK7(powerset(sK1))))))) = empty_set )
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_18746,c_12356]) ).
tcf(c_23174,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(relation_dom(relation_dom(sK7(powerset(sK7(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_12356]) ).
tcf(c_23265,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(relation_dom(relation_dom(relation_image(X0,empty_set)))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_12356]) ).
tcf(c_23266,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(powerset(relation_dom(relation_image(X0,empty_set)))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_12318]) ).
tcf(c_23267,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(powerset(relation_dom(relation_image(X0,empty_set)))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_12212]) ).
tcf(c_23268,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(powerset(relation_dom(relation_image(X0,empty_set)))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_12135]) ).
tcf(c_23269,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(relation_dom(relation_dom(relation_image(X0,empty_set)))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_12099]) ).
tcf(c_23270,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(relation_dom(relation_dom(relation_image(X0,empty_set)))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_12063]) ).
tcf(c_23271,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(relation_dom(relation_dom(relation_image(X0,empty_set)))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_12027]) ).
tcf(c_23272,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_18616,c_11953]) ).
tcf(c_23273,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(powerset(relation_dom(relation_image(X0,empty_set)))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_11431]) ).
tcf(c_23274,plain,
! [X0: $i] :
( ( relation_image(X0,empty_set) = sK7(powerset(sK1)) )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_19450]) ).
tcf(c_23275,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(relation_image(X1,empty_set))) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18616,c_9347]) ).
tcf(c_23276,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_image(X1,empty_set))) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18616,c_9319]) ).
tcf(c_23277,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(relation_image(X1,empty_set))) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18616,c_6877]) ).
tcf(c_23278,plain,
! [X0: $i,X1: $i] :
( ( relation_image(relation_dom(relation_image(X0,empty_set)),X1) = sK1 )
| ( apply(relation_dom(relation_image(X0,empty_set)),sK3(relation_dom(relation_image(X0,empty_set)),X1,sK1)) = sK2(relation_dom(relation_image(X0,empty_set)),X1,sK1) )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_18242]) ).
tcf(c_23279,plain,
! [X0: $i] :
( ( relation_dom(sK7(sK6(powerset(relation_image(X0,empty_set))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_10680]) ).
tcf(c_23280,plain,
! [X0: $i] :
( ( identity_relation(sK7(sK6(powerset(relation_image(X0,empty_set))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_10678]) ).
tcf(c_23281,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(powerset(relation_image(X0,empty_set))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_15645]) ).
tcf(c_23282,plain,
! [X0: $i] :
( ( relation_image(sK7(sK6(sK6(powerset(relation_image(X0,empty_set))))),sK1) = sK1 )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_16314]) ).
tcf(c_23283,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X1,sK7(sK6(sK6(powerset(relation_image(X0,empty_set)))))) = sK1 )
| ~ empty(sK0)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_15105]) ).
tcf(c_23284,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(sK6(powerset(relation_image(X0,empty_set))))) = relation_image(X1,sK1) )
| ~ empty(sK0)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_15101]) ).
tcf(c_23285,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(identity_relation(relation_image(X0,empty_set))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_9748]) ).
tcf(c_23286,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(relation_image(X0,empty_set))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_9682]) ).
tcf(c_23287,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(relation_dom(relation_image(X0,empty_set))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_11340]) ).
tcf(c_23288,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(relation_dom(relation_image(X0,empty_set))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_9747]) ).
tcf(c_23289,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(relation_dom(relation_image(X0,empty_set))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_9681]) ).
tcf(c_23290,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(identity_relation(relation_image(X0,empty_set))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_9115]) ).
tcf(c_23291,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(identity_relation(relation_image(X0,empty_set))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_9088]) ).
tcf(c_23292,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(relation_dom(relation_image(X0,empty_set))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_9114]) ).
tcf(c_23293,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(relation_dom(relation_image(X0,empty_set))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_9087]) ).
tcf(c_23294,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(powerset(relation_image(X0,empty_set))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_8009]) ).
tcf(c_23295,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(powerset(relation_image(X0,empty_set))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_7966]) ).
tcf(c_23296,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(powerset(relation_image(X0,empty_set))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_7938]) ).
tcf(c_23297,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(relation_dom(relation_image(X0,empty_set))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_9017]) ).
tcf(c_23298,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(relation_dom(relation_image(X0,empty_set))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_8992]) ).
tcf(c_23299,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(relation_dom(relation_image(X0,empty_set))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_8957]) ).
tcf(c_23300,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_18616,c_8561]) ).
tcf(c_23301,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(powerset(relation_image(X0,empty_set))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_6875]) ).
tcf(c_23302,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(relation_image(X0,empty_set)))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_10681]) ).
tcf(c_23303,plain,
! [X0: $i] :
( ( relation_image(sK7(sK6(powerset(relation_image(X0,empty_set)))),sK1) = sK1 )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_11188]) ).
tcf(c_23304,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X1,sK7(sK6(powerset(relation_image(X0,empty_set))))) = sK1 )
| ~ empty(sK0)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_10420]) ).
tcf(c_23305,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(powerset(relation_image(X0,empty_set)))) = relation_image(X1,sK1) )
| ~ empty(sK0)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_10418]) ).
tcf(c_23306,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(relation_image(X0,empty_set)))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_8006]) ).
tcf(c_23307,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(relation_image(X0,empty_set)))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_7963]) ).
tcf(c_23308,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_image(X1,empty_set)) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18616,c_5794]) ).
tcf(c_23309,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_image(X1,empty_set)) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18616,c_5793]) ).
tcf(c_23310,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(relation_image(X0,empty_set)))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_6878]) ).
tcf(c_23311,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(relation_image(X0,empty_set)))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_6876]) ).
tcf(c_23312,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(relation_image(X0,empty_set)))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_8005]) ).
tcf(c_23313,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(relation_image(X0,empty_set)))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_7962]) ).
tcf(c_23314,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(relation_image(X0,empty_set)))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_7934]) ).
tcf(c_23315,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X1,sK7(powerset(relation_image(X0,empty_set)))) = sK1 )
| ~ empty(sK0)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_7111]) ).
tcf(c_23316,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(relation_image(X0,empty_set))) = relation_image(X1,sK1) )
| ~ empty(sK0)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_6946]) ).
tcf(c_23317,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_18616,c_6133]) ).
tcf(c_23318,plain,
! [X0: $i] :
( ( relation_image(sK7(powerset(relation_image(X0,empty_set))),sK1) = sK1 )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_8316]) ).
tcf(c_23320,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X1,relation_image(X0,empty_set)) = sK1 )
| ~ empty(sK0)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_7107]) ).
tcf(c_23321,plain,
! [X0: $i] :
( ( relation_image(relation_dom(relation_image(X0,empty_set)),sK1) = sK1 )
| ~ empty(sK0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_8131]) ).
tcf(c_23322,plain,
! [X0: $i] :
( ( sK7(powerset(relation_image(X0,empty_set))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_6879]) ).
tcf(c_23323,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_image(X0,empty_set))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_6106]) ).
tcf(c_23324,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_image(X0,empty_set))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_6105]) ).
tcf(c_23325,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_image(X0,empty_set))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_5747]) ).
tcf(c_23326,plain,
! [X0: $i] :
( ( identity_relation(relation_image(X0,empty_set)) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_5776]) ).
tcf(c_23327,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X1,empty_set) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18616,c_51]) ).
tcf(c_23328,plain,
! [X0: $i] :
( ( relation_dom(relation_image(X0,empty_set)) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_5663]) ).
tcf(c_23329,plain,
! [X0: $i] :
( ( relation_image(X0,empty_set) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_52]) ).
tcf(c_23330,plain,
! [X0: $i] :
( function(relation_image(X0,empty_set))
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_98]) ).
tcf(c_23331,plain,
! [X0: $i] :
( relation(relation_image(X0,empty_set))
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_80]) ).
tcf(c_23871,plain,
( empty(sK7(powerset(empty_set)))
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_11339,c_18755]) ).
tcf(c_23872,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(relation_dom(relation_dom(sK7(powerset(sK7(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_12356]) ).
tcf(c_23873,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(powerset(relation_dom(sK7(powerset(sK7(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_12318]) ).
tcf(c_23874,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(powerset(relation_dom(sK7(powerset(sK7(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_12212]) ).
tcf(c_23875,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(powerset(relation_dom(sK7(powerset(sK7(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_12135]) ).
tcf(c_23876,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(relation_dom(relation_dom(sK7(powerset(sK7(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_12099]) ).
tcf(c_23877,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(relation_dom(relation_dom(sK7(powerset(sK7(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_12063]) ).
tcf(c_23878,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(relation_dom(relation_dom(sK7(powerset(sK7(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_12027]) ).
tcf(c_23879,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK7(powerset(sK7(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_11953]) ).
tcf(c_23880,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(powerset(relation_dom(sK7(powerset(sK7(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_11431]) ).
tcf(c_23881,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(sK6(powerset(X0))))) = sK7(powerset(sK1)) )
| ~ empty(sK0)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_19450]) ).
tcf(c_23882,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(sK7(powerset(sK7(sK6(powerset(X0))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_9347]) ).
tcf(c_23883,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK7(powerset(sK7(sK6(powerset(X0))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_9319]) ).
tcf(c_23884,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(sK7(powerset(sK7(sK6(powerset(X0))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_6877]) ).
tcf(c_23885,plain,
! [X0: $i,X1: $i] :
( ( relation_image(relation_dom(sK7(powerset(sK7(sK6(powerset(X0)))))),X1) = sK1 )
| ( apply(relation_dom(sK7(powerset(sK7(sK6(powerset(X0)))))),sK3(relation_dom(sK7(powerset(sK7(sK6(powerset(X0)))))),X1,sK1)) = sK2(relation_dom(sK7(powerset(sK7(sK6(powerset(X0)))))),X1,sK1) )
| ~ empty(sK0)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_18242]) ).
tcf(c_23886,plain,
! [X0: $i] :
( ( relation_dom(sK7(sK6(powerset(sK7(powerset(sK7(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_10680]) ).
tcf(c_23887,plain,
! [X0: $i] :
( ( identity_relation(sK7(sK6(powerset(sK7(powerset(sK7(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_10678]) ).
tcf(c_23888,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(powerset(sK7(powerset(sK7(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_15645]) ).
tcf(c_23889,plain,
! [X0: $i] :
( ( relation_image(sK7(sK6(sK6(powerset(sK7(powerset(sK7(sK6(powerset(X0))))))))),sK1) = sK1 )
| ~ empty(sK0)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_16314]) ).
tcf(c_23890,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X1,sK7(sK6(sK6(powerset(sK7(powerset(sK7(sK6(powerset(X0)))))))))) = sK1 )
| ~ empty(sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_15105]) ).
tcf(c_23891,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(sK6(powerset(sK7(powerset(sK7(sK6(powerset(X0))))))))) = relation_image(X1,sK1) )
| ~ empty(sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_15101]) ).
tcf(c_23892,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(identity_relation(sK7(powerset(sK7(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_9748]) ).
tcf(c_23893,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(sK7(powerset(sK7(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_9682]) ).
tcf(c_23894,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(relation_dom(sK7(powerset(sK7(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_11340]) ).
tcf(c_23895,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(relation_dom(sK7(powerset(sK7(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_9747]) ).
tcf(c_23896,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(relation_dom(sK7(powerset(sK7(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_9681]) ).
tcf(c_23897,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(identity_relation(sK7(powerset(sK7(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_9115]) ).
tcf(c_23898,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(identity_relation(sK7(powerset(sK7(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_9088]) ).
tcf(c_23899,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(relation_dom(sK7(powerset(sK7(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_9114]) ).
tcf(c_23900,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(relation_dom(sK7(powerset(sK7(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_9087]) ).
tcf(c_23901,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(powerset(sK7(powerset(sK7(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_8009]) ).
tcf(c_23902,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(powerset(sK7(powerset(sK7(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_7966]) ).
tcf(c_23903,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(powerset(sK7(powerset(sK7(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_7938]) ).
tcf(c_23904,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(relation_dom(sK7(powerset(sK7(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_9017]) ).
tcf(c_23905,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(relation_dom(sK7(powerset(sK7(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_8992]) ).
tcf(c_23906,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(relation_dom(sK7(powerset(sK7(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_8957]) ).
tcf(c_23907,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK7(powerset(sK7(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_8561]) ).
tcf(c_23908,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(powerset(sK7(powerset(sK7(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_6875]) ).
tcf(c_23909,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(sK7(powerset(sK7(sK6(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_10681]) ).
tcf(c_23910,plain,
! [X0: $i] :
( ( relation_image(sK7(sK6(powerset(sK7(powerset(sK7(sK6(powerset(X0)))))))),sK1) = sK1 )
| ~ empty(sK0)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_11188]) ).
tcf(c_23911,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X1,sK7(sK6(powerset(sK7(powerset(sK7(sK6(powerset(X0))))))))) = sK1 )
| ~ empty(sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_10420]) ).
tcf(c_23912,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(powerset(sK7(powerset(sK7(sK6(powerset(X0)))))))) = relation_image(X1,sK1) )
| ~ empty(sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_10418]) ).
tcf(c_23913,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(sK7(powerset(sK7(sK6(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_8006]) ).
tcf(c_23914,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(sK7(powerset(sK7(sK6(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_7963]) ).
tcf(c_23915,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK7(powerset(sK7(sK6(powerset(X0)))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_5794]) ).
tcf(c_23916,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(powerset(sK7(sK6(powerset(X0)))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_5793]) ).
tcf(c_23917,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(sK7(powerset(sK7(sK6(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_6878]) ).
tcf(c_23918,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(sK7(powerset(sK7(sK6(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_6876]) ).
tcf(c_23919,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(sK7(powerset(sK7(sK6(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_8005]) ).
tcf(c_23920,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(sK7(powerset(sK7(sK6(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_7962]) ).
tcf(c_23921,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(sK7(powerset(sK7(sK6(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_7934]) ).
tcf(c_23922,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X1,sK7(powerset(sK7(powerset(sK7(sK6(powerset(X0)))))))) = sK1 )
| ~ empty(sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_7111]) ).
tcf(c_23923,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(sK7(powerset(sK7(sK6(powerset(X0))))))) = relation_image(X1,sK1) )
| ~ empty(sK0)
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_6946]) ).
tcf(c_23924,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK7(powerset(sK7(sK6(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_6133]) ).
tcf(c_23925,plain,
! [X0: $i] :
( ( relation_image(sK7(powerset(sK7(powerset(sK7(sK6(powerset(X0))))))),sK1) = sK1 )
| ~ empty(sK0)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_8316]) ).
tcf(c_23928,plain,
! [X0: $i] :
( ( relation_image(relation_dom(sK7(powerset(sK7(sK6(powerset(X0)))))),sK1) = sK1 )
| ~ empty(sK0)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_8131]) ).
tcf(c_23937,plain,
! [X0: $i] :
( function(sK7(powerset(sK7(sK6(powerset(X0))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_98]) ).
tcf(c_23938,plain,
! [X0: $i] :
( relation(sK7(powerset(sK7(sK6(powerset(X0))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_80]) ).
tcf(c_24236,plain,
~ empty(sK0),
inference(global_subsumption_just,[status(thm)],[c_19422,c_49,c_5857,c_6237,c_6638,c_8112,c_13256,c_22498]) ).
tcf(c_24238,plain,
apply(identity_relation(powerset(sK0)),sK6(sK0)) = sK6(sK0),
inference(superposition,[status(thm)],[c_5806,c_24236]) ).
tcf(c_24239,plain,
apply(identity_relation(sK0),sK7(sK0)) = sK7(sK0),
inference(superposition,[status(thm)],[c_5807,c_24236]) ).
tcf(c_24251,plain,
( ( sK7(powerset(powerset(empty_set))) = empty_set )
| ( apply(identity_relation(powerset(empty_set)),empty_set) = empty_set ) ),
inference(superposition,[status(thm)],[c_8004,c_9423]) ).
tcf(c_24253,plain,
( ( sK7(powerset(sK6(sK6(powerset(empty_set))))) = empty_set )
| ( apply(identity_relation(sK6(sK6(powerset(empty_set)))),empty_set) = empty_set ) ),
inference(superposition,[status(thm)],[c_16755,c_9423]) ).
tcf(c_24254,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK7(powerset(X0)) = empty_set )
| ( relation_image(identity_relation(X0),X1) = X2 )
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),relation_dom(identity_relation(X0)))
| ~ in(sK2(identity_relation(X0),X1,X2),X2)
| ( sK2(identity_relation(X0),X1,X2) != sK7(X0) ) ),
inference(superposition,[status(thm)],[c_9423,c_53]) ).
tcf(c_24255,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0),relation_image(identity_relation(X0),X1))
| ( sK7(powerset(X0)) = empty_set )
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),relation_dom(identity_relation(X0))) ),
inference(superposition,[status(thm)],[c_9423,c_57]) ).
tcf(c_24258,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0),relation_image(identity_relation(X0),X1))
| ( sK7(powerset(X0)) = empty_set )
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),X0) ),
inference(light_normalisation,[status(thm)],[c_24255,c_121]) ).
tcf(c_24259,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0),relation_image(identity_relation(X0),X1))
| ( sK7(powerset(X0)) = empty_set )
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_24258,c_62,c_63]) ).
tcf(c_24264,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK7(powerset(X0)) = empty_set )
| ( relation_image(identity_relation(X0),X1) = X2 )
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),X0)
| ~ in(sK2(identity_relation(X0),X1,X2),X2)
| ( sK2(identity_relation(X0),X1,X2) != sK7(X0) ) ),
inference(light_normalisation,[status(thm)],[c_24254,c_121]) ).
tcf(c_24265,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK7(powerset(X0)) = empty_set )
| ( relation_image(identity_relation(X0),X1) = X2 )
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),X0)
| ~ in(sK2(identity_relation(X0),X1,X2),X2)
| ( sK2(identity_relation(X0),X1,X2) != sK7(X0) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_24264,c_62,c_63]) ).
tcf(c_24290,plain,
( function(sK7(powerset(empty_set)))
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_11339,c_23937]) ).
tcf(c_24291,plain,
( function(empty_set)
| ~ empty(empty_set) ),
inference(light_normalisation,[status(thm)],[c_24290,c_8004]) ).
tcf(c_24296,plain,
( relation(sK7(powerset(empty_set)))
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_11339,c_23938]) ).
tcf(c_24297,plain,
( relation(empty_set)
| ~ empty(empty_set) ),
inference(light_normalisation,[status(thm)],[c_24296,c_8004]) ).
tcf(c_24298,plain,
! [X0: $i] :
( in(sK7(sK0),relation_image(identity_relation(sK0),X0))
| ~ function(identity_relation(sK0))
| ~ relation(identity_relation(sK0))
| ~ in(sK7(sK0),X0)
| ~ in(sK7(sK0),relation_dom(identity_relation(sK0))) ),
inference(superposition,[status(thm)],[c_24239,c_57]) ).
tcf(c_24299,plain,
! [X0: $i] :
( in(sK7(sK0),relation_image(identity_relation(sK0),X0))
| ~ in(sK7(sK0),X0)
| ~ in(sK7(sK0),relation_dom(identity_relation(sK0))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_24298,c_62,c_63]) ).
tcf(c_24315,plain,
( ( identity_relation(identity_relation(empty_set)) = empty_set )
| ( apply(empty_set,sK7(empty_set)) = sK7(empty_set) ) ),
inference(superposition,[status(thm)],[c_6104,c_9424]) ).
tcf(c_24316,plain,
( ( identity_relation(identity_relation(powerset(empty_set))) = empty_set )
| ( apply(identity_relation(powerset(empty_set)),empty_set) = empty_set ) ),
inference(superposition,[status(thm)],[c_8004,c_9424]) ).
tcf(c_24318,plain,
( ( identity_relation(identity_relation(sK6(sK6(powerset(empty_set))))) = empty_set )
| ( apply(identity_relation(sK6(sK6(powerset(empty_set)))),empty_set) = empty_set ) ),
inference(superposition,[status(thm)],[c_16755,c_9424]) ).
tcf(c_24319,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(identity_relation(X0)) = empty_set )
| ( relation_image(identity_relation(X0),X1) = X2 )
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),relation_dom(identity_relation(X0)))
| ~ in(sK2(identity_relation(X0),X1,X2),X2)
| ( sK2(identity_relation(X0),X1,X2) != sK7(X0) ) ),
inference(superposition,[status(thm)],[c_9424,c_53]) ).
tcf(c_24320,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0),relation_image(identity_relation(X0),X1))
| ( identity_relation(identity_relation(X0)) = empty_set )
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),relation_dom(identity_relation(X0))) ),
inference(superposition,[status(thm)],[c_9424,c_57]) ).
tcf(c_24324,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0),relation_image(identity_relation(X0),X1))
| ( identity_relation(identity_relation(X0)) = empty_set )
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),X0) ),
inference(light_normalisation,[status(thm)],[c_24320,c_121]) ).
tcf(c_24325,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0),relation_image(identity_relation(X0),X1))
| ( identity_relation(identity_relation(X0)) = empty_set )
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_24324,c_62,c_63]) ).
tcf(c_24330,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(identity_relation(X0)) = empty_set )
| ( relation_image(identity_relation(X0),X1) = X2 )
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),X0)
| ~ in(sK2(identity_relation(X0),X1,X2),X2)
| ( sK2(identity_relation(X0),X1,X2) != sK7(X0) ) ),
inference(light_normalisation,[status(thm)],[c_24319,c_121]) ).
tcf(c_24331,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(identity_relation(X0)) = empty_set )
| ( relation_image(identity_relation(X0),X1) = X2 )
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),X0)
| ~ in(sK2(identity_relation(X0),X1,X2),X2)
| ( sK2(identity_relation(X0),X1,X2) != sK7(X0) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_24330,c_62,c_63]) ).
tcf(c_24344,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(relation_dom(relation_dom(X0))))) = empty_set )
| ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) ) ),
inference(superposition,[status(thm)],[c_5806,c_12755]) ).
tcf(c_24345,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( relation_dom(sK7(powerset(relation_dom(relation_dom(X0))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_12755]) ).
tcf(c_24346,plain,
relation_dom(sK7(powerset(relation_dom(relation_dom(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_12755]) ).
tcf(c_24347,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(relation_dom(relation_dom(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_12755]) ).
tcf(c_24348,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(relation_dom(relation_dom(identity_relation(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_12755]) ).
tcf(c_24349,plain,
( ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ( relation_dom(sK7(powerset(relation_dom(relation_dom(sK1))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5890,c_12755]) ).
tcf(c_24350,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(relation_dom(relation_dom(sK7(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_12755]) ).
tcf(c_24351,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(relation_dom(relation_dom(sK7(sK6(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_12755]) ).
tcf(c_24352,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(relation_dom(relation_dom(sK7(sK6(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_12755]) ).
tcf(c_24353,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(relation_dom(relation_dom(relation_image(X0,empty_set)))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_12755]) ).
tcf(c_24354,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(relation_dom(relation_dom(sK7(powerset(sK7(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_12755]) ).
tcf(c_24355,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(relation_dom(relation_dom(sK7(powerset(sK7(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_12755]) ).
tcf(c_24392,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(identity_relation(relation_dom(X0))))) = empty_set )
| ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) ) ),
inference(superposition,[status(thm)],[c_5806,c_12871]) ).
tcf(c_24393,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( identity_relation(sK7(powerset(identity_relation(relation_dom(X0))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_12871]) ).
tcf(c_24394,plain,
identity_relation(sK7(powerset(identity_relation(relation_dom(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_12871]) ).
tcf(c_24395,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(identity_relation(relation_dom(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_12871]) ).
tcf(c_24396,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(identity_relation(relation_dom(identity_relation(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_12871]) ).
tcf(c_24397,plain,
( ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ( identity_relation(sK7(powerset(identity_relation(relation_dom(sK1))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5890,c_12871]) ).
tcf(c_24398,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(identity_relation(relation_dom(sK7(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_12871]) ).
tcf(c_24399,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(identity_relation(relation_dom(sK7(sK6(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_12871]) ).
tcf(c_24400,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(identity_relation(relation_dom(sK7(sK6(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_12871]) ).
tcf(c_24401,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(identity_relation(relation_dom(relation_image(X0,empty_set)))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_12871]) ).
tcf(c_24402,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(identity_relation(relation_dom(sK7(powerset(sK7(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_12871]) ).
tcf(c_24403,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(identity_relation(relation_dom(sK7(powerset(sK7(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_12871]) ).
tcf(c_24440,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(identity_relation(relation_dom(X0))))) = empty_set )
| ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) ) ),
inference(superposition,[status(thm)],[c_5806,c_12909]) ).
tcf(c_24441,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( relation_dom(sK7(powerset(identity_relation(relation_dom(X0))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_12909]) ).
tcf(c_24442,plain,
relation_dom(sK7(powerset(identity_relation(relation_dom(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_12909]) ).
tcf(c_24443,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(identity_relation(relation_dom(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_12909]) ).
tcf(c_24444,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(identity_relation(relation_dom(identity_relation(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_12909]) ).
tcf(c_24445,plain,
( ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ( relation_dom(sK7(powerset(identity_relation(relation_dom(sK1))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5890,c_12909]) ).
tcf(c_24446,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(identity_relation(relation_dom(sK7(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_12909]) ).
tcf(c_24447,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(identity_relation(relation_dom(sK7(sK6(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_12909]) ).
tcf(c_24448,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(identity_relation(relation_dom(sK7(sK6(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_12909]) ).
tcf(c_24449,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(identity_relation(relation_dom(relation_image(X0,empty_set)))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_12909]) ).
tcf(c_24450,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(identity_relation(relation_dom(sK7(powerset(sK7(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_12909]) ).
tcf(c_24451,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(identity_relation(relation_dom(sK7(powerset(sK7(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_12909]) ).
tcf(c_24488,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(relation_dom(relation_dom(X0))))) = empty_set )
| ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) ) ),
inference(superposition,[status(thm)],[c_5806,c_13044]) ).
tcf(c_24489,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( identity_relation(identity_relation(identity_relation(relation_dom(relation_dom(X0))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_13044]) ).
tcf(c_24490,plain,
identity_relation(identity_relation(identity_relation(relation_dom(relation_dom(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_13044]) ).
tcf(c_24491,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(relation_dom(relation_dom(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_13044]) ).
tcf(c_24492,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(relation_dom(relation_dom(identity_relation(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_13044]) ).
tcf(c_24493,plain,
( ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ( identity_relation(identity_relation(identity_relation(relation_dom(relation_dom(sK1))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5890,c_13044]) ).
tcf(c_24494,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(relation_dom(relation_dom(sK7(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_13044]) ).
tcf(c_24495,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(relation_dom(relation_dom(sK7(sK6(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_13044]) ).
tcf(c_24496,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(relation_dom(relation_dom(sK7(sK6(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_13044]) ).
tcf(c_24497,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(relation_dom(relation_dom(relation_image(X0,empty_set)))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_13044]) ).
tcf(c_24498,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(relation_dom(relation_dom(sK7(powerset(sK7(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_13044]) ).
tcf(c_24499,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(relation_dom(relation_dom(sK7(powerset(sK7(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_13044]) ).
tcf(c_24548,plain,
( ( identity_relation(relation_dom(empty_set)) = empty_set )
| ( apply(empty_set,sK7(empty_set)) = sK7(empty_set) ) ),
inference(superposition,[status(thm)],[c_6104,c_9425]) ).
tcf(c_24549,plain,
( ( identity_relation(relation_dom(powerset(empty_set))) = empty_set )
| ( apply(identity_relation(powerset(empty_set)),empty_set) = empty_set ) ),
inference(superposition,[status(thm)],[c_8004,c_9425]) ).
tcf(c_24551,plain,
( ( identity_relation(relation_dom(sK6(sK6(powerset(empty_set))))) = empty_set )
| ( apply(identity_relation(sK6(sK6(powerset(empty_set)))),empty_set) = empty_set ) ),
inference(superposition,[status(thm)],[c_16755,c_9425]) ).
tcf(c_24552,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(relation_dom(X0)) = empty_set )
| ( relation_image(identity_relation(X0),X1) = X2 )
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),relation_dom(identity_relation(X0)))
| ~ in(sK2(identity_relation(X0),X1,X2),X2)
| ( sK2(identity_relation(X0),X1,X2) != sK7(X0) ) ),
inference(superposition,[status(thm)],[c_9425,c_53]) ).
tcf(c_24553,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0),relation_image(identity_relation(X0),X1))
| ( identity_relation(relation_dom(X0)) = empty_set )
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),relation_dom(identity_relation(X0))) ),
inference(superposition,[status(thm)],[c_9425,c_57]) ).
tcf(c_24557,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0),relation_image(identity_relation(X0),X1))
| ( identity_relation(relation_dom(X0)) = empty_set )
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),X0) ),
inference(light_normalisation,[status(thm)],[c_24553,c_121]) ).
tcf(c_24558,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0),relation_image(identity_relation(X0),X1))
| ( identity_relation(relation_dom(X0)) = empty_set )
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_24557,c_62,c_63]) ).
tcf(c_24563,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(relation_dom(X0)) = empty_set )
| ( relation_image(identity_relation(X0),X1) = X2 )
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),X0)
| ~ in(sK2(identity_relation(X0),X1,X2),X2)
| ( sK2(identity_relation(X0),X1,X2) != sK7(X0) ) ),
inference(light_normalisation,[status(thm)],[c_24552,c_121]) ).
tcf(c_24564,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(relation_dom(X0)) = empty_set )
| ( relation_image(identity_relation(X0),X1) = X2 )
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),X0)
| ~ in(sK2(identity_relation(X0),X1,X2),X2)
| ( sK2(identity_relation(X0),X1,X2) != sK7(X0) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_24563,c_62,c_63]) ).
tcf(c_24577,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(relation_dom(relation_dom(X0))))) = empty_set )
| ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) ) ),
inference(superposition,[status(thm)],[c_5806,c_13649]) ).
tcf(c_24578,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( sK7(powerset(identity_relation(relation_dom(relation_dom(X0))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_13649]) ).
tcf(c_24579,plain,
sK7(powerset(identity_relation(relation_dom(relation_dom(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_13649]) ).
tcf(c_24580,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(relation_dom(relation_dom(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_13649]) ).
tcf(c_24581,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(relation_dom(relation_dom(identity_relation(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_13649]) ).
tcf(c_24582,plain,
( ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ( sK7(powerset(identity_relation(relation_dom(relation_dom(sK1))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5890,c_13649]) ).
tcf(c_24583,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(relation_dom(relation_dom(sK7(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_13649]) ).
tcf(c_24584,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(relation_dom(relation_dom(sK7(sK6(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_13649]) ).
tcf(c_24585,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(relation_dom(relation_dom(sK7(sK6(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_13649]) ).
tcf(c_24586,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(relation_dom(relation_dom(relation_image(X0,empty_set)))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_13649]) ).
tcf(c_24587,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(relation_dom(relation_dom(sK7(powerset(sK7(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_13649]) ).
tcf(c_24588,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(relation_dom(relation_dom(sK7(powerset(sK7(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_13649]) ).
tcf(c_24625,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(relation_dom(relation_dom(X0))))) = empty_set )
| ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) ) ),
inference(superposition,[status(thm)],[c_5806,c_13817]) ).
tcf(c_24626,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( sK7(sK6(powerset(relation_dom(relation_dom(X0))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_13817]) ).
tcf(c_24627,plain,
sK7(sK6(powerset(relation_dom(relation_dom(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_13817]) ).
tcf(c_24628,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(relation_dom(relation_dom(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_13817]) ).
tcf(c_24629,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(relation_dom(relation_dom(identity_relation(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_13817]) ).
tcf(c_24630,plain,
( ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ( sK7(sK6(powerset(relation_dom(relation_dom(sK1))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5890,c_13817]) ).
tcf(c_24631,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(relation_dom(relation_dom(sK7(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_13817]) ).
tcf(c_24632,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(relation_dom(relation_dom(sK7(sK6(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_13817]) ).
tcf(c_24633,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(relation_dom(relation_dom(sK7(sK6(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_13817]) ).
tcf(c_24634,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(relation_dom(relation_dom(relation_image(X0,empty_set)))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_13817]) ).
tcf(c_24635,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(relation_dom(relation_dom(sK7(powerset(sK7(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_13817]) ).
tcf(c_24636,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(relation_dom(relation_dom(sK7(powerset(sK7(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_13817]) ).
tcf(c_24673,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(relation_dom(X0))))) = empty_set )
| ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) ) ),
inference(superposition,[status(thm)],[c_5806,c_13853]) ).
tcf(c_24674,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( identity_relation(identity_relation(identity_relation(identity_relation(relation_dom(X0))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_13853]) ).
tcf(c_24675,plain,
identity_relation(identity_relation(identity_relation(identity_relation(relation_dom(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_13853]) ).
tcf(c_24676,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(relation_dom(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_13853]) ).
tcf(c_24677,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(relation_dom(identity_relation(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_13853]) ).
tcf(c_24678,plain,
( ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ( identity_relation(identity_relation(identity_relation(identity_relation(relation_dom(sK1))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5890,c_13853]) ).
tcf(c_24679,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(relation_dom(sK7(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_13853]) ).
tcf(c_24680,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(relation_dom(sK7(sK6(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_13853]) ).
tcf(c_24681,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(relation_dom(sK7(sK6(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_13853]) ).
tcf(c_24682,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(relation_dom(relation_image(X0,empty_set)))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_13853]) ).
tcf(c_24683,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(relation_dom(sK7(powerset(sK7(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_13853]) ).
tcf(c_24684,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(relation_dom(sK7(powerset(sK7(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_13853]) ).
tcf(c_24721,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(identity_relation(relation_dom(X0))))) = empty_set )
| ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) ) ),
inference(superposition,[status(thm)],[c_5806,c_13969]) ).
tcf(c_24722,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( sK7(powerset(identity_relation(identity_relation(relation_dom(X0))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_13969]) ).
tcf(c_24723,plain,
sK7(powerset(identity_relation(identity_relation(relation_dom(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_13969]) ).
tcf(c_24724,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(identity_relation(relation_dom(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_13969]) ).
tcf(c_24725,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(identity_relation(relation_dom(identity_relation(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_13969]) ).
tcf(c_24726,plain,
( ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ( sK7(powerset(identity_relation(identity_relation(relation_dom(sK1))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5890,c_13969]) ).
tcf(c_24727,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(identity_relation(relation_dom(sK7(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_13969]) ).
tcf(c_24728,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(identity_relation(relation_dom(sK7(sK6(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_13969]) ).
tcf(c_24729,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(identity_relation(relation_dom(sK7(sK6(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_13969]) ).
tcf(c_24730,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(identity_relation(relation_dom(relation_image(X0,empty_set)))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_13969]) ).
tcf(c_24731,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(identity_relation(relation_dom(sK7(powerset(sK7(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_13969]) ).
tcf(c_24732,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(identity_relation(relation_dom(sK7(powerset(sK7(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_13969]) ).
tcf(c_24787,plain,
( ( relation_dom(relation_dom(empty_set)) = empty_set )
| ( apply(empty_set,sK7(empty_set)) = sK7(empty_set) ) ),
inference(superposition,[status(thm)],[c_6104,c_9426]) ).
tcf(c_24788,plain,
( ( relation_dom(relation_dom(powerset(empty_set))) = empty_set )
| ( apply(identity_relation(powerset(empty_set)),empty_set) = empty_set ) ),
inference(superposition,[status(thm)],[c_8004,c_9426]) ).
tcf(c_24790,plain,
( ( relation_dom(relation_dom(sK6(sK6(powerset(empty_set))))) = empty_set )
| ( apply(identity_relation(sK6(sK6(powerset(empty_set)))),empty_set) = empty_set ) ),
inference(superposition,[status(thm)],[c_16755,c_9426]) ).
tcf(c_24791,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_dom(X0)) = empty_set )
| ( relation_image(identity_relation(X0),X1) = X2 )
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),relation_dom(identity_relation(X0)))
| ~ in(sK2(identity_relation(X0),X1,X2),X2)
| ( sK2(identity_relation(X0),X1,X2) != sK7(X0) ) ),
inference(superposition,[status(thm)],[c_9426,c_53]) ).
tcf(c_24792,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0),relation_image(identity_relation(X0),X1))
| ( relation_dom(relation_dom(X0)) = empty_set )
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),relation_dom(identity_relation(X0))) ),
inference(superposition,[status(thm)],[c_9426,c_57]) ).
tcf(c_24796,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0),relation_image(identity_relation(X0),X1))
| ( relation_dom(relation_dom(X0)) = empty_set )
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),X0) ),
inference(light_normalisation,[status(thm)],[c_24792,c_121]) ).
tcf(c_24797,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0),relation_image(identity_relation(X0),X1))
| ( relation_dom(relation_dom(X0)) = empty_set )
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_24796,c_62,c_63]) ).
tcf(c_24802,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_dom(X0)) = empty_set )
| ( relation_image(identity_relation(X0),X1) = X2 )
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),X0)
| ~ in(sK2(identity_relation(X0),X1,X2),X2)
| ( sK2(identity_relation(X0),X1,X2) != sK7(X0) ) ),
inference(light_normalisation,[status(thm)],[c_24791,c_121]) ).
tcf(c_24803,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_dom(X0)) = empty_set )
| ( relation_image(identity_relation(X0),X1) = X2 )
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),X0)
| ~ in(sK2(identity_relation(X0),X1,X2),X2)
| ( sK2(identity_relation(X0),X1,X2) != sK7(X0) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_24802,c_62,c_63]) ).
tcf(c_24816,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(powerset(relation_dom(X0))))) = empty_set )
| ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) ) ),
inference(superposition,[status(thm)],[c_5806,c_16756]) ).
tcf(c_24817,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( sK7(sK6(sK6(powerset(relation_dom(X0))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_16756]) ).
tcf(c_24818,plain,
sK7(sK6(sK6(powerset(relation_dom(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_16756]) ).
tcf(c_24819,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(powerset(relation_dom(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_16756]) ).
tcf(c_24820,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(powerset(relation_dom(identity_relation(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_16756]) ).
tcf(c_24821,plain,
( ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ( sK7(sK6(sK6(powerset(relation_dom(sK1))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5890,c_16756]) ).
tcf(c_24822,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(powerset(relation_dom(sK7(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_16756]) ).
tcf(c_24823,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(powerset(relation_dom(sK7(sK6(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_16756]) ).
tcf(c_24824,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(powerset(relation_dom(sK7(sK6(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_16756]) ).
tcf(c_24825,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(powerset(relation_dom(relation_image(X0,empty_set)))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_16756]) ).
tcf(c_24826,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(powerset(relation_dom(sK7(powerset(sK7(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_16756]) ).
tcf(c_24827,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(powerset(relation_dom(sK7(powerset(sK7(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_16756]) ).
tcf(c_24872,plain,
! [X0: $i] :
( ( identity_relation(sK7(sK6(powerset(relation_dom(X0))))) = empty_set )
| ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) ) ),
inference(superposition,[status(thm)],[c_5806,c_17479]) ).
tcf(c_24873,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( identity_relation(sK7(sK6(powerset(relation_dom(X0))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_17479]) ).
tcf(c_24874,plain,
identity_relation(sK7(sK6(powerset(relation_dom(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_17479]) ).
tcf(c_24875,plain,
! [X0: $i] :
( ( identity_relation(sK7(sK6(powerset(relation_dom(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_17479]) ).
tcf(c_24876,plain,
! [X0: $i] :
( ( identity_relation(sK7(sK6(powerset(relation_dom(identity_relation(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_17479]) ).
tcf(c_24877,plain,
( ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ( identity_relation(sK7(sK6(powerset(relation_dom(sK1))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5890,c_17479]) ).
tcf(c_24878,plain,
! [X0: $i] :
( ( identity_relation(sK7(sK6(powerset(relation_dom(sK7(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_17479]) ).
tcf(c_24879,plain,
! [X0: $i] :
( ( identity_relation(sK7(sK6(powerset(relation_dom(sK7(sK6(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_17479]) ).
tcf(c_24880,plain,
! [X0: $i] :
( ( identity_relation(sK7(sK6(powerset(relation_dom(sK7(sK6(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_17479]) ).
tcf(c_24881,plain,
! [X0: $i] :
( ( identity_relation(sK7(sK6(powerset(relation_dom(relation_image(X0,empty_set)))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_17479]) ).
tcf(c_24882,plain,
! [X0: $i] :
( ( identity_relation(sK7(sK6(powerset(relation_dom(sK7(powerset(sK7(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_17479]) ).
tcf(c_24883,plain,
! [X0: $i] :
( ( identity_relation(sK7(sK6(powerset(relation_dom(sK7(powerset(sK7(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_17479]) ).
tcf(c_24936,plain,
! [X0: $i] :
( element(sK3(X0,sK1,empty_set),sK0)
| ( relation_image(X0,sK1) = relation_image(empty_set,empty_set) )
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18922,c_18609]) ).
tcf(c_24938,plain,
! [X0: $i] :
( element(sK3(X0,sK1,empty_set),sK0)
| ( relation_image(X0,sK1) = relation_image(empty_set,empty_set) )
| ~ function(X0)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_24936,c_5610,c_82]) ).
tcf(c_24956,plain,
! [X0: $i] :
( element(sK2(X0,empty_set,sK1),sK0)
| ( relation_image(X0,relation_image(empty_set,empty_set)) = sK1 )
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18922,c_18613]) ).
tcf(c_24958,plain,
! [X0: $i] :
( element(sK2(X0,empty_set,sK1),sK0)
| ( relation_image(X0,relation_image(empty_set,empty_set)) = sK1 )
| ~ function(X0)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_24956,c_5610,c_82]) ).
tcf(c_24964,plain,
! [X0: $i,X1: $i] :
( ~ relation(X0)
| ~ function(X0)
| ( apply(X0,sK3(X0,X1,sK1)) = sK2(X0,X1,sK1) )
| ( relation_image(X0,X1) = sK1 )
| in(sK2(X0,X1,sK1),sK0) ),
inference(global_subsumption_just,[status(thm)],[c_8123,c_49,c_5857,c_6237,c_6638,c_8112,c_8123,c_13256,c_22498]) ).
tcf(c_24965,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,X1,sK1),sK0)
| ( relation_image(X0,X1) = sK1 )
| ( apply(X0,sK3(X0,X1,sK1)) = sK2(X0,X1,sK1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(renaming,[status(thm)],[c_24964]) ).
tcf(c_24977,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X0,X1) = sK1 )
| ( apply(X0,sK3(X0,X1,sK1)) = sK2(X0,X1,sK1) )
| ( apply(identity_relation(sK0),sK2(X0,X1,sK1)) = sK2(X0,X1,sK1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_24965,c_151]) ).
tcf(c_24978,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X0,X1) = sK1 )
| ( apply(X0,sK3(X0,X1,sK1)) = sK2(X0,X1,sK1) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK0,sK2(X0,X1,sK1)) ),
inference(superposition,[status(thm)],[c_24965,c_85]) ).
tcf(c_25003,plain,
! [X0: $i] :
( element(sK3(X0,sK1,empty_set),sK0)
| element(sK2(X0,sK1,sK7(sK6(powerset(empty_set)))),empty_set)
| ( sK7(sK6(powerset(empty_set))) = relation_image(X0,sK1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_11339,c_10564]) ).
tcf(c_25004,plain,
! [X0: $i] :
( element(sK2(X0,sK1,empty_set),empty_set)
| element(sK3(X0,sK1,sK7(sK6(powerset(empty_set)))),sK0)
| ( sK7(sK6(powerset(empty_set))) = relation_image(X0,sK1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_11339,c_10564]) ).
tcf(c_25006,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,X2)
| element(sK3(X1,sK1,sK7(sK6(powerset(powerset(X2))))),sK0)
| ( sK7(sK6(powerset(powerset(X2)))) = relation_image(X1,sK1) )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,sK2(X1,sK1,sK7(sK6(powerset(powerset(X2)))))) ),
inference(superposition,[status(thm)],[c_10564,c_65]) ).
tcf(c_25007,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK3(X1,sK1,sK7(sK6(powerset(powerset(X2))))),sK0)
| ( sK7(sK6(powerset(powerset(X2)))) = relation_image(X1,sK1) )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X2)
| ~ in(X0,sK2(X1,sK1,sK7(sK6(powerset(powerset(X2)))))) ),
inference(superposition,[status(thm)],[c_10564,c_64]) ).
tcf(c_25008,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| element(sK3(X0,sK1,sK7(sK6(powerset(X1)))),sK0)
| in(sK2(X0,sK1,sK7(sK6(powerset(X1)))),X1)
| ( sK7(sK6(powerset(X1))) = relation_image(X0,sK1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_10564,c_71]) ).
tcf(c_25041,plain,
! [X0: $i] :
( element(sK3(X0,empty_set,sK1),empty_set)
| element(sK2(X0,sK7(sK6(powerset(empty_set))),sK1),sK0)
| ( relation_image(X0,sK7(sK6(powerset(empty_set)))) = sK1 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_11339,c_10566]) ).
tcf(c_25042,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,X2)
| element(sK2(X1,sK7(sK6(powerset(powerset(X2)))),sK1),sK0)
| ( relation_image(X1,sK7(sK6(powerset(powerset(X2))))) = sK1 )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,sK3(X1,sK7(sK6(powerset(powerset(X2)))),sK1)) ),
inference(superposition,[status(thm)],[c_10566,c_65]) ).
tcf(c_25043,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X1,sK7(sK6(powerset(powerset(X2)))),sK1),sK0)
| ( relation_image(X1,sK7(sK6(powerset(powerset(X2))))) = sK1 )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X2)
| ~ in(X0,sK3(X1,sK7(sK6(powerset(powerset(X2)))),sK1)) ),
inference(superposition,[status(thm)],[c_10566,c_64]) ).
tcf(c_25044,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| element(sK2(X0,sK7(sK6(powerset(X1))),sK1),sK0)
| in(sK3(X0,sK7(sK6(powerset(X1))),sK1),X1)
| ( relation_image(X0,sK7(sK6(powerset(X1)))) = sK1 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_10566,c_71]) ).
tcf(c_25071,plain,
( ( identity_relation(powerset(empty_set)) = empty_set )
| ( apply(identity_relation(powerset(empty_set)),empty_set) = empty_set ) ),
inference(superposition,[status(thm)],[c_8004,c_9427]) ).
tcf(c_25073,plain,
( ( identity_relation(sK6(sK6(powerset(empty_set)))) = empty_set )
| ( apply(identity_relation(sK6(sK6(powerset(empty_set)))),empty_set) = empty_set ) ),
inference(superposition,[status(thm)],[c_16755,c_9427]) ).
tcf(c_25074,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(X0) = empty_set )
| ( relation_image(identity_relation(X0),X1) = X2 )
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),relation_dom(identity_relation(X0)))
| ~ in(sK2(identity_relation(X0),X1,X2),X2)
| ( sK2(identity_relation(X0),X1,X2) != sK7(X0) ) ),
inference(superposition,[status(thm)],[c_9427,c_53]) ).
tcf(c_25075,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0),relation_image(identity_relation(X0),X1))
| ( identity_relation(X0) = empty_set )
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),relation_dom(identity_relation(X0))) ),
inference(superposition,[status(thm)],[c_9427,c_57]) ).
tcf(c_25078,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0),relation_image(identity_relation(X0),X1))
| ( identity_relation(X0) = empty_set )
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),X0) ),
inference(light_normalisation,[status(thm)],[c_25075,c_121]) ).
tcf(c_25079,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0),relation_image(identity_relation(X0),X1))
| ( identity_relation(X0) = empty_set )
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_25078,c_62,c_63]) ).
tcf(c_25084,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(X0) = empty_set )
| ( relation_image(identity_relation(X0),X1) = X2 )
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),X0)
| ~ in(sK2(identity_relation(X0),X1,X2),X2)
| ( sK2(identity_relation(X0),X1,X2) != sK7(X0) ) ),
inference(light_normalisation,[status(thm)],[c_25074,c_121]) ).
tcf(c_25085,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(X0) = empty_set )
| ( relation_image(identity_relation(X0),X1) = X2 )
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),X0)
| ~ in(sK2(identity_relation(X0),X1,X2),X2)
| ( sK2(identity_relation(X0),X1,X2) != sK7(X0) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_25084,c_62,c_63]) ).
tcf(c_25096,plain,
! [X0: $i] :
( ( relation_dom(sK7(sK6(powerset(relation_dom(X0))))) = empty_set )
| ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) ) ),
inference(superposition,[status(thm)],[c_5806,c_17536]) ).
tcf(c_25097,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( relation_dom(sK7(sK6(powerset(relation_dom(X0))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_17536]) ).
tcf(c_25098,plain,
relation_dom(sK7(sK6(powerset(relation_dom(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_17536]) ).
tcf(c_25099,plain,
! [X0: $i] :
( ( relation_dom(sK7(sK6(powerset(relation_dom(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_17536]) ).
tcf(c_25100,plain,
! [X0: $i] :
( ( relation_dom(sK7(sK6(powerset(relation_dom(identity_relation(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_17536]) ).
tcf(c_25101,plain,
( ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ( relation_dom(sK7(sK6(powerset(relation_dom(sK1))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5890,c_17536]) ).
tcf(c_25102,plain,
! [X0: $i] :
( ( relation_dom(sK7(sK6(powerset(relation_dom(sK7(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_17536]) ).
tcf(c_25103,plain,
! [X0: $i] :
( ( relation_dom(sK7(sK6(powerset(relation_dom(sK7(sK6(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_17536]) ).
tcf(c_25104,plain,
! [X0: $i] :
( ( relation_dom(sK7(sK6(powerset(relation_dom(sK7(sK6(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_17536]) ).
tcf(c_25105,plain,
! [X0: $i] :
( ( relation_dom(sK7(sK6(powerset(relation_dom(relation_image(X0,empty_set)))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_17536]) ).
tcf(c_25106,plain,
! [X0: $i] :
( ( relation_dom(sK7(sK6(powerset(relation_dom(sK7(powerset(sK7(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_17536]) ).
tcf(c_25107,plain,
! [X0: $i] :
( ( relation_dom(sK7(sK6(powerset(relation_dom(sK7(powerset(sK7(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_17536]) ).
tcf(c_25146,plain,
! [X0: $i] :
( ( relation_image(X0,empty_set) = empty_set )
| ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16950,c_23329]) ).
tcf(c_25147,plain,
! [X0: $i] :
( ( relation_image(X0,empty_set) = empty_set )
| ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_9431,c_23329]) ).
tcf(c_25148,plain,
! [X0: $i] :
( ( relation_image(identity_relation(X0),empty_set) = empty_set )
| ~ relation(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_62,c_23329]) ).
tcf(c_25149,plain,
( ( relation_image(sK14,empty_set) = empty_set )
| ~ relation(sK14) ),
inference(superposition,[status(thm)],[c_97,c_23329]) ).
tcf(c_25150,plain,
( ( relation_image(empty_set,empty_set) = empty_set )
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_5610,c_23329]) ).
tcf(c_25151,plain,
! [X0: $i] :
( ( relation_image(relation_dom(X0),empty_set) = empty_set )
| ~ empty(X0)
| ~ relation(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_5622,c_23329]) ).
tcf(c_25152,plain,
( ( relation_image(sK1,empty_set) = empty_set )
| ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_5909,c_23329]) ).
tcf(c_25153,plain,
! [X0: $i] :
( ( relation_image(sK7(powerset(X0)),empty_set) = empty_set )
| ~ empty(X0)
| ~ relation(sK7(powerset(X0))) ),
inference(superposition,[status(thm)],[c_6880,c_23329]) ).
tcf(c_25154,plain,
! [X0: $i] :
( ( relation_image(sK7(sK6(powerset(X0))),empty_set) = empty_set )
| ~ empty(X0)
| ~ relation(sK7(sK6(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_10682,c_23329]) ).
tcf(c_25155,plain,
! [X0: $i] :
( ( relation_image(sK7(sK6(sK6(powerset(X0)))),empty_set) = empty_set )
| ~ empty(X0)
| ~ relation(sK7(sK6(sK6(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_15646,c_23329]) ).
tcf(c_25156,plain,
! [X0: $i] :
( ( relation_image(sK7(powerset(sK7(powerset(X0)))),empty_set) = empty_set )
| ~ empty(X0)
| ~ relation(sK7(powerset(sK7(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_20633,c_23329]) ).
tcf(c_25157,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_23330,c_23329]) ).
tcf(c_25158,plain,
! [X0: $i] :
( ( relation_image(sK7(powerset(sK7(sK6(powerset(X0))))),empty_set) = empty_set )
| ~ empty(X0)
| ~ relation(sK7(powerset(sK7(sK6(powerset(X0)))))) ),
inference(superposition,[status(thm)],[c_23937,c_23329]) ).
tcf(c_25159,plain,
relation_image(sK14,empty_set) = empty_set,
inference(forward_subsumption_resolution,[status(thm)],[c_25149,c_96]) ).
tcf(c_25160,plain,
! [X0: $i] : relation_image(identity_relation(X0),empty_set) = empty_set,
inference(forward_subsumption_resolution,[status(thm)],[c_25148,c_63]) ).
tcf(c_25202,plain,
! [X0: $i] :
( element(sK2(X0,empty_set,sK1),sK0)
| ( relation_image(X0,relation_image(sK14,empty_set)) = sK1 )
| ~ function(sK14)
| ~ relation(sK14)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_25159,c_18613]) ).
tcf(c_25203,plain,
! [X0: $i] :
( element(sK3(X0,sK1,empty_set),sK0)
| ( relation_image(X0,sK1) = relation_image(sK14,empty_set) )
| ~ function(sK14)
| ~ relation(sK14)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_25159,c_18609]) ).
tcf(c_25208,plain,
! [X0: $i] :
( element(sK3(X0,sK1,empty_set),sK0)
| ( relation_image(X0,sK1) = empty_set )
| ~ function(sK14)
| ~ relation(sK14)
| ~ function(X0)
| ~ relation(X0) ),
inference(light_normalisation,[status(thm)],[c_25203,c_25159]) ).
tcf(c_25210,plain,
! [X0: $i] :
( element(sK2(X0,empty_set,sK1),sK0)
| ( relation_image(X0,empty_set) = sK1 )
| ~ function(sK14)
| ~ relation(sK14)
| ~ function(X0)
| ~ relation(X0) ),
inference(light_normalisation,[status(thm)],[c_25202,c_25159]) ).
tcf(c_25212,plain,
relation_image(empty_set,empty_set) = empty_set,
inference(superposition,[status(thm)],[c_6104,c_25160]) ).
tcf(c_25215,plain,
! [X0: $i,X1: $i] :
( element(sK2(X1,empty_set,sK1),sK0)
| ( relation_image(X1,relation_image(identity_relation(X0),empty_set)) = sK1 )
| ~ function(X1)
| ~ relation(X1)
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_25160,c_18613]) ).
tcf(c_25216,plain,
! [X0: $i,X1: $i] :
( element(sK3(X1,sK1,empty_set),sK0)
| ( relation_image(identity_relation(X0),empty_set) = relation_image(X1,sK1) )
| ~ function(X1)
| ~ relation(X1)
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_25160,c_18609]) ).
tcf(c_25221,plain,
! [X0: $i,X1: $i] :
( element(sK3(X1,sK1,empty_set),sK0)
| ( relation_image(X1,sK1) = empty_set )
| ~ function(X1)
| ~ relation(X1)
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0)) ),
inference(light_normalisation,[status(thm)],[c_25216,c_25160]) ).
tcf(c_25223,plain,
! [X0: $i,X1: $i] :
( element(sK2(X1,empty_set,sK1),sK0)
| ( relation_image(X1,empty_set) = sK1 )
| ~ function(X1)
| ~ relation(X1)
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0)) ),
inference(light_normalisation,[status(thm)],[c_25215,c_25160]) ).
tcf(c_25241,plain,
! [X0: $i] :
( element(sK3(X0,sK1,empty_set),sK0)
| element(sK2(X0,sK1,sK7(sK6(sK6(powerset(empty_set))))),empty_set)
| ( sK7(sK6(sK6(powerset(empty_set)))) = relation_image(X0,sK1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16755,c_15386]) ).
tcf(c_25242,plain,
! [X0: $i] :
( element(sK2(X0,sK1,empty_set),empty_set)
| element(sK3(X0,sK1,sK7(sK6(sK6(powerset(empty_set))))),sK0)
| ( sK7(sK6(sK6(powerset(empty_set)))) = relation_image(X0,sK1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16755,c_15386]) ).
tcf(c_25244,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,X2)
| element(sK3(X1,sK1,sK7(sK6(sK6(powerset(powerset(X2)))))),sK0)
| ( sK7(sK6(sK6(powerset(powerset(X2))))) = relation_image(X1,sK1) )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,sK2(X1,sK1,sK7(sK6(sK6(powerset(powerset(X2))))))) ),
inference(superposition,[status(thm)],[c_15386,c_65]) ).
tcf(c_25245,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK3(X1,sK1,sK7(sK6(sK6(powerset(powerset(X2)))))),sK0)
| ( sK7(sK6(sK6(powerset(powerset(X2))))) = relation_image(X1,sK1) )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X2)
| ~ in(X0,sK2(X1,sK1,sK7(sK6(sK6(powerset(powerset(X2))))))) ),
inference(superposition,[status(thm)],[c_15386,c_64]) ).
tcf(c_25246,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| element(sK3(X0,sK1,sK7(sK6(sK6(powerset(X1))))),sK0)
| in(sK2(X0,sK1,sK7(sK6(sK6(powerset(X1))))),X1)
| ( sK7(sK6(sK6(powerset(X1)))) = relation_image(X0,sK1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_15386,c_71]) ).
tcf(c_25279,plain,
! [X0: $i] :
( element(sK3(X0,empty_set,sK1),empty_set)
| element(sK2(X0,sK7(sK6(sK6(powerset(empty_set)))),sK1),sK0)
| ( relation_image(X0,sK7(sK6(sK6(powerset(empty_set))))) = sK1 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16755,c_15390]) ).
tcf(c_25280,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,X2)
| element(sK2(X1,sK7(sK6(sK6(powerset(powerset(X2))))),sK1),sK0)
| ( relation_image(X1,sK7(sK6(sK6(powerset(powerset(X2)))))) = sK1 )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,sK3(X1,sK7(sK6(sK6(powerset(powerset(X2))))),sK1)) ),
inference(superposition,[status(thm)],[c_15390,c_65]) ).
tcf(c_25281,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X1,sK7(sK6(sK6(powerset(powerset(X2))))),sK1),sK0)
| ( relation_image(X1,sK7(sK6(sK6(powerset(powerset(X2)))))) = sK1 )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X2)
| ~ in(X0,sK3(X1,sK7(sK6(sK6(powerset(powerset(X2))))),sK1)) ),
inference(superposition,[status(thm)],[c_15390,c_64]) ).
tcf(c_25282,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| element(sK2(X0,sK7(sK6(sK6(powerset(X1)))),sK1),sK0)
| in(sK3(X0,sK7(sK6(sK6(powerset(X1)))),sK1),X1)
| ( relation_image(X0,sK7(sK6(sK6(powerset(X1))))) = sK1 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_15390,c_71]) ).
tcf(c_25313,plain,
( ( relation_dom(powerset(empty_set)) = empty_set )
| ( apply(identity_relation(powerset(empty_set)),empty_set) = empty_set ) ),
inference(superposition,[status(thm)],[c_8004,c_9429]) ).
tcf(c_25315,plain,
( ( relation_dom(sK6(sK6(powerset(empty_set)))) = empty_set )
| ( apply(identity_relation(sK6(sK6(powerset(empty_set)))),empty_set) = empty_set ) ),
inference(superposition,[status(thm)],[c_16755,c_9429]) ).
tcf(c_25316,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(X0) = empty_set )
| ( relation_image(identity_relation(X0),X1) = X2 )
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),relation_dom(identity_relation(X0)))
| ~ in(sK2(identity_relation(X0),X1,X2),X2)
| ( sK2(identity_relation(X0),X1,X2) != sK7(X0) ) ),
inference(superposition,[status(thm)],[c_9429,c_53]) ).
tcf(c_25317,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0),relation_image(identity_relation(X0),X1))
| ( relation_dom(X0) = empty_set )
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),relation_dom(identity_relation(X0))) ),
inference(superposition,[status(thm)],[c_9429,c_57]) ).
tcf(c_25320,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0),relation_image(identity_relation(X0),X1))
| ( relation_dom(X0) = empty_set )
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),X0) ),
inference(light_normalisation,[status(thm)],[c_25317,c_121]) ).
tcf(c_25321,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0),relation_image(identity_relation(X0),X1))
| ( relation_dom(X0) = empty_set )
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_25320,c_62,c_63]) ).
tcf(c_25326,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(X0) = empty_set )
| ( relation_image(identity_relation(X0),X1) = X2 )
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),X0)
| ~ in(sK2(identity_relation(X0),X1,X2),X2)
| ( sK2(identity_relation(X0),X1,X2) != sK7(X0) ) ),
inference(light_normalisation,[status(thm)],[c_25316,c_121]) ).
tcf(c_25327,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(X0) = empty_set )
| ( relation_image(identity_relation(X0),X1) = X2 )
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),X0)
| ~ in(sK2(identity_relation(X0),X1,X2),X2)
| ( sK2(identity_relation(X0),X1,X2) != sK7(X0) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_25326,c_62,c_63]) ).
tcf(c_25341,plain,
( ( powerset(empty_set) = empty_set )
| ( apply(identity_relation(powerset(empty_set)),empty_set) = empty_set ) ),
inference(superposition,[status(thm)],[c_8004,c_9430]) ).
tcf(c_25343,plain,
( ( sK6(sK6(powerset(empty_set))) = empty_set )
| ( apply(identity_relation(sK6(sK6(powerset(empty_set)))),empty_set) = empty_set ) ),
inference(superposition,[status(thm)],[c_16755,c_9430]) ).
tcf(c_25344,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = empty_set )
| ( relation_image(identity_relation(X0),X1) = X2 )
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),relation_dom(identity_relation(X0)))
| ~ in(sK2(identity_relation(X0),X1,X2),X2)
| ( sK2(identity_relation(X0),X1,X2) != sK7(X0) ) ),
inference(superposition,[status(thm)],[c_9430,c_53]) ).
tcf(c_25345,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0),relation_image(identity_relation(X0),X1))
| ( X0 = empty_set )
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),relation_dom(identity_relation(X0))) ),
inference(superposition,[status(thm)],[c_9430,c_57]) ).
tcf(c_25348,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0),relation_image(identity_relation(X0),X1))
| ( X0 = empty_set )
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),X0) ),
inference(light_normalisation,[status(thm)],[c_25345,c_121]) ).
tcf(c_25349,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0),relation_image(identity_relation(X0),X1))
| ( X0 = empty_set )
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_25348,c_62,c_63]) ).
tcf(c_25354,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = empty_set )
| ( relation_image(identity_relation(X0),X1) = X2 )
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),X0)
| ~ in(sK2(identity_relation(X0),X1,X2),X2)
| ( sK2(identity_relation(X0),X1,X2) != sK7(X0) ) ),
inference(light_normalisation,[status(thm)],[c_25344,c_121]) ).
tcf(c_25355,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = empty_set )
| ( relation_image(identity_relation(X0),X1) = X2 )
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),X0)
| ~ in(sK2(identity_relation(X0),X1,X2),X2)
| ( sK2(identity_relation(X0),X1,X2) != sK7(X0) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_25354,c_62,c_63]) ).
tcf(c_25366,plain,
! [X0: $i] :
( ( relation_dom(sK7(sK6(powerset(relation_dom(X0))))) = empty_set )
| ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_10348,c_17536]) ).
tcf(c_25367,plain,
! [X0: $i] :
( ( identity_relation(sK7(sK6(powerset(relation_dom(X0))))) = empty_set )
| ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_10348,c_17479]) ).
tcf(c_25368,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(powerset(relation_dom(X0))))) = empty_set )
| ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_10348,c_16756]) ).
tcf(c_25369,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(identity_relation(relation_dom(X0))))) = empty_set )
| ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_10348,c_13969]) ).
tcf(c_25370,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(relation_dom(X0))))) = empty_set )
| ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_10348,c_13853]) ).
tcf(c_25371,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(relation_dom(relation_dom(X0))))) = empty_set )
| ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_10348,c_13817]) ).
tcf(c_25372,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(relation_dom(relation_dom(X0))))) = empty_set )
| ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_10348,c_13649]) ).
tcf(c_25373,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(relation_dom(relation_dom(X0))))) = empty_set )
| ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_10348,c_13044]) ).
tcf(c_25374,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(identity_relation(relation_dom(X0))))) = empty_set )
| ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_10348,c_12909]) ).
tcf(c_25375,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(identity_relation(relation_dom(X0))))) = empty_set )
| ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_10348,c_12871]) ).
tcf(c_25376,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(relation_dom(relation_dom(X0))))) = empty_set )
| ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_10348,c_12755]) ).
tcf(c_25377,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(relation_dom(relation_dom(X0))))) = empty_set )
| ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_10348,c_12356]) ).
tcf(c_25378,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(powerset(relation_dom(X0))))) = empty_set )
| ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_10348,c_12318]) ).
tcf(c_25379,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(powerset(relation_dom(X0))))) = empty_set )
| ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_10348,c_12212]) ).
tcf(c_25380,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(powerset(relation_dom(X0))))) = empty_set )
| ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_10348,c_12135]) ).
tcf(c_25381,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(relation_dom(relation_dom(X0))))) = empty_set )
| ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_10348,c_12099]) ).
tcf(c_25382,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(relation_dom(relation_dom(X0))))) = empty_set )
| ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_10348,c_12063]) ).
tcf(c_25383,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(relation_dom(relation_dom(X0))))) = empty_set )
| ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_10348,c_12027]) ).
tcf(c_25384,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(X0))))) = empty_set )
| ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_10348,c_11953]) ).
tcf(c_25385,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(powerset(relation_dom(X0))))) = empty_set )
| ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_10348,c_11431]) ).
tcf(c_25386,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(X1)) = X0 )
| ( apply(identity_relation(X1),sK7(sK6(X1))) = sK7(sK6(X1)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10348,c_9347]) ).
tcf(c_25387,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(X1)) = X0 )
| ( apply(identity_relation(X1),sK7(sK6(X1))) = sK7(sK6(X1)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10348,c_9319]) ).
tcf(c_25388,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(X1)) = X0 )
| ( apply(identity_relation(X1),sK7(sK6(X1))) = sK7(sK6(X1)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10348,c_6877]) ).
tcf(c_25389,plain,
! [X0: $i] :
( ( relation_dom(sK7(sK6(powerset(X0)))) = empty_set )
| ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_10348,c_10680]) ).
tcf(c_25390,plain,
! [X0: $i] :
( ( identity_relation(sK7(sK6(powerset(X0)))) = empty_set )
| ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_10348,c_10678]) ).
tcf(c_25391,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(powerset(X0)))) = empty_set )
| ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_10348,c_15645]) ).
tcf(c_25392,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(identity_relation(X0)))) = empty_set )
| ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_10348,c_9748]) ).
tcf(c_25393,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(X0)))) = empty_set )
| ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_10348,c_9682]) ).
tcf(c_25394,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(relation_dom(X0)))) = empty_set )
| ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_10348,c_11340]) ).
tcf(c_25395,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(relation_dom(X0)))) = empty_set )
| ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_10348,c_9747]) ).
tcf(c_25396,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(relation_dom(X0)))) = empty_set )
| ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_10348,c_9681]) ).
tcf(c_25397,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(identity_relation(X0)))) = empty_set )
| ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_10348,c_9115]) ).
tcf(c_25398,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(identity_relation(X0)))) = empty_set )
| ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_10348,c_9088]) ).
tcf(c_25399,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(relation_dom(X0)))) = empty_set )
| ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_10348,c_9114]) ).
tcf(c_25400,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(relation_dom(X0)))) = empty_set )
| ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_10348,c_9087]) ).
tcf(c_25401,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(powerset(X0)))) = empty_set )
| ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_10348,c_8009]) ).
tcf(c_25402,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(powerset(X0)))) = empty_set )
| ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_10348,c_7966]) ).
tcf(c_25403,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(powerset(X0)))) = empty_set )
| ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_10348,c_7938]) ).
tcf(c_25404,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(relation_dom(X0)))) = empty_set )
| ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_10348,c_9017]) ).
tcf(c_25405,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(relation_dom(X0)))) = empty_set )
| ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_10348,c_8992]) ).
tcf(c_25406,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(relation_dom(X0)))) = empty_set )
| ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_10348,c_8957]) ).
tcf(c_25407,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(X0)))) = empty_set )
| ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_10348,c_8561]) ).
tcf(c_25408,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(powerset(X0)))) = empty_set )
| ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_10348,c_6875]) ).
tcf(c_25409,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(X0))) = empty_set )
| ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_10348,c_10681]) ).
tcf(c_25410,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(X0))) = empty_set )
| ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_10348,c_8006]) ).
tcf(c_25411,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(X0))) = empty_set )
| ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_10348,c_7963]) ).
tcf(c_25412,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(X1) = X0 )
| ( apply(identity_relation(X1),sK7(sK6(X1))) = sK7(sK6(X1)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10348,c_5794]) ).
tcf(c_25413,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(X1) = X0 )
| ( apply(identity_relation(X1),sK7(sK6(X1))) = sK7(sK6(X1)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10348,c_5793]) ).
tcf(c_25414,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(X0))) = empty_set )
| ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_10348,c_6878]) ).
tcf(c_25415,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(X0))) = empty_set )
| ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_10348,c_6876]) ).
tcf(c_25416,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(X0))) = empty_set )
| ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_10348,c_8005]) ).
tcf(c_25417,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(X0))) = empty_set )
| ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_10348,c_7962]) ).
tcf(c_25418,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(X0))) = empty_set )
| ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_10348,c_7934]) ).
tcf(c_25419,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(X0))) = empty_set )
| ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_10348,c_6133]) ).
tcf(c_25420,plain,
! [X0: $i] :
( ( sK7(powerset(X0)) = empty_set )
| ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_10348,c_6879]) ).
tcf(c_25421,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(X0)) = empty_set )
| ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_10348,c_6106]) ).
tcf(c_25422,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(X0)) = empty_set )
| ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_10348,c_6105]) ).
tcf(c_25423,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(X0)) = empty_set )
| ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_10348,c_5747]) ).
tcf(c_25424,plain,
! [X0: $i] :
( ( identity_relation(X0) = empty_set )
| ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_10348,c_5776]) ).
tcf(c_25425,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( apply(identity_relation(X1),sK7(sK6(X1))) = sK7(sK6(X1)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10348,c_51]) ).
tcf(c_25426,plain,
! [X0: $i] :
( ( relation_dom(X0) = empty_set )
| ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_10348,c_5663]) ).
tcf(c_25427,plain,
! [X0: $i] :
( ( X0 = empty_set )
| ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_10348,c_52]) ).
tcf(c_25428,plain,
! [X0: $i] :
( function(X0)
| ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_10348,c_98]) ).
tcf(c_25429,plain,
! [X0: $i] :
( relation(X0)
| ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_10348,c_80]) ).
tcf(c_25430,plain,
! [X0: $i] :
( empty(X0)
| ( apply(identity_relation(sK6(X0)),sK7(sK6(sK6(X0)))) = sK7(sK6(sK6(X0))) ) ),
inference(superposition,[status(thm)],[c_10348,c_69]) ).
tcf(c_25431,plain,
! [X0: $i] : apply(identity_relation(powerset(X0)),sK7(sK6(powerset(X0)))) = sK7(sK6(powerset(X0))),
inference(superposition,[status(thm)],[c_10348,c_70]) ).
tcf(c_25432,plain,
apply(identity_relation(sK8),sK7(sK6(sK8))) = sK7(sK6(sK8)),
inference(superposition,[status(thm)],[c_10348,c_74]) ).
tcf(c_25433,plain,
apply(identity_relation(sK9),sK7(sK6(sK9))) = sK7(sK6(sK9)),
inference(superposition,[status(thm)],[c_10348,c_75]) ).
tcf(c_25434,plain,
! [X0: $i] :
( empty(X0)
| ( apply(identity_relation(relation_dom(X0)),sK7(sK6(relation_dom(X0)))) = sK7(sK6(relation_dom(X0))) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_10348,c_88]) ).
tcf(c_25435,plain,
! [X0: $i] :
( function(X0)
| ( apply(identity_relation(identity_relation(X0)),sK7(sK6(identity_relation(X0)))) = sK7(sK6(identity_relation(X0))) ) ),
inference(superposition,[status(thm)],[c_10348,c_5644]) ).
tcf(c_25436,plain,
! [X0: $i] :
( relation(X0)
| ( apply(identity_relation(identity_relation(X0)),sK7(sK6(identity_relation(X0)))) = sK7(sK6(identity_relation(X0))) ) ),
inference(superposition,[status(thm)],[c_10348,c_5633]) ).
tcf(c_25437,plain,
! [X0: $i] :
( empty(X0)
| ( apply(identity_relation(identity_relation(X0)),sK7(sK6(identity_relation(X0)))) = sK7(sK6(identity_relation(X0))) ) ),
inference(superposition,[status(thm)],[c_10348,c_5621]) ).
tcf(c_25438,plain,
apply(identity_relation(sK0),sK7(sK6(sK0))) = sK7(sK6(sK0)),
inference(superposition,[status(thm)],[c_10348,c_24236]) ).
tcf(c_25439,plain,
apply(identity_relation(sK6(powerset(empty_set))),sK7(sK6(sK6(powerset(empty_set))))) = sK7(sK6(sK6(powerset(empty_set)))),
inference(superposition,[status(thm)],[c_10348,c_11408]) ).
tcf(c_25663,plain,
! [X0: $i] :
( element(sK3(X0,sK1,empty_set),sK0)
| ( relation_image(X0,sK1) = relation_image(sK14,empty_set) )
| ( apply(sK14,sK4(sK14,empty_set,sK2(X0,sK1,relation_image(sK14,empty_set)))) = sK2(X0,sK1,relation_image(sK14,empty_set)) )
| ~ function(sK14)
| ~ relation(sK14)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_25159,c_7277]) ).
tcf(c_25664,plain,
! [X0: $i,X1: $i] :
( element(sK3(X0,sK1,empty_set),sK0)
| ( relation_image(X0,sK1) = relation_image(empty_set,X1) )
| ( apply(empty_set,sK4(empty_set,X1,sK2(X0,sK1,relation_image(empty_set,X1)))) = sK2(X0,sK1,relation_image(empty_set,X1)) )
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18922,c_7277]) ).
tcf(c_25665,plain,
! [X0: $i,X1: $i] :
( element(sK3(X1,sK1,empty_set),sK0)
| ( relation_image(identity_relation(X0),empty_set) = relation_image(X1,sK1) )
| ( apply(identity_relation(X0),sK4(identity_relation(X0),empty_set,sK2(X1,sK1,relation_image(identity_relation(X0),empty_set)))) = sK2(X1,sK1,relation_image(identity_relation(X0),empty_set)) )
| ~ function(X1)
| ~ relation(X1)
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_25160,c_7277]) ).
tcf(c_25667,plain,
! [X0: $i,X1: $i] :
( element(sK3(X0,sK1,empty_set),sK0)
| ( relation_image(X0,sK1) = relation_image(empty_set,X1) )
| ( apply(empty_set,sK4(empty_set,X1,sK2(X0,sK1,relation_image(empty_set,X1)))) = sK2(X0,sK1,relation_image(empty_set,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_25664,c_5610,c_82]) ).
tcf(c_25673,plain,
! [X0: $i] :
( element(sK3(X0,sK1,empty_set),sK0)
| ( relation_image(X0,sK1) = empty_set )
| ( apply(sK14,sK4(sK14,empty_set,sK2(X0,sK1,empty_set))) = sK2(X0,sK1,empty_set) )
| ~ function(sK14)
| ~ relation(sK14)
| ~ function(X0)
| ~ relation(X0) ),
inference(light_normalisation,[status(thm)],[c_25663,c_25159]) ).
tcf(c_25674,plain,
! [X0: $i] :
( element(sK3(X0,sK1,empty_set),sK0)
| ( relation_image(X0,sK1) = empty_set )
| ( apply(sK14,sK4(sK14,empty_set,sK2(X0,sK1,empty_set))) = sK2(X0,sK1,empty_set) )
| ~ function(X0)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_25673,c_97,c_96]) ).
tcf(c_25680,plain,
! [X0: $i,X1: $i] :
( element(sK3(X1,sK1,empty_set),sK0)
| ( relation_image(X1,sK1) = empty_set )
| ( apply(identity_relation(X0),sK4(identity_relation(X0),empty_set,sK2(X1,sK1,empty_set))) = sK2(X1,sK1,empty_set) )
| ~ function(X1)
| ~ relation(X1)
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0)) ),
inference(light_normalisation,[status(thm)],[c_25665,c_25160]) ).
tcf(c_25681,plain,
! [X0: $i,X1: $i] :
( element(sK3(X0,sK1,empty_set),sK0)
| ( relation_image(X0,sK1) = empty_set )
| ( apply(identity_relation(X1),sK4(identity_relation(X1),empty_set,sK2(X0,sK1,empty_set))) = sK2(X0,sK1,empty_set) )
| ~ function(X0)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_25680,c_62,c_63]) ).
tcf(c_25702,plain,
! [X0: $i] :
( element(sK2(X0,empty_set,sK1),sK0)
| ( relation_image(X0,relation_image(sK14,empty_set)) = sK1 )
| ( apply(sK14,sK4(sK14,empty_set,sK3(X0,relation_image(sK14,empty_set),sK1))) = sK3(X0,relation_image(sK14,empty_set),sK1) )
| ~ function(sK14)
| ~ relation(sK14)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_25159,c_7399]) ).
tcf(c_25703,plain,
! [X0: $i,X1: $i] :
( element(sK2(X0,empty_set,sK1),sK0)
| ( relation_image(X0,relation_image(empty_set,X1)) = sK1 )
| ( apply(empty_set,sK4(empty_set,X1,sK3(X0,relation_image(empty_set,X1),sK1))) = sK3(X0,relation_image(empty_set,X1),sK1) )
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18922,c_7399]) ).
tcf(c_25704,plain,
! [X0: $i,X1: $i] :
( element(sK2(X1,empty_set,sK1),sK0)
| ( relation_image(X1,relation_image(identity_relation(X0),empty_set)) = sK1 )
| ( apply(identity_relation(X0),sK4(identity_relation(X0),empty_set,sK3(X1,relation_image(identity_relation(X0),empty_set),sK1))) = sK3(X1,relation_image(identity_relation(X0),empty_set),sK1) )
| ~ function(X1)
| ~ relation(X1)
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_25160,c_7399]) ).
tcf(c_25706,plain,
! [X0: $i,X1: $i] :
( element(sK2(X0,empty_set,sK1),sK0)
| ( relation_image(X0,relation_image(empty_set,X1)) = sK1 )
| ( apply(empty_set,sK4(empty_set,X1,sK3(X0,relation_image(empty_set,X1),sK1))) = sK3(X0,relation_image(empty_set,X1),sK1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_25703,c_5610,c_82]) ).
tcf(c_25712,plain,
! [X0: $i] :
( element(sK2(X0,empty_set,sK1),sK0)
| ( relation_image(X0,empty_set) = sK1 )
| ( apply(sK14,sK4(sK14,empty_set,sK3(X0,empty_set,sK1))) = sK3(X0,empty_set,sK1) )
| ~ function(sK14)
| ~ relation(sK14)
| ~ function(X0)
| ~ relation(X0) ),
inference(light_normalisation,[status(thm)],[c_25702,c_25159]) ).
tcf(c_25713,plain,
! [X0: $i] :
( element(sK2(X0,empty_set,sK1),sK0)
| ( relation_image(X0,empty_set) = sK1 )
| ( apply(sK14,sK4(sK14,empty_set,sK3(X0,empty_set,sK1))) = sK3(X0,empty_set,sK1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_25712,c_97,c_96]) ).
tcf(c_25719,plain,
! [X0: $i,X1: $i] :
( element(sK2(X1,empty_set,sK1),sK0)
| ( relation_image(X1,empty_set) = sK1 )
| ( apply(identity_relation(X0),sK4(identity_relation(X0),empty_set,sK3(X1,empty_set,sK1))) = sK3(X1,empty_set,sK1) )
| ~ function(X1)
| ~ relation(X1)
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0)) ),
inference(light_normalisation,[status(thm)],[c_25704,c_25160]) ).
tcf(c_25720,plain,
! [X0: $i,X1: $i] :
( element(sK2(X0,empty_set,sK1),sK0)
| ( relation_image(X0,empty_set) = sK1 )
| ( apply(identity_relation(X1),sK4(identity_relation(X1),empty_set,sK3(X0,empty_set,sK1))) = sK3(X0,empty_set,sK1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_25719,c_62,c_63]) ).
tcf(c_25731,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(sK8),X0) = X1 )
| ~ function(identity_relation(sK8))
| ~ relation(identity_relation(sK8))
| ~ in(sK7(sK6(sK8)),X0)
| ~ in(sK7(sK6(sK8)),relation_dom(identity_relation(sK8)))
| ~ in(sK2(identity_relation(sK8),X0,X1),X1)
| ( sK2(identity_relation(sK8),X0,X1) != sK7(sK6(sK8)) ) ),
inference(superposition,[status(thm)],[c_25432,c_53]) ).
tcf(c_25732,plain,
! [X0: $i] :
( in(sK7(sK6(sK8)),relation_image(identity_relation(sK8),X0))
| ~ function(identity_relation(sK8))
| ~ relation(identity_relation(sK8))
| ~ in(sK7(sK6(sK8)),X0)
| ~ in(sK7(sK6(sK8)),relation_dom(identity_relation(sK8))) ),
inference(superposition,[status(thm)],[c_25432,c_57]) ).
tcf(c_25733,plain,
! [X0: $i] :
( in(sK7(sK6(sK8)),relation_image(identity_relation(sK8),X0))
| ~ in(sK7(sK6(sK8)),X0)
| ~ in(sK7(sK6(sK8)),relation_dom(identity_relation(sK8))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_25732,c_62,c_63]) ).
tcf(c_25737,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(sK8),X0) = X1 )
| ~ in(sK7(sK6(sK8)),X0)
| ~ in(sK7(sK6(sK8)),relation_dom(identity_relation(sK8)))
| ~ in(sK2(identity_relation(sK8),X0,X1),X1)
| ( sK2(identity_relation(sK8),X0,X1) != sK7(sK6(sK8)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_25731,c_62,c_63]) ).
tcf(c_25745,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(sK9),X0) = X1 )
| ~ function(identity_relation(sK9))
| ~ relation(identity_relation(sK9))
| ~ in(sK7(sK6(sK9)),X0)
| ~ in(sK7(sK6(sK9)),relation_dom(identity_relation(sK9)))
| ~ in(sK2(identity_relation(sK9),X0,X1),X1)
| ( sK2(identity_relation(sK9),X0,X1) != sK7(sK6(sK9)) ) ),
inference(superposition,[status(thm)],[c_25433,c_53]) ).
tcf(c_25746,plain,
! [X0: $i] :
( in(sK7(sK6(sK9)),relation_image(identity_relation(sK9),X0))
| ~ function(identity_relation(sK9))
| ~ relation(identity_relation(sK9))
| ~ in(sK7(sK6(sK9)),X0)
| ~ in(sK7(sK6(sK9)),relation_dom(identity_relation(sK9))) ),
inference(superposition,[status(thm)],[c_25433,c_57]) ).
tcf(c_25747,plain,
! [X0: $i] :
( in(sK7(sK6(sK9)),relation_image(identity_relation(sK9),X0))
| ~ in(sK7(sK6(sK9)),X0)
| ~ in(sK7(sK6(sK9)),relation_dom(identity_relation(sK9))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_25746,c_62,c_63]) ).
tcf(c_25751,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(sK9),X0) = X1 )
| ~ in(sK7(sK6(sK9)),X0)
| ~ in(sK7(sK6(sK9)),relation_dom(identity_relation(sK9)))
| ~ in(sK2(identity_relation(sK9),X0,X1),X1)
| ( sK2(identity_relation(sK9),X0,X1) != sK7(sK6(sK9)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_25745,c_62,c_63]) ).
tcf(c_25765,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(powerset(X1))) = X0 )
| ( apply(identity_relation(X1),sK7(sK6(X1))) = sK7(sK6(X1)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10348,c_10679]) ).
tcf(c_25766,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(powerset(X1))) = X0 )
| ( apply(identity_relation(powerset(X1)),sK6(X1)) = sK6(X1) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5806,c_10679]) ).
tcf(c_25767,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(powerset(X1))) = X0 )
| ( apply(identity_relation(X1),sK7(X1)) = sK7(X1) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5807,c_10679]) ).
tcf(c_25768,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(empty_set))) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_83,c_10679]) ).
tcf(c_25769,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(powerset(relation_dom(X0)))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_10679]) ).
tcf(c_25770,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(powerset(identity_relation(X0)))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_10679]) ).
tcf(c_25771,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(sK1))) = X0 )
| ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5890,c_10679]) ).
tcf(c_25772,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(powerset(sK7(powerset(X0))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_10679]) ).
tcf(c_25773,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(powerset(sK7(sK6(powerset(X0)))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_10679]) ).
tcf(c_25774,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(powerset(sK7(sK6(sK6(powerset(X0))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_10679]) ).
tcf(c_25775,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(powerset(relation_image(X1,empty_set)))) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18616,c_10679]) ).
tcf(c_25776,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(powerset(sK7(powerset(sK7(powerset(X0))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_10679]) ).
tcf(c_25777,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(powerset(sK7(powerset(sK7(sK6(powerset(X0)))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_10679]) ).
tcf(c_25816,plain,
apply(identity_relation(sK0),sK7(sK6(sK1))) = sK7(sK6(sK1)),
inference(global_subsumption_just,[status(thm)],[c_11020,c_49,c_6237,c_6638,c_8112,c_11020,c_13256,c_22498]) ).
tcf(c_25818,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(sK0),X0) = X1 )
| ~ function(identity_relation(sK0))
| ~ relation(identity_relation(sK0))
| ~ in(sK7(sK6(sK1)),X0)
| ~ in(sK7(sK6(sK1)),relation_dom(identity_relation(sK0)))
| ~ in(sK2(identity_relation(sK0),X0,X1),X1)
| ( sK2(identity_relation(sK0),X0,X1) != sK7(sK6(sK1)) ) ),
inference(superposition,[status(thm)],[c_25816,c_53]) ).
tcf(c_25819,plain,
! [X0: $i] :
( in(sK7(sK6(sK1)),relation_image(identity_relation(sK0),X0))
| ~ function(identity_relation(sK0))
| ~ relation(identity_relation(sK0))
| ~ in(sK7(sK6(sK1)),X0)
| ~ in(sK7(sK6(sK1)),relation_dom(identity_relation(sK0))) ),
inference(superposition,[status(thm)],[c_25816,c_57]) ).
tcf(c_25820,plain,
! [X0: $i] :
( in(sK7(sK6(sK1)),relation_image(identity_relation(sK0),X0))
| ~ in(sK7(sK6(sK1)),X0)
| ~ in(sK7(sK6(sK1)),relation_dom(identity_relation(sK0))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_25819,c_62,c_63]) ).
tcf(c_25824,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(sK0),X0) = X1 )
| ~ in(sK7(sK6(sK1)),X0)
| ~ in(sK7(sK6(sK1)),relation_dom(identity_relation(sK0)))
| ~ in(sK2(identity_relation(sK0),X0,X1),X1)
| ( sK2(identity_relation(sK0),X0,X1) != sK7(sK6(sK1)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_25818,c_62,c_63]) ).
tcf(c_25832,plain,
! [X0: $i] :
( in(sK6(sK0),relation_image(identity_relation(powerset(sK0)),X0))
| ~ function(identity_relation(powerset(sK0)))
| ~ relation(identity_relation(powerset(sK0)))
| ~ in(sK6(sK0),X0)
| ~ in(sK6(sK0),relation_dom(identity_relation(powerset(sK0)))) ),
inference(superposition,[status(thm)],[c_24238,c_57]) ).
tcf(c_25833,plain,
! [X0: $i] :
( in(sK6(sK0),relation_image(identity_relation(powerset(sK0)),X0))
| ~ in(sK6(sK0),X0)
| ~ in(sK6(sK0),relation_dom(identity_relation(powerset(sK0)))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_25832,c_62,c_63]) ).
tcf(c_25842,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(identity_relation(X0)))) = empty_set )
| ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_10348,c_11341]) ).
tcf(c_25843,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(identity_relation(X0)))) = empty_set )
| ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) ) ),
inference(superposition,[status(thm)],[c_5806,c_11341]) ).
tcf(c_25844,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(identity_relation(X0)))) = empty_set )
| ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) ) ),
inference(superposition,[status(thm)],[c_5807,c_11341]) ).
tcf(c_25845,plain,
sK7(sK6(powerset(identity_relation(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_11341]) ).
tcf(c_25846,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(identity_relation(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_11341]) ).
tcf(c_25847,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(identity_relation(identity_relation(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_11341]) ).
tcf(c_25848,plain,
( ( sK7(sK6(powerset(identity_relation(sK1)))) = empty_set )
| ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) ) ),
inference(superposition,[status(thm)],[c_5890,c_11341]) ).
tcf(c_25849,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(identity_relation(sK7(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_11341]) ).
tcf(c_25850,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(identity_relation(sK7(sK6(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_11341]) ).
tcf(c_25851,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(identity_relation(sK7(sK6(sK6(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_11341]) ).
tcf(c_25852,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(identity_relation(relation_image(X0,empty_set))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_11341]) ).
tcf(c_25853,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(identity_relation(sK7(powerset(sK7(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_11341]) ).
tcf(c_25854,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(identity_relation(sK7(powerset(sK7(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_11341]) ).
tcf(c_25892,plain,
in(empty_set,sK6(sK6(powerset(empty_set)))),
inference(global_subsumption_just,[status(thm)],[c_16842,c_103,c_6362,c_6911,c_8986,c_16843]) ).
tcf(c_25894,plain,
apply(identity_relation(sK6(sK6(powerset(empty_set)))),empty_set) = empty_set,
inference(superposition,[status(thm)],[c_25892,c_151]) ).
tcf(c_25895,plain,
~ in(sK6(sK6(powerset(empty_set))),empty_set),
inference(superposition,[status(thm)],[c_25892,c_85]) ).
tcf(c_25896,plain,
~ empty(sK6(sK6(powerset(empty_set)))),
inference(superposition,[status(thm)],[c_25892,c_84]) ).
tcf(c_25899,plain,
apply(identity_relation(sK6(sK6(powerset(empty_set)))),sK7(sK6(sK6(sK6(powerset(empty_set)))))) = sK7(sK6(sK6(sK6(powerset(empty_set))))),
inference(superposition,[status(thm)],[c_10348,c_25896]) ).
tcf(c_25900,plain,
apply(identity_relation(powerset(sK6(sK6(powerset(empty_set))))),sK6(sK6(sK6(powerset(empty_set))))) = sK6(sK6(sK6(powerset(empty_set)))),
inference(superposition,[status(thm)],[c_5806,c_25896]) ).
tcf(c_25901,plain,
apply(identity_relation(sK6(sK6(powerset(empty_set)))),sK7(sK6(sK6(powerset(empty_set))))) = sK7(sK6(sK6(powerset(empty_set)))),
inference(superposition,[status(thm)],[c_5807,c_25896]) ).
tcf(c_25903,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(sK0),X0) = X1 )
| ~ function(identity_relation(sK0))
| ~ relation(identity_relation(sK0))
| ~ in(sK7(sK6(sK0)),X0)
| ~ in(sK7(sK6(sK0)),relation_dom(identity_relation(sK0)))
| ~ in(sK2(identity_relation(sK0),X0,X1),X1)
| ( sK2(identity_relation(sK0),X0,X1) != sK7(sK6(sK0)) ) ),
inference(superposition,[status(thm)],[c_25438,c_53]) ).
tcf(c_25904,plain,
! [X0: $i] :
( in(sK7(sK6(sK0)),relation_image(identity_relation(sK0),X0))
| ~ function(identity_relation(sK0))
| ~ relation(identity_relation(sK0))
| ~ in(sK7(sK6(sK0)),X0)
| ~ in(sK7(sK6(sK0)),relation_dom(identity_relation(sK0))) ),
inference(superposition,[status(thm)],[c_25438,c_57]) ).
tcf(c_25905,plain,
! [X0: $i] :
( in(sK7(sK6(sK0)),relation_image(identity_relation(sK0),X0))
| ~ in(sK7(sK6(sK0)),X0)
| ~ in(sK7(sK6(sK0)),relation_dom(identity_relation(sK0))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_25904,c_62,c_63]) ).
tcf(c_25909,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(sK0),X0) = X1 )
| ~ in(sK7(sK6(sK0)),X0)
| ~ in(sK7(sK6(sK0)),relation_dom(identity_relation(sK0)))
| ~ in(sK2(identity_relation(sK0),X0,X1),X1)
| ( sK2(identity_relation(sK0),X0,X1) != sK7(sK6(sK0)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_25903,c_62,c_63]) ).
tcf(c_25923,plain,
! [X0: $i] :
( in(empty_set,relation_image(identity_relation(sK6(sK6(powerset(empty_set)))),X0))
| ~ in(empty_set,X0)
| ~ function(identity_relation(sK6(sK6(powerset(empty_set)))))
| ~ relation(identity_relation(sK6(sK6(powerset(empty_set)))))
| ~ in(empty_set,relation_dom(identity_relation(sK6(sK6(powerset(empty_set)))))) ),
inference(superposition,[status(thm)],[c_25894,c_57]) ).
tcf(c_25924,plain,
! [X0: $i] :
( in(empty_set,relation_image(identity_relation(sK6(sK6(powerset(empty_set)))),X0))
| ~ in(empty_set,X0)
| ~ in(empty_set,relation_dom(identity_relation(sK6(sK6(powerset(empty_set)))))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_25923,c_62,c_63]) ).
tcf(c_25932,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(identity_relation(relation_dom(X0))))) = empty_set )
| ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_10348,c_25846]) ).
tcf(c_25933,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(identity_relation(relation_dom(X0))))) = empty_set )
| ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) ) ),
inference(superposition,[status(thm)],[c_5806,c_25846]) ).
tcf(c_25934,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( sK7(sK6(powerset(identity_relation(relation_dom(X0))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_25846]) ).
tcf(c_25935,plain,
sK7(sK6(powerset(identity_relation(relation_dom(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_25846]) ).
tcf(c_25936,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(identity_relation(relation_dom(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_25846]) ).
tcf(c_25937,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(identity_relation(relation_dom(identity_relation(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_25846]) ).
tcf(c_25938,plain,
( ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ( sK7(sK6(powerset(identity_relation(relation_dom(sK1))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5890,c_25846]) ).
tcf(c_25939,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(identity_relation(relation_dom(sK7(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_25846]) ).
tcf(c_25940,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(identity_relation(relation_dom(sK7(sK6(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_25846]) ).
tcf(c_25941,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(identity_relation(relation_dom(sK7(sK6(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_25846]) ).
tcf(c_25942,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(identity_relation(relation_dom(relation_image(X0,empty_set)))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_25846]) ).
tcf(c_25943,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(identity_relation(relation_dom(sK7(powerset(sK7(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_25846]) ).
tcf(c_25944,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(identity_relation(relation_dom(sK7(powerset(sK7(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_25846]) ).
tcf(c_25980,plain,
! [X0: $i] :
( in(sK7(sK6(sK7(powerset(X0)))),X0)
| empty(sK7(powerset(X0))) ),
inference(global_subsumption_just,[status(thm)],[c_16078,c_6837,c_16078]) ).
tcf(c_25981,plain,
! [X0: $i] :
( empty(sK7(powerset(X0)))
| in(sK7(sK6(sK7(powerset(X0)))),X0) ),
inference(renaming,[status(thm)],[c_25980]) ).
tcf(c_25987,plain,
( empty(sK7(powerset(empty_set)))
| in(sK7(sK6(empty_set)),empty_set) ),
inference(superposition,[status(thm)],[c_8004,c_25981]) ).
tcf(c_25988,plain,
! [X0: $i,X1: $i] :
( empty(sK7(powerset(relation_image(X0,X1))))
| ( apply(X0,sK4(X0,X1,sK7(sK6(sK7(powerset(relation_image(X0,X1))))))) = sK7(sK6(sK7(powerset(relation_image(X0,X1))))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_25981,c_60]) ).
tcf(c_25989,plain,
! [X0: $i] :
( empty(sK7(powerset(X0)))
| ( apply(identity_relation(X0),sK7(sK6(sK7(powerset(X0))))) = sK7(sK6(sK7(powerset(X0)))) ) ),
inference(superposition,[status(thm)],[c_25981,c_151]) ).
tcf(c_25990,plain,
! [X0: $i] :
( empty(sK7(powerset(X0)))
| ~ in(X0,sK7(sK6(sK7(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_25981,c_85]) ).
tcf(c_25993,plain,
( empty(sK7(powerset(sK1)))
| element(sK7(sK6(sK7(powerset(sK1)))),sK0) ),
inference(superposition,[status(thm)],[c_25981,c_5838]) ).
tcf(c_25994,plain,
! [X0: $i] :
( empty(X0)
| empty(sK7(powerset(sK6(X0))))
| element(sK7(sK6(sK7(powerset(sK6(X0))))),X0) ),
inference(superposition,[status(thm)],[c_25981,c_5839]) ).
tcf(c_25995,plain,
! [X0: $i] :
( empty(sK7(powerset(sK7(powerset(X0)))))
| element(sK7(sK6(sK7(powerset(sK7(powerset(X0)))))),X0) ),
inference(superposition,[status(thm)],[c_25981,c_5840]) ).
tcf(c_25999,plain,
! [X0: $i] :
( empty(sK7(powerset(sK7(sK6(powerset(X0))))))
| element(sK7(sK6(sK7(powerset(sK7(sK6(powerset(X0))))))),X0) ),
inference(superposition,[status(thm)],[c_25981,c_9820]) ).
tcf(c_26001,plain,
! [X0: $i] :
( empty(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))
| element(sK7(sK6(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))),X0) ),
inference(superposition,[status(thm)],[c_25981,c_14092]) ).
tcf(c_26003,plain,
( empty(empty_set)
| in(sK7(sK6(empty_set)),empty_set) ),
inference(light_normalisation,[status(thm)],[c_25987,c_8004]) ).
tcf(c_26119,plain,
( empty(sK7(powerset(empty_set)))
| ~ in(empty_set,sK7(sK6(empty_set))) ),
inference(superposition,[status(thm)],[c_8004,c_25990]) ).
tcf(c_26120,plain,
( empty(empty_set)
| ~ in(empty_set,sK7(sK6(empty_set))) ),
inference(light_normalisation,[status(thm)],[c_26119,c_8004]) ).
tcf(c_26126,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(identity_relation(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_25846]) ).
tcf(c_26127,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(identity_relation(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_11341]) ).
tcf(c_26128,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(powerset(sK7(powerset(sK7(sK6(sK6(powerset(X0))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_10679]) ).
tcf(c_26129,plain,
! [X0: $i] :
( ( relation_dom(sK7(sK6(powerset(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_17536]) ).
tcf(c_26130,plain,
! [X0: $i] :
( ( identity_relation(sK7(sK6(powerset(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_17479]) ).
tcf(c_26131,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(powerset(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_16756]) ).
tcf(c_26132,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(identity_relation(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_13969]) ).
tcf(c_26133,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_13853]) ).
tcf(c_26134,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(relation_dom(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_13817]) ).
tcf(c_26135,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(relation_dom(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_13649]) ).
tcf(c_26136,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(relation_dom(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_13044]) ).
tcf(c_26137,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(identity_relation(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_12909]) ).
tcf(c_26138,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(identity_relation(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_12871]) ).
tcf(c_26139,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(relation_dom(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_12755]) ).
tcf(c_26140,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(relation_dom(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_12356]) ).
tcf(c_26141,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(powerset(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_12318]) ).
tcf(c_26142,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(powerset(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_12212]) ).
tcf(c_26143,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(powerset(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_12135]) ).
tcf(c_26144,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(relation_dom(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_12099]) ).
tcf(c_26145,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(relation_dom(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_12063]) ).
tcf(c_26146,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(relation_dom(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_12027]) ).
tcf(c_26147,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_11953]) ).
tcf(c_26148,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(powerset(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_11431]) ).
tcf(c_26149,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_9347]) ).
tcf(c_26150,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_9319]) ).
tcf(c_26151,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_6877]) ).
tcf(c_26152,plain,
! [X0: $i] :
( ( relation_dom(sK7(sK6(powerset(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_10680]) ).
tcf(c_26153,plain,
! [X0: $i] :
( ( identity_relation(sK7(sK6(powerset(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_10678]) ).
tcf(c_26154,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(powerset(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_15645]) ).
tcf(c_26155,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(identity_relation(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_9748]) ).
tcf(c_26156,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_9682]) ).
tcf(c_26157,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_11340]) ).
tcf(c_26158,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_9747]) ).
tcf(c_26159,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_9681]) ).
tcf(c_26160,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(identity_relation(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_9115]) ).
tcf(c_26161,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(identity_relation(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_9088]) ).
tcf(c_26162,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_9114]) ).
tcf(c_26163,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_9087]) ).
tcf(c_26164,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(powerset(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_8009]) ).
tcf(c_26165,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(powerset(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_7966]) ).
tcf(c_26166,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(powerset(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_7938]) ).
tcf(c_26167,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_9017]) ).
tcf(c_26168,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_8992]) ).
tcf(c_26169,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_8957]) ).
tcf(c_26170,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_8561]) ).
tcf(c_26171,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(powerset(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_6875]) ).
tcf(c_26172,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(sK7(powerset(sK7(sK6(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_10681]) ).
tcf(c_26173,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(sK7(powerset(sK7(sK6(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_8006]) ).
tcf(c_26174,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(sK7(powerset(sK7(sK6(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_7963]) ).
tcf(c_26175,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK7(powerset(sK7(sK6(sK6(powerset(X0))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_5794]) ).
tcf(c_26176,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_5793]) ).
tcf(c_26177,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(sK7(powerset(sK7(sK6(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_6878]) ).
tcf(c_26178,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(sK7(powerset(sK7(sK6(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_6876]) ).
tcf(c_26179,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_8005]) ).
tcf(c_26180,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_7962]) ).
tcf(c_26181,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_7934]) ).
tcf(c_26182,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_6133]) ).
tcf(c_26191,plain,
! [X0: $i] :
( function(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_98]) ).
tcf(c_26192,plain,
! [X0: $i] :
( relation(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_80]) ).
tcf(c_26579,plain,
( empty(sK0)
| empty(sK7(powerset(sK1)))
| in(sK7(sK6(sK7(powerset(sK1)))),sK0) ),
inference(superposition,[status(thm)],[c_25993,c_71]) ).
tcf(c_26580,plain,
( empty(sK7(powerset(sK1)))
| in(sK7(sK6(sK7(powerset(sK1)))),sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_26579,c_24236]) ).
tcf(c_26588,plain,
! [X0: $i] :
( ( relation_image(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))),empty_set) = empty_set )
| ~ empty(X0)
| ~ relation(sK7(powerset(sK7(sK6(sK6(powerset(X0))))))) ),
inference(superposition,[status(thm)],[c_26191,c_23329]) ).
tcf(c_26597,plain,
( empty(sK7(powerset(sK1)))
| ( apply(identity_relation(sK0),sK7(sK6(sK7(powerset(sK1))))) = sK7(sK6(sK7(powerset(sK1)))) ) ),
inference(superposition,[status(thm)],[c_26580,c_151]) ).
tcf(c_26598,plain,
( empty(sK7(powerset(sK1)))
| ~ in(sK0,sK7(sK6(sK7(powerset(sK1))))) ),
inference(superposition,[status(thm)],[c_26580,c_85]) ).
tcf(c_26622,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(identity_relation(powerset(powerset(X0))),X1) = X2 )
| ~ function(identity_relation(powerset(powerset(X0))))
| ~ relation(identity_relation(powerset(powerset(X0))))
| ~ in(sK6(powerset(X0)),X1)
| ~ in(sK6(powerset(X0)),relation_dom(identity_relation(powerset(powerset(X0)))))
| ~ in(sK2(identity_relation(powerset(powerset(X0))),X1,X2),X2)
| ( sK2(identity_relation(powerset(powerset(X0))),X1,X2) != sK6(powerset(X0)) ) ),
inference(superposition,[status(thm)],[c_16953,c_53]) ).
tcf(c_26623,plain,
! [X0: $i,X1: $i] :
( in(sK6(powerset(X0)),relation_image(identity_relation(powerset(powerset(X0))),X1))
| ~ function(identity_relation(powerset(powerset(X0))))
| ~ relation(identity_relation(powerset(powerset(X0))))
| ~ in(sK6(powerset(X0)),X1)
| ~ in(sK6(powerset(X0)),relation_dom(identity_relation(powerset(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_16953,c_57]) ).
tcf(c_26624,plain,
! [X0: $i,X1: $i] :
( in(sK6(powerset(X0)),relation_image(identity_relation(powerset(powerset(X0))),X1))
| ~ in(sK6(powerset(X0)),X1)
| ~ in(sK6(powerset(X0)),relation_dom(identity_relation(powerset(powerset(X0))))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_26623,c_62,c_63]) ).
tcf(c_26628,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(identity_relation(powerset(powerset(X0))),X1) = X2 )
| ~ in(sK6(powerset(X0)),X1)
| ~ in(sK6(powerset(X0)),relation_dom(identity_relation(powerset(powerset(X0)))))
| ~ in(sK2(identity_relation(powerset(powerset(X0))),X1,X2),X2)
| ( sK2(identity_relation(powerset(powerset(X0))),X1,X2) != sK6(powerset(X0)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_26622,c_62,c_63]) ).
tcf(c_26642,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(relation_dom(X1))) = X0 )
| ( apply(identity_relation(X1),sK7(sK6(X1))) = sK7(sK6(X1)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10348,c_18503]) ).
tcf(c_26643,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(relation_dom(X1))) = X0 )
| ( apply(identity_relation(powerset(X1)),sK6(X1)) = sK6(X1) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5806,c_18503]) ).
tcf(c_26644,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(relation_dom(X1))) = X0 )
| ( apply(identity_relation(X1),sK7(X1)) = sK7(X1) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5807,c_18503]) ).
tcf(c_26645,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(empty_set))) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_83,c_18503]) ).
tcf(c_26646,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(relation_dom(relation_dom(X0)))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_18503]) ).
tcf(c_26647,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(relation_dom(identity_relation(X0)))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_18503]) ).
tcf(c_26648,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(sK1))) = X0 )
| ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5890,c_18503]) ).
tcf(c_26649,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(relation_dom(sK7(powerset(X0))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_18503]) ).
tcf(c_26650,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(relation_dom(sK7(sK6(powerset(X0)))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_18503]) ).
tcf(c_26651,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(relation_dom(sK7(sK6(sK6(powerset(X0))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_18503]) ).
tcf(c_26652,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(relation_dom(relation_image(X1,empty_set)))) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18616,c_18503]) ).
tcf(c_26653,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(relation_dom(sK7(powerset(sK7(powerset(X0))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_18503]) ).
tcf(c_26654,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(relation_dom(sK7(powerset(sK7(sK6(powerset(X0)))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_18503]) ).
tcf(c_26655,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_18503]) ).
tcf(c_26727,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK7(powerset(X0))))) = empty_set )
| ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_10348,c_8565]) ).
tcf(c_26728,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK7(powerset(X0))))) = empty_set )
| ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) ) ),
inference(superposition,[status(thm)],[c_5806,c_8565]) ).
tcf(c_26729,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( relation_dom(relation_dom(relation_dom(sK7(powerset(X0))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_8565]) ).
tcf(c_26730,plain,
relation_dom(relation_dom(relation_dom(sK7(powerset(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_8565]) ).
tcf(c_26731,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK7(powerset(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_8565]) ).
tcf(c_26732,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK7(powerset(identity_relation(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_8565]) ).
tcf(c_26733,plain,
( ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ( relation_dom(relation_dom(relation_dom(sK7(powerset(sK1))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5890,c_8565]) ).
tcf(c_26737,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK7(powerset(relation_image(X0,empty_set)))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_8565]) ).
tcf(c_26738,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK7(powerset(sK7(powerset(sK7(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_8565]) ).
tcf(c_26739,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK7(powerset(sK7(powerset(sK7(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_8565]) ).
tcf(c_26740,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK7(powerset(sK7(powerset(sK7(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_8565]) ).
tcf(c_26805,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(sK7(powerset(X0))))) = empty_set )
| ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_10348,c_8961]) ).
tcf(c_26806,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(sK7(powerset(X0))))) = empty_set )
| ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) ) ),
inference(superposition,[status(thm)],[c_5806,c_8961]) ).
tcf(c_26807,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( identity_relation(relation_dom(relation_dom(sK7(powerset(X0))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_8961]) ).
tcf(c_26808,plain,
identity_relation(relation_dom(relation_dom(sK7(powerset(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_8961]) ).
tcf(c_26809,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(sK7(powerset(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_8961]) ).
tcf(c_26810,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(sK7(powerset(identity_relation(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_8961]) ).
tcf(c_26811,plain,
( ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ( identity_relation(relation_dom(relation_dom(sK7(powerset(sK1))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5890,c_8961]) ).
tcf(c_26815,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(sK7(powerset(relation_image(X0,empty_set)))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_8961]) ).
tcf(c_26816,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(sK7(powerset(sK7(powerset(sK7(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_8961]) ).
tcf(c_26817,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(sK7(powerset(sK7(powerset(sK7(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_8961]) ).
tcf(c_26818,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(sK7(powerset(sK7(powerset(sK7(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_8961]) ).
tcf(c_26854,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(sK7(powerset(X0))))) = empty_set )
| ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_10348,c_8996]) ).
tcf(c_26855,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(sK7(powerset(X0))))) = empty_set )
| ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) ) ),
inference(superposition,[status(thm)],[c_5806,c_8996]) ).
tcf(c_26856,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( identity_relation(identity_relation(relation_dom(sK7(powerset(X0))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_8996]) ).
tcf(c_26857,plain,
identity_relation(identity_relation(relation_dom(sK7(powerset(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_8996]) ).
tcf(c_26858,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(sK7(powerset(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_8996]) ).
tcf(c_26859,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(sK7(powerset(identity_relation(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_8996]) ).
tcf(c_26860,plain,
( ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ( identity_relation(identity_relation(relation_dom(sK7(powerset(sK1))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5890,c_8996]) ).
tcf(c_26864,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(sK7(powerset(relation_image(X0,empty_set)))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_8996]) ).
tcf(c_26865,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(sK7(powerset(sK7(powerset(sK7(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_8996]) ).
tcf(c_26866,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(sK7(powerset(sK7(powerset(sK7(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_8996]) ).
tcf(c_26867,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(sK7(powerset(sK7(powerset(sK7(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_8996]) ).
tcf(c_26905,plain,
apply(identity_relation(sK0),sK7(sK6(sK6(sK1)))) = sK7(sK6(sK6(sK1))),
inference(global_subsumption_just,[status(thm)],[c_14213,c_49,c_6237,c_6638,c_8112,c_13256,c_14213,c_22498]) ).
tcf(c_26907,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(sK0),X0) = X1 )
| ~ function(identity_relation(sK0))
| ~ relation(identity_relation(sK0))
| ~ in(sK7(sK6(sK6(sK1))),X0)
| ~ in(sK2(identity_relation(sK0),X0,X1),X1)
| ~ in(sK7(sK6(sK6(sK1))),relation_dom(identity_relation(sK0)))
| ( sK2(identity_relation(sK0),X0,X1) != sK7(sK6(sK6(sK1))) ) ),
inference(superposition,[status(thm)],[c_26905,c_53]) ).
tcf(c_26908,plain,
! [X0: $i] :
( in(sK7(sK6(sK6(sK1))),relation_image(identity_relation(sK0),X0))
| ~ function(identity_relation(sK0))
| ~ relation(identity_relation(sK0))
| ~ in(sK7(sK6(sK6(sK1))),X0)
| ~ in(sK7(sK6(sK6(sK1))),relation_dom(identity_relation(sK0))) ),
inference(superposition,[status(thm)],[c_26905,c_57]) ).
tcf(c_26909,plain,
! [X0: $i] :
( in(sK7(sK6(sK6(sK1))),relation_image(identity_relation(sK0),X0))
| ~ in(sK7(sK6(sK6(sK1))),X0)
| ~ in(sK7(sK6(sK6(sK1))),relation_dom(identity_relation(sK0))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_26908,c_62,c_63]) ).
tcf(c_26913,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(sK0),X0) = X1 )
| ~ in(sK7(sK6(sK6(sK1))),X0)
| ~ in(sK2(identity_relation(sK0),X0,X1),X1)
| ~ in(sK7(sK6(sK6(sK1))),relation_dom(identity_relation(sK0)))
| ( sK2(identity_relation(sK0),X0,X1) != sK7(sK6(sK6(sK1))) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_26907,c_62,c_63]) ).
tcf(c_26960,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(X1))) = X0 )
| ( apply(identity_relation(X1),sK7(sK6(X1))) = sK7(sK6(X1)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10348,c_20393]) ).
tcf(c_26961,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(X1))) = X0 )
| ( apply(identity_relation(powerset(X1)),sK6(X1)) = sK6(X1) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5806,c_20393]) ).
tcf(c_26962,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(X1))) = X0 )
| ( apply(identity_relation(X1),sK7(X1)) = sK7(X1) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5807,c_20393]) ).
tcf(c_26963,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(empty_set))) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_83,c_20393]) ).
tcf(c_26964,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(X0)))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_20393]) ).
tcf(c_26965,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(identity_relation(X0)))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_20393]) ).
tcf(c_26966,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK1))) = X0 )
| ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5890,c_20393]) ).
tcf(c_26967,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(sK7(powerset(X0))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_20393]) ).
tcf(c_26968,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(sK7(sK6(powerset(X0)))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_20393]) ).
tcf(c_26969,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(sK7(sK6(sK6(powerset(X0))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_20393]) ).
tcf(c_26970,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_image(X1,empty_set)))) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18616,c_20393]) ).
tcf(c_26971,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(sK7(powerset(sK7(powerset(X0))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_20393]) ).
tcf(c_26972,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(sK7(powerset(sK7(sK6(powerset(X0)))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_20393]) ).
tcf(c_26973,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_20393]) ).
tcf(c_27085,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(relation_dom(X1))) = X0 )
| ( apply(identity_relation(X1),sK7(sK6(X1))) = sK7(sK6(X1)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10348,c_20489]) ).
tcf(c_27086,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(relation_dom(X1))) = X0 )
| ( apply(identity_relation(powerset(X1)),sK6(X1)) = sK6(X1) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5806,c_20489]) ).
tcf(c_27087,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(relation_dom(X1))) = X0 )
| ( apply(identity_relation(X1),sK7(X1)) = sK7(X1) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5807,c_20489]) ).
tcf(c_27088,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(empty_set))) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_83,c_20489]) ).
tcf(c_27089,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(relation_dom(relation_dom(X0)))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_20489]) ).
tcf(c_27090,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(relation_dom(identity_relation(X0)))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_20489]) ).
tcf(c_27091,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(sK1))) = X0 )
| ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5890,c_20489]) ).
tcf(c_27092,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(relation_dom(sK7(powerset(X0))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_20489]) ).
tcf(c_27093,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(relation_dom(sK7(sK6(powerset(X0)))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_20489]) ).
tcf(c_27094,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(relation_dom(sK7(sK6(sK6(powerset(X0))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_20489]) ).
tcf(c_27095,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(relation_dom(relation_image(X1,empty_set)))) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18616,c_20489]) ).
tcf(c_27096,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(relation_dom(sK7(powerset(sK7(powerset(X0))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_20489]) ).
tcf(c_27097,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(relation_dom(sK7(powerset(sK7(sK6(powerset(X0)))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_20489]) ).
tcf(c_27098,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_20489]) ).
tcf(c_27179,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( relation_dom(relation_dom(sK7(powerset(relation_dom(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10348,c_21512]) ).
tcf(c_27180,plain,
! [X0: $i] :
( ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ( relation_dom(relation_dom(sK7(powerset(relation_dom(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_21512]) ).
tcf(c_27181,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( relation_dom(relation_dom(sK7(powerset(relation_dom(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_21512]) ).
tcf(c_27182,plain,
relation_dom(relation_dom(sK7(powerset(relation_dom(relation_dom(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_21512]) ).
tcf(c_27183,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(powerset(relation_dom(relation_dom(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_21512]) ).
tcf(c_27184,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(powerset(relation_dom(relation_dom(identity_relation(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_21512]) ).
tcf(c_27185,plain,
( ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ( relation_dom(relation_dom(sK7(powerset(relation_dom(relation_dom(sK1)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5890,c_21512]) ).
tcf(c_27186,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(powerset(relation_dom(relation_dom(sK7(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_21512]) ).
tcf(c_27187,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(powerset(relation_dom(relation_dom(sK7(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_21512]) ).
tcf(c_27188,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(powerset(relation_dom(relation_dom(sK7(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_21512]) ).
tcf(c_27189,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(powerset(relation_dom(relation_dom(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_21512]) ).
tcf(c_27190,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(powerset(relation_dom(relation_dom(sK7(powerset(sK7(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_21512]) ).
tcf(c_27191,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(powerset(relation_dom(relation_dom(sK7(powerset(sK7(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_21512]) ).
tcf(c_27192,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(powerset(relation_dom(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_21512]) ).
tcf(c_27246,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10348,c_21763]) ).
tcf(c_27247,plain,
! [X0: $i] :
( ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_21763]) ).
tcf(c_27248,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_21763]) ).
tcf(c_27249,plain,
relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_21763]) ).
tcf(c_27250,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_86,c_21763]) ).
tcf(c_27251,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(identity_relation(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_21763]) ).
tcf(c_27252,plain,
( ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK1)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5890,c_21763]) ).
tcf(c_27253,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK7(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_21763]) ).
tcf(c_27254,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK7(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_21763]) ).
tcf(c_27255,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK7(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_21763]) ).
tcf(c_27256,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_18616,c_21763]) ).
tcf(c_27257,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK7(powerset(sK7(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_21763]) ).
tcf(c_27258,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK7(powerset(sK7(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_21763]) ).
tcf(c_27259,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_21763]) ).
tcf(c_27363,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(sK7(powerset(X0))))) = empty_set )
| ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_10348,c_9021]) ).
tcf(c_27364,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(sK7(powerset(X0))))) = empty_set )
| ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) ) ),
inference(superposition,[status(thm)],[c_5806,c_9021]) ).
tcf(c_27365,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( sK7(powerset(relation_dom(sK7(powerset(X0))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_9021]) ).
tcf(c_27366,plain,
sK7(powerset(relation_dom(sK7(powerset(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_9021]) ).
tcf(c_27367,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(sK7(powerset(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_9021]) ).
tcf(c_27368,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(sK7(powerset(identity_relation(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_9021]) ).
tcf(c_27369,plain,
( ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ( sK7(powerset(relation_dom(sK7(powerset(sK1))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5890,c_9021]) ).
tcf(c_27373,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(sK7(powerset(relation_image(X0,empty_set)))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_9021]) ).
tcf(c_27374,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(sK7(powerset(sK7(powerset(sK7(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_9021]) ).
tcf(c_27375,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(sK7(powerset(sK7(powerset(sK7(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_9021]) ).
tcf(c_27376,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(sK7(powerset(sK7(powerset(sK7(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_9021]) ).
tcf(c_27448,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(sK7(powerset(X0))))) = empty_set )
| ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_10348,c_9091]) ).
tcf(c_27449,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(sK7(powerset(X0))))) = empty_set )
| ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) ) ),
inference(superposition,[status(thm)],[c_5806,c_9091]) ).
tcf(c_27450,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( identity_relation(sK7(powerset(sK7(powerset(X0))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_9091]) ).
tcf(c_27451,plain,
identity_relation(sK7(powerset(sK7(powerset(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_9091]) ).
tcf(c_27452,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(sK7(powerset(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_9091]) ).
tcf(c_27453,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(sK7(powerset(identity_relation(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_9091]) ).
tcf(c_27454,plain,
( ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ( identity_relation(sK7(powerset(sK7(powerset(sK1))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5890,c_9091]) ).
tcf(c_27458,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(sK7(powerset(relation_image(X0,empty_set)))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_9091]) ).
tcf(c_27459,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(sK7(powerset(sK7(powerset(sK7(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_9091]) ).
tcf(c_27460,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(sK7(powerset(sK7(powerset(sK7(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_9091]) ).
tcf(c_27461,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(sK7(powerset(sK7(powerset(sK7(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_9091]) ).
tcf(c_27584,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(sK7(powerset(X0))))) = empty_set )
| ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_10348,c_9118]) ).
tcf(c_27585,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(sK7(powerset(X0))))) = empty_set )
| ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) ) ),
inference(superposition,[status(thm)],[c_5806,c_9118]) ).
tcf(c_27586,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( relation_dom(sK7(powerset(sK7(powerset(X0))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_9118]) ).
tcf(c_27587,plain,
relation_dom(sK7(powerset(sK7(powerset(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_9118]) ).
tcf(c_27588,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(sK7(powerset(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_9118]) ).
tcf(c_27589,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(sK7(powerset(identity_relation(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_9118]) ).
tcf(c_27590,plain,
( ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ( relation_dom(sK7(powerset(sK7(powerset(sK1))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5890,c_9118]) ).
tcf(c_27594,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(sK7(powerset(relation_image(X0,empty_set)))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_9118]) ).
tcf(c_27595,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(sK7(powerset(sK7(powerset(sK7(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_9118]) ).
tcf(c_27596,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(sK7(powerset(sK7(powerset(sK7(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_9118]) ).
tcf(c_27597,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(sK7(powerset(sK7(powerset(sK7(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_9118]) ).
tcf(c_27710,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(X1)) = X0 )
| ( apply(identity_relation(X1),sK7(sK6(X1))) = sK7(sK6(X1)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10348,c_9348]) ).
tcf(c_27711,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(X1)) = X0 )
| ( apply(identity_relation(powerset(X1)),sK6(X1)) = sK6(X1) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5806,c_9348]) ).
tcf(c_27712,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(X1)) = X0 )
| ( apply(identity_relation(X1),sK7(X1)) = sK7(X1) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5807,c_9348]) ).
tcf(c_27713,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(empty_set)) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_83,c_9348]) ).
tcf(c_27714,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(relation_dom(X0))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_9348]) ).
tcf(c_27715,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(identity_relation(X0))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_9348]) ).
tcf(c_27716,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK1)) = X0 )
| ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5890,c_9348]) ).
tcf(c_27717,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(sK7(powerset(X0)))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_9348]) ).
tcf(c_27718,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(sK7(sK6(powerset(X0))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_9348]) ).
tcf(c_27719,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(sK7(sK6(sK6(powerset(X0)))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_9348]) ).
tcf(c_27720,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(relation_image(X1,empty_set))) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18616,c_9348]) ).
tcf(c_27721,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(sK7(powerset(sK7(powerset(X0)))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_9348]) ).
tcf(c_27722,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(sK7(powerset(sK7(sK6(powerset(X0))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_9348]) ).
tcf(c_27723,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_9348]) ).
tcf(c_27825,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( identity_relation(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10348,c_21914]) ).
tcf(c_27826,plain,
! [X0: $i] :
( ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ( identity_relation(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_21914]) ).
tcf(c_27827,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( identity_relation(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_21914]) ).
tcf(c_27828,plain,
identity_relation(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_21914]) ).
tcf(c_27829,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_21914]) ).
tcf(c_27830,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(identity_relation(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_21914]) ).
tcf(c_27831,plain,
( ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ( identity_relation(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK1)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5890,c_21914]) ).
tcf(c_27832,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK7(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_21914]) ).
tcf(c_27833,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK7(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_21914]) ).
tcf(c_27834,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK7(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_21914]) ).
tcf(c_27835,plain,
! [X0: $i] :
( ( identity_relation(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_18616,c_21914]) ).
tcf(c_27836,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK7(powerset(sK7(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_21914]) ).
tcf(c_27837,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK7(powerset(sK7(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_21914]) ).
tcf(c_27838,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_21914]) ).
tcf(c_27905,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( identity_relation(identity_relation(relation_dom(relation_dom(relation_dom(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10348,c_22031]) ).
tcf(c_27906,plain,
! [X0: $i] :
( ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ( identity_relation(identity_relation(relation_dom(relation_dom(relation_dom(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_22031]) ).
tcf(c_27907,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( identity_relation(identity_relation(relation_dom(relation_dom(relation_dom(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_22031]) ).
tcf(c_27908,plain,
identity_relation(identity_relation(relation_dom(relation_dom(relation_dom(relation_dom(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_22031]) ).
tcf(c_27909,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_22031]) ).
tcf(c_27910,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(relation_dom(relation_dom(relation_dom(identity_relation(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_22031]) ).
tcf(c_27911,plain,
( ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ( identity_relation(identity_relation(relation_dom(relation_dom(relation_dom(relation_dom(sK1)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5890,c_22031]) ).
tcf(c_27912,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(relation_dom(relation_dom(relation_dom(sK7(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_22031]) ).
tcf(c_27913,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(relation_dom(relation_dom(relation_dom(sK7(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_22031]) ).
tcf(c_27914,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(relation_dom(relation_dom(relation_dom(sK7(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_22031]) ).
tcf(c_27915,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(relation_dom(relation_dom(relation_dom(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_22031]) ).
tcf(c_27916,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(relation_dom(relation_dom(relation_dom(sK7(powerset(sK7(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_22031]) ).
tcf(c_27917,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(relation_dom(relation_dom(relation_dom(sK7(powerset(sK7(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_22031]) ).
tcf(c_27918,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(relation_dom(relation_dom(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_22031]) ).
tcf(c_28043,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( sK7(powerset(relation_dom(relation_dom(relation_dom(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10348,c_22121]) ).
tcf(c_28044,plain,
! [X0: $i] :
( ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ( sK7(powerset(relation_dom(relation_dom(relation_dom(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_22121]) ).
tcf(c_28045,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( sK7(powerset(relation_dom(relation_dom(relation_dom(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_22121]) ).
tcf(c_28046,plain,
sK7(powerset(relation_dom(relation_dom(relation_dom(relation_dom(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_22121]) ).
tcf(c_28047,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_22121]) ).
tcf(c_28048,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(relation_dom(relation_dom(relation_dom(identity_relation(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_22121]) ).
tcf(c_28049,plain,
( ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ( sK7(powerset(relation_dom(relation_dom(relation_dom(relation_dom(sK1)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5890,c_22121]) ).
tcf(c_28050,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(relation_dom(relation_dom(relation_dom(sK7(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_22121]) ).
tcf(c_28051,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(relation_dom(relation_dom(relation_dom(sK7(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_22121]) ).
tcf(c_28052,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(relation_dom(relation_dom(relation_dom(sK7(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_22121]) ).
tcf(c_28053,plain,
! [X0: $i] :
( ( sK7(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_18616,c_22121]) ).
tcf(c_28054,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(relation_dom(relation_dom(relation_dom(sK7(powerset(sK7(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_22121]) ).
tcf(c_28055,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(relation_dom(relation_dom(relation_dom(sK7(powerset(sK7(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_22121]) ).
tcf(c_28056,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(relation_dom(relation_dom(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_22121]) ).
tcf(c_28249,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( identity_relation(relation_dom(sK7(powerset(relation_dom(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10348,c_22338]) ).
tcf(c_28250,plain,
! [X0: $i] :
( ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ( identity_relation(relation_dom(sK7(powerset(relation_dom(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_22338]) ).
tcf(c_28251,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( identity_relation(relation_dom(sK7(powerset(relation_dom(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_22338]) ).
tcf(c_28252,plain,
identity_relation(relation_dom(sK7(powerset(relation_dom(relation_dom(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_22338]) ).
tcf(c_28253,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(powerset(relation_dom(relation_dom(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_22338]) ).
tcf(c_28254,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(powerset(relation_dom(relation_dom(identity_relation(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_22338]) ).
tcf(c_28255,plain,
( ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ( identity_relation(relation_dom(sK7(powerset(relation_dom(relation_dom(sK1)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5890,c_22338]) ).
tcf(c_28256,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(powerset(relation_dom(relation_dom(sK7(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_22338]) ).
tcf(c_28257,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(powerset(relation_dom(relation_dom(sK7(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_22338]) ).
tcf(c_28258,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(powerset(relation_dom(relation_dom(sK7(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_22338]) ).
tcf(c_28259,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(powerset(relation_dom(relation_dom(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_22338]) ).
tcf(c_28260,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(powerset(relation_dom(relation_dom(sK7(powerset(sK7(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_22338]) ).
tcf(c_28261,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(powerset(relation_dom(relation_dom(sK7(powerset(sK7(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_22338]) ).
tcf(c_28262,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(powerset(relation_dom(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_22338]) ).
tcf(c_28425,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(sK7(powerset(X0))))) = empty_set )
| ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_10348,c_9685]) ).
tcf(c_28426,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(sK7(powerset(X0))))) = empty_set )
| ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) ) ),
inference(superposition,[status(thm)],[c_5806,c_9685]) ).
tcf(c_28427,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( identity_relation(identity_relation(identity_relation(sK7(powerset(X0))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_9685]) ).
tcf(c_28428,plain,
identity_relation(identity_relation(identity_relation(sK7(powerset(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_9685]) ).
tcf(c_28429,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(sK7(powerset(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_9685]) ).
tcf(c_28430,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(sK7(powerset(identity_relation(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_9685]) ).
tcf(c_28431,plain,
( ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ( identity_relation(identity_relation(identity_relation(sK7(powerset(sK1))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5890,c_9685]) ).
tcf(c_28435,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(sK7(powerset(relation_image(X0,empty_set)))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_9685]) ).
tcf(c_28436,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(sK7(powerset(sK7(powerset(sK7(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_9685]) ).
tcf(c_28437,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(sK7(powerset(sK7(powerset(sK7(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_9685]) ).
tcf(c_28438,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(sK7(powerset(sK7(powerset(sK7(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_9685]) ).
tcf(c_28568,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(sK7(powerset(X0))))) = empty_set )
| ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_10348,c_9751]) ).
tcf(c_28569,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(sK7(powerset(X0))))) = empty_set )
| ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) ) ),
inference(superposition,[status(thm)],[c_5806,c_9751]) ).
tcf(c_28570,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( sK7(powerset(identity_relation(sK7(powerset(X0))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_9751]) ).
tcf(c_28571,plain,
sK7(powerset(identity_relation(sK7(powerset(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_9751]) ).
tcf(c_28572,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(sK7(powerset(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_9751]) ).
tcf(c_28573,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(sK7(powerset(identity_relation(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_9751]) ).
tcf(c_28574,plain,
( ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ( sK7(powerset(identity_relation(sK7(powerset(sK1))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5890,c_9751]) ).
tcf(c_28578,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(sK7(powerset(relation_image(X0,empty_set)))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_9751]) ).
tcf(c_28579,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(sK7(powerset(sK7(powerset(sK7(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_9751]) ).
tcf(c_28580,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(sK7(powerset(sK7(powerset(sK7(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_9751]) ).
tcf(c_28581,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(sK7(powerset(sK7(powerset(sK7(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_9751]) ).
tcf(c_28653,plain,
( element(sK7(empty_set),empty_set)
| empty(sK7(sK6(powerset(empty_set)))) ),
inference(superposition,[status(thm)],[c_11339,c_10563]) ).
tcf(c_28654,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| empty(sK7(sK6(powerset(powerset(X1)))))
| ~ in(X0,sK7(sK7(sK6(powerset(powerset(X1)))))) ),
inference(superposition,[status(thm)],[c_10563,c_65]) ).
tcf(c_28655,plain,
! [X0: $i,X1: $i] :
( empty(sK7(sK6(powerset(powerset(X1)))))
| ~ empty(X1)
| ~ in(X0,sK7(sK7(sK6(powerset(powerset(X1)))))) ),
inference(superposition,[status(thm)],[c_10563,c_64]) ).
tcf(c_28656,plain,
! [X0: $i] :
( empty(X0)
| empty(sK7(sK6(powerset(X0))))
| in(sK7(sK7(sK6(powerset(X0)))),X0) ),
inference(superposition,[status(thm)],[c_10563,c_71]) ).
tcf(c_28713,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(sK6(powerset(X0))))) = empty_set )
| ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_10348,c_10674]) ).
tcf(c_28714,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(sK6(powerset(X0))))) = empty_set )
| ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) ) ),
inference(superposition,[status(thm)],[c_5806,c_10674]) ).
tcf(c_28715,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( sK7(powerset(sK7(sK6(powerset(X0))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_10674]) ).
tcf(c_28716,plain,
sK7(powerset(sK7(sK6(powerset(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_10674]) ).
tcf(c_28717,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(sK6(powerset(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_10674]) ).
tcf(c_28718,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(sK6(powerset(identity_relation(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_10674]) ).
tcf(c_28719,plain,
( ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ( sK7(powerset(sK7(sK6(powerset(sK1))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5890,c_10674]) ).
tcf(c_28720,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(sK6(powerset(sK7(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_10674]) ).
tcf(c_28721,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(sK6(powerset(sK7(sK6(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_10674]) ).
tcf(c_28722,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(sK6(powerset(sK7(sK6(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_10674]) ).
tcf(c_28723,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(sK6(powerset(relation_image(X0,empty_set)))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_10674]) ).
tcf(c_28724,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(sK6(powerset(sK7(powerset(sK7(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_10674]) ).
tcf(c_28725,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(sK6(powerset(sK7(powerset(sK7(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_10674]) ).
tcf(c_28726,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(sK6(powerset(sK7(powerset(sK7(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_10674]) ).
tcf(c_28823,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( identity_relation(identity_relation(sK7(powerset(relation_dom(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10348,c_22426]) ).
tcf(c_28824,plain,
! [X0: $i] :
( ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ( identity_relation(identity_relation(sK7(powerset(relation_dom(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_22426]) ).
tcf(c_28825,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( identity_relation(identity_relation(sK7(powerset(relation_dom(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_22426]) ).
tcf(c_28826,plain,
identity_relation(identity_relation(sK7(powerset(relation_dom(relation_dom(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_22426]) ).
tcf(c_28827,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(powerset(relation_dom(relation_dom(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_22426]) ).
tcf(c_28828,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(powerset(relation_dom(relation_dom(identity_relation(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_22426]) ).
tcf(c_28829,plain,
( ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ( identity_relation(identity_relation(sK7(powerset(relation_dom(relation_dom(sK1)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5890,c_22426]) ).
tcf(c_28830,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(powerset(relation_dom(relation_dom(sK7(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_22426]) ).
tcf(c_28831,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(powerset(relation_dom(relation_dom(sK7(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_22426]) ).
tcf(c_28832,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(powerset(relation_dom(relation_dom(sK7(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_22426]) ).
tcf(c_28833,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(powerset(relation_dom(relation_dom(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_22426]) ).
tcf(c_28834,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(powerset(relation_dom(relation_dom(sK7(powerset(sK7(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_22426]) ).
tcf(c_28835,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(powerset(relation_dom(relation_dom(sK7(powerset(sK7(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_22426]) ).
tcf(c_28836,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(powerset(relation_dom(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_22426]) ).
tcf(c_28895,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( sK7(powerset(sK7(powerset(relation_dom(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10348,c_22515]) ).
tcf(c_28896,plain,
! [X0: $i] :
( ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ( sK7(powerset(sK7(powerset(relation_dom(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_22515]) ).
tcf(c_28897,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( sK7(powerset(sK7(powerset(relation_dom(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_22515]) ).
tcf(c_28898,plain,
sK7(powerset(sK7(powerset(relation_dom(relation_dom(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_22515]) ).
tcf(c_28899,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(powerset(relation_dom(relation_dom(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_22515]) ).
tcf(c_28900,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(powerset(relation_dom(relation_dom(identity_relation(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_22515]) ).
tcf(c_28901,plain,
( ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ( sK7(powerset(sK7(powerset(relation_dom(relation_dom(sK1)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5890,c_22515]) ).
tcf(c_28902,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(powerset(relation_dom(relation_dom(sK7(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_22515]) ).
tcf(c_28903,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(powerset(relation_dom(relation_dom(sK7(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_22515]) ).
tcf(c_28904,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(powerset(relation_dom(relation_dom(sK7(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_22515]) ).
tcf(c_28905,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(powerset(relation_dom(relation_dom(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_22515]) ).
tcf(c_28906,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(powerset(relation_dom(relation_dom(sK7(powerset(sK7(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_22515]) ).
tcf(c_28907,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(powerset(relation_dom(relation_dom(sK7(powerset(sK7(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_22515]) ).
tcf(c_28908,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(powerset(relation_dom(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_22515]) ).
tcf(c_29038,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( identity_relation(sK7(powerset(relation_dom(relation_dom(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10348,c_23164]) ).
tcf(c_29039,plain,
! [X0: $i] :
( ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ( identity_relation(sK7(powerset(relation_dom(relation_dom(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_23164]) ).
tcf(c_29040,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( identity_relation(sK7(powerset(relation_dom(relation_dom(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_23164]) ).
tcf(c_29041,plain,
identity_relation(sK7(powerset(relation_dom(relation_dom(relation_dom(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_23164]) ).
tcf(c_29042,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(relation_dom(relation_dom(relation_dom(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_23164]) ).
tcf(c_29043,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(relation_dom(relation_dom(relation_dom(identity_relation(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_23164]) ).
tcf(c_29044,plain,
( ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ( identity_relation(sK7(powerset(relation_dom(relation_dom(relation_dom(sK1)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5890,c_23164]) ).
tcf(c_29045,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(relation_dom(relation_dom(relation_dom(sK7(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_23164]) ).
tcf(c_29046,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(relation_dom(relation_dom(relation_dom(sK7(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_23164]) ).
tcf(c_29047,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(relation_dom(relation_dom(relation_dom(sK7(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_23164]) ).
tcf(c_29048,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(relation_dom(relation_dom(relation_dom(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_23164]) ).
tcf(c_29049,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(relation_dom(relation_dom(relation_dom(sK7(powerset(sK7(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_23164]) ).
tcf(c_29050,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(relation_dom(relation_dom(relation_dom(sK7(powerset(sK7(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_23164]) ).
tcf(c_29051,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(relation_dom(relation_dom(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_23164]) ).
tcf(c_29094,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( relation_dom(sK7(powerset(relation_dom(relation_dom(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10348,c_24347]) ).
tcf(c_29095,plain,
! [X0: $i] :
( ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ( relation_dom(sK7(powerset(relation_dom(relation_dom(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_24347]) ).
tcf(c_29096,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( relation_dom(sK7(powerset(relation_dom(relation_dom(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_24347]) ).
tcf(c_29097,plain,
relation_dom(sK7(powerset(relation_dom(relation_dom(relation_dom(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_24347]) ).
tcf(c_29098,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(relation_dom(relation_dom(relation_dom(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_24347]) ).
tcf(c_29099,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(relation_dom(relation_dom(relation_dom(identity_relation(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_24347]) ).
tcf(c_29100,plain,
( ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ( relation_dom(sK7(powerset(relation_dom(relation_dom(relation_dom(sK1)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5890,c_24347]) ).
tcf(c_29101,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(relation_dom(relation_dom(relation_dom(sK7(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_24347]) ).
tcf(c_29102,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(relation_dom(relation_dom(relation_dom(sK7(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_24347]) ).
tcf(c_29103,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(relation_dom(relation_dom(relation_dom(sK7(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_24347]) ).
tcf(c_29104,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(relation_dom(relation_dom(relation_dom(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_24347]) ).
tcf(c_29105,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(relation_dom(relation_dom(relation_dom(sK7(powerset(sK7(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_24347]) ).
tcf(c_29106,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(relation_dom(relation_dom(relation_dom(sK7(powerset(sK7(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_24347]) ).
tcf(c_29107,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(relation_dom(relation_dom(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_24347]) ).
tcf(c_29190,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(sK6(powerset(X0))))) = empty_set )
| ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_10348,c_10675]) ).
tcf(c_29191,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(sK6(powerset(X0))))) = empty_set )
| ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) ) ),
inference(superposition,[status(thm)],[c_5806,c_10675]) ).
tcf(c_29192,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( identity_relation(identity_relation(sK7(sK6(powerset(X0))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_10675]) ).
tcf(c_29193,plain,
identity_relation(identity_relation(sK7(sK6(powerset(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_10675]) ).
tcf(c_29194,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(sK6(powerset(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_10675]) ).
tcf(c_29195,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(sK6(powerset(identity_relation(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_10675]) ).
tcf(c_29196,plain,
( ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ( identity_relation(identity_relation(sK7(sK6(powerset(sK1))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5890,c_10675]) ).
tcf(c_29197,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(sK6(powerset(sK7(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_10675]) ).
tcf(c_29198,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(sK6(powerset(sK7(sK6(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_10675]) ).
tcf(c_29199,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(sK6(powerset(sK7(sK6(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_10675]) ).
tcf(c_29200,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(sK6(powerset(relation_image(X0,empty_set)))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_10675]) ).
tcf(c_29201,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(sK6(powerset(sK7(powerset(sK7(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_10675]) ).
tcf(c_29202,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(sK6(powerset(sK7(powerset(sK7(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_10675]) ).
tcf(c_29203,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(sK6(powerset(sK7(powerset(sK7(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_10675]) ).
tcf(c_29304,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(sK6(powerset(X0))))) = empty_set )
| ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_10348,c_10676]) ).
tcf(c_29305,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(sK6(powerset(X0))))) = empty_set )
| ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) ) ),
inference(superposition,[status(thm)],[c_5806,c_10676]) ).
tcf(c_29306,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( identity_relation(relation_dom(sK7(sK6(powerset(X0))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_10676]) ).
tcf(c_29307,plain,
identity_relation(relation_dom(sK7(sK6(powerset(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_10676]) ).
tcf(c_29308,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(sK6(powerset(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_10676]) ).
tcf(c_29309,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(sK6(powerset(identity_relation(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_10676]) ).
tcf(c_29310,plain,
( ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ( identity_relation(relation_dom(sK7(sK6(powerset(sK1))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5890,c_10676]) ).
tcf(c_29311,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(sK6(powerset(sK7(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_10676]) ).
tcf(c_29312,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(sK6(powerset(sK7(sK6(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_10676]) ).
tcf(c_29313,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(sK6(powerset(sK7(sK6(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_10676]) ).
tcf(c_29314,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(sK6(powerset(relation_image(X0,empty_set)))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_10676]) ).
tcf(c_29315,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(sK6(powerset(sK7(powerset(sK7(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_10676]) ).
tcf(c_29316,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(sK6(powerset(sK7(powerset(sK7(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_10676]) ).
tcf(c_29317,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(sK6(powerset(sK7(powerset(sK7(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_10676]) ).
tcf(c_29438,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(sK6(powerset(X0))))) = empty_set )
| ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_10348,c_10677]) ).
tcf(c_29439,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(sK6(powerset(X0))))) = empty_set )
| ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) ) ),
inference(superposition,[status(thm)],[c_5806,c_10677]) ).
tcf(c_29440,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( relation_dom(relation_dom(sK7(sK6(powerset(X0))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_10677]) ).
tcf(c_29441,plain,
relation_dom(relation_dom(sK7(sK6(powerset(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_10677]) ).
tcf(c_29442,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(sK6(powerset(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_10677]) ).
tcf(c_29443,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(sK6(powerset(identity_relation(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_10677]) ).
tcf(c_29444,plain,
( ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ( relation_dom(relation_dom(sK7(sK6(powerset(sK1))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5890,c_10677]) ).
tcf(c_29445,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(sK6(powerset(sK7(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_10677]) ).
tcf(c_29446,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(sK6(powerset(sK7(sK6(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_10677]) ).
tcf(c_29447,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(sK6(powerset(sK7(sK6(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_10677]) ).
tcf(c_29448,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(sK6(powerset(relation_image(X0,empty_set)))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_10677]) ).
tcf(c_29449,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(sK6(powerset(sK7(powerset(sK7(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_10677]) ).
tcf(c_29450,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(sK6(powerset(sK7(powerset(sK7(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_10677]) ).
tcf(c_29451,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(sK6(powerset(sK7(powerset(sK7(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_10677]) ).
tcf(c_29565,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(sK7(powerset(X0))))) = empty_set )
| ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_10348,c_11345]) ).
tcf(c_29566,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(sK7(powerset(X0))))) = empty_set )
| ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) ) ),
inference(superposition,[status(thm)],[c_5806,c_11345]) ).
tcf(c_29567,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( sK7(sK6(powerset(sK7(powerset(X0))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_11345]) ).
tcf(c_29568,plain,
sK7(sK6(powerset(sK7(powerset(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_11345]) ).
tcf(c_29569,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(sK7(powerset(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_11345]) ).
tcf(c_29570,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(sK7(powerset(identity_relation(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_11345]) ).
tcf(c_29571,plain,
( ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ( sK7(sK6(powerset(sK7(powerset(sK1))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5890,c_11345]) ).
tcf(c_29575,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(sK7(powerset(relation_image(X0,empty_set)))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_11345]) ).
tcf(c_29576,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(sK7(powerset(sK7(powerset(sK7(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_11345]) ).
tcf(c_29577,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(sK7(powerset(sK7(powerset(sK7(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_11345]) ).
tcf(c_29578,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(sK7(powerset(sK7(powerset(sK7(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_11345]) ).
tcf(c_29620,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( identity_relation(sK7(powerset(identity_relation(relation_dom(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10348,c_24395]) ).
tcf(c_29621,plain,
! [X0: $i] :
( ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ( identity_relation(sK7(powerset(identity_relation(relation_dom(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_24395]) ).
tcf(c_29622,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( identity_relation(sK7(powerset(identity_relation(relation_dom(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_24395]) ).
tcf(c_29623,plain,
identity_relation(sK7(powerset(identity_relation(relation_dom(relation_dom(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_24395]) ).
tcf(c_29624,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(identity_relation(relation_dom(relation_dom(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_24395]) ).
tcf(c_29625,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(identity_relation(relation_dom(relation_dom(identity_relation(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_24395]) ).
tcf(c_29626,plain,
( ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ( identity_relation(sK7(powerset(identity_relation(relation_dom(relation_dom(sK1)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5890,c_24395]) ).
tcf(c_29627,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(identity_relation(relation_dom(relation_dom(sK7(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_24395]) ).
tcf(c_29628,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(identity_relation(relation_dom(relation_dom(sK7(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_24395]) ).
tcf(c_29629,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(identity_relation(relation_dom(relation_dom(sK7(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_24395]) ).
tcf(c_29630,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(identity_relation(relation_dom(relation_dom(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_24395]) ).
tcf(c_29631,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(identity_relation(relation_dom(relation_dom(sK7(powerset(sK7(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_24395]) ).
tcf(c_29632,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(identity_relation(relation_dom(relation_dom(sK7(powerset(sK7(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_24395]) ).
tcf(c_29633,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(identity_relation(relation_dom(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_24395]) ).
tcf(c_29787,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( relation_dom(sK7(powerset(identity_relation(relation_dom(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10348,c_24443]) ).
tcf(c_29788,plain,
! [X0: $i] :
( ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ( relation_dom(sK7(powerset(identity_relation(relation_dom(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_24443]) ).
tcf(c_29789,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( relation_dom(sK7(powerset(identity_relation(relation_dom(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_24443]) ).
tcf(c_29790,plain,
relation_dom(sK7(powerset(identity_relation(relation_dom(relation_dom(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_24443]) ).
tcf(c_29791,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(identity_relation(relation_dom(relation_dom(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_24443]) ).
tcf(c_29792,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(identity_relation(relation_dom(relation_dom(identity_relation(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_24443]) ).
tcf(c_29793,plain,
( ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ( relation_dom(sK7(powerset(identity_relation(relation_dom(relation_dom(sK1)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5890,c_24443]) ).
tcf(c_29794,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(identity_relation(relation_dom(relation_dom(sK7(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_24443]) ).
tcf(c_29795,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(identity_relation(relation_dom(relation_dom(sK7(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_24443]) ).
tcf(c_29796,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(identity_relation(relation_dom(relation_dom(sK7(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_24443]) ).
tcf(c_29797,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(identity_relation(relation_dom(relation_dom(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_24443]) ).
tcf(c_29798,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(identity_relation(relation_dom(relation_dom(sK7(powerset(sK7(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_24443]) ).
tcf(c_29799,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(identity_relation(relation_dom(relation_dom(sK7(powerset(sK7(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_24443]) ).
tcf(c_29800,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(identity_relation(relation_dom(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_24443]) ).
tcf(c_29843,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( identity_relation(identity_relation(identity_relation(relation_dom(relation_dom(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10348,c_24491]) ).
tcf(c_29844,plain,
! [X0: $i] :
( ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ( identity_relation(identity_relation(identity_relation(relation_dom(relation_dom(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_24491]) ).
tcf(c_29845,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( identity_relation(identity_relation(identity_relation(relation_dom(relation_dom(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_24491]) ).
tcf(c_29846,plain,
identity_relation(identity_relation(identity_relation(relation_dom(relation_dom(relation_dom(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_24491]) ).
tcf(c_29847,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(relation_dom(relation_dom(relation_dom(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_24491]) ).
tcf(c_29848,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(relation_dom(relation_dom(relation_dom(identity_relation(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_24491]) ).
tcf(c_29849,plain,
( ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ( identity_relation(identity_relation(identity_relation(relation_dom(relation_dom(relation_dom(sK1)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5890,c_24491]) ).
tcf(c_29850,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(relation_dom(relation_dom(relation_dom(sK7(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_24491]) ).
tcf(c_29851,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(relation_dom(relation_dom(relation_dom(sK7(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_24491]) ).
tcf(c_29852,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(relation_dom(relation_dom(relation_dom(sK7(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_24491]) ).
tcf(c_29853,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(relation_dom(relation_dom(relation_dom(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_24491]) ).
tcf(c_29854,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(relation_dom(relation_dom(relation_dom(sK7(powerset(sK7(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_24491]) ).
tcf(c_29855,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(relation_dom(relation_dom(relation_dom(sK7(powerset(sK7(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_24491]) ).
tcf(c_29856,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(relation_dom(relation_dom(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_24491]) ).
tcf(c_29975,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( sK7(powerset(identity_relation(relation_dom(relation_dom(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10348,c_24580]) ).
tcf(c_29976,plain,
! [X0: $i] :
( ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ( sK7(powerset(identity_relation(relation_dom(relation_dom(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_24580]) ).
tcf(c_29977,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( sK7(powerset(identity_relation(relation_dom(relation_dom(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_24580]) ).
tcf(c_29978,plain,
sK7(powerset(identity_relation(relation_dom(relation_dom(relation_dom(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_24580]) ).
tcf(c_29979,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(relation_dom(relation_dom(relation_dom(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_24580]) ).
tcf(c_29980,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(relation_dom(relation_dom(relation_dom(identity_relation(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_24580]) ).
tcf(c_29981,plain,
( ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ( sK7(powerset(identity_relation(relation_dom(relation_dom(relation_dom(sK1)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5890,c_24580]) ).
tcf(c_29982,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(relation_dom(relation_dom(relation_dom(sK7(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_24580]) ).
tcf(c_29983,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(relation_dom(relation_dom(relation_dom(sK7(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_24580]) ).
tcf(c_29984,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(relation_dom(relation_dom(relation_dom(sK7(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_24580]) ).
tcf(c_29985,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(relation_dom(relation_dom(relation_dom(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_24580]) ).
tcf(c_29986,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(relation_dom(relation_dom(relation_dom(sK7(powerset(sK7(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_24580]) ).
tcf(c_29987,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(relation_dom(relation_dom(relation_dom(sK7(powerset(sK7(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_24580]) ).
tcf(c_29988,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(relation_dom(relation_dom(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_24580]) ).
tcf(c_30064,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(powerset(identity_relation(X0))))) = empty_set )
| ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_10348,c_11432]) ).
tcf(c_30065,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(powerset(identity_relation(X0))))) = empty_set )
| ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) ) ),
inference(superposition,[status(thm)],[c_5806,c_11432]) ).
tcf(c_30066,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( relation_dom(relation_dom(sK7(powerset(identity_relation(X0))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_11432]) ).
tcf(c_30067,plain,
relation_dom(relation_dom(sK7(powerset(identity_relation(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_11432]) ).
tcf(c_30068,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(powerset(identity_relation(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_11432]) ).
tcf(c_30069,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(powerset(identity_relation(identity_relation(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_11432]) ).
tcf(c_30070,plain,
( ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ( relation_dom(relation_dom(sK7(powerset(identity_relation(sK1))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5890,c_11432]) ).
tcf(c_30071,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(powerset(identity_relation(sK7(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_11432]) ).
tcf(c_30072,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(powerset(identity_relation(sK7(sK6(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_11432]) ).
tcf(c_30073,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(powerset(identity_relation(sK7(sK6(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_11432]) ).
tcf(c_30074,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(powerset(identity_relation(relation_image(X0,empty_set)))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_11432]) ).
tcf(c_30075,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(powerset(identity_relation(sK7(powerset(sK7(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_11432]) ).
tcf(c_30076,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(powerset(identity_relation(sK7(powerset(sK7(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_11432]) ).
tcf(c_30077,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(powerset(identity_relation(sK7(powerset(sK7(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_11432]) ).
tcf(c_30154,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(powerset(identity_relation(X0))))) = empty_set )
| ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_10348,c_12136]) ).
tcf(c_30155,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(powerset(identity_relation(X0))))) = empty_set )
| ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) ) ),
inference(superposition,[status(thm)],[c_5806,c_12136]) ).
tcf(c_30156,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( identity_relation(relation_dom(sK7(powerset(identity_relation(X0))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_12136]) ).
tcf(c_30157,plain,
identity_relation(relation_dom(sK7(powerset(identity_relation(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_12136]) ).
tcf(c_30158,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(powerset(identity_relation(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_12136]) ).
tcf(c_30159,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(powerset(identity_relation(identity_relation(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_12136]) ).
tcf(c_30160,plain,
( ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ( identity_relation(relation_dom(sK7(powerset(identity_relation(sK1))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5890,c_12136]) ).
tcf(c_30161,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(powerset(identity_relation(sK7(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_12136]) ).
tcf(c_30162,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(powerset(identity_relation(sK7(sK6(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_12136]) ).
tcf(c_30163,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(powerset(identity_relation(sK7(sK6(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_12136]) ).
tcf(c_30164,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(powerset(identity_relation(relation_image(X0,empty_set)))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_12136]) ).
tcf(c_30165,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(powerset(identity_relation(sK7(powerset(sK7(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_12136]) ).
tcf(c_30166,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(powerset(identity_relation(sK7(powerset(sK7(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_12136]) ).
tcf(c_30167,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(powerset(identity_relation(sK7(powerset(sK7(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_12136]) ).
tcf(c_30244,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(powerset(identity_relation(X0))))) = empty_set )
| ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_10348,c_12213]) ).
tcf(c_30245,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(powerset(identity_relation(X0))))) = empty_set )
| ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) ) ),
inference(superposition,[status(thm)],[c_5806,c_12213]) ).
tcf(c_30246,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( identity_relation(identity_relation(sK7(powerset(identity_relation(X0))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_12213]) ).
tcf(c_30247,plain,
identity_relation(identity_relation(sK7(powerset(identity_relation(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_12213]) ).
tcf(c_30248,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(powerset(identity_relation(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_12213]) ).
tcf(c_30249,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(powerset(identity_relation(identity_relation(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_12213]) ).
tcf(c_30250,plain,
( ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ( identity_relation(identity_relation(sK7(powerset(identity_relation(sK1))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5890,c_12213]) ).
tcf(c_30251,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(powerset(identity_relation(sK7(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_12213]) ).
tcf(c_30252,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(powerset(identity_relation(sK7(sK6(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_12213]) ).
tcf(c_30253,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(powerset(identity_relation(sK7(sK6(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_12213]) ).
tcf(c_30254,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(powerset(identity_relation(relation_image(X0,empty_set)))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_12213]) ).
tcf(c_30255,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(powerset(identity_relation(sK7(powerset(sK7(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_12213]) ).
tcf(c_30256,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(powerset(identity_relation(sK7(powerset(sK7(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_12213]) ).
tcf(c_30257,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(powerset(identity_relation(sK7(powerset(sK7(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_12213]) ).
tcf(c_30351,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(powerset(identity_relation(X0))))) = empty_set )
| ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_10348,c_12319]) ).
tcf(c_30352,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(powerset(identity_relation(X0))))) = empty_set )
| ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) ) ),
inference(superposition,[status(thm)],[c_5806,c_12319]) ).
tcf(c_30353,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( sK7(powerset(sK7(powerset(identity_relation(X0))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_12319]) ).
tcf(c_30354,plain,
sK7(powerset(sK7(powerset(identity_relation(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_12319]) ).
tcf(c_30355,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(powerset(identity_relation(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_12319]) ).
tcf(c_30356,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(powerset(identity_relation(identity_relation(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_12319]) ).
tcf(c_30357,plain,
( ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ( sK7(powerset(sK7(powerset(identity_relation(sK1))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5890,c_12319]) ).
tcf(c_30358,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(powerset(identity_relation(sK7(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_12319]) ).
tcf(c_30359,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(powerset(identity_relation(sK7(sK6(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_12319]) ).
tcf(c_30360,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(powerset(identity_relation(sK7(sK6(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_12319]) ).
tcf(c_30361,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(powerset(identity_relation(relation_image(X0,empty_set)))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_12319]) ).
tcf(c_30362,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(powerset(identity_relation(sK7(powerset(sK7(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_12319]) ).
tcf(c_30363,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(powerset(identity_relation(sK7(powerset(sK7(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_12319]) ).
tcf(c_30364,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(powerset(identity_relation(sK7(powerset(sK7(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_12319]) ).
tcf(c_30471,plain,
( ( apply(empty_set,sK7(empty_set)) = sK7(empty_set) )
| ( identity_relation(identity_relation(identity_relation(empty_set))) = empty_set ) ),
inference(superposition,[status(thm)],[c_6104,c_9679]) ).
tcf(c_30472,plain,
( ( apply(identity_relation(powerset(empty_set)),empty_set) = empty_set )
| ( identity_relation(identity_relation(identity_relation(powerset(empty_set)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8004,c_9679]) ).
tcf(c_30475,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(identity_relation(identity_relation(X0))) = empty_set )
| ( relation_image(identity_relation(X0),X1) = X2 )
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),relation_dom(identity_relation(X0)))
| ~ in(sK2(identity_relation(X0),X1,X2),X2)
| ( sK2(identity_relation(X0),X1,X2) != sK7(X0) ) ),
inference(superposition,[status(thm)],[c_9679,c_53]) ).
tcf(c_30476,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0),relation_image(identity_relation(X0),X1))
| ( identity_relation(identity_relation(identity_relation(X0))) = empty_set )
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),relation_dom(identity_relation(X0))) ),
inference(superposition,[status(thm)],[c_9679,c_57]) ).
tcf(c_30478,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0),relation_image(identity_relation(X0),X1))
| ( identity_relation(identity_relation(identity_relation(X0))) = empty_set )
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),X0) ),
inference(light_normalisation,[status(thm)],[c_30476,c_121]) ).
tcf(c_30479,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0),relation_image(identity_relation(X0),X1))
| ( identity_relation(identity_relation(identity_relation(X0))) = empty_set )
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_30478,c_62,c_63]) ).
tcf(c_30484,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(identity_relation(identity_relation(X0))) = empty_set )
| ( relation_image(identity_relation(X0),X1) = X2 )
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),X0)
| ~ in(sK2(identity_relation(X0),X1,X2),X2)
| ( sK2(identity_relation(X0),X1,X2) != sK7(X0) ) ),
inference(light_normalisation,[status(thm)],[c_30475,c_121]) ).
tcf(c_30485,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(identity_relation(identity_relation(X0))) = empty_set )
| ( relation_image(identity_relation(X0),X1) = X2 )
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),X0)
| ~ in(sK2(identity_relation(X0),X1,X2),X2)
| ( sK2(identity_relation(X0),X1,X2) != sK7(X0) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_30484,c_62,c_63]) ).
tcf(c_30497,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( sK7(sK6(powerset(relation_dom(relation_dom(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10348,c_24628]) ).
tcf(c_30498,plain,
! [X0: $i] :
( ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ( sK7(sK6(powerset(relation_dom(relation_dom(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_24628]) ).
tcf(c_30499,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( sK7(sK6(powerset(relation_dom(relation_dom(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_24628]) ).
tcf(c_30500,plain,
sK7(sK6(powerset(relation_dom(relation_dom(relation_dom(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_24628]) ).
tcf(c_30501,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(relation_dom(relation_dom(relation_dom(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_24628]) ).
tcf(c_30502,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(relation_dom(relation_dom(relation_dom(identity_relation(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_24628]) ).
tcf(c_30503,plain,
( ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ( sK7(sK6(powerset(relation_dom(relation_dom(relation_dom(sK1)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5890,c_24628]) ).
tcf(c_30504,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(relation_dom(relation_dom(relation_dom(sK7(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_24628]) ).
tcf(c_30505,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(relation_dom(relation_dom(relation_dom(sK7(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_24628]) ).
tcf(c_30506,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(relation_dom(relation_dom(relation_dom(sK7(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_24628]) ).
tcf(c_30507,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(relation_dom(relation_dom(relation_dom(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_24628]) ).
tcf(c_30508,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(relation_dom(relation_dom(relation_dom(sK7(powerset(sK7(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_24628]) ).
tcf(c_30509,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(relation_dom(relation_dom(relation_dom(sK7(powerset(sK7(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_24628]) ).
tcf(c_30510,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(relation_dom(relation_dom(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_24628]) ).
tcf(c_30574,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( identity_relation(identity_relation(identity_relation(identity_relation(relation_dom(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10348,c_24676]) ).
tcf(c_30575,plain,
! [X0: $i] :
( ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ( identity_relation(identity_relation(identity_relation(identity_relation(relation_dom(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_24676]) ).
tcf(c_30576,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( identity_relation(identity_relation(identity_relation(identity_relation(relation_dom(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_24676]) ).
tcf(c_30577,plain,
identity_relation(identity_relation(identity_relation(identity_relation(relation_dom(relation_dom(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_24676]) ).
tcf(c_30578,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(relation_dom(relation_dom(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_24676]) ).
tcf(c_30579,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(relation_dom(relation_dom(identity_relation(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_24676]) ).
tcf(c_30580,plain,
( ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ( identity_relation(identity_relation(identity_relation(identity_relation(relation_dom(relation_dom(sK1)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5890,c_24676]) ).
tcf(c_30581,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(relation_dom(relation_dom(sK7(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_24676]) ).
tcf(c_30582,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(relation_dom(relation_dom(sK7(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_24676]) ).
tcf(c_30583,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(relation_dom(relation_dom(sK7(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_24676]) ).
tcf(c_30584,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(relation_dom(relation_dom(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_24676]) ).
tcf(c_30585,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(relation_dom(relation_dom(sK7(powerset(sK7(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_24676]) ).
tcf(c_30586,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(relation_dom(relation_dom(sK7(powerset(sK7(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_24676]) ).
tcf(c_30587,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(relation_dom(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_24676]) ).
tcf(c_30682,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( sK7(powerset(identity_relation(identity_relation(relation_dom(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10348,c_24724]) ).
tcf(c_30683,plain,
! [X0: $i] :
( ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ( sK7(powerset(identity_relation(identity_relation(relation_dom(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_24724]) ).
tcf(c_30684,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( sK7(powerset(identity_relation(identity_relation(relation_dom(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_24724]) ).
tcf(c_30685,plain,
sK7(powerset(identity_relation(identity_relation(relation_dom(relation_dom(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_24724]) ).
tcf(c_30686,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(identity_relation(relation_dom(relation_dom(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_24724]) ).
tcf(c_30687,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(identity_relation(relation_dom(relation_dom(identity_relation(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_24724]) ).
tcf(c_30688,plain,
( ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ( sK7(powerset(identity_relation(identity_relation(relation_dom(relation_dom(sK1)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5890,c_24724]) ).
tcf(c_30689,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(identity_relation(relation_dom(relation_dom(sK7(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_24724]) ).
tcf(c_30690,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(identity_relation(relation_dom(relation_dom(sK7(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_24724]) ).
tcf(c_30691,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(identity_relation(relation_dom(relation_dom(sK7(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_24724]) ).
tcf(c_30692,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(identity_relation(relation_dom(relation_dom(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_24724]) ).
tcf(c_30693,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(identity_relation(relation_dom(relation_dom(sK7(powerset(sK7(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_24724]) ).
tcf(c_30694,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(identity_relation(relation_dom(relation_dom(sK7(powerset(sK7(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_24724]) ).
tcf(c_30695,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(identity_relation(relation_dom(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_24724]) ).
tcf(c_30759,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( sK7(sK6(sK6(powerset(relation_dom(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10348,c_24819]) ).
tcf(c_30760,plain,
! [X0: $i] :
( ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ( sK7(sK6(sK6(powerset(relation_dom(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_24819]) ).
tcf(c_30761,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( sK7(sK6(sK6(powerset(relation_dom(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_24819]) ).
tcf(c_30762,plain,
sK7(sK6(sK6(powerset(relation_dom(relation_dom(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_24819]) ).
tcf(c_30763,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(powerset(relation_dom(relation_dom(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_24819]) ).
tcf(c_30764,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(powerset(relation_dom(relation_dom(identity_relation(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_24819]) ).
tcf(c_30765,plain,
( ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ( sK7(sK6(sK6(powerset(relation_dom(relation_dom(sK1)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5890,c_24819]) ).
tcf(c_30766,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(powerset(relation_dom(relation_dom(sK7(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_24819]) ).
tcf(c_30767,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(powerset(relation_dom(relation_dom(sK7(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_24819]) ).
tcf(c_30768,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(powerset(relation_dom(relation_dom(sK7(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_24819]) ).
tcf(c_30769,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(powerset(relation_dom(relation_dom(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_24819]) ).
tcf(c_30770,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(powerset(relation_dom(relation_dom(sK7(powerset(sK7(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_24819]) ).
tcf(c_30771,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(powerset(relation_dom(relation_dom(sK7(powerset(sK7(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_24819]) ).
tcf(c_30772,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(powerset(relation_dom(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_24819]) ).
tcf(c_30938,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(identity_relation(identity_relation(X0))))) = empty_set )
| ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_10348,c_12872]) ).
tcf(c_30939,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(identity_relation(identity_relation(X0))))) = empty_set )
| ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) ) ),
inference(superposition,[status(thm)],[c_5806,c_12872]) ).
tcf(c_30940,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( identity_relation(sK7(powerset(identity_relation(identity_relation(X0))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_12872]) ).
tcf(c_30941,plain,
identity_relation(sK7(powerset(identity_relation(identity_relation(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_12872]) ).
tcf(c_30942,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(identity_relation(identity_relation(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_12872]) ).
tcf(c_30943,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(identity_relation(identity_relation(identity_relation(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_12872]) ).
tcf(c_30944,plain,
( ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ( identity_relation(sK7(powerset(identity_relation(identity_relation(sK1))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5890,c_12872]) ).
tcf(c_30945,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(identity_relation(identity_relation(sK7(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_12872]) ).
tcf(c_30946,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(identity_relation(identity_relation(sK7(sK6(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_12872]) ).
tcf(c_30947,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(identity_relation(identity_relation(sK7(sK6(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_12872]) ).
tcf(c_30948,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(identity_relation(identity_relation(relation_image(X0,empty_set)))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_12872]) ).
tcf(c_30949,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(identity_relation(identity_relation(sK7(powerset(sK7(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_12872]) ).
tcf(c_30950,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(identity_relation(identity_relation(sK7(powerset(sK7(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_12872]) ).
tcf(c_30951,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(identity_relation(identity_relation(sK7(powerset(sK7(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_12872]) ).
tcf(c_31010,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(identity_relation(identity_relation(X0))))) = empty_set )
| ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_10348,c_12910]) ).
tcf(c_31011,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(identity_relation(identity_relation(X0))))) = empty_set )
| ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) ) ),
inference(superposition,[status(thm)],[c_5806,c_12910]) ).
tcf(c_31012,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( relation_dom(sK7(powerset(identity_relation(identity_relation(X0))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_12910]) ).
tcf(c_31013,plain,
relation_dom(sK7(powerset(identity_relation(identity_relation(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_12910]) ).
tcf(c_31014,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(identity_relation(identity_relation(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_12910]) ).
tcf(c_31015,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(identity_relation(identity_relation(identity_relation(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_12910]) ).
tcf(c_31016,plain,
( ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ( relation_dom(sK7(powerset(identity_relation(identity_relation(sK1))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5890,c_12910]) ).
tcf(c_31017,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(identity_relation(identity_relation(sK7(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_12910]) ).
tcf(c_31018,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(identity_relation(identity_relation(sK7(sK6(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_12910]) ).
tcf(c_31019,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(identity_relation(identity_relation(sK7(sK6(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_12910]) ).
tcf(c_31020,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(identity_relation(identity_relation(relation_image(X0,empty_set)))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_12910]) ).
tcf(c_31021,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(identity_relation(identity_relation(sK7(powerset(sK7(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_12910]) ).
tcf(c_31022,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(identity_relation(identity_relation(sK7(powerset(sK7(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_12910]) ).
tcf(c_31023,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(identity_relation(identity_relation(sK7(powerset(sK7(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_12910]) ).
tcf(c_31138,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(identity_relation(X0))))) = empty_set )
| ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_10348,c_13854]) ).
tcf(c_31139,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(identity_relation(X0))))) = empty_set )
| ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) ) ),
inference(superposition,[status(thm)],[c_5806,c_13854]) ).
tcf(c_31140,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( identity_relation(identity_relation(identity_relation(identity_relation(identity_relation(X0))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_13854]) ).
tcf(c_31141,plain,
identity_relation(identity_relation(identity_relation(identity_relation(identity_relation(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_13854]) ).
tcf(c_31142,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(identity_relation(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_13854]) ).
tcf(c_31143,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(identity_relation(identity_relation(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_13854]) ).
tcf(c_31144,plain,
( ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ( identity_relation(identity_relation(identity_relation(identity_relation(identity_relation(sK1))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5890,c_13854]) ).
tcf(c_31145,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(identity_relation(sK7(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_13854]) ).
tcf(c_31146,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(identity_relation(sK7(sK6(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_13854]) ).
tcf(c_31147,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(identity_relation(sK7(sK6(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_13854]) ).
tcf(c_31148,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(identity_relation(relation_image(X0,empty_set)))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_13854]) ).
tcf(c_31149,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(identity_relation(sK7(powerset(sK7(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_13854]) ).
tcf(c_31150,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(identity_relation(sK7(powerset(sK7(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_13854]) ).
tcf(c_31151,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(identity_relation(sK7(powerset(sK7(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_13854]) ).
tcf(c_31218,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(identity_relation(identity_relation(X0))))) = empty_set )
| ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_10348,c_13970]) ).
tcf(c_31219,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(identity_relation(identity_relation(X0))))) = empty_set )
| ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) ) ),
inference(superposition,[status(thm)],[c_5806,c_13970]) ).
tcf(c_31220,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( sK7(powerset(identity_relation(identity_relation(identity_relation(X0))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_13970]) ).
tcf(c_31221,plain,
sK7(powerset(identity_relation(identity_relation(identity_relation(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_13970]) ).
tcf(c_31222,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(identity_relation(identity_relation(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_13970]) ).
tcf(c_31223,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(identity_relation(identity_relation(identity_relation(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_13970]) ).
tcf(c_31224,plain,
( ( apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1) )
| ( sK7(powerset(identity_relation(identity_relation(identity_relation(sK1))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5890,c_13970]) ).
tcf(c_31225,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(identity_relation(identity_relation(sK7(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_13970]) ).
tcf(c_31226,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(identity_relation(identity_relation(sK7(sK6(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_13970]) ).
tcf(c_31227,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(identity_relation(identity_relation(sK7(sK6(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_13970]) ).
tcf(c_31228,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(identity_relation(identity_relation(relation_image(X0,empty_set)))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_13970]) ).
tcf(c_31229,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(identity_relation(identity_relation(sK7(powerset(sK7(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_13970]) ).
tcf(c_31230,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(identity_relation(identity_relation(sK7(powerset(sK7(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_13970]) ).
tcf(c_31231,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(identity_relation(identity_relation(sK7(powerset(sK7(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_13970]) ).
tcf(c_31308,plain,
function(empty_set),
inference(superposition,[status(thm)],[c_83,c_98]) ).
tcf(c_31351,plain,
! [X0: $i] : sK5(X0) = empty_set,
inference(superposition,[status(thm)],[c_67,c_52]) ).
tcf(c_31355,plain,
! [X0: $i] :
( ( relation_dom(X0) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_52]) ).
tcf(c_31362,plain,
! [X0: $i] : element(empty_set,powerset(X0)),
inference(demodulation,[status(thm)],[c_66,c_31351]) ).
tcf(c_31439,plain,
relation_dom(empty_set) = empty_set,
inference(superposition,[status(thm)],[c_83,c_31355]) ).
tcf(c_31480,plain,
! [X0: $i] :
( empty(X0)
| in(sK7(X0),X0) ),
inference(superposition,[status(thm)],[c_73,c_71]) ).
tcf(c_31525,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ in(X0,empty_set) ),
inference(superposition,[status(thm)],[c_31362,c_64]) ).
tcf(c_31536,plain,
! [X0: $i] :
( element(X0,sK0)
| ~ in(X0,sK1) ),
inference(superposition,[status(thm)],[c_50,c_65]) ).
tcf(c_31537,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| element(X0,X1)
| ~ in(X0,sK6(X1)) ),
inference(superposition,[status(thm)],[c_68,c_65]) ).
tcf(c_31549,plain,
! [X0: $i] : ~ in(X0,empty_set),
inference(global_subsumption_just,[status(thm)],[c_31525,c_8375]) ).
tcf(c_32182,plain,
! [X0: $i,X1: $i] :
( element(sK2(X0,X1,sK1),sK0)
| in(sK3(X0,X1,sK1),relation_dom(X0))
| ( relation_image(X0,X1) = sK1 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_54,c_31536]) ).
tcf(c_32767,plain,
! [X0: $i] :
( in(sK3(empty_set,X0,sK1),empty_set)
| element(sK2(empty_set,X0,sK1),sK0)
| ( relation_image(empty_set,X0) = sK1 )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_31439,c_32182]) ).
tcf(c_32777,plain,
! [X0: $i] :
( element(sK2(empty_set,X0,sK1),sK0)
| ( relation_image(empty_set,X0) = sK1 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_32767,c_31549,c_31308,c_82]) ).
tcf(c_33471,plain,
! [X0: $i] :
( empty(X0)
| empty(sK6(X0))
| element(sK7(sK6(X0)),X0) ),
inference(superposition,[status(thm)],[c_31480,c_31537]) ).
tcf(c_33539,plain,
! [X0: $i] :
( empty(X0)
| element(sK7(sK6(X0)),X0) ),
inference(global_subsumption_just,[status(thm)],[c_33471,c_69,c_8391]) ).
tcf(c_33547,plain,
! [X0: $i] :
( empty(X0)
| in(sK7(sK6(X0)),X0) ),
inference(superposition,[status(thm)],[c_33539,c_71]) ).
tcf(c_33941,plain,
! [X0: $i] :
( empty(X0)
| empty(sK6(X0))
| element(sK7(sK6(sK6(X0))),X0) ),
inference(superposition,[status(thm)],[c_33547,c_31537]) ).
tcf(c_34057,plain,
! [X0: $i] :
( empty(X0)
| element(sK7(sK6(sK6(X0))),X0) ),
inference(global_subsumption_just,[status(thm)],[c_33941,c_69,c_10354]) ).
tcf(c_34065,plain,
! [X0: $i] :
( empty(X0)
| in(sK7(sK6(sK6(X0))),X0) ),
inference(superposition,[status(thm)],[c_34057,c_71]) ).
tcf(c_34392,plain,
! [X0: $i] :
( empty(X0)
| empty(sK6(X0))
| element(sK7(sK6(sK6(sK6(X0)))),X0) ),
inference(superposition,[status(thm)],[c_34065,c_31537]) ).
tcf(c_34523,plain,
! [X0: $i] :
( empty(X0)
| element(sK7(sK6(sK6(sK6(X0)))),X0) ),
inference(global_subsumption_just,[status(thm)],[c_34392,c_69,c_14108]) ).
tcf(c_34531,plain,
! [X0: $i] :
( empty(X0)
| in(sK7(sK6(sK6(sK6(X0)))),X0) ),
inference(superposition,[status(thm)],[c_34523,c_71]) ).
tcf(c_34754,plain,
( empty(sK1)
| element(sK7(sK6(sK6(sK6(sK1)))),sK0) ),
inference(superposition,[status(thm)],[c_34531,c_31536]) ).
tcf(c_35445,plain,
apply(identity_relation(sK0),sK7(sK1)) = sK7(sK1),
inference(global_subsumption_just,[status(thm)],[c_9683,c_49,c_5890,c_6237,c_6638,c_8112,c_13256,c_22498]) ).
tcf(c_35447,plain,
! [X0: $i] :
( in(sK7(sK1),relation_image(identity_relation(sK0),X0))
| ~ function(identity_relation(sK0))
| ~ relation(identity_relation(sK0))
| ~ in(sK7(sK1),X0)
| ~ in(sK7(sK1),relation_dom(identity_relation(sK0))) ),
inference(superposition,[status(thm)],[c_35445,c_57]) ).
tcf(c_35448,plain,
! [X0: $i] :
( in(sK7(sK1),relation_image(identity_relation(sK0),X0))
| ~ in(sK7(sK1),X0)
| ~ in(sK7(sK1),relation_dom(identity_relation(sK0))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_35447,c_62,c_63]) ).
tcf(c_35456,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( identity_relation(sK7(sK6(powerset(relation_dom(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10348,c_24875]) ).
tcf(c_35457,plain,
! [X0: $i] :
( ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ( identity_relation(sK7(sK6(powerset(relation_dom(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_24875]) ).
tcf(c_35458,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( identity_relation(sK7(sK6(powerset(relation_dom(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_24875]) ).
tcf(c_35459,plain,
identity_relation(sK7(sK6(powerset(relation_dom(relation_dom(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_24875]) ).
tcf(c_35460,plain,
! [X0: $i] :
( ( identity_relation(sK7(sK6(powerset(relation_dom(relation_dom(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_24875]) ).
tcf(c_35461,plain,
! [X0: $i] :
( ( identity_relation(sK7(sK6(powerset(relation_dom(relation_dom(identity_relation(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_24875]) ).
tcf(c_35462,plain,
! [X0: $i] :
( ( identity_relation(sK7(sK6(powerset(relation_dom(relation_dom(sK7(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_24875]) ).
tcf(c_35463,plain,
! [X0: $i] :
( ( identity_relation(sK7(sK6(powerset(relation_dom(relation_dom(sK7(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_24875]) ).
tcf(c_35464,plain,
! [X0: $i] :
( ( identity_relation(sK7(sK6(powerset(relation_dom(relation_dom(sK7(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_24875]) ).
tcf(c_35465,plain,
! [X0: $i] :
( ( identity_relation(sK7(sK6(powerset(relation_dom(relation_dom(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_24875]) ).
tcf(c_35466,plain,
! [X0: $i] :
( ( identity_relation(sK7(sK6(powerset(relation_dom(relation_dom(sK7(powerset(sK7(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_24875]) ).
tcf(c_35467,plain,
! [X0: $i] :
( ( identity_relation(sK7(sK6(powerset(relation_dom(relation_dom(sK7(powerset(sK7(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_24875]) ).
tcf(c_35468,plain,
! [X0: $i] :
( ( identity_relation(sK7(sK6(powerset(relation_dom(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_24875]) ).
tcf(c_35509,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( relation_dom(sK7(sK6(powerset(relation_dom(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10348,c_25099]) ).
tcf(c_35510,plain,
! [X0: $i] :
( ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ( relation_dom(sK7(sK6(powerset(relation_dom(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_25099]) ).
tcf(c_35511,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( relation_dom(sK7(sK6(powerset(relation_dom(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_25099]) ).
tcf(c_35512,plain,
relation_dom(sK7(sK6(powerset(relation_dom(relation_dom(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_25099]) ).
tcf(c_35513,plain,
! [X0: $i] :
( ( relation_dom(sK7(sK6(powerset(relation_dom(relation_dom(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_25099]) ).
tcf(c_35514,plain,
! [X0: $i] :
( ( relation_dom(sK7(sK6(powerset(relation_dom(relation_dom(identity_relation(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_25099]) ).
tcf(c_35515,plain,
! [X0: $i] :
( ( relation_dom(sK7(sK6(powerset(relation_dom(relation_dom(sK7(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_25099]) ).
tcf(c_35516,plain,
! [X0: $i] :
( ( relation_dom(sK7(sK6(powerset(relation_dom(relation_dom(sK7(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_25099]) ).
tcf(c_35517,plain,
! [X0: $i] :
( ( relation_dom(sK7(sK6(powerset(relation_dom(relation_dom(sK7(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_25099]) ).
tcf(c_35518,plain,
! [X0: $i] :
( ( relation_dom(sK7(sK6(powerset(relation_dom(relation_dom(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_25099]) ).
tcf(c_35519,plain,
! [X0: $i] :
( ( relation_dom(sK7(sK6(powerset(relation_dom(relation_dom(sK7(powerset(sK7(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_25099]) ).
tcf(c_35520,plain,
! [X0: $i] :
( ( relation_dom(sK7(sK6(powerset(relation_dom(relation_dom(sK7(powerset(sK7(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_25099]) ).
tcf(c_35521,plain,
! [X0: $i] :
( ( relation_dom(sK7(sK6(powerset(relation_dom(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_25099]) ).
tcf(c_35562,plain,
! [X0: $i] :
( ( relation_image(X0,empty_set) = empty_set )
| ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_25428,c_23329]) ).
tcf(c_35570,plain,
! [X0: $i] :
( empty(X0)
| element(sK7(sK6(sK6(sK6(X0)))),X0) ),
inference(global_subsumption_just,[status(thm)],[c_14108,c_34523]) ).
tcf(c_35576,plain,
! [X0: $i,X1: $i] :
( empty(powerset(X1))
| element(X0,X1)
| ~ in(X0,sK7(sK6(sK6(sK6(powerset(X1)))))) ),
inference(superposition,[status(thm)],[c_35570,c_65]) ).
tcf(c_35577,plain,
! [X0: $i,X1: $i] :
( empty(powerset(X1))
| ~ empty(X1)
| ~ in(X0,sK7(sK6(sK6(sK6(powerset(X1)))))) ),
inference(superposition,[status(thm)],[c_35570,c_64]) ).
tcf(c_35578,plain,
! [X0: $i] :
( empty(X0)
| in(sK7(sK6(sK6(sK6(X0)))),X0) ),
inference(superposition,[status(thm)],[c_35570,c_71]) ).
tcf(c_35581,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ in(X0,sK7(sK6(sK6(sK6(powerset(X1)))))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_35577,c_70]) ).
tcf(c_35584,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| ~ in(X0,sK7(sK6(sK6(sK6(powerset(X1)))))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_35576,c_70]) ).
tcf(c_35591,plain,
! [X0: $i,X1: $i] :
( empty(relation_image(X0,X1))
| ( apply(X0,sK4(X0,X1,sK7(sK6(sK6(sK6(relation_image(X0,X1))))))) = sK7(sK6(sK6(sK6(relation_image(X0,X1))))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_35578,c_60]) ).
tcf(c_35592,plain,
! [X0: $i] :
( empty(X0)
| ( apply(identity_relation(X0),sK7(sK6(sK6(sK6(X0))))) = sK7(sK6(sK6(sK6(X0)))) ) ),
inference(superposition,[status(thm)],[c_35578,c_151]) ).
tcf(c_35593,plain,
! [X0: $i] :
( empty(X0)
| ~ in(X0,sK7(sK6(sK6(sK6(X0))))) ),
inference(superposition,[status(thm)],[c_35578,c_85]) ).
tcf(c_35596,plain,
( empty(sK1)
| element(sK7(sK6(sK6(sK6(sK1)))),sK0) ),
inference(superposition,[status(thm)],[c_35578,c_5838]) ).
tcf(c_35597,plain,
! [X0: $i] :
( empty(X0)
| empty(sK6(X0))
| element(sK7(sK6(sK6(sK6(sK6(X0))))),X0) ),
inference(superposition,[status(thm)],[c_35578,c_5839]) ).
tcf(c_35598,plain,
! [X0: $i] :
( empty(sK7(powerset(X0)))
| element(sK7(sK6(sK6(sK6(sK7(powerset(X0)))))),X0) ),
inference(superposition,[status(thm)],[c_35578,c_5840]) ).
tcf(c_35602,plain,
! [X0: $i] :
( empty(sK7(sK6(powerset(X0))))
| element(sK7(sK6(sK6(sK6(sK7(sK6(powerset(X0))))))),X0) ),
inference(superposition,[status(thm)],[c_35578,c_9820]) ).
tcf(c_35604,plain,
! [X0: $i] :
( empty(sK7(sK6(sK6(powerset(X0)))))
| element(sK7(sK6(sK6(sK6(sK7(sK6(sK6(powerset(X0)))))))),X0) ),
inference(superposition,[status(thm)],[c_35578,c_14092]) ).
tcf(c_35642,plain,
element(sK7(sK6(sK6(sK6(sK1)))),sK0),
inference(global_subsumption_just,[status(thm)],[c_35596,c_49,c_6237,c_6638,c_8112,c_13256,c_22498,c_34754]) ).
tcf(c_35644,plain,
( empty(sK0)
| in(sK7(sK6(sK6(sK6(sK1)))),sK0) ),
inference(superposition,[status(thm)],[c_35642,c_71]) ).
tcf(c_35645,plain,
in(sK7(sK6(sK6(sK6(sK1)))),sK0),
inference(forward_subsumption_resolution,[status(thm)],[c_35644,c_24236]) ).
tcf(c_35646,plain,
apply(identity_relation(sK0),sK7(sK6(sK6(sK6(sK1))))) = sK7(sK6(sK6(sK6(sK1)))),
inference(superposition,[status(thm)],[c_35645,c_151]) ).
tcf(c_35647,plain,
~ in(sK0,sK7(sK6(sK6(sK6(sK1))))),
inference(superposition,[status(thm)],[c_35645,c_85]) ).
tcf(c_35666,plain,
( ( sK7(powerset(identity_relation(empty_set))) = empty_set )
| ( apply(empty_set,sK7(empty_set)) = sK7(empty_set) ) ),
inference(superposition,[status(thm)],[c_6104,c_9745]) ).
tcf(c_35667,plain,
( ( sK7(powerset(identity_relation(powerset(empty_set)))) = empty_set )
| ( apply(identity_relation(powerset(empty_set)),empty_set) = empty_set ) ),
inference(superposition,[status(thm)],[c_8004,c_9745]) ).
tcf(c_35670,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK7(powerset(identity_relation(X0))) = empty_set )
| ( relation_image(identity_relation(X0),X1) = X2 )
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),relation_dom(identity_relation(X0)))
| ~ in(sK2(identity_relation(X0),X1,X2),X2)
| ( sK2(identity_relation(X0),X1,X2) != sK7(X0) ) ),
inference(superposition,[status(thm)],[c_9745,c_53]) ).
tcf(c_35671,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0),relation_image(identity_relation(X0),X1))
| ( sK7(powerset(identity_relation(X0))) = empty_set )
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),relation_dom(identity_relation(X0))) ),
inference(superposition,[status(thm)],[c_9745,c_57]) ).
tcf(c_35673,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0),relation_image(identity_relation(X0),X1))
| ( sK7(powerset(identity_relation(X0))) = empty_set )
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),X0) ),
inference(light_normalisation,[status(thm)],[c_35671,c_121]) ).
tcf(c_35674,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0),relation_image(identity_relation(X0),X1))
| ( sK7(powerset(identity_relation(X0))) = empty_set )
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_35673,c_62,c_63]) ).
tcf(c_35679,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK7(powerset(identity_relation(X0))) = empty_set )
| ( relation_image(identity_relation(X0),X1) = X2 )
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),X0)
| ~ in(sK2(identity_relation(X0),X1,X2),X2)
| ( sK2(identity_relation(X0),X1,X2) != sK7(X0) ) ),
inference(light_normalisation,[status(thm)],[c_35670,c_121]) ).
tcf(c_35680,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK7(powerset(identity_relation(X0))) = empty_set )
| ( relation_image(identity_relation(X0),X1) = X2 )
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),X0)
| ~ in(sK2(identity_relation(X0),X1,X2),X2)
| ( sK2(identity_relation(X0),X1,X2) != sK7(X0) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_35679,c_62,c_63]) ).
tcf(c_35715,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK7(sK6(sK6(sK6(powerset(X0))))) = relation_image(X1,X2) )
| ( apply(X1,sK3(X1,X2,sK7(sK6(sK6(sK6(powerset(X0))))))) = sK2(X1,X2,sK7(sK6(sK6(sK6(powerset(X0)))))) )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_56,c_35581]) ).
tcf(c_35716,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(X1,X2,sK7(sK6(sK6(sK6(powerset(X0)))))),relation_dom(X1))
| ( sK7(sK6(sK6(sK6(powerset(X0))))) = relation_image(X1,X2) )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_54,c_35581]) ).
tcf(c_35717,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(X1,X2,sK7(sK6(sK6(sK6(powerset(X0)))))),X2)
| ( sK7(sK6(sK6(sK6(powerset(X0))))) = relation_image(X1,X2) )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_55,c_35581]) ).
tcf(c_35718,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,sK7(sK6(sK6(sK6(powerset(X0))))),X2),X2)
| ( relation_image(X1,sK7(sK6(sK6(sK6(powerset(X0)))))) = X2 )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_55,c_35581]) ).
tcf(c_35719,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ function(X1)
| ~ relation(X1)
| ~ empty(X2)
| ~ in(X0,relation_image(X1,sK7(sK6(sK6(sK6(powerset(X2))))))) ),
inference(superposition,[status(thm)],[c_59,c_35581]) ).
tcf(c_35721,plain,
! [X0: $i,X1: $i] :
( in(sK3(X1,sK1,sK7(sK6(sK6(sK6(powerset(X0)))))),sK0)
| ( sK7(sK6(sK6(sK6(powerset(X0))))) = relation_image(X1,sK1) )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11821,c_35581]) ).
tcf(c_35722,plain,
! [X0: $i,X1: $i] :
( element(sK3(X1,sK1,sK7(sK6(sK6(sK6(powerset(X0)))))),sK0)
| ( sK7(sK6(sK6(sK6(powerset(X0))))) = relation_image(X1,sK1) )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6475,c_35581]) ).
tcf(c_35723,plain,
! [X0: $i,X1: $i] :
( in(sK2(X1,sK7(sK6(sK6(sK6(powerset(X0))))),sK1),sK0)
| ( relation_image(X1,sK7(sK6(sK6(sK6(powerset(X0)))))) = sK1 )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12513,c_35581]) ).
tcf(c_35724,plain,
! [X0: $i,X1: $i] :
( element(sK2(X1,sK7(sK6(sK6(sK6(powerset(X0))))),sK1),sK0)
| ( relation_image(X1,sK7(sK6(sK6(sK6(powerset(X0)))))) = sK1 )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6486,c_35581]) ).
tcf(c_35728,plain,
! [X0: $i] :
( empty(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25981,c_35581]) ).
tcf(c_35729,plain,
! [X0: $i] :
( empty(sK7(sK6(sK6(sK6(powerset(X0))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35578,c_35581]) ).
tcf(c_35923,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X0,X1,sK7(sK6(sK6(sK6(powerset(X2)))))),X2)
| ( sK7(sK6(sK6(sK6(powerset(X2))))) = relation_image(X0,X1) )
| ( apply(X0,sK3(X0,X1,sK7(sK6(sK6(sK6(powerset(X2))))))) = sK2(X0,X1,sK7(sK6(sK6(sK6(powerset(X2)))))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_56,c_35584]) ).
tcf(c_35924,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X0,X2,sK7(sK6(sK6(sK6(powerset(X1)))))),X1)
| in(sK3(X0,X2,sK7(sK6(sK6(sK6(powerset(X1)))))),relation_dom(X0))
| ( sK7(sK6(sK6(sK6(powerset(X1))))) = relation_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_54,c_35584]) ).
tcf(c_35925,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(X0,X2,sK7(sK6(sK6(sK6(powerset(X1)))))),X2)
| element(sK2(X0,X2,sK7(sK6(sK6(sK6(powerset(X1)))))),X1)
| ( sK7(sK6(sK6(sK6(powerset(X1))))) = relation_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_55,c_35584]) ).
tcf(c_35926,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,sK7(sK6(sK6(sK6(powerset(X1))))),X2),X2)
| element(sK3(X0,sK7(sK6(sK6(sK6(powerset(X1))))),X2),X1)
| ( relation_image(X0,sK7(sK6(sK6(sK6(powerset(X1)))))) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_55,c_35584]) ).
tcf(c_35927,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK4(X1,sK7(sK6(sK6(sK6(powerset(X2))))),X0),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,sK7(sK6(sK6(sK6(powerset(X2))))))) ),
inference(superposition,[status(thm)],[c_59,c_35584]) ).
tcf(c_35928,plain,
! [X0: $i] :
( empty(sK7(sK6(sK6(sK6(powerset(X0))))))
| element(sK7(sK7(sK6(sK6(sK6(powerset(X0)))))),X0) ),
inference(superposition,[status(thm)],[c_5703,c_35584]) ).
tcf(c_35929,plain,
! [X0: $i,X1: $i] :
( in(sK3(X0,sK1,sK7(sK6(sK6(sK6(powerset(X1)))))),sK0)
| element(sK2(X0,sK1,sK7(sK6(sK6(sK6(powerset(X1)))))),X1)
| ( sK7(sK6(sK6(sK6(powerset(X1))))) = relation_image(X0,sK1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_11821,c_35584]) ).
tcf(c_35930,plain,
! [X0: $i,X1: $i] :
( element(sK3(X0,sK1,sK7(sK6(sK6(sK6(powerset(X1)))))),sK0)
| element(sK2(X0,sK1,sK7(sK6(sK6(sK6(powerset(X1)))))),X1)
| ( sK7(sK6(sK6(sK6(powerset(X1))))) = relation_image(X0,sK1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6475,c_35584]) ).
tcf(c_35931,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,sK7(sK6(sK6(sK6(powerset(X1))))),sK1),sK0)
| element(sK3(X0,sK7(sK6(sK6(sK6(powerset(X1))))),sK1),X1)
| ( relation_image(X0,sK7(sK6(sK6(sK6(powerset(X1)))))) = sK1 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_12513,c_35584]) ).
tcf(c_35932,plain,
! [X0: $i,X1: $i] :
( element(sK2(X0,sK7(sK6(sK6(sK6(powerset(X1))))),sK1),sK0)
| element(sK3(X0,sK7(sK6(sK6(sK6(powerset(X1))))),sK1),X1)
| ( relation_image(X0,sK7(sK6(sK6(sK6(powerset(X1)))))) = sK1 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6486,c_35584]) ).
tcf(c_35933,plain,
! [X0: $i] :
( empty(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))
| element(sK7(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0)))))))),X0) ),
inference(superposition,[status(thm)],[c_18732,c_35584]) ).
tcf(c_35934,plain,
! [X0: $i] :
( empty(sK7(sK6(sK6(sK6(powerset(X0))))))
| element(sK7(sK6(sK7(sK6(sK6(sK6(powerset(X0))))))),X0) ),
inference(superposition,[status(thm)],[c_9814,c_35584]) ).
tcf(c_35935,plain,
! [X0: $i] :
( empty(sK7(sK6(sK6(sK6(powerset(X0))))))
| element(sK7(sK6(sK6(sK7(sK6(sK6(sK6(powerset(X0)))))))),X0) ),
inference(superposition,[status(thm)],[c_14086,c_35584]) ).
tcf(c_35936,plain,
! [X0: $i] :
( empty(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))
| element(sK7(sK6(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))),X0) ),
inference(superposition,[status(thm)],[c_25981,c_35584]) ).
tcf(c_35937,plain,
! [X0: $i] :
( empty(sK7(sK6(sK6(sK6(powerset(X0))))))
| element(sK7(sK6(sK6(sK6(sK7(sK6(sK6(sK6(powerset(X0))))))))),X0) ),
inference(superposition,[status(thm)],[c_35578,c_35584]) ).
tcf(c_36160,plain,
! [X0: $i] :
( ( relation_dom(sK7(sK6(powerset(relation_dom(relation_dom(sK7(sK6(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_25099]) ).
tcf(c_36161,plain,
! [X0: $i] :
( ( identity_relation(sK7(sK6(powerset(relation_dom(relation_dom(sK7(sK6(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_24875]) ).
tcf(c_36162,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(identity_relation(identity_relation(sK7(sK6(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_13970]) ).
tcf(c_36163,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(identity_relation(sK7(sK6(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_13854]) ).
tcf(c_36164,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(identity_relation(identity_relation(sK7(sK6(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_12910]) ).
tcf(c_36165,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(identity_relation(identity_relation(sK7(sK6(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_12872]) ).
tcf(c_36166,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(powerset(relation_dom(relation_dom(sK7(sK6(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_24819]) ).
tcf(c_36167,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(identity_relation(relation_dom(relation_dom(sK7(sK6(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_24724]) ).
tcf(c_36168,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(relation_dom(relation_dom(sK7(sK6(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_24676]) ).
tcf(c_36169,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(relation_dom(relation_dom(relation_dom(sK7(sK6(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_24628]) ).
tcf(c_36170,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(powerset(identity_relation(sK7(sK6(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_12319]) ).
tcf(c_36171,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(powerset(identity_relation(sK7(sK6(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_12213]) ).
tcf(c_36172,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(powerset(identity_relation(sK7(sK6(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_12136]) ).
tcf(c_36173,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(powerset(identity_relation(sK7(sK6(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_11432]) ).
tcf(c_36174,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(relation_dom(relation_dom(relation_dom(sK7(sK6(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_24580]) ).
tcf(c_36175,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(relation_dom(relation_dom(relation_dom(sK7(sK6(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_24491]) ).
tcf(c_36176,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(identity_relation(relation_dom(relation_dom(sK7(sK6(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_24443]) ).
tcf(c_36177,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(identity_relation(relation_dom(relation_dom(sK7(sK6(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_24395]) ).
tcf(c_36178,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_11345]) ).
tcf(c_36179,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(sK6(powerset(sK7(sK6(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_10677]) ).
tcf(c_36180,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(sK6(powerset(sK7(sK6(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_10676]) ).
tcf(c_36181,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(sK6(powerset(sK7(sK6(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_10675]) ).
tcf(c_36182,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(relation_dom(relation_dom(relation_dom(sK7(sK6(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_24347]) ).
tcf(c_36183,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(relation_dom(relation_dom(relation_dom(sK7(sK6(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_23164]) ).
tcf(c_36184,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(powerset(relation_dom(relation_dom(sK7(sK6(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_22515]) ).
tcf(c_36185,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(powerset(relation_dom(relation_dom(sK7(sK6(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_22426]) ).
tcf(c_36186,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(sK6(powerset(sK7(sK6(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_10674]) ).
tcf(c_36187,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_9751]) ).
tcf(c_36188,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_9685]) ).
tcf(c_36189,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(powerset(relation_dom(relation_dom(sK7(sK6(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_22338]) ).
tcf(c_36190,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(relation_dom(relation_dom(relation_dom(sK7(sK6(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_22121]) ).
tcf(c_36191,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(relation_dom(relation_dom(relation_dom(sK7(sK6(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_22031]) ).
tcf(c_36192,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK7(sK6(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_21914]) ).
tcf(c_36193,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(sK7(sK6(sK6(sK6(powerset(X0))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_9348]) ).
tcf(c_36194,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_9118]) ).
tcf(c_36195,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_9091]) ).
tcf(c_36196,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_9021]) ).
tcf(c_36197,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK7(sK6(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_21763]) ).
tcf(c_36198,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(powerset(relation_dom(relation_dom(sK7(sK6(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_21512]) ).
tcf(c_36199,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(relation_dom(sK7(sK6(sK6(sK6(powerset(X0)))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_20489]) ).
tcf(c_36200,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(sK7(sK6(sK6(sK6(powerset(X0)))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_20393]) ).
tcf(c_36201,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_8996]) ).
tcf(c_36202,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_8961]) ).
tcf(c_36203,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_8565]) ).
tcf(c_36204,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(relation_dom(sK7(sK6(sK6(sK6(powerset(X0)))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_18503]) ).
tcf(c_36205,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(identity_relation(relation_dom(sK7(sK6(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_25846]) ).
tcf(c_36206,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(identity_relation(sK7(sK6(sK6(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_11341]) ).
tcf(c_36207,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(powerset(sK7(sK6(sK6(sK6(powerset(X0)))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_10679]) ).
tcf(c_36208,plain,
! [X0: $i] :
( ( relation_dom(sK7(sK6(powerset(relation_dom(sK7(sK6(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_17536]) ).
tcf(c_36209,plain,
! [X0: $i] :
( ( identity_relation(sK7(sK6(powerset(relation_dom(sK7(sK6(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_17479]) ).
tcf(c_36210,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(powerset(relation_dom(sK7(sK6(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_16756]) ).
tcf(c_36211,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(identity_relation(relation_dom(sK7(sK6(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_13969]) ).
tcf(c_36212,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(relation_dom(sK7(sK6(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_13853]) ).
tcf(c_36213,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(relation_dom(relation_dom(sK7(sK6(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_13817]) ).
tcf(c_36214,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(relation_dom(relation_dom(sK7(sK6(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_13649]) ).
tcf(c_36215,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(relation_dom(relation_dom(sK7(sK6(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_13044]) ).
tcf(c_36216,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(identity_relation(relation_dom(sK7(sK6(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_12909]) ).
tcf(c_36217,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(identity_relation(relation_dom(sK7(sK6(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_12871]) ).
tcf(c_36218,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(relation_dom(relation_dom(sK7(sK6(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_12755]) ).
tcf(c_36219,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(relation_dom(relation_dom(sK7(sK6(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_12356]) ).
tcf(c_36220,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(powerset(relation_dom(sK7(sK6(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_12318]) ).
tcf(c_36221,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(powerset(relation_dom(sK7(sK6(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_12212]) ).
tcf(c_36222,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(powerset(relation_dom(sK7(sK6(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_12135]) ).
tcf(c_36223,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(relation_dom(relation_dom(sK7(sK6(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_12099]) ).
tcf(c_36224,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(relation_dom(relation_dom(sK7(sK6(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_12063]) ).
tcf(c_36225,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(relation_dom(relation_dom(sK7(sK6(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_12027]) ).
tcf(c_36226,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK7(sK6(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_11953]) ).
tcf(c_36227,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(powerset(relation_dom(sK7(sK6(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_11431]) ).
tcf(c_36228,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(sK7(sK6(sK6(sK6(powerset(X0))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_9347]) ).
tcf(c_36229,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK7(sK6(sK6(sK6(powerset(X0))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_9319]) ).
tcf(c_36230,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_6877]) ).
tcf(c_36231,plain,
! [X0: $i] :
( ( relation_dom(sK7(sK6(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_10680]) ).
tcf(c_36232,plain,
! [X0: $i] :
( ( identity_relation(sK7(sK6(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_10678]) ).
tcf(c_36233,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_15645]) ).
tcf(c_36234,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(identity_relation(sK7(sK6(sK6(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_9748]) ).
tcf(c_36235,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(sK7(sK6(sK6(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_9682]) ).
tcf(c_36236,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(relation_dom(sK7(sK6(sK6(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_11340]) ).
tcf(c_36237,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(relation_dom(sK7(sK6(sK6(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_9747]) ).
tcf(c_36238,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(relation_dom(sK7(sK6(sK6(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_9681]) ).
tcf(c_36239,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(identity_relation(sK7(sK6(sK6(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_9115]) ).
tcf(c_36240,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(identity_relation(sK7(sK6(sK6(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_9088]) ).
tcf(c_36241,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(relation_dom(sK7(sK6(sK6(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_9114]) ).
tcf(c_36242,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(relation_dom(sK7(sK6(sK6(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_9087]) ).
tcf(c_36243,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_8009]) ).
tcf(c_36244,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_7966]) ).
tcf(c_36245,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_7938]) ).
tcf(c_36246,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(relation_dom(sK7(sK6(sK6(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_9017]) ).
tcf(c_36247,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(relation_dom(sK7(sK6(sK6(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_8992]) ).
tcf(c_36248,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(relation_dom(sK7(sK6(sK6(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_8957]) ).
tcf(c_36249,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK7(sK6(sK6(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_8561]) ).
tcf(c_36250,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_6875]) ).
tcf(c_36251,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(sK7(sK6(sK6(sK6(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_10681]) ).
tcf(c_36252,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(sK7(sK6(sK6(sK6(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_8006]) ).
tcf(c_36253,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(sK7(sK6(sK6(sK6(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_7963]) ).
tcf(c_36254,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK7(sK6(sK6(sK6(powerset(X0)))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_5794]) ).
tcf(c_36255,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(sK6(sK6(sK6(powerset(X0)))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_5793]) ).
tcf(c_36256,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_6878]) ).
tcf(c_36257,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_6876]) ).
tcf(c_36258,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(sK7(sK6(sK6(sK6(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_8005]) ).
tcf(c_36259,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(sK7(sK6(sK6(sK6(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_7962]) ).
tcf(c_36260,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(sK7(sK6(sK6(sK6(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_7934]) ).
tcf(c_36261,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK7(sK6(sK6(sK6(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_6133]) ).
tcf(c_36262,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_6879]) ).
tcf(c_36263,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(sK6(sK6(sK6(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_6106]) ).
tcf(c_36264,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(sK6(sK6(sK6(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_6105]) ).
tcf(c_36265,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(sK6(sK6(sK6(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_5747]) ).
tcf(c_36266,plain,
! [X0: $i] :
( ( identity_relation(sK7(sK6(sK6(sK6(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_5776]) ).
tcf(c_36267,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(sK6(sK6(powerset(X0))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_51]) ).
tcf(c_36268,plain,
! [X0: $i] :
( ( relation_dom(sK7(sK6(sK6(sK6(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_5663]) ).
tcf(c_36269,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(sK6(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_52]) ).
tcf(c_36270,plain,
! [X0: $i] :
( function(sK7(sK6(sK6(sK6(powerset(X0))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_98]) ).
tcf(c_36271,plain,
! [X0: $i] :
( relation(sK7(sK6(sK6(sK6(powerset(X0))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_80]) ).
tcf(c_37138,plain,
! [X0: $i] :
( ( relation_image(sK7(sK6(sK6(sK6(powerset(X0))))),empty_set) = empty_set )
| ~ empty(X0)
| ~ relation(sK7(sK6(sK6(sK6(powerset(X0)))))) ),
inference(superposition,[status(thm)],[c_36270,c_23329]) ).
tcf(c_37227,plain,
( empty(sK7(powerset(empty_set)))
| element(sK7(sK6(sK6(empty_set))),empty_set) ),
inference(superposition,[status(thm)],[c_8004,c_14109]) ).
tcf(c_37228,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| empty(sK7(powerset(powerset(X1))))
| ~ in(X0,sK7(sK6(sK6(sK7(powerset(powerset(X1))))))) ),
inference(superposition,[status(thm)],[c_14109,c_65]) ).
tcf(c_37229,plain,
! [X0: $i,X1: $i] :
( empty(sK7(powerset(powerset(X1))))
| ~ empty(X1)
| ~ in(X0,sK7(sK6(sK6(sK7(powerset(powerset(X1))))))) ),
inference(superposition,[status(thm)],[c_14109,c_64]) ).
tcf(c_37230,plain,
! [X0: $i] :
( empty(X0)
| empty(sK7(powerset(X0)))
| in(sK7(sK6(sK6(sK7(powerset(X0))))),X0) ),
inference(superposition,[status(thm)],[c_14109,c_71]) ).
tcf(c_37231,plain,
( empty(empty_set)
| element(sK7(sK6(sK6(empty_set))),empty_set) ),
inference(light_normalisation,[status(thm)],[c_37227,c_8004]) ).
tcf(c_37274,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,X2)
| element(sK3(X1,sK1,sK7(sK6(sK6(sK6(powerset(powerset(X2))))))),sK0)
| ( sK7(sK6(sK6(sK6(powerset(powerset(X2)))))) = relation_image(X1,sK1) )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,sK2(X1,sK1,sK7(sK6(sK6(sK6(powerset(powerset(X2)))))))) ),
inference(superposition,[status(thm)],[c_35930,c_65]) ).
tcf(c_37275,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK3(X1,sK1,sK7(sK6(sK6(sK6(powerset(powerset(X2))))))),sK0)
| ( sK7(sK6(sK6(sK6(powerset(powerset(X2)))))) = relation_image(X1,sK1) )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X2)
| ~ in(X0,sK2(X1,sK1,sK7(sK6(sK6(sK6(powerset(powerset(X2)))))))) ),
inference(superposition,[status(thm)],[c_35930,c_64]) ).
tcf(c_37276,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| element(sK3(X0,sK1,sK7(sK6(sK6(sK6(powerset(X1)))))),sK0)
| in(sK2(X0,sK1,sK7(sK6(sK6(sK6(powerset(X1)))))),X1)
| ( sK7(sK6(sK6(sK6(powerset(X1))))) = relation_image(X0,sK1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_35930,c_71]) ).
tcf(c_37307,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,X2)
| element(sK2(X1,sK7(sK6(sK6(sK6(powerset(powerset(X2)))))),sK1),sK0)
| ( relation_image(X1,sK7(sK6(sK6(sK6(powerset(powerset(X2))))))) = sK1 )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,sK3(X1,sK7(sK6(sK6(sK6(powerset(powerset(X2)))))),sK1)) ),
inference(superposition,[status(thm)],[c_35932,c_65]) ).
tcf(c_37308,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X1,sK7(sK6(sK6(sK6(powerset(powerset(X2)))))),sK1),sK0)
| ( relation_image(X1,sK7(sK6(sK6(sK6(powerset(powerset(X2))))))) = sK1 )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X2)
| ~ in(X0,sK3(X1,sK7(sK6(sK6(sK6(powerset(powerset(X2)))))),sK1)) ),
inference(superposition,[status(thm)],[c_35932,c_64]) ).
tcf(c_37309,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| element(sK2(X0,sK7(sK6(sK6(sK6(powerset(X1))))),sK1),sK0)
| in(sK3(X0,sK7(sK6(sK6(sK6(powerset(X1))))),sK1),X1)
| ( relation_image(X0,sK7(sK6(sK6(sK6(powerset(X1)))))) = sK1 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_35932,c_71]) ).
tcf(c_37338,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(sK6(powerset(X0))))) = empty_set )
| ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_10348,c_36269]) ).
tcf(c_37339,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(sK6(powerset(X0))))) = empty_set )
| ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) ) ),
inference(superposition,[status(thm)],[c_5806,c_36269]) ).
tcf(c_37340,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( sK7(sK6(sK6(sK6(powerset(X0))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_36269]) ).
tcf(c_37341,plain,
sK7(sK6(sK6(sK6(powerset(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_36269]) ).
tcf(c_37342,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(sK6(powerset(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_36269]) ).
tcf(c_37343,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(sK6(powerset(identity_relation(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_36269]) ).
tcf(c_37344,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(sK6(powerset(sK7(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_36269]) ).
tcf(c_37345,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(sK6(powerset(sK7(sK6(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_36269]) ).
tcf(c_37346,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(sK6(powerset(sK7(sK6(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_36269]) ).
tcf(c_37347,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(sK6(powerset(relation_image(X0,empty_set)))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_36269]) ).
tcf(c_37348,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(sK6(powerset(sK7(powerset(sK7(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_36269]) ).
tcf(c_37349,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(sK6(powerset(sK7(powerset(sK7(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_36269]) ).
tcf(c_37350,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(sK6(powerset(sK7(powerset(sK7(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_36269]) ).
tcf(c_37351,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(sK6(powerset(sK7(sK6(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_36269]) ).
tcf(c_37425,plain,
( ( sK7(powerset(identity_relation(sK6(sK6(sK6(powerset(empty_set))))))) = empty_set )
| ( apply(identity_relation(sK6(sK6(sK6(powerset(empty_set))))),empty_set) = empty_set ) ),
inference(superposition,[status(thm)],[c_37341,c_9745]) ).
tcf(c_37426,plain,
( ( apply(identity_relation(sK6(sK6(sK6(powerset(empty_set))))),empty_set) = empty_set )
| ( identity_relation(identity_relation(identity_relation(sK6(sK6(sK6(powerset(empty_set))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_37341,c_9679]) ).
tcf(c_37427,plain,
( ( sK6(sK6(sK6(powerset(empty_set)))) = empty_set )
| ( apply(identity_relation(sK6(sK6(sK6(powerset(empty_set))))),empty_set) = empty_set ) ),
inference(superposition,[status(thm)],[c_37341,c_9430]) ).
tcf(c_37428,plain,
( ( relation_dom(sK6(sK6(sK6(powerset(empty_set))))) = empty_set )
| ( apply(identity_relation(sK6(sK6(sK6(powerset(empty_set))))),empty_set) = empty_set ) ),
inference(superposition,[status(thm)],[c_37341,c_9429]) ).
tcf(c_37429,plain,
( ( identity_relation(sK6(sK6(sK6(powerset(empty_set))))) = empty_set )
| ( apply(identity_relation(sK6(sK6(sK6(powerset(empty_set))))),empty_set) = empty_set ) ),
inference(superposition,[status(thm)],[c_37341,c_9427]) ).
tcf(c_37430,plain,
( ( relation_dom(relation_dom(sK6(sK6(sK6(powerset(empty_set)))))) = empty_set )
| ( apply(identity_relation(sK6(sK6(sK6(powerset(empty_set))))),empty_set) = empty_set ) ),
inference(superposition,[status(thm)],[c_37341,c_9426]) ).
tcf(c_37431,plain,
( ( identity_relation(relation_dom(sK6(sK6(sK6(powerset(empty_set)))))) = empty_set )
| ( apply(identity_relation(sK6(sK6(sK6(powerset(empty_set))))),empty_set) = empty_set ) ),
inference(superposition,[status(thm)],[c_37341,c_9425]) ).
tcf(c_37432,plain,
( ( identity_relation(identity_relation(sK6(sK6(sK6(powerset(empty_set)))))) = empty_set )
| ( apply(identity_relation(sK6(sK6(sK6(powerset(empty_set))))),empty_set) = empty_set ) ),
inference(superposition,[status(thm)],[c_37341,c_9424]) ).
tcf(c_37433,plain,
( ( sK7(powerset(sK6(sK6(sK6(powerset(empty_set)))))) = empty_set )
| ( apply(identity_relation(sK6(sK6(sK6(powerset(empty_set))))),empty_set) = empty_set ) ),
inference(superposition,[status(thm)],[c_37341,c_9423]) ).
tcf(c_37434,plain,
( ( apply(identity_relation(sK6(sK6(sK6(powerset(empty_set))))),empty_set) = empty_set )
| ( relation_dom(relation_dom(relation_dom(sK6(sK6(sK6(powerset(empty_set))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_37341,c_9418]) ).
tcf(c_37435,plain,
( ( apply(identity_relation(sK6(sK6(sK6(powerset(empty_set))))),empty_set) = empty_set )
| ( identity_relation(relation_dom(relation_dom(sK6(sK6(sK6(powerset(empty_set))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_37341,c_9415]) ).
tcf(c_37436,plain,
( ( apply(identity_relation(sK6(sK6(sK6(powerset(empty_set))))),empty_set) = empty_set )
| ( identity_relation(identity_relation(relation_dom(sK6(sK6(sK6(powerset(empty_set))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_37341,c_9414]) ).
tcf(c_37437,plain,
( ( sK7(powerset(relation_dom(sK6(sK6(sK6(powerset(empty_set))))))) = empty_set )
| ( apply(identity_relation(sK6(sK6(sK6(powerset(empty_set))))),empty_set) = empty_set ) ),
inference(superposition,[status(thm)],[c_37341,c_9413]) ).
tcf(c_37438,plain,
( ( apply(identity_relation(sK6(sK6(sK6(powerset(empty_set))))),empty_set) = empty_set )
| ( identity_relation(sK7(powerset(sK6(sK6(sK6(powerset(empty_set))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_37341,c_9412]) ).
tcf(c_37439,plain,
( ( apply(identity_relation(sK6(sK6(sK6(powerset(empty_set))))),empty_set) = empty_set )
| ( relation_dom(sK7(powerset(sK6(sK6(sK6(powerset(empty_set))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_37341,c_9411]) ).
tcf(c_37440,plain,
( empty(sK6(sK6(sK6(powerset(empty_set)))))
| ~ in(sK6(sK6(sK6(powerset(empty_set)))),empty_set) ),
inference(superposition,[status(thm)],[c_37341,c_5724]) ).
tcf(c_37441,plain,
( empty(sK6(sK6(sK6(powerset(empty_set)))))
| in(empty_set,sK6(sK6(sK6(powerset(empty_set))))) ),
inference(superposition,[status(thm)],[c_37341,c_5703]) ).
tcf(c_37442,plain,
element(empty_set,sK6(sK6(sK6(powerset(empty_set))))),
inference(superposition,[status(thm)],[c_37341,c_73]) ).
tcf(c_37452,plain,
! [X0: $i] :
( element(sK2(X0,empty_set,sK1),sK0)
| ( relation_image(X0,sK7(sK6(sK6(sK6(powerset(empty_set)))))) = sK1 )
| ~ empty(empty_set)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_37341,c_35724]) ).
tcf(c_37453,plain,
! [X0: $i] :
( element(sK3(X0,sK1,empty_set),sK0)
| ( sK7(sK6(sK6(sK6(powerset(empty_set))))) = relation_image(X0,sK1) )
| ~ empty(empty_set)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_37341,c_35722]) ).
tcf(c_37457,plain,
! [X0: $i] :
( element(sK3(X0,empty_set,sK1),empty_set)
| element(sK2(X0,sK7(sK6(sK6(sK6(powerset(empty_set))))),sK1),sK0)
| ( relation_image(X0,sK7(sK6(sK6(sK6(powerset(empty_set)))))) = sK1 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_37341,c_35932]) ).
tcf(c_37458,plain,
! [X0: $i] :
( element(sK2(X0,sK1,empty_set),empty_set)
| element(sK3(X0,sK1,sK7(sK6(sK6(sK6(powerset(empty_set)))))),sK0)
| ( sK7(sK6(sK6(sK6(powerset(empty_set))))) = relation_image(X0,sK1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_37341,c_35930]) ).
tcf(c_37459,plain,
! [X0: $i] :
( element(sK3(X0,sK1,empty_set),sK0)
| element(sK2(X0,sK1,sK7(sK6(sK6(sK6(powerset(empty_set)))))),empty_set)
| ( sK7(sK6(sK6(sK6(powerset(empty_set))))) = relation_image(X0,sK1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_37341,c_35930]) ).
tcf(c_37556,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( sK7(sK6(powerset(identity_relation(relation_dom(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10348,c_25936]) ).
tcf(c_37557,plain,
! [X0: $i] :
( ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ( sK7(sK6(powerset(identity_relation(relation_dom(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_25936]) ).
tcf(c_37558,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( sK7(sK6(powerset(identity_relation(relation_dom(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_25936]) ).
tcf(c_37559,plain,
sK7(sK6(powerset(identity_relation(relation_dom(relation_dom(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_25936]) ).
tcf(c_37560,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(identity_relation(relation_dom(relation_dom(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_25936]) ).
tcf(c_37561,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(identity_relation(relation_dom(relation_dom(identity_relation(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_25936]) ).
tcf(c_37562,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(identity_relation(relation_dom(relation_dom(sK7(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_25936]) ).
tcf(c_37563,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(identity_relation(relation_dom(relation_dom(sK7(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_25936]) ).
tcf(c_37564,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(identity_relation(relation_dom(relation_dom(sK7(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_25936]) ).
tcf(c_37565,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(identity_relation(relation_dom(relation_dom(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_25936]) ).
tcf(c_37566,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(identity_relation(relation_dom(relation_dom(sK7(powerset(sK7(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_25936]) ).
tcf(c_37567,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(identity_relation(relation_dom(relation_dom(sK7(powerset(sK7(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_25936]) ).
tcf(c_37568,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(identity_relation(relation_dom(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_25936]) ).
tcf(c_37569,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(identity_relation(relation_dom(relation_dom(sK7(sK6(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_25936]) ).
tcf(c_37660,plain,
! [X0: $i] :
( ( identity_relation(sK7(sK6(sK6(powerset(X0))))) = empty_set )
| ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_10348,c_15642]) ).
tcf(c_37661,plain,
! [X0: $i] :
( ( identity_relation(sK7(sK6(sK6(powerset(X0))))) = empty_set )
| ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) ) ),
inference(superposition,[status(thm)],[c_5806,c_15642]) ).
tcf(c_37662,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( identity_relation(sK7(sK6(sK6(powerset(X0))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_15642]) ).
tcf(c_37663,plain,
identity_relation(sK7(sK6(sK6(powerset(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_15642]) ).
tcf(c_37664,plain,
! [X0: $i] :
( ( identity_relation(sK7(sK6(sK6(powerset(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_15642]) ).
tcf(c_37665,plain,
! [X0: $i] :
( ( identity_relation(sK7(sK6(sK6(powerset(identity_relation(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_15642]) ).
tcf(c_37666,plain,
! [X0: $i] :
( ( identity_relation(sK7(sK6(sK6(powerset(sK7(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_15642]) ).
tcf(c_37667,plain,
! [X0: $i] :
( ( identity_relation(sK7(sK6(sK6(powerset(sK7(sK6(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_15642]) ).
tcf(c_37668,plain,
! [X0: $i] :
( ( identity_relation(sK7(sK6(sK6(powerset(sK7(sK6(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_15642]) ).
tcf(c_37669,plain,
! [X0: $i] :
( ( identity_relation(sK7(sK6(sK6(powerset(relation_image(X0,empty_set)))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_15642]) ).
tcf(c_37670,plain,
! [X0: $i] :
( ( identity_relation(sK7(sK6(sK6(powerset(sK7(powerset(sK7(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_15642]) ).
tcf(c_37671,plain,
! [X0: $i] :
( ( identity_relation(sK7(sK6(sK6(powerset(sK7(powerset(sK7(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_15642]) ).
tcf(c_37672,plain,
! [X0: $i] :
( ( identity_relation(sK7(sK6(sK6(powerset(sK7(powerset(sK7(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_15642]) ).
tcf(c_37673,plain,
! [X0: $i] :
( ( identity_relation(sK7(sK6(sK6(powerset(sK7(sK6(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_15642]) ).
tcf(c_37776,plain,
! [X0: $i] :
( ( relation_dom(sK7(sK6(sK6(powerset(X0))))) = empty_set )
| ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_10348,c_15644]) ).
tcf(c_37777,plain,
! [X0: $i] :
( ( relation_dom(sK7(sK6(sK6(powerset(X0))))) = empty_set )
| ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) ) ),
inference(superposition,[status(thm)],[c_5806,c_15644]) ).
tcf(c_37778,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( relation_dom(sK7(sK6(sK6(powerset(X0))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_15644]) ).
tcf(c_37779,plain,
relation_dom(sK7(sK6(sK6(powerset(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_15644]) ).
tcf(c_37780,plain,
! [X0: $i] :
( ( relation_dom(sK7(sK6(sK6(powerset(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_15644]) ).
tcf(c_37781,plain,
! [X0: $i] :
( ( relation_dom(sK7(sK6(sK6(powerset(identity_relation(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_15644]) ).
tcf(c_37782,plain,
! [X0: $i] :
( ( relation_dom(sK7(sK6(sK6(powerset(sK7(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_15644]) ).
tcf(c_37783,plain,
! [X0: $i] :
( ( relation_dom(sK7(sK6(sK6(powerset(sK7(sK6(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_15644]) ).
tcf(c_37784,plain,
! [X0: $i] :
( ( relation_dom(sK7(sK6(sK6(powerset(sK7(sK6(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_15644]) ).
tcf(c_37785,plain,
! [X0: $i] :
( ( relation_dom(sK7(sK6(sK6(powerset(relation_image(X0,empty_set)))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_15644]) ).
tcf(c_37786,plain,
! [X0: $i] :
( ( relation_dom(sK7(sK6(sK6(powerset(sK7(powerset(sK7(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_15644]) ).
tcf(c_37787,plain,
! [X0: $i] :
( ( relation_dom(sK7(sK6(sK6(powerset(sK7(powerset(sK7(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_15644]) ).
tcf(c_37788,plain,
! [X0: $i] :
( ( relation_dom(sK7(sK6(sK6(powerset(sK7(powerset(sK7(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_15644]) ).
tcf(c_37789,plain,
! [X0: $i] :
( ( relation_dom(sK7(sK6(sK6(powerset(sK7(sK6(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_15644]) ).
tcf(c_37885,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(powerset(identity_relation(X0))))) = empty_set )
| ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_10348,c_16757]) ).
tcf(c_37886,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(powerset(identity_relation(X0))))) = empty_set )
| ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) ) ),
inference(superposition,[status(thm)],[c_5806,c_16757]) ).
tcf(c_37887,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( sK7(sK6(sK6(powerset(identity_relation(X0))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_16757]) ).
tcf(c_37888,plain,
sK7(sK6(sK6(powerset(identity_relation(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_16757]) ).
tcf(c_37889,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(powerset(identity_relation(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_16757]) ).
tcf(c_37890,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(powerset(identity_relation(identity_relation(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_16757]) ).
tcf(c_37891,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(powerset(identity_relation(sK7(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_16757]) ).
tcf(c_37892,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(powerset(identity_relation(sK7(sK6(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_16757]) ).
tcf(c_37893,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(powerset(identity_relation(sK7(sK6(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_16757]) ).
tcf(c_37894,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(powerset(identity_relation(relation_image(X0,empty_set)))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_16757]) ).
tcf(c_37895,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(powerset(identity_relation(sK7(powerset(sK7(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_16757]) ).
tcf(c_37896,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(powerset(identity_relation(sK7(powerset(sK7(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_16757]) ).
tcf(c_37897,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(powerset(identity_relation(sK7(powerset(sK7(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_16757]) ).
tcf(c_37898,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(powerset(identity_relation(sK7(sK6(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_16757]) ).
tcf(c_37965,plain,
! [X0: $i] :
( ( identity_relation(sK7(sK6(powerset(identity_relation(X0))))) = empty_set )
| ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_10348,c_17480]) ).
tcf(c_37966,plain,
! [X0: $i] :
( ( identity_relation(sK7(sK6(powerset(identity_relation(X0))))) = empty_set )
| ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) ) ),
inference(superposition,[status(thm)],[c_5806,c_17480]) ).
tcf(c_37967,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( identity_relation(sK7(sK6(powerset(identity_relation(X0))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_17480]) ).
tcf(c_37968,plain,
identity_relation(sK7(sK6(powerset(identity_relation(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_17480]) ).
tcf(c_37969,plain,
! [X0: $i] :
( ( identity_relation(sK7(sK6(powerset(identity_relation(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_17480]) ).
tcf(c_37970,plain,
! [X0: $i] :
( ( identity_relation(sK7(sK6(powerset(identity_relation(identity_relation(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_17480]) ).
tcf(c_37971,plain,
! [X0: $i] :
( ( identity_relation(sK7(sK6(powerset(identity_relation(sK7(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_17480]) ).
tcf(c_37972,plain,
! [X0: $i] :
( ( identity_relation(sK7(sK6(powerset(identity_relation(sK7(sK6(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_17480]) ).
tcf(c_37973,plain,
! [X0: $i] :
( ( identity_relation(sK7(sK6(powerset(identity_relation(sK7(sK6(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_17480]) ).
tcf(c_37974,plain,
! [X0: $i] :
( ( identity_relation(sK7(sK6(powerset(identity_relation(relation_image(X0,empty_set)))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_17480]) ).
tcf(c_37975,plain,
! [X0: $i] :
( ( identity_relation(sK7(sK6(powerset(identity_relation(sK7(powerset(sK7(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_17480]) ).
tcf(c_37976,plain,
! [X0: $i] :
( ( identity_relation(sK7(sK6(powerset(identity_relation(sK7(powerset(sK7(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_17480]) ).
tcf(c_37977,plain,
! [X0: $i] :
( ( identity_relation(sK7(sK6(powerset(identity_relation(sK7(powerset(sK7(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_17480]) ).
tcf(c_37978,plain,
! [X0: $i] :
( ( identity_relation(sK7(sK6(powerset(identity_relation(sK7(sK6(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_17480]) ).
tcf(c_38085,plain,
( ( sK7(sK6(powerset(powerset(empty_set)))) = empty_set )
| ( apply(identity_relation(powerset(empty_set)),empty_set) = empty_set ) ),
inference(superposition,[status(thm)],[c_8004,c_11338]) ).
tcf(c_38088,plain,
( ( sK7(sK6(powerset(sK6(sK6(sK6(powerset(empty_set))))))) = empty_set )
| ( apply(identity_relation(sK6(sK6(sK6(powerset(empty_set))))),empty_set) = empty_set ) ),
inference(superposition,[status(thm)],[c_37341,c_11338]) ).
tcf(c_38089,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK7(sK6(powerset(X0))) = empty_set )
| ( relation_image(identity_relation(X0),X1) = X2 )
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),relation_dom(identity_relation(X0)))
| ~ in(sK2(identity_relation(X0),X1,X2),X2)
| ( sK2(identity_relation(X0),X1,X2) != sK7(X0) ) ),
inference(superposition,[status(thm)],[c_11338,c_53]) ).
tcf(c_38090,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0),relation_image(identity_relation(X0),X1))
| ( sK7(sK6(powerset(X0))) = empty_set )
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),relation_dom(identity_relation(X0))) ),
inference(superposition,[status(thm)],[c_11338,c_57]) ).
tcf(c_38093,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0),relation_image(identity_relation(X0),X1))
| ( sK7(sK6(powerset(X0))) = empty_set )
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),X0) ),
inference(light_normalisation,[status(thm)],[c_38090,c_121]) ).
tcf(c_38094,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0),relation_image(identity_relation(X0),X1))
| ( sK7(sK6(powerset(X0))) = empty_set )
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_38093,c_62,c_63]) ).
tcf(c_38099,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK7(sK6(powerset(X0))) = empty_set )
| ( relation_image(identity_relation(X0),X1) = X2 )
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),X0)
| ~ in(sK2(identity_relation(X0),X1,X2),X2)
| ( sK2(identity_relation(X0),X1,X2) != sK7(X0) ) ),
inference(light_normalisation,[status(thm)],[c_38089,c_121]) ).
tcf(c_38100,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK7(sK6(powerset(X0))) = empty_set )
| ( relation_image(identity_relation(X0),X1) = X2 )
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),X0)
| ~ in(sK2(identity_relation(X0),X1,X2),X2)
| ( sK2(identity_relation(X0),X1,X2) != sK7(X0) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_38099,c_62,c_63]) ).
tcf(c_38111,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( relation_dom(relation_dom(relation_dom(sK7(powerset(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10348,c_26731]) ).
tcf(c_38112,plain,
! [X0: $i] :
( ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ( relation_dom(relation_dom(relation_dom(sK7(powerset(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_26731]) ).
tcf(c_38113,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( relation_dom(relation_dom(relation_dom(sK7(powerset(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_26731]) ).
tcf(c_38114,plain,
relation_dom(relation_dom(relation_dom(sK7(powerset(relation_dom(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_26731]) ).
tcf(c_38115,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK7(powerset(relation_dom(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_26731]) ).
tcf(c_38116,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK7(powerset(relation_dom(identity_relation(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_26731]) ).
tcf(c_38117,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK7(powerset(relation_dom(sK7(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_26731]) ).
tcf(c_38118,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK7(powerset(relation_dom(sK7(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_26731]) ).
tcf(c_38119,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK7(powerset(relation_dom(sK7(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_26731]) ).
tcf(c_38120,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK7(powerset(relation_dom(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_26731]) ).
tcf(c_38121,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK7(powerset(relation_dom(sK7(powerset(sK7(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_26731]) ).
tcf(c_38122,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK7(powerset(relation_dom(sK7(powerset(sK7(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_26731]) ).
tcf(c_38123,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK7(powerset(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_26731]) ).
tcf(c_38124,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK7(powerset(relation_dom(sK7(sK6(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_26731]) ).
tcf(c_38245,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( identity_relation(relation_dom(relation_dom(sK7(powerset(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10348,c_26809]) ).
tcf(c_38246,plain,
! [X0: $i] :
( ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ( identity_relation(relation_dom(relation_dom(sK7(powerset(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_26809]) ).
tcf(c_38247,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( identity_relation(relation_dom(relation_dom(sK7(powerset(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_26809]) ).
tcf(c_38248,plain,
identity_relation(relation_dom(relation_dom(sK7(powerset(relation_dom(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_26809]) ).
tcf(c_38249,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(sK7(powerset(relation_dom(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_26809]) ).
tcf(c_38250,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(sK7(powerset(relation_dom(identity_relation(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_26809]) ).
tcf(c_38251,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(sK7(powerset(relation_dom(sK7(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_26809]) ).
tcf(c_38252,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(sK7(powerset(relation_dom(sK7(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_26809]) ).
tcf(c_38253,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(sK7(powerset(relation_dom(sK7(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_26809]) ).
tcf(c_38254,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(sK7(powerset(relation_dom(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_26809]) ).
tcf(c_38255,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(sK7(powerset(relation_dom(sK7(powerset(sK7(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_26809]) ).
tcf(c_38256,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(sK7(powerset(relation_dom(sK7(powerset(sK7(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_26809]) ).
tcf(c_38257,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(sK7(powerset(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_26809]) ).
tcf(c_38258,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(sK7(powerset(relation_dom(sK7(sK6(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_26809]) ).
tcf(c_38333,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( identity_relation(identity_relation(relation_dom(sK7(powerset(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10348,c_26858]) ).
tcf(c_38334,plain,
! [X0: $i] :
( ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ( identity_relation(identity_relation(relation_dom(sK7(powerset(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_26858]) ).
tcf(c_38335,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( identity_relation(identity_relation(relation_dom(sK7(powerset(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_26858]) ).
tcf(c_38336,plain,
identity_relation(identity_relation(relation_dom(sK7(powerset(relation_dom(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_26858]) ).
tcf(c_38337,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(sK7(powerset(relation_dom(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_26858]) ).
tcf(c_38338,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(sK7(powerset(relation_dom(identity_relation(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_26858]) ).
tcf(c_38339,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(sK7(powerset(relation_dom(sK7(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_26858]) ).
tcf(c_38340,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(sK7(powerset(relation_dom(sK7(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_26858]) ).
tcf(c_38341,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(sK7(powerset(relation_dom(sK7(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_26858]) ).
tcf(c_38342,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(sK7(powerset(relation_dom(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_26858]) ).
tcf(c_38343,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(sK7(powerset(relation_dom(sK7(powerset(sK7(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_26858]) ).
tcf(c_38344,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(sK7(powerset(relation_dom(sK7(powerset(sK7(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_26858]) ).
tcf(c_38345,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(sK7(powerset(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_26858]) ).
tcf(c_38346,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(sK7(powerset(relation_dom(sK7(sK6(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_26858]) ).
tcf(c_38434,plain,
! [X0: $i] : element(sK2(empty_set,X0,sK1),sK0),
inference(global_subsumption_just,[status(thm)],[c_32777,c_83,c_49,c_6237,c_6638,c_8030,c_8112,c_13256,c_14431,c_22498]) ).
tcf(c_38444,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( sK7(powerset(relation_dom(sK7(powerset(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10348,c_27367]) ).
tcf(c_38445,plain,
! [X0: $i] :
( ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ( sK7(powerset(relation_dom(sK7(powerset(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_27367]) ).
tcf(c_38446,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( sK7(powerset(relation_dom(sK7(powerset(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_27367]) ).
tcf(c_38447,plain,
sK7(powerset(relation_dom(sK7(powerset(relation_dom(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_27367]) ).
tcf(c_38448,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(sK7(powerset(relation_dom(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_27367]) ).
tcf(c_38449,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(sK7(powerset(relation_dom(identity_relation(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_27367]) ).
tcf(c_38450,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(sK7(powerset(relation_dom(sK7(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_27367]) ).
tcf(c_38451,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(sK7(powerset(relation_dom(sK7(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_27367]) ).
tcf(c_38452,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(sK7(powerset(relation_dom(sK7(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_27367]) ).
tcf(c_38453,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(sK7(powerset(relation_dom(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_27367]) ).
tcf(c_38454,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(sK7(powerset(relation_dom(sK7(powerset(sK7(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_27367]) ).
tcf(c_38455,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(sK7(powerset(relation_dom(sK7(powerset(sK7(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_27367]) ).
tcf(c_38456,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(sK7(powerset(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_27367]) ).
tcf(c_38457,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(sK7(powerset(relation_dom(sK7(sK6(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_27367]) ).
tcf(c_38678,plain,
! [X0: $i] :
( ( relation_dom(sK7(sK6(powerset(identity_relation(X0))))) = empty_set )
| ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_10348,c_17537]) ).
tcf(c_38679,plain,
! [X0: $i] :
( ( relation_dom(sK7(sK6(powerset(identity_relation(X0))))) = empty_set )
| ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) ) ),
inference(superposition,[status(thm)],[c_5806,c_17537]) ).
tcf(c_38680,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( relation_dom(sK7(sK6(powerset(identity_relation(X0))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_17537]) ).
tcf(c_38681,plain,
relation_dom(sK7(sK6(powerset(identity_relation(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_17537]) ).
tcf(c_38682,plain,
! [X0: $i] :
( ( relation_dom(sK7(sK6(powerset(identity_relation(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_17537]) ).
tcf(c_38683,plain,
! [X0: $i] :
( ( relation_dom(sK7(sK6(powerset(identity_relation(identity_relation(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_17537]) ).
tcf(c_38684,plain,
! [X0: $i] :
( ( relation_dom(sK7(sK6(powerset(identity_relation(sK7(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_17537]) ).
tcf(c_38685,plain,
! [X0: $i] :
( ( relation_dom(sK7(sK6(powerset(identity_relation(sK7(sK6(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_17537]) ).
tcf(c_38686,plain,
! [X0: $i] :
( ( relation_dom(sK7(sK6(powerset(identity_relation(sK7(sK6(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_17537]) ).
tcf(c_38687,plain,
! [X0: $i] :
( ( relation_dom(sK7(sK6(powerset(identity_relation(relation_image(X0,empty_set)))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_17537]) ).
tcf(c_38688,plain,
! [X0: $i] :
( ( relation_dom(sK7(sK6(powerset(identity_relation(sK7(powerset(sK7(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_17537]) ).
tcf(c_38689,plain,
! [X0: $i] :
( ( relation_dom(sK7(sK6(powerset(identity_relation(sK7(powerset(sK7(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_17537]) ).
tcf(c_38690,plain,
! [X0: $i] :
( ( relation_dom(sK7(sK6(powerset(identity_relation(sK7(powerset(sK7(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_17537]) ).
tcf(c_38691,plain,
! [X0: $i] :
( ( relation_dom(sK7(sK6(powerset(identity_relation(sK7(sK6(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_17537]) ).
tcf(c_38739,plain,
( empty(sK7(powerset(empty_set)))
| ~ function(sK14)
| ~ relation(sK14) ),
inference(superposition,[status(thm)],[c_25159,c_18752]) ).
tcf(c_38740,plain,
( empty(sK7(powerset(empty_set)))
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_18922,c_18752]) ).
tcf(c_38741,plain,
! [X0: $i] :
( empty(sK7(powerset(empty_set)))
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_25160,c_18752]) ).
tcf(c_38742,plain,
! [X0: $i] :
( ( relation_dom(sK7(sK6(powerset(identity_relation(sK7(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_17537]) ).
tcf(c_38743,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(sK7(powerset(relation_dom(sK7(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_27367]) ).
tcf(c_38744,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(sK7(powerset(relation_dom(sK7(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_26858]) ).
tcf(c_38745,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(sK7(powerset(relation_dom(sK7(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_26809]) ).
tcf(c_38746,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK7(powerset(relation_dom(sK7(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_26731]) ).
tcf(c_38747,plain,
! [X0: $i] :
( ( identity_relation(sK7(sK6(powerset(identity_relation(sK7(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_17480]) ).
tcf(c_38748,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(powerset(identity_relation(sK7(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_16757]) ).
tcf(c_38749,plain,
! [X0: $i] :
( ( relation_dom(sK7(sK6(sK6(powerset(sK7(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_15644]) ).
tcf(c_38750,plain,
! [X0: $i] :
( ( identity_relation(sK7(sK6(sK6(powerset(sK7(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_15642]) ).
tcf(c_38751,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(identity_relation(relation_dom(relation_dom(sK7(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_25936]) ).
tcf(c_38752,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(sK6(powerset(sK7(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_36269]) ).
tcf(c_38753,plain,
! [X0: $i] :
( ( relation_dom(sK7(sK6(powerset(relation_dom(relation_dom(sK7(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_25099]) ).
tcf(c_38754,plain,
! [X0: $i] :
( ( identity_relation(sK7(sK6(powerset(relation_dom(relation_dom(sK7(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_24875]) ).
tcf(c_38755,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(identity_relation(identity_relation(sK7(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_13970]) ).
tcf(c_38756,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(identity_relation(sK7(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_13854]) ).
tcf(c_38757,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(identity_relation(identity_relation(sK7(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_12910]) ).
tcf(c_38758,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(identity_relation(identity_relation(sK7(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_12872]) ).
tcf(c_38759,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(powerset(relation_dom(relation_dom(sK7(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_24819]) ).
tcf(c_38760,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(identity_relation(relation_dom(relation_dom(sK7(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_24724]) ).
tcf(c_38761,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(relation_dom(relation_dom(sK7(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_24676]) ).
tcf(c_38762,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(relation_dom(relation_dom(relation_dom(sK7(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_24628]) ).
tcf(c_38763,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(powerset(identity_relation(sK7(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_12319]) ).
tcf(c_38764,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(powerset(identity_relation(sK7(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_12213]) ).
tcf(c_38765,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(powerset(identity_relation(sK7(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_12136]) ).
tcf(c_38766,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(powerset(identity_relation(sK7(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_11432]) ).
tcf(c_38767,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(relation_dom(relation_dom(relation_dom(sK7(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_24580]) ).
tcf(c_38768,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(relation_dom(relation_dom(relation_dom(sK7(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_24491]) ).
tcf(c_38769,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(identity_relation(relation_dom(relation_dom(sK7(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_24443]) ).
tcf(c_38770,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(identity_relation(relation_dom(relation_dom(sK7(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_24395]) ).
tcf(c_38771,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(sK7(powerset(sK7(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_11345]) ).
tcf(c_38772,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(sK6(powerset(sK7(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_10677]) ).
tcf(c_38773,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(sK6(powerset(sK7(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_10676]) ).
tcf(c_38774,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(sK6(powerset(sK7(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_10675]) ).
tcf(c_38775,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(relation_dom(relation_dom(relation_dom(sK7(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_24347]) ).
tcf(c_38776,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(relation_dom(relation_dom(relation_dom(sK7(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_23164]) ).
tcf(c_38777,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(powerset(relation_dom(relation_dom(sK7(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_22515]) ).
tcf(c_38778,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(powerset(relation_dom(relation_dom(sK7(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_22426]) ).
tcf(c_38779,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(sK6(powerset(sK7(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_10674]) ).
tcf(c_38780,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(sK7(powerset(sK7(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_9751]) ).
tcf(c_38781,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(sK7(powerset(sK7(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_9685]) ).
tcf(c_38782,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(powerset(relation_dom(relation_dom(sK7(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_22338]) ).
tcf(c_38783,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(relation_dom(relation_dom(relation_dom(sK7(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_22121]) ).
tcf(c_38784,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(relation_dom(relation_dom(relation_dom(sK7(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_22031]) ).
tcf(c_38785,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK7(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_21914]) ).
tcf(c_38786,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(sK7(powerset(relation_image(X1,empty_set))))) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18752,c_9348]) ).
tcf(c_38787,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(sK7(powerset(sK7(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_9118]) ).
tcf(c_38788,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(sK7(powerset(sK7(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_9091]) ).
tcf(c_38789,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(sK7(powerset(sK7(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_9021]) ).
tcf(c_38790,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK7(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_21763]) ).
tcf(c_38791,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(powerset(relation_dom(relation_dom(sK7(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_21512]) ).
tcf(c_38792,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(relation_dom(sK7(powerset(relation_image(X1,empty_set)))))) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18752,c_20489]) ).
tcf(c_38793,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(sK7(powerset(relation_image(X1,empty_set)))))) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18752,c_20393]) ).
tcf(c_38794,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(sK7(powerset(sK7(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_8996]) ).
tcf(c_38795,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(sK7(powerset(sK7(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_8961]) ).
tcf(c_38796,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK7(powerset(sK7(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_8565]) ).
tcf(c_38797,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(relation_dom(sK7(powerset(relation_image(X1,empty_set)))))) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18752,c_18503]) ).
tcf(c_38798,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(identity_relation(relation_dom(sK7(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_25846]) ).
tcf(c_38799,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(identity_relation(sK7(powerset(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_11341]) ).
tcf(c_38800,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(powerset(sK7(powerset(relation_image(X1,empty_set)))))) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18752,c_10679]) ).
tcf(c_38801,plain,
! [X0: $i] :
( ( relation_dom(sK7(sK6(powerset(relation_dom(sK7(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_17536]) ).
tcf(c_38802,plain,
! [X0: $i] :
( ( identity_relation(sK7(sK6(powerset(relation_dom(sK7(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_17479]) ).
tcf(c_38803,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(powerset(relation_dom(sK7(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_16756]) ).
tcf(c_38804,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(identity_relation(relation_dom(sK7(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_13969]) ).
tcf(c_38805,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(relation_dom(sK7(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_13853]) ).
tcf(c_38806,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(relation_dom(relation_dom(sK7(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_13817]) ).
tcf(c_38807,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(relation_dom(relation_dom(sK7(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_13649]) ).
tcf(c_38808,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(relation_dom(relation_dom(sK7(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_13044]) ).
tcf(c_38809,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(identity_relation(relation_dom(sK7(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_12909]) ).
tcf(c_38810,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(identity_relation(relation_dom(sK7(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_12871]) ).
tcf(c_38811,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(relation_dom(relation_dom(sK7(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_12755]) ).
tcf(c_38812,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(relation_dom(relation_dom(sK7(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_12356]) ).
tcf(c_38813,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(powerset(relation_dom(sK7(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_12318]) ).
tcf(c_38814,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(powerset(relation_dom(sK7(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_12212]) ).
tcf(c_38815,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(powerset(relation_dom(sK7(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_12135]) ).
tcf(c_38816,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(relation_dom(relation_dom(sK7(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_12099]) ).
tcf(c_38817,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(relation_dom(relation_dom(sK7(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_12063]) ).
tcf(c_38818,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(relation_dom(relation_dom(sK7(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_12027]) ).
tcf(c_38819,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK7(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_11953]) ).
tcf(c_38820,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(powerset(relation_dom(sK7(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_11431]) ).
tcf(c_38821,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(sK7(powerset(relation_image(X1,empty_set))))) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18752,c_9347]) ).
tcf(c_38822,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK7(powerset(relation_image(X1,empty_set))))) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18752,c_9319]) ).
tcf(c_38823,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(sK7(powerset(relation_image(X1,empty_set))))) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18752,c_6877]) ).
tcf(c_38824,plain,
! [X0: $i] :
( ( relation_dom(sK7(sK6(powerset(sK7(powerset(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_10680]) ).
tcf(c_38825,plain,
! [X0: $i] :
( ( identity_relation(sK7(sK6(powerset(sK7(powerset(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_10678]) ).
tcf(c_38826,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(powerset(sK7(powerset(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_15645]) ).
tcf(c_38827,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(identity_relation(sK7(powerset(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_9748]) ).
tcf(c_38828,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(sK7(powerset(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_9682]) ).
tcf(c_38829,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(relation_dom(sK7(powerset(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_11340]) ).
tcf(c_38830,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(relation_dom(sK7(powerset(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_9747]) ).
tcf(c_38831,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(relation_dom(sK7(powerset(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_9681]) ).
tcf(c_38832,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(identity_relation(sK7(powerset(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_9115]) ).
tcf(c_38833,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(identity_relation(sK7(powerset(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_9088]) ).
tcf(c_38834,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(relation_dom(sK7(powerset(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_9114]) ).
tcf(c_38835,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(relation_dom(sK7(powerset(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_9087]) ).
tcf(c_38836,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(powerset(sK7(powerset(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_8009]) ).
tcf(c_38837,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(powerset(sK7(powerset(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_7966]) ).
tcf(c_38838,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(powerset(sK7(powerset(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_7938]) ).
tcf(c_38839,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(relation_dom(sK7(powerset(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_9017]) ).
tcf(c_38840,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(relation_dom(sK7(powerset(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_8992]) ).
tcf(c_38841,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(relation_dom(sK7(powerset(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_8957]) ).
tcf(c_38842,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK7(powerset(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_8561]) ).
tcf(c_38843,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(powerset(sK7(powerset(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_6875]) ).
tcf(c_38847,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK7(powerset(relation_image(X1,empty_set)))) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18752,c_5794]) ).
tcf(c_38848,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(powerset(relation_image(X1,empty_set)))) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18752,c_5793]) ).
tcf(c_38863,plain,
! [X0: $i] :
( function(sK7(powerset(relation_image(X0,empty_set))))
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_98]) ).
tcf(c_38864,plain,
! [X0: $i] :
( relation(sK7(powerset(relation_image(X0,empty_set))))
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_80]) ).
tcf(c_38865,plain,
( empty(empty_set)
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(light_normalisation,[status(thm)],[c_38740,c_8004]) ).
tcf(c_38866,plain,
( empty(empty_set)
| ~ function(sK14)
| ~ relation(sK14) ),
inference(light_normalisation,[status(thm)],[c_38739,c_8004]) ).
tcf(c_38873,plain,
! [X0: $i] :
( empty(empty_set)
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0)) ),
inference(light_normalisation,[status(thm)],[c_38741,c_8004]) ).
tcf(c_39547,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(identity_relation(identity_relation(X0))))) = empty_set )
| ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_10348,c_25847]) ).
tcf(c_39548,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(identity_relation(identity_relation(X0))))) = empty_set )
| ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) ) ),
inference(superposition,[status(thm)],[c_5806,c_25847]) ).
tcf(c_39549,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( sK7(sK6(powerset(identity_relation(identity_relation(X0))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_25847]) ).
tcf(c_39550,plain,
sK7(sK6(powerset(identity_relation(identity_relation(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_25847]) ).
tcf(c_39551,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(identity_relation(identity_relation(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_25847]) ).
tcf(c_39552,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(identity_relation(identity_relation(identity_relation(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_25847]) ).
tcf(c_39553,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(identity_relation(identity_relation(sK7(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_25847]) ).
tcf(c_39554,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(identity_relation(identity_relation(sK7(sK6(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_25847]) ).
tcf(c_39555,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(identity_relation(identity_relation(sK7(sK6(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_25847]) ).
tcf(c_39556,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(identity_relation(identity_relation(relation_image(X0,empty_set)))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_25847]) ).
tcf(c_39557,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(identity_relation(identity_relation(sK7(powerset(sK7(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_25847]) ).
tcf(c_39558,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(identity_relation(identity_relation(sK7(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_25847]) ).
tcf(c_39559,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(identity_relation(identity_relation(sK7(powerset(sK7(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_25847]) ).
tcf(c_39560,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(identity_relation(identity_relation(sK7(powerset(sK7(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_25847]) ).
tcf(c_39561,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(identity_relation(identity_relation(sK7(sK6(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_25847]) ).
tcf(c_39612,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(identity_relation(identity_relation(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_25847]) ).
tcf(c_39613,plain,
! [X0: $i] :
( ( relation_dom(sK7(sK6(powerset(identity_relation(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_17537]) ).
tcf(c_39614,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(sK7(powerset(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_27367]) ).
tcf(c_39615,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(sK7(powerset(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_26858]) ).
tcf(c_39616,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(sK7(powerset(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_26809]) ).
tcf(c_39617,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK7(powerset(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_26731]) ).
tcf(c_39618,plain,
! [X0: $i] :
( ( identity_relation(sK7(sK6(powerset(identity_relation(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_17480]) ).
tcf(c_39619,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(powerset(identity_relation(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_16757]) ).
tcf(c_39620,plain,
! [X0: $i] :
( ( relation_dom(sK7(sK6(sK6(powerset(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_15644]) ).
tcf(c_39621,plain,
! [X0: $i] :
( ( identity_relation(sK7(sK6(sK6(powerset(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_15642]) ).
tcf(c_39622,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(identity_relation(relation_dom(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_25936]) ).
tcf(c_39623,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(sK6(powerset(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_36269]) ).
tcf(c_39624,plain,
! [X0: $i] :
( ( relation_dom(sK7(sK6(powerset(relation_dom(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_25099]) ).
tcf(c_39625,plain,
! [X0: $i] :
( ( identity_relation(sK7(sK6(powerset(relation_dom(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_24875]) ).
tcf(c_39626,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(identity_relation(identity_relation(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_13970]) ).
tcf(c_39627,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(identity_relation(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_13854]) ).
tcf(c_39628,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(identity_relation(identity_relation(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_12910]) ).
tcf(c_39629,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(identity_relation(identity_relation(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_12872]) ).
tcf(c_39630,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(powerset(relation_dom(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_24819]) ).
tcf(c_39631,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(identity_relation(relation_dom(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_24724]) ).
tcf(c_39632,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(relation_dom(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_24676]) ).
tcf(c_39633,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(relation_dom(relation_dom(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_24628]) ).
tcf(c_39634,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(powerset(identity_relation(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_12319]) ).
tcf(c_39635,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(powerset(identity_relation(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_12213]) ).
tcf(c_39636,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(powerset(identity_relation(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_12136]) ).
tcf(c_39637,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(powerset(identity_relation(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_11432]) ).
tcf(c_39638,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(relation_dom(relation_dom(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_24580]) ).
tcf(c_39639,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(relation_dom(relation_dom(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_24491]) ).
tcf(c_39640,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(identity_relation(relation_dom(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_24443]) ).
tcf(c_39641,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(identity_relation(relation_dom(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_24395]) ).
tcf(c_39642,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(sK7(powerset(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_11345]) ).
tcf(c_39643,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(sK6(powerset(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_10677]) ).
tcf(c_39644,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(sK6(powerset(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_10676]) ).
tcf(c_39645,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(sK6(powerset(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_10675]) ).
tcf(c_39646,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(relation_dom(relation_dom(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_24347]) ).
tcf(c_39647,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(relation_dom(relation_dom(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_23164]) ).
tcf(c_39648,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(powerset(relation_dom(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_22515]) ).
tcf(c_39649,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(powerset(relation_dom(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_22426]) ).
tcf(c_39650,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(sK6(powerset(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_10674]) ).
tcf(c_39651,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(sK7(powerset(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_9751]) ).
tcf(c_39652,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(sK7(powerset(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_9685]) ).
tcf(c_39653,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(powerset(relation_dom(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_22338]) ).
tcf(c_39654,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(relation_dom(relation_dom(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_22121]) ).
tcf(c_39655,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(relation_dom(relation_dom(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_22031]) ).
tcf(c_39656,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_21914]) ).
tcf(c_39657,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_9348]) ).
tcf(c_39658,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(sK7(powerset(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_9118]) ).
tcf(c_39659,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(sK7(powerset(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_9091]) ).
tcf(c_39660,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(sK7(powerset(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_9021]) ).
tcf(c_39661,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_21763]) ).
tcf(c_39662,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(powerset(relation_dom(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_21512]) ).
tcf(c_39663,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0)))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_20489]) ).
tcf(c_39664,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0)))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_20393]) ).
tcf(c_39665,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(sK7(powerset(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_8996]) ).
tcf(c_39666,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(sK7(powerset(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_8961]) ).
tcf(c_39667,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK7(powerset(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_8565]) ).
tcf(c_39668,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0)))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_18503]) ).
tcf(c_39669,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(identity_relation(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_25846]) ).
tcf(c_39670,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(identity_relation(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_11341]) ).
tcf(c_39671,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(powerset(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0)))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_10679]) ).
tcf(c_39672,plain,
! [X0: $i] :
( ( relation_dom(sK7(sK6(powerset(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_17536]) ).
tcf(c_39673,plain,
! [X0: $i] :
( ( identity_relation(sK7(sK6(powerset(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_17479]) ).
tcf(c_39674,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(powerset(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_16756]) ).
tcf(c_39675,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(identity_relation(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_13969]) ).
tcf(c_39676,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_13853]) ).
tcf(c_39677,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(relation_dom(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_13817]) ).
tcf(c_39678,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(relation_dom(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_13649]) ).
tcf(c_39679,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(relation_dom(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_13044]) ).
tcf(c_39680,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(identity_relation(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_12909]) ).
tcf(c_39681,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(identity_relation(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_12871]) ).
tcf(c_39682,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(relation_dom(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_12755]) ).
tcf(c_39683,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(relation_dom(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_12356]) ).
tcf(c_39684,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(powerset(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_12318]) ).
tcf(c_39685,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(powerset(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_12212]) ).
tcf(c_39686,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(powerset(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_12135]) ).
tcf(c_39687,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(relation_dom(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_12099]) ).
tcf(c_39688,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(relation_dom(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_12063]) ).
tcf(c_39689,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(relation_dom(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_12027]) ).
tcf(c_39690,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_11953]) ).
tcf(c_39691,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(powerset(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_11431]) ).
tcf(c_39692,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_9347]) ).
tcf(c_39693,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_9319]) ).
tcf(c_39694,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_6877]) ).
tcf(c_39695,plain,
! [X0: $i] :
( ( relation_dom(sK7(sK6(powerset(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_10680]) ).
tcf(c_39696,plain,
! [X0: $i] :
( ( identity_relation(sK7(sK6(powerset(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_10678]) ).
tcf(c_39697,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(powerset(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_15645]) ).
tcf(c_39698,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(identity_relation(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_9748]) ).
tcf(c_39699,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_9682]) ).
tcf(c_39700,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_11340]) ).
tcf(c_39701,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_9747]) ).
tcf(c_39702,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_9681]) ).
tcf(c_39703,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(identity_relation(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_9115]) ).
tcf(c_39704,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(identity_relation(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_9088]) ).
tcf(c_39705,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_9114]) ).
tcf(c_39706,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_9087]) ).
tcf(c_39707,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(powerset(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_8009]) ).
tcf(c_39708,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(powerset(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_7966]) ).
tcf(c_39709,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(powerset(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_7938]) ).
tcf(c_39710,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_9017]) ).
tcf(c_39711,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_8992]) ).
tcf(c_39712,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_8957]) ).
tcf(c_39713,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_8561]) ).
tcf(c_39714,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(powerset(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_6875]) ).
tcf(c_39718,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0)))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_5794]) ).
tcf(c_39719,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0)))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_5793]) ).
tcf(c_39734,plain,
! [X0: $i] :
( function(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_98]) ).
tcf(c_39735,plain,
! [X0: $i] :
( relation(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_80]) ).
tcf(c_40490,plain,
( function(sK7(powerset(empty_set)))
| ~ function(sK14)
| ~ relation(sK14) ),
inference(superposition,[status(thm)],[c_25159,c_38863]) ).
tcf(c_40491,plain,
( function(sK7(powerset(empty_set)))
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_18922,c_38863]) ).
tcf(c_40492,plain,
! [X0: $i] :
( function(sK7(powerset(empty_set)))
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_25160,c_38863]) ).
tcf(c_40493,plain,
! [X0: $i] :
( ( relation_image(sK7(powerset(relation_image(X0,empty_set))),empty_set) = empty_set )
| ~ function(X0)
| ~ relation(X0)
| ~ relation(sK7(powerset(relation_image(X0,empty_set)))) ),
inference(superposition,[status(thm)],[c_38863,c_23329]) ).
tcf(c_40495,plain,
( function(empty_set)
| ~ function(sK14)
| ~ relation(sK14) ),
inference(light_normalisation,[status(thm)],[c_40490,c_8004]) ).
tcf(c_40496,plain,
! [X0: $i] :
( function(empty_set)
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0)) ),
inference(light_normalisation,[status(thm)],[c_40492,c_8004]) ).
tcf(c_40536,plain,
( relation(sK7(powerset(empty_set)))
| ~ function(sK14)
| ~ relation(sK14) ),
inference(superposition,[status(thm)],[c_25159,c_38864]) ).
tcf(c_40537,plain,
( relation(sK7(powerset(empty_set)))
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_18922,c_38864]) ).
tcf(c_40538,plain,
! [X0: $i] :
( relation(sK7(powerset(empty_set)))
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_25160,c_38864]) ).
tcf(c_40540,plain,
( relation(empty_set)
| ~ function(sK14)
| ~ relation(sK14) ),
inference(light_normalisation,[status(thm)],[c_40536,c_8004]) ).
tcf(c_40541,plain,
! [X0: $i] :
( relation(empty_set)
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0)) ),
inference(light_normalisation,[status(thm)],[c_40538,c_8004]) ).
tcf(c_40547,plain,
! [X0: $i] :
( ( relation_image(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))),empty_set) = empty_set )
| ~ empty(X0)
| ~ relation(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0)))))))) ),
inference(superposition,[status(thm)],[c_39734,c_23329]) ).
tcf(c_40563,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(powerset(X1))) = X0 )
| ( apply(identity_relation(X1),sK7(sK6(X1))) = sK7(sK6(X1)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10348,c_9323]) ).
tcf(c_40564,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(powerset(X1))) = X0 )
| ( apply(identity_relation(powerset(X1)),sK6(X1)) = sK6(X1) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5806,c_9323]) ).
tcf(c_40565,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(powerset(X1))) = X0 )
| ( apply(identity_relation(X1),sK7(X1)) = sK7(X1) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5807,c_9323]) ).
tcf(c_40566,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(empty_set))) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_83,c_9323]) ).
tcf(c_40567,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(powerset(relation_dom(X0)))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_9323]) ).
tcf(c_40568,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(powerset(identity_relation(X0)))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_9323]) ).
tcf(c_40573,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(powerset(sK7(powerset(sK7(powerset(X0))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_9323]) ).
tcf(c_40574,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(powerset(sK7(powerset(relation_image(X1,empty_set)))))) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18752,c_9323]) ).
tcf(c_40575,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(powerset(sK7(powerset(sK7(sK6(powerset(X0)))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_9323]) ).
tcf(c_40576,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(powerset(sK7(powerset(sK7(sK6(sK6(powerset(X0))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_9323]) ).
tcf(c_40578,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(powerset(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0)))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_9323]) ).
tcf(c_40634,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK7(powerset(X1))) = X0 )
| ( apply(identity_relation(X1),sK7(sK6(X1))) = sK7(sK6(X1)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10348,c_9351]) ).
tcf(c_40635,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK7(powerset(X1))) = X0 )
| ( apply(identity_relation(powerset(X1)),sK6(X1)) = sK6(X1) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5806,c_9351]) ).
tcf(c_40636,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK7(powerset(X1))) = X0 )
| ( apply(identity_relation(X1),sK7(X1)) = sK7(X1) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5807,c_9351]) ).
tcf(c_40637,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(empty_set))) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_83,c_9351]) ).
tcf(c_40638,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK7(powerset(relation_dom(X0)))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_9351]) ).
tcf(c_40639,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK7(powerset(identity_relation(X0)))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_9351]) ).
tcf(c_40644,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK7(powerset(sK7(powerset(sK7(powerset(X0))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_9351]) ).
tcf(c_40645,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK7(powerset(sK7(powerset(relation_image(X1,empty_set)))))) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18752,c_9351]) ).
tcf(c_40646,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK7(powerset(sK7(powerset(sK7(sK6(powerset(X0)))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_9351]) ).
tcf(c_40647,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK7(powerset(sK7(powerset(sK7(sK6(sK6(powerset(X0))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_9351]) ).
tcf(c_40649,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK7(powerset(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0)))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_9351]) ).
tcf(c_40715,plain,
( empty(sK7(sK6(powerset(empty_set))))
| element(sK7(sK6(empty_set)),empty_set) ),
inference(superposition,[status(thm)],[c_11339,c_10568]) ).
tcf(c_40716,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| empty(sK7(sK6(powerset(powerset(X1)))))
| ~ in(X0,sK7(sK6(sK7(sK6(powerset(powerset(X1))))))) ),
inference(superposition,[status(thm)],[c_10568,c_65]) ).
tcf(c_40717,plain,
! [X0: $i,X1: $i] :
( empty(sK7(sK6(powerset(powerset(X1)))))
| ~ empty(X1)
| ~ in(X0,sK7(sK6(sK7(sK6(powerset(powerset(X1))))))) ),
inference(superposition,[status(thm)],[c_10568,c_64]) ).
tcf(c_40718,plain,
! [X0: $i] :
( empty(X0)
| empty(sK7(sK6(powerset(X0))))
| in(sK7(sK6(sK7(sK6(powerset(X0))))),X0) ),
inference(superposition,[status(thm)],[c_10568,c_71]) ).
tcf(c_40764,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( sK7(powerset(identity_relation(sK7(sK6(powerset(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10348,c_10658]) ).
tcf(c_40765,plain,
! [X0: $i] :
( ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ( sK7(powerset(identity_relation(sK7(sK6(powerset(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_10658]) ).
tcf(c_40766,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( sK7(powerset(identity_relation(sK7(sK6(powerset(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_10658]) ).
tcf(c_40767,plain,
sK7(powerset(identity_relation(sK7(sK6(powerset(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_10658]) ).
tcf(c_40768,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(sK7(sK6(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_10658]) ).
tcf(c_40769,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(sK7(sK6(powerset(identity_relation(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_10658]) ).
tcf(c_40770,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(sK7(sK6(powerset(sK7(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_10658]) ).
tcf(c_40771,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(sK7(sK6(powerset(sK7(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_10658]) ).
tcf(c_40772,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(sK7(sK6(powerset(sK7(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_10658]) ).
tcf(c_40773,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(sK7(sK6(powerset(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_10658]) ).
tcf(c_40774,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(sK7(sK6(powerset(sK7(powerset(sK7(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_10658]) ).
tcf(c_40775,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(sK7(sK6(powerset(sK7(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_10658]) ).
tcf(c_40776,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(sK7(sK6(powerset(sK7(powerset(sK7(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_10658]) ).
tcf(c_40777,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(sK7(sK6(powerset(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_10658]) ).
tcf(c_40778,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(sK7(sK6(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_10658]) ).
tcf(c_40779,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(sK7(sK6(powerset(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_10658]) ).
tcf(c_40891,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( sK7(powerset(identity_relation(sK7(sK6(powerset(sK7(powerset(sK1)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_10658]) ).
tcf(c_40892,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(sK7(powerset(sK1))))) = X0 )
| ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21309,c_9351]) ).
tcf(c_40893,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(sK7(powerset(sK1))))) = X0 )
| ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21309,c_9323]) ).
tcf(c_40894,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( sK7(sK6(powerset(identity_relation(identity_relation(sK7(powerset(sK1))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_25847]) ).
tcf(c_40895,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( relation_dom(sK7(sK6(powerset(identity_relation(sK7(powerset(sK1))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_17537]) ).
tcf(c_40896,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( sK7(powerset(relation_dom(sK7(powerset(relation_dom(sK7(powerset(sK1)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_27367]) ).
tcf(c_40897,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( identity_relation(identity_relation(relation_dom(sK7(powerset(relation_dom(sK7(powerset(sK1)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_26858]) ).
tcf(c_40898,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( identity_relation(relation_dom(relation_dom(sK7(powerset(relation_dom(sK7(powerset(sK1)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_26809]) ).
tcf(c_40899,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( relation_dom(relation_dom(relation_dom(sK7(powerset(relation_dom(sK7(powerset(sK1)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_26731]) ).
tcf(c_40900,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( identity_relation(sK7(sK6(powerset(identity_relation(sK7(powerset(sK1))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_17480]) ).
tcf(c_40901,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( sK7(sK6(sK6(powerset(identity_relation(sK7(powerset(sK1))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_16757]) ).
tcf(c_40902,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( relation_dom(sK7(sK6(sK6(powerset(sK7(powerset(sK1))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_15644]) ).
tcf(c_40903,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( identity_relation(sK7(sK6(sK6(powerset(sK7(powerset(sK1))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_15642]) ).
tcf(c_40904,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( sK7(sK6(powerset(identity_relation(relation_dom(relation_dom(sK7(powerset(sK1)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_25936]) ).
tcf(c_40905,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( sK7(sK6(sK6(sK6(powerset(sK7(powerset(sK1))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_36269]) ).
tcf(c_40906,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( relation_dom(sK7(sK6(powerset(relation_dom(relation_dom(sK7(powerset(sK1)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_25099]) ).
tcf(c_40907,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( identity_relation(sK7(sK6(powerset(relation_dom(relation_dom(sK7(powerset(sK1)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_24875]) ).
tcf(c_40908,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( sK7(powerset(identity_relation(identity_relation(identity_relation(sK7(powerset(sK1))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_13970]) ).
tcf(c_40909,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( identity_relation(identity_relation(identity_relation(identity_relation(identity_relation(sK7(powerset(sK1))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_13854]) ).
tcf(c_40910,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( relation_dom(sK7(powerset(identity_relation(identity_relation(sK7(powerset(sK1))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_12910]) ).
tcf(c_40911,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( identity_relation(sK7(powerset(identity_relation(identity_relation(sK7(powerset(sK1))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_12872]) ).
tcf(c_40912,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( sK7(sK6(sK6(powerset(relation_dom(relation_dom(sK7(powerset(sK1)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_24819]) ).
tcf(c_40913,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( sK7(powerset(identity_relation(identity_relation(relation_dom(relation_dom(sK7(powerset(sK1)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_24724]) ).
tcf(c_40914,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( identity_relation(identity_relation(identity_relation(identity_relation(relation_dom(relation_dom(sK7(powerset(sK1)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_24676]) ).
tcf(c_40915,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( sK7(sK6(powerset(relation_dom(relation_dom(relation_dom(sK7(powerset(sK1)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_24628]) ).
tcf(c_40916,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( sK7(powerset(sK7(powerset(identity_relation(sK7(powerset(sK1))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_12319]) ).
tcf(c_40917,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( identity_relation(identity_relation(sK7(powerset(identity_relation(sK7(powerset(sK1))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_12213]) ).
tcf(c_40918,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( identity_relation(relation_dom(sK7(powerset(identity_relation(sK7(powerset(sK1))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_12136]) ).
tcf(c_40919,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( relation_dom(relation_dom(sK7(powerset(identity_relation(sK7(powerset(sK1))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_11432]) ).
tcf(c_40920,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( sK7(powerset(identity_relation(relation_dom(relation_dom(relation_dom(sK7(powerset(sK1)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_24580]) ).
tcf(c_40921,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( identity_relation(identity_relation(identity_relation(relation_dom(relation_dom(relation_dom(sK7(powerset(sK1)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_24491]) ).
tcf(c_40922,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( relation_dom(sK7(powerset(identity_relation(relation_dom(relation_dom(sK7(powerset(sK1)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_24443]) ).
tcf(c_40923,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( identity_relation(sK7(powerset(identity_relation(relation_dom(relation_dom(sK7(powerset(sK1)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_24395]) ).
tcf(c_40924,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( sK7(sK6(powerset(sK7(powerset(sK7(powerset(sK1))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_11345]) ).
tcf(c_40925,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( relation_dom(relation_dom(sK7(sK6(powerset(sK7(powerset(sK1))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_10677]) ).
tcf(c_40926,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( identity_relation(relation_dom(sK7(sK6(powerset(sK7(powerset(sK1))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_10676]) ).
tcf(c_40927,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( identity_relation(identity_relation(sK7(sK6(powerset(sK7(powerset(sK1))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_10675]) ).
tcf(c_40928,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( relation_dom(sK7(powerset(relation_dom(relation_dom(relation_dom(sK7(powerset(sK1)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_24347]) ).
tcf(c_40929,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( identity_relation(sK7(powerset(relation_dom(relation_dom(relation_dom(sK7(powerset(sK1)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_23164]) ).
tcf(c_40930,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( sK7(powerset(sK7(powerset(relation_dom(relation_dom(sK7(powerset(sK1)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_22515]) ).
tcf(c_40931,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( identity_relation(identity_relation(sK7(powerset(relation_dom(relation_dom(sK7(powerset(sK1)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_22426]) ).
tcf(c_40932,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( sK7(powerset(sK7(sK6(powerset(sK7(powerset(sK1))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_10674]) ).
tcf(c_40933,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( sK7(powerset(identity_relation(sK7(powerset(sK7(powerset(sK1))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_9751]) ).
tcf(c_40934,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( identity_relation(identity_relation(identity_relation(sK7(powerset(sK7(powerset(sK1))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_9685]) ).
tcf(c_40935,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( identity_relation(relation_dom(sK7(powerset(relation_dom(relation_dom(sK7(powerset(sK1)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_22338]) ).
tcf(c_40936,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( sK7(powerset(relation_dom(relation_dom(relation_dom(relation_dom(sK7(powerset(sK1)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_22121]) ).
tcf(c_40937,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( identity_relation(identity_relation(relation_dom(relation_dom(relation_dom(relation_dom(sK7(powerset(sK1)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_22031]) ).
tcf(c_40938,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( identity_relation(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK7(powerset(sK1)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_21914]) ).
tcf(c_40939,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(powerset(sK1)))) = X0 )
| ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21309,c_9348]) ).
tcf(c_40940,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( relation_dom(sK7(powerset(sK7(powerset(sK7(powerset(sK1))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_9118]) ).
tcf(c_40941,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( identity_relation(sK7(powerset(sK7(powerset(sK7(powerset(sK1))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_9091]) ).
tcf(c_40942,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( sK7(powerset(relation_dom(sK7(powerset(sK7(powerset(sK1))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_9021]) ).
tcf(c_40943,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK7(powerset(sK1)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_21763]) ).
tcf(c_40944,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( relation_dom(relation_dom(sK7(powerset(relation_dom(relation_dom(sK7(powerset(sK1)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_21512]) ).
tcf(c_40945,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(sK7(powerset(sK1))))) = X0 )
| ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21309,c_20489]) ).
tcf(c_40946,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK7(powerset(sK1))))) = X0 )
| ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21309,c_20393]) ).
tcf(c_40947,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( identity_relation(identity_relation(relation_dom(sK7(powerset(sK7(powerset(sK1))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_8996]) ).
tcf(c_40948,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( identity_relation(relation_dom(relation_dom(sK7(powerset(sK7(powerset(sK1))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_8961]) ).
tcf(c_40949,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( relation_dom(relation_dom(relation_dom(sK7(powerset(sK7(powerset(sK1))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_8565]) ).
tcf(c_40950,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(sK7(powerset(sK1))))) = X0 )
| ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21309,c_18503]) ).
tcf(c_40951,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( sK7(sK6(powerset(identity_relation(relation_dom(sK7(powerset(sK1))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_25846]) ).
tcf(c_40952,plain,
( ( sK7(sK6(powerset(identity_relation(sK7(powerset(sK1)))))) = empty_set )
| ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) ) ),
inference(superposition,[status(thm)],[c_21309,c_11341]) ).
tcf(c_40953,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(sK7(powerset(sK1))))) = X0 )
| ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21309,c_10679]) ).
tcf(c_40954,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( relation_dom(sK7(sK6(powerset(relation_dom(sK7(powerset(sK1))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_17536]) ).
tcf(c_40955,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( identity_relation(sK7(sK6(powerset(relation_dom(sK7(powerset(sK1))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_17479]) ).
tcf(c_40956,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( sK7(sK6(sK6(powerset(relation_dom(sK7(powerset(sK1))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_16756]) ).
tcf(c_40957,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( sK7(powerset(identity_relation(identity_relation(relation_dom(sK7(powerset(sK1))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_13969]) ).
tcf(c_40958,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( identity_relation(identity_relation(identity_relation(identity_relation(relation_dom(sK7(powerset(sK1))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_13853]) ).
tcf(c_40959,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( sK7(sK6(powerset(relation_dom(relation_dom(sK7(powerset(sK1))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_13817]) ).
tcf(c_40960,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( sK7(powerset(identity_relation(relation_dom(relation_dom(sK7(powerset(sK1))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_13649]) ).
tcf(c_40961,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( identity_relation(identity_relation(identity_relation(relation_dom(relation_dom(sK7(powerset(sK1))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_13044]) ).
tcf(c_40962,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( relation_dom(sK7(powerset(identity_relation(relation_dom(sK7(powerset(sK1))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_12909]) ).
tcf(c_40963,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( identity_relation(sK7(powerset(identity_relation(relation_dom(sK7(powerset(sK1))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_12871]) ).
tcf(c_40964,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( relation_dom(sK7(powerset(relation_dom(relation_dom(sK7(powerset(sK1))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_12755]) ).
tcf(c_40965,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( identity_relation(sK7(powerset(relation_dom(relation_dom(sK7(powerset(sK1))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_12356]) ).
tcf(c_40966,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( sK7(powerset(sK7(powerset(relation_dom(sK7(powerset(sK1))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_12318]) ).
tcf(c_40967,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( identity_relation(identity_relation(sK7(powerset(relation_dom(sK7(powerset(sK1))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_12212]) ).
tcf(c_40968,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( identity_relation(relation_dom(sK7(powerset(relation_dom(sK7(powerset(sK1))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_12135]) ).
tcf(c_40969,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( sK7(powerset(relation_dom(relation_dom(relation_dom(sK7(powerset(sK1))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_12099]) ).
tcf(c_40970,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( identity_relation(identity_relation(relation_dom(relation_dom(relation_dom(sK7(powerset(sK1))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_12063]) ).
tcf(c_40971,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( identity_relation(relation_dom(relation_dom(relation_dom(relation_dom(sK7(powerset(sK1))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_12027]) ).
tcf(c_40972,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK7(powerset(sK1))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_11953]) ).
tcf(c_40973,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( relation_dom(relation_dom(sK7(powerset(relation_dom(sK7(powerset(sK1))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_11431]) ).
tcf(c_40974,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(powerset(sK1)))) = X0 )
| ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21309,c_9347]) ).
tcf(c_40975,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(powerset(sK1)))) = X0 )
| ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21309,c_9319]) ).
tcf(c_40976,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(powerset(sK1)))) = X0 )
| ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21309,c_6877]) ).
tcf(c_40977,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( relation_dom(sK7(sK6(powerset(sK7(powerset(sK1)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_10680]) ).
tcf(c_40978,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( identity_relation(sK7(sK6(powerset(sK7(powerset(sK1)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_10678]) ).
tcf(c_40979,plain,
( ( sK7(sK6(sK6(powerset(sK7(powerset(sK1)))))) = empty_set )
| ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) ) ),
inference(superposition,[status(thm)],[c_21309,c_15645]) ).
tcf(c_40980,plain,
( ( sK7(powerset(identity_relation(identity_relation(sK7(powerset(sK1)))))) = empty_set )
| ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) ) ),
inference(superposition,[status(thm)],[c_21309,c_9748]) ).
tcf(c_40981,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( identity_relation(identity_relation(identity_relation(identity_relation(sK7(powerset(sK1)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_9682]) ).
tcf(c_40982,plain,
( ( sK7(sK6(powerset(relation_dom(sK7(powerset(sK1)))))) = empty_set )
| ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) ) ),
inference(superposition,[status(thm)],[c_21309,c_11340]) ).
tcf(c_40983,plain,
( ( sK7(powerset(identity_relation(relation_dom(sK7(powerset(sK1)))))) = empty_set )
| ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) ) ),
inference(superposition,[status(thm)],[c_21309,c_9747]) ).
tcf(c_40984,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( identity_relation(identity_relation(identity_relation(relation_dom(sK7(powerset(sK1)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_9681]) ).
tcf(c_40985,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( relation_dom(sK7(powerset(identity_relation(sK7(powerset(sK1)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_9115]) ).
tcf(c_40986,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( identity_relation(sK7(powerset(identity_relation(sK7(powerset(sK1)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_9088]) ).
tcf(c_40987,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( relation_dom(sK7(powerset(relation_dom(sK7(powerset(sK1)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_9114]) ).
tcf(c_40988,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( identity_relation(sK7(powerset(relation_dom(sK7(powerset(sK1)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_9087]) ).
tcf(c_40989,plain,
( ( sK7(powerset(sK7(powerset(sK7(powerset(sK1)))))) = empty_set )
| ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) ) ),
inference(superposition,[status(thm)],[c_21309,c_8009]) ).
tcf(c_40990,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( identity_relation(identity_relation(sK7(powerset(sK7(powerset(sK1)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_7966]) ).
tcf(c_40991,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( identity_relation(relation_dom(sK7(powerset(sK7(powerset(sK1)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_7938]) ).
tcf(c_40992,plain,
( ( sK7(powerset(relation_dom(relation_dom(sK7(powerset(sK1)))))) = empty_set )
| ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) ) ),
inference(superposition,[status(thm)],[c_21309,c_9017]) ).
tcf(c_40993,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( identity_relation(identity_relation(relation_dom(relation_dom(sK7(powerset(sK1)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_8992]) ).
tcf(c_40994,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( identity_relation(relation_dom(relation_dom(relation_dom(sK7(powerset(sK1)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_8957]) ).
tcf(c_40995,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( relation_dom(relation_dom(relation_dom(relation_dom(sK7(powerset(sK1)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_8561]) ).
tcf(c_40996,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( relation_dom(relation_dom(sK7(powerset(sK7(powerset(sK1)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_6875]) ).
tcf(c_40997,plain,
( ( sK7(sK6(powerset(sK7(powerset(sK1))))) = empty_set )
| ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) ) ),
inference(superposition,[status(thm)],[c_21309,c_10681]) ).
tcf(c_40998,plain,
( ( sK7(powerset(identity_relation(sK7(powerset(sK1))))) = empty_set )
| ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) ) ),
inference(superposition,[status(thm)],[c_21309,c_8006]) ).
tcf(c_40999,plain,
( ( identity_relation(identity_relation(identity_relation(sK7(powerset(sK1))))) = empty_set )
| ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) ) ),
inference(superposition,[status(thm)],[c_21309,c_7963]) ).
tcf(c_41000,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(sK1))) = X0 )
| ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21309,c_5794]) ).
tcf(c_41001,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(sK1))) = X0 )
| ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21309,c_5793]) ).
tcf(c_41002,plain,
( ( relation_dom(sK7(powerset(sK7(powerset(sK1))))) = empty_set )
| ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) ) ),
inference(superposition,[status(thm)],[c_21309,c_6878]) ).
tcf(c_41003,plain,
( ( identity_relation(sK7(powerset(sK7(powerset(sK1))))) = empty_set )
| ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) ) ),
inference(superposition,[status(thm)],[c_21309,c_6876]) ).
tcf(c_41004,plain,
( ( sK7(powerset(relation_dom(sK7(powerset(sK1))))) = empty_set )
| ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) ) ),
inference(superposition,[status(thm)],[c_21309,c_8005]) ).
tcf(c_41005,plain,
( ( identity_relation(identity_relation(relation_dom(sK7(powerset(sK1))))) = empty_set )
| ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) ) ),
inference(superposition,[status(thm)],[c_21309,c_7962]) ).
tcf(c_41006,plain,
( ( identity_relation(relation_dom(relation_dom(sK7(powerset(sK1))))) = empty_set )
| ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) ) ),
inference(superposition,[status(thm)],[c_21309,c_7934]) ).
tcf(c_41007,plain,
( ( relation_dom(relation_dom(relation_dom(sK7(powerset(sK1))))) = empty_set )
| ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) ) ),
inference(superposition,[status(thm)],[c_21309,c_6133]) ).
tcf(c_41008,plain,
( ( sK7(powerset(sK7(powerset(sK1)))) = empty_set )
| ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) ) ),
inference(superposition,[status(thm)],[c_21309,c_6879]) ).
tcf(c_41009,plain,
( ( identity_relation(identity_relation(sK7(powerset(sK1)))) = empty_set )
| ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) ) ),
inference(superposition,[status(thm)],[c_21309,c_6106]) ).
tcf(c_41010,plain,
( ( identity_relation(relation_dom(sK7(powerset(sK1)))) = empty_set )
| ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) ) ),
inference(superposition,[status(thm)],[c_21309,c_6105]) ).
tcf(c_41011,plain,
( ( relation_dom(relation_dom(sK7(powerset(sK1)))) = empty_set )
| ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) ) ),
inference(superposition,[status(thm)],[c_21309,c_5747]) ).
tcf(c_41012,plain,
( ( identity_relation(sK7(powerset(sK1))) = empty_set )
| ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) ) ),
inference(superposition,[status(thm)],[c_21309,c_5776]) ).
tcf(c_41013,plain,
! [X0: $i] :
( ( sK7(powerset(sK1)) = X0 )
| ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21309,c_51]) ).
tcf(c_41014,plain,
( ( relation_dom(sK7(powerset(sK1))) = empty_set )
| ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) ) ),
inference(superposition,[status(thm)],[c_21309,c_5663]) ).
tcf(c_41015,plain,
( ( sK7(powerset(sK1)) = empty_set )
| ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) ) ),
inference(superposition,[status(thm)],[c_21309,c_52]) ).
tcf(c_41016,plain,
( function(sK7(powerset(sK1)))
| ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) ) ),
inference(superposition,[status(thm)],[c_21309,c_98]) ).
tcf(c_41017,plain,
( relation(sK7(powerset(sK1)))
| ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) ) ),
inference(superposition,[status(thm)],[c_21309,c_80]) ).
tcf(c_42010,plain,
! [X0: $i] : element(sK2(empty_set,X0,sK1),sK0),
inference(global_subsumption_just,[status(thm)],[c_7603,c_38434]) ).
tcf(c_42012,plain,
! [X0: $i] :
( empty(sK0)
| in(sK2(empty_set,X0,sK1),sK0) ),
inference(superposition,[status(thm)],[c_42010,c_71]) ).
tcf(c_42013,plain,
! [X0: $i] : in(sK2(empty_set,X0,sK1),sK0),
inference(forward_subsumption_resolution,[status(thm)],[c_42012,c_24236]) ).
tcf(c_42018,plain,
( ( apply(empty_set,sK7(empty_set)) = sK7(empty_set) )
| ( relation_dom(relation_dom(sK7(powerset(empty_set)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_6104,c_11429]) ).
tcf(c_42019,plain,
( ( apply(identity_relation(powerset(empty_set)),empty_set) = empty_set )
| ( relation_dom(relation_dom(sK7(powerset(powerset(empty_set))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8004,c_11429]) ).
tcf(c_42022,plain,
( ( apply(identity_relation(sK6(sK6(sK6(powerset(empty_set))))),empty_set) = empty_set )
| ( relation_dom(relation_dom(sK7(powerset(sK6(sK6(sK6(powerset(empty_set)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_37341,c_11429]) ).
tcf(c_42023,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(identity_relation(X0),X1) = X2 )
| ( relation_dom(relation_dom(sK7(powerset(X0)))) = empty_set )
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),relation_dom(identity_relation(X0)))
| ~ in(sK2(identity_relation(X0),X1,X2),X2)
| ( sK2(identity_relation(X0),X1,X2) != sK7(X0) ) ),
inference(superposition,[status(thm)],[c_11429,c_53]) ).
tcf(c_42024,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0),relation_image(identity_relation(X0),X1))
| ( relation_dom(relation_dom(sK7(powerset(X0)))) = empty_set )
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),relation_dom(identity_relation(X0))) ),
inference(superposition,[status(thm)],[c_11429,c_57]) ).
tcf(c_42028,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0),relation_image(identity_relation(X0),X1))
| ( relation_dom(relation_dom(sK7(powerset(X0)))) = empty_set )
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),X0) ),
inference(light_normalisation,[status(thm)],[c_42024,c_121]) ).
tcf(c_42029,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0),relation_image(identity_relation(X0),X1))
| ( relation_dom(relation_dom(sK7(powerset(X0)))) = empty_set )
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_42028,c_62,c_63]) ).
tcf(c_42034,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(identity_relation(X0),X1) = X2 )
| ( relation_dom(relation_dom(sK7(powerset(X0)))) = empty_set )
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),X0)
| ~ in(sK2(identity_relation(X0),X1,X2),X2)
| ( sK2(identity_relation(X0),X1,X2) != sK7(X0) ) ),
inference(light_normalisation,[status(thm)],[c_42023,c_121]) ).
tcf(c_42035,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(identity_relation(X0),X1) = X2 )
| ( relation_dom(relation_dom(sK7(powerset(X0)))) = empty_set )
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),X0)
| ~ in(sK2(identity_relation(X0),X1,X2),X2)
| ( sK2(identity_relation(X0),X1,X2) != sK7(X0) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_42034,c_62,c_63]) ).
tcf(c_42047,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( identity_relation(sK7(powerset(sK7(powerset(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10348,c_27452]) ).
tcf(c_42048,plain,
! [X0: $i] :
( ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ( identity_relation(sK7(powerset(sK7(powerset(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_27452]) ).
tcf(c_42049,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( identity_relation(sK7(powerset(sK7(powerset(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_27452]) ).
tcf(c_42050,plain,
identity_relation(sK7(powerset(sK7(powerset(relation_dom(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_27452]) ).
tcf(c_42051,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(sK7(powerset(relation_dom(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_27452]) ).
tcf(c_42052,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(sK7(powerset(relation_dom(identity_relation(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_27452]) ).
tcf(c_42053,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(sK7(powerset(relation_dom(sK7(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_27452]) ).
tcf(c_42054,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(sK7(powerset(relation_dom(sK7(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_27452]) ).
tcf(c_42055,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(sK7(powerset(relation_dom(sK7(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_27452]) ).
tcf(c_42056,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(sK7(powerset(relation_dom(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_27452]) ).
tcf(c_42057,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( identity_relation(sK7(powerset(sK7(powerset(relation_dom(sK7(powerset(sK1)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_27452]) ).
tcf(c_42058,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(sK7(powerset(relation_dom(sK7(powerset(sK7(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_27452]) ).
tcf(c_42059,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(sK7(powerset(relation_dom(sK7(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_27452]) ).
tcf(c_42060,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(sK7(powerset(relation_dom(sK7(powerset(sK7(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_27452]) ).
tcf(c_42061,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(sK7(powerset(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_27452]) ).
tcf(c_42062,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(sK7(powerset(relation_dom(sK7(sK6(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_27452]) ).
tcf(c_42063,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(sK7(powerset(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_27452]) ).
tcf(c_42145,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( relation_dom(sK7(powerset(sK7(powerset(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10348,c_27588]) ).
tcf(c_42146,plain,
! [X0: $i] :
( ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ( relation_dom(sK7(powerset(sK7(powerset(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_27588]) ).
tcf(c_42147,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( relation_dom(sK7(powerset(sK7(powerset(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_27588]) ).
tcf(c_42148,plain,
relation_dom(sK7(powerset(sK7(powerset(relation_dom(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_27588]) ).
tcf(c_42149,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(sK7(powerset(relation_dom(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_27588]) ).
tcf(c_42150,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(sK7(powerset(relation_dom(identity_relation(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_27588]) ).
tcf(c_42151,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(sK7(powerset(relation_dom(sK7(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_27588]) ).
tcf(c_42152,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(sK7(powerset(relation_dom(sK7(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_27588]) ).
tcf(c_42153,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(sK7(powerset(relation_dom(sK7(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_27588]) ).
tcf(c_42154,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(sK7(powerset(relation_dom(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_27588]) ).
tcf(c_42155,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( relation_dom(sK7(powerset(sK7(powerset(relation_dom(sK7(powerset(sK1)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_27588]) ).
tcf(c_42156,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(sK7(powerset(relation_dom(sK7(powerset(sK7(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_27588]) ).
tcf(c_42157,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(sK7(powerset(relation_dom(sK7(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_27588]) ).
tcf(c_42158,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(sK7(powerset(relation_dom(sK7(powerset(sK7(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_27588]) ).
tcf(c_42159,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(sK7(powerset(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_27588]) ).
tcf(c_42160,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(sK7(powerset(relation_dom(sK7(sK6(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_27588]) ).
tcf(c_42161,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(sK7(powerset(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_27588]) ).
tcf(c_42262,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(relation_dom(X1))) = X0 )
| ( apply(identity_relation(X1),sK7(sK6(X1))) = sK7(sK6(X1)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10348,c_27714]) ).
tcf(c_42263,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(relation_dom(X1))) = X0 )
| ( apply(identity_relation(powerset(X1)),sK6(X1)) = sK6(X1) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5806,c_27714]) ).
tcf(c_42264,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(relation_dom(X1))) = X0 )
| ( apply(identity_relation(X1),sK7(X1)) = sK7(X1) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5807,c_27714]) ).
tcf(c_42265,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(empty_set))) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_83,c_27714]) ).
tcf(c_42266,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(relation_dom(relation_dom(X0)))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_27714]) ).
tcf(c_42267,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(relation_dom(identity_relation(X0)))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_27714]) ).
tcf(c_42268,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(relation_dom(sK7(powerset(X0))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_27714]) ).
tcf(c_42269,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(relation_dom(sK7(sK6(powerset(X0)))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_27714]) ).
tcf(c_42270,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(relation_dom(sK7(sK6(sK6(powerset(X0))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_27714]) ).
tcf(c_42271,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(relation_dom(relation_image(X1,empty_set)))) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18616,c_27714]) ).
tcf(c_42272,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(sK7(powerset(sK1))))) = X0 )
| ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21309,c_27714]) ).
tcf(c_42273,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(relation_dom(sK7(powerset(sK7(powerset(X0))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_27714]) ).
tcf(c_42274,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(relation_dom(sK7(powerset(relation_image(X1,empty_set)))))) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18752,c_27714]) ).
tcf(c_42275,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(relation_dom(sK7(powerset(sK7(sK6(powerset(X0)))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_27714]) ).
tcf(c_42276,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_27714]) ).
tcf(c_42277,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(relation_dom(sK7(sK6(sK6(sK6(powerset(X0)))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_27714]) ).
tcf(c_42278,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0)))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_27714]) ).
tcf(c_42379,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( identity_relation(identity_relation(identity_relation(sK7(powerset(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10348,c_28429]) ).
tcf(c_42380,plain,
! [X0: $i] :
( ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ( identity_relation(identity_relation(identity_relation(sK7(powerset(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_28429]) ).
tcf(c_42381,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( identity_relation(identity_relation(identity_relation(sK7(powerset(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_28429]) ).
tcf(c_42382,plain,
identity_relation(identity_relation(identity_relation(sK7(powerset(relation_dom(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_28429]) ).
tcf(c_42383,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(sK7(powerset(relation_dom(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_28429]) ).
tcf(c_42384,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(sK7(powerset(relation_dom(identity_relation(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_28429]) ).
tcf(c_42385,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(sK7(powerset(relation_dom(sK7(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_28429]) ).
tcf(c_42386,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(sK7(powerset(relation_dom(sK7(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_28429]) ).
tcf(c_42387,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(sK7(powerset(relation_dom(sK7(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_28429]) ).
tcf(c_42388,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(sK7(powerset(relation_dom(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_28429]) ).
tcf(c_42389,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( identity_relation(identity_relation(identity_relation(sK7(powerset(relation_dom(sK7(powerset(sK1)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_28429]) ).
tcf(c_42390,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(sK7(powerset(relation_dom(sK7(powerset(sK7(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_28429]) ).
tcf(c_42391,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(sK7(powerset(relation_dom(sK7(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_28429]) ).
tcf(c_42392,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(sK7(powerset(relation_dom(sK7(powerset(sK7(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_28429]) ).
tcf(c_42393,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(sK7(powerset(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_28429]) ).
tcf(c_42394,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(sK7(powerset(relation_dom(sK7(sK6(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_28429]) ).
tcf(c_42395,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(sK7(powerset(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_28429]) ).
tcf(c_42454,plain,
! [X0: $i] : apply(identity_relation(sK0),sK2(empty_set,X0,sK1)) = sK2(empty_set,X0,sK1),
inference(superposition,[status(thm)],[c_42013,c_151]) ).
tcf(c_42455,plain,
! [X0: $i] : ~ in(sK0,sK2(empty_set,X0,sK1)),
inference(superposition,[status(thm)],[c_42013,c_85]) ).
tcf(c_42482,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( identity_relation(identity_relation(identity_relation(sK7(sK6(powerset(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10348,c_10659]) ).
tcf(c_42483,plain,
! [X0: $i] :
( ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ( identity_relation(identity_relation(identity_relation(sK7(sK6(powerset(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_10659]) ).
tcf(c_42484,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( identity_relation(identity_relation(identity_relation(sK7(sK6(powerset(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_10659]) ).
tcf(c_42485,plain,
identity_relation(identity_relation(identity_relation(sK7(sK6(powerset(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_10659]) ).
tcf(c_42486,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(sK7(sK6(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_10659]) ).
tcf(c_42487,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(sK7(sK6(powerset(identity_relation(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_10659]) ).
tcf(c_42488,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(sK7(sK6(powerset(sK7(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_10659]) ).
tcf(c_42489,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(sK7(sK6(powerset(sK7(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_10659]) ).
tcf(c_42490,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(sK7(sK6(powerset(sK7(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_10659]) ).
tcf(c_42491,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(sK7(sK6(powerset(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_10659]) ).
tcf(c_42492,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( identity_relation(identity_relation(identity_relation(sK7(sK6(powerset(sK7(powerset(sK1)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_10659]) ).
tcf(c_42493,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(sK7(sK6(powerset(sK7(powerset(sK7(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_10659]) ).
tcf(c_42494,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(sK7(sK6(powerset(sK7(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_10659]) ).
tcf(c_42495,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(sK7(sK6(powerset(sK7(powerset(sK7(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_10659]) ).
tcf(c_42496,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(sK7(sK6(powerset(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_10659]) ).
tcf(c_42497,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(sK7(sK6(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_10659]) ).
tcf(c_42498,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(sK7(sK6(powerset(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_10659]) ).
tcf(c_42628,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( relation_dom(sK7(powerset(sK7(sK6(powerset(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10348,c_10662]) ).
tcf(c_42629,plain,
! [X0: $i] :
( ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ( relation_dom(sK7(powerset(sK7(sK6(powerset(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_10662]) ).
tcf(c_42630,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( relation_dom(sK7(powerset(sK7(sK6(powerset(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_10662]) ).
tcf(c_42631,plain,
relation_dom(sK7(powerset(sK7(sK6(powerset(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_10662]) ).
tcf(c_42632,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(sK7(sK6(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_10662]) ).
tcf(c_42633,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(sK7(sK6(powerset(identity_relation(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_10662]) ).
tcf(c_42634,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(sK7(sK6(powerset(sK7(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_10662]) ).
tcf(c_42635,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(sK7(sK6(powerset(sK7(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_10662]) ).
tcf(c_42636,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(sK7(sK6(powerset(sK7(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_10662]) ).
tcf(c_42637,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(sK7(sK6(powerset(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_10662]) ).
tcf(c_42638,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( relation_dom(sK7(powerset(sK7(sK6(powerset(sK7(powerset(sK1)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_10662]) ).
tcf(c_42639,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(sK7(sK6(powerset(sK7(powerset(sK7(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_10662]) ).
tcf(c_42640,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(sK7(sK6(powerset(sK7(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_10662]) ).
tcf(c_42641,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(sK7(sK6(powerset(sK7(powerset(sK7(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_10662]) ).
tcf(c_42642,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(sK7(sK6(powerset(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_10662]) ).
tcf(c_42643,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(sK7(sK6(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_10662]) ).
tcf(c_42644,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(sK7(sK6(powerset(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_10662]) ).
tcf(c_42754,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( sK7(powerset(identity_relation(sK7(powerset(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10348,c_28572]) ).
tcf(c_42755,plain,
! [X0: $i] :
( ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ( sK7(powerset(identity_relation(sK7(powerset(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_28572]) ).
tcf(c_42756,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( sK7(powerset(identity_relation(sK7(powerset(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_28572]) ).
tcf(c_42757,plain,
sK7(powerset(identity_relation(sK7(powerset(relation_dom(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_28572]) ).
tcf(c_42758,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(sK7(powerset(relation_dom(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_28572]) ).
tcf(c_42759,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(sK7(powerset(relation_dom(identity_relation(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_28572]) ).
tcf(c_42760,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(sK7(powerset(relation_dom(sK7(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_28572]) ).
tcf(c_42761,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(sK7(powerset(relation_dom(sK7(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_28572]) ).
tcf(c_42762,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(sK7(powerset(relation_dom(sK7(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_28572]) ).
tcf(c_42763,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(sK7(powerset(relation_dom(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_28572]) ).
tcf(c_42764,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( sK7(powerset(identity_relation(sK7(powerset(relation_dom(sK7(powerset(sK1)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_28572]) ).
tcf(c_42765,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(sK7(powerset(relation_dom(sK7(powerset(sK7(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_28572]) ).
tcf(c_42766,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(sK7(powerset(relation_dom(sK7(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_28572]) ).
tcf(c_42767,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(sK7(powerset(relation_dom(sK7(powerset(sK7(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_28572]) ).
tcf(c_42768,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(sK7(powerset(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_28572]) ).
tcf(c_42769,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(sK7(powerset(relation_dom(sK7(sK6(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_28572]) ).
tcf(c_42770,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(sK7(powerset(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_28572]) ).
tcf(c_42958,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( sK7(powerset(sK7(sK6(powerset(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10348,c_28717]) ).
tcf(c_42959,plain,
! [X0: $i] :
( ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ( sK7(powerset(sK7(sK6(powerset(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_28717]) ).
tcf(c_42960,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( sK7(powerset(sK7(sK6(powerset(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_28717]) ).
tcf(c_42961,plain,
sK7(powerset(sK7(sK6(powerset(relation_dom(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_28717]) ).
tcf(c_42962,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(sK6(powerset(relation_dom(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_28717]) ).
tcf(c_42963,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(sK6(powerset(relation_dom(identity_relation(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_28717]) ).
tcf(c_42964,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(sK6(powerset(relation_dom(sK7(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_28717]) ).
tcf(c_42965,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(sK6(powerset(relation_dom(sK7(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_28717]) ).
tcf(c_42966,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(sK6(powerset(relation_dom(sK7(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_28717]) ).
tcf(c_42967,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(sK6(powerset(relation_dom(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_28717]) ).
tcf(c_42968,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( sK7(powerset(sK7(sK6(powerset(relation_dom(sK7(powerset(sK1)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_28717]) ).
tcf(c_42969,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(sK6(powerset(relation_dom(sK7(powerset(sK7(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_28717]) ).
tcf(c_42970,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(sK6(powerset(relation_dom(sK7(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_28717]) ).
tcf(c_42971,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(sK6(powerset(relation_dom(sK7(powerset(sK7(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_28717]) ).
tcf(c_42972,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(sK6(powerset(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_28717]) ).
tcf(c_42973,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(sK6(powerset(relation_dom(sK7(sK6(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_28717]) ).
tcf(c_42974,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(sK6(powerset(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_28717]) ).
tcf(c_43121,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( identity_relation(identity_relation(sK7(sK6(powerset(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10348,c_29194]) ).
tcf(c_43122,plain,
! [X0: $i] :
( ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ( identity_relation(identity_relation(sK7(sK6(powerset(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_29194]) ).
tcf(c_43123,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( identity_relation(identity_relation(sK7(sK6(powerset(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_29194]) ).
tcf(c_43124,plain,
identity_relation(identity_relation(sK7(sK6(powerset(relation_dom(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_29194]) ).
tcf(c_43125,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(sK6(powerset(relation_dom(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_29194]) ).
tcf(c_43126,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(sK6(powerset(relation_dom(identity_relation(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_29194]) ).
tcf(c_43127,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(sK6(powerset(relation_dom(sK7(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_29194]) ).
tcf(c_43128,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(sK6(powerset(relation_dom(sK7(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_29194]) ).
tcf(c_43129,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(sK6(powerset(relation_dom(sK7(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_29194]) ).
tcf(c_43130,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(sK6(powerset(relation_dom(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_29194]) ).
tcf(c_43131,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( identity_relation(identity_relation(sK7(sK6(powerset(relation_dom(sK7(powerset(sK1)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_29194]) ).
tcf(c_43132,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(sK6(powerset(relation_dom(sK7(powerset(sK7(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_29194]) ).
tcf(c_43133,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(sK6(powerset(relation_dom(sK7(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_29194]) ).
tcf(c_43134,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(sK6(powerset(relation_dom(sK7(powerset(sK7(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_29194]) ).
tcf(c_43135,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(sK6(powerset(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_29194]) ).
tcf(c_43136,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(sK6(powerset(relation_dom(sK7(sK6(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_29194]) ).
tcf(c_43137,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(sK6(powerset(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_29194]) ).
tcf(c_43423,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( identity_relation(relation_dom(sK7(sK6(powerset(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10348,c_29308]) ).
tcf(c_43424,plain,
! [X0: $i] :
( ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ( identity_relation(relation_dom(sK7(sK6(powerset(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_29308]) ).
tcf(c_43425,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( identity_relation(relation_dom(sK7(sK6(powerset(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_29308]) ).
tcf(c_43426,plain,
identity_relation(relation_dom(sK7(sK6(powerset(relation_dom(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_29308]) ).
tcf(c_43427,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(sK6(powerset(relation_dom(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_29308]) ).
tcf(c_43428,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(sK6(powerset(relation_dom(identity_relation(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_29308]) ).
tcf(c_43429,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(sK6(powerset(relation_dom(sK7(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_29308]) ).
tcf(c_43430,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(sK6(powerset(relation_dom(sK7(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_29308]) ).
tcf(c_43431,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(sK6(powerset(relation_dom(sK7(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_29308]) ).
tcf(c_43432,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(sK6(powerset(relation_dom(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_29308]) ).
tcf(c_43433,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( identity_relation(relation_dom(sK7(sK6(powerset(relation_dom(sK7(powerset(sK1)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_29308]) ).
tcf(c_43434,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(sK6(powerset(relation_dom(sK7(powerset(sK7(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_29308]) ).
tcf(c_43435,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(sK6(powerset(relation_dom(sK7(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_29308]) ).
tcf(c_43436,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(sK6(powerset(relation_dom(sK7(powerset(sK7(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_29308]) ).
tcf(c_43437,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(sK6(powerset(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_29308]) ).
tcf(c_43438,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(sK6(powerset(relation_dom(sK7(sK6(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_29308]) ).
tcf(c_43439,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(sK6(powerset(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_29308]) ).
tcf(c_43579,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( identity_relation(sK7(powerset(sK7(sK6(powerset(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10348,c_10663]) ).
tcf(c_43580,plain,
! [X0: $i] :
( ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ( identity_relation(sK7(powerset(sK7(sK6(powerset(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_10663]) ).
tcf(c_43581,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( identity_relation(sK7(powerset(sK7(sK6(powerset(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_10663]) ).
tcf(c_43582,plain,
identity_relation(sK7(powerset(sK7(sK6(powerset(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_10663]) ).
tcf(c_43583,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(sK7(sK6(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_10663]) ).
tcf(c_43584,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(sK7(sK6(powerset(identity_relation(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_10663]) ).
tcf(c_43585,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(sK7(sK6(powerset(sK7(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_10663]) ).
tcf(c_43586,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(sK7(sK6(powerset(sK7(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_10663]) ).
tcf(c_43587,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(sK7(sK6(powerset(sK7(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_10663]) ).
tcf(c_43588,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(sK7(sK6(powerset(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_10663]) ).
tcf(c_43589,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( identity_relation(sK7(powerset(sK7(sK6(powerset(sK7(powerset(sK1)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_10663]) ).
tcf(c_43590,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(sK7(sK6(powerset(sK7(powerset(sK7(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_10663]) ).
tcf(c_43591,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(sK7(sK6(powerset(sK7(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_10663]) ).
tcf(c_43592,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(sK7(sK6(powerset(sK7(powerset(sK7(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_10663]) ).
tcf(c_43593,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(sK7(sK6(powerset(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_10663]) ).
tcf(c_43594,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(sK7(sK6(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_10663]) ).
tcf(c_43595,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(sK7(sK6(powerset(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_10663]) ).
tcf(c_43696,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( sK7(powerset(relation_dom(sK7(sK6(powerset(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10348,c_10664]) ).
tcf(c_43697,plain,
! [X0: $i] :
( ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ( sK7(powerset(relation_dom(sK7(sK6(powerset(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_10664]) ).
tcf(c_43698,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( sK7(powerset(relation_dom(sK7(sK6(powerset(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_10664]) ).
tcf(c_43699,plain,
sK7(powerset(relation_dom(sK7(sK6(powerset(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_10664]) ).
tcf(c_43700,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(sK7(sK6(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_10664]) ).
tcf(c_43701,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(sK7(sK6(powerset(identity_relation(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_10664]) ).
tcf(c_43702,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(sK7(sK6(powerset(sK7(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_10664]) ).
tcf(c_43703,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(sK7(sK6(powerset(sK7(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_10664]) ).
tcf(c_43704,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(sK7(sK6(powerset(sK7(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_10664]) ).
tcf(c_43705,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(sK7(sK6(powerset(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_10664]) ).
tcf(c_43706,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( sK7(powerset(relation_dom(sK7(sK6(powerset(sK7(powerset(sK1)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_10664]) ).
tcf(c_43707,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(sK7(sK6(powerset(sK7(powerset(sK7(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_10664]) ).
tcf(c_43708,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(sK7(sK6(powerset(sK7(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_10664]) ).
tcf(c_43709,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(sK7(sK6(powerset(sK7(powerset(sK7(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_10664]) ).
tcf(c_43710,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(sK7(sK6(powerset(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_10664]) ).
tcf(c_43711,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(sK7(sK6(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_10664]) ).
tcf(c_43712,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(sK7(sK6(powerset(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_10664]) ).
tcf(c_43823,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( identity_relation(identity_relation(relation_dom(sK7(sK6(powerset(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10348,c_10665]) ).
tcf(c_43824,plain,
! [X0: $i] :
( ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ( identity_relation(identity_relation(relation_dom(sK7(sK6(powerset(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_10665]) ).
tcf(c_43825,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( identity_relation(identity_relation(relation_dom(sK7(sK6(powerset(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_10665]) ).
tcf(c_43826,plain,
identity_relation(identity_relation(relation_dom(sK7(sK6(powerset(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_10665]) ).
tcf(c_43827,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(sK7(sK6(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_10665]) ).
tcf(c_43828,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(sK7(sK6(powerset(identity_relation(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_10665]) ).
tcf(c_43829,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(sK7(sK6(powerset(sK7(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_10665]) ).
tcf(c_43830,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(sK7(sK6(powerset(sK7(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_10665]) ).
tcf(c_43831,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(sK7(sK6(powerset(sK7(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_10665]) ).
tcf(c_43832,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(sK7(sK6(powerset(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_10665]) ).
tcf(c_43833,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( identity_relation(identity_relation(relation_dom(sK7(sK6(powerset(sK7(powerset(sK1)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_10665]) ).
tcf(c_43834,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(sK7(sK6(powerset(sK7(powerset(sK7(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_10665]) ).
tcf(c_43835,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(sK7(sK6(powerset(sK7(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_10665]) ).
tcf(c_43836,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(sK7(sK6(powerset(sK7(powerset(sK7(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_10665]) ).
tcf(c_43837,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(sK7(sK6(powerset(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_10665]) ).
tcf(c_43838,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(sK7(sK6(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_10665]) ).
tcf(c_43839,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(sK7(sK6(powerset(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_10665]) ).
tcf(c_43977,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( identity_relation(relation_dom(relation_dom(sK7(sK6(powerset(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10348,c_10666]) ).
tcf(c_43978,plain,
! [X0: $i] :
( ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ( identity_relation(relation_dom(relation_dom(sK7(sK6(powerset(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_10666]) ).
tcf(c_43979,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( identity_relation(relation_dom(relation_dom(sK7(sK6(powerset(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_10666]) ).
tcf(c_43980,plain,
identity_relation(relation_dom(relation_dom(sK7(sK6(powerset(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_10666]) ).
tcf(c_43981,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(sK7(sK6(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_10666]) ).
tcf(c_43982,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(sK7(sK6(powerset(identity_relation(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_10666]) ).
tcf(c_43983,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(sK7(sK6(powerset(sK7(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_10666]) ).
tcf(c_43984,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(sK7(sK6(powerset(sK7(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_10666]) ).
tcf(c_43985,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(sK7(sK6(powerset(sK7(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_10666]) ).
tcf(c_43986,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(sK7(sK6(powerset(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_10666]) ).
tcf(c_43987,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( identity_relation(relation_dom(relation_dom(sK7(sK6(powerset(sK7(powerset(sK1)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_10666]) ).
tcf(c_43988,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(sK7(sK6(powerset(sK7(powerset(sK7(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_10666]) ).
tcf(c_43989,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(sK7(sK6(powerset(sK7(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_10666]) ).
tcf(c_43990,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(sK7(sK6(powerset(sK7(powerset(sK7(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_10666]) ).
tcf(c_43991,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(sK7(sK6(powerset(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_10666]) ).
tcf(c_43992,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(sK7(sK6(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_10666]) ).
tcf(c_43993,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(sK7(sK6(powerset(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_10666]) ).
tcf(c_44145,plain,
! [X0: $i] :
( ( relation_image(X0,sK1) = empty_set )
| ( apply(identity_relation(sK0),sK3(X0,sK1,empty_set)) = sK3(X0,sK1,empty_set) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_11847,c_151]) ).
tcf(c_44146,plain,
! [X0: $i] :
( ( relation_image(X0,sK1) = empty_set )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK0,sK3(X0,sK1,empty_set)) ),
inference(superposition,[status(thm)],[c_11847,c_85]) ).
tcf(c_44165,plain,
! [X0: $i] :
( ( relation_image(X0,empty_set) = sK1 )
| ( apply(identity_relation(sK0),sK2(X0,empty_set,sK1)) = sK2(X0,empty_set,sK1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_12535,c_151]) ).
tcf(c_44166,plain,
! [X0: $i] :
( ( relation_image(X0,empty_set) = sK1 )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK0,sK2(X0,empty_set,sK1)) ),
inference(superposition,[status(thm)],[c_12535,c_85]) ).
tcf(c_44183,plain,
( ( apply(empty_set,sK7(empty_set)) = sK7(empty_set) )
| ( relation_dom(relation_dom(relation_dom(relation_dom(empty_set)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_6104,c_11951]) ).
tcf(c_44184,plain,
( ( apply(identity_relation(powerset(empty_set)),empty_set) = empty_set )
| ( relation_dom(relation_dom(relation_dom(relation_dom(powerset(empty_set))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8004,c_11951]) ).
tcf(c_44187,plain,
( ( apply(identity_relation(sK6(sK6(sK6(powerset(empty_set))))),empty_set) = empty_set )
| ( relation_dom(relation_dom(relation_dom(relation_dom(sK6(sK6(sK6(powerset(empty_set)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_37341,c_11951]) ).
tcf(c_44188,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(identity_relation(X0),X1) = X2 )
| ( relation_dom(relation_dom(relation_dom(relation_dom(X0)))) = empty_set )
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),relation_dom(identity_relation(X0)))
| ~ in(sK2(identity_relation(X0),X1,X2),X2)
| ( sK2(identity_relation(X0),X1,X2) != sK7(X0) ) ),
inference(superposition,[status(thm)],[c_11951,c_53]) ).
tcf(c_44189,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0),relation_image(identity_relation(X0),X1))
| ( relation_dom(relation_dom(relation_dom(relation_dom(X0)))) = empty_set )
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),relation_dom(identity_relation(X0))) ),
inference(superposition,[status(thm)],[c_11951,c_57]) ).
tcf(c_44193,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0),relation_image(identity_relation(X0),X1))
| ( relation_dom(relation_dom(relation_dom(relation_dom(X0)))) = empty_set )
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),X0) ),
inference(light_normalisation,[status(thm)],[c_44189,c_121]) ).
tcf(c_44194,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0),relation_image(identity_relation(X0),X1))
| ( relation_dom(relation_dom(relation_dom(relation_dom(X0)))) = empty_set )
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_44193,c_62,c_63]) ).
tcf(c_44199,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(identity_relation(X0),X1) = X2 )
| ( relation_dom(relation_dom(relation_dom(relation_dom(X0)))) = empty_set )
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),X0)
| ~ in(sK2(identity_relation(X0),X1,X2),X2)
| ( sK2(identity_relation(X0),X1,X2) != sK7(X0) ) ),
inference(light_normalisation,[status(thm)],[c_44188,c_121]) ).
tcf(c_44200,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(identity_relation(X0),X1) = X2 )
| ( relation_dom(relation_dom(relation_dom(relation_dom(X0)))) = empty_set )
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),X0)
| ~ in(sK2(identity_relation(X0),X1,X2),X2)
| ( sK2(identity_relation(X0),X1,X2) != sK7(X0) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_44199,c_62,c_63]) ).
tcf(c_44212,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( relation_dom(relation_dom(sK7(sK6(powerset(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10348,c_29442]) ).
tcf(c_44213,plain,
! [X0: $i] :
( ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ( relation_dom(relation_dom(sK7(sK6(powerset(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_29442]) ).
tcf(c_44214,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( relation_dom(relation_dom(sK7(sK6(powerset(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_29442]) ).
tcf(c_44215,plain,
relation_dom(relation_dom(sK7(sK6(powerset(relation_dom(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_29442]) ).
tcf(c_44216,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(sK6(powerset(relation_dom(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_29442]) ).
tcf(c_44217,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(sK6(powerset(relation_dom(identity_relation(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_29442]) ).
tcf(c_44218,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(sK6(powerset(relation_dom(sK7(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_29442]) ).
tcf(c_44219,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(sK6(powerset(relation_dom(sK7(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_29442]) ).
tcf(c_44220,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(sK6(powerset(relation_dom(sK7(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_29442]) ).
tcf(c_44221,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(sK6(powerset(relation_dom(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_29442]) ).
tcf(c_44222,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( relation_dom(relation_dom(sK7(sK6(powerset(relation_dom(sK7(powerset(sK1)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_29442]) ).
tcf(c_44223,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(sK6(powerset(relation_dom(sK7(powerset(sK7(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_29442]) ).
tcf(c_44224,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(sK6(powerset(relation_dom(sK7(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_29442]) ).
tcf(c_44225,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(sK6(powerset(relation_dom(sK7(powerset(sK7(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_29442]) ).
tcf(c_44226,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(sK6(powerset(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_29442]) ).
tcf(c_44227,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(sK6(powerset(relation_dom(sK7(sK6(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_29442]) ).
tcf(c_44228,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(sK6(powerset(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_29442]) ).
tcf(c_44311,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( sK7(sK6(powerset(sK7(powerset(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10348,c_29569]) ).
tcf(c_44312,plain,
! [X0: $i] :
( ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ( sK7(sK6(powerset(sK7(powerset(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_29569]) ).
tcf(c_44313,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( sK7(sK6(powerset(sK7(powerset(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_29569]) ).
tcf(c_44314,plain,
sK7(sK6(powerset(sK7(powerset(relation_dom(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_29569]) ).
tcf(c_44315,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(sK7(powerset(relation_dom(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_29569]) ).
tcf(c_44316,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(sK7(powerset(relation_dom(identity_relation(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_29569]) ).
tcf(c_44317,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(sK7(powerset(relation_dom(sK7(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_29569]) ).
tcf(c_44318,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(sK7(powerset(relation_dom(sK7(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_29569]) ).
tcf(c_44319,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(sK7(powerset(relation_dom(sK7(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_29569]) ).
tcf(c_44320,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(sK7(powerset(relation_dom(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_29569]) ).
tcf(c_44321,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( sK7(sK6(powerset(sK7(powerset(relation_dom(sK7(powerset(sK1)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_29569]) ).
tcf(c_44322,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(sK7(powerset(relation_dom(sK7(powerset(sK7(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_29569]) ).
tcf(c_44323,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(sK7(powerset(relation_dom(sK7(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_29569]) ).
tcf(c_44324,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(sK7(powerset(relation_dom(sK7(powerset(sK7(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_29569]) ).
tcf(c_44325,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(sK7(powerset(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_29569]) ).
tcf(c_44326,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(sK7(powerset(relation_dom(sK7(sK6(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_29569]) ).
tcf(c_44327,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(sK7(powerset(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_29569]) ).
tcf(c_44594,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( relation_dom(relation_dom(sK7(powerset(identity_relation(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10348,c_30068]) ).
tcf(c_44595,plain,
! [X0: $i] :
( ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ( relation_dom(relation_dom(sK7(powerset(identity_relation(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_30068]) ).
tcf(c_44596,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( relation_dom(relation_dom(sK7(powerset(identity_relation(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_30068]) ).
tcf(c_44597,plain,
relation_dom(relation_dom(sK7(powerset(identity_relation(relation_dom(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_30068]) ).
tcf(c_44598,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(powerset(identity_relation(relation_dom(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_30068]) ).
tcf(c_44599,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(powerset(identity_relation(relation_dom(identity_relation(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_30068]) ).
tcf(c_44600,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(powerset(identity_relation(relation_dom(sK7(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_30068]) ).
tcf(c_44601,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(powerset(identity_relation(relation_dom(sK7(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_30068]) ).
tcf(c_44602,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(powerset(identity_relation(relation_dom(sK7(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_30068]) ).
tcf(c_44603,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(powerset(identity_relation(relation_dom(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_30068]) ).
tcf(c_44604,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( relation_dom(relation_dom(sK7(powerset(identity_relation(relation_dom(sK7(powerset(sK1)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_30068]) ).
tcf(c_44605,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(powerset(identity_relation(relation_dom(sK7(powerset(sK7(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_30068]) ).
tcf(c_44606,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(powerset(identity_relation(relation_dom(sK7(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_30068]) ).
tcf(c_44607,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(powerset(identity_relation(relation_dom(sK7(powerset(sK7(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_30068]) ).
tcf(c_44608,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(powerset(identity_relation(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_30068]) ).
tcf(c_44609,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(powerset(identity_relation(relation_dom(sK7(sK6(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_30068]) ).
tcf(c_44610,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(powerset(identity_relation(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_30068]) ).
tcf(c_44874,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( identity_relation(relation_dom(sK7(powerset(identity_relation(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10348,c_30158]) ).
tcf(c_44875,plain,
! [X0: $i] :
( ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ( identity_relation(relation_dom(sK7(powerset(identity_relation(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_30158]) ).
tcf(c_44876,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( identity_relation(relation_dom(sK7(powerset(identity_relation(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_30158]) ).
tcf(c_44877,plain,
identity_relation(relation_dom(sK7(powerset(identity_relation(relation_dom(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_30158]) ).
tcf(c_44878,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(powerset(identity_relation(relation_dom(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_30158]) ).
tcf(c_44879,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(powerset(identity_relation(relation_dom(identity_relation(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_30158]) ).
tcf(c_44880,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(powerset(identity_relation(relation_dom(sK7(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_30158]) ).
tcf(c_44881,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(powerset(identity_relation(relation_dom(sK7(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_30158]) ).
tcf(c_44882,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(powerset(identity_relation(relation_dom(sK7(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_30158]) ).
tcf(c_44883,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(powerset(identity_relation(relation_dom(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_30158]) ).
tcf(c_44884,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( identity_relation(relation_dom(sK7(powerset(identity_relation(relation_dom(sK7(powerset(sK1)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_30158]) ).
tcf(c_44885,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(powerset(identity_relation(relation_dom(sK7(powerset(sK7(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_30158]) ).
tcf(c_44886,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(powerset(identity_relation(relation_dom(sK7(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_30158]) ).
tcf(c_44887,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(powerset(identity_relation(relation_dom(sK7(powerset(sK7(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_30158]) ).
tcf(c_44888,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(powerset(identity_relation(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_30158]) ).
tcf(c_44889,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(powerset(identity_relation(relation_dom(sK7(sK6(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_30158]) ).
tcf(c_44890,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(powerset(identity_relation(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_30158]) ).
tcf(c_45013,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( relation_dom(relation_dom(relation_dom(sK7(sK6(powerset(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10348,c_10669]) ).
tcf(c_45014,plain,
! [X0: $i] :
( ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ( relation_dom(relation_dom(relation_dom(sK7(sK6(powerset(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_10669]) ).
tcf(c_45015,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( relation_dom(relation_dom(relation_dom(sK7(sK6(powerset(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_10669]) ).
tcf(c_45016,plain,
relation_dom(relation_dom(relation_dom(sK7(sK6(powerset(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_10669]) ).
tcf(c_45017,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK7(sK6(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_10669]) ).
tcf(c_45018,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK7(sK6(powerset(identity_relation(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_10669]) ).
tcf(c_45019,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK7(sK6(powerset(sK7(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_10669]) ).
tcf(c_45020,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK7(sK6(powerset(sK7(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_10669]) ).
tcf(c_45021,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK7(sK6(powerset(sK7(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_10669]) ).
tcf(c_45022,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK7(sK6(powerset(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_10669]) ).
tcf(c_45023,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( relation_dom(relation_dom(relation_dom(sK7(sK6(powerset(sK7(powerset(sK1)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_10669]) ).
tcf(c_45024,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK7(sK6(powerset(sK7(powerset(sK7(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_10669]) ).
tcf(c_45025,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK7(sK6(powerset(sK7(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_10669]) ).
tcf(c_45026,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK7(sK6(powerset(sK7(powerset(sK7(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_10669]) ).
tcf(c_45027,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK7(sK6(powerset(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_10669]) ).
tcf(c_45028,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK7(sK6(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_10669]) ).
tcf(c_45029,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK7(sK6(powerset(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_10669]) ).
tcf(c_45246,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( sK7(sK6(powerset(sK7(sK6(powerset(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10348,c_11346]) ).
tcf(c_45247,plain,
! [X0: $i] :
( ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ( sK7(sK6(powerset(sK7(sK6(powerset(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_11346]) ).
tcf(c_45248,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( sK7(sK6(powerset(sK7(sK6(powerset(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_11346]) ).
tcf(c_45249,plain,
sK7(sK6(powerset(sK7(sK6(powerset(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_11346]) ).
tcf(c_45250,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(sK7(sK6(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_11346]) ).
tcf(c_45251,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(sK7(sK6(powerset(identity_relation(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_11346]) ).
tcf(c_45252,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(sK7(sK6(powerset(sK7(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_11346]) ).
tcf(c_45253,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(sK7(sK6(powerset(sK7(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_11346]) ).
tcf(c_45254,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(sK7(sK6(powerset(sK7(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_11346]) ).
tcf(c_45255,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(sK7(sK6(powerset(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_11346]) ).
tcf(c_45256,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( sK7(sK6(powerset(sK7(sK6(powerset(sK7(powerset(sK1)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_11346]) ).
tcf(c_45257,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(sK7(sK6(powerset(sK7(powerset(sK7(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_11346]) ).
tcf(c_45258,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(sK7(sK6(powerset(sK7(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_11346]) ).
tcf(c_45259,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(sK7(sK6(powerset(sK7(powerset(sK7(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_11346]) ).
tcf(c_45260,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(sK7(sK6(powerset(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_11346]) ).
tcf(c_45261,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(sK7(sK6(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_11346]) ).
tcf(c_45262,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(sK7(sK6(powerset(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_11346]) ).
tcf(c_45317,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( relation_dom(relation_dom(sK7(powerset(sK7(powerset(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10348,c_11436]) ).
tcf(c_45318,plain,
! [X0: $i] :
( ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ( relation_dom(relation_dom(sK7(powerset(sK7(powerset(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_11436]) ).
tcf(c_45319,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( relation_dom(relation_dom(sK7(powerset(sK7(powerset(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_11436]) ).
tcf(c_45320,plain,
relation_dom(relation_dom(sK7(powerset(sK7(powerset(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_11436]) ).
tcf(c_45321,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(powerset(sK7(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_11436]) ).
tcf(c_45322,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(powerset(sK7(powerset(identity_relation(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_11436]) ).
tcf(c_45327,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( relation_dom(relation_dom(sK7(powerset(sK7(powerset(sK7(powerset(sK1)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_11436]) ).
tcf(c_45328,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(powerset(sK7(powerset(sK7(powerset(sK7(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_11436]) ).
tcf(c_45329,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(powerset(sK7(powerset(sK7(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_11436]) ).
tcf(c_45330,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(powerset(sK7(powerset(sK7(powerset(sK7(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_11436]) ).
tcf(c_45331,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(powerset(sK7(powerset(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_11436]) ).
tcf(c_45333,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(powerset(sK7(powerset(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_11436]) ).
tcf(c_45404,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( relation_dom(relation_dom(relation_dom(relation_dom(sK7(powerset(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10348,c_11958]) ).
tcf(c_45405,plain,
! [X0: $i] :
( ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ( relation_dom(relation_dom(relation_dom(relation_dom(sK7(powerset(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_11958]) ).
tcf(c_45406,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( relation_dom(relation_dom(relation_dom(relation_dom(sK7(powerset(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_11958]) ).
tcf(c_45407,plain,
relation_dom(relation_dom(relation_dom(relation_dom(sK7(powerset(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_11958]) ).
tcf(c_45408,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK7(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_11958]) ).
tcf(c_45409,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK7(powerset(identity_relation(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_11958]) ).
tcf(c_45414,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( relation_dom(relation_dom(relation_dom(relation_dom(sK7(powerset(sK7(powerset(sK1)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_11958]) ).
tcf(c_45415,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK7(powerset(sK7(powerset(sK7(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_11958]) ).
tcf(c_45416,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK7(powerset(sK7(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_11958]) ).
tcf(c_45417,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK7(powerset(sK7(powerset(sK7(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_11958]) ).
tcf(c_45418,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK7(powerset(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_11958]) ).
tcf(c_45420,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK7(powerset(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_11958]) ).
tcf(c_45463,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( identity_relation(identity_relation(sK7(powerset(identity_relation(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10348,c_30248]) ).
tcf(c_45464,plain,
! [X0: $i] :
( ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ( identity_relation(identity_relation(sK7(powerset(identity_relation(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_30248]) ).
tcf(c_45465,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( identity_relation(identity_relation(sK7(powerset(identity_relation(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_30248]) ).
tcf(c_45466,plain,
identity_relation(identity_relation(sK7(powerset(identity_relation(relation_dom(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_30248]) ).
tcf(c_45467,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(powerset(identity_relation(relation_dom(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_30248]) ).
tcf(c_45468,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(powerset(identity_relation(relation_dom(identity_relation(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_30248]) ).
tcf(c_45469,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(powerset(identity_relation(relation_dom(sK7(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_30248]) ).
tcf(c_45470,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(powerset(identity_relation(relation_dom(sK7(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_30248]) ).
tcf(c_45471,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(powerset(identity_relation(relation_dom(sK7(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_30248]) ).
tcf(c_45472,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(powerset(identity_relation(relation_dom(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_30248]) ).
tcf(c_45473,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( identity_relation(identity_relation(sK7(powerset(identity_relation(relation_dom(sK7(powerset(sK1)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_30248]) ).
tcf(c_45474,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(powerset(identity_relation(relation_dom(sK7(powerset(sK7(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_30248]) ).
tcf(c_45475,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(powerset(identity_relation(relation_dom(sK7(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_30248]) ).
tcf(c_45476,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(powerset(identity_relation(relation_dom(sK7(powerset(sK7(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_30248]) ).
tcf(c_45477,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(powerset(identity_relation(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_30248]) ).
tcf(c_45478,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(powerset(identity_relation(relation_dom(sK7(sK6(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_30248]) ).
tcf(c_45479,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(powerset(identity_relation(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_30248]) ).
tcf(c_45557,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( sK7(powerset(sK7(powerset(identity_relation(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10348,c_30355]) ).
tcf(c_45558,plain,
! [X0: $i] :
( ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ( sK7(powerset(sK7(powerset(identity_relation(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_30355]) ).
tcf(c_45559,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( sK7(powerset(sK7(powerset(identity_relation(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_30355]) ).
tcf(c_45560,plain,
sK7(powerset(sK7(powerset(identity_relation(relation_dom(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_30355]) ).
tcf(c_45561,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(powerset(identity_relation(relation_dom(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_30355]) ).
tcf(c_45562,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(powerset(identity_relation(relation_dom(identity_relation(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_30355]) ).
tcf(c_45563,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(powerset(identity_relation(relation_dom(sK7(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_30355]) ).
tcf(c_45564,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(powerset(identity_relation(relation_dom(sK7(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_30355]) ).
tcf(c_45565,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(powerset(identity_relation(relation_dom(sK7(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_30355]) ).
tcf(c_45566,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(powerset(identity_relation(relation_dom(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_30355]) ).
tcf(c_45567,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( sK7(powerset(sK7(powerset(identity_relation(relation_dom(sK7(powerset(sK1)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_30355]) ).
tcf(c_45568,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(powerset(identity_relation(relation_dom(sK7(powerset(sK7(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_30355]) ).
tcf(c_45569,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(powerset(identity_relation(relation_dom(sK7(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_30355]) ).
tcf(c_45570,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(powerset(identity_relation(relation_dom(sK7(powerset(sK7(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_30355]) ).
tcf(c_45571,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(powerset(identity_relation(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_30355]) ).
tcf(c_45572,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(powerset(identity_relation(relation_dom(sK7(sK6(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_30355]) ).
tcf(c_45573,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(powerset(identity_relation(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_30355]) ).
tcf(c_45689,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( identity_relation(sK7(powerset(identity_relation(identity_relation(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10348,c_30942]) ).
tcf(c_45690,plain,
! [X0: $i] :
( ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ( identity_relation(sK7(powerset(identity_relation(identity_relation(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_30942]) ).
tcf(c_45691,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( identity_relation(sK7(powerset(identity_relation(identity_relation(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_30942]) ).
tcf(c_45692,plain,
identity_relation(sK7(powerset(identity_relation(identity_relation(relation_dom(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_30942]) ).
tcf(c_45693,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(identity_relation(identity_relation(relation_dom(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_30942]) ).
tcf(c_45694,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(identity_relation(identity_relation(relation_dom(identity_relation(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_30942]) ).
tcf(c_45695,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(identity_relation(identity_relation(relation_dom(sK7(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_30942]) ).
tcf(c_45696,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(identity_relation(identity_relation(relation_dom(sK7(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_30942]) ).
tcf(c_45697,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(identity_relation(identity_relation(relation_dom(sK7(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_30942]) ).
tcf(c_45698,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(identity_relation(identity_relation(relation_dom(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_30942]) ).
tcf(c_45699,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( identity_relation(sK7(powerset(identity_relation(identity_relation(relation_dom(sK7(powerset(sK1)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_30942]) ).
tcf(c_45700,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(identity_relation(identity_relation(relation_dom(sK7(powerset(sK7(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_30942]) ).
tcf(c_45701,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(identity_relation(identity_relation(relation_dom(sK7(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_30942]) ).
tcf(c_45702,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(identity_relation(identity_relation(relation_dom(sK7(powerset(sK7(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_30942]) ).
tcf(c_45703,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(identity_relation(identity_relation(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_30942]) ).
tcf(c_45704,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(identity_relation(identity_relation(relation_dom(sK7(sK6(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_30942]) ).
tcf(c_45705,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(identity_relation(identity_relation(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_30942]) ).
tcf(c_45758,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( relation_dom(sK7(powerset(identity_relation(identity_relation(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10348,c_31014]) ).
tcf(c_45759,plain,
! [X0: $i] :
( ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ( relation_dom(sK7(powerset(identity_relation(identity_relation(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_31014]) ).
tcf(c_45760,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( relation_dom(sK7(powerset(identity_relation(identity_relation(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_31014]) ).
tcf(c_45761,plain,
relation_dom(sK7(powerset(identity_relation(identity_relation(relation_dom(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_31014]) ).
tcf(c_45762,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(identity_relation(identity_relation(relation_dom(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_31014]) ).
tcf(c_45763,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(identity_relation(identity_relation(relation_dom(identity_relation(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_31014]) ).
tcf(c_45764,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(identity_relation(identity_relation(relation_dom(sK7(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_31014]) ).
tcf(c_45765,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(identity_relation(identity_relation(relation_dom(sK7(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_31014]) ).
tcf(c_45766,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(identity_relation(identity_relation(relation_dom(sK7(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_31014]) ).
tcf(c_45767,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(identity_relation(identity_relation(relation_dom(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_31014]) ).
tcf(c_45768,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( relation_dom(sK7(powerset(identity_relation(identity_relation(relation_dom(sK7(powerset(sK1)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_31014]) ).
tcf(c_45769,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(identity_relation(identity_relation(relation_dom(sK7(powerset(sK7(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_31014]) ).
tcf(c_45770,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(identity_relation(identity_relation(relation_dom(sK7(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_31014]) ).
tcf(c_45771,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(identity_relation(identity_relation(relation_dom(sK7(powerset(sK7(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_31014]) ).
tcf(c_45772,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(identity_relation(identity_relation(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_31014]) ).
tcf(c_45773,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(identity_relation(identity_relation(relation_dom(sK7(sK6(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_31014]) ).
tcf(c_45774,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(identity_relation(identity_relation(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_31014]) ).
tcf(c_45979,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( identity_relation(relation_dom(relation_dom(relation_dom(sK7(powerset(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10348,c_12032]) ).
tcf(c_45980,plain,
! [X0: $i] :
( ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ( identity_relation(relation_dom(relation_dom(relation_dom(sK7(powerset(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_12032]) ).
tcf(c_45981,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( identity_relation(relation_dom(relation_dom(relation_dom(sK7(powerset(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_12032]) ).
tcf(c_45982,plain,
identity_relation(relation_dom(relation_dom(relation_dom(sK7(powerset(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_12032]) ).
tcf(c_45983,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(relation_dom(sK7(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_12032]) ).
tcf(c_45984,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(relation_dom(sK7(powerset(identity_relation(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_12032]) ).
tcf(c_45989,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( identity_relation(relation_dom(relation_dom(relation_dom(sK7(powerset(sK7(powerset(sK1)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_12032]) ).
tcf(c_45990,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(relation_dom(sK7(powerset(sK7(powerset(sK7(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_12032]) ).
tcf(c_45991,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(relation_dom(sK7(powerset(sK7(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_12032]) ).
tcf(c_45992,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(relation_dom(sK7(powerset(sK7(powerset(sK7(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_12032]) ).
tcf(c_45993,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(relation_dom(sK7(powerset(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_12032]) ).
tcf(c_45995,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(relation_dom(sK7(powerset(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_12032]) ).
tcf(c_46223,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( identity_relation(identity_relation(relation_dom(relation_dom(sK7(powerset(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10348,c_12068]) ).
tcf(c_46224,plain,
! [X0: $i] :
( ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ( identity_relation(identity_relation(relation_dom(relation_dom(sK7(powerset(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_12068]) ).
tcf(c_46225,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( identity_relation(identity_relation(relation_dom(relation_dom(sK7(powerset(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_12068]) ).
tcf(c_46226,plain,
identity_relation(identity_relation(relation_dom(relation_dom(sK7(powerset(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_12068]) ).
tcf(c_46227,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(relation_dom(sK7(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_12068]) ).
tcf(c_46228,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(relation_dom(sK7(powerset(identity_relation(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_12068]) ).
tcf(c_46233,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( identity_relation(identity_relation(relation_dom(relation_dom(sK7(powerset(sK7(powerset(sK1)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_12068]) ).
tcf(c_46234,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(relation_dom(sK7(powerset(sK7(powerset(sK7(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_12068]) ).
tcf(c_46235,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(relation_dom(sK7(powerset(sK7(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_12068]) ).
tcf(c_46236,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(relation_dom(sK7(powerset(sK7(powerset(sK7(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_12068]) ).
tcf(c_46237,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(relation_dom(sK7(powerset(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_12068]) ).
tcf(c_46239,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(relation_dom(sK7(powerset(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_12068]) ).
tcf(c_46406,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( sK7(powerset(relation_dom(relation_dom(sK7(powerset(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10348,c_12104]) ).
tcf(c_46407,plain,
! [X0: $i] :
( ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ( sK7(powerset(relation_dom(relation_dom(sK7(powerset(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_12104]) ).
tcf(c_46408,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( sK7(powerset(relation_dom(relation_dom(sK7(powerset(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_12104]) ).
tcf(c_46409,plain,
sK7(powerset(relation_dom(relation_dom(sK7(powerset(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_12104]) ).
tcf(c_46410,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(relation_dom(sK7(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_12104]) ).
tcf(c_46411,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(relation_dom(sK7(powerset(identity_relation(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_12104]) ).
tcf(c_46416,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( sK7(powerset(relation_dom(relation_dom(sK7(powerset(sK7(powerset(sK1)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_12104]) ).
tcf(c_46417,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(relation_dom(sK7(powerset(sK7(powerset(sK7(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_12104]) ).
tcf(c_46418,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(relation_dom(sK7(powerset(sK7(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_12104]) ).
tcf(c_46419,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(relation_dom(sK7(powerset(sK7(powerset(sK7(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_12104]) ).
tcf(c_46420,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(relation_dom(sK7(powerset(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_12104]) ).
tcf(c_46422,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(relation_dom(sK7(powerset(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_12104]) ).
tcf(c_46568,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( identity_relation(relation_dom(sK7(powerset(sK7(powerset(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10348,c_12140]) ).
tcf(c_46569,plain,
! [X0: $i] :
( ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ( identity_relation(relation_dom(sK7(powerset(sK7(powerset(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_12140]) ).
tcf(c_46570,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( identity_relation(relation_dom(sK7(powerset(sK7(powerset(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_12140]) ).
tcf(c_46571,plain,
identity_relation(relation_dom(sK7(powerset(sK7(powerset(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_12140]) ).
tcf(c_46572,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(powerset(sK7(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_12140]) ).
tcf(c_46573,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(powerset(sK7(powerset(identity_relation(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_12140]) ).
tcf(c_46578,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( identity_relation(relation_dom(sK7(powerset(sK7(powerset(sK7(powerset(sK1)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_12140]) ).
tcf(c_46579,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(powerset(sK7(powerset(sK7(powerset(sK7(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_12140]) ).
tcf(c_46580,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(powerset(sK7(powerset(sK7(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_12140]) ).
tcf(c_46581,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(powerset(sK7(powerset(sK7(powerset(sK7(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_12140]) ).
tcf(c_46582,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(powerset(sK7(powerset(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_12140]) ).
tcf(c_46584,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(powerset(sK7(powerset(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_12140]) ).
tcf(c_46623,plain,
( ( apply(empty_set,sK7(empty_set)) = sK7(empty_set) )
| ( identity_relation(relation_dom(relation_dom(relation_dom(empty_set)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_6104,c_12025]) ).
tcf(c_46624,plain,
( ( apply(identity_relation(powerset(empty_set)),empty_set) = empty_set )
| ( identity_relation(relation_dom(relation_dom(relation_dom(powerset(empty_set))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8004,c_12025]) ).
tcf(c_46627,plain,
( ( apply(identity_relation(sK6(sK6(sK6(powerset(empty_set))))),empty_set) = empty_set )
| ( identity_relation(relation_dom(relation_dom(relation_dom(sK6(sK6(sK6(powerset(empty_set)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_37341,c_12025]) ).
tcf(c_46628,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(identity_relation(X0),X1) = X2 )
| ( identity_relation(relation_dom(relation_dom(relation_dom(X0)))) = empty_set )
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),relation_dom(identity_relation(X0)))
| ~ in(sK2(identity_relation(X0),X1,X2),X2)
| ( sK2(identity_relation(X0),X1,X2) != sK7(X0) ) ),
inference(superposition,[status(thm)],[c_12025,c_53]) ).
tcf(c_46629,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0),relation_image(identity_relation(X0),X1))
| ( identity_relation(relation_dom(relation_dom(relation_dom(X0)))) = empty_set )
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),relation_dom(identity_relation(X0))) ),
inference(superposition,[status(thm)],[c_12025,c_57]) ).
tcf(c_46633,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0),relation_image(identity_relation(X0),X1))
| ( identity_relation(relation_dom(relation_dom(relation_dom(X0)))) = empty_set )
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),X0) ),
inference(light_normalisation,[status(thm)],[c_46629,c_121]) ).
tcf(c_46634,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0),relation_image(identity_relation(X0),X1))
| ( identity_relation(relation_dom(relation_dom(relation_dom(X0)))) = empty_set )
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_46633,c_62,c_63]) ).
tcf(c_46639,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(identity_relation(X0),X1) = X2 )
| ( identity_relation(relation_dom(relation_dom(relation_dom(X0)))) = empty_set )
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),X0)
| ~ in(sK2(identity_relation(X0),X1,X2),X2)
| ( sK2(identity_relation(X0),X1,X2) != sK7(X0) ) ),
inference(light_normalisation,[status(thm)],[c_46628,c_121]) ).
tcf(c_46640,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(identity_relation(X0),X1) = X2 )
| ( identity_relation(relation_dom(relation_dom(relation_dom(X0)))) = empty_set )
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),X0)
| ~ in(sK2(identity_relation(X0),X1,X2),X2)
| ( sK2(identity_relation(X0),X1,X2) != sK7(X0) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_46639,c_62,c_63]) ).
tcf(c_46669,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( identity_relation(identity_relation(identity_relation(identity_relation(identity_relation(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10348,c_31142]) ).
tcf(c_46670,plain,
! [X0: $i] :
( ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ( identity_relation(identity_relation(identity_relation(identity_relation(identity_relation(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_31142]) ).
tcf(c_46671,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( identity_relation(identity_relation(identity_relation(identity_relation(identity_relation(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_31142]) ).
tcf(c_46672,plain,
identity_relation(identity_relation(identity_relation(identity_relation(identity_relation(relation_dom(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_31142]) ).
tcf(c_46673,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(identity_relation(relation_dom(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_31142]) ).
tcf(c_46674,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(identity_relation(relation_dom(identity_relation(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_31142]) ).
tcf(c_46675,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(identity_relation(relation_dom(sK7(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_31142]) ).
tcf(c_46676,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(identity_relation(relation_dom(sK7(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_31142]) ).
tcf(c_46677,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(identity_relation(relation_dom(sK7(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_31142]) ).
tcf(c_46678,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(identity_relation(relation_dom(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_31142]) ).
tcf(c_46679,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( identity_relation(identity_relation(identity_relation(identity_relation(identity_relation(relation_dom(sK7(powerset(sK1)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_31142]) ).
tcf(c_46680,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(identity_relation(relation_dom(sK7(powerset(sK7(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_31142]) ).
tcf(c_46681,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(identity_relation(relation_dom(sK7(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_31142]) ).
tcf(c_46682,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(identity_relation(relation_dom(sK7(powerset(sK7(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_31142]) ).
tcf(c_46683,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(identity_relation(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_31142]) ).
tcf(c_46684,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(identity_relation(relation_dom(sK7(sK6(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_31142]) ).
tcf(c_46685,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(identity_relation(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_31142]) ).
tcf(c_46826,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( sK7(powerset(identity_relation(identity_relation(identity_relation(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10348,c_31222]) ).
tcf(c_46827,plain,
! [X0: $i] :
( ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ( sK7(powerset(identity_relation(identity_relation(identity_relation(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_31222]) ).
tcf(c_46828,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( sK7(powerset(identity_relation(identity_relation(identity_relation(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_31222]) ).
tcf(c_46829,plain,
sK7(powerset(identity_relation(identity_relation(identity_relation(relation_dom(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_31222]) ).
tcf(c_46830,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(identity_relation(identity_relation(relation_dom(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_31222]) ).
tcf(c_46831,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(identity_relation(identity_relation(relation_dom(identity_relation(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_31222]) ).
tcf(c_46832,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(identity_relation(identity_relation(relation_dom(sK7(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_31222]) ).
tcf(c_46833,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(identity_relation(identity_relation(relation_dom(sK7(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_31222]) ).
tcf(c_46834,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(identity_relation(identity_relation(relation_dom(sK7(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_31222]) ).
tcf(c_46835,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(identity_relation(identity_relation(relation_dom(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_31222]) ).
tcf(c_46836,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( sK7(powerset(identity_relation(identity_relation(identity_relation(relation_dom(sK7(powerset(sK1)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_31222]) ).
tcf(c_46837,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(identity_relation(identity_relation(relation_dom(sK7(powerset(sK7(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_31222]) ).
tcf(c_46838,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(identity_relation(identity_relation(relation_dom(sK7(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_31222]) ).
tcf(c_46839,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(identity_relation(identity_relation(relation_dom(sK7(powerset(sK7(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_31222]) ).
tcf(c_46840,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(identity_relation(identity_relation(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_31222]) ).
tcf(c_46841,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(identity_relation(identity_relation(relation_dom(sK7(sK6(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_31222]) ).
tcf(c_46842,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(identity_relation(identity_relation(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_31222]) ).
tcf(c_46969,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( sK7(sK6(sK6(sK6(powerset(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10348,c_37342]) ).
tcf(c_46970,plain,
! [X0: $i] :
( ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ( sK7(sK6(sK6(sK6(powerset(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_37342]) ).
tcf(c_46971,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( sK7(sK6(sK6(sK6(powerset(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_37342]) ).
tcf(c_46972,plain,
sK7(sK6(sK6(sK6(powerset(relation_dom(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_37342]) ).
tcf(c_46973,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(sK6(powerset(relation_dom(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_37342]) ).
tcf(c_46974,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(sK6(powerset(relation_dom(identity_relation(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_37342]) ).
tcf(c_46975,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(sK6(powerset(relation_dom(sK7(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_37342]) ).
tcf(c_46976,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(sK6(powerset(relation_dom(sK7(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_37342]) ).
tcf(c_46977,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(sK6(powerset(relation_dom(sK7(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_37342]) ).
tcf(c_46978,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(sK6(powerset(relation_dom(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_37342]) ).
tcf(c_46979,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( sK7(sK6(sK6(sK6(powerset(relation_dom(sK7(powerset(sK1)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_37342]) ).
tcf(c_46980,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(sK6(powerset(relation_dom(sK7(powerset(sK7(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_37342]) ).
tcf(c_46981,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(sK6(powerset(relation_dom(sK7(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_37342]) ).
tcf(c_46982,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(sK6(powerset(relation_dom(sK7(powerset(sK7(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_37342]) ).
tcf(c_46983,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(sK6(powerset(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_37342]) ).
tcf(c_46984,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(sK6(powerset(relation_dom(sK7(sK6(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_37342]) ).
tcf(c_46985,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(sK6(powerset(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_37342]) ).
tcf(c_47124,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( identity_relation(sK7(sK6(sK6(powerset(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10348,c_37664]) ).
tcf(c_47125,plain,
! [X0: $i] :
( ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ( identity_relation(sK7(sK6(sK6(powerset(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_37664]) ).
tcf(c_47126,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( identity_relation(sK7(sK6(sK6(powerset(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_37664]) ).
tcf(c_47127,plain,
identity_relation(sK7(sK6(sK6(powerset(relation_dom(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_37664]) ).
tcf(c_47128,plain,
! [X0: $i] :
( ( identity_relation(sK7(sK6(sK6(powerset(relation_dom(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_37664]) ).
tcf(c_47129,plain,
! [X0: $i] :
( ( identity_relation(sK7(sK6(sK6(powerset(relation_dom(identity_relation(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_37664]) ).
tcf(c_47130,plain,
! [X0: $i] :
( ( identity_relation(sK7(sK6(sK6(powerset(relation_dom(sK7(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_37664]) ).
tcf(c_47131,plain,
! [X0: $i] :
( ( identity_relation(sK7(sK6(sK6(powerset(relation_dom(sK7(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_37664]) ).
tcf(c_47132,plain,
! [X0: $i] :
( ( identity_relation(sK7(sK6(sK6(powerset(relation_dom(sK7(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_37664]) ).
tcf(c_47133,plain,
! [X0: $i] :
( ( identity_relation(sK7(sK6(sK6(powerset(relation_dom(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_37664]) ).
tcf(c_47134,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( identity_relation(sK7(sK6(sK6(powerset(relation_dom(sK7(powerset(sK1)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_37664]) ).
tcf(c_47135,plain,
! [X0: $i] :
( ( identity_relation(sK7(sK6(sK6(powerset(relation_dom(sK7(powerset(sK7(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_37664]) ).
tcf(c_47136,plain,
! [X0: $i] :
( ( identity_relation(sK7(sK6(sK6(powerset(relation_dom(sK7(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_37664]) ).
tcf(c_47137,plain,
! [X0: $i] :
( ( identity_relation(sK7(sK6(sK6(powerset(relation_dom(sK7(powerset(sK7(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_37664]) ).
tcf(c_47138,plain,
! [X0: $i] :
( ( identity_relation(sK7(sK6(sK6(powerset(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_37664]) ).
tcf(c_47139,plain,
! [X0: $i] :
( ( identity_relation(sK7(sK6(sK6(powerset(relation_dom(sK7(sK6(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_37664]) ).
tcf(c_47140,plain,
! [X0: $i] :
( ( identity_relation(sK7(sK6(sK6(powerset(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_37664]) ).
tcf(c_47338,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( identity_relation(identity_relation(sK7(powerset(sK7(powerset(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10348,c_12217]) ).
tcf(c_47339,plain,
! [X0: $i] :
( ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ( identity_relation(identity_relation(sK7(powerset(sK7(powerset(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_12217]) ).
tcf(c_47340,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( identity_relation(identity_relation(sK7(powerset(sK7(powerset(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_12217]) ).
tcf(c_47341,plain,
identity_relation(identity_relation(sK7(powerset(sK7(powerset(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_12217]) ).
tcf(c_47342,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(powerset(sK7(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_12217]) ).
tcf(c_47343,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(powerset(sK7(powerset(identity_relation(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_12217]) ).
tcf(c_47348,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( identity_relation(identity_relation(sK7(powerset(sK7(powerset(sK7(powerset(sK1)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_12217]) ).
tcf(c_47349,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(powerset(sK7(powerset(sK7(powerset(sK7(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_12217]) ).
tcf(c_47350,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(powerset(sK7(powerset(sK7(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_12217]) ).
tcf(c_47351,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(powerset(sK7(powerset(sK7(powerset(sK7(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_12217]) ).
tcf(c_47352,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(powerset(sK7(powerset(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_12217]) ).
tcf(c_47354,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(powerset(sK7(powerset(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_12217]) ).
tcf(c_47688,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( sK7(powerset(sK7(powerset(sK7(powerset(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10348,c_12323]) ).
tcf(c_47689,plain,
! [X0: $i] :
( ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ( sK7(powerset(sK7(powerset(sK7(powerset(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_12323]) ).
tcf(c_47690,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( sK7(powerset(sK7(powerset(sK7(powerset(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_12323]) ).
tcf(c_47691,plain,
sK7(powerset(sK7(powerset(sK7(powerset(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_12323]) ).
tcf(c_47692,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(powerset(sK7(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_12323]) ).
tcf(c_47693,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(powerset(sK7(powerset(identity_relation(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_12323]) ).
tcf(c_47698,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( sK7(powerset(sK7(powerset(sK7(powerset(sK7(powerset(sK1)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_12323]) ).
tcf(c_47699,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(powerset(sK7(powerset(sK7(powerset(sK7(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_12323]) ).
tcf(c_47700,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(powerset(sK7(powerset(sK7(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_12323]) ).
tcf(c_47701,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(powerset(sK7(powerset(sK7(powerset(sK7(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_12323]) ).
tcf(c_47702,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(powerset(sK7(powerset(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_12323]) ).
tcf(c_47704,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(powerset(sK7(powerset(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_12323]) ).
tcf(c_47816,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( identity_relation(sK7(powerset(relation_dom(sK7(powerset(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10348,c_12361]) ).
tcf(c_47817,plain,
! [X0: $i] :
( ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ( identity_relation(sK7(powerset(relation_dom(sK7(powerset(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_12361]) ).
tcf(c_47818,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( identity_relation(sK7(powerset(relation_dom(sK7(powerset(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_12361]) ).
tcf(c_47819,plain,
identity_relation(sK7(powerset(relation_dom(sK7(powerset(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_12361]) ).
tcf(c_47820,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(relation_dom(sK7(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_12361]) ).
tcf(c_47821,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(relation_dom(sK7(powerset(identity_relation(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_12361]) ).
tcf(c_47826,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( identity_relation(sK7(powerset(relation_dom(sK7(powerset(sK7(powerset(sK1)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_12361]) ).
tcf(c_47827,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(relation_dom(sK7(powerset(sK7(powerset(sK7(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_12361]) ).
tcf(c_47828,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(relation_dom(sK7(powerset(sK7(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_12361]) ).
tcf(c_47829,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(relation_dom(sK7(powerset(sK7(powerset(sK7(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_12361]) ).
tcf(c_47830,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(relation_dom(sK7(powerset(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_12361]) ).
tcf(c_47832,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(relation_dom(sK7(powerset(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_12361]) ).
tcf(c_48059,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( relation_dom(sK7(powerset(relation_dom(sK7(powerset(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10348,c_12760]) ).
tcf(c_48060,plain,
! [X0: $i] :
( ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ( relation_dom(sK7(powerset(relation_dom(sK7(powerset(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_12760]) ).
tcf(c_48061,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( relation_dom(sK7(powerset(relation_dom(sK7(powerset(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_12760]) ).
tcf(c_48062,plain,
relation_dom(sK7(powerset(relation_dom(sK7(powerset(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_12760]) ).
tcf(c_48063,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(relation_dom(sK7(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_12760]) ).
tcf(c_48064,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(relation_dom(sK7(powerset(identity_relation(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_12760]) ).
tcf(c_48069,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( relation_dom(sK7(powerset(relation_dom(sK7(powerset(sK7(powerset(sK1)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_12760]) ).
tcf(c_48070,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(relation_dom(sK7(powerset(sK7(powerset(sK7(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_12760]) ).
tcf(c_48071,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(relation_dom(sK7(powerset(sK7(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_12760]) ).
tcf(c_48072,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(relation_dom(sK7(powerset(sK7(powerset(sK7(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_12760]) ).
tcf(c_48073,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(relation_dom(sK7(powerset(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_12760]) ).
tcf(c_48075,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(relation_dom(sK7(powerset(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_12760]) ).
tcf(c_48141,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( relation_dom(sK7(sK6(sK6(powerset(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10348,c_37780]) ).
tcf(c_48142,plain,
! [X0: $i] :
( ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ( relation_dom(sK7(sK6(sK6(powerset(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_37780]) ).
tcf(c_48143,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( relation_dom(sK7(sK6(sK6(powerset(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_37780]) ).
tcf(c_48144,plain,
relation_dom(sK7(sK6(sK6(powerset(relation_dom(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_37780]) ).
tcf(c_48145,plain,
! [X0: $i] :
( ( relation_dom(sK7(sK6(sK6(powerset(relation_dom(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_37780]) ).
tcf(c_48146,plain,
! [X0: $i] :
( ( relation_dom(sK7(sK6(sK6(powerset(relation_dom(identity_relation(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_37780]) ).
tcf(c_48147,plain,
! [X0: $i] :
( ( relation_dom(sK7(sK6(sK6(powerset(relation_dom(sK7(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_37780]) ).
tcf(c_48148,plain,
! [X0: $i] :
( ( relation_dom(sK7(sK6(sK6(powerset(relation_dom(sK7(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_37780]) ).
tcf(c_48149,plain,
! [X0: $i] :
( ( relation_dom(sK7(sK6(sK6(powerset(relation_dom(sK7(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_37780]) ).
tcf(c_48150,plain,
! [X0: $i] :
( ( relation_dom(sK7(sK6(sK6(powerset(relation_dom(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_37780]) ).
tcf(c_48151,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( relation_dom(sK7(sK6(sK6(powerset(relation_dom(sK7(powerset(sK1)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_37780]) ).
tcf(c_48152,plain,
! [X0: $i] :
( ( relation_dom(sK7(sK6(sK6(powerset(relation_dom(sK7(powerset(sK7(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_37780]) ).
tcf(c_48153,plain,
! [X0: $i] :
( ( relation_dom(sK7(sK6(sK6(powerset(relation_dom(sK7(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_37780]) ).
tcf(c_48154,plain,
! [X0: $i] :
( ( relation_dom(sK7(sK6(sK6(powerset(relation_dom(sK7(powerset(sK7(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_37780]) ).
tcf(c_48155,plain,
! [X0: $i] :
( ( relation_dom(sK7(sK6(sK6(powerset(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_37780]) ).
tcf(c_48156,plain,
! [X0: $i] :
( ( relation_dom(sK7(sK6(sK6(powerset(relation_dom(sK7(sK6(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_37780]) ).
tcf(c_48157,plain,
! [X0: $i] :
( ( relation_dom(sK7(sK6(sK6(powerset(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_37780]) ).
tcf(c_48250,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( sK7(sK6(sK6(powerset(identity_relation(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10348,c_37889]) ).
tcf(c_48251,plain,
! [X0: $i] :
( ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ( sK7(sK6(sK6(powerset(identity_relation(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_37889]) ).
tcf(c_48252,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( sK7(sK6(sK6(powerset(identity_relation(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_37889]) ).
tcf(c_48253,plain,
sK7(sK6(sK6(powerset(identity_relation(relation_dom(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_37889]) ).
tcf(c_48254,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(powerset(identity_relation(relation_dom(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_37889]) ).
tcf(c_48255,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(powerset(identity_relation(relation_dom(identity_relation(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_37889]) ).
tcf(c_48256,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(powerset(identity_relation(relation_dom(sK7(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_37889]) ).
tcf(c_48257,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(powerset(identity_relation(relation_dom(sK7(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_37889]) ).
tcf(c_48258,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(powerset(identity_relation(relation_dom(sK7(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_37889]) ).
tcf(c_48259,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(powerset(identity_relation(relation_dom(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_37889]) ).
tcf(c_48260,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( sK7(sK6(sK6(powerset(identity_relation(relation_dom(sK7(powerset(sK1)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_37889]) ).
tcf(c_48261,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(powerset(identity_relation(relation_dom(sK7(powerset(sK7(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_37889]) ).
tcf(c_48262,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(powerset(identity_relation(relation_dom(sK7(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_37889]) ).
tcf(c_48263,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(powerset(identity_relation(relation_dom(sK7(powerset(sK7(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_37889]) ).
tcf(c_48264,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(powerset(identity_relation(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_37889]) ).
tcf(c_48265,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(powerset(identity_relation(relation_dom(sK7(sK6(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_37889]) ).
tcf(c_48266,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(powerset(identity_relation(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_37889]) ).
tcf(c_48436,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( identity_relation(sK7(sK6(powerset(identity_relation(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10348,c_37969]) ).
tcf(c_48437,plain,
! [X0: $i] :
( ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ( identity_relation(sK7(sK6(powerset(identity_relation(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_37969]) ).
tcf(c_48438,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( identity_relation(sK7(sK6(powerset(identity_relation(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_37969]) ).
tcf(c_48439,plain,
identity_relation(sK7(sK6(powerset(identity_relation(relation_dom(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_37969]) ).
tcf(c_48440,plain,
! [X0: $i] :
( ( identity_relation(sK7(sK6(powerset(identity_relation(relation_dom(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_37969]) ).
tcf(c_48441,plain,
! [X0: $i] :
( ( identity_relation(sK7(sK6(powerset(identity_relation(relation_dom(identity_relation(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_37969]) ).
tcf(c_48442,plain,
! [X0: $i] :
( ( identity_relation(sK7(sK6(powerset(identity_relation(relation_dom(sK7(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_37969]) ).
tcf(c_48443,plain,
! [X0: $i] :
( ( identity_relation(sK7(sK6(powerset(identity_relation(relation_dom(sK7(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_37969]) ).
tcf(c_48444,plain,
! [X0: $i] :
( ( identity_relation(sK7(sK6(powerset(identity_relation(relation_dom(sK7(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_37969]) ).
tcf(c_48445,plain,
! [X0: $i] :
( ( identity_relation(sK7(sK6(powerset(identity_relation(relation_dom(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_37969]) ).
tcf(c_48446,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( identity_relation(sK7(sK6(powerset(identity_relation(relation_dom(sK7(powerset(sK1)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_37969]) ).
tcf(c_48447,plain,
! [X0: $i] :
( ( identity_relation(sK7(sK6(powerset(identity_relation(relation_dom(sK7(powerset(sK7(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_37969]) ).
tcf(c_48448,plain,
! [X0: $i] :
( ( identity_relation(sK7(sK6(powerset(identity_relation(relation_dom(sK7(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_37969]) ).
tcf(c_48449,plain,
! [X0: $i] :
( ( identity_relation(sK7(sK6(powerset(identity_relation(relation_dom(sK7(powerset(sK7(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_37969]) ).
tcf(c_48450,plain,
! [X0: $i] :
( ( identity_relation(sK7(sK6(powerset(identity_relation(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_37969]) ).
tcf(c_48451,plain,
! [X0: $i] :
( ( identity_relation(sK7(sK6(powerset(identity_relation(relation_dom(sK7(sK6(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_37969]) ).
tcf(c_48452,plain,
! [X0: $i] :
( ( identity_relation(sK7(sK6(powerset(identity_relation(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_37969]) ).
tcf(c_48575,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( relation_dom(sK7(sK6(powerset(identity_relation(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10348,c_38682]) ).
tcf(c_48576,plain,
! [X0: $i] :
( ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ( relation_dom(sK7(sK6(powerset(identity_relation(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_38682]) ).
tcf(c_48577,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( relation_dom(sK7(sK6(powerset(identity_relation(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_38682]) ).
tcf(c_48578,plain,
relation_dom(sK7(sK6(powerset(identity_relation(relation_dom(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_38682]) ).
tcf(c_48579,plain,
! [X0: $i] :
( ( relation_dom(sK7(sK6(powerset(identity_relation(relation_dom(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_38682]) ).
tcf(c_48580,plain,
! [X0: $i] :
( ( relation_dom(sK7(sK6(powerset(identity_relation(relation_dom(identity_relation(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_38682]) ).
tcf(c_48581,plain,
! [X0: $i] :
( ( relation_dom(sK7(sK6(powerset(identity_relation(relation_dom(sK7(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_38682]) ).
tcf(c_48582,plain,
! [X0: $i] :
( ( relation_dom(sK7(sK6(powerset(identity_relation(relation_dom(sK7(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_38682]) ).
tcf(c_48583,plain,
! [X0: $i] :
( ( relation_dom(sK7(sK6(powerset(identity_relation(relation_dom(sK7(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_38682]) ).
tcf(c_48584,plain,
! [X0: $i] :
( ( relation_dom(sK7(sK6(powerset(identity_relation(relation_dom(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_38682]) ).
tcf(c_48585,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( relation_dom(sK7(sK6(powerset(identity_relation(relation_dom(sK7(powerset(sK1)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_38682]) ).
tcf(c_48586,plain,
! [X0: $i] :
( ( relation_dom(sK7(sK6(powerset(identity_relation(relation_dom(sK7(powerset(sK7(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_38682]) ).
tcf(c_48587,plain,
! [X0: $i] :
( ( relation_dom(sK7(sK6(powerset(identity_relation(relation_dom(sK7(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_38682]) ).
tcf(c_48588,plain,
! [X0: $i] :
( ( relation_dom(sK7(sK6(powerset(identity_relation(relation_dom(sK7(powerset(sK7(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_38682]) ).
tcf(c_48589,plain,
! [X0: $i] :
( ( relation_dom(sK7(sK6(powerset(identity_relation(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_38682]) ).
tcf(c_48590,plain,
! [X0: $i] :
( ( relation_dom(sK7(sK6(powerset(identity_relation(relation_dom(sK7(sK6(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_38682]) ).
tcf(c_48591,plain,
! [X0: $i] :
( ( relation_dom(sK7(sK6(powerset(identity_relation(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_38682]) ).
tcf(c_48761,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( identity_relation(sK7(powerset(identity_relation(sK7(powerset(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10348,c_12876]) ).
tcf(c_48762,plain,
! [X0: $i] :
( ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ( identity_relation(sK7(powerset(identity_relation(sK7(powerset(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_12876]) ).
tcf(c_48763,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( identity_relation(sK7(powerset(identity_relation(sK7(powerset(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_12876]) ).
tcf(c_48764,plain,
identity_relation(sK7(powerset(identity_relation(sK7(powerset(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_12876]) ).
tcf(c_48765,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(identity_relation(sK7(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_12876]) ).
tcf(c_48766,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(identity_relation(sK7(powerset(identity_relation(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_12876]) ).
tcf(c_48771,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( identity_relation(sK7(powerset(identity_relation(sK7(powerset(sK7(powerset(sK1)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_12876]) ).
tcf(c_48772,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(identity_relation(sK7(powerset(sK7(powerset(sK7(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_12876]) ).
tcf(c_48773,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(identity_relation(sK7(powerset(sK7(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_12876]) ).
tcf(c_48774,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(identity_relation(sK7(powerset(sK7(powerset(sK7(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_12876]) ).
tcf(c_48775,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(identity_relation(sK7(powerset(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_12876]) ).
tcf(c_48777,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(identity_relation(sK7(powerset(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_12876]) ).
tcf(c_48816,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( relation_dom(sK7(powerset(identity_relation(sK7(powerset(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10348,c_12914]) ).
tcf(c_48817,plain,
! [X0: $i] :
( ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ( relation_dom(sK7(powerset(identity_relation(sK7(powerset(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_12914]) ).
tcf(c_48818,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( relation_dom(sK7(powerset(identity_relation(sK7(powerset(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_12914]) ).
tcf(c_48819,plain,
relation_dom(sK7(powerset(identity_relation(sK7(powerset(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_12914]) ).
tcf(c_48820,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(identity_relation(sK7(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_12914]) ).
tcf(c_48821,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(identity_relation(sK7(powerset(identity_relation(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_12914]) ).
tcf(c_48826,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( relation_dom(sK7(powerset(identity_relation(sK7(powerset(sK7(powerset(sK1)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_12914]) ).
tcf(c_48827,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(identity_relation(sK7(powerset(sK7(powerset(sK7(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_12914]) ).
tcf(c_48828,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(identity_relation(sK7(powerset(sK7(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_12914]) ).
tcf(c_48829,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(identity_relation(sK7(powerset(sK7(powerset(sK7(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_12914]) ).
tcf(c_48830,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(identity_relation(sK7(powerset(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_12914]) ).
tcf(c_48832,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(identity_relation(sK7(powerset(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_12914]) ).
tcf(c_48871,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( identity_relation(identity_relation(identity_relation(relation_dom(sK7(powerset(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10348,c_13049]) ).
tcf(c_48872,plain,
! [X0: $i] :
( ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ( identity_relation(identity_relation(identity_relation(relation_dom(sK7(powerset(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_13049]) ).
tcf(c_48873,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( identity_relation(identity_relation(identity_relation(relation_dom(sK7(powerset(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_13049]) ).
tcf(c_48874,plain,
identity_relation(identity_relation(identity_relation(relation_dom(sK7(powerset(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_13049]) ).
tcf(c_48875,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(relation_dom(sK7(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_13049]) ).
tcf(c_48876,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(relation_dom(sK7(powerset(identity_relation(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_13049]) ).
tcf(c_48881,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( identity_relation(identity_relation(identity_relation(relation_dom(sK7(powerset(sK7(powerset(sK1)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_13049]) ).
tcf(c_48882,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(relation_dom(sK7(powerset(sK7(powerset(sK7(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_13049]) ).
tcf(c_48883,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(relation_dom(sK7(powerset(sK7(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_13049]) ).
tcf(c_48884,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(relation_dom(sK7(powerset(sK7(powerset(sK7(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_13049]) ).
tcf(c_48885,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(relation_dom(sK7(powerset(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_13049]) ).
tcf(c_48887,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(relation_dom(sK7(powerset(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_13049]) ).
tcf(c_48992,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( sK7(powerset(identity_relation(relation_dom(sK7(powerset(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10348,c_13654]) ).
tcf(c_48993,plain,
! [X0: $i] :
( ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ( sK7(powerset(identity_relation(relation_dom(sK7(powerset(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_13654]) ).
tcf(c_48994,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( sK7(powerset(identity_relation(relation_dom(sK7(powerset(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_13654]) ).
tcf(c_48995,plain,
sK7(powerset(identity_relation(relation_dom(sK7(powerset(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_13654]) ).
tcf(c_48996,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(relation_dom(sK7(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_13654]) ).
tcf(c_48997,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(relation_dom(sK7(powerset(identity_relation(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_13654]) ).
tcf(c_49002,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( sK7(powerset(identity_relation(relation_dom(sK7(powerset(sK7(powerset(sK1)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_13654]) ).
tcf(c_49003,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(relation_dom(sK7(powerset(sK7(powerset(sK7(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_13654]) ).
tcf(c_49004,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(relation_dom(sK7(powerset(sK7(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_13654]) ).
tcf(c_49005,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(relation_dom(sK7(powerset(sK7(powerset(sK7(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_13654]) ).
tcf(c_49006,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(relation_dom(sK7(powerset(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_13654]) ).
tcf(c_49008,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(relation_dom(sK7(powerset(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_13654]) ).
tcf(c_49063,plain,
( ( apply(empty_set,sK7(empty_set)) = sK7(empty_set) )
| ( identity_relation(identity_relation(relation_dom(relation_dom(empty_set)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_6104,c_12061]) ).
tcf(c_49064,plain,
( ( apply(identity_relation(powerset(empty_set)),empty_set) = empty_set )
| ( identity_relation(identity_relation(relation_dom(relation_dom(powerset(empty_set))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8004,c_12061]) ).
tcf(c_49067,plain,
( ( apply(identity_relation(sK6(sK6(sK6(powerset(empty_set))))),empty_set) = empty_set )
| ( identity_relation(identity_relation(relation_dom(relation_dom(sK6(sK6(sK6(powerset(empty_set)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_37341,c_12061]) ).
tcf(c_49068,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(identity_relation(X0),X1) = X2 )
| ( identity_relation(identity_relation(relation_dom(relation_dom(X0)))) = empty_set )
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),relation_dom(identity_relation(X0)))
| ~ in(sK2(identity_relation(X0),X1,X2),X2)
| ( sK2(identity_relation(X0),X1,X2) != sK7(X0) ) ),
inference(superposition,[status(thm)],[c_12061,c_53]) ).
tcf(c_49069,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0),relation_image(identity_relation(X0),X1))
| ( identity_relation(identity_relation(relation_dom(relation_dom(X0)))) = empty_set )
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),relation_dom(identity_relation(X0))) ),
inference(superposition,[status(thm)],[c_12061,c_57]) ).
tcf(c_49073,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0),relation_image(identity_relation(X0),X1))
| ( identity_relation(identity_relation(relation_dom(relation_dom(X0)))) = empty_set )
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),X0) ),
inference(light_normalisation,[status(thm)],[c_49069,c_121]) ).
tcf(c_49074,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0),relation_image(identity_relation(X0),X1))
| ( identity_relation(identity_relation(relation_dom(relation_dom(X0)))) = empty_set )
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_49073,c_62,c_63]) ).
tcf(c_49079,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(identity_relation(X0),X1) = X2 )
| ( identity_relation(identity_relation(relation_dom(relation_dom(X0)))) = empty_set )
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),X0)
| ~ in(sK2(identity_relation(X0),X1,X2),X2)
| ( sK2(identity_relation(X0),X1,X2) != sK7(X0) ) ),
inference(light_normalisation,[status(thm)],[c_49068,c_121]) ).
tcf(c_49080,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(identity_relation(X0),X1) = X2 )
| ( identity_relation(identity_relation(relation_dom(relation_dom(X0)))) = empty_set )
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),X0)
| ~ in(sK2(identity_relation(X0),X1,X2),X2)
| ( sK2(identity_relation(X0),X1,X2) != sK7(X0) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_49079,c_62,c_63]) ).
tcf(c_49092,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( sK7(sK6(powerset(identity_relation(identity_relation(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10348,c_39551]) ).
tcf(c_49093,plain,
! [X0: $i] :
( ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ( sK7(sK6(powerset(identity_relation(identity_relation(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_39551]) ).
tcf(c_49094,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( sK7(sK6(powerset(identity_relation(identity_relation(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_39551]) ).
tcf(c_49095,plain,
sK7(sK6(powerset(identity_relation(identity_relation(relation_dom(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_39551]) ).
tcf(c_49096,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(identity_relation(identity_relation(relation_dom(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_39551]) ).
tcf(c_49097,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(identity_relation(identity_relation(relation_dom(identity_relation(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_39551]) ).
tcf(c_49098,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(identity_relation(identity_relation(relation_dom(sK7(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_39551]) ).
tcf(c_49099,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(identity_relation(identity_relation(relation_dom(sK7(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_39551]) ).
tcf(c_49100,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(identity_relation(identity_relation(relation_dom(sK7(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_39551]) ).
tcf(c_49101,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(identity_relation(identity_relation(relation_dom(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_39551]) ).
tcf(c_49102,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( sK7(sK6(powerset(identity_relation(identity_relation(relation_dom(sK7(powerset(sK1)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_39551]) ).
tcf(c_49103,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(identity_relation(identity_relation(relation_dom(sK7(powerset(sK7(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_39551]) ).
tcf(c_49104,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(identity_relation(identity_relation(relation_dom(sK7(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_39551]) ).
tcf(c_49105,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(identity_relation(identity_relation(relation_dom(sK7(powerset(sK7(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_39551]) ).
tcf(c_49106,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(identity_relation(identity_relation(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_39551]) ).
tcf(c_49107,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(identity_relation(identity_relation(relation_dom(sK7(sK6(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_39551]) ).
tcf(c_49108,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(identity_relation(identity_relation(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_39551]) ).
tcf(c_49157,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(identity_relation(sK0),X0) = X1 )
| ~ function(identity_relation(sK0))
| ~ relation(identity_relation(sK0))
| ~ in(sK2(empty_set,X2,sK1),X0)
| ~ in(sK2(identity_relation(sK0),X0,X1),X1)
| ~ in(sK2(empty_set,X2,sK1),relation_dom(identity_relation(sK0)))
| ( sK2(identity_relation(sK0),X0,X1) != sK2(empty_set,X2,sK1) ) ),
inference(superposition,[status(thm)],[c_42454,c_53]) ).
tcf(c_49158,plain,
! [X0: $i,X1: $i] :
( in(sK2(empty_set,X0,sK1),relation_image(identity_relation(sK0),X1))
| ~ function(identity_relation(sK0))
| ~ relation(identity_relation(sK0))
| ~ in(sK2(empty_set,X0,sK1),X1)
| ~ in(sK2(empty_set,X0,sK1),relation_dom(identity_relation(sK0))) ),
inference(superposition,[status(thm)],[c_42454,c_57]) ).
tcf(c_49159,plain,
! [X0: $i,X1: $i] :
( in(sK2(empty_set,X0,sK1),relation_image(identity_relation(sK0),X1))
| ~ in(sK2(empty_set,X0,sK1),X1)
| ~ in(sK2(empty_set,X0,sK1),relation_dom(identity_relation(sK0))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_49158,c_62,c_63]) ).
tcf(c_49163,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(identity_relation(sK0),X0) = X1 )
| ~ in(sK2(empty_set,X2,sK1),X0)
| ~ in(sK2(identity_relation(sK0),X0,X1),X1)
| ~ in(sK2(empty_set,X2,sK1),relation_dom(identity_relation(sK0)))
| ( sK2(identity_relation(sK0),X0,X1) != sK2(empty_set,X2,sK1) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_49157,c_62,c_63]) ).
tcf(c_49175,plain,
! [X0: $i,X1: $i] :
( in(sK4(empty_set,X1,X0),empty_set)
| ~ in(X0,relation_image(identity_relation(empty_set),X1)) ),
inference(superposition,[status(thm)],[c_6104,c_6013]) ).
tcf(c_49176,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( apply(X1,sK4(X1,X2,sK4(identity_relation(relation_image(X1,X2)),X3,X0))) = sK4(identity_relation(relation_image(X1,X2)),X3,X0) )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(identity_relation(relation_image(X1,X2)),X3)) ),
inference(superposition,[status(thm)],[c_6013,c_60]) ).
tcf(c_49177,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(identity_relation(X1),sK4(identity_relation(X1),X2,X0)) = sK4(identity_relation(X1),X2,X0) )
| ~ in(X0,relation_image(identity_relation(X1),X2)) ),
inference(superposition,[status(thm)],[c_6013,c_151]) ).
tcf(c_49178,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(X2,relation_image(identity_relation(X0),X1))
| ~ in(X0,sK4(identity_relation(X0),X1,X2)) ),
inference(superposition,[status(thm)],[c_6013,c_85]) ).
tcf(c_49179,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(X1)
| ~ in(X0,relation_image(identity_relation(X1),X2)) ),
inference(superposition,[status(thm)],[c_6013,c_84]) ).
tcf(c_49180,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK4(identity_relation(X1),X2,X0),X1)
| ~ in(X0,relation_image(identity_relation(X1),X2)) ),
inference(superposition,[status(thm)],[c_6013,c_72]) ).
tcf(c_49181,plain,
! [X0: $i,X1: $i] :
( element(sK4(identity_relation(sK1),X1,X0),sK0)
| ~ in(X0,relation_image(identity_relation(sK1),X1)) ),
inference(superposition,[status(thm)],[c_6013,c_5838]) ).
tcf(c_49182,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X1)
| element(sK4(identity_relation(sK6(X1)),X2,X0),X1)
| ~ in(X0,relation_image(identity_relation(sK6(X1)),X2)) ),
inference(superposition,[status(thm)],[c_6013,c_5839]) ).
tcf(c_49183,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK4(identity_relation(sK7(powerset(X1))),X2,X0),X1)
| ~ in(X0,relation_image(identity_relation(sK7(powerset(X1))),X2)) ),
inference(superposition,[status(thm)],[c_6013,c_5840]) ).
tcf(c_49184,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(X1)
| ~ in(X0,relation_image(identity_relation(sK7(powerset(X1))),X2)) ),
inference(superposition,[status(thm)],[c_6013,c_5822]) ).
tcf(c_49185,plain,
! [X0: $i,X1: $i] : ~ in(X0,relation_image(identity_relation(empty_set),X1)),
inference(superposition,[status(thm)],[c_6013,c_8375]) ).
tcf(c_49186,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(identity_relation(relation_image(X1,empty_set)),X2)) ),
inference(superposition,[status(thm)],[c_6013,c_8512]) ).
tcf(c_49187,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK4(identity_relation(sK7(sK6(powerset(X1)))),X2,X0),X1)
| ~ in(X0,relation_image(identity_relation(sK7(sK6(powerset(X1)))),X2)) ),
inference(superposition,[status(thm)],[c_6013,c_9820]) ).
tcf(c_49188,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(X1)
| ~ in(X0,relation_image(identity_relation(sK7(sK6(powerset(X1)))),X2)) ),
inference(superposition,[status(thm)],[c_6013,c_9817]) ).
tcf(c_49189,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK4(identity_relation(sK7(sK6(sK6(powerset(X1))))),X2,X0),X1)
| ~ in(X0,relation_image(identity_relation(sK7(sK6(sK6(powerset(X1))))),X2)) ),
inference(superposition,[status(thm)],[c_6013,c_14092]) ).
tcf(c_49190,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(X1)
| ~ in(X0,relation_image(identity_relation(sK7(sK6(sK6(powerset(X1))))),X2)) ),
inference(superposition,[status(thm)],[c_6013,c_14089]) ).
tcf(c_49191,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK4(identity_relation(sK7(sK6(sK6(sK6(powerset(X1)))))),X2,X0),X1)
| ~ in(X0,relation_image(identity_relation(sK7(sK6(sK6(sK6(powerset(X1)))))),X2)) ),
inference(superposition,[status(thm)],[c_6013,c_35584]) ).
tcf(c_49192,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(X1)
| ~ in(X0,relation_image(identity_relation(sK7(sK6(sK6(sK6(powerset(X1)))))),X2)) ),
inference(superposition,[status(thm)],[c_6013,c_35581]) ).
tcf(c_49307,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(identity_relation(X0),X3) = relation_image(X1,X2) )
| ( apply(X1,sK3(X1,X2,relation_image(identity_relation(X0),X3))) = sK2(X1,X2,relation_image(identity_relation(X0),X3)) )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_56,c_49179]) ).
tcf(c_49308,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK3(X1,X3,relation_image(identity_relation(X0),X2)),relation_dom(X1))
| ( relation_image(identity_relation(X0),X2) = relation_image(X1,X3) )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_54,c_49179]) ).
tcf(c_49309,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK3(X1,X3,relation_image(identity_relation(X0),X2)),X3)
| ( relation_image(identity_relation(X0),X2) = relation_image(X1,X3) )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_55,c_49179]) ).
tcf(c_49310,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,relation_image(identity_relation(X0),X2),X3),X3)
| ( relation_image(X1,relation_image(identity_relation(X0),X2)) = X3 )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_55,c_49179]) ).
tcf(c_49311,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(X1)
| ~ function(identity_relation(X1))
| ~ relation(identity_relation(X1))
| ~ in(X0,X2)
| ~ in(X0,relation_dom(identity_relation(X1))) ),
inference(superposition,[status(thm)],[c_57,c_49179]) ).
tcf(c_49312,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ function(X1)
| ~ relation(X1)
| ~ empty(X2)
| ~ in(X0,relation_image(X1,relation_image(identity_relation(X2),X3))) ),
inference(superposition,[status(thm)],[c_59,c_49179]) ).
tcf(c_49314,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ empty(X1)
| ~ in(X0,relation_image(identity_relation(relation_image(identity_relation(X1),X2)),X3)) ),
inference(superposition,[status(thm)],[c_6013,c_49179]) ).
tcf(c_49315,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(X1,sK1,relation_image(identity_relation(X0),X2)),sK0)
| ( relation_image(identity_relation(X0),X2) = relation_image(X1,sK1) )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11821,c_49179]) ).
tcf(c_49316,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK3(X1,sK1,relation_image(identity_relation(X0),X2)),sK0)
| ( relation_image(identity_relation(X0),X2) = relation_image(X1,sK1) )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6475,c_49179]) ).
tcf(c_49317,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,relation_image(identity_relation(X0),X2),sK1),sK0)
| ( relation_image(X1,relation_image(identity_relation(X0),X2)) = sK1 )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12513,c_49179]) ).
tcf(c_49318,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X1,relation_image(identity_relation(X0),X2),sK1),sK0)
| ( relation_image(X1,relation_image(identity_relation(X0),X2)) = sK1 )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6486,c_49179]) ).
tcf(c_49322,plain,
! [X0: $i,X1: $i] :
( empty(sK7(powerset(relation_image(identity_relation(X0),X1))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25981,c_49179]) ).
tcf(c_49323,plain,
! [X0: $i,X1: $i] :
( empty(relation_image(identity_relation(X0),X1))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35578,c_49179]) ).
tcf(c_49325,plain,
! [X0: $i,X1: $i] :
( ~ empty(empty_set)
| ~ in(X0,relation_image(empty_set,X1)) ),
inference(superposition,[status(thm)],[c_6104,c_49179]) ).
tcf(c_49337,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(X1)
| ~ in(X0,X2)
| ~ in(X0,relation_dom(identity_relation(X1))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_49311,c_62,c_63]) ).
tcf(c_49483,plain,
! [X0: $i] :
( empty(relation_image(empty_set,X0))
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_6104,c_49323]) ).
tcf(c_49484,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(powerset(identity_relation(identity_relation(relation_dom(relation_image(identity_relation(X0),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_39551]) ).
tcf(c_49485,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(identity_relation(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_13654]) ).
tcf(c_49486,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(identity_relation(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_13049]) ).
tcf(c_49487,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(powerset(identity_relation(sK7(powerset(relation_image(identity_relation(X0),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_12914]) ).
tcf(c_49488,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK7(powerset(identity_relation(sK7(powerset(relation_image(identity_relation(X0),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_12876]) ).
tcf(c_49489,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(sK6(powerset(identity_relation(relation_dom(relation_image(identity_relation(X0),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_38682]) ).
tcf(c_49490,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK7(sK6(powerset(identity_relation(relation_dom(relation_image(identity_relation(X0),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_37969]) ).
tcf(c_49491,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(sK6(powerset(identity_relation(relation_dom(relation_image(identity_relation(X0),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_37889]) ).
tcf(c_49492,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(sK6(sK6(powerset(relation_dom(relation_image(identity_relation(X0),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_37780]) ).
tcf(c_49493,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(powerset(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_12760]) ).
tcf(c_49494,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK7(powerset(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_12361]) ).
tcf(c_49495,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(sK7(powerset(sK7(powerset(relation_image(identity_relation(X0),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_12323]) ).
tcf(c_49496,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(sK7(powerset(sK7(powerset(relation_image(identity_relation(X0),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_12217]) ).
tcf(c_49497,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK7(sK6(sK6(powerset(relation_dom(relation_image(identity_relation(X0),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_37664]) ).
tcf(c_49498,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(sK6(sK6(powerset(relation_dom(relation_image(identity_relation(X0),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_37342]) ).
tcf(c_49499,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(identity_relation(identity_relation(identity_relation(relation_dom(relation_image(identity_relation(X0),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_31222]) ).
tcf(c_49500,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(identity_relation(relation_dom(relation_image(identity_relation(X0),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_31142]) ).
tcf(c_49501,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(sK7(powerset(sK7(powerset(relation_image(identity_relation(X0),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_12140]) ).
tcf(c_49502,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(relation_dom(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_12104]) ).
tcf(c_49503,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(relation_dom(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_12068]) ).
tcf(c_49504,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(relation_dom(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_12032]) ).
tcf(c_49505,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(powerset(identity_relation(identity_relation(relation_dom(relation_image(identity_relation(X0),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_31014]) ).
tcf(c_49506,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK7(powerset(identity_relation(identity_relation(relation_dom(relation_image(identity_relation(X0),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_30942]) ).
tcf(c_49507,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(sK7(powerset(identity_relation(relation_dom(relation_image(identity_relation(X0),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_30355]) ).
tcf(c_49508,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(sK7(powerset(identity_relation(relation_dom(relation_image(identity_relation(X0),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_30248]) ).
tcf(c_49509,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_11958]) ).
tcf(c_49510,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK7(powerset(sK7(powerset(relation_image(identity_relation(X0),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_11436]) ).
tcf(c_49511,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(powerset(sK7(sK6(powerset(relation_image(identity_relation(X0),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_11346]) ).
tcf(c_49512,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(sK7(sK6(powerset(relation_image(identity_relation(X0),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_10669]) ).
tcf(c_49513,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(sK7(powerset(identity_relation(relation_dom(relation_image(identity_relation(X0),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_30158]) ).
tcf(c_49514,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK7(powerset(identity_relation(relation_dom(relation_image(identity_relation(X0),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_30068]) ).
tcf(c_49515,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(powerset(sK7(powerset(relation_dom(relation_image(identity_relation(X0),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_29569]) ).
tcf(c_49516,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK7(sK6(powerset(relation_dom(relation_image(identity_relation(X0),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_29442]) ).
tcf(c_49517,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(relation_dom(sK7(sK6(powerset(relation_image(identity_relation(X0),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_10666]) ).
tcf(c_49518,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(relation_dom(sK7(sK6(powerset(relation_image(identity_relation(X0),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_10665]) ).
tcf(c_49519,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(relation_dom(sK7(sK6(powerset(relation_image(identity_relation(X0),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_10664]) ).
tcf(c_49520,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK7(powerset(sK7(sK6(powerset(relation_image(identity_relation(X0),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_10663]) ).
tcf(c_49521,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(sK7(sK6(powerset(relation_dom(relation_image(identity_relation(X0),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_29308]) ).
tcf(c_49522,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(sK7(sK6(powerset(relation_dom(relation_image(identity_relation(X0),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_29194]) ).
tcf(c_49523,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(sK7(sK6(powerset(relation_dom(relation_image(identity_relation(X0),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_28717]) ).
tcf(c_49524,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(identity_relation(sK7(powerset(relation_dom(relation_image(identity_relation(X0),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_28572]) ).
tcf(c_49525,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(powerset(sK7(sK6(powerset(relation_image(identity_relation(X0),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_10662]) ).
tcf(c_49526,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(identity_relation(sK7(sK6(powerset(relation_image(identity_relation(X0),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_10659]) ).
tcf(c_49527,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(identity_relation(sK7(powerset(relation_dom(relation_image(identity_relation(X0),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_28429]) ).
tcf(c_49528,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(identity_relation(relation_dom(relation_image(identity_relation(X0),X2)))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_27714]) ).
tcf(c_49529,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(powerset(sK7(powerset(relation_dom(relation_image(identity_relation(X0),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_27588]) ).
tcf(c_49530,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK7(powerset(sK7(powerset(relation_dom(relation_image(identity_relation(X0),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_27452]) ).
tcf(c_49531,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(identity_relation(sK7(sK6(powerset(relation_image(identity_relation(X0),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_10658]) ).
tcf(c_49532,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(sK7(powerset(relation_image(identity_relation(X0),X2)))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_9351]) ).
tcf(c_49533,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(sK7(powerset(relation_image(identity_relation(X0),X2)))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_9323]) ).
tcf(c_49534,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(powerset(identity_relation(identity_relation(relation_image(identity_relation(X0),X1)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_25847]) ).
tcf(c_49535,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(sK6(powerset(identity_relation(relation_image(identity_relation(X0),X1)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_17537]) ).
tcf(c_49536,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(relation_dom(sK7(powerset(relation_dom(relation_image(identity_relation(X0),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_27367]) ).
tcf(c_49537,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(relation_dom(sK7(powerset(relation_dom(relation_image(identity_relation(X0),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_26858]) ).
tcf(c_49538,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(relation_dom(sK7(powerset(relation_dom(relation_image(identity_relation(X0),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_26809]) ).
tcf(c_49539,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(sK7(powerset(relation_dom(relation_image(identity_relation(X0),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_26731]) ).
tcf(c_49540,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK7(sK6(powerset(identity_relation(relation_image(identity_relation(X0),X1)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_17480]) ).
tcf(c_49541,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(sK6(powerset(identity_relation(relation_image(identity_relation(X0),X1)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_16757]) ).
tcf(c_49542,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(sK6(sK6(powerset(relation_image(identity_relation(X0),X1)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_15644]) ).
tcf(c_49543,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK7(sK6(sK6(powerset(relation_image(identity_relation(X0),X1)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_15642]) ).
tcf(c_49544,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(powerset(identity_relation(relation_dom(relation_dom(relation_image(identity_relation(X0),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_25936]) ).
tcf(c_49545,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(sK6(sK6(powerset(relation_image(identity_relation(X0),X1)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_36269]) ).
tcf(c_49546,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(sK6(powerset(relation_dom(relation_dom(relation_image(identity_relation(X0),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_25099]) ).
tcf(c_49547,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK7(sK6(powerset(relation_dom(relation_dom(relation_image(identity_relation(X0),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_24875]) ).
tcf(c_49548,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(identity_relation(identity_relation(identity_relation(relation_image(identity_relation(X0),X1)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_13970]) ).
tcf(c_49549,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(identity_relation(relation_image(identity_relation(X0),X1)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_13854]) ).
tcf(c_49550,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(powerset(identity_relation(identity_relation(relation_image(identity_relation(X0),X1)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_12910]) ).
tcf(c_49551,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK7(powerset(identity_relation(identity_relation(relation_image(identity_relation(X0),X1)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_12872]) ).
tcf(c_49552,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(sK6(powerset(relation_dom(relation_dom(relation_image(identity_relation(X0),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_24819]) ).
tcf(c_49553,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(identity_relation(identity_relation(relation_dom(relation_dom(relation_image(identity_relation(X0),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_24724]) ).
tcf(c_49554,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(relation_dom(relation_dom(relation_image(identity_relation(X0),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_24676]) ).
tcf(c_49555,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(powerset(relation_dom(relation_dom(relation_dom(relation_image(identity_relation(X0),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_24628]) ).
tcf(c_49556,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(sK7(powerset(identity_relation(relation_image(identity_relation(X0),X1)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_12319]) ).
tcf(c_49557,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(sK7(powerset(identity_relation(relation_image(identity_relation(X0),X1)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_12213]) ).
tcf(c_49558,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(sK7(powerset(identity_relation(relation_image(identity_relation(X0),X1)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_12136]) ).
tcf(c_49559,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK7(powerset(identity_relation(relation_image(identity_relation(X0),X1)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_11432]) ).
tcf(c_49560,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(identity_relation(relation_dom(relation_dom(relation_dom(relation_image(identity_relation(X0),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_24580]) ).
tcf(c_49561,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(identity_relation(relation_dom(relation_dom(relation_dom(relation_image(identity_relation(X0),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_24491]) ).
tcf(c_49562,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(powerset(identity_relation(relation_dom(relation_dom(relation_image(identity_relation(X0),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_24443]) ).
tcf(c_49563,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK7(powerset(identity_relation(relation_dom(relation_dom(relation_image(identity_relation(X0),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_24395]) ).
tcf(c_49564,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(powerset(sK7(powerset(relation_image(identity_relation(X0),X1)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_11345]) ).
tcf(c_49565,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK7(sK6(powerset(relation_image(identity_relation(X0),X1)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_10677]) ).
tcf(c_49566,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(sK7(sK6(powerset(relation_image(identity_relation(X0),X1)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_10676]) ).
tcf(c_49567,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(sK7(sK6(powerset(relation_image(identity_relation(X0),X1)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_10675]) ).
tcf(c_49568,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(powerset(relation_dom(relation_dom(relation_dom(relation_image(identity_relation(X0),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_24347]) ).
tcf(c_49569,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK7(powerset(relation_dom(relation_dom(relation_dom(relation_image(identity_relation(X0),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_23164]) ).
tcf(c_49570,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(sK7(powerset(relation_dom(relation_dom(relation_image(identity_relation(X0),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_22515]) ).
tcf(c_49571,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(sK7(powerset(relation_dom(relation_dom(relation_image(identity_relation(X0),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_22426]) ).
tcf(c_49572,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(sK7(sK6(powerset(relation_image(identity_relation(X0),X1)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_10674]) ).
tcf(c_49573,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(identity_relation(sK7(powerset(relation_image(identity_relation(X0),X1)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_9751]) ).
tcf(c_49574,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(identity_relation(sK7(powerset(relation_image(identity_relation(X0),X1)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_9685]) ).
tcf(c_49575,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(sK7(powerset(relation_dom(relation_dom(relation_image(identity_relation(X0),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_22338]) ).
tcf(c_49576,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(relation_dom(relation_dom(relation_dom(relation_dom(relation_image(identity_relation(X0),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_22121]) ).
tcf(c_49577,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(relation_dom(relation_dom(relation_dom(relation_dom(relation_image(identity_relation(X0),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_22031]) ).
tcf(c_49578,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_image(identity_relation(X0),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_21914]) ).
tcf(c_49579,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(identity_relation(relation_image(identity_relation(X0),X2))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_9348]) ).
tcf(c_49580,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(powerset(sK7(powerset(relation_image(identity_relation(X0),X1)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_9118]) ).
tcf(c_49581,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK7(powerset(sK7(powerset(relation_image(identity_relation(X0),X1)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_9091]) ).
tcf(c_49582,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X1)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_9021]) ).
tcf(c_49583,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_image(identity_relation(X0),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_21763]) ).
tcf(c_49584,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK7(powerset(relation_dom(relation_dom(relation_image(identity_relation(X0),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_21512]) ).
tcf(c_49585,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(relation_dom(relation_dom(relation_image(identity_relation(X0),X2)))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_20489]) ).
tcf(c_49586,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_image(identity_relation(X0),X2)))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_20393]) ).
tcf(c_49587,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X1)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_8996]) ).
tcf(c_49588,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X1)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_8961]) ).
tcf(c_49589,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X1)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_8565]) ).
tcf(c_49590,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK7(powerset(relation_dom(relation_image(identity_relation(X0),X2)))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_18503]) ).
tcf(c_49591,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(powerset(identity_relation(relation_dom(relation_image(identity_relation(X0),X1)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_25846]) ).
tcf(c_49592,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(powerset(identity_relation(relation_image(identity_relation(X0),X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_11341]) ).
tcf(c_49593,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK7(sK6(powerset(relation_image(identity_relation(X0),X2)))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_10679]) ).
tcf(c_49594,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(sK6(powerset(relation_dom(relation_image(identity_relation(X0),X1)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_17536]) ).
tcf(c_49595,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK7(sK6(powerset(relation_dom(relation_image(identity_relation(X0),X1)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_17479]) ).
tcf(c_49596,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(sK6(powerset(relation_dom(relation_image(identity_relation(X0),X1)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_16756]) ).
tcf(c_49597,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(identity_relation(identity_relation(relation_dom(relation_image(identity_relation(X0),X1)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_13969]) ).
tcf(c_49598,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(relation_dom(relation_image(identity_relation(X0),X1)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_13853]) ).
tcf(c_49599,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(powerset(relation_dom(relation_dom(relation_image(identity_relation(X0),X1)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_13817]) ).
tcf(c_49600,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(identity_relation(relation_dom(relation_dom(relation_image(identity_relation(X0),X1)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_13649]) ).
tcf(c_49601,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(identity_relation(relation_dom(relation_dom(relation_image(identity_relation(X0),X1)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_13044]) ).
tcf(c_49602,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(powerset(identity_relation(relation_dom(relation_image(identity_relation(X0),X1)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_12909]) ).
tcf(c_49603,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK7(powerset(identity_relation(relation_dom(relation_image(identity_relation(X0),X1)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_12871]) ).
tcf(c_49604,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(powerset(relation_dom(relation_dom(relation_image(identity_relation(X0),X1)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_12755]) ).
tcf(c_49605,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK7(powerset(relation_dom(relation_dom(relation_image(identity_relation(X0),X1)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_12356]) ).
tcf(c_49606,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(sK7(powerset(relation_dom(relation_image(identity_relation(X0),X1)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_12318]) ).
tcf(c_49607,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(sK7(powerset(relation_dom(relation_image(identity_relation(X0),X1)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_12212]) ).
tcf(c_49608,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(sK7(powerset(relation_dom(relation_image(identity_relation(X0),X1)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_12135]) ).
tcf(c_49609,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(relation_dom(relation_dom(relation_dom(relation_image(identity_relation(X0),X1)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_12099]) ).
tcf(c_49610,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(relation_dom(relation_dom(relation_dom(relation_image(identity_relation(X0),X1)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_12063]) ).
tcf(c_49611,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(relation_dom(relation_dom(relation_dom(relation_image(identity_relation(X0),X1)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_12027]) ).
tcf(c_49612,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_image(identity_relation(X0),X1)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_11953]) ).
tcf(c_49613,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK7(powerset(relation_dom(relation_image(identity_relation(X0),X1)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_11431]) ).
tcf(c_49614,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(relation_dom(relation_image(identity_relation(X0),X2))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_9347]) ).
tcf(c_49615,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_dom(relation_image(identity_relation(X0),X2))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_9319]) ).
tcf(c_49616,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK7(powerset(relation_image(identity_relation(X0),X2))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_6877]) ).
tcf(c_49617,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(sK6(powerset(relation_image(identity_relation(X0),X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_10680]) ).
tcf(c_49618,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK7(sK6(powerset(relation_image(identity_relation(X0),X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_10678]) ).
tcf(c_49619,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(sK6(powerset(relation_image(identity_relation(X0),X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_15645]) ).
tcf(c_49620,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(identity_relation(identity_relation(relation_image(identity_relation(X0),X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_9748]) ).
tcf(c_49621,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(relation_image(identity_relation(X0),X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_9682]) ).
tcf(c_49622,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(powerset(relation_dom(relation_image(identity_relation(X0),X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_11340]) ).
tcf(c_49623,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(identity_relation(relation_dom(relation_image(identity_relation(X0),X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_9747]) ).
tcf(c_49624,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(identity_relation(relation_dom(relation_image(identity_relation(X0),X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_9681]) ).
tcf(c_49625,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(powerset(identity_relation(relation_image(identity_relation(X0),X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_9115]) ).
tcf(c_49626,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK7(powerset(identity_relation(relation_image(identity_relation(X0),X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_9088]) ).
tcf(c_49627,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(powerset(relation_dom(relation_image(identity_relation(X0),X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_9114]) ).
tcf(c_49628,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK7(powerset(relation_dom(relation_image(identity_relation(X0),X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_9087]) ).
tcf(c_49629,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(sK7(powerset(relation_image(identity_relation(X0),X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_8009]) ).
tcf(c_49630,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(sK7(powerset(relation_image(identity_relation(X0),X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_7966]) ).
tcf(c_49631,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_7938]) ).
tcf(c_49632,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(relation_dom(relation_dom(relation_image(identity_relation(X0),X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_9017]) ).
tcf(c_49633,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(relation_dom(relation_dom(relation_image(identity_relation(X0),X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_8992]) ).
tcf(c_49634,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(relation_dom(relation_dom(relation_image(identity_relation(X0),X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_8957]) ).
tcf(c_49635,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_image(identity_relation(X0),X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_8561]) ).
tcf(c_49636,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_6875]) ).
tcf(c_49637,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(powerset(relation_image(identity_relation(X0),X1)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_10681]) ).
tcf(c_49638,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(identity_relation(relation_image(identity_relation(X0),X1)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_8006]) ).
tcf(c_49639,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(identity_relation(relation_image(identity_relation(X0),X1)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_7963]) ).
tcf(c_49640,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(relation_image(identity_relation(X0),X2)) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_5794]) ).
tcf(c_49641,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_image(identity_relation(X0),X2)) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_5793]) ).
tcf(c_49642,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(powerset(relation_image(identity_relation(X0),X1)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_6878]) ).
tcf(c_49643,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK7(powerset(relation_image(identity_relation(X0),X1)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_6876]) ).
tcf(c_49644,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(relation_dom(relation_image(identity_relation(X0),X1)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_8005]) ).
tcf(c_49645,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(relation_dom(relation_image(identity_relation(X0),X1)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_7962]) ).
tcf(c_49646,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(relation_dom(relation_image(identity_relation(X0),X1)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_7934]) ).
tcf(c_49647,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_image(identity_relation(X0),X1)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_6133]) ).
tcf(c_49648,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(relation_image(identity_relation(X0),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_6879]) ).
tcf(c_49649,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(relation_image(identity_relation(X0),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_6106]) ).
tcf(c_49650,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(relation_image(identity_relation(X0),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_6105]) ).
tcf(c_49651,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_image(identity_relation(X0),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_5747]) ).
tcf(c_49652,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_image(identity_relation(X0),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_5776]) ).
tcf(c_49653,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(identity_relation(X0),X2) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_51]) ).
tcf(c_49654,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_image(identity_relation(X0),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_5663]) ).
tcf(c_49655,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(X0),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_52]) ).
tcf(c_49656,plain,
! [X0: $i,X1: $i] :
( function(relation_image(identity_relation(X0),X1))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_98]) ).
tcf(c_49657,plain,
! [X0: $i,X1: $i] :
( relation(relation_image(identity_relation(X0),X1))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_80]) ).
tcf(c_51255,plain,
! [X0: $i] :
( function(relation_image(empty_set,X0))
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_6104,c_49656]) ).
tcf(c_51256,plain,
! [X0: $i,X1: $i] :
( ( relation_image(relation_image(identity_relation(X0),X1),empty_set) = empty_set )
| ~ empty(X0)
| ~ relation(relation_image(identity_relation(X0),X1)) ),
inference(superposition,[status(thm)],[c_49656,c_23329]) ).
tcf(c_51267,plain,
! [X0: $i] :
( relation(relation_image(empty_set,X0))
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_6104,c_49657]) ).
tcf(c_51273,plain,
! [X0: $i] :
( empty(sK7(powerset(empty_set)))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25160,c_49322]) ).
tcf(c_51274,plain,
! [X0: $i] :
( empty(sK7(powerset(relation_image(empty_set,X0))))
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_6104,c_49322]) ).
tcf(c_51275,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(powerset(identity_relation(identity_relation(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_39551]) ).
tcf(c_51276,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(identity_relation(relation_dom(sK7(powerset(sK7(powerset(relation_image(identity_relation(X0),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_13654]) ).
tcf(c_51277,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(identity_relation(relation_dom(sK7(powerset(sK7(powerset(relation_image(identity_relation(X0),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_13049]) ).
tcf(c_51278,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(powerset(identity_relation(sK7(powerset(sK7(powerset(relation_image(identity_relation(X0),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_12914]) ).
tcf(c_51279,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK7(powerset(identity_relation(sK7(powerset(sK7(powerset(relation_image(identity_relation(X0),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_12876]) ).
tcf(c_51280,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(sK6(powerset(identity_relation(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_38682]) ).
tcf(c_51281,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK7(sK6(powerset(identity_relation(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_37969]) ).
tcf(c_51282,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(sK6(powerset(identity_relation(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_37889]) ).
tcf(c_51283,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(sK6(sK6(powerset(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_37780]) ).
tcf(c_51284,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(powerset(relation_dom(sK7(powerset(sK7(powerset(relation_image(identity_relation(X0),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_12760]) ).
tcf(c_51285,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK7(powerset(relation_dom(sK7(powerset(sK7(powerset(relation_image(identity_relation(X0),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_12361]) ).
tcf(c_51286,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(sK7(powerset(sK7(powerset(sK7(powerset(relation_image(identity_relation(X0),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_12323]) ).
tcf(c_51287,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(sK7(powerset(sK7(powerset(sK7(powerset(relation_image(identity_relation(X0),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_12217]) ).
tcf(c_51288,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK7(sK6(sK6(powerset(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_37664]) ).
tcf(c_51289,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(sK6(sK6(powerset(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_37342]) ).
tcf(c_51290,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(identity_relation(identity_relation(identity_relation(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_31222]) ).
tcf(c_51291,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(identity_relation(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_31142]) ).
tcf(c_51292,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(sK7(powerset(sK7(powerset(sK7(powerset(relation_image(identity_relation(X0),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_12140]) ).
tcf(c_51293,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(relation_dom(relation_dom(sK7(powerset(sK7(powerset(relation_image(identity_relation(X0),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_12104]) ).
tcf(c_51294,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(relation_dom(relation_dom(sK7(powerset(sK7(powerset(relation_image(identity_relation(X0),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_12068]) ).
tcf(c_51295,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(relation_dom(relation_dom(sK7(powerset(sK7(powerset(relation_image(identity_relation(X0),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_12032]) ).
tcf(c_51296,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(powerset(identity_relation(identity_relation(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_31014]) ).
tcf(c_51297,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK7(powerset(identity_relation(identity_relation(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_30942]) ).
tcf(c_51298,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(sK7(powerset(identity_relation(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_30355]) ).
tcf(c_51299,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(sK7(powerset(identity_relation(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_30248]) ).
tcf(c_51300,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK7(powerset(sK7(powerset(relation_image(identity_relation(X0),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_11958]) ).
tcf(c_51301,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK7(powerset(sK7(powerset(sK7(powerset(relation_image(identity_relation(X0),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_11436]) ).
tcf(c_51302,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(powerset(sK7(sK6(powerset(sK7(powerset(relation_image(identity_relation(X0),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_11346]) ).
tcf(c_51303,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(sK7(sK6(powerset(sK7(powerset(relation_image(identity_relation(X0),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_10669]) ).
tcf(c_51304,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(sK7(powerset(identity_relation(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_30158]) ).
tcf(c_51305,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK7(powerset(identity_relation(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_30068]) ).
tcf(c_51306,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(powerset(sK7(powerset(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_29569]) ).
tcf(c_51307,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK7(sK6(powerset(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_29442]) ).
tcf(c_51308,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(relation_dom(sK7(sK6(powerset(sK7(powerset(relation_image(identity_relation(X0),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_10666]) ).
tcf(c_51309,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(relation_dom(sK7(sK6(powerset(sK7(powerset(relation_image(identity_relation(X0),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_10665]) ).
tcf(c_51310,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(relation_dom(sK7(sK6(powerset(sK7(powerset(relation_image(identity_relation(X0),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_10664]) ).
tcf(c_51311,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK7(powerset(sK7(sK6(powerset(sK7(powerset(relation_image(identity_relation(X0),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_10663]) ).
tcf(c_51312,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(sK7(sK6(powerset(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_29308]) ).
tcf(c_51313,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(sK7(sK6(powerset(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_29194]) ).
tcf(c_51314,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(sK7(sK6(powerset(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_28717]) ).
tcf(c_51315,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(identity_relation(sK7(powerset(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_28572]) ).
tcf(c_51316,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(powerset(sK7(sK6(powerset(sK7(powerset(relation_image(identity_relation(X0),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_10662]) ).
tcf(c_51317,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(identity_relation(sK7(sK6(powerset(sK7(powerset(relation_image(identity_relation(X0),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_10659]) ).
tcf(c_51318,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(identity_relation(sK7(powerset(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_28429]) ).
tcf(c_51319,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(identity_relation(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X2)))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_27714]) ).
tcf(c_51320,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(powerset(sK7(powerset(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_27588]) ).
tcf(c_51321,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK7(powerset(sK7(powerset(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_27452]) ).
tcf(c_51322,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(identity_relation(sK7(sK6(powerset(sK7(powerset(relation_image(identity_relation(X0),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_10658]) ).
tcf(c_51323,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(sK7(powerset(sK7(powerset(relation_image(identity_relation(X0),X2)))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_9351]) ).
tcf(c_51324,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(sK7(powerset(sK7(powerset(relation_image(identity_relation(X0),X2)))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_9323]) ).
tcf(c_51325,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(powerset(identity_relation(identity_relation(sK7(powerset(relation_image(identity_relation(X0),X1)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_25847]) ).
tcf(c_51326,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(sK6(powerset(identity_relation(sK7(powerset(relation_image(identity_relation(X0),X1)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_17537]) ).
tcf(c_51327,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(relation_dom(sK7(powerset(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_27367]) ).
tcf(c_51328,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(relation_dom(sK7(powerset(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_26858]) ).
tcf(c_51329,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(relation_dom(sK7(powerset(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_26809]) ).
tcf(c_51330,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(sK7(powerset(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_26731]) ).
tcf(c_51331,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK7(sK6(powerset(identity_relation(sK7(powerset(relation_image(identity_relation(X0),X1)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_17480]) ).
tcf(c_51332,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(sK6(powerset(identity_relation(sK7(powerset(relation_image(identity_relation(X0),X1)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_16757]) ).
tcf(c_51333,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(sK6(sK6(powerset(sK7(powerset(relation_image(identity_relation(X0),X1)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_15644]) ).
tcf(c_51334,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK7(sK6(sK6(powerset(sK7(powerset(relation_image(identity_relation(X0),X1)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_15642]) ).
tcf(c_51335,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(powerset(identity_relation(relation_dom(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_25936]) ).
tcf(c_51336,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(sK6(sK6(powerset(sK7(powerset(relation_image(identity_relation(X0),X1)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_36269]) ).
tcf(c_51337,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(sK6(powerset(relation_dom(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_25099]) ).
tcf(c_51338,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK7(sK6(powerset(relation_dom(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_24875]) ).
tcf(c_51339,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(identity_relation(identity_relation(identity_relation(sK7(powerset(relation_image(identity_relation(X0),X1)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_13970]) ).
tcf(c_51340,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(identity_relation(sK7(powerset(relation_image(identity_relation(X0),X1)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_13854]) ).
tcf(c_51341,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(powerset(identity_relation(identity_relation(sK7(powerset(relation_image(identity_relation(X0),X1)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_12910]) ).
tcf(c_51342,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK7(powerset(identity_relation(identity_relation(sK7(powerset(relation_image(identity_relation(X0),X1)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_12872]) ).
tcf(c_51343,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(sK6(powerset(relation_dom(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_24819]) ).
tcf(c_51344,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(identity_relation(identity_relation(relation_dom(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_24724]) ).
tcf(c_51345,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(relation_dom(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_24676]) ).
tcf(c_51346,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(powerset(relation_dom(relation_dom(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_24628]) ).
tcf(c_51347,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(sK7(powerset(identity_relation(sK7(powerset(relation_image(identity_relation(X0),X1)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_12319]) ).
tcf(c_51348,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(sK7(powerset(identity_relation(sK7(powerset(relation_image(identity_relation(X0),X1)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_12213]) ).
tcf(c_51349,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(sK7(powerset(identity_relation(sK7(powerset(relation_image(identity_relation(X0),X1)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_12136]) ).
tcf(c_51350,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK7(powerset(identity_relation(sK7(powerset(relation_image(identity_relation(X0),X1)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_11432]) ).
tcf(c_51351,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(identity_relation(relation_dom(relation_dom(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_24580]) ).
tcf(c_51352,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(identity_relation(relation_dom(relation_dom(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_24491]) ).
tcf(c_51353,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(powerset(identity_relation(relation_dom(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_24443]) ).
tcf(c_51354,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK7(powerset(identity_relation(relation_dom(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_24395]) ).
tcf(c_51355,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(powerset(sK7(powerset(sK7(powerset(relation_image(identity_relation(X0),X1)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_11345]) ).
tcf(c_51356,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK7(sK6(powerset(sK7(powerset(relation_image(identity_relation(X0),X1)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_10677]) ).
tcf(c_51357,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(sK7(sK6(powerset(sK7(powerset(relation_image(identity_relation(X0),X1)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_10676]) ).
tcf(c_51358,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(sK7(sK6(powerset(sK7(powerset(relation_image(identity_relation(X0),X1)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_10675]) ).
tcf(c_51359,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(powerset(relation_dom(relation_dom(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_24347]) ).
tcf(c_51360,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK7(powerset(relation_dom(relation_dom(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_23164]) ).
tcf(c_51361,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(sK7(powerset(relation_dom(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_22515]) ).
tcf(c_51362,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(sK7(powerset(relation_dom(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_22426]) ).
tcf(c_51363,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(sK7(sK6(powerset(sK7(powerset(relation_image(identity_relation(X0),X1)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_10674]) ).
tcf(c_51364,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(identity_relation(sK7(powerset(sK7(powerset(relation_image(identity_relation(X0),X1)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_9751]) ).
tcf(c_51365,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(identity_relation(sK7(powerset(sK7(powerset(relation_image(identity_relation(X0),X1)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_9685]) ).
tcf(c_51366,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(sK7(powerset(relation_dom(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_22338]) ).
tcf(c_51367,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(relation_dom(relation_dom(relation_dom(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_22121]) ).
tcf(c_51368,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(relation_dom(relation_dom(relation_dom(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_22031]) ).
tcf(c_51369,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_21914]) ).
tcf(c_51370,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(identity_relation(sK7(powerset(relation_image(identity_relation(X0),X2))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_9348]) ).
tcf(c_51371,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(powerset(sK7(powerset(sK7(powerset(relation_image(identity_relation(X0),X1)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_9118]) ).
tcf(c_51372,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK7(powerset(sK7(powerset(sK7(powerset(relation_image(identity_relation(X0),X1)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_9091]) ).
tcf(c_51373,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(relation_dom(sK7(powerset(sK7(powerset(relation_image(identity_relation(X0),X1)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_9021]) ).
tcf(c_51374,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_21763]) ).
tcf(c_51375,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK7(powerset(relation_dom(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_21512]) ).
tcf(c_51376,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(relation_dom(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X2)))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_20489]) ).
tcf(c_51377,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_dom(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X2)))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_20393]) ).
tcf(c_51378,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(relation_dom(sK7(powerset(sK7(powerset(relation_image(identity_relation(X0),X1)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_8996]) ).
tcf(c_51379,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(relation_dom(sK7(powerset(sK7(powerset(relation_image(identity_relation(X0),X1)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_8961]) ).
tcf(c_51380,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(sK7(powerset(sK7(powerset(relation_image(identity_relation(X0),X1)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_8565]) ).
tcf(c_51381,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK7(powerset(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X2)))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_18503]) ).
tcf(c_51382,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(powerset(identity_relation(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X1)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_25846]) ).
tcf(c_51383,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(powerset(identity_relation(sK7(powerset(relation_image(identity_relation(X0),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_11341]) ).
tcf(c_51384,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK7(sK6(powerset(sK7(powerset(relation_image(identity_relation(X0),X2)))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_10679]) ).
tcf(c_51385,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(sK6(powerset(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X1)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_17536]) ).
tcf(c_51386,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK7(sK6(powerset(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X1)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_17479]) ).
tcf(c_51387,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(sK6(powerset(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X1)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_16756]) ).
tcf(c_51388,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(identity_relation(identity_relation(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X1)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_13969]) ).
tcf(c_51389,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X1)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_13853]) ).
tcf(c_51390,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(powerset(relation_dom(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X1)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_13817]) ).
tcf(c_51391,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(identity_relation(relation_dom(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X1)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_13649]) ).
tcf(c_51392,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(identity_relation(relation_dom(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X1)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_13044]) ).
tcf(c_51393,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(powerset(identity_relation(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X1)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_12909]) ).
tcf(c_51394,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK7(powerset(identity_relation(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X1)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_12871]) ).
tcf(c_51395,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(powerset(relation_dom(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X1)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_12755]) ).
tcf(c_51396,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK7(powerset(relation_dom(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X1)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_12356]) ).
tcf(c_51397,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(sK7(powerset(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X1)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_12318]) ).
tcf(c_51398,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(sK7(powerset(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X1)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_12212]) ).
tcf(c_51399,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(sK7(powerset(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X1)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_12135]) ).
tcf(c_51400,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(relation_dom(relation_dom(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X1)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_12099]) ).
tcf(c_51401,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(relation_dom(relation_dom(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X1)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_12063]) ).
tcf(c_51402,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(relation_dom(relation_dom(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X1)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_12027]) ).
tcf(c_51403,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X1)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_11953]) ).
tcf(c_51404,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK7(powerset(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X1)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_11431]) ).
tcf(c_51405,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X2))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_9347]) ).
tcf(c_51406,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X2))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_9319]) ).
tcf(c_51407,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK7(powerset(sK7(powerset(relation_image(identity_relation(X0),X2))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_6877]) ).
tcf(c_51408,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(sK6(powerset(sK7(powerset(relation_image(identity_relation(X0),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_10680]) ).
tcf(c_51409,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK7(sK6(powerset(sK7(powerset(relation_image(identity_relation(X0),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_10678]) ).
tcf(c_51410,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(sK6(powerset(sK7(powerset(relation_image(identity_relation(X0),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_15645]) ).
tcf(c_51411,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(identity_relation(identity_relation(sK7(powerset(relation_image(identity_relation(X0),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_9748]) ).
tcf(c_51412,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(sK7(powerset(relation_image(identity_relation(X0),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_9682]) ).
tcf(c_51413,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(powerset(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_11340]) ).
tcf(c_51447,plain,
! [X0: $i,X1: $i] :
( function(sK7(powerset(relation_image(identity_relation(X0),X1))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_98]) ).
tcf(c_51448,plain,
! [X0: $i,X1: $i] :
( relation(sK7(powerset(relation_image(identity_relation(X0),X1))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_80]) ).
tcf(c_51449,plain,
! [X0: $i] :
( empty(empty_set)
| ~ empty(X0) ),
inference(light_normalisation,[status(thm)],[c_51273,c_8004]) ).
tcf(c_52588,plain,
! [X0: $i,X1: $i] :
( empty(sK0)
| in(sK4(identity_relation(sK1),X1,X0),sK0)
| ~ in(X0,relation_image(identity_relation(sK1),X1)) ),
inference(superposition,[status(thm)],[c_49181,c_71]) ).
tcf(c_52589,plain,
! [X0: $i,X1: $i] :
( in(sK4(identity_relation(sK1),X1,X0),sK0)
| ~ in(X0,relation_image(identity_relation(sK1),X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_52588,c_24236]) ).
tcf(c_52630,plain,
! [X0: $i,X1: $i] :
( element(sK3(X1,sK1,empty_set),sK0)
| ( relation_image(identity_relation(X0),empty_set) = relation_image(X1,sK1) )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25160,c_49316]) ).
tcf(c_52631,plain,
! [X0: $i,X1: $i] :
( element(sK3(X0,sK1,relation_image(empty_set,X1)),sK0)
| ( relation_image(identity_relation(empty_set),X1) = relation_image(X0,sK1) )
| ~ empty(empty_set)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6104,c_49316]) ).
tcf(c_52634,plain,
! [X0: $i,X1: $i] :
( element(sK3(X0,sK1,relation_image(empty_set,X1)),sK0)
| ( relation_image(X0,sK1) = relation_image(empty_set,X1) )
| ~ empty(empty_set)
| ~ function(X0)
| ~ relation(X0) ),
inference(light_normalisation,[status(thm)],[c_52631,c_6104]) ).
tcf(c_52646,plain,
! [X0: $i,X1: $i] :
( element(sK2(X1,empty_set,sK1),sK0)
| ( relation_image(X1,relation_image(identity_relation(X0),empty_set)) = sK1 )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25160,c_49318]) ).
tcf(c_52647,plain,
! [X0: $i,X1: $i] :
( element(sK2(X0,relation_image(empty_set,X1),sK1),sK0)
| ( relation_image(X0,relation_image(identity_relation(empty_set),X1)) = sK1 )
| ~ empty(empty_set)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6104,c_49318]) ).
tcf(c_52650,plain,
! [X0: $i,X1: $i] :
( element(sK2(X0,relation_image(empty_set,X1),sK1),sK0)
| ( relation_image(X0,relation_image(empty_set,X1)) = sK1 )
| ~ empty(empty_set)
| ~ function(X0)
| ~ relation(X0) ),
inference(light_normalisation,[status(thm)],[c_52647,c_6104]) ).
tcf(c_52656,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(sK0),sK4(identity_relation(sK1),X1,X0)) = sK4(identity_relation(sK1),X1,X0) )
| ~ in(X0,relation_image(identity_relation(sK1),X1)) ),
inference(superposition,[status(thm)],[c_52589,c_151]) ).
tcf(c_52657,plain,
! [X0: $i,X1: $i] :
( ~ in(X1,relation_image(identity_relation(sK1),X0))
| ~ in(sK0,sK4(identity_relation(sK1),X0,X1)) ),
inference(superposition,[status(thm)],[c_52589,c_85]) ).
tcf(c_52678,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(X0),X1) = empty_set )
| ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_10348,c_49655]) ).
tcf(c_52679,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(X0),X1) = empty_set )
| ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) ) ),
inference(superposition,[status(thm)],[c_5806,c_49655]) ).
tcf(c_52680,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(X0),X1) = empty_set )
| ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) ) ),
inference(superposition,[status(thm)],[c_5807,c_49655]) ).
tcf(c_52681,plain,
! [X0: $i] : relation_image(identity_relation(empty_set),X0) = empty_set,
inference(superposition,[status(thm)],[c_83,c_49655]) ).
tcf(c_52682,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(relation_dom(X0)),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_49655]) ).
tcf(c_52683,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(identity_relation(X0)),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_49655]) ).
tcf(c_52684,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(sK7(powerset(X0))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_49655]) ).
tcf(c_52685,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(sK7(sK6(powerset(X0)))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_49655]) ).
tcf(c_52686,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(sK7(sK6(sK6(powerset(X0))))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_49655]) ).
tcf(c_52687,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(relation_image(X0,empty_set)),X1) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_49655]) ).
tcf(c_52688,plain,
! [X0: $i] :
( ( relation_image(identity_relation(sK7(powerset(sK1))),X0) = empty_set )
| ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) ) ),
inference(superposition,[status(thm)],[c_21309,c_49655]) ).
tcf(c_52689,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(sK7(powerset(sK7(powerset(X0))))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_49655]) ).
tcf(c_52690,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(sK7(powerset(relation_image(X0,empty_set)))),X1) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_49655]) ).
tcf(c_52691,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(sK7(powerset(sK7(sK6(powerset(X0)))))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_49655]) ).
tcf(c_52692,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(sK7(powerset(sK7(sK6(sK6(powerset(X0))))))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_49655]) ).
tcf(c_52693,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(identity_relation(relation_image(identity_relation(X0),X1)),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_49655]) ).
tcf(c_52694,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(sK7(sK6(sK6(sK6(powerset(X0)))))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_49655]) ).
tcf(c_52695,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0)))))))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_49655]) ).
tcf(c_52696,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(identity_relation(sK7(powerset(relation_image(identity_relation(X0),X1)))),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_49655]) ).
tcf(c_52802,plain,
! [X0: $i] :
( function(sK7(powerset(empty_set)))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25160,c_51447]) ).
tcf(c_52803,plain,
! [X0: $i] :
( function(sK7(powerset(relation_image(empty_set,X0))))
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_6104,c_51447]) ).
tcf(c_52804,plain,
! [X0: $i,X1: $i] :
( ( relation_image(sK7(powerset(relation_image(identity_relation(X0),X1))),empty_set) = empty_set )
| ~ empty(X0)
| ~ relation(sK7(powerset(relation_image(identity_relation(X0),X1)))) ),
inference(superposition,[status(thm)],[c_51447,c_23329]) ).
tcf(c_52805,plain,
! [X0: $i] :
( function(empty_set)
| ~ empty(X0) ),
inference(light_normalisation,[status(thm)],[c_52802,c_8004]) ).
tcf(c_52863,plain,
! [X0: $i] :
( relation(sK7(powerset(empty_set)))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25160,c_51448]) ).
tcf(c_52864,plain,
! [X0: $i] :
( relation(sK7(powerset(relation_image(empty_set,X0))))
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_6104,c_51448]) ).
tcf(c_52865,plain,
! [X0: $i] :
( relation(empty_set)
| ~ empty(X0) ),
inference(light_normalisation,[status(thm)],[c_52863,c_8004]) ).
tcf(c_52871,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(relation_dom(X0)),X1) = empty_set )
| ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_10348,c_52682]) ).
tcf(c_52872,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(relation_dom(X0)),X1) = empty_set )
| ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) ) ),
inference(superposition,[status(thm)],[c_5806,c_52682]) ).
tcf(c_52873,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( relation_image(identity_relation(relation_dom(X0)),X1) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_52682]) ).
tcf(c_52874,plain,
! [X0: $i] : relation_image(identity_relation(relation_dom(empty_set)),X0) = empty_set,
inference(superposition,[status(thm)],[c_83,c_52682]) ).
tcf(c_52875,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(relation_dom(relation_dom(X0))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_52682]) ).
tcf(c_52876,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(relation_dom(identity_relation(X0))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_52682]) ).
tcf(c_52877,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(relation_dom(sK7(powerset(X0)))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_52682]) ).
tcf(c_52878,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(relation_dom(sK7(sK6(powerset(X0))))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_52682]) ).
tcf(c_52879,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(relation_dom(sK7(sK6(sK6(powerset(X0)))))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_52682]) ).
tcf(c_52880,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(relation_dom(relation_image(X0,empty_set))),X1) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_52682]) ).
tcf(c_52881,plain,
! [X0: $i] :
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( relation_image(identity_relation(relation_dom(sK7(powerset(sK1)))),X0) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_52682]) ).
tcf(c_52882,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(relation_dom(sK7(powerset(sK7(powerset(X0)))))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_52682]) ).
tcf(c_52883,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(relation_dom(sK7(powerset(relation_image(X0,empty_set))))),X1) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_52682]) ).
tcf(c_52884,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(relation_dom(sK7(powerset(sK7(sK6(powerset(X0))))))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_52682]) ).
tcf(c_52885,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_52682]) ).
tcf(c_52886,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(identity_relation(relation_dom(relation_image(identity_relation(X0),X1))),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_52682]) ).
tcf(c_52887,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(relation_dom(sK7(sK6(sK6(sK6(powerset(X0))))))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_52682]) ).
tcf(c_52888,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_52682]) ).
tcf(c_52889,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(identity_relation(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X1))))),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_52682]) ).
tcf(c_53057,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_image(identity_relation(X0),X1)) = empty_set )
| ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_10348,c_49652]) ).
tcf(c_53058,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_image(identity_relation(X0),X1)) = empty_set )
| ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) ) ),
inference(superposition,[status(thm)],[c_5806,c_49652]) ).
tcf(c_53059,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( identity_relation(relation_image(identity_relation(X0),X1)) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_49652]) ).
tcf(c_53060,plain,
! [X0: $i] : identity_relation(relation_image(identity_relation(empty_set),X0)) = empty_set,
inference(superposition,[status(thm)],[c_83,c_49652]) ).
tcf(c_53061,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_image(identity_relation(relation_dom(X0)),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_49652]) ).
tcf(c_53062,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_image(identity_relation(identity_relation(X0)),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_49652]) ).
tcf(c_53063,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_image(identity_relation(sK7(powerset(X0))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_49652]) ).
tcf(c_53064,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_image(identity_relation(sK7(sK6(powerset(X0)))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_49652]) ).
tcf(c_53065,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_image(identity_relation(sK7(sK6(sK6(powerset(X0))))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_49652]) ).
tcf(c_53066,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_image(identity_relation(relation_image(X0,empty_set)),X1)) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_49652]) ).
tcf(c_53067,plain,
! [X0: $i] :
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( identity_relation(relation_image(identity_relation(sK7(powerset(sK1))),X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_49652]) ).
tcf(c_53068,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_image(identity_relation(sK7(powerset(sK7(powerset(X0))))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_49652]) ).
tcf(c_53069,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_image(identity_relation(sK7(powerset(relation_image(X0,empty_set)))),X1)) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_49652]) ).
tcf(c_53070,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_image(identity_relation(sK7(powerset(sK7(sK6(powerset(X0)))))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_49652]) ).
tcf(c_53071,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_image(identity_relation(sK7(powerset(sK7(sK6(sK6(powerset(X0))))))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_49652]) ).
tcf(c_53072,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(relation_image(identity_relation(relation_image(identity_relation(X0),X1)),X2)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_49652]) ).
tcf(c_53073,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_image(identity_relation(sK7(sK6(sK6(sK6(powerset(X0)))))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_49652]) ).
tcf(c_53074,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_image(identity_relation(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0)))))))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_49652]) ).
tcf(c_53075,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(relation_image(identity_relation(sK7(powerset(relation_image(identity_relation(X0),X1)))),X2)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_49652]) ).
tcf(c_53233,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_image(identity_relation(X0),X1)) = empty_set )
| ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_10348,c_49654]) ).
tcf(c_53234,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_image(identity_relation(X0),X1)) = empty_set )
| ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) ) ),
inference(superposition,[status(thm)],[c_5806,c_49654]) ).
tcf(c_53235,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( relation_dom(relation_image(identity_relation(X0),X1)) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_49654]) ).
tcf(c_53236,plain,
! [X0: $i] : relation_dom(relation_image(identity_relation(empty_set),X0)) = empty_set,
inference(superposition,[status(thm)],[c_83,c_49654]) ).
tcf(c_53237,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_image(identity_relation(relation_dom(X0)),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_49654]) ).
tcf(c_53238,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_image(identity_relation(identity_relation(X0)),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_49654]) ).
tcf(c_53239,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_49654]) ).
tcf(c_53240,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_image(identity_relation(sK7(sK6(powerset(X0)))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_49654]) ).
tcf(c_53241,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_image(identity_relation(sK7(sK6(sK6(powerset(X0))))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_49654]) ).
tcf(c_53242,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_image(identity_relation(relation_image(X0,empty_set)),X1)) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_49654]) ).
tcf(c_53243,plain,
! [X0: $i] :
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( relation_dom(relation_image(identity_relation(sK7(powerset(sK1))),X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_49654]) ).
tcf(c_53244,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_image(identity_relation(sK7(powerset(sK7(powerset(X0))))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_49654]) ).
tcf(c_53245,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_image(identity_relation(sK7(powerset(relation_image(X0,empty_set)))),X1)) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_49654]) ).
tcf(c_53246,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_image(identity_relation(sK7(powerset(sK7(sK6(powerset(X0)))))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_49654]) ).
tcf(c_53247,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_image(identity_relation(sK7(powerset(sK7(sK6(sK6(powerset(X0))))))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_49654]) ).
tcf(c_53248,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_image(identity_relation(relation_image(identity_relation(X0),X1)),X2)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_49654]) ).
tcf(c_53249,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_image(identity_relation(sK7(sK6(sK6(sK6(powerset(X0)))))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_49654]) ).
tcf(c_53250,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_image(identity_relation(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0)))))))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_49654]) ).
tcf(c_53251,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_image(identity_relation(sK7(powerset(relation_image(identity_relation(X0),X1)))),X2)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_49654]) ).
tcf(c_53467,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(identity_relation(X0)),X1) = empty_set )
| ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_10348,c_52683]) ).
tcf(c_53468,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(identity_relation(X0)),X1) = empty_set )
| ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) ) ),
inference(superposition,[status(thm)],[c_5806,c_52683]) ).
tcf(c_53469,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( relation_image(identity_relation(identity_relation(X0)),X1) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_52683]) ).
tcf(c_53470,plain,
! [X0: $i] : relation_image(identity_relation(identity_relation(empty_set)),X0) = empty_set,
inference(superposition,[status(thm)],[c_83,c_52683]) ).
tcf(c_53471,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(identity_relation(relation_dom(X0))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_52683]) ).
tcf(c_53472,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(identity_relation(identity_relation(X0))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_52683]) ).
tcf(c_53473,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(identity_relation(sK7(powerset(X0)))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_52683]) ).
tcf(c_53474,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(identity_relation(sK7(sK6(powerset(X0))))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_52683]) ).
tcf(c_53475,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(identity_relation(sK7(sK6(sK6(powerset(X0)))))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_52683]) ).
tcf(c_53476,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(identity_relation(relation_image(X0,empty_set))),X1) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_52683]) ).
tcf(c_53477,plain,
! [X0: $i] :
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( relation_image(identity_relation(identity_relation(sK7(powerset(sK1)))),X0) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_52683]) ).
tcf(c_53478,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(identity_relation(sK7(powerset(sK7(powerset(X0)))))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_52683]) ).
tcf(c_53479,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(identity_relation(sK7(powerset(relation_image(X0,empty_set))))),X1) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_52683]) ).
tcf(c_53480,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(identity_relation(sK7(powerset(sK7(sK6(powerset(X0))))))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_52683]) ).
tcf(c_53481,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(identity_relation(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_52683]) ).
tcf(c_53482,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(identity_relation(identity_relation(relation_image(identity_relation(X0),X1))),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_52683]) ).
tcf(c_53483,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(identity_relation(sK7(sK6(sK6(sK6(powerset(X0))))))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_52683]) ).
tcf(c_53484,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(identity_relation(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_52683]) ).
tcf(c_53485,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(identity_relation(identity_relation(sK7(powerset(relation_image(identity_relation(X0),X1))))),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_52683]) ).
tcf(c_53592,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(identity_relation(sK7(powerset(X0))),X3) = relation_image(X1,X2) )
| ( apply(X1,sK3(X1,X2,relation_image(identity_relation(sK7(powerset(X0))),X3))) = sK2(X1,X2,relation_image(identity_relation(sK7(powerset(X0))),X3)) )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_56,c_49184]) ).
tcf(c_53593,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK3(X1,X3,relation_image(identity_relation(sK7(powerset(X0))),X2)),relation_dom(X1))
| ( relation_image(identity_relation(sK7(powerset(X0))),X2) = relation_image(X1,X3) )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_54,c_49184]) ).
tcf(c_53594,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK3(X1,X3,relation_image(identity_relation(sK7(powerset(X0))),X2)),X3)
| ( relation_image(identity_relation(sK7(powerset(X0))),X2) = relation_image(X1,X3) )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_55,c_49184]) ).
tcf(c_53595,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,relation_image(identity_relation(sK7(powerset(X0))),X2),X3),X3)
| ( relation_image(X1,relation_image(identity_relation(sK7(powerset(X0))),X2)) = X3 )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_55,c_49184]) ).
tcf(c_53596,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(X1)
| ~ in(X0,X2)
| ~ function(identity_relation(sK7(powerset(X1))))
| ~ relation(identity_relation(sK7(powerset(X1))))
| ~ in(X0,relation_dom(identity_relation(sK7(powerset(X1))))) ),
inference(superposition,[status(thm)],[c_57,c_49184]) ).
tcf(c_53597,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ function(X1)
| ~ relation(X1)
| ~ empty(X2)
| ~ in(X0,relation_image(X1,relation_image(identity_relation(sK7(powerset(X2))),X3))) ),
inference(superposition,[status(thm)],[c_59,c_49184]) ).
tcf(c_53599,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ empty(X1)
| ~ in(X0,relation_image(identity_relation(relation_image(identity_relation(sK7(powerset(X1))),X2)),X3)) ),
inference(superposition,[status(thm)],[c_6013,c_49184]) ).
tcf(c_53600,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(X1,sK1,relation_image(identity_relation(sK7(powerset(X0))),X2)),sK0)
| ( relation_image(identity_relation(sK7(powerset(X0))),X2) = relation_image(X1,sK1) )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11821,c_49184]) ).
tcf(c_53601,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK3(X1,sK1,relation_image(identity_relation(sK7(powerset(X0))),X2)),sK0)
| ( relation_image(identity_relation(sK7(powerset(X0))),X2) = relation_image(X1,sK1) )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6475,c_49184]) ).
tcf(c_53602,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,relation_image(identity_relation(sK7(powerset(X0))),X2),sK1),sK0)
| ( relation_image(X1,relation_image(identity_relation(sK7(powerset(X0))),X2)) = sK1 )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12513,c_49184]) ).
tcf(c_53603,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X1,relation_image(identity_relation(sK7(powerset(X0))),X2),sK1),sK0)
| ( relation_image(X1,relation_image(identity_relation(sK7(powerset(X0))),X2)) = sK1 )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6486,c_49184]) ).
tcf(c_53607,plain,
! [X0: $i,X1: $i] :
( empty(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25981,c_49184]) ).
tcf(c_53608,plain,
! [X0: $i,X1: $i] :
( empty(relation_image(identity_relation(sK7(powerset(X0))),X1))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35578,c_49184]) ).
tcf(c_53610,plain,
! [X0: $i,X1: $i] :
( ~ empty(empty_set)
| ~ in(X0,relation_image(identity_relation(empty_set),X1)) ),
inference(superposition,[status(thm)],[c_8004,c_49184]) ).
tcf(c_53623,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(X1)
| ~ in(X0,X2)
| ~ in(X0,relation_dom(identity_relation(sK7(powerset(X1))))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_53596,c_62,c_63]) ).
tcf(c_53716,plain,
! [X0: $i,X1: $i] :
( element(sK3(X1,sK1,empty_set),sK0)
| ( relation_image(identity_relation(sK7(powerset(X0))),empty_set) = relation_image(X1,sK1) )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25160,c_53601]) ).
tcf(c_53717,plain,
! [X0: $i,X1: $i] :
( element(sK3(X0,sK1,relation_image(identity_relation(empty_set),X1)),sK0)
| ( relation_image(identity_relation(sK7(powerset(empty_set))),X1) = relation_image(X0,sK1) )
| ~ empty(empty_set)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8004,c_53601]) ).
tcf(c_53737,plain,
! [X0: $i,X1: $i] :
( element(sK2(X1,empty_set,sK1),sK0)
| ( relation_image(X1,relation_image(identity_relation(sK7(powerset(X0))),empty_set)) = sK1 )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25160,c_53603]) ).
tcf(c_53738,plain,
! [X0: $i,X1: $i] :
( element(sK2(X0,relation_image(identity_relation(empty_set),X1),sK1),sK0)
| ( relation_image(X0,relation_image(identity_relation(sK7(powerset(empty_set))),X1)) = sK1 )
| ~ empty(empty_set)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8004,c_53603]) ).
tcf(c_53766,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(X0))) = empty_set )
| ( apply(identity_relation(identity_relation(X0)),sK7(identity_relation(X0))) = sK7(identity_relation(X0)) ) ),
inference(superposition,[status(thm)],[c_121,c_12097]) ).
tcf(c_53768,plain,
( ( apply(empty_set,sK7(empty_set)) = sK7(empty_set) )
| ( sK7(powerset(relation_dom(relation_dom(empty_set)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_6104,c_12097]) ).
tcf(c_53769,plain,
( ( apply(identity_relation(powerset(empty_set)),empty_set) = empty_set )
| ( sK7(powerset(relation_dom(relation_dom(powerset(empty_set))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8004,c_12097]) ).
tcf(c_53773,plain,
( ( apply(identity_relation(sK6(sK6(sK6(powerset(empty_set))))),empty_set) = empty_set )
| ( sK7(powerset(relation_dom(relation_dom(sK6(sK6(sK6(powerset(empty_set)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_37341,c_12097]) ).
tcf(c_53774,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( apply(identity_relation(powerset(relation_dom(relation_dom(X0)))),empty_set) = empty_set )
| ( sK7(powerset(relation_dom(relation_dom(powerset(relation_dom(relation_dom(X0))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_12097,c_12097]) ).
tcf(c_53775,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( apply(identity_relation(powerset(relation_dom(relation_dom(X0)))),empty_set) = empty_set )
| ( identity_relation(identity_relation(relation_dom(relation_dom(powerset(relation_dom(relation_dom(X0))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_12097,c_12061]) ).
tcf(c_53776,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( apply(identity_relation(powerset(relation_dom(relation_dom(X0)))),empty_set) = empty_set )
| ( identity_relation(relation_dom(relation_dom(relation_dom(powerset(relation_dom(relation_dom(X0))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_12097,c_12025]) ).
tcf(c_53777,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( apply(identity_relation(powerset(relation_dom(relation_dom(X0)))),empty_set) = empty_set )
| ( relation_dom(relation_dom(relation_dom(relation_dom(powerset(relation_dom(relation_dom(X0))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_12097,c_11951]) ).
tcf(c_53778,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( apply(identity_relation(powerset(relation_dom(relation_dom(X0)))),empty_set) = empty_set )
| ( relation_dom(relation_dom(sK7(powerset(powerset(relation_dom(relation_dom(X0))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_12097,c_11429]) ).
tcf(c_53779,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( sK7(sK6(powerset(powerset(relation_dom(relation_dom(X0)))))) = empty_set )
| ( apply(identity_relation(powerset(relation_dom(relation_dom(X0)))),empty_set) = empty_set ) ),
inference(superposition,[status(thm)],[c_12097,c_11338]) ).
tcf(c_53780,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( sK7(powerset(identity_relation(powerset(relation_dom(relation_dom(X0)))))) = empty_set )
| ( apply(identity_relation(powerset(relation_dom(relation_dom(X0)))),empty_set) = empty_set ) ),
inference(superposition,[status(thm)],[c_12097,c_9745]) ).
tcf(c_53781,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( apply(identity_relation(powerset(relation_dom(relation_dom(X0)))),empty_set) = empty_set )
| ( identity_relation(identity_relation(identity_relation(powerset(relation_dom(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_12097,c_9679]) ).
tcf(c_53782,plain,
! [X0: $i] :
( ( powerset(relation_dom(relation_dom(X0))) = empty_set )
| ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( apply(identity_relation(powerset(relation_dom(relation_dom(X0)))),empty_set) = empty_set ) ),
inference(superposition,[status(thm)],[c_12097,c_9430]) ).
tcf(c_53783,plain,
! [X0: $i] :
( ( relation_dom(powerset(relation_dom(relation_dom(X0)))) = empty_set )
| ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( apply(identity_relation(powerset(relation_dom(relation_dom(X0)))),empty_set) = empty_set ) ),
inference(superposition,[status(thm)],[c_12097,c_9429]) ).
tcf(c_53784,plain,
! [X0: $i] :
( ( identity_relation(powerset(relation_dom(relation_dom(X0)))) = empty_set )
| ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( apply(identity_relation(powerset(relation_dom(relation_dom(X0)))),empty_set) = empty_set ) ),
inference(superposition,[status(thm)],[c_12097,c_9427]) ).
tcf(c_53785,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( relation_dom(relation_dom(powerset(relation_dom(relation_dom(X0))))) = empty_set )
| ( apply(identity_relation(powerset(relation_dom(relation_dom(X0)))),empty_set) = empty_set ) ),
inference(superposition,[status(thm)],[c_12097,c_9426]) ).
tcf(c_53786,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( identity_relation(relation_dom(powerset(relation_dom(relation_dom(X0))))) = empty_set )
| ( apply(identity_relation(powerset(relation_dom(relation_dom(X0)))),empty_set) = empty_set ) ),
inference(superposition,[status(thm)],[c_12097,c_9425]) ).
tcf(c_53787,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( identity_relation(identity_relation(powerset(relation_dom(relation_dom(X0))))) = empty_set )
| ( apply(identity_relation(powerset(relation_dom(relation_dom(X0)))),empty_set) = empty_set ) ),
inference(superposition,[status(thm)],[c_12097,c_9424]) ).
tcf(c_53788,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( sK7(powerset(powerset(relation_dom(relation_dom(X0))))) = empty_set )
| ( apply(identity_relation(powerset(relation_dom(relation_dom(X0)))),empty_set) = empty_set ) ),
inference(superposition,[status(thm)],[c_12097,c_9423]) ).
tcf(c_53789,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( apply(identity_relation(powerset(relation_dom(relation_dom(X0)))),empty_set) = empty_set )
| ( relation_dom(relation_dom(relation_dom(powerset(relation_dom(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_12097,c_9418]) ).
tcf(c_53790,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( apply(identity_relation(powerset(relation_dom(relation_dom(X0)))),empty_set) = empty_set )
| ( identity_relation(relation_dom(relation_dom(powerset(relation_dom(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_12097,c_9415]) ).
tcf(c_53791,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( apply(identity_relation(powerset(relation_dom(relation_dom(X0)))),empty_set) = empty_set )
| ( identity_relation(identity_relation(relation_dom(powerset(relation_dom(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_12097,c_9414]) ).
tcf(c_53792,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( sK7(powerset(relation_dom(powerset(relation_dom(relation_dom(X0)))))) = empty_set )
| ( apply(identity_relation(powerset(relation_dom(relation_dom(X0)))),empty_set) = empty_set ) ),
inference(superposition,[status(thm)],[c_12097,c_9413]) ).
tcf(c_53793,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( apply(identity_relation(powerset(relation_dom(relation_dom(X0)))),empty_set) = empty_set )
| ( identity_relation(sK7(powerset(powerset(relation_dom(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_12097,c_9412]) ).
tcf(c_53794,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( apply(identity_relation(powerset(relation_dom(relation_dom(X0)))),empty_set) = empty_set )
| ( relation_dom(sK7(powerset(powerset(relation_dom(relation_dom(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_12097,c_9411]) ).
tcf(c_53795,plain,
! [X0: $i] :
( empty(powerset(relation_dom(relation_dom(X0))))
| ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ~ in(powerset(relation_dom(relation_dom(X0))),empty_set) ),
inference(superposition,[status(thm)],[c_12097,c_5724]) ).
tcf(c_53796,plain,
! [X0: $i] :
( empty(powerset(relation_dom(relation_dom(X0))))
| in(empty_set,powerset(relation_dom(relation_dom(X0))))
| ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) ) ),
inference(superposition,[status(thm)],[c_12097,c_5703]) ).
tcf(c_53797,plain,
! [X0: $i] :
( element(empty_set,powerset(relation_dom(relation_dom(X0))))
| ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) ) ),
inference(superposition,[status(thm)],[c_12097,c_73]) ).
tcf(c_53798,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(identity_relation(X2),sK7(X2)) = sK7(X2) )
| ~ empty(relation_dom(relation_dom(X2)))
| ~ in(X0,relation_image(identity_relation(empty_set),X1)) ),
inference(superposition,[status(thm)],[c_12097,c_49184]) ).
tcf(c_53799,plain,
! [X0: $i,X1: $i] :
( element(sK3(X0,empty_set,sK1),relation_dom(relation_dom(X1)))
| element(sK2(X0,sK7(powerset(relation_dom(relation_dom(X1)))),sK1),sK0)
| ( apply(identity_relation(X1),sK7(X1)) = sK7(X1) )
| ( relation_image(X0,sK7(powerset(relation_dom(relation_dom(X1))))) = sK1 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_12097,c_7843]) ).
tcf(c_53800,plain,
! [X0: $i,X1: $i] :
( element(sK2(X0,sK1,empty_set),relation_dom(relation_dom(X1)))
| element(sK3(X0,sK1,sK7(powerset(relation_dom(relation_dom(X1))))),sK0)
| ( sK7(powerset(relation_dom(relation_dom(X1)))) = relation_image(X0,sK1) )
| ( apply(identity_relation(X1),sK7(X1)) = sK7(X1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_12097,c_7841]) ).
tcf(c_53801,plain,
! [X0: $i,X1: $i] :
( element(sK3(X0,sK1,empty_set),sK0)
| element(sK2(X0,sK1,sK7(powerset(relation_dom(relation_dom(X1))))),relation_dom(relation_dom(X1)))
| ( sK7(powerset(relation_dom(relation_dom(X1)))) = relation_image(X0,sK1) )
| ( apply(identity_relation(X1),sK7(X1)) = sK7(X1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_12097,c_7841]) ).
tcf(c_53803,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ~ in(X1,empty_set)
| ~ empty(relation_dom(relation_dom(X0))) ),
inference(superposition,[status(thm)],[c_12097,c_5822]) ).
tcf(c_53804,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X1,relation_image(identity_relation(empty_set),X2),sK1),sK0)
| ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( relation_image(X1,relation_image(identity_relation(sK7(powerset(relation_dom(relation_dom(X0))))),X2)) = sK1 )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(relation_dom(relation_dom(X0))) ),
inference(superposition,[status(thm)],[c_12097,c_53603]) ).
tcf(c_53805,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK3(X1,sK1,relation_image(identity_relation(empty_set),X2)),sK0)
| ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( relation_image(identity_relation(sK7(powerset(relation_dom(relation_dom(X0))))),X2) = relation_image(X1,sK1) )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(relation_dom(relation_dom(X0))) ),
inference(superposition,[status(thm)],[c_12097,c_53601]) ).
tcf(c_53806,plain,
! [X0: $i] :
( empty(sK7(powerset(relation_dom(relation_dom(X0)))))
| element(sK7(sK6(sK6(empty_set))),relation_dom(relation_dom(X0)))
| ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) ) ),
inference(superposition,[status(thm)],[c_12097,c_14109]) ).
tcf(c_53807,plain,
! [X0: $i] :
( empty(sK7(powerset(relation_dom(relation_dom(X0)))))
| ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ~ in(relation_dom(relation_dom(X0)),sK7(sK6(empty_set))) ),
inference(superposition,[status(thm)],[c_12097,c_25990]) ).
tcf(c_53808,plain,
! [X0: $i] :
( empty(sK7(powerset(relation_dom(relation_dom(X0)))))
| in(sK7(sK6(empty_set)),relation_dom(relation_dom(X0)))
| ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) ) ),
inference(superposition,[status(thm)],[c_12097,c_25981]) ).
tcf(c_53809,plain,
! [X0: $i] :
( relation(sK7(powerset(empty_set)))
| ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ~ empty(relation_dom(relation_dom(X0))) ),
inference(superposition,[status(thm)],[c_12097,c_20634]) ).
tcf(c_53810,plain,
! [X0: $i] :
( function(sK7(powerset(empty_set)))
| ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ~ empty(relation_dom(relation_dom(X0))) ),
inference(superposition,[status(thm)],[c_12097,c_20633]) ).
tcf(c_53811,plain,
! [X0: $i] :
( empty(sK7(powerset(empty_set)))
| ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ~ empty(relation_dom(relation_dom(X0))) ),
inference(superposition,[status(thm)],[c_12097,c_18749]) ).
tcf(c_53812,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( apply(identity_relation(powerset(relation_dom(relation_dom(X0)))),empty_set) = empty_set ) ),
inference(superposition,[status(thm)],[c_12097,c_9434]) ).
tcf(c_53813,plain,
! [X0: $i] :
( empty(sK7(powerset(relation_dom(relation_dom(X0)))))
| ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ~ in(relation_dom(relation_dom(X0)),sK7(empty_set)) ),
inference(superposition,[status(thm)],[c_12097,c_18741]) ).
tcf(c_53814,plain,
! [X0: $i] :
( in(sK7(empty_set),relation_dom(relation_dom(X0)))
| empty(sK7(powerset(relation_dom(relation_dom(X0)))))
| ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) ) ),
inference(superposition,[status(thm)],[c_12097,c_18732]) ).
tcf(c_53815,plain,
! [X0: $i] :
( empty(sK7(powerset(relation_dom(relation_dom(X0)))))
| element(sK7(sK6(empty_set)),relation_dom(relation_dom(X0)))
| ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) ) ),
inference(superposition,[status(thm)],[c_12097,c_10355]) ).
tcf(c_53816,plain,
! [X0: $i,X1: $i] :
( element(sK2(X1,empty_set,sK1),sK0)
| ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( relation_image(X1,sK7(powerset(relation_dom(relation_dom(X0))))) = sK1 )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(relation_dom(relation_dom(X0))) ),
inference(superposition,[status(thm)],[c_12097,c_7406]) ).
tcf(c_53817,plain,
! [X0: $i,X1: $i] :
( element(sK3(X1,sK1,empty_set),sK0)
| ( sK7(powerset(relation_dom(relation_dom(X0)))) = relation_image(X1,sK1) )
| ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(relation_dom(relation_dom(X0))) ),
inference(superposition,[status(thm)],[c_12097,c_7284]) ).
tcf(c_53818,plain,
! [X0: $i] :
( empty(sK7(powerset(relation_dom(relation_dom(X0)))))
| element(sK7(empty_set),relation_dom(relation_dom(X0)))
| ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) ) ),
inference(superposition,[status(thm)],[c_12097,c_7840]) ).
tcf(c_53822,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(identity_relation(X0),X1) = X2 )
| ( sK7(powerset(relation_dom(relation_dom(X0)))) = empty_set )
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),relation_dom(identity_relation(X0)))
| ~ in(sK2(identity_relation(X0),X1,X2),X2)
| ( sK2(identity_relation(X0),X1,X2) != sK7(X0) ) ),
inference(superposition,[status(thm)],[c_12097,c_53]) ).
tcf(c_53823,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0),relation_image(identity_relation(X0),X1))
| ( sK7(powerset(relation_dom(relation_dom(X0)))) = empty_set )
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),relation_dom(identity_relation(X0))) ),
inference(superposition,[status(thm)],[c_12097,c_57]) ).
tcf(c_53825,plain,
! [X0: $i] :
( empty(empty_set)
| ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ~ empty(relation_dom(relation_dom(X0))) ),
inference(light_normalisation,[status(thm)],[c_53811,c_8004]) ).
tcf(c_53826,plain,
! [X0: $i] :
( function(empty_set)
| ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ~ empty(relation_dom(relation_dom(X0))) ),
inference(light_normalisation,[status(thm)],[c_53810,c_8004]) ).
tcf(c_53827,plain,
! [X0: $i] :
( relation(empty_set)
| ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ~ empty(relation_dom(relation_dom(X0))) ),
inference(light_normalisation,[status(thm)],[c_53809,c_8004]) ).
tcf(c_53836,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(identity_relation(X2),sK7(X2)) = sK7(X2) )
| ~ empty(relation_dom(relation_dom(X2)))
| ~ in(X0,relation_image(empty_set,X1)) ),
inference(light_normalisation,[status(thm)],[c_53798,c_6104]) ).
tcf(c_53857,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0),relation_image(identity_relation(X0),X1))
| ( sK7(powerset(relation_dom(relation_dom(X0)))) = empty_set )
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),X0) ),
inference(light_normalisation,[status(thm)],[c_53823,c_121]) ).
tcf(c_53858,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0),relation_image(identity_relation(X0),X1))
| ( sK7(powerset(relation_dom(relation_dom(X0)))) = empty_set )
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_53857,c_62,c_63]) ).
tcf(c_53875,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK3(X1,sK1,relation_image(empty_set,X2)),sK0)
| ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( relation_image(identity_relation(sK7(powerset(relation_dom(relation_dom(X0))))),X2) = relation_image(X1,sK1) )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(relation_dom(relation_dom(X0))) ),
inference(light_normalisation,[status(thm)],[c_53805,c_6104]) ).
tcf(c_53882,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X1,relation_image(empty_set,X2),sK1),sK0)
| ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( relation_image(X1,relation_image(identity_relation(sK7(powerset(relation_dom(relation_dom(X0))))),X2)) = sK1 )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(relation_dom(relation_dom(X0))) ),
inference(light_normalisation,[status(thm)],[c_53804,c_6104]) ).
tcf(c_53907,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(identity_relation(X0),X1) = X2 )
| ( sK7(powerset(relation_dom(relation_dom(X0)))) = empty_set )
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),X0)
| ~ in(sK2(identity_relation(X0),X1,X2),X2)
| ( sK2(identity_relation(X0),X1,X2) != sK7(X0) ) ),
inference(light_normalisation,[status(thm)],[c_53822,c_121]) ).
tcf(c_53908,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(identity_relation(X0),X1) = X2 )
| ( sK7(powerset(relation_dom(relation_dom(X0)))) = empty_set )
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),X0)
| ~ in(sK2(identity_relation(X0),X1,X2),X2)
| ( sK2(identity_relation(X0),X1,X2) != sK7(X0) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_53907,c_62,c_63]) ).
tcf(c_54049,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( relation_image(identity_relation(relation_dom(relation_dom(X0))),X1) = empty_set ) ),
inference(superposition,[status(thm)],[c_10348,c_52875]) ).
tcf(c_54050,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ( relation_image(identity_relation(relation_dom(relation_dom(X0))),X1) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_52875]) ).
tcf(c_54051,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( relation_image(identity_relation(relation_dom(relation_dom(X0))),X1) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_52875]) ).
tcf(c_54052,plain,
! [X0: $i] : relation_image(identity_relation(relation_dom(relation_dom(empty_set))),X0) = empty_set,
inference(superposition,[status(thm)],[c_83,c_52875]) ).
tcf(c_54053,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(relation_dom(relation_dom(relation_dom(X0)))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_52875]) ).
tcf(c_54054,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(relation_dom(relation_dom(identity_relation(X0)))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_52875]) ).
tcf(c_54055,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(relation_dom(relation_dom(sK7(powerset(X0))))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_52875]) ).
tcf(c_54056,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(relation_dom(relation_dom(sK7(sK6(powerset(X0)))))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_52875]) ).
tcf(c_54057,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(relation_dom(relation_dom(sK7(sK6(sK6(powerset(X0))))))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_52875]) ).
tcf(c_54058,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(relation_dom(relation_dom(relation_image(X0,empty_set)))),X1) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_52875]) ).
tcf(c_54059,plain,
! [X0: $i] :
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( relation_image(identity_relation(relation_dom(relation_dom(sK7(powerset(sK1))))),X0) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_52875]) ).
tcf(c_54060,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(relation_dom(relation_dom(sK7(powerset(sK7(powerset(X0))))))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_52875]) ).
tcf(c_54061,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(relation_dom(relation_dom(sK7(powerset(relation_image(X0,empty_set)))))),X1) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_52875]) ).
tcf(c_54062,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(relation_dom(relation_dom(sK7(powerset(sK7(sK6(powerset(X0)))))))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_52875]) ).
tcf(c_54063,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(relation_dom(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0))))))))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_52875]) ).
tcf(c_54064,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(identity_relation(relation_dom(relation_dom(relation_image(identity_relation(X0),X1)))),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_52875]) ).
tcf(c_54065,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(relation_dom(relation_dom(sK7(sK6(sK6(sK6(powerset(X0)))))))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_52875]) ).
tcf(c_54066,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(relation_dom(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0)))))))))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_52875]) ).
tcf(c_54067,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(identity_relation(relation_dom(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X1)))))),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_52875]) ).
tcf(c_54159,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( identity_relation(relation_image(identity_relation(relation_dom(X0)),X1)) = empty_set ) ),
inference(superposition,[status(thm)],[c_10348,c_53061]) ).
tcf(c_54160,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ( identity_relation(relation_image(identity_relation(relation_dom(X0)),X1)) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_53061]) ).
tcf(c_54161,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( identity_relation(relation_image(identity_relation(relation_dom(X0)),X1)) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_53061]) ).
tcf(c_54162,plain,
! [X0: $i] : identity_relation(relation_image(identity_relation(relation_dom(empty_set)),X0)) = empty_set,
inference(superposition,[status(thm)],[c_83,c_53061]) ).
tcf(c_54163,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_image(identity_relation(relation_dom(relation_dom(X0))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_53061]) ).
tcf(c_54164,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_image(identity_relation(relation_dom(identity_relation(X0))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_53061]) ).
tcf(c_54165,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_image(identity_relation(relation_dom(sK7(powerset(X0)))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_53061]) ).
tcf(c_54166,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_image(identity_relation(relation_dom(sK7(sK6(powerset(X0))))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_53061]) ).
tcf(c_54167,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_image(identity_relation(relation_dom(sK7(sK6(sK6(powerset(X0)))))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_53061]) ).
tcf(c_54168,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_image(identity_relation(relation_dom(relation_image(X0,empty_set))),X1)) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_53061]) ).
tcf(c_54169,plain,
! [X0: $i] :
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( identity_relation(relation_image(identity_relation(relation_dom(sK7(powerset(sK1)))),X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_53061]) ).
tcf(c_54170,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_image(identity_relation(relation_dom(sK7(powerset(sK7(powerset(X0)))))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_53061]) ).
tcf(c_54171,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_image(identity_relation(relation_dom(sK7(powerset(relation_image(X0,empty_set))))),X1)) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_53061]) ).
tcf(c_54172,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_image(identity_relation(relation_dom(sK7(powerset(sK7(sK6(powerset(X0))))))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_53061]) ).
tcf(c_54173,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_image(identity_relation(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_53061]) ).
tcf(c_54174,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(relation_image(identity_relation(relation_dom(relation_image(identity_relation(X0),X1))),X2)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_53061]) ).
tcf(c_54175,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_image(identity_relation(relation_dom(sK7(sK6(sK6(sK6(powerset(X0))))))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_53061]) ).
tcf(c_54176,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_image(identity_relation(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_53061]) ).
tcf(c_54177,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(relation_image(identity_relation(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X1))))),X2)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_53061]) ).
tcf(c_54361,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( relation_dom(relation_image(identity_relation(relation_dom(X0)),X1)) = empty_set ) ),
inference(superposition,[status(thm)],[c_10348,c_53237]) ).
tcf(c_54362,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ( relation_dom(relation_image(identity_relation(relation_dom(X0)),X1)) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_53237]) ).
tcf(c_54363,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( relation_dom(relation_image(identity_relation(relation_dom(X0)),X1)) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_53237]) ).
tcf(c_54364,plain,
! [X0: $i] : relation_dom(relation_image(identity_relation(relation_dom(empty_set)),X0)) = empty_set,
inference(superposition,[status(thm)],[c_83,c_53237]) ).
tcf(c_54365,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_image(identity_relation(relation_dom(relation_dom(X0))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_53237]) ).
tcf(c_54366,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_image(identity_relation(relation_dom(identity_relation(X0))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_53237]) ).
tcf(c_54367,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_image(identity_relation(relation_dom(sK7(powerset(X0)))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_53237]) ).
tcf(c_54368,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_image(identity_relation(relation_dom(sK7(sK6(powerset(X0))))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_53237]) ).
tcf(c_54369,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_image(identity_relation(relation_dom(sK7(sK6(sK6(powerset(X0)))))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_53237]) ).
tcf(c_54370,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_image(identity_relation(relation_dom(relation_image(X0,empty_set))),X1)) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_53237]) ).
tcf(c_54371,plain,
! [X0: $i] :
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( relation_dom(relation_image(identity_relation(relation_dom(sK7(powerset(sK1)))),X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_53237]) ).
tcf(c_54372,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_image(identity_relation(relation_dom(sK7(powerset(sK7(powerset(X0)))))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_53237]) ).
tcf(c_54373,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_image(identity_relation(relation_dom(sK7(powerset(relation_image(X0,empty_set))))),X1)) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_53237]) ).
tcf(c_54374,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_image(identity_relation(relation_dom(sK7(powerset(sK7(sK6(powerset(X0))))))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_53237]) ).
tcf(c_54375,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_image(identity_relation(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_53237]) ).
tcf(c_54376,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_image(identity_relation(relation_dom(relation_image(identity_relation(X0),X1))),X2)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_53237]) ).
tcf(c_54377,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_image(identity_relation(relation_dom(sK7(sK6(sK6(sK6(powerset(X0))))))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_53237]) ).
tcf(c_54378,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_image(identity_relation(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_53237]) ).
tcf(c_54379,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_image(identity_relation(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X1))))),X2)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_53237]) ).
tcf(c_54625,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( relation_image(identity_relation(identity_relation(relation_dom(X0))),X1) = empty_set ) ),
inference(superposition,[status(thm)],[c_10348,c_53471]) ).
tcf(c_54626,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ( relation_image(identity_relation(identity_relation(relation_dom(X0))),X1) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_53471]) ).
tcf(c_54627,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( relation_image(identity_relation(identity_relation(relation_dom(X0))),X1) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_53471]) ).
tcf(c_54628,plain,
! [X0: $i] : relation_image(identity_relation(identity_relation(relation_dom(empty_set))),X0) = empty_set,
inference(superposition,[status(thm)],[c_83,c_53471]) ).
tcf(c_54629,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(identity_relation(relation_dom(relation_dom(X0)))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_53471]) ).
tcf(c_54630,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(identity_relation(relation_dom(identity_relation(X0)))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_53471]) ).
tcf(c_54631,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(identity_relation(relation_dom(sK7(powerset(X0))))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_53471]) ).
tcf(c_54632,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(identity_relation(relation_dom(sK7(sK6(powerset(X0)))))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_53471]) ).
tcf(c_54633,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(identity_relation(relation_dom(sK7(sK6(sK6(powerset(X0))))))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_53471]) ).
tcf(c_54634,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(identity_relation(relation_dom(relation_image(X0,empty_set)))),X1) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_53471]) ).
tcf(c_54635,plain,
! [X0: $i] :
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( relation_image(identity_relation(identity_relation(relation_dom(sK7(powerset(sK1))))),X0) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_53471]) ).
tcf(c_54636,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(identity_relation(relation_dom(sK7(powerset(sK7(powerset(X0))))))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_53471]) ).
tcf(c_54637,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(identity_relation(relation_dom(sK7(powerset(relation_image(X0,empty_set)))))),X1) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_53471]) ).
tcf(c_54638,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(identity_relation(relation_dom(sK7(powerset(sK7(sK6(powerset(X0)))))))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_53471]) ).
tcf(c_54639,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(identity_relation(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0))))))))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_53471]) ).
tcf(c_54640,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(identity_relation(identity_relation(relation_dom(relation_image(identity_relation(X0),X1)))),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_53471]) ).
tcf(c_54641,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(identity_relation(relation_dom(sK7(sK6(sK6(sK6(powerset(X0)))))))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_53471]) ).
tcf(c_54642,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(identity_relation(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0)))))))))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_53471]) ).
tcf(c_54643,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(identity_relation(identity_relation(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X1)))))),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_53471]) ).
tcf(c_55027,plain,
! [X0: $i] :
( empty(relation_image(identity_relation(empty_set),X0))
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_8004,c_53608]) ).
tcf(c_55028,plain,
! [X0: $i,X1: $i] :
( empty(relation_image(identity_relation(empty_set),X1))
| ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ~ empty(relation_dom(relation_dom(X0))) ),
inference(superposition,[status(thm)],[c_12097,c_53608]) ).
tcf(c_55029,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(identity_relation(identity_relation(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X1)))),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_53471]) ).
tcf(c_55030,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_image(identity_relation(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X1))),X2)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_53237]) ).
tcf(c_55031,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(relation_image(identity_relation(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X1))),X2)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_53061]) ).
tcf(c_55032,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(identity_relation(relation_dom(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X1)))),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_52875]) ).
tcf(c_55033,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(identity_relation(identity_relation(relation_image(identity_relation(sK7(powerset(X0))),X1))),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_52683]) ).
tcf(c_55034,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_image(identity_relation(relation_image(identity_relation(sK7(powerset(X0))),X1)),X2)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_49654]) ).
tcf(c_55035,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(relation_image(identity_relation(relation_image(identity_relation(sK7(powerset(X0))),X1)),X2)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_49652]) ).
tcf(c_55036,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(identity_relation(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X1))),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_52682]) ).
tcf(c_55037,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(identity_relation(relation_image(identity_relation(sK7(powerset(X0))),X1)),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_49655]) ).
tcf(c_55038,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(powerset(identity_relation(identity_relation(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_39551]) ).
tcf(c_55039,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(identity_relation(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_13654]) ).
tcf(c_55040,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(identity_relation(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_13049]) ).
tcf(c_55041,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(powerset(identity_relation(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_12914]) ).
tcf(c_55042,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK7(powerset(identity_relation(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_12876]) ).
tcf(c_55043,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(sK6(powerset(identity_relation(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_38682]) ).
tcf(c_55044,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK7(sK6(powerset(identity_relation(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_37969]) ).
tcf(c_55045,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(sK6(powerset(identity_relation(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_37889]) ).
tcf(c_55046,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(sK6(sK6(powerset(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_37780]) ).
tcf(c_55047,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(powerset(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_12760]) ).
tcf(c_55048,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK7(powerset(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_12361]) ).
tcf(c_55049,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(sK7(powerset(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_12323]) ).
tcf(c_55050,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(sK7(powerset(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_12217]) ).
tcf(c_55051,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK7(sK6(sK6(powerset(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_37664]) ).
tcf(c_55052,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(sK6(sK6(powerset(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_37342]) ).
tcf(c_55053,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(identity_relation(identity_relation(identity_relation(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_31222]) ).
tcf(c_55054,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(identity_relation(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_31142]) ).
tcf(c_55055,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(sK7(powerset(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_12140]) ).
tcf(c_55056,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(relation_dom(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_12104]) ).
tcf(c_55057,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(relation_dom(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_12068]) ).
tcf(c_55058,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(relation_dom(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_12032]) ).
tcf(c_55059,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(powerset(identity_relation(identity_relation(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_31014]) ).
tcf(c_55060,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK7(powerset(identity_relation(identity_relation(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_30942]) ).
tcf(c_55061,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(sK7(powerset(identity_relation(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_30355]) ).
tcf(c_55062,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(sK7(powerset(identity_relation(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_30248]) ).
tcf(c_55063,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_11958]) ).
tcf(c_55064,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK7(powerset(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_11436]) ).
tcf(c_55065,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(powerset(sK7(sK6(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_11346]) ).
tcf(c_55066,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(sK7(sK6(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_10669]) ).
tcf(c_55067,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(sK7(powerset(identity_relation(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_30158]) ).
tcf(c_55068,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK7(powerset(identity_relation(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_30068]) ).
tcf(c_55069,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(powerset(sK7(powerset(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_29569]) ).
tcf(c_55070,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK7(sK6(powerset(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_29442]) ).
tcf(c_55071,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(relation_dom(sK7(sK6(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_10666]) ).
tcf(c_55072,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(relation_dom(sK7(sK6(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_10665]) ).
tcf(c_55073,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(relation_dom(sK7(sK6(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_10664]) ).
tcf(c_55074,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK7(powerset(sK7(sK6(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_10663]) ).
tcf(c_55075,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(sK7(sK6(powerset(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_29308]) ).
tcf(c_55076,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(sK7(sK6(powerset(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_29194]) ).
tcf(c_55077,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(sK7(sK6(powerset(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_28717]) ).
tcf(c_55078,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(identity_relation(sK7(powerset(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_28572]) ).
tcf(c_55079,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(powerset(sK7(sK6(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_10662]) ).
tcf(c_55080,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(identity_relation(sK7(sK6(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_10659]) ).
tcf(c_55081,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(identity_relation(sK7(powerset(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_28429]) ).
tcf(c_55082,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(identity_relation(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X2)))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_27714]) ).
tcf(c_55083,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(powerset(sK7(powerset(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_27588]) ).
tcf(c_55084,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK7(powerset(sK7(powerset(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_27452]) ).
tcf(c_55085,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(identity_relation(sK7(sK6(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_10658]) ).
tcf(c_55086,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X2)))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_9351]) ).
tcf(c_55087,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X2)))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_9323]) ).
tcf(c_55088,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(powerset(identity_relation(identity_relation(relation_image(identity_relation(sK7(powerset(X0))),X1)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_25847]) ).
tcf(c_55089,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(sK6(powerset(identity_relation(relation_image(identity_relation(sK7(powerset(X0))),X1)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_17537]) ).
tcf(c_55090,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(relation_dom(sK7(powerset(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_27367]) ).
tcf(c_55091,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(relation_dom(sK7(powerset(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_26858]) ).
tcf(c_55092,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(relation_dom(sK7(powerset(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_26809]) ).
tcf(c_55093,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(sK7(powerset(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_26731]) ).
tcf(c_55094,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK7(sK6(powerset(identity_relation(relation_image(identity_relation(sK7(powerset(X0))),X1)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_17480]) ).
tcf(c_55095,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(sK6(powerset(identity_relation(relation_image(identity_relation(sK7(powerset(X0))),X1)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_16757]) ).
tcf(c_55096,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(sK6(sK6(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_15644]) ).
tcf(c_55097,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK7(sK6(sK6(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_15642]) ).
tcf(c_55098,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(powerset(identity_relation(relation_dom(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_25936]) ).
tcf(c_55099,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(sK6(sK6(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_36269]) ).
tcf(c_55100,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(sK6(powerset(relation_dom(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_25099]) ).
tcf(c_55101,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK7(sK6(powerset(relation_dom(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_24875]) ).
tcf(c_55102,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(identity_relation(identity_relation(identity_relation(relation_image(identity_relation(sK7(powerset(X0))),X1)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_13970]) ).
tcf(c_55103,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(identity_relation(relation_image(identity_relation(sK7(powerset(X0))),X1)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_13854]) ).
tcf(c_55104,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(powerset(identity_relation(identity_relation(relation_image(identity_relation(sK7(powerset(X0))),X1)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_12910]) ).
tcf(c_55105,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK7(powerset(identity_relation(identity_relation(relation_image(identity_relation(sK7(powerset(X0))),X1)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_12872]) ).
tcf(c_55106,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(sK6(powerset(relation_dom(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_24819]) ).
tcf(c_55107,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(identity_relation(identity_relation(relation_dom(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_24724]) ).
tcf(c_55108,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(relation_dom(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_24676]) ).
tcf(c_55109,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(powerset(relation_dom(relation_dom(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_24628]) ).
tcf(c_55110,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(sK7(powerset(identity_relation(relation_image(identity_relation(sK7(powerset(X0))),X1)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_12319]) ).
tcf(c_55111,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(sK7(powerset(identity_relation(relation_image(identity_relation(sK7(powerset(X0))),X1)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_12213]) ).
tcf(c_55112,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(sK7(powerset(identity_relation(relation_image(identity_relation(sK7(powerset(X0))),X1)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_12136]) ).
tcf(c_55113,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK7(powerset(identity_relation(relation_image(identity_relation(sK7(powerset(X0))),X1)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_11432]) ).
tcf(c_55114,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(identity_relation(relation_dom(relation_dom(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_24580]) ).
tcf(c_55115,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(identity_relation(relation_dom(relation_dom(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_24491]) ).
tcf(c_55116,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(powerset(identity_relation(relation_dom(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_24443]) ).
tcf(c_55117,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK7(powerset(identity_relation(relation_dom(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_24395]) ).
tcf(c_55118,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(powerset(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_11345]) ).
tcf(c_55119,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK7(sK6(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_10677]) ).
tcf(c_55120,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(sK7(sK6(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_10676]) ).
tcf(c_55121,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(sK7(sK6(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_10675]) ).
tcf(c_55122,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(powerset(relation_dom(relation_dom(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_24347]) ).
tcf(c_55123,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK7(powerset(relation_dom(relation_dom(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_23164]) ).
tcf(c_55124,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(sK7(powerset(relation_dom(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_22515]) ).
tcf(c_55125,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(sK7(powerset(relation_dom(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_22426]) ).
tcf(c_55126,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(sK7(sK6(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_10674]) ).
tcf(c_55127,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(identity_relation(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_9751]) ).
tcf(c_55128,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(identity_relation(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_9685]) ).
tcf(c_55129,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(sK7(powerset(relation_dom(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_22338]) ).
tcf(c_55130,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(relation_dom(relation_dom(relation_dom(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_22121]) ).
tcf(c_55131,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(relation_dom(relation_dom(relation_dom(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_22031]) ).
tcf(c_55132,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_21914]) ).
tcf(c_55133,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(identity_relation(relation_image(identity_relation(sK7(powerset(X0))),X2))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_9348]) ).
tcf(c_55134,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(powerset(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_9118]) ).
tcf(c_55135,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK7(powerset(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_9091]) ).
tcf(c_55136,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_9021]) ).
tcf(c_55137,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_21763]) ).
tcf(c_55138,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK7(powerset(relation_dom(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_21512]) ).
tcf(c_55139,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(relation_dom(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X2)))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_20489]) ).
tcf(c_55140,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X2)))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_20393]) ).
tcf(c_55141,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_8996]) ).
tcf(c_55142,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_8961]) ).
tcf(c_55143,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_8565]) ).
tcf(c_55144,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK7(powerset(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X2)))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_18503]) ).
tcf(c_55145,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(powerset(identity_relation(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X1)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_25846]) ).
tcf(c_55146,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(powerset(identity_relation(relation_image(identity_relation(sK7(powerset(X0))),X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_11341]) ).
tcf(c_55147,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK7(sK6(powerset(relation_image(identity_relation(sK7(powerset(X0))),X2)))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_10679]) ).
tcf(c_55148,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(sK6(powerset(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X1)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_17536]) ).
tcf(c_55149,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK7(sK6(powerset(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X1)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_17479]) ).
tcf(c_55150,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(sK6(powerset(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X1)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_16756]) ).
tcf(c_55151,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(identity_relation(identity_relation(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X1)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_13969]) ).
tcf(c_55152,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X1)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_13853]) ).
tcf(c_55153,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(powerset(relation_dom(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X1)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_13817]) ).
tcf(c_55154,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(identity_relation(relation_dom(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X1)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_13649]) ).
tcf(c_55155,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(identity_relation(relation_dom(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X1)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_13044]) ).
tcf(c_55156,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(powerset(identity_relation(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X1)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_12909]) ).
tcf(c_55157,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK7(powerset(identity_relation(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X1)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_12871]) ).
tcf(c_55158,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(powerset(relation_dom(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X1)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_12755]) ).
tcf(c_55159,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK7(powerset(relation_dom(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X1)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_12356]) ).
tcf(c_55160,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(sK7(powerset(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X1)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_12318]) ).
tcf(c_55161,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(sK7(powerset(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X1)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_12212]) ).
tcf(c_55162,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(sK7(powerset(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X1)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_12135]) ).
tcf(c_55163,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(relation_dom(relation_dom(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X1)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_12099]) ).
tcf(c_55164,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(relation_dom(relation_dom(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X1)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_12063]) ).
tcf(c_55165,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(relation_dom(relation_dom(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X1)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_12027]) ).
tcf(c_55166,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X1)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_11953]) ).
tcf(c_55167,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK7(powerset(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X1)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_11431]) ).
tcf(c_55168,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X2))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_9347]) ).
tcf(c_55169,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X2))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_9319]) ).
tcf(c_55170,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X2))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_6877]) ).
tcf(c_55171,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(sK6(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_10680]) ).
tcf(c_55172,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK7(sK6(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_10678]) ).
tcf(c_55173,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(sK6(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_15645]) ).
tcf(c_55174,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(identity_relation(identity_relation(relation_image(identity_relation(sK7(powerset(X0))),X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_9748]) ).
tcf(c_55175,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(relation_image(identity_relation(sK7(powerset(X0))),X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_9682]) ).
tcf(c_55176,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(powerset(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_11340]) ).
tcf(c_55177,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(identity_relation(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_9747]) ).
tcf(c_55178,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(identity_relation(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_9681]) ).
tcf(c_55179,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(powerset(identity_relation(relation_image(identity_relation(sK7(powerset(X0))),X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_9115]) ).
tcf(c_55180,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK7(powerset(identity_relation(relation_image(identity_relation(sK7(powerset(X0))),X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_9088]) ).
tcf(c_55181,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(powerset(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_9114]) ).
tcf(c_55182,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK7(powerset(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_9087]) ).
tcf(c_55183,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_8009]) ).
tcf(c_55184,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_7966]) ).
tcf(c_55185,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_7938]) ).
tcf(c_55186,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(relation_dom(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_9017]) ).
tcf(c_55187,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(relation_dom(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_8992]) ).
tcf(c_55188,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(relation_dom(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_8957]) ).
tcf(c_55189,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_8561]) ).
tcf(c_55190,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_6875]) ).
tcf(c_55191,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_10681]) ).
tcf(c_55192,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(identity_relation(relation_image(identity_relation(sK7(powerset(X0))),X1)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_8006]) ).
tcf(c_55193,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(identity_relation(relation_image(identity_relation(sK7(powerset(X0))),X1)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_7963]) ).
tcf(c_55194,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(relation_image(identity_relation(sK7(powerset(X0))),X2)) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_5794]) ).
tcf(c_55195,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X2)) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_5793]) ).
tcf(c_55196,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_6878]) ).
tcf(c_55197,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_6876]) ).
tcf(c_55198,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X1)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_8005]) ).
tcf(c_55199,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X1)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_7962]) ).
tcf(c_55200,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X1)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_7934]) ).
tcf(c_55201,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X1)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_6133]) ).
tcf(c_55202,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_6879]) ).
tcf(c_55203,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(relation_image(identity_relation(sK7(powerset(X0))),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_6106]) ).
tcf(c_55204,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_6105]) ).
tcf(c_55205,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_5747]) ).
tcf(c_55207,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(identity_relation(sK7(powerset(X0))),X2) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_51]) ).
tcf(c_55210,plain,
! [X0: $i,X1: $i] :
( function(relation_image(identity_relation(sK7(powerset(X0))),X1))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_98]) ).
tcf(c_55211,plain,
! [X0: $i,X1: $i] :
( relation(relation_image(identity_relation(sK7(powerset(X0))),X1))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_80]) ).
tcf(c_55587,plain,
! [X0: $i,X1: $i] :
( empty(relation_image(empty_set,X1))
| ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ~ empty(relation_dom(relation_dom(X0))) ),
inference(light_normalisation,[status(thm)],[c_55028,c_6104]) ).
tcf(c_56792,plain,
! [X0: $i] :
( function(relation_image(identity_relation(empty_set),X0))
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_8004,c_55210]) ).
tcf(c_56793,plain,
! [X0: $i,X1: $i] :
( function(relation_image(identity_relation(empty_set),X1))
| ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ~ empty(relation_dom(relation_dom(X0))) ),
inference(superposition,[status(thm)],[c_12097,c_55210]) ).
tcf(c_56794,plain,
! [X0: $i,X1: $i] :
( ( relation_image(relation_image(identity_relation(sK7(powerset(X0))),X1),empty_set) = empty_set )
| ~ empty(X0)
| ~ relation(relation_image(identity_relation(sK7(powerset(X0))),X1)) ),
inference(superposition,[status(thm)],[c_55210,c_23329]) ).
tcf(c_56796,plain,
! [X0: $i,X1: $i] :
( function(relation_image(empty_set,X1))
| ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ~ empty(relation_dom(relation_dom(X0))) ),
inference(light_normalisation,[status(thm)],[c_56793,c_6104]) ).
tcf(c_56820,plain,
! [X0: $i] :
( relation(relation_image(identity_relation(empty_set),X0))
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_8004,c_55211]) ).
tcf(c_56821,plain,
! [X0: $i,X1: $i] :
( relation(relation_image(identity_relation(empty_set),X1))
| ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ~ empty(relation_dom(relation_dom(X0))) ),
inference(superposition,[status(thm)],[c_12097,c_55211]) ).
tcf(c_56823,plain,
! [X0: $i,X1: $i] :
( relation(relation_image(empty_set,X1))
| ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ~ empty(relation_dom(relation_dom(X0))) ),
inference(light_normalisation,[status(thm)],[c_56821,c_6104]) ).
tcf(c_56831,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(relation_image(identity_relation(X0),X1))) = empty_set )
| ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_10348,c_49648]) ).
tcf(c_56832,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(relation_image(identity_relation(X0),X1))) = empty_set )
| ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) ) ),
inference(superposition,[status(thm)],[c_5806,c_49648]) ).
tcf(c_56833,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( sK7(powerset(relation_image(identity_relation(X0),X1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_49648]) ).
tcf(c_56834,plain,
! [X0: $i] : sK7(powerset(relation_image(identity_relation(empty_set),X0))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_49648]) ).
tcf(c_56835,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(relation_image(identity_relation(relation_dom(X0)),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_49648]) ).
tcf(c_56836,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(relation_image(identity_relation(identity_relation(X0)),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_49648]) ).
tcf(c_56838,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(relation_image(identity_relation(sK7(sK6(powerset(X0)))),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_49648]) ).
tcf(c_56839,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(relation_image(identity_relation(sK7(sK6(sK6(powerset(X0))))),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_49648]) ).
tcf(c_56840,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(relation_image(identity_relation(relation_image(X0,empty_set)),X1))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_49648]) ).
tcf(c_56841,plain,
! [X0: $i] :
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( sK7(powerset(relation_image(identity_relation(sK7(powerset(sK1))),X0))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_49648]) ).
tcf(c_56842,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(relation_image(identity_relation(sK7(powerset(sK7(powerset(X0))))),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_49648]) ).
tcf(c_56843,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(relation_image(identity_relation(sK7(powerset(relation_image(X0,empty_set)))),X1))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_49648]) ).
tcf(c_56844,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(relation_image(identity_relation(sK7(powerset(sK7(sK6(powerset(X0)))))),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_49648]) ).
tcf(c_56845,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(relation_image(identity_relation(sK7(powerset(sK7(sK6(sK6(powerset(X0))))))),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_49648]) ).
tcf(c_56846,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK7(powerset(relation_image(identity_relation(relation_image(identity_relation(X0),X1)),X2))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_49648]) ).
tcf(c_56847,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(relation_image(identity_relation(sK7(sK6(sK6(sK6(powerset(X0)))))),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_49648]) ).
tcf(c_56848,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(relation_image(identity_relation(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0)))))))),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_49648]) ).
tcf(c_56849,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK7(powerset(relation_image(identity_relation(sK7(powerset(relation_image(identity_relation(X0),X1)))),X2))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_49648]) ).
tcf(c_56850,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK7(powerset(relation_image(identity_relation(relation_image(identity_relation(sK7(powerset(X0))),X1)),X2))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_49648]) ).
tcf(c_56955,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(X1)
| ~ in(X0,X2)
| ~ in(X0,X1) ),
inference(demodulation,[status(thm)],[c_49337,c_121]) ).
tcf(c_56962,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(identity_relation(X1),X2) = X0 )
| ( apply(identity_relation(X1),sK7(sK6(X1))) = sK7(sK6(X1)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10348,c_49653]) ).
tcf(c_56963,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(identity_relation(X1),X2) = X0 )
| ( apply(identity_relation(powerset(X1)),sK6(X1)) = sK6(X1) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5806,c_49653]) ).
tcf(c_56964,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(identity_relation(X1),X2) = X0 )
| ( apply(identity_relation(X1),sK7(X1)) = sK7(X1) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5807,c_49653]) ).
tcf(c_56965,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(empty_set),X1) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_83,c_49653]) ).
tcf(c_56966,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(identity_relation(relation_dom(X0)),X2) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_49653]) ).
tcf(c_56967,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(identity_relation(identity_relation(X0)),X2) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_49653]) ).
tcf(c_56969,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(identity_relation(sK7(sK6(powerset(X0)))),X2) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_49653]) ).
tcf(c_56970,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(identity_relation(sK7(sK6(sK6(powerset(X0))))),X2) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_49653]) ).
tcf(c_56971,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(identity_relation(relation_image(X1,empty_set)),X2) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18616,c_49653]) ).
tcf(c_56972,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(sK7(powerset(sK1))),X1) = X0 )
| ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21309,c_49653]) ).
tcf(c_56973,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(identity_relation(sK7(powerset(sK7(powerset(X0))))),X2) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_49653]) ).
tcf(c_56974,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(identity_relation(sK7(powerset(relation_image(X1,empty_set)))),X2) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18752,c_49653]) ).
tcf(c_56975,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(identity_relation(sK7(powerset(sK7(sK6(powerset(X0)))))),X2) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_49653]) ).
tcf(c_56976,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(identity_relation(sK7(powerset(sK7(sK6(sK6(powerset(X0))))))),X2) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_49653]) ).
tcf(c_56977,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(identity_relation(relation_image(identity_relation(X0),X2)),X3) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_49653]) ).
tcf(c_56978,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(identity_relation(sK7(sK6(sK6(sK6(powerset(X0)))))),X2) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_49653]) ).
tcf(c_56979,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(identity_relation(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0)))))))),X2) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_49653]) ).
tcf(c_56980,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(identity_relation(sK7(powerset(relation_image(identity_relation(X0),X2)))),X3) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_49653]) ).
tcf(c_56981,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(identity_relation(relation_image(identity_relation(sK7(powerset(X0))),X2)),X3) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_49653]) ).
tcf(c_57126,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( relation_image(identity_relation(relation_dom(relation_dom(relation_dom(X0)))),X1) = empty_set ) ),
inference(superposition,[status(thm)],[c_10348,c_54053]) ).
tcf(c_57127,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ( relation_image(identity_relation(relation_dom(relation_dom(relation_dom(X0)))),X1) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_54053]) ).
tcf(c_57128,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( relation_image(identity_relation(relation_dom(relation_dom(relation_dom(X0)))),X1) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_54053]) ).
tcf(c_57129,plain,
! [X0: $i] : relation_image(identity_relation(relation_dom(relation_dom(relation_dom(empty_set)))),X0) = empty_set,
inference(superposition,[status(thm)],[c_83,c_54053]) ).
tcf(c_57130,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(relation_dom(relation_dom(relation_dom(relation_dom(X0))))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_54053]) ).
tcf(c_57131,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(relation_dom(relation_dom(relation_dom(identity_relation(X0))))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_54053]) ).
tcf(c_57132,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(relation_dom(relation_dom(relation_dom(sK7(powerset(X0)))))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_54053]) ).
tcf(c_57133,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(relation_dom(relation_dom(relation_dom(sK7(sK6(powerset(X0))))))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_54053]) ).
tcf(c_57134,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(relation_dom(relation_dom(relation_dom(sK7(sK6(sK6(powerset(X0)))))))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_54053]) ).
tcf(c_57135,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(relation_dom(relation_dom(relation_dom(relation_image(X0,empty_set))))),X1) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_54053]) ).
tcf(c_57136,plain,
! [X0: $i] :
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( relation_image(identity_relation(relation_dom(relation_dom(relation_dom(sK7(powerset(sK1)))))),X0) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_54053]) ).
tcf(c_57137,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(relation_dom(relation_dom(relation_dom(sK7(powerset(sK7(powerset(X0)))))))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_54053]) ).
tcf(c_57138,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(relation_dom(relation_dom(relation_dom(sK7(powerset(relation_image(X0,empty_set))))))),X1) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_54053]) ).
tcf(c_57139,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(relation_dom(relation_dom(relation_dom(sK7(powerset(sK7(sK6(powerset(X0))))))))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_54053]) ).
tcf(c_57140,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(relation_dom(relation_dom(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_54053]) ).
tcf(c_57141,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(identity_relation(relation_dom(relation_dom(relation_dom(relation_image(identity_relation(X0),X1))))),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_54053]) ).
tcf(c_57142,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(relation_dom(relation_dom(relation_dom(sK7(sK6(sK6(sK6(powerset(X0))))))))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_54053]) ).
tcf(c_57143,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(relation_dom(relation_dom(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_54053]) ).
tcf(c_57144,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(identity_relation(relation_dom(relation_dom(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X1))))))),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_54053]) ).
tcf(c_57145,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(identity_relation(relation_dom(relation_dom(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X1))))),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_54053]) ).
tcf(c_57399,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( identity_relation(relation_image(identity_relation(relation_dom(relation_dom(X0))),X1)) = empty_set ) ),
inference(superposition,[status(thm)],[c_10348,c_54163]) ).
tcf(c_57400,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ( identity_relation(relation_image(identity_relation(relation_dom(relation_dom(X0))),X1)) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_54163]) ).
tcf(c_57401,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( identity_relation(relation_image(identity_relation(relation_dom(relation_dom(X0))),X1)) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_54163]) ).
tcf(c_57402,plain,
! [X0: $i] : identity_relation(relation_image(identity_relation(relation_dom(relation_dom(empty_set))),X0)) = empty_set,
inference(superposition,[status(thm)],[c_83,c_54163]) ).
tcf(c_57403,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_image(identity_relation(relation_dom(relation_dom(relation_dom(X0)))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_54163]) ).
tcf(c_57404,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_image(identity_relation(relation_dom(relation_dom(identity_relation(X0)))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_54163]) ).
tcf(c_57405,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_image(identity_relation(relation_dom(relation_dom(sK7(powerset(X0))))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_54163]) ).
tcf(c_57406,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_image(identity_relation(relation_dom(relation_dom(sK7(sK6(powerset(X0)))))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_54163]) ).
tcf(c_57407,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_image(identity_relation(relation_dom(relation_dom(sK7(sK6(sK6(powerset(X0))))))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_54163]) ).
tcf(c_57408,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_image(identity_relation(relation_dom(relation_dom(relation_image(X0,empty_set)))),X1)) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_54163]) ).
tcf(c_57409,plain,
! [X0: $i] :
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( identity_relation(relation_image(identity_relation(relation_dom(relation_dom(sK7(powerset(sK1))))),X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_54163]) ).
tcf(c_57410,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_image(identity_relation(relation_dom(relation_dom(sK7(powerset(sK7(powerset(X0))))))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_54163]) ).
tcf(c_57411,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_image(identity_relation(relation_dom(relation_dom(sK7(powerset(relation_image(X0,empty_set)))))),X1)) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_54163]) ).
tcf(c_57412,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_image(identity_relation(relation_dom(relation_dom(sK7(powerset(sK7(sK6(powerset(X0)))))))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_54163]) ).
tcf(c_57413,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_image(identity_relation(relation_dom(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0))))))))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_54163]) ).
tcf(c_57414,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(relation_image(identity_relation(relation_dom(relation_dom(relation_image(identity_relation(X0),X1)))),X2)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_54163]) ).
tcf(c_57415,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_image(identity_relation(relation_dom(relation_dom(sK7(sK6(sK6(sK6(powerset(X0)))))))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_54163]) ).
tcf(c_57416,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_image(identity_relation(relation_dom(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0)))))))))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_54163]) ).
tcf(c_57417,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(relation_image(identity_relation(relation_dom(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X1)))))),X2)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_54163]) ).
tcf(c_57418,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(relation_image(identity_relation(relation_dom(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X1)))),X2)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_54163]) ).
tcf(c_57511,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( identity_relation(identity_relation(relation_image(identity_relation(X0),X1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10348,c_49649]) ).
tcf(c_57512,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ( identity_relation(identity_relation(relation_image(identity_relation(X0),X1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_49649]) ).
tcf(c_57513,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( identity_relation(identity_relation(relation_image(identity_relation(X0),X1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_49649]) ).
tcf(c_57514,plain,
! [X0: $i] : identity_relation(identity_relation(relation_image(identity_relation(empty_set),X0))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_49649]) ).
tcf(c_57515,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(relation_image(identity_relation(relation_dom(X0)),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_49649]) ).
tcf(c_57516,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(relation_image(identity_relation(identity_relation(X0)),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_49649]) ).
tcf(c_57518,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(relation_image(identity_relation(sK7(sK6(powerset(X0)))),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_49649]) ).
tcf(c_57519,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(relation_image(identity_relation(sK7(sK6(sK6(powerset(X0))))),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_49649]) ).
tcf(c_57520,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(relation_image(identity_relation(relation_image(X0,empty_set)),X1))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_49649]) ).
tcf(c_57521,plain,
! [X0: $i] :
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( identity_relation(identity_relation(relation_image(identity_relation(sK7(powerset(sK1))),X0))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_49649]) ).
tcf(c_57522,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(relation_image(identity_relation(sK7(powerset(sK7(powerset(X0))))),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_49649]) ).
tcf(c_57523,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(relation_image(identity_relation(sK7(powerset(relation_image(X0,empty_set)))),X1))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_49649]) ).
tcf(c_57524,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(relation_image(identity_relation(sK7(powerset(sK7(sK6(powerset(X0)))))),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_49649]) ).
tcf(c_57525,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(relation_image(identity_relation(sK7(powerset(sK7(sK6(sK6(powerset(X0))))))),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_49649]) ).
tcf(c_57526,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(identity_relation(relation_image(identity_relation(relation_image(identity_relation(X0),X1)),X2))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_49649]) ).
tcf(c_57527,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(relation_image(identity_relation(sK7(sK6(sK6(sK6(powerset(X0)))))),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_49649]) ).
tcf(c_57528,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(relation_image(identity_relation(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0)))))))),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_49649]) ).
tcf(c_57529,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(identity_relation(relation_image(identity_relation(sK7(powerset(relation_image(identity_relation(X0),X1)))),X2))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_49649]) ).
tcf(c_57530,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(identity_relation(relation_image(identity_relation(relation_image(identity_relation(sK7(powerset(X0))),X1)),X2))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_49649]) ).
tcf(c_57806,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( identity_relation(relation_dom(relation_image(identity_relation(X0),X1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10348,c_49650]) ).
tcf(c_57807,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ( identity_relation(relation_dom(relation_image(identity_relation(X0),X1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_49650]) ).
tcf(c_57808,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( identity_relation(relation_dom(relation_image(identity_relation(X0),X1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_49650]) ).
tcf(c_57809,plain,
! [X0: $i] : identity_relation(relation_dom(relation_image(identity_relation(empty_set),X0))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_49650]) ).
tcf(c_57810,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(relation_image(identity_relation(relation_dom(X0)),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_49650]) ).
tcf(c_57811,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(relation_image(identity_relation(identity_relation(X0)),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_49650]) ).
tcf(c_57813,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(relation_image(identity_relation(sK7(sK6(powerset(X0)))),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_49650]) ).
tcf(c_57814,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(relation_image(identity_relation(sK7(sK6(sK6(powerset(X0))))),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_49650]) ).
tcf(c_57815,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(relation_image(identity_relation(relation_image(X0,empty_set)),X1))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_49650]) ).
tcf(c_57816,plain,
! [X0: $i] :
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( identity_relation(relation_dom(relation_image(identity_relation(sK7(powerset(sK1))),X0))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_49650]) ).
tcf(c_57817,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(relation_image(identity_relation(sK7(powerset(sK7(powerset(X0))))),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_49650]) ).
tcf(c_57818,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(relation_image(identity_relation(sK7(powerset(relation_image(X0,empty_set)))),X1))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_49650]) ).
tcf(c_57819,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(relation_image(identity_relation(sK7(powerset(sK7(sK6(powerset(X0)))))),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_49650]) ).
tcf(c_57820,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(relation_image(identity_relation(sK7(powerset(sK7(sK6(sK6(powerset(X0))))))),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_49650]) ).
tcf(c_57821,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(relation_dom(relation_image(identity_relation(relation_image(identity_relation(X0),X1)),X2))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_49650]) ).
tcf(c_57822,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(relation_image(identity_relation(sK7(sK6(sK6(sK6(powerset(X0)))))),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_49650]) ).
tcf(c_57823,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(relation_image(identity_relation(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0)))))))),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_49650]) ).
tcf(c_57824,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(relation_dom(relation_image(identity_relation(sK7(powerset(relation_image(identity_relation(X0),X1)))),X2))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_49650]) ).
tcf(c_57825,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(relation_dom(relation_image(identity_relation(relation_image(identity_relation(sK7(powerset(X0))),X1)),X2))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_49650]) ).
tcf(c_58045,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( relation_dom(relation_dom(relation_image(identity_relation(X0),X1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10348,c_49651]) ).
tcf(c_58046,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ( relation_dom(relation_dom(relation_image(identity_relation(X0),X1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_49651]) ).
tcf(c_58047,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( relation_dom(relation_dom(relation_image(identity_relation(X0),X1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_49651]) ).
tcf(c_58048,plain,
! [X0: $i] : relation_dom(relation_dom(relation_image(identity_relation(empty_set),X0))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_49651]) ).
tcf(c_58049,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_image(identity_relation(relation_dom(X0)),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_49651]) ).
tcf(c_58050,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_image(identity_relation(identity_relation(X0)),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_49651]) ).
tcf(c_58052,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_image(identity_relation(sK7(sK6(powerset(X0)))),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_49651]) ).
tcf(c_58053,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_image(identity_relation(sK7(sK6(sK6(powerset(X0))))),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_49651]) ).
tcf(c_58054,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_image(identity_relation(relation_image(X0,empty_set)),X1))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_49651]) ).
tcf(c_58055,plain,
! [X0: $i] :
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( relation_dom(relation_dom(relation_image(identity_relation(sK7(powerset(sK1))),X0))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_49651]) ).
tcf(c_58056,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_image(identity_relation(sK7(powerset(sK7(powerset(X0))))),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_49651]) ).
tcf(c_58057,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_image(identity_relation(sK7(powerset(relation_image(X0,empty_set)))),X1))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_49651]) ).
tcf(c_58058,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_image(identity_relation(sK7(powerset(sK7(sK6(powerset(X0)))))),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_49651]) ).
tcf(c_58059,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_image(identity_relation(sK7(powerset(sK7(sK6(sK6(powerset(X0))))))),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_49651]) ).
tcf(c_58060,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_dom(relation_image(identity_relation(relation_image(identity_relation(X0),X1)),X2))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_49651]) ).
tcf(c_58061,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_image(identity_relation(sK7(sK6(sK6(sK6(powerset(X0)))))),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_49651]) ).
tcf(c_58062,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_image(identity_relation(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0)))))))),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_49651]) ).
tcf(c_58063,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_dom(relation_image(identity_relation(sK7(powerset(relation_image(identity_relation(X0),X1)))),X2))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_49651]) ).
tcf(c_58064,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_dom(relation_image(identity_relation(relation_image(identity_relation(sK7(powerset(X0))),X1)),X2))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_49651]) ).
tcf(c_58126,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( relation_image(identity_relation(sK7(powerset(X0))),X1) = empty_set ) ),
inference(superposition,[status(thm)],[c_10348,c_52684]) ).
tcf(c_58127,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ( relation_image(identity_relation(sK7(powerset(X0))),X1) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_52684]) ).
tcf(c_58128,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( relation_image(identity_relation(sK7(powerset(X0))),X1) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_52684]) ).
tcf(c_58129,plain,
! [X0: $i] : relation_image(identity_relation(sK7(powerset(empty_set))),X0) = empty_set,
inference(superposition,[status(thm)],[c_83,c_52684]) ).
tcf(c_58130,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(sK7(powerset(relation_dom(X0)))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_52684]) ).
tcf(c_58131,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(sK7(powerset(identity_relation(X0)))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_52684]) ).
tcf(c_58136,plain,
! [X0: $i] :
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( relation_image(identity_relation(sK7(powerset(sK7(powerset(sK1))))),X0) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_52684]) ).
tcf(c_58137,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(sK7(powerset(sK7(powerset(sK7(powerset(X0))))))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_52684]) ).
tcf(c_58138,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(sK7(powerset(sK7(powerset(relation_image(X0,empty_set)))))),X1) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_52684]) ).
tcf(c_58139,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(sK7(powerset(sK7(powerset(sK7(sK6(powerset(X0)))))))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_52684]) ).
tcf(c_58140,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(sK7(powerset(sK7(powerset(sK7(sK6(sK6(powerset(X0))))))))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_52684]) ).
tcf(c_58143,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(sK7(powerset(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0)))))))))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_52684]) ).
tcf(c_58144,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(identity_relation(sK7(powerset(sK7(powerset(relation_image(identity_relation(X0),X1)))))),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_52684]) ).
tcf(c_58145,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(identity_relation(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1)))),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_52684]) ).
tcf(c_58243,plain,
( ( apply(empty_set,sK7(empty_set)) = sK7(empty_set) )
| ( identity_relation(relation_dom(sK7(powerset(empty_set)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_6104,c_12133]) ).
tcf(c_58244,plain,
( ( apply(identity_relation(powerset(empty_set)),empty_set) = empty_set )
| ( identity_relation(relation_dom(sK7(powerset(powerset(empty_set))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8004,c_12133]) ).
tcf(c_58245,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( apply(identity_relation(powerset(relation_dom(relation_dom(X0)))),empty_set) = empty_set )
| ( identity_relation(relation_dom(sK7(powerset(powerset(relation_dom(relation_dom(X0))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_12097,c_12133]) ).
tcf(c_58248,plain,
( ( apply(identity_relation(sK6(sK6(sK6(powerset(empty_set))))),empty_set) = empty_set )
| ( identity_relation(relation_dom(sK7(powerset(sK6(sK6(sK6(powerset(empty_set)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_37341,c_12133]) ).
tcf(c_58249,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(identity_relation(X0),X1) = X2 )
| ( identity_relation(relation_dom(sK7(powerset(X0)))) = empty_set )
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),relation_dom(identity_relation(X0)))
| ~ in(sK2(identity_relation(X0),X1,X2),X2)
| ( sK2(identity_relation(X0),X1,X2) != sK7(X0) ) ),
inference(superposition,[status(thm)],[c_12133,c_53]) ).
tcf(c_58250,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0),relation_image(identity_relation(X0),X1))
| ( identity_relation(relation_dom(sK7(powerset(X0)))) = empty_set )
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),relation_dom(identity_relation(X0))) ),
inference(superposition,[status(thm)],[c_12133,c_57]) ).
tcf(c_58254,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0),relation_image(identity_relation(X0),X1))
| ( identity_relation(relation_dom(sK7(powerset(X0)))) = empty_set )
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),X0) ),
inference(light_normalisation,[status(thm)],[c_58250,c_121]) ).
tcf(c_58255,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0),relation_image(identity_relation(X0),X1))
| ( identity_relation(relation_dom(sK7(powerset(X0)))) = empty_set )
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_58254,c_62,c_63]) ).
tcf(c_58260,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(identity_relation(X0),X1) = X2 )
| ( identity_relation(relation_dom(sK7(powerset(X0)))) = empty_set )
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),X0)
| ~ in(sK2(identity_relation(X0),X1,X2),X2)
| ( sK2(identity_relation(X0),X1,X2) != sK7(X0) ) ),
inference(light_normalisation,[status(thm)],[c_58249,c_121]) ).
tcf(c_58261,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(identity_relation(X0),X1) = X2 )
| ( identity_relation(relation_dom(sK7(powerset(X0)))) = empty_set )
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),X0)
| ~ in(sK2(identity_relation(X0),X1,X2),X2)
| ( sK2(identity_relation(X0),X1,X2) != sK7(X0) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_58260,c_62,c_63]) ).
tcf(c_58273,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( relation_dom(relation_image(identity_relation(relation_dom(relation_dom(X0))),X1)) = empty_set ) ),
inference(superposition,[status(thm)],[c_10348,c_54365]) ).
tcf(c_58274,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ( relation_dom(relation_image(identity_relation(relation_dom(relation_dom(X0))),X1)) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_54365]) ).
tcf(c_58275,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( relation_dom(relation_image(identity_relation(relation_dom(relation_dom(X0))),X1)) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_54365]) ).
tcf(c_58276,plain,
! [X0: $i] : relation_dom(relation_image(identity_relation(relation_dom(relation_dom(empty_set))),X0)) = empty_set,
inference(superposition,[status(thm)],[c_83,c_54365]) ).
tcf(c_58277,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_image(identity_relation(relation_dom(relation_dom(relation_dom(X0)))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_54365]) ).
tcf(c_58278,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_image(identity_relation(relation_dom(relation_dom(identity_relation(X0)))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_54365]) ).
tcf(c_58279,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_image(identity_relation(relation_dom(relation_dom(sK7(powerset(X0))))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_54365]) ).
tcf(c_58280,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_image(identity_relation(relation_dom(relation_dom(sK7(sK6(powerset(X0)))))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_54365]) ).
tcf(c_58281,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_image(identity_relation(relation_dom(relation_dom(sK7(sK6(sK6(powerset(X0))))))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_54365]) ).
tcf(c_58282,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_image(identity_relation(relation_dom(relation_dom(relation_image(X0,empty_set)))),X1)) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_54365]) ).
tcf(c_58283,plain,
! [X0: $i] :
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( relation_dom(relation_image(identity_relation(relation_dom(relation_dom(sK7(powerset(sK1))))),X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_54365]) ).
tcf(c_58284,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_image(identity_relation(relation_dom(relation_dom(sK7(powerset(sK7(powerset(X0))))))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_54365]) ).
tcf(c_58285,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_image(identity_relation(relation_dom(relation_dom(sK7(powerset(relation_image(X0,empty_set)))))),X1)) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_54365]) ).
tcf(c_58286,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_image(identity_relation(relation_dom(relation_dom(sK7(powerset(sK7(sK6(powerset(X0)))))))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_54365]) ).
tcf(c_58287,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_image(identity_relation(relation_dom(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0))))))))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_54365]) ).
tcf(c_58288,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_image(identity_relation(relation_dom(relation_dom(relation_image(identity_relation(X0),X1)))),X2)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_54365]) ).
tcf(c_58289,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_image(identity_relation(relation_dom(relation_dom(sK7(sK6(sK6(sK6(powerset(X0)))))))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_54365]) ).
tcf(c_58290,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_image(identity_relation(relation_dom(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0)))))))))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_54365]) ).
tcf(c_58291,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_image(identity_relation(relation_dom(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X1)))))),X2)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_54365]) ).
tcf(c_58292,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_image(identity_relation(relation_dom(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X1)))),X2)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_54365]) ).
tcf(c_58355,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( relation_image(identity_relation(identity_relation(relation_dom(relation_dom(X0)))),X1) = empty_set ) ),
inference(superposition,[status(thm)],[c_10348,c_54629]) ).
tcf(c_58356,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ( relation_image(identity_relation(identity_relation(relation_dom(relation_dom(X0)))),X1) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_54629]) ).
tcf(c_58357,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( relation_image(identity_relation(identity_relation(relation_dom(relation_dom(X0)))),X1) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_54629]) ).
tcf(c_58358,plain,
! [X0: $i] : relation_image(identity_relation(identity_relation(relation_dom(relation_dom(empty_set)))),X0) = empty_set,
inference(superposition,[status(thm)],[c_83,c_54629]) ).
tcf(c_58359,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(identity_relation(relation_dom(relation_dom(relation_dom(X0))))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_54629]) ).
tcf(c_58360,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(identity_relation(relation_dom(relation_dom(identity_relation(X0))))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_54629]) ).
tcf(c_58361,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(identity_relation(relation_dom(relation_dom(sK7(powerset(X0)))))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_54629]) ).
tcf(c_58362,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(identity_relation(relation_dom(relation_dom(sK7(sK6(powerset(X0))))))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_54629]) ).
tcf(c_58363,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(identity_relation(relation_dom(relation_dom(sK7(sK6(sK6(powerset(X0)))))))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_54629]) ).
tcf(c_58364,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(identity_relation(relation_dom(relation_dom(relation_image(X0,empty_set))))),X1) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_54629]) ).
tcf(c_58365,plain,
! [X0: $i] :
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( relation_image(identity_relation(identity_relation(relation_dom(relation_dom(sK7(powerset(sK1)))))),X0) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_54629]) ).
tcf(c_58366,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(identity_relation(relation_dom(relation_dom(sK7(powerset(sK7(powerset(X0)))))))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_54629]) ).
tcf(c_58367,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(identity_relation(relation_dom(relation_dom(sK7(powerset(relation_image(X0,empty_set))))))),X1) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_54629]) ).
tcf(c_58368,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(identity_relation(relation_dom(relation_dom(sK7(powerset(sK7(sK6(powerset(X0))))))))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_54629]) ).
tcf(c_58369,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(identity_relation(relation_dom(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_54629]) ).
tcf(c_58370,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(identity_relation(identity_relation(relation_dom(relation_dom(relation_image(identity_relation(X0),X1))))),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_54629]) ).
tcf(c_58371,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(identity_relation(relation_dom(relation_dom(sK7(sK6(sK6(sK6(powerset(X0))))))))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_54629]) ).
tcf(c_58372,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(identity_relation(relation_dom(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_54629]) ).
tcf(c_58373,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(identity_relation(identity_relation(relation_dom(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X1))))))),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_54629]) ).
tcf(c_58374,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(identity_relation(identity_relation(relation_dom(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X1))))),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_54629]) ).
tcf(c_58467,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( sK7(powerset(relation_image(identity_relation(relation_dom(X0)),X1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10348,c_56835]) ).
tcf(c_58468,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ( sK7(powerset(relation_image(identity_relation(relation_dom(X0)),X1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_56835]) ).
tcf(c_58469,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( sK7(powerset(relation_image(identity_relation(relation_dom(X0)),X1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_56835]) ).
tcf(c_58470,plain,
! [X0: $i] : sK7(powerset(relation_image(identity_relation(relation_dom(empty_set)),X0))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_56835]) ).
tcf(c_58471,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(relation_image(identity_relation(relation_dom(relation_dom(X0))),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_56835]) ).
tcf(c_58472,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(relation_image(identity_relation(relation_dom(identity_relation(X0))),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_56835]) ).
tcf(c_58473,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(relation_image(identity_relation(relation_dom(sK7(powerset(X0)))),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_56835]) ).
tcf(c_58474,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(relation_image(identity_relation(relation_dom(sK7(sK6(powerset(X0))))),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_56835]) ).
tcf(c_58475,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(relation_image(identity_relation(relation_dom(sK7(sK6(sK6(powerset(X0)))))),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_56835]) ).
tcf(c_58476,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(relation_image(identity_relation(relation_dom(relation_image(X0,empty_set))),X1))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_56835]) ).
tcf(c_58477,plain,
! [X0: $i] :
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( sK7(powerset(relation_image(identity_relation(relation_dom(sK7(powerset(sK1)))),X0))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_56835]) ).
tcf(c_58478,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(relation_image(identity_relation(relation_dom(sK7(powerset(sK7(powerset(X0)))))),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_56835]) ).
tcf(c_58479,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(relation_image(identity_relation(relation_dom(sK7(powerset(relation_image(X0,empty_set))))),X1))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_56835]) ).
tcf(c_58480,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(relation_image(identity_relation(relation_dom(sK7(powerset(sK7(sK6(powerset(X0))))))),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_56835]) ).
tcf(c_58481,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(relation_image(identity_relation(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_56835]) ).
tcf(c_58482,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK7(powerset(relation_image(identity_relation(relation_dom(relation_image(identity_relation(X0),X1))),X2))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_56835]) ).
tcf(c_58483,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(relation_image(identity_relation(relation_dom(sK7(sK6(sK6(sK6(powerset(X0))))))),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_56835]) ).
tcf(c_58484,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(relation_image(identity_relation(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_56835]) ).
tcf(c_58485,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK7(powerset(relation_image(identity_relation(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X1))))),X2))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_56835]) ).
tcf(c_58486,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK7(powerset(relation_image(identity_relation(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X1))),X2))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_56835]) ).
tcf(c_58598,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( identity_relation(identity_relation(relation_image(identity_relation(relation_dom(X0)),X1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10348,c_57515]) ).
tcf(c_58599,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ( identity_relation(identity_relation(relation_image(identity_relation(relation_dom(X0)),X1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_57515]) ).
tcf(c_58600,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( identity_relation(identity_relation(relation_image(identity_relation(relation_dom(X0)),X1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_57515]) ).
tcf(c_58601,plain,
! [X0: $i] : identity_relation(identity_relation(relation_image(identity_relation(relation_dom(empty_set)),X0))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_57515]) ).
tcf(c_58602,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(relation_image(identity_relation(relation_dom(relation_dom(X0))),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_57515]) ).
tcf(c_58603,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(relation_image(identity_relation(relation_dom(identity_relation(X0))),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_57515]) ).
tcf(c_58604,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(relation_image(identity_relation(relation_dom(sK7(powerset(X0)))),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_57515]) ).
tcf(c_58605,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(relation_image(identity_relation(relation_dom(sK7(sK6(powerset(X0))))),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_57515]) ).
tcf(c_58606,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(relation_image(identity_relation(relation_dom(sK7(sK6(sK6(powerset(X0)))))),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_57515]) ).
tcf(c_58607,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(relation_image(identity_relation(relation_dom(relation_image(X0,empty_set))),X1))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_57515]) ).
tcf(c_58608,plain,
! [X0: $i] :
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( identity_relation(identity_relation(relation_image(identity_relation(relation_dom(sK7(powerset(sK1)))),X0))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_57515]) ).
tcf(c_58609,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(relation_image(identity_relation(relation_dom(sK7(powerset(sK7(powerset(X0)))))),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_57515]) ).
tcf(c_58610,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(relation_image(identity_relation(relation_dom(sK7(powerset(relation_image(X0,empty_set))))),X1))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_57515]) ).
tcf(c_58611,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(relation_image(identity_relation(relation_dom(sK7(powerset(sK7(sK6(powerset(X0))))))),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_57515]) ).
tcf(c_58612,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(relation_image(identity_relation(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_57515]) ).
tcf(c_58613,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(identity_relation(relation_image(identity_relation(relation_dom(relation_image(identity_relation(X0),X1))),X2))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_57515]) ).
tcf(c_58614,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(relation_image(identity_relation(relation_dom(sK7(sK6(sK6(sK6(powerset(X0))))))),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_57515]) ).
tcf(c_58615,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(relation_image(identity_relation(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_57515]) ).
tcf(c_58616,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(identity_relation(relation_image(identity_relation(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X1))))),X2))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_57515]) ).
tcf(c_58617,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(identity_relation(relation_image(identity_relation(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X1))),X2))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_57515]) ).
tcf(c_58750,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( identity_relation(relation_image(identity_relation(identity_relation(X0)),X1)) = empty_set ) ),
inference(superposition,[status(thm)],[c_10348,c_53062]) ).
tcf(c_58751,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ( identity_relation(relation_image(identity_relation(identity_relation(X0)),X1)) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_53062]) ).
tcf(c_58752,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( identity_relation(relation_image(identity_relation(identity_relation(X0)),X1)) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_53062]) ).
tcf(c_58753,plain,
! [X0: $i] : identity_relation(relation_image(identity_relation(identity_relation(empty_set)),X0)) = empty_set,
inference(superposition,[status(thm)],[c_83,c_53062]) ).
tcf(c_58754,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_image(identity_relation(identity_relation(relation_dom(X0))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_53062]) ).
tcf(c_58755,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_image(identity_relation(identity_relation(identity_relation(X0))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_53062]) ).
tcf(c_58756,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_image(identity_relation(identity_relation(sK7(powerset(X0)))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_53062]) ).
tcf(c_58757,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_image(identity_relation(identity_relation(sK7(sK6(powerset(X0))))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_53062]) ).
tcf(c_58758,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_image(identity_relation(identity_relation(sK7(sK6(sK6(powerset(X0)))))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_53062]) ).
tcf(c_58759,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_image(identity_relation(identity_relation(relation_image(X0,empty_set))),X1)) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_53062]) ).
tcf(c_58760,plain,
! [X0: $i] :
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( identity_relation(relation_image(identity_relation(identity_relation(sK7(powerset(sK1)))),X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_53062]) ).
tcf(c_58761,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_image(identity_relation(identity_relation(sK7(powerset(sK7(powerset(X0)))))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_53062]) ).
tcf(c_58762,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_image(identity_relation(identity_relation(sK7(powerset(relation_image(X0,empty_set))))),X1)) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_53062]) ).
tcf(c_58763,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_image(identity_relation(identity_relation(sK7(powerset(sK7(sK6(powerset(X0))))))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_53062]) ).
tcf(c_58764,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_image(identity_relation(identity_relation(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_53062]) ).
tcf(c_58765,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(relation_image(identity_relation(identity_relation(relation_image(identity_relation(X0),X1))),X2)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_53062]) ).
tcf(c_58766,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_image(identity_relation(identity_relation(sK7(sK6(sK6(sK6(powerset(X0))))))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_53062]) ).
tcf(c_58767,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_image(identity_relation(identity_relation(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_53062]) ).
tcf(c_58768,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(relation_image(identity_relation(identity_relation(sK7(powerset(relation_image(identity_relation(X0),X1))))),X2)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_53062]) ).
tcf(c_58769,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(relation_image(identity_relation(identity_relation(relation_image(identity_relation(sK7(powerset(X0))),X1))),X2)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_53062]) ).
tcf(c_59007,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( relation_dom(relation_image(identity_relation(identity_relation(X0)),X1)) = empty_set ) ),
inference(superposition,[status(thm)],[c_10348,c_53238]) ).
tcf(c_59008,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ( relation_dom(relation_image(identity_relation(identity_relation(X0)),X1)) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_53238]) ).
tcf(c_59009,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( relation_dom(relation_image(identity_relation(identity_relation(X0)),X1)) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_53238]) ).
tcf(c_59010,plain,
! [X0: $i] : relation_dom(relation_image(identity_relation(identity_relation(empty_set)),X0)) = empty_set,
inference(superposition,[status(thm)],[c_83,c_53238]) ).
tcf(c_59011,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_image(identity_relation(identity_relation(relation_dom(X0))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_53238]) ).
tcf(c_59012,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_image(identity_relation(identity_relation(identity_relation(X0))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_53238]) ).
tcf(c_59013,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_image(identity_relation(identity_relation(sK7(powerset(X0)))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_53238]) ).
tcf(c_59014,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_image(identity_relation(identity_relation(sK7(sK6(powerset(X0))))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_53238]) ).
tcf(c_59015,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_image(identity_relation(identity_relation(sK7(sK6(sK6(powerset(X0)))))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_53238]) ).
tcf(c_59016,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_image(identity_relation(identity_relation(relation_image(X0,empty_set))),X1)) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_53238]) ).
tcf(c_59017,plain,
! [X0: $i] :
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( relation_dom(relation_image(identity_relation(identity_relation(sK7(powerset(sK1)))),X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_53238]) ).
tcf(c_59018,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_image(identity_relation(identity_relation(sK7(powerset(sK7(powerset(X0)))))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_53238]) ).
tcf(c_59019,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_image(identity_relation(identity_relation(sK7(powerset(relation_image(X0,empty_set))))),X1)) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_53238]) ).
tcf(c_59020,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_image(identity_relation(identity_relation(sK7(powerset(sK7(sK6(powerset(X0))))))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_53238]) ).
tcf(c_59021,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_image(identity_relation(identity_relation(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_53238]) ).
tcf(c_59022,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_image(identity_relation(identity_relation(relation_image(identity_relation(X0),X1))),X2)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_53238]) ).
tcf(c_59023,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_image(identity_relation(identity_relation(sK7(sK6(sK6(sK6(powerset(X0))))))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_53238]) ).
tcf(c_59024,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_image(identity_relation(identity_relation(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_53238]) ).
tcf(c_59025,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_image(identity_relation(identity_relation(sK7(powerset(relation_image(identity_relation(X0),X1))))),X2)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_53238]) ).
tcf(c_59026,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_image(identity_relation(identity_relation(relation_image(identity_relation(sK7(powerset(X0))),X1))),X2)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_53238]) ).
tcf(c_59148,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( relation_image(identity_relation(identity_relation(identity_relation(X0))),X1) = empty_set ) ),
inference(superposition,[status(thm)],[c_10348,c_53472]) ).
tcf(c_59149,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ( relation_image(identity_relation(identity_relation(identity_relation(X0))),X1) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_53472]) ).
tcf(c_59150,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( relation_image(identity_relation(identity_relation(identity_relation(X0))),X1) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_53472]) ).
tcf(c_59151,plain,
! [X0: $i] : relation_image(identity_relation(identity_relation(identity_relation(empty_set))),X0) = empty_set,
inference(superposition,[status(thm)],[c_83,c_53472]) ).
tcf(c_59152,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(identity_relation(identity_relation(relation_dom(X0)))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_53472]) ).
tcf(c_59153,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(identity_relation(identity_relation(identity_relation(X0)))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_53472]) ).
tcf(c_59154,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(identity_relation(identity_relation(sK7(powerset(X0))))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_53472]) ).
tcf(c_59155,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(identity_relation(identity_relation(sK7(sK6(powerset(X0)))))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_53472]) ).
tcf(c_59156,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(identity_relation(identity_relation(sK7(sK6(sK6(powerset(X0))))))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_53472]) ).
tcf(c_59157,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(identity_relation(identity_relation(relation_image(X0,empty_set)))),X1) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_53472]) ).
tcf(c_59158,plain,
! [X0: $i] :
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( relation_image(identity_relation(identity_relation(identity_relation(sK7(powerset(sK1))))),X0) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_53472]) ).
tcf(c_59159,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(identity_relation(identity_relation(sK7(powerset(sK7(powerset(X0))))))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_53472]) ).
tcf(c_59160,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(identity_relation(identity_relation(sK7(powerset(relation_image(X0,empty_set)))))),X1) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_53472]) ).
tcf(c_59161,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(identity_relation(identity_relation(sK7(powerset(sK7(sK6(powerset(X0)))))))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_53472]) ).
tcf(c_59162,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(identity_relation(identity_relation(sK7(powerset(sK7(sK6(sK6(powerset(X0))))))))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_53472]) ).
tcf(c_59163,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(identity_relation(identity_relation(identity_relation(relation_image(identity_relation(X0),X1)))),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_53472]) ).
tcf(c_59164,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(identity_relation(identity_relation(sK7(sK6(sK6(sK6(powerset(X0)))))))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_53472]) ).
tcf(c_59165,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(identity_relation(identity_relation(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0)))))))))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_53472]) ).
tcf(c_59166,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(identity_relation(identity_relation(identity_relation(sK7(powerset(relation_image(identity_relation(X0),X1)))))),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_53472]) ).
tcf(c_59167,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(identity_relation(identity_relation(identity_relation(relation_image(identity_relation(sK7(powerset(X0))),X1)))),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_53472]) ).
tcf(c_59278,plain,
! [X0: $i] :
( empty(sK7(powerset(relation_image(identity_relation(empty_set),X0))))
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_8004,c_53607]) ).
tcf(c_59279,plain,
! [X0: $i,X1: $i] :
( empty(sK7(powerset(relation_image(identity_relation(empty_set),X1))))
| ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ~ empty(relation_dom(relation_dom(X0))) ),
inference(superposition,[status(thm)],[c_12097,c_53607]) ).
tcf(c_59280,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(identity_relation(identity_relation(identity_relation(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1)))))),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_53472]) ).
tcf(c_59281,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_image(identity_relation(identity_relation(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))),X2)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_53238]) ).
tcf(c_59282,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(relation_image(identity_relation(identity_relation(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))),X2)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_53062]) ).
tcf(c_59283,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(identity_relation(relation_image(identity_relation(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))),X2))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_57515]) ).
tcf(c_59284,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK7(powerset(relation_image(identity_relation(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))),X2))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_56835]) ).
tcf(c_59285,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(identity_relation(identity_relation(relation_dom(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_54629]) ).
tcf(c_59286,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_image(identity_relation(relation_dom(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1)))))),X2)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_54365]) ).
tcf(c_59287,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(identity_relation(sK7(powerset(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1)))))),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_52684]) ).
tcf(c_59288,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_dom(relation_image(identity_relation(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1)))),X2))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_49651]) ).
tcf(c_59289,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(relation_dom(relation_image(identity_relation(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1)))),X2))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_49650]) ).
tcf(c_59290,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(identity_relation(relation_image(identity_relation(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1)))),X2))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_49649]) ).
tcf(c_59291,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(relation_image(identity_relation(relation_dom(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1)))))),X2)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_54163]) ).
tcf(c_59292,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(identity_relation(relation_dom(relation_dom(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_54053]) ).
tcf(c_59293,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(identity_relation(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X2)))),X3) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_49653]) ).
tcf(c_59294,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK7(powerset(relation_image(identity_relation(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1)))),X2))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_49648]) ).
tcf(c_59295,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(identity_relation(identity_relation(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1)))))),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_53471]) ).
tcf(c_59296,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_image(identity_relation(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))),X2)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_53237]) ).
tcf(c_59297,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(relation_image(identity_relation(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))),X2)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_53061]) ).
tcf(c_59298,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(identity_relation(relation_dom(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1)))))),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_52875]) ).
tcf(c_59299,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(identity_relation(identity_relation(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_52683]) ).
tcf(c_59300,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_image(identity_relation(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1)))),X2)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_49654]) ).
tcf(c_59301,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(relation_image(identity_relation(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1)))),X2)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_49652]) ).
tcf(c_59302,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(identity_relation(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_52682]) ).
tcf(c_59304,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(powerset(identity_relation(identity_relation(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_39551]) ).
tcf(c_59305,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(identity_relation(relation_dom(sK7(powerset(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_13654]) ).
tcf(c_59306,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(identity_relation(relation_dom(sK7(powerset(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_13049]) ).
tcf(c_59307,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(powerset(identity_relation(sK7(powerset(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_12914]) ).
tcf(c_59308,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK7(powerset(identity_relation(sK7(powerset(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_12876]) ).
tcf(c_59309,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(sK6(powerset(identity_relation(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_38682]) ).
tcf(c_59310,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK7(sK6(powerset(identity_relation(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_37969]) ).
tcf(c_59311,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(sK6(powerset(identity_relation(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_37889]) ).
tcf(c_59312,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(sK6(sK6(powerset(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_37780]) ).
tcf(c_59313,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(powerset(relation_dom(sK7(powerset(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_12760]) ).
tcf(c_59314,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK7(powerset(relation_dom(sK7(powerset(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_12361]) ).
tcf(c_59315,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(sK7(powerset(sK7(powerset(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_12323]) ).
tcf(c_59316,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(sK7(powerset(sK7(powerset(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_12217]) ).
tcf(c_59317,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK7(sK6(sK6(powerset(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_37664]) ).
tcf(c_59318,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(sK6(sK6(powerset(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_37342]) ).
tcf(c_59319,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(identity_relation(identity_relation(identity_relation(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_31222]) ).
tcf(c_59320,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(identity_relation(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_31142]) ).
tcf(c_59321,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(sK7(powerset(sK7(powerset(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_12140]) ).
tcf(c_59322,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(relation_dom(relation_dom(sK7(powerset(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_12104]) ).
tcf(c_59323,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(relation_dom(relation_dom(sK7(powerset(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_12068]) ).
tcf(c_59324,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(relation_dom(relation_dom(sK7(powerset(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_12032]) ).
tcf(c_59325,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(powerset(identity_relation(identity_relation(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_31014]) ).
tcf(c_59326,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK7(powerset(identity_relation(identity_relation(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_30942]) ).
tcf(c_59327,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(sK7(powerset(identity_relation(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_30355]) ).
tcf(c_59328,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(sK7(powerset(identity_relation(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_30248]) ).
tcf(c_59329,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK7(powerset(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_11958]) ).
tcf(c_59330,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK7(powerset(sK7(powerset(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_11436]) ).
tcf(c_59331,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(powerset(sK7(sK6(powerset(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_11346]) ).
tcf(c_59332,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(sK7(sK6(powerset(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_10669]) ).
tcf(c_59333,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(sK7(powerset(identity_relation(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_30158]) ).
tcf(c_59334,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK7(powerset(identity_relation(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_30068]) ).
tcf(c_59335,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(powerset(sK7(powerset(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_29569]) ).
tcf(c_59336,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK7(sK6(powerset(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_29442]) ).
tcf(c_59337,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(relation_dom(sK7(sK6(powerset(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_10666]) ).
tcf(c_59338,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(relation_dom(sK7(sK6(powerset(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_10665]) ).
tcf(c_59339,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(relation_dom(sK7(sK6(powerset(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_10664]) ).
tcf(c_59340,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK7(powerset(sK7(sK6(powerset(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_10663]) ).
tcf(c_59341,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(sK7(sK6(powerset(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_29308]) ).
tcf(c_59342,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(sK7(sK6(powerset(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_29194]) ).
tcf(c_59343,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(sK7(sK6(powerset(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_28717]) ).
tcf(c_59344,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(identity_relation(sK7(powerset(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_28572]) ).
tcf(c_59345,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(powerset(sK7(sK6(powerset(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_10662]) ).
tcf(c_59346,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(identity_relation(sK7(sK6(powerset(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_10659]) ).
tcf(c_59347,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(identity_relation(sK7(powerset(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_28429]) ).
tcf(c_59348,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(identity_relation(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X2)))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_27714]) ).
tcf(c_59349,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(powerset(sK7(powerset(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_27588]) ).
tcf(c_59350,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK7(powerset(sK7(powerset(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_27452]) ).
tcf(c_59351,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(identity_relation(sK7(sK6(powerset(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_10658]) ).
tcf(c_59352,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(sK7(powerset(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X2)))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_9351]) ).
tcf(c_59353,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(sK7(powerset(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X2)))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_9323]) ).
tcf(c_59354,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(powerset(identity_relation(identity_relation(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_25847]) ).
tcf(c_59355,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(sK6(powerset(identity_relation(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_17537]) ).
tcf(c_59356,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(relation_dom(sK7(powerset(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_27367]) ).
tcf(c_59357,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(relation_dom(sK7(powerset(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_26858]) ).
tcf(c_59358,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(relation_dom(sK7(powerset(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_26809]) ).
tcf(c_59359,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(sK7(powerset(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_26731]) ).
tcf(c_59360,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK7(sK6(powerset(identity_relation(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_17480]) ).
tcf(c_59361,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(sK6(powerset(identity_relation(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_16757]) ).
tcf(c_59362,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(sK6(sK6(powerset(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_15644]) ).
tcf(c_59363,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK7(sK6(sK6(powerset(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_15642]) ).
tcf(c_59364,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(powerset(identity_relation(relation_dom(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_25936]) ).
tcf(c_59365,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(sK6(sK6(powerset(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_36269]) ).
tcf(c_59366,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(sK6(powerset(relation_dom(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_25099]) ).
tcf(c_59367,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK7(sK6(powerset(relation_dom(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_24875]) ).
tcf(c_59368,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(identity_relation(identity_relation(identity_relation(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_13970]) ).
tcf(c_59369,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(identity_relation(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_13854]) ).
tcf(c_59370,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(powerset(identity_relation(identity_relation(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_12910]) ).
tcf(c_59371,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK7(powerset(identity_relation(identity_relation(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_12872]) ).
tcf(c_59372,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(sK6(powerset(relation_dom(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_24819]) ).
tcf(c_59373,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(identity_relation(identity_relation(relation_dom(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_24724]) ).
tcf(c_59374,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(relation_dom(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_24676]) ).
tcf(c_59375,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(powerset(relation_dom(relation_dom(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_24628]) ).
tcf(c_59376,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(sK7(powerset(identity_relation(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_12319]) ).
tcf(c_59377,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(sK7(powerset(identity_relation(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_12213]) ).
tcf(c_59378,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(sK7(powerset(identity_relation(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_12136]) ).
tcf(c_59379,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK7(powerset(identity_relation(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_11432]) ).
tcf(c_59380,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(identity_relation(relation_dom(relation_dom(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_24580]) ).
tcf(c_59381,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(identity_relation(relation_dom(relation_dom(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_24491]) ).
tcf(c_59382,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(powerset(identity_relation(relation_dom(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_24443]) ).
tcf(c_59383,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK7(powerset(identity_relation(relation_dom(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_24395]) ).
tcf(c_59384,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(powerset(sK7(powerset(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_11345]) ).
tcf(c_59385,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK7(sK6(powerset(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_10677]) ).
tcf(c_59386,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(sK7(sK6(powerset(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_10676]) ).
tcf(c_59387,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(sK7(sK6(powerset(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_10675]) ).
tcf(c_59388,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(powerset(relation_dom(relation_dom(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_24347]) ).
tcf(c_59389,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK7(powerset(relation_dom(relation_dom(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_23164]) ).
tcf(c_59390,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(sK7(powerset(relation_dom(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_22515]) ).
tcf(c_59391,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(sK7(powerset(relation_dom(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_22426]) ).
tcf(c_59392,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(sK7(sK6(powerset(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_10674]) ).
tcf(c_59393,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(identity_relation(sK7(powerset(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_9751]) ).
tcf(c_59394,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(identity_relation(sK7(powerset(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_9685]) ).
tcf(c_59395,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(sK7(powerset(relation_dom(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_22338]) ).
tcf(c_59396,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(relation_dom(relation_dom(relation_dom(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_22121]) ).
tcf(c_59397,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(relation_dom(relation_dom(relation_dom(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_22031]) ).
tcf(c_59398,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_21914]) ).
tcf(c_59399,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(identity_relation(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X2))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_9348]) ).
tcf(c_59400,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(powerset(sK7(powerset(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_9118]) ).
tcf(c_59401,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK7(powerset(sK7(powerset(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_9091]) ).
tcf(c_59402,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(relation_dom(sK7(powerset(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_9021]) ).
tcf(c_59403,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_21763]) ).
tcf(c_59404,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK7(powerset(relation_dom(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_21512]) ).
tcf(c_59405,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(relation_dom(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X2)))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_20489]) ).
tcf(c_59406,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_dom(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X2)))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_20393]) ).
tcf(c_59407,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(relation_dom(sK7(powerset(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_8996]) ).
tcf(c_59408,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(relation_dom(sK7(powerset(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_8961]) ).
tcf(c_59409,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(sK7(powerset(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_8565]) ).
tcf(c_59410,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK7(powerset(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X2)))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_18503]) ).
tcf(c_59411,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(powerset(identity_relation(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_25846]) ).
tcf(c_59412,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(powerset(identity_relation(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_11341]) ).
tcf(c_59413,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK7(sK6(powerset(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X2)))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_10679]) ).
tcf(c_59414,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(sK6(powerset(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_17536]) ).
tcf(c_59415,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK7(sK6(powerset(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_17479]) ).
tcf(c_59416,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(sK6(powerset(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_16756]) ).
tcf(c_59417,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(identity_relation(identity_relation(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_13969]) ).
tcf(c_59418,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_13853]) ).
tcf(c_59419,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(powerset(relation_dom(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_13817]) ).
tcf(c_59420,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(identity_relation(relation_dom(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_13649]) ).
tcf(c_59421,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(identity_relation(relation_dom(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_13044]) ).
tcf(c_59422,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(powerset(identity_relation(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_12909]) ).
tcf(c_59423,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK7(powerset(identity_relation(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_12871]) ).
tcf(c_59424,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(powerset(relation_dom(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_12755]) ).
tcf(c_59425,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK7(powerset(relation_dom(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_12356]) ).
tcf(c_59426,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(sK7(powerset(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_12318]) ).
tcf(c_59427,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(sK7(powerset(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_12212]) ).
tcf(c_59428,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(sK7(powerset(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_12135]) ).
tcf(c_59429,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(relation_dom(relation_dom(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_12099]) ).
tcf(c_59430,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(relation_dom(relation_dom(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_12063]) ).
tcf(c_59431,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(relation_dom(relation_dom(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_12027]) ).
tcf(c_59432,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_11953]) ).
tcf(c_59433,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK7(powerset(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_11431]) ).
tcf(c_59434,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X2))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_9347]) ).
tcf(c_59435,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X2))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_9319]) ).
tcf(c_59436,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK7(powerset(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X2))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_6877]) ).
tcf(c_59437,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(sK6(powerset(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_10680]) ).
tcf(c_59438,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK7(sK6(powerset(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_10678]) ).
tcf(c_59439,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(sK6(powerset(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_15645]) ).
tcf(c_59440,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(identity_relation(identity_relation(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_9748]) ).
tcf(c_59441,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_9682]) ).
tcf(c_59442,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(powerset(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_11340]) ).
tcf(c_59476,plain,
! [X0: $i,X1: $i] :
( function(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_98]) ).
tcf(c_59477,plain,
! [X0: $i,X1: $i] :
( relation(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_80]) ).
tcf(c_59819,plain,
! [X0: $i,X1: $i] :
( empty(sK7(powerset(relation_image(empty_set,X1))))
| ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ~ empty(relation_dom(relation_dom(X0))) ),
inference(light_normalisation,[status(thm)],[c_59279,c_6104]) ).
tcf(c_60976,plain,
! [X0: $i] :
( function(sK7(powerset(relation_image(identity_relation(empty_set),X0))))
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_8004,c_59476]) ).
tcf(c_60977,plain,
! [X0: $i,X1: $i] :
( function(sK7(powerset(relation_image(identity_relation(empty_set),X1))))
| ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ~ empty(relation_dom(relation_dom(X0))) ),
inference(superposition,[status(thm)],[c_12097,c_59476]) ).
tcf(c_60978,plain,
! [X0: $i,X1: $i] :
( ( relation_image(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))),empty_set) = empty_set )
| ~ empty(X0)
| ~ relation(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1)))) ),
inference(superposition,[status(thm)],[c_59476,c_23329]) ).
tcf(c_60980,plain,
! [X0: $i,X1: $i] :
( function(sK7(powerset(relation_image(empty_set,X1))))
| ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ~ empty(relation_dom(relation_dom(X0))) ),
inference(light_normalisation,[status(thm)],[c_60977,c_6104]) ).
tcf(c_60994,plain,
! [X0: $i] :
( relation(sK7(powerset(relation_image(identity_relation(empty_set),X0))))
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_8004,c_59477]) ).
tcf(c_60995,plain,
! [X0: $i,X1: $i] :
( relation(sK7(powerset(relation_image(identity_relation(empty_set),X1))))
| ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ~ empty(relation_dom(relation_dom(X0))) ),
inference(superposition,[status(thm)],[c_12097,c_59477]) ).
tcf(c_60997,plain,
! [X0: $i,X1: $i] :
( relation(sK7(powerset(relation_image(empty_set,X1))))
| ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ~ empty(relation_dom(relation_dom(X0))) ),
inference(light_normalisation,[status(thm)],[c_60995,c_6104]) ).
tcf(c_61006,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( identity_relation(relation_dom(relation_image(identity_relation(relation_dom(X0)),X1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10348,c_57810]) ).
tcf(c_61007,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ( identity_relation(relation_dom(relation_image(identity_relation(relation_dom(X0)),X1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_57810]) ).
tcf(c_61008,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( identity_relation(relation_dom(relation_image(identity_relation(relation_dom(X0)),X1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_57810]) ).
tcf(c_61009,plain,
! [X0: $i] : identity_relation(relation_dom(relation_image(identity_relation(relation_dom(empty_set)),X0))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_57810]) ).
tcf(c_61010,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(relation_image(identity_relation(relation_dom(relation_dom(X0))),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_57810]) ).
tcf(c_61011,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(relation_image(identity_relation(relation_dom(identity_relation(X0))),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_57810]) ).
tcf(c_61012,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(relation_image(identity_relation(relation_dom(sK7(powerset(X0)))),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_57810]) ).
tcf(c_61013,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(relation_image(identity_relation(relation_dom(sK7(sK6(powerset(X0))))),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_57810]) ).
tcf(c_61014,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(relation_image(identity_relation(relation_dom(sK7(sK6(sK6(powerset(X0)))))),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_57810]) ).
tcf(c_61015,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(relation_image(identity_relation(relation_dom(relation_image(X0,empty_set))),X1))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_57810]) ).
tcf(c_61016,plain,
! [X0: $i] :
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( identity_relation(relation_dom(relation_image(identity_relation(relation_dom(sK7(powerset(sK1)))),X0))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_57810]) ).
tcf(c_61017,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(relation_image(identity_relation(relation_dom(sK7(powerset(sK7(powerset(X0)))))),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_57810]) ).
tcf(c_61018,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(relation_image(identity_relation(relation_dom(sK7(powerset(relation_image(X0,empty_set))))),X1))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_57810]) ).
tcf(c_61019,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(relation_image(identity_relation(relation_dom(sK7(powerset(sK7(sK6(powerset(X0))))))),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_57810]) ).
tcf(c_61020,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(relation_image(identity_relation(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_57810]) ).
tcf(c_61021,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(relation_dom(relation_image(identity_relation(relation_dom(relation_image(identity_relation(X0),X1))),X2))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_57810]) ).
tcf(c_61022,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(relation_image(identity_relation(relation_dom(sK7(sK6(sK6(sK6(powerset(X0))))))),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_57810]) ).
tcf(c_61023,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(relation_image(identity_relation(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_57810]) ).
tcf(c_61024,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(relation_dom(relation_image(identity_relation(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X1))))),X2))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_57810]) ).
tcf(c_61025,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(relation_dom(relation_image(identity_relation(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X1))),X2))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_57810]) ).
tcf(c_61026,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(relation_dom(relation_image(identity_relation(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))),X2))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_57810]) ).
tcf(c_61128,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( relation_dom(relation_dom(relation_image(identity_relation(relation_dom(X0)),X1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10348,c_58049]) ).
tcf(c_61129,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ( relation_dom(relation_dom(relation_image(identity_relation(relation_dom(X0)),X1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_58049]) ).
tcf(c_61130,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( relation_dom(relation_dom(relation_image(identity_relation(relation_dom(X0)),X1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_58049]) ).
tcf(c_61131,plain,
! [X0: $i] : relation_dom(relation_dom(relation_image(identity_relation(relation_dom(empty_set)),X0))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_58049]) ).
tcf(c_61132,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_image(identity_relation(relation_dom(relation_dom(X0))),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_58049]) ).
tcf(c_61133,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_image(identity_relation(relation_dom(identity_relation(X0))),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_58049]) ).
tcf(c_61134,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_image(identity_relation(relation_dom(sK7(powerset(X0)))),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_58049]) ).
tcf(c_61135,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_image(identity_relation(relation_dom(sK7(sK6(powerset(X0))))),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_58049]) ).
tcf(c_61136,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_image(identity_relation(relation_dom(sK7(sK6(sK6(powerset(X0)))))),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_58049]) ).
tcf(c_61137,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_image(identity_relation(relation_dom(relation_image(X0,empty_set))),X1))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_58049]) ).
tcf(c_61138,plain,
! [X0: $i] :
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( relation_dom(relation_dom(relation_image(identity_relation(relation_dom(sK7(powerset(sK1)))),X0))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_58049]) ).
tcf(c_61139,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_image(identity_relation(relation_dom(sK7(powerset(sK7(powerset(X0)))))),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_58049]) ).
tcf(c_61140,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_image(identity_relation(relation_dom(sK7(powerset(relation_image(X0,empty_set))))),X1))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_58049]) ).
tcf(c_61141,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_image(identity_relation(relation_dom(sK7(powerset(sK7(sK6(powerset(X0))))))),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_58049]) ).
tcf(c_61142,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_image(identity_relation(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_58049]) ).
tcf(c_61143,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_dom(relation_image(identity_relation(relation_dom(relation_image(identity_relation(X0),X1))),X2))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_58049]) ).
tcf(c_61144,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_image(identity_relation(relation_dom(sK7(sK6(sK6(sK6(powerset(X0))))))),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_58049]) ).
tcf(c_61145,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_image(identity_relation(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_58049]) ).
tcf(c_61146,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_dom(relation_image(identity_relation(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X1))))),X2))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_58049]) ).
tcf(c_61147,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_dom(relation_image(identity_relation(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X1))),X2))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_58049]) ).
tcf(c_61148,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_dom(relation_image(identity_relation(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))),X2))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_58049]) ).
tcf(c_61265,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( sK7(sK6(powerset(relation_dom(sK7(powerset(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10348,c_13822]) ).
tcf(c_61266,plain,
! [X0: $i] :
( ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ( sK7(sK6(powerset(relation_dom(sK7(powerset(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_13822]) ).
tcf(c_61267,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( sK7(sK6(powerset(relation_dom(sK7(powerset(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_13822]) ).
tcf(c_61268,plain,
sK7(sK6(powerset(relation_dom(sK7(powerset(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_13822]) ).
tcf(c_61269,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(relation_dom(sK7(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_13822]) ).
tcf(c_61270,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(relation_dom(sK7(powerset(identity_relation(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_13822]) ).
tcf(c_61275,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( sK7(sK6(powerset(relation_dom(sK7(powerset(sK7(powerset(sK1)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_13822]) ).
tcf(c_61276,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(relation_dom(sK7(powerset(sK7(powerset(sK7(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_13822]) ).
tcf(c_61277,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(relation_dom(sK7(powerset(sK7(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_13822]) ).
tcf(c_61278,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(relation_dom(sK7(powerset(sK7(powerset(sK7(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_13822]) ).
tcf(c_61279,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(relation_dom(sK7(powerset(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_13822]) ).
tcf(c_61282,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(relation_dom(sK7(powerset(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_13822]) ).
tcf(c_61283,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(powerset(relation_dom(sK7(powerset(sK7(powerset(relation_image(identity_relation(X0),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_13822]) ).
tcf(c_61285,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(powerset(relation_dom(sK7(powerset(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_13822]) ).
tcf(c_61330,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( identity_relation(identity_relation(identity_relation(identity_relation(sK7(powerset(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10348,c_13858]) ).
tcf(c_61331,plain,
! [X0: $i] :
( ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ( identity_relation(identity_relation(identity_relation(identity_relation(sK7(powerset(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_13858]) ).
tcf(c_61332,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( identity_relation(identity_relation(identity_relation(identity_relation(sK7(powerset(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_13858]) ).
tcf(c_61333,plain,
identity_relation(identity_relation(identity_relation(identity_relation(sK7(powerset(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_13858]) ).
tcf(c_61334,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(sK7(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_13858]) ).
tcf(c_61335,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(sK7(powerset(identity_relation(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_13858]) ).
tcf(c_61340,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( identity_relation(identity_relation(identity_relation(identity_relation(sK7(powerset(sK7(powerset(sK1)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_13858]) ).
tcf(c_61341,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(sK7(powerset(sK7(powerset(sK7(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_13858]) ).
tcf(c_61342,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(sK7(powerset(sK7(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_13858]) ).
tcf(c_61343,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(sK7(powerset(sK7(powerset(sK7(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_13858]) ).
tcf(c_61344,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(sK7(powerset(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_13858]) ).
tcf(c_61347,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(sK7(powerset(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_13858]) ).
tcf(c_61348,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(sK7(powerset(sK7(powerset(relation_image(identity_relation(X0),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_13858]) ).
tcf(c_61350,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(sK7(powerset(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_13858]) ).
tcf(c_61480,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( sK7(powerset(identity_relation(identity_relation(sK7(powerset(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10348,c_13974]) ).
tcf(c_61481,plain,
! [X0: $i] :
( ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ( sK7(powerset(identity_relation(identity_relation(sK7(powerset(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_13974]) ).
tcf(c_61482,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( sK7(powerset(identity_relation(identity_relation(sK7(powerset(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_13974]) ).
tcf(c_61483,plain,
sK7(powerset(identity_relation(identity_relation(sK7(powerset(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_13974]) ).
tcf(c_61484,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(identity_relation(sK7(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_13974]) ).
tcf(c_61485,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(identity_relation(sK7(powerset(identity_relation(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_13974]) ).
tcf(c_61490,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( sK7(powerset(identity_relation(identity_relation(sK7(powerset(sK7(powerset(sK1)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_13974]) ).
tcf(c_61491,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(identity_relation(sK7(powerset(sK7(powerset(sK7(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_13974]) ).
tcf(c_61492,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(identity_relation(sK7(powerset(sK7(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_13974]) ).
tcf(c_61493,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(identity_relation(sK7(powerset(sK7(powerset(sK7(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_13974]) ).
tcf(c_61494,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(identity_relation(sK7(powerset(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_13974]) ).
tcf(c_61497,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(identity_relation(sK7(powerset(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_13974]) ).
tcf(c_61498,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(identity_relation(identity_relation(sK7(powerset(sK7(powerset(relation_image(identity_relation(X0),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_13974]) ).
tcf(c_61500,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(identity_relation(identity_relation(sK7(powerset(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_13974]) ).
tcf(c_61680,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( sK7(powerset(sK7(sK6(sK6(powerset(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10348,c_15638]) ).
tcf(c_61681,plain,
! [X0: $i] :
( ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ( sK7(powerset(sK7(sK6(sK6(powerset(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_15638]) ).
tcf(c_61682,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( sK7(powerset(sK7(sK6(sK6(powerset(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_15638]) ).
tcf(c_61683,plain,
sK7(powerset(sK7(sK6(sK6(powerset(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_15638]) ).
tcf(c_61684,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(sK6(sK6(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_15638]) ).
tcf(c_61685,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(sK6(sK6(powerset(identity_relation(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_15638]) ).
tcf(c_61686,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(sK6(sK6(powerset(sK7(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_15638]) ).
tcf(c_61687,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(sK6(sK6(powerset(sK7(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_15638]) ).
tcf(c_61688,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(sK6(sK6(powerset(sK7(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_15638]) ).
tcf(c_61689,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(sK6(sK6(powerset(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_15638]) ).
tcf(c_61690,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( sK7(powerset(sK7(sK6(sK6(powerset(sK7(powerset(sK1)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_15638]) ).
tcf(c_61691,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(sK6(sK6(powerset(sK7(powerset(sK7(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_15638]) ).
tcf(c_61692,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(sK6(sK6(powerset(sK7(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_15638]) ).
tcf(c_61693,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(sK6(sK6(powerset(sK7(powerset(sK7(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_15638]) ).
tcf(c_61694,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(sK6(sK6(powerset(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_15638]) ).
tcf(c_61695,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(sK7(sK6(sK6(powerset(relation_image(identity_relation(X0),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_15638]) ).
tcf(c_61696,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(sK6(sK6(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_15638]) ).
tcf(c_61697,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(sK6(sK6(powerset(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_15638]) ).
tcf(c_61698,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(sK7(sK6(sK6(powerset(sK7(powerset(relation_image(identity_relation(X0),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_15638]) ).
tcf(c_61699,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(sK7(sK6(sK6(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_15638]) ).
tcf(c_61700,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(sK7(sK6(sK6(powerset(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_15638]) ).
tcf(c_62096,plain,
( ( apply(empty_set,sK7(empty_set)) = sK7(empty_set) )
| ( identity_relation(identity_relation(sK7(powerset(empty_set)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_6104,c_12210]) ).
tcf(c_62097,plain,
( ( apply(identity_relation(powerset(empty_set)),empty_set) = empty_set )
| ( identity_relation(identity_relation(sK7(powerset(powerset(empty_set))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8004,c_12210]) ).
tcf(c_62098,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( apply(identity_relation(powerset(relation_dom(relation_dom(X0)))),empty_set) = empty_set )
| ( identity_relation(identity_relation(sK7(powerset(powerset(relation_dom(relation_dom(X0))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_12097,c_12210]) ).
tcf(c_62101,plain,
( ( apply(identity_relation(sK6(sK6(sK6(powerset(empty_set))))),empty_set) = empty_set )
| ( identity_relation(identity_relation(sK7(powerset(sK6(sK6(sK6(powerset(empty_set)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_37341,c_12210]) ).
tcf(c_62102,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(identity_relation(X0),X1) = X2 )
| ( identity_relation(identity_relation(sK7(powerset(X0)))) = empty_set )
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),relation_dom(identity_relation(X0)))
| ~ in(sK2(identity_relation(X0),X1,X2),X2)
| ( sK2(identity_relation(X0),X1,X2) != sK7(X0) ) ),
inference(superposition,[status(thm)],[c_12210,c_53]) ).
tcf(c_62103,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0),relation_image(identity_relation(X0),X1))
| ( identity_relation(identity_relation(sK7(powerset(X0)))) = empty_set )
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),relation_dom(identity_relation(X0))) ),
inference(superposition,[status(thm)],[c_12210,c_57]) ).
tcf(c_62107,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0),relation_image(identity_relation(X0),X1))
| ( identity_relation(identity_relation(sK7(powerset(X0)))) = empty_set )
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),X0) ),
inference(light_normalisation,[status(thm)],[c_62103,c_121]) ).
tcf(c_62108,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0),relation_image(identity_relation(X0),X1))
| ( identity_relation(identity_relation(sK7(powerset(X0)))) = empty_set )
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_62107,c_62,c_63]) ).
tcf(c_62113,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(identity_relation(X0),X1) = X2 )
| ( identity_relation(identity_relation(sK7(powerset(X0)))) = empty_set )
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),X0)
| ~ in(sK2(identity_relation(X0),X1,X2),X2)
| ( sK2(identity_relation(X0),X1,X2) != sK7(X0) ) ),
inference(light_normalisation,[status(thm)],[c_62102,c_121]) ).
tcf(c_62114,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(identity_relation(X0),X1) = X2 )
| ( identity_relation(identity_relation(sK7(powerset(X0)))) = empty_set )
| ~ in(sK7(X0),X1)
| ~ in(sK7(X0),X0)
| ~ in(sK2(identity_relation(X0),X1,X2),X2)
| ( sK2(identity_relation(X0),X1,X2) != sK7(X0) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_62113,c_62,c_63]) ).
tcf(c_62126,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( relation_image(identity_relation(sK7(powerset(relation_dom(X0)))),X1) = empty_set ) ),
inference(superposition,[status(thm)],[c_10348,c_58130]) ).
tcf(c_62127,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ( relation_image(identity_relation(sK7(powerset(relation_dom(X0)))),X1) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_58130]) ).
tcf(c_62128,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( relation_image(identity_relation(sK7(powerset(relation_dom(X0)))),X1) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_58130]) ).
tcf(c_62129,plain,
! [X0: $i] : relation_image(identity_relation(sK7(powerset(relation_dom(empty_set)))),X0) = empty_set,
inference(superposition,[status(thm)],[c_83,c_58130]) ).
tcf(c_62130,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(sK7(powerset(relation_dom(relation_dom(X0))))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_58130]) ).
tcf(c_62131,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(sK7(powerset(relation_dom(identity_relation(X0))))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_58130]) ).
tcf(c_62132,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(sK7(powerset(relation_dom(sK7(powerset(X0)))))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_58130]) ).
tcf(c_62133,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(sK7(powerset(relation_dom(sK7(sK6(powerset(X0))))))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_58130]) ).
tcf(c_62134,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(sK7(powerset(relation_dom(sK7(sK6(sK6(powerset(X0)))))))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_58130]) ).
tcf(c_62135,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(sK7(powerset(relation_dom(relation_image(X0,empty_set))))),X1) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_58130]) ).
tcf(c_62136,plain,
! [X0: $i] :
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( relation_image(identity_relation(sK7(powerset(relation_dom(sK7(powerset(sK1)))))),X0) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_58130]) ).
tcf(c_62137,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(sK7(powerset(relation_dom(sK7(powerset(sK7(powerset(X0)))))))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_58130]) ).
tcf(c_62138,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(sK7(powerset(relation_dom(sK7(powerset(relation_image(X0,empty_set))))))),X1) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_58130]) ).
tcf(c_62139,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(sK7(powerset(relation_dom(sK7(powerset(sK7(sK6(powerset(X0))))))))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_58130]) ).
tcf(c_62140,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(sK7(powerset(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_58130]) ).
tcf(c_62141,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(identity_relation(sK7(powerset(relation_dom(relation_image(identity_relation(X0),X1))))),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_58130]) ).
tcf(c_62142,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(sK7(powerset(relation_dom(sK7(sK6(sK6(sK6(powerset(X0))))))))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_58130]) ).
tcf(c_62143,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(sK7(powerset(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_58130]) ).
tcf(c_62144,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(identity_relation(sK7(powerset(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X1))))))),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_58130]) ).
tcf(c_62145,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(identity_relation(sK7(powerset(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X1))))),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_58130]) ).
tcf(c_62146,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(identity_relation(sK7(powerset(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_58130]) ).
tcf(c_62406,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( identity_relation(relation_image(identity_relation(identity_relation(relation_dom(X0))),X1)) = empty_set ) ),
inference(superposition,[status(thm)],[c_10348,c_58754]) ).
tcf(c_62407,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ( identity_relation(relation_image(identity_relation(identity_relation(relation_dom(X0))),X1)) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_58754]) ).
tcf(c_62408,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( identity_relation(relation_image(identity_relation(identity_relation(relation_dom(X0))),X1)) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_58754]) ).
tcf(c_62409,plain,
! [X0: $i] : identity_relation(relation_image(identity_relation(identity_relation(relation_dom(empty_set))),X0)) = empty_set,
inference(superposition,[status(thm)],[c_83,c_58754]) ).
tcf(c_62410,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_image(identity_relation(identity_relation(relation_dom(relation_dom(X0)))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_58754]) ).
tcf(c_62411,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_image(identity_relation(identity_relation(relation_dom(identity_relation(X0)))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_58754]) ).
tcf(c_62412,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_image(identity_relation(identity_relation(relation_dom(sK7(powerset(X0))))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_58754]) ).
tcf(c_62413,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_image(identity_relation(identity_relation(relation_dom(sK7(sK6(powerset(X0)))))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_58754]) ).
tcf(c_62414,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_image(identity_relation(identity_relation(relation_dom(sK7(sK6(sK6(powerset(X0))))))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_58754]) ).
tcf(c_62415,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_image(identity_relation(identity_relation(relation_dom(relation_image(X0,empty_set)))),X1)) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_58754]) ).
tcf(c_62416,plain,
! [X0: $i] :
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( identity_relation(relation_image(identity_relation(identity_relation(relation_dom(sK7(powerset(sK1))))),X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_58754]) ).
tcf(c_62417,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_image(identity_relation(identity_relation(relation_dom(sK7(powerset(sK7(powerset(X0))))))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_58754]) ).
tcf(c_62418,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_image(identity_relation(identity_relation(relation_dom(sK7(powerset(relation_image(X0,empty_set)))))),X1)) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_58754]) ).
tcf(c_62419,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_image(identity_relation(identity_relation(relation_dom(sK7(powerset(sK7(sK6(powerset(X0)))))))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_58754]) ).
tcf(c_62420,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_image(identity_relation(identity_relation(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0))))))))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_58754]) ).
tcf(c_62421,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(relation_image(identity_relation(identity_relation(relation_dom(relation_image(identity_relation(X0),X1)))),X2)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_58754]) ).
tcf(c_62422,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_image(identity_relation(identity_relation(relation_dom(sK7(sK6(sK6(sK6(powerset(X0)))))))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_58754]) ).
tcf(c_62423,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_image(identity_relation(identity_relation(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0)))))))))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_58754]) ).
tcf(c_62424,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(relation_image(identity_relation(identity_relation(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X1)))))),X2)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_58754]) ).
tcf(c_62425,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(relation_image(identity_relation(identity_relation(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X1)))),X2)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_58754]) ).
tcf(c_62426,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(relation_image(identity_relation(identity_relation(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1)))))),X2)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_58754]) ).
tcf(c_62523,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( relation_dom(relation_image(identity_relation(identity_relation(relation_dom(X0))),X1)) = empty_set ) ),
inference(superposition,[status(thm)],[c_10348,c_59011]) ).
tcf(c_62524,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ( relation_dom(relation_image(identity_relation(identity_relation(relation_dom(X0))),X1)) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_59011]) ).
tcf(c_62525,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( relation_dom(relation_image(identity_relation(identity_relation(relation_dom(X0))),X1)) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_59011]) ).
tcf(c_62526,plain,
! [X0: $i] : relation_dom(relation_image(identity_relation(identity_relation(relation_dom(empty_set))),X0)) = empty_set,
inference(superposition,[status(thm)],[c_83,c_59011]) ).
tcf(c_62527,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_image(identity_relation(identity_relation(relation_dom(relation_dom(X0)))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_59011]) ).
tcf(c_62528,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_image(identity_relation(identity_relation(relation_dom(identity_relation(X0)))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_59011]) ).
tcf(c_62529,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_image(identity_relation(identity_relation(relation_dom(sK7(powerset(X0))))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_59011]) ).
tcf(c_62530,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_image(identity_relation(identity_relation(relation_dom(sK7(sK6(powerset(X0)))))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_59011]) ).
tcf(c_62531,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_image(identity_relation(identity_relation(relation_dom(sK7(sK6(sK6(powerset(X0))))))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_59011]) ).
tcf(c_62532,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_image(identity_relation(identity_relation(relation_dom(relation_image(X0,empty_set)))),X1)) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_59011]) ).
tcf(c_62533,plain,
! [X0: $i] :
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( relation_dom(relation_image(identity_relation(identity_relation(relation_dom(sK7(powerset(sK1))))),X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_59011]) ).
tcf(c_62534,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_image(identity_relation(identity_relation(relation_dom(sK7(powerset(sK7(powerset(X0))))))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_59011]) ).
tcf(c_62535,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_image(identity_relation(identity_relation(relation_dom(sK7(powerset(relation_image(X0,empty_set)))))),X1)) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_59011]) ).
tcf(c_62536,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_image(identity_relation(identity_relation(relation_dom(sK7(powerset(sK7(sK6(powerset(X0)))))))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_59011]) ).
tcf(c_62537,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_image(identity_relation(identity_relation(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0))))))))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_59011]) ).
tcf(c_62538,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_image(identity_relation(identity_relation(relation_dom(relation_image(identity_relation(X0),X1)))),X2)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_59011]) ).
tcf(c_62539,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_image(identity_relation(identity_relation(relation_dom(sK7(sK6(sK6(sK6(powerset(X0)))))))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_59011]) ).
tcf(c_62540,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_image(identity_relation(identity_relation(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0)))))))))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_59011]) ).
tcf(c_62541,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_image(identity_relation(identity_relation(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X1)))))),X2)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_59011]) ).
tcf(c_62542,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_image(identity_relation(identity_relation(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X1)))),X2)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_59011]) ).
tcf(c_62543,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_image(identity_relation(identity_relation(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1)))))),X2)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_59011]) ).
tcf(c_62618,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( relation_image(identity_relation(identity_relation(identity_relation(relation_dom(X0)))),X1) = empty_set ) ),
inference(superposition,[status(thm)],[c_10348,c_59152]) ).
tcf(c_62619,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ( relation_image(identity_relation(identity_relation(identity_relation(relation_dom(X0)))),X1) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_59152]) ).
tcf(c_62620,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( relation_image(identity_relation(identity_relation(identity_relation(relation_dom(X0)))),X1) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_59152]) ).
tcf(c_62621,plain,
! [X0: $i] : relation_image(identity_relation(identity_relation(identity_relation(relation_dom(empty_set)))),X0) = empty_set,
inference(superposition,[status(thm)],[c_83,c_59152]) ).
tcf(c_62622,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(identity_relation(identity_relation(relation_dom(relation_dom(X0))))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_59152]) ).
tcf(c_62623,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(identity_relation(identity_relation(relation_dom(identity_relation(X0))))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_59152]) ).
tcf(c_62624,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(identity_relation(identity_relation(relation_dom(sK7(powerset(X0)))))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_59152]) ).
tcf(c_62625,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(identity_relation(identity_relation(relation_dom(sK7(sK6(powerset(X0))))))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_59152]) ).
tcf(c_62626,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(identity_relation(identity_relation(relation_dom(sK7(sK6(sK6(powerset(X0)))))))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_59152]) ).
tcf(c_62627,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(identity_relation(identity_relation(relation_dom(relation_image(X0,empty_set))))),X1) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_59152]) ).
tcf(c_62628,plain,
! [X0: $i] :
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( relation_image(identity_relation(identity_relation(identity_relation(relation_dom(sK7(powerset(sK1)))))),X0) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_59152]) ).
tcf(c_62629,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(identity_relation(identity_relation(relation_dom(sK7(powerset(sK7(powerset(X0)))))))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_59152]) ).
tcf(c_62630,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(identity_relation(identity_relation(relation_dom(sK7(powerset(relation_image(X0,empty_set))))))),X1) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_59152]) ).
tcf(c_62631,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(identity_relation(identity_relation(relation_dom(sK7(powerset(sK7(sK6(powerset(X0))))))))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_59152]) ).
tcf(c_62632,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(identity_relation(identity_relation(relation_dom(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_59152]) ).
tcf(c_62633,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(identity_relation(identity_relation(identity_relation(relation_dom(relation_image(identity_relation(X0),X1))))),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_59152]) ).
tcf(c_62634,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(identity_relation(identity_relation(relation_dom(sK7(sK6(sK6(sK6(powerset(X0))))))))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_59152]) ).
tcf(c_62635,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(identity_relation(identity_relation(relation_dom(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_59152]) ).
tcf(c_62636,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(identity_relation(identity_relation(identity_relation(relation_dom(sK7(powerset(relation_image(identity_relation(X0),X1))))))),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_59152]) ).
tcf(c_62637,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(identity_relation(identity_relation(identity_relation(relation_dom(relation_image(identity_relation(sK7(powerset(X0))),X1))))),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_59152]) ).
tcf(c_62638,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(identity_relation(identity_relation(identity_relation(relation_dom(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_59152]) ).
tcf(c_62720,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( identity_relation(identity_relation(sK7(sK6(sK6(powerset(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10348,c_15639]) ).
tcf(c_62721,plain,
! [X0: $i] :
( ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ( identity_relation(identity_relation(sK7(sK6(sK6(powerset(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_15639]) ).
tcf(c_62722,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( identity_relation(identity_relation(sK7(sK6(sK6(powerset(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_15639]) ).
tcf(c_62723,plain,
identity_relation(identity_relation(sK7(sK6(sK6(powerset(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_15639]) ).
tcf(c_62724,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(sK6(sK6(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_15639]) ).
tcf(c_62725,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(sK6(sK6(powerset(identity_relation(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_15639]) ).
tcf(c_62726,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(sK6(sK6(powerset(sK7(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_15639]) ).
tcf(c_62727,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(sK6(sK6(powerset(sK7(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_15639]) ).
tcf(c_62728,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(sK6(sK6(powerset(sK7(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_15639]) ).
tcf(c_62729,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(sK6(sK6(powerset(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_15639]) ).
tcf(c_62730,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( identity_relation(identity_relation(sK7(sK6(sK6(powerset(sK7(powerset(sK1)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_15639]) ).
tcf(c_62731,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(sK6(sK6(powerset(sK7(powerset(sK7(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_15639]) ).
tcf(c_62732,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(sK6(sK6(powerset(sK7(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_15639]) ).
tcf(c_62733,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(sK6(sK6(powerset(sK7(powerset(sK7(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_15639]) ).
tcf(c_62734,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(sK6(sK6(powerset(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_15639]) ).
tcf(c_62735,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(sK7(sK6(sK6(powerset(relation_image(identity_relation(X0),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_15639]) ).
tcf(c_62736,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(sK6(sK6(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_15639]) ).
tcf(c_62737,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(sK6(sK6(powerset(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_15639]) ).
tcf(c_62738,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(sK7(sK6(sK6(powerset(sK7(powerset(relation_image(identity_relation(X0),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_15639]) ).
tcf(c_62739,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(sK7(sK6(sK6(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_15639]) ).
tcf(c_62740,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(sK7(sK6(sK6(powerset(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_15639]) ).
tcf(c_63002,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( identity_relation(relation_dom(sK7(sK6(sK6(powerset(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10348,c_15640]) ).
tcf(c_63003,plain,
! [X0: $i] :
( ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ( identity_relation(relation_dom(sK7(sK6(sK6(powerset(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_15640]) ).
tcf(c_63004,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( identity_relation(relation_dom(sK7(sK6(sK6(powerset(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_15640]) ).
tcf(c_63005,plain,
identity_relation(relation_dom(sK7(sK6(sK6(powerset(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_15640]) ).
tcf(c_63006,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(sK6(sK6(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_15640]) ).
tcf(c_63007,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(sK6(sK6(powerset(identity_relation(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_15640]) ).
tcf(c_63008,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(sK6(sK6(powerset(sK7(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_15640]) ).
tcf(c_63009,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(sK6(sK6(powerset(sK7(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_15640]) ).
tcf(c_63010,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(sK6(sK6(powerset(sK7(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_15640]) ).
tcf(c_63011,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(sK6(sK6(powerset(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_15640]) ).
tcf(c_63012,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( identity_relation(relation_dom(sK7(sK6(sK6(powerset(sK7(powerset(sK1)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_15640]) ).
tcf(c_63013,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(sK6(sK6(powerset(sK7(powerset(sK7(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_15640]) ).
tcf(c_63014,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(sK6(sK6(powerset(sK7(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_15640]) ).
tcf(c_63015,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(sK6(sK6(powerset(sK7(powerset(sK7(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_15640]) ).
tcf(c_63016,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(sK6(sK6(powerset(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_15640]) ).
tcf(c_63017,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(sK7(sK6(sK6(powerset(relation_image(identity_relation(X0),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_15640]) ).
tcf(c_63018,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(sK6(sK6(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_15640]) ).
tcf(c_63019,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(sK6(sK6(powerset(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_15640]) ).
tcf(c_63020,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(sK7(sK6(sK6(powerset(sK7(powerset(relation_image(identity_relation(X0),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_15640]) ).
tcf(c_63021,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(sK7(sK6(sK6(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_15640]) ).
tcf(c_63022,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(sK7(sK6(sK6(powerset(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_15640]) ).
tcf(c_63103,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( relation_dom(relation_dom(sK7(sK6(sK6(powerset(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10348,c_15641]) ).
tcf(c_63104,plain,
! [X0: $i] :
( ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ( relation_dom(relation_dom(sK7(sK6(sK6(powerset(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_15641]) ).
tcf(c_63105,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( relation_dom(relation_dom(sK7(sK6(sK6(powerset(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_15641]) ).
tcf(c_63106,plain,
relation_dom(relation_dom(sK7(sK6(sK6(powerset(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_15641]) ).
tcf(c_63107,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(sK6(sK6(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_15641]) ).
tcf(c_63108,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(sK6(sK6(powerset(identity_relation(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_15641]) ).
tcf(c_63109,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(sK6(sK6(powerset(sK7(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_15641]) ).
tcf(c_63110,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(sK6(sK6(powerset(sK7(sK6(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_15641]) ).
tcf(c_63111,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(sK6(sK6(powerset(sK7(sK6(sK6(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_15641]) ).
tcf(c_63112,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(sK6(sK6(powerset(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18616,c_15641]) ).
tcf(c_63113,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( relation_dom(relation_dom(sK7(sK6(sK6(powerset(sK7(powerset(sK1)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_15641]) ).
tcf(c_63114,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(sK6(sK6(powerset(sK7(powerset(sK7(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_15641]) ).
tcf(c_63115,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(sK6(sK6(powerset(sK7(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_15641]) ).
tcf(c_63116,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(sK6(sK6(powerset(sK7(powerset(sK7(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_15641]) ).
tcf(c_63117,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(sK6(sK6(powerset(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_15641]) ).
tcf(c_63118,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK7(sK6(sK6(powerset(relation_image(identity_relation(X0),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_15641]) ).
tcf(c_63119,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(sK6(sK6(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_15641]) ).
tcf(c_63120,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(sK6(sK6(powerset(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_15641]) ).
tcf(c_63121,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK7(sK6(sK6(powerset(sK7(powerset(relation_image(identity_relation(X0),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_15641]) ).
tcf(c_63122,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK7(sK6(sK6(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_15641]) ).
tcf(c_63123,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK7(sK6(sK6(powerset(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_15641]) ).
tcf(c_63308,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( sK7(sK6(sK6(powerset(sK7(powerset(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10348,c_16761]) ).
tcf(c_63309,plain,
! [X0: $i] :
( ( apply(identity_relation(powerset(X0)),sK6(X0)) = sK6(X0) )
| ( sK7(sK6(sK6(powerset(sK7(powerset(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5806,c_16761]) ).
tcf(c_63310,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK7(X0)) = sK7(X0) )
| ( sK7(sK6(sK6(powerset(sK7(powerset(X0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5807,c_16761]) ).
tcf(c_63311,plain,
sK7(sK6(sK6(powerset(sK7(powerset(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_83,c_16761]) ).
tcf(c_63312,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(powerset(sK7(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_16761]) ).
tcf(c_63313,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(powerset(sK7(powerset(identity_relation(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_16761]) ).
tcf(c_63318,plain,
( ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ( sK7(sK6(sK6(powerset(sK7(powerset(sK7(powerset(sK1)))))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_21309,c_16761]) ).
tcf(c_63319,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(powerset(sK7(powerset(sK7(powerset(sK7(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_16761]) ).
tcf(c_63320,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(powerset(sK7(powerset(sK7(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_18752,c_16761]) ).
tcf(c_63321,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(powerset(sK7(powerset(sK7(powerset(sK7(sK6(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_16761]) ).
tcf(c_63322,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(powerset(sK7(powerset(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_16761]) ).
tcf(c_63325,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(powerset(sK7(powerset(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_16761]) ).
tcf(c_63326,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(sK6(powerset(sK7(powerset(sK7(powerset(relation_image(identity_relation(X0),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_16761]) ).
tcf(c_63328,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(sK6(powerset(sK7(powerset(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X1))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_16761]) ).
tcf(c_63391,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(powerset(sK7(powerset(X0)))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_16761]) ).
tcf(c_63392,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(sK6(sK6(powerset(X0)))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_15641]) ).
tcf(c_63393,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(sK6(sK6(powerset(X0)))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_15640]) ).
tcf(c_63394,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(sK6(sK6(powerset(X0)))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_15639]) ).
tcf(c_63395,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( relation_image(identity_relation(identity_relation(identity_relation(relation_dom(X0)))),X1) = empty_set ) ),
inference(superposition,[status(thm)],[c_9433,c_59152]) ).
tcf(c_63396,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( relation_dom(relation_image(identity_relation(identity_relation(relation_dom(X0))),X1)) = empty_set ) ),
inference(superposition,[status(thm)],[c_9433,c_59011]) ).
tcf(c_63397,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( identity_relation(relation_image(identity_relation(identity_relation(relation_dom(X0))),X1)) = empty_set ) ),
inference(superposition,[status(thm)],[c_9433,c_58754]) ).
tcf(c_63398,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( relation_image(identity_relation(sK7(powerset(relation_dom(X0)))),X1) = empty_set ) ),
inference(superposition,[status(thm)],[c_9433,c_58130]) ).
tcf(c_63399,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(sK6(sK6(powerset(X0)))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_15638]) ).
tcf(c_63400,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(identity_relation(sK7(powerset(X0)))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_13974]) ).
tcf(c_63401,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(sK7(powerset(X0)))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_13858]) ).
tcf(c_63402,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(relation_dom(sK7(powerset(X0)))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_13822]) ).
tcf(c_63403,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( relation_dom(relation_dom(relation_image(identity_relation(relation_dom(X0)),X1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_9433,c_58049]) ).
tcf(c_63404,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( identity_relation(relation_dom(relation_image(identity_relation(relation_dom(X0)),X1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_9433,c_57810]) ).
tcf(c_63405,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(identity_relation(identity_relation(X0))),X1) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_53472]) ).
tcf(c_63406,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_image(identity_relation(identity_relation(X0)),X1)) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_53238]) ).
tcf(c_63407,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_image(identity_relation(identity_relation(X0)),X1)) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_53062]) ).
tcf(c_63408,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( identity_relation(identity_relation(relation_image(identity_relation(relation_dom(X0)),X1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_9433,c_57515]) ).
tcf(c_63409,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(relation_image(identity_relation(relation_dom(X0)),X1))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_56835]) ).
tcf(c_63410,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( relation_image(identity_relation(identity_relation(relation_dom(relation_dom(X0)))),X1) = empty_set ) ),
inference(superposition,[status(thm)],[c_9433,c_54629]) ).
tcf(c_63411,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( relation_dom(relation_image(identity_relation(relation_dom(relation_dom(X0))),X1)) = empty_set ) ),
inference(superposition,[status(thm)],[c_9433,c_54365]) ).
tcf(c_63412,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(sK7(powerset(X0))),X1) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_52684]) ).
tcf(c_63413,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_image(identity_relation(X0),X1))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_49651]) ).
tcf(c_63414,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(relation_image(identity_relation(X0),X1))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_49650]) ).
tcf(c_63415,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(relation_image(identity_relation(X0),X1))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_49649]) ).
tcf(c_63416,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( identity_relation(relation_image(identity_relation(relation_dom(relation_dom(X0))),X1)) = empty_set ) ),
inference(superposition,[status(thm)],[c_9433,c_54163]) ).
tcf(c_63417,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) )
| ( relation_image(identity_relation(relation_dom(relation_dom(relation_dom(X0)))),X1) = empty_set ) ),
inference(superposition,[status(thm)],[c_9433,c_54053]) ).
tcf(c_63418,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(identity_relation(X1),X2) = X0 )
| ( apply(identity_relation(sK6(X1)),sK7(sK6(X1))) = sK7(sK6(X1)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9433,c_49653]) ).
tcf(c_63419,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(relation_image(identity_relation(X0),X1))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_49648]) ).
tcf(c_63420,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(identity_relation(relation_dom(X0))),X1) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_53471]) ).
tcf(c_63421,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_image(identity_relation(relation_dom(X0)),X1)) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_53237]) ).
tcf(c_63422,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_image(identity_relation(relation_dom(X0)),X1)) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_53061]) ).
tcf(c_63423,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(relation_dom(relation_dom(X0))),X1) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_52875]) ).
tcf(c_63424,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(identity_relation(X0)),X1) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_52683]) ).
tcf(c_63425,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_image(identity_relation(X0),X1)) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_49654]) ).
tcf(c_63426,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_image(identity_relation(X0),X1)) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_49652]) ).
tcf(c_63427,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(relation_dom(X0)),X1) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_52682]) ).
tcf(c_63428,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(X0),X1) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_49655]) ).
tcf(c_63429,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(identity_relation(identity_relation(relation_dom(X0)))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_39551]) ).
tcf(c_63430,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(relation_dom(sK7(powerset(X0)))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_13654]) ).
tcf(c_63431,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(relation_dom(sK7(powerset(X0)))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_13049]) ).
tcf(c_63432,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(identity_relation(sK7(powerset(X0)))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_12914]) ).
tcf(c_63433,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(identity_relation(sK7(powerset(X0)))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_12876]) ).
tcf(c_63434,plain,
! [X0: $i] :
( ( relation_dom(sK7(sK6(powerset(identity_relation(relation_dom(X0)))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_38682]) ).
tcf(c_63435,plain,
! [X0: $i] :
( ( identity_relation(sK7(sK6(powerset(identity_relation(relation_dom(X0)))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_37969]) ).
tcf(c_63436,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(powerset(identity_relation(relation_dom(X0)))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_37889]) ).
tcf(c_63437,plain,
! [X0: $i] :
( ( relation_dom(sK7(sK6(sK6(powerset(relation_dom(X0)))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_37780]) ).
tcf(c_63438,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(relation_dom(sK7(powerset(X0)))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_12760]) ).
tcf(c_63439,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(relation_dom(sK7(powerset(X0)))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_12361]) ).
tcf(c_63440,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(powerset(sK7(powerset(X0)))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_12323]) ).
tcf(c_63441,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(powerset(sK7(powerset(X0)))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_12217]) ).
tcf(c_63442,plain,
! [X0: $i] :
( ( identity_relation(sK7(sK6(sK6(powerset(relation_dom(X0)))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_37664]) ).
tcf(c_63443,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(sK6(powerset(relation_dom(X0)))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_37342]) ).
tcf(c_63444,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(identity_relation(identity_relation(relation_dom(X0)))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_31222]) ).
tcf(c_63445,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(identity_relation(relation_dom(X0)))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_31142]) ).
tcf(c_63446,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(powerset(sK7(powerset(X0)))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_12140]) ).
tcf(c_63447,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(relation_dom(sK7(powerset(X0)))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_12104]) ).
tcf(c_63448,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(relation_dom(sK7(powerset(X0)))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_12068]) ).
tcf(c_63449,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(relation_dom(sK7(powerset(X0)))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_12032]) ).
tcf(c_63450,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(identity_relation(identity_relation(relation_dom(X0)))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_31014]) ).
tcf(c_63451,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(identity_relation(identity_relation(relation_dom(X0)))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_30942]) ).
tcf(c_63452,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(powerset(identity_relation(relation_dom(X0)))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_30355]) ).
tcf(c_63453,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(powerset(identity_relation(relation_dom(X0)))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_30248]) ).
tcf(c_63454,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK7(powerset(X0)))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_11958]) ).
tcf(c_63455,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(powerset(sK7(powerset(X0)))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_11436]) ).
tcf(c_63456,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(sK7(sK6(powerset(X0)))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_11346]) ).
tcf(c_63457,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK7(sK6(powerset(X0)))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_10669]) ).
tcf(c_63458,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(powerset(identity_relation(relation_dom(X0)))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_30158]) ).
tcf(c_63459,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(powerset(identity_relation(relation_dom(X0)))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_30068]) ).
tcf(c_63460,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(sK7(powerset(relation_dom(X0)))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_29569]) ).
tcf(c_63461,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(sK6(powerset(relation_dom(X0)))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_29442]) ).
tcf(c_63462,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(sK7(sK6(powerset(X0)))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_10666]) ).
tcf(c_63463,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(sK7(sK6(powerset(X0)))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_10665]) ).
tcf(c_63464,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(sK7(sK6(powerset(X0)))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_10664]) ).
tcf(c_63465,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(sK7(sK6(powerset(X0)))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_10663]) ).
tcf(c_63466,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(sK6(powerset(relation_dom(X0)))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_29308]) ).
tcf(c_63467,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(sK6(powerset(relation_dom(X0)))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_29194]) ).
tcf(c_63468,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(sK6(powerset(relation_dom(X0)))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_28717]) ).
tcf(c_63469,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(sK7(powerset(relation_dom(X0)))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_28572]) ).
tcf(c_63470,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(sK7(sK6(powerset(X0)))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_10662]) ).
tcf(c_63471,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(sK7(sK6(powerset(X0)))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_10659]) ).
tcf(c_63472,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(sK7(powerset(relation_dom(X0)))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_28429]) ).
tcf(c_63473,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(relation_dom(X1))) = X0 )
| ( apply(identity_relation(sK6(X1)),sK7(sK6(X1))) = sK7(sK6(X1)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9433,c_27714]) ).
tcf(c_63474,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(sK7(powerset(relation_dom(X0)))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_27588]) ).
tcf(c_63475,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(sK7(powerset(relation_dom(X0)))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_27452]) ).
tcf(c_63476,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(sK7(sK6(powerset(X0)))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_10658]) ).
tcf(c_63477,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK7(powerset(X1))) = X0 )
| ( apply(identity_relation(sK6(X1)),sK7(sK6(X1))) = sK7(sK6(X1)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9433,c_9351]) ).
tcf(c_63478,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(powerset(X1))) = X0 )
| ( apply(identity_relation(sK6(X1)),sK7(sK6(X1))) = sK7(sK6(X1)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9433,c_9323]) ).
tcf(c_63479,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(identity_relation(identity_relation(X0))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_25847]) ).
tcf(c_63480,plain,
! [X0: $i] :
( ( relation_dom(sK7(sK6(powerset(identity_relation(X0))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_17537]) ).
tcf(c_63481,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(sK7(powerset(relation_dom(X0)))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_27367]) ).
tcf(c_63482,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(sK7(powerset(relation_dom(X0)))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_26858]) ).
tcf(c_63483,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(sK7(powerset(relation_dom(X0)))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_26809]) ).
tcf(c_63484,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK7(powerset(relation_dom(X0)))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_26731]) ).
tcf(c_63485,plain,
! [X0: $i] :
( ( identity_relation(sK7(sK6(powerset(identity_relation(X0))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_17480]) ).
tcf(c_63486,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(powerset(identity_relation(X0))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_16757]) ).
tcf(c_63487,plain,
! [X0: $i] :
( ( relation_dom(sK7(sK6(sK6(powerset(X0))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_15644]) ).
tcf(c_63488,plain,
! [X0: $i] :
( ( identity_relation(sK7(sK6(sK6(powerset(X0))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_15642]) ).
tcf(c_63489,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(identity_relation(relation_dom(relation_dom(X0)))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_25936]) ).
tcf(c_63490,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(sK6(powerset(X0))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_36269]) ).
tcf(c_63491,plain,
! [X0: $i] :
( ( relation_dom(sK7(sK6(powerset(relation_dom(relation_dom(X0)))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_25099]) ).
tcf(c_63492,plain,
! [X0: $i] :
( ( identity_relation(sK7(sK6(powerset(relation_dom(relation_dom(X0)))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_24875]) ).
tcf(c_63493,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(identity_relation(identity_relation(X0))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_13970]) ).
tcf(c_63494,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(identity_relation(X0))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_13854]) ).
tcf(c_63495,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(identity_relation(identity_relation(X0))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_12910]) ).
tcf(c_63496,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(identity_relation(identity_relation(X0))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_12872]) ).
tcf(c_63497,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(powerset(relation_dom(relation_dom(X0)))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_24819]) ).
tcf(c_63498,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(identity_relation(relation_dom(relation_dom(X0)))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_24724]) ).
tcf(c_63499,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(relation_dom(relation_dom(X0)))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_24676]) ).
tcf(c_63500,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(relation_dom(relation_dom(relation_dom(X0)))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_24628]) ).
tcf(c_63501,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(powerset(identity_relation(X0))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_12319]) ).
tcf(c_63502,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(powerset(identity_relation(X0))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_12213]) ).
tcf(c_63503,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(powerset(identity_relation(X0))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_12136]) ).
tcf(c_63504,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(powerset(identity_relation(X0))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_11432]) ).
tcf(c_63505,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(relation_dom(relation_dom(relation_dom(X0)))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_24580]) ).
tcf(c_63506,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(relation_dom(relation_dom(relation_dom(X0)))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_24491]) ).
tcf(c_63507,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(identity_relation(relation_dom(relation_dom(X0)))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_24443]) ).
tcf(c_63508,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(identity_relation(relation_dom(relation_dom(X0)))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_24395]) ).
tcf(c_63509,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(sK7(powerset(X0))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_11345]) ).
tcf(c_63510,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(sK6(powerset(X0))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_10677]) ).
tcf(c_63511,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(sK6(powerset(X0))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_10676]) ).
tcf(c_63512,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(sK6(powerset(X0))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_10675]) ).
tcf(c_63513,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(relation_dom(relation_dom(relation_dom(X0)))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_24347]) ).
tcf(c_63514,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(relation_dom(relation_dom(relation_dom(X0)))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_23164]) ).
tcf(c_63515,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(powerset(relation_dom(relation_dom(X0)))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_22515]) ).
tcf(c_63516,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(powerset(relation_dom(relation_dom(X0)))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_22426]) ).
tcf(c_63517,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(sK6(powerset(X0))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_10674]) ).
tcf(c_63518,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(sK7(powerset(X0))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_9751]) ).
tcf(c_63519,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(sK7(powerset(X0))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_9685]) ).
tcf(c_63520,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(powerset(relation_dom(relation_dom(X0)))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_22338]) ).
tcf(c_63521,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(relation_dom(relation_dom(relation_dom(X0)))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_22121]) ).
tcf(c_63522,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(relation_dom(relation_dom(relation_dom(X0)))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_22031]) ).
tcf(c_63523,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(X0)))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_21914]) ).
tcf(c_63524,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(X1)) = X0 )
| ( apply(identity_relation(sK6(X1)),sK7(sK6(X1))) = sK7(sK6(X1)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9433,c_9348]) ).
tcf(c_63525,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(sK7(powerset(X0))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_9118]) ).
tcf(c_63526,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(sK7(powerset(X0))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_9091]) ).
tcf(c_63527,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(sK7(powerset(X0))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_9021]) ).
tcf(c_63528,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(X0)))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_21763]) ).
tcf(c_63529,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(powerset(relation_dom(relation_dom(X0)))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_21512]) ).
tcf(c_63530,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(relation_dom(X1))) = X0 )
| ( apply(identity_relation(sK6(X1)),sK7(sK6(X1))) = sK7(sK6(X1)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9433,c_20489]) ).
tcf(c_63531,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(X1))) = X0 )
| ( apply(identity_relation(sK6(X1)),sK7(sK6(X1))) = sK7(sK6(X1)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9433,c_20393]) ).
tcf(c_63532,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(sK7(powerset(X0))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_8996]) ).
tcf(c_63533,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(sK7(powerset(X0))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_8961]) ).
tcf(c_63534,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK7(powerset(X0))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_8565]) ).
tcf(c_63535,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(relation_dom(X1))) = X0 )
| ( apply(identity_relation(sK6(X1)),sK7(sK6(X1))) = sK7(sK6(X1)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9433,c_18503]) ).
tcf(c_63536,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(identity_relation(relation_dom(X0))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_25846]) ).
tcf(c_63537,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(identity_relation(X0)))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_11341]) ).
tcf(c_63538,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(powerset(X1))) = X0 )
| ( apply(identity_relation(sK6(X1)),sK7(sK6(X1))) = sK7(sK6(X1)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9433,c_10679]) ).
tcf(c_63539,plain,
! [X0: $i] :
( ( relation_dom(sK7(sK6(powerset(relation_dom(X0))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_17536]) ).
tcf(c_63540,plain,
! [X0: $i] :
( ( identity_relation(sK7(sK6(powerset(relation_dom(X0))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_17479]) ).
tcf(c_63541,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(powerset(relation_dom(X0))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_16756]) ).
tcf(c_63542,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(identity_relation(relation_dom(X0))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_13969]) ).
tcf(c_63543,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(relation_dom(X0))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_13853]) ).
tcf(c_63544,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(relation_dom(relation_dom(X0))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_13817]) ).
tcf(c_63545,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(relation_dom(relation_dom(X0))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_13649]) ).
tcf(c_63546,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(relation_dom(relation_dom(X0))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_13044]) ).
tcf(c_63547,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(identity_relation(relation_dom(X0))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_12909]) ).
tcf(c_63548,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(identity_relation(relation_dom(X0))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_12871]) ).
tcf(c_63549,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(relation_dom(relation_dom(X0))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_12755]) ).
tcf(c_63550,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(relation_dom(relation_dom(X0))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_12356]) ).
tcf(c_63551,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(powerset(relation_dom(X0))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_12318]) ).
tcf(c_63552,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(powerset(relation_dom(X0))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_12212]) ).
tcf(c_63553,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(powerset(relation_dom(X0))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_12135]) ).
tcf(c_63554,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(relation_dom(relation_dom(X0))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_12099]) ).
tcf(c_63555,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(relation_dom(relation_dom(X0))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_12063]) ).
tcf(c_63556,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(relation_dom(relation_dom(X0))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_12027]) ).
tcf(c_63557,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(X0))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_11953]) ).
tcf(c_63558,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(powerset(relation_dom(X0))))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_11431]) ).
tcf(c_63559,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(X1)) = X0 )
| ( apply(identity_relation(sK6(X1)),sK7(sK6(X1))) = sK7(sK6(X1)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9433,c_9347]) ).
tcf(c_63560,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(X1)) = X0 )
| ( apply(identity_relation(sK6(X1)),sK7(sK6(X1))) = sK7(sK6(X1)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9433,c_9319]) ).
tcf(c_63561,plain,
! [X0: $i,X1: $i] :
( ( sK7(powerset(X1)) = X0 )
| ( apply(identity_relation(sK6(X1)),sK7(sK6(X1))) = sK7(sK6(X1)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9433,c_6877]) ).
tcf(c_63562,plain,
! [X0: $i] :
( ( relation_dom(sK7(sK6(powerset(X0)))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_10680]) ).
tcf(c_63563,plain,
! [X0: $i] :
( ( identity_relation(sK7(sK6(powerset(X0)))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_10678]) ).
tcf(c_63564,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(powerset(X0)))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_15645]) ).
tcf(c_63565,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(identity_relation(X0)))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_9748]) ).
tcf(c_63566,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(X0)))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_9682]) ).
tcf(c_63567,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(relation_dom(X0)))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_11340]) ).
tcf(c_63568,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(relation_dom(X0)))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_9747]) ).
tcf(c_63569,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(relation_dom(X0)))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_9681]) ).
tcf(c_63570,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(identity_relation(X0)))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_9115]) ).
tcf(c_63571,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(identity_relation(X0)))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_9088]) ).
tcf(c_63572,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(relation_dom(X0)))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_9114]) ).
tcf(c_63573,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(relation_dom(X0)))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_9087]) ).
tcf(c_63574,plain,
! [X0: $i] :
( ( sK7(powerset(sK7(powerset(X0)))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_8009]) ).
tcf(c_63575,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK7(powerset(X0)))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_7966]) ).
tcf(c_63576,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK7(powerset(X0)))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_7938]) ).
tcf(c_63577,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(relation_dom(X0)))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_9017]) ).
tcf(c_63578,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(relation_dom(X0)))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_8992]) ).
tcf(c_63579,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(relation_dom(X0)))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_8957]) ).
tcf(c_63580,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(X0)))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_8561]) ).
tcf(c_63581,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK7(powerset(X0)))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_6875]) ).
tcf(c_63582,plain,
! [X0: $i] :
( ( sK7(sK6(powerset(X0))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_10681]) ).
tcf(c_63583,plain,
! [X0: $i] :
( ( sK7(powerset(identity_relation(X0))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_8006]) ).
tcf(c_63584,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(X0))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_7963]) ).
tcf(c_63585,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(X1) = X0 )
| ( apply(identity_relation(sK6(X1)),sK7(sK6(X1))) = sK7(sK6(X1)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9433,c_5794]) ).
tcf(c_63586,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(X1) = X0 )
| ( apply(identity_relation(sK6(X1)),sK7(sK6(X1))) = sK7(sK6(X1)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9433,c_5793]) ).
tcf(c_63587,plain,
! [X0: $i] :
( ( relation_dom(sK7(powerset(X0))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_6878]) ).
tcf(c_63588,plain,
! [X0: $i] :
( ( identity_relation(sK7(powerset(X0))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_6876]) ).
tcf(c_63589,plain,
! [X0: $i] :
( ( sK7(powerset(relation_dom(X0))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_8005]) ).
tcf(c_63590,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(X0))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_7962]) ).
tcf(c_63591,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(X0))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_7934]) ).
tcf(c_63592,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(X0))) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_6133]) ).
tcf(c_63593,plain,
! [X0: $i] :
( ( sK7(powerset(X0)) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_6879]) ).
tcf(c_63594,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(X0)) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_6106]) ).
tcf(c_63595,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(X0)) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_6105]) ).
tcf(c_63596,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(X0)) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_5747]) ).
tcf(c_63597,plain,
! [X0: $i] :
( ( identity_relation(X0) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_5776]) ).
tcf(c_63598,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( apply(identity_relation(sK6(X1)),sK7(sK6(X1))) = sK7(sK6(X1)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9433,c_51]) ).
tcf(c_63599,plain,
! [X0: $i] :
( ( relation_dom(X0) = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_5663]) ).
tcf(c_63600,plain,
! [X0: $i] :
( ( X0 = empty_set )
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_52]) ).
tcf(c_63601,plain,
! [X0: $i] :
( function(X0)
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_98]) ).
tcf(c_63602,plain,
! [X0: $i] :
( relation(X0)
| ( apply(identity_relation(sK6(X0)),sK7(sK6(X0))) = sK7(sK6(X0)) ) ),
inference(superposition,[status(thm)],[c_9433,c_80]) ).
tcf(c_63603,plain,
! [X0: $i] :
( empty(X0)
| ( apply(identity_relation(sK6(sK6(X0))),sK7(sK6(sK6(X0)))) = sK7(sK6(sK6(X0))) ) ),
inference(superposition,[status(thm)],[c_9433,c_69]) ).
tcf(c_63604,plain,
! [X0: $i] : apply(identity_relation(sK6(powerset(X0))),sK7(sK6(powerset(X0)))) = sK7(sK6(powerset(X0))),
inference(superposition,[status(thm)],[c_9433,c_70]) ).
tcf(c_63605,plain,
apply(identity_relation(sK6(sK8)),sK7(sK6(sK8))) = sK7(sK6(sK8)),
inference(superposition,[status(thm)],[c_9433,c_74]) ).
tcf(c_63606,plain,
apply(identity_relation(sK6(sK9)),sK7(sK6(sK9))) = sK7(sK6(sK9)),
inference(superposition,[status(thm)],[c_9433,c_75]) ).
tcf(c_63607,plain,
! [X0: $i] :
( empty(X0)
| ( apply(identity_relation(sK6(relation_dom(X0))),sK7(sK6(relation_dom(X0)))) = sK7(sK6(relation_dom(X0))) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_9433,c_88]) ).
tcf(c_63608,plain,
! [X0: $i] :
( function(X0)
| ( apply(identity_relation(sK6(identity_relation(X0))),sK7(sK6(identity_relation(X0)))) = sK7(sK6(identity_relation(X0))) ) ),
inference(superposition,[status(thm)],[c_9433,c_5644]) ).
tcf(c_63609,plain,
! [X0: $i] :
( relation(X0)
| ( apply(identity_relation(sK6(identity_relation(X0))),sK7(sK6(identity_relation(X0)))) = sK7(sK6(identity_relation(X0))) ) ),
inference(superposition,[status(thm)],[c_9433,c_5633]) ).
tcf(c_63610,plain,
! [X0: $i] :
( empty(X0)
| ( apply(identity_relation(sK6(identity_relation(X0))),sK7(sK6(identity_relation(X0)))) = sK7(sK6(identity_relation(X0))) ) ),
inference(superposition,[status(thm)],[c_9433,c_5621]) ).
tcf(c_63611,plain,
apply(identity_relation(sK6(sK0)),sK7(sK6(sK0))) = sK7(sK6(sK0)),
inference(superposition,[status(thm)],[c_9433,c_24236]) ).
tcf(c_63613,plain,
apply(identity_relation(sK6(sK6(sK6(powerset(empty_set))))),sK7(sK6(sK6(sK6(powerset(empty_set)))))) = sK7(sK6(sK6(sK6(powerset(empty_set))))),
inference(superposition,[status(thm)],[c_9433,c_25896]) ).
tcf(c_63722,plain,
apply(identity_relation(sK6(sK6(sK6(powerset(empty_set))))),empty_set) = empty_set,
inference(light_normalisation,[status(thm)],[c_63613,c_37341]) ).
tcf(c_65105,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(sK6(sK8)),X0) = X1 )
| ~ function(identity_relation(sK6(sK8)))
| ~ relation(identity_relation(sK6(sK8)))
| ~ in(sK7(sK6(sK8)),X0)
| ~ in(sK7(sK6(sK8)),relation_dom(identity_relation(sK6(sK8))))
| ~ in(sK2(identity_relation(sK6(sK8)),X0,X1),X1)
| ( sK2(identity_relation(sK6(sK8)),X0,X1) != sK7(sK6(sK8)) ) ),
inference(superposition,[status(thm)],[c_63605,c_53]) ).
tcf(c_65106,plain,
! [X0: $i] :
( in(sK7(sK6(sK8)),relation_image(identity_relation(sK6(sK8)),X0))
| ~ function(identity_relation(sK6(sK8)))
| ~ relation(identity_relation(sK6(sK8)))
| ~ in(sK7(sK6(sK8)),X0)
| ~ in(sK7(sK6(sK8)),relation_dom(identity_relation(sK6(sK8)))) ),
inference(superposition,[status(thm)],[c_63605,c_57]) ).
tcf(c_65107,plain,
! [X0: $i] :
( in(sK7(sK6(sK8)),relation_image(identity_relation(sK6(sK8)),X0))
| ~ in(sK7(sK6(sK8)),X0)
| ~ in(sK7(sK6(sK8)),relation_dom(identity_relation(sK6(sK8)))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_65106,c_62,c_63]) ).
tcf(c_65111,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(sK6(sK8)),X0) = X1 )
| ~ in(sK7(sK6(sK8)),X0)
| ~ in(sK7(sK6(sK8)),relation_dom(identity_relation(sK6(sK8))))
| ~ in(sK2(identity_relation(sK6(sK8)),X0,X1),X1)
| ( sK2(identity_relation(sK6(sK8)),X0,X1) != sK7(sK6(sK8)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_65105,c_62,c_63]) ).
tcf(c_65117,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(sK6(sK9)),X0) = X1 )
| ~ function(identity_relation(sK6(sK9)))
| ~ relation(identity_relation(sK6(sK9)))
| ~ in(sK7(sK6(sK9)),X0)
| ~ in(sK7(sK6(sK9)),relation_dom(identity_relation(sK6(sK9))))
| ~ in(sK2(identity_relation(sK6(sK9)),X0,X1),X1)
| ( sK2(identity_relation(sK6(sK9)),X0,X1) != sK7(sK6(sK9)) ) ),
inference(superposition,[status(thm)],[c_63606,c_53]) ).
tcf(c_65118,plain,
! [X0: $i] :
( in(sK7(sK6(sK9)),relation_image(identity_relation(sK6(sK9)),X0))
| ~ function(identity_relation(sK6(sK9)))
| ~ relation(identity_relation(sK6(sK9)))
| ~ in(sK7(sK6(sK9)),X0)
| ~ in(sK7(sK6(sK9)),relation_dom(identity_relation(sK6(sK9)))) ),
inference(superposition,[status(thm)],[c_63606,c_57]) ).
tcf(c_65119,plain,
! [X0: $i] :
( in(sK7(sK6(sK9)),relation_image(identity_relation(sK6(sK9)),X0))
| ~ in(sK7(sK6(sK9)),X0)
| ~ in(sK7(sK6(sK9)),relation_dom(identity_relation(sK6(sK9)))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_65118,c_62,c_63]) ).
tcf(c_65123,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(sK6(sK9)),X0) = X1 )
| ~ in(sK7(sK6(sK9)),X0)
| ~ in(sK7(sK6(sK9)),relation_dom(identity_relation(sK6(sK9))))
| ~ in(sK2(identity_relation(sK6(sK9)),X0,X1),X1)
| ( sK2(identity_relation(sK6(sK9)),X0,X1) != sK7(sK6(sK9)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_65117,c_62,c_63]) ).
tcf(c_65152,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(sK6(powerset(X1)))) = X0 )
| ( apply(identity_relation(sK6(X1)),sK7(sK6(X1))) = sK7(sK6(X1)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9433,c_15643]) ).
tcf(c_65153,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(sK6(powerset(X1)))) = X0 )
| ( apply(identity_relation(X1),sK7(sK6(X1))) = sK7(sK6(X1)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10348,c_15643]) ).
tcf(c_65154,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(sK6(powerset(X1)))) = X0 )
| ( apply(identity_relation(powerset(X1)),sK6(X1)) = sK6(X1) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5806,c_15643]) ).
tcf(c_65155,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(sK6(powerset(X1)))) = X0 )
| ( apply(identity_relation(X1),sK7(X1)) = sK7(X1) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5807,c_15643]) ).
tcf(c_65156,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(powerset(empty_set)))) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_83,c_15643]) ).
tcf(c_65157,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(sK6(powerset(relation_dom(X0))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_86,c_15643]) ).
tcf(c_65158,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(sK6(powerset(identity_relation(X0))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5767,c_15643]) ).
tcf(c_65159,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(sK6(powerset(sK7(powerset(X0)))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6837,c_15643]) ).
tcf(c_65160,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(sK6(powerset(sK7(sK6(powerset(X0))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10421,c_15643]) ).
tcf(c_65161,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(sK6(powerset(sK7(sK6(sK6(powerset(X0)))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15107,c_15643]) ).
tcf(c_65162,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(sK6(powerset(relation_image(X1,empty_set))))) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18616,c_15643]) ).
tcf(c_65163,plain,
! [X0: $i] :
( ( sK7(sK6(sK6(powerset(sK7(powerset(sK1)))))) = X0 )
| ( apply(identity_relation(sK0),sK7(sK7(powerset(sK1)))) = sK7(sK7(powerset(sK1))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21309,c_15643]) ).
tcf(c_65164,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(sK6(powerset(sK7(powerset(sK7(powerset(X0)))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18749,c_15643]) ).
tcf(c_65165,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(sK6(powerset(sK7(powerset(relation_image(X1,empty_set))))))) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18752,c_15643]) ).
tcf(c_65166,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(sK6(powerset(sK7(powerset(sK7(sK6(powerset(X0))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18755,c_15643]) ).
tcf(c_65167,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(sK6(powerset(sK7(powerset(sK7(sK6(sK6(powerset(X0)))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18757,c_15643]) ).
tcf(c_65168,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK7(sK6(sK6(powerset(relation_image(identity_relation(X0),X2))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49323,c_15643]) ).
tcf(c_65169,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(sK6(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35729,c_15643]) ).
tcf(c_65170,plain,
! [X0: $i,X1: $i] :
( ( sK7(sK6(sK6(powerset(sK7(powerset(sK7(sK6(sK6(sK6(powerset(X0))))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_35728,c_15643]) ).
tcf(c_65171,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK7(sK6(sK6(powerset(sK7(powerset(relation_image(identity_relation(X0),X2))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_49322,c_15643]) ).
tcf(c_65172,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK7(sK6(sK6(powerset(relation_image(identity_relation(sK7(powerset(X0))),X2))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53608,c_15643]) ).
tcf(c_65173,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK7(sK6(sK6(powerset(sK7(powerset(relation_image(identity_relation(sK7(powerset(X0))),X2))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53607,c_15643]) ).
tcf(c_65303,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_65173,c_65172,c_65171,c_65170,c_65169,c_65168,c_65167,c_65166,c_65165,c_65164,c_65163,c_65162,c_65161,c_65160,c_65159,c_65158,c_65157,c_65156,c_65155,c_65154,c_65153,c_65152,c_63722,c_63613,c_63594,c_63593,c_63590,c_63589,c_63588,c_63587,c_63584,c_63583,c_63582,c_63581,c_63578,c_63577,c_63576,c_63575,c_63574,c_63573,c_63572,c_63571,c_63570,c_63569,c_63568,c_63567,c_63566,c_63565,c_63564,c_63563,c_63562,c_63561,c_63558,c_63555,c_63554,c_63553,c_63552,c_63551,c_63550,c_63549,c_63548,c_63547,c_63546,c_63545,c_63544,c_63543,c_63542,c_63541,c_63540,c_63539,c_63538,c_63537,c_63536,c_63535,c_63534,c_63533,c_63532,c_63531,c_63530,c_63529,c_63528,c_63527,c_63526,c_63525,c_63523,c_63522,c_63521,c_63520,c_63519,c_63518,c_63517,c_63516,c_63515,c_63514,c_63513,c_63512,c_63511,c_63510,c_63509,c_63508,c_63507,c_63506,c_63505,c_63504,c_63503,c_63502,c_63501,c_63500,c_63499,c_63498,c_63497,c_63496,c_63495,c_63494,c_63493,c_63492,c_63491,c_63490,c_63489,c_63488,c_63487,c_63486,c_63485,c_63484,c_63483,c_63482,c_63481,c_63480,c_63479,c_63478,c_63477,c_63476,c_63475,c_63474,c_63473,c_63472,c_63471,c_63470,c_63469,c_63468,c_63467,c_63466,c_63465,c_63464,c_63463,c_63462,c_63461,c_63460,c_63459,c_63458,c_63457,c_63456,c_63455,c_63454,c_63453,c_63452,c_63451,c_63450,c_63449,c_63448,c_63447,c_63446,c_63445,c_63444,c_63443,c_63442,c_63441,c_63440,c_63439,c_63438,c_63437,c_63436,c_63435,c_63434,c_63433,c_63432,c_63431,c_63430,c_63429,c_63428,c_63427,c_63426,c_63425,c_63424,c_63423,c_63422,c_63421,c_63420,c_63419,c_63418,c_63417,c_63416,c_63415,c_63414,c_63413,c_63412,c_63411,c_63410,c_63409,c_63408,c_63407,c_63406,c_63405,c_63404,c_63403,c_63402,c_63401,c_63400,c_63399,c_63398,c_63397,c_63396,c_63395,c_63394,c_63393,c_63392,c_63391,c_63328,c_63326,c_63325,c_63322,c_63321,c_63320,c_63319,c_63318,c_63313,c_63312,c_63311,c_63310,c_63309,c_63308,c_63123,c_63122,c_63121,c_63120,c_63119,c_63118,c_63117,c_63116,c_63115,c_63114,c_63113,c_63112,c_63111,c_63110,c_63109,c_63108,c_63107,c_63106,c_63105,c_63104,c_63103,c_63022,c_63021,c_63020,c_63019,c_63018,c_63017,c_63016,c_63015,c_63014,c_63013,c_63012,c_63011,c_63010,c_63009,c_63008,c_63007,c_63006,c_63005,c_63004,c_63003,c_63002,c_62740,c_62739,c_62738,c_62737,c_62736,c_62735,c_62734,c_62733,c_62732,c_62731,c_62730,c_62729,c_62728,c_62727,c_62726,c_62725,c_62724,c_62723,c_62722,c_62721,c_62720,c_62638,c_62637,c_62636,c_62635,c_62634,c_62633,c_62632,c_62631,c_62630,c_62629,c_62628,c_62627,c_62626,c_62625,c_62624,c_62623,c_62622,c_62621,c_62620,c_62619,c_62618,c_62543,c_62542,c_62541,c_62540,c_62539,c_62538,c_62537,c_62536,c_62535,c_62534,c_62533,c_62532,c_62531,c_62530,c_62529,c_62528,c_62527,c_62526,c_62525,c_62524,c_62523,c_62426,c_62425,c_62424,c_62423,c_62422,c_62421,c_62420,c_62419,c_62418,c_62417,c_62416,c_62415,c_62414,c_62413,c_62412,c_62411,c_62410,c_62409,c_62408,c_62407,c_62406,c_62146,c_62145,c_62144,c_62143,c_62142,c_62141,c_62140,c_62139,c_62138,c_62137,c_62136,c_62135,c_62134,c_62133,c_62132,c_62131,c_62130,c_62129,c_62128,c_62127,c_62126,c_62114,c_62113,c_62108,c_62107,c_62103,c_62102,c_62101,c_62098,c_62097,c_62096,c_61700,c_61699,c_61698,c_61697,c_61696,c_61695,c_61694,c_61693,c_61692,c_61691,c_61690,c_61689,c_61688,c_61687,c_61686,c_61685,c_61684,c_61683,c_61682,c_61681,c_61680,c_61500,c_61498,c_61497,c_61494,c_61493,c_61492,c_61491,c_61490,c_61485,c_61484,c_61483,c_61482,c_61481,c_61480,c_61350,c_61348,c_61347,c_61344,c_61343,c_61342,c_61341,c_61340,c_61335,c_61334,c_61333,c_61332,c_61331,c_61330,c_61285,c_61283,c_61282,c_61279,c_61278,c_61277,c_61276,c_61275,c_61270,c_61269,c_61268,c_61267,c_61266,c_61265,c_61148,c_61147,c_61146,c_61145,c_61144,c_61143,c_61142,c_61141,c_61140,c_61139,c_61138,c_61137,c_61136,c_61135,c_61134,c_61133,c_61132,c_61131,c_61130,c_61129,c_61128,c_61026,c_61025,c_61024,c_61023,c_61022,c_61021,c_61020,c_61019,c_61018,c_61017,c_61016,c_61015,c_61014,c_61013,c_61012,c_61011,c_61010,c_61009,c_61008,c_61007,c_61006,c_60997,c_60995,c_60994,c_60980,c_60978,c_60977,c_60976,c_59819,c_59477,c_59476,c_59442,c_59441,c_59440,c_59439,c_59438,c_59437,c_59436,c_59435,c_59434,c_59433,c_59432,c_59431,c_59430,c_59429,c_59428,c_59427,c_59426,c_59425,c_59424,c_59423,c_59422,c_59421,c_59420,c_59419,c_59418,c_59417,c_59416,c_59415,c_59414,c_59413,c_59412,c_59411,c_59410,c_59409,c_59408,c_59407,c_59406,c_59405,c_59404,c_59403,c_59402,c_59401,c_59400,c_59399,c_59398,c_59397,c_59396,c_59395,c_59394,c_59393,c_59392,c_59391,c_59390,c_59389,c_59388,c_59387,c_59386,c_59385,c_59384,c_59383,c_59382,c_59381,c_59380,c_59379,c_59378,c_59377,c_59376,c_59375,c_59374,c_59373,c_59372,c_59371,c_59370,c_59369,c_59368,c_59367,c_59366,c_59365,c_59364,c_59363,c_59362,c_59361,c_59360,c_59359,c_59358,c_59357,c_59356,c_59355,c_59354,c_59353,c_59352,c_59351,c_59350,c_59349,c_59348,c_59347,c_59346,c_59345,c_59344,c_59343,c_59342,c_59341,c_59340,c_59339,c_59338,c_59337,c_59336,c_59335,c_59334,c_59333,c_59332,c_59331,c_59330,c_59329,c_59328,c_59327,c_59326,c_59325,c_59324,c_59323,c_59322,c_59321,c_59320,c_59319,c_59318,c_59317,c_59316,c_59315,c_59314,c_59313,c_59312,c_59311,c_59310,c_59309,c_59308,c_59307,c_59306,c_59305,c_59304,c_59302,c_59301,c_59300,c_59299,c_59298,c_59297,c_59296,c_59295,c_59294,c_59293,c_59292,c_59291,c_59290,c_59289,c_59288,c_59287,c_59286,c_59285,c_59284,c_59283,c_59282,c_59281,c_59280,c_59279,c_59278,c_59167,c_59166,c_59165,c_59164,c_59163,c_59162,c_59161,c_59160,c_59159,c_59158,c_59157,c_59156,c_59155,c_59154,c_59153,c_59152,c_59151,c_59150,c_59149,c_59148,c_59026,c_59025,c_59024,c_59023,c_59022,c_59021,c_59020,c_59019,c_59018,c_59017,c_59016,c_59015,c_59014,c_59013,c_59012,c_59011,c_59010,c_59009,c_59008,c_59007,c_58769,c_58768,c_58767,c_58766,c_58765,c_58764,c_58763,c_58762,c_58761,c_58760,c_58759,c_58758,c_58757,c_58756,c_58755,c_58754,c_58753,c_58752,c_58751,c_58750,c_58617,c_58616,c_58615,c_58614,c_58613,c_58612,c_58611,c_58610,c_58609,c_58608,c_58607,c_58606,c_58605,c_58604,c_58603,c_58602,c_58601,c_58600,c_58599,c_58598,c_58486,c_58485,c_58484,c_58483,c_58482,c_58481,c_58480,c_58479,c_58478,c_58477,c_58476,c_58475,c_58474,c_58473,c_58472,c_58471,c_58470,c_58469,c_58468,c_58467,c_58374,c_58373,c_58372,c_58371,c_58370,c_58369,c_58368,c_58367,c_58366,c_58365,c_58364,c_58363,c_58362,c_58361,c_58360,c_58359,c_58358,c_58357,c_58356,c_58355,c_58292,c_58291,c_58290,c_58289,c_58288,c_58287,c_58286,c_58285,c_58284,c_58283,c_58282,c_58281,c_58280,c_58279,c_58278,c_58277,c_58276,c_58275,c_58274,c_58273,c_58261,c_58260,c_58255,c_58254,c_58250,c_58249,c_58248,c_58245,c_58244,c_58243,c_58145,c_58144,c_58143,c_58140,c_58139,c_58138,c_58137,c_58136,c_58131,c_58130,c_58129,c_58128,c_58127,c_58126,c_58064,c_58063,c_58062,c_58061,c_58060,c_58059,c_58058,c_58057,c_58056,c_58055,c_58054,c_58053,c_58052,c_58050,c_58049,c_58048,c_58047,c_58046,c_58045,c_57825,c_57824,c_57823,c_57822,c_57821,c_57820,c_57819,c_57818,c_57817,c_57816,c_57815,c_57814,c_57813,c_57811,c_57810,c_57809,c_57808,c_57807,c_57806,c_57530,c_57529,c_57528,c_57527,c_57526,c_57525,c_57524,c_57523,c_57522,c_57521,c_57520,c_57519,c_57518,c_57516,c_57515,c_57514,c_57513,c_57512,c_57511,c_57418,c_57417,c_57416,c_57415,c_57414,c_57413,c_57412,c_57411,c_57410,c_57409,c_57408,c_57407,c_57406,c_57405,c_57404,c_57403,c_57402,c_57401,c_57400,c_57399,c_57145,c_57144,c_57143,c_57142,c_57141,c_57140,c_57139,c_57138,c_57137,c_57136,c_57135,c_57134,c_57133,c_57132,c_57131,c_57130,c_57129,c_57128,c_57127,c_57126,c_56981,c_56980,c_56979,c_56978,c_56977,c_56976,c_56975,c_56974,c_56973,c_56972,c_56971,c_56970,c_56969,c_56967,c_56966,c_56965,c_56964,c_56963,c_56962,c_56955,c_56850,c_56849,c_56848,c_56847,c_56846,c_56845,c_56844,c_56843,c_56842,c_56841,c_56840,c_56839,c_56838,c_56836,c_56835,c_56834,c_56833,c_56832,c_56831,c_56823,c_56821,c_56820,c_56796,c_56794,c_56793,c_56792,c_65123,c_65119,c_65118,c_65117,c_65111,c_65107,c_65106,c_65105,c_55587,c_55211,c_55210,c_55207,c_55205,c_55204,c_55203,c_55202,c_55201,c_55200,c_55199,c_55198,c_55197,c_55196,c_55195,c_55194,c_55193,c_55192,c_55191,c_55190,c_55189,c_55188,c_55187,c_55186,c_55185,c_55184,c_55183,c_55182,c_55181,c_55180,c_55179,c_55178,c_55177,c_55176,c_55175,c_55174,c_55173,c_55172,c_55171,c_55170,c_55169,c_55168,c_55167,c_55166,c_55165,c_55164,c_55163,c_55162,c_55161,c_55160,c_55159,c_55158,c_55157,c_55156,c_55155,c_55154,c_55153,c_55152,c_55151,c_55150,c_55149,c_55148,c_55147,c_55146,c_55145,c_55144,c_55143,c_55142,c_55141,c_55140,c_55139,c_55138,c_55137,c_55136,c_55135,c_55134,c_55133,c_55132,c_55131,c_55130,c_55129,c_55128,c_55127,c_55126,c_55125,c_55124,c_55123,c_55122,c_55121,c_55120,c_55119,c_55118,c_55117,c_55116,c_55115,c_55114,c_55113,c_55112,c_55111,c_55110,c_55109,c_55108,c_55107,c_55106,c_55105,c_55104,c_55103,c_55102,c_55101,c_55100,c_55099,c_55098,c_55097,c_55096,c_55095,c_55094,c_55093,c_55092,c_55091,c_55090,c_55089,c_55088,c_55087,c_55086,c_55085,c_55084,c_55083,c_55082,c_55081,c_55080,c_55079,c_55078,c_55077,c_55076,c_55075,c_55074,c_55073,c_55072,c_55071,c_55070,c_55069,c_55068,c_55067,c_55066,c_55065,c_55064,c_55063,c_55062,c_55061,c_55060,c_55059,c_55058,c_55057,c_55056,c_55055,c_55054,c_55053,c_55052,c_55051,c_55050,c_55049,c_55048,c_55047,c_55046,c_55045,c_55044,c_55043,c_55042,c_55041,c_55040,c_55039,c_55038,c_55037,c_55036,c_55035,c_55034,c_55033,c_55032,c_55031,c_55030,c_55029,c_55028,c_55027,c_54643,c_54642,c_54641,c_54640,c_54639,c_54638,c_54637,c_54636,c_54635,c_54634,c_54633,c_54632,c_54631,c_54630,c_54629,c_54628,c_54627,c_54626,c_54625,c_54379,c_54378,c_54377,c_54376,c_54375,c_54374,c_54373,c_54372,c_54371,c_54370,c_54369,c_54368,c_54367,c_54366,c_54365,c_54364,c_54363,c_54362,c_54361,c_54177,c_54176,c_54175,c_54174,c_54173,c_54172,c_54171,c_54170,c_54169,c_54168,c_54167,c_54166,c_54165,c_54164,c_54163,c_54162,c_54161,c_54160,c_54159,c_54067,c_54066,c_54065,c_54064,c_54063,c_54062,c_54061,c_54060,c_54059,c_54058,c_54057,c_54056,c_54055,c_54054,c_54053,c_54052,c_54051,c_54050,c_54049,c_53908,c_53907,c_53882,c_53875,c_53858,c_53857,c_53836,c_53823,c_53822,c_53825,c_53826,c_53827,c_53818,c_53817,c_53816,c_53815,c_53814,c_53813,c_53812,c_53811,c_53810,c_53809,c_53808,c_53807,c_53806,c_53805,c_53804,c_53803,c_53801,c_53800,c_53799,c_53798,c_53797,c_53796,c_53795,c_53794,c_53793,c_53792,c_53791,c_53790,c_53789,c_53788,c_53787,c_53786,c_53785,c_53784,c_53783,c_53782,c_53781,c_53780,c_53779,c_53778,c_53777,c_53776,c_53775,c_53773,c_53774,c_53769,c_53768,c_53766,c_53738,c_53737,c_53717,c_53716,c_53623,c_53610,c_53607,c_53603,c_53602,c_53601,c_53600,c_53599,c_53608,c_53597,c_53596,c_53595,c_53594,c_53593,c_53592,c_53485,c_53484,c_53483,c_53482,c_53481,c_53480,c_53479,c_53478,c_53477,c_53476,c_53475,c_53474,c_53473,c_53472,c_53471,c_53470,c_53469,c_53468,c_53467,c_53251,c_53250,c_53249,c_53248,c_53247,c_53246,c_53245,c_53244,c_53243,c_53242,c_53241,c_53240,c_53239,c_53238,c_53237,c_53236,c_53235,c_53234,c_53233,c_53075,c_53074,c_53073,c_53072,c_53071,c_53070,c_53069,c_53068,c_53067,c_53066,c_53065,c_53064,c_53063,c_53062,c_53061,c_53060,c_53059,c_53058,c_53057,c_52889,c_52888,c_52887,c_52886,c_52885,c_52884,c_52883,c_52882,c_52881,c_52880,c_52879,c_52878,c_52877,c_52876,c_52875,c_52874,c_52873,c_52872,c_52871,c_52865,c_52864,c_52863,c_52805,c_52804,c_52803,c_52802,c_52696,c_52695,c_52694,c_52693,c_52692,c_52691,c_52690,c_52689,c_52688,c_52687,c_52686,c_52685,c_52684,c_52683,c_52682,c_52681,c_52680,c_52679,c_52678,c_52646,c_52630,c_51448,c_51447,c_51413,c_51412,c_51411,c_51410,c_51409,c_51408,c_51407,c_51406,c_51405,c_51404,c_51403,c_51402,c_51401,c_51400,c_51399,c_51398,c_51397,c_51396,c_51395,c_51394,c_51393,c_51392,c_51391,c_51390,c_51389,c_51388,c_51387,c_51386,c_51385,c_51384,c_51383,c_51382,c_51381,c_51380,c_51379,c_51378,c_51377,c_51376,c_51375,c_51374,c_51373,c_51372,c_51371,c_51370,c_51369,c_51368,c_51367,c_51366,c_51365,c_51364,c_51363,c_51362,c_51361,c_51360,c_51359,c_51358,c_51357,c_51356,c_51355,c_51354,c_51353,c_51352,c_51351,c_51350,c_51349,c_51348,c_51347,c_51346,c_51345,c_51344,c_51343,c_51342,c_51341,c_51340,c_51339,c_51338,c_51337,c_51336,c_51335,c_51334,c_51333,c_51332,c_51331,c_51330,c_51329,c_51328,c_51327,c_51326,c_51325,c_51324,c_51323,c_51322,c_51321,c_51320,c_51319,c_51318,c_51317,c_51316,c_51315,c_51314,c_51313,c_51312,c_51311,c_51310,c_51309,c_51308,c_51307,c_51306,c_51305,c_51304,c_51303,c_51302,c_51301,c_51300,c_51299,c_51298,c_51297,c_51296,c_51295,c_51294,c_51293,c_51292,c_51291,c_51290,c_51289,c_51288,c_51287,c_51286,c_51285,c_51284,c_51283,c_51282,c_51281,c_51280,c_51279,c_51278,c_51277,c_51276,c_51275,c_51274,c_51273,c_51267,c_51256,c_51255,c_49657,c_49656,c_49655,c_49654,c_49653,c_49652,c_49651,c_49650,c_49649,c_49648,c_49647,c_49646,c_49645,c_49644,c_49643,c_49642,c_49641,c_49640,c_49639,c_49638,c_49637,c_49636,c_49635,c_49634,c_49633,c_49632,c_49631,c_49630,c_49629,c_49628,c_49627,c_49626,c_49625,c_49624,c_49623,c_49622,c_49621,c_49620,c_49619,c_49618,c_49617,c_49616,c_49615,c_49614,c_49613,c_49612,c_49611,c_49610,c_49609,c_49608,c_49607,c_49606,c_49605,c_49604,c_49603,c_49602,c_49601,c_49600,c_49599,c_49598,c_49597,c_49596,c_49595,c_49594,c_49593,c_49592,c_49591,c_49590,c_49589,c_49588,c_49587,c_49586,c_49585,c_49584,c_49583,c_49582,c_49581,c_49580,c_49579,c_49578,c_49577,c_49576,c_49575,c_49574,c_49573,c_49572,c_49571,c_49570,c_49569,c_49568,c_49567,c_49566,c_49565,c_49564,c_49563,c_49562,c_49561,c_49560,c_49559,c_49558,c_49557,c_49556,c_49555,c_49554,c_49553,c_49552,c_49551,c_49550,c_49549,c_49548,c_49547,c_49546,c_49545,c_49544,c_49543,c_49542,c_49541,c_49540,c_49539,c_49538,c_49537,c_49536,c_49535,c_49534,c_49533,c_49532,c_49531,c_49530,c_49529,c_49528,c_49527,c_49526,c_49525,c_49524,c_49523,c_49522,c_49521,c_49520,c_49519,c_49518,c_49517,c_49516,c_49515,c_49514,c_49513,c_49512,c_49511,c_49510,c_49509,c_49508,c_49507,c_49506,c_49505,c_49504,c_49503,c_49502,c_49501,c_49500,c_49499,c_49498,c_49497,c_49496,c_49495,c_49494,c_49493,c_49492,c_49491,c_49490,c_49489,c_49488,c_49487,c_49486,c_49485,c_49484,c_49483,c_51449,c_49322,c_49192,c_49191,c_49163,c_49159,c_49158,c_49157,c_49108,c_49107,c_49106,c_49105,c_49104,c_49103,c_49102,c_49101,c_49100,c_49099,c_49098,c_49097,c_49096,c_49095,c_49094,c_49093,c_49092,c_49080,c_49079,c_49074,c_49073,c_49069,c_49068,c_49067,c_49064,c_49063,c_49008,c_49006,c_49005,c_49004,c_49003,c_49002,c_48997,c_48996,c_48995,c_48994,c_48993,c_48992,c_48887,c_48885,c_48884,c_48883,c_48882,c_48881,c_48876,c_48875,c_48874,c_48873,c_48872,c_48871,c_48832,c_48830,c_48829,c_48828,c_48827,c_48826,c_48821,c_48820,c_48819,c_48818,c_48817,c_48816,c_48777,c_48775,c_48774,c_48773,c_48772,c_48771,c_48766,c_48765,c_48764,c_48763,c_48762,c_48761,c_48591,c_48590,c_48589,c_48588,c_48587,c_48586,c_48585,c_48584,c_48583,c_48582,c_48581,c_48580,c_48579,c_48578,c_48577,c_48576,c_48575,c_48452,c_48451,c_48450,c_48449,c_48448,c_48447,c_48446,c_48445,c_48444,c_48443,c_48442,c_48441,c_48440,c_48439,c_48438,c_48437,c_48436,c_48266,c_48265,c_48264,c_48263,c_48262,c_48261,c_48260,c_48259,c_48258,c_48257,c_48256,c_48255,c_48254,c_48253,c_48252,c_48251,c_48250,c_48157,c_48156,c_48155,c_48154,c_48153,c_48152,c_48151,c_48150,c_48149,c_48148,c_48147,c_48146,c_48145,c_48144,c_48143,c_48142,c_48141,c_48075,c_48073,c_48072,c_48071,c_48070,c_48069,c_48064,c_48063,c_48062,c_48061,c_48060,c_48059,c_47832,c_47830,c_47829,c_47828,c_47827,c_47826,c_47821,c_47820,c_47819,c_47818,c_47817,c_47816,c_47704,c_47702,c_47701,c_47700,c_47699,c_47698,c_47693,c_47692,c_47691,c_47690,c_47689,c_47688,c_47354,c_47352,c_47351,c_47350,c_47349,c_47348,c_47343,c_47342,c_47341,c_47340,c_47339,c_47338,c_47140,c_47139,c_47138,c_47137,c_47136,c_47135,c_47134,c_47133,c_47132,c_47131,c_47130,c_47129,c_47128,c_47127,c_47126,c_47125,c_47124,c_46985,c_46984,c_46983,c_46982,c_46981,c_46980,c_46979,c_46978,c_46977,c_46976,c_46975,c_46974,c_46973,c_46972,c_46971,c_46970,c_46969,c_46842,c_46841,c_46840,c_46839,c_46838,c_46837,c_46836,c_46835,c_46834,c_46833,c_46832,c_46831,c_46830,c_46829,c_46828,c_46827,c_46826,c_46685,c_46684,c_46683,c_46682,c_46681,c_46680,c_46679,c_46678,c_46677,c_46676,c_46675,c_46674,c_46673,c_46672,c_46671,c_46670,c_46669,c_46640,c_46639,c_46634,c_46633,c_46629,c_46628,c_46627,c_46624,c_46623,c_46584,c_46582,c_46581,c_46580,c_46579,c_46578,c_46573,c_46572,c_46571,c_46570,c_46569,c_46568,c_46422,c_46420,c_46419,c_46418,c_46417,c_46416,c_46411,c_46410,c_46409,c_46408,c_46407,c_46406,c_46239,c_46237,c_46236,c_46235,c_46234,c_46233,c_46228,c_46227,c_46226,c_46225,c_46224,c_46223,c_45995,c_45993,c_45992,c_45991,c_45990,c_45989,c_45984,c_45983,c_45982,c_45981,c_45980,c_45979,c_45774,c_45773,c_45772,c_45771,c_45770,c_45769,c_45768,c_45767,c_45766,c_45765,c_45764,c_45763,c_45762,c_45761,c_45760,c_45759,c_45758,c_45705,c_45704,c_45703,c_45702,c_45701,c_45700,c_45699,c_45698,c_45697,c_45696,c_45695,c_45694,c_45693,c_45692,c_45691,c_45690,c_45689,c_45573,c_45572,c_45571,c_45570,c_45569,c_45568,c_45567,c_45566,c_45565,c_45564,c_45563,c_45562,c_45561,c_45560,c_45559,c_45558,c_45557,c_45479,c_45478,c_45477,c_45476,c_45475,c_45474,c_45473,c_45472,c_45471,c_45470,c_45469,c_45468,c_45467,c_45466,c_45465,c_45464,c_45463,c_45420,c_45418,c_45417,c_45416,c_45415,c_45414,c_45409,c_45408,c_45407,c_45406,c_45405,c_45404,c_45333,c_45331,c_45330,c_45329,c_45328,c_45327,c_45322,c_45321,c_45320,c_45319,c_45318,c_45317,c_45262,c_45261,c_45260,c_45259,c_45258,c_45257,c_45256,c_45255,c_45254,c_45253,c_45252,c_45251,c_45250,c_45249,c_45248,c_45247,c_45246,c_45029,c_45028,c_45027,c_45026,c_45025,c_45024,c_45023,c_45022,c_45021,c_45020,c_45019,c_45018,c_45017,c_45016,c_45015,c_45014,c_45013,c_44890,c_44889,c_44888,c_44887,c_44886,c_44885,c_44884,c_44883,c_44882,c_44881,c_44880,c_44879,c_44878,c_44877,c_44876,c_44875,c_44874,c_63611,c_63609,c_63610,c_63608,c_63607,c_63606,c_63605,c_63604,c_63603,c_63602,c_63601,c_63600,c_63599,c_63597,c_63598,c_63596,c_63595,c_63592,c_63591,c_63586,c_63585,c_63560,c_63559,c_63524,c_63580,c_63557,c_63579,c_63556,c_44610,c_44609,c_44608,c_44607,c_44606,c_44605,c_44604,c_44603,c_44602,c_44601,c_44600,c_44599,c_44598,c_44597,c_44596,c_44595,c_44594,c_44327,c_44326,c_44325,c_44324,c_44323,c_44322,c_44321,c_44320,c_44319,c_44318,c_44317,c_44316,c_44315,c_44314,c_44313,c_44312,c_44311,c_44228,c_44227,c_44226,c_44225,c_44224,c_44223,c_44222,c_44221,c_44220,c_44219,c_44218,c_44217,c_44216,c_44215,c_44214,c_44213,c_44212,c_44200,c_44199,c_44194,c_44193,c_44189,c_44188,c_44187,c_44184,c_44183,c_43993,c_43992,c_43991,c_43990,c_43989,c_43988,c_43987,c_43986,c_43985,c_43984,c_43983,c_43982,c_43981,c_43980,c_43979,c_43978,c_43977,c_43839,c_43838,c_43837,c_43836,c_43835,c_43834,c_43833,c_43832,c_43831,c_43830,c_43829,c_43828,c_43827,c_43826,c_43825,c_43824,c_43823,c_43712,c_43711,c_43710,c_43709,c_43708,c_43707,c_43706,c_43705,c_43704,c_43703,c_43702,c_43701,c_43700,c_43699,c_43698,c_43697,c_43696,c_43595,c_43594,c_43593,c_43592,c_43591,c_43590,c_43589,c_43588,c_43587,c_43586,c_43585,c_43584,c_43583,c_43582,c_43581,c_43580,c_43579,c_43439,c_43438,c_43437,c_43436,c_43435,c_43434,c_43433,c_43432,c_43431,c_43430,c_43429,c_43428,c_43427,c_43426,c_43425,c_43424,c_43423,c_43137,c_43136,c_43135,c_43134,c_43133,c_43132,c_43131,c_43130,c_43129,c_43128,c_43127,c_43126,c_43125,c_43124,c_43123,c_43122,c_43121,c_42974,c_42973,c_42972,c_42971,c_42970,c_42969,c_42968,c_42967,c_42966,c_42965,c_42964,c_42963,c_42962,c_42961,c_42960,c_42959,c_42958,c_42770,c_42769,c_42768,c_42767,c_42766,c_42765,c_42764,c_42763,c_42762,c_42761,c_42760,c_42759,c_42758,c_42757,c_42756,c_42755,c_42754,c_42644,c_42643,c_42642,c_42641,c_42640,c_42639,c_42638,c_42637,c_42636,c_42635,c_42634,c_42633,c_42632,c_42631,c_42630,c_42629,c_42628,c_42498,c_42497,c_42496,c_42495,c_42494,c_42493,c_42492,c_42491,c_42490,c_42489,c_42488,c_42487,c_42486,c_42485,c_42484,c_42483,c_42482,c_42395,c_42394,c_42393,c_42392,c_42391,c_42390,c_42389,c_42388,c_42387,c_42386,c_42385,c_42384,c_42383,c_42382,c_42381,c_42380,c_42379,c_42278,c_42277,c_42276,c_42275,c_42274,c_42273,c_42272,c_42271,c_42270,c_42269,c_42268,c_42267,c_42266,c_42265,c_42264,c_42263,c_42262,c_42161,c_42160,c_42159,c_42158,c_42157,c_42156,c_42155,c_42154,c_42153,c_42152,c_42151,c_42150,c_42149,c_42148,c_42147,c_42146,c_42145,c_42063,c_42062,c_42061,c_42060,c_42059,c_42058,c_42057,c_42056,c_42055,c_42054,c_42053,c_42052,c_42051,c_42050,c_42049,c_42048,c_42047,c_42035,c_42034,c_42029,c_42028,c_42024,c_42023,c_42022,c_42019,c_42018,c_41017,c_41016,c_41015,c_41014,c_41013,c_41012,c_41011,c_41010,c_41009,c_41008,c_41007,c_41006,c_41005,c_41004,c_41003,c_41002,c_41001,c_41000,c_40999,c_40998,c_40997,c_40996,c_40995,c_40994,c_40993,c_40992,c_40991,c_40990,c_40989,c_40988,c_40987,c_40986,c_40985,c_40984,c_40983,c_40982,c_40981,c_40980,c_40979,c_40978,c_40977,c_40976,c_40975,c_40974,c_40973,c_40972,c_40971,c_40970,c_40969,c_40968,c_40967,c_40966,c_40965,c_40964,c_40963,c_40962,c_40961,c_40960,c_40959,c_40958,c_40957,c_40956,c_40955,c_40954,c_40953,c_40952,c_40951,c_40950,c_40949,c_40948,c_40947,c_40946,c_40945,c_40944,c_40943,c_40942,c_40941,c_40940,c_40939,c_40938,c_40937,c_40936,c_40935,c_40934,c_40933,c_40932,c_40931,c_40930,c_40929,c_40928,c_40927,c_40926,c_40925,c_40924,c_40923,c_40922,c_40921,c_40920,c_40919,c_40918,c_40917,c_40916,c_40915,c_40914,c_40913,c_40912,c_40911,c_40910,c_40909,c_40908,c_40907,c_40906,c_40905,c_40904,c_40903,c_40902,c_40901,c_40900,c_40899,c_40898,c_40897,c_40896,c_40895,c_40894,c_40893,c_40892,c_40891,c_40779,c_40778,c_40777,c_40776,c_40775,c_40774,c_40773,c_40772,c_40771,c_40770,c_40769,c_40768,c_40767,c_40766,c_40765,c_40764,c_40718,c_40717,c_40716,c_40715,c_40649,c_40647,c_40646,c_40645,c_40644,c_40639,c_40638,c_40637,c_40636,c_40635,c_40634,c_40578,c_40576,c_40575,c_40574,c_40573,c_40568,c_40567,c_40566,c_40565,c_40564,c_40563,c_40547,c_40541,c_40540,c_40538,c_40537,c_40536,c_40496,c_40495,c_40493,c_40492,c_40491,c_40490,c_39735,c_39734,c_39719,c_39718,c_39714,c_39713,c_39712,c_39711,c_39710,c_39709,c_39708,c_39707,c_39706,c_39705,c_39704,c_39703,c_39702,c_39701,c_39700,c_39699,c_39698,c_39697,c_39696,c_39695,c_39694,c_39693,c_39692,c_39691,c_39690,c_39689,c_39688,c_39687,c_39686,c_39685,c_39684,c_39683,c_39682,c_39681,c_39680,c_39679,c_39678,c_39677,c_39676,c_39675,c_39674,c_39673,c_39672,c_39671,c_39670,c_39669,c_39668,c_39667,c_39666,c_39665,c_39664,c_39663,c_39662,c_39661,c_39660,c_39659,c_39658,c_39657,c_39656,c_39655,c_39654,c_39653,c_39652,c_39651,c_39650,c_39649,c_39648,c_39647,c_39646,c_39645,c_39644,c_39643,c_39642,c_39641,c_39640,c_39639,c_39638,c_39637,c_39636,c_39635,c_39634,c_39633,c_39632,c_39631,c_39630,c_39629,c_39628,c_39627,c_39626,c_39625,c_39624,c_39623,c_39622,c_39621,c_39620,c_39619,c_39618,c_39617,c_39616,c_39615,c_39614,c_39613,c_39612,c_39561,c_39560,c_39559,c_39558,c_39557,c_39556,c_39555,c_39554,c_39553,c_39552,c_39551,c_39550,c_39549,c_39548,c_39547,c_42455,c_42454,c_38873,c_38866,c_38865,c_38864,c_38863,c_38848,c_38847,c_38843,c_38842,c_38841,c_38840,c_38839,c_38838,c_38837,c_38836,c_38835,c_38834,c_38833,c_38832,c_38831,c_38830,c_38829,c_38828,c_38827,c_38826,c_38825,c_38824,c_38823,c_38822,c_38821,c_38820,c_38819,c_38818,c_38817,c_38816,c_38815,c_38814,c_38813,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_38789,c_38788,c_38787,c_38786,c_38785,c_38784,c_38783,c_38782,c_38781,c_38780,c_38779,c_38778,c_38777,c_38776,c_38775,c_38774,c_38773,c_38772,c_38771,c_38770,c_38769,c_38768,c_38767,c_38766,c_38765,c_38764,c_38763,c_38762,c_38761,c_38760,c_38759,c_38758,c_38757,c_38756,c_38755,c_38754,c_38753,c_38752,c_38751,c_38750,c_38749,c_38748,c_38747,c_38746,c_38745,c_38744,c_38743,c_38742,c_38741,c_38740,c_38739,c_38691,c_38690,c_38689,c_38688,c_38687,c_38686,c_38685,c_38684,c_38683,c_38682,c_38681,c_38680,c_38679,c_38678,c_38457,c_38456,c_38455,c_38454,c_38453,c_38452,c_38451,c_38450,c_38449,c_38448,c_38447,c_38446,c_38445,c_38444,c_42013,c_42012,c_42010,c_38346,c_38345,c_38344,c_38343,c_38342,c_38341,c_38340,c_38339,c_38338,c_38337,c_38336,c_38335,c_38334,c_38333,c_38258,c_38257,c_38256,c_38255,c_38254,c_38253,c_38252,c_38251,c_38250,c_38249,c_38248,c_38247,c_38246,c_38245,c_38124,c_38123,c_38122,c_38121,c_38120,c_38119,c_38118,c_38117,c_38116,c_38115,c_38114,c_38113,c_38112,c_38111,c_38100,c_38099,c_38094,c_38093,c_38090,c_38089,c_38088,c_38085,c_37978,c_37977,c_37976,c_37975,c_37974,c_37973,c_37972,c_37971,c_37970,c_37969,c_37968,c_37967,c_37966,c_37965,c_37898,c_37897,c_37896,c_37895,c_37894,c_37893,c_37892,c_37891,c_37890,c_37889,c_37888,c_37887,c_37886,c_37885,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_37673,c_37672,c_37671,c_37670,c_37669,c_37668,c_37667,c_37666,c_37665,c_37664,c_37663,c_37662,c_37661,c_37660,c_37569,c_37568,c_37567,c_37566,c_37565,c_37564,c_37563,c_37562,c_37561,c_37560,c_37559,c_37558,c_37557,c_37556,c_37459,c_37458,c_37457,c_37453,c_37452,c_37442,c_37441,c_37440,c_37439,c_37438,c_37437,c_37436,c_37435,c_37434,c_37433,c_37432,c_37431,c_37430,c_37429,c_37428,c_37427,c_37426,c_37425,c_37351,c_37350,c_37349,c_37348,c_37347,c_37346,c_37345,c_37344,c_37343,c_37342,c_37341,c_37340,c_37339,c_37338,c_37309,c_37308,c_37307,c_37276,c_37275,c_37274,c_37231,c_37227,c_37138,c_49187,c_36271,c_36270,c_36269,c_36268,c_36267,c_36266,c_36265,c_36264,c_36263,c_36262,c_36261,c_36260,c_36259,c_36258,c_36257,c_36256,c_36255,c_36254,c_36253,c_36252,c_36251,c_36250,c_36249,c_36248,c_36247,c_36246,c_36245,c_36244,c_36243,c_36242,c_36241,c_36240,c_36239,c_36238,c_36237,c_36236,c_36235,c_36234,c_36233,c_36232,c_36231,c_36230,c_36229,c_36228,c_36227,c_36226,c_36225,c_36224,c_36223,c_36222,c_36221,c_36220,c_36219,c_36218,c_36217,c_36216,c_36215,c_36214,c_36213,c_36212,c_36211,c_36210,c_36209,c_36208,c_36207,c_36206,c_36205,c_36204,c_36203,c_36202,c_36201,c_36200,c_36199,c_36198,c_36197,c_36196,c_36195,c_36194,c_36193,c_36192,c_36191,c_36190,c_36189,c_36188,c_36187,c_36186,c_36185,c_36184,c_36183,c_36182,c_36181,c_36180,c_36179,c_36178,c_36177,c_36176,c_36175,c_36174,c_36173,c_36172,c_36171,c_36170,c_36169,c_36168,c_36167,c_36166,c_36165,c_36164,c_36163,c_36162,c_36161,c_36160,c_35937,c_35936,c_35935,c_35934,c_35933,c_35932,c_35931,c_35930,c_35929,c_35928,c_35927,c_35926,c_35925,c_35924,c_35923,c_35728,c_35724,c_35723,c_35722,c_35721,c_35729,c_35719,c_35718,c_35717,c_35716,c_35715,c_35680,c_35679,c_35674,c_35673,c_35671,c_35670,c_35667,c_35666,c_35602,c_35562,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_35468,c_35467,c_35466,c_35465,c_35464,c_35463,c_35462,c_35461,c_35460,c_35459,c_35458,c_35457,c_35456,c_49188,c_35647,c_35646,c_35645,c_35644,c_35642,c_37230,c_37229,c_37228,c_35604,c_35598,c_35597,c_35596,c_35593,c_35592,c_35591,c_35584,c_35581,c_35578,c_35577,c_35576,c_35570,c_49189,c_49317,c_52650,c_52647,c_49315,c_52634,c_52631,c_49190,c_49337,c_49325,c_49318,c_49316,c_49314,c_49323,c_49312,c_49311,c_49310,c_49309,c_49308,c_49307,c_49182,c_49183,c_49184,c_44146,c_44145,c_44166,c_44165,c_52657,c_52656,c_52589,c_52588,c_49186,c_49185,c_49181,c_49180,c_49179,c_49178,c_49177,c_49176,c_49175,c_31231,c_31230,c_31229,c_31228,c_31227,c_31226,c_31225,c_31224,c_31223,c_31222,c_31221,c_31220,c_31219,c_31218,c_31151,c_31150,c_31149,c_31148,c_31147,c_31146,c_31145,c_31144,c_31143,c_31142,c_31141,c_31140,c_31139,c_31138,c_31023,c_31022,c_31021,c_31020,c_31019,c_31018,c_31017,c_31016,c_31015,c_31014,c_31013,c_31012,c_31011,c_31010,c_30951,c_30950,c_30949,c_30948,c_30947,c_30946,c_30945,c_30944,c_30943,c_30942,c_30941,c_30940,c_30939,c_30938,c_30772,c_30771,c_30770,c_30769,c_30768,c_30767,c_30766,c_30765,c_30764,c_30763,c_30762,c_30761,c_30760,c_30759,c_30695,c_30694,c_30693,c_30692,c_30691,c_30690,c_30689,c_30688,c_30687,c_30686,c_30685,c_30684,c_30683,c_30682,c_30587,c_30586,c_30585,c_30584,c_30583,c_30582,c_30581,c_30580,c_30579,c_30578,c_30577,c_30576,c_30575,c_30574,c_30510,c_30509,c_30508,c_30507,c_30506,c_30505,c_30504,c_30503,c_30502,c_30501,c_30500,c_30499,c_30498,c_30497,c_30485,c_30484,c_30479,c_30478,c_30476,c_30475,c_30472,c_30471,c_30364,c_30363,c_30362,c_30361,c_30360,c_30359,c_30358,c_30357,c_30356,c_30355,c_30354,c_30353,c_30352,c_30351,c_30257,c_30256,c_30255,c_30254,c_30253,c_30252,c_30251,c_30250,c_30249,c_30248,c_30247,c_30246,c_30245,c_30244,c_30167,c_30166,c_30165,c_30164,c_30163,c_30162,c_30161,c_30160,c_30159,c_30158,c_30157,c_30156,c_30155,c_30154,c_30077,c_30076,c_30075,c_30074,c_30073,c_30072,c_30071,c_30070,c_30069,c_30068,c_30067,c_30066,c_30065,c_30064,c_29988,c_29987,c_29986,c_29985,c_29984,c_29983,c_29982,c_29981,c_29980,c_29979,c_29978,c_29977,c_29976,c_29975,c_29856,c_29855,c_29854,c_29853,c_29852,c_29851,c_29850,c_29849,c_29848,c_29847,c_29846,c_29845,c_29844,c_29843,c_29800,c_29799,c_29798,c_29797,c_29796,c_29795,c_29794,c_29793,c_29792,c_29791,c_29790,c_29789,c_29788,c_29787,c_29633,c_29632,c_29631,c_29630,c_29629,c_29628,c_29627,c_29626,c_29625,c_29624,c_29623,c_29622,c_29621,c_29620,c_29578,c_29577,c_29576,c_29575,c_29571,c_29570,c_29569,c_29568,c_29567,c_29566,c_29565,c_29451,c_29450,c_29449,c_29448,c_29447,c_29446,c_29445,c_29444,c_29443,c_29442,c_29441,c_29440,c_29439,c_29438,c_29317,c_29316,c_29315,c_29314,c_29313,c_29312,c_29311,c_29310,c_29309,c_29308,c_29307,c_29306,c_29305,c_29304,c_29203,c_29202,c_29201,c_29200,c_29199,c_29198,c_29197,c_29196,c_29195,c_29194,c_29193,c_29192,c_29191,c_29190,c_29107,c_29106,c_29105,c_29104,c_29103,c_29102,c_29101,c_29100,c_29099,c_29098,c_29097,c_29096,c_29095,c_29094,c_29051,c_29050,c_29049,c_29048,c_29047,c_29046,c_29045,c_29044,c_29043,c_29042,c_29041,c_29040,c_29039,c_29038,c_28908,c_28907,c_28906,c_28905,c_28904,c_28903,c_28902,c_28901,c_28900,c_28899,c_28898,c_28897,c_28896,c_28895,c_28836,c_28835,c_28834,c_28833,c_28832,c_28831,c_28830,c_28829,c_28828,c_28827,c_28826,c_28825,c_28824,c_28823,c_28726,c_28725,c_28724,c_28723,c_28722,c_28721,c_28720,c_28719,c_28718,c_28717,c_28716,c_28715,c_28714,c_28713,c_28656,c_28655,c_28654,c_28653,c_28581,c_28580,c_28579,c_28578,c_28574,c_28573,c_28572,c_28571,c_28570,c_28569,c_28568,c_28438,c_28437,c_28436,c_28435,c_28431,c_28430,c_28429,c_28428,c_28427,c_28426,c_28425,c_28262,c_28261,c_28260,c_28259,c_28258,c_28257,c_28256,c_28255,c_28254,c_28253,c_28252,c_28251,c_28250,c_28249,c_28056,c_28055,c_28054,c_28053,c_28052,c_28051,c_28050,c_28049,c_28048,c_28047,c_28046,c_28045,c_28044,c_28043,c_27918,c_27917,c_27916,c_27915,c_27914,c_27913,c_27912,c_27911,c_27910,c_27909,c_27908,c_27907,c_27906,c_27905,c_27838,c_27837,c_27836,c_27835,c_27834,c_27833,c_27832,c_27831,c_27830,c_27829,c_27828,c_27827,c_27826,c_27825,c_27723,c_27722,c_27721,c_27720,c_27719,c_27718,c_27717,c_27716,c_27715,c_27714,c_27713,c_27712,c_27711,c_27710,c_27597,c_27596,c_27595,c_27594,c_27590,c_27589,c_27588,c_27587,c_27586,c_27585,c_27584,c_27461,c_27460,c_27459,c_27458,c_27454,c_27453,c_27452,c_27451,c_27450,c_27449,c_27448,c_27376,c_27375,c_27374,c_27373,c_27369,c_27368,c_27367,c_27366,c_27365,c_27364,c_27363,c_27259,c_27258,c_27257,c_27256,c_27255,c_27254,c_27253,c_27252,c_27251,c_27250,c_27249,c_27248,c_27247,c_27246,c_27192,c_27191,c_27190,c_27189,c_27188,c_27187,c_27186,c_27185,c_27184,c_27183,c_27182,c_27181,c_27180,c_27179,c_27098,c_27097,c_27096,c_27095,c_27094,c_27093,c_27092,c_27091,c_27090,c_27089,c_27088,c_27087,c_27086,c_27085,c_26973,c_26972,c_26971,c_26970,c_26969,c_26968,c_26967,c_26966,c_26965,c_26964,c_26963,c_26962,c_26961,c_26960,c_26913,c_26909,c_26908,c_26907,c_26905,c_26867,c_26866,c_26865,c_26864,c_26860,c_26859,c_26858,c_26857,c_26856,c_26855,c_26854,c_26818,c_26817,c_26816,c_26815,c_26811,c_26810,c_26809,c_26808,c_26807,c_26806,c_26805,c_26740,c_26739,c_26738,c_26737,c_26733,c_26732,c_26731,c_26730,c_26729,c_26728,c_26727,c_26655,c_26654,c_26653,c_26652,c_26651,c_26650,c_26649,c_26648,c_26647,c_26646,c_26645,c_26644,c_26643,c_26642,c_26628,c_26624,c_26623,c_26622,c_26598,c_26597,c_26588,c_26580,c_26579,c_26192,c_26191,c_26182,c_26181,c_26180,c_26179,c_26178,c_26177,c_26176,c_26175,c_26174,c_26173,c_26172,c_26171,c_26170,c_26169,c_26168,c_26167,c_26166,c_26165,c_26164,c_26163,c_26162,c_26161,c_26160,c_26159,c_26158,c_26157,c_26156,c_26155,c_26154,c_26153,c_26152,c_26151,c_26150,c_26149,c_26148,c_26147,c_26146,c_26145,c_26144,c_26143,c_26142,c_26141,c_26140,c_26139,c_26138,c_26137,c_26136,c_26135,c_26134,c_26133,c_26132,c_26131,c_26130,c_26129,c_26128,c_26127,c_26126,c_26120,c_26119,c_26003,c_26001,c_25999,c_25995,c_25994,c_25993,c_25990,c_25989,c_25988,c_25987,c_25981,c_25944,c_25943,c_25942,c_25941,c_25940,c_25939,c_25938,c_25937,c_25936,c_25935,c_25934,c_25933,c_25932,c_25924,c_25923,c_25909,c_25905,c_25904,c_25903,c_25901,c_25900,c_25899,c_25896,c_25895,c_25894,c_25892,c_25854,c_25853,c_25852,c_25851,c_25850,c_25849,c_25848,c_25847,c_25846,c_25845,c_25844,c_25843,c_25842,c_25833,c_25832,c_25824,c_25820,c_25819,c_25818,c_25777,c_25776,c_25775,c_25774,c_25773,c_25772,c_25771,c_25770,c_25769,c_25768,c_25767,c_25766,c_25765,c_25751,c_25747,c_25746,c_25745,c_25737,c_25733,c_25732,c_25731,c_25720,c_25719,c_25713,c_25712,c_25706,c_25704,c_25703,c_25702,c_25681,c_25680,c_25674,c_25673,c_25667,c_25665,c_25664,c_25663,c_25439,c_25438,c_25437,c_25436,c_25435,c_25434,c_25433,c_25432,c_25431,c_25430,c_25429,c_25428,c_25427,c_25426,c_25425,c_25424,c_25423,c_25422,c_25421,c_25420,c_25419,c_25418,c_25417,c_25416,c_25415,c_25414,c_25413,c_25412,c_25411,c_25410,c_25409,c_25408,c_25407,c_25406,c_25405,c_25404,c_25403,c_25402,c_25401,c_25400,c_25399,c_25398,c_25397,c_25396,c_25395,c_25394,c_25393,c_25392,c_25391,c_25390,c_25389,c_25388,c_25387,c_25386,c_25385,c_25384,c_25383,c_25382,c_25381,c_25380,c_25379,c_25378,c_25377,c_25376,c_25375,c_25374,c_25373,c_25372,c_25371,c_25370,c_25369,c_25368,c_25367,c_25366,c_25355,c_25354,c_25349,c_25348,c_25345,c_25344,c_25343,c_25341,c_25327,c_25326,c_25321,c_25320,c_25317,c_25316,c_25315,c_25313,c_25282,c_25281,c_25280,c_25279,c_25246,c_25245,c_25244,c_25242,c_25241,c_25223,c_25221,c_25216,c_25215,c_25210,c_25208,c_25203,c_25202,c_25160,c_25159,c_25158,c_25157,c_25156,c_25155,c_25154,c_25153,c_25152,c_25151,c_25150,c_25149,c_25148,c_25147,c_25146,c_25107,c_25106,c_25105,c_25104,c_25103,c_25102,c_25101,c_25100,c_25099,c_25098,c_25097,c_25096,c_25085,c_25084,c_25079,c_25078,c_25075,c_25074,c_25073,c_25071,c_25044,c_25043,c_25042,c_25041,c_25008,c_25007,c_25006,c_25004,c_25003,c_24978,c_24977,c_24965,c_24958,c_24956,c_24938,c_24936,c_24883,c_24882,c_24881,c_24880,c_24879,c_24878,c_24877,c_24876,c_24875,c_24874,c_24873,c_24872,c_24827,c_24826,c_24825,c_24824,c_24823,c_24822,c_24821,c_24820,c_24819,c_24818,c_24817,c_24816,c_24803,c_24802,c_24797,c_24796,c_24792,c_24791,c_24790,c_24788,c_24787,c_24732,c_24731,c_24730,c_24729,c_24728,c_24727,c_24726,c_24725,c_24724,c_24723,c_24722,c_24721,c_24684,c_24683,c_24682,c_24681,c_24680,c_24679,c_24678,c_24677,c_24676,c_24675,c_24674,c_24673,c_24636,c_24635,c_24634,c_24633,c_24632,c_24631,c_24630,c_24629,c_24628,c_24627,c_24626,c_24625,c_24588,c_24587,c_24586,c_24585,c_24584,c_24583,c_24582,c_24581,c_24580,c_24579,c_24578,c_24577,c_24564,c_24563,c_24558,c_24557,c_24553,c_24552,c_24551,c_24549,c_24548,c_24499,c_24498,c_24497,c_24496,c_24495,c_24494,c_24493,c_24492,c_24491,c_24490,c_24489,c_24488,c_24451,c_24450,c_24449,c_24448,c_24447,c_24446,c_24445,c_24444,c_24443,c_24442,c_24441,c_24440,c_24403,c_24402,c_24401,c_24400,c_24399,c_24398,c_24397,c_24396,c_24395,c_24394,c_24393,c_24392,c_24355,c_24354,c_24353,c_24352,c_24351,c_24350,c_24349,c_24348,c_24347,c_24346,c_24345,c_24344,c_24331,c_24330,c_24325,c_24324,c_24320,c_24319,c_24318,c_24316,c_24315,c_24299,c_24298,c_24297,c_24265,c_24264,c_24259,c_24258,c_24255,c_24254,c_24253,c_24251,c_24239,c_24238,c_23938,c_23937,c_23928,c_23925,c_23924,c_23923,c_23922,c_23921,c_23920,c_23919,c_23918,c_23917,c_23916,c_23915,c_23914,c_23913,c_23912,c_23911,c_23910,c_23909,c_23908,c_23907,c_23906,c_23905,c_23904,c_23903,c_23902,c_23901,c_23900,c_23899,c_23898,c_23897,c_23896,c_23895,c_23894,c_23893,c_23892,c_23891,c_23890,c_23889,c_23888,c_23887,c_23886,c_23885,c_23884,c_23883,c_23882,c_23881,c_23880,c_23879,c_23878,c_23877,c_23876,c_23875,c_23874,c_23873,c_23872,c_23331,c_23330,c_23329,c_23328,c_23327,c_23326,c_23325,c_23324,c_23323,c_23322,c_23321,c_23320,c_23318,c_23317,c_23316,c_23315,c_23314,c_23313,c_23312,c_23311,c_23310,c_23309,c_23308,c_23307,c_23306,c_23305,c_23304,c_23303,c_23302,c_23301,c_23300,c_23299,c_23298,c_23297,c_23296,c_23295,c_23294,c_23293,c_23292,c_23291,c_23290,c_23289,c_23288,c_23287,c_23286,c_23285,c_23284,c_23283,c_23282,c_23281,c_23280,c_23279,c_23278,c_23277,c_23276,c_23275,c_23274,c_23273,c_23272,c_23271,c_23270,c_23269,c_23268,c_23267,c_23266,c_23265,c_23174,c_23173,c_23172,c_23171,c_23170,c_23169,c_23168,c_23167,c_23166,c_23165,c_23164,c_23163,c_23162,c_23161,c_25816,c_35448,c_35447,c_35445,c_24236,c_22525,c_22524,c_22523,c_22522,c_22521,c_22520,c_22519,c_22518,c_22517,c_22516,c_22515,c_22514,c_22513,c_22512,c_22436,c_22435,c_22434,c_22433,c_22432,c_22431,c_22430,c_22429,c_22428,c_22427,c_22426,c_22425,c_22424,c_22423,c_22348,c_22347,c_22346,c_22345,c_22344,c_22343,c_22342,c_22341,c_22340,c_22339,c_22338,c_22337,c_22336,c_22335,c_22315,c_22314,c_22309,c_22308,c_22304,c_22303,c_22302,c_22300,c_22299,c_22287,c_22286,c_22277,c_22276,c_22267,c_22266,c_22257,c_22256,c_22240,c_22239,c_22230,c_22229,c_22220,c_22219,c_22210,c_22209,c_22131,c_22130,c_22129,c_22128,c_22127,c_22126,c_22125,c_22124,c_22123,c_22122,c_22121,c_22120,c_22119,c_22118,c_22041,c_22040,c_22039,c_22038,c_22037,c_22036,c_22035,c_22034,c_22033,c_22032,c_22031,c_22030,c_22029,c_22028,c_21924,c_21923,c_21922,c_21921,c_21920,c_21919,c_21918,c_21917,c_21916,c_21915,c_21914,c_21913,c_21912,c_21911,c_21773,c_21772,c_21771,c_21770,c_21769,c_21768,c_21767,c_21766,c_21765,c_21764,c_21763,c_21762,c_21761,c_21760,c_21747,c_21746,c_21741,c_21740,c_21736,c_21735,c_21734,c_21732,c_21731,c_21700,c_21699,c_21686,c_21685,c_21666,c_21665,c_21656,c_21655,c_21646,c_21645,c_21636,c_21635,c_21626,c_21625,c_21616,c_21615,c_21522,c_21521,c_21520,c_21519,c_21518,c_21517,c_21516,c_21515,c_21514,c_21513,c_21512,c_21511,c_21510,c_21509,c_21371,c_21369,c_21368,c_21367,c_21366,c_21365,c_21364,c_21363,c_21362,c_21361,c_21347,c_21346,c_21341,c_21340,c_21336,c_21335,c_21334,c_21332,c_21331,c_21322,c_21321,c_21310,c_21309,c_21304,c_21220,c_21218,c_21217,c_21216,c_21215,c_21214,c_21213,c_21212,c_21211,c_21210,c_21208,c_21207,c_21196,c_21195,c_21168,c_21167,c_21150,c_21149,c_21140,c_21139,c_21130,c_21129,c_20634,c_20633,c_20624,c_20621,c_20620,c_20619,c_20618,c_20617,c_20616,c_20615,c_20614,c_20613,c_20612,c_20611,c_20610,c_20609,c_20608,c_20607,c_20606,c_20605,c_20604,c_20603,c_20602,c_20601,c_20600,c_20599,c_20598,c_20597,c_20596,c_20595,c_20594,c_20593,c_20592,c_20591,c_20590,c_20589,c_20588,c_20587,c_20586,c_20585,c_20584,c_20583,c_20582,c_20581,c_20580,c_20579,c_20578,c_20560,c_20556,c_20555,c_20554,c_20498,c_20497,c_20496,c_20495,c_20494,c_20493,c_20492,c_20491,c_20490,c_20489,c_20488,c_20487,c_20486,c_20402,c_20401,c_20400,c_20399,c_20398,c_20397,c_20396,c_20395,c_20394,c_20393,c_20392,c_20391,c_20390,c_20375,c_20374,c_20369,c_20368,c_20364,c_20363,c_20362,c_20360,c_20359,c_20269,c_20268,c_20259,c_20258,c_20195,c_20194,c_20185,c_20184,c_20175,c_20174,c_20125,c_20124,c_20108,c_20107,c_20052,c_20046,c_20040,c_20031,c_20030,c_20029,c_20004,c_20003,c_19998,c_19997,c_19993,c_19992,c_19991,c_19989,c_19988,c_19876,c_19875,c_19874,c_19873,c_19872,c_19871,c_19870,c_19869,c_19868,c_19867,c_19866,c_19822,c_19454,c_19453,c_19452,c_19451,c_19450,c_19449,c_19448,c_19447,c_19446,c_19445,c_19444,c_19443,c_19441,c_19440,c_19439,c_19438,c_19437,c_19436,c_19435,c_19434,c_19433,c_19432,c_19431,c_19430,c_19429,c_19428,c_19427,c_19426,c_19425,c_19424,c_19423,c_19422,c_19421,c_19420,c_19419,c_19418,c_19417,c_19416,c_19415,c_19414,c_19413,c_19412,c_19411,c_19410,c_19409,c_19408,c_19407,c_19406,c_19405,c_19404,c_19403,c_19402,c_19401,c_19400,c_18919,c_18918,c_18917,c_18916,c_18915,c_18914,c_18911,c_18910,c_18909,c_18908,c_18907,c_18906,c_18905,c_18904,c_18903,c_18902,c_18901,c_18900,c_18899,c_18898,c_18897,c_18896,c_18895,c_18894,c_18893,c_18892,c_18891,c_18890,c_18889,c_18888,c_18887,c_18886,c_18885,c_18884,c_18883,c_18882,c_18881,c_18880,c_18879,c_18878,c_18877,c_18876,c_18875,c_18874,c_18873,c_18872,c_18871,c_18870,c_18761,c_18757,c_18756,c_18755,c_18754,c_18753,c_18752,c_18751,c_18750,c_18749,c_18748,c_18747,c_18746,c_18745,c_18744,c_18741,c_18740,c_18739,c_18738,c_18732,c_18615,c_18614,c_18613,c_18612,c_18611,c_18610,c_18609,c_18608,c_18616,c_18606,c_18604,c_18603,c_18602,c_18601,c_18511,c_18510,c_18509,c_18508,c_18507,c_18506,c_18505,c_18504,c_18503,c_18502,c_18501,c_18500,c_18405,c_18399,c_18398,c_18397,c_18396,c_18395,c_18393,c_18392,c_18389,c_18388,c_18387,c_18386,c_18385,c_18374,c_18373,c_18368,c_18367,c_18363,c_18362,c_18361,c_18359,c_18358,c_18266,c_18264,c_18263,c_18262,c_18261,c_18260,c_18259,c_18258,c_18257,c_18256,c_18255,c_18254,c_18253,c_18242,c_18234,c_18208,c_18189,c_18181,c_18180,c_18179,c_18178,c_18177,c_18176,c_17675,c_17674,c_17673,c_17672,c_17671,c_17670,c_17669,c_17668,c_17667,c_17666,c_17665,c_17664,c_17663,c_17662,c_17661,c_17660,c_17659,c_17658,c_17657,c_17656,c_17655,c_17654,c_17653,c_17652,c_17651,c_17650,c_17649,c_17648,c_17647,c_17646,c_17645,c_17644,c_17643,c_17642,c_17641,c_17640,c_17639,c_17638,c_17637,c_17636,c_17635,c_17634,c_17633,c_17632,c_17631,c_17630,c_17629,c_17628,c_17627,c_17626,c_17625,c_17624,c_17623,c_17543,c_17542,c_17541,c_17540,c_17539,c_17538,c_17537,c_17536,c_17535,c_17534,c_17533,c_17486,c_17485,c_17484,c_17483,c_17482,c_17481,c_17480,c_17479,c_17478,c_17477,c_17476,c_17467,c_17466,c_17422,c_17421,c_16972,c_16971,c_16970,c_16969,c_16968,c_16967,c_16966,c_16965,c_16964,c_16963,c_16962,c_16961,c_16960,c_16959,c_16958,c_16957,c_16956,c_16955,c_16954,c_16953,c_16952,c_16951,c_16950,c_16949,c_16948,c_16947,c_16946,c_16945,c_16944,c_16943,c_16942,c_16941,c_16940,c_16939,c_16938,c_16937,c_16936,c_16935,c_16934,c_16933,c_16932,c_16931,c_16930,c_16929,c_16928,c_16927,c_16926,c_16925,c_16924,c_16923,c_16922,c_16921,c_16920,c_16919,c_16918,c_16917,c_16916,c_16915,c_16914,c_16913,c_16912,c_16911,c_16910,c_16909,c_16908,c_16907,c_16906,c_16905,c_16904,c_16903,c_16902,c_16901,c_16851,c_16850,c_16843,c_16842,c_16841,c_16763,c_16762,c_16761,c_16760,c_16759,c_16758,c_16757,c_16756,c_16755,c_16754,c_16744,c_16743,c_16568,c_16561,c_16554,c_16553,c_16552,c_16551,c_16550,c_16549,c_16548,c_16547,c_16546,c_16545,c_16544,c_16543,c_16506,c_16505,c_16504,c_16473,c_16472,c_16471,c_16332,c_16331,c_16330,c_16329,c_16328,c_16327,c_16326,c_16325,c_16324,c_16323,c_16314,c_16237,c_16236,c_16235,c_16234,c_16233,c_16232,c_16231,c_16230,c_16229,c_16228,c_16110,c_16109,c_16108,c_16107,c_16106,c_16105,c_16104,c_16103,c_16102,c_16101,c_16079,c_16078,c_16077,c_16076,c_16075,c_15984,c_15983,c_15982,c_15981,c_15980,c_15979,c_15978,c_15977,c_15976,c_15975,c_15647,c_15646,c_15645,c_15644,c_15643,c_15642,c_15641,c_15640,c_15639,c_15638,c_15637,c_15634,c_15633,c_15632,c_15631,c_15630,c_15629,c_15628,c_15627,c_15626,c_15625,c_15624,c_15623,c_15622,c_15621,c_15620,c_15619,c_15618,c_15617,c_15616,c_15615,c_15614,c_15613,c_15612,c_15611,c_15610,c_15609,c_15608,c_15607,c_15606,c_15605,c_15604,c_15603,c_15602,c_15601,c_15394,c_15393,c_15392,c_15391,c_15390,c_15389,c_15388,c_15387,c_15386,c_15385,c_15384,c_15383,c_15382,c_15381,c_15380,c_15379,c_15106,c_15105,c_15104,c_15103,c_15102,c_15101,c_15100,c_15099,c_15107,c_15097,c_15096,c_15095,c_15094,c_15093,c_15051,c_15050,c_14875,c_14868,c_14861,c_14860,c_14859,c_14858,c_14857,c_14856,c_14855,c_14854,c_14853,c_14852,c_14851,c_14721,c_14720,c_14719,c_14718,c_14717,c_14716,c_14715,c_14714,c_14711,c_14710,c_14709,c_14708,c_14707,c_14484,c_14483,c_14482,c_14481,c_14480,c_14479,c_14478,c_14477,c_14474,c_14473,c_14472,c_14471,c_14470,c_14387,c_14386,c_14385,c_14384,c_14256,c_14255,c_14254,c_14253,c_14251,c_14250,c_14234,c_14233,c_14226,c_14221,c_14214,c_14213,c_14208,c_14203,c_14114,c_14109,c_14108,c_14106,c_14103,c_14102,c_14101,c_14092,c_14089,c_14086,c_14085,c_14084,c_14078,c_13975,c_13974,c_13973,c_13972,c_13971,c_13970,c_13969,c_13968,c_13967,c_13859,c_13858,c_13857,c_13856,c_13855,c_13854,c_13853,c_13852,c_13851,c_13823,c_13822,c_13821,c_13820,c_13819,c_13818,c_13817,c_13816,c_13815,c_13720,c_13719,c_13718,c_13717,c_13716,c_13715,c_13714,c_13713,c_13712,c_13655,c_13654,c_13653,c_13652,c_13651,c_13650,c_13649,c_13648,c_13647,c_13637,c_13636,c_13560,c_13553,c_13546,c_13545,c_13544,c_13516,c_13509,c_13502,c_13501,c_13500,c_13407,c_13406,c_13402,c_13398,c_13397,c_13396,c_13395,c_13394,c_13393,c_13392,c_13391,c_13390,c_13389,c_13388,c_18970,c_13292,c_13288,c_13284,c_13283,c_13282,c_13281,c_13280,c_13279,c_13278,c_13277,c_13276,c_13275,c_13217,c_13213,c_13209,c_13208,c_13207,c_13206,c_13205,c_13204,c_13203,c_13202,c_13201,c_13200,c_13162,c_13161,c_13160,c_13120,c_13119,c_13118,c_13102,c_13094,c_13050,c_13049,c_13048,c_13047,c_13046,c_13045,c_13044,c_13043,c_13042,c_13032,c_12915,c_12914,c_12913,c_12912,c_12911,c_12910,c_12909,c_12908,c_12907,c_12877,c_12876,c_12875,c_12874,c_12873,c_12872,c_12871,c_12870,c_12869,c_12829,c_12828,c_12827,c_12826,c_12825,c_12824,c_12789,c_12761,c_12760,c_12759,c_12758,c_12757,c_12756,c_12755,c_12754,c_12753,c_12743,c_12742,c_12734,c_12720,c_12659,c_12658,c_12646,c_12639,c_12635,c_12634,c_12633,c_12539,c_12538,c_12535,c_12534,c_12533,c_12532,c_12530,c_12529,c_12528,c_12527,c_12526,c_12525,c_12513,c_12479,c_20039,c_20027,c_12362,c_12361,c_12360,c_12359,c_12358,c_12357,c_12356,c_12355,c_12354,c_12324,c_12323,c_12322,c_12321,c_12320,c_12319,c_12318,c_12317,c_12316,c_12218,c_12217,c_12216,c_12215,c_12214,c_12213,c_12212,c_12211,c_12210,c_12141,c_12140,c_12139,c_12138,c_12137,c_12136,c_12135,c_12134,c_12133,c_12105,c_12104,c_12103,c_12102,c_12101,c_12100,c_12099,c_12098,c_12097,c_12069,c_12068,c_12067,c_12066,c_12065,c_12064,c_12063,c_12062,c_12061,c_12033,c_12032,c_12031,c_12030,c_12029,c_12028,c_12027,c_12026,c_12025,c_11959,c_11958,c_11957,c_11956,c_11955,c_11954,c_11953,c_11952,c_11951,c_11941,c_11940,c_11851,c_11850,c_11847,c_11846,c_11845,c_11844,c_11842,c_11841,c_11840,c_11839,c_11838,c_11837,c_11834,c_11833,c_11821,c_11811,c_11804,c_11797,c_11796,c_11795,c_11646,c_11639,c_11632,c_11631,c_11630,c_11596,c_11595,c_11594,c_11593,c_11561,c_11560,c_11559,c_11558,c_11542,c_11538,c_11536,c_11535,c_11516,c_11515,c_11514,c_11437,c_11436,c_11435,c_11434,c_11433,c_11432,c_11431,c_11430,c_11429,c_11421,c_11420,c_11411,c_11408,c_11407,c_11406,c_11404,c_11395,c_11393,c_11392,c_11391,c_11390,c_11346,c_11345,c_11344,c_11343,c_11342,c_11341,c_11340,c_11339,c_11338,c_11324,c_11323,c_11310,c_11309,c_11308,c_11270,c_11269,c_11205,c_11204,c_11203,c_11202,c_11201,c_11200,c_11199,c_11198,c_11197,c_11188,c_11119,c_11118,c_11117,c_11116,c_11115,c_11114,c_11113,c_11112,c_11111,c_11046,c_11045,c_11044,c_11043,c_11042,c_11041,c_11040,c_11039,c_11038,c_11021,c_11020,c_11015,c_10830,c_10829,c_10828,c_10827,c_10826,c_10825,c_10683,c_10682,c_10681,c_10680,c_10679,c_10678,c_10677,c_10676,c_10675,c_10674,c_10673,c_10670,c_10669,c_10668,c_10667,c_10666,c_10665,c_10664,c_10663,c_10662,c_10661,c_10660,c_10659,c_10658,c_10650,c_10568,c_10567,c_10566,c_10565,c_10564,c_10563,c_10562,c_10561,c_10560,c_10559,c_10558,c_10420,c_10419,c_10418,c_10417,c_10421,c_10415,c_10414,c_10413,c_10412,c_10411,c_10355,c_10354,c_10352,c_10349,c_10348,c_10347,c_10337,c_10336,c_10307,c_10306,c_10305,c_10290,c_10288,c_10287,c_10210,c_10205,c_10200,c_10199,c_10198,c_10197,c_10196,c_10195,c_10194,c_10193,c_10139,c_10134,c_10129,c_10128,c_10127,c_10126,c_10125,c_10124,c_10123,c_10122,c_10067,c_10057,c_10036,c_10033,c_10032,c_9877,c_9876,c_9875,c_9874,c_9873,c_9872,c_9871,c_9870,c_9869,c_9868,c_9867,c_9866,c_9865,c_9864,c_9863,c_9862,c_9861,c_9860,c_9859,c_9858,c_9857,c_9856,c_9855,c_9854,c_9853,c_9852,c_9820,c_9817,c_9814,c_9813,c_9812,c_9806,c_9751,c_9750,c_9749,c_9748,c_9747,c_9746,c_9745,c_9685,c_9684,c_9683,c_9682,c_9681,c_9680,c_9679,c_9670,c_9669,c_9664,c_9663,c_25212,c_18924,c_18923,c_18922,c_18921,c_18920,c_18400,c_18390,c_9449,c_9448,c_9447,c_9446,c_9445,c_9444,c_9443,c_9442,c_9441,c_9440,c_9439,c_9438,c_9437,c_9436,c_9435,c_9434,c_9433,c_9432,c_9431,c_9430,c_9429,c_9428,c_9427,c_9426,c_9425,c_9424,c_9423,c_9422,c_9421,c_9420,c_9419,c_9418,c_9417,c_9416,c_9415,c_9414,c_9413,c_9412,c_9411,c_9410,c_9409,c_9351,c_9350,c_9349,c_9348,c_9347,c_9346,c_9323,c_9322,c_9321,c_9320,c_9319,c_9318,c_9306,c_9305,c_9232,c_9229,c_9226,c_9225,c_9224,c_9223,c_9222,c_9221,c_9220,c_9219,c_9208,c_9191,c_9174,c_9152,c_9151,c_9150,c_9149,c_9148,c_9118,c_9117,c_9116,c_9115,c_9114,c_9113,c_9091,c_9090,c_9089,c_9088,c_9087,c_9086,c_18383,c_9021,c_9020,c_9019,c_9018,c_9017,c_9016,c_8996,c_8995,c_8994,c_8993,c_8992,c_8991,c_8961,c_8960,c_8959,c_8958,c_8957,c_8956,c_8938,c_8937,c_8915,c_8914,c_8896,c_8880,c_8879,c_8824,c_8823,c_8822,c_8821,c_8820,c_8819,c_8726,c_8725,c_8724,c_8723,c_8722,c_8721,c_8701,c_8694,c_8693,c_8692,c_8691,c_8681,c_8673,c_8658,c_8565,c_8564,c_8563,c_8562,c_8561,c_8560,c_8516,c_8514,c_8512,c_8511,c_8510,c_8509,c_8508,c_8395,c_8394,c_8393,c_8392,c_8391,c_8390,c_8389,c_8388,c_8387,c_8386,c_8375,c_8371,c_8368,c_8357,c_8356,c_8330,c_8329,c_8328,c_8327,c_8326,c_8325,c_8316,c_8302,c_8301,c_8212,c_8211,c_8210,c_8209,c_8208,c_8147,c_8145,c_8144,c_8143,c_8142,c_8141,c_8140,c_8131,c_8123,c_8077,c_8073,c_8069,c_8068,c_8067,c_8066,c_8065,c_8064,c_8063,c_8062,c_8009,c_8008,c_8007,c_8006,c_8005,c_8004,c_7966,c_7965,c_7964,c_7963,c_7962,c_7961,c_7938,c_7937,c_7936,c_7935,c_7934,c_7933,c_7844,c_7843,c_7842,c_7841,c_7840,c_7839,c_7838,c_7837,c_7836,c_7835,c_7712,c_7711,c_7710,c_7709,c_7708,c_7707,c_7706,c_7705,c_7704,c_7703,c_7702,c_7701,c_7685,c_7684,c_7617,c_7603,c_7597,c_7596,c_7595,c_7594,c_7593,c_7592,c_7574,c_7408,c_7407,c_7406,c_7403,c_7402,c_7401,c_7400,c_7399,c_7398,c_7286,c_7285,c_7284,c_7282,c_7281,c_7280,c_7279,c_7278,c_7277,c_7276,c_7237,c_7223,c_7217,c_7216,c_7215,c_7214,c_7213,c_7212,c_7115,c_7114,c_7113,c_7112,c_7111,c_7108,c_7107,c_7106,c_7105,c_7104,c_7058,c_7055,c_7052,c_7051,c_7050,c_7049,c_7048,c_7047,c_7046,c_7045,c_6950,c_6949,c_6948,c_6946,c_6945,c_6943,c_6941,c_6940,c_6939,c_6919,c_24290,c_24296,c_6881,c_6880,c_6879,c_6878,c_6877,c_6876,c_6875,c_23871,c_6837,c_6836,c_6835,c_6834,c_6833,c_6826,c_6825,c_6758,c_6724,c_6703,c_6702,c_6701,c_6700,c_6699,c_6698,c_6697,c_6696,c_6695,c_6694,c_6693,c_6692,c_6691,c_6690,c_6689,c_6688,c_6687,c_6491,c_6490,c_6489,c_6488,c_6487,c_6486,c_6485,c_6484,c_6483,c_6482,c_6481,c_6480,c_6479,c_6478,c_6477,c_6476,c_6475,c_6474,c_6473,c_6472,c_6471,c_6470,c_6440,c_6435,c_6431,c_6427,c_6389,c_6388,c_6387,c_6386,c_6385,c_6384,c_6383,c_6382,c_6381,c_6380,c_6379,c_6342,c_6339,c_6336,c_6335,c_6334,c_6333,c_6332,c_6331,c_6330,c_6284,c_6283,c_6258,c_6257,c_6247,c_6200,c_6199,c_6198,c_6197,c_6196,c_6195,c_6194,c_6179,c_6158,c_6157,c_6135,c_6134,c_6133,c_6132,c_6107,c_6106,c_6105,c_6104,c_6094,c_6076,c_6075,c_6045,c_6044,c_6039,c_6038,c_6037,c_6036,c_6035,c_6034,c_6013,c_6002,c_5997,c_5996,c_5995,c_5994,c_5993,c_5992,c_5949,c_5948,c_5947,c_5946,c_5945,c_5944,c_5943,c_5910,c_5909,c_5908,c_5907,c_5906,c_5891,c_5890,c_5885,c_5880,c_5873,c_5857,c_5841,c_5840,c_5839,c_5838,c_5823,c_5822,c_5820,c_20553,c_5808,c_5807,c_5806,c_5805,c_5794,c_5793,c_5776,c_5775,c_5767,c_5765,c_5747,c_5746,c_5733,c_5724,c_5716,c_5714,c_5713,c_5711,c_5710,c_5707,c_5706,c_5703,c_5702,c_5701,c_8369,c_5669,c_5664,c_5663,c_5661,c_5660,c_5659,c_5644,c_5633,c_5622,c_5621,c_5610,c_5609,c_5608,c_5607,c_5594,c_5593,c_151,c_121,c_24291,c_98,c_97,c_96,c_95,c_94,c_93,c_90,c_89,c_88,c_87,c_86,c_85,c_84,c_82,c_83,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_62,c_63,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
% 0.00/0.02 % Problem : SEU081+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.35 % Computer : n016.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Thu Sep 24 12:47:42 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.40 Running first-order theorem proving
% 0.13/0.40 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
% 0.13/0.41
% 0.13/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.41
% 0.13/0.42 % Detected problem language: tptp
% 0.13/0.43 % Proving...
% 34.69/5.80 % SZS status Started for theBenchmark.p
% 34.69/5.80 % SZS status Theorem for theBenchmark.p
% 34.69/5.80
% 34.69/5.80 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 34.69/5.80
% 34.69/5.80 % ------ iProver source info
% 34.69/5.80
% 34.69/5.80 % git: date: 2026-07-19 20:42:38 +0200
% 34.69/5.80 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 34.69/5.80 % git: non_committed_changes: false
% 34.69/5.80
% 34.69/5.80 % ------ Parsing...
% 34.69/5.80 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 34.69/5.80
% 34.69/5.80 % ------ 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 %
% 34.69/5.80
% 34.69/5.80 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 34.69/5.80
% 34.69/5.80 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 34.69/5.80 % ------ Proving...
% 34.69/5.80 % ------ Problem Properties
% 34.69/5.80
% 34.69/5.80 %
% 34.69/5.80 % clauses 48
% 34.69/5.80 % conjectures 2
% 34.69/5.80 % EPR 21
% 34.69/5.80 % Horn 42
% 34.69/5.80 % unary 22
% 34.69/5.80 % binary 11
% 34.69/5.80 % lits 106
% 34.69/5.80 % lits eq 15
% 34.69/5.80 % fd_pure 0
% 34.69/5.80 % fd_pseudo 0
% 34.69/5.80 % fd_cond 1
% 34.69/5.80 % fd_pseudo_cond 5
% 34.69/5.80 % AC symbols 0
% 34.69/5.80
% 34.69/5.80 % ------ Schedule dynamic 5 is on
% 34.69/5.80
% 34.69/5.80 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 34.69/5.80
% 34.69/5.80
% 34.69/5.80 % ------
% 34.69/5.80 % Current options:
% 34.69/5.80 % ------
% 34.69/5.80
% 34.69/5.80
% 34.69/5.80 %
% 34.69/5.80
% 34.69/5.80 % ------ Proving...
% 34.69/5.80 %
% 34.69/5.80
% 34.69/5.80 % SZS status Theorem for theBenchmark.p
% 34.69/5.80
% 34.69/5.80 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 34.73/5.96
% 34.73/5.96
%------------------------------------------------------------------------------