%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU071+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 : n012.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 02:55:17 PM UTC 2026
% Result : Theorem 7.17s 7.76s
% Output : CNFRefutation 13.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 44
% Number of leaves : 34
% Syntax : Number of formulae : 3948 ( 222 unt; 0 def)
% Number of atoms : 12480 (4307 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 14550 (6018 ~;8372 |; 122 &)
% ( 18 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 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 : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 25 ( 25 usr; 10 con; 0-3 aty)
% Number of variables : 7367 ( 1 sgn7334 !; 33 ?;7049 :)
% 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(f4,axiom,
! [X0] :
( ( function(X0)
& empty(X0)
& relation(X0) )
=> ( one_to_one(X0)
& function(X0)
& relation(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_funct_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] :
( ( function(X0)
& relation(X0) )
=> ! [X1,X2] :
( X2 = relation_inverse_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d13_funct_1) ).
fof(f7,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f8,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( one_to_one(X0)
<=> ! [X1,X2] :
( ( apply(X0,X1) = apply(X0,X2)
& in(X2,relation_dom(X0))
& in(X1,relation_dom(X0)) )
=> X1 = X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_funct_1) ).
fof(f9,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f11,axiom,
! [X0] : ~ empty(powerset(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(f12,axiom,
empty(empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(f13,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_relat_1) ).
fof(f14,axiom,
! [X0] :
( ( relation(X0)
& ~ empty(X0) )
=> ~ empty(relation_dom(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_relat_1) ).
fof(f15,axiom,
! [X0] :
( empty(X0)
=> ( relation(relation_dom(X0))
& empty(relation_dom(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc7_relat_1) ).
fof(f16,axiom,
? [X0] :
( function(X0)
& relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_funct_1) ).
fof(f17,axiom,
? [X0] :
( relation(X0)
& empty(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_relat_1) ).
fof(f18,axiom,
! [X0] :
( ~ empty(X0)
=> ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_subset_1) ).
fof(f19,axiom,
? [X0] : empty(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(f20,axiom,
? [X0] :
( function(X0)
& empty(X0)
& relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_funct_1) ).
fof(f21,axiom,
? [X0] :
( relation(X0)
& ~ empty(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_relat_1) ).
fof(f22,axiom,
! [X0] :
? [X1] :
( empty(X1)
& element(X1,powerset(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).
fof(f23,axiom,
? [X0] : ~ empty(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f24,axiom,
? [X0] :
( one_to_one(X0)
& function(X0)
& relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_funct_1) ).
fof(f26,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f27,conjecture,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ( one_to_one(X1)
=> subset(relation_inverse_image(X1,relation_image(X1,X0)),X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t152_funct_1) ).
fof(f28,negated_conjecture,
~ ! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ( one_to_one(X1)
=> subset(relation_inverse_image(X1,relation_image(X1,X0)),X0) ) ),
inference(negated_conjecture,[status(cth)],[f27]) ).
fof(f29,axiom,
! [X0,X1] :
( in(X0,X1)
=> element(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
fof(f30,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(f31,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
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] : subset(X0,X0),
inference(rectify,[],[f26]) ).
fof(f38,plain,
? [X0,X1] :
( function(X1)
& relation(X1)
& one_to_one(X1)
& ~ subset(relation_inverse_image(X1,relation_image(X1,X0)),X0) ),
inference(ennf_transformation,[],[f28]) ).
fof(f39,plain,
? [X0,X1] :
( function(X1)
& relation(X1)
& one_to_one(X1)
& ~ subset(relation_inverse_image(X1,relation_image(X1,X0)),X0) ),
inference(flattening,[],[f38]) ).
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] :
( ~ empty(X0)
| function(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f43,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( X2 = relation_inverse_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) ) ) ) ),
inference(ennf_transformation,[],[f6]) ).
fof(f44,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( X2 = relation_inverse_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) ) ) ) ),
inference(flattening,[],[f43]) ).
fof(f45,plain,
! [X0] :
( ~ empty(X0)
| relation(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f46,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ( one_to_one(X0)
<=> ! [X1,X2] :
( apply(X0,X1) != apply(X0,X2)
| ~ in(X2,relation_dom(X0))
| ~ in(X1,relation_dom(X0))
| X1 = X2 ) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f47,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ( one_to_one(X0)
<=> ! [X1,X2] :
( apply(X0,X1) != apply(X0,X2)
| ~ in(X2,relation_dom(X0))
| ~ in(X1,relation_dom(X0))
| X1 = X2 ) ) ),
inference(flattening,[],[f46]) ).
fof(f48,plain,
! [X0] :
( ~ function(X0)
| ~ empty(X0)
| ~ relation(X0)
| ( one_to_one(X0)
& function(X0)
& relation(X0) ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f49,plain,
! [X0] :
( ~ function(X0)
| ~ empty(X0)
| ~ relation(X0)
| ( one_to_one(X0)
& function(X0)
& relation(X0) ) ),
inference(flattening,[],[f48]) ).
fof(f50,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f51,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(ennf_transformation,[],[f36]) ).
fof(f52,plain,
! [X0] :
( ~ empty(X0)
| X0 = empty_set ),
inference(ennf_transformation,[],[f34]) ).
fof(f53,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f35]) ).
fof(f54,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(ennf_transformation,[],[f30]) ).
fof(f55,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(flattening,[],[f54]) ).
fof(f56,plain,
! [X0,X1] :
( ~ in(X0,X1)
| element(X0,X1) ),
inference(ennf_transformation,[],[f29]) ).
fof(f57,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ in(X1,X0) ),
inference(ennf_transformation,[],[f1]) ).
fof(f58,plain,
! [X0] :
( ~ empty(X0)
| ( relation(relation_dom(X0))
& empty(relation_dom(X0)) ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f59,plain,
! [X0] :
( ~ relation(X0)
| empty(X0)
| ~ empty(relation_dom(X0)) ),
inference(ennf_transformation,[],[f14]) ).
fof(f60,plain,
! [X0] :
( ~ relation(X0)
| empty(X0)
| ~ empty(relation_dom(X0)) ),
inference(flattening,[],[f59]) ).
fof(f61,plain,
! [X0,X1,X2] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f33]) ).
fof(f62,plain,
! [X0,X1,X2] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(ennf_transformation,[],[f32]) ).
fof(f63,plain,
! [X0,X1,X2] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(flattening,[],[f62]) ).
fof(f64,plain,
! [X0] :
( empty(X0)
| ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) ) ),
inference(ennf_transformation,[],[f18]) ).
fof(f65,plain,
( function(sK1)
& relation(sK1)
& one_to_one(sK1)
& ~ subset(relation_inverse_image(sK1,relation_image(sK1,sK0)),sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f39]) ).
fof(f66,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(f67,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,[],[f66]) ).
fof(f68,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))],[f67]) ).
fof(f69,plain,
( function(sK5)
& empty(sK5)
& relation(sK5) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X0,sK5)],[f20]) ).
fof(f70,plain,
( function(sK6)
& relation(sK6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X0,sK6)],[f16]) ).
fof(f71,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( ( relation_inverse_image(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) ) )
& ( ~ in(apply(X0,X3),X1)
| ~ in(X3,relation_dom(X0))
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) ) )
& ( ~ in(X3,X2)
| ~ in(apply(X0,X3),X1)
| ~ in(X3,relation_dom(X0)) ) )
| X2 = relation_inverse_image(X0,X1) ) ) ),
inference(nnf_transformation,[],[f44]) ).
fof(f72,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( ( relation_inverse_image(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) ) )
& ( ~ in(apply(X0,X3),X1)
| ~ in(X3,relation_dom(X0))
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) ) )
& ( ~ in(X3,X2)
| ~ in(apply(X0,X3),X1)
| ~ in(X3,relation_dom(X0)) ) )
| X2 = relation_inverse_image(X0,X1) ) ) ),
inference(flattening,[],[f71]) ).
fof(f73,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( ( relation_inverse_image(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| ( in(apply(X0,X4),X1)
& in(X4,relation_dom(X0)) ) )
& ( ~ in(apply(X0,X4),X1)
| ~ in(X4,relation_dom(X0))
| in(X4,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) ) )
& ( ~ in(X3,X2)
| ~ in(apply(X0,X3),X1)
| ~ in(X3,relation_dom(X0)) ) )
| X2 = relation_inverse_image(X0,X1) ) ) ),
inference(rectify,[],[f72]) ).
fof(f74,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( ( relation_inverse_image(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| ( in(apply(X0,X4),X1)
& in(X4,relation_dom(X0)) ) )
& ( ~ in(apply(X0,X4),X1)
| ~ in(X4,relation_dom(X0))
| in(X4,X2) ) ) )
& ( ( ( in(sK7(X0,X1,X2),X2)
| ( in(apply(X0,sK7(X0,X1,X2)),X1)
& in(sK7(X0,X1,X2),relation_dom(X0)) ) )
& ( ~ in(sK7(X0,X1,X2),X2)
| ~ in(apply(X0,sK7(X0,X1,X2)),X1)
| ~ in(sK7(X0,X1,X2),relation_dom(X0)) ) )
| X2 = relation_inverse_image(X0,X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X3,sK7(X0,X1,X2))],[f73]) ).
fof(f75,plain,
( relation(sK8)
& ~ empty(sK8) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(X0,sK8)],[f21]) ).
fof(f76,plain,
( relation(sK9)
& empty(sK9) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(X0,sK9)],[f17]) ).
fof(f77,plain,
( one_to_one(sK10)
& function(sK10)
& relation(sK10) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(X0,sK10)],[f24]) ).
fof(f78,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ( ( ~ one_to_one(X0)
| ! [X1,X2] :
( apply(X0,X1) != apply(X0,X2)
| ~ in(X2,relation_dom(X0))
| ~ in(X1,relation_dom(X0))
| X1 = X2 ) )
& ( ? [X1,X2] :
( apply(X0,X1) = apply(X0,X2)
& in(X2,relation_dom(X0))
& in(X1,relation_dom(X0))
& X1 != X2 )
| one_to_one(X0) ) ) ),
inference(nnf_transformation,[],[f47]) ).
fof(f79,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ( ( ~ one_to_one(X0)
| ! [X3,X4] :
( apply(X0,X4) != apply(X0,X3)
| ~ in(X4,relation_dom(X0))
| ~ in(X3,relation_dom(X0))
| X3 = X4 ) )
& ( ? [X1,X2] :
( apply(X0,X1) = apply(X0,X2)
& in(X2,relation_dom(X0))
& in(X1,relation_dom(X0))
& X1 != X2 )
| one_to_one(X0) ) ) ),
inference(rectify,[],[f78]) ).
fof(f80,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ( ( ~ one_to_one(X0)
| ! [X3,X4] :
( apply(X0,X4) != apply(X0,X3)
| ~ in(X4,relation_dom(X0))
| ~ in(X3,relation_dom(X0))
| X3 = X4 ) )
& ( ( apply(X0,sK11(X0)) = apply(X0,sK12(X0))
& in(sK12(X0),relation_dom(X0))
& in(sK11(X0),relation_dom(X0))
& sK11(X0) != sK12(X0) )
| one_to_one(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11,sK12]),skolemize(X1,sK11(X0)),skolemize(X2,sK12(X0))],[f79]) ).
fof(f81,plain,
! [X0,X1] :
( ( ~ element(X0,powerset(X1))
| subset(X0,X1) )
& ( ~ subset(X0,X1)
| element(X0,powerset(X1)) ) ),
inference(nnf_transformation,[],[f31]) ).
fof(f82,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) )
& ( ? [X2] :
( in(X2,X0)
& ~ in(X2,X1) )
| subset(X0,X1) ) ),
inference(nnf_transformation,[],[f50]) ).
fof(f83,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ in(X3,X0)
| in(X3,X1) ) )
& ( ? [X2] :
( in(X2,X0)
& ~ in(X2,X1) )
| subset(X0,X1) ) ),
inference(rectify,[],[f82]) ).
fof(f84,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ in(X3,X0)
| in(X3,X1) ) )
& ( ( in(sK13(X0,X1),X0)
& ~ in(sK13(X0,X1),X1) )
| subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(X2,sK13(X0,X1))],[f83]) ).
fof(f85,plain,
~ empty(sK14),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(X0,sK14)],[f23]) ).
fof(f86,plain,
empty(sK15),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(X0,sK15)],[f19]) ).
fof(f87,plain,
! [X0] :
( empty(sK16(X0))
& element(sK16(X0),powerset(X0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(X1,sK16(X0))],[f22]) ).
fof(f88,plain,
! [X0] :
( empty(X0)
| ( ~ empty(sK17(X0))
& element(sK17(X0),powerset(X0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(X1,sK17(X0))],[f64]) ).
fof(f89,plain,
! [X0] : element(sK18(X0),X0),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(X1,sK18(X0))],[f9]) ).
fof(f90,plain,
function(sK1),
inference(cnf_transformation,[],[f65]) ).
fof(f91,plain,
relation(sK1),
inference(cnf_transformation,[],[f65]) ).
fof(f92,plain,
one_to_one(sK1),
inference(cnf_transformation,[],[f65]) ).
fof(f93,plain,
~ subset(relation_inverse_image(sK1,relation_image(sK1,sK0)),sK0),
inference(cnf_transformation,[],[f65]) ).
fof(f94,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,[],[f68]) ).
fof(f95,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,[],[f68]) ).
fof(f96,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,[],[f68]) ).
fof(f97,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,[],[f68]) ).
fof(f98,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,[],[f68]) ).
fof(f99,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,[],[f68]) ).
fof(f100,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,[],[f68]) ).
fof(f101,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,[],[f68]) ).
fof(f102,plain,
function(sK5),
inference(cnf_transformation,[],[f69]) ).
fof(f103,plain,
empty(sK5),
inference(cnf_transformation,[],[f69]) ).
fof(f104,plain,
relation(sK5),
inference(cnf_transformation,[],[f69]) ).
fof(f105,plain,
function(sK6),
inference(cnf_transformation,[],[f70]) ).
fof(f106,plain,
relation(sK6),
inference(cnf_transformation,[],[f70]) ).
fof(f107,plain,
! [X0] :
( ~ empty(X0)
| function(X0) ),
inference(cnf_transformation,[],[f42]) ).
fof(f108,plain,
! [X2,X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| relation_inverse_image(X0,X1) != X2
| ~ in(X4,X2)
| in(apply(X0,X4),X1) ),
inference(cnf_transformation,[],[f74]) ).
fof(f109,plain,
! [X2,X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| relation_inverse_image(X0,X1) != X2
| ~ in(X4,X2)
| in(X4,relation_dom(X0)) ),
inference(cnf_transformation,[],[f74]) ).
fof(f110,plain,
! [X2,X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| relation_inverse_image(X0,X1) != X2
| ~ in(apply(X0,X4),X1)
| ~ in(X4,relation_dom(X0))
| in(X4,X2) ),
inference(cnf_transformation,[],[f74]) ).
fof(f111,plain,
! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| in(sK7(X0,X1,X2),X2)
| in(apply(X0,sK7(X0,X1,X2)),X1)
| relation_inverse_image(X0,X1) = X2 ),
inference(cnf_transformation,[],[f74]) ).
fof(f112,plain,
! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| in(sK7(X0,X1,X2),X2)
| in(sK7(X0,X1,X2),relation_dom(X0))
| relation_inverse_image(X0,X1) = X2 ),
inference(cnf_transformation,[],[f74]) ).
fof(f113,plain,
! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(sK7(X0,X1,X2),X2)
| ~ in(apply(X0,sK7(X0,X1,X2)),X1)
| ~ in(sK7(X0,X1,X2),relation_dom(X0))
| relation_inverse_image(X0,X1) = X2 ),
inference(cnf_transformation,[],[f74]) ).
fof(f114,plain,
relation(sK8),
inference(cnf_transformation,[],[f75]) ).
fof(f115,plain,
~ empty(sK8),
inference(cnf_transformation,[],[f75]) ).
fof(f116,plain,
relation(sK9),
inference(cnf_transformation,[],[f76]) ).
fof(f117,plain,
empty(sK9),
inference(cnf_transformation,[],[f76]) ).
fof(f118,plain,
! [X0] :
( ~ empty(X0)
| relation(X0) ),
inference(cnf_transformation,[],[f45]) ).
fof(f119,plain,
one_to_one(sK10),
inference(cnf_transformation,[],[f77]) ).
fof(f120,plain,
function(sK10),
inference(cnf_transformation,[],[f77]) ).
fof(f121,plain,
relation(sK10),
inference(cnf_transformation,[],[f77]) ).
fof(f122,plain,
! [X3,X0,X4] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| apply(X0,X4) != apply(X0,X3)
| ~ in(X4,relation_dom(X0))
| ~ in(X3,relation_dom(X0))
| X3 = X4 ),
inference(cnf_transformation,[],[f80]) ).
fof(f123,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| apply(X0,sK11(X0)) = apply(X0,sK12(X0))
| one_to_one(X0) ),
inference(cnf_transformation,[],[f80]) ).
fof(f124,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| in(sK12(X0),relation_dom(X0))
| one_to_one(X0) ),
inference(cnf_transformation,[],[f80]) ).
fof(f125,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| in(sK11(X0),relation_dom(X0))
| one_to_one(X0) ),
inference(cnf_transformation,[],[f80]) ).
fof(f126,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| sK11(X0) != sK12(X0)
| one_to_one(X0) ),
inference(cnf_transformation,[],[f80]) ).
fof(f127,plain,
! [X0] :
( ~ function(X0)
| ~ empty(X0)
| ~ relation(X0)
| one_to_one(X0) ),
inference(cnf_transformation,[],[f49]) ).
fof(f130,plain,
! [X0,X1] :
( ~ element(X0,powerset(X1))
| subset(X0,X1) ),
inference(cnf_transformation,[],[f81]) ).
fof(f131,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f81]) ).
fof(f132,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f37]) ).
fof(f133,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f84]) ).
fof(f134,plain,
! [X0,X1] :
( in(sK13(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f84]) ).
fof(f135,plain,
! [X0,X1] :
( ~ in(sK13(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f84]) ).
fof(f136,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(cnf_transformation,[],[f51]) ).
fof(f137,plain,
! [X0] :
( ~ empty(X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f52]) ).
fof(f138,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f53]) ).
fof(f139,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(cnf_transformation,[],[f55]) ).
fof(f140,plain,
! [X0,X1] :
( ~ in(X0,X1)
| element(X0,X1) ),
inference(cnf_transformation,[],[f56]) ).
fof(f141,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ in(X1,X0) ),
inference(cnf_transformation,[],[f57]) ).
fof(f142,plain,
! [X0] :
( ~ empty(X0)
| relation(relation_dom(X0)) ),
inference(cnf_transformation,[],[f58]) ).
fof(f143,plain,
! [X0] :
( ~ empty(X0)
| empty(relation_dom(X0)) ),
inference(cnf_transformation,[],[f58]) ).
fof(f144,plain,
! [X0] :
( ~ relation(X0)
| empty(X0)
| ~ empty(relation_dom(X0)) ),
inference(cnf_transformation,[],[f60]) ).
fof(f145,plain,
~ empty(sK14),
inference(cnf_transformation,[],[f85]) ).
fof(f146,plain,
empty(sK15),
inference(cnf_transformation,[],[f86]) ).
fof(f147,plain,
! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f61]) ).
fof(f148,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(cnf_transformation,[],[f63]) ).
fof(f149,plain,
! [X0] : empty(sK16(X0)),
inference(cnf_transformation,[],[f87]) ).
fof(f150,plain,
! [X0] : element(sK16(X0),powerset(X0)),
inference(cnf_transformation,[],[f87]) ).
fof(f151,plain,
! [X0] :
( empty(X0)
| ~ empty(sK17(X0)) ),
inference(cnf_transformation,[],[f88]) ).
fof(f152,plain,
! [X0] :
( empty(X0)
| element(sK17(X0),powerset(X0)) ),
inference(cnf_transformation,[],[f88]) ).
fof(f153,plain,
! [X0] : ~ empty(powerset(X0)),
inference(cnf_transformation,[],[f11]) ).
fof(f154,plain,
! [X0] : element(sK18(X0),X0),
inference(cnf_transformation,[],[f89]) ).
fof(f155,plain,
relation(empty_set),
inference(cnf_transformation,[],[f13]) ).
fof(f157,plain,
empty(empty_set),
inference(cnf_transformation,[],[f12]) ).
fof(f158,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,[],[f97]) ).
fof(f159,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,[],[f158]) ).
fof(f160,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,[],[f96]) ).
fof(f161,plain,
! [X0,X1,X6] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X6,relation_image(X0,X1))
| in(sK4(X0,X1,X6),X1) ),
inference(equality_resolution,[],[f95]) ).
fof(f162,plain,
! [X0,X1,X6] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X6,relation_image(X0,X1))
| apply(X0,sK4(X0,X1,X6)) = X6 ),
inference(equality_resolution,[],[f94]) ).
fof(f163,plain,
! [X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(apply(X0,X4),X1)
| ~ in(X4,relation_dom(X0))
| in(X4,relation_inverse_image(X0,X1)) ),
inference(equality_resolution,[],[f110]) ).
fof(f164,plain,
! [X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X4,relation_inverse_image(X0,X1))
| in(X4,relation_dom(X0)) ),
inference(equality_resolution,[],[f109]) ).
fof(f165,plain,
! [X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X4,relation_inverse_image(X0,X1))
| in(apply(X0,X4),X1) ),
inference(equality_resolution,[],[f108]) ).
tcf(c_49,negated_conjecture,
~ subset(relation_inverse_image(sK1,relation_image(sK1,sK0)),sK0),
inference(cnf_transformation,[],[f93]) ).
tcf(c_50,negated_conjecture,
one_to_one(sK1),
inference(cnf_transformation,[],[f92]) ).
tcf(c_51,negated_conjecture,
relation(sK1),
inference(cnf_transformation,[],[f91]) ).
tcf(c_52,negated_conjecture,
function(sK1),
inference(cnf_transformation,[],[f90]) ).
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,[],[f101]) ).
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,[],[f100]) ).
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,[],[f99]) ).
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,[],[f98]) ).
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,[],[f159]) ).
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,[],[f160]) ).
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,[],[f161]) ).
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,[],[f162]) ).
tcf(c_61,plain,
relation(sK5),
inference(cnf_transformation,[],[f104]) ).
tcf(c_62,plain,
empty(sK5),
inference(cnf_transformation,[],[f103]) ).
tcf(c_63,plain,
function(sK5),
inference(cnf_transformation,[],[f102]) ).
tcf(c_64,plain,
relation(sK6),
inference(cnf_transformation,[],[f106]) ).
tcf(c_65,plain,
function(sK6),
inference(cnf_transformation,[],[f105]) ).
tcf(c_66,plain,
! [X0: $i] :
( function(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f107]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_inverse_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK7(X0,X1,X2),X2)
| ~ in(sK7(X0,X1,X2),relation_dom(X0))
| ~ in(apply(X0,sK7(X0,X1,X2)),X1) ),
inference(cnf_transformation,[],[f113]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X1,X2),X2)
| in(sK7(X0,X1,X2),relation_dom(X0))
| ( relation_inverse_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f112]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X1,X2),X2)
| in(apply(X0,sK7(X0,X1,X2)),X1)
| ( relation_inverse_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f111]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,relation_inverse_image(X0,X2))
| ~ function(X0)
| ~ relation(X0)
| ~ in(X1,relation_dom(X0))
| ~ in(apply(X0,X1),X2) ),
inference(cnf_transformation,[],[f163]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_inverse_image(X1,X2)) ),
inference(cnf_transformation,[],[f164]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X1,X0),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_inverse_image(X1,X2)) ),
inference(cnf_transformation,[],[f165]) ).
tcf(c_73,plain,
~ empty(sK8),
inference(cnf_transformation,[],[f115]) ).
tcf(c_74,plain,
relation(sK8),
inference(cnf_transformation,[],[f114]) ).
tcf(c_75,plain,
empty(sK9),
inference(cnf_transformation,[],[f117]) ).
tcf(c_76,plain,
relation(sK9),
inference(cnf_transformation,[],[f116]) ).
tcf(c_77,plain,
! [X0: $i] :
( relation(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f118]) ).
tcf(c_78,plain,
relation(sK10),
inference(cnf_transformation,[],[f121]) ).
tcf(c_79,plain,
function(sK10),
inference(cnf_transformation,[],[f120]) ).
tcf(c_80,plain,
one_to_one(sK10),
inference(cnf_transformation,[],[f119]) ).
tcf(c_81,plain,
! [X0: $i] :
( one_to_one(X0)
| ~ function(X0)
| ~ relation(X0)
| ( sK11(X0) != sK12(X0) ) ),
inference(cnf_transformation,[],[f126]) ).
tcf(c_82,plain,
! [X0: $i] :
( one_to_one(X0)
| in(sK11(X0),relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f125]) ).
tcf(c_83,plain,
! [X0: $i] :
( one_to_one(X0)
| in(sK12(X0),relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f124]) ).
tcf(c_84,plain,
! [X0: $i] :
( one_to_one(X0)
| ( apply(X0,sK11(X0)) = apply(X0,sK12(X0)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f123]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| ~ in(X2,relation_dom(X0))
| ~ in(X1,relation_dom(X0))
| ( apply(X0,X1) != apply(X0,X2) ) ),
inference(cnf_transformation,[],[f122]) ).
tcf(c_86,plain,
! [X0: $i] :
( one_to_one(X0)
| ~ empty(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f127]) ).
tcf(c_87,plain,
! [X0: $i,X1: $i] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f131]) ).
tcf(c_88,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f130]) ).
tcf(c_89,plain,
! [X0: $i] : subset(X0,X0),
inference(cnf_transformation,[],[f132]) ).
tcf(c_90,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ in(sK13(X0,X1),X1) ),
inference(cnf_transformation,[],[f135]) ).
tcf(c_91,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| in(sK13(X0,X1),X0) ),
inference(cnf_transformation,[],[f134]) ).
tcf(c_92,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,X1)
| ~ in(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f133]) ).
tcf(c_93,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f136]) ).
tcf(c_94,plain,
! [X0: $i] :
( ( X0 = empty_set )
| ~ empty(X0) ),
inference(cnf_transformation,[],[f137]) ).
tcf(c_95,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f138]) ).
tcf(c_96,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f139]) ).
tcf(c_97,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f140]) ).
tcf(c_98,plain,
! [X0: $i,X1: $i] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f141]) ).
tcf(c_99,plain,
! [X0: $i] :
( empty(relation_dom(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f143]) ).
tcf(c_100,plain,
! [X0: $i] :
( relation(relation_dom(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f142]) ).
tcf(c_101,plain,
! [X0: $i] :
( empty(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(cnf_transformation,[],[f144]) ).
tcf(c_102,plain,
~ empty(sK14),
inference(cnf_transformation,[],[f145]) ).
tcf(c_103,plain,
empty(sK15),
inference(cnf_transformation,[],[f146]) ).
tcf(c_104,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(X1)
| ~ in(X2,X0)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f147]) ).
tcf(c_105,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X2,X1)
| ~ in(X2,X0)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f148]) ).
tcf(c_106,plain,
! [X0: $i] : element(sK16(X0),powerset(X0)),
inference(cnf_transformation,[],[f150]) ).
tcf(c_107,plain,
! [X0: $i] : empty(sK16(X0)),
inference(cnf_transformation,[],[f149]) ).
tcf(c_108,plain,
! [X0: $i] :
( empty(X0)
| element(sK17(X0),powerset(X0)) ),
inference(cnf_transformation,[],[f152]) ).
tcf(c_109,plain,
! [X0: $i] :
( empty(X0)
| ~ empty(sK17(X0)) ),
inference(cnf_transformation,[],[f151]) ).
tcf(c_110,plain,
! [X0: $i] : ~ empty(powerset(X0)),
inference(cnf_transformation,[],[f153]) ).
tcf(c_111,plain,
! [X0: $i] : element(sK18(X0),X0),
inference(cnf_transformation,[],[f154]) ).
tcf(c_113,plain,
relation(empty_set),
inference(cnf_transformation,[],[f155]) ).
tcf(c_114,plain,
empty(empty_set),
inference(cnf_transformation,[],[f157]) ).
tcf(c_145,plain,
! [X0: $i] :
( one_to_one(X0)
| ~ empty(X0) ),
inference(global_subsumption_just,[status(thm)],[c_86,c_77,c_66,c_86]) ).
tcf(c_149,plain,
! [X0: $i,X1: $i] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_87]) ).
tcf(c_299,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(X1)
| ~ in(X2,X0)
| ~ subset(X0,X1) ),
inference(bin_hyper_res,[status(thm)],[c_104,c_149]) ).
tcf(c_300,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X2,X1)
| ~ in(X2,X0)
| ~ subset(X0,X1) ),
inference(bin_hyper_res,[status(thm)],[c_105,c_149]) ).
tcf(c_5773,plain,
! [X0: $i] :
( one_to_one(X0)
| ~ empty(X0) ),
inference(prop_impl_just,[status(thm)],[c_145]) ).
tcf(c_11187,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| ~ empty(X1)
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_12346,plain,
! [X0: $i] : subset(sK18(powerset(X0)),X0),
inference(superposition,[status(thm)],[c_111,c_88]) ).
tcf(c_12352,plain,
function(sK9),
inference(superposition,[status(thm)],[c_75,c_66]) ).
tcf(c_12353,plain,
function(sK15),
inference(superposition,[status(thm)],[c_103,c_66]) ).
tcf(c_12354,plain,
! [X0: $i] : function(sK16(X0)),
inference(superposition,[status(thm)],[c_107,c_66]) ).
tcf(c_12355,plain,
function(empty_set),
inference(superposition,[status(thm)],[c_114,c_66]) ).
tcf(c_12363,plain,
relation(sK15),
inference(superposition,[status(thm)],[c_103,c_77]) ).
tcf(c_12364,plain,
! [X0: $i] : relation(sK16(X0)),
inference(superposition,[status(thm)],[c_107,c_77]) ).
tcf(c_12367,plain,
! [X0: $i] : subset(sK16(X0),X0),
inference(superposition,[status(thm)],[c_106,c_88]) ).
tcf(c_12373,plain,
one_to_one(sK5),
inference(superposition,[status(thm)],[c_62,c_5773]) ).
tcf(c_12374,plain,
one_to_one(sK9),
inference(superposition,[status(thm)],[c_75,c_5773]) ).
tcf(c_12375,plain,
one_to_one(sK15),
inference(superposition,[status(thm)],[c_103,c_5773]) ).
tcf(c_12376,plain,
! [X0: $i] : one_to_one(sK16(X0)),
inference(superposition,[status(thm)],[c_107,c_5773]) ).
tcf(c_12377,plain,
one_to_one(empty_set),
inference(superposition,[status(thm)],[c_114,c_5773]) ).
tcf(c_12383,plain,
! [X0: $i] :
( one_to_one(relation_dom(X0))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_99,c_5773]) ).
tcf(c_12385,plain,
! [X0: $i] :
( function(relation_dom(X0))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_99,c_66]) ).
tcf(c_12404,plain,
sK5 = empty_set,
inference(superposition,[status(thm)],[c_62,c_94]) ).
tcf(c_12405,plain,
sK9 = empty_set,
inference(superposition,[status(thm)],[c_75,c_94]) ).
tcf(c_12406,plain,
! [X0: $i] :
( ( relation_dom(X0) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_99,c_94]) ).
tcf(c_12407,plain,
empty_set = sK15,
inference(superposition,[status(thm)],[c_103,c_94]) ).
tcf(c_12408,plain,
! [X0: $i] : sK16(X0) = empty_set,
inference(superposition,[status(thm)],[c_107,c_94]) ).
tcf(c_12424,plain,
! [X0: $i] : subset(empty_set,X0),
inference(demodulation,[status(thm)],[c_12367,c_12408]) ).
tcf(c_12428,plain,
! [X0: $i] : element(empty_set,powerset(X0)),
inference(demodulation,[status(thm)],[c_106,c_12408]) ).
tcf(c_12455,plain,
! [X0: $i] :
( empty(X0)
| subset(sK17(X0),X0) ),
inference(superposition,[status(thm)],[c_108,c_88]) ).
tcf(c_12475,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| element(sK13(X0,X1),X0) ),
inference(superposition,[status(thm)],[c_91,c_97]) ).
tcf(c_12476,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_91,c_95]) ).
tcf(c_12485,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ in(X0,sK13(X0,X1)) ),
inference(superposition,[status(thm)],[c_91,c_98]) ).
tcf(c_12499,plain,
! [X0: $i,X1: $i] :
( empty(powerset(X1))
| in(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_87,c_96]) ).
tcf(c_12500,plain,
! [X0: $i] :
( empty(X0)
| empty(powerset(X0))
| in(sK17(X0),powerset(X0)) ),
inference(superposition,[status(thm)],[c_108,c_96]) ).
tcf(c_12501,plain,
! [X0: $i] :
( empty(X0)
| in(sK18(X0),X0) ),
inference(superposition,[status(thm)],[c_111,c_96]) ).
tcf(c_12502,plain,
! [X0: $i] :
( empty(powerset(X0))
| in(empty_set,powerset(X0)) ),
inference(superposition,[status(thm)],[c_12428,c_96]) ).
tcf(c_12505,plain,
! [X0: $i] : in(empty_set,powerset(X0)),
inference(forward_subsumption_resolution,[status(thm)],[c_12502,c_110]) ).
tcf(c_12506,plain,
! [X0: $i] :
( empty(X0)
| in(sK17(X0),powerset(X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12500,c_110]) ).
tcf(c_12509,plain,
! [X0: $i,X1: $i] :
( in(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12499,c_110]) ).
tcf(c_12513,plain,
! [X0: $i] : ~ in(powerset(X0),empty_set),
inference(superposition,[status(thm)],[c_12505,c_98]) ).
tcf(c_12521,plain,
~ empty(relation_inverse_image(sK1,relation_image(sK1,sK0))),
inference(superposition,[status(thm)],[c_12476,c_49]) ).
tcf(c_12526,plain,
! [X0: $i] :
( empty(X0)
| ~ in(X0,sK18(X0)) ),
inference(superposition,[status(thm)],[c_12501,c_98]) ).
tcf(c_12536,plain,
! [X0: $i] :
( empty(X0)
| ~ in(powerset(X0),sK17(X0)) ),
inference(superposition,[status(thm)],[c_12506,c_98]) ).
tcf(c_12550,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(X0)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_99,c_12406]) ).
tcf(c_12551,plain,
relation_dom(empty_set) = empty_set,
inference(superposition,[status(thm)],[c_114,c_12406]) ).
tcf(c_12563,plain,
! [X0: $i,X1: $i] :
( subset(powerset(X0),X1)
| subset(sK13(powerset(X0),X1),X0) ),
inference(superposition,[status(thm)],[c_12475,c_88]) ).
tcf(c_12572,plain,
! [X0: $i,X1: $i] :
( subset(X0,powerset(X1))
| ~ subset(sK13(X0,powerset(X1)),X1) ),
inference(superposition,[status(thm)],[c_12509,c_90]) ).
tcf(c_12573,plain,
! [X0: $i,X1: $i] :
( ~ subset(X1,X0)
| ~ in(powerset(X0),X1) ),
inference(superposition,[status(thm)],[c_12509,c_98]) ).
tcf(c_12575,plain,
! [X0: $i,X1: $i] :
( ~ empty(powerset(X1))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_12509,c_95]) ).
tcf(c_12604,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(X0) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_99,c_93]) ).
tcf(c_12618,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| in(X0,X1)
| ~ in(X0,sK17(X1)) ),
inference(superposition,[status(thm)],[c_12455,c_92]) ).
tcf(c_12619,plain,
! [X0: $i,X1: $i] :
( in(X0,X1)
| ~ in(X0,sK18(powerset(X1))) ),
inference(superposition,[status(thm)],[c_12346,c_92]) ).
tcf(c_12620,plain,
! [X0: $i,X1: $i] :
( in(X0,X1)
| ~ in(X0,empty_set) ),
inference(superposition,[status(thm)],[c_12424,c_92]) ).
tcf(c_12621,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X1)
| subset(powerset(X1),X2)
| ~ in(X0,sK13(powerset(X1),X2)) ),
inference(superposition,[status(thm)],[c_12563,c_92]) ).
tcf(c_12645,plain,
! [X0: $i] :
( one_to_one(X0)
| ~ function(X0)
| ~ relation(X0)
| ~ in(relation_dom(X0),sK11(X0)) ),
inference(superposition,[status(thm)],[c_82,c_98]) ).
tcf(c_12646,plain,
! [X0: $i] :
( one_to_one(X0)
| element(sK11(X0),relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_82,c_97]) ).
tcf(c_12647,plain,
! [X0: $i] :
( one_to_one(X0)
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_82,c_95]) ).
tcf(c_12674,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_99,c_12550]) ).
tcf(c_12675,plain,
relation_dom(relation_dom(empty_set)) = empty_set,
inference(superposition,[status(thm)],[c_114,c_12550]) ).
tcf(c_12684,plain,
! [X0: $i,X1: $i] :
( ~ subset(powerset(X1),X0)
| ~ subset(powerset(X0),X1) ),
inference(superposition,[status(thm)],[c_12509,c_12573]) ).
tcf(c_12692,plain,
! [X0: $i,X1: $i] :
( subset(sK18(powerset(X0)),X1)
| in(sK13(sK18(powerset(X0)),X1),X0) ),
inference(superposition,[status(thm)],[c_91,c_12619]) ).
tcf(c_12693,plain,
! [X0: $i] :
( empty(sK18(powerset(X0)))
| in(sK18(sK18(powerset(X0))),X0) ),
inference(superposition,[status(thm)],[c_12501,c_12619]) ).
tcf(c_12705,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| subset(sK17(X0),X1)
| in(sK13(sK17(X0),X1),X0) ),
inference(superposition,[status(thm)],[c_91,c_12618]) ).
tcf(c_12706,plain,
! [X0: $i] :
( empty(X0)
| empty(sK17(X0))
| in(sK18(sK17(X0)),X0) ),
inference(superposition,[status(thm)],[c_12501,c_12618]) ).
tcf(c_12718,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_99,c_12674]) ).
tcf(c_12719,plain,
relation_dom(relation_dom(relation_dom(empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_114,c_12674]) ).
tcf(c_12728,plain,
! [X0: $i,X1: $i] :
( ~ empty(powerset(X1))
| ~ subset(powerset(X0),X1) ),
inference(superposition,[status(thm)],[c_12476,c_12684]) ).
tcf(c_12729,plain,
! [X0: $i] : ~ subset(powerset(powerset(X0)),X0),
inference(superposition,[status(thm)],[c_89,c_12684]) ).
tcf(c_12731,plain,
! [X0: $i] : ~ empty(powerset(powerset(X0))),
inference(superposition,[status(thm)],[c_12476,c_12729]) ).
tcf(c_12736,plain,
! [X0: $i] :
( empty(sK18(powerset(X0)))
| ~ in(X0,sK18(sK18(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_12693,c_98]) ).
tcf(c_12737,plain,
! [X0: $i] :
( empty(sK18(powerset(X0)))
| element(sK18(sK18(powerset(X0))),X0) ),
inference(superposition,[status(thm)],[c_12693,c_97]) ).
tcf(c_12738,plain,
! [X0: $i] :
( empty(sK18(powerset(X0)))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12693,c_95]) ).
tcf(c_12739,plain,
! [X0: $i] :
( empty(X0)
| empty(sK18(powerset(sK17(X0))))
| in(sK18(sK18(powerset(sK17(X0)))),X0) ),
inference(superposition,[status(thm)],[c_12693,c_12618]) ).
tcf(c_12740,plain,
! [X0: $i] :
( empty(sK18(powerset(sK18(powerset(X0)))))
| in(sK18(sK18(powerset(sK18(powerset(X0))))),X0) ),
inference(superposition,[status(thm)],[c_12693,c_12619]) ).
tcf(c_12741,plain,
! [X0: $i] :
( empty(sK18(powerset(empty_set)))
| in(sK18(sK18(powerset(empty_set))),X0) ),
inference(superposition,[status(thm)],[c_12693,c_12620]) ).
tcf(c_12765,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK18(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12738,c_12674]) ).
tcf(c_12766,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK18(powerset(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12738,c_12550]) ).
tcf(c_12767,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(X0)) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12738,c_93]) ).
tcf(c_12768,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12738,c_12406]) ).
tcf(c_12769,plain,
! [X0: $i] :
( ( sK18(powerset(X0)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12738,c_94]) ).
tcf(c_12770,plain,
! [X0: $i] :
( one_to_one(sK18(powerset(X0)))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12738,c_5773]) ).
tcf(c_12771,plain,
! [X0: $i] :
( relation(sK18(powerset(X0)))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12738,c_77]) ).
tcf(c_12772,plain,
! [X0: $i] :
( function(sK18(powerset(X0)))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12738,c_66]) ).
tcf(c_12806,plain,
! [X0: $i,X1: $i] :
( subset(X0,powerset(X1))
| ~ empty(sK13(X0,powerset(X1))) ),
inference(superposition,[status(thm)],[c_12476,c_12572]) ).
tcf(c_12807,plain,
! [X0: $i] : subset(powerset(X0),powerset(X0)),
inference(superposition,[status(thm)],[c_12563,c_12572]) ).
tcf(c_12820,plain,
! [X0: $i] :
( one_to_one(X0)
| ~ function(X0)
| ~ relation(X0)
| ~ in(relation_dom(X0),sK12(X0)) ),
inference(superposition,[status(thm)],[c_83,c_98]) ).
tcf(c_12821,plain,
! [X0: $i] :
( one_to_one(X0)
| element(sK12(X0),relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_83,c_97]) ).
tcf(c_12839,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(relation_inverse_image(X0,X1),X2)
| in(sK13(relation_inverse_image(X0,X1),X2),relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_91,c_71]) ).
tcf(c_12840,plain,
! [X0: $i,X1: $i] :
( empty(relation_inverse_image(X0,X1))
| in(sK18(relation_inverse_image(X0,X1)),relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_12501,c_71]) ).
tcf(c_12841,plain,
! [X0: $i,X1: $i] :
( empty(sK18(powerset(relation_inverse_image(X0,X1))))
| in(sK18(sK18(powerset(relation_inverse_image(X0,X1)))),relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_12693,c_71]) ).
tcf(c_12865,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(relation_inverse_image(X0,X1),X2)
| in(apply(X0,sK13(relation_inverse_image(X0,X1),X2)),X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_91,c_72]) ).
tcf(c_12866,plain,
! [X0: $i,X1: $i] :
( empty(relation_inverse_image(X0,X1))
| in(apply(X0,sK18(relation_inverse_image(X0,X1))),X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_12501,c_72]) ).
tcf(c_12867,plain,
! [X0: $i,X1: $i] :
( empty(sK18(powerset(relation_inverse_image(X0,X1))))
| in(apply(X0,sK18(sK18(powerset(relation_inverse_image(X0,X1))))),X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_12693,c_72]) ).
tcf(c_12891,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X2,sK4(X1,relation_inverse_image(X2,X3),X0)),X3)
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,relation_inverse_image(X2,X3))) ),
inference(superposition,[status(thm)],[c_59,c_72]) ).
tcf(c_12892,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK4(X1,relation_inverse_image(X2,X3),X0),relation_dom(X2))
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,relation_inverse_image(X2,X3))) ),
inference(superposition,[status(thm)],[c_59,c_71]) ).
tcf(c_12893,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_98]) ).
tcf(c_12894,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_97]) ).
tcf(c_12895,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(X2)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_59,c_95]) ).
tcf(c_12896,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X2)
| in(sK4(X1,sK17(X2),X0),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,sK17(X2))) ),
inference(superposition,[status(thm)],[c_59,c_12618]) ).
tcf(c_12897,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK4(X1,sK18(powerset(X2)),X0),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,sK18(powerset(X2)))) ),
inference(superposition,[status(thm)],[c_59,c_12619]) ).
tcf(c_12898,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK4(X1,empty_set,X0),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,empty_set)) ),
inference(superposition,[status(thm)],[c_59,c_12620]) ).
tcf(c_12957,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_99,c_12769]) ).
tcf(c_12958,plain,
sK18(powerset(empty_set)) = empty_set,
inference(superposition,[status(thm)],[c_114,c_12769]) ).
tcf(c_12959,plain,
! [X0: $i] :
( ( sK18(powerset(sK18(powerset(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12738,c_12769]) ).
tcf(c_12968,plain,
( empty(powerset(empty_set))
| ~ in(powerset(empty_set),empty_set) ),
inference(superposition,[status(thm)],[c_12958,c_12526]) ).
tcf(c_12969,plain,
( empty(powerset(empty_set))
| in(empty_set,powerset(empty_set)) ),
inference(superposition,[status(thm)],[c_12958,c_12501]) ).
tcf(c_12970,plain,
element(empty_set,powerset(empty_set)),
inference(superposition,[status(thm)],[c_12958,c_111]) ).
tcf(c_12975,plain,
( empty(sK18(powerset(empty_set)))
| in(sK18(empty_set),empty_set) ),
inference(superposition,[status(thm)],[c_12958,c_12693]) ).
tcf(c_12976,plain,
subset(empty_set,empty_set),
inference(superposition,[status(thm)],[c_12958,c_12346]) ).
tcf(c_12978,plain,
( empty(empty_set)
| in(sK18(empty_set),empty_set) ),
inference(light_normalisation,[status(thm)],[c_12975,c_12958]) ).
tcf(c_12981,plain,
! [X0: $i] :
( empty(X0)
| in(sK18(sK17(X0)),X0) ),
inference(global_subsumption_just,[status(thm)],[c_12706,c_109,c_12706]) ).
tcf(c_12988,plain,
! [X0: $i,X1: $i] :
( empty(relation_inverse_image(X0,X1))
| in(apply(X0,sK18(sK17(relation_inverse_image(X0,X1)))),X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_12981,c_72]) ).
tcf(c_12989,plain,
! [X0: $i,X1: $i] :
( empty(relation_inverse_image(X0,X1))
| in(sK18(sK17(relation_inverse_image(X0,X1))),relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_12981,c_71]) ).
tcf(c_12990,plain,
! [X0: $i] :
( empty(X0)
| ~ in(X0,sK18(sK17(X0))) ),
inference(superposition,[status(thm)],[c_12981,c_98]) ).
tcf(c_12991,plain,
! [X0: $i] :
( empty(X0)
| element(sK18(sK17(X0)),X0) ),
inference(superposition,[status(thm)],[c_12981,c_97]) ).
tcf(c_12993,plain,
! [X0: $i] :
( empty(X0)
| empty(sK17(X0))
| in(sK18(sK17(sK17(X0))),X0) ),
inference(superposition,[status(thm)],[c_12981,c_12618]) ).
tcf(c_12994,plain,
! [X0: $i] :
( empty(sK18(powerset(X0)))
| in(sK18(sK17(sK18(powerset(X0)))),X0) ),
inference(superposition,[status(thm)],[c_12981,c_12619]) ).
tcf(c_13027,plain,
! [X0: $i] :
( empty(powerset(X0))
| subset(sK18(sK17(powerset(X0))),X0) ),
inference(superposition,[status(thm)],[c_12991,c_88]) ).
tcf(c_13029,plain,
! [X0: $i] : subset(sK18(sK17(powerset(X0))),X0),
inference(forward_subsumption_resolution,[status(thm)],[c_13027,c_110]) ).
tcf(c_13032,plain,
! [X0: $i,X1: $i] :
( in(X0,X1)
| ~ in(X0,sK18(sK17(powerset(X1)))) ),
inference(superposition,[status(thm)],[c_13029,c_92]) ).
tcf(c_13044,plain,
( element(sK18(empty_set),empty_set)
| empty(sK18(powerset(empty_set))) ),
inference(superposition,[status(thm)],[c_12958,c_12737]) ).
tcf(c_13045,plain,
! [X0: $i] :
( empty(sK18(powerset(powerset(X0))))
| subset(sK18(sK18(powerset(powerset(X0)))),X0) ),
inference(superposition,[status(thm)],[c_12737,c_88]) ).
tcf(c_13047,plain,
( empty(empty_set)
| element(sK18(empty_set),empty_set) ),
inference(light_normalisation,[status(thm)],[c_13044,c_12958]) ).
tcf(c_13057,plain,
! [X0: $i] :
( empty(empty_set)
| in(sK18(empty_set),X0) ),
inference(light_normalisation,[status(thm)],[c_12741,c_12958]) ).
tcf(c_13062,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(relation_dom(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_99,c_12768]) ).
tcf(c_13063,plain,
relation_dom(sK18(powerset(empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_114,c_12768]) ).
tcf(c_13064,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(sK18(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12738,c_12768]) ).
tcf(c_13085,plain,
( one_to_one(sK6)
| ( apply(sK6,sK11(sK6)) = apply(sK6,sK12(sK6)) )
| ~ function(sK6) ),
inference(superposition,[status(thm)],[c_64,c_84]) ).
tcf(c_13086,plain,
( one_to_one(sK8)
| ( apply(sK8,sK11(sK8)) = apply(sK8,sK12(sK8)) )
| ~ function(sK8) ),
inference(superposition,[status(thm)],[c_74,c_84]) ).
tcf(c_13088,plain,
! [X0: $i] :
( one_to_one(relation_dom(X0))
| ( apply(relation_dom(X0),sK11(relation_dom(X0))) = apply(relation_dom(X0),sK12(relation_dom(X0))) )
| ~ empty(X0)
| ~ function(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_100,c_84]) ).
tcf(c_13090,plain,
! [X0: $i] :
( one_to_one(sK18(powerset(X0)))
| ( apply(sK18(powerset(X0)),sK11(sK18(powerset(X0)))) = apply(sK18(powerset(X0)),sK12(sK18(powerset(X0)))) )
| ~ empty(X0)
| ~ function(sK18(powerset(X0))) ),
inference(superposition,[status(thm)],[c_12771,c_84]) ).
tcf(c_13094,plain,
( one_to_one(sK6)
| ( apply(sK6,sK11(sK6)) = apply(sK6,sK12(sK6)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_13085,c_65]) ).
tcf(c_13114,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_12551,c_58]) ).
tcf(c_13115,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_98]) ).
tcf(c_13116,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_97]) ).
tcf(c_13117,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_95]) ).
tcf(c_13122,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_13114,c_12355,c_113]) ).
tcf(c_13145,plain,
! [X0: $i] :
( ~ empty(empty_set)
| ~ in(X0,empty_set) ),
inference(instantiation,[status(thm)],[c_95]) ).
tcf(c_13155,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_13156,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(relation_image(X0,X1),X2)
| ( apply(X0,sK4(X0,X1,sK13(relation_image(X0,X1),X2))) = sK13(relation_image(X0,X1),X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_91,c_60]) ).
tcf(c_13157,plain,
! [X0: $i,X1: $i] :
( empty(relation_image(X0,X1))
| ( apply(X0,sK4(X0,X1,sK18(relation_image(X0,X1)))) = sK18(relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_12501,c_60]) ).
tcf(c_13158,plain,
! [X0: $i,X1: $i] :
( empty(sK18(powerset(relation_image(X0,X1))))
| ( apply(X0,sK4(X0,X1,sK18(sK18(powerset(relation_image(X0,X1)))))) = sK18(sK18(powerset(relation_image(X0,X1)))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_12693,c_60]) ).
tcf(c_13159,plain,
! [X0: $i,X1: $i] :
( empty(relation_image(X0,X1))
| ( apply(X0,sK4(X0,X1,sK18(sK17(relation_image(X0,X1))))) = sK18(sK17(relation_image(X0,X1))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_12981,c_60]) ).
tcf(c_13197,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_13198,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_98]) ).
tcf(c_13199,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_97]) ).
tcf(c_13200,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ function(X1)
| ~ relation(X1)
| ~ in(X0,X2)
| ~ empty(relation_image(X1,X2))
| ~ in(X0,relation_dom(X1)) ),
inference(superposition,[status(thm)],[c_57,c_95]) ).
tcf(c_13229,plain,
! [X0: $i] :
( empty(X0)
| ~ empty(empty_set)
| ( X0 != empty_set ) ),
inference(instantiation,[status(thm)],[c_11187]) ).
tcf(c_13241,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,relation_inverse_image(X1,relation_image(X1,X2)))
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,X2)
| ~ in(X0,relation_dom(X1)) ),
inference(superposition,[status(thm)],[c_57,c_70]) ).
tcf(c_13242,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,relation_inverse_image(X0,powerset(X2)))
| ~ function(X0)
| ~ relation(X0)
| ~ in(X1,relation_dom(X0))
| ~ subset(apply(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_12509,c_70]) ).
tcf(c_13258,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(relation_dom(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_99,c_12957]) ).
tcf(c_13259,plain,
sK18(powerset(relation_dom(empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_114,c_12957]) ).
tcf(c_13260,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(sK18(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12738,c_12957]) ).
tcf(c_13272,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK4(X1,sK18(sK17(powerset(X2))),X0),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,sK18(sK17(powerset(X2))))) ),
inference(superposition,[status(thm)],[c_59,c_13032]) ).
tcf(c_13273,plain,
! [X0: $i,X1: $i] :
( subset(sK18(sK17(powerset(X0))),X1)
| in(sK13(sK18(sK17(powerset(X0))),X1),X0) ),
inference(superposition,[status(thm)],[c_91,c_13032]) ).
tcf(c_13274,plain,
! [X0: $i] :
( empty(sK18(sK17(powerset(X0))))
| in(sK18(sK18(sK17(powerset(X0)))),X0) ),
inference(superposition,[status(thm)],[c_12501,c_13032]) ).
tcf(c_13275,plain,
! [X0: $i] :
( empty(sK18(powerset(sK18(sK17(powerset(X0))))))
| in(sK18(sK18(powerset(sK18(sK17(powerset(X0)))))),X0) ),
inference(superposition,[status(thm)],[c_12693,c_13032]) ).
tcf(c_13276,plain,
! [X0: $i] :
( empty(sK18(sK17(powerset(X0))))
| in(sK18(sK17(sK18(sK17(powerset(X0))))),X0) ),
inference(superposition,[status(thm)],[c_12981,c_13032]) ).
tcf(c_13313,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ in(X0,sK18(powerset(X1))) ),
inference(superposition,[status(thm)],[c_12346,c_299]) ).
tcf(c_13314,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ in(X0,empty_set) ),
inference(superposition,[status(thm)],[c_12424,c_299]) ).
tcf(c_13315,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(powerset(X1),X2)
| ~ empty(X1)
| ~ in(X0,sK13(powerset(X1),X2)) ),
inference(superposition,[status(thm)],[c_12563,c_299]) ).
tcf(c_13316,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ in(X0,sK18(sK17(powerset(X1)))) ),
inference(superposition,[status(thm)],[c_13029,c_299]) ).
tcf(c_13338,plain,
! [X0: $i] : ~ in(X0,empty_set),
inference(global_subsumption_just,[status(thm)],[c_13314,c_114,c_13145]) ).
tcf(c_13341,plain,
! [X0: $i,X1: $i] :
( ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,empty_set)) ),
inference(superposition,[status(thm)],[c_59,c_13338]) ).
tcf(c_13344,plain,
empty(sK18(powerset(empty_set))),
inference(superposition,[status(thm)],[c_12693,c_13338]) ).
tcf(c_13355,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(X2)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,sK18(powerset(X2)))) ),
inference(superposition,[status(thm)],[c_59,c_13313]) ).
tcf(c_13356,plain,
! [X0: $i,X1: $i] :
( subset(sK18(powerset(X0)),X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_91,c_13313]) ).
tcf(c_13358,plain,
! [X0: $i] :
( empty(sK18(powerset(sK18(powerset(X0)))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12693,c_13313]) ).
tcf(c_13383,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(sK18(powerset(sK18(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13358,c_12957]) ).
tcf(c_13384,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(sK18(powerset(sK18(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13358,c_12768]) ).
tcf(c_13385,plain,
! [X0: $i] :
( ( sK18(powerset(sK18(powerset(sK18(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13358,c_12769]) ).
tcf(c_13386,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK18(powerset(sK18(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13358,c_12674]) ).
tcf(c_13387,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK18(powerset(sK18(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13358,c_12550]) ).
tcf(c_13388,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK18(powerset(X0)))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13358,c_93]) ).
tcf(c_13391,plain,
! [X0: $i] :
( one_to_one(sK18(powerset(sK18(powerset(X0)))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13358,c_5773]) ).
tcf(c_13392,plain,
! [X0: $i] :
( relation(sK18(powerset(sK18(powerset(X0)))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13358,c_77]) ).
tcf(c_13393,plain,
! [X0: $i] :
( function(sK18(powerset(sK18(powerset(X0)))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13358,c_66]) ).
tcf(c_13451,plain,
! [X0: $i] :
( one_to_one(sK18(powerset(sK18(powerset(X0)))))
| ( apply(sK18(powerset(sK18(powerset(X0)))),sK11(sK18(powerset(sK18(powerset(X0)))))) = apply(sK18(powerset(sK18(powerset(X0)))),sK12(sK18(powerset(sK18(powerset(X0)))))) )
| ~ empty(X0)
| ~ function(sK18(powerset(sK18(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_13392,c_84]) ).
tcf(c_13466,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(X2)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,sK18(sK17(powerset(X2))))) ),
inference(superposition,[status(thm)],[c_59,c_13316]) ).
tcf(c_13467,plain,
! [X0: $i,X1: $i] :
( subset(sK18(sK17(powerset(X0))),X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_91,c_13316]) ).
tcf(c_13469,plain,
! [X0: $i] :
( empty(sK18(powerset(sK18(sK17(powerset(X0))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12693,c_13316]) ).
tcf(c_13470,plain,
! [X0: $i] :
( empty(sK18(sK17(powerset(X0))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12981,c_13316]) ).
tcf(c_13488,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(sK18(sK17(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13470,c_12957]) ).
tcf(c_13489,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(sK18(sK17(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13470,c_12768]) ).
tcf(c_13490,plain,
! [X0: $i] :
( ( sK18(powerset(sK18(sK17(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13470,c_12769]) ).
tcf(c_13491,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK18(sK17(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13470,c_12674]) ).
tcf(c_13492,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK18(sK17(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13470,c_12550]) ).
tcf(c_13493,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(powerset(X0))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13470,c_93]) ).
tcf(c_13494,plain,
! [X0: $i] :
( ( relation_dom(sK18(sK17(powerset(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13470,c_12406]) ).
tcf(c_13495,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13470,c_94]) ).
tcf(c_13496,plain,
! [X0: $i] :
( one_to_one(sK18(sK17(powerset(X0))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13470,c_5773]) ).
tcf(c_13497,plain,
! [X0: $i] :
( relation(sK18(sK17(powerset(X0))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13470,c_77]) ).
tcf(c_13498,plain,
! [X0: $i] :
( function(sK18(sK17(powerset(X0))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13470,c_66]) ).
tcf(c_13555,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_13556,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,relation_inverse_image(X1,X2),X3),X3)
| in(apply(X1,sK3(X0,relation_inverse_image(X1,X2),X3)),X2)
| ( relation_image(X0,relation_inverse_image(X1,X2)) = X3 )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_55,c_72]) ).
tcf(c_13557,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,relation_inverse_image(X1,X2),X3),X3)
| in(sK3(X0,relation_inverse_image(X1,X2),X3),relation_dom(X1))
| ( relation_image(X0,relation_inverse_image(X1,X2)) = X3 )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_55,c_71]) ).
tcf(c_13558,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_98]) ).
tcf(c_13559,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK3(X0,X1,X2),X1)
| in(sK2(X0,X1,X2),X2)
| ( relation_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_55,c_97]) ).
tcf(c_13560,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,X2),X2)
| ( relation_image(X0,X1) = X2 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_55,c_95]) ).
tcf(c_13561,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X1)
| in(sK3(X0,sK17(X1),X2),X1)
| in(sK2(X0,sK17(X1),X2),X2)
| ( relation_image(X0,sK17(X1)) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_55,c_12618]) ).
tcf(c_13562,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,sK18(powerset(X1)),X2),X2)
| ( relation_image(X0,sK18(powerset(X1))) = X2 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_55,c_13313]) ).
tcf(c_13563,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(X0,sK18(powerset(X1)),X2),X1)
| in(sK2(X0,sK18(powerset(X1)),X2),X2)
| ( relation_image(X0,sK18(powerset(X1))) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_55,c_12619]) ).
tcf(c_13564,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_13338]) ).
tcf(c_13565,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,sK18(sK17(powerset(X1))),X2),X2)
| ( relation_image(X0,sK18(sK17(powerset(X1)))) = X2 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_55,c_13316]) ).
tcf(c_13566,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(X0,sK18(sK17(powerset(X1))),X2),X1)
| in(sK2(X0,sK18(sK17(powerset(X1))),X2),X2)
| ( relation_image(X0,sK18(sK17(powerset(X1)))) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_55,c_13032]) ).
tcf(c_13567,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_13568,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK3(X0,X2,relation_inverse_image(X1,X3)),X2)
| in(apply(X1,sK2(X0,X2,relation_inverse_image(X1,X3))),X3)
| ( relation_image(X0,X2) = relation_inverse_image(X1,X3) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_55,c_72]) ).
tcf(c_13569,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK3(X0,X2,relation_inverse_image(X1,X3)),X2)
| in(sK2(X0,X2,relation_inverse_image(X1,X3)),relation_dom(X1))
| ( relation_image(X0,X2) = relation_inverse_image(X1,X3) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_55,c_71]) ).
tcf(c_13570,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_98]) ).
tcf(c_13571,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X0,X1,X2),X2)
| in(sK3(X0,X1,X2),X1)
| ( relation_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_55,c_97]) ).
tcf(c_13572,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(X0,X2,X1),X2)
| ( relation_image(X0,X2) = X1 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_55,c_95]) ).
tcf(c_13573,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X2)
| in(sK3(X0,X1,sK17(X2)),X1)
| in(sK2(X0,X1,sK17(X2)),X2)
| ( relation_image(X0,X1) = sK17(X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_55,c_12618]) ).
tcf(c_13574,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(X0,X2,sK18(powerset(X1))),X2)
| ( relation_image(X0,X2) = sK18(powerset(X1)) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_55,c_13313]) ).
tcf(c_13575,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(X0,X1,sK18(powerset(X2))),X1)
| in(sK2(X0,X1,sK18(powerset(X2))),X2)
| ( relation_image(X0,X1) = sK18(powerset(X2)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_55,c_12619]) ).
tcf(c_13576,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_13338]) ).
tcf(c_13577,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(X0,X2,sK18(sK17(powerset(X1)))),X2)
| ( sK18(sK17(powerset(X1))) = relation_image(X0,X2) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_55,c_13316]) ).
tcf(c_13578,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(X0,X2,sK18(sK17(powerset(X1)))),X2)
| in(sK2(X0,X2,sK18(sK17(powerset(X1)))),X1)
| ( sK18(sK17(powerset(X1))) = relation_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_55,c_13032]) ).
tcf(c_13775,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_12551,c_54]) ).
tcf(c_13776,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_13777,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK3(X0,X2,relation_inverse_image(X1,X3)),relation_dom(X0))
| in(apply(X1,sK2(X0,X2,relation_inverse_image(X1,X3))),X3)
| ( relation_image(X0,X2) = relation_inverse_image(X1,X3) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_54,c_72]) ).
tcf(c_13778,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK3(X0,X2,relation_inverse_image(X1,X3)),relation_dom(X0))
| in(sK2(X0,X2,relation_inverse_image(X1,X3)),relation_dom(X1))
| ( relation_image(X0,X2) = relation_inverse_image(X1,X3) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_54,c_71]) ).
tcf(c_13779,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_98]) ).
tcf(c_13780,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_97]) ).
tcf(c_13781,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(X0,X2,X1),relation_dom(X0))
| ( relation_image(X0,X2) = X1 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_54,c_95]) ).
tcf(c_13782,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X2)
| in(sK2(X0,X1,sK17(X2)),X2)
| in(sK3(X0,X1,sK17(X2)),relation_dom(X0))
| ( relation_image(X0,X1) = sK17(X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_54,c_12618]) ).
tcf(c_13783,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(X0,X2,sK18(powerset(X1))),relation_dom(X0))
| ( relation_image(X0,X2) = sK18(powerset(X1)) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_54,c_13313]) ).
tcf(c_13784,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,sK18(powerset(X2))),X2)
| in(sK3(X0,X1,sK18(powerset(X2))),relation_dom(X0))
| ( relation_image(X0,X1) = sK18(powerset(X2)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_54,c_12619]) ).
tcf(c_13785,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_13338]) ).
tcf(c_13786,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(X0,X2,sK18(sK17(powerset(X1)))),relation_dom(X0))
| ( sK18(sK17(powerset(X1))) = relation_image(X0,X2) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_54,c_13316]) ).
tcf(c_13787,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X2,sK18(sK17(powerset(X1)))),X1)
| in(sK3(X0,X2,sK18(sK17(powerset(X1)))),relation_dom(X0))
| ( sK18(sK17(powerset(X1))) = relation_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_54,c_13032]) ).
tcf(c_13788,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_98]) ).
tcf(c_13789,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_97]) ).
tcf(c_13790,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_95]) ).
tcf(c_13805,plain,
! [X0: $i,X1: $i] :
( in(sK2(empty_set,X0,X1),X1)
| ( relation_image(empty_set,X0) = X1 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_13775,c_13338,c_12355,c_113]) ).
tcf(c_13920,plain,
! [X0: $i,X1: $i] :
( in(sK7(empty_set,X0,X1),empty_set)
| in(sK7(empty_set,X0,X1),X1)
| ( relation_inverse_image(empty_set,X0) = X1 )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_12551,c_68]) ).
tcf(c_13921,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X3,relation_image(X1,X2)),relation_dom(X0))
| ( relation_image(X1,X2) = relation_inverse_image(X0,X3) )
| ( apply(X1,sK4(X1,X2,sK7(X0,X3,relation_image(X1,X2)))) = sK7(X0,X3,relation_image(X1,X2)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_68,c_60]) ).
tcf(c_13922,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X2,relation_inverse_image(X1,X3)),relation_dom(X0))
| in(apply(X1,sK7(X0,X2,relation_inverse_image(X1,X3))),X3)
| ( relation_inverse_image(X0,X2) = relation_inverse_image(X1,X3) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_68,c_72]) ).
tcf(c_13923,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X2,relation_inverse_image(X1,X3)),relation_dom(X1))
| in(sK7(X0,X2,relation_inverse_image(X1,X3)),relation_dom(X0))
| ( relation_inverse_image(X0,X2) = relation_inverse_image(X1,X3) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_68,c_71]) ).
tcf(c_13924,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X1,X2,X0),relation_dom(X1))
| ( relation_inverse_image(X1,X2) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,sK7(X1,X2,X0)) ),
inference(superposition,[status(thm)],[c_68,c_98]) ).
tcf(c_13925,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK7(X0,X1,X2),X2)
| in(sK7(X0,X1,X2),relation_dom(X0))
| ( relation_inverse_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_68,c_97]) ).
tcf(c_13926,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X2,X1),relation_dom(X0))
| ( relation_inverse_image(X0,X2) = X1 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_68,c_95]) ).
tcf(c_13927,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X2)
| in(sK7(X0,X1,sK17(X2)),X2)
| in(sK7(X0,X1,sK17(X2)),relation_dom(X0))
| ( relation_inverse_image(X0,X1) = sK17(X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_68,c_12618]) ).
tcf(c_13928,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X2,sK18(powerset(X1))),relation_dom(X0))
| ( relation_inverse_image(X0,X2) = sK18(powerset(X1)) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_68,c_13313]) ).
tcf(c_13929,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X1,sK18(powerset(X2))),X2)
| in(sK7(X0,X1,sK18(powerset(X2))),relation_dom(X0))
| ( relation_inverse_image(X0,X1) = sK18(powerset(X2)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_68,c_12619]) ).
tcf(c_13930,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0,X1,empty_set),relation_dom(X0))
| ( relation_inverse_image(X0,X1) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_68,c_13338]) ).
tcf(c_13931,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X2,sK18(sK17(powerset(X1)))),relation_dom(X0))
| ( sK18(sK17(powerset(X1))) = relation_inverse_image(X0,X2) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_68,c_13316]) ).
tcf(c_13932,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X2,sK18(sK17(powerset(X1)))),X1)
| in(sK7(X0,X2,sK18(sK17(powerset(X1)))),relation_dom(X0))
| ( sK18(sK17(powerset(X1))) = relation_inverse_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_68,c_13032]) ).
tcf(c_13933,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X1,X2),X2)
| ( relation_inverse_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0)
| ~ in(relation_dom(X0),sK7(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_68,c_98]) ).
tcf(c_13934,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X1,X2),X2)
| element(sK7(X0,X1,X2),relation_dom(X0))
| ( relation_inverse_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_68,c_97]) ).
tcf(c_13935,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X1,X2),X2)
| ( relation_inverse_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_68,c_95]) ).
tcf(c_13936,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0,X1,relation_dom(X0)),relation_dom(X0))
| ( relation_inverse_image(X0,X1) = relation_dom(X0) )
| ~ function(X0)
| ~ relation(X0) ),
inference(equality_factoring,[status(thm)],[c_68]) ).
tcf(c_13956,plain,
! [X0: $i,X1: $i] :
( in(sK7(empty_set,X0,X1),X1)
| ( relation_inverse_image(empty_set,X0) = X1 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_13920,c_13338,c_12355,c_113]) ).
tcf(c_14068,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X0,sK7(X0,X3,relation_image(X1,X2))),X3)
| ( relation_image(X1,X2) = relation_inverse_image(X0,X3) )
| ( apply(X1,sK4(X1,X2,sK7(X0,X3,relation_image(X1,X2)))) = sK7(X0,X3,relation_image(X1,X2)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_69,c_60]) ).
tcf(c_14069,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X1,sK7(X0,X2,relation_inverse_image(X1,X3))),X3)
| in(apply(X0,sK7(X0,X2,relation_inverse_image(X1,X3))),X2)
| ( relation_inverse_image(X0,X2) = relation_inverse_image(X1,X3) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_69,c_72]) ).
tcf(c_14070,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X2,relation_inverse_image(X1,X3)),relation_dom(X1))
| in(apply(X0,sK7(X0,X2,relation_inverse_image(X1,X3))),X2)
| ( relation_inverse_image(X0,X2) = relation_inverse_image(X1,X3) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_69,c_71]) ).
tcf(c_14071,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X1,sK7(X1,X2,X0)),X2)
| ( relation_inverse_image(X1,X2) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,sK7(X1,X2,X0)) ),
inference(superposition,[status(thm)],[c_69,c_98]) ).
tcf(c_14072,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK7(X0,X1,X2),X2)
| in(apply(X0,sK7(X0,X1,X2)),X1)
| ( relation_inverse_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_69,c_97]) ).
tcf(c_14073,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X0,sK7(X0,X2,X1)),X2)
| ( relation_inverse_image(X0,X2) = X1 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_69,c_95]) ).
tcf(c_14074,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X2)
| in(sK7(X0,X1,sK17(X2)),X2)
| in(apply(X0,sK7(X0,X1,sK17(X2))),X1)
| ( relation_inverse_image(X0,X1) = sK17(X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_69,c_12618]) ).
tcf(c_14075,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X0,sK7(X0,X2,sK18(powerset(X1)))),X2)
| ( relation_inverse_image(X0,X2) = sK18(powerset(X1)) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_69,c_13313]) ).
tcf(c_14076,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X1,sK18(powerset(X2))),X2)
| in(apply(X0,sK7(X0,X1,sK18(powerset(X2)))),X1)
| ( relation_inverse_image(X0,X1) = sK18(powerset(X2)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_69,c_12619]) ).
tcf(c_14077,plain,
! [X0: $i,X1: $i] :
( in(apply(X0,sK7(X0,X1,empty_set)),X1)
| ( relation_inverse_image(X0,X1) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_69,c_13338]) ).
tcf(c_14078,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X0,sK7(X0,X2,sK18(sK17(powerset(X1))))),X2)
| ( sK18(sK17(powerset(X1))) = relation_inverse_image(X0,X2) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_69,c_13316]) ).
tcf(c_14079,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X2,sK18(sK17(powerset(X1)))),X1)
| in(apply(X0,sK7(X0,X2,sK18(sK17(powerset(X1))))),X2)
| ( sK18(sK17(powerset(X1))) = relation_inverse_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_69,c_13032]) ).
tcf(c_14080,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,relation_image(X1,X2),X3),X3)
| ( relation_inverse_image(X0,relation_image(X1,X2)) = X3 )
| ( apply(X1,sK4(X1,X2,apply(X0,sK7(X0,relation_image(X1,X2),X3)))) = apply(X0,sK7(X0,relation_image(X1,X2),X3)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_69,c_60]) ).
tcf(c_14081,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X1,X2),X2)
| in(sK7(X0,X1,X2),relation_inverse_image(X0,X1))
| ( relation_inverse_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK7(X0,X1,X2),relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_69,c_70]) ).
tcf(c_14082,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,relation_inverse_image(X1,X2),X3),X3)
| in(apply(X1,apply(X0,sK7(X0,relation_inverse_image(X1,X2),X3))),X2)
| ( relation_inverse_image(X0,relation_inverse_image(X1,X2)) = X3 )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_69,c_72]) ).
tcf(c_14083,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,relation_inverse_image(X1,X2),X3),X3)
| in(apply(X0,sK7(X0,relation_inverse_image(X1,X2),X3)),relation_dom(X1))
| ( relation_inverse_image(X0,relation_inverse_image(X1,X2)) = X3 )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_69,c_71]) ).
tcf(c_14084,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X1,X0,X2),X2)
| ( relation_inverse_image(X1,X0) = X2 )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,apply(X1,sK7(X1,X0,X2))) ),
inference(superposition,[status(thm)],[c_69,c_98]) ).
tcf(c_14085,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X1,X2),X2)
| element(apply(X0,sK7(X0,X1,X2)),X1)
| ( relation_inverse_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_69,c_97]) ).
tcf(c_14086,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X1,X2),X2)
| ( relation_inverse_image(X0,X1) = X2 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_69,c_95]) ).
tcf(c_14087,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X1)
| in(sK7(X0,sK17(X1),X2),X2)
| in(apply(X0,sK7(X0,sK17(X1),X2)),X1)
| ( relation_inverse_image(X0,sK17(X1)) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_69,c_12618]) ).
tcf(c_14088,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,sK18(powerset(X1)),X2),X2)
| ( relation_inverse_image(X0,sK18(powerset(X1))) = X2 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_69,c_13313]) ).
tcf(c_14089,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,sK18(powerset(X1)),X2),X2)
| in(apply(X0,sK7(X0,sK18(powerset(X1)),X2)),X1)
| ( relation_inverse_image(X0,sK18(powerset(X1))) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_69,c_12619]) ).
tcf(c_14090,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0,empty_set,X1),X1)
| ( relation_inverse_image(X0,empty_set) = X1 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_69,c_13338]) ).
tcf(c_14091,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,sK18(sK17(powerset(X1))),X2),X2)
| ( relation_inverse_image(X0,sK18(sK17(powerset(X1)))) = X2 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_69,c_13316]) ).
tcf(c_14092,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,sK18(sK17(powerset(X1))),X2),X2)
| in(apply(X0,sK7(X0,sK18(sK17(powerset(X1))),X2)),X1)
| ( relation_inverse_image(X0,sK18(sK17(powerset(X1)))) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_69,c_13032]) ).
tcf(c_14279,plain,
function(empty_set),
inference(superposition,[status(thm)],[c_114,c_66]) ).
tcf(c_14309,plain,
! [X0: $i] :
( empty(powerset(X0))
| ~ empty(empty_set)
| ( powerset(X0) != empty_set ) ),
inference(instantiation,[status(thm)],[c_13229]) ).
tcf(c_14315,plain,
! [X0: $i] :
( one_to_one(sK18(sK17(powerset(X0))))
| ( apply(sK18(sK17(powerset(X0))),sK11(sK18(sK17(powerset(X0))))) = apply(sK18(sK17(powerset(X0))),sK12(sK18(sK17(powerset(X0))))) )
| ~ empty(X0)
| ~ function(sK18(sK17(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_13497,c_84]) ).
tcf(c_14335,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(sK18(powerset(sK18(sK17(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13469,c_12957]) ).
tcf(c_14336,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(sK18(powerset(sK18(sK17(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13469,c_12768]) ).
tcf(c_14337,plain,
! [X0: $i] :
( ( sK18(powerset(sK18(powerset(sK18(sK17(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13469,c_12769]) ).
tcf(c_14338,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK18(powerset(sK18(sK17(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13469,c_12674]) ).
tcf(c_14339,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK18(powerset(sK18(sK17(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13469,c_12550]) ).
tcf(c_14340,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK18(sK17(powerset(X0))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13469,c_93]) ).
tcf(c_14343,plain,
! [X0: $i] :
( one_to_one(sK18(powerset(sK18(sK17(powerset(X0))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13469,c_5773]) ).
tcf(c_14344,plain,
! [X0: $i] :
( relation(sK18(powerset(sK18(sK17(powerset(X0))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13469,c_77]) ).
tcf(c_14345,plain,
! [X0: $i] :
( function(sK18(powerset(sK18(sK17(powerset(X0))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13469,c_66]) ).
tcf(c_14374,plain,
! [X0: $i] : subset(sK16(X0),X0),
inference(superposition,[status(thm)],[c_106,c_88]) ).
tcf(c_14397,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(relation_dom(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_99,c_13495]) ).
tcf(c_14398,plain,
sK18(sK17(powerset(empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_114,c_13495]) ).
tcf(c_14399,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(sK18(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12738,c_13495]) ).
tcf(c_14400,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(sK18(powerset(sK18(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13358,c_13495]) ).
tcf(c_14401,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(sK18(sK17(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13470,c_13495]) ).
tcf(c_14402,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(sK18(powerset(sK18(sK17(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13469,c_13495]) ).
tcf(c_14424,plain,
( empty(sK17(powerset(empty_set)))
| ~ in(sK17(powerset(empty_set)),empty_set) ),
inference(superposition,[status(thm)],[c_14398,c_12526]) ).
tcf(c_14425,plain,
( empty(sK17(powerset(empty_set)))
| in(empty_set,sK17(powerset(empty_set))) ),
inference(superposition,[status(thm)],[c_14398,c_12501]) ).
tcf(c_14426,plain,
element(empty_set,sK17(powerset(empty_set))),
inference(superposition,[status(thm)],[c_14398,c_111]) ).
tcf(c_14428,plain,
( empty(powerset(empty_set))
| element(empty_set,powerset(empty_set)) ),
inference(superposition,[status(thm)],[c_14398,c_12991]) ).
tcf(c_14430,plain,
( empty(sK18(powerset(empty_set)))
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_14398,c_13469]) ).
tcf(c_14450,plain,
( empty(powerset(empty_set))
| empty(sK17(powerset(empty_set)))
| in(empty_set,powerset(empty_set)) ),
inference(superposition,[status(thm)],[c_14425,c_12618]) ).
tcf(c_14455,plain,
( one_to_one(sK18(powerset(empty_set)))
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_14398,c_14343]) ).
tcf(c_14456,plain,
( one_to_one(empty_set)
| ~ empty(empty_set) ),
inference(light_normalisation,[status(thm)],[c_14455,c_12958]) ).
tcf(c_14461,plain,
( relation(sK18(powerset(empty_set)))
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_14398,c_14344]) ).
tcf(c_14462,plain,
! [X0: $i] :
( one_to_one(sK18(powerset(sK18(sK17(powerset(X0))))))
| ( apply(sK18(powerset(sK18(sK17(powerset(X0))))),sK11(sK18(powerset(sK18(sK17(powerset(X0))))))) = apply(sK18(powerset(sK18(sK17(powerset(X0))))),sK12(sK18(powerset(sK18(sK17(powerset(X0))))))) )
| ~ empty(X0)
| ~ function(sK18(powerset(sK18(sK17(powerset(X0)))))) ),
inference(superposition,[status(thm)],[c_14344,c_84]) ).
tcf(c_14463,plain,
( relation(empty_set)
| ~ empty(empty_set) ),
inference(light_normalisation,[status(thm)],[c_14461,c_12958]) ).
tcf(c_14473,plain,
( function(sK18(powerset(empty_set)))
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_14398,c_14345]) ).
tcf(c_14474,plain,
( function(empty_set)
| ~ empty(empty_set) ),
inference(light_normalisation,[status(thm)],[c_14473,c_12958]) ).
tcf(c_14484,plain,
! [X0: $i] :
( one_to_one(X0)
| empty(relation_dom(X0))
| in(sK11(X0),relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_12646,c_96]) ).
tcf(c_14500,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_14501,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X1,sK2(X0,X2,relation_inverse_image(X1,X3))),X3)
| ( relation_image(X0,X2) = relation_inverse_image(X1,X3) )
| ( apply(X0,sK3(X0,X2,relation_inverse_image(X1,X3))) = sK2(X0,X2,relation_inverse_image(X1,X3)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_56,c_72]) ).
tcf(c_14502,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,X2,relation_inverse_image(X1,X3)),relation_dom(X1))
| ( relation_image(X0,X2) = relation_inverse_image(X1,X3) )
| ( apply(X0,sK3(X0,X2,relation_inverse_image(X1,X3))) = sK2(X0,X2,relation_inverse_image(X1,X3)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_56,c_71]) ).
tcf(c_14503,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_98]) ).
tcf(c_14504,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_97]) ).
tcf(c_14505,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X0,X2) = X1 )
| ( apply(X0,sK3(X0,X2,X1)) = sK2(X0,X2,X1) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_56,c_95]) ).
tcf(c_14506,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X2)
| in(sK2(X0,X1,sK17(X2)),X2)
| ( relation_image(X0,X1) = sK17(X2) )
| ( apply(X0,sK3(X0,X1,sK17(X2))) = sK2(X0,X1,sK17(X2)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_56,c_12618]) ).
tcf(c_14507,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X0,X2) = sK18(powerset(X1)) )
| ( apply(X0,sK3(X0,X2,sK18(powerset(X1)))) = sK2(X0,X2,sK18(powerset(X1))) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_56,c_13313]) ).
tcf(c_14508,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,sK18(powerset(X2))),X2)
| ( relation_image(X0,X1) = sK18(powerset(X2)) )
| ( apply(X0,sK3(X0,X1,sK18(powerset(X2)))) = sK2(X0,X1,sK18(powerset(X2))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_56,c_12619]) ).
tcf(c_14509,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_13338]) ).
tcf(c_14510,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK18(sK17(powerset(X1))) = relation_image(X0,X2) )
| ( apply(X0,sK3(X0,X2,sK18(sK17(powerset(X1))))) = sK2(X0,X2,sK18(sK17(powerset(X1)))) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_56,c_13316]) ).
tcf(c_14511,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,sK18(sK17(powerset(X2)))),X2)
| ( sK18(sK17(powerset(X2))) = relation_image(X0,X1) )
| ( apply(X0,sK3(X0,X1,sK18(sK17(powerset(X2))))) = sK2(X0,X1,sK18(sK17(powerset(X2)))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_56,c_13032]) ).
tcf(c_14638,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_inverse_image(X0,relation_image(X0,X1)) = X2 )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK7(X0,relation_image(X0,X1),X2),X2)
| ~ in(sK7(X0,relation_image(X0,X1),X2),X1)
| ~ in(sK7(X0,relation_image(X0,X1),X2),relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_57,c_67]) ).
tcf(c_14640,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_inverse_image(X0,powerset(X1)) = X2 )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK7(X0,powerset(X1),X2),X2)
| ~ in(sK7(X0,powerset(X1),X2),relation_dom(X0))
| ~ subset(apply(X0,sK7(X0,powerset(X1),X2)),X1) ),
inference(superposition,[status(thm)],[c_12509,c_67]) ).
tcf(c_14688,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| element(X0,X1)
| ~ in(X0,sK17(X1)) ),
inference(superposition,[status(thm)],[c_12455,c_300]) ).
tcf(c_14689,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| ~ in(X0,sK18(powerset(X1))) ),
inference(superposition,[status(thm)],[c_12346,c_300]) ).
tcf(c_14691,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,X1)
| subset(powerset(X1),X2)
| ~ in(X0,sK13(powerset(X1),X2)) ),
inference(superposition,[status(thm)],[c_12563,c_300]) ).
tcf(c_14693,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| ~ in(X0,sK18(sK17(powerset(X1)))) ),
inference(superposition,[status(thm)],[c_13029,c_300]) ).
tcf(c_14717,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X0,X1,sK18(powerset(X2))),X2)
| ( relation_image(X0,X1) = sK18(powerset(X2)) )
| ( apply(X0,sK3(X0,X1,sK18(powerset(X2)))) = sK2(X0,X1,sK18(powerset(X2))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_56,c_14689]) ).
tcf(c_14718,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X0,X1,sK18(powerset(X2))),X2)
| in(sK3(X0,X1,sK18(powerset(X2))),relation_dom(X0))
| ( relation_image(X0,X1) = sK18(powerset(X2)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_54,c_14689]) ).
tcf(c_14719,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X0,X1,sK18(powerset(X2))),X2)
| in(sK3(X0,X1,sK18(powerset(X2))),X1)
| ( relation_image(X0,X1) = sK18(powerset(X2)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_55,c_14689]) ).
tcf(c_14720,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK3(X0,sK18(powerset(X1)),X2),X1)
| in(sK2(X0,sK18(powerset(X1)),X2),X2)
| ( relation_image(X0,sK18(powerset(X1))) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_55,c_14689]) ).
tcf(c_14721,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK4(X1,sK18(powerset(X2)),X0),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,sK18(powerset(X2)))) ),
inference(superposition,[status(thm)],[c_59,c_14689]) ).
tcf(c_14722,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,sK18(powerset(X1)),X2),X2)
| element(apply(X0,sK7(X0,sK18(powerset(X1)),X2)),X1)
| ( relation_inverse_image(X0,sK18(powerset(X1))) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_69,c_14689]) ).
tcf(c_14723,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK7(X0,X1,sK18(powerset(X2))),X2)
| in(apply(X0,sK7(X0,X1,sK18(powerset(X2)))),X1)
| ( relation_inverse_image(X0,X1) = sK18(powerset(X2)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_69,c_14689]) ).
tcf(c_14724,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK7(X0,X1,sK18(powerset(X2))),X2)
| in(sK7(X0,X1,sK18(powerset(X2))),relation_dom(X0))
| ( relation_inverse_image(X0,X1) = sK18(powerset(X2)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_68,c_14689]) ).
tcf(c_14725,plain,
! [X0: $i,X1: $i] :
( subset(sK18(powerset(X0)),X1)
| element(sK13(sK18(powerset(X0)),X1),X0) ),
inference(superposition,[status(thm)],[c_91,c_14689]) ).
tcf(c_14727,plain,
! [X0: $i] :
( empty(sK18(powerset(sK18(powerset(X0)))))
| element(sK18(sK18(powerset(sK18(powerset(X0))))),X0) ),
inference(superposition,[status(thm)],[c_12693,c_14689]) ).
tcf(c_14728,plain,
! [X0: $i] :
( empty(sK18(powerset(X0)))
| element(sK18(sK17(sK18(powerset(X0)))),X0) ),
inference(superposition,[status(thm)],[c_12981,c_14689]) ).
tcf(c_14820,plain,
! [X0: $i] :
( ( relation_dom(X0) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_99,c_94]) ).
tcf(c_14822,plain,
! [X0: $i] : sK16(X0) = empty_set,
inference(superposition,[status(thm)],[c_107,c_94]) ).
tcf(c_14838,plain,
! [X0: $i] : subset(empty_set,X0),
inference(demodulation,[status(thm)],[c_14374,c_14822]) ).
tcf(c_14957,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X2)
| element(sK2(X0,X1,sK17(X2)),X2)
| ( relation_image(X0,X1) = sK17(X2) )
| ( apply(X0,sK3(X0,X1,sK17(X2))) = sK2(X0,X1,sK17(X2)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_56,c_14688]) ).
tcf(c_14958,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X2)
| element(sK2(X0,X1,sK17(X2)),X2)
| in(sK3(X0,X1,sK17(X2)),relation_dom(X0))
| ( relation_image(X0,X1) = sK17(X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_54,c_14688]) ).
tcf(c_14959,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X2)
| element(sK2(X0,X1,sK17(X2)),X2)
| in(sK3(X0,X1,sK17(X2)),X1)
| ( relation_image(X0,X1) = sK17(X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_55,c_14688]) ).
tcf(c_14960,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X1)
| element(sK3(X0,sK17(X1),X2),X1)
| in(sK2(X0,sK17(X1),X2),X2)
| ( relation_image(X0,sK17(X1)) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_55,c_14688]) ).
tcf(c_14961,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X2)
| element(sK4(X1,sK17(X2),X0),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,sK17(X2))) ),
inference(superposition,[status(thm)],[c_59,c_14688]) ).
tcf(c_14962,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X1)
| in(sK7(X0,sK17(X1),X2),X2)
| element(apply(X0,sK7(X0,sK17(X1),X2)),X1)
| ( relation_inverse_image(X0,sK17(X1)) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_69,c_14688]) ).
tcf(c_14963,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X2)
| element(sK7(X0,X1,sK17(X2)),X2)
| in(apply(X0,sK7(X0,X1,sK17(X2))),X1)
| ( relation_inverse_image(X0,X1) = sK17(X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_69,c_14688]) ).
tcf(c_14964,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X2)
| element(sK7(X0,X1,sK17(X2)),X2)
| in(sK7(X0,X1,sK17(X2)),relation_dom(X0))
| ( relation_inverse_image(X0,X1) = sK17(X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_68,c_14688]) ).
tcf(c_14965,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| subset(sK17(X0),X1)
| element(sK13(sK17(X0),X1),X0) ),
inference(superposition,[status(thm)],[c_91,c_14688]) ).
tcf(c_14966,plain,
! [X0: $i] :
( empty(X0)
| empty(sK17(X0))
| element(sK18(sK17(X0)),X0) ),
inference(superposition,[status(thm)],[c_12501,c_14688]) ).
tcf(c_14967,plain,
! [X0: $i] :
( empty(X0)
| empty(sK18(powerset(sK17(X0))))
| element(sK18(sK18(powerset(sK17(X0)))),X0) ),
inference(superposition,[status(thm)],[c_12693,c_14688]) ).
tcf(c_14968,plain,
! [X0: $i] :
( empty(X0)
| empty(sK17(X0))
| element(sK18(sK17(sK17(X0))),X0) ),
inference(superposition,[status(thm)],[c_12981,c_14688]) ).
tcf(c_14969,plain,
( empty(powerset(empty_set))
| element(empty_set,powerset(empty_set))
| empty(sK17(powerset(empty_set))) ),
inference(superposition,[status(thm)],[c_14425,c_14688]) ).
tcf(c_15045,plain,
relation_dom(empty_set) = empty_set,
inference(superposition,[status(thm)],[c_114,c_14820]) ).
tcf(c_15080,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X0,X1,sK18(sK17(powerset(X2)))),X2)
| ( sK18(sK17(powerset(X2))) = relation_image(X0,X1) )
| ( apply(X0,sK3(X0,X1,sK18(sK17(powerset(X2))))) = sK2(X0,X1,sK18(sK17(powerset(X2)))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_56,c_14693]) ).
tcf(c_15081,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X0,X2,sK18(sK17(powerset(X1)))),X1)
| in(sK3(X0,X2,sK18(sK17(powerset(X1)))),relation_dom(X0))
| ( sK18(sK17(powerset(X1))) = relation_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_54,c_14693]) ).
tcf(c_15082,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X0,X2,sK18(sK17(powerset(X1)))),X1)
| in(sK3(X0,X2,sK18(sK17(powerset(X1)))),X2)
| ( sK18(sK17(powerset(X1))) = relation_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_55,c_14693]) ).
tcf(c_15083,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK3(X0,sK18(sK17(powerset(X1))),X2),X1)
| in(sK2(X0,sK18(sK17(powerset(X1))),X2),X2)
| ( relation_image(X0,sK18(sK17(powerset(X1)))) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_55,c_14693]) ).
tcf(c_15084,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK4(X1,sK18(sK17(powerset(X2))),X0),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,sK18(sK17(powerset(X2))))) ),
inference(superposition,[status(thm)],[c_59,c_14693]) ).
tcf(c_15085,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,sK18(sK17(powerset(X1))),X2),X2)
| element(apply(X0,sK7(X0,sK18(sK17(powerset(X1))),X2)),X1)
| ( relation_inverse_image(X0,sK18(sK17(powerset(X1)))) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_69,c_14693]) ).
tcf(c_15086,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK7(X0,X2,sK18(sK17(powerset(X1)))),X1)
| in(apply(X0,sK7(X0,X2,sK18(sK17(powerset(X1))))),X2)
| ( sK18(sK17(powerset(X1))) = relation_inverse_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_69,c_14693]) ).
tcf(c_15087,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK7(X0,X2,sK18(sK17(powerset(X1)))),X1)
| in(sK7(X0,X2,sK18(sK17(powerset(X1)))),relation_dom(X0))
| ( sK18(sK17(powerset(X1))) = relation_inverse_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_68,c_14693]) ).
tcf(c_15088,plain,
! [X0: $i,X1: $i] :
( subset(sK18(sK17(powerset(X0))),X1)
| element(sK13(sK18(sK17(powerset(X0))),X1),X0) ),
inference(superposition,[status(thm)],[c_91,c_14693]) ).
tcf(c_15089,plain,
! [X0: $i] :
( empty(sK18(sK17(powerset(X0))))
| element(sK18(sK18(sK17(powerset(X0)))),X0) ),
inference(superposition,[status(thm)],[c_12501,c_14693]) ).
tcf(c_15090,plain,
! [X0: $i] :
( empty(sK18(powerset(sK18(sK17(powerset(X0))))))
| element(sK18(sK18(powerset(sK18(sK17(powerset(X0)))))),X0) ),
inference(superposition,[status(thm)],[c_12693,c_14693]) ).
tcf(c_15091,plain,
! [X0: $i] :
( empty(sK18(sK17(powerset(X0))))
| element(sK18(sK17(sK18(sK17(powerset(X0))))),X0) ),
inference(superposition,[status(thm)],[c_12981,c_14693]) ).
tcf(c_15210,plain,
! [X0: $i,X1: $i] :
( in(X0,X1)
| ~ in(X0,empty_set) ),
inference(superposition,[status(thm)],[c_14838,c_92]) ).
tcf(c_15230,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(X0)) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_99,c_12604]) ).
tcf(c_15231,plain,
! [X0: $i] :
( ( relation_dom(empty_set) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_114,c_12604]) ).
tcf(c_15232,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(powerset(X0))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12738,c_12604]) ).
tcf(c_15233,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(powerset(sK18(powerset(X0))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13358,c_12604]) ).
tcf(c_15234,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(sK17(powerset(X0)))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13470,c_12604]) ).
tcf(c_15235,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(powerset(sK18(sK17(powerset(X0)))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13469,c_12604]) ).
tcf(c_15261,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_99,c_12718]) ).
tcf(c_15262,plain,
relation_dom(relation_dom(relation_dom(relation_dom(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_114,c_12718]) ).
tcf(c_15263,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK18(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12738,c_12718]) ).
tcf(c_15264,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK18(powerset(sK18(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13358,c_12718]) ).
tcf(c_15265,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK18(sK17(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13470,c_12718]) ).
tcf(c_15266,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK18(powerset(sK18(sK17(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13469,c_12718]) ).
tcf(c_15311,plain,
( empty(sK18(powerset(empty_set)))
| ~ in(empty_set,sK18(empty_set)) ),
inference(superposition,[status(thm)],[c_12958,c_12736]) ).
tcf(c_15312,plain,
( empty(empty_set)
| ~ in(empty_set,sK18(empty_set)) ),
inference(light_normalisation,[status(thm)],[c_15311,c_12958]) ).
tcf(c_15317,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK18(powerset(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_99,c_12766]) ).
tcf(c_15318,plain,
relation_dom(relation_dom(sK18(powerset(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_114,c_12766]) ).
tcf(c_15320,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK18(powerset(sK18(powerset(sK18(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13358,c_12766]) ).
tcf(c_15322,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK18(powerset(sK18(powerset(sK18(sK17(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13469,c_12766]) ).
tcf(c_15355,plain,
! [X0: $i] :
( ( sK18(powerset(sK18(powerset(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_99,c_12959]) ).
tcf(c_15356,plain,
sK18(powerset(sK18(powerset(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_114,c_12959]) ).
tcf(c_15358,plain,
! [X0: $i] :
( ( sK18(powerset(sK18(powerset(sK18(powerset(sK18(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13358,c_12959]) ).
tcf(c_15360,plain,
! [X0: $i] :
( ( sK18(powerset(sK18(powerset(sK18(powerset(sK18(sK17(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13469,c_12959]) ).
tcf(c_15371,plain,
! [X0: $i] :
( empty(X0)
| in(sK18(sK17(sK17(X0))),X0) ),
inference(global_subsumption_just,[status(thm)],[c_12993,c_109,c_12993]) ).
tcf(c_15378,plain,
! [X0: $i,X1: $i] :
( empty(relation_image(X0,X1))
| ( apply(X0,sK4(X0,X1,sK18(sK17(sK17(relation_image(X0,X1)))))) = sK18(sK17(sK17(relation_image(X0,X1)))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_15371,c_60]) ).
tcf(c_15379,plain,
! [X0: $i,X1: $i] :
( empty(relation_inverse_image(X0,X1))
| in(apply(X0,sK18(sK17(sK17(relation_inverse_image(X0,X1))))),X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_15371,c_72]) ).
tcf(c_15380,plain,
! [X0: $i,X1: $i] :
( empty(relation_inverse_image(X0,X1))
| in(sK18(sK17(sK17(relation_inverse_image(X0,X1)))),relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_15371,c_71]) ).
tcf(c_15381,plain,
! [X0: $i] :
( empty(X0)
| ~ in(X0,sK18(sK17(sK17(X0)))) ),
inference(superposition,[status(thm)],[c_15371,c_98]) ).
tcf(c_15382,plain,
! [X0: $i] :
( empty(X0)
| element(sK18(sK17(sK17(X0))),X0) ),
inference(superposition,[status(thm)],[c_15371,c_97]) ).
tcf(c_15384,plain,
! [X0: $i] :
( empty(X0)
| empty(sK17(X0))
| element(sK18(sK17(sK17(sK17(X0)))),X0) ),
inference(superposition,[status(thm)],[c_15371,c_14688]) ).
tcf(c_15385,plain,
! [X0: $i] :
( empty(X0)
| empty(sK17(X0))
| in(sK18(sK17(sK17(sK17(X0)))),X0) ),
inference(superposition,[status(thm)],[c_15371,c_12618]) ).
tcf(c_15386,plain,
! [X0: $i] :
( empty(sK18(powerset(X0)))
| element(sK18(sK17(sK17(sK18(powerset(X0))))),X0) ),
inference(superposition,[status(thm)],[c_15371,c_14689]) ).
tcf(c_15388,plain,
! [X0: $i] :
( empty(sK18(powerset(X0)))
| in(sK18(sK17(sK17(sK18(powerset(X0))))),X0) ),
inference(superposition,[status(thm)],[c_15371,c_12619]) ).
tcf(c_15390,plain,
! [X0: $i] :
( empty(sK18(sK17(powerset(X0))))
| element(sK18(sK17(sK17(sK18(sK17(powerset(X0)))))),X0) ),
inference(superposition,[status(thm)],[c_15371,c_14693]) ).
tcf(c_15392,plain,
! [X0: $i] :
( empty(sK18(sK17(powerset(X0))))
| in(sK18(sK17(sK17(sK18(sK17(powerset(X0)))))),X0) ),
inference(superposition,[status(thm)],[c_15371,c_13032]) ).
tcf(c_15434,plain,
! [X0: $i] : ~ in(X0,empty_set),
inference(global_subsumption_just,[status(thm)],[c_15210,c_114,c_13145]) ).
tcf(c_15472,plain,
! [X0: $i] :
( empty(powerset(X0))
| subset(sK18(sK17(sK17(powerset(X0)))),X0) ),
inference(superposition,[status(thm)],[c_15382,c_88]) ).
tcf(c_15474,plain,
! [X0: $i] : subset(sK18(sK17(sK17(powerset(X0)))),X0),
inference(forward_subsumption_resolution,[status(thm)],[c_15472,c_110]) ).
tcf(c_15476,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| ~ in(X0,sK18(sK17(sK17(powerset(X1))))) ),
inference(superposition,[status(thm)],[c_15474,c_300]) ).
tcf(c_15477,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ in(X0,sK18(sK17(sK17(powerset(X1))))) ),
inference(superposition,[status(thm)],[c_15474,c_299]) ).
tcf(c_15478,plain,
! [X0: $i,X1: $i] :
( in(X0,X1)
| ~ in(X0,sK18(sK17(sK17(powerset(X1))))) ),
inference(superposition,[status(thm)],[c_15474,c_92]) ).
tcf(c_15527,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(relation_dom(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_99,c_13062]) ).
tcf(c_15528,plain,
relation_dom(sK18(powerset(relation_dom(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_114,c_13062]) ).
tcf(c_15529,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(relation_dom(sK18(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12738,c_13062]) ).
tcf(c_15530,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(relation_dom(sK18(powerset(sK18(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13358,c_13062]) ).
tcf(c_15531,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(relation_dom(sK18(sK17(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13470,c_13062]) ).
tcf(c_15532,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(relation_dom(sK18(powerset(sK18(sK17(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13469,c_13062]) ).
tcf(c_15553,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(relation_dom(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_99,c_13258]) ).
tcf(c_15554,plain,
sK18(powerset(relation_dom(relation_dom(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_114,c_13258]) ).
tcf(c_15555,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(relation_dom(sK18(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12738,c_13258]) ).
tcf(c_15556,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(relation_dom(sK18(powerset(sK18(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13358,c_13258]) ).
tcf(c_15557,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(relation_dom(sK18(sK17(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13470,c_13258]) ).
tcf(c_15558,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(relation_dom(sK18(powerset(sK18(sK17(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13469,c_13258]) ).
tcf(c_15588,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(relation_dom(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_99,c_14397]) ).
tcf(c_15589,plain,
sK18(sK17(powerset(relation_dom(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_114,c_14397]) ).
tcf(c_15590,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(relation_dom(sK18(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12738,c_14397]) ).
tcf(c_15591,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(relation_dom(sK18(powerset(sK18(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13358,c_14397]) ).
tcf(c_15592,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(relation_dom(sK18(sK17(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13470,c_14397]) ).
tcf(c_15593,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(relation_dom(sK18(powerset(sK18(sK17(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13469,c_14397]) ).
tcf(c_15645,plain,
( empty(sK18(powerset(empty_set)))
| in(sK18(sK17(empty_set)),empty_set) ),
inference(superposition,[status(thm)],[c_12958,c_12994]) ).
tcf(c_15646,plain,
! [X0: $i,X1: $i] :
( empty(sK18(powerset(relation_image(X0,X1))))
| ( apply(X0,sK4(X0,X1,sK18(sK17(sK18(powerset(relation_image(X0,X1))))))) = sK18(sK17(sK18(powerset(relation_image(X0,X1))))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_12994,c_60]) ).
tcf(c_15647,plain,
! [X0: $i,X1: $i] :
( empty(sK18(powerset(relation_inverse_image(X0,X1))))
| in(apply(X0,sK18(sK17(sK18(powerset(relation_inverse_image(X0,X1)))))),X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_12994,c_72]) ).
tcf(c_15648,plain,
! [X0: $i,X1: $i] :
( empty(sK18(powerset(relation_inverse_image(X0,X1))))
| in(sK18(sK17(sK18(powerset(relation_inverse_image(X0,X1))))),relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_12994,c_71]) ).
tcf(c_15649,plain,
! [X0: $i] :
( empty(sK18(powerset(X0)))
| ~ in(X0,sK18(sK17(sK18(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_12994,c_98]) ).
tcf(c_15652,plain,
! [X0: $i] :
( empty(X0)
| empty(sK18(powerset(sK17(X0))))
| element(sK18(sK17(sK18(powerset(sK17(X0))))),X0) ),
inference(superposition,[status(thm)],[c_12994,c_14688]) ).
tcf(c_15653,plain,
! [X0: $i] :
( empty(X0)
| empty(sK18(powerset(sK17(X0))))
| in(sK18(sK17(sK18(powerset(sK17(X0))))),X0) ),
inference(superposition,[status(thm)],[c_12994,c_12618]) ).
tcf(c_15654,plain,
! [X0: $i] :
( empty(sK18(powerset(sK18(powerset(X0)))))
| element(sK18(sK17(sK18(powerset(sK18(powerset(X0)))))),X0) ),
inference(superposition,[status(thm)],[c_12994,c_14689]) ).
tcf(c_15656,plain,
! [X0: $i] :
( empty(sK18(powerset(sK18(powerset(X0)))))
| in(sK18(sK17(sK18(powerset(sK18(powerset(X0)))))),X0) ),
inference(superposition,[status(thm)],[c_12994,c_12619]) ).
tcf(c_15658,plain,
! [X0: $i] :
( empty(sK18(powerset(sK18(sK17(powerset(X0))))))
| element(sK18(sK17(sK18(powerset(sK18(sK17(powerset(X0))))))),X0) ),
inference(superposition,[status(thm)],[c_12994,c_14693]) ).
tcf(c_15660,plain,
! [X0: $i] :
( empty(sK18(powerset(sK18(sK17(powerset(X0))))))
| in(sK18(sK17(sK18(powerset(sK18(sK17(powerset(X0))))))),X0) ),
inference(superposition,[status(thm)],[c_12994,c_13032]) ).
tcf(c_15661,plain,
( empty(empty_set)
| in(sK18(sK17(empty_set)),empty_set) ),
inference(light_normalisation,[status(thm)],[c_15645,c_12958]) ).
tcf(c_15716,plain,
! [X0: $i] :
( ( relation_dom(sK18(sK17(powerset(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_99,c_13494]) ).
tcf(c_15717,plain,
relation_dom(sK18(sK17(powerset(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_114,c_13494]) ).
tcf(c_15718,plain,
! [X0: $i] :
( ( relation_dom(sK18(sK17(powerset(sK18(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12738,c_13494]) ).
tcf(c_15719,plain,
! [X0: $i] :
( ( relation_dom(sK18(sK17(powerset(sK18(powerset(sK18(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13358,c_13494]) ).
tcf(c_15720,plain,
! [X0: $i] :
( ( relation_dom(sK18(sK17(powerset(sK18(sK17(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13470,c_13494]) ).
tcf(c_15721,plain,
! [X0: $i] :
( ( relation_dom(sK18(sK17(powerset(sK18(powerset(sK18(sK17(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13469,c_13494]) ).
tcf(c_15742,plain,
( empty(sK18(powerset(empty_set)))
| element(sK18(sK17(empty_set)),empty_set) ),
inference(superposition,[status(thm)],[c_12958,c_14728]) ).
tcf(c_15743,plain,
! [X0: $i] :
( empty(sK18(powerset(powerset(X0))))
| subset(sK18(sK17(sK18(powerset(powerset(X0))))),X0) ),
inference(superposition,[status(thm)],[c_14728,c_88]) ).
tcf(c_15745,plain,
( empty(empty_set)
| element(sK18(sK17(empty_set)),empty_set) ),
inference(light_normalisation,[status(thm)],[c_15742,c_12958]) ).
tcf(c_15755,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X0,X1,sK18(sK17(sK17(powerset(X2))))),X2)
| ( sK18(sK17(sK17(powerset(X2)))) = relation_image(X0,X1) )
| ( apply(X0,sK3(X0,X1,sK18(sK17(sK17(powerset(X2)))))) = sK2(X0,X1,sK18(sK17(sK17(powerset(X2))))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_56,c_15476]) ).
tcf(c_15756,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X0,X2,sK18(sK17(sK17(powerset(X1))))),X1)
| in(sK3(X0,X2,sK18(sK17(sK17(powerset(X1))))),relation_dom(X0))
| ( sK18(sK17(sK17(powerset(X1)))) = relation_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_54,c_15476]) ).
tcf(c_15757,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X0,X2,sK18(sK17(sK17(powerset(X1))))),X1)
| in(sK3(X0,X2,sK18(sK17(sK17(powerset(X1))))),X2)
| ( sK18(sK17(sK17(powerset(X1)))) = relation_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_55,c_15476]) ).
tcf(c_15758,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK3(X0,sK18(sK17(sK17(powerset(X1)))),X2),X1)
| in(sK2(X0,sK18(sK17(sK17(powerset(X1)))),X2),X2)
| ( relation_image(X0,sK18(sK17(sK17(powerset(X1))))) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_55,c_15476]) ).
tcf(c_15759,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK4(X1,sK18(sK17(sK17(powerset(X2)))),X0),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,sK18(sK17(sK17(powerset(X2)))))) ),
inference(superposition,[status(thm)],[c_59,c_15476]) ).
tcf(c_15760,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,sK18(sK17(sK17(powerset(X1)))),X2),X2)
| element(apply(X0,sK7(X0,sK18(sK17(sK17(powerset(X1)))),X2)),X1)
| ( relation_inverse_image(X0,sK18(sK17(sK17(powerset(X1))))) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_69,c_15476]) ).
tcf(c_15761,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK7(X0,X2,sK18(sK17(sK17(powerset(X1))))),X1)
| in(apply(X0,sK7(X0,X2,sK18(sK17(sK17(powerset(X1)))))),X2)
| ( sK18(sK17(sK17(powerset(X1)))) = relation_inverse_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_69,c_15476]) ).
tcf(c_15762,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK7(X0,X2,sK18(sK17(sK17(powerset(X1))))),X1)
| in(sK7(X0,X2,sK18(sK17(sK17(powerset(X1))))),relation_dom(X0))
| ( sK18(sK17(sK17(powerset(X1)))) = relation_inverse_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_68,c_15476]) ).
tcf(c_15763,plain,
! [X0: $i,X1: $i] :
( subset(sK18(sK17(sK17(powerset(X0)))),X1)
| element(sK13(sK18(sK17(sK17(powerset(X0)))),X1),X0) ),
inference(superposition,[status(thm)],[c_91,c_15476]) ).
tcf(c_15764,plain,
! [X0: $i] :
( empty(sK18(sK17(sK17(powerset(X0)))))
| element(sK18(sK18(sK17(sK17(powerset(X0))))),X0) ),
inference(superposition,[status(thm)],[c_12501,c_15476]) ).
tcf(c_15765,plain,
! [X0: $i] :
( empty(sK18(powerset(sK18(sK17(sK17(powerset(X0)))))))
| element(sK18(sK18(powerset(sK18(sK17(sK17(powerset(X0))))))),X0) ),
inference(superposition,[status(thm)],[c_12693,c_15476]) ).
tcf(c_15766,plain,
! [X0: $i] :
( empty(sK18(sK17(sK17(powerset(X0)))))
| element(sK18(sK17(sK18(sK17(sK17(powerset(X0)))))),X0) ),
inference(superposition,[status(thm)],[c_12981,c_15476]) ).
tcf(c_15767,plain,
! [X0: $i] :
( empty(sK18(sK17(sK17(powerset(X0)))))
| element(sK18(sK17(sK17(sK18(sK17(sK17(powerset(X0))))))),X0) ),
inference(superposition,[status(thm)],[c_15371,c_15476]) ).
tcf(c_15768,plain,
! [X0: $i] :
( empty(sK18(powerset(sK18(sK17(sK17(powerset(X0)))))))
| element(sK18(sK17(sK18(powerset(sK18(sK17(sK17(powerset(X0)))))))),X0) ),
inference(superposition,[status(thm)],[c_12994,c_15476]) ).
tcf(c_15874,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK18(sK17(sK17(powerset(X1)))) = relation_image(X0,X2) )
| ( apply(X0,sK3(X0,X2,sK18(sK17(sK17(powerset(X1)))))) = sK2(X0,X2,sK18(sK17(sK17(powerset(X1))))) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_56,c_15477]) ).
tcf(c_15875,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(X0,X2,sK18(sK17(sK17(powerset(X1))))),relation_dom(X0))
| ( sK18(sK17(sK17(powerset(X1)))) = relation_image(X0,X2) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_54,c_15477]) ).
tcf(c_15876,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(X0,X2,sK18(sK17(sK17(powerset(X1))))),X2)
| ( sK18(sK17(sK17(powerset(X1)))) = relation_image(X0,X2) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_55,c_15477]) ).
tcf(c_15877,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,sK18(sK17(sK17(powerset(X1)))),X2),X2)
| ( relation_image(X0,sK18(sK17(sK17(powerset(X1))))) = X2 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_55,c_15477]) ).
tcf(c_15878,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(X2)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,sK18(sK17(sK17(powerset(X2)))))) ),
inference(superposition,[status(thm)],[c_59,c_15477]) ).
tcf(c_15879,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,sK18(sK17(sK17(powerset(X1)))),X2),X2)
| ( relation_inverse_image(X0,sK18(sK17(sK17(powerset(X1))))) = X2 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_69,c_15477]) ).
tcf(c_15880,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X0,sK7(X0,X2,sK18(sK17(sK17(powerset(X1)))))),X2)
| ( sK18(sK17(sK17(powerset(X1)))) = relation_inverse_image(X0,X2) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_69,c_15477]) ).
tcf(c_15881,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X2,sK18(sK17(sK17(powerset(X1))))),relation_dom(X0))
| ( sK18(sK17(sK17(powerset(X1)))) = relation_inverse_image(X0,X2) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_68,c_15477]) ).
tcf(c_15882,plain,
! [X0: $i,X1: $i] :
( subset(sK18(sK17(sK17(powerset(X0)))),X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_91,c_15477]) ).
tcf(c_15885,plain,
! [X0: $i] :
( empty(sK18(sK17(sK17(powerset(X0)))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12981,c_15477]) ).
tcf(c_15887,plain,
! [X0: $i] :
( empty(sK18(powerset(sK18(sK17(sK17(powerset(X0)))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12994,c_15477]) ).
tcf(c_15957,plain,
! [X0: $i] :
( ( relation_dom(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15885,c_13494]) ).
tcf(c_15958,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(relation_dom(sK18(sK17(sK17(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15885,c_14397]) ).
tcf(c_15959,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(relation_dom(sK18(sK17(sK17(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15885,c_13258]) ).
tcf(c_15960,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(relation_dom(sK18(sK17(sK17(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15885,c_13062]) ).
tcf(c_15961,plain,
! [X0: $i] :
( ( sK18(powerset(sK18(powerset(sK18(sK17(sK17(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15885,c_12959]) ).
tcf(c_15962,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK18(powerset(sK18(sK17(sK17(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15885,c_12766]) ).
tcf(c_15963,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK18(sK17(sK17(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15885,c_12718]) ).
tcf(c_15964,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(sK17(sK17(powerset(X0))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15885,c_12604]) ).
tcf(c_15965,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15885,c_13495]) ).
tcf(c_15966,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(sK18(sK17(sK17(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15885,c_12957]) ).
tcf(c_15967,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(sK18(sK17(sK17(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15885,c_12768]) ).
tcf(c_15968,plain,
! [X0: $i] :
( ( sK18(powerset(sK18(sK17(sK17(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15885,c_12769]) ).
tcf(c_15969,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK18(sK17(sK17(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15885,c_12674]) ).
tcf(c_15970,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK18(sK17(sK17(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15885,c_12550]) ).
tcf(c_15971,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(sK17(powerset(X0)))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15885,c_93]) ).
tcf(c_15972,plain,
! [X0: $i] :
( ( relation_dom(sK18(sK17(sK17(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15885,c_12406]) ).
tcf(c_15973,plain,
! [X0: $i] :
( ( sK18(sK17(sK17(powerset(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15885,c_94]) ).
tcf(c_15974,plain,
! [X0: $i] :
( one_to_one(sK18(sK17(sK17(powerset(X0)))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15885,c_5773]) ).
tcf(c_15975,plain,
! [X0: $i] :
( relation(sK18(sK17(sK17(powerset(X0)))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15885,c_77]) ).
tcf(c_15976,plain,
! [X0: $i] :
( function(sK18(sK17(sK17(powerset(X0)))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15885,c_66]) ).
tcf(c_16098,plain,
! [X0: $i] :
( one_to_one(sK18(sK17(sK17(powerset(X0)))))
| ( apply(sK18(sK17(sK17(powerset(X0)))),sK11(sK18(sK17(sK17(powerset(X0)))))) = apply(sK18(sK17(sK17(powerset(X0)))),sK12(sK18(sK17(sK17(powerset(X0)))))) )
| ~ empty(X0)
| ~ function(sK18(sK17(sK17(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_15975,c_84]) ).
tcf(c_16142,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,sK18(sK17(sK17(powerset(X2))))),X2)
| ( sK18(sK17(sK17(powerset(X2)))) = relation_image(X0,X1) )
| ( apply(X0,sK3(X0,X1,sK18(sK17(sK17(powerset(X2)))))) = sK2(X0,X1,sK18(sK17(sK17(powerset(X2))))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_56,c_15478]) ).
tcf(c_16143,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X2,sK18(sK17(sK17(powerset(X1))))),X1)
| in(sK3(X0,X2,sK18(sK17(sK17(powerset(X1))))),relation_dom(X0))
| ( sK18(sK17(sK17(powerset(X1)))) = relation_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_54,c_15478]) ).
tcf(c_16144,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(X0,X2,sK18(sK17(sK17(powerset(X1))))),X2)
| in(sK2(X0,X2,sK18(sK17(sK17(powerset(X1))))),X1)
| ( sK18(sK17(sK17(powerset(X1)))) = relation_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_55,c_15478]) ).
tcf(c_16145,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(X0,sK18(sK17(sK17(powerset(X1)))),X2),X1)
| in(sK2(X0,sK18(sK17(sK17(powerset(X1)))),X2),X2)
| ( relation_image(X0,sK18(sK17(sK17(powerset(X1))))) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_55,c_15478]) ).
tcf(c_16146,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK4(X1,sK18(sK17(sK17(powerset(X2)))),X0),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,sK18(sK17(sK17(powerset(X2)))))) ),
inference(superposition,[status(thm)],[c_59,c_15478]) ).
tcf(c_16147,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,sK18(sK17(sK17(powerset(X1)))),X2),X2)
| in(apply(X0,sK7(X0,sK18(sK17(sK17(powerset(X1)))),X2)),X1)
| ( relation_inverse_image(X0,sK18(sK17(sK17(powerset(X1))))) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_69,c_15478]) ).
tcf(c_16148,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X2,sK18(sK17(sK17(powerset(X1))))),X1)
| in(apply(X0,sK7(X0,X2,sK18(sK17(sK17(powerset(X1)))))),X2)
| ( sK18(sK17(sK17(powerset(X1)))) = relation_inverse_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_69,c_15478]) ).
tcf(c_16149,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X2,sK18(sK17(sK17(powerset(X1))))),X1)
| in(sK7(X0,X2,sK18(sK17(sK17(powerset(X1))))),relation_dom(X0))
| ( sK18(sK17(sK17(powerset(X1)))) = relation_inverse_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_68,c_15478]) ).
tcf(c_16150,plain,
! [X0: $i,X1: $i] :
( subset(sK18(sK17(sK17(powerset(X0)))),X1)
| in(sK13(sK18(sK17(sK17(powerset(X0)))),X1),X0) ),
inference(superposition,[status(thm)],[c_91,c_15478]) ).
tcf(c_16151,plain,
! [X0: $i] :
( empty(sK18(sK17(sK17(powerset(X0)))))
| in(sK18(sK18(sK17(sK17(powerset(X0))))),X0) ),
inference(superposition,[status(thm)],[c_12501,c_15478]) ).
tcf(c_16152,plain,
! [X0: $i] :
( empty(sK18(powerset(sK18(sK17(sK17(powerset(X0)))))))
| in(sK18(sK18(powerset(sK18(sK17(sK17(powerset(X0))))))),X0) ),
inference(superposition,[status(thm)],[c_12693,c_15478]) ).
tcf(c_16153,plain,
! [X0: $i] :
( empty(sK18(sK17(sK17(powerset(X0)))))
| in(sK18(sK17(sK18(sK17(sK17(powerset(X0)))))),X0) ),
inference(superposition,[status(thm)],[c_12981,c_15478]) ).
tcf(c_16154,plain,
! [X0: $i] :
( empty(sK18(sK17(sK17(powerset(X0)))))
| in(sK18(sK17(sK17(sK18(sK17(sK17(powerset(X0))))))),X0) ),
inference(superposition,[status(thm)],[c_15371,c_15478]) ).
tcf(c_16155,plain,
! [X0: $i] :
( empty(sK18(powerset(sK18(sK17(sK17(powerset(X0)))))))
| in(sK18(sK17(sK18(powerset(sK18(sK17(sK17(powerset(X0)))))))),X0) ),
inference(superposition,[status(thm)],[c_12994,c_15478]) ).
tcf(c_16250,plain,
! [X0: $i] :
( one_to_one(X0)
| ~ empty(relation_dom(X0))
| ~ relation(X0) ),
inference(global_subsumption_just,[status(thm)],[c_12647,c_101,c_145]) ).
tcf(c_16251,plain,
! [X0: $i] :
( one_to_one(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(renaming,[status(thm)],[c_16250]) ).
tcf(c_16287,plain,
! [X0: $i] :
( ( sK18(sK17(sK17(powerset(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_99,c_15973]) ).
tcf(c_16288,plain,
sK18(sK17(sK17(powerset(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_114,c_15973]) ).
tcf(c_16289,plain,
! [X0: $i] :
( ( sK18(sK17(sK17(powerset(sK18(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12738,c_15973]) ).
tcf(c_16290,plain,
! [X0: $i] :
( ( sK18(sK17(sK17(powerset(sK18(powerset(sK18(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13358,c_15973]) ).
tcf(c_16291,plain,
! [X0: $i] :
( ( sK18(sK17(sK17(powerset(sK18(sK17(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13470,c_15973]) ).
tcf(c_16292,plain,
! [X0: $i] :
( ( sK18(sK17(sK17(powerset(sK18(powerset(sK18(sK17(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13469,c_15973]) ).
tcf(c_16293,plain,
! [X0: $i] :
( ( sK18(sK17(sK17(powerset(sK18(sK17(sK17(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15885,c_15973]) ).
tcf(c_16364,plain,
( empty(sK17(sK17(powerset(empty_set))))
| ~ in(sK17(sK17(powerset(empty_set))),empty_set) ),
inference(superposition,[status(thm)],[c_16288,c_12526]) ).
tcf(c_16365,plain,
( empty(sK17(sK17(powerset(empty_set))))
| in(empty_set,sK17(sK17(powerset(empty_set)))) ),
inference(superposition,[status(thm)],[c_16288,c_12501]) ).
tcf(c_16366,plain,
element(empty_set,sK17(sK17(powerset(empty_set)))),
inference(superposition,[status(thm)],[c_16288,c_111]) ).
tcf(c_16389,plain,
! [X0: $i] :
( in(sK13(empty_set,X0),empty_set)
| subset(sK18(powerset(empty_set)),X0) ),
inference(superposition,[status(thm)],[c_12958,c_12692]) ).
tcf(c_16390,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK18(powerset(relation_image(X0,X1))),X2)
| ( apply(X0,sK4(X0,X1,sK13(sK18(powerset(relation_image(X0,X1))),X2))) = sK13(sK18(powerset(relation_image(X0,X1))),X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_12692,c_60]) ).
tcf(c_16391,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK18(powerset(relation_inverse_image(X0,X1))),X2)
| in(apply(X0,sK13(sK18(powerset(relation_inverse_image(X0,X1))),X2)),X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_12692,c_72]) ).
tcf(c_16392,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK18(powerset(relation_inverse_image(X0,X1))),X2)
| in(sK13(sK18(powerset(relation_inverse_image(X0,X1))),X2),relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_12692,c_71]) ).
tcf(c_16394,plain,
! [X0: $i,X1: $i] :
( subset(sK18(powerset(X0)),X1)
| ~ in(X0,sK13(sK18(powerset(X0)),X1)) ),
inference(superposition,[status(thm)],[c_12692,c_98]) ).
tcf(c_16397,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| subset(sK18(powerset(sK17(X0))),X1)
| element(sK13(sK18(powerset(sK17(X0))),X1),X0) ),
inference(superposition,[status(thm)],[c_12692,c_14688]) ).
tcf(c_16398,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| subset(sK18(powerset(sK17(X0))),X1)
| in(sK13(sK18(powerset(sK17(X0))),X1),X0) ),
inference(superposition,[status(thm)],[c_12692,c_12618]) ).
tcf(c_16399,plain,
! [X0: $i,X1: $i] :
( subset(sK18(powerset(sK18(powerset(X0)))),X1)
| element(sK13(sK18(powerset(sK18(powerset(X0)))),X1),X0) ),
inference(superposition,[status(thm)],[c_12692,c_14689]) ).
tcf(c_16400,plain,
! [X0: $i,X1: $i] :
( subset(sK18(powerset(sK18(powerset(X0)))),X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12692,c_13313]) ).
tcf(c_16401,plain,
! [X0: $i,X1: $i] :
( subset(sK18(powerset(sK18(powerset(X0)))),X1)
| in(sK13(sK18(powerset(sK18(powerset(X0)))),X1),X0) ),
inference(superposition,[status(thm)],[c_12692,c_12619]) ).
tcf(c_16402,plain,
! [X0: $i] : subset(sK18(powerset(empty_set)),X0),
inference(superposition,[status(thm)],[c_12692,c_13338]) ).
tcf(c_16403,plain,
! [X0: $i,X1: $i] :
( subset(sK18(powerset(sK18(sK17(powerset(X0))))),X1)
| element(sK13(sK18(powerset(sK18(sK17(powerset(X0))))),X1),X0) ),
inference(superposition,[status(thm)],[c_12692,c_14693]) ).
tcf(c_16404,plain,
! [X0: $i,X1: $i] :
( subset(sK18(powerset(sK18(sK17(powerset(X0))))),X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12692,c_13316]) ).
tcf(c_16405,plain,
! [X0: $i,X1: $i] :
( subset(sK18(powerset(sK18(sK17(powerset(X0))))),X1)
| in(sK13(sK18(powerset(sK18(sK17(powerset(X0))))),X1),X0) ),
inference(superposition,[status(thm)],[c_12692,c_13032]) ).
tcf(c_16406,plain,
! [X0: $i,X1: $i] :
( subset(sK18(powerset(sK18(sK17(sK17(powerset(X0)))))),X1)
| in(sK13(sK18(powerset(sK18(sK17(sK17(powerset(X0)))))),X1),X0) ),
inference(superposition,[status(thm)],[c_12692,c_15478]) ).
tcf(c_16407,plain,
! [X0: $i,X1: $i] :
( subset(sK18(powerset(sK18(sK17(sK17(powerset(X0)))))),X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12692,c_15477]) ).
tcf(c_16408,plain,
! [X0: $i,X1: $i] :
( subset(sK18(powerset(sK18(sK17(sK17(powerset(X0)))))),X1)
| element(sK13(sK18(powerset(sK18(sK17(sK17(powerset(X0)))))),X1),X0) ),
inference(superposition,[status(thm)],[c_12692,c_15476]) ).
tcf(c_16412,plain,
! [X0: $i] :
( subset(empty_set,X0)
| in(sK13(empty_set,X0),empty_set) ),
inference(light_normalisation,[status(thm)],[c_16389,c_12958]) ).
tcf(c_16503,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,X2)
| ~ empty(X1)
| ~ in(X0,sK18(powerset(sK18(powerset(X1))))) ),
inference(superposition,[status(thm)],[c_16400,c_300]) ).
tcf(c_16504,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(X2)
| ~ empty(X1)
| ~ in(X0,sK18(powerset(sK18(powerset(X1))))) ),
inference(superposition,[status(thm)],[c_16400,c_299]) ).
tcf(c_16505,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ empty(X1)
| ~ in(X0,sK18(powerset(sK18(powerset(X1))))) ),
inference(superposition,[status(thm)],[c_16400,c_92]) ).
tcf(c_16523,plain,
! [X0: $i] :
( ( sK18(sK17(sK17(powerset(sK18(powerset(sK18(sK17(sK17(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15887,c_15973]) ).
tcf(c_16524,plain,
! [X0: $i] :
( ( relation_dom(sK18(sK17(powerset(sK18(powerset(sK18(sK17(sK17(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15887,c_13494]) ).
tcf(c_16525,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(relation_dom(sK18(powerset(sK18(sK17(sK17(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15887,c_14397]) ).
tcf(c_16526,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(relation_dom(sK18(powerset(sK18(sK17(sK17(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15887,c_13258]) ).
tcf(c_16527,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(relation_dom(sK18(powerset(sK18(sK17(sK17(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15887,c_13062]) ).
tcf(c_16528,plain,
! [X0: $i] :
( ( sK18(powerset(sK18(powerset(sK18(powerset(sK18(sK17(sK17(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15887,c_12959]) ).
tcf(c_16529,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK18(powerset(sK18(powerset(sK18(sK17(sK17(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15887,c_12766]) ).
tcf(c_16530,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK18(powerset(sK18(sK17(sK17(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15887,c_12718]) ).
tcf(c_16531,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(powerset(sK18(sK17(sK17(powerset(X0))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15887,c_12604]) ).
tcf(c_16532,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(sK18(powerset(sK18(sK17(sK17(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15887,c_13495]) ).
tcf(c_16533,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(sK18(powerset(sK18(sK17(sK17(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15887,c_12957]) ).
tcf(c_16534,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(sK18(powerset(sK18(sK17(sK17(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15887,c_12768]) ).
tcf(c_16536,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK18(powerset(sK18(sK17(sK17(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15887,c_12674]) ).
tcf(c_16538,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK18(sK17(sK17(powerset(X0)))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15887,c_93]) ).
tcf(c_16541,plain,
! [X0: $i] :
( one_to_one(sK18(powerset(sK18(sK17(sK17(powerset(X0)))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15887,c_5773]) ).
tcf(c_16542,plain,
! [X0: $i] :
( relation(sK18(powerset(sK18(sK17(sK17(powerset(X0)))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15887,c_77]) ).
tcf(c_16543,plain,
! [X0: $i] :
( function(sK18(powerset(sK18(sK17(sK17(powerset(X0)))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15887,c_66]) ).
tcf(c_16674,plain,
( empty(sK17(powerset(empty_set)))
| empty(sK17(sK17(powerset(empty_set))))
| in(empty_set,sK17(powerset(empty_set))) ),
inference(superposition,[status(thm)],[c_16365,c_12618]) ).
tcf(c_16682,plain,
! [X0: $i] :
( subset(sK18(powerset(empty_set)),X0)
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_14398,c_16404]) ).
tcf(c_16683,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,X2)
| ~ empty(X1)
| ~ in(X0,sK18(powerset(sK18(sK17(powerset(X1)))))) ),
inference(superposition,[status(thm)],[c_16404,c_300]) ).
tcf(c_16684,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(X2)
| ~ empty(X1)
| ~ in(X0,sK18(powerset(sK18(sK17(powerset(X1)))))) ),
inference(superposition,[status(thm)],[c_16404,c_299]) ).
tcf(c_16685,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ empty(X1)
| ~ in(X0,sK18(powerset(sK18(sK17(powerset(X1)))))) ),
inference(superposition,[status(thm)],[c_16404,c_92]) ).
tcf(c_16686,plain,
! [X0: $i] :
( subset(empty_set,X0)
| ~ empty(empty_set) ),
inference(light_normalisation,[status(thm)],[c_16682,c_12958]) ).
tcf(c_16709,plain,
! [X0: $i] :
( one_to_one(sK18(powerset(sK18(sK17(sK17(powerset(X0)))))))
| ( apply(sK18(powerset(sK18(sK17(sK17(powerset(X0)))))),sK11(sK18(powerset(sK18(sK17(sK17(powerset(X0)))))))) = apply(sK18(powerset(sK18(sK17(sK17(powerset(X0)))))),sK12(sK18(powerset(sK18(sK17(sK17(powerset(X0)))))))) )
| ~ empty(X0)
| ~ function(sK18(powerset(sK18(sK17(sK17(powerset(X0))))))) ),
inference(superposition,[status(thm)],[c_16542,c_84]) ).
tcf(c_16726,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(relation_image(X0,X1))
| subset(sK17(relation_image(X0,X1)),X2)
| ( apply(X0,sK4(X0,X1,sK13(sK17(relation_image(X0,X1)),X2))) = sK13(sK17(relation_image(X0,X1)),X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_12705,c_60]) ).
tcf(c_16727,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(relation_inverse_image(X0,X1))
| subset(sK17(relation_inverse_image(X0,X1)),X2)
| in(apply(X0,sK13(sK17(relation_inverse_image(X0,X1)),X2)),X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_12705,c_72]) ).
tcf(c_16728,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(relation_inverse_image(X0,X1))
| subset(sK17(relation_inverse_image(X0,X1)),X2)
| in(sK13(sK17(relation_inverse_image(X0,X1)),X2),relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_12705,c_71]) ).
tcf(c_16730,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| subset(sK17(X0),X1)
| ~ in(X0,sK13(sK17(X0),X1)) ),
inference(superposition,[status(thm)],[c_12705,c_98]) ).
tcf(c_16733,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| empty(sK17(X0))
| subset(sK17(sK17(X0)),X1)
| element(sK13(sK17(sK17(X0)),X1),X0) ),
inference(superposition,[status(thm)],[c_12705,c_14688]) ).
tcf(c_16734,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| empty(sK17(X0))
| subset(sK17(sK17(X0)),X1)
| in(sK13(sK17(sK17(X0)),X1),X0) ),
inference(superposition,[status(thm)],[c_12705,c_12618]) ).
tcf(c_16735,plain,
! [X0: $i,X1: $i] :
( empty(sK18(powerset(X0)))
| subset(sK17(sK18(powerset(X0))),X1)
| element(sK13(sK17(sK18(powerset(X0))),X1),X0) ),
inference(superposition,[status(thm)],[c_12705,c_14689]) ).
tcf(c_16736,plain,
! [X0: $i,X1: $i] :
( empty(sK18(powerset(X0)))
| subset(sK17(sK18(powerset(X0))),X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12705,c_13313]) ).
tcf(c_16737,plain,
! [X0: $i,X1: $i] :
( empty(sK18(powerset(X0)))
| subset(sK17(sK18(powerset(X0))),X1)
| in(sK13(sK17(sK18(powerset(X0))),X1),X0) ),
inference(superposition,[status(thm)],[c_12705,c_12619]) ).
tcf(c_16739,plain,
! [X0: $i,X1: $i] :
( empty(sK18(sK17(powerset(X0))))
| subset(sK17(sK18(sK17(powerset(X0)))),X1)
| element(sK13(sK17(sK18(sK17(powerset(X0)))),X1),X0) ),
inference(superposition,[status(thm)],[c_12705,c_14693]) ).
tcf(c_16740,plain,
! [X0: $i,X1: $i] :
( empty(sK18(sK17(powerset(X0))))
| subset(sK17(sK18(sK17(powerset(X0)))),X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12705,c_13316]) ).
tcf(c_16741,plain,
! [X0: $i,X1: $i] :
( empty(sK18(sK17(powerset(X0))))
| subset(sK17(sK18(sK17(powerset(X0)))),X1)
| in(sK13(sK17(sK18(sK17(powerset(X0)))),X1),X0) ),
inference(superposition,[status(thm)],[c_12705,c_13032]) ).
tcf(c_16742,plain,
! [X0: $i,X1: $i] :
( empty(sK18(sK17(sK17(powerset(X0)))))
| subset(sK17(sK18(sK17(sK17(powerset(X0))))),X1)
| in(sK13(sK17(sK18(sK17(sK17(powerset(X0))))),X1),X0) ),
inference(superposition,[status(thm)],[c_12705,c_15478]) ).
tcf(c_16743,plain,
! [X0: $i,X1: $i] :
( empty(sK18(sK17(sK17(powerset(X0)))))
| subset(sK17(sK18(sK17(sK17(powerset(X0))))),X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12705,c_15477]) ).
tcf(c_16744,plain,
! [X0: $i,X1: $i] :
( empty(sK18(sK17(sK17(powerset(X0)))))
| subset(sK17(sK18(sK17(sK17(powerset(X0))))),X1)
| element(sK13(sK17(sK18(sK17(sK17(powerset(X0))))),X1),X0) ),
inference(superposition,[status(thm)],[c_12705,c_15476]) ).
tcf(c_16852,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK18(powerset(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_99,c_12765]) ).
tcf(c_16853,plain,
relation_dom(relation_dom(relation_dom(sK18(powerset(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_114,c_12765]) ).
tcf(c_16855,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK18(powerset(sK18(powerset(sK18(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13358,c_12765]) ).
tcf(c_16857,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK18(powerset(sK18(powerset(sK18(sK17(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13469,c_12765]) ).
tcf(c_16859,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK18(powerset(sK18(powerset(sK18(sK17(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15887,c_12765]) ).
tcf(c_16879,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(relation_dom(X0))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_99,c_12767]) ).
tcf(c_16880,plain,
! [X0: $i] :
( ( sK18(powerset(empty_set)) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_114,c_12767]) ).
tcf(c_16882,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK18(powerset(sK18(powerset(X0)))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13358,c_12767]) ).
tcf(c_16884,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK18(powerset(sK18(sK17(powerset(X0))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13469,c_12767]) ).
tcf(c_16886,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK18(powerset(sK18(sK17(sK17(powerset(X0)))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15887,c_12767]) ).
tcf(c_16908,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| empty(sK18(powerset(powerset(X1))))
| ~ in(X0,sK18(sK18(powerset(powerset(X1))))) ),
inference(superposition,[status(thm)],[c_13045,c_300]) ).
tcf(c_16909,plain,
! [X0: $i,X1: $i] :
( empty(sK18(powerset(powerset(X1))))
| ~ empty(X1)
| ~ in(X0,sK18(sK18(powerset(powerset(X1))))) ),
inference(superposition,[status(thm)],[c_13045,c_299]) ).
tcf(c_16910,plain,
! [X0: $i,X1: $i] :
( in(X0,X1)
| empty(sK18(powerset(powerset(X1))))
| ~ in(X0,sK18(sK18(powerset(powerset(X1))))) ),
inference(superposition,[status(thm)],[c_13045,c_92]) ).
tcf(c_16986,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(sK18(powerset(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_99,c_13064]) ).
tcf(c_16987,plain,
relation_dom(sK18(powerset(sK18(powerset(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_114,c_13064]) ).
tcf(c_16989,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(sK18(powerset(sK18(powerset(sK18(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13358,c_13064]) ).
tcf(c_16991,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(sK18(powerset(sK18(powerset(sK18(sK17(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13469,c_13064]) ).
tcf(c_16993,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(sK18(powerset(sK18(powerset(sK18(sK17(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15887,c_13064]) ).
tcf(c_17015,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_15045,c_58]) ).
tcf(c_17023,plain,
! [X0: $i,X1: $i] : ~ in(X0,relation_image(empty_set,X1)),
inference(forward_subsumption_resolution,[status(thm)],[c_17015,c_15434,c_14279,c_113]) ).
tcf(c_17042,plain,
! [X0: $i] :
( one_to_one(X0)
| empty(relation_dom(X0))
| in(sK12(X0),relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_12821,c_96]) ).
tcf(c_17048,plain,
! [X0: $i,X1: $i] : ~ in(X0,relation_image(empty_set,X1)),
inference(global_subsumption_just,[status(thm)],[c_13122,c_17023]) ).
tcf(c_17050,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_17048]) ).
tcf(c_17051,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_17048]) ).
tcf(c_17052,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_17048]) ).
tcf(c_17053,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_17048]) ).
tcf(c_17054,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_17048]) ).
tcf(c_17055,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_17048]) ).
tcf(c_17056,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,relation_image(empty_set,X1),X2),X2)
| ( relation_inverse_image(X0,relation_image(empty_set,X1)) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_69,c_17048]) ).
tcf(c_17057,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X0,sK7(X0,X1,relation_image(empty_set,X2))),X1)
| ( relation_inverse_image(X0,X1) = relation_image(empty_set,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_69,c_17048]) ).
tcf(c_17058,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X1,relation_image(empty_set,X2)),relation_dom(X0))
| ( relation_inverse_image(X0,X1) = relation_image(empty_set,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_68,c_17048]) ).
tcf(c_17059,plain,
! [X0: $i,X1: $i] : subset(relation_image(empty_set,X0),X1),
inference(superposition,[status(thm)],[c_91,c_17048]) ).
tcf(c_17061,plain,
! [X0: $i,X1: $i] : subset(sK18(powerset(relation_image(empty_set,X0))),X1),
inference(superposition,[status(thm)],[c_12692,c_17048]) ).
tcf(c_17064,plain,
! [X0: $i] : empty(relation_image(empty_set,X0)),
inference(superposition,[status(thm)],[c_12981,c_17048]) ).
tcf(c_17066,plain,
! [X0: $i] : empty(sK18(powerset(relation_image(empty_set,X0)))),
inference(superposition,[status(thm)],[c_12994,c_17048]) ).
tcf(c_17070,plain,
! [X0: $i,X1: $i] :
( ~ function(empty_set)
| ~ relation(empty_set)
| ~ in(X0,empty_set)
| ~ in(X0,X1) ),
inference(light_normalisation,[status(thm)],[c_17054,c_12551]) ).
tcf(c_17161,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_13341]) ).
tcf(c_17162,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_13341]) ).
tcf(c_17163,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_13341]) ).
tcf(c_17164,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_13341]) ).
tcf(c_17166,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_13341]) ).
tcf(c_17167,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,relation_image(X1,empty_set),X2),X2)
| ( relation_inverse_image(X0,relation_image(X1,empty_set)) = X2 )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_69,c_13341]) ).
tcf(c_17168,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X0,sK7(X0,X2,relation_image(X1,empty_set))),X2)
| ( relation_inverse_image(X0,X2) = relation_image(X1,empty_set) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_69,c_13341]) ).
tcf(c_17169,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X2,relation_image(X1,empty_set)),relation_dom(X0))
| ( relation_inverse_image(X0,X2) = relation_image(X1,empty_set) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_68,c_13341]) ).
tcf(c_17170,plain,
! [X0: $i,X1: $i] :
( subset(relation_image(X0,empty_set),X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_91,c_13341]) ).
tcf(c_17172,plain,
! [X0: $i,X1: $i] :
( subset(sK18(powerset(relation_image(X0,empty_set))),X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_12692,c_13341]) ).
tcf(c_17174,plain,
! [X0: $i,X1: $i] :
( empty(relation_image(X0,empty_set))
| subset(sK17(relation_image(X0,empty_set)),X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_12705,c_13341]) ).
tcf(c_17175,plain,
! [X0: $i] :
( empty(relation_image(X0,empty_set))
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_12981,c_13341]) ).
tcf(c_17177,plain,
! [X0: $i] :
( empty(sK18(powerset(relation_image(X0,empty_set))))
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_12994,c_13341]) ).
tcf(c_17296,plain,
! [X0: $i] : relation_dom(sK18(powerset(sK18(powerset(relation_image(empty_set,X0)))))) = empty_set,
inference(superposition,[status(thm)],[c_17064,c_13064]) ).
tcf(c_17297,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(relation_image(empty_set,X1))) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17064,c_12767]) ).
tcf(c_17298,plain,
! [X0: $i] : relation_dom(relation_dom(relation_dom(sK18(powerset(relation_image(empty_set,X0)))))) = empty_set,
inference(superposition,[status(thm)],[c_17064,c_12765]) ).
tcf(c_17299,plain,
! [X0: $i] : sK18(sK17(sK17(powerset(relation_image(empty_set,X0))))) = empty_set,
inference(superposition,[status(thm)],[c_17064,c_15973]) ).
tcf(c_17300,plain,
! [X0: $i] : relation_dom(sK18(sK17(powerset(relation_image(empty_set,X0))))) = empty_set,
inference(superposition,[status(thm)],[c_17064,c_13494]) ).
tcf(c_17301,plain,
! [X0: $i] : sK18(sK17(powerset(relation_dom(relation_image(empty_set,X0))))) = empty_set,
inference(superposition,[status(thm)],[c_17064,c_14397]) ).
tcf(c_17302,plain,
! [X0: $i] : sK18(powerset(relation_dom(relation_dom(relation_image(empty_set,X0))))) = empty_set,
inference(superposition,[status(thm)],[c_17064,c_13258]) ).
tcf(c_17303,plain,
! [X0: $i] : relation_dom(sK18(powerset(relation_dom(relation_image(empty_set,X0))))) = empty_set,
inference(superposition,[status(thm)],[c_17064,c_13062]) ).
tcf(c_17304,plain,
! [X0: $i] : sK18(powerset(sK18(powerset(relation_image(empty_set,X0))))) = empty_set,
inference(superposition,[status(thm)],[c_17064,c_12959]) ).
tcf(c_17305,plain,
! [X0: $i] : relation_dom(relation_dom(sK18(powerset(relation_image(empty_set,X0))))) = empty_set,
inference(superposition,[status(thm)],[c_17064,c_12766]) ).
tcf(c_17306,plain,
! [X0: $i] : relation_dom(relation_dom(relation_dom(relation_dom(relation_image(empty_set,X0))))) = empty_set,
inference(superposition,[status(thm)],[c_17064,c_12718]) ).
tcf(c_17307,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_image(empty_set,X1)) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17064,c_12604]) ).
tcf(c_17308,plain,
! [X0: $i] : sK18(sK17(powerset(relation_image(empty_set,X0)))) = empty_set,
inference(superposition,[status(thm)],[c_17064,c_13495]) ).
tcf(c_17309,plain,
! [X0: $i] : sK18(powerset(relation_dom(relation_image(empty_set,X0)))) = empty_set,
inference(superposition,[status(thm)],[c_17064,c_12957]) ).
tcf(c_17310,plain,
! [X0: $i] : relation_dom(sK18(powerset(relation_image(empty_set,X0)))) = empty_set,
inference(superposition,[status(thm)],[c_17064,c_12768]) ).
tcf(c_17311,plain,
! [X0: $i] : sK18(powerset(relation_image(empty_set,X0))) = empty_set,
inference(superposition,[status(thm)],[c_17064,c_12769]) ).
tcf(c_17312,plain,
! [X0: $i] : relation_dom(relation_dom(relation_dom(relation_image(empty_set,X0)))) = empty_set,
inference(superposition,[status(thm)],[c_17064,c_12674]) ).
tcf(c_17313,plain,
! [X0: $i] : relation_dom(relation_dom(relation_image(empty_set,X0))) = empty_set,
inference(superposition,[status(thm)],[c_17064,c_12550]) ).
tcf(c_17314,plain,
! [X0: $i,X1: $i] :
( ( relation_image(empty_set,X1) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17064,c_93]) ).
tcf(c_17315,plain,
! [X0: $i] : relation_dom(relation_image(empty_set,X0)) = empty_set,
inference(superposition,[status(thm)],[c_17064,c_12406]) ).
tcf(c_17316,plain,
! [X0: $i] : relation_image(empty_set,X0) = empty_set,
inference(superposition,[status(thm)],[c_17064,c_94]) ).
tcf(c_17317,plain,
! [X0: $i] : one_to_one(relation_image(empty_set,X0)),
inference(superposition,[status(thm)],[c_17064,c_5773]) ).
tcf(c_17318,plain,
! [X0: $i] : relation(relation_image(empty_set,X0)),
inference(superposition,[status(thm)],[c_17064,c_77]) ).
tcf(c_17319,plain,
! [X0: $i] : function(relation_image(empty_set,X0)),
inference(superposition,[status(thm)],[c_17064,c_66]) ).
tcf(c_17420,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_17316,c_57]) ).
tcf(c_17424,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_17420,c_12551]) ).
tcf(c_17437,plain,
! [X0: $i] :
( subset(sK18(powerset(empty_set)),X0)
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_17316,c_17172]) ).
tcf(c_17438,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,X2)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,sK18(powerset(relation_image(X1,empty_set)))) ),
inference(superposition,[status(thm)],[c_17172,c_300]) ).
tcf(c_17439,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(X2)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,sK18(powerset(relation_image(X1,empty_set)))) ),
inference(superposition,[status(thm)],[c_17172,c_299]) ).
tcf(c_17440,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,sK18(powerset(relation_image(X1,empty_set)))) ),
inference(superposition,[status(thm)],[c_17172,c_92]) ).
tcf(c_17441,plain,
! [X0: $i] :
( subset(empty_set,X0)
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(light_normalisation,[status(thm)],[c_17437,c_12958]) ).
tcf(c_17462,plain,
! [X0: $i] :
( element(sK13(empty_set,X0),empty_set)
| subset(sK18(powerset(empty_set)),X0) ),
inference(superposition,[status(thm)],[c_12958,c_14725]) ).
tcf(c_17463,plain,
! [X0: $i,X1: $i] :
( subset(sK18(powerset(powerset(X0))),X1)
| subset(sK13(sK18(powerset(powerset(X0))),X1),X0) ),
inference(superposition,[status(thm)],[c_14725,c_88]) ).
tcf(c_17465,plain,
! [X0: $i] :
( subset(empty_set,X0)
| element(sK13(empty_set,X0),empty_set) ),
inference(light_normalisation,[status(thm)],[c_17462,c_12958]) ).
tcf(c_17475,plain,
! [X0: $i,X1: $i] :
( empty(powerset(X0))
| subset(sK17(powerset(X0)),X1)
| subset(sK13(sK17(powerset(X0)),X1),X0) ),
inference(superposition,[status(thm)],[c_14965,c_88]) ).
tcf(c_17477,plain,
! [X0: $i,X1: $i] :
( subset(sK17(powerset(X0)),X1)
| subset(sK13(sK17(powerset(X0)),X1),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17475,c_110]) ).
tcf(c_17487,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(X0))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_99,c_15230]) ).
tcf(c_17488,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(empty_set)) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_114,c_15230]) ).
tcf(c_17489,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK18(powerset(X0)))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12738,c_15230]) ).
tcf(c_17490,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK18(powerset(sK18(powerset(X0)))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13358,c_15230]) ).
tcf(c_17491,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK18(sK17(powerset(X0))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13470,c_15230]) ).
tcf(c_17492,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK18(powerset(sK18(sK17(powerset(X0))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13469,c_15230]) ).
tcf(c_17493,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK18(sK17(sK17(powerset(X0)))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15885,c_15230]) ).
tcf(c_17494,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK18(powerset(sK18(sK17(sK17(powerset(X0)))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15887,c_15230]) ).
tcf(c_17533,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_image(X0,empty_set))) = X1 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17175,c_15230]) ).
tcf(c_17534,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(sK18(powerset(relation_image(X0,empty_set)))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17175,c_13064]) ).
tcf(c_17535,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(relation_image(X0,empty_set))) = X1 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17175,c_12767]) ).
tcf(c_17536,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK18(powerset(relation_image(X0,empty_set)))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17175,c_12765]) ).
tcf(c_17537,plain,
! [X0: $i] :
( ( sK18(sK17(sK17(powerset(relation_image(X0,empty_set))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17175,c_15973]) ).
tcf(c_17538,plain,
! [X0: $i] :
( ( relation_dom(sK18(sK17(powerset(relation_image(X0,empty_set))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17175,c_13494]) ).
tcf(c_17539,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(relation_dom(relation_image(X0,empty_set))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17175,c_14397]) ).
tcf(c_17540,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(relation_dom(relation_image(X0,empty_set))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17175,c_13258]) ).
tcf(c_17541,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(relation_dom(relation_image(X0,empty_set))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17175,c_13062]) ).
tcf(c_17542,plain,
! [X0: $i] :
( ( sK18(powerset(sK18(powerset(relation_image(X0,empty_set))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17175,c_12959]) ).
tcf(c_17543,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK18(powerset(relation_image(X0,empty_set))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17175,c_12766]) ).
tcf(c_17544,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_17175,c_12718]) ).
tcf(c_17545,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_image(X0,empty_set)) = X1 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17175,c_12604]) ).
tcf(c_17546,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(relation_image(X0,empty_set)))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17175,c_13495]) ).
tcf(c_17547,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(relation_image(X0,empty_set)))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17175,c_12957]) ).
tcf(c_17548,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(relation_image(X0,empty_set)))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17175,c_12768]) ).
tcf(c_17549,plain,
! [X0: $i] :
( ( sK18(powerset(relation_image(X0,empty_set))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17175,c_12769]) ).
tcf(c_17550,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_17175,c_12674]) ).
tcf(c_17551,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_image(X0,empty_set))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17175,c_12550]) ).
tcf(c_17552,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X0,empty_set) = X1 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17175,c_93]) ).
tcf(c_17553,plain,
! [X0: $i] :
( ( relation_dom(relation_image(X0,empty_set)) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17175,c_12406]) ).
tcf(c_17554,plain,
! [X0: $i] :
( ( relation_image(X0,empty_set) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17175,c_94]) ).
tcf(c_17555,plain,
! [X0: $i] :
( one_to_one(relation_image(X0,empty_set))
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17175,c_5773]) ).
tcf(c_17556,plain,
! [X0: $i] :
( relation(relation_image(X0,empty_set))
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17175,c_77]) ).
tcf(c_17557,plain,
! [X0: $i] :
( function(relation_image(X0,empty_set))
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17175,c_66]) ).
tcf(c_17715,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,X1)
| subset(sK18(powerset(powerset(X1))),X2)
| ~ in(X0,sK13(sK18(powerset(powerset(X1))),X2)) ),
inference(superposition,[status(thm)],[c_17463,c_300]) ).
tcf(c_17716,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK18(powerset(powerset(X1))),X2)
| ~ empty(X1)
| ~ in(X0,sK13(sK18(powerset(powerset(X1))),X2)) ),
inference(superposition,[status(thm)],[c_17463,c_299]) ).
tcf(c_17717,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X1)
| subset(sK18(powerset(powerset(X1))),X2)
| ~ in(X0,sK13(sK18(powerset(powerset(X1))),X2)) ),
inference(superposition,[status(thm)],[c_17463,c_92]) ).
tcf(c_17718,plain,
! [X0: $i] : subset(sK18(powerset(powerset(X0))),powerset(X0)),
inference(superposition,[status(thm)],[c_17463,c_12572]) ).
tcf(c_17745,plain,
! [X0: $i] :
( one_to_one(relation_image(X0,empty_set))
| ( apply(relation_image(X0,empty_set),sK11(relation_image(X0,empty_set))) = apply(relation_image(X0,empty_set),sK12(relation_image(X0,empty_set))) )
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_image(X0,empty_set)) ),
inference(superposition,[status(thm)],[c_17556,c_84]) ).
tcf(c_17763,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_99,c_15261]) ).
tcf(c_17764,plain,
relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_114,c_15261]) ).
tcf(c_17765,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK18(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12738,c_15261]) ).
tcf(c_17766,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK18(powerset(sK18(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13358,c_15261]) ).
tcf(c_17767,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK18(sK17(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13470,c_15261]) ).
tcf(c_17768,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK18(powerset(sK18(sK17(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13469,c_15261]) ).
tcf(c_17769,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK18(sK17(sK17(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15885,c_15261]) ).
tcf(c_17770,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK18(powerset(sK18(sK17(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15887,c_15261]) ).
tcf(c_17771,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_17175,c_15261]) ).
tcf(c_17840,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(sK18(powerset(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_99,c_13260]) ).
tcf(c_17841,plain,
sK18(powerset(relation_dom(sK18(powerset(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_114,c_13260]) ).
tcf(c_17843,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(sK18(powerset(sK18(powerset(sK18(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13358,c_13260]) ).
tcf(c_17845,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(sK18(powerset(sK18(powerset(sK18(sK17(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13469,c_13260]) ).
tcf(c_17847,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(sK18(powerset(sK18(powerset(sK18(sK17(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15887,c_13260]) ).
tcf(c_17848,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(sK18(powerset(relation_image(X0,empty_set)))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17175,c_13260]) ).
tcf(c_17870,plain,
( in(sK18(empty_set),empty_set)
| empty(sK18(sK17(powerset(empty_set)))) ),
inference(superposition,[status(thm)],[c_14398,c_13274]) ).
tcf(c_17871,plain,
! [X0: $i,X1: $i] :
( empty(sK18(sK17(powerset(relation_image(X0,X1)))))
| ( apply(X0,sK4(X0,X1,sK18(sK18(sK17(powerset(relation_image(X0,X1))))))) = sK18(sK18(sK17(powerset(relation_image(X0,X1))))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13274,c_60]) ).
tcf(c_17872,plain,
! [X0: $i,X1: $i] :
( empty(sK18(sK17(powerset(relation_inverse_image(X0,X1)))))
| in(apply(X0,sK18(sK18(sK17(powerset(relation_inverse_image(X0,X1)))))),X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13274,c_72]) ).
tcf(c_17873,plain,
! [X0: $i,X1: $i] :
( empty(sK18(sK17(powerset(relation_inverse_image(X0,X1)))))
| in(sK18(sK18(sK17(powerset(relation_inverse_image(X0,X1))))),relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13274,c_71]) ).
tcf(c_17874,plain,
! [X0: $i] :
( empty(sK18(sK17(powerset(X0))))
| ~ in(X0,sK18(sK18(sK17(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_13274,c_98]) ).
tcf(c_17877,plain,
! [X0: $i] :
( empty(X0)
| empty(sK18(sK17(powerset(sK17(X0)))))
| element(sK18(sK18(sK17(powerset(sK17(X0))))),X0) ),
inference(superposition,[status(thm)],[c_13274,c_14688]) ).
tcf(c_17878,plain,
! [X0: $i] :
( empty(X0)
| empty(sK18(sK17(powerset(sK17(X0)))))
| in(sK18(sK18(sK17(powerset(sK17(X0))))),X0) ),
inference(superposition,[status(thm)],[c_13274,c_12618]) ).
tcf(c_17879,plain,
! [X0: $i] :
( empty(sK18(sK17(powerset(sK18(powerset(X0))))))
| element(sK18(sK18(sK17(powerset(sK18(powerset(X0)))))),X0) ),
inference(superposition,[status(thm)],[c_13274,c_14689]) ).
tcf(c_17880,plain,
! [X0: $i] :
( empty(sK18(sK17(powerset(sK18(powerset(X0))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13274,c_13313]) ).
tcf(c_17881,plain,
! [X0: $i] :
( empty(sK18(sK17(powerset(sK18(powerset(X0))))))
| in(sK18(sK18(sK17(powerset(sK18(powerset(X0)))))),X0) ),
inference(superposition,[status(thm)],[c_13274,c_12619]) ).
tcf(c_17882,plain,
empty(sK18(sK17(powerset(empty_set)))),
inference(superposition,[status(thm)],[c_13274,c_13338]) ).
tcf(c_17883,plain,
! [X0: $i] :
( empty(sK18(sK17(powerset(relation_image(X0,empty_set)))))
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13274,c_13341]) ).
tcf(c_17884,plain,
! [X0: $i] :
( empty(sK18(sK17(powerset(sK18(sK17(powerset(X0)))))))
| element(sK18(sK18(sK17(powerset(sK18(sK17(powerset(X0))))))),X0) ),
inference(superposition,[status(thm)],[c_13274,c_14693]) ).
tcf(c_17885,plain,
! [X0: $i] :
( empty(sK18(sK17(powerset(sK18(sK17(powerset(X0)))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13274,c_13316]) ).
tcf(c_17886,plain,
! [X0: $i] :
( empty(sK18(sK17(powerset(sK18(sK17(powerset(X0)))))))
| in(sK18(sK18(sK17(powerset(sK18(sK17(powerset(X0))))))),X0) ),
inference(superposition,[status(thm)],[c_13274,c_13032]) ).
tcf(c_17887,plain,
! [X0: $i] :
( empty(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0))))))))
| in(sK18(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0)))))))),X0) ),
inference(superposition,[status(thm)],[c_13274,c_15478]) ).
tcf(c_17888,plain,
! [X0: $i] :
( empty(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0))))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13274,c_15477]) ).
tcf(c_17889,plain,
! [X0: $i] :
( empty(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0))))))))
| element(sK18(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0)))))))),X0) ),
inference(superposition,[status(thm)],[c_13274,c_15476]) ).
tcf(c_18099,plain,
( empty(sK18(sK17(powerset(empty_set))))
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_12958,c_17880]) ).
tcf(c_18100,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(sK18(powerset(sK18(sK17(powerset(sK18(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17880,c_13260]) ).
tcf(c_18101,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK18(sK17(powerset(sK18(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17880,c_15261]) ).
tcf(c_18102,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK18(sK17(powerset(sK18(powerset(X0))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17880,c_15230]) ).
tcf(c_18103,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(sK18(powerset(sK18(sK17(powerset(sK18(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17880,c_13064]) ).
tcf(c_18104,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK18(sK17(powerset(sK18(powerset(X0))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17880,c_12767]) ).
tcf(c_18105,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK18(powerset(sK18(sK17(powerset(sK18(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17880,c_12765]) ).
tcf(c_18106,plain,
! [X0: $i] :
( ( sK18(sK17(sK17(powerset(sK18(sK17(powerset(sK18(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17880,c_15973]) ).
tcf(c_18107,plain,
! [X0: $i] :
( ( relation_dom(sK18(sK17(powerset(sK18(sK17(powerset(sK18(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17880,c_13494]) ).
tcf(c_18108,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(relation_dom(sK18(sK17(powerset(sK18(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17880,c_14397]) ).
tcf(c_18109,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(relation_dom(sK18(sK17(powerset(sK18(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17880,c_13258]) ).
tcf(c_18110,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(relation_dom(sK18(sK17(powerset(sK18(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17880,c_13062]) ).
tcf(c_18111,plain,
! [X0: $i] :
( ( sK18(powerset(sK18(powerset(sK18(sK17(powerset(sK18(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17880,c_12959]) ).
tcf(c_18112,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK18(powerset(sK18(sK17(powerset(sK18(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17880,c_12766]) ).
tcf(c_18113,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK18(sK17(powerset(sK18(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17880,c_12718]) ).
tcf(c_18114,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(sK17(powerset(sK18(powerset(X0)))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17880,c_12604]) ).
tcf(c_18115,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(sK18(sK17(powerset(sK18(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17880,c_13495]) ).
tcf(c_18116,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(sK18(sK17(powerset(sK18(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17880,c_12957]) ).
tcf(c_18117,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(sK18(sK17(powerset(sK18(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17880,c_12768]) ).
tcf(c_18118,plain,
! [X0: $i] :
( ( sK18(powerset(sK18(sK17(powerset(sK18(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17880,c_12769]) ).
tcf(c_18119,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK18(sK17(powerset(sK18(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17880,c_12674]) ).
tcf(c_18120,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK18(sK17(powerset(sK18(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17880,c_12550]) ).
tcf(c_18121,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(powerset(sK18(powerset(X0))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17880,c_93]) ).
tcf(c_18124,plain,
! [X0: $i] :
( one_to_one(sK18(sK17(powerset(sK18(powerset(X0))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17880,c_5773]) ).
tcf(c_18125,plain,
! [X0: $i] :
( relation(sK18(sK17(powerset(sK18(powerset(X0))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17880,c_77]) ).
tcf(c_18126,plain,
! [X0: $i] :
( function(sK18(sK17(powerset(sK18(powerset(X0))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17880,c_66]) ).
tcf(c_18259,plain,
( one_to_one(sK18(sK17(powerset(empty_set))))
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_12958,c_18124]) ).
tcf(c_18265,plain,
( relation(sK18(sK17(powerset(empty_set))))
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_12958,c_18125]) ).
tcf(c_18266,plain,
! [X0: $i] :
( one_to_one(sK18(sK17(powerset(sK18(powerset(X0))))))
| ( apply(sK18(sK17(powerset(sK18(powerset(X0))))),sK11(sK18(sK17(powerset(sK18(powerset(X0))))))) = apply(sK18(sK17(powerset(sK18(powerset(X0))))),sK12(sK18(sK17(powerset(sK18(powerset(X0))))))) )
| ~ empty(X0)
| ~ function(sK18(sK17(powerset(sK18(powerset(X0)))))) ),
inference(superposition,[status(thm)],[c_18125,c_84]) ).
tcf(c_18277,plain,
( function(sK18(sK17(powerset(empty_set))))
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_12958,c_18126]) ).
tcf(c_18284,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(sK18(powerset(sK18(sK17(powerset(sK18(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17885,c_13260]) ).
tcf(c_18285,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK18(sK17(powerset(sK18(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17885,c_15261]) ).
tcf(c_18286,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK18(sK17(powerset(sK18(sK17(powerset(X0)))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17885,c_15230]) ).
tcf(c_18287,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(sK18(powerset(sK18(sK17(powerset(sK18(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17885,c_13064]) ).
tcf(c_18288,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK18(sK17(powerset(sK18(sK17(powerset(X0)))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17885,c_12767]) ).
tcf(c_18289,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK18(powerset(sK18(sK17(powerset(sK18(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17885,c_12765]) ).
tcf(c_18290,plain,
! [X0: $i] :
( ( sK18(sK17(sK17(powerset(sK18(sK17(powerset(sK18(sK17(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17885,c_15973]) ).
tcf(c_18291,plain,
! [X0: $i] :
( ( relation_dom(sK18(sK17(powerset(sK18(sK17(powerset(sK18(sK17(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17885,c_13494]) ).
tcf(c_18292,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(relation_dom(sK18(sK17(powerset(sK18(sK17(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17885,c_14397]) ).
tcf(c_18293,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(relation_dom(sK18(sK17(powerset(sK18(sK17(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17885,c_13258]) ).
tcf(c_18294,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(relation_dom(sK18(sK17(powerset(sK18(sK17(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17885,c_13062]) ).
tcf(c_18295,plain,
! [X0: $i] :
( ( sK18(powerset(sK18(powerset(sK18(sK17(powerset(sK18(sK17(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17885,c_12959]) ).
tcf(c_18296,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK18(powerset(sK18(sK17(powerset(sK18(sK17(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17885,c_12766]) ).
tcf(c_18297,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK18(sK17(powerset(sK18(sK17(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17885,c_12718]) ).
tcf(c_18298,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(sK17(powerset(sK18(sK17(powerset(X0))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17885,c_12604]) ).
tcf(c_18299,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(sK18(sK17(powerset(sK18(sK17(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17885,c_13495]) ).
tcf(c_18300,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(sK18(sK17(powerset(sK18(sK17(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17885,c_12957]) ).
tcf(c_18301,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(sK18(sK17(powerset(sK18(sK17(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17885,c_12768]) ).
tcf(c_18302,plain,
! [X0: $i] :
( ( sK18(powerset(sK18(sK17(powerset(sK18(sK17(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17885,c_12769]) ).
tcf(c_18303,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK18(sK17(powerset(sK18(sK17(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17885,c_12674]) ).
tcf(c_18304,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK18(sK17(powerset(sK18(sK17(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17885,c_12550]) ).
tcf(c_18305,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(powerset(sK18(sK17(powerset(X0)))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17885,c_93]) ).
tcf(c_18308,plain,
! [X0: $i] :
( one_to_one(sK18(sK17(powerset(sK18(sK17(powerset(X0)))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17885,c_5773]) ).
tcf(c_18309,plain,
! [X0: $i] :
( relation(sK18(sK17(powerset(sK18(sK17(powerset(X0)))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17885,c_77]) ).
tcf(c_18310,plain,
! [X0: $i] :
( function(sK18(sK17(powerset(sK18(sK17(powerset(X0)))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17885,c_66]) ).
tcf(c_18545,plain,
! [X0: $i] :
( one_to_one(sK18(sK17(powerset(sK18(sK17(powerset(X0)))))))
| ( apply(sK18(sK17(powerset(sK18(sK17(powerset(X0)))))),sK11(sK18(sK17(powerset(sK18(sK17(powerset(X0)))))))) = apply(sK18(sK17(powerset(sK18(sK17(powerset(X0)))))),sK12(sK18(sK17(powerset(sK18(sK17(powerset(X0)))))))) )
| ~ empty(X0)
| ~ function(sK18(sK17(powerset(sK18(sK17(powerset(X0))))))) ),
inference(superposition,[status(thm)],[c_18309,c_84]) ).
tcf(c_18555,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,X1)
| subset(sK17(powerset(X1)),X2)
| ~ in(X0,sK13(sK17(powerset(X1)),X2)) ),
inference(superposition,[status(thm)],[c_17477,c_300]) ).
tcf(c_18556,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK17(powerset(X1)),X2)
| ~ empty(X1)
| ~ in(X0,sK13(sK17(powerset(X1)),X2)) ),
inference(superposition,[status(thm)],[c_17477,c_299]) ).
tcf(c_18557,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X1)
| subset(sK17(powerset(X1)),X2)
| ~ in(X0,sK13(sK17(powerset(X1)),X2)) ),
inference(superposition,[status(thm)],[c_17477,c_92]) ).
tcf(c_18558,plain,
! [X0: $i] : subset(sK17(powerset(X0)),powerset(X0)),
inference(superposition,[status(thm)],[c_17477,c_12572]) ).
tcf(c_18581,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK18(powerset(relation_dom(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_99,c_15317]) ).
tcf(c_18582,plain,
relation_dom(relation_dom(sK18(powerset(relation_dom(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_114,c_15317]) ).
tcf(c_18583,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK18(powerset(relation_dom(sK18(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12738,c_15317]) ).
tcf(c_18584,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK18(powerset(relation_dom(sK18(powerset(sK18(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13358,c_15317]) ).
tcf(c_18585,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK18(powerset(relation_dom(sK18(sK17(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13470,c_15317]) ).
tcf(c_18586,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK18(powerset(relation_dom(sK18(powerset(sK18(sK17(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13469,c_15317]) ).
tcf(c_18587,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK18(powerset(relation_dom(sK18(sK17(sK17(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15885,c_15317]) ).
tcf(c_18588,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK18(powerset(relation_dom(sK18(powerset(sK18(sK17(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15887,c_15317]) ).
tcf(c_18589,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK18(powerset(relation_dom(relation_image(X0,empty_set)))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17175,c_15317]) ).
tcf(c_18590,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK18(powerset(relation_dom(sK18(sK17(powerset(sK18(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17880,c_15317]) ).
tcf(c_18591,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK18(powerset(relation_dom(sK18(sK17(powerset(sK18(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17885,c_15317]) ).
tcf(c_18628,plain,
! [X0: $i] :
( ( sK18(powerset(sK18(powerset(relation_dom(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_99,c_15355]) ).
tcf(c_18629,plain,
sK18(powerset(sK18(powerset(relation_dom(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_114,c_15355]) ).
tcf(c_18630,plain,
! [X0: $i] :
( ( sK18(powerset(sK18(powerset(relation_dom(sK18(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12738,c_15355]) ).
tcf(c_18631,plain,
! [X0: $i] :
( ( sK18(powerset(sK18(powerset(relation_dom(sK18(powerset(sK18(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13358,c_15355]) ).
tcf(c_18632,plain,
! [X0: $i] :
( ( sK18(powerset(sK18(powerset(relation_dom(sK18(sK17(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13470,c_15355]) ).
tcf(c_18633,plain,
! [X0: $i] :
( ( sK18(powerset(sK18(powerset(relation_dom(sK18(powerset(sK18(sK17(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13469,c_15355]) ).
tcf(c_18634,plain,
! [X0: $i] :
( ( sK18(powerset(sK18(powerset(relation_dom(sK18(sK17(sK17(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15885,c_15355]) ).
tcf(c_18635,plain,
! [X0: $i] :
( ( sK18(powerset(sK18(powerset(relation_dom(sK18(powerset(sK18(sK17(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15887,c_15355]) ).
tcf(c_18636,plain,
! [X0: $i] :
( ( sK18(powerset(sK18(powerset(relation_dom(relation_image(X0,empty_set)))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17175,c_15355]) ).
tcf(c_18637,plain,
! [X0: $i] :
( ( sK18(powerset(sK18(powerset(relation_dom(sK18(sK17(powerset(sK18(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17880,c_15355]) ).
tcf(c_18638,plain,
! [X0: $i] :
( ( sK18(powerset(sK18(powerset(relation_dom(sK18(sK17(powerset(sK18(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17885,c_15355]) ).
tcf(c_18708,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(relation_dom(relation_dom(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_99,c_15527]) ).
tcf(c_18709,plain,
relation_dom(sK18(powerset(relation_dom(relation_dom(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_114,c_15527]) ).
tcf(c_18710,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(relation_dom(relation_dom(sK18(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12738,c_15527]) ).
tcf(c_18711,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(relation_dom(relation_dom(sK18(powerset(sK18(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13358,c_15527]) ).
tcf(c_18712,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(relation_dom(relation_dom(sK18(sK17(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13470,c_15527]) ).
tcf(c_18713,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(relation_dom(relation_dom(sK18(powerset(sK18(sK17(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13469,c_15527]) ).
tcf(c_18714,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(relation_dom(relation_dom(sK18(sK17(sK17(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15885,c_15527]) ).
tcf(c_18715,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(relation_dom(relation_dom(sK18(powerset(sK18(sK17(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15887,c_15527]) ).
tcf(c_18716,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(relation_dom(relation_dom(relation_image(X0,empty_set)))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17175,c_15527]) ).
tcf(c_18717,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(relation_dom(relation_dom(sK18(sK17(powerset(sK18(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17880,c_15527]) ).
tcf(c_18718,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(relation_dom(relation_dom(sK18(sK17(powerset(sK18(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17885,c_15527]) ).
tcf(c_18765,plain,
! [X0: $i,X1: $i] :
( element(X0,powerset(X1))
| ~ in(X0,sK17(powerset(X1))) ),
inference(superposition,[status(thm)],[c_18558,c_300]) ).
tcf(c_18766,plain,
! [X0: $i,X1: $i] :
( ~ empty(powerset(X1))
| ~ in(X0,sK17(powerset(X1))) ),
inference(superposition,[status(thm)],[c_18558,c_299]) ).
tcf(c_18767,plain,
! [X0: $i,X1: $i] :
( in(X0,powerset(X1))
| ~ in(X0,sK17(powerset(X1))) ),
inference(superposition,[status(thm)],[c_18558,c_92]) ).
tcf(c_18876,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X0,X1,sK17(powerset(X2))),powerset(X2))
| ( relation_image(X0,X1) = sK17(powerset(X2)) )
| ( apply(X0,sK3(X0,X1,sK17(powerset(X2)))) = sK2(X0,X1,sK17(powerset(X2))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_56,c_18765]) ).
tcf(c_18877,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X0,X1,sK17(powerset(X2))),powerset(X2))
| in(sK3(X0,X1,sK17(powerset(X2))),relation_dom(X0))
| ( relation_image(X0,X1) = sK17(powerset(X2)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_54,c_18765]) ).
tcf(c_18878,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(X0,X1,sK17(powerset(X2))),X1)
| element(sK2(X0,X1,sK17(powerset(X2))),powerset(X2))
| ( relation_image(X0,X1) = sK17(powerset(X2)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_55,c_18765]) ).
tcf(c_18879,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,sK17(powerset(X1)),X2),X2)
| element(sK3(X0,sK17(powerset(X1)),X2),powerset(X1))
| ( relation_image(X0,sK17(powerset(X1))) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_55,c_18765]) ).
tcf(c_18880,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK4(X1,sK17(powerset(X2)),X0),powerset(X2))
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,sK17(powerset(X2)))) ),
inference(superposition,[status(thm)],[c_59,c_18765]) ).
tcf(c_18881,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,sK17(powerset(X1)),X2),X2)
| element(apply(X0,sK7(X0,sK17(powerset(X1)),X2)),powerset(X1))
| ( relation_inverse_image(X0,sK17(powerset(X1))) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_69,c_18765]) ).
tcf(c_18882,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK7(X0,X1,sK17(powerset(X2))),powerset(X2))
| in(apply(X0,sK7(X0,X1,sK17(powerset(X2)))),X1)
| ( relation_inverse_image(X0,X1) = sK17(powerset(X2)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_69,c_18765]) ).
tcf(c_18883,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK7(X0,X1,sK17(powerset(X2))),powerset(X2))
| in(sK7(X0,X1,sK17(powerset(X2))),relation_dom(X0))
| ( relation_inverse_image(X0,X1) = sK17(powerset(X2)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_68,c_18765]) ).
tcf(c_18884,plain,
! [X0: $i,X1: $i] :
( subset(sK17(powerset(X0)),X1)
| element(sK13(sK17(powerset(X0)),X1),powerset(X0)) ),
inference(superposition,[status(thm)],[c_91,c_18765]) ).
tcf(c_18885,plain,
! [X0: $i] :
( empty(sK17(powerset(X0)))
| element(sK18(sK17(powerset(X0))),powerset(X0)) ),
inference(superposition,[status(thm)],[c_12501,c_18765]) ).
tcf(c_18886,plain,
! [X0: $i,X1: $i] :
( subset(sK18(powerset(sK17(powerset(X0)))),X1)
| element(sK13(sK18(powerset(sK17(powerset(X0)))),X1),powerset(X0)) ),
inference(superposition,[status(thm)],[c_12692,c_18765]) ).
tcf(c_18887,plain,
! [X0: $i] :
( empty(sK18(powerset(sK17(powerset(X0)))))
| element(sK18(sK18(powerset(sK17(powerset(X0))))),powerset(X0)) ),
inference(superposition,[status(thm)],[c_12693,c_18765]) ).
tcf(c_18888,plain,
! [X0: $i,X1: $i] :
( empty(sK17(powerset(X0)))
| subset(sK17(sK17(powerset(X0))),X1)
| element(sK13(sK17(sK17(powerset(X0))),X1),powerset(X0)) ),
inference(superposition,[status(thm)],[c_12705,c_18765]) ).
tcf(c_18889,plain,
! [X0: $i] :
( empty(sK17(powerset(X0)))
| element(sK18(sK17(sK17(powerset(X0)))),powerset(X0)) ),
inference(superposition,[status(thm)],[c_12981,c_18765]) ).
tcf(c_18890,plain,
! [X0: $i] :
( empty(sK17(powerset(X0)))
| element(sK18(sK17(sK17(sK17(powerset(X0))))),powerset(X0)) ),
inference(superposition,[status(thm)],[c_15371,c_18765]) ).
tcf(c_18891,plain,
! [X0: $i] :
( empty(sK18(powerset(sK17(powerset(X0)))))
| element(sK18(sK17(sK18(powerset(sK17(powerset(X0)))))),powerset(X0)) ),
inference(superposition,[status(thm)],[c_12994,c_18765]) ).
tcf(c_18892,plain,
! [X0: $i] :
( empty(sK18(sK17(powerset(sK17(powerset(X0))))))
| element(sK18(sK18(sK17(powerset(sK17(powerset(X0)))))),powerset(X0)) ),
inference(superposition,[status(thm)],[c_13274,c_18765]) ).
tcf(c_18893,plain,
( element(empty_set,powerset(empty_set))
| empty(sK17(powerset(empty_set))) ),
inference(superposition,[status(thm)],[c_14425,c_18765]) ).
tcf(c_18993,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,sK17(powerset(X2))),powerset(X2))
| ( relation_image(X0,X1) = sK17(powerset(X2)) )
| ( apply(X0,sK3(X0,X1,sK17(powerset(X2)))) = sK2(X0,X1,sK17(powerset(X2))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_56,c_18767]) ).
tcf(c_18994,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(X0,X1,sK17(powerset(X2))),relation_dom(X0))
| in(sK2(X0,X1,sK17(powerset(X2))),powerset(X2))
| ( relation_image(X0,X1) = sK17(powerset(X2)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_54,c_18767]) ).
tcf(c_18995,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(X0,X1,sK17(powerset(X2))),X1)
| in(sK2(X0,X1,sK17(powerset(X2))),powerset(X2))
| ( relation_image(X0,X1) = sK17(powerset(X2)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_55,c_18767]) ).
tcf(c_18996,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,sK17(powerset(X1)),X2),X2)
| in(sK3(X0,sK17(powerset(X1)),X2),powerset(X1))
| ( relation_image(X0,sK17(powerset(X1))) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_55,c_18767]) ).
tcf(c_18997,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK4(X1,sK17(powerset(X2)),X0),powerset(X2))
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,sK17(powerset(X2)))) ),
inference(superposition,[status(thm)],[c_59,c_18767]) ).
tcf(c_18998,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,sK17(powerset(X1)),X2),X2)
| in(apply(X0,sK7(X0,sK17(powerset(X1)),X2)),powerset(X1))
| ( relation_inverse_image(X0,sK17(powerset(X1))) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_69,c_18767]) ).
tcf(c_18999,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X1,sK17(powerset(X2))),powerset(X2))
| in(apply(X0,sK7(X0,X1,sK17(powerset(X2)))),X1)
| ( relation_inverse_image(X0,X1) = sK17(powerset(X2)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_69,c_18767]) ).
tcf(c_19000,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X1,sK17(powerset(X2))),powerset(X2))
| in(sK7(X0,X1,sK17(powerset(X2))),relation_dom(X0))
| ( relation_inverse_image(X0,X1) = sK17(powerset(X2)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_68,c_18767]) ).
tcf(c_19001,plain,
! [X0: $i,X1: $i] :
( subset(sK17(powerset(X0)),X1)
| in(sK13(sK17(powerset(X0)),X1),powerset(X0)) ),
inference(superposition,[status(thm)],[c_91,c_18767]) ).
tcf(c_19002,plain,
! [X0: $i] :
( empty(sK17(powerset(X0)))
| in(sK18(sK17(powerset(X0))),powerset(X0)) ),
inference(superposition,[status(thm)],[c_12501,c_18767]) ).
tcf(c_19003,plain,
! [X0: $i,X1: $i] :
( subset(sK18(powerset(sK17(powerset(X0)))),X1)
| in(sK13(sK18(powerset(sK17(powerset(X0)))),X1),powerset(X0)) ),
inference(superposition,[status(thm)],[c_12692,c_18767]) ).
tcf(c_19004,plain,
! [X0: $i] :
( empty(sK18(powerset(sK17(powerset(X0)))))
| in(sK18(sK18(powerset(sK17(powerset(X0))))),powerset(X0)) ),
inference(superposition,[status(thm)],[c_12693,c_18767]) ).
tcf(c_19005,plain,
! [X0: $i,X1: $i] :
( empty(sK17(powerset(X0)))
| subset(sK17(sK17(powerset(X0))),X1)
| in(sK13(sK17(sK17(powerset(X0))),X1),powerset(X0)) ),
inference(superposition,[status(thm)],[c_12705,c_18767]) ).
tcf(c_19006,plain,
! [X0: $i] :
( empty(sK17(powerset(X0)))
| in(sK18(sK17(sK17(powerset(X0)))),powerset(X0)) ),
inference(superposition,[status(thm)],[c_12981,c_18767]) ).
tcf(c_19007,plain,
! [X0: $i] :
( empty(sK17(powerset(X0)))
| in(sK18(sK17(sK17(sK17(powerset(X0))))),powerset(X0)) ),
inference(superposition,[status(thm)],[c_15371,c_18767]) ).
tcf(c_19008,plain,
! [X0: $i] :
( empty(sK18(powerset(sK17(powerset(X0)))))
| in(sK18(sK17(sK18(powerset(sK17(powerset(X0)))))),powerset(X0)) ),
inference(superposition,[status(thm)],[c_12994,c_18767]) ).
tcf(c_19009,plain,
! [X0: $i] :
( empty(sK18(sK17(powerset(sK17(powerset(X0))))))
| in(sK18(sK18(sK17(powerset(sK17(powerset(X0)))))),powerset(X0)) ),
inference(superposition,[status(thm)],[c_13274,c_18767]) ).
tcf(c_19010,plain,
( empty(sK17(powerset(empty_set)))
| in(empty_set,powerset(empty_set)) ),
inference(superposition,[status(thm)],[c_14425,c_18767]) ).
tcf(c_19122,plain,
! [X0: $i] :
( empty(sK17(powerset(X0)))
| ~ in(powerset(X0),sK18(sK17(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_19002,c_98]) ).
tcf(c_19132,plain,
! [X0: $i] :
( ( sK18(powerset(sK18(sK17(powerset(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_99,c_13490]) ).
tcf(c_19133,plain,
sK18(powerset(sK18(sK17(powerset(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_114,c_13490]) ).
tcf(c_19135,plain,
! [X0: $i] :
( ( sK18(powerset(sK18(sK17(powerset(sK18(powerset(sK18(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13358,c_13490]) ).
tcf(c_19137,plain,
! [X0: $i] :
( ( sK18(powerset(sK18(sK17(powerset(sK18(powerset(sK18(sK17(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13469,c_13490]) ).
tcf(c_19138,plain,
! [X0: $i] :
( ( sK18(powerset(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15885,c_13490]) ).
tcf(c_19139,plain,
! [X0: $i] :
( ( sK18(powerset(sK18(sK17(powerset(sK18(powerset(sK18(sK17(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15887,c_13490]) ).
tcf(c_19140,plain,
! [X0: $i] :
( ( sK18(powerset(sK18(sK17(powerset(relation_image(X0,empty_set)))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17175,c_13490]) ).
tcf(c_19141,plain,
! [X0: $i] :
( ( sK18(powerset(sK18(sK17(powerset(sK18(sK17(powerset(sK18(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17880,c_13490]) ).
tcf(c_19142,plain,
! [X0: $i] :
( ( sK18(powerset(sK18(sK17(powerset(sK18(sK17(powerset(sK18(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17885,c_13490]) ).
tcf(c_19196,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK18(sK17(powerset(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_99,c_13492]) ).
tcf(c_19197,plain,
relation_dom(relation_dom(sK18(sK17(powerset(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_114,c_13492]) ).
tcf(c_19199,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK18(sK17(powerset(sK18(powerset(sK18(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13358,c_13492]) ).
tcf(c_19201,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK18(sK17(powerset(sK18(powerset(sK18(sK17(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13469,c_13492]) ).
tcf(c_19202,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15885,c_13492]) ).
tcf(c_19203,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK18(sK17(powerset(sK18(powerset(sK18(sK17(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15887,c_13492]) ).
tcf(c_19204,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK18(sK17(powerset(relation_image(X0,empty_set)))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17175,c_13492]) ).
tcf(c_19205,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK18(sK17(powerset(sK18(sK17(powerset(sK18(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17880,c_13492]) ).
tcf(c_19206,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK18(sK17(powerset(sK18(sK17(powerset(sK18(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17885,c_13492]) ).
tcf(c_19241,plain,
! [X0: $i,X1: $i] :
( in(sK2(empty_set,X1,X0),X0)
| ( X0 = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_13805,c_17316]) ).
tcf(c_19248,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X0,X1) = empty_set )
| ( apply(X0,sK4(X0,X1,sK2(empty_set,X2,relation_image(X0,X1)))) = sK2(empty_set,X2,relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_19241,c_60]) ).
tcf(c_19249,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X0,sK2(empty_set,X2,relation_inverse_image(X0,X1))),X1)
| ( relation_inverse_image(X0,X1) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_19241,c_72]) ).
tcf(c_19250,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(empty_set,X2,relation_inverse_image(X0,X1)),relation_dom(X0))
| ( relation_inverse_image(X0,X1) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_19241,c_71]) ).
tcf(c_19251,plain,
! [X0: $i,X1: $i] :
( ( X0 = empty_set )
| ~ in(X0,sK2(empty_set,X1,X0)) ),
inference(superposition,[status(thm)],[c_19241,c_98]) ).
tcf(c_19252,plain,
! [X0: $i,X1: $i] :
( element(sK2(empty_set,X1,X0),X0)
| ( X0 = empty_set ) ),
inference(superposition,[status(thm)],[c_19241,c_97]) ).
tcf(c_19254,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| element(sK2(empty_set,X1,sK17(X0)),X0)
| ( sK17(X0) = empty_set ) ),
inference(superposition,[status(thm)],[c_19241,c_14688]) ).
tcf(c_19255,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| in(sK2(empty_set,X1,sK17(X0)),X0)
| ( sK17(X0) = empty_set ) ),
inference(superposition,[status(thm)],[c_19241,c_12618]) ).
tcf(c_19256,plain,
! [X0: $i,X1: $i] :
( element(sK2(empty_set,X1,sK18(powerset(X0))),X0)
| ( sK18(powerset(X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_19241,c_14689]) ).
tcf(c_19258,plain,
! [X0: $i,X1: $i] :
( in(sK2(empty_set,X1,sK18(powerset(X0))),X0)
| ( sK18(powerset(X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_19241,c_12619]) ).
tcf(c_19261,plain,
! [X0: $i,X1: $i] :
( element(sK2(empty_set,X1,sK18(sK17(powerset(X0)))),X0)
| ( sK18(sK17(powerset(X0))) = empty_set ) ),
inference(superposition,[status(thm)],[c_19241,c_14693]) ).
tcf(c_19263,plain,
! [X0: $i,X1: $i] :
( in(sK2(empty_set,X1,sK18(sK17(powerset(X0)))),X0)
| ( sK18(sK17(powerset(X0))) = empty_set ) ),
inference(superposition,[status(thm)],[c_19241,c_13032]) ).
tcf(c_19264,plain,
! [X0: $i,X1: $i] :
( in(sK2(empty_set,X1,sK18(sK17(sK17(powerset(X0))))),X0)
| ( sK18(sK17(sK17(powerset(X0)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_19241,c_15478]) ).
tcf(c_19266,plain,
! [X0: $i,X1: $i] :
( element(sK2(empty_set,X1,sK18(sK17(sK17(powerset(X0))))),X0)
| ( sK18(sK17(sK17(powerset(X0)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_19241,c_15476]) ).
tcf(c_19267,plain,
! [X0: $i,X1: $i] :
( in(sK2(empty_set,X1,sK17(powerset(X0))),powerset(X0))
| ( sK17(powerset(X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_19241,c_18767]) ).
tcf(c_19268,plain,
! [X0: $i,X1: $i] :
( element(sK2(empty_set,X1,sK17(powerset(X0))),powerset(X0))
| ( sK17(powerset(X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_19241,c_18765]) ).
tcf(c_19471,plain,
! [X0: $i,X1: $i] :
( subset(sK2(empty_set,X1,powerset(X0)),X0)
| ( powerset(X0) = empty_set ) ),
inference(superposition,[status(thm)],[c_19252,c_88]) ).
tcf(c_19484,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X0,X1) = relation_inverse_image(empty_set,X2) )
| ( apply(X0,sK4(X0,X1,sK7(empty_set,X2,relation_image(X0,X1)))) = sK7(empty_set,X2,relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13956,c_60]) ).
tcf(c_19485,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X0,sK7(empty_set,X2,relation_inverse_image(X0,X1))),X1)
| ( relation_inverse_image(X0,X1) = relation_inverse_image(empty_set,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13956,c_72]) ).
tcf(c_19486,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(empty_set,X2,relation_inverse_image(X0,X1)),relation_dom(X0))
| ( relation_inverse_image(X0,X1) = relation_inverse_image(empty_set,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13956,c_71]) ).
tcf(c_19487,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse_image(empty_set,X1) = X0 )
| ~ in(X0,sK7(empty_set,X1,X0)) ),
inference(superposition,[status(thm)],[c_13956,c_98]) ).
tcf(c_19488,plain,
! [X0: $i,X1: $i] :
( element(sK7(empty_set,X0,X1),X1)
| ( relation_inverse_image(empty_set,X0) = X1 ) ),
inference(superposition,[status(thm)],[c_13956,c_97]) ).
tcf(c_19489,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse_image(empty_set,X1) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13956,c_95]) ).
tcf(c_19490,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| element(sK7(empty_set,X0,sK17(X1)),X1)
| ( relation_inverse_image(empty_set,X0) = sK17(X1) ) ),
inference(superposition,[status(thm)],[c_13956,c_14688]) ).
tcf(c_19491,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| in(sK7(empty_set,X0,sK17(X1)),X1)
| ( relation_inverse_image(empty_set,X0) = sK17(X1) ) ),
inference(superposition,[status(thm)],[c_13956,c_12618]) ).
tcf(c_19492,plain,
! [X0: $i,X1: $i] :
( element(sK7(empty_set,X0,sK18(powerset(X1))),X1)
| ( relation_inverse_image(empty_set,X0) = sK18(powerset(X1)) ) ),
inference(superposition,[status(thm)],[c_13956,c_14689]) ).
tcf(c_19493,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse_image(empty_set,X1) = sK18(powerset(X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13956,c_13313]) ).
tcf(c_19494,plain,
! [X0: $i,X1: $i] :
( in(sK7(empty_set,X0,sK18(powerset(X1))),X1)
| ( relation_inverse_image(empty_set,X0) = sK18(powerset(X1)) ) ),
inference(superposition,[status(thm)],[c_13956,c_12619]) ).
tcf(c_19495,plain,
! [X0: $i] : relation_inverse_image(empty_set,X0) = empty_set,
inference(superposition,[status(thm)],[c_13956,c_13338]) ).
tcf(c_19496,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X0,empty_set) = relation_inverse_image(empty_set,X1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13956,c_13341]) ).
tcf(c_19497,plain,
! [X0: $i,X1: $i] :
( element(sK7(empty_set,X1,sK18(sK17(powerset(X0)))),X0)
| ( sK18(sK17(powerset(X0))) = relation_inverse_image(empty_set,X1) ) ),
inference(superposition,[status(thm)],[c_13956,c_14693]) ).
tcf(c_19498,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(powerset(X0))) = relation_inverse_image(empty_set,X1) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13956,c_13316]) ).
tcf(c_19499,plain,
! [X0: $i,X1: $i] :
( in(sK7(empty_set,X1,sK18(sK17(powerset(X0)))),X0)
| ( sK18(sK17(powerset(X0))) = relation_inverse_image(empty_set,X1) ) ),
inference(superposition,[status(thm)],[c_13956,c_13032]) ).
tcf(c_19500,plain,
! [X0: $i,X1: $i] :
( in(sK7(empty_set,X1,sK18(sK17(sK17(powerset(X0))))),X0)
| ( sK18(sK17(sK17(powerset(X0)))) = relation_inverse_image(empty_set,X1) ) ),
inference(superposition,[status(thm)],[c_13956,c_15478]) ).
tcf(c_19501,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(sK17(powerset(X0)))) = relation_inverse_image(empty_set,X1) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13956,c_15477]) ).
tcf(c_19502,plain,
! [X0: $i,X1: $i] :
( element(sK7(empty_set,X1,sK18(sK17(sK17(powerset(X0))))),X0)
| ( sK18(sK17(sK17(powerset(X0)))) = relation_inverse_image(empty_set,X1) ) ),
inference(superposition,[status(thm)],[c_13956,c_15476]) ).
tcf(c_19503,plain,
! [X0: $i,X1: $i] :
( in(sK7(empty_set,X0,sK17(powerset(X1))),powerset(X1))
| ( relation_inverse_image(empty_set,X0) = sK17(powerset(X1)) ) ),
inference(superposition,[status(thm)],[c_13956,c_18767]) ).
tcf(c_19504,plain,
! [X0: $i,X1: $i] :
( element(sK7(empty_set,X0,sK17(powerset(X1))),powerset(X1))
| ( relation_inverse_image(empty_set,X0) = sK17(powerset(X1)) ) ),
inference(superposition,[status(thm)],[c_13956,c_18765]) ).
tcf(c_19554,plain,
! [X0: $i,X1: $i] :
( in(sK7(empty_set,X1,X0),X0)
| ( X0 = empty_set ) ),
inference(demodulation,[status(thm)],[c_13956,c_19495]) ).
tcf(c_19616,plain,
! [X0: $i,X1: $i] : subset(sK2(empty_set,X1,powerset(X0)),X0),
inference(global_subsumption_just,[status(thm)],[c_19471,c_114,c_110,c_14309,c_19471]) ).
tcf(c_19617,plain,
! [X0: $i,X1: $i] : subset(sK2(empty_set,X0,powerset(X1)),X1),
inference(renaming,[status(thm)],[c_19616]) ).
tcf(c_19619,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,X2)
| ~ in(X0,sK2(empty_set,X1,powerset(X2))) ),
inference(superposition,[status(thm)],[c_19617,c_300]) ).
tcf(c_19620,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(X2)
| ~ in(X0,sK2(empty_set,X1,powerset(X2))) ),
inference(superposition,[status(thm)],[c_19617,c_299]) ).
tcf(c_19621,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ in(X0,sK2(empty_set,X1,powerset(X2))) ),
inference(superposition,[status(thm)],[c_19617,c_92]) ).
tcf(c_19641,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,X1,sK2(empty_set,X2,powerset(X3))),X3)
| ( sK2(empty_set,X2,powerset(X3)) = relation_image(X0,X1) )
| ( apply(X0,sK3(X0,X1,sK2(empty_set,X2,powerset(X3)))) = sK2(X0,X1,sK2(empty_set,X2,powerset(X3))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_56,c_19621]) ).
tcf(c_19642,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,X3,sK2(empty_set,X1,powerset(X2))),X2)
| in(sK3(X0,X3,sK2(empty_set,X1,powerset(X2))),relation_dom(X0))
| ( sK2(empty_set,X1,powerset(X2)) = relation_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_54,c_19621]) ).
tcf(c_19643,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK3(X0,X3,sK2(empty_set,X1,powerset(X2))),X3)
| in(sK2(X0,X3,sK2(empty_set,X1,powerset(X2))),X2)
| ( sK2(empty_set,X1,powerset(X2)) = relation_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_55,c_19621]) ).
tcf(c_19644,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK3(X0,sK2(empty_set,X1,powerset(X2)),X3),X2)
| in(sK2(X0,sK2(empty_set,X1,powerset(X2)),X3),X3)
| ( relation_image(X0,sK2(empty_set,X1,powerset(X2))) = X3 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_55,c_19621]) ).
tcf(c_19645,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK4(X1,sK2(empty_set,X2,powerset(X3)),X0),X3)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,sK2(empty_set,X2,powerset(X3)))) ),
inference(superposition,[status(thm)],[c_59,c_19621]) ).
tcf(c_19646,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,sK2(empty_set,X1,powerset(X2)),X3),X3)
| in(apply(X0,sK7(X0,sK2(empty_set,X1,powerset(X2)),X3)),X2)
| ( relation_inverse_image(X0,sK2(empty_set,X1,powerset(X2))) = X3 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_69,c_19621]) ).
tcf(c_19647,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X3,sK2(empty_set,X1,powerset(X2))),X2)
| in(apply(X0,sK7(X0,X3,sK2(empty_set,X1,powerset(X2)))),X3)
| ( sK2(empty_set,X1,powerset(X2)) = relation_inverse_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_69,c_19621]) ).
tcf(c_19648,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X3,sK2(empty_set,X1,powerset(X2))),X2)
| in(sK7(X0,X3,sK2(empty_set,X1,powerset(X2))),relation_dom(X0))
| ( sK2(empty_set,X1,powerset(X2)) = relation_inverse_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_68,c_19621]) ).
tcf(c_19649,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(empty_set,X0,powerset(X1)),X2)
| in(sK13(sK2(empty_set,X0,powerset(X1)),X2),X1) ),
inference(superposition,[status(thm)],[c_91,c_19621]) ).
tcf(c_19650,plain,
! [X0: $i,X1: $i] :
( empty(sK2(empty_set,X0,powerset(X1)))
| in(sK18(sK2(empty_set,X0,powerset(X1))),X1) ),
inference(superposition,[status(thm)],[c_12501,c_19621]) ).
tcf(c_19651,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK18(powerset(sK2(empty_set,X0,powerset(X1)))),X2)
| in(sK13(sK18(powerset(sK2(empty_set,X0,powerset(X1)))),X2),X1) ),
inference(superposition,[status(thm)],[c_12692,c_19621]) ).
tcf(c_19652,plain,
! [X0: $i,X1: $i] :
( empty(sK18(powerset(sK2(empty_set,X0,powerset(X1)))))
| in(sK18(sK18(powerset(sK2(empty_set,X0,powerset(X1))))),X1) ),
inference(superposition,[status(thm)],[c_12693,c_19621]) ).
tcf(c_19653,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(sK2(empty_set,X0,powerset(X1)))
| subset(sK17(sK2(empty_set,X0,powerset(X1))),X2)
| in(sK13(sK17(sK2(empty_set,X0,powerset(X1))),X2),X1) ),
inference(superposition,[status(thm)],[c_12705,c_19621]) ).
tcf(c_19654,plain,
! [X0: $i,X1: $i] :
( empty(sK2(empty_set,X0,powerset(X1)))
| in(sK18(sK17(sK2(empty_set,X0,powerset(X1)))),X1) ),
inference(superposition,[status(thm)],[c_12981,c_19621]) ).
tcf(c_19655,plain,
! [X0: $i,X1: $i] :
( empty(sK2(empty_set,X0,powerset(X1)))
| in(sK18(sK17(sK17(sK2(empty_set,X0,powerset(X1))))),X1) ),
inference(superposition,[status(thm)],[c_15371,c_19621]) ).
tcf(c_19656,plain,
! [X0: $i,X1: $i] :
( empty(sK18(powerset(sK2(empty_set,X0,powerset(X1)))))
| in(sK18(sK17(sK18(powerset(sK2(empty_set,X0,powerset(X1)))))),X1) ),
inference(superposition,[status(thm)],[c_12994,c_19621]) ).
tcf(c_19657,plain,
! [X0: $i,X1: $i] :
( empty(sK18(sK17(powerset(sK2(empty_set,X0,powerset(X1))))))
| in(sK18(sK18(sK17(powerset(sK2(empty_set,X0,powerset(X1)))))),X1) ),
inference(superposition,[status(thm)],[c_13274,c_19621]) ).
tcf(c_19658,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(empty_set,X2,sK2(empty_set,X0,powerset(X1))),X1)
| ( sK2(empty_set,X0,powerset(X1)) = empty_set ) ),
inference(superposition,[status(thm)],[c_19241,c_19621]) ).
tcf(c_19765,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(relation_dom(relation_dom(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_99,c_15553]) ).
tcf(c_19766,plain,
sK18(powerset(relation_dom(relation_dom(relation_dom(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_114,c_15553]) ).
tcf(c_19767,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(relation_dom(relation_dom(sK18(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12738,c_15553]) ).
tcf(c_19768,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(relation_dom(relation_dom(sK18(powerset(sK18(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13358,c_15553]) ).
tcf(c_19769,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(relation_dom(relation_dom(sK18(sK17(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13470,c_15553]) ).
tcf(c_19770,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(relation_dom(relation_dom(sK18(powerset(sK18(sK17(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13469,c_15553]) ).
tcf(c_19771,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(relation_dom(relation_dom(sK18(sK17(sK17(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15885,c_15553]) ).
tcf(c_19772,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(relation_dom(relation_dom(sK18(powerset(sK18(sK17(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15887,c_15553]) ).
tcf(c_19773,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(relation_dom(relation_dom(relation_image(X0,empty_set)))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17175,c_15553]) ).
tcf(c_19774,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(relation_dom(relation_dom(sK18(sK17(powerset(sK18(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17880,c_15553]) ).
tcf(c_19775,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(relation_dom(relation_dom(sK18(sK17(powerset(sK18(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17885,c_15553]) ).
tcf(c_19830,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(relation_dom(relation_dom(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_99,c_15588]) ).
tcf(c_19831,plain,
sK18(sK17(powerset(relation_dom(relation_dom(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_114,c_15588]) ).
tcf(c_19832,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(relation_dom(relation_dom(sK18(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12738,c_15588]) ).
tcf(c_19833,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(relation_dom(relation_dom(sK18(powerset(sK18(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13358,c_15588]) ).
tcf(c_19834,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(relation_dom(relation_dom(sK18(sK17(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13470,c_15588]) ).
tcf(c_19835,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(relation_dom(relation_dom(sK18(powerset(sK18(sK17(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13469,c_15588]) ).
tcf(c_19836,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(relation_dom(relation_dom(sK18(sK17(sK17(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15885,c_15588]) ).
tcf(c_19837,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(relation_dom(relation_dom(sK18(powerset(sK18(sK17(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15887,c_15588]) ).
tcf(c_19838,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(relation_dom(relation_dom(relation_image(X0,empty_set)))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17175,c_15588]) ).
tcf(c_19839,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(relation_dom(relation_dom(sK18(sK17(powerset(sK18(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17880,c_15588]) ).
tcf(c_19840,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(relation_dom(relation_dom(sK18(sK17(powerset(sK18(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17885,c_15588]) ).
tcf(c_19877,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X0,X1) = empty_set )
| ( apply(X0,sK4(X0,X1,sK7(empty_set,X2,relation_image(X0,X1)))) = sK7(empty_set,X2,relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_19554,c_60]) ).
tcf(c_19878,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X0,sK7(empty_set,X2,relation_inverse_image(X0,X1))),X1)
| ( relation_inverse_image(X0,X1) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_19554,c_72]) ).
tcf(c_19879,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(empty_set,X2,relation_inverse_image(X0,X1)),relation_dom(X0))
| ( relation_inverse_image(X0,X1) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_19554,c_71]) ).
tcf(c_19880,plain,
! [X0: $i,X1: $i] :
( ( X0 = empty_set )
| ~ in(X0,sK7(empty_set,X1,X0)) ),
inference(superposition,[status(thm)],[c_19554,c_98]) ).
tcf(c_19881,plain,
! [X0: $i,X1: $i] :
( element(sK7(empty_set,X1,X0),X0)
| ( X0 = empty_set ) ),
inference(superposition,[status(thm)],[c_19554,c_97]) ).
tcf(c_19883,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| element(sK7(empty_set,X1,sK17(X0)),X0)
| ( sK17(X0) = empty_set ) ),
inference(superposition,[status(thm)],[c_19554,c_14688]) ).
tcf(c_19884,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| in(sK7(empty_set,X1,sK17(X0)),X0)
| ( sK17(X0) = empty_set ) ),
inference(superposition,[status(thm)],[c_19554,c_12618]) ).
tcf(c_19885,plain,
! [X0: $i,X1: $i] :
( element(sK7(empty_set,X1,sK18(powerset(X0))),X0)
| ( sK18(powerset(X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_19554,c_14689]) ).
tcf(c_19887,plain,
! [X0: $i,X1: $i] :
( in(sK7(empty_set,X1,sK18(powerset(X0))),X0)
| ( sK18(powerset(X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_19554,c_12619]) ).
tcf(c_19890,plain,
! [X0: $i,X1: $i] :
( element(sK7(empty_set,X1,sK18(sK17(powerset(X0)))),X0)
| ( sK18(sK17(powerset(X0))) = empty_set ) ),
inference(superposition,[status(thm)],[c_19554,c_14693]) ).
tcf(c_19892,plain,
! [X0: $i,X1: $i] :
( in(sK7(empty_set,X1,sK18(sK17(powerset(X0)))),X0)
| ( sK18(sK17(powerset(X0))) = empty_set ) ),
inference(superposition,[status(thm)],[c_19554,c_13032]) ).
tcf(c_19893,plain,
! [X0: $i,X1: $i] :
( in(sK7(empty_set,X1,sK18(sK17(sK17(powerset(X0))))),X0)
| ( sK18(sK17(sK17(powerset(X0)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_19554,c_15478]) ).
tcf(c_19895,plain,
! [X0: $i,X1: $i] :
( element(sK7(empty_set,X1,sK18(sK17(sK17(powerset(X0))))),X0)
| ( sK18(sK17(sK17(powerset(X0)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_19554,c_15476]) ).
tcf(c_19896,plain,
! [X0: $i,X1: $i] :
( in(sK7(empty_set,X1,sK17(powerset(X0))),powerset(X0))
| ( sK17(powerset(X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_19554,c_18767]) ).
tcf(c_19897,plain,
! [X0: $i,X1: $i] :
( element(sK7(empty_set,X1,sK17(powerset(X0))),powerset(X0))
| ( sK17(powerset(X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_19554,c_18765]) ).
tcf(c_19898,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(empty_set,X2,sK2(empty_set,X0,powerset(X1))),X1)
| ( sK2(empty_set,X0,powerset(X1)) = empty_set ) ),
inference(superposition,[status(thm)],[c_19554,c_19621]) ).
tcf(c_20029,plain,
! [X0: $i,X1: $i] :
( subset(sK7(empty_set,X1,powerset(X0)),X0)
| ( powerset(X0) = empty_set ) ),
inference(superposition,[status(thm)],[c_19881,c_88]) ).
tcf(c_20039,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X0,X1,sK2(empty_set,X2,powerset(X3))),X3)
| ( sK2(empty_set,X2,powerset(X3)) = relation_image(X0,X1) )
| ( apply(X0,sK3(X0,X1,sK2(empty_set,X2,powerset(X3)))) = sK2(X0,X1,sK2(empty_set,X2,powerset(X3))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_56,c_19619]) ).
tcf(c_20040,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X0,X3,sK2(empty_set,X1,powerset(X2))),X2)
| in(sK3(X0,X3,sK2(empty_set,X1,powerset(X2))),relation_dom(X0))
| ( sK2(empty_set,X1,powerset(X2)) = relation_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_54,c_19619]) ).
tcf(c_20041,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X0,X3,sK2(empty_set,X1,powerset(X2))),X2)
| in(sK3(X0,X3,sK2(empty_set,X1,powerset(X2))),X3)
| ( sK2(empty_set,X1,powerset(X2)) = relation_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_55,c_19619]) ).
tcf(c_20042,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK3(X0,sK2(empty_set,X1,powerset(X2)),X3),X2)
| in(sK2(X0,sK2(empty_set,X1,powerset(X2)),X3),X3)
| ( relation_image(X0,sK2(empty_set,X1,powerset(X2))) = X3 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_55,c_19619]) ).
tcf(c_20043,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK4(X1,sK2(empty_set,X2,powerset(X3)),X0),X3)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,sK2(empty_set,X2,powerset(X3)))) ),
inference(superposition,[status(thm)],[c_59,c_19619]) ).
tcf(c_20044,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,sK2(empty_set,X1,powerset(X2)),X3),X3)
| element(apply(X0,sK7(X0,sK2(empty_set,X1,powerset(X2)),X3)),X2)
| ( relation_inverse_image(X0,sK2(empty_set,X1,powerset(X2))) = X3 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_69,c_19619]) ).
tcf(c_20045,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK7(X0,X3,sK2(empty_set,X1,powerset(X2))),X2)
| in(apply(X0,sK7(X0,X3,sK2(empty_set,X1,powerset(X2)))),X3)
| ( sK2(empty_set,X1,powerset(X2)) = relation_inverse_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_69,c_19619]) ).
tcf(c_20046,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK7(X0,X3,sK2(empty_set,X1,powerset(X2))),X2)
| in(sK7(X0,X3,sK2(empty_set,X1,powerset(X2))),relation_dom(X0))
| ( sK2(empty_set,X1,powerset(X2)) = relation_inverse_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_68,c_19619]) ).
tcf(c_20047,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(empty_set,X0,powerset(X1)),X2)
| element(sK13(sK2(empty_set,X0,powerset(X1)),X2),X1) ),
inference(superposition,[status(thm)],[c_91,c_19619]) ).
tcf(c_20048,plain,
! [X0: $i,X1: $i] :
( empty(sK2(empty_set,X0,powerset(X1)))
| element(sK18(sK2(empty_set,X0,powerset(X1))),X1) ),
inference(superposition,[status(thm)],[c_12501,c_19619]) ).
tcf(c_20049,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK18(powerset(sK2(empty_set,X0,powerset(X1)))),X2)
| element(sK13(sK18(powerset(sK2(empty_set,X0,powerset(X1)))),X2),X1) ),
inference(superposition,[status(thm)],[c_12692,c_19619]) ).
tcf(c_20050,plain,
! [X0: $i,X1: $i] :
( empty(sK18(powerset(sK2(empty_set,X0,powerset(X1)))))
| element(sK18(sK18(powerset(sK2(empty_set,X0,powerset(X1))))),X1) ),
inference(superposition,[status(thm)],[c_12693,c_19619]) ).
tcf(c_20051,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(sK2(empty_set,X0,powerset(X1)))
| subset(sK17(sK2(empty_set,X0,powerset(X1))),X2)
| element(sK13(sK17(sK2(empty_set,X0,powerset(X1))),X2),X1) ),
inference(superposition,[status(thm)],[c_12705,c_19619]) ).
tcf(c_20052,plain,
! [X0: $i,X1: $i] :
( empty(sK2(empty_set,X0,powerset(X1)))
| element(sK18(sK17(sK2(empty_set,X0,powerset(X1)))),X1) ),
inference(superposition,[status(thm)],[c_12981,c_19619]) ).
tcf(c_20053,plain,
! [X0: $i,X1: $i] :
( empty(sK2(empty_set,X0,powerset(X1)))
| element(sK18(sK17(sK17(sK2(empty_set,X0,powerset(X1))))),X1) ),
inference(superposition,[status(thm)],[c_15371,c_19619]) ).
tcf(c_20054,plain,
! [X0: $i,X1: $i] :
( empty(sK18(powerset(sK2(empty_set,X0,powerset(X1)))))
| element(sK18(sK17(sK18(powerset(sK2(empty_set,X0,powerset(X1)))))),X1) ),
inference(superposition,[status(thm)],[c_12994,c_19619]) ).
tcf(c_20055,plain,
! [X0: $i,X1: $i] :
( empty(sK18(sK17(powerset(sK2(empty_set,X0,powerset(X1))))))
| element(sK18(sK18(sK17(powerset(sK2(empty_set,X0,powerset(X1)))))),X1) ),
inference(superposition,[status(thm)],[c_13274,c_19619]) ).
tcf(c_20056,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(empty_set,X2,sK2(empty_set,X0,powerset(X1))),X1)
| ( sK2(empty_set,X0,powerset(X1)) = empty_set ) ),
inference(superposition,[status(thm)],[c_19241,c_19619]) ).
tcf(c_20057,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK7(empty_set,X2,sK2(empty_set,X0,powerset(X1))),X1)
| ( sK2(empty_set,X0,powerset(X1)) = empty_set ) ),
inference(superposition,[status(thm)],[c_19554,c_19619]) ).
tcf(c_20173,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK2(empty_set,X3,powerset(X1)) = relation_image(X0,X2) )
| ( apply(X0,sK3(X0,X2,sK2(empty_set,X3,powerset(X1)))) = sK2(X0,X2,sK2(empty_set,X3,powerset(X1))) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_56,c_19620]) ).
tcf(c_20174,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK3(X0,X3,sK2(empty_set,X2,powerset(X1))),relation_dom(X0))
| ( sK2(empty_set,X2,powerset(X1)) = relation_image(X0,X3) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_54,c_19620]) ).
tcf(c_20175,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK3(X0,X3,sK2(empty_set,X2,powerset(X1))),X3)
| ( sK2(empty_set,X2,powerset(X1)) = relation_image(X0,X3) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_55,c_19620]) ).
tcf(c_20176,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,sK2(empty_set,X2,powerset(X1)),X3),X3)
| ( relation_image(X0,sK2(empty_set,X2,powerset(X1))) = X3 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_55,c_19620]) ).
tcf(c_20177,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ empty(X3)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,sK2(empty_set,X2,powerset(X3)))) ),
inference(superposition,[status(thm)],[c_59,c_19620]) ).
tcf(c_20178,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,sK2(empty_set,X2,powerset(X1)),X3),X3)
| ( relation_inverse_image(X0,sK2(empty_set,X2,powerset(X1))) = X3 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_69,c_19620]) ).
tcf(c_20179,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X0,sK7(X0,X3,sK2(empty_set,X2,powerset(X1)))),X3)
| ( sK2(empty_set,X2,powerset(X1)) = relation_inverse_image(X0,X3) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_69,c_19620]) ).
tcf(c_20180,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X3,sK2(empty_set,X2,powerset(X1))),relation_dom(X0))
| ( sK2(empty_set,X2,powerset(X1)) = relation_inverse_image(X0,X3) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_68,c_19620]) ).
tcf(c_20181,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(empty_set,X1,powerset(X0)),X2)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_91,c_19620]) ).
tcf(c_20183,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK18(powerset(sK2(empty_set,X1,powerset(X0)))),X2)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12692,c_19620]) ).
tcf(c_20185,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(sK2(empty_set,X1,powerset(X0)))
| subset(sK17(sK2(empty_set,X1,powerset(X0))),X2)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12705,c_19620]) ).
tcf(c_20186,plain,
! [X0: $i,X1: $i] :
( empty(sK2(empty_set,X1,powerset(X0)))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12981,c_19620]) ).
tcf(c_20188,plain,
! [X0: $i,X1: $i] :
( empty(sK18(powerset(sK2(empty_set,X1,powerset(X0)))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12994,c_19620]) ).
tcf(c_20189,plain,
! [X0: $i,X1: $i] :
( empty(sK18(sK17(powerset(sK2(empty_set,X1,powerset(X0))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13274,c_19620]) ).
tcf(c_20190,plain,
! [X0: $i,X1: $i] :
( ( sK2(empty_set,X1,powerset(X0)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_19241,c_19620]) ).
tcf(c_20308,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(powerset(relation_dom(relation_dom(sK2(empty_set,X1,powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20186,c_15588]) ).
tcf(c_20309,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(relation_dom(relation_dom(relation_dom(sK2(empty_set,X1,powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20186,c_15553]) ).
tcf(c_20310,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK18(sK17(powerset(sK2(empty_set,X1,powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20186,c_13492]) ).
tcf(c_20311,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK18(sK17(powerset(sK2(empty_set,X1,powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20186,c_13490]) ).
tcf(c_20312,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(powerset(relation_dom(relation_dom(sK2(empty_set,X1,powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20186,c_15527]) ).
tcf(c_20313,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK18(powerset(relation_dom(sK2(empty_set,X1,powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20186,c_15355]) ).
tcf(c_20314,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK18(powerset(relation_dom(sK2(empty_set,X1,powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20186,c_15317]) ).
tcf(c_20315,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(relation_dom(sK18(powerset(sK2(empty_set,X1,powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20186,c_13260]) ).
tcf(c_20316,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK2(empty_set,X1,powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20186,c_15261]) ).
tcf(c_20317,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_dom(sK2(empty_set,X2,powerset(X0)))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20186,c_15230]) ).
tcf(c_20318,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(powerset(sK18(powerset(sK2(empty_set,X1,powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20186,c_13064]) ).
tcf(c_20319,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK18(powerset(sK2(empty_set,X2,powerset(X0)))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20186,c_12767]) ).
tcf(c_20320,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(sK18(powerset(sK2(empty_set,X1,powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20186,c_12765]) ).
tcf(c_20321,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(sK17(powerset(sK2(empty_set,X1,powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20186,c_15973]) ).
tcf(c_20322,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(sK17(powerset(sK2(empty_set,X1,powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20186,c_13494]) ).
tcf(c_20323,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(powerset(relation_dom(sK2(empty_set,X1,powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20186,c_14397]) ).
tcf(c_20324,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(relation_dom(relation_dom(sK2(empty_set,X1,powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20186,c_13258]) ).
tcf(c_20325,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(powerset(relation_dom(sK2(empty_set,X1,powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20186,c_13062]) ).
tcf(c_20326,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK18(powerset(sK2(empty_set,X1,powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20186,c_12959]) ).
tcf(c_20327,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK18(powerset(sK2(empty_set,X1,powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20186,c_12766]) ).
tcf(c_20328,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK2(empty_set,X1,powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20186,c_12718]) ).
tcf(c_20329,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(sK2(empty_set,X2,powerset(X0))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20186,c_12604]) ).
tcf(c_20330,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(powerset(sK2(empty_set,X1,powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20186,c_13495]) ).
tcf(c_20331,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(relation_dom(sK2(empty_set,X1,powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20186,c_12957]) ).
tcf(c_20332,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(powerset(sK2(empty_set,X1,powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20186,c_12768]) ).
tcf(c_20333,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK2(empty_set,X1,powerset(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20186,c_12769]) ).
tcf(c_20334,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(sK2(empty_set,X1,powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20186,c_12674]) ).
tcf(c_20335,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK2(empty_set,X1,powerset(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20186,c_12550]) ).
tcf(c_20336,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK2(empty_set,X2,powerset(X0)) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20186,c_93]) ).
tcf(c_20337,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK2(empty_set,X1,powerset(X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20186,c_12406]) ).
tcf(c_20339,plain,
! [X0: $i,X1: $i] :
( one_to_one(sK2(empty_set,X1,powerset(X0)))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20186,c_5773]) ).
tcf(c_20340,plain,
! [X0: $i,X1: $i] :
( relation(sK2(empty_set,X1,powerset(X0)))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20186,c_77]) ).
tcf(c_20341,plain,
! [X0: $i,X1: $i] :
( function(sK2(empty_set,X1,powerset(X0)))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20186,c_66]) ).
tcf(c_20573,plain,
! [X0: $i,X1: $i] :
( one_to_one(sK2(empty_set,X0,powerset(X1)))
| ( apply(sK2(empty_set,X0,powerset(X1)),sK11(sK2(empty_set,X0,powerset(X1)))) = apply(sK2(empty_set,X0,powerset(X1)),sK12(sK2(empty_set,X0,powerset(X1)))) )
| ~ empty(X1)
| ~ function(sK2(empty_set,X0,powerset(X1))) ),
inference(superposition,[status(thm)],[c_20340,c_84]) ).
tcf(c_20598,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(powerset(relation_dom(relation_dom(sK18(powerset(sK2(empty_set,X1,powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20188,c_15588]) ).
tcf(c_20599,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(relation_dom(relation_dom(relation_dom(sK18(powerset(sK2(empty_set,X1,powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20188,c_15553]) ).
tcf(c_20600,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK18(sK17(powerset(sK18(powerset(sK2(empty_set,X1,powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20188,c_13492]) ).
tcf(c_20601,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK18(sK17(powerset(sK18(powerset(sK2(empty_set,X1,powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20188,c_13490]) ).
tcf(c_20602,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(powerset(relation_dom(relation_dom(sK18(powerset(sK2(empty_set,X1,powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20188,c_15527]) ).
tcf(c_20603,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK18(powerset(relation_dom(sK18(powerset(sK2(empty_set,X1,powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20188,c_15355]) ).
tcf(c_20604,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK18(powerset(relation_dom(sK18(powerset(sK2(empty_set,X1,powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20188,c_15317]) ).
tcf(c_20605,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(relation_dom(sK18(powerset(sK18(powerset(sK2(empty_set,X1,powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20188,c_13260]) ).
tcf(c_20606,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK18(powerset(sK2(empty_set,X1,powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20188,c_15261]) ).
tcf(c_20607,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_dom(sK18(powerset(sK2(empty_set,X2,powerset(X0)))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20188,c_15230]) ).
tcf(c_20608,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(powerset(sK18(powerset(sK18(powerset(sK2(empty_set,X1,powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20188,c_13064]) ).
tcf(c_20609,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK18(powerset(sK18(powerset(sK2(empty_set,X2,powerset(X0)))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20188,c_12767]) ).
tcf(c_20610,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(sK18(powerset(sK18(powerset(sK2(empty_set,X1,powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20188,c_12765]) ).
tcf(c_20611,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(sK17(powerset(sK18(powerset(sK2(empty_set,X1,powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20188,c_15973]) ).
tcf(c_20612,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(sK17(powerset(sK18(powerset(sK2(empty_set,X1,powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20188,c_13494]) ).
tcf(c_20613,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(powerset(relation_dom(sK18(powerset(sK2(empty_set,X1,powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20188,c_14397]) ).
tcf(c_20614,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(relation_dom(relation_dom(sK18(powerset(sK2(empty_set,X1,powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20188,c_13258]) ).
tcf(c_20615,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(powerset(relation_dom(sK18(powerset(sK2(empty_set,X1,powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20188,c_13062]) ).
tcf(c_20616,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK18(powerset(sK18(powerset(sK2(empty_set,X1,powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20188,c_12959]) ).
tcf(c_20617,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK18(powerset(sK18(powerset(sK2(empty_set,X1,powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20188,c_12766]) ).
tcf(c_20618,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK18(powerset(sK2(empty_set,X1,powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20188,c_12718]) ).
tcf(c_20619,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(sK18(powerset(sK2(empty_set,X2,powerset(X0))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20188,c_12604]) ).
tcf(c_20620,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(powerset(sK18(powerset(sK2(empty_set,X1,powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20188,c_13495]) ).
tcf(c_20629,plain,
! [X0: $i,X1: $i] :
( one_to_one(sK18(powerset(sK2(empty_set,X1,powerset(X0)))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20188,c_5773]) ).
tcf(c_20630,plain,
! [X0: $i,X1: $i] :
( relation(sK18(powerset(sK2(empty_set,X1,powerset(X0)))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20188,c_77]) ).
tcf(c_20631,plain,
! [X0: $i,X1: $i] :
( function(sK18(powerset(sK2(empty_set,X1,powerset(X0)))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20188,c_66]) ).
tcf(c_20793,plain,
! [X0: $i,X1: $i] : subset(sK7(empty_set,X1,powerset(X0)),X0),
inference(global_subsumption_just,[status(thm)],[c_20029,c_114,c_110,c_14309,c_20029]) ).
tcf(c_20794,plain,
! [X0: $i,X1: $i] : subset(sK7(empty_set,X0,powerset(X1)),X1),
inference(renaming,[status(thm)],[c_20793]) ).
tcf(c_20796,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,X2)
| ~ in(X0,sK7(empty_set,X1,powerset(X2))) ),
inference(superposition,[status(thm)],[c_20794,c_300]) ).
tcf(c_20797,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(X2)
| ~ in(X0,sK7(empty_set,X1,powerset(X2))) ),
inference(superposition,[status(thm)],[c_20794,c_299]) ).
tcf(c_20798,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ in(X0,sK7(empty_set,X1,powerset(X2))) ),
inference(superposition,[status(thm)],[c_20794,c_92]) ).
tcf(c_20821,plain,
! [X0: $i,X1: $i] :
( one_to_one(sK18(powerset(sK2(empty_set,X0,powerset(X1)))))
| ( apply(sK18(powerset(sK2(empty_set,X0,powerset(X1)))),sK11(sK18(powerset(sK2(empty_set,X0,powerset(X1)))))) = apply(sK18(powerset(sK2(empty_set,X0,powerset(X1)))),sK12(sK18(powerset(sK2(empty_set,X0,powerset(X1)))))) )
| ~ empty(X1)
| ~ function(sK18(powerset(sK2(empty_set,X0,powerset(X1))))) ),
inference(superposition,[status(thm)],[c_20630,c_84]) ).
tcf(c_20836,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,X1,sK7(empty_set,X2,powerset(X3))),X3)
| ( sK7(empty_set,X2,powerset(X3)) = relation_image(X0,X1) )
| ( apply(X0,sK3(X0,X1,sK7(empty_set,X2,powerset(X3)))) = sK2(X0,X1,sK7(empty_set,X2,powerset(X3))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_56,c_20798]) ).
tcf(c_20837,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,X3,sK7(empty_set,X1,powerset(X2))),X2)
| in(sK3(X0,X3,sK7(empty_set,X1,powerset(X2))),relation_dom(X0))
| ( sK7(empty_set,X1,powerset(X2)) = relation_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_54,c_20798]) ).
tcf(c_20838,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK3(X0,X3,sK7(empty_set,X1,powerset(X2))),X3)
| in(sK2(X0,X3,sK7(empty_set,X1,powerset(X2))),X2)
| ( sK7(empty_set,X1,powerset(X2)) = relation_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_55,c_20798]) ).
tcf(c_20839,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK3(X0,sK7(empty_set,X1,powerset(X2)),X3),X2)
| in(sK2(X0,sK7(empty_set,X1,powerset(X2)),X3),X3)
| ( relation_image(X0,sK7(empty_set,X1,powerset(X2))) = X3 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_55,c_20798]) ).
tcf(c_20840,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK4(X1,sK7(empty_set,X2,powerset(X3)),X0),X3)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,sK7(empty_set,X2,powerset(X3)))) ),
inference(superposition,[status(thm)],[c_59,c_20798]) ).
tcf(c_20841,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,sK7(empty_set,X1,powerset(X2)),X3),X3)
| in(apply(X0,sK7(X0,sK7(empty_set,X1,powerset(X2)),X3)),X2)
| ( relation_inverse_image(X0,sK7(empty_set,X1,powerset(X2))) = X3 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_69,c_20798]) ).
tcf(c_20842,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X3,sK7(empty_set,X1,powerset(X2))),X2)
| in(apply(X0,sK7(X0,X3,sK7(empty_set,X1,powerset(X2)))),X3)
| ( sK7(empty_set,X1,powerset(X2)) = relation_inverse_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_69,c_20798]) ).
tcf(c_20843,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X3,sK7(empty_set,X1,powerset(X2))),X2)
| in(sK7(X0,X3,sK7(empty_set,X1,powerset(X2))),relation_dom(X0))
| ( sK7(empty_set,X1,powerset(X2)) = relation_inverse_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_68,c_20798]) ).
tcf(c_20844,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK7(empty_set,X0,powerset(X1)),X2)
| in(sK13(sK7(empty_set,X0,powerset(X1)),X2),X1) ),
inference(superposition,[status(thm)],[c_91,c_20798]) ).
tcf(c_20845,plain,
! [X0: $i,X1: $i] :
( empty(sK7(empty_set,X0,powerset(X1)))
| in(sK18(sK7(empty_set,X0,powerset(X1))),X1) ),
inference(superposition,[status(thm)],[c_12501,c_20798]) ).
tcf(c_20846,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK18(powerset(sK7(empty_set,X0,powerset(X1)))),X2)
| in(sK13(sK18(powerset(sK7(empty_set,X0,powerset(X1)))),X2),X1) ),
inference(superposition,[status(thm)],[c_12692,c_20798]) ).
tcf(c_20847,plain,
! [X0: $i,X1: $i] :
( empty(sK18(powerset(sK7(empty_set,X0,powerset(X1)))))
| in(sK18(sK18(powerset(sK7(empty_set,X0,powerset(X1))))),X1) ),
inference(superposition,[status(thm)],[c_12693,c_20798]) ).
tcf(c_20848,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(sK7(empty_set,X0,powerset(X1)))
| subset(sK17(sK7(empty_set,X0,powerset(X1))),X2)
| in(sK13(sK17(sK7(empty_set,X0,powerset(X1))),X2),X1) ),
inference(superposition,[status(thm)],[c_12705,c_20798]) ).
tcf(c_20849,plain,
! [X0: $i,X1: $i] :
( empty(sK7(empty_set,X0,powerset(X1)))
| in(sK18(sK17(sK7(empty_set,X0,powerset(X1)))),X1) ),
inference(superposition,[status(thm)],[c_12981,c_20798]) ).
tcf(c_20850,plain,
! [X0: $i,X1: $i] :
( empty(sK7(empty_set,X0,powerset(X1)))
| in(sK18(sK17(sK17(sK7(empty_set,X0,powerset(X1))))),X1) ),
inference(superposition,[status(thm)],[c_15371,c_20798]) ).
tcf(c_20851,plain,
! [X0: $i,X1: $i] :
( empty(sK18(powerset(sK7(empty_set,X0,powerset(X1)))))
| in(sK18(sK17(sK18(powerset(sK7(empty_set,X0,powerset(X1)))))),X1) ),
inference(superposition,[status(thm)],[c_12994,c_20798]) ).
tcf(c_20852,plain,
! [X0: $i,X1: $i] :
( empty(sK18(sK17(powerset(sK7(empty_set,X0,powerset(X1))))))
| in(sK18(sK18(sK17(powerset(sK7(empty_set,X0,powerset(X1)))))),X1) ),
inference(superposition,[status(thm)],[c_13274,c_20798]) ).
tcf(c_20853,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(empty_set,X2,sK7(empty_set,X0,powerset(X1))),X1)
| ( sK7(empty_set,X0,powerset(X1)) = empty_set ) ),
inference(superposition,[status(thm)],[c_19241,c_20798]) ).
tcf(c_20854,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(empty_set,X2,sK7(empty_set,X0,powerset(X1))),X1)
| ( sK7(empty_set,X0,powerset(X1)) = empty_set ) ),
inference(superposition,[status(thm)],[c_19554,c_20798]) ).
tcf(c_21015,plain,
! [X0: $i,X1: $i] :
( ( sK2(empty_set,X1,powerset(relation_dom(X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_99,c_20190]) ).
tcf(c_21016,plain,
! [X0: $i] : sK2(empty_set,X0,powerset(empty_set)) = empty_set,
inference(superposition,[status(thm)],[c_114,c_20190]) ).
tcf(c_21017,plain,
! [X0: $i,X1: $i] :
( ( sK2(empty_set,X1,powerset(sK18(powerset(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12738,c_20190]) ).
tcf(c_21018,plain,
! [X0: $i,X1: $i] :
( ( sK2(empty_set,X1,powerset(sK18(powerset(sK18(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13358,c_20190]) ).
tcf(c_21019,plain,
! [X0: $i,X1: $i] :
( ( sK2(empty_set,X1,powerset(sK18(sK17(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13470,c_20190]) ).
tcf(c_21020,plain,
! [X0: $i,X1: $i] :
( ( sK2(empty_set,X1,powerset(sK18(powerset(sK18(sK17(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13469,c_20190]) ).
tcf(c_21021,plain,
! [X0: $i,X1: $i] :
( ( sK2(empty_set,X1,powerset(sK18(sK17(sK17(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15885,c_20190]) ).
tcf(c_21022,plain,
! [X0: $i,X1: $i] :
( ( sK2(empty_set,X1,powerset(sK18(powerset(sK18(sK17(sK17(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15887,c_20190]) ).
tcf(c_21023,plain,
! [X0: $i,X1: $i] :
( ( sK2(empty_set,X1,powerset(relation_image(X0,empty_set))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17175,c_20190]) ).
tcf(c_21024,plain,
! [X0: $i,X1: $i] :
( ( sK2(empty_set,X1,powerset(sK18(sK17(powerset(sK18(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17880,c_20190]) ).
tcf(c_21025,plain,
! [X0: $i,X1: $i] :
( ( sK2(empty_set,X1,powerset(sK18(sK17(powerset(sK18(sK17(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17885,c_20190]) ).
tcf(c_21026,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK2(empty_set,X1,powerset(sK2(empty_set,X2,powerset(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20186,c_20190]) ).
tcf(c_21027,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK2(empty_set,X1,powerset(sK18(powerset(sK2(empty_set,X2,powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20188,c_20190]) ).
tcf(c_21074,plain,
! [X0: $i,X1: $i] :
( ( relation_image(empty_set,X1) = powerset(empty_set) )
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ in(X0,X1)
| ~ in(X0,relation_dom(empty_set))
| ~ in(sK2(empty_set,X1,powerset(empty_set)),powerset(empty_set))
| ( apply(empty_set,X0) != empty_set ) ),
inference(superposition,[status(thm)],[c_21016,c_53]) ).
tcf(c_21075,plain,
! [X0: $i] :
( in(empty_set,powerset(empty_set))
| ( relation_image(empty_set,X0) = powerset(empty_set) )
| ( apply(empty_set,sK3(empty_set,X0,powerset(empty_set))) = sK2(empty_set,X0,powerset(empty_set)) )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_21016,c_56]) ).
tcf(c_21076,plain,
! [X0: $i] :
( in(empty_set,powerset(empty_set))
| in(sK3(empty_set,X0,powerset(empty_set)),relation_dom(empty_set))
| ( relation_image(empty_set,X0) = powerset(empty_set) )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_21016,c_54]) ).
tcf(c_21077,plain,
! [X0: $i] :
( in(empty_set,powerset(empty_set))
| in(sK3(empty_set,X0,powerset(empty_set)),X0)
| ( relation_image(empty_set,X0) = powerset(empty_set) )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_21016,c_55]) ).
tcf(c_21078,plain,
( ( powerset(empty_set) = empty_set )
| ~ in(powerset(empty_set),empty_set) ),
inference(superposition,[status(thm)],[c_21016,c_19251]) ).
tcf(c_21079,plain,
( element(empty_set,powerset(empty_set))
| ( powerset(empty_set) = empty_set ) ),
inference(superposition,[status(thm)],[c_21016,c_19252]) ).
tcf(c_21080,plain,
( in(empty_set,powerset(empty_set))
| ( powerset(empty_set) = empty_set ) ),
inference(superposition,[status(thm)],[c_21016,c_19241]) ).
tcf(c_21094,plain,
! [X0: $i] :
( in(empty_set,powerset(empty_set))
| in(sK3(empty_set,X0,powerset(empty_set)),X0)
| ( powerset(empty_set) = empty_set )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(light_normalisation,[status(thm)],[c_21077,c_17316]) ).
tcf(c_21095,plain,
! [X0: $i] :
( in(empty_set,powerset(empty_set))
| in(sK3(empty_set,X0,powerset(empty_set)),empty_set)
| ( powerset(empty_set) = empty_set )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(light_normalisation,[status(thm)],[c_21076,c_12551,c_17316]) ).
tcf(c_21096,plain,
! [X0: $i] :
( in(empty_set,powerset(empty_set))
| ( powerset(empty_set) = empty_set )
| ( apply(empty_set,sK3(empty_set,X0,powerset(empty_set))) = empty_set )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(light_normalisation,[status(thm)],[c_21075,c_17316,c_21016]) ).
tcf(c_21097,plain,
! [X0: $i,X1: $i] :
( ( relation_image(empty_set,X1) = powerset(empty_set) )
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ in(X0,empty_set)
| ~ in(X0,X1)
| ~ in(sK2(empty_set,X1,powerset(empty_set)),powerset(empty_set))
| ( apply(empty_set,X0) != empty_set ) ),
inference(light_normalisation,[status(thm)],[c_21074,c_12551]) ).
tcf(c_21102,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X0,X1,sK7(empty_set,X2,powerset(X3))),X3)
| ( sK7(empty_set,X2,powerset(X3)) = relation_image(X0,X1) )
| ( apply(X0,sK3(X0,X1,sK7(empty_set,X2,powerset(X3)))) = sK2(X0,X1,sK7(empty_set,X2,powerset(X3))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_56,c_20796]) ).
tcf(c_21103,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X0,X3,sK7(empty_set,X1,powerset(X2))),X2)
| in(sK3(X0,X3,sK7(empty_set,X1,powerset(X2))),relation_dom(X0))
| ( sK7(empty_set,X1,powerset(X2)) = relation_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_54,c_20796]) ).
tcf(c_21104,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X0,X3,sK7(empty_set,X1,powerset(X2))),X2)
| in(sK3(X0,X3,sK7(empty_set,X1,powerset(X2))),X3)
| ( sK7(empty_set,X1,powerset(X2)) = relation_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_55,c_20796]) ).
tcf(c_21105,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK3(X0,sK7(empty_set,X1,powerset(X2)),X3),X2)
| in(sK2(X0,sK7(empty_set,X1,powerset(X2)),X3),X3)
| ( relation_image(X0,sK7(empty_set,X1,powerset(X2))) = X3 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_55,c_20796]) ).
tcf(c_21106,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK4(X1,sK7(empty_set,X2,powerset(X3)),X0),X3)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,sK7(empty_set,X2,powerset(X3)))) ),
inference(superposition,[status(thm)],[c_59,c_20796]) ).
tcf(c_21107,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,sK7(empty_set,X1,powerset(X2)),X3),X3)
| element(apply(X0,sK7(X0,sK7(empty_set,X1,powerset(X2)),X3)),X2)
| ( relation_inverse_image(X0,sK7(empty_set,X1,powerset(X2))) = X3 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_69,c_20796]) ).
tcf(c_21108,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK7(X0,X3,sK7(empty_set,X1,powerset(X2))),X2)
| in(apply(X0,sK7(X0,X3,sK7(empty_set,X1,powerset(X2)))),X3)
| ( sK7(empty_set,X1,powerset(X2)) = relation_inverse_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_69,c_20796]) ).
tcf(c_21109,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK7(X0,X3,sK7(empty_set,X1,powerset(X2))),X2)
| in(sK7(X0,X3,sK7(empty_set,X1,powerset(X2))),relation_dom(X0))
| ( sK7(empty_set,X1,powerset(X2)) = relation_inverse_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_68,c_20796]) ).
tcf(c_21110,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK7(empty_set,X0,powerset(X1)),X2)
| element(sK13(sK7(empty_set,X0,powerset(X1)),X2),X1) ),
inference(superposition,[status(thm)],[c_91,c_20796]) ).
tcf(c_21111,plain,
! [X0: $i,X1: $i] :
( empty(sK7(empty_set,X0,powerset(X1)))
| element(sK18(sK7(empty_set,X0,powerset(X1))),X1) ),
inference(superposition,[status(thm)],[c_12501,c_20796]) ).
tcf(c_21112,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK18(powerset(sK7(empty_set,X0,powerset(X1)))),X2)
| element(sK13(sK18(powerset(sK7(empty_set,X0,powerset(X1)))),X2),X1) ),
inference(superposition,[status(thm)],[c_12692,c_20796]) ).
tcf(c_21113,plain,
! [X0: $i,X1: $i] :
( empty(sK18(powerset(sK7(empty_set,X0,powerset(X1)))))
| element(sK18(sK18(powerset(sK7(empty_set,X0,powerset(X1))))),X1) ),
inference(superposition,[status(thm)],[c_12693,c_20796]) ).
tcf(c_21114,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(sK7(empty_set,X0,powerset(X1)))
| subset(sK17(sK7(empty_set,X0,powerset(X1))),X2)
| element(sK13(sK17(sK7(empty_set,X0,powerset(X1))),X2),X1) ),
inference(superposition,[status(thm)],[c_12705,c_20796]) ).
tcf(c_21115,plain,
! [X0: $i,X1: $i] :
( empty(sK7(empty_set,X0,powerset(X1)))
| element(sK18(sK17(sK7(empty_set,X0,powerset(X1)))),X1) ),
inference(superposition,[status(thm)],[c_12981,c_20796]) ).
tcf(c_21116,plain,
! [X0: $i,X1: $i] :
( empty(sK7(empty_set,X0,powerset(X1)))
| element(sK18(sK17(sK17(sK7(empty_set,X0,powerset(X1))))),X1) ),
inference(superposition,[status(thm)],[c_15371,c_20796]) ).
tcf(c_21117,plain,
! [X0: $i,X1: $i] :
( empty(sK18(powerset(sK7(empty_set,X0,powerset(X1)))))
| element(sK18(sK17(sK18(powerset(sK7(empty_set,X0,powerset(X1)))))),X1) ),
inference(superposition,[status(thm)],[c_12994,c_20796]) ).
tcf(c_21118,plain,
! [X0: $i,X1: $i] :
( empty(sK18(sK17(powerset(sK7(empty_set,X0,powerset(X1))))))
| element(sK18(sK18(sK17(powerset(sK7(empty_set,X0,powerset(X1)))))),X1) ),
inference(superposition,[status(thm)],[c_13274,c_20796]) ).
tcf(c_21119,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(empty_set,X2,sK7(empty_set,X0,powerset(X1))),X1)
| ( sK7(empty_set,X0,powerset(X1)) = empty_set ) ),
inference(superposition,[status(thm)],[c_19241,c_20796]) ).
tcf(c_21120,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK7(empty_set,X2,sK7(empty_set,X0,powerset(X1))),X1)
| ( sK7(empty_set,X0,powerset(X1)) = empty_set ) ),
inference(superposition,[status(thm)],[c_19554,c_20796]) ).
tcf(c_21286,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK7(empty_set,X3,powerset(X1)) = relation_image(X0,X2) )
| ( apply(X0,sK3(X0,X2,sK7(empty_set,X3,powerset(X1)))) = sK2(X0,X2,sK7(empty_set,X3,powerset(X1))) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_56,c_20797]) ).
tcf(c_21287,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK3(X0,X3,sK7(empty_set,X2,powerset(X1))),relation_dom(X0))
| ( sK7(empty_set,X2,powerset(X1)) = relation_image(X0,X3) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_54,c_20797]) ).
tcf(c_21288,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK3(X0,X3,sK7(empty_set,X2,powerset(X1))),X3)
| ( sK7(empty_set,X2,powerset(X1)) = relation_image(X0,X3) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_55,c_20797]) ).
tcf(c_21289,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,sK7(empty_set,X2,powerset(X1)),X3),X3)
| ( relation_image(X0,sK7(empty_set,X2,powerset(X1))) = X3 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_55,c_20797]) ).
tcf(c_21290,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ empty(X3)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,sK7(empty_set,X2,powerset(X3)))) ),
inference(superposition,[status(thm)],[c_59,c_20797]) ).
tcf(c_21291,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,sK7(empty_set,X2,powerset(X1)),X3),X3)
| ( relation_inverse_image(X0,sK7(empty_set,X2,powerset(X1))) = X3 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_69,c_20797]) ).
tcf(c_21292,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X0,sK7(X0,X3,sK7(empty_set,X2,powerset(X1)))),X3)
| ( sK7(empty_set,X2,powerset(X1)) = relation_inverse_image(X0,X3) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_69,c_20797]) ).
tcf(c_21293,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X3,sK7(empty_set,X2,powerset(X1))),relation_dom(X0))
| ( sK7(empty_set,X2,powerset(X1)) = relation_inverse_image(X0,X3) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_68,c_20797]) ).
tcf(c_21294,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK7(empty_set,X1,powerset(X0)),X2)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_91,c_20797]) ).
tcf(c_21296,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK18(powerset(sK7(empty_set,X1,powerset(X0)))),X2)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12692,c_20797]) ).
tcf(c_21298,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(sK7(empty_set,X1,powerset(X0)))
| subset(sK17(sK7(empty_set,X1,powerset(X0))),X2)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12705,c_20797]) ).
tcf(c_21299,plain,
! [X0: $i,X1: $i] :
( empty(sK7(empty_set,X1,powerset(X0)))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12981,c_20797]) ).
tcf(c_21301,plain,
! [X0: $i,X1: $i] :
( empty(sK18(powerset(sK7(empty_set,X1,powerset(X0)))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12994,c_20797]) ).
tcf(c_21302,plain,
! [X0: $i,X1: $i] :
( empty(sK18(sK17(powerset(sK7(empty_set,X1,powerset(X0))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13274,c_20797]) ).
tcf(c_21303,plain,
! [X0: $i,X1: $i] :
( ( sK7(empty_set,X1,powerset(X0)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_19241,c_20797]) ).
tcf(c_21399,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK2(empty_set,X1,powerset(sK7(empty_set,X2,powerset(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21299,c_20190]) ).
tcf(c_21400,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(powerset(relation_dom(relation_dom(sK7(empty_set,X1,powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21299,c_15588]) ).
tcf(c_21401,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(relation_dom(relation_dom(relation_dom(sK7(empty_set,X1,powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21299,c_15553]) ).
tcf(c_21402,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK18(sK17(powerset(sK7(empty_set,X1,powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21299,c_13492]) ).
tcf(c_21403,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK18(sK17(powerset(sK7(empty_set,X1,powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21299,c_13490]) ).
tcf(c_21404,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(powerset(relation_dom(relation_dom(sK7(empty_set,X1,powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21299,c_15527]) ).
tcf(c_21405,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK18(powerset(relation_dom(sK7(empty_set,X1,powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21299,c_15355]) ).
tcf(c_21406,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK18(powerset(relation_dom(sK7(empty_set,X1,powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21299,c_15317]) ).
tcf(c_21407,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(relation_dom(sK18(powerset(sK7(empty_set,X1,powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21299,c_13260]) ).
tcf(c_21408,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK7(empty_set,X1,powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21299,c_15261]) ).
tcf(c_21409,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_dom(sK7(empty_set,X2,powerset(X0)))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21299,c_15230]) ).
tcf(c_21410,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(powerset(sK18(powerset(sK7(empty_set,X1,powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21299,c_13064]) ).
tcf(c_21411,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK18(powerset(sK7(empty_set,X2,powerset(X0)))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21299,c_12767]) ).
tcf(c_21412,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(sK18(powerset(sK7(empty_set,X1,powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21299,c_12765]) ).
tcf(c_21413,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(sK17(powerset(sK7(empty_set,X1,powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21299,c_15973]) ).
tcf(c_21414,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(sK17(powerset(sK7(empty_set,X1,powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21299,c_13494]) ).
tcf(c_21415,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(powerset(relation_dom(sK7(empty_set,X1,powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21299,c_14397]) ).
tcf(c_21416,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(relation_dom(relation_dom(sK7(empty_set,X1,powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21299,c_13258]) ).
tcf(c_21417,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(powerset(relation_dom(sK7(empty_set,X1,powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21299,c_13062]) ).
tcf(c_21418,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK18(powerset(sK7(empty_set,X1,powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21299,c_12959]) ).
tcf(c_21419,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK18(powerset(sK7(empty_set,X1,powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21299,c_12766]) ).
tcf(c_21420,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK7(empty_set,X1,powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21299,c_12718]) ).
tcf(c_21421,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(sK7(empty_set,X2,powerset(X0))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21299,c_12604]) ).
tcf(c_21422,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(powerset(sK7(empty_set,X1,powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21299,c_13495]) ).
tcf(c_21423,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(relation_dom(sK7(empty_set,X1,powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21299,c_12957]) ).
tcf(c_21424,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(powerset(sK7(empty_set,X1,powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21299,c_12768]) ).
tcf(c_21425,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK7(empty_set,X1,powerset(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21299,c_12769]) ).
tcf(c_21426,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(sK7(empty_set,X1,powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21299,c_12674]) ).
tcf(c_21427,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK7(empty_set,X1,powerset(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21299,c_12550]) ).
tcf(c_21428,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK7(empty_set,X2,powerset(X0)) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21299,c_93]) ).
tcf(c_21429,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(empty_set,X1,powerset(X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21299,c_12406]) ).
tcf(c_21431,plain,
! [X0: $i,X1: $i] :
( one_to_one(sK7(empty_set,X1,powerset(X0)))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21299,c_5773]) ).
tcf(c_21432,plain,
! [X0: $i,X1: $i] :
( relation(sK7(empty_set,X1,powerset(X0)))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21299,c_77]) ).
tcf(c_21433,plain,
! [X0: $i,X1: $i] :
( function(sK7(empty_set,X1,powerset(X0)))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21299,c_66]) ).
tcf(c_21752,plain,
! [X0: $i,X1: $i] :
( one_to_one(sK7(empty_set,X0,powerset(X1)))
| ( apply(sK7(empty_set,X0,powerset(X1)),sK11(sK7(empty_set,X0,powerset(X1)))) = apply(sK7(empty_set,X0,powerset(X1)),sK12(sK7(empty_set,X0,powerset(X1)))) )
| ~ empty(X1)
| ~ function(sK7(empty_set,X0,powerset(X1))) ),
inference(superposition,[status(thm)],[c_21432,c_84]) ).
tcf(c_21773,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK2(empty_set,X1,powerset(sK18(powerset(sK7(empty_set,X2,powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21301,c_20190]) ).
tcf(c_21774,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(powerset(relation_dom(relation_dom(sK18(powerset(sK7(empty_set,X1,powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21301,c_15588]) ).
tcf(c_21775,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(relation_dom(relation_dom(relation_dom(sK18(powerset(sK7(empty_set,X1,powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21301,c_15553]) ).
tcf(c_21776,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK18(sK17(powerset(sK18(powerset(sK7(empty_set,X1,powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21301,c_13492]) ).
tcf(c_21777,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK18(sK17(powerset(sK18(powerset(sK7(empty_set,X1,powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21301,c_13490]) ).
tcf(c_21778,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(powerset(relation_dom(relation_dom(sK18(powerset(sK7(empty_set,X1,powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21301,c_15527]) ).
tcf(c_21779,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK18(powerset(relation_dom(sK18(powerset(sK7(empty_set,X1,powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21301,c_15355]) ).
tcf(c_21780,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK18(powerset(relation_dom(sK18(powerset(sK7(empty_set,X1,powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21301,c_15317]) ).
tcf(c_21781,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(relation_dom(sK18(powerset(sK18(powerset(sK7(empty_set,X1,powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21301,c_13260]) ).
tcf(c_21782,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK18(powerset(sK7(empty_set,X1,powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21301,c_15261]) ).
tcf(c_21783,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_dom(sK18(powerset(sK7(empty_set,X2,powerset(X0)))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21301,c_15230]) ).
tcf(c_21784,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(powerset(sK18(powerset(sK18(powerset(sK7(empty_set,X1,powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21301,c_13064]) ).
tcf(c_21785,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK18(powerset(sK18(powerset(sK7(empty_set,X2,powerset(X0)))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21301,c_12767]) ).
tcf(c_21786,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(sK18(powerset(sK18(powerset(sK7(empty_set,X1,powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21301,c_12765]) ).
tcf(c_21787,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(sK17(powerset(sK18(powerset(sK7(empty_set,X1,powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21301,c_15973]) ).
tcf(c_21788,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(sK17(powerset(sK18(powerset(sK7(empty_set,X1,powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21301,c_13494]) ).
tcf(c_21789,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(powerset(relation_dom(sK18(powerset(sK7(empty_set,X1,powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21301,c_14397]) ).
tcf(c_21790,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(relation_dom(relation_dom(sK18(powerset(sK7(empty_set,X1,powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21301,c_13258]) ).
tcf(c_21791,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(powerset(relation_dom(sK18(powerset(sK7(empty_set,X1,powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21301,c_13062]) ).
tcf(c_21792,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK18(powerset(sK18(powerset(sK7(empty_set,X1,powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21301,c_12959]) ).
tcf(c_21793,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK18(powerset(sK18(powerset(sK7(empty_set,X1,powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21301,c_12766]) ).
tcf(c_21794,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK18(powerset(sK7(empty_set,X1,powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21301,c_12718]) ).
tcf(c_21795,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(sK18(powerset(sK7(empty_set,X2,powerset(X0))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21301,c_12604]) ).
tcf(c_21796,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(powerset(sK18(powerset(sK7(empty_set,X1,powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21301,c_13495]) ).
tcf(c_21805,plain,
! [X0: $i,X1: $i] :
( one_to_one(sK18(powerset(sK7(empty_set,X1,powerset(X0)))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21301,c_5773]) ).
tcf(c_21806,plain,
! [X0: $i,X1: $i] :
( relation(sK18(powerset(sK7(empty_set,X1,powerset(X0)))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21301,c_77]) ).
tcf(c_21807,plain,
! [X0: $i,X1: $i] :
( function(sK18(powerset(sK7(empty_set,X1,powerset(X0)))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21301,c_66]) ).
tcf(c_21941,plain,
! [X0: $i,X1: $i] :
( ( sK7(empty_set,X1,powerset(relation_dom(X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_99,c_21303]) ).
tcf(c_21942,plain,
! [X0: $i] : sK7(empty_set,X0,powerset(empty_set)) = empty_set,
inference(superposition,[status(thm)],[c_114,c_21303]) ).
tcf(c_21943,plain,
! [X0: $i,X1: $i] :
( ( sK7(empty_set,X1,powerset(sK18(powerset(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12738,c_21303]) ).
tcf(c_21944,plain,
! [X0: $i,X1: $i] :
( ( sK7(empty_set,X1,powerset(sK18(powerset(sK18(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13358,c_21303]) ).
tcf(c_21945,plain,
! [X0: $i,X1: $i] :
( ( sK7(empty_set,X1,powerset(sK18(sK17(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13470,c_21303]) ).
tcf(c_21946,plain,
! [X0: $i,X1: $i] :
( ( sK7(empty_set,X1,powerset(sK18(powerset(sK18(sK17(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13469,c_21303]) ).
tcf(c_21947,plain,
! [X0: $i,X1: $i] :
( ( sK7(empty_set,X1,powerset(sK18(sK17(sK17(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15885,c_21303]) ).
tcf(c_21948,plain,
! [X0: $i,X1: $i] :
( ( sK7(empty_set,X1,powerset(sK18(powerset(sK18(sK17(sK17(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15887,c_21303]) ).
tcf(c_21949,plain,
! [X0: $i,X1: $i] :
( ( sK7(empty_set,X1,powerset(relation_image(X0,empty_set))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17175,c_21303]) ).
tcf(c_21950,plain,
! [X0: $i,X1: $i] :
( ( sK7(empty_set,X1,powerset(sK18(sK17(powerset(sK18(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17880,c_21303]) ).
tcf(c_21951,plain,
! [X0: $i,X1: $i] :
( ( sK7(empty_set,X1,powerset(sK18(sK17(powerset(sK18(sK17(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17885,c_21303]) ).
tcf(c_21952,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK7(empty_set,X1,powerset(sK2(empty_set,X2,powerset(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20186,c_21303]) ).
tcf(c_21953,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK7(empty_set,X1,powerset(sK18(powerset(sK2(empty_set,X2,powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20188,c_21303]) ).
tcf(c_21954,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK7(empty_set,X1,powerset(sK7(empty_set,X2,powerset(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21299,c_21303]) ).
tcf(c_21955,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK7(empty_set,X1,powerset(sK18(powerset(sK7(empty_set,X2,powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21301,c_21303]) ).
tcf(c_22062,plain,
! [X0: $i] :
( ( relation_inverse_image(empty_set,X0) = powerset(empty_set) )
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ in(apply(empty_set,empty_set),X0)
| ~ in(sK7(empty_set,X0,powerset(empty_set)),powerset(empty_set))
| ~ in(sK7(empty_set,X0,powerset(empty_set)),relation_dom(empty_set)) ),
inference(superposition,[status(thm)],[c_21942,c_67]) ).
tcf(c_22063,plain,
! [X0: $i] :
( in(apply(empty_set,empty_set),X0)
| in(sK7(empty_set,X0,powerset(empty_set)),powerset(empty_set))
| ( relation_inverse_image(empty_set,X0) = powerset(empty_set) )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_21942,c_69]) ).
tcf(c_22064,plain,
! [X0: $i] :
( in(empty_set,powerset(empty_set))
| in(apply(empty_set,sK7(empty_set,X0,powerset(empty_set))),X0)
| ( relation_inverse_image(empty_set,X0) = powerset(empty_set) )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_21942,c_69]) ).
tcf(c_22065,plain,
! [X0: $i] :
( in(empty_set,relation_dom(empty_set))
| in(sK7(empty_set,X0,powerset(empty_set)),powerset(empty_set))
| ( relation_inverse_image(empty_set,X0) = powerset(empty_set) )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_21942,c_68]) ).
tcf(c_22066,plain,
! [X0: $i] :
( in(empty_set,powerset(empty_set))
| in(sK7(empty_set,X0,powerset(empty_set)),relation_dom(empty_set))
| ( relation_inverse_image(empty_set,X0) = powerset(empty_set) )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_21942,c_68]) ).
tcf(c_22080,plain,
( in(empty_set,empty_set)
| in(empty_set,powerset(empty_set))
| ( powerset(empty_set) = empty_set )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(light_normalisation,[status(thm)],[c_22066,c_12551,c_19495,c_21942]) ).
tcf(c_22082,plain,
! [X0: $i] :
( in(empty_set,powerset(empty_set))
| in(apply(empty_set,empty_set),X0)
| ( powerset(empty_set) = empty_set )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(light_normalisation,[status(thm)],[c_22064,c_19495,c_21942]) ).
tcf(c_22084,plain,
! [X0: $i] :
( ( powerset(empty_set) = empty_set )
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ in(empty_set,empty_set)
| ~ in(empty_set,powerset(empty_set))
| ~ in(apply(empty_set,empty_set),X0) ),
inference(light_normalisation,[status(thm)],[c_22062,c_12551,c_19495,c_21942]) ).
tcf(c_22093,plain,
! [X0: $i,X1: $i] :
( subset(empty_set,X1)
| ( apply(empty_set,sK4(empty_set,X0,sK13(relation_image(empty_set,X0),X1))) = sK13(relation_image(empty_set,X0),X1) )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_17316,c_13156]) ).
tcf(c_22094,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(X0,X3)
| ( apply(X1,sK4(X1,X2,sK13(relation_image(X1,X2),X3))) = sK13(relation_image(X1,X2),X3) )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_13156,c_300]) ).
tcf(c_22095,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( apply(X1,sK4(X1,X2,sK13(relation_image(X1,X2),X3))) = sK13(relation_image(X1,X2),X3) )
| ~ empty(X3)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_13156,c_299]) ).
tcf(c_22096,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,X3)
| ( apply(X1,sK4(X1,X2,sK13(relation_image(X1,X2),X3))) = sK13(relation_image(X1,X2),X3) )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_13156,c_92]) ).
tcf(c_22097,plain,
! [X0: $i,X1: $i] :
( subset(empty_set,X1)
| ( apply(empty_set,sK4(empty_set,X0,sK13(empty_set,X1))) = sK13(empty_set,X1) )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(light_normalisation,[status(thm)],[c_22093,c_17316]) ).
tcf(c_22167,plain,
! [X0: $i,X1: $i] :
( one_to_one(sK18(powerset(sK7(empty_set,X0,powerset(X1)))))
| ( apply(sK18(powerset(sK7(empty_set,X0,powerset(X1)))),sK11(sK18(powerset(sK7(empty_set,X0,powerset(X1)))))) = apply(sK18(powerset(sK7(empty_set,X0,powerset(X1)))),sK12(sK18(powerset(sK7(empty_set,X0,powerset(X1)))))) )
| ~ empty(X1)
| ~ function(sK18(powerset(sK7(empty_set,X0,powerset(X1))))) ),
inference(superposition,[status(thm)],[c_21806,c_84]) ).
tcf(c_22182,plain,
( empty(sK18(powerset(empty_set)))
| ~ in(empty_set,sK18(sK17(empty_set))) ),
inference(superposition,[status(thm)],[c_12958,c_15649]) ).
tcf(c_22183,plain,
( empty(empty_set)
| ~ in(empty_set,sK18(sK17(empty_set))) ),
inference(light_normalisation,[status(thm)],[c_22182,c_12958]) ).
tcf(c_22188,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(sK18(powerset(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_99,c_14399]) ).
tcf(c_22189,plain,
sK18(sK17(powerset(sK18(powerset(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_114,c_14399]) ).
tcf(c_22191,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(sK18(powerset(sK18(powerset(sK18(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13358,c_14399]) ).
tcf(c_22193,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(sK18(powerset(sK18(powerset(sK18(sK17(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13469,c_14399]) ).
tcf(c_22195,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(sK18(powerset(sK18(powerset(sK18(sK17(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15887,c_14399]) ).
tcf(c_22196,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(sK18(powerset(relation_image(X0,empty_set)))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17175,c_14399]) ).
tcf(c_22197,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(sK18(powerset(sK18(sK17(powerset(sK18(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17880,c_14399]) ).
tcf(c_22198,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(sK18(powerset(sK18(sK17(powerset(sK18(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17885,c_14399]) ).
tcf(c_22200,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(powerset(sK18(powerset(sK18(powerset(sK2(empty_set,X1,powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20188,c_14399]) ).
tcf(c_22202,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(powerset(sK18(powerset(sK18(powerset(sK7(empty_set,X1,powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21301,c_14399]) ).
tcf(c_22236,plain,
( element(sK18(empty_set),empty_set)
| empty(sK18(sK17(powerset(empty_set)))) ),
inference(superposition,[status(thm)],[c_14398,c_15089]) ).
tcf(c_22237,plain,
! [X0: $i] :
( empty(sK18(sK17(powerset(powerset(X0)))))
| subset(sK18(sK18(sK17(powerset(powerset(X0))))),X0) ),
inference(superposition,[status(thm)],[c_15089,c_88]) ).
tcf(c_22262,plain,
! [X0: $i] :
( empty(X0)
| element(sK18(sK17(sK17(sK17(X0)))),X0) ),
inference(global_subsumption_just,[status(thm)],[c_15384,c_109,c_15384]) ).
tcf(c_22269,plain,
! [X0: $i] :
( empty(powerset(X0))
| subset(sK18(sK17(sK17(sK17(powerset(X0))))),X0) ),
inference(superposition,[status(thm)],[c_22262,c_88]) ).
tcf(c_22270,plain,
! [X0: $i] :
( empty(X0)
| in(sK18(sK17(sK17(sK17(X0)))),X0) ),
inference(superposition,[status(thm)],[c_22262,c_96]) ).
tcf(c_22273,plain,
! [X0: $i] : subset(sK18(sK17(sK17(sK17(powerset(X0))))),X0),
inference(forward_subsumption_resolution,[status(thm)],[c_22269,c_110]) ).
tcf(c_22276,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| ~ in(X0,sK18(sK17(sK17(sK17(powerset(X1)))))) ),
inference(superposition,[status(thm)],[c_22273,c_300]) ).
tcf(c_22277,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ in(X0,sK18(sK17(sK17(sK17(powerset(X1)))))) ),
inference(superposition,[status(thm)],[c_22273,c_299]) ).
tcf(c_22278,plain,
! [X0: $i,X1: $i] :
( in(X0,X1)
| ~ in(X0,sK18(sK17(sK17(sK17(powerset(X1)))))) ),
inference(superposition,[status(thm)],[c_22273,c_92]) ).
tcf(c_22292,plain,
! [X0: $i,X1: $i] :
( empty(relation_image(X0,X1))
| ( apply(X0,sK4(X0,X1,sK18(sK17(sK17(sK17(relation_image(X0,X1))))))) = sK18(sK17(sK17(sK17(relation_image(X0,X1))))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_22270,c_60]) ).
tcf(c_22293,plain,
! [X0: $i,X1: $i] :
( empty(relation_inverse_image(X0,X1))
| in(apply(X0,sK18(sK17(sK17(sK17(relation_inverse_image(X0,X1)))))),X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_22270,c_72]) ).
tcf(c_22294,plain,
! [X0: $i,X1: $i] :
( empty(relation_inverse_image(X0,X1))
| in(sK18(sK17(sK17(sK17(relation_inverse_image(X0,X1))))),relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_22270,c_71]) ).
tcf(c_22295,plain,
! [X0: $i] :
( empty(X0)
| ~ in(X0,sK18(sK17(sK17(sK17(X0))))) ),
inference(superposition,[status(thm)],[c_22270,c_98]) ).
tcf(c_22298,plain,
! [X0: $i] :
( empty(X0)
| empty(sK17(X0))
| element(sK18(sK17(sK17(sK17(sK17(X0))))),X0) ),
inference(superposition,[status(thm)],[c_22270,c_14688]) ).
tcf(c_22299,plain,
! [X0: $i] :
( empty(X0)
| empty(sK17(X0))
| in(sK18(sK17(sK17(sK17(sK17(X0))))),X0) ),
inference(superposition,[status(thm)],[c_22270,c_12618]) ).
tcf(c_22300,plain,
! [X0: $i] :
( empty(sK18(powerset(X0)))
| element(sK18(sK17(sK17(sK17(sK18(powerset(X0)))))),X0) ),
inference(superposition,[status(thm)],[c_22270,c_14689]) ).
tcf(c_22302,plain,
! [X0: $i] :
( empty(sK18(powerset(X0)))
| in(sK18(sK17(sK17(sK17(sK18(powerset(X0)))))),X0) ),
inference(superposition,[status(thm)],[c_22270,c_12619]) ).
tcf(c_22305,plain,
! [X0: $i] :
( empty(sK18(sK17(powerset(X0))))
| element(sK18(sK17(sK17(sK17(sK18(sK17(powerset(X0))))))),X0) ),
inference(superposition,[status(thm)],[c_22270,c_14693]) ).
tcf(c_22307,plain,
! [X0: $i] :
( empty(sK18(sK17(powerset(X0))))
| in(sK18(sK17(sK17(sK17(sK18(sK17(powerset(X0))))))),X0) ),
inference(superposition,[status(thm)],[c_22270,c_13032]) ).
tcf(c_22308,plain,
! [X0: $i] :
( empty(sK18(sK17(sK17(powerset(X0)))))
| in(sK18(sK17(sK17(sK17(sK18(sK17(sK17(powerset(X0)))))))),X0) ),
inference(superposition,[status(thm)],[c_22270,c_15478]) ).
tcf(c_22310,plain,
! [X0: $i] :
( empty(sK18(sK17(sK17(powerset(X0)))))
| element(sK18(sK17(sK17(sK17(sK18(sK17(sK17(powerset(X0)))))))),X0) ),
inference(superposition,[status(thm)],[c_22270,c_15476]) ).
tcf(c_22311,plain,
! [X0: $i] :
( empty(sK17(powerset(X0)))
| in(sK18(sK17(sK17(sK17(sK17(powerset(X0)))))),powerset(X0)) ),
inference(superposition,[status(thm)],[c_22270,c_18767]) ).
tcf(c_22312,plain,
! [X0: $i] :
( empty(sK17(powerset(X0)))
| element(sK18(sK17(sK17(sK17(sK17(powerset(X0)))))),powerset(X0)) ),
inference(superposition,[status(thm)],[c_22270,c_18765]) ).
tcf(c_22314,plain,
! [X0: $i,X1: $i] :
( empty(sK2(empty_set,X0,powerset(X1)))
| element(sK18(sK17(sK17(sK17(sK2(empty_set,X0,powerset(X1)))))),X1) ),
inference(superposition,[status(thm)],[c_22270,c_19619]) ).
tcf(c_22315,plain,
! [X0: $i,X1: $i] :
( empty(sK2(empty_set,X0,powerset(X1)))
| in(sK18(sK17(sK17(sK17(sK2(empty_set,X0,powerset(X1)))))),X1) ),
inference(superposition,[status(thm)],[c_22270,c_19621]) ).
tcf(c_22317,plain,
! [X0: $i,X1: $i] :
( empty(sK7(empty_set,X0,powerset(X1)))
| element(sK18(sK17(sK17(sK17(sK7(empty_set,X0,powerset(X1)))))),X1) ),
inference(superposition,[status(thm)],[c_22270,c_20796]) ).
tcf(c_22318,plain,
! [X0: $i,X1: $i] :
( empty(sK7(empty_set,X0,powerset(X1)))
| in(sK18(sK17(sK17(sK17(sK7(empty_set,X0,powerset(X1)))))),X1) ),
inference(superposition,[status(thm)],[c_22270,c_20798]) ).
tcf(c_22438,plain,
( empty(sK18(powerset(empty_set)))
| element(sK18(sK17(sK17(empty_set))),empty_set) ),
inference(superposition,[status(thm)],[c_12958,c_15386]) ).
tcf(c_22439,plain,
! [X0: $i] :
( empty(sK18(powerset(powerset(X0))))
| subset(sK18(sK17(sK17(sK18(powerset(powerset(X0)))))),X0) ),
inference(superposition,[status(thm)],[c_15386,c_88]) ).
tcf(c_22441,plain,
( empty(empty_set)
| element(sK18(sK17(sK17(empty_set))),empty_set) ),
inference(light_normalisation,[status(thm)],[c_22438,c_12958]) ).
tcf(c_22449,plain,
( empty(sK18(powerset(empty_set)))
| in(sK18(sK17(sK17(empty_set))),empty_set) ),
inference(superposition,[status(thm)],[c_12958,c_15388]) ).
tcf(c_22450,plain,
! [X0: $i,X1: $i] :
( empty(sK18(powerset(relation_image(X0,X1))))
| ( apply(X0,sK4(X0,X1,sK18(sK17(sK17(sK18(powerset(relation_image(X0,X1)))))))) = sK18(sK17(sK17(sK18(powerset(relation_image(X0,X1)))))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_15388,c_60]) ).
tcf(c_22451,plain,
! [X0: $i,X1: $i] :
( empty(sK18(powerset(relation_inverse_image(X0,X1))))
| in(apply(X0,sK18(sK17(sK17(sK18(powerset(relation_inverse_image(X0,X1))))))),X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_15388,c_72]) ).
tcf(c_22452,plain,
! [X0: $i,X1: $i] :
( empty(sK18(powerset(relation_inverse_image(X0,X1))))
| in(sK18(sK17(sK17(sK18(powerset(relation_inverse_image(X0,X1)))))),relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_15388,c_71]) ).
tcf(c_22453,plain,
! [X0: $i] :
( empty(sK18(powerset(X0)))
| ~ in(X0,sK18(sK17(sK17(sK18(powerset(X0)))))) ),
inference(superposition,[status(thm)],[c_15388,c_98]) ).
tcf(c_22456,plain,
! [X0: $i] :
( empty(X0)
| empty(sK18(powerset(sK17(X0))))
| element(sK18(sK17(sK17(sK18(powerset(sK17(X0)))))),X0) ),
inference(superposition,[status(thm)],[c_15388,c_14688]) ).
tcf(c_22457,plain,
! [X0: $i] :
( empty(X0)
| empty(sK18(powerset(sK17(X0))))
| in(sK18(sK17(sK17(sK18(powerset(sK17(X0)))))),X0) ),
inference(superposition,[status(thm)],[c_15388,c_12618]) ).
tcf(c_22458,plain,
! [X0: $i] :
( empty(sK18(powerset(sK18(powerset(X0)))))
| element(sK18(sK17(sK17(sK18(powerset(sK18(powerset(X0))))))),X0) ),
inference(superposition,[status(thm)],[c_15388,c_14689]) ).
tcf(c_22460,plain,
! [X0: $i] :
( empty(sK18(powerset(sK18(powerset(X0)))))
| in(sK18(sK17(sK17(sK18(powerset(sK18(powerset(X0))))))),X0) ),
inference(superposition,[status(thm)],[c_15388,c_12619]) ).
tcf(c_22463,plain,
! [X0: $i] :
( empty(sK18(powerset(sK18(sK17(powerset(X0))))))
| element(sK18(sK17(sK17(sK18(powerset(sK18(sK17(powerset(X0)))))))),X0) ),
inference(superposition,[status(thm)],[c_15388,c_14693]) ).
tcf(c_22465,plain,
! [X0: $i] :
( empty(sK18(powerset(sK18(sK17(powerset(X0))))))
| in(sK18(sK17(sK17(sK18(powerset(sK18(sK17(powerset(X0)))))))),X0) ),
inference(superposition,[status(thm)],[c_15388,c_13032]) ).
tcf(c_22466,plain,
! [X0: $i] :
( empty(sK18(powerset(sK18(sK17(sK17(powerset(X0)))))))
| in(sK18(sK17(sK17(sK18(powerset(sK18(sK17(sK17(powerset(X0))))))))),X0) ),
inference(superposition,[status(thm)],[c_15388,c_15478]) ).
tcf(c_22468,plain,
! [X0: $i] :
( empty(sK18(powerset(sK18(sK17(sK17(powerset(X0)))))))
| element(sK18(sK17(sK17(sK18(powerset(sK18(sK17(sK17(powerset(X0))))))))),X0) ),
inference(superposition,[status(thm)],[c_15388,c_15476]) ).
tcf(c_22469,plain,
! [X0: $i] :
( empty(sK18(powerset(sK17(powerset(X0)))))
| in(sK18(sK17(sK17(sK18(powerset(sK17(powerset(X0))))))),powerset(X0)) ),
inference(superposition,[status(thm)],[c_15388,c_18767]) ).
tcf(c_22470,plain,
! [X0: $i] :
( empty(sK18(powerset(sK17(powerset(X0)))))
| element(sK18(sK17(sK17(sK18(powerset(sK17(powerset(X0))))))),powerset(X0)) ),
inference(superposition,[status(thm)],[c_15388,c_18765]) ).
tcf(c_22472,plain,
! [X0: $i,X1: $i] :
( empty(sK18(powerset(sK2(empty_set,X0,powerset(X1)))))
| element(sK18(sK17(sK17(sK18(powerset(sK2(empty_set,X0,powerset(X1))))))),X1) ),
inference(superposition,[status(thm)],[c_15388,c_19619]) ).
tcf(c_22473,plain,
! [X0: $i,X1: $i] :
( empty(sK18(powerset(sK2(empty_set,X0,powerset(X1)))))
| in(sK18(sK17(sK17(sK18(powerset(sK2(empty_set,X0,powerset(X1))))))),X1) ),
inference(superposition,[status(thm)],[c_15388,c_19621]) ).
tcf(c_22475,plain,
! [X0: $i,X1: $i] :
( empty(sK18(powerset(sK7(empty_set,X0,powerset(X1)))))
| element(sK18(sK17(sK17(sK18(powerset(sK7(empty_set,X0,powerset(X1))))))),X1) ),
inference(superposition,[status(thm)],[c_15388,c_20796]) ).
tcf(c_22476,plain,
! [X0: $i,X1: $i] :
( empty(sK18(powerset(sK7(empty_set,X0,powerset(X1)))))
| in(sK18(sK17(sK17(sK18(powerset(sK7(empty_set,X0,powerset(X1))))))),X1) ),
inference(superposition,[status(thm)],[c_15388,c_20798]) ).
tcf(c_22477,plain,
( empty(empty_set)
| in(sK18(sK17(sK17(empty_set))),empty_set) ),
inference(light_normalisation,[status(thm)],[c_22449,c_12958]) ).
tcf(c_22613,plain,
! [X0: $i] :
( ( relation_dom(sK18(sK17(powerset(relation_dom(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_99,c_15716]) ).
tcf(c_22614,plain,
relation_dom(sK18(sK17(powerset(relation_dom(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_114,c_15716]) ).
tcf(c_22615,plain,
! [X0: $i] :
( ( relation_dom(sK18(sK17(powerset(relation_dom(sK18(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12738,c_15716]) ).
tcf(c_22616,plain,
! [X0: $i] :
( ( relation_dom(sK18(sK17(powerset(relation_dom(sK18(powerset(sK18(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13358,c_15716]) ).
tcf(c_22617,plain,
! [X0: $i] :
( ( relation_dom(sK18(sK17(powerset(relation_dom(sK18(sK17(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13470,c_15716]) ).
tcf(c_22618,plain,
! [X0: $i] :
( ( relation_dom(sK18(sK17(powerset(relation_dom(sK18(powerset(sK18(sK17(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13469,c_15716]) ).
tcf(c_22619,plain,
! [X0: $i] :
( ( relation_dom(sK18(sK17(powerset(relation_dom(sK18(sK17(sK17(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15885,c_15716]) ).
tcf(c_22620,plain,
! [X0: $i] :
( ( relation_dom(sK18(sK17(powerset(relation_dom(sK18(powerset(sK18(sK17(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15887,c_15716]) ).
tcf(c_22621,plain,
! [X0: $i] :
( ( relation_dom(sK18(sK17(powerset(relation_dom(relation_image(X0,empty_set)))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17175,c_15716]) ).
tcf(c_22622,plain,
! [X0: $i] :
( ( relation_dom(sK18(sK17(powerset(relation_dom(sK18(sK17(powerset(sK18(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17880,c_15716]) ).
tcf(c_22623,plain,
! [X0: $i] :
( ( relation_dom(sK18(sK17(powerset(relation_dom(sK18(sK17(powerset(sK18(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17885,c_15716]) ).
tcf(c_22624,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(sK17(powerset(relation_dom(sK2(empty_set,X1,powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20186,c_15716]) ).
tcf(c_22625,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(sK17(powerset(relation_dom(sK18(powerset(sK2(empty_set,X1,powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20188,c_15716]) ).
tcf(c_22626,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(sK17(powerset(relation_dom(sK7(empty_set,X1,powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21299,c_15716]) ).
tcf(c_22627,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(sK17(powerset(relation_dom(sK18(powerset(sK7(empty_set,X1,powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21301,c_15716]) ).
tcf(c_22713,plain,
! [X0: $i] :
( ( relation_dom(sK18(sK17(sK17(powerset(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_99,c_15972]) ).
tcf(c_22714,plain,
relation_dom(sK18(sK17(sK17(powerset(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_114,c_15972]) ).
tcf(c_22715,plain,
! [X0: $i] :
( ( relation_dom(sK18(sK17(sK17(powerset(sK18(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12738,c_15972]) ).
tcf(c_22716,plain,
! [X0: $i] :
( ( relation_dom(sK18(sK17(sK17(powerset(sK18(powerset(sK18(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13358,c_15972]) ).
tcf(c_22717,plain,
! [X0: $i] :
( ( relation_dom(sK18(sK17(sK17(powerset(sK18(sK17(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13470,c_15972]) ).
tcf(c_22718,plain,
! [X0: $i] :
( ( relation_dom(sK18(sK17(sK17(powerset(sK18(powerset(sK18(sK17(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13469,c_15972]) ).
tcf(c_22719,plain,
! [X0: $i] :
( ( relation_dom(sK18(sK17(sK17(powerset(sK18(sK17(sK17(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15885,c_15972]) ).
tcf(c_22720,plain,
! [X0: $i] :
( ( relation_dom(sK18(sK17(sK17(powerset(sK18(powerset(sK18(sK17(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15887,c_15972]) ).
tcf(c_22721,plain,
! [X0: $i] :
( ( relation_dom(sK18(sK17(sK17(powerset(relation_image(X0,empty_set)))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17175,c_15972]) ).
tcf(c_22722,plain,
! [X0: $i] :
( ( relation_dom(sK18(sK17(sK17(powerset(sK18(sK17(powerset(sK18(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17880,c_15972]) ).
tcf(c_22723,plain,
! [X0: $i] :
( ( relation_dom(sK18(sK17(sK17(powerset(sK18(sK17(powerset(sK18(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17885,c_15972]) ).
tcf(c_22724,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(sK17(sK17(powerset(sK2(empty_set,X1,powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20186,c_15972]) ).
tcf(c_22725,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(sK17(sK17(powerset(sK18(powerset(sK2(empty_set,X1,powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20188,c_15972]) ).
tcf(c_22726,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(sK17(sK17(powerset(sK7(empty_set,X1,powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21299,c_15972]) ).
tcf(c_22727,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(sK17(sK17(powerset(sK18(powerset(sK7(empty_set,X1,powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21301,c_15972]) ).
tcf(c_22812,plain,
! [X0: $i] :
( ( sK18(sK17(sK17(powerset(relation_dom(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_99,c_16287]) ).
tcf(c_22813,plain,
sK18(sK17(sK17(powerset(relation_dom(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_114,c_16287]) ).
tcf(c_22814,plain,
! [X0: $i] :
( ( sK18(sK17(sK17(powerset(relation_dom(sK18(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12738,c_16287]) ).
tcf(c_22815,plain,
! [X0: $i] :
( ( sK18(sK17(sK17(powerset(relation_dom(sK18(powerset(sK18(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13358,c_16287]) ).
tcf(c_22816,plain,
! [X0: $i] :
( ( sK18(sK17(sK17(powerset(relation_dom(sK18(sK17(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13470,c_16287]) ).
tcf(c_22817,plain,
! [X0: $i] :
( ( sK18(sK17(sK17(powerset(relation_dom(sK18(powerset(sK18(sK17(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13469,c_16287]) ).
tcf(c_22818,plain,
! [X0: $i] :
( ( sK18(sK17(sK17(powerset(relation_dom(sK18(sK17(sK17(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15885,c_16287]) ).
tcf(c_22819,plain,
! [X0: $i] :
( ( sK18(sK17(sK17(powerset(relation_dom(sK18(powerset(sK18(sK17(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15887,c_16287]) ).
tcf(c_22820,plain,
! [X0: $i] :
( ( sK18(sK17(sK17(powerset(relation_dom(relation_image(X0,empty_set)))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17175,c_16287]) ).
tcf(c_22821,plain,
! [X0: $i] :
( ( sK18(sK17(sK17(powerset(relation_dom(sK18(sK17(powerset(sK18(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17880,c_16287]) ).
tcf(c_22822,plain,
! [X0: $i] :
( ( sK18(sK17(sK17(powerset(relation_dom(sK18(sK17(powerset(sK18(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17885,c_16287]) ).
tcf(c_22823,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(sK17(powerset(relation_dom(sK2(empty_set,X1,powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20186,c_16287]) ).
tcf(c_22824,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(sK17(powerset(relation_dom(sK18(powerset(sK2(empty_set,X1,powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20188,c_16287]) ).
tcf(c_22825,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(sK17(powerset(relation_dom(sK7(empty_set,X1,powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21299,c_16287]) ).
tcf(c_22826,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(sK17(powerset(relation_dom(sK18(powerset(sK7(empty_set,X1,powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21301,c_16287]) ).
tcf(c_22944,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(sK17(powerset(relation_dom(relation_image(X0,X1)))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(relation_image(X0,X1)))) = sK18(relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13157,c_16287]) ).
tcf(c_22945,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(sK17(sK17(powerset(relation_image(X0,X1)))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(relation_image(X0,X1)))) = sK18(relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13157,c_15972]) ).
tcf(c_22946,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(sK17(powerset(relation_dom(relation_image(X0,X1)))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(relation_image(X0,X1)))) = sK18(relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13157,c_15716]) ).
tcf(c_22947,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(powerset(sK18(powerset(relation_image(X0,X1)))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(relation_image(X0,X1)))) = sK18(relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13157,c_14399]) ).
tcf(c_22948,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK7(empty_set,X2,powerset(relation_image(X0,X1))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(relation_image(X0,X1)))) = sK18(relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13157,c_21303]) ).
tcf(c_22949,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK2(empty_set,X2,powerset(relation_image(X0,X1))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(relation_image(X0,X1)))) = sK18(relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13157,c_20190]) ).
tcf(c_22950,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(powerset(relation_dom(relation_dom(relation_image(X0,X1)))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(relation_image(X0,X1)))) = sK18(relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13157,c_15588]) ).
tcf(c_22951,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(relation_dom(relation_dom(relation_dom(relation_image(X0,X1)))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(relation_image(X0,X1)))) = sK18(relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13157,c_15553]) ).
tcf(c_22952,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK18(sK17(powerset(relation_image(X0,X1)))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(relation_image(X0,X1)))) = sK18(relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13157,c_13492]) ).
tcf(c_22953,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK18(sK17(powerset(relation_image(X0,X1)))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(relation_image(X0,X1)))) = sK18(relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13157,c_13490]) ).
tcf(c_22954,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(powerset(relation_dom(relation_dom(relation_image(X0,X1)))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(relation_image(X0,X1)))) = sK18(relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13157,c_15527]) ).
tcf(c_22955,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK18(powerset(relation_dom(relation_image(X0,X1)))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(relation_image(X0,X1)))) = sK18(relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13157,c_15355]) ).
tcf(c_22956,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK18(powerset(relation_dom(relation_image(X0,X1)))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(relation_image(X0,X1)))) = sK18(relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13157,c_15317]) ).
tcf(c_22957,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(relation_dom(sK18(powerset(relation_image(X0,X1)))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(relation_image(X0,X1)))) = sK18(relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13157,c_13260]) ).
tcf(c_22958,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_image(X0,X1)))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(relation_image(X0,X1)))) = sK18(relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13157,c_15261]) ).
tcf(c_22959,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_dom(relation_image(X0,X2))) = X1 )
| ( apply(X0,sK4(X0,X2,sK18(relation_image(X0,X2)))) = sK18(relation_image(X0,X2)) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13157,c_15230]) ).
tcf(c_22960,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(powerset(sK18(powerset(relation_image(X0,X1)))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(relation_image(X0,X1)))) = sK18(relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13157,c_13064]) ).
tcf(c_22961,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK18(powerset(relation_image(X0,X2))) = X1 )
| ( apply(X0,sK4(X0,X2,sK18(relation_image(X0,X2)))) = sK18(relation_image(X0,X2)) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13157,c_12767]) ).
tcf(c_22962,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(sK18(powerset(relation_image(X0,X1)))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(relation_image(X0,X1)))) = sK18(relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13157,c_12765]) ).
tcf(c_22963,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(sK17(powerset(relation_image(X0,X1))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(relation_image(X0,X1)))) = sK18(relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13157,c_15973]) ).
tcf(c_22964,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(sK17(powerset(relation_image(X0,X1))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(relation_image(X0,X1)))) = sK18(relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13157,c_13494]) ).
tcf(c_22965,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(powerset(relation_dom(relation_image(X0,X1))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(relation_image(X0,X1)))) = sK18(relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13157,c_14397]) ).
tcf(c_22966,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(relation_dom(relation_dom(relation_image(X0,X1))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(relation_image(X0,X1)))) = sK18(relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13157,c_13258]) ).
tcf(c_22967,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(powerset(relation_dom(relation_image(X0,X1))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(relation_image(X0,X1)))) = sK18(relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13157,c_13062]) ).
tcf(c_22968,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK18(powerset(relation_image(X0,X1))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(relation_image(X0,X1)))) = sK18(relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13157,c_12959]) ).
tcf(c_22969,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK18(powerset(relation_image(X0,X1))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(relation_image(X0,X1)))) = sK18(relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13157,c_12766]) ).
tcf(c_22970,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_image(X0,X1))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(relation_image(X0,X1)))) = sK18(relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13157,c_12718]) ).
tcf(c_22971,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_image(X0,X2)) = X1 )
| ( apply(X0,sK4(X0,X2,sK18(relation_image(X0,X2)))) = sK18(relation_image(X0,X2)) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13157,c_12604]) ).
tcf(c_22972,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(powerset(relation_image(X0,X1)))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(relation_image(X0,X1)))) = sK18(relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13157,c_13495]) ).
tcf(c_22973,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(relation_dom(relation_image(X0,X1)))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(relation_image(X0,X1)))) = sK18(relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13157,c_12957]) ).
tcf(c_22974,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(powerset(relation_image(X0,X1)))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(relation_image(X0,X1)))) = sK18(relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13157,c_12768]) ).
tcf(c_22975,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(relation_image(X0,X1))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(relation_image(X0,X1)))) = sK18(relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13157,c_12769]) ).
tcf(c_22976,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_image(X0,X1)))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(relation_image(X0,X1)))) = sK18(relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13157,c_12674]) ).
tcf(c_22977,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_image(X0,X1))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(relation_image(X0,X1)))) = sK18(relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13157,c_12550]) ).
tcf(c_22978,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X0,X2) = X1 )
| ( apply(X0,sK4(X0,X2,sK18(relation_image(X0,X2)))) = sK18(relation_image(X0,X2)) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13157,c_93]) ).
tcf(c_22979,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_image(X0,X1)) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(relation_image(X0,X1)))) = sK18(relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13157,c_12406]) ).
tcf(c_22980,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X0,X1) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(relation_image(X0,X1)))) = sK18(relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13157,c_94]) ).
tcf(c_22981,plain,
! [X0: $i,X1: $i] :
( one_to_one(relation_image(X0,X1))
| ( apply(X0,sK4(X0,X1,sK18(relation_image(X0,X1)))) = sK18(relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13157,c_5773]) ).
tcf(c_22982,plain,
! [X0: $i,X1: $i] :
( relation(relation_image(X0,X1))
| ( apply(X0,sK4(X0,X1,sK18(relation_image(X0,X1)))) = sK18(relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13157,c_77]) ).
tcf(c_22983,plain,
! [X0: $i,X1: $i] :
( function(relation_image(X0,X1))
| ( apply(X0,sK4(X0,X1,sK18(relation_image(X0,X1)))) = sK18(relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13157,c_66]) ).
tcf(c_23306,plain,
( ( relation_image(sK1,empty_set) = empty_set )
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_52,c_17554]) ).
tcf(c_23307,plain,
( ( relation_image(sK6,empty_set) = empty_set )
| ~ relation(sK6) ),
inference(superposition,[status(thm)],[c_65,c_17554]) ).
tcf(c_23308,plain,
( ( relation_image(sK10,empty_set) = empty_set )
| ~ relation(sK10) ),
inference(superposition,[status(thm)],[c_79,c_17554]) ).
tcf(c_23309,plain,
! [X0: $i] :
( ( relation_image(relation_dom(X0),empty_set) = empty_set )
| ~ empty(X0)
| ~ relation(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_12385,c_17554]) ).
tcf(c_23310,plain,
( ( relation_image(empty_set,empty_set) = empty_set )
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_12355,c_17554]) ).
tcf(c_23311,plain,
! [X0: $i] :
( ( relation_image(sK18(powerset(X0)),empty_set) = empty_set )
| ~ empty(X0)
| ~ relation(sK18(powerset(X0))) ),
inference(superposition,[status(thm)],[c_12772,c_17554]) ).
tcf(c_23312,plain,
! [X0: $i] :
( ( relation_image(sK18(powerset(sK18(powerset(X0)))),empty_set) = empty_set )
| ~ empty(X0)
| ~ relation(sK18(powerset(sK18(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_13393,c_17554]) ).
tcf(c_23313,plain,
! [X0: $i] :
( ( relation_image(sK18(sK17(powerset(X0))),empty_set) = empty_set )
| ~ empty(X0)
| ~ relation(sK18(sK17(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_13498,c_17554]) ).
tcf(c_23314,plain,
! [X0: $i] :
( ( relation_image(sK18(powerset(sK18(sK17(powerset(X0))))),empty_set) = empty_set )
| ~ empty(X0)
| ~ relation(sK18(powerset(sK18(sK17(powerset(X0)))))) ),
inference(superposition,[status(thm)],[c_14345,c_17554]) ).
tcf(c_23315,plain,
! [X0: $i] :
( ( relation_image(sK18(sK17(sK17(powerset(X0)))),empty_set) = empty_set )
| ~ empty(X0)
| ~ relation(sK18(sK17(sK17(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_15976,c_17554]) ).
tcf(c_23316,plain,
! [X0: $i] :
( ( relation_image(sK18(powerset(sK18(sK17(sK17(powerset(X0)))))),empty_set) = empty_set )
| ~ empty(X0)
| ~ relation(sK18(powerset(sK18(sK17(sK17(powerset(X0))))))) ),
inference(superposition,[status(thm)],[c_16543,c_17554]) ).
tcf(c_23317,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_17557,c_17554]) ).
tcf(c_23318,plain,
! [X0: $i] :
( ( relation_image(sK18(sK17(powerset(sK18(powerset(X0))))),empty_set) = empty_set )
| ~ empty(X0)
| ~ relation(sK18(sK17(powerset(sK18(powerset(X0)))))) ),
inference(superposition,[status(thm)],[c_18126,c_17554]) ).
tcf(c_23319,plain,
! [X0: $i] :
( ( relation_image(sK18(sK17(powerset(sK18(sK17(powerset(X0)))))),empty_set) = empty_set )
| ~ empty(X0)
| ~ relation(sK18(sK17(powerset(sK18(sK17(powerset(X0))))))) ),
inference(superposition,[status(thm)],[c_18310,c_17554]) ).
tcf(c_23320,plain,
! [X0: $i,X1: $i] :
( ( relation_image(sK2(empty_set,X0,powerset(X1)),empty_set) = empty_set )
| ~ empty(X1)
| ~ relation(sK2(empty_set,X0,powerset(X1))) ),
inference(superposition,[status(thm)],[c_20341,c_17554]) ).
tcf(c_23321,plain,
! [X0: $i,X1: $i] :
( ( relation_image(sK18(powerset(sK2(empty_set,X0,powerset(X1)))),empty_set) = empty_set )
| ~ empty(X1)
| ~ relation(sK18(powerset(sK2(empty_set,X0,powerset(X1))))) ),
inference(superposition,[status(thm)],[c_20631,c_17554]) ).
tcf(c_23322,plain,
! [X0: $i,X1: $i] :
( ( relation_image(sK7(empty_set,X0,powerset(X1)),empty_set) = empty_set )
| ~ empty(X1)
| ~ relation(sK7(empty_set,X0,powerset(X1))) ),
inference(superposition,[status(thm)],[c_21433,c_17554]) ).
tcf(c_23323,plain,
! [X0: $i,X1: $i] :
( ( relation_image(sK18(powerset(sK7(empty_set,X0,powerset(X1)))),empty_set) = empty_set )
| ~ empty(X1)
| ~ relation(sK18(powerset(sK7(empty_set,X0,powerset(X1))))) ),
inference(superposition,[status(thm)],[c_21807,c_17554]) ).
tcf(c_23324,plain,
relation_image(sK10,empty_set) = empty_set,
inference(forward_subsumption_resolution,[status(thm)],[c_23308,c_78]) ).
tcf(c_23325,plain,
relation_image(sK6,empty_set) = empty_set,
inference(forward_subsumption_resolution,[status(thm)],[c_23307,c_64]) ).
tcf(c_23326,plain,
relation_image(sK1,empty_set) = empty_set,
inference(forward_subsumption_resolution,[status(thm)],[c_23306,c_51]) ).
tcf(c_23459,plain,
! [X0: $i] :
( subset(sK18(powerset(empty_set)),X0)
| ~ function(sK10)
| ~ relation(sK10) ),
inference(superposition,[status(thm)],[c_23324,c_17172]) ).
tcf(c_23461,plain,
! [X0: $i] :
( subset(empty_set,X0)
| ~ function(sK10)
| ~ relation(sK10) ),
inference(light_normalisation,[status(thm)],[c_23459,c_12958]) ).
tcf(c_23471,plain,
! [X0: $i] :
( subset(sK18(powerset(empty_set)),X0)
| ~ function(sK6)
| ~ relation(sK6) ),
inference(superposition,[status(thm)],[c_23325,c_17172]) ).
tcf(c_23473,plain,
! [X0: $i] :
( subset(empty_set,X0)
| ~ function(sK6)
| ~ relation(sK6) ),
inference(light_normalisation,[status(thm)],[c_23471,c_12958]) ).
tcf(c_23483,plain,
! [X0: $i] :
( subset(sK18(powerset(empty_set)),X0)
| ~ function(sK1)
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_23326,c_17172]) ).
tcf(c_23485,plain,
! [X0: $i] :
( subset(empty_set,X0)
| ~ function(sK1)
| ~ relation(sK1) ),
inference(light_normalisation,[status(thm)],[c_23483,c_12958]) ).
tcf(c_23491,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,X2)
| ~ empty(X1)
| ~ in(X0,sK18(powerset(sK18(sK17(sK17(powerset(X1))))))) ),
inference(superposition,[status(thm)],[c_16407,c_300]) ).
tcf(c_23492,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(X2)
| ~ empty(X1)
| ~ in(X0,sK18(powerset(sK18(sK17(sK17(powerset(X1))))))) ),
inference(superposition,[status(thm)],[c_16407,c_299]) ).
tcf(c_23493,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ empty(X1)
| ~ in(X0,sK18(powerset(sK18(sK17(sK17(powerset(X1))))))) ),
inference(superposition,[status(thm)],[c_16407,c_92]) ).
tcf(c_23512,plain,
( empty(sK18(powerset(empty_set)))
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_17316,c_17177]) ).
tcf(c_23513,plain,
( empty(sK18(powerset(empty_set)))
| ~ function(sK1)
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_23326,c_17177]) ).
tcf(c_23514,plain,
( empty(sK18(powerset(empty_set)))
| ~ function(sK6)
| ~ relation(sK6) ),
inference(superposition,[status(thm)],[c_23325,c_17177]) ).
tcf(c_23515,plain,
( empty(sK18(powerset(empty_set)))
| ~ function(sK10)
| ~ relation(sK10) ),
inference(superposition,[status(thm)],[c_23324,c_17177]) ).
tcf(c_23516,plain,
! [X0: $i] :
( ( sK18(sK17(sK17(powerset(relation_dom(sK18(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17177,c_16287]) ).
tcf(c_23517,plain,
! [X0: $i] :
( ( relation_dom(sK18(sK17(sK17(powerset(sK18(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17177,c_15972]) ).
tcf(c_23518,plain,
! [X0: $i] :
( ( relation_dom(sK18(sK17(powerset(relation_dom(sK18(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17177,c_15716]) ).
tcf(c_23519,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(sK18(powerset(sK18(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17177,c_14399]) ).
tcf(c_23520,plain,
! [X0: $i,X1: $i] :
( ( sK7(empty_set,X1,powerset(sK18(powerset(relation_image(X0,empty_set))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17177,c_21303]) ).
tcf(c_23521,plain,
! [X0: $i,X1: $i] :
( ( sK2(empty_set,X1,powerset(sK18(powerset(relation_image(X0,empty_set))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17177,c_20190]) ).
tcf(c_23522,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(relation_dom(relation_dom(sK18(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17177,c_15588]) ).
tcf(c_23523,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(relation_dom(relation_dom(sK18(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17177,c_15553]) ).
tcf(c_23524,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK18(sK17(powerset(sK18(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17177,c_13492]) ).
tcf(c_23525,plain,
! [X0: $i] :
( ( sK18(powerset(sK18(sK17(powerset(sK18(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17177,c_13490]) ).
tcf(c_23526,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(relation_dom(relation_dom(sK18(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17177,c_15527]) ).
tcf(c_23527,plain,
! [X0: $i] :
( ( sK18(powerset(sK18(powerset(relation_dom(sK18(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17177,c_15355]) ).
tcf(c_23528,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK18(powerset(relation_dom(sK18(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17177,c_15317]) ).
tcf(c_23529,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(sK18(powerset(sK18(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17177,c_13260]) ).
tcf(c_23530,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK18(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17177,c_15261]) ).
tcf(c_23531,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK18(powerset(relation_image(X0,empty_set))))) = X1 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17177,c_15230]) ).
tcf(c_23532,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(sK18(powerset(sK18(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17177,c_13064]) ).
tcf(c_23533,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK18(powerset(relation_image(X0,empty_set))))) = X1 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17177,c_12767]) ).
tcf(c_23534,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK18(powerset(sK18(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17177,c_12765]) ).
tcf(c_23535,plain,
! [X0: $i] :
( ( sK18(sK17(sK17(powerset(sK18(powerset(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17177,c_15973]) ).
tcf(c_23536,plain,
! [X0: $i] :
( ( relation_dom(sK18(sK17(powerset(sK18(powerset(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17177,c_13494]) ).
tcf(c_23537,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(relation_dom(sK18(powerset(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17177,c_14397]) ).
tcf(c_23538,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(relation_dom(sK18(powerset(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17177,c_13258]) ).
tcf(c_23539,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(relation_dom(sK18(powerset(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17177,c_13062]) ).
tcf(c_23540,plain,
! [X0: $i] :
( ( sK18(powerset(sK18(powerset(sK18(powerset(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17177,c_12959]) ).
tcf(c_23541,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK18(powerset(sK18(powerset(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17177,c_12766]) ).
tcf(c_23542,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK18(powerset(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17177,c_12718]) ).
tcf(c_23543,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(powerset(relation_image(X0,empty_set)))) = X1 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17177,c_12604]) ).
tcf(c_23553,plain,
! [X0: $i] :
( one_to_one(sK18(powerset(relation_image(X0,empty_set))))
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17177,c_5773]) ).
tcf(c_23554,plain,
! [X0: $i] :
( relation(sK18(powerset(relation_image(X0,empty_set))))
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17177,c_77]) ).
tcf(c_23555,plain,
! [X0: $i] :
( function(sK18(powerset(relation_image(X0,empty_set))))
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17177,c_66]) ).
tcf(c_23556,plain,
( empty(empty_set)
| ~ function(sK10)
| ~ relation(sK10) ),
inference(light_normalisation,[status(thm)],[c_23515,c_12958]) ).
tcf(c_23557,plain,
( empty(empty_set)
| ~ function(sK6)
| ~ relation(sK6) ),
inference(light_normalisation,[status(thm)],[c_23514,c_12958]) ).
tcf(c_23558,plain,
( empty(empty_set)
| ~ function(sK1)
| ~ relation(sK1) ),
inference(light_normalisation,[status(thm)],[c_23513,c_12958]) ).
tcf(c_23559,plain,
( empty(empty_set)
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(light_normalisation,[status(thm)],[c_23512,c_12958]) ).
tcf(c_23802,plain,
! [X0: $i] :
( ( sK18(sK17(sK17(powerset(relation_dom(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17888,c_16287]) ).
tcf(c_23803,plain,
! [X0: $i] :
( ( relation_dom(sK18(sK17(sK17(powerset(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17888,c_15972]) ).
tcf(c_23804,plain,
! [X0: $i] :
( ( relation_dom(sK18(sK17(powerset(relation_dom(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17888,c_15716]) ).
tcf(c_23805,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(sK18(powerset(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17888,c_14399]) ).
tcf(c_23806,plain,
! [X0: $i,X1: $i] :
( ( sK7(empty_set,X1,powerset(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17888,c_21303]) ).
tcf(c_23807,plain,
! [X0: $i,X1: $i] :
( ( sK2(empty_set,X1,powerset(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17888,c_20190]) ).
tcf(c_23808,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(relation_dom(relation_dom(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17888,c_15588]) ).
tcf(c_23809,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(relation_dom(relation_dom(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17888,c_15553]) ).
tcf(c_23810,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK18(sK17(powerset(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17888,c_13492]) ).
tcf(c_23811,plain,
! [X0: $i] :
( ( sK18(powerset(sK18(sK17(powerset(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17888,c_13490]) ).
tcf(c_23812,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(relation_dom(relation_dom(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17888,c_15527]) ).
tcf(c_23813,plain,
! [X0: $i] :
( ( sK18(powerset(sK18(powerset(relation_dom(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17888,c_15355]) ).
tcf(c_23814,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK18(powerset(relation_dom(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17888,c_15317]) ).
tcf(c_23815,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(sK18(powerset(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17888,c_13260]) ).
tcf(c_23816,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17888,c_15261]) ).
tcf(c_23817,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17888,c_15230]) ).
tcf(c_23818,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(sK18(powerset(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17888,c_13064]) ).
tcf(c_23819,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17888,c_12767]) ).
tcf(c_23820,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK18(powerset(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17888,c_12765]) ).
tcf(c_23821,plain,
! [X0: $i] :
( ( sK18(sK17(sK17(powerset(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17888,c_15973]) ).
tcf(c_23822,plain,
! [X0: $i] :
( ( relation_dom(sK18(sK17(powerset(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17888,c_13494]) ).
tcf(c_23823,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(relation_dom(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17888,c_14397]) ).
tcf(c_23824,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(relation_dom(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17888,c_13258]) ).
tcf(c_23825,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(relation_dom(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17888,c_13062]) ).
tcf(c_23826,plain,
! [X0: $i] :
( ( sK18(powerset(sK18(powerset(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17888,c_12959]) ).
tcf(c_23827,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK18(powerset(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17888,c_12766]) ).
tcf(c_23828,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17888,c_12718]) ).
tcf(c_23829,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0)))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17888,c_12604]) ).
tcf(c_23830,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17888,c_13495]) ).
tcf(c_23831,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17888,c_12957]) ).
tcf(c_23832,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17888,c_12768]) ).
tcf(c_23834,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17888,c_12674]) ).
tcf(c_23836,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17888,c_93]) ).
tcf(c_23839,plain,
! [X0: $i] :
( one_to_one(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0))))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17888,c_5773]) ).
tcf(c_23840,plain,
! [X0: $i] :
( relation(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0))))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17888,c_77]) ).
tcf(c_23841,plain,
! [X0: $i] :
( function(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0))))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17888,c_66]) ).
tcf(c_24031,plain,
! [X0: $i] :
( empty(sK17(powerset(X0)))
| ~ in(powerset(X0),sK18(sK17(sK17(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_19006,c_98]) ).
tcf(c_24041,plain,
( empty(sK17(powerset(empty_set)))
| ~ in(powerset(empty_set),empty_set) ),
inference(superposition,[status(thm)],[c_14398,c_19122]) ).
tcf(c_24049,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(X0,X3)
| ~ empty(X2)
| ~ in(X0,sK18(powerset(sK2(empty_set,X1,powerset(X2))))) ),
inference(superposition,[status(thm)],[c_20183,c_300]) ).
tcf(c_24050,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ empty(X3)
| ~ empty(X2)
| ~ in(X0,sK18(powerset(sK2(empty_set,X1,powerset(X2))))) ),
inference(superposition,[status(thm)],[c_20183,c_299]) ).
tcf(c_24051,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,X3)
| ~ empty(X2)
| ~ in(X0,sK18(powerset(sK2(empty_set,X1,powerset(X2))))) ),
inference(superposition,[status(thm)],[c_20183,c_92]) ).
tcf(c_24069,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(sK17(powerset(relation_dom(sK18(sK17(powerset(sK2(empty_set,X1,powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20189,c_16287]) ).
tcf(c_24070,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(sK17(sK17(powerset(sK18(sK17(powerset(sK2(empty_set,X1,powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20189,c_15972]) ).
tcf(c_24071,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(sK17(powerset(relation_dom(sK18(sK17(powerset(sK2(empty_set,X1,powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20189,c_15716]) ).
tcf(c_24072,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(powerset(sK18(powerset(sK18(sK17(powerset(sK2(empty_set,X1,powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20189,c_14399]) ).
tcf(c_24073,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK7(empty_set,X1,powerset(sK18(sK17(powerset(sK2(empty_set,X2,powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20189,c_21303]) ).
tcf(c_24074,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK2(empty_set,X1,powerset(sK18(sK17(powerset(sK2(empty_set,X2,powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20189,c_20190]) ).
tcf(c_24075,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(powerset(relation_dom(relation_dom(sK18(sK17(powerset(sK2(empty_set,X1,powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20189,c_15588]) ).
tcf(c_24076,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(relation_dom(relation_dom(relation_dom(sK18(sK17(powerset(sK2(empty_set,X1,powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20189,c_15553]) ).
tcf(c_24077,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK18(sK17(powerset(sK18(sK17(powerset(sK2(empty_set,X1,powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20189,c_13492]) ).
tcf(c_24078,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK18(sK17(powerset(sK18(sK17(powerset(sK2(empty_set,X1,powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20189,c_13490]) ).
tcf(c_24079,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(powerset(relation_dom(relation_dom(sK18(sK17(powerset(sK2(empty_set,X1,powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20189,c_15527]) ).
tcf(c_24080,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK18(powerset(relation_dom(sK18(sK17(powerset(sK2(empty_set,X1,powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20189,c_15355]) ).
tcf(c_24081,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK18(powerset(relation_dom(sK18(sK17(powerset(sK2(empty_set,X1,powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20189,c_15317]) ).
tcf(c_24082,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(relation_dom(sK18(powerset(sK18(sK17(powerset(sK2(empty_set,X1,powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20189,c_13260]) ).
tcf(c_24083,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK18(sK17(powerset(sK2(empty_set,X1,powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20189,c_15261]) ).
tcf(c_24084,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_dom(sK18(sK17(powerset(sK2(empty_set,X2,powerset(X0))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20189,c_15230]) ).
tcf(c_24085,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(powerset(sK18(powerset(sK18(sK17(powerset(sK2(empty_set,X1,powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20189,c_13064]) ).
tcf(c_24086,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK18(powerset(sK18(sK17(powerset(sK2(empty_set,X2,powerset(X0))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20189,c_12767]) ).
tcf(c_24087,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(sK18(powerset(sK18(sK17(powerset(sK2(empty_set,X1,powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20189,c_12765]) ).
tcf(c_24088,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(sK17(powerset(sK18(sK17(powerset(sK2(empty_set,X1,powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20189,c_15973]) ).
tcf(c_24089,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(sK17(powerset(sK18(sK17(powerset(sK2(empty_set,X1,powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20189,c_13494]) ).
tcf(c_24090,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(powerset(relation_dom(sK18(sK17(powerset(sK2(empty_set,X1,powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20189,c_14397]) ).
tcf(c_24091,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(relation_dom(relation_dom(sK18(sK17(powerset(sK2(empty_set,X1,powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20189,c_13258]) ).
tcf(c_24092,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(powerset(relation_dom(sK18(sK17(powerset(sK2(empty_set,X1,powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20189,c_13062]) ).
tcf(c_24093,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK18(powerset(sK18(sK17(powerset(sK2(empty_set,X1,powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20189,c_12959]) ).
tcf(c_24094,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK18(powerset(sK18(sK17(powerset(sK2(empty_set,X1,powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20189,c_12766]) ).
tcf(c_24095,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK18(sK17(powerset(sK2(empty_set,X1,powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20189,c_12718]) ).
tcf(c_24096,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(sK18(sK17(powerset(sK2(empty_set,X2,powerset(X0)))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20189,c_12604]) ).
tcf(c_24097,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(powerset(sK18(sK17(powerset(sK2(empty_set,X1,powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20189,c_13495]) ).
tcf(c_24098,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(relation_dom(sK18(sK17(powerset(sK2(empty_set,X1,powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20189,c_12957]) ).
tcf(c_24099,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(powerset(sK18(sK17(powerset(sK2(empty_set,X1,powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20189,c_12768]) ).
tcf(c_24101,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(sK18(sK17(powerset(sK2(empty_set,X1,powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20189,c_12674]) ).
tcf(c_24103,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK18(sK17(powerset(sK2(empty_set,X2,powerset(X0))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20189,c_93]) ).
tcf(c_24106,plain,
! [X0: $i,X1: $i] :
( one_to_one(sK18(sK17(powerset(sK2(empty_set,X1,powerset(X0))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20189,c_5773]) ).
tcf(c_24107,plain,
! [X0: $i,X1: $i] :
( relation(sK18(sK17(powerset(sK2(empty_set,X1,powerset(X0))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20189,c_77]) ).
tcf(c_24108,plain,
! [X0: $i,X1: $i] :
( function(sK18(sK17(powerset(sK2(empty_set,X1,powerset(X0))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20189,c_66]) ).
tcf(c_24409,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK2(empty_set,X1,powerset(relation_dom(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_99,c_20337]) ).
tcf(c_24410,plain,
! [X0: $i] : relation_dom(sK2(empty_set,X0,powerset(empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_114,c_20337]) ).
tcf(c_24411,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK2(empty_set,X1,powerset(sK18(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12738,c_20337]) ).
tcf(c_24412,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK2(empty_set,X1,powerset(sK18(powerset(sK18(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13358,c_20337]) ).
tcf(c_24413,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(sK2(empty_set,X2,powerset(relation_image(X0,X1)))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(relation_image(X0,X1)))) = sK18(relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13157,c_20337]) ).
tcf(c_24414,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK2(empty_set,X1,powerset(sK18(sK17(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13470,c_20337]) ).
tcf(c_24415,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK2(empty_set,X1,powerset(sK18(powerset(sK18(sK17(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13469,c_20337]) ).
tcf(c_24416,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK2(empty_set,X1,powerset(sK18(sK17(sK17(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15885,c_20337]) ).
tcf(c_24417,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK2(empty_set,X1,powerset(sK18(powerset(sK18(sK17(sK17(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15887,c_20337]) ).
tcf(c_24418,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK2(empty_set,X1,powerset(relation_image(X0,empty_set)))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17175,c_20337]) ).
tcf(c_24419,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK2(empty_set,X1,powerset(sK18(powerset(relation_image(X0,empty_set)))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17177,c_20337]) ).
tcf(c_24420,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK2(empty_set,X1,powerset(sK18(sK17(powerset(sK18(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17880,c_20337]) ).
tcf(c_24421,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK2(empty_set,X1,powerset(sK18(sK17(powerset(sK18(sK17(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17885,c_20337]) ).
tcf(c_24422,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK2(empty_set,X1,powerset(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17888,c_20337]) ).
tcf(c_24423,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(sK2(empty_set,X1,powerset(sK2(empty_set,X2,powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20186,c_20337]) ).
tcf(c_24424,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(sK2(empty_set,X1,powerset(sK18(powerset(sK2(empty_set,X2,powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20188,c_20337]) ).
tcf(c_24425,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(sK2(empty_set,X1,powerset(sK18(sK17(powerset(sK2(empty_set,X2,powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20189,c_20337]) ).
tcf(c_24426,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(sK2(empty_set,X1,powerset(sK7(empty_set,X2,powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21299,c_20337]) ).
tcf(c_24427,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(sK2(empty_set,X1,powerset(sK18(powerset(sK7(empty_set,X2,powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21301,c_20337]) ).
tcf(c_24511,plain,
! [X0: $i,X1: $i] :
( ( sK2(empty_set,X1,powerset(relation_dom(relation_dom(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_99,c_21015]) ).
tcf(c_24512,plain,
! [X0: $i] : sK2(empty_set,X0,powerset(relation_dom(empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_114,c_21015]) ).
tcf(c_24513,plain,
! [X0: $i,X1: $i] :
( ( sK2(empty_set,X1,powerset(relation_dom(sK18(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12738,c_21015]) ).
tcf(c_24514,plain,
! [X0: $i,X1: $i] :
( ( sK2(empty_set,X1,powerset(relation_dom(sK18(powerset(sK18(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13358,c_21015]) ).
tcf(c_24515,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK2(empty_set,X2,powerset(relation_dom(relation_image(X0,X1)))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(relation_image(X0,X1)))) = sK18(relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13157,c_21015]) ).
tcf(c_24516,plain,
! [X0: $i,X1: $i] :
( ( sK2(empty_set,X1,powerset(relation_dom(sK18(sK17(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13470,c_21015]) ).
tcf(c_24517,plain,
! [X0: $i,X1: $i] :
( ( sK2(empty_set,X1,powerset(relation_dom(sK18(powerset(sK18(sK17(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13469,c_21015]) ).
tcf(c_24518,plain,
! [X0: $i,X1: $i] :
( ( sK2(empty_set,X1,powerset(relation_dom(sK18(sK17(sK17(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15885,c_21015]) ).
tcf(c_24519,plain,
! [X0: $i,X1: $i] :
( ( sK2(empty_set,X1,powerset(relation_dom(sK18(powerset(sK18(sK17(sK17(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15887,c_21015]) ).
tcf(c_24520,plain,
! [X0: $i,X1: $i] :
( ( sK2(empty_set,X1,powerset(relation_dom(relation_image(X0,empty_set)))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17175,c_21015]) ).
tcf(c_24521,plain,
! [X0: $i,X1: $i] :
( ( sK2(empty_set,X1,powerset(relation_dom(sK18(powerset(relation_image(X0,empty_set)))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17177,c_21015]) ).
tcf(c_24522,plain,
! [X0: $i,X1: $i] :
( ( sK2(empty_set,X1,powerset(relation_dom(sK18(sK17(powerset(sK18(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17880,c_21015]) ).
tcf(c_24523,plain,
! [X0: $i,X1: $i] :
( ( sK2(empty_set,X1,powerset(relation_dom(sK18(sK17(powerset(sK18(sK17(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17885,c_21015]) ).
tcf(c_24524,plain,
! [X0: $i,X1: $i] :
( ( sK2(empty_set,X1,powerset(relation_dom(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17888,c_21015]) ).
tcf(c_24525,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK2(empty_set,X1,powerset(relation_dom(sK2(empty_set,X2,powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20186,c_21015]) ).
tcf(c_24526,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK2(empty_set,X1,powerset(relation_dom(sK18(powerset(sK2(empty_set,X2,powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20188,c_21015]) ).
tcf(c_24527,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK2(empty_set,X1,powerset(relation_dom(sK18(sK17(powerset(sK2(empty_set,X2,powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20189,c_21015]) ).
tcf(c_24528,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK2(empty_set,X1,powerset(relation_dom(sK7(empty_set,X2,powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21299,c_21015]) ).
tcf(c_24529,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK2(empty_set,X1,powerset(relation_dom(sK18(powerset(sK7(empty_set,X2,powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21301,c_21015]) ).
tcf(c_24664,plain,
( one_to_one(sK18(powerset(empty_set)))
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_17316,c_23553]) ).
tcf(c_24665,plain,
( one_to_one(sK18(powerset(empty_set)))
| ~ function(sK1)
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_23326,c_23553]) ).
tcf(c_24666,plain,
( one_to_one(sK18(powerset(empty_set)))
| ~ function(sK6)
| ~ relation(sK6) ),
inference(superposition,[status(thm)],[c_23325,c_23553]) ).
tcf(c_24667,plain,
( one_to_one(sK18(powerset(empty_set)))
| ~ function(sK10)
| ~ relation(sK10) ),
inference(superposition,[status(thm)],[c_23324,c_23553]) ).
tcf(c_24668,plain,
( one_to_one(empty_set)
| ~ function(sK10)
| ~ relation(sK10) ),
inference(light_normalisation,[status(thm)],[c_24667,c_12958]) ).
tcf(c_24669,plain,
( one_to_one(empty_set)
| ~ function(sK6)
| ~ relation(sK6) ),
inference(light_normalisation,[status(thm)],[c_24666,c_12958]) ).
tcf(c_24670,plain,
( one_to_one(empty_set)
| ~ function(sK1)
| ~ relation(sK1) ),
inference(light_normalisation,[status(thm)],[c_24665,c_12958]) ).
tcf(c_24671,plain,
( one_to_one(empty_set)
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(light_normalisation,[status(thm)],[c_24664,c_12958]) ).
tcf(c_24676,plain,
! [X0: $i,X1: $i] :
( ( sK7(empty_set,X1,powerset(relation_dom(relation_dom(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_99,c_21941]) ).
tcf(c_24677,plain,
! [X0: $i] : sK7(empty_set,X0,powerset(relation_dom(empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_114,c_21941]) ).
tcf(c_24678,plain,
! [X0: $i,X1: $i] :
( ( sK7(empty_set,X1,powerset(relation_dom(sK18(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12738,c_21941]) ).
tcf(c_24679,plain,
! [X0: $i,X1: $i] :
( ( sK7(empty_set,X1,powerset(relation_dom(sK18(powerset(sK18(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13358,c_21941]) ).
tcf(c_24680,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK7(empty_set,X2,powerset(relation_dom(relation_image(X0,X1)))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(relation_image(X0,X1)))) = sK18(relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13157,c_21941]) ).
tcf(c_24681,plain,
! [X0: $i,X1: $i] :
( ( sK7(empty_set,X1,powerset(relation_dom(sK18(sK17(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13470,c_21941]) ).
tcf(c_24682,plain,
! [X0: $i,X1: $i] :
( ( sK7(empty_set,X1,powerset(relation_dom(sK18(powerset(sK18(sK17(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13469,c_21941]) ).
tcf(c_24683,plain,
! [X0: $i,X1: $i] :
( ( sK7(empty_set,X1,powerset(relation_dom(sK18(sK17(sK17(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15885,c_21941]) ).
tcf(c_24684,plain,
! [X0: $i,X1: $i] :
( ( sK7(empty_set,X1,powerset(relation_dom(sK18(powerset(sK18(sK17(sK17(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15887,c_21941]) ).
tcf(c_24685,plain,
! [X0: $i,X1: $i] :
( ( sK7(empty_set,X1,powerset(relation_dom(relation_image(X0,empty_set)))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17175,c_21941]) ).
tcf(c_24686,plain,
! [X0: $i,X1: $i] :
( ( sK7(empty_set,X1,powerset(relation_dom(sK18(powerset(relation_image(X0,empty_set)))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17177,c_21941]) ).
tcf(c_24687,plain,
! [X0: $i,X1: $i] :
( ( sK7(empty_set,X1,powerset(relation_dom(sK18(sK17(powerset(sK18(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17880,c_21941]) ).
tcf(c_24688,plain,
! [X0: $i,X1: $i] :
( ( sK7(empty_set,X1,powerset(relation_dom(sK18(sK17(powerset(sK18(sK17(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17885,c_21941]) ).
tcf(c_24689,plain,
! [X0: $i,X1: $i] :
( ( sK7(empty_set,X1,powerset(relation_dom(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17888,c_21941]) ).
tcf(c_24690,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK7(empty_set,X1,powerset(relation_dom(sK2(empty_set,X2,powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20186,c_21941]) ).
tcf(c_24691,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK7(empty_set,X1,powerset(relation_dom(sK18(powerset(sK2(empty_set,X2,powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20188,c_21941]) ).
tcf(c_24692,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK7(empty_set,X1,powerset(relation_dom(sK18(sK17(powerset(sK2(empty_set,X2,powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20189,c_21941]) ).
tcf(c_24693,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK7(empty_set,X1,powerset(relation_dom(sK7(empty_set,X2,powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21299,c_21941]) ).
tcf(c_24694,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK7(empty_set,X1,powerset(relation_dom(sK18(powerset(sK7(empty_set,X2,powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21301,c_21941]) ).
tcf(c_24880,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,sK18(sK17(sK17(sK17(powerset(X2)))))),X2)
| ( sK18(sK17(sK17(sK17(powerset(X2))))) = relation_image(X0,X1) )
| ( apply(X0,sK3(X0,X1,sK18(sK17(sK17(sK17(powerset(X2))))))) = sK2(X0,X1,sK18(sK17(sK17(sK17(powerset(X2)))))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_56,c_22278]) ).
tcf(c_24881,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X2,sK18(sK17(sK17(sK17(powerset(X1)))))),X1)
| in(sK3(X0,X2,sK18(sK17(sK17(sK17(powerset(X1)))))),relation_dom(X0))
| ( sK18(sK17(sK17(sK17(powerset(X1))))) = relation_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_54,c_22278]) ).
tcf(c_24882,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(X0,X2,sK18(sK17(sK17(sK17(powerset(X1)))))),X2)
| in(sK2(X0,X2,sK18(sK17(sK17(sK17(powerset(X1)))))),X1)
| ( sK18(sK17(sK17(sK17(powerset(X1))))) = relation_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_55,c_22278]) ).
tcf(c_24883,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(X0,sK18(sK17(sK17(sK17(powerset(X1))))),X2),X1)
| in(sK2(X0,sK18(sK17(sK17(sK17(powerset(X1))))),X2),X2)
| ( relation_image(X0,sK18(sK17(sK17(sK17(powerset(X1)))))) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_55,c_22278]) ).
tcf(c_24884,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK4(X1,sK18(sK17(sK17(sK17(powerset(X2))))),X0),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,sK18(sK17(sK17(sK17(powerset(X2))))))) ),
inference(superposition,[status(thm)],[c_59,c_22278]) ).
tcf(c_24885,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,sK18(sK17(sK17(sK17(powerset(X1))))),X2),X2)
| in(apply(X0,sK7(X0,sK18(sK17(sK17(sK17(powerset(X1))))),X2)),X1)
| ( relation_inverse_image(X0,sK18(sK17(sK17(sK17(powerset(X1)))))) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_69,c_22278]) ).
tcf(c_24886,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X2,sK18(sK17(sK17(sK17(powerset(X1)))))),X1)
| in(apply(X0,sK7(X0,X2,sK18(sK17(sK17(sK17(powerset(X1))))))),X2)
| ( sK18(sK17(sK17(sK17(powerset(X1))))) = relation_inverse_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_69,c_22278]) ).
tcf(c_24887,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X2,sK18(sK17(sK17(sK17(powerset(X1)))))),X1)
| in(sK7(X0,X2,sK18(sK17(sK17(sK17(powerset(X1)))))),relation_dom(X0))
| ( sK18(sK17(sK17(sK17(powerset(X1))))) = relation_inverse_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_68,c_22278]) ).
tcf(c_24888,plain,
! [X0: $i,X1: $i] :
( subset(sK18(sK17(sK17(sK17(powerset(X0))))),X1)
| in(sK13(sK18(sK17(sK17(sK17(powerset(X0))))),X1),X0) ),
inference(superposition,[status(thm)],[c_91,c_22278]) ).
tcf(c_24889,plain,
! [X0: $i] :
( empty(sK18(sK17(sK17(sK17(powerset(X0))))))
| in(sK18(sK18(sK17(sK17(sK17(powerset(X0)))))),X0) ),
inference(superposition,[status(thm)],[c_12501,c_22278]) ).
tcf(c_24890,plain,
! [X0: $i,X1: $i] :
( subset(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0))))))),X1)
| in(sK13(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0))))))),X1),X0) ),
inference(superposition,[status(thm)],[c_12692,c_22278]) ).
tcf(c_24891,plain,
! [X0: $i] :
( empty(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0))))))))
| in(sK18(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0)))))))),X0) ),
inference(superposition,[status(thm)],[c_12693,c_22278]) ).
tcf(c_24892,plain,
! [X0: $i,X1: $i] :
( empty(sK18(sK17(sK17(sK17(powerset(X0))))))
| subset(sK17(sK18(sK17(sK17(sK17(powerset(X0)))))),X1)
| in(sK13(sK17(sK18(sK17(sK17(sK17(powerset(X0)))))),X1),X0) ),
inference(superposition,[status(thm)],[c_12705,c_22278]) ).
tcf(c_24893,plain,
! [X0: $i] :
( empty(sK18(sK17(sK17(sK17(powerset(X0))))))
| in(sK18(sK17(sK18(sK17(sK17(sK17(powerset(X0))))))),X0) ),
inference(superposition,[status(thm)],[c_12981,c_22278]) ).
tcf(c_24894,plain,
! [X0: $i] :
( empty(sK18(sK17(sK17(sK17(powerset(X0))))))
| in(sK18(sK17(sK17(sK18(sK17(sK17(sK17(powerset(X0)))))))),X0) ),
inference(superposition,[status(thm)],[c_15371,c_22278]) ).
tcf(c_24895,plain,
! [X0: $i] :
( empty(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0))))))))
| in(sK18(sK17(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0))))))))),X0) ),
inference(superposition,[status(thm)],[c_12994,c_22278]) ).
tcf(c_24896,plain,
! [X0: $i] :
( empty(sK18(sK17(powerset(sK18(sK17(sK17(sK17(powerset(X0)))))))))
| in(sK18(sK18(sK17(powerset(sK18(sK17(sK17(sK17(powerset(X0))))))))),X0) ),
inference(superposition,[status(thm)],[c_13274,c_22278]) ).
tcf(c_24897,plain,
! [X0: $i] :
( empty(sK18(sK17(sK17(sK17(powerset(X0))))))
| in(sK18(sK17(sK17(sK17(sK18(sK17(sK17(sK17(powerset(X0))))))))),X0) ),
inference(superposition,[status(thm)],[c_22270,c_22278]) ).
tcf(c_24898,plain,
! [X0: $i] :
( empty(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0))))))))
| in(sK18(sK17(sK17(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0)))))))))),X0) ),
inference(superposition,[status(thm)],[c_15388,c_22278]) ).
tcf(c_24899,plain,
! [X0: $i,X1: $i] :
( in(sK2(empty_set,X1,sK18(sK17(sK17(sK17(powerset(X0)))))),X0)
| ( sK18(sK17(sK17(sK17(powerset(X0))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_19241,c_22278]) ).
tcf(c_24900,plain,
! [X0: $i,X1: $i] :
( in(sK7(empty_set,X1,sK18(sK17(sK17(sK17(powerset(X0)))))),X0)
| ( sK18(sK17(sK17(sK17(powerset(X0))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_19554,c_22278]) ).
tcf(c_25008,plain,
( relation(sK18(powerset(empty_set)))
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_17316,c_23554]) ).
tcf(c_25009,plain,
( relation(sK18(powerset(empty_set)))
| ~ function(sK1)
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_23326,c_23554]) ).
tcf(c_25010,plain,
( relation(sK18(powerset(empty_set)))
| ~ function(sK6)
| ~ relation(sK6) ),
inference(superposition,[status(thm)],[c_23325,c_23554]) ).
tcf(c_25011,plain,
( relation(sK18(powerset(empty_set)))
| ~ function(sK10)
| ~ relation(sK10) ),
inference(superposition,[status(thm)],[c_23324,c_23554]) ).
tcf(c_25012,plain,
! [X0: $i] :
( one_to_one(sK18(powerset(relation_image(X0,empty_set))))
| ( apply(sK18(powerset(relation_image(X0,empty_set))),sK11(sK18(powerset(relation_image(X0,empty_set))))) = apply(sK18(powerset(relation_image(X0,empty_set))),sK12(sK18(powerset(relation_image(X0,empty_set))))) )
| ~ function(X0)
| ~ relation(X0)
| ~ function(sK18(powerset(relation_image(X0,empty_set)))) ),
inference(superposition,[status(thm)],[c_23554,c_84]) ).
tcf(c_25013,plain,
( relation(empty_set)
| ~ function(sK10)
| ~ relation(sK10) ),
inference(light_normalisation,[status(thm)],[c_25011,c_12958]) ).
tcf(c_25014,plain,
( relation(empty_set)
| ~ function(sK6)
| ~ relation(sK6) ),
inference(light_normalisation,[status(thm)],[c_25010,c_12958]) ).
tcf(c_25015,plain,
( relation(empty_set)
| ~ function(sK1)
| ~ relation(sK1) ),
inference(light_normalisation,[status(thm)],[c_25009,c_12958]) ).
tcf(c_25029,plain,
( function(sK18(powerset(empty_set)))
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_17316,c_23555]) ).
tcf(c_25030,plain,
( function(sK18(powerset(empty_set)))
| ~ function(sK1)
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_23326,c_23555]) ).
tcf(c_25031,plain,
( function(sK18(powerset(empty_set)))
| ~ function(sK6)
| ~ relation(sK6) ),
inference(superposition,[status(thm)],[c_23325,c_23555]) ).
tcf(c_25032,plain,
( function(sK18(powerset(empty_set)))
| ~ function(sK10)
| ~ relation(sK10) ),
inference(superposition,[status(thm)],[c_23324,c_23555]) ).
tcf(c_25033,plain,
! [X0: $i] :
( ( relation_image(sK18(powerset(relation_image(X0,empty_set))),empty_set) = empty_set )
| ~ function(X0)
| ~ relation(X0)
| ~ relation(sK18(powerset(relation_image(X0,empty_set)))) ),
inference(superposition,[status(thm)],[c_23555,c_17554]) ).
tcf(c_25034,plain,
( function(empty_set)
| ~ function(sK10)
| ~ relation(sK10) ),
inference(light_normalisation,[status(thm)],[c_25032,c_12958]) ).
tcf(c_25035,plain,
( function(empty_set)
| ~ function(sK6)
| ~ relation(sK6) ),
inference(light_normalisation,[status(thm)],[c_25031,c_12958]) ).
tcf(c_25036,plain,
( function(empty_set)
| ~ function(sK1)
| ~ relation(sK1) ),
inference(light_normalisation,[status(thm)],[c_25030,c_12958]) ).
tcf(c_25048,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(X0,X3)
| ~ empty(X2)
| ~ in(X0,sK18(powerset(sK7(empty_set,X1,powerset(X2))))) ),
inference(superposition,[status(thm)],[c_21296,c_300]) ).
tcf(c_25049,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ empty(X3)
| ~ empty(X2)
| ~ in(X0,sK18(powerset(sK7(empty_set,X1,powerset(X2))))) ),
inference(superposition,[status(thm)],[c_21296,c_299]) ).
tcf(c_25050,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,X3)
| ~ empty(X2)
| ~ in(X0,sK18(powerset(sK7(empty_set,X1,powerset(X2))))) ),
inference(superposition,[status(thm)],[c_21296,c_92]) ).
tcf(c_25068,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK7(empty_set,X1,powerset(relation_dom(sK18(sK17(powerset(sK7(empty_set,X2,powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21302,c_21941]) ).
tcf(c_25069,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK2(empty_set,X1,powerset(relation_dom(sK18(sK17(powerset(sK7(empty_set,X2,powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21302,c_21015]) ).
tcf(c_25070,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(sK2(empty_set,X1,powerset(sK18(sK17(powerset(sK7(empty_set,X2,powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21302,c_20337]) ).
tcf(c_25071,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(sK17(powerset(relation_dom(sK18(sK17(powerset(sK7(empty_set,X1,powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21302,c_16287]) ).
tcf(c_25072,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(sK17(sK17(powerset(sK18(sK17(powerset(sK7(empty_set,X1,powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21302,c_15972]) ).
tcf(c_25073,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(sK17(powerset(relation_dom(sK18(sK17(powerset(sK7(empty_set,X1,powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21302,c_15716]) ).
tcf(c_25074,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(powerset(sK18(powerset(sK18(sK17(powerset(sK7(empty_set,X1,powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21302,c_14399]) ).
tcf(c_25075,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK7(empty_set,X1,powerset(sK18(sK17(powerset(sK7(empty_set,X2,powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21302,c_21303]) ).
tcf(c_25076,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK2(empty_set,X1,powerset(sK18(sK17(powerset(sK7(empty_set,X2,powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21302,c_20190]) ).
tcf(c_25077,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(powerset(relation_dom(relation_dom(sK18(sK17(powerset(sK7(empty_set,X1,powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21302,c_15588]) ).
tcf(c_25078,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(relation_dom(relation_dom(relation_dom(sK18(sK17(powerset(sK7(empty_set,X1,powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21302,c_15553]) ).
tcf(c_25079,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK18(sK17(powerset(sK18(sK17(powerset(sK7(empty_set,X1,powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21302,c_13492]) ).
tcf(c_25080,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK18(sK17(powerset(sK18(sK17(powerset(sK7(empty_set,X1,powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21302,c_13490]) ).
tcf(c_25081,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(powerset(relation_dom(relation_dom(sK18(sK17(powerset(sK7(empty_set,X1,powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21302,c_15527]) ).
tcf(c_25082,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK18(powerset(relation_dom(sK18(sK17(powerset(sK7(empty_set,X1,powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21302,c_15355]) ).
tcf(c_25083,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK18(powerset(relation_dom(sK18(sK17(powerset(sK7(empty_set,X1,powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21302,c_15317]) ).
tcf(c_25084,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(relation_dom(sK18(powerset(sK18(sK17(powerset(sK7(empty_set,X1,powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21302,c_13260]) ).
tcf(c_25085,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK18(sK17(powerset(sK7(empty_set,X1,powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21302,c_15261]) ).
tcf(c_25086,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_dom(sK18(sK17(powerset(sK7(empty_set,X2,powerset(X0))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21302,c_15230]) ).
tcf(c_25087,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(powerset(sK18(powerset(sK18(sK17(powerset(sK7(empty_set,X1,powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21302,c_13064]) ).
tcf(c_25088,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK18(powerset(sK18(sK17(powerset(sK7(empty_set,X2,powerset(X0))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21302,c_12767]) ).
tcf(c_25089,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(sK18(powerset(sK18(sK17(powerset(sK7(empty_set,X1,powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21302,c_12765]) ).
tcf(c_25090,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(sK17(powerset(sK18(sK17(powerset(sK7(empty_set,X1,powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21302,c_15973]) ).
tcf(c_25091,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(sK17(powerset(sK18(sK17(powerset(sK7(empty_set,X1,powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21302,c_13494]) ).
tcf(c_25092,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(powerset(relation_dom(sK18(sK17(powerset(sK7(empty_set,X1,powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21302,c_14397]) ).
tcf(c_25093,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(relation_dom(relation_dom(sK18(sK17(powerset(sK7(empty_set,X1,powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21302,c_13258]) ).
tcf(c_25094,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(powerset(relation_dom(sK18(sK17(powerset(sK7(empty_set,X1,powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21302,c_13062]) ).
tcf(c_25095,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK18(powerset(sK18(sK17(powerset(sK7(empty_set,X1,powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21302,c_12959]) ).
tcf(c_25096,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK18(powerset(sK18(sK17(powerset(sK7(empty_set,X1,powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21302,c_12766]) ).
tcf(c_25097,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK18(sK17(powerset(sK7(empty_set,X1,powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21302,c_12718]) ).
tcf(c_25098,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(sK18(sK17(powerset(sK7(empty_set,X2,powerset(X0)))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21302,c_12604]) ).
tcf(c_25099,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(powerset(sK18(sK17(powerset(sK7(empty_set,X1,powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21302,c_13495]) ).
tcf(c_25100,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(relation_dom(sK18(sK17(powerset(sK7(empty_set,X1,powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21302,c_12957]) ).
tcf(c_25101,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(powerset(sK18(sK17(powerset(sK7(empty_set,X1,powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21302,c_12768]) ).
tcf(c_25103,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(sK18(sK17(powerset(sK7(empty_set,X1,powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21302,c_12674]) ).
tcf(c_25105,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK18(sK17(powerset(sK7(empty_set,X2,powerset(X0))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21302,c_93]) ).
tcf(c_25108,plain,
! [X0: $i,X1: $i] :
( one_to_one(sK18(sK17(powerset(sK7(empty_set,X1,powerset(X0))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21302,c_5773]) ).
tcf(c_25109,plain,
! [X0: $i,X1: $i] :
( relation(sK18(sK17(powerset(sK7(empty_set,X1,powerset(X0))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21302,c_77]) ).
tcf(c_25110,plain,
! [X0: $i,X1: $i] :
( function(sK18(sK17(powerset(sK7(empty_set,X1,powerset(X0))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21302,c_66]) ).
tcf(c_25384,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(empty_set,X1,powerset(relation_dom(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_99,c_21429]) ).
tcf(c_25385,plain,
! [X0: $i] : relation_dom(sK7(empty_set,X0,powerset(empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_114,c_21429]) ).
tcf(c_25386,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(empty_set,X1,powerset(sK18(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12738,c_21429]) ).
tcf(c_25387,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(empty_set,X1,powerset(sK18(powerset(sK18(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13358,c_21429]) ).
tcf(c_25388,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(sK7(empty_set,X2,powerset(relation_image(X0,X1)))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(relation_image(X0,X1)))) = sK18(relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13157,c_21429]) ).
tcf(c_25389,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(empty_set,X1,powerset(sK18(sK17(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13470,c_21429]) ).
tcf(c_25390,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(empty_set,X1,powerset(sK18(powerset(sK18(sK17(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13469,c_21429]) ).
tcf(c_25391,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(empty_set,X1,powerset(sK18(sK17(sK17(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15885,c_21429]) ).
tcf(c_25392,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(empty_set,X1,powerset(sK18(powerset(sK18(sK17(sK17(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15887,c_21429]) ).
tcf(c_25393,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(empty_set,X1,powerset(relation_image(X0,empty_set)))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17175,c_21429]) ).
tcf(c_25394,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(empty_set,X1,powerset(sK18(powerset(relation_image(X0,empty_set)))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17177,c_21429]) ).
tcf(c_25395,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(empty_set,X1,powerset(sK18(sK17(powerset(sK18(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17880,c_21429]) ).
tcf(c_25396,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(empty_set,X1,powerset(sK18(sK17(powerset(sK18(sK17(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17885,c_21429]) ).
tcf(c_25397,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(empty_set,X1,powerset(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17888,c_21429]) ).
tcf(c_25398,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(sK7(empty_set,X1,powerset(sK2(empty_set,X2,powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20186,c_21429]) ).
tcf(c_25399,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(sK7(empty_set,X1,powerset(sK18(powerset(sK2(empty_set,X2,powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20188,c_21429]) ).
tcf(c_25400,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(sK7(empty_set,X1,powerset(sK18(sK17(powerset(sK2(empty_set,X2,powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20189,c_21429]) ).
tcf(c_25401,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(sK7(empty_set,X1,powerset(sK7(empty_set,X2,powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21299,c_21429]) ).
tcf(c_25402,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(sK7(empty_set,X1,powerset(sK18(powerset(sK7(empty_set,X2,powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21301,c_21429]) ).
tcf(c_25403,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(sK7(empty_set,X1,powerset(sK18(sK17(powerset(sK7(empty_set,X2,powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21302,c_21429]) ).
tcf(c_25485,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X0,X1,sK18(sK17(sK17(sK17(powerset(X2)))))),X2)
| ( sK18(sK17(sK17(sK17(powerset(X2))))) = relation_image(X0,X1) )
| ( apply(X0,sK3(X0,X1,sK18(sK17(sK17(sK17(powerset(X2))))))) = sK2(X0,X1,sK18(sK17(sK17(sK17(powerset(X2)))))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_56,c_22276]) ).
tcf(c_25486,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X0,X2,sK18(sK17(sK17(sK17(powerset(X1)))))),X1)
| in(sK3(X0,X2,sK18(sK17(sK17(sK17(powerset(X1)))))),relation_dom(X0))
| ( sK18(sK17(sK17(sK17(powerset(X1))))) = relation_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_54,c_22276]) ).
tcf(c_25487,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X0,X2,sK18(sK17(sK17(sK17(powerset(X1)))))),X1)
| in(sK3(X0,X2,sK18(sK17(sK17(sK17(powerset(X1)))))),X2)
| ( sK18(sK17(sK17(sK17(powerset(X1))))) = relation_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_55,c_22276]) ).
tcf(c_25488,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK3(X0,sK18(sK17(sK17(sK17(powerset(X1))))),X2),X1)
| in(sK2(X0,sK18(sK17(sK17(sK17(powerset(X1))))),X2),X2)
| ( relation_image(X0,sK18(sK17(sK17(sK17(powerset(X1)))))) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_55,c_22276]) ).
tcf(c_25489,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK4(X1,sK18(sK17(sK17(sK17(powerset(X2))))),X0),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,sK18(sK17(sK17(sK17(powerset(X2))))))) ),
inference(superposition,[status(thm)],[c_59,c_22276]) ).
tcf(c_25490,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,sK18(sK17(sK17(sK17(powerset(X1))))),X2),X2)
| element(apply(X0,sK7(X0,sK18(sK17(sK17(sK17(powerset(X1))))),X2)),X1)
| ( relation_inverse_image(X0,sK18(sK17(sK17(sK17(powerset(X1)))))) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_69,c_22276]) ).
tcf(c_25491,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK7(X0,X2,sK18(sK17(sK17(sK17(powerset(X1)))))),X1)
| in(apply(X0,sK7(X0,X2,sK18(sK17(sK17(sK17(powerset(X1))))))),X2)
| ( sK18(sK17(sK17(sK17(powerset(X1))))) = relation_inverse_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_69,c_22276]) ).
tcf(c_25492,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK7(X0,X2,sK18(sK17(sK17(sK17(powerset(X1)))))),X1)
| in(sK7(X0,X2,sK18(sK17(sK17(sK17(powerset(X1)))))),relation_dom(X0))
| ( sK18(sK17(sK17(sK17(powerset(X1))))) = relation_inverse_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_68,c_22276]) ).
tcf(c_25493,plain,
! [X0: $i,X1: $i] :
( subset(sK18(sK17(sK17(sK17(powerset(X0))))),X1)
| element(sK13(sK18(sK17(sK17(sK17(powerset(X0))))),X1),X0) ),
inference(superposition,[status(thm)],[c_91,c_22276]) ).
tcf(c_25494,plain,
! [X0: $i] :
( empty(sK18(sK17(sK17(sK17(powerset(X0))))))
| element(sK18(sK18(sK17(sK17(sK17(powerset(X0)))))),X0) ),
inference(superposition,[status(thm)],[c_12501,c_22276]) ).
tcf(c_25495,plain,
! [X0: $i,X1: $i] :
( subset(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0))))))),X1)
| element(sK13(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0))))))),X1),X0) ),
inference(superposition,[status(thm)],[c_12692,c_22276]) ).
tcf(c_25496,plain,
! [X0: $i] :
( empty(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0))))))))
| element(sK18(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0)))))))),X0) ),
inference(superposition,[status(thm)],[c_12693,c_22276]) ).
tcf(c_25497,plain,
! [X0: $i,X1: $i] :
( empty(sK18(sK17(sK17(sK17(powerset(X0))))))
| subset(sK17(sK18(sK17(sK17(sK17(powerset(X0)))))),X1)
| element(sK13(sK17(sK18(sK17(sK17(sK17(powerset(X0)))))),X1),X0) ),
inference(superposition,[status(thm)],[c_12705,c_22276]) ).
tcf(c_25498,plain,
! [X0: $i] :
( empty(sK18(sK17(sK17(sK17(powerset(X0))))))
| element(sK18(sK17(sK18(sK17(sK17(sK17(powerset(X0))))))),X0) ),
inference(superposition,[status(thm)],[c_12981,c_22276]) ).
tcf(c_25499,plain,
! [X0: $i] :
( empty(sK18(sK17(sK17(sK17(powerset(X0))))))
| element(sK18(sK17(sK17(sK18(sK17(sK17(sK17(powerset(X0)))))))),X0) ),
inference(superposition,[status(thm)],[c_15371,c_22276]) ).
tcf(c_25500,plain,
! [X0: $i] :
( empty(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0))))))))
| element(sK18(sK17(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0))))))))),X0) ),
inference(superposition,[status(thm)],[c_12994,c_22276]) ).
tcf(c_25501,plain,
! [X0: $i] :
( empty(sK18(sK17(powerset(sK18(sK17(sK17(sK17(powerset(X0)))))))))
| element(sK18(sK18(sK17(powerset(sK18(sK17(sK17(sK17(powerset(X0))))))))),X0) ),
inference(superposition,[status(thm)],[c_13274,c_22276]) ).
tcf(c_25502,plain,
! [X0: $i] :
( empty(sK18(sK17(sK17(sK17(powerset(X0))))))
| element(sK18(sK17(sK17(sK17(sK18(sK17(sK17(sK17(powerset(X0))))))))),X0) ),
inference(superposition,[status(thm)],[c_22270,c_22276]) ).
tcf(c_25503,plain,
! [X0: $i] :
( empty(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0))))))))
| element(sK18(sK17(sK17(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0)))))))))),X0) ),
inference(superposition,[status(thm)],[c_15388,c_22276]) ).
tcf(c_25504,plain,
! [X0: $i,X1: $i] :
( element(sK2(empty_set,X1,sK18(sK17(sK17(sK17(powerset(X0)))))),X0)
| ( sK18(sK17(sK17(sK17(powerset(X0))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_19241,c_22276]) ).
tcf(c_25505,plain,
! [X0: $i,X1: $i] :
( element(sK7(empty_set,X1,sK18(sK17(sK17(sK17(powerset(X0)))))),X0)
| ( sK18(sK17(sK17(sK17(powerset(X0))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_19554,c_22276]) ).
tcf(c_25666,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK18(sK17(sK17(sK17(powerset(X1))))) = relation_image(X0,X2) )
| ( apply(X0,sK3(X0,X2,sK18(sK17(sK17(sK17(powerset(X1))))))) = sK2(X0,X2,sK18(sK17(sK17(sK17(powerset(X1)))))) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_56,c_22277]) ).
tcf(c_25667,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(X0,X2,sK18(sK17(sK17(sK17(powerset(X1)))))),relation_dom(X0))
| ( sK18(sK17(sK17(sK17(powerset(X1))))) = relation_image(X0,X2) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_54,c_22277]) ).
tcf(c_25668,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(X0,X2,sK18(sK17(sK17(sK17(powerset(X1)))))),X2)
| ( sK18(sK17(sK17(sK17(powerset(X1))))) = relation_image(X0,X2) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_55,c_22277]) ).
tcf(c_25669,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,sK18(sK17(sK17(sK17(powerset(X1))))),X2),X2)
| ( relation_image(X0,sK18(sK17(sK17(sK17(powerset(X1)))))) = X2 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_55,c_22277]) ).
tcf(c_25670,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(X2)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,sK18(sK17(sK17(sK17(powerset(X2))))))) ),
inference(superposition,[status(thm)],[c_59,c_22277]) ).
tcf(c_25671,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,sK18(sK17(sK17(sK17(powerset(X1))))),X2),X2)
| ( relation_inverse_image(X0,sK18(sK17(sK17(sK17(powerset(X1)))))) = X2 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_69,c_22277]) ).
tcf(c_25672,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X0,sK7(X0,X2,sK18(sK17(sK17(sK17(powerset(X1))))))),X2)
| ( sK18(sK17(sK17(sK17(powerset(X1))))) = relation_inverse_image(X0,X2) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_69,c_22277]) ).
tcf(c_25673,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X2,sK18(sK17(sK17(sK17(powerset(X1)))))),relation_dom(X0))
| ( sK18(sK17(sK17(sK17(powerset(X1))))) = relation_inverse_image(X0,X2) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_68,c_22277]) ).
tcf(c_25674,plain,
! [X0: $i,X1: $i] :
( subset(sK18(sK17(sK17(sK17(powerset(X0))))),X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_91,c_22277]) ).
tcf(c_25676,plain,
! [X0: $i,X1: $i] :
( subset(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0))))))),X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12692,c_22277]) ).
tcf(c_25678,plain,
! [X0: $i,X1: $i] :
( empty(sK18(sK17(sK17(sK17(powerset(X0))))))
| subset(sK17(sK18(sK17(sK17(sK17(powerset(X0)))))),X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12705,c_22277]) ).
tcf(c_25682,plain,
! [X0: $i] :
( empty(sK18(sK17(powerset(sK18(sK17(sK17(sK17(powerset(X0)))))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13274,c_22277]) ).
tcf(c_25683,plain,
! [X0: $i] :
( empty(sK18(sK17(sK17(sK17(powerset(X0))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_22270,c_22277]) ).
tcf(c_25684,plain,
! [X0: $i] :
( empty(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0))))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15388,c_22277]) ).
tcf(c_25685,plain,
! [X0: $i] :
( ( sK18(sK17(sK17(sK17(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_19241,c_22277]) ).
tcf(c_25821,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(empty_set,X1,powerset(sK18(sK17(sK17(sK17(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25683,c_21429]) ).
tcf(c_25822,plain,
! [X0: $i,X1: $i] :
( ( sK7(empty_set,X1,powerset(relation_dom(sK18(sK17(sK17(sK17(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25683,c_21941]) ).
tcf(c_25823,plain,
! [X0: $i,X1: $i] :
( ( sK2(empty_set,X1,powerset(relation_dom(sK18(sK17(sK17(sK17(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25683,c_21015]) ).
tcf(c_25824,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK2(empty_set,X1,powerset(sK18(sK17(sK17(sK17(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25683,c_20337]) ).
tcf(c_25825,plain,
! [X0: $i] :
( ( sK18(sK17(sK17(powerset(relation_dom(sK18(sK17(sK17(sK17(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25683,c_16287]) ).
tcf(c_25826,plain,
! [X0: $i] :
( ( relation_dom(sK18(sK17(sK17(powerset(sK18(sK17(sK17(sK17(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25683,c_15972]) ).
tcf(c_25827,plain,
! [X0: $i] :
( ( relation_dom(sK18(sK17(powerset(relation_dom(sK18(sK17(sK17(sK17(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25683,c_15716]) ).
tcf(c_25828,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25683,c_14399]) ).
tcf(c_25829,plain,
! [X0: $i,X1: $i] :
( ( sK7(empty_set,X1,powerset(sK18(sK17(sK17(sK17(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25683,c_21303]) ).
tcf(c_25830,plain,
! [X0: $i,X1: $i] :
( ( sK2(empty_set,X1,powerset(sK18(sK17(sK17(sK17(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25683,c_20190]) ).
tcf(c_25831,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(relation_dom(relation_dom(sK18(sK17(sK17(sK17(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25683,c_15588]) ).
tcf(c_25832,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(relation_dom(relation_dom(sK18(sK17(sK17(sK17(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25683,c_15553]) ).
tcf(c_25833,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK18(sK17(powerset(sK18(sK17(sK17(sK17(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25683,c_13492]) ).
tcf(c_25834,plain,
! [X0: $i] :
( ( sK18(powerset(sK18(sK17(powerset(sK18(sK17(sK17(sK17(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25683,c_13490]) ).
tcf(c_25835,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(relation_dom(relation_dom(sK18(sK17(sK17(sK17(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25683,c_15527]) ).
tcf(c_25836,plain,
! [X0: $i] :
( ( sK18(powerset(sK18(powerset(relation_dom(sK18(sK17(sK17(sK17(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25683,c_15355]) ).
tcf(c_25837,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK18(powerset(relation_dom(sK18(sK17(sK17(sK17(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25683,c_15317]) ).
tcf(c_25838,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25683,c_13260]) ).
tcf(c_25839,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK18(sK17(sK17(sK17(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25683,c_15261]) ).
tcf(c_25840,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK18(sK17(sK17(sK17(powerset(X0))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25683,c_15230]) ).
tcf(c_25841,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25683,c_13064]) ).
tcf(c_25842,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25683,c_12767]) ).
tcf(c_25843,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25683,c_12765]) ).
tcf(c_25844,plain,
! [X0: $i] :
( ( sK18(sK17(sK17(powerset(sK18(sK17(sK17(sK17(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25683,c_15973]) ).
tcf(c_25845,plain,
! [X0: $i] :
( ( relation_dom(sK18(sK17(powerset(sK18(sK17(sK17(sK17(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25683,c_13494]) ).
tcf(c_25846,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(relation_dom(sK18(sK17(sK17(sK17(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25683,c_14397]) ).
tcf(c_25847,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(relation_dom(sK18(sK17(sK17(sK17(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25683,c_13258]) ).
tcf(c_25848,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(relation_dom(sK18(sK17(sK17(sK17(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25683,c_13062]) ).
tcf(c_25849,plain,
! [X0: $i] :
( ( sK18(powerset(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25683,c_12959]) ).
tcf(c_25850,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25683,c_12766]) ).
tcf(c_25851,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK18(sK17(sK17(sK17(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25683,c_12718]) ).
tcf(c_25852,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(sK17(sK17(sK17(powerset(X0)))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25683,c_12604]) ).
tcf(c_25853,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(sK18(sK17(sK17(sK17(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25683,c_13495]) ).
tcf(c_25854,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(sK18(sK17(sK17(sK17(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25683,c_12957]) ).
tcf(c_25855,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25683,c_12768]) ).
tcf(c_25856,plain,
! [X0: $i] :
( ( sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25683,c_12769]) ).
tcf(c_25857,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK18(sK17(sK17(sK17(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25683,c_12674]) ).
tcf(c_25858,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK18(sK17(sK17(sK17(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25683,c_12550]) ).
tcf(c_25859,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(sK17(sK17(powerset(X0))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25683,c_93]) ).
tcf(c_25860,plain,
! [X0: $i] :
( ( relation_dom(sK18(sK17(sK17(sK17(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25683,c_12406]) ).
tcf(c_25862,plain,
! [X0: $i] :
( one_to_one(sK18(sK17(sK17(sK17(powerset(X0))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25683,c_5773]) ).
tcf(c_25863,plain,
! [X0: $i] :
( relation(sK18(sK17(sK17(sK17(powerset(X0))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25683,c_77]) ).
tcf(c_25864,plain,
! [X0: $i] :
( function(sK18(sK17(sK17(sK17(powerset(X0))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25683,c_66]) ).
tcf(c_26198,plain,
! [X0: $i] :
( one_to_one(sK18(sK17(sK17(sK17(powerset(X0))))))
| ( apply(sK18(sK17(sK17(sK17(powerset(X0))))),sK11(sK18(sK17(sK17(sK17(powerset(X0))))))) = apply(sK18(sK17(sK17(sK17(powerset(X0))))),sK12(sK18(sK17(sK17(sK17(powerset(X0))))))) )
| ~ empty(X0)
| ~ function(sK18(sK17(sK17(sK17(powerset(X0)))))) ),
inference(superposition,[status(thm)],[c_25863,c_84]) ).
tcf(c_26208,plain,
! [X0: $i] :
( ( relation_image(sK18(sK17(sK17(sK17(powerset(X0))))),empty_set) = empty_set )
| ~ empty(X0)
| ~ relation(sK18(sK17(sK17(sK17(powerset(X0)))))) ),
inference(superposition,[status(thm)],[c_25864,c_17554]) ).
tcf(c_26230,plain,
! [X0: $i] :
( one_to_one(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0))))))))
| ( apply(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0))))))),sK11(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0))))))))) = apply(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0))))))),sK12(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0))))))))) )
| ~ empty(X0)
| ~ function(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0)))))))) ),
inference(superposition,[status(thm)],[c_23840,c_84]) ).
tcf(c_26244,plain,
! [X0: $i] :
( empty(sK18(powerset(empty_set)))
| ( apply(empty_set,sK4(empty_set,X0,sK18(sK18(powerset(relation_image(empty_set,X0)))))) = sK18(sK18(powerset(relation_image(empty_set,X0)))) )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_17316,c_13158]) ).
tcf(c_26245,plain,
( empty(sK18(powerset(empty_set)))
| ( apply(sK1,sK4(sK1,empty_set,sK18(sK18(powerset(relation_image(sK1,empty_set)))))) = sK18(sK18(powerset(relation_image(sK1,empty_set)))) )
| ~ function(sK1)
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_23326,c_13158]) ).
tcf(c_26246,plain,
( empty(sK18(powerset(empty_set)))
| ( apply(sK6,sK4(sK6,empty_set,sK18(sK18(powerset(relation_image(sK6,empty_set)))))) = sK18(sK18(powerset(relation_image(sK6,empty_set)))) )
| ~ function(sK6)
| ~ relation(sK6) ),
inference(superposition,[status(thm)],[c_23325,c_13158]) ).
tcf(c_26247,plain,
( empty(sK18(powerset(empty_set)))
| ( apply(sK10,sK4(sK10,empty_set,sK18(sK18(powerset(relation_image(sK10,empty_set)))))) = sK18(sK18(powerset(relation_image(sK10,empty_set)))) )
| ~ function(sK10)
| ~ relation(sK10) ),
inference(superposition,[status(thm)],[c_23324,c_13158]) ).
tcf(c_26248,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(sK7(empty_set,X2,powerset(sK18(powerset(relation_image(X0,X1)))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK18(powerset(relation_image(X0,X1)))))) = sK18(sK18(powerset(relation_image(X0,X1)))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13158,c_21429]) ).
tcf(c_26249,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK7(empty_set,X2,powerset(relation_dom(sK18(powerset(relation_image(X0,X1)))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK18(powerset(relation_image(X0,X1)))))) = sK18(sK18(powerset(relation_image(X0,X1)))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13158,c_21941]) ).
tcf(c_26250,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK2(empty_set,X2,powerset(relation_dom(sK18(powerset(relation_image(X0,X1)))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK18(powerset(relation_image(X0,X1)))))) = sK18(sK18(powerset(relation_image(X0,X1)))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13158,c_21015]) ).
tcf(c_26251,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(sK2(empty_set,X2,powerset(sK18(powerset(relation_image(X0,X1)))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK18(powerset(relation_image(X0,X1)))))) = sK18(sK18(powerset(relation_image(X0,X1)))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13158,c_20337]) ).
tcf(c_26252,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(sK17(powerset(relation_dom(sK18(powerset(relation_image(X0,X1)))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK18(powerset(relation_image(X0,X1)))))) = sK18(sK18(powerset(relation_image(X0,X1)))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13158,c_16287]) ).
tcf(c_26253,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(sK17(sK17(powerset(sK18(powerset(relation_image(X0,X1)))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK18(powerset(relation_image(X0,X1)))))) = sK18(sK18(powerset(relation_image(X0,X1)))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13158,c_15972]) ).
tcf(c_26254,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(sK17(powerset(relation_dom(sK18(powerset(relation_image(X0,X1)))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK18(powerset(relation_image(X0,X1)))))) = sK18(sK18(powerset(relation_image(X0,X1)))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13158,c_15716]) ).
tcf(c_26255,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(powerset(sK18(powerset(sK18(powerset(relation_image(X0,X1)))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK18(powerset(relation_image(X0,X1)))))) = sK18(sK18(powerset(relation_image(X0,X1)))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13158,c_14399]) ).
tcf(c_26256,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK7(empty_set,X2,powerset(sK18(powerset(relation_image(X0,X1))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK18(powerset(relation_image(X0,X1)))))) = sK18(sK18(powerset(relation_image(X0,X1)))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13158,c_21303]) ).
tcf(c_26257,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK2(empty_set,X2,powerset(sK18(powerset(relation_image(X0,X1))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK18(powerset(relation_image(X0,X1)))))) = sK18(sK18(powerset(relation_image(X0,X1)))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13158,c_20190]) ).
tcf(c_26258,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(powerset(relation_dom(relation_dom(sK18(powerset(relation_image(X0,X1)))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK18(powerset(relation_image(X0,X1)))))) = sK18(sK18(powerset(relation_image(X0,X1)))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13158,c_15588]) ).
tcf(c_26259,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(relation_dom(relation_dom(relation_dom(sK18(powerset(relation_image(X0,X1)))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK18(powerset(relation_image(X0,X1)))))) = sK18(sK18(powerset(relation_image(X0,X1)))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13158,c_15553]) ).
tcf(c_26260,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK18(sK17(powerset(sK18(powerset(relation_image(X0,X1)))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK18(powerset(relation_image(X0,X1)))))) = sK18(sK18(powerset(relation_image(X0,X1)))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13158,c_13492]) ).
tcf(c_26261,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK18(sK17(powerset(sK18(powerset(relation_image(X0,X1)))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK18(powerset(relation_image(X0,X1)))))) = sK18(sK18(powerset(relation_image(X0,X1)))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13158,c_13490]) ).
tcf(c_26262,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(powerset(relation_dom(relation_dom(sK18(powerset(relation_image(X0,X1)))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK18(powerset(relation_image(X0,X1)))))) = sK18(sK18(powerset(relation_image(X0,X1)))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13158,c_15527]) ).
tcf(c_26263,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK18(powerset(relation_dom(sK18(powerset(relation_image(X0,X1)))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK18(powerset(relation_image(X0,X1)))))) = sK18(sK18(powerset(relation_image(X0,X1)))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13158,c_15355]) ).
tcf(c_26264,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK18(powerset(relation_dom(sK18(powerset(relation_image(X0,X1)))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK18(powerset(relation_image(X0,X1)))))) = sK18(sK18(powerset(relation_image(X0,X1)))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13158,c_15317]) ).
tcf(c_26265,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(relation_dom(sK18(powerset(sK18(powerset(relation_image(X0,X1)))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK18(powerset(relation_image(X0,X1)))))) = sK18(sK18(powerset(relation_image(X0,X1)))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13158,c_13260]) ).
tcf(c_26266,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK18(powerset(relation_image(X0,X1)))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK18(powerset(relation_image(X0,X1)))))) = sK18(sK18(powerset(relation_image(X0,X1)))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13158,c_15261]) ).
tcf(c_26267,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_dom(sK18(powerset(relation_image(X0,X2))))) = X1 )
| ( apply(X0,sK4(X0,X2,sK18(sK18(powerset(relation_image(X0,X2)))))) = sK18(sK18(powerset(relation_image(X0,X2)))) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13158,c_15230]) ).
tcf(c_26268,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(powerset(sK18(powerset(sK18(powerset(relation_image(X0,X1)))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK18(powerset(relation_image(X0,X1)))))) = sK18(sK18(powerset(relation_image(X0,X1)))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13158,c_13064]) ).
tcf(c_26269,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK18(powerset(sK18(powerset(relation_image(X0,X2))))) = X1 )
| ( apply(X0,sK4(X0,X2,sK18(sK18(powerset(relation_image(X0,X2)))))) = sK18(sK18(powerset(relation_image(X0,X2)))) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13158,c_12767]) ).
tcf(c_26270,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(sK18(powerset(sK18(powerset(relation_image(X0,X1)))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK18(powerset(relation_image(X0,X1)))))) = sK18(sK18(powerset(relation_image(X0,X1)))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13158,c_12765]) ).
tcf(c_26271,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(sK17(powerset(sK18(powerset(relation_image(X0,X1))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK18(powerset(relation_image(X0,X1)))))) = sK18(sK18(powerset(relation_image(X0,X1)))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13158,c_15973]) ).
tcf(c_26272,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(sK17(powerset(sK18(powerset(relation_image(X0,X1))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK18(powerset(relation_image(X0,X1)))))) = sK18(sK18(powerset(relation_image(X0,X1)))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13158,c_13494]) ).
tcf(c_26273,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(powerset(relation_dom(sK18(powerset(relation_image(X0,X1))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK18(powerset(relation_image(X0,X1)))))) = sK18(sK18(powerset(relation_image(X0,X1)))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13158,c_14397]) ).
tcf(c_26274,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(relation_dom(relation_dom(sK18(powerset(relation_image(X0,X1))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK18(powerset(relation_image(X0,X1)))))) = sK18(sK18(powerset(relation_image(X0,X1)))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13158,c_13258]) ).
tcf(c_26275,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(powerset(relation_dom(sK18(powerset(relation_image(X0,X1))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK18(powerset(relation_image(X0,X1)))))) = sK18(sK18(powerset(relation_image(X0,X1)))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13158,c_13062]) ).
tcf(c_26276,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK18(powerset(sK18(powerset(relation_image(X0,X1))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK18(powerset(relation_image(X0,X1)))))) = sK18(sK18(powerset(relation_image(X0,X1)))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13158,c_12959]) ).
tcf(c_26277,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK18(powerset(sK18(powerset(relation_image(X0,X1))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK18(powerset(relation_image(X0,X1)))))) = sK18(sK18(powerset(relation_image(X0,X1)))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13158,c_12766]) ).
tcf(c_26278,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK18(powerset(relation_image(X0,X1))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK18(powerset(relation_image(X0,X1)))))) = sK18(sK18(powerset(relation_image(X0,X1)))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13158,c_12718]) ).
tcf(c_26279,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(sK18(powerset(relation_image(X0,X2)))) = X1 )
| ( apply(X0,sK4(X0,X2,sK18(sK18(powerset(relation_image(X0,X2)))))) = sK18(sK18(powerset(relation_image(X0,X2)))) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13158,c_12604]) ).
tcf(c_26280,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(powerset(sK18(powerset(relation_image(X0,X1)))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK18(powerset(relation_image(X0,X1)))))) = sK18(sK18(powerset(relation_image(X0,X1)))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13158,c_13495]) ).
tcf(c_26281,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(relation_dom(sK18(powerset(relation_image(X0,X1)))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK18(powerset(relation_image(X0,X1)))))) = sK18(sK18(powerset(relation_image(X0,X1)))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13158,c_12957]) ).
tcf(c_26282,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(powerset(sK18(powerset(relation_image(X0,X1)))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK18(powerset(relation_image(X0,X1)))))) = sK18(sK18(powerset(relation_image(X0,X1)))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13158,c_12768]) ).
tcf(c_26283,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK18(powerset(relation_image(X0,X1))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK18(powerset(relation_image(X0,X1)))))) = sK18(sK18(powerset(relation_image(X0,X1)))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13158,c_12769]) ).
tcf(c_26284,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(sK18(powerset(relation_image(X0,X1)))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK18(powerset(relation_image(X0,X1)))))) = sK18(sK18(powerset(relation_image(X0,X1)))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13158,c_12674]) ).
tcf(c_26285,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK18(powerset(relation_image(X0,X1))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK18(powerset(relation_image(X0,X1)))))) = sK18(sK18(powerset(relation_image(X0,X1)))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13158,c_12550]) ).
tcf(c_26286,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK18(powerset(relation_image(X0,X2))) = X1 )
| ( apply(X0,sK4(X0,X2,sK18(sK18(powerset(relation_image(X0,X2)))))) = sK18(sK18(powerset(relation_image(X0,X2)))) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13158,c_93]) ).
tcf(c_26287,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(powerset(relation_image(X0,X1)))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK18(powerset(relation_image(X0,X1)))))) = sK18(sK18(powerset(relation_image(X0,X1)))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13158,c_12406]) ).
tcf(c_26288,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(relation_image(X0,X1))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK18(powerset(relation_image(X0,X1)))))) = sK18(sK18(powerset(relation_image(X0,X1)))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13158,c_94]) ).
tcf(c_26289,plain,
! [X0: $i,X1: $i] :
( one_to_one(sK18(powerset(relation_image(X0,X1))))
| ( apply(X0,sK4(X0,X1,sK18(sK18(powerset(relation_image(X0,X1)))))) = sK18(sK18(powerset(relation_image(X0,X1)))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13158,c_5773]) ).
tcf(c_26290,plain,
! [X0: $i,X1: $i] :
( relation(sK18(powerset(relation_image(X0,X1))))
| ( apply(X0,sK4(X0,X1,sK18(sK18(powerset(relation_image(X0,X1)))))) = sK18(sK18(powerset(relation_image(X0,X1)))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13158,c_77]) ).
tcf(c_26291,plain,
! [X0: $i,X1: $i] :
( function(sK18(powerset(relation_image(X0,X1))))
| ( apply(X0,sK4(X0,X1,sK18(sK18(powerset(relation_image(X0,X1)))))) = sK18(sK18(powerset(relation_image(X0,X1)))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13158,c_66]) ).
tcf(c_26292,plain,
( empty(empty_set)
| ( apply(sK10,sK4(sK10,empty_set,sK18(empty_set))) = sK18(empty_set) )
| ~ function(sK10)
| ~ relation(sK10) ),
inference(light_normalisation,[status(thm)],[c_26247,c_12958,c_23324]) ).
tcf(c_26293,plain,
( empty(empty_set)
| ( apply(sK6,sK4(sK6,empty_set,sK18(empty_set))) = sK18(empty_set) )
| ~ function(sK6)
| ~ relation(sK6) ),
inference(light_normalisation,[status(thm)],[c_26246,c_12958,c_23325]) ).
tcf(c_26294,plain,
( empty(empty_set)
| ( apply(sK1,sK4(sK1,empty_set,sK18(empty_set))) = sK18(empty_set) )
| ~ function(sK1)
| ~ relation(sK1) ),
inference(light_normalisation,[status(thm)],[c_26245,c_12958,c_23326]) ).
tcf(c_26295,plain,
! [X0: $i] :
( empty(empty_set)
| ( apply(empty_set,sK4(empty_set,X0,sK18(empty_set))) = sK18(empty_set) )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(light_normalisation,[status(thm)],[c_26244,c_12958,c_17316]) ).
tcf(c_26583,plain,
! [X0: $i] :
( ( relation_image(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0))))))),empty_set) = empty_set )
| ~ empty(X0)
| ~ relation(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0)))))))) ),
inference(superposition,[status(thm)],[c_23841,c_17554]) ).
tcf(c_26598,plain,
! [X0: $i,X1: $i] :
( one_to_one(sK18(sK17(powerset(sK2(empty_set,X0,powerset(X1))))))
| ( apply(sK18(sK17(powerset(sK2(empty_set,X0,powerset(X1))))),sK11(sK18(sK17(powerset(sK2(empty_set,X0,powerset(X1))))))) = apply(sK18(sK17(powerset(sK2(empty_set,X0,powerset(X1))))),sK12(sK18(sK17(powerset(sK2(empty_set,X0,powerset(X1))))))) )
| ~ empty(X1)
| ~ function(sK18(sK17(powerset(sK2(empty_set,X0,powerset(X1)))))) ),
inference(superposition,[status(thm)],[c_24107,c_84]) ).
tcf(c_26621,plain,
! [X0: $i,X1: $i] :
( ( relation_image(sK18(sK17(powerset(sK2(empty_set,X0,powerset(X1))))),empty_set) = empty_set )
| ~ empty(X1)
| ~ relation(sK18(sK17(powerset(sK2(empty_set,X0,powerset(X1)))))) ),
inference(superposition,[status(thm)],[c_24108,c_17554]) ).
tcf(c_26636,plain,
! [X0: $i,X1: $i] :
( one_to_one(sK18(sK17(powerset(sK7(empty_set,X0,powerset(X1))))))
| ( apply(sK18(sK17(powerset(sK7(empty_set,X0,powerset(X1))))),sK11(sK18(sK17(powerset(sK7(empty_set,X0,powerset(X1))))))) = apply(sK18(sK17(powerset(sK7(empty_set,X0,powerset(X1))))),sK12(sK18(sK17(powerset(sK7(empty_set,X0,powerset(X1))))))) )
| ~ empty(X1)
| ~ function(sK18(sK17(powerset(sK7(empty_set,X0,powerset(X1)))))) ),
inference(superposition,[status(thm)],[c_25109,c_84]) ).
tcf(c_26647,plain,
! [X0: $i,X1: $i] :
( ( relation_image(sK18(sK17(powerset(sK7(empty_set,X0,powerset(X1))))),empty_set) = empty_set )
| ~ empty(X1)
| ~ relation(sK18(sK17(powerset(sK7(empty_set,X0,powerset(X1)))))) ),
inference(superposition,[status(thm)],[c_25110,c_17554]) ).
tcf(c_26656,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(empty_set,X1,powerset(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25684,c_21429]) ).
tcf(c_26657,plain,
! [X0: $i,X1: $i] :
( ( sK7(empty_set,X1,powerset(relation_dom(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25684,c_21941]) ).
tcf(c_26658,plain,
! [X0: $i,X1: $i] :
( ( sK2(empty_set,X1,powerset(relation_dom(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25684,c_21015]) ).
tcf(c_26659,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK2(empty_set,X1,powerset(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25684,c_20337]) ).
tcf(c_26660,plain,
! [X0: $i] :
( ( sK18(sK17(sK17(powerset(relation_dom(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25684,c_16287]) ).
tcf(c_26661,plain,
! [X0: $i] :
( ( relation_dom(sK18(sK17(sK17(powerset(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25684,c_15972]) ).
tcf(c_26662,plain,
! [X0: $i] :
( ( relation_dom(sK18(sK17(powerset(relation_dom(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25684,c_15716]) ).
tcf(c_26663,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(sK18(powerset(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25684,c_14399]) ).
tcf(c_26664,plain,
! [X0: $i,X1: $i] :
( ( sK7(empty_set,X1,powerset(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25684,c_21303]) ).
tcf(c_26665,plain,
! [X0: $i,X1: $i] :
( ( sK2(empty_set,X1,powerset(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25684,c_20190]) ).
tcf(c_26666,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(relation_dom(relation_dom(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25684,c_15588]) ).
tcf(c_26667,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(relation_dom(relation_dom(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25684,c_15553]) ).
tcf(c_26668,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK18(sK17(powerset(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25684,c_13492]) ).
tcf(c_26669,plain,
! [X0: $i] :
( ( sK18(powerset(sK18(sK17(powerset(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25684,c_13490]) ).
tcf(c_26670,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(relation_dom(relation_dom(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25684,c_15527]) ).
tcf(c_26671,plain,
! [X0: $i] :
( ( sK18(powerset(sK18(powerset(relation_dom(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25684,c_15355]) ).
tcf(c_26672,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK18(powerset(relation_dom(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25684,c_15317]) ).
tcf(c_26673,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(sK18(powerset(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25684,c_13260]) ).
tcf(c_26674,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25684,c_15261]) ).
tcf(c_26675,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25684,c_15230]) ).
tcf(c_26676,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(sK18(powerset(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25684,c_13064]) ).
tcf(c_26677,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25684,c_12767]) ).
tcf(c_26678,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK18(powerset(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25684,c_12765]) ).
tcf(c_26679,plain,
! [X0: $i] :
( ( sK18(sK17(sK17(powerset(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25684,c_15973]) ).
tcf(c_26680,plain,
! [X0: $i] :
( ( relation_dom(sK18(sK17(powerset(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25684,c_13494]) ).
tcf(c_26681,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(relation_dom(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25684,c_14397]) ).
tcf(c_26682,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(relation_dom(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25684,c_13258]) ).
tcf(c_26683,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(relation_dom(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25684,c_13062]) ).
tcf(c_26684,plain,
! [X0: $i] :
( ( sK18(powerset(sK18(powerset(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25684,c_12959]) ).
tcf(c_26685,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK18(powerset(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25684,c_12766]) ).
tcf(c_26686,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25684,c_12718]) ).
tcf(c_26687,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0)))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25684,c_12604]) ).
tcf(c_26697,plain,
! [X0: $i] :
( one_to_one(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0))))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25684,c_5773]) ).
tcf(c_26698,plain,
! [X0: $i] :
( relation(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0))))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25684,c_77]) ).
tcf(c_26699,plain,
! [X0: $i] :
( function(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0))))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25684,c_66]) ).
tcf(c_26954,plain,
! [X0: $i] :
( ( sK18(sK17(sK17(sK17(powerset(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_99,c_25685]) ).
tcf(c_26955,plain,
sK18(sK17(sK17(sK17(powerset(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_114,c_25685]) ).
tcf(c_26956,plain,
! [X0: $i] :
( ( sK18(sK17(sK17(sK17(powerset(sK18(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12738,c_25685]) ).
tcf(c_26957,plain,
! [X0: $i] :
( ( sK18(sK17(sK17(sK17(powerset(sK18(powerset(sK18(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13358,c_25685]) ).
tcf(c_26958,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(sK17(sK17(powerset(relation_image(X0,X1)))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(relation_image(X0,X1)))) = sK18(relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13157,c_25685]) ).
tcf(c_26959,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(sK17(sK17(powerset(sK18(powerset(relation_image(X0,X1)))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK18(powerset(relation_image(X0,X1)))))) = sK18(sK18(powerset(relation_image(X0,X1)))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13158,c_25685]) ).
tcf(c_26960,plain,
! [X0: $i] :
( ( sK18(sK17(sK17(sK17(powerset(sK18(sK17(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13470,c_25685]) ).
tcf(c_26961,plain,
! [X0: $i] :
( ( sK18(sK17(sK17(sK17(powerset(sK18(powerset(sK18(sK17(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13469,c_25685]) ).
tcf(c_26962,plain,
! [X0: $i] :
( ( sK18(sK17(sK17(sK17(powerset(sK18(sK17(sK17(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15885,c_25685]) ).
tcf(c_26963,plain,
! [X0: $i] :
( ( sK18(sK17(sK17(sK17(powerset(sK18(powerset(sK18(sK17(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15887,c_25685]) ).
tcf(c_26964,plain,
! [X0: $i] :
( ( sK18(sK17(sK17(sK17(powerset(relation_image(X0,empty_set)))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17175,c_25685]) ).
tcf(c_26965,plain,
! [X0: $i] :
( ( sK18(sK17(sK17(sK17(powerset(sK18(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17177,c_25685]) ).
tcf(c_26966,plain,
! [X0: $i] :
( ( sK18(sK17(sK17(sK17(powerset(sK18(sK17(powerset(sK18(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17880,c_25685]) ).
tcf(c_26967,plain,
! [X0: $i] :
( ( sK18(sK17(sK17(sK17(powerset(sK18(sK17(powerset(sK18(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17885,c_25685]) ).
tcf(c_26968,plain,
! [X0: $i] :
( ( sK18(sK17(sK17(sK17(powerset(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17888,c_25685]) ).
tcf(c_26969,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(sK17(sK17(powerset(sK2(empty_set,X1,powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20186,c_25685]) ).
tcf(c_26970,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(sK17(sK17(powerset(sK18(powerset(sK2(empty_set,X1,powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20188,c_25685]) ).
tcf(c_26971,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(sK17(sK17(powerset(sK18(sK17(powerset(sK2(empty_set,X1,powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20189,c_25685]) ).
tcf(c_26972,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(sK17(sK17(powerset(sK7(empty_set,X1,powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21299,c_25685]) ).
tcf(c_26973,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(sK17(sK17(powerset(sK18(powerset(sK7(empty_set,X1,powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21301,c_25685]) ).
tcf(c_26974,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(sK17(sK17(powerset(sK18(sK17(powerset(sK7(empty_set,X1,powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21302,c_25685]) ).
tcf(c_26975,plain,
! [X0: $i] :
( ( sK18(sK17(sK17(sK17(powerset(sK18(sK17(sK17(sK17(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25683,c_25685]) ).
tcf(c_26976,plain,
! [X0: $i] :
( ( sK18(sK17(sK17(sK17(powerset(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25684,c_25685]) ).
tcf(c_27186,plain,
( empty(sK17(sK17(sK17(powerset(empty_set)))))
| ~ in(sK17(sK17(sK17(powerset(empty_set)))),empty_set) ),
inference(superposition,[status(thm)],[c_26955,c_12526]) ).
tcf(c_27187,plain,
( empty(sK17(sK17(sK17(powerset(empty_set)))))
| in(empty_set,sK17(sK17(sK17(powerset(empty_set))))) ),
inference(superposition,[status(thm)],[c_26955,c_12501]) ).
tcf(c_27188,plain,
element(empty_set,sK17(sK17(sK17(powerset(empty_set))))),
inference(superposition,[status(thm)],[c_26955,c_111]) ).
tcf(c_27221,plain,
! [X0: $i] :
( one_to_one(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0))))))))
| ( apply(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0))))))),sK11(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0))))))))) = apply(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0))))))),sK12(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0))))))))) )
| ~ empty(X0)
| ~ function(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0)))))))) ),
inference(superposition,[status(thm)],[c_26698,c_84]) ).
tcf(c_27232,plain,
! [X0: $i] :
( ( relation_image(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0))))))),empty_set) = empty_set )
| ~ empty(X0)
| ~ relation(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0)))))))) ),
inference(superposition,[status(thm)],[c_26699,c_17554]) ).
tcf(c_27241,plain,
( empty(sK18(sK17(powerset(empty_set))))
| in(sK18(sK17(empty_set)),empty_set) ),
inference(superposition,[status(thm)],[c_14398,c_13276]) ).
tcf(c_27242,plain,
! [X0: $i,X1: $i] :
( empty(sK18(sK17(powerset(relation_image(X0,X1)))))
| ( apply(X0,sK4(X0,X1,sK18(sK17(sK18(sK17(powerset(relation_image(X0,X1)))))))) = sK18(sK17(sK18(sK17(powerset(relation_image(X0,X1)))))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13276,c_60]) ).
tcf(c_27243,plain,
! [X0: $i,X1: $i] :
( empty(sK18(sK17(powerset(relation_inverse_image(X0,X1)))))
| in(apply(X0,sK18(sK17(sK18(sK17(powerset(relation_inverse_image(X0,X1))))))),X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13276,c_72]) ).
tcf(c_27244,plain,
! [X0: $i,X1: $i] :
( empty(sK18(sK17(powerset(relation_inverse_image(X0,X1)))))
| in(sK18(sK17(sK18(sK17(powerset(relation_inverse_image(X0,X1)))))),relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13276,c_71]) ).
tcf(c_27245,plain,
! [X0: $i] :
( empty(sK18(sK17(powerset(X0))))
| ~ in(X0,sK18(sK17(sK18(sK17(powerset(X0)))))) ),
inference(superposition,[status(thm)],[c_13276,c_98]) ).
tcf(c_27248,plain,
! [X0: $i] :
( empty(X0)
| empty(sK18(sK17(powerset(sK17(X0)))))
| element(sK18(sK17(sK18(sK17(powerset(sK17(X0)))))),X0) ),
inference(superposition,[status(thm)],[c_13276,c_14688]) ).
tcf(c_27249,plain,
! [X0: $i] :
( empty(X0)
| empty(sK18(sK17(powerset(sK17(X0)))))
| in(sK18(sK17(sK18(sK17(powerset(sK17(X0)))))),X0) ),
inference(superposition,[status(thm)],[c_13276,c_12618]) ).
tcf(c_27250,plain,
! [X0: $i] :
( empty(sK18(sK17(powerset(sK18(powerset(X0))))))
| element(sK18(sK17(sK18(sK17(powerset(sK18(powerset(X0))))))),X0) ),
inference(superposition,[status(thm)],[c_13276,c_14689]) ).
tcf(c_27252,plain,
! [X0: $i] :
( empty(sK18(sK17(powerset(sK18(powerset(X0))))))
| in(sK18(sK17(sK18(sK17(powerset(sK18(powerset(X0))))))),X0) ),
inference(superposition,[status(thm)],[c_13276,c_12619]) ).
tcf(c_27255,plain,
! [X0: $i] :
( empty(sK18(sK17(powerset(sK18(sK17(powerset(X0)))))))
| element(sK18(sK17(sK18(sK17(powerset(sK18(sK17(powerset(X0)))))))),X0) ),
inference(superposition,[status(thm)],[c_13276,c_14693]) ).
tcf(c_27257,plain,
! [X0: $i] :
( empty(sK18(sK17(powerset(sK18(sK17(powerset(X0)))))))
| in(sK18(sK17(sK18(sK17(powerset(sK18(sK17(powerset(X0)))))))),X0) ),
inference(superposition,[status(thm)],[c_13276,c_13032]) ).
tcf(c_27258,plain,
! [X0: $i] :
( empty(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0))))))))
| in(sK18(sK17(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0))))))))),X0) ),
inference(superposition,[status(thm)],[c_13276,c_15478]) ).
tcf(c_27260,plain,
! [X0: $i] :
( empty(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0))))))))
| element(sK18(sK17(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0))))))))),X0) ),
inference(superposition,[status(thm)],[c_13276,c_15476]) ).
tcf(c_27261,plain,
! [X0: $i] :
( empty(sK18(sK17(powerset(sK17(powerset(X0))))))
| in(sK18(sK17(sK18(sK17(powerset(sK17(powerset(X0))))))),powerset(X0)) ),
inference(superposition,[status(thm)],[c_13276,c_18767]) ).
tcf(c_27262,plain,
! [X0: $i] :
( empty(sK18(sK17(powerset(sK17(powerset(X0))))))
| element(sK18(sK17(sK18(sK17(powerset(sK17(powerset(X0))))))),powerset(X0)) ),
inference(superposition,[status(thm)],[c_13276,c_18765]) ).
tcf(c_27264,plain,
! [X0: $i,X1: $i] :
( empty(sK18(sK17(powerset(sK2(empty_set,X0,powerset(X1))))))
| element(sK18(sK17(sK18(sK17(powerset(sK2(empty_set,X0,powerset(X1))))))),X1) ),
inference(superposition,[status(thm)],[c_13276,c_19619]) ).
tcf(c_27265,plain,
! [X0: $i,X1: $i] :
( empty(sK18(sK17(powerset(sK2(empty_set,X0,powerset(X1))))))
| in(sK18(sK17(sK18(sK17(powerset(sK2(empty_set,X0,powerset(X1))))))),X1) ),
inference(superposition,[status(thm)],[c_13276,c_19621]) ).
tcf(c_27267,plain,
! [X0: $i,X1: $i] :
( empty(sK18(sK17(powerset(sK7(empty_set,X0,powerset(X1))))))
| element(sK18(sK17(sK18(sK17(powerset(sK7(empty_set,X0,powerset(X1))))))),X1) ),
inference(superposition,[status(thm)],[c_13276,c_20796]) ).
tcf(c_27268,plain,
! [X0: $i,X1: $i] :
( empty(sK18(sK17(powerset(sK7(empty_set,X0,powerset(X1))))))
| in(sK18(sK17(sK18(sK17(powerset(sK7(empty_set,X0,powerset(X1))))))),X1) ),
inference(superposition,[status(thm)],[c_13276,c_20798]) ).
tcf(c_27270,plain,
! [X0: $i] :
( empty(sK18(sK17(powerset(sK18(sK17(sK17(sK17(powerset(X0)))))))))
| element(sK18(sK17(sK18(sK17(powerset(sK18(sK17(sK17(sK17(powerset(X0)))))))))),X0) ),
inference(superposition,[status(thm)],[c_13276,c_22276]) ).
tcf(c_27271,plain,
! [X0: $i] :
( empty(sK18(sK17(powerset(sK18(sK17(sK17(sK17(powerset(X0)))))))))
| in(sK18(sK17(sK18(sK17(powerset(sK18(sK17(sK17(sK17(powerset(X0)))))))))),X0) ),
inference(superposition,[status(thm)],[c_13276,c_22278]) ).
tcf(c_27345,plain,
! [X0: $i] :
( ( sK18(powerset(sK18(powerset(sK18(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_99,c_13385]) ).
tcf(c_27346,plain,
sK18(powerset(sK18(powerset(sK18(powerset(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_114,c_13385]) ).
tcf(c_27348,plain,
! [X0: $i] :
( ( sK18(powerset(sK18(powerset(sK18(powerset(sK18(powerset(sK18(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13358,c_13385]) ).
tcf(c_27349,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK18(powerset(sK18(powerset(relation_image(X0,X1))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(relation_image(X0,X1)))) = sK18(relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13157,c_13385]) ).
tcf(c_27350,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK18(powerset(sK18(powerset(sK18(powerset(relation_image(X0,X1))))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK18(powerset(relation_image(X0,X1)))))) = sK18(sK18(powerset(relation_image(X0,X1)))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13158,c_13385]) ).
tcf(c_27352,plain,
! [X0: $i] :
( ( sK18(powerset(sK18(powerset(sK18(powerset(sK18(powerset(sK18(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13469,c_13385]) ).
tcf(c_27354,plain,
! [X0: $i] :
( ( sK18(powerset(sK18(powerset(sK18(powerset(sK18(powerset(sK18(sK17(sK17(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15887,c_13385]) ).
tcf(c_27356,plain,
! [X0: $i] :
( ( sK18(powerset(sK18(powerset(sK18(powerset(sK18(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17177,c_13385]) ).
tcf(c_27357,plain,
! [X0: $i] :
( ( sK18(powerset(sK18(powerset(sK18(powerset(sK18(sK17(powerset(sK18(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17880,c_13385]) ).
tcf(c_27358,plain,
! [X0: $i] :
( ( sK18(powerset(sK18(powerset(sK18(powerset(sK18(sK17(powerset(sK18(sK17(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17885,c_13385]) ).
tcf(c_27359,plain,
! [X0: $i] :
( ( sK18(powerset(sK18(powerset(sK18(powerset(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17888,c_13385]) ).
tcf(c_27361,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK18(powerset(sK18(powerset(sK18(powerset(sK2(empty_set,X1,powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20188,c_13385]) ).
tcf(c_27362,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK18(powerset(sK18(powerset(sK18(sK17(powerset(sK2(empty_set,X1,powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20189,c_13385]) ).
tcf(c_27364,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK18(powerset(sK18(powerset(sK18(powerset(sK7(empty_set,X1,powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21301,c_13385]) ).
tcf(c_27365,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK18(powerset(sK18(powerset(sK18(sK17(powerset(sK7(empty_set,X1,powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21302,c_13385]) ).
tcf(c_27367,plain,
! [X0: $i] :
( ( sK18(powerset(sK18(powerset(sK18(powerset(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25684,c_13385]) ).
tcf(c_27431,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK18(powerset(sK18(powerset(relation_image(X0,X1))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK17(relation_image(X0,X1))))) = sK18(sK17(relation_image(X0,X1))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13159,c_13385]) ).
tcf(c_27432,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(sK17(sK17(powerset(relation_image(X0,X1)))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK17(relation_image(X0,X1))))) = sK18(sK17(relation_image(X0,X1))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13159,c_25685]) ).
tcf(c_27433,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(sK7(empty_set,X2,powerset(relation_image(X0,X1)))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK17(relation_image(X0,X1))))) = sK18(sK17(relation_image(X0,X1))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13159,c_21429]) ).
tcf(c_27434,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK7(empty_set,X2,powerset(relation_dom(relation_image(X0,X1)))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK17(relation_image(X0,X1))))) = sK18(sK17(relation_image(X0,X1))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13159,c_21941]) ).
tcf(c_27435,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK2(empty_set,X2,powerset(relation_dom(relation_image(X0,X1)))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK17(relation_image(X0,X1))))) = sK18(sK17(relation_image(X0,X1))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13159,c_21015]) ).
tcf(c_27436,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(sK2(empty_set,X2,powerset(relation_image(X0,X1)))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK17(relation_image(X0,X1))))) = sK18(sK17(relation_image(X0,X1))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13159,c_20337]) ).
tcf(c_27437,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(sK17(powerset(relation_dom(relation_image(X0,X1)))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK17(relation_image(X0,X1))))) = sK18(sK17(relation_image(X0,X1))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13159,c_16287]) ).
tcf(c_27438,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(sK17(sK17(powerset(relation_image(X0,X1)))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK17(relation_image(X0,X1))))) = sK18(sK17(relation_image(X0,X1))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13159,c_15972]) ).
tcf(c_27439,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(sK17(powerset(relation_dom(relation_image(X0,X1)))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK17(relation_image(X0,X1))))) = sK18(sK17(relation_image(X0,X1))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13159,c_15716]) ).
tcf(c_27440,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(powerset(sK18(powerset(relation_image(X0,X1)))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK17(relation_image(X0,X1))))) = sK18(sK17(relation_image(X0,X1))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13159,c_14399]) ).
tcf(c_27441,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK7(empty_set,X2,powerset(relation_image(X0,X1))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK17(relation_image(X0,X1))))) = sK18(sK17(relation_image(X0,X1))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13159,c_21303]) ).
tcf(c_27442,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK2(empty_set,X2,powerset(relation_image(X0,X1))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK17(relation_image(X0,X1))))) = sK18(sK17(relation_image(X0,X1))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13159,c_20190]) ).
tcf(c_27443,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(powerset(relation_dom(relation_dom(relation_image(X0,X1)))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK17(relation_image(X0,X1))))) = sK18(sK17(relation_image(X0,X1))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13159,c_15588]) ).
tcf(c_27444,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(relation_dom(relation_dom(relation_dom(relation_image(X0,X1)))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK17(relation_image(X0,X1))))) = sK18(sK17(relation_image(X0,X1))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13159,c_15553]) ).
tcf(c_27445,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK18(sK17(powerset(relation_image(X0,X1)))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK17(relation_image(X0,X1))))) = sK18(sK17(relation_image(X0,X1))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13159,c_13492]) ).
tcf(c_27446,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK18(sK17(powerset(relation_image(X0,X1)))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK17(relation_image(X0,X1))))) = sK18(sK17(relation_image(X0,X1))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13159,c_13490]) ).
tcf(c_27447,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(powerset(relation_dom(relation_dom(relation_image(X0,X1)))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK17(relation_image(X0,X1))))) = sK18(sK17(relation_image(X0,X1))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13159,c_15527]) ).
tcf(c_27448,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK18(powerset(relation_dom(relation_image(X0,X1)))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK17(relation_image(X0,X1))))) = sK18(sK17(relation_image(X0,X1))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13159,c_15355]) ).
tcf(c_27449,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK18(powerset(relation_dom(relation_image(X0,X1)))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK17(relation_image(X0,X1))))) = sK18(sK17(relation_image(X0,X1))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13159,c_15317]) ).
tcf(c_27450,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(relation_dom(sK18(powerset(relation_image(X0,X1)))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK17(relation_image(X0,X1))))) = sK18(sK17(relation_image(X0,X1))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13159,c_13260]) ).
tcf(c_27451,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_image(X0,X1)))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK17(relation_image(X0,X1))))) = sK18(sK17(relation_image(X0,X1))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13159,c_15261]) ).
tcf(c_27452,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_dom(relation_image(X0,X2))) = X1 )
| ( apply(X0,sK4(X0,X2,sK18(sK17(relation_image(X0,X2))))) = sK18(sK17(relation_image(X0,X2))) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13159,c_15230]) ).
tcf(c_27453,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(powerset(sK18(powerset(relation_image(X0,X1)))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK17(relation_image(X0,X1))))) = sK18(sK17(relation_image(X0,X1))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13159,c_13064]) ).
tcf(c_27454,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK18(powerset(relation_image(X0,X2))) = X1 )
| ( apply(X0,sK4(X0,X2,sK18(sK17(relation_image(X0,X2))))) = sK18(sK17(relation_image(X0,X2))) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13159,c_12767]) ).
tcf(c_27455,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(sK18(powerset(relation_image(X0,X1)))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK17(relation_image(X0,X1))))) = sK18(sK17(relation_image(X0,X1))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13159,c_12765]) ).
tcf(c_27456,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(sK17(powerset(relation_image(X0,X1))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK17(relation_image(X0,X1))))) = sK18(sK17(relation_image(X0,X1))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13159,c_15973]) ).
tcf(c_27457,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(sK17(powerset(relation_image(X0,X1))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK17(relation_image(X0,X1))))) = sK18(sK17(relation_image(X0,X1))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13159,c_13494]) ).
tcf(c_27458,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(powerset(relation_dom(relation_image(X0,X1))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK17(relation_image(X0,X1))))) = sK18(sK17(relation_image(X0,X1))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13159,c_14397]) ).
tcf(c_27459,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(relation_dom(relation_dom(relation_image(X0,X1))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK17(relation_image(X0,X1))))) = sK18(sK17(relation_image(X0,X1))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13159,c_13258]) ).
tcf(c_27460,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(powerset(relation_dom(relation_image(X0,X1))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK17(relation_image(X0,X1))))) = sK18(sK17(relation_image(X0,X1))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13159,c_13062]) ).
tcf(c_27461,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK18(powerset(relation_image(X0,X1))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK17(relation_image(X0,X1))))) = sK18(sK17(relation_image(X0,X1))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13159,c_12959]) ).
tcf(c_27462,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK18(powerset(relation_image(X0,X1))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK17(relation_image(X0,X1))))) = sK18(sK17(relation_image(X0,X1))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13159,c_12766]) ).
tcf(c_27463,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_image(X0,X1))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK17(relation_image(X0,X1))))) = sK18(sK17(relation_image(X0,X1))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13159,c_12718]) ).
tcf(c_27464,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_image(X0,X2)) = X1 )
| ( apply(X0,sK4(X0,X2,sK18(sK17(relation_image(X0,X2))))) = sK18(sK17(relation_image(X0,X2))) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13159,c_12604]) ).
tcf(c_27465,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(powerset(relation_image(X0,X1)))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK17(relation_image(X0,X1))))) = sK18(sK17(relation_image(X0,X1))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13159,c_13495]) ).
tcf(c_27466,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(relation_dom(relation_image(X0,X1)))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK17(relation_image(X0,X1))))) = sK18(sK17(relation_image(X0,X1))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13159,c_12957]) ).
tcf(c_27467,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(powerset(relation_image(X0,X1)))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK17(relation_image(X0,X1))))) = sK18(sK17(relation_image(X0,X1))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13159,c_12768]) ).
tcf(c_27468,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(relation_image(X0,X1))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK17(relation_image(X0,X1))))) = sK18(sK17(relation_image(X0,X1))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13159,c_12769]) ).
tcf(c_27469,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_image(X0,X1)))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK17(relation_image(X0,X1))))) = sK18(sK17(relation_image(X0,X1))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13159,c_12674]) ).
tcf(c_27470,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_image(X0,X1))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK17(relation_image(X0,X1))))) = sK18(sK17(relation_image(X0,X1))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13159,c_12550]) ).
tcf(c_27471,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X0,X2) = X1 )
| ( apply(X0,sK4(X0,X2,sK18(sK17(relation_image(X0,X2))))) = sK18(sK17(relation_image(X0,X2))) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13159,c_93]) ).
tcf(c_27472,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_image(X0,X1)) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK17(relation_image(X0,X1))))) = sK18(sK17(relation_image(X0,X1))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13159,c_12406]) ).
tcf(c_27473,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X0,X1) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK17(relation_image(X0,X1))))) = sK18(sK17(relation_image(X0,X1))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13159,c_94]) ).
tcf(c_27474,plain,
! [X0: $i,X1: $i] :
( one_to_one(relation_image(X0,X1))
| ( apply(X0,sK4(X0,X1,sK18(sK17(relation_image(X0,X1))))) = sK18(sK17(relation_image(X0,X1))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13159,c_5773]) ).
tcf(c_27475,plain,
! [X0: $i,X1: $i] :
( relation(relation_image(X0,X1))
| ( apply(X0,sK4(X0,X1,sK18(sK17(relation_image(X0,X1))))) = sK18(sK17(relation_image(X0,X1))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13159,c_77]) ).
tcf(c_27476,plain,
! [X0: $i,X1: $i] :
( function(relation_image(X0,X1))
| ( apply(X0,sK4(X0,X1,sK18(sK17(relation_image(X0,X1))))) = sK18(sK17(relation_image(X0,X1))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13159,c_66]) ).
tcf(c_27874,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(powerset(relation_dom(X0)))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_99,c_13493]) ).
tcf(c_27875,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(empty_set))) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_114,c_13493]) ).
tcf(c_27877,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(powerset(sK18(powerset(sK18(powerset(X0))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13358,c_13493]) ).
tcf(c_27878,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK18(sK17(powerset(relation_image(X0,X2)))) = X1 )
| ( apply(X0,sK4(X0,X2,sK18(sK17(relation_image(X0,X2))))) = sK18(sK17(relation_image(X0,X2))) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13159,c_13493]) ).
tcf(c_27879,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK18(sK17(powerset(relation_image(X0,X2)))) = X1 )
| ( apply(X0,sK4(X0,X2,sK18(relation_image(X0,X2)))) = sK18(relation_image(X0,X2)) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13157,c_13493]) ).
tcf(c_27880,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK18(sK17(powerset(sK18(powerset(relation_image(X0,X2)))))) = X1 )
| ( apply(X0,sK4(X0,X2,sK18(sK18(powerset(relation_image(X0,X2)))))) = sK18(sK18(powerset(relation_image(X0,X2)))) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13158,c_13493]) ).
tcf(c_27882,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(powerset(sK18(powerset(sK18(sK17(powerset(X0)))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13469,c_13493]) ).
tcf(c_27884,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(powerset(sK18(powerset(sK18(sK17(sK17(powerset(X0))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15887,c_13493]) ).
tcf(c_27885,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(powerset(relation_image(X0,empty_set)))) = X1 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17175,c_13493]) ).
tcf(c_27886,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(powerset(sK18(powerset(relation_image(X0,empty_set)))))) = X1 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17177,c_13493]) ).
tcf(c_27887,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(powerset(sK18(sK17(powerset(sK18(powerset(X0)))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17880,c_13493]) ).
tcf(c_27888,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(powerset(sK18(sK17(powerset(sK18(sK17(powerset(X0))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17885,c_13493]) ).
tcf(c_27889,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(powerset(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0)))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17888,c_13493]) ).
tcf(c_27891,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK18(sK17(powerset(sK18(powerset(sK2(empty_set,X2,powerset(X0))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20188,c_13493]) ).
tcf(c_27892,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK18(sK17(powerset(sK18(sK17(powerset(sK2(empty_set,X2,powerset(X0)))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20189,c_13493]) ).
tcf(c_27894,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK18(sK17(powerset(sK18(powerset(sK7(empty_set,X2,powerset(X0))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21301,c_13493]) ).
tcf(c_27895,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK18(sK17(powerset(sK18(sK17(powerset(sK7(empty_set,X2,powerset(X0)))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21302,c_13493]) ).
tcf(c_27896,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(powerset(sK18(sK17(sK17(sK17(powerset(X0)))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25683,c_13493]) ).
tcf(c_27897,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(powerset(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0)))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25684,c_13493]) ).
tcf(c_28089,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| empty(sK18(powerset(powerset(X1))))
| ~ in(X0,sK18(sK17(sK18(powerset(powerset(X1)))))) ),
inference(superposition,[status(thm)],[c_15743,c_300]) ).
tcf(c_28090,plain,
! [X0: $i,X1: $i] :
( empty(sK18(powerset(powerset(X1))))
| ~ empty(X1)
| ~ in(X0,sK18(sK17(sK18(powerset(powerset(X1)))))) ),
inference(superposition,[status(thm)],[c_15743,c_299]) ).
tcf(c_28091,plain,
! [X0: $i,X1: $i] :
( in(X0,X1)
| empty(sK18(powerset(powerset(X1))))
| ~ in(X0,sK18(sK17(sK18(powerset(powerset(X1)))))) ),
inference(superposition,[status(thm)],[c_15743,c_92]) ).
tcf(c_28108,plain,
! [X0: $i] :
( subset(sK18(powerset(empty_set)),X0)
| ~ in(empty_set,sK13(empty_set,X0)) ),
inference(superposition,[status(thm)],[c_12958,c_16394]) ).
tcf(c_28109,plain,
! [X0: $i] :
( subset(empty_set,X0)
| ~ in(empty_set,sK13(empty_set,X0)) ),
inference(light_normalisation,[status(thm)],[c_28108,c_12958]) ).
tcf(c_28120,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK18(powerset(sK18(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_99,c_13387]) ).
tcf(c_28121,plain,
relation_dom(relation_dom(sK18(powerset(sK18(powerset(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_114,c_13387]) ).
tcf(c_28123,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK18(powerset(sK18(powerset(sK18(powerset(sK18(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13358,c_13387]) ).
tcf(c_28124,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK18(powerset(sK18(powerset(relation_image(X0,X1))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK17(relation_image(X0,X1))))) = sK18(sK17(relation_image(X0,X1))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13159,c_13387]) ).
tcf(c_28125,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK18(powerset(sK18(powerset(relation_image(X0,X1))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(relation_image(X0,X1)))) = sK18(relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13157,c_13387]) ).
tcf(c_28126,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK18(powerset(sK18(powerset(sK18(powerset(relation_image(X0,X1))))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK18(powerset(relation_image(X0,X1)))))) = sK18(sK18(powerset(relation_image(X0,X1)))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13158,c_13387]) ).
tcf(c_28128,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK18(powerset(sK18(powerset(sK18(powerset(sK18(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13469,c_13387]) ).
tcf(c_28130,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK18(powerset(sK18(powerset(sK18(powerset(sK18(sK17(sK17(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15887,c_13387]) ).
tcf(c_28132,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK18(powerset(sK18(powerset(sK18(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17177,c_13387]) ).
tcf(c_28133,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK18(powerset(sK18(powerset(sK18(sK17(powerset(sK18(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17880,c_13387]) ).
tcf(c_28134,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK18(powerset(sK18(powerset(sK18(sK17(powerset(sK18(sK17(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17885,c_13387]) ).
tcf(c_28135,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK18(powerset(sK18(powerset(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17888,c_13387]) ).
tcf(c_28137,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK18(powerset(sK18(powerset(sK18(powerset(sK2(empty_set,X1,powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20188,c_13387]) ).
tcf(c_28138,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK18(powerset(sK18(powerset(sK18(sK17(powerset(sK2(empty_set,X1,powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20189,c_13387]) ).
tcf(c_28140,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK18(powerset(sK18(powerset(sK18(powerset(sK7(empty_set,X1,powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21301,c_13387]) ).
tcf(c_28141,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK18(powerset(sK18(powerset(sK18(sK17(powerset(sK7(empty_set,X1,powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21302,c_13387]) ).
tcf(c_28143,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK18(powerset(sK18(powerset(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25684,c_13387]) ).
tcf(c_28259,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(sK18(sK17(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_99,c_13488]) ).
tcf(c_28260,plain,
sK18(powerset(relation_dom(sK18(sK17(powerset(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_114,c_13488]) ).
tcf(c_28262,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(sK18(sK17(powerset(sK18(powerset(sK18(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13358,c_13488]) ).
tcf(c_28263,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(relation_dom(sK18(sK17(powerset(relation_image(X0,X1))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK17(relation_image(X0,X1))))) = sK18(sK17(relation_image(X0,X1))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13159,c_13488]) ).
tcf(c_28264,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(relation_dom(sK18(sK17(powerset(relation_image(X0,X1))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(relation_image(X0,X1)))) = sK18(relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13157,c_13488]) ).
tcf(c_28265,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(relation_dom(sK18(sK17(powerset(sK18(powerset(relation_image(X0,X1))))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK18(powerset(relation_image(X0,X1)))))) = sK18(sK18(powerset(relation_image(X0,X1)))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13158,c_13488]) ).
tcf(c_28267,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(sK18(sK17(powerset(sK18(powerset(sK18(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13469,c_13488]) ).
tcf(c_28269,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(sK18(sK17(powerset(sK18(powerset(sK18(sK17(sK17(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15887,c_13488]) ).
tcf(c_28270,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(sK18(sK17(powerset(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17175,c_13488]) ).
tcf(c_28271,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(sK18(sK17(powerset(sK18(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17177,c_13488]) ).
tcf(c_28272,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(sK18(sK17(powerset(sK18(sK17(powerset(sK18(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17880,c_13488]) ).
tcf(c_28273,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(sK18(sK17(powerset(sK18(sK17(powerset(sK18(sK17(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17885,c_13488]) ).
tcf(c_28274,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(sK18(sK17(powerset(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17888,c_13488]) ).
tcf(c_28276,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(relation_dom(sK18(sK17(powerset(sK18(powerset(sK2(empty_set,X1,powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20188,c_13488]) ).
tcf(c_28277,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(relation_dom(sK18(sK17(powerset(sK18(sK17(powerset(sK2(empty_set,X1,powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20189,c_13488]) ).
tcf(c_28279,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(relation_dom(sK18(sK17(powerset(sK18(powerset(sK7(empty_set,X1,powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21301,c_13488]) ).
tcf(c_28280,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(relation_dom(sK18(sK17(powerset(sK18(sK17(powerset(sK7(empty_set,X1,powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21302,c_13488]) ).
tcf(c_28281,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(sK18(sK17(powerset(sK18(sK17(sK17(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25683,c_13488]) ).
tcf(c_28282,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(sK18(sK17(powerset(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25684,c_13488]) ).
tcf(c_28381,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(sK18(sK17(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_99,c_13489]) ).
tcf(c_28382,plain,
relation_dom(sK18(powerset(sK18(sK17(powerset(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_114,c_13489]) ).
tcf(c_28384,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(sK18(sK17(powerset(sK18(powerset(sK18(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13358,c_13489]) ).
tcf(c_28385,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(powerset(sK18(sK17(powerset(relation_image(X0,X1))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK17(relation_image(X0,X1))))) = sK18(sK17(relation_image(X0,X1))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13159,c_13489]) ).
tcf(c_28386,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(powerset(sK18(sK17(powerset(relation_image(X0,X1))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(relation_image(X0,X1)))) = sK18(relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13157,c_13489]) ).
tcf(c_28387,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(powerset(sK18(sK17(powerset(sK18(powerset(relation_image(X0,X1))))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK18(powerset(relation_image(X0,X1)))))) = sK18(sK18(powerset(relation_image(X0,X1)))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13158,c_13489]) ).
tcf(c_28389,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(sK18(sK17(powerset(sK18(powerset(sK18(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13469,c_13489]) ).
tcf(c_28391,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(sK18(sK17(powerset(sK18(powerset(sK18(sK17(sK17(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15887,c_13489]) ).
tcf(c_28392,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(sK18(sK17(powerset(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17175,c_13489]) ).
tcf(c_28393,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(sK18(sK17(powerset(sK18(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17177,c_13489]) ).
tcf(c_28394,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(sK18(sK17(powerset(sK18(sK17(powerset(sK18(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17880,c_13489]) ).
tcf(c_28395,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(sK18(sK17(powerset(sK18(sK17(powerset(sK18(sK17(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17885,c_13489]) ).
tcf(c_28396,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(sK18(sK17(powerset(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17888,c_13489]) ).
tcf(c_28398,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(powerset(sK18(sK17(powerset(sK18(powerset(sK2(empty_set,X1,powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20188,c_13489]) ).
tcf(c_28399,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(powerset(sK18(sK17(powerset(sK18(sK17(powerset(sK2(empty_set,X1,powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20189,c_13489]) ).
tcf(c_28401,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(powerset(sK18(sK17(powerset(sK18(powerset(sK7(empty_set,X1,powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21301,c_13489]) ).
tcf(c_28402,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(powerset(sK18(sK17(powerset(sK18(sK17(powerset(sK7(empty_set,X1,powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21302,c_13489]) ).
tcf(c_28403,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(sK18(sK17(powerset(sK18(sK17(sK17(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25683,c_13489]) ).
tcf(c_28404,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(sK18(sK17(powerset(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25684,c_13489]) ).
tcf(c_28578,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK18(sK17(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_99,c_13491]) ).
tcf(c_28579,plain,
relation_dom(relation_dom(relation_dom(sK18(sK17(powerset(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_114,c_13491]) ).
tcf(c_28581,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK18(sK17(powerset(sK18(powerset(sK18(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13358,c_13491]) ).
tcf(c_28582,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(sK18(sK17(powerset(relation_image(X0,X1))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK17(relation_image(X0,X1))))) = sK18(sK17(relation_image(X0,X1))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13159,c_13491]) ).
tcf(c_28583,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(sK18(sK17(powerset(relation_image(X0,X1))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(relation_image(X0,X1)))) = sK18(relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13157,c_13491]) ).
tcf(c_28584,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(sK18(sK17(powerset(sK18(powerset(relation_image(X0,X1))))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK18(powerset(relation_image(X0,X1)))))) = sK18(sK18(powerset(relation_image(X0,X1)))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13158,c_13491]) ).
tcf(c_28586,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK18(sK17(powerset(sK18(powerset(sK18(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13469,c_13491]) ).
tcf(c_28588,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK18(sK17(powerset(sK18(powerset(sK18(sK17(sK17(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15887,c_13491]) ).
tcf(c_28589,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK18(sK17(powerset(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17175,c_13491]) ).
tcf(c_28590,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK18(sK17(powerset(sK18(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17177,c_13491]) ).
tcf(c_28591,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK18(sK17(powerset(sK18(sK17(powerset(sK18(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17880,c_13491]) ).
tcf(c_28592,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK18(sK17(powerset(sK18(sK17(powerset(sK18(sK17(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17885,c_13491]) ).
tcf(c_28593,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK18(sK17(powerset(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17888,c_13491]) ).
tcf(c_28595,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(sK18(sK17(powerset(sK18(powerset(sK2(empty_set,X1,powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20188,c_13491]) ).
tcf(c_28596,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(sK18(sK17(powerset(sK18(sK17(powerset(sK2(empty_set,X1,powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20189,c_13491]) ).
tcf(c_28598,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(sK18(sK17(powerset(sK18(powerset(sK7(empty_set,X1,powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21301,c_13491]) ).
tcf(c_28599,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(sK18(sK17(powerset(sK18(sK17(powerset(sK7(empty_set,X1,powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21302,c_13491]) ).
tcf(c_28600,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK18(sK17(powerset(sK18(sK17(sK17(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25683,c_13491]) ).
tcf(c_28601,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK18(sK17(powerset(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25684,c_13491]) ).
tcf(c_28669,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(sK18(sK17(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_99,c_14401]) ).
tcf(c_28670,plain,
sK18(sK17(powerset(sK18(sK17(powerset(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_114,c_14401]) ).
tcf(c_28672,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(sK18(sK17(powerset(sK18(powerset(sK18(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13358,c_14401]) ).
tcf(c_28673,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(powerset(sK18(sK17(powerset(relation_image(X0,X1))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK17(relation_image(X0,X1))))) = sK18(sK17(relation_image(X0,X1))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13159,c_14401]) ).
tcf(c_28674,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(powerset(sK18(sK17(powerset(relation_image(X0,X1))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(relation_image(X0,X1)))) = sK18(relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13157,c_14401]) ).
tcf(c_28675,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(powerset(sK18(sK17(powerset(sK18(powerset(relation_image(X0,X1))))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK18(powerset(relation_image(X0,X1)))))) = sK18(sK18(powerset(relation_image(X0,X1)))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13158,c_14401]) ).
tcf(c_28677,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(sK18(sK17(powerset(sK18(powerset(sK18(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13469,c_14401]) ).
tcf(c_28679,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(sK18(sK17(powerset(sK18(powerset(sK18(sK17(sK17(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15887,c_14401]) ).
tcf(c_28680,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(sK18(sK17(powerset(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17175,c_14401]) ).
tcf(c_28681,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(sK18(sK17(powerset(sK18(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17177,c_14401]) ).
tcf(c_28682,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(sK18(sK17(powerset(sK18(sK17(powerset(sK18(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17880,c_14401]) ).
tcf(c_28683,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(sK18(sK17(powerset(sK18(sK17(powerset(sK18(sK17(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17885,c_14401]) ).
tcf(c_28684,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(sK18(sK17(powerset(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17888,c_14401]) ).
tcf(c_28686,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(powerset(sK18(sK17(powerset(sK18(powerset(sK2(empty_set,X1,powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20188,c_14401]) ).
tcf(c_28687,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(powerset(sK18(sK17(powerset(sK18(sK17(powerset(sK2(empty_set,X1,powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20189,c_14401]) ).
tcf(c_28689,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(powerset(sK18(sK17(powerset(sK18(powerset(sK7(empty_set,X1,powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21301,c_14401]) ).
tcf(c_28690,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(powerset(sK18(sK17(powerset(sK18(sK17(powerset(sK7(empty_set,X1,powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21302,c_14401]) ).
tcf(c_28691,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(sK18(sK17(powerset(sK18(sK17(sK17(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25683,c_14401]) ).
tcf(c_28692,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(sK18(sK17(powerset(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25684,c_14401]) ).
tcf(c_28854,plain,
( element(sK18(sK17(empty_set)),empty_set)
| empty(sK18(sK17(powerset(empty_set)))) ),
inference(superposition,[status(thm)],[c_14398,c_15091]) ).
tcf(c_28855,plain,
! [X0: $i] :
( empty(sK18(sK17(powerset(powerset(X0)))))
| subset(sK18(sK17(sK18(sK17(powerset(powerset(X0)))))),X0) ),
inference(superposition,[status(thm)],[c_15091,c_88]) ).
tcf(c_28867,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(powerset(relation_dom(X0)))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_99,c_15232]) ).
tcf(c_28868,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(empty_set))) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_114,c_15232]) ).
tcf(c_28870,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(powerset(sK18(powerset(sK18(powerset(X0))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13358,c_15232]) ).
tcf(c_28871,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(sK18(powerset(relation_image(X0,X2)))) = X1 )
| ( apply(X0,sK4(X0,X2,sK18(sK17(relation_image(X0,X2))))) = sK18(sK17(relation_image(X0,X2))) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13159,c_15232]) ).
tcf(c_28872,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(sK18(powerset(relation_image(X0,X2)))) = X1 )
| ( apply(X0,sK4(X0,X2,sK18(relation_image(X0,X2)))) = sK18(relation_image(X0,X2)) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13157,c_15232]) ).
tcf(c_28873,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(sK18(powerset(sK18(powerset(relation_image(X0,X2)))))) = X1 )
| ( apply(X0,sK4(X0,X2,sK18(sK18(powerset(relation_image(X0,X2)))))) = sK18(sK18(powerset(relation_image(X0,X2)))) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13158,c_15232]) ).
tcf(c_28875,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(powerset(sK18(powerset(sK18(sK17(powerset(X0)))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13469,c_15232]) ).
tcf(c_28877,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(powerset(sK18(powerset(sK18(sK17(sK17(powerset(X0))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15887,c_15232]) ).
tcf(c_28879,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(powerset(sK18(powerset(relation_image(X0,empty_set)))))) = X1 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17177,c_15232]) ).
tcf(c_28880,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(powerset(sK18(sK17(powerset(sK18(powerset(X0)))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17880,c_15232]) ).
tcf(c_28881,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(powerset(sK18(sK17(powerset(sK18(sK17(powerset(X0))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17885,c_15232]) ).
tcf(c_28882,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(powerset(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0)))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17888,c_15232]) ).
tcf(c_28884,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(sK18(powerset(sK18(powerset(sK2(empty_set,X2,powerset(X0))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20188,c_15232]) ).
tcf(c_28885,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(sK18(powerset(sK18(sK17(powerset(sK2(empty_set,X2,powerset(X0)))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20189,c_15232]) ).
tcf(c_28887,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(sK18(powerset(sK18(powerset(sK7(empty_set,X2,powerset(X0))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21301,c_15232]) ).
tcf(c_28888,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(sK18(powerset(sK18(sK17(powerset(sK7(empty_set,X2,powerset(X0)))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21302,c_15232]) ).
tcf(c_28890,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(powerset(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0)))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25684,c_15232]) ).
tcf(c_29063,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK18(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_99,c_15263]) ).
tcf(c_29064,plain,
relation_dom(relation_dom(relation_dom(relation_dom(sK18(powerset(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_114,c_15263]) ).
tcf(c_29066,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK18(powerset(sK18(powerset(sK18(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13358,c_15263]) ).
tcf(c_29067,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK18(powerset(relation_image(X0,X1))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK17(relation_image(X0,X1))))) = sK18(sK17(relation_image(X0,X1))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13159,c_15263]) ).
tcf(c_29068,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK18(powerset(relation_image(X0,X1))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(relation_image(X0,X1)))) = sK18(relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13157,c_15263]) ).
tcf(c_29069,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK18(powerset(sK18(powerset(relation_image(X0,X1))))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK18(powerset(relation_image(X0,X1)))))) = sK18(sK18(powerset(relation_image(X0,X1)))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13158,c_15263]) ).
tcf(c_29071,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK18(powerset(sK18(powerset(sK18(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13469,c_15263]) ).
tcf(c_29073,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK18(powerset(sK18(powerset(sK18(sK17(sK17(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15887,c_15263]) ).
tcf(c_29075,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK18(powerset(sK18(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17177,c_15263]) ).
tcf(c_29076,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK18(powerset(sK18(sK17(powerset(sK18(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17880,c_15263]) ).
tcf(c_29077,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK18(powerset(sK18(sK17(powerset(sK18(sK17(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17885,c_15263]) ).
tcf(c_29078,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK18(powerset(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17888,c_15263]) ).
tcf(c_29080,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK18(powerset(sK18(powerset(sK2(empty_set,X1,powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20188,c_15263]) ).
tcf(c_29081,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK18(powerset(sK18(sK17(powerset(sK2(empty_set,X1,powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20189,c_15263]) ).
tcf(c_29083,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK18(powerset(sK18(powerset(sK7(empty_set,X1,powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21301,c_15263]) ).
tcf(c_29084,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK18(powerset(sK18(sK17(powerset(sK7(empty_set,X1,powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21302,c_15263]) ).
tcf(c_29086,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK18(powerset(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25684,c_15263]) ).
tcf(c_29238,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(relation_dom(sK18(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_99,c_15529]) ).
tcf(c_29239,plain,
relation_dom(sK18(powerset(relation_dom(sK18(powerset(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_114,c_15529]) ).
tcf(c_29241,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(relation_dom(sK18(powerset(sK18(powerset(sK18(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13358,c_15529]) ).
tcf(c_29242,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(powerset(relation_dom(sK18(powerset(relation_image(X0,X1))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK17(relation_image(X0,X1))))) = sK18(sK17(relation_image(X0,X1))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13159,c_15529]) ).
tcf(c_29243,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(powerset(relation_dom(sK18(powerset(relation_image(X0,X1))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(relation_image(X0,X1)))) = sK18(relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13157,c_15529]) ).
tcf(c_29244,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(powerset(relation_dom(sK18(powerset(sK18(powerset(relation_image(X0,X1))))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK18(powerset(relation_image(X0,X1)))))) = sK18(sK18(powerset(relation_image(X0,X1)))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13158,c_15529]) ).
tcf(c_29246,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(relation_dom(sK18(powerset(sK18(powerset(sK18(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13469,c_15529]) ).
tcf(c_29248,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(relation_dom(sK18(powerset(sK18(powerset(sK18(sK17(sK17(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15887,c_15529]) ).
tcf(c_29250,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(relation_dom(sK18(powerset(sK18(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17177,c_15529]) ).
tcf(c_29251,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(relation_dom(sK18(powerset(sK18(sK17(powerset(sK18(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17880,c_15529]) ).
tcf(c_29252,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(relation_dom(sK18(powerset(sK18(sK17(powerset(sK18(sK17(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17885,c_15529]) ).
tcf(c_29253,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(relation_dom(sK18(powerset(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17888,c_15529]) ).
tcf(c_29255,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(powerset(relation_dom(sK18(powerset(sK18(powerset(sK2(empty_set,X1,powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20188,c_15529]) ).
tcf(c_29256,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(powerset(relation_dom(sK18(powerset(sK18(sK17(powerset(sK2(empty_set,X1,powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20189,c_15529]) ).
tcf(c_29258,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(powerset(relation_dom(sK18(powerset(sK18(powerset(sK7(empty_set,X1,powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21301,c_15529]) ).
tcf(c_29259,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(powerset(relation_dom(sK18(powerset(sK18(sK17(powerset(sK7(empty_set,X1,powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21302,c_15529]) ).
tcf(c_29261,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(relation_dom(sK18(powerset(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25684,c_15529]) ).
tcf(c_29351,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(relation_dom(sK18(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_99,c_15555]) ).
tcf(c_29352,plain,
sK18(powerset(relation_dom(relation_dom(sK18(powerset(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_114,c_15555]) ).
tcf(c_29354,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(relation_dom(sK18(powerset(sK18(powerset(sK18(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13358,c_15555]) ).
tcf(c_29355,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(relation_dom(relation_dom(sK18(powerset(relation_image(X0,X1))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK17(relation_image(X0,X1))))) = sK18(sK17(relation_image(X0,X1))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13159,c_15555]) ).
tcf(c_29356,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(relation_dom(relation_dom(sK18(powerset(relation_image(X0,X1))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(relation_image(X0,X1)))) = sK18(relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13157,c_15555]) ).
tcf(c_29357,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(relation_dom(relation_dom(sK18(powerset(sK18(powerset(relation_image(X0,X1))))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK18(powerset(relation_image(X0,X1)))))) = sK18(sK18(powerset(relation_image(X0,X1)))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13158,c_15555]) ).
tcf(c_29359,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(relation_dom(sK18(powerset(sK18(powerset(sK18(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13469,c_15555]) ).
tcf(c_29361,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(relation_dom(sK18(powerset(sK18(powerset(sK18(sK17(sK17(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15887,c_15555]) ).
tcf(c_29363,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(relation_dom(sK18(powerset(sK18(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17177,c_15555]) ).
tcf(c_29364,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(relation_dom(sK18(powerset(sK18(sK17(powerset(sK18(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17880,c_15555]) ).
tcf(c_29365,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(relation_dom(sK18(powerset(sK18(sK17(powerset(sK18(sK17(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17885,c_15555]) ).
tcf(c_29366,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(relation_dom(sK18(powerset(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17888,c_15555]) ).
tcf(c_29368,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(relation_dom(relation_dom(sK18(powerset(sK18(powerset(sK2(empty_set,X1,powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20188,c_15555]) ).
tcf(c_29369,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(relation_dom(relation_dom(sK18(powerset(sK18(sK17(powerset(sK2(empty_set,X1,powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20189,c_15555]) ).
tcf(c_29371,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(relation_dom(relation_dom(sK18(powerset(sK18(powerset(sK7(empty_set,X1,powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21301,c_15555]) ).
tcf(c_29372,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(relation_dom(relation_dom(sK18(powerset(sK18(sK17(powerset(sK7(empty_set,X1,powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21302,c_15555]) ).
tcf(c_29374,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(relation_dom(sK18(powerset(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25684,c_15555]) ).
tcf(c_29478,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(relation_dom(sK18(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_99,c_15590]) ).
tcf(c_29479,plain,
sK18(sK17(powerset(relation_dom(sK18(powerset(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_114,c_15590]) ).
tcf(c_29481,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(relation_dom(sK18(powerset(sK18(powerset(sK18(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13358,c_15590]) ).
tcf(c_29482,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(powerset(relation_dom(sK18(powerset(relation_image(X0,X1))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK17(relation_image(X0,X1))))) = sK18(sK17(relation_image(X0,X1))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13159,c_15590]) ).
tcf(c_29483,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(powerset(relation_dom(sK18(powerset(relation_image(X0,X1))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(relation_image(X0,X1)))) = sK18(relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13157,c_15590]) ).
tcf(c_29484,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(powerset(relation_dom(sK18(powerset(sK18(powerset(relation_image(X0,X1))))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK18(powerset(relation_image(X0,X1)))))) = sK18(sK18(powerset(relation_image(X0,X1)))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13158,c_15590]) ).
tcf(c_29486,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(relation_dom(sK18(powerset(sK18(powerset(sK18(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13469,c_15590]) ).
tcf(c_29488,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(relation_dom(sK18(powerset(sK18(powerset(sK18(sK17(sK17(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15887,c_15590]) ).
tcf(c_29490,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(relation_dom(sK18(powerset(sK18(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17177,c_15590]) ).
tcf(c_29491,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(relation_dom(sK18(powerset(sK18(sK17(powerset(sK18(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17880,c_15590]) ).
tcf(c_29492,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(relation_dom(sK18(powerset(sK18(sK17(powerset(sK18(sK17(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17885,c_15590]) ).
tcf(c_29493,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(relation_dom(sK18(powerset(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17888,c_15590]) ).
tcf(c_29495,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(powerset(relation_dom(sK18(powerset(sK18(powerset(sK2(empty_set,X1,powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20188,c_15590]) ).
tcf(c_29496,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(powerset(relation_dom(sK18(powerset(sK18(sK17(powerset(sK2(empty_set,X1,powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20189,c_15590]) ).
tcf(c_29498,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(powerset(relation_dom(sK18(powerset(sK18(powerset(sK7(empty_set,X1,powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21301,c_15590]) ).
tcf(c_29499,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(powerset(relation_dom(sK18(powerset(sK18(sK17(powerset(sK7(empty_set,X1,powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21302,c_15590]) ).
tcf(c_29501,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(relation_dom(sK18(powerset(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25684,c_15590]) ).
tcf(c_29586,plain,
! [X0: $i] :
( ( relation_dom(sK18(sK17(powerset(sK18(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_99,c_15718]) ).
tcf(c_29587,plain,
relation_dom(sK18(sK17(powerset(sK18(powerset(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_114,c_15718]) ).
tcf(c_29589,plain,
! [X0: $i] :
( ( relation_dom(sK18(sK17(powerset(sK18(powerset(sK18(powerset(sK18(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13358,c_15718]) ).
tcf(c_29590,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(sK17(powerset(sK18(powerset(relation_image(X0,X1))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK17(relation_image(X0,X1))))) = sK18(sK17(relation_image(X0,X1))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13159,c_15718]) ).
tcf(c_29591,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(sK17(powerset(sK18(powerset(relation_image(X0,X1))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(relation_image(X0,X1)))) = sK18(relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13157,c_15718]) ).
tcf(c_29592,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(sK17(powerset(sK18(powerset(sK18(powerset(relation_image(X0,X1))))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK18(powerset(relation_image(X0,X1)))))) = sK18(sK18(powerset(relation_image(X0,X1)))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13158,c_15718]) ).
tcf(c_29594,plain,
! [X0: $i] :
( ( relation_dom(sK18(sK17(powerset(sK18(powerset(sK18(powerset(sK18(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13469,c_15718]) ).
tcf(c_29596,plain,
! [X0: $i] :
( ( relation_dom(sK18(sK17(powerset(sK18(powerset(sK18(powerset(sK18(sK17(sK17(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15887,c_15718]) ).
tcf(c_29598,plain,
! [X0: $i] :
( ( relation_dom(sK18(sK17(powerset(sK18(powerset(sK18(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17177,c_15718]) ).
tcf(c_29599,plain,
! [X0: $i] :
( ( relation_dom(sK18(sK17(powerset(sK18(powerset(sK18(sK17(powerset(sK18(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17880,c_15718]) ).
tcf(c_29600,plain,
! [X0: $i] :
( ( relation_dom(sK18(sK17(powerset(sK18(powerset(sK18(sK17(powerset(sK18(sK17(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17885,c_15718]) ).
tcf(c_29601,plain,
! [X0: $i] :
( ( relation_dom(sK18(sK17(powerset(sK18(powerset(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17888,c_15718]) ).
tcf(c_29603,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(sK17(powerset(sK18(powerset(sK18(powerset(sK2(empty_set,X1,powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20188,c_15718]) ).
tcf(c_29604,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(sK17(powerset(sK18(powerset(sK18(sK17(powerset(sK2(empty_set,X1,powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20189,c_15718]) ).
tcf(c_29606,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(sK17(powerset(sK18(powerset(sK18(powerset(sK7(empty_set,X1,powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21301,c_15718]) ).
tcf(c_29607,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(sK17(powerset(sK18(powerset(sK18(sK17(powerset(sK7(empty_set,X1,powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21302,c_15718]) ).
tcf(c_29609,plain,
! [X0: $i] :
( ( relation_dom(sK18(sK17(powerset(sK18(powerset(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25684,c_15718]) ).
tcf(c_29847,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X0,X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK3(sK1,X2,relation_image(X0,X1))) = sK2(sK1,X2,relation_image(X0,X1)) )
| ( apply(X0,sK4(X0,X1,sK2(sK1,X2,relation_image(X0,X1)))) = sK2(sK1,X2,relation_image(X0,X1)) )
| ~ relation(sK1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_52,c_14500]) ).
tcf(c_29848,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X0,X1) = relation_image(sK6,X2) )
| ( apply(sK6,sK3(sK6,X2,relation_image(X0,X1))) = sK2(sK6,X2,relation_image(X0,X1)) )
| ( apply(X0,sK4(X0,X1,sK2(sK6,X2,relation_image(X0,X1)))) = sK2(sK6,X2,relation_image(X0,X1)) )
| ~ relation(sK6)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_65,c_14500]) ).
tcf(c_29849,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X0,X1) = relation_image(sK10,X2) )
| ( apply(sK10,sK3(sK10,X2,relation_image(X0,X1))) = sK2(sK10,X2,relation_image(X0,X1)) )
| ( apply(X0,sK4(X0,X1,sK2(sK10,X2,relation_image(X0,X1)))) = sK2(sK10,X2,relation_image(X0,X1)) )
| ~ relation(sK10)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_79,c_14500]) ).
tcf(c_29850,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(relation_dom(X0),X3) = relation_image(X1,X2) )
| ( apply(relation_dom(X0),sK3(relation_dom(X0),X3,relation_image(X1,X2))) = sK2(relation_dom(X0),X3,relation_image(X1,X2)) )
| ( apply(X1,sK4(X1,X2,sK2(relation_dom(X0),X3,relation_image(X1,X2)))) = sK2(relation_dom(X0),X3,relation_image(X1,X2)) )
| ~ empty(X0)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_12385,c_14500]) ).
tcf(c_29851,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X0,X1) = relation_image(empty_set,X2) )
| ( apply(empty_set,sK3(empty_set,X2,relation_image(X0,X1))) = sK2(empty_set,X2,relation_image(X0,X1)) )
| ( apply(X0,sK4(X0,X1,sK2(empty_set,X2,relation_image(X0,X1)))) = sK2(empty_set,X2,relation_image(X0,X1)) )
| ~ relation(empty_set)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_12355,c_14500]) ).
tcf(c_29852,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(sK18(powerset(X0)),X3) = relation_image(X1,X2) )
| ( apply(sK18(powerset(X0)),sK3(sK18(powerset(X0)),X3,relation_image(X1,X2))) = sK2(sK18(powerset(X0)),X3,relation_image(X1,X2)) )
| ( apply(X1,sK4(X1,X2,sK2(sK18(powerset(X0)),X3,relation_image(X1,X2)))) = sK2(sK18(powerset(X0)),X3,relation_image(X1,X2)) )
| ~ empty(X0)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(sK18(powerset(X0))) ),
inference(superposition,[status(thm)],[c_12772,c_14500]) ).
tcf(c_29853,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(sK18(powerset(sK18(powerset(X0)))),X2) = relation_image(X1,X3) )
| ( apply(X1,sK4(X1,X3,sK2(sK18(powerset(sK18(powerset(X0)))),X2,relation_image(X1,X3)))) = sK2(sK18(powerset(sK18(powerset(X0)))),X2,relation_image(X1,X3)) )
| ( apply(sK18(powerset(sK18(powerset(X0)))),sK3(sK18(powerset(sK18(powerset(X0)))),X2,relation_image(X1,X3))) = sK2(sK18(powerset(sK18(powerset(X0)))),X2,relation_image(X1,X3)) )
| ~ empty(X0)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(sK18(powerset(sK18(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_13393,c_14500]) ).
tcf(c_29854,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(sK18(sK17(powerset(X0))),X3) = relation_image(X1,X2) )
| ( apply(sK18(sK17(powerset(X0))),sK3(sK18(sK17(powerset(X0))),X3,relation_image(X1,X2))) = sK2(sK18(sK17(powerset(X0))),X3,relation_image(X1,X2)) )
| ( apply(X1,sK4(X1,X2,sK2(sK18(sK17(powerset(X0))),X3,relation_image(X1,X2)))) = sK2(sK18(sK17(powerset(X0))),X3,relation_image(X1,X2)) )
| ~ empty(X0)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(sK18(sK17(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_13498,c_14500]) ).
tcf(c_29855,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(sK18(powerset(sK18(sK17(powerset(X0))))),X2) = relation_image(X1,X3) )
| ( apply(X1,sK4(X1,X3,sK2(sK18(powerset(sK18(sK17(powerset(X0))))),X2,relation_image(X1,X3)))) = sK2(sK18(powerset(sK18(sK17(powerset(X0))))),X2,relation_image(X1,X3)) )
| ( apply(sK18(powerset(sK18(sK17(powerset(X0))))),sK3(sK18(powerset(sK18(sK17(powerset(X0))))),X2,relation_image(X1,X3))) = sK2(sK18(powerset(sK18(sK17(powerset(X0))))),X2,relation_image(X1,X3)) )
| ~ empty(X0)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(sK18(powerset(sK18(sK17(powerset(X0)))))) ),
inference(superposition,[status(thm)],[c_14345,c_14500]) ).
tcf(c_29856,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(sK18(sK17(sK17(powerset(X0)))),X2) = relation_image(X1,X3) )
| ( apply(X1,sK4(X1,X3,sK2(sK18(sK17(sK17(powerset(X0)))),X2,relation_image(X1,X3)))) = sK2(sK18(sK17(sK17(powerset(X0)))),X2,relation_image(X1,X3)) )
| ( apply(sK18(sK17(sK17(powerset(X0)))),sK3(sK18(sK17(sK17(powerset(X0)))),X2,relation_image(X1,X3))) = sK2(sK18(sK17(sK17(powerset(X0)))),X2,relation_image(X1,X3)) )
| ~ empty(X0)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(sK18(sK17(sK17(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_15976,c_14500]) ).
tcf(c_29857,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(sK18(powerset(sK18(sK17(sK17(powerset(X0)))))),X2) = relation_image(X1,X3) )
| ( apply(X1,sK4(X1,X3,sK2(sK18(powerset(sK18(sK17(sK17(powerset(X0)))))),X2,relation_image(X1,X3)))) = sK2(sK18(powerset(sK18(sK17(sK17(powerset(X0)))))),X2,relation_image(X1,X3)) )
| ( apply(sK18(powerset(sK18(sK17(sK17(powerset(X0)))))),sK3(sK18(powerset(sK18(sK17(sK17(powerset(X0)))))),X2,relation_image(X1,X3))) = sK2(sK18(powerset(sK18(sK17(sK17(powerset(X0)))))),X2,relation_image(X1,X3)) )
| ~ empty(X0)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(sK18(powerset(sK18(sK17(sK17(powerset(X0))))))) ),
inference(superposition,[status(thm)],[c_16543,c_14500]) ).
tcf(c_29858,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(relation_image(X0,empty_set),X3) = relation_image(X1,X2) )
| ( apply(relation_image(X0,empty_set),sK3(relation_image(X0,empty_set),X3,relation_image(X1,X2))) = sK2(relation_image(X0,empty_set),X3,relation_image(X1,X2)) )
| ( apply(X1,sK4(X1,X2,sK2(relation_image(X0,empty_set),X3,relation_image(X1,X2)))) = sK2(relation_image(X0,empty_set),X3,relation_image(X1,X2)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_image(X0,empty_set)) ),
inference(superposition,[status(thm)],[c_17557,c_14500]) ).
tcf(c_29859,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(sK18(sK17(powerset(sK18(powerset(X0))))),X2) = relation_image(X1,X3) )
| ( apply(X1,sK4(X1,X3,sK2(sK18(sK17(powerset(sK18(powerset(X0))))),X2,relation_image(X1,X3)))) = sK2(sK18(sK17(powerset(sK18(powerset(X0))))),X2,relation_image(X1,X3)) )
| ( apply(sK18(sK17(powerset(sK18(powerset(X0))))),sK3(sK18(sK17(powerset(sK18(powerset(X0))))),X2,relation_image(X1,X3))) = sK2(sK18(sK17(powerset(sK18(powerset(X0))))),X2,relation_image(X1,X3)) )
| ~ empty(X0)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(sK18(sK17(powerset(sK18(powerset(X0)))))) ),
inference(superposition,[status(thm)],[c_18126,c_14500]) ).
tcf(c_29860,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(sK18(sK17(powerset(sK18(sK17(powerset(X0)))))),X2) = relation_image(X1,X3) )
| ( apply(X1,sK4(X1,X3,sK2(sK18(sK17(powerset(sK18(sK17(powerset(X0)))))),X2,relation_image(X1,X3)))) = sK2(sK18(sK17(powerset(sK18(sK17(powerset(X0)))))),X2,relation_image(X1,X3)) )
| ( apply(sK18(sK17(powerset(sK18(sK17(powerset(X0)))))),sK3(sK18(sK17(powerset(sK18(sK17(powerset(X0)))))),X2,relation_image(X1,X3))) = sK2(sK18(sK17(powerset(sK18(sK17(powerset(X0)))))),X2,relation_image(X1,X3)) )
| ~ empty(X0)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(sK18(sK17(powerset(sK18(sK17(powerset(X0))))))) ),
inference(superposition,[status(thm)],[c_18310,c_14500]) ).
tcf(c_29861,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( relation_image(sK2(empty_set,X0,powerset(X1)),X3) = relation_image(X2,X4) )
| ( apply(X2,sK4(X2,X4,sK2(sK2(empty_set,X0,powerset(X1)),X3,relation_image(X2,X4)))) = sK2(sK2(empty_set,X0,powerset(X1)),X3,relation_image(X2,X4)) )
| ( apply(sK2(empty_set,X0,powerset(X1)),sK3(sK2(empty_set,X0,powerset(X1)),X3,relation_image(X2,X4))) = sK2(sK2(empty_set,X0,powerset(X1)),X3,relation_image(X2,X4)) )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ relation(sK2(empty_set,X0,powerset(X1))) ),
inference(superposition,[status(thm)],[c_20341,c_14500]) ).
tcf(c_29862,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( relation_image(sK18(powerset(sK2(empty_set,X0,powerset(X1)))),X3) = relation_image(X2,X4) )
| ( apply(X2,sK4(X2,X4,sK2(sK18(powerset(sK2(empty_set,X0,powerset(X1)))),X3,relation_image(X2,X4)))) = sK2(sK18(powerset(sK2(empty_set,X0,powerset(X1)))),X3,relation_image(X2,X4)) )
| ( apply(sK18(powerset(sK2(empty_set,X0,powerset(X1)))),sK3(sK18(powerset(sK2(empty_set,X0,powerset(X1)))),X3,relation_image(X2,X4))) = sK2(sK18(powerset(sK2(empty_set,X0,powerset(X1)))),X3,relation_image(X2,X4)) )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ relation(sK18(powerset(sK2(empty_set,X0,powerset(X1))))) ),
inference(superposition,[status(thm)],[c_20631,c_14500]) ).
tcf(c_29863,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( relation_image(sK7(empty_set,X0,powerset(X1)),X3) = relation_image(X2,X4) )
| ( apply(X2,sK4(X2,X4,sK2(sK7(empty_set,X0,powerset(X1)),X3,relation_image(X2,X4)))) = sK2(sK7(empty_set,X0,powerset(X1)),X3,relation_image(X2,X4)) )
| ( apply(sK7(empty_set,X0,powerset(X1)),sK3(sK7(empty_set,X0,powerset(X1)),X3,relation_image(X2,X4))) = sK2(sK7(empty_set,X0,powerset(X1)),X3,relation_image(X2,X4)) )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ relation(sK7(empty_set,X0,powerset(X1))) ),
inference(superposition,[status(thm)],[c_21433,c_14500]) ).
tcf(c_29864,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( relation_image(sK18(powerset(sK7(empty_set,X0,powerset(X1)))),X3) = relation_image(X2,X4) )
| ( apply(X2,sK4(X2,X4,sK2(sK18(powerset(sK7(empty_set,X0,powerset(X1)))),X3,relation_image(X2,X4)))) = sK2(sK18(powerset(sK7(empty_set,X0,powerset(X1)))),X3,relation_image(X2,X4)) )
| ( apply(sK18(powerset(sK7(empty_set,X0,powerset(X1)))),sK3(sK18(powerset(sK7(empty_set,X0,powerset(X1)))),X3,relation_image(X2,X4))) = sK2(sK18(powerset(sK7(empty_set,X0,powerset(X1)))),X3,relation_image(X2,X4)) )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ relation(sK18(powerset(sK7(empty_set,X0,powerset(X1))))) ),
inference(superposition,[status(thm)],[c_21807,c_14500]) ).
tcf(c_29865,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(sK18(powerset(relation_image(X0,empty_set))),X2) = relation_image(X1,X3) )
| ( apply(X1,sK4(X1,X3,sK2(sK18(powerset(relation_image(X0,empty_set))),X2,relation_image(X1,X3)))) = sK2(sK18(powerset(relation_image(X0,empty_set))),X2,relation_image(X1,X3)) )
| ( apply(sK18(powerset(relation_image(X0,empty_set))),sK3(sK18(powerset(relation_image(X0,empty_set))),X2,relation_image(X1,X3))) = sK2(sK18(powerset(relation_image(X0,empty_set))),X2,relation_image(X1,X3)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(sK18(powerset(relation_image(X0,empty_set)))) ),
inference(superposition,[status(thm)],[c_23555,c_14500]) ).
tcf(c_29866,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0))))))),X2) = relation_image(X1,X3) )
| ( apply(X1,sK4(X1,X3,sK2(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0))))))),X2,relation_image(X1,X3)))) = sK2(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0))))))),X2,relation_image(X1,X3)) )
| ( apply(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0))))))),sK3(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0))))))),X2,relation_image(X1,X3))) = sK2(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0))))))),X2,relation_image(X1,X3)) )
| ~ empty(X0)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0)))))))) ),
inference(superposition,[status(thm)],[c_23841,c_14500]) ).
tcf(c_29867,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( relation_image(sK18(sK17(powerset(sK2(empty_set,X0,powerset(X1))))),X3) = relation_image(X2,X4) )
| ( apply(X2,sK4(X2,X4,sK2(sK18(sK17(powerset(sK2(empty_set,X0,powerset(X1))))),X3,relation_image(X2,X4)))) = sK2(sK18(sK17(powerset(sK2(empty_set,X0,powerset(X1))))),X3,relation_image(X2,X4)) )
| ( apply(sK18(sK17(powerset(sK2(empty_set,X0,powerset(X1))))),sK3(sK18(sK17(powerset(sK2(empty_set,X0,powerset(X1))))),X3,relation_image(X2,X4))) = sK2(sK18(sK17(powerset(sK2(empty_set,X0,powerset(X1))))),X3,relation_image(X2,X4)) )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ relation(sK18(sK17(powerset(sK2(empty_set,X0,powerset(X1)))))) ),
inference(superposition,[status(thm)],[c_24108,c_14500]) ).
tcf(c_29868,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( relation_image(sK18(sK17(powerset(sK7(empty_set,X0,powerset(X1))))),X3) = relation_image(X2,X4) )
| ( apply(X2,sK4(X2,X4,sK2(sK18(sK17(powerset(sK7(empty_set,X0,powerset(X1))))),X3,relation_image(X2,X4)))) = sK2(sK18(sK17(powerset(sK7(empty_set,X0,powerset(X1))))),X3,relation_image(X2,X4)) )
| ( apply(sK18(sK17(powerset(sK7(empty_set,X0,powerset(X1))))),sK3(sK18(sK17(powerset(sK7(empty_set,X0,powerset(X1))))),X3,relation_image(X2,X4))) = sK2(sK18(sK17(powerset(sK7(empty_set,X0,powerset(X1))))),X3,relation_image(X2,X4)) )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ relation(sK18(sK17(powerset(sK7(empty_set,X0,powerset(X1)))))) ),
inference(superposition,[status(thm)],[c_25110,c_14500]) ).
tcf(c_29869,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(sK18(sK17(sK17(sK17(powerset(X0))))),X2) = relation_image(X1,X3) )
| ( apply(X1,sK4(X1,X3,sK2(sK18(sK17(sK17(sK17(powerset(X0))))),X2,relation_image(X1,X3)))) = sK2(sK18(sK17(sK17(sK17(powerset(X0))))),X2,relation_image(X1,X3)) )
| ( apply(sK18(sK17(sK17(sK17(powerset(X0))))),sK3(sK18(sK17(sK17(sK17(powerset(X0))))),X2,relation_image(X1,X3))) = sK2(sK18(sK17(sK17(sK17(powerset(X0))))),X2,relation_image(X1,X3)) )
| ~ empty(X0)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(sK18(sK17(sK17(sK17(powerset(X0)))))) ),
inference(superposition,[status(thm)],[c_25864,c_14500]) ).
tcf(c_29870,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0))))))),X2) = relation_image(X1,X3) )
| ( apply(X1,sK4(X1,X3,sK2(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0))))))),X2,relation_image(X1,X3)))) = sK2(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0))))))),X2,relation_image(X1,X3)) )
| ( apply(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0))))))),sK3(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0))))))),X2,relation_image(X1,X3))) = sK2(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0))))))),X2,relation_image(X1,X3)) )
| ~ empty(X0)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0)))))))) ),
inference(superposition,[status(thm)],[c_26699,c_14500]) ).
tcf(c_29871,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X0,X1) = relation_image(empty_set,X2) )
| ( apply(empty_set,sK3(empty_set,X2,relation_image(X0,X1))) = sK2(empty_set,X2,relation_image(X0,X1)) )
| ( apply(X0,sK4(X0,X1,sK2(empty_set,X2,relation_image(X0,X1)))) = sK2(empty_set,X2,relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_29851,c_113]) ).
tcf(c_29877,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X0,X1) = relation_image(sK10,X2) )
| ( apply(sK10,sK3(sK10,X2,relation_image(X0,X1))) = sK2(sK10,X2,relation_image(X0,X1)) )
| ( apply(X0,sK4(X0,X1,sK2(sK10,X2,relation_image(X0,X1)))) = sK2(sK10,X2,relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_29849,c_78]) ).
tcf(c_29883,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X0,X1) = relation_image(sK6,X2) )
| ( apply(sK6,sK3(sK6,X2,relation_image(X0,X1))) = sK2(sK6,X2,relation_image(X0,X1)) )
| ( apply(X0,sK4(X0,X1,sK2(sK6,X2,relation_image(X0,X1)))) = sK2(sK6,X2,relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_29848,c_64]) ).
tcf(c_29889,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X0,X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK3(sK1,X2,relation_image(X0,X1))) = sK2(sK1,X2,relation_image(X0,X1)) )
| ( apply(X0,sK4(X0,X1,sK2(sK1,X2,relation_image(X0,X1)))) = sK2(sK1,X2,relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_29847,c_51]) ).
tcf(c_30094,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK18(powerset(relation_dom(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_99,c_16852]) ).
tcf(c_30095,plain,
relation_dom(relation_dom(relation_dom(sK18(powerset(relation_dom(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_114,c_16852]) ).
tcf(c_30096,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK18(powerset(relation_dom(sK18(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12738,c_16852]) ).
tcf(c_30097,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK18(powerset(relation_dom(sK18(powerset(sK18(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13358,c_16852]) ).
tcf(c_30098,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(sK18(powerset(relation_dom(relation_image(X0,X1))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK17(relation_image(X0,X1))))) = sK18(sK17(relation_image(X0,X1))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13159,c_16852]) ).
tcf(c_30099,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(sK18(powerset(relation_dom(relation_image(X0,X1))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(relation_image(X0,X1)))) = sK18(relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13157,c_16852]) ).
tcf(c_30100,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(sK18(powerset(relation_dom(sK18(powerset(relation_image(X0,X1))))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK18(powerset(relation_image(X0,X1)))))) = sK18(sK18(powerset(relation_image(X0,X1)))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13158,c_16852]) ).
tcf(c_30101,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK18(powerset(relation_dom(sK18(sK17(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13470,c_16852]) ).
tcf(c_30102,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK18(powerset(relation_dom(sK18(powerset(sK18(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13469,c_16852]) ).
tcf(c_30103,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK18(powerset(relation_dom(sK18(sK17(sK17(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15885,c_16852]) ).
tcf(c_30104,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK18(powerset(relation_dom(sK18(powerset(sK18(sK17(sK17(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15887,c_16852]) ).
tcf(c_30105,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK18(powerset(relation_dom(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17175,c_16852]) ).
tcf(c_30106,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK18(powerset(relation_dom(sK18(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17177,c_16852]) ).
tcf(c_30107,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK18(powerset(relation_dom(sK18(sK17(powerset(sK18(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17880,c_16852]) ).
tcf(c_30108,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK18(powerset(relation_dom(sK18(sK17(powerset(sK18(sK17(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17885,c_16852]) ).
tcf(c_30109,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK18(powerset(relation_dom(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17888,c_16852]) ).
tcf(c_30110,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(sK18(powerset(relation_dom(sK2(empty_set,X1,powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20186,c_16852]) ).
tcf(c_30111,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(sK18(powerset(relation_dom(sK18(powerset(sK2(empty_set,X1,powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20188,c_16852]) ).
tcf(c_30112,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(sK18(powerset(relation_dom(sK18(sK17(powerset(sK2(empty_set,X1,powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20189,c_16852]) ).
tcf(c_30113,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(sK18(powerset(relation_dom(sK7(empty_set,X1,powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21299,c_16852]) ).
tcf(c_30114,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(sK18(powerset(relation_dom(sK18(powerset(sK7(empty_set,X1,powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21301,c_16852]) ).
tcf(c_30115,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(sK18(powerset(relation_dom(sK18(sK17(powerset(sK7(empty_set,X1,powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21302,c_16852]) ).
tcf(c_30116,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK18(powerset(relation_dom(sK18(sK17(sK17(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25683,c_16852]) ).
tcf(c_30117,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK18(powerset(relation_dom(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25684,c_16852]) ).
tcf(c_30250,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(relation_dom(relation_dom(X0)))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_99,c_16879]) ).
tcf(c_30251,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(empty_set))) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_114,c_16879]) ).
tcf(c_30252,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(relation_dom(sK18(powerset(X0))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12738,c_16879]) ).
tcf(c_30253,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(relation_dom(sK18(powerset(sK18(powerset(X0))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13358,c_16879]) ).
tcf(c_30254,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK18(powerset(relation_dom(relation_image(X0,X2)))) = X1 )
| ( apply(X0,sK4(X0,X2,sK18(sK17(relation_image(X0,X2))))) = sK18(sK17(relation_image(X0,X2))) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13159,c_16879]) ).
tcf(c_30255,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK18(powerset(relation_dom(relation_image(X0,X2)))) = X1 )
| ( apply(X0,sK4(X0,X2,sK18(relation_image(X0,X2)))) = sK18(relation_image(X0,X2)) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13157,c_16879]) ).
tcf(c_30256,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK18(powerset(relation_dom(sK18(powerset(relation_image(X0,X2)))))) = X1 )
| ( apply(X0,sK4(X0,X2,sK18(sK18(powerset(relation_image(X0,X2)))))) = sK18(sK18(powerset(relation_image(X0,X2)))) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13158,c_16879]) ).
tcf(c_30257,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(relation_dom(sK18(sK17(powerset(X0)))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13470,c_16879]) ).
tcf(c_30258,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(relation_dom(sK18(powerset(sK18(sK17(powerset(X0)))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13469,c_16879]) ).
tcf(c_30259,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(relation_dom(sK18(sK17(sK17(powerset(X0))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15885,c_16879]) ).
tcf(c_30260,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(relation_dom(sK18(powerset(sK18(sK17(sK17(powerset(X0))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15887,c_16879]) ).
tcf(c_30261,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(relation_dom(relation_image(X0,empty_set)))) = X1 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17175,c_16879]) ).
tcf(c_30262,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(relation_dom(sK18(powerset(relation_image(X0,empty_set)))))) = X1 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17177,c_16879]) ).
tcf(c_30263,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(relation_dom(sK18(sK17(powerset(sK18(powerset(X0)))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17880,c_16879]) ).
tcf(c_30264,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(relation_dom(sK18(sK17(powerset(sK18(sK17(powerset(X0))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17885,c_16879]) ).
tcf(c_30265,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(relation_dom(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0)))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17888,c_16879]) ).
tcf(c_30266,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK18(powerset(relation_dom(sK2(empty_set,X2,powerset(X0))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20186,c_16879]) ).
tcf(c_30267,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK18(powerset(relation_dom(sK18(powerset(sK2(empty_set,X2,powerset(X0))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20188,c_16879]) ).
tcf(c_30268,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK18(powerset(relation_dom(sK18(sK17(powerset(sK2(empty_set,X2,powerset(X0)))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20189,c_16879]) ).
tcf(c_30269,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK18(powerset(relation_dom(sK7(empty_set,X2,powerset(X0))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21299,c_16879]) ).
tcf(c_30270,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK18(powerset(relation_dom(sK18(powerset(sK7(empty_set,X2,powerset(X0))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21301,c_16879]) ).
tcf(c_30271,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK18(powerset(relation_dom(sK18(sK17(powerset(sK7(empty_set,X2,powerset(X0)))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21302,c_16879]) ).
tcf(c_30272,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(relation_dom(sK18(sK17(sK17(sK17(powerset(X0)))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25683,c_16879]) ).
tcf(c_30273,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(relation_dom(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0)))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25684,c_16879]) ).
tcf(c_30479,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(sK18(powerset(relation_dom(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_99,c_16986]) ).
tcf(c_30480,plain,
relation_dom(sK18(powerset(sK18(powerset(relation_dom(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_114,c_16986]) ).
tcf(c_30481,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(sK18(powerset(relation_dom(sK18(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12738,c_16986]) ).
tcf(c_30482,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(sK18(powerset(relation_dom(sK18(powerset(sK18(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13358,c_16986]) ).
tcf(c_30483,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(powerset(sK18(powerset(relation_dom(relation_image(X0,X1))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK17(relation_image(X0,X1))))) = sK18(sK17(relation_image(X0,X1))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13159,c_16986]) ).
tcf(c_30484,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(powerset(sK18(powerset(relation_dom(relation_image(X0,X1))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(relation_image(X0,X1)))) = sK18(relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13157,c_16986]) ).
tcf(c_30485,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(powerset(sK18(powerset(relation_dom(sK18(powerset(relation_image(X0,X1))))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK18(powerset(relation_image(X0,X1)))))) = sK18(sK18(powerset(relation_image(X0,X1)))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13158,c_16986]) ).
tcf(c_30486,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(sK18(powerset(relation_dom(sK18(sK17(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13470,c_16986]) ).
tcf(c_30487,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(sK18(powerset(relation_dom(sK18(powerset(sK18(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13469,c_16986]) ).
tcf(c_30488,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(sK18(powerset(relation_dom(sK18(sK17(sK17(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15885,c_16986]) ).
tcf(c_30489,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(sK18(powerset(relation_dom(sK18(powerset(sK18(sK17(sK17(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15887,c_16986]) ).
tcf(c_30490,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(sK18(powerset(relation_dom(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17175,c_16986]) ).
tcf(c_30491,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(sK18(powerset(relation_dom(sK18(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17177,c_16986]) ).
tcf(c_30492,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(sK18(powerset(relation_dom(sK18(sK17(powerset(sK18(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17880,c_16986]) ).
tcf(c_30493,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(sK18(powerset(relation_dom(sK18(sK17(powerset(sK18(sK17(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17885,c_16986]) ).
tcf(c_30494,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(sK18(powerset(relation_dom(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17888,c_16986]) ).
tcf(c_30495,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(powerset(sK18(powerset(relation_dom(sK2(empty_set,X1,powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20186,c_16986]) ).
tcf(c_30496,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(powerset(sK18(powerset(relation_dom(sK18(powerset(sK2(empty_set,X1,powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20188,c_16986]) ).
tcf(c_30497,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(powerset(sK18(powerset(relation_dom(sK18(sK17(powerset(sK2(empty_set,X1,powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20189,c_16986]) ).
tcf(c_30498,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(powerset(sK18(powerset(relation_dom(sK7(empty_set,X1,powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21299,c_16986]) ).
tcf(c_30499,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(powerset(sK18(powerset(relation_dom(sK18(powerset(sK7(empty_set,X1,powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21301,c_16986]) ).
tcf(c_30500,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(powerset(sK18(powerset(relation_dom(sK18(sK17(powerset(sK7(empty_set,X1,powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21302,c_16986]) ).
tcf(c_30501,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(sK18(powerset(relation_dom(sK18(sK17(sK17(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25683,c_16986]) ).
tcf(c_30502,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(sK18(powerset(relation_dom(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25684,c_16986]) ).
tcf(c_30612,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(X0)))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_99,c_17487]) ).
tcf(c_30613,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(empty_set))) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_114,c_17487]) ).
tcf(c_30614,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(sK18(powerset(X0))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12738,c_17487]) ).
tcf(c_30615,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(sK18(powerset(sK18(powerset(X0))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13358,c_17487]) ).
tcf(c_30616,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_image(X0,X2)))) = X1 )
| ( apply(X0,sK4(X0,X2,sK18(sK17(relation_image(X0,X2))))) = sK18(sK17(relation_image(X0,X2))) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13159,c_17487]) ).
tcf(c_30617,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_image(X0,X2)))) = X1 )
| ( apply(X0,sK4(X0,X2,sK18(relation_image(X0,X2)))) = sK18(relation_image(X0,X2)) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13157,c_17487]) ).
tcf(c_30618,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_dom(relation_dom(sK18(powerset(relation_image(X0,X2)))))) = X1 )
| ( apply(X0,sK4(X0,X2,sK18(sK18(powerset(relation_image(X0,X2)))))) = sK18(sK18(powerset(relation_image(X0,X2)))) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13158,c_17487]) ).
tcf(c_30619,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(sK18(sK17(powerset(X0)))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13470,c_17487]) ).
tcf(c_30620,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(sK18(powerset(sK18(sK17(powerset(X0)))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13469,c_17487]) ).
tcf(c_30621,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(sK18(sK17(sK17(powerset(X0))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15885,c_17487]) ).
tcf(c_30622,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(sK18(powerset(sK18(sK17(sK17(powerset(X0))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15887,c_17487]) ).
tcf(c_30623,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_image(X0,empty_set)))) = X1 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17175,c_17487]) ).
tcf(c_30624,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(sK18(powerset(relation_image(X0,empty_set)))))) = X1 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17177,c_17487]) ).
tcf(c_30625,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(sK18(sK17(powerset(sK18(powerset(X0)))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17880,c_17487]) ).
tcf(c_30626,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(sK18(sK17(powerset(sK18(sK17(powerset(X0))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17885,c_17487]) ).
tcf(c_30627,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0)))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17888,c_17487]) ).
tcf(c_30628,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_dom(relation_dom(sK2(empty_set,X2,powerset(X0))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20186,c_17487]) ).
tcf(c_30629,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_dom(relation_dom(sK18(powerset(sK2(empty_set,X2,powerset(X0))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20188,c_17487]) ).
tcf(c_30630,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_dom(relation_dom(sK18(sK17(powerset(sK2(empty_set,X2,powerset(X0)))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20189,c_17487]) ).
tcf(c_30631,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_dom(relation_dom(sK7(empty_set,X2,powerset(X0))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21299,c_17487]) ).
tcf(c_30632,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_dom(relation_dom(sK18(powerset(sK7(empty_set,X2,powerset(X0))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21301,c_17487]) ).
tcf(c_30633,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_dom(relation_dom(sK18(sK17(powerset(sK7(empty_set,X2,powerset(X0)))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21302,c_17487]) ).
tcf(c_30634,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(sK18(sK17(sK17(sK17(powerset(X0)))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25683,c_17487]) ).
tcf(c_30635,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0)))))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25684,c_17487]) ).
tcf(c_30849,plain,
! [X0: $i] :
( ( sK18(powerset(sK18(sK17(sK17(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_99,c_15968]) ).
tcf(c_30850,plain,
sK18(powerset(sK18(sK17(sK17(powerset(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_114,c_15968]) ).
tcf(c_30851,plain,
! [X0: $i] :
( ( sK18(powerset(sK18(sK17(sK17(powerset(sK18(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12738,c_15968]) ).
tcf(c_30852,plain,
! [X0: $i] :
( ( sK18(powerset(sK18(sK17(sK17(powerset(sK18(powerset(sK18(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13358,c_15968]) ).
tcf(c_30853,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK18(sK17(sK17(powerset(relation_image(X0,X1))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK17(relation_image(X0,X1))))) = sK18(sK17(relation_image(X0,X1))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13159,c_15968]) ).
tcf(c_30854,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK18(sK17(sK17(powerset(relation_image(X0,X1))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(relation_image(X0,X1)))) = sK18(relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13157,c_15968]) ).
tcf(c_30855,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK18(sK17(sK17(powerset(sK18(powerset(relation_image(X0,X1))))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK18(powerset(relation_image(X0,X1)))))) = sK18(sK18(powerset(relation_image(X0,X1)))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13158,c_15968]) ).
tcf(c_30856,plain,
! [X0: $i] :
( ( sK18(powerset(sK18(sK17(sK17(powerset(sK18(sK17(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13470,c_15968]) ).
tcf(c_30857,plain,
! [X0: $i] :
( ( sK18(powerset(sK18(sK17(sK17(powerset(sK18(powerset(sK18(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13469,c_15968]) ).
tcf(c_30858,plain,
! [X0: $i] :
( ( sK18(powerset(sK18(sK17(sK17(powerset(sK18(sK17(sK17(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15885,c_15968]) ).
tcf(c_30859,plain,
! [X0: $i] :
( ( sK18(powerset(sK18(sK17(sK17(powerset(sK18(powerset(sK18(sK17(sK17(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15887,c_15968]) ).
tcf(c_30860,plain,
! [X0: $i] :
( ( sK18(powerset(sK18(sK17(sK17(powerset(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17175,c_15968]) ).
tcf(c_30861,plain,
! [X0: $i] :
( ( sK18(powerset(sK18(sK17(sK17(powerset(sK18(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17177,c_15968]) ).
tcf(c_30862,plain,
! [X0: $i] :
( ( sK18(powerset(sK18(sK17(sK17(powerset(sK18(sK17(powerset(sK18(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17880,c_15968]) ).
tcf(c_30863,plain,
! [X0: $i] :
( ( sK18(powerset(sK18(sK17(sK17(powerset(sK18(sK17(powerset(sK18(sK17(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17885,c_15968]) ).
tcf(c_30864,plain,
! [X0: $i] :
( ( sK18(powerset(sK18(sK17(sK17(powerset(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17888,c_15968]) ).
tcf(c_30865,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK18(sK17(sK17(powerset(sK2(empty_set,X1,powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20186,c_15968]) ).
tcf(c_30866,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK18(sK17(sK17(powerset(sK18(powerset(sK2(empty_set,X1,powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20188,c_15968]) ).
tcf(c_30867,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK18(sK17(sK17(powerset(sK18(sK17(powerset(sK2(empty_set,X1,powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20189,c_15968]) ).
tcf(c_30868,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK18(sK17(sK17(powerset(sK7(empty_set,X1,powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21299,c_15968]) ).
tcf(c_30869,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK18(sK17(sK17(powerset(sK18(powerset(sK7(empty_set,X1,powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21301,c_15968]) ).
tcf(c_30870,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK18(sK17(sK17(powerset(sK18(sK17(powerset(sK7(empty_set,X1,powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21302,c_15968]) ).
tcf(c_30871,plain,
! [X0: $i] :
( ( sK18(powerset(sK18(sK17(sK17(powerset(sK18(sK17(sK17(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25683,c_15968]) ).
tcf(c_30872,plain,
! [X0: $i] :
( ( sK18(powerset(sK18(sK17(sK17(powerset(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25684,c_15968]) ).
tcf(c_31116,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK18(sK17(sK17(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_99,c_15970]) ).
tcf(c_31117,plain,
relation_dom(relation_dom(sK18(sK17(sK17(powerset(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_114,c_15970]) ).
tcf(c_31118,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK18(sK17(sK17(powerset(sK18(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12738,c_15970]) ).
tcf(c_31119,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK18(sK17(sK17(powerset(sK18(powerset(sK18(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13358,c_15970]) ).
tcf(c_31120,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK18(sK17(sK17(powerset(relation_image(X0,X1))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK17(relation_image(X0,X1))))) = sK18(sK17(relation_image(X0,X1))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13159,c_15970]) ).
tcf(c_31121,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK18(sK17(sK17(powerset(relation_image(X0,X1))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(relation_image(X0,X1)))) = sK18(relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13157,c_15970]) ).
tcf(c_31122,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK18(sK17(sK17(powerset(sK18(powerset(relation_image(X0,X1))))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK18(powerset(relation_image(X0,X1)))))) = sK18(sK18(powerset(relation_image(X0,X1)))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13158,c_15970]) ).
tcf(c_31123,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK18(sK17(sK17(powerset(sK18(sK17(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13470,c_15970]) ).
tcf(c_31124,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK18(sK17(sK17(powerset(sK18(powerset(sK18(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13469,c_15970]) ).
tcf(c_31125,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK18(sK17(sK17(powerset(sK18(sK17(sK17(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15885,c_15970]) ).
tcf(c_31126,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK18(sK17(sK17(powerset(sK18(powerset(sK18(sK17(sK17(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15887,c_15970]) ).
tcf(c_31127,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK18(sK17(sK17(powerset(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17175,c_15970]) ).
tcf(c_31128,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK18(sK17(sK17(powerset(sK18(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17177,c_15970]) ).
tcf(c_31129,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK18(sK17(sK17(powerset(sK18(sK17(powerset(sK18(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17880,c_15970]) ).
tcf(c_31130,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK18(sK17(sK17(powerset(sK18(sK17(powerset(sK18(sK17(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17885,c_15970]) ).
tcf(c_31131,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK18(sK17(sK17(powerset(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17888,c_15970]) ).
tcf(c_31132,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK18(sK17(sK17(powerset(sK2(empty_set,X1,powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20186,c_15970]) ).
tcf(c_31133,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK18(sK17(sK17(powerset(sK18(powerset(sK2(empty_set,X1,powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20188,c_15970]) ).
tcf(c_31134,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK18(sK17(sK17(powerset(sK18(sK17(powerset(sK2(empty_set,X1,powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20189,c_15970]) ).
tcf(c_31135,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK18(sK17(sK17(powerset(sK7(empty_set,X1,powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21299,c_15970]) ).
tcf(c_31136,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK18(sK17(sK17(powerset(sK18(powerset(sK7(empty_set,X1,powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21301,c_15970]) ).
tcf(c_31137,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK18(sK17(sK17(powerset(sK18(sK17(powerset(sK7(empty_set,X1,powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21302,c_15970]) ).
tcf(c_31138,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK18(sK17(sK17(powerset(sK18(sK17(sK17(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25683,c_15970]) ).
tcf(c_31139,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK18(sK17(sK17(powerset(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25684,c_15970]) ).
tcf(c_31268,plain,
! [X0: $i] :
( ( sK18(sK17(sK17(powerset(sK18(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_99,c_16289]) ).
tcf(c_31269,plain,
sK18(sK17(sK17(powerset(sK18(powerset(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_114,c_16289]) ).
tcf(c_31271,plain,
! [X0: $i] :
( ( sK18(sK17(sK17(powerset(sK18(powerset(sK18(powerset(sK18(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13358,c_16289]) ).
tcf(c_31272,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(sK17(powerset(sK18(powerset(relation_image(X0,X1))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK17(relation_image(X0,X1))))) = sK18(sK17(relation_image(X0,X1))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13159,c_16289]) ).
tcf(c_31273,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(sK17(powerset(sK18(powerset(relation_image(X0,X1))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(relation_image(X0,X1)))) = sK18(relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13157,c_16289]) ).
tcf(c_31274,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(sK17(powerset(sK18(powerset(sK18(powerset(relation_image(X0,X1))))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK18(powerset(relation_image(X0,X1)))))) = sK18(sK18(powerset(relation_image(X0,X1)))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13158,c_16289]) ).
tcf(c_31276,plain,
! [X0: $i] :
( ( sK18(sK17(sK17(powerset(sK18(powerset(sK18(powerset(sK18(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13469,c_16289]) ).
tcf(c_31278,plain,
! [X0: $i] :
( ( sK18(sK17(sK17(powerset(sK18(powerset(sK18(powerset(sK18(sK17(sK17(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15887,c_16289]) ).
tcf(c_31280,plain,
! [X0: $i] :
( ( sK18(sK17(sK17(powerset(sK18(powerset(sK18(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17177,c_16289]) ).
tcf(c_31281,plain,
! [X0: $i] :
( ( sK18(sK17(sK17(powerset(sK18(powerset(sK18(sK17(powerset(sK18(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17880,c_16289]) ).
tcf(c_31282,plain,
! [X0: $i] :
( ( sK18(sK17(sK17(powerset(sK18(powerset(sK18(sK17(powerset(sK18(sK17(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17885,c_16289]) ).
tcf(c_31283,plain,
! [X0: $i] :
( ( sK18(sK17(sK17(powerset(sK18(powerset(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17888,c_16289]) ).
tcf(c_31285,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(sK17(powerset(sK18(powerset(sK18(powerset(sK2(empty_set,X1,powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20188,c_16289]) ).
tcf(c_31286,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(sK17(powerset(sK18(powerset(sK18(sK17(powerset(sK2(empty_set,X1,powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20189,c_16289]) ).
tcf(c_31288,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(sK17(powerset(sK18(powerset(sK18(powerset(sK7(empty_set,X1,powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21301,c_16289]) ).
tcf(c_31289,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(sK17(powerset(sK18(powerset(sK18(sK17(powerset(sK7(empty_set,X1,powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21302,c_16289]) ).
tcf(c_31291,plain,
! [X0: $i] :
( ( sK18(sK17(sK17(powerset(sK18(powerset(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25684,c_16289]) ).
tcf(c_31475,plain,
! [X0: $i,X1: $i] :
( ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X0))) = sK2(sK1,X1,relation_image(sK1,X0)) )
| ( apply(sK1,sK4(sK1,X0,sK2(sK1,X1,relation_image(sK1,X0)))) = sK2(sK1,X1,relation_image(sK1,X0)) )
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_52,c_29889]) ).
tcf(c_31476,plain,
! [X0: $i,X1: $i] :
( ( relation_image(sK1,X1) = relation_image(sK6,X0) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK6,X0))) = sK2(sK1,X1,relation_image(sK6,X0)) )
| ( apply(sK6,sK4(sK6,X0,sK2(sK1,X1,relation_image(sK6,X0)))) = sK2(sK1,X1,relation_image(sK6,X0)) )
| ~ relation(sK6) ),
inference(superposition,[status(thm)],[c_65,c_29889]) ).
tcf(c_31477,plain,
! [X0: $i,X1: $i] :
( ( relation_image(sK1,X1) = relation_image(sK10,X0) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK10,X0))) = sK2(sK1,X1,relation_image(sK10,X0)) )
| ( apply(sK10,sK4(sK10,X0,sK2(sK1,X1,relation_image(sK10,X0)))) = sK2(sK1,X1,relation_image(sK10,X0)) )
| ~ relation(sK10) ),
inference(superposition,[status(thm)],[c_79,c_29889]) ).
tcf(c_31478,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(relation_dom(X0),X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK3(sK1,X2,relation_image(relation_dom(X0),X1))) = sK2(sK1,X2,relation_image(relation_dom(X0),X1)) )
| ( apply(relation_dom(X0),sK4(relation_dom(X0),X1,sK2(sK1,X2,relation_image(relation_dom(X0),X1)))) = sK2(sK1,X2,relation_image(relation_dom(X0),X1)) )
| ~ empty(X0)
| ~ relation(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_12385,c_29889]) ).
tcf(c_31479,plain,
! [X0: $i,X1: $i] :
( ( relation_image(sK1,X1) = relation_image(empty_set,X0) )
| ( apply(sK1,sK3(sK1,X1,relation_image(empty_set,X0))) = sK2(sK1,X1,relation_image(empty_set,X0)) )
| ( apply(empty_set,sK4(empty_set,X0,sK2(sK1,X1,relation_image(empty_set,X0)))) = sK2(sK1,X1,relation_image(empty_set,X0)) )
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_12355,c_29889]) ).
tcf(c_31480,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK18(powerset(X0)),X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK3(sK1,X2,relation_image(sK18(powerset(X0)),X1))) = sK2(sK1,X2,relation_image(sK18(powerset(X0)),X1)) )
| ( apply(sK18(powerset(X0)),sK4(sK18(powerset(X0)),X1,sK2(sK1,X2,relation_image(sK18(powerset(X0)),X1)))) = sK2(sK1,X2,relation_image(sK18(powerset(X0)),X1)) )
| ~ empty(X0)
| ~ relation(sK18(powerset(X0))) ),
inference(superposition,[status(thm)],[c_12772,c_29889]) ).
tcf(c_31481,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK18(powerset(sK18(powerset(X0)))),X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK3(sK1,X2,relation_image(sK18(powerset(sK18(powerset(X0)))),X1))) = sK2(sK1,X2,relation_image(sK18(powerset(sK18(powerset(X0)))),X1)) )
| ( apply(sK18(powerset(sK18(powerset(X0)))),sK4(sK18(powerset(sK18(powerset(X0)))),X1,sK2(sK1,X2,relation_image(sK18(powerset(sK18(powerset(X0)))),X1)))) = sK2(sK1,X2,relation_image(sK18(powerset(sK18(powerset(X0)))),X1)) )
| ~ empty(X0)
| ~ relation(sK18(powerset(sK18(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_13393,c_29889]) ).
tcf(c_31482,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK18(sK17(powerset(X0))),X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK3(sK1,X2,relation_image(sK18(sK17(powerset(X0))),X1))) = sK2(sK1,X2,relation_image(sK18(sK17(powerset(X0))),X1)) )
| ( apply(sK18(sK17(powerset(X0))),sK4(sK18(sK17(powerset(X0))),X1,sK2(sK1,X2,relation_image(sK18(sK17(powerset(X0))),X1)))) = sK2(sK1,X2,relation_image(sK18(sK17(powerset(X0))),X1)) )
| ~ empty(X0)
| ~ relation(sK18(sK17(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_13498,c_29889]) ).
tcf(c_31483,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK18(powerset(sK18(sK17(powerset(X0))))),X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK3(sK1,X2,relation_image(sK18(powerset(sK18(sK17(powerset(X0))))),X1))) = sK2(sK1,X2,relation_image(sK18(powerset(sK18(sK17(powerset(X0))))),X1)) )
| ( apply(sK18(powerset(sK18(sK17(powerset(X0))))),sK4(sK18(powerset(sK18(sK17(powerset(X0))))),X1,sK2(sK1,X2,relation_image(sK18(powerset(sK18(sK17(powerset(X0))))),X1)))) = sK2(sK1,X2,relation_image(sK18(powerset(sK18(sK17(powerset(X0))))),X1)) )
| ~ empty(X0)
| ~ relation(sK18(powerset(sK18(sK17(powerset(X0)))))) ),
inference(superposition,[status(thm)],[c_14345,c_29889]) ).
tcf(c_31484,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK18(sK17(sK17(powerset(X0)))),X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK3(sK1,X2,relation_image(sK18(sK17(sK17(powerset(X0)))),X1))) = sK2(sK1,X2,relation_image(sK18(sK17(sK17(powerset(X0)))),X1)) )
| ( apply(sK18(sK17(sK17(powerset(X0)))),sK4(sK18(sK17(sK17(powerset(X0)))),X1,sK2(sK1,X2,relation_image(sK18(sK17(sK17(powerset(X0)))),X1)))) = sK2(sK1,X2,relation_image(sK18(sK17(sK17(powerset(X0)))),X1)) )
| ~ empty(X0)
| ~ relation(sK18(sK17(sK17(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_15976,c_29889]) ).
tcf(c_31485,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK18(powerset(sK18(sK17(sK17(powerset(X0)))))),X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK3(sK1,X2,relation_image(sK18(powerset(sK18(sK17(sK17(powerset(X0)))))),X1))) = sK2(sK1,X2,relation_image(sK18(powerset(sK18(sK17(sK17(powerset(X0)))))),X1)) )
| ( apply(sK18(powerset(sK18(sK17(sK17(powerset(X0)))))),sK4(sK18(powerset(sK18(sK17(sK17(powerset(X0)))))),X1,sK2(sK1,X2,relation_image(sK18(powerset(sK18(sK17(sK17(powerset(X0)))))),X1)))) = sK2(sK1,X2,relation_image(sK18(powerset(sK18(sK17(sK17(powerset(X0)))))),X1)) )
| ~ empty(X0)
| ~ relation(sK18(powerset(sK18(sK17(sK17(powerset(X0))))))) ),
inference(superposition,[status(thm)],[c_16543,c_29889]) ).
tcf(c_31486,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(relation_image(X0,empty_set),X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK3(sK1,X2,relation_image(relation_image(X0,empty_set),X1))) = sK2(sK1,X2,relation_image(relation_image(X0,empty_set),X1)) )
| ( apply(relation_image(X0,empty_set),sK4(relation_image(X0,empty_set),X1,sK2(sK1,X2,relation_image(relation_image(X0,empty_set),X1)))) = sK2(sK1,X2,relation_image(relation_image(X0,empty_set),X1)) )
| ~ function(X0)
| ~ relation(X0)
| ~ relation(relation_image(X0,empty_set)) ),
inference(superposition,[status(thm)],[c_17557,c_29889]) ).
tcf(c_31487,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK18(sK17(powerset(sK18(powerset(X0))))),X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK3(sK1,X2,relation_image(sK18(sK17(powerset(sK18(powerset(X0))))),X1))) = sK2(sK1,X2,relation_image(sK18(sK17(powerset(sK18(powerset(X0))))),X1)) )
| ( apply(sK18(sK17(powerset(sK18(powerset(X0))))),sK4(sK18(sK17(powerset(sK18(powerset(X0))))),X1,sK2(sK1,X2,relation_image(sK18(sK17(powerset(sK18(powerset(X0))))),X1)))) = sK2(sK1,X2,relation_image(sK18(sK17(powerset(sK18(powerset(X0))))),X1)) )
| ~ empty(X0)
| ~ relation(sK18(sK17(powerset(sK18(powerset(X0)))))) ),
inference(superposition,[status(thm)],[c_18126,c_29889]) ).
tcf(c_31488,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK18(sK17(powerset(sK18(sK17(powerset(X0)))))),X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK3(sK1,X2,relation_image(sK18(sK17(powerset(sK18(sK17(powerset(X0)))))),X1))) = sK2(sK1,X2,relation_image(sK18(sK17(powerset(sK18(sK17(powerset(X0)))))),X1)) )
| ( apply(sK18(sK17(powerset(sK18(sK17(powerset(X0)))))),sK4(sK18(sK17(powerset(sK18(sK17(powerset(X0)))))),X1,sK2(sK1,X2,relation_image(sK18(sK17(powerset(sK18(sK17(powerset(X0)))))),X1)))) = sK2(sK1,X2,relation_image(sK18(sK17(powerset(sK18(sK17(powerset(X0)))))),X1)) )
| ~ empty(X0)
| ~ relation(sK18(sK17(powerset(sK18(sK17(powerset(X0))))))) ),
inference(superposition,[status(thm)],[c_18310,c_29889]) ).
tcf(c_31489,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(sK2(empty_set,X0,powerset(X1)),X2) = relation_image(sK1,X3) )
| ( apply(sK1,sK3(sK1,X3,relation_image(sK2(empty_set,X0,powerset(X1)),X2))) = sK2(sK1,X3,relation_image(sK2(empty_set,X0,powerset(X1)),X2)) )
| ( apply(sK2(empty_set,X0,powerset(X1)),sK4(sK2(empty_set,X0,powerset(X1)),X2,sK2(sK1,X3,relation_image(sK2(empty_set,X0,powerset(X1)),X2)))) = sK2(sK1,X3,relation_image(sK2(empty_set,X0,powerset(X1)),X2)) )
| ~ empty(X1)
| ~ relation(sK2(empty_set,X0,powerset(X1))) ),
inference(superposition,[status(thm)],[c_20341,c_29889]) ).
tcf(c_31490,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(sK18(powerset(sK2(empty_set,X0,powerset(X1)))),X2) = relation_image(sK1,X3) )
| ( apply(sK1,sK3(sK1,X3,relation_image(sK18(powerset(sK2(empty_set,X0,powerset(X1)))),X2))) = sK2(sK1,X3,relation_image(sK18(powerset(sK2(empty_set,X0,powerset(X1)))),X2)) )
| ( apply(sK18(powerset(sK2(empty_set,X0,powerset(X1)))),sK4(sK18(powerset(sK2(empty_set,X0,powerset(X1)))),X2,sK2(sK1,X3,relation_image(sK18(powerset(sK2(empty_set,X0,powerset(X1)))),X2)))) = sK2(sK1,X3,relation_image(sK18(powerset(sK2(empty_set,X0,powerset(X1)))),X2)) )
| ~ empty(X1)
| ~ relation(sK18(powerset(sK2(empty_set,X0,powerset(X1))))) ),
inference(superposition,[status(thm)],[c_20631,c_29889]) ).
tcf(c_31491,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(sK7(empty_set,X0,powerset(X1)),X2) = relation_image(sK1,X3) )
| ( apply(sK1,sK3(sK1,X3,relation_image(sK7(empty_set,X0,powerset(X1)),X2))) = sK2(sK1,X3,relation_image(sK7(empty_set,X0,powerset(X1)),X2)) )
| ( apply(sK7(empty_set,X0,powerset(X1)),sK4(sK7(empty_set,X0,powerset(X1)),X2,sK2(sK1,X3,relation_image(sK7(empty_set,X0,powerset(X1)),X2)))) = sK2(sK1,X3,relation_image(sK7(empty_set,X0,powerset(X1)),X2)) )
| ~ empty(X1)
| ~ relation(sK7(empty_set,X0,powerset(X1))) ),
inference(superposition,[status(thm)],[c_21433,c_29889]) ).
tcf(c_31492,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(sK18(powerset(sK7(empty_set,X0,powerset(X1)))),X2) = relation_image(sK1,X3) )
| ( apply(sK1,sK3(sK1,X3,relation_image(sK18(powerset(sK7(empty_set,X0,powerset(X1)))),X2))) = sK2(sK1,X3,relation_image(sK18(powerset(sK7(empty_set,X0,powerset(X1)))),X2)) )
| ( apply(sK18(powerset(sK7(empty_set,X0,powerset(X1)))),sK4(sK18(powerset(sK7(empty_set,X0,powerset(X1)))),X2,sK2(sK1,X3,relation_image(sK18(powerset(sK7(empty_set,X0,powerset(X1)))),X2)))) = sK2(sK1,X3,relation_image(sK18(powerset(sK7(empty_set,X0,powerset(X1)))),X2)) )
| ~ empty(X1)
| ~ relation(sK18(powerset(sK7(empty_set,X0,powerset(X1))))) ),
inference(superposition,[status(thm)],[c_21807,c_29889]) ).
tcf(c_31493,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK18(powerset(relation_image(X0,empty_set))),X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK3(sK1,X2,relation_image(sK18(powerset(relation_image(X0,empty_set))),X1))) = sK2(sK1,X2,relation_image(sK18(powerset(relation_image(X0,empty_set))),X1)) )
| ( apply(sK18(powerset(relation_image(X0,empty_set))),sK4(sK18(powerset(relation_image(X0,empty_set))),X1,sK2(sK1,X2,relation_image(sK18(powerset(relation_image(X0,empty_set))),X1)))) = sK2(sK1,X2,relation_image(sK18(powerset(relation_image(X0,empty_set))),X1)) )
| ~ function(X0)
| ~ relation(X0)
| ~ relation(sK18(powerset(relation_image(X0,empty_set)))) ),
inference(superposition,[status(thm)],[c_23555,c_29889]) ).
tcf(c_31494,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0))))))),X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK3(sK1,X2,relation_image(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0))))))),X1))) = sK2(sK1,X2,relation_image(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0))))))),X1)) )
| ( apply(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0))))))),sK4(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0))))))),X1,sK2(sK1,X2,relation_image(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0))))))),X1)))) = sK2(sK1,X2,relation_image(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0))))))),X1)) )
| ~ empty(X0)
| ~ relation(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0)))))))) ),
inference(superposition,[status(thm)],[c_23841,c_29889]) ).
tcf(c_31495,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(sK18(sK17(powerset(sK2(empty_set,X0,powerset(X1))))),X2) = relation_image(sK1,X3) )
| ( apply(sK1,sK3(sK1,X3,relation_image(sK18(sK17(powerset(sK2(empty_set,X0,powerset(X1))))),X2))) = sK2(sK1,X3,relation_image(sK18(sK17(powerset(sK2(empty_set,X0,powerset(X1))))),X2)) )
| ( apply(sK18(sK17(powerset(sK2(empty_set,X0,powerset(X1))))),sK4(sK18(sK17(powerset(sK2(empty_set,X0,powerset(X1))))),X2,sK2(sK1,X3,relation_image(sK18(sK17(powerset(sK2(empty_set,X0,powerset(X1))))),X2)))) = sK2(sK1,X3,relation_image(sK18(sK17(powerset(sK2(empty_set,X0,powerset(X1))))),X2)) )
| ~ empty(X1)
| ~ relation(sK18(sK17(powerset(sK2(empty_set,X0,powerset(X1)))))) ),
inference(superposition,[status(thm)],[c_24108,c_29889]) ).
tcf(c_31496,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(sK18(sK17(powerset(sK7(empty_set,X0,powerset(X1))))),X2) = relation_image(sK1,X3) )
| ( apply(sK1,sK3(sK1,X3,relation_image(sK18(sK17(powerset(sK7(empty_set,X0,powerset(X1))))),X2))) = sK2(sK1,X3,relation_image(sK18(sK17(powerset(sK7(empty_set,X0,powerset(X1))))),X2)) )
| ( apply(sK18(sK17(powerset(sK7(empty_set,X0,powerset(X1))))),sK4(sK18(sK17(powerset(sK7(empty_set,X0,powerset(X1))))),X2,sK2(sK1,X3,relation_image(sK18(sK17(powerset(sK7(empty_set,X0,powerset(X1))))),X2)))) = sK2(sK1,X3,relation_image(sK18(sK17(powerset(sK7(empty_set,X0,powerset(X1))))),X2)) )
| ~ empty(X1)
| ~ relation(sK18(sK17(powerset(sK7(empty_set,X0,powerset(X1)))))) ),
inference(superposition,[status(thm)],[c_25110,c_29889]) ).
tcf(c_31497,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK18(sK17(sK17(sK17(powerset(X0))))),X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK3(sK1,X2,relation_image(sK18(sK17(sK17(sK17(powerset(X0))))),X1))) = sK2(sK1,X2,relation_image(sK18(sK17(sK17(sK17(powerset(X0))))),X1)) )
| ( apply(sK18(sK17(sK17(sK17(powerset(X0))))),sK4(sK18(sK17(sK17(sK17(powerset(X0))))),X1,sK2(sK1,X2,relation_image(sK18(sK17(sK17(sK17(powerset(X0))))),X1)))) = sK2(sK1,X2,relation_image(sK18(sK17(sK17(sK17(powerset(X0))))),X1)) )
| ~ empty(X0)
| ~ relation(sK18(sK17(sK17(sK17(powerset(X0)))))) ),
inference(superposition,[status(thm)],[c_25864,c_29889]) ).
tcf(c_31498,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0))))))),X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK3(sK1,X2,relation_image(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0))))))),X1))) = sK2(sK1,X2,relation_image(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0))))))),X1)) )
| ( apply(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0))))))),sK4(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0))))))),X1,sK2(sK1,X2,relation_image(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0))))))),X1)))) = sK2(sK1,X2,relation_image(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0))))))),X1)) )
| ~ empty(X0)
| ~ relation(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0)))))))) ),
inference(superposition,[status(thm)],[c_26699,c_29889]) ).
tcf(c_31499,plain,
! [X0: $i,X1: $i] :
( ( relation_image(sK1,X1) = empty_set )
| ( apply(sK1,sK3(sK1,X1,empty_set)) = sK2(sK1,X1,empty_set) )
| ( apply(empty_set,sK4(empty_set,X0,sK2(sK1,X1,empty_set))) = sK2(sK1,X1,empty_set) )
| ~ relation(empty_set) ),
inference(light_normalisation,[status(thm)],[c_31479,c_17316]) ).
tcf(c_31500,plain,
! [X0: $i,X1: $i] :
( ( relation_image(sK1,X1) = empty_set )
| ( apply(sK1,sK3(sK1,X1,empty_set)) = sK2(sK1,X1,empty_set) )
| ( apply(empty_set,sK4(empty_set,X0,sK2(sK1,X1,empty_set))) = sK2(sK1,X1,empty_set) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_31499,c_113]) ).
tcf(c_31504,plain,
! [X0: $i,X1: $i] :
( ( relation_image(sK1,X1) = relation_image(sK10,X0) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK10,X0))) = sK2(sK1,X1,relation_image(sK10,X0)) )
| ( apply(sK10,sK4(sK10,X0,sK2(sK1,X1,relation_image(sK10,X0)))) = sK2(sK1,X1,relation_image(sK10,X0)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_31477,c_78]) ).
tcf(c_31508,plain,
! [X0: $i,X1: $i] :
( ( relation_image(sK1,X1) = relation_image(sK6,X0) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK6,X0))) = sK2(sK1,X1,relation_image(sK6,X0)) )
| ( apply(sK6,sK4(sK6,X0,sK2(sK1,X1,relation_image(sK6,X0)))) = sK2(sK1,X1,relation_image(sK6,X0)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_31476,c_64]) ).
tcf(c_31512,plain,
! [X0: $i,X1: $i] :
( ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X0))) = sK2(sK1,X1,relation_image(sK1,X0)) )
| ( apply(sK1,sK4(sK1,X0,sK2(sK1,X1,relation_image(sK1,X0)))) = sK2(sK1,X1,relation_image(sK1,X0)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_31475,c_51]) ).
tcf(c_31735,plain,
! [X0: $i] :
( ( relation_image(sK1,X0) = relation_image(sK1,empty_set) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,empty_set))) = sK2(sK1,X0,relation_image(sK1,empty_set)) )
| ( apply(sK1,sK4(sK1,empty_set,sK2(sK1,X0,empty_set))) = sK2(sK1,X0,empty_set) ) ),
inference(superposition,[status(thm)],[c_23326,c_31512]) ).
tcf(c_31736,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(sK1,X2) = X3 )
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(sK2(sK1,X2,X3),X3)
| ~ in(sK4(sK1,X1,sK2(sK1,X0,relation_image(sK1,X1))),X2)
| ~ in(sK4(sK1,X1,sK2(sK1,X0,relation_image(sK1,X1))),relation_dom(sK1))
| ( sK2(sK1,X0,relation_image(sK1,X1)) != sK2(sK1,X2,X3) ) ),
inference(superposition,[status(thm)],[c_31512,c_53]) ).
tcf(c_31737,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(sK1,X1,relation_image(sK1,X0)),relation_image(sK1,X2))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X0))) = sK2(sK1,X1,relation_image(sK1,X0)) )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(sK4(sK1,X0,sK2(sK1,X1,relation_image(sK1,X0))),X2)
| ~ in(sK4(sK1,X0,sK2(sK1,X1,relation_image(sK1,X0))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_31512,c_57]) ).
tcf(c_31739,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK4(sK1,X0,sK2(sK1,X1,relation_image(sK1,X0))),relation_inverse_image(sK1,X2))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X0))) = sK2(sK1,X1,relation_image(sK1,X0)) )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(sK2(sK1,X1,relation_image(sK1,X0)),X2)
| ~ in(sK4(sK1,X0,sK2(sK1,X1,relation_image(sK1,X0))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_31512,c_70]) ).
tcf(c_31740,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ( sK4(sK1,X1,sK2(sK1,X0,relation_image(sK1,X1))) = X2 )
| ~ function(sK1)
| ~ relation(sK1)
| ~ one_to_one(sK1)
| ~ in(X2,relation_dom(sK1))
| ~ in(sK4(sK1,X1,sK2(sK1,X0,relation_image(sK1,X1))),relation_dom(sK1))
| ( sK2(sK1,X0,relation_image(sK1,X1)) != apply(sK1,X2) ) ),
inference(superposition,[status(thm)],[c_31512,c_85]) ).
tcf(c_31741,plain,
! [X0: $i] :
( ( relation_image(sK1,X0) = empty_set )
| ( apply(sK1,sK3(sK1,X0,empty_set)) = sK2(sK1,X0,empty_set) )
| ( apply(sK1,sK4(sK1,empty_set,sK2(sK1,X0,empty_set))) = sK2(sK1,X0,empty_set) ) ),
inference(light_normalisation,[status(thm)],[c_31735,c_23326]) ).
tcf(c_31745,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK4(sK1,X0,sK2(sK1,X1,relation_image(sK1,X0))),relation_inverse_image(sK1,X2))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X0))) = sK2(sK1,X1,relation_image(sK1,X0)) )
| ~ in(sK2(sK1,X1,relation_image(sK1,X0)),X2)
| ~ in(sK4(sK1,X0,sK2(sK1,X1,relation_image(sK1,X0))),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_31739,c_52,c_51]) ).
tcf(c_31751,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(sK1,X1,relation_image(sK1,X0)),relation_image(sK1,X2))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X0))) = sK2(sK1,X1,relation_image(sK1,X0)) )
| ~ in(sK4(sK1,X0,sK2(sK1,X1,relation_image(sK1,X0))),X2)
| ~ in(sK4(sK1,X0,sK2(sK1,X1,relation_image(sK1,X0))),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_31737,c_52,c_51]) ).
tcf(c_31757,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ( sK4(sK1,X1,sK2(sK1,X0,relation_image(sK1,X1))) = X2 )
| ~ in(X2,relation_dom(sK1))
| ~ in(sK4(sK1,X1,sK2(sK1,X0,relation_image(sK1,X1))),relation_dom(sK1))
| ( sK2(sK1,X0,relation_image(sK1,X1)) != apply(sK1,X2) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_31740,c_52,c_51,c_50]) ).
tcf(c_31764,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(sK1,X2) = X3 )
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ in(sK2(sK1,X2,X3),X3)
| ~ in(sK4(sK1,X1,sK2(sK1,X0,relation_image(sK1,X1))),X2)
| ~ in(sK4(sK1,X1,sK2(sK1,X0,relation_image(sK1,X1))),relation_dom(sK1))
| ( sK2(sK1,X0,relation_image(sK1,X1)) != sK2(sK1,X2,X3) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_31736,c_52,c_51]) ).
tcf(c_31833,plain,
! [X0: $i,X1: $i] :
( in(sK4(sK1,empty_set,sK2(sK1,X0,empty_set)),relation_inverse_image(sK1,X1))
| ( relation_image(sK1,X0) = relation_image(sK1,empty_set) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,empty_set))) = sK2(sK1,X0,relation_image(sK1,empty_set)) )
| ~ in(sK2(sK1,X0,relation_image(sK1,empty_set)),X1)
| ~ in(sK4(sK1,empty_set,sK2(sK1,X0,relation_image(sK1,empty_set))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_23326,c_31745]) ).
tcf(c_31834,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(sK1,sK4(sK1,X0,sK2(sK1,X1,relation_image(sK1,X0)))),X2)
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X0))) = sK2(sK1,X1,relation_image(sK1,X0)) )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(sK2(sK1,X1,relation_image(sK1,X0)),X2)
| ~ in(sK4(sK1,X0,sK2(sK1,X1,relation_image(sK1,X0))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_31745,c_72]) ).
tcf(c_31836,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK1,X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK3(sK1,X2,relation_image(sK1,X1))) = sK2(sK1,X2,relation_image(sK1,X1)) )
| ~ in(sK2(sK1,X2,relation_image(sK1,X1)),X0)
| ~ in(sK4(sK1,X1,sK2(sK1,X2,relation_image(sK1,X1))),relation_dom(sK1))
| ~ in(relation_inverse_image(sK1,X0),sK4(sK1,X1,sK2(sK1,X2,relation_image(sK1,X1)))) ),
inference(superposition,[status(thm)],[c_31745,c_98]) ).
tcf(c_31837,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK4(sK1,X0,sK2(sK1,X1,relation_image(sK1,X0))),relation_inverse_image(sK1,X2))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X0))) = sK2(sK1,X1,relation_image(sK1,X0)) )
| ~ in(sK2(sK1,X1,relation_image(sK1,X0)),X2)
| ~ in(sK4(sK1,X0,sK2(sK1,X1,relation_image(sK1,X0))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_31745,c_97]) ).
tcf(c_31838,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X0))) = sK2(sK1,X1,relation_image(sK1,X0)) )
| ~ empty(relation_inverse_image(sK1,X2))
| ~ in(sK2(sK1,X1,relation_image(sK1,X0)),X2)
| ~ in(sK4(sK1,X0,sK2(sK1,X1,relation_image(sK1,X0))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_31745,c_95]) ).
tcf(c_31844,plain,
! [X0: $i,X1: $i] :
( in(sK4(sK1,empty_set,sK2(sK1,X0,empty_set)),relation_inverse_image(sK1,X1))
| ( relation_image(sK1,X0) = empty_set )
| ( apply(sK1,sK3(sK1,X0,empty_set)) = sK2(sK1,X0,empty_set) )
| ~ in(sK2(sK1,X0,empty_set),X1)
| ~ in(sK4(sK1,empty_set,sK2(sK1,X0,empty_set)),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_31833,c_23326]) ).
tcf(c_31860,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(sK1,sK4(sK1,X0,sK2(sK1,X1,relation_image(sK1,X0)))),X2)
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X0))) = sK2(sK1,X1,relation_image(sK1,X0)) )
| ~ in(sK2(sK1,X1,relation_image(sK1,X0)),X2)
| ~ in(sK4(sK1,X0,sK2(sK1,X1,relation_image(sK1,X0))),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_31834,c_52,c_51]) ).
tcf(c_31881,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(sK1,X1,relation_image(sK1,X0)),relation_image(sK1,X2))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X0))) = sK2(sK1,X1,relation_image(sK1,X0)) )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(sK2(sK1,X1,relation_image(sK1,X0)),relation_image(sK1,X0))
| ~ in(sK4(sK1,X0,sK2(sK1,X1,relation_image(sK1,X0))),X2) ),
inference(superposition,[status(thm)],[c_58,c_31751]) ).
tcf(c_31882,plain,
! [X0: $i,X1: $i] :
( in(sK2(sK1,X0,relation_image(sK1,relation_dom(sK1))),relation_image(sK1,X1))
| ( relation_image(sK1,relation_dom(sK1)) = relation_image(sK1,X0) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,relation_dom(sK1)))) = sK2(sK1,X0,relation_image(sK1,relation_dom(sK1))) )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(sK2(sK1,X0,relation_image(sK1,relation_dom(sK1))),relation_image(sK1,relation_dom(sK1)))
| ~ in(sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,relation_dom(sK1)))),X1) ),
inference(superposition,[status(thm)],[c_59,c_31751]) ).
tcf(c_31883,plain,
! [X0: $i,X1: $i] :
( in(sK2(sK1,X0,relation_image(sK1,empty_set)),relation_image(sK1,X1))
| ( relation_image(sK1,X0) = relation_image(sK1,empty_set) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,empty_set))) = sK2(sK1,X0,relation_image(sK1,empty_set)) )
| ~ in(sK4(sK1,empty_set,sK2(sK1,X0,empty_set)),relation_dom(sK1))
| ~ in(sK4(sK1,empty_set,sK2(sK1,X0,relation_image(sK1,empty_set))),X1) ),
inference(superposition,[status(thm)],[c_23326,c_31751]) ).
tcf(c_31884,plain,
! [X0: $i,X1: $i] :
( in(sK2(sK1,X0,empty_set),relation_image(sK1,X1))
| ( relation_image(sK1,X0) = empty_set )
| ( apply(sK1,sK3(sK1,X0,empty_set)) = sK2(sK1,X0,empty_set) )
| ~ in(sK4(sK1,empty_set,sK2(sK1,X0,empty_set)),X1)
| ~ in(sK4(sK1,empty_set,sK2(sK1,X0,empty_set)),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_31883,c_23326]) ).
tcf(c_31890,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(sK1,X1,relation_image(sK1,X0)),relation_image(sK1,X2))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X0))) = sK2(sK1,X1,relation_image(sK1,X0)) )
| ~ in(sK2(sK1,X1,relation_image(sK1,X0)),relation_image(sK1,X0))
| ~ in(sK4(sK1,X0,sK2(sK1,X1,relation_image(sK1,X0))),X2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_31881,c_52,c_51]) ).
tcf(c_31896,plain,
! [X0: $i,X1: $i] :
( in(sK2(sK1,X0,relation_image(sK1,relation_dom(sK1))),relation_image(sK1,X1))
| ( relation_image(sK1,relation_dom(sK1)) = relation_image(sK1,X0) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,relation_dom(sK1)))) = sK2(sK1,X0,relation_image(sK1,relation_dom(sK1))) )
| ~ in(sK2(sK1,X0,relation_image(sK1,relation_dom(sK1))),relation_image(sK1,relation_dom(sK1)))
| ~ in(sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,relation_dom(sK1)))),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_31882,c_52,c_51]) ).
tcf(c_31914,plain,
! [X0: $i,X1: $i] :
( in(sK2(sK1,X0,relation_image(sK1,X1)),relation_image(sK1,relation_dom(sK1)))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),relation_image(sK1,X1)) ),
inference(superposition,[status(thm)],[c_58,c_31890]) ).
tcf(c_31916,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(sK1,X1,relation_image(sK1,X0)),relation_image(sK1,powerset(X2)))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X0))) = sK2(sK1,X1,relation_image(sK1,X0)) )
| ~ in(sK2(sK1,X1,relation_image(sK1,X0)),relation_image(sK1,X0))
| ~ subset(sK4(sK1,X0,sK2(sK1,X1,relation_image(sK1,X0))),X2) ),
inference(superposition,[status(thm)],[c_12509,c_31890]) ).
tcf(c_31917,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(sK1,X1,relation_image(sK1,X0)),relation_image(sK1,relation_inverse_image(sK1,X2)))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X0))) = sK2(sK1,X1,relation_image(sK1,X0)) )
| ~ in(sK2(sK1,X1,relation_image(sK1,X0)),X2)
| ~ in(sK2(sK1,X1,relation_image(sK1,X0)),relation_image(sK1,X0))
| ~ in(sK4(sK1,X0,sK2(sK1,X1,relation_image(sK1,X0))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_31745,c_31890]) ).
tcf(c_31918,plain,
! [X0: $i,X1: $i] :
( in(sK2(sK1,X0,relation_image(sK1,empty_set)),relation_image(sK1,X1))
| ( relation_image(sK1,X0) = relation_image(sK1,empty_set) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,empty_set))) = sK2(sK1,X0,relation_image(sK1,empty_set)) )
| ~ in(sK4(sK1,empty_set,sK2(sK1,X0,empty_set)),X1)
| ~ in(sK2(sK1,X0,relation_image(sK1,empty_set)),relation_image(sK1,empty_set)) ),
inference(superposition,[status(thm)],[c_23326,c_31890]) ).
tcf(c_31919,plain,
! [X0: $i,X1: $i] :
( in(sK2(sK1,X0,relation_image(sK1,X1)),relation_image(sK1,relation_dom(sK1)))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),relation_image(sK1,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_31914,c_52,c_51]) ).
tcf(c_31924,plain,
! [X0: $i,X1: $i] :
( in(sK2(sK1,X0,empty_set),relation_image(sK1,X1))
| ( relation_image(sK1,X0) = empty_set )
| ( apply(sK1,sK3(sK1,X0,empty_set)) = sK2(sK1,X0,empty_set) )
| ~ in(sK2(sK1,X0,empty_set),empty_set)
| ~ in(sK4(sK1,empty_set,sK2(sK1,X0,empty_set)),X1) ),
inference(light_normalisation,[status(thm)],[c_31918,c_23326]) ).
tcf(c_31947,plain,
! [X0: $i,X1: $i] :
( in(sK2(sK1,X0,relation_image(sK1,X1)),relation_image(sK1,relation_dom(sK1)))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ function(sK1)
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_56,c_31919]) ).
tcf(c_31952,plain,
! [X0: $i,X1: $i] :
( in(sK2(sK1,X0,relation_image(sK1,X1)),relation_image(sK1,relation_dom(sK1)))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_31947,c_52,c_51]) ).
tcf(c_31966,plain,
! [X0: $i] :
( in(sK2(sK1,X0,empty_set),relation_image(sK1,relation_dom(sK1)))
| ( relation_image(sK1,X0) = relation_image(sK1,empty_set) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,empty_set))) = sK2(sK1,X0,relation_image(sK1,empty_set)) ) ),
inference(superposition,[status(thm)],[c_23326,c_31952]) ).
tcf(c_31967,plain,
! [X0: $i,X1: $i] :
( ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1)))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ function(sK1)
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_31952,c_60]) ).
tcf(c_31968,plain,
! [X0: $i,X1: $i] :
( ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ in(relation_image(sK1,relation_dom(sK1)),sK2(sK1,X0,relation_image(sK1,X1))) ),
inference(superposition,[status(thm)],[c_31952,c_98]) ).
tcf(c_31969,plain,
! [X0: $i,X1: $i] :
( element(sK2(sK1,X0,relation_image(sK1,X1)),relation_image(sK1,relation_dom(sK1)))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) ) ),
inference(superposition,[status(thm)],[c_31952,c_97]) ).
tcf(c_31970,plain,
! [X0: $i,X1: $i] :
( ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ empty(relation_image(sK1,relation_dom(sK1))) ),
inference(superposition,[status(thm)],[c_31952,c_95]) ).
tcf(c_31974,plain,
! [X0: $i] :
( in(sK2(sK1,X0,empty_set),relation_image(sK1,relation_dom(sK1)))
| ( relation_image(sK1,X0) = empty_set )
| ( apply(sK1,sK3(sK1,X0,empty_set)) = sK2(sK1,X0,empty_set) ) ),
inference(light_normalisation,[status(thm)],[c_31966,c_23326]) ).
tcf(c_31984,plain,
! [X0: $i,X1: $i] :
( ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1)))) = sK2(sK1,X0,relation_image(sK1,X1)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_31967,c_52,c_51]) ).
tcf(c_31999,plain,
! [X0: $i] :
( ( relation_image(sK1,X0) = relation_image(sK1,empty_set) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,empty_set))) = sK2(sK1,X0,relation_image(sK1,empty_set)) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK2(sK1,X0,empty_set))) = sK2(sK1,X0,empty_set) ) ),
inference(superposition,[status(thm)],[c_23326,c_31984]) ).
tcf(c_32000,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(sK1,X2) = X3 )
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(sK2(sK1,X2,X3),X3)
| ~ in(sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1))),X2)
| ~ in(sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1))),relation_dom(sK1))
| ( sK2(sK1,X0,relation_image(sK1,X1)) != sK2(sK1,X2,X3) ) ),
inference(superposition,[status(thm)],[c_31984,c_53]) ).
tcf(c_32001,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(sK1,X0,relation_image(sK1,X1)),relation_image(sK1,X2))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1))),X2)
| ~ in(sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_31984,c_57]) ).
tcf(c_32003,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1))),relation_inverse_image(sK1,X2))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),X2)
| ~ in(sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_31984,c_70]) ).
tcf(c_32004,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ( sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1))) = X2 )
| ~ function(sK1)
| ~ relation(sK1)
| ~ one_to_one(sK1)
| ~ in(X2,relation_dom(sK1))
| ~ in(sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1))),relation_dom(sK1))
| ( sK2(sK1,X0,relation_image(sK1,X1)) != apply(sK1,X2) ) ),
inference(superposition,[status(thm)],[c_31984,c_85]) ).
tcf(c_32005,plain,
! [X0: $i] :
( ( relation_image(sK1,X0) = empty_set )
| ( apply(sK1,sK3(sK1,X0,empty_set)) = sK2(sK1,X0,empty_set) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK2(sK1,X0,empty_set))) = sK2(sK1,X0,empty_set) ) ),
inference(light_normalisation,[status(thm)],[c_31999,c_23326]) ).
tcf(c_32009,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1))),relation_inverse_image(sK1,X2))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),X2)
| ~ in(sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1))),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_32003,c_52,c_51]) ).
tcf(c_32015,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(sK1,X0,relation_image(sK1,X1)),relation_image(sK1,X2))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ in(sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1))),X2)
| ~ in(sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1))),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_32001,c_52,c_51]) ).
tcf(c_32021,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ( sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1))) = X2 )
| ~ in(X2,relation_dom(sK1))
| ~ in(sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1))),relation_dom(sK1))
| ( sK2(sK1,X0,relation_image(sK1,X1)) != apply(sK1,X2) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_32004,c_52,c_51,c_50]) ).
tcf(c_32028,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(sK1,X2) = X3 )
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ in(sK2(sK1,X2,X3),X3)
| ~ in(sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1))),X2)
| ~ in(sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1))),relation_dom(sK1))
| ( sK2(sK1,X0,relation_image(sK1,X1)) != sK2(sK1,X2,X3) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_32000,c_52,c_51]) ).
tcf(c_32105,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(empty_set,X0) = X1 )
| ( relation_image(sK1,X2) = empty_set )
| ( apply(sK1,sK3(sK1,X2,empty_set)) = sK2(sK1,X2,empty_set) )
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ in(sK2(empty_set,X0,X1),X1)
| ~ in(sK4(empty_set,X3,sK2(sK1,X2,empty_set)),X0)
| ~ in(sK4(empty_set,X3,sK2(sK1,X2,empty_set)),relation_dom(empty_set))
| ( sK2(empty_set,X0,X1) != sK2(sK1,X2,empty_set) ) ),
inference(superposition,[status(thm)],[c_31500,c_53]) ).
tcf(c_32106,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(sK1,X1,empty_set),relation_image(empty_set,X2))
| ( relation_image(sK1,X1) = empty_set )
| ( apply(sK1,sK3(sK1,X1,empty_set)) = sK2(sK1,X1,empty_set) )
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ in(sK4(empty_set,X0,sK2(sK1,X1,empty_set)),X2)
| ~ in(sK4(empty_set,X0,sK2(sK1,X1,empty_set)),relation_dom(empty_set)) ),
inference(superposition,[status(thm)],[c_31500,c_57]) ).
tcf(c_32108,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK4(empty_set,X0,sK2(sK1,X1,empty_set)),relation_inverse_image(empty_set,X2))
| ( relation_image(sK1,X1) = empty_set )
| ( apply(sK1,sK3(sK1,X1,empty_set)) = sK2(sK1,X1,empty_set) )
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ in(sK2(sK1,X1,empty_set),X2)
| ~ in(sK4(empty_set,X0,sK2(sK1,X1,empty_set)),relation_dom(empty_set)) ),
inference(superposition,[status(thm)],[c_31500,c_70]) ).
tcf(c_32109,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK1,X0) = empty_set )
| ( apply(sK1,sK3(sK1,X0,empty_set)) = sK2(sK1,X0,empty_set) )
| ( sK4(empty_set,X2,sK2(sK1,X0,empty_set)) = X1 )
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ one_to_one(empty_set)
| ~ in(X1,relation_dom(empty_set))
| ~ in(sK4(empty_set,X2,sK2(sK1,X0,empty_set)),relation_dom(empty_set))
| ( sK2(sK1,X0,empty_set) != apply(empty_set,X1) ) ),
inference(superposition,[status(thm)],[c_31500,c_85]) ).
tcf(c_32110,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK4(empty_set,X0,sK2(sK1,X1,empty_set)),relation_inverse_image(empty_set,X2))
| ( relation_image(sK1,X1) = empty_set )
| ( apply(sK1,sK3(sK1,X1,empty_set)) = sK2(sK1,X1,empty_set) )
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ in(sK2(sK1,X1,empty_set),X2)
| ~ in(sK4(empty_set,X0,sK2(sK1,X1,empty_set)),empty_set) ),
inference(light_normalisation,[status(thm)],[c_32108,c_12551]) ).
tcf(c_32111,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(sK1,X1,empty_set),relation_image(empty_set,X2))
| ( relation_image(sK1,X1) = empty_set )
| ( apply(sK1,sK3(sK1,X1,empty_set)) = sK2(sK1,X1,empty_set) )
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ in(sK4(empty_set,X0,sK2(sK1,X1,empty_set)),empty_set)
| ~ in(sK4(empty_set,X0,sK2(sK1,X1,empty_set)),X2) ),
inference(light_normalisation,[status(thm)],[c_32106,c_12551]) ).
tcf(c_32112,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK1,X0) = empty_set )
| ( apply(sK1,sK3(sK1,X0,empty_set)) = sK2(sK1,X0,empty_set) )
| ( sK4(empty_set,X2,sK2(sK1,X0,empty_set)) = X1 )
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ one_to_one(empty_set)
| ~ in(X1,empty_set)
| ~ in(sK4(empty_set,X2,sK2(sK1,X0,empty_set)),empty_set)
| ( sK2(sK1,X0,empty_set) != apply(empty_set,X1) ) ),
inference(light_normalisation,[status(thm)],[c_32109,c_12551]) ).
tcf(c_32113,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = empty_set )
| ( relation_image(sK1,X2) = empty_set )
| ( apply(sK1,sK3(sK1,X2,empty_set)) = sK2(sK1,X2,empty_set) )
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ in(sK2(empty_set,X0,X1),X1)
| ~ in(sK4(empty_set,X3,sK2(sK1,X2,empty_set)),empty_set)
| ~ in(sK4(empty_set,X3,sK2(sK1,X2,empty_set)),X0)
| ( sK2(empty_set,X0,X1) != sK2(sK1,X2,empty_set) ) ),
inference(light_normalisation,[status(thm)],[c_32105,c_12551,c_17316]) ).
tcf(c_32118,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_99,c_17763]) ).
tcf(c_32119,plain,
relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_114,c_17763]) ).
tcf(c_32120,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK18(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12738,c_17763]) ).
tcf(c_32121,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK18(powerset(sK18(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13358,c_17763]) ).
tcf(c_32122,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_image(X0,X1))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK17(relation_image(X0,X1))))) = sK18(sK17(relation_image(X0,X1))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13159,c_17763]) ).
tcf(c_32123,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_image(X0,X1))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(relation_image(X0,X1)))) = sK18(relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13157,c_17763]) ).
tcf(c_32124,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK18(powerset(relation_image(X0,X1))))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK18(powerset(relation_image(X0,X1)))))) = sK18(sK18(powerset(relation_image(X0,X1)))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13158,c_17763]) ).
tcf(c_32125,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK18(sK17(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13470,c_17763]) ).
tcf(c_32126,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK18(powerset(sK18(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13469,c_17763]) ).
tcf(c_32127,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK18(sK17(sK17(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15885,c_17763]) ).
tcf(c_32128,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK18(powerset(sK18(sK17(sK17(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15887,c_17763]) ).
tcf(c_32129,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_17175,c_17763]) ).
tcf(c_32130,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK18(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17177,c_17763]) ).
tcf(c_32131,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK18(sK17(powerset(sK18(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17880,c_17763]) ).
tcf(c_32132,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK18(sK17(powerset(sK18(sK17(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17885,c_17763]) ).
tcf(c_32133,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17888,c_17763]) ).
tcf(c_32134,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK2(empty_set,X1,powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20186,c_17763]) ).
tcf(c_32135,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK18(powerset(sK2(empty_set,X1,powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20188,c_17763]) ).
tcf(c_32136,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK18(sK17(powerset(sK2(empty_set,X1,powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20189,c_17763]) ).
tcf(c_32137,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK7(empty_set,X1,powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21299,c_17763]) ).
tcf(c_32138,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK18(powerset(sK7(empty_set,X1,powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21301,c_17763]) ).
tcf(c_32139,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK18(sK17(powerset(sK7(empty_set,X1,powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21302,c_17763]) ).
tcf(c_32140,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK18(sK17(sK17(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25683,c_17763]) ).
tcf(c_32141,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25684,c_17763]) ).
tcf(c_32224,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(sK18(powerset(relation_dom(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_99,c_17840]) ).
tcf(c_32225,plain,
sK18(powerset(relation_dom(sK18(powerset(relation_dom(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_114,c_17840]) ).
tcf(c_32226,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(sK18(powerset(relation_dom(sK18(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12738,c_17840]) ).
tcf(c_32227,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(sK18(powerset(relation_dom(sK18(powerset(sK18(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13358,c_17840]) ).
tcf(c_32228,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(relation_dom(sK18(powerset(relation_dom(relation_image(X0,X1))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK17(relation_image(X0,X1))))) = sK18(sK17(relation_image(X0,X1))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13159,c_17840]) ).
tcf(c_32229,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(relation_dom(sK18(powerset(relation_dom(relation_image(X0,X1))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(relation_image(X0,X1)))) = sK18(relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13157,c_17840]) ).
tcf(c_32230,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(relation_dom(sK18(powerset(relation_dom(sK18(powerset(relation_image(X0,X1))))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK18(powerset(relation_image(X0,X1)))))) = sK18(sK18(powerset(relation_image(X0,X1)))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13158,c_17840]) ).
tcf(c_32231,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(sK18(powerset(relation_dom(sK18(sK17(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13470,c_17840]) ).
tcf(c_32232,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(sK18(powerset(relation_dom(sK18(powerset(sK18(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13469,c_17840]) ).
tcf(c_32233,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(sK18(powerset(relation_dom(sK18(sK17(sK17(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15885,c_17840]) ).
tcf(c_32234,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(sK18(powerset(relation_dom(sK18(powerset(sK18(sK17(sK17(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15887,c_17840]) ).
tcf(c_32235,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(sK18(powerset(relation_dom(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17175,c_17840]) ).
tcf(c_32236,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(sK18(powerset(relation_dom(sK18(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17177,c_17840]) ).
tcf(c_32237,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(sK18(powerset(relation_dom(sK18(sK17(powerset(sK18(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17880,c_17840]) ).
tcf(c_32238,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(sK18(powerset(relation_dom(sK18(sK17(powerset(sK18(sK17(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17885,c_17840]) ).
tcf(c_32239,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(sK18(powerset(relation_dom(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17888,c_17840]) ).
tcf(c_32240,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(relation_dom(sK18(powerset(relation_dom(sK2(empty_set,X1,powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20186,c_17840]) ).
tcf(c_32241,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(relation_dom(sK18(powerset(relation_dom(sK18(powerset(sK2(empty_set,X1,powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20188,c_17840]) ).
tcf(c_32242,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(relation_dom(sK18(powerset(relation_dom(sK18(sK17(powerset(sK2(empty_set,X1,powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20189,c_17840]) ).
tcf(c_32243,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(relation_dom(sK18(powerset(relation_dom(sK7(empty_set,X1,powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21299,c_17840]) ).
tcf(c_32244,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(relation_dom(sK18(powerset(relation_dom(sK18(powerset(sK7(empty_set,X1,powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21301,c_17840]) ).
tcf(c_32245,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(relation_dom(sK18(powerset(relation_dom(sK18(sK17(powerset(sK7(empty_set,X1,powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21302,c_17840]) ).
tcf(c_32246,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(sK18(powerset(relation_dom(sK18(sK17(sK17(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25683,c_17840]) ).
tcf(c_32247,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(sK18(powerset(relation_dom(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25684,c_17840]) ).
tcf(c_32412,plain,
( empty(sK18(sK17(powerset(empty_set))))
| ~ in(empty_set,sK18(empty_set)) ),
inference(superposition,[status(thm)],[c_14398,c_17874]) ).
tcf(c_32418,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK18(powerset(relation_dom(relation_dom(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_99,c_18581]) ).
tcf(c_32419,plain,
relation_dom(relation_dom(sK18(powerset(relation_dom(relation_dom(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_114,c_18581]) ).
tcf(c_32420,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK18(powerset(relation_dom(relation_dom(sK18(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12738,c_18581]) ).
tcf(c_32421,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK18(powerset(relation_dom(relation_dom(sK18(powerset(sK18(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13358,c_18581]) ).
tcf(c_32422,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK18(powerset(relation_dom(relation_dom(relation_image(X0,X1))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK17(relation_image(X0,X1))))) = sK18(sK17(relation_image(X0,X1))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13159,c_18581]) ).
tcf(c_32423,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK18(powerset(relation_dom(relation_dom(relation_image(X0,X1))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(relation_image(X0,X1)))) = sK18(relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13157,c_18581]) ).
tcf(c_32424,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK18(powerset(relation_dom(relation_dom(sK18(powerset(relation_image(X0,X1))))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK18(powerset(relation_image(X0,X1)))))) = sK18(sK18(powerset(relation_image(X0,X1)))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13158,c_18581]) ).
tcf(c_32425,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK18(powerset(relation_dom(relation_dom(sK18(sK17(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13470,c_18581]) ).
tcf(c_32426,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK18(powerset(relation_dom(relation_dom(sK18(powerset(sK18(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13469,c_18581]) ).
tcf(c_32427,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK18(powerset(relation_dom(relation_dom(sK18(sK17(sK17(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15885,c_18581]) ).
tcf(c_32428,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK18(powerset(relation_dom(relation_dom(sK18(powerset(sK18(sK17(sK17(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15887,c_18581]) ).
tcf(c_32429,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK18(powerset(relation_dom(relation_dom(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17175,c_18581]) ).
tcf(c_32430,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK18(powerset(relation_dom(relation_dom(sK18(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17177,c_18581]) ).
tcf(c_32431,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK18(powerset(relation_dom(relation_dom(sK18(sK17(powerset(sK18(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17880,c_18581]) ).
tcf(c_32432,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK18(powerset(relation_dom(relation_dom(sK18(sK17(powerset(sK18(sK17(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17885,c_18581]) ).
tcf(c_32433,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK18(powerset(relation_dom(relation_dom(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17888,c_18581]) ).
tcf(c_32434,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK18(powerset(relation_dom(relation_dom(sK2(empty_set,X1,powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20186,c_18581]) ).
tcf(c_32435,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK18(powerset(relation_dom(relation_dom(sK18(powerset(sK2(empty_set,X1,powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20188,c_18581]) ).
tcf(c_32436,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK18(powerset(relation_dom(relation_dom(sK18(sK17(powerset(sK2(empty_set,X1,powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20189,c_18581]) ).
tcf(c_32437,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK18(powerset(relation_dom(relation_dom(sK7(empty_set,X1,powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21299,c_18581]) ).
tcf(c_32438,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK18(powerset(relation_dom(relation_dom(sK18(powerset(sK7(empty_set,X1,powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21301,c_18581]) ).
tcf(c_32439,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK18(powerset(relation_dom(relation_dom(sK18(sK17(powerset(sK7(empty_set,X1,powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21302,c_18581]) ).
tcf(c_32440,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK18(powerset(relation_dom(relation_dom(sK18(sK17(sK17(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25683,c_18581]) ).
tcf(c_32441,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK18(powerset(relation_dom(relation_dom(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25684,c_18581]) ).
tcf(c_32584,plain,
( ( relation_dom(relation_image(sK1,empty_set)) = empty_set )
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_52,c_17553]) ).
tcf(c_32585,plain,
( ( relation_dom(relation_image(sK6,empty_set)) = empty_set )
| ~ relation(sK6) ),
inference(superposition,[status(thm)],[c_65,c_17553]) ).
tcf(c_32586,plain,
( ( relation_dom(relation_image(sK10,empty_set)) = empty_set )
| ~ relation(sK10) ),
inference(superposition,[status(thm)],[c_79,c_17553]) ).
tcf(c_32587,plain,
! [X0: $i] :
( ( relation_dom(relation_image(relation_dom(X0),empty_set)) = empty_set )
| ~ empty(X0)
| ~ relation(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_12385,c_17553]) ).
tcf(c_32588,plain,
( ( relation_dom(relation_image(empty_set,empty_set)) = empty_set )
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_12355,c_17553]) ).
tcf(c_32589,plain,
! [X0: $i] :
( ( relation_dom(relation_image(sK18(powerset(X0)),empty_set)) = empty_set )
| ~ empty(X0)
| ~ relation(sK18(powerset(X0))) ),
inference(superposition,[status(thm)],[c_12772,c_17553]) ).
tcf(c_32590,plain,
! [X0: $i] :
( ( relation_dom(relation_image(sK18(powerset(sK18(powerset(X0)))),empty_set)) = empty_set )
| ~ empty(X0)
| ~ relation(sK18(powerset(sK18(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_13393,c_17553]) ).
tcf(c_32591,plain,
! [X0: $i] :
( ( relation_dom(relation_image(sK18(sK17(powerset(X0))),empty_set)) = empty_set )
| ~ empty(X0)
| ~ relation(sK18(sK17(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_13498,c_17553]) ).
tcf(c_32592,plain,
! [X0: $i] :
( ( relation_dom(relation_image(sK18(powerset(sK18(sK17(powerset(X0))))),empty_set)) = empty_set )
| ~ empty(X0)
| ~ relation(sK18(powerset(sK18(sK17(powerset(X0)))))) ),
inference(superposition,[status(thm)],[c_14345,c_17553]) ).
tcf(c_32593,plain,
! [X0: $i] :
( ( relation_dom(relation_image(sK18(sK17(sK17(powerset(X0)))),empty_set)) = empty_set )
| ~ empty(X0)
| ~ relation(sK18(sK17(sK17(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_15976,c_17553]) ).
tcf(c_32594,plain,
! [X0: $i] :
( ( relation_dom(relation_image(sK18(powerset(sK18(sK17(sK17(powerset(X0)))))),empty_set)) = empty_set )
| ~ empty(X0)
| ~ relation(sK18(powerset(sK18(sK17(sK17(powerset(X0))))))) ),
inference(superposition,[status(thm)],[c_16543,c_17553]) ).
tcf(c_32595,plain,
! [X0: $i] :
( ( relation_dom(relation_image(relation_image(X0,empty_set),empty_set)) = empty_set )
| ~ function(X0)
| ~ relation(X0)
| ~ relation(relation_image(X0,empty_set)) ),
inference(superposition,[status(thm)],[c_17557,c_17553]) ).
tcf(c_32596,plain,
! [X0: $i] :
( ( relation_dom(relation_image(sK18(sK17(powerset(sK18(powerset(X0))))),empty_set)) = empty_set )
| ~ empty(X0)
| ~ relation(sK18(sK17(powerset(sK18(powerset(X0)))))) ),
inference(superposition,[status(thm)],[c_18126,c_17553]) ).
tcf(c_32597,plain,
! [X0: $i] :
( ( relation_dom(relation_image(sK18(sK17(powerset(sK18(sK17(powerset(X0)))))),empty_set)) = empty_set )
| ~ empty(X0)
| ~ relation(sK18(sK17(powerset(sK18(sK17(powerset(X0))))))) ),
inference(superposition,[status(thm)],[c_18310,c_17553]) ).
tcf(c_32598,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_image(sK2(empty_set,X0,powerset(X1)),empty_set)) = empty_set )
| ~ empty(X1)
| ~ relation(sK2(empty_set,X0,powerset(X1))) ),
inference(superposition,[status(thm)],[c_20341,c_17553]) ).
tcf(c_32599,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_image(sK18(powerset(sK2(empty_set,X0,powerset(X1)))),empty_set)) = empty_set )
| ~ empty(X1)
| ~ relation(sK18(powerset(sK2(empty_set,X0,powerset(X1))))) ),
inference(superposition,[status(thm)],[c_20631,c_17553]) ).
tcf(c_32600,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_image(sK7(empty_set,X0,powerset(X1)),empty_set)) = empty_set )
| ~ empty(X1)
| ~ relation(sK7(empty_set,X0,powerset(X1))) ),
inference(superposition,[status(thm)],[c_21433,c_17553]) ).
tcf(c_32601,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_image(sK18(powerset(sK7(empty_set,X0,powerset(X1)))),empty_set)) = empty_set )
| ~ empty(X1)
| ~ relation(sK18(powerset(sK7(empty_set,X0,powerset(X1))))) ),
inference(superposition,[status(thm)],[c_21807,c_17553]) ).
tcf(c_32602,plain,
! [X0: $i] :
( ( relation_dom(relation_image(sK18(powerset(relation_image(X0,empty_set))),empty_set)) = empty_set )
| ~ function(X0)
| ~ relation(X0)
| ~ relation(sK18(powerset(relation_image(X0,empty_set)))) ),
inference(superposition,[status(thm)],[c_23555,c_17553]) ).
tcf(c_32603,plain,
! [X0: $i] :
( ( relation_dom(relation_image(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0))))))),empty_set)) = empty_set )
| ~ empty(X0)
| ~ relation(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0)))))))) ),
inference(superposition,[status(thm)],[c_23841,c_17553]) ).
tcf(c_32604,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_image(sK18(sK17(powerset(sK2(empty_set,X0,powerset(X1))))),empty_set)) = empty_set )
| ~ empty(X1)
| ~ relation(sK18(sK17(powerset(sK2(empty_set,X0,powerset(X1)))))) ),
inference(superposition,[status(thm)],[c_24108,c_17553]) ).
tcf(c_32605,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_image(sK18(sK17(powerset(sK7(empty_set,X0,powerset(X1))))),empty_set)) = empty_set )
| ~ empty(X1)
| ~ relation(sK18(sK17(powerset(sK7(empty_set,X0,powerset(X1)))))) ),
inference(superposition,[status(thm)],[c_25110,c_17553]) ).
tcf(c_32606,plain,
! [X0: $i] :
( ( relation_dom(relation_image(sK18(sK17(sK17(sK17(powerset(X0))))),empty_set)) = empty_set )
| ~ empty(X0)
| ~ relation(sK18(sK17(sK17(sK17(powerset(X0)))))) ),
inference(superposition,[status(thm)],[c_25864,c_17553]) ).
tcf(c_32607,plain,
! [X0: $i] :
( ( relation_dom(relation_image(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0))))))),empty_set)) = empty_set )
| ~ empty(X0)
| ~ relation(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0)))))))) ),
inference(superposition,[status(thm)],[c_26699,c_17553]) ).
tcf(c_32608,plain,
relation_dom(relation_image(empty_set,empty_set)) = empty_set,
inference(forward_subsumption_resolution,[status(thm)],[c_32588,c_113]) ).
tcf(c_32700,plain,
( empty(sK18(sK17(powerset(empty_set))))
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_17316,c_17883]) ).
tcf(c_32701,plain,
( empty(sK18(sK17(powerset(empty_set))))
| ~ function(sK1)
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_23326,c_17883]) ).
tcf(c_32702,plain,
( empty(sK18(sK17(powerset(empty_set))))
| ~ function(sK6)
| ~ relation(sK6) ),
inference(superposition,[status(thm)],[c_23325,c_17883]) ).
tcf(c_32703,plain,
( empty(sK18(sK17(powerset(empty_set))))
| ~ function(sK10)
| ~ relation(sK10) ),
inference(superposition,[status(thm)],[c_23324,c_17883]) ).
tcf(c_32704,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK18(powerset(relation_dom(relation_dom(sK18(sK17(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17883,c_18581]) ).
tcf(c_32705,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(sK18(powerset(relation_dom(sK18(sK17(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17883,c_17840]) ).
tcf(c_32706,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK18(sK17(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17883,c_17763]) ).
tcf(c_32707,plain,
! [X0: $i] :
( ( sK18(sK17(sK17(powerset(sK18(powerset(sK18(sK17(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17883,c_16289]) ).
tcf(c_32708,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK18(sK17(sK17(powerset(sK18(sK17(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17883,c_15970]) ).
tcf(c_32709,plain,
! [X0: $i] :
( ( sK18(powerset(sK18(sK17(sK17(powerset(sK18(sK17(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17883,c_15968]) ).
tcf(c_32710,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(sK18(sK17(powerset(relation_image(X0,empty_set))))))) = X1 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17883,c_17487]) ).
tcf(c_32711,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(sK18(powerset(relation_dom(sK18(sK17(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17883,c_16986]) ).
tcf(c_32712,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(relation_dom(sK18(sK17(powerset(relation_image(X0,empty_set))))))) = X1 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17883,c_16879]) ).
tcf(c_32713,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK18(powerset(relation_dom(sK18(sK17(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17883,c_16852]) ).
tcf(c_32714,plain,
! [X0: $i] :
( ( relation_dom(sK18(sK17(powerset(sK18(powerset(sK18(sK17(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17883,c_15718]) ).
tcf(c_32715,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(relation_dom(sK18(powerset(sK18(sK17(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17883,c_15590]) ).
tcf(c_32716,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(relation_dom(sK18(powerset(sK18(sK17(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17883,c_15555]) ).
tcf(c_32717,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(relation_dom(sK18(powerset(sK18(sK17(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17883,c_15529]) ).
tcf(c_32718,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK18(powerset(sK18(sK17(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17883,c_15263]) ).
tcf(c_32719,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(powerset(sK18(sK17(powerset(relation_image(X0,empty_set))))))) = X1 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17883,c_15232]) ).
tcf(c_32720,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(sK18(sK17(powerset(sK18(sK17(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17883,c_14401]) ).
tcf(c_32721,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK18(sK17(powerset(sK18(sK17(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17883,c_13491]) ).
tcf(c_32722,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(sK18(sK17(powerset(sK18(sK17(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17883,c_13489]) ).
tcf(c_32723,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(sK18(sK17(powerset(sK18(sK17(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17883,c_13488]) ).
tcf(c_32724,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK18(powerset(sK18(powerset(sK18(sK17(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17883,c_13387]) ).
tcf(c_32725,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(powerset(sK18(sK17(powerset(relation_image(X0,empty_set))))))) = X1 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17883,c_13493]) ).
tcf(c_32726,plain,
! [X0: $i] :
( ( sK18(powerset(sK18(powerset(sK18(powerset(sK18(sK17(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17883,c_13385]) ).
tcf(c_32727,plain,
! [X0: $i] :
( ( sK18(sK17(sK17(sK17(powerset(sK18(sK17(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17883,c_25685]) ).
tcf(c_32728,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK7(empty_set,X1,powerset(sK18(sK17(powerset(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17883,c_21429]) ).
tcf(c_32729,plain,
! [X0: $i,X1: $i] :
( ( sK7(empty_set,X1,powerset(relation_dom(sK18(sK17(powerset(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17883,c_21941]) ).
tcf(c_32730,plain,
! [X0: $i,X1: $i] :
( ( sK2(empty_set,X1,powerset(relation_dom(sK18(sK17(powerset(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17883,c_21015]) ).
tcf(c_32731,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK2(empty_set,X1,powerset(sK18(sK17(powerset(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17883,c_20337]) ).
tcf(c_32732,plain,
! [X0: $i] :
( ( sK18(sK17(sK17(powerset(relation_dom(sK18(sK17(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17883,c_16287]) ).
tcf(c_32733,plain,
! [X0: $i] :
( ( relation_dom(sK18(sK17(sK17(powerset(sK18(sK17(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17883,c_15972]) ).
tcf(c_32734,plain,
! [X0: $i] :
( ( relation_dom(sK18(sK17(powerset(relation_dom(sK18(sK17(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17883,c_15716]) ).
tcf(c_32735,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(sK18(powerset(sK18(sK17(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17883,c_14399]) ).
tcf(c_32736,plain,
! [X0: $i,X1: $i] :
( ( sK7(empty_set,X1,powerset(sK18(sK17(powerset(relation_image(X0,empty_set)))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17883,c_21303]) ).
tcf(c_32737,plain,
! [X0: $i,X1: $i] :
( ( sK2(empty_set,X1,powerset(sK18(sK17(powerset(relation_image(X0,empty_set)))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17883,c_20190]) ).
tcf(c_32738,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(relation_dom(relation_dom(sK18(sK17(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17883,c_15588]) ).
tcf(c_32739,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(relation_dom(relation_dom(sK18(sK17(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17883,c_15553]) ).
tcf(c_32740,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK18(sK17(powerset(sK18(sK17(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17883,c_13492]) ).
tcf(c_32741,plain,
! [X0: $i] :
( ( sK18(powerset(sK18(sK17(powerset(sK18(sK17(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17883,c_13490]) ).
tcf(c_32742,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(relation_dom(relation_dom(sK18(sK17(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17883,c_15527]) ).
tcf(c_32743,plain,
! [X0: $i] :
( ( sK18(powerset(sK18(powerset(relation_dom(sK18(sK17(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17883,c_15355]) ).
tcf(c_32744,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK18(powerset(relation_dom(sK18(sK17(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17883,c_15317]) ).
tcf(c_32745,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(sK18(powerset(sK18(sK17(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17883,c_13260]) ).
tcf(c_32746,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK18(sK17(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17883,c_15261]) ).
tcf(c_32747,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK18(sK17(powerset(relation_image(X0,empty_set)))))) = X1 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17883,c_15230]) ).
tcf(c_32748,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(sK18(powerset(sK18(sK17(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17883,c_13064]) ).
tcf(c_32749,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK18(sK17(powerset(relation_image(X0,empty_set)))))) = X1 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17883,c_12767]) ).
tcf(c_32750,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK18(powerset(sK18(sK17(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17883,c_12765]) ).
tcf(c_32751,plain,
! [X0: $i] :
( ( sK18(sK17(sK17(powerset(sK18(sK17(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17883,c_15973]) ).
tcf(c_32752,plain,
! [X0: $i] :
( ( relation_dom(sK18(sK17(powerset(sK18(sK17(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17883,c_13494]) ).
tcf(c_32753,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(relation_dom(sK18(sK17(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17883,c_14397]) ).
tcf(c_32754,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(relation_dom(sK18(sK17(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17883,c_13258]) ).
tcf(c_32755,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(relation_dom(sK18(sK17(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17883,c_13062]) ).
tcf(c_32756,plain,
! [X0: $i] :
( ( sK18(powerset(sK18(powerset(sK18(sK17(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17883,c_12959]) ).
tcf(c_32757,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK18(powerset(sK18(sK17(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17883,c_12766]) ).
tcf(c_32758,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK18(sK17(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17883,c_12718]) ).
tcf(c_32759,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(sK17(powerset(relation_image(X0,empty_set))))) = X1 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17883,c_12604]) ).
tcf(c_32769,plain,
! [X0: $i] :
( one_to_one(sK18(sK17(powerset(relation_image(X0,empty_set)))))
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17883,c_5773]) ).
tcf(c_32770,plain,
! [X0: $i] :
( relation(sK18(sK17(powerset(relation_image(X0,empty_set)))))
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17883,c_77]) ).
tcf(c_32771,plain,
! [X0: $i] :
( function(sK18(sK17(powerset(relation_image(X0,empty_set)))))
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17883,c_66]) ).
tcf(c_33199,plain,
! [X0: $i] :
( ( sK18(powerset(sK18(powerset(relation_dom(relation_dom(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_99,c_18628]) ).
tcf(c_33200,plain,
sK18(powerset(sK18(powerset(relation_dom(relation_dom(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_114,c_18628]) ).
tcf(c_33201,plain,
! [X0: $i] :
( ( sK18(powerset(sK18(powerset(relation_dom(relation_dom(sK18(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12738,c_18628]) ).
tcf(c_33202,plain,
! [X0: $i] :
( ( sK18(powerset(sK18(powerset(relation_dom(relation_dom(sK18(powerset(sK18(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13358,c_18628]) ).
tcf(c_33203,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK18(powerset(relation_dom(relation_dom(relation_image(X0,X1))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK17(relation_image(X0,X1))))) = sK18(sK17(relation_image(X0,X1))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13159,c_18628]) ).
tcf(c_33204,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK18(powerset(relation_dom(relation_dom(relation_image(X0,X1))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(relation_image(X0,X1)))) = sK18(relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13157,c_18628]) ).
tcf(c_33205,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK18(powerset(relation_dom(relation_dom(sK18(powerset(relation_image(X0,X1))))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK18(powerset(relation_image(X0,X1)))))) = sK18(sK18(powerset(relation_image(X0,X1)))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13158,c_18628]) ).
tcf(c_33206,plain,
! [X0: $i] :
( ( sK18(powerset(sK18(powerset(relation_dom(relation_dom(sK18(sK17(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13470,c_18628]) ).
tcf(c_33207,plain,
! [X0: $i] :
( ( sK18(powerset(sK18(powerset(relation_dom(relation_dom(sK18(powerset(sK18(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13469,c_18628]) ).
tcf(c_33208,plain,
! [X0: $i] :
( ( sK18(powerset(sK18(powerset(relation_dom(relation_dom(sK18(sK17(sK17(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15885,c_18628]) ).
tcf(c_33209,plain,
! [X0: $i] :
( ( sK18(powerset(sK18(powerset(relation_dom(relation_dom(sK18(powerset(sK18(sK17(sK17(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15887,c_18628]) ).
tcf(c_33210,plain,
! [X0: $i] :
( ( sK18(powerset(sK18(powerset(relation_dom(relation_dom(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17175,c_18628]) ).
tcf(c_33211,plain,
! [X0: $i] :
( ( sK18(powerset(sK18(powerset(relation_dom(relation_dom(sK18(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17177,c_18628]) ).
tcf(c_33212,plain,
! [X0: $i] :
( ( sK18(powerset(sK18(powerset(relation_dom(relation_dom(sK18(sK17(powerset(sK18(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17880,c_18628]) ).
tcf(c_33213,plain,
! [X0: $i] :
( ( sK18(powerset(sK18(powerset(relation_dom(relation_dom(sK18(sK17(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17883,c_18628]) ).
tcf(c_33214,plain,
! [X0: $i] :
( ( sK18(powerset(sK18(powerset(relation_dom(relation_dom(sK18(sK17(powerset(sK18(sK17(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17885,c_18628]) ).
tcf(c_33215,plain,
! [X0: $i] :
( ( sK18(powerset(sK18(powerset(relation_dom(relation_dom(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17888,c_18628]) ).
tcf(c_33216,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK18(powerset(relation_dom(relation_dom(sK2(empty_set,X1,powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20186,c_18628]) ).
tcf(c_33217,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK18(powerset(relation_dom(relation_dom(sK18(powerset(sK2(empty_set,X1,powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20188,c_18628]) ).
tcf(c_33218,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK18(powerset(relation_dom(relation_dom(sK18(sK17(powerset(sK2(empty_set,X1,powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20189,c_18628]) ).
tcf(c_33219,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK18(powerset(relation_dom(relation_dom(sK7(empty_set,X1,powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21299,c_18628]) ).
tcf(c_33220,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK18(powerset(relation_dom(relation_dom(sK18(powerset(sK7(empty_set,X1,powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21301,c_18628]) ).
tcf(c_33221,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK18(powerset(relation_dom(relation_dom(sK18(sK17(powerset(sK7(empty_set,X1,powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21302,c_18628]) ).
tcf(c_33222,plain,
! [X0: $i] :
( ( sK18(powerset(sK18(powerset(relation_dom(relation_dom(sK18(sK17(sK17(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25683,c_18628]) ).
tcf(c_33223,plain,
! [X0: $i] :
( ( sK18(powerset(sK18(powerset(relation_dom(relation_dom(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25684,c_18628]) ).
tcf(c_33335,plain,
! [X0: $i,X1: $i] :
( in(apply(sK1,sK4(sK1,empty_set,sK2(sK1,X0,empty_set))),X1)
| ( relation_image(sK1,X0) = relation_image(sK1,empty_set) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,empty_set))) = sK2(sK1,X0,relation_image(sK1,empty_set)) )
| ~ in(sK2(sK1,X0,relation_image(sK1,empty_set)),X1)
| ~ in(sK4(sK1,empty_set,sK2(sK1,X0,relation_image(sK1,empty_set))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_23326,c_31860]) ).
tcf(c_33336,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X0))) = sK2(sK1,X1,relation_image(sK1,X0)) )
| ( apply(X2,sK4(X2,X3,apply(sK1,sK4(sK1,X0,sK2(sK1,X1,relation_image(sK1,X0)))))) = apply(sK1,sK4(sK1,X0,sK2(sK1,X1,relation_image(sK1,X0)))) )
| ~ function(X2)
| ~ relation(X2)
| ~ in(sK2(sK1,X1,relation_image(sK1,X0)),relation_image(X2,X3))
| ~ in(sK4(sK1,X0,sK2(sK1,X1,relation_image(sK1,X0))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_31860,c_60]) ).
tcf(c_33338,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X2,apply(sK1,sK4(sK1,X0,sK2(sK1,X1,relation_image(sK1,X0))))),X3)
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X0))) = sK2(sK1,X1,relation_image(sK1,X0)) )
| ~ function(X2)
| ~ relation(X2)
| ~ in(sK2(sK1,X1,relation_image(sK1,X0)),relation_inverse_image(X2,X3))
| ~ in(sK4(sK1,X0,sK2(sK1,X1,relation_image(sK1,X0))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_31860,c_72]) ).
tcf(c_33339,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(sK1,sK4(sK1,X0,sK2(sK1,X1,relation_image(sK1,X0)))),relation_dom(X2))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X0))) = sK2(sK1,X1,relation_image(sK1,X0)) )
| ~ function(X2)
| ~ relation(X2)
| ~ in(sK2(sK1,X1,relation_image(sK1,X0)),relation_inverse_image(X2,X3))
| ~ in(sK4(sK1,X0,sK2(sK1,X1,relation_image(sK1,X0))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_31860,c_71]) ).
tcf(c_33340,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK1,X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK3(sK1,X2,relation_image(sK1,X1))) = sK2(sK1,X2,relation_image(sK1,X1)) )
| ~ in(sK2(sK1,X2,relation_image(sK1,X1)),X0)
| ~ in(sK4(sK1,X1,sK2(sK1,X2,relation_image(sK1,X1))),relation_dom(sK1))
| ~ in(X0,apply(sK1,sK4(sK1,X1,sK2(sK1,X2,relation_image(sK1,X1))))) ),
inference(superposition,[status(thm)],[c_31860,c_98]) ).
tcf(c_33341,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(apply(sK1,sK4(sK1,X0,sK2(sK1,X1,relation_image(sK1,X0)))),X2)
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X0))) = sK2(sK1,X1,relation_image(sK1,X0)) )
| ~ in(sK2(sK1,X1,relation_image(sK1,X0)),X2)
| ~ in(sK4(sK1,X0,sK2(sK1,X1,relation_image(sK1,X0))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_31860,c_97]) ).
tcf(c_33342,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X0))) = sK2(sK1,X1,relation_image(sK1,X0)) )
| ~ empty(X2)
| ~ in(sK2(sK1,X1,relation_image(sK1,X0)),X2)
| ~ in(sK4(sK1,X0,sK2(sK1,X1,relation_image(sK1,X0))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_31860,c_95]) ).
tcf(c_33343,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(apply(sK1,sK4(sK1,X1,sK2(sK1,X0,relation_image(sK1,X1)))),X2)
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ in(sK4(sK1,X1,sK2(sK1,X0,relation_image(sK1,X1))),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK13(apply(sK1,sK4(sK1,X1,sK2(sK1,X0,relation_image(sK1,X1)))),X2)) ),
inference(superposition,[status(thm)],[c_31860,c_12485]) ).
tcf(c_33344,plain,
! [X0: $i,X1: $i] :
( empty(apply(sK1,sK4(sK1,X1,sK2(sK1,X0,relation_image(sK1,X1)))))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ in(sK4(sK1,X1,sK2(sK1,X0,relation_image(sK1,X1))),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK18(apply(sK1,sK4(sK1,X1,sK2(sK1,X0,relation_image(sK1,X1)))))) ),
inference(superposition,[status(thm)],[c_31860,c_12526]) ).
tcf(c_33345,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X2)
| element(apply(sK1,sK4(sK1,X0,sK2(sK1,X1,relation_image(sK1,X0)))),X2)
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X0))) = sK2(sK1,X1,relation_image(sK1,X0)) )
| ~ in(sK2(sK1,X1,relation_image(sK1,X0)),sK17(X2))
| ~ in(sK4(sK1,X0,sK2(sK1,X1,relation_image(sK1,X0))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_31860,c_14688]) ).
tcf(c_33346,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X2)
| in(apply(sK1,sK4(sK1,X0,sK2(sK1,X1,relation_image(sK1,X0)))),X2)
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X0))) = sK2(sK1,X1,relation_image(sK1,X0)) )
| ~ in(sK2(sK1,X1,relation_image(sK1,X0)),sK17(X2))
| ~ in(sK4(sK1,X0,sK2(sK1,X1,relation_image(sK1,X0))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_31860,c_12618]) ).
tcf(c_33347,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(apply(sK1,sK4(sK1,X0,sK2(sK1,X1,relation_image(sK1,X0)))),X2)
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X0))) = sK2(sK1,X1,relation_image(sK1,X0)) )
| ~ in(sK2(sK1,X1,relation_image(sK1,X0)),sK18(powerset(X2)))
| ~ in(sK4(sK1,X0,sK2(sK1,X1,relation_image(sK1,X0))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_31860,c_14689]) ).
tcf(c_33348,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X0))) = sK2(sK1,X1,relation_image(sK1,X0)) )
| ~ empty(X2)
| ~ in(sK2(sK1,X1,relation_image(sK1,X0)),sK18(powerset(X2)))
| ~ in(sK4(sK1,X0,sK2(sK1,X1,relation_image(sK1,X0))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_31860,c_13313]) ).
tcf(c_33349,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(sK1,sK4(sK1,X0,sK2(sK1,X1,relation_image(sK1,X0)))),X2)
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X0))) = sK2(sK1,X1,relation_image(sK1,X0)) )
| ~ in(sK2(sK1,X1,relation_image(sK1,X0)),sK18(powerset(X2)))
| ~ in(sK4(sK1,X0,sK2(sK1,X1,relation_image(sK1,X0))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_31860,c_12619]) ).
tcf(c_33350,plain,
! [X0: $i,X1: $i] :
( ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X0))) = sK2(sK1,X1,relation_image(sK1,X0)) )
| ~ in(sK2(sK1,X1,relation_image(sK1,X0)),empty_set)
| ~ in(sK4(sK1,X0,sK2(sK1,X1,relation_image(sK1,X0))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_31860,c_13338]) ).
tcf(c_33351,plain,
! [X0: $i,X1: $i] :
( empty(sK18(powerset(apply(sK1,sK4(sK1,X1,sK2(sK1,X0,relation_image(sK1,X1)))))))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ in(sK4(sK1,X1,sK2(sK1,X0,relation_image(sK1,X1))),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK18(sK18(powerset(apply(sK1,sK4(sK1,X1,sK2(sK1,X0,relation_image(sK1,X1)))))))) ),
inference(superposition,[status(thm)],[c_31860,c_12736]) ).
tcf(c_33352,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X0))) = sK2(sK1,X1,relation_image(sK1,X0)) )
| ~ function(X2)
| ~ relation(X2)
| ~ in(sK2(sK1,X1,relation_image(sK1,X0)),relation_image(X2,empty_set))
| ~ in(sK4(sK1,X0,sK2(sK1,X1,relation_image(sK1,X0))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_31860,c_13341]) ).
tcf(c_33353,plain,
! [X0: $i,X1: $i] :
( empty(apply(sK1,sK4(sK1,X1,sK2(sK1,X0,relation_image(sK1,X1)))))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ in(sK4(sK1,X1,sK2(sK1,X0,relation_image(sK1,X1))),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK18(sK17(apply(sK1,sK4(sK1,X1,sK2(sK1,X0,relation_image(sK1,X1))))))) ),
inference(superposition,[status(thm)],[c_31860,c_12990]) ).
tcf(c_33354,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(apply(sK1,sK4(sK1,X0,sK2(sK1,X1,relation_image(sK1,X0)))),X2)
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X0))) = sK2(sK1,X1,relation_image(sK1,X0)) )
| ~ in(sK2(sK1,X1,relation_image(sK1,X0)),sK18(sK17(powerset(X2))))
| ~ in(sK4(sK1,X0,sK2(sK1,X1,relation_image(sK1,X0))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_31860,c_14693]) ).
tcf(c_33355,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X0))) = sK2(sK1,X1,relation_image(sK1,X0)) )
| ~ empty(X2)
| ~ in(sK2(sK1,X1,relation_image(sK1,X0)),sK18(sK17(powerset(X2))))
| ~ in(sK4(sK1,X0,sK2(sK1,X1,relation_image(sK1,X0))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_31860,c_13316]) ).
tcf(c_33356,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(sK1,sK4(sK1,X0,sK2(sK1,X1,relation_image(sK1,X0)))),X2)
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X0))) = sK2(sK1,X1,relation_image(sK1,X0)) )
| ~ in(sK2(sK1,X1,relation_image(sK1,X0)),sK18(sK17(powerset(X2))))
| ~ in(sK4(sK1,X0,sK2(sK1,X1,relation_image(sK1,X0))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_31860,c_13032]) ).
tcf(c_33357,plain,
! [X0: $i,X1: $i] :
( empty(apply(sK1,sK4(sK1,X1,sK2(sK1,X0,relation_image(sK1,X1)))))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ in(sK4(sK1,X1,sK2(sK1,X0,relation_image(sK1,X1))),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK18(sK17(sK17(apply(sK1,sK4(sK1,X1,sK2(sK1,X0,relation_image(sK1,X1)))))))) ),
inference(superposition,[status(thm)],[c_31860,c_15381]) ).
tcf(c_33358,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(sK1,sK4(sK1,X0,sK2(sK1,X1,relation_image(sK1,X0)))),X2)
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X0))) = sK2(sK1,X1,relation_image(sK1,X0)) )
| ~ in(sK2(sK1,X1,relation_image(sK1,X0)),sK18(sK17(sK17(powerset(X2)))))
| ~ in(sK4(sK1,X0,sK2(sK1,X1,relation_image(sK1,X0))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_31860,c_15478]) ).
tcf(c_33359,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X0))) = sK2(sK1,X1,relation_image(sK1,X0)) )
| ~ empty(X2)
| ~ in(sK2(sK1,X1,relation_image(sK1,X0)),sK18(sK17(sK17(powerset(X2)))))
| ~ in(sK4(sK1,X0,sK2(sK1,X1,relation_image(sK1,X0))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_31860,c_15477]) ).
tcf(c_33360,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(apply(sK1,sK4(sK1,X0,sK2(sK1,X1,relation_image(sK1,X0)))),X2)
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X0))) = sK2(sK1,X1,relation_image(sK1,X0)) )
| ~ in(sK2(sK1,X1,relation_image(sK1,X0)),sK18(sK17(sK17(powerset(X2)))))
| ~ in(sK4(sK1,X0,sK2(sK1,X1,relation_image(sK1,X0))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_31860,c_15476]) ).
tcf(c_33361,plain,
! [X0: $i,X1: $i] :
( empty(sK18(powerset(apply(sK1,sK4(sK1,X1,sK2(sK1,X0,relation_image(sK1,X1)))))))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ in(sK4(sK1,X1,sK2(sK1,X0,relation_image(sK1,X1))),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK18(sK17(sK18(powerset(apply(sK1,sK4(sK1,X1,sK2(sK1,X0,relation_image(sK1,X1))))))))) ),
inference(superposition,[status(thm)],[c_31860,c_15649]) ).
tcf(c_33362,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK18(powerset(apply(sK1,sK4(sK1,X1,sK2(sK1,X0,relation_image(sK1,X1)))))),X2)
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ in(sK4(sK1,X1,sK2(sK1,X0,relation_image(sK1,X1))),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK13(sK18(powerset(apply(sK1,sK4(sK1,X1,sK2(sK1,X0,relation_image(sK1,X1)))))),X2)) ),
inference(superposition,[status(thm)],[c_31860,c_16394]) ).
tcf(c_33363,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(apply(sK1,sK4(sK1,X1,sK2(sK1,X0,relation_image(sK1,X1)))))
| subset(sK17(apply(sK1,sK4(sK1,X1,sK2(sK1,X0,relation_image(sK1,X1))))),X2)
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ in(sK4(sK1,X1,sK2(sK1,X0,relation_image(sK1,X1))),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK13(sK17(apply(sK1,sK4(sK1,X1,sK2(sK1,X0,relation_image(sK1,X1))))),X2)) ),
inference(superposition,[status(thm)],[c_31860,c_16730]) ).
tcf(c_33364,plain,
! [X0: $i,X1: $i] :
( empty(sK18(sK17(powerset(apply(sK1,sK4(sK1,X1,sK2(sK1,X0,relation_image(sK1,X1))))))))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ in(sK4(sK1,X1,sK2(sK1,X0,relation_image(sK1,X1))),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK18(sK18(sK17(powerset(apply(sK1,sK4(sK1,X1,sK2(sK1,X0,relation_image(sK1,X1))))))))) ),
inference(superposition,[status(thm)],[c_31860,c_17874]) ).
tcf(c_33365,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(sK1,sK4(sK1,X0,sK2(sK1,X1,relation_image(sK1,X0)))),powerset(X2))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X0))) = sK2(sK1,X1,relation_image(sK1,X0)) )
| ~ in(sK2(sK1,X1,relation_image(sK1,X0)),sK17(powerset(X2)))
| ~ in(sK4(sK1,X0,sK2(sK1,X1,relation_image(sK1,X0))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_31860,c_18767]) ).
tcf(c_33366,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(apply(sK1,sK4(sK1,X0,sK2(sK1,X1,relation_image(sK1,X0)))),powerset(X2))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X0))) = sK2(sK1,X1,relation_image(sK1,X0)) )
| ~ in(sK2(sK1,X1,relation_image(sK1,X0)),sK17(powerset(X2)))
| ~ in(sK4(sK1,X0,sK2(sK1,X1,relation_image(sK1,X0))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_31860,c_18765]) ).
tcf(c_33367,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ( apply(sK1,sK4(sK1,X1,sK2(sK1,X0,relation_image(sK1,X1)))) = empty_set )
| ~ in(sK4(sK1,X1,sK2(sK1,X0,relation_image(sK1,X1))),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK2(empty_set,X2,apply(sK1,sK4(sK1,X1,sK2(sK1,X0,relation_image(sK1,X1)))))) ),
inference(superposition,[status(thm)],[c_31860,c_19251]) ).
tcf(c_33368,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ( apply(sK1,sK4(sK1,X1,sK2(sK1,X0,relation_image(sK1,X1)))) = empty_set )
| ~ in(sK4(sK1,X1,sK2(sK1,X0,relation_image(sK1,X1))),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK7(empty_set,X2,apply(sK1,sK4(sK1,X1,sK2(sK1,X0,relation_image(sK1,X1)))))) ),
inference(superposition,[status(thm)],[c_31860,c_19880]) ).
tcf(c_33369,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ empty(X3)
| ~ in(sK4(sK1,X1,sK2(sK1,X0,relation_image(sK1,X1))),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK2(empty_set,X2,powerset(X3))) ),
inference(superposition,[status(thm)],[c_31860,c_19620]) ).
tcf(c_33370,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(apply(sK1,sK4(sK1,X1,sK2(sK1,X0,relation_image(sK1,X1)))),X3)
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ in(sK4(sK1,X1,sK2(sK1,X0,relation_image(sK1,X1))),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK2(empty_set,X2,powerset(X3))) ),
inference(superposition,[status(thm)],[c_31860,c_19619]) ).
tcf(c_33371,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(sK1,sK4(sK1,X1,sK2(sK1,X0,relation_image(sK1,X1)))),X3)
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ in(sK4(sK1,X1,sK2(sK1,X0,relation_image(sK1,X1))),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK2(empty_set,X2,powerset(X3))) ),
inference(superposition,[status(thm)],[c_31860,c_19621]) ).
tcf(c_33372,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ empty(X3)
| ~ in(sK4(sK1,X1,sK2(sK1,X0,relation_image(sK1,X1))),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK7(empty_set,X2,powerset(X3))) ),
inference(superposition,[status(thm)],[c_31860,c_20797]) ).
tcf(c_33373,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(apply(sK1,sK4(sK1,X1,sK2(sK1,X0,relation_image(sK1,X1)))),X3)
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ in(sK4(sK1,X1,sK2(sK1,X0,relation_image(sK1,X1))),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK7(empty_set,X2,powerset(X3))) ),
inference(superposition,[status(thm)],[c_31860,c_20796]) ).
tcf(c_33374,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(sK1,sK4(sK1,X1,sK2(sK1,X0,relation_image(sK1,X1)))),X3)
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ in(sK4(sK1,X1,sK2(sK1,X0,relation_image(sK1,X1))),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK7(empty_set,X2,powerset(X3))) ),
inference(superposition,[status(thm)],[c_31860,c_20798]) ).
tcf(c_33375,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ empty(X2)
| ~ in(sK4(sK1,X1,sK2(sK1,X0,relation_image(sK1,X1))),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK18(sK17(sK17(sK17(powerset(X2)))))) ),
inference(superposition,[status(thm)],[c_31860,c_22277]) ).
tcf(c_33376,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(apply(sK1,sK4(sK1,X1,sK2(sK1,X0,relation_image(sK1,X1)))),X2)
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ in(sK4(sK1,X1,sK2(sK1,X0,relation_image(sK1,X1))),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK18(sK17(sK17(sK17(powerset(X2)))))) ),
inference(superposition,[status(thm)],[c_31860,c_22276]) ).
tcf(c_33377,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(sK1,sK4(sK1,X1,sK2(sK1,X0,relation_image(sK1,X1)))),X2)
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ in(sK4(sK1,X1,sK2(sK1,X0,relation_image(sK1,X1))),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK18(sK17(sK17(sK17(powerset(X2)))))) ),
inference(superposition,[status(thm)],[c_31860,c_22278]) ).
tcf(c_33378,plain,
! [X0: $i,X1: $i] :
( empty(apply(sK1,sK4(sK1,X1,sK2(sK1,X0,relation_image(sK1,X1)))))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ in(sK4(sK1,X1,sK2(sK1,X0,relation_image(sK1,X1))),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK18(sK17(sK17(sK17(apply(sK1,sK4(sK1,X1,sK2(sK1,X0,relation_image(sK1,X1))))))))) ),
inference(superposition,[status(thm)],[c_31860,c_22295]) ).
tcf(c_33420,plain,
! [X0: $i,X1: $i] :
( in(apply(sK1,sK4(sK1,empty_set,sK2(sK1,X0,empty_set))),X1)
| ( relation_image(sK1,X0) = empty_set )
| ( apply(sK1,sK3(sK1,X0,empty_set)) = sK2(sK1,X0,empty_set) )
| ~ in(sK2(sK1,X0,empty_set),X1)
| ~ in(sK4(sK1,empty_set,sK2(sK1,X0,empty_set)),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_33335,c_23326]) ).
tcf(c_33739,plain,
! [X0: $i,X1: $i] :
( in(sK4(sK1,relation_dom(sK1),sK2(sK1,X0,empty_set)),relation_inverse_image(sK1,X1))
| ( relation_image(sK1,X0) = relation_image(sK1,empty_set) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,empty_set))) = sK2(sK1,X0,relation_image(sK1,empty_set)) )
| ~ in(sK2(sK1,X0,relation_image(sK1,empty_set)),X1)
| ~ in(sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,empty_set))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_23326,c_32009]) ).
tcf(c_33740,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(sK1,sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1)))),X2)
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),X2)
| ~ in(sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_32009,c_72]) ).
tcf(c_33742,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK1,X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X2))) = sK2(sK1,X1,relation_image(sK1,X2)) )
| ~ in(sK2(sK1,X1,relation_image(sK1,X2)),X0)
| ~ in(sK4(sK1,relation_dom(sK1),sK2(sK1,X1,relation_image(sK1,X2))),relation_dom(sK1))
| ~ in(relation_inverse_image(sK1,X0),sK4(sK1,relation_dom(sK1),sK2(sK1,X1,relation_image(sK1,X2)))) ),
inference(superposition,[status(thm)],[c_32009,c_98]) ).
tcf(c_33743,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1))),relation_inverse_image(sK1,X2))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),X2)
| ~ in(sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_32009,c_97]) ).
tcf(c_33744,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ empty(relation_inverse_image(sK1,X2))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),X2)
| ~ in(sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_32009,c_95]) ).
tcf(c_33745,plain,
! [X0: $i,X1: $i] :
( in(sK2(sK1,X0,relation_image(sK1,relation_dom(sK1))),relation_image(sK1,relation_inverse_image(sK1,X1)))
| ( relation_image(sK1,relation_dom(sK1)) = relation_image(sK1,X0) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,relation_dom(sK1)))) = sK2(sK1,X0,relation_image(sK1,relation_dom(sK1))) )
| ~ in(sK2(sK1,X0,relation_image(sK1,relation_dom(sK1))),X1)
| ~ in(sK2(sK1,X0,relation_image(sK1,relation_dom(sK1))),relation_image(sK1,relation_dom(sK1)))
| ~ in(sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,relation_dom(sK1)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_32009,c_31890]) ).
tcf(c_33751,plain,
! [X0: $i,X1: $i] :
( in(sK4(sK1,relation_dom(sK1),sK2(sK1,X0,empty_set)),relation_inverse_image(sK1,X1))
| ( relation_image(sK1,X0) = empty_set )
| ( apply(sK1,sK3(sK1,X0,empty_set)) = sK2(sK1,X0,empty_set) )
| ~ in(sK2(sK1,X0,empty_set),X1)
| ~ in(sK4(sK1,relation_dom(sK1),sK2(sK1,X0,empty_set)),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_33739,c_23326]) ).
tcf(c_33767,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(sK1,sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1)))),X2)
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),X2)
| ~ in(sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1))),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_33740,c_52,c_51]) ).
tcf(c_33795,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(sK1,X0,relation_image(sK1,X1)),relation_image(sK1,X2))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),relation_image(sK1,relation_dom(sK1)))
| ~ in(sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1))),X2) ),
inference(superposition,[status(thm)],[c_58,c_32015]) ).
tcf(c_33797,plain,
! [X0: $i,X1: $i] :
( in(sK2(sK1,X0,relation_image(sK1,empty_set)),relation_image(sK1,X1))
| ( relation_image(sK1,X0) = relation_image(sK1,empty_set) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,empty_set))) = sK2(sK1,X0,relation_image(sK1,empty_set)) )
| ~ in(sK4(sK1,relation_dom(sK1),sK2(sK1,X0,empty_set)),relation_dom(sK1))
| ~ in(sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,empty_set))),X1) ),
inference(superposition,[status(thm)],[c_23326,c_32015]) ).
tcf(c_33798,plain,
! [X0: $i,X1: $i] :
( in(sK2(sK1,X0,empty_set),relation_image(sK1,X1))
| ( relation_image(sK1,X0) = empty_set )
| ( apply(sK1,sK3(sK1,X0,empty_set)) = sK2(sK1,X0,empty_set) )
| ~ in(sK4(sK1,relation_dom(sK1),sK2(sK1,X0,empty_set)),X1)
| ~ in(sK4(sK1,relation_dom(sK1),sK2(sK1,X0,empty_set)),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_33797,c_23326]) ).
tcf(c_33804,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(sK1,X0,relation_image(sK1,X1)),relation_image(sK1,X2))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),relation_image(sK1,relation_dom(sK1)))
| ~ in(sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1))),X2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_33795,c_52,c_51]) ).
tcf(c_33812,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(sK1,X0,relation_image(sK1,X1)),relation_image(sK1,X2))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ in(sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1))),X2) ),
inference(global_subsumption_just,[status(thm)],[c_33804,c_31952,c_33804]) ).
tcf(c_33825,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(sK1,X0,relation_image(sK1,X1)),relation_image(sK1,powerset(X2)))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ subset(sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1))),X2) ),
inference(superposition,[status(thm)],[c_12509,c_33812]) ).
tcf(c_33826,plain,
! [X0: $i,X1: $i] :
( in(sK2(sK1,X0,relation_image(sK1,relation_dom(sK1))),relation_image(sK1,relation_inverse_image(sK1,X1)))
| ( relation_image(sK1,relation_dom(sK1)) = relation_image(sK1,X0) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,relation_dom(sK1)))) = sK2(sK1,X0,relation_image(sK1,relation_dom(sK1))) )
| ~ in(sK2(sK1,X0,relation_image(sK1,relation_dom(sK1))),X1)
| ~ in(sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,relation_dom(sK1)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_31745,c_33812]) ).
tcf(c_33827,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(sK1,X0,relation_image(sK1,X1)),relation_image(sK1,relation_inverse_image(sK1,X2)))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),X2)
| ~ in(sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_32009,c_33812]) ).
tcf(c_33828,plain,
! [X0: $i,X1: $i] :
( in(sK2(sK1,X0,relation_image(sK1,empty_set)),relation_image(sK1,X1))
| ( relation_image(sK1,X0) = relation_image(sK1,empty_set) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,empty_set))) = sK2(sK1,X0,relation_image(sK1,empty_set)) )
| ~ in(sK4(sK1,relation_dom(sK1),sK2(sK1,X0,empty_set)),X1) ),
inference(superposition,[status(thm)],[c_23326,c_33812]) ).
tcf(c_33829,plain,
! [X0: $i,X1: $i] :
( in(sK2(sK1,X0,empty_set),relation_image(sK1,X1))
| ( relation_image(sK1,X0) = empty_set )
| ( apply(sK1,sK3(sK1,X0,empty_set)) = sK2(sK1,X0,empty_set) )
| ~ in(sK4(sK1,relation_dom(sK1),sK2(sK1,X0,empty_set)),X1) ),
inference(light_normalisation,[status(thm)],[c_33828,c_23326]) ).
tcf(c_33949,plain,
! [X0: $i,X1: $i] :
( in(apply(sK1,sK4(sK1,relation_dom(sK1),sK2(sK1,X0,empty_set))),X1)
| ( relation_image(sK1,X0) = relation_image(sK1,empty_set) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,empty_set))) = sK2(sK1,X0,relation_image(sK1,empty_set)) )
| ~ in(sK2(sK1,X0,relation_image(sK1,empty_set)),X1)
| ~ in(sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,empty_set))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_23326,c_33767]) ).
tcf(c_33950,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ( apply(X2,sK4(X2,X3,apply(sK1,sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1)))))) = apply(sK1,sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1)))) )
| ~ function(X2)
| ~ relation(X2)
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),relation_image(X2,X3))
| ~ in(sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_33767,c_60]) ).
tcf(c_33952,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X2,apply(sK1,sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1))))),X3)
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ function(X2)
| ~ relation(X2)
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),relation_inverse_image(X2,X3))
| ~ in(sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_33767,c_72]) ).
tcf(c_33953,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(sK1,sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1)))),relation_dom(X2))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ function(X2)
| ~ relation(X2)
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),relation_inverse_image(X2,X3))
| ~ in(sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_33767,c_71]) ).
tcf(c_33954,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK1,X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X2))) = sK2(sK1,X1,relation_image(sK1,X2)) )
| ~ in(sK2(sK1,X1,relation_image(sK1,X2)),X0)
| ~ in(sK4(sK1,relation_dom(sK1),sK2(sK1,X1,relation_image(sK1,X2))),relation_dom(sK1))
| ~ in(X0,apply(sK1,sK4(sK1,relation_dom(sK1),sK2(sK1,X1,relation_image(sK1,X2))))) ),
inference(superposition,[status(thm)],[c_33767,c_98]) ).
tcf(c_33955,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(apply(sK1,sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1)))),X2)
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),X2)
| ~ in(sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_33767,c_97]) ).
tcf(c_33956,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ empty(X2)
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),X2)
| ~ in(sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_33767,c_95]) ).
tcf(c_33957,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(apply(sK1,sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1)))),X2)
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ in(sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1))),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK13(apply(sK1,sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1)))),X2)) ),
inference(superposition,[status(thm)],[c_33767,c_12485]) ).
tcf(c_33958,plain,
! [X0: $i,X1: $i] :
( empty(apply(sK1,sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1)))))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ in(sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1))),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK18(apply(sK1,sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1)))))) ),
inference(superposition,[status(thm)],[c_33767,c_12526]) ).
tcf(c_33959,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X2)
| element(apply(sK1,sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1)))),X2)
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK17(X2))
| ~ in(sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_33767,c_14688]) ).
tcf(c_33960,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X2)
| in(apply(sK1,sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1)))),X2)
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK17(X2))
| ~ in(sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_33767,c_12618]) ).
tcf(c_33961,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(apply(sK1,sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1)))),X2)
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK18(powerset(X2)))
| ~ in(sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_33767,c_14689]) ).
tcf(c_33962,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ empty(X2)
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK18(powerset(X2)))
| ~ in(sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_33767,c_13313]) ).
tcf(c_33963,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(sK1,sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1)))),X2)
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK18(powerset(X2)))
| ~ in(sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_33767,c_12619]) ).
tcf(c_33964,plain,
! [X0: $i,X1: $i] :
( ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),empty_set)
| ~ in(sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_33767,c_13338]) ).
tcf(c_33965,plain,
! [X0: $i,X1: $i] :
( empty(sK18(powerset(apply(sK1,sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1)))))))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ in(sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1))),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK18(sK18(powerset(apply(sK1,sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1)))))))) ),
inference(superposition,[status(thm)],[c_33767,c_12736]) ).
tcf(c_33966,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ function(X2)
| ~ relation(X2)
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),relation_image(X2,empty_set))
| ~ in(sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_33767,c_13341]) ).
tcf(c_33967,plain,
! [X0: $i,X1: $i] :
( empty(apply(sK1,sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1)))))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ in(sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1))),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK18(sK17(apply(sK1,sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1))))))) ),
inference(superposition,[status(thm)],[c_33767,c_12990]) ).
tcf(c_33968,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(apply(sK1,sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1)))),X2)
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK18(sK17(powerset(X2))))
| ~ in(sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_33767,c_14693]) ).
tcf(c_33969,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ empty(X2)
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK18(sK17(powerset(X2))))
| ~ in(sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_33767,c_13316]) ).
tcf(c_33970,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(sK1,sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1)))),X2)
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK18(sK17(powerset(X2))))
| ~ in(sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_33767,c_13032]) ).
tcf(c_33971,plain,
! [X0: $i,X1: $i] :
( empty(apply(sK1,sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1)))))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ in(sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1))),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK18(sK17(sK17(apply(sK1,sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1)))))))) ),
inference(superposition,[status(thm)],[c_33767,c_15381]) ).
tcf(c_33972,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(sK1,sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1)))),X2)
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK18(sK17(sK17(powerset(X2)))))
| ~ in(sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_33767,c_15478]) ).
tcf(c_33973,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ empty(X2)
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK18(sK17(sK17(powerset(X2)))))
| ~ in(sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_33767,c_15477]) ).
tcf(c_33974,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(apply(sK1,sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1)))),X2)
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK18(sK17(sK17(powerset(X2)))))
| ~ in(sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_33767,c_15476]) ).
tcf(c_33975,plain,
! [X0: $i,X1: $i] :
( empty(sK18(powerset(apply(sK1,sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1)))))))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ in(sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1))),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK18(sK17(sK18(powerset(apply(sK1,sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1))))))))) ),
inference(superposition,[status(thm)],[c_33767,c_15649]) ).
tcf(c_33976,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK18(powerset(apply(sK1,sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1)))))),X2)
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ in(sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1))),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK13(sK18(powerset(apply(sK1,sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1)))))),X2)) ),
inference(superposition,[status(thm)],[c_33767,c_16394]) ).
tcf(c_33977,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(apply(sK1,sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1)))))
| subset(sK17(apply(sK1,sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1))))),X2)
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ in(sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1))),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK13(sK17(apply(sK1,sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1))))),X2)) ),
inference(superposition,[status(thm)],[c_33767,c_16730]) ).
tcf(c_33978,plain,
! [X0: $i,X1: $i] :
( empty(sK18(sK17(powerset(apply(sK1,sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1))))))))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ in(sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1))),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK18(sK18(sK17(powerset(apply(sK1,sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1))))))))) ),
inference(superposition,[status(thm)],[c_33767,c_17874]) ).
tcf(c_33979,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(sK1,sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1)))),powerset(X2))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK17(powerset(X2)))
| ~ in(sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_33767,c_18767]) ).
tcf(c_33980,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(apply(sK1,sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1)))),powerset(X2))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK17(powerset(X2)))
| ~ in(sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_33767,c_18765]) ).
tcf(c_33981,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1)))) = empty_set )
| ~ in(sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1))),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK2(empty_set,X2,apply(sK1,sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1)))))) ),
inference(superposition,[status(thm)],[c_33767,c_19251]) ).
tcf(c_33982,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1)))) = empty_set )
| ~ in(sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1))),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK7(empty_set,X2,apply(sK1,sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1)))))) ),
inference(superposition,[status(thm)],[c_33767,c_19880]) ).
tcf(c_33983,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ empty(X3)
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK2(empty_set,X2,powerset(X3)))
| ~ in(sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_33767,c_19620]) ).
tcf(c_33984,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(apply(sK1,sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1)))),X3)
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK2(empty_set,X2,powerset(X3)))
| ~ in(sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_33767,c_19619]) ).
tcf(c_33985,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(sK1,sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1)))),X3)
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK2(empty_set,X2,powerset(X3)))
| ~ in(sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_33767,c_19621]) ).
tcf(c_33986,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ empty(X3)
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK7(empty_set,X2,powerset(X3)))
| ~ in(sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_33767,c_20797]) ).
tcf(c_33987,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(apply(sK1,sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1)))),X3)
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK7(empty_set,X2,powerset(X3)))
| ~ in(sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_33767,c_20796]) ).
tcf(c_33988,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(sK1,sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1)))),X3)
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK7(empty_set,X2,powerset(X3)))
| ~ in(sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_33767,c_20798]) ).
tcf(c_33989,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ empty(X2)
| ~ in(sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1))),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK18(sK17(sK17(sK17(powerset(X2)))))) ),
inference(superposition,[status(thm)],[c_33767,c_22277]) ).
tcf(c_33990,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(apply(sK1,sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1)))),X2)
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ in(sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1))),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK18(sK17(sK17(sK17(powerset(X2)))))) ),
inference(superposition,[status(thm)],[c_33767,c_22276]) ).
tcf(c_33991,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(sK1,sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1)))),X2)
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ in(sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1))),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK18(sK17(sK17(sK17(powerset(X2)))))) ),
inference(superposition,[status(thm)],[c_33767,c_22278]) ).
tcf(c_33992,plain,
! [X0: $i,X1: $i] :
( empty(apply(sK1,sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1)))))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ in(sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1))),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK18(sK17(sK17(sK17(apply(sK1,sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1))))))))) ),
inference(superposition,[status(thm)],[c_33767,c_22295]) ).
tcf(c_34034,plain,
! [X0: $i,X1: $i] :
( in(apply(sK1,sK4(sK1,relation_dom(sK1),sK2(sK1,X0,empty_set))),X1)
| ( relation_image(sK1,X0) = empty_set )
| ( apply(sK1,sK3(sK1,X0,empty_set)) = sK2(sK1,X0,empty_set) )
| ~ in(sK2(sK1,X0,empty_set),X1)
| ~ in(sK4(sK1,relation_dom(sK1),sK2(sK1,X0,empty_set)),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_33949,c_23326]) ).
tcf(c_34346,plain,
! [X0: $i,X1: $i] :
( ( relation_image(sK1,X0) = relation_image(sK1,empty_set) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,empty_set))) = sK2(sK1,X0,relation_image(sK1,empty_set)) )
| ( sK4(sK1,empty_set,sK2(sK1,X0,relation_image(sK1,empty_set))) = X1 )
| ~ in(X1,relation_dom(sK1))
| ~ in(sK4(sK1,empty_set,sK2(sK1,X0,relation_image(sK1,empty_set))),relation_dom(sK1))
| ( sK2(sK1,X0,empty_set) != apply(sK1,X1) ) ),
inference(superposition,[status(thm)],[c_23326,c_31757]) ).
tcf(c_34347,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(sK1,X2) = relation_image(sK1,X3) )
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X2,relation_image(sK1,X3))) = sK2(sK1,X2,relation_image(sK1,X3)) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ( sK4(sK1,X1,sK2(sK1,X0,relation_image(sK1,X1))) = sK4(sK1,X3,sK2(sK1,X2,relation_image(sK1,X3))) )
| ~ in(sK4(sK1,X3,sK2(sK1,X2,relation_image(sK1,X3))),relation_dom(sK1))
| ~ in(sK4(sK1,X1,sK2(sK1,X0,relation_image(sK1,X1))),relation_dom(sK1))
| ( sK2(sK1,X0,relation_image(sK1,X1)) != sK2(sK1,X2,relation_image(sK1,X3)) ) ),
inference(superposition,[status(thm)],[c_31512,c_31757]) ).
tcf(c_34348,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(sK1,X2) = relation_image(sK1,X3) )
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X2,relation_image(sK1,X3))) = sK2(sK1,X2,relation_image(sK1,X3)) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ( sK4(sK1,relation_dom(sK1),sK2(sK1,X2,relation_image(sK1,X3))) = sK4(sK1,X1,sK2(sK1,X0,relation_image(sK1,X1))) )
| ~ in(sK4(sK1,X1,sK2(sK1,X0,relation_image(sK1,X1))),relation_dom(sK1))
| ~ in(sK4(sK1,relation_dom(sK1),sK2(sK1,X2,relation_image(sK1,X3))),relation_dom(sK1))
| ( sK2(sK1,X0,relation_image(sK1,X1)) != sK2(sK1,X2,relation_image(sK1,X3)) ) ),
inference(superposition,[status(thm)],[c_31984,c_31757]) ).
tcf(c_34349,plain,
! [X0: $i,X1: $i] :
( ( relation_image(sK1,X0) = empty_set )
| ( apply(sK1,sK3(sK1,X0,empty_set)) = sK2(sK1,X0,empty_set) )
| ( sK4(sK1,empty_set,sK2(sK1,X0,empty_set)) = X1 )
| ~ in(X1,relation_dom(sK1))
| ~ in(sK4(sK1,empty_set,sK2(sK1,X0,empty_set)),relation_dom(sK1))
| ( sK2(sK1,X0,empty_set) != apply(sK1,X1) ) ),
inference(light_normalisation,[status(thm)],[c_34346,c_23326]) ).
tcf(c_34387,plain,
! [X0: $i,X1: $i] :
( ( relation_image(sK1,X0) = relation_image(sK1,empty_set) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,empty_set))) = sK2(sK1,X0,relation_image(sK1,empty_set)) )
| ( sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,empty_set))) = X1 )
| ~ in(X1,relation_dom(sK1))
| ~ in(sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,empty_set))),relation_dom(sK1))
| ( sK2(sK1,X0,empty_set) != apply(sK1,X1) ) ),
inference(superposition,[status(thm)],[c_23326,c_32021]) ).
tcf(c_34388,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(sK1,X2) = relation_image(sK1,X3) )
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X2,relation_image(sK1,X3))) = sK2(sK1,X2,relation_image(sK1,X3)) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ( sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1))) = sK4(sK1,X3,sK2(sK1,X2,relation_image(sK1,X3))) )
| ~ in(sK4(sK1,X3,sK2(sK1,X2,relation_image(sK1,X3))),relation_dom(sK1))
| ~ in(sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1))),relation_dom(sK1))
| ( sK2(sK1,X0,relation_image(sK1,X1)) != sK2(sK1,X2,relation_image(sK1,X3)) ) ),
inference(superposition,[status(thm)],[c_31512,c_32021]) ).
tcf(c_34389,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(sK1,X2) = relation_image(sK1,X3) )
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X2,relation_image(sK1,X3))) = sK2(sK1,X2,relation_image(sK1,X3)) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ( sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1))) = sK4(sK1,relation_dom(sK1),sK2(sK1,X2,relation_image(sK1,X3))) )
| ~ in(sK4(sK1,relation_dom(sK1),sK2(sK1,X2,relation_image(sK1,X3))),relation_dom(sK1))
| ~ in(sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1))),relation_dom(sK1))
| ( sK2(sK1,X0,relation_image(sK1,X1)) != sK2(sK1,X2,relation_image(sK1,X3)) ) ),
inference(superposition,[status(thm)],[c_31984,c_32021]) ).
tcf(c_34390,plain,
! [X0: $i,X1: $i] :
( ( relation_image(sK1,X0) = empty_set )
| ( apply(sK1,sK3(sK1,X0,empty_set)) = sK2(sK1,X0,empty_set) )
| ( sK4(sK1,relation_dom(sK1),sK2(sK1,X0,empty_set)) = X1 )
| ~ in(X1,relation_dom(sK1))
| ~ in(sK4(sK1,relation_dom(sK1),sK2(sK1,X0,empty_set)),relation_dom(sK1))
| ( sK2(sK1,X0,empty_set) != apply(sK1,X1) ) ),
inference(light_normalisation,[status(thm)],[c_34387,c_23326]) ).
tcf(c_34421,plain,
( one_to_one(sK18(sK17(powerset(empty_set))))
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_17316,c_32769]) ).
tcf(c_34422,plain,
( one_to_one(sK18(sK17(powerset(empty_set))))
| ~ function(sK1)
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_23326,c_32769]) ).
tcf(c_34423,plain,
( one_to_one(sK18(sK17(powerset(empty_set))))
| ~ function(sK6)
| ~ relation(sK6) ),
inference(superposition,[status(thm)],[c_23325,c_32769]) ).
tcf(c_34424,plain,
( one_to_one(sK18(sK17(powerset(empty_set))))
| ~ function(sK10)
| ~ relation(sK10) ),
inference(superposition,[status(thm)],[c_23324,c_32769]) ).
tcf(c_34433,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(relation_dom(relation_dom(relation_dom(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_99,c_18708]) ).
tcf(c_34434,plain,
relation_dom(sK18(powerset(relation_dom(relation_dom(relation_dom(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_114,c_18708]) ).
tcf(c_34435,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(relation_dom(relation_dom(relation_dom(sK18(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12738,c_18708]) ).
tcf(c_34436,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(relation_dom(relation_dom(relation_dom(sK18(powerset(sK18(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13358,c_18708]) ).
tcf(c_34437,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(powerset(relation_dom(relation_dom(relation_dom(relation_image(X0,X1))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK17(relation_image(X0,X1))))) = sK18(sK17(relation_image(X0,X1))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13159,c_18708]) ).
tcf(c_34438,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(powerset(relation_dom(relation_dom(relation_dom(relation_image(X0,X1))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(relation_image(X0,X1)))) = sK18(relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13157,c_18708]) ).
tcf(c_34439,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(powerset(relation_dom(relation_dom(relation_dom(sK18(powerset(relation_image(X0,X1))))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK18(powerset(relation_image(X0,X1)))))) = sK18(sK18(powerset(relation_image(X0,X1)))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13158,c_18708]) ).
tcf(c_34440,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(relation_dom(relation_dom(relation_dom(sK18(sK17(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13470,c_18708]) ).
tcf(c_34441,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(relation_dom(relation_dom(relation_dom(sK18(powerset(sK18(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13469,c_18708]) ).
tcf(c_34442,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(relation_dom(relation_dom(relation_dom(sK18(sK17(sK17(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15885,c_18708]) ).
tcf(c_34443,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(relation_dom(relation_dom(relation_dom(sK18(powerset(sK18(sK17(sK17(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15887,c_18708]) ).
tcf(c_34444,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(relation_dom(relation_dom(relation_dom(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17175,c_18708]) ).
tcf(c_34445,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(relation_dom(relation_dom(relation_dom(sK18(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17177,c_18708]) ).
tcf(c_34446,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(relation_dom(relation_dom(relation_dom(sK18(sK17(powerset(sK18(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17880,c_18708]) ).
tcf(c_34447,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(relation_dom(relation_dom(relation_dom(sK18(sK17(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17883,c_18708]) ).
tcf(c_34448,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(relation_dom(relation_dom(relation_dom(sK18(sK17(powerset(sK18(sK17(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17885,c_18708]) ).
tcf(c_34449,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(relation_dom(relation_dom(relation_dom(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17888,c_18708]) ).
tcf(c_34450,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(powerset(relation_dom(relation_dom(relation_dom(sK2(empty_set,X1,powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20186,c_18708]) ).
tcf(c_34451,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(powerset(relation_dom(relation_dom(relation_dom(sK18(powerset(sK2(empty_set,X1,powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20188,c_18708]) ).
tcf(c_34452,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(powerset(relation_dom(relation_dom(relation_dom(sK18(sK17(powerset(sK2(empty_set,X1,powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20189,c_18708]) ).
tcf(c_34453,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(powerset(relation_dom(relation_dom(relation_dom(sK7(empty_set,X1,powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21299,c_18708]) ).
tcf(c_34454,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(powerset(relation_dom(relation_dom(relation_dom(sK18(powerset(sK7(empty_set,X1,powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21301,c_18708]) ).
tcf(c_34455,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(powerset(relation_dom(relation_dom(relation_dom(sK18(sK17(powerset(sK7(empty_set,X1,powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21302,c_18708]) ).
tcf(c_34456,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(relation_dom(relation_dom(relation_dom(sK18(sK17(sK17(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25683,c_18708]) ).
tcf(c_34457,plain,
! [X0: $i] :
( ( relation_dom(sK18(powerset(relation_dom(relation_dom(relation_dom(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25684,c_18708]) ).
tcf(c_34648,plain,
! [X0: $i,X1: $i] :
( subset(sK17(powerset(X0)),X1)
| ~ in(powerset(X0),sK13(sK17(powerset(X0)),X1)) ),
inference(superposition,[status(thm)],[c_19001,c_98]) ).
tcf(c_34658,plain,
! [X0: $i] :
( ( sK18(powerset(sK18(sK17(powerset(relation_dom(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_99,c_19132]) ).
tcf(c_34659,plain,
sK18(powerset(sK18(sK17(powerset(relation_dom(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_114,c_19132]) ).
tcf(c_34660,plain,
! [X0: $i] :
( ( sK18(powerset(sK18(sK17(powerset(relation_dom(sK18(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12738,c_19132]) ).
tcf(c_34661,plain,
! [X0: $i] :
( ( sK18(powerset(sK18(sK17(powerset(relation_dom(sK18(powerset(sK18(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13358,c_19132]) ).
tcf(c_34662,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK18(sK17(powerset(relation_dom(relation_image(X0,X1))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK17(relation_image(X0,X1))))) = sK18(sK17(relation_image(X0,X1))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13159,c_19132]) ).
tcf(c_34663,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK18(sK17(powerset(relation_dom(relation_image(X0,X1))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(relation_image(X0,X1)))) = sK18(relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13157,c_19132]) ).
tcf(c_34664,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK18(sK17(powerset(relation_dom(sK18(powerset(relation_image(X0,X1))))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK18(powerset(relation_image(X0,X1)))))) = sK18(sK18(powerset(relation_image(X0,X1)))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13158,c_19132]) ).
tcf(c_34665,plain,
! [X0: $i] :
( ( sK18(powerset(sK18(sK17(powerset(relation_dom(sK18(sK17(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13470,c_19132]) ).
tcf(c_34666,plain,
! [X0: $i] :
( ( sK18(powerset(sK18(sK17(powerset(relation_dom(sK18(powerset(sK18(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13469,c_19132]) ).
tcf(c_34667,plain,
! [X0: $i] :
( ( sK18(powerset(sK18(sK17(powerset(relation_dom(sK18(sK17(sK17(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15885,c_19132]) ).
tcf(c_34668,plain,
! [X0: $i] :
( ( sK18(powerset(sK18(sK17(powerset(relation_dom(sK18(powerset(sK18(sK17(sK17(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15887,c_19132]) ).
tcf(c_34669,plain,
! [X0: $i] :
( ( sK18(powerset(sK18(sK17(powerset(relation_dom(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17175,c_19132]) ).
tcf(c_34670,plain,
! [X0: $i] :
( ( sK18(powerset(sK18(sK17(powerset(relation_dom(sK18(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17177,c_19132]) ).
tcf(c_34671,plain,
! [X0: $i] :
( ( sK18(powerset(sK18(sK17(powerset(relation_dom(sK18(sK17(powerset(sK18(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17880,c_19132]) ).
tcf(c_34672,plain,
! [X0: $i] :
( ( sK18(powerset(sK18(sK17(powerset(relation_dom(sK18(sK17(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17883,c_19132]) ).
tcf(c_34673,plain,
! [X0: $i] :
( ( sK18(powerset(sK18(sK17(powerset(relation_dom(sK18(sK17(powerset(sK18(sK17(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17885,c_19132]) ).
tcf(c_34674,plain,
! [X0: $i] :
( ( sK18(powerset(sK18(sK17(powerset(relation_dom(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17888,c_19132]) ).
tcf(c_34675,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK18(sK17(powerset(relation_dom(sK2(empty_set,X1,powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20186,c_19132]) ).
tcf(c_34676,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK18(sK17(powerset(relation_dom(sK18(powerset(sK2(empty_set,X1,powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20188,c_19132]) ).
tcf(c_34677,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK18(sK17(powerset(relation_dom(sK18(sK17(powerset(sK2(empty_set,X1,powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20189,c_19132]) ).
tcf(c_34678,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK18(sK17(powerset(relation_dom(sK7(empty_set,X1,powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21299,c_19132]) ).
tcf(c_34679,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK18(sK17(powerset(relation_dom(sK18(powerset(sK7(empty_set,X1,powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21301,c_19132]) ).
tcf(c_34680,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK18(sK17(powerset(relation_dom(sK18(sK17(powerset(sK7(empty_set,X1,powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21302,c_19132]) ).
tcf(c_34681,plain,
! [X0: $i] :
( ( sK18(powerset(sK18(sK17(powerset(relation_dom(sK18(sK17(sK17(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25683,c_19132]) ).
tcf(c_34682,plain,
! [X0: $i] :
( ( sK18(powerset(sK18(sK17(powerset(relation_dom(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25684,c_19132]) ).
tcf(c_34912,plain,
! [X0: $i] :
( empty(sK17(powerset(X0)))
| ~ in(powerset(X0),sK18(sK17(sK17(sK17(powerset(X0)))))) ),
inference(superposition,[status(thm)],[c_19007,c_98]) ).
tcf(c_34922,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK18(sK17(powerset(relation_dom(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_99,c_19196]) ).
tcf(c_34923,plain,
relation_dom(relation_dom(sK18(sK17(powerset(relation_dom(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_114,c_19196]) ).
tcf(c_34924,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK18(sK17(powerset(relation_dom(sK18(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12738,c_19196]) ).
tcf(c_34925,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK18(sK17(powerset(relation_dom(sK18(powerset(sK18(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13358,c_19196]) ).
tcf(c_34926,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK18(sK17(powerset(relation_dom(relation_image(X0,X1))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK17(relation_image(X0,X1))))) = sK18(sK17(relation_image(X0,X1))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13159,c_19196]) ).
tcf(c_34927,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK18(sK17(powerset(relation_dom(relation_image(X0,X1))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(relation_image(X0,X1)))) = sK18(relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13157,c_19196]) ).
tcf(c_34928,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK18(sK17(powerset(relation_dom(sK18(powerset(relation_image(X0,X1))))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK18(powerset(relation_image(X0,X1)))))) = sK18(sK18(powerset(relation_image(X0,X1)))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13158,c_19196]) ).
tcf(c_34929,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK18(sK17(powerset(relation_dom(sK18(sK17(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13470,c_19196]) ).
tcf(c_34930,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK18(sK17(powerset(relation_dom(sK18(powerset(sK18(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13469,c_19196]) ).
tcf(c_34931,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK18(sK17(powerset(relation_dom(sK18(sK17(sK17(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15885,c_19196]) ).
tcf(c_34932,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK18(sK17(powerset(relation_dom(sK18(powerset(sK18(sK17(sK17(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15887,c_19196]) ).
tcf(c_34933,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK18(sK17(powerset(relation_dom(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17175,c_19196]) ).
tcf(c_34934,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK18(sK17(powerset(relation_dom(sK18(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17177,c_19196]) ).
tcf(c_34935,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK18(sK17(powerset(relation_dom(sK18(sK17(powerset(sK18(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17880,c_19196]) ).
tcf(c_34936,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK18(sK17(powerset(relation_dom(sK18(sK17(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17883,c_19196]) ).
tcf(c_34937,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK18(sK17(powerset(relation_dom(sK18(sK17(powerset(sK18(sK17(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17885,c_19196]) ).
tcf(c_34938,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK18(sK17(powerset(relation_dom(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17888,c_19196]) ).
tcf(c_34939,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK18(sK17(powerset(relation_dom(sK2(empty_set,X1,powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20186,c_19196]) ).
tcf(c_34940,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK18(sK17(powerset(relation_dom(sK18(powerset(sK2(empty_set,X1,powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20188,c_19196]) ).
tcf(c_34941,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK18(sK17(powerset(relation_dom(sK18(sK17(powerset(sK2(empty_set,X1,powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20189,c_19196]) ).
tcf(c_34942,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK18(sK17(powerset(relation_dom(sK7(empty_set,X1,powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21299,c_19196]) ).
tcf(c_34943,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK18(sK17(powerset(relation_dom(sK18(powerset(sK7(empty_set,X1,powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21301,c_19196]) ).
tcf(c_34944,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK18(sK17(powerset(relation_dom(sK18(sK17(powerset(sK7(empty_set,X1,powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21302,c_19196]) ).
tcf(c_34945,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK18(sK17(powerset(relation_dom(sK18(sK17(sK17(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25683,c_19196]) ).
tcf(c_34946,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK18(sK17(powerset(relation_dom(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25684,c_19196]) ).
tcf(c_35116,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK1,X2) = relation_image(sK1,empty_set) )
| ( relation_image(sK1,X0) = X1 )
| ( apply(sK1,sK3(sK1,X2,relation_image(sK1,empty_set))) = sK2(sK1,X2,relation_image(sK1,empty_set)) )
| ~ in(sK2(sK1,X0,X1),X1)
| ~ in(sK4(sK1,empty_set,sK2(sK1,X2,relation_image(sK1,empty_set))),X0)
| ~ in(sK4(sK1,empty_set,sK2(sK1,X2,relation_image(sK1,empty_set))),relation_dom(sK1))
| ( sK2(sK1,X0,X1) != sK2(sK1,X2,empty_set) ) ),
inference(superposition,[status(thm)],[c_23326,c_31764]) ).
tcf(c_35117,plain,
! [X0: $i,X1: $i] :
( ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X0))) = sK2(sK1,X1,relation_image(sK1,X0)) )
| ~ in(sK2(sK1,X1,relation_image(sK1,X0)),relation_image(sK1,X0))
| ~ in(sK4(sK1,X0,sK2(sK1,X1,relation_image(sK1,X0))),X1)
| ~ in(sK4(sK1,X0,sK2(sK1,X1,relation_image(sK1,X0))),relation_dom(sK1)) ),
inference(equality_resolution,[status(thm)],[c_31764]) ).
tcf(c_35123,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK1,X2) = empty_set )
| ( relation_image(sK1,X0) = X1 )
| ( apply(sK1,sK3(sK1,X2,empty_set)) = sK2(sK1,X2,empty_set) )
| ~ in(sK2(sK1,X0,X1),X1)
| ~ in(sK4(sK1,empty_set,sK2(sK1,X2,empty_set)),X0)
| ~ in(sK4(sK1,empty_set,sK2(sK1,X2,empty_set)),relation_dom(sK1))
| ( sK2(sK1,X0,X1) != sK2(sK1,X2,empty_set) ) ),
inference(light_normalisation,[status(thm)],[c_35116,c_23326]) ).
tcf(c_35147,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK1,X2) = relation_image(sK1,empty_set) )
| ( relation_image(sK1,X0) = X1 )
| ( apply(sK1,sK3(sK1,X2,relation_image(sK1,empty_set))) = sK2(sK1,X2,relation_image(sK1,empty_set)) )
| ~ in(sK2(sK1,X0,X1),X1)
| ~ in(sK4(sK1,relation_dom(sK1),sK2(sK1,X2,relation_image(sK1,empty_set))),X0)
| ~ in(sK4(sK1,relation_dom(sK1),sK2(sK1,X2,relation_image(sK1,empty_set))),relation_dom(sK1))
| ( sK2(sK1,X0,X1) != sK2(sK1,X2,empty_set) ) ),
inference(superposition,[status(thm)],[c_23326,c_32028]) ).
tcf(c_35148,plain,
! [X0: $i,X1: $i] :
( ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),relation_image(sK1,X1))
| ~ in(sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1))),X0)
| ~ in(sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1))),relation_dom(sK1)) ),
inference(equality_resolution,[status(thm)],[c_32028]) ).
tcf(c_35154,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK1,X2) = empty_set )
| ( relation_image(sK1,X0) = X1 )
| ( apply(sK1,sK3(sK1,X2,empty_set)) = sK2(sK1,X2,empty_set) )
| ~ in(sK2(sK1,X0,X1),X1)
| ~ in(sK4(sK1,relation_dom(sK1),sK2(sK1,X2,empty_set)),X0)
| ~ in(sK4(sK1,relation_dom(sK1),sK2(sK1,X2,empty_set)),relation_dom(sK1))
| ( sK2(sK1,X0,X1) != sK2(sK1,X2,empty_set) ) ),
inference(light_normalisation,[status(thm)],[c_35147,c_23326]) ).
tcf(c_35176,plain,
! [X0: $i] :
( ( relation_image(sK1,X0) = empty_set )
| ( apply(sK1,sK3(sK1,X0,empty_set)) = sK2(sK1,X0,empty_set) )
| ~ in(relation_image(sK1,relation_dom(sK1)),sK2(sK1,X0,empty_set)) ),
inference(superposition,[status(thm)],[c_31974,c_98]) ).
tcf(c_35177,plain,
! [X0: $i] :
( element(sK2(sK1,X0,empty_set),relation_image(sK1,relation_dom(sK1)))
| ( relation_image(sK1,X0) = empty_set )
| ( apply(sK1,sK3(sK1,X0,empty_set)) = sK2(sK1,X0,empty_set) ) ),
inference(superposition,[status(thm)],[c_31974,c_97]) ).
tcf(c_35178,plain,
! [X0: $i] :
( ( relation_image(sK1,X0) = empty_set )
| ( apply(sK1,sK3(sK1,X0,empty_set)) = sK2(sK1,X0,empty_set) )
| ~ empty(relation_image(sK1,relation_dom(sK1))) ),
inference(superposition,[status(thm)],[c_31974,c_95]) ).
tcf(c_35212,plain,
! [X0: $i,X1: $i] :
( ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))) = sK18(sK17(relation_image(sK1,relation_dom(sK1)))) )
| ~ function(sK1)
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_13159,c_31970]) ).
tcf(c_35213,plain,
! [X0: $i,X1: $i] :
( ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) )
| ~ function(sK1)
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_13157,c_31970]) ).
tcf(c_35214,plain,
! [X0: $i,X1: $i] :
( ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_35213,c_52,c_51]) ).
tcf(c_35218,plain,
! [X0: $i,X1: $i] :
( ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))) = sK18(sK17(relation_image(sK1,relation_dom(sK1)))) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_35212,c_52,c_51]) ).
tcf(c_35363,plain,
! [X0: $i] :
( ( relation_image(sK1,X0) = relation_image(sK1,empty_set) )
| ( apply(sK1,sK3(sK1,X0,empty_set)) = sK2(sK1,X0,empty_set) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) ) ),
inference(superposition,[status(thm)],[c_23326,c_35214]) ).
tcf(c_35364,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(sK1,X2) = X3 )
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(sK2(sK1,X2,X3),X3)
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),X2)
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1))
| ( sK2(sK1,X0,relation_image(sK1,X1)) != sK2(sK1,X2,X3) ) ),
inference(superposition,[status(thm)],[c_35214,c_53]) ).
tcf(c_35365,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(sK1,X0,relation_image(sK1,X1)),relation_image(sK1,X2))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),X2)
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_35214,c_57]) ).
tcf(c_35367,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(sK1,X0,relation_image(sK1,X1)),relation_inverse_image(sK1,X2))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),X2)
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_35214,c_70]) ).
tcf(c_35368,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( sK3(sK1,X0,relation_image(sK1,X1)) = X2 )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) )
| ~ function(sK1)
| ~ relation(sK1)
| ~ one_to_one(sK1)
| ~ in(X2,relation_dom(sK1))
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1))
| ( sK2(sK1,X0,relation_image(sK1,X1)) != apply(sK1,X2) ) ),
inference(superposition,[status(thm)],[c_35214,c_85]) ).
tcf(c_35369,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(sK1,X2) = relation_image(sK1,X3) )
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ( sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1))) = sK3(sK1,X2,relation_image(sK1,X3)) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) )
| ~ in(sK3(sK1,X2,relation_image(sK1,X3)),relation_dom(sK1))
| ~ in(sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1))),relation_dom(sK1))
| ( sK2(sK1,X0,relation_image(sK1,X1)) != sK2(sK1,X2,relation_image(sK1,X3)) ) ),
inference(superposition,[status(thm)],[c_35214,c_32021]) ).
tcf(c_35370,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(sK1,X2) = relation_image(sK1,X3) )
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ( sK4(sK1,X1,sK2(sK1,X0,relation_image(sK1,X1))) = sK3(sK1,X2,relation_image(sK1,X3)) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) )
| ~ in(sK3(sK1,X2,relation_image(sK1,X3)),relation_dom(sK1))
| ~ in(sK4(sK1,X1,sK2(sK1,X0,relation_image(sK1,X1))),relation_dom(sK1))
| ( sK2(sK1,X0,relation_image(sK1,X1)) != sK2(sK1,X2,relation_image(sK1,X3)) ) ),
inference(superposition,[status(thm)],[c_35214,c_31757]) ).
tcf(c_35371,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(sK1,X2) = relation_image(sK1,X3) )
| ( relation_image(sK1,X0) = X1 )
| ( apply(sK1,sK3(sK1,X2,relation_image(sK1,X3))) = sK2(sK1,X2,relation_image(sK1,X3)) )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(sK2(sK1,X0,X1),X1)
| ~ in(sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1)))),X0)
| ~ in(sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1)))),relation_dom(sK1))
| ( sK18(relation_image(sK1,relation_dom(sK1))) != sK2(sK1,X0,X1) ) ),
inference(superposition,[status(thm)],[c_35214,c_53]) ).
tcf(c_35372,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK18(relation_image(sK1,relation_dom(sK1))),relation_image(sK1,X0))
| ( relation_image(sK1,X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X2))) = sK2(sK1,X1,relation_image(sK1,X2)) )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1)))),X0)
| ~ in(sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_35214,c_57]) ).
tcf(c_35374,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1)))),relation_inverse_image(sK1,X0))
| ( relation_image(sK1,X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X2))) = sK2(sK1,X1,relation_image(sK1,X2)) )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(sK18(relation_image(sK1,relation_dom(sK1))),X0)
| ~ in(sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_35214,c_70]) ).
tcf(c_35375,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK1,X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X2))) = sK2(sK1,X1,relation_image(sK1,X2)) )
| ( sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1)))) = X0 )
| ~ function(sK1)
| ~ relation(sK1)
| ~ one_to_one(sK1)
| ~ in(X0,relation_dom(sK1))
| ~ in(sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1)))),relation_dom(sK1))
| ( sK18(relation_image(sK1,relation_dom(sK1))) != apply(sK1,X0) ) ),
inference(superposition,[status(thm)],[c_35214,c_85]) ).
tcf(c_35376,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(sK1,X2) = relation_image(sK1,X3) )
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X2,relation_image(sK1,X3))) = sK2(sK1,X2,relation_image(sK1,X3)) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ( sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1))) = sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1)))) )
| ~ in(sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1)))),relation_dom(sK1))
| ~ in(sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1))),relation_dom(sK1))
| ( sK2(sK1,X0,relation_image(sK1,X1)) != sK18(relation_image(sK1,relation_dom(sK1))) ) ),
inference(superposition,[status(thm)],[c_35214,c_32021]) ).
tcf(c_35377,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(sK1,X2) = relation_image(sK1,X3) )
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X2,relation_image(sK1,X3))) = sK2(sK1,X2,relation_image(sK1,X3)) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ( sK4(sK1,X1,sK2(sK1,X0,relation_image(sK1,X1))) = sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1)))) )
| ~ in(sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1)))),relation_dom(sK1))
| ~ in(sK4(sK1,X1,sK2(sK1,X0,relation_image(sK1,X1))),relation_dom(sK1))
| ( sK2(sK1,X0,relation_image(sK1,X1)) != sK18(relation_image(sK1,relation_dom(sK1))) ) ),
inference(superposition,[status(thm)],[c_35214,c_31757]) ).
tcf(c_35378,plain,
! [X0: $i] :
( ( relation_image(sK1,X0) = empty_set )
| ( apply(sK1,sK3(sK1,X0,empty_set)) = sK2(sK1,X0,empty_set) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) ) ),
inference(light_normalisation,[status(thm)],[c_35363,c_23326]) ).
tcf(c_35382,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(sK1,X0,relation_image(sK1,X1)),relation_inverse_image(sK1,X2))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) )
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),X2)
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_35367,c_52,c_51]) ).
tcf(c_35388,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(sK1,X0,relation_image(sK1,X1)),relation_image(sK1,X2))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) )
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),X2)
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_35365,c_52,c_51]) ).
tcf(c_35394,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1)))),relation_inverse_image(sK1,X0))
| ( relation_image(sK1,X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X2))) = sK2(sK1,X1,relation_image(sK1,X2)) )
| ~ in(sK18(relation_image(sK1,relation_dom(sK1))),X0)
| ~ in(sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1)))),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_35374,c_52,c_51]) ).
tcf(c_35400,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK18(relation_image(sK1,relation_dom(sK1))),relation_image(sK1,X0))
| ( relation_image(sK1,X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X2))) = sK2(sK1,X1,relation_image(sK1,X2)) )
| ~ in(sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1)))),X0)
| ~ in(sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1)))),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_35372,c_52,c_51]) ).
tcf(c_35406,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( sK3(sK1,X0,relation_image(sK1,X1)) = X2 )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) )
| ~ in(X2,relation_dom(sK1))
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1))
| ( sK2(sK1,X0,relation_image(sK1,X1)) != apply(sK1,X2) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_35368,c_52,c_51,c_50]) ).
tcf(c_35413,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK1,X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X2))) = sK2(sK1,X1,relation_image(sK1,X2)) )
| ( sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1)))) = X0 )
| ~ in(X0,relation_dom(sK1))
| ~ in(sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1)))),relation_dom(sK1))
| ( sK18(relation_image(sK1,relation_dom(sK1))) != apply(sK1,X0) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_35375,c_52,c_51,c_50]) ).
tcf(c_35420,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(sK1,X2) = X3 )
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) )
| ~ in(sK2(sK1,X2,X3),X3)
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),X2)
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1))
| ( sK2(sK1,X0,relation_image(sK1,X1)) != sK2(sK1,X2,X3) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_35364,c_52,c_51]) ).
tcf(c_35428,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(sK1,X2) = relation_image(sK1,X3) )
| ( relation_image(sK1,X0) = X1 )
| ( apply(sK1,sK3(sK1,X2,relation_image(sK1,X3))) = sK2(sK1,X2,relation_image(sK1,X3)) )
| ~ in(sK2(sK1,X0,X1),X1)
| ~ in(sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1)))),X0)
| ~ in(sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1)))),relation_dom(sK1))
| ( sK18(relation_image(sK1,relation_dom(sK1))) != sK2(sK1,X0,X1) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_35371,c_52,c_51]) ).
tcf(c_35566,plain,
! [X0: $i] :
( ( relation_image(sK1,X0) = relation_image(sK1,empty_set) )
| ( apply(sK1,sK3(sK1,X0,empty_set)) = sK2(sK1,X0,empty_set) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))) = sK18(sK17(relation_image(sK1,relation_dom(sK1)))) ) ),
inference(superposition,[status(thm)],[c_23326,c_35218]) ).
tcf(c_35567,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(sK1,X2) = X3 )
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))) = sK18(sK17(relation_image(sK1,relation_dom(sK1)))) )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(sK2(sK1,X2,X3),X3)
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),X2)
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1))
| ( sK2(sK1,X0,relation_image(sK1,X1)) != sK2(sK1,X2,X3) ) ),
inference(superposition,[status(thm)],[c_35218,c_53]) ).
tcf(c_35568,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(sK1,X0,relation_image(sK1,X1)),relation_image(sK1,X2))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))) = sK18(sK17(relation_image(sK1,relation_dom(sK1)))) )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),X2)
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_35218,c_57]) ).
tcf(c_35570,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(sK1,X0,relation_image(sK1,X1)),relation_inverse_image(sK1,X2))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))) = sK18(sK17(relation_image(sK1,relation_dom(sK1)))) )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),X2)
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_35218,c_70]) ).
tcf(c_35571,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( sK3(sK1,X0,relation_image(sK1,X1)) = X2 )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))) = sK18(sK17(relation_image(sK1,relation_dom(sK1)))) )
| ~ function(sK1)
| ~ relation(sK1)
| ~ one_to_one(sK1)
| ~ in(X2,relation_dom(sK1))
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1))
| ( sK2(sK1,X0,relation_image(sK1,X1)) != apply(sK1,X2) ) ),
inference(superposition,[status(thm)],[c_35218,c_85]) ).
tcf(c_35572,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(sK1,X2) = relation_image(sK1,X3) )
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ( sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1))) = sK3(sK1,X2,relation_image(sK1,X3)) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))) = sK18(sK17(relation_image(sK1,relation_dom(sK1)))) )
| ~ in(sK3(sK1,X2,relation_image(sK1,X3)),relation_dom(sK1))
| ~ in(sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1))),relation_dom(sK1))
| ( sK2(sK1,X0,relation_image(sK1,X1)) != sK2(sK1,X2,relation_image(sK1,X3)) ) ),
inference(superposition,[status(thm)],[c_35218,c_32021]) ).
tcf(c_35573,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(sK1,X2) = relation_image(sK1,X3) )
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ( sK4(sK1,X1,sK2(sK1,X0,relation_image(sK1,X1))) = sK3(sK1,X2,relation_image(sK1,X3)) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))) = sK18(sK17(relation_image(sK1,relation_dom(sK1)))) )
| ~ in(sK3(sK1,X2,relation_image(sK1,X3)),relation_dom(sK1))
| ~ in(sK4(sK1,X1,sK2(sK1,X0,relation_image(sK1,X1))),relation_dom(sK1))
| ( sK2(sK1,X0,relation_image(sK1,X1)) != sK2(sK1,X2,relation_image(sK1,X3)) ) ),
inference(superposition,[status(thm)],[c_35218,c_31757]) ).
tcf(c_35574,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(sK1,X2) = relation_image(sK1,X3) )
| ( relation_image(sK1,X0) = X1 )
| ( apply(sK1,sK3(sK1,X2,relation_image(sK1,X3))) = sK2(sK1,X2,relation_image(sK1,X3)) )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(sK2(sK1,X0,X1),X1)
| ~ in(sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1))))),X0)
| ~ in(sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1))))),relation_dom(sK1))
| ( sK18(sK17(relation_image(sK1,relation_dom(sK1)))) != sK2(sK1,X0,X1) ) ),
inference(superposition,[status(thm)],[c_35218,c_53]) ).
tcf(c_35575,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK18(sK17(relation_image(sK1,relation_dom(sK1)))),relation_image(sK1,X0))
| ( relation_image(sK1,X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X2))) = sK2(sK1,X1,relation_image(sK1,X2)) )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1))))),X0)
| ~ in(sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1))))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_35218,c_57]) ).
tcf(c_35577,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1))))),relation_inverse_image(sK1,X0))
| ( relation_image(sK1,X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X2))) = sK2(sK1,X1,relation_image(sK1,X2)) )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(sK18(sK17(relation_image(sK1,relation_dom(sK1)))),X0)
| ~ in(sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1))))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_35218,c_70]) ).
tcf(c_35578,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK1,X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X2))) = sK2(sK1,X1,relation_image(sK1,X2)) )
| ( sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1))))) = X0 )
| ~ function(sK1)
| ~ relation(sK1)
| ~ one_to_one(sK1)
| ~ in(X0,relation_dom(sK1))
| ~ in(sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1))))),relation_dom(sK1))
| ( sK18(sK17(relation_image(sK1,relation_dom(sK1)))) != apply(sK1,X0) ) ),
inference(superposition,[status(thm)],[c_35218,c_85]) ).
tcf(c_35579,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(sK1,X2) = relation_image(sK1,X3) )
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X2,relation_image(sK1,X3))) = sK2(sK1,X2,relation_image(sK1,X3)) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ( sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1))) = sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1))))) )
| ~ in(sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1))))),relation_dom(sK1))
| ~ in(sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1))),relation_dom(sK1))
| ( sK2(sK1,X0,relation_image(sK1,X1)) != sK18(sK17(relation_image(sK1,relation_dom(sK1)))) ) ),
inference(superposition,[status(thm)],[c_35218,c_32021]) ).
tcf(c_35580,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(sK1,X2) = relation_image(sK1,X3) )
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X2,relation_image(sK1,X3))) = sK2(sK1,X2,relation_image(sK1,X3)) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ( sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1))))) = sK4(sK1,X1,sK2(sK1,X0,relation_image(sK1,X1))) )
| ~ in(sK4(sK1,X1,sK2(sK1,X0,relation_image(sK1,X1))),relation_dom(sK1))
| ~ in(sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1))))),relation_dom(sK1))
| ( sK2(sK1,X0,relation_image(sK1,X1)) != sK18(sK17(relation_image(sK1,relation_dom(sK1)))) ) ),
inference(superposition,[status(thm)],[c_35218,c_31757]) ).
tcf(c_35581,plain,
! [X0: $i] :
( ( relation_image(sK1,X0) = empty_set )
| ( apply(sK1,sK3(sK1,X0,empty_set)) = sK2(sK1,X0,empty_set) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))) = sK18(sK17(relation_image(sK1,relation_dom(sK1)))) ) ),
inference(light_normalisation,[status(thm)],[c_35566,c_23326]) ).
tcf(c_35585,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(sK1,X0,relation_image(sK1,X1)),relation_inverse_image(sK1,X2))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))) = sK18(sK17(relation_image(sK1,relation_dom(sK1)))) )
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),X2)
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_35570,c_52,c_51]) ).
tcf(c_35591,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(sK1,X0,relation_image(sK1,X1)),relation_image(sK1,X2))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))) = sK18(sK17(relation_image(sK1,relation_dom(sK1)))) )
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),X2)
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_35568,c_52,c_51]) ).
tcf(c_35597,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1))))),relation_inverse_image(sK1,X0))
| ( relation_image(sK1,X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X2))) = sK2(sK1,X1,relation_image(sK1,X2)) )
| ~ in(sK18(sK17(relation_image(sK1,relation_dom(sK1)))),X0)
| ~ in(sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1))))),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_35577,c_52,c_51]) ).
tcf(c_35603,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK18(sK17(relation_image(sK1,relation_dom(sK1)))),relation_image(sK1,X0))
| ( relation_image(sK1,X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X2))) = sK2(sK1,X1,relation_image(sK1,X2)) )
| ~ in(sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1))))),X0)
| ~ in(sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1))))),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_35575,c_52,c_51]) ).
tcf(c_35609,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( sK3(sK1,X0,relation_image(sK1,X1)) = X2 )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))) = sK18(sK17(relation_image(sK1,relation_dom(sK1)))) )
| ~ in(X2,relation_dom(sK1))
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1))
| ( sK2(sK1,X0,relation_image(sK1,X1)) != apply(sK1,X2) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_35571,c_52,c_51,c_50]) ).
tcf(c_35616,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK1,X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X2))) = sK2(sK1,X1,relation_image(sK1,X2)) )
| ( sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1))))) = X0 )
| ~ in(X0,relation_dom(sK1))
| ~ in(sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1))))),relation_dom(sK1))
| ( sK18(sK17(relation_image(sK1,relation_dom(sK1)))) != apply(sK1,X0) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_35578,c_52,c_51,c_50]) ).
tcf(c_35623,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(sK1,X2) = X3 )
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))) = sK18(sK17(relation_image(sK1,relation_dom(sK1)))) )
| ~ in(sK2(sK1,X2,X3),X3)
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),X2)
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1))
| ( sK2(sK1,X0,relation_image(sK1,X1)) != sK2(sK1,X2,X3) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_35567,c_52,c_51]) ).
tcf(c_35631,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(sK1,X2) = relation_image(sK1,X3) )
| ( relation_image(sK1,X0) = X1 )
| ( apply(sK1,sK3(sK1,X2,relation_image(sK1,X3))) = sK2(sK1,X2,relation_image(sK1,X3)) )
| ~ in(sK2(sK1,X0,X1),X1)
| ~ in(sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1))))),X0)
| ~ in(sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1))))),relation_dom(sK1))
| ( sK18(sK17(relation_image(sK1,relation_dom(sK1)))) != sK2(sK1,X0,X1) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_35574,c_52,c_51]) ).
tcf(c_35694,plain,
! [X0: $i,X1: $i] :
( in(sK3(sK1,X0,empty_set),relation_inverse_image(sK1,X1))
| ( relation_image(sK1,X0) = relation_image(sK1,empty_set) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) )
| ~ in(sK2(sK1,X0,relation_image(sK1,empty_set)),X1)
| ~ in(sK3(sK1,X0,relation_image(sK1,empty_set)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_23326,c_35382]) ).
tcf(c_35695,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))),X2)
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),X2)
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_35382,c_72]) ).
tcf(c_35697,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK1,X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) )
| ~ in(sK2(sK1,X1,relation_image(sK1,X2)),X0)
| ~ in(sK3(sK1,X1,relation_image(sK1,X2)),relation_dom(sK1))
| ~ in(relation_inverse_image(sK1,X0),sK3(sK1,X1,relation_image(sK1,X2))) ),
inference(superposition,[status(thm)],[c_35382,c_98]) ).
tcf(c_35698,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK3(sK1,X0,relation_image(sK1,X1)),relation_inverse_image(sK1,X2))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) )
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),X2)
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_35382,c_97]) ).
tcf(c_35699,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) )
| ~ empty(relation_inverse_image(sK1,X2))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),X2)
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_35382,c_95]) ).
tcf(c_35705,plain,
! [X0: $i,X1: $i] :
( in(sK3(sK1,X0,empty_set),relation_inverse_image(sK1,X1))
| ( relation_image(sK1,X0) = empty_set )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) )
| ~ in(sK2(sK1,X0,empty_set),X1)
| ~ in(sK3(sK1,X0,empty_set),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_35694,c_23326]) ).
tcf(c_35721,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))),X2)
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) )
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),X2)
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_35695,c_52,c_51]) ).
tcf(c_35742,plain,
! [X0: $i,X1: $i] :
( in(sK2(sK1,X0,empty_set),relation_image(sK1,X1))
| ( relation_image(sK1,X0) = relation_image(sK1,empty_set) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) )
| ~ in(sK3(sK1,X0,relation_image(sK1,empty_set)),X1)
| ~ in(sK3(sK1,X0,relation_image(sK1,empty_set)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_23326,c_35388]) ).
tcf(c_35743,plain,
! [X0: $i,X1: $i] :
( in(sK2(sK1,X0,relation_image(sK1,X1)),empty_set)
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) )
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),empty_set)
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_23326,c_35388]) ).
tcf(c_35744,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) )
| ( apply(sK1,sK4(sK1,X2,sK2(sK1,X0,relation_image(sK1,X1)))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),X2)
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_35388,c_60]) ).
tcf(c_35745,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK1,X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) )
| ~ in(sK3(sK1,X1,relation_image(sK1,X2)),X0)
| ~ in(sK3(sK1,X1,relation_image(sK1,X2)),relation_dom(sK1))
| ~ in(relation_image(sK1,X0),sK2(sK1,X1,relation_image(sK1,X2))) ),
inference(superposition,[status(thm)],[c_35388,c_98]) ).
tcf(c_35746,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(sK1,X0,relation_image(sK1,X1)),relation_image(sK1,X2))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) )
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),X2)
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_35388,c_97]) ).
tcf(c_35747,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) )
| ~ empty(relation_image(sK1,X2))
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),X2)
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_35388,c_95]) ).
tcf(c_35748,plain,
! [X0: $i,X1: $i] :
( ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),empty_set)
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_35388,c_13341]) ).
tcf(c_35754,plain,
! [X0: $i,X1: $i] :
( in(sK2(sK1,X0,empty_set),relation_image(sK1,X1))
| ( relation_image(sK1,X0) = empty_set )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) )
| ~ in(sK3(sK1,X0,empty_set),X1)
| ~ in(sK3(sK1,X0,empty_set),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_35742,c_23326]) ).
tcf(c_35770,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) )
| ( apply(sK1,sK4(sK1,X2,sK2(sK1,X0,relation_image(sK1,X1)))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),X2)
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_35744,c_52,c_51]) ).
tcf(c_35787,plain,
( relation(sK18(sK17(powerset(empty_set))))
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_17316,c_32770]) ).
tcf(c_35788,plain,
( relation(sK18(sK17(powerset(empty_set))))
| ~ function(sK1)
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_23326,c_32770]) ).
tcf(c_35789,plain,
( relation(sK18(sK17(powerset(empty_set))))
| ~ function(sK6)
| ~ relation(sK6) ),
inference(superposition,[status(thm)],[c_23325,c_32770]) ).
tcf(c_35790,plain,
( relation(sK18(sK17(powerset(empty_set))))
| ~ function(sK10)
| ~ relation(sK10) ),
inference(superposition,[status(thm)],[c_23324,c_32770]) ).
tcf(c_35791,plain,
! [X0: $i] :
( one_to_one(sK18(sK17(powerset(relation_image(X0,empty_set)))))
| ( apply(sK18(sK17(powerset(relation_image(X0,empty_set)))),sK11(sK18(sK17(powerset(relation_image(X0,empty_set)))))) = apply(sK18(sK17(powerset(relation_image(X0,empty_set)))),sK12(sK18(sK17(powerset(relation_image(X0,empty_set)))))) )
| ~ function(X0)
| ~ relation(X0)
| ~ function(sK18(sK17(powerset(relation_image(X0,empty_set))))) ),
inference(superposition,[status(thm)],[c_32770,c_84]) ).
tcf(c_35806,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_99,c_19765]) ).
tcf(c_35807,plain,
sK18(powerset(relation_dom(relation_dom(relation_dom(relation_dom(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_114,c_19765]) ).
tcf(c_35808,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(relation_dom(relation_dom(relation_dom(sK18(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12738,c_19765]) ).
tcf(c_35809,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(relation_dom(relation_dom(relation_dom(sK18(powerset(sK18(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13358,c_19765]) ).
tcf(c_35810,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(relation_dom(relation_dom(relation_dom(relation_dom(relation_image(X0,X1))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK17(relation_image(X0,X1))))) = sK18(sK17(relation_image(X0,X1))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13159,c_19765]) ).
tcf(c_35811,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(relation_dom(relation_dom(relation_dom(relation_dom(relation_image(X0,X1))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(relation_image(X0,X1)))) = sK18(relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13157,c_19765]) ).
tcf(c_35812,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(relation_dom(relation_dom(relation_dom(relation_dom(sK18(powerset(relation_image(X0,X1))))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK18(powerset(relation_image(X0,X1)))))) = sK18(sK18(powerset(relation_image(X0,X1)))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13158,c_19765]) ).
tcf(c_35813,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(relation_dom(relation_dom(relation_dom(sK18(sK17(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13470,c_19765]) ).
tcf(c_35814,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(relation_dom(relation_dom(relation_dom(sK18(powerset(sK18(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13469,c_19765]) ).
tcf(c_35815,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(relation_dom(relation_dom(relation_dom(sK18(sK17(sK17(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15885,c_19765]) ).
tcf(c_35816,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(relation_dom(relation_dom(relation_dom(sK18(powerset(sK18(sK17(sK17(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15887,c_19765]) ).
tcf(c_35817,plain,
! [X0: $i] :
( ( sK18(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_17175,c_19765]) ).
tcf(c_35818,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(relation_dom(relation_dom(relation_dom(sK18(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17177,c_19765]) ).
tcf(c_35819,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(relation_dom(relation_dom(relation_dom(sK18(sK17(powerset(sK18(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17880,c_19765]) ).
tcf(c_35820,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(relation_dom(relation_dom(relation_dom(sK18(sK17(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17883,c_19765]) ).
tcf(c_35821,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(relation_dom(relation_dom(relation_dom(sK18(sK17(powerset(sK18(sK17(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17885,c_19765]) ).
tcf(c_35822,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(relation_dom(relation_dom(relation_dom(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17888,c_19765]) ).
tcf(c_35823,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(relation_dom(relation_dom(relation_dom(relation_dom(sK2(empty_set,X1,powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20186,c_19765]) ).
tcf(c_35824,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(relation_dom(relation_dom(relation_dom(relation_dom(sK18(powerset(sK2(empty_set,X1,powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20188,c_19765]) ).
tcf(c_35825,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(relation_dom(relation_dom(relation_dom(relation_dom(sK18(sK17(powerset(sK2(empty_set,X1,powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20189,c_19765]) ).
tcf(c_35826,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(relation_dom(relation_dom(relation_dom(relation_dom(sK7(empty_set,X1,powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21299,c_19765]) ).
tcf(c_35827,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(relation_dom(relation_dom(relation_dom(relation_dom(sK18(powerset(sK7(empty_set,X1,powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21301,c_19765]) ).
tcf(c_35828,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(relation_dom(relation_dom(relation_dom(relation_dom(sK18(sK17(powerset(sK7(empty_set,X1,powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21302,c_19765]) ).
tcf(c_35829,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(relation_dom(relation_dom(relation_dom(sK18(sK17(sK17(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25683,c_19765]) ).
tcf(c_35830,plain,
! [X0: $i] :
( ( sK18(powerset(relation_dom(relation_dom(relation_dom(relation_dom(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25684,c_19765]) ).
tcf(c_35954,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(relation_dom(relation_dom(relation_dom(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_99,c_19830]) ).
tcf(c_35955,plain,
sK18(sK17(powerset(relation_dom(relation_dom(relation_dom(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_114,c_19830]) ).
tcf(c_35956,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(relation_dom(relation_dom(relation_dom(sK18(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12738,c_19830]) ).
tcf(c_35957,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(relation_dom(relation_dom(relation_dom(sK18(powerset(sK18(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13358,c_19830]) ).
tcf(c_35958,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(powerset(relation_dom(relation_dom(relation_dom(relation_image(X0,X1))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK17(relation_image(X0,X1))))) = sK18(sK17(relation_image(X0,X1))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13159,c_19830]) ).
tcf(c_35959,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(powerset(relation_dom(relation_dom(relation_dom(relation_image(X0,X1))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(relation_image(X0,X1)))) = sK18(relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13157,c_19830]) ).
tcf(c_35960,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(powerset(relation_dom(relation_dom(relation_dom(sK18(powerset(relation_image(X0,X1))))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK18(powerset(relation_image(X0,X1)))))) = sK18(sK18(powerset(relation_image(X0,X1)))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13158,c_19830]) ).
tcf(c_35961,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(relation_dom(relation_dom(relation_dom(sK18(sK17(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13470,c_19830]) ).
tcf(c_35962,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(relation_dom(relation_dom(relation_dom(sK18(powerset(sK18(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13469,c_19830]) ).
tcf(c_35963,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(relation_dom(relation_dom(relation_dom(sK18(sK17(sK17(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15885,c_19830]) ).
tcf(c_35964,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(relation_dom(relation_dom(relation_dom(sK18(powerset(sK18(sK17(sK17(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15887,c_19830]) ).
tcf(c_35965,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(relation_dom(relation_dom(relation_dom(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17175,c_19830]) ).
tcf(c_35966,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(relation_dom(relation_dom(relation_dom(sK18(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17177,c_19830]) ).
tcf(c_35967,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(relation_dom(relation_dom(relation_dom(sK18(sK17(powerset(sK18(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17880,c_19830]) ).
tcf(c_35968,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(relation_dom(relation_dom(relation_dom(sK18(sK17(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17883,c_19830]) ).
tcf(c_35969,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(relation_dom(relation_dom(relation_dom(sK18(sK17(powerset(sK18(sK17(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17885,c_19830]) ).
tcf(c_35970,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(relation_dom(relation_dom(relation_dom(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17888,c_19830]) ).
tcf(c_35971,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(powerset(relation_dom(relation_dom(relation_dom(sK2(empty_set,X1,powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20186,c_19830]) ).
tcf(c_35972,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(powerset(relation_dom(relation_dom(relation_dom(sK18(powerset(sK2(empty_set,X1,powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20188,c_19830]) ).
tcf(c_35973,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(powerset(relation_dom(relation_dom(relation_dom(sK18(sK17(powerset(sK2(empty_set,X1,powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20189,c_19830]) ).
tcf(c_35974,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(powerset(relation_dom(relation_dom(relation_dom(sK7(empty_set,X1,powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21299,c_19830]) ).
tcf(c_35975,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(powerset(relation_dom(relation_dom(relation_dom(sK18(powerset(sK7(empty_set,X1,powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21301,c_19830]) ).
tcf(c_35976,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(powerset(relation_dom(relation_dom(relation_dom(sK18(sK17(powerset(sK7(empty_set,X1,powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21302,c_19830]) ).
tcf(c_35977,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(relation_dom(relation_dom(relation_dom(sK18(sK17(sK17(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25683,c_19830]) ).
tcf(c_35978,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(relation_dom(relation_dom(relation_dom(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25684,c_19830]) ).
tcf(c_36123,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(sK18(powerset(relation_dom(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_99,c_22188]) ).
tcf(c_36124,plain,
sK18(sK17(powerset(sK18(powerset(relation_dom(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_114,c_22188]) ).
tcf(c_36125,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(sK18(powerset(relation_dom(sK18(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12738,c_22188]) ).
tcf(c_36126,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(sK18(powerset(relation_dom(sK18(powerset(sK18(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13358,c_22188]) ).
tcf(c_36127,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(powerset(sK18(powerset(relation_dom(relation_image(X0,X1))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK17(relation_image(X0,X1))))) = sK18(sK17(relation_image(X0,X1))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13159,c_22188]) ).
tcf(c_36128,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(powerset(sK18(powerset(relation_dom(relation_image(X0,X1))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(relation_image(X0,X1)))) = sK18(relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13157,c_22188]) ).
tcf(c_36129,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(powerset(sK18(powerset(relation_dom(sK18(powerset(relation_image(X0,X1))))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK18(powerset(relation_image(X0,X1)))))) = sK18(sK18(powerset(relation_image(X0,X1)))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13158,c_22188]) ).
tcf(c_36130,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(sK18(powerset(relation_dom(sK18(sK17(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13470,c_22188]) ).
tcf(c_36131,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(sK18(powerset(relation_dom(sK18(powerset(sK18(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13469,c_22188]) ).
tcf(c_36132,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(sK18(powerset(relation_dom(sK18(sK17(sK17(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15885,c_22188]) ).
tcf(c_36133,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(sK18(powerset(relation_dom(sK18(powerset(sK18(sK17(sK17(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15887,c_22188]) ).
tcf(c_36134,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(sK18(powerset(relation_dom(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17175,c_22188]) ).
tcf(c_36135,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(sK18(powerset(relation_dom(sK18(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17177,c_22188]) ).
tcf(c_36136,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(sK18(powerset(relation_dom(sK18(sK17(powerset(sK18(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17880,c_22188]) ).
tcf(c_36137,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(sK18(powerset(relation_dom(sK18(sK17(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17883,c_22188]) ).
tcf(c_36138,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(sK18(powerset(relation_dom(sK18(sK17(powerset(sK18(sK17(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17885,c_22188]) ).
tcf(c_36139,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(sK18(powerset(relation_dom(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17888,c_22188]) ).
tcf(c_36140,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(powerset(sK18(powerset(relation_dom(sK2(empty_set,X1,powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20186,c_22188]) ).
tcf(c_36141,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(powerset(sK18(powerset(relation_dom(sK18(powerset(sK2(empty_set,X1,powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20188,c_22188]) ).
tcf(c_36142,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(powerset(sK18(powerset(relation_dom(sK18(sK17(powerset(sK2(empty_set,X1,powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20189,c_22188]) ).
tcf(c_36143,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(powerset(sK18(powerset(relation_dom(sK7(empty_set,X1,powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21299,c_22188]) ).
tcf(c_36144,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(powerset(sK18(powerset(relation_dom(sK18(powerset(sK7(empty_set,X1,powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21301,c_22188]) ).
tcf(c_36145,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(powerset(sK18(powerset(relation_dom(sK18(sK17(powerset(sK7(empty_set,X1,powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21302,c_22188]) ).
tcf(c_36146,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(sK18(powerset(relation_dom(sK18(sK17(sK17(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25683,c_22188]) ).
tcf(c_36147,plain,
! [X0: $i] :
( ( sK18(sK17(powerset(sK18(powerset(relation_dom(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25684,c_22188]) ).
tcf(c_36502,plain,
! [X0: $i,X1: $i] :
( empty(sK18(powerset(apply(sK1,sK4(sK1,X1,sK2(sK1,X0,relation_image(sK1,X1)))))))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ in(sK4(sK1,X1,sK2(sK1,X0,relation_image(sK1,X1))),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK18(sK17(sK17(sK18(powerset(apply(sK1,sK4(sK1,X1,sK2(sK1,X0,relation_image(sK1,X1)))))))))) ),
inference(superposition,[status(thm)],[c_31860,c_22453]) ).
tcf(c_36503,plain,
! [X0: $i,X1: $i] :
( empty(sK18(powerset(apply(sK1,sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1)))))))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ in(sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1))),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK18(sK17(sK17(sK18(powerset(apply(sK1,sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1)))))))))) ),
inference(superposition,[status(thm)],[c_33767,c_22453]) ).
tcf(c_36504,plain,
( empty(sK18(powerset(empty_set)))
| ~ in(empty_set,sK18(sK17(sK17(empty_set)))) ),
inference(superposition,[status(thm)],[c_12958,c_22453]) ).
tcf(c_36505,plain,
( empty(empty_set)
| ~ in(empty_set,sK18(sK17(sK17(empty_set)))) ),
inference(light_normalisation,[status(thm)],[c_36504,c_12958]) ).
tcf(c_36523,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK2(empty_set,X1,powerset(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_99,c_20333]) ).
tcf(c_36524,plain,
! [X0: $i] : sK18(powerset(sK2(empty_set,X0,powerset(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_114,c_20333]) ).
tcf(c_36525,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK2(empty_set,X1,powerset(sK18(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12738,c_20333]) ).
tcf(c_36526,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK2(empty_set,X1,powerset(sK18(powerset(sK18(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13358,c_20333]) ).
tcf(c_36527,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK18(powerset(sK2(empty_set,X2,powerset(relation_image(X0,X1))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK17(relation_image(X0,X1))))) = sK18(sK17(relation_image(X0,X1))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13159,c_20333]) ).
tcf(c_36528,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK18(powerset(sK2(empty_set,X2,powerset(relation_image(X0,X1))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(relation_image(X0,X1)))) = sK18(relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13157,c_20333]) ).
tcf(c_36529,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK18(powerset(sK2(empty_set,X2,powerset(sK18(powerset(relation_image(X0,X1))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK18(powerset(relation_image(X0,X1)))))) = sK18(sK18(powerset(relation_image(X0,X1)))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13158,c_20333]) ).
tcf(c_36530,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK2(empty_set,X1,powerset(sK18(sK17(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13470,c_20333]) ).
tcf(c_36531,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK2(empty_set,X1,powerset(sK18(powerset(sK18(sK17(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13469,c_20333]) ).
tcf(c_36532,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK2(empty_set,X1,powerset(sK18(sK17(sK17(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15885,c_20333]) ).
tcf(c_36533,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK2(empty_set,X1,powerset(sK18(powerset(sK18(sK17(sK17(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15887,c_20333]) ).
tcf(c_36534,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK2(empty_set,X1,powerset(relation_image(X0,empty_set))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17175,c_20333]) ).
tcf(c_36535,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK2(empty_set,X1,powerset(sK18(powerset(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17177,c_20333]) ).
tcf(c_36536,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK2(empty_set,X1,powerset(sK18(sK17(powerset(sK18(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17880,c_20333]) ).
tcf(c_36537,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK2(empty_set,X1,powerset(sK18(sK17(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17883,c_20333]) ).
tcf(c_36538,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK2(empty_set,X1,powerset(sK18(sK17(powerset(sK18(sK17(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17885,c_20333]) ).
tcf(c_36539,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK2(empty_set,X1,powerset(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17888,c_20333]) ).
tcf(c_36540,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK18(powerset(sK2(empty_set,X1,powerset(sK2(empty_set,X2,powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20186,c_20333]) ).
tcf(c_36541,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK18(powerset(sK2(empty_set,X1,powerset(sK18(powerset(sK2(empty_set,X2,powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20188,c_20333]) ).
tcf(c_36542,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK18(powerset(sK2(empty_set,X1,powerset(sK18(sK17(powerset(sK2(empty_set,X2,powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20189,c_20333]) ).
tcf(c_36543,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK18(powerset(sK2(empty_set,X1,powerset(sK7(empty_set,X2,powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21299,c_20333]) ).
tcf(c_36544,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK18(powerset(sK2(empty_set,X1,powerset(sK18(powerset(sK7(empty_set,X2,powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21301,c_20333]) ).
tcf(c_36545,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK18(powerset(sK2(empty_set,X1,powerset(sK18(sK17(powerset(sK7(empty_set,X2,powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21302,c_20333]) ).
tcf(c_36546,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK2(empty_set,X1,powerset(sK18(sK17(sK17(sK17(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25683,c_20333]) ).
tcf(c_36547,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK2(empty_set,X1,powerset(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25684,c_20333]) ).
tcf(c_36765,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK2(empty_set,X1,powerset(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_99,c_20335]) ).
tcf(c_36766,plain,
! [X0: $i] : relation_dom(relation_dom(sK2(empty_set,X0,powerset(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_114,c_20335]) ).
tcf(c_36767,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK2(empty_set,X1,powerset(sK18(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12738,c_20335]) ).
tcf(c_36768,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK2(empty_set,X1,powerset(sK18(powerset(sK18(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13358,c_20335]) ).
tcf(c_36769,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_dom(sK2(empty_set,X2,powerset(relation_image(X0,X1))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK17(relation_image(X0,X1))))) = sK18(sK17(relation_image(X0,X1))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13159,c_20335]) ).
tcf(c_36770,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_dom(sK2(empty_set,X2,powerset(relation_image(X0,X1))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(relation_image(X0,X1)))) = sK18(relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13157,c_20335]) ).
tcf(c_36771,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_dom(sK2(empty_set,X2,powerset(sK18(powerset(relation_image(X0,X1))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK18(powerset(relation_image(X0,X1)))))) = sK18(sK18(powerset(relation_image(X0,X1)))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13158,c_20335]) ).
tcf(c_36772,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK2(empty_set,X1,powerset(sK18(sK17(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13470,c_20335]) ).
tcf(c_36773,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK2(empty_set,X1,powerset(sK18(powerset(sK18(sK17(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13469,c_20335]) ).
tcf(c_36774,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK2(empty_set,X1,powerset(sK18(sK17(sK17(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15885,c_20335]) ).
tcf(c_36775,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK2(empty_set,X1,powerset(sK18(powerset(sK18(sK17(sK17(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15887,c_20335]) ).
tcf(c_36776,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK2(empty_set,X1,powerset(relation_image(X0,empty_set))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17175,c_20335]) ).
tcf(c_36777,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK2(empty_set,X1,powerset(sK18(powerset(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17177,c_20335]) ).
tcf(c_36778,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK2(empty_set,X1,powerset(sK18(sK17(powerset(sK18(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17880,c_20335]) ).
tcf(c_36779,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK2(empty_set,X1,powerset(sK18(sK17(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17883,c_20335]) ).
tcf(c_36780,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK2(empty_set,X1,powerset(sK18(sK17(powerset(sK18(sK17(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17885,c_20335]) ).
tcf(c_36781,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK2(empty_set,X1,powerset(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17888,c_20335]) ).
tcf(c_36782,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_dom(sK2(empty_set,X1,powerset(sK2(empty_set,X2,powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20186,c_20335]) ).
tcf(c_36783,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_dom(sK2(empty_set,X1,powerset(sK18(powerset(sK2(empty_set,X2,powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20188,c_20335]) ).
tcf(c_36784,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_dom(sK2(empty_set,X1,powerset(sK18(sK17(powerset(sK2(empty_set,X2,powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20189,c_20335]) ).
tcf(c_36785,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_dom(sK2(empty_set,X1,powerset(sK7(empty_set,X2,powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21299,c_20335]) ).
tcf(c_36786,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_dom(sK2(empty_set,X1,powerset(sK18(powerset(sK7(empty_set,X2,powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21301,c_20335]) ).
tcf(c_36787,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_dom(sK2(empty_set,X1,powerset(sK18(sK17(powerset(sK7(empty_set,X2,powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21302,c_20335]) ).
tcf(c_36788,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK2(empty_set,X1,powerset(sK18(sK17(sK17(sK17(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25683,c_20335]) ).
tcf(c_36789,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK2(empty_set,X1,powerset(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25684,c_20335]) ).
tcf(c_36994,plain,
! [X0: $i,X1: $i] :
( ( sK2(empty_set,X1,powerset(sK18(powerset(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_99,c_21017]) ).
tcf(c_36995,plain,
! [X0: $i] : sK2(empty_set,X0,powerset(sK18(powerset(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_114,c_21017]) ).
tcf(c_36997,plain,
! [X0: $i,X1: $i] :
( ( sK2(empty_set,X1,powerset(sK18(powerset(sK18(powerset(sK18(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13358,c_21017]) ).
tcf(c_36998,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK2(empty_set,X2,powerset(sK18(powerset(relation_image(X0,X1))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK17(relation_image(X0,X1))))) = sK18(sK17(relation_image(X0,X1))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13159,c_21017]) ).
tcf(c_36999,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK2(empty_set,X2,powerset(sK18(powerset(relation_image(X0,X1))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(relation_image(X0,X1)))) = sK18(relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13157,c_21017]) ).
tcf(c_37000,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK2(empty_set,X2,powerset(sK18(powerset(sK18(powerset(relation_image(X0,X1))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK18(powerset(relation_image(X0,X1)))))) = sK18(sK18(powerset(relation_image(X0,X1)))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13158,c_21017]) ).
tcf(c_37002,plain,
! [X0: $i,X1: $i] :
( ( sK2(empty_set,X1,powerset(sK18(powerset(sK18(powerset(sK18(sK17(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13469,c_21017]) ).
tcf(c_37004,plain,
! [X0: $i,X1: $i] :
( ( sK2(empty_set,X1,powerset(sK18(powerset(sK18(powerset(sK18(sK17(sK17(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15887,c_21017]) ).
tcf(c_37006,plain,
! [X0: $i,X1: $i] :
( ( sK2(empty_set,X1,powerset(sK18(powerset(sK18(powerset(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17177,c_21017]) ).
tcf(c_37007,plain,
! [X0: $i,X1: $i] :
( ( sK2(empty_set,X1,powerset(sK18(powerset(sK18(sK17(powerset(sK18(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17880,c_21017]) ).
tcf(c_37008,plain,
! [X0: $i,X1: $i] :
( ( sK2(empty_set,X1,powerset(sK18(powerset(sK18(sK17(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17883,c_21017]) ).
tcf(c_37009,plain,
! [X0: $i,X1: $i] :
( ( sK2(empty_set,X1,powerset(sK18(powerset(sK18(sK17(powerset(sK18(sK17(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17885,c_21017]) ).
tcf(c_37010,plain,
! [X0: $i,X1: $i] :
( ( sK2(empty_set,X1,powerset(sK18(powerset(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17888,c_21017]) ).
tcf(c_37012,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK2(empty_set,X1,powerset(sK18(powerset(sK18(powerset(sK2(empty_set,X2,powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20188,c_21017]) ).
tcf(c_37013,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK2(empty_set,X1,powerset(sK18(powerset(sK18(sK17(powerset(sK2(empty_set,X2,powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20189,c_21017]) ).
tcf(c_37015,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK2(empty_set,X1,powerset(sK18(powerset(sK18(powerset(sK7(empty_set,X2,powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21301,c_21017]) ).
tcf(c_37016,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK2(empty_set,X1,powerset(sK18(powerset(sK18(sK17(powerset(sK7(empty_set,X2,powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21302,c_21017]) ).
tcf(c_37018,plain,
! [X0: $i,X1: $i] :
( ( sK2(empty_set,X1,powerset(sK18(powerset(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25684,c_21017]) ).
tcf(c_37182,plain,
! [X0: $i,X1: $i] :
( in(apply(sK1,sK3(sK1,X0,empty_set)),X1)
| ( relation_image(sK1,X0) = relation_image(sK1,empty_set) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) )
| ~ in(sK2(sK1,X0,relation_image(sK1,empty_set)),X1)
| ~ in(sK3(sK1,X0,relation_image(sK1,empty_set)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_23326,c_35721]) ).
tcf(c_37183,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) )
| ( apply(X2,sK4(X2,X3,apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))))) = apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) )
| ~ function(X2)
| ~ relation(X2)
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),relation_image(X2,X3)) ),
inference(superposition,[status(thm)],[c_35721,c_60]) ).
tcf(c_37185,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X2,apply(sK1,sK3(sK1,X0,relation_image(sK1,X1)))),X3)
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) )
| ~ function(X2)
| ~ relation(X2)
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),relation_inverse_image(X2,X3)) ),
inference(superposition,[status(thm)],[c_35721,c_72]) ).
tcf(c_37186,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))),relation_dom(X2))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) )
| ~ function(X2)
| ~ relation(X2)
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),relation_inverse_image(X2,X3)) ),
inference(superposition,[status(thm)],[c_35721,c_71]) ).
tcf(c_37187,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK1,X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) )
| ~ in(sK2(sK1,X1,relation_image(sK1,X2)),X0)
| ~ in(sK3(sK1,X1,relation_image(sK1,X2)),relation_dom(sK1))
| ~ in(X0,apply(sK1,sK3(sK1,X1,relation_image(sK1,X2)))) ),
inference(superposition,[status(thm)],[c_35721,c_98]) ).
tcf(c_37188,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))),X2)
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) )
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),X2)
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_35721,c_97]) ).
tcf(c_37189,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) )
| ~ empty(X2)
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),X2)
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_35721,c_95]) ).
tcf(c_37190,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))),X2)
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) )
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK13(apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))),X2)) ),
inference(superposition,[status(thm)],[c_35721,c_12485]) ).
tcf(c_37191,plain,
! [X0: $i,X1: $i] :
( empty(apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) )
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK18(apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))))) ),
inference(superposition,[status(thm)],[c_35721,c_12526]) ).
tcf(c_37192,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X2)
| element(apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))),X2)
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) )
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK17(X2)) ),
inference(superposition,[status(thm)],[c_35721,c_14688]) ).
tcf(c_37193,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X2)
| in(apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))),X2)
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) )
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK17(X2)) ),
inference(superposition,[status(thm)],[c_35721,c_12618]) ).
tcf(c_37194,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))),X2)
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) )
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK18(powerset(X2))) ),
inference(superposition,[status(thm)],[c_35721,c_14689]) ).
tcf(c_37195,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) )
| ~ empty(X2)
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK18(powerset(X2))) ),
inference(superposition,[status(thm)],[c_35721,c_13313]) ).
tcf(c_37196,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))),X2)
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) )
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK18(powerset(X2))) ),
inference(superposition,[status(thm)],[c_35721,c_12619]) ).
tcf(c_37197,plain,
! [X0: $i,X1: $i] :
( ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) )
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),empty_set)
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_35721,c_13338]) ).
tcf(c_37198,plain,
! [X0: $i,X1: $i] :
( empty(sK18(powerset(apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))))))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) )
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK18(sK18(powerset(apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))))))) ),
inference(superposition,[status(thm)],[c_35721,c_12736]) ).
tcf(c_37199,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) )
| ~ function(X2)
| ~ relation(X2)
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),relation_image(X2,empty_set)) ),
inference(superposition,[status(thm)],[c_35721,c_13341]) ).
tcf(c_37200,plain,
! [X0: $i,X1: $i] :
( empty(apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) )
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK18(sK17(apply(sK1,sK3(sK1,X0,relation_image(sK1,X1)))))) ),
inference(superposition,[status(thm)],[c_35721,c_12990]) ).
tcf(c_37201,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))),X2)
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) )
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK18(sK17(powerset(X2)))) ),
inference(superposition,[status(thm)],[c_35721,c_14693]) ).
tcf(c_37202,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) )
| ~ empty(X2)
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK18(sK17(powerset(X2)))) ),
inference(superposition,[status(thm)],[c_35721,c_13316]) ).
tcf(c_37203,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))),X2)
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) )
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK18(sK17(powerset(X2)))) ),
inference(superposition,[status(thm)],[c_35721,c_13032]) ).
tcf(c_37204,plain,
! [X0: $i,X1: $i] :
( empty(apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) )
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK18(sK17(sK17(apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))))))) ),
inference(superposition,[status(thm)],[c_35721,c_15381]) ).
tcf(c_37205,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))),X2)
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) )
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK18(sK17(sK17(powerset(X2))))) ),
inference(superposition,[status(thm)],[c_35721,c_15478]) ).
tcf(c_37206,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) )
| ~ empty(X2)
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK18(sK17(sK17(powerset(X2))))) ),
inference(superposition,[status(thm)],[c_35721,c_15477]) ).
tcf(c_37207,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))),X2)
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) )
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK18(sK17(sK17(powerset(X2))))) ),
inference(superposition,[status(thm)],[c_35721,c_15476]) ).
tcf(c_37208,plain,
! [X0: $i,X1: $i] :
( empty(sK18(powerset(apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))))))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) )
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK18(sK17(sK18(powerset(apply(sK1,sK3(sK1,X0,relation_image(sK1,X1)))))))) ),
inference(superposition,[status(thm)],[c_35721,c_15649]) ).
tcf(c_37209,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK18(powerset(apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))))),X2)
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) )
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK13(sK18(powerset(apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))))),X2)) ),
inference(superposition,[status(thm)],[c_35721,c_16394]) ).
tcf(c_37210,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))))
| subset(sK17(apply(sK1,sK3(sK1,X0,relation_image(sK1,X1)))),X2)
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) )
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK13(sK17(apply(sK1,sK3(sK1,X0,relation_image(sK1,X1)))),X2)) ),
inference(superposition,[status(thm)],[c_35721,c_16730]) ).
tcf(c_37211,plain,
! [X0: $i,X1: $i] :
( empty(sK18(sK17(powerset(apply(sK1,sK3(sK1,X0,relation_image(sK1,X1)))))))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) )
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK18(sK18(sK17(powerset(apply(sK1,sK3(sK1,X0,relation_image(sK1,X1)))))))) ),
inference(superposition,[status(thm)],[c_35721,c_17874]) ).
tcf(c_37212,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))),powerset(X2))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) )
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK17(powerset(X2))) ),
inference(superposition,[status(thm)],[c_35721,c_18767]) ).
tcf(c_37213,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))),powerset(X2))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) )
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK17(powerset(X2))) ),
inference(superposition,[status(thm)],[c_35721,c_18765]) ).
tcf(c_37214,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = empty_set )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) )
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK2(empty_set,X2,apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))))) ),
inference(superposition,[status(thm)],[c_35721,c_19251]) ).
tcf(c_37215,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = empty_set )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) )
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK7(empty_set,X2,apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))))) ),
inference(superposition,[status(thm)],[c_35721,c_19880]) ).
tcf(c_37216,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) )
| ~ empty(X3)
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK2(empty_set,X2,powerset(X3))) ),
inference(superposition,[status(thm)],[c_35721,c_19620]) ).
tcf(c_37217,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))),X3)
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) )
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK2(empty_set,X2,powerset(X3))) ),
inference(superposition,[status(thm)],[c_35721,c_19619]) ).
tcf(c_37218,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))),X3)
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) )
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK2(empty_set,X2,powerset(X3))) ),
inference(superposition,[status(thm)],[c_35721,c_19621]) ).
tcf(c_37219,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) )
| ~ empty(X3)
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK7(empty_set,X2,powerset(X3))) ),
inference(superposition,[status(thm)],[c_35721,c_20797]) ).
tcf(c_37220,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))),X3)
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) )
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK7(empty_set,X2,powerset(X3))) ),
inference(superposition,[status(thm)],[c_35721,c_20796]) ).
tcf(c_37221,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))),X3)
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) )
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK7(empty_set,X2,powerset(X3))) ),
inference(superposition,[status(thm)],[c_35721,c_20798]) ).
tcf(c_37222,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) )
| ~ empty(X2)
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK18(sK17(sK17(sK17(powerset(X2)))))) ),
inference(superposition,[status(thm)],[c_35721,c_22277]) ).
tcf(c_37223,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))),X2)
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) )
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK18(sK17(sK17(sK17(powerset(X2)))))) ),
inference(superposition,[status(thm)],[c_35721,c_22276]) ).
tcf(c_37224,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))),X2)
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) )
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK18(sK17(sK17(sK17(powerset(X2)))))) ),
inference(superposition,[status(thm)],[c_35721,c_22278]) ).
tcf(c_37225,plain,
! [X0: $i,X1: $i] :
( empty(apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) )
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK18(sK17(sK17(sK17(apply(sK1,sK3(sK1,X0,relation_image(sK1,X1)))))))) ),
inference(superposition,[status(thm)],[c_35721,c_22295]) ).
tcf(c_37226,plain,
! [X0: $i,X1: $i] :
( empty(sK18(powerset(apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))))))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) )
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK18(sK17(sK17(sK18(powerset(apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))))))))) ),
inference(superposition,[status(thm)],[c_35721,c_22453]) ).
tcf(c_37268,plain,
! [X0: $i,X1: $i] :
( in(apply(sK1,sK3(sK1,X0,empty_set)),X1)
| ( relation_image(sK1,X0) = empty_set )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) )
| ~ in(sK2(sK1,X0,empty_set),X1)
| ~ in(sK3(sK1,X0,empty_set),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_37182,c_23326]) ).
tcf(c_37684,plain,
! [X0: $i,X1: $i] :
( in(sK3(sK1,X0,empty_set),relation_inverse_image(sK1,X1))
| ( relation_image(sK1,X0) = relation_image(sK1,empty_set) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))) = sK18(sK17(relation_image(sK1,relation_dom(sK1)))) )
| ~ in(sK2(sK1,X0,relation_image(sK1,empty_set)),X1)
| ~ in(sK3(sK1,X0,relation_image(sK1,empty_set)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_23326,c_35585]) ).
tcf(c_37685,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))),X2)
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))) = sK18(sK17(relation_image(sK1,relation_dom(sK1)))) )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),X2)
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_35585,c_72]) ).
tcf(c_37687,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK1,X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))) = sK18(sK17(relation_image(sK1,relation_dom(sK1)))) )
| ~ in(sK2(sK1,X1,relation_image(sK1,X2)),X0)
| ~ in(sK3(sK1,X1,relation_image(sK1,X2)),relation_dom(sK1))
| ~ in(relation_inverse_image(sK1,X0),sK3(sK1,X1,relation_image(sK1,X2))) ),
inference(superposition,[status(thm)],[c_35585,c_98]) ).
tcf(c_37688,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK3(sK1,X0,relation_image(sK1,X1)),relation_inverse_image(sK1,X2))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))) = sK18(sK17(relation_image(sK1,relation_dom(sK1)))) )
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),X2)
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_35585,c_97]) ).
tcf(c_37689,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))) = sK18(sK17(relation_image(sK1,relation_dom(sK1)))) )
| ~ empty(relation_inverse_image(sK1,X2))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),X2)
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_35585,c_95]) ).
tcf(c_37695,plain,
! [X0: $i,X1: $i] :
( in(sK3(sK1,X0,empty_set),relation_inverse_image(sK1,X1))
| ( relation_image(sK1,X0) = empty_set )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))) = sK18(sK17(relation_image(sK1,relation_dom(sK1)))) )
| ~ in(sK2(sK1,X0,empty_set),X1)
| ~ in(sK3(sK1,X0,empty_set),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_37684,c_23326]) ).
tcf(c_37711,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))),X2)
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))) = sK18(sK17(relation_image(sK1,relation_dom(sK1)))) )
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),X2)
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_37685,c_52,c_51]) ).
tcf(c_37769,plain,
! [X0: $i,X1: $i] :
( in(sK2(sK1,X0,empty_set),relation_image(sK1,X1))
| ( relation_image(sK1,X0) = relation_image(sK1,empty_set) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))) = sK18(sK17(relation_image(sK1,relation_dom(sK1)))) )
| ~ in(sK3(sK1,X0,relation_image(sK1,empty_set)),X1)
| ~ in(sK3(sK1,X0,relation_image(sK1,empty_set)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_23326,c_35591]) ).
tcf(c_37770,plain,
! [X0: $i,X1: $i] :
( in(sK2(sK1,X0,relation_image(sK1,X1)),empty_set)
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))) = sK18(sK17(relation_image(sK1,relation_dom(sK1)))) )
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),empty_set)
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_23326,c_35591]) ).
tcf(c_37771,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,X2,sK2(sK1,X0,relation_image(sK1,X1)))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))) = sK18(sK17(relation_image(sK1,relation_dom(sK1)))) )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),X2)
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_35591,c_60]) ).
tcf(c_37772,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK1,X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))) = sK18(sK17(relation_image(sK1,relation_dom(sK1)))) )
| ~ in(sK3(sK1,X1,relation_image(sK1,X2)),X0)
| ~ in(sK3(sK1,X1,relation_image(sK1,X2)),relation_dom(sK1))
| ~ in(relation_image(sK1,X0),sK2(sK1,X1,relation_image(sK1,X2))) ),
inference(superposition,[status(thm)],[c_35591,c_98]) ).
tcf(c_37773,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(sK1,X0,relation_image(sK1,X1)),relation_image(sK1,X2))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))) = sK18(sK17(relation_image(sK1,relation_dom(sK1)))) )
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),X2)
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_35591,c_97]) ).
tcf(c_37774,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))) = sK18(sK17(relation_image(sK1,relation_dom(sK1)))) )
| ~ empty(relation_image(sK1,X2))
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),X2)
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_35591,c_95]) ).
tcf(c_37775,plain,
! [X0: $i,X1: $i] :
( ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))) = sK18(sK17(relation_image(sK1,relation_dom(sK1)))) )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),empty_set)
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_35591,c_13341]) ).
tcf(c_37781,plain,
! [X0: $i,X1: $i] :
( in(sK2(sK1,X0,empty_set),relation_image(sK1,X1))
| ( relation_image(sK1,X0) = empty_set )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))) = sK18(sK17(relation_image(sK1,relation_dom(sK1)))) )
| ~ in(sK3(sK1,X0,empty_set),X1)
| ~ in(sK3(sK1,X0,empty_set),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_37769,c_23326]) ).
tcf(c_37797,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,X2,sK2(sK1,X0,relation_image(sK1,X1)))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))) = sK18(sK17(relation_image(sK1,relation_dom(sK1)))) )
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),X2)
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_37771,c_52,c_51]) ).
tcf(c_37868,plain,
! [X0: $i,X1: $i] :
( in(apply(sK1,sK3(sK1,X0,empty_set)),X1)
| ( relation_image(sK1,X0) = relation_image(sK1,empty_set) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))) = sK18(sK17(relation_image(sK1,relation_dom(sK1)))) )
| ~ in(sK2(sK1,X0,relation_image(sK1,empty_set)),X1)
| ~ in(sK3(sK1,X0,relation_image(sK1,empty_set)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_23326,c_37711]) ).
tcf(c_37869,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))) = sK18(sK17(relation_image(sK1,relation_dom(sK1)))) )
| ( apply(X2,sK4(X2,X3,apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))))) = apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) )
| ~ function(X2)
| ~ relation(X2)
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),relation_image(X2,X3)) ),
inference(superposition,[status(thm)],[c_37711,c_60]) ).
tcf(c_37871,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X2,apply(sK1,sK3(sK1,X0,relation_image(sK1,X1)))),X3)
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))) = sK18(sK17(relation_image(sK1,relation_dom(sK1)))) )
| ~ function(X2)
| ~ relation(X2)
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),relation_inverse_image(X2,X3)) ),
inference(superposition,[status(thm)],[c_37711,c_72]) ).
tcf(c_37872,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))),relation_dom(X2))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))) = sK18(sK17(relation_image(sK1,relation_dom(sK1)))) )
| ~ function(X2)
| ~ relation(X2)
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),relation_inverse_image(X2,X3)) ),
inference(superposition,[status(thm)],[c_37711,c_71]) ).
tcf(c_37873,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK1,X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))) = sK18(sK17(relation_image(sK1,relation_dom(sK1)))) )
| ~ in(sK2(sK1,X1,relation_image(sK1,X2)),X0)
| ~ in(sK3(sK1,X1,relation_image(sK1,X2)),relation_dom(sK1))
| ~ in(X0,apply(sK1,sK3(sK1,X1,relation_image(sK1,X2)))) ),
inference(superposition,[status(thm)],[c_37711,c_98]) ).
tcf(c_37874,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))),X2)
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))) = sK18(sK17(relation_image(sK1,relation_dom(sK1)))) )
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),X2)
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_37711,c_97]) ).
tcf(c_37875,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))) = sK18(sK17(relation_image(sK1,relation_dom(sK1)))) )
| ~ empty(X2)
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),X2)
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_37711,c_95]) ).
tcf(c_37876,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))),X2)
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))) = sK18(sK17(relation_image(sK1,relation_dom(sK1)))) )
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK13(apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))),X2)) ),
inference(superposition,[status(thm)],[c_37711,c_12485]) ).
tcf(c_37877,plain,
! [X0: $i,X1: $i] :
( empty(apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))) = sK18(sK17(relation_image(sK1,relation_dom(sK1)))) )
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK18(apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))))) ),
inference(superposition,[status(thm)],[c_37711,c_12526]) ).
tcf(c_37878,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X2)
| element(apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))),X2)
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))) = sK18(sK17(relation_image(sK1,relation_dom(sK1)))) )
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK17(X2)) ),
inference(superposition,[status(thm)],[c_37711,c_14688]) ).
tcf(c_37879,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X2)
| in(apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))),X2)
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))) = sK18(sK17(relation_image(sK1,relation_dom(sK1)))) )
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK17(X2)) ),
inference(superposition,[status(thm)],[c_37711,c_12618]) ).
tcf(c_37880,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))),X2)
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))) = sK18(sK17(relation_image(sK1,relation_dom(sK1)))) )
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK18(powerset(X2))) ),
inference(superposition,[status(thm)],[c_37711,c_14689]) ).
tcf(c_37881,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))) = sK18(sK17(relation_image(sK1,relation_dom(sK1)))) )
| ~ empty(X2)
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK18(powerset(X2))) ),
inference(superposition,[status(thm)],[c_37711,c_13313]) ).
tcf(c_37882,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))),X2)
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))) = sK18(sK17(relation_image(sK1,relation_dom(sK1)))) )
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK18(powerset(X2))) ),
inference(superposition,[status(thm)],[c_37711,c_12619]) ).
tcf(c_37883,plain,
! [X0: $i,X1: $i] :
( ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))) = sK18(sK17(relation_image(sK1,relation_dom(sK1)))) )
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),empty_set)
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_37711,c_13338]) ).
tcf(c_37884,plain,
! [X0: $i,X1: $i] :
( empty(sK18(powerset(apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))))))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))) = sK18(sK17(relation_image(sK1,relation_dom(sK1)))) )
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK18(sK18(powerset(apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))))))) ),
inference(superposition,[status(thm)],[c_37711,c_12736]) ).
tcf(c_37885,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))) = sK18(sK17(relation_image(sK1,relation_dom(sK1)))) )
| ~ function(X2)
| ~ relation(X2)
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),relation_image(X2,empty_set)) ),
inference(superposition,[status(thm)],[c_37711,c_13341]) ).
tcf(c_37886,plain,
! [X0: $i,X1: $i] :
( empty(apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))) = sK18(sK17(relation_image(sK1,relation_dom(sK1)))) )
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK18(sK17(apply(sK1,sK3(sK1,X0,relation_image(sK1,X1)))))) ),
inference(superposition,[status(thm)],[c_37711,c_12990]) ).
tcf(c_37887,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))),X2)
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))) = sK18(sK17(relation_image(sK1,relation_dom(sK1)))) )
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK18(sK17(powerset(X2)))) ),
inference(superposition,[status(thm)],[c_37711,c_14693]) ).
tcf(c_37888,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))) = sK18(sK17(relation_image(sK1,relation_dom(sK1)))) )
| ~ empty(X2)
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK18(sK17(powerset(X2)))) ),
inference(superposition,[status(thm)],[c_37711,c_13316]) ).
tcf(c_37889,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))),X2)
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))) = sK18(sK17(relation_image(sK1,relation_dom(sK1)))) )
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK18(sK17(powerset(X2)))) ),
inference(superposition,[status(thm)],[c_37711,c_13032]) ).
tcf(c_37890,plain,
! [X0: $i,X1: $i] :
( empty(apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))) = sK18(sK17(relation_image(sK1,relation_dom(sK1)))) )
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK18(sK17(sK17(apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))))))) ),
inference(superposition,[status(thm)],[c_37711,c_15381]) ).
tcf(c_37891,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))),X2)
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))) = sK18(sK17(relation_image(sK1,relation_dom(sK1)))) )
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK18(sK17(sK17(powerset(X2))))) ),
inference(superposition,[status(thm)],[c_37711,c_15478]) ).
tcf(c_37892,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))) = sK18(sK17(relation_image(sK1,relation_dom(sK1)))) )
| ~ empty(X2)
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK18(sK17(sK17(powerset(X2))))) ),
inference(superposition,[status(thm)],[c_37711,c_15477]) ).
tcf(c_37893,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))),X2)
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))) = sK18(sK17(relation_image(sK1,relation_dom(sK1)))) )
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK18(sK17(sK17(powerset(X2))))) ),
inference(superposition,[status(thm)],[c_37711,c_15476]) ).
tcf(c_37894,plain,
! [X0: $i,X1: $i] :
( empty(sK18(powerset(apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))))))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))) = sK18(sK17(relation_image(sK1,relation_dom(sK1)))) )
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK18(sK17(sK18(powerset(apply(sK1,sK3(sK1,X0,relation_image(sK1,X1)))))))) ),
inference(superposition,[status(thm)],[c_37711,c_15649]) ).
tcf(c_37895,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK18(powerset(apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))))),X2)
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))) = sK18(sK17(relation_image(sK1,relation_dom(sK1)))) )
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK13(sK18(powerset(apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))))),X2)) ),
inference(superposition,[status(thm)],[c_37711,c_16394]) ).
tcf(c_37896,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))))
| subset(sK17(apply(sK1,sK3(sK1,X0,relation_image(sK1,X1)))),X2)
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))) = sK18(sK17(relation_image(sK1,relation_dom(sK1)))) )
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK13(sK17(apply(sK1,sK3(sK1,X0,relation_image(sK1,X1)))),X2)) ),
inference(superposition,[status(thm)],[c_37711,c_16730]) ).
tcf(c_37897,plain,
! [X0: $i,X1: $i] :
( empty(sK18(sK17(powerset(apply(sK1,sK3(sK1,X0,relation_image(sK1,X1)))))))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))) = sK18(sK17(relation_image(sK1,relation_dom(sK1)))) )
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK18(sK18(sK17(powerset(apply(sK1,sK3(sK1,X0,relation_image(sK1,X1)))))))) ),
inference(superposition,[status(thm)],[c_37711,c_17874]) ).
tcf(c_37898,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))),powerset(X2))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))) = sK18(sK17(relation_image(sK1,relation_dom(sK1)))) )
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK17(powerset(X2))) ),
inference(superposition,[status(thm)],[c_37711,c_18767]) ).
tcf(c_37899,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))),powerset(X2))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))) = sK18(sK17(relation_image(sK1,relation_dom(sK1)))) )
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK17(powerset(X2))) ),
inference(superposition,[status(thm)],[c_37711,c_18765]) ).
tcf(c_37900,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = empty_set )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))) = sK18(sK17(relation_image(sK1,relation_dom(sK1)))) )
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK2(empty_set,X2,apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))))) ),
inference(superposition,[status(thm)],[c_37711,c_19251]) ).
tcf(c_37901,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = empty_set )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))) = sK18(sK17(relation_image(sK1,relation_dom(sK1)))) )
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK7(empty_set,X2,apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))))) ),
inference(superposition,[status(thm)],[c_37711,c_19880]) ).
tcf(c_37902,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))) = sK18(sK17(relation_image(sK1,relation_dom(sK1)))) )
| ~ empty(X3)
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK2(empty_set,X2,powerset(X3))) ),
inference(superposition,[status(thm)],[c_37711,c_19620]) ).
tcf(c_37903,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))),X3)
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))) = sK18(sK17(relation_image(sK1,relation_dom(sK1)))) )
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK2(empty_set,X2,powerset(X3))) ),
inference(superposition,[status(thm)],[c_37711,c_19619]) ).
tcf(c_37904,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))),X3)
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))) = sK18(sK17(relation_image(sK1,relation_dom(sK1)))) )
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK2(empty_set,X2,powerset(X3))) ),
inference(superposition,[status(thm)],[c_37711,c_19621]) ).
tcf(c_37905,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))) = sK18(sK17(relation_image(sK1,relation_dom(sK1)))) )
| ~ empty(X3)
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK7(empty_set,X2,powerset(X3))) ),
inference(superposition,[status(thm)],[c_37711,c_20797]) ).
tcf(c_37906,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))),X3)
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))) = sK18(sK17(relation_image(sK1,relation_dom(sK1)))) )
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK7(empty_set,X2,powerset(X3))) ),
inference(superposition,[status(thm)],[c_37711,c_20796]) ).
tcf(c_37907,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))),X3)
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))) = sK18(sK17(relation_image(sK1,relation_dom(sK1)))) )
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK7(empty_set,X2,powerset(X3))) ),
inference(superposition,[status(thm)],[c_37711,c_20798]) ).
tcf(c_37908,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))) = sK18(sK17(relation_image(sK1,relation_dom(sK1)))) )
| ~ empty(X2)
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK18(sK17(sK17(sK17(powerset(X2)))))) ),
inference(superposition,[status(thm)],[c_37711,c_22277]) ).
tcf(c_37909,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))),X2)
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))) = sK18(sK17(relation_image(sK1,relation_dom(sK1)))) )
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK18(sK17(sK17(sK17(powerset(X2)))))) ),
inference(superposition,[status(thm)],[c_37711,c_22276]) ).
tcf(c_37910,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))),X2)
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))) = sK18(sK17(relation_image(sK1,relation_dom(sK1)))) )
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK18(sK17(sK17(sK17(powerset(X2)))))) ),
inference(superposition,[status(thm)],[c_37711,c_22278]) ).
tcf(c_37911,plain,
! [X0: $i,X1: $i] :
( empty(apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))) = sK18(sK17(relation_image(sK1,relation_dom(sK1)))) )
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK18(sK17(sK17(sK17(apply(sK1,sK3(sK1,X0,relation_image(sK1,X1)))))))) ),
inference(superposition,[status(thm)],[c_37711,c_22295]) ).
tcf(c_37912,plain,
! [X0: $i,X1: $i] :
( empty(sK18(powerset(apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))))))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))) = sK18(sK17(relation_image(sK1,relation_dom(sK1)))) )
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK18(sK17(sK17(sK18(powerset(apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))))))))) ),
inference(superposition,[status(thm)],[c_37711,c_22453]) ).
tcf(c_37954,plain,
! [X0: $i,X1: $i] :
( in(apply(sK1,sK3(sK1,X0,empty_set)),X1)
| ( relation_image(sK1,X0) = empty_set )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))) = sK18(sK17(relation_image(sK1,relation_dom(sK1)))) )
| ~ in(sK2(sK1,X0,empty_set),X1)
| ~ in(sK3(sK1,X0,empty_set),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_37868,c_23326]) ).
tcf(c_38396,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))),X0)
| ( relation_image(sK1,X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X2))) = sK2(sK1,X1,relation_image(sK1,X2)) )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(sK18(relation_image(sK1,relation_dom(sK1))),X0)
| ~ in(sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_35394,c_72]) ).
tcf(c_38398,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK1,X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X2))) = sK2(sK1,X1,relation_image(sK1,X2)) )
| ~ in(sK18(relation_image(sK1,relation_dom(sK1))),X0)
| ~ in(sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1)))),relation_dom(sK1))
| ~ in(relation_inverse_image(sK1,X0),sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) ),
inference(superposition,[status(thm)],[c_35394,c_98]) ).
tcf(c_38399,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1)))),relation_inverse_image(sK1,X0))
| ( relation_image(sK1,X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X2))) = sK2(sK1,X1,relation_image(sK1,X2)) )
| ~ in(sK18(relation_image(sK1,relation_dom(sK1))),X0)
| ~ in(sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_35394,c_97]) ).
tcf(c_38400,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK1,X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X2))) = sK2(sK1,X1,relation_image(sK1,X2)) )
| ~ empty(relation_inverse_image(sK1,X0))
| ~ in(sK18(relation_image(sK1,relation_dom(sK1))),X0)
| ~ in(sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_35394,c_95]) ).
tcf(c_38416,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))),X0)
| ( relation_image(sK1,X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X2))) = sK2(sK1,X1,relation_image(sK1,X2)) )
| ~ in(sK18(relation_image(sK1,relation_dom(sK1))),X0)
| ~ in(sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1)))),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_38396,c_52,c_51]) ).
tcf(c_38476,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK18(relation_image(sK1,relation_dom(sK1))),relation_image(sK1,X0))
| ( relation_image(sK1,X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X2))) = sK2(sK1,X1,relation_image(sK1,X2)) )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(sK18(relation_image(sK1,relation_dom(sK1))),relation_image(sK1,relation_dom(sK1)))
| ~ in(sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1)))),X0) ),
inference(superposition,[status(thm)],[c_58,c_35400]) ).
tcf(c_38478,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK18(relation_image(sK1,relation_dom(sK1))),relation_image(sK1,X0))
| ( relation_image(sK1,X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X2))) = sK2(sK1,X1,relation_image(sK1,X2)) )
| ~ in(sK18(relation_image(sK1,relation_dom(sK1))),relation_image(sK1,relation_dom(sK1)))
| ~ in(sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1)))),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_38476,c_52,c_51]) ).
tcf(c_38497,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK18(relation_image(sK1,relation_dom(sK1))),relation_image(sK1,powerset(X0)))
| ( relation_image(sK1,X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X2))) = sK2(sK1,X1,relation_image(sK1,X2)) )
| ~ in(sK18(relation_image(sK1,relation_dom(sK1))),relation_image(sK1,relation_dom(sK1)))
| ~ subset(sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1)))),X0) ),
inference(superposition,[status(thm)],[c_12509,c_38478]) ).
tcf(c_38498,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK18(relation_image(sK1,relation_dom(sK1))),relation_image(sK1,relation_inverse_image(sK1,X0)))
| ( relation_image(sK1,X3) = relation_image(sK1,X4) )
| ( relation_image(sK1,X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK3(sK1,X3,relation_image(sK1,X4))) = sK2(sK1,X3,relation_image(sK1,X4)) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X2))) = sK2(sK1,X1,relation_image(sK1,X2)) )
| ~ in(sK18(relation_image(sK1,relation_dom(sK1))),X0)
| ~ in(sK18(relation_image(sK1,relation_dom(sK1))),relation_image(sK1,relation_dom(sK1)))
| ~ in(sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_35394,c_38478]) ).
tcf(c_38550,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(sK1,X2) = relation_image(sK1,X3) )
| ( apply(sK1,sK3(sK1,X2,relation_image(sK1,X3))) = sK2(sK1,X2,relation_image(sK1,X3)) )
| ( apply(X0,sK4(X0,X1,apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))))) = apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK18(relation_image(sK1,relation_dom(sK1))),relation_image(X0,X1))
| ~ in(sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_38416,c_60]) ).
tcf(c_38552,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X0,apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1)))))),X1)
| ( relation_image(sK1,X2) = relation_image(sK1,X3) )
| ( apply(sK1,sK3(sK1,X2,relation_image(sK1,X3))) = sK2(sK1,X2,relation_image(sK1,X3)) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK18(relation_image(sK1,relation_dom(sK1))),relation_inverse_image(X0,X1))
| ~ in(sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_38416,c_72]) ).
tcf(c_38553,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))),relation_dom(X0))
| ( relation_image(sK1,X2) = relation_image(sK1,X3) )
| ( apply(sK1,sK3(sK1,X2,relation_image(sK1,X3))) = sK2(sK1,X2,relation_image(sK1,X3)) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK18(relation_image(sK1,relation_dom(sK1))),relation_inverse_image(X0,X1))
| ~ in(sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_38416,c_71]) ).
tcf(c_38554,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK1,X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X2))) = sK2(sK1,X1,relation_image(sK1,X2)) )
| ~ in(sK18(relation_image(sK1,relation_dom(sK1))),X0)
| ~ in(sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1)))),relation_dom(sK1))
| ~ in(X0,apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1)))))) ),
inference(superposition,[status(thm)],[c_38416,c_98]) ).
tcf(c_38555,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))),X0)
| ( relation_image(sK1,X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X2))) = sK2(sK1,X1,relation_image(sK1,X2)) )
| ~ in(sK18(relation_image(sK1,relation_dom(sK1))),X0)
| ~ in(sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_38416,c_97]) ).
tcf(c_38556,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK1,X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X2))) = sK2(sK1,X1,relation_image(sK1,X2)) )
| ~ empty(X0)
| ~ in(sK18(relation_image(sK1,relation_dom(sK1))),X0)
| ~ in(sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_38416,c_95]) ).
tcf(c_38557,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))),X0)
| ( relation_image(sK1,X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X2))) = sK2(sK1,X1,relation_image(sK1,X2)) )
| ~ in(sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1)))),relation_dom(sK1))
| ~ in(sK18(relation_image(sK1,relation_dom(sK1))),sK13(apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))),X0)) ),
inference(superposition,[status(thm)],[c_38416,c_12485]) ).
tcf(c_38558,plain,
! [X0: $i,X1: $i] :
( empty(apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ in(sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1)))),relation_dom(sK1))
| ~ in(sK18(relation_image(sK1,relation_dom(sK1))),sK18(apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))))) ),
inference(superposition,[status(thm)],[c_38416,c_12526]) ).
tcf(c_38559,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X0)
| element(apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))),X0)
| ( relation_image(sK1,X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X2))) = sK2(sK1,X1,relation_image(sK1,X2)) )
| ~ in(sK18(relation_image(sK1,relation_dom(sK1))),sK17(X0))
| ~ in(sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_38416,c_14688]) ).
tcf(c_38560,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X0)
| in(apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))),X0)
| ( relation_image(sK1,X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X2))) = sK2(sK1,X1,relation_image(sK1,X2)) )
| ~ in(sK18(relation_image(sK1,relation_dom(sK1))),sK17(X0))
| ~ in(sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_38416,c_12618]) ).
tcf(c_38561,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))),X0)
| ( relation_image(sK1,X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X2))) = sK2(sK1,X1,relation_image(sK1,X2)) )
| ~ in(sK18(relation_image(sK1,relation_dom(sK1))),sK18(powerset(X0)))
| ~ in(sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_38416,c_14689]) ).
tcf(c_38562,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK1,X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X2))) = sK2(sK1,X1,relation_image(sK1,X2)) )
| ~ empty(X0)
| ~ in(sK18(relation_image(sK1,relation_dom(sK1))),sK18(powerset(X0)))
| ~ in(sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_38416,c_13313]) ).
tcf(c_38563,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))),X0)
| ( relation_image(sK1,X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X2))) = sK2(sK1,X1,relation_image(sK1,X2)) )
| ~ in(sK18(relation_image(sK1,relation_dom(sK1))),sK18(powerset(X0)))
| ~ in(sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_38416,c_12619]) ).
tcf(c_38564,plain,
! [X0: $i,X1: $i] :
( ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ in(sK18(relation_image(sK1,relation_dom(sK1))),empty_set)
| ~ in(sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_38416,c_13338]) ).
tcf(c_38565,plain,
! [X0: $i,X1: $i] :
( empty(sK18(powerset(apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))))))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ in(sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1)))),relation_dom(sK1))
| ~ in(sK18(relation_image(sK1,relation_dom(sK1))),sK18(sK18(powerset(apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))))))) ),
inference(superposition,[status(thm)],[c_38416,c_12736]) ).
tcf(c_38566,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK1,X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X2))) = sK2(sK1,X1,relation_image(sK1,X2)) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK18(relation_image(sK1,relation_dom(sK1))),relation_image(X0,empty_set))
| ~ in(sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_38416,c_13341]) ).
tcf(c_38567,plain,
! [X0: $i,X1: $i] :
( empty(apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ in(sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1)))),relation_dom(sK1))
| ~ in(sK18(relation_image(sK1,relation_dom(sK1))),sK18(sK17(apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1)))))))) ),
inference(superposition,[status(thm)],[c_38416,c_12990]) ).
tcf(c_38568,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))),X0)
| ( relation_image(sK1,X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X2))) = sK2(sK1,X1,relation_image(sK1,X2)) )
| ~ in(sK18(relation_image(sK1,relation_dom(sK1))),sK18(sK17(powerset(X0))))
| ~ in(sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_38416,c_14693]) ).
tcf(c_38569,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK1,X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X2))) = sK2(sK1,X1,relation_image(sK1,X2)) )
| ~ empty(X0)
| ~ in(sK18(relation_image(sK1,relation_dom(sK1))),sK18(sK17(powerset(X0))))
| ~ in(sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_38416,c_13316]) ).
tcf(c_38570,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))),X0)
| ( relation_image(sK1,X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X2))) = sK2(sK1,X1,relation_image(sK1,X2)) )
| ~ in(sK18(relation_image(sK1,relation_dom(sK1))),sK18(sK17(powerset(X0))))
| ~ in(sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_38416,c_13032]) ).
tcf(c_38571,plain,
! [X0: $i,X1: $i] :
( empty(apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ in(sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1)))),relation_dom(sK1))
| ~ in(sK18(relation_image(sK1,relation_dom(sK1))),sK18(sK17(sK17(apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))))))) ),
inference(superposition,[status(thm)],[c_38416,c_15381]) ).
tcf(c_38572,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))),X0)
| ( relation_image(sK1,X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X2))) = sK2(sK1,X1,relation_image(sK1,X2)) )
| ~ in(sK18(relation_image(sK1,relation_dom(sK1))),sK18(sK17(sK17(powerset(X0)))))
| ~ in(sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_38416,c_15478]) ).
tcf(c_38573,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK1,X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X2))) = sK2(sK1,X1,relation_image(sK1,X2)) )
| ~ empty(X0)
| ~ in(sK18(relation_image(sK1,relation_dom(sK1))),sK18(sK17(sK17(powerset(X0)))))
| ~ in(sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_38416,c_15477]) ).
tcf(c_38574,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))),X0)
| ( relation_image(sK1,X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X2))) = sK2(sK1,X1,relation_image(sK1,X2)) )
| ~ in(sK18(relation_image(sK1,relation_dom(sK1))),sK18(sK17(sK17(powerset(X0)))))
| ~ in(sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_38416,c_15476]) ).
tcf(c_38575,plain,
! [X0: $i,X1: $i] :
( empty(sK18(powerset(apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))))))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ in(sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1)))),relation_dom(sK1))
| ~ in(sK18(relation_image(sK1,relation_dom(sK1))),sK18(sK17(sK18(powerset(apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1)))))))))) ),
inference(superposition,[status(thm)],[c_38416,c_15649]) ).
tcf(c_38576,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK18(powerset(apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))))),X0)
| ( relation_image(sK1,X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X2))) = sK2(sK1,X1,relation_image(sK1,X2)) )
| ~ in(sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1)))),relation_dom(sK1))
| ~ in(sK18(relation_image(sK1,relation_dom(sK1))),sK13(sK18(powerset(apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))))),X0)) ),
inference(superposition,[status(thm)],[c_38416,c_16394]) ).
tcf(c_38577,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))))
| subset(sK17(apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1)))))),X0)
| ( relation_image(sK1,X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X2))) = sK2(sK1,X1,relation_image(sK1,X2)) )
| ~ in(sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1)))),relation_dom(sK1))
| ~ in(sK18(relation_image(sK1,relation_dom(sK1))),sK13(sK17(apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1)))))),X0)) ),
inference(superposition,[status(thm)],[c_38416,c_16730]) ).
tcf(c_38578,plain,
! [X0: $i,X1: $i] :
( empty(sK18(sK17(powerset(apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1)))))))))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ in(sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1)))),relation_dom(sK1))
| ~ in(sK18(relation_image(sK1,relation_dom(sK1))),sK18(sK18(sK17(powerset(apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1)))))))))) ),
inference(superposition,[status(thm)],[c_38416,c_17874]) ).
tcf(c_38579,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))),powerset(X0))
| ( relation_image(sK1,X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X2))) = sK2(sK1,X1,relation_image(sK1,X2)) )
| ~ in(sK18(relation_image(sK1,relation_dom(sK1))),sK17(powerset(X0)))
| ~ in(sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_38416,c_18767]) ).
tcf(c_38580,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))),powerset(X0))
| ( relation_image(sK1,X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X2))) = sK2(sK1,X1,relation_image(sK1,X2)) )
| ~ in(sK18(relation_image(sK1,relation_dom(sK1))),sK17(powerset(X0)))
| ~ in(sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_38416,c_18765]) ).
tcf(c_38581,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK1,X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X2))) = sK2(sK1,X1,relation_image(sK1,X2)) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = empty_set )
| ~ in(sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1)))),relation_dom(sK1))
| ~ in(sK18(relation_image(sK1,relation_dom(sK1))),sK2(empty_set,X0,apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))))) ),
inference(superposition,[status(thm)],[c_38416,c_19251]) ).
tcf(c_38582,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK1,X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X2))) = sK2(sK1,X1,relation_image(sK1,X2)) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = empty_set )
| ~ in(sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1)))),relation_dom(sK1))
| ~ in(sK18(relation_image(sK1,relation_dom(sK1))),sK7(empty_set,X0,apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))))) ),
inference(superposition,[status(thm)],[c_38416,c_19880]) ).
tcf(c_38583,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(sK1,X2) = relation_image(sK1,X3) )
| ( apply(sK1,sK3(sK1,X2,relation_image(sK1,X3))) = sK2(sK1,X2,relation_image(sK1,X3)) )
| ~ empty(X1)
| ~ in(sK18(relation_image(sK1,relation_dom(sK1))),sK2(empty_set,X0,powerset(X1)))
| ~ in(sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_38416,c_19620]) ).
tcf(c_38584,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))),X1)
| ( relation_image(sK1,X2) = relation_image(sK1,X3) )
| ( apply(sK1,sK3(sK1,X2,relation_image(sK1,X3))) = sK2(sK1,X2,relation_image(sK1,X3)) )
| ~ in(sK18(relation_image(sK1,relation_dom(sK1))),sK2(empty_set,X0,powerset(X1)))
| ~ in(sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_38416,c_19619]) ).
tcf(c_38585,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))),X1)
| ( relation_image(sK1,X2) = relation_image(sK1,X3) )
| ( apply(sK1,sK3(sK1,X2,relation_image(sK1,X3))) = sK2(sK1,X2,relation_image(sK1,X3)) )
| ~ in(sK18(relation_image(sK1,relation_dom(sK1))),sK2(empty_set,X0,powerset(X1)))
| ~ in(sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_38416,c_19621]) ).
tcf(c_38586,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(sK1,X2) = relation_image(sK1,X3) )
| ( apply(sK1,sK3(sK1,X2,relation_image(sK1,X3))) = sK2(sK1,X2,relation_image(sK1,X3)) )
| ~ empty(X1)
| ~ in(sK18(relation_image(sK1,relation_dom(sK1))),sK7(empty_set,X0,powerset(X1)))
| ~ in(sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_38416,c_20797]) ).
tcf(c_38587,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))),X1)
| ( relation_image(sK1,X2) = relation_image(sK1,X3) )
| ( apply(sK1,sK3(sK1,X2,relation_image(sK1,X3))) = sK2(sK1,X2,relation_image(sK1,X3)) )
| ~ in(sK18(relation_image(sK1,relation_dom(sK1))),sK7(empty_set,X0,powerset(X1)))
| ~ in(sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_38416,c_20796]) ).
tcf(c_38588,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))),X1)
| ( relation_image(sK1,X2) = relation_image(sK1,X3) )
| ( apply(sK1,sK3(sK1,X2,relation_image(sK1,X3))) = sK2(sK1,X2,relation_image(sK1,X3)) )
| ~ in(sK18(relation_image(sK1,relation_dom(sK1))),sK7(empty_set,X0,powerset(X1)))
| ~ in(sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_38416,c_20798]) ).
tcf(c_38589,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK1,X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X2))) = sK2(sK1,X1,relation_image(sK1,X2)) )
| ~ empty(X0)
| ~ in(sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1)))),relation_dom(sK1))
| ~ in(sK18(relation_image(sK1,relation_dom(sK1))),sK18(sK17(sK17(sK17(powerset(X0)))))) ),
inference(superposition,[status(thm)],[c_38416,c_22277]) ).
tcf(c_38590,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))),X0)
| ( relation_image(sK1,X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X2))) = sK2(sK1,X1,relation_image(sK1,X2)) )
| ~ in(sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1)))),relation_dom(sK1))
| ~ in(sK18(relation_image(sK1,relation_dom(sK1))),sK18(sK17(sK17(sK17(powerset(X0)))))) ),
inference(superposition,[status(thm)],[c_38416,c_22276]) ).
tcf(c_38591,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))),X0)
| ( relation_image(sK1,X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X2))) = sK2(sK1,X1,relation_image(sK1,X2)) )
| ~ in(sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1)))),relation_dom(sK1))
| ~ in(sK18(relation_image(sK1,relation_dom(sK1))),sK18(sK17(sK17(sK17(powerset(X0)))))) ),
inference(superposition,[status(thm)],[c_38416,c_22278]) ).
tcf(c_38592,plain,
! [X0: $i,X1: $i] :
( empty(apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ in(sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1)))),relation_dom(sK1))
| ~ in(sK18(relation_image(sK1,relation_dom(sK1))),sK18(sK17(sK17(sK17(apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1)))))))))) ),
inference(superposition,[status(thm)],[c_38416,c_22295]) ).
tcf(c_38593,plain,
! [X0: $i,X1: $i] :
( empty(sK18(powerset(apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))))))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ in(sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1)))),relation_dom(sK1))
| ~ in(sK18(relation_image(sK1,relation_dom(sK1))),sK18(sK17(sK17(sK18(powerset(apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))))))))) ),
inference(superposition,[status(thm)],[c_38416,c_22453]) ).
tcf(c_39167,plain,
( function(sK18(sK17(powerset(empty_set))))
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_17316,c_32771]) ).
tcf(c_39168,plain,
( function(sK18(sK17(powerset(empty_set))))
| ~ function(sK1)
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_23326,c_32771]) ).
tcf(c_39169,plain,
( function(sK18(sK17(powerset(empty_set))))
| ~ function(sK6)
| ~ relation(sK6) ),
inference(superposition,[status(thm)],[c_23325,c_32771]) ).
tcf(c_39170,plain,
( function(sK18(sK17(powerset(empty_set))))
| ~ function(sK10)
| ~ relation(sK10) ),
inference(superposition,[status(thm)],[c_23324,c_32771]) ).
tcf(c_39171,plain,
! [X0: $i] :
( ( relation_dom(relation_image(sK18(sK17(powerset(relation_image(X0,empty_set)))),empty_set)) = empty_set )
| ~ function(X0)
| ~ relation(X0)
| ~ relation(sK18(sK17(powerset(relation_image(X0,empty_set))))) ),
inference(superposition,[status(thm)],[c_32771,c_17553]) ).
tcf(c_39172,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK18(sK17(powerset(relation_image(X0,empty_set)))),X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK3(sK1,X2,relation_image(sK18(sK17(powerset(relation_image(X0,empty_set)))),X1))) = sK2(sK1,X2,relation_image(sK18(sK17(powerset(relation_image(X0,empty_set)))),X1)) )
| ( apply(sK18(sK17(powerset(relation_image(X0,empty_set)))),sK4(sK18(sK17(powerset(relation_image(X0,empty_set)))),X1,sK2(sK1,X2,relation_image(sK18(sK17(powerset(relation_image(X0,empty_set)))),X1)))) = sK2(sK1,X2,relation_image(sK18(sK17(powerset(relation_image(X0,empty_set)))),X1)) )
| ~ function(X0)
| ~ relation(X0)
| ~ relation(sK18(sK17(powerset(relation_image(X0,empty_set))))) ),
inference(superposition,[status(thm)],[c_32771,c_29889]) ).
tcf(c_39173,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(sK18(sK17(powerset(relation_image(X0,empty_set)))),X2) = relation_image(X1,X3) )
| ( apply(X1,sK4(X1,X3,sK2(sK18(sK17(powerset(relation_image(X0,empty_set)))),X2,relation_image(X1,X3)))) = sK2(sK18(sK17(powerset(relation_image(X0,empty_set)))),X2,relation_image(X1,X3)) )
| ( apply(sK18(sK17(powerset(relation_image(X0,empty_set)))),sK3(sK18(sK17(powerset(relation_image(X0,empty_set)))),X2,relation_image(X1,X3))) = sK2(sK18(sK17(powerset(relation_image(X0,empty_set)))),X2,relation_image(X1,X3)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(sK18(sK17(powerset(relation_image(X0,empty_set))))) ),
inference(superposition,[status(thm)],[c_32771,c_14500]) ).
tcf(c_39174,plain,
! [X0: $i] :
( ( relation_image(sK18(sK17(powerset(relation_image(X0,empty_set)))),empty_set) = empty_set )
| ~ function(X0)
| ~ relation(X0)
| ~ relation(sK18(sK17(powerset(relation_image(X0,empty_set))))) ),
inference(superposition,[status(thm)],[c_32771,c_17554]) ).
tcf(c_39212,plain,
! [X0: $i] :
( ( relation_dom(sK18(sK17(powerset(relation_dom(relation_dom(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_99,c_22613]) ).
tcf(c_39213,plain,
relation_dom(sK18(sK17(powerset(relation_dom(relation_dom(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_114,c_22613]) ).
tcf(c_39214,plain,
! [X0: $i] :
( ( relation_dom(sK18(sK17(powerset(relation_dom(relation_dom(sK18(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12738,c_22613]) ).
tcf(c_39215,plain,
! [X0: $i] :
( ( relation_dom(sK18(sK17(powerset(relation_dom(relation_dom(sK18(powerset(sK18(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13358,c_22613]) ).
tcf(c_39216,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(sK17(powerset(relation_dom(relation_dom(relation_image(X0,X1))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK17(relation_image(X0,X1))))) = sK18(sK17(relation_image(X0,X1))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13159,c_22613]) ).
tcf(c_39217,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(sK17(powerset(relation_dom(relation_dom(relation_image(X0,X1))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(relation_image(X0,X1)))) = sK18(relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13157,c_22613]) ).
tcf(c_39218,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(sK17(powerset(relation_dom(relation_dom(sK18(powerset(relation_image(X0,X1))))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK18(powerset(relation_image(X0,X1)))))) = sK18(sK18(powerset(relation_image(X0,X1)))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13158,c_22613]) ).
tcf(c_39219,plain,
! [X0: $i] :
( ( relation_dom(sK18(sK17(powerset(relation_dom(relation_dom(sK18(sK17(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13470,c_22613]) ).
tcf(c_39220,plain,
! [X0: $i] :
( ( relation_dom(sK18(sK17(powerset(relation_dom(relation_dom(sK18(powerset(sK18(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13469,c_22613]) ).
tcf(c_39221,plain,
! [X0: $i] :
( ( relation_dom(sK18(sK17(powerset(relation_dom(relation_dom(sK18(sK17(sK17(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15885,c_22613]) ).
tcf(c_39222,plain,
! [X0: $i] :
( ( relation_dom(sK18(sK17(powerset(relation_dom(relation_dom(sK18(powerset(sK18(sK17(sK17(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15887,c_22613]) ).
tcf(c_39223,plain,
! [X0: $i] :
( ( relation_dom(sK18(sK17(powerset(relation_dom(relation_dom(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17175,c_22613]) ).
tcf(c_39224,plain,
! [X0: $i] :
( ( relation_dom(sK18(sK17(powerset(relation_dom(relation_dom(sK18(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17177,c_22613]) ).
tcf(c_39225,plain,
! [X0: $i] :
( ( relation_dom(sK18(sK17(powerset(relation_dom(relation_dom(sK18(sK17(powerset(sK18(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17880,c_22613]) ).
tcf(c_39226,plain,
! [X0: $i] :
( ( relation_dom(sK18(sK17(powerset(relation_dom(relation_dom(sK18(sK17(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17883,c_22613]) ).
tcf(c_39227,plain,
! [X0: $i] :
( ( relation_dom(sK18(sK17(powerset(relation_dom(relation_dom(sK18(sK17(powerset(sK18(sK17(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17885,c_22613]) ).
tcf(c_39228,plain,
! [X0: $i] :
( ( relation_dom(sK18(sK17(powerset(relation_dom(relation_dom(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17888,c_22613]) ).
tcf(c_39229,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(sK17(powerset(relation_dom(relation_dom(sK2(empty_set,X1,powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20186,c_22613]) ).
tcf(c_39230,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(sK17(powerset(relation_dom(relation_dom(sK18(powerset(sK2(empty_set,X1,powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20188,c_22613]) ).
tcf(c_39231,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(sK17(powerset(relation_dom(relation_dom(sK18(sK17(powerset(sK2(empty_set,X1,powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20189,c_22613]) ).
tcf(c_39232,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(sK17(powerset(relation_dom(relation_dom(sK7(empty_set,X1,powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21299,c_22613]) ).
tcf(c_39233,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(sK17(powerset(relation_dom(relation_dom(sK18(powerset(sK7(empty_set,X1,powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21301,c_22613]) ).
tcf(c_39234,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(sK17(powerset(relation_dom(relation_dom(sK18(sK17(powerset(sK7(empty_set,X1,powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21302,c_22613]) ).
tcf(c_39235,plain,
! [X0: $i] :
( ( relation_dom(sK18(sK17(powerset(relation_dom(relation_dom(sK18(sK17(sK17(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25683,c_22613]) ).
tcf(c_39236,plain,
! [X0: $i] :
( ( relation_dom(sK18(sK17(powerset(relation_dom(relation_dom(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25684,c_22613]) ).
tcf(c_39483,plain,
! [X0: $i] :
( ( relation_dom(sK18(sK17(sK17(powerset(relation_dom(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_99,c_22713]) ).
tcf(c_39484,plain,
relation_dom(sK18(sK17(sK17(powerset(relation_dom(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_114,c_22713]) ).
tcf(c_39485,plain,
! [X0: $i] :
( ( relation_dom(sK18(sK17(sK17(powerset(relation_dom(sK18(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12738,c_22713]) ).
tcf(c_39486,plain,
! [X0: $i] :
( ( relation_dom(sK18(sK17(sK17(powerset(relation_dom(sK18(powerset(sK18(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13358,c_22713]) ).
tcf(c_39487,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(sK17(sK17(powerset(relation_dom(relation_image(X0,X1))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK17(relation_image(X0,X1))))) = sK18(sK17(relation_image(X0,X1))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13159,c_22713]) ).
tcf(c_39488,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(sK17(sK17(powerset(relation_dom(relation_image(X0,X1))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(relation_image(X0,X1)))) = sK18(relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13157,c_22713]) ).
tcf(c_39489,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(sK17(sK17(powerset(relation_dom(sK18(powerset(relation_image(X0,X1))))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK18(powerset(relation_image(X0,X1)))))) = sK18(sK18(powerset(relation_image(X0,X1)))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13158,c_22713]) ).
tcf(c_39490,plain,
! [X0: $i] :
( ( relation_dom(sK18(sK17(sK17(powerset(relation_dom(sK18(sK17(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13470,c_22713]) ).
tcf(c_39491,plain,
! [X0: $i] :
( ( relation_dom(sK18(sK17(sK17(powerset(relation_dom(sK18(powerset(sK18(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13469,c_22713]) ).
tcf(c_39492,plain,
! [X0: $i] :
( ( relation_dom(sK18(sK17(sK17(powerset(relation_dom(sK18(sK17(sK17(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15885,c_22713]) ).
tcf(c_39493,plain,
! [X0: $i] :
( ( relation_dom(sK18(sK17(sK17(powerset(relation_dom(sK18(powerset(sK18(sK17(sK17(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15887,c_22713]) ).
tcf(c_39494,plain,
! [X0: $i] :
( ( relation_dom(sK18(sK17(sK17(powerset(relation_dom(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17175,c_22713]) ).
tcf(c_39495,plain,
! [X0: $i] :
( ( relation_dom(sK18(sK17(sK17(powerset(relation_dom(sK18(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17177,c_22713]) ).
tcf(c_39496,plain,
! [X0: $i] :
( ( relation_dom(sK18(sK17(sK17(powerset(relation_dom(sK18(sK17(powerset(sK18(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17880,c_22713]) ).
tcf(c_39497,plain,
! [X0: $i] :
( ( relation_dom(sK18(sK17(sK17(powerset(relation_dom(sK18(sK17(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17883,c_22713]) ).
tcf(c_39498,plain,
! [X0: $i] :
( ( relation_dom(sK18(sK17(sK17(powerset(relation_dom(sK18(sK17(powerset(sK18(sK17(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17885,c_22713]) ).
tcf(c_39499,plain,
! [X0: $i] :
( ( relation_dom(sK18(sK17(sK17(powerset(relation_dom(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17888,c_22713]) ).
tcf(c_39500,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(sK17(sK17(powerset(relation_dom(sK2(empty_set,X1,powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20186,c_22713]) ).
tcf(c_39501,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(sK17(sK17(powerset(relation_dom(sK18(powerset(sK2(empty_set,X1,powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20188,c_22713]) ).
tcf(c_39502,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(sK17(sK17(powerset(relation_dom(sK18(sK17(powerset(sK2(empty_set,X1,powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20189,c_22713]) ).
tcf(c_39503,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(sK17(sK17(powerset(relation_dom(sK7(empty_set,X1,powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21299,c_22713]) ).
tcf(c_39504,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(sK17(sK17(powerset(relation_dom(sK18(powerset(sK7(empty_set,X1,powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21301,c_22713]) ).
tcf(c_39505,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK18(sK17(sK17(powerset(relation_dom(sK18(sK17(powerset(sK7(empty_set,X1,powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21302,c_22713]) ).
tcf(c_39506,plain,
! [X0: $i] :
( ( relation_dom(sK18(sK17(sK17(powerset(relation_dom(sK18(sK17(sK17(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25683,c_22713]) ).
tcf(c_39507,plain,
! [X0: $i] :
( ( relation_dom(sK18(sK17(sK17(powerset(relation_dom(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25684,c_22713]) ).
tcf(c_39721,plain,
! [X0: $i] :
( ( sK18(sK17(sK17(powerset(relation_dom(relation_dom(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_99,c_22812]) ).
tcf(c_39722,plain,
sK18(sK17(sK17(powerset(relation_dom(relation_dom(empty_set)))))) = empty_set,
inference(superposition,[status(thm)],[c_114,c_22812]) ).
tcf(c_39723,plain,
! [X0: $i] :
( ( sK18(sK17(sK17(powerset(relation_dom(relation_dom(sK18(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12738,c_22812]) ).
tcf(c_39724,plain,
! [X0: $i] :
( ( sK18(sK17(sK17(powerset(relation_dom(relation_dom(sK18(powerset(sK18(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13358,c_22812]) ).
tcf(c_39725,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(sK17(powerset(relation_dom(relation_dom(relation_image(X0,X1))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK17(relation_image(X0,X1))))) = sK18(sK17(relation_image(X0,X1))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13159,c_22812]) ).
tcf(c_39726,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(sK17(powerset(relation_dom(relation_dom(relation_image(X0,X1))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(relation_image(X0,X1)))) = sK18(relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13157,c_22812]) ).
tcf(c_39727,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(sK17(powerset(relation_dom(relation_dom(sK18(powerset(relation_image(X0,X1))))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK18(powerset(relation_image(X0,X1)))))) = sK18(sK18(powerset(relation_image(X0,X1)))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13158,c_22812]) ).
tcf(c_39728,plain,
! [X0: $i] :
( ( sK18(sK17(sK17(powerset(relation_dom(relation_dom(sK18(sK17(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13470,c_22812]) ).
tcf(c_39729,plain,
! [X0: $i] :
( ( sK18(sK17(sK17(powerset(relation_dom(relation_dom(sK18(powerset(sK18(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13469,c_22812]) ).
tcf(c_39730,plain,
! [X0: $i] :
( ( sK18(sK17(sK17(powerset(relation_dom(relation_dom(sK18(sK17(sK17(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15885,c_22812]) ).
tcf(c_39731,plain,
! [X0: $i] :
( ( sK18(sK17(sK17(powerset(relation_dom(relation_dom(sK18(powerset(sK18(sK17(sK17(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15887,c_22812]) ).
tcf(c_39732,plain,
! [X0: $i] :
( ( sK18(sK17(sK17(powerset(relation_dom(relation_dom(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17175,c_22812]) ).
tcf(c_39733,plain,
! [X0: $i] :
( ( sK18(sK17(sK17(powerset(relation_dom(relation_dom(sK18(powerset(relation_image(X0,empty_set))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17177,c_22812]) ).
tcf(c_39734,plain,
! [X0: $i] :
( ( sK18(sK17(sK17(powerset(relation_dom(relation_dom(sK18(sK17(powerset(sK18(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17880,c_22812]) ).
tcf(c_39735,plain,
! [X0: $i] :
( ( sK18(sK17(sK17(powerset(relation_dom(relation_dom(sK18(sK17(powerset(relation_image(X0,empty_set)))))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17883,c_22812]) ).
tcf(c_39736,plain,
! [X0: $i] :
( ( sK18(sK17(sK17(powerset(relation_dom(relation_dom(sK18(sK17(powerset(sK18(sK17(powerset(X0)))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17885,c_22812]) ).
tcf(c_39737,plain,
! [X0: $i] :
( ( sK18(sK17(sK17(powerset(relation_dom(relation_dom(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17888,c_22812]) ).
tcf(c_39738,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(sK17(powerset(relation_dom(relation_dom(sK2(empty_set,X1,powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20186,c_22812]) ).
tcf(c_39739,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(sK17(powerset(relation_dom(relation_dom(sK18(powerset(sK2(empty_set,X1,powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20188,c_22812]) ).
tcf(c_39740,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(sK17(powerset(relation_dom(relation_dom(sK18(sK17(powerset(sK2(empty_set,X1,powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20189,c_22812]) ).
tcf(c_39741,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(sK17(powerset(relation_dom(relation_dom(sK7(empty_set,X1,powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21299,c_22812]) ).
tcf(c_39742,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(sK17(powerset(relation_dom(relation_dom(sK18(powerset(sK7(empty_set,X1,powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21301,c_22812]) ).
tcf(c_39743,plain,
! [X0: $i,X1: $i] :
( ( sK18(sK17(sK17(powerset(relation_dom(relation_dom(sK18(sK17(powerset(sK7(empty_set,X1,powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21302,c_22812]) ).
tcf(c_39744,plain,
! [X0: $i] :
( ( sK18(sK17(sK17(powerset(relation_dom(relation_dom(sK18(sK17(sK17(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25683,c_22812]) ).
tcf(c_39745,plain,
! [X0: $i] :
( ( sK18(sK17(sK17(powerset(relation_dom(relation_dom(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0))))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25684,c_22812]) ).
tcf(c_39941,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK7(empty_set,X1,powerset(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_99,c_21425]) ).
tcf(c_39942,plain,
! [X0: $i] : sK18(powerset(sK7(empty_set,X0,powerset(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_114,c_21425]) ).
tcf(c_39943,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK7(empty_set,X1,powerset(sK18(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12738,c_21425]) ).
tcf(c_39944,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK7(empty_set,X1,powerset(sK18(powerset(sK18(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13358,c_21425]) ).
tcf(c_39945,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK18(powerset(sK7(empty_set,X2,powerset(relation_image(X0,X1))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK17(relation_image(X0,X1))))) = sK18(sK17(relation_image(X0,X1))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13159,c_21425]) ).
tcf(c_39946,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK18(powerset(sK7(empty_set,X2,powerset(relation_image(X0,X1))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(relation_image(X0,X1)))) = sK18(relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13157,c_21425]) ).
tcf(c_39947,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK18(powerset(sK7(empty_set,X2,powerset(sK18(powerset(relation_image(X0,X1))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK18(powerset(relation_image(X0,X1)))))) = sK18(sK18(powerset(relation_image(X0,X1)))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13158,c_21425]) ).
tcf(c_39948,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK7(empty_set,X1,powerset(sK18(sK17(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13470,c_21425]) ).
tcf(c_39949,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK7(empty_set,X1,powerset(sK18(powerset(sK18(sK17(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13469,c_21425]) ).
tcf(c_39950,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK7(empty_set,X1,powerset(sK18(sK17(sK17(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15885,c_21425]) ).
tcf(c_39951,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK7(empty_set,X1,powerset(sK18(powerset(sK18(sK17(sK17(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15887,c_21425]) ).
tcf(c_39952,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK7(empty_set,X1,powerset(relation_image(X0,empty_set))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17175,c_21425]) ).
tcf(c_39953,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK7(empty_set,X1,powerset(sK18(powerset(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17177,c_21425]) ).
tcf(c_39954,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK7(empty_set,X1,powerset(sK18(sK17(powerset(sK18(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17880,c_21425]) ).
tcf(c_39955,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK7(empty_set,X1,powerset(sK18(sK17(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17883,c_21425]) ).
tcf(c_39956,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK7(empty_set,X1,powerset(sK18(sK17(powerset(sK18(sK17(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17885,c_21425]) ).
tcf(c_39957,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK7(empty_set,X1,powerset(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17888,c_21425]) ).
tcf(c_39958,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK18(powerset(sK7(empty_set,X1,powerset(sK2(empty_set,X2,powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20186,c_21425]) ).
tcf(c_39959,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK18(powerset(sK7(empty_set,X1,powerset(sK18(powerset(sK2(empty_set,X2,powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20188,c_21425]) ).
tcf(c_39960,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK18(powerset(sK7(empty_set,X1,powerset(sK18(sK17(powerset(sK2(empty_set,X2,powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20189,c_21425]) ).
tcf(c_39961,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK18(powerset(sK7(empty_set,X1,powerset(sK7(empty_set,X2,powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21299,c_21425]) ).
tcf(c_39962,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK18(powerset(sK7(empty_set,X1,powerset(sK18(powerset(sK7(empty_set,X2,powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21301,c_21425]) ).
tcf(c_39963,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK18(powerset(sK7(empty_set,X1,powerset(sK18(sK17(powerset(sK7(empty_set,X2,powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21302,c_21425]) ).
tcf(c_39964,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK7(empty_set,X1,powerset(sK18(sK17(sK17(sK17(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25683,c_21425]) ).
tcf(c_39965,plain,
! [X0: $i,X1: $i] :
( ( sK18(powerset(sK7(empty_set,X1,powerset(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25684,c_21425]) ).
tcf(c_40115,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK7(empty_set,X1,powerset(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_99,c_21427]) ).
tcf(c_40116,plain,
! [X0: $i] : relation_dom(relation_dom(sK7(empty_set,X0,powerset(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_114,c_21427]) ).
tcf(c_40117,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK7(empty_set,X1,powerset(sK18(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12738,c_21427]) ).
tcf(c_40118,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK7(empty_set,X1,powerset(sK18(powerset(sK18(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13358,c_21427]) ).
tcf(c_40119,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_dom(sK7(empty_set,X2,powerset(relation_image(X0,X1))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK17(relation_image(X0,X1))))) = sK18(sK17(relation_image(X0,X1))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13159,c_21427]) ).
tcf(c_40120,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_dom(sK7(empty_set,X2,powerset(relation_image(X0,X1))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(relation_image(X0,X1)))) = sK18(relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13157,c_21427]) ).
tcf(c_40121,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_dom(sK7(empty_set,X2,powerset(sK18(powerset(relation_image(X0,X1))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK18(powerset(relation_image(X0,X1)))))) = sK18(sK18(powerset(relation_image(X0,X1)))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13158,c_21427]) ).
tcf(c_40122,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK7(empty_set,X1,powerset(sK18(sK17(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13470,c_21427]) ).
tcf(c_40123,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK7(empty_set,X1,powerset(sK18(powerset(sK18(sK17(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13469,c_21427]) ).
tcf(c_40124,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK7(empty_set,X1,powerset(sK18(sK17(sK17(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15885,c_21427]) ).
tcf(c_40125,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK7(empty_set,X1,powerset(sK18(powerset(sK18(sK17(sK17(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15887,c_21427]) ).
tcf(c_40126,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK7(empty_set,X1,powerset(relation_image(X0,empty_set))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17175,c_21427]) ).
tcf(c_40127,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK7(empty_set,X1,powerset(sK18(powerset(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17177,c_21427]) ).
tcf(c_40128,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK7(empty_set,X1,powerset(sK18(sK17(powerset(sK18(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17880,c_21427]) ).
tcf(c_40129,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK7(empty_set,X1,powerset(sK18(sK17(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17883,c_21427]) ).
tcf(c_40130,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK7(empty_set,X1,powerset(sK18(sK17(powerset(sK18(sK17(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17885,c_21427]) ).
tcf(c_40131,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK7(empty_set,X1,powerset(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17888,c_21427]) ).
tcf(c_40132,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_dom(sK7(empty_set,X1,powerset(sK2(empty_set,X2,powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20186,c_21427]) ).
tcf(c_40133,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_dom(sK7(empty_set,X1,powerset(sK18(powerset(sK2(empty_set,X2,powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20188,c_21427]) ).
tcf(c_40134,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_dom(sK7(empty_set,X1,powerset(sK18(sK17(powerset(sK2(empty_set,X2,powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20189,c_21427]) ).
tcf(c_40135,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_dom(sK7(empty_set,X1,powerset(sK7(empty_set,X2,powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21299,c_21427]) ).
tcf(c_40136,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_dom(sK7(empty_set,X1,powerset(sK18(powerset(sK7(empty_set,X2,powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21301,c_21427]) ).
tcf(c_40137,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_dom(sK7(empty_set,X1,powerset(sK18(sK17(powerset(sK7(empty_set,X2,powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21302,c_21427]) ).
tcf(c_40138,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK7(empty_set,X1,powerset(sK18(sK17(sK17(sK17(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25683,c_21427]) ).
tcf(c_40139,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK7(empty_set,X1,powerset(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25684,c_21427]) ).
tcf(c_40341,plain,
! [X0: $i,X1: $i] :
( ( sK7(empty_set,X1,powerset(sK18(powerset(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_99,c_21943]) ).
tcf(c_40342,plain,
! [X0: $i] : sK7(empty_set,X0,powerset(sK18(powerset(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_114,c_21943]) ).
tcf(c_40344,plain,
! [X0: $i,X1: $i] :
( ( sK7(empty_set,X1,powerset(sK18(powerset(sK18(powerset(sK18(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13358,c_21943]) ).
tcf(c_40345,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK7(empty_set,X2,powerset(sK18(powerset(relation_image(X0,X1))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK17(relation_image(X0,X1))))) = sK18(sK17(relation_image(X0,X1))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13159,c_21943]) ).
tcf(c_40346,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK7(empty_set,X2,powerset(sK18(powerset(relation_image(X0,X1))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(relation_image(X0,X1)))) = sK18(relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13157,c_21943]) ).
tcf(c_40347,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK7(empty_set,X2,powerset(sK18(powerset(sK18(powerset(relation_image(X0,X1))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK18(powerset(relation_image(X0,X1)))))) = sK18(sK18(powerset(relation_image(X0,X1)))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13158,c_21943]) ).
tcf(c_40349,plain,
! [X0: $i,X1: $i] :
( ( sK7(empty_set,X1,powerset(sK18(powerset(sK18(powerset(sK18(sK17(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13469,c_21943]) ).
tcf(c_40351,plain,
! [X0: $i,X1: $i] :
( ( sK7(empty_set,X1,powerset(sK18(powerset(sK18(powerset(sK18(sK17(sK17(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15887,c_21943]) ).
tcf(c_40353,plain,
! [X0: $i,X1: $i] :
( ( sK7(empty_set,X1,powerset(sK18(powerset(sK18(powerset(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17177,c_21943]) ).
tcf(c_40354,plain,
! [X0: $i,X1: $i] :
( ( sK7(empty_set,X1,powerset(sK18(powerset(sK18(sK17(powerset(sK18(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17880,c_21943]) ).
tcf(c_40355,plain,
! [X0: $i,X1: $i] :
( ( sK7(empty_set,X1,powerset(sK18(powerset(sK18(sK17(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17883,c_21943]) ).
tcf(c_40356,plain,
! [X0: $i,X1: $i] :
( ( sK7(empty_set,X1,powerset(sK18(powerset(sK18(sK17(powerset(sK18(sK17(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17885,c_21943]) ).
tcf(c_40357,plain,
! [X0: $i,X1: $i] :
( ( sK7(empty_set,X1,powerset(sK18(powerset(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17888,c_21943]) ).
tcf(c_40359,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK7(empty_set,X1,powerset(sK18(powerset(sK18(powerset(sK2(empty_set,X2,powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20188,c_21943]) ).
tcf(c_40360,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK7(empty_set,X1,powerset(sK18(powerset(sK18(sK17(powerset(sK2(empty_set,X2,powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20189,c_21943]) ).
tcf(c_40362,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK7(empty_set,X1,powerset(sK18(powerset(sK18(powerset(sK7(empty_set,X2,powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21301,c_21943]) ).
tcf(c_40363,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK7(empty_set,X1,powerset(sK18(powerset(sK18(sK17(powerset(sK7(empty_set,X2,powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21302,c_21943]) ).
tcf(c_40365,plain,
! [X0: $i,X1: $i] :
( ( sK7(empty_set,X1,powerset(sK18(powerset(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25684,c_21943]) ).
tcf(c_40613,plain,
! [X0: $i] :
( empty(X0)
| element(sK18(sK17(sK17(sK17(sK17(X0))))),X0) ),
inference(global_subsumption_just,[status(thm)],[c_22298,c_109,c_22298]) ).
tcf(c_40620,plain,
! [X0: $i] :
( empty(powerset(X0))
| subset(sK18(sK17(sK17(sK17(sK17(powerset(X0)))))),X0) ),
inference(superposition,[status(thm)],[c_40613,c_88]) ).
tcf(c_40621,plain,
! [X0: $i] :
( empty(X0)
| in(sK18(sK17(sK17(sK17(sK17(X0))))),X0) ),
inference(superposition,[status(thm)],[c_40613,c_96]) ).
tcf(c_40624,plain,
! [X0: $i] : subset(sK18(sK17(sK17(sK17(sK17(powerset(X0)))))),X0),
inference(forward_subsumption_resolution,[status(thm)],[c_40620,c_110]) ).
tcf(c_40708,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))),X0)
| ( relation_image(sK1,X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X2))) = sK2(sK1,X1,relation_image(sK1,X2)) )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(sK18(sK17(relation_image(sK1,relation_dom(sK1)))),X0)
| ~ in(sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1))))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_35597,c_72]) ).
tcf(c_40710,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK1,X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X2))) = sK2(sK1,X1,relation_image(sK1,X2)) )
| ~ in(sK18(sK17(relation_image(sK1,relation_dom(sK1)))),X0)
| ~ in(sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1))))),relation_dom(sK1))
| ~ in(relation_inverse_image(sK1,X0),sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))) ),
inference(superposition,[status(thm)],[c_35597,c_98]) ).
tcf(c_40711,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1))))),relation_inverse_image(sK1,X0))
| ( relation_image(sK1,X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X2))) = sK2(sK1,X1,relation_image(sK1,X2)) )
| ~ in(sK18(sK17(relation_image(sK1,relation_dom(sK1)))),X0)
| ~ in(sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1))))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_35597,c_97]) ).
tcf(c_40712,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK1,X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X2))) = sK2(sK1,X1,relation_image(sK1,X2)) )
| ~ empty(relation_inverse_image(sK1,X0))
| ~ in(sK18(sK17(relation_image(sK1,relation_dom(sK1)))),X0)
| ~ in(sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1))))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_35597,c_95]) ).
tcf(c_40728,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))),X0)
| ( relation_image(sK1,X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X2))) = sK2(sK1,X1,relation_image(sK1,X2)) )
| ~ in(sK18(sK17(relation_image(sK1,relation_dom(sK1)))),X0)
| ~ in(sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1))))),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_40708,c_52,c_51]) ).
tcf(c_40748,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK18(sK17(relation_image(sK1,relation_dom(sK1)))),relation_image(sK1,X0))
| ( relation_image(sK1,X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X2))) = sK2(sK1,X1,relation_image(sK1,X2)) )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(sK18(sK17(relation_image(sK1,relation_dom(sK1)))),relation_image(sK1,relation_dom(sK1)))
| ~ in(sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1))))),X0) ),
inference(superposition,[status(thm)],[c_58,c_35603]) ).
tcf(c_40750,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK18(sK17(relation_image(sK1,relation_dom(sK1)))),relation_image(sK1,X0))
| ( relation_image(sK1,X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X2))) = sK2(sK1,X1,relation_image(sK1,X2)) )
| ~ in(sK18(sK17(relation_image(sK1,relation_dom(sK1)))),relation_image(sK1,relation_dom(sK1)))
| ~ in(sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1))))),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_40748,c_52,c_51]) ).
tcf(c_40769,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK18(sK17(relation_image(sK1,relation_dom(sK1)))),relation_image(sK1,powerset(X0)))
| ( relation_image(sK1,X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X2))) = sK2(sK1,X1,relation_image(sK1,X2)) )
| ~ in(sK18(sK17(relation_image(sK1,relation_dom(sK1)))),relation_image(sK1,relation_dom(sK1)))
| ~ subset(sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1))))),X0) ),
inference(superposition,[status(thm)],[c_12509,c_40750]) ).
tcf(c_40770,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK18(sK17(relation_image(sK1,relation_dom(sK1)))),relation_image(sK1,relation_inverse_image(sK1,X0)))
| ( relation_image(sK1,X3) = relation_image(sK1,X4) )
| ( relation_image(sK1,X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK3(sK1,X3,relation_image(sK1,X4))) = sK2(sK1,X3,relation_image(sK1,X4)) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X2))) = sK2(sK1,X1,relation_image(sK1,X2)) )
| ~ in(sK18(sK17(relation_image(sK1,relation_dom(sK1)))),X0)
| ~ in(sK18(sK17(relation_image(sK1,relation_dom(sK1)))),relation_image(sK1,relation_dom(sK1)))
| ~ in(sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1))))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_35597,c_40750]) ).
tcf(c_40797,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(sK1,X2) = relation_image(sK1,X3) )
| ( apply(sK1,sK3(sK1,X2,relation_image(sK1,X3))) = sK2(sK1,X2,relation_image(sK1,X3)) )
| ( apply(X0,sK4(X0,X1,apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))))) = apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK18(sK17(relation_image(sK1,relation_dom(sK1)))),relation_image(X0,X1))
| ~ in(sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1))))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_40728,c_60]) ).
tcf(c_40799,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X0,apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1))))))),X1)
| ( relation_image(sK1,X2) = relation_image(sK1,X3) )
| ( apply(sK1,sK3(sK1,X2,relation_image(sK1,X3))) = sK2(sK1,X2,relation_image(sK1,X3)) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK18(sK17(relation_image(sK1,relation_dom(sK1)))),relation_inverse_image(X0,X1))
| ~ in(sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1))))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_40728,c_72]) ).
tcf(c_40800,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))),relation_dom(X0))
| ( relation_image(sK1,X2) = relation_image(sK1,X3) )
| ( apply(sK1,sK3(sK1,X2,relation_image(sK1,X3))) = sK2(sK1,X2,relation_image(sK1,X3)) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK18(sK17(relation_image(sK1,relation_dom(sK1)))),relation_inverse_image(X0,X1))
| ~ in(sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1))))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_40728,c_71]) ).
tcf(c_40801,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK1,X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X2))) = sK2(sK1,X1,relation_image(sK1,X2)) )
| ~ in(sK18(sK17(relation_image(sK1,relation_dom(sK1)))),X0)
| ~ in(sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1))))),relation_dom(sK1))
| ~ in(X0,apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1))))))) ),
inference(superposition,[status(thm)],[c_40728,c_98]) ).
tcf(c_40802,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))),X0)
| ( relation_image(sK1,X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X2))) = sK2(sK1,X1,relation_image(sK1,X2)) )
| ~ in(sK18(sK17(relation_image(sK1,relation_dom(sK1)))),X0)
| ~ in(sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1))))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_40728,c_97]) ).
tcf(c_40803,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK1,X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X2))) = sK2(sK1,X1,relation_image(sK1,X2)) )
| ~ empty(X0)
| ~ in(sK18(sK17(relation_image(sK1,relation_dom(sK1)))),X0)
| ~ in(sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1))))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_40728,c_95]) ).
tcf(c_40804,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))),X0)
| ( relation_image(sK1,X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X2))) = sK2(sK1,X1,relation_image(sK1,X2)) )
| ~ in(sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1))))),relation_dom(sK1))
| ~ in(sK18(sK17(relation_image(sK1,relation_dom(sK1)))),sK13(apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))),X0)) ),
inference(superposition,[status(thm)],[c_40728,c_12485]) ).
tcf(c_40805,plain,
! [X0: $i,X1: $i] :
( empty(apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ in(sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1))))),relation_dom(sK1))
| ~ in(sK18(sK17(relation_image(sK1,relation_dom(sK1)))),sK18(apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))))) ),
inference(superposition,[status(thm)],[c_40728,c_12526]) ).
tcf(c_40806,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X0)
| element(apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))),X0)
| ( relation_image(sK1,X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X2))) = sK2(sK1,X1,relation_image(sK1,X2)) )
| ~ in(sK18(sK17(relation_image(sK1,relation_dom(sK1)))),sK17(X0))
| ~ in(sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1))))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_40728,c_14688]) ).
tcf(c_40807,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X0)
| in(apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))),X0)
| ( relation_image(sK1,X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X2))) = sK2(sK1,X1,relation_image(sK1,X2)) )
| ~ in(sK18(sK17(relation_image(sK1,relation_dom(sK1)))),sK17(X0))
| ~ in(sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1))))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_40728,c_12618]) ).
tcf(c_40808,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))),X0)
| ( relation_image(sK1,X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X2))) = sK2(sK1,X1,relation_image(sK1,X2)) )
| ~ in(sK18(sK17(relation_image(sK1,relation_dom(sK1)))),sK18(powerset(X0)))
| ~ in(sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1))))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_40728,c_14689]) ).
tcf(c_40809,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK1,X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X2))) = sK2(sK1,X1,relation_image(sK1,X2)) )
| ~ empty(X0)
| ~ in(sK18(sK17(relation_image(sK1,relation_dom(sK1)))),sK18(powerset(X0)))
| ~ in(sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1))))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_40728,c_13313]) ).
tcf(c_40810,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))),X0)
| ( relation_image(sK1,X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X2))) = sK2(sK1,X1,relation_image(sK1,X2)) )
| ~ in(sK18(sK17(relation_image(sK1,relation_dom(sK1)))),sK18(powerset(X0)))
| ~ in(sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1))))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_40728,c_12619]) ).
tcf(c_40811,plain,
! [X0: $i,X1: $i] :
( ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ in(sK18(sK17(relation_image(sK1,relation_dom(sK1)))),empty_set)
| ~ in(sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1))))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_40728,c_13338]) ).
tcf(c_40812,plain,
! [X0: $i,X1: $i] :
( empty(sK18(powerset(apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))))))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ in(sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1))))),relation_dom(sK1))
| ~ in(sK18(sK17(relation_image(sK1,relation_dom(sK1)))),sK18(sK18(powerset(apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))))))) ),
inference(superposition,[status(thm)],[c_40728,c_12736]) ).
tcf(c_40813,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK1,X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X2))) = sK2(sK1,X1,relation_image(sK1,X2)) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK18(sK17(relation_image(sK1,relation_dom(sK1)))),relation_image(X0,empty_set))
| ~ in(sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1))))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_40728,c_13341]) ).
tcf(c_40814,plain,
! [X0: $i,X1: $i] :
( empty(apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ in(sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1))))),relation_dom(sK1))
| ~ in(sK18(sK17(relation_image(sK1,relation_dom(sK1)))),sK18(sK17(apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1))))))))) ),
inference(superposition,[status(thm)],[c_40728,c_12990]) ).
tcf(c_40815,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))),X0)
| ( relation_image(sK1,X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X2))) = sK2(sK1,X1,relation_image(sK1,X2)) )
| ~ in(sK18(sK17(relation_image(sK1,relation_dom(sK1)))),sK18(sK17(powerset(X0))))
| ~ in(sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1))))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_40728,c_14693]) ).
tcf(c_40816,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK1,X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X2))) = sK2(sK1,X1,relation_image(sK1,X2)) )
| ~ empty(X0)
| ~ in(sK18(sK17(relation_image(sK1,relation_dom(sK1)))),sK18(sK17(powerset(X0))))
| ~ in(sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1))))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_40728,c_13316]) ).
tcf(c_40817,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))),X0)
| ( relation_image(sK1,X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X2))) = sK2(sK1,X1,relation_image(sK1,X2)) )
| ~ in(sK18(sK17(relation_image(sK1,relation_dom(sK1)))),sK18(sK17(powerset(X0))))
| ~ in(sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1))))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_40728,c_13032]) ).
tcf(c_40818,plain,
! [X0: $i,X1: $i] :
( empty(apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ in(sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1))))),relation_dom(sK1))
| ~ in(sK18(sK17(relation_image(sK1,relation_dom(sK1)))),sK18(sK17(sK17(apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))))))) ),
inference(superposition,[status(thm)],[c_40728,c_15381]) ).
tcf(c_40819,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))),X0)
| ( relation_image(sK1,X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X2))) = sK2(sK1,X1,relation_image(sK1,X2)) )
| ~ in(sK18(sK17(relation_image(sK1,relation_dom(sK1)))),sK18(sK17(sK17(powerset(X0)))))
| ~ in(sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1))))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_40728,c_15478]) ).
tcf(c_40820,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK1,X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X2))) = sK2(sK1,X1,relation_image(sK1,X2)) )
| ~ empty(X0)
| ~ in(sK18(sK17(relation_image(sK1,relation_dom(sK1)))),sK18(sK17(sK17(powerset(X0)))))
| ~ in(sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1))))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_40728,c_15477]) ).
tcf(c_40821,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))),X0)
| ( relation_image(sK1,X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X2))) = sK2(sK1,X1,relation_image(sK1,X2)) )
| ~ in(sK18(sK17(relation_image(sK1,relation_dom(sK1)))),sK18(sK17(sK17(powerset(X0)))))
| ~ in(sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1))))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_40728,c_15476]) ).
tcf(c_40822,plain,
! [X0: $i,X1: $i] :
( empty(sK18(powerset(apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))))))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ in(sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1))))),relation_dom(sK1))
| ~ in(sK18(sK17(relation_image(sK1,relation_dom(sK1)))),sK18(sK17(sK18(powerset(apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1))))))))))) ),
inference(superposition,[status(thm)],[c_40728,c_15649]) ).
tcf(c_40823,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK18(powerset(apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))))),X0)
| ( relation_image(sK1,X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X2))) = sK2(sK1,X1,relation_image(sK1,X2)) )
| ~ in(sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1))))),relation_dom(sK1))
| ~ in(sK18(sK17(relation_image(sK1,relation_dom(sK1)))),sK13(sK18(powerset(apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))))),X0)) ),
inference(superposition,[status(thm)],[c_40728,c_16394]) ).
tcf(c_40824,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))))
| subset(sK17(apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1))))))),X0)
| ( relation_image(sK1,X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X2))) = sK2(sK1,X1,relation_image(sK1,X2)) )
| ~ in(sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1))))),relation_dom(sK1))
| ~ in(sK18(sK17(relation_image(sK1,relation_dom(sK1)))),sK13(sK17(apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1))))))),X0)) ),
inference(superposition,[status(thm)],[c_40728,c_16730]) ).
tcf(c_40825,plain,
! [X0: $i,X1: $i] :
( empty(sK18(sK17(powerset(apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1))))))))))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ in(sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1))))),relation_dom(sK1))
| ~ in(sK18(sK17(relation_image(sK1,relation_dom(sK1)))),sK18(sK18(sK17(powerset(apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1))))))))))) ),
inference(superposition,[status(thm)],[c_40728,c_17874]) ).
tcf(c_40826,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))),powerset(X0))
| ( relation_image(sK1,X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X2))) = sK2(sK1,X1,relation_image(sK1,X2)) )
| ~ in(sK18(sK17(relation_image(sK1,relation_dom(sK1)))),sK17(powerset(X0)))
| ~ in(sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1))))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_40728,c_18767]) ).
tcf(c_40827,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))),powerset(X0))
| ( relation_image(sK1,X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X2))) = sK2(sK1,X1,relation_image(sK1,X2)) )
| ~ in(sK18(sK17(relation_image(sK1,relation_dom(sK1)))),sK17(powerset(X0)))
| ~ in(sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1))))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_40728,c_18765]) ).
tcf(c_40828,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK1,X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X2))) = sK2(sK1,X1,relation_image(sK1,X2)) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))) = empty_set )
| ~ in(sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1))))),relation_dom(sK1))
| ~ in(sK18(sK17(relation_image(sK1,relation_dom(sK1)))),sK2(empty_set,X0,apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))))) ),
inference(superposition,[status(thm)],[c_40728,c_19251]) ).
tcf(c_40829,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK1,X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X2))) = sK2(sK1,X1,relation_image(sK1,X2)) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))) = empty_set )
| ~ in(sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1))))),relation_dom(sK1))
| ~ in(sK18(sK17(relation_image(sK1,relation_dom(sK1)))),sK7(empty_set,X0,apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))))) ),
inference(superposition,[status(thm)],[c_40728,c_19880]) ).
tcf(c_40830,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(sK1,X2) = relation_image(sK1,X3) )
| ( apply(sK1,sK3(sK1,X2,relation_image(sK1,X3))) = sK2(sK1,X2,relation_image(sK1,X3)) )
| ~ empty(X1)
| ~ in(sK18(sK17(relation_image(sK1,relation_dom(sK1)))),sK2(empty_set,X0,powerset(X1)))
| ~ in(sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1))))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_40728,c_19620]) ).
tcf(c_40831,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))),X1)
| ( relation_image(sK1,X2) = relation_image(sK1,X3) )
| ( apply(sK1,sK3(sK1,X2,relation_image(sK1,X3))) = sK2(sK1,X2,relation_image(sK1,X3)) )
| ~ in(sK18(sK17(relation_image(sK1,relation_dom(sK1)))),sK2(empty_set,X0,powerset(X1)))
| ~ in(sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1))))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_40728,c_19619]) ).
tcf(c_40832,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))),X1)
| ( relation_image(sK1,X2) = relation_image(sK1,X3) )
| ( apply(sK1,sK3(sK1,X2,relation_image(sK1,X3))) = sK2(sK1,X2,relation_image(sK1,X3)) )
| ~ in(sK18(sK17(relation_image(sK1,relation_dom(sK1)))),sK2(empty_set,X0,powerset(X1)))
| ~ in(sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1))))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_40728,c_19621]) ).
tcf(c_40833,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(sK1,X2) = relation_image(sK1,X3) )
| ( apply(sK1,sK3(sK1,X2,relation_image(sK1,X3))) = sK2(sK1,X2,relation_image(sK1,X3)) )
| ~ empty(X1)
| ~ in(sK18(sK17(relation_image(sK1,relation_dom(sK1)))),sK7(empty_set,X0,powerset(X1)))
| ~ in(sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1))))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_40728,c_20797]) ).
tcf(c_40834,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))),X1)
| ( relation_image(sK1,X2) = relation_image(sK1,X3) )
| ( apply(sK1,sK3(sK1,X2,relation_image(sK1,X3))) = sK2(sK1,X2,relation_image(sK1,X3)) )
| ~ in(sK18(sK17(relation_image(sK1,relation_dom(sK1)))),sK7(empty_set,X0,powerset(X1)))
| ~ in(sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1))))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_40728,c_20796]) ).
tcf(c_40835,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))),X1)
| ( relation_image(sK1,X2) = relation_image(sK1,X3) )
| ( apply(sK1,sK3(sK1,X2,relation_image(sK1,X3))) = sK2(sK1,X2,relation_image(sK1,X3)) )
| ~ in(sK18(sK17(relation_image(sK1,relation_dom(sK1)))),sK7(empty_set,X0,powerset(X1)))
| ~ in(sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1))))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_40728,c_20798]) ).
tcf(c_40836,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK1,X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X2))) = sK2(sK1,X1,relation_image(sK1,X2)) )
| ~ empty(X0)
| ~ in(sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1))))),relation_dom(sK1))
| ~ in(sK18(sK17(relation_image(sK1,relation_dom(sK1)))),sK18(sK17(sK17(sK17(powerset(X0)))))) ),
inference(superposition,[status(thm)],[c_40728,c_22277]) ).
tcf(c_40837,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))),X0)
| ( relation_image(sK1,X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X2))) = sK2(sK1,X1,relation_image(sK1,X2)) )
| ~ in(sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1))))),relation_dom(sK1))
| ~ in(sK18(sK17(relation_image(sK1,relation_dom(sK1)))),sK18(sK17(sK17(sK17(powerset(X0)))))) ),
inference(superposition,[status(thm)],[c_40728,c_22276]) ).
tcf(c_40838,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))),X0)
| ( relation_image(sK1,X1) = relation_image(sK1,X2) )
| ( apply(sK1,sK3(sK1,X1,relation_image(sK1,X2))) = sK2(sK1,X1,relation_image(sK1,X2)) )
| ~ in(sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1))))),relation_dom(sK1))
| ~ in(sK18(sK17(relation_image(sK1,relation_dom(sK1)))),sK18(sK17(sK17(sK17(powerset(X0)))))) ),
inference(superposition,[status(thm)],[c_40728,c_22278]) ).
tcf(c_40839,plain,
! [X0: $i,X1: $i] :
( empty(apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ in(sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1))))),relation_dom(sK1))
| ~ in(sK18(sK17(relation_image(sK1,relation_dom(sK1)))),sK18(sK17(sK17(sK17(apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1))))))))))) ),
inference(superposition,[status(thm)],[c_40728,c_22295]) ).
tcf(c_40840,plain,
! [X0: $i,X1: $i] :
( empty(sK18(powerset(apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))))))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ in(sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1))))),relation_dom(sK1))
| ~ in(sK18(sK17(relation_image(sK1,relation_dom(sK1)))),sK18(sK17(sK17(sK18(powerset(apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))))))))) ),
inference(superposition,[status(thm)],[c_40728,c_22453]) ).
tcf(c_41123,plain,
! [X0: $i,X1: $i] :
( ( relation_image(sK1,X0) = relation_image(sK1,empty_set) )
| ( sK3(sK1,X0,relation_image(sK1,empty_set)) = X1 )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) )
| ~ in(X1,relation_dom(sK1))
| ~ in(sK3(sK1,X0,relation_image(sK1,empty_set)),relation_dom(sK1))
| ( sK2(sK1,X0,empty_set) != apply(sK1,X1) ) ),
inference(superposition,[status(thm)],[c_23326,c_35406]) ).
tcf(c_41124,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(sK1,X2) = relation_image(sK1,X3) )
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X2,relation_image(sK1,X3))) = sK2(sK1,X2,relation_image(sK1,X3)) )
| ( sK4(sK1,X3,sK2(sK1,X2,relation_image(sK1,X3))) = sK3(sK1,X0,relation_image(sK1,X1)) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) )
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1))
| ~ in(sK4(sK1,X3,sK2(sK1,X2,relation_image(sK1,X3))),relation_dom(sK1))
| ( sK2(sK1,X0,relation_image(sK1,X1)) != sK2(sK1,X2,relation_image(sK1,X3)) ) ),
inference(superposition,[status(thm)],[c_31512,c_35406]) ).
tcf(c_41125,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(sK1,X2) = relation_image(sK1,X3) )
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( sK3(sK1,X0,relation_image(sK1,X1)) = sK3(sK1,X2,relation_image(sK1,X3)) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))) = sK18(sK17(relation_image(sK1,relation_dom(sK1)))) )
| ~ in(sK3(sK1,X2,relation_image(sK1,X3)),relation_dom(sK1))
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1))
| ( sK2(sK1,X0,relation_image(sK1,X1)) != sK2(sK1,X2,relation_image(sK1,X3)) ) ),
inference(superposition,[status(thm)],[c_35218,c_35406]) ).
tcf(c_41126,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(sK1,X2) = relation_image(sK1,X3) )
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( sK3(sK1,X0,relation_image(sK1,X1)) = sK3(sK1,X2,relation_image(sK1,X3)) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) )
| ~ in(sK3(sK1,X2,relation_image(sK1,X3)),relation_dom(sK1))
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1))
| ( sK2(sK1,X0,relation_image(sK1,X1)) != sK2(sK1,X2,relation_image(sK1,X3)) ) ),
inference(superposition,[status(thm)],[c_35214,c_35406]) ).
tcf(c_41127,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(sK1,X2) = relation_image(sK1,X3) )
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X2,relation_image(sK1,X3))) = sK2(sK1,X2,relation_image(sK1,X3)) )
| ( sK4(sK1,relation_dom(sK1),sK2(sK1,X2,relation_image(sK1,X3))) = sK3(sK1,X0,relation_image(sK1,X1)) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) )
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1))
| ~ in(sK4(sK1,relation_dom(sK1),sK2(sK1,X2,relation_image(sK1,X3))),relation_dom(sK1))
| ( sK2(sK1,X0,relation_image(sK1,X1)) != sK2(sK1,X2,relation_image(sK1,X3)) ) ),
inference(superposition,[status(thm)],[c_31984,c_35406]) ).
tcf(c_41128,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(sK1,X2) = relation_image(sK1,X3) )
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X2,relation_image(sK1,X3))) = sK2(sK1,X2,relation_image(sK1,X3)) )
| ( sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1))))) = sK3(sK1,X0,relation_image(sK1,X1)) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) )
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1))
| ~ in(sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1))))),relation_dom(sK1))
| ( sK2(sK1,X0,relation_image(sK1,X1)) != sK18(sK17(relation_image(sK1,relation_dom(sK1)))) ) ),
inference(superposition,[status(thm)],[c_35218,c_35406]) ).
tcf(c_41129,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(sK1,X2) = relation_image(sK1,X3) )
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X2,relation_image(sK1,X3))) = sK2(sK1,X2,relation_image(sK1,X3)) )
| ( sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1)))) = sK3(sK1,X0,relation_image(sK1,X1)) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) )
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1))
| ~ in(sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1)))),relation_dom(sK1))
| ( sK2(sK1,X0,relation_image(sK1,X1)) != sK18(relation_image(sK1,relation_dom(sK1))) ) ),
inference(superposition,[status(thm)],[c_35214,c_35406]) ).
tcf(c_41130,plain,
! [X0: $i,X1: $i] :
( ( relation_image(sK1,X0) = empty_set )
| ( sK3(sK1,X0,empty_set) = X1 )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) )
| ~ in(X1,relation_dom(sK1))
| ~ in(sK3(sK1,X0,empty_set),relation_dom(sK1))
| ( sK2(sK1,X0,empty_set) != apply(sK1,X1) ) ),
inference(light_normalisation,[status(thm)],[c_41123,c_23326]) ).
tcf(c_41245,plain,
! [X0: $i,X1: $i] :
( ( relation_image(sK1,X0) = relation_image(sK1,empty_set) )
| ( sK3(sK1,X0,relation_image(sK1,empty_set)) = X1 )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))) = sK18(sK17(relation_image(sK1,relation_dom(sK1)))) )
| ~ in(X1,relation_dom(sK1))
| ~ in(sK3(sK1,X0,relation_image(sK1,empty_set)),relation_dom(sK1))
| ( sK2(sK1,X0,empty_set) != apply(sK1,X1) ) ),
inference(superposition,[status(thm)],[c_23326,c_35609]) ).
tcf(c_41246,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(sK1,X2) = relation_image(sK1,X3) )
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X2,relation_image(sK1,X3))) = sK2(sK1,X2,relation_image(sK1,X3)) )
| ( sK4(sK1,X3,sK2(sK1,X2,relation_image(sK1,X3))) = sK3(sK1,X0,relation_image(sK1,X1)) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))) = sK18(sK17(relation_image(sK1,relation_dom(sK1)))) )
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1))
| ~ in(sK4(sK1,X3,sK2(sK1,X2,relation_image(sK1,X3))),relation_dom(sK1))
| ( sK2(sK1,X0,relation_image(sK1,X1)) != sK2(sK1,X2,relation_image(sK1,X3)) ) ),
inference(superposition,[status(thm)],[c_31512,c_35609]) ).
tcf(c_41247,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(sK1,X2) = relation_image(sK1,X3) )
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( sK3(sK1,X0,relation_image(sK1,X1)) = sK3(sK1,X2,relation_image(sK1,X3)) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))) = sK18(sK17(relation_image(sK1,relation_dom(sK1)))) )
| ~ in(sK3(sK1,X2,relation_image(sK1,X3)),relation_dom(sK1))
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1))
| ( sK2(sK1,X0,relation_image(sK1,X1)) != sK2(sK1,X2,relation_image(sK1,X3)) ) ),
inference(superposition,[status(thm)],[c_35218,c_35609]) ).
tcf(c_41249,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(sK1,X2) = relation_image(sK1,X3) )
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X2,relation_image(sK1,X3))) = sK2(sK1,X2,relation_image(sK1,X3)) )
| ( sK4(sK1,relation_dom(sK1),sK2(sK1,X2,relation_image(sK1,X3))) = sK3(sK1,X0,relation_image(sK1,X1)) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))) = sK18(sK17(relation_image(sK1,relation_dom(sK1)))) )
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1))
| ~ in(sK4(sK1,relation_dom(sK1),sK2(sK1,X2,relation_image(sK1,X3))),relation_dom(sK1))
| ( sK2(sK1,X0,relation_image(sK1,X1)) != sK2(sK1,X2,relation_image(sK1,X3)) ) ),
inference(superposition,[status(thm)],[c_31984,c_35609]) ).
tcf(c_41250,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(sK1,X2) = relation_image(sK1,X3) )
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X2,relation_image(sK1,X3))) = sK2(sK1,X2,relation_image(sK1,X3)) )
| ( sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1))))) = sK3(sK1,X0,relation_image(sK1,X1)) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))) = sK18(sK17(relation_image(sK1,relation_dom(sK1)))) )
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1))
| ~ in(sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1))))),relation_dom(sK1))
| ( sK2(sK1,X0,relation_image(sK1,X1)) != sK18(sK17(relation_image(sK1,relation_dom(sK1)))) ) ),
inference(superposition,[status(thm)],[c_35218,c_35609]) ).
tcf(c_41251,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(sK1,X2) = relation_image(sK1,X3) )
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X2,relation_image(sK1,X3))) = sK2(sK1,X2,relation_image(sK1,X3)) )
| ( sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1)))) = sK3(sK1,X0,relation_image(sK1,X1)) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))) = sK18(sK17(relation_image(sK1,relation_dom(sK1)))) )
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1))
| ~ in(sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1)))),relation_dom(sK1))
| ( sK2(sK1,X0,relation_image(sK1,X1)) != sK18(relation_image(sK1,relation_dom(sK1))) ) ),
inference(superposition,[status(thm)],[c_35214,c_35609]) ).
tcf(c_41252,plain,
! [X0: $i,X1: $i] :
( ( relation_image(sK1,X0) = empty_set )
| ( sK3(sK1,X0,empty_set) = X1 )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))) = sK18(sK17(relation_image(sK1,relation_dom(sK1)))) )
| ~ in(X1,relation_dom(sK1))
| ~ in(sK3(sK1,X0,empty_set),relation_dom(sK1))
| ( sK2(sK1,X0,empty_set) != apply(sK1,X1) ) ),
inference(light_normalisation,[status(thm)],[c_41245,c_23326]) ).
tcf(c_41509,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(sK1,X0,relation_image(sK1,X1)),relation_image(sK1,X1))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) )
| ( apply(sK1,sK4(sK1,X2,sK2(sK1,X0,relation_image(sK1,X1)))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),X2) ),
inference(superposition,[status(thm)],[c_54,c_35770]) ).
tcf(c_41510,plain,
! [X0: $i,X1: $i] :
( in(sK2(sK1,relation_dom(sK1),relation_image(sK1,X0)),relation_image(sK1,X0))
| ( relation_image(sK1,relation_dom(sK1)) = relation_image(sK1,X0) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) )
| ( apply(sK1,sK4(sK1,X1,sK2(sK1,relation_dom(sK1),relation_image(sK1,X0)))) = sK2(sK1,relation_dom(sK1),relation_image(sK1,X0)) )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(sK3(sK1,relation_dom(sK1),relation_image(sK1,X0)),X1) ),
inference(superposition,[status(thm)],[c_55,c_35770]) ).
tcf(c_41511,plain,
! [X0: $i,X1: $i] :
( ( relation_image(sK1,X0) = relation_image(sK1,empty_set) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) )
| ( apply(sK1,sK4(sK1,X1,sK2(sK1,X0,relation_image(sK1,empty_set)))) = sK2(sK1,X0,relation_image(sK1,empty_set)) )
| ~ in(sK3(sK1,X0,empty_set),relation_dom(sK1))
| ~ in(sK3(sK1,X0,relation_image(sK1,empty_set)),X1) ),
inference(superposition,[status(thm)],[c_23326,c_35770]) ).
tcf(c_41512,plain,
! [X0: $i,X1: $i] :
( ( relation_image(sK1,X0) = empty_set )
| ( apply(sK1,sK4(sK1,X1,sK2(sK1,X0,empty_set))) = sK2(sK1,X0,empty_set) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) )
| ~ in(sK3(sK1,X0,empty_set),X1)
| ~ in(sK3(sK1,X0,empty_set),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_41511,c_23326]) ).
tcf(c_41518,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(sK1,X0,relation_image(sK1,X1)),relation_image(sK1,X1))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) )
| ( apply(sK1,sK4(sK1,X2,sK2(sK1,X0,relation_image(sK1,X1)))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),X2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_41509,c_52,c_51]) ).
tcf(c_41524,plain,
! [X0: $i,X1: $i] :
( in(sK2(sK1,relation_dom(sK1),relation_image(sK1,X0)),relation_image(sK1,X0))
| ( relation_image(sK1,relation_dom(sK1)) = relation_image(sK1,X0) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) )
| ( apply(sK1,sK4(sK1,X1,sK2(sK1,relation_dom(sK1),relation_image(sK1,X0)))) = sK2(sK1,relation_dom(sK1),relation_image(sK1,X0)) )
| ~ in(sK3(sK1,relation_dom(sK1),relation_image(sK1,X0)),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_41510,c_52,c_51]) ).
tcf(c_41634,plain,
! [X0: $i,X1: $i] :
( in(sK2(sK1,X0,relation_image(sK1,X1)),relation_image(sK1,X1))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1)))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ function(sK1)
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_54,c_41518]) ).
tcf(c_41635,plain,
! [X0: $i,X1: $i] :
( in(sK2(sK1,X0,relation_image(sK1,X1)),relation_image(sK1,X1))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) )
| ( apply(sK1,sK4(sK1,X0,sK2(sK1,X0,relation_image(sK1,X1)))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ function(sK1)
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_55,c_41518]) ).
tcf(c_41636,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(sK1,X0,relation_image(sK1,X1)),relation_image(sK1,X1))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) )
| ( apply(sK1,sK4(sK1,powerset(X2),sK2(sK1,X0,relation_image(sK1,X1)))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ subset(sK3(sK1,X0,relation_image(sK1,X1)),X2) ),
inference(superposition,[status(thm)],[c_12509,c_41518]) ).
tcf(c_41637,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(sK1,X0,relation_image(sK1,X1)),relation_image(sK1,X1))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))) = sK18(sK17(relation_image(sK1,relation_dom(sK1)))) )
| ( apply(sK1,sK4(sK1,relation_inverse_image(sK1,X2),sK2(sK1,X0,relation_image(sK1,X1)))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),X2)
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_35585,c_41518]) ).
tcf(c_41638,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(sK1,X0,relation_image(sK1,X1)),relation_image(sK1,X1))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) )
| ( apply(sK1,sK4(sK1,relation_inverse_image(sK1,X2),sK2(sK1,X0,relation_image(sK1,X1)))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),X2)
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_35382,c_41518]) ).
tcf(c_41639,plain,
! [X0: $i,X1: $i] :
( in(sK2(sK1,X0,relation_image(sK1,empty_set)),relation_image(sK1,empty_set))
| ( relation_image(sK1,X0) = relation_image(sK1,empty_set) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) )
| ( apply(sK1,sK4(sK1,X1,sK2(sK1,X0,relation_image(sK1,empty_set)))) = sK2(sK1,X0,relation_image(sK1,empty_set)) )
| ~ in(sK3(sK1,X0,empty_set),X1) ),
inference(superposition,[status(thm)],[c_23326,c_41518]) ).
tcf(c_41640,plain,
! [X0: $i,X1: $i] :
( in(sK2(sK1,X0,relation_image(sK1,X1)),relation_image(sK1,X1))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) )
| ( apply(sK1,sK4(sK1,X0,sK2(sK1,X0,relation_image(sK1,X1)))) = sK2(sK1,X0,relation_image(sK1,X1)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_41635,c_52,c_51]) ).
tcf(c_41645,plain,
! [X0: $i,X1: $i] :
( in(sK2(sK1,X0,empty_set),empty_set)
| ( relation_image(sK1,X0) = empty_set )
| ( apply(sK1,sK4(sK1,X1,sK2(sK1,X0,empty_set))) = sK2(sK1,X0,empty_set) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) )
| ~ in(sK3(sK1,X0,empty_set),X1) ),
inference(light_normalisation,[status(thm)],[c_41639,c_23326]) ).
tcf(c_41646,plain,
! [X0: $i,X1: $i] :
( ( relation_image(sK1,X0) = empty_set )
| ( apply(sK1,sK4(sK1,X1,sK2(sK1,X0,empty_set))) = sK2(sK1,X0,empty_set) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) )
| ~ in(sK3(sK1,X0,empty_set),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_41645,c_13338]) ).
tcf(c_41651,plain,
! [X0: $i,X1: $i] :
( in(sK2(sK1,X0,relation_image(sK1,X1)),relation_image(sK1,X1))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1)))) = sK2(sK1,X0,relation_image(sK1,X1)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_41634,c_52,c_51]) ).
tcf(c_41680,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| ~ in(X0,sK18(sK17(sK17(sK17(sK17(powerset(X1))))))) ),
inference(superposition,[status(thm)],[c_40624,c_300]) ).
tcf(c_41681,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ in(X0,sK18(sK17(sK17(sK17(sK17(powerset(X1))))))) ),
inference(superposition,[status(thm)],[c_40624,c_299]) ).
tcf(c_41682,plain,
! [X0: $i,X1: $i] :
( in(X0,X1)
| ~ in(X0,sK18(sK17(sK17(sK17(sK17(powerset(X1))))))) ),
inference(superposition,[status(thm)],[c_40624,c_92]) ).
tcf(c_41696,plain,
! [X0: $i,X1: $i] :
( empty(relation_image(X0,X1))
| ( apply(X0,sK4(X0,X1,sK18(sK17(sK17(sK17(sK17(relation_image(X0,X1)))))))) = sK18(sK17(sK17(sK17(sK17(relation_image(X0,X1)))))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_40621,c_60]) ).
tcf(c_41697,plain,
! [X0: $i,X1: $i] :
( empty(relation_inverse_image(X0,X1))
| in(apply(X0,sK18(sK17(sK17(sK17(sK17(relation_inverse_image(X0,X1))))))),X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_40621,c_72]) ).
tcf(c_41698,plain,
! [X0: $i,X1: $i] :
( empty(relation_inverse_image(X0,X1))
| in(sK18(sK17(sK17(sK17(sK17(relation_inverse_image(X0,X1)))))),relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_40621,c_71]) ).
tcf(c_41699,plain,
! [X0: $i] :
( empty(X0)
| ~ in(X0,sK18(sK17(sK17(sK17(sK17(X0)))))) ),
inference(superposition,[status(thm)],[c_40621,c_98]) ).
tcf(c_41702,plain,
! [X0: $i] :
( empty(X0)
| empty(sK17(X0))
| element(sK18(sK17(sK17(sK17(sK17(sK17(X0)))))),X0) ),
inference(superposition,[status(thm)],[c_40621,c_14688]) ).
tcf(c_41703,plain,
! [X0: $i] :
( empty(X0)
| empty(sK17(X0))
| in(sK18(sK17(sK17(sK17(sK17(sK17(X0)))))),X0) ),
inference(superposition,[status(thm)],[c_40621,c_12618]) ).
tcf(c_41704,plain,
! [X0: $i] :
( empty(sK18(powerset(X0)))
| element(sK18(sK17(sK17(sK17(sK17(sK18(powerset(X0))))))),X0) ),
inference(superposition,[status(thm)],[c_40621,c_14689]) ).
tcf(c_41706,plain,
! [X0: $i] :
( empty(sK18(powerset(X0)))
| in(sK18(sK17(sK17(sK17(sK17(sK18(powerset(X0))))))),X0) ),
inference(superposition,[status(thm)],[c_40621,c_12619]) ).
tcf(c_41709,plain,
! [X0: $i] :
( empty(sK18(sK17(powerset(X0))))
| element(sK18(sK17(sK17(sK17(sK17(sK18(sK17(powerset(X0)))))))),X0) ),
inference(superposition,[status(thm)],[c_40621,c_14693]) ).
tcf(c_41711,plain,
! [X0: $i] :
( empty(sK18(sK17(powerset(X0))))
| in(sK18(sK17(sK17(sK17(sK17(sK18(sK17(powerset(X0)))))))),X0) ),
inference(superposition,[status(thm)],[c_40621,c_13032]) ).
tcf(c_41712,plain,
! [X0: $i] :
( empty(sK18(sK17(sK17(powerset(X0)))))
| in(sK18(sK17(sK17(sK17(sK17(sK18(sK17(sK17(powerset(X0))))))))),X0) ),
inference(superposition,[status(thm)],[c_40621,c_15478]) ).
tcf(c_41714,plain,
! [X0: $i] :
( empty(sK18(sK17(sK17(powerset(X0)))))
| element(sK18(sK17(sK17(sK17(sK17(sK18(sK17(sK17(powerset(X0))))))))),X0) ),
inference(superposition,[status(thm)],[c_40621,c_15476]) ).
tcf(c_41715,plain,
! [X0: $i] :
( empty(sK17(powerset(X0)))
| in(sK18(sK17(sK17(sK17(sK17(sK17(powerset(X0))))))),powerset(X0)) ),
inference(superposition,[status(thm)],[c_40621,c_18767]) ).
tcf(c_41716,plain,
! [X0: $i] :
( empty(sK17(powerset(X0)))
| element(sK18(sK17(sK17(sK17(sK17(sK17(powerset(X0))))))),powerset(X0)) ),
inference(superposition,[status(thm)],[c_40621,c_18765]) ).
tcf(c_41718,plain,
! [X0: $i,X1: $i] :
( empty(sK2(empty_set,X0,powerset(X1)))
| element(sK18(sK17(sK17(sK17(sK17(sK2(empty_set,X0,powerset(X1))))))),X1) ),
inference(superposition,[status(thm)],[c_40621,c_19619]) ).
tcf(c_41719,plain,
! [X0: $i,X1: $i] :
( empty(sK2(empty_set,X0,powerset(X1)))
| in(sK18(sK17(sK17(sK17(sK17(sK2(empty_set,X0,powerset(X1))))))),X1) ),
inference(superposition,[status(thm)],[c_40621,c_19621]) ).
tcf(c_41721,plain,
! [X0: $i,X1: $i] :
( empty(sK7(empty_set,X0,powerset(X1)))
| element(sK18(sK17(sK17(sK17(sK17(sK7(empty_set,X0,powerset(X1))))))),X1) ),
inference(superposition,[status(thm)],[c_40621,c_20796]) ).
tcf(c_41722,plain,
! [X0: $i,X1: $i] :
( empty(sK7(empty_set,X0,powerset(X1)))
| in(sK18(sK17(sK17(sK17(sK17(sK7(empty_set,X0,powerset(X1))))))),X1) ),
inference(superposition,[status(thm)],[c_40621,c_20798]) ).
tcf(c_41724,plain,
! [X0: $i] :
( empty(sK18(sK17(sK17(sK17(powerset(X0))))))
| element(sK18(sK17(sK17(sK17(sK17(sK18(sK17(sK17(sK17(powerset(X0)))))))))),X0) ),
inference(superposition,[status(thm)],[c_40621,c_22276]) ).
tcf(c_41725,plain,
! [X0: $i] :
( empty(sK18(sK17(sK17(sK17(powerset(X0))))))
| in(sK18(sK17(sK17(sK17(sK17(sK18(sK17(sK17(sK17(powerset(X0)))))))))),X0) ),
inference(superposition,[status(thm)],[c_40621,c_22278]) ).
tcf(c_41855,plain,
! [X0: $i,X1: $i] :
( empty(apply(sK1,sK4(sK1,X1,sK2(sK1,X0,relation_image(sK1,X1)))))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ in(sK4(sK1,X1,sK2(sK1,X0,relation_image(sK1,X1))),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK18(sK17(sK17(sK17(sK17(apply(sK1,sK4(sK1,X1,sK2(sK1,X0,relation_image(sK1,X1)))))))))) ),
inference(superposition,[status(thm)],[c_31860,c_41699]) ).
tcf(c_41856,plain,
! [X0: $i,X1: $i] :
( empty(apply(sK1,sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1)))))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ in(sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1))),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK18(sK17(sK17(sK17(sK17(apply(sK1,sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1)))))))))) ),
inference(superposition,[status(thm)],[c_33767,c_41699]) ).
tcf(c_41857,plain,
! [X0: $i,X1: $i] :
( empty(apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))) = sK18(sK17(relation_image(sK1,relation_dom(sK1)))) )
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK18(sK17(sK17(sK17(sK17(apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))))))))) ),
inference(superposition,[status(thm)],[c_37711,c_41699]) ).
tcf(c_41858,plain,
! [X0: $i,X1: $i] :
( empty(apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) )
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1))
| ~ in(sK2(sK1,X0,relation_image(sK1,X1)),sK18(sK17(sK17(sK17(sK17(apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))))))))) ),
inference(superposition,[status(thm)],[c_35721,c_41699]) ).
tcf(c_41859,plain,
! [X0: $i,X1: $i] :
( empty(apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ in(sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1)))),relation_dom(sK1))
| ~ in(sK18(relation_image(sK1,relation_dom(sK1))),sK18(sK17(sK17(sK17(sK17(apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))))))))) ),
inference(superposition,[status(thm)],[c_38416,c_41699]) ).
tcf(c_41860,plain,
! [X0: $i,X1: $i] :
( empty(apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ in(sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1))))),relation_dom(sK1))
| ~ in(sK18(sK17(relation_image(sK1,relation_dom(sK1)))),sK18(sK17(sK17(sK17(sK17(apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))))))))) ),
inference(superposition,[status(thm)],[c_40728,c_41699]) ).
tcf(c_41916,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK2(empty_set,X1,powerset(relation_dom(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_99,c_24409]) ).
tcf(c_41917,plain,
! [X0: $i] : relation_dom(sK2(empty_set,X0,powerset(relation_dom(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_114,c_24409]) ).
tcf(c_41918,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK2(empty_set,X1,powerset(relation_dom(sK18(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12738,c_24409]) ).
tcf(c_41919,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK2(empty_set,X1,powerset(relation_dom(sK18(powerset(sK18(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13358,c_24409]) ).
tcf(c_41920,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(sK2(empty_set,X2,powerset(relation_dom(relation_image(X0,X1))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK17(relation_image(X0,X1))))) = sK18(sK17(relation_image(X0,X1))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13159,c_24409]) ).
tcf(c_41921,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(sK2(empty_set,X2,powerset(relation_dom(relation_image(X0,X1))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(relation_image(X0,X1)))) = sK18(relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13157,c_24409]) ).
tcf(c_41922,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(sK2(empty_set,X2,powerset(relation_dom(sK18(powerset(relation_image(X0,X1))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK18(powerset(relation_image(X0,X1)))))) = sK18(sK18(powerset(relation_image(X0,X1)))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13158,c_24409]) ).
tcf(c_41923,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK2(empty_set,X1,powerset(relation_dom(sK18(sK17(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13470,c_24409]) ).
tcf(c_41924,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK2(empty_set,X1,powerset(relation_dom(sK18(powerset(sK18(sK17(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13469,c_24409]) ).
tcf(c_41925,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK2(empty_set,X1,powerset(relation_dom(sK18(sK17(sK17(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15885,c_24409]) ).
tcf(c_41926,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK2(empty_set,X1,powerset(relation_dom(sK18(powerset(sK18(sK17(sK17(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15887,c_24409]) ).
tcf(c_41927,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK2(empty_set,X1,powerset(relation_dom(relation_image(X0,empty_set))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17175,c_24409]) ).
tcf(c_41928,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK2(empty_set,X1,powerset(relation_dom(sK18(powerset(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17177,c_24409]) ).
tcf(c_41929,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK2(empty_set,X1,powerset(relation_dom(sK18(sK17(powerset(sK18(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17880,c_24409]) ).
tcf(c_41930,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK2(empty_set,X1,powerset(relation_dom(sK18(sK17(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17883,c_24409]) ).
tcf(c_41931,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK2(empty_set,X1,powerset(relation_dom(sK18(sK17(powerset(sK18(sK17(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17885,c_24409]) ).
tcf(c_41932,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK2(empty_set,X1,powerset(relation_dom(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17888,c_24409]) ).
tcf(c_41933,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(sK2(empty_set,X1,powerset(relation_dom(sK2(empty_set,X2,powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20186,c_24409]) ).
tcf(c_41934,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(sK2(empty_set,X1,powerset(relation_dom(sK18(powerset(sK2(empty_set,X2,powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20188,c_24409]) ).
tcf(c_41935,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(sK2(empty_set,X1,powerset(relation_dom(sK18(sK17(powerset(sK2(empty_set,X2,powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20189,c_24409]) ).
tcf(c_41936,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(sK2(empty_set,X1,powerset(relation_dom(sK7(empty_set,X2,powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21299,c_24409]) ).
tcf(c_41937,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(sK2(empty_set,X1,powerset(relation_dom(sK18(powerset(sK7(empty_set,X2,powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21301,c_24409]) ).
tcf(c_41938,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(sK2(empty_set,X1,powerset(relation_dom(sK18(sK17(powerset(sK7(empty_set,X2,powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21302,c_24409]) ).
tcf(c_41939,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK2(empty_set,X1,powerset(relation_dom(sK18(sK17(sK17(sK17(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25683,c_24409]) ).
tcf(c_41940,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK2(empty_set,X1,powerset(relation_dom(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25684,c_24409]) ).
tcf(c_42105,plain,
! [X0: $i] : sK16(X0) = empty_set,
inference(superposition,[status(thm)],[c_107,c_94]) ).
tcf(c_42124,plain,
! [X0: $i] : element(empty_set,powerset(X0)),
inference(demodulation,[status(thm)],[c_106,c_42105]) ).
tcf(c_42157,plain,
! [X0: $i] : subset(empty_set,X0),
inference(superposition,[status(thm)],[c_42124,c_88]) ).
tcf(c_42321,plain,
! [X0: $i,X1: $i] :
( in(X0,X1)
| ~ in(X0,empty_set) ),
inference(superposition,[status(thm)],[c_42157,c_92]) ).
tcf(c_42353,plain,
! [X0: $i] : ~ in(X0,empty_set),
inference(global_subsumption_just,[status(thm)],[c_42321,c_114,c_13145]) ).
tcf(c_43565,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X0,X2) = X1 )
| ( apply(X0,sK3(X0,X2,X1)) = sK2(X0,X2,X1) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_56,c_95]) ).
tcf(c_45909,plain,
! [X0: $i,X1: $i] :
( ( relation_image(sK1,X1) = X0 )
| ( apply(sK1,sK3(sK1,X1,X0)) = sK2(sK1,X1,X0) )
| ~ relation(sK1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_52,c_43565]) ).
tcf(c_45929,plain,
! [X0: $i,X1: $i] :
( ( relation_image(sK1,X1) = X0 )
| ( apply(sK1,sK3(sK1,X1,X0)) = sK2(sK1,X1,X0) )
| ~ empty(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_45909,c_51]) ).
tcf(c_46308,plain,
! [X0: $i] :
( ( relation_image(sK1,X0) = empty_set )
| ( apply(sK1,sK3(sK1,X0,empty_set)) = sK2(sK1,X0,empty_set) ) ),
inference(superposition,[status(thm)],[c_114,c_45929]) ).
tcf(c_46357,plain,
! [X0: $i,X1: $i] :
( in(sK2(sK1,X0,empty_set),relation_image(sK1,X1))
| ( relation_image(sK1,X0) = empty_set )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(sK3(sK1,X0,empty_set),X1)
| ~ in(sK3(sK1,X0,empty_set),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_46308,c_57]) ).
tcf(c_46368,plain,
! [X0: $i,X1: $i] :
( in(sK2(sK1,X0,empty_set),relation_image(sK1,X1))
| ( relation_image(sK1,X0) = empty_set )
| ~ in(sK3(sK1,X0,empty_set),X1)
| ~ in(sK3(sK1,X0,empty_set),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_46357,c_52,c_51]) ).
tcf(c_46448,plain,
! [X0: $i,X1: $i] :
( ( relation_image(sK1,X0) = empty_set )
| ( apply(sK1,sK4(sK1,X1,sK2(sK1,X0,empty_set))) = sK2(sK1,X0,empty_set) )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(sK3(sK1,X0,empty_set),X1)
| ~ in(sK3(sK1,X0,empty_set),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_46368,c_60]) ).
tcf(c_46464,plain,
! [X0: $i,X1: $i] :
( ( relation_image(sK1,X0) = empty_set )
| ( apply(sK1,sK4(sK1,X1,sK2(sK1,X0,empty_set))) = sK2(sK1,X0,empty_set) )
| ~ in(sK3(sK1,X0,empty_set),X1)
| ~ in(sK3(sK1,X0,empty_set),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_46448,c_52,c_51]) ).
tcf(c_46633,plain,
! [X0: $i,X1: $i] :
( in(sK2(sK1,X0,empty_set),empty_set)
| ( relation_image(sK1,X0) = empty_set )
| ( apply(sK1,sK4(sK1,X1,sK2(sK1,X0,empty_set))) = sK2(sK1,X0,empty_set) )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(sK3(sK1,X0,empty_set),X1) ),
inference(superposition,[status(thm)],[c_54,c_46464]) ).
tcf(c_46635,plain,
! [X0: $i,X1: $i] :
( ( relation_image(sK1,X0) = empty_set )
| ( apply(sK1,sK4(sK1,X1,sK2(sK1,X0,empty_set))) = sK2(sK1,X0,empty_set) )
| ~ in(sK3(sK1,X0,empty_set),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_46633,c_42353,c_52,c_51]) ).
tcf(c_46650,plain,
! [X0: $i] :
( in(sK2(sK1,X0,empty_set),empty_set)
| ( relation_image(sK1,X0) = empty_set )
| ( apply(sK1,sK4(sK1,X0,sK2(sK1,X0,empty_set))) = sK2(sK1,X0,empty_set) )
| ~ function(sK1)
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_55,c_46635]) ).
tcf(c_46656,plain,
! [X0: $i] :
( ( relation_image(sK1,X0) = empty_set )
| ( apply(sK1,sK4(sK1,X0,sK2(sK1,X0,empty_set))) = sK2(sK1,X0,empty_set) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_46650,c_42353,c_52,c_51]) ).
tcf(c_47010,plain,
! [X0: $i,X1: $i] :
( ( sK2(empty_set,X1,powerset(relation_dom(relation_dom(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_99,c_24511]) ).
tcf(c_47011,plain,
! [X0: $i] : sK2(empty_set,X0,powerset(relation_dom(relation_dom(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_114,c_24511]) ).
tcf(c_47012,plain,
! [X0: $i,X1: $i] :
( ( sK2(empty_set,X1,powerset(relation_dom(relation_dom(sK18(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12738,c_24511]) ).
tcf(c_47013,plain,
! [X0: $i,X1: $i] :
( ( sK2(empty_set,X1,powerset(relation_dom(relation_dom(sK18(powerset(sK18(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13358,c_24511]) ).
tcf(c_47014,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK2(empty_set,X2,powerset(relation_dom(relation_dom(relation_image(X0,X1))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK17(relation_image(X0,X1))))) = sK18(sK17(relation_image(X0,X1))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13159,c_24511]) ).
tcf(c_47015,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK2(empty_set,X2,powerset(relation_dom(relation_dom(relation_image(X0,X1))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(relation_image(X0,X1)))) = sK18(relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13157,c_24511]) ).
tcf(c_47016,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK2(empty_set,X2,powerset(relation_dom(relation_dom(sK18(powerset(relation_image(X0,X1))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK18(powerset(relation_image(X0,X1)))))) = sK18(sK18(powerset(relation_image(X0,X1)))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13158,c_24511]) ).
tcf(c_47017,plain,
! [X0: $i,X1: $i] :
( ( sK2(empty_set,X1,powerset(relation_dom(relation_dom(sK18(sK17(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13470,c_24511]) ).
tcf(c_47018,plain,
! [X0: $i,X1: $i] :
( ( sK2(empty_set,X1,powerset(relation_dom(relation_dom(sK18(powerset(sK18(sK17(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13469,c_24511]) ).
tcf(c_47019,plain,
! [X0: $i,X1: $i] :
( ( sK2(empty_set,X1,powerset(relation_dom(relation_dom(sK18(sK17(sK17(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15885,c_24511]) ).
tcf(c_47020,plain,
! [X0: $i,X1: $i] :
( ( sK2(empty_set,X1,powerset(relation_dom(relation_dom(sK18(powerset(sK18(sK17(sK17(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15887,c_24511]) ).
tcf(c_47021,plain,
! [X0: $i,X1: $i] :
( ( sK2(empty_set,X1,powerset(relation_dom(relation_dom(relation_image(X0,empty_set))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17175,c_24511]) ).
tcf(c_47022,plain,
! [X0: $i,X1: $i] :
( ( sK2(empty_set,X1,powerset(relation_dom(relation_dom(sK18(powerset(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17177,c_24511]) ).
tcf(c_47023,plain,
! [X0: $i,X1: $i] :
( ( sK2(empty_set,X1,powerset(relation_dom(relation_dom(sK18(sK17(powerset(sK18(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17880,c_24511]) ).
tcf(c_47024,plain,
! [X0: $i,X1: $i] :
( ( sK2(empty_set,X1,powerset(relation_dom(relation_dom(sK18(sK17(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17883,c_24511]) ).
tcf(c_47025,plain,
! [X0: $i,X1: $i] :
( ( sK2(empty_set,X1,powerset(relation_dom(relation_dom(sK18(sK17(powerset(sK18(sK17(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17885,c_24511]) ).
tcf(c_47026,plain,
! [X0: $i,X1: $i] :
( ( sK2(empty_set,X1,powerset(relation_dom(relation_dom(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17888,c_24511]) ).
tcf(c_47027,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK2(empty_set,X1,powerset(relation_dom(relation_dom(sK2(empty_set,X2,powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20186,c_24511]) ).
tcf(c_47028,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK2(empty_set,X1,powerset(relation_dom(relation_dom(sK18(powerset(sK2(empty_set,X2,powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20188,c_24511]) ).
tcf(c_47029,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK2(empty_set,X1,powerset(relation_dom(relation_dom(sK18(sK17(powerset(sK2(empty_set,X2,powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20189,c_24511]) ).
tcf(c_47030,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK2(empty_set,X1,powerset(relation_dom(relation_dom(sK7(empty_set,X2,powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21299,c_24511]) ).
tcf(c_47031,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK2(empty_set,X1,powerset(relation_dom(relation_dom(sK18(powerset(sK7(empty_set,X2,powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21301,c_24511]) ).
tcf(c_47032,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK2(empty_set,X1,powerset(relation_dom(relation_dom(sK18(sK17(powerset(sK7(empty_set,X2,powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21302,c_24511]) ).
tcf(c_47033,plain,
! [X0: $i,X1: $i] :
( ( sK2(empty_set,X1,powerset(relation_dom(relation_dom(sK18(sK17(sK17(sK17(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25683,c_24511]) ).
tcf(c_47034,plain,
! [X0: $i,X1: $i] :
( ( sK2(empty_set,X1,powerset(relation_dom(relation_dom(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25684,c_24511]) ).
tcf(c_47194,plain,
( empty(sK18(powerset(empty_set)))
| element(sK18(sK17(sK17(sK17(empty_set)))),empty_set) ),
inference(superposition,[status(thm)],[c_12958,c_22300]) ).
tcf(c_47195,plain,
! [X0: $i] :
( empty(sK18(powerset(powerset(X0))))
| subset(sK18(sK17(sK17(sK17(sK18(powerset(powerset(X0))))))),X0) ),
inference(superposition,[status(thm)],[c_22300,c_88]) ).
tcf(c_47197,plain,
( empty(empty_set)
| element(sK18(sK17(sK17(sK17(empty_set)))),empty_set) ),
inference(light_normalisation,[status(thm)],[c_47194,c_12958]) ).
tcf(c_47205,plain,
( empty(sK18(powerset(empty_set)))
| in(sK18(sK17(sK17(sK17(empty_set)))),empty_set) ),
inference(superposition,[status(thm)],[c_12958,c_22302]) ).
tcf(c_47206,plain,
! [X0: $i,X1: $i] :
( empty(sK18(powerset(relation_image(X0,X1))))
| ( apply(X0,sK4(X0,X1,sK18(sK17(sK17(sK17(sK18(powerset(relation_image(X0,X1))))))))) = sK18(sK17(sK17(sK17(sK18(powerset(relation_image(X0,X1))))))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_22302,c_60]) ).
tcf(c_47207,plain,
! [X0: $i,X1: $i] :
( empty(sK18(powerset(relation_inverse_image(X0,X1))))
| in(apply(X0,sK18(sK17(sK17(sK17(sK18(powerset(relation_inverse_image(X0,X1)))))))),X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_22302,c_72]) ).
tcf(c_47208,plain,
! [X0: $i,X1: $i] :
( empty(sK18(powerset(relation_inverse_image(X0,X1))))
| in(sK18(sK17(sK17(sK17(sK18(powerset(relation_inverse_image(X0,X1))))))),relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_22302,c_71]) ).
tcf(c_47209,plain,
! [X0: $i] :
( empty(sK18(powerset(X0)))
| ~ in(X0,sK18(sK17(sK17(sK17(sK18(powerset(X0))))))) ),
inference(superposition,[status(thm)],[c_22302,c_98]) ).
tcf(c_47212,plain,
! [X0: $i] :
( empty(X0)
| empty(sK18(powerset(sK17(X0))))
| element(sK18(sK17(sK17(sK17(sK18(powerset(sK17(X0))))))),X0) ),
inference(superposition,[status(thm)],[c_22302,c_14688]) ).
tcf(c_47213,plain,
! [X0: $i] :
( empty(X0)
| empty(sK18(powerset(sK17(X0))))
| in(sK18(sK17(sK17(sK17(sK18(powerset(sK17(X0))))))),X0) ),
inference(superposition,[status(thm)],[c_22302,c_12618]) ).
tcf(c_47214,plain,
! [X0: $i] :
( empty(sK18(powerset(sK18(powerset(X0)))))
| element(sK18(sK17(sK17(sK17(sK18(powerset(sK18(powerset(X0)))))))),X0) ),
inference(superposition,[status(thm)],[c_22302,c_14689]) ).
tcf(c_47216,plain,
! [X0: $i] :
( empty(sK18(powerset(sK18(powerset(X0)))))
| in(sK18(sK17(sK17(sK17(sK18(powerset(sK18(powerset(X0)))))))),X0) ),
inference(superposition,[status(thm)],[c_22302,c_12619]) ).
tcf(c_47219,plain,
! [X0: $i] :
( empty(sK18(powerset(sK18(sK17(powerset(X0))))))
| element(sK18(sK17(sK17(sK17(sK18(powerset(sK18(sK17(powerset(X0))))))))),X0) ),
inference(superposition,[status(thm)],[c_22302,c_14693]) ).
tcf(c_47221,plain,
! [X0: $i] :
( empty(sK18(powerset(sK18(sK17(powerset(X0))))))
| in(sK18(sK17(sK17(sK17(sK18(powerset(sK18(sK17(powerset(X0))))))))),X0) ),
inference(superposition,[status(thm)],[c_22302,c_13032]) ).
tcf(c_47222,plain,
! [X0: $i] :
( empty(sK18(powerset(sK18(sK17(sK17(powerset(X0)))))))
| in(sK18(sK17(sK17(sK17(sK18(powerset(sK18(sK17(sK17(powerset(X0)))))))))),X0) ),
inference(superposition,[status(thm)],[c_22302,c_15478]) ).
tcf(c_47224,plain,
! [X0: $i] :
( empty(sK18(powerset(sK18(sK17(sK17(powerset(X0)))))))
| element(sK18(sK17(sK17(sK17(sK18(powerset(sK18(sK17(sK17(powerset(X0)))))))))),X0) ),
inference(superposition,[status(thm)],[c_22302,c_15476]) ).
tcf(c_47225,plain,
! [X0: $i] :
( empty(sK18(powerset(sK17(powerset(X0)))))
| in(sK18(sK17(sK17(sK17(sK18(powerset(sK17(powerset(X0)))))))),powerset(X0)) ),
inference(superposition,[status(thm)],[c_22302,c_18767]) ).
tcf(c_47226,plain,
! [X0: $i] :
( empty(sK18(powerset(sK17(powerset(X0)))))
| element(sK18(sK17(sK17(sK17(sK18(powerset(sK17(powerset(X0)))))))),powerset(X0)) ),
inference(superposition,[status(thm)],[c_22302,c_18765]) ).
tcf(c_47228,plain,
! [X0: $i,X1: $i] :
( empty(sK18(powerset(sK2(empty_set,X0,powerset(X1)))))
| element(sK18(sK17(sK17(sK17(sK18(powerset(sK2(empty_set,X0,powerset(X1)))))))),X1) ),
inference(superposition,[status(thm)],[c_22302,c_19619]) ).
tcf(c_47229,plain,
! [X0: $i,X1: $i] :
( empty(sK18(powerset(sK2(empty_set,X0,powerset(X1)))))
| in(sK18(sK17(sK17(sK17(sK18(powerset(sK2(empty_set,X0,powerset(X1)))))))),X1) ),
inference(superposition,[status(thm)],[c_22302,c_19621]) ).
tcf(c_47231,plain,
! [X0: $i,X1: $i] :
( empty(sK18(powerset(sK7(empty_set,X0,powerset(X1)))))
| element(sK18(sK17(sK17(sK17(sK18(powerset(sK7(empty_set,X0,powerset(X1)))))))),X1) ),
inference(superposition,[status(thm)],[c_22302,c_20796]) ).
tcf(c_47232,plain,
! [X0: $i,X1: $i] :
( empty(sK18(powerset(sK7(empty_set,X0,powerset(X1)))))
| in(sK18(sK17(sK17(sK17(sK18(powerset(sK7(empty_set,X0,powerset(X1)))))))),X1) ),
inference(superposition,[status(thm)],[c_22302,c_20798]) ).
tcf(c_47234,plain,
! [X0: $i] :
( empty(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0))))))))
| element(sK18(sK17(sK17(sK17(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0))))))))))),X0) ),
inference(superposition,[status(thm)],[c_22302,c_22276]) ).
tcf(c_47235,plain,
! [X0: $i] :
( empty(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0))))))))
| in(sK18(sK17(sK17(sK17(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0))))))))))),X0) ),
inference(superposition,[status(thm)],[c_22302,c_22278]) ).
tcf(c_47236,plain,
( empty(empty_set)
| in(sK18(sK17(sK17(sK17(empty_set)))),empty_set) ),
inference(light_normalisation,[status(thm)],[c_47205,c_12958]) ).
tcf(c_47376,plain,
! [X0: $i,X1: $i] :
( ( sK7(empty_set,X1,powerset(relation_dom(relation_dom(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_99,c_24676]) ).
tcf(c_47377,plain,
! [X0: $i] : sK7(empty_set,X0,powerset(relation_dom(relation_dom(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_114,c_24676]) ).
tcf(c_47378,plain,
! [X0: $i,X1: $i] :
( ( sK7(empty_set,X1,powerset(relation_dom(relation_dom(sK18(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12738,c_24676]) ).
tcf(c_47379,plain,
! [X0: $i,X1: $i] :
( ( sK7(empty_set,X1,powerset(relation_dom(relation_dom(sK18(powerset(sK18(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13358,c_24676]) ).
tcf(c_47380,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK7(empty_set,X2,powerset(relation_dom(relation_dom(relation_image(X0,X1))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK17(relation_image(X0,X1))))) = sK18(sK17(relation_image(X0,X1))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13159,c_24676]) ).
tcf(c_47381,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK7(empty_set,X2,powerset(relation_dom(relation_dom(relation_image(X0,X1))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(relation_image(X0,X1)))) = sK18(relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13157,c_24676]) ).
tcf(c_47382,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK7(empty_set,X2,powerset(relation_dom(relation_dom(sK18(powerset(relation_image(X0,X1))))))) = empty_set )
| ( apply(X0,sK4(X0,X1,sK18(sK18(powerset(relation_image(X0,X1)))))) = sK18(sK18(powerset(relation_image(X0,X1)))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_13158,c_24676]) ).
tcf(c_47383,plain,
! [X0: $i,X1: $i] :
( ( sK7(empty_set,X1,powerset(relation_dom(relation_dom(sK18(sK17(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13470,c_24676]) ).
tcf(c_47384,plain,
! [X0: $i,X1: $i] :
( ( sK7(empty_set,X1,powerset(relation_dom(relation_dom(sK18(powerset(sK18(sK17(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_13469,c_24676]) ).
tcf(c_47385,plain,
! [X0: $i,X1: $i] :
( ( sK7(empty_set,X1,powerset(relation_dom(relation_dom(sK18(sK17(sK17(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15885,c_24676]) ).
tcf(c_47386,plain,
! [X0: $i,X1: $i] :
( ( sK7(empty_set,X1,powerset(relation_dom(relation_dom(sK18(powerset(sK18(sK17(sK17(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_15887,c_24676]) ).
tcf(c_47387,plain,
! [X0: $i,X1: $i] :
( ( sK7(empty_set,X1,powerset(relation_dom(relation_dom(relation_image(X0,empty_set))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17175,c_24676]) ).
tcf(c_47388,plain,
! [X0: $i,X1: $i] :
( ( sK7(empty_set,X1,powerset(relation_dom(relation_dom(sK18(powerset(relation_image(X0,empty_set))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17177,c_24676]) ).
tcf(c_47389,plain,
! [X0: $i,X1: $i] :
( ( sK7(empty_set,X1,powerset(relation_dom(relation_dom(sK18(sK17(powerset(sK18(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17880,c_24676]) ).
tcf(c_47390,plain,
! [X0: $i,X1: $i] :
( ( sK7(empty_set,X1,powerset(relation_dom(relation_dom(sK18(sK17(powerset(relation_image(X0,empty_set)))))))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17883,c_24676]) ).
tcf(c_47391,plain,
! [X0: $i,X1: $i] :
( ( sK7(empty_set,X1,powerset(relation_dom(relation_dom(sK18(sK17(powerset(sK18(sK17(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17885,c_24676]) ).
tcf(c_47392,plain,
! [X0: $i,X1: $i] :
( ( sK7(empty_set,X1,powerset(relation_dom(relation_dom(sK18(sK17(powerset(sK18(sK17(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17888,c_24676]) ).
tcf(c_47393,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK7(empty_set,X1,powerset(relation_dom(relation_dom(sK2(empty_set,X2,powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20186,c_24676]) ).
tcf(c_47394,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK7(empty_set,X1,powerset(relation_dom(relation_dom(sK18(powerset(sK2(empty_set,X2,powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20188,c_24676]) ).
tcf(c_47395,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK7(empty_set,X1,powerset(relation_dom(relation_dom(sK18(sK17(powerset(sK2(empty_set,X2,powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20189,c_24676]) ).
tcf(c_47396,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK7(empty_set,X1,powerset(relation_dom(relation_dom(sK7(empty_set,X2,powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21299,c_24676]) ).
tcf(c_47397,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK7(empty_set,X1,powerset(relation_dom(relation_dom(sK18(powerset(sK7(empty_set,X2,powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21301,c_24676]) ).
tcf(c_47398,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK7(empty_set,X1,powerset(relation_dom(relation_dom(sK18(sK17(powerset(sK7(empty_set,X2,powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21302,c_24676]) ).
tcf(c_47399,plain,
! [X0: $i,X1: $i] :
( ( sK7(empty_set,X1,powerset(relation_dom(relation_dom(sK18(sK17(sK17(sK17(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25683,c_24676]) ).
tcf(c_47400,plain,
! [X0: $i,X1: $i] :
( ( sK7(empty_set,X1,powerset(relation_dom(relation_dom(sK18(powerset(sK18(sK17(sK17(sK17(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25684,c_24676]) ).
tcf(c_47677,plain,
! [X0: $i] :
( in(sK2(sK1,X0,empty_set),empty_set)
| ( relation_image(sK1,X0) = relation_image(sK1,empty_set) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) )
| ( apply(sK1,sK4(sK1,X0,sK2(sK1,X0,relation_image(sK1,empty_set)))) = sK2(sK1,X0,relation_image(sK1,empty_set)) ) ),
inference(superposition,[status(thm)],[c_23326,c_41640]) ).
tcf(c_47679,plain,
! [X0: $i,X1: $i] :
( ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) )
| ( apply(sK1,sK4(sK1,X1,sK2(sK1,X0,relation_image(sK1,X1)))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ( apply(sK1,sK4(sK1,X0,sK2(sK1,X0,relation_image(sK1,X1)))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ~ function(sK1)
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_41640,c_60]) ).
tcf(c_47680,plain,
! [X0: $i,X1: $i] :
( ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) )
| ( apply(sK1,sK4(sK1,X1,sK2(sK1,X1,relation_image(sK1,X0)))) = sK2(sK1,X1,relation_image(sK1,X0)) )
| ~ in(relation_image(sK1,X0),sK2(sK1,X1,relation_image(sK1,X0))) ),
inference(superposition,[status(thm)],[c_41640,c_98]) ).
tcf(c_47681,plain,
! [X0: $i,X1: $i] :
( element(sK2(sK1,X0,relation_image(sK1,X1)),relation_image(sK1,X1))
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) )
| ( apply(sK1,sK4(sK1,X0,sK2(sK1,X0,relation_image(sK1,X1)))) = sK2(sK1,X0,relation_image(sK1,X1)) ) ),
inference(superposition,[status(thm)],[c_41640,c_97]) ).
tcf(c_47682,plain,
! [X0: $i,X1: $i] :
( ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) )
| ( apply(sK1,sK4(sK1,X1,sK2(sK1,X1,relation_image(sK1,X0)))) = sK2(sK1,X1,relation_image(sK1,X0)) )
| ~ empty(relation_image(sK1,X0)) ),
inference(superposition,[status(thm)],[c_41640,c_95]) ).
tcf(c_47683,plain,
! [X0: $i] :
( ( relation_image(sK1,X0) = relation_image(sK1,empty_set) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) )
| ( apply(sK1,sK4(sK1,X0,sK2(sK1,X0,relation_image(sK1,empty_set)))) = sK2(sK1,X0,relation_image(sK1,empty_set)) )
| ~ function(sK1)
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_41640,c_13341]) ).
tcf(c_47688,plain,
! [X0: $i] :
( ( relation_image(sK1,X0) = empty_set )
| ( apply(sK1,sK4(sK1,X0,sK2(sK1,X0,empty_set))) = sK2(sK1,X0,empty_set) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) )
| ~ function(sK1)
| ~ relation(sK1) ),
inference(light_normalisation,[status(thm)],[c_47683,c_23326]) ).
tcf(c_47689,plain,
! [X0: $i] :
( ( relation_image(sK1,X0) = empty_set )
| ( apply(sK1,sK4(sK1,X0,sK2(sK1,X0,empty_set))) = sK2(sK1,X0,empty_set) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_47688,c_52,c_51]) ).
tcf(c_47693,plain,
! [X0: $i] :
( in(sK2(sK1,X0,empty_set),empty_set)
| ( relation_image(sK1,X0) = empty_set )
| ( apply(sK1,sK4(sK1,X0,sK2(sK1,X0,empty_set))) = sK2(sK1,X0,empty_set) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) ) ),
inference(light_normalisation,[status(thm)],[c_47677,c_23326]) ).
tcf(c_47703,plain,
! [X0: $i,X1: $i] :
( ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) )
| ( apply(sK1,sK4(sK1,X1,sK2(sK1,X0,relation_image(sK1,X1)))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ( apply(sK1,sK4(sK1,X0,sK2(sK1,X0,relation_image(sK1,X1)))) = sK2(sK1,X0,relation_image(sK1,X1)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_47679,c_52,c_51]) ).
tcf(c_47744,plain,
! [X0: $i] :
( ( relation_image(sK1,X0) = empty_set )
| ( apply(sK1,sK4(sK1,X0,sK2(sK1,X0,empty_set))) = sK2(sK1,X0,empty_set) ) ),
inference(global_subsumption_just,[status(thm)],[c_47689,c_46656]) ).
tcf(c_47750,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK1,X2) = empty_set )
| ( relation_image(sK1,X0) = X1 )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(sK2(sK1,X0,X1),X1)
| ~ in(sK4(sK1,X2,sK2(sK1,X2,empty_set)),X0)
| ~ in(sK4(sK1,X2,sK2(sK1,X2,empty_set)),relation_dom(sK1))
| ( sK2(sK1,X0,X1) != sK2(sK1,X2,empty_set) ) ),
inference(superposition,[status(thm)],[c_47744,c_53]) ).
tcf(c_47751,plain,
! [X0: $i,X1: $i] :
( in(sK2(sK1,X0,empty_set),relation_image(sK1,X1))
| ( relation_image(sK1,X0) = empty_set )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(sK4(sK1,X0,sK2(sK1,X0,empty_set)),X1)
| ~ in(sK4(sK1,X0,sK2(sK1,X0,empty_set)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_47744,c_57]) ).
tcf(c_47753,plain,
! [X0: $i,X1: $i] :
( in(sK4(sK1,X0,sK2(sK1,X0,empty_set)),relation_inverse_image(sK1,X1))
| ( relation_image(sK1,X0) = empty_set )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(sK2(sK1,X0,empty_set),X1)
| ~ in(sK4(sK1,X0,sK2(sK1,X0,empty_set)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_47744,c_70]) ).
tcf(c_47754,plain,
! [X0: $i,X1: $i] :
( ( relation_image(sK1,X0) = empty_set )
| ( sK4(sK1,X0,sK2(sK1,X0,empty_set)) = X1 )
| ~ function(sK1)
| ~ relation(sK1)
| ~ one_to_one(sK1)
| ~ in(X1,relation_dom(sK1))
| ~ in(sK4(sK1,X0,sK2(sK1,X0,empty_set)),relation_dom(sK1))
| ( sK2(sK1,X0,empty_set) != apply(sK1,X1) ) ),
inference(superposition,[status(thm)],[c_47744,c_85]) ).
tcf(c_47755,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK1,X2) = empty_set )
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( sK4(sK1,X2,sK2(sK1,X2,empty_set)) = sK3(sK1,X0,relation_image(sK1,X1)) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(sK17(relation_image(sK1,relation_dom(sK1)))))) = sK18(sK17(relation_image(sK1,relation_dom(sK1)))) )
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1))
| ~ in(sK4(sK1,X2,sK2(sK1,X2,empty_set)),relation_dom(sK1))
| ( sK2(sK1,X0,relation_image(sK1,X1)) != sK2(sK1,X2,empty_set) ) ),
inference(superposition,[status(thm)],[c_47744,c_35609]) ).
tcf(c_47756,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK1,X2) = empty_set )
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( sK4(sK1,X2,sK2(sK1,X2,empty_set)) = sK3(sK1,X0,relation_image(sK1,X1)) )
| ( apply(sK1,sK4(sK1,relation_dom(sK1),sK18(relation_image(sK1,relation_dom(sK1))))) = sK18(relation_image(sK1,relation_dom(sK1))) )
| ~ in(sK3(sK1,X0,relation_image(sK1,X1)),relation_dom(sK1))
| ~ in(sK4(sK1,X2,sK2(sK1,X2,empty_set)),relation_dom(sK1))
| ( sK2(sK1,X0,relation_image(sK1,X1)) != sK2(sK1,X2,empty_set) ) ),
inference(superposition,[status(thm)],[c_47744,c_35406]) ).
tcf(c_47757,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK1,X2) = empty_set )
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ( sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1))) = sK4(sK1,X2,sK2(sK1,X2,empty_set)) )
| ~ in(sK4(sK1,X2,sK2(sK1,X2,empty_set)),relation_dom(sK1))
| ~ in(sK4(sK1,relation_dom(sK1),sK2(sK1,X0,relation_image(sK1,X1))),relation_dom(sK1))
| ( sK2(sK1,X0,relation_image(sK1,X1)) != sK2(sK1,X2,empty_set) ) ),
inference(superposition,[status(thm)],[c_47744,c_32021]) ).
tcf(c_47758,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK1,X2) = empty_set )
| ( relation_image(sK1,X0) = relation_image(sK1,X1) )
| ( apply(sK1,sK3(sK1,X0,relation_image(sK1,X1))) = sK2(sK1,X0,relation_image(sK1,X1)) )
| ( sK4(sK1,X1,sK2(sK1,X0,relation_image(sK1,X1))) = sK4(sK1,X2,sK2(sK1,X2,empty_set)) )
| ~ in(sK4(sK1,X2,sK2(sK1,X2,empty_set)),relation_dom(sK1))
| ~ in(sK4(sK1,X1,sK2(sK1,X0,relation_image(sK1,X1))),relation_dom(sK1))
| ( sK2(sK1,X0,relation_image(sK1,X1)) != sK2(sK1,X2,empty_set) ) ),
inference(superposition,[status(thm)],[c_47744,c_31757]) ).
tcf(c_47759,plain,
! [X0: $i,X1: $i] :
( in(sK4(sK1,X0,sK2(sK1,X0,empty_set)),relation_inverse_image(sK1,X1))
| ( relation_image(sK1,X0) = empty_set )
| ~ in(sK2(sK1,X0,empty_set),X1)
| ~ in(sK4(sK1,X0,sK2(sK1,X0,empty_set)),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_47753,c_52,c_51]) ).
tcf(c_47764,plain,
! [X0: $i,X1: $i] :
( in(sK2(sK1,X0,empty_set),relation_image(sK1,X1))
| ( relation_image(sK1,X0) = empty_set )
| ~ in(sK4(sK1,X0,sK2(sK1,X0,empty_set)),X1)
| ~ in(sK4(sK1,X0,sK2(sK1,X0,empty_set)),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_47751,c_52,c_51]) ).
tcf(c_47769,plain,
! [X0: $i,X1: $i] :
( ( relation_image(sK1,X0) = empty_set )
| ( sK4(sK1,X0,sK2(sK1,X0,empty_set)) = X1 )
| ~ in(X1,relation_dom(sK1))
| ~ in(sK4(sK1,X0,sK2(sK1,X0,empty_set)),relation_dom(sK1))
| ( sK2(sK1,X0,empty_set) != apply(sK1,X1) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_47754,c_52,c_51,c_50]) ).
tcf(c_47775,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK1,X2) = empty_set )
| ( relation_image(sK1,X0) = X1 )
| ~ in(sK2(sK1,X0,X1),X1)
| ~ in(sK4(sK1,X2,sK2(sK1,X2,empty_set)),X0)
| ~ in(sK4(sK1,X2,sK2(sK1,X2,empty_set)),relation_dom(sK1))
| ( sK2(sK1,X0,X1) != sK2(sK1,X2,empty_set) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_47750,c_52,c_51]) ).
tcf(c_47826,plain,
! [X0: $i,X1: $i] :
( in(apply(sK1,sK4(sK1,X0,sK2(sK1,X0,empty_set))),X1)
| ( relation_image(sK1,X0) = empty_set )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(sK2(sK1,X0,empty_set),X1)
| ~ in(sK4(sK1,X0,sK2(sK1,X0,empty_set)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_47759,c_72]) ).
tcf(c_47828,plain,
! [X0: $i,X1: $i] :
( ( relation_image(sK1,X1) = empty_set )
| ~ in(sK2(sK1,X1,empty_set),X0)
| ~ in(sK4(sK1,X1,sK2(sK1,X1,empty_set)),relation_dom(sK1))
| ~ in(relation_inverse_image(sK1,X0),sK4(sK1,X1,sK2(sK1,X1,empty_set))) ),
inference(superposition,[status(thm)],[c_47759,c_98]) ).
tcf(c_47829,plain,
! [X0: $i,X1: $i] :
( element(sK4(sK1,X0,sK2(sK1,X0,empty_set)),relation_inverse_image(sK1,X1))
| ( relation_image(sK1,X0) = empty_set )
| ~ in(sK2(sK1,X0,empty_set),X1)
| ~ in(sK4(sK1,X0,sK2(sK1,X0,empty_set)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_47759,c_97]) ).
tcf(c_47830,plain,
! [X0: $i,X1: $i] :
( ( relation_image(sK1,X0) = empty_set )
| ~ empty(relation_inverse_image(sK1,X1))
| ~ in(sK2(sK1,X0,empty_set),X1)
| ~ in(sK4(sK1,X0,sK2(sK1,X0,empty_set)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_47759,c_95]) ).
tcf(c_47843,plain,
! [X0: $i,X1: $i] :
( in(apply(sK1,sK4(sK1,X0,sK2(sK1,X0,empty_set))),X1)
| ( relation_image(sK1,X0) = empty_set )
| ~ in(sK2(sK1,X0,empty_set),X1)
| ~ in(sK4(sK1,X0,sK2(sK1,X0,empty_set)),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_47826,c_52,c_51]) ).
tcf(c_47866,plain,
! [X0: $i,X1: $i] :
( in(sK2(sK1,X0,empty_set),relation_image(sK1,X1))
| ( relation_image(sK1,X0) = empty_set )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(sK2(sK1,X0,empty_set),relation_image(sK1,X0))
| ~ in(sK4(sK1,X0,sK2(sK1,X0,empty_set)),X1) ),
inference(superposition,[status(thm)],[c_58,c_47764]) ).
tcf(c_47867,plain,
! [X0: $i] :
( in(sK2(sK1,relation_dom(sK1),empty_set),relation_image(sK1,X0))
| ( relation_image(sK1,relation_dom(sK1)) = empty_set )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(sK2(sK1,relation_dom(sK1),empty_set),relation_image(sK1,relation_dom(sK1)))
| ~ in(sK4(sK1,relation_dom(sK1),sK2(sK1,relation_dom(sK1),empty_set)),X0) ),
inference(superposition,[status(thm)],[c_59,c_47764]) ).
tcf(c_47868,plain,
! [X0: $i,X1: $i] :
( in(sK2(sK1,X0,empty_set),relation_image(sK1,X1))
| ( relation_image(sK1,X0) = empty_set )
| ~ in(sK2(sK1,X0,empty_set),relation_image(sK1,X0))
| ~ in(sK4(sK1,X0,sK2(sK1,X0,empty_set)),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_47866,c_52,c_51]) ).
tcf(c_47873,plain,
! [X0: $i] :
( in(sK2(sK1,relation_dom(sK1),empty_set),relation_image(sK1,X0))
| ( relation_image(sK1,relation_dom(sK1)) = empty_set )
| ~ in(sK2(sK1,relation_dom(sK1),empty_set),relation_image(sK1,relation_dom(sK1)))
| ~ in(sK4(sK1,relation_dom(sK1),sK2(sK1,relation_dom(sK1),empty_set)),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_47867,c_52,c_51]) ).
tcf(c_47887,plain,
! [X0: $i] :
( in(sK2(sK1,X0,empty_set),relation_image(sK1,relation_dom(sK1)))
| ( relation_image(sK1,X0) = empty_set )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(sK2(sK1,X0,empty_set),relation_image(sK1,X0)) ),
inference(superposition,[status(thm)],[c_58,c_47868]) ).
tcf(c_47889,plain,
! [X0: $i,X1: $i] :
( in(sK2(sK1,X0,empty_set),relation_image(sK1,powerset(X1)))
| ( relation_image(sK1,X0) = empty_set )
| ~ in(sK2(sK1,X0,empty_set),relation_image(sK1,X0))
| ~ subset(sK4(sK1,X0,sK2(sK1,X0,empty_set)),X1) ),
inference(superposition,[status(thm)],[c_12509,c_47868]) ).
tcf(c_47890,plain,
! [X0: $i,X1: $i] :
( in(sK2(sK1,X0,empty_set),relation_image(sK1,relation_inverse_image(sK1,X1)))
| ( relation_image(sK1,X0) = empty_set )
| ~ in(sK2(sK1,X0,empty_set),X1)
| ~ in(sK2(sK1,X0,empty_set),relation_image(sK1,X0))
| ~ in(sK4(sK1,X0,sK2(sK1,X0,empty_set)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_47759,c_47868]) ).
tcf(c_47891,plain,
! [X0: $i] :
( in(sK2(sK1,X0,empty_set),relation_image(sK1,relation_dom(sK1)))
| ( relation_image(sK1,X0) = empty_set )
| ~ in(sK2(sK1,X0,empty_set),relation_image(sK1,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_47887,c_52,c_51]) ).
tcf(c_47934,plain,
( in(sK2(sK1,relation_dom(sK1),empty_set),relation_image(sK1,relation_dom(sK1)))
| ( relation_image(sK1,relation_dom(sK1)) = empty_set )
| ( apply(sK1,sK3(sK1,relation_dom(sK1),empty_set)) = sK2(sK1,relation_dom(sK1),empty_set) ) ),
inference(superposition,[status(thm)],[c_31974,c_47891]) ).
tcf(c_47948,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK1,X0) = empty_set )
| ( apply(X1,sK4(X1,X2,apply(sK1,sK4(sK1,X0,sK2(sK1,X0,empty_set))))) = apply(sK1,sK4(sK1,X0,sK2(sK1,X0,empty_set))) )
| ~ function(X1)
| ~ relation(X1)
| ~ in(sK2(sK1,X0,empty_set),relation_image(X1,X2))
| ~ in(sK4(sK1,X0,sK2(sK1,X0,empty_set)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_47843,c_60]) ).
tcf(c_47950,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X1,apply(sK1,sK4(sK1,X0,sK2(sK1,X0,empty_set)))),X2)
| ( relation_image(sK1,X0) = empty_set )
| ~ function(X1)
| ~ relation(X1)
| ~ in(sK2(sK1,X0,empty_set),relation_inverse_image(X1,X2))
| ~ in(sK4(sK1,X0,sK2(sK1,X0,empty_set)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_47843,c_72]) ).
tcf(c_47951,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(sK1,sK4(sK1,X0,sK2(sK1,X0,empty_set))),relation_dom(X1))
| ( relation_image(sK1,X0) = empty_set )
| ~ function(X1)
| ~ relation(X1)
| ~ in(sK2(sK1,X0,empty_set),relation_inverse_image(X1,X2))
| ~ in(sK4(sK1,X0,sK2(sK1,X0,empty_set)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_47843,c_71]) ).
tcf(c_47952,plain,
! [X0: $i,X1: $i] :
( ( relation_image(sK1,X1) = empty_set )
| ~ in(sK2(sK1,X1,empty_set),X0)
| ~ in(sK4(sK1,X1,sK2(sK1,X1,empty_set)),relation_dom(sK1))
| ~ in(X0,apply(sK1,sK4(sK1,X1,sK2(sK1,X1,empty_set)))) ),
inference(superposition,[status(thm)],[c_47843,c_98]) ).
tcf(c_47953,plain,
! [X0: $i,X1: $i] :
( element(apply(sK1,sK4(sK1,X0,sK2(sK1,X0,empty_set))),X1)
| ( relation_image(sK1,X0) = empty_set )
| ~ in(sK2(sK1,X0,empty_set),X1)
| ~ in(sK4(sK1,X0,sK2(sK1,X0,empty_set)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_47843,c_97]) ).
tcf(c_47954,plain,
! [X0: $i,X1: $i] :
( ( relation_image(sK1,X0) = empty_set )
| ~ empty(X1)
| ~ in(sK2(sK1,X0,empty_set),X1)
| ~ in(sK4(sK1,X0,sK2(sK1,X0,empty_set)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_47843,c_95]) ).
tcf(c_47955,plain,
! [X0: $i,X1: $i] :
( subset(apply(sK1,sK4(sK1,X0,sK2(sK1,X0,empty_set))),X1)
| ( relation_image(sK1,X0) = empty_set )
| ~ in(sK4(sK1,X0,sK2(sK1,X0,empty_set)),relation_dom(sK1))
| ~ in(sK2(sK1,X0,empty_set),sK13(apply(sK1,sK4(sK1,X0,sK2(sK1,X0,empty_set))),X1)) ),
inference(superposition,[status(thm)],[c_47843,c_12485]) ).
tcf(c_47956,plain,
! [X0: $i] :
( empty(apply(sK1,sK4(sK1,X0,sK2(sK1,X0,empty_set))))
| ( relation_image(sK1,X0) = empty_set )
| ~ in(sK4(sK1,X0,sK2(sK1,X0,empty_set)),relation_dom(sK1))
| ~ in(sK2(sK1,X0,empty_set),sK18(apply(sK1,sK4(sK1,X0,sK2(sK1,X0,empty_set))))) ),
inference(superposition,[status(thm)],[c_47843,c_12526]) ).
tcf(c_47957,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| element(apply(sK1,sK4(sK1,X0,sK2(sK1,X0,empty_set))),X1)
| ( relation_image(sK1,X0) = empty_set )
| ~ in(sK2(sK1,X0,empty_set),sK17(X1))
| ~ in(sK4(sK1,X0,sK2(sK1,X0,empty_set)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_47843,c_14688]) ).
tcf(c_47958,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| in(apply(sK1,sK4(sK1,X0,sK2(sK1,X0,empty_set))),X1)
| ( relation_image(sK1,X0) = empty_set )
| ~ in(sK2(sK1,X0,empty_set),sK17(X1))
| ~ in(sK4(sK1,X0,sK2(sK1,X0,empty_set)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_47843,c_12618]) ).
tcf(c_47959,plain,
! [X0: $i,X1: $i] :
( element(apply(sK1,sK4(sK1,X0,sK2(sK1,X0,empty_set))),X1)
| ( relation_image(sK1,X0) = empty_set )
| ~ in(sK2(sK1,X0,empty_set),sK18(powerset(X1)))
| ~ in(sK4(sK1,X0,sK2(sK1,X0,empty_set)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_47843,c_14689]) ).
tcf(c_47960,plain,
! [X0: $i,X1: $i] :
( ( relation_image(sK1,X0) = empty_set )
| ~ empty(X1)
| ~ in(sK2(sK1,X0,empty_set),sK18(powerset(X1)))
| ~ in(sK4(sK1,X0,sK2(sK1,X0,empty_set)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_47843,c_13313]) ).
tcf(c_47961,plain,
! [X0: $i,X1: $i] :
( in(apply(sK1,sK4(sK1,X0,sK2(sK1,X0,empty_set))),X1)
| ( relation_image(sK1,X0) = empty_set )
| ~ in(sK2(sK1,X0,empty_set),sK18(powerset(X1)))
| ~ in(sK4(sK1,X0,sK2(sK1,X0,empty_set)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_47843,c_12619]) ).
tcf(c_47962,plain,
! [X0: $i] :
( ( relation_image(sK1,X0) = empty_set )
| ~ in(sK2(sK1,X0,empty_set),empty_set)
| ~ in(sK4(sK1,X0,sK2(sK1,X0,empty_set)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_47843,c_13338]) ).
tcf(c_47963,plain,
! [X0: $i] :
( empty(sK18(powerset(apply(sK1,sK4(sK1,X0,sK2(sK1,X0,empty_set))))))
| ( relation_image(sK1,X0) = empty_set )
| ~ in(sK4(sK1,X0,sK2(sK1,X0,empty_set)),relation_dom(sK1))
| ~ in(sK2(sK1,X0,empty_set),sK18(sK18(powerset(apply(sK1,sK4(sK1,X0,sK2(sK1,X0,empty_set))))))) ),
inference(superposition,[status(thm)],[c_47843,c_12736]) ).
tcf(c_47964,plain,
! [X0: $i,X1: $i] :
( ( relation_image(sK1,X0) = empty_set )
| ~ function(X1)
| ~ relation(X1)
| ~ in(sK2(sK1,X0,empty_set),relation_image(X1,empty_set))
| ~ in(sK4(sK1,X0,sK2(sK1,X0,empty_set)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_47843,c_13341]) ).
tcf(c_47965,plain,
! [X0: $i] :
( empty(apply(sK1,sK4(sK1,X0,sK2(sK1,X0,empty_set))))
| ( relation_image(sK1,X0) = empty_set )
| ~ in(sK4(sK1,X0,sK2(sK1,X0,empty_set)),relation_dom(sK1))
| ~ in(sK2(sK1,X0,empty_set),sK18(sK17(apply(sK1,sK4(sK1,X0,sK2(sK1,X0,empty_set)))))) ),
inference(superposition,[status(thm)],[c_47843,c_12990]) ).
tcf(c_47966,plain,
! [X0: $i,X1: $i] :
( element(apply(sK1,sK4(sK1,X0,sK2(sK1,X0,empty_set))),X1)
| ( relation_image(sK1,X0) = empty_set )
| ~ in(sK2(sK1,X0,empty_set),sK18(sK17(powerset(X1))))
| ~ in(sK4(sK1,X0,sK2(sK1,X0,empty_set)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_47843,c_14693]) ).
tcf(c_47967,plain,
! [X0: $i,X1: $i] :
( ( relation_image(sK1,X0) = empty_set )
| ~ empty(X1)
| ~ in(sK2(sK1,X0,empty_set),sK18(sK17(powerset(X1))))
| ~ in(sK4(sK1,X0,sK2(sK1,X0,empty_set)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_47843,c_13316]) ).
tcf(c_47968,plain,
! [X0: $i,X1: $i] :
( in(apply(sK1,sK4(sK1,X0,sK2(sK1,X0,empty_set))),X1)
| ( relation_image(sK1,X0) = empty_set )
| ~ in(sK2(sK1,X0,empty_set),sK18(sK17(powerset(X1))))
| ~ in(sK4(sK1,X0,sK2(sK1,X0,empty_set)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_47843,c_13032]) ).
tcf(c_47969,plain,
! [X0: $i] :
( empty(apply(sK1,sK4(sK1,X0,sK2(sK1,X0,empty_set))))
| ( relation_image(sK1,X0) = empty_set )
| ~ in(sK4(sK1,X0,sK2(sK1,X0,empty_set)),relation_dom(sK1))
| ~ in(sK2(sK1,X0,empty_set),sK18(sK17(sK17(apply(sK1,sK4(sK1,X0,sK2(sK1,X0,empty_set))))))) ),
inference(superposition,[status(thm)],[c_47843,c_15381]) ).
tcf(c_47970,plain,
! [X0: $i,X1: $i] :
( in(apply(sK1,sK4(sK1,X0,sK2(sK1,X0,empty_set))),X1)
| ( relation_image(sK1,X0) = empty_set )
| ~ in(sK2(sK1,X0,empty_set),sK18(sK17(sK17(powerset(X1)))))
| ~ in(sK4(sK1,X0,sK2(sK1,X0,empty_set)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_47843,c_15478]) ).
tcf(c_47971,plain,
! [X0: $i,X1: $i] :
( ( relation_image(sK1,X0) = empty_set )
| ~ empty(X1)
| ~ in(sK2(sK1,X0,empty_set),sK18(sK17(sK17(powerset(X1)))))
| ~ in(sK4(sK1,X0,sK2(sK1,X0,empty_set)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_47843,c_15477]) ).
tcf(c_47972,plain,
! [X0: $i,X1: $i] :
( element(apply(sK1,sK4(sK1,X0,sK2(sK1,X0,empty_set))),X1)
| ( relation_image(sK1,X0) = empty_set )
| ~ in(sK2(sK1,X0,empty_set),sK18(sK17(sK17(powerset(X1)))))
| ~ in(sK4(sK1,X0,sK2(sK1,X0,empty_set)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_47843,c_15476]) ).
tcf(c_47973,plain,
! [X0: $i] :
( empty(sK18(powerset(apply(sK1,sK4(sK1,X0,sK2(sK1,X0,empty_set))))))
| ( relation_image(sK1,X0) = empty_set )
| ~ in(sK4(sK1,X0,sK2(sK1,X0,empty_set)),relation_dom(sK1))
| ~ in(sK2(sK1,X0,empty_set),sK18(sK17(sK18(powerset(apply(sK1,sK4(sK1,X0,sK2(sK1,X0,empty_set)))))))) ),
inference(superposition,[status(thm)],[c_47843,c_15649]) ).
tcf(c_47974,plain,
! [X0: $i,X1: $i] :
( subset(sK18(powerset(apply(sK1,sK4(sK1,X0,sK2(sK1,X0,empty_set))))),X1)
| ( relation_image(sK1,X0) = empty_set )
| ~ in(sK4(sK1,X0,sK2(sK1,X0,empty_set)),relation_dom(sK1))
| ~ in(sK2(sK1,X0,empty_set),sK13(sK18(powerset(apply(sK1,sK4(sK1,X0,sK2(sK1,X0,empty_set))))),X1)) ),
inference(superposition,[status(thm)],[c_47843,c_16394]) ).
tcf(c_47975,plain,
! [X0: $i,X1: $i] :
( empty(apply(sK1,sK4(sK1,X0,sK2(sK1,X0,empty_set))))
| subset(sK17(apply(sK1,sK4(sK1,X0,sK2(sK1,X0,empty_set)))),X1)
| ( relation_image(sK1,X0) = empty_set )
| ~ in(sK4(sK1,X0,sK2(sK1,X0,empty_set)),relation_dom(sK1))
| ~ in(sK2(sK1,X0,empty_set),sK13(sK17(apply(sK1,sK4(sK1,X0,sK2(sK1,X0,empty_set)))),X1)) ),
inference(superposition,[status(thm)],[c_47843,c_16730]) ).
tcf(c_47976,plain,
! [X0: $i] :
( empty(sK18(sK17(powerset(apply(sK1,sK4(sK1,X0,sK2(sK1,X0,empty_set)))))))
| ( relation_image(sK1,X0) = empty_set )
| ~ in(sK4(sK1,X0,sK2(sK1,X0,empty_set)),relation_dom(sK1))
| ~ in(sK2(sK1,X0,empty_set),sK18(sK18(sK17(powerset(apply(sK1,sK4(sK1,X0,sK2(sK1,X0,empty_set)))))))) ),
inference(superposition,[status(thm)],[c_47843,c_17874]) ).
tcf(c_47977,plain,
! [X0: $i,X1: $i] :
( in(apply(sK1,sK4(sK1,X0,sK2(sK1,X0,empty_set))),powerset(X1))
| ( relation_image(sK1,X0) = empty_set )
| ~ in(sK2(sK1,X0,empty_set),sK17(powerset(X1)))
| ~ in(sK4(sK1,X0,sK2(sK1,X0,empty_set)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_47843,c_18767]) ).
tcf(c_47978,plain,
! [X0: $i,X1: $i] :
( element(apply(sK1,sK4(sK1,X0,sK2(sK1,X0,empty_set))),powerset(X1))
| ( relation_image(sK1,X0) = empty_set )
| ~ in(sK2(sK1,X0,empty_set),sK17(powerset(X1)))
| ~ in(sK4(sK1,X0,sK2(sK1,X0,empty_set)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_47843,c_18765]) ).
tcf(c_47979,plain,
! [X0: $i,X1: $i] :
( ( relation_image(sK1,X0) = empty_set )
| ( apply(sK1,sK4(sK1,X0,sK2(sK1,X0,empty_set))) = empty_set )
| ~ in(sK4(sK1,X0,sK2(sK1,X0,empty_set)),relation_dom(sK1))
| ~ in(sK2(sK1,X0,empty_set),sK2(empty_set,X1,apply(sK1,sK4(sK1,X0,sK2(sK1,X0,empty_set))))) ),
inference(superposition,[status(thm)],[c_47843,c_19251]) ).
tcf(c_47980,plain,
! [X0: $i,X1: $i] :
( ( relation_image(sK1,X0) = empty_set )
| ( apply(sK1,sK4(sK1,X0,sK2(sK1,X0,empty_set))) = empty_set )
| ~ in(sK4(sK1,X0,sK2(sK1,X0,empty_set)),relation_dom(sK1))
| ~ in(sK2(sK1,X0,empty_set),sK7(empty_set,X1,apply(sK1,sK4(sK1,X0,sK2(sK1,X0,empty_set))))) ),
inference(superposition,[status(thm)],[c_47843,c_19880]) ).
tcf(c_47981,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK1,X0) = empty_set )
| ~ empty(X2)
| ~ in(sK4(sK1,X0,sK2(sK1,X0,empty_set)),relation_dom(sK1))
| ~ in(sK2(sK1,X0,empty_set),sK2(empty_set,X1,powerset(X2))) ),
inference(superposition,[status(thm)],[c_47843,c_19620]) ).
tcf(c_47982,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(apply(sK1,sK4(sK1,X0,sK2(sK1,X0,empty_set))),X2)
| ( relation_image(sK1,X0) = empty_set )
| ~ in(sK4(sK1,X0,sK2(sK1,X0,empty_set)),relation_dom(sK1))
| ~ in(sK2(sK1,X0,empty_set),sK2(empty_set,X1,powerset(X2))) ),
inference(superposition,[status(thm)],[c_47843,c_19619]) ).
tcf(c_47983,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(sK1,sK4(sK1,X0,sK2(sK1,X0,empty_set))),X2)
| ( relation_image(sK1,X0) = empty_set )
| ~ in(sK4(sK1,X0,sK2(sK1,X0,empty_set)),relation_dom(sK1))
| ~ in(sK2(sK1,X0,empty_set),sK2(empty_set,X1,powerset(X2))) ),
inference(superposition,[status(thm)],[c_47843,c_19621]) ).
tcf(c_47984,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(sK1,X0) = empty_set )
| ~ empty(X2)
| ~ in(sK4(sK1,X0,sK2(sK1,X0,empty_set)),relation_dom(sK1))
| ~ in(sK2(sK1,X0,empty_set),sK7(empty_set,X1,powerset(X2))) ),
inference(superposition,[status(thm)],[c_47843,c_20797]) ).
tcf(c_47985,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(apply(sK1,sK4(sK1,X0,sK2(sK1,X0,empty_set))),X2)
| ( relation_image(sK1,X0) = empty_set )
| ~ in(sK4(sK1,X0,sK2(sK1,X0,empty_set)),relation_dom(sK1))
| ~ in(sK2(sK1,X0,empty_set),sK7(empty_set,X1,powerset(X2))) ),
inference(superposition,[status(thm)],[c_47843,c_20796]) ).
tcf(c_47986,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(sK1,sK4(sK1,X0,sK2(sK1,X0,empty_set))),X2)
| ( relation_image(sK1,X0) = empty_set )
| ~ in(sK4(sK1,X0,sK2(sK1,X0,empty_set)),relation_dom(sK1))
| ~ in(sK2(sK1,X0,empty_set),sK7(empty_set,X1,powerset(X2))) ),
inference(superposition,[status(thm)],[c_47843,c_20798]) ).
tcf(c_47987,plain,
! [X0: $i,X1: $i] :
( ( relation_image(sK1,X0) = empty_set )
| ~ empty(X1)
| ~ in(sK4(sK1,X0,sK2(sK1,X0,empty_set)),relation_dom(sK1))
| ~ in(sK2(sK1,X0,empty_set),sK18(sK17(sK17(sK17(powerset(X1)))))) ),
inference(superposition,[status(thm)],[c_47843,c_22277]) ).
tcf(c_47988,plain,
! [X0: $i,X1: $i] :
( element(apply(sK1,sK4(sK1,X0,sK2(sK1,X0,empty_set))),X1)
| ( relation_image(sK1,X0) = empty_set )
| ~ in(sK4(sK1,X0,sK2(sK1,X0,empty_set)),relation_dom(sK1))
| ~ in(sK2(sK1,X0,empty_set),sK18(sK17(sK17(sK17(powerset(X1)))))) ),
inference(superposition,[status(thm)],[c_47843,c_22276]) ).
tcf(c_47989,plain,
! [X0: $i,X1: $i] :
( in(apply(sK1,sK4(sK1,X0,sK2(sK1,X0,empty_set))),X1)
| ( relation_image(sK1,X0) = empty_set )
| ~ in(sK4(sK1,X0,sK2(sK1,X0,empty_set)),relation_dom(sK1))
| ~ in(sK2(sK1,X0,empty_set),sK18(sK17(sK17(sK17(powerset(X1)))))) ),
inference(superposition,[status(thm)],[c_47843,c_22278]) ).
tcf(c_47990,plain,
! [X0: $i] :
( empty(apply(sK1,sK4(sK1,X0,sK2(sK1,X0,empty_set))))
| ( relation_image(sK1,X0) = empty_set )
| ~ in(sK4(sK1,X0,sK2(sK1,X0,empty_set)),relation_dom(sK1))
| ~ in(sK2(sK1,X0,empty_set),sK18(sK17(sK17(sK17(apply(sK1,sK4(sK1,X0,sK2(sK1,X0,empty_set)))))))) ),
inference(superposition,[status(thm)],[c_47843,c_22295]) ).
tcf(c_47991,plain,
! [X0: $i] :
( empty(sK18(powerset(apply(sK1,sK4(sK1,X0,sK2(sK1,X0,empty_set))))))
| ( relation_image(sK1,X0) = empty_set )
| ~ in(sK4(sK1,X0,sK2(sK1,X0,empty_set)),relation_dom(sK1))
| ~ in(sK2(sK1,X0,empty_set),sK18(sK17(sK17(sK18(powerset(apply(sK1,sK4(sK1,X0,sK2(sK1,X0,empty_set))))))))) ),
inference(superposition,[status(thm)],[c_47843,c_22453]) ).
tcf(c_47992,plain,
! [X0: $i] :
( empty(apply(sK1,sK4(sK1,X0,sK2(sK1,X0,empty_set))))
| ( relation_image(sK1,X0) = empty_set )
| ~ in(sK4(sK1,X0,sK2(sK1,X0,empty_set)),relation_dom(sK1))
| ~ in(sK2(sK1,X0,empty_set),sK18(sK17(sK17(sK17(sK17(apply(sK1,sK4(sK1,X0,sK2(sK1,X0,empty_set))))))))) ),
inference(superposition,[status(thm)],[c_47843,c_41699]) ).
tcf(c_48316,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_47992,c_47991,c_47990,c_47989,c_47988,c_47987,c_47986,c_47985,c_47984,c_47983,c_47982,c_47981,c_47980,c_47979,c_47978,c_47977,c_47976,c_47975,c_47974,c_47973,c_47972,c_47971,c_47970,c_47969,c_47968,c_47967,c_47966,c_47965,c_47964,c_47963,c_47962,c_47961,c_47960,c_47959,c_47958,c_47957,c_47956,c_47955,c_47954,c_47953,c_47952,c_47951,c_47950,c_47948,c_47934,c_47891,c_47890,c_47889,c_47887,c_47873,c_47868,c_47867,c_47866,c_47843,c_47830,c_47829,c_47828,c_47826,c_47775,c_47769,c_47764,c_47759,c_47758,c_47757,c_47756,c_47755,c_47753,c_47754,c_47751,c_47750,c_47703,c_47693,c_47689,c_47688,c_47683,c_47682,c_47681,c_47680,c_47679,c_47677,c_47400,c_47399,c_47398,c_47397,c_47396,c_47395,c_47394,c_47393,c_47392,c_47391,c_47390,c_47389,c_47388,c_47387,c_47386,c_47385,c_47384,c_47383,c_47382,c_47381,c_47380,c_47379,c_47378,c_47377,c_47376,c_47236,c_47235,c_47234,c_47232,c_47231,c_47229,c_47228,c_47226,c_47225,c_47224,c_47222,c_47221,c_47219,c_47216,c_47214,c_47213,c_47212,c_47209,c_47208,c_47207,c_47206,c_47205,c_47197,c_47195,c_47194,c_47034,c_47033,c_47032,c_47031,c_47030,c_47029,c_47028,c_47027,c_47026,c_47025,c_47024,c_47023,c_47022,c_47021,c_47020,c_47019,c_47018,c_47017,c_47016,c_47015,c_47014,c_47013,c_47012,c_47011,c_47010,c_47744,c_41940,c_41939,c_41938,c_41937,c_41936,c_41935,c_41934,c_41933,c_41932,c_41931,c_41930,c_41929,c_41928,c_41927,c_41926,c_41925,c_41924,c_41923,c_41922,c_41921,c_41920,c_41919,c_41918,c_41917,c_41916,c_41860,c_41859,c_41858,c_41857,c_41856,c_41855,c_41725,c_41724,c_41722,c_41721,c_41719,c_41718,c_41716,c_41715,c_41714,c_41712,c_41711,c_41709,c_41706,c_41704,c_41703,c_41702,c_41699,c_41698,c_41697,c_41696,c_41682,c_41681,c_41680,c_41651,c_41646,c_41645,c_41640,c_41639,c_41638,c_41637,c_41636,c_41635,c_41634,c_41524,c_41518,c_41512,c_41511,c_41510,c_41509,c_41252,c_41251,c_41250,c_41249,c_41247,c_41246,c_41245,c_41130,c_41129,c_41128,c_41127,c_41126,c_41125,c_41124,c_41123,c_40840,c_40839,c_40838,c_40837,c_40836,c_40835,c_40834,c_40833,c_40832,c_40831,c_40830,c_40829,c_40828,c_40827,c_40826,c_40825,c_40824,c_40823,c_40822,c_40821,c_40820,c_40819,c_40818,c_40817,c_40816,c_40815,c_40814,c_40813,c_40812,c_40811,c_40810,c_40809,c_40808,c_40807,c_40806,c_40805,c_40804,c_40803,c_40802,c_40801,c_40800,c_40799,c_40797,c_40770,c_40769,c_40750,c_40748,c_40728,c_40712,c_40711,c_40710,c_40708,c_40624,c_40621,c_40620,c_40613,c_40365,c_40363,c_40362,c_40360,c_40359,c_40357,c_40356,c_40355,c_40354,c_40353,c_40351,c_40349,c_40347,c_40346,c_40345,c_40344,c_40342,c_40341,c_40139,c_40138,c_40137,c_40136,c_40135,c_40134,c_40133,c_40132,c_40131,c_40130,c_40129,c_40128,c_40127,c_40126,c_40125,c_40124,c_40123,c_40122,c_40121,c_40120,c_40119,c_40118,c_40117,c_40116,c_40115,c_39965,c_39964,c_39963,c_39962,c_39961,c_39960,c_39959,c_39958,c_39957,c_39956,c_39955,c_39954,c_39953,c_39952,c_39951,c_39950,c_39949,c_39948,c_39947,c_39946,c_39945,c_39944,c_39943,c_39942,c_39941,c_39745,c_39744,c_39743,c_39742,c_39741,c_39740,c_39739,c_39738,c_39737,c_39736,c_39735,c_39734,c_39733,c_39732,c_39731,c_39730,c_39729,c_39728,c_39727,c_39726,c_39725,c_39724,c_39723,c_39722,c_39721,c_39507,c_39506,c_39505,c_39504,c_39503,c_39502,c_39501,c_39500,c_39499,c_39498,c_39497,c_39496,c_39495,c_39494,c_39493,c_39492,c_39491,c_39490,c_39489,c_39488,c_39487,c_39486,c_39485,c_39484,c_39483,c_39236,c_39235,c_39234,c_39233,c_39232,c_39231,c_39230,c_39229,c_39228,c_39227,c_39226,c_39225,c_39224,c_39223,c_39222,c_39221,c_39220,c_39219,c_39218,c_39217,c_39216,c_39215,c_39214,c_39213,c_39212,c_39174,c_39173,c_39172,c_39171,c_39170,c_39169,c_39168,c_39167,c_38593,c_38592,c_38591,c_38590,c_38589,c_38588,c_38587,c_38586,c_38585,c_38584,c_38583,c_38582,c_38581,c_38580,c_38579,c_38578,c_38577,c_38576,c_38575,c_38574,c_38573,c_38572,c_38571,c_38570,c_38569,c_38568,c_38567,c_38566,c_38565,c_38564,c_38563,c_38562,c_38561,c_38560,c_38559,c_38558,c_38557,c_38556,c_38555,c_38554,c_38553,c_38552,c_38550,c_38498,c_38497,c_38478,c_38476,c_38416,c_38400,c_38399,c_38398,c_38396,c_37954,c_37912,c_37911,c_37910,c_37909,c_37908,c_37907,c_37906,c_37905,c_37904,c_37903,c_37902,c_37901,c_37900,c_37899,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_37884,c_37883,c_37882,c_37881,c_37880,c_37879,c_37878,c_37877,c_37876,c_37875,c_37874,c_37873,c_37872,c_37871,c_37869,c_37868,c_37797,c_37781,c_37775,c_37774,c_37773,c_37772,c_37771,c_37770,c_37769,c_37711,c_37695,c_37689,c_37688,c_37687,c_37685,c_37684,c_37268,c_37226,c_37225,c_37224,c_37223,c_37222,c_37221,c_37220,c_37219,c_37218,c_37217,c_37216,c_37215,c_37214,c_37213,c_37212,c_37211,c_37210,c_37209,c_37208,c_37207,c_37206,c_37205,c_37204,c_37203,c_37202,c_37201,c_37200,c_37199,c_37198,c_37197,c_37196,c_37195,c_37194,c_37193,c_37192,c_37191,c_37190,c_37189,c_37188,c_37187,c_37186,c_37185,c_37183,c_37182,c_37018,c_37016,c_37015,c_37013,c_37012,c_37010,c_37009,c_37008,c_37007,c_37006,c_37004,c_37002,c_37000,c_36999,c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).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEU071+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.02 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.03/5.51 % Computer : n012.cluster.edu
% 0.03/5.51 % Model : x86_64 x86_64
% 0.03/5.51 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/5.51 % Memory : 8046.5625MB
% 0.03/5.51 % OS : Linux 6.8.0-71-generic
% 0.03/5.51 % CPULimit : 300
% 0.03/5.51 % WCLimit : 300
% 0.03/5.51 % DateTime : Thu Sep 24 12:41:21 UTC 2026
% 0.03/5.52 % CPUTime :
% 0.03/5.52 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.03/5.54 Running first-order theorem proving
% 0.03/5.54 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
% 0.03/5.54
% 0.03/5.54 % ======== iProver multi-core TPTP/SMT =========
% 0.03/5.54
% 0.03/5.54 % Detected problem language: tptp
% 0.03/5.55 % Proving...
% 7.17/7.76 % SZS status Started for theBenchmark.p
% 7.17/7.76 % SZS status Theorem for theBenchmark.p
% 7.17/7.76
% 7.17/7.76 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 7.17/7.76
% 7.17/7.76 % ------ iProver source info
% 7.17/7.76
% 7.17/7.76 % git: date: 2026-07-19 20:42:38 +0200
% 7.17/7.76 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 7.17/7.76 % git: non_committed_changes: false
% 7.17/7.76
% 7.17/7.76 % ------ Parsing...
% 7.17/7.76 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 7.17/7.76
% 7.17/7.76 % ------ 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 %
% 7.17/7.76
% 7.17/7.76 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 7.17/7.76
% 7.17/7.76 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 7.17/7.76 % ------ Proving...
% 7.17/7.76 % ------ Problem Properties
% 7.17/7.76
% 7.17/7.76 %
% 7.17/7.76 % clauses 65
% 7.17/7.76 % conjectures 4
% 7.17/7.76 % EPR 32
% 7.17/7.76 % Horn 54
% 7.17/7.76 % unary 25
% 7.17/7.76 % binary 15
% 7.17/7.76 % lits 164
% 7.17/7.76 % lits eq 16
% 7.17/7.76 % fd_pure 0
% 7.17/7.76 % fd_pseudo 0
% 7.17/7.76 % fd_cond 1
% 7.17/7.76 % fd_pseudo_cond 9
% 7.17/7.76 % AC symbols 0
% 7.17/7.76
% 7.17/7.76 % ------ Schedule dynamic 5 is on
% 7.17/7.76
% 7.17/7.76 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 7.17/7.76
% 7.17/7.76
% 7.17/7.76 % ------
% 7.17/7.76 % Current options:
% 7.17/7.76 % ------
% 7.17/7.76
% 7.17/7.76
% 7.17/7.76 %
% 7.17/7.76
% 7.17/7.76 % ------ Proving...
% 7.17/7.76 %
% 7.17/7.76
% 7.17/7.76 % SZS status Theorem for theBenchmark.p
% 7.17/7.76
% 7.17/7.76 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 13.33/7.80
% 13.33/7.80
%------------------------------------------------------------------------------