%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET998+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 : n005.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 02:49:17 PM UTC 2026
% Result : Theorem 10.72s 2.79s
% Output : CNFRefutation 14.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 32
% Syntax : Number of formulae : 2365 ( 108 unt; 0 def)
% Number of atoms : 10635 (2945 equ)
% Maximal formula atoms : 17 ( 4 avg)
% Number of connectives : 14608 (6338 ~;8083 |; 132 &)
% ( 19 <=>; 36 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 24 ( 24 usr; 9 con; 0-4 aty)
% Number of variables : 3605 ( 0 sgn3566 !; 39 ?;3278 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( in(X0,X1)
=> ~ in(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f2,axiom,
! [X0] :
( empty(X0)
=> function(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_funct_1) ).
fof(f3,axiom,
! [X0] :
( empty(X0)
=> relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relat_1) ).
fof(f5,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ! [X1,X2] :
( ( ~ in(X1,relation_dom(X0))
=> ( X2 = apply(X0,X1)
<=> X2 = empty_set ) )
& ( in(X1,relation_dom(X0))
=> ( X2 = apply(X0,X1)
<=> in(ordered_pair(X1,X2),X0) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_funct_1) ).
fof(f6,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( X1 = relation_dom(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_relat_1) ).
fof(f8,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ( X2 = relation_composition(X0,X1)
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ? [X5] :
( in(ordered_pair(X5,X4),X1)
& in(ordered_pair(X3,X5),X0) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_relat_1) ).
fof(f9,axiom,
! [X0,X1] :
( ( relation(X1)
& relation(X0) )
=> relation(relation_composition(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_relat_1) ).
fof(f10,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f11,axiom,
! [X0,X1] :
( ( relation(X1)
& empty(X0) )
=> ( relation(relation_composition(X1,X0))
& empty(relation_composition(X1,X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc10_relat_1) ).
fof(f13,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1)
& function(X0)
& relation(X0) )
=> ( function(relation_composition(X0,X1))
& relation(relation_composition(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_funct_1) ).
fof(f14,axiom,
! [X0] : ~ empty(powerset(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(f15,axiom,
empty(empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(f16,axiom,
! [X0,X1] : ~ empty(ordered_pair(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
fof(f19,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_relat_1) ).
fof(f20,axiom,
! [X0] :
( ( relation(X0)
& ~ empty(X0) )
=> ~ empty(relation_dom(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_relat_1) ).
fof(f21,axiom,
! [X0] :
( empty(X0)
=> ( relation(relation_dom(X0))
& empty(relation_dom(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc7_relat_1) ).
fof(f22,axiom,
! [X0,X1] :
( ( relation(X1)
& empty(X0) )
=> ( relation(relation_composition(X0,X1))
& empty(relation_composition(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc9_relat_1) ).
fof(f23,axiom,
? [X0] :
( function(X0)
& relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_funct_1) ).
fof(f24,axiom,
? [X0] :
( relation(X0)
& empty(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_relat_1) ).
fof(f25,axiom,
! [X0] :
( ~ empty(X0)
=> ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_subset_1) ).
fof(f26,axiom,
? [X0] : empty(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(f27,axiom,
? [X0] :
( relation(X0)
& ~ empty(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_relat_1) ).
fof(f28,axiom,
! [X0] :
? [X1] :
( empty(X1)
& element(X1,powerset(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).
fof(f29,axiom,
? [X0] : ~ empty(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f32,axiom,
! [X0,X1] :
( in(X0,X1)
=> element(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
fof(f33,conjecture,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ! [X1] :
( ( function(X1)
& relation(X1) )
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( ( ! [X3] :
( in(X3,relation_dom(X2))
=> apply(X2,X3) = apply(X1,apply(X0,X3)) )
& ! [X3] :
( in(X3,relation_dom(X2))
<=> ( in(apply(X0,X3),relation_dom(X1))
& in(X3,relation_dom(X0)) ) ) )
=> X2 = relation_composition(X0,X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_funct_1) ).
fof(f34,negated_conjecture,
~ ! [X0] :
( ( function(X0)
& relation(X0) )
=> ! [X1] :
( ( function(X1)
& relation(X1) )
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( ( ! [X3] :
( in(X3,relation_dom(X2))
=> apply(X2,X3) = apply(X1,apply(X0,X3)) )
& ! [X3] :
( in(X3,relation_dom(X2))
<=> ( in(apply(X0,X3),relation_dom(X1))
& in(X3,relation_dom(X0)) ) ) )
=> X2 = relation_composition(X0,X1) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f33]) ).
fof(f35,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(f37,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X2))
& in(X0,X1) )
=> element(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
fof(f38,axiom,
! [X0,X1,X2] :
~ ( empty(X2)
& element(X1,powerset(X2))
& in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
fof(f39,axiom,
! [X0] :
( empty(X0)
=> X0 = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(f40,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(f41,axiom,
! [X0,X1] :
~ ( empty(X1)
& X0 != X1
& empty(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
fof(f42,plain,
~ ! [X0] :
( ( function(X0)
& relation(X0) )
=> ! [X1] :
( ( function(X1)
& relation(X1) )
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( ( ! [X4] :
( in(X4,relation_dom(X2))
=> apply(X2,X4) = apply(X1,apply(X0,X4)) )
& ! [X3] :
( in(X3,relation_dom(X2))
<=> ( in(apply(X0,X3),relation_dom(X1))
& in(X3,relation_dom(X0)) ) ) )
=> X2 = relation_composition(X0,X1) ) ) ) ),
inference(rectify,[],[f34]) ).
fof(f43,plain,
? [X0] :
( function(X0)
& relation(X0)
& ? [X1] :
( function(X1)
& relation(X1)
& ? [X2] :
( function(X2)
& relation(X2)
& ! [X4] :
( ~ in(X4,relation_dom(X2))
| apply(X2,X4) = apply(X1,apply(X0,X4)) )
& ! [X3] :
( in(X3,relation_dom(X2))
<=> ( in(apply(X0,X3),relation_dom(X1))
& in(X3,relation_dom(X0)) ) )
& relation_composition(X0,X1) != X2 ) ) ),
inference(ennf_transformation,[],[f42]) ).
fof(f44,plain,
? [X0] :
( function(X0)
& relation(X0)
& ? [X1] :
( function(X1)
& relation(X1)
& ? [X2] :
( function(X2)
& relation(X2)
& ! [X4] :
( ~ in(X4,relation_dom(X2))
| apply(X2,X4) = apply(X1,apply(X0,X4)) )
& ! [X3] :
( in(X3,relation_dom(X2))
<=> ( in(apply(X0,X3),relation_dom(X1))
& in(X3,relation_dom(X0)) ) )
& relation_composition(X0,X1) != X2 ) ) ),
inference(flattening,[],[f43]) ).
fof(f45,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(ennf_transformation,[],[f41]) ).
fof(f46,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f40]) ).
fof(f47,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(ennf_transformation,[],[f35]) ).
fof(f48,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(flattening,[],[f47]) ).
fof(f49,plain,
! [X0,X1] :
( ~ in(X0,X1)
| element(X0,X1) ),
inference(ennf_transformation,[],[f32]) ).
fof(f50,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ in(X1,X0) ),
inference(ennf_transformation,[],[f1]) ).
fof(f51,plain,
! [X0] :
( ~ empty(X0)
| ( relation(relation_dom(X0))
& empty(relation_dom(X0)) ) ),
inference(ennf_transformation,[],[f21]) ).
fof(f52,plain,
! [X0] :
( ~ relation(X0)
| empty(X0)
| ~ empty(relation_dom(X0)) ),
inference(ennf_transformation,[],[f20]) ).
fof(f53,plain,
! [X0] :
( ~ relation(X0)
| empty(X0)
| ~ empty(relation_dom(X0)) ),
inference(flattening,[],[f52]) ).
fof(f54,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( X1 = relation_dom(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) ) ),
inference(ennf_transformation,[],[f6]) ).
fof(f55,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( ( in(X1,relation_dom(X0))
| ( X2 = apply(X0,X1)
<=> X2 = empty_set ) )
& ( ~ in(X1,relation_dom(X0))
| ( X2 = apply(X0,X1)
<=> in(ordered_pair(X1,X2),X0) ) ) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f56,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( ( in(X1,relation_dom(X0))
| ( X2 = apply(X0,X1)
<=> X2 = empty_set ) )
& ( ~ in(X1,relation_dom(X0))
| ( X2 = apply(X0,X1)
<=> in(ordered_pair(X1,X2),X0) ) ) ) ),
inference(flattening,[],[f55]) ).
fof(f57,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0)
| ( function(relation_composition(X0,X1))
& relation(relation_composition(X0,X1)) ) ),
inference(ennf_transformation,[],[f13]) ).
fof(f58,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0)
| ( function(relation_composition(X0,X1))
& relation(relation_composition(X0,X1)) ) ),
inference(flattening,[],[f57]) ).
fof(f59,plain,
! [X0] :
( ~ empty(X0)
| function(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f60,plain,
! [X0] :
( ~ empty(X0)
| relation(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f61,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ empty(X0)
| ( relation(relation_composition(X0,X1))
& empty(relation_composition(X0,X1)) ) ),
inference(ennf_transformation,[],[f22]) ).
fof(f62,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ empty(X0)
| ( relation(relation_composition(X0,X1))
& empty(relation_composition(X0,X1)) ) ),
inference(flattening,[],[f61]) ).
fof(f63,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ empty(X0)
| ( relation(relation_composition(X1,X0))
& empty(relation_composition(X1,X0)) ) ),
inference(ennf_transformation,[],[f11]) ).
fof(f64,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ empty(X0)
| ( relation(relation_composition(X1,X0))
& empty(relation_composition(X1,X0)) ) ),
inference(flattening,[],[f63]) ).
fof(f65,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ relation(X0)
| relation(relation_composition(X0,X1)) ),
inference(ennf_transformation,[],[f9]) ).
fof(f66,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ relation(X0)
| relation(relation_composition(X0,X1)) ),
inference(flattening,[],[f65]) ).
fof(f67,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ~ relation(X1)
| ! [X2] :
( ~ relation(X2)
| ( X2 = relation_composition(X0,X1)
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ? [X5] :
( in(ordered_pair(X5,X4),X1)
& in(ordered_pair(X3,X5),X0) ) ) ) ) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f68,plain,
! [X0,X1,X2] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f38]) ).
fof(f69,plain,
! [X0,X1,X2] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(ennf_transformation,[],[f37]) ).
fof(f70,plain,
! [X0,X1,X2] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(flattening,[],[f69]) ).
fof(f71,plain,
! [X0] :
( empty(X0)
| ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) ) ),
inference(ennf_transformation,[],[f25]) ).
fof(f72,plain,
! [X0] :
( ~ empty(X0)
| X0 = empty_set ),
inference(ennf_transformation,[],[f39]) ).
fof(f73,plain,
? [X0] :
( function(X0)
& relation(X0)
& ? [X1] :
( function(X1)
& relation(X1)
& ? [X2] :
( function(X2)
& relation(X2)
& ! [X4] :
( ~ in(X4,relation_dom(X2))
| apply(X2,X4) = apply(X1,apply(X0,X4)) )
& ! [X3] :
( ( ~ in(X3,relation_dom(X2))
| ( in(apply(X0,X3),relation_dom(X1))
& in(X3,relation_dom(X0)) ) )
& ( ~ in(apply(X0,X3),relation_dom(X1))
| ~ in(X3,relation_dom(X0))
| in(X3,relation_dom(X2)) ) )
& relation_composition(X0,X1) != X2 ) ) ),
inference(nnf_transformation,[],[f44]) ).
fof(f74,plain,
? [X0] :
( function(X0)
& relation(X0)
& ? [X1] :
( function(X1)
& relation(X1)
& ? [X2] :
( function(X2)
& relation(X2)
& ! [X4] :
( ~ in(X4,relation_dom(X2))
| apply(X2,X4) = apply(X1,apply(X0,X4)) )
& ! [X3] :
( ( ~ in(X3,relation_dom(X2))
| ( in(apply(X0,X3),relation_dom(X1))
& in(X3,relation_dom(X0)) ) )
& ( ~ in(apply(X0,X3),relation_dom(X1))
| ~ in(X3,relation_dom(X0))
| in(X3,relation_dom(X2)) ) )
& relation_composition(X0,X1) != X2 ) ) ),
inference(flattening,[],[f73]) ).
fof(f75,plain,
( function(sK0)
& relation(sK0)
& function(sK1)
& relation(sK1)
& function(sK2)
& relation(sK2)
& ! [X4] :
( ~ in(X4,relation_dom(sK2))
| apply(sK2,X4) = apply(sK1,apply(sK0,X4)) )
& ! [X3] :
( ( ~ in(X3,relation_dom(sK2))
| ( in(apply(sK0,X3),relation_dom(sK1))
& in(X3,relation_dom(sK0)) ) )
& ( ~ in(apply(sK0,X3),relation_dom(sK1))
| ~ in(X3,relation_dom(sK0))
| in(X3,relation_dom(sK2)) ) )
& sK2 != relation_composition(sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f74]) ).
fof(f76,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( relation_dom(X0) != X1
| ! [X2] :
( ( ~ in(X2,X1)
| ? [X3] : in(ordered_pair(X2,X3),X0) )
& ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
| in(X2,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| ? [X3] : in(ordered_pair(X2,X3),X0) )
& ( ~ in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X2,X3),X0) ) )
| X1 = relation_dom(X0) ) ) ),
inference(nnf_transformation,[],[f54]) ).
fof(f77,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( relation_dom(X0) != X1
| ! [X5] :
( ( ~ in(X5,X1)
| ? [X7] : in(ordered_pair(X5,X7),X0) )
& ( ! [X6] : ~ in(ordered_pair(X5,X6),X0)
| in(X5,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| ? [X4] : in(ordered_pair(X2,X4),X0) )
& ( ~ in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X2,X3),X0) ) )
| X1 = relation_dom(X0) ) ) ),
inference(rectify,[],[f76]) ).
fof(f78,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( relation_dom(X0) != X1
| ! [X5] :
( ( ~ in(X5,X1)
| in(ordered_pair(X5,sK5(X0,X5)),X0) )
& ( ! [X6] : ~ in(ordered_pair(X5,X6),X0)
| in(X5,X1) ) ) )
& ( ( ( in(sK3(X0,X1),X1)
| in(ordered_pair(sK3(X0,X1),sK4(X0,X1)),X0) )
& ( ~ in(sK3(X0,X1),X1)
| ! [X3] : ~ in(ordered_pair(sK3(X0,X1),X3),X0) ) )
| X1 = relation_dom(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5]),skolemize(X2,sK3(X0,X1)),skolemize(X4,sK4(X0,X1)),skolemize(X7,sK5(X0,X5))],[f77]) ).
fof(f79,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( ( in(X1,relation_dom(X0))
| ( ( apply(X0,X1) != X2
| X2 = empty_set )
& ( empty_set != X2
| X2 = apply(X0,X1) ) ) )
& ( ~ in(X1,relation_dom(X0))
| ( ( apply(X0,X1) != X2
| in(ordered_pair(X1,X2),X0) )
& ( ~ in(ordered_pair(X1,X2),X0)
| X2 = apply(X0,X1) ) ) ) ) ),
inference(nnf_transformation,[],[f56]) ).
fof(f80,plain,
( function(sK6)
& relation(sK6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X0,sK6)],[f23]) ).
fof(f81,plain,
( relation(sK7)
& ~ empty(sK7) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X0,sK7)],[f27]) ).
fof(f82,plain,
( relation(sK8)
& empty(sK8) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(X0,sK8)],[f24]) ).
fof(f83,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ~ relation(X1)
| ! [X2] :
( ~ relation(X2)
| ( ( relation_composition(X0,X1) != X2
| ! [X3,X4] :
( ( ~ in(ordered_pair(X3,X4),X2)
| ? [X5] :
( in(ordered_pair(X5,X4),X1)
& in(ordered_pair(X3,X5),X0) ) )
& ( ! [X5] :
( ~ in(ordered_pair(X5,X4),X1)
| ~ in(ordered_pair(X3,X5),X0) )
| in(ordered_pair(X3,X4),X2) ) ) )
& ( ? [X3,X4] :
( ( in(ordered_pair(X3,X4),X2)
| ? [X5] :
( in(ordered_pair(X5,X4),X1)
& in(ordered_pair(X3,X5),X0) ) )
& ( ~ in(ordered_pair(X3,X4),X2)
| ! [X5] :
( ~ in(ordered_pair(X5,X4),X1)
| ~ in(ordered_pair(X3,X5),X0) ) ) )
| X2 = relation_composition(X0,X1) ) ) ) ) ),
inference(nnf_transformation,[],[f67]) ).
fof(f84,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ~ relation(X1)
| ! [X2] :
( ~ relation(X2)
| ( ( relation_composition(X0,X1) != X2
| ! [X7,X8] :
( ( ~ in(ordered_pair(X7,X8),X2)
| ? [X10] :
( in(ordered_pair(X10,X8),X1)
& in(ordered_pair(X7,X10),X0) ) )
& ( ! [X9] :
( ~ in(ordered_pair(X9,X8),X1)
| ~ in(ordered_pair(X7,X9),X0) )
| in(ordered_pair(X7,X8),X2) ) ) )
& ( ? [X3,X4] :
( ( in(ordered_pair(X3,X4),X2)
| ? [X6] :
( in(ordered_pair(X6,X4),X1)
& in(ordered_pair(X3,X6),X0) ) )
& ( ~ in(ordered_pair(X3,X4),X2)
| ! [X5] :
( ~ in(ordered_pair(X5,X4),X1)
| ~ in(ordered_pair(X3,X5),X0) ) ) )
| X2 = relation_composition(X0,X1) ) ) ) ) ),
inference(rectify,[],[f83]) ).
fof(f85,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ~ relation(X1)
| ! [X2] :
( ~ relation(X2)
| ( ( relation_composition(X0,X1) != X2
| ! [X7,X8] :
( ( ~ in(ordered_pair(X7,X8),X2)
| ( in(ordered_pair(sK12(X0,X1,X7,X8),X8),X1)
& in(ordered_pair(X7,sK12(X0,X1,X7,X8)),X0) ) )
& ( ! [X9] :
( ~ in(ordered_pair(X9,X8),X1)
| ~ in(ordered_pair(X7,X9),X0) )
| in(ordered_pair(X7,X8),X2) ) ) )
& ( ( ( in(ordered_pair(sK9(X0,X1,X2),sK10(X0,X1,X2)),X2)
| ( in(ordered_pair(sK11(X0,X1,X2),sK10(X0,X1,X2)),X1)
& in(ordered_pair(sK9(X0,X1,X2),sK11(X0,X1,X2)),X0) ) )
& ( ~ in(ordered_pair(sK9(X0,X1,X2),sK10(X0,X1,X2)),X2)
| ! [X5] :
( ~ in(ordered_pair(X5,sK10(X0,X1,X2)),X1)
| ~ in(ordered_pair(sK9(X0,X1,X2),X5),X0) ) ) )
| X2 = relation_composition(X0,X1) ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK10,sK11,sK12]),skolemize(X3,sK9(X0,X1,X2)),skolemize(X4,sK10(X0,X1,X2)),skolemize(X6,sK11(X0,X1,X2)),skolemize(X10,sK12(X0,X1,X7,X8))],[f84]) ).
fof(f86,plain,
~ empty(sK13),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(X0,sK13)],[f29]) ).
fof(f87,plain,
empty(sK14),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(X0,sK14)],[f26]) ).
fof(f88,plain,
! [X0] :
( empty(sK15(X0))
& element(sK15(X0),powerset(X0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(X1,sK15(X0))],[f28]) ).
fof(f89,plain,
! [X0] :
( empty(X0)
| ( ~ empty(sK16(X0))
& element(sK16(X0),powerset(X0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(X1,sK16(X0))],[f71]) ).
fof(f90,plain,
! [X0] : element(sK17(X0),X0),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(X1,sK17(X0))],[f10]) ).
fof(f91,plain,
function(sK0),
inference(cnf_transformation,[],[f75]) ).
fof(f92,plain,
relation(sK0),
inference(cnf_transformation,[],[f75]) ).
fof(f93,plain,
function(sK1),
inference(cnf_transformation,[],[f75]) ).
fof(f94,plain,
relation(sK1),
inference(cnf_transformation,[],[f75]) ).
fof(f95,plain,
function(sK2),
inference(cnf_transformation,[],[f75]) ).
fof(f96,plain,
relation(sK2),
inference(cnf_transformation,[],[f75]) ).
fof(f97,plain,
! [X4] :
( ~ in(X4,relation_dom(sK2))
| apply(sK2,X4) = apply(sK1,apply(sK0,X4)) ),
inference(cnf_transformation,[],[f75]) ).
fof(f98,plain,
! [X3] :
( ~ in(X3,relation_dom(sK2))
| in(apply(sK0,X3),relation_dom(sK1)) ),
inference(cnf_transformation,[],[f75]) ).
fof(f99,plain,
! [X3] :
( ~ in(X3,relation_dom(sK2))
| in(X3,relation_dom(sK0)) ),
inference(cnf_transformation,[],[f75]) ).
fof(f100,plain,
! [X3] :
( ~ in(apply(sK0,X3),relation_dom(sK1))
| ~ in(X3,relation_dom(sK0))
| in(X3,relation_dom(sK2)) ),
inference(cnf_transformation,[],[f75]) ).
fof(f101,plain,
sK2 != relation_composition(sK0,sK1),
inference(cnf_transformation,[],[f75]) ).
fof(f102,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(cnf_transformation,[],[f45]) ).
fof(f103,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f46]) ).
fof(f104,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(cnf_transformation,[],[f48]) ).
fof(f105,plain,
! [X0,X1] :
( ~ in(X0,X1)
| element(X0,X1) ),
inference(cnf_transformation,[],[f49]) ).
fof(f106,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ in(X1,X0) ),
inference(cnf_transformation,[],[f50]) ).
fof(f107,plain,
! [X0] :
( ~ empty(X0)
| relation(relation_dom(X0)) ),
inference(cnf_transformation,[],[f51]) ).
fof(f108,plain,
! [X0] :
( ~ empty(X0)
| empty(relation_dom(X0)) ),
inference(cnf_transformation,[],[f51]) ).
fof(f109,plain,
! [X0] :
( ~ relation(X0)
| empty(X0)
| ~ empty(relation_dom(X0)) ),
inference(cnf_transformation,[],[f53]) ).
fof(f110,plain,
! [X0,X1,X5] :
( ~ relation(X0)
| relation_dom(X0) != X1
| ~ in(X5,X1)
| in(ordered_pair(X5,sK5(X0,X5)),X0) ),
inference(cnf_transformation,[],[f78]) ).
fof(f111,plain,
! [X0,X1,X6,X5] :
( ~ relation(X0)
| relation_dom(X0) != X1
| ~ in(ordered_pair(X5,X6),X0)
| in(X5,X1) ),
inference(cnf_transformation,[],[f78]) ).
fof(f112,plain,
! [X0,X1] :
( ~ relation(X0)
| in(sK3(X0,X1),X1)
| in(ordered_pair(sK3(X0,X1),sK4(X0,X1)),X0)
| relation_dom(X0) = X1 ),
inference(cnf_transformation,[],[f78]) ).
fof(f113,plain,
! [X3,X0,X1] :
( ~ relation(X0)
| ~ in(sK3(X0,X1),X1)
| ~ in(ordered_pair(sK3(X0,X1),X3),X0)
| relation_dom(X0) = X1 ),
inference(cnf_transformation,[],[f78]) ).
fof(f114,plain,
! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| in(X1,relation_dom(X0))
| apply(X0,X1) != X2
| empty_set = X2 ),
inference(cnf_transformation,[],[f79]) ).
fof(f116,plain,
! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X1,relation_dom(X0))
| apply(X0,X1) != X2
| in(ordered_pair(X1,X2),X0) ),
inference(cnf_transformation,[],[f79]) ).
fof(f117,plain,
! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X1,relation_dom(X0))
| ~ in(ordered_pair(X1,X2),X0)
| apply(X0,X1) = X2 ),
inference(cnf_transformation,[],[f79]) ).
fof(f118,plain,
function(sK6),
inference(cnf_transformation,[],[f80]) ).
fof(f119,plain,
relation(sK6),
inference(cnf_transformation,[],[f80]) ).
fof(f120,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0)
| function(relation_composition(X0,X1)) ),
inference(cnf_transformation,[],[f58]) ).
fof(f121,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0)
| relation(relation_composition(X0,X1)) ),
inference(cnf_transformation,[],[f58]) ).
fof(f122,plain,
! [X0] :
( ~ empty(X0)
| function(X0) ),
inference(cnf_transformation,[],[f59]) ).
fof(f123,plain,
relation(sK7),
inference(cnf_transformation,[],[f81]) ).
fof(f124,plain,
~ empty(sK7),
inference(cnf_transformation,[],[f81]) ).
fof(f125,plain,
relation(sK8),
inference(cnf_transformation,[],[f82]) ).
fof(f126,plain,
empty(sK8),
inference(cnf_transformation,[],[f82]) ).
fof(f127,plain,
! [X0] :
( ~ empty(X0)
| relation(X0) ),
inference(cnf_transformation,[],[f60]) ).
fof(f128,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ empty(X0)
| relation(relation_composition(X0,X1)) ),
inference(cnf_transformation,[],[f62]) ).
fof(f129,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ empty(X0)
| empty(relation_composition(X0,X1)) ),
inference(cnf_transformation,[],[f62]) ).
fof(f130,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ empty(X0)
| relation(relation_composition(X1,X0)) ),
inference(cnf_transformation,[],[f64]) ).
fof(f131,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ empty(X0)
| empty(relation_composition(X1,X0)) ),
inference(cnf_transformation,[],[f64]) ).
fof(f132,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ relation(X0)
| relation(relation_composition(X0,X1)) ),
inference(cnf_transformation,[],[f66]) ).
fof(f133,plain,
! [X2,X0,X1,X8,X7] :
( ~ relation(X0)
| ~ relation(X1)
| ~ relation(X2)
| relation_composition(X0,X1) != X2
| ~ in(ordered_pair(X7,X8),X2)
| in(ordered_pair(sK12(X0,X1,X7,X8),X8),X1) ),
inference(cnf_transformation,[],[f85]) ).
fof(f134,plain,
! [X2,X0,X1,X8,X7] :
( ~ relation(X0)
| ~ relation(X1)
| ~ relation(X2)
| relation_composition(X0,X1) != X2
| ~ in(ordered_pair(X7,X8),X2)
| in(ordered_pair(X7,sK12(X0,X1,X7,X8)),X0) ),
inference(cnf_transformation,[],[f85]) ).
fof(f135,plain,
! [X2,X0,X1,X8,X9,X7] :
( ~ relation(X0)
| ~ relation(X1)
| ~ relation(X2)
| relation_composition(X0,X1) != X2
| ~ in(ordered_pair(X9,X8),X1)
| ~ in(ordered_pair(X7,X9),X0)
| in(ordered_pair(X7,X8),X2) ),
inference(cnf_transformation,[],[f85]) ).
fof(f136,plain,
! [X2,X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| ~ relation(X2)
| in(ordered_pair(sK9(X0,X1,X2),sK10(X0,X1,X2)),X2)
| in(ordered_pair(sK11(X0,X1,X2),sK10(X0,X1,X2)),X1)
| relation_composition(X0,X1) = X2 ),
inference(cnf_transformation,[],[f85]) ).
fof(f137,plain,
! [X2,X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| ~ relation(X2)
| in(ordered_pair(sK9(X0,X1,X2),sK10(X0,X1,X2)),X2)
| in(ordered_pair(sK9(X0,X1,X2),sK11(X0,X1,X2)),X0)
| relation_composition(X0,X1) = X2 ),
inference(cnf_transformation,[],[f85]) ).
fof(f138,plain,
! [X2,X0,X1,X5] :
( ~ relation(X0)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(sK9(X0,X1,X2),sK10(X0,X1,X2)),X2)
| ~ in(ordered_pair(X5,sK10(X0,X1,X2)),X1)
| ~ in(ordered_pair(sK9(X0,X1,X2),X5),X0)
| relation_composition(X0,X1) = X2 ),
inference(cnf_transformation,[],[f85]) ).
fof(f139,plain,
~ empty(sK13),
inference(cnf_transformation,[],[f86]) ).
fof(f140,plain,
empty(sK14),
inference(cnf_transformation,[],[f87]) ).
fof(f141,plain,
! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f68]) ).
fof(f142,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(cnf_transformation,[],[f70]) ).
fof(f143,plain,
! [X0] : empty(sK15(X0)),
inference(cnf_transformation,[],[f88]) ).
fof(f144,plain,
! [X0] : element(sK15(X0),powerset(X0)),
inference(cnf_transformation,[],[f88]) ).
fof(f145,plain,
! [X0] :
( empty(X0)
| ~ empty(sK16(X0)) ),
inference(cnf_transformation,[],[f89]) ).
fof(f146,plain,
! [X0] :
( empty(X0)
| element(sK16(X0),powerset(X0)) ),
inference(cnf_transformation,[],[f89]) ).
fof(f147,plain,
! [X0] : element(sK17(X0),X0),
inference(cnf_transformation,[],[f90]) ).
fof(f148,plain,
! [X0,X1] : ~ empty(ordered_pair(X0,X1)),
inference(cnf_transformation,[],[f16]) ).
fof(f149,plain,
! [X0] :
( ~ empty(X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f72]) ).
fof(f150,plain,
relation(empty_set),
inference(cnf_transformation,[],[f19]) ).
fof(f152,plain,
empty(empty_set),
inference(cnf_transformation,[],[f15]) ).
fof(f153,plain,
! [X0] : ~ empty(powerset(X0)),
inference(cnf_transformation,[],[f14]) ).
fof(f154,plain,
! [X0,X6,X5] :
( ~ relation(X0)
| ~ in(ordered_pair(X5,X6),X0)
| in(X5,relation_dom(X0)) ),
inference(equality_resolution,[],[f111]) ).
fof(f155,plain,
! [X0,X5] :
( ~ relation(X0)
| ~ in(X5,relation_dom(X0))
| in(ordered_pair(X5,sK5(X0,X5)),X0) ),
inference(equality_resolution,[],[f110]) ).
fof(f156,plain,
! [X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X1,relation_dom(X0))
| in(ordered_pair(X1,apply(X0,X1)),X0) ),
inference(equality_resolution,[],[f116]) ).
fof(f158,plain,
! [X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| in(X1,relation_dom(X0))
| apply(X0,X1) = empty_set ),
inference(equality_resolution,[],[f114]) ).
fof(f159,plain,
! [X0,X1,X8,X9,X7] :
( ~ relation(X0)
| ~ relation(X1)
| ~ relation(relation_composition(X0,X1))
| ~ in(ordered_pair(X9,X8),X1)
| ~ in(ordered_pair(X7,X9),X0)
| in(ordered_pair(X7,X8),relation_composition(X0,X1)) ),
inference(equality_resolution,[],[f135]) ).
fof(f160,plain,
! [X0,X1,X8,X7] :
( ~ relation(X0)
| ~ relation(X1)
| ~ relation(relation_composition(X0,X1))
| ~ in(ordered_pair(X7,X8),relation_composition(X0,X1))
| in(ordered_pair(X7,sK12(X0,X1,X7,X8)),X0) ),
inference(equality_resolution,[],[f134]) ).
fof(f161,plain,
! [X0,X1,X8,X7] :
( ~ relation(X0)
| ~ relation(X1)
| ~ relation(relation_composition(X0,X1))
| ~ in(ordered_pair(X7,X8),relation_composition(X0,X1))
| in(ordered_pair(sK12(X0,X1,X7,X8),X8),X1) ),
inference(equality_resolution,[],[f133]) ).
tcf(c_49,negated_conjecture,
relation_composition(sK0,sK1) != sK2,
inference(cnf_transformation,[],[f101]) ).
tcf(c_50,negated_conjecture,
! [X0: $i] :
( in(X0,relation_dom(sK2))
| ~ in(X0,relation_dom(sK0))
| ~ in(apply(sK0,X0),relation_dom(sK1)) ),
inference(cnf_transformation,[],[f100]) ).
tcf(c_51,negated_conjecture,
! [X0: $i] :
( in(X0,relation_dom(sK0))
| ~ in(X0,relation_dom(sK2)) ),
inference(cnf_transformation,[],[f99]) ).
tcf(c_52,negated_conjecture,
! [X0: $i] :
( in(apply(sK0,X0),relation_dom(sK1))
| ~ in(X0,relation_dom(sK2)) ),
inference(cnf_transformation,[],[f98]) ).
tcf(c_53,negated_conjecture,
! [X0: $i] :
( ( apply(sK1,apply(sK0,X0)) = apply(sK2,X0) )
| ~ in(X0,relation_dom(sK2)) ),
inference(cnf_transformation,[],[f97]) ).
tcf(c_54,negated_conjecture,
relation(sK2),
inference(cnf_transformation,[],[f96]) ).
tcf(c_55,negated_conjecture,
function(sK2),
inference(cnf_transformation,[],[f95]) ).
tcf(c_56,negated_conjecture,
relation(sK1),
inference(cnf_transformation,[],[f94]) ).
tcf(c_57,negated_conjecture,
function(sK1),
inference(cnf_transformation,[],[f93]) ).
tcf(c_58,negated_conjecture,
relation(sK0),
inference(cnf_transformation,[],[f92]) ).
tcf(c_59,negated_conjecture,
function(sK0),
inference(cnf_transformation,[],[f91]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f102]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f103]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f104]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f105]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f106]) ).
tcf(c_65,plain,
! [X0: $i] :
( empty(relation_dom(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f108]) ).
tcf(c_66,plain,
! [X0: $i] :
( relation(relation_dom(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f107]) ).
tcf(c_67,plain,
! [X0: $i] :
( empty(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(cnf_transformation,[],[f109]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(X0) = X1 )
| ~ relation(X0)
| ~ in(sK3(X0,X1),X1)
| ~ in(ordered_pair(sK3(X0,X1),X2),X0) ),
inference(cnf_transformation,[],[f113]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i] :
( in(sK3(X0,X1),X1)
| in(ordered_pair(sK3(X0,X1),sK4(X0,X1)),X0)
| ( relation_dom(X0) = X1 )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f112]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,relation_dom(X2))
| ~ relation(X2)
| ~ in(ordered_pair(X0,X1),X2) ),
inference(cnf_transformation,[],[f154]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(X0,sK5(X1,X0)),X1)
| ~ relation(X1)
| ~ in(X0,relation_dom(X1)) ),
inference(cnf_transformation,[],[f155]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(X2,X0) = X1 )
| ~ function(X2)
| ~ relation(X2)
| ~ in(X0,relation_dom(X2))
| ~ in(ordered_pair(X0,X1),X2) ),
inference(cnf_transformation,[],[f117]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(X0,apply(X1,X0)),X1)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_dom(X1)) ),
inference(cnf_transformation,[],[f156]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i] :
( in(X1,relation_dom(X0))
| ( apply(X0,X1) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f158]) ).
tcf(c_76,plain,
relation(sK6),
inference(cnf_transformation,[],[f119]) ).
tcf(c_77,plain,
function(sK6),
inference(cnf_transformation,[],[f118]) ).
tcf(c_78,plain,
! [X0: $i,X1: $i] :
( relation(relation_composition(X0,X1))
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f121]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i] :
( function(relation_composition(X0,X1))
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f120]) ).
tcf(c_80,plain,
! [X0: $i] :
( function(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f122]) ).
tcf(c_81,plain,
~ empty(sK7),
inference(cnf_transformation,[],[f124]) ).
tcf(c_82,plain,
relation(sK7),
inference(cnf_transformation,[],[f123]) ).
tcf(c_83,plain,
empty(sK8),
inference(cnf_transformation,[],[f126]) ).
tcf(c_84,plain,
relation(sK8),
inference(cnf_transformation,[],[f125]) ).
tcf(c_85,plain,
! [X0: $i] :
( relation(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f127]) ).
tcf(c_86,plain,
! [X0: $i,X1: $i] :
( empty(relation_composition(X1,X0))
| ~ empty(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f129]) ).
tcf(c_87,plain,
! [X0: $i,X1: $i] :
( relation(relation_composition(X1,X0))
| ~ empty(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f128]) ).
tcf(c_88,plain,
! [X0: $i,X1: $i] :
( empty(relation_composition(X0,X1))
| ~ empty(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f131]) ).
tcf(c_89,plain,
! [X0: $i,X1: $i] :
( relation(relation_composition(X0,X1))
| ~ empty(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f130]) ).
tcf(c_90,plain,
! [X0: $i,X1: $i] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f132]) ).
tcf(c_91,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_composition(X0,X1) = X2 )
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(ordered_pair(X3,sK10(X0,X1,X2)),X1)
| ~ in(ordered_pair(sK9(X0,X1,X2),X3),X0)
| ~ in(ordered_pair(sK9(X0,X1,X2),sK10(X0,X1,X2)),X2) ),
inference(cnf_transformation,[],[f138]) ).
tcf(c_92,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(ordered_pair(sK9(X0,X1,X2),sK11(X0,X1,X2)),X0)
| in(ordered_pair(sK9(X0,X1,X2),sK10(X0,X1,X2)),X2)
| ( relation_composition(X0,X1) = X2 )
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f137]) ).
tcf(c_93,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(ordered_pair(sK11(X0,X1,X2),sK10(X0,X1,X2)),X1)
| in(ordered_pair(sK9(X0,X1,X2),sK10(X0,X1,X2)),X2)
| ( relation_composition(X0,X1) = X2 )
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f136]) ).
tcf(c_94,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(ordered_pair(X0,X3),relation_composition(X2,X4))
| ~ relation(X4)
| ~ relation(X2)
| ~ relation(relation_composition(X2,X4))
| ~ in(ordered_pair(X1,X3),X4)
| ~ in(ordered_pair(X0,X1),X2) ),
inference(cnf_transformation,[],[f159]) ).
tcf(c_95,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(ordered_pair(X0,sK12(X2,X3,X0,X1)),X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(relation_composition(X2,X3))
| ~ in(ordered_pair(X0,X1),relation_composition(X2,X3)) ),
inference(cnf_transformation,[],[f160]) ).
tcf(c_96,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(ordered_pair(sK12(X2,X3,X0,X1),X1),X3)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(relation_composition(X2,X3))
| ~ in(ordered_pair(X0,X1),relation_composition(X2,X3)) ),
inference(cnf_transformation,[],[f161]) ).
tcf(c_97,plain,
~ empty(sK13),
inference(cnf_transformation,[],[f139]) ).
tcf(c_98,plain,
empty(sK14),
inference(cnf_transformation,[],[f140]) ).
tcf(c_99,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(X1)
| ~ in(X2,X0)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f141]) ).
tcf(c_100,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X2,X1)
| ~ in(X2,X0)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f142]) ).
tcf(c_101,plain,
! [X0: $i] : element(sK15(X0),powerset(X0)),
inference(cnf_transformation,[],[f144]) ).
tcf(c_102,plain,
! [X0: $i] : empty(sK15(X0)),
inference(cnf_transformation,[],[f143]) ).
tcf(c_103,plain,
! [X0: $i] :
( empty(X0)
| element(sK16(X0),powerset(X0)) ),
inference(cnf_transformation,[],[f146]) ).
tcf(c_104,plain,
! [X0: $i] :
( empty(X0)
| ~ empty(sK16(X0)) ),
inference(cnf_transformation,[],[f145]) ).
tcf(c_105,plain,
! [X0: $i] : element(sK17(X0),X0),
inference(cnf_transformation,[],[f147]) ).
tcf(c_106,plain,
! [X0: $i,X1: $i] : ~ empty(ordered_pair(X0,X1)),
inference(cnf_transformation,[],[f148]) ).
tcf(c_107,plain,
! [X0: $i] :
( ( X0 = empty_set )
| ~ empty(X0) ),
inference(cnf_transformation,[],[f149]) ).
tcf(c_109,plain,
relation(empty_set),
inference(cnf_transformation,[],[f150]) ).
tcf(c_110,plain,
empty(empty_set),
inference(cnf_transformation,[],[f152]) ).
tcf(c_111,plain,
! [X0: $i] : ~ empty(powerset(X0)),
inference(cnf_transformation,[],[f153]) ).
tcf(c_126,plain,
( empty(sK0)
| ~ relation(sK0)
| ~ empty(relation_dom(sK0)) ),
inference(instantiation,[status(thm)],[c_67]) ).
tcf(c_150,plain,
! [X0: $i,X1: $i] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(global_subsumption_just,[status(thm)],[c_78,c_90]) ).
tcf(c_152,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(X2,X0) = X1 )
| ~ function(X2)
| ~ relation(X2)
| ~ in(ordered_pair(X0,X1),X2) ),
inference(global_subsumption_just,[status(thm)],[c_72,c_70,c_72]) ).
tcf(c_299,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(ordered_pair(X0,X3),relation_composition(X2,X4))
| ~ relation(X4)
| ~ relation(X2)
| ~ in(ordered_pair(X1,X3),X4)
| ~ in(ordered_pair(X0,X1),X2) ),
inference(backward_subsumption_resolution,[status(thm)],[c_94,c_150]) ).
tcf(c_300,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(ordered_pair(sK12(X2,X3,X0,X1),X1),X3)
| ~ relation(X3)
| ~ relation(X2)
| ~ in(ordered_pair(X0,X1),relation_composition(X2,X3)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_96,c_150]) ).
tcf(c_301,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(ordered_pair(X0,sK12(X2,X3,X0,X1)),X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ in(ordered_pair(X0,X1),relation_composition(X2,X3)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_95,c_150]) ).
tcf(c_2008,plain,
function(sK8),
inference(superposition,[status(thm)],[c_83,c_80]) ).
tcf(c_2009,plain,
function(sK14),
inference(superposition,[status(thm)],[c_98,c_80]) ).
tcf(c_2010,plain,
! [X0: $i] : function(sK15(X0)),
inference(superposition,[status(thm)],[c_102,c_80]) ).
tcf(c_2011,plain,
function(empty_set),
inference(superposition,[status(thm)],[c_110,c_80]) ).
tcf(c_2018,plain,
relation(sK14),
inference(superposition,[status(thm)],[c_98,c_85]) ).
tcf(c_2019,plain,
! [X0: $i] : relation(sK15(X0)),
inference(superposition,[status(thm)],[c_102,c_85]) ).
tcf(c_2027,plain,
! [X0: $i] :
( function(relation_dom(X0))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_65,c_80]) ).
tcf(c_2047,plain,
! [X0: $i] :
( ~ empty(relation_dom(sK1))
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_52,c_61]) ).
tcf(c_2063,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ relation(X2)
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2))
| ~ in(ordered_pair(X0,X1),relation_composition(X2,relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_300,c_2047]) ).
tcf(c_2064,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(sK1,apply(sK0,ordered_pair(sK12(X2,relation_dom(sK2),X0,X1),X1))) = apply(sK2,ordered_pair(sK12(X2,relation_dom(sK2),X0,X1),X1)) )
| ~ relation(X2)
| ~ relation(relation_dom(sK2))
| ~ in(ordered_pair(X0,X1),relation_composition(X2,relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_300,c_53]) ).
tcf(c_2065,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(ordered_pair(sK12(X2,relation_dom(sK2),X0,X1),X1),relation_dom(sK0))
| ~ relation(X2)
| ~ relation(relation_dom(sK2))
| ~ in(ordered_pair(X0,X1),relation_composition(X2,relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_300,c_51]) ).
tcf(c_2066,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ empty(X3)
| ~ relation(X3)
| ~ relation(X2)
| ~ in(ordered_pair(X0,X1),relation_composition(X2,X3)) ),
inference(superposition,[status(thm)],[c_300,c_61]) ).
tcf(c_2067,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(ordered_pair(sK12(X2,X3,X0,X1),X4),relation_composition(X3,X5))
| ~ relation(X5)
| ~ relation(X3)
| ~ relation(X2)
| ~ in(ordered_pair(X1,X4),X5)
| ~ in(ordered_pair(X0,X1),relation_composition(X2,X3)) ),
inference(superposition,[status(thm)],[c_300,c_299]) ).
tcf(c_2068,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( apply(X3,sK12(X2,X3,X0,X1)) = X1 )
| ~ function(X3)
| ~ relation(X3)
| ~ relation(X2)
| ~ in(ordered_pair(X0,X1),relation_composition(X2,X3)) ),
inference(superposition,[status(thm)],[c_300,c_152]) ).
tcf(c_2106,plain,
! [X0: $i] :
( element(apply(sK0,X0),relation_dom(sK1))
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_52,c_63]) ).
tcf(c_2107,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(ordered_pair(sK12(X2,X3,X0,X1),X1),X3)
| ~ relation(X3)
| ~ relation(X2)
| ~ in(ordered_pair(X0,X1),relation_composition(X2,X3)) ),
inference(superposition,[status(thm)],[c_300,c_63]) ).
tcf(c_2124,plain,
! [X0: $i] :
( ( relation_dom(X0) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_65,c_107]) ).
tcf(c_2125,plain,
empty_set = sK8,
inference(superposition,[status(thm)],[c_83,c_107]) ).
tcf(c_2126,plain,
empty_set = sK14,
inference(superposition,[status(thm)],[c_98,c_107]) ).
tcf(c_2127,plain,
! [X0: $i] : sK15(X0) = empty_set,
inference(superposition,[status(thm)],[c_102,c_107]) ).
tcf(c_2139,plain,
! [X0: $i] : element(empty_set,powerset(X0)),
inference(demodulation,[status(thm)],[c_101,c_2127]) ).
tcf(c_2148,plain,
! [X0: $i] :
( ~ in(X0,relation_dom(sK2))
| ~ in(relation_dom(sK1),apply(sK0,X0)) ),
inference(superposition,[status(thm)],[c_52,c_64]) ).
tcf(c_2149,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ relation(X1)
| ~ relation(X0)
| ~ in(ordered_pair(X2,X3),relation_composition(X1,X0))
| ~ in(X0,ordered_pair(sK12(X1,X0,X2,X3),X3)) ),
inference(superposition,[status(thm)],[c_300,c_64]) ).
tcf(c_2174,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ relation(X0)
| ~ relation(relation_dom(sK2))
| ~ in(ordered_pair(X1,X2),relation_composition(X0,relation_dom(sK2)))
| ~ in(relation_dom(sK0),ordered_pair(sK12(X0,relation_dom(sK2),X1,X2),X2)) ),
inference(superposition,[status(thm)],[c_2065,c_64]) ).
tcf(c_2175,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(ordered_pair(sK12(X2,relation_dom(sK2),X0,X1),X1),relation_dom(sK0))
| ~ relation(X2)
| ~ relation(relation_dom(sK2))
| ~ in(ordered_pair(X0,X1),relation_composition(X2,relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_2065,c_63]) ).
tcf(c_2176,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ relation(X2)
| ~ empty(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(ordered_pair(X0,X1),relation_composition(X2,relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_2065,c_61]) ).
tcf(c_2177,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(ordered_pair(sK12(X2,relation_dom(sK2),X0,X1),X3),relation_composition(relation_dom(sK0),X4))
| ~ relation(X4)
| ~ relation(X2)
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(ordered_pair(X1,X3),X4)
| ~ in(ordered_pair(X0,X1),relation_composition(X2,relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_2065,c_299]) ).
tcf(c_2178,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(relation_dom(sK0),sK12(X2,relation_dom(sK2),X0,X1)) = X1 )
| ~ relation(X2)
| ~ function(relation_dom(sK0))
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(ordered_pair(X0,X1),relation_composition(X2,relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_2065,c_152]) ).
tcf(c_2217,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( apply(sK1,apply(sK0,ordered_pair(sK12(X3,relation_dom(sK2),sK12(X2,relation_composition(X3,relation_dom(sK2)),X0,X1),X1),X1))) = apply(sK2,ordered_pair(sK12(X3,relation_dom(sK2),sK12(X2,relation_composition(X3,relation_dom(sK2)),X0,X1),X1),X1)) )
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(relation_dom(sK2))
| ~ relation(relation_composition(X3,relation_dom(sK2)))
| ~ in(ordered_pair(X0,X1),relation_composition(X2,relation_composition(X3,relation_dom(sK2)))) ),
inference(superposition,[status(thm)],[c_300,c_2064]) ).
tcf(c_2233,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ relation(X3)
| ~ relation(X2)
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2))
| ~ relation(relation_composition(X3,relation_dom(sK2)))
| ~ in(ordered_pair(X0,X1),relation_composition(X2,relation_composition(X3,relation_dom(sK2)))) ),
inference(superposition,[status(thm)],[c_300,c_2063]) ).
tcf(c_2249,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ relation(X3)
| ~ relation(X2)
| ~ empty(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ relation(relation_composition(X3,relation_dom(sK2)))
| ~ in(ordered_pair(X0,X1),relation_composition(X2,relation_composition(X3,relation_dom(sK2)))) ),
inference(superposition,[status(thm)],[c_300,c_2176]) ).
tcf(c_2281,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ relation(X2)
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2))
| ~ in(ordered_pair(X0,X1),relation_composition(relation_dom(sK2),X2)) ),
inference(superposition,[status(thm)],[c_301,c_2047]) ).
tcf(c_2282,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(sK1,apply(sK0,ordered_pair(X0,sK12(relation_dom(sK2),X2,X0,X1)))) = apply(sK2,ordered_pair(X0,sK12(relation_dom(sK2),X2,X0,X1))) )
| ~ relation(X2)
| ~ relation(relation_dom(sK2))
| ~ in(ordered_pair(X0,X1),relation_composition(relation_dom(sK2),X2)) ),
inference(superposition,[status(thm)],[c_301,c_53]) ).
tcf(c_2283,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(ordered_pair(X0,sK12(relation_dom(sK2),X2,X0,X1)),relation_dom(sK0))
| ~ relation(X2)
| ~ relation(relation_dom(sK2))
| ~ in(ordered_pair(X0,X1),relation_composition(relation_dom(sK2),X2)) ),
inference(superposition,[status(thm)],[c_301,c_51]) ).
tcf(c_2284,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ relation(X2)
| ~ relation(X0)
| ~ in(ordered_pair(X1,X3),relation_composition(X0,X2))
| ~ in(X0,ordered_pair(X1,sK12(X0,X2,X1,X3))) ),
inference(superposition,[status(thm)],[c_301,c_64]) ).
tcf(c_2285,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(ordered_pair(X0,sK12(X2,X3,X0,X1)),X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ in(ordered_pair(X0,X1),relation_composition(X2,X3)) ),
inference(superposition,[status(thm)],[c_301,c_63]) ).
tcf(c_2286,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ empty(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ in(ordered_pair(X0,X1),relation_composition(X2,X3)) ),
inference(superposition,[status(thm)],[c_301,c_61]) ).
tcf(c_2287,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(ordered_pair(X2,X4),relation_composition(X0,X5))
| ~ relation(X5)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(ordered_pair(X2,X3),relation_composition(X0,X1))
| ~ in(ordered_pair(sK12(X0,X1,X2,X3),X4),X5) ),
inference(superposition,[status(thm)],[c_301,c_299]) ).
tcf(c_2288,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK12(X2,X3,X0,X1) = apply(X2,X0) )
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ in(ordered_pair(X0,X1),relation_composition(X2,X3)) ),
inference(superposition,[status(thm)],[c_301,c_152]) ).
tcf(c_2289,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ relation(X3)
| ~ relation(X2)
| ~ empty(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ relation(relation_composition(X2,relation_dom(sK2)))
| ~ in(ordered_pair(X0,X1),relation_composition(relation_composition(X2,relation_dom(sK2)),X3)) ),
inference(superposition,[status(thm)],[c_301,c_2176]) ).
tcf(c_2290,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ relation(X3)
| ~ relation(X2)
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2))
| ~ relation(relation_composition(X2,relation_dom(sK2)))
| ~ in(ordered_pair(X0,X1),relation_composition(relation_composition(X2,relation_dom(sK2)),X3)) ),
inference(superposition,[status(thm)],[c_301,c_2063]) ).
tcf(c_2291,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( apply(sK1,apply(sK0,ordered_pair(sK12(X2,relation_dom(sK2),X0,sK12(relation_composition(X2,relation_dom(sK2)),X3,X0,X1)),sK12(relation_composition(X2,relation_dom(sK2)),X3,X0,X1)))) = apply(sK2,ordered_pair(sK12(X2,relation_dom(sK2),X0,sK12(relation_composition(X2,relation_dom(sK2)),X3,X0,X1)),sK12(relation_composition(X2,relation_dom(sK2)),X3,X0,X1))) )
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(relation_dom(sK2))
| ~ relation(relation_composition(X2,relation_dom(sK2)))
| ~ in(ordered_pair(X0,X1),relation_composition(relation_composition(X2,relation_dom(sK2)),X3)) ),
inference(superposition,[status(thm)],[c_301,c_2064]) ).
tcf(c_2360,plain,
! [X0: $i] :
( empty(X0)
| empty(powerset(X0))
| in(sK16(X0),powerset(X0)) ),
inference(superposition,[status(thm)],[c_103,c_62]) ).
tcf(c_2361,plain,
! [X0: $i] :
( empty(X0)
| in(sK17(X0),X0) ),
inference(superposition,[status(thm)],[c_105,c_62]) ).
tcf(c_2363,plain,
! [X0: $i] :
( empty(powerset(X0))
| in(empty_set,powerset(X0)) ),
inference(superposition,[status(thm)],[c_2139,c_62]) ).
tcf(c_2367,plain,
! [X0: $i] : in(empty_set,powerset(X0)),
inference(forward_subsumption_resolution,[status(thm)],[c_2363,c_111]) ).
tcf(c_2368,plain,
! [X0: $i] :
( empty(X0)
| in(sK16(X0),powerset(X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2360,c_111]) ).
tcf(c_2387,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(X0) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_65,c_60]) ).
tcf(c_2399,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_composition(X1,X0) = X2 )
| ~ empty(X2)
| ~ empty(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_86,c_60]) ).
tcf(c_2400,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(X1,X0) = empty_set )
| ~ empty(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_86,c_107]) ).
tcf(c_2402,plain,
! [X0: $i,X1: $i] :
( function(relation_composition(X1,X0))
| ~ empty(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_86,c_80]) ).
tcf(c_2416,plain,
! [X0: $i] : ~ in(powerset(X0),empty_set),
inference(superposition,[status(thm)],[c_2367,c_64]) ).
tcf(c_2424,plain,
( empty(relation_dom(sK2))
| ~ empty(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_2361,c_2047]) ).
tcf(c_2425,plain,
( empty(relation_dom(sK2))
| ( apply(sK1,apply(sK0,sK17(relation_dom(sK2)))) = apply(sK2,sK17(relation_dom(sK2))) ) ),
inference(superposition,[status(thm)],[c_2361,c_53]) ).
tcf(c_2426,plain,
( empty(relation_dom(sK2))
| in(sK17(relation_dom(sK2)),relation_dom(sK0)) ),
inference(superposition,[status(thm)],[c_2361,c_51]) ).
tcf(c_2427,plain,
! [X0: $i] :
( empty(X0)
| ~ in(X0,sK17(X0)) ),
inference(superposition,[status(thm)],[c_2361,c_64]) ).
tcf(c_2443,plain,
! [X0: $i] :
( empty(X0)
| ~ in(powerset(X0),sK16(X0)) ),
inference(superposition,[status(thm)],[c_2368,c_64]) ).
tcf(c_2453,plain,
( empty(relation_dom(sK2))
| ~ in(relation_dom(sK0),sK17(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_2426,c_64]) ).
tcf(c_2454,plain,
( empty(relation_dom(sK2))
| element(sK17(relation_dom(sK2)),relation_dom(sK0)) ),
inference(superposition,[status(thm)],[c_2426,c_63]) ).
tcf(c_2455,plain,
( empty(relation_dom(sK2))
| ~ empty(relation_dom(sK0)) ),
inference(superposition,[status(thm)],[c_2426,c_61]) ).
tcf(c_2466,plain,
! [X0: $i] :
( ( relation_dom(sK2) = X0 )
| ( apply(sK1,apply(sK0,sK17(relation_dom(sK2)))) = apply(sK2,sK17(relation_dom(sK2))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2425,c_60]) ).
tcf(c_2467,plain,
( ( relation_dom(sK2) = empty_set )
| ( apply(sK1,apply(sK0,sK17(relation_dom(sK2)))) = apply(sK2,sK17(relation_dom(sK2))) ) ),
inference(superposition,[status(thm)],[c_2425,c_107]) ).
tcf(c_2468,plain,
( relation(relation_dom(sK2))
| ( apply(sK1,apply(sK0,sK17(relation_dom(sK2)))) = apply(sK2,sK17(relation_dom(sK2))) ) ),
inference(superposition,[status(thm)],[c_2425,c_85]) ).
tcf(c_2469,plain,
( function(relation_dom(sK2))
| ( apply(sK1,apply(sK0,sK17(relation_dom(sK2)))) = apply(sK2,sK17(relation_dom(sK2))) ) ),
inference(superposition,[status(thm)],[c_2425,c_80]) ).
tcf(c_2470,plain,
( empty(sK2)
| ( apply(sK1,apply(sK0,sK17(relation_dom(sK2)))) = apply(sK2,sK17(relation_dom(sK2))) )
| ~ relation(sK2) ),
inference(superposition,[status(thm)],[c_2425,c_67]) ).
tcf(c_2475,plain,
( empty(sK2)
| ( apply(sK1,apply(sK0,sK17(relation_dom(sK2)))) = apply(sK2,sK17(relation_dom(sK2))) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2470,c_54]) ).
tcf(c_2488,plain,
! [X0: $i] :
( ( X0 = sK2 )
| ( apply(sK1,apply(sK0,sK17(relation_dom(sK2)))) = apply(sK2,sK17(relation_dom(sK2))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2475,c_60]) ).
tcf(c_2489,plain,
( ( sK2 = empty_set )
| ( apply(sK1,apply(sK0,sK17(relation_dom(sK2)))) = apply(sK2,sK17(relation_dom(sK2))) ) ),
inference(superposition,[status(thm)],[c_2475,c_107]) ).
tcf(c_2506,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ relation(X1)
| ~ relation(relation_dom(sK2))
| ~ in(ordered_pair(X0,X2),relation_composition(relation_dom(sK2),X1))
| ~ in(relation_dom(sK0),ordered_pair(X0,sK12(relation_dom(sK2),X1,X0,X2))) ),
inference(superposition,[status(thm)],[c_2283,c_64]) ).
tcf(c_2507,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(ordered_pair(X0,sK12(relation_dom(sK2),X2,X0,X1)),relation_dom(sK0))
| ~ relation(X2)
| ~ relation(relation_dom(sK2))
| ~ in(ordered_pair(X0,X1),relation_composition(relation_dom(sK2),X2)) ),
inference(superposition,[status(thm)],[c_2283,c_63]) ).
tcf(c_2508,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ relation(X2)
| ~ empty(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(ordered_pair(X0,X1),relation_composition(relation_dom(sK2),X2)) ),
inference(superposition,[status(thm)],[c_2283,c_61]) ).
tcf(c_2509,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(ordered_pair(X1,X3),relation_composition(relation_dom(sK0),X4))
| ~ relation(X4)
| ~ relation(X0)
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(ordered_pair(X1,X2),relation_composition(relation_dom(sK2),X0))
| ~ in(ordered_pair(sK12(relation_dom(sK2),X0,X1,X2),X3),X4) ),
inference(superposition,[status(thm)],[c_2283,c_299]) ).
tcf(c_2510,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK12(relation_dom(sK2),X2,X0,X1) = apply(relation_dom(sK0),X0) )
| ~ relation(X2)
| ~ function(relation_dom(sK0))
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(ordered_pair(X0,X1),relation_composition(relation_dom(sK2),X2)) ),
inference(superposition,[status(thm)],[c_2283,c_152]) ).
tcf(c_2549,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( apply(sK1,apply(sK0,ordered_pair(X0,sK12(relation_dom(sK2),X2,X0,sK12(relation_composition(relation_dom(sK2),X2),X3,X0,X1))))) = apply(sK2,ordered_pair(X0,sK12(relation_dom(sK2),X2,X0,sK12(relation_composition(relation_dom(sK2),X2),X3,X0,X1)))) )
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(relation_dom(sK2))
| ~ relation(relation_composition(relation_dom(sK2),X2))
| ~ in(ordered_pair(X0,X1),relation_composition(relation_composition(relation_dom(sK2),X2),X3)) ),
inference(superposition,[status(thm)],[c_301,c_2282]) ).
tcf(c_2550,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( apply(sK1,apply(sK0,ordered_pair(sK12(X2,relation_composition(relation_dom(sK2),X3),X0,X1),sK12(relation_dom(sK2),X3,sK12(X2,relation_composition(relation_dom(sK2),X3),X0,X1),X1)))) = apply(sK2,ordered_pair(sK12(X2,relation_composition(relation_dom(sK2),X3),X0,X1),sK12(relation_dom(sK2),X3,sK12(X2,relation_composition(relation_dom(sK2),X3),X0,X1),X1))) )
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(relation_dom(sK2))
| ~ relation(relation_composition(relation_dom(sK2),X3))
| ~ in(ordered_pair(X0,X1),relation_composition(X2,relation_composition(relation_dom(sK2),X3))) ),
inference(superposition,[status(thm)],[c_300,c_2282]) ).
tcf(c_2565,plain,
( ( relation_composition(sK0,sK1) = sK2 )
| ~ empty(sK2)
| ~ empty(relation_composition(sK0,sK1)) ),
inference(instantiation,[status(thm)],[c_60]) ).
tcf(c_2570,plain,
( empty(relation_dom(sK2))
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_65,c_2424]) ).
tcf(c_2577,plain,
( empty(relation_dom(sK2))
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_65,c_2455]) ).
tcf(c_2606,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_composition(X0,X1) = X2 )
| ~ empty(X2)
| ~ empty(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_88,c_60]) ).
tcf(c_2607,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(X0,X1) = empty_set )
| ~ empty(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_88,c_107]) ).
tcf(c_2609,plain,
! [X0: $i,X1: $i] :
( function(relation_composition(X0,X1))
| ~ empty(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_88,c_80]) ).
tcf(c_2636,plain,
! [X0: $i] :
( ( relation_dom(sK2) = X0 )
| ~ empty(sK1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2570,c_60]) ).
tcf(c_2637,plain,
( ( relation_dom(sK2) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_2570,c_107]) ).
tcf(c_2638,plain,
( relation(relation_dom(sK2))
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_2570,c_85]) ).
tcf(c_2639,plain,
( function(relation_dom(sK2))
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_2570,c_80]) ).
tcf(c_2640,plain,
( empty(sK2)
| ~ empty(sK1)
| ~ relation(sK2) ),
inference(superposition,[status(thm)],[c_2570,c_67]) ).
tcf(c_2645,plain,
( empty(sK2)
| ~ empty(sK1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2640,c_54]) ).
tcf(c_2667,plain,
! [X0: $i] :
( ( relation_dom(sK2) = X0 )
| ~ empty(sK0)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2577,c_60]) ).
tcf(c_2668,plain,
( ( relation_dom(sK2) = empty_set )
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_2577,c_107]) ).
tcf(c_2669,plain,
( relation(relation_dom(sK2))
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_2577,c_85]) ).
tcf(c_2670,plain,
( function(relation_dom(sK2))
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_2577,c_80]) ).
tcf(c_2671,plain,
( empty(sK2)
| ~ empty(sK0)
| ~ relation(sK2) ),
inference(superposition,[status(thm)],[c_2577,c_67]) ).
tcf(c_2676,plain,
( empty(sK2)
| ~ empty(sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2671,c_54]) ).
tcf(c_2721,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ relation(X3)
| ~ relation(X2)
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2))
| ~ relation(relation_composition(relation_dom(sK2),X2))
| ~ in(ordered_pair(X0,X1),relation_composition(relation_composition(relation_dom(sK2),X2),X3)) ),
inference(superposition,[status(thm)],[c_301,c_2281]) ).
tcf(c_2722,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ relation(X3)
| ~ relation(X2)
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2))
| ~ relation(relation_composition(relation_dom(sK2),X3))
| ~ in(ordered_pair(X0,X1),relation_composition(X2,relation_composition(relation_dom(sK2),X3))) ),
inference(superposition,[status(thm)],[c_300,c_2281]) ).
tcf(c_2737,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ relation(X2)
| ~ empty(relation_dom(sK0))
| ~ in(ordered_pair(X0,X1),relation_composition(relation_dom(sK2),X2)) ),
inference(global_subsumption_just,[status(thm)],[c_2508,c_58,c_126,c_2508,c_2669]) ).
tcf(c_2746,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ relation(X3)
| ~ relation(X2)
| ~ empty(relation_dom(sK0))
| ~ relation(relation_composition(relation_dom(sK2),X2))
| ~ in(ordered_pair(X0,X1),relation_composition(relation_composition(relation_dom(sK2),X2),X3)) ),
inference(superposition,[status(thm)],[c_301,c_2737]) ).
tcf(c_2747,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ relation(X3)
| ~ relation(X2)
| ~ empty(relation_dom(sK0))
| ~ relation(relation_composition(relation_dom(sK2),X3))
| ~ in(ordered_pair(X0,X1),relation_composition(X2,relation_composition(relation_dom(sK2),X3))) ),
inference(superposition,[status(thm)],[c_300,c_2737]) ).
tcf(c_2770,plain,
! [X0: $i] :
( ( relation_dom(X0) = sK2 )
| ( apply(sK1,apply(sK0,sK17(relation_dom(sK2)))) = apply(sK2,sK17(relation_dom(sK2))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_65,c_2488]) ).
tcf(c_2771,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(X1,X0) = sK2 )
| ( apply(sK1,apply(sK0,sK17(relation_dom(sK2)))) = apply(sK2,sK17(relation_dom(sK2))) )
| ~ empty(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_86,c_2488]) ).
tcf(c_2772,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(X0,X1) = sK2 )
| ( apply(sK1,apply(sK0,sK17(relation_dom(sK2)))) = apply(sK2,sK17(relation_dom(sK2))) )
| ~ empty(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_88,c_2488]) ).
tcf(c_2776,plain,
( ( relation_dom(sK2) = sK2 )
| ( apply(sK1,apply(sK0,sK17(relation_dom(sK2)))) = apply(sK2,sK17(relation_dom(sK2))) ) ),
inference(superposition,[status(thm)],[c_2425,c_2488]) ).
tcf(c_2811,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(ordered_pair(X4,X5),X1)
| ~ in(ordered_pair(X3,X4),relation_composition(X2,X0))
| ~ in(relation_composition(X0,X1),ordered_pair(sK12(X2,X0,X3,X4),X5)) ),
inference(superposition,[status(thm)],[c_2067,c_64]) ).
tcf(c_2812,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( element(ordered_pair(sK12(X2,X3,X0,X1),X4),relation_composition(X3,X5))
| ~ relation(X5)
| ~ relation(X3)
| ~ relation(X2)
| ~ in(ordered_pair(X1,X4),X5)
| ~ in(ordered_pair(X0,X1),relation_composition(X2,X3)) ),
inference(superposition,[status(thm)],[c_2067,c_63]) ).
tcf(c_2813,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ~ relation(X5)
| ~ relation(X3)
| ~ relation(X2)
| ~ empty(relation_composition(X3,X5))
| ~ in(ordered_pair(X1,X4),X5)
| ~ in(ordered_pair(X0,X1),relation_composition(X2,X3)) ),
inference(superposition,[status(thm)],[c_2067,c_61]) ).
tcf(c_2814,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
( in(ordered_pair(sK12(X2,X3,X0,X1),X6),relation_composition(relation_composition(X3,X5),X7))
| ~ relation(X7)
| ~ relation(X5)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(relation_composition(X3,X5))
| ~ in(ordered_pair(X4,X6),X7)
| ~ in(ordered_pair(X1,X4),X5)
| ~ in(ordered_pair(X0,X1),relation_composition(X2,X3)) ),
inference(superposition,[status(thm)],[c_2067,c_299]) ).
tcf(c_2815,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( apply(relation_composition(X3,X5),sK12(X2,X3,X0,X1)) = X4 )
| ~ relation(X5)
| ~ relation(X3)
| ~ relation(X2)
| ~ function(relation_composition(X3,X5))
| ~ relation(relation_composition(X3,X5))
| ~ in(ordered_pair(X1,X4),X5)
| ~ in(ordered_pair(X0,X1),relation_composition(X2,X3)) ),
inference(superposition,[status(thm)],[c_2067,c_152]) ).
tcf(c_2816,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ relation(X3)
| ~ relation(X2)
| ~ empty(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(ordered_pair(X1,X4),relation_dom(sK2))
| ~ in(ordered_pair(X0,X1),relation_composition(X2,X3)) ),
inference(superposition,[status(thm)],[c_2067,c_2176]) ).
tcf(c_2817,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ relation(X3)
| ~ relation(X2)
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2))
| ~ in(ordered_pair(X1,X4),relation_dom(sK2))
| ~ in(ordered_pair(X0,X1),relation_composition(X2,X3)) ),
inference(superposition,[status(thm)],[c_2067,c_2063]) ).
tcf(c_2818,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( apply(sK1,apply(sK0,ordered_pair(sK12(X3,relation_dom(sK2),sK12(X2,X3,X0,X1),X4),X4))) = apply(sK2,ordered_pair(sK12(X3,relation_dom(sK2),sK12(X2,X3,X0,X1),X4),X4)) )
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(relation_dom(sK2))
| ~ in(ordered_pair(X1,X4),relation_dom(sK2))
| ~ in(ordered_pair(X0,X1),relation_composition(X2,X3)) ),
inference(superposition,[status(thm)],[c_2067,c_2064]) ).
tcf(c_2819,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ relation(X4)
| ~ relation(X2)
| ~ empty(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(ordered_pair(X1,X3),X4)
| ~ in(ordered_pair(X0,X1),relation_composition(X2,relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_2067,c_2737]) ).
tcf(c_2820,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ relation(X4)
| ~ relation(X2)
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2))
| ~ in(ordered_pair(X1,X3),X4)
| ~ in(ordered_pair(X0,X1),relation_composition(X2,relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_2067,c_2281]) ).
tcf(c_2821,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( apply(sK1,apply(sK0,ordered_pair(sK12(X2,relation_dom(sK2),X0,X1),sK12(relation_dom(sK2),X4,sK12(X2,relation_dom(sK2),X0,X1),X3)))) = apply(sK2,ordered_pair(sK12(X2,relation_dom(sK2),X0,X1),sK12(relation_dom(sK2),X4,sK12(X2,relation_dom(sK2),X0,X1),X3))) )
| ~ relation(X4)
| ~ relation(X2)
| ~ relation(relation_dom(sK2))
| ~ in(ordered_pair(X1,X3),X4)
| ~ in(ordered_pair(X0,X1),relation_composition(X2,relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_2067,c_2282]) ).
tcf(c_2907,plain,
( relation(relation_dom(empty_set))
| ~ empty(empty_set) ),
inference(instantiation,[status(thm)],[c_66]) ).
tcf(c_2913,plain,
! [X0: $i] :
( ~ empty(empty_set)
| ~ in(X0,empty_set) ),
inference(instantiation,[status(thm)],[c_61]) ).
tcf(c_2925,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ in(X0,sK17(powerset(X1))) ),
inference(superposition,[status(thm)],[c_105,c_99]) ).
tcf(c_2926,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ in(X0,empty_set) ),
inference(superposition,[status(thm)],[c_2139,c_99]) ).
tcf(c_2939,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| element(X0,X1)
| ~ in(X0,sK16(X1)) ),
inference(superposition,[status(thm)],[c_103,c_100]) ).
tcf(c_2940,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| ~ in(X0,sK17(powerset(X1))) ),
inference(superposition,[status(thm)],[c_105,c_100]) ).
tcf(c_2941,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| ~ in(X0,empty_set) ),
inference(superposition,[status(thm)],[c_2139,c_100]) ).
tcf(c_2959,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,relation_dom(X2))
| ~ relation(X3)
| ~ relation(X2)
| ~ in(ordered_pair(X0,X1),relation_composition(X2,X3)) ),
inference(superposition,[status(thm)],[c_301,c_70]) ).
tcf(c_2960,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X2,X3,X0,X1),relation_dom(X3))
| ~ relation(X3)
| ~ relation(X2)
| ~ in(ordered_pair(X0,X1),relation_composition(X2,X3)) ),
inference(superposition,[status(thm)],[c_300,c_70]) ).
tcf(c_2961,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(X2,relation_dom(sK2),X0,X1),relation_dom(relation_dom(sK0)))
| ~ relation(X2)
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(ordered_pair(X0,X1),relation_composition(X2,relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_2065,c_70]) ).
tcf(c_2962,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK12(X2,X3,X0,X1),relation_dom(relation_composition(X3,X5)))
| ~ relation(X5)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(relation_composition(X3,X5))
| ~ in(ordered_pair(X1,X4),X5)
| ~ in(ordered_pair(X0,X1),relation_composition(X2,X3)) ),
inference(superposition,[status(thm)],[c_2067,c_70]) ).
tcf(c_2963,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,relation_dom(relation_dom(sK0)))
| ~ relation(X2)
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(ordered_pair(X0,X1),relation_composition(relation_dom(sK2),X2)) ),
inference(superposition,[status(thm)],[c_2283,c_70]) ).
tcf(c_3017,plain,
! [X0: $i] :
( ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2))
| ~ in(X0,relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_71,c_2047]) ).
tcf(c_3018,plain,
! [X0: $i] :
( ( apply(sK1,apply(sK0,ordered_pair(X0,sK5(relation_dom(sK2),X0)))) = apply(sK2,ordered_pair(X0,sK5(relation_dom(sK2),X0))) )
| ~ relation(relation_dom(sK2))
| ~ in(X0,relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_71,c_53]) ).
tcf(c_3019,plain,
! [X0: $i] :
( in(ordered_pair(X0,sK5(relation_dom(sK2),X0)),relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(X0,relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_71,c_51]) ).
tcf(c_3020,plain,
! [X0: $i,X1: $i] :
( ~ relation(X0)
| ~ in(X1,relation_dom(X0))
| ~ in(X0,ordered_pair(X1,sK5(X0,X1))) ),
inference(superposition,[status(thm)],[c_71,c_64]) ).
tcf(c_3021,plain,
! [X0: $i,X1: $i] :
( element(ordered_pair(X0,sK5(X1,X0)),X1)
| ~ relation(X1)
| ~ in(X0,relation_dom(X1)) ),
inference(superposition,[status(thm)],[c_71,c_63]) ).
tcf(c_3022,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ relation(X1)
| ~ in(X0,relation_dom(X1)) ),
inference(superposition,[status(thm)],[c_71,c_61]) ).
tcf(c_3024,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(ordered_pair(X1,X2),relation_composition(X0,X3))
| ~ relation(X3)
| ~ relation(X0)
| ~ in(X1,relation_dom(X0))
| ~ in(ordered_pair(sK5(X0,X1),X2),X3) ),
inference(superposition,[status(thm)],[c_71,c_299]) ).
tcf(c_3025,plain,
! [X0: $i,X1: $i] :
( ( apply(X1,X0) = sK5(X1,X0) )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_dom(X1)) ),
inference(superposition,[status(thm)],[c_71,c_152]) ).
tcf(c_3026,plain,
! [X0: $i,X1: $i] :
( ~ relation(X1)
| ~ empty(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ relation(relation_composition(X1,relation_dom(sK2)))
| ~ in(X0,relation_dom(relation_composition(X1,relation_dom(sK2)))) ),
inference(superposition,[status(thm)],[c_71,c_2176]) ).
tcf(c_3027,plain,
! [X0: $i,X1: $i] :
( ~ relation(X1)
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2))
| ~ relation(relation_composition(X1,relation_dom(sK2)))
| ~ in(X0,relation_dom(relation_composition(X1,relation_dom(sK2)))) ),
inference(superposition,[status(thm)],[c_71,c_2063]) ).
tcf(c_3028,plain,
! [X0: $i,X1: $i] :
( ( apply(sK1,apply(sK0,ordered_pair(sK12(X1,relation_dom(sK2),X0,sK5(relation_composition(X1,relation_dom(sK2)),X0)),sK5(relation_composition(X1,relation_dom(sK2)),X0)))) = apply(sK2,ordered_pair(sK12(X1,relation_dom(sK2),X0,sK5(relation_composition(X1,relation_dom(sK2)),X0)),sK5(relation_composition(X1,relation_dom(sK2)),X0))) )
| ~ relation(X1)
| ~ relation(relation_dom(sK2))
| ~ relation(relation_composition(X1,relation_dom(sK2)))
| ~ in(X0,relation_dom(relation_composition(X1,relation_dom(sK2)))) ),
inference(superposition,[status(thm)],[c_71,c_2064]) ).
tcf(c_3029,plain,
! [X0: $i,X1: $i] :
( ~ relation(X1)
| ~ empty(relation_dom(sK0))
| ~ relation(relation_composition(relation_dom(sK2),X1))
| ~ in(X0,relation_dom(relation_composition(relation_dom(sK2),X1))) ),
inference(superposition,[status(thm)],[c_71,c_2737]) ).
tcf(c_3030,plain,
! [X0: $i,X1: $i] :
( ~ relation(X1)
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2))
| ~ relation(relation_composition(relation_dom(sK2),X1))
| ~ in(X0,relation_dom(relation_composition(relation_dom(sK2),X1))) ),
inference(superposition,[status(thm)],[c_71,c_2281]) ).
tcf(c_3031,plain,
! [X0: $i,X1: $i] :
( ( apply(sK1,apply(sK0,ordered_pair(X0,sK12(relation_dom(sK2),X1,X0,sK5(relation_composition(relation_dom(sK2),X1),X0))))) = apply(sK2,ordered_pair(X0,sK12(relation_dom(sK2),X1,X0,sK5(relation_composition(relation_dom(sK2),X1),X0)))) )
| ~ relation(X1)
| ~ relation(relation_dom(sK2))
| ~ relation(relation_composition(relation_dom(sK2),X1))
| ~ in(X0,relation_dom(relation_composition(relation_dom(sK2),X1))) ),
inference(superposition,[status(thm)],[c_71,c_2282]) ).
tcf(c_3131,plain,
! [X0: $i] :
( ~ relation(relation_dom(sK2))
| ~ in(X0,relation_dom(relation_dom(sK2)))
| ~ in(relation_dom(sK0),ordered_pair(X0,sK5(relation_dom(sK2),X0))) ),
inference(superposition,[status(thm)],[c_3019,c_64]) ).
tcf(c_3132,plain,
! [X0: $i] :
( element(ordered_pair(X0,sK5(relation_dom(sK2),X0)),relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(X0,relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_3019,c_63]) ).
tcf(c_3133,plain,
! [X0: $i] :
( ~ empty(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(X0,relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_3019,c_61]) ).
tcf(c_3134,plain,
! [X0: $i] :
( in(X0,relation_dom(relation_dom(sK0)))
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(X0,relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_3019,c_70]) ).
tcf(c_3135,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(ordered_pair(X0,X1),relation_composition(relation_dom(sK0),X2))
| ~ relation(X2)
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(X0,relation_dom(relation_dom(sK2)))
| ~ in(ordered_pair(sK5(relation_dom(sK2),X0),X1),X2) ),
inference(superposition,[status(thm)],[c_3019,c_299]) ).
tcf(c_3136,plain,
! [X0: $i] :
( ( apply(relation_dom(sK0),X0) = sK5(relation_dom(sK2),X0) )
| ~ function(relation_dom(sK0))
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(X0,relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_3019,c_152]) ).
tcf(c_3187,plain,
! [X0: $i] :
( ( apply(sK1,apply(sK0,ordered_pair(ordered_pair(X0,sK5(relation_dom(relation_dom(sK2)),X0)),sK5(relation_dom(sK2),ordered_pair(X0,sK5(relation_dom(relation_dom(sK2)),X0)))))) = apply(sK2,ordered_pair(ordered_pair(X0,sK5(relation_dom(relation_dom(sK2)),X0)),sK5(relation_dom(sK2),ordered_pair(X0,sK5(relation_dom(relation_dom(sK2)),X0))))) )
| ~ relation(relation_dom(sK2))
| ~ relation(relation_dom(relation_dom(sK2)))
| ~ in(X0,relation_dom(relation_dom(relation_dom(sK2)))) ),
inference(superposition,[status(thm)],[c_71,c_3018]) ).
tcf(c_3188,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(sK1,apply(sK0,ordered_pair(ordered_pair(X0,sK12(relation_dom(relation_dom(sK2)),X2,X0,X1)),sK5(relation_dom(sK2),ordered_pair(X0,sK12(relation_dom(relation_dom(sK2)),X2,X0,X1)))))) = apply(sK2,ordered_pair(ordered_pair(X0,sK12(relation_dom(relation_dom(sK2)),X2,X0,X1)),sK5(relation_dom(sK2),ordered_pair(X0,sK12(relation_dom(relation_dom(sK2)),X2,X0,X1))))) )
| ~ relation(X2)
| ~ relation(relation_dom(sK2))
| ~ relation(relation_dom(relation_dom(sK2)))
| ~ in(ordered_pair(X0,X1),relation_composition(relation_dom(relation_dom(sK2)),X2)) ),
inference(superposition,[status(thm)],[c_301,c_3018]) ).
tcf(c_3189,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(sK1,apply(sK0,ordered_pair(ordered_pair(sK12(X2,relation_dom(relation_dom(sK2)),X0,X1),X1),sK5(relation_dom(sK2),ordered_pair(sK12(X2,relation_dom(relation_dom(sK2)),X0,X1),X1))))) = apply(sK2,ordered_pair(ordered_pair(sK12(X2,relation_dom(relation_dom(sK2)),X0,X1),X1),sK5(relation_dom(sK2),ordered_pair(sK12(X2,relation_dom(relation_dom(sK2)),X0,X1),X1)))) )
| ~ relation(X2)
| ~ relation(relation_dom(sK2))
| ~ relation(relation_dom(relation_dom(sK2)))
| ~ in(ordered_pair(X0,X1),relation_composition(X2,relation_dom(relation_dom(sK2)))) ),
inference(superposition,[status(thm)],[c_300,c_3018]) ).
tcf(c_3190,plain,
( empty(relation_dom(relation_dom(sK2)))
| ( apply(sK1,apply(sK0,ordered_pair(sK17(relation_dom(relation_dom(sK2))),sK5(relation_dom(sK2),sK17(relation_dom(relation_dom(sK2))))))) = apply(sK2,ordered_pair(sK17(relation_dom(relation_dom(sK2))),sK5(relation_dom(sK2),sK17(relation_dom(relation_dom(sK2)))))) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_2361,c_3018]) ).
tcf(c_3217,plain,
! [X0: $i] :
( ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2))
| ~ relation(relation_dom(relation_dom(sK2)))
| ~ in(X0,relation_dom(relation_dom(relation_dom(sK2)))) ),
inference(superposition,[status(thm)],[c_71,c_3017]) ).
tcf(c_3218,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ relation(X2)
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2))
| ~ relation(relation_dom(relation_dom(sK2)))
| ~ in(ordered_pair(X0,X1),relation_composition(relation_dom(relation_dom(sK2)),X2)) ),
inference(superposition,[status(thm)],[c_301,c_3017]) ).
tcf(c_3219,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ relation(X2)
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2))
| ~ relation(relation_dom(relation_dom(sK2)))
| ~ in(ordered_pair(X0,X1),relation_composition(X2,relation_dom(relation_dom(sK2)))) ),
inference(superposition,[status(thm)],[c_300,c_3017]) ).
tcf(c_3220,plain,
( empty(relation_dom(relation_dom(sK2)))
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_2361,c_3017]) ).
tcf(c_3241,plain,
! [X0: $i] :
( ~ empty(relation_dom(sK0))
| ~ in(X0,relation_dom(relation_dom(sK2))) ),
inference(global_subsumption_just,[status(thm)],[c_3133,c_58,c_126,c_2669,c_3133]) ).
tcf(c_3248,plain,
! [X0: $i] :
( ~ empty(relation_dom(sK0))
| ~ relation(relation_dom(relation_dom(sK2)))
| ~ in(X0,relation_dom(relation_dom(relation_dom(sK2)))) ),
inference(superposition,[status(thm)],[c_71,c_3241]) ).
tcf(c_3249,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ relation(X2)
| ~ empty(relation_dom(sK0))
| ~ relation(relation_dom(relation_dom(sK2)))
| ~ in(ordered_pair(X0,X1),relation_composition(relation_dom(relation_dom(sK2)),X2)) ),
inference(superposition,[status(thm)],[c_301,c_3241]) ).
tcf(c_3250,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ relation(X2)
| ~ empty(relation_dom(sK0))
| ~ relation(relation_dom(relation_dom(sK2)))
| ~ in(ordered_pair(X0,X1),relation_composition(X2,relation_dom(relation_dom(sK2)))) ),
inference(superposition,[status(thm)],[c_300,c_3241]) ).
tcf(c_3251,plain,
( empty(relation_dom(relation_dom(sK2)))
| ~ empty(relation_dom(sK0)) ),
inference(superposition,[status(thm)],[c_2361,c_3241]) ).
tcf(c_3294,plain,
! [X0: $i] :
( in(ordered_pair(X0,sK5(relation_dom(relation_dom(sK2)),X0)),relation_dom(relation_dom(sK0)))
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ relation(relation_dom(relation_dom(sK2)))
| ~ in(X0,relation_dom(relation_dom(relation_dom(sK2)))) ),
inference(superposition,[status(thm)],[c_71,c_3134]) ).
tcf(c_3295,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(ordered_pair(X0,sK12(relation_dom(relation_dom(sK2)),X2,X0,X1)),relation_dom(relation_dom(sK0)))
| ~ relation(X2)
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ relation(relation_dom(relation_dom(sK2)))
| ~ in(ordered_pair(X0,X1),relation_composition(relation_dom(relation_dom(sK2)),X2)) ),
inference(superposition,[status(thm)],[c_301,c_3134]) ).
tcf(c_3296,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(ordered_pair(sK12(X2,relation_dom(relation_dom(sK2)),X0,X1),X1),relation_dom(relation_dom(sK0)))
| ~ relation(X2)
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ relation(relation_dom(relation_dom(sK2)))
| ~ in(ordered_pair(X0,X1),relation_composition(X2,relation_dom(relation_dom(sK2)))) ),
inference(superposition,[status(thm)],[c_300,c_3134]) ).
tcf(c_3297,plain,
( empty(relation_dom(relation_dom(sK2)))
| in(sK17(relation_dom(relation_dom(sK2))),relation_dom(relation_dom(sK0)))
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_2361,c_3134]) ).
tcf(c_3343,plain,
! [X0: $i] :
( ( relation_dom(X0) = relation_dom(sK2) )
| ( apply(sK1,apply(sK0,sK17(relation_dom(sK2)))) = apply(sK2,sK17(relation_dom(sK2))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_65,c_2466]) ).
tcf(c_3344,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(X1,X0) = relation_dom(sK2) )
| ( apply(sK1,apply(sK0,sK17(relation_dom(sK2)))) = apply(sK2,sK17(relation_dom(sK2))) )
| ~ empty(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_86,c_2466]) ).
tcf(c_3345,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(X0,X1) = relation_dom(sK2) )
| ( apply(sK1,apply(sK0,sK17(relation_dom(sK2)))) = apply(sK2,sK17(relation_dom(sK2))) )
| ~ empty(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_88,c_2466]) ).
tcf(c_3374,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(X2,sK12(X1,X2,X0,sK5(relation_composition(X1,X2),X0))) = sK5(relation_composition(X1,X2),X0) )
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(relation_composition(X1,X2))
| ~ in(X0,relation_dom(relation_composition(X1,X2))) ),
inference(superposition,[status(thm)],[c_71,c_2068]) ).
tcf(c_3375,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( apply(X3,sK12(X2,X3,X0,sK12(relation_composition(X2,X3),X4,X0,X1))) = sK12(relation_composition(X2,X3),X4,X0,X1) )
| ~ function(X3)
| ~ relation(X4)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(relation_composition(X2,X3))
| ~ in(ordered_pair(X0,X1),relation_composition(relation_composition(X2,X3),X4)) ),
inference(superposition,[status(thm)],[c_301,c_2068]) ).
tcf(c_3376,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( apply(X4,sK12(X3,X4,sK12(X2,relation_composition(X3,X4),X0,X1),X1)) = X1 )
| ~ function(X4)
| ~ relation(X4)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(relation_composition(X3,X4))
| ~ in(ordered_pair(X0,X1),relation_composition(X2,relation_composition(X3,X4))) ),
inference(superposition,[status(thm)],[c_300,c_2068]) ).
tcf(c_3377,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( apply(X5,sK12(X3,X5,sK12(X2,X3,X0,X1),X4)) = X4 )
| ~ function(X5)
| ~ relation(X5)
| ~ relation(X3)
| ~ relation(X2)
| ~ in(ordered_pair(X1,X4),X5)
| ~ in(ordered_pair(X0,X1),relation_composition(X2,X3)) ),
inference(superposition,[status(thm)],[c_2067,c_2068]) ).
tcf(c_3427,plain,
! [X0: $i] :
( ( apply(sK2,X0) = empty_set )
| ~ function(sK2)
| ~ relation(sK2)
| ~ empty(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_75,c_2047]) ).
tcf(c_3428,plain,
! [X0: $i] :
( ( apply(sK2,X0) = empty_set )
| ( apply(sK1,apply(sK0,X0)) = apply(sK2,X0) )
| ~ function(sK2)
| ~ relation(sK2) ),
inference(superposition,[status(thm)],[c_75,c_53]) ).
tcf(c_3429,plain,
! [X0: $i] :
( in(X0,relation_dom(sK0))
| ( apply(sK2,X0) = empty_set )
| ~ function(sK2)
| ~ relation(sK2) ),
inference(superposition,[status(thm)],[c_75,c_51]) ).
tcf(c_3430,plain,
! [X0: $i] :
( in(X0,relation_dom(sK2))
| ( apply(sK1,apply(sK0,X0)) = empty_set )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(X0,relation_dom(sK0)) ),
inference(superposition,[status(thm)],[c_75,c_50]) ).
tcf(c_3431,plain,
! [X0: $i,X1: $i] :
( ( apply(X0,X1) = empty_set )
| ~ function(X0)
| ~ relation(X0)
| ~ in(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_75,c_64]) ).
tcf(c_3432,plain,
! [X0: $i,X1: $i] :
( element(X1,relation_dom(X0))
| ( apply(X0,X1) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_75,c_63]) ).
tcf(c_3433,plain,
! [X0: $i,X1: $i] :
( ( apply(X0,X1) = empty_set )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_75,c_61]) ).
tcf(c_3434,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,relation_dom(relation_dom(X0)))
| ( apply(X0,ordered_pair(X1,X2)) = empty_set )
| ~ function(X0)
| ~ relation(X0)
| ~ relation(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_75,c_70]) ).
tcf(c_3435,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(ordered_pair(X4,X1),relation_composition(relation_dom(X3),X2))
| ( apply(X3,ordered_pair(X4,X0)) = empty_set )
| ~ function(X3)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(relation_dom(X3))
| ~ in(ordered_pair(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_75,c_299]) ).
tcf(c_3436,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(relation_dom(X0),X1) = X2 )
| ( apply(X0,ordered_pair(X1,X2)) = empty_set )
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom(X0))
| ~ relation(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_75,c_152]) ).
tcf(c_3437,plain,
! [X0: $i] :
( in(X0,relation_dom(relation_dom(sK0)))
| ( apply(relation_dom(sK2),X0) = empty_set )
| ~ function(relation_dom(sK2))
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_75,c_3134]) ).
tcf(c_3438,plain,
! [X0: $i] :
( ( apply(relation_dom(sK2),X0) = empty_set )
| ~ empty(relation_dom(sK0))
| ~ function(relation_dom(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_75,c_3241]) ).
tcf(c_3439,plain,
! [X0: $i] :
( ( apply(relation_dom(sK2),X0) = empty_set )
| ~ empty(relation_dom(sK1))
| ~ function(relation_dom(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_75,c_3017]) ).
tcf(c_3440,plain,
! [X0: $i] :
( ( apply(relation_dom(sK2),X0) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(X0,sK5(relation_dom(sK2),X0)))) = apply(sK2,ordered_pair(X0,sK5(relation_dom(sK2),X0))) )
| ~ function(relation_dom(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_75,c_3018]) ).
tcf(c_3449,plain,
! [X0: $i] :
( in(X0,relation_dom(sK0))
| ( apply(sK2,X0) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3429,c_55,c_54]) ).
tcf(c_3452,plain,
! [X0: $i] :
( ( apply(sK2,X0) = empty_set )
| ~ empty(relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3427,c_55,c_54]) ).
tcf(c_3467,plain,
! [X0: $i] :
( ( apply(sK2,X0) = empty_set )
| ( apply(sK1,apply(sK0,X0)) = apply(sK2,X0) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3428,c_55,c_54]) ).
tcf(c_3475,plain,
! [X0: $i] :
( in(X0,relation_dom(sK2))
| ( apply(sK1,apply(sK0,X0)) = empty_set )
| ~ in(X0,relation_dom(sK0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3430,c_57,c_56]) ).
tcf(c_3546,plain,
( in(ordered_pair(apply(sK0,sK17(relation_dom(sK2))),apply(sK2,sK17(relation_dom(sK2)))),sK1)
| ( relation_dom(sK2) = sK2 )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_2776,c_73]) ).
tcf(c_3547,plain,
( in(ordered_pair(apply(sK0,sK17(relation_dom(sK2))),apply(sK2,sK17(relation_dom(sK2)))),sK1)
| ( sK2 = empty_set )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_2489,c_73]) ).
tcf(c_3548,plain,
( in(ordered_pair(apply(sK0,sK17(relation_dom(sK2))),apply(sK2,sK17(relation_dom(sK2)))),sK1)
| ( relation_dom(sK2) = empty_set )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_2467,c_73]) ).
tcf(c_3549,plain,
! [X0: $i] :
( ~ empty(relation_dom(sK1))
| ~ function(relation_dom(sK2))
| ~ relation(relation_dom(sK2))
| ~ in(X0,relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_73,c_2047]) ).
tcf(c_3550,plain,
! [X0: $i] :
( ( apply(sK1,apply(sK0,ordered_pair(X0,apply(relation_dom(sK2),X0)))) = apply(sK2,ordered_pair(X0,apply(relation_dom(sK2),X0))) )
| ~ function(relation_dom(sK2))
| ~ relation(relation_dom(sK2))
| ~ in(X0,relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_73,c_53]) ).
tcf(c_3551,plain,
! [X0: $i] :
( in(ordered_pair(X0,apply(relation_dom(sK2),X0)),relation_dom(sK0))
| ~ function(relation_dom(sK2))
| ~ relation(relation_dom(sK2))
| ~ in(X0,relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_73,c_51]) ).
tcf(c_3552,plain,
! [X0: $i,X1: $i] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X1,relation_dom(X0))
| ~ in(X0,ordered_pair(X1,apply(X0,X1))) ),
inference(superposition,[status(thm)],[c_73,c_64]) ).
tcf(c_3553,plain,
! [X0: $i,X1: $i] :
( element(ordered_pair(X0,apply(X1,X0)),X1)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_dom(X1)) ),
inference(superposition,[status(thm)],[c_73,c_63]) ).
tcf(c_3554,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_dom(X1)) ),
inference(superposition,[status(thm)],[c_73,c_61]) ).
tcf(c_3556,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(ordered_pair(X1,X2),relation_composition(X0,X3))
| ~ function(X0)
| ~ relation(X3)
| ~ relation(X0)
| ~ in(X1,relation_dom(X0))
| ~ in(ordered_pair(apply(X0,X1),X2),X3) ),
inference(superposition,[status(thm)],[c_73,c_299]) ).
tcf(c_3558,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(X2,sK12(X1,X2,X0,apply(relation_composition(X1,X2),X0))) = apply(relation_composition(X1,X2),X0) )
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ function(relation_composition(X1,X2))
| ~ relation(relation_composition(X1,X2))
| ~ in(X0,relation_dom(relation_composition(X1,X2))) ),
inference(superposition,[status(thm)],[c_73,c_2068]) ).
tcf(c_3559,plain,
! [X0: $i,X1: $i] :
( ~ relation(X1)
| ~ empty(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ function(relation_composition(X1,relation_dom(sK2)))
| ~ relation(relation_composition(X1,relation_dom(sK2)))
| ~ in(X0,relation_dom(relation_composition(X1,relation_dom(sK2)))) ),
inference(superposition,[status(thm)],[c_73,c_2176]) ).
tcf(c_3560,plain,
! [X0: $i,X1: $i] :
( ~ relation(X1)
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2))
| ~ function(relation_composition(X1,relation_dom(sK2)))
| ~ relation(relation_composition(X1,relation_dom(sK2)))
| ~ in(X0,relation_dom(relation_composition(X1,relation_dom(sK2)))) ),
inference(superposition,[status(thm)],[c_73,c_2063]) ).
tcf(c_3561,plain,
! [X0: $i,X1: $i] :
( ( apply(sK1,apply(sK0,ordered_pair(sK12(X1,relation_dom(sK2),X0,apply(relation_composition(X1,relation_dom(sK2)),X0)),apply(relation_composition(X1,relation_dom(sK2)),X0)))) = apply(sK2,ordered_pair(sK12(X1,relation_dom(sK2),X0,apply(relation_composition(X1,relation_dom(sK2)),X0)),apply(relation_composition(X1,relation_dom(sK2)),X0))) )
| ~ relation(X1)
| ~ relation(relation_dom(sK2))
| ~ function(relation_composition(X1,relation_dom(sK2)))
| ~ relation(relation_composition(X1,relation_dom(sK2)))
| ~ in(X0,relation_dom(relation_composition(X1,relation_dom(sK2)))) ),
inference(superposition,[status(thm)],[c_73,c_2064]) ).
tcf(c_3562,plain,
! [X0: $i,X1: $i] :
( ~ relation(X1)
| ~ empty(relation_dom(sK0))
| ~ function(relation_composition(relation_dom(sK2),X1))
| ~ relation(relation_composition(relation_dom(sK2),X1))
| ~ in(X0,relation_dom(relation_composition(relation_dom(sK2),X1))) ),
inference(superposition,[status(thm)],[c_73,c_2737]) ).
tcf(c_3563,plain,
! [X0: $i,X1: $i] :
( ~ relation(X1)
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2))
| ~ function(relation_composition(relation_dom(sK2),X1))
| ~ relation(relation_composition(relation_dom(sK2),X1))
| ~ in(X0,relation_dom(relation_composition(relation_dom(sK2),X1))) ),
inference(superposition,[status(thm)],[c_73,c_2281]) ).
tcf(c_3564,plain,
! [X0: $i,X1: $i] :
( ( apply(sK1,apply(sK0,ordered_pair(X0,sK12(relation_dom(sK2),X1,X0,apply(relation_composition(relation_dom(sK2),X1),X0))))) = apply(sK2,ordered_pair(X0,sK12(relation_dom(sK2),X1,X0,apply(relation_composition(relation_dom(sK2),X1),X0)))) )
| ~ relation(X1)
| ~ relation(relation_dom(sK2))
| ~ function(relation_composition(relation_dom(sK2),X1))
| ~ relation(relation_composition(relation_dom(sK2),X1))
| ~ in(X0,relation_dom(relation_composition(relation_dom(sK2),X1))) ),
inference(superposition,[status(thm)],[c_73,c_2282]) ).
tcf(c_3565,plain,
! [X0: $i] :
( in(ordered_pair(X0,apply(relation_dom(relation_dom(sK2)),X0)),relation_dom(relation_dom(sK0)))
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ function(relation_dom(relation_dom(sK2)))
| ~ relation(relation_dom(relation_dom(sK2)))
| ~ in(X0,relation_dom(relation_dom(relation_dom(sK2)))) ),
inference(superposition,[status(thm)],[c_73,c_3134]) ).
tcf(c_3566,plain,
! [X0: $i] :
( ~ empty(relation_dom(sK0))
| ~ function(relation_dom(relation_dom(sK2)))
| ~ relation(relation_dom(relation_dom(sK2)))
| ~ in(X0,relation_dom(relation_dom(relation_dom(sK2)))) ),
inference(superposition,[status(thm)],[c_73,c_3241]) ).
tcf(c_3567,plain,
! [X0: $i] :
( ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2))
| ~ function(relation_dom(relation_dom(sK2)))
| ~ relation(relation_dom(relation_dom(sK2)))
| ~ in(X0,relation_dom(relation_dom(relation_dom(sK2)))) ),
inference(superposition,[status(thm)],[c_73,c_3017]) ).
tcf(c_3568,plain,
! [X0: $i] :
( ( apply(sK1,apply(sK0,ordered_pair(ordered_pair(X0,apply(relation_dom(relation_dom(sK2)),X0)),sK5(relation_dom(sK2),ordered_pair(X0,apply(relation_dom(relation_dom(sK2)),X0)))))) = apply(sK2,ordered_pair(ordered_pair(X0,apply(relation_dom(relation_dom(sK2)),X0)),sK5(relation_dom(sK2),ordered_pair(X0,apply(relation_dom(relation_dom(sK2)),X0))))) )
| ~ relation(relation_dom(sK2))
| ~ function(relation_dom(relation_dom(sK2)))
| ~ relation(relation_dom(relation_dom(sK2)))
| ~ in(X0,relation_dom(relation_dom(relation_dom(sK2)))) ),
inference(superposition,[status(thm)],[c_73,c_3018]) ).
tcf(c_3627,plain,
( in(ordered_pair(apply(sK0,sK17(relation_dom(sK2))),apply(sK2,sK17(relation_dom(sK2)))),sK1)
| ( sK2 = empty_set )
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3547,c_57,c_56]) ).
tcf(c_3631,plain,
( in(ordered_pair(apply(sK0,sK17(relation_dom(sK2))),apply(sK2,sK17(relation_dom(sK2)))),sK1)
| ( relation_dom(sK2) = empty_set )
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3548,c_57,c_56]) ).
tcf(c_3635,plain,
( in(ordered_pair(apply(sK0,sK17(relation_dom(sK2))),apply(sK2,sK17(relation_dom(sK2)))),sK1)
| ( relation_dom(sK2) = sK2 )
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3546,c_57,c_56]) ).
tcf(c_3762,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(X0) = X1 )
| ~ relation(X0)
| ~ in(sK3(X0,X1),X1)
| ~ in(sK3(X0,X1),relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_71,c_68]) ).
tcf(c_3763,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(X0) = X1 )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK3(X0,X1),X1)
| ~ in(sK3(X0,X1),relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_73,c_68]) ).
tcf(c_3764,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_dom(X0)) = X1 )
| ( apply(X0,ordered_pair(sK3(relation_dom(X0),X1),X2)) = empty_set )
| ~ function(X0)
| ~ relation(X0)
| ~ relation(relation_dom(X0))
| ~ in(sK3(relation_dom(X0),X1),X1) ),
inference(superposition,[status(thm)],[c_75,c_68]) ).
tcf(c_3765,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_dom(X0) = X1 )
| ~ relation(X3)
| ~ relation(X0)
| ~ in(sK3(X0,X1),X1)
| ~ in(ordered_pair(sK3(X0,X1),X2),relation_composition(X0,X3)) ),
inference(superposition,[status(thm)],[c_301,c_68]) ).
tcf(c_3766,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_dom(sK0)) = X0 )
| ~ relation(X2)
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(sK3(relation_dom(sK0),X0),X0)
| ~ in(ordered_pair(sK3(relation_dom(sK0),X0),X1),relation_composition(relation_dom(sK2),X2)) ),
inference(superposition,[status(thm)],[c_2283,c_68]) ).
tcf(c_3767,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK0)) = X0 )
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(sK3(relation_dom(sK0),X0),X0)
| ~ in(sK3(relation_dom(sK0),X0),relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_3019,c_68]) ).
tcf(c_3809,plain,
! [X0: $i] : ~ in(X0,empty_set),
inference(global_subsumption_just,[status(thm)],[c_2926,c_110,c_2913]) ).
tcf(c_3812,plain,
! [X0: $i] :
( ~ relation(empty_set)
| ~ in(X0,relation_dom(empty_set)) ),
inference(superposition,[status(thm)],[c_71,c_3809]) ).
tcf(c_3814,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ relation(empty_set)
| ~ relation(X2)
| ~ in(ordered_pair(X0,X1),relation_composition(empty_set,X2)) ),
inference(superposition,[status(thm)],[c_301,c_3809]) ).
tcf(c_3815,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ relation(empty_set)
| ~ relation(X2)
| ~ in(ordered_pair(X0,X1),relation_composition(X2,empty_set)) ),
inference(superposition,[status(thm)],[c_300,c_3809]) ).
tcf(c_3817,plain,
! [X0: $i] : ~ in(X0,relation_dom(empty_set)),
inference(forward_subsumption_resolution,[status(thm)],[c_3812,c_109]) ).
tcf(c_3818,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ relation(X2)
| ~ in(ordered_pair(X0,X1),relation_composition(X2,empty_set)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3815,c_109]) ).
tcf(c_3821,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ relation(X2)
| ~ in(ordered_pair(X0,X1),relation_composition(empty_set,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3814,c_109]) ).
tcf(c_3827,plain,
! [X0: $i] :
( ~ relation(relation_dom(empty_set))
| ~ in(X0,relation_dom(relation_dom(empty_set))) ),
inference(superposition,[status(thm)],[c_71,c_3817]) ).
tcf(c_3829,plain,
! [X0: $i] :
( ( apply(empty_set,X0) = empty_set )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_75,c_3817]) ).
tcf(c_3830,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ relation(X2)
| ~ relation(relation_dom(empty_set))
| ~ in(ordered_pair(X0,X1),relation_composition(relation_dom(empty_set),X2)) ),
inference(superposition,[status(thm)],[c_301,c_3817]) ).
tcf(c_3831,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ relation(X2)
| ~ relation(relation_dom(empty_set))
| ~ in(ordered_pair(X0,X1),relation_composition(X2,relation_dom(empty_set))) ),
inference(superposition,[status(thm)],[c_300,c_3817]) ).
tcf(c_3832,plain,
empty(relation_dom(empty_set)),
inference(superposition,[status(thm)],[c_2361,c_3817]) ).
tcf(c_3835,plain,
! [X0: $i] : apply(empty_set,X0) = empty_set,
inference(forward_subsumption_resolution,[status(thm)],[c_3829,c_2011,c_109]) ).
tcf(c_3854,plain,
( ( relation_dom(sK2) = relation_dom(empty_set) )
| ( apply(sK1,apply(sK0,sK17(relation_dom(sK2)))) = apply(sK2,sK17(relation_dom(sK2))) ) ),
inference(superposition,[status(thm)],[c_3832,c_2466]) ).
tcf(c_3855,plain,
( ( relation_dom(empty_set) = sK2 )
| ( apply(sK1,apply(sK0,sK17(relation_dom(sK2)))) = apply(sK2,sK17(relation_dom(sK2))) ) ),
inference(superposition,[status(thm)],[c_3832,c_2488]) ).
tcf(c_3856,plain,
! [X0: $i] :
( ( relation_dom(empty_set) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3832,c_60]) ).
tcf(c_3857,plain,
relation_dom(empty_set) = empty_set,
inference(superposition,[status(thm)],[c_3832,c_107]) ).
tcf(c_3858,plain,
relation(relation_dom(empty_set)),
inference(superposition,[status(thm)],[c_3832,c_85]) ).
tcf(c_3859,plain,
function(relation_dom(empty_set)),
inference(superposition,[status(thm)],[c_3832,c_80]) ).
tcf(c_3889,plain,
! [X0: $i] :
( ( apply(sK2,X0) = empty_set )
| ~ in(relation_dom(sK0),X0) ),
inference(superposition,[status(thm)],[c_3449,c_64]) ).
tcf(c_3890,plain,
! [X0: $i] :
( element(X0,relation_dom(sK0))
| ( apply(sK2,X0) = empty_set ) ),
inference(superposition,[status(thm)],[c_3449,c_63]) ).
tcf(c_3891,plain,
! [X0: $i] :
( ( apply(sK2,X0) = empty_set )
| ~ empty(relation_dom(sK0)) ),
inference(superposition,[status(thm)],[c_3449,c_61]) ).
tcf(c_3892,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK0)) = X0 )
| ( apply(sK2,ordered_pair(sK3(relation_dom(sK0),X0),X1)) = empty_set )
| ~ relation(relation_dom(sK0))
| ~ in(sK3(relation_dom(sK0),X0),X0) ),
inference(superposition,[status(thm)],[c_3449,c_68]) ).
tcf(c_3893,plain,
! [X0: $i,X1: $i] :
( in(X0,relation_dom(relation_dom(sK0)))
| ( apply(sK2,ordered_pair(X0,X1)) = empty_set )
| ~ relation(relation_dom(sK0)) ),
inference(superposition,[status(thm)],[c_3449,c_70]) ).
tcf(c_3894,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(ordered_pair(X3,X1),relation_composition(relation_dom(sK0),X2))
| ( apply(sK2,ordered_pair(X3,X0)) = empty_set )
| ~ relation(X2)
| ~ relation(relation_dom(sK0))
| ~ in(ordered_pair(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_3449,c_299]) ).
tcf(c_3895,plain,
! [X0: $i,X1: $i] :
( ( apply(relation_dom(sK0),X0) = X1 )
| ( apply(sK2,ordered_pair(X0,X1)) = empty_set )
| ~ function(relation_dom(sK0))
| ~ relation(relation_dom(sK0)) ),
inference(superposition,[status(thm)],[c_3449,c_152]) ).
tcf(c_3941,plain,
! [X0: $i] :
( ( apply(sK2,X0) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_65,c_3452]) ).
tcf(c_3964,plain,
! [X0: $i] :
( in(ordered_pair(apply(sK0,X0),apply(sK2,X0)),sK1)
| ( apply(sK2,X0) = empty_set )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(apply(sK0,X0),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_3467,c_73]) ).
tcf(c_3965,plain,
! [X0: $i] :
( in(ordered_pair(apply(sK0,X0),apply(sK2,X0)),sK1)
| ( apply(sK2,X0) = empty_set )
| ~ in(apply(sK0,X0),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3964,c_57,c_56]) ).
tcf(c_3991,plain,
! [X0: $i] :
( in(X0,relation_dom(sK2))
| ( apply(sK2,X0) = empty_set )
| ( apply(sK1,apply(sK0,X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_3449,c_3475]) ).
tcf(c_3992,plain,
! [X0: $i] :
( in(ordered_pair(X0,sK5(relation_dom(sK0),X0)),relation_dom(sK2))
| ( apply(sK1,apply(sK0,ordered_pair(X0,sK5(relation_dom(sK0),X0)))) = empty_set )
| ~ relation(relation_dom(sK0))
| ~ in(X0,relation_dom(relation_dom(sK0))) ),
inference(superposition,[status(thm)],[c_71,c_3475]) ).
tcf(c_3993,plain,
! [X0: $i] :
( in(ordered_pair(X0,apply(relation_dom(sK0),X0)),relation_dom(sK2))
| ( apply(sK1,apply(sK0,ordered_pair(X0,apply(relation_dom(sK0),X0)))) = empty_set )
| ~ function(relation_dom(sK0))
| ~ relation(relation_dom(sK0))
| ~ in(X0,relation_dom(relation_dom(sK0))) ),
inference(superposition,[status(thm)],[c_73,c_3475]) ).
tcf(c_3994,plain,
! [X0: $i] :
( in(X0,relation_dom(sK2))
| ( apply(sK0,X0) = empty_set )
| ( apply(sK1,apply(sK0,X0)) = empty_set )
| ~ function(sK0)
| ~ relation(sK0) ),
inference(superposition,[status(thm)],[c_75,c_3475]) ).
tcf(c_3995,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(ordered_pair(X0,sK12(relation_dom(sK0),X2,X0,X1)),relation_dom(sK2))
| ( apply(sK1,apply(sK0,ordered_pair(X0,sK12(relation_dom(sK0),X2,X0,X1)))) = empty_set )
| ~ relation(X2)
| ~ relation(relation_dom(sK0))
| ~ in(ordered_pair(X0,X1),relation_composition(relation_dom(sK0),X2)) ),
inference(superposition,[status(thm)],[c_301,c_3475]) ).
tcf(c_3996,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(ordered_pair(sK12(X2,relation_dom(sK0),X0,X1),X1),relation_dom(sK2))
| ( apply(sK1,apply(sK0,ordered_pair(sK12(X2,relation_dom(sK0),X0,X1),X1))) = empty_set )
| ~ relation(X2)
| ~ relation(relation_dom(sK0))
| ~ in(ordered_pair(X0,X1),relation_composition(X2,relation_dom(sK0))) ),
inference(superposition,[status(thm)],[c_300,c_3475]) ).
tcf(c_3997,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(ordered_pair(sK12(X2,relation_dom(sK2),X0,X1),X1),relation_dom(sK2))
| ( apply(sK1,apply(sK0,ordered_pair(sK12(X2,relation_dom(sK2),X0,X1),X1))) = empty_set )
| ~ relation(X2)
| ~ relation(relation_dom(sK2))
| ~ in(ordered_pair(X0,X1),relation_composition(X2,relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_2065,c_3475]) ).
tcf(c_3998,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(ordered_pair(X0,sK12(relation_dom(sK2),X2,X0,X1)),relation_dom(sK2))
| ( apply(sK1,apply(sK0,ordered_pair(X0,sK12(relation_dom(sK2),X2,X0,X1)))) = empty_set )
| ~ relation(X2)
| ~ relation(relation_dom(sK2))
| ~ in(ordered_pair(X0,X1),relation_composition(relation_dom(sK2),X2)) ),
inference(superposition,[status(thm)],[c_2283,c_3475]) ).
tcf(c_3999,plain,
( empty(relation_dom(sK0))
| in(sK17(relation_dom(sK0)),relation_dom(sK2))
| ( apply(sK1,apply(sK0,sK17(relation_dom(sK0)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_2361,c_3475]) ).
tcf(c_4000,plain,
( empty(relation_dom(sK2))
| in(sK17(relation_dom(sK2)),relation_dom(sK2))
| ( apply(sK1,apply(sK0,sK17(relation_dom(sK2)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_2426,c_3475]) ).
tcf(c_4001,plain,
! [X0: $i] :
( in(ordered_pair(X0,sK5(relation_dom(sK2),X0)),relation_dom(sK2))
| ( apply(sK1,apply(sK0,ordered_pair(X0,sK5(relation_dom(sK2),X0)))) = empty_set )
| ~ relation(relation_dom(sK2))
| ~ in(X0,relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_3019,c_3475]) ).
tcf(c_4011,plain,
! [X0: $i] :
( in(X0,relation_dom(sK2))
| ( apply(sK0,X0) = empty_set )
| ( apply(sK1,apply(sK0,X0)) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3994,c_59,c_58]) ).
tcf(c_4108,plain,
! [X0: $i] :
( ( apply(sK0,X0) = empty_set )
| ( apply(sK1,apply(sK0,X0)) = empty_set )
| ~ empty(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_4011,c_2047]) ).
tcf(c_4109,plain,
! [X0: $i] :
( ( apply(sK0,X0) = empty_set )
| ( apply(sK1,apply(sK0,X0)) = empty_set )
| ( apply(sK1,apply(sK0,X0)) = apply(sK2,X0) ) ),
inference(superposition,[status(thm)],[c_4011,c_53]) ).
tcf(c_4110,plain,
! [X0: $i] :
( in(X0,relation_dom(sK0))
| ( apply(sK0,X0) = empty_set )
| ( apply(sK1,apply(sK0,X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_4011,c_51]) ).
tcf(c_4111,plain,
! [X0: $i] :
( ( apply(sK0,X0) = empty_set )
| ( apply(sK1,apply(sK0,X0)) = empty_set )
| ~ in(relation_dom(sK2),X0) ),
inference(superposition,[status(thm)],[c_4011,c_64]) ).
tcf(c_4112,plain,
! [X0: $i] :
( element(X0,relation_dom(sK2))
| ( apply(sK0,X0) = empty_set )
| ( apply(sK1,apply(sK0,X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_4011,c_63]) ).
tcf(c_4113,plain,
! [X0: $i] :
( ( apply(sK0,X0) = empty_set )
| ( apply(sK1,apply(sK0,X0)) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4011,c_61]) ).
tcf(c_4114,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK2)) = X0 )
| ( apply(sK0,ordered_pair(sK3(relation_dom(sK2),X0),X1)) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(sK3(relation_dom(sK2),X0),X1))) = empty_set )
| ~ relation(relation_dom(sK2))
| ~ in(sK3(relation_dom(sK2),X0),X0) ),
inference(superposition,[status(thm)],[c_4011,c_68]) ).
tcf(c_4115,plain,
! [X0: $i,X1: $i] :
( in(X0,relation_dom(relation_dom(sK2)))
| ( apply(sK0,ordered_pair(X0,X1)) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(X0,X1))) = empty_set )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4011,c_70]) ).
tcf(c_4116,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(ordered_pair(X3,X1),relation_composition(relation_dom(sK2),X2))
| ( apply(sK0,ordered_pair(X3,X0)) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(X3,X0))) = empty_set )
| ~ relation(X2)
| ~ relation(relation_dom(sK2))
| ~ in(ordered_pair(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_4011,c_299]) ).
tcf(c_4117,plain,
! [X0: $i,X1: $i] :
( ( apply(relation_dom(sK2),X0) = X1 )
| ( apply(sK0,ordered_pair(X0,X1)) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(X0,X1))) = empty_set )
| ~ function(relation_dom(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4011,c_152]) ).
tcf(c_4188,plain,
! [X0: $i] :
( ( apply(sK0,X0) = empty_set )
| ( apply(sK1,apply(sK0,X0)) = empty_set )
| ~ in(relation_dom(sK0),X0) ),
inference(superposition,[status(thm)],[c_4110,c_64]) ).
tcf(c_4189,plain,
! [X0: $i] :
( element(X0,relation_dom(sK0))
| ( apply(sK0,X0) = empty_set )
| ( apply(sK1,apply(sK0,X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_4110,c_63]) ).
tcf(c_4190,plain,
! [X0: $i] :
( ( apply(sK0,X0) = empty_set )
| ( apply(sK1,apply(sK0,X0)) = empty_set )
| ~ empty(relation_dom(sK0)) ),
inference(superposition,[status(thm)],[c_4110,c_61]) ).
tcf(c_4191,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK0)) = X0 )
| ( apply(sK0,ordered_pair(sK3(relation_dom(sK0),X0),X1)) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(sK3(relation_dom(sK0),X0),X1))) = empty_set )
| ~ relation(relation_dom(sK0))
| ~ in(sK3(relation_dom(sK0),X0),X0) ),
inference(superposition,[status(thm)],[c_4110,c_68]) ).
tcf(c_4192,plain,
! [X0: $i,X1: $i] :
( in(X0,relation_dom(relation_dom(sK0)))
| ( apply(sK0,ordered_pair(X0,X1)) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(X0,X1))) = empty_set )
| ~ relation(relation_dom(sK0)) ),
inference(superposition,[status(thm)],[c_4110,c_70]) ).
tcf(c_4193,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(ordered_pair(X3,X1),relation_composition(relation_dom(sK0),X2))
| ( apply(sK0,ordered_pair(X3,X0)) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(X3,X0))) = empty_set )
| ~ relation(X2)
| ~ relation(relation_dom(sK0))
| ~ in(ordered_pair(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_4110,c_299]) ).
tcf(c_4194,plain,
! [X0: $i,X1: $i] :
( ( apply(relation_dom(sK0),X0) = X1 )
| ( apply(sK0,ordered_pair(X0,X1)) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(X0,X1))) = empty_set )
| ~ function(relation_dom(sK0))
| ~ relation(relation_dom(sK0)) ),
inference(superposition,[status(thm)],[c_4110,c_152]) ).
tcf(c_4252,plain,
! [X0: $i] :
( ( apply(sK2,X0) = empty_set )
| ~ in(apply(sK0,X0),relation_dom(sK1))
| ~ in(sK1,ordered_pair(apply(sK0,X0),apply(sK2,X0))) ),
inference(superposition,[status(thm)],[c_3965,c_64]) ).
tcf(c_4253,plain,
! [X0: $i] :
( element(ordered_pair(apply(sK0,X0),apply(sK2,X0)),sK1)
| ( apply(sK2,X0) = empty_set )
| ~ in(apply(sK0,X0),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_3965,c_63]) ).
tcf(c_4256,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(ordered_pair(apply(sK0,X0),X1),relation_composition(sK1,X2))
| ( apply(sK2,X0) = empty_set )
| ~ relation(sK1)
| ~ relation(X2)
| ~ in(apply(sK0,X0),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,X0),X1),X2) ),
inference(superposition,[status(thm)],[c_3965,c_299]) ).
tcf(c_4264,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(ordered_pair(apply(sK0,X0),X1),relation_composition(sK1,X2))
| ( apply(sK2,X0) = empty_set )
| ~ relation(X2)
| ~ in(apply(sK0,X0),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,X0),X1),X2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4256,c_56]) ).
tcf(c_4293,plain,
! [X0: $i] :
( in(ordered_pair(X0,apply(relation_dom(sK2),X0)),relation_dom(sK2))
| ( apply(sK1,apply(sK0,ordered_pair(X0,apply(relation_dom(sK2),X0)))) = empty_set )
| ~ function(relation_dom(sK2))
| ~ relation(relation_dom(sK2))
| ~ in(X0,relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_3551,c_3475]) ).
tcf(c_4294,plain,
! [X0: $i] :
( ~ function(relation_dom(sK2))
| ~ relation(relation_dom(sK2))
| ~ in(X0,relation_dom(relation_dom(sK2)))
| ~ in(relation_dom(sK0),ordered_pair(X0,apply(relation_dom(sK2),X0))) ),
inference(superposition,[status(thm)],[c_3551,c_64]) ).
tcf(c_4295,plain,
! [X0: $i] :
( element(ordered_pair(X0,apply(relation_dom(sK2),X0)),relation_dom(sK0))
| ~ function(relation_dom(sK2))
| ~ relation(relation_dom(sK2))
| ~ in(X0,relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_3551,c_63]) ).
tcf(c_4296,plain,
! [X0: $i] :
( ~ empty(relation_dom(sK0))
| ~ function(relation_dom(sK2))
| ~ relation(relation_dom(sK2))
| ~ in(X0,relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_3551,c_61]) ).
tcf(c_4297,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK0)) = X0 )
| ~ function(relation_dom(sK2))
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(sK3(relation_dom(sK0),X0),X0)
| ~ in(sK3(relation_dom(sK0),X0),relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_3551,c_68]) ).
tcf(c_4298,plain,
! [X0: $i] :
( in(X0,relation_dom(relation_dom(sK0)))
| ~ function(relation_dom(sK2))
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(X0,relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_3551,c_70]) ).
tcf(c_4299,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(ordered_pair(X0,X1),relation_composition(relation_dom(sK0),X2))
| ~ relation(X2)
| ~ function(relation_dom(sK2))
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(X0,relation_dom(relation_dom(sK2)))
| ~ in(ordered_pair(apply(relation_dom(sK2),X0),X1),X2) ),
inference(superposition,[status(thm)],[c_3551,c_299]) ).
tcf(c_4300,plain,
! [X0: $i] :
( ( apply(relation_dom(sK2),X0) = apply(relation_dom(sK0),X0) )
| ~ function(relation_dom(sK0))
| ~ function(relation_dom(sK2))
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(X0,relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_3551,c_152]) ).
tcf(c_4452,plain,
! [X0: $i] :
( in(ordered_pair(X0,empty_set),empty_set)
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ in(X0,relation_dom(empty_set)) ),
inference(superposition,[status(thm)],[c_3835,c_73]) ).
tcf(c_4453,plain,
! [X0: $i] :
( in(ordered_pair(X0,empty_set),empty_set)
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ in(X0,empty_set) ),
inference(light_normalisation,[status(thm)],[c_4452,c_3857]) ).
tcf(c_4462,plain,
! [X0: $i] :
( in(sK3(relation_dom(sK2),X0),X0)
| ( relation_dom(relation_dom(sK2)) = X0 )
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_69,c_2047]) ).
tcf(c_4463,plain,
! [X0: $i] :
( in(sK3(relation_dom(sK2),X0),X0)
| ( relation_dom(relation_dom(sK2)) = X0 )
| ( apply(sK1,apply(sK0,ordered_pair(sK3(relation_dom(sK2),X0),sK4(relation_dom(sK2),X0)))) = apply(sK2,ordered_pair(sK3(relation_dom(sK2),X0),sK4(relation_dom(sK2),X0))) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_69,c_53]) ).
tcf(c_4464,plain,
! [X0: $i] :
( in(sK3(relation_dom(sK2),X0),X0)
| in(ordered_pair(sK3(relation_dom(sK2),X0),sK4(relation_dom(sK2),X0)),relation_dom(sK0))
| ( relation_dom(relation_dom(sK2)) = X0 )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_69,c_51]) ).
tcf(c_4465,plain,
! [X0: $i] :
( in(sK3(relation_dom(sK0),X0),X0)
| in(ordered_pair(sK3(relation_dom(sK0),X0),sK4(relation_dom(sK0),X0)),relation_dom(sK2))
| ( relation_dom(relation_dom(sK0)) = X0 )
| ( apply(sK1,apply(sK0,ordered_pair(sK3(relation_dom(sK0),X0),sK4(relation_dom(sK0),X0)))) = empty_set )
| ~ relation(relation_dom(sK0)) ),
inference(superposition,[status(thm)],[c_69,c_3475]) ).
tcf(c_4466,plain,
! [X0: $i,X1: $i] :
( in(sK3(X0,X1),X1)
| ( relation_dom(X0) = X1 )
| ~ relation(X0)
| ~ in(X0,ordered_pair(sK3(X0,X1),sK4(X0,X1))) ),
inference(superposition,[status(thm)],[c_69,c_64]) ).
tcf(c_4467,plain,
! [X0: $i,X1: $i] :
( in(sK3(X0,X1),X1)
| element(ordered_pair(sK3(X0,X1),sK4(X0,X1)),X0)
| ( relation_dom(X0) = X1 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_69,c_63]) ).
tcf(c_4468,plain,
! [X0: $i,X1: $i] :
( in(sK3(X0,X1),X1)
| ( relation_dom(X0) = X1 )
| ~ empty(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_69,c_61]) ).
tcf(c_4470,plain,
! [X0: $i,X1: $i] :
( in(sK3(X0,X1),X1)
| in(sK3(X0,X1),relation_dom(X0))
| ( relation_dom(X0) = X1 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_69,c_70]) ).
tcf(c_4471,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK3(X0,X1),X1)
| in(ordered_pair(sK3(X0,X1),X2),relation_composition(X0,X3))
| ( relation_dom(X0) = X1 )
| ~ relation(X3)
| ~ relation(X0)
| ~ in(ordered_pair(sK4(X0,X1),X2),X3) ),
inference(superposition,[status(thm)],[c_69,c_299]) ).
tcf(c_4472,plain,
! [X0: $i,X1: $i] :
( in(sK3(X0,X1),X1)
| ( relation_dom(X0) = X1 )
| ( apply(X0,sK3(X0,X1)) = sK4(X0,X1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_69,c_152]) ).
tcf(c_4473,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(relation_composition(X0,X1),X2),X2)
| ( relation_dom(relation_composition(X0,X1)) = X2 )
| ( apply(X1,sK12(X0,X1,sK3(relation_composition(X0,X1),X2),sK4(relation_composition(X0,X1),X2))) = sK4(relation_composition(X0,X1),X2) )
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_composition(X0,X1)) ),
inference(superposition,[status(thm)],[c_69,c_2068]) ).
tcf(c_4474,plain,
! [X0: $i,X1: $i] :
( in(sK3(relation_composition(X0,relation_dom(sK2)),X1),X1)
| ( relation_dom(relation_composition(X0,relation_dom(sK2))) = X1 )
| ~ relation(X0)
| ~ empty(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ relation(relation_composition(X0,relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_69,c_2176]) ).
tcf(c_4475,plain,
! [X0: $i,X1: $i] :
( in(sK3(relation_composition(X0,relation_dom(sK2)),X1),X1)
| ( relation_dom(relation_composition(X0,relation_dom(sK2))) = X1 )
| ~ relation(X0)
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2))
| ~ relation(relation_composition(X0,relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_69,c_2063]) ).
tcf(c_4476,plain,
! [X0: $i,X1: $i] :
( in(sK3(relation_composition(X0,relation_dom(sK2)),X1),X1)
| ( relation_dom(relation_composition(X0,relation_dom(sK2))) = X1 )
| ( apply(sK1,apply(sK0,ordered_pair(sK12(X0,relation_dom(sK2),sK3(relation_composition(X0,relation_dom(sK2)),X1),sK4(relation_composition(X0,relation_dom(sK2)),X1)),sK4(relation_composition(X0,relation_dom(sK2)),X1)))) = apply(sK2,ordered_pair(sK12(X0,relation_dom(sK2),sK3(relation_composition(X0,relation_dom(sK2)),X1),sK4(relation_composition(X0,relation_dom(sK2)),X1)),sK4(relation_composition(X0,relation_dom(sK2)),X1))) )
| ~ relation(X0)
| ~ relation(relation_dom(sK2))
| ~ relation(relation_composition(X0,relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_69,c_2064]) ).
tcf(c_4477,plain,
! [X0: $i,X1: $i] :
( in(sK3(relation_composition(relation_dom(sK2),X0),X1),X1)
| ( relation_dom(relation_composition(relation_dom(sK2),X0)) = X1 )
| ~ relation(X0)
| ~ empty(relation_dom(sK0))
| ~ relation(relation_composition(relation_dom(sK2),X0)) ),
inference(superposition,[status(thm)],[c_69,c_2737]) ).
tcf(c_4478,plain,
! [X0: $i,X1: $i] :
( in(sK3(relation_composition(relation_dom(sK2),X0),X1),X1)
| ( relation_dom(relation_composition(relation_dom(sK2),X0)) = X1 )
| ~ relation(X0)
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2))
| ~ relation(relation_composition(relation_dom(sK2),X0)) ),
inference(superposition,[status(thm)],[c_69,c_2281]) ).
tcf(c_4479,plain,
! [X0: $i,X1: $i] :
( in(sK3(relation_composition(relation_dom(sK2),X0),X1),X1)
| ( relation_dom(relation_composition(relation_dom(sK2),X0)) = X1 )
| ( apply(sK1,apply(sK0,ordered_pair(sK3(relation_composition(relation_dom(sK2),X0),X1),sK12(relation_dom(sK2),X0,sK3(relation_composition(relation_dom(sK2),X0),X1),sK4(relation_composition(relation_dom(sK2),X0),X1))))) = apply(sK2,ordered_pair(sK3(relation_composition(relation_dom(sK2),X0),X1),sK12(relation_dom(sK2),X0,sK3(relation_composition(relation_dom(sK2),X0),X1),sK4(relation_composition(relation_dom(sK2),X0),X1)))) )
| ~ relation(X0)
| ~ relation(relation_dom(sK2))
| ~ relation(relation_composition(relation_dom(sK2),X0)) ),
inference(superposition,[status(thm)],[c_69,c_2282]) ).
tcf(c_4480,plain,
! [X0: $i] :
( in(sK3(empty_set,X0),X0)
| ( relation_dom(empty_set) = X0 )
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_69,c_3809]) ).
tcf(c_4481,plain,
! [X0: $i] :
( in(sK3(relation_dom(relation_dom(sK2)),X0),X0)
| in(ordered_pair(sK3(relation_dom(relation_dom(sK2)),X0),sK4(relation_dom(relation_dom(sK2)),X0)),relation_dom(relation_dom(sK0)))
| ( relation_dom(relation_dom(relation_dom(sK2))) = X0 )
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ relation(relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_69,c_3134]) ).
tcf(c_4482,plain,
! [X0: $i] :
( in(sK3(relation_dom(relation_dom(sK2)),X0),X0)
| ( relation_dom(relation_dom(relation_dom(sK2))) = X0 )
| ~ empty(relation_dom(sK0))
| ~ relation(relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_69,c_3241]) ).
tcf(c_4483,plain,
! [X0: $i] :
( in(sK3(relation_dom(relation_dom(sK2)),X0),X0)
| ( relation_dom(relation_dom(relation_dom(sK2))) = X0 )
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2))
| ~ relation(relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_69,c_3017]) ).
tcf(c_4484,plain,
! [X0: $i] :
( in(sK3(relation_dom(relation_dom(sK2)),X0),X0)
| ( relation_dom(relation_dom(relation_dom(sK2))) = X0 )
| ( apply(sK1,apply(sK0,ordered_pair(ordered_pair(sK3(relation_dom(relation_dom(sK2)),X0),sK4(relation_dom(relation_dom(sK2)),X0)),sK5(relation_dom(sK2),ordered_pair(sK3(relation_dom(relation_dom(sK2)),X0),sK4(relation_dom(relation_dom(sK2)),X0)))))) = apply(sK2,ordered_pair(ordered_pair(sK3(relation_dom(relation_dom(sK2)),X0),sK4(relation_dom(relation_dom(sK2)),X0)),sK5(relation_dom(sK2),ordered_pair(sK3(relation_dom(relation_dom(sK2)),X0),sK4(relation_dom(relation_dom(sK2)),X0))))) )
| ~ relation(relation_dom(sK2))
| ~ relation(relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_69,c_3018]) ).
tcf(c_4485,plain,
! [X0: $i] :
( in(sK3(empty_set,X0),X0)
| ( X0 = empty_set )
| ~ relation(empty_set) ),
inference(light_normalisation,[status(thm)],[c_4480,c_3857]) ).
tcf(c_4486,plain,
! [X0: $i] :
( in(sK3(empty_set,X0),X0)
| ( X0 = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4485,c_109]) ).
tcf(c_4701,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK9(relation_dom(sK2),X0,X1),sK10(relation_dom(sK2),X0,X1)),X1)
| ( relation_composition(relation_dom(sK2),X0) = X1 )
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_92,c_2047]) ).
tcf(c_4702,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK9(relation_dom(sK2),X0,X1),sK10(relation_dom(sK2),X0,X1)),X1)
| ( relation_composition(relation_dom(sK2),X0) = X1 )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(relation_dom(sK2),X0,X1),sK11(relation_dom(sK2),X0,X1)))) = apply(sK2,ordered_pair(sK9(relation_dom(sK2),X0,X1),sK11(relation_dom(sK2),X0,X1))) )
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_92,c_53]) ).
tcf(c_4703,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK9(relation_dom(sK2),X0,X1),sK10(relation_dom(sK2),X0,X1)),X1)
| in(ordered_pair(sK9(relation_dom(sK2),X0,X1),sK11(relation_dom(sK2),X0,X1)),relation_dom(sK0))
| ( relation_composition(relation_dom(sK2),X0) = X1 )
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_92,c_51]) ).
tcf(c_4704,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK9(relation_dom(sK0),X0,X1),sK10(relation_dom(sK0),X0,X1)),X1)
| in(ordered_pair(sK9(relation_dom(sK0),X0,X1),sK11(relation_dom(sK0),X0,X1)),relation_dom(sK2))
| ( relation_composition(relation_dom(sK0),X0) = X1 )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(relation_dom(sK0),X0,X1),sK11(relation_dom(sK0),X0,X1)))) = empty_set )
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK0)) ),
inference(superposition,[status(thm)],[c_92,c_3475]) ).
tcf(c_4705,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(ordered_pair(sK9(X0,X1,X2),sK10(X0,X1,X2)),X2)
| ( relation_composition(X0,X1) = X2 )
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(X0,ordered_pair(sK9(X0,X1,X2),sK11(X0,X1,X2))) ),
inference(superposition,[status(thm)],[c_92,c_64]) ).
tcf(c_4706,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(ordered_pair(sK9(X0,X1,X2),sK11(X0,X1,X2)),X0)
| in(ordered_pair(sK9(X0,X1,X2),sK10(X0,X1,X2)),X2)
| ( relation_composition(X0,X1) = X2 )
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_92,c_63]) ).
tcf(c_4707,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(ordered_pair(sK9(X0,X1,X2),sK10(X0,X1,X2)),X2)
| ( relation_composition(X0,X1) = X2 )
| ~ empty(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_92,c_61]) ).
tcf(c_4708,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK9(X0,X1,X2),relation_dom(X0))
| in(ordered_pair(sK9(X0,X1,X2),sK10(X0,X1,X2)),X2)
| ( relation_composition(X0,X1) = X2 )
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_92,c_70]) ).
tcf(c_4709,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(ordered_pair(sK9(X0,X1,X2),X3),relation_composition(X0,X4))
| in(ordered_pair(sK9(X0,X1,X2),sK10(X0,X1,X2)),X2)
| ( relation_composition(X0,X1) = X2 )
| ~ relation(X4)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(ordered_pair(sK11(X0,X1,X2),X3),X4) ),
inference(superposition,[status(thm)],[c_92,c_299]) ).
tcf(c_4710,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(ordered_pair(sK9(X0,X1,X2),sK10(X0,X1,X2)),X2)
| ( relation_composition(X0,X1) = X2 )
| ( apply(X0,sK9(X0,X1,X2)) = sK11(X0,X1,X2) )
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_92,c_152]) ).
tcf(c_4711,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(ordered_pair(sK9(relation_composition(X0,X1),X2,X3),sK10(relation_composition(X0,X1),X2,X3)),X3)
| ( relation_composition(relation_composition(X0,X1),X2) = X3 )
| ( apply(X1,sK12(X0,X1,sK9(relation_composition(X0,X1),X2,X3),sK11(relation_composition(X0,X1),X2,X3))) = sK11(relation_composition(X0,X1),X2,X3) )
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_composition(X0,X1)) ),
inference(superposition,[status(thm)],[c_92,c_2068]) ).
tcf(c_4712,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(ordered_pair(sK9(relation_composition(X0,relation_dom(sK2)),X1,X2),sK10(relation_composition(X0,relation_dom(sK2)),X1,X2)),X2)
| ( relation_composition(relation_composition(X0,relation_dom(sK2)),X1) = X2 )
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ relation(relation_composition(X0,relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_92,c_2176]) ).
tcf(c_4713,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(ordered_pair(sK9(relation_composition(X0,relation_dom(sK2)),X1,X2),sK10(relation_composition(X0,relation_dom(sK2)),X1,X2)),X2)
| ( relation_composition(relation_composition(X0,relation_dom(sK2)),X1) = X2 )
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2))
| ~ relation(relation_composition(X0,relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_92,c_2063]) ).
tcf(c_4714,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(ordered_pair(sK9(relation_composition(X0,relation_dom(sK2)),X1,X2),sK10(relation_composition(X0,relation_dom(sK2)),X1,X2)),X2)
| ( relation_composition(relation_composition(X0,relation_dom(sK2)),X1) = X2 )
| ( apply(sK1,apply(sK0,ordered_pair(sK12(X0,relation_dom(sK2),sK9(relation_composition(X0,relation_dom(sK2)),X1,X2),sK11(relation_composition(X0,relation_dom(sK2)),X1,X2)),sK11(relation_composition(X0,relation_dom(sK2)),X1,X2)))) = apply(sK2,ordered_pair(sK12(X0,relation_dom(sK2),sK9(relation_composition(X0,relation_dom(sK2)),X1,X2),sK11(relation_composition(X0,relation_dom(sK2)),X1,X2)),sK11(relation_composition(X0,relation_dom(sK2)),X1,X2))) )
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2))
| ~ relation(relation_composition(X0,relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_92,c_2064]) ).
tcf(c_4715,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(ordered_pair(sK9(relation_composition(relation_dom(sK2),X0),X1,X2),sK10(relation_composition(relation_dom(sK2),X0),X1,X2)),X2)
| ( relation_composition(relation_composition(relation_dom(sK2),X0),X1) = X2 )
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(sK0))
| ~ relation(relation_composition(relation_dom(sK2),X0)) ),
inference(superposition,[status(thm)],[c_92,c_2737]) ).
tcf(c_4716,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(ordered_pair(sK9(relation_composition(relation_dom(sK2),X0),X1,X2),sK10(relation_composition(relation_dom(sK2),X0),X1,X2)),X2)
| ( relation_composition(relation_composition(relation_dom(sK2),X0),X1) = X2 )
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2))
| ~ relation(relation_composition(relation_dom(sK2),X0)) ),
inference(superposition,[status(thm)],[c_92,c_2281]) ).
tcf(c_4717,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(ordered_pair(sK9(relation_composition(relation_dom(sK2),X0),X1,X2),sK10(relation_composition(relation_dom(sK2),X0),X1,X2)),X2)
| ( relation_composition(relation_composition(relation_dom(sK2),X0),X1) = X2 )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(relation_composition(relation_dom(sK2),X0),X1,X2),sK12(relation_dom(sK2),X0,sK9(relation_composition(relation_dom(sK2),X0),X1,X2),sK11(relation_composition(relation_dom(sK2),X0),X1,X2))))) = apply(sK2,ordered_pair(sK9(relation_composition(relation_dom(sK2),X0),X1,X2),sK12(relation_dom(sK2),X0,sK9(relation_composition(relation_dom(sK2),X0),X1,X2),sK11(relation_composition(relation_dom(sK2),X0),X1,X2)))) )
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2))
| ~ relation(relation_composition(relation_dom(sK2),X0)) ),
inference(superposition,[status(thm)],[c_92,c_2282]) ).
tcf(c_4718,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK9(empty_set,X0,X1),sK10(empty_set,X0,X1)),X1)
| ( relation_composition(empty_set,X0) = X1 )
| ~ relation(empty_set)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_92,c_3809]) ).
tcf(c_4719,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK9(relation_dom(relation_dom(sK2)),X0,X1),sK10(relation_dom(relation_dom(sK2)),X0,X1)),X1)
| in(ordered_pair(sK9(relation_dom(relation_dom(sK2)),X0,X1),sK11(relation_dom(relation_dom(sK2)),X0,X1)),relation_dom(relation_dom(sK0)))
| ( relation_composition(relation_dom(relation_dom(sK2)),X0) = X1 )
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ relation(relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_92,c_3134]) ).
tcf(c_4720,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK9(relation_dom(relation_dom(sK2)),X0,X1),sK10(relation_dom(relation_dom(sK2)),X0,X1)),X1)
| ( relation_composition(relation_dom(relation_dom(sK2)),X0) = X1 )
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(sK0))
| ~ relation(relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_92,c_3241]) ).
tcf(c_4721,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK9(relation_dom(relation_dom(sK2)),X0,X1),sK10(relation_dom(relation_dom(sK2)),X0,X1)),X1)
| ( relation_composition(relation_dom(relation_dom(sK2)),X0) = X1 )
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2))
| ~ relation(relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_92,c_3017]) ).
tcf(c_4722,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK9(relation_dom(relation_dom(sK2)),X0,X1),sK10(relation_dom(relation_dom(sK2)),X0,X1)),X1)
| ( relation_composition(relation_dom(relation_dom(sK2)),X0) = X1 )
| ( apply(sK1,apply(sK0,ordered_pair(ordered_pair(sK9(relation_dom(relation_dom(sK2)),X0,X1),sK11(relation_dom(relation_dom(sK2)),X0,X1)),sK5(relation_dom(sK2),ordered_pair(sK9(relation_dom(relation_dom(sK2)),X0,X1),sK11(relation_dom(relation_dom(sK2)),X0,X1)))))) = apply(sK2,ordered_pair(ordered_pair(sK9(relation_dom(relation_dom(sK2)),X0,X1),sK11(relation_dom(relation_dom(sK2)),X0,X1)),sK5(relation_dom(sK2),ordered_pair(sK9(relation_dom(relation_dom(sK2)),X0,X1),sK11(relation_dom(relation_dom(sK2)),X0,X1))))) )
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2))
| ~ relation(relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_92,c_3018]) ).
tcf(c_4723,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK9(X0,X1,relation_dom(sK2)),sK11(X0,X1,relation_dom(sK2))),X0)
| ( relation_composition(X0,X1) = relation_dom(sK2) )
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_92,c_2047]) ).
tcf(c_4724,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK9(X0,X1,relation_dom(sK2)),sK11(X0,X1,relation_dom(sK2))),X0)
| ( relation_composition(X0,X1) = relation_dom(sK2) )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(X0,X1,relation_dom(sK2)),sK10(X0,X1,relation_dom(sK2))))) = apply(sK2,ordered_pair(sK9(X0,X1,relation_dom(sK2)),sK10(X0,X1,relation_dom(sK2)))) )
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_92,c_53]) ).
tcf(c_4725,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK9(X0,X1,relation_dom(sK2)),sK11(X0,X1,relation_dom(sK2))),X0)
| in(ordered_pair(sK9(X0,X1,relation_dom(sK2)),sK10(X0,X1,relation_dom(sK2))),relation_dom(sK0))
| ( relation_composition(X0,X1) = relation_dom(sK2) )
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_92,c_51]) ).
tcf(c_4726,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK9(X0,X1,relation_dom(sK0)),sK11(X0,X1,relation_dom(sK0))),X0)
| in(ordered_pair(sK9(X0,X1,relation_dom(sK0)),sK10(X0,X1,relation_dom(sK0))),relation_dom(sK2))
| ( relation_composition(X0,X1) = relation_dom(sK0) )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(X0,X1,relation_dom(sK0)),sK10(X0,X1,relation_dom(sK0))))) = empty_set )
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK0)) ),
inference(superposition,[status(thm)],[c_92,c_3475]) ).
tcf(c_4727,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(ordered_pair(sK9(X1,X2,X0),sK11(X1,X2,X0)),X1)
| ( relation_composition(X1,X2) = X0 )
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(X0,ordered_pair(sK9(X1,X2,X0),sK10(X1,X2,X0))) ),
inference(superposition,[status(thm)],[c_92,c_64]) ).
tcf(c_4728,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(ordered_pair(sK9(X0,X1,X2),sK10(X0,X1,X2)),X2)
| in(ordered_pair(sK9(X0,X1,X2),sK11(X0,X1,X2)),X0)
| ( relation_composition(X0,X1) = X2 )
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_92,c_63]) ).
tcf(c_4729,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(ordered_pair(sK9(X0,X1,X2),sK11(X0,X1,X2)),X0)
| ( relation_composition(X0,X1) = X2 )
| ~ empty(X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_92,c_61]) ).
tcf(c_4730,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK9(X0,X1,X2),relation_dom(X2))
| in(ordered_pair(sK9(X0,X1,X2),sK11(X0,X1,X2)),X0)
| ( relation_composition(X0,X1) = X2 )
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_92,c_70]) ).
tcf(c_4731,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(ordered_pair(sK9(X0,X1,X2),X3),relation_composition(X2,X4))
| in(ordered_pair(sK9(X0,X1,X2),sK11(X0,X1,X2)),X0)
| ( relation_composition(X0,X1) = X2 )
| ~ relation(X4)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(ordered_pair(sK10(X0,X1,X2),X3),X4) ),
inference(superposition,[status(thm)],[c_92,c_299]) ).
tcf(c_4732,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(ordered_pair(sK9(X0,X1,X2),sK11(X0,X1,X2)),X0)
| ( relation_composition(X0,X1) = X2 )
| ( apply(X2,sK9(X0,X1,X2)) = sK10(X0,X1,X2) )
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_92,c_152]) ).
tcf(c_4733,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(ordered_pair(sK9(X2,X3,relation_composition(X0,X1)),sK11(X2,X3,relation_composition(X0,X1))),X2)
| ( relation_composition(X0,X1) = relation_composition(X2,X3) )
| ( apply(X1,sK12(X0,X1,sK9(X2,X3,relation_composition(X0,X1)),sK10(X2,X3,relation_composition(X0,X1)))) = sK10(X2,X3,relation_composition(X0,X1)) )
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_composition(X0,X1)) ),
inference(superposition,[status(thm)],[c_92,c_2068]) ).
tcf(c_4734,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(ordered_pair(sK9(X1,X2,relation_composition(X0,relation_dom(sK2))),sK11(X1,X2,relation_composition(X0,relation_dom(sK2)))),X1)
| ( relation_composition(X0,relation_dom(sK2)) = relation_composition(X1,X2) )
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ relation(relation_composition(X0,relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_92,c_2176]) ).
tcf(c_4735,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(ordered_pair(sK9(X1,X2,relation_composition(X0,relation_dom(sK2))),sK11(X1,X2,relation_composition(X0,relation_dom(sK2)))),X1)
| ( relation_composition(X0,relation_dom(sK2)) = relation_composition(X1,X2) )
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2))
| ~ relation(relation_composition(X0,relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_92,c_2063]) ).
tcf(c_4736,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(ordered_pair(sK9(X1,X2,relation_composition(X0,relation_dom(sK2))),sK11(X1,X2,relation_composition(X0,relation_dom(sK2)))),X1)
| ( relation_composition(X0,relation_dom(sK2)) = relation_composition(X1,X2) )
| ( apply(sK1,apply(sK0,ordered_pair(sK12(X0,relation_dom(sK2),sK9(X1,X2,relation_composition(X0,relation_dom(sK2))),sK10(X1,X2,relation_composition(X0,relation_dom(sK2)))),sK10(X1,X2,relation_composition(X0,relation_dom(sK2)))))) = apply(sK2,ordered_pair(sK12(X0,relation_dom(sK2),sK9(X1,X2,relation_composition(X0,relation_dom(sK2))),sK10(X1,X2,relation_composition(X0,relation_dom(sK2)))),sK10(X1,X2,relation_composition(X0,relation_dom(sK2))))) )
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2))
| ~ relation(relation_composition(X0,relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_92,c_2064]) ).
tcf(c_4737,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(ordered_pair(sK9(X1,X2,relation_composition(relation_dom(sK2),X0)),sK11(X1,X2,relation_composition(relation_dom(sK2),X0))),X1)
| ( relation_composition(relation_dom(sK2),X0) = relation_composition(X1,X2) )
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(sK0))
| ~ relation(relation_composition(relation_dom(sK2),X0)) ),
inference(superposition,[status(thm)],[c_92,c_2737]) ).
tcf(c_4738,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(ordered_pair(sK9(X1,X2,relation_composition(relation_dom(sK2),X0)),sK11(X1,X2,relation_composition(relation_dom(sK2),X0))),X1)
| ( relation_composition(relation_dom(sK2),X0) = relation_composition(X1,X2) )
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2))
| ~ relation(relation_composition(relation_dom(sK2),X0)) ),
inference(superposition,[status(thm)],[c_92,c_2281]) ).
tcf(c_4739,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(ordered_pair(sK9(X1,X2,relation_composition(relation_dom(sK2),X0)),sK11(X1,X2,relation_composition(relation_dom(sK2),X0))),X1)
| ( relation_composition(relation_dom(sK2),X0) = relation_composition(X1,X2) )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(X1,X2,relation_composition(relation_dom(sK2),X0)),sK12(relation_dom(sK2),X0,sK9(X1,X2,relation_composition(relation_dom(sK2),X0)),sK10(X1,X2,relation_composition(relation_dom(sK2),X0)))))) = apply(sK2,ordered_pair(sK9(X1,X2,relation_composition(relation_dom(sK2),X0)),sK12(relation_dom(sK2),X0,sK9(X1,X2,relation_composition(relation_dom(sK2),X0)),sK10(X1,X2,relation_composition(relation_dom(sK2),X0))))) )
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2))
| ~ relation(relation_composition(relation_dom(sK2),X0)) ),
inference(superposition,[status(thm)],[c_92,c_2282]) ).
tcf(c_4740,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK9(X0,X1,empty_set),sK11(X0,X1,empty_set)),X0)
| ( relation_composition(X0,X1) = empty_set )
| ~ relation(empty_set)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_92,c_3809]) ).
tcf(c_4741,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK9(X0,X1,relation_dom(relation_dom(sK2))),sK11(X0,X1,relation_dom(relation_dom(sK2)))),X0)
| in(ordered_pair(sK9(X0,X1,relation_dom(relation_dom(sK2))),sK10(X0,X1,relation_dom(relation_dom(sK2)))),relation_dom(relation_dom(sK0)))
| ( relation_composition(X0,X1) = relation_dom(relation_dom(sK2)) )
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ relation(relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_92,c_3134]) ).
tcf(c_4742,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK9(X0,X1,relation_dom(relation_dom(sK2))),sK11(X0,X1,relation_dom(relation_dom(sK2)))),X0)
| ( relation_composition(X0,X1) = relation_dom(relation_dom(sK2)) )
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(sK0))
| ~ relation(relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_92,c_3241]) ).
tcf(c_4743,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK9(X0,X1,relation_dom(relation_dom(sK2))),sK11(X0,X1,relation_dom(relation_dom(sK2)))),X0)
| ( relation_composition(X0,X1) = relation_dom(relation_dom(sK2)) )
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2))
| ~ relation(relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_92,c_3017]) ).
tcf(c_4744,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK9(X0,X1,relation_dom(relation_dom(sK2))),sK11(X0,X1,relation_dom(relation_dom(sK2)))),X0)
| ( relation_composition(X0,X1) = relation_dom(relation_dom(sK2)) )
| ( apply(sK1,apply(sK0,ordered_pair(ordered_pair(sK9(X0,X1,relation_dom(relation_dom(sK2))),sK10(X0,X1,relation_dom(relation_dom(sK2)))),sK5(relation_dom(sK2),ordered_pair(sK9(X0,X1,relation_dom(relation_dom(sK2))),sK10(X0,X1,relation_dom(relation_dom(sK2)))))))) = apply(sK2,ordered_pair(ordered_pair(sK9(X0,X1,relation_dom(relation_dom(sK2))),sK10(X0,X1,relation_dom(relation_dom(sK2)))),sK5(relation_dom(sK2),ordered_pair(sK9(X0,X1,relation_dom(relation_dom(sK2))),sK10(X0,X1,relation_dom(relation_dom(sK2))))))) )
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2))
| ~ relation(relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_92,c_3018]) ).
tcf(c_4745,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK9(X0,X1,empty_set),sK11(X0,X1,empty_set)),X0)
| ( relation_composition(X0,X1) = empty_set )
| ~ relation(X1)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4740,c_109]) ).
tcf(c_4750,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK9(empty_set,X0,X1),sK10(empty_set,X0,X1)),X1)
| ( relation_composition(empty_set,X0) = X1 )
| ~ relation(X1)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4718,c_109]) ).
tcf(c_5255,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK9(X0,relation_dom(sK2),X1),sK10(X0,relation_dom(sK2),X1)),X1)
| ( relation_composition(X0,relation_dom(sK2)) = X1 )
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_93,c_2047]) ).
tcf(c_5256,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK9(X0,relation_dom(sK2),X1),sK10(X0,relation_dom(sK2),X1)),X1)
| ( relation_composition(X0,relation_dom(sK2)) = X1 )
| ( apply(sK1,apply(sK0,ordered_pair(sK11(X0,relation_dom(sK2),X1),sK10(X0,relation_dom(sK2),X1)))) = apply(sK2,ordered_pair(sK11(X0,relation_dom(sK2),X1),sK10(X0,relation_dom(sK2),X1))) )
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_93,c_53]) ).
tcf(c_5257,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK9(X0,relation_dom(sK2),X1),sK10(X0,relation_dom(sK2),X1)),X1)
| in(ordered_pair(sK11(X0,relation_dom(sK2),X1),sK10(X0,relation_dom(sK2),X1)),relation_dom(sK0))
| ( relation_composition(X0,relation_dom(sK2)) = X1 )
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_93,c_51]) ).
tcf(c_5258,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK9(X0,relation_dom(sK0),X1),sK10(X0,relation_dom(sK0),X1)),X1)
| in(ordered_pair(sK11(X0,relation_dom(sK0),X1),sK10(X0,relation_dom(sK0),X1)),relation_dom(sK2))
| ( relation_composition(X0,relation_dom(sK0)) = X1 )
| ( apply(sK1,apply(sK0,ordered_pair(sK11(X0,relation_dom(sK0),X1),sK10(X0,relation_dom(sK0),X1)))) = empty_set )
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK0)) ),
inference(superposition,[status(thm)],[c_93,c_3475]) ).
tcf(c_5259,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(ordered_pair(sK9(X1,X0,X2),sK10(X1,X0,X2)),X2)
| ( relation_composition(X1,X0) = X2 )
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(X0,ordered_pair(sK11(X1,X0,X2),sK10(X1,X0,X2))) ),
inference(superposition,[status(thm)],[c_93,c_64]) ).
tcf(c_5260,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(ordered_pair(sK11(X0,X1,X2),sK10(X0,X1,X2)),X1)
| in(ordered_pair(sK9(X0,X1,X2),sK10(X0,X1,X2)),X2)
| ( relation_composition(X0,X1) = X2 )
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_93,c_63]) ).
tcf(c_5261,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(ordered_pair(sK9(X0,X1,X2),sK10(X0,X1,X2)),X2)
| ( relation_composition(X0,X1) = X2 )
| ~ empty(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_93,c_61]) ).
tcf(c_5262,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(X0,X1,X2),relation_dom(X1))
| in(ordered_pair(sK9(X0,X1,X2),sK10(X0,X1,X2)),X2)
| ( relation_composition(X0,X1) = X2 )
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_93,c_70]) ).
tcf(c_5263,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(ordered_pair(sK11(X0,X1,X2),X3),relation_composition(X1,X4))
| in(ordered_pair(sK9(X0,X1,X2),sK10(X0,X1,X2)),X2)
| ( relation_composition(X0,X1) = X2 )
| ~ relation(X4)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(ordered_pair(sK10(X0,X1,X2),X3),X4) ),
inference(superposition,[status(thm)],[c_93,c_299]) ).
tcf(c_5264,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(ordered_pair(sK9(X0,X1,X2),sK10(X0,X1,X2)),X2)
| ( relation_composition(X0,X1) = X2 )
| ( apply(X1,sK11(X0,X1,X2)) = sK10(X0,X1,X2) )
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_93,c_152]) ).
tcf(c_5265,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(ordered_pair(sK9(X2,relation_composition(X0,X1),X3),sK10(X2,relation_composition(X0,X1),X3)),X3)
| ( relation_composition(X2,relation_composition(X0,X1)) = X3 )
| ( apply(X1,sK12(X0,X1,sK11(X2,relation_composition(X0,X1),X3),sK10(X2,relation_composition(X0,X1),X3))) = sK10(X2,relation_composition(X0,X1),X3) )
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_composition(X0,X1)) ),
inference(superposition,[status(thm)],[c_93,c_2068]) ).
tcf(c_5266,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(ordered_pair(sK9(X1,relation_composition(X0,relation_dom(sK2)),X2),sK10(X1,relation_composition(X0,relation_dom(sK2)),X2)),X2)
| ( relation_composition(X1,relation_composition(X0,relation_dom(sK2))) = X2 )
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ relation(relation_composition(X0,relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_93,c_2176]) ).
tcf(c_5267,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(ordered_pair(sK9(X1,relation_composition(X0,relation_dom(sK2)),X2),sK10(X1,relation_composition(X0,relation_dom(sK2)),X2)),X2)
| ( relation_composition(X1,relation_composition(X0,relation_dom(sK2))) = X2 )
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2))
| ~ relation(relation_composition(X0,relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_93,c_2063]) ).
tcf(c_5268,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(ordered_pair(sK9(X1,relation_composition(X0,relation_dom(sK2)),X2),sK10(X1,relation_composition(X0,relation_dom(sK2)),X2)),X2)
| ( relation_composition(X1,relation_composition(X0,relation_dom(sK2))) = X2 )
| ( apply(sK1,apply(sK0,ordered_pair(sK12(X0,relation_dom(sK2),sK11(X1,relation_composition(X0,relation_dom(sK2)),X2),sK10(X1,relation_composition(X0,relation_dom(sK2)),X2)),sK10(X1,relation_composition(X0,relation_dom(sK2)),X2)))) = apply(sK2,ordered_pair(sK12(X0,relation_dom(sK2),sK11(X1,relation_composition(X0,relation_dom(sK2)),X2),sK10(X1,relation_composition(X0,relation_dom(sK2)),X2)),sK10(X1,relation_composition(X0,relation_dom(sK2)),X2))) )
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2))
| ~ relation(relation_composition(X0,relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_93,c_2064]) ).
tcf(c_5269,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(ordered_pair(sK9(X1,relation_composition(relation_dom(sK2),X0),X2),sK10(X1,relation_composition(relation_dom(sK2),X0),X2)),X2)
| ( relation_composition(X1,relation_composition(relation_dom(sK2),X0)) = X2 )
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(sK0))
| ~ relation(relation_composition(relation_dom(sK2),X0)) ),
inference(superposition,[status(thm)],[c_93,c_2737]) ).
tcf(c_5270,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(ordered_pair(sK9(X1,relation_composition(relation_dom(sK2),X0),X2),sK10(X1,relation_composition(relation_dom(sK2),X0),X2)),X2)
| ( relation_composition(X1,relation_composition(relation_dom(sK2),X0)) = X2 )
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2))
| ~ relation(relation_composition(relation_dom(sK2),X0)) ),
inference(superposition,[status(thm)],[c_93,c_2281]) ).
tcf(c_5271,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(ordered_pair(sK9(X1,relation_composition(relation_dom(sK2),X0),X2),sK10(X1,relation_composition(relation_dom(sK2),X0),X2)),X2)
| ( relation_composition(X1,relation_composition(relation_dom(sK2),X0)) = X2 )
| ( apply(sK1,apply(sK0,ordered_pair(sK11(X1,relation_composition(relation_dom(sK2),X0),X2),sK12(relation_dom(sK2),X0,sK11(X1,relation_composition(relation_dom(sK2),X0),X2),sK10(X1,relation_composition(relation_dom(sK2),X0),X2))))) = apply(sK2,ordered_pair(sK11(X1,relation_composition(relation_dom(sK2),X0),X2),sK12(relation_dom(sK2),X0,sK11(X1,relation_composition(relation_dom(sK2),X0),X2),sK10(X1,relation_composition(relation_dom(sK2),X0),X2)))) )
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2))
| ~ relation(relation_composition(relation_dom(sK2),X0)) ),
inference(superposition,[status(thm)],[c_93,c_2282]) ).
tcf(c_5272,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK9(X0,empty_set,X1),sK10(X0,empty_set,X1)),X1)
| ( relation_composition(X0,empty_set) = X1 )
| ~ relation(empty_set)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_93,c_3809]) ).
tcf(c_5273,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK9(X0,relation_dom(relation_dom(sK2)),X1),sK10(X0,relation_dom(relation_dom(sK2)),X1)),X1)
| in(ordered_pair(sK11(X0,relation_dom(relation_dom(sK2)),X1),sK10(X0,relation_dom(relation_dom(sK2)),X1)),relation_dom(relation_dom(sK0)))
| ( relation_composition(X0,relation_dom(relation_dom(sK2))) = X1 )
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ relation(relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_93,c_3134]) ).
tcf(c_5274,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK9(X0,relation_dom(relation_dom(sK2)),X1),sK10(X0,relation_dom(relation_dom(sK2)),X1)),X1)
| ( relation_composition(X0,relation_dom(relation_dom(sK2))) = X1 )
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(sK0))
| ~ relation(relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_93,c_3241]) ).
tcf(c_5275,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK9(X0,relation_dom(relation_dom(sK2)),X1),sK10(X0,relation_dom(relation_dom(sK2)),X1)),X1)
| ( relation_composition(X0,relation_dom(relation_dom(sK2))) = X1 )
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2))
| ~ relation(relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_93,c_3017]) ).
tcf(c_5276,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK9(X0,relation_dom(relation_dom(sK2)),X1),sK10(X0,relation_dom(relation_dom(sK2)),X1)),X1)
| ( relation_composition(X0,relation_dom(relation_dom(sK2))) = X1 )
| ( apply(sK1,apply(sK0,ordered_pair(ordered_pair(sK11(X0,relation_dom(relation_dom(sK2)),X1),sK10(X0,relation_dom(relation_dom(sK2)),X1)),sK5(relation_dom(sK2),ordered_pair(sK11(X0,relation_dom(relation_dom(sK2)),X1),sK10(X0,relation_dom(relation_dom(sK2)),X1)))))) = apply(sK2,ordered_pair(ordered_pair(sK11(X0,relation_dom(relation_dom(sK2)),X1),sK10(X0,relation_dom(relation_dom(sK2)),X1)),sK5(relation_dom(sK2),ordered_pair(sK11(X0,relation_dom(relation_dom(sK2)),X1),sK10(X0,relation_dom(relation_dom(sK2)),X1))))) )
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2))
| ~ relation(relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_93,c_3018]) ).
tcf(c_5277,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK11(X0,X1,relation_dom(sK2)),sK10(X0,X1,relation_dom(sK2))),X1)
| ( relation_composition(X0,X1) = relation_dom(sK2) )
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_93,c_2047]) ).
tcf(c_5278,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK11(X0,X1,relation_dom(sK2)),sK10(X0,X1,relation_dom(sK2))),X1)
| ( relation_composition(X0,X1) = relation_dom(sK2) )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(X0,X1,relation_dom(sK2)),sK10(X0,X1,relation_dom(sK2))))) = apply(sK2,ordered_pair(sK9(X0,X1,relation_dom(sK2)),sK10(X0,X1,relation_dom(sK2)))) )
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_93,c_53]) ).
tcf(c_5279,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK11(X0,X1,relation_dom(sK2)),sK10(X0,X1,relation_dom(sK2))),X1)
| in(ordered_pair(sK9(X0,X1,relation_dom(sK2)),sK10(X0,X1,relation_dom(sK2))),relation_dom(sK0))
| ( relation_composition(X0,X1) = relation_dom(sK2) )
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_93,c_51]) ).
tcf(c_5280,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK11(X0,X1,relation_dom(sK0)),sK10(X0,X1,relation_dom(sK0))),X1)
| in(ordered_pair(sK9(X0,X1,relation_dom(sK0)),sK10(X0,X1,relation_dom(sK0))),relation_dom(sK2))
| ( relation_composition(X0,X1) = relation_dom(sK0) )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(X0,X1,relation_dom(sK0)),sK10(X0,X1,relation_dom(sK0))))) = empty_set )
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK0)) ),
inference(superposition,[status(thm)],[c_93,c_3475]) ).
tcf(c_5281,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(ordered_pair(sK11(X1,X2,X0),sK10(X1,X2,X0)),X2)
| ( relation_composition(X1,X2) = X0 )
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(X0,ordered_pair(sK9(X1,X2,X0),sK10(X1,X2,X0))) ),
inference(superposition,[status(thm)],[c_93,c_64]) ).
tcf(c_5282,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(ordered_pair(sK9(X0,X1,X2),sK10(X0,X1,X2)),X2)
| in(ordered_pair(sK11(X0,X1,X2),sK10(X0,X1,X2)),X1)
| ( relation_composition(X0,X1) = X2 )
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_93,c_63]) ).
tcf(c_5283,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(ordered_pair(sK11(X0,X1,X2),sK10(X0,X1,X2)),X1)
| ( relation_composition(X0,X1) = X2 )
| ~ empty(X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_93,c_61]) ).
tcf(c_5284,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK9(X0,X1,X2),relation_dom(X2))
| in(ordered_pair(sK11(X0,X1,X2),sK10(X0,X1,X2)),X1)
| ( relation_composition(X0,X1) = X2 )
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_93,c_70]) ).
tcf(c_5285,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(ordered_pair(sK9(X0,X1,X2),X3),relation_composition(X2,X4))
| in(ordered_pair(sK11(X0,X1,X2),sK10(X0,X1,X2)),X1)
| ( relation_composition(X0,X1) = X2 )
| ~ relation(X4)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(ordered_pair(sK10(X0,X1,X2),X3),X4) ),
inference(superposition,[status(thm)],[c_93,c_299]) ).
tcf(c_5286,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(ordered_pair(sK11(X0,X1,X2),sK10(X0,X1,X2)),X1)
| ( relation_composition(X0,X1) = X2 )
| ( apply(X2,sK9(X0,X1,X2)) = sK10(X0,X1,X2) )
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_93,c_152]) ).
tcf(c_5287,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(ordered_pair(sK11(X2,X3,relation_composition(X0,X1)),sK10(X2,X3,relation_composition(X0,X1))),X3)
| ( relation_composition(X0,X1) = relation_composition(X2,X3) )
| ( apply(X1,sK12(X0,X1,sK9(X2,X3,relation_composition(X0,X1)),sK10(X2,X3,relation_composition(X0,X1)))) = sK10(X2,X3,relation_composition(X0,X1)) )
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_composition(X0,X1)) ),
inference(superposition,[status(thm)],[c_93,c_2068]) ).
tcf(c_5288,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(ordered_pair(sK11(X1,X2,relation_composition(X0,relation_dom(sK2))),sK10(X1,X2,relation_composition(X0,relation_dom(sK2)))),X2)
| ( relation_composition(X0,relation_dom(sK2)) = relation_composition(X1,X2) )
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ relation(relation_composition(X0,relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_93,c_2176]) ).
tcf(c_5289,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(ordered_pair(sK11(X1,X2,relation_composition(X0,relation_dom(sK2))),sK10(X1,X2,relation_composition(X0,relation_dom(sK2)))),X2)
| ( relation_composition(X0,relation_dom(sK2)) = relation_composition(X1,X2) )
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2))
| ~ relation(relation_composition(X0,relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_93,c_2063]) ).
tcf(c_5290,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(ordered_pair(sK11(X1,X2,relation_composition(X0,relation_dom(sK2))),sK10(X1,X2,relation_composition(X0,relation_dom(sK2)))),X2)
| ( relation_composition(X0,relation_dom(sK2)) = relation_composition(X1,X2) )
| ( apply(sK1,apply(sK0,ordered_pair(sK12(X0,relation_dom(sK2),sK9(X1,X2,relation_composition(X0,relation_dom(sK2))),sK10(X1,X2,relation_composition(X0,relation_dom(sK2)))),sK10(X1,X2,relation_composition(X0,relation_dom(sK2)))))) = apply(sK2,ordered_pair(sK12(X0,relation_dom(sK2),sK9(X1,X2,relation_composition(X0,relation_dom(sK2))),sK10(X1,X2,relation_composition(X0,relation_dom(sK2)))),sK10(X1,X2,relation_composition(X0,relation_dom(sK2))))) )
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2))
| ~ relation(relation_composition(X0,relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_93,c_2064]) ).
tcf(c_5291,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(ordered_pair(sK11(X1,X2,relation_composition(relation_dom(sK2),X0)),sK10(X1,X2,relation_composition(relation_dom(sK2),X0))),X2)
| ( relation_composition(relation_dom(sK2),X0) = relation_composition(X1,X2) )
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(sK0))
| ~ relation(relation_composition(relation_dom(sK2),X0)) ),
inference(superposition,[status(thm)],[c_93,c_2737]) ).
tcf(c_5292,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(ordered_pair(sK11(X1,X2,relation_composition(relation_dom(sK2),X0)),sK10(X1,X2,relation_composition(relation_dom(sK2),X0))),X2)
| ( relation_composition(relation_dom(sK2),X0) = relation_composition(X1,X2) )
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2))
| ~ relation(relation_composition(relation_dom(sK2),X0)) ),
inference(superposition,[status(thm)],[c_93,c_2281]) ).
tcf(c_5293,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(ordered_pair(sK11(X1,X2,relation_composition(relation_dom(sK2),X0)),sK10(X1,X2,relation_composition(relation_dom(sK2),X0))),X2)
| ( relation_composition(relation_dom(sK2),X0) = relation_composition(X1,X2) )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(X1,X2,relation_composition(relation_dom(sK2),X0)),sK12(relation_dom(sK2),X0,sK9(X1,X2,relation_composition(relation_dom(sK2),X0)),sK10(X1,X2,relation_composition(relation_dom(sK2),X0)))))) = apply(sK2,ordered_pair(sK9(X1,X2,relation_composition(relation_dom(sK2),X0)),sK12(relation_dom(sK2),X0,sK9(X1,X2,relation_composition(relation_dom(sK2),X0)),sK10(X1,X2,relation_composition(relation_dom(sK2),X0))))) )
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2))
| ~ relation(relation_composition(relation_dom(sK2),X0)) ),
inference(superposition,[status(thm)],[c_93,c_2282]) ).
tcf(c_5294,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK11(X0,X1,empty_set),sK10(X0,X1,empty_set)),X1)
| ( relation_composition(X0,X1) = empty_set )
| ~ relation(empty_set)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_93,c_3809]) ).
tcf(c_5295,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK11(X0,X1,relation_dom(relation_dom(sK2))),sK10(X0,X1,relation_dom(relation_dom(sK2)))),X1)
| in(ordered_pair(sK9(X0,X1,relation_dom(relation_dom(sK2))),sK10(X0,X1,relation_dom(relation_dom(sK2)))),relation_dom(relation_dom(sK0)))
| ( relation_composition(X0,X1) = relation_dom(relation_dom(sK2)) )
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ relation(relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_93,c_3134]) ).
tcf(c_5296,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK11(X0,X1,relation_dom(relation_dom(sK2))),sK10(X0,X1,relation_dom(relation_dom(sK2)))),X1)
| ( relation_composition(X0,X1) = relation_dom(relation_dom(sK2)) )
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(sK0))
| ~ relation(relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_93,c_3241]) ).
tcf(c_5297,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK11(X0,X1,relation_dom(relation_dom(sK2))),sK10(X0,X1,relation_dom(relation_dom(sK2)))),X1)
| ( relation_composition(X0,X1) = relation_dom(relation_dom(sK2)) )
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2))
| ~ relation(relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_93,c_3017]) ).
tcf(c_5298,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK11(X0,X1,relation_dom(relation_dom(sK2))),sK10(X0,X1,relation_dom(relation_dom(sK2)))),X1)
| ( relation_composition(X0,X1) = relation_dom(relation_dom(sK2)) )
| ( apply(sK1,apply(sK0,ordered_pair(ordered_pair(sK9(X0,X1,relation_dom(relation_dom(sK2))),sK10(X0,X1,relation_dom(relation_dom(sK2)))),sK5(relation_dom(sK2),ordered_pair(sK9(X0,X1,relation_dom(relation_dom(sK2))),sK10(X0,X1,relation_dom(relation_dom(sK2)))))))) = apply(sK2,ordered_pair(ordered_pair(sK9(X0,X1,relation_dom(relation_dom(sK2))),sK10(X0,X1,relation_dom(relation_dom(sK2)))),sK5(relation_dom(sK2),ordered_pair(sK9(X0,X1,relation_dom(relation_dom(sK2))),sK10(X0,X1,relation_dom(relation_dom(sK2))))))) )
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2))
| ~ relation(relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_93,c_3018]) ).
tcf(c_5299,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK11(X0,X1,empty_set),sK10(X0,X1,empty_set)),X1)
| ( relation_composition(X0,X1) = empty_set )
| ~ relation(X1)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5294,c_109]) ).
tcf(c_5304,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK9(X0,empty_set,X1),sK10(X0,empty_set,X1)),X1)
| ( relation_composition(X0,empty_set) = X1 )
| ~ relation(X1)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5272,c_109]) ).
tcf(c_5782,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_composition(X0,X1) = relation_dom(sK2) )
| ( apply(sK0,ordered_pair(sK9(X0,X1,relation_dom(sK2)),sK10(X0,X1,relation_dom(sK2)))) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(X0,X1,relation_dom(sK2)),sK10(X0,X1,relation_dom(sK2))))) = empty_set )
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2))
| ~ in(ordered_pair(X2,sK10(X0,X1,relation_dom(sK2))),X1)
| ~ in(ordered_pair(sK9(X0,X1,relation_dom(sK2)),X2),X0) ),
inference(superposition,[status(thm)],[c_4011,c_91]) ).
tcf(c_5783,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_composition(X0,X1) = relation_dom(sK0) )
| ( apply(sK0,ordered_pair(sK9(X0,X1,relation_dom(sK0)),sK10(X0,X1,relation_dom(sK0)))) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(X0,X1,relation_dom(sK0)),sK10(X0,X1,relation_dom(sK0))))) = empty_set )
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK0))
| ~ in(ordered_pair(X2,sK10(X0,X1,relation_dom(sK0))),X1)
| ~ in(ordered_pair(sK9(X0,X1,relation_dom(sK0)),X2),X0) ),
inference(superposition,[status(thm)],[c_4110,c_91]) ).
tcf(c_5784,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_composition(X0,X1) = relation_dom(sK0) )
| ( apply(sK2,ordered_pair(sK9(X0,X1,relation_dom(sK0)),sK10(X0,X1,relation_dom(sK0)))) = empty_set )
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK0))
| ~ in(ordered_pair(X2,sK10(X0,X1,relation_dom(sK0))),X1)
| ~ in(ordered_pair(sK9(X0,X1,relation_dom(sK0)),X2),X0) ),
inference(superposition,[status(thm)],[c_3449,c_91]) ).
tcf(c_5785,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_composition(X0,X1) = relation_dom(X2) )
| ( apply(X2,ordered_pair(sK9(X0,X1,relation_dom(X2)),sK10(X0,X1,relation_dom(X2)))) = empty_set )
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(X2))
| ~ in(ordered_pair(X3,sK10(X0,X1,relation_dom(X2))),X1)
| ~ in(ordered_pair(sK9(X0,X1,relation_dom(X2)),X3),X0) ),
inference(superposition,[status(thm)],[c_75,c_91]) ).
tcf(c_5786,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(ordered_pair(sK11(X0,X1,X2),sK10(X0,X1,X2)),X1)
| ( relation_composition(X0,X1) = X2 )
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(ordered_pair(X3,sK10(X0,X1,X2)),X1)
| ~ in(ordered_pair(sK9(X0,X1,X2),X3),X0) ),
inference(superposition,[status(thm)],[c_93,c_91]) ).
tcf(c_5787,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(ordered_pair(sK9(X0,X1,X2),sK11(X0,X1,X2)),X0)
| ( relation_composition(X0,X1) = X2 )
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(ordered_pair(X3,sK10(X0,X1,X2)),X1)
| ~ in(ordered_pair(sK9(X0,X1,X2),X3),X0) ),
inference(superposition,[status(thm)],[c_92,c_91]) ).
tcf(c_5862,plain,
! [X0: $i] :
( in(ordered_pair(apply(sK0,X0),apply(sK2,X0)),sK1)
| ( apply(sK0,X0) = empty_set )
| ( apply(sK1,apply(sK0,X0)) = empty_set )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(apply(sK0,X0),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_4109,c_73]) ).
tcf(c_5863,plain,
! [X0: $i] :
( in(ordered_pair(apply(sK0,X0),apply(sK2,X0)),sK1)
| ( apply(sK0,X0) = empty_set )
| ( apply(sK1,apply(sK0,X0)) = empty_set )
| ~ in(apply(sK0,X0),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5862,c_57,c_56]) ).
tcf(c_5875,plain,
( ( sK2 = empty_set )
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(sK1,ordered_pair(apply(sK0,sK17(relation_dom(sK2))),apply(sK2,sK17(relation_dom(sK2))))) ),
inference(superposition,[status(thm)],[c_3627,c_64]) ).
tcf(c_5876,plain,
( element(ordered_pair(apply(sK0,sK17(relation_dom(sK2))),apply(sK2,sK17(relation_dom(sK2)))),sK1)
| ( sK2 = empty_set )
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_3627,c_63]) ).
tcf(c_5877,plain,
( ( sK2 = empty_set )
| ~ empty(sK1)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_3627,c_61]) ).
tcf(c_5879,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(apply(sK0,sK17(relation_dom(sK2))),X0),relation_composition(sK1,X1))
| ( sK2 = empty_set )
| ~ relation(sK1)
| ~ relation(X1)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),X1) ),
inference(superposition,[status(thm)],[c_3627,c_299]) ).
tcf(c_5890,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(apply(sK0,sK17(relation_dom(sK2))),X0),relation_composition(sK1,X1))
| ( sK2 = empty_set )
| ~ relation(X1)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5879,c_56]) ).
tcf(c_5916,plain,
( ( relation_dom(sK2) = empty_set )
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(sK1,ordered_pair(apply(sK0,sK17(relation_dom(sK2))),apply(sK2,sK17(relation_dom(sK2))))) ),
inference(superposition,[status(thm)],[c_3631,c_64]) ).
tcf(c_5917,plain,
( element(ordered_pair(apply(sK0,sK17(relation_dom(sK2))),apply(sK2,sK17(relation_dom(sK2)))),sK1)
| ( relation_dom(sK2) = empty_set )
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_3631,c_63]) ).
tcf(c_5920,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(apply(sK0,sK17(relation_dom(sK2))),X0),relation_composition(sK1,X1))
| ( relation_dom(sK2) = empty_set )
| ~ relation(sK1)
| ~ relation(X1)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),X1) ),
inference(superposition,[status(thm)],[c_3631,c_299]) ).
tcf(c_5928,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(apply(sK0,sK17(relation_dom(sK2))),X0),relation_composition(sK1,X1))
| ( relation_dom(sK2) = empty_set )
| ~ relation(X1)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5920,c_56]) ).
tcf(c_5960,plain,
( ( relation_dom(sK2) = sK2 )
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(sK1,ordered_pair(apply(sK0,sK17(relation_dom(sK2))),apply(sK2,sK17(relation_dom(sK2))))) ),
inference(superposition,[status(thm)],[c_3635,c_64]) ).
tcf(c_5961,plain,
( element(ordered_pair(apply(sK0,sK17(relation_dom(sK2))),apply(sK2,sK17(relation_dom(sK2)))),sK1)
| ( relation_dom(sK2) = sK2 )
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_3635,c_63]) ).
tcf(c_5962,plain,
( ( relation_dom(sK2) = sK2 )
| ~ empty(sK1)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_3635,c_61]) ).
tcf(c_5964,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(apply(sK0,sK17(relation_dom(sK2))),X0),relation_composition(sK1,X1))
| ( relation_dom(sK2) = sK2 )
| ~ relation(sK1)
| ~ relation(X1)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),X1) ),
inference(superposition,[status(thm)],[c_3635,c_299]) ).
tcf(c_5975,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(apply(sK0,sK17(relation_dom(sK2))),X0),relation_composition(sK1,X1))
| ( relation_dom(sK2) = sK2 )
| ~ relation(X1)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5964,c_56]) ).
tcf(c_5990,plain,
! [X0: $i] :
( in(sK3(relation_dom(sK2),X0),X0)
| in(ordered_pair(sK3(relation_dom(sK2),X0),sK4(relation_dom(sK2),X0)),relation_dom(sK2))
| ( relation_dom(relation_dom(sK2)) = X0 )
| ( apply(sK1,apply(sK0,ordered_pair(sK3(relation_dom(sK2),X0),sK4(relation_dom(sK2),X0)))) = empty_set )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4464,c_3475]) ).
tcf(c_5991,plain,
! [X0: $i] :
( in(sK3(relation_dom(sK2),X0),X0)
| ( relation_dom(relation_dom(sK2)) = X0 )
| ~ relation(relation_dom(sK2))
| ~ in(relation_dom(sK0),ordered_pair(sK3(relation_dom(sK2),X0),sK4(relation_dom(sK2),X0))) ),
inference(superposition,[status(thm)],[c_4464,c_64]) ).
tcf(c_5992,plain,
! [X0: $i] :
( in(sK3(relation_dom(sK2),X0),X0)
| element(ordered_pair(sK3(relation_dom(sK2),X0),sK4(relation_dom(sK2),X0)),relation_dom(sK0))
| ( relation_dom(relation_dom(sK2)) = X0 )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4464,c_63]) ).
tcf(c_5993,plain,
! [X0: $i] :
( in(sK3(relation_dom(sK2),X0),X0)
| ( relation_dom(relation_dom(sK2)) = X0 )
| ~ empty(relation_dom(sK0))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4464,c_61]) ).
tcf(c_5994,plain,
! [X0: $i] :
( in(sK3(relation_dom(sK2),X0),X0)
| in(sK3(relation_dom(sK2),X0),relation_dom(relation_dom(sK0)))
| ( relation_dom(relation_dom(sK2)) = X0 )
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4464,c_70]) ).
tcf(c_5995,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(relation_dom(sK2),X0),X0)
| in(ordered_pair(sK3(relation_dom(sK2),X0),X1),relation_composition(relation_dom(sK0),X2))
| ( relation_dom(relation_dom(sK2)) = X0 )
| ~ relation(X2)
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(ordered_pair(sK4(relation_dom(sK2),X0),X1),X2) ),
inference(superposition,[status(thm)],[c_4464,c_299]) ).
tcf(c_5996,plain,
! [X0: $i] :
( in(sK3(relation_dom(sK2),X0),X0)
| ( relation_dom(relation_dom(sK2)) = X0 )
| ( apply(relation_dom(sK0),sK3(relation_dom(sK2),X0)) = sK4(relation_dom(sK2),X0) )
| ~ function(relation_dom(sK0))
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4464,c_152]) ).
tcf(c_6060,plain,
! [X0: $i] :
( in(ordered_pair(apply(sK0,X0),apply(sK2,X0)),sK1)
| ( apply(sK0,X0) = empty_set )
| ( apply(sK1,apply(sK0,X0)) = empty_set ) ),
inference(global_subsumption_just,[status(thm)],[c_5863,c_52,c_4011,c_5863]) ).
tcf(c_6069,plain,
! [X0: $i] :
( ( apply(sK0,X0) = empty_set )
| ( apply(sK1,apply(sK0,X0)) = empty_set )
| ~ in(sK1,ordered_pair(apply(sK0,X0),apply(sK2,X0))) ),
inference(superposition,[status(thm)],[c_6060,c_64]) ).
tcf(c_6070,plain,
! [X0: $i] :
( element(ordered_pair(apply(sK0,X0),apply(sK2,X0)),sK1)
| ( apply(sK0,X0) = empty_set )
| ( apply(sK1,apply(sK0,X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_6060,c_63]) ).
tcf(c_6071,plain,
! [X0: $i] :
( ( apply(sK0,X0) = empty_set )
| ( apply(sK1,apply(sK0,X0)) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_6060,c_61]) ).
tcf(c_6072,plain,
! [X0: $i] :
( in(apply(sK0,X0),relation_dom(sK1))
| ( apply(sK0,X0) = empty_set )
| ( apply(sK1,apply(sK0,X0)) = empty_set )
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_6060,c_70]) ).
tcf(c_6073,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(ordered_pair(apply(sK0,X0),X1),relation_composition(sK1,X2))
| ( apply(sK0,X0) = empty_set )
| ( apply(sK1,apply(sK0,X0)) = empty_set )
| ~ relation(sK1)
| ~ relation(X2)
| ~ in(ordered_pair(apply(sK2,X0),X1),X2) ),
inference(superposition,[status(thm)],[c_6060,c_299]) ).
tcf(c_6078,plain,
! [X0: $i] :
( in(apply(sK0,X0),relation_dom(sK1))
| ( apply(sK0,X0) = empty_set )
| ( apply(sK1,apply(sK0,X0)) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6072,c_56]) ).
tcf(c_6088,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(ordered_pair(apply(sK0,X0),X1),relation_composition(sK1,X2))
| ( apply(sK0,X0) = empty_set )
| ( apply(sK1,apply(sK0,X0)) = empty_set )
| ~ relation(X2)
| ~ in(ordered_pair(apply(sK2,X0),X1),X2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6073,c_56]) ).
tcf(c_6121,plain,
! [X0: $i] :
( ( apply(sK0,X0) = empty_set )
| ( apply(sK1,apply(sK0,X0)) = empty_set )
| ~ in(relation_dom(sK1),apply(sK0,X0)) ),
inference(superposition,[status(thm)],[c_6078,c_64]) ).
tcf(c_6122,plain,
! [X0: $i] :
( element(apply(sK0,X0),relation_dom(sK1))
| ( apply(sK0,X0) = empty_set )
| ( apply(sK1,apply(sK0,X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_6078,c_63]) ).
tcf(c_6142,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(sK2,X1) = empty_set )
| ~ relation(X0)
| ~ in(apply(sK0,X1),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,X1),X2),X0)
| ~ in(relation_composition(sK1,X0),ordered_pair(apply(sK0,X1),X2)) ),
inference(superposition,[status(thm)],[c_4264,c_64]) ).
tcf(c_6143,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(ordered_pair(apply(sK0,X0),X1),relation_composition(sK1,X2))
| ( apply(sK2,X0) = empty_set )
| ~ relation(X2)
| ~ in(apply(sK0,X0),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,X0),X1),X2) ),
inference(superposition,[status(thm)],[c_4264,c_63]) ).
tcf(c_6144,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(sK2,X0) = empty_set )
| ~ relation(X2)
| ~ empty(relation_composition(sK1,X2))
| ~ in(apply(sK0,X0),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,X0),X1),X2) ),
inference(superposition,[status(thm)],[c_4264,c_61]) ).
tcf(c_6145,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(sK0,X0),relation_dom(relation_composition(sK1,X2)))
| ( apply(sK2,X0) = empty_set )
| ~ relation(X2)
| ~ relation(relation_composition(sK1,X2))
| ~ in(apply(sK0,X0),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,X0),X1),X2) ),
inference(superposition,[status(thm)],[c_4264,c_70]) ).
tcf(c_6146,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(ordered_pair(apply(sK0,X0),X3),relation_composition(relation_composition(sK1,X2),X4))
| ( apply(sK2,X0) = empty_set )
| ~ relation(X4)
| ~ relation(X2)
| ~ relation(relation_composition(sK1,X2))
| ~ in(ordered_pair(X1,X3),X4)
| ~ in(apply(sK0,X0),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,X0),X1),X2) ),
inference(superposition,[status(thm)],[c_4264,c_299]) ).
tcf(c_6147,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(sK2,X0) = empty_set )
| ( apply(relation_composition(sK1,X2),apply(sK0,X0)) = X1 )
| ~ relation(X2)
| ~ function(relation_composition(sK1,X2))
| ~ relation(relation_composition(sK1,X2))
| ~ in(apply(sK0,X0),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,X0),X1),X2) ),
inference(superposition,[status(thm)],[c_4264,c_152]) ).
tcf(c_6148,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(sK2,X0) = empty_set )
| ( apply(X2,sK12(sK1,X2,apply(sK0,X0),X1)) = X1 )
| ~ relation(sK1)
| ~ function(X2)
| ~ relation(X2)
| ~ in(apply(sK0,X0),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,X0),X1),X2) ),
inference(superposition,[status(thm)],[c_4264,c_2068]) ).
tcf(c_6149,plain,
! [X0: $i,X1: $i] :
( ( apply(sK2,X0) = empty_set )
| ~ relation(sK1)
| ~ empty(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,X0),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,X0),X1),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4264,c_2176]) ).
tcf(c_6150,plain,
! [X0: $i,X1: $i] :
( ( apply(sK2,X0) = empty_set )
| ~ relation(sK1)
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,X0),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,X0),X1),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4264,c_2063]) ).
tcf(c_6151,plain,
! [X0: $i,X1: $i] :
( ( apply(sK2,X0) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,X0),X1),X1))) = apply(sK2,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,X0),X1),X1)) )
| ~ relation(sK1)
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,X0),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,X0),X1),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4264,c_2064]) ).
tcf(c_6175,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(sK2,X0) = empty_set )
| ( apply(X2,sK12(sK1,X2,apply(sK0,X0),X1)) = X1 )
| ~ function(X2)
| ~ relation(X2)
| ~ in(apply(sK0,X0),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,X0),X1),X2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6148,c_56]) ).
tcf(c_6197,plain,
! [X0: $i,X1: $i] :
( ( apply(sK2,X0) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,X0),X1),X1))) = apply(sK2,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,X0),X1),X1)) )
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,X0),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,X0),X1),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6151,c_56]) ).
tcf(c_6244,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(X0)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_65,c_2124]) ).
tcf(c_6245,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_composition(X1,X0)) = empty_set )
| ~ empty(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_86,c_2124]) ).
tcf(c_6246,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_composition(X0,X1)) = empty_set )
| ~ empty(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_88,c_2124]) ).
tcf(c_6248,plain,
( ( relation_dom(relation_dom(sK2)) = empty_set )
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_2577,c_2124]) ).
tcf(c_6249,plain,
( ( relation_dom(relation_dom(sK2)) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_2570,c_2124]) ).
tcf(c_6250,plain,
( ( relation_dom(relation_dom(sK2)) = empty_set )
| ( apply(sK1,apply(sK0,sK17(relation_dom(sK2)))) = apply(sK2,sK17(relation_dom(sK2))) ) ),
inference(superposition,[status(thm)],[c_2425,c_2124]) ).
tcf(c_6284,plain,
( ( relation_dom(relation_dom(relation_dom(sK2))) = empty_set )
| ~ empty(relation_dom(sK0)) ),
inference(superposition,[status(thm)],[c_3251,c_2124]) ).
tcf(c_6285,plain,
( ( relation_dom(relation_dom(sK2)) = relation_dom(sK2) )
| ( apply(sK1,apply(sK0,sK17(relation_dom(sK2)))) = apply(sK2,sK17(relation_dom(sK2))) )
| ~ empty(relation_dom(sK0)) ),
inference(superposition,[status(thm)],[c_3251,c_2466]) ).
tcf(c_6286,plain,
( ( relation_dom(relation_dom(sK2)) = sK2 )
| ( apply(sK1,apply(sK0,sK17(relation_dom(sK2)))) = apply(sK2,sK17(relation_dom(sK2))) )
| ~ empty(relation_dom(sK0)) ),
inference(superposition,[status(thm)],[c_3251,c_2488]) ).
tcf(c_6287,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK2)) = X0 )
| ~ empty(X0)
| ~ empty(relation_dom(sK0)) ),
inference(superposition,[status(thm)],[c_3251,c_60]) ).
tcf(c_6288,plain,
( ( relation_dom(relation_dom(sK2)) = empty_set )
| ~ empty(relation_dom(sK0)) ),
inference(superposition,[status(thm)],[c_3251,c_107]) ).
tcf(c_6289,plain,
( relation(relation_dom(relation_dom(sK2)))
| ~ empty(relation_dom(sK0)) ),
inference(superposition,[status(thm)],[c_3251,c_85]) ).
tcf(c_6290,plain,
( function(relation_dom(relation_dom(sK2)))
| ~ empty(relation_dom(sK0)) ),
inference(superposition,[status(thm)],[c_3251,c_80]) ).
tcf(c_6367,plain,
! [X0: $i] :
( in(sK3(relation_dom(relation_dom(sK2)),X0),X0)
| ( relation_dom(relation_dom(relation_dom(sK2))) = X0 )
| ( apply(sK1,apply(sK0,ordered_pair(ordered_pair(sK3(relation_dom(relation_dom(sK2)),X0),sK4(relation_dom(relation_dom(sK2)),X0)),apply(relation_dom(sK2),ordered_pair(sK3(relation_dom(relation_dom(sK2)),X0),sK4(relation_dom(relation_dom(sK2)),X0)))))) = apply(sK2,ordered_pair(ordered_pair(sK3(relation_dom(relation_dom(sK2)),X0),sK4(relation_dom(relation_dom(sK2)),X0)),apply(relation_dom(sK2),ordered_pair(sK3(relation_dom(relation_dom(sK2)),X0),sK4(relation_dom(relation_dom(sK2)),X0))))) )
| ~ function(relation_dom(sK2))
| ~ relation(relation_dom(sK2))
| ~ relation(relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_69,c_3550]) ).
tcf(c_6368,plain,
! [X0: $i] :
( ( apply(sK1,apply(sK0,ordered_pair(ordered_pair(X0,sK5(relation_dom(relation_dom(sK2)),X0)),apply(relation_dom(sK2),ordered_pair(X0,sK5(relation_dom(relation_dom(sK2)),X0)))))) = apply(sK2,ordered_pair(ordered_pair(X0,sK5(relation_dom(relation_dom(sK2)),X0)),apply(relation_dom(sK2),ordered_pair(X0,sK5(relation_dom(relation_dom(sK2)),X0))))) )
| ~ function(relation_dom(sK2))
| ~ relation(relation_dom(sK2))
| ~ relation(relation_dom(relation_dom(sK2)))
| ~ in(X0,relation_dom(relation_dom(relation_dom(sK2)))) ),
inference(superposition,[status(thm)],[c_71,c_3550]) ).
tcf(c_6369,plain,
! [X0: $i] :
( ( apply(sK1,apply(sK0,ordered_pair(ordered_pair(X0,apply(relation_dom(relation_dom(sK2)),X0)),apply(relation_dom(sK2),ordered_pair(X0,apply(relation_dom(relation_dom(sK2)),X0)))))) = apply(sK2,ordered_pair(ordered_pair(X0,apply(relation_dom(relation_dom(sK2)),X0)),apply(relation_dom(sK2),ordered_pair(X0,apply(relation_dom(relation_dom(sK2)),X0))))) )
| ~ function(relation_dom(sK2))
| ~ relation(relation_dom(sK2))
| ~ function(relation_dom(relation_dom(sK2)))
| ~ relation(relation_dom(relation_dom(sK2)))
| ~ in(X0,relation_dom(relation_dom(relation_dom(sK2)))) ),
inference(superposition,[status(thm)],[c_73,c_3550]) ).
tcf(c_6370,plain,
! [X0: $i] :
( ( apply(relation_dom(sK2),X0) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(X0,apply(relation_dom(sK2),X0)))) = apply(sK2,ordered_pair(X0,apply(relation_dom(sK2),X0))) )
| ~ function(relation_dom(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_75,c_3550]) ).
tcf(c_6371,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK11(X0,X1,relation_dom(relation_dom(sK2))),sK10(X0,X1,relation_dom(relation_dom(sK2)))),X1)
| ( relation_composition(X0,X1) = relation_dom(relation_dom(sK2)) )
| ( apply(sK1,apply(sK0,ordered_pair(ordered_pair(sK9(X0,X1,relation_dom(relation_dom(sK2))),sK10(X0,X1,relation_dom(relation_dom(sK2)))),apply(relation_dom(sK2),ordered_pair(sK9(X0,X1,relation_dom(relation_dom(sK2))),sK10(X0,X1,relation_dom(relation_dom(sK2)))))))) = apply(sK2,ordered_pair(ordered_pair(sK9(X0,X1,relation_dom(relation_dom(sK2))),sK10(X0,X1,relation_dom(relation_dom(sK2)))),apply(relation_dom(sK2),ordered_pair(sK9(X0,X1,relation_dom(relation_dom(sK2))),sK10(X0,X1,relation_dom(relation_dom(sK2))))))) )
| ~ relation(X1)
| ~ relation(X0)
| ~ function(relation_dom(sK2))
| ~ relation(relation_dom(sK2))
| ~ relation(relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_93,c_3550]) ).
tcf(c_6372,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK9(X0,X1,relation_dom(relation_dom(sK2))),sK11(X0,X1,relation_dom(relation_dom(sK2)))),X0)
| ( relation_composition(X0,X1) = relation_dom(relation_dom(sK2)) )
| ( apply(sK1,apply(sK0,ordered_pair(ordered_pair(sK9(X0,X1,relation_dom(relation_dom(sK2))),sK10(X0,X1,relation_dom(relation_dom(sK2)))),apply(relation_dom(sK2),ordered_pair(sK9(X0,X1,relation_dom(relation_dom(sK2))),sK10(X0,X1,relation_dom(relation_dom(sK2)))))))) = apply(sK2,ordered_pair(ordered_pair(sK9(X0,X1,relation_dom(relation_dom(sK2))),sK10(X0,X1,relation_dom(relation_dom(sK2)))),apply(relation_dom(sK2),ordered_pair(sK9(X0,X1,relation_dom(relation_dom(sK2))),sK10(X0,X1,relation_dom(relation_dom(sK2))))))) )
| ~ relation(X1)
| ~ relation(X0)
| ~ function(relation_dom(sK2))
| ~ relation(relation_dom(sK2))
| ~ relation(relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_92,c_3550]) ).
tcf(c_6373,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK9(relation_dom(relation_dom(sK2)),X0,X1),sK10(relation_dom(relation_dom(sK2)),X0,X1)),X1)
| ( relation_composition(relation_dom(relation_dom(sK2)),X0) = X1 )
| ( apply(sK1,apply(sK0,ordered_pair(ordered_pair(sK9(relation_dom(relation_dom(sK2)),X0,X1),sK11(relation_dom(relation_dom(sK2)),X0,X1)),apply(relation_dom(sK2),ordered_pair(sK9(relation_dom(relation_dom(sK2)),X0,X1),sK11(relation_dom(relation_dom(sK2)),X0,X1)))))) = apply(sK2,ordered_pair(ordered_pair(sK9(relation_dom(relation_dom(sK2)),X0,X1),sK11(relation_dom(relation_dom(sK2)),X0,X1)),apply(relation_dom(sK2),ordered_pair(sK9(relation_dom(relation_dom(sK2)),X0,X1),sK11(relation_dom(relation_dom(sK2)),X0,X1))))) )
| ~ relation(X1)
| ~ relation(X0)
| ~ function(relation_dom(sK2))
| ~ relation(relation_dom(sK2))
| ~ relation(relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_92,c_3550]) ).
tcf(c_6374,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK9(X0,relation_dom(relation_dom(sK2)),X1),sK10(X0,relation_dom(relation_dom(sK2)),X1)),X1)
| ( relation_composition(X0,relation_dom(relation_dom(sK2))) = X1 )
| ( apply(sK1,apply(sK0,ordered_pair(ordered_pair(sK11(X0,relation_dom(relation_dom(sK2)),X1),sK10(X0,relation_dom(relation_dom(sK2)),X1)),apply(relation_dom(sK2),ordered_pair(sK11(X0,relation_dom(relation_dom(sK2)),X1),sK10(X0,relation_dom(relation_dom(sK2)),X1)))))) = apply(sK2,ordered_pair(ordered_pair(sK11(X0,relation_dom(relation_dom(sK2)),X1),sK10(X0,relation_dom(relation_dom(sK2)),X1)),apply(relation_dom(sK2),ordered_pair(sK11(X0,relation_dom(relation_dom(sK2)),X1),sK10(X0,relation_dom(relation_dom(sK2)),X1))))) )
| ~ relation(X1)
| ~ relation(X0)
| ~ function(relation_dom(sK2))
| ~ relation(relation_dom(sK2))
| ~ relation(relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_93,c_3550]) ).
tcf(c_6375,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(sK1,apply(sK0,ordered_pair(ordered_pair(X0,sK12(relation_dom(relation_dom(sK2)),X2,X0,X1)),apply(relation_dom(sK2),ordered_pair(X0,sK12(relation_dom(relation_dom(sK2)),X2,X0,X1)))))) = apply(sK2,ordered_pair(ordered_pair(X0,sK12(relation_dom(relation_dom(sK2)),X2,X0,X1)),apply(relation_dom(sK2),ordered_pair(X0,sK12(relation_dom(relation_dom(sK2)),X2,X0,X1))))) )
| ~ relation(X2)
| ~ function(relation_dom(sK2))
| ~ relation(relation_dom(sK2))
| ~ relation(relation_dom(relation_dom(sK2)))
| ~ in(ordered_pair(X0,X1),relation_composition(relation_dom(relation_dom(sK2)),X2)) ),
inference(superposition,[status(thm)],[c_301,c_3550]) ).
tcf(c_6376,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(sK1,apply(sK0,ordered_pair(ordered_pair(sK12(X2,relation_dom(relation_dom(sK2)),X0,X1),X1),apply(relation_dom(sK2),ordered_pair(sK12(X2,relation_dom(relation_dom(sK2)),X0,X1),X1))))) = apply(sK2,ordered_pair(ordered_pair(sK12(X2,relation_dom(relation_dom(sK2)),X0,X1),X1),apply(relation_dom(sK2),ordered_pair(sK12(X2,relation_dom(relation_dom(sK2)),X0,X1),X1)))) )
| ~ relation(X2)
| ~ function(relation_dom(sK2))
| ~ relation(relation_dom(sK2))
| ~ relation(relation_dom(relation_dom(sK2)))
| ~ in(ordered_pair(X0,X1),relation_composition(X2,relation_dom(relation_dom(sK2)))) ),
inference(superposition,[status(thm)],[c_300,c_3550]) ).
tcf(c_6377,plain,
( empty(relation_dom(relation_dom(sK2)))
| ( apply(sK1,apply(sK0,ordered_pair(sK17(relation_dom(relation_dom(sK2))),apply(relation_dom(sK2),sK17(relation_dom(relation_dom(sK2))))))) = apply(sK2,ordered_pair(sK17(relation_dom(relation_dom(sK2))),apply(relation_dom(sK2),sK17(relation_dom(relation_dom(sK2)))))) )
| ~ function(relation_dom(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_2361,c_3550]) ).
tcf(c_6493,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(sK0,X1) = empty_set )
| ( apply(sK1,apply(sK0,X1)) = empty_set )
| ~ relation(X0)
| ~ in(ordered_pair(apply(sK2,X1),X2),X0)
| ~ in(relation_composition(sK1,X0),ordered_pair(apply(sK0,X1),X2)) ),
inference(superposition,[status(thm)],[c_6088,c_64]) ).
tcf(c_6494,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(ordered_pair(apply(sK0,X0),X1),relation_composition(sK1,X2))
| ( apply(sK0,X0) = empty_set )
| ( apply(sK1,apply(sK0,X0)) = empty_set )
| ~ relation(X2)
| ~ in(ordered_pair(apply(sK2,X0),X1),X2) ),
inference(superposition,[status(thm)],[c_6088,c_63]) ).
tcf(c_6495,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(sK0,X0) = empty_set )
| ( apply(sK1,apply(sK0,X0)) = empty_set )
| ~ relation(X2)
| ~ empty(relation_composition(sK1,X2))
| ~ in(ordered_pair(apply(sK2,X0),X1),X2) ),
inference(superposition,[status(thm)],[c_6088,c_61]) ).
tcf(c_6496,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(sK0,X0),relation_dom(relation_composition(sK1,X2)))
| ( apply(sK0,X0) = empty_set )
| ( apply(sK1,apply(sK0,X0)) = empty_set )
| ~ relation(X2)
| ~ relation(relation_composition(sK1,X2))
| ~ in(ordered_pair(apply(sK2,X0),X1),X2) ),
inference(superposition,[status(thm)],[c_6088,c_70]) ).
tcf(c_6497,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(ordered_pair(apply(sK0,X0),X3),relation_composition(relation_composition(sK1,X2),X4))
| ( apply(sK0,X0) = empty_set )
| ( apply(sK1,apply(sK0,X0)) = empty_set )
| ~ relation(X4)
| ~ relation(X2)
| ~ relation(relation_composition(sK1,X2))
| ~ in(ordered_pair(X1,X3),X4)
| ~ in(ordered_pair(apply(sK2,X0),X1),X2) ),
inference(superposition,[status(thm)],[c_6088,c_299]) ).
tcf(c_6498,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(sK0,X0) = empty_set )
| ( apply(sK1,apply(sK0,X0)) = empty_set )
| ( apply(relation_composition(sK1,X2),apply(sK0,X0)) = X1 )
| ~ relation(X2)
| ~ function(relation_composition(sK1,X2))
| ~ relation(relation_composition(sK1,X2))
| ~ in(ordered_pair(apply(sK2,X0),X1),X2) ),
inference(superposition,[status(thm)],[c_6088,c_152]) ).
tcf(c_6499,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(sK0,X0) = empty_set )
| ( apply(sK1,apply(sK0,X0)) = empty_set )
| ( apply(X2,sK12(sK1,X2,apply(sK0,X0),X1)) = X1 )
| ~ relation(sK1)
| ~ function(X2)
| ~ relation(X2)
| ~ in(ordered_pair(apply(sK2,X0),X1),X2) ),
inference(superposition,[status(thm)],[c_6088,c_2068]) ).
tcf(c_6500,plain,
! [X0: $i,X1: $i] :
( ( apply(sK0,X0) = empty_set )
| ( apply(sK1,apply(sK0,X0)) = empty_set )
| ~ relation(sK1)
| ~ empty(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(ordered_pair(apply(sK2,X0),X1),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6088,c_2176]) ).
tcf(c_6501,plain,
! [X0: $i,X1: $i] :
( ( apply(sK0,X0) = empty_set )
| ( apply(sK1,apply(sK0,X0)) = empty_set )
| ~ relation(sK1)
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2))
| ~ in(ordered_pair(apply(sK2,X0),X1),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6088,c_2063]) ).
tcf(c_6502,plain,
! [X0: $i,X1: $i] :
( ( apply(sK0,X0) = empty_set )
| ( apply(sK1,apply(sK0,X0)) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,X0),X1),X1))) = apply(sK2,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,X0),X1),X1)) )
| ~ relation(sK1)
| ~ relation(relation_dom(sK2))
| ~ in(ordered_pair(apply(sK2,X0),X1),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6088,c_2064]) ).
tcf(c_6526,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(sK0,X0) = empty_set )
| ( apply(sK1,apply(sK0,X0)) = empty_set )
| ( apply(X2,sK12(sK1,X2,apply(sK0,X0),X1)) = X1 )
| ~ function(X2)
| ~ relation(X2)
| ~ in(ordered_pair(apply(sK2,X0),X1),X2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6499,c_56]) ).
tcf(c_6548,plain,
! [X0: $i,X1: $i] :
( ( apply(sK0,X0) = empty_set )
| ( apply(sK1,apply(sK0,X0)) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,X0),X1),X1))) = apply(sK2,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,X0),X1),X1)) )
| ~ relation(relation_dom(sK2))
| ~ in(ordered_pair(apply(sK2,X0),X1),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6502,c_56]) ).
tcf(c_6604,plain,
! [X0: $i,X1: $i] :
( ( sK2 = empty_set )
| ~ relation(X0)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X1),X0)
| ~ in(relation_composition(sK1,X0),ordered_pair(apply(sK0,sK17(relation_dom(sK2))),X1)) ),
inference(superposition,[status(thm)],[c_5890,c_64]) ).
tcf(c_6605,plain,
! [X0: $i,X1: $i] :
( element(ordered_pair(apply(sK0,sK17(relation_dom(sK2))),X0),relation_composition(sK1,X1))
| ( sK2 = empty_set )
| ~ relation(X1)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),X1) ),
inference(superposition,[status(thm)],[c_5890,c_63]) ).
tcf(c_6606,plain,
! [X0: $i,X1: $i] :
( ( sK2 = empty_set )
| ~ relation(X1)
| ~ empty(relation_composition(sK1,X1))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),X1) ),
inference(superposition,[status(thm)],[c_5890,c_61]) ).
tcf(c_6607,plain,
! [X0: $i,X1: $i] :
( in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(relation_composition(sK1,X1)))
| ( sK2 = empty_set )
| ~ relation(X1)
| ~ relation(relation_composition(sK1,X1))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),X1) ),
inference(superposition,[status(thm)],[c_5890,c_70]) ).
tcf(c_6608,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(ordered_pair(apply(sK0,sK17(relation_dom(sK2))),X2),relation_composition(relation_composition(sK1,X1),X3))
| ( sK2 = empty_set )
| ~ relation(X3)
| ~ relation(X1)
| ~ relation(relation_composition(sK1,X1))
| ~ in(ordered_pair(X0,X2),X3)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),X1) ),
inference(superposition,[status(thm)],[c_5890,c_299]) ).
tcf(c_6609,plain,
! [X0: $i,X1: $i] :
( ( sK2 = empty_set )
| ( apply(relation_composition(sK1,X1),apply(sK0,sK17(relation_dom(sK2)))) = X0 )
| ~ relation(X1)
| ~ function(relation_composition(sK1,X1))
| ~ relation(relation_composition(sK1,X1))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),X1) ),
inference(superposition,[status(thm)],[c_5890,c_152]) ).
tcf(c_6610,plain,
! [X0: $i,X1: $i] :
( ( sK2 = empty_set )
| ( apply(X1,sK12(sK1,X1,apply(sK0,sK17(relation_dom(sK2))),X0)) = X0 )
| ~ relation(sK1)
| ~ function(X1)
| ~ relation(X1)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),X1) ),
inference(superposition,[status(thm)],[c_5890,c_2068]) ).
tcf(c_6611,plain,
! [X0: $i] :
( ( sK2 = empty_set )
| ~ relation(sK1)
| ~ empty(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5890,c_2176]) ).
tcf(c_6612,plain,
! [X0: $i] :
( ( sK2 = empty_set )
| ~ relation(sK1)
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5890,c_2063]) ).
tcf(c_6613,plain,
! [X0: $i] :
( ( sK2 = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,sK17(relation_dom(sK2))),X0),X0))) = apply(sK2,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,sK17(relation_dom(sK2))),X0),X0)) )
| ~ relation(sK1)
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5890,c_2064]) ).
tcf(c_6619,plain,
! [X0: $i] :
( ( sK2 = empty_set )
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6612,c_56]) ).
tcf(c_6625,plain,
! [X0: $i] :
( ( sK2 = empty_set )
| ~ empty(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6611,c_56]) ).
tcf(c_6647,plain,
! [X0: $i,X1: $i] :
( ( sK2 = empty_set )
| ( apply(X1,sK12(sK1,X1,apply(sK0,sK17(relation_dom(sK2))),X0)) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6610,c_56]) ).
tcf(c_6669,plain,
! [X0: $i] :
( ( sK2 = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,sK17(relation_dom(sK2))),X0),X0))) = apply(sK2,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,sK17(relation_dom(sK2))),X0),X0)) )
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6613,c_56]) ).
tcf(c_6726,plain,
! [X0: $i] :
( ( sK2 = empty_set )
| ~ empty(relation_dom(sK0))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1)) ),
inference(global_subsumption_just,[status(thm)],[c_6625,c_58,c_126,c_2669,c_6625]) ).
tcf(c_6727,plain,
! [X0: $i] :
( ( sK2 = empty_set )
| ~ empty(relation_dom(sK0))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),relation_dom(sK2)) ),
inference(renaming,[status(thm)],[c_6726]) ).
tcf(c_6737,plain,
! [X0: $i] :
( ( sK2 = empty_set )
| ( apply(sK0,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0)) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0))) = empty_set )
| ~ empty(relation_dom(sK0))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_4011,c_6727]) ).
tcf(c_6738,plain,
( ( sK2 = empty_set )
| ~ empty(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(apply(sK2,sK17(relation_dom(sK2))),relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_71,c_6727]) ).
tcf(c_6739,plain,
( ( sK2 = empty_set )
| ~ empty(relation_dom(sK0))
| ~ function(relation_dom(sK2))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(apply(sK2,sK17(relation_dom(sK2))),relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_73,c_6727]) ).
tcf(c_6740,plain,
! [X0: $i] :
( ( sK2 = empty_set )
| ( apply(sK2,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0)) = empty_set )
| ~ function(sK2)
| ~ relation(sK2)
| ~ empty(relation_dom(sK0))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_75,c_6727]) ).
tcf(c_6741,plain,
! [X0: $i,X1: $i] :
( ( sK2 = empty_set )
| ~ relation(X1)
| ~ empty(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),relation_composition(relation_dom(sK2),X1)) ),
inference(superposition,[status(thm)],[c_301,c_6727]) ).
tcf(c_6747,plain,
! [X0: $i] :
( ( sK2 = empty_set )
| ( apply(sK2,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0)) = empty_set )
| ~ empty(relation_dom(sK0))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6740,c_55,c_54]) ).
tcf(c_6792,plain,
! [X0: $i] :
( ( sK2 = empty_set )
| ( apply(sK0,sK17(relation_dom(sK2))) = empty_set )
| ( apply(sK1,apply(sK0,sK17(relation_dom(sK2)))) = empty_set )
| ( apply(sK2,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0)) = empty_set )
| ~ empty(relation_dom(sK0)) ),
inference(superposition,[status(thm)],[c_6078,c_6747]) ).
tcf(c_6793,plain,
! [X0: $i] :
( ( sK2 = empty_set )
| ( apply(sK2,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0)) = empty_set )
| ~ empty(relation_dom(sK0))
| ~ in(sK17(relation_dom(sK2)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_52,c_6747]) ).
tcf(c_6794,plain,
! [X0: $i] :
( ( sK2 = empty_set )
| ( apply(sK1,apply(sK0,sK17(relation_dom(sK2)))) = empty_set )
| ( apply(sK2,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0)) = empty_set )
| ~ function(sK1)
| ~ relation(sK1)
| ~ empty(relation_dom(sK0)) ),
inference(superposition,[status(thm)],[c_75,c_6747]) ).
tcf(c_6799,plain,
! [X0: $i] :
( ( sK2 = empty_set )
| ( apply(sK1,apply(sK0,sK17(relation_dom(sK2)))) = empty_set )
| ( apply(sK2,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0)) = empty_set )
| ~ empty(relation_dom(sK0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6794,c_57,c_56]) ).
tcf(c_6850,plain,
! [X0: $i] :
( ( sK2 = empty_set )
| ( apply(sK2,sK17(relation_dom(sK2))) = empty_set )
| ( apply(sK2,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0)) = empty_set )
| ~ function(sK2)
| ~ relation(sK2)
| ~ empty(relation_dom(sK0)) ),
inference(superposition,[status(thm)],[c_75,c_6793]) ).
tcf(c_6851,plain,
! [X0: $i] :
( empty(relation_dom(sK2))
| ( sK2 = empty_set )
| ( apply(sK2,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0)) = empty_set )
| ~ empty(relation_dom(sK0)) ),
inference(superposition,[status(thm)],[c_2361,c_6793]) ).
tcf(c_6856,plain,
! [X0: $i] :
( ( sK2 = empty_set )
| ( apply(sK2,sK17(relation_dom(sK2))) = empty_set )
| ( apply(sK2,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0)) = empty_set )
| ~ empty(relation_dom(sK0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6850,c_55,c_54]) ).
tcf(c_6870,plain,
! [X0: $i] :
( ( sK2 = empty_set )
| ( apply(sK2,sK17(relation_dom(sK2))) = empty_set )
| ( apply(sK2,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0)) = empty_set )
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_65,c_6856]) ).
tcf(c_6903,plain,
! [X0: $i,X1: $i] :
( in(sK3(sK17(powerset(X0)),X1),X1)
| ( relation_dom(sK17(powerset(X0))) = X1 )
| ~ empty(X0)
| ~ relation(sK17(powerset(X0))) ),
inference(superposition,[status(thm)],[c_69,c_2925]) ).
tcf(c_6904,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ relation(sK17(powerset(X1)))
| ~ in(X0,relation_dom(sK17(powerset(X1)))) ),
inference(superposition,[status(thm)],[c_71,c_2925]) ).
tcf(c_6905,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ function(sK17(powerset(X1)))
| ~ relation(sK17(powerset(X1)))
| ~ in(X0,relation_dom(sK17(powerset(X1)))) ),
inference(superposition,[status(thm)],[c_73,c_2925]) ).
tcf(c_6906,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(ordered_pair(sK11(X1,X2,sK17(powerset(X0))),sK10(X1,X2,sK17(powerset(X0)))),X2)
| ( relation_composition(X1,X2) = sK17(powerset(X0)) )
| ~ empty(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(sK17(powerset(X0))) ),
inference(superposition,[status(thm)],[c_93,c_2925]) ).
tcf(c_6907,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(ordered_pair(sK9(X1,X2,sK17(powerset(X0))),sK11(X1,X2,sK17(powerset(X0)))),X1)
| ( relation_composition(X1,X2) = sK17(powerset(X0)) )
| ~ empty(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(sK17(powerset(X0))) ),
inference(superposition,[status(thm)],[c_92,c_2925]) ).
tcf(c_6908,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(ordered_pair(sK9(sK17(powerset(X0)),X1,X2),sK10(sK17(powerset(X0)),X1,X2)),X2)
| ( relation_composition(sK17(powerset(X0)),X1) = X2 )
| ~ empty(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(sK17(powerset(X0))) ),
inference(superposition,[status(thm)],[c_92,c_2925]) ).
tcf(c_6909,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(ordered_pair(sK9(X1,sK17(powerset(X0)),X2),sK10(X1,sK17(powerset(X0)),X2)),X2)
| ( relation_composition(X1,sK17(powerset(X0))) = X2 )
| ~ empty(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(sK17(powerset(X0))) ),
inference(superposition,[status(thm)],[c_93,c_2925]) ).
tcf(c_6910,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ empty(X2)
| ~ relation(X3)
| ~ relation(sK17(powerset(X2)))
| ~ in(ordered_pair(X0,X1),relation_composition(sK17(powerset(X2)),X3)) ),
inference(superposition,[status(thm)],[c_301,c_2925]) ).
tcf(c_6911,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ empty(X3)
| ~ relation(X2)
| ~ relation(sK17(powerset(X3)))
| ~ in(ordered_pair(X0,X1),relation_composition(X2,sK17(powerset(X3)))) ),
inference(superposition,[status(thm)],[c_300,c_2925]) ).
tcf(c_6912,plain,
! [X0: $i] :
( empty(sK17(powerset(X0)))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2361,c_2925]) ).
tcf(c_7004,plain,
! [X0: $i,X1: $i] :
( in(sK3(sK17(powerset(X0)),X1),X1)
| element(ordered_pair(sK3(sK17(powerset(X0)),X1),sK4(sK17(powerset(X0)),X1)),X0)
| ( relation_dom(sK17(powerset(X0))) = X1 )
| ~ relation(sK17(powerset(X0))) ),
inference(superposition,[status(thm)],[c_69,c_2940]) ).
tcf(c_7005,plain,
! [X0: $i,X1: $i] :
( element(ordered_pair(X0,sK5(sK17(powerset(X1)),X0)),X1)
| ~ relation(sK17(powerset(X1)))
| ~ in(X0,relation_dom(sK17(powerset(X1)))) ),
inference(superposition,[status(thm)],[c_71,c_2940]) ).
tcf(c_7006,plain,
! [X0: $i,X1: $i] :
( element(ordered_pair(X0,apply(sK17(powerset(X1)),X0)),X1)
| ~ function(sK17(powerset(X1)))
| ~ relation(sK17(powerset(X1)))
| ~ in(X0,relation_dom(sK17(powerset(X1)))) ),
inference(superposition,[status(thm)],[c_73,c_2940]) ).
tcf(c_7007,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(ordered_pair(sK9(X1,X2,sK17(powerset(X0))),sK10(X1,X2,sK17(powerset(X0)))),X0)
| in(ordered_pair(sK11(X1,X2,sK17(powerset(X0))),sK10(X1,X2,sK17(powerset(X0)))),X2)
| ( relation_composition(X1,X2) = sK17(powerset(X0)) )
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(sK17(powerset(X0))) ),
inference(superposition,[status(thm)],[c_93,c_2940]) ).
tcf(c_7008,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(ordered_pair(sK9(X1,X2,sK17(powerset(X0))),sK10(X1,X2,sK17(powerset(X0)))),X0)
| in(ordered_pair(sK9(X1,X2,sK17(powerset(X0))),sK11(X1,X2,sK17(powerset(X0)))),X1)
| ( relation_composition(X1,X2) = sK17(powerset(X0)) )
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(sK17(powerset(X0))) ),
inference(superposition,[status(thm)],[c_92,c_2940]) ).
tcf(c_7009,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(ordered_pair(sK9(sK17(powerset(X0)),X1,X2),sK11(sK17(powerset(X0)),X1,X2)),X0)
| in(ordered_pair(sK9(sK17(powerset(X0)),X1,X2),sK10(sK17(powerset(X0)),X1,X2)),X2)
| ( relation_composition(sK17(powerset(X0)),X1) = X2 )
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(sK17(powerset(X0))) ),
inference(superposition,[status(thm)],[c_92,c_2940]) ).
tcf(c_7010,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(ordered_pair(sK11(X1,sK17(powerset(X0)),X2),sK10(X1,sK17(powerset(X0)),X2)),X0)
| in(ordered_pair(sK9(X1,sK17(powerset(X0)),X2),sK10(X1,sK17(powerset(X0)),X2)),X2)
| ( relation_composition(X1,sK17(powerset(X0))) = X2 )
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(sK17(powerset(X0))) ),
inference(superposition,[status(thm)],[c_93,c_2940]) ).
tcf(c_7011,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(ordered_pair(X0,sK12(sK17(powerset(X2)),X3,X0,X1)),X2)
| ~ relation(X3)
| ~ relation(sK17(powerset(X2)))
| ~ in(ordered_pair(X0,X1),relation_composition(sK17(powerset(X2)),X3)) ),
inference(superposition,[status(thm)],[c_301,c_2940]) ).
tcf(c_7012,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(ordered_pair(sK12(X2,sK17(powerset(X3)),X0,X1),X1),X3)
| ~ relation(X2)
| ~ relation(sK17(powerset(X3)))
| ~ in(ordered_pair(X0,X1),relation_composition(X2,sK17(powerset(X3)))) ),
inference(superposition,[status(thm)],[c_300,c_2940]) ).
tcf(c_7013,plain,
! [X0: $i] :
( empty(sK17(powerset(X0)))
| element(sK17(sK17(powerset(X0))),X0) ),
inference(superposition,[status(thm)],[c_2361,c_2940]) ).
tcf(c_7079,plain,
( ( relation_dom(sK2) = empty_set )
| ~ empty(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_4486,c_2047]) ).
tcf(c_7080,plain,
( ( relation_dom(sK2) = empty_set )
| ( apply(sK1,apply(sK0,sK3(empty_set,relation_dom(sK2)))) = apply(sK2,sK3(empty_set,relation_dom(sK2))) ) ),
inference(superposition,[status(thm)],[c_4486,c_53]) ).
tcf(c_7081,plain,
( in(sK3(empty_set,relation_dom(sK2)),relation_dom(sK0))
| ( relation_dom(sK2) = empty_set ) ),
inference(superposition,[status(thm)],[c_4486,c_51]) ).
tcf(c_7082,plain,
( in(sK3(empty_set,relation_dom(sK0)),relation_dom(sK2))
| ( relation_dom(sK0) = empty_set )
| ( apply(sK1,apply(sK0,sK3(empty_set,relation_dom(sK0)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_4486,c_3475]) ).
tcf(c_7083,plain,
! [X0: $i] :
( ( X0 = empty_set )
| ~ in(X0,sK3(empty_set,X0)) ),
inference(superposition,[status(thm)],[c_4486,c_64]) ).
tcf(c_7084,plain,
! [X0: $i] :
( element(sK3(empty_set,X0),X0)
| ( X0 = empty_set ) ),
inference(superposition,[status(thm)],[c_4486,c_63]) ).
tcf(c_7087,plain,
! [X0: $i] :
( element(sK3(empty_set,sK17(powerset(X0))),X0)
| ( sK17(powerset(X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_4486,c_2940]) ).
tcf(c_7088,plain,
! [X0: $i] :
( ( sK17(powerset(X0)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_4486,c_2925]) ).
tcf(c_7089,plain,
( ( relation_dom(relation_dom(sK2)) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(sK3(empty_set,relation_dom(relation_dom(sK2))),apply(relation_dom(sK2),sK3(empty_set,relation_dom(relation_dom(sK2))))))) = apply(sK2,ordered_pair(sK3(empty_set,relation_dom(relation_dom(sK2))),apply(relation_dom(sK2),sK3(empty_set,relation_dom(relation_dom(sK2)))))) )
| ~ function(relation_dom(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4486,c_3550]) ).
tcf(c_7090,plain,
( in(sK3(empty_set,relation_dom(relation_dom(sK2))),relation_dom(relation_dom(sK0)))
| ( relation_dom(relation_dom(sK2)) = empty_set )
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4486,c_3134]) ).
tcf(c_7092,plain,
( ( relation_dom(relation_dom(sK2)) = empty_set )
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4486,c_3017]) ).
tcf(c_7093,plain,
( ( relation_dom(relation_dom(sK2)) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(sK3(empty_set,relation_dom(relation_dom(sK2))),sK5(relation_dom(sK2),sK3(empty_set,relation_dom(relation_dom(sK2))))))) = apply(sK2,ordered_pair(sK3(empty_set,relation_dom(relation_dom(sK2))),sK5(relation_dom(sK2),sK3(empty_set,relation_dom(relation_dom(sK2)))))) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4486,c_3018]) ).
tcf(c_7141,plain,
( empty(sK2)
| ~ relation(sK2)
| ~ empty(relation_dom(sK2)) ),
inference(instantiation,[status(thm)],[c_67]) ).
tcf(c_7171,plain,
! [X0: $i] :
( ( relation_dom(sK17(powerset(X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6912,c_2124]) ).
tcf(c_7172,plain,
! [X0: $i] :
( ( sK17(powerset(X0)) = relation_dom(sK2) )
| ( apply(sK1,apply(sK0,sK17(relation_dom(sK2)))) = apply(sK2,sK17(relation_dom(sK2))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6912,c_2466]) ).
tcf(c_7173,plain,
! [X0: $i] :
( ( sK17(powerset(X0)) = sK2 )
| ( apply(sK1,apply(sK0,sK17(relation_dom(sK2)))) = apply(sK2,sK17(relation_dom(sK2))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6912,c_2488]) ).
tcf(c_7174,plain,
! [X0: $i,X1: $i] :
( ( sK17(powerset(X0)) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6912,c_60]) ).
tcf(c_7176,plain,
! [X0: $i] :
( relation(sK17(powerset(X0)))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6912,c_85]) ).
tcf(c_7177,plain,
! [X0: $i] :
( function(sK17(powerset(X0)))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6912,c_80]) ).
tcf(c_7227,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_65,c_6244]) ).
tcf(c_7228,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_composition(X1,X0))) = empty_set )
| ~ empty(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_86,c_6244]) ).
tcf(c_7229,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_composition(X0,X1))) = empty_set )
| ~ empty(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_88,c_6244]) ).
tcf(c_7230,plain,
relation_dom(relation_dom(empty_set)) = empty_set,
inference(superposition,[status(thm)],[c_110,c_6244]) ).
tcf(c_7231,plain,
( ( relation_dom(relation_dom(relation_dom(sK2))) = empty_set )
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_2577,c_6244]) ).
tcf(c_7232,plain,
( ( relation_dom(relation_dom(relation_dom(sK2))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_2570,c_6244]) ).
tcf(c_7233,plain,
( ( relation_dom(relation_dom(relation_dom(sK2))) = empty_set )
| ( apply(sK1,apply(sK0,sK17(relation_dom(sK2)))) = apply(sK2,sK17(relation_dom(sK2))) ) ),
inference(superposition,[status(thm)],[c_2425,c_6244]) ).
tcf(c_7235,plain,
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK2)))) = empty_set )
| ~ empty(relation_dom(sK0)) ),
inference(superposition,[status(thm)],[c_3251,c_6244]) ).
tcf(c_7236,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK17(powerset(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6912,c_6244]) ).
tcf(c_7267,plain,
( in(sK3(empty_set,relation_dom(sK2)),relation_dom(sK2))
| ( relation_dom(sK2) = empty_set )
| ( apply(sK1,apply(sK0,sK3(empty_set,relation_dom(sK2)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_7081,c_3475]) ).
tcf(c_7268,plain,
( ( relation_dom(sK2) = empty_set )
| ~ in(relation_dom(sK0),sK3(empty_set,relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_7081,c_64]) ).
tcf(c_7269,plain,
( element(sK3(empty_set,relation_dom(sK2)),relation_dom(sK0))
| ( relation_dom(sK2) = empty_set ) ),
inference(superposition,[status(thm)],[c_7081,c_63]) ).
tcf(c_7270,plain,
( ( relation_dom(sK2) = empty_set )
| ~ empty(relation_dom(sK0)) ),
inference(superposition,[status(thm)],[c_7081,c_61]) ).
tcf(c_7368,plain,
( in(ordered_pair(apply(sK0,sK3(empty_set,relation_dom(sK2))),apply(sK2,sK3(empty_set,relation_dom(sK2)))),sK1)
| ( relation_dom(sK2) = empty_set )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(apply(sK0,sK3(empty_set,relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_7080,c_73]) ).
tcf(c_7369,plain,
( in(ordered_pair(apply(sK0,sK3(empty_set,relation_dom(sK2))),apply(sK2,sK3(empty_set,relation_dom(sK2)))),sK1)
| ( relation_dom(sK2) = empty_set )
| ~ in(apply(sK0,sK3(empty_set,relation_dom(sK2))),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7368,c_57,c_56]) ).
tcf(c_7381,plain,
! [X0: $i] :
( ( sK2 = empty_set )
| ( apply(sK1,apply(sK0,sK17(relation_dom(sK2)))) = empty_set )
| ( apply(sK2,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0)) = empty_set )
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_65,c_6799]) ).
tcf(c_7393,plain,
( ( relation_dom(sK2) = empty_set )
| ~ in(apply(sK0,sK3(empty_set,relation_dom(sK2))),relation_dom(sK1))
| ~ in(sK1,ordered_pair(apply(sK0,sK3(empty_set,relation_dom(sK2))),apply(sK2,sK3(empty_set,relation_dom(sK2))))) ),
inference(superposition,[status(thm)],[c_7369,c_64]) ).
tcf(c_7394,plain,
( element(ordered_pair(apply(sK0,sK3(empty_set,relation_dom(sK2))),apply(sK2,sK3(empty_set,relation_dom(sK2)))),sK1)
| ( relation_dom(sK2) = empty_set )
| ~ in(apply(sK0,sK3(empty_set,relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_7369,c_63]) ).
tcf(c_7397,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(apply(sK0,sK3(empty_set,relation_dom(sK2))),X0),relation_composition(sK1,X1))
| ( relation_dom(sK2) = empty_set )
| ~ relation(sK1)
| ~ relation(X1)
| ~ in(apply(sK0,sK3(empty_set,relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK3(empty_set,relation_dom(sK2))),X0),X1) ),
inference(superposition,[status(thm)],[c_7369,c_299]) ).
tcf(c_7405,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(apply(sK0,sK3(empty_set,relation_dom(sK2))),X0),relation_composition(sK1,X1))
| ( relation_dom(sK2) = empty_set )
| ~ relation(X1)
| ~ in(apply(sK0,sK3(empty_set,relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK3(empty_set,relation_dom(sK2))),X0),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7397,c_56]) ).
tcf(c_7422,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK2) = empty_set )
| ~ relation(X0)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X1),X0)
| ~ in(relation_composition(sK1,X0),ordered_pair(apply(sK0,sK17(relation_dom(sK2))),X1)) ),
inference(superposition,[status(thm)],[c_5928,c_64]) ).
tcf(c_7423,plain,
! [X0: $i,X1: $i] :
( element(ordered_pair(apply(sK0,sK17(relation_dom(sK2))),X0),relation_composition(sK1,X1))
| ( relation_dom(sK2) = empty_set )
| ~ relation(X1)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),X1) ),
inference(superposition,[status(thm)],[c_5928,c_63]) ).
tcf(c_7424,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK2) = empty_set )
| ~ relation(X1)
| ~ empty(relation_composition(sK1,X1))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),X1) ),
inference(superposition,[status(thm)],[c_5928,c_61]) ).
tcf(c_7425,plain,
! [X0: $i,X1: $i] :
( in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(relation_composition(sK1,X1)))
| ( relation_dom(sK2) = empty_set )
| ~ relation(X1)
| ~ relation(relation_composition(sK1,X1))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),X1) ),
inference(superposition,[status(thm)],[c_5928,c_70]) ).
tcf(c_7426,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(ordered_pair(apply(sK0,sK17(relation_dom(sK2))),X2),relation_composition(relation_composition(sK1,X1),X3))
| ( relation_dom(sK2) = empty_set )
| ~ relation(X3)
| ~ relation(X1)
| ~ relation(relation_composition(sK1,X1))
| ~ in(ordered_pair(X0,X2),X3)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),X1) ),
inference(superposition,[status(thm)],[c_5928,c_299]) ).
tcf(c_7427,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK2) = empty_set )
| ( apply(relation_composition(sK1,X1),apply(sK0,sK17(relation_dom(sK2)))) = X0 )
| ~ relation(X1)
| ~ function(relation_composition(sK1,X1))
| ~ relation(relation_composition(sK1,X1))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),X1) ),
inference(superposition,[status(thm)],[c_5928,c_152]) ).
tcf(c_7428,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK2) = empty_set )
| ( apply(X1,sK12(sK1,X1,apply(sK0,sK17(relation_dom(sK2))),X0)) = X0 )
| ~ relation(sK1)
| ~ function(X1)
| ~ relation(X1)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),X1) ),
inference(superposition,[status(thm)],[c_5928,c_2068]) ).
tcf(c_7429,plain,
! [X0: $i] :
( ( relation_dom(sK2) = empty_set )
| ~ relation(sK1)
| ~ empty(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5928,c_2176]) ).
tcf(c_7430,plain,
! [X0: $i] :
( ( relation_dom(sK2) = empty_set )
| ~ relation(sK1)
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5928,c_2063]) ).
tcf(c_7431,plain,
! [X0: $i] :
( ( relation_dom(sK2) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,sK17(relation_dom(sK2))),X0),X0))) = apply(sK2,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,sK17(relation_dom(sK2))),X0),X0)) )
| ~ relation(sK1)
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5928,c_2064]) ).
tcf(c_7455,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK2) = empty_set )
| ( apply(X1,sK12(sK1,X1,apply(sK0,sK17(relation_dom(sK2))),X0)) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7428,c_56]) ).
tcf(c_7477,plain,
! [X0: $i] :
( ( relation_dom(sK2) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,sK17(relation_dom(sK2))),X0),X0))) = apply(sK2,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,sK17(relation_dom(sK2))),X0),X0)) )
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7431,c_56]) ).
tcf(c_7501,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK2) = sK2 )
| ~ relation(X0)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X1),X0)
| ~ in(relation_composition(sK1,X0),ordered_pair(apply(sK0,sK17(relation_dom(sK2))),X1)) ),
inference(superposition,[status(thm)],[c_5975,c_64]) ).
tcf(c_7502,plain,
! [X0: $i,X1: $i] :
( element(ordered_pair(apply(sK0,sK17(relation_dom(sK2))),X0),relation_composition(sK1,X1))
| ( relation_dom(sK2) = sK2 )
| ~ relation(X1)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),X1) ),
inference(superposition,[status(thm)],[c_5975,c_63]) ).
tcf(c_7503,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK2) = sK2 )
| ~ relation(X1)
| ~ empty(relation_composition(sK1,X1))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),X1) ),
inference(superposition,[status(thm)],[c_5975,c_61]) ).
tcf(c_7504,plain,
! [X0: $i,X1: $i] :
( in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(relation_composition(sK1,X1)))
| ( relation_dom(sK2) = sK2 )
| ~ relation(X1)
| ~ relation(relation_composition(sK1,X1))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),X1) ),
inference(superposition,[status(thm)],[c_5975,c_70]) ).
tcf(c_7505,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(ordered_pair(apply(sK0,sK17(relation_dom(sK2))),X2),relation_composition(relation_composition(sK1,X1),X3))
| ( relation_dom(sK2) = sK2 )
| ~ relation(X3)
| ~ relation(X1)
| ~ relation(relation_composition(sK1,X1))
| ~ in(ordered_pair(X0,X2),X3)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),X1) ),
inference(superposition,[status(thm)],[c_5975,c_299]) ).
tcf(c_7506,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK2) = sK2 )
| ( apply(relation_composition(sK1,X1),apply(sK0,sK17(relation_dom(sK2)))) = X0 )
| ~ relation(X1)
| ~ function(relation_composition(sK1,X1))
| ~ relation(relation_composition(sK1,X1))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),X1) ),
inference(superposition,[status(thm)],[c_5975,c_152]) ).
tcf(c_7507,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK2) = sK2 )
| ( apply(X1,sK12(sK1,X1,apply(sK0,sK17(relation_dom(sK2))),X0)) = X0 )
| ~ relation(sK1)
| ~ function(X1)
| ~ relation(X1)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),X1) ),
inference(superposition,[status(thm)],[c_5975,c_2068]) ).
tcf(c_7508,plain,
! [X0: $i] :
( ( relation_dom(sK2) = sK2 )
| ~ relation(sK1)
| ~ empty(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5975,c_2176]) ).
tcf(c_7509,plain,
! [X0: $i] :
( ( relation_dom(sK2) = sK2 )
| ~ relation(sK1)
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5975,c_2063]) ).
tcf(c_7510,plain,
! [X0: $i] :
( ( relation_dom(sK2) = sK2 )
| ( apply(sK1,apply(sK0,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,sK17(relation_dom(sK2))),X0),X0))) = apply(sK2,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,sK17(relation_dom(sK2))),X0),X0)) )
| ~ relation(sK1)
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5975,c_2064]) ).
tcf(c_7516,plain,
! [X0: $i] :
( ( relation_dom(sK2) = sK2 )
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7509,c_56]) ).
tcf(c_7522,plain,
! [X0: $i] :
( ( relation_dom(sK2) = sK2 )
| ~ empty(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7508,c_56]) ).
tcf(c_7544,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK2) = sK2 )
| ( apply(X1,sK12(sK1,X1,apply(sK0,sK17(relation_dom(sK2))),X0)) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7507,c_56]) ).
tcf(c_7566,plain,
! [X0: $i] :
( ( relation_dom(sK2) = sK2 )
| ( apply(sK1,apply(sK0,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,sK17(relation_dom(sK2))),X0),X0))) = apply(sK2,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,sK17(relation_dom(sK2))),X0),X0)) )
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7510,c_56]) ).
tcf(c_7602,plain,
! [X0: $i] :
( ( relation_dom(sK2) = sK2 )
| ~ empty(relation_dom(sK0))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1)) ),
inference(global_subsumption_just,[status(thm)],[c_7522,c_58,c_126,c_2669,c_7522]) ).
tcf(c_7603,plain,
! [X0: $i] :
( ( relation_dom(sK2) = sK2 )
| ~ empty(relation_dom(sK0))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),relation_dom(sK2)) ),
inference(renaming,[status(thm)],[c_7602]) ).
tcf(c_7613,plain,
! [X0: $i] :
( ( relation_dom(sK2) = sK2 )
| ( apply(sK0,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0)) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0))) = empty_set )
| ~ empty(relation_dom(sK0))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_4011,c_7603]) ).
tcf(c_7614,plain,
( ( relation_dom(sK2) = sK2 )
| ~ empty(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(apply(sK2,sK17(relation_dom(sK2))),relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_71,c_7603]) ).
tcf(c_7615,plain,
( ( relation_dom(sK2) = sK2 )
| ~ empty(relation_dom(sK0))
| ~ function(relation_dom(sK2))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(apply(sK2,sK17(relation_dom(sK2))),relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_73,c_7603]) ).
tcf(c_7616,plain,
! [X0: $i] :
( ( relation_dom(sK2) = sK2 )
| ( apply(sK2,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0)) = empty_set )
| ~ function(sK2)
| ~ relation(sK2)
| ~ empty(relation_dom(sK0))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_75,c_7603]) ).
tcf(c_7617,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK2) = sK2 )
| ~ relation(X1)
| ~ empty(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),relation_composition(relation_dom(sK2),X1)) ),
inference(superposition,[status(thm)],[c_301,c_7603]) ).
tcf(c_7623,plain,
! [X0: $i] :
( ( relation_dom(sK2) = sK2 )
| ( apply(sK2,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0)) = empty_set )
| ~ empty(relation_dom(sK0))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7616,c_55,c_54]) ).
tcf(c_7679,plain,
( in(ordered_pair(apply(sK0,sK17(relation_dom(sK2))),apply(sK2,sK17(relation_dom(sK2)))),sK1)
| ( relation_dom(relation_dom(sK2)) = empty_set )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_6250,c_73]) ).
tcf(c_7680,plain,
( in(ordered_pair(apply(sK0,sK17(relation_dom(sK2))),apply(sK2,sK17(relation_dom(sK2)))),sK1)
| ( relation_dom(relation_dom(sK2)) = empty_set )
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7679,c_57,c_56]) ).
tcf(c_7689,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| ( powerset(X1) = empty_set )
| ~ in(X0,sK3(empty_set,powerset(X1))) ),
inference(superposition,[status(thm)],[c_7084,c_100]) ).
tcf(c_7690,plain,
! [X0: $i,X1: $i] :
( ( powerset(X1) = empty_set )
| ~ empty(X1)
| ~ in(X0,sK3(empty_set,powerset(X1))) ),
inference(superposition,[status(thm)],[c_7084,c_99]) ).
tcf(c_7733,plain,
! [X0: $i] :
( ( sK17(powerset(relation_dom(X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_65,c_7088]) ).
tcf(c_7734,plain,
! [X0: $i,X1: $i] :
( ( sK17(powerset(relation_composition(X1,X0))) = empty_set )
| ~ empty(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_86,c_7088]) ).
tcf(c_7735,plain,
! [X0: $i,X1: $i] :
( ( sK17(powerset(relation_composition(X0,X1))) = empty_set )
| ~ empty(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_88,c_7088]) ).
tcf(c_7736,plain,
sK17(powerset(empty_set)) = empty_set,
inference(superposition,[status(thm)],[c_110,c_7088]) ).
tcf(c_7737,plain,
( ( sK17(powerset(relation_dom(sK2))) = empty_set )
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_2577,c_7088]) ).
tcf(c_7738,plain,
( ( sK17(powerset(relation_dom(sK2))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_2570,c_7088]) ).
tcf(c_7739,plain,
( ( sK17(powerset(relation_dom(sK2))) = empty_set )
| ( apply(sK1,apply(sK0,sK17(relation_dom(sK2)))) = apply(sK2,sK17(relation_dom(sK2))) ) ),
inference(superposition,[status(thm)],[c_2425,c_7088]) ).
tcf(c_7740,plain,
( ( sK17(powerset(sK2)) = empty_set )
| ( apply(sK1,apply(sK0,sK17(relation_dom(sK2)))) = apply(sK2,sK17(relation_dom(sK2))) ) ),
inference(superposition,[status(thm)],[c_2475,c_7088]) ).
tcf(c_7741,plain,
( ( sK17(powerset(relation_dom(relation_dom(sK2)))) = empty_set )
| ~ empty(relation_dom(sK0)) ),
inference(superposition,[status(thm)],[c_3251,c_7088]) ).
tcf(c_7742,plain,
! [X0: $i] :
( ( sK17(powerset(sK17(powerset(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6912,c_7088]) ).
tcf(c_7870,plain,
( ( relation_dom(relation_dom(sK2)) = empty_set )
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(sK1,ordered_pair(apply(sK0,sK17(relation_dom(sK2))),apply(sK2,sK17(relation_dom(sK2))))) ),
inference(superposition,[status(thm)],[c_7680,c_64]) ).
tcf(c_7871,plain,
( element(ordered_pair(apply(sK0,sK17(relation_dom(sK2))),apply(sK2,sK17(relation_dom(sK2)))),sK1)
| ( relation_dom(relation_dom(sK2)) = empty_set )
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_7680,c_63]) ).
tcf(c_7874,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(apply(sK0,sK17(relation_dom(sK2))),X0),relation_composition(sK1,X1))
| ( relation_dom(relation_dom(sK2)) = empty_set )
| ~ relation(sK1)
| ~ relation(X1)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),X1) ),
inference(superposition,[status(thm)],[c_7680,c_299]) ).
tcf(c_7882,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(apply(sK0,sK17(relation_dom(sK2))),X0),relation_composition(sK1,X1))
| ( relation_dom(relation_dom(sK2)) = empty_set )
| ~ relation(X1)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7874,c_56]) ).
tcf(c_7918,plain,
! [X0: $i] :
( ( relation_dom(sK2) = sK2 )
| ( apply(sK0,sK17(relation_dom(sK2))) = empty_set )
| ( apply(sK1,apply(sK0,sK17(relation_dom(sK2)))) = empty_set )
| ( apply(sK2,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0)) = empty_set )
| ~ empty(relation_dom(sK0)) ),
inference(superposition,[status(thm)],[c_6078,c_7623]) ).
tcf(c_7919,plain,
! [X0: $i] :
( ( relation_dom(sK2) = sK2 )
| ( apply(sK2,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0)) = empty_set )
| ~ empty(relation_dom(sK0))
| ~ in(sK17(relation_dom(sK2)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_52,c_7623]) ).
tcf(c_7920,plain,
! [X0: $i] :
( ( relation_dom(sK2) = sK2 )
| ( apply(sK1,apply(sK0,sK17(relation_dom(sK2)))) = empty_set )
| ( apply(sK2,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0)) = empty_set )
| ~ function(sK1)
| ~ relation(sK1)
| ~ empty(relation_dom(sK0)) ),
inference(superposition,[status(thm)],[c_75,c_7623]) ).
tcf(c_7925,plain,
! [X0: $i] :
( ( relation_dom(sK2) = sK2 )
| ( apply(sK1,apply(sK0,sK17(relation_dom(sK2)))) = empty_set )
| ( apply(sK2,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0)) = empty_set )
| ~ empty(relation_dom(sK0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7920,c_57,c_56]) ).
tcf(c_7946,plain,
! [X0: $i] :
( ( relation_dom(sK2) = sK2 )
| ( apply(sK2,sK17(relation_dom(sK2))) = empty_set )
| ( apply(sK2,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0)) = empty_set )
| ~ function(sK2)
| ~ relation(sK2)
| ~ empty(relation_dom(sK0)) ),
inference(superposition,[status(thm)],[c_75,c_7919]) ).
tcf(c_7947,plain,
! [X0: $i] :
( empty(relation_dom(sK2))
| ( relation_dom(sK2) = sK2 )
| ( apply(sK2,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0)) = empty_set )
| ~ empty(relation_dom(sK0)) ),
inference(superposition,[status(thm)],[c_2361,c_7919]) ).
tcf(c_7952,plain,
! [X0: $i] :
( ( relation_dom(sK2) = sK2 )
| ( apply(sK2,sK17(relation_dom(sK2))) = empty_set )
| ( apply(sK2,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0)) = empty_set )
| ~ empty(relation_dom(sK0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7946,c_55,c_54]) ).
tcf(c_7966,plain,
! [X0: $i] :
( ( relation_dom(sK2) = sK2 )
| ( apply(sK2,sK17(relation_dom(sK2))) = empty_set )
| ( apply(sK2,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0)) = empty_set )
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_65,c_7952]) ).
tcf(c_7980,plain,
! [X0: $i] :
( ( relation_dom(sK2) = sK2 )
| ( apply(sK1,apply(sK0,sK17(relation_dom(sK2)))) = empty_set )
| ( apply(sK2,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0)) = empty_set )
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_65,c_7925]) ).
tcf(c_7998,plain,
! [X0: $i,X1: $i] :
( ( apply(sK2,X0) = empty_set )
| ( apply(sK0,ordered_pair(apply(sK2,X0),X1)) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(apply(sK2,X0),X1))) = empty_set )
| ( apply(relation_dom(sK2),sK12(sK1,relation_dom(sK2),apply(sK0,X0),X1)) = X1 )
| ~ function(relation_dom(sK2))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,X0),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_4011,c_6175]) ).
tcf(c_7999,plain,
! [X0: $i,X1: $i] :
( ( apply(sK2,X0) = empty_set )
| ( apply(sK0,ordered_pair(apply(sK2,X0),X1)) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(apply(sK2,X0),X1))) = empty_set )
| ( apply(relation_dom(sK0),sK12(sK1,relation_dom(sK0),apply(sK0,X0),X1)) = X1 )
| ~ function(relation_dom(sK0))
| ~ relation(relation_dom(sK0))
| ~ in(apply(sK0,X0),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_4110,c_6175]) ).
tcf(c_8000,plain,
! [X0: $i,X1: $i] :
( ( apply(sK2,X0) = empty_set )
| ( apply(sK2,ordered_pair(apply(sK2,X0),X1)) = empty_set )
| ( apply(relation_dom(sK0),sK12(sK1,relation_dom(sK0),apply(sK0,X0),X1)) = X1 )
| ~ function(relation_dom(sK0))
| ~ relation(relation_dom(sK0))
| ~ in(apply(sK0,X0),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_3449,c_6175]) ).
tcf(c_8001,plain,
! [X0: $i,X1: $i] :
( ( apply(sK2,X0) = empty_set )
| ( apply(X1,sK12(sK1,X1,apply(sK0,X0),sK5(X1,apply(sK2,X0)))) = sK5(X1,apply(sK2,X0)) )
| ~ function(X1)
| ~ relation(X1)
| ~ in(apply(sK0,X0),relation_dom(sK1))
| ~ in(apply(sK2,X0),relation_dom(X1)) ),
inference(superposition,[status(thm)],[c_71,c_6175]) ).
tcf(c_8002,plain,
! [X0: $i,X1: $i] :
( ( apply(sK2,X0) = empty_set )
| ( apply(X1,sK12(sK1,X1,apply(sK0,X0),apply(X1,apply(sK2,X0)))) = apply(X1,apply(sK2,X0)) )
| ~ function(X1)
| ~ relation(X1)
| ~ in(apply(sK0,X0),relation_dom(sK1))
| ~ in(apply(sK2,X0),relation_dom(X1)) ),
inference(superposition,[status(thm)],[c_73,c_6175]) ).
tcf(c_8003,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(sK2,X0) = empty_set )
| ( apply(X1,ordered_pair(apply(sK2,X0),X2)) = empty_set )
| ( apply(relation_dom(X1),sK12(sK1,relation_dom(X1),apply(sK0,X0),X2)) = X2 )
| ~ function(X1)
| ~ relation(X1)
| ~ function(relation_dom(X1))
| ~ relation(relation_dom(X1))
| ~ in(apply(sK0,X0),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_75,c_6175]) ).
tcf(c_8004,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( apply(sK2,X0) = empty_set )
| ( apply(X2,sK12(sK1,X2,apply(sK0,X0),sK12(X2,X3,apply(sK2,X0),X1))) = sK12(X2,X3,apply(sK2,X0),X1) )
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ in(apply(sK0,X0),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,X0),X1),relation_composition(X2,X3)) ),
inference(superposition,[status(thm)],[c_301,c_6175]) ).
tcf(c_8005,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(sK2,X0) = empty_set )
| ( apply(relation_dom(sK0),sK12(sK1,relation_dom(sK0),apply(sK0,X0),sK12(relation_dom(sK2),X2,apply(sK2,X0),X1))) = sK12(relation_dom(sK2),X2,apply(sK2,X0),X1) )
| ~ relation(X2)
| ~ function(relation_dom(sK0))
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,X0),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,X0),X1),relation_composition(relation_dom(sK2),X2)) ),
inference(superposition,[status(thm)],[c_2283,c_6175]) ).
tcf(c_8006,plain,
! [X0: $i] :
( ( apply(sK2,X0) = empty_set )
| ( apply(relation_dom(sK0),sK12(sK1,relation_dom(sK0),apply(sK0,X0),sK5(relation_dom(sK2),apply(sK2,X0)))) = sK5(relation_dom(sK2),apply(sK2,X0)) )
| ~ function(relation_dom(sK0))
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,X0),relation_dom(sK1))
| ~ in(apply(sK2,X0),relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_3019,c_6175]) ).
tcf(c_8007,plain,
! [X0: $i] :
( ( apply(sK2,X0) = empty_set )
| ( apply(relation_dom(sK0),sK12(sK1,relation_dom(sK0),apply(sK0,X0),apply(relation_dom(sK2),apply(sK2,X0)))) = apply(relation_dom(sK2),apply(sK2,X0)) )
| ~ function(relation_dom(sK0))
| ~ function(relation_dom(sK2))
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,X0),relation_dom(sK1))
| ~ in(apply(sK2,X0),relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_3551,c_6175]) ).
tcf(c_8106,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK2)) = empty_set )
| ~ relation(X0)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X1),X0)
| ~ in(relation_composition(sK1,X0),ordered_pair(apply(sK0,sK17(relation_dom(sK2))),X1)) ),
inference(superposition,[status(thm)],[c_7882,c_64]) ).
tcf(c_8107,plain,
! [X0: $i,X1: $i] :
( element(ordered_pair(apply(sK0,sK17(relation_dom(sK2))),X0),relation_composition(sK1,X1))
| ( relation_dom(relation_dom(sK2)) = empty_set )
| ~ relation(X1)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),X1) ),
inference(superposition,[status(thm)],[c_7882,c_63]) ).
tcf(c_8108,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK2)) = empty_set )
| ~ relation(X1)
| ~ empty(relation_composition(sK1,X1))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),X1) ),
inference(superposition,[status(thm)],[c_7882,c_61]) ).
tcf(c_8109,plain,
! [X0: $i,X1: $i] :
( in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(relation_composition(sK1,X1)))
| ( relation_dom(relation_dom(sK2)) = empty_set )
| ~ relation(X1)
| ~ relation(relation_composition(sK1,X1))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),X1) ),
inference(superposition,[status(thm)],[c_7882,c_70]) ).
tcf(c_8110,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(ordered_pair(apply(sK0,sK17(relation_dom(sK2))),X2),relation_composition(relation_composition(sK1,X1),X3))
| ( relation_dom(relation_dom(sK2)) = empty_set )
| ~ relation(X3)
| ~ relation(X1)
| ~ relation(relation_composition(sK1,X1))
| ~ in(ordered_pair(X0,X2),X3)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),X1) ),
inference(superposition,[status(thm)],[c_7882,c_299]) ).
tcf(c_8111,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK2)) = empty_set )
| ( apply(relation_composition(sK1,X1),apply(sK0,sK17(relation_dom(sK2)))) = X0 )
| ~ relation(X1)
| ~ function(relation_composition(sK1,X1))
| ~ relation(relation_composition(sK1,X1))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),X1) ),
inference(superposition,[status(thm)],[c_7882,c_152]) ).
tcf(c_8112,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK2)) = empty_set )
| ( apply(X1,sK12(sK1,X1,apply(sK0,sK17(relation_dom(sK2))),X0)) = X0 )
| ~ relation(sK1)
| ~ function(X1)
| ~ relation(X1)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),X1) ),
inference(superposition,[status(thm)],[c_7882,c_2068]) ).
tcf(c_8113,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK2)) = empty_set )
| ~ relation(sK1)
| ~ empty(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_7882,c_2176]) ).
tcf(c_8114,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK2)) = empty_set )
| ~ relation(sK1)
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_7882,c_2063]) ).
tcf(c_8115,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK2)) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,sK17(relation_dom(sK2))),X0),X0))) = apply(sK2,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,sK17(relation_dom(sK2))),X0),X0)) )
| ~ relation(sK1)
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_7882,c_2064]) ).
tcf(c_8139,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK2)) = empty_set )
| ( apply(X1,sK12(sK1,X1,apply(sK0,sK17(relation_dom(sK2))),X0)) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8112,c_56]) ).
tcf(c_8161,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK2)) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,sK17(relation_dom(sK2))),X0),X0))) = apply(sK2,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,sK17(relation_dom(sK2))),X0),X0)) )
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8115,c_56]) ).
tcf(c_8201,plain,
! [X0: $i,X1: $i] :
( ( apply(sK0,X0) = empty_set )
| ( apply(sK1,apply(sK0,X0)) = empty_set )
| ( apply(sK0,ordered_pair(apply(sK2,X0),X1)) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(apply(sK2,X0),X1))) = empty_set )
| ( apply(relation_dom(sK2),sK12(sK1,relation_dom(sK2),apply(sK0,X0),X1)) = X1 )
| ~ function(relation_dom(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4011,c_6526]) ).
tcf(c_8202,plain,
! [X0: $i,X1: $i] :
( ( apply(sK0,X0) = empty_set )
| ( apply(sK1,apply(sK0,X0)) = empty_set )
| ( apply(sK0,ordered_pair(apply(sK2,X0),X1)) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(apply(sK2,X0),X1))) = empty_set )
| ( apply(relation_dom(sK0),sK12(sK1,relation_dom(sK0),apply(sK0,X0),X1)) = X1 )
| ~ function(relation_dom(sK0))
| ~ relation(relation_dom(sK0)) ),
inference(superposition,[status(thm)],[c_4110,c_6526]) ).
tcf(c_8203,plain,
! [X0: $i,X1: $i] :
( ( apply(sK0,X0) = empty_set )
| ( apply(sK1,apply(sK0,X0)) = empty_set )
| ( apply(sK2,ordered_pair(apply(sK2,X0),X1)) = empty_set )
| ( apply(relation_dom(sK0),sK12(sK1,relation_dom(sK0),apply(sK0,X0),X1)) = X1 )
| ~ function(relation_dom(sK0))
| ~ relation(relation_dom(sK0)) ),
inference(superposition,[status(thm)],[c_3449,c_6526]) ).
tcf(c_8204,plain,
! [X0: $i,X1: $i] :
( ( apply(sK0,X0) = empty_set )
| ( apply(sK1,apply(sK0,X0)) = empty_set )
| ( apply(X1,sK12(sK1,X1,apply(sK0,X0),sK5(X1,apply(sK2,X0)))) = sK5(X1,apply(sK2,X0)) )
| ~ function(X1)
| ~ relation(X1)
| ~ in(apply(sK2,X0),relation_dom(X1)) ),
inference(superposition,[status(thm)],[c_71,c_6526]) ).
tcf(c_8205,plain,
! [X0: $i,X1: $i] :
( ( apply(sK0,X0) = empty_set )
| ( apply(sK1,apply(sK0,X0)) = empty_set )
| ( apply(X1,sK12(sK1,X1,apply(sK0,X0),apply(X1,apply(sK2,X0)))) = apply(X1,apply(sK2,X0)) )
| ~ function(X1)
| ~ relation(X1)
| ~ in(apply(sK2,X0),relation_dom(X1)) ),
inference(superposition,[status(thm)],[c_73,c_6526]) ).
tcf(c_8206,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(sK0,X1) = empty_set )
| ( apply(sK1,apply(sK0,X1)) = empty_set )
| ( apply(X0,ordered_pair(apply(sK2,X1),X2)) = empty_set )
| ( apply(relation_dom(X0),sK12(sK1,relation_dom(X0),apply(sK0,X1),X2)) = X2 )
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom(X0))
| ~ relation(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_75,c_6526]) ).
tcf(c_8207,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( apply(sK0,X0) = empty_set )
| ( apply(sK1,apply(sK0,X0)) = empty_set )
| ( apply(X2,sK12(sK1,X2,apply(sK0,X0),sK12(X2,X3,apply(sK2,X0),X1))) = sK12(X2,X3,apply(sK2,X0),X1) )
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ in(ordered_pair(apply(sK2,X0),X1),relation_composition(X2,X3)) ),
inference(superposition,[status(thm)],[c_301,c_6526]) ).
tcf(c_8208,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(sK0,X0) = empty_set )
| ( apply(sK1,apply(sK0,X0)) = empty_set )
| ( apply(relation_dom(sK0),sK12(sK1,relation_dom(sK0),apply(sK0,X0),sK12(relation_dom(sK2),X2,apply(sK2,X0),X1))) = sK12(relation_dom(sK2),X2,apply(sK2,X0),X1) )
| ~ relation(X2)
| ~ function(relation_dom(sK0))
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(ordered_pair(apply(sK2,X0),X1),relation_composition(relation_dom(sK2),X2)) ),
inference(superposition,[status(thm)],[c_2283,c_6526]) ).
tcf(c_8209,plain,
! [X0: $i] :
( ( apply(sK0,X0) = empty_set )
| ( apply(sK1,apply(sK0,X0)) = empty_set )
| ( apply(relation_dom(sK0),sK12(sK1,relation_dom(sK0),apply(sK0,X0),sK5(relation_dom(sK2),apply(sK2,X0)))) = sK5(relation_dom(sK2),apply(sK2,X0)) )
| ~ function(relation_dom(sK0))
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK2,X0),relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_3019,c_6526]) ).
tcf(c_8210,plain,
! [X0: $i] :
( ( apply(sK0,X0) = empty_set )
| ( apply(sK1,apply(sK0,X0)) = empty_set )
| ( apply(relation_dom(sK0),sK12(sK1,relation_dom(sK0),apply(sK0,X0),apply(relation_dom(sK2),apply(sK2,X0)))) = apply(relation_dom(sK2),apply(sK2,X0)) )
| ~ function(relation_dom(sK0))
| ~ function(relation_dom(sK2))
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK2,X0),relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_3551,c_6526]) ).
tcf(c_8322,plain,
( in(ordered_pair(apply(sK0,sK17(relation_dom(sK2))),apply(sK2,sK17(relation_dom(sK2)))),sK1)
| ( relation_dom(relation_dom(relation_dom(sK2))) = empty_set )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_7233,c_73]) ).
tcf(c_8323,plain,
( in(ordered_pair(apply(sK0,sK17(relation_dom(sK2))),apply(sK2,sK17(relation_dom(sK2)))),sK1)
| ( relation_dom(relation_dom(relation_dom(sK2))) = empty_set )
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8322,c_57,c_56]) ).
tcf(c_8327,plain,
( empty(powerset(empty_set))
| ~ in(powerset(empty_set),empty_set) ),
inference(superposition,[status(thm)],[c_7736,c_2427]) ).
tcf(c_8328,plain,
( empty(powerset(empty_set))
| in(empty_set,powerset(empty_set)) ),
inference(superposition,[status(thm)],[c_7736,c_2361]) ).
tcf(c_8329,plain,
element(empty_set,powerset(empty_set)),
inference(superposition,[status(thm)],[c_7736,c_105]) ).
tcf(c_8341,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| in(sK3(sK16(X0),X1),X1)
| element(ordered_pair(sK3(sK16(X0),X1),sK4(sK16(X0),X1)),X0)
| ( relation_dom(sK16(X0)) = X1 )
| ~ relation(sK16(X0)) ),
inference(superposition,[status(thm)],[c_69,c_2939]) ).
tcf(c_8342,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| element(ordered_pair(X0,sK5(sK16(X1),X0)),X1)
| ~ relation(sK16(X1))
| ~ in(X0,relation_dom(sK16(X1))) ),
inference(superposition,[status(thm)],[c_71,c_2939]) ).
tcf(c_8343,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| element(ordered_pair(X0,apply(sK16(X1),X0)),X1)
| ~ function(sK16(X1))
| ~ relation(sK16(X1))
| ~ in(X0,relation_dom(sK16(X1))) ),
inference(superposition,[status(thm)],[c_73,c_2939]) ).
tcf(c_8344,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X0)
| element(ordered_pair(sK9(X1,X2,sK16(X0)),sK10(X1,X2,sK16(X0))),X0)
| in(ordered_pair(sK11(X1,X2,sK16(X0)),sK10(X1,X2,sK16(X0))),X2)
| ( relation_composition(X1,X2) = sK16(X0) )
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(sK16(X0)) ),
inference(superposition,[status(thm)],[c_93,c_2939]) ).
tcf(c_8345,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X0)
| element(ordered_pair(sK9(X1,X2,sK16(X0)),sK10(X1,X2,sK16(X0))),X0)
| in(ordered_pair(sK9(X1,X2,sK16(X0)),sK11(X1,X2,sK16(X0))),X1)
| ( relation_composition(X1,X2) = sK16(X0) )
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(sK16(X0)) ),
inference(superposition,[status(thm)],[c_92,c_2939]) ).
tcf(c_8346,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X0)
| element(ordered_pair(sK9(sK16(X0),X1,X2),sK11(sK16(X0),X1,X2)),X0)
| in(ordered_pair(sK9(sK16(X0),X1,X2),sK10(sK16(X0),X1,X2)),X2)
| ( relation_composition(sK16(X0),X1) = X2 )
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(sK16(X0)) ),
inference(superposition,[status(thm)],[c_92,c_2939]) ).
tcf(c_8347,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X0)
| element(ordered_pair(sK11(X1,sK16(X0),X2),sK10(X1,sK16(X0),X2)),X0)
| in(ordered_pair(sK9(X1,sK16(X0),X2),sK10(X1,sK16(X0),X2)),X2)
| ( relation_composition(X1,sK16(X0)) = X2 )
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(sK16(X0)) ),
inference(superposition,[status(thm)],[c_93,c_2939]) ).
tcf(c_8348,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( empty(X2)
| element(ordered_pair(X0,sK12(sK16(X2),X3,X0,X1)),X2)
| ~ relation(X3)
| ~ relation(sK16(X2))
| ~ in(ordered_pair(X0,X1),relation_composition(sK16(X2),X3)) ),
inference(superposition,[status(thm)],[c_301,c_2939]) ).
tcf(c_8349,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( empty(X3)
| element(ordered_pair(sK12(X2,sK16(X3),X0,X1),X1),X3)
| ~ relation(X2)
| ~ relation(sK16(X3))
| ~ in(ordered_pair(X0,X1),relation_composition(X2,sK16(X3))) ),
inference(superposition,[status(thm)],[c_300,c_2939]) ).
tcf(c_8350,plain,
! [X0: $i] :
( empty(X0)
| empty(sK16(X0))
| element(sK17(sK16(X0)),X0) ),
inference(superposition,[status(thm)],[c_2361,c_2939]) ).
tcf(c_8351,plain,
! [X0: $i] :
( empty(X0)
| element(sK3(empty_set,sK16(X0)),X0)
| ( sK16(X0) = empty_set ) ),
inference(superposition,[status(thm)],[c_4486,c_2939]) ).
tcf(c_8451,plain,
! [X0: $i] : ~ in(X0,relation_dom(relation_dom(empty_set))),
inference(global_subsumption_just,[status(thm)],[c_3827,c_110,c_2907,c_3827]) ).
tcf(c_8464,plain,
! [X0: $i] :
( ( apply(sK2,X0) = empty_set )
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_65,c_3891]) ).
tcf(c_8481,plain,
( element(sK17(empty_set),empty_set)
| empty(sK17(powerset(empty_set))) ),
inference(superposition,[status(thm)],[c_7736,c_7013]) ).
tcf(c_8482,plain,
! [X0: $i] :
( empty(X0)
| empty(sK17(powerset(X0)))
| in(sK17(sK17(powerset(X0))),X0) ),
inference(superposition,[status(thm)],[c_7013,c_62]) ).
tcf(c_8483,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| empty(sK17(powerset(powerset(X1))))
| ~ in(X0,sK17(sK17(powerset(powerset(X1))))) ),
inference(superposition,[status(thm)],[c_7013,c_100]) ).
tcf(c_8484,plain,
! [X0: $i,X1: $i] :
( empty(sK17(powerset(powerset(X1))))
| ~ empty(X1)
| ~ in(X0,sK17(sK17(powerset(powerset(X1))))) ),
inference(superposition,[status(thm)],[c_7013,c_99]) ).
tcf(c_8485,plain,
( empty(empty_set)
| element(sK17(empty_set),empty_set) ),
inference(light_normalisation,[status(thm)],[c_8481,c_7736]) ).
tcf(c_8504,plain,
( ( relation_dom(relation_dom(relation_dom(sK2))) = empty_set )
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(sK1,ordered_pair(apply(sK0,sK17(relation_dom(sK2))),apply(sK2,sK17(relation_dom(sK2))))) ),
inference(superposition,[status(thm)],[c_8323,c_64]) ).
tcf(c_8505,plain,
( element(ordered_pair(apply(sK0,sK17(relation_dom(sK2))),apply(sK2,sK17(relation_dom(sK2)))),sK1)
| ( relation_dom(relation_dom(relation_dom(sK2))) = empty_set )
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8323,c_63]) ).
tcf(c_8508,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(apply(sK0,sK17(relation_dom(sK2))),X0),relation_composition(sK1,X1))
| ( relation_dom(relation_dom(relation_dom(sK2))) = empty_set )
| ~ relation(sK1)
| ~ relation(X1)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),X1) ),
inference(superposition,[status(thm)],[c_8323,c_299]) ).
tcf(c_8516,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(apply(sK0,sK17(relation_dom(sK2))),X0),relation_composition(sK1,X1))
| ( relation_dom(relation_dom(relation_dom(sK2))) = empty_set )
| ~ relation(X1)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8508,c_56]) ).
tcf(c_8533,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(sK2))) = empty_set )
| ~ relation(X0)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X1),X0)
| ~ in(relation_composition(sK1,X0),ordered_pair(apply(sK0,sK17(relation_dom(sK2))),X1)) ),
inference(superposition,[status(thm)],[c_8516,c_64]) ).
tcf(c_8534,plain,
! [X0: $i,X1: $i] :
( element(ordered_pair(apply(sK0,sK17(relation_dom(sK2))),X0),relation_composition(sK1,X1))
| ( relation_dom(relation_dom(relation_dom(sK2))) = empty_set )
| ~ relation(X1)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),X1) ),
inference(superposition,[status(thm)],[c_8516,c_63]) ).
tcf(c_8535,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(sK2))) = empty_set )
| ~ relation(X1)
| ~ empty(relation_composition(sK1,X1))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),X1) ),
inference(superposition,[status(thm)],[c_8516,c_61]) ).
tcf(c_8536,plain,
! [X0: $i,X1: $i] :
( in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(relation_composition(sK1,X1)))
| ( relation_dom(relation_dom(relation_dom(sK2))) = empty_set )
| ~ relation(X1)
| ~ relation(relation_composition(sK1,X1))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),X1) ),
inference(superposition,[status(thm)],[c_8516,c_70]) ).
tcf(c_8537,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(ordered_pair(apply(sK0,sK17(relation_dom(sK2))),X2),relation_composition(relation_composition(sK1,X1),X3))
| ( relation_dom(relation_dom(relation_dom(sK2))) = empty_set )
| ~ relation(X3)
| ~ relation(X1)
| ~ relation(relation_composition(sK1,X1))
| ~ in(ordered_pair(X0,X2),X3)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),X1) ),
inference(superposition,[status(thm)],[c_8516,c_299]) ).
tcf(c_8538,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(sK2))) = empty_set )
| ( apply(relation_composition(sK1,X1),apply(sK0,sK17(relation_dom(sK2)))) = X0 )
| ~ relation(X1)
| ~ function(relation_composition(sK1,X1))
| ~ relation(relation_composition(sK1,X1))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),X1) ),
inference(superposition,[status(thm)],[c_8516,c_152]) ).
tcf(c_8539,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(sK2))) = empty_set )
| ( apply(X1,sK12(sK1,X1,apply(sK0,sK17(relation_dom(sK2))),X0)) = X0 )
| ~ relation(sK1)
| ~ function(X1)
| ~ relation(X1)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),X1) ),
inference(superposition,[status(thm)],[c_8516,c_2068]) ).
tcf(c_8540,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK2))) = empty_set )
| ~ relation(sK1)
| ~ empty(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_8516,c_2176]) ).
tcf(c_8541,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK2))) = empty_set )
| ~ relation(sK1)
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_8516,c_2063]) ).
tcf(c_8542,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK2))) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,sK17(relation_dom(sK2))),X0),X0))) = apply(sK2,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,sK17(relation_dom(sK2))),X0),X0)) )
| ~ relation(sK1)
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_8516,c_2064]) ).
tcf(c_8548,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK2))) = empty_set )
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8541,c_56]) ).
tcf(c_8571,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(sK2))) = empty_set )
| ( apply(X1,sK12(sK1,X1,apply(sK0,sK17(relation_dom(sK2))),X0)) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8539,c_56]) ).
tcf(c_8593,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK2))) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,sK17(relation_dom(sK2))),X0),X0))) = apply(sK2,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,sK17(relation_dom(sK2))),X0),X0)) )
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8542,c_56]) ).
tcf(c_8654,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK2) = empty_set )
| ~ relation(X0)
| ~ in(apply(sK0,sK3(empty_set,relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK3(empty_set,relation_dom(sK2))),X1),X0)
| ~ in(relation_composition(sK1,X0),ordered_pair(apply(sK0,sK3(empty_set,relation_dom(sK2))),X1)) ),
inference(superposition,[status(thm)],[c_7405,c_64]) ).
tcf(c_8655,plain,
! [X0: $i,X1: $i] :
( element(ordered_pair(apply(sK0,sK3(empty_set,relation_dom(sK2))),X0),relation_composition(sK1,X1))
| ( relation_dom(sK2) = empty_set )
| ~ relation(X1)
| ~ in(apply(sK0,sK3(empty_set,relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK3(empty_set,relation_dom(sK2))),X0),X1) ),
inference(superposition,[status(thm)],[c_7405,c_63]) ).
tcf(c_8656,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK2) = empty_set )
| ~ relation(X1)
| ~ empty(relation_composition(sK1,X1))
| ~ in(apply(sK0,sK3(empty_set,relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK3(empty_set,relation_dom(sK2))),X0),X1) ),
inference(superposition,[status(thm)],[c_7405,c_61]) ).
tcf(c_8657,plain,
! [X0: $i,X1: $i] :
( in(apply(sK0,sK3(empty_set,relation_dom(sK2))),relation_dom(relation_composition(sK1,X1)))
| ( relation_dom(sK2) = empty_set )
| ~ relation(X1)
| ~ relation(relation_composition(sK1,X1))
| ~ in(apply(sK0,sK3(empty_set,relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK3(empty_set,relation_dom(sK2))),X0),X1) ),
inference(superposition,[status(thm)],[c_7405,c_70]) ).
tcf(c_8658,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(ordered_pair(apply(sK0,sK3(empty_set,relation_dom(sK2))),X2),relation_composition(relation_composition(sK1,X1),X3))
| ( relation_dom(sK2) = empty_set )
| ~ relation(X3)
| ~ relation(X1)
| ~ relation(relation_composition(sK1,X1))
| ~ in(ordered_pair(X0,X2),X3)
| ~ in(apply(sK0,sK3(empty_set,relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK3(empty_set,relation_dom(sK2))),X0),X1) ),
inference(superposition,[status(thm)],[c_7405,c_299]) ).
tcf(c_8659,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK2) = empty_set )
| ( apply(relation_composition(sK1,X1),apply(sK0,sK3(empty_set,relation_dom(sK2)))) = X0 )
| ~ relation(X1)
| ~ function(relation_composition(sK1,X1))
| ~ relation(relation_composition(sK1,X1))
| ~ in(apply(sK0,sK3(empty_set,relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK3(empty_set,relation_dom(sK2))),X0),X1) ),
inference(superposition,[status(thm)],[c_7405,c_152]) ).
tcf(c_8660,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK2) = empty_set )
| ( apply(X1,sK12(sK1,X1,apply(sK0,sK3(empty_set,relation_dom(sK2))),X0)) = X0 )
| ~ relation(sK1)
| ~ function(X1)
| ~ relation(X1)
| ~ in(apply(sK0,sK3(empty_set,relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK3(empty_set,relation_dom(sK2))),X0),X1) ),
inference(superposition,[status(thm)],[c_7405,c_2068]) ).
tcf(c_8661,plain,
! [X0: $i] :
( ( relation_dom(sK2) = empty_set )
| ~ relation(sK1)
| ~ empty(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK3(empty_set,relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK3(empty_set,relation_dom(sK2))),X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_7405,c_2176]) ).
tcf(c_8662,plain,
! [X0: $i] :
( ( relation_dom(sK2) = empty_set )
| ~ relation(sK1)
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK3(empty_set,relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK3(empty_set,relation_dom(sK2))),X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_7405,c_2063]) ).
tcf(c_8663,plain,
! [X0: $i] :
( ( relation_dom(sK2) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,sK3(empty_set,relation_dom(sK2))),X0),X0))) = apply(sK2,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,sK3(empty_set,relation_dom(sK2))),X0),X0)) )
| ~ relation(sK1)
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK3(empty_set,relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK3(empty_set,relation_dom(sK2))),X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_7405,c_2064]) ).
tcf(c_8687,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK2) = empty_set )
| ( apply(X1,sK12(sK1,X1,apply(sK0,sK3(empty_set,relation_dom(sK2))),X0)) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ in(apply(sK0,sK3(empty_set,relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK3(empty_set,relation_dom(sK2))),X0),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8660,c_56]) ).
tcf(c_8709,plain,
! [X0: $i] :
( ( relation_dom(sK2) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,sK3(empty_set,relation_dom(sK2))),X0),X0))) = apply(sK2,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,sK3(empty_set,relation_dom(sK2))),X0),X0)) )
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK3(empty_set,relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK3(empty_set,relation_dom(sK2))),X0),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8663,c_56]) ).
tcf(c_8781,plain,
( ( relation_dom(relation_dom(sK2)) = relation_dom(sK2) )
| ( apply(sK1,apply(sK0,ordered_pair(sK3(relation_dom(sK2),relation_dom(sK2)),sK4(relation_dom(sK2),relation_dom(sK2))))) = apply(sK2,ordered_pair(sK3(relation_dom(sK2),relation_dom(sK2)),sK4(relation_dom(sK2),relation_dom(sK2)))) )
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4463,c_2047]) ).
tcf(c_8782,plain,
( ( relation_dom(relation_dom(sK2)) = relation_dom(sK2) )
| ( apply(sK1,apply(sK0,sK3(relation_dom(sK2),relation_dom(sK2)))) = apply(sK2,sK3(relation_dom(sK2),relation_dom(sK2))) )
| ( apply(sK1,apply(sK0,ordered_pair(sK3(relation_dom(sK2),relation_dom(sK2)),sK4(relation_dom(sK2),relation_dom(sK2))))) = apply(sK2,ordered_pair(sK3(relation_dom(sK2),relation_dom(sK2)),sK4(relation_dom(sK2),relation_dom(sK2)))) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4463,c_53]) ).
tcf(c_8783,plain,
( in(sK3(relation_dom(sK2),relation_dom(sK2)),relation_dom(sK0))
| ( relation_dom(relation_dom(sK2)) = relation_dom(sK2) )
| ( apply(sK1,apply(sK0,ordered_pair(sK3(relation_dom(sK2),relation_dom(sK2)),sK4(relation_dom(sK2),relation_dom(sK2))))) = apply(sK2,ordered_pair(sK3(relation_dom(sK2),relation_dom(sK2)),sK4(relation_dom(sK2),relation_dom(sK2)))) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4463,c_51]) ).
tcf(c_8784,plain,
( in(sK3(relation_dom(sK2),relation_dom(sK0)),relation_dom(sK2))
| ( relation_dom(relation_dom(sK2)) = relation_dom(sK0) )
| ( apply(sK1,apply(sK0,sK3(relation_dom(sK2),relation_dom(sK0)))) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(sK3(relation_dom(sK2),relation_dom(sK0)),sK4(relation_dom(sK2),relation_dom(sK0))))) = apply(sK2,ordered_pair(sK3(relation_dom(sK2),relation_dom(sK0)),sK4(relation_dom(sK2),relation_dom(sK0)))) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4463,c_3475]) ).
tcf(c_8785,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK2)) = X0 )
| ( apply(sK1,apply(sK0,ordered_pair(sK3(relation_dom(sK2),X0),sK4(relation_dom(sK2),X0)))) = apply(sK2,ordered_pair(sK3(relation_dom(sK2),X0),sK4(relation_dom(sK2),X0))) )
| ~ relation(relation_dom(sK2))
| ~ in(X0,sK3(relation_dom(sK2),X0)) ),
inference(superposition,[status(thm)],[c_4463,c_64]) ).
tcf(c_8786,plain,
! [X0: $i] :
( element(sK3(relation_dom(sK2),X0),X0)
| ( relation_dom(relation_dom(sK2)) = X0 )
| ( apply(sK1,apply(sK0,ordered_pair(sK3(relation_dom(sK2),X0),sK4(relation_dom(sK2),X0)))) = apply(sK2,ordered_pair(sK3(relation_dom(sK2),X0),sK4(relation_dom(sK2),X0))) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4463,c_63]) ).
tcf(c_8787,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK2)) = X0 )
| ( apply(sK1,apply(sK0,ordered_pair(sK3(relation_dom(sK2),X0),sK4(relation_dom(sK2),X0)))) = apply(sK2,ordered_pair(sK3(relation_dom(sK2),X0),sK4(relation_dom(sK2),X0))) )
| ~ empty(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4463,c_61]) ).
tcf(c_8788,plain,
( ( relation_dom(relation_dom(sK2)) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(sK3(relation_dom(sK2),empty_set),sK4(relation_dom(sK2),empty_set)))) = apply(sK2,ordered_pair(sK3(relation_dom(sK2),empty_set),sK4(relation_dom(sK2),empty_set))) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4463,c_3809]) ).
tcf(c_8789,plain,
! [X0: $i] :
( empty(X0)
| element(sK3(relation_dom(sK2),sK16(X0)),X0)
| ( relation_dom(relation_dom(sK2)) = sK16(X0) )
| ( apply(sK1,apply(sK0,ordered_pair(sK3(relation_dom(sK2),sK16(X0)),sK4(relation_dom(sK2),sK16(X0))))) = apply(sK2,ordered_pair(sK3(relation_dom(sK2),sK16(X0)),sK4(relation_dom(sK2),sK16(X0)))) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4463,c_2939]) ).
tcf(c_8790,plain,
! [X0: $i] :
( element(sK3(relation_dom(sK2),sK17(powerset(X0))),X0)
| ( sK17(powerset(X0)) = relation_dom(relation_dom(sK2)) )
| ( apply(sK1,apply(sK0,ordered_pair(sK3(relation_dom(sK2),sK17(powerset(X0))),sK4(relation_dom(sK2),sK17(powerset(X0)))))) = apply(sK2,ordered_pair(sK3(relation_dom(sK2),sK17(powerset(X0))),sK4(relation_dom(sK2),sK17(powerset(X0))))) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4463,c_2940]) ).
tcf(c_8791,plain,
! [X0: $i] :
( ( sK17(powerset(X0)) = relation_dom(relation_dom(sK2)) )
| ( apply(sK1,apply(sK0,ordered_pair(sK3(relation_dom(sK2),sK17(powerset(X0))),sK4(relation_dom(sK2),sK17(powerset(X0)))))) = apply(sK2,ordered_pair(sK3(relation_dom(sK2),sK17(powerset(X0))),sK4(relation_dom(sK2),sK17(powerset(X0))))) )
| ~ empty(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4463,c_2925]) ).
tcf(c_8860,plain,
! [X0: $i] :
( ( sK2 = empty_set )
| ( apply(sK0,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0)) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0))) = empty_set )
| ( apply(relation_dom(sK2),sK12(sK1,relation_dom(sK2),apply(sK0,sK17(relation_dom(sK2))),X0)) = X0 )
| ~ function(relation_dom(sK2))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_4011,c_6647]) ).
tcf(c_8861,plain,
! [X0: $i] :
( ( sK2 = empty_set )
| ( apply(sK0,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0)) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0))) = empty_set )
| ( apply(relation_dom(sK0),sK12(sK1,relation_dom(sK0),apply(sK0,sK17(relation_dom(sK2))),X0)) = X0 )
| ~ function(relation_dom(sK0))
| ~ relation(relation_dom(sK0))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_4110,c_6647]) ).
tcf(c_8862,plain,
! [X0: $i] :
( ( sK2 = empty_set )
| ( apply(sK2,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0)) = empty_set )
| ( apply(relation_dom(sK0),sK12(sK1,relation_dom(sK0),apply(sK0,sK17(relation_dom(sK2))),X0)) = X0 )
| ~ function(relation_dom(sK0))
| ~ relation(relation_dom(sK0))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_3449,c_6647]) ).
tcf(c_8863,plain,
! [X0: $i] :
( ( sK2 = empty_set )
| ( apply(X0,sK12(sK1,X0,apply(sK0,sK17(relation_dom(sK2))),sK5(X0,apply(sK2,sK17(relation_dom(sK2)))))) = sK5(X0,apply(sK2,sK17(relation_dom(sK2)))) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(apply(sK2,sK17(relation_dom(sK2))),relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_71,c_6647]) ).
tcf(c_8864,plain,
! [X0: $i] :
( ( sK2 = empty_set )
| ( apply(X0,sK12(sK1,X0,apply(sK0,sK17(relation_dom(sK2))),apply(X0,apply(sK2,sK17(relation_dom(sK2)))))) = apply(X0,apply(sK2,sK17(relation_dom(sK2)))) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(apply(sK2,sK17(relation_dom(sK2))),relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_73,c_6647]) ).
tcf(c_8865,plain,
! [X0: $i,X1: $i] :
( ( sK2 = empty_set )
| ( apply(X0,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X1)) = empty_set )
| ( apply(relation_dom(X0),sK12(sK1,relation_dom(X0),apply(sK0,sK17(relation_dom(sK2))),X1)) = X1 )
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom(X0))
| ~ relation(relation_dom(X0))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_75,c_6647]) ).
tcf(c_8866,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK2 = empty_set )
| ( apply(X1,sK12(sK1,X1,apply(sK0,sK17(relation_dom(sK2))),sK12(X1,X2,apply(sK2,sK17(relation_dom(sK2))),X0))) = sK12(X1,X2,apply(sK2,sK17(relation_dom(sK2))),X0) )
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),relation_composition(X1,X2)) ),
inference(superposition,[status(thm)],[c_301,c_6647]) ).
tcf(c_8867,plain,
! [X0: $i,X1: $i] :
( ( sK2 = empty_set )
| ( apply(relation_dom(sK0),sK12(sK1,relation_dom(sK0),apply(sK0,sK17(relation_dom(sK2))),sK12(relation_dom(sK2),X1,apply(sK2,sK17(relation_dom(sK2))),X0))) = sK12(relation_dom(sK2),X1,apply(sK2,sK17(relation_dom(sK2))),X0) )
| ~ relation(X1)
| ~ function(relation_dom(sK0))
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),relation_composition(relation_dom(sK2),X1)) ),
inference(superposition,[status(thm)],[c_2283,c_6647]) ).
tcf(c_8868,plain,
( ( sK2 = empty_set )
| ( apply(relation_dom(sK0),sK12(sK1,relation_dom(sK0),apply(sK0,sK17(relation_dom(sK2))),sK5(relation_dom(sK2),apply(sK2,sK17(relation_dom(sK2)))))) = sK5(relation_dom(sK2),apply(sK2,sK17(relation_dom(sK2)))) )
| ~ function(relation_dom(sK0))
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(apply(sK2,sK17(relation_dom(sK2))),relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_3019,c_6647]) ).
tcf(c_8869,plain,
( ( sK2 = empty_set )
| ( apply(relation_dom(sK0),sK12(sK1,relation_dom(sK0),apply(sK0,sK17(relation_dom(sK2))),apply(relation_dom(sK2),apply(sK2,sK17(relation_dom(sK2)))))) = apply(relation_dom(sK2),apply(sK2,sK17(relation_dom(sK2)))) )
| ~ function(relation_dom(sK0))
| ~ function(relation_dom(sK2))
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(apply(sK2,sK17(relation_dom(sK2))),relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_3551,c_6647]) ).
tcf(c_9037,plain,
! [X0: $i] :
( in(ordered_pair(sK9(relation_dom(sK2),X0,relation_dom(sK2)),sK11(relation_dom(sK2),X0,relation_dom(sK2))),relation_dom(sK0))
| ( relation_composition(relation_dom(sK2),X0) = relation_dom(sK2) )
| ~ relation(X0)
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4703,c_2047]) ).
tcf(c_9038,plain,
! [X0: $i] :
( in(ordered_pair(sK9(relation_dom(sK2),X0,relation_dom(sK2)),sK11(relation_dom(sK2),X0,relation_dom(sK2))),relation_dom(sK0))
| ( relation_composition(relation_dom(sK2),X0) = relation_dom(sK2) )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(relation_dom(sK2),X0,relation_dom(sK2)),sK10(relation_dom(sK2),X0,relation_dom(sK2))))) = apply(sK2,ordered_pair(sK9(relation_dom(sK2),X0,relation_dom(sK2)),sK10(relation_dom(sK2),X0,relation_dom(sK2)))) )
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4703,c_53]) ).
tcf(c_9039,plain,
! [X0: $i] :
( in(ordered_pair(sK9(relation_dom(sK2),X0,relation_dom(sK2)),sK11(relation_dom(sK2),X0,relation_dom(sK2))),relation_dom(sK0))
| in(ordered_pair(sK9(relation_dom(sK2),X0,relation_dom(sK2)),sK10(relation_dom(sK2),X0,relation_dom(sK2))),relation_dom(sK0))
| ( relation_composition(relation_dom(sK2),X0) = relation_dom(sK2) )
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4703,c_51]) ).
tcf(c_9040,plain,
! [X0: $i] :
( in(ordered_pair(sK9(relation_dom(sK2),X0,relation_dom(sK0)),sK11(relation_dom(sK2),X0,relation_dom(sK0))),relation_dom(sK0))
| in(ordered_pair(sK9(relation_dom(sK2),X0,relation_dom(sK0)),sK10(relation_dom(sK2),X0,relation_dom(sK0))),relation_dom(sK2))
| ( relation_composition(relation_dom(sK2),X0) = relation_dom(sK0) )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(relation_dom(sK2),X0,relation_dom(sK0)),sK10(relation_dom(sK2),X0,relation_dom(sK0))))) = empty_set )
| ~ relation(X0)
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4703,c_3475]) ).
tcf(c_9041,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK9(relation_dom(sK2),X1,X0),sK11(relation_dom(sK2),X1,X0)),relation_dom(sK0))
| ( relation_composition(relation_dom(sK2),X1) = X0 )
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2))
| ~ in(X0,ordered_pair(sK9(relation_dom(sK2),X1,X0),sK10(relation_dom(sK2),X1,X0))) ),
inference(superposition,[status(thm)],[c_4703,c_64]) ).
tcf(c_9042,plain,
! [X0: $i,X1: $i] :
( element(ordered_pair(sK9(relation_dom(sK2),X0,X1),sK10(relation_dom(sK2),X0,X1)),X1)
| in(ordered_pair(sK9(relation_dom(sK2),X0,X1),sK11(relation_dom(sK2),X0,X1)),relation_dom(sK0))
| ( relation_composition(relation_dom(sK2),X0) = X1 )
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4703,c_63]) ).
tcf(c_9043,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK9(relation_dom(sK2),X0,X1),sK11(relation_dom(sK2),X0,X1)),relation_dom(sK0))
| ( relation_composition(relation_dom(sK2),X0) = X1 )
| ~ empty(X1)
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4703,c_61]) ).
tcf(c_9044,plain,
! [X0: $i,X1: $i] :
( in(sK9(relation_dom(sK2),X0,X1),relation_dom(X1))
| in(ordered_pair(sK9(relation_dom(sK2),X0,X1),sK11(relation_dom(sK2),X0,X1)),relation_dom(sK0))
| ( relation_composition(relation_dom(sK2),X0) = X1 )
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4703,c_70]) ).
tcf(c_9045,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(ordered_pair(sK9(relation_dom(sK2),X0,X1),X2),relation_composition(X1,X3))
| in(ordered_pair(sK9(relation_dom(sK2),X0,X1),sK11(relation_dom(sK2),X0,X1)),relation_dom(sK0))
| ( relation_composition(relation_dom(sK2),X0) = X1 )
| ~ relation(X3)
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2))
| ~ in(ordered_pair(sK10(relation_dom(sK2),X0,X1),X2),X3) ),
inference(superposition,[status(thm)],[c_4703,c_299]) ).
tcf(c_9046,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK9(relation_dom(sK2),X0,X1),sK11(relation_dom(sK2),X0,X1)),relation_dom(sK0))
| ( relation_composition(relation_dom(sK2),X0) = X1 )
| ( apply(X1,sK9(relation_dom(sK2),X0,X1)) = sK10(relation_dom(sK2),X0,X1) )
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4703,c_152]) ).
tcf(c_9047,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(ordered_pair(sK9(relation_dom(sK2),X0,X1),sK11(relation_dom(sK2),X0,X1)),relation_dom(sK0))
| ( relation_composition(relation_dom(sK2),X0) = X1 )
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2))
| ~ in(ordered_pair(X2,sK10(relation_dom(sK2),X0,X1)),X0)
| ~ in(ordered_pair(sK9(relation_dom(sK2),X0,X1),X2),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4703,c_91]) ).
tcf(c_9048,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(ordered_pair(sK9(relation_dom(sK2),X2,relation_composition(X0,X1)),sK11(relation_dom(sK2),X2,relation_composition(X0,X1))),relation_dom(sK0))
| ( relation_composition(relation_dom(sK2),X2) = relation_composition(X0,X1) )
| ( apply(X1,sK12(X0,X1,sK9(relation_dom(sK2),X2,relation_composition(X0,X1)),sK10(relation_dom(sK2),X2,relation_composition(X0,X1)))) = sK10(relation_dom(sK2),X2,relation_composition(X0,X1)) )
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2))
| ~ relation(relation_composition(X0,X1)) ),
inference(superposition,[status(thm)],[c_4703,c_2068]) ).
tcf(c_9049,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK9(relation_dom(sK2),X1,relation_composition(X0,relation_dom(sK2))),sK11(relation_dom(sK2),X1,relation_composition(X0,relation_dom(sK2)))),relation_dom(sK0))
| ( relation_composition(relation_dom(sK2),X1) = relation_composition(X0,relation_dom(sK2)) )
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ relation(relation_composition(X0,relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_4703,c_2176]) ).
tcf(c_9050,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK9(relation_dom(sK2),X1,relation_composition(X0,relation_dom(sK2))),sK11(relation_dom(sK2),X1,relation_composition(X0,relation_dom(sK2)))),relation_dom(sK0))
| ( relation_composition(relation_dom(sK2),X1) = relation_composition(X0,relation_dom(sK2)) )
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2))
| ~ relation(relation_composition(X0,relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_4703,c_2063]) ).
tcf(c_9051,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK9(relation_dom(sK2),X1,relation_composition(X0,relation_dom(sK2))),sK11(relation_dom(sK2),X1,relation_composition(X0,relation_dom(sK2)))),relation_dom(sK0))
| ( relation_composition(relation_dom(sK2),X1) = relation_composition(X0,relation_dom(sK2)) )
| ( apply(sK1,apply(sK0,ordered_pair(sK12(X0,relation_dom(sK2),sK9(relation_dom(sK2),X1,relation_composition(X0,relation_dom(sK2))),sK10(relation_dom(sK2),X1,relation_composition(X0,relation_dom(sK2)))),sK10(relation_dom(sK2),X1,relation_composition(X0,relation_dom(sK2)))))) = apply(sK2,ordered_pair(sK12(X0,relation_dom(sK2),sK9(relation_dom(sK2),X1,relation_composition(X0,relation_dom(sK2))),sK10(relation_dom(sK2),X1,relation_composition(X0,relation_dom(sK2)))),sK10(relation_dom(sK2),X1,relation_composition(X0,relation_dom(sK2))))) )
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2))
| ~ relation(relation_composition(X0,relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_4703,c_2064]) ).
tcf(c_9052,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK9(relation_dom(sK2),X1,relation_composition(relation_dom(sK2),X0)),sK11(relation_dom(sK2),X1,relation_composition(relation_dom(sK2),X0))),relation_dom(sK0))
| ( relation_composition(relation_dom(sK2),X0) = relation_composition(relation_dom(sK2),X1) )
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ relation(relation_composition(relation_dom(sK2),X0)) ),
inference(superposition,[status(thm)],[c_4703,c_2737]) ).
tcf(c_9053,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK9(relation_dom(sK2),X1,relation_composition(relation_dom(sK2),X0)),sK11(relation_dom(sK2),X1,relation_composition(relation_dom(sK2),X0))),relation_dom(sK0))
| ( relation_composition(relation_dom(sK2),X0) = relation_composition(relation_dom(sK2),X1) )
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2))
| ~ relation(relation_composition(relation_dom(sK2),X0)) ),
inference(superposition,[status(thm)],[c_4703,c_2281]) ).
tcf(c_9054,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK9(relation_dom(sK2),X1,relation_composition(relation_dom(sK2),X0)),sK11(relation_dom(sK2),X1,relation_composition(relation_dom(sK2),X0))),relation_dom(sK0))
| ( relation_composition(relation_dom(sK2),X0) = relation_composition(relation_dom(sK2),X1) )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(relation_dom(sK2),X1,relation_composition(relation_dom(sK2),X0)),sK12(relation_dom(sK2),X0,sK9(relation_dom(sK2),X1,relation_composition(relation_dom(sK2),X0)),sK10(relation_dom(sK2),X1,relation_composition(relation_dom(sK2),X0)))))) = apply(sK2,ordered_pair(sK9(relation_dom(sK2),X1,relation_composition(relation_dom(sK2),X0)),sK12(relation_dom(sK2),X0,sK9(relation_dom(sK2),X1,relation_composition(relation_dom(sK2),X0)),sK10(relation_dom(sK2),X1,relation_composition(relation_dom(sK2),X0))))) )
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2))
| ~ relation(relation_composition(relation_dom(sK2),X0)) ),
inference(superposition,[status(thm)],[c_4703,c_2282]) ).
tcf(c_9055,plain,
! [X0: $i] :
( in(ordered_pair(sK9(relation_dom(sK2),X0,empty_set),sK11(relation_dom(sK2),X0,empty_set)),relation_dom(sK0))
| ( relation_composition(relation_dom(sK2),X0) = empty_set )
| ~ relation(empty_set)
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4703,c_3809]) ).
tcf(c_9056,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| element(ordered_pair(sK9(relation_dom(sK2),X1,sK16(X0)),sK10(relation_dom(sK2),X1,sK16(X0))),X0)
| in(ordered_pair(sK9(relation_dom(sK2),X1,sK16(X0)),sK11(relation_dom(sK2),X1,sK16(X0))),relation_dom(sK0))
| ( relation_composition(relation_dom(sK2),X1) = sK16(X0) )
| ~ relation(X1)
| ~ relation(relation_dom(sK2))
| ~ relation(sK16(X0)) ),
inference(superposition,[status(thm)],[c_4703,c_2939]) ).
tcf(c_9057,plain,
! [X0: $i,X1: $i] :
( element(ordered_pair(sK9(relation_dom(sK2),X1,sK17(powerset(X0))),sK10(relation_dom(sK2),X1,sK17(powerset(X0)))),X0)
| in(ordered_pair(sK9(relation_dom(sK2),X1,sK17(powerset(X0))),sK11(relation_dom(sK2),X1,sK17(powerset(X0)))),relation_dom(sK0))
| ( relation_composition(relation_dom(sK2),X1) = sK17(powerset(X0)) )
| ~ relation(X1)
| ~ relation(relation_dom(sK2))
| ~ relation(sK17(powerset(X0))) ),
inference(superposition,[status(thm)],[c_4703,c_2940]) ).
tcf(c_9058,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK9(relation_dom(sK2),X1,sK17(powerset(X0))),sK11(relation_dom(sK2),X1,sK17(powerset(X0)))),relation_dom(sK0))
| ( relation_composition(relation_dom(sK2),X1) = sK17(powerset(X0)) )
| ~ empty(X0)
| ~ relation(X1)
| ~ relation(relation_dom(sK2))
| ~ relation(sK17(powerset(X0))) ),
inference(superposition,[status(thm)],[c_4703,c_2925]) ).
tcf(c_9059,plain,
! [X0: $i] :
( in(ordered_pair(sK9(relation_dom(sK2),X0,relation_dom(relation_dom(sK2))),sK11(relation_dom(sK2),X0,relation_dom(relation_dom(sK2)))),relation_dom(sK0))
| ( relation_composition(relation_dom(sK2),X0) = relation_dom(relation_dom(sK2)) )
| ( apply(sK1,apply(sK0,ordered_pair(ordered_pair(sK9(relation_dom(sK2),X0,relation_dom(relation_dom(sK2))),sK10(relation_dom(sK2),X0,relation_dom(relation_dom(sK2)))),apply(relation_dom(sK2),ordered_pair(sK9(relation_dom(sK2),X0,relation_dom(relation_dom(sK2))),sK10(relation_dom(sK2),X0,relation_dom(relation_dom(sK2)))))))) = apply(sK2,ordered_pair(ordered_pair(sK9(relation_dom(sK2),X0,relation_dom(relation_dom(sK2))),sK10(relation_dom(sK2),X0,relation_dom(relation_dom(sK2)))),apply(relation_dom(sK2),ordered_pair(sK9(relation_dom(sK2),X0,relation_dom(relation_dom(sK2))),sK10(relation_dom(sK2),X0,relation_dom(relation_dom(sK2))))))) )
| ~ relation(X0)
| ~ function(relation_dom(sK2))
| ~ relation(relation_dom(sK2))
| ~ relation(relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_4703,c_3550]) ).
tcf(c_9060,plain,
! [X0: $i] :
( in(ordered_pair(sK9(relation_dom(sK2),X0,relation_dom(relation_dom(sK2))),sK11(relation_dom(sK2),X0,relation_dom(relation_dom(sK2)))),relation_dom(sK0))
| in(ordered_pair(sK9(relation_dom(sK2),X0,relation_dom(relation_dom(sK2))),sK10(relation_dom(sK2),X0,relation_dom(relation_dom(sK2)))),relation_dom(relation_dom(sK0)))
| ( relation_composition(relation_dom(sK2),X0) = relation_dom(relation_dom(sK2)) )
| ~ relation(X0)
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ relation(relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_4703,c_3134]) ).
tcf(c_9061,plain,
! [X0: $i] :
( in(ordered_pair(sK9(relation_dom(sK2),X0,relation_dom(relation_dom(sK2))),sK11(relation_dom(sK2),X0,relation_dom(relation_dom(sK2)))),relation_dom(sK0))
| ( relation_composition(relation_dom(sK2),X0) = relation_dom(relation_dom(sK2)) )
| ~ relation(X0)
| ~ empty(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ relation(relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_4703,c_3241]) ).
tcf(c_9062,plain,
! [X0: $i] :
( in(ordered_pair(sK9(relation_dom(sK2),X0,relation_dom(relation_dom(sK2))),sK11(relation_dom(sK2),X0,relation_dom(relation_dom(sK2)))),relation_dom(sK0))
| ( relation_composition(relation_dom(sK2),X0) = relation_dom(relation_dom(sK2)) )
| ~ relation(X0)
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2))
| ~ relation(relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_4703,c_3017]) ).
tcf(c_9063,plain,
! [X0: $i] :
( in(ordered_pair(sK9(relation_dom(sK2),X0,relation_dom(relation_dom(sK2))),sK11(relation_dom(sK2),X0,relation_dom(relation_dom(sK2)))),relation_dom(sK0))
| ( relation_composition(relation_dom(sK2),X0) = relation_dom(relation_dom(sK2)) )
| ( apply(sK1,apply(sK0,ordered_pair(ordered_pair(sK9(relation_dom(sK2),X0,relation_dom(relation_dom(sK2))),sK10(relation_dom(sK2),X0,relation_dom(relation_dom(sK2)))),sK5(relation_dom(sK2),ordered_pair(sK9(relation_dom(sK2),X0,relation_dom(relation_dom(sK2))),sK10(relation_dom(sK2),X0,relation_dom(relation_dom(sK2)))))))) = apply(sK2,ordered_pair(ordered_pair(sK9(relation_dom(sK2),X0,relation_dom(relation_dom(sK2))),sK10(relation_dom(sK2),X0,relation_dom(relation_dom(sK2)))),sK5(relation_dom(sK2),ordered_pair(sK9(relation_dom(sK2),X0,relation_dom(relation_dom(sK2))),sK10(relation_dom(sK2),X0,relation_dom(relation_dom(sK2))))))) )
| ~ relation(X0)
| ~ relation(relation_dom(sK2))
| ~ relation(relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_4703,c_3018]) ).
tcf(c_9064,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK9(relation_dom(sK2),X0,X1),sK10(relation_dom(sK2),X0,X1)),X1)
| in(ordered_pair(sK9(relation_dom(sK2),X0,X1),sK11(relation_dom(sK2),X0,X1)),relation_dom(sK2))
| ( relation_composition(relation_dom(sK2),X0) = X1 )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(relation_dom(sK2),X0,X1),sK11(relation_dom(sK2),X0,X1)))) = empty_set )
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4703,c_3475]) ).
tcf(c_9065,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK9(relation_dom(sK2),X0,X1),sK10(relation_dom(sK2),X0,X1)),X1)
| ( relation_composition(relation_dom(sK2),X0) = X1 )
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2))
| ~ in(relation_dom(sK0),ordered_pair(sK9(relation_dom(sK2),X0,X1),sK11(relation_dom(sK2),X0,X1))) ),
inference(superposition,[status(thm)],[c_4703,c_64]) ).
tcf(c_9066,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK9(relation_dom(sK2),X0,X1),sK10(relation_dom(sK2),X0,X1)),X1)
| element(ordered_pair(sK9(relation_dom(sK2),X0,X1),sK11(relation_dom(sK2),X0,X1)),relation_dom(sK0))
| ( relation_composition(relation_dom(sK2),X0) = X1 )
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4703,c_63]) ).
tcf(c_9067,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK9(relation_dom(sK2),X0,X1),sK10(relation_dom(sK2),X0,X1)),X1)
| ( relation_composition(relation_dom(sK2),X0) = X1 )
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(sK0))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4703,c_61]) ).
tcf(c_9068,plain,
! [X0: $i,X1: $i] :
( in(sK9(relation_dom(sK2),X0,X1),relation_dom(relation_dom(sK0)))
| in(ordered_pair(sK9(relation_dom(sK2),X0,X1),sK10(relation_dom(sK2),X0,X1)),X1)
| ( relation_composition(relation_dom(sK2),X0) = X1 )
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4703,c_70]) ).
tcf(c_9069,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(ordered_pair(sK9(relation_dom(sK2),X0,X1),X2),relation_composition(relation_dom(sK0),X3))
| in(ordered_pair(sK9(relation_dom(sK2),X0,X1),sK10(relation_dom(sK2),X0,X1)),X1)
| ( relation_composition(relation_dom(sK2),X0) = X1 )
| ~ relation(X3)
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(ordered_pair(sK11(relation_dom(sK2),X0,X1),X2),X3) ),
inference(superposition,[status(thm)],[c_4703,c_299]) ).
tcf(c_9070,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK9(relation_dom(sK2),X0,X1),sK10(relation_dom(sK2),X0,X1)),X1)
| ( relation_composition(relation_dom(sK2),X0) = X1 )
| ( apply(relation_dom(sK0),sK9(relation_dom(sK2),X0,X1)) = sK11(relation_dom(sK2),X0,X1) )
| ~ relation(X1)
| ~ relation(X0)
| ~ function(relation_dom(sK0))
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4703,c_152]) ).
tcf(c_9071,plain,
! [X0: $i] :
( in(ordered_pair(sK9(relation_dom(sK2),X0,empty_set),sK11(relation_dom(sK2),X0,empty_set)),relation_dom(sK0))
| ( relation_composition(relation_dom(sK2),X0) = empty_set )
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9055,c_109]) ).
tcf(c_9372,plain,
! [X0: $i] :
( in(ordered_pair(sK9(relation_dom(sK2),X0,relation_dom(sK2)),sK10(relation_dom(sK2),X0,relation_dom(sK2))),relation_dom(sK0))
| ( relation_composition(relation_dom(sK2),X0) = relation_dom(sK2) )
| ~ relation(X0)
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4725,c_2047]) ).
tcf(c_9373,plain,
! [X0: $i] :
( in(ordered_pair(sK9(relation_dom(sK2),X0,relation_dom(sK2)),sK10(relation_dom(sK2),X0,relation_dom(sK2))),relation_dom(sK0))
| ( relation_composition(relation_dom(sK2),X0) = relation_dom(sK2) )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(relation_dom(sK2),X0,relation_dom(sK2)),sK11(relation_dom(sK2),X0,relation_dom(sK2))))) = apply(sK2,ordered_pair(sK9(relation_dom(sK2),X0,relation_dom(sK2)),sK11(relation_dom(sK2),X0,relation_dom(sK2)))) )
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4725,c_53]) ).
tcf(c_9375,plain,
! [X0: $i] :
( in(ordered_pair(sK9(relation_dom(sK0),X0,relation_dom(sK2)),sK11(relation_dom(sK0),X0,relation_dom(sK2))),relation_dom(sK2))
| in(ordered_pair(sK9(relation_dom(sK0),X0,relation_dom(sK2)),sK10(relation_dom(sK0),X0,relation_dom(sK2))),relation_dom(sK0))
| ( relation_composition(relation_dom(sK0),X0) = relation_dom(sK2) )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(relation_dom(sK0),X0,relation_dom(sK2)),sK11(relation_dom(sK0),X0,relation_dom(sK2))))) = empty_set )
| ~ relation(X0)
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4725,c_3475]) ).
tcf(c_9376,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK9(X0,X1,relation_dom(sK2)),sK10(X0,X1,relation_dom(sK2))),relation_dom(sK0))
| ( relation_composition(X0,X1) = relation_dom(sK2) )
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2))
| ~ in(X0,ordered_pair(sK9(X0,X1,relation_dom(sK2)),sK11(X0,X1,relation_dom(sK2)))) ),
inference(superposition,[status(thm)],[c_4725,c_64]) ).
tcf(c_9377,plain,
! [X0: $i,X1: $i] :
( element(ordered_pair(sK9(X0,X1,relation_dom(sK2)),sK11(X0,X1,relation_dom(sK2))),X0)
| in(ordered_pair(sK9(X0,X1,relation_dom(sK2)),sK10(X0,X1,relation_dom(sK2))),relation_dom(sK0))
| ( relation_composition(X0,X1) = relation_dom(sK2) )
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4725,c_63]) ).
tcf(c_9378,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK9(X0,X1,relation_dom(sK2)),sK10(X0,X1,relation_dom(sK2))),relation_dom(sK0))
| ( relation_composition(X0,X1) = relation_dom(sK2) )
| ~ empty(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4725,c_61]) ).
tcf(c_9379,plain,
! [X0: $i,X1: $i] :
( in(sK9(X0,X1,relation_dom(sK2)),relation_dom(X0))
| in(ordered_pair(sK9(X0,X1,relation_dom(sK2)),sK10(X0,X1,relation_dom(sK2))),relation_dom(sK0))
| ( relation_composition(X0,X1) = relation_dom(sK2) )
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4725,c_70]) ).
tcf(c_9380,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(ordered_pair(sK9(X0,X1,relation_dom(sK2)),X2),relation_composition(X0,X3))
| in(ordered_pair(sK9(X0,X1,relation_dom(sK2)),sK10(X0,X1,relation_dom(sK2))),relation_dom(sK0))
| ( relation_composition(X0,X1) = relation_dom(sK2) )
| ~ relation(X3)
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2))
| ~ in(ordered_pair(sK11(X0,X1,relation_dom(sK2)),X2),X3) ),
inference(superposition,[status(thm)],[c_4725,c_299]) ).
tcf(c_9381,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK9(X0,X1,relation_dom(sK2)),sK10(X0,X1,relation_dom(sK2))),relation_dom(sK0))
| ( relation_composition(X0,X1) = relation_dom(sK2) )
| ( apply(X0,sK9(X0,X1,relation_dom(sK2))) = sK11(X0,X1,relation_dom(sK2)) )
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4725,c_152]) ).
tcf(c_9382,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(ordered_pair(sK9(relation_composition(X0,X1),X2,relation_dom(sK2)),sK10(relation_composition(X0,X1),X2,relation_dom(sK2))),relation_dom(sK0))
| ( relation_composition(relation_composition(X0,X1),X2) = relation_dom(sK2) )
| ( apply(X1,sK12(X0,X1,sK9(relation_composition(X0,X1),X2,relation_dom(sK2)),sK11(relation_composition(X0,X1),X2,relation_dom(sK2)))) = sK11(relation_composition(X0,X1),X2,relation_dom(sK2)) )
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2))
| ~ relation(relation_composition(X0,X1)) ),
inference(superposition,[status(thm)],[c_4725,c_2068]) ).
tcf(c_9383,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK9(relation_composition(X0,relation_dom(sK2)),X1,relation_dom(sK2)),sK10(relation_composition(X0,relation_dom(sK2)),X1,relation_dom(sK2))),relation_dom(sK0))
| ( relation_composition(relation_composition(X0,relation_dom(sK2)),X1) = relation_dom(sK2) )
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ relation(relation_composition(X0,relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_4725,c_2176]) ).
tcf(c_9384,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK9(relation_composition(X0,relation_dom(sK2)),X1,relation_dom(sK2)),sK10(relation_composition(X0,relation_dom(sK2)),X1,relation_dom(sK2))),relation_dom(sK0))
| ( relation_composition(relation_composition(X0,relation_dom(sK2)),X1) = relation_dom(sK2) )
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2))
| ~ relation(relation_composition(X0,relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_4725,c_2063]) ).
tcf(c_9385,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK9(relation_composition(X0,relation_dom(sK2)),X1,relation_dom(sK2)),sK10(relation_composition(X0,relation_dom(sK2)),X1,relation_dom(sK2))),relation_dom(sK0))
| ( relation_composition(relation_composition(X0,relation_dom(sK2)),X1) = relation_dom(sK2) )
| ( apply(sK1,apply(sK0,ordered_pair(sK12(X0,relation_dom(sK2),sK9(relation_composition(X0,relation_dom(sK2)),X1,relation_dom(sK2)),sK11(relation_composition(X0,relation_dom(sK2)),X1,relation_dom(sK2))),sK11(relation_composition(X0,relation_dom(sK2)),X1,relation_dom(sK2))))) = apply(sK2,ordered_pair(sK12(X0,relation_dom(sK2),sK9(relation_composition(X0,relation_dom(sK2)),X1,relation_dom(sK2)),sK11(relation_composition(X0,relation_dom(sK2)),X1,relation_dom(sK2))),sK11(relation_composition(X0,relation_dom(sK2)),X1,relation_dom(sK2)))) )
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2))
| ~ relation(relation_composition(X0,relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_4725,c_2064]) ).
tcf(c_9386,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK9(relation_composition(relation_dom(sK2),X0),X1,relation_dom(sK2)),sK10(relation_composition(relation_dom(sK2),X0),X1,relation_dom(sK2))),relation_dom(sK0))
| ( relation_composition(relation_composition(relation_dom(sK2),X0),X1) = relation_dom(sK2) )
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ relation(relation_composition(relation_dom(sK2),X0)) ),
inference(superposition,[status(thm)],[c_4725,c_2737]) ).
tcf(c_9387,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK9(relation_composition(relation_dom(sK2),X0),X1,relation_dom(sK2)),sK10(relation_composition(relation_dom(sK2),X0),X1,relation_dom(sK2))),relation_dom(sK0))
| ( relation_composition(relation_composition(relation_dom(sK2),X0),X1) = relation_dom(sK2) )
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2))
| ~ relation(relation_composition(relation_dom(sK2),X0)) ),
inference(superposition,[status(thm)],[c_4725,c_2281]) ).
tcf(c_9388,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK9(relation_composition(relation_dom(sK2),X0),X1,relation_dom(sK2)),sK10(relation_composition(relation_dom(sK2),X0),X1,relation_dom(sK2))),relation_dom(sK0))
| ( relation_composition(relation_composition(relation_dom(sK2),X0),X1) = relation_dom(sK2) )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(relation_composition(relation_dom(sK2),X0),X1,relation_dom(sK2)),sK12(relation_dom(sK2),X0,sK9(relation_composition(relation_dom(sK2),X0),X1,relation_dom(sK2)),sK11(relation_composition(relation_dom(sK2),X0),X1,relation_dom(sK2)))))) = apply(sK2,ordered_pair(sK9(relation_composition(relation_dom(sK2),X0),X1,relation_dom(sK2)),sK12(relation_dom(sK2),X0,sK9(relation_composition(relation_dom(sK2),X0),X1,relation_dom(sK2)),sK11(relation_composition(relation_dom(sK2),X0),X1,relation_dom(sK2))))) )
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2))
| ~ relation(relation_composition(relation_dom(sK2),X0)) ),
inference(superposition,[status(thm)],[c_4725,c_2282]) ).
tcf(c_9389,plain,
! [X0: $i] :
( in(ordered_pair(sK9(empty_set,X0,relation_dom(sK2)),sK10(empty_set,X0,relation_dom(sK2))),relation_dom(sK0))
| ( relation_composition(empty_set,X0) = relation_dom(sK2) )
| ~ relation(empty_set)
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4725,c_3809]) ).
tcf(c_9390,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| element(ordered_pair(sK9(sK16(X0),X1,relation_dom(sK2)),sK11(sK16(X0),X1,relation_dom(sK2))),X0)
| in(ordered_pair(sK9(sK16(X0),X1,relation_dom(sK2)),sK10(sK16(X0),X1,relation_dom(sK2))),relation_dom(sK0))
| ( relation_composition(sK16(X0),X1) = relation_dom(sK2) )
| ~ relation(X1)
| ~ relation(relation_dom(sK2))
| ~ relation(sK16(X0)) ),
inference(superposition,[status(thm)],[c_4725,c_2939]) ).
tcf(c_9391,plain,
! [X0: $i,X1: $i] :
( element(ordered_pair(sK9(sK17(powerset(X0)),X1,relation_dom(sK2)),sK11(sK17(powerset(X0)),X1,relation_dom(sK2))),X0)
| in(ordered_pair(sK9(sK17(powerset(X0)),X1,relation_dom(sK2)),sK10(sK17(powerset(X0)),X1,relation_dom(sK2))),relation_dom(sK0))
| ( relation_composition(sK17(powerset(X0)),X1) = relation_dom(sK2) )
| ~ relation(X1)
| ~ relation(relation_dom(sK2))
| ~ relation(sK17(powerset(X0))) ),
inference(superposition,[status(thm)],[c_4725,c_2940]) ).
tcf(c_9392,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK9(sK17(powerset(X0)),X1,relation_dom(sK2)),sK10(sK17(powerset(X0)),X1,relation_dom(sK2))),relation_dom(sK0))
| ( relation_composition(sK17(powerset(X0)),X1) = relation_dom(sK2) )
| ~ empty(X0)
| ~ relation(X1)
| ~ relation(relation_dom(sK2))
| ~ relation(sK17(powerset(X0))) ),
inference(superposition,[status(thm)],[c_4725,c_2925]) ).
tcf(c_9393,plain,
! [X0: $i] :
( in(ordered_pair(sK9(relation_dom(relation_dom(sK2)),X0,relation_dom(sK2)),sK10(relation_dom(relation_dom(sK2)),X0,relation_dom(sK2))),relation_dom(sK0))
| ( relation_composition(relation_dom(relation_dom(sK2)),X0) = relation_dom(sK2) )
| ( apply(sK1,apply(sK0,ordered_pair(ordered_pair(sK9(relation_dom(relation_dom(sK2)),X0,relation_dom(sK2)),sK11(relation_dom(relation_dom(sK2)),X0,relation_dom(sK2))),apply(relation_dom(sK2),ordered_pair(sK9(relation_dom(relation_dom(sK2)),X0,relation_dom(sK2)),sK11(relation_dom(relation_dom(sK2)),X0,relation_dom(sK2))))))) = apply(sK2,ordered_pair(ordered_pair(sK9(relation_dom(relation_dom(sK2)),X0,relation_dom(sK2)),sK11(relation_dom(relation_dom(sK2)),X0,relation_dom(sK2))),apply(relation_dom(sK2),ordered_pair(sK9(relation_dom(relation_dom(sK2)),X0,relation_dom(sK2)),sK11(relation_dom(relation_dom(sK2)),X0,relation_dom(sK2)))))) )
| ~ relation(X0)
| ~ function(relation_dom(sK2))
| ~ relation(relation_dom(sK2))
| ~ relation(relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_4725,c_3550]) ).
tcf(c_9394,plain,
! [X0: $i] :
( in(ordered_pair(sK9(relation_dom(relation_dom(sK2)),X0,relation_dom(sK2)),sK10(relation_dom(relation_dom(sK2)),X0,relation_dom(sK2))),relation_dom(sK0))
| in(ordered_pair(sK9(relation_dom(relation_dom(sK2)),X0,relation_dom(sK2)),sK11(relation_dom(relation_dom(sK2)),X0,relation_dom(sK2))),relation_dom(relation_dom(sK0)))
| ( relation_composition(relation_dom(relation_dom(sK2)),X0) = relation_dom(sK2) )
| ~ relation(X0)
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ relation(relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_4725,c_3134]) ).
tcf(c_9395,plain,
! [X0: $i] :
( in(ordered_pair(sK9(relation_dom(relation_dom(sK2)),X0,relation_dom(sK2)),sK10(relation_dom(relation_dom(sK2)),X0,relation_dom(sK2))),relation_dom(sK0))
| ( relation_composition(relation_dom(relation_dom(sK2)),X0) = relation_dom(sK2) )
| ~ relation(X0)
| ~ empty(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ relation(relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_4725,c_3241]) ).
tcf(c_9396,plain,
! [X0: $i] :
( in(ordered_pair(sK9(relation_dom(relation_dom(sK2)),X0,relation_dom(sK2)),sK10(relation_dom(relation_dom(sK2)),X0,relation_dom(sK2))),relation_dom(sK0))
| ( relation_composition(relation_dom(relation_dom(sK2)),X0) = relation_dom(sK2) )
| ~ relation(X0)
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2))
| ~ relation(relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_4725,c_3017]) ).
tcf(c_9397,plain,
! [X0: $i] :
( in(ordered_pair(sK9(relation_dom(relation_dom(sK2)),X0,relation_dom(sK2)),sK10(relation_dom(relation_dom(sK2)),X0,relation_dom(sK2))),relation_dom(sK0))
| ( relation_composition(relation_dom(relation_dom(sK2)),X0) = relation_dom(sK2) )
| ( apply(sK1,apply(sK0,ordered_pair(ordered_pair(sK9(relation_dom(relation_dom(sK2)),X0,relation_dom(sK2)),sK11(relation_dom(relation_dom(sK2)),X0,relation_dom(sK2))),sK5(relation_dom(sK2),ordered_pair(sK9(relation_dom(relation_dom(sK2)),X0,relation_dom(sK2)),sK11(relation_dom(relation_dom(sK2)),X0,relation_dom(sK2))))))) = apply(sK2,ordered_pair(ordered_pair(sK9(relation_dom(relation_dom(sK2)),X0,relation_dom(sK2)),sK11(relation_dom(relation_dom(sK2)),X0,relation_dom(sK2))),sK5(relation_dom(sK2),ordered_pair(sK9(relation_dom(relation_dom(sK2)),X0,relation_dom(sK2)),sK11(relation_dom(relation_dom(sK2)),X0,relation_dom(sK2)))))) )
| ~ relation(X0)
| ~ relation(relation_dom(sK2))
| ~ relation(relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_4725,c_3018]) ).
tcf(c_9398,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK9(X0,X1,relation_dom(sK2)),sK11(X0,X1,relation_dom(sK2))),X0)
| in(ordered_pair(sK9(X0,X1,relation_dom(sK2)),sK10(X0,X1,relation_dom(sK2))),relation_dom(sK2))
| ( relation_composition(X0,X1) = relation_dom(sK2) )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(X0,X1,relation_dom(sK2)),sK10(X0,X1,relation_dom(sK2))))) = empty_set )
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4725,c_3475]) ).
tcf(c_9399,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK9(X0,X1,relation_dom(sK2)),sK11(X0,X1,relation_dom(sK2))),X0)
| ( relation_composition(X0,X1) = relation_dom(sK2) )
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2))
| ~ in(relation_dom(sK0),ordered_pair(sK9(X0,X1,relation_dom(sK2)),sK10(X0,X1,relation_dom(sK2)))) ),
inference(superposition,[status(thm)],[c_4725,c_64]) ).
tcf(c_9400,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK9(X0,X1,relation_dom(sK2)),sK11(X0,X1,relation_dom(sK2))),X0)
| element(ordered_pair(sK9(X0,X1,relation_dom(sK2)),sK10(X0,X1,relation_dom(sK2))),relation_dom(sK0))
| ( relation_composition(X0,X1) = relation_dom(sK2) )
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4725,c_63]) ).
tcf(c_9401,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK9(X0,X1,relation_dom(sK2)),sK11(X0,X1,relation_dom(sK2))),X0)
| ( relation_composition(X0,X1) = relation_dom(sK2) )
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(sK0))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4725,c_61]) ).
tcf(c_9402,plain,
! [X0: $i,X1: $i] :
( in(sK9(X0,X1,relation_dom(sK2)),relation_dom(relation_dom(sK0)))
| in(ordered_pair(sK9(X0,X1,relation_dom(sK2)),sK11(X0,X1,relation_dom(sK2))),X0)
| ( relation_composition(X0,X1) = relation_dom(sK2) )
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4725,c_70]) ).
tcf(c_9403,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(ordered_pair(sK9(X0,X1,relation_dom(sK2)),X2),relation_composition(relation_dom(sK0),X3))
| in(ordered_pair(sK9(X0,X1,relation_dom(sK2)),sK11(X0,X1,relation_dom(sK2))),X0)
| ( relation_composition(X0,X1) = relation_dom(sK2) )
| ~ relation(X3)
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(ordered_pair(sK10(X0,X1,relation_dom(sK2)),X2),X3) ),
inference(superposition,[status(thm)],[c_4725,c_299]) ).
tcf(c_9404,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK9(X0,X1,relation_dom(sK2)),sK11(X0,X1,relation_dom(sK2))),X0)
| ( relation_composition(X0,X1) = relation_dom(sK2) )
| ( apply(relation_dom(sK0),sK9(X0,X1,relation_dom(sK2))) = sK10(X0,X1,relation_dom(sK2)) )
| ~ relation(X1)
| ~ relation(X0)
| ~ function(relation_dom(sK0))
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4725,c_152]) ).
tcf(c_9405,plain,
! [X0: $i] :
( in(ordered_pair(sK9(empty_set,X0,relation_dom(sK2)),sK10(empty_set,X0,relation_dom(sK2))),relation_dom(sK0))
| ( relation_composition(empty_set,X0) = relation_dom(sK2) )
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9389,c_109]) ).
tcf(c_9780,plain,
( in(ordered_pair(apply(sK0,sK17(relation_dom(sK2))),apply(sK2,sK17(relation_dom(sK2)))),sK1)
| ( sK17(powerset(relation_dom(sK2))) = empty_set )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_7739,c_73]) ).
tcf(c_9781,plain,
( in(ordered_pair(apply(sK0,sK17(relation_dom(sK2))),apply(sK2,sK17(relation_dom(sK2)))),sK1)
| ( sK17(powerset(relation_dom(sK2))) = empty_set )
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9780,c_57,c_56]) ).
tcf(c_9793,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_65,c_7227]) ).
tcf(c_9794,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_composition(X1,X0)))) = empty_set )
| ~ empty(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_86,c_7227]) ).
tcf(c_9795,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_composition(X0,X1)))) = empty_set )
| ~ empty(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_88,c_7227]) ).
tcf(c_9796,plain,
relation_dom(relation_dom(relation_dom(empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_110,c_7227]) ).
tcf(c_9797,plain,
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK2)))) = empty_set )
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_2577,c_7227]) ).
tcf(c_9798,plain,
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK2)))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_2570,c_7227]) ).
tcf(c_9799,plain,
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK2)))) = empty_set )
| ( apply(sK1,apply(sK0,sK17(relation_dom(sK2)))) = apply(sK2,sK17(relation_dom(sK2))) ) ),
inference(superposition,[status(thm)],[c_2425,c_7227]) ).
tcf(c_9801,plain,
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK2))))) = empty_set )
| ~ empty(relation_dom(sK0)) ),
inference(superposition,[status(thm)],[c_3251,c_7227]) ).
tcf(c_9802,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK17(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6912,c_7227]) ).
tcf(c_9849,plain,
! [X0: $i] :
( ( sK17(powerset(relation_dom(relation_dom(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_65,c_7733]) ).
tcf(c_9850,plain,
! [X0: $i,X1: $i] :
( ( sK17(powerset(relation_dom(relation_composition(X1,X0)))) = empty_set )
| ~ empty(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_86,c_7733]) ).
tcf(c_9851,plain,
! [X0: $i,X1: $i] :
( ( sK17(powerset(relation_dom(relation_composition(X0,X1)))) = empty_set )
| ~ empty(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_88,c_7733]) ).
tcf(c_9852,plain,
sK17(powerset(relation_dom(empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_110,c_7733]) ).
tcf(c_9853,plain,
( ( sK17(powerset(relation_dom(relation_dom(sK2)))) = empty_set )
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_2577,c_7733]) ).
tcf(c_9854,plain,
( ( sK17(powerset(relation_dom(relation_dom(sK2)))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_2570,c_7733]) ).
tcf(c_9855,plain,
( ( sK17(powerset(relation_dom(relation_dom(sK2)))) = empty_set )
| ( apply(sK1,apply(sK0,sK17(relation_dom(sK2)))) = apply(sK2,sK17(relation_dom(sK2))) ) ),
inference(superposition,[status(thm)],[c_2425,c_7733]) ).
tcf(c_9857,plain,
( ( sK17(powerset(relation_dom(relation_dom(relation_dom(sK2))))) = empty_set )
| ~ empty(relation_dom(sK0)) ),
inference(superposition,[status(thm)],[c_3251,c_7733]) ).
tcf(c_9858,plain,
! [X0: $i] :
( ( sK17(powerset(relation_dom(sK17(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6912,c_7733]) ).
tcf(c_9929,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(X0)) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_65,c_2387]) ).
tcf(c_9930,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_composition(X1,X0)) = X2 )
| ~ empty(X2)
| ~ empty(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_86,c_2387]) ).
tcf(c_9931,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_composition(X0,X1)) = X2 )
| ~ empty(X2)
| ~ empty(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_88,c_2387]) ).
tcf(c_9933,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK2)) = X0 )
| ~ empty(sK0)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2577,c_2387]) ).
tcf(c_9934,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK2)) = X0 )
| ~ empty(sK1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2570,c_2387]) ).
tcf(c_9935,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK2)) = X0 )
| ( apply(sK1,apply(sK0,sK17(relation_dom(sK2)))) = apply(sK2,sK17(relation_dom(sK2))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2425,c_2387]) ).
tcf(c_9937,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK2))) = X0 )
| ~ empty(X0)
| ~ empty(relation_dom(sK0)) ),
inference(superposition,[status(thm)],[c_3251,c_2387]) ).
tcf(c_9938,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK17(powerset(X0))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6912,c_2387]) ).
tcf(c_9976,plain,
! [X0: $i] :
( ( relation_dom(sK17(powerset(relation_dom(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_65,c_7171]) ).
tcf(c_9977,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK17(powerset(relation_composition(X1,X0)))) = empty_set )
| ~ empty(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_86,c_7171]) ).
tcf(c_9978,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK17(powerset(relation_composition(X0,X1)))) = empty_set )
| ~ empty(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_88,c_7171]) ).
tcf(c_9979,plain,
relation_dom(sK17(powerset(empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_110,c_7171]) ).
tcf(c_9980,plain,
( ( relation_dom(sK17(powerset(relation_dom(sK2)))) = empty_set )
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_2577,c_7171]) ).
tcf(c_9981,plain,
( ( relation_dom(sK17(powerset(relation_dom(sK2)))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_2570,c_7171]) ).
tcf(c_9982,plain,
( ( relation_dom(sK17(powerset(relation_dom(sK2)))) = empty_set )
| ( apply(sK1,apply(sK0,sK17(relation_dom(sK2)))) = apply(sK2,sK17(relation_dom(sK2))) ) ),
inference(superposition,[status(thm)],[c_2425,c_7171]) ).
tcf(c_9983,plain,
( ( relation_dom(sK17(powerset(sK2))) = empty_set )
| ( apply(sK1,apply(sK0,sK17(relation_dom(sK2)))) = apply(sK2,sK17(relation_dom(sK2))) ) ),
inference(superposition,[status(thm)],[c_2475,c_7171]) ).
tcf(c_9984,plain,
( ( relation_dom(sK17(powerset(relation_dom(relation_dom(sK2))))) = empty_set )
| ~ empty(relation_dom(sK0)) ),
inference(superposition,[status(thm)],[c_3251,c_7171]) ).
tcf(c_9985,plain,
! [X0: $i] :
( ( relation_dom(sK17(powerset(sK17(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6912,c_7171]) ).
tcf(c_10043,plain,
( ( sK17(powerset(relation_dom(sK2))) = empty_set )
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(sK1,ordered_pair(apply(sK0,sK17(relation_dom(sK2))),apply(sK2,sK17(relation_dom(sK2))))) ),
inference(superposition,[status(thm)],[c_9781,c_64]) ).
tcf(c_10044,plain,
( element(ordered_pair(apply(sK0,sK17(relation_dom(sK2))),apply(sK2,sK17(relation_dom(sK2)))),sK1)
| ( sK17(powerset(relation_dom(sK2))) = empty_set )
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_9781,c_63]) ).
tcf(c_10047,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(apply(sK0,sK17(relation_dom(sK2))),X0),relation_composition(sK1,X1))
| ( sK17(powerset(relation_dom(sK2))) = empty_set )
| ~ relation(sK1)
| ~ relation(X1)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),X1) ),
inference(superposition,[status(thm)],[c_9781,c_299]) ).
tcf(c_10055,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(apply(sK0,sK17(relation_dom(sK2))),X0),relation_composition(sK1,X1))
| ( sK17(powerset(relation_dom(sK2))) = empty_set )
| ~ relation(X1)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_10047,c_56]) ).
tcf(c_10095,plain,
! [X0: $i,X1: $i] :
( ( sK17(powerset(relation_dom(sK2))) = empty_set )
| ~ relation(X0)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X1),X0)
| ~ in(relation_composition(sK1,X0),ordered_pair(apply(sK0,sK17(relation_dom(sK2))),X1)) ),
inference(superposition,[status(thm)],[c_10055,c_64]) ).
tcf(c_10096,plain,
! [X0: $i,X1: $i] :
( element(ordered_pair(apply(sK0,sK17(relation_dom(sK2))),X0),relation_composition(sK1,X1))
| ( sK17(powerset(relation_dom(sK2))) = empty_set )
| ~ relation(X1)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),X1) ),
inference(superposition,[status(thm)],[c_10055,c_63]) ).
tcf(c_10097,plain,
! [X0: $i,X1: $i] :
( ( sK17(powerset(relation_dom(sK2))) = empty_set )
| ~ relation(X1)
| ~ empty(relation_composition(sK1,X1))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),X1) ),
inference(superposition,[status(thm)],[c_10055,c_61]) ).
tcf(c_10098,plain,
! [X0: $i,X1: $i] :
( in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(relation_composition(sK1,X1)))
| ( sK17(powerset(relation_dom(sK2))) = empty_set )
| ~ relation(X1)
| ~ relation(relation_composition(sK1,X1))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),X1) ),
inference(superposition,[status(thm)],[c_10055,c_70]) ).
tcf(c_10099,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(ordered_pair(apply(sK0,sK17(relation_dom(sK2))),X2),relation_composition(relation_composition(sK1,X1),X3))
| ( sK17(powerset(relation_dom(sK2))) = empty_set )
| ~ relation(X3)
| ~ relation(X1)
| ~ relation(relation_composition(sK1,X1))
| ~ in(ordered_pair(X0,X2),X3)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),X1) ),
inference(superposition,[status(thm)],[c_10055,c_299]) ).
tcf(c_10100,plain,
! [X0: $i,X1: $i] :
( ( sK17(powerset(relation_dom(sK2))) = empty_set )
| ( apply(relation_composition(sK1,X1),apply(sK0,sK17(relation_dom(sK2)))) = X0 )
| ~ relation(X1)
| ~ function(relation_composition(sK1,X1))
| ~ relation(relation_composition(sK1,X1))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),X1) ),
inference(superposition,[status(thm)],[c_10055,c_152]) ).
tcf(c_10101,plain,
! [X0: $i,X1: $i] :
( ( sK17(powerset(relation_dom(sK2))) = empty_set )
| ( apply(X1,sK12(sK1,X1,apply(sK0,sK17(relation_dom(sK2))),X0)) = X0 )
| ~ relation(sK1)
| ~ function(X1)
| ~ relation(X1)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),X1) ),
inference(superposition,[status(thm)],[c_10055,c_2068]) ).
tcf(c_10102,plain,
! [X0: $i] :
( ( sK17(powerset(relation_dom(sK2))) = empty_set )
| ~ relation(sK1)
| ~ empty(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_10055,c_2176]) ).
tcf(c_10103,plain,
! [X0: $i] :
( ( sK17(powerset(relation_dom(sK2))) = empty_set )
| ~ relation(sK1)
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_10055,c_2063]) ).
tcf(c_10104,plain,
! [X0: $i] :
( ( sK17(powerset(relation_dom(sK2))) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,sK17(relation_dom(sK2))),X0),X0))) = apply(sK2,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,sK17(relation_dom(sK2))),X0),X0)) )
| ~ relation(sK1)
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_10055,c_2064]) ).
tcf(c_10110,plain,
! [X0: $i] :
( ( sK17(powerset(relation_dom(sK2))) = empty_set )
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_10103,c_56]) ).
tcf(c_10116,plain,
! [X0: $i] :
( ( sK17(powerset(relation_dom(sK2))) = empty_set )
| ~ empty(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_10102,c_56]) ).
tcf(c_10138,plain,
! [X0: $i,X1: $i] :
( ( sK17(powerset(relation_dom(sK2))) = empty_set )
| ( apply(X1,sK12(sK1,X1,apply(sK0,sK17(relation_dom(sK2))),X0)) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_10101,c_56]) ).
tcf(c_10160,plain,
! [X0: $i] :
( ( sK17(powerset(relation_dom(sK2))) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,sK17(relation_dom(sK2))),X0),X0))) = apply(sK2,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,sK17(relation_dom(sK2))),X0),X0)) )
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_10104,c_56]) ).
tcf(c_10196,plain,
( ( sK17(powerset(relation_dom(sK2))) = empty_set )
| ~ empty(relation_dom(sK0)) ),
inference(global_subsumption_just,[status(thm)],[c_10116,c_58,c_126,c_7737]) ).
tcf(c_10215,plain,
! [X0: $i] :
( in(ordered_pair(sK11(X0,relation_dom(sK2),relation_dom(sK2)),sK10(X0,relation_dom(sK2),relation_dom(sK2))),relation_dom(sK0))
| ( relation_composition(X0,relation_dom(sK2)) = relation_dom(sK2) )
| ~ relation(X0)
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5257,c_2047]) ).
tcf(c_10216,plain,
! [X0: $i] :
( in(ordered_pair(sK11(X0,relation_dom(sK2),relation_dom(sK2)),sK10(X0,relation_dom(sK2),relation_dom(sK2))),relation_dom(sK0))
| ( relation_composition(X0,relation_dom(sK2)) = relation_dom(sK2) )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(X0,relation_dom(sK2),relation_dom(sK2)),sK10(X0,relation_dom(sK2),relation_dom(sK2))))) = apply(sK2,ordered_pair(sK9(X0,relation_dom(sK2),relation_dom(sK2)),sK10(X0,relation_dom(sK2),relation_dom(sK2)))) )
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5257,c_53]) ).
tcf(c_10217,plain,
! [X0: $i] :
( in(ordered_pair(sK11(X0,relation_dom(sK2),relation_dom(sK2)),sK10(X0,relation_dom(sK2),relation_dom(sK2))),relation_dom(sK0))
| in(ordered_pair(sK9(X0,relation_dom(sK2),relation_dom(sK2)),sK10(X0,relation_dom(sK2),relation_dom(sK2))),relation_dom(sK0))
| ( relation_composition(X0,relation_dom(sK2)) = relation_dom(sK2) )
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5257,c_51]) ).
tcf(c_10218,plain,
! [X0: $i] :
( in(ordered_pair(sK11(X0,relation_dom(sK2),relation_dom(sK0)),sK10(X0,relation_dom(sK2),relation_dom(sK0))),relation_dom(sK0))
| in(ordered_pair(sK9(X0,relation_dom(sK2),relation_dom(sK0)),sK10(X0,relation_dom(sK2),relation_dom(sK0))),relation_dom(sK2))
| ( relation_composition(X0,relation_dom(sK2)) = relation_dom(sK0) )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(X0,relation_dom(sK2),relation_dom(sK0)),sK10(X0,relation_dom(sK2),relation_dom(sK0))))) = empty_set )
| ~ relation(X0)
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5257,c_3475]) ).
tcf(c_10219,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK11(X1,relation_dom(sK2),X0),sK10(X1,relation_dom(sK2),X0)),relation_dom(sK0))
| ( relation_composition(X1,relation_dom(sK2)) = X0 )
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2))
| ~ in(X0,ordered_pair(sK9(X1,relation_dom(sK2),X0),sK10(X1,relation_dom(sK2),X0))) ),
inference(superposition,[status(thm)],[c_5257,c_64]) ).
tcf(c_10220,plain,
! [X0: $i,X1: $i] :
( element(ordered_pair(sK9(X0,relation_dom(sK2),X1),sK10(X0,relation_dom(sK2),X1)),X1)
| in(ordered_pair(sK11(X0,relation_dom(sK2),X1),sK10(X0,relation_dom(sK2),X1)),relation_dom(sK0))
| ( relation_composition(X0,relation_dom(sK2)) = X1 )
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5257,c_63]) ).
tcf(c_10221,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK11(X0,relation_dom(sK2),X1),sK10(X0,relation_dom(sK2),X1)),relation_dom(sK0))
| ( relation_composition(X0,relation_dom(sK2)) = X1 )
| ~ empty(X1)
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5257,c_61]) ).
tcf(c_10222,plain,
! [X0: $i,X1: $i] :
( in(sK9(X0,relation_dom(sK2),X1),relation_dom(X1))
| in(ordered_pair(sK11(X0,relation_dom(sK2),X1),sK10(X0,relation_dom(sK2),X1)),relation_dom(sK0))
| ( relation_composition(X0,relation_dom(sK2)) = X1 )
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5257,c_70]) ).
tcf(c_10223,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(ordered_pair(sK9(X0,relation_dom(sK2),X1),X2),relation_composition(X1,X3))
| in(ordered_pair(sK11(X0,relation_dom(sK2),X1),sK10(X0,relation_dom(sK2),X1)),relation_dom(sK0))
| ( relation_composition(X0,relation_dom(sK2)) = X1 )
| ~ relation(X3)
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2))
| ~ in(ordered_pair(sK10(X0,relation_dom(sK2),X1),X2),X3) ),
inference(superposition,[status(thm)],[c_5257,c_299]) ).
tcf(c_10224,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK11(X0,relation_dom(sK2),X1),sK10(X0,relation_dom(sK2),X1)),relation_dom(sK0))
| ( relation_composition(X0,relation_dom(sK2)) = X1 )
| ( apply(X1,sK9(X0,relation_dom(sK2),X1)) = sK10(X0,relation_dom(sK2),X1) )
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5257,c_152]) ).
tcf(c_10225,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(ordered_pair(sK11(X1,relation_dom(sK2),X2),sK10(X1,relation_dom(sK2),X2)),relation_dom(sK0))
| ( relation_composition(X1,relation_dom(sK2)) = X2 )
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(relation_dom(sK2))
| ~ in(ordered_pair(sK9(X1,relation_dom(sK2),X2),X0),X1)
| ~ in(ordered_pair(X0,sK10(X1,relation_dom(sK2),X2)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5257,c_91]) ).
tcf(c_10226,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(ordered_pair(sK11(X2,relation_dom(sK2),relation_composition(X0,X1)),sK10(X2,relation_dom(sK2),relation_composition(X0,X1))),relation_dom(sK0))
| ( relation_composition(X2,relation_dom(sK2)) = relation_composition(X0,X1) )
| ( apply(X1,sK12(X0,X1,sK9(X2,relation_dom(sK2),relation_composition(X0,X1)),sK10(X2,relation_dom(sK2),relation_composition(X0,X1)))) = sK10(X2,relation_dom(sK2),relation_composition(X0,X1)) )
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2))
| ~ relation(relation_composition(X0,X1)) ),
inference(superposition,[status(thm)],[c_5257,c_2068]) ).
tcf(c_10227,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK11(X1,relation_dom(sK2),relation_composition(X0,relation_dom(sK2))),sK10(X1,relation_dom(sK2),relation_composition(X0,relation_dom(sK2)))),relation_dom(sK0))
| ( relation_composition(X0,relation_dom(sK2)) = relation_composition(X1,relation_dom(sK2)) )
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ relation(relation_composition(X0,relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_5257,c_2176]) ).
tcf(c_10228,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK11(X1,relation_dom(sK2),relation_composition(X0,relation_dom(sK2))),sK10(X1,relation_dom(sK2),relation_composition(X0,relation_dom(sK2)))),relation_dom(sK0))
| ( relation_composition(X0,relation_dom(sK2)) = relation_composition(X1,relation_dom(sK2)) )
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2))
| ~ relation(relation_composition(X0,relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_5257,c_2063]) ).
tcf(c_10229,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK11(X1,relation_dom(sK2),relation_composition(X0,relation_dom(sK2))),sK10(X1,relation_dom(sK2),relation_composition(X0,relation_dom(sK2)))),relation_dom(sK0))
| ( relation_composition(X0,relation_dom(sK2)) = relation_composition(X1,relation_dom(sK2)) )
| ( apply(sK1,apply(sK0,ordered_pair(sK12(X0,relation_dom(sK2),sK9(X1,relation_dom(sK2),relation_composition(X0,relation_dom(sK2))),sK10(X1,relation_dom(sK2),relation_composition(X0,relation_dom(sK2)))),sK10(X1,relation_dom(sK2),relation_composition(X0,relation_dom(sK2)))))) = apply(sK2,ordered_pair(sK12(X0,relation_dom(sK2),sK9(X1,relation_dom(sK2),relation_composition(X0,relation_dom(sK2))),sK10(X1,relation_dom(sK2),relation_composition(X0,relation_dom(sK2)))),sK10(X1,relation_dom(sK2),relation_composition(X0,relation_dom(sK2))))) )
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2))
| ~ relation(relation_composition(X0,relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_5257,c_2064]) ).
tcf(c_10230,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK11(X1,relation_dom(sK2),relation_composition(relation_dom(sK2),X0)),sK10(X1,relation_dom(sK2),relation_composition(relation_dom(sK2),X0))),relation_dom(sK0))
| ( relation_composition(relation_dom(sK2),X0) = relation_composition(X1,relation_dom(sK2)) )
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ relation(relation_composition(relation_dom(sK2),X0)) ),
inference(superposition,[status(thm)],[c_5257,c_2737]) ).
tcf(c_10231,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK11(X1,relation_dom(sK2),relation_composition(relation_dom(sK2),X0)),sK10(X1,relation_dom(sK2),relation_composition(relation_dom(sK2),X0))),relation_dom(sK0))
| ( relation_composition(relation_dom(sK2),X0) = relation_composition(X1,relation_dom(sK2)) )
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2))
| ~ relation(relation_composition(relation_dom(sK2),X0)) ),
inference(superposition,[status(thm)],[c_5257,c_2281]) ).
tcf(c_10232,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK11(X1,relation_dom(sK2),relation_composition(relation_dom(sK2),X0)),sK10(X1,relation_dom(sK2),relation_composition(relation_dom(sK2),X0))),relation_dom(sK0))
| ( relation_composition(relation_dom(sK2),X0) = relation_composition(X1,relation_dom(sK2)) )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(X1,relation_dom(sK2),relation_composition(relation_dom(sK2),X0)),sK12(relation_dom(sK2),X0,sK9(X1,relation_dom(sK2),relation_composition(relation_dom(sK2),X0)),sK10(X1,relation_dom(sK2),relation_composition(relation_dom(sK2),X0)))))) = apply(sK2,ordered_pair(sK9(X1,relation_dom(sK2),relation_composition(relation_dom(sK2),X0)),sK12(relation_dom(sK2),X0,sK9(X1,relation_dom(sK2),relation_composition(relation_dom(sK2),X0)),sK10(X1,relation_dom(sK2),relation_composition(relation_dom(sK2),X0))))) )
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2))
| ~ relation(relation_composition(relation_dom(sK2),X0)) ),
inference(superposition,[status(thm)],[c_5257,c_2282]) ).
tcf(c_10233,plain,
! [X0: $i] :
( in(ordered_pair(sK11(X0,relation_dom(sK2),empty_set),sK10(X0,relation_dom(sK2),empty_set)),relation_dom(sK0))
| ( relation_composition(X0,relation_dom(sK2)) = empty_set )
| ~ relation(empty_set)
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5257,c_3809]) ).
tcf(c_10234,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| element(ordered_pair(sK9(X1,relation_dom(sK2),sK16(X0)),sK10(X1,relation_dom(sK2),sK16(X0))),X0)
| in(ordered_pair(sK11(X1,relation_dom(sK2),sK16(X0)),sK10(X1,relation_dom(sK2),sK16(X0))),relation_dom(sK0))
| ( relation_composition(X1,relation_dom(sK2)) = sK16(X0) )
| ~ relation(X1)
| ~ relation(relation_dom(sK2))
| ~ relation(sK16(X0)) ),
inference(superposition,[status(thm)],[c_5257,c_2939]) ).
tcf(c_10235,plain,
! [X0: $i,X1: $i] :
( element(ordered_pair(sK9(X1,relation_dom(sK2),sK17(powerset(X0))),sK10(X1,relation_dom(sK2),sK17(powerset(X0)))),X0)
| in(ordered_pair(sK11(X1,relation_dom(sK2),sK17(powerset(X0))),sK10(X1,relation_dom(sK2),sK17(powerset(X0)))),relation_dom(sK0))
| ( relation_composition(X1,relation_dom(sK2)) = sK17(powerset(X0)) )
| ~ relation(X1)
| ~ relation(relation_dom(sK2))
| ~ relation(sK17(powerset(X0))) ),
inference(superposition,[status(thm)],[c_5257,c_2940]) ).
tcf(c_10236,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK11(X1,relation_dom(sK2),sK17(powerset(X0))),sK10(X1,relation_dom(sK2),sK17(powerset(X0)))),relation_dom(sK0))
| ( relation_composition(X1,relation_dom(sK2)) = sK17(powerset(X0)) )
| ~ empty(X0)
| ~ relation(X1)
| ~ relation(relation_dom(sK2))
| ~ relation(sK17(powerset(X0))) ),
inference(superposition,[status(thm)],[c_5257,c_2925]) ).
tcf(c_10237,plain,
! [X0: $i] :
( in(ordered_pair(sK11(X0,relation_dom(sK2),relation_dom(relation_dom(sK2))),sK10(X0,relation_dom(sK2),relation_dom(relation_dom(sK2)))),relation_dom(sK0))
| ( relation_composition(X0,relation_dom(sK2)) = relation_dom(relation_dom(sK2)) )
| ( apply(sK1,apply(sK0,ordered_pair(ordered_pair(sK9(X0,relation_dom(sK2),relation_dom(relation_dom(sK2))),sK10(X0,relation_dom(sK2),relation_dom(relation_dom(sK2)))),apply(relation_dom(sK2),ordered_pair(sK9(X0,relation_dom(sK2),relation_dom(relation_dom(sK2))),sK10(X0,relation_dom(sK2),relation_dom(relation_dom(sK2)))))))) = apply(sK2,ordered_pair(ordered_pair(sK9(X0,relation_dom(sK2),relation_dom(relation_dom(sK2))),sK10(X0,relation_dom(sK2),relation_dom(relation_dom(sK2)))),apply(relation_dom(sK2),ordered_pair(sK9(X0,relation_dom(sK2),relation_dom(relation_dom(sK2))),sK10(X0,relation_dom(sK2),relation_dom(relation_dom(sK2))))))) )
| ~ relation(X0)
| ~ function(relation_dom(sK2))
| ~ relation(relation_dom(sK2))
| ~ relation(relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_5257,c_3550]) ).
tcf(c_10238,plain,
! [X0: $i] :
( in(ordered_pair(sK11(X0,relation_dom(sK2),relation_dom(relation_dom(sK2))),sK10(X0,relation_dom(sK2),relation_dom(relation_dom(sK2)))),relation_dom(sK0))
| in(ordered_pair(sK9(X0,relation_dom(sK2),relation_dom(relation_dom(sK2))),sK10(X0,relation_dom(sK2),relation_dom(relation_dom(sK2)))),relation_dom(relation_dom(sK0)))
| ( relation_composition(X0,relation_dom(sK2)) = relation_dom(relation_dom(sK2)) )
| ~ relation(X0)
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ relation(relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_5257,c_3134]) ).
tcf(c_10239,plain,
! [X0: $i] :
( in(ordered_pair(sK11(X0,relation_dom(sK2),relation_dom(relation_dom(sK2))),sK10(X0,relation_dom(sK2),relation_dom(relation_dom(sK2)))),relation_dom(sK0))
| ( relation_composition(X0,relation_dom(sK2)) = relation_dom(relation_dom(sK2)) )
| ~ relation(X0)
| ~ empty(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ relation(relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_5257,c_3241]) ).
tcf(c_10240,plain,
! [X0: $i] :
( in(ordered_pair(sK11(X0,relation_dom(sK2),relation_dom(relation_dom(sK2))),sK10(X0,relation_dom(sK2),relation_dom(relation_dom(sK2)))),relation_dom(sK0))
| ( relation_composition(X0,relation_dom(sK2)) = relation_dom(relation_dom(sK2)) )
| ~ relation(X0)
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2))
| ~ relation(relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_5257,c_3017]) ).
tcf(c_10241,plain,
! [X0: $i] :
( in(ordered_pair(sK11(X0,relation_dom(sK2),relation_dom(relation_dom(sK2))),sK10(X0,relation_dom(sK2),relation_dom(relation_dom(sK2)))),relation_dom(sK0))
| ( relation_composition(X0,relation_dom(sK2)) = relation_dom(relation_dom(sK2)) )
| ( apply(sK1,apply(sK0,ordered_pair(ordered_pair(sK9(X0,relation_dom(sK2),relation_dom(relation_dom(sK2))),sK10(X0,relation_dom(sK2),relation_dom(relation_dom(sK2)))),sK5(relation_dom(sK2),ordered_pair(sK9(X0,relation_dom(sK2),relation_dom(relation_dom(sK2))),sK10(X0,relation_dom(sK2),relation_dom(relation_dom(sK2)))))))) = apply(sK2,ordered_pair(ordered_pair(sK9(X0,relation_dom(sK2),relation_dom(relation_dom(sK2))),sK10(X0,relation_dom(sK2),relation_dom(relation_dom(sK2)))),sK5(relation_dom(sK2),ordered_pair(sK9(X0,relation_dom(sK2),relation_dom(relation_dom(sK2))),sK10(X0,relation_dom(sK2),relation_dom(relation_dom(sK2))))))) )
| ~ relation(X0)
| ~ relation(relation_dom(sK2))
| ~ relation(relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_5257,c_3018]) ).
tcf(c_10242,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK9(X0,relation_dom(sK2),X1),sK10(X0,relation_dom(sK2),X1)),X1)
| in(ordered_pair(sK11(X0,relation_dom(sK2),X1),sK10(X0,relation_dom(sK2),X1)),relation_dom(sK2))
| ( relation_composition(X0,relation_dom(sK2)) = X1 )
| ( apply(sK1,apply(sK0,ordered_pair(sK11(X0,relation_dom(sK2),X1),sK10(X0,relation_dom(sK2),X1)))) = empty_set )
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5257,c_3475]) ).
tcf(c_10243,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK9(X0,relation_dom(sK2),X1),sK10(X0,relation_dom(sK2),X1)),X1)
| ( relation_composition(X0,relation_dom(sK2)) = X1 )
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2))
| ~ in(relation_dom(sK0),ordered_pair(sK11(X0,relation_dom(sK2),X1),sK10(X0,relation_dom(sK2),X1))) ),
inference(superposition,[status(thm)],[c_5257,c_64]) ).
tcf(c_10244,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK9(X0,relation_dom(sK2),X1),sK10(X0,relation_dom(sK2),X1)),X1)
| element(ordered_pair(sK11(X0,relation_dom(sK2),X1),sK10(X0,relation_dom(sK2),X1)),relation_dom(sK0))
| ( relation_composition(X0,relation_dom(sK2)) = X1 )
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5257,c_63]) ).
tcf(c_10245,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK9(X0,relation_dom(sK2),X1),sK10(X0,relation_dom(sK2),X1)),X1)
| ( relation_composition(X0,relation_dom(sK2)) = X1 )
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(sK0))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5257,c_61]) ).
tcf(c_10246,plain,
! [X0: $i,X1: $i] :
( in(sK11(X0,relation_dom(sK2),X1),relation_dom(relation_dom(sK0)))
| in(ordered_pair(sK9(X0,relation_dom(sK2),X1),sK10(X0,relation_dom(sK2),X1)),X1)
| ( relation_composition(X0,relation_dom(sK2)) = X1 )
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5257,c_70]) ).
tcf(c_10247,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(ordered_pair(sK11(X0,relation_dom(sK2),X1),X2),relation_composition(relation_dom(sK0),X3))
| in(ordered_pair(sK9(X0,relation_dom(sK2),X1),sK10(X0,relation_dom(sK2),X1)),X1)
| ( relation_composition(X0,relation_dom(sK2)) = X1 )
| ~ relation(X3)
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(ordered_pair(sK10(X0,relation_dom(sK2),X1),X2),X3) ),
inference(superposition,[status(thm)],[c_5257,c_299]) ).
tcf(c_10248,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK9(X0,relation_dom(sK2),X1),sK10(X0,relation_dom(sK2),X1)),X1)
| ( relation_composition(X0,relation_dom(sK2)) = X1 )
| ( apply(relation_dom(sK0),sK11(X0,relation_dom(sK2),X1)) = sK10(X0,relation_dom(sK2),X1) )
| ~ relation(X1)
| ~ relation(X0)
| ~ function(relation_dom(sK0))
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5257,c_152]) ).
tcf(c_10249,plain,
! [X0: $i] :
( in(ordered_pair(sK11(X0,relation_dom(sK2),empty_set),sK10(X0,relation_dom(sK2),empty_set)),relation_dom(sK0))
| ( relation_composition(X0,relation_dom(sK2)) = empty_set )
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_10233,c_109]) ).
tcf(c_10661,plain,
! [X0: $i] :
( in(ordered_pair(sK9(X0,relation_dom(sK2),relation_dom(sK2)),sK10(X0,relation_dom(sK2),relation_dom(sK2))),relation_dom(sK0))
| ( relation_composition(X0,relation_dom(sK2)) = relation_dom(sK2) )
| ~ relation(X0)
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5279,c_2047]) ).
tcf(c_10662,plain,
! [X0: $i] :
( in(ordered_pair(sK9(X0,relation_dom(sK2),relation_dom(sK2)),sK10(X0,relation_dom(sK2),relation_dom(sK2))),relation_dom(sK0))
| ( relation_composition(X0,relation_dom(sK2)) = relation_dom(sK2) )
| ( apply(sK1,apply(sK0,ordered_pair(sK11(X0,relation_dom(sK2),relation_dom(sK2)),sK10(X0,relation_dom(sK2),relation_dom(sK2))))) = apply(sK2,ordered_pair(sK11(X0,relation_dom(sK2),relation_dom(sK2)),sK10(X0,relation_dom(sK2),relation_dom(sK2)))) )
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5279,c_53]) ).
tcf(c_10664,plain,
! [X0: $i] :
( in(ordered_pair(sK11(X0,relation_dom(sK0),relation_dom(sK2)),sK10(X0,relation_dom(sK0),relation_dom(sK2))),relation_dom(sK2))
| in(ordered_pair(sK9(X0,relation_dom(sK0),relation_dom(sK2)),sK10(X0,relation_dom(sK0),relation_dom(sK2))),relation_dom(sK0))
| ( relation_composition(X0,relation_dom(sK0)) = relation_dom(sK2) )
| ( apply(sK1,apply(sK0,ordered_pair(sK11(X0,relation_dom(sK0),relation_dom(sK2)),sK10(X0,relation_dom(sK0),relation_dom(sK2))))) = empty_set )
| ~ relation(X0)
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5279,c_3475]) ).
tcf(c_10665,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK9(X1,X0,relation_dom(sK2)),sK10(X1,X0,relation_dom(sK2))),relation_dom(sK0))
| ( relation_composition(X1,X0) = relation_dom(sK2) )
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2))
| ~ in(X0,ordered_pair(sK11(X1,X0,relation_dom(sK2)),sK10(X1,X0,relation_dom(sK2)))) ),
inference(superposition,[status(thm)],[c_5279,c_64]) ).
tcf(c_10666,plain,
! [X0: $i,X1: $i] :
( element(ordered_pair(sK11(X0,X1,relation_dom(sK2)),sK10(X0,X1,relation_dom(sK2))),X1)
| in(ordered_pair(sK9(X0,X1,relation_dom(sK2)),sK10(X0,X1,relation_dom(sK2))),relation_dom(sK0))
| ( relation_composition(X0,X1) = relation_dom(sK2) )
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5279,c_63]) ).
tcf(c_10667,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK9(X0,X1,relation_dom(sK2)),sK10(X0,X1,relation_dom(sK2))),relation_dom(sK0))
| ( relation_composition(X0,X1) = relation_dom(sK2) )
| ~ empty(X1)
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5279,c_61]) ).
tcf(c_10668,plain,
! [X0: $i,X1: $i] :
( in(sK11(X0,X1,relation_dom(sK2)),relation_dom(X1))
| in(ordered_pair(sK9(X0,X1,relation_dom(sK2)),sK10(X0,X1,relation_dom(sK2))),relation_dom(sK0))
| ( relation_composition(X0,X1) = relation_dom(sK2) )
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5279,c_70]) ).
tcf(c_10669,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(ordered_pair(sK11(X0,X1,relation_dom(sK2)),X2),relation_composition(X1,X3))
| in(ordered_pair(sK9(X0,X1,relation_dom(sK2)),sK10(X0,X1,relation_dom(sK2))),relation_dom(sK0))
| ( relation_composition(X0,X1) = relation_dom(sK2) )
| ~ relation(X3)
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2))
| ~ in(ordered_pair(sK10(X0,X1,relation_dom(sK2)),X2),X3) ),
inference(superposition,[status(thm)],[c_5279,c_299]) ).
tcf(c_10670,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK9(X0,X1,relation_dom(sK2)),sK10(X0,X1,relation_dom(sK2))),relation_dom(sK0))
| ( relation_composition(X0,X1) = relation_dom(sK2) )
| ( apply(X1,sK11(X0,X1,relation_dom(sK2))) = sK10(X0,X1,relation_dom(sK2)) )
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5279,c_152]) ).
tcf(c_10671,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(ordered_pair(sK9(X2,relation_composition(X0,X1),relation_dom(sK2)),sK10(X2,relation_composition(X0,X1),relation_dom(sK2))),relation_dom(sK0))
| ( relation_composition(X2,relation_composition(X0,X1)) = relation_dom(sK2) )
| ( apply(X1,sK12(X0,X1,sK11(X2,relation_composition(X0,X1),relation_dom(sK2)),sK10(X2,relation_composition(X0,X1),relation_dom(sK2)))) = sK10(X2,relation_composition(X0,X1),relation_dom(sK2)) )
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2))
| ~ relation(relation_composition(X0,X1)) ),
inference(superposition,[status(thm)],[c_5279,c_2068]) ).
tcf(c_10672,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK9(X1,relation_composition(X0,relation_dom(sK2)),relation_dom(sK2)),sK10(X1,relation_composition(X0,relation_dom(sK2)),relation_dom(sK2))),relation_dom(sK0))
| ( relation_composition(X1,relation_composition(X0,relation_dom(sK2))) = relation_dom(sK2) )
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ relation(relation_composition(X0,relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_5279,c_2176]) ).
tcf(c_10673,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK9(X1,relation_composition(X0,relation_dom(sK2)),relation_dom(sK2)),sK10(X1,relation_composition(X0,relation_dom(sK2)),relation_dom(sK2))),relation_dom(sK0))
| ( relation_composition(X1,relation_composition(X0,relation_dom(sK2))) = relation_dom(sK2) )
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2))
| ~ relation(relation_composition(X0,relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_5279,c_2063]) ).
tcf(c_10674,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK9(X1,relation_composition(X0,relation_dom(sK2)),relation_dom(sK2)),sK10(X1,relation_composition(X0,relation_dom(sK2)),relation_dom(sK2))),relation_dom(sK0))
| ( relation_composition(X1,relation_composition(X0,relation_dom(sK2))) = relation_dom(sK2) )
| ( apply(sK1,apply(sK0,ordered_pair(sK12(X0,relation_dom(sK2),sK11(X1,relation_composition(X0,relation_dom(sK2)),relation_dom(sK2)),sK10(X1,relation_composition(X0,relation_dom(sK2)),relation_dom(sK2))),sK10(X1,relation_composition(X0,relation_dom(sK2)),relation_dom(sK2))))) = apply(sK2,ordered_pair(sK12(X0,relation_dom(sK2),sK11(X1,relation_composition(X0,relation_dom(sK2)),relation_dom(sK2)),sK10(X1,relation_composition(X0,relation_dom(sK2)),relation_dom(sK2))),sK10(X1,relation_composition(X0,relation_dom(sK2)),relation_dom(sK2)))) )
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2))
| ~ relation(relation_composition(X0,relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_5279,c_2064]) ).
tcf(c_10675,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK9(X1,relation_composition(relation_dom(sK2),X0),relation_dom(sK2)),sK10(X1,relation_composition(relation_dom(sK2),X0),relation_dom(sK2))),relation_dom(sK0))
| ( relation_composition(X1,relation_composition(relation_dom(sK2),X0)) = relation_dom(sK2) )
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ relation(relation_composition(relation_dom(sK2),X0)) ),
inference(superposition,[status(thm)],[c_5279,c_2737]) ).
tcf(c_10676,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK9(X1,relation_composition(relation_dom(sK2),X0),relation_dom(sK2)),sK10(X1,relation_composition(relation_dom(sK2),X0),relation_dom(sK2))),relation_dom(sK0))
| ( relation_composition(X1,relation_composition(relation_dom(sK2),X0)) = relation_dom(sK2) )
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2))
| ~ relation(relation_composition(relation_dom(sK2),X0)) ),
inference(superposition,[status(thm)],[c_5279,c_2281]) ).
tcf(c_10677,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK9(X1,relation_composition(relation_dom(sK2),X0),relation_dom(sK2)),sK10(X1,relation_composition(relation_dom(sK2),X0),relation_dom(sK2))),relation_dom(sK0))
| ( relation_composition(X1,relation_composition(relation_dom(sK2),X0)) = relation_dom(sK2) )
| ( apply(sK1,apply(sK0,ordered_pair(sK11(X1,relation_composition(relation_dom(sK2),X0),relation_dom(sK2)),sK12(relation_dom(sK2),X0,sK11(X1,relation_composition(relation_dom(sK2),X0),relation_dom(sK2)),sK10(X1,relation_composition(relation_dom(sK2),X0),relation_dom(sK2)))))) = apply(sK2,ordered_pair(sK11(X1,relation_composition(relation_dom(sK2),X0),relation_dom(sK2)),sK12(relation_dom(sK2),X0,sK11(X1,relation_composition(relation_dom(sK2),X0),relation_dom(sK2)),sK10(X1,relation_composition(relation_dom(sK2),X0),relation_dom(sK2))))) )
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2))
| ~ relation(relation_composition(relation_dom(sK2),X0)) ),
inference(superposition,[status(thm)],[c_5279,c_2282]) ).
tcf(c_10678,plain,
! [X0: $i] :
( in(ordered_pair(sK9(X0,empty_set,relation_dom(sK2)),sK10(X0,empty_set,relation_dom(sK2))),relation_dom(sK0))
| ( relation_composition(X0,empty_set) = relation_dom(sK2) )
| ~ relation(empty_set)
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5279,c_3809]) ).
tcf(c_10679,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| element(ordered_pair(sK11(X1,sK16(X0),relation_dom(sK2)),sK10(X1,sK16(X0),relation_dom(sK2))),X0)
| in(ordered_pair(sK9(X1,sK16(X0),relation_dom(sK2)),sK10(X1,sK16(X0),relation_dom(sK2))),relation_dom(sK0))
| ( relation_composition(X1,sK16(X0)) = relation_dom(sK2) )
| ~ relation(X1)
| ~ relation(relation_dom(sK2))
| ~ relation(sK16(X0)) ),
inference(superposition,[status(thm)],[c_5279,c_2939]) ).
tcf(c_10680,plain,
! [X0: $i,X1: $i] :
( element(ordered_pair(sK11(X1,sK17(powerset(X0)),relation_dom(sK2)),sK10(X1,sK17(powerset(X0)),relation_dom(sK2))),X0)
| in(ordered_pair(sK9(X1,sK17(powerset(X0)),relation_dom(sK2)),sK10(X1,sK17(powerset(X0)),relation_dom(sK2))),relation_dom(sK0))
| ( relation_composition(X1,sK17(powerset(X0))) = relation_dom(sK2) )
| ~ relation(X1)
| ~ relation(relation_dom(sK2))
| ~ relation(sK17(powerset(X0))) ),
inference(superposition,[status(thm)],[c_5279,c_2940]) ).
tcf(c_10681,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK9(X1,sK17(powerset(X0)),relation_dom(sK2)),sK10(X1,sK17(powerset(X0)),relation_dom(sK2))),relation_dom(sK0))
| ( relation_composition(X1,sK17(powerset(X0))) = relation_dom(sK2) )
| ~ empty(X0)
| ~ relation(X1)
| ~ relation(relation_dom(sK2))
| ~ relation(sK17(powerset(X0))) ),
inference(superposition,[status(thm)],[c_5279,c_2925]) ).
tcf(c_10682,plain,
! [X0: $i] :
( in(ordered_pair(sK9(X0,relation_dom(relation_dom(sK2)),relation_dom(sK2)),sK10(X0,relation_dom(relation_dom(sK2)),relation_dom(sK2))),relation_dom(sK0))
| ( relation_composition(X0,relation_dom(relation_dom(sK2))) = relation_dom(sK2) )
| ( apply(sK1,apply(sK0,ordered_pair(ordered_pair(sK11(X0,relation_dom(relation_dom(sK2)),relation_dom(sK2)),sK10(X0,relation_dom(relation_dom(sK2)),relation_dom(sK2))),apply(relation_dom(sK2),ordered_pair(sK11(X0,relation_dom(relation_dom(sK2)),relation_dom(sK2)),sK10(X0,relation_dom(relation_dom(sK2)),relation_dom(sK2))))))) = apply(sK2,ordered_pair(ordered_pair(sK11(X0,relation_dom(relation_dom(sK2)),relation_dom(sK2)),sK10(X0,relation_dom(relation_dom(sK2)),relation_dom(sK2))),apply(relation_dom(sK2),ordered_pair(sK11(X0,relation_dom(relation_dom(sK2)),relation_dom(sK2)),sK10(X0,relation_dom(relation_dom(sK2)),relation_dom(sK2)))))) )
| ~ relation(X0)
| ~ function(relation_dom(sK2))
| ~ relation(relation_dom(sK2))
| ~ relation(relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_5279,c_3550]) ).
tcf(c_10683,plain,
! [X0: $i] :
( in(ordered_pair(sK9(X0,relation_dom(relation_dom(sK2)),relation_dom(sK2)),sK10(X0,relation_dom(relation_dom(sK2)),relation_dom(sK2))),relation_dom(sK0))
| in(ordered_pair(sK11(X0,relation_dom(relation_dom(sK2)),relation_dom(sK2)),sK10(X0,relation_dom(relation_dom(sK2)),relation_dom(sK2))),relation_dom(relation_dom(sK0)))
| ( relation_composition(X0,relation_dom(relation_dom(sK2))) = relation_dom(sK2) )
| ~ relation(X0)
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ relation(relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_5279,c_3134]) ).
tcf(c_10684,plain,
! [X0: $i] :
( in(ordered_pair(sK9(X0,relation_dom(relation_dom(sK2)),relation_dom(sK2)),sK10(X0,relation_dom(relation_dom(sK2)),relation_dom(sK2))),relation_dom(sK0))
| ( relation_composition(X0,relation_dom(relation_dom(sK2))) = relation_dom(sK2) )
| ~ relation(X0)
| ~ empty(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ relation(relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_5279,c_3241]) ).
tcf(c_10685,plain,
! [X0: $i] :
( in(ordered_pair(sK9(X0,relation_dom(relation_dom(sK2)),relation_dom(sK2)),sK10(X0,relation_dom(relation_dom(sK2)),relation_dom(sK2))),relation_dom(sK0))
| ( relation_composition(X0,relation_dom(relation_dom(sK2))) = relation_dom(sK2) )
| ~ relation(X0)
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2))
| ~ relation(relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_5279,c_3017]) ).
tcf(c_10686,plain,
! [X0: $i] :
( in(ordered_pair(sK9(X0,relation_dom(relation_dom(sK2)),relation_dom(sK2)),sK10(X0,relation_dom(relation_dom(sK2)),relation_dom(sK2))),relation_dom(sK0))
| ( relation_composition(X0,relation_dom(relation_dom(sK2))) = relation_dom(sK2) )
| ( apply(sK1,apply(sK0,ordered_pair(ordered_pair(sK11(X0,relation_dom(relation_dom(sK2)),relation_dom(sK2)),sK10(X0,relation_dom(relation_dom(sK2)),relation_dom(sK2))),sK5(relation_dom(sK2),ordered_pair(sK11(X0,relation_dom(relation_dom(sK2)),relation_dom(sK2)),sK10(X0,relation_dom(relation_dom(sK2)),relation_dom(sK2))))))) = apply(sK2,ordered_pair(ordered_pair(sK11(X0,relation_dom(relation_dom(sK2)),relation_dom(sK2)),sK10(X0,relation_dom(relation_dom(sK2)),relation_dom(sK2))),sK5(relation_dom(sK2),ordered_pair(sK11(X0,relation_dom(relation_dom(sK2)),relation_dom(sK2)),sK10(X0,relation_dom(relation_dom(sK2)),relation_dom(sK2)))))) )
| ~ relation(X0)
| ~ relation(relation_dom(sK2))
| ~ relation(relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_5279,c_3018]) ).
tcf(c_10687,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK11(X0,X1,relation_dom(sK2)),sK10(X0,X1,relation_dom(sK2))),X1)
| in(ordered_pair(sK9(X0,X1,relation_dom(sK2)),sK10(X0,X1,relation_dom(sK2))),relation_dom(sK2))
| ( relation_composition(X0,X1) = relation_dom(sK2) )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(X0,X1,relation_dom(sK2)),sK10(X0,X1,relation_dom(sK2))))) = empty_set )
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5279,c_3475]) ).
tcf(c_10688,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK11(X0,X1,relation_dom(sK2)),sK10(X0,X1,relation_dom(sK2))),X1)
| ( relation_composition(X0,X1) = relation_dom(sK2) )
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2))
| ~ in(relation_dom(sK0),ordered_pair(sK9(X0,X1,relation_dom(sK2)),sK10(X0,X1,relation_dom(sK2)))) ),
inference(superposition,[status(thm)],[c_5279,c_64]) ).
tcf(c_10689,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK11(X0,X1,relation_dom(sK2)),sK10(X0,X1,relation_dom(sK2))),X1)
| element(ordered_pair(sK9(X0,X1,relation_dom(sK2)),sK10(X0,X1,relation_dom(sK2))),relation_dom(sK0))
| ( relation_composition(X0,X1) = relation_dom(sK2) )
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5279,c_63]) ).
tcf(c_10690,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK11(X0,X1,relation_dom(sK2)),sK10(X0,X1,relation_dom(sK2))),X1)
| ( relation_composition(X0,X1) = relation_dom(sK2) )
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(sK0))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5279,c_61]) ).
tcf(c_10691,plain,
! [X0: $i,X1: $i] :
( in(sK9(X0,X1,relation_dom(sK2)),relation_dom(relation_dom(sK0)))
| in(ordered_pair(sK11(X0,X1,relation_dom(sK2)),sK10(X0,X1,relation_dom(sK2))),X1)
| ( relation_composition(X0,X1) = relation_dom(sK2) )
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5279,c_70]) ).
tcf(c_10692,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(ordered_pair(sK9(X0,X1,relation_dom(sK2)),X2),relation_composition(relation_dom(sK0),X3))
| in(ordered_pair(sK11(X0,X1,relation_dom(sK2)),sK10(X0,X1,relation_dom(sK2))),X1)
| ( relation_composition(X0,X1) = relation_dom(sK2) )
| ~ relation(X3)
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(ordered_pair(sK10(X0,X1,relation_dom(sK2)),X2),X3) ),
inference(superposition,[status(thm)],[c_5279,c_299]) ).
tcf(c_10693,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK11(X0,X1,relation_dom(sK2)),sK10(X0,X1,relation_dom(sK2))),X1)
| ( relation_composition(X0,X1) = relation_dom(sK2) )
| ( apply(relation_dom(sK0),sK9(X0,X1,relation_dom(sK2))) = sK10(X0,X1,relation_dom(sK2)) )
| ~ relation(X1)
| ~ relation(X0)
| ~ function(relation_dom(sK0))
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5279,c_152]) ).
tcf(c_10694,plain,
! [X0: $i] :
( in(ordered_pair(sK9(X0,empty_set,relation_dom(sK2)),sK10(X0,empty_set,relation_dom(sK2))),relation_dom(sK0))
| ( relation_composition(X0,empty_set) = relation_dom(sK2) )
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_10678,c_109]) ).
tcf(c_11081,plain,
! [X0: $i] :
( ( relation_dom(sK2) = empty_set )
| ( apply(sK0,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0)) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0))) = empty_set )
| ( apply(relation_dom(sK2),sK12(sK1,relation_dom(sK2),apply(sK0,sK17(relation_dom(sK2))),X0)) = X0 )
| ~ function(relation_dom(sK2))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_4011,c_7455]) ).
tcf(c_11082,plain,
! [X0: $i] :
( ( relation_dom(sK2) = empty_set )
| ( apply(sK0,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0)) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0))) = empty_set )
| ( apply(relation_dom(sK0),sK12(sK1,relation_dom(sK0),apply(sK0,sK17(relation_dom(sK2))),X0)) = X0 )
| ~ function(relation_dom(sK0))
| ~ relation(relation_dom(sK0))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_4110,c_7455]) ).
tcf(c_11083,plain,
! [X0: $i] :
( ( relation_dom(sK2) = empty_set )
| ( apply(sK2,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0)) = empty_set )
| ( apply(relation_dom(sK0),sK12(sK1,relation_dom(sK0),apply(sK0,sK17(relation_dom(sK2))),X0)) = X0 )
| ~ function(relation_dom(sK0))
| ~ relation(relation_dom(sK0))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_3449,c_7455]) ).
tcf(c_11084,plain,
! [X0: $i] :
( ( relation_dom(sK2) = empty_set )
| ( apply(X0,sK12(sK1,X0,apply(sK0,sK17(relation_dom(sK2))),sK5(X0,apply(sK2,sK17(relation_dom(sK2)))))) = sK5(X0,apply(sK2,sK17(relation_dom(sK2)))) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(apply(sK2,sK17(relation_dom(sK2))),relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_71,c_7455]) ).
tcf(c_11085,plain,
! [X0: $i] :
( ( relation_dom(sK2) = empty_set )
| ( apply(X0,sK12(sK1,X0,apply(sK0,sK17(relation_dom(sK2))),apply(X0,apply(sK2,sK17(relation_dom(sK2)))))) = apply(X0,apply(sK2,sK17(relation_dom(sK2)))) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(apply(sK2,sK17(relation_dom(sK2))),relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_73,c_7455]) ).
tcf(c_11086,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK2) = empty_set )
| ( apply(X0,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X1)) = empty_set )
| ( apply(relation_dom(X0),sK12(sK1,relation_dom(X0),apply(sK0,sK17(relation_dom(sK2))),X1)) = X1 )
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom(X0))
| ~ relation(relation_dom(X0))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_75,c_7455]) ).
tcf(c_11087,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(sK2) = empty_set )
| ( apply(X1,sK12(sK1,X1,apply(sK0,sK17(relation_dom(sK2))),sK12(X1,X2,apply(sK2,sK17(relation_dom(sK2))),X0))) = sK12(X1,X2,apply(sK2,sK17(relation_dom(sK2))),X0) )
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),relation_composition(X1,X2)) ),
inference(superposition,[status(thm)],[c_301,c_7455]) ).
tcf(c_11088,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK2) = empty_set )
| ( apply(relation_dom(sK0),sK12(sK1,relation_dom(sK0),apply(sK0,sK17(relation_dom(sK2))),sK12(relation_dom(sK2),X1,apply(sK2,sK17(relation_dom(sK2))),X0))) = sK12(relation_dom(sK2),X1,apply(sK2,sK17(relation_dom(sK2))),X0) )
| ~ relation(X1)
| ~ function(relation_dom(sK0))
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),relation_composition(relation_dom(sK2),X1)) ),
inference(superposition,[status(thm)],[c_2283,c_7455]) ).
tcf(c_11089,plain,
( ( relation_dom(sK2) = empty_set )
| ( apply(relation_dom(sK0),sK12(sK1,relation_dom(sK0),apply(sK0,sK17(relation_dom(sK2))),sK5(relation_dom(sK2),apply(sK2,sK17(relation_dom(sK2)))))) = sK5(relation_dom(sK2),apply(sK2,sK17(relation_dom(sK2)))) )
| ~ function(relation_dom(sK0))
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(apply(sK2,sK17(relation_dom(sK2))),relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_3019,c_7455]) ).
tcf(c_11090,plain,
( ( relation_dom(sK2) = empty_set )
| ( apply(relation_dom(sK0),sK12(sK1,relation_dom(sK0),apply(sK0,sK17(relation_dom(sK2))),apply(relation_dom(sK2),apply(sK2,sK17(relation_dom(sK2)))))) = apply(relation_dom(sK2),apply(sK2,sK17(relation_dom(sK2)))) )
| ~ function(relation_dom(sK0))
| ~ function(relation_dom(sK2))
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(apply(sK2,sK17(relation_dom(sK2))),relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_3551,c_7455]) ).
tcf(c_11181,plain,
! [X0: $i] :
( ( relation_dom(sK2) = sK2 )
| ( apply(sK0,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0)) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0))) = empty_set )
| ( apply(relation_dom(sK2),sK12(sK1,relation_dom(sK2),apply(sK0,sK17(relation_dom(sK2))),X0)) = X0 )
| ~ function(relation_dom(sK2))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_4011,c_7544]) ).
tcf(c_11182,plain,
! [X0: $i] :
( ( relation_dom(sK2) = sK2 )
| ( apply(sK0,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0)) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0))) = empty_set )
| ( apply(relation_dom(sK0),sK12(sK1,relation_dom(sK0),apply(sK0,sK17(relation_dom(sK2))),X0)) = X0 )
| ~ function(relation_dom(sK0))
| ~ relation(relation_dom(sK0))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_4110,c_7544]) ).
tcf(c_11183,plain,
! [X0: $i] :
( ( relation_dom(sK2) = sK2 )
| ( apply(sK2,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0)) = empty_set )
| ( apply(relation_dom(sK0),sK12(sK1,relation_dom(sK0),apply(sK0,sK17(relation_dom(sK2))),X0)) = X0 )
| ~ function(relation_dom(sK0))
| ~ relation(relation_dom(sK0))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_3449,c_7544]) ).
tcf(c_11184,plain,
! [X0: $i] :
( ( relation_dom(sK2) = sK2 )
| ( apply(X0,sK12(sK1,X0,apply(sK0,sK17(relation_dom(sK2))),sK5(X0,apply(sK2,sK17(relation_dom(sK2)))))) = sK5(X0,apply(sK2,sK17(relation_dom(sK2)))) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(apply(sK2,sK17(relation_dom(sK2))),relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_71,c_7544]) ).
tcf(c_11185,plain,
! [X0: $i] :
( ( relation_dom(sK2) = sK2 )
| ( apply(X0,sK12(sK1,X0,apply(sK0,sK17(relation_dom(sK2))),apply(X0,apply(sK2,sK17(relation_dom(sK2)))))) = apply(X0,apply(sK2,sK17(relation_dom(sK2)))) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(apply(sK2,sK17(relation_dom(sK2))),relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_73,c_7544]) ).
tcf(c_11186,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK2) = sK2 )
| ( apply(X0,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X1)) = empty_set )
| ( apply(relation_dom(X0),sK12(sK1,relation_dom(X0),apply(sK0,sK17(relation_dom(sK2))),X1)) = X1 )
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom(X0))
| ~ relation(relation_dom(X0))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_75,c_7544]) ).
tcf(c_11187,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(sK2) = sK2 )
| ( apply(X1,sK12(sK1,X1,apply(sK0,sK17(relation_dom(sK2))),sK12(X1,X2,apply(sK2,sK17(relation_dom(sK2))),X0))) = sK12(X1,X2,apply(sK2,sK17(relation_dom(sK2))),X0) )
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),relation_composition(X1,X2)) ),
inference(superposition,[status(thm)],[c_301,c_7544]) ).
tcf(c_11188,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK2) = sK2 )
| ( apply(relation_dom(sK0),sK12(sK1,relation_dom(sK0),apply(sK0,sK17(relation_dom(sK2))),sK12(relation_dom(sK2),X1,apply(sK2,sK17(relation_dom(sK2))),X0))) = sK12(relation_dom(sK2),X1,apply(sK2,sK17(relation_dom(sK2))),X0) )
| ~ relation(X1)
| ~ function(relation_dom(sK0))
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),relation_composition(relation_dom(sK2),X1)) ),
inference(superposition,[status(thm)],[c_2283,c_7544]) ).
tcf(c_11189,plain,
( ( relation_dom(sK2) = sK2 )
| ( apply(relation_dom(sK0),sK12(sK1,relation_dom(sK0),apply(sK0,sK17(relation_dom(sK2))),sK5(relation_dom(sK2),apply(sK2,sK17(relation_dom(sK2)))))) = sK5(relation_dom(sK2),apply(sK2,sK17(relation_dom(sK2)))) )
| ~ function(relation_dom(sK0))
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(apply(sK2,sK17(relation_dom(sK2))),relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_3019,c_7544]) ).
tcf(c_11190,plain,
( ( relation_dom(sK2) = sK2 )
| ( apply(relation_dom(sK0),sK12(sK1,relation_dom(sK0),apply(sK0,sK17(relation_dom(sK2))),apply(relation_dom(sK2),apply(sK2,sK17(relation_dom(sK2)))))) = apply(relation_dom(sK2),apply(sK2,sK17(relation_dom(sK2)))) )
| ~ function(relation_dom(sK0))
| ~ function(relation_dom(sK2))
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(apply(sK2,sK17(relation_dom(sK2))),relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_3551,c_7544]) ).
tcf(c_11291,plain,
( in(ordered_pair(apply(sK0,sK17(relation_dom(sK2))),apply(sK2,sK17(relation_dom(sK2)))),sK1)
| ( sK17(powerset(sK2)) = empty_set )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_7740,c_73]) ).
tcf(c_11292,plain,
( in(ordered_pair(apply(sK0,sK17(relation_dom(sK2))),apply(sK2,sK17(relation_dom(sK2)))),sK1)
| ( sK17(powerset(sK2)) = empty_set )
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11291,c_57,c_56]) ).
tcf(c_11302,plain,
! [X0: $i] :
( ( relation_dom(X0) = relation_dom(sK2) )
| ~ empty(sK1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_65,c_2636]) ).
tcf(c_11303,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(X1,X0) = relation_dom(sK2) )
| ~ empty(sK1)
| ~ empty(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_86,c_2636]) ).
tcf(c_11304,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(X0,X1) = relation_dom(sK2) )
| ~ empty(sK1)
| ~ empty(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_88,c_2636]) ).
tcf(c_11310,plain,
( ( relation_dom(relation_dom(sK2)) = relation_dom(sK2) )
| ~ empty(sK1)
| ~ empty(relation_dom(sK0)) ),
inference(superposition,[status(thm)],[c_3251,c_2636]) ).
tcf(c_11311,plain,
! [X0: $i] :
( ( sK17(powerset(X0)) = relation_dom(sK2) )
| ~ empty(sK1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6912,c_2636]) ).
tcf(c_11356,plain,
! [X0: $i] :
( ( relation_dom(X0) = relation_dom(sK2) )
| ~ empty(sK0)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_65,c_2667]) ).
tcf(c_11357,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(X1,X0) = relation_dom(sK2) )
| ~ empty(sK0)
| ~ empty(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_86,c_2667]) ).
tcf(c_11358,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(X0,X1) = relation_dom(sK2) )
| ~ empty(sK0)
| ~ empty(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_88,c_2667]) ).
tcf(c_11364,plain,
( ( relation_dom(relation_dom(sK2)) = relation_dom(sK2) )
| ~ empty(sK0)
| ~ empty(relation_dom(sK0)) ),
inference(superposition,[status(thm)],[c_3251,c_2667]) ).
tcf(c_11365,plain,
! [X0: $i] :
( ( sK17(powerset(X0)) = relation_dom(sK2) )
| ~ empty(sK0)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6912,c_2667]) ).
tcf(c_11389,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ in(X0,relation_dom(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3022,c_85]) ).
tcf(c_11396,plain,
! [X0: $i] :
( ( apply(sK0,X0) = empty_set )
| ( apply(sK1,apply(sK0,X0)) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_4011,c_11389]) ).
tcf(c_11397,plain,
! [X0: $i] :
( ( apply(sK0,X0) = empty_set )
| ( apply(sK1,apply(sK0,X0)) = empty_set )
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_4110,c_11389]) ).
tcf(c_11400,plain,
! [X0: $i] :
( ~ empty(sK1)
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_52,c_11389]) ).
tcf(c_11401,plain,
! [X0: $i,X1: $i] :
( in(sK3(relation_dom(X0),X1),X1)
| ( relation_dom(relation_dom(X0)) = X1 )
| ~ empty(X0)
| ~ relation(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_69,c_11389]) ).
tcf(c_11402,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ relation(relation_dom(X1))
| ~ in(X0,relation_dom(relation_dom(X1))) ),
inference(superposition,[status(thm)],[c_71,c_11389]) ).
tcf(c_11403,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ function(relation_dom(X1))
| ~ relation(relation_dom(X1))
| ~ in(X0,relation_dom(relation_dom(X1))) ),
inference(superposition,[status(thm)],[c_73,c_11389]) ).
tcf(c_11404,plain,
! [X0: $i,X1: $i] :
( ( apply(X0,X1) = empty_set )
| ~ empty(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_75,c_11389]) ).
tcf(c_11405,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(ordered_pair(sK11(X1,X2,relation_dom(X0)),sK10(X1,X2,relation_dom(X0))),X2)
| ( relation_composition(X1,X2) = relation_dom(X0) )
| ~ empty(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_93,c_11389]) ).
tcf(c_11406,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(ordered_pair(sK9(X1,X2,relation_dom(X0)),sK11(X1,X2,relation_dom(X0))),X1)
| ( relation_composition(X1,X2) = relation_dom(X0) )
| ~ empty(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_92,c_11389]) ).
tcf(c_11407,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(ordered_pair(sK9(relation_dom(X0),X1,X2),sK10(relation_dom(X0),X1,X2)),X2)
| ( relation_composition(relation_dom(X0),X1) = X2 )
| ~ empty(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_92,c_11389]) ).
tcf(c_11408,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(ordered_pair(sK9(X1,relation_dom(X0),X2),sK10(X1,relation_dom(X0),X2)),X2)
| ( relation_composition(X1,relation_dom(X0)) = X2 )
| ~ empty(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_93,c_11389]) ).
tcf(c_11409,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ empty(X2)
| ~ relation(X3)
| ~ relation(relation_dom(X2))
| ~ in(ordered_pair(X0,X1),relation_composition(relation_dom(X2),X3)) ),
inference(superposition,[status(thm)],[c_301,c_11389]) ).
tcf(c_11410,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ empty(X3)
| ~ relation(X2)
| ~ relation(relation_dom(X3))
| ~ in(ordered_pair(X0,X1),relation_composition(X2,relation_dom(X3))) ),
inference(superposition,[status(thm)],[c_300,c_11389]) ).
tcf(c_11411,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(sK0)
| ~ relation(X2)
| ~ relation(relation_dom(sK2))
| ~ in(ordered_pair(X0,X1),relation_composition(X2,relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_2065,c_11389]) ).
tcf(c_11412,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(sK0)
| ~ relation(X2)
| ~ relation(relation_dom(sK2))
| ~ in(ordered_pair(X0,X1),relation_composition(relation_dom(sK2),X2)) ),
inference(superposition,[status(thm)],[c_2283,c_11389]) ).
tcf(c_11415,plain,
! [X0: $i] :
( ~ empty(sK0)
| ~ relation(relation_dom(sK2))
| ~ in(X0,relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_3019,c_11389]) ).
tcf(c_11416,plain,
! [X0: $i] :
( ~ empty(sK0)
| ~ function(relation_dom(sK2))
| ~ relation(relation_dom(sK2))
| ~ in(X0,relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_3551,c_11389]) ).
tcf(c_11417,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK2)) = relation_dom(X0) )
| ( apply(sK1,apply(sK0,ordered_pair(sK3(relation_dom(sK2),relation_dom(X0)),sK4(relation_dom(sK2),relation_dom(X0))))) = apply(sK2,ordered_pair(sK3(relation_dom(sK2),relation_dom(X0)),sK4(relation_dom(sK2),relation_dom(X0)))) )
| ~ empty(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4463,c_11389]) ).
tcf(c_11418,plain,
! [X0: $i] :
( in(sK3(relation_dom(sK2),X0),X0)
| ( relation_dom(relation_dom(sK2)) = X0 )
| ~ empty(sK0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4464,c_11389]) ).
tcf(c_11420,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK9(relation_dom(sK2),X1,relation_dom(X0)),sK11(relation_dom(sK2),X1,relation_dom(X0))),relation_dom(sK0))
| ( relation_composition(relation_dom(sK2),X1) = relation_dom(X0) )
| ~ empty(X0)
| ~ relation(X1)
| ~ relation(relation_dom(sK2))
| ~ relation(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_4703,c_11389]) ).
tcf(c_11421,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK9(relation_dom(sK2),X0,X1),sK10(relation_dom(sK2),X0,X1)),X1)
| ( relation_composition(relation_dom(sK2),X0) = X1 )
| ~ empty(sK0)
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4703,c_11389]) ).
tcf(c_11422,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK9(relation_dom(X0),X1,relation_dom(sK2)),sK10(relation_dom(X0),X1,relation_dom(sK2))),relation_dom(sK0))
| ( relation_composition(relation_dom(X0),X1) = relation_dom(sK2) )
| ~ empty(X0)
| ~ relation(X1)
| ~ relation(relation_dom(sK2))
| ~ relation(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_4725,c_11389]) ).
tcf(c_11423,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK11(X0,X1,relation_dom(sK2)),sK10(X0,X1,relation_dom(sK2))),X1)
| ( relation_composition(X0,X1) = relation_dom(sK2) )
| ~ empty(sK0)
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5279,c_11389]) ).
tcf(c_11424,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK9(X0,X1,relation_dom(sK2)),sK11(X0,X1,relation_dom(sK2))),X0)
| ( relation_composition(X0,X1) = relation_dom(sK2) )
| ~ empty(sK0)
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4725,c_11389]) ).
tcf(c_11425,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK11(X1,relation_dom(sK2),relation_dom(X0)),sK10(X1,relation_dom(sK2),relation_dom(X0))),relation_dom(sK0))
| ( relation_composition(X1,relation_dom(sK2)) = relation_dom(X0) )
| ~ empty(X0)
| ~ relation(X1)
| ~ relation(relation_dom(sK2))
| ~ relation(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_5257,c_11389]) ).
tcf(c_11426,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK9(X0,relation_dom(sK2),X1),sK10(X0,relation_dom(sK2),X1)),X1)
| ( relation_composition(X0,relation_dom(sK2)) = X1 )
| ~ empty(sK0)
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5257,c_11389]) ).
tcf(c_11427,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK9(X1,relation_dom(X0),relation_dom(sK2)),sK10(X1,relation_dom(X0),relation_dom(sK2))),relation_dom(sK0))
| ( relation_composition(X1,relation_dom(X0)) = relation_dom(sK2) )
| ~ empty(X0)
| ~ relation(X1)
| ~ relation(relation_dom(sK2))
| ~ relation(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_5279,c_11389]) ).
tcf(c_11774,plain,
! [X0: $i] :
( in(sK3(relation_dom(sK2),X0),X0)
| ( relation_dom(relation_dom(sK2)) = X0 )
| ~ empty(sK1)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_69,c_11400]) ).
tcf(c_11775,plain,
! [X0: $i] :
( ~ empty(sK1)
| ~ relation(relation_dom(sK2))
| ~ in(X0,relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_71,c_11400]) ).
tcf(c_11776,plain,
! [X0: $i] :
( ~ empty(sK1)
| ~ function(relation_dom(sK2))
| ~ relation(relation_dom(sK2))
| ~ in(X0,relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_73,c_11400]) ).
tcf(c_11778,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK11(X0,X1,relation_dom(sK2)),sK10(X0,X1,relation_dom(sK2))),X1)
| ( relation_composition(X0,X1) = relation_dom(sK2) )
| ~ empty(sK1)
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_93,c_11400]) ).
tcf(c_11779,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK9(X0,X1,relation_dom(sK2)),sK11(X0,X1,relation_dom(sK2))),X0)
| ( relation_composition(X0,X1) = relation_dom(sK2) )
| ~ empty(sK1)
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_92,c_11400]) ).
tcf(c_11780,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK9(relation_dom(sK2),X0,X1),sK10(relation_dom(sK2),X0,X1)),X1)
| ( relation_composition(relation_dom(sK2),X0) = X1 )
| ~ empty(sK1)
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_92,c_11400]) ).
tcf(c_11781,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK9(X0,relation_dom(sK2),X1),sK10(X0,relation_dom(sK2),X1)),X1)
| ( relation_composition(X0,relation_dom(sK2)) = X1 )
| ~ empty(sK1)
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_93,c_11400]) ).
tcf(c_11782,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(sK1)
| ~ relation(X2)
| ~ relation(relation_dom(sK2))
| ~ in(ordered_pair(X0,X1),relation_composition(relation_dom(sK2),X2)) ),
inference(superposition,[status(thm)],[c_301,c_11400]) ).
tcf(c_11783,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(sK1)
| ~ relation(X2)
| ~ relation(relation_dom(sK2))
| ~ in(ordered_pair(X0,X1),relation_composition(X2,relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_300,c_11400]) ).
tcf(c_11785,plain,
( ( relation_dom(relation_dom(sK2)) = relation_dom(sK2) )
| ( apply(sK1,apply(sK0,ordered_pair(sK3(relation_dom(sK2),relation_dom(sK2)),sK4(relation_dom(sK2),relation_dom(sK2))))) = apply(sK2,ordered_pair(sK3(relation_dom(sK2),relation_dom(sK2)),sK4(relation_dom(sK2),relation_dom(sK2)))) )
| ~ empty(sK1)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4463,c_11400]) ).
tcf(c_11787,plain,
! [X0: $i] :
( in(ordered_pair(sK9(relation_dom(sK2),X0,relation_dom(sK2)),sK11(relation_dom(sK2),X0,relation_dom(sK2))),relation_dom(sK0))
| ( relation_composition(relation_dom(sK2),X0) = relation_dom(sK2) )
| ~ empty(sK1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4703,c_11400]) ).
tcf(c_11788,plain,
! [X0: $i] :
( in(ordered_pair(sK9(relation_dom(sK2),X0,relation_dom(sK2)),sK10(relation_dom(sK2),X0,relation_dom(sK2))),relation_dom(sK0))
| ( relation_composition(relation_dom(sK2),X0) = relation_dom(sK2) )
| ~ empty(sK1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4725,c_11400]) ).
tcf(c_11789,plain,
! [X0: $i] :
( in(ordered_pair(sK11(X0,relation_dom(sK2),relation_dom(sK2)),sK10(X0,relation_dom(sK2),relation_dom(sK2))),relation_dom(sK0))
| ( relation_composition(X0,relation_dom(sK2)) = relation_dom(sK2) )
| ~ empty(sK1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5257,c_11400]) ).
tcf(c_11790,plain,
! [X0: $i] :
( in(ordered_pair(sK9(X0,relation_dom(sK2),relation_dom(sK2)),sK10(X0,relation_dom(sK2),relation_dom(sK2))),relation_dom(sK0))
| ( relation_composition(X0,relation_dom(sK2)) = relation_dom(sK2) )
| ~ empty(sK1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5279,c_11400]) ).
tcf(c_11924,plain,
! [X0: $i] :
( empty(X0)
| element(sK17(sK16(X0)),X0) ),
inference(global_subsumption_just,[status(thm)],[c_8350,c_104,c_8350]) ).
tcf(c_11931,plain,
! [X0: $i] :
( empty(X0)
| in(sK17(sK16(X0)),X0) ),
inference(superposition,[status(thm)],[c_11924,c_62]) ).
tcf(c_11932,plain,
! [X0: $i,X1: $i] :
( empty(powerset(X1))
| element(X0,X1)
| ~ in(X0,sK17(sK16(powerset(X1)))) ),
inference(superposition,[status(thm)],[c_11924,c_100]) ).
tcf(c_11933,plain,
! [X0: $i,X1: $i] :
( empty(powerset(X1))
| ~ empty(X1)
| ~ in(X0,sK17(sK16(powerset(X1)))) ),
inference(superposition,[status(thm)],[c_11924,c_99]) ).
tcf(c_11936,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ in(X0,sK17(sK16(powerset(X1)))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11933,c_111]) ).
tcf(c_11939,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| ~ in(X0,sK17(sK16(powerset(X1)))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11932,c_111]) ).
tcf(c_11951,plain,
( empty(relation_dom(sK2))
| ( apply(sK1,apply(sK0,sK17(sK16(relation_dom(sK2))))) = apply(sK2,sK17(sK16(relation_dom(sK2)))) ) ),
inference(superposition,[status(thm)],[c_11931,c_53]) ).
tcf(c_11952,plain,
( empty(relation_dom(sK2))
| in(sK17(sK16(relation_dom(sK2))),relation_dom(sK0)) ),
inference(superposition,[status(thm)],[c_11931,c_51]) ).
tcf(c_11953,plain,
( empty(relation_dom(sK0))
| in(sK17(sK16(relation_dom(sK0))),relation_dom(sK2))
| ( apply(sK1,apply(sK0,sK17(sK16(relation_dom(sK0))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11931,c_3475]) ).
tcf(c_11954,plain,
! [X0: $i] :
( empty(X0)
| ~ in(X0,sK17(sK16(X0))) ),
inference(superposition,[status(thm)],[c_11931,c_64]) ).
tcf(c_11959,plain,
! [X0: $i] :
( empty(X0)
| empty(sK16(X0))
| element(sK17(sK16(sK16(X0))),X0) ),
inference(superposition,[status(thm)],[c_11931,c_2939]) ).
tcf(c_11960,plain,
! [X0: $i] :
( empty(sK17(powerset(X0)))
| element(sK17(sK16(sK17(powerset(X0)))),X0) ),
inference(superposition,[status(thm)],[c_11931,c_2940]) ).
tcf(c_11962,plain,
( empty(relation_dom(relation_dom(sK2)))
| ( apply(sK1,apply(sK0,ordered_pair(sK17(sK16(relation_dom(relation_dom(sK2)))),apply(relation_dom(sK2),sK17(sK16(relation_dom(relation_dom(sK2)))))))) = apply(sK2,ordered_pair(sK17(sK16(relation_dom(relation_dom(sK2)))),apply(relation_dom(sK2),sK17(sK16(relation_dom(relation_dom(sK2))))))) )
| ~ function(relation_dom(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_11931,c_3550]) ).
tcf(c_11963,plain,
( empty(relation_dom(relation_dom(sK2)))
| in(sK17(sK16(relation_dom(relation_dom(sK2)))),relation_dom(relation_dom(sK0)))
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_11931,c_3134]) ).
tcf(c_11966,plain,
( empty(relation_dom(relation_dom(sK2)))
| ( apply(sK1,apply(sK0,ordered_pair(sK17(sK16(relation_dom(relation_dom(sK2)))),sK5(relation_dom(sK2),sK17(sK16(relation_dom(relation_dom(sK2)))))))) = apply(sK2,ordered_pair(sK17(sK16(relation_dom(relation_dom(sK2)))),sK5(relation_dom(sK2),sK17(sK16(relation_dom(relation_dom(sK2))))))) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_11931,c_3018]) ).
tcf(c_12003,plain,
( empty(relation_dom(sK2))
| in(sK17(sK16(relation_dom(sK2))),relation_dom(sK2))
| ( apply(sK1,apply(sK0,sK17(sK16(relation_dom(sK2))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_11952,c_3475]) ).
tcf(c_12004,plain,
( empty(relation_dom(sK2))
| ~ in(relation_dom(sK0),sK17(sK16(relation_dom(sK2)))) ),
inference(superposition,[status(thm)],[c_11952,c_64]) ).
tcf(c_12005,plain,
( empty(relation_dom(sK2))
| element(sK17(sK16(relation_dom(sK2))),relation_dom(sK0)) ),
inference(superposition,[status(thm)],[c_11952,c_63]) ).
tcf(c_12021,plain,
( ( relation_dom(sK17(powerset(relation_dom(sK2)))) = empty_set )
| ( apply(sK1,apply(sK0,sK17(sK16(relation_dom(sK2))))) = apply(sK2,sK17(sK16(relation_dom(sK2)))) ) ),
inference(superposition,[status(thm)],[c_11951,c_7171]) ).
tcf(c_12022,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK2)) = X0 )
| ( apply(sK1,apply(sK0,sK17(sK16(relation_dom(sK2))))) = apply(sK2,sK17(sK16(relation_dom(sK2)))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11951,c_2387]) ).
tcf(c_12023,plain,
( ( sK17(powerset(relation_dom(relation_dom(sK2)))) = empty_set )
| ( apply(sK1,apply(sK0,sK17(sK16(relation_dom(sK2))))) = apply(sK2,sK17(sK16(relation_dom(sK2)))) ) ),
inference(superposition,[status(thm)],[c_11951,c_7733]) ).
tcf(c_12024,plain,
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK2)))) = empty_set )
| ( apply(sK1,apply(sK0,sK17(sK16(relation_dom(sK2))))) = apply(sK2,sK17(sK16(relation_dom(sK2)))) ) ),
inference(superposition,[status(thm)],[c_11951,c_7227]) ).
tcf(c_12025,plain,
( ( sK17(powerset(relation_dom(sK2))) = empty_set )
| ( apply(sK1,apply(sK0,sK17(sK16(relation_dom(sK2))))) = apply(sK2,sK17(sK16(relation_dom(sK2)))) ) ),
inference(superposition,[status(thm)],[c_11951,c_7088]) ).
tcf(c_12026,plain,
( ( relation_dom(relation_dom(relation_dom(sK2))) = empty_set )
| ( apply(sK1,apply(sK0,sK17(sK16(relation_dom(sK2))))) = apply(sK2,sK17(sK16(relation_dom(sK2)))) ) ),
inference(superposition,[status(thm)],[c_11951,c_6244]) ).
tcf(c_12027,plain,
( ( relation_dom(relation_dom(sK2)) = empty_set )
| ( apply(sK1,apply(sK0,sK17(sK16(relation_dom(sK2))))) = apply(sK2,sK17(sK16(relation_dom(sK2)))) ) ),
inference(superposition,[status(thm)],[c_11951,c_2124]) ).
tcf(c_12030,plain,
! [X0: $i] :
( ( relation_dom(sK2) = X0 )
| ( apply(sK1,apply(sK0,sK17(sK16(relation_dom(sK2))))) = apply(sK2,sK17(sK16(relation_dom(sK2)))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11951,c_60]) ).
tcf(c_12031,plain,
( ( relation_dom(sK2) = empty_set )
| ( apply(sK1,apply(sK0,sK17(sK16(relation_dom(sK2))))) = apply(sK2,sK17(sK16(relation_dom(sK2)))) ) ),
inference(superposition,[status(thm)],[c_11951,c_107]) ).
tcf(c_12032,plain,
( relation(relation_dom(sK2))
| ( apply(sK1,apply(sK0,sK17(sK16(relation_dom(sK2))))) = apply(sK2,sK17(sK16(relation_dom(sK2)))) ) ),
inference(superposition,[status(thm)],[c_11951,c_85]) ).
tcf(c_12033,plain,
( function(relation_dom(sK2))
| ( apply(sK1,apply(sK0,sK17(sK16(relation_dom(sK2))))) = apply(sK2,sK17(sK16(relation_dom(sK2)))) ) ),
inference(superposition,[status(thm)],[c_11951,c_80]) ).
tcf(c_12034,plain,
( empty(sK2)
| ( apply(sK1,apply(sK0,sK17(sK16(relation_dom(sK2))))) = apply(sK2,sK17(sK16(relation_dom(sK2)))) )
| ~ relation(sK2) ),
inference(superposition,[status(thm)],[c_11951,c_67]) ).
tcf(c_12039,plain,
( empty(sK2)
| ( apply(sK1,apply(sK0,sK17(sK16(relation_dom(sK2))))) = apply(sK2,sK17(sK16(relation_dom(sK2)))) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12034,c_54]) ).
tcf(c_12066,plain,
( ( relation_dom(sK2) = sK2 )
| ( apply(sK1,apply(sK0,sK17(sK16(relation_dom(sK2))))) = apply(sK2,sK17(sK16(relation_dom(sK2)))) )
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_12039,c_2667]) ).
tcf(c_12067,plain,
( ( relation_dom(sK2) = sK2 )
| ( apply(sK1,apply(sK0,sK17(sK16(relation_dom(sK2))))) = apply(sK2,sK17(sK16(relation_dom(sK2)))) )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_12039,c_2636]) ).
tcf(c_12068,plain,
( ( relation_dom(sK17(powerset(sK2))) = empty_set )
| ( apply(sK1,apply(sK0,sK17(sK16(relation_dom(sK2))))) = apply(sK2,sK17(sK16(relation_dom(sK2)))) ) ),
inference(superposition,[status(thm)],[c_12039,c_7171]) ).
tcf(c_12072,plain,
( ( sK17(powerset(sK2)) = empty_set )
| ( apply(sK1,apply(sK0,sK17(sK16(relation_dom(sK2))))) = apply(sK2,sK17(sK16(relation_dom(sK2)))) ) ),
inference(superposition,[status(thm)],[c_12039,c_7088]) ).
tcf(c_12077,plain,
! [X0: $i] :
( ( X0 = sK2 )
| ( apply(sK1,apply(sK0,sK17(sK16(relation_dom(sK2))))) = apply(sK2,sK17(sK16(relation_dom(sK2)))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12039,c_60]) ).
tcf(c_12078,plain,
( ( sK2 = empty_set )
| ( apply(sK1,apply(sK0,sK17(sK16(relation_dom(sK2))))) = apply(sK2,sK17(sK16(relation_dom(sK2)))) ) ),
inference(superposition,[status(thm)],[c_12039,c_107]) ).
tcf(c_12103,plain,
( ( sK17(powerset(sK2)) = empty_set )
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(sK1,ordered_pair(apply(sK0,sK17(relation_dom(sK2))),apply(sK2,sK17(relation_dom(sK2))))) ),
inference(superposition,[status(thm)],[c_11292,c_64]) ).
tcf(c_12104,plain,
( element(ordered_pair(apply(sK0,sK17(relation_dom(sK2))),apply(sK2,sK17(relation_dom(sK2)))),sK1)
| ( sK17(powerset(sK2)) = empty_set )
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_11292,c_63]) ).
tcf(c_12105,plain,
( ( sK17(powerset(sK2)) = empty_set )
| ~ empty(sK1)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_11292,c_61]) ).
tcf(c_12107,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(apply(sK0,sK17(relation_dom(sK2))),X0),relation_composition(sK1,X1))
| ( sK17(powerset(sK2)) = empty_set )
| ~ relation(sK1)
| ~ relation(X1)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),X1) ),
inference(superposition,[status(thm)],[c_11292,c_299]) ).
tcf(c_12118,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(apply(sK0,sK17(relation_dom(sK2))),X0),relation_composition(sK1,X1))
| ( sK17(powerset(sK2)) = empty_set )
| ~ relation(X1)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12107,c_56]) ).
tcf(c_12135,plain,
! [X0: $i,X1: $i] :
( ( sK17(powerset(sK2)) = empty_set )
| ~ relation(X0)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X1),X0)
| ~ in(relation_composition(sK1,X0),ordered_pair(apply(sK0,sK17(relation_dom(sK2))),X1)) ),
inference(superposition,[status(thm)],[c_12118,c_64]) ).
tcf(c_12136,plain,
! [X0: $i,X1: $i] :
( element(ordered_pair(apply(sK0,sK17(relation_dom(sK2))),X0),relation_composition(sK1,X1))
| ( sK17(powerset(sK2)) = empty_set )
| ~ relation(X1)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),X1) ),
inference(superposition,[status(thm)],[c_12118,c_63]) ).
tcf(c_12137,plain,
! [X0: $i,X1: $i] :
( ( sK17(powerset(sK2)) = empty_set )
| ~ relation(X1)
| ~ empty(relation_composition(sK1,X1))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),X1) ),
inference(superposition,[status(thm)],[c_12118,c_61]) ).
tcf(c_12138,plain,
! [X0: $i,X1: $i] :
( in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(relation_composition(sK1,X1)))
| ( sK17(powerset(sK2)) = empty_set )
| ~ relation(X1)
| ~ relation(relation_composition(sK1,X1))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),X1) ),
inference(superposition,[status(thm)],[c_12118,c_70]) ).
tcf(c_12139,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(ordered_pair(apply(sK0,sK17(relation_dom(sK2))),X2),relation_composition(relation_composition(sK1,X1),X3))
| ( sK17(powerset(sK2)) = empty_set )
| ~ relation(X3)
| ~ relation(X1)
| ~ relation(relation_composition(sK1,X1))
| ~ in(ordered_pair(X0,X2),X3)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),X1) ),
inference(superposition,[status(thm)],[c_12118,c_299]) ).
tcf(c_12140,plain,
! [X0: $i,X1: $i] :
( ( sK17(powerset(sK2)) = empty_set )
| ( apply(relation_composition(sK1,X1),apply(sK0,sK17(relation_dom(sK2)))) = X0 )
| ~ relation(X1)
| ~ function(relation_composition(sK1,X1))
| ~ relation(relation_composition(sK1,X1))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),X1) ),
inference(superposition,[status(thm)],[c_12118,c_152]) ).
tcf(c_12141,plain,
! [X0: $i,X1: $i] :
( ( sK17(powerset(sK2)) = empty_set )
| ( apply(X1,sK12(sK1,X1,apply(sK0,sK17(relation_dom(sK2))),X0)) = X0 )
| ~ relation(sK1)
| ~ function(X1)
| ~ relation(X1)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),X1) ),
inference(superposition,[status(thm)],[c_12118,c_2068]) ).
tcf(c_12142,plain,
! [X0: $i] :
( ( sK17(powerset(sK2)) = empty_set )
| ~ relation(sK1)
| ~ empty(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_12118,c_2176]) ).
tcf(c_12143,plain,
! [X0: $i] :
( ( sK17(powerset(sK2)) = empty_set )
| ~ relation(sK1)
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_12118,c_2063]) ).
tcf(c_12144,plain,
! [X0: $i] :
( ( sK17(powerset(sK2)) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,sK17(relation_dom(sK2))),X0),X0))) = apply(sK2,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,sK17(relation_dom(sK2))),X0),X0)) )
| ~ relation(sK1)
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_12118,c_2064]) ).
tcf(c_12150,plain,
! [X0: $i] :
( ( sK17(powerset(sK2)) = empty_set )
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12143,c_56]) ).
tcf(c_12156,plain,
! [X0: $i] :
( ( sK17(powerset(sK2)) = empty_set )
| ~ empty(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12142,c_56]) ).
tcf(c_12178,plain,
! [X0: $i,X1: $i] :
( ( sK17(powerset(sK2)) = empty_set )
| ( apply(X1,sK12(sK1,X1,apply(sK0,sK17(relation_dom(sK2))),X0)) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12141,c_56]) ).
tcf(c_12200,plain,
! [X0: $i] :
( ( sK17(powerset(sK2)) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,sK17(relation_dom(sK2))),X0),X0))) = apply(sK2,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,sK17(relation_dom(sK2))),X0),X0)) )
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12144,c_56]) ).
tcf(c_12233,plain,
! [X0: $i] :
( ( sK17(powerset(sK2)) = empty_set )
| ~ empty(relation_dom(sK0))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1)) ),
inference(global_subsumption_just,[status(thm)],[c_12156,c_58,c_126,c_2669,c_12156]) ).
tcf(c_12234,plain,
! [X0: $i] :
( ( sK17(powerset(sK2)) = empty_set )
| ~ empty(relation_dom(sK0))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),relation_dom(sK2)) ),
inference(renaming,[status(thm)],[c_12233]) ).
tcf(c_12244,plain,
! [X0: $i] :
( ( sK17(powerset(sK2)) = empty_set )
| ( apply(sK0,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0)) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0))) = empty_set )
| ~ empty(relation_dom(sK0))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_4011,c_12234]) ).
tcf(c_12245,plain,
( ( sK17(powerset(sK2)) = empty_set )
| ~ empty(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(apply(sK2,sK17(relation_dom(sK2))),relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_71,c_12234]) ).
tcf(c_12246,plain,
( ( sK17(powerset(sK2)) = empty_set )
| ~ empty(relation_dom(sK0))
| ~ function(relation_dom(sK2))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(apply(sK2,sK17(relation_dom(sK2))),relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_73,c_12234]) ).
tcf(c_12247,plain,
! [X0: $i] :
( ( sK17(powerset(sK2)) = empty_set )
| ( apply(sK2,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0)) = empty_set )
| ~ function(sK2)
| ~ relation(sK2)
| ~ empty(relation_dom(sK0))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_75,c_12234]) ).
tcf(c_12248,plain,
! [X0: $i,X1: $i] :
( ( sK17(powerset(sK2)) = empty_set )
| ~ relation(X1)
| ~ empty(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),relation_composition(relation_dom(sK2),X1)) ),
inference(superposition,[status(thm)],[c_301,c_12234]) ).
tcf(c_12254,plain,
! [X0: $i] :
( ( sK17(powerset(sK2)) = empty_set )
| ( apply(sK2,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0)) = empty_set )
| ~ empty(relation_dom(sK0))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12247,c_55,c_54]) ).
tcf(c_12283,plain,
( in(ordered_pair(apply(sK0,sK17(relation_dom(sK2))),apply(sK2,sK17(relation_dom(sK2)))),sK1)
| ( relation_dom(relation_dom(relation_dom(relation_dom(sK2)))) = empty_set )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_9799,c_73]) ).
tcf(c_12284,plain,
( in(ordered_pair(apply(sK0,sK17(relation_dom(sK2))),apply(sK2,sK17(relation_dom(sK2)))),sK1)
| ( relation_dom(relation_dom(relation_dom(relation_dom(sK2)))) = empty_set )
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12283,c_57,c_56]) ).
tcf(c_12292,plain,
! [X0: $i,X1: $i] :
( in(sK3(sK17(sK16(powerset(X0))),X1),X1)
| ( relation_dom(sK17(sK16(powerset(X0)))) = X1 )
| ~ empty(X0)
| ~ relation(sK17(sK16(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_69,c_11936]) ).
tcf(c_12293,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ relation(sK17(sK16(powerset(X1))))
| ~ in(X0,relation_dom(sK17(sK16(powerset(X1))))) ),
inference(superposition,[status(thm)],[c_71,c_11936]) ).
tcf(c_12294,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ function(sK17(sK16(powerset(X1))))
| ~ relation(sK17(sK16(powerset(X1))))
| ~ in(X0,relation_dom(sK17(sK16(powerset(X1))))) ),
inference(superposition,[status(thm)],[c_73,c_11936]) ).
tcf(c_12295,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(ordered_pair(sK11(X1,X2,sK17(sK16(powerset(X0)))),sK10(X1,X2,sK17(sK16(powerset(X0))))),X2)
| ( sK17(sK16(powerset(X0))) = relation_composition(X1,X2) )
| ~ empty(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(sK17(sK16(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_93,c_11936]) ).
tcf(c_12296,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(ordered_pair(sK9(X1,X2,sK17(sK16(powerset(X0)))),sK11(X1,X2,sK17(sK16(powerset(X0))))),X1)
| ( sK17(sK16(powerset(X0))) = relation_composition(X1,X2) )
| ~ empty(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(sK17(sK16(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_92,c_11936]) ).
tcf(c_12297,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(ordered_pair(sK9(sK17(sK16(powerset(X0))),X1,X2),sK10(sK17(sK16(powerset(X0))),X1,X2)),X2)
| ( relation_composition(sK17(sK16(powerset(X0))),X1) = X2 )
| ~ empty(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(sK17(sK16(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_92,c_11936]) ).
tcf(c_12298,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(ordered_pair(sK9(X1,sK17(sK16(powerset(X0))),X2),sK10(X1,sK17(sK16(powerset(X0))),X2)),X2)
| ( relation_composition(X1,sK17(sK16(powerset(X0)))) = X2 )
| ~ empty(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(sK17(sK16(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_93,c_11936]) ).
tcf(c_12299,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ empty(X2)
| ~ relation(X3)
| ~ relation(sK17(sK16(powerset(X2))))
| ~ in(ordered_pair(X0,X1),relation_composition(sK17(sK16(powerset(X2))),X3)) ),
inference(superposition,[status(thm)],[c_301,c_11936]) ).
tcf(c_12300,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ empty(X3)
| ~ relation(X2)
| ~ relation(sK17(sK16(powerset(X3))))
| ~ in(ordered_pair(X0,X1),relation_composition(X2,sK17(sK16(powerset(X3))))) ),
inference(superposition,[status(thm)],[c_300,c_11936]) ).
tcf(c_12302,plain,
! [X0: $i] :
( ( sK17(sK16(powerset(X0))) = relation_dom(relation_dom(sK2)) )
| ( apply(sK1,apply(sK0,ordered_pair(sK3(relation_dom(sK2),sK17(sK16(powerset(X0)))),sK4(relation_dom(sK2),sK17(sK16(powerset(X0))))))) = apply(sK2,ordered_pair(sK3(relation_dom(sK2),sK17(sK16(powerset(X0)))),sK4(relation_dom(sK2),sK17(sK16(powerset(X0)))))) )
| ~ empty(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4463,c_11936]) ).
tcf(c_12303,plain,
! [X0: $i] :
( ( sK17(sK16(powerset(X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_4486,c_11936]) ).
tcf(c_12304,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK9(relation_dom(sK2),X1,sK17(sK16(powerset(X0)))),sK11(relation_dom(sK2),X1,sK17(sK16(powerset(X0))))),relation_dom(sK0))
| ( relation_composition(relation_dom(sK2),X1) = sK17(sK16(powerset(X0))) )
| ~ empty(X0)
| ~ relation(X1)
| ~ relation(relation_dom(sK2))
| ~ relation(sK17(sK16(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_4703,c_11936]) ).
tcf(c_12305,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK9(sK17(sK16(powerset(X0))),X1,relation_dom(sK2)),sK10(sK17(sK16(powerset(X0))),X1,relation_dom(sK2))),relation_dom(sK0))
| ( relation_composition(sK17(sK16(powerset(X0))),X1) = relation_dom(sK2) )
| ~ empty(X0)
| ~ relation(X1)
| ~ relation(relation_dom(sK2))
| ~ relation(sK17(sK16(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_4725,c_11936]) ).
tcf(c_12306,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK11(X1,relation_dom(sK2),sK17(sK16(powerset(X0)))),sK10(X1,relation_dom(sK2),sK17(sK16(powerset(X0))))),relation_dom(sK0))
| ( relation_composition(X1,relation_dom(sK2)) = sK17(sK16(powerset(X0))) )
| ~ empty(X0)
| ~ relation(X1)
| ~ relation(relation_dom(sK2))
| ~ relation(sK17(sK16(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_5257,c_11936]) ).
tcf(c_12307,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK9(X1,sK17(sK16(powerset(X0))),relation_dom(sK2)),sK10(X1,sK17(sK16(powerset(X0))),relation_dom(sK2))),relation_dom(sK0))
| ( relation_composition(X1,sK17(sK16(powerset(X0)))) = relation_dom(sK2) )
| ~ empty(X0)
| ~ relation(X1)
| ~ relation(relation_dom(sK2))
| ~ relation(sK17(sK16(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_5279,c_11936]) ).
tcf(c_12308,plain,
! [X0: $i] :
( empty(sK17(sK16(powerset(X0))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11931,c_11936]) ).
tcf(c_12485,plain,
! [X0: $i,X1: $i] :
( in(sK3(sK17(sK16(powerset(X0))),X1),X1)
| element(ordered_pair(sK3(sK17(sK16(powerset(X0))),X1),sK4(sK17(sK16(powerset(X0))),X1)),X0)
| ( relation_dom(sK17(sK16(powerset(X0)))) = X1 )
| ~ relation(sK17(sK16(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_69,c_11939]) ).
tcf(c_12486,plain,
! [X0: $i,X1: $i] :
( element(ordered_pair(X0,sK5(sK17(sK16(powerset(X1))),X0)),X1)
| ~ relation(sK17(sK16(powerset(X1))))
| ~ in(X0,relation_dom(sK17(sK16(powerset(X1))))) ),
inference(superposition,[status(thm)],[c_71,c_11939]) ).
tcf(c_12487,plain,
! [X0: $i,X1: $i] :
( element(ordered_pair(X0,apply(sK17(sK16(powerset(X1))),X0)),X1)
| ~ function(sK17(sK16(powerset(X1))))
| ~ relation(sK17(sK16(powerset(X1))))
| ~ in(X0,relation_dom(sK17(sK16(powerset(X1))))) ),
inference(superposition,[status(thm)],[c_73,c_11939]) ).
tcf(c_12488,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(ordered_pair(sK9(X1,X2,sK17(sK16(powerset(X0)))),sK10(X1,X2,sK17(sK16(powerset(X0))))),X0)
| in(ordered_pair(sK11(X1,X2,sK17(sK16(powerset(X0)))),sK10(X1,X2,sK17(sK16(powerset(X0))))),X2)
| ( sK17(sK16(powerset(X0))) = relation_composition(X1,X2) )
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(sK17(sK16(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_93,c_11939]) ).
tcf(c_12489,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(ordered_pair(sK9(X1,X2,sK17(sK16(powerset(X0)))),sK10(X1,X2,sK17(sK16(powerset(X0))))),X0)
| in(ordered_pair(sK9(X1,X2,sK17(sK16(powerset(X0)))),sK11(X1,X2,sK17(sK16(powerset(X0))))),X1)
| ( sK17(sK16(powerset(X0))) = relation_composition(X1,X2) )
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(sK17(sK16(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_92,c_11939]) ).
tcf(c_12490,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(ordered_pair(sK9(sK17(sK16(powerset(X0))),X1,X2),sK11(sK17(sK16(powerset(X0))),X1,X2)),X0)
| in(ordered_pair(sK9(sK17(sK16(powerset(X0))),X1,X2),sK10(sK17(sK16(powerset(X0))),X1,X2)),X2)
| ( relation_composition(sK17(sK16(powerset(X0))),X1) = X2 )
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(sK17(sK16(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_92,c_11939]) ).
tcf(c_12491,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(ordered_pair(sK11(X1,sK17(sK16(powerset(X0))),X2),sK10(X1,sK17(sK16(powerset(X0))),X2)),X0)
| in(ordered_pair(sK9(X1,sK17(sK16(powerset(X0))),X2),sK10(X1,sK17(sK16(powerset(X0))),X2)),X2)
| ( relation_composition(X1,sK17(sK16(powerset(X0)))) = X2 )
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(sK17(sK16(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_93,c_11939]) ).
tcf(c_12492,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(ordered_pair(X0,sK12(sK17(sK16(powerset(X2))),X3,X0,X1)),X2)
| ~ relation(X3)
| ~ relation(sK17(sK16(powerset(X2))))
| ~ in(ordered_pair(X0,X1),relation_composition(sK17(sK16(powerset(X2))),X3)) ),
inference(superposition,[status(thm)],[c_301,c_11939]) ).
tcf(c_12493,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(ordered_pair(sK12(X2,sK17(sK16(powerset(X3))),X0,X1),X1),X3)
| ~ relation(X2)
| ~ relation(sK17(sK16(powerset(X3))))
| ~ in(ordered_pair(X0,X1),relation_composition(X2,sK17(sK16(powerset(X3))))) ),
inference(superposition,[status(thm)],[c_300,c_11939]) ).
tcf(c_12494,plain,
! [X0: $i] :
( empty(sK17(sK16(powerset(X0))))
| element(sK17(sK17(sK16(powerset(X0)))),X0) ),
inference(superposition,[status(thm)],[c_2361,c_11939]) ).
tcf(c_12495,plain,
! [X0: $i] :
( element(sK3(relation_dom(sK2),sK17(sK16(powerset(X0)))),X0)
| ( sK17(sK16(powerset(X0))) = relation_dom(relation_dom(sK2)) )
| ( apply(sK1,apply(sK0,ordered_pair(sK3(relation_dom(sK2),sK17(sK16(powerset(X0)))),sK4(relation_dom(sK2),sK17(sK16(powerset(X0))))))) = apply(sK2,ordered_pair(sK3(relation_dom(sK2),sK17(sK16(powerset(X0)))),sK4(relation_dom(sK2),sK17(sK16(powerset(X0)))))) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4463,c_11939]) ).
tcf(c_12496,plain,
! [X0: $i] :
( element(sK3(empty_set,sK17(sK16(powerset(X0)))),X0)
| ( sK17(sK16(powerset(X0))) = empty_set ) ),
inference(superposition,[status(thm)],[c_4486,c_11939]) ).
tcf(c_12497,plain,
! [X0: $i,X1: $i] :
( element(ordered_pair(sK9(relation_dom(sK2),X1,sK17(sK16(powerset(X0)))),sK10(relation_dom(sK2),X1,sK17(sK16(powerset(X0))))),X0)
| in(ordered_pair(sK9(relation_dom(sK2),X1,sK17(sK16(powerset(X0)))),sK11(relation_dom(sK2),X1,sK17(sK16(powerset(X0))))),relation_dom(sK0))
| ( relation_composition(relation_dom(sK2),X1) = sK17(sK16(powerset(X0))) )
| ~ relation(X1)
| ~ relation(relation_dom(sK2))
| ~ relation(sK17(sK16(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_4703,c_11939]) ).
tcf(c_12498,plain,
! [X0: $i,X1: $i] :
( element(ordered_pair(sK9(sK17(sK16(powerset(X0))),X1,relation_dom(sK2)),sK11(sK17(sK16(powerset(X0))),X1,relation_dom(sK2))),X0)
| in(ordered_pair(sK9(sK17(sK16(powerset(X0))),X1,relation_dom(sK2)),sK10(sK17(sK16(powerset(X0))),X1,relation_dom(sK2))),relation_dom(sK0))
| ( relation_composition(sK17(sK16(powerset(X0))),X1) = relation_dom(sK2) )
| ~ relation(X1)
| ~ relation(relation_dom(sK2))
| ~ relation(sK17(sK16(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_4725,c_11939]) ).
tcf(c_12499,plain,
! [X0: $i,X1: $i] :
( element(ordered_pair(sK9(X1,relation_dom(sK2),sK17(sK16(powerset(X0)))),sK10(X1,relation_dom(sK2),sK17(sK16(powerset(X0))))),X0)
| in(ordered_pair(sK11(X1,relation_dom(sK2),sK17(sK16(powerset(X0)))),sK10(X1,relation_dom(sK2),sK17(sK16(powerset(X0))))),relation_dom(sK0))
| ( relation_composition(X1,relation_dom(sK2)) = sK17(sK16(powerset(X0))) )
| ~ relation(X1)
| ~ relation(relation_dom(sK2))
| ~ relation(sK17(sK16(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_5257,c_11939]) ).
tcf(c_12500,plain,
! [X0: $i,X1: $i] :
( element(ordered_pair(sK11(X1,sK17(sK16(powerset(X0))),relation_dom(sK2)),sK10(X1,sK17(sK16(powerset(X0))),relation_dom(sK2))),X0)
| in(ordered_pair(sK9(X1,sK17(sK16(powerset(X0))),relation_dom(sK2)),sK10(X1,sK17(sK16(powerset(X0))),relation_dom(sK2))),relation_dom(sK0))
| ( relation_composition(X1,sK17(sK16(powerset(X0)))) = relation_dom(sK2) )
| ~ relation(X1)
| ~ relation(relation_dom(sK2))
| ~ relation(sK17(sK16(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_5279,c_11939]) ).
tcf(c_12501,plain,
! [X0: $i] :
( empty(sK17(sK16(powerset(X0))))
| element(sK17(sK16(sK17(sK16(powerset(X0))))),X0) ),
inference(superposition,[status(thm)],[c_11931,c_11939]) ).
tcf(c_12638,plain,
! [X0: $i,X1: $i] :
( in(sK3(relation_composition(X0,empty_set),X1),X1)
| ( relation_dom(relation_composition(X0,empty_set)) = X1 )
| ~ relation(X0)
| ~ relation(relation_composition(X0,empty_set)) ),
inference(superposition,[status(thm)],[c_69,c_3818]) ).
tcf(c_12639,plain,
! [X0: $i,X1: $i] :
( ~ relation(X1)
| ~ relation(relation_composition(X1,empty_set))
| ~ in(X0,relation_dom(relation_composition(X1,empty_set))) ),
inference(superposition,[status(thm)],[c_71,c_3818]) ).
tcf(c_12640,plain,
! [X0: $i,X1: $i] :
( ~ relation(X1)
| ~ function(relation_composition(X1,empty_set))
| ~ relation(relation_composition(X1,empty_set))
| ~ in(X0,relation_dom(relation_composition(X1,empty_set))) ),
inference(superposition,[status(thm)],[c_73,c_3818]) ).
tcf(c_12641,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(ordered_pair(sK11(X1,X2,relation_composition(X0,empty_set)),sK10(X1,X2,relation_composition(X0,empty_set))),X2)
| ( relation_composition(X1,X2) = relation_composition(X0,empty_set) )
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_composition(X0,empty_set)) ),
inference(superposition,[status(thm)],[c_93,c_3818]) ).
tcf(c_12642,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(ordered_pair(sK9(X1,X2,relation_composition(X0,empty_set)),sK11(X1,X2,relation_composition(X0,empty_set))),X1)
| ( relation_composition(X1,X2) = relation_composition(X0,empty_set) )
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_composition(X0,empty_set)) ),
inference(superposition,[status(thm)],[c_92,c_3818]) ).
tcf(c_12643,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(ordered_pair(sK9(relation_composition(X0,empty_set),X1,X2),sK10(relation_composition(X0,empty_set),X1,X2)),X2)
| ( relation_composition(relation_composition(X0,empty_set),X1) = X2 )
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_composition(X0,empty_set)) ),
inference(superposition,[status(thm)],[c_92,c_3818]) ).
tcf(c_12644,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(ordered_pair(sK9(X1,relation_composition(X0,empty_set),X2),sK10(X1,relation_composition(X0,empty_set),X2)),X2)
| ( relation_composition(X1,relation_composition(X0,empty_set)) = X2 )
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_composition(X0,empty_set)) ),
inference(superposition,[status(thm)],[c_93,c_3818]) ).
tcf(c_12645,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ relation(X3)
| ~ relation(X2)
| ~ relation(relation_composition(X2,empty_set))
| ~ in(ordered_pair(X0,X1),relation_composition(relation_composition(X2,empty_set),X3)) ),
inference(superposition,[status(thm)],[c_301,c_3818]) ).
tcf(c_12646,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ relation(X3)
| ~ relation(X2)
| ~ relation(relation_composition(X3,empty_set))
| ~ in(ordered_pair(X0,X1),relation_composition(X2,relation_composition(X3,empty_set))) ),
inference(superposition,[status(thm)],[c_300,c_3818]) ).
tcf(c_12647,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ relation(empty_set)
| ~ relation(X3)
| ~ relation(X2)
| ~ in(ordered_pair(X1,X4),empty_set)
| ~ in(ordered_pair(X0,X1),relation_composition(X2,X3)) ),
inference(superposition,[status(thm)],[c_2067,c_3818]) ).
tcf(c_12648,plain,
! [X0: $i,X1: $i] :
( ( apply(sK0,X0) = empty_set )
| ( apply(sK1,apply(sK0,X0)) = empty_set )
| ~ relation(empty_set)
| ~ relation(sK1)
| ~ in(ordered_pair(apply(sK2,X0),X1),empty_set) ),
inference(superposition,[status(thm)],[c_6088,c_3818]) ).
tcf(c_12649,plain,
! [X0: $i,X1: $i] :
( ( apply(sK2,X0) = empty_set )
| ~ relation(empty_set)
| ~ relation(sK1)
| ~ in(apply(sK0,X0),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,X0),X1),empty_set) ),
inference(superposition,[status(thm)],[c_4264,c_3818]) ).
tcf(c_12650,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK9(relation_dom(sK2),X1,relation_composition(X0,empty_set)),sK11(relation_dom(sK2),X1,relation_composition(X0,empty_set))),relation_dom(sK0))
| ( relation_composition(relation_dom(sK2),X1) = relation_composition(X0,empty_set) )
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2))
| ~ relation(relation_composition(X0,empty_set)) ),
inference(superposition,[status(thm)],[c_4703,c_3818]) ).
tcf(c_12651,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK9(relation_composition(X0,empty_set),X1,relation_dom(sK2)),sK10(relation_composition(X0,empty_set),X1,relation_dom(sK2))),relation_dom(sK0))
| ( relation_composition(relation_composition(X0,empty_set),X1) = relation_dom(sK2) )
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2))
| ~ relation(relation_composition(X0,empty_set)) ),
inference(superposition,[status(thm)],[c_4725,c_3818]) ).
tcf(c_12652,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK11(X1,relation_dom(sK2),relation_composition(X0,empty_set)),sK10(X1,relation_dom(sK2),relation_composition(X0,empty_set))),relation_dom(sK0))
| ( relation_composition(X1,relation_dom(sK2)) = relation_composition(X0,empty_set) )
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2))
| ~ relation(relation_composition(X0,empty_set)) ),
inference(superposition,[status(thm)],[c_5257,c_3818]) ).
tcf(c_12653,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK9(X1,relation_composition(X0,empty_set),relation_dom(sK2)),sK10(X1,relation_composition(X0,empty_set),relation_dom(sK2))),relation_dom(sK0))
| ( relation_composition(X1,relation_composition(X0,empty_set)) = relation_dom(sK2) )
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2))
| ~ relation(relation_composition(X0,empty_set)) ),
inference(superposition,[status(thm)],[c_5279,c_3818]) ).
tcf(c_12654,plain,
! [X0: $i] :
( ( sK17(powerset(sK2)) = empty_set )
| ~ relation(empty_set)
| ~ relation(sK1)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),empty_set) ),
inference(superposition,[status(thm)],[c_12118,c_3818]) ).
tcf(c_12655,plain,
! [X0: $i] :
( ( sK17(powerset(relation_dom(sK2))) = empty_set )
| ~ relation(empty_set)
| ~ relation(sK1)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),empty_set) ),
inference(superposition,[status(thm)],[c_10055,c_3818]) ).
tcf(c_12656,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK2))) = empty_set )
| ~ relation(empty_set)
| ~ relation(sK1)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),empty_set) ),
inference(superposition,[status(thm)],[c_8516,c_3818]) ).
tcf(c_12657,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK2)) = empty_set )
| ~ relation(empty_set)
| ~ relation(sK1)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),empty_set) ),
inference(superposition,[status(thm)],[c_7882,c_3818]) ).
tcf(c_12658,plain,
! [X0: $i] :
( ( relation_dom(sK2) = sK2 )
| ~ relation(empty_set)
| ~ relation(sK1)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),empty_set) ),
inference(superposition,[status(thm)],[c_5975,c_3818]) ).
tcf(c_12659,plain,
! [X0: $i] :
( ( relation_dom(sK2) = empty_set )
| ~ relation(empty_set)
| ~ relation(sK1)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),empty_set) ),
inference(superposition,[status(thm)],[c_5928,c_3818]) ).
tcf(c_12660,plain,
! [X0: $i] :
( ( sK2 = empty_set )
| ~ relation(empty_set)
| ~ relation(sK1)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),empty_set) ),
inference(superposition,[status(thm)],[c_5890,c_3818]) ).
tcf(c_12661,plain,
! [X0: $i] :
( ( relation_dom(sK2) = empty_set )
| ~ relation(empty_set)
| ~ relation(sK1)
| ~ in(apply(sK0,sK3(empty_set,relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK3(empty_set,relation_dom(sK2))),X0),empty_set) ),
inference(superposition,[status(thm)],[c_7405,c_3818]) ).
tcf(c_12769,plain,
! [X0: $i] :
( ( sK17(sK16(powerset(X0))) = relation_dom(sK2) )
| ~ empty(sK0)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12308,c_2667]) ).
tcf(c_12770,plain,
! [X0: $i] :
( ( sK17(sK16(powerset(X0))) = relation_dom(sK2) )
| ~ empty(sK1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12308,c_2636]) ).
tcf(c_12771,plain,
! [X0: $i] :
( ( relation_dom(sK17(powerset(sK17(sK16(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12308,c_7171]) ).
tcf(c_12772,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK17(sK16(powerset(X0)))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12308,c_2387]) ).
tcf(c_12773,plain,
! [X0: $i] :
( ( sK17(powerset(relation_dom(sK17(sK16(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12308,c_7733]) ).
tcf(c_12774,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK17(sK16(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12308,c_7227]) ).
tcf(c_12775,plain,
! [X0: $i] :
( ( sK17(powerset(sK17(sK16(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12308,c_7088]) ).
tcf(c_12776,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK17(sK16(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12308,c_6244]) ).
tcf(c_12777,plain,
! [X0: $i] :
( ( relation_dom(sK17(sK16(powerset(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12308,c_2124]) ).
tcf(c_12778,plain,
! [X0: $i] :
( ( sK17(sK16(powerset(X0))) = relation_dom(sK2) )
| ( apply(sK1,apply(sK0,sK17(relation_dom(sK2)))) = apply(sK2,sK17(relation_dom(sK2))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12308,c_2466]) ).
tcf(c_12779,plain,
! [X0: $i] :
( ( sK17(sK16(powerset(X0))) = sK2 )
| ( apply(sK1,apply(sK0,sK17(relation_dom(sK2)))) = apply(sK2,sK17(relation_dom(sK2))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12308,c_2488]) ).
tcf(c_12780,plain,
! [X0: $i,X1: $i] :
( ( sK17(sK16(powerset(X0))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12308,c_60]) ).
tcf(c_12782,plain,
! [X0: $i] :
( relation(sK17(sK16(powerset(X0))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12308,c_85]) ).
tcf(c_12783,plain,
! [X0: $i] :
( function(sK17(sK16(powerset(X0))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12308,c_80]) ).
tcf(c_12877,plain,
! [X0: $i] :
( ( sK17(sK16(powerset(relation_dom(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_65,c_12303]) ).
tcf(c_12878,plain,
! [X0: $i,X1: $i] :
( ( sK17(sK16(powerset(relation_composition(X1,X0)))) = empty_set )
| ~ empty(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_86,c_12303]) ).
tcf(c_12879,plain,
! [X0: $i,X1: $i] :
( ( sK17(sK16(powerset(relation_composition(X0,X1)))) = empty_set )
| ~ empty(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_88,c_12303]) ).
tcf(c_12880,plain,
sK17(sK16(powerset(empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_110,c_12303]) ).
tcf(c_12881,plain,
( ( sK17(sK16(powerset(relation_dom(sK2)))) = empty_set )
| ( apply(sK1,apply(sK0,sK17(sK16(relation_dom(sK2))))) = apply(sK2,sK17(sK16(relation_dom(sK2)))) ) ),
inference(superposition,[status(thm)],[c_11951,c_12303]) ).
tcf(c_12882,plain,
( ( sK17(sK16(powerset(relation_dom(sK2)))) = empty_set )
| ~ empty(sK0) ),
inference(superposition,[status(thm)],[c_2577,c_12303]) ).
tcf(c_12883,plain,
( ( sK17(sK16(powerset(relation_dom(sK2)))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_2570,c_12303]) ).
tcf(c_12884,plain,
( ( sK17(sK16(powerset(relation_dom(sK2)))) = empty_set )
| ( apply(sK1,apply(sK0,sK17(relation_dom(sK2)))) = apply(sK2,sK17(relation_dom(sK2))) ) ),
inference(superposition,[status(thm)],[c_2425,c_12303]) ).
tcf(c_12885,plain,
( ( sK17(sK16(powerset(sK2))) = empty_set )
| ( apply(sK1,apply(sK0,sK17(sK16(relation_dom(sK2))))) = apply(sK2,sK17(sK16(relation_dom(sK2)))) ) ),
inference(superposition,[status(thm)],[c_12039,c_12303]) ).
tcf(c_12886,plain,
( ( sK17(sK16(powerset(sK2))) = empty_set )
| ( apply(sK1,apply(sK0,sK17(relation_dom(sK2)))) = apply(sK2,sK17(relation_dom(sK2))) ) ),
inference(superposition,[status(thm)],[c_2475,c_12303]) ).
tcf(c_12887,plain,
( ( sK17(sK16(powerset(relation_dom(relation_dom(sK2))))) = empty_set )
| ~ empty(relation_dom(sK0)) ),
inference(superposition,[status(thm)],[c_3251,c_12303]) ).
tcf(c_12888,plain,
! [X0: $i] :
( ( sK17(sK16(powerset(sK17(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6912,c_12303]) ).
tcf(c_12889,plain,
! [X0: $i] :
( ( sK17(sK16(powerset(sK17(sK16(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12308,c_12303]) ).
tcf(c_12968,plain,
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK2)))) = empty_set )
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(sK1,ordered_pair(apply(sK0,sK17(relation_dom(sK2))),apply(sK2,sK17(relation_dom(sK2))))) ),
inference(superposition,[status(thm)],[c_12284,c_64]) ).
tcf(c_12969,plain,
( element(ordered_pair(apply(sK0,sK17(relation_dom(sK2))),apply(sK2,sK17(relation_dom(sK2)))),sK1)
| ( relation_dom(relation_dom(relation_dom(relation_dom(sK2)))) = empty_set )
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_12284,c_63]) ).
tcf(c_12972,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(apply(sK0,sK17(relation_dom(sK2))),X0),relation_composition(sK1,X1))
| ( relation_dom(relation_dom(relation_dom(relation_dom(sK2)))) = empty_set )
| ~ relation(sK1)
| ~ relation(X1)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),X1) ),
inference(superposition,[status(thm)],[c_12284,c_299]) ).
tcf(c_12980,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(apply(sK0,sK17(relation_dom(sK2))),X0),relation_composition(sK1,X1))
| ( relation_dom(relation_dom(relation_dom(relation_dom(sK2)))) = empty_set )
| ~ relation(X1)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12972,c_56]) ).
tcf(c_12997,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK2)))) = empty_set )
| ~ relation(X0)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X1),X0)
| ~ in(relation_composition(sK1,X0),ordered_pair(apply(sK0,sK17(relation_dom(sK2))),X1)) ),
inference(superposition,[status(thm)],[c_12980,c_64]) ).
tcf(c_12998,plain,
! [X0: $i,X1: $i] :
( element(ordered_pair(apply(sK0,sK17(relation_dom(sK2))),X0),relation_composition(sK1,X1))
| ( relation_dom(relation_dom(relation_dom(relation_dom(sK2)))) = empty_set )
| ~ relation(X1)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),X1) ),
inference(superposition,[status(thm)],[c_12980,c_63]) ).
tcf(c_12999,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK2)))) = empty_set )
| ~ relation(X1)
| ~ empty(relation_composition(sK1,X1))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),X1) ),
inference(superposition,[status(thm)],[c_12980,c_61]) ).
tcf(c_13000,plain,
! [X0: $i,X1: $i] :
( in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(relation_composition(sK1,X1)))
| ( relation_dom(relation_dom(relation_dom(relation_dom(sK2)))) = empty_set )
| ~ relation(X1)
| ~ relation(relation_composition(sK1,X1))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),X1) ),
inference(superposition,[status(thm)],[c_12980,c_70]) ).
tcf(c_13001,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(ordered_pair(apply(sK0,sK17(relation_dom(sK2))),X2),relation_composition(relation_composition(sK1,X1),X3))
| ( relation_dom(relation_dom(relation_dom(relation_dom(sK2)))) = empty_set )
| ~ relation(X3)
| ~ relation(X1)
| ~ relation(relation_composition(sK1,X1))
| ~ in(ordered_pair(X0,X2),X3)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),X1) ),
inference(superposition,[status(thm)],[c_12980,c_299]) ).
tcf(c_13002,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK2)))) = empty_set )
| ( apply(relation_composition(sK1,X1),apply(sK0,sK17(relation_dom(sK2)))) = X0 )
| ~ relation(X1)
| ~ function(relation_composition(sK1,X1))
| ~ relation(relation_composition(sK1,X1))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),X1) ),
inference(superposition,[status(thm)],[c_12980,c_152]) ).
tcf(c_13003,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK2)))) = empty_set )
| ( apply(X1,sK12(sK1,X1,apply(sK0,sK17(relation_dom(sK2))),X0)) = X0 )
| ~ relation(sK1)
| ~ function(X1)
| ~ relation(X1)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),X1) ),
inference(superposition,[status(thm)],[c_12980,c_2068]) ).
tcf(c_13004,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK2)))) = empty_set )
| ~ relation(sK1)
| ~ empty(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_12980,c_2176]) ).
tcf(c_13005,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK2)))) = empty_set )
| ~ relation(sK1)
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_12980,c_2063]) ).
tcf(c_13006,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK2)))) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,sK17(relation_dom(sK2))),X0),X0))) = apply(sK2,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,sK17(relation_dom(sK2))),X0),X0)) )
| ~ relation(sK1)
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_12980,c_2064]) ).
tcf(c_13007,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK2)))) = empty_set )
| ~ relation(empty_set)
| ~ relation(sK1)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),empty_set) ),
inference(superposition,[status(thm)],[c_12980,c_3818]) ).
tcf(c_13013,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK2)))) = empty_set )
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_13005,c_56]) ).
tcf(c_13036,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK2)))) = empty_set )
| ( apply(X1,sK12(sK1,X1,apply(sK0,sK17(relation_dom(sK2))),X0)) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_13003,c_56]) ).
tcf(c_13058,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK2)))) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,sK17(relation_dom(sK2))),X0),X0))) = apply(sK2,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,sK17(relation_dom(sK2))),X0),X0)) )
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_13006,c_56]) ).
tcf(c_13096,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK2)) = empty_set )
| ( apply(sK0,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0)) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0))) = empty_set )
| ( apply(relation_dom(sK2),sK12(sK1,relation_dom(sK2),apply(sK0,sK17(relation_dom(sK2))),X0)) = X0 )
| ~ function(relation_dom(sK2))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_4011,c_8139]) ).
tcf(c_13097,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK2)) = empty_set )
| ( apply(sK0,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0)) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0))) = empty_set )
| ( apply(relation_dom(sK0),sK12(sK1,relation_dom(sK0),apply(sK0,sK17(relation_dom(sK2))),X0)) = X0 )
| ~ function(relation_dom(sK0))
| ~ relation(relation_dom(sK0))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_4110,c_8139]) ).
tcf(c_13098,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK2)) = empty_set )
| ( apply(sK2,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0)) = empty_set )
| ( apply(relation_dom(sK0),sK12(sK1,relation_dom(sK0),apply(sK0,sK17(relation_dom(sK2))),X0)) = X0 )
| ~ function(relation_dom(sK0))
| ~ relation(relation_dom(sK0))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_3449,c_8139]) ).
tcf(c_13099,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK2)) = empty_set )
| ( apply(X0,sK12(sK1,X0,apply(sK0,sK17(relation_dom(sK2))),sK5(X0,apply(sK2,sK17(relation_dom(sK2)))))) = sK5(X0,apply(sK2,sK17(relation_dom(sK2)))) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(apply(sK2,sK17(relation_dom(sK2))),relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_71,c_8139]) ).
tcf(c_13100,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK2)) = empty_set )
| ( apply(X0,sK12(sK1,X0,apply(sK0,sK17(relation_dom(sK2))),apply(X0,apply(sK2,sK17(relation_dom(sK2)))))) = apply(X0,apply(sK2,sK17(relation_dom(sK2)))) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(apply(sK2,sK17(relation_dom(sK2))),relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_73,c_8139]) ).
tcf(c_13101,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK2)) = empty_set )
| ( apply(X0,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X1)) = empty_set )
| ( apply(relation_dom(X0),sK12(sK1,relation_dom(X0),apply(sK0,sK17(relation_dom(sK2))),X1)) = X1 )
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom(X0))
| ~ relation(relation_dom(X0))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_75,c_8139]) ).
tcf(c_13102,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_dom(sK2)) = empty_set )
| ( apply(X1,sK12(sK1,X1,apply(sK0,sK17(relation_dom(sK2))),sK12(X1,X2,apply(sK2,sK17(relation_dom(sK2))),X0))) = sK12(X1,X2,apply(sK2,sK17(relation_dom(sK2))),X0) )
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),relation_composition(X1,X2)) ),
inference(superposition,[status(thm)],[c_301,c_8139]) ).
tcf(c_13103,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK2)) = empty_set )
| ( apply(relation_dom(sK0),sK12(sK1,relation_dom(sK0),apply(sK0,sK17(relation_dom(sK2))),sK12(relation_dom(sK2),X1,apply(sK2,sK17(relation_dom(sK2))),X0))) = sK12(relation_dom(sK2),X1,apply(sK2,sK17(relation_dom(sK2))),X0) )
| ~ relation(X1)
| ~ function(relation_dom(sK0))
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),relation_composition(relation_dom(sK2),X1)) ),
inference(superposition,[status(thm)],[c_2283,c_8139]) ).
tcf(c_13104,plain,
( ( relation_dom(relation_dom(sK2)) = empty_set )
| ( apply(relation_dom(sK0),sK12(sK1,relation_dom(sK0),apply(sK0,sK17(relation_dom(sK2))),sK5(relation_dom(sK2),apply(sK2,sK17(relation_dom(sK2)))))) = sK5(relation_dom(sK2),apply(sK2,sK17(relation_dom(sK2)))) )
| ~ function(relation_dom(sK0))
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(apply(sK2,sK17(relation_dom(sK2))),relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_3019,c_8139]) ).
tcf(c_13105,plain,
( ( relation_dom(relation_dom(sK2)) = empty_set )
| ( apply(relation_dom(sK0),sK12(sK1,relation_dom(sK0),apply(sK0,sK17(relation_dom(sK2))),apply(relation_dom(sK2),apply(sK2,sK17(relation_dom(sK2)))))) = apply(relation_dom(sK2),apply(sK2,sK17(relation_dom(sK2)))) )
| ~ function(relation_dom(sK0))
| ~ function(relation_dom(sK2))
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(apply(sK2,sK17(relation_dom(sK2))),relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_3551,c_8139]) ).
tcf(c_13220,plain,
! [X0: $i] :
( ( sK17(powerset(sK2)) = empty_set )
| ( apply(sK0,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0)) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0))) = empty_set )
| ( apply(relation_dom(sK2),sK12(sK1,relation_dom(sK2),apply(sK0,sK17(relation_dom(sK2))),X0)) = X0 )
| ~ function(relation_dom(sK2))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_4011,c_12178]) ).
tcf(c_13221,plain,
! [X0: $i] :
( ( sK17(powerset(sK2)) = empty_set )
| ( apply(sK0,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0)) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0))) = empty_set )
| ( apply(relation_dom(sK0),sK12(sK1,relation_dom(sK0),apply(sK0,sK17(relation_dom(sK2))),X0)) = X0 )
| ~ function(relation_dom(sK0))
| ~ relation(relation_dom(sK0))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_4110,c_12178]) ).
tcf(c_13222,plain,
! [X0: $i] :
( ( sK17(powerset(sK2)) = empty_set )
| ( apply(sK2,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0)) = empty_set )
| ( apply(relation_dom(sK0),sK12(sK1,relation_dom(sK0),apply(sK0,sK17(relation_dom(sK2))),X0)) = X0 )
| ~ function(relation_dom(sK0))
| ~ relation(relation_dom(sK0))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_3449,c_12178]) ).
tcf(c_13223,plain,
! [X0: $i] :
( ( sK17(powerset(sK2)) = empty_set )
| ( apply(X0,sK12(sK1,X0,apply(sK0,sK17(relation_dom(sK2))),sK5(X0,apply(sK2,sK17(relation_dom(sK2)))))) = sK5(X0,apply(sK2,sK17(relation_dom(sK2)))) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(apply(sK2,sK17(relation_dom(sK2))),relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_71,c_12178]) ).
tcf(c_13224,plain,
! [X0: $i] :
( ( sK17(powerset(sK2)) = empty_set )
| ( apply(X0,sK12(sK1,X0,apply(sK0,sK17(relation_dom(sK2))),apply(X0,apply(sK2,sK17(relation_dom(sK2)))))) = apply(X0,apply(sK2,sK17(relation_dom(sK2)))) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(apply(sK2,sK17(relation_dom(sK2))),relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_73,c_12178]) ).
tcf(c_13225,plain,
! [X0: $i,X1: $i] :
( ( sK17(powerset(sK2)) = empty_set )
| ( apply(X0,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X1)) = empty_set )
| ( apply(relation_dom(X0),sK12(sK1,relation_dom(X0),apply(sK0,sK17(relation_dom(sK2))),X1)) = X1 )
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom(X0))
| ~ relation(relation_dom(X0))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_75,c_12178]) ).
tcf(c_13226,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK17(powerset(sK2)) = empty_set )
| ( apply(X1,sK12(sK1,X1,apply(sK0,sK17(relation_dom(sK2))),sK12(X1,X2,apply(sK2,sK17(relation_dom(sK2))),X0))) = sK12(X1,X2,apply(sK2,sK17(relation_dom(sK2))),X0) )
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),relation_composition(X1,X2)) ),
inference(superposition,[status(thm)],[c_301,c_12178]) ).
tcf(c_13227,plain,
! [X0: $i,X1: $i] :
( ( sK17(powerset(sK2)) = empty_set )
| ( apply(relation_dom(sK0),sK12(sK1,relation_dom(sK0),apply(sK0,sK17(relation_dom(sK2))),sK12(relation_dom(sK2),X1,apply(sK2,sK17(relation_dom(sK2))),X0))) = sK12(relation_dom(sK2),X1,apply(sK2,sK17(relation_dom(sK2))),X0) )
| ~ relation(X1)
| ~ function(relation_dom(sK0))
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),relation_composition(relation_dom(sK2),X1)) ),
inference(superposition,[status(thm)],[c_2283,c_12178]) ).
tcf(c_13228,plain,
( ( sK17(powerset(sK2)) = empty_set )
| ( apply(relation_dom(sK0),sK12(sK1,relation_dom(sK0),apply(sK0,sK17(relation_dom(sK2))),sK5(relation_dom(sK2),apply(sK2,sK17(relation_dom(sK2)))))) = sK5(relation_dom(sK2),apply(sK2,sK17(relation_dom(sK2)))) )
| ~ function(relation_dom(sK0))
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(apply(sK2,sK17(relation_dom(sK2))),relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_3019,c_12178]) ).
tcf(c_13229,plain,
( ( sK17(powerset(sK2)) = empty_set )
| ( apply(relation_dom(sK0),sK12(sK1,relation_dom(sK0),apply(sK0,sK17(relation_dom(sK2))),apply(relation_dom(sK2),apply(sK2,sK17(relation_dom(sK2)))))) = apply(relation_dom(sK2),apply(sK2,sK17(relation_dom(sK2)))) )
| ~ function(relation_dom(sK0))
| ~ function(relation_dom(sK2))
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(apply(sK2,sK17(relation_dom(sK2))),relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_3551,c_12178]) ).
tcf(c_13392,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK2))) = empty_set )
| ( apply(sK0,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0)) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0))) = empty_set )
| ( apply(relation_dom(sK2),sK12(sK1,relation_dom(sK2),apply(sK0,sK17(relation_dom(sK2))),X0)) = X0 )
| ~ function(relation_dom(sK2))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_4011,c_8571]) ).
tcf(c_13393,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK2))) = empty_set )
| ( apply(sK0,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0)) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0))) = empty_set )
| ( apply(relation_dom(sK0),sK12(sK1,relation_dom(sK0),apply(sK0,sK17(relation_dom(sK2))),X0)) = X0 )
| ~ function(relation_dom(sK0))
| ~ relation(relation_dom(sK0))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_4110,c_8571]) ).
tcf(c_13394,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK2))) = empty_set )
| ( apply(sK2,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0)) = empty_set )
| ( apply(relation_dom(sK0),sK12(sK1,relation_dom(sK0),apply(sK0,sK17(relation_dom(sK2))),X0)) = X0 )
| ~ function(relation_dom(sK0))
| ~ relation(relation_dom(sK0))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_3449,c_8571]) ).
tcf(c_13395,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK2))) = empty_set )
| ( apply(X0,sK12(sK1,X0,apply(sK0,sK17(relation_dom(sK2))),sK5(X0,apply(sK2,sK17(relation_dom(sK2)))))) = sK5(X0,apply(sK2,sK17(relation_dom(sK2)))) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(apply(sK2,sK17(relation_dom(sK2))),relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_71,c_8571]) ).
tcf(c_13396,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK2))) = empty_set )
| ( apply(X0,sK12(sK1,X0,apply(sK0,sK17(relation_dom(sK2))),apply(X0,apply(sK2,sK17(relation_dom(sK2)))))) = apply(X0,apply(sK2,sK17(relation_dom(sK2)))) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(apply(sK2,sK17(relation_dom(sK2))),relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_73,c_8571]) ).
tcf(c_13397,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(sK2))) = empty_set )
| ( apply(X0,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X1)) = empty_set )
| ( apply(relation_dom(X0),sK12(sK1,relation_dom(X0),apply(sK0,sK17(relation_dom(sK2))),X1)) = X1 )
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom(X0))
| ~ relation(relation_dom(X0))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_75,c_8571]) ).
tcf(c_13398,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_dom(relation_dom(sK2))) = empty_set )
| ( apply(X1,sK12(sK1,X1,apply(sK0,sK17(relation_dom(sK2))),sK12(X1,X2,apply(sK2,sK17(relation_dom(sK2))),X0))) = sK12(X1,X2,apply(sK2,sK17(relation_dom(sK2))),X0) )
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),relation_composition(X1,X2)) ),
inference(superposition,[status(thm)],[c_301,c_8571]) ).
tcf(c_13399,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(sK2))) = empty_set )
| ( apply(relation_dom(sK0),sK12(sK1,relation_dom(sK0),apply(sK0,sK17(relation_dom(sK2))),sK12(relation_dom(sK2),X1,apply(sK2,sK17(relation_dom(sK2))),X0))) = sK12(relation_dom(sK2),X1,apply(sK2,sK17(relation_dom(sK2))),X0) )
| ~ relation(X1)
| ~ function(relation_dom(sK0))
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),relation_composition(relation_dom(sK2),X1)) ),
inference(superposition,[status(thm)],[c_2283,c_8571]) ).
tcf(c_13400,plain,
( ( relation_dom(relation_dom(relation_dom(sK2))) = empty_set )
| ( apply(relation_dom(sK0),sK12(sK1,relation_dom(sK0),apply(sK0,sK17(relation_dom(sK2))),sK5(relation_dom(sK2),apply(sK2,sK17(relation_dom(sK2)))))) = sK5(relation_dom(sK2),apply(sK2,sK17(relation_dom(sK2)))) )
| ~ function(relation_dom(sK0))
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(apply(sK2,sK17(relation_dom(sK2))),relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_3019,c_8571]) ).
tcf(c_13401,plain,
( ( relation_dom(relation_dom(relation_dom(sK2))) = empty_set )
| ( apply(relation_dom(sK0),sK12(sK1,relation_dom(sK0),apply(sK0,sK17(relation_dom(sK2))),apply(relation_dom(sK2),apply(sK2,sK17(relation_dom(sK2)))))) = apply(relation_dom(sK2),apply(sK2,sK17(relation_dom(sK2)))) )
| ~ function(relation_dom(sK0))
| ~ function(relation_dom(sK2))
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(apply(sK2,sK17(relation_dom(sK2))),relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_3551,c_8571]) ).
tcf(c_13505,plain,
! [X0: $i] :
( ( sK17(powerset(relation_dom(sK2))) = empty_set )
| ( apply(sK0,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0)) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0))) = empty_set )
| ( apply(relation_dom(sK2),sK12(sK1,relation_dom(sK2),apply(sK0,sK17(relation_dom(sK2))),X0)) = X0 )
| ~ function(relation_dom(sK2))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_4011,c_10138]) ).
tcf(c_13506,plain,
! [X0: $i] :
( ( sK17(powerset(relation_dom(sK2))) = empty_set )
| ( apply(sK0,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0)) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0))) = empty_set )
| ( apply(relation_dom(sK0),sK12(sK1,relation_dom(sK0),apply(sK0,sK17(relation_dom(sK2))),X0)) = X0 )
| ~ function(relation_dom(sK0))
| ~ relation(relation_dom(sK0))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_4110,c_10138]) ).
tcf(c_13507,plain,
! [X0: $i] :
( ( sK17(powerset(relation_dom(sK2))) = empty_set )
| ( apply(sK2,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0)) = empty_set )
| ( apply(relation_dom(sK0),sK12(sK1,relation_dom(sK0),apply(sK0,sK17(relation_dom(sK2))),X0)) = X0 )
| ~ function(relation_dom(sK0))
| ~ relation(relation_dom(sK0))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_3449,c_10138]) ).
tcf(c_13508,plain,
! [X0: $i] :
( ( sK17(powerset(relation_dom(sK2))) = empty_set )
| ( apply(X0,sK12(sK1,X0,apply(sK0,sK17(relation_dom(sK2))),sK5(X0,apply(sK2,sK17(relation_dom(sK2)))))) = sK5(X0,apply(sK2,sK17(relation_dom(sK2)))) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(apply(sK2,sK17(relation_dom(sK2))),relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_71,c_10138]) ).
tcf(c_13509,plain,
! [X0: $i] :
( ( sK17(powerset(relation_dom(sK2))) = empty_set )
| ( apply(X0,sK12(sK1,X0,apply(sK0,sK17(relation_dom(sK2))),apply(X0,apply(sK2,sK17(relation_dom(sK2)))))) = apply(X0,apply(sK2,sK17(relation_dom(sK2)))) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(apply(sK2,sK17(relation_dom(sK2))),relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_73,c_10138]) ).
tcf(c_13510,plain,
! [X0: $i,X1: $i] :
( ( sK17(powerset(relation_dom(sK2))) = empty_set )
| ( apply(X0,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X1)) = empty_set )
| ( apply(relation_dom(X0),sK12(sK1,relation_dom(X0),apply(sK0,sK17(relation_dom(sK2))),X1)) = X1 )
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom(X0))
| ~ relation(relation_dom(X0))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_75,c_10138]) ).
tcf(c_13511,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK17(powerset(relation_dom(sK2))) = empty_set )
| ( apply(X1,sK12(sK1,X1,apply(sK0,sK17(relation_dom(sK2))),sK12(X1,X2,apply(sK2,sK17(relation_dom(sK2))),X0))) = sK12(X1,X2,apply(sK2,sK17(relation_dom(sK2))),X0) )
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),relation_composition(X1,X2)) ),
inference(superposition,[status(thm)],[c_301,c_10138]) ).
tcf(c_13512,plain,
! [X0: $i,X1: $i] :
( ( sK17(powerset(relation_dom(sK2))) = empty_set )
| ( apply(relation_dom(sK0),sK12(sK1,relation_dom(sK0),apply(sK0,sK17(relation_dom(sK2))),sK12(relation_dom(sK2),X1,apply(sK2,sK17(relation_dom(sK2))),X0))) = sK12(relation_dom(sK2),X1,apply(sK2,sK17(relation_dom(sK2))),X0) )
| ~ relation(X1)
| ~ function(relation_dom(sK0))
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),relation_composition(relation_dom(sK2),X1)) ),
inference(superposition,[status(thm)],[c_2283,c_10138]) ).
tcf(c_13513,plain,
( ( sK17(powerset(relation_dom(sK2))) = empty_set )
| ( apply(relation_dom(sK0),sK12(sK1,relation_dom(sK0),apply(sK0,sK17(relation_dom(sK2))),sK5(relation_dom(sK2),apply(sK2,sK17(relation_dom(sK2)))))) = sK5(relation_dom(sK2),apply(sK2,sK17(relation_dom(sK2)))) )
| ~ function(relation_dom(sK0))
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(apply(sK2,sK17(relation_dom(sK2))),relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_3019,c_10138]) ).
tcf(c_13514,plain,
( ( sK17(powerset(relation_dom(sK2))) = empty_set )
| ( apply(relation_dom(sK0),sK12(sK1,relation_dom(sK0),apply(sK0,sK17(relation_dom(sK2))),apply(relation_dom(sK2),apply(sK2,sK17(relation_dom(sK2)))))) = apply(relation_dom(sK2),apply(sK2,sK17(relation_dom(sK2)))) )
| ~ function(relation_dom(sK0))
| ~ function(relation_dom(sK2))
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(apply(sK2,sK17(relation_dom(sK2))),relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_3551,c_10138]) ).
tcf(c_13623,plain,
! [X0: $i] :
( ( relation_dom(sK2) = empty_set )
| ( apply(sK0,ordered_pair(apply(sK2,sK3(empty_set,relation_dom(sK2))),X0)) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(apply(sK2,sK3(empty_set,relation_dom(sK2))),X0))) = empty_set )
| ( apply(relation_dom(sK2),sK12(sK1,relation_dom(sK2),apply(sK0,sK3(empty_set,relation_dom(sK2))),X0)) = X0 )
| ~ function(relation_dom(sK2))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK3(empty_set,relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_4011,c_8687]) ).
tcf(c_13624,plain,
! [X0: $i] :
( ( relation_dom(sK2) = empty_set )
| ( apply(sK0,ordered_pair(apply(sK2,sK3(empty_set,relation_dom(sK2))),X0)) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(apply(sK2,sK3(empty_set,relation_dom(sK2))),X0))) = empty_set )
| ( apply(relation_dom(sK0),sK12(sK1,relation_dom(sK0),apply(sK0,sK3(empty_set,relation_dom(sK2))),X0)) = X0 )
| ~ function(relation_dom(sK0))
| ~ relation(relation_dom(sK0))
| ~ in(apply(sK0,sK3(empty_set,relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_4110,c_8687]) ).
tcf(c_13625,plain,
! [X0: $i] :
( ( relation_dom(sK2) = empty_set )
| ( apply(sK2,ordered_pair(apply(sK2,sK3(empty_set,relation_dom(sK2))),X0)) = empty_set )
| ( apply(relation_dom(sK0),sK12(sK1,relation_dom(sK0),apply(sK0,sK3(empty_set,relation_dom(sK2))),X0)) = X0 )
| ~ function(relation_dom(sK0))
| ~ relation(relation_dom(sK0))
| ~ in(apply(sK0,sK3(empty_set,relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_3449,c_8687]) ).
tcf(c_13626,plain,
! [X0: $i] :
( ( relation_dom(sK2) = empty_set )
| ( apply(X0,sK12(sK1,X0,apply(sK0,sK3(empty_set,relation_dom(sK2))),sK5(X0,apply(sK2,sK3(empty_set,relation_dom(sK2)))))) = sK5(X0,apply(sK2,sK3(empty_set,relation_dom(sK2)))) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(apply(sK0,sK3(empty_set,relation_dom(sK2))),relation_dom(sK1))
| ~ in(apply(sK2,sK3(empty_set,relation_dom(sK2))),relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_71,c_8687]) ).
tcf(c_13627,plain,
! [X0: $i] :
( ( relation_dom(sK2) = empty_set )
| ( apply(X0,sK12(sK1,X0,apply(sK0,sK3(empty_set,relation_dom(sK2))),apply(X0,apply(sK2,sK3(empty_set,relation_dom(sK2)))))) = apply(X0,apply(sK2,sK3(empty_set,relation_dom(sK2)))) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(apply(sK0,sK3(empty_set,relation_dom(sK2))),relation_dom(sK1))
| ~ in(apply(sK2,sK3(empty_set,relation_dom(sK2))),relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_73,c_8687]) ).
tcf(c_13628,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK2) = empty_set )
| ( apply(X0,ordered_pair(apply(sK2,sK3(empty_set,relation_dom(sK2))),X1)) = empty_set )
| ( apply(relation_dom(X0),sK12(sK1,relation_dom(X0),apply(sK0,sK3(empty_set,relation_dom(sK2))),X1)) = X1 )
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom(X0))
| ~ relation(relation_dom(X0))
| ~ in(apply(sK0,sK3(empty_set,relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_75,c_8687]) ).
tcf(c_13629,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(sK2) = empty_set )
| ( apply(X1,sK12(sK1,X1,apply(sK0,sK3(empty_set,relation_dom(sK2))),sK12(X1,X2,apply(sK2,sK3(empty_set,relation_dom(sK2))),X0))) = sK12(X1,X2,apply(sK2,sK3(empty_set,relation_dom(sK2))),X0) )
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(apply(sK0,sK3(empty_set,relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK3(empty_set,relation_dom(sK2))),X0),relation_composition(X1,X2)) ),
inference(superposition,[status(thm)],[c_301,c_8687]) ).
tcf(c_13630,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK2) = empty_set )
| ( apply(relation_dom(sK0),sK12(sK1,relation_dom(sK0),apply(sK0,sK3(empty_set,relation_dom(sK2))),sK12(relation_dom(sK2),X1,apply(sK2,sK3(empty_set,relation_dom(sK2))),X0))) = sK12(relation_dom(sK2),X1,apply(sK2,sK3(empty_set,relation_dom(sK2))),X0) )
| ~ relation(X1)
| ~ function(relation_dom(sK0))
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK3(empty_set,relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK3(empty_set,relation_dom(sK2))),X0),relation_composition(relation_dom(sK2),X1)) ),
inference(superposition,[status(thm)],[c_2283,c_8687]) ).
tcf(c_13631,plain,
( ( relation_dom(sK2) = empty_set )
| ( apply(relation_dom(sK0),sK12(sK1,relation_dom(sK0),apply(sK0,sK3(empty_set,relation_dom(sK2))),sK5(relation_dom(sK2),apply(sK2,sK3(empty_set,relation_dom(sK2)))))) = sK5(relation_dom(sK2),apply(sK2,sK3(empty_set,relation_dom(sK2)))) )
| ~ function(relation_dom(sK0))
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK3(empty_set,relation_dom(sK2))),relation_dom(sK1))
| ~ in(apply(sK2,sK3(empty_set,relation_dom(sK2))),relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_3019,c_8687]) ).
tcf(c_13632,plain,
( ( relation_dom(sK2) = empty_set )
| ( apply(relation_dom(sK0),sK12(sK1,relation_dom(sK0),apply(sK0,sK3(empty_set,relation_dom(sK2))),apply(relation_dom(sK2),apply(sK2,sK3(empty_set,relation_dom(sK2)))))) = apply(relation_dom(sK2),apply(sK2,sK3(empty_set,relation_dom(sK2)))) )
| ~ function(relation_dom(sK0))
| ~ function(relation_dom(sK2))
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK3(empty_set,relation_dom(sK2))),relation_dom(sK1))
| ~ in(apply(sK2,sK3(empty_set,relation_dom(sK2))),relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_3551,c_8687]) ).
tcf(c_13719,plain,
( in(ordered_pair(apply(sK0,sK17(relation_dom(sK2))),apply(sK2,sK17(relation_dom(sK2)))),sK1)
| ( sK17(powerset(relation_dom(relation_dom(sK2)))) = empty_set )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_9855,c_73]) ).
tcf(c_13720,plain,
( in(ordered_pair(apply(sK0,sK17(relation_dom(sK2))),apply(sK2,sK17(relation_dom(sK2)))),sK1)
| ( sK17(powerset(relation_dom(relation_dom(sK2)))) = empty_set )
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_13719,c_57,c_56]) ).
tcf(c_13724,plain,
( empty(sK16(powerset(empty_set)))
| ~ in(sK16(powerset(empty_set)),empty_set) ),
inference(superposition,[status(thm)],[c_12880,c_2427]) ).
tcf(c_13725,plain,
( empty(sK16(powerset(empty_set)))
| in(empty_set,sK16(powerset(empty_set))) ),
inference(superposition,[status(thm)],[c_12880,c_2361]) ).
tcf(c_13726,plain,
element(empty_set,sK16(powerset(empty_set))),
inference(superposition,[status(thm)],[c_12880,c_105]) ).
tcf(c_13729,plain,
( empty(powerset(empty_set))
| element(empty_set,powerset(empty_set)) ),
inference(superposition,[status(thm)],[c_12880,c_11924]) ).
tcf(c_13746,plain,
! [X0: $i,X1: $i] :
( in(sK3(relation_composition(empty_set,X0),X1),X1)
| ( relation_dom(relation_composition(empty_set,X0)) = X1 )
| ~ relation(X0)
| ~ relation(relation_composition(empty_set,X0)) ),
inference(superposition,[status(thm)],[c_69,c_3821]) ).
tcf(c_13747,plain,
! [X0: $i,X1: $i] :
( ~ relation(X1)
| ~ relation(relation_composition(empty_set,X1))
| ~ in(X0,relation_dom(relation_composition(empty_set,X1))) ),
inference(superposition,[status(thm)],[c_71,c_3821]) ).
tcf(c_13748,plain,
! [X0: $i,X1: $i] :
( ~ relation(X1)
| ~ function(relation_composition(empty_set,X1))
| ~ relation(relation_composition(empty_set,X1))
| ~ in(X0,relation_dom(relation_composition(empty_set,X1))) ),
inference(superposition,[status(thm)],[c_73,c_3821]) ).
tcf(c_13749,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(ordered_pair(sK11(X1,X2,relation_composition(empty_set,X0)),sK10(X1,X2,relation_composition(empty_set,X0))),X2)
| ( relation_composition(X1,X2) = relation_composition(empty_set,X0) )
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_composition(empty_set,X0)) ),
inference(superposition,[status(thm)],[c_93,c_3821]) ).
tcf(c_13750,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(ordered_pair(sK9(X1,X2,relation_composition(empty_set,X0)),sK11(X1,X2,relation_composition(empty_set,X0))),X1)
| ( relation_composition(X1,X2) = relation_composition(empty_set,X0) )
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_composition(empty_set,X0)) ),
inference(superposition,[status(thm)],[c_92,c_3821]) ).
tcf(c_13751,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(ordered_pair(sK9(relation_composition(empty_set,X0),X1,X2),sK10(relation_composition(empty_set,X0),X1,X2)),X2)
| ( relation_composition(relation_composition(empty_set,X0),X1) = X2 )
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_composition(empty_set,X0)) ),
inference(superposition,[status(thm)],[c_92,c_3821]) ).
tcf(c_13752,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(ordered_pair(sK9(X1,relation_composition(empty_set,X0),X2),sK10(X1,relation_composition(empty_set,X0),X2)),X2)
| ( relation_composition(X1,relation_composition(empty_set,X0)) = X2 )
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_composition(empty_set,X0)) ),
inference(superposition,[status(thm)],[c_93,c_3821]) ).
tcf(c_13753,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ relation(X3)
| ~ relation(X2)
| ~ relation(relation_composition(empty_set,X2))
| ~ in(ordered_pair(X0,X1),relation_composition(relation_composition(empty_set,X2),X3)) ),
inference(superposition,[status(thm)],[c_301,c_3821]) ).
tcf(c_13754,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ relation(X3)
| ~ relation(X2)
| ~ relation(relation_composition(empty_set,X3))
| ~ in(ordered_pair(X0,X1),relation_composition(X2,relation_composition(empty_set,X3))) ),
inference(superposition,[status(thm)],[c_300,c_3821]) ).
tcf(c_13755,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ relation(empty_set)
| ~ relation(X4)
| ~ relation(X2)
| ~ in(ordered_pair(X1,X3),X4)
| ~ in(ordered_pair(X0,X1),relation_composition(X2,empty_set)) ),
inference(superposition,[status(thm)],[c_2067,c_3821]) ).
tcf(c_13756,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK9(relation_dom(sK2),X1,relation_composition(empty_set,X0)),sK11(relation_dom(sK2),X1,relation_composition(empty_set,X0))),relation_dom(sK0))
| ( relation_composition(relation_dom(sK2),X1) = relation_composition(empty_set,X0) )
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2))
| ~ relation(relation_composition(empty_set,X0)) ),
inference(superposition,[status(thm)],[c_4703,c_3821]) ).
tcf(c_13757,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK9(relation_composition(empty_set,X0),X1,relation_dom(sK2)),sK10(relation_composition(empty_set,X0),X1,relation_dom(sK2))),relation_dom(sK0))
| ( relation_composition(relation_composition(empty_set,X0),X1) = relation_dom(sK2) )
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2))
| ~ relation(relation_composition(empty_set,X0)) ),
inference(superposition,[status(thm)],[c_4725,c_3821]) ).
tcf(c_13758,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK11(X1,relation_dom(sK2),relation_composition(empty_set,X0)),sK10(X1,relation_dom(sK2),relation_composition(empty_set,X0))),relation_dom(sK0))
| ( relation_composition(X1,relation_dom(sK2)) = relation_composition(empty_set,X0) )
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2))
| ~ relation(relation_composition(empty_set,X0)) ),
inference(superposition,[status(thm)],[c_5257,c_3821]) ).
tcf(c_13759,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK9(X1,relation_composition(empty_set,X0),relation_dom(sK2)),sK10(X1,relation_composition(empty_set,X0),relation_dom(sK2))),relation_dom(sK0))
| ( relation_composition(X1,relation_composition(empty_set,X0)) = relation_dom(sK2) )
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2))
| ~ relation(relation_composition(empty_set,X0)) ),
inference(superposition,[status(thm)],[c_5279,c_3821]) ).
tcf(c_13779,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ relation(X4)
| ~ relation(X2)
| ~ in(ordered_pair(X1,X3),X4)
| ~ in(ordered_pair(X0,X1),relation_composition(X2,empty_set)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_13755,c_109]) ).
tcf(c_13919,plain,
( ( apply(sK0,relation_dom(sK0)) = empty_set )
| ( apply(sK2,relation_dom(sK2)) = empty_set )
| ( apply(sK1,apply(sK0,relation_dom(sK0))) = empty_set ) ),
inference(superposition,[status(thm)],[c_4011,c_3889]) ).
tcf(c_13921,plain,
apply(sK2,relation_dom(sK0)) = empty_set,
inference(superposition,[status(thm)],[c_3449,c_3889]) ).
tcf(c_13922,plain,
! [X0: $i] :
( ( apply(sK2,relation_dom(X0)) = empty_set )
| ( apply(X0,relation_dom(sK0)) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_75,c_3889]) ).
tcf(c_13932,plain,
( empty(relation_composition(sK0,sK1))
| ~ empty(sK0)
| ~ relation(sK1) ),
inference(instantiation,[status(thm)],[c_86]) ).
tcf(c_13933,plain,
! [X0: $i,X1: $i] :
( ( apply(sK0,relation_dom(sK0)) = empty_set )
| ( apply(sK1,apply(sK0,relation_dom(sK0))) = empty_set )
| ( apply(X1,sK12(sK1,X1,apply(sK0,relation_dom(sK0)),X0)) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ in(ordered_pair(empty_set,X0),X1) ),
inference(superposition,[status(thm)],[c_13921,c_6526]) ).
tcf(c_13935,plain,
( in(ordered_pair(apply(sK0,relation_dom(sK0)),empty_set),sK1)
| ( apply(sK0,relation_dom(sK0)) = empty_set )
| ( apply(sK1,apply(sK0,relation_dom(sK0))) = empty_set ) ),
inference(superposition,[status(thm)],[c_13921,c_6060]) ).
tcf(c_13937,plain,
( in(ordered_pair(relation_dom(sK0),empty_set),sK2)
| ~ function(sK2)
| ~ relation(sK2)
| ~ in(relation_dom(sK0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_13921,c_73]) ).
tcf(c_13938,plain,
( in(ordered_pair(relation_dom(sK0),empty_set),sK2)
| ~ in(relation_dom(sK0),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_13937,c_55,c_54]) ).
tcf(c_13951,plain,
( empty(relation_composition(sK0,sK1))
| ~ empty(sK1)
| ~ relation(sK0) ),
inference(instantiation,[status(thm)],[c_88]) ).
tcf(c_13971,plain,
( empty(powerset(empty_set))
| element(empty_set,powerset(empty_set))
| empty(sK16(powerset(empty_set))) ),
inference(superposition,[status(thm)],[c_13725,c_2939]) ).
tcf(c_13972,plain,
~ empty(relation_dom(sK0)),
inference(global_subsumption_just,[status(thm)],[c_6284,c_58,c_56,c_54,c_49,c_126,c_2455,c_2565,c_7141,c_13932]) ).
tcf(c_13974,plain,
~ empty(sK0),
inference(superposition,[status(thm)],[c_65,c_13972]) ).
tcf(c_13979,plain,
( ~ in(relation_dom(sK0),relation_dom(sK2))
| ~ in(sK2,ordered_pair(relation_dom(sK0),empty_set)) ),
inference(superposition,[status(thm)],[c_13938,c_64]) ).
tcf(c_13980,plain,
( element(ordered_pair(relation_dom(sK0),empty_set),sK2)
| ~ in(relation_dom(sK0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_13938,c_63]) ).
tcf(c_13981,plain,
( ~ empty(sK2)
| ~ in(relation_dom(sK0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_13938,c_61]) ).
tcf(c_13983,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(relation_dom(sK0),X0),relation_composition(sK2,X1))
| ~ relation(sK2)
| ~ relation(X1)
| ~ in(relation_dom(sK0),relation_dom(sK2))
| ~ in(ordered_pair(empty_set,X0),X1) ),
inference(superposition,[status(thm)],[c_13938,c_299]) ).
tcf(c_13991,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(relation_dom(sK0),X0),relation_composition(sK2,X1))
| ~ relation(X1)
| ~ in(relation_dom(sK0),relation_dom(sK2))
| ~ in(ordered_pair(empty_set,X0),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_13983,c_54]) ).
tcf(c_14005,plain,
! [X0: $i,X1: $i] :
( ~ relation(X0)
| ~ in(relation_dom(sK0),relation_dom(sK2))
| ~ in(ordered_pair(empty_set,X1),X0)
| ~ in(relation_composition(sK2,X0),ordered_pair(relation_dom(sK0),X1)) ),
inference(superposition,[status(thm)],[c_13991,c_64]) ).
tcf(c_14006,plain,
! [X0: $i,X1: $i] :
( element(ordered_pair(relation_dom(sK0),X0),relation_composition(sK2,X1))
| ~ relation(X1)
| ~ in(relation_dom(sK0),relation_dom(sK2))
| ~ in(ordered_pair(empty_set,X0),X1) ),
inference(superposition,[status(thm)],[c_13991,c_63]) ).
tcf(c_14007,plain,
! [X0: $i,X1: $i] :
( ~ relation(X1)
| ~ empty(relation_composition(sK2,X1))
| ~ in(relation_dom(sK0),relation_dom(sK2))
| ~ in(ordered_pair(empty_set,X0),X1) ),
inference(superposition,[status(thm)],[c_13991,c_61]) ).
tcf(c_14008,plain,
! [X0: $i,X1: $i] :
( in(relation_dom(sK0),relation_dom(relation_composition(sK2,X1)))
| ~ relation(X1)
| ~ relation(relation_composition(sK2,X1))
| ~ in(relation_dom(sK0),relation_dom(sK2))
| ~ in(ordered_pair(empty_set,X0),X1) ),
inference(superposition,[status(thm)],[c_13991,c_70]) ).
tcf(c_14009,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(ordered_pair(relation_dom(sK0),X1),relation_composition(relation_composition(sK2,X3),X2))
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(relation_composition(sK2,X3))
| ~ in(relation_dom(sK0),relation_dom(sK2))
| ~ in(ordered_pair(empty_set,X0),X3)
| ~ in(ordered_pair(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_13991,c_299]) ).
tcf(c_14010,plain,
! [X0: $i,X1: $i] :
( ( apply(relation_composition(sK2,X1),relation_dom(sK0)) = X0 )
| ~ relation(X1)
| ~ function(relation_composition(sK2,X1))
| ~ relation(relation_composition(sK2,X1))
| ~ in(relation_dom(sK0),relation_dom(sK2))
| ~ in(ordered_pair(empty_set,X0),X1) ),
inference(superposition,[status(thm)],[c_13991,c_152]) ).
tcf(c_14011,plain,
! [X0: $i,X1: $i] :
( ( apply(X1,sK12(sK2,X1,relation_dom(sK0),X0)) = X0 )
| ~ relation(sK2)
| ~ function(X1)
| ~ relation(X1)
| ~ in(relation_dom(sK0),relation_dom(sK2))
| ~ in(ordered_pair(empty_set,X0),X1) ),
inference(superposition,[status(thm)],[c_13991,c_2068]) ).
tcf(c_14012,plain,
! [X0: $i] :
( ~ relation(sK2)
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2))
| ~ in(relation_dom(sK0),relation_dom(sK2))
| ~ in(ordered_pair(empty_set,X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_13991,c_2063]) ).
tcf(c_14013,plain,
! [X0: $i] :
( ( apply(sK1,apply(sK0,ordered_pair(sK12(sK2,relation_dom(sK2),relation_dom(sK0),X0),X0))) = apply(sK2,ordered_pair(sK12(sK2,relation_dom(sK2),relation_dom(sK0),X0),X0)) )
| ~ relation(sK2)
| ~ relation(relation_dom(sK2))
| ~ in(relation_dom(sK0),relation_dom(sK2))
| ~ in(ordered_pair(empty_set,X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_13991,c_2064]) ).
tcf(c_14014,plain,
! [X0: $i] :
( ~ relation(empty_set)
| ~ relation(sK2)
| ~ in(relation_dom(sK0),relation_dom(sK2))
| ~ in(ordered_pair(empty_set,X0),empty_set) ),
inference(superposition,[status(thm)],[c_13991,c_3818]) ).
tcf(c_14023,plain,
! [X0: $i] :
( ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2))
| ~ in(relation_dom(sK0),relation_dom(sK2))
| ~ in(ordered_pair(empty_set,X0),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14012,c_54]) ).
tcf(c_14037,plain,
! [X0: $i,X1: $i] :
( ( apply(X1,sK12(sK2,X1,relation_dom(sK0),X0)) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ in(relation_dom(sK0),relation_dom(sK2))
| ~ in(ordered_pair(empty_set,X0),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14011,c_54]) ).
tcf(c_14056,plain,
! [X0: $i] :
( ( apply(sK1,apply(sK0,ordered_pair(sK12(sK2,relation_dom(sK2),relation_dom(sK0),X0),X0))) = apply(sK2,ordered_pair(sK12(sK2,relation_dom(sK2),relation_dom(sK0),X0),X0)) )
| ~ relation(relation_dom(sK2))
| ~ in(relation_dom(sK0),relation_dom(sK2))
| ~ in(ordered_pair(empty_set,X0),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14013,c_54]) ).
tcf(c_14070,plain,
( ~ empty(relation_dom(sK1))
| ~ in(relation_dom(sK0),relation_dom(sK2)) ),
inference(global_subsumption_just,[status(thm)],[c_14023,c_54,c_2424,c_7141,c_13981]) ).
tcf(c_14082,plain,
! [X0: $i] :
( ( apply(sK0,ordered_pair(empty_set,X0)) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(empty_set,X0))) = empty_set )
| ( apply(relation_dom(sK2),sK12(sK2,relation_dom(sK2),relation_dom(sK0),X0)) = X0 )
| ~ function(relation_dom(sK2))
| ~ relation(relation_dom(sK2))
| ~ in(relation_dom(sK0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4011,c_14037]) ).
tcf(c_14083,plain,
! [X0: $i] :
( ( apply(sK0,ordered_pair(empty_set,X0)) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(empty_set,X0))) = empty_set )
| ( apply(relation_dom(sK0),sK12(sK2,relation_dom(sK0),relation_dom(sK0),X0)) = X0 )
| ~ function(relation_dom(sK0))
| ~ relation(relation_dom(sK0))
| ~ in(relation_dom(sK0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4110,c_14037]) ).
tcf(c_14084,plain,
! [X0: $i] :
( ( apply(sK2,ordered_pair(empty_set,X0)) = empty_set )
| ( apply(relation_dom(sK0),sK12(sK2,relation_dom(sK0),relation_dom(sK0),X0)) = X0 )
| ~ function(relation_dom(sK0))
| ~ relation(relation_dom(sK0))
| ~ in(relation_dom(sK0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_3449,c_14037]) ).
tcf(c_14085,plain,
! [X0: $i] :
( ( apply(X0,sK12(sK2,X0,relation_dom(sK0),sK5(X0,empty_set))) = sK5(X0,empty_set) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(empty_set,relation_dom(X0))
| ~ in(relation_dom(sK0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_71,c_14037]) ).
tcf(c_14086,plain,
! [X0: $i] :
( ( apply(X0,sK12(sK2,X0,relation_dom(sK0),apply(X0,empty_set))) = apply(X0,empty_set) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(empty_set,relation_dom(X0))
| ~ in(relation_dom(sK0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_73,c_14037]) ).
tcf(c_14087,plain,
! [X0: $i,X1: $i] :
( ( apply(X0,ordered_pair(empty_set,X1)) = empty_set )
| ( apply(relation_dom(X0),sK12(sK2,relation_dom(X0),relation_dom(sK0),X1)) = X1 )
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom(X0))
| ~ relation(relation_dom(X0))
| ~ in(relation_dom(sK0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_75,c_14037]) ).
tcf(c_14088,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(X1,sK12(sK2,X1,relation_dom(sK0),sK12(X1,X2,empty_set,X0))) = sK12(X1,X2,empty_set,X0) )
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(relation_dom(sK0),relation_dom(sK2))
| ~ in(ordered_pair(empty_set,X0),relation_composition(X1,X2)) ),
inference(superposition,[status(thm)],[c_301,c_14037]) ).
tcf(c_14089,plain,
! [X0: $i,X1: $i] :
( ( apply(relation_dom(sK0),sK12(sK2,relation_dom(sK0),relation_dom(sK0),sK12(relation_dom(sK2),X1,empty_set,X0))) = sK12(relation_dom(sK2),X1,empty_set,X0) )
| ~ relation(X1)
| ~ function(relation_dom(sK0))
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(relation_dom(sK0),relation_dom(sK2))
| ~ in(ordered_pair(empty_set,X0),relation_composition(relation_dom(sK2),X1)) ),
inference(superposition,[status(thm)],[c_2283,c_14037]) ).
tcf(c_14090,plain,
( ( apply(relation_dom(sK0),sK12(sK2,relation_dom(sK0),relation_dom(sK0),sK5(relation_dom(sK2),empty_set))) = sK5(relation_dom(sK2),empty_set) )
| ~ function(relation_dom(sK0))
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(empty_set,relation_dom(relation_dom(sK2)))
| ~ in(relation_dom(sK0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_3019,c_14037]) ).
tcf(c_14091,plain,
( ( apply(relation_dom(sK0),sK12(sK2,relation_dom(sK0),relation_dom(sK0),apply(relation_dom(sK2),empty_set))) = apply(relation_dom(sK2),empty_set) )
| ~ function(relation_dom(sK0))
| ~ function(relation_dom(sK2))
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(empty_set,relation_dom(relation_dom(sK2)))
| ~ in(relation_dom(sK0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_3551,c_14037]) ).
tcf(c_14166,plain,
( ( sK17(powerset(relation_dom(relation_dom(sK2)))) = empty_set )
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(sK1,ordered_pair(apply(sK0,sK17(relation_dom(sK2))),apply(sK2,sK17(relation_dom(sK2))))) ),
inference(superposition,[status(thm)],[c_13720,c_64]) ).
tcf(c_14167,plain,
( element(ordered_pair(apply(sK0,sK17(relation_dom(sK2))),apply(sK2,sK17(relation_dom(sK2)))),sK1)
| ( sK17(powerset(relation_dom(relation_dom(sK2)))) = empty_set )
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_13720,c_63]) ).
tcf(c_14170,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(apply(sK0,sK17(relation_dom(sK2))),X0),relation_composition(sK1,X1))
| ( sK17(powerset(relation_dom(relation_dom(sK2)))) = empty_set )
| ~ relation(sK1)
| ~ relation(X1)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),X1) ),
inference(superposition,[status(thm)],[c_13720,c_299]) ).
tcf(c_14178,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(apply(sK0,sK17(relation_dom(sK2))),X0),relation_composition(sK1,X1))
| ( sK17(powerset(relation_dom(relation_dom(sK2)))) = empty_set )
| ~ relation(X1)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14170,c_56]) ).
tcf(c_14195,plain,
! [X0: $i,X1: $i] :
( ( sK17(powerset(relation_dom(relation_dom(sK2)))) = empty_set )
| ~ relation(X0)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X1),X0)
| ~ in(relation_composition(sK1,X0),ordered_pair(apply(sK0,sK17(relation_dom(sK2))),X1)) ),
inference(superposition,[status(thm)],[c_14178,c_64]) ).
tcf(c_14196,plain,
! [X0: $i,X1: $i] :
( element(ordered_pair(apply(sK0,sK17(relation_dom(sK2))),X0),relation_composition(sK1,X1))
| ( sK17(powerset(relation_dom(relation_dom(sK2)))) = empty_set )
| ~ relation(X1)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),X1) ),
inference(superposition,[status(thm)],[c_14178,c_63]) ).
tcf(c_14197,plain,
! [X0: $i,X1: $i] :
( ( sK17(powerset(relation_dom(relation_dom(sK2)))) = empty_set )
| ~ relation(X1)
| ~ empty(relation_composition(sK1,X1))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),X1) ),
inference(superposition,[status(thm)],[c_14178,c_61]) ).
tcf(c_14198,plain,
! [X0: $i,X1: $i] :
( in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(relation_composition(sK1,X1)))
| ( sK17(powerset(relation_dom(relation_dom(sK2)))) = empty_set )
| ~ relation(X1)
| ~ relation(relation_composition(sK1,X1))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),X1) ),
inference(superposition,[status(thm)],[c_14178,c_70]) ).
tcf(c_14199,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(ordered_pair(apply(sK0,sK17(relation_dom(sK2))),X2),relation_composition(relation_composition(sK1,X1),X3))
| ( sK17(powerset(relation_dom(relation_dom(sK2)))) = empty_set )
| ~ relation(X3)
| ~ relation(X1)
| ~ relation(relation_composition(sK1,X1))
| ~ in(ordered_pair(X0,X2),X3)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),X1) ),
inference(superposition,[status(thm)],[c_14178,c_299]) ).
tcf(c_14200,plain,
! [X0: $i,X1: $i] :
( ( sK17(powerset(relation_dom(relation_dom(sK2)))) = empty_set )
| ( apply(relation_composition(sK1,X1),apply(sK0,sK17(relation_dom(sK2)))) = X0 )
| ~ relation(X1)
| ~ function(relation_composition(sK1,X1))
| ~ relation(relation_composition(sK1,X1))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),X1) ),
inference(superposition,[status(thm)],[c_14178,c_152]) ).
tcf(c_14201,plain,
! [X0: $i,X1: $i] :
( ( sK17(powerset(relation_dom(relation_dom(sK2)))) = empty_set )
| ( apply(X1,sK12(sK1,X1,apply(sK0,sK17(relation_dom(sK2))),X0)) = X0 )
| ~ relation(sK1)
| ~ function(X1)
| ~ relation(X1)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),X1) ),
inference(superposition,[status(thm)],[c_14178,c_2068]) ).
tcf(c_14202,plain,
! [X0: $i] :
( ( sK17(powerset(relation_dom(relation_dom(sK2)))) = empty_set )
| ~ relation(sK1)
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_14178,c_2063]) ).
tcf(c_14203,plain,
! [X0: $i] :
( ( sK17(powerset(relation_dom(relation_dom(sK2)))) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,sK17(relation_dom(sK2))),X0),X0))) = apply(sK2,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,sK17(relation_dom(sK2))),X0),X0)) )
| ~ relation(sK1)
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_14178,c_2064]) ).
tcf(c_14204,plain,
! [X0: $i] :
( ( sK17(powerset(relation_dom(relation_dom(sK2)))) = empty_set )
| ~ relation(empty_set)
| ~ relation(sK1)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),empty_set) ),
inference(superposition,[status(thm)],[c_14178,c_3818]) ).
tcf(c_14210,plain,
! [X0: $i] :
( ( sK17(powerset(relation_dom(relation_dom(sK2)))) = empty_set )
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14202,c_56]) ).
tcf(c_14232,plain,
! [X0: $i,X1: $i] :
( ( sK17(powerset(relation_dom(relation_dom(sK2)))) = empty_set )
| ( apply(X1,sK12(sK1,X1,apply(sK0,sK17(relation_dom(sK2))),X0)) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14201,c_56]) ).
tcf(c_14254,plain,
! [X0: $i] :
( ( sK17(powerset(relation_dom(relation_dom(sK2)))) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,sK17(relation_dom(sK2))),X0),X0))) = apply(sK2,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,sK17(relation_dom(sK2))),X0),X0)) )
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14203,c_56]) ).
tcf(c_14277,plain,
! [X0: $i] :
( ( apply(sK0,ordered_pair(empty_set,X0)) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(empty_set,X0))) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(sK12(sK2,relation_dom(sK2),relation_dom(sK0),X0),X0))) = apply(sK2,ordered_pair(sK12(sK2,relation_dom(sK2),relation_dom(sK0),X0),X0)) )
| ~ relation(relation_dom(sK2))
| ~ in(relation_dom(sK0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4011,c_14056]) ).
tcf(c_14278,plain,
( ( apply(sK1,apply(sK0,ordered_pair(sK12(sK2,relation_dom(sK2),relation_dom(sK0),sK5(relation_dom(sK2),empty_set)),sK5(relation_dom(sK2),empty_set)))) = apply(sK2,ordered_pair(sK12(sK2,relation_dom(sK2),relation_dom(sK0),sK5(relation_dom(sK2),empty_set)),sK5(relation_dom(sK2),empty_set))) )
| ~ relation(relation_dom(sK2))
| ~ in(empty_set,relation_dom(relation_dom(sK2)))
| ~ in(relation_dom(sK0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_71,c_14056]) ).
tcf(c_14279,plain,
( ( apply(sK1,apply(sK0,ordered_pair(sK12(sK2,relation_dom(sK2),relation_dom(sK0),apply(relation_dom(sK2),empty_set)),apply(relation_dom(sK2),empty_set)))) = apply(sK2,ordered_pair(sK12(sK2,relation_dom(sK2),relation_dom(sK0),apply(relation_dom(sK2),empty_set)),apply(relation_dom(sK2),empty_set))) )
| ~ function(relation_dom(sK2))
| ~ relation(relation_dom(sK2))
| ~ in(empty_set,relation_dom(relation_dom(sK2)))
| ~ in(relation_dom(sK0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_73,c_14056]) ).
tcf(c_14280,plain,
! [X0: $i] :
( ( apply(sK2,ordered_pair(empty_set,X0)) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(sK12(sK2,relation_dom(sK2),relation_dom(sK0),X0),X0))) = apply(sK2,ordered_pair(sK12(sK2,relation_dom(sK2),relation_dom(sK0),X0),X0)) )
| ~ function(sK2)
| ~ relation(sK2)
| ~ relation(relation_dom(sK2))
| ~ in(relation_dom(sK0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_75,c_14056]) ).
tcf(c_14281,plain,
! [X0: $i,X1: $i] :
( ( apply(sK1,apply(sK0,ordered_pair(sK12(sK2,relation_dom(sK2),relation_dom(sK0),sK12(relation_dom(sK2),X1,empty_set,X0)),sK12(relation_dom(sK2),X1,empty_set,X0)))) = apply(sK2,ordered_pair(sK12(sK2,relation_dom(sK2),relation_dom(sK0),sK12(relation_dom(sK2),X1,empty_set,X0)),sK12(relation_dom(sK2),X1,empty_set,X0))) )
| ~ relation(X1)
| ~ relation(relation_dom(sK2))
| ~ in(relation_dom(sK0),relation_dom(sK2))
| ~ in(ordered_pair(empty_set,X0),relation_composition(relation_dom(sK2),X1)) ),
inference(superposition,[status(thm)],[c_301,c_14056]) ).
tcf(c_14282,plain,
! [X0: $i] :
( ( apply(sK2,ordered_pair(empty_set,X0)) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(sK12(sK2,relation_dom(sK2),relation_dom(sK0),X0),X0))) = apply(sK2,ordered_pair(sK12(sK2,relation_dom(sK2),relation_dom(sK0),X0),X0)) )
| ~ relation(relation_dom(sK2))
| ~ in(relation_dom(sK0),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14280,c_55,c_54]) ).
tcf(c_14313,plain,
( in(ordered_pair(apply(sK0,sK17(relation_dom(sK2))),apply(sK2,sK17(relation_dom(sK2)))),sK1)
| ( relation_dom(sK17(powerset(relation_dom(sK2)))) = empty_set )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_9982,c_73]) ).
tcf(c_14314,plain,
( in(ordered_pair(apply(sK0,sK17(relation_dom(sK2))),apply(sK2,sK17(relation_dom(sK2)))),sK1)
| ( relation_dom(sK17(powerset(relation_dom(sK2)))) = empty_set )
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14313,c_57,c_56]) ).
tcf(c_14322,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_65,c_9793]) ).
tcf(c_14323,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_composition(X1,X0))))) = empty_set )
| ~ empty(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_86,c_9793]) ).
tcf(c_14324,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_composition(X0,X1))))) = empty_set )
| ~ empty(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_88,c_9793]) ).
tcf(c_14325,plain,
relation_dom(relation_dom(relation_dom(relation_dom(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_110,c_9793]) ).
tcf(c_14326,plain,
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK2))))) = empty_set )
| ( apply(sK1,apply(sK0,sK17(sK16(relation_dom(sK2))))) = apply(sK2,sK17(sK16(relation_dom(sK2)))) ) ),
inference(superposition,[status(thm)],[c_11951,c_9793]) ).
tcf(c_14327,plain,
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK2))))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_2570,c_9793]) ).
tcf(c_14328,plain,
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK2))))) = empty_set )
| ( apply(sK1,apply(sK0,sK17(relation_dom(sK2)))) = apply(sK2,sK17(relation_dom(sK2))) ) ),
inference(superposition,[status(thm)],[c_2425,c_9793]) ).
tcf(c_14331,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK17(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6912,c_9793]) ).
tcf(c_14332,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK17(sK16(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12308,c_9793]) ).
tcf(c_14356,plain,
! [X0: $i] :
( ( sK17(powerset(relation_dom(relation_dom(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_65,c_9849]) ).
tcf(c_14357,plain,
! [X0: $i,X1: $i] :
( ( sK17(powerset(relation_dom(relation_dom(relation_composition(X1,X0))))) = empty_set )
| ~ empty(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_86,c_9849]) ).
tcf(c_14358,plain,
! [X0: $i,X1: $i] :
( ( sK17(powerset(relation_dom(relation_dom(relation_composition(X0,X1))))) = empty_set )
| ~ empty(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_88,c_9849]) ).
tcf(c_14359,plain,
sK17(powerset(relation_dom(relation_dom(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_110,c_9849]) ).
tcf(c_14360,plain,
( ( sK17(powerset(relation_dom(relation_dom(relation_dom(sK2))))) = empty_set )
| ( apply(sK1,apply(sK0,sK17(sK16(relation_dom(sK2))))) = apply(sK2,sK17(sK16(relation_dom(sK2)))) ) ),
inference(superposition,[status(thm)],[c_11951,c_9849]) ).
tcf(c_14361,plain,
( ( sK17(powerset(relation_dom(relation_dom(relation_dom(sK2))))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_2570,c_9849]) ).
tcf(c_14362,plain,
( ( sK17(powerset(relation_dom(relation_dom(relation_dom(sK2))))) = empty_set )
| ( apply(sK1,apply(sK0,sK17(relation_dom(sK2)))) = apply(sK2,sK17(relation_dom(sK2))) ) ),
inference(superposition,[status(thm)],[c_2425,c_9849]) ).
tcf(c_14365,plain,
! [X0: $i] :
( ( sK17(powerset(relation_dom(relation_dom(sK17(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6912,c_9849]) ).
tcf(c_14366,plain,
! [X0: $i] :
( ( sK17(powerset(relation_dom(relation_dom(sK17(sK16(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12308,c_9849]) ).
tcf(c_14390,plain,
! [X0: $i] :
( ( relation_dom(sK17(powerset(relation_dom(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_65,c_9976]) ).
tcf(c_14391,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK17(powerset(relation_dom(relation_composition(X1,X0))))) = empty_set )
| ~ empty(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_86,c_9976]) ).
tcf(c_14392,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK17(powerset(relation_dom(relation_composition(X0,X1))))) = empty_set )
| ~ empty(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_88,c_9976]) ).
tcf(c_14393,plain,
relation_dom(sK17(powerset(relation_dom(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_110,c_9976]) ).
tcf(c_14394,plain,
( ( relation_dom(sK17(powerset(relation_dom(relation_dom(sK2))))) = empty_set )
| ( apply(sK1,apply(sK0,sK17(sK16(relation_dom(sK2))))) = apply(sK2,sK17(sK16(relation_dom(sK2)))) ) ),
inference(superposition,[status(thm)],[c_11951,c_9976]) ).
tcf(c_14395,plain,
( ( relation_dom(sK17(powerset(relation_dom(relation_dom(sK2))))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_2570,c_9976]) ).
tcf(c_14396,plain,
( ( relation_dom(sK17(powerset(relation_dom(relation_dom(sK2))))) = empty_set )
| ( apply(sK1,apply(sK0,sK17(relation_dom(sK2)))) = apply(sK2,sK17(relation_dom(sK2))) ) ),
inference(superposition,[status(thm)],[c_2425,c_9976]) ).
tcf(c_14399,plain,
! [X0: $i] :
( ( relation_dom(sK17(powerset(relation_dom(sK17(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6912,c_9976]) ).
tcf(c_14400,plain,
! [X0: $i] :
( ( relation_dom(sK17(powerset(relation_dom(sK17(sK16(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12308,c_9976]) ).
tcf(c_14435,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK17(powerset(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_65,c_7236]) ).
tcf(c_14436,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK17(powerset(relation_composition(X1,X0))))) = empty_set )
| ~ empty(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_86,c_7236]) ).
tcf(c_14437,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK17(powerset(relation_composition(X0,X1))))) = empty_set )
| ~ empty(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_88,c_7236]) ).
tcf(c_14438,plain,
relation_dom(relation_dom(sK17(powerset(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_110,c_7236]) ).
tcf(c_14439,plain,
( ( relation_dom(relation_dom(sK17(powerset(relation_dom(sK2))))) = empty_set )
| ( apply(sK1,apply(sK0,sK17(sK16(relation_dom(sK2))))) = apply(sK2,sK17(sK16(relation_dom(sK2)))) ) ),
inference(superposition,[status(thm)],[c_11951,c_7236]) ).
tcf(c_14440,plain,
( ( relation_dom(relation_dom(sK17(powerset(relation_dom(sK2))))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_2570,c_7236]) ).
tcf(c_14441,plain,
( ( relation_dom(relation_dom(sK17(powerset(relation_dom(sK2))))) = empty_set )
| ( apply(sK1,apply(sK0,sK17(relation_dom(sK2)))) = apply(sK2,sK17(relation_dom(sK2))) ) ),
inference(superposition,[status(thm)],[c_2425,c_7236]) ).
tcf(c_14442,plain,
( ( relation_dom(relation_dom(sK17(powerset(sK2)))) = empty_set )
| ( apply(sK1,apply(sK0,sK17(sK16(relation_dom(sK2))))) = apply(sK2,sK17(sK16(relation_dom(sK2)))) ) ),
inference(superposition,[status(thm)],[c_12039,c_7236]) ).
tcf(c_14443,plain,
( ( relation_dom(relation_dom(sK17(powerset(sK2)))) = empty_set )
| ( apply(sK1,apply(sK0,sK17(relation_dom(sK2)))) = apply(sK2,sK17(relation_dom(sK2))) ) ),
inference(superposition,[status(thm)],[c_2475,c_7236]) ).
tcf(c_14444,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK17(powerset(sK17(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6912,c_7236]) ).
tcf(c_14445,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK17(powerset(sK17(sK16(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12308,c_7236]) ).
tcf(c_14485,plain,
! [X0: $i] :
( ( sK17(powerset(sK17(powerset(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_65,c_7742]) ).
tcf(c_14486,plain,
! [X0: $i,X1: $i] :
( ( sK17(powerset(sK17(powerset(relation_composition(X1,X0))))) = empty_set )
| ~ empty(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_86,c_7742]) ).
tcf(c_14487,plain,
! [X0: $i,X1: $i] :
( ( sK17(powerset(sK17(powerset(relation_composition(X0,X1))))) = empty_set )
| ~ empty(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_88,c_7742]) ).
tcf(c_14488,plain,
sK17(powerset(sK17(powerset(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_110,c_7742]) ).
tcf(c_14489,plain,
( ( sK17(powerset(sK17(powerset(relation_dom(sK2))))) = empty_set )
| ( apply(sK1,apply(sK0,sK17(sK16(relation_dom(sK2))))) = apply(sK2,sK17(sK16(relation_dom(sK2)))) ) ),
inference(superposition,[status(thm)],[c_11951,c_7742]) ).
tcf(c_14490,plain,
( ( sK17(powerset(sK17(powerset(relation_dom(sK2))))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_2570,c_7742]) ).
tcf(c_14491,plain,
( ( sK17(powerset(sK17(powerset(relation_dom(sK2))))) = empty_set )
| ( apply(sK1,apply(sK0,sK17(relation_dom(sK2)))) = apply(sK2,sK17(relation_dom(sK2))) ) ),
inference(superposition,[status(thm)],[c_2425,c_7742]) ).
tcf(c_14492,plain,
( ( sK17(powerset(sK17(powerset(sK2)))) = empty_set )
| ( apply(sK1,apply(sK0,sK17(sK16(relation_dom(sK2))))) = apply(sK2,sK17(sK16(relation_dom(sK2)))) ) ),
inference(superposition,[status(thm)],[c_12039,c_7742]) ).
tcf(c_14493,plain,
( ( sK17(powerset(sK17(powerset(sK2)))) = empty_set )
| ( apply(sK1,apply(sK0,sK17(relation_dom(sK2)))) = apply(sK2,sK17(relation_dom(sK2))) ) ),
inference(superposition,[status(thm)],[c_2475,c_7742]) ).
tcf(c_14494,plain,
! [X0: $i] :
( ( sK17(powerset(sK17(powerset(sK17(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6912,c_7742]) ).
tcf(c_14495,plain,
! [X0: $i] :
( ( sK17(powerset(sK17(powerset(sK17(sK16(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12308,c_7742]) ).
tcf(c_14574,plain,
~ empty(sK1),
inference(global_subsumption_just,[status(thm)],[c_9798,c_58,c_49,c_2565,c_2645,c_13951]) ).
tcf(c_14582,plain,
( ( relation_dom(sK17(powerset(relation_dom(sK2)))) = empty_set )
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(sK1,ordered_pair(apply(sK0,sK17(relation_dom(sK2))),apply(sK2,sK17(relation_dom(sK2))))) ),
inference(superposition,[status(thm)],[c_14314,c_64]) ).
tcf(c_14583,plain,
( element(ordered_pair(apply(sK0,sK17(relation_dom(sK2))),apply(sK2,sK17(relation_dom(sK2)))),sK1)
| ( relation_dom(sK17(powerset(relation_dom(sK2)))) = empty_set )
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_14314,c_63]) ).
tcf(c_14586,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(apply(sK0,sK17(relation_dom(sK2))),X0),relation_composition(sK1,X1))
| ( relation_dom(sK17(powerset(relation_dom(sK2)))) = empty_set )
| ~ relation(sK1)
| ~ relation(X1)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),X1) ),
inference(superposition,[status(thm)],[c_14314,c_299]) ).
tcf(c_14594,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(apply(sK0,sK17(relation_dom(sK2))),X0),relation_composition(sK1,X1))
| ( relation_dom(sK17(powerset(relation_dom(sK2)))) = empty_set )
| ~ relation(X1)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14586,c_56]) ).
tcf(c_14611,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK17(powerset(relation_dom(sK2)))) = empty_set )
| ~ relation(X0)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X1),X0)
| ~ in(relation_composition(sK1,X0),ordered_pair(apply(sK0,sK17(relation_dom(sK2))),X1)) ),
inference(superposition,[status(thm)],[c_14594,c_64]) ).
tcf(c_14612,plain,
! [X0: $i,X1: $i] :
( element(ordered_pair(apply(sK0,sK17(relation_dom(sK2))),X0),relation_composition(sK1,X1))
| ( relation_dom(sK17(powerset(relation_dom(sK2)))) = empty_set )
| ~ relation(X1)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),X1) ),
inference(superposition,[status(thm)],[c_14594,c_63]) ).
tcf(c_14613,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK17(powerset(relation_dom(sK2)))) = empty_set )
| ~ relation(X1)
| ~ empty(relation_composition(sK1,X1))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),X1) ),
inference(superposition,[status(thm)],[c_14594,c_61]) ).
tcf(c_14614,plain,
! [X0: $i,X1: $i] :
( in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(relation_composition(sK1,X1)))
| ( relation_dom(sK17(powerset(relation_dom(sK2)))) = empty_set )
| ~ relation(X1)
| ~ relation(relation_composition(sK1,X1))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),X1) ),
inference(superposition,[status(thm)],[c_14594,c_70]) ).
tcf(c_14615,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(ordered_pair(apply(sK0,sK17(relation_dom(sK2))),X2),relation_composition(relation_composition(sK1,X1),X3))
| ( relation_dom(sK17(powerset(relation_dom(sK2)))) = empty_set )
| ~ relation(X3)
| ~ relation(X1)
| ~ relation(relation_composition(sK1,X1))
| ~ in(ordered_pair(X0,X2),X3)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),X1) ),
inference(superposition,[status(thm)],[c_14594,c_299]) ).
tcf(c_14616,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK17(powerset(relation_dom(sK2)))) = empty_set )
| ( apply(relation_composition(sK1,X1),apply(sK0,sK17(relation_dom(sK2)))) = X0 )
| ~ relation(X1)
| ~ function(relation_composition(sK1,X1))
| ~ relation(relation_composition(sK1,X1))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),X1) ),
inference(superposition,[status(thm)],[c_14594,c_152]) ).
tcf(c_14617,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK17(powerset(relation_dom(sK2)))) = empty_set )
| ( apply(X1,sK12(sK1,X1,apply(sK0,sK17(relation_dom(sK2))),X0)) = X0 )
| ~ relation(sK1)
| ~ function(X1)
| ~ relation(X1)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),X1) ),
inference(superposition,[status(thm)],[c_14594,c_2068]) ).
tcf(c_14618,plain,
! [X0: $i] :
( ( relation_dom(sK17(powerset(relation_dom(sK2)))) = empty_set )
| ~ relation(sK1)
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_14594,c_2063]) ).
tcf(c_14619,plain,
! [X0: $i] :
( ( relation_dom(sK17(powerset(relation_dom(sK2)))) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,sK17(relation_dom(sK2))),X0),X0))) = apply(sK2,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,sK17(relation_dom(sK2))),X0),X0)) )
| ~ relation(sK1)
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_14594,c_2064]) ).
tcf(c_14620,plain,
! [X0: $i] :
( ( relation_dom(sK17(powerset(relation_dom(sK2)))) = empty_set )
| ~ relation(empty_set)
| ~ relation(sK1)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),empty_set) ),
inference(superposition,[status(thm)],[c_14594,c_3818]) ).
tcf(c_14626,plain,
! [X0: $i] :
( ( relation_dom(sK17(powerset(relation_dom(sK2)))) = empty_set )
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14618,c_56]) ).
tcf(c_14648,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK17(powerset(relation_dom(sK2)))) = empty_set )
| ( apply(X1,sK12(sK1,X1,apply(sK0,sK17(relation_dom(sK2))),X0)) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14617,c_56]) ).
tcf(c_14670,plain,
! [X0: $i] :
( ( relation_dom(sK17(powerset(relation_dom(sK2)))) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,sK17(relation_dom(sK2))),X0),X0))) = apply(sK2,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,sK17(relation_dom(sK2))),X0),X0)) )
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14619,c_56]) ).
tcf(c_14693,plain,
! [X0: $i] :
( ( apply(sK0,relation_dom(sK0)) = empty_set )
| ( apply(sK2,ordered_pair(empty_set,X0)) = empty_set )
| ( apply(sK1,apply(sK0,relation_dom(sK0))) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(sK12(sK2,relation_dom(sK2),relation_dom(sK0),X0),X0))) = apply(sK2,ordered_pair(sK12(sK2,relation_dom(sK2),relation_dom(sK0),X0),X0)) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4011,c_14282]) ).
tcf(c_14711,plain,
! [X0: $i] :
( in(ordered_pair(sK9(relation_dom(sK2),X0,relation_dom(sK2)),sK11(relation_dom(sK2),X0,relation_dom(sK2))),relation_dom(sK2))
| in(ordered_pair(sK9(relation_dom(sK2),X0,relation_dom(sK2)),sK10(relation_dom(sK2),X0,relation_dom(sK2))),relation_dom(sK0))
| ( relation_composition(relation_dom(sK2),X0) = relation_dom(sK2) )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(relation_dom(sK2),X0,relation_dom(sK2)),sK11(relation_dom(sK2),X0,relation_dom(sK2))))) = empty_set )
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_9039,c_3475]) ).
tcf(c_14712,plain,
! [X0: $i] :
( in(ordered_pair(sK9(relation_dom(sK2),X0,relation_dom(sK2)),sK10(relation_dom(sK2),X0,relation_dom(sK2))),relation_dom(sK0))
| ( relation_composition(relation_dom(sK2),X0) = relation_dom(sK2) )
| ~ relation(X0)
| ~ relation(relation_dom(sK2))
| ~ in(relation_dom(sK0),ordered_pair(sK9(relation_dom(sK2),X0,relation_dom(sK2)),sK11(relation_dom(sK2),X0,relation_dom(sK2)))) ),
inference(superposition,[status(thm)],[c_9039,c_64]) ).
tcf(c_14713,plain,
! [X0: $i] :
( element(ordered_pair(sK9(relation_dom(sK2),X0,relation_dom(sK2)),sK11(relation_dom(sK2),X0,relation_dom(sK2))),relation_dom(sK0))
| in(ordered_pair(sK9(relation_dom(sK2),X0,relation_dom(sK2)),sK10(relation_dom(sK2),X0,relation_dom(sK2))),relation_dom(sK0))
| ( relation_composition(relation_dom(sK2),X0) = relation_dom(sK2) )
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_9039,c_63]) ).
tcf(c_14715,plain,
! [X0: $i] :
( in(sK9(relation_dom(sK2),X0,relation_dom(sK2)),relation_dom(relation_dom(sK0)))
| in(ordered_pair(sK9(relation_dom(sK2),X0,relation_dom(sK2)),sK10(relation_dom(sK2),X0,relation_dom(sK2))),relation_dom(sK0))
| ( relation_composition(relation_dom(sK2),X0) = relation_dom(sK2) )
| ~ relation(X0)
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_9039,c_70]) ).
tcf(c_14716,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(ordered_pair(sK9(relation_dom(sK2),X0,relation_dom(sK2)),X1),relation_composition(relation_dom(sK0),X2))
| in(ordered_pair(sK9(relation_dom(sK2),X0,relation_dom(sK2)),sK10(relation_dom(sK2),X0,relation_dom(sK2))),relation_dom(sK0))
| ( relation_composition(relation_dom(sK2),X0) = relation_dom(sK2) )
| ~ relation(X2)
| ~ relation(X0)
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(ordered_pair(sK11(relation_dom(sK2),X0,relation_dom(sK2)),X1),X2) ),
inference(superposition,[status(thm)],[c_9039,c_299]) ).
tcf(c_14717,plain,
! [X0: $i] :
( in(ordered_pair(sK9(relation_dom(sK2),X0,relation_dom(sK2)),sK10(relation_dom(sK2),X0,relation_dom(sK2))),relation_dom(sK0))
| ( relation_composition(relation_dom(sK2),X0) = relation_dom(sK2) )
| ( apply(relation_dom(sK0),sK9(relation_dom(sK2),X0,relation_dom(sK2))) = sK11(relation_dom(sK2),X0,relation_dom(sK2)) )
| ~ relation(X0)
| ~ function(relation_dom(sK0))
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_9039,c_152]) ).
tcf(c_14772,plain,
! [X0: $i] :
( in(ordered_pair(sK11(X0,relation_dom(sK2),relation_dom(sK2)),sK10(X0,relation_dom(sK2),relation_dom(sK2))),relation_dom(sK2))
| in(ordered_pair(sK9(X0,relation_dom(sK2),relation_dom(sK2)),sK10(X0,relation_dom(sK2),relation_dom(sK2))),relation_dom(sK0))
| ( relation_composition(X0,relation_dom(sK2)) = relation_dom(sK2) )
| ( apply(sK1,apply(sK0,ordered_pair(sK11(X0,relation_dom(sK2),relation_dom(sK2)),sK10(X0,relation_dom(sK2),relation_dom(sK2))))) = empty_set )
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_10217,c_3475]) ).
tcf(c_14773,plain,
! [X0: $i] :
( in(ordered_pair(sK9(X0,relation_dom(sK2),relation_dom(sK2)),sK10(X0,relation_dom(sK2),relation_dom(sK2))),relation_dom(sK0))
| ( relation_composition(X0,relation_dom(sK2)) = relation_dom(sK2) )
| ~ relation(X0)
| ~ relation(relation_dom(sK2))
| ~ in(relation_dom(sK0),ordered_pair(sK11(X0,relation_dom(sK2),relation_dom(sK2)),sK10(X0,relation_dom(sK2),relation_dom(sK2)))) ),
inference(superposition,[status(thm)],[c_10217,c_64]) ).
tcf(c_14774,plain,
! [X0: $i] :
( element(ordered_pair(sK11(X0,relation_dom(sK2),relation_dom(sK2)),sK10(X0,relation_dom(sK2),relation_dom(sK2))),relation_dom(sK0))
| in(ordered_pair(sK9(X0,relation_dom(sK2),relation_dom(sK2)),sK10(X0,relation_dom(sK2),relation_dom(sK2))),relation_dom(sK0))
| ( relation_composition(X0,relation_dom(sK2)) = relation_dom(sK2) )
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_10217,c_63]) ).
tcf(c_14776,plain,
! [X0: $i] :
( in(sK11(X0,relation_dom(sK2),relation_dom(sK2)),relation_dom(relation_dom(sK0)))
| in(ordered_pair(sK9(X0,relation_dom(sK2),relation_dom(sK2)),sK10(X0,relation_dom(sK2),relation_dom(sK2))),relation_dom(sK0))
| ( relation_composition(X0,relation_dom(sK2)) = relation_dom(sK2) )
| ~ relation(X0)
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_10217,c_70]) ).
tcf(c_14777,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(ordered_pair(sK11(X0,relation_dom(sK2),relation_dom(sK2)),X1),relation_composition(relation_dom(sK0),X2))
| in(ordered_pair(sK9(X0,relation_dom(sK2),relation_dom(sK2)),sK10(X0,relation_dom(sK2),relation_dom(sK2))),relation_dom(sK0))
| ( relation_composition(X0,relation_dom(sK2)) = relation_dom(sK2) )
| ~ relation(X2)
| ~ relation(X0)
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(ordered_pair(sK10(X0,relation_dom(sK2),relation_dom(sK2)),X1),X2) ),
inference(superposition,[status(thm)],[c_10217,c_299]) ).
tcf(c_14778,plain,
! [X0: $i] :
( in(ordered_pair(sK9(X0,relation_dom(sK2),relation_dom(sK2)),sK10(X0,relation_dom(sK2),relation_dom(sK2))),relation_dom(sK0))
| ( relation_composition(X0,relation_dom(sK2)) = relation_dom(sK2) )
| ( apply(relation_dom(sK0),sK11(X0,relation_dom(sK2),relation_dom(sK2))) = sK10(X0,relation_dom(sK2),relation_dom(sK2)) )
| ~ relation(X0)
| ~ function(relation_dom(sK0))
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_10217,c_152]) ).
tcf(c_14847,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK2)))) = empty_set )
| ( apply(sK0,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0)) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0))) = empty_set )
| ( apply(relation_dom(sK2),sK12(sK1,relation_dom(sK2),apply(sK0,sK17(relation_dom(sK2))),X0)) = X0 )
| ~ function(relation_dom(sK2))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_4011,c_13036]) ).
tcf(c_14848,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK2)))) = empty_set )
| ( apply(sK0,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0)) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0))) = empty_set )
| ( apply(relation_dom(sK0),sK12(sK1,relation_dom(sK0),apply(sK0,sK17(relation_dom(sK2))),X0)) = X0 )
| ~ function(relation_dom(sK0))
| ~ relation(relation_dom(sK0))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_4110,c_13036]) ).
tcf(c_14849,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK2)))) = empty_set )
| ( apply(sK2,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0)) = empty_set )
| ( apply(relation_dom(sK0),sK12(sK1,relation_dom(sK0),apply(sK0,sK17(relation_dom(sK2))),X0)) = X0 )
| ~ function(relation_dom(sK0))
| ~ relation(relation_dom(sK0))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_3449,c_13036]) ).
tcf(c_14850,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK2)))) = empty_set )
| ( apply(X0,sK12(sK1,X0,apply(sK0,sK17(relation_dom(sK2))),sK5(X0,apply(sK2,sK17(relation_dom(sK2)))))) = sK5(X0,apply(sK2,sK17(relation_dom(sK2)))) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(apply(sK2,sK17(relation_dom(sK2))),relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_71,c_13036]) ).
tcf(c_14851,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK2)))) = empty_set )
| ( apply(X0,sK12(sK1,X0,apply(sK0,sK17(relation_dom(sK2))),apply(X0,apply(sK2,sK17(relation_dom(sK2)))))) = apply(X0,apply(sK2,sK17(relation_dom(sK2)))) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(apply(sK2,sK17(relation_dom(sK2))),relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_73,c_13036]) ).
tcf(c_14852,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK2)))) = empty_set )
| ( apply(X0,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X1)) = empty_set )
| ( apply(relation_dom(X0),sK12(sK1,relation_dom(X0),apply(sK0,sK17(relation_dom(sK2))),X1)) = X1 )
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom(X0))
| ~ relation(relation_dom(X0))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_75,c_13036]) ).
tcf(c_14853,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK2)))) = empty_set )
| ( apply(X1,sK12(sK1,X1,apply(sK0,sK17(relation_dom(sK2))),sK12(X1,X2,apply(sK2,sK17(relation_dom(sK2))),X0))) = sK12(X1,X2,apply(sK2,sK17(relation_dom(sK2))),X0) )
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),relation_composition(X1,X2)) ),
inference(superposition,[status(thm)],[c_301,c_13036]) ).
tcf(c_14854,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK2)))) = empty_set )
| ( apply(relation_dom(sK0),sK12(sK1,relation_dom(sK0),apply(sK0,sK17(relation_dom(sK2))),sK12(relation_dom(sK2),X1,apply(sK2,sK17(relation_dom(sK2))),X0))) = sK12(relation_dom(sK2),X1,apply(sK2,sK17(relation_dom(sK2))),X0) )
| ~ relation(X1)
| ~ function(relation_dom(sK0))
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),relation_composition(relation_dom(sK2),X1)) ),
inference(superposition,[status(thm)],[c_2283,c_13036]) ).
tcf(c_14855,plain,
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK2)))) = empty_set )
| ( apply(relation_dom(sK0),sK12(sK1,relation_dom(sK0),apply(sK0,sK17(relation_dom(sK2))),sK5(relation_dom(sK2),apply(sK2,sK17(relation_dom(sK2)))))) = sK5(relation_dom(sK2),apply(sK2,sK17(relation_dom(sK2)))) )
| ~ function(relation_dom(sK0))
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(apply(sK2,sK17(relation_dom(sK2))),relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_3019,c_13036]) ).
tcf(c_14856,plain,
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK2)))) = empty_set )
| ( apply(relation_dom(sK0),sK12(sK1,relation_dom(sK0),apply(sK0,sK17(relation_dom(sK2))),apply(relation_dom(sK2),apply(sK2,sK17(relation_dom(sK2)))))) = apply(relation_dom(sK2),apply(sK2,sK17(relation_dom(sK2)))) )
| ~ function(relation_dom(sK0))
| ~ function(relation_dom(sK2))
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(apply(sK2,sK17(relation_dom(sK2))),relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_3551,c_13036]) ).
tcf(c_14959,plain,
! [X0: $i] :
( ( sK17(powerset(relation_dom(relation_dom(sK2)))) = empty_set )
| ( apply(sK0,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0)) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0))) = empty_set )
| ( apply(relation_dom(sK2),sK12(sK1,relation_dom(sK2),apply(sK0,sK17(relation_dom(sK2))),X0)) = X0 )
| ~ function(relation_dom(sK2))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_4011,c_14232]) ).
tcf(c_14960,plain,
! [X0: $i] :
( ( sK17(powerset(relation_dom(relation_dom(sK2)))) = empty_set )
| ( apply(sK0,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0)) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0))) = empty_set )
| ( apply(relation_dom(sK0),sK12(sK1,relation_dom(sK0),apply(sK0,sK17(relation_dom(sK2))),X0)) = X0 )
| ~ function(relation_dom(sK0))
| ~ relation(relation_dom(sK0))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_4110,c_14232]) ).
tcf(c_14961,plain,
! [X0: $i] :
( ( sK17(powerset(relation_dom(relation_dom(sK2)))) = empty_set )
| ( apply(sK2,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0)) = empty_set )
| ( apply(relation_dom(sK0),sK12(sK1,relation_dom(sK0),apply(sK0,sK17(relation_dom(sK2))),X0)) = X0 )
| ~ function(relation_dom(sK0))
| ~ relation(relation_dom(sK0))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_3449,c_14232]) ).
tcf(c_14962,plain,
! [X0: $i] :
( ( sK17(powerset(relation_dom(relation_dom(sK2)))) = empty_set )
| ( apply(X0,sK12(sK1,X0,apply(sK0,sK17(relation_dom(sK2))),sK5(X0,apply(sK2,sK17(relation_dom(sK2)))))) = sK5(X0,apply(sK2,sK17(relation_dom(sK2)))) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(apply(sK2,sK17(relation_dom(sK2))),relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_71,c_14232]) ).
tcf(c_14963,plain,
! [X0: $i] :
( ( sK17(powerset(relation_dom(relation_dom(sK2)))) = empty_set )
| ( apply(X0,sK12(sK1,X0,apply(sK0,sK17(relation_dom(sK2))),apply(X0,apply(sK2,sK17(relation_dom(sK2)))))) = apply(X0,apply(sK2,sK17(relation_dom(sK2)))) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(apply(sK2,sK17(relation_dom(sK2))),relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_73,c_14232]) ).
tcf(c_14964,plain,
! [X0: $i,X1: $i] :
( ( sK17(powerset(relation_dom(relation_dom(sK2)))) = empty_set )
| ( apply(X0,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X1)) = empty_set )
| ( apply(relation_dom(X0),sK12(sK1,relation_dom(X0),apply(sK0,sK17(relation_dom(sK2))),X1)) = X1 )
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom(X0))
| ~ relation(relation_dom(X0))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_75,c_14232]) ).
tcf(c_14965,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK17(powerset(relation_dom(relation_dom(sK2)))) = empty_set )
| ( apply(X1,sK12(sK1,X1,apply(sK0,sK17(relation_dom(sK2))),sK12(X1,X2,apply(sK2,sK17(relation_dom(sK2))),X0))) = sK12(X1,X2,apply(sK2,sK17(relation_dom(sK2))),X0) )
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),relation_composition(X1,X2)) ),
inference(superposition,[status(thm)],[c_301,c_14232]) ).
tcf(c_14966,plain,
! [X0: $i,X1: $i] :
( ( sK17(powerset(relation_dom(relation_dom(sK2)))) = empty_set )
| ( apply(relation_dom(sK0),sK12(sK1,relation_dom(sK0),apply(sK0,sK17(relation_dom(sK2))),sK12(relation_dom(sK2),X1,apply(sK2,sK17(relation_dom(sK2))),X0))) = sK12(relation_dom(sK2),X1,apply(sK2,sK17(relation_dom(sK2))),X0) )
| ~ relation(X1)
| ~ function(relation_dom(sK0))
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),relation_composition(relation_dom(sK2),X1)) ),
inference(superposition,[status(thm)],[c_2283,c_14232]) ).
tcf(c_14967,plain,
( ( sK17(powerset(relation_dom(relation_dom(sK2)))) = empty_set )
| ( apply(relation_dom(sK0),sK12(sK1,relation_dom(sK0),apply(sK0,sK17(relation_dom(sK2))),sK5(relation_dom(sK2),apply(sK2,sK17(relation_dom(sK2)))))) = sK5(relation_dom(sK2),apply(sK2,sK17(relation_dom(sK2)))) )
| ~ function(relation_dom(sK0))
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(apply(sK2,sK17(relation_dom(sK2))),relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_3019,c_14232]) ).
tcf(c_14968,plain,
( ( sK17(powerset(relation_dom(relation_dom(sK2)))) = empty_set )
| ( apply(relation_dom(sK0),sK12(sK1,relation_dom(sK0),apply(sK0,sK17(relation_dom(sK2))),apply(relation_dom(sK2),apply(sK2,sK17(relation_dom(sK2)))))) = apply(relation_dom(sK2),apply(sK2,sK17(relation_dom(sK2)))) )
| ~ function(relation_dom(sK0))
| ~ function(relation_dom(sK2))
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(apply(sK2,sK17(relation_dom(sK2))),relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_3551,c_14232]) ).
tcf(c_15079,plain,
( in(ordered_pair(apply(sK0,sK17(relation_dom(sK2))),apply(sK2,sK17(relation_dom(sK2)))),sK1)
| ( relation_dom(sK17(powerset(sK2))) = empty_set )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_9983,c_73]) ).
tcf(c_15080,plain,
( in(ordered_pair(apply(sK0,sK17(relation_dom(sK2))),apply(sK2,sK17(relation_dom(sK2)))),sK1)
| ( relation_dom(sK17(powerset(sK2))) = empty_set )
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_15079,c_57,c_56]) ).
tcf(c_15095,plain,
! [X0: $i] :
( ( sK17(sK16(powerset(relation_dom(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_65,c_12877]) ).
tcf(c_15096,plain,
! [X0: $i,X1: $i] :
( ( sK17(sK16(powerset(relation_dom(relation_composition(X1,X0))))) = empty_set )
| ~ empty(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_86,c_12877]) ).
tcf(c_15097,plain,
! [X0: $i,X1: $i] :
( ( sK17(sK16(powerset(relation_dom(relation_composition(X0,X1))))) = empty_set )
| ~ empty(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_88,c_12877]) ).
tcf(c_15098,plain,
sK17(sK16(powerset(relation_dom(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_110,c_12877]) ).
tcf(c_15099,plain,
( ( sK17(sK16(powerset(relation_dom(relation_dom(sK2))))) = empty_set )
| ( apply(sK1,apply(sK0,sK17(sK16(relation_dom(sK2))))) = apply(sK2,sK17(sK16(relation_dom(sK2)))) ) ),
inference(superposition,[status(thm)],[c_11951,c_12877]) ).
tcf(c_15100,plain,
( ( sK17(sK16(powerset(relation_dom(relation_dom(sK2))))) = empty_set )
| ( apply(sK1,apply(sK0,sK17(relation_dom(sK2)))) = apply(sK2,sK17(relation_dom(sK2))) ) ),
inference(superposition,[status(thm)],[c_2425,c_12877]) ).
tcf(c_15103,plain,
! [X0: $i] :
( ( sK17(sK16(powerset(relation_dom(sK17(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6912,c_12877]) ).
tcf(c_15104,plain,
! [X0: $i] :
( ( sK17(sK16(powerset(relation_dom(sK17(sK16(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12308,c_12877]) ).
tcf(c_15142,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(relation_dom(X1),X0) = empty_set )
| ~ empty(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_65,c_2400]) ).
tcf(c_15143,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_composition(relation_composition(X2,X0),X1) = empty_set )
| ~ empty(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_86,c_2400]) ).
tcf(c_15144,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_composition(relation_composition(X0,X2),X1) = empty_set )
| ~ empty(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_88,c_2400]) ).
tcf(c_15145,plain,
! [X0: $i] :
( ( relation_composition(empty_set,X0) = empty_set )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_110,c_2400]) ).
tcf(c_15146,plain,
! [X0: $i] :
( ( relation_composition(relation_dom(sK2),X0) = empty_set )
| ( apply(sK1,apply(sK0,sK17(sK16(relation_dom(sK2))))) = apply(sK2,sK17(sK16(relation_dom(sK2)))) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_11951,c_2400]) ).
tcf(c_15147,plain,
! [X0: $i] :
( ( relation_composition(relation_dom(sK2),X0) = empty_set )
| ( apply(sK1,apply(sK0,sK17(relation_dom(sK2)))) = apply(sK2,sK17(relation_dom(sK2))) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_2425,c_2400]) ).
tcf(c_15148,plain,
! [X0: $i] :
( ( relation_composition(sK2,X0) = empty_set )
| ( apply(sK1,apply(sK0,sK17(sK16(relation_dom(sK2))))) = apply(sK2,sK17(sK16(relation_dom(sK2)))) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_12039,c_2400]) ).
tcf(c_15149,plain,
! [X0: $i] :
( ( relation_composition(sK2,X0) = empty_set )
| ( apply(sK1,apply(sK0,sK17(relation_dom(sK2)))) = apply(sK2,sK17(relation_dom(sK2))) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_2475,c_2400]) ).
tcf(c_15150,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(sK17(powerset(X1)),X0) = empty_set )
| ~ empty(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6912,c_2400]) ).
tcf(c_15151,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(sK17(sK16(powerset(X1))),X0) = empty_set )
| ~ empty(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_12308,c_2400]) ).
tcf(c_15261,plain,
relation_composition(empty_set,sK2) = empty_set,
inference(superposition,[status(thm)],[c_54,c_15145]) ).
tcf(c_15262,plain,
relation_composition(empty_set,sK1) = empty_set,
inference(superposition,[status(thm)],[c_56,c_15145]) ).
tcf(c_15263,plain,
relation_composition(empty_set,sK0) = empty_set,
inference(superposition,[status(thm)],[c_58,c_15145]) ).
tcf(c_15264,plain,
! [X0: $i] :
( ( relation_composition(empty_set,relation_dom(X0)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_66,c_15145]) ).
tcf(c_15265,plain,
relation_composition(empty_set,sK6) = empty_set,
inference(superposition,[status(thm)],[c_76,c_15145]) ).
tcf(c_15266,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(empty_set,relation_composition(X0,X1)) = empty_set )
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_90,c_15145]) ).
tcf(c_15267,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(empty_set,relation_composition(X0,X1)) = empty_set )
| ~ empty(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_89,c_15145]) ).
tcf(c_15268,plain,
relation_composition(empty_set,sK7) = empty_set,
inference(superposition,[status(thm)],[c_82,c_15145]) ).
tcf(c_15269,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(empty_set,relation_composition(X1,X0)) = empty_set )
| ~ empty(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_87,c_15145]) ).
tcf(c_15270,plain,
relation_composition(empty_set,empty_set) = empty_set,
inference(superposition,[status(thm)],[c_109,c_15145]) ).
tcf(c_15271,plain,
( ( relation_composition(empty_set,relation_dom(sK2)) = empty_set )
| ( apply(sK1,apply(sK0,sK17(relation_dom(sK2)))) = apply(sK2,sK17(relation_dom(sK2))) ) ),
inference(superposition,[status(thm)],[c_2468,c_15145]) ).
tcf(c_15272,plain,
! [X0: $i] :
( ( relation_composition(empty_set,sK17(powerset(X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7176,c_15145]) ).
tcf(c_15273,plain,
! [X0: $i] :
( ( relation_composition(empty_set,sK17(sK16(powerset(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12782,c_15145]) ).
tcf(c_15299,plain,
! [X0: $i,X1: $i] :
( ( apply(sK2,sK12(empty_set,sK2,X0,X1)) = X1 )
| ~ function(sK2)
| ~ relation(empty_set)
| ~ relation(sK2)
| ~ in(ordered_pair(X0,X1),empty_set) ),
inference(superposition,[status(thm)],[c_15261,c_2068]) ).
tcf(c_15308,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(ordered_pair(sK12(X2,empty_set,X0,X1),X3),empty_set)
| ~ relation(empty_set)
| ~ relation(sK2)
| ~ relation(X2)
| ~ in(ordered_pair(X1,X3),sK2)
| ~ in(ordered_pair(X0,X1),relation_composition(X2,empty_set)) ),
inference(superposition,[status(thm)],[c_15261,c_2067]) ).
tcf(c_15309,plain,
! [X0: $i,X1: $i] :
( ~ relation(sK2)
| ~ in(ordered_pair(X0,X1),empty_set) ),
inference(superposition,[status(thm)],[c_15261,c_3821]) ).
tcf(c_15310,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ relation(X2)
| ~ in(ordered_pair(X1,X3),sK2)
| ~ in(ordered_pair(X0,X1),relation_composition(X2,empty_set)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_15308,c_3809,c_109,c_54]) ).
tcf(c_15326,plain,
! [X0: $i,X1: $i] :
( ( apply(sK1,sK12(empty_set,sK1,X0,X1)) = X1 )
| ~ function(sK1)
| ~ relation(empty_set)
| ~ relation(sK1)
| ~ in(ordered_pair(X0,X1),empty_set) ),
inference(superposition,[status(thm)],[c_15262,c_2068]) ).
tcf(c_15335,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(ordered_pair(sK12(X2,empty_set,X0,X1),X3),empty_set)
| ~ relation(empty_set)
| ~ relation(sK1)
| ~ relation(X2)
| ~ in(ordered_pair(X1,X3),sK1)
| ~ in(ordered_pair(X0,X1),relation_composition(X2,empty_set)) ),
inference(superposition,[status(thm)],[c_15262,c_2067]) ).
tcf(c_15336,plain,
! [X0: $i,X1: $i] :
( ~ relation(sK1)
| ~ in(ordered_pair(X0,X1),empty_set) ),
inference(superposition,[status(thm)],[c_15262,c_3821]) ).
tcf(c_15337,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ relation(X2)
| ~ in(ordered_pair(X1,X3),sK1)
| ~ in(ordered_pair(X0,X1),relation_composition(X2,empty_set)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_15335,c_3809,c_109,c_56]) ).
tcf(c_15341,plain,
! [X0: $i,X1: $i] :
( ( apply(sK0,sK12(empty_set,sK0,X0,X1)) = X1 )
| ~ function(sK0)
| ~ relation(empty_set)
| ~ relation(sK0)
| ~ in(ordered_pair(X0,X1),empty_set) ),
inference(superposition,[status(thm)],[c_15263,c_2068]) ).
tcf(c_15350,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(ordered_pair(sK12(X2,empty_set,X0,X1),X3),empty_set)
| ~ relation(empty_set)
| ~ relation(sK0)
| ~ relation(X2)
| ~ in(ordered_pair(X1,X3),sK0)
| ~ in(ordered_pair(X0,X1),relation_composition(X2,empty_set)) ),
inference(superposition,[status(thm)],[c_15263,c_2067]) ).
tcf(c_15351,plain,
! [X0: $i,X1: $i] :
( ~ relation(sK0)
| ~ in(ordered_pair(X0,X1),empty_set) ),
inference(superposition,[status(thm)],[c_15263,c_3821]) ).
tcf(c_15352,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ relation(X2)
| ~ in(ordered_pair(X1,X3),sK0)
| ~ in(ordered_pair(X0,X1),relation_composition(X2,empty_set)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_15350,c_3809,c_109,c_58]) ).
tcf(c_15356,plain,
! [X0: $i,X1: $i] :
( ( apply(sK6,sK12(empty_set,sK6,X0,X1)) = X1 )
| ~ function(sK6)
| ~ relation(sK6)
| ~ relation(empty_set)
| ~ in(ordered_pair(X0,X1),empty_set) ),
inference(superposition,[status(thm)],[c_15265,c_2068]) ).
tcf(c_15365,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(ordered_pair(sK12(X2,empty_set,X0,X1),X3),empty_set)
| ~ relation(sK6)
| ~ relation(empty_set)
| ~ relation(X2)
| ~ in(ordered_pair(X1,X3),sK6)
| ~ in(ordered_pair(X0,X1),relation_composition(X2,empty_set)) ),
inference(superposition,[status(thm)],[c_15265,c_2067]) ).
tcf(c_15366,plain,
! [X0: $i,X1: $i] :
( ~ relation(sK6)
| ~ in(ordered_pair(X0,X1),empty_set) ),
inference(superposition,[status(thm)],[c_15265,c_3821]) ).
tcf(c_15367,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ relation(X2)
| ~ in(ordered_pair(X1,X3),sK6)
| ~ in(ordered_pair(X0,X1),relation_composition(X2,empty_set)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_15365,c_3809,c_76,c_109]) ).
tcf(c_15383,plain,
( ( relation_dom(sK17(powerset(sK2))) = empty_set )
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(sK1,ordered_pair(apply(sK0,sK17(relation_dom(sK2))),apply(sK2,sK17(relation_dom(sK2))))) ),
inference(superposition,[status(thm)],[c_15080,c_64]) ).
tcf(c_15384,plain,
( element(ordered_pair(apply(sK0,sK17(relation_dom(sK2))),apply(sK2,sK17(relation_dom(sK2)))),sK1)
| ( relation_dom(sK17(powerset(sK2))) = empty_set )
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_15080,c_63]) ).
tcf(c_15387,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(apply(sK0,sK17(relation_dom(sK2))),X0),relation_composition(sK1,X1))
| ( relation_dom(sK17(powerset(sK2))) = empty_set )
| ~ relation(sK1)
| ~ relation(X1)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),X1) ),
inference(superposition,[status(thm)],[c_15080,c_299]) ).
tcf(c_15395,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(apply(sK0,sK17(relation_dom(sK2))),X0),relation_composition(sK1,X1))
| ( relation_dom(sK17(powerset(sK2))) = empty_set )
| ~ relation(X1)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_15387,c_56]) ).
tcf(c_15412,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK17(powerset(sK2))) = empty_set )
| ~ relation(X0)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X1),X0)
| ~ in(relation_composition(sK1,X0),ordered_pair(apply(sK0,sK17(relation_dom(sK2))),X1)) ),
inference(superposition,[status(thm)],[c_15395,c_64]) ).
tcf(c_15413,plain,
! [X0: $i,X1: $i] :
( element(ordered_pair(apply(sK0,sK17(relation_dom(sK2))),X0),relation_composition(sK1,X1))
| ( relation_dom(sK17(powerset(sK2))) = empty_set )
| ~ relation(X1)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),X1) ),
inference(superposition,[status(thm)],[c_15395,c_63]) ).
tcf(c_15414,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK17(powerset(sK2))) = empty_set )
| ~ relation(X1)
| ~ empty(relation_composition(sK1,X1))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),X1) ),
inference(superposition,[status(thm)],[c_15395,c_61]) ).
tcf(c_15415,plain,
! [X0: $i,X1: $i] :
( in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(relation_composition(sK1,X1)))
| ( relation_dom(sK17(powerset(sK2))) = empty_set )
| ~ relation(X1)
| ~ relation(relation_composition(sK1,X1))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),X1) ),
inference(superposition,[status(thm)],[c_15395,c_70]) ).
tcf(c_15416,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(ordered_pair(apply(sK0,sK17(relation_dom(sK2))),X2),relation_composition(relation_composition(sK1,X1),X3))
| ( relation_dom(sK17(powerset(sK2))) = empty_set )
| ~ relation(X3)
| ~ relation(X1)
| ~ relation(relation_composition(sK1,X1))
| ~ in(ordered_pair(X0,X2),X3)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),X1) ),
inference(superposition,[status(thm)],[c_15395,c_299]) ).
tcf(c_15417,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK17(powerset(sK2))) = empty_set )
| ( apply(relation_composition(sK1,X1),apply(sK0,sK17(relation_dom(sK2)))) = X0 )
| ~ relation(X1)
| ~ function(relation_composition(sK1,X1))
| ~ relation(relation_composition(sK1,X1))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),X1) ),
inference(superposition,[status(thm)],[c_15395,c_152]) ).
tcf(c_15418,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK17(powerset(sK2))) = empty_set )
| ( apply(X1,sK12(sK1,X1,apply(sK0,sK17(relation_dom(sK2))),X0)) = X0 )
| ~ relation(sK1)
| ~ function(X1)
| ~ relation(X1)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),X1) ),
inference(superposition,[status(thm)],[c_15395,c_2068]) ).
tcf(c_15419,plain,
! [X0: $i] :
( ( relation_dom(sK17(powerset(sK2))) = empty_set )
| ~ relation(sK1)
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_15395,c_2063]) ).
tcf(c_15420,plain,
! [X0: $i] :
( ( relation_dom(sK17(powerset(sK2))) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,sK17(relation_dom(sK2))),X0),X0))) = apply(sK2,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,sK17(relation_dom(sK2))),X0),X0)) )
| ~ relation(sK1)
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_15395,c_2064]) ).
tcf(c_15421,plain,
! [X0: $i] :
( ( relation_dom(sK17(powerset(sK2))) = empty_set )
| ~ relation(empty_set)
| ~ relation(sK1)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),empty_set) ),
inference(superposition,[status(thm)],[c_15395,c_3818]) ).
tcf(c_15427,plain,
! [X0: $i] :
( ( relation_dom(sK17(powerset(sK2))) = empty_set )
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_15419,c_56]) ).
tcf(c_15449,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK17(powerset(sK2))) = empty_set )
| ( apply(X1,sK12(sK1,X1,apply(sK0,sK17(relation_dom(sK2))),X0)) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_15418,c_56]) ).
tcf(c_15471,plain,
! [X0: $i] :
( ( relation_dom(sK17(powerset(sK2))) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,sK17(relation_dom(sK2))),X0),X0))) = apply(sK2,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,sK17(relation_dom(sK2))),X0),X0)) )
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_15420,c_56]) ).
tcf(c_15644,plain,
! [X0: $i] :
( ( relation_dom(sK17(powerset(sK2))) = empty_set )
| ( apply(sK0,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0)) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0))) = empty_set )
| ( apply(relation_dom(sK2),sK12(sK1,relation_dom(sK2),apply(sK0,sK17(relation_dom(sK2))),X0)) = X0 )
| ~ function(relation_dom(sK2))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_4011,c_15449]) ).
tcf(c_15645,plain,
! [X0: $i] :
( ( relation_dom(sK17(powerset(sK2))) = empty_set )
| ( apply(sK0,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0)) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0))) = empty_set )
| ( apply(relation_dom(sK0),sK12(sK1,relation_dom(sK0),apply(sK0,sK17(relation_dom(sK2))),X0)) = X0 )
| ~ function(relation_dom(sK0))
| ~ relation(relation_dom(sK0))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_4110,c_15449]) ).
tcf(c_15646,plain,
! [X0: $i] :
( ( relation_dom(sK17(powerset(sK2))) = empty_set )
| ( apply(sK2,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0)) = empty_set )
| ( apply(relation_dom(sK0),sK12(sK1,relation_dom(sK0),apply(sK0,sK17(relation_dom(sK2))),X0)) = X0 )
| ~ function(relation_dom(sK0))
| ~ relation(relation_dom(sK0))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_3449,c_15449]) ).
tcf(c_15647,plain,
! [X0: $i] :
( ( relation_dom(sK17(powerset(sK2))) = empty_set )
| ( apply(X0,sK12(sK1,X0,apply(sK0,sK17(relation_dom(sK2))),sK5(X0,apply(sK2,sK17(relation_dom(sK2)))))) = sK5(X0,apply(sK2,sK17(relation_dom(sK2)))) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(apply(sK2,sK17(relation_dom(sK2))),relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_71,c_15449]) ).
tcf(c_15648,plain,
! [X0: $i] :
( ( relation_dom(sK17(powerset(sK2))) = empty_set )
| ( apply(X0,sK12(sK1,X0,apply(sK0,sK17(relation_dom(sK2))),apply(X0,apply(sK2,sK17(relation_dom(sK2)))))) = apply(X0,apply(sK2,sK17(relation_dom(sK2)))) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(apply(sK2,sK17(relation_dom(sK2))),relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_73,c_15449]) ).
tcf(c_15649,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK17(powerset(sK2))) = empty_set )
| ( apply(X0,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X1)) = empty_set )
| ( apply(relation_dom(X0),sK12(sK1,relation_dom(X0),apply(sK0,sK17(relation_dom(sK2))),X1)) = X1 )
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom(X0))
| ~ relation(relation_dom(X0))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_75,c_15449]) ).
tcf(c_15650,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(sK17(powerset(sK2))) = empty_set )
| ( apply(X1,sK12(sK1,X1,apply(sK0,sK17(relation_dom(sK2))),sK12(X1,X2,apply(sK2,sK17(relation_dom(sK2))),X0))) = sK12(X1,X2,apply(sK2,sK17(relation_dom(sK2))),X0) )
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),relation_composition(X1,X2)) ),
inference(superposition,[status(thm)],[c_301,c_15449]) ).
tcf(c_15651,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK17(powerset(sK2))) = empty_set )
| ( apply(relation_dom(sK0),sK12(sK1,relation_dom(sK0),apply(sK0,sK17(relation_dom(sK2))),sK12(relation_dom(sK2),X1,apply(sK2,sK17(relation_dom(sK2))),X0))) = sK12(relation_dom(sK2),X1,apply(sK2,sK17(relation_dom(sK2))),X0) )
| ~ relation(X1)
| ~ function(relation_dom(sK0))
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),relation_composition(relation_dom(sK2),X1)) ),
inference(superposition,[status(thm)],[c_2283,c_15449]) ).
tcf(c_15652,plain,
( ( relation_dom(sK17(powerset(sK2))) = empty_set )
| ( apply(relation_dom(sK0),sK12(sK1,relation_dom(sK0),apply(sK0,sK17(relation_dom(sK2))),sK5(relation_dom(sK2),apply(sK2,sK17(relation_dom(sK2)))))) = sK5(relation_dom(sK2),apply(sK2,sK17(relation_dom(sK2)))) )
| ~ function(relation_dom(sK0))
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(apply(sK2,sK17(relation_dom(sK2))),relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_3019,c_15449]) ).
tcf(c_15653,plain,
( ( relation_dom(sK17(powerset(sK2))) = empty_set )
| ( apply(relation_dom(sK0),sK12(sK1,relation_dom(sK0),apply(sK0,sK17(relation_dom(sK2))),apply(relation_dom(sK2),apply(sK2,sK17(relation_dom(sK2)))))) = apply(relation_dom(sK2),apply(sK2,sK17(relation_dom(sK2)))) )
| ~ function(relation_dom(sK0))
| ~ function(relation_dom(sK2))
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(apply(sK2,sK17(relation_dom(sK2))),relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_3551,c_15449]) ).
tcf(c_15761,plain,
! [X0: $i] :
( ( relation_dom(sK17(powerset(relation_dom(sK2)))) = empty_set )
| ( apply(sK0,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0)) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0))) = empty_set )
| ( apply(relation_dom(sK2),sK12(sK1,relation_dom(sK2),apply(sK0,sK17(relation_dom(sK2))),X0)) = X0 )
| ~ function(relation_dom(sK2))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_4011,c_14648]) ).
tcf(c_15762,plain,
! [X0: $i] :
( ( relation_dom(sK17(powerset(relation_dom(sK2)))) = empty_set )
| ( apply(sK0,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0)) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0))) = empty_set )
| ( apply(relation_dom(sK0),sK12(sK1,relation_dom(sK0),apply(sK0,sK17(relation_dom(sK2))),X0)) = X0 )
| ~ function(relation_dom(sK0))
| ~ relation(relation_dom(sK0))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_4110,c_14648]) ).
tcf(c_15763,plain,
! [X0: $i] :
( ( relation_dom(sK17(powerset(relation_dom(sK2)))) = empty_set )
| ( apply(sK2,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0)) = empty_set )
| ( apply(relation_dom(sK0),sK12(sK1,relation_dom(sK0),apply(sK0,sK17(relation_dom(sK2))),X0)) = X0 )
| ~ function(relation_dom(sK0))
| ~ relation(relation_dom(sK0))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_3449,c_14648]) ).
tcf(c_15764,plain,
! [X0: $i] :
( ( relation_dom(sK17(powerset(relation_dom(sK2)))) = empty_set )
| ( apply(X0,sK12(sK1,X0,apply(sK0,sK17(relation_dom(sK2))),sK5(X0,apply(sK2,sK17(relation_dom(sK2)))))) = sK5(X0,apply(sK2,sK17(relation_dom(sK2)))) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(apply(sK2,sK17(relation_dom(sK2))),relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_71,c_14648]) ).
tcf(c_15765,plain,
! [X0: $i] :
( ( relation_dom(sK17(powerset(relation_dom(sK2)))) = empty_set )
| ( apply(X0,sK12(sK1,X0,apply(sK0,sK17(relation_dom(sK2))),apply(X0,apply(sK2,sK17(relation_dom(sK2)))))) = apply(X0,apply(sK2,sK17(relation_dom(sK2)))) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(apply(sK2,sK17(relation_dom(sK2))),relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_73,c_14648]) ).
tcf(c_15766,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK17(powerset(relation_dom(sK2)))) = empty_set )
| ( apply(X0,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X1)) = empty_set )
| ( apply(relation_dom(X0),sK12(sK1,relation_dom(X0),apply(sK0,sK17(relation_dom(sK2))),X1)) = X1 )
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom(X0))
| ~ relation(relation_dom(X0))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_75,c_14648]) ).
tcf(c_15767,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(sK17(powerset(relation_dom(sK2)))) = empty_set )
| ( apply(X1,sK12(sK1,X1,apply(sK0,sK17(relation_dom(sK2))),sK12(X1,X2,apply(sK2,sK17(relation_dom(sK2))),X0))) = sK12(X1,X2,apply(sK2,sK17(relation_dom(sK2))),X0) )
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),relation_composition(X1,X2)) ),
inference(superposition,[status(thm)],[c_301,c_14648]) ).
tcf(c_15768,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK17(powerset(relation_dom(sK2)))) = empty_set )
| ( apply(relation_dom(sK0),sK12(sK1,relation_dom(sK0),apply(sK0,sK17(relation_dom(sK2))),sK12(relation_dom(sK2),X1,apply(sK2,sK17(relation_dom(sK2))),X0))) = sK12(relation_dom(sK2),X1,apply(sK2,sK17(relation_dom(sK2))),X0) )
| ~ relation(X1)
| ~ function(relation_dom(sK0))
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),relation_composition(relation_dom(sK2),X1)) ),
inference(superposition,[status(thm)],[c_2283,c_14648]) ).
tcf(c_15769,plain,
( ( relation_dom(sK17(powerset(relation_dom(sK2)))) = empty_set )
| ( apply(relation_dom(sK0),sK12(sK1,relation_dom(sK0),apply(sK0,sK17(relation_dom(sK2))),sK5(relation_dom(sK2),apply(sK2,sK17(relation_dom(sK2)))))) = sK5(relation_dom(sK2),apply(sK2,sK17(relation_dom(sK2)))) )
| ~ function(relation_dom(sK0))
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(apply(sK2,sK17(relation_dom(sK2))),relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_3019,c_14648]) ).
tcf(c_15770,plain,
( ( relation_dom(sK17(powerset(relation_dom(sK2)))) = empty_set )
| ( apply(relation_dom(sK0),sK12(sK1,relation_dom(sK0),apply(sK0,sK17(relation_dom(sK2))),apply(relation_dom(sK2),apply(sK2,sK17(relation_dom(sK2)))))) = apply(relation_dom(sK2),apply(sK2,sK17(relation_dom(sK2)))) )
| ~ function(relation_dom(sK0))
| ~ function(relation_dom(sK2))
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(apply(sK2,sK17(relation_dom(sK2))),relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_3551,c_14648]) ).
tcf(c_15884,plain,
( in(ordered_pair(apply(sK0,sK17(sK16(relation_dom(sK2)))),apply(sK2,sK17(sK16(relation_dom(sK2))))),sK1)
| ( relation_dom(sK17(powerset(relation_dom(sK2)))) = empty_set )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_12021,c_73]) ).
tcf(c_15885,plain,
( in(ordered_pair(apply(sK0,sK17(sK16(relation_dom(sK2)))),apply(sK2,sK17(sK16(relation_dom(sK2))))),sK1)
| ( relation_dom(sK17(powerset(relation_dom(sK2)))) = empty_set )
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_15884,c_57,c_56]) ).
tcf(c_15889,plain,
! [X0: $i,X1: $i] :
( ( apply(sK7,sK12(empty_set,sK7,X0,X1)) = X1 )
| ~ function(sK7)
| ~ relation(sK7)
| ~ relation(empty_set)
| ~ in(ordered_pair(X0,X1),empty_set) ),
inference(superposition,[status(thm)],[c_15268,c_2068]) ).
tcf(c_15898,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(ordered_pair(sK12(X2,empty_set,X0,X1),X3),empty_set)
| ~ relation(sK7)
| ~ relation(empty_set)
| ~ relation(X2)
| ~ in(ordered_pair(X1,X3),sK7)
| ~ in(ordered_pair(X0,X1),relation_composition(X2,empty_set)) ),
inference(superposition,[status(thm)],[c_15268,c_2067]) ).
tcf(c_15899,plain,
! [X0: $i,X1: $i] :
( ~ relation(sK7)
| ~ in(ordered_pair(X0,X1),empty_set) ),
inference(superposition,[status(thm)],[c_15268,c_3821]) ).
tcf(c_15900,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ relation(X2)
| ~ in(ordered_pair(X1,X3),sK7)
| ~ in(ordered_pair(X0,X1),relation_composition(X2,empty_set)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_15898,c_3809,c_82,c_109]) ).
tcf(c_15904,plain,
! [X0: $i,X1: $i] :
( ( apply(empty_set,sK12(empty_set,empty_set,X0,X1)) = X1 )
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ in(ordered_pair(X0,X1),empty_set) ),
inference(superposition,[status(thm)],[c_15270,c_2068]) ).
tcf(c_15913,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(ordered_pair(sK12(X2,empty_set,X0,X1),X3),empty_set)
| ~ relation(empty_set)
| ~ relation(X2)
| ~ in(ordered_pair(X1,X3),empty_set)
| ~ in(ordered_pair(X0,X1),relation_composition(X2,empty_set)) ),
inference(superposition,[status(thm)],[c_15270,c_2067]) ).
tcf(c_15914,plain,
! [X0: $i,X1: $i] :
( ~ relation(empty_set)
| ~ in(ordered_pair(X0,X1),empty_set) ),
inference(superposition,[status(thm)],[c_15270,c_3821]) ).
tcf(c_15920,plain,
! [X0: $i] :
( ( relation_composition(empty_set,relation_dom(relation_dom(X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_65,c_15264]) ).
tcf(c_15921,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(empty_set,relation_dom(relation_composition(X1,X0))) = empty_set )
| ~ empty(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_86,c_15264]) ).
tcf(c_15922,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(empty_set,relation_dom(relation_composition(X0,X1))) = empty_set )
| ~ empty(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_88,c_15264]) ).
tcf(c_15923,plain,
relation_composition(empty_set,relation_dom(empty_set)) = empty_set,
inference(superposition,[status(thm)],[c_110,c_15264]) ).
tcf(c_15924,plain,
( ( relation_composition(empty_set,relation_dom(relation_dom(sK2))) = empty_set )
| ( apply(sK1,apply(sK0,sK17(sK16(relation_dom(sK2))))) = apply(sK2,sK17(sK16(relation_dom(sK2)))) ) ),
inference(superposition,[status(thm)],[c_11951,c_15264]) ).
tcf(c_15925,plain,
( ( relation_composition(empty_set,relation_dom(relation_dom(sK2))) = empty_set )
| ( apply(sK1,apply(sK0,sK17(relation_dom(sK2)))) = apply(sK2,sK17(relation_dom(sK2))) ) ),
inference(superposition,[status(thm)],[c_2425,c_15264]) ).
tcf(c_15926,plain,
( ( relation_composition(empty_set,relation_dom(sK2)) = empty_set )
| ( apply(sK1,apply(sK0,sK17(sK16(relation_dom(sK2))))) = apply(sK2,sK17(sK16(relation_dom(sK2)))) ) ),
inference(superposition,[status(thm)],[c_12039,c_15264]) ).
tcf(c_15928,plain,
! [X0: $i] :
( ( relation_composition(empty_set,relation_dom(sK17(powerset(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6912,c_15264]) ).
tcf(c_15929,plain,
! [X0: $i] :
( ( relation_composition(empty_set,relation_dom(sK17(sK16(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12308,c_15264]) ).
tcf(c_15953,plain,
! [X0: $i] :
( ( relation_composition(empty_set,relation_dom(relation_dom(relation_dom(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_65,c_15920]) ).
tcf(c_15954,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(empty_set,relation_dom(relation_dom(relation_composition(X1,X0)))) = empty_set )
| ~ empty(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_86,c_15920]) ).
tcf(c_15955,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(empty_set,relation_dom(relation_dom(relation_composition(X0,X1)))) = empty_set )
| ~ empty(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_88,c_15920]) ).
tcf(c_15956,plain,
relation_composition(empty_set,relation_dom(relation_dom(empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_110,c_15920]) ).
tcf(c_15957,plain,
( ( relation_composition(empty_set,relation_dom(relation_dom(relation_dom(sK2)))) = empty_set )
| ( apply(sK1,apply(sK0,sK17(sK16(relation_dom(sK2))))) = apply(sK2,sK17(sK16(relation_dom(sK2)))) ) ),
inference(superposition,[status(thm)],[c_11951,c_15920]) ).
tcf(c_15958,plain,
( ( relation_composition(empty_set,relation_dom(relation_dom(relation_dom(sK2)))) = empty_set )
| ( apply(sK1,apply(sK0,sK17(relation_dom(sK2)))) = apply(sK2,sK17(relation_dom(sK2))) ) ),
inference(superposition,[status(thm)],[c_2425,c_15920]) ).
tcf(c_15961,plain,
! [X0: $i] :
( ( relation_composition(empty_set,relation_dom(relation_dom(sK17(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6912,c_15920]) ).
tcf(c_15962,plain,
! [X0: $i] :
( ( relation_composition(empty_set,relation_dom(relation_dom(sK17(sK16(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12308,c_15920]) ).
tcf(c_16012,plain,
( ( relation_dom(sK17(powerset(relation_dom(sK2)))) = empty_set )
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(sK1,ordered_pair(apply(sK0,sK17(sK16(relation_dom(sK2)))),apply(sK2,sK17(sK16(relation_dom(sK2)))))) ),
inference(superposition,[status(thm)],[c_15885,c_64]) ).
tcf(c_16013,plain,
( element(ordered_pair(apply(sK0,sK17(sK16(relation_dom(sK2)))),apply(sK2,sK17(sK16(relation_dom(sK2))))),sK1)
| ( relation_dom(sK17(powerset(relation_dom(sK2)))) = empty_set )
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_15885,c_63]) ).
tcf(c_16016,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(apply(sK0,sK17(sK16(relation_dom(sK2)))),X0),relation_composition(sK1,X1))
| ( relation_dom(sK17(powerset(relation_dom(sK2)))) = empty_set )
| ~ relation(sK1)
| ~ relation(X1)
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0),X1) ),
inference(superposition,[status(thm)],[c_15885,c_299]) ).
tcf(c_16024,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(apply(sK0,sK17(sK16(relation_dom(sK2)))),X0),relation_composition(sK1,X1))
| ( relation_dom(sK17(powerset(relation_dom(sK2)))) = empty_set )
| ~ relation(X1)
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16016,c_56]) ).
tcf(c_16041,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK17(powerset(relation_dom(sK2)))) = empty_set )
| ~ relation(X0)
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X1),X0)
| ~ in(relation_composition(sK1,X0),ordered_pair(apply(sK0,sK17(sK16(relation_dom(sK2)))),X1)) ),
inference(superposition,[status(thm)],[c_16024,c_64]) ).
tcf(c_16042,plain,
! [X0: $i,X1: $i] :
( element(ordered_pair(apply(sK0,sK17(sK16(relation_dom(sK2)))),X0),relation_composition(sK1,X1))
| ( relation_dom(sK17(powerset(relation_dom(sK2)))) = empty_set )
| ~ relation(X1)
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0),X1) ),
inference(superposition,[status(thm)],[c_16024,c_63]) ).
tcf(c_16043,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK17(powerset(relation_dom(sK2)))) = empty_set )
| ~ relation(X1)
| ~ empty(relation_composition(sK1,X1))
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0),X1) ),
inference(superposition,[status(thm)],[c_16024,c_61]) ).
tcf(c_16044,plain,
! [X0: $i,X1: $i] :
( in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(relation_composition(sK1,X1)))
| ( relation_dom(sK17(powerset(relation_dom(sK2)))) = empty_set )
| ~ relation(X1)
| ~ relation(relation_composition(sK1,X1))
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0),X1) ),
inference(superposition,[status(thm)],[c_16024,c_70]) ).
tcf(c_16045,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(ordered_pair(apply(sK0,sK17(sK16(relation_dom(sK2)))),X2),relation_composition(relation_composition(sK1,X1),X3))
| ( relation_dom(sK17(powerset(relation_dom(sK2)))) = empty_set )
| ~ relation(X3)
| ~ relation(X1)
| ~ relation(relation_composition(sK1,X1))
| ~ in(ordered_pair(X0,X2),X3)
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0),X1) ),
inference(superposition,[status(thm)],[c_16024,c_299]) ).
tcf(c_16046,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK17(powerset(relation_dom(sK2)))) = empty_set )
| ( apply(relation_composition(sK1,X1),apply(sK0,sK17(sK16(relation_dom(sK2))))) = X0 )
| ~ relation(X1)
| ~ function(relation_composition(sK1,X1))
| ~ relation(relation_composition(sK1,X1))
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0),X1) ),
inference(superposition,[status(thm)],[c_16024,c_152]) ).
tcf(c_16047,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK17(powerset(relation_dom(sK2)))) = empty_set )
| ( apply(X1,sK12(sK1,X1,apply(sK0,sK17(sK16(relation_dom(sK2)))),X0)) = X0 )
| ~ relation(sK1)
| ~ function(X1)
| ~ relation(X1)
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0),X1) ),
inference(superposition,[status(thm)],[c_16024,c_2068]) ).
tcf(c_16048,plain,
! [X0: $i] :
( ( relation_dom(sK17(powerset(relation_dom(sK2)))) = empty_set )
| ~ relation(sK1)
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_16024,c_2063]) ).
tcf(c_16049,plain,
! [X0: $i] :
( ( relation_dom(sK17(powerset(relation_dom(sK2)))) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,sK17(sK16(relation_dom(sK2)))),X0),X0))) = apply(sK2,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,sK17(sK16(relation_dom(sK2)))),X0),X0)) )
| ~ relation(sK1)
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_16024,c_2064]) ).
tcf(c_16050,plain,
! [X0: $i] :
( ( relation_dom(sK17(powerset(relation_dom(sK2)))) = empty_set )
| ~ relation(empty_set)
| ~ relation(sK1)
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0),empty_set) ),
inference(superposition,[status(thm)],[c_16024,c_3818]) ).
tcf(c_16056,plain,
! [X0: $i] :
( ( relation_dom(sK17(powerset(relation_dom(sK2)))) = empty_set )
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16048,c_56]) ).
tcf(c_16078,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK17(powerset(relation_dom(sK2)))) = empty_set )
| ( apply(X1,sK12(sK1,X1,apply(sK0,sK17(sK16(relation_dom(sK2)))),X0)) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16047,c_56]) ).
tcf(c_16100,plain,
! [X0: $i] :
( ( relation_dom(sK17(powerset(relation_dom(sK2)))) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,sK17(sK16(relation_dom(sK2)))),X0),X0))) = apply(sK2,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,sK17(sK16(relation_dom(sK2)))),X0),X0)) )
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16049,c_56]) ).
tcf(c_16133,plain,
( in(sK3(relation_dom(sK2),relation_dom(sK2)),relation_dom(sK2))
| ( relation_dom(relation_dom(sK2)) = relation_dom(sK2) )
| ( apply(sK1,apply(sK0,sK3(relation_dom(sK2),relation_dom(sK2)))) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(sK3(relation_dom(sK2),relation_dom(sK2)),sK4(relation_dom(sK2),relation_dom(sK2))))) = apply(sK2,ordered_pair(sK3(relation_dom(sK2),relation_dom(sK2)),sK4(relation_dom(sK2),relation_dom(sK2)))) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_8783,c_3475]) ).
tcf(c_16134,plain,
( ( relation_dom(relation_dom(sK2)) = relation_dom(sK2) )
| ( apply(sK1,apply(sK0,ordered_pair(sK3(relation_dom(sK2),relation_dom(sK2)),sK4(relation_dom(sK2),relation_dom(sK2))))) = apply(sK2,ordered_pair(sK3(relation_dom(sK2),relation_dom(sK2)),sK4(relation_dom(sK2),relation_dom(sK2)))) )
| ~ relation(relation_dom(sK2))
| ~ in(relation_dom(sK0),sK3(relation_dom(sK2),relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_8783,c_64]) ).
tcf(c_16135,plain,
( element(sK3(relation_dom(sK2),relation_dom(sK2)),relation_dom(sK0))
| ( relation_dom(relation_dom(sK2)) = relation_dom(sK2) )
| ( apply(sK1,apply(sK0,ordered_pair(sK3(relation_dom(sK2),relation_dom(sK2)),sK4(relation_dom(sK2),relation_dom(sK2))))) = apply(sK2,ordered_pair(sK3(relation_dom(sK2),relation_dom(sK2)),sK4(relation_dom(sK2),relation_dom(sK2)))) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_8783,c_63]) ).
tcf(c_16163,plain,
! [X0: $i] :
( ( relation_dom(sK17(powerset(relation_dom(sK2)))) = empty_set )
| ( apply(sK0,ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0)) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0))) = empty_set )
| ( apply(relation_dom(sK2),sK12(sK1,relation_dom(sK2),apply(sK0,sK17(sK16(relation_dom(sK2)))),X0)) = X0 )
| ~ function(relation_dom(sK2))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_4011,c_16078]) ).
tcf(c_16164,plain,
! [X0: $i] :
( ( relation_dom(sK17(powerset(relation_dom(sK2)))) = empty_set )
| ( apply(sK0,ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0)) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0))) = empty_set )
| ( apply(relation_dom(sK0),sK12(sK1,relation_dom(sK0),apply(sK0,sK17(sK16(relation_dom(sK2)))),X0)) = X0 )
| ~ function(relation_dom(sK0))
| ~ relation(relation_dom(sK0))
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_4110,c_16078]) ).
tcf(c_16165,plain,
! [X0: $i] :
( ( relation_dom(sK17(powerset(relation_dom(sK2)))) = empty_set )
| ( apply(sK2,ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0)) = empty_set )
| ( apply(relation_dom(sK0),sK12(sK1,relation_dom(sK0),apply(sK0,sK17(sK16(relation_dom(sK2)))),X0)) = X0 )
| ~ function(relation_dom(sK0))
| ~ relation(relation_dom(sK0))
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_3449,c_16078]) ).
tcf(c_16166,plain,
! [X0: $i] :
( ( relation_dom(sK17(powerset(relation_dom(sK2)))) = empty_set )
| ( apply(X0,sK12(sK1,X0,apply(sK0,sK17(sK16(relation_dom(sK2)))),sK5(X0,apply(sK2,sK17(sK16(relation_dom(sK2))))))) = sK5(X0,apply(sK2,sK17(sK16(relation_dom(sK2))))) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(apply(sK2,sK17(sK16(relation_dom(sK2)))),relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_71,c_16078]) ).
tcf(c_16167,plain,
! [X0: $i] :
( ( relation_dom(sK17(powerset(relation_dom(sK2)))) = empty_set )
| ( apply(X0,sK12(sK1,X0,apply(sK0,sK17(sK16(relation_dom(sK2)))),apply(X0,apply(sK2,sK17(sK16(relation_dom(sK2))))))) = apply(X0,apply(sK2,sK17(sK16(relation_dom(sK2))))) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(apply(sK2,sK17(sK16(relation_dom(sK2)))),relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_73,c_16078]) ).
tcf(c_16168,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK17(powerset(relation_dom(sK2)))) = empty_set )
| ( apply(X0,ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X1)) = empty_set )
| ( apply(relation_dom(X0),sK12(sK1,relation_dom(X0),apply(sK0,sK17(sK16(relation_dom(sK2)))),X1)) = X1 )
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom(X0))
| ~ relation(relation_dom(X0))
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_75,c_16078]) ).
tcf(c_16169,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(sK17(powerset(relation_dom(sK2)))) = empty_set )
| ( apply(X1,sK12(sK1,X1,apply(sK0,sK17(sK16(relation_dom(sK2)))),sK12(X1,X2,apply(sK2,sK17(sK16(relation_dom(sK2)))),X0))) = sK12(X1,X2,apply(sK2,sK17(sK16(relation_dom(sK2)))),X0) )
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0),relation_composition(X1,X2)) ),
inference(superposition,[status(thm)],[c_301,c_16078]) ).
tcf(c_16170,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK17(powerset(relation_dom(sK2)))) = empty_set )
| ( apply(relation_dom(sK0),sK12(sK1,relation_dom(sK0),apply(sK0,sK17(sK16(relation_dom(sK2)))),sK12(relation_dom(sK2),X1,apply(sK2,sK17(sK16(relation_dom(sK2)))),X0))) = sK12(relation_dom(sK2),X1,apply(sK2,sK17(sK16(relation_dom(sK2)))),X0) )
| ~ relation(X1)
| ~ function(relation_dom(sK0))
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0),relation_composition(relation_dom(sK2),X1)) ),
inference(superposition,[status(thm)],[c_2283,c_16078]) ).
tcf(c_16171,plain,
( ( relation_dom(sK17(powerset(relation_dom(sK2)))) = empty_set )
| ( apply(relation_dom(sK0),sK12(sK1,relation_dom(sK0),apply(sK0,sK17(sK16(relation_dom(sK2)))),sK5(relation_dom(sK2),apply(sK2,sK17(sK16(relation_dom(sK2))))))) = sK5(relation_dom(sK2),apply(sK2,sK17(sK16(relation_dom(sK2))))) )
| ~ function(relation_dom(sK0))
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(apply(sK2,sK17(sK16(relation_dom(sK2)))),relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_3019,c_16078]) ).
tcf(c_16172,plain,
( ( relation_dom(sK17(powerset(relation_dom(sK2)))) = empty_set )
| ( apply(relation_dom(sK0),sK12(sK1,relation_dom(sK0),apply(sK0,sK17(sK16(relation_dom(sK2)))),apply(relation_dom(sK2),apply(sK2,sK17(sK16(relation_dom(sK2))))))) = apply(relation_dom(sK2),apply(sK2,sK17(sK16(relation_dom(sK2))))) )
| ~ function(relation_dom(sK0))
| ~ function(relation_dom(sK2))
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(apply(sK2,sK17(sK16(relation_dom(sK2)))),relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_3551,c_16078]) ).
tcf(c_16281,plain,
! [X0: $i,X1: $i] :
( ( apply(sK2,X0) = empty_set )
| ( apply(sK0,ordered_pair(apply(sK2,X0),X1)) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(apply(sK2,X0),X1))) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,X0),X1),X1))) = apply(sK2,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,X0),X1),X1)) )
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,X0),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_4011,c_6197]) ).
tcf(c_16282,plain,
! [X0: $i] :
( ( apply(sK2,X0) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,X0),sK5(relation_dom(sK2),apply(sK2,X0))),sK5(relation_dom(sK2),apply(sK2,X0))))) = apply(sK2,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,X0),sK5(relation_dom(sK2),apply(sK2,X0))),sK5(relation_dom(sK2),apply(sK2,X0)))) )
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,X0),relation_dom(sK1))
| ~ in(apply(sK2,X0),relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_71,c_6197]) ).
tcf(c_16283,plain,
! [X0: $i] :
( ( apply(sK2,X0) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,X0),apply(relation_dom(sK2),apply(sK2,X0))),apply(relation_dom(sK2),apply(sK2,X0))))) = apply(sK2,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,X0),apply(relation_dom(sK2),apply(sK2,X0))),apply(relation_dom(sK2),apply(sK2,X0)))) )
| ~ function(relation_dom(sK2))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,X0),relation_dom(sK1))
| ~ in(apply(sK2,X0),relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_73,c_6197]) ).
tcf(c_16284,plain,
! [X0: $i,X1: $i] :
( ( apply(sK2,X0) = empty_set )
| ( apply(sK2,ordered_pair(apply(sK2,X0),X1)) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,X0),X1),X1))) = apply(sK2,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,X0),X1),X1)) )
| ~ function(sK2)
| ~ relation(sK2)
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,X0),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_75,c_6197]) ).
tcf(c_16285,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(sK2,X0) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,X0),sK12(relation_dom(sK2),X2,apply(sK2,X0),X1)),sK12(relation_dom(sK2),X2,apply(sK2,X0),X1)))) = apply(sK2,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,X0),sK12(relation_dom(sK2),X2,apply(sK2,X0),X1)),sK12(relation_dom(sK2),X2,apply(sK2,X0),X1))) )
| ~ relation(X2)
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,X0),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,X0),X1),relation_composition(relation_dom(sK2),X2)) ),
inference(superposition,[status(thm)],[c_301,c_6197]) ).
tcf(c_16287,plain,
! [X0: $i,X1: $i] :
( ( apply(sK2,X0) = empty_set )
| ( apply(sK2,ordered_pair(apply(sK2,X0),X1)) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,X0),X1),X1))) = apply(sK2,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,X0),X1),X1)) )
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,X0),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16284,c_55,c_54]) ).
tcf(c_16341,plain,
! [X0: $i,X1: $i] :
( ( apply(sK0,X0) = empty_set )
| ( apply(sK1,apply(sK0,X0)) = empty_set )
| ( apply(sK0,ordered_pair(apply(sK2,X0),X1)) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(apply(sK2,X0),X1))) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,X0),X1),X1))) = apply(sK2,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,X0),X1),X1)) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4011,c_6548]) ).
tcf(c_16342,plain,
! [X0: $i] :
( ( apply(sK0,X0) = empty_set )
| ( apply(sK1,apply(sK0,X0)) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,X0),sK5(relation_dom(sK2),apply(sK2,X0))),sK5(relation_dom(sK2),apply(sK2,X0))))) = apply(sK2,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,X0),sK5(relation_dom(sK2),apply(sK2,X0))),sK5(relation_dom(sK2),apply(sK2,X0)))) )
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK2,X0),relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_71,c_6548]) ).
tcf(c_16343,plain,
! [X0: $i] :
( ( apply(sK0,X0) = empty_set )
| ( apply(sK1,apply(sK0,X0)) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,X0),apply(relation_dom(sK2),apply(sK2,X0))),apply(relation_dom(sK2),apply(sK2,X0))))) = apply(sK2,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,X0),apply(relation_dom(sK2),apply(sK2,X0))),apply(relation_dom(sK2),apply(sK2,X0)))) )
| ~ function(relation_dom(sK2))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK2,X0),relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_73,c_6548]) ).
tcf(c_16344,plain,
! [X0: $i,X1: $i] :
( ( apply(sK0,X0) = empty_set )
| ( apply(sK1,apply(sK0,X0)) = empty_set )
| ( apply(sK2,ordered_pair(apply(sK2,X0),X1)) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,X0),X1),X1))) = apply(sK2,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,X0),X1),X1)) )
| ~ function(sK2)
| ~ relation(sK2)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_75,c_6548]) ).
tcf(c_16345,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(sK0,X0) = empty_set )
| ( apply(sK1,apply(sK0,X0)) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,X0),sK12(relation_dom(sK2),X2,apply(sK2,X0),X1)),sK12(relation_dom(sK2),X2,apply(sK2,X0),X1)))) = apply(sK2,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,X0),sK12(relation_dom(sK2),X2,apply(sK2,X0),X1)),sK12(relation_dom(sK2),X2,apply(sK2,X0),X1))) )
| ~ relation(X2)
| ~ relation(relation_dom(sK2))
| ~ in(ordered_pair(apply(sK2,X0),X1),relation_composition(relation_dom(sK2),X2)) ),
inference(superposition,[status(thm)],[c_301,c_6548]) ).
tcf(c_16346,plain,
! [X0: $i] :
( ( apply(sK0,relation_dom(sK0)) = empty_set )
| ( apply(sK1,apply(sK0,relation_dom(sK0))) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,relation_dom(sK0)),X0),X0))) = apply(sK2,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,relation_dom(sK0)),X0),X0)) )
| ~ relation(relation_dom(sK2))
| ~ in(ordered_pair(empty_set,X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_13921,c_6548]) ).
tcf(c_16352,plain,
! [X0: $i,X1: $i] :
( ( apply(sK0,X0) = empty_set )
| ( apply(sK1,apply(sK0,X0)) = empty_set )
| ( apply(sK2,ordered_pair(apply(sK2,X0),X1)) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,X0),X1),X1))) = apply(sK2,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,X0),X1),X1)) )
| ~ relation(relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16344,c_55,c_54]) ).
tcf(c_16398,plain,
! [X0: $i,X1: $i] :
( ( apply(sK2,X0) = empty_set )
| ( apply(sK2,ordered_pair(apply(sK2,X0),X1)) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,X0),X1),X1))) = apply(sK2,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,X0),X1),X1)) )
| ~ relation(relation_dom(sK2))
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_52,c_16287]) ).
tcf(c_16399,plain,
! [X0: $i,X1: $i] :
( ( apply(sK2,X0) = empty_set )
| ( apply(sK1,apply(sK0,X0)) = empty_set )
| ( apply(sK2,ordered_pair(apply(sK2,X0),X1)) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,X0),X1),X1))) = apply(sK2,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,X0),X1),X1)) )
| ~ function(sK1)
| ~ relation(sK1)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_75,c_16287]) ).
tcf(c_16405,plain,
! [X0: $i,X1: $i] :
( ( apply(sK2,X0) = empty_set )
| ( apply(sK1,apply(sK0,X0)) = empty_set )
| ( apply(sK2,ordered_pair(apply(sK2,X0),X1)) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,X0),X1),X1))) = apply(sK2,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,X0),X1),X1)) )
| ~ relation(relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16399,c_57,c_56]) ).
tcf(c_16427,plain,
( in(ordered_pair(apply(sK0,sK17(sK16(relation_dom(sK2)))),apply(sK2,sK17(sK16(relation_dom(sK2))))),sK1)
| ( sK17(powerset(relation_dom(relation_dom(sK2)))) = empty_set )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_12023,c_73]) ).
tcf(c_16428,plain,
( in(ordered_pair(apply(sK0,sK17(sK16(relation_dom(sK2)))),apply(sK2,sK17(sK16(relation_dom(sK2))))),sK1)
| ( sK17(powerset(relation_dom(relation_dom(sK2)))) = empty_set )
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16427,c_57,c_56]) ).
tcf(c_16438,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(X0,relation_dom(X1)) = empty_set )
| ~ empty(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_65,c_2607]) ).
tcf(c_16439,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_composition(X1,relation_composition(X2,X0)) = empty_set )
| ~ empty(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_86,c_2607]) ).
tcf(c_16440,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_composition(X1,relation_composition(X0,X2)) = empty_set )
| ~ empty(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_88,c_2607]) ).
tcf(c_16441,plain,
! [X0: $i] :
( ( relation_composition(X0,empty_set) = empty_set )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_110,c_2607]) ).
tcf(c_16442,plain,
! [X0: $i] :
( ( relation_composition(X0,relation_dom(sK2)) = empty_set )
| ( apply(sK1,apply(sK0,sK17(sK16(relation_dom(sK2))))) = apply(sK2,sK17(sK16(relation_dom(sK2)))) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_11951,c_2607]) ).
tcf(c_16443,plain,
! [X0: $i] :
( ( relation_composition(X0,relation_dom(sK2)) = empty_set )
| ( apply(sK1,apply(sK0,sK17(relation_dom(sK2)))) = apply(sK2,sK17(relation_dom(sK2))) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_2425,c_2607]) ).
tcf(c_16444,plain,
! [X0: $i] :
( ( relation_composition(X0,sK2) = empty_set )
| ( apply(sK1,apply(sK0,sK17(sK16(relation_dom(sK2))))) = apply(sK2,sK17(sK16(relation_dom(sK2)))) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_12039,c_2607]) ).
tcf(c_16445,plain,
! [X0: $i] :
( ( relation_composition(X0,sK2) = empty_set )
| ( apply(sK1,apply(sK0,sK17(relation_dom(sK2)))) = apply(sK2,sK17(relation_dom(sK2))) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_2475,c_2607]) ).
tcf(c_16446,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(X0,sK17(powerset(X1))) = empty_set )
| ~ empty(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6912,c_2607]) ).
tcf(c_16447,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(X0,sK17(sK16(powerset(X1)))) = empty_set )
| ~ empty(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_12308,c_2607]) ).
tcf(c_16858,plain,
relation_composition(sK2,empty_set) = empty_set,
inference(superposition,[status(thm)],[c_54,c_16441]) ).
tcf(c_16859,plain,
relation_composition(sK1,empty_set) = empty_set,
inference(superposition,[status(thm)],[c_56,c_16441]) ).
tcf(c_16860,plain,
relation_composition(sK0,empty_set) = empty_set,
inference(superposition,[status(thm)],[c_58,c_16441]) ).
tcf(c_16861,plain,
! [X0: $i] :
( ( relation_composition(relation_dom(X0),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_66,c_16441]) ).
tcf(c_16862,plain,
relation_composition(sK6,empty_set) = empty_set,
inference(superposition,[status(thm)],[c_76,c_16441]) ).
tcf(c_16863,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(relation_composition(X0,X1),empty_set) = empty_set )
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_90,c_16441]) ).
tcf(c_16864,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(relation_composition(X0,X1),empty_set) = empty_set )
| ~ empty(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_89,c_16441]) ).
tcf(c_16865,plain,
relation_composition(sK7,empty_set) = empty_set,
inference(superposition,[status(thm)],[c_82,c_16441]) ).
tcf(c_16866,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(relation_composition(X1,X0),empty_set) = empty_set )
| ~ empty(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_87,c_16441]) ).
tcf(c_16868,plain,
( ( relation_composition(relation_dom(sK2),empty_set) = empty_set )
| ( apply(sK1,apply(sK0,sK17(relation_dom(sK2)))) = apply(sK2,sK17(relation_dom(sK2))) ) ),
inference(superposition,[status(thm)],[c_2468,c_16441]) ).
tcf(c_16869,plain,
! [X0: $i] :
( ( relation_composition(sK17(powerset(X0)),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7176,c_16441]) ).
tcf(c_16870,plain,
! [X0: $i] :
( ( relation_composition(sK17(sK16(powerset(X0))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12782,c_16441]) ).
tcf(c_16889,plain,
! [X0: $i,X1: $i] :
( ( apply(empty_set,sK12(sK2,empty_set,X0,X1)) = X1 )
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ relation(sK2)
| ~ in(ordered_pair(X0,X1),empty_set) ),
inference(superposition,[status(thm)],[c_16858,c_2068]) ).
tcf(c_16898,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(ordered_pair(sK12(X2,sK2,X0,X1),X3),empty_set)
| ~ relation(empty_set)
| ~ relation(sK2)
| ~ relation(X2)
| ~ in(ordered_pair(X1,X3),empty_set)
| ~ in(ordered_pair(X0,X1),relation_composition(X2,sK2)) ),
inference(superposition,[status(thm)],[c_16858,c_2067]) ).
tcf(c_16899,plain,
! [X0: $i] :
( in(ordered_pair(relation_dom(sK0),X0),empty_set)
| ~ relation(empty_set)
| ~ in(relation_dom(sK0),relation_dom(sK2))
| ~ in(ordered_pair(empty_set,X0),empty_set) ),
inference(superposition,[status(thm)],[c_16858,c_13991]) ).
tcf(c_16903,plain,
! [X0: $i,X1: $i] :
( ( apply(empty_set,sK12(sK1,empty_set,X0,X1)) = X1 )
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ relation(sK1)
| ~ in(ordered_pair(X0,X1),empty_set) ),
inference(superposition,[status(thm)],[c_16859,c_2068]) ).
tcf(c_16912,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(ordered_pair(sK12(X2,sK1,X0,X1),X3),empty_set)
| ~ relation(empty_set)
| ~ relation(sK1)
| ~ relation(X2)
| ~ in(ordered_pair(X1,X3),empty_set)
| ~ in(ordered_pair(X0,X1),relation_composition(X2,sK1)) ),
inference(superposition,[status(thm)],[c_16859,c_2067]) ).
tcf(c_16913,plain,
! [X0: $i] :
( in(ordered_pair(apply(sK0,sK17(sK16(relation_dom(sK2)))),X0),empty_set)
| ( relation_dom(sK17(powerset(relation_dom(sK2)))) = empty_set )
| ~ relation(empty_set)
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0),empty_set) ),
inference(superposition,[status(thm)],[c_16859,c_16024]) ).
tcf(c_16914,plain,
! [X0: $i] :
( in(ordered_pair(apply(sK0,sK17(relation_dom(sK2))),X0),empty_set)
| ( relation_dom(sK17(powerset(sK2))) = empty_set )
| ~ relation(empty_set)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),empty_set) ),
inference(superposition,[status(thm)],[c_16859,c_15395]) ).
tcf(c_16915,plain,
! [X0: $i] :
( in(ordered_pair(apply(sK0,sK17(relation_dom(sK2))),X0),empty_set)
| ( relation_dom(sK17(powerset(relation_dom(sK2)))) = empty_set )
| ~ relation(empty_set)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),empty_set) ),
inference(superposition,[status(thm)],[c_16859,c_14594]) ).
tcf(c_16916,plain,
! [X0: $i] :
( in(ordered_pair(apply(sK0,sK17(relation_dom(sK2))),X0),empty_set)
| ( sK17(powerset(relation_dom(relation_dom(sK2)))) = empty_set )
| ~ relation(empty_set)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),empty_set) ),
inference(superposition,[status(thm)],[c_16859,c_14178]) ).
tcf(c_16917,plain,
! [X0: $i] :
( in(ordered_pair(apply(sK0,sK17(relation_dom(sK2))),X0),empty_set)
| ( relation_dom(relation_dom(relation_dom(relation_dom(sK2)))) = empty_set )
| ~ relation(empty_set)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),empty_set) ),
inference(superposition,[status(thm)],[c_16859,c_12980]) ).
tcf(c_16918,plain,
! [X0: $i] :
( in(ordered_pair(apply(sK0,sK17(relation_dom(sK2))),X0),empty_set)
| ( sK17(powerset(sK2)) = empty_set )
| ~ relation(empty_set)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),empty_set) ),
inference(superposition,[status(thm)],[c_16859,c_12118]) ).
tcf(c_16919,plain,
! [X0: $i] :
( in(ordered_pair(apply(sK0,sK17(relation_dom(sK2))),X0),empty_set)
| ( sK17(powerset(relation_dom(sK2))) = empty_set )
| ~ relation(empty_set)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),empty_set) ),
inference(superposition,[status(thm)],[c_16859,c_10055]) ).
tcf(c_16920,plain,
! [X0: $i] :
( in(ordered_pair(apply(sK0,sK3(empty_set,relation_dom(sK2))),X0),empty_set)
| ( relation_dom(sK2) = empty_set )
| ~ relation(empty_set)
| ~ in(apply(sK0,sK3(empty_set,relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK3(empty_set,relation_dom(sK2))),X0),empty_set) ),
inference(superposition,[status(thm)],[c_16859,c_7405]) ).
tcf(c_16921,plain,
! [X0: $i] :
( in(ordered_pair(apply(sK0,sK17(relation_dom(sK2))),X0),empty_set)
| ( relation_dom(relation_dom(relation_dom(sK2))) = empty_set )
| ~ relation(empty_set)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),empty_set) ),
inference(superposition,[status(thm)],[c_16859,c_8516]) ).
tcf(c_16922,plain,
! [X0: $i] :
( in(ordered_pair(apply(sK0,sK17(relation_dom(sK2))),X0),empty_set)
| ( relation_dom(relation_dom(sK2)) = empty_set )
| ~ relation(empty_set)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),empty_set) ),
inference(superposition,[status(thm)],[c_16859,c_7882]) ).
tcf(c_16923,plain,
! [X0: $i] :
( in(ordered_pair(apply(sK0,sK17(relation_dom(sK2))),X0),empty_set)
| ( relation_dom(sK2) = sK2 )
| ~ relation(empty_set)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),empty_set) ),
inference(superposition,[status(thm)],[c_16859,c_5975]) ).
tcf(c_16924,plain,
! [X0: $i] :
( in(ordered_pair(apply(sK0,sK17(relation_dom(sK2))),X0),empty_set)
| ( relation_dom(sK2) = empty_set )
| ~ relation(empty_set)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),empty_set) ),
inference(superposition,[status(thm)],[c_16859,c_5928]) ).
tcf(c_16925,plain,
! [X0: $i] :
( in(ordered_pair(apply(sK0,sK17(relation_dom(sK2))),X0),empty_set)
| ( sK2 = empty_set )
| ~ relation(empty_set)
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),empty_set) ),
inference(superposition,[status(thm)],[c_16859,c_5890]) ).
tcf(c_16927,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(apply(sK0,X0),X1),empty_set)
| ( apply(sK0,X0) = empty_set )
| ( apply(sK1,apply(sK0,X0)) = empty_set )
| ~ relation(empty_set)
| ~ in(ordered_pair(apply(sK2,X0),X1),empty_set) ),
inference(superposition,[status(thm)],[c_16859,c_6088]) ).
tcf(c_16928,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(apply(sK0,X0),X1),empty_set)
| ( apply(sK2,X0) = empty_set )
| ~ relation(empty_set)
| ~ in(apply(sK0,X0),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,X0),X1),empty_set) ),
inference(superposition,[status(thm)],[c_16859,c_4264]) ).
tcf(c_16929,plain,
! [X0: $i,X1: $i] :
( ( apply(empty_set,sK12(sK0,empty_set,X0,X1)) = X1 )
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ relation(sK0)
| ~ in(ordered_pair(X0,X1),empty_set) ),
inference(superposition,[status(thm)],[c_16860,c_2068]) ).
tcf(c_16938,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(ordered_pair(sK12(X2,sK0,X0,X1),X3),empty_set)
| ~ relation(empty_set)
| ~ relation(sK0)
| ~ relation(X2)
| ~ in(ordered_pair(X1,X3),empty_set)
| ~ in(ordered_pair(X0,X1),relation_composition(X2,sK0)) ),
inference(superposition,[status(thm)],[c_16860,c_2067]) ).
tcf(c_16940,plain,
! [X0: $i,X1: $i] :
( ( apply(empty_set,sK12(sK6,empty_set,X0,X1)) = X1 )
| ~ function(empty_set)
| ~ relation(sK6)
| ~ relation(empty_set)
| ~ in(ordered_pair(X0,X1),empty_set) ),
inference(superposition,[status(thm)],[c_16862,c_2068]) ).
tcf(c_16949,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(ordered_pair(sK12(X2,sK6,X0,X1),X3),empty_set)
| ~ relation(sK6)
| ~ relation(empty_set)
| ~ relation(X2)
| ~ in(ordered_pair(X1,X3),empty_set)
| ~ in(ordered_pair(X0,X1),relation_composition(X2,sK6)) ),
inference(superposition,[status(thm)],[c_16862,c_2067]) ).
tcf(c_16951,plain,
! [X0: $i,X1: $i] :
( ( apply(empty_set,sK12(sK7,empty_set,X0,X1)) = X1 )
| ~ function(empty_set)
| ~ relation(sK7)
| ~ relation(empty_set)
| ~ in(ordered_pair(X0,X1),empty_set) ),
inference(superposition,[status(thm)],[c_16865,c_2068]) ).
tcf(c_16960,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(ordered_pair(sK12(X2,sK7,X0,X1),X3),empty_set)
| ~ relation(sK7)
| ~ relation(empty_set)
| ~ relation(X2)
| ~ in(ordered_pair(X1,X3),empty_set)
| ~ in(ordered_pair(X0,X1),relation_composition(X2,sK7)) ),
inference(superposition,[status(thm)],[c_16865,c_2067]) ).
tcf(c_16966,plain,
! [X0: $i] :
( ( relation_composition(relation_dom(relation_dom(X0)),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_65,c_16861]) ).
tcf(c_16967,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(relation_dom(relation_composition(X1,X0)),empty_set) = empty_set )
| ~ empty(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_86,c_16861]) ).
tcf(c_16968,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(relation_dom(relation_composition(X0,X1)),empty_set) = empty_set )
| ~ empty(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_88,c_16861]) ).
tcf(c_16969,plain,
relation_composition(relation_dom(empty_set),empty_set) = empty_set,
inference(superposition,[status(thm)],[c_110,c_16861]) ).
tcf(c_16970,plain,
( ( relation_composition(relation_dom(relation_dom(sK2)),empty_set) = empty_set )
| ( apply(sK1,apply(sK0,sK17(sK16(relation_dom(sK2))))) = apply(sK2,sK17(sK16(relation_dom(sK2)))) ) ),
inference(superposition,[status(thm)],[c_11951,c_16861]) ).
tcf(c_16971,plain,
( ( relation_composition(relation_dom(relation_dom(sK2)),empty_set) = empty_set )
| ( apply(sK1,apply(sK0,sK17(relation_dom(sK2)))) = apply(sK2,sK17(relation_dom(sK2))) ) ),
inference(superposition,[status(thm)],[c_2425,c_16861]) ).
tcf(c_16972,plain,
( ( relation_composition(relation_dom(sK2),empty_set) = empty_set )
| ( apply(sK1,apply(sK0,sK17(sK16(relation_dom(sK2))))) = apply(sK2,sK17(sK16(relation_dom(sK2)))) ) ),
inference(superposition,[status(thm)],[c_12039,c_16861]) ).
tcf(c_16974,plain,
! [X0: $i] :
( ( relation_composition(relation_dom(sK17(powerset(X0))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6912,c_16861]) ).
tcf(c_16975,plain,
! [X0: $i] :
( ( relation_composition(relation_dom(sK17(sK16(powerset(X0)))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12308,c_16861]) ).
tcf(c_17027,plain,
( ( sK17(powerset(relation_dom(relation_dom(sK2)))) = empty_set )
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(sK1,ordered_pair(apply(sK0,sK17(sK16(relation_dom(sK2)))),apply(sK2,sK17(sK16(relation_dom(sK2)))))) ),
inference(superposition,[status(thm)],[c_16428,c_64]) ).
tcf(c_17028,plain,
( element(ordered_pair(apply(sK0,sK17(sK16(relation_dom(sK2)))),apply(sK2,sK17(sK16(relation_dom(sK2))))),sK1)
| ( sK17(powerset(relation_dom(relation_dom(sK2)))) = empty_set )
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_16428,c_63]) ).
tcf(c_17031,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(apply(sK0,sK17(sK16(relation_dom(sK2)))),X0),relation_composition(sK1,X1))
| ( sK17(powerset(relation_dom(relation_dom(sK2)))) = empty_set )
| ~ relation(sK1)
| ~ relation(X1)
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0),X1) ),
inference(superposition,[status(thm)],[c_16428,c_299]) ).
tcf(c_17039,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(apply(sK0,sK17(sK16(relation_dom(sK2)))),X0),relation_composition(sK1,X1))
| ( sK17(powerset(relation_dom(relation_dom(sK2)))) = empty_set )
| ~ relation(X1)
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17031,c_56]) ).
tcf(c_17056,plain,
! [X0: $i] :
( in(ordered_pair(apply(sK0,sK17(sK16(relation_dom(sK2)))),X0),empty_set)
| ( sK17(powerset(relation_dom(relation_dom(sK2)))) = empty_set )
| ~ relation(empty_set)
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0),empty_set) ),
inference(superposition,[status(thm)],[c_16859,c_17039]) ).
tcf(c_17057,plain,
! [X0: $i,X1: $i] :
( ( sK17(powerset(relation_dom(relation_dom(sK2)))) = empty_set )
| ~ relation(X0)
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X1),X0)
| ~ in(relation_composition(sK1,X0),ordered_pair(apply(sK0,sK17(sK16(relation_dom(sK2)))),X1)) ),
inference(superposition,[status(thm)],[c_17039,c_64]) ).
tcf(c_17058,plain,
! [X0: $i,X1: $i] :
( element(ordered_pair(apply(sK0,sK17(sK16(relation_dom(sK2)))),X0),relation_composition(sK1,X1))
| ( sK17(powerset(relation_dom(relation_dom(sK2)))) = empty_set )
| ~ relation(X1)
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0),X1) ),
inference(superposition,[status(thm)],[c_17039,c_63]) ).
tcf(c_17059,plain,
! [X0: $i,X1: $i] :
( ( sK17(powerset(relation_dom(relation_dom(sK2)))) = empty_set )
| ~ relation(X1)
| ~ empty(relation_composition(sK1,X1))
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0),X1) ),
inference(superposition,[status(thm)],[c_17039,c_61]) ).
tcf(c_17060,plain,
! [X0: $i,X1: $i] :
( in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(relation_composition(sK1,X1)))
| ( sK17(powerset(relation_dom(relation_dom(sK2)))) = empty_set )
| ~ relation(X1)
| ~ relation(relation_composition(sK1,X1))
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0),X1) ),
inference(superposition,[status(thm)],[c_17039,c_70]) ).
tcf(c_17061,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(ordered_pair(apply(sK0,sK17(sK16(relation_dom(sK2)))),X2),relation_composition(relation_composition(sK1,X1),X3))
| ( sK17(powerset(relation_dom(relation_dom(sK2)))) = empty_set )
| ~ relation(X3)
| ~ relation(X1)
| ~ relation(relation_composition(sK1,X1))
| ~ in(ordered_pair(X0,X2),X3)
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0),X1) ),
inference(superposition,[status(thm)],[c_17039,c_299]) ).
tcf(c_17062,plain,
! [X0: $i,X1: $i] :
( ( sK17(powerset(relation_dom(relation_dom(sK2)))) = empty_set )
| ( apply(relation_composition(sK1,X1),apply(sK0,sK17(sK16(relation_dom(sK2))))) = X0 )
| ~ relation(X1)
| ~ function(relation_composition(sK1,X1))
| ~ relation(relation_composition(sK1,X1))
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0),X1) ),
inference(superposition,[status(thm)],[c_17039,c_152]) ).
tcf(c_17063,plain,
! [X0: $i,X1: $i] :
( ( sK17(powerset(relation_dom(relation_dom(sK2)))) = empty_set )
| ( apply(X1,sK12(sK1,X1,apply(sK0,sK17(sK16(relation_dom(sK2)))),X0)) = X0 )
| ~ relation(sK1)
| ~ function(X1)
| ~ relation(X1)
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0),X1) ),
inference(superposition,[status(thm)],[c_17039,c_2068]) ).
tcf(c_17064,plain,
! [X0: $i] :
( ( sK17(powerset(relation_dom(relation_dom(sK2)))) = empty_set )
| ~ relation(sK1)
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_17039,c_2063]) ).
tcf(c_17065,plain,
! [X0: $i] :
( ( sK17(powerset(relation_dom(relation_dom(sK2)))) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,sK17(sK16(relation_dom(sK2)))),X0),X0))) = apply(sK2,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,sK17(sK16(relation_dom(sK2)))),X0),X0)) )
| ~ relation(sK1)
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_17039,c_2064]) ).
tcf(c_17066,plain,
! [X0: $i] :
( ( sK17(powerset(relation_dom(relation_dom(sK2)))) = empty_set )
| ~ relation(empty_set)
| ~ relation(sK1)
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0),empty_set) ),
inference(superposition,[status(thm)],[c_17039,c_3818]) ).
tcf(c_17072,plain,
! [X0: $i] :
( ( sK17(powerset(relation_dom(relation_dom(sK2)))) = empty_set )
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17064,c_56]) ).
tcf(c_17094,plain,
! [X0: $i,X1: $i] :
( ( sK17(powerset(relation_dom(relation_dom(sK2)))) = empty_set )
| ( apply(X1,sK12(sK1,X1,apply(sK0,sK17(sK16(relation_dom(sK2)))),X0)) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17063,c_56]) ).
tcf(c_17116,plain,
! [X0: $i] :
( ( sK17(powerset(relation_dom(relation_dom(sK2)))) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,sK17(sK16(relation_dom(sK2)))),X0),X0))) = apply(sK2,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,sK17(sK16(relation_dom(sK2)))),X0),X0)) )
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17065,c_56]) ).
tcf(c_17143,plain,
! [X0: $i] :
( ( sK17(powerset(relation_dom(relation_dom(sK2)))) = empty_set )
| ( apply(sK0,ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0)) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0))) = empty_set )
| ( apply(relation_dom(sK2),sK12(sK1,relation_dom(sK2),apply(sK0,sK17(sK16(relation_dom(sK2)))),X0)) = X0 )
| ~ function(relation_dom(sK2))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_4011,c_17094]) ).
tcf(c_17144,plain,
! [X0: $i] :
( ( sK17(powerset(relation_dom(relation_dom(sK2)))) = empty_set )
| ( apply(sK0,ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0)) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0))) = empty_set )
| ( apply(relation_dom(sK0),sK12(sK1,relation_dom(sK0),apply(sK0,sK17(sK16(relation_dom(sK2)))),X0)) = X0 )
| ~ function(relation_dom(sK0))
| ~ relation(relation_dom(sK0))
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_4110,c_17094]) ).
tcf(c_17145,plain,
! [X0: $i] :
( ( sK17(powerset(relation_dom(relation_dom(sK2)))) = empty_set )
| ( apply(sK2,ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0)) = empty_set )
| ( apply(relation_dom(sK0),sK12(sK1,relation_dom(sK0),apply(sK0,sK17(sK16(relation_dom(sK2)))),X0)) = X0 )
| ~ function(relation_dom(sK0))
| ~ relation(relation_dom(sK0))
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_3449,c_17094]) ).
tcf(c_17146,plain,
! [X0: $i] :
( ( sK17(powerset(relation_dom(relation_dom(sK2)))) = empty_set )
| ( apply(X0,sK12(sK1,X0,apply(sK0,sK17(sK16(relation_dom(sK2)))),sK5(X0,apply(sK2,sK17(sK16(relation_dom(sK2))))))) = sK5(X0,apply(sK2,sK17(sK16(relation_dom(sK2))))) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(apply(sK2,sK17(sK16(relation_dom(sK2)))),relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_71,c_17094]) ).
tcf(c_17147,plain,
! [X0: $i] :
( ( sK17(powerset(relation_dom(relation_dom(sK2)))) = empty_set )
| ( apply(X0,sK12(sK1,X0,apply(sK0,sK17(sK16(relation_dom(sK2)))),apply(X0,apply(sK2,sK17(sK16(relation_dom(sK2))))))) = apply(X0,apply(sK2,sK17(sK16(relation_dom(sK2))))) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(apply(sK2,sK17(sK16(relation_dom(sK2)))),relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_73,c_17094]) ).
tcf(c_17148,plain,
! [X0: $i,X1: $i] :
( ( sK17(powerset(relation_dom(relation_dom(sK2)))) = empty_set )
| ( apply(X0,ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X1)) = empty_set )
| ( apply(relation_dom(X0),sK12(sK1,relation_dom(X0),apply(sK0,sK17(sK16(relation_dom(sK2)))),X1)) = X1 )
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom(X0))
| ~ relation(relation_dom(X0))
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_75,c_17094]) ).
tcf(c_17149,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK17(powerset(relation_dom(relation_dom(sK2)))) = empty_set )
| ( apply(X1,sK12(sK1,X1,apply(sK0,sK17(sK16(relation_dom(sK2)))),sK12(X1,X2,apply(sK2,sK17(sK16(relation_dom(sK2)))),X0))) = sK12(X1,X2,apply(sK2,sK17(sK16(relation_dom(sK2)))),X0) )
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0),relation_composition(X1,X2)) ),
inference(superposition,[status(thm)],[c_301,c_17094]) ).
tcf(c_17150,plain,
! [X0: $i,X1: $i] :
( ( sK17(powerset(relation_dom(relation_dom(sK2)))) = empty_set )
| ( apply(relation_dom(sK0),sK12(sK1,relation_dom(sK0),apply(sK0,sK17(sK16(relation_dom(sK2)))),sK12(relation_dom(sK2),X1,apply(sK2,sK17(sK16(relation_dom(sK2)))),X0))) = sK12(relation_dom(sK2),X1,apply(sK2,sK17(sK16(relation_dom(sK2)))),X0) )
| ~ relation(X1)
| ~ function(relation_dom(sK0))
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0),relation_composition(relation_dom(sK2),X1)) ),
inference(superposition,[status(thm)],[c_2283,c_17094]) ).
tcf(c_17151,plain,
( ( sK17(powerset(relation_dom(relation_dom(sK2)))) = empty_set )
| ( apply(relation_dom(sK0),sK12(sK1,relation_dom(sK0),apply(sK0,sK17(sK16(relation_dom(sK2)))),sK5(relation_dom(sK2),apply(sK2,sK17(sK16(relation_dom(sK2))))))) = sK5(relation_dom(sK2),apply(sK2,sK17(sK16(relation_dom(sK2))))) )
| ~ function(relation_dom(sK0))
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(apply(sK2,sK17(sK16(relation_dom(sK2)))),relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_3019,c_17094]) ).
tcf(c_17152,plain,
( ( sK17(powerset(relation_dom(relation_dom(sK2)))) = empty_set )
| ( apply(relation_dom(sK0),sK12(sK1,relation_dom(sK0),apply(sK0,sK17(sK16(relation_dom(sK2)))),apply(relation_dom(sK2),apply(sK2,sK17(sK16(relation_dom(sK2))))))) = apply(relation_dom(sK2),apply(sK2,sK17(sK16(relation_dom(sK2))))) )
| ~ function(relation_dom(sK0))
| ~ function(relation_dom(sK2))
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(apply(sK2,sK17(sK16(relation_dom(sK2)))),relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_3551,c_17094]) ).
tcf(c_17266,plain,
! [X0: $i,X1: $i] :
( ( apply(sK2,X0) = empty_set )
| ( apply(sK2,ordered_pair(apply(sK2,X0),X1)) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,X0),X1),X1))) = apply(sK2,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,X0),X1),X1)) )
| ~ function(sK2)
| ~ relation(sK2)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_75,c_16398]) ).
tcf(c_17281,plain,
! [X0: $i,X1: $i] :
( ( apply(sK2,X0) = empty_set )
| ( apply(sK2,ordered_pair(apply(sK2,X0),X1)) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,X0),X1),X1))) = apply(sK2,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,X0),X1),X1)) )
| ~ relation(relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17266,c_55,c_54]) ).
tcf(c_17299,plain,
! [X0: $i,X1: $i] :
( ( apply(sK2,X0) = empty_set )
| ( apply(sK2,ordered_pair(apply(sK2,X0),X1)) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,X0),X1),X1))) = apply(sK2,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,X0),X1),X1)) )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_66,c_17281]) ).
tcf(c_17300,plain,
! [X0: $i,X1: $i] :
( ( apply(sK2,X0) = empty_set )
| ( apply(sK1,apply(sK0,sK17(relation_dom(sK2)))) = apply(sK2,sK17(relation_dom(sK2))) )
| ( apply(sK2,ordered_pair(apply(sK2,X0),X1)) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,X0),X1),X1))) = apply(sK2,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,X0),X1),X1)) ) ),
inference(superposition,[status(thm)],[c_2468,c_17281]) ).
tcf(c_17321,plain,
! [X0: $i,X1: $i] :
( ( apply(sK0,X0) = empty_set )
| ( apply(sK1,apply(sK0,X0)) = empty_set )
| ( apply(sK2,ordered_pair(apply(sK2,X0),X1)) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,X0),X1),X1))) = apply(sK2,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,X0),X1),X1)) )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_66,c_16352]) ).
tcf(c_17322,plain,
! [X0: $i,X1: $i] :
( ( apply(sK0,X0) = empty_set )
| ( apply(sK1,apply(sK0,X0)) = empty_set )
| ( apply(sK1,apply(sK0,sK17(relation_dom(sK2)))) = apply(sK2,sK17(relation_dom(sK2))) )
| ( apply(sK2,ordered_pair(apply(sK2,X0),X1)) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,X0),X1),X1))) = apply(sK2,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,X0),X1),X1)) ) ),
inference(superposition,[status(thm)],[c_2468,c_16352]) ).
tcf(c_17340,plain,
( in(ordered_pair(apply(sK0,sK17(sK16(relation_dom(sK2)))),apply(sK2,sK17(sK16(relation_dom(sK2))))),sK1)
| ( relation_dom(relation_dom(relation_dom(relation_dom(sK2)))) = empty_set )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_12024,c_73]) ).
tcf(c_17341,plain,
( in(ordered_pair(apply(sK0,sK17(sK16(relation_dom(sK2)))),apply(sK2,sK17(sK16(relation_dom(sK2))))),sK1)
| ( relation_dom(relation_dom(relation_dom(relation_dom(sK2)))) = empty_set )
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17340,c_57,c_56]) ).
tcf(c_17349,plain,
! [X0: $i] :
( ( relation_composition(relation_dom(relation_dom(relation_dom(X0))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_65,c_16966]) ).
tcf(c_17350,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(relation_dom(relation_dom(relation_composition(X1,X0))),empty_set) = empty_set )
| ~ empty(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_86,c_16966]) ).
tcf(c_17351,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(relation_dom(relation_dom(relation_composition(X0,X1))),empty_set) = empty_set )
| ~ empty(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_88,c_16966]) ).
tcf(c_17352,plain,
relation_composition(relation_dom(relation_dom(empty_set)),empty_set) = empty_set,
inference(superposition,[status(thm)],[c_110,c_16966]) ).
tcf(c_17353,plain,
( ( relation_composition(relation_dom(relation_dom(relation_dom(sK2))),empty_set) = empty_set )
| ( apply(sK1,apply(sK0,sK17(sK16(relation_dom(sK2))))) = apply(sK2,sK17(sK16(relation_dom(sK2)))) ) ),
inference(superposition,[status(thm)],[c_11951,c_16966]) ).
tcf(c_17354,plain,
( ( relation_composition(relation_dom(relation_dom(relation_dom(sK2))),empty_set) = empty_set )
| ( apply(sK1,apply(sK0,sK17(relation_dom(sK2)))) = apply(sK2,sK17(relation_dom(sK2))) ) ),
inference(superposition,[status(thm)],[c_2425,c_16966]) ).
tcf(c_17357,plain,
! [X0: $i] :
( ( relation_composition(relation_dom(relation_dom(sK17(powerset(X0)))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6912,c_16966]) ).
tcf(c_17358,plain,
! [X0: $i] :
( ( relation_composition(relation_dom(relation_dom(sK17(sK16(powerset(X0))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12308,c_16966]) ).
tcf(c_17410,plain,
! [X0: $i,X1: $i] :
( ( sK17(powerset(relation_dom(X0))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_65,c_7174]) ).
tcf(c_17411,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK17(powerset(relation_composition(X1,X0))) = X2 )
| ~ empty(X2)
| ~ empty(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_86,c_7174]) ).
tcf(c_17412,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK17(powerset(relation_composition(X0,X1))) = X2 )
| ~ empty(X2)
| ~ empty(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_88,c_7174]) ).
tcf(c_17413,plain,
! [X0: $i] :
( ( sK17(powerset(empty_set)) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_110,c_7174]) ).
tcf(c_17414,plain,
! [X0: $i] :
( ( sK17(powerset(relation_dom(sK2))) = X0 )
| ( apply(sK1,apply(sK0,sK17(sK16(relation_dom(sK2))))) = apply(sK2,sK17(sK16(relation_dom(sK2)))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11951,c_7174]) ).
tcf(c_17415,plain,
! [X0: $i] :
( ( sK17(powerset(relation_dom(sK2))) = X0 )
| ( apply(sK1,apply(sK0,sK17(relation_dom(sK2)))) = apply(sK2,sK17(relation_dom(sK2))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2425,c_7174]) ).
tcf(c_17416,plain,
! [X0: $i] :
( ( sK17(powerset(sK2)) = X0 )
| ( apply(sK1,apply(sK0,sK17(sK16(relation_dom(sK2))))) = apply(sK2,sK17(sK16(relation_dom(sK2)))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12039,c_7174]) ).
tcf(c_17417,plain,
! [X0: $i] :
( ( sK17(powerset(sK2)) = X0 )
| ( apply(sK1,apply(sK0,sK17(relation_dom(sK2)))) = apply(sK2,sK17(relation_dom(sK2))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2475,c_7174]) ).
tcf(c_17418,plain,
! [X0: $i,X1: $i] :
( ( sK17(powerset(sK17(powerset(X0)))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6912,c_7174]) ).
tcf(c_17419,plain,
! [X0: $i,X1: $i] :
( ( sK17(powerset(sK17(sK16(powerset(X0))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12308,c_7174]) ).
tcf(c_17455,plain,
! [X0: $i] :
( in(sK17(sK17(powerset(X0))),X0)
| empty(sK17(powerset(X0))) ),
inference(global_subsumption_just,[status(thm)],[c_8482,c_6912,c_8482]) ).
tcf(c_17456,plain,
! [X0: $i] :
( empty(sK17(powerset(X0)))
| in(sK17(sK17(powerset(X0))),X0) ),
inference(renaming,[status(thm)],[c_17455]) ).
tcf(c_17462,plain,
( empty(sK17(powerset(empty_set)))
| in(sK17(empty_set),empty_set) ),
inference(superposition,[status(thm)],[c_7736,c_17456]) ).
tcf(c_17463,plain,
( empty(sK17(powerset(relation_dom(sK2))))
| ~ empty(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_17456,c_2047]) ).
tcf(c_17464,plain,
( empty(sK17(powerset(relation_dom(sK2))))
| ( apply(sK1,apply(sK0,sK17(sK17(powerset(relation_dom(sK2)))))) = apply(sK2,sK17(sK17(powerset(relation_dom(sK2))))) ) ),
inference(superposition,[status(thm)],[c_17456,c_53]) ).
tcf(c_17465,plain,
( empty(sK17(powerset(relation_dom(sK2))))
| in(sK17(sK17(powerset(relation_dom(sK2)))),relation_dom(sK0)) ),
inference(superposition,[status(thm)],[c_17456,c_51]) ).
tcf(c_17466,plain,
( empty(sK17(powerset(relation_dom(sK0))))
| in(sK17(sK17(powerset(relation_dom(sK0)))),relation_dom(sK2))
| ( apply(sK1,apply(sK0,sK17(sK17(powerset(relation_dom(sK0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_17456,c_3475]) ).
tcf(c_17467,plain,
! [X0: $i] :
( empty(sK17(powerset(X0)))
| ~ in(X0,sK17(sK17(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_17456,c_64]) ).
tcf(c_17470,plain,
! [X0: $i] :
( empty(sK17(powerset(relation_dom(X0))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17456,c_11389]) ).
tcf(c_17471,plain,
empty(sK17(powerset(empty_set))),
inference(superposition,[status(thm)],[c_17456,c_3809]) ).
tcf(c_17472,plain,
! [X0: $i] :
( empty(X0)
| empty(sK17(powerset(sK16(X0))))
| element(sK17(sK17(powerset(sK16(X0)))),X0) ),
inference(superposition,[status(thm)],[c_17456,c_2939]) ).
tcf(c_17473,plain,
! [X0: $i] :
( empty(sK17(powerset(sK17(powerset(X0)))))
| element(sK17(sK17(powerset(sK17(powerset(X0))))),X0) ),
inference(superposition,[status(thm)],[c_17456,c_2940]) ).
tcf(c_17474,plain,
! [X0: $i] :
( empty(sK17(powerset(sK17(powerset(X0)))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17456,c_2925]) ).
tcf(c_17475,plain,
( empty(sK17(powerset(relation_dom(relation_dom(sK2)))))
| ( apply(sK1,apply(sK0,ordered_pair(sK17(sK17(powerset(relation_dom(relation_dom(sK2))))),apply(relation_dom(sK2),sK17(sK17(powerset(relation_dom(relation_dom(sK2))))))))) = apply(sK2,ordered_pair(sK17(sK17(powerset(relation_dom(relation_dom(sK2))))),apply(relation_dom(sK2),sK17(sK17(powerset(relation_dom(relation_dom(sK2)))))))) )
| ~ function(relation_dom(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_17456,c_3550]) ).
tcf(c_17476,plain,
( empty(sK17(powerset(relation_dom(relation_dom(sK2)))))
| in(sK17(sK17(powerset(relation_dom(relation_dom(sK2))))),relation_dom(relation_dom(sK0)))
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_17456,c_3134]) ).
tcf(c_17477,plain,
( empty(sK17(powerset(relation_dom(relation_dom(sK2)))))
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_17456,c_3017]) ).
tcf(c_17478,plain,
( empty(sK17(powerset(relation_dom(relation_dom(sK2)))))
| ( apply(sK1,apply(sK0,ordered_pair(sK17(sK17(powerset(relation_dom(relation_dom(sK2))))),sK5(relation_dom(sK2),sK17(sK17(powerset(relation_dom(relation_dom(sK2))))))))) = apply(sK2,ordered_pair(sK17(sK17(powerset(relation_dom(relation_dom(sK2))))),sK5(relation_dom(sK2),sK17(sK17(powerset(relation_dom(relation_dom(sK2)))))))) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_17456,c_3018]) ).
tcf(c_17479,plain,
! [X0: $i] :
( empty(sK17(powerset(sK17(sK16(powerset(X0))))))
| element(sK17(sK17(powerset(sK17(sK16(powerset(X0)))))),X0) ),
inference(superposition,[status(thm)],[c_17456,c_11939]) ).
tcf(c_17480,plain,
! [X0: $i] :
( empty(sK17(powerset(sK17(sK16(powerset(X0))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17456,c_11936]) ).
tcf(c_17484,plain,
( empty(empty_set)
| in(sK17(empty_set),empty_set) ),
inference(light_normalisation,[status(thm)],[c_17462,c_7736]) ).
tcf(c_17557,plain,
( empty(sK17(powerset(empty_set)))
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_3857,c_17470]) ).
tcf(c_17558,plain,
! [X0: $i,X1: $i] :
( ( sK17(powerset(sK17(powerset(relation_dom(X0))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17470,c_7174]) ).
tcf(c_17559,plain,
! [X0: $i] :
( ( relation_composition(relation_dom(relation_dom(sK17(powerset(relation_dom(X0))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17470,c_16966]) ).
tcf(c_17560,plain,
! [X0: $i] :
( ( relation_composition(relation_dom(sK17(powerset(relation_dom(X0)))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17470,c_16861]) ).
tcf(c_17561,plain,
! [X0: $i] :
( ( relation_composition(empty_set,relation_dom(relation_dom(sK17(powerset(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17470,c_15920]) ).
tcf(c_17562,plain,
! [X0: $i] :
( ( relation_composition(empty_set,relation_dom(sK17(powerset(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17470,c_15264]) ).
tcf(c_17563,plain,
! [X0: $i] :
( ( sK17(sK16(powerset(relation_dom(sK17(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17470,c_12877]) ).
tcf(c_17564,plain,
! [X0: $i] :
( ( sK17(powerset(sK17(powerset(sK17(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17470,c_7742]) ).
tcf(c_17565,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK17(powerset(sK17(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17470,c_7236]) ).
tcf(c_17566,plain,
! [X0: $i] :
( ( relation_dom(sK17(powerset(relation_dom(sK17(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17470,c_9976]) ).
tcf(c_17567,plain,
! [X0: $i] :
( ( sK17(powerset(relation_dom(relation_dom(sK17(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17470,c_9849]) ).
tcf(c_17568,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK17(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17470,c_9793]) ).
tcf(c_17569,plain,
! [X0: $i] :
( ( sK17(sK16(powerset(sK17(powerset(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17470,c_12303]) ).
tcf(c_17570,plain,
! [X0: $i] :
( ( relation_dom(sK17(powerset(sK17(powerset(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17470,c_7171]) ).
tcf(c_17571,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK17(powerset(relation_dom(X0)))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17470,c_2387]) ).
tcf(c_17572,plain,
! [X0: $i] :
( ( sK17(powerset(relation_dom(sK17(powerset(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17470,c_7733]) ).
tcf(c_17573,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK17(powerset(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17470,c_7227]) ).
tcf(c_17577,plain,
! [X0: $i] :
( ( sK17(powerset(relation_dom(X0))) = relation_dom(sK2) )
| ( apply(sK1,apply(sK0,sK17(relation_dom(sK2)))) = apply(sK2,sK17(relation_dom(sK2))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17470,c_2466]) ).
tcf(c_17578,plain,
! [X0: $i] :
( ( sK17(powerset(relation_dom(X0))) = sK2 )
| ( apply(sK1,apply(sK0,sK17(relation_dom(sK2)))) = apply(sK2,sK17(relation_dom(sK2))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17470,c_2488]) ).
tcf(c_17581,plain,
! [X0: $i] :
( relation(sK17(powerset(relation_dom(X0))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17470,c_85]) ).
tcf(c_17582,plain,
! [X0: $i] :
( function(sK17(powerset(relation_dom(X0))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17470,c_80]) ).
tcf(c_17583,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(X0,sK17(powerset(relation_dom(X1)))) = empty_set )
| ~ empty(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17470,c_2607]) ).
tcf(c_17584,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(sK17(powerset(relation_dom(X1))),X0) = empty_set )
| ~ empty(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17470,c_2400]) ).
tcf(c_17670,plain,
( relation(sK17(powerset(empty_set)))
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_3857,c_17581]) ).
tcf(c_17671,plain,
! [X0: $i] :
( ( relation_composition(sK17(powerset(relation_dom(X0))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17581,c_16441]) ).
tcf(c_17672,plain,
! [X0: $i] :
( ( relation_composition(empty_set,sK17(powerset(relation_dom(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17581,c_15145]) ).
tcf(c_17673,plain,
( relation(empty_set)
| ~ empty(empty_set) ),
inference(light_normalisation,[status(thm)],[c_17670,c_7736]) ).
tcf(c_17682,plain,
( function(sK17(powerset(empty_set)))
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_3857,c_17582]) ).
tcf(c_17683,plain,
( function(empty_set)
| ~ empty(empty_set) ),
inference(light_normalisation,[status(thm)],[c_17682,c_7736]) ).
tcf(c_17688,plain,
! [X0: $i] :
( ( sK17(powerset(sK17(powerset(relation_dom(sK2))))) = X0 )
| ~ empty(X0)
| ~ empty(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_17463,c_7174]) ).
tcf(c_17689,plain,
( ( relation_composition(relation_dom(relation_dom(sK17(powerset(relation_dom(sK2))))),empty_set) = empty_set )
| ~ empty(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_17463,c_16966]) ).
tcf(c_17690,plain,
( ( relation_composition(relation_dom(sK17(powerset(relation_dom(sK2)))),empty_set) = empty_set )
| ~ empty(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_17463,c_16861]) ).
tcf(c_17691,plain,
( ( relation_composition(empty_set,relation_dom(relation_dom(sK17(powerset(relation_dom(sK2)))))) = empty_set )
| ~ empty(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_17463,c_15920]) ).
tcf(c_17692,plain,
( ( relation_composition(empty_set,relation_dom(sK17(powerset(relation_dom(sK2))))) = empty_set )
| ~ empty(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_17463,c_15264]) ).
tcf(c_17693,plain,
( ( sK17(sK16(powerset(relation_dom(sK17(powerset(relation_dom(sK2))))))) = empty_set )
| ~ empty(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_17463,c_12877]) ).
tcf(c_17694,plain,
( ( sK17(powerset(sK17(powerset(sK17(powerset(relation_dom(sK2))))))) = empty_set )
| ~ empty(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_17463,c_7742]) ).
tcf(c_17695,plain,
( ( relation_dom(relation_dom(sK17(powerset(sK17(powerset(relation_dom(sK2))))))) = empty_set )
| ~ empty(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_17463,c_7236]) ).
tcf(c_17696,plain,
( ( relation_dom(sK17(powerset(relation_dom(sK17(powerset(relation_dom(sK2))))))) = empty_set )
| ~ empty(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_17463,c_9976]) ).
tcf(c_17697,plain,
( ( sK17(powerset(relation_dom(relation_dom(sK17(powerset(relation_dom(sK2))))))) = empty_set )
| ~ empty(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_17463,c_9849]) ).
tcf(c_17698,plain,
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK17(powerset(relation_dom(sK2))))))) = empty_set )
| ~ empty(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_17463,c_9793]) ).
tcf(c_17699,plain,
( ( sK17(sK16(powerset(sK17(powerset(relation_dom(sK2)))))) = empty_set )
| ~ empty(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_17463,c_12303]) ).
tcf(c_17700,plain,
( ( relation_dom(sK17(powerset(sK17(powerset(relation_dom(sK2)))))) = empty_set )
| ~ empty(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_17463,c_7171]) ).
tcf(c_17701,plain,
! [X0: $i] :
( ( relation_dom(sK17(powerset(relation_dom(sK2)))) = X0 )
| ~ empty(X0)
| ~ empty(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_17463,c_2387]) ).
tcf(c_17702,plain,
( ( sK17(powerset(relation_dom(sK17(powerset(relation_dom(sK2)))))) = empty_set )
| ~ empty(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_17463,c_7733]) ).
tcf(c_17703,plain,
( ( relation_dom(relation_dom(relation_dom(sK17(powerset(relation_dom(sK2)))))) = empty_set )
| ~ empty(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_17463,c_7227]) ).
tcf(c_17704,plain,
( ( sK17(powerset(sK17(powerset(relation_dom(sK2))))) = empty_set )
| ~ empty(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_17463,c_7088]) ).
tcf(c_17705,plain,
( ( relation_dom(relation_dom(sK17(powerset(relation_dom(sK2))))) = empty_set )
| ~ empty(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_17463,c_6244]) ).
tcf(c_17706,plain,
( ( relation_dom(sK17(powerset(relation_dom(sK2)))) = empty_set )
| ~ empty(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_17463,c_2124]) ).
tcf(c_17707,plain,
( ( sK17(powerset(relation_dom(sK2))) = relation_dom(sK2) )
| ( apply(sK1,apply(sK0,sK17(relation_dom(sK2)))) = apply(sK2,sK17(relation_dom(sK2))) )
| ~ empty(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_17463,c_2466]) ).
tcf(c_17708,plain,
( ( sK17(powerset(relation_dom(sK2))) = sK2 )
| ( apply(sK1,apply(sK0,sK17(relation_dom(sK2)))) = apply(sK2,sK17(relation_dom(sK2))) )
| ~ empty(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_17463,c_2488]) ).
tcf(c_17709,plain,
! [X0: $i] :
( ( sK17(powerset(relation_dom(sK2))) = X0 )
| ~ empty(X0)
| ~ empty(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_17463,c_60]) ).
tcf(c_17710,plain,
( ( sK17(powerset(relation_dom(sK2))) = empty_set )
| ~ empty(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_17463,c_107]) ).
tcf(c_17711,plain,
( relation(sK17(powerset(relation_dom(sK2))))
| ~ empty(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_17463,c_85]) ).
tcf(c_17712,plain,
( function(sK17(powerset(relation_dom(sK2))))
| ~ empty(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_17463,c_80]) ).
tcf(c_17713,plain,
! [X0: $i] :
( ( relation_composition(X0,sK17(powerset(relation_dom(sK2)))) = empty_set )
| ~ relation(X0)
| ~ empty(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_17463,c_2607]) ).
tcf(c_17714,plain,
! [X0: $i] :
( ( relation_composition(sK17(powerset(relation_dom(sK2))),X0) = empty_set )
| ~ relation(X0)
| ~ empty(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_17463,c_2400]) ).
tcf(c_17814,plain,
( empty(sK17(powerset(relation_dom(sK2))))
| in(sK17(sK17(powerset(relation_dom(sK2)))),relation_dom(sK2))
| ( apply(sK1,apply(sK0,sK17(sK17(powerset(relation_dom(sK2)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_17465,c_3475]) ).
tcf(c_17815,plain,
( empty(sK17(powerset(relation_dom(sK2))))
| ~ in(relation_dom(sK0),sK17(sK17(powerset(relation_dom(sK2))))) ),
inference(superposition,[status(thm)],[c_17465,c_64]) ).
tcf(c_17816,plain,
( empty(sK17(powerset(relation_dom(sK2))))
| element(sK17(sK17(powerset(relation_dom(sK2)))),relation_dom(sK0)) ),
inference(superposition,[status(thm)],[c_17465,c_63]) ).
tcf(c_17830,plain,
! [X0: $i] :
( ( sK17(powerset(sK17(powerset(relation_dom(sK2))))) = X0 )
| ( apply(sK1,apply(sK0,sK17(sK17(powerset(relation_dom(sK2)))))) = apply(sK2,sK17(sK17(powerset(relation_dom(sK2))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17464,c_7174]) ).
tcf(c_17831,plain,
( ( relation_composition(relation_dom(relation_dom(sK17(powerset(relation_dom(sK2))))),empty_set) = empty_set )
| ( apply(sK1,apply(sK0,sK17(sK17(powerset(relation_dom(sK2)))))) = apply(sK2,sK17(sK17(powerset(relation_dom(sK2))))) ) ),
inference(superposition,[status(thm)],[c_17464,c_16966]) ).
tcf(c_17832,plain,
( ( relation_composition(relation_dom(sK17(powerset(relation_dom(sK2)))),empty_set) = empty_set )
| ( apply(sK1,apply(sK0,sK17(sK17(powerset(relation_dom(sK2)))))) = apply(sK2,sK17(sK17(powerset(relation_dom(sK2))))) ) ),
inference(superposition,[status(thm)],[c_17464,c_16861]) ).
tcf(c_17833,plain,
( ( relation_composition(empty_set,relation_dom(relation_dom(sK17(powerset(relation_dom(sK2)))))) = empty_set )
| ( apply(sK1,apply(sK0,sK17(sK17(powerset(relation_dom(sK2)))))) = apply(sK2,sK17(sK17(powerset(relation_dom(sK2))))) ) ),
inference(superposition,[status(thm)],[c_17464,c_15920]) ).
tcf(c_17834,plain,
( ( relation_composition(empty_set,relation_dom(sK17(powerset(relation_dom(sK2))))) = empty_set )
| ( apply(sK1,apply(sK0,sK17(sK17(powerset(relation_dom(sK2)))))) = apply(sK2,sK17(sK17(powerset(relation_dom(sK2))))) ) ),
inference(superposition,[status(thm)],[c_17464,c_15264]) ).
tcf(c_17835,plain,
( ( sK17(sK16(powerset(relation_dom(sK17(powerset(relation_dom(sK2))))))) = empty_set )
| ( apply(sK1,apply(sK0,sK17(sK17(powerset(relation_dom(sK2)))))) = apply(sK2,sK17(sK17(powerset(relation_dom(sK2))))) ) ),
inference(superposition,[status(thm)],[c_17464,c_12877]) ).
tcf(c_17836,plain,
( ( sK17(powerset(sK17(powerset(sK17(powerset(relation_dom(sK2))))))) = empty_set )
| ( apply(sK1,apply(sK0,sK17(sK17(powerset(relation_dom(sK2)))))) = apply(sK2,sK17(sK17(powerset(relation_dom(sK2))))) ) ),
inference(superposition,[status(thm)],[c_17464,c_7742]) ).
tcf(c_17837,plain,
( ( relation_dom(relation_dom(sK17(powerset(sK17(powerset(relation_dom(sK2))))))) = empty_set )
| ( apply(sK1,apply(sK0,sK17(sK17(powerset(relation_dom(sK2)))))) = apply(sK2,sK17(sK17(powerset(relation_dom(sK2))))) ) ),
inference(superposition,[status(thm)],[c_17464,c_7236]) ).
tcf(c_17838,plain,
( ( relation_dom(sK17(powerset(relation_dom(sK17(powerset(relation_dom(sK2))))))) = empty_set )
| ( apply(sK1,apply(sK0,sK17(sK17(powerset(relation_dom(sK2)))))) = apply(sK2,sK17(sK17(powerset(relation_dom(sK2))))) ) ),
inference(superposition,[status(thm)],[c_17464,c_9976]) ).
tcf(c_17839,plain,
( ( sK17(powerset(relation_dom(relation_dom(sK17(powerset(relation_dom(sK2))))))) = empty_set )
| ( apply(sK1,apply(sK0,sK17(sK17(powerset(relation_dom(sK2)))))) = apply(sK2,sK17(sK17(powerset(relation_dom(sK2))))) ) ),
inference(superposition,[status(thm)],[c_17464,c_9849]) ).
tcf(c_17840,plain,
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK17(powerset(relation_dom(sK2))))))) = empty_set )
| ( apply(sK1,apply(sK0,sK17(sK17(powerset(relation_dom(sK2)))))) = apply(sK2,sK17(sK17(powerset(relation_dom(sK2))))) ) ),
inference(superposition,[status(thm)],[c_17464,c_9793]) ).
tcf(c_17841,plain,
( ( sK17(sK16(powerset(sK17(powerset(relation_dom(sK2)))))) = empty_set )
| ( apply(sK1,apply(sK0,sK17(sK17(powerset(relation_dom(sK2)))))) = apply(sK2,sK17(sK17(powerset(relation_dom(sK2))))) ) ),
inference(superposition,[status(thm)],[c_17464,c_12303]) ).
tcf(c_17842,plain,
( ( relation_dom(sK17(powerset(sK17(powerset(relation_dom(sK2)))))) = empty_set )
| ( apply(sK1,apply(sK0,sK17(sK17(powerset(relation_dom(sK2)))))) = apply(sK2,sK17(sK17(powerset(relation_dom(sK2))))) ) ),
inference(superposition,[status(thm)],[c_17464,c_7171]) ).
tcf(c_17843,plain,
! [X0: $i] :
( ( relation_dom(sK17(powerset(relation_dom(sK2)))) = X0 )
| ( apply(sK1,apply(sK0,sK17(sK17(powerset(relation_dom(sK2)))))) = apply(sK2,sK17(sK17(powerset(relation_dom(sK2))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17464,c_2387]) ).
tcf(c_17844,plain,
( ( sK17(powerset(relation_dom(sK17(powerset(relation_dom(sK2)))))) = empty_set )
| ( apply(sK1,apply(sK0,sK17(sK17(powerset(relation_dom(sK2)))))) = apply(sK2,sK17(sK17(powerset(relation_dom(sK2))))) ) ),
inference(superposition,[status(thm)],[c_17464,c_7733]) ).
tcf(c_17845,plain,
( ( relation_dom(relation_dom(relation_dom(sK17(powerset(relation_dom(sK2)))))) = empty_set )
| ( apply(sK1,apply(sK0,sK17(sK17(powerset(relation_dom(sK2)))))) = apply(sK2,sK17(sK17(powerset(relation_dom(sK2))))) ) ),
inference(superposition,[status(thm)],[c_17464,c_7227]) ).
tcf(c_17846,plain,
( ( sK17(powerset(sK17(powerset(relation_dom(sK2))))) = empty_set )
| ( apply(sK1,apply(sK0,sK17(sK17(powerset(relation_dom(sK2)))))) = apply(sK2,sK17(sK17(powerset(relation_dom(sK2))))) ) ),
inference(superposition,[status(thm)],[c_17464,c_7088]) ).
tcf(c_17847,plain,
( ( relation_dom(relation_dom(sK17(powerset(relation_dom(sK2))))) = empty_set )
| ( apply(sK1,apply(sK0,sK17(sK17(powerset(relation_dom(sK2)))))) = apply(sK2,sK17(sK17(powerset(relation_dom(sK2))))) ) ),
inference(superposition,[status(thm)],[c_17464,c_6244]) ).
tcf(c_17848,plain,
( ( relation_dom(sK17(powerset(relation_dom(sK2)))) = empty_set )
| ( apply(sK1,apply(sK0,sK17(sK17(powerset(relation_dom(sK2)))))) = apply(sK2,sK17(sK17(powerset(relation_dom(sK2))))) ) ),
inference(superposition,[status(thm)],[c_17464,c_2124]) ).
tcf(c_17849,plain,
( ( sK17(powerset(relation_dom(sK2))) = relation_dom(sK2) )
| ( apply(sK1,apply(sK0,sK17(relation_dom(sK2)))) = apply(sK2,sK17(relation_dom(sK2))) )
| ( apply(sK1,apply(sK0,sK17(sK17(powerset(relation_dom(sK2)))))) = apply(sK2,sK17(sK17(powerset(relation_dom(sK2))))) ) ),
inference(superposition,[status(thm)],[c_17464,c_2466]) ).
tcf(c_17850,plain,
( ( sK17(powerset(relation_dom(sK2))) = sK2 )
| ( apply(sK1,apply(sK0,sK17(relation_dom(sK2)))) = apply(sK2,sK17(relation_dom(sK2))) )
| ( apply(sK1,apply(sK0,sK17(sK17(powerset(relation_dom(sK2)))))) = apply(sK2,sK17(sK17(powerset(relation_dom(sK2))))) ) ),
inference(superposition,[status(thm)],[c_17464,c_2488]) ).
tcf(c_17851,plain,
! [X0: $i] :
( ( sK17(powerset(relation_dom(sK2))) = X0 )
| ( apply(sK1,apply(sK0,sK17(sK17(powerset(relation_dom(sK2)))))) = apply(sK2,sK17(sK17(powerset(relation_dom(sK2))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17464,c_60]) ).
tcf(c_17852,plain,
( ( sK17(powerset(relation_dom(sK2))) = empty_set )
| ( apply(sK1,apply(sK0,sK17(sK17(powerset(relation_dom(sK2)))))) = apply(sK2,sK17(sK17(powerset(relation_dom(sK2))))) ) ),
inference(superposition,[status(thm)],[c_17464,c_107]) ).
tcf(c_17853,plain,
( relation(sK17(powerset(relation_dom(sK2))))
| ( apply(sK1,apply(sK0,sK17(sK17(powerset(relation_dom(sK2)))))) = apply(sK2,sK17(sK17(powerset(relation_dom(sK2))))) ) ),
inference(superposition,[status(thm)],[c_17464,c_85]) ).
tcf(c_17854,plain,
( function(sK17(powerset(relation_dom(sK2))))
| ( apply(sK1,apply(sK0,sK17(sK17(powerset(relation_dom(sK2)))))) = apply(sK2,sK17(sK17(powerset(relation_dom(sK2))))) ) ),
inference(superposition,[status(thm)],[c_17464,c_80]) ).
tcf(c_17855,plain,
! [X0: $i] :
( ( relation_composition(X0,sK17(powerset(relation_dom(sK2)))) = empty_set )
| ( apply(sK1,apply(sK0,sK17(sK17(powerset(relation_dom(sK2)))))) = apply(sK2,sK17(sK17(powerset(relation_dom(sK2))))) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17464,c_2607]) ).
tcf(c_17856,plain,
! [X0: $i] :
( ( relation_composition(sK17(powerset(relation_dom(sK2))),X0) = empty_set )
| ( apply(sK1,apply(sK0,sK17(sK17(powerset(relation_dom(sK2)))))) = apply(sK2,sK17(sK17(powerset(relation_dom(sK2))))) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17464,c_2400]) ).
tcf(c_18314,plain,
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK2)))) = empty_set )
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(sK1,ordered_pair(apply(sK0,sK17(sK16(relation_dom(sK2)))),apply(sK2,sK17(sK16(relation_dom(sK2)))))) ),
inference(superposition,[status(thm)],[c_17341,c_64]) ).
tcf(c_18315,plain,
( element(ordered_pair(apply(sK0,sK17(sK16(relation_dom(sK2)))),apply(sK2,sK17(sK16(relation_dom(sK2))))),sK1)
| ( relation_dom(relation_dom(relation_dom(relation_dom(sK2)))) = empty_set )
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_17341,c_63]) ).
tcf(c_18318,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(apply(sK0,sK17(sK16(relation_dom(sK2)))),X0),relation_composition(sK1,X1))
| ( relation_dom(relation_dom(relation_dom(relation_dom(sK2)))) = empty_set )
| ~ relation(sK1)
| ~ relation(X1)
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0),X1) ),
inference(superposition,[status(thm)],[c_17341,c_299]) ).
tcf(c_18326,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(apply(sK0,sK17(sK16(relation_dom(sK2)))),X0),relation_composition(sK1,X1))
| ( relation_dom(relation_dom(relation_dom(relation_dom(sK2)))) = empty_set )
| ~ relation(X1)
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18318,c_56]) ).
tcf(c_18343,plain,
! [X0: $i] :
( in(ordered_pair(apply(sK0,sK17(sK16(relation_dom(sK2)))),X0),empty_set)
| ( relation_dom(relation_dom(relation_dom(relation_dom(sK2)))) = empty_set )
| ~ relation(empty_set)
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0),empty_set) ),
inference(superposition,[status(thm)],[c_16859,c_18326]) ).
tcf(c_18344,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK2)))) = empty_set )
| ~ relation(X0)
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X1),X0)
| ~ in(relation_composition(sK1,X0),ordered_pair(apply(sK0,sK17(sK16(relation_dom(sK2)))),X1)) ),
inference(superposition,[status(thm)],[c_18326,c_64]) ).
tcf(c_18345,plain,
! [X0: $i,X1: $i] :
( element(ordered_pair(apply(sK0,sK17(sK16(relation_dom(sK2)))),X0),relation_composition(sK1,X1))
| ( relation_dom(relation_dom(relation_dom(relation_dom(sK2)))) = empty_set )
| ~ relation(X1)
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0),X1) ),
inference(superposition,[status(thm)],[c_18326,c_63]) ).
tcf(c_18346,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK2)))) = empty_set )
| ~ relation(X1)
| ~ empty(relation_composition(sK1,X1))
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0),X1) ),
inference(superposition,[status(thm)],[c_18326,c_61]) ).
tcf(c_18347,plain,
! [X0: $i,X1: $i] :
( in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(relation_composition(sK1,X1)))
| ( relation_dom(relation_dom(relation_dom(relation_dom(sK2)))) = empty_set )
| ~ relation(X1)
| ~ relation(relation_composition(sK1,X1))
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0),X1) ),
inference(superposition,[status(thm)],[c_18326,c_70]) ).
tcf(c_18348,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(ordered_pair(apply(sK0,sK17(sK16(relation_dom(sK2)))),X2),relation_composition(relation_composition(sK1,X1),X3))
| ( relation_dom(relation_dom(relation_dom(relation_dom(sK2)))) = empty_set )
| ~ relation(X3)
| ~ relation(X1)
| ~ relation(relation_composition(sK1,X1))
| ~ in(ordered_pair(X0,X2),X3)
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0),X1) ),
inference(superposition,[status(thm)],[c_18326,c_299]) ).
tcf(c_18349,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK2)))) = empty_set )
| ( apply(relation_composition(sK1,X1),apply(sK0,sK17(sK16(relation_dom(sK2))))) = X0 )
| ~ relation(X1)
| ~ function(relation_composition(sK1,X1))
| ~ relation(relation_composition(sK1,X1))
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0),X1) ),
inference(superposition,[status(thm)],[c_18326,c_152]) ).
tcf(c_18350,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK2)))) = empty_set )
| ( apply(X1,sK12(sK1,X1,apply(sK0,sK17(sK16(relation_dom(sK2)))),X0)) = X0 )
| ~ relation(sK1)
| ~ function(X1)
| ~ relation(X1)
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0),X1) ),
inference(superposition,[status(thm)],[c_18326,c_2068]) ).
tcf(c_18351,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK2)))) = empty_set )
| ~ relation(sK1)
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_18326,c_2063]) ).
tcf(c_18352,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK2)))) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,sK17(sK16(relation_dom(sK2)))),X0),X0))) = apply(sK2,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,sK17(sK16(relation_dom(sK2)))),X0),X0)) )
| ~ relation(sK1)
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_18326,c_2064]) ).
tcf(c_18353,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK2)))) = empty_set )
| ~ relation(empty_set)
| ~ relation(sK1)
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0),empty_set) ),
inference(superposition,[status(thm)],[c_18326,c_3818]) ).
tcf(c_18359,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK2)))) = empty_set )
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18351,c_56]) ).
tcf(c_18381,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK2)))) = empty_set )
| ( apply(X1,sK12(sK1,X1,apply(sK0,sK17(sK16(relation_dom(sK2)))),X0)) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18350,c_56]) ).
tcf(c_18403,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK2)))) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,sK17(sK16(relation_dom(sK2)))),X0),X0))) = apply(sK2,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,sK17(sK16(relation_dom(sK2)))),X0),X0)) )
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18352,c_56]) ).
tcf(c_18464,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK2)))) = empty_set )
| ( apply(sK0,ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0)) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0))) = empty_set )
| ( apply(relation_dom(sK2),sK12(sK1,relation_dom(sK2),apply(sK0,sK17(sK16(relation_dom(sK2)))),X0)) = X0 )
| ~ function(relation_dom(sK2))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_4011,c_18381]) ).
tcf(c_18465,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK2)))) = empty_set )
| ( apply(sK0,ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0)) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0))) = empty_set )
| ( apply(relation_dom(sK0),sK12(sK1,relation_dom(sK0),apply(sK0,sK17(sK16(relation_dom(sK2)))),X0)) = X0 )
| ~ function(relation_dom(sK0))
| ~ relation(relation_dom(sK0))
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_4110,c_18381]) ).
tcf(c_18466,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK2)))) = empty_set )
| ( apply(sK2,ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0)) = empty_set )
| ( apply(relation_dom(sK0),sK12(sK1,relation_dom(sK0),apply(sK0,sK17(sK16(relation_dom(sK2)))),X0)) = X0 )
| ~ function(relation_dom(sK0))
| ~ relation(relation_dom(sK0))
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_3449,c_18381]) ).
tcf(c_18467,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK2)))) = empty_set )
| ( apply(X0,sK12(sK1,X0,apply(sK0,sK17(sK16(relation_dom(sK2)))),sK5(X0,apply(sK2,sK17(sK16(relation_dom(sK2))))))) = sK5(X0,apply(sK2,sK17(sK16(relation_dom(sK2))))) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(apply(sK2,sK17(sK16(relation_dom(sK2)))),relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_71,c_18381]) ).
tcf(c_18468,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK2)))) = empty_set )
| ( apply(X0,sK12(sK1,X0,apply(sK0,sK17(sK16(relation_dom(sK2)))),apply(X0,apply(sK2,sK17(sK16(relation_dom(sK2))))))) = apply(X0,apply(sK2,sK17(sK16(relation_dom(sK2))))) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(apply(sK2,sK17(sK16(relation_dom(sK2)))),relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_73,c_18381]) ).
tcf(c_18469,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK2)))) = empty_set )
| ( apply(X0,ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X1)) = empty_set )
| ( apply(relation_dom(X0),sK12(sK1,relation_dom(X0),apply(sK0,sK17(sK16(relation_dom(sK2)))),X1)) = X1 )
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom(X0))
| ~ relation(relation_dom(X0))
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_75,c_18381]) ).
tcf(c_18470,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK2)))) = empty_set )
| ( apply(X1,sK12(sK1,X1,apply(sK0,sK17(sK16(relation_dom(sK2)))),sK12(X1,X2,apply(sK2,sK17(sK16(relation_dom(sK2)))),X0))) = sK12(X1,X2,apply(sK2,sK17(sK16(relation_dom(sK2)))),X0) )
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0),relation_composition(X1,X2)) ),
inference(superposition,[status(thm)],[c_301,c_18381]) ).
tcf(c_18471,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK2)))) = empty_set )
| ( apply(relation_dom(sK0),sK12(sK1,relation_dom(sK0),apply(sK0,sK17(sK16(relation_dom(sK2)))),sK12(relation_dom(sK2),X1,apply(sK2,sK17(sK16(relation_dom(sK2)))),X0))) = sK12(relation_dom(sK2),X1,apply(sK2,sK17(sK16(relation_dom(sK2)))),X0) )
| ~ relation(X1)
| ~ function(relation_dom(sK0))
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0),relation_composition(relation_dom(sK2),X1)) ),
inference(superposition,[status(thm)],[c_2283,c_18381]) ).
tcf(c_18472,plain,
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK2)))) = empty_set )
| ( apply(relation_dom(sK0),sK12(sK1,relation_dom(sK0),apply(sK0,sK17(sK16(relation_dom(sK2)))),sK5(relation_dom(sK2),apply(sK2,sK17(sK16(relation_dom(sK2))))))) = sK5(relation_dom(sK2),apply(sK2,sK17(sK16(relation_dom(sK2))))) )
| ~ function(relation_dom(sK0))
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(apply(sK2,sK17(sK16(relation_dom(sK2)))),relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_3019,c_18381]) ).
tcf(c_18473,plain,
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK2)))) = empty_set )
| ( apply(relation_dom(sK0),sK12(sK1,relation_dom(sK0),apply(sK0,sK17(sK16(relation_dom(sK2)))),apply(relation_dom(sK2),apply(sK2,sK17(sK16(relation_dom(sK2))))))) = apply(relation_dom(sK2),apply(sK2,sK17(sK16(relation_dom(sK2))))) )
| ~ function(relation_dom(sK0))
| ~ function(relation_dom(sK2))
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(apply(sK2,sK17(sK16(relation_dom(sK2)))),relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_3551,c_18381]) ).
tcf(c_18560,plain,
( ( relation_dom(relation_dom(sK2)) = relation_dom(sK2) )
| ( apply(sK1,apply(sK0,sK3(relation_dom(sK2),relation_dom(sK2)))) = apply(sK2,sK3(relation_dom(sK2),relation_dom(sK2))) )
| ( apply(sK1,apply(sK0,ordered_pair(sK3(relation_dom(sK2),relation_dom(sK2)),sK4(relation_dom(sK2),relation_dom(sK2))))) = apply(sK2,ordered_pair(sK3(relation_dom(sK2),relation_dom(sK2)),sK4(relation_dom(sK2),relation_dom(sK2)))) )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_66,c_8782]) ).
tcf(c_18561,plain,
( ( relation_dom(relation_dom(sK2)) = relation_dom(sK2) )
| ( apply(sK1,apply(sK0,sK17(relation_dom(sK2)))) = apply(sK2,sK17(relation_dom(sK2))) )
| ( apply(sK1,apply(sK0,sK3(relation_dom(sK2),relation_dom(sK2)))) = apply(sK2,sK3(relation_dom(sK2),relation_dom(sK2))) )
| ( apply(sK1,apply(sK0,ordered_pair(sK3(relation_dom(sK2),relation_dom(sK2)),sK4(relation_dom(sK2),relation_dom(sK2))))) = apply(sK2,ordered_pair(sK3(relation_dom(sK2),relation_dom(sK2)),sK4(relation_dom(sK2),relation_dom(sK2)))) ) ),
inference(superposition,[status(thm)],[c_2468,c_8782]) ).
tcf(c_18582,plain,
! [X0: $i] :
( ( relation_composition(relation_dom(sK2),X0) = relation_dom(sK2) )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(relation_dom(sK2),X0,relation_dom(sK2)),sK11(relation_dom(sK2),X0,relation_dom(sK2))))) = apply(sK2,ordered_pair(sK9(relation_dom(sK2),X0,relation_dom(sK2)),sK11(relation_dom(sK2),X0,relation_dom(sK2)))) )
| ~ relation(X0)
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4702,c_2047]) ).
tcf(c_18583,plain,
! [X0: $i] :
( ( relation_composition(relation_dom(sK2),X0) = relation_dom(sK2) )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(relation_dom(sK2),X0,relation_dom(sK2)),sK11(relation_dom(sK2),X0,relation_dom(sK2))))) = apply(sK2,ordered_pair(sK9(relation_dom(sK2),X0,relation_dom(sK2)),sK11(relation_dom(sK2),X0,relation_dom(sK2)))) )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(relation_dom(sK2),X0,relation_dom(sK2)),sK10(relation_dom(sK2),X0,relation_dom(sK2))))) = apply(sK2,ordered_pair(sK9(relation_dom(sK2),X0,relation_dom(sK2)),sK10(relation_dom(sK2),X0,relation_dom(sK2)))) )
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4702,c_53]) ).
tcf(c_18585,plain,
! [X0: $i] :
( in(ordered_pair(sK9(relation_dom(sK2),X0,relation_dom(sK0)),sK10(relation_dom(sK2),X0,relation_dom(sK0))),relation_dom(sK2))
| ( relation_composition(relation_dom(sK2),X0) = relation_dom(sK0) )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(relation_dom(sK2),X0,relation_dom(sK0)),sK11(relation_dom(sK2),X0,relation_dom(sK0))))) = apply(sK2,ordered_pair(sK9(relation_dom(sK2),X0,relation_dom(sK0)),sK11(relation_dom(sK2),X0,relation_dom(sK0)))) )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(relation_dom(sK2),X0,relation_dom(sK0)),sK10(relation_dom(sK2),X0,relation_dom(sK0))))) = empty_set )
| ~ relation(X0)
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4702,c_3475]) ).
tcf(c_18586,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(relation_dom(sK2),X1) = X0 )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(relation_dom(sK2),X1,X0),sK11(relation_dom(sK2),X1,X0)))) = apply(sK2,ordered_pair(sK9(relation_dom(sK2),X1,X0),sK11(relation_dom(sK2),X1,X0))) )
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2))
| ~ in(X0,ordered_pair(sK9(relation_dom(sK2),X1,X0),sK10(relation_dom(sK2),X1,X0))) ),
inference(superposition,[status(thm)],[c_4702,c_64]) ).
tcf(c_18587,plain,
! [X0: $i,X1: $i] :
( element(ordered_pair(sK9(relation_dom(sK2),X0,X1),sK10(relation_dom(sK2),X0,X1)),X1)
| ( relation_composition(relation_dom(sK2),X0) = X1 )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(relation_dom(sK2),X0,X1),sK11(relation_dom(sK2),X0,X1)))) = apply(sK2,ordered_pair(sK9(relation_dom(sK2),X0,X1),sK11(relation_dom(sK2),X0,X1))) )
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4702,c_63]) ).
tcf(c_18588,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(relation_dom(sK2),X0) = X1 )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(relation_dom(sK2),X0,X1),sK11(relation_dom(sK2),X0,X1)))) = apply(sK2,ordered_pair(sK9(relation_dom(sK2),X0,X1),sK11(relation_dom(sK2),X0,X1))) )
| ~ empty(X1)
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4702,c_61]) ).
tcf(c_18589,plain,
! [X0: $i,X1: $i] :
( in(sK9(relation_dom(sK2),X0,X1),relation_dom(X1))
| ( relation_composition(relation_dom(sK2),X0) = X1 )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(relation_dom(sK2),X0,X1),sK11(relation_dom(sK2),X0,X1)))) = apply(sK2,ordered_pair(sK9(relation_dom(sK2),X0,X1),sK11(relation_dom(sK2),X0,X1))) )
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4702,c_70]) ).
tcf(c_18590,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(ordered_pair(sK9(relation_dom(sK2),X0,X1),X2),relation_composition(X1,X3))
| ( relation_composition(relation_dom(sK2),X0) = X1 )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(relation_dom(sK2),X0,X1),sK11(relation_dom(sK2),X0,X1)))) = apply(sK2,ordered_pair(sK9(relation_dom(sK2),X0,X1),sK11(relation_dom(sK2),X0,X1))) )
| ~ relation(X3)
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2))
| ~ in(ordered_pair(sK10(relation_dom(sK2),X0,X1),X2),X3) ),
inference(superposition,[status(thm)],[c_4702,c_299]) ).
tcf(c_18591,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(relation_dom(sK2),X0) = X1 )
| ( apply(X1,sK9(relation_dom(sK2),X0,X1)) = sK10(relation_dom(sK2),X0,X1) )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(relation_dom(sK2),X0,X1),sK11(relation_dom(sK2),X0,X1)))) = apply(sK2,ordered_pair(sK9(relation_dom(sK2),X0,X1),sK11(relation_dom(sK2),X0,X1))) )
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4702,c_152]) ).
tcf(c_18592,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(relation_dom(sK2),X1) = relation_dom(X0) )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(relation_dom(sK2),X1,relation_dom(X0)),sK11(relation_dom(sK2),X1,relation_dom(X0))))) = apply(sK2,ordered_pair(sK9(relation_dom(sK2),X1,relation_dom(X0)),sK11(relation_dom(sK2),X1,relation_dom(X0)))) )
| ~ empty(X0)
| ~ relation(X1)
| ~ relation(relation_dom(sK2))
| ~ relation(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_4702,c_11389]) ).
tcf(c_18593,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_composition(relation_dom(sK2),X0) = X1 )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(relation_dom(sK2),X0,X1),sK11(relation_dom(sK2),X0,X1)))) = apply(sK2,ordered_pair(sK9(relation_dom(sK2),X0,X1),sK11(relation_dom(sK2),X0,X1))) )
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2))
| ~ in(ordered_pair(X2,sK10(relation_dom(sK2),X0,X1)),X0)
| ~ in(ordered_pair(sK9(relation_dom(sK2),X0,X1),X2),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4702,c_91]) ).
tcf(c_18594,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_composition(relation_dom(sK2),X2) = relation_composition(X0,X1) )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(relation_dom(sK2),X2,relation_composition(X0,X1)),sK11(relation_dom(sK2),X2,relation_composition(X0,X1))))) = apply(sK2,ordered_pair(sK9(relation_dom(sK2),X2,relation_composition(X0,X1)),sK11(relation_dom(sK2),X2,relation_composition(X0,X1)))) )
| ( apply(X1,sK12(X0,X1,sK9(relation_dom(sK2),X2,relation_composition(X0,X1)),sK10(relation_dom(sK2),X2,relation_composition(X0,X1)))) = sK10(relation_dom(sK2),X2,relation_composition(X0,X1)) )
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2))
| ~ relation(relation_composition(X0,X1)) ),
inference(superposition,[status(thm)],[c_4702,c_2068]) ).
tcf(c_18595,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(relation_dom(sK2),X1) = relation_composition(X0,relation_dom(sK2)) )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(relation_dom(sK2),X1,relation_composition(X0,relation_dom(sK2))),sK11(relation_dom(sK2),X1,relation_composition(X0,relation_dom(sK2)))))) = apply(sK2,ordered_pair(sK9(relation_dom(sK2),X1,relation_composition(X0,relation_dom(sK2))),sK11(relation_dom(sK2),X1,relation_composition(X0,relation_dom(sK2))))) )
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2))
| ~ relation(relation_composition(X0,relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_4702,c_2063]) ).
tcf(c_18596,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(relation_dom(sK2),X1) = relation_composition(X0,relation_dom(sK2)) )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(relation_dom(sK2),X1,relation_composition(X0,relation_dom(sK2))),sK11(relation_dom(sK2),X1,relation_composition(X0,relation_dom(sK2)))))) = apply(sK2,ordered_pair(sK9(relation_dom(sK2),X1,relation_composition(X0,relation_dom(sK2))),sK11(relation_dom(sK2),X1,relation_composition(X0,relation_dom(sK2))))) )
| ( apply(sK1,apply(sK0,ordered_pair(sK12(X0,relation_dom(sK2),sK9(relation_dom(sK2),X1,relation_composition(X0,relation_dom(sK2))),sK10(relation_dom(sK2),X1,relation_composition(X0,relation_dom(sK2)))),sK10(relation_dom(sK2),X1,relation_composition(X0,relation_dom(sK2)))))) = apply(sK2,ordered_pair(sK12(X0,relation_dom(sK2),sK9(relation_dom(sK2),X1,relation_composition(X0,relation_dom(sK2))),sK10(relation_dom(sK2),X1,relation_composition(X0,relation_dom(sK2)))),sK10(relation_dom(sK2),X1,relation_composition(X0,relation_dom(sK2))))) )
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2))
| ~ relation(relation_composition(X0,relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_4702,c_2064]) ).
tcf(c_18597,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(relation_dom(sK2),X0) = relation_composition(relation_dom(sK2),X1) )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(relation_dom(sK2),X1,relation_composition(relation_dom(sK2),X0)),sK11(relation_dom(sK2),X1,relation_composition(relation_dom(sK2),X0))))) = apply(sK2,ordered_pair(sK9(relation_dom(sK2),X1,relation_composition(relation_dom(sK2),X0)),sK11(relation_dom(sK2),X1,relation_composition(relation_dom(sK2),X0)))) )
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2))
| ~ relation(relation_composition(relation_dom(sK2),X0)) ),
inference(superposition,[status(thm)],[c_4702,c_2281]) ).
tcf(c_18598,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(relation_dom(sK2),X0) = relation_composition(relation_dom(sK2),X1) )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(relation_dom(sK2),X1,relation_composition(relation_dom(sK2),X0)),sK11(relation_dom(sK2),X1,relation_composition(relation_dom(sK2),X0))))) = apply(sK2,ordered_pair(sK9(relation_dom(sK2),X1,relation_composition(relation_dom(sK2),X0)),sK11(relation_dom(sK2),X1,relation_composition(relation_dom(sK2),X0)))) )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(relation_dom(sK2),X1,relation_composition(relation_dom(sK2),X0)),sK12(relation_dom(sK2),X0,sK9(relation_dom(sK2),X1,relation_composition(relation_dom(sK2),X0)),sK10(relation_dom(sK2),X1,relation_composition(relation_dom(sK2),X0)))))) = apply(sK2,ordered_pair(sK9(relation_dom(sK2),X1,relation_composition(relation_dom(sK2),X0)),sK12(relation_dom(sK2),X0,sK9(relation_dom(sK2),X1,relation_composition(relation_dom(sK2),X0)),sK10(relation_dom(sK2),X1,relation_composition(relation_dom(sK2),X0))))) )
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2))
| ~ relation(relation_composition(relation_dom(sK2),X0)) ),
inference(superposition,[status(thm)],[c_4702,c_2282]) ).
tcf(c_18599,plain,
! [X0: $i] :
( ( relation_composition(relation_dom(sK2),X0) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(relation_dom(sK2),X0,empty_set),sK11(relation_dom(sK2),X0,empty_set)))) = apply(sK2,ordered_pair(sK9(relation_dom(sK2),X0,empty_set),sK11(relation_dom(sK2),X0,empty_set))) )
| ~ relation(empty_set)
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4702,c_3809]) ).
tcf(c_18600,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| element(ordered_pair(sK9(relation_dom(sK2),X1,sK16(X0)),sK10(relation_dom(sK2),X1,sK16(X0))),X0)
| ( relation_composition(relation_dom(sK2),X1) = sK16(X0) )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(relation_dom(sK2),X1,sK16(X0)),sK11(relation_dom(sK2),X1,sK16(X0))))) = apply(sK2,ordered_pair(sK9(relation_dom(sK2),X1,sK16(X0)),sK11(relation_dom(sK2),X1,sK16(X0)))) )
| ~ relation(X1)
| ~ relation(relation_dom(sK2))
| ~ relation(sK16(X0)) ),
inference(superposition,[status(thm)],[c_4702,c_2939]) ).
tcf(c_18601,plain,
! [X0: $i,X1: $i] :
( element(ordered_pair(sK9(relation_dom(sK2),X1,sK17(powerset(X0))),sK10(relation_dom(sK2),X1,sK17(powerset(X0)))),X0)
| ( relation_composition(relation_dom(sK2),X1) = sK17(powerset(X0)) )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(relation_dom(sK2),X1,sK17(powerset(X0))),sK11(relation_dom(sK2),X1,sK17(powerset(X0)))))) = apply(sK2,ordered_pair(sK9(relation_dom(sK2),X1,sK17(powerset(X0))),sK11(relation_dom(sK2),X1,sK17(powerset(X0))))) )
| ~ relation(X1)
| ~ relation(relation_dom(sK2))
| ~ relation(sK17(powerset(X0))) ),
inference(superposition,[status(thm)],[c_4702,c_2940]) ).
tcf(c_18602,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(relation_dom(sK2),X1) = sK17(powerset(X0)) )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(relation_dom(sK2),X1,sK17(powerset(X0))),sK11(relation_dom(sK2),X1,sK17(powerset(X0)))))) = apply(sK2,ordered_pair(sK9(relation_dom(sK2),X1,sK17(powerset(X0))),sK11(relation_dom(sK2),X1,sK17(powerset(X0))))) )
| ~ empty(X0)
| ~ relation(X1)
| ~ relation(relation_dom(sK2))
| ~ relation(sK17(powerset(X0))) ),
inference(superposition,[status(thm)],[c_4702,c_2925]) ).
tcf(c_18603,plain,
! [X0: $i] :
( ( relation_composition(relation_dom(sK2),X0) = relation_dom(relation_dom(sK2)) )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(relation_dom(sK2),X0,relation_dom(relation_dom(sK2))),sK11(relation_dom(sK2),X0,relation_dom(relation_dom(sK2)))))) = apply(sK2,ordered_pair(sK9(relation_dom(sK2),X0,relation_dom(relation_dom(sK2))),sK11(relation_dom(sK2),X0,relation_dom(relation_dom(sK2))))) )
| ( apply(sK1,apply(sK0,ordered_pair(ordered_pair(sK9(relation_dom(sK2),X0,relation_dom(relation_dom(sK2))),sK10(relation_dom(sK2),X0,relation_dom(relation_dom(sK2)))),apply(relation_dom(sK2),ordered_pair(sK9(relation_dom(sK2),X0,relation_dom(relation_dom(sK2))),sK10(relation_dom(sK2),X0,relation_dom(relation_dom(sK2)))))))) = apply(sK2,ordered_pair(ordered_pair(sK9(relation_dom(sK2),X0,relation_dom(relation_dom(sK2))),sK10(relation_dom(sK2),X0,relation_dom(relation_dom(sK2)))),apply(relation_dom(sK2),ordered_pair(sK9(relation_dom(sK2),X0,relation_dom(relation_dom(sK2))),sK10(relation_dom(sK2),X0,relation_dom(relation_dom(sK2))))))) )
| ~ relation(X0)
| ~ function(relation_dom(sK2))
| ~ relation(relation_dom(sK2))
| ~ relation(relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_4702,c_3550]) ).
tcf(c_18604,plain,
! [X0: $i] :
( in(ordered_pair(sK9(relation_dom(sK2),X0,relation_dom(relation_dom(sK2))),sK10(relation_dom(sK2),X0,relation_dom(relation_dom(sK2)))),relation_dom(relation_dom(sK0)))
| ( relation_composition(relation_dom(sK2),X0) = relation_dom(relation_dom(sK2)) )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(relation_dom(sK2),X0,relation_dom(relation_dom(sK2))),sK11(relation_dom(sK2),X0,relation_dom(relation_dom(sK2)))))) = apply(sK2,ordered_pair(sK9(relation_dom(sK2),X0,relation_dom(relation_dom(sK2))),sK11(relation_dom(sK2),X0,relation_dom(relation_dom(sK2))))) )
| ~ relation(X0)
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ relation(relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_4702,c_3134]) ).
tcf(c_18605,plain,
! [X0: $i] :
( ( relation_composition(relation_dom(sK2),X0) = relation_dom(relation_dom(sK2)) )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(relation_dom(sK2),X0,relation_dom(relation_dom(sK2))),sK11(relation_dom(sK2),X0,relation_dom(relation_dom(sK2)))))) = apply(sK2,ordered_pair(sK9(relation_dom(sK2),X0,relation_dom(relation_dom(sK2))),sK11(relation_dom(sK2),X0,relation_dom(relation_dom(sK2))))) )
| ~ relation(X0)
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2))
| ~ relation(relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_4702,c_3017]) ).
tcf(c_18606,plain,
! [X0: $i] :
( ( relation_composition(relation_dom(sK2),X0) = relation_dom(relation_dom(sK2)) )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(relation_dom(sK2),X0,relation_dom(relation_dom(sK2))),sK11(relation_dom(sK2),X0,relation_dom(relation_dom(sK2)))))) = apply(sK2,ordered_pair(sK9(relation_dom(sK2),X0,relation_dom(relation_dom(sK2))),sK11(relation_dom(sK2),X0,relation_dom(relation_dom(sK2))))) )
| ( apply(sK1,apply(sK0,ordered_pair(ordered_pair(sK9(relation_dom(sK2),X0,relation_dom(relation_dom(sK2))),sK10(relation_dom(sK2),X0,relation_dom(relation_dom(sK2)))),sK5(relation_dom(sK2),ordered_pair(sK9(relation_dom(sK2),X0,relation_dom(relation_dom(sK2))),sK10(relation_dom(sK2),X0,relation_dom(relation_dom(sK2)))))))) = apply(sK2,ordered_pair(ordered_pair(sK9(relation_dom(sK2),X0,relation_dom(relation_dom(sK2))),sK10(relation_dom(sK2),X0,relation_dom(relation_dom(sK2)))),sK5(relation_dom(sK2),ordered_pair(sK9(relation_dom(sK2),X0,relation_dom(relation_dom(sK2))),sK10(relation_dom(sK2),X0,relation_dom(relation_dom(sK2))))))) )
| ~ relation(X0)
| ~ relation(relation_dom(sK2))
| ~ relation(relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_4702,c_3018]) ).
tcf(c_18607,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(relation_dom(sK2),X1) = relation_composition(empty_set,X0) )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(relation_dom(sK2),X1,relation_composition(empty_set,X0)),sK11(relation_dom(sK2),X1,relation_composition(empty_set,X0))))) = apply(sK2,ordered_pair(sK9(relation_dom(sK2),X1,relation_composition(empty_set,X0)),sK11(relation_dom(sK2),X1,relation_composition(empty_set,X0)))) )
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2))
| ~ relation(relation_composition(empty_set,X0)) ),
inference(superposition,[status(thm)],[c_4702,c_3821]) ).
tcf(c_18608,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(relation_dom(sK2),X1) = relation_composition(X0,empty_set) )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(relation_dom(sK2),X1,relation_composition(X0,empty_set)),sK11(relation_dom(sK2),X1,relation_composition(X0,empty_set))))) = apply(sK2,ordered_pair(sK9(relation_dom(sK2),X1,relation_composition(X0,empty_set)),sK11(relation_dom(sK2),X1,relation_composition(X0,empty_set)))) )
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2))
| ~ relation(relation_composition(X0,empty_set)) ),
inference(superposition,[status(thm)],[c_4702,c_3818]) ).
tcf(c_18609,plain,
! [X0: $i,X1: $i] :
( element(ordered_pair(sK9(relation_dom(sK2),X1,sK17(sK16(powerset(X0)))),sK10(relation_dom(sK2),X1,sK17(sK16(powerset(X0))))),X0)
| ( relation_composition(relation_dom(sK2),X1) = sK17(sK16(powerset(X0))) )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(relation_dom(sK2),X1,sK17(sK16(powerset(X0)))),sK11(relation_dom(sK2),X1,sK17(sK16(powerset(X0))))))) = apply(sK2,ordered_pair(sK9(relation_dom(sK2),X1,sK17(sK16(powerset(X0)))),sK11(relation_dom(sK2),X1,sK17(sK16(powerset(X0)))))) )
| ~ relation(X1)
| ~ relation(relation_dom(sK2))
| ~ relation(sK17(sK16(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_4702,c_11939]) ).
tcf(c_18610,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(relation_dom(sK2),X1) = sK17(sK16(powerset(X0))) )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(relation_dom(sK2),X1,sK17(sK16(powerset(X0)))),sK11(relation_dom(sK2),X1,sK17(sK16(powerset(X0))))))) = apply(sK2,ordered_pair(sK9(relation_dom(sK2),X1,sK17(sK16(powerset(X0)))),sK11(relation_dom(sK2),X1,sK17(sK16(powerset(X0)))))) )
| ~ empty(X0)
| ~ relation(X1)
| ~ relation(relation_dom(sK2))
| ~ relation(sK17(sK16(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_4702,c_11936]) ).
tcf(c_18611,plain,
! [X0: $i] :
( ( relation_composition(relation_dom(sK2),X0) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(relation_dom(sK2),X0,empty_set),sK11(relation_dom(sK2),X0,empty_set)))) = apply(sK2,ordered_pair(sK9(relation_dom(sK2),X0,empty_set),sK11(relation_dom(sK2),X0,empty_set))) )
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18599,c_109]) ).
tcf(c_18912,plain,
( in(ordered_pair(apply(sK0,sK17(sK16(relation_dom(sK2)))),apply(sK2,sK17(sK16(relation_dom(sK2))))),sK1)
| ( sK17(powerset(relation_dom(sK2))) = empty_set )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_12025,c_73]) ).
tcf(c_18913,plain,
( in(ordered_pair(apply(sK0,sK17(sK16(relation_dom(sK2)))),apply(sK2,sK17(sK16(relation_dom(sK2))))),sK1)
| ( sK17(powerset(relation_dom(sK2))) = empty_set )
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18912,c_57,c_56]) ).
tcf(c_18921,plain,
( ( relation_composition(sK17(powerset(relation_dom(sK2))),empty_set) = empty_set )
| ~ empty(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_17711,c_16441]) ).
tcf(c_18922,plain,
( ( relation_composition(empty_set,sK17(powerset(relation_dom(sK2)))) = empty_set )
| ~ empty(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_17711,c_15145]) ).
tcf(c_18935,plain,
( empty(sK17(powerset(empty_set)))
| ~ in(empty_set,sK17(empty_set)) ),
inference(superposition,[status(thm)],[c_7736,c_17467]) ).
tcf(c_18936,plain,
( empty(empty_set)
| ~ in(empty_set,sK17(empty_set)) ),
inference(light_normalisation,[status(thm)],[c_18935,c_7736]) ).
tcf(c_18947,plain,
! [X0: $i,X1: $i] :
( ( sK17(powerset(sK17(powerset(sK17(powerset(X0)))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17474,c_7174]) ).
tcf(c_18948,plain,
! [X0: $i] :
( ( relation_composition(relation_dom(relation_dom(sK17(powerset(sK17(powerset(X0)))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17474,c_16966]) ).
tcf(c_18949,plain,
! [X0: $i] :
( ( relation_composition(relation_dom(sK17(powerset(sK17(powerset(X0))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17474,c_16861]) ).
tcf(c_18950,plain,
! [X0: $i] :
( ( relation_composition(empty_set,relation_dom(relation_dom(sK17(powerset(sK17(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17474,c_15920]) ).
tcf(c_18951,plain,
! [X0: $i] :
( ( relation_composition(empty_set,relation_dom(sK17(powerset(sK17(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17474,c_15264]) ).
tcf(c_18952,plain,
! [X0: $i] :
( ( sK17(sK16(powerset(relation_dom(sK17(powerset(sK17(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17474,c_12877]) ).
tcf(c_18953,plain,
! [X0: $i] :
( ( sK17(powerset(sK17(powerset(sK17(powerset(sK17(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17474,c_7742]) ).
tcf(c_18954,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK17(powerset(sK17(powerset(sK17(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17474,c_7236]) ).
tcf(c_18955,plain,
! [X0: $i] :
( ( relation_dom(sK17(powerset(relation_dom(sK17(powerset(sK17(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17474,c_9976]) ).
tcf(c_18956,plain,
! [X0: $i] :
( ( sK17(powerset(relation_dom(relation_dom(sK17(powerset(sK17(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17474,c_9849]) ).
tcf(c_18957,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK17(powerset(sK17(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17474,c_9793]) ).
tcf(c_18958,plain,
! [X0: $i] :
( ( sK17(sK16(powerset(sK17(powerset(sK17(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17474,c_12303]) ).
tcf(c_18959,plain,
! [X0: $i] :
( ( relation_dom(sK17(powerset(sK17(powerset(sK17(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17474,c_7171]) ).
tcf(c_18960,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK17(powerset(sK17(powerset(X0))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17474,c_2387]) ).
tcf(c_18961,plain,
! [X0: $i] :
( ( sK17(powerset(relation_dom(sK17(powerset(sK17(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17474,c_7733]) ).
tcf(c_18962,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK17(powerset(sK17(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17474,c_7227]) ).
tcf(c_18966,plain,
! [X0: $i] :
( ( sK17(powerset(sK17(powerset(X0)))) = relation_dom(sK2) )
| ( apply(sK1,apply(sK0,sK17(relation_dom(sK2)))) = apply(sK2,sK17(relation_dom(sK2))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17474,c_2466]) ).
tcf(c_18967,plain,
! [X0: $i] :
( ( sK17(powerset(sK17(powerset(X0)))) = sK2 )
| ( apply(sK1,apply(sK0,sK17(relation_dom(sK2)))) = apply(sK2,sK17(relation_dom(sK2))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17474,c_2488]) ).
tcf(c_18970,plain,
! [X0: $i] :
( relation(sK17(powerset(sK17(powerset(X0)))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17474,c_85]) ).
tcf(c_18971,plain,
! [X0: $i] :
( function(sK17(powerset(sK17(powerset(X0)))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17474,c_80]) ).
tcf(c_18972,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(X0,sK17(powerset(sK17(powerset(X1))))) = empty_set )
| ~ empty(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17474,c_2607]) ).
tcf(c_18973,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(sK17(powerset(sK17(powerset(X1)))),X0) = empty_set )
| ~ empty(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17474,c_2400]) ).
tcf(c_19029,plain,
! [X0: $i] :
( ( relation_composition(sK17(powerset(sK17(powerset(X0)))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18970,c_16441]) ).
tcf(c_19030,plain,
! [X0: $i] :
( ( relation_composition(empty_set,sK17(powerset(sK17(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_18970,c_15145]) ).
tcf(c_19045,plain,
! [X0: $i,X1: $i] :
( ( sK17(powerset(sK17(powerset(sK17(sK16(powerset(X0))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17480,c_7174]) ).
tcf(c_19046,plain,
! [X0: $i] :
( ( relation_composition(relation_dom(relation_dom(sK17(powerset(sK17(sK16(powerset(X0))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17480,c_16966]) ).
tcf(c_19047,plain,
! [X0: $i] :
( ( relation_composition(relation_dom(sK17(powerset(sK17(sK16(powerset(X0)))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17480,c_16861]) ).
tcf(c_19048,plain,
! [X0: $i] :
( ( relation_composition(empty_set,relation_dom(relation_dom(sK17(powerset(sK17(sK16(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17480,c_15920]) ).
tcf(c_19049,plain,
! [X0: $i] :
( ( relation_composition(empty_set,relation_dom(sK17(powerset(sK17(sK16(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17480,c_15264]) ).
tcf(c_19050,plain,
! [X0: $i] :
( ( sK17(sK16(powerset(relation_dom(sK17(powerset(sK17(sK16(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17480,c_12877]) ).
tcf(c_19051,plain,
! [X0: $i] :
( ( sK17(powerset(sK17(powerset(sK17(powerset(sK17(sK16(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17480,c_7742]) ).
tcf(c_19052,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK17(powerset(sK17(powerset(sK17(sK16(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17480,c_7236]) ).
tcf(c_19053,plain,
! [X0: $i] :
( ( relation_dom(sK17(powerset(relation_dom(sK17(powerset(sK17(sK16(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17480,c_9976]) ).
tcf(c_19054,plain,
! [X0: $i] :
( ( sK17(powerset(relation_dom(relation_dom(sK17(powerset(sK17(sK16(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17480,c_9849]) ).
tcf(c_19055,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK17(powerset(sK17(sK16(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17480,c_9793]) ).
tcf(c_19056,plain,
! [X0: $i] :
( ( sK17(sK16(powerset(sK17(powerset(sK17(sK16(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17480,c_12303]) ).
tcf(c_19057,plain,
! [X0: $i] :
( ( relation_dom(sK17(powerset(sK17(powerset(sK17(sK16(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17480,c_7171]) ).
tcf(c_19058,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK17(powerset(sK17(sK16(powerset(X0)))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17480,c_2387]) ).
tcf(c_19059,plain,
! [X0: $i] :
( ( sK17(powerset(relation_dom(sK17(powerset(sK17(sK16(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17480,c_7733]) ).
tcf(c_19060,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK17(powerset(sK17(sK16(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17480,c_7227]) ).
tcf(c_19064,plain,
! [X0: $i] :
( ( sK17(powerset(sK17(sK16(powerset(X0))))) = relation_dom(sK2) )
| ( apply(sK1,apply(sK0,sK17(relation_dom(sK2)))) = apply(sK2,sK17(relation_dom(sK2))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17480,c_2466]) ).
tcf(c_19065,plain,
! [X0: $i] :
( ( sK17(powerset(sK17(sK16(powerset(X0))))) = sK2 )
| ( apply(sK1,apply(sK0,sK17(relation_dom(sK2)))) = apply(sK2,sK17(relation_dom(sK2))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17480,c_2488]) ).
tcf(c_19068,plain,
! [X0: $i] :
( relation(sK17(powerset(sK17(sK16(powerset(X0))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17480,c_85]) ).
tcf(c_19069,plain,
! [X0: $i] :
( function(sK17(powerset(sK17(sK16(powerset(X0))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17480,c_80]) ).
tcf(c_19070,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(X0,sK17(powerset(sK17(sK16(powerset(X1)))))) = empty_set )
| ~ empty(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17480,c_2607]) ).
tcf(c_19071,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(sK17(powerset(sK17(sK16(powerset(X1))))),X0) = empty_set )
| ~ empty(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17480,c_2400]) ).
tcf(c_19160,plain,
( ( sK17(powerset(relation_dom(sK2))) = empty_set )
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(sK1,ordered_pair(apply(sK0,sK17(sK16(relation_dom(sK2)))),apply(sK2,sK17(sK16(relation_dom(sK2)))))) ),
inference(superposition,[status(thm)],[c_18913,c_64]) ).
tcf(c_19161,plain,
( element(ordered_pair(apply(sK0,sK17(sK16(relation_dom(sK2)))),apply(sK2,sK17(sK16(relation_dom(sK2))))),sK1)
| ( sK17(powerset(relation_dom(sK2))) = empty_set )
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_18913,c_63]) ).
tcf(c_19164,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(apply(sK0,sK17(sK16(relation_dom(sK2)))),X0),relation_composition(sK1,X1))
| ( sK17(powerset(relation_dom(sK2))) = empty_set )
| ~ relation(sK1)
| ~ relation(X1)
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0),X1) ),
inference(superposition,[status(thm)],[c_18913,c_299]) ).
tcf(c_19172,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(apply(sK0,sK17(sK16(relation_dom(sK2)))),X0),relation_composition(sK1,X1))
| ( sK17(powerset(relation_dom(sK2))) = empty_set )
| ~ relation(X1)
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_19164,c_56]) ).
tcf(c_19189,plain,
! [X0: $i] :
( in(ordered_pair(apply(sK0,sK17(sK16(relation_dom(sK2)))),X0),empty_set)
| ( sK17(powerset(relation_dom(sK2))) = empty_set )
| ~ relation(empty_set)
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0),empty_set) ),
inference(superposition,[status(thm)],[c_16859,c_19172]) ).
tcf(c_19190,plain,
! [X0: $i,X1: $i] :
( ( sK17(powerset(relation_dom(sK2))) = empty_set )
| ~ relation(X0)
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X1),X0)
| ~ in(relation_composition(sK1,X0),ordered_pair(apply(sK0,sK17(sK16(relation_dom(sK2)))),X1)) ),
inference(superposition,[status(thm)],[c_19172,c_64]) ).
tcf(c_19191,plain,
! [X0: $i,X1: $i] :
( element(ordered_pair(apply(sK0,sK17(sK16(relation_dom(sK2)))),X0),relation_composition(sK1,X1))
| ( sK17(powerset(relation_dom(sK2))) = empty_set )
| ~ relation(X1)
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0),X1) ),
inference(superposition,[status(thm)],[c_19172,c_63]) ).
tcf(c_19192,plain,
! [X0: $i,X1: $i] :
( ( sK17(powerset(relation_dom(sK2))) = empty_set )
| ~ relation(X1)
| ~ empty(relation_composition(sK1,X1))
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0),X1) ),
inference(superposition,[status(thm)],[c_19172,c_61]) ).
tcf(c_19193,plain,
! [X0: $i,X1: $i] :
( in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(relation_composition(sK1,X1)))
| ( sK17(powerset(relation_dom(sK2))) = empty_set )
| ~ relation(X1)
| ~ relation(relation_composition(sK1,X1))
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0),X1) ),
inference(superposition,[status(thm)],[c_19172,c_70]) ).
tcf(c_19194,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(ordered_pair(apply(sK0,sK17(sK16(relation_dom(sK2)))),X2),relation_composition(relation_composition(sK1,X1),X3))
| ( sK17(powerset(relation_dom(sK2))) = empty_set )
| ~ relation(X3)
| ~ relation(X1)
| ~ relation(relation_composition(sK1,X1))
| ~ in(ordered_pair(X0,X2),X3)
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0),X1) ),
inference(superposition,[status(thm)],[c_19172,c_299]) ).
tcf(c_19195,plain,
! [X0: $i,X1: $i] :
( ( sK17(powerset(relation_dom(sK2))) = empty_set )
| ( apply(relation_composition(sK1,X1),apply(sK0,sK17(sK16(relation_dom(sK2))))) = X0 )
| ~ relation(X1)
| ~ function(relation_composition(sK1,X1))
| ~ relation(relation_composition(sK1,X1))
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0),X1) ),
inference(superposition,[status(thm)],[c_19172,c_152]) ).
tcf(c_19196,plain,
! [X0: $i,X1: $i] :
( ( sK17(powerset(relation_dom(sK2))) = empty_set )
| ( apply(X1,sK12(sK1,X1,apply(sK0,sK17(sK16(relation_dom(sK2)))),X0)) = X0 )
| ~ relation(sK1)
| ~ function(X1)
| ~ relation(X1)
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0),X1) ),
inference(superposition,[status(thm)],[c_19172,c_2068]) ).
tcf(c_19197,plain,
! [X0: $i] :
( ( sK17(powerset(relation_dom(sK2))) = empty_set )
| ~ relation(sK1)
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_19172,c_2063]) ).
tcf(c_19198,plain,
! [X0: $i] :
( ( sK17(powerset(relation_dom(sK2))) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,sK17(sK16(relation_dom(sK2)))),X0),X0))) = apply(sK2,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,sK17(sK16(relation_dom(sK2)))),X0),X0)) )
| ~ relation(sK1)
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_19172,c_2064]) ).
tcf(c_19199,plain,
! [X0: $i] :
( ( sK17(powerset(relation_dom(sK2))) = empty_set )
| ~ relation(empty_set)
| ~ relation(sK1)
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0),empty_set) ),
inference(superposition,[status(thm)],[c_19172,c_3818]) ).
tcf(c_19222,plain,
! [X0: $i,X1: $i] :
( ( sK17(powerset(relation_dom(sK2))) = empty_set )
| ( apply(X1,sK12(sK1,X1,apply(sK0,sK17(sK16(relation_dom(sK2)))),X0)) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_19196,c_56]) ).
tcf(c_19244,plain,
! [X0: $i] :
( ( sK17(powerset(relation_dom(sK2))) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,sK17(sK16(relation_dom(sK2)))),X0),X0))) = apply(sK2,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,sK17(sK16(relation_dom(sK2)))),X0),X0)) )
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_19198,c_56]) ).
tcf(c_19367,plain,
! [X0: $i] :
( ( sK17(powerset(relation_dom(sK2))) = empty_set )
| ( apply(sK0,ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0)) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0))) = empty_set )
| ( apply(relation_dom(sK2),sK12(sK1,relation_dom(sK2),apply(sK0,sK17(sK16(relation_dom(sK2)))),X0)) = X0 )
| ~ function(relation_dom(sK2))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_4011,c_19222]) ).
tcf(c_19368,plain,
! [X0: $i] :
( ( sK17(powerset(relation_dom(sK2))) = empty_set )
| ( apply(sK0,ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0)) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0))) = empty_set )
| ( apply(relation_dom(sK0),sK12(sK1,relation_dom(sK0),apply(sK0,sK17(sK16(relation_dom(sK2)))),X0)) = X0 )
| ~ function(relation_dom(sK0))
| ~ relation(relation_dom(sK0))
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_4110,c_19222]) ).
tcf(c_19369,plain,
! [X0: $i] :
( ( sK17(powerset(relation_dom(sK2))) = empty_set )
| ( apply(sK2,ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0)) = empty_set )
| ( apply(relation_dom(sK0),sK12(sK1,relation_dom(sK0),apply(sK0,sK17(sK16(relation_dom(sK2)))),X0)) = X0 )
| ~ function(relation_dom(sK0))
| ~ relation(relation_dom(sK0))
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_3449,c_19222]) ).
tcf(c_19370,plain,
! [X0: $i] :
( ( sK17(powerset(relation_dom(sK2))) = empty_set )
| ( apply(X0,sK12(sK1,X0,apply(sK0,sK17(sK16(relation_dom(sK2)))),sK5(X0,apply(sK2,sK17(sK16(relation_dom(sK2))))))) = sK5(X0,apply(sK2,sK17(sK16(relation_dom(sK2))))) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(apply(sK2,sK17(sK16(relation_dom(sK2)))),relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_71,c_19222]) ).
tcf(c_19371,plain,
! [X0: $i] :
( ( sK17(powerset(relation_dom(sK2))) = empty_set )
| ( apply(X0,sK12(sK1,X0,apply(sK0,sK17(sK16(relation_dom(sK2)))),apply(X0,apply(sK2,sK17(sK16(relation_dom(sK2))))))) = apply(X0,apply(sK2,sK17(sK16(relation_dom(sK2))))) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(apply(sK2,sK17(sK16(relation_dom(sK2)))),relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_73,c_19222]) ).
tcf(c_19372,plain,
! [X0: $i,X1: $i] :
( ( sK17(powerset(relation_dom(sK2))) = empty_set )
| ( apply(X0,ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X1)) = empty_set )
| ( apply(relation_dom(X0),sK12(sK1,relation_dom(X0),apply(sK0,sK17(sK16(relation_dom(sK2)))),X1)) = X1 )
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom(X0))
| ~ relation(relation_dom(X0))
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_75,c_19222]) ).
tcf(c_19373,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK17(powerset(relation_dom(sK2))) = empty_set )
| ( apply(X1,sK12(sK1,X1,apply(sK0,sK17(sK16(relation_dom(sK2)))),sK12(X1,X2,apply(sK2,sK17(sK16(relation_dom(sK2)))),X0))) = sK12(X1,X2,apply(sK2,sK17(sK16(relation_dom(sK2)))),X0) )
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0),relation_composition(X1,X2)) ),
inference(superposition,[status(thm)],[c_301,c_19222]) ).
tcf(c_19374,plain,
! [X0: $i,X1: $i] :
( ( sK17(powerset(relation_dom(sK2))) = empty_set )
| ( apply(relation_dom(sK0),sK12(sK1,relation_dom(sK0),apply(sK0,sK17(sK16(relation_dom(sK2)))),sK12(relation_dom(sK2),X1,apply(sK2,sK17(sK16(relation_dom(sK2)))),X0))) = sK12(relation_dom(sK2),X1,apply(sK2,sK17(sK16(relation_dom(sK2)))),X0) )
| ~ relation(X1)
| ~ function(relation_dom(sK0))
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0),relation_composition(relation_dom(sK2),X1)) ),
inference(superposition,[status(thm)],[c_2283,c_19222]) ).
tcf(c_19375,plain,
( ( sK17(powerset(relation_dom(sK2))) = empty_set )
| ( apply(relation_dom(sK0),sK12(sK1,relation_dom(sK0),apply(sK0,sK17(sK16(relation_dom(sK2)))),sK5(relation_dom(sK2),apply(sK2,sK17(sK16(relation_dom(sK2))))))) = sK5(relation_dom(sK2),apply(sK2,sK17(sK16(relation_dom(sK2))))) )
| ~ function(relation_dom(sK0))
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(apply(sK2,sK17(sK16(relation_dom(sK2)))),relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_3019,c_19222]) ).
tcf(c_19376,plain,
( ( sK17(powerset(relation_dom(sK2))) = empty_set )
| ( apply(relation_dom(sK0),sK12(sK1,relation_dom(sK0),apply(sK0,sK17(sK16(relation_dom(sK2)))),apply(relation_dom(sK2),apply(sK2,sK17(sK16(relation_dom(sK2))))))) = apply(relation_dom(sK2),apply(sK2,sK17(sK16(relation_dom(sK2))))) )
| ~ function(relation_dom(sK0))
| ~ function(relation_dom(sK2))
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(apply(sK2,sK17(sK16(relation_dom(sK2)))),relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_3551,c_19222]) ).
tcf(c_19467,plain,
! [X0: $i] :
( ( relation_composition(relation_dom(sK2),X0) = relation_dom(sK2) )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(relation_dom(sK2),X0,relation_dom(sK2)),sK10(relation_dom(sK2),X0,relation_dom(sK2))))) = apply(sK2,ordered_pair(sK9(relation_dom(sK2),X0,relation_dom(sK2)),sK10(relation_dom(sK2),X0,relation_dom(sK2)))) )
| ~ relation(X0)
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4724,c_2047]) ).
tcf(c_19470,plain,
! [X0: $i] :
( in(ordered_pair(sK9(relation_dom(sK0),X0,relation_dom(sK2)),sK11(relation_dom(sK0),X0,relation_dom(sK2))),relation_dom(sK2))
| ( relation_composition(relation_dom(sK0),X0) = relation_dom(sK2) )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(relation_dom(sK0),X0,relation_dom(sK2)),sK11(relation_dom(sK0),X0,relation_dom(sK2))))) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(relation_dom(sK0),X0,relation_dom(sK2)),sK10(relation_dom(sK0),X0,relation_dom(sK2))))) = apply(sK2,ordered_pair(sK9(relation_dom(sK0),X0,relation_dom(sK2)),sK10(relation_dom(sK0),X0,relation_dom(sK2)))) )
| ~ relation(X0)
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4724,c_3475]) ).
tcf(c_19471,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(X0,X1) = relation_dom(sK2) )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(X0,X1,relation_dom(sK2)),sK10(X0,X1,relation_dom(sK2))))) = apply(sK2,ordered_pair(sK9(X0,X1,relation_dom(sK2)),sK10(X0,X1,relation_dom(sK2)))) )
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2))
| ~ in(X0,ordered_pair(sK9(X0,X1,relation_dom(sK2)),sK11(X0,X1,relation_dom(sK2)))) ),
inference(superposition,[status(thm)],[c_4724,c_64]) ).
tcf(c_19472,plain,
! [X0: $i,X1: $i] :
( element(ordered_pair(sK9(X0,X1,relation_dom(sK2)),sK11(X0,X1,relation_dom(sK2))),X0)
| ( relation_composition(X0,X1) = relation_dom(sK2) )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(X0,X1,relation_dom(sK2)),sK10(X0,X1,relation_dom(sK2))))) = apply(sK2,ordered_pair(sK9(X0,X1,relation_dom(sK2)),sK10(X0,X1,relation_dom(sK2)))) )
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4724,c_63]) ).
tcf(c_19473,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(X0,X1) = relation_dom(sK2) )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(X0,X1,relation_dom(sK2)),sK10(X0,X1,relation_dom(sK2))))) = apply(sK2,ordered_pair(sK9(X0,X1,relation_dom(sK2)),sK10(X0,X1,relation_dom(sK2)))) )
| ~ empty(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4724,c_61]) ).
tcf(c_19474,plain,
! [X0: $i,X1: $i] :
( in(sK9(X0,X1,relation_dom(sK2)),relation_dom(X0))
| ( relation_composition(X0,X1) = relation_dom(sK2) )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(X0,X1,relation_dom(sK2)),sK10(X0,X1,relation_dom(sK2))))) = apply(sK2,ordered_pair(sK9(X0,X1,relation_dom(sK2)),sK10(X0,X1,relation_dom(sK2)))) )
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4724,c_70]) ).
tcf(c_19475,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(ordered_pair(sK9(X0,X1,relation_dom(sK2)),X2),relation_composition(X0,X3))
| ( relation_composition(X0,X1) = relation_dom(sK2) )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(X0,X1,relation_dom(sK2)),sK10(X0,X1,relation_dom(sK2))))) = apply(sK2,ordered_pair(sK9(X0,X1,relation_dom(sK2)),sK10(X0,X1,relation_dom(sK2)))) )
| ~ relation(X3)
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2))
| ~ in(ordered_pair(sK11(X0,X1,relation_dom(sK2)),X2),X3) ),
inference(superposition,[status(thm)],[c_4724,c_299]) ).
tcf(c_19476,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(X0,X1) = relation_dom(sK2) )
| ( apply(X0,sK9(X0,X1,relation_dom(sK2))) = sK11(X0,X1,relation_dom(sK2)) )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(X0,X1,relation_dom(sK2)),sK10(X0,X1,relation_dom(sK2))))) = apply(sK2,ordered_pair(sK9(X0,X1,relation_dom(sK2)),sK10(X0,X1,relation_dom(sK2)))) )
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4724,c_152]) ).
tcf(c_19477,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(relation_dom(X0),X1) = relation_dom(sK2) )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(relation_dom(X0),X1,relation_dom(sK2)),sK10(relation_dom(X0),X1,relation_dom(sK2))))) = apply(sK2,ordered_pair(sK9(relation_dom(X0),X1,relation_dom(sK2)),sK10(relation_dom(X0),X1,relation_dom(sK2)))) )
| ~ empty(X0)
| ~ relation(X1)
| ~ relation(relation_dom(sK2))
| ~ relation(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_4724,c_11389]) ).
tcf(c_19478,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_composition(relation_composition(X0,X1),X2) = relation_dom(sK2) )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(relation_composition(X0,X1),X2,relation_dom(sK2)),sK10(relation_composition(X0,X1),X2,relation_dom(sK2))))) = apply(sK2,ordered_pair(sK9(relation_composition(X0,X1),X2,relation_dom(sK2)),sK10(relation_composition(X0,X1),X2,relation_dom(sK2)))) )
| ( apply(X1,sK12(X0,X1,sK9(relation_composition(X0,X1),X2,relation_dom(sK2)),sK11(relation_composition(X0,X1),X2,relation_dom(sK2)))) = sK11(relation_composition(X0,X1),X2,relation_dom(sK2)) )
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2))
| ~ relation(relation_composition(X0,X1)) ),
inference(superposition,[status(thm)],[c_4724,c_2068]) ).
tcf(c_19479,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(relation_composition(X0,relation_dom(sK2)),X1) = relation_dom(sK2) )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(relation_composition(X0,relation_dom(sK2)),X1,relation_dom(sK2)),sK10(relation_composition(X0,relation_dom(sK2)),X1,relation_dom(sK2))))) = apply(sK2,ordered_pair(sK9(relation_composition(X0,relation_dom(sK2)),X1,relation_dom(sK2)),sK10(relation_composition(X0,relation_dom(sK2)),X1,relation_dom(sK2)))) )
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2))
| ~ relation(relation_composition(X0,relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_4724,c_2063]) ).
tcf(c_19480,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(relation_composition(X0,relation_dom(sK2)),X1) = relation_dom(sK2) )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(relation_composition(X0,relation_dom(sK2)),X1,relation_dom(sK2)),sK10(relation_composition(X0,relation_dom(sK2)),X1,relation_dom(sK2))))) = apply(sK2,ordered_pair(sK9(relation_composition(X0,relation_dom(sK2)),X1,relation_dom(sK2)),sK10(relation_composition(X0,relation_dom(sK2)),X1,relation_dom(sK2)))) )
| ( apply(sK1,apply(sK0,ordered_pair(sK12(X0,relation_dom(sK2),sK9(relation_composition(X0,relation_dom(sK2)),X1,relation_dom(sK2)),sK11(relation_composition(X0,relation_dom(sK2)),X1,relation_dom(sK2))),sK11(relation_composition(X0,relation_dom(sK2)),X1,relation_dom(sK2))))) = apply(sK2,ordered_pair(sK12(X0,relation_dom(sK2),sK9(relation_composition(X0,relation_dom(sK2)),X1,relation_dom(sK2)),sK11(relation_composition(X0,relation_dom(sK2)),X1,relation_dom(sK2))),sK11(relation_composition(X0,relation_dom(sK2)),X1,relation_dom(sK2)))) )
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2))
| ~ relation(relation_composition(X0,relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_4724,c_2064]) ).
tcf(c_19481,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(relation_composition(relation_dom(sK2),X0),X1) = relation_dom(sK2) )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(relation_composition(relation_dom(sK2),X0),X1,relation_dom(sK2)),sK10(relation_composition(relation_dom(sK2),X0),X1,relation_dom(sK2))))) = apply(sK2,ordered_pair(sK9(relation_composition(relation_dom(sK2),X0),X1,relation_dom(sK2)),sK10(relation_composition(relation_dom(sK2),X0),X1,relation_dom(sK2)))) )
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2))
| ~ relation(relation_composition(relation_dom(sK2),X0)) ),
inference(superposition,[status(thm)],[c_4724,c_2281]) ).
tcf(c_19482,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(relation_composition(relation_dom(sK2),X0),X1) = relation_dom(sK2) )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(relation_composition(relation_dom(sK2),X0),X1,relation_dom(sK2)),sK10(relation_composition(relation_dom(sK2),X0),X1,relation_dom(sK2))))) = apply(sK2,ordered_pair(sK9(relation_composition(relation_dom(sK2),X0),X1,relation_dom(sK2)),sK10(relation_composition(relation_dom(sK2),X0),X1,relation_dom(sK2)))) )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(relation_composition(relation_dom(sK2),X0),X1,relation_dom(sK2)),sK12(relation_dom(sK2),X0,sK9(relation_composition(relation_dom(sK2),X0),X1,relation_dom(sK2)),sK11(relation_composition(relation_dom(sK2),X0),X1,relation_dom(sK2)))))) = apply(sK2,ordered_pair(sK9(relation_composition(relation_dom(sK2),X0),X1,relation_dom(sK2)),sK12(relation_dom(sK2),X0,sK9(relation_composition(relation_dom(sK2),X0),X1,relation_dom(sK2)),sK11(relation_composition(relation_dom(sK2),X0),X1,relation_dom(sK2))))) )
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2))
| ~ relation(relation_composition(relation_dom(sK2),X0)) ),
inference(superposition,[status(thm)],[c_4724,c_2282]) ).
tcf(c_19483,plain,
! [X0: $i] :
( ( relation_composition(empty_set,X0) = relation_dom(sK2) )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(empty_set,X0,relation_dom(sK2)),sK10(empty_set,X0,relation_dom(sK2))))) = apply(sK2,ordered_pair(sK9(empty_set,X0,relation_dom(sK2)),sK10(empty_set,X0,relation_dom(sK2)))) )
| ~ relation(empty_set)
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4724,c_3809]) ).
tcf(c_19484,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| element(ordered_pair(sK9(sK16(X0),X1,relation_dom(sK2)),sK11(sK16(X0),X1,relation_dom(sK2))),X0)
| ( relation_composition(sK16(X0),X1) = relation_dom(sK2) )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(sK16(X0),X1,relation_dom(sK2)),sK10(sK16(X0),X1,relation_dom(sK2))))) = apply(sK2,ordered_pair(sK9(sK16(X0),X1,relation_dom(sK2)),sK10(sK16(X0),X1,relation_dom(sK2)))) )
| ~ relation(X1)
| ~ relation(relation_dom(sK2))
| ~ relation(sK16(X0)) ),
inference(superposition,[status(thm)],[c_4724,c_2939]) ).
tcf(c_19485,plain,
! [X0: $i,X1: $i] :
( element(ordered_pair(sK9(sK17(powerset(X0)),X1,relation_dom(sK2)),sK11(sK17(powerset(X0)),X1,relation_dom(sK2))),X0)
| ( relation_composition(sK17(powerset(X0)),X1) = relation_dom(sK2) )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(sK17(powerset(X0)),X1,relation_dom(sK2)),sK10(sK17(powerset(X0)),X1,relation_dom(sK2))))) = apply(sK2,ordered_pair(sK9(sK17(powerset(X0)),X1,relation_dom(sK2)),sK10(sK17(powerset(X0)),X1,relation_dom(sK2)))) )
| ~ relation(X1)
| ~ relation(relation_dom(sK2))
| ~ relation(sK17(powerset(X0))) ),
inference(superposition,[status(thm)],[c_4724,c_2940]) ).
tcf(c_19486,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(sK17(powerset(X0)),X1) = relation_dom(sK2) )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(sK17(powerset(X0)),X1,relation_dom(sK2)),sK10(sK17(powerset(X0)),X1,relation_dom(sK2))))) = apply(sK2,ordered_pair(sK9(sK17(powerset(X0)),X1,relation_dom(sK2)),sK10(sK17(powerset(X0)),X1,relation_dom(sK2)))) )
| ~ empty(X0)
| ~ relation(X1)
| ~ relation(relation_dom(sK2))
| ~ relation(sK17(powerset(X0))) ),
inference(superposition,[status(thm)],[c_4724,c_2925]) ).
tcf(c_19487,plain,
! [X0: $i] :
( ( relation_composition(relation_dom(relation_dom(sK2)),X0) = relation_dom(sK2) )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(relation_dom(relation_dom(sK2)),X0,relation_dom(sK2)),sK10(relation_dom(relation_dom(sK2)),X0,relation_dom(sK2))))) = apply(sK2,ordered_pair(sK9(relation_dom(relation_dom(sK2)),X0,relation_dom(sK2)),sK10(relation_dom(relation_dom(sK2)),X0,relation_dom(sK2)))) )
| ( apply(sK1,apply(sK0,ordered_pair(ordered_pair(sK9(relation_dom(relation_dom(sK2)),X0,relation_dom(sK2)),sK11(relation_dom(relation_dom(sK2)),X0,relation_dom(sK2))),apply(relation_dom(sK2),ordered_pair(sK9(relation_dom(relation_dom(sK2)),X0,relation_dom(sK2)),sK11(relation_dom(relation_dom(sK2)),X0,relation_dom(sK2))))))) = apply(sK2,ordered_pair(ordered_pair(sK9(relation_dom(relation_dom(sK2)),X0,relation_dom(sK2)),sK11(relation_dom(relation_dom(sK2)),X0,relation_dom(sK2))),apply(relation_dom(sK2),ordered_pair(sK9(relation_dom(relation_dom(sK2)),X0,relation_dom(sK2)),sK11(relation_dom(relation_dom(sK2)),X0,relation_dom(sK2)))))) )
| ~ relation(X0)
| ~ function(relation_dom(sK2))
| ~ relation(relation_dom(sK2))
| ~ relation(relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_4724,c_3550]) ).
tcf(c_19488,plain,
! [X0: $i] :
( in(ordered_pair(sK9(relation_dom(relation_dom(sK2)),X0,relation_dom(sK2)),sK11(relation_dom(relation_dom(sK2)),X0,relation_dom(sK2))),relation_dom(relation_dom(sK0)))
| ( relation_composition(relation_dom(relation_dom(sK2)),X0) = relation_dom(sK2) )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(relation_dom(relation_dom(sK2)),X0,relation_dom(sK2)),sK10(relation_dom(relation_dom(sK2)),X0,relation_dom(sK2))))) = apply(sK2,ordered_pair(sK9(relation_dom(relation_dom(sK2)),X0,relation_dom(sK2)),sK10(relation_dom(relation_dom(sK2)),X0,relation_dom(sK2)))) )
| ~ relation(X0)
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ relation(relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_4724,c_3134]) ).
tcf(c_19489,plain,
! [X0: $i] :
( ( relation_composition(relation_dom(relation_dom(sK2)),X0) = relation_dom(sK2) )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(relation_dom(relation_dom(sK2)),X0,relation_dom(sK2)),sK10(relation_dom(relation_dom(sK2)),X0,relation_dom(sK2))))) = apply(sK2,ordered_pair(sK9(relation_dom(relation_dom(sK2)),X0,relation_dom(sK2)),sK10(relation_dom(relation_dom(sK2)),X0,relation_dom(sK2)))) )
| ~ relation(X0)
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2))
| ~ relation(relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_4724,c_3017]) ).
tcf(c_19490,plain,
! [X0: $i] :
( ( relation_composition(relation_dom(relation_dom(sK2)),X0) = relation_dom(sK2) )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(relation_dom(relation_dom(sK2)),X0,relation_dom(sK2)),sK10(relation_dom(relation_dom(sK2)),X0,relation_dom(sK2))))) = apply(sK2,ordered_pair(sK9(relation_dom(relation_dom(sK2)),X0,relation_dom(sK2)),sK10(relation_dom(relation_dom(sK2)),X0,relation_dom(sK2)))) )
| ( apply(sK1,apply(sK0,ordered_pair(ordered_pair(sK9(relation_dom(relation_dom(sK2)),X0,relation_dom(sK2)),sK11(relation_dom(relation_dom(sK2)),X0,relation_dom(sK2))),sK5(relation_dom(sK2),ordered_pair(sK9(relation_dom(relation_dom(sK2)),X0,relation_dom(sK2)),sK11(relation_dom(relation_dom(sK2)),X0,relation_dom(sK2))))))) = apply(sK2,ordered_pair(ordered_pair(sK9(relation_dom(relation_dom(sK2)),X0,relation_dom(sK2)),sK11(relation_dom(relation_dom(sK2)),X0,relation_dom(sK2))),sK5(relation_dom(sK2),ordered_pair(sK9(relation_dom(relation_dom(sK2)),X0,relation_dom(sK2)),sK11(relation_dom(relation_dom(sK2)),X0,relation_dom(sK2)))))) )
| ~ relation(X0)
| ~ relation(relation_dom(sK2))
| ~ relation(relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_4724,c_3018]) ).
tcf(c_19491,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(relation_composition(empty_set,X0),X1) = relation_dom(sK2) )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(relation_composition(empty_set,X0),X1,relation_dom(sK2)),sK10(relation_composition(empty_set,X0),X1,relation_dom(sK2))))) = apply(sK2,ordered_pair(sK9(relation_composition(empty_set,X0),X1,relation_dom(sK2)),sK10(relation_composition(empty_set,X0),X1,relation_dom(sK2)))) )
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2))
| ~ relation(relation_composition(empty_set,X0)) ),
inference(superposition,[status(thm)],[c_4724,c_3821]) ).
tcf(c_19492,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(relation_composition(X0,empty_set),X1) = relation_dom(sK2) )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(relation_composition(X0,empty_set),X1,relation_dom(sK2)),sK10(relation_composition(X0,empty_set),X1,relation_dom(sK2))))) = apply(sK2,ordered_pair(sK9(relation_composition(X0,empty_set),X1,relation_dom(sK2)),sK10(relation_composition(X0,empty_set),X1,relation_dom(sK2)))) )
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2))
| ~ relation(relation_composition(X0,empty_set)) ),
inference(superposition,[status(thm)],[c_4724,c_3818]) ).
tcf(c_19493,plain,
! [X0: $i,X1: $i] :
( element(ordered_pair(sK9(sK17(sK16(powerset(X0))),X1,relation_dom(sK2)),sK11(sK17(sK16(powerset(X0))),X1,relation_dom(sK2))),X0)
| ( relation_composition(sK17(sK16(powerset(X0))),X1) = relation_dom(sK2) )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(sK17(sK16(powerset(X0))),X1,relation_dom(sK2)),sK10(sK17(sK16(powerset(X0))),X1,relation_dom(sK2))))) = apply(sK2,ordered_pair(sK9(sK17(sK16(powerset(X0))),X1,relation_dom(sK2)),sK10(sK17(sK16(powerset(X0))),X1,relation_dom(sK2)))) )
| ~ relation(X1)
| ~ relation(relation_dom(sK2))
| ~ relation(sK17(sK16(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_4724,c_11939]) ).
tcf(c_19494,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(sK17(sK16(powerset(X0))),X1) = relation_dom(sK2) )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(sK17(sK16(powerset(X0))),X1,relation_dom(sK2)),sK10(sK17(sK16(powerset(X0))),X1,relation_dom(sK2))))) = apply(sK2,ordered_pair(sK9(sK17(sK16(powerset(X0))),X1,relation_dom(sK2)),sK10(sK17(sK16(powerset(X0))),X1,relation_dom(sK2)))) )
| ~ empty(X0)
| ~ relation(X1)
| ~ relation(relation_dom(sK2))
| ~ relation(sK17(sK16(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_4724,c_11936]) ).
tcf(c_19495,plain,
! [X0: $i] :
( ( relation_composition(empty_set,X0) = relation_dom(sK2) )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(empty_set,X0,relation_dom(sK2)),sK10(empty_set,X0,relation_dom(sK2))))) = apply(sK2,ordered_pair(sK9(empty_set,X0,relation_dom(sK2)),sK10(empty_set,X0,relation_dom(sK2)))) )
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_19483,c_109]) ).
tcf(c_19697,plain,
! [X0: $i] :
( ( relation_composition(X0,relation_dom(sK2)) = relation_dom(sK2) )
| ( apply(sK1,apply(sK0,ordered_pair(sK11(X0,relation_dom(sK2),relation_dom(sK2)),sK10(X0,relation_dom(sK2),relation_dom(sK2))))) = apply(sK2,ordered_pair(sK11(X0,relation_dom(sK2),relation_dom(sK2)),sK10(X0,relation_dom(sK2),relation_dom(sK2)))) )
| ~ relation(X0)
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5256,c_2047]) ).
tcf(c_19698,plain,
! [X0: $i] :
( ( relation_composition(X0,relation_dom(sK2)) = relation_dom(sK2) )
| ( apply(sK1,apply(sK0,ordered_pair(sK11(X0,relation_dom(sK2),relation_dom(sK2)),sK10(X0,relation_dom(sK2),relation_dom(sK2))))) = apply(sK2,ordered_pair(sK11(X0,relation_dom(sK2),relation_dom(sK2)),sK10(X0,relation_dom(sK2),relation_dom(sK2)))) )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(X0,relation_dom(sK2),relation_dom(sK2)),sK10(X0,relation_dom(sK2),relation_dom(sK2))))) = apply(sK2,ordered_pair(sK9(X0,relation_dom(sK2),relation_dom(sK2)),sK10(X0,relation_dom(sK2),relation_dom(sK2)))) )
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5256,c_53]) ).
tcf(c_19700,plain,
! [X0: $i] :
( in(ordered_pair(sK9(X0,relation_dom(sK2),relation_dom(sK0)),sK10(X0,relation_dom(sK2),relation_dom(sK0))),relation_dom(sK2))
| ( relation_composition(X0,relation_dom(sK2)) = relation_dom(sK0) )
| ( apply(sK1,apply(sK0,ordered_pair(sK11(X0,relation_dom(sK2),relation_dom(sK0)),sK10(X0,relation_dom(sK2),relation_dom(sK0))))) = apply(sK2,ordered_pair(sK11(X0,relation_dom(sK2),relation_dom(sK0)),sK10(X0,relation_dom(sK2),relation_dom(sK0)))) )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(X0,relation_dom(sK2),relation_dom(sK0)),sK10(X0,relation_dom(sK2),relation_dom(sK0))))) = empty_set )
| ~ relation(X0)
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5256,c_3475]) ).
tcf(c_19701,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(X1,relation_dom(sK2)) = X0 )
| ( apply(sK1,apply(sK0,ordered_pair(sK11(X1,relation_dom(sK2),X0),sK10(X1,relation_dom(sK2),X0)))) = apply(sK2,ordered_pair(sK11(X1,relation_dom(sK2),X0),sK10(X1,relation_dom(sK2),X0))) )
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2))
| ~ in(X0,ordered_pair(sK9(X1,relation_dom(sK2),X0),sK10(X1,relation_dom(sK2),X0))) ),
inference(superposition,[status(thm)],[c_5256,c_64]) ).
tcf(c_19702,plain,
! [X0: $i,X1: $i] :
( element(ordered_pair(sK9(X0,relation_dom(sK2),X1),sK10(X0,relation_dom(sK2),X1)),X1)
| ( relation_composition(X0,relation_dom(sK2)) = X1 )
| ( apply(sK1,apply(sK0,ordered_pair(sK11(X0,relation_dom(sK2),X1),sK10(X0,relation_dom(sK2),X1)))) = apply(sK2,ordered_pair(sK11(X0,relation_dom(sK2),X1),sK10(X0,relation_dom(sK2),X1))) )
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5256,c_63]) ).
tcf(c_19703,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(X0,relation_dom(sK2)) = X1 )
| ( apply(sK1,apply(sK0,ordered_pair(sK11(X0,relation_dom(sK2),X1),sK10(X0,relation_dom(sK2),X1)))) = apply(sK2,ordered_pair(sK11(X0,relation_dom(sK2),X1),sK10(X0,relation_dom(sK2),X1))) )
| ~ empty(X1)
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5256,c_61]) ).
tcf(c_19704,plain,
! [X0: $i,X1: $i] :
( in(sK9(X0,relation_dom(sK2),X1),relation_dom(X1))
| ( relation_composition(X0,relation_dom(sK2)) = X1 )
| ( apply(sK1,apply(sK0,ordered_pair(sK11(X0,relation_dom(sK2),X1),sK10(X0,relation_dom(sK2),X1)))) = apply(sK2,ordered_pair(sK11(X0,relation_dom(sK2),X1),sK10(X0,relation_dom(sK2),X1))) )
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5256,c_70]) ).
tcf(c_19705,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(ordered_pair(sK9(X0,relation_dom(sK2),X1),X2),relation_composition(X1,X3))
| ( relation_composition(X0,relation_dom(sK2)) = X1 )
| ( apply(sK1,apply(sK0,ordered_pair(sK11(X0,relation_dom(sK2),X1),sK10(X0,relation_dom(sK2),X1)))) = apply(sK2,ordered_pair(sK11(X0,relation_dom(sK2),X1),sK10(X0,relation_dom(sK2),X1))) )
| ~ relation(X3)
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2))
| ~ in(ordered_pair(sK10(X0,relation_dom(sK2),X1),X2),X3) ),
inference(superposition,[status(thm)],[c_5256,c_299]) ).
tcf(c_19706,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(X0,relation_dom(sK2)) = X1 )
| ( apply(X1,sK9(X0,relation_dom(sK2),X1)) = sK10(X0,relation_dom(sK2),X1) )
| ( apply(sK1,apply(sK0,ordered_pair(sK11(X0,relation_dom(sK2),X1),sK10(X0,relation_dom(sK2),X1)))) = apply(sK2,ordered_pair(sK11(X0,relation_dom(sK2),X1),sK10(X0,relation_dom(sK2),X1))) )
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5256,c_152]) ).
tcf(c_19707,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(X1,relation_dom(sK2)) = relation_dom(X0) )
| ( apply(sK1,apply(sK0,ordered_pair(sK11(X1,relation_dom(sK2),relation_dom(X0)),sK10(X1,relation_dom(sK2),relation_dom(X0))))) = apply(sK2,ordered_pair(sK11(X1,relation_dom(sK2),relation_dom(X0)),sK10(X1,relation_dom(sK2),relation_dom(X0)))) )
| ~ empty(X0)
| ~ relation(X1)
| ~ relation(relation_dom(sK2))
| ~ relation(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_5256,c_11389]) ).
tcf(c_19708,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_composition(X1,relation_dom(sK2)) = X2 )
| ( apply(sK1,apply(sK0,ordered_pair(sK11(X1,relation_dom(sK2),X2),sK10(X1,relation_dom(sK2),X2)))) = apply(sK2,ordered_pair(sK11(X1,relation_dom(sK2),X2),sK10(X1,relation_dom(sK2),X2))) )
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(relation_dom(sK2))
| ~ in(ordered_pair(sK9(X1,relation_dom(sK2),X2),X0),X1)
| ~ in(ordered_pair(X0,sK10(X1,relation_dom(sK2),X2)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5256,c_91]) ).
tcf(c_19709,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_composition(X2,relation_dom(sK2)) = relation_composition(X0,X1) )
| ( apply(sK1,apply(sK0,ordered_pair(sK11(X2,relation_dom(sK2),relation_composition(X0,X1)),sK10(X2,relation_dom(sK2),relation_composition(X0,X1))))) = apply(sK2,ordered_pair(sK11(X2,relation_dom(sK2),relation_composition(X0,X1)),sK10(X2,relation_dom(sK2),relation_composition(X0,X1)))) )
| ( apply(X1,sK12(X0,X1,sK9(X2,relation_dom(sK2),relation_composition(X0,X1)),sK10(X2,relation_dom(sK2),relation_composition(X0,X1)))) = sK10(X2,relation_dom(sK2),relation_composition(X0,X1)) )
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2))
| ~ relation(relation_composition(X0,X1)) ),
inference(superposition,[status(thm)],[c_5256,c_2068]) ).
tcf(c_19710,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(X0,relation_dom(sK2)) = relation_composition(X1,relation_dom(sK2)) )
| ( apply(sK1,apply(sK0,ordered_pair(sK11(X1,relation_dom(sK2),relation_composition(X0,relation_dom(sK2))),sK10(X1,relation_dom(sK2),relation_composition(X0,relation_dom(sK2)))))) = apply(sK2,ordered_pair(sK11(X1,relation_dom(sK2),relation_composition(X0,relation_dom(sK2))),sK10(X1,relation_dom(sK2),relation_composition(X0,relation_dom(sK2))))) )
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2))
| ~ relation(relation_composition(X0,relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_5256,c_2063]) ).
tcf(c_19711,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(X0,relation_dom(sK2)) = relation_composition(X1,relation_dom(sK2)) )
| ( apply(sK1,apply(sK0,ordered_pair(sK11(X1,relation_dom(sK2),relation_composition(X0,relation_dom(sK2))),sK10(X1,relation_dom(sK2),relation_composition(X0,relation_dom(sK2)))))) = apply(sK2,ordered_pair(sK11(X1,relation_dom(sK2),relation_composition(X0,relation_dom(sK2))),sK10(X1,relation_dom(sK2),relation_composition(X0,relation_dom(sK2))))) )
| ( apply(sK1,apply(sK0,ordered_pair(sK12(X0,relation_dom(sK2),sK9(X1,relation_dom(sK2),relation_composition(X0,relation_dom(sK2))),sK10(X1,relation_dom(sK2),relation_composition(X0,relation_dom(sK2)))),sK10(X1,relation_dom(sK2),relation_composition(X0,relation_dom(sK2)))))) = apply(sK2,ordered_pair(sK12(X0,relation_dom(sK2),sK9(X1,relation_dom(sK2),relation_composition(X0,relation_dom(sK2))),sK10(X1,relation_dom(sK2),relation_composition(X0,relation_dom(sK2)))),sK10(X1,relation_dom(sK2),relation_composition(X0,relation_dom(sK2))))) )
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2))
| ~ relation(relation_composition(X0,relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_5256,c_2064]) ).
tcf(c_19712,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(relation_dom(sK2),X0) = relation_composition(X1,relation_dom(sK2)) )
| ( apply(sK1,apply(sK0,ordered_pair(sK11(X1,relation_dom(sK2),relation_composition(relation_dom(sK2),X0)),sK10(X1,relation_dom(sK2),relation_composition(relation_dom(sK2),X0))))) = apply(sK2,ordered_pair(sK11(X1,relation_dom(sK2),relation_composition(relation_dom(sK2),X0)),sK10(X1,relation_dom(sK2),relation_composition(relation_dom(sK2),X0)))) )
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2))
| ~ relation(relation_composition(relation_dom(sK2),X0)) ),
inference(superposition,[status(thm)],[c_5256,c_2281]) ).
tcf(c_19713,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(relation_dom(sK2),X0) = relation_composition(X1,relation_dom(sK2)) )
| ( apply(sK1,apply(sK0,ordered_pair(sK11(X1,relation_dom(sK2),relation_composition(relation_dom(sK2),X0)),sK10(X1,relation_dom(sK2),relation_composition(relation_dom(sK2),X0))))) = apply(sK2,ordered_pair(sK11(X1,relation_dom(sK2),relation_composition(relation_dom(sK2),X0)),sK10(X1,relation_dom(sK2),relation_composition(relation_dom(sK2),X0)))) )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(X1,relation_dom(sK2),relation_composition(relation_dom(sK2),X0)),sK12(relation_dom(sK2),X0,sK9(X1,relation_dom(sK2),relation_composition(relation_dom(sK2),X0)),sK10(X1,relation_dom(sK2),relation_composition(relation_dom(sK2),X0)))))) = apply(sK2,ordered_pair(sK9(X1,relation_dom(sK2),relation_composition(relation_dom(sK2),X0)),sK12(relation_dom(sK2),X0,sK9(X1,relation_dom(sK2),relation_composition(relation_dom(sK2),X0)),sK10(X1,relation_dom(sK2),relation_composition(relation_dom(sK2),X0))))) )
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2))
| ~ relation(relation_composition(relation_dom(sK2),X0)) ),
inference(superposition,[status(thm)],[c_5256,c_2282]) ).
tcf(c_19714,plain,
! [X0: $i] :
( ( relation_composition(X0,relation_dom(sK2)) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(sK11(X0,relation_dom(sK2),empty_set),sK10(X0,relation_dom(sK2),empty_set)))) = apply(sK2,ordered_pair(sK11(X0,relation_dom(sK2),empty_set),sK10(X0,relation_dom(sK2),empty_set))) )
| ~ relation(empty_set)
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5256,c_3809]) ).
tcf(c_19715,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| element(ordered_pair(sK9(X1,relation_dom(sK2),sK16(X0)),sK10(X1,relation_dom(sK2),sK16(X0))),X0)
| ( relation_composition(X1,relation_dom(sK2)) = sK16(X0) )
| ( apply(sK1,apply(sK0,ordered_pair(sK11(X1,relation_dom(sK2),sK16(X0)),sK10(X1,relation_dom(sK2),sK16(X0))))) = apply(sK2,ordered_pair(sK11(X1,relation_dom(sK2),sK16(X0)),sK10(X1,relation_dom(sK2),sK16(X0)))) )
| ~ relation(X1)
| ~ relation(relation_dom(sK2))
| ~ relation(sK16(X0)) ),
inference(superposition,[status(thm)],[c_5256,c_2939]) ).
tcf(c_19716,plain,
! [X0: $i,X1: $i] :
( element(ordered_pair(sK9(X1,relation_dom(sK2),sK17(powerset(X0))),sK10(X1,relation_dom(sK2),sK17(powerset(X0)))),X0)
| ( relation_composition(X1,relation_dom(sK2)) = sK17(powerset(X0)) )
| ( apply(sK1,apply(sK0,ordered_pair(sK11(X1,relation_dom(sK2),sK17(powerset(X0))),sK10(X1,relation_dom(sK2),sK17(powerset(X0)))))) = apply(sK2,ordered_pair(sK11(X1,relation_dom(sK2),sK17(powerset(X0))),sK10(X1,relation_dom(sK2),sK17(powerset(X0))))) )
| ~ relation(X1)
| ~ relation(relation_dom(sK2))
| ~ relation(sK17(powerset(X0))) ),
inference(superposition,[status(thm)],[c_5256,c_2940]) ).
tcf(c_19717,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(X1,relation_dom(sK2)) = sK17(powerset(X0)) )
| ( apply(sK1,apply(sK0,ordered_pair(sK11(X1,relation_dom(sK2),sK17(powerset(X0))),sK10(X1,relation_dom(sK2),sK17(powerset(X0)))))) = apply(sK2,ordered_pair(sK11(X1,relation_dom(sK2),sK17(powerset(X0))),sK10(X1,relation_dom(sK2),sK17(powerset(X0))))) )
| ~ empty(X0)
| ~ relation(X1)
| ~ relation(relation_dom(sK2))
| ~ relation(sK17(powerset(X0))) ),
inference(superposition,[status(thm)],[c_5256,c_2925]) ).
tcf(c_19718,plain,
! [X0: $i] :
( ( relation_composition(X0,relation_dom(sK2)) = relation_dom(relation_dom(sK2)) )
| ( apply(sK1,apply(sK0,ordered_pair(sK11(X0,relation_dom(sK2),relation_dom(relation_dom(sK2))),sK10(X0,relation_dom(sK2),relation_dom(relation_dom(sK2)))))) = apply(sK2,ordered_pair(sK11(X0,relation_dom(sK2),relation_dom(relation_dom(sK2))),sK10(X0,relation_dom(sK2),relation_dom(relation_dom(sK2))))) )
| ( apply(sK1,apply(sK0,ordered_pair(ordered_pair(sK9(X0,relation_dom(sK2),relation_dom(relation_dom(sK2))),sK10(X0,relation_dom(sK2),relation_dom(relation_dom(sK2)))),apply(relation_dom(sK2),ordered_pair(sK9(X0,relation_dom(sK2),relation_dom(relation_dom(sK2))),sK10(X0,relation_dom(sK2),relation_dom(relation_dom(sK2)))))))) = apply(sK2,ordered_pair(ordered_pair(sK9(X0,relation_dom(sK2),relation_dom(relation_dom(sK2))),sK10(X0,relation_dom(sK2),relation_dom(relation_dom(sK2)))),apply(relation_dom(sK2),ordered_pair(sK9(X0,relation_dom(sK2),relation_dom(relation_dom(sK2))),sK10(X0,relation_dom(sK2),relation_dom(relation_dom(sK2))))))) )
| ~ relation(X0)
| ~ function(relation_dom(sK2))
| ~ relation(relation_dom(sK2))
| ~ relation(relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_5256,c_3550]) ).
tcf(c_19719,plain,
! [X0: $i] :
( in(ordered_pair(sK9(X0,relation_dom(sK2),relation_dom(relation_dom(sK2))),sK10(X0,relation_dom(sK2),relation_dom(relation_dom(sK2)))),relation_dom(relation_dom(sK0)))
| ( relation_composition(X0,relation_dom(sK2)) = relation_dom(relation_dom(sK2)) )
| ( apply(sK1,apply(sK0,ordered_pair(sK11(X0,relation_dom(sK2),relation_dom(relation_dom(sK2))),sK10(X0,relation_dom(sK2),relation_dom(relation_dom(sK2)))))) = apply(sK2,ordered_pair(sK11(X0,relation_dom(sK2),relation_dom(relation_dom(sK2))),sK10(X0,relation_dom(sK2),relation_dom(relation_dom(sK2))))) )
| ~ relation(X0)
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ relation(relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_5256,c_3134]) ).
tcf(c_19720,plain,
! [X0: $i] :
( ( relation_composition(X0,relation_dom(sK2)) = relation_dom(relation_dom(sK2)) )
| ( apply(sK1,apply(sK0,ordered_pair(sK11(X0,relation_dom(sK2),relation_dom(relation_dom(sK2))),sK10(X0,relation_dom(sK2),relation_dom(relation_dom(sK2)))))) = apply(sK2,ordered_pair(sK11(X0,relation_dom(sK2),relation_dom(relation_dom(sK2))),sK10(X0,relation_dom(sK2),relation_dom(relation_dom(sK2))))) )
| ~ relation(X0)
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2))
| ~ relation(relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_5256,c_3017]) ).
tcf(c_19721,plain,
! [X0: $i] :
( ( relation_composition(X0,relation_dom(sK2)) = relation_dom(relation_dom(sK2)) )
| ( apply(sK1,apply(sK0,ordered_pair(sK11(X0,relation_dom(sK2),relation_dom(relation_dom(sK2))),sK10(X0,relation_dom(sK2),relation_dom(relation_dom(sK2)))))) = apply(sK2,ordered_pair(sK11(X0,relation_dom(sK2),relation_dom(relation_dom(sK2))),sK10(X0,relation_dom(sK2),relation_dom(relation_dom(sK2))))) )
| ( apply(sK1,apply(sK0,ordered_pair(ordered_pair(sK9(X0,relation_dom(sK2),relation_dom(relation_dom(sK2))),sK10(X0,relation_dom(sK2),relation_dom(relation_dom(sK2)))),sK5(relation_dom(sK2),ordered_pair(sK9(X0,relation_dom(sK2),relation_dom(relation_dom(sK2))),sK10(X0,relation_dom(sK2),relation_dom(relation_dom(sK2)))))))) = apply(sK2,ordered_pair(ordered_pair(sK9(X0,relation_dom(sK2),relation_dom(relation_dom(sK2))),sK10(X0,relation_dom(sK2),relation_dom(relation_dom(sK2)))),sK5(relation_dom(sK2),ordered_pair(sK9(X0,relation_dom(sK2),relation_dom(relation_dom(sK2))),sK10(X0,relation_dom(sK2),relation_dom(relation_dom(sK2))))))) )
| ~ relation(X0)
| ~ relation(relation_dom(sK2))
| ~ relation(relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_5256,c_3018]) ).
tcf(c_19722,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(X1,relation_dom(sK2)) = relation_composition(empty_set,X0) )
| ( apply(sK1,apply(sK0,ordered_pair(sK11(X1,relation_dom(sK2),relation_composition(empty_set,X0)),sK10(X1,relation_dom(sK2),relation_composition(empty_set,X0))))) = apply(sK2,ordered_pair(sK11(X1,relation_dom(sK2),relation_composition(empty_set,X0)),sK10(X1,relation_dom(sK2),relation_composition(empty_set,X0)))) )
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2))
| ~ relation(relation_composition(empty_set,X0)) ),
inference(superposition,[status(thm)],[c_5256,c_3821]) ).
tcf(c_19723,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(X1,relation_dom(sK2)) = relation_composition(X0,empty_set) )
| ( apply(sK1,apply(sK0,ordered_pair(sK11(X1,relation_dom(sK2),relation_composition(X0,empty_set)),sK10(X1,relation_dom(sK2),relation_composition(X0,empty_set))))) = apply(sK2,ordered_pair(sK11(X1,relation_dom(sK2),relation_composition(X0,empty_set)),sK10(X1,relation_dom(sK2),relation_composition(X0,empty_set)))) )
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2))
| ~ relation(relation_composition(X0,empty_set)) ),
inference(superposition,[status(thm)],[c_5256,c_3818]) ).
tcf(c_19724,plain,
! [X0: $i,X1: $i] :
( element(ordered_pair(sK9(X1,relation_dom(sK2),sK17(sK16(powerset(X0)))),sK10(X1,relation_dom(sK2),sK17(sK16(powerset(X0))))),X0)
| ( relation_composition(X1,relation_dom(sK2)) = sK17(sK16(powerset(X0))) )
| ( apply(sK1,apply(sK0,ordered_pair(sK11(X1,relation_dom(sK2),sK17(sK16(powerset(X0)))),sK10(X1,relation_dom(sK2),sK17(sK16(powerset(X0))))))) = apply(sK2,ordered_pair(sK11(X1,relation_dom(sK2),sK17(sK16(powerset(X0)))),sK10(X1,relation_dom(sK2),sK17(sK16(powerset(X0)))))) )
| ~ relation(X1)
| ~ relation(relation_dom(sK2))
| ~ relation(sK17(sK16(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_5256,c_11939]) ).
tcf(c_19725,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(X1,relation_dom(sK2)) = sK17(sK16(powerset(X0))) )
| ( apply(sK1,apply(sK0,ordered_pair(sK11(X1,relation_dom(sK2),sK17(sK16(powerset(X0)))),sK10(X1,relation_dom(sK2),sK17(sK16(powerset(X0))))))) = apply(sK2,ordered_pair(sK11(X1,relation_dom(sK2),sK17(sK16(powerset(X0)))),sK10(X1,relation_dom(sK2),sK17(sK16(powerset(X0)))))) )
| ~ empty(X0)
| ~ relation(X1)
| ~ relation(relation_dom(sK2))
| ~ relation(sK17(sK16(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_5256,c_11936]) ).
tcf(c_19726,plain,
! [X0: $i] :
( ( relation_composition(X0,relation_dom(sK2)) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(sK11(X0,relation_dom(sK2),empty_set),sK10(X0,relation_dom(sK2),empty_set)))) = apply(sK2,ordered_pair(sK11(X0,relation_dom(sK2),empty_set),sK10(X0,relation_dom(sK2),empty_set))) )
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_19714,c_109]) ).
tcf(c_20102,plain,
! [X0: $i] :
( ( relation_composition(X0,relation_dom(sK2)) = relation_dom(sK2) )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(X0,relation_dom(sK2),relation_dom(sK2)),sK10(X0,relation_dom(sK2),relation_dom(sK2))))) = apply(sK2,ordered_pair(sK9(X0,relation_dom(sK2),relation_dom(sK2)),sK10(X0,relation_dom(sK2),relation_dom(sK2)))) )
| ~ relation(X0)
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5278,c_2047]) ).
tcf(c_20105,plain,
! [X0: $i] :
( in(ordered_pair(sK11(X0,relation_dom(sK0),relation_dom(sK2)),sK10(X0,relation_dom(sK0),relation_dom(sK2))),relation_dom(sK2))
| ( relation_composition(X0,relation_dom(sK0)) = relation_dom(sK2) )
| ( apply(sK1,apply(sK0,ordered_pair(sK11(X0,relation_dom(sK0),relation_dom(sK2)),sK10(X0,relation_dom(sK0),relation_dom(sK2))))) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(X0,relation_dom(sK0),relation_dom(sK2)),sK10(X0,relation_dom(sK0),relation_dom(sK2))))) = apply(sK2,ordered_pair(sK9(X0,relation_dom(sK0),relation_dom(sK2)),sK10(X0,relation_dom(sK0),relation_dom(sK2)))) )
| ~ relation(X0)
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5278,c_3475]) ).
tcf(c_20106,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(X1,X0) = relation_dom(sK2) )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(X1,X0,relation_dom(sK2)),sK10(X1,X0,relation_dom(sK2))))) = apply(sK2,ordered_pair(sK9(X1,X0,relation_dom(sK2)),sK10(X1,X0,relation_dom(sK2)))) )
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2))
| ~ in(X0,ordered_pair(sK11(X1,X0,relation_dom(sK2)),sK10(X1,X0,relation_dom(sK2)))) ),
inference(superposition,[status(thm)],[c_5278,c_64]) ).
tcf(c_20107,plain,
! [X0: $i,X1: $i] :
( element(ordered_pair(sK11(X0,X1,relation_dom(sK2)),sK10(X0,X1,relation_dom(sK2))),X1)
| ( relation_composition(X0,X1) = relation_dom(sK2) )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(X0,X1,relation_dom(sK2)),sK10(X0,X1,relation_dom(sK2))))) = apply(sK2,ordered_pair(sK9(X0,X1,relation_dom(sK2)),sK10(X0,X1,relation_dom(sK2)))) )
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5278,c_63]) ).
tcf(c_20108,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(X0,X1) = relation_dom(sK2) )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(X0,X1,relation_dom(sK2)),sK10(X0,X1,relation_dom(sK2))))) = apply(sK2,ordered_pair(sK9(X0,X1,relation_dom(sK2)),sK10(X0,X1,relation_dom(sK2)))) )
| ~ empty(X1)
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5278,c_61]) ).
tcf(c_20109,plain,
! [X0: $i,X1: $i] :
( in(sK11(X0,X1,relation_dom(sK2)),relation_dom(X1))
| ( relation_composition(X0,X1) = relation_dom(sK2) )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(X0,X1,relation_dom(sK2)),sK10(X0,X1,relation_dom(sK2))))) = apply(sK2,ordered_pair(sK9(X0,X1,relation_dom(sK2)),sK10(X0,X1,relation_dom(sK2)))) )
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5278,c_70]) ).
tcf(c_20110,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(ordered_pair(sK11(X0,X1,relation_dom(sK2)),X2),relation_composition(X1,X3))
| ( relation_composition(X0,X1) = relation_dom(sK2) )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(X0,X1,relation_dom(sK2)),sK10(X0,X1,relation_dom(sK2))))) = apply(sK2,ordered_pair(sK9(X0,X1,relation_dom(sK2)),sK10(X0,X1,relation_dom(sK2)))) )
| ~ relation(X3)
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2))
| ~ in(ordered_pair(sK10(X0,X1,relation_dom(sK2)),X2),X3) ),
inference(superposition,[status(thm)],[c_5278,c_299]) ).
tcf(c_20111,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(X0,X1) = relation_dom(sK2) )
| ( apply(X1,sK11(X0,X1,relation_dom(sK2))) = sK10(X0,X1,relation_dom(sK2)) )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(X0,X1,relation_dom(sK2)),sK10(X0,X1,relation_dom(sK2))))) = apply(sK2,ordered_pair(sK9(X0,X1,relation_dom(sK2)),sK10(X0,X1,relation_dom(sK2)))) )
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5278,c_152]) ).
tcf(c_20112,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(X1,relation_dom(X0)) = relation_dom(sK2) )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(X1,relation_dom(X0),relation_dom(sK2)),sK10(X1,relation_dom(X0),relation_dom(sK2))))) = apply(sK2,ordered_pair(sK9(X1,relation_dom(X0),relation_dom(sK2)),sK10(X1,relation_dom(X0),relation_dom(sK2)))) )
| ~ empty(X0)
| ~ relation(X1)
| ~ relation(relation_dom(sK2))
| ~ relation(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_5278,c_11389]) ).
tcf(c_20113,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_composition(X2,relation_composition(X0,X1)) = relation_dom(sK2) )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(X2,relation_composition(X0,X1),relation_dom(sK2)),sK10(X2,relation_composition(X0,X1),relation_dom(sK2))))) = apply(sK2,ordered_pair(sK9(X2,relation_composition(X0,X1),relation_dom(sK2)),sK10(X2,relation_composition(X0,X1),relation_dom(sK2)))) )
| ( apply(X1,sK12(X0,X1,sK11(X2,relation_composition(X0,X1),relation_dom(sK2)),sK10(X2,relation_composition(X0,X1),relation_dom(sK2)))) = sK10(X2,relation_composition(X0,X1),relation_dom(sK2)) )
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2))
| ~ relation(relation_composition(X0,X1)) ),
inference(superposition,[status(thm)],[c_5278,c_2068]) ).
tcf(c_20114,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(X1,relation_composition(X0,relation_dom(sK2))) = relation_dom(sK2) )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(X1,relation_composition(X0,relation_dom(sK2)),relation_dom(sK2)),sK10(X1,relation_composition(X0,relation_dom(sK2)),relation_dom(sK2))))) = apply(sK2,ordered_pair(sK9(X1,relation_composition(X0,relation_dom(sK2)),relation_dom(sK2)),sK10(X1,relation_composition(X0,relation_dom(sK2)),relation_dom(sK2)))) )
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2))
| ~ relation(relation_composition(X0,relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_5278,c_2063]) ).
tcf(c_20115,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(X1,relation_composition(X0,relation_dom(sK2))) = relation_dom(sK2) )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(X1,relation_composition(X0,relation_dom(sK2)),relation_dom(sK2)),sK10(X1,relation_composition(X0,relation_dom(sK2)),relation_dom(sK2))))) = apply(sK2,ordered_pair(sK9(X1,relation_composition(X0,relation_dom(sK2)),relation_dom(sK2)),sK10(X1,relation_composition(X0,relation_dom(sK2)),relation_dom(sK2)))) )
| ( apply(sK1,apply(sK0,ordered_pair(sK12(X0,relation_dom(sK2),sK11(X1,relation_composition(X0,relation_dom(sK2)),relation_dom(sK2)),sK10(X1,relation_composition(X0,relation_dom(sK2)),relation_dom(sK2))),sK10(X1,relation_composition(X0,relation_dom(sK2)),relation_dom(sK2))))) = apply(sK2,ordered_pair(sK12(X0,relation_dom(sK2),sK11(X1,relation_composition(X0,relation_dom(sK2)),relation_dom(sK2)),sK10(X1,relation_composition(X0,relation_dom(sK2)),relation_dom(sK2))),sK10(X1,relation_composition(X0,relation_dom(sK2)),relation_dom(sK2)))) )
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2))
| ~ relation(relation_composition(X0,relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_5278,c_2064]) ).
tcf(c_20116,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(X1,relation_composition(relation_dom(sK2),X0)) = relation_dom(sK2) )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(X1,relation_composition(relation_dom(sK2),X0),relation_dom(sK2)),sK10(X1,relation_composition(relation_dom(sK2),X0),relation_dom(sK2))))) = apply(sK2,ordered_pair(sK9(X1,relation_composition(relation_dom(sK2),X0),relation_dom(sK2)),sK10(X1,relation_composition(relation_dom(sK2),X0),relation_dom(sK2)))) )
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2))
| ~ relation(relation_composition(relation_dom(sK2),X0)) ),
inference(superposition,[status(thm)],[c_5278,c_2281]) ).
tcf(c_20117,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(X1,relation_composition(relation_dom(sK2),X0)) = relation_dom(sK2) )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(X1,relation_composition(relation_dom(sK2),X0),relation_dom(sK2)),sK10(X1,relation_composition(relation_dom(sK2),X0),relation_dom(sK2))))) = apply(sK2,ordered_pair(sK9(X1,relation_composition(relation_dom(sK2),X0),relation_dom(sK2)),sK10(X1,relation_composition(relation_dom(sK2),X0),relation_dom(sK2)))) )
| ( apply(sK1,apply(sK0,ordered_pair(sK11(X1,relation_composition(relation_dom(sK2),X0),relation_dom(sK2)),sK12(relation_dom(sK2),X0,sK11(X1,relation_composition(relation_dom(sK2),X0),relation_dom(sK2)),sK10(X1,relation_composition(relation_dom(sK2),X0),relation_dom(sK2)))))) = apply(sK2,ordered_pair(sK11(X1,relation_composition(relation_dom(sK2),X0),relation_dom(sK2)),sK12(relation_dom(sK2),X0,sK11(X1,relation_composition(relation_dom(sK2),X0),relation_dom(sK2)),sK10(X1,relation_composition(relation_dom(sK2),X0),relation_dom(sK2))))) )
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2))
| ~ relation(relation_composition(relation_dom(sK2),X0)) ),
inference(superposition,[status(thm)],[c_5278,c_2282]) ).
tcf(c_20118,plain,
! [X0: $i] :
( ( relation_composition(X0,empty_set) = relation_dom(sK2) )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(X0,empty_set,relation_dom(sK2)),sK10(X0,empty_set,relation_dom(sK2))))) = apply(sK2,ordered_pair(sK9(X0,empty_set,relation_dom(sK2)),sK10(X0,empty_set,relation_dom(sK2)))) )
| ~ relation(empty_set)
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5278,c_3809]) ).
tcf(c_20119,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| element(ordered_pair(sK11(X1,sK16(X0),relation_dom(sK2)),sK10(X1,sK16(X0),relation_dom(sK2))),X0)
| ( relation_composition(X1,sK16(X0)) = relation_dom(sK2) )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(X1,sK16(X0),relation_dom(sK2)),sK10(X1,sK16(X0),relation_dom(sK2))))) = apply(sK2,ordered_pair(sK9(X1,sK16(X0),relation_dom(sK2)),sK10(X1,sK16(X0),relation_dom(sK2)))) )
| ~ relation(X1)
| ~ relation(relation_dom(sK2))
| ~ relation(sK16(X0)) ),
inference(superposition,[status(thm)],[c_5278,c_2939]) ).
tcf(c_20120,plain,
! [X0: $i,X1: $i] :
( element(ordered_pair(sK11(X1,sK17(powerset(X0)),relation_dom(sK2)),sK10(X1,sK17(powerset(X0)),relation_dom(sK2))),X0)
| ( relation_composition(X1,sK17(powerset(X0))) = relation_dom(sK2) )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(X1,sK17(powerset(X0)),relation_dom(sK2)),sK10(X1,sK17(powerset(X0)),relation_dom(sK2))))) = apply(sK2,ordered_pair(sK9(X1,sK17(powerset(X0)),relation_dom(sK2)),sK10(X1,sK17(powerset(X0)),relation_dom(sK2)))) )
| ~ relation(X1)
| ~ relation(relation_dom(sK2))
| ~ relation(sK17(powerset(X0))) ),
inference(superposition,[status(thm)],[c_5278,c_2940]) ).
tcf(c_20121,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(X1,sK17(powerset(X0))) = relation_dom(sK2) )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(X1,sK17(powerset(X0)),relation_dom(sK2)),sK10(X1,sK17(powerset(X0)),relation_dom(sK2))))) = apply(sK2,ordered_pair(sK9(X1,sK17(powerset(X0)),relation_dom(sK2)),sK10(X1,sK17(powerset(X0)),relation_dom(sK2)))) )
| ~ empty(X0)
| ~ relation(X1)
| ~ relation(relation_dom(sK2))
| ~ relation(sK17(powerset(X0))) ),
inference(superposition,[status(thm)],[c_5278,c_2925]) ).
tcf(c_20122,plain,
! [X0: $i] :
( ( relation_composition(X0,relation_dom(relation_dom(sK2))) = relation_dom(sK2) )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(X0,relation_dom(relation_dom(sK2)),relation_dom(sK2)),sK10(X0,relation_dom(relation_dom(sK2)),relation_dom(sK2))))) = apply(sK2,ordered_pair(sK9(X0,relation_dom(relation_dom(sK2)),relation_dom(sK2)),sK10(X0,relation_dom(relation_dom(sK2)),relation_dom(sK2)))) )
| ( apply(sK1,apply(sK0,ordered_pair(ordered_pair(sK11(X0,relation_dom(relation_dom(sK2)),relation_dom(sK2)),sK10(X0,relation_dom(relation_dom(sK2)),relation_dom(sK2))),apply(relation_dom(sK2),ordered_pair(sK11(X0,relation_dom(relation_dom(sK2)),relation_dom(sK2)),sK10(X0,relation_dom(relation_dom(sK2)),relation_dom(sK2))))))) = apply(sK2,ordered_pair(ordered_pair(sK11(X0,relation_dom(relation_dom(sK2)),relation_dom(sK2)),sK10(X0,relation_dom(relation_dom(sK2)),relation_dom(sK2))),apply(relation_dom(sK2),ordered_pair(sK11(X0,relation_dom(relation_dom(sK2)),relation_dom(sK2)),sK10(X0,relation_dom(relation_dom(sK2)),relation_dom(sK2)))))) )
| ~ relation(X0)
| ~ function(relation_dom(sK2))
| ~ relation(relation_dom(sK2))
| ~ relation(relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_5278,c_3550]) ).
tcf(c_20123,plain,
! [X0: $i] :
( in(ordered_pair(sK11(X0,relation_dom(relation_dom(sK2)),relation_dom(sK2)),sK10(X0,relation_dom(relation_dom(sK2)),relation_dom(sK2))),relation_dom(relation_dom(sK0)))
| ( relation_composition(X0,relation_dom(relation_dom(sK2))) = relation_dom(sK2) )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(X0,relation_dom(relation_dom(sK2)),relation_dom(sK2)),sK10(X0,relation_dom(relation_dom(sK2)),relation_dom(sK2))))) = apply(sK2,ordered_pair(sK9(X0,relation_dom(relation_dom(sK2)),relation_dom(sK2)),sK10(X0,relation_dom(relation_dom(sK2)),relation_dom(sK2)))) )
| ~ relation(X0)
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ relation(relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_5278,c_3134]) ).
tcf(c_20124,plain,
! [X0: $i] :
( ( relation_composition(X0,relation_dom(relation_dom(sK2))) = relation_dom(sK2) )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(X0,relation_dom(relation_dom(sK2)),relation_dom(sK2)),sK10(X0,relation_dom(relation_dom(sK2)),relation_dom(sK2))))) = apply(sK2,ordered_pair(sK9(X0,relation_dom(relation_dom(sK2)),relation_dom(sK2)),sK10(X0,relation_dom(relation_dom(sK2)),relation_dom(sK2)))) )
| ~ relation(X0)
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2))
| ~ relation(relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_5278,c_3017]) ).
tcf(c_20125,plain,
! [X0: $i] :
( ( relation_composition(X0,relation_dom(relation_dom(sK2))) = relation_dom(sK2) )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(X0,relation_dom(relation_dom(sK2)),relation_dom(sK2)),sK10(X0,relation_dom(relation_dom(sK2)),relation_dom(sK2))))) = apply(sK2,ordered_pair(sK9(X0,relation_dom(relation_dom(sK2)),relation_dom(sK2)),sK10(X0,relation_dom(relation_dom(sK2)),relation_dom(sK2)))) )
| ( apply(sK1,apply(sK0,ordered_pair(ordered_pair(sK11(X0,relation_dom(relation_dom(sK2)),relation_dom(sK2)),sK10(X0,relation_dom(relation_dom(sK2)),relation_dom(sK2))),sK5(relation_dom(sK2),ordered_pair(sK11(X0,relation_dom(relation_dom(sK2)),relation_dom(sK2)),sK10(X0,relation_dom(relation_dom(sK2)),relation_dom(sK2))))))) = apply(sK2,ordered_pair(ordered_pair(sK11(X0,relation_dom(relation_dom(sK2)),relation_dom(sK2)),sK10(X0,relation_dom(relation_dom(sK2)),relation_dom(sK2))),sK5(relation_dom(sK2),ordered_pair(sK11(X0,relation_dom(relation_dom(sK2)),relation_dom(sK2)),sK10(X0,relation_dom(relation_dom(sK2)),relation_dom(sK2)))))) )
| ~ relation(X0)
| ~ relation(relation_dom(sK2))
| ~ relation(relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_5278,c_3018]) ).
tcf(c_20126,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(X1,relation_composition(empty_set,X0)) = relation_dom(sK2) )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(X1,relation_composition(empty_set,X0),relation_dom(sK2)),sK10(X1,relation_composition(empty_set,X0),relation_dom(sK2))))) = apply(sK2,ordered_pair(sK9(X1,relation_composition(empty_set,X0),relation_dom(sK2)),sK10(X1,relation_composition(empty_set,X0),relation_dom(sK2)))) )
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2))
| ~ relation(relation_composition(empty_set,X0)) ),
inference(superposition,[status(thm)],[c_5278,c_3821]) ).
tcf(c_20127,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(X1,relation_composition(X0,empty_set)) = relation_dom(sK2) )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(X1,relation_composition(X0,empty_set),relation_dom(sK2)),sK10(X1,relation_composition(X0,empty_set),relation_dom(sK2))))) = apply(sK2,ordered_pair(sK9(X1,relation_composition(X0,empty_set),relation_dom(sK2)),sK10(X1,relation_composition(X0,empty_set),relation_dom(sK2)))) )
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2))
| ~ relation(relation_composition(X0,empty_set)) ),
inference(superposition,[status(thm)],[c_5278,c_3818]) ).
tcf(c_20128,plain,
! [X0: $i,X1: $i] :
( element(ordered_pair(sK11(X1,sK17(sK16(powerset(X0))),relation_dom(sK2)),sK10(X1,sK17(sK16(powerset(X0))),relation_dom(sK2))),X0)
| ( relation_composition(X1,sK17(sK16(powerset(X0)))) = relation_dom(sK2) )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(X1,sK17(sK16(powerset(X0))),relation_dom(sK2)),sK10(X1,sK17(sK16(powerset(X0))),relation_dom(sK2))))) = apply(sK2,ordered_pair(sK9(X1,sK17(sK16(powerset(X0))),relation_dom(sK2)),sK10(X1,sK17(sK16(powerset(X0))),relation_dom(sK2)))) )
| ~ relation(X1)
| ~ relation(relation_dom(sK2))
| ~ relation(sK17(sK16(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_5278,c_11939]) ).
tcf(c_20129,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(X1,sK17(sK16(powerset(X0)))) = relation_dom(sK2) )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(X1,sK17(sK16(powerset(X0))),relation_dom(sK2)),sK10(X1,sK17(sK16(powerset(X0))),relation_dom(sK2))))) = apply(sK2,ordered_pair(sK9(X1,sK17(sK16(powerset(X0))),relation_dom(sK2)),sK10(X1,sK17(sK16(powerset(X0))),relation_dom(sK2)))) )
| ~ empty(X0)
| ~ relation(X1)
| ~ relation(relation_dom(sK2))
| ~ relation(sK17(sK16(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_5278,c_11936]) ).
tcf(c_20130,plain,
! [X0: $i] :
( ( relation_composition(X0,empty_set) = relation_dom(sK2) )
| ( apply(sK1,apply(sK0,ordered_pair(sK9(X0,empty_set,relation_dom(sK2)),sK10(X0,empty_set,relation_dom(sK2))))) = apply(sK2,ordered_pair(sK9(X0,empty_set,relation_dom(sK2)),sK10(X0,empty_set,relation_dom(sK2)))) )
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_20118,c_109]) ).
tcf(c_20541,plain,
! [X0: $i] :
( ( sK2 = empty_set )
| ( apply(sK0,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0)) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0))) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,sK17(relation_dom(sK2))),X0),X0))) = apply(sK2,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,sK17(relation_dom(sK2))),X0),X0)) )
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_4011,c_6669]) ).
tcf(c_20542,plain,
( ( sK2 = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,sK17(relation_dom(sK2))),sK5(relation_dom(sK2),apply(sK2,sK17(relation_dom(sK2))))),sK5(relation_dom(sK2),apply(sK2,sK17(relation_dom(sK2))))))) = apply(sK2,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,sK17(relation_dom(sK2))),sK5(relation_dom(sK2),apply(sK2,sK17(relation_dom(sK2))))),sK5(relation_dom(sK2),apply(sK2,sK17(relation_dom(sK2)))))) )
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(apply(sK2,sK17(relation_dom(sK2))),relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_71,c_6669]) ).
tcf(c_20543,plain,
( ( sK2 = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,sK17(relation_dom(sK2))),apply(relation_dom(sK2),apply(sK2,sK17(relation_dom(sK2))))),apply(relation_dom(sK2),apply(sK2,sK17(relation_dom(sK2))))))) = apply(sK2,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,sK17(relation_dom(sK2))),apply(relation_dom(sK2),apply(sK2,sK17(relation_dom(sK2))))),apply(relation_dom(sK2),apply(sK2,sK17(relation_dom(sK2)))))) )
| ~ function(relation_dom(sK2))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(apply(sK2,sK17(relation_dom(sK2))),relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_73,c_6669]) ).
tcf(c_20544,plain,
! [X0: $i] :
( ( sK2 = empty_set )
| ( apply(sK2,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0)) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,sK17(relation_dom(sK2))),X0),X0))) = apply(sK2,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,sK17(relation_dom(sK2))),X0),X0)) )
| ~ function(sK2)
| ~ relation(sK2)
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_75,c_6669]) ).
tcf(c_20545,plain,
! [X0: $i,X1: $i] :
( ( sK2 = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,sK17(relation_dom(sK2))),sK12(relation_dom(sK2),X1,apply(sK2,sK17(relation_dom(sK2))),X0)),sK12(relation_dom(sK2),X1,apply(sK2,sK17(relation_dom(sK2))),X0)))) = apply(sK2,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,sK17(relation_dom(sK2))),sK12(relation_dom(sK2),X1,apply(sK2,sK17(relation_dom(sK2))),X0)),sK12(relation_dom(sK2),X1,apply(sK2,sK17(relation_dom(sK2))),X0))) )
| ~ relation(X1)
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),relation_composition(relation_dom(sK2),X1)) ),
inference(superposition,[status(thm)],[c_301,c_6669]) ).
tcf(c_20546,plain,
! [X0: $i] :
( ( sK2 = empty_set )
| ( apply(sK2,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0)) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,sK17(relation_dom(sK2))),X0),X0))) = apply(sK2,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,sK17(relation_dom(sK2))),X0),X0)) )
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_20544,c_55,c_54]) ).
tcf(c_20588,plain,
! [X0: $i] :
( ( relation_dom(sK2) = empty_set )
| ( apply(sK0,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0)) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0))) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,sK17(relation_dom(sK2))),X0),X0))) = apply(sK2,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,sK17(relation_dom(sK2))),X0),X0)) )
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_4011,c_7477]) ).
tcf(c_20589,plain,
( ( relation_dom(sK2) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,sK17(relation_dom(sK2))),sK5(relation_dom(sK2),apply(sK2,sK17(relation_dom(sK2))))),sK5(relation_dom(sK2),apply(sK2,sK17(relation_dom(sK2))))))) = apply(sK2,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,sK17(relation_dom(sK2))),sK5(relation_dom(sK2),apply(sK2,sK17(relation_dom(sK2))))),sK5(relation_dom(sK2),apply(sK2,sK17(relation_dom(sK2)))))) )
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(apply(sK2,sK17(relation_dom(sK2))),relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_71,c_7477]) ).
tcf(c_20590,plain,
( ( relation_dom(sK2) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,sK17(relation_dom(sK2))),apply(relation_dom(sK2),apply(sK2,sK17(relation_dom(sK2))))),apply(relation_dom(sK2),apply(sK2,sK17(relation_dom(sK2))))))) = apply(sK2,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,sK17(relation_dom(sK2))),apply(relation_dom(sK2),apply(sK2,sK17(relation_dom(sK2))))),apply(relation_dom(sK2),apply(sK2,sK17(relation_dom(sK2)))))) )
| ~ function(relation_dom(sK2))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(apply(sK2,sK17(relation_dom(sK2))),relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_73,c_7477]) ).
tcf(c_20591,plain,
! [X0: $i] :
( ( relation_dom(sK2) = empty_set )
| ( apply(sK2,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0)) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,sK17(relation_dom(sK2))),X0),X0))) = apply(sK2,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,sK17(relation_dom(sK2))),X0),X0)) )
| ~ function(sK2)
| ~ relation(sK2)
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_75,c_7477]) ).
tcf(c_20592,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK2) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,sK17(relation_dom(sK2))),sK12(relation_dom(sK2),X1,apply(sK2,sK17(relation_dom(sK2))),X0)),sK12(relation_dom(sK2),X1,apply(sK2,sK17(relation_dom(sK2))),X0)))) = apply(sK2,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,sK17(relation_dom(sK2))),sK12(relation_dom(sK2),X1,apply(sK2,sK17(relation_dom(sK2))),X0)),sK12(relation_dom(sK2),X1,apply(sK2,sK17(relation_dom(sK2))),X0))) )
| ~ relation(X1)
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),relation_composition(relation_dom(sK2),X1)) ),
inference(superposition,[status(thm)],[c_301,c_7477]) ).
tcf(c_20593,plain,
! [X0: $i] :
( ( relation_dom(sK2) = empty_set )
| ( apply(sK2,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0)) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,sK17(relation_dom(sK2))),X0),X0))) = apply(sK2,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,sK17(relation_dom(sK2))),X0),X0)) )
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_20591,c_55,c_54]) ).
tcf(c_20629,plain,
( in(ordered_pair(apply(sK0,sK17(sK16(relation_dom(sK2)))),apply(sK2,sK17(sK16(relation_dom(sK2))))),sK1)
| ( relation_dom(relation_dom(relation_dom(sK2))) = empty_set )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_12026,c_73]) ).
tcf(c_20630,plain,
( in(ordered_pair(apply(sK0,sK17(sK16(relation_dom(sK2)))),apply(sK2,sK17(sK16(relation_dom(sK2))))),sK1)
| ( relation_dom(relation_dom(relation_dom(sK2))) = empty_set )
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_20629,c_57,c_56]) ).
tcf(c_20639,plain,
! [X0: $i] :
( ( relation_composition(sK17(powerset(sK17(sK16(powerset(X0))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_19068,c_16441]) ).
tcf(c_20640,plain,
! [X0: $i] :
( ( relation_composition(empty_set,sK17(powerset(sK17(sK16(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_19068,c_15145]) ).
tcf(c_20656,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(X0))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_65,c_9929]) ).
tcf(c_20657,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_dom(relation_composition(X1,X0))) = X2 )
| ~ empty(X2)
| ~ empty(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_86,c_9929]) ).
tcf(c_20658,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_dom(relation_composition(X0,X1))) = X2 )
| ~ empty(X2)
| ~ empty(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_88,c_9929]) ).
tcf(c_20659,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(empty_set)) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_110,c_9929]) ).
tcf(c_20660,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK2))) = X0 )
| ( apply(sK1,apply(sK0,sK17(sK16(relation_dom(sK2))))) = apply(sK2,sK17(sK16(relation_dom(sK2)))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11951,c_9929]) ).
tcf(c_20661,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK2))) = X0 )
| ( apply(sK1,apply(sK0,sK17(relation_dom(sK2)))) = apply(sK2,sK17(relation_dom(sK2))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2425,c_9929]) ).
tcf(c_20664,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK17(powerset(X0)))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6912,c_9929]) ).
tcf(c_20665,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK17(sK16(powerset(X0))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12308,c_9929]) ).
tcf(c_20666,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK17(powerset(relation_dom(sK2))))) = X0 )
| ( apply(sK1,apply(sK0,sK17(sK17(powerset(relation_dom(sK2)))))) = apply(sK2,sK17(sK17(powerset(relation_dom(sK2))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17464,c_9929]) ).
tcf(c_20667,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK17(powerset(relation_dom(sK2))))) = X0 )
| ~ empty(X0)
| ~ empty(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_17463,c_9929]) ).
tcf(c_20668,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK17(powerset(relation_dom(X0))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17470,c_9929]) ).
tcf(c_20669,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK17(powerset(sK17(powerset(X0)))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17474,c_9929]) ).
tcf(c_20670,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK17(powerset(sK17(sK16(powerset(X0))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17480,c_9929]) ).
tcf(c_20762,plain,
! [X0: $i] :
( empty(X0)
| element(sK17(sK16(sK16(X0))),X0) ),
inference(global_subsumption_just,[status(thm)],[c_11959,c_104,c_11959]) ).
tcf(c_20769,plain,
! [X0: $i] :
( empty(X0)
| in(sK17(sK16(sK16(X0))),X0) ),
inference(superposition,[status(thm)],[c_20762,c_62]) ).
tcf(c_20770,plain,
! [X0: $i,X1: $i] :
( empty(powerset(X1))
| element(X0,X1)
| ~ in(X0,sK17(sK16(sK16(powerset(X1))))) ),
inference(superposition,[status(thm)],[c_20762,c_100]) ).
tcf(c_20771,plain,
! [X0: $i,X1: $i] :
( empty(powerset(X1))
| ~ empty(X1)
| ~ in(X0,sK17(sK16(sK16(powerset(X1))))) ),
inference(superposition,[status(thm)],[c_20762,c_99]) ).
tcf(c_20774,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ in(X0,sK17(sK16(sK16(powerset(X1))))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_20771,c_111]) ).
tcf(c_20777,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| ~ in(X0,sK17(sK16(sK16(powerset(X1))))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_20770,c_111]) ).
tcf(c_20787,plain,
( empty(relation_dom(sK2))
| ( apply(sK1,apply(sK0,sK17(sK16(sK16(relation_dom(sK2)))))) = apply(sK2,sK17(sK16(sK16(relation_dom(sK2))))) ) ),
inference(superposition,[status(thm)],[c_20769,c_53]) ).
tcf(c_20788,plain,
( empty(relation_dom(sK2))
| in(sK17(sK16(sK16(relation_dom(sK2)))),relation_dom(sK0)) ),
inference(superposition,[status(thm)],[c_20769,c_51]) ).
tcf(c_20789,plain,
( empty(relation_dom(sK0))
| in(sK17(sK16(sK16(relation_dom(sK0)))),relation_dom(sK2))
| ( apply(sK1,apply(sK0,sK17(sK16(sK16(relation_dom(sK0)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_20769,c_3475]) ).
tcf(c_20790,plain,
! [X0: $i] :
( empty(X0)
| ~ in(X0,sK17(sK16(sK16(X0)))) ),
inference(superposition,[status(thm)],[c_20769,c_64]) ).
tcf(c_20795,plain,
! [X0: $i] :
( empty(X0)
| empty(sK16(X0))
| element(sK17(sK16(sK16(sK16(X0)))),X0) ),
inference(superposition,[status(thm)],[c_20769,c_2939]) ).
tcf(c_20796,plain,
! [X0: $i] :
( empty(sK17(powerset(X0)))
| element(sK17(sK16(sK16(sK17(powerset(X0))))),X0) ),
inference(superposition,[status(thm)],[c_20769,c_2940]) ).
tcf(c_20798,plain,
( empty(relation_dom(relation_dom(sK2)))
| ( apply(sK1,apply(sK0,ordered_pair(sK17(sK16(sK16(relation_dom(relation_dom(sK2))))),apply(relation_dom(sK2),sK17(sK16(sK16(relation_dom(relation_dom(sK2))))))))) = apply(sK2,ordered_pair(sK17(sK16(sK16(relation_dom(relation_dom(sK2))))),apply(relation_dom(sK2),sK17(sK16(sK16(relation_dom(relation_dom(sK2)))))))) )
| ~ function(relation_dom(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_20769,c_3550]) ).
tcf(c_20799,plain,
( empty(relation_dom(relation_dom(sK2)))
| in(sK17(sK16(sK16(relation_dom(relation_dom(sK2))))),relation_dom(relation_dom(sK0)))
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_20769,c_3134]) ).
tcf(c_20801,plain,
( empty(relation_dom(relation_dom(sK2)))
| ( apply(sK1,apply(sK0,ordered_pair(sK17(sK16(sK16(relation_dom(relation_dom(sK2))))),sK5(relation_dom(sK2),sK17(sK16(sK16(relation_dom(relation_dom(sK2))))))))) = apply(sK2,ordered_pair(sK17(sK16(sK16(relation_dom(relation_dom(sK2))))),sK5(relation_dom(sK2),sK17(sK16(sK16(relation_dom(relation_dom(sK2)))))))) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_20769,c_3018]) ).
tcf(c_20802,plain,
! [X0: $i] :
( empty(sK17(sK16(powerset(X0))))
| element(sK17(sK16(sK16(sK17(sK16(powerset(X0)))))),X0) ),
inference(superposition,[status(thm)],[c_20769,c_11939]) ).
tcf(c_20821,plain,
( in(sK17(sK16(sK16(relation_dom(sK0)))),relation_dom(sK2))
| ( apply(sK1,apply(sK0,sK17(sK16(sK16(relation_dom(sK0)))))) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_20789,c_13972]) ).
tcf(c_20915,plain,
( empty(sK17(powerset(empty_set)))
| element(sK17(sK16(empty_set)),empty_set) ),
inference(superposition,[status(thm)],[c_7736,c_11960]) ).
tcf(c_20916,plain,
! [X0: $i] :
( empty(X0)
| empty(sK17(powerset(X0)))
| in(sK17(sK16(sK17(powerset(X0)))),X0) ),
inference(superposition,[status(thm)],[c_11960,c_62]) ).
tcf(c_20917,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| empty(sK17(powerset(powerset(X1))))
| ~ in(X0,sK17(sK16(sK17(powerset(powerset(X1)))))) ),
inference(superposition,[status(thm)],[c_11960,c_100]) ).
tcf(c_20918,plain,
! [X0: $i,X1: $i] :
( empty(sK17(powerset(powerset(X1))))
| ~ empty(X1)
| ~ in(X0,sK17(sK16(sK17(powerset(powerset(X1)))))) ),
inference(superposition,[status(thm)],[c_11960,c_99]) ).
tcf(c_20919,plain,
( empty(empty_set)
| element(sK17(sK16(empty_set)),empty_set) ),
inference(light_normalisation,[status(thm)],[c_20915,c_7736]) ).
tcf(c_20974,plain,
( empty(relation_dom(sK2))
| in(sK17(sK16(sK16(relation_dom(sK2)))),relation_dom(sK2))
| ( apply(sK1,apply(sK0,sK17(sK16(sK16(relation_dom(sK2)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_20788,c_3475]) ).
tcf(c_20975,plain,
( empty(relation_dom(sK2))
| ~ in(relation_dom(sK0),sK17(sK16(sK16(relation_dom(sK2))))) ),
inference(superposition,[status(thm)],[c_20788,c_64]) ).
tcf(c_20976,plain,
( empty(relation_dom(sK2))
| element(sK17(sK16(sK16(relation_dom(sK2)))),relation_dom(sK0)) ),
inference(superposition,[status(thm)],[c_20788,c_63]) ).
tcf(c_20990,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK2))) = X0 )
| ( apply(sK1,apply(sK0,sK17(sK16(sK16(relation_dom(sK2)))))) = apply(sK2,sK17(sK16(sK16(relation_dom(sK2))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20787,c_9929]) ).
tcf(c_20991,plain,
! [X0: $i] :
( ( sK17(powerset(relation_dom(sK2))) = X0 )
| ( apply(sK1,apply(sK0,sK17(sK16(sK16(relation_dom(sK2)))))) = apply(sK2,sK17(sK16(sK16(relation_dom(sK2))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20787,c_7174]) ).
tcf(c_20992,plain,
( ( relation_composition(relation_dom(relation_dom(relation_dom(sK2))),empty_set) = empty_set )
| ( apply(sK1,apply(sK0,sK17(sK16(sK16(relation_dom(sK2)))))) = apply(sK2,sK17(sK16(sK16(relation_dom(sK2))))) ) ),
inference(superposition,[status(thm)],[c_20787,c_16966]) ).
tcf(c_20993,plain,
( ( relation_composition(relation_dom(relation_dom(sK2)),empty_set) = empty_set )
| ( apply(sK1,apply(sK0,sK17(sK16(sK16(relation_dom(sK2)))))) = apply(sK2,sK17(sK16(sK16(relation_dom(sK2))))) ) ),
inference(superposition,[status(thm)],[c_20787,c_16861]) ).
tcf(c_20994,plain,
( ( relation_composition(empty_set,relation_dom(relation_dom(relation_dom(sK2)))) = empty_set )
| ( apply(sK1,apply(sK0,sK17(sK16(sK16(relation_dom(sK2)))))) = apply(sK2,sK17(sK16(sK16(relation_dom(sK2))))) ) ),
inference(superposition,[status(thm)],[c_20787,c_15920]) ).
tcf(c_20995,plain,
( ( relation_composition(empty_set,relation_dom(relation_dom(sK2))) = empty_set )
| ( apply(sK1,apply(sK0,sK17(sK16(sK16(relation_dom(sK2)))))) = apply(sK2,sK17(sK16(sK16(relation_dom(sK2))))) ) ),
inference(superposition,[status(thm)],[c_20787,c_15264]) ).
tcf(c_20996,plain,
( ( sK17(sK16(powerset(relation_dom(relation_dom(sK2))))) = empty_set )
| ( apply(sK1,apply(sK0,sK17(sK16(sK16(relation_dom(sK2)))))) = apply(sK2,sK17(sK16(sK16(relation_dom(sK2))))) ) ),
inference(superposition,[status(thm)],[c_20787,c_12877]) ).
tcf(c_20997,plain,
( ( sK17(powerset(sK17(powerset(relation_dom(sK2))))) = empty_set )
| ( apply(sK1,apply(sK0,sK17(sK16(sK16(relation_dom(sK2)))))) = apply(sK2,sK17(sK16(sK16(relation_dom(sK2))))) ) ),
inference(superposition,[status(thm)],[c_20787,c_7742]) ).
tcf(c_20998,plain,
( ( relation_dom(relation_dom(sK17(powerset(relation_dom(sK2))))) = empty_set )
| ( apply(sK1,apply(sK0,sK17(sK16(sK16(relation_dom(sK2)))))) = apply(sK2,sK17(sK16(sK16(relation_dom(sK2))))) ) ),
inference(superposition,[status(thm)],[c_20787,c_7236]) ).
tcf(c_20999,plain,
( ( relation_dom(sK17(powerset(relation_dom(relation_dom(sK2))))) = empty_set )
| ( apply(sK1,apply(sK0,sK17(sK16(sK16(relation_dom(sK2)))))) = apply(sK2,sK17(sK16(sK16(relation_dom(sK2))))) ) ),
inference(superposition,[status(thm)],[c_20787,c_9976]) ).
tcf(c_21000,plain,
( ( sK17(powerset(relation_dom(relation_dom(relation_dom(sK2))))) = empty_set )
| ( apply(sK1,apply(sK0,sK17(sK16(sK16(relation_dom(sK2)))))) = apply(sK2,sK17(sK16(sK16(relation_dom(sK2))))) ) ),
inference(superposition,[status(thm)],[c_20787,c_9849]) ).
tcf(c_21001,plain,
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK2))))) = empty_set )
| ( apply(sK1,apply(sK0,sK17(sK16(sK16(relation_dom(sK2)))))) = apply(sK2,sK17(sK16(sK16(relation_dom(sK2))))) ) ),
inference(superposition,[status(thm)],[c_20787,c_9793]) ).
tcf(c_21002,plain,
( ( sK17(sK16(powerset(relation_dom(sK2)))) = empty_set )
| ( apply(sK1,apply(sK0,sK17(sK16(sK16(relation_dom(sK2)))))) = apply(sK2,sK17(sK16(sK16(relation_dom(sK2))))) ) ),
inference(superposition,[status(thm)],[c_20787,c_12303]) ).
tcf(c_21003,plain,
( ( relation_dom(sK17(powerset(relation_dom(sK2)))) = empty_set )
| ( apply(sK1,apply(sK0,sK17(sK16(sK16(relation_dom(sK2)))))) = apply(sK2,sK17(sK16(sK16(relation_dom(sK2))))) ) ),
inference(superposition,[status(thm)],[c_20787,c_7171]) ).
tcf(c_21004,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK2)) = X0 )
| ( apply(sK1,apply(sK0,sK17(sK16(sK16(relation_dom(sK2)))))) = apply(sK2,sK17(sK16(sK16(relation_dom(sK2))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20787,c_2387]) ).
tcf(c_21005,plain,
( ( sK17(powerset(relation_dom(relation_dom(sK2)))) = empty_set )
| ( apply(sK1,apply(sK0,sK17(sK16(sK16(relation_dom(sK2)))))) = apply(sK2,sK17(sK16(sK16(relation_dom(sK2))))) ) ),
inference(superposition,[status(thm)],[c_20787,c_7733]) ).
tcf(c_21006,plain,
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK2)))) = empty_set )
| ( apply(sK1,apply(sK0,sK17(sK16(sK16(relation_dom(sK2)))))) = apply(sK2,sK17(sK16(sK16(relation_dom(sK2))))) ) ),
inference(superposition,[status(thm)],[c_20787,c_7227]) ).
tcf(c_21007,plain,
( ( sK17(powerset(relation_dom(sK2))) = empty_set )
| ( apply(sK1,apply(sK0,sK17(sK16(sK16(relation_dom(sK2)))))) = apply(sK2,sK17(sK16(sK16(relation_dom(sK2))))) ) ),
inference(superposition,[status(thm)],[c_20787,c_7088]) ).
tcf(c_21008,plain,
( ( relation_dom(relation_dom(relation_dom(sK2))) = empty_set )
| ( apply(sK1,apply(sK0,sK17(sK16(sK16(relation_dom(sK2)))))) = apply(sK2,sK17(sK16(sK16(relation_dom(sK2))))) ) ),
inference(superposition,[status(thm)],[c_20787,c_6244]) ).
tcf(c_21009,plain,
( ( relation_dom(relation_dom(sK2)) = empty_set )
| ( apply(sK1,apply(sK0,sK17(sK16(sK16(relation_dom(sK2)))))) = apply(sK2,sK17(sK16(sK16(relation_dom(sK2))))) ) ),
inference(superposition,[status(thm)],[c_20787,c_2124]) ).
tcf(c_21012,plain,
! [X0: $i] :
( ( relation_dom(sK2) = X0 )
| ( apply(sK1,apply(sK0,sK17(sK16(sK16(relation_dom(sK2)))))) = apply(sK2,sK17(sK16(sK16(relation_dom(sK2))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20787,c_60]) ).
tcf(c_21013,plain,
( ( relation_dom(sK2) = empty_set )
| ( apply(sK1,apply(sK0,sK17(sK16(sK16(relation_dom(sK2)))))) = apply(sK2,sK17(sK16(sK16(relation_dom(sK2))))) ) ),
inference(superposition,[status(thm)],[c_20787,c_107]) ).
tcf(c_21014,plain,
( relation(relation_dom(sK2))
| ( apply(sK1,apply(sK0,sK17(sK16(sK16(relation_dom(sK2)))))) = apply(sK2,sK17(sK16(sK16(relation_dom(sK2))))) ) ),
inference(superposition,[status(thm)],[c_20787,c_85]) ).
tcf(c_21015,plain,
( function(relation_dom(sK2))
| ( apply(sK1,apply(sK0,sK17(sK16(sK16(relation_dom(sK2)))))) = apply(sK2,sK17(sK16(sK16(relation_dom(sK2))))) ) ),
inference(superposition,[status(thm)],[c_20787,c_80]) ).
tcf(c_21016,plain,
! [X0: $i] :
( ( relation_composition(X0,relation_dom(sK2)) = empty_set )
| ( apply(sK1,apply(sK0,sK17(sK16(sK16(relation_dom(sK2)))))) = apply(sK2,sK17(sK16(sK16(relation_dom(sK2))))) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_20787,c_2607]) ).
tcf(c_21017,plain,
! [X0: $i] :
( ( relation_composition(relation_dom(sK2),X0) = empty_set )
| ( apply(sK1,apply(sK0,sK17(sK16(sK16(relation_dom(sK2)))))) = apply(sK2,sK17(sK16(sK16(relation_dom(sK2))))) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_20787,c_2400]) ).
tcf(c_21018,plain,
( empty(sK2)
| ( apply(sK1,apply(sK0,sK17(sK16(sK16(relation_dom(sK2)))))) = apply(sK2,sK17(sK16(sK16(relation_dom(sK2))))) )
| ~ relation(sK2) ),
inference(superposition,[status(thm)],[c_20787,c_67]) ).
tcf(c_21023,plain,
( empty(sK2)
| ( apply(sK1,apply(sK0,sK17(sK16(sK16(relation_dom(sK2)))))) = apply(sK2,sK17(sK16(sK16(relation_dom(sK2))))) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_21018,c_54]) ).
tcf(c_21204,plain,
! [X0: $i] :
( ( sK17(powerset(sK2)) = X0 )
| ( apply(sK1,apply(sK0,sK17(sK16(sK16(relation_dom(sK2)))))) = apply(sK2,sK17(sK16(sK16(relation_dom(sK2))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21023,c_7174]) ).
tcf(c_21206,plain,
( ( relation_composition(relation_dom(sK2),empty_set) = empty_set )
| ( apply(sK1,apply(sK0,sK17(sK16(sK16(relation_dom(sK2)))))) = apply(sK2,sK17(sK16(sK16(relation_dom(sK2))))) ) ),
inference(superposition,[status(thm)],[c_21023,c_16861]) ).
tcf(c_21208,plain,
( ( relation_composition(empty_set,relation_dom(sK2)) = empty_set )
| ( apply(sK1,apply(sK0,sK17(sK16(sK16(relation_dom(sK2)))))) = apply(sK2,sK17(sK16(sK16(relation_dom(sK2))))) ) ),
inference(superposition,[status(thm)],[c_21023,c_15264]) ).
tcf(c_21210,plain,
( ( sK17(powerset(sK17(powerset(sK2)))) = empty_set )
| ( apply(sK1,apply(sK0,sK17(sK16(sK16(relation_dom(sK2)))))) = apply(sK2,sK17(sK16(sK16(relation_dom(sK2))))) ) ),
inference(superposition,[status(thm)],[c_21023,c_7742]) ).
tcf(c_21211,plain,
( ( relation_dom(relation_dom(sK17(powerset(sK2)))) = empty_set )
| ( apply(sK1,apply(sK0,sK17(sK16(sK16(relation_dom(sK2)))))) = apply(sK2,sK17(sK16(sK16(relation_dom(sK2))))) ) ),
inference(superposition,[status(thm)],[c_21023,c_7236]) ).
tcf(c_21215,plain,
( ( sK17(sK16(powerset(sK2))) = empty_set )
| ( apply(sK1,apply(sK0,sK17(sK16(sK16(relation_dom(sK2)))))) = apply(sK2,sK17(sK16(sK16(relation_dom(sK2))))) ) ),
inference(superposition,[status(thm)],[c_21023,c_12303]) ).
tcf(c_21216,plain,
( ( relation_dom(sK17(powerset(sK2))) = empty_set )
| ( apply(sK1,apply(sK0,sK17(sK16(sK16(relation_dom(sK2)))))) = apply(sK2,sK17(sK16(sK16(relation_dom(sK2))))) ) ),
inference(superposition,[status(thm)],[c_21023,c_7171]) ).
tcf(c_21220,plain,
( ( sK17(powerset(sK2)) = empty_set )
| ( apply(sK1,apply(sK0,sK17(sK16(sK16(relation_dom(sK2)))))) = apply(sK2,sK17(sK16(sK16(relation_dom(sK2))))) ) ),
inference(superposition,[status(thm)],[c_21023,c_7088]) ).
tcf(c_21225,plain,
! [X0: $i] :
( ( X0 = sK2 )
| ( apply(sK1,apply(sK0,sK17(sK16(sK16(relation_dom(sK2)))))) = apply(sK2,sK17(sK16(sK16(relation_dom(sK2))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_21023,c_60]) ).
tcf(c_21226,plain,
( ( sK2 = empty_set )
| ( apply(sK1,apply(sK0,sK17(sK16(sK16(relation_dom(sK2)))))) = apply(sK2,sK17(sK16(sK16(relation_dom(sK2))))) ) ),
inference(superposition,[status(thm)],[c_21023,c_107]) ).
tcf(c_21229,plain,
! [X0: $i] :
( ( relation_composition(X0,sK2) = empty_set )
| ( apply(sK1,apply(sK0,sK17(sK16(sK16(relation_dom(sK2)))))) = apply(sK2,sK17(sK16(sK16(relation_dom(sK2))))) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_21023,c_2607]) ).
tcf(c_21230,plain,
! [X0: $i] :
( ( relation_composition(sK2,X0) = empty_set )
| ( apply(sK1,apply(sK0,sK17(sK16(sK16(relation_dom(sK2)))))) = apply(sK2,sK17(sK16(sK16(relation_dom(sK2))))) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_21023,c_2400]) ).
tcf(c_21267,plain,
( ( relation_dom(relation_dom(relation_dom(sK2))) = empty_set )
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(sK1,ordered_pair(apply(sK0,sK17(sK16(relation_dom(sK2)))),apply(sK2,sK17(sK16(relation_dom(sK2)))))) ),
inference(superposition,[status(thm)],[c_20630,c_64]) ).
tcf(c_21268,plain,
( element(ordered_pair(apply(sK0,sK17(sK16(relation_dom(sK2)))),apply(sK2,sK17(sK16(relation_dom(sK2))))),sK1)
| ( relation_dom(relation_dom(relation_dom(sK2))) = empty_set )
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_20630,c_63]) ).
tcf(c_21271,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(apply(sK0,sK17(sK16(relation_dom(sK2)))),X0),relation_composition(sK1,X1))
| ( relation_dom(relation_dom(relation_dom(sK2))) = empty_set )
| ~ relation(sK1)
| ~ relation(X1)
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0),X1) ),
inference(superposition,[status(thm)],[c_20630,c_299]) ).
tcf(c_21279,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(apply(sK0,sK17(sK16(relation_dom(sK2)))),X0),relation_composition(sK1,X1))
| ( relation_dom(relation_dom(relation_dom(sK2))) = empty_set )
| ~ relation(X1)
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_21271,c_56]) ).
tcf(c_21296,plain,
! [X0: $i] :
( in(ordered_pair(apply(sK0,sK17(sK16(relation_dom(sK2)))),X0),empty_set)
| ( relation_dom(relation_dom(relation_dom(sK2))) = empty_set )
| ~ relation(empty_set)
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0),empty_set) ),
inference(superposition,[status(thm)],[c_16859,c_21279]) ).
tcf(c_21297,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(sK2))) = empty_set )
| ~ relation(X0)
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X1),X0)
| ~ in(relation_composition(sK1,X0),ordered_pair(apply(sK0,sK17(sK16(relation_dom(sK2)))),X1)) ),
inference(superposition,[status(thm)],[c_21279,c_64]) ).
tcf(c_21298,plain,
! [X0: $i,X1: $i] :
( element(ordered_pair(apply(sK0,sK17(sK16(relation_dom(sK2)))),X0),relation_composition(sK1,X1))
| ( relation_dom(relation_dom(relation_dom(sK2))) = empty_set )
| ~ relation(X1)
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0),X1) ),
inference(superposition,[status(thm)],[c_21279,c_63]) ).
tcf(c_21299,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(sK2))) = empty_set )
| ~ relation(X1)
| ~ empty(relation_composition(sK1,X1))
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0),X1) ),
inference(superposition,[status(thm)],[c_21279,c_61]) ).
tcf(c_21300,plain,
! [X0: $i,X1: $i] :
( in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(relation_composition(sK1,X1)))
| ( relation_dom(relation_dom(relation_dom(sK2))) = empty_set )
| ~ relation(X1)
| ~ relation(relation_composition(sK1,X1))
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0),X1) ),
inference(superposition,[status(thm)],[c_21279,c_70]) ).
tcf(c_21301,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(ordered_pair(apply(sK0,sK17(sK16(relation_dom(sK2)))),X2),relation_composition(relation_composition(sK1,X1),X3))
| ( relation_dom(relation_dom(relation_dom(sK2))) = empty_set )
| ~ relation(X3)
| ~ relation(X1)
| ~ relation(relation_composition(sK1,X1))
| ~ in(ordered_pair(X0,X2),X3)
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0),X1) ),
inference(superposition,[status(thm)],[c_21279,c_299]) ).
tcf(c_21302,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(sK2))) = empty_set )
| ( apply(relation_composition(sK1,X1),apply(sK0,sK17(sK16(relation_dom(sK2))))) = X0 )
| ~ relation(X1)
| ~ function(relation_composition(sK1,X1))
| ~ relation(relation_composition(sK1,X1))
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0),X1) ),
inference(superposition,[status(thm)],[c_21279,c_152]) ).
tcf(c_21303,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(sK2))) = empty_set )
| ( apply(X1,sK12(sK1,X1,apply(sK0,sK17(sK16(relation_dom(sK2)))),X0)) = X0 )
| ~ relation(sK1)
| ~ function(X1)
| ~ relation(X1)
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0),X1) ),
inference(superposition,[status(thm)],[c_21279,c_2068]) ).
tcf(c_21304,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK2))) = empty_set )
| ~ relation(sK1)
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_21279,c_2063]) ).
tcf(c_21305,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK2))) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,sK17(sK16(relation_dom(sK2)))),X0),X0))) = apply(sK2,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,sK17(sK16(relation_dom(sK2)))),X0),X0)) )
| ~ relation(sK1)
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_21279,c_2064]) ).
tcf(c_21306,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK2))) = empty_set )
| ~ relation(empty_set)
| ~ relation(sK1)
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0),empty_set) ),
inference(superposition,[status(thm)],[c_21279,c_3818]) ).
tcf(c_21312,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK2))) = empty_set )
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_21304,c_56]) ).
tcf(c_21334,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(sK2))) = empty_set )
| ( apply(X1,sK12(sK1,X1,apply(sK0,sK17(sK16(relation_dom(sK2)))),X0)) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_21303,c_56]) ).
tcf(c_21356,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK2))) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,sK17(sK16(relation_dom(sK2)))),X0),X0))) = apply(sK2,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,sK17(sK16(relation_dom(sK2)))),X0),X0)) )
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_21305,c_56]) ).
tcf(c_21383,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK2))) = empty_set )
| ( apply(sK0,ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0)) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0))) = empty_set )
| ( apply(relation_dom(sK2),sK12(sK1,relation_dom(sK2),apply(sK0,sK17(sK16(relation_dom(sK2)))),X0)) = X0 )
| ~ function(relation_dom(sK2))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_4011,c_21334]) ).
tcf(c_21384,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK2))) = empty_set )
| ( apply(sK0,ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0)) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0))) = empty_set )
| ( apply(relation_dom(sK0),sK12(sK1,relation_dom(sK0),apply(sK0,sK17(sK16(relation_dom(sK2)))),X0)) = X0 )
| ~ function(relation_dom(sK0))
| ~ relation(relation_dom(sK0))
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_4110,c_21334]) ).
tcf(c_21385,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK2))) = empty_set )
| ( apply(sK2,ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0)) = empty_set )
| ( apply(relation_dom(sK0),sK12(sK1,relation_dom(sK0),apply(sK0,sK17(sK16(relation_dom(sK2)))),X0)) = X0 )
| ~ function(relation_dom(sK0))
| ~ relation(relation_dom(sK0))
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_3449,c_21334]) ).
tcf(c_21386,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK2))) = empty_set )
| ( apply(X0,sK12(sK1,X0,apply(sK0,sK17(sK16(relation_dom(sK2)))),sK5(X0,apply(sK2,sK17(sK16(relation_dom(sK2))))))) = sK5(X0,apply(sK2,sK17(sK16(relation_dom(sK2))))) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(apply(sK2,sK17(sK16(relation_dom(sK2)))),relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_71,c_21334]) ).
tcf(c_21387,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK2))) = empty_set )
| ( apply(X0,sK12(sK1,X0,apply(sK0,sK17(sK16(relation_dom(sK2)))),apply(X0,apply(sK2,sK17(sK16(relation_dom(sK2))))))) = apply(X0,apply(sK2,sK17(sK16(relation_dom(sK2))))) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(apply(sK2,sK17(sK16(relation_dom(sK2)))),relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_73,c_21334]) ).
tcf(c_21388,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(sK2))) = empty_set )
| ( apply(X0,ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X1)) = empty_set )
| ( apply(relation_dom(X0),sK12(sK1,relation_dom(X0),apply(sK0,sK17(sK16(relation_dom(sK2)))),X1)) = X1 )
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom(X0))
| ~ relation(relation_dom(X0))
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_75,c_21334]) ).
tcf(c_21389,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_dom(relation_dom(sK2))) = empty_set )
| ( apply(X1,sK12(sK1,X1,apply(sK0,sK17(sK16(relation_dom(sK2)))),sK12(X1,X2,apply(sK2,sK17(sK16(relation_dom(sK2)))),X0))) = sK12(X1,X2,apply(sK2,sK17(sK16(relation_dom(sK2)))),X0) )
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0),relation_composition(X1,X2)) ),
inference(superposition,[status(thm)],[c_301,c_21334]) ).
tcf(c_21390,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(sK2))) = empty_set )
| ( apply(relation_dom(sK0),sK12(sK1,relation_dom(sK0),apply(sK0,sK17(sK16(relation_dom(sK2)))),sK12(relation_dom(sK2),X1,apply(sK2,sK17(sK16(relation_dom(sK2)))),X0))) = sK12(relation_dom(sK2),X1,apply(sK2,sK17(sK16(relation_dom(sK2)))),X0) )
| ~ relation(X1)
| ~ function(relation_dom(sK0))
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(sK16(relation_dom(sK2)))),X0),relation_composition(relation_dom(sK2),X1)) ),
inference(superposition,[status(thm)],[c_2283,c_21334]) ).
tcf(c_21391,plain,
( ( relation_dom(relation_dom(relation_dom(sK2))) = empty_set )
| ( apply(relation_dom(sK0),sK12(sK1,relation_dom(sK0),apply(sK0,sK17(sK16(relation_dom(sK2)))),sK5(relation_dom(sK2),apply(sK2,sK17(sK16(relation_dom(sK2))))))) = sK5(relation_dom(sK2),apply(sK2,sK17(sK16(relation_dom(sK2))))) )
| ~ function(relation_dom(sK0))
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(apply(sK2,sK17(sK16(relation_dom(sK2)))),relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_3019,c_21334]) ).
tcf(c_21392,plain,
( ( relation_dom(relation_dom(relation_dom(sK2))) = empty_set )
| ( apply(relation_dom(sK0),sK12(sK1,relation_dom(sK0),apply(sK0,sK17(sK16(relation_dom(sK2)))),apply(relation_dom(sK2),apply(sK2,sK17(sK16(relation_dom(sK2))))))) = apply(relation_dom(sK2),apply(sK2,sK17(sK16(relation_dom(sK2))))) )
| ~ function(relation_dom(sK0))
| ~ function(relation_dom(sK2))
| ~ relation(relation_dom(sK0))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1))
| ~ in(apply(sK2,sK17(sK16(relation_dom(sK2)))),relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_3551,c_21334]) ).
tcf(c_21596,plain,
! [X0: $i] :
( ( relation_dom(sK2) = sK2 )
| ( apply(sK0,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0)) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0))) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,sK17(relation_dom(sK2))),X0),X0))) = apply(sK2,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,sK17(relation_dom(sK2))),X0),X0)) )
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_4011,c_7566]) ).
tcf(c_21597,plain,
( ( relation_dom(sK2) = sK2 )
| ( apply(sK1,apply(sK0,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,sK17(relation_dom(sK2))),sK5(relation_dom(sK2),apply(sK2,sK17(relation_dom(sK2))))),sK5(relation_dom(sK2),apply(sK2,sK17(relation_dom(sK2))))))) = apply(sK2,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,sK17(relation_dom(sK2))),sK5(relation_dom(sK2),apply(sK2,sK17(relation_dom(sK2))))),sK5(relation_dom(sK2),apply(sK2,sK17(relation_dom(sK2)))))) )
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(apply(sK2,sK17(relation_dom(sK2))),relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_71,c_7566]) ).
tcf(c_21598,plain,
( ( relation_dom(sK2) = sK2 )
| ( apply(sK1,apply(sK0,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,sK17(relation_dom(sK2))),apply(relation_dom(sK2),apply(sK2,sK17(relation_dom(sK2))))),apply(relation_dom(sK2),apply(sK2,sK17(relation_dom(sK2))))))) = apply(sK2,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,sK17(relation_dom(sK2))),apply(relation_dom(sK2),apply(sK2,sK17(relation_dom(sK2))))),apply(relation_dom(sK2),apply(sK2,sK17(relation_dom(sK2)))))) )
| ~ function(relation_dom(sK2))
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(apply(sK2,sK17(relation_dom(sK2))),relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_73,c_7566]) ).
tcf(c_21599,plain,
! [X0: $i] :
( ( relation_dom(sK2) = sK2 )
| ( apply(sK2,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0)) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,sK17(relation_dom(sK2))),X0),X0))) = apply(sK2,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,sK17(relation_dom(sK2))),X0),X0)) )
| ~ function(sK2)
| ~ relation(sK2)
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_75,c_7566]) ).
tcf(c_21600,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK2) = sK2 )
| ( apply(sK1,apply(sK0,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,sK17(relation_dom(sK2))),sK12(relation_dom(sK2),X1,apply(sK2,sK17(relation_dom(sK2))),X0)),sK12(relation_dom(sK2),X1,apply(sK2,sK17(relation_dom(sK2))),X0)))) = apply(sK2,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,sK17(relation_dom(sK2))),sK12(relation_dom(sK2),X1,apply(sK2,sK17(relation_dom(sK2))),X0)),sK12(relation_dom(sK2),X1,apply(sK2,sK17(relation_dom(sK2))),X0))) )
| ~ relation(X1)
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1))
| ~ in(ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0),relation_composition(relation_dom(sK2),X1)) ),
inference(superposition,[status(thm)],[c_301,c_7566]) ).
tcf(c_21601,plain,
! [X0: $i] :
( ( relation_dom(sK2) = sK2 )
| ( apply(sK2,ordered_pair(apply(sK2,sK17(relation_dom(sK2))),X0)) = empty_set )
| ( apply(sK1,apply(sK0,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,sK17(relation_dom(sK2))),X0),X0))) = apply(sK2,ordered_pair(sK12(sK1,relation_dom(sK2),apply(sK0,sK17(relation_dom(sK2))),X0),X0)) )
| ~ relation(relation_dom(sK2))
| ~ in(apply(sK0,sK17(relation_dom(sK2))),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_21599,c_55,c_54]) ).
tcf(c_21659,plain,
( in(ordered_pair(apply(sK0,sK17(sK16(relation_dom(sK2)))),apply(sK2,sK17(sK16(relation_dom(sK2))))),sK1)
| ( relation_dom(relation_dom(sK2)) = empty_set )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_12027,c_73]) ).
tcf(c_21660,plain,
( in(ordered_pair(apply(sK0,sK17(sK16(relation_dom(sK2)))),apply(sK2,sK17(sK16(relation_dom(sK2))))),sK1)
| ( relation_dom(relation_dom(sK2)) = empty_set )
| ~ in(apply(sK0,sK17(sK16(relation_dom(sK2)))),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_21659,c_57,c_56]) ).
tcf(c_21695,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_21660,c_21659,c_21601,c_21600,c_21599,c_21598,c_21597,c_21596,c_21392,c_21391,c_21390,c_21389,c_21388,c_21387,c_21386,c_21385,c_21384,c_21383,c_21356,c_21334,c_21312,c_21306,c_21305,c_21304,c_21303,c_21302,c_21301,c_21300,c_21299,c_21298,c_21297,c_21296,c_21279,c_21271,c_21268,c_21267,c_21230,c_21229,c_21226,c_21225,c_21220,c_21216,c_21215,c_21211,c_21210,c_21208,c_21206,c_21204,c_21023,c_21018,c_21017,c_21016,c_21015,c_21014,c_21013,c_21012,c_21009,c_21008,c_21007,c_21006,c_21005,c_21004,c_21003,c_21002,c_21001,c_21000,c_20999,c_20998,c_20997,c_20996,c_20995,c_20994,c_20993,c_20992,c_20991,c_20990,c_20976,c_20975,c_20974,c_20919,c_20918,c_20917,c_20916,c_20915,c_20821,c_20802,c_20801,c_20799,c_20798,c_20796,c_20795,c_20790,c_20789,c_20788,c_20787,c_20777,c_20774,c_20771,c_20770,c_20769,c_20762,c_20670,c_20669,c_20668,c_20667,c_20666,c_20665,c_20664,c_20661,c_20660,c_20659,c_20658,c_20657,c_20656,c_20640,c_20639,c_20630,c_20629,c_20593,c_20592,c_20591,c_20590,c_20589,c_20588,c_20546,c_20545,c_20544,c_20543,c_20542,c_20541,c_20130,c_20129,c_20128,c_20127,c_20126,c_20125,c_20124,c_20123,c_20122,c_20121,c_20120,c_20119,c_20118,c_20117,c_20116,c_20115,c_20114,c_20113,c_20112,c_20111,c_20110,c_20109,c_20108,c_20107,c_20106,c_20105,c_20102,c_19726,c_19725,c_19724,c_19723,c_19722,c_19721,c_19720,c_19719,c_19718,c_19717,c_19716,c_19715,c_19714,c_19713,c_19712,c_19711,c_19710,c_19709,c_19708,c_19707,c_19706,c_19705,c_19704,c_19703,c_19702,c_19701,c_19700,c_19698,c_19697,c_19495,c_19494,c_19493,c_19492,c_19491,c_19490,c_19489,c_19488,c_19487,c_19486,c_19485,c_19484,c_19483,c_19482,c_19481,c_19480,c_19479,c_19478,c_19477,c_19476,c_19475,c_19474,c_19473,c_19472,c_19471,c_19470,c_19467,c_19376,c_19375,c_19374,c_19373,c_19372,c_19371,c_19370,c_19369,c_19368,c_19367,c_19244,c_19222,c_19199,c_19198,c_19197,c_19196,c_19195,c_19194,c_19193,c_19192,c_19191,c_19190,c_19189,c_19172,c_19164,c_19161,c_19160,c_19071,c_19070,c_19069,c_19068,c_19065,c_19064,c_19060,c_19059,c_19058,c_19057,c_19056,c_19055,c_19054,c_19053,c_19052,c_19051,c_19050,c_19049,c_19048,c_19047,c_19046,c_19045,c_19030,c_19029,c_18973,c_18972,c_18971,c_18970,c_18967,c_18966,c_18962,c_18961,c_18960,c_18959,c_18958,c_18957,c_18956,c_18955,c_18954,c_18953,c_18952,c_18951,c_18950,c_18949,c_18948,c_18947,c_18936,c_18935,c_18922,c_18921,c_18913,c_18912,c_18611,c_18610,c_18609,c_18608,c_18607,c_18606,c_18605,c_18604,c_18603,c_18602,c_18601,c_18600,c_18599,c_18598,c_18597,c_18596,c_18595,c_18594,c_18593,c_18592,c_18591,c_18590,c_18589,c_18588,c_18587,c_18586,c_18585,c_18583,c_18582,c_18561,c_18560,c_18473,c_18472,c_18471,c_18470,c_18469,c_18468,c_18467,c_18466,c_18465,c_18464,c_18403,c_18381,c_18359,c_18353,c_18352,c_18351,c_18350,c_18349,c_18348,c_18347,c_18346,c_18345,c_18344,c_18343,c_18326,c_18318,c_18315,c_18314,c_17856,c_17855,c_17854,c_17853,c_17852,c_17851,c_17850,c_17849,c_17848,c_17847,c_17846,c_17845,c_17844,c_17843,c_17842,c_17841,c_17840,c_17839,c_17838,c_17837,c_17836,c_17835,c_17834,c_17833,c_17832,c_17831,c_17830,c_17816,c_17815,c_17814,c_17714,c_17713,c_17712,c_17711,c_17710,c_17709,c_17708,c_17707,c_17706,c_17705,c_17704,c_17703,c_17702,c_17701,c_17700,c_17699,c_17698,c_17697,c_17696,c_17695,c_17694,c_17693,c_17692,c_17691,c_17690,c_17689,c_17688,c_17683,c_17682,c_17673,c_17672,c_17671,c_17670,c_17584,c_17583,c_17582,c_17581,c_17578,c_17577,c_17573,c_17572,c_17571,c_17570,c_17569,c_17568,c_17567,c_17566,c_17565,c_17564,c_17563,c_17562,c_17561,c_17560,c_17559,c_17558,c_17557,c_17484,c_17480,c_17479,c_17478,c_17477,c_17476,c_17475,c_17474,c_17473,c_17472,c_17471,c_17470,c_17467,c_17466,c_17465,c_17464,c_17463,c_17462,c_17456,c_17419,c_17418,c_17417,c_17416,c_17415,c_17414,c_17413,c_17412,c_17411,c_17410,c_17358,c_17357,c_17354,c_17353,c_17352,c_17351,c_17350,c_17349,c_17341,c_17340,c_17322,c_17321,c_17300,c_17299,c_17281,c_17266,c_17152,c_17151,c_17150,c_17149,c_17148,c_17147,c_17146,c_17145,c_17144,c_17143,c_17116,c_17094,c_17072,c_17066,c_17065,c_17064,c_17063,c_17062,c_17061,c_17060,c_17059,c_17058,c_17057,c_17056,c_17039,c_17031,c_17028,c_17027,c_16975,c_16974,c_16972,c_16971,c_16970,c_16969,c_16968,c_16967,c_16966,c_16960,c_16951,c_16949,c_16940,c_16938,c_16929,c_16928,c_16927,c_16925,c_16924,c_16923,c_16922,c_16921,c_16920,c_16919,c_16918,c_16917,c_16916,c_16915,c_16914,c_16913,c_16912,c_16903,c_16899,c_16898,c_16889,c_16870,c_16869,c_16868,c_16866,c_16865,c_16864,c_16863,c_16862,c_16861,c_16860,c_16859,c_16858,c_16447,c_16446,c_16445,c_16444,c_16443,c_16442,c_16441,c_16440,c_16439,c_16438,c_16428,c_16427,c_16405,c_16399,c_16398,c_16352,c_16346,c_16345,c_16344,c_16343,c_16342,c_16341,c_16287,c_16285,c_16284,c_16283,c_16282,c_16281,c_16172,c_16171,c_16170,c_16169,c_16168,c_16167,c_16166,c_16165,c_16164,c_16163,c_16135,c_16134,c_16133,c_16100,c_16078,c_16056,c_16050,c_16049,c_16048,c_16047,c_16046,c_16045,c_16044,c_16043,c_16042,c_16041,c_16024,c_16016,c_16013,c_16012,c_15962,c_15961,c_15958,c_15957,c_15956,c_15955,c_15954,c_15953,c_15929,c_15928,c_15926,c_15925,c_15924,c_15923,c_15922,c_15921,c_15920,c_15914,c_15913,c_15904,c_15900,c_15899,c_15898,c_15889,c_15885,c_15884,c_15770,c_15769,c_15768,c_15767,c_15766,c_15765,c_15764,c_15763,c_15762,c_15761,c_15653,c_15652,c_15651,c_15650,c_15649,c_15648,c_15647,c_15646,c_15645,c_15644,c_15471,c_15449,c_15427,c_15421,c_15420,c_15419,c_15418,c_15417,c_15416,c_15415,c_15414,c_15413,c_15412,c_15395,c_15387,c_15384,c_15383,c_15367,c_15366,c_15365,c_15356,c_15352,c_15351,c_15350,c_15341,c_15337,c_15336,c_15335,c_15326,c_15310,c_15309,c_15308,c_15299,c_15273,c_15272,c_15271,c_15270,c_15269,c_15268,c_15267,c_15266,c_15265,c_15264,c_15263,c_15262,c_15261,c_15151,c_15150,c_15149,c_15148,c_15147,c_15146,c_15145,c_15144,c_15143,c_15142,c_15104,c_15103,c_15100,c_15099,c_15098,c_15097,c_15096,c_15095,c_15080,c_15079,c_14968,c_14967,c_14966,c_14965,c_14964,c_14963,c_14962,c_14961,c_14960,c_14959,c_14856,c_14855,c_14854,c_14853,c_14852,c_14851,c_14850,c_14849,c_14848,c_14847,c_14778,c_14777,c_14776,c_14774,c_14773,c_14772,c_14717,c_14716,c_14715,c_14713,c_14712,c_14711,c_14693,c_14670,c_14648,c_14626,c_14620,c_14619,c_14618,c_14617,c_14616,c_14615,c_14614,c_14613,c_14612,c_14611,c_14594,c_14586,c_14583,c_14582,c_14574,c_14495,c_14494,c_14493,c_14492,c_14491,c_14490,c_14489,c_14488,c_14487,c_14486,c_14485,c_14445,c_14444,c_14443,c_14442,c_14441,c_14440,c_14439,c_14438,c_14437,c_14436,c_14435,c_14400,c_14399,c_14396,c_14395,c_14394,c_14393,c_14392,c_14391,c_14390,c_14366,c_14365,c_14362,c_14361,c_14360,c_14359,c_14358,c_14357,c_14356,c_14332,c_14331,c_14328,c_14327,c_14326,c_14325,c_14324,c_14323,c_14322,c_14314,c_14313,c_14282,c_14281,c_14280,c_14279,c_14278,c_14277,c_14254,c_14232,c_14210,c_14204,c_14203,c_14202,c_14201,c_14200,c_14199,c_14198,c_14197,c_14196,c_14195,c_14178,c_14170,c_14167,c_14166,c_14091,c_14090,c_14089,c_14088,c_14087,c_14086,c_14085,c_14084,c_14083,c_14082,c_14070,c_14056,c_14037,c_14023,c_14014,c_14013,c_14012,c_14011,c_14010,c_14009,c_14008,c_14007,c_14006,c_14005,c_13991,c_13983,c_13981,c_13980,c_13979,c_13974,c_13972,c_13971,c_13938,c_13937,c_13935,c_13933,c_13922,c_13921,c_13919,c_13779,c_13759,c_13758,c_13757,c_13756,c_13755,c_13754,c_13753,c_13752,c_13751,c_13750,c_13749,c_13748,c_13747,c_13746,c_13729,c_13726,c_13725,c_13724,c_13720,c_13719,c_13632,c_13631,c_13630,c_13629,c_13628,c_13627,c_13626,c_13625,c_13624,c_13623,c_13514,c_13513,c_13512,c_13511,c_13510,c_13509,c_13508,c_13507,c_13506,c_13505,c_13401,c_13400,c_13399,c_13398,c_13397,c_13396,c_13395,c_13394,c_13393,c_13392,c_13229,c_13228,c_13227,c_13226,c_13225,c_13224,c_13223,c_13222,c_13221,c_13220,c_13105,c_13104,c_13103,c_13102,c_13101,c_13100,c_13099,c_13098,c_13097,c_13096,c_13058,c_13036,c_13013,c_13007,c_13006,c_13005,c_13004,c_13003,c_13002,c_13001,c_13000,c_12999,c_12998,c_12997,c_12980,c_12972,c_12969,c_12968,c_12889,c_12888,c_12887,c_12886,c_12885,c_12884,c_12883,c_12882,c_12881,c_12880,c_12879,c_12878,c_12877,c_12783,c_12782,c_12780,c_12779,c_12778,c_12777,c_12776,c_12775,c_12774,c_12773,c_12772,c_12771,c_12770,c_12769,c_12661,c_12660,c_12659,c_12658,c_12657,c_12656,c_12655,c_12654,c_12653,c_12652,c_12651,c_12650,c_12649,c_12648,c_12647,c_12646,c_12645,c_12644,c_12643,c_12642,c_12641,c_12640,c_12639,c_12638,c_12501,c_12500,c_12499,c_12498,c_12497,c_12496,c_12495,c_12494,c_12493,c_12492,c_12491,c_12490,c_12489,c_12488,c_12487,c_12486,c_12485,c_12307,c_12306,c_12305,c_12304,c_12303,c_12302,c_12308,c_12300,c_12299,c_12298,c_12297,c_12296,c_12295,c_12294,c_12293,c_12292,c_12284,c_12283,c_12254,c_12248,c_12247,c_12246,c_12245,c_12244,c_12234,c_12200,c_12178,c_12156,c_12150,c_12144,c_12143,c_12142,c_12141,c_12140,c_12139,c_12138,c_12137,c_12136,c_12135,c_12118,c_12107,c_12105,c_12104,c_12103,c_12078,c_12077,c_12072,c_12068,c_12067,c_12066,c_12039,c_12034,c_12033,c_12032,c_12031,c_12030,c_12027,c_12026,c_12025,c_12024,c_12023,c_12022,c_12021,c_12005,c_12004,c_12003,c_11966,c_11963,c_11962,c_11960,c_11959,c_11954,c_11953,c_11952,c_11951,c_11939,c_11936,c_11933,c_11932,c_11931,c_11924,c_11790,c_11789,c_11788,c_11787,c_11785,c_11783,c_11782,c_11781,c_11780,c_11779,c_11778,c_11776,c_11775,c_11774,c_11427,c_11426,c_11425,c_11424,c_11423,c_11422,c_11421,c_11420,c_11418,c_11417,c_11416,c_11415,c_11412,c_11411,c_11410,c_11409,c_11408,c_11407,c_11406,c_11405,c_11404,c_11403,c_11402,c_11401,c_11400,c_11397,c_11396,c_11389,c_11365,c_11364,c_11358,c_11357,c_11356,c_11311,c_11310,c_11304,c_11303,c_11302,c_11292,c_11291,c_11190,c_11189,c_11188,c_11187,c_11186,c_11185,c_11184,c_11183,c_11182,c_11181,c_11090,c_11089,c_11088,c_11087,c_11086,c_11085,c_11084,c_11083,c_11082,c_11081,c_10694,c_10693,c_10692,c_10691,c_10690,c_10689,c_10688,c_10687,c_10686,c_10685,c_10684,c_10683,c_10682,c_10681,c_10680,c_10679,c_10678,c_10677,c_10676,c_10675,c_10674,c_10673,c_10672,c_10671,c_10670,c_10669,c_10668,c_10667,c_10666,c_10665,c_10664,c_10662,c_10661,c_10249,c_10248,c_10247,c_10246,c_10245,c_10244,c_10243,c_10242,c_10241,c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).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET998+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n005.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 12:32:47 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.41
% 0.09/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.41
% 0.09/0.41 % Detected problem language: tptp
% 0.09/0.42 % Proving...
% 10.72/2.79 % SZS status Started for theBenchmark.p
% 10.72/2.79 % SZS status Theorem for theBenchmark.p
% 10.72/2.79
% 10.72/2.79 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 10.72/2.79
% 10.72/2.79 % ------ iProver source info
% 10.72/2.79
% 10.72/2.79 % git: date: 2026-07-19 20:42:38 +0200
% 10.72/2.79 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 10.72/2.79 % git: non_committed_changes: false
% 10.72/2.79
% 10.72/2.79 % ------ Parsing...
% 10.72/2.79 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 10.72/2.79
% 10.72/2.79 % ------ 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 %
% 10.72/2.79
% 10.72/2.79 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 10.72/2.79
% 10.72/2.79 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 10.72/2.79 % ------ Proving...
% 10.72/2.79 % ------ Problem Properties
% 10.72/2.79
% 10.72/2.79 %
% 10.72/2.79 % clauses 60
% 10.72/2.79 % conjectures 11
% 10.72/2.79 % EPR 24
% 10.72/2.79 % Horn 54
% 10.72/2.79 % unary 22
% 10.72/2.79 % binary 13
% 10.72/2.79 % lits 144
% 10.72/2.79 % lits eq 11
% 10.72/2.79 % fd_pure 0
% 10.72/2.79 % fd_pseudo 0
% 10.72/2.79 % fd_cond 1
% 10.72/2.79 % fd_pseudo_cond 7
% 10.72/2.79 % AC symbols 0
% 10.72/2.79
% 10.72/2.79 % ------ Schedule dynamic 5 is on
% 10.72/2.79
% 10.72/2.79 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 10.72/2.79
% 10.72/2.79
% 10.72/2.79 % ------
% 10.72/2.79 % Current options:
% 10.72/2.79 % ------
% 10.72/2.79
% 10.72/2.79
% 10.72/2.79 %
% 10.72/2.79
% 10.72/2.79 % ------ Proving...
% 10.72/2.79 %
% 10.72/2.79
% 10.72/2.79 % SZS status Theorem for theBenchmark.p
% 10.72/2.79
% 10.72/2.79 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 14.94/2.86
% 14.94/2.86
%------------------------------------------------------------------------------